Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(2.28179 - 3.95218i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28179 | + | 3.95218i | −0.806734 | + | 1.39730i | 0.108380 | + | 0.994110i | \(0.465434\pi\) |
−0.915114 | + | 0.403195i | \(0.867900\pi\) | |||||||
\(3\) | 1.09409 | + | 5.07966i | 0.210557 | + | 0.977582i | ||||
\(4\) | −6.41313 | − | 11.1079i | −0.801641 | − | 1.38848i | ||||
\(5\) | −10.3955 | − | 18.0055i | −0.929801 | − | 1.61046i | −0.783652 | − | 0.621200i | \(-0.786645\pi\) |
−0.146149 | − | 0.989263i | \(-0.546688\pi\) | |||||||
\(6\) | −22.5722 | − | 7.26670i | −1.53584 | − | 0.494437i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | 22.0250 | 0.973376 | ||||||||
\(9\) | −24.6060 | + | 11.1152i | −0.911332 | + | 0.411673i | ||||
\(10\) | 94.8813 | 3.00041 | ||||||||
\(11\) | −22.6993 | + | 39.3163i | −0.622190 | + | 1.07766i | 0.366887 | + | 0.930265i | \(0.380423\pi\) |
−0.989077 | + | 0.147399i | \(0.952910\pi\) | |||||||
\(12\) | 49.4077 | − | 44.7295i | 1.18856 | − | 1.07602i | ||||
\(13\) | −14.6521 | − | 25.3782i | −0.312597 | − | 0.541434i | 0.666327 | − | 0.745660i | \(-0.267866\pi\) |
−0.978924 | + | 0.204226i | \(0.934532\pi\) | |||||||
\(14\) | 15.9725 | + | 27.6652i | 0.304917 | + | 0.528132i | ||||
\(15\) | 80.0884 | − | 72.5052i | 1.37858 | − | 1.24805i | ||||
\(16\) | 1.04863 | − | 1.81629i | 0.0163849 | − | 0.0283795i | ||||
\(17\) | −98.0555 | −1.39894 | −0.699469 | − | 0.714663i | \(-0.746580\pi\) | ||||
−0.699469 | + | 0.714663i | \(0.746580\pi\) | |||||||
\(18\) | 12.2165 | − | 122.610i | 0.159970 | − | 1.60552i | ||||
\(19\) | 31.1554 | 0.376186 | 0.188093 | − | 0.982151i | \(-0.439769\pi\) | ||||
0.188093 | + | 0.982151i | \(0.439769\pi\) | |||||||
\(20\) | −133.335 | + | 230.943i | −1.49073 | + | 2.58202i | ||||
\(21\) | 34.6231 | + | 11.1463i | 0.359780 | + | 0.115825i | ||||
\(22\) | −103.590 | − | 179.423i | −1.00388 | − | 1.73878i | ||||
\(23\) | −4.19596 | − | 7.26761i | −0.0380399 | − | 0.0658870i | 0.846379 | − | 0.532582i | \(-0.178778\pi\) |
−0.884419 | + | 0.466695i | \(0.845445\pi\) | |||||||
\(24\) | 24.0972 | + | 111.879i | 0.204951 | + | 0.951554i | ||||
\(25\) | −153.632 | + | 266.099i | −1.22906 | + | 2.12879i | ||||
\(26\) | 133.732 | 1.00873 | ||||||||
\(27\) | −83.3823 | − | 112.829i | −0.594331 | − | 0.804220i | ||||
\(28\) | −89.7838 | −0.605983 | ||||||||
\(29\) | 36.1332 | − | 62.5845i | 0.231371 | − | 0.400747i | −0.726841 | − | 0.686806i | \(-0.759012\pi\) |
0.958212 | + | 0.286059i | \(0.0923455\pi\) | |||||||
\(30\) | 103.808 | + | 481.965i | 0.631757 | + | 2.93315i | ||||
\(31\) | 15.4299 | + | 26.7254i | 0.0893965 | + | 0.154839i | 0.907256 | − | 0.420578i | \(-0.138173\pi\) |
−0.817860 | + | 0.575418i | \(0.804840\pi\) | |||||||
\(32\) | 92.8855 | + | 160.882i | 0.513125 | + | 0.888758i | ||||
\(33\) | −224.548 | − | 72.2893i | −1.18451 | − | 0.381332i | ||||
\(34\) | 223.742 | − | 387.533i | 1.12857 | − | 1.95474i | ||||
\(35\) | −145.537 | −0.702863 | ||||||||
\(36\) | 281.267 | + | 202.036i | 1.30216 | + | 0.935354i | ||||
\(37\) | −196.369 | −0.872511 | −0.436255 | − | 0.899823i | \(-0.643696\pi\) | ||||
−0.436255 | + | 0.899823i | \(0.643696\pi\) | |||||||
\(38\) | −71.0900 | + | 123.131i | −0.303482 | + | 0.525646i | ||||
\(39\) | 112.882 | − | 102.194i | 0.463477 | − | 0.419592i | ||||
\(40\) | −228.961 | − | 396.571i | −0.905046 | − | 1.56759i | ||||
\(41\) | −106.336 | − | 184.180i | −0.405048 | − | 0.701564i | 0.589279 | − | 0.807930i | \(-0.299412\pi\) |
−0.994327 | + | 0.106366i | \(0.966079\pi\) | |||||||
\(42\) | −123.055 | + | 111.403i | −0.452089 | + | 0.409283i | ||||
\(43\) | −118.438 | + | 205.141i | −0.420039 | + | 0.727529i | −0.995943 | − | 0.0899887i | \(-0.971317\pi\) |
0.575904 | + | 0.817517i | \(0.304650\pi\) | |||||||
\(44\) | 582.293 | 1.99509 | ||||||||
\(45\) | 455.925 | + | 327.495i | 1.51034 | + | 1.08489i | ||||
\(46\) | 38.2972 | 0.122752 | ||||||||
\(47\) | 110.018 | − | 190.557i | 0.341442 | − | 0.591395i | −0.643259 | − | 0.765649i | \(-0.722418\pi\) |
0.984701 | + | 0.174254i | \(0.0557513\pi\) | |||||||
\(48\) | 10.3734 | + | 3.33953i | 0.0311932 | + | 0.0100421i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −701.114 | − | 1214.36i | −1.98305 | − | 3.43474i | ||||
\(51\) | −107.281 | − | 498.089i | −0.294556 | − | 1.36758i | ||||
\(52\) | −187.932 | + | 325.507i | −0.501181 | + | 0.868071i | ||||
\(53\) | 55.9028 | 0.144884 | 0.0724419 | − | 0.997373i | \(-0.476921\pi\) | ||||
0.0724419 | + | 0.997373i | \(0.476921\pi\) | |||||||
\(54\) | 636.181 | − | 72.0896i | 1.60321 | − | 0.181670i | ||||
\(55\) | 943.880 | 2.31405 | ||||||||
\(56\) | 77.0874 | − | 133.519i | 0.183951 | − | 0.318612i | ||||
\(57\) | 34.0866 | + | 158.259i | 0.0792085 | + | 0.367752i | ||||
\(58\) | 164.897 | + | 285.609i | 0.373310 | + | 0.646592i | ||||
\(59\) | 327.326 | + | 566.946i | 0.722275 | + | 1.25102i | 0.960086 | + | 0.279706i | \(0.0902370\pi\) |
−0.237810 | + | 0.971312i | \(0.576430\pi\) | |||||||
\(60\) | −1318.99 | − | 424.626i | −2.83802 | − | 0.913650i | ||||
\(61\) | −174.391 | + | 302.055i | −0.366041 | + | 0.634002i | −0.988943 | − | 0.148298i | \(-0.952620\pi\) |
0.622901 | + | 0.782300i | \(0.285954\pi\) | |||||||
\(62\) | −140.831 | −0.288477 | ||||||||
\(63\) | −18.7387 | + | 188.069i | −0.0374739 | + | 0.376102i | ||||
\(64\) | −831.002 | −1.62305 | ||||||||
\(65\) | −304.632 | + | 527.638i | −0.581306 | + | 1.00685i | ||||
\(66\) | 798.072 | − | 722.506i | 1.48842 | − | 1.34749i | ||||
\(67\) | −105.247 | − | 182.293i | −0.191910 | − | 0.332398i | 0.753973 | − | 0.656905i | \(-0.228135\pi\) |
−0.945883 | + | 0.324507i | \(0.894802\pi\) | |||||||
\(68\) | 628.842 | + | 1089.19i | 1.12145 | + | 1.94240i | ||||
\(69\) | 32.3263 | − | 29.2654i | 0.0564004 | − | 0.0510601i | ||||
\(70\) | 332.085 | − | 575.187i | 0.567024 | − | 0.982115i | ||||
\(71\) | −548.252 | −0.916416 | −0.458208 | − | 0.888845i | \(-0.651508\pi\) | ||||
−0.458208 | + | 0.888845i | \(0.651508\pi\) | |||||||
\(72\) | −541.946 | + | 244.811i | −0.887068 | + | 0.400713i | ||||
\(73\) | −266.888 | −0.427902 | −0.213951 | − | 0.976844i | \(-0.568633\pi\) | ||||
−0.213951 | + | 0.976844i | \(0.568633\pi\) | |||||||
\(74\) | 448.073 | − | 776.086i | 0.703884 | − | 1.21916i | ||||
\(75\) | −1519.78 | − | 489.266i | −2.33986 | − | 0.753274i | ||||
\(76\) | −199.803 | − | 346.070i | −0.301566 | − | 0.522328i | ||||
\(77\) | 158.895 | + | 275.214i | 0.235166 | + | 0.407319i | ||||
\(78\) | 146.314 | + | 679.314i | 0.212395 | + | 0.986117i | ||||
\(79\) | 134.946 | − | 233.733i | 0.192185 | − | 0.332874i | −0.753789 | − | 0.657116i | \(-0.771776\pi\) |
0.945974 | + | 0.324242i | \(0.105109\pi\) | |||||||
\(80\) | −43.6042 | −0.0609388 | ||||||||
\(81\) | 481.906 | − | 546.999i | 0.661051 | − | 0.750341i | ||||
\(82\) | 970.550 | 1.30706 | ||||||||
\(83\) | −312.634 | + | 541.499i | −0.413447 | + | 0.716111i | −0.995264 | − | 0.0972088i | \(-0.969009\pi\) |
0.581817 | + | 0.813320i | \(0.302342\pi\) | |||||||
\(84\) | −98.2311 | − | 456.071i | −0.127594 | − | 0.592398i | ||||
\(85\) | 1019.34 | + | 1765.54i | 1.30073 | + | 2.25294i | ||||
\(86\) | −540.503 | − | 936.178i | −0.677720 | − | 1.17384i | ||||
\(87\) | 357.441 | + | 115.072i | 0.440479 | + | 0.141804i | ||||
\(88\) | −499.951 | + | 865.941i | −0.605625 | + | 1.04897i | ||||
\(89\) | 1605.63 | 1.91232 | 0.956162 | − | 0.292838i | \(-0.0945996\pi\) | ||||
0.956162 | + | 0.292838i | \(0.0945996\pi\) | |||||||
\(90\) | −2334.64 | + | 1054.62i | −2.73437 | + | 1.23519i | ||||
\(91\) | −205.129 | −0.236301 | ||||||||
\(92\) | −53.8184 | + | 93.2162i | −0.0609887 | + | 0.105635i | ||||
\(93\) | −118.874 | + | 107.618i | −0.132545 | + | 0.119995i | ||||
\(94\) | 502.076 | + | 869.621i | 0.550906 | + | 0.954198i | ||||
\(95\) | −323.875 | − | 560.969i | −0.349778 | − | 0.605833i | ||||
\(96\) | −715.603 | + | 647.846i | −0.760791 | + | 0.688755i | ||||
\(97\) | 145.549 | − | 252.099i | 0.152354 | − | 0.263884i | −0.779739 | − | 0.626105i | \(-0.784648\pi\) |
0.932092 | + | 0.362221i | \(0.117981\pi\) | |||||||
\(98\) | 223.615 | 0.230496 | ||||||||
\(99\) | 121.530 | − | 1219.72i | 0.123376 | − | 1.23825i | ||||
\(100\) | 3941.06 | 3.94106 | ||||||||
\(101\) | 726.307 | − | 1258.00i | 0.715547 | − | 1.23936i | −0.247201 | − | 0.968964i | \(-0.579511\pi\) |
0.962748 | − | 0.270399i | \(-0.0871557\pi\) | |||||||
\(102\) | 2213.33 | + | 712.540i | 2.14855 | + | 0.691686i | ||||
\(103\) | 28.1341 | + | 48.7296i | 0.0269139 | + | 0.0466162i | 0.879169 | − | 0.476511i | \(-0.158099\pi\) |
−0.852255 | + | 0.523127i | \(0.824765\pi\) | |||||||
\(104\) | −322.712 | − | 558.954i | −0.304275 | − | 0.527019i | ||||
\(105\) | −159.230 | − | 739.278i | −0.147993 | − | 0.687106i | ||||
\(106\) | −127.558 | + | 220.938i | −0.116883 | + | 0.202447i | ||||
\(107\) | −300.124 | −0.271160 | −0.135580 | − | 0.990766i | \(-0.543290\pi\) | ||||
−0.135580 | + | 0.990766i | \(0.543290\pi\) | |||||||
\(108\) | −718.547 | + | 1649.79i | −0.640206 | + | 1.46991i | ||||
\(109\) | −936.906 | −0.823296 | −0.411648 | − | 0.911343i | \(-0.635047\pi\) | ||||
−0.411648 | + | 0.911343i | \(0.635047\pi\) | |||||||
\(110\) | −2153.74 | + | 3730.38i | −1.86682 | + | 3.23343i | ||||
\(111\) | −214.845 | − | 997.489i | −0.183713 | − | 0.852951i | ||||
\(112\) | −7.34044 | − | 12.7140i | −0.00619291 | − | 0.0107264i | ||||
\(113\) | −697.297 | − | 1207.75i | −0.580498 | − | 1.00545i | −0.995420 | − | 0.0955946i | \(-0.969525\pi\) |
0.414923 | − | 0.909857i | \(-0.363809\pi\) | |||||||
\(114\) | −703.245 | − | 226.397i | −0.577763 | − | 0.186000i | ||||
\(115\) | −87.2381 | + | 151.101i | −0.0707391 | + | 0.122524i | ||||
\(116\) | −926.907 | −0.741906 | ||||||||
\(117\) | 642.612 | + | 461.594i | 0.507773 | + | 0.364738i | ||||
\(118\) | −2987.56 | −2.33074 | ||||||||
\(119\) | −343.194 | + | 594.430i | −0.264375 | + | 0.457910i | ||||
\(120\) | 1763.95 | − | 1596.93i | 1.34188 | − | 1.21482i | ||||
\(121\) | −365.014 | − | 632.222i | −0.274240 | − | 0.474998i | ||||
\(122\) | −795.849 | − | 1378.45i | −0.590596 | − | 1.02294i | ||||
\(123\) | 819.232 | − | 741.662i | 0.600550 | − | 0.543686i | ||||
\(124\) | 197.908 | − | 342.786i | 0.143328 | − | 0.248251i | ||||
\(125\) | 3789.47 | 2.71152 | ||||||||
\(126\) | −700.523 | − | 503.192i | −0.495298 | − | 0.355777i | ||||
\(127\) | −2387.37 | −1.66807 | −0.834034 | − | 0.551714i | \(-0.813974\pi\) | ||||
−0.834034 | + | 0.551714i | \(0.813974\pi\) | |||||||
\(128\) | 1153.09 | − | 1997.21i | 0.796247 | − | 1.37914i | ||||
\(129\) | −1171.63 | − | 377.185i | −0.799661 | − | 0.257436i | ||||
\(130\) | −1390.21 | − | 2407.92i | −0.937920 | − | 1.62452i | ||||
\(131\) | −1060.00 | − | 1835.97i | −0.706963 | − | 1.22450i | −0.965978 | − | 0.258623i | \(-0.916731\pi\) |
0.259015 | − | 0.965873i | \(-0.416602\pi\) | |||||||
\(132\) | 637.078 | + | 2957.85i | 0.420080 | + | 1.95036i | ||||
\(133\) | 109.044 | − | 188.869i | 0.0710925 | − | 0.123136i | ||||
\(134\) | 960.606 | 0.619282 | ||||||||
\(135\) | −1164.74 | + | 2674.26i | −0.742557 | + | 1.70491i | ||||
\(136\) | −2159.67 | −1.36169 | ||||||||
\(137\) | 32.9508 | − | 57.0725i | 0.0205487 | − | 0.0355915i | −0.855568 | − | 0.517690i | \(-0.826792\pi\) |
0.876117 | + | 0.482099i | \(0.160125\pi\) | |||||||
\(138\) | 41.9004 | + | 194.537i | 0.0258463 | + | 0.120000i | ||||
\(139\) | 981.641 | + | 1700.25i | 0.599005 | + | 1.03751i | 0.992968 | + | 0.118381i | \(0.0377705\pi\) |
−0.393963 | + | 0.919126i | \(0.628896\pi\) | |||||||
\(140\) | 933.346 | + | 1616.60i | 0.563444 | + | 0.975914i | ||||
\(141\) | 1088.33 | + | 350.369i | 0.650030 | + | 0.209265i | ||||
\(142\) | 1251.00 | − | 2166.79i | 0.739304 | − | 1.28051i | ||||
\(143\) | 1330.37 | 0.777979 | ||||||||
\(144\) | −5.61429 | + | 56.3472i | −0.00324901 | + | 0.0326083i | ||||
\(145\) | −1502.49 | −0.860517 | ||||||||
\(146\) | 608.982 | − | 1054.79i | 0.345203 | − | 0.597910i | ||||
\(147\) | 188.752 | − | 170.880i | 0.105905 | − | 0.0958769i | ||||
\(148\) | 1259.34 | + | 2181.24i | 0.699440 | + | 1.21147i | ||||
\(149\) | 1316.91 | + | 2280.95i | 0.724063 | + | 1.25411i | 0.959359 | + | 0.282190i | \(0.0910607\pi\) |
−0.235296 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(150\) | 5401.49 | − | 4890.04i | 2.94020 | − | 2.66180i | ||||
\(151\) | 368.737 | − | 638.671i | 0.198724 | − | 0.344200i | −0.749391 | − | 0.662128i | \(-0.769654\pi\) |
0.948115 | + | 0.317927i | \(0.102987\pi\) | |||||||
\(152\) | 686.197 | 0.366170 | ||||||||
\(153\) | 2412.75 | − | 1089.90i | 1.27490 | − | 0.575905i | ||||
\(154\) | −1450.26 | −0.758865 | ||||||||
\(155\) | 320.803 | − | 555.646i | 0.166242 | − | 0.287939i | ||||
\(156\) | −1859.08 | − | 598.497i | −0.954138 | − | 0.307167i | ||||
\(157\) | −1173.36 | − | 2032.32i | −0.596462 | − | 1.03310i | −0.993339 | − | 0.115230i | \(-0.963239\pi\) |
0.396877 | − | 0.917872i | \(-0.370094\pi\) | |||||||
\(158\) | 615.837 | + | 1066.66i | 0.310084 | + | 0.537082i | ||||
\(159\) | 61.1624 | + | 283.967i | 0.0305063 | + | 0.141636i | ||||
\(160\) | 1931.18 | − | 3344.90i | 0.954207 | − | 1.65274i | ||||
\(161\) | −58.7434 | −0.0287555 | ||||||||
\(162\) | 1062.23 | + | 3152.71i | 0.515163 | + | 1.52902i | ||||
\(163\) | −572.002 | −0.274863 | −0.137431 | − | 0.990511i | \(-0.543885\pi\) | ||||
−0.137431 | + | 0.990511i | \(0.543885\pi\) | |||||||
\(164\) | −1363.90 | + | 2362.34i | −0.649406 | + | 1.12480i | ||||
\(165\) | 1032.69 | + | 4794.59i | 0.487239 | + | 2.26217i | ||||
\(166\) | −1426.73 | − | 2471.17i | −0.667083 | − | 1.15542i | ||||
\(167\) | −271.886 | − | 470.920i | −0.125983 | − | 0.218209i | 0.796134 | − | 0.605121i | \(-0.206875\pi\) |
−0.922117 | + | 0.386912i | \(0.873542\pi\) | |||||||
\(168\) | 762.574 | + | 245.497i | 0.350201 | + | 0.112741i | ||||
\(169\) | 669.132 | − | 1158.97i | 0.304566 | − | 0.527524i | ||||
\(170\) | −9303.63 | −4.19739 | ||||||||
\(171\) | −766.608 | + | 346.297i | −0.342830 | + | 0.154866i | ||||
\(172\) | 3038.24 | 1.34688 | ||||||||
\(173\) | −1017.23 | + | 1761.89i | −0.447042 | + | 0.774299i | −0.998192 | − | 0.0601072i | \(-0.980856\pi\) |
0.551150 | + | 0.834406i | \(0.314189\pi\) | |||||||
\(174\) | −1270.39 | + | 1150.10i | −0.553494 | + | 0.501086i | ||||
\(175\) | 1075.43 | + | 1862.69i | 0.464541 | + | 0.804608i | ||||
\(176\) | 47.6064 | + | 82.4568i | 0.0203890 | + | 0.0353148i | ||||
\(177\) | −2521.77 | + | 2282.99i | −1.07089 | + | 0.969493i | ||||
\(178\) | −3663.72 | + | 6345.75i | −1.54274 | + | 2.67210i | ||||
\(179\) | −931.218 | −0.388841 | −0.194420 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194420 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(180\) | 713.865 | − | 7164.62i | 0.295602 | − | 2.96678i | ||||
\(181\) | 1002.74 | 0.411785 | 0.205892 | − | 0.978575i | \(-0.433990\pi\) | ||||
0.205892 | + | 0.978575i | \(0.433990\pi\) | |||||||
\(182\) | 468.062 | − | 810.708i | 0.190632 | − | 0.330185i | ||||
\(183\) | −1725.13 | − | 555.376i | −0.696861 | − | 0.224342i | ||||
\(184\) | −92.4159 | − | 160.069i | −0.0370271 | − | 0.0641328i | ||||
\(185\) | 2041.35 | + | 3535.73i | 0.811261 | + | 1.40515i | ||||
\(186\) | −154.081 | − | 715.374i | −0.0607408 | − | 0.282010i | ||||
\(187\) | 2225.79 | − | 3855.18i | 0.870405 | − | 1.50759i | ||||
\(188\) | −2822.24 | −1.09486 | ||||||||
\(189\) | −975.828 | + | 110.577i | −0.375561 | + | 0.0425572i | ||||
\(190\) | 2956.06 | 1.12871 | ||||||||
\(191\) | 1921.54 | − | 3328.21i | 0.727947 | − | 1.26084i | −0.229803 | − | 0.973237i | \(-0.573808\pi\) |
0.957750 | − | 0.287604i | \(-0.0928586\pi\) | |||||||
\(192\) | −909.187 | − | 4221.21i | −0.341745 | − | 1.58666i | ||||
\(193\) | 1733.05 | + | 3001.73i | 0.646361 | + | 1.11953i | 0.983985 | + | 0.178250i | \(0.0570435\pi\) |
−0.337624 | + | 0.941281i | \(0.609623\pi\) | |||||||
\(194\) | 664.227 | + | 1150.47i | 0.245818 | + | 0.425769i | ||||
\(195\) | −3013.51 | − | 970.146i | −1.10668 | − | 0.356275i | ||||
\(196\) | −314.243 | + | 544.285i | −0.114520 | + | 0.198355i | ||||
\(197\) | −3691.99 | −1.33525 | −0.667623 | − | 0.744500i | \(-0.732688\pi\) | ||||
−0.667623 | + | 0.744500i | \(0.732688\pi\) | |||||||
\(198\) | 4543.25 | + | 3263.45i | 1.63068 | + | 1.17133i | ||||
\(199\) | −481.783 | −0.171622 | −0.0858108 | − | 0.996311i | \(-0.527348\pi\) | ||||
−0.0858108 | + | 0.996311i | \(0.527348\pi\) | |||||||
\(200\) | −3383.75 | + | 5860.83i | −1.19634 | + | 2.07212i | ||||
\(201\) | 810.839 | − | 734.064i | 0.284538 | − | 0.257596i | ||||
\(202\) | 3314.56 | + | 5740.98i | 1.15451 | + | 1.99967i | ||||
\(203\) | −252.932 | − | 438.092i | −0.0874501 | − | 0.151468i | ||||
\(204\) | −4844.70 | + | 4385.97i | −1.66273 | + | 1.50529i | ||||
\(205\) | −2210.84 | + | 3829.29i | −0.753228 | + | 1.30463i | ||||
\(206\) | −256.784 | −0.0868494 | ||||||||
\(207\) | 184.026 | + | 132.188i | 0.0617909 | + | 0.0443849i | ||||
\(208\) | −61.4588 | −0.0204875 | ||||||||
\(209\) | −707.204 | + | 1224.91i | −0.234059 | + | 0.405402i | ||||
\(210\) | 3285.09 | + | 1057.57i | 1.07949 | + | 0.347521i | ||||
\(211\) | −574.892 | − | 995.742i | −0.187570 | − | 0.324880i | 0.756870 | − | 0.653566i | \(-0.226728\pi\) |
−0.944439 | + | 0.328686i | \(0.893394\pi\) | |||||||
\(212\) | −358.512 | − | 620.960i | −0.116145 | − | 0.201169i | ||||
\(213\) | −599.834 | − | 2784.93i | −0.192958 | − | 0.895871i | ||||
\(214\) | 684.820 | − | 1186.14i | 0.218754 | − | 0.378893i | ||||
\(215\) | 4924.90 | 1.56221 | ||||||||
\(216\) | −1836.49 | − | 2485.06i | −0.578508 | − | 0.782809i | ||||
\(217\) | 216.018 | 0.0675774 | ||||||||
\(218\) | 2137.82 | − | 3702.82i | 0.664182 | − | 1.15040i | ||||
\(219\) | −291.998 | − | 1355.70i | −0.0900978 | − | 0.418309i | ||||
\(220\) | −6053.22 | − | 10484.5i | −1.85504 | − | 3.21302i | ||||
\(221\) | 1436.72 | + | 2488.47i | 0.437304 | + | 0.757433i | ||||
\(222\) | 4432.48 | + | 1426.96i | 1.34004 | + | 0.431401i | ||||
\(223\) | 1007.98 | − | 1745.87i | 0.302687 | − | 0.524269i | −0.674057 | − | 0.738680i | \(-0.735450\pi\) |
0.976744 | + | 0.214411i | \(0.0687830\pi\) | |||||||
\(224\) | 1300.40 | 0.387886 | ||||||||
\(225\) | 822.534 | − | 8255.28i | 0.243714 | − | 2.44601i | ||||
\(226\) | 6364.34 | 1.87323 | ||||||||
\(227\) | −1521.10 | + | 2634.62i | −0.444753 | + | 0.770335i | −0.998035 | − | 0.0626590i | \(-0.980042\pi\) |
0.553282 | + | 0.832994i | \(0.313375\pi\) | |||||||
\(228\) | 1539.31 | − | 1393.56i | 0.447121 | − | 0.404785i | ||||
\(229\) | −2040.67 | − | 3534.54i | −0.588870 | − | 1.01995i | −0.994381 | − | 0.105863i | \(-0.966240\pi\) |
0.405511 | − | 0.914090i | \(-0.367094\pi\) | |||||||
\(230\) | −398.118 | − | 689.560i | −0.114135 | − | 0.197688i | ||||
\(231\) | −1224.15 | + | 1108.24i | −0.348672 | + | 0.315657i | ||||
\(232\) | 795.833 | − | 1378.42i | 0.225211 | − | 0.390077i | ||||
\(233\) | 2667.57 | 0.750035 | 0.375017 | − | 0.927018i | \(-0.377637\pi\) | ||||
0.375017 | + | 0.927018i | \(0.377637\pi\) | |||||||
\(234\) | −3290.61 | + | 1486.46i | −0.919289 | + | 0.415268i | ||||
\(235\) | −4574.77 | −1.26989 | ||||||||
\(236\) | 4198.37 | − | 7271.79i | 1.15801 | − | 2.00573i | ||||
\(237\) | 1334.93 | + | 429.756i | 0.365878 | + | 0.117788i | ||||
\(238\) | −1566.19 | − | 2712.73i | −0.426560 | − | 0.738824i | ||||
\(239\) | 2986.31 | + | 5172.45i | 0.808237 | + | 1.39991i | 0.914084 | + | 0.405525i | \(0.132911\pi\) |
−0.105848 | + | 0.994382i | \(0.533756\pi\) | |||||||
\(240\) | −47.7068 | − | 221.495i | −0.0128311 | − | 0.0595726i | ||||
\(241\) | 1320.63 | − | 2287.40i | 0.352984 | − | 0.611387i | −0.633787 | − | 0.773508i | \(-0.718500\pi\) |
0.986771 | + | 0.162121i | \(0.0518336\pi\) | |||||||
\(242\) | 3331.54 | 0.884956 | ||||||||
\(243\) | 3305.82 | + | 1849.46i | 0.872709 | + | 0.488241i | ||||
\(244\) | 4473.57 | 1.17373 | ||||||||
\(245\) | −509.379 | + | 882.270i | −0.132829 | + | 0.230066i | ||||
\(246\) | 1061.86 | + | 4930.07i | 0.275211 | + | 1.27776i | ||||
\(247\) | −456.492 | − | 790.667i | −0.117595 | − | 0.203680i | ||||
\(248\) | 339.843 | + | 588.626i | 0.0870164 | + | 0.150717i | ||||
\(249\) | −3092.68 | − | 995.631i | −0.787111 | − | 0.253396i | ||||
\(250\) | −8646.77 | + | 14976.6i | −2.18748 | + | 3.78882i | ||||
\(251\) | −7001.16 | −1.76060 | −0.880298 | − | 0.474422i | \(-0.842657\pi\) | ||||
−0.880298 | + | 0.474422i | \(0.842657\pi\) | |||||||
\(252\) | 2209.22 | − | 997.962i | 0.552252 | − | 0.249467i | ||||
\(253\) | 380.981 | 0.0946721 | ||||||||
\(254\) | 5447.47 | − | 9435.29i | 1.34569 | − | 2.33080i | ||||
\(255\) | −7853.11 | + | 7109.53i | −1.92855 | + | 1.74595i | ||||
\(256\) | 1938.20 | + | 3357.06i | 0.473193 | + | 0.819595i | ||||
\(257\) | −2893.85 | − | 5012.30i | −0.702388 | − | 1.21657i | −0.967626 | − | 0.252388i | \(-0.918784\pi\) |
0.265239 | − | 0.964183i | \(-0.414549\pi\) | |||||||
\(258\) | 4164.11 | − | 3769.83i | 1.00483 | − | 0.909687i | ||||
\(259\) | −687.292 | + | 1190.43i | −0.164889 | + | 0.285596i | ||||
\(260\) | 7814.57 | 1.86400 | ||||||||
\(261\) | −193.454 | + | 1941.58i | −0.0458793 | + | 0.460462i | ||||
\(262\) | 9674.74 | 2.28133 | ||||||||
\(263\) | 3743.32 | − | 6483.62i | 0.877653 | − | 1.52014i | 0.0237442 | − | 0.999718i | \(-0.492441\pi\) |
0.853909 | − | 0.520422i | \(-0.174225\pi\) | |||||||
\(264\) | −4945.68 | − | 1592.17i | −1.15297 | − | 0.371179i | ||||
\(265\) | −581.137 | − | 1006.56i | −0.134713 | − | 0.233330i | ||||
\(266\) | 497.630 | + | 861.920i | 0.114705 | + | 0.198676i | ||||
\(267\) | 1756.70 | + | 8156.08i | 0.402653 | + | 1.86945i | ||||
\(268\) | −1349.93 | + | 2338.14i | −0.307686 | + | 0.532928i | ||||
\(269\) | −3249.42 | −0.736508 | −0.368254 | − | 0.929725i | \(-0.620044\pi\) | ||||
−0.368254 | + | 0.929725i | \(0.620044\pi\) | |||||||
\(270\) | −7911.42 | − | 10705.4i | −1.78324 | − | 2.41299i | ||||
\(271\) | −3946.32 | −0.884581 | −0.442291 | − | 0.896872i | \(-0.645834\pi\) | ||||
−0.442291 | + | 0.896872i | \(0.645834\pi\) | |||||||
\(272\) | −102.824 | + | 178.097i | −0.0229215 | + | 0.0397012i | ||||
\(273\) | −224.429 | − | 1041.99i | −0.0497548 | − | 0.231004i | ||||
\(274\) | 150.374 | + | 260.455i | 0.0331547 | + | 0.0574257i | ||||
\(275\) | −6974.69 | − | 12080.5i | −1.52942 | − | 2.64903i | ||||
\(276\) | −532.389 | − | 171.393i | −0.116109 | − | 0.0373791i | ||||
\(277\) | −2327.13 | + | 4030.71i | −0.504779 | + | 0.874303i | 0.495206 | + | 0.868776i | \(0.335093\pi\) |
−0.999985 | + | 0.00552735i | \(0.998241\pi\) | |||||||
\(278\) | −8959.60 | −1.93295 | ||||||||
\(279\) | −676.724 | − | 486.097i | −0.145213 | − | 0.104308i | ||||
\(280\) | −3205.45 | −0.684150 | ||||||||
\(281\) | −3223.44 | + | 5583.17i | −0.684322 | + | 1.18528i | 0.289327 | + | 0.957230i | \(0.406569\pi\) |
−0.973649 | + | 0.228051i | \(0.926765\pi\) | |||||||
\(282\) | −3868.07 | + | 3501.82i | −0.816809 | + | 0.739469i | ||||
\(283\) | 1819.23 | + | 3151.00i | 0.382127 | + | 0.661864i | 0.991366 | − | 0.131123i | \(-0.0418583\pi\) |
−0.609239 | + | 0.792987i | \(0.708525\pi\) | |||||||
\(284\) | 3516.01 | + | 6089.91i | 0.734636 | + | 1.27243i | ||||
\(285\) | 2495.18 | − | 2258.93i | 0.518603 | − | 0.469499i | ||||
\(286\) | −3035.62 | + | 5257.85i | −0.627622 | + | 1.08707i | ||||
\(287\) | −1488.71 | −0.306187 | ||||||||
\(288\) | −4073.77 | − | 2926.23i | −0.833504 | − | 0.598713i | ||||
\(289\) | 4701.88 | 0.957029 | ||||||||
\(290\) | 3428.36 | − | 5938.10i | 0.694208 | − | 1.20240i | ||||
\(291\) | 1439.82 | + | 463.524i | 0.290048 | + | 0.0933755i | ||||
\(292\) | 1711.59 | + | 2964.55i | 0.343024 | + | 0.594135i | ||||
\(293\) | −3163.73 | − | 5479.74i | −0.630809 | − | 1.09259i | −0.987387 | − | 0.158328i | \(-0.949390\pi\) |
0.356578 | − | 0.934266i | \(-0.383944\pi\) | |||||||
\(294\) | 244.654 | + | 1135.89i | 0.0485324 | + | 0.225328i | ||||
\(295\) | 6805.43 | − | 11787.4i | 1.34314 | − | 2.32639i | ||||
\(296\) | −4325.03 | −0.849281 | ||||||||
\(297\) | 6328.74 | − | 717.148i | 1.23647 | − | 0.140112i | ||||
\(298\) | −12019.6 | −2.33651 | ||||||||
\(299\) | −122.959 | + | 212.972i | −0.0237823 | + | 0.0411922i | ||||
\(300\) | 4311.85 | + | 20019.2i | 0.829817 | + | 3.85271i | ||||
\(301\) | 829.068 | + | 1435.99i | 0.158760 | + | 0.274980i | ||||
\(302\) | 1682.76 | + | 2914.62i | 0.320635 | + | 0.555357i | ||||
\(303\) | 7184.86 | + | 2313.03i | 1.36224 | + | 0.438549i | ||||
\(304\) | 32.6706 | − | 56.5871i | 0.00616377 | − | 0.0106760i | ||||
\(305\) | 7251.53 | 1.36138 | ||||||||
\(306\) | −1197.89 | + | 12022.5i | −0.223788 | + | 2.24602i | ||||
\(307\) | 2712.80 | 0.504324 | 0.252162 | − | 0.967685i | \(-0.418858\pi\) | ||||
0.252162 | + | 0.967685i | \(0.418858\pi\) | |||||||
\(308\) | 2038.03 | − | 3529.96i | 0.377037 | − | 0.653047i | ||||
\(309\) | −216.749 | + | 196.226i | −0.0399043 | + | 0.0361259i | ||||
\(310\) | 1464.01 | + | 2535.74i | 0.268226 | + | 0.464581i | ||||
\(311\) | −1523.04 | − | 2637.98i | −0.277696 | − | 0.480983i | 0.693116 | − | 0.720826i | \(-0.256237\pi\) |
−0.970812 | + | 0.239843i | \(0.922904\pi\) | |||||||
\(312\) | 2486.22 | − | 2250.81i | 0.451137 | − | 0.408421i | ||||
\(313\) | −2190.26 | + | 3793.65i | −0.395531 | + | 0.685079i | −0.993169 | − | 0.116687i | \(-0.962773\pi\) |
0.597638 | + | 0.801766i | \(0.296106\pi\) | |||||||
\(314\) | 10709.5 | 1.92475 | ||||||||
\(315\) | 3581.07 | − | 1617.67i | 0.640542 | − | 0.289350i | ||||
\(316\) | −3461.70 | −0.616253 | ||||||||
\(317\) | −3453.12 | + | 5980.99i | −0.611820 | + | 1.05970i | 0.379114 | + | 0.925350i | \(0.376229\pi\) |
−0.990934 | + | 0.134353i | \(0.957105\pi\) | |||||||
\(318\) | −1261.85 | − | 406.229i | −0.222519 | − | 0.0716358i | ||||
\(319\) | 1640.39 | + | 2841.25i | 0.287914 | + | 0.498681i | ||||
\(320\) | 8638.67 | + | 14962.6i | 1.50911 | + | 2.61386i | ||||
\(321\) | −328.361 | − | 1524.53i | −0.0570945 | − | 0.265081i | ||||
\(322\) | 134.040 | − | 232.164i | 0.0231980 | − | 0.0401801i | ||||
\(323\) | −3054.96 | −0.526261 | ||||||||
\(324\) | −9166.51 | − | 1844.97i | −1.57176 | − | 0.316353i | ||||
\(325\) | 9004.16 | 1.53680 | ||||||||
\(326\) | 1305.19 | − | 2260.65i | 0.221741 | − | 0.384067i | ||||
\(327\) | −1025.06 | − | 4759.17i | −0.173351 | − | 0.804839i | ||||
\(328\) | −2342.06 | − | 4056.57i | −0.394264 | − | 0.682885i | ||||
\(329\) | −770.126 | − | 1333.90i | −0.129053 | − | 0.223526i | ||||
\(330\) | −21305.4 | − | 6858.90i | −3.55402 | − | 1.14415i | ||||
\(331\) | −2851.26 | + | 4938.52i | −0.473472 | + | 0.820078i | −0.999539 | − | 0.0303654i | \(-0.990333\pi\) |
0.526067 | + | 0.850443i | \(0.323666\pi\) | |||||||
\(332\) | 8019.85 | 1.32574 | ||||||||
\(333\) | 4831.85 | − | 2182.68i | 0.795147 | − | 0.359189i | ||||
\(334\) | 2481.54 | 0.406539 | ||||||||
\(335\) | −2188.19 | + | 3790.06i | −0.356876 | + | 0.618128i | ||||
\(336\) | 56.5518 | − | 51.1972i | 0.00918201 | − | 0.00831260i | ||||
\(337\) | −614.807 | − | 1064.88i | −0.0993788 | − | 0.172129i | 0.812049 | − | 0.583589i | \(-0.198352\pi\) |
−0.911428 | + | 0.411460i | \(0.865019\pi\) | |||||||
\(338\) | 3053.63 | + | 5289.05i | 0.491408 | + | 0.851143i | ||||
\(339\) | 5372.08 | − | 4863.42i | 0.860683 | − | 0.779188i | ||||
\(340\) | 13074.3 | − | 22645.3i | 2.08544 | − | 3.61209i | ||||
\(341\) | −1400.99 | −0.222486 | ||||||||
\(342\) | 380.610 | − | 3819.95i | 0.0601784 | − | 0.603974i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −2608.60 | + | 4518.23i | −0.408856 | + | 0.708159i | ||||
\(345\) | −862.987 | − | 277.823i | −0.134671 | − | 0.0433550i | ||||
\(346\) | −4642.19 | − | 8040.50i | −0.721288 | − | 1.24931i | ||||
\(347\) | −2192.74 | − | 3797.94i | −0.339229 | − | 0.587562i | 0.645059 | − | 0.764133i | \(-0.276833\pi\) |
−0.984288 | + | 0.176571i | \(0.943500\pi\) | |||||||
\(348\) | −1014.12 | − | 4708.37i | −0.156213 | − | 0.725274i | ||||
\(349\) | −1460.02 | + | 2528.82i | −0.223934 | + | 0.387865i | −0.955999 | − | 0.293370i | \(-0.905223\pi\) |
0.732065 | + | 0.681235i | \(0.238557\pi\) | |||||||
\(350\) | −9815.59 | −1.49904 | ||||||||
\(351\) | −1641.67 | + | 3769.28i | −0.249646 | + | 0.573188i | ||||
\(352\) | −8433.73 | −1.27704 | ||||||||
\(353\) | −5565.95 | + | 9640.52i | −0.839223 | + | 1.45358i | 0.0513214 | + | 0.998682i | \(0.483657\pi\) |
−0.890545 | + | 0.454895i | \(0.849677\pi\) | |||||||
\(354\) | −3268.64 | − | 15175.8i | −0.490753 | − | 2.27849i | ||||
\(355\) | 5699.35 | + | 9871.56i | 0.852084 | + | 1.47585i | ||||
\(356\) | −10297.1 | − | 17835.2i | −1.53300 | − | 2.65523i | ||||
\(357\) | −3394.99 | − | 1092.95i | −0.503310 | − | 0.162032i | ||||
\(358\) | 2124.84 | − | 3680.34i | 0.313691 | − | 0.543329i | ||||
\(359\) | 7640.81 | 1.12330 | 0.561652 | − | 0.827373i | \(-0.310166\pi\) | ||||
0.561652 | + | 0.827373i | \(0.310166\pi\) | |||||||
\(360\) | 10041.7 | + | 7213.08i | 1.47013 | + | 1.05601i | ||||
\(361\) | −5888.34 | −0.858484 | ||||||||
\(362\) | −2288.04 | + | 3963.00i | −0.332201 | + | 0.575389i | ||||
\(363\) | 2812.12 | − | 2545.85i | 0.406606 | − | 0.368106i | ||||
\(364\) | 1315.52 | + | 2278.55i | 0.189429 | + | 0.328100i | ||||
\(365\) | 2774.43 | + | 4805.45i | 0.397864 | + | 0.689121i | ||||
\(366\) | 6131.34 | − | 5550.78i | 0.875656 | − | 0.792744i | ||||
\(367\) | −2204.25 | + | 3817.87i | −0.313518 | + | 0.543028i | −0.979121 | − | 0.203277i | \(-0.934841\pi\) |
0.665604 | + | 0.746305i | \(0.268174\pi\) | |||||||
\(368\) | −17.6001 | −0.00249312 | ||||||||
\(369\) | 4663.70 | + | 3349.98i | 0.657948 | + | 0.472610i | ||||
\(370\) | −18631.8 | −2.61789 | ||||||||
\(371\) | 195.660 | − | 338.893i | 0.0273804 | − | 0.0474243i | ||||
\(372\) | 1957.77 | + | 630.267i | 0.272864 | + | 0.0878436i | ||||
\(373\) | −2302.17 | − | 3987.47i | −0.319575 | − | 0.553521i | 0.660824 | − | 0.750541i | \(-0.270207\pi\) |
−0.980399 | + | 0.197020i | \(0.936874\pi\) | |||||||
\(374\) | 10157.6 | + | 17593.4i | 1.40437 | + | 2.43244i | ||||
\(375\) | 4146.00 | + | 19249.2i | 0.570930 | + | 2.65073i | ||||
\(376\) | 2423.15 | − | 4197.01i | 0.332352 | − | 0.575650i | ||||
\(377\) | −2117.71 | −0.289304 | ||||||||
\(378\) | 1789.61 | − | 4108.96i | 0.243513 | − | 0.559106i | ||||
\(379\) | 14679.5 | 1.98954 | 0.994770 | − | 0.102143i | \(-0.0325700\pi\) | ||||
0.994770 | + | 0.102143i | \(0.0325700\pi\) | |||||||
\(380\) | −4154.11 | + | 7195.13i | −0.560793 | + | 0.971321i | ||||
\(381\) | −2611.98 | − | 12127.0i | −0.351223 | − | 1.63067i | ||||
\(382\) | 8769.10 | + | 15188.5i | 1.17452 | + | 2.03433i | ||||
\(383\) | −911.873 | − | 1579.41i | −0.121657 | − | 0.210716i | 0.798764 | − | 0.601644i | \(-0.205487\pi\) |
−0.920421 | + | 0.390928i | \(0.872154\pi\) | |||||||
\(384\) | 11406.7 | + | 3672.18i | 1.51588 | + | 0.488009i | ||||
\(385\) | 3303.58 | − | 5721.97i | 0.437314 | − | 0.757451i | ||||
\(386\) | −15817.8 | −2.08577 | ||||||||
\(387\) | 634.108 | − | 6364.16i | 0.0832908 | − | 0.835939i | ||||
\(388\) | −3733.71 | −0.488532 | ||||||||
\(389\) | −4306.80 | + | 7459.59i | −0.561345 | + | 0.972278i | 0.436035 | + | 0.899930i | \(0.356383\pi\) |
−0.997379 | + | 0.0723480i | \(0.976951\pi\) | |||||||
\(390\) | 10710.4 | − | 9696.27i | 1.39062 | − | 1.25895i | ||||
\(391\) | 411.437 | + | 712.629i | 0.0532155 | + | 0.0921719i | ||||
\(392\) | −539.612 | − | 934.636i | −0.0695269 | − | 0.120424i | ||||
\(393\) | 8166.36 | − | 7393.12i | 1.04819 | − | 0.948941i | ||||
\(394\) | 8424.34 | − | 14591.4i | 1.07719 | − | 1.86575i | ||||
\(395\) | −5611.32 | −0.714775 | ||||||||
\(396\) | −14327.9 | + | 6472.29i | −1.81819 | + | 0.821325i | ||||
\(397\) | −5497.04 | −0.694933 | −0.347467 | − | 0.937692i | \(-0.612958\pi\) | ||||
−0.347467 | + | 0.937692i | \(0.612958\pi\) | |||||||
\(398\) | 1099.33 | − | 1904.09i | 0.138453 | − | 0.239808i | ||||
\(399\) | 1078.70 | + | 347.267i | 0.135344 | + | 0.0435716i | ||||
\(400\) | 322.208 | + | 558.081i | 0.0402760 | + | 0.0697602i | ||||
\(401\) | 4310.52 | + | 7466.04i | 0.536801 | + | 0.929767i | 0.999074 | + | 0.0430288i | \(0.0137007\pi\) |
−0.462273 | + | 0.886738i | \(0.652966\pi\) | |||||||
\(402\) | 1050.99 | + | 4879.56i | 0.130394 | + | 0.605398i | ||||
\(403\) | 452.161 | − | 783.165i | 0.0558902 | − | 0.0968046i | ||||
\(404\) | −18631.6 | −2.29445 | ||||||||
\(405\) | −14858.6 | − | 2990.64i | −1.82304 | − | 0.366929i | ||||
\(406\) | 2308.55 | 0.282196 | ||||||||
\(407\) | 4457.44 | − | 7720.51i | 0.542867 | − | 0.940274i | ||||
\(408\) | −2362.87 | − | 10970.4i | −0.286714 | − | 1.33117i | ||||
\(409\) | −4699.45 | − | 8139.69i | −0.568149 | − | 0.984063i | −0.996749 | − | 0.0805684i | \(-0.974326\pi\) |
0.428600 | − | 0.903494i | \(-0.359007\pi\) | |||||||
\(410\) | −10089.3 | − | 17475.3i | −1.21531 | − | 2.10498i | ||||
\(411\) | 325.960 | + | 104.937i | 0.0391202 | + | 0.0125940i | ||||
\(412\) | 360.854 | − | 625.018i | 0.0431505 | − | 0.0747389i | ||||
\(413\) | 4582.57 | 0.545989 | ||||||||
\(414\) | −942.338 | + | 425.680i | −0.111868 | + | 0.0505338i | ||||
\(415\) | 13000.0 | 1.53769 | ||||||||
\(416\) | 2721.94 | − | 4714.53i | 0.320803 | − | 0.555646i | ||||
\(417\) | −7562.71 | + | 6846.63i | −0.888124 | + | 0.804031i | ||||
\(418\) | −3227.38 | − | 5589.99i | −0.377647 | − | 0.654104i | ||||
\(419\) | 297.363 | + | 515.048i | 0.0346710 | + | 0.0600519i | 0.882840 | − | 0.469673i | \(-0.155628\pi\) |
−0.848169 | + | 0.529725i | \(0.822295\pi\) | |||||||
\(420\) | −7190.64 | + | 6509.79i | −0.835398 | + | 0.756298i | ||||
\(421\) | −1558.89 | + | 2700.07i | −0.180464 | + | 0.312574i | −0.942039 | − | 0.335504i | \(-0.891093\pi\) |
0.761574 | + | 0.648078i | \(0.224427\pi\) | |||||||
\(422\) | 5247.13 | 0.605276 | ||||||||
\(423\) | −589.027 | + | 5911.70i | −0.0677056 | + | 0.679520i | ||||
\(424\) | 1231.26 | 0.141026 | ||||||||
\(425\) | 15064.5 | − | 26092.5i | 1.71938 | − | 2.97805i | ||||
\(426\) | 12375.2 | + | 3983.98i | 1.40747 | + | 0.453109i | ||||
\(427\) | 1220.74 | + | 2114.38i | 0.138351 | + | 0.239630i | ||||
\(428\) | 1924.73 | + | 3333.73i | 0.217373 | + | 0.376500i | ||||
\(429\) | 1455.54 | + | 6757.82i | 0.163809 | + | 0.760538i | ||||
\(430\) | −11237.6 | + | 19464.1i | −1.26029 | + | 2.18288i | ||||
\(431\) | −8465.93 | −0.946148 | −0.473074 | − | 0.881023i | \(-0.656856\pi\) | ||||
−0.473074 | + | 0.881023i | \(0.656856\pi\) | |||||||
\(432\) | −292.367 | + | 33.1300i | −0.0325614 | + | 0.00368974i | ||||
\(433\) | 5368.98 | 0.595881 | 0.297941 | − | 0.954584i | \(-0.403700\pi\) | ||||
0.297941 | + | 0.954584i | \(0.403700\pi\) | |||||||
\(434\) | −492.909 | + | 853.743i | −0.0545170 | + | 0.0944262i | ||||
\(435\) | −1643.85 | − | 7632.14i | −0.181188 | − | 0.841225i | ||||
\(436\) | 6008.50 | + | 10407.0i | 0.659988 | + | 1.14313i | ||||
\(437\) | −130.727 | − | 226.425i | −0.0143101 | − | 0.0247858i | ||||
\(438\) | 6024.24 | + | 1939.40i | 0.657191 | + | 0.211571i | ||||
\(439\) | 8896.36 | − | 15408.9i | 0.967198 | − | 1.67524i | 0.263609 | − | 0.964630i | \(-0.415087\pi\) |
0.703589 | − | 0.710607i | \(-0.251580\pi\) | |||||||
\(440\) | 20788.9 | 2.25244 | ||||||||
\(441\) | 1074.52 | + | 771.838i | 0.116026 | + | 0.0833428i | ||||
\(442\) | −13113.2 | −1.41115 | ||||||||
\(443\) | −4431.80 | + | 7676.10i | −0.475307 | + | 0.823256i | −0.999600 | − | 0.0282821i | \(-0.990996\pi\) |
0.524293 | + | 0.851538i | \(0.324330\pi\) | |||||||
\(444\) | −9702.15 | + | 8783.49i | −1.03703 | + | 0.938842i | ||||
\(445\) | −16691.4 | − | 28910.3i | −1.77808 | − | 3.07973i | ||||
\(446\) | 4599.99 | + | 7967.41i | 0.488376 | + | 0.845892i | ||||
\(447\) | −10145.7 | + | 9185.01i | −1.07354 | + | 0.971893i | ||||
\(448\) | −2908.51 | + | 5037.68i | −0.306728 | + | 0.531268i | ||||
\(449\) | 114.115 | 0.0119943 | 0.00599714 | − | 0.999982i | \(-0.498091\pi\) | ||||
0.00599714 | + | 0.999982i | \(0.498091\pi\) | |||||||
\(450\) | 30749.5 | + | 22087.6i | 3.22121 | + | 2.31382i | ||||
\(451\) | 9655.04 | 1.00807 | ||||||||
\(452\) | −8943.71 | + | 15491.0i | −0.930701 | + | 1.61202i | ||||
\(453\) | 3647.66 | + | 1174.30i | 0.378327 | + | 0.121795i | ||||
\(454\) | −6941.66 | − | 12023.3i | −0.717595 | − | 1.24291i | ||||
\(455\) | 2132.42 | + | 3693.46i | 0.219713 | + | 0.380554i | ||||
\(456\) | 750.758 | + | 3485.65i | 0.0770997 | + | 0.357961i | ||||
\(457\) | −4031.28 | + | 6982.39i | −0.412638 | + | 0.714710i | −0.995177 | − | 0.0980929i | \(-0.968726\pi\) |
0.582540 | + | 0.812802i | \(0.302059\pi\) | |||||||
\(458\) | 18625.5 | 1.90025 | ||||||||
\(459\) | 8176.10 | + | 11063.5i | 0.831433 | + | 1.12505i | ||||
\(460\) | 2237.87 | 0.226829 | ||||||||
\(461\) | −2064.94 | + | 3576.57i | −0.208620 | + | 0.361340i | −0.951280 | − | 0.308329i | \(-0.900230\pi\) |
0.742660 | + | 0.669668i | \(0.233564\pi\) | |||||||
\(462\) | −1586.71 | − | 7366.83i | −0.159784 | − | 0.741852i | ||||
\(463\) | −5909.24 | − | 10235.1i | −0.593144 | − | 1.02736i | −0.993806 | − | 0.111130i | \(-0.964553\pi\) |
0.400662 | − | 0.916226i | \(-0.368780\pi\) | |||||||
\(464\) | −75.7810 | − | 131.256i | −0.00758199 | − | 0.0131324i | ||||
\(465\) | 3173.48 | + | 1021.64i | 0.316488 | + | 0.101887i | ||||
\(466\) | −6086.83 | + | 10542.7i | −0.605079 | + | 1.04803i | ||||
\(467\) | 1590.26 | 0.157577 | 0.0787884 | − | 0.996891i | \(-0.474895\pi\) | ||||
0.0787884 | + | 0.996891i | \(0.474895\pi\) | |||||||
\(468\) | 1006.17 | − | 10098.3i | 0.0993807 | − | 0.997424i | ||||
\(469\) | −1473.46 | −0.145070 | ||||||||
\(470\) | 10438.7 | − | 18080.3i | 1.02447 | − | 1.77443i | ||||
\(471\) | 9039.76 | − | 8183.82i | 0.884353 | − | 0.800617i | ||||
\(472\) | 7209.35 | + | 12487.0i | 0.703045 | + | 1.21771i | ||||
\(473\) | −5376.93 | − | 9313.11i | −0.522688 | − | 0.905322i | ||||
\(474\) | −4744.50 | + | 4295.26i | −0.459751 | + | 0.416219i | ||||
\(475\) | −4786.48 | + | 8290.42i | −0.462355 | + | 0.800822i | ||||
\(476\) | 8803.79 | 0.847734 | ||||||||
\(477\) | −1375.54 | + | 621.369i | −0.132037 | + | 0.0596447i | ||||
\(478\) | −27256.6 | −2.60813 | ||||||||
\(479\) | −6567.28 | + | 11374.9i | −0.626444 | + | 1.08503i | 0.361816 | + | 0.932249i | \(0.382157\pi\) |
−0.988260 | + | 0.152783i | \(0.951177\pi\) | |||||||
\(480\) | 19103.8 | + | 6150.13i | 1.81660 | + | 0.584821i | ||||
\(481\) | 2877.22 | + | 4983.50i | 0.272744 | + | 0.472407i | ||||
\(482\) | 6026.80 | + | 10438.7i | 0.569529 | + | 0.986453i | ||||
\(483\) | −64.2703 | − | 298.397i | −0.00605466 | − | 0.0281108i | ||||
\(484\) | −4681.76 | + | 8109.04i | −0.439684 | + | 0.761555i | ||||
\(485\) | −6052.23 | −0.566635 | ||||||||
\(486\) | −14852.6 | + | 8845.09i | −1.38627 | + | 0.825559i | ||||
\(487\) | −18337.9 | −1.70631 | −0.853153 | − | 0.521661i | \(-0.825313\pi\) | ||||
−0.853153 | + | 0.521661i | \(0.825313\pi\) | |||||||
\(488\) | −3840.97 | + | 6652.75i | −0.356296 | + | 0.617122i | ||||
\(489\) | −625.819 | − | 2905.58i | −0.0578743 | − | 0.268701i | ||||
\(490\) | −2324.59 | − | 4026.31i | −0.214315 | − | 0.371204i | ||||
\(491\) | 4048.59 | + | 7012.36i | 0.372119 | + | 0.644528i | 0.989891 | − | 0.141828i | \(-0.0452981\pi\) |
−0.617773 | + | 0.786357i | \(0.711965\pi\) | |||||||
\(492\) | −13492.1 | − | 4343.54i | −1.23632 | − | 0.398012i | ||||
\(493\) | −3543.06 | + | 6136.76i | −0.323674 | + | 0.560620i | ||||
\(494\) | 4166.47 | 0.379471 | ||||||||
\(495\) | −23225.1 | + | 10491.4i | −2.10887 | + | 0.952632i | ||||
\(496\) | 64.7212 | 0.00585901 | ||||||||
\(497\) | −1918.88 | + | 3323.60i | −0.173186 | + | 0.299968i | ||||
\(498\) | 10991.8 | − | 9950.99i | 0.989061 | − | 0.895411i | ||||
\(499\) | 301.177 | + | 521.655i | 0.0270191 | + | 0.0467985i | 0.879219 | − | 0.476418i | \(-0.158065\pi\) |
−0.852200 | + | 0.523217i | \(0.824732\pi\) | |||||||
\(500\) | −24302.3 | − | 42092.9i | −2.17367 | − | 3.76490i | ||||
\(501\) | 2094.65 | − | 1896.32i | 0.186790 | − | 0.169104i | ||||
\(502\) | 15975.2 | − | 27669.8i | 1.42033 | − | 2.46009i | ||||
\(503\) | 11416.3 | 1.01198 | 0.505992 | − | 0.862538i | \(-0.331126\pi\) | ||||
0.505992 | + | 0.862538i | \(0.331126\pi\) | |||||||
\(504\) | −412.719 | + | 4142.21i | −0.0364761 | + | 0.366089i | ||||
\(505\) | −30201.3 | −2.66126 | ||||||||
\(506\) | −869.317 | + | 1505.70i | −0.0763752 | + | 0.132286i | ||||
\(507\) | 6619.26 | + | 2130.95i | 0.579826 | + | 0.186664i | ||||
\(508\) | 15310.5 | + | 26518.5i | 1.33719 | + | 2.31608i | ||||
\(509\) | −6406.07 | − | 11095.6i | −0.557847 | − | 0.966220i | −0.997676 | − | 0.0681380i | \(-0.978294\pi\) |
0.439829 | − | 0.898082i | \(-0.355039\pi\) | |||||||
\(510\) | −10179.0 | − | 47259.3i | −0.883789 | − | 4.10329i | ||||
\(511\) | −934.108 | + | 1617.92i | −0.0808659 | + | 0.140064i | ||||
\(512\) | 759.150 | 0.0655273 | ||||||||
\(513\) | −2597.81 | − | 3515.23i | −0.223579 | − | 0.302536i | ||||
\(514\) | 26412.7 | 2.26656 | ||||||||
\(515\) | 584.935 | − | 1013.14i | 0.0500491 | − | 0.0866876i | ||||
\(516\) | 3324.09 | + | 15433.2i | 0.283595 | + | 1.31669i | ||||
\(517\) | 4994.66 | + | 8651.00i | 0.424884 | + | 0.735920i | ||||
\(518\) | −3136.51 | − | 5432.60i | −0.266043 | − | 0.460801i | ||||
\(519\) | −10062.7 | − | 3239.51i | −0.851068 | − | 0.273986i | ||||
\(520\) | −6709.51 | + | 11621.2i | −0.565830 | + | 0.980046i | ||||
\(521\) | 3033.32 | 0.255071 | 0.127536 | − | 0.991834i | \(-0.459293\pi\) | ||||
0.127536 | + | 0.991834i | \(0.459293\pi\) | |||||||
\(522\) | −7232.04 | − | 5194.84i | −0.606394 | − | 0.435578i | ||||
\(523\) | 12789.3 | 1.06928 | 0.534642 | − | 0.845078i | \(-0.320446\pi\) | ||||
0.534642 | + | 0.845078i | \(0.320446\pi\) | |||||||
\(524\) | −13595.8 | + | 23548.6i | −1.13346 | + | 1.96321i | ||||
\(525\) | −8285.25 | + | 7500.76i | −0.688758 | + | 0.623543i | ||||
\(526\) | 17082.9 | + | 29588.5i | 1.41607 | + | 2.45270i | ||||
\(527\) | −1512.99 | − | 2620.57i | −0.125060 | − | 0.216611i | ||||
\(528\) | −366.767 | + | 332.039i | −0.0302301 | + | 0.0273677i | ||||
\(529\) | 6048.29 | − | 10475.9i | 0.497106 | − | 0.861013i | ||||
\(530\) | 5304.13 | 0.434711 | ||||||||
\(531\) | −14355.9 | − | 10312.0i | −1.17324 | − | 0.842751i | ||||
\(532\) | −2797.25 | −0.227962 | ||||||||
\(533\) | −3116.11 | + | 5397.25i | −0.253234 | + | 0.438614i | ||||
\(534\) | −36242.7 | − | 11667.7i | −2.93703 | − | 0.945523i | ||||
\(535\) | 3119.94 | + | 5403.89i | 0.252124 | + | 0.436692i | ||||
\(536\) | −2318.06 | − | 4015.01i | −0.186801 | − | 0.323548i | ||||
\(537\) | −1018.83 | − | 4730.28i | −0.0818731 | − | 0.380124i | ||||
\(538\) | 7414.49 | − | 12842.3i | 0.594166 | − | 1.02913i | ||||
\(539\) | 2224.53 | 0.177768 | ||||||||
\(540\) | 37174.9 | − | 4212.52i | 2.96251 | − | 0.335700i | ||||
\(541\) | 3836.05 | 0.304851 | 0.152426 | − | 0.988315i | \(-0.451292\pi\) | ||||
0.152426 | + | 0.988315i | \(0.451292\pi\) | |||||||
\(542\) | 9004.66 | − | 15596.5i | 0.713622 | − | 1.23603i | ||||
\(543\) | 1097.08 | + | 5093.58i | 0.0867041 | + | 0.402553i | ||||
\(544\) | −9107.93 | − | 15775.4i | −0.717830 | − | 1.24332i | ||||
\(545\) | 9739.60 | + | 16869.5i | 0.765502 | + | 1.32589i | ||||
\(546\) | 4630.22 | + | 1490.62i | 0.362922 | + | 0.116836i | ||||
\(547\) | −2438.27 | + | 4223.20i | −0.190590 | + | 0.330112i | −0.945446 | − | 0.325779i | \(-0.894373\pi\) |
0.754856 | + | 0.655891i | \(0.227707\pi\) | |||||||
\(548\) | −845.271 | −0.0658908 | ||||||||
\(549\) | 933.676 | − | 9370.73i | 0.0725834 | − | 0.728476i | ||||
\(550\) | 63659.1 | 4.93533 | ||||||||
\(551\) | 1125.74 | − | 1949.84i | 0.0870386 | − | 0.150755i | ||||
\(552\) | 711.986 | − | 644.571i | 0.0548988 | − | 0.0497006i | ||||
\(553\) | −944.622 | − | 1636.13i | −0.0726391 | − | 0.125815i | ||||
\(554\) | −10620.1 | − | 18394.5i | −0.814445 | − | 1.41066i | ||||
\(555\) | −15726.9 | + | 14237.8i | −1.20283 | + | 1.08894i | ||||
\(556\) | 12590.8 | − | 21807.9i | 0.960374 | − | 1.66342i | ||||
\(557\) | 26004.6 | 1.97819 | 0.989095 | − | 0.147276i | \(-0.0470506\pi\) | ||||
0.989095 | + | 0.147276i | \(0.0470506\pi\) | |||||||
\(558\) | 3465.28 | − | 1565.36i | 0.262898 | − | 0.118758i | ||||
\(559\) | 6941.48 | 0.525212 | ||||||||
\(560\) | −152.615 | + | 264.337i | −0.0115163 | + | 0.0199469i | ||||
\(561\) | 22018.2 | + | 7088.36i | 1.65706 | + | 0.533460i | ||||
\(562\) | −14710.4 | − | 25479.2i | −1.10413 | − | 1.91241i | ||||
\(563\) | −7675.11 | − | 13293.7i | −0.574542 | − | 0.995137i | −0.996091 | − | 0.0883309i | \(-0.971847\pi\) |
0.421549 | − | 0.906806i | \(-0.361487\pi\) | |||||||
\(564\) | −3087.77 | − | 14336.0i | −0.230529 | − | 1.07031i | ||||
\(565\) | −14497.5 | + | 25110.4i | −1.07949 | + | 1.86974i | ||||
\(566\) | −16604.4 | −1.23310 | ||||||||
\(567\) | −1629.33 | − | 4835.90i | −0.120680 | − | 0.358181i | ||||
\(568\) | −12075.2 | −0.892017 | ||||||||
\(569\) | 10436.7 | − | 18077.0i | 0.768947 | − | 1.33186i | −0.169187 | − | 0.985584i | \(-0.554114\pi\) |
0.938134 | − | 0.346272i | \(-0.112552\pi\) | |||||||
\(570\) | 3234.18 | + | 15015.8i | 0.237658 | + | 1.10341i | ||||
\(571\) | 3.53471 | + | 6.12229i | 0.000259059 | + | 0.000448704i | 0.866155 | − | 0.499776i | \(-0.166584\pi\) |
−0.865896 | + | 0.500224i | \(0.833251\pi\) | |||||||
\(572\) | −8531.82 | − | 14777.5i | −0.623660 | − | 1.08021i | ||||
\(573\) | 19008.5 | + | 6119.44i | 1.38585 | + | 0.446149i | ||||
\(574\) | 3396.92 | − | 5883.64i | 0.247012 | − | 0.427837i | ||||
\(575\) | 2578.54 | 0.187013 | ||||||||
\(576\) | 20447.6 | − | 9236.73i | 1.47914 | − | 0.668166i | ||||
\(577\) | −13121.5 | −0.946715 | −0.473357 | − | 0.880870i | \(-0.656958\pi\) | ||||
−0.473357 | + | 0.880870i | \(0.656958\pi\) | |||||||
\(578\) | −10728.7 | + | 18582.7i | −0.772068 | + | 1.33726i | ||||
\(579\) | −13351.7 | + | 12087.5i | −0.958337 | + | 0.867596i | ||||
\(580\) | 9635.65 | + | 16689.4i | 0.689825 | + | 1.19481i | ||||
\(581\) | 2188.44 | + | 3790.49i | 0.156268 | + | 0.270664i | ||||
\(582\) | −5117.30 | + | 4632.76i | −0.364466 | + | 0.329956i | ||||
\(583\) | −1268.95 | + | 2197.89i | −0.0901452 | + | 0.156136i | ||||
\(584\) | −5878.20 | −0.416510 | ||||||||
\(585\) | 1630.97 | − | 16369.1i | 0.115269 | − | 1.15688i | ||||
\(586\) | 28875.9 | 2.03558 | ||||||||
\(587\) | 1918.15 | − | 3322.34i | 0.134873 | − | 0.233607i | −0.790676 | − | 0.612235i | \(-0.790271\pi\) |
0.925549 | + | 0.378628i | \(0.123604\pi\) | |||||||
\(588\) | −3108.59 | − | 1000.75i | −0.218021 | − | 0.0701878i | ||||
\(589\) | 480.724 | + | 832.638i | 0.0336297 | + | 0.0582483i | ||||
\(590\) | 31057.1 | + | 53792.5i | 2.16712 | + | 3.75357i | ||||
\(591\) | −4039.35 | − | 18754.1i | −0.281145 | − | 1.30531i | ||||
\(592\) | −205.919 | + | 356.663i | −0.0142960 | + | 0.0247614i | ||||
\(593\) | 2999.00 | 0.207680 | 0.103840 | − | 0.994594i | \(-0.466887\pi\) | ||||
0.103840 | + | 0.994594i | \(0.466887\pi\) | |||||||
\(594\) | −11606.5 | + | 26648.7i | −0.801721 | + | 1.84075i | ||||
\(595\) | 14270.7 | 0.983263 | ||||||||
\(596\) | 16891.0 | − | 29256.1i | 1.16088 | − | 2.01070i | ||||
\(597\) | −527.112 | − | 2447.30i | −0.0361361 | − | 0.167774i | ||||
\(598\) | −561.134 | − | 971.913i | −0.0383720 | − | 0.0664623i | ||||
\(599\) | −4181.01 | − | 7241.73i | −0.285195 | − | 0.493972i | 0.687462 | − | 0.726221i | \(-0.258725\pi\) |
−0.972656 | + | 0.232249i | \(0.925392\pi\) | |||||||
\(600\) | −33473.2 | − | 10776.1i | −2.27756 | − | 0.733219i | ||||
\(601\) | 7265.07 | − | 12583.5i | 0.493092 | − | 0.854061i | −0.506876 | − | 0.862019i | \(-0.669200\pi\) |
0.999968 | + | 0.00795794i | \(0.00253312\pi\) | |||||||
\(602\) | −7567.04 | −0.512308 | ||||||||
\(603\) | 4615.92 | + | 3315.66i | 0.311733 | + | 0.223921i | ||||
\(604\) | −9459.02 | −0.637222 | ||||||||
\(605\) | −7588.99 | + | 13144.5i | −0.509977 | + | 0.883307i | ||||
\(606\) | −25535.9 | + | 23118.0i | −1.71175 | + | 1.54968i | ||||
\(607\) | 6504.64 | + | 11266.4i | 0.434951 | + | 0.753357i | 0.997292 | − | 0.0735487i | \(-0.0234324\pi\) |
−0.562341 | + | 0.826906i | \(0.690099\pi\) | |||||||
\(608\) | 2893.88 | + | 5012.35i | 0.193030 | + | 0.334338i | ||||
\(609\) | 1948.63 | − | 1764.12i | 0.129659 | − | 0.117382i | ||||
\(610\) | −16546.5 | + | 28659.3i | −1.09827 | + | 1.90227i | ||||
\(611\) | −6447.98 | −0.426935 | ||||||||
\(612\) | −27579.8 | − | 19810.8i | −1.82164 | − | 1.30850i | ||||
\(613\) | 3740.67 | 0.246467 | 0.123233 | − | 0.992378i | \(-0.460674\pi\) | ||||
0.123233 | + | 0.992378i | \(0.460674\pi\) | |||||||
\(614\) | −6190.03 | + | 10721.5i | −0.406856 | + | 0.704695i | ||||
\(615\) | −21870.3 | − | 7040.75i | −1.43398 | − | 0.461643i | ||||
\(616\) | 3499.66 | + | 6061.58i | 0.228905 | + | 0.396474i | ||||
\(617\) | −11342.8 | − | 19646.3i | −0.740104 | − | 1.28190i | −0.952448 | − | 0.304703i | \(-0.901443\pi\) |
0.212344 | − | 0.977195i | \(-0.431890\pi\) | |||||||
\(618\) | −280.944 | − | 1304.38i | −0.0182867 | − | 0.0849024i | ||||
\(619\) | 594.523 | − | 1029.74i | 0.0386040 | − | 0.0668641i | −0.846078 | − | 0.533059i | \(-0.821042\pi\) |
0.884682 | + | 0.466195i | \(0.154376\pi\) | |||||||
\(620\) | −8229.39 | −0.533065 | ||||||||
\(621\) | −470.128 | + | 1079.42i | −0.0303794 | + | 0.0697512i | ||||
\(622\) | 13901.0 | 0.896107 | ||||||||
\(623\) | 5619.72 | − | 9733.64i | 0.361395 | − | 0.625955i | ||||
\(624\) | −67.2412 | − | 312.190i | −0.00431378 | − | 0.0200282i | ||||
\(625\) | −20189.3 | − | 34968.9i | −1.29212 | − | 2.23801i | ||||
\(626\) | −9995.45 | − | 17312.6i | −0.638176 | − | 1.10535i | ||||
\(627\) | −6995.89 | − | 2252.20i | −0.445596 | − | 0.143452i | ||||
\(628\) | −15049.8 | + | 26067.1i | −0.956296 | + | 1.65635i | ||||
\(629\) | 19255.1 | 1.22059 | ||||||||
\(630\) | −1777.95 | + | 17844.2i | −0.112437 | + | 1.12846i | ||||
\(631\) | 23574.4 | 1.48729 | 0.743646 | − | 0.668574i | \(-0.233095\pi\) | ||||
0.743646 | + | 0.668574i | \(0.233095\pi\) | |||||||
\(632\) | 2972.18 | − | 5147.97i | 0.187068 | − | 0.324012i | ||||
\(633\) | 4429.05 | − | 4009.69i | 0.278103 | − | 0.251770i | ||||
\(634\) | −15758.6 | − | 27294.7i | −0.987152 | − | 1.70980i | ||||
\(635\) | 24817.8 | + | 42985.8i | 1.55097 | + | 2.68636i | ||||
\(636\) | 2762.03 | − | 2500.50i | 0.172204 | − | 0.155898i | ||||
\(637\) | −717.953 | + | 1243.53i | −0.0446567 | + | 0.0773477i | ||||
\(638\) | −14972.1 | −0.929079 | ||||||||
\(639\) | 13490.3 | − | 6093.91i | 0.835159 | − | 0.377264i | ||||
\(640\) | −47947.7 | −2.96140 | ||||||||
\(641\) | 6996.33 | − | 12118.0i | 0.431105 | − | 0.746696i | −0.565863 | − | 0.824499i | \(-0.691457\pi\) |
0.996969 | + | 0.0778026i | \(0.0247904\pi\) | |||||||
\(642\) | 6774.45 | + | 2180.91i | 0.416459 | + | 0.134071i | ||||
\(643\) | −5948.33 | − | 10302.8i | −0.364820 | − | 0.631886i | 0.623927 | − | 0.781482i | \(-0.285536\pi\) |
−0.988747 | + | 0.149596i | \(0.952203\pi\) | |||||||
\(644\) | 376.729 | + | 652.513i | 0.0230515 | + | 0.0399264i | ||||
\(645\) | 5388.26 | + | 25016.8i | 0.328934 | + | 1.52719i | ||||
\(646\) | 6970.77 | − | 12073.7i | 0.424553 | − | 0.735347i | ||||
\(647\) | −5011.63 | −0.304525 | −0.152262 | − | 0.988340i | \(-0.548656\pi\) | ||||
−0.152262 | + | 0.988340i | \(0.548656\pi\) | |||||||
\(648\) | 10614.0 | − | 12047.6i | 0.643451 | − | 0.730364i | ||||
\(649\) | −29720.3 | −1.79757 | ||||||||
\(650\) | −20545.6 | + | 35586.0i | −1.23979 | + | 2.14738i | ||||
\(651\) | 236.343 | + | 1097.30i | 0.0142289 | + | 0.0660624i | ||||
\(652\) | 3668.32 | + | 6353.72i | 0.220341 | + | 0.381642i | ||||
\(653\) | 6238.61 | + | 10805.6i | 0.373868 | + | 0.647558i | 0.990157 | − | 0.139962i | \(-0.0446981\pi\) |
−0.616289 | + | 0.787520i | \(0.711365\pi\) | |||||||
\(654\) | 21148.0 | + | 6808.22i | 1.26445 | + | 0.407068i | ||||
\(655\) | −22038.3 | + | 38171.5i | −1.31467 | + | 2.27708i | ||||
\(656\) | −446.032 | −0.0265467 | ||||||||
\(657\) | 6567.03 | − | 2966.50i | 0.389961 | − | 0.176156i | ||||
\(658\) | 7029.06 | 0.416446 | ||||||||
\(659\) | −14463.6 | + | 25051.6i | −0.854962 | + | 1.48084i | 0.0217183 | + | 0.999764i | \(0.493086\pi\) |
−0.876680 | + | 0.481073i | \(0.840247\pi\) | |||||||
\(660\) | 46634.9 | − | 42219.3i | 2.75040 | − | 2.48997i | ||||
\(661\) | 12339.9 | + | 21373.3i | 0.726121 | + | 1.25768i | 0.958511 | + | 0.285056i | \(0.0920123\pi\) |
−0.232389 | + | 0.972623i | \(0.574654\pi\) | |||||||
\(662\) | −13011.9 | − | 22537.3i | −0.763933 | − | 1.32317i | ||||
\(663\) | −11068.7 | + | 10020.7i | −0.648375 | + | 0.586983i | ||||
\(664\) | −6885.77 | + | 11926.5i | −0.402439 | + | 0.697045i | ||||
\(665\) | −4534.26 | −0.264407 | ||||||||
\(666\) | −2398.94 | + | 24076.7i | −0.139575 | + | 1.40083i | ||||
\(667\) | −606.453 | −0.0352053 | ||||||||
\(668\) | −3487.28 | + | 6040.14i | −0.201986 | + | 0.349850i | ||||
\(669\) | 9971.24 | + | 3210.06i | 0.576249 | + | 0.185513i | ||||
\(670\) | −9985.98 | − | 17296.2i | −0.575809 | − | 0.997330i | ||||
\(671\) | −7917.11 | − | 13712.8i | −0.455494 | − | 0.788939i | ||||
\(672\) | 1422.74 | + | 6605.58i | 0.0816720 | + | 0.379190i | ||||
\(673\) | 537.810 | − | 931.515i | 0.0308040 | − | 0.0533540i | −0.850212 | − | 0.526440i | \(-0.823527\pi\) |
0.881016 | + | 0.473086i | \(0.156860\pi\) | |||||||
\(674\) | 5611.44 | 0.320689 | ||||||||
\(675\) | 42833.9 | − | 4853.78i | 2.44249 | − | 0.276774i | ||||
\(676\) | −17164.9 | −0.976610 | ||||||||
\(677\) | −11518.6 | + | 19950.8i | −0.653908 | + | 1.13260i | 0.328259 | + | 0.944588i | \(0.393538\pi\) |
−0.982166 | + | 0.188013i | \(0.939795\pi\) | |||||||
\(678\) | 6963.14 | + | 32328.7i | 0.394421 | + | 1.83123i | ||||
\(679\) | −1018.85 | − | 1764.69i | −0.0575843 | − | 0.0997389i | ||||
\(680\) | 22450.8 | + | 38886.0i | 1.26610 | + | 2.19296i | ||||
\(681\) | −15047.2 | − | 4844.17i | −0.846711 | − | 0.272583i | ||||
\(682\) | 3196.76 | − | 5536.95i | 0.179487 | − | 0.310881i | ||||
\(683\) | −1233.44 | −0.0691015 | −0.0345508 | − | 0.999403i | \(-0.511000\pi\) | ||||
−0.0345508 | + | 0.999403i | \(0.511000\pi\) | |||||||
\(684\) | 8762.97 | + | 6294.52i | 0.489855 | + | 0.351867i | ||||
\(685\) | −1370.16 | −0.0764249 | ||||||||
\(686\) | 782.654 | − | 1355.60i | 0.0435596 | − | 0.0754474i | ||||
\(687\) | 15721.6 | − | 14233.0i | 0.873097 | − | 0.790427i | ||||
\(688\) | 248.397 | + | 430.236i | 0.0137646 | + | 0.0238410i | ||||
\(689\) | −819.093 | − | 1418.71i | −0.0452902 | − | 0.0784450i | ||||
\(690\) | 3067.16 | − | 2776.74i | 0.169224 | − | 0.153201i | ||||
\(691\) | 15214.0 | − | 26351.4i | 0.837578 | − | 1.45073i | −0.0543356 | − | 0.998523i | \(-0.517304\pi\) |
0.891914 | − | 0.452205i | \(-0.149363\pi\) | |||||||
\(692\) | 26094.4 | 1.43347 | ||||||||
\(693\) | −6968.81 | − | 5005.76i | −0.381996 | − | 0.274391i | ||||
\(694\) | 20013.5 | 1.09467 | ||||||||
\(695\) | 20409.3 | − | 35349.9i | 1.11391 | − | 1.92935i | ||||
\(696\) | 7872.63 | + | 2534.45i | 0.428752 | + | 0.138029i | ||||
\(697\) | 10426.9 | + | 18059.9i | 0.566637 | + | 0.981444i | ||||
\(698\) | −6662.90 | − | 11540.5i | −0.361310 | − | 0.625808i | ||||
\(699\) | 2918.55 | + | 13550.3i | 0.157925 | + | 0.733220i | ||||
\(700\) | 13793.7 | − | 23891.4i | 0.744790 | − | 1.29001i | ||||
\(701\) | 359.627 | 0.0193765 | 0.00968825 | − | 0.999953i | \(-0.496916\pi\) | ||||
0.00968825 | + | 0.999953i | \(0.496916\pi\) | |||||||
\(702\) | −11150.9 | − | 15088.9i | −0.599521 | − | 0.811242i | ||||
\(703\) | −6117.96 | −0.328226 | ||||||||
\(704\) | 18863.1 | − | 32671.9i | 1.00985 | − | 1.74910i | ||||
\(705\) | −5005.19 | − | 23238.3i | −0.267385 | − | 1.24142i | ||||
\(706\) | −25400.7 | − | 43995.3i | −1.35406 | − | 2.34530i | ||||
\(707\) | −5084.15 | − | 8806.00i | −0.270451 | − | 0.468435i | ||||
\(708\) | 41531.6 | + | 13370.3i | 2.20460 | + | 0.709729i | ||||
\(709\) | −16634.0 | + | 28810.9i | −0.881103 | + | 1.52611i | −0.0309861 | + | 0.999520i | \(0.509865\pi\) |
−0.850116 | + | 0.526595i | \(0.823469\pi\) | |||||||
\(710\) | −52018.8 | −2.74962 | ||||||||
\(711\) | −722.489 | + | 7251.18i | −0.0381089 | + | 0.382476i | ||||
\(712\) | 35364.1 | 1.86141 | ||||||||
\(713\) | 129.486 | − | 224.277i | 0.00680126 | − | 0.0117801i | ||||
\(714\) | 12066.2 | − | 10923.7i | 0.632445 | − | 0.572562i | ||||
\(715\) | −13829.8 | − | 23954.0i | −0.723366 | − | 1.25291i | ||||
\(716\) | 5972.02 | + | 10343.8i | 0.311711 | + | 0.539899i | ||||
\(717\) | −23007.0 | + | 20828.6i | −1.19834 | + | 1.08488i | ||||
\(718\) | −17434.7 | + | 30197.8i | −0.906209 | + | 1.56960i | ||||
\(719\) | −8882.66 | −0.460733 | −0.230367 | − | 0.973104i | \(-0.573993\pi\) | ||||
−0.230367 | + | 0.973104i | \(0.573993\pi\) | |||||||
\(720\) | 1072.92 | − | 484.669i | 0.0555354 | − | 0.0250869i | ||||
\(721\) | 393.877 | 0.0203450 | ||||||||
\(722\) | 13436.0 | − | 23271.8i | 0.692569 | − | 1.19956i | ||||
\(723\) | 13064.1 | + | 4205.74i | 0.672004 | + | 0.216339i | ||||
\(724\) | −6430.69 | − | 11138.3i | −0.330103 | − | 0.571756i | ||||
\(725\) | 11102.5 | + | 19230.0i | 0.568738 | + | 0.985083i | ||||
\(726\) | 3644.99 | + | 16923.1i | 0.186333 | + | 0.865116i | ||||
\(727\) | 8494.42 | − | 14712.8i | 0.433343 | − | 0.750573i | −0.563815 | − | 0.825901i | \(-0.690667\pi\) |
0.997159 | + | 0.0753280i | \(0.0240004\pi\) | |||||||
\(728\) | −4517.97 | −0.230010 | ||||||||
\(729\) | −5777.77 | + | 18815.9i | −0.293541 | + | 0.955946i | ||||
\(730\) | −25322.7 | −1.28388 | ||||||||
\(731\) | 11613.5 | − | 20115.2i | 0.587609 | − | 1.01777i | ||||
\(732\) | 4894.47 | + | 22724.2i | 0.247138 | + | 1.14742i | ||||
\(733\) | 10991.9 | + | 19038.5i | 0.553882 | + | 0.959351i | 0.997990 | + | 0.0633778i | \(0.0201873\pi\) |
−0.444108 | + | 0.895973i | \(0.646479\pi\) | |||||||
\(734\) | −10059.3 | − | 17423.2i | −0.505851 | − | 0.876159i | ||||
\(735\) | −5038.94 | − | 1622.19i | −0.252876 | − | 0.0814089i | ||||
\(736\) | 779.487 | − | 1350.11i | 0.0390384 | − | 0.0676165i | ||||
\(737\) | 9556.12 | 0.477618 | ||||||||
\(738\) | −23881.3 | + | 10787.8i | −1.19117 | + | 0.538083i | ||||
\(739\) | 18909.8 | 0.941284 | 0.470642 | − | 0.882324i | \(-0.344022\pi\) | ||||
0.470642 | + | 0.882324i | \(0.344022\pi\) | |||||||
\(740\) | 26182.9 | − | 45350.2i | 1.30068 | − | 2.25284i | ||||
\(741\) | 3516.88 | − | 3183.88i | 0.174353 | − | 0.157845i | ||||
\(742\) | 892.909 | + | 1546.56i | 0.0441775 | + | 0.0765177i | ||||
\(743\) | 5004.66 | + | 8668.33i | 0.247111 | + | 0.428008i | 0.962723 | − | 0.270489i | \(-0.0871855\pi\) |
−0.715612 | + | 0.698498i | \(0.753852\pi\) | |||||||
\(744\) | −2618.20 | + | 2370.30i | −0.129016 | + | 0.116800i | ||||
\(745\) | 27379.8 | − | 47423.2i | 1.34647 | − | 2.33215i | ||||
\(746\) | 21012.2 | 1.03125 | ||||||||
\(747\) | 1673.82 | − | 16799.1i | 0.0819836 | − | 0.822819i | ||||
\(748\) | −57097.0 | −2.79101 | ||||||||
\(749\) | −1050.43 | + | 1819.40i | −0.0512443 | + | 0.0887578i | ||||
\(750\) | −85536.6 | − | 27536.9i | −4.16447 | − | 1.34068i | ||||
\(751\) | 14626.9 | + | 25334.5i | 0.710708 | + | 1.23098i | 0.964592 | + | 0.263747i | \(0.0849585\pi\) |
−0.253884 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(752\) | −230.737 | − | 399.649i | −0.0111890 | − | 0.0193799i | ||||
\(753\) | −7659.87 | − | 35563.5i | −0.370705 | − | 1.72113i | ||||
\(754\) | 4832.17 | − | 8369.56i | 0.233391 | − | 0.404246i | ||||
\(755\) | −15332.8 | −0.739096 | ||||||||
\(756\) | 7486.38 | + | 10130.2i | 0.360155 | + | 0.487344i | ||||
\(757\) | −20805.2 | −0.998912 | −0.499456 | − | 0.866339i | \(-0.666467\pi\) | ||||
−0.499456 | + | 0.866339i | \(0.666467\pi\) | |||||||
\(758\) | −33495.5 | + | 58016.0i | −1.60503 | + | 2.77999i | ||||
\(759\) | 416.825 | + | 1935.25i | 0.0199339 | + | 0.0925497i | ||||
\(760\) | −7133.35 | − | 12355.3i | −0.340466 | − | 0.589704i | ||||
\(761\) | −5062.52 | − | 8768.54i | −0.241151 | − | 0.417687i | 0.719891 | − | 0.694087i | \(-0.244192\pi\) |
−0.961043 | + | 0.276400i | \(0.910858\pi\) | |||||||
\(762\) | 53888.1 | + | 17348.3i | 2.56189 | + | 0.824753i | ||||
\(763\) | −3279.17 | + | 5679.69i | −0.155588 | + | 0.269487i | ||||
\(764\) | −49292.3 | −2.33421 | ||||||||
\(765\) | −44706.0 | − | 32112.7i | −2.11287 | − | 1.51770i | ||||
\(766\) | 8322.81 | 0.392579 | ||||||||
\(767\) | 9592.04 | − | 16613.9i | 0.451562 | − | 0.782129i | ||||
\(768\) | −14932.2 | + | 13518.3i | −0.701587 | + | 0.635157i | ||||
\(769\) | 18632.4 | + | 32272.3i | 0.873735 | + | 1.51335i | 0.858104 | + | 0.513475i | \(0.171642\pi\) |
0.0156305 | + | 0.999878i | \(0.495024\pi\) | |||||||
\(770\) | 15076.2 | + | 26112.7i | 0.705593 | + | 1.22212i | ||||
\(771\) | 22294.7 | − | 20183.7i | 1.04140 | − | 0.942798i | ||||
\(772\) | 22228.6 | − | 38501.0i | 1.03630 | − | 1.79492i | ||||
\(773\) | 16637.3 | 0.774130 | 0.387065 | − | 0.922052i | \(-0.373489\pi\) | ||||
0.387065 | + | 0.922052i | \(0.373489\pi\) | |||||||
\(774\) | 23705.4 | + | 17027.8i | 1.10087 | + | 0.790763i | ||||
\(775\) | −9482.13 | −0.439494 | ||||||||
\(776\) | 3205.73 | − | 5552.48i | 0.148297 | − | 0.256859i | ||||
\(777\) | −6798.91 | − | 2188.79i | −0.313912 | − | 0.101058i | ||||
\(778\) | −19654.4 | − | 34042.4i | −0.905713 | − | 1.56874i | ||||
\(779\) | −3312.95 | − | 5738.20i | −0.152373 | − | 0.263918i | ||||
\(780\) | 8549.80 | + | 39695.4i | 0.392477 | + | 1.82221i | ||||
\(781\) | 12444.9 | − | 21555.2i | 0.570185 | − | 0.987589i | ||||
\(782\) | −3755.25 | −0.171723 | ||||||||
\(783\) | −10074.2 | + | 1141.57i | −0.459800 | + | 0.0521028i | ||||
\(784\) | −102.766 | −0.00468140 | ||||||||
\(785\) | −24395.4 | + | 42254.0i | −1.10918 | + | 1.92116i | ||||
\(786\) | 10585.0 | + | 49144.4i | 0.480349 | + | 2.23018i | ||||
\(787\) | −6559.92 | − | 11362.1i | −0.297123 | − | 0.514633i | 0.678353 | − | 0.734736i | \(-0.262694\pi\) |
−0.975477 | + | 0.220103i | \(0.929361\pi\) | |||||||
\(788\) | 23677.2 | + | 41010.1i | 1.07039 | + | 1.85397i | ||||
\(789\) | 37030.1 | + | 11921.2i | 1.67086 | + | 0.537902i | ||||
\(790\) | 12803.9 | − | 22176.9i | 0.576634 | − | 0.998759i | ||||
\(791\) | −9762.16 | −0.438815 | ||||||||
\(792\) | 2676.69 | − | 26864.3i | 0.120091 | − | 1.20528i | ||||
\(793\) | 10220.8 | 0.457694 | ||||||||
\(794\) | 12543.1 | − | 21725.3i | 0.560626 | − | 0.971033i | ||||
\(795\) | 4477.16 | − | 4053.24i | 0.199734 | − | 0.180822i | ||||
\(796\) | 3089.74 | + | 5351.58i | 0.137579 | + | 0.238294i | ||||
\(797\) | 191.253 | + | 331.260i | 0.00850004 | + | 0.0147225i | 0.870244 | − | 0.492621i | \(-0.163961\pi\) |
−0.861744 | + | 0.507343i | \(0.830628\pi\) | |||||||
\(798\) | −3833.82 | + | 3470.81i | −0.170070 | + | 0.153966i | ||||
\(799\) | −10787.9 | + | 18685.1i | −0.477657 | + | 0.827325i | ||||
\(800\) | −57080.9 | −2.52264 | ||||||||
\(801\) | −39508.2 | + | 17846.9i | −1.74276 | + | 0.787252i | ||||
\(802\) | −39342.8 | −1.73222 | ||||||||
\(803\) | 6058.16 | − | 10493.0i | 0.266236 | − | 0.461135i | ||||
\(804\) | −13353.9 | − | 4299.04i | −0.585766 | − | 0.188576i | ||||
\(805\) | 610.666 | + | 1057.71i | 0.0267368 | + | 0.0463096i | ||||
\(806\) | 2063.47 | + | 3574.04i | 0.0901770 | + | 0.156191i | ||||
\(807\) | −3555.14 | − | 16506.0i | −0.155077 | − | 0.719997i | ||||
\(808\) | 15996.9 | − | 27707.4i | 0.696496 | − | 1.20637i | ||||
\(809\) | 2590.19 | 0.112566 | 0.0562831 | − | 0.998415i | \(-0.482075\pi\) | ||||
0.0562831 | + | 0.998415i | \(0.482075\pi\) | |||||||
\(810\) | 45723.9 | − | 51900.0i | 1.98342 | − | 2.25133i | ||||
\(811\) | −20167.1 | −0.873199 | −0.436599 | − | 0.899656i | \(-0.643817\pi\) | ||||
−0.436599 | + | 0.899656i | \(0.643817\pi\) | |||||||
\(812\) | −3244.17 | + | 5619.07i | −0.140207 | + | 0.242846i | ||||
\(813\) | −4317.61 | − | 20046.0i | −0.186255 | − | 0.864751i | ||||
\(814\) | 20341.9 | + | 35233.1i | 0.875899 | + | 1.51710i | ||||
\(815\) | 5946.24 | + | 10299.2i | 0.255568 | + | 0.442656i | ||||
\(816\) | −1017.17 | − | 327.460i | −0.0436374 | − | 0.0140483i | ||||
\(817\) | −3689.99 | + | 6391.25i | −0.158013 | + | 0.273686i | ||||
\(818\) | 42892.6 | 1.83338 | ||||||||
\(819\) | 5047.41 | − | 2280.05i | 0.215349 | − | 0.0972788i | ||||
\(820\) | 56713.6 | 2.41527 | ||||||||
\(821\) | −14806.3 | + | 25645.2i | −0.629407 | + | 1.09016i | 0.358264 | + | 0.933620i | \(0.383369\pi\) |
−0.987671 | + | 0.156544i | \(0.949965\pi\) | |||||||
\(822\) | −1158.50 | + | 1048.81i | −0.0491573 | + | 0.0445028i | ||||
\(823\) | −5118.30 | − | 8865.16i | −0.216784 | − | 0.375480i | 0.737039 | − | 0.675850i | \(-0.236223\pi\) |
−0.953823 | + | 0.300370i | \(0.902890\pi\) | |||||||
\(824\) | 619.652 | + | 1073.27i | 0.0261973 | + | 0.0453751i | ||||
\(825\) | 53734.0 | − | 48646.2i | 2.26761 | − | 2.05290i | ||||
\(826\) | −10456.5 | + | 18111.1i | −0.440468 | + | 0.762913i | ||||
\(827\) | −8733.00 | −0.367202 | −0.183601 | − | 0.983001i | \(-0.558775\pi\) | ||||
−0.183601 | + | 0.983001i | \(0.558775\pi\) | |||||||
\(828\) | 288.139 | − | 2891.87i | 0.0120936 | − | 0.121376i | ||||
\(829\) | 10394.4 | 0.435481 | 0.217741 | − | 0.976007i | \(-0.430131\pi\) | ||||
0.217741 | + | 0.976007i | \(0.430131\pi\) | |||||||
\(830\) | −29663.1 | + | 51378.1i | −1.24051 | + | 2.14863i | ||||
\(831\) | −23020.7 | − | 7411.11i | −0.960987 | − | 0.309372i | ||||
\(832\) | 12175.9 | + | 21089.3i | 0.507361 | + | 0.878775i | ||||
\(833\) | 2402.36 | + | 4161.01i | 0.0999242 | + | 0.173074i | ||||
\(834\) | −9802.57 | − | 45511.7i | −0.406997 | − | 1.88962i | ||||
\(835\) | −5652.77 | + | 9790.89i | −0.234278 | + | 0.405782i | ||||
\(836\) | 18141.6 | 0.750525 | ||||||||
\(837\) | 1728.81 | − | 3969.36i | 0.0713938 | − | 0.163920i | ||||
\(838\) | −2714.08 | −0.111881 | ||||||||
\(839\) | 14344.8 | − | 24846.0i | 0.590272 | − | 1.02238i | −0.403924 | − | 0.914793i | \(-0.632354\pi\) |
0.994196 | − | 0.107588i | \(-0.0343128\pi\) | |||||||
\(840\) | −3507.03 | − | 16282.6i | −0.144053 | − | 0.668813i | ||||
\(841\) | 9583.28 | + | 16598.7i | 0.392935 | + | 0.680583i | ||||
\(842\) | −7114.11 | − | 12322.0i | −0.291174 | − | 0.504328i | ||||
\(843\) | −31887.3 | − | 10265.5i | −1.30280 | − | 0.419412i | ||||
\(844\) | −7373.71 | + | 12771.6i | −0.300727 | + | 0.520874i | ||||
\(845\) | −27823.8 | −1.13274 | ||||||||
\(846\) | −22020.0 | − | 15817.2i | −0.894876 | − | 0.642797i | ||||
\(847\) | −5110.19 | −0.207306 | ||||||||
\(848\) | 58.6215 | − | 101.535i | 0.00237391 | − | 0.00411172i | ||||
\(849\) | −14015.6 | + | 12688.5i | −0.566566 | + | 0.512920i | ||||
\(850\) | 68748.1 | + | 119075.i | 2.77416 | + | 4.80499i | ||||
\(851\) | 823.957 | + | 1427.13i | 0.0331902 | + | 0.0574871i | ||||
\(852\) | −27087.9 | + | 24523.0i | −1.08922 | + | 0.986085i | ||||
\(853\) | −11064.3 | + | 19163.9i | −0.444120 | + | 0.769239i | −0.997990 | − | 0.0633642i | \(-0.979817\pi\) |
0.553870 | + | 0.832603i | \(0.313150\pi\) | |||||||
\(854\) | −11141.9 | −0.446449 | ||||||||
\(855\) | 14204.5 | + | 10203.2i | 0.568169 | + | 0.408121i | ||||
\(856\) | −6610.22 | −0.263940 | ||||||||
\(857\) | −2393.76 | + | 4146.11i | −0.0954132 | + | 0.165261i | −0.909781 | − | 0.415089i | \(-0.863751\pi\) |
0.814368 | + | 0.580349i | \(0.197084\pi\) | |||||||
\(858\) | −30029.3 | − | 9667.39i | −1.19485 | − | 0.384661i | ||||
\(859\) | −5787.93 | − | 10025.0i | −0.229897 | − | 0.398194i | 0.727880 | − | 0.685704i | \(-0.240506\pi\) |
−0.957777 | + | 0.287511i | \(0.907172\pi\) | |||||||
\(860\) | −31584.0 | − | 54705.1i | −1.25233 | − | 2.16910i | ||||
\(861\) | −1628.78 | − | 7562.15i | −0.0644699 | − | 0.299323i | ||||
\(862\) | 19317.5 | − | 33458.8i | 0.763290 | − | 1.32206i | ||||
\(863\) | 4683.61 | 0.184741 | 0.0923707 | − | 0.995725i | \(-0.470556\pi\) | ||||
0.0923707 | + | 0.995725i | \(0.470556\pi\) | |||||||
\(864\) | 10407.2 | − | 23894.9i | 0.409791 | − | 0.940882i | ||||
\(865\) | 42298.2 | 1.66264 | ||||||||
\(866\) | −12250.9 | + | 21219.1i | −0.480718 | + | 0.832628i | ||||
\(867\) | 5144.26 | + | 23884.0i | 0.201509 | + | 0.935574i | ||||
\(868\) | −1385.35 | − | 2399.50i | −0.0541728 | − | 0.0938300i | ||||
\(869\) | 6126.35 | + | 10611.2i | 0.239151 | + | 0.414222i | ||||
\(870\) | 33914.5 | + | 10918.1i | 1.32162 | + | 0.425471i | ||||
\(871\) | −3084.18 | + | 5341.96i | −0.119981 | + | 0.207813i | ||||
\(872\) | −20635.3 | −0.801377 | ||||||||
\(873\) | −779.259 | + | 7820.95i | −0.0302107 | + | 0.303206i | ||||
\(874\) | 1193.16 | 0.0461777 | ||||||||
\(875\) | 13263.1 | − | 22972.4i | 0.512429 | − | 0.887554i | ||||
\(876\) | −13186.3 | + | 11937.8i | −0.508589 | + | 0.460433i | ||||
\(877\) | 11435.6 | + | 19807.1i | 0.440313 | + | 0.762644i | 0.997712 | − | 0.0676002i | \(-0.0215342\pi\) |
−0.557400 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(878\) | 40599.2 | + | 70319.9i | 1.56054 | + | 2.70294i | ||||
\(879\) | 24373.8 | − | 22066.0i | 0.935278 | − | 0.846720i | ||||
\(880\) | 989.785 | − | 1714.36i | 0.0379155 | − | 0.0656716i | ||||
\(881\) | −20712.8 | −0.792091 | −0.396045 | − | 0.918231i | \(-0.629618\pi\) | ||||
−0.396045 | + | 0.918231i | \(0.629618\pi\) | |||||||
\(882\) | −5502.27 | + | 2485.52i | −0.210058 | + | 0.0948888i | ||||
\(883\) | −21641.0 | −0.824775 | −0.412388 | − | 0.911008i | \(-0.635305\pi\) | ||||
−0.412388 | + | 0.911008i | \(0.635305\pi\) | |||||||
\(884\) | 18427.7 | − | 31917.8i | 0.701122 | − | 1.21438i | ||||
\(885\) | 67321.5 | + | 21672.9i | 2.55705 | + | 0.823195i | ||||
\(886\) | −20224.9 | − | 35030.5i | −0.766893 | − | 1.32830i | ||||
\(887\) | −13479.5 | − | 23347.1i | −0.510255 | − | 0.883787i | −0.999929 | − | 0.0118818i | \(-0.996218\pi\) |
0.489675 | − | 0.871905i | \(-0.337116\pi\) | |||||||
\(888\) | −4731.95 | − | 21969.7i | −0.178822 | − | 0.830242i | ||||
\(889\) | −8355.78 | + | 14472.6i | −0.315235 | + | 0.546003i | ||||
\(890\) | 152345. | 5.73776 | ||||||||
\(891\) | 10567.1 | + | 31363.2i | 0.397317 | + | 1.17925i | ||||
\(892\) | −25857.1 | −0.970585 | ||||||||
\(893\) | 3427.65 | − | 5936.87i | 0.128446 | − | 0.222475i | ||||
\(894\) | −13150.5 | − | 61055.7i | −0.491967 | − | 2.28412i | ||||
\(895\) | 9680.47 | + | 16767.1i | 0.361545 | + | 0.626214i | ||||
\(896\) | −8071.62 | − | 13980.5i | −0.300953 | − | 0.521266i | ||||
\(897\) | −1216.35 | − | 391.582i | −0.0452763 | − | 0.0145759i | ||||
\(898\) | −260.387 | + | 451.003i | −0.00967620 | + | 0.0167597i | ||||
\(899\) | 2230.12 | 0.0827351 | ||||||||
\(900\) | −96973.5 | + | 43805.5i | −3.59161 | + | 1.62243i | ||||
\(901\) | −5481.58 | −0.202683 | ||||||||
\(902\) | −22030.8 | + | 38158.4i | −0.813242 | + | 1.40858i | ||||
\(903\) | −6387.26 | + | 5782.48i | −0.235387 | + | 0.213100i | ||||
\(904\) | −15358.0 | − | 26600.8i | −0.565042 | − | 0.978682i | ||||
\(905\) | −10424.0 | − | 18054.8i | −0.382878 | − | 0.663164i | ||||
\(906\) | −12964.2 | + | 11736.7i | −0.475395 | + | 0.430381i | ||||
\(907\) | 10184.2 | − | 17639.5i | 0.372833 | − | 0.645765i | −0.617167 | − | 0.786832i | \(-0.711720\pi\) |
0.990000 | + | 0.141067i | \(0.0450532\pi\) | |||||||
\(908\) | 39020.0 | 1.42613 | ||||||||
\(909\) | −3888.58 | + | 39027.3i | −0.141888 | + | 1.42404i | ||||
\(910\) | −19462.9 | −0.709001 | ||||||||
\(911\) | −10750.9 | + | 18621.1i | −0.390991 | + | 0.677217i | −0.992581 | − | 0.121589i | \(-0.961201\pi\) |
0.601589 | + | 0.798806i | \(0.294534\pi\) | |||||||
\(912\) | 323.188 | + | 104.044i | 0.0117344 | + | 0.00377769i | ||||
\(913\) | −14193.1 | − | 24583.2i | −0.514485 | − | 0.891113i | ||||
\(914\) | −18397.1 | − | 31864.7i | −0.665778 | − | 1.15316i | ||||
\(915\) | 7933.80 | + | 36835.3i | 0.286648 | + | 1.33086i | ||||
\(916\) | −26174.2 | + | 45335.0i | −0.944125 | + | 1.63527i | ||||
\(917\) | −14839.9 | −0.534414 | ||||||||
\(918\) | −62381.1 | + | 7068.79i | −2.24279 | + | 0.254145i | ||||
\(919\) | −2461.02 | −0.0883369 | −0.0441685 | − | 0.999024i | \(-0.514064\pi\) | ||||
−0.0441685 | + | 0.999024i | \(0.514064\pi\) | |||||||
\(920\) | −1921.42 | + | 3327.99i | −0.0688557 | + | 0.119262i | ||||
\(921\) | 2968.03 | + | 13780.1i | 0.106189 | + | 0.493018i | ||||
\(922\) | −9423.50 | − | 16322.0i | −0.336601 | − | 0.583010i | ||||
\(923\) | 8033.04 | + | 13913.6i | 0.286469 | + | 0.496179i | ||||
\(924\) | 20160.8 | + | 6490.40i | 0.717794 | + | 0.231081i | ||||
\(925\) | 30168.7 | − | 52253.7i | 1.07237 | − | 1.85740i | ||||
\(926\) | 53934.6 | 1.91404 | ||||||||
\(927\) | −1233.90 | − | 886.324i | −0.0437181 | − | 0.0314031i | ||||
\(928\) | 13425.0 | 0.474889 | ||||||||
\(929\) | −866.047 | + | 1500.04i | −0.0305857 | + | 0.0529759i | −0.880913 | − | 0.473278i | \(-0.843071\pi\) |
0.850327 | + | 0.526254i | \(0.176404\pi\) | |||||||
\(930\) | −11278.9 | + | 10211.0i | −0.397689 | + | 0.360034i | ||||
\(931\) | −763.307 | − | 1322.09i | −0.0268704 | − | 0.0465409i | ||||
\(932\) | −17107.4 | − | 29631.0i | −0.601259 | − | 1.04141i | ||||
\(933\) | 11733.7 | − | 10622.7i | 0.411730 | − | 0.372745i | ||||
\(934\) | −3628.63 | + | 6284.97i | −0.127123 | + | 0.220183i | ||||
\(935\) | −92552.7 | −3.23721 | ||||||||
\(936\) | 14153.5 | + | 10166.6i | 0.494255 | + | 0.355027i | ||||
\(937\) | 35120.9 | 1.22449 | 0.612247 | − | 0.790667i | \(-0.290266\pi\) | ||||
0.612247 | + | 0.790667i | \(0.290266\pi\) | |||||||
\(938\) | 3362.12 | − | 5823.37i | 0.117033 | − | 0.202708i | ||||
\(939\) | −21666.8 | − | 6975.23i | −0.753002 | − | 0.242415i | ||||
\(940\) | 29338.6 | + | 50815.9i | 1.01800 | + | 1.76322i | ||||
\(941\) | 6463.99 | + | 11196.0i | 0.223932 | + | 0.387862i | 0.955999 | − | 0.293371i | \(-0.0947773\pi\) |
−0.732066 | + | 0.681233i | \(0.761444\pi\) | |||||||
\(942\) | 11717.1 | + | 54400.5i | 0.405268 | + | 1.88160i | ||||
\(943\) | −892.366 | + | 1545.62i | −0.0308160 | + | 0.0533748i | ||||
\(944\) | 1372.98 | 0.0473376 | ||||||||
\(945\) | 12135.2 | + | 16420.8i | 0.417734 | + | 0.565257i | ||||
\(946\) | 49076.1 | 1.68668 | ||||||||
\(947\) | 1601.47 | − | 2773.83i | 0.0549533 | − | 0.0951819i | −0.837240 | − | 0.546835i | \(-0.815832\pi\) |
0.892193 | + | 0.451654i | \(0.149166\pi\) | |||||||
\(948\) | −3787.40 | − | 17584.3i | −0.129756 | − | 0.602438i | ||||
\(949\) | 3910.47 | + | 6773.13i | 0.133761 | + | 0.231681i | ||||
\(950\) | −21843.5 | − | 37834.0i | −0.745995 | − | 1.29210i | ||||
\(951\) | −34159.4 | − | 10997.0i | −1.16477 | − | 0.374976i | ||||
\(952\) | −7558.85 | + | 13092.3i | −0.257336 | + | 0.445719i | ||||
\(953\) | −36827.2 | −1.25178 | −0.625891 | − | 0.779910i | \(-0.715265\pi\) | ||||
−0.625891 | + | 0.779910i | \(0.715265\pi\) | |||||||
\(954\) | 682.936 | − | 6854.21i | 0.0231770 | − | 0.232614i | ||||
\(955\) | −79901.5 | −2.70738 | ||||||||
\(956\) | 38303.2 | − | 66343.1i | 1.29583 | − | 2.24444i | ||||
\(957\) | −12637.8 | + | 11441.2i | −0.426879 | + | 0.386460i | ||||
\(958\) | −29970.3 | − | 51910.1i | −1.01075 | − | 1.75067i | ||||
\(959\) | −230.656 | − | 399.507i | −0.00776669 | − | 0.0134523i | ||||
\(960\) | −66553.6 | + | 60251.9i | −2.23751 | + | 2.02565i | ||||
\(961\) | 14419.3 | − | 24975.0i | 0.484017 | − | 0.838341i | ||||
\(962\) | −26260.9 | −0.880129 | ||||||||
\(963\) | 7384.84 | − | 3335.93i | 0.247116 | − | 0.111629i | ||||
\(964\) | −33877.5 | −1.13187 | ||||||||
\(965\) | 36031.8 | − | 62409.0i | 1.20197 | − | 2.08188i | ||||
\(966\) | 1325.97 | + | 426.871i | 0.0441639 | + | 0.0142177i | ||||
\(967\) | −490.524 | − | 849.612i | −0.0163125 | − | 0.0282541i | 0.857754 | − | 0.514061i | \(-0.171859\pi\) |
−0.874066 | + | 0.485806i | \(0.838526\pi\) | |||||||
\(968\) | −8039.42 | − | 13924.7i | −0.266939 | − | 0.462351i | ||||
\(969\) | −3342.38 | − | 15518.1i | −0.110808 | − | 0.514463i | ||||
\(970\) | 13809.9 | − | 23919.5i | 0.457124 | − | 0.791761i | ||||
\(971\) | 35299.7 | 1.16666 | 0.583328 | − | 0.812237i | \(-0.301750\pi\) | ||||
0.583328 | + | 0.812237i | \(0.301750\pi\) | |||||||
\(972\) | −657.116 | − | 48581.3i | −0.0216841 | − | 1.60313i | ||||
\(973\) | 13743.0 | 0.452805 | ||||||||
\(974\) | 41843.3 | − | 72474.7i | 1.37654 | − | 2.38423i | ||||
\(975\) | 9851.32 | + | 45738.1i | 0.323584 | + | 1.50235i | ||||
\(976\) | 365.745 | + | 633.489i | 0.0119951 | + | 0.0207761i | ||||
\(977\) | 19802.8 | + | 34299.4i | 0.648462 | + | 1.12317i | 0.983490 | + | 0.180961i | \(0.0579207\pi\) |
−0.335029 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(978\) | 12911.3 | + | 4156.57i | 0.422146 | + | 0.135902i | ||||
\(979\) | −36446.7 | + | 63127.6i | −1.18983 | + | 2.06084i | ||||
\(980\) | 13066.8 | 0.425924 | ||||||||
\(981\) | 23053.5 | − | 10413.9i | 0.750296 | − | 0.338929i | ||||
\(982\) | −36952.1 | −1.20080 | ||||||||
\(983\) | 5834.71 | − | 10106.0i | 0.189317 | − | 0.327906i | −0.755706 | − | 0.654911i | \(-0.772706\pi\) |
0.945023 | + | 0.327005i | \(0.106039\pi\) | |||||||
\(984\) | 18043.6 | − | 16335.1i | 0.584561 | − | 0.529211i | ||||
\(985\) | 38380.0 | + | 66476.2i | 1.24151 | + | 2.15036i | ||||
\(986\) | −16169.0 | − | 28005.6i | −0.522238 | − | 0.904543i | ||||
\(987\) | 5933.17 | − | 5371.38i | 0.191342 | − | 0.173225i | ||||
\(988\) | −5855.08 | + | 10141.3i | −0.188537 | + | 0.326556i | ||||
\(989\) | 1987.85 | 0.0639129 | ||||||||
\(990\) | 11530.9 | − | 115729.i | 0.370178 | − | 3.71525i | ||||
\(991\) | 37428.6 | 1.19976 | 0.599879 | − | 0.800091i | \(-0.295215\pi\) | ||||
0.599879 | + | 0.800091i | \(0.295215\pi\) | |||||||
\(992\) | −2866.42 | + | 4964.79i | −0.0917430 | + | 0.158904i | ||||
\(993\) | −28205.6 | − | 9080.26i | −0.901386 | − | 0.290185i | ||||
\(994\) | −8756.97 | − | 15167.5i | −0.279431 | − | 0.483988i | ||||
\(995\) | 5008.37 | + | 8674.76i | 0.159574 | + | 0.276390i | ||||
\(996\) | 8774.41 | + | 40738.2i | 0.279144 | + | 1.29602i | ||||
\(997\) | −5306.23 | + | 9190.66i | −0.168556 | + | 0.291947i | −0.937912 | − | 0.346873i | \(-0.887244\pi\) |
0.769357 | + | 0.638820i | \(0.220577\pi\) | |||||||
\(998\) | −2748.89 | −0.0871891 | ||||||||
\(999\) | 16373.7 | + | 22156.1i | 0.518560 | + | 0.701691i |
(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 | 63.4.f.b.43.2 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.7 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.2 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.2 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.7 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.2 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.2 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.7 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.7 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.2 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.7 | 8 | 9.7 | even | 3 |