Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.6 | ||
Root | \(2.05188 - 3.55396i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.4.e.q.226.6 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.75899 | + | 4.77871i | 0.975449 | + | 1.68953i | 0.678445 | + | 0.734651i | \(0.262654\pi\) |
0.297004 | + | 0.954876i | \(0.404012\pi\) | |||||||
\(3\) | 1.93020 | − | 3.34320i | 0.371466 | − | 0.643398i | −0.618325 | − | 0.785922i | \(-0.712188\pi\) |
0.989791 | + | 0.142524i | \(0.0455218\pi\) | |||||||
\(4\) | −11.2240 | + | 19.4406i | −1.40300 | + | 2.43007i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 21.3015 | 1.44939 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −79.7239 | −3.52333 | ||||||||
\(9\) | 6.04869 | + | 10.4766i | 0.224026 | + | 0.388024i | ||||
\(10\) | 13.7949 | − | 23.8935i | 0.436234 | − | 0.755580i | ||||
\(11\) | −17.2605 | + | 29.8961i | −0.473113 | + | 0.819456i | −0.999526 | − | 0.0307725i | \(-0.990203\pi\) |
0.526413 | + | 0.850229i | \(0.323537\pi\) | |||||||
\(12\) | 43.3291 | + | 75.0482i | 1.04234 | + | 1.80538i | ||||
\(13\) | −68.8935 | −1.46982 | −0.734908 | − | 0.678167i | \(-0.762775\pi\) | ||||
−0.734908 | + | 0.678167i | \(0.762775\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −19.3020 | −0.332250 | ||||||||
\(16\) | −130.165 | − | 225.452i | −2.03383 | − | 3.52269i | ||||
\(17\) | −45.7173 | + | 79.1847i | −0.652239 | + | 1.12971i | 0.330339 | + | 0.943862i | \(0.392837\pi\) |
−0.982578 | + | 0.185849i | \(0.940496\pi\) | |||||||
\(18\) | −33.3765 | + | 57.8098i | −0.437051 | + | 0.756995i | ||||
\(19\) | 5.91392 | + | 10.2432i | 0.0714077 | + | 0.123682i | 0.899518 | − | 0.436883i | \(-0.143918\pi\) |
−0.828111 | + | 0.560564i | \(0.810584\pi\) | |||||||
\(20\) | 112.240 | 1.25488 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −190.486 | −1.84599 | ||||||||
\(23\) | 0.0520827 | + | 0.0902099i | 0.000472174 | + | 0.000817829i | 0.866261 | − | 0.499591i | \(-0.166516\pi\) |
−0.865789 | + | 0.500409i | \(0.833183\pi\) | |||||||
\(24\) | −153.883 | + | 266.533i | −1.30880 | + | 2.26691i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −190.076 | − | 329.222i | −1.43373 | − | 2.48330i | ||||
\(27\) | 150.931 | 1.07580 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 190.863 | 1.22215 | 0.611076 | − | 0.791572i | \(-0.290737\pi\) | ||||
0.611076 | + | 0.791572i | \(0.290737\pi\) | |||||||
\(30\) | −53.2538 | − | 92.2384i | −0.324093 | − | 0.561345i | ||||
\(31\) | 79.9010 | − | 138.393i | 0.462924 | − | 0.801807i | −0.536181 | − | 0.844103i | \(-0.680134\pi\) |
0.999105 | + | 0.0422954i | \(0.0134671\pi\) | |||||||
\(32\) | 399.352 | − | 691.697i | 2.20613 | − | 3.82112i | ||||
\(33\) | 66.6324 | + | 115.411i | 0.351491 | + | 0.608801i | ||||
\(34\) | −504.534 | −2.54491 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −271.562 | −1.25723 | ||||||||
\(37\) | 88.9538 | + | 154.073i | 0.395241 | + | 0.684577i | 0.993132 | − | 0.117000i | \(-0.0373277\pi\) |
−0.597891 | + | 0.801577i | \(0.703994\pi\) | |||||||
\(38\) | −32.6328 | + | 56.5217i | −0.139309 | + | 0.241290i | ||||
\(39\) | −132.978 | + | 230.324i | −0.545987 | + | 0.945678i | ||||
\(40\) | 199.310 | + | 345.215i | 0.787841 | + | 1.36458i | ||||
\(41\) | −145.247 | −0.553264 | −0.276632 | − | 0.960976i | \(-0.589218\pi\) | ||||
−0.276632 | + | 0.960976i | \(0.589218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.25729 | 0.0292843 | 0.0146421 | − | 0.999893i | \(-0.495339\pi\) | ||||
0.0146421 | + | 0.999893i | \(0.495339\pi\) | |||||||
\(44\) | −387.465 | − | 671.109i | −1.32756 | − | 2.29940i | ||||
\(45\) | 30.2435 | − | 52.3832i | 0.100187 | − | 0.173529i | ||||
\(46\) | −0.287391 | + | 0.497776i | −0.000921163 | + | 0.00159550i | ||||
\(47\) | 130.264 | + | 225.624i | 0.404277 | + | 0.700228i | 0.994237 | − | 0.107204i | \(-0.0341899\pi\) |
−0.589960 | + | 0.807432i | \(0.700857\pi\) | |||||||
\(48\) | −1004.98 | −3.02199 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −137.949 | −0.390180 | ||||||||
\(51\) | 176.487 | + | 305.684i | 0.484570 | + | 0.839300i | ||||
\(52\) | 773.262 | − | 1339.33i | 2.06216 | − | 3.57176i | ||||
\(53\) | −176.554 | + | 305.800i | −0.457576 | + | 0.792544i | −0.998832 | − | 0.0483132i | \(-0.984615\pi\) |
0.541257 | + | 0.840857i | \(0.317949\pi\) | |||||||
\(54\) | 416.417 | + | 721.256i | 1.04939 | + | 1.81760i | ||||
\(55\) | 172.605 | 0.423165 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 45.6601 | 0.106102 | ||||||||
\(58\) | 526.589 | + | 912.079i | 1.19215 | + | 2.06486i | ||||
\(59\) | 120.247 | − | 208.274i | 0.265337 | − | 0.459576i | −0.702315 | − | 0.711866i | \(-0.747850\pi\) |
0.967652 | + | 0.252290i | \(0.0811836\pi\) | |||||||
\(60\) | 216.645 | − | 375.241i | 0.466147 | − | 0.807390i | ||||
\(61\) | 389.094 | + | 673.931i | 0.816695 | + | 1.41456i | 0.908104 | + | 0.418744i | \(0.137530\pi\) |
−0.0914091 | + | 0.995813i | \(0.529137\pi\) | |||||||
\(62\) | 881.783 | 1.80623 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2324.58 | 4.54020 | ||||||||
\(65\) | 172.234 | + | 298.318i | 0.328661 | + | 0.569257i | ||||
\(66\) | −367.676 | + | 636.833i | −0.685724 | + | 1.18771i | ||||
\(67\) | −75.9723 | + | 131.588i | −0.138530 | + | 0.239940i | −0.926940 | − | 0.375209i | \(-0.877571\pi\) |
0.788411 | + | 0.615149i | \(0.210904\pi\) | |||||||
\(68\) | −1026.26 | − | 1777.54i | −1.83019 | − | 3.16998i | ||||
\(69\) | 0.402119 | 0.000701587 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −311.449 | −0.520594 | −0.260297 | − | 0.965529i | \(-0.583820\pi\) | ||||
−0.260297 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(72\) | −482.225 | − | 835.238i | −0.789316 | − | 1.36714i | ||||
\(73\) | 319.944 | − | 554.159i | 0.512967 | − | 0.888485i | −0.486920 | − | 0.873447i | \(-0.661880\pi\) |
0.999887 | − | 0.0150383i | \(-0.00478701\pi\) | |||||||
\(74\) | −490.845 | + | 850.168i | −0.771075 | + | 1.33554i | ||||
\(75\) | 48.2549 | + | 83.5799i | 0.0742933 | + | 0.128680i | ||||
\(76\) | −265.512 | −0.400740 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1467.54 | −2.13033 | ||||||||
\(79\) | −195.593 | − | 338.777i | −0.278556 | − | 0.482473i | 0.692470 | − | 0.721447i | \(-0.256522\pi\) |
−0.971026 | + | 0.238973i | \(0.923189\pi\) | |||||||
\(80\) | −650.825 | + | 1127.26i | −0.909556 | + | 1.57540i | ||||
\(81\) | 128.012 | − | 221.723i | 0.175599 | − | 0.304147i | ||||
\(82\) | −400.736 | − | 694.095i | −0.539681 | − | 0.934755i | ||||
\(83\) | −493.205 | −0.652245 | −0.326122 | − | 0.945328i | \(-0.605742\pi\) | ||||
−0.326122 | + | 0.945328i | \(0.605742\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 457.173 | 0.583381 | ||||||||
\(86\) | 22.7817 | + | 39.4591i | 0.0285653 | + | 0.0494766i | ||||
\(87\) | 368.403 | − | 638.093i | 0.453988 | − | 0.786331i | ||||
\(88\) | 1376.08 | − | 2383.44i | 1.66694 | − | 2.88722i | ||||
\(89\) | 236.925 | + | 410.366i | 0.282180 | + | 0.488749i | 0.971921 | − | 0.235306i | \(-0.0756092\pi\) |
−0.689742 | + | 0.724056i | \(0.742276\pi\) | |||||||
\(90\) | 333.765 | 0.390910 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.33831 | −0.00264984 | ||||||||
\(93\) | −308.449 | − | 534.249i | −0.343921 | − | 0.595689i | ||||
\(94\) | −718.795 | + | 1244.99i | −0.788703 | + | 1.36607i | ||||
\(95\) | 29.5696 | − | 51.2160i | 0.0319345 | − | 0.0553121i | ||||
\(96\) | −1541.65 | − | 2670.22i | −1.63900 | − | 2.83884i | ||||
\(97\) | −839.005 | −0.878227 | −0.439114 | − | 0.898431i | \(-0.644707\pi\) | ||||
−0.439114 | + | 0.898431i | \(0.644707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −417.615 | −0.423958 | ||||||||
\(100\) | −280.600 | − | 486.014i | −0.280600 | − | 0.486014i | ||||
\(101\) | 443.720 | − | 768.546i | 0.437146 | − | 0.757160i | −0.560322 | − | 0.828275i | \(-0.689322\pi\) |
0.997468 | + | 0.0711152i | \(0.0226558\pi\) | |||||||
\(102\) | −973.848 | + | 1686.75i | −0.945347 | + | 1.63739i | ||||
\(103\) | 309.544 | + | 536.145i | 0.296119 | + | 0.512893i | 0.975245 | − | 0.221129i | \(-0.0709742\pi\) |
−0.679126 | + | 0.734022i | \(0.737641\pi\) | |||||||
\(104\) | 5492.46 | 5.17865 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1948.44 | −1.78537 | ||||||||
\(107\) | 1075.65 | + | 1863.08i | 0.971841 | + | 1.68328i | 0.689990 | + | 0.723819i | \(0.257615\pi\) |
0.281851 | + | 0.959458i | \(0.409052\pi\) | |||||||
\(108\) | −1694.05 | + | 2934.19i | −1.50936 | + | 2.61428i | ||||
\(109\) | 203.538 | − | 352.539i | 0.178857 | − | 0.309790i | −0.762632 | − | 0.646832i | \(-0.776093\pi\) |
0.941489 | + | 0.337043i | \(0.109427\pi\) | |||||||
\(110\) | 476.216 | + | 824.830i | 0.412776 | + | 0.714950i | ||||
\(111\) | 686.793 | 0.587275 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −349.581 | −0.291025 | −0.145513 | − | 0.989356i | \(-0.546483\pi\) | ||||
−0.145513 | + | 0.989356i | \(0.546483\pi\) | |||||||
\(114\) | 125.976 | + | 218.196i | 0.103497 | + | 0.179263i | ||||
\(115\) | 0.260414 | − | 0.451050i | 0.000211163 | − | 0.000365744i | ||||
\(116\) | −2142.25 | + | 3710.49i | −1.71468 | + | 2.96992i | ||||
\(117\) | −416.715 | − | 721.772i | −0.329277 | − | 0.570324i | ||||
\(118\) | 1327.04 | 1.03529 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1538.83 | 1.17063 | ||||||||
\(121\) | 69.6478 | + | 120.633i | 0.0523274 | + | 0.0906337i | ||||
\(122\) | −2147.01 | + | 3718.73i | −1.59329 | + | 2.75966i | ||||
\(123\) | −280.356 | + | 485.591i | −0.205519 | + | 0.355969i | ||||
\(124\) | 1793.62 | + | 3106.64i | 1.29897 | + | 2.24987i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1183.78 | 0.827114 | 0.413557 | − | 0.910478i | \(-0.364286\pi\) | ||||
0.413557 | + | 0.910478i | \(0.364286\pi\) | |||||||
\(128\) | 3218.68 | + | 5574.92i | 2.22261 | + | 3.84967i | ||||
\(129\) | 15.9382 | − | 27.6057i | 0.0108781 | − | 0.0188415i | ||||
\(130\) | −950.381 | + | 1646.11i | −0.641184 | + | 1.11056i | ||||
\(131\) | 111.679 | + | 193.433i | 0.0744840 | + | 0.129010i | 0.900862 | − | 0.434106i | \(-0.142936\pi\) |
−0.826378 | + | 0.563116i | \(0.809602\pi\) | |||||||
\(132\) | −2991.53 | −1.97257 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −838.426 | −0.540515 | ||||||||
\(135\) | −377.328 | − | 653.551i | −0.240557 | − | 0.416657i | ||||
\(136\) | 3644.76 | − | 6312.91i | 2.29806 | − | 3.98035i | ||||
\(137\) | −1018.33 | + | 1763.80i | −0.635050 | + | 1.09994i | 0.351454 | + | 0.936205i | \(0.385687\pi\) |
−0.986504 | + | 0.163734i | \(0.947646\pi\) | |||||||
\(138\) | 1.10944 | + | 1.92161i | 0.000684362 | + | 0.00118535i | ||||
\(139\) | −2687.00 | −1.63963 | −0.819815 | − | 0.572629i | \(-0.805924\pi\) | ||||
−0.819815 | + | 0.572629i | \(0.805924\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1005.74 | 0.600701 | ||||||||
\(142\) | −859.283 | − | 1488.32i | −0.507813 | − | 0.879557i | ||||
\(143\) | 1189.14 | − | 2059.65i | 0.695390 | − | 1.20445i | ||||
\(144\) | 1574.66 | − | 2727.38i | 0.911259 | − | 1.57835i | ||||
\(145\) | −477.158 | − | 826.462i | −0.273282 | − | 0.473337i | ||||
\(146\) | 3530.88 | 2.00149 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3993.68 | −2.21810 | ||||||||
\(149\) | −336.750 | − | 583.268i | −0.185152 | − | 0.320693i | 0.758476 | − | 0.651701i | \(-0.225944\pi\) |
−0.943628 | + | 0.331009i | \(0.892611\pi\) | |||||||
\(150\) | −266.269 | + | 461.192i | −0.144939 | + | 0.251041i | ||||
\(151\) | 1062.59 | − | 1840.46i | 0.572664 | − | 0.991884i | −0.423627 | − | 0.905837i | \(-0.639243\pi\) |
0.996291 | − | 0.0860467i | \(-0.0274234\pi\) | |||||||
\(152\) | −471.480 | − | 816.628i | −0.251593 | − | 0.435772i | ||||
\(153\) | −1106.12 | −0.584473 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −799.010 | −0.414052 | ||||||||
\(156\) | −2985.09 | − | 5170.33i | −1.53204 | − | 2.65358i | ||||
\(157\) | −1406.52 | + | 2436.16i | −0.714983 | + | 1.23839i | 0.247984 | + | 0.968764i | \(0.420232\pi\) |
−0.962966 | + | 0.269622i | \(0.913101\pi\) | |||||||
\(158\) | 1079.28 | − | 1869.36i | 0.543435 | − | 0.941257i | ||||
\(159\) | 681.566 | + | 1180.51i | 0.339948 | + | 0.588807i | ||||
\(160\) | −3993.52 | −1.97322 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1412.73 | 0.685153 | ||||||||
\(163\) | 672.210 | + | 1164.30i | 0.323016 | + | 0.559480i | 0.981109 | − | 0.193457i | \(-0.0619699\pi\) |
−0.658093 | + | 0.752937i | \(0.728637\pi\) | |||||||
\(164\) | 1630.26 | − | 2823.69i | 0.776231 | − | 1.34447i | ||||
\(165\) | 333.162 | − | 577.054i | 0.157192 | − | 0.272264i | ||||
\(166\) | −1360.75 | − | 2356.88i | −0.636232 | − | 1.10199i | ||||
\(167\) | −1451.24 | −0.672456 | −0.336228 | − | 0.941781i | \(-0.609151\pi\) | ||||
−0.336228 | + | 0.941781i | \(0.609151\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2549.31 | 1.16036 | ||||||||
\(170\) | 1261.33 | + | 2184.69i | 0.569058 | + | 0.985638i | ||||
\(171\) | −71.5429 | + | 123.916i | −0.0319943 | + | 0.0554157i | ||||
\(172\) | −92.6799 | + | 160.526i | −0.0410859 | + | 0.0711629i | ||||
\(173\) | −989.579 | − | 1714.00i | −0.434892 | − | 0.753255i | 0.562395 | − | 0.826869i | \(-0.309880\pi\) |
−0.997287 | + | 0.0736139i | \(0.976547\pi\) | |||||||
\(174\) | 4065.68 | 1.77137 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8986.87 | 3.84893 | ||||||||
\(177\) | −464.201 | − | 804.020i | −0.197127 | − | 0.341434i | ||||
\(178\) | −1307.35 | + | 2264.39i | −0.550504 | + | 0.953501i | ||||
\(179\) | 2179.33 | − | 3774.71i | 0.910005 | − | 1.57617i | 0.0959500 | − | 0.995386i | \(-0.469411\pi\) |
0.814055 | − | 0.580788i | \(-0.197256\pi\) | |||||||
\(180\) | 678.906 | + | 1175.90i | 0.281126 | + | 0.486924i | ||||
\(181\) | 377.923 | 0.155198 | 0.0775988 | − | 0.996985i | \(-0.475275\pi\) | ||||
0.0775988 | + | 0.996985i | \(0.475275\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3004.11 | 1.21350 | ||||||||
\(184\) | −4.15224 | − | 7.19189i | −0.00166362 | − | 0.00288148i | ||||
\(185\) | 444.769 | − | 770.363i | 0.176757 | − | 0.306152i | ||||
\(186\) | 1702.01 | − | 2947.97i | 0.670955 | − | 1.16213i | ||||
\(187\) | −1578.21 | − | 2733.54i | −0.617166 | − | 1.06896i | ||||
\(188\) | −5848.36 | −2.26880 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 326.328 | 0.124602 | ||||||||
\(191\) | 1212.97 | + | 2100.93i | 0.459517 | + | 0.795906i | 0.998935 | − | 0.0461315i | \(-0.0146893\pi\) |
−0.539419 | + | 0.842038i | \(0.681356\pi\) | |||||||
\(192\) | 4486.90 | − | 7771.54i | 1.68653 | − | 2.92116i | ||||
\(193\) | 311.461 | − | 539.467i | 0.116163 | − | 0.201200i | −0.802081 | − | 0.597215i | \(-0.796274\pi\) |
0.918244 | + | 0.396015i | \(0.129607\pi\) | |||||||
\(194\) | −2314.80 | − | 4009.36i | −0.856666 | − | 1.48379i | ||||
\(195\) | 1329.78 | 0.488346 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2842.29 | 1.02794 | 0.513971 | − | 0.857807i | \(-0.328174\pi\) | ||||
0.513971 | + | 0.857807i | \(0.328174\pi\) | |||||||
\(198\) | −1152.19 | − | 1995.66i | −0.413550 | − | 0.716289i | ||||
\(199\) | −433.682 | + | 751.159i | −0.154487 | + | 0.267579i | −0.932872 | − | 0.360208i | \(-0.882706\pi\) |
0.778385 | + | 0.627787i | \(0.216039\pi\) | |||||||
\(200\) | 996.549 | − | 1726.07i | 0.352333 | − | 0.610259i | ||||
\(201\) | 293.283 | + | 507.980i | 0.102918 | + | 0.178260i | ||||
\(202\) | 4896.87 | 1.70566 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7923.55 | −2.71941 | ||||||||
\(205\) | 363.119 | + | 628.940i | 0.123714 | + | 0.214278i | ||||
\(206\) | −1708.05 | + | 2958.44i | −0.577698 | + | 1.00060i | ||||
\(207\) | −0.630065 | + | 1.09130i | −0.000211558 | + | 0.000366429i | ||||
\(208\) | 8967.52 | + | 15532.2i | 2.98935 | + | 5.17771i | ||||
\(209\) | −408.309 | −0.135136 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5975.92 | −1.94976 | −0.974880 | − | 0.222730i | \(-0.928503\pi\) | ||||
−0.974880 | + | 0.222730i | \(0.928503\pi\) | |||||||
\(212\) | −3963.28 | − | 6864.61i | −1.28396 | − | 2.22388i | ||||
\(213\) | −601.157 | + | 1041.23i | −0.193383 | + | 0.334949i | ||||
\(214\) | −5935.40 | + | 10280.4i | −1.89596 | + | 3.28390i | ||||
\(215\) | −20.6432 | − | 35.7551i | −0.00654817 | − | 0.0113418i | ||||
\(216\) | −12032.8 | −3.79042 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2246.24 | 0.697864 | ||||||||
\(219\) | −1235.11 | − | 2139.27i | −0.381100 | − | 0.660084i | ||||
\(220\) | −1937.33 | + | 3355.55i | −0.593702 | + | 1.02832i | ||||
\(221\) | 3149.62 | − | 5455.31i | 0.958672 | − | 1.66047i | ||||
\(222\) | 1894.85 | + | 3281.98i | 0.572857 | + | 0.992217i | ||||
\(223\) | 5181.58 | 1.55598 | 0.777992 | − | 0.628274i | \(-0.216238\pi\) | ||||
0.777992 | + | 0.628274i | \(0.216238\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −302.435 | −0.0896102 | ||||||||
\(226\) | −964.491 | − | 1670.55i | −0.283880 | − | 0.491695i | ||||
\(227\) | 1876.53 | − | 3250.24i | 0.548677 | − | 0.950336i | −0.449689 | − | 0.893185i | \(-0.648465\pi\) |
0.998366 | − | 0.0571507i | \(-0.0182016\pi\) | |||||||
\(228\) | −512.489 | + | 887.658i | −0.148862 | + | 0.257836i | ||||
\(229\) | −3129.07 | − | 5419.71i | −0.902947 | − | 1.56395i | −0.823650 | − | 0.567099i | \(-0.808066\pi\) |
−0.0792969 | − | 0.996851i | \(-0.525268\pi\) | |||||||
\(230\) | 2.87391 | 0.000823913 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15216.4 | −4.30605 | ||||||||
\(233\) | −889.981 | − | 1541.49i | −0.250234 | − | 0.433419i | 0.713356 | − | 0.700802i | \(-0.247174\pi\) |
−0.963590 | + | 0.267383i | \(0.913841\pi\) | |||||||
\(234\) | 2299.42 | − | 3982.72i | 0.642385 | − | 1.11264i | ||||
\(235\) | 651.322 | − | 1128.12i | 0.180798 | − | 0.313151i | ||||
\(236\) | 2699.31 | + | 4675.35i | 0.744536 | + | 1.28957i | ||||
\(237\) | −1510.13 | −0.413897 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3519.46 | 0.952532 | 0.476266 | − | 0.879301i | \(-0.341990\pi\) | ||||
0.476266 | + | 0.879301i | \(0.341990\pi\) | |||||||
\(240\) | 2512.44 | + | 4351.67i | 0.675739 | + | 1.17041i | ||||
\(241\) | 181.465 | − | 314.307i | 0.0485029 | − | 0.0840095i | −0.840755 | − | 0.541416i | \(-0.817888\pi\) |
0.889258 | + | 0.457407i | \(0.151222\pi\) | |||||||
\(242\) | −384.315 | + | 665.652i | −0.102085 | + | 0.176817i | ||||
\(243\) | 1543.39 | + | 2673.24i | 0.407444 | + | 0.705713i | ||||
\(244\) | −17468.8 | −4.58330 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3093.99 | −0.801894 | ||||||||
\(247\) | −407.430 | − | 705.690i | −0.104956 | − | 0.181789i | ||||
\(248\) | −6370.01 | + | 11033.2i | −1.63103 | + | 2.82503i | ||||
\(249\) | −951.983 | + | 1648.88i | −0.242287 | + | 0.419653i | ||||
\(250\) | 344.873 | + | 597.338i | 0.0872468 | + | 0.151116i | ||||
\(251\) | 5333.85 | 1.34131 | 0.670656 | − | 0.741768i | \(-0.266012\pi\) | ||||
0.670656 | + | 0.741768i | \(0.266012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.59590 | −0.000893567 | ||||||||
\(254\) | 3266.03 | + | 5656.93i | 0.806807 | + | 1.39743i | ||||
\(255\) | 882.433 | − | 1528.42i | 0.216706 | − | 0.375346i | ||||
\(256\) | −8462.27 | + | 14657.1i | −2.06598 | + | 3.57839i | ||||
\(257\) | −1219.39 | − | 2112.04i | −0.295966 | − | 0.512629i | 0.679243 | − | 0.733914i | \(-0.262308\pi\) |
−0.975209 | + | 0.221285i | \(0.928975\pi\) | |||||||
\(258\) | 175.893 | 0.0424442 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −7732.62 | −1.84445 | ||||||||
\(261\) | 1154.47 | + | 1999.61i | 0.273793 | + | 0.474224i | ||||
\(262\) | −616.239 | + | 1067.36i | −0.145311 | + | 0.251685i | ||||
\(263\) | −763.126 | + | 1321.77i | −0.178921 | + | 0.309901i | −0.941511 | − | 0.336981i | \(-0.890594\pi\) |
0.762590 | + | 0.646882i | \(0.223927\pi\) | |||||||
\(264\) | −5312.19 | − | 9200.99i | −1.23842 | − | 2.14501i | ||||
\(265\) | 1765.54 | 0.409268 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1829.25 | 0.419281 | ||||||||
\(268\) | −1705.43 | − | 2953.89i | −0.388715 | − | 0.673274i | ||||
\(269\) | −3782.06 | + | 6550.72i | −0.857235 | + | 1.48478i | 0.0173203 | + | 0.999850i | \(0.494487\pi\) |
−0.874556 | + | 0.484925i | \(0.838847\pi\) | |||||||
\(270\) | 2082.09 | − | 3606.28i | 0.469303 | − | 0.812856i | ||||
\(271\) | 2141.34 | + | 3708.91i | 0.479990 | + | 0.831367i | 0.999737 | − | 0.0229535i | \(-0.00730696\pi\) |
−0.519747 | + | 0.854320i | \(0.673974\pi\) | |||||||
\(272\) | 23803.2 | 5.30617 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11238.2 | −2.47784 | ||||||||
\(275\) | −431.513 | − | 747.403i | −0.0946227 | − | 0.163891i | ||||
\(276\) | −4.51339 | + | 7.81743i | −0.000984328 | + | 0.00170491i | ||||
\(277\) | 2004.20 | − | 3471.38i | 0.434732 | − | 0.752979i | −0.562541 | − | 0.826769i | \(-0.690176\pi\) |
0.997274 | + | 0.0737905i | \(0.0235096\pi\) | |||||||
\(278\) | −7413.40 | − | 12840.4i | −1.59937 | − | 2.77020i | ||||
\(279\) | 1933.18 | 0.414827 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6935.44 | 1.47236 | 0.736181 | − | 0.676785i | \(-0.236627\pi\) | ||||
0.736181 | + | 0.676785i | \(0.236627\pi\) | |||||||
\(282\) | 2774.83 | + | 4806.15i | 0.585953 | + | 1.01490i | ||||
\(283\) | −1333.32 | + | 2309.38i | −0.280062 | + | 0.485082i | −0.971400 | − | 0.237450i | \(-0.923688\pi\) |
0.691338 | + | 0.722532i | \(0.257022\pi\) | |||||||
\(284\) | 3495.71 | − | 6054.74i | 0.730394 | − | 1.26508i | ||||
\(285\) | −114.150 | − | 197.714i | −0.0237252 | − | 0.0410932i | ||||
\(286\) | 13123.3 | 2.71327 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 9662.22 | 1.97692 | ||||||||
\(289\) | −1723.64 | − | 2985.43i | −0.350832 | − | 0.607660i | ||||
\(290\) | 2632.95 | − | 4560.40i | 0.533144 | − | 0.923433i | ||||
\(291\) | −1619.44 | + | 2804.96i | −0.326232 | + | 0.565050i | ||||
\(292\) | 7182.11 | + | 12439.8i | 1.43939 | + | 2.49309i | ||||
\(293\) | −5939.10 | −1.18418 | −0.592092 | − | 0.805870i | \(-0.701698\pi\) | ||||
−0.592092 | + | 0.805870i | \(0.701698\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1202.47 | −0.237324 | ||||||||
\(296\) | −7091.74 | − | 12283.3i | −1.39256 | − | 2.41199i | ||||
\(297\) | −2605.15 | + | 4512.26i | −0.508977 | + | 0.881575i | ||||
\(298\) | 1858.18 | − | 3218.46i | 0.361213 | − | 0.625639i | ||||
\(299\) | −3.58816 | − | 6.21488i | −0.000694009 | − | 0.00120206i | ||||
\(300\) | −2166.45 | −0.416934 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11726.7 | 2.23442 | ||||||||
\(303\) | −1712.93 | − | 2966.89i | −0.324770 | − | 0.562519i | ||||
\(304\) | 1539.57 | − | 2666.61i | 0.290462 | − | 0.503095i | ||||
\(305\) | 1945.47 | − | 3369.65i | 0.365237 | − | 0.632609i | ||||
\(306\) | −3051.77 | − | 5285.82i | −0.570124 | − | 0.987484i | ||||
\(307\) | −10381.5 | −1.92998 | −0.964992 | − | 0.262278i | \(-0.915526\pi\) | ||||
−0.964992 | + | 0.262278i | \(0.915526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2389.92 | 0.439993 | ||||||||
\(310\) | −2204.46 | − | 3818.23i | −0.403886 | − | 0.699551i | ||||
\(311\) | 2120.27 | − | 3672.42i | 0.386590 | − | 0.669594i | −0.605398 | − | 0.795923i | \(-0.706986\pi\) |
0.991988 | + | 0.126329i | \(0.0403194\pi\) | |||||||
\(312\) | 10601.5 | − | 18362.4i | 1.92369 | − | 3.33194i | ||||
\(313\) | −141.951 | − | 245.867i | −0.0256344 | − | 0.0444001i | 0.852924 | − | 0.522036i | \(-0.174827\pi\) |
−0.878558 | + | 0.477636i | \(0.841494\pi\) | |||||||
\(314\) | −15522.2 | −2.78972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8781.36 | 1.56326 | ||||||||
\(317\) | −869.746 | − | 1506.44i | −0.154100 | − | 0.266910i | 0.778631 | − | 0.627482i | \(-0.215915\pi\) |
−0.932731 | + | 0.360573i | \(0.882581\pi\) | |||||||
\(318\) | −3760.86 | + | 6514.01i | −0.663204 | + | 1.14870i | ||||
\(319\) | −3294.40 | + | 5706.07i | −0.578217 | + | 1.00150i | ||||
\(320\) | −5811.46 | − | 10065.7i | −1.01522 | − | 1.75841i | ||||
\(321\) | 8304.85 | 1.44402 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1081.47 | −0.186300 | ||||||||
\(324\) | 2873.62 | + | 4977.25i | 0.492733 | + | 0.853438i | ||||
\(325\) | 861.169 | − | 1491.59i | 0.146982 | − | 0.254580i | ||||
\(326\) | −3709.24 | + | 6424.59i | −0.630171 | + | 1.09149i | ||||
\(327\) | −785.737 | − | 1360.94i | −0.132879 | − | 0.230153i | ||||
\(328\) | 11579.7 | 1.94933 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3676.76 | 0.613330 | ||||||||
\(331\) | −2803.48 | − | 4855.77i | −0.465538 | − | 0.806336i | 0.533687 | − | 0.845682i | \(-0.320806\pi\) |
−0.999226 | + | 0.0393458i | \(0.987473\pi\) | |||||||
\(332\) | 5535.75 | − | 9588.19i | 0.915101 | − | 1.58500i | ||||
\(333\) | −1076.11 | + | 1863.87i | −0.177088 | + | 0.306726i | ||||
\(334\) | −4003.94 | − | 6935.04i | −0.655946 | − | 1.13613i | ||||
\(335\) | 759.723 | 0.123905 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9427.44 | −1.52387 | −0.761937 | − | 0.647652i | \(-0.775751\pi\) | ||||
−0.761937 | + | 0.647652i | \(0.775751\pi\) | |||||||
\(338\) | 7033.52 | + | 12182.4i | 1.13187 | + | 1.96046i | ||||
\(339\) | −674.760 | + | 1168.72i | −0.108106 | + | 0.187245i | ||||
\(340\) | −5131.32 | + | 8887.70i | −0.818484 | + | 1.41766i | ||||
\(341\) | 2758.27 | + | 4777.46i | 0.438031 | + | 0.758692i | ||||
\(342\) | −789.544 | −0.124835 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −658.303 | −0.103178 | ||||||||
\(345\) | −1.00530 | − | 1.74123i | −0.000156880 | − | 0.000271723i | ||||
\(346\) | 5460.47 | − | 9457.81i | 0.848430 | − | 1.46952i | ||||
\(347\) | −5817.11 | + | 10075.5i | −0.899939 | + | 1.55874i | −0.0723679 | + | 0.997378i | \(0.523056\pi\) |
−0.827571 | + | 0.561361i | \(0.810278\pi\) | |||||||
\(348\) | 8269.93 | + | 14323.9i | 1.27389 | + | 2.20645i | ||||
\(349\) | 1317.10 | 0.202013 | 0.101006 | − | 0.994886i | \(-0.467794\pi\) | ||||
0.101006 | + | 0.994886i | \(0.467794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10398.2 | −1.58124 | ||||||||
\(352\) | 13786.0 | + | 23878.1i | 2.08750 | + | 3.61565i | ||||
\(353\) | 2924.41 | − | 5065.23i | 0.440937 | − | 0.763725i | −0.556822 | − | 0.830632i | \(-0.687980\pi\) |
0.997759 | + | 0.0669064i | \(0.0213129\pi\) | |||||||
\(354\) | 2561.45 | − | 4436.56i | 0.384575 | − | 0.666104i | ||||
\(355\) | 778.622 | + | 1348.61i | 0.116408 | + | 0.201625i | ||||
\(356\) | −10637.0 | −1.58359 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 24051.0 | 3.55065 | ||||||||
\(359\) | 6211.00 | + | 10757.8i | 0.913104 | + | 1.58154i | 0.809654 | + | 0.586907i | \(0.199655\pi\) |
0.103450 | + | 0.994635i | \(0.467012\pi\) | |||||||
\(360\) | −2411.13 | + | 4176.19i | −0.352993 | + | 0.611402i | ||||
\(361\) | 3359.55 | − | 5818.91i | 0.489802 | − | 0.848362i | ||||
\(362\) | 1042.68 | + | 1805.98i | 0.151387 | + | 0.262211i | ||||
\(363\) | 537.735 | 0.0777515 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3199.44 | −0.458812 | ||||||||
\(366\) | 8288.30 | + | 14355.8i | 1.18371 | + | 2.05024i | ||||
\(367\) | −3295.39 | + | 5707.78i | −0.468713 | + | 0.811836i | −0.999361 | − | 0.0357573i | \(-0.988616\pi\) |
0.530647 | + | 0.847593i | \(0.321949\pi\) | |||||||
\(368\) | 13.5587 | − | 23.4844i | 0.00192064 | − | 0.00332665i | ||||
\(369\) | −878.557 | − | 1521.71i | −0.123945 | − | 0.214680i | ||||
\(370\) | 4908.45 | 0.689670 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13848.1 | 1.93009 | ||||||||
\(373\) | −172.139 | − | 298.154i | −0.0238955 | − | 0.0413882i | 0.853830 | − | 0.520551i | \(-0.174274\pi\) |
−0.877726 | + | 0.479163i | \(0.840940\pi\) | |||||||
\(374\) | 8708.52 | − | 15083.6i | 1.20403 | − | 2.08544i | ||||
\(375\) | 241.274 | − | 417.900i | 0.0332250 | − | 0.0575473i | ||||
\(376\) | −10385.2 | − | 17987.7i | −1.42440 | − | 2.46713i | ||||
\(377\) | −13149.2 | −1.79634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5241.23 | 0.710353 | 0.355177 | − | 0.934799i | \(-0.384421\pi\) | ||||
0.355177 | + | 0.934799i | \(0.384421\pi\) | |||||||
\(380\) | 663.779 | + | 1149.70i | 0.0896083 | + | 0.155206i | ||||
\(381\) | 2284.93 | − | 3957.61i | 0.307245 | − | 0.532164i | ||||
\(382\) | −6693.16 | + | 11592.9i | −0.896470 | + | 1.55273i | ||||
\(383\) | 3798.69 | + | 6579.52i | 0.506798 | + | 0.877801i | 0.999969 | + | 0.00786802i | \(0.00250450\pi\) |
−0.493171 | + | 0.869933i | \(0.664162\pi\) | |||||||
\(384\) | 24850.7 | 3.30250 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3437.27 | 0.453245 | ||||||||
\(387\) | 49.9458 | + | 86.5086i | 0.00656043 | + | 0.0113630i | ||||
\(388\) | 9417.01 | − | 16310.7i | 1.23216 | − | 2.13416i | ||||
\(389\) | −1550.92 | + | 2686.27i | −0.202146 | + | 0.350127i | −0.949220 | − | 0.314614i | \(-0.898125\pi\) |
0.747074 | + | 0.664741i | \(0.231458\pi\) | |||||||
\(390\) | 3668.84 | + | 6354.62i | 0.476357 | + | 0.825074i | ||||
\(391\) | −9.52432 | −0.00123188 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 862.246 | 0.110673 | ||||||||
\(394\) | 7841.84 | + | 13582.5i | 1.00271 | + | 1.73674i | ||||
\(395\) | −977.965 | + | 1693.89i | −0.124574 | + | 0.215769i | ||||
\(396\) | 4687.31 | − | 8118.67i | 0.594814 | − | 1.03025i | ||||
\(397\) | −1466.03 | − | 2539.24i | −0.185335 | − | 0.321009i | 0.758355 | − | 0.651842i | \(-0.226004\pi\) |
−0.943689 | + | 0.330833i | \(0.892670\pi\) | |||||||
\(398\) | −4786.09 | −0.602777 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6508.25 | 0.813531 | ||||||||
\(401\) | −44.6187 | − | 77.2819i | −0.00555649 | − | 0.00962413i | 0.863234 | − | 0.504804i | \(-0.168435\pi\) |
−0.868790 | + | 0.495180i | \(0.835102\pi\) | |||||||
\(402\) | −1618.33 | + | 2803.02i | −0.200783 | + | 0.347766i | ||||
\(403\) | −5504.65 | + | 9534.34i | −0.680413 | + | 1.17851i | ||||
\(404\) | 9960.64 | + | 17252.3i | 1.22663 | + | 2.12459i | ||||
\(405\) | −1280.12 | −0.157061 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6141.56 | −0.747975 | ||||||||
\(408\) | −14070.2 | − | 24370.3i | −1.70730 | − | 2.95713i | ||||
\(409\) | 73.6942 | − | 127.642i | 0.00890940 | − | 0.0154315i | −0.861536 | − | 0.507696i | \(-0.830497\pi\) |
0.870446 | + | 0.492264i | \(0.163831\pi\) | |||||||
\(410\) | −2003.68 | + | 3470.47i | −0.241353 | + | 0.418035i | ||||
\(411\) | 3931.16 | + | 6808.96i | 0.471800 | + | 0.817181i | ||||
\(412\) | −13897.3 | −1.66182 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.95336 | −0.000825457 | ||||||||
\(415\) | 1233.01 | + | 2135.64i | 0.145846 | + | 0.252613i | ||||
\(416\) | −27512.7 | + | 47653.4i | −3.24260 | + | 5.61635i | ||||
\(417\) | −5186.44 | + | 8983.17i | −0.609067 | + | 1.05493i | ||||
\(418\) | −1126.52 | − | 1951.19i | −0.131818 | − | 0.228315i | ||||
\(419\) | 3781.67 | 0.440923 | 0.220462 | − | 0.975396i | \(-0.429244\pi\) | ||||
0.220462 | + | 0.975396i | \(0.429244\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10899.2 | −1.26175 | −0.630874 | − | 0.775885i | \(-0.717304\pi\) | ||||
−0.630874 | + | 0.775885i | \(0.717304\pi\) | |||||||
\(422\) | −16487.5 | − | 28557.2i | −1.90189 | − | 3.29417i | ||||
\(423\) | −1575.86 | + | 2729.47i | −0.181137 | + | 0.313738i | ||||
\(424\) | 14075.5 | − | 24379.6i | 1.61219 | − | 2.79240i | ||||
\(425\) | −1142.93 | − | 1979.62i | −0.130448 | − | 0.225942i | ||||
\(426\) | −6634.33 | −0.754541 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −48292.4 | −5.45398 | ||||||||
\(429\) | −4590.54 | − | 7951.05i | −0.516628 | − | 0.894826i | ||||
\(430\) | 113.909 | − | 197.296i | 0.0127748 | − | 0.0221266i | ||||
\(431\) | 5641.69 | − | 9771.69i | 0.630512 | − | 1.09208i | −0.356936 | − | 0.934129i | \(-0.616178\pi\) |
0.987447 | − | 0.157949i | \(-0.0504882\pi\) | |||||||
\(432\) | −19646.0 | − | 34027.8i | −2.18800 | − | 3.78973i | ||||
\(433\) | 8906.19 | 0.988462 | 0.494231 | − | 0.869331i | \(-0.335450\pi\) | ||||
0.494231 | + | 0.869331i | \(0.335450\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3684.03 | −0.406059 | ||||||||
\(436\) | 4569.03 | + | 7913.80i | 0.501874 | + | 0.869271i | ||||
\(437\) | −0.616026 | + | 1.06699i | −6.74337e−5 | + | 0.000116799i | ||||
\(438\) | 6815.29 | − | 11804.4i | 0.743487 | − | 1.28776i | ||||
\(439\) | 4074.74 | + | 7057.67i | 0.443000 | + | 0.767298i | 0.997910 | − | 0.0646116i | \(-0.0205809\pi\) |
−0.554911 | + | 0.831910i | \(0.687248\pi\) | |||||||
\(440\) | −13760.8 | −1.49095 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 34759.1 | 3.74054 | ||||||||
\(443\) | 5736.39 | + | 9935.71i | 0.615223 | + | 1.06560i | 0.990345 | + | 0.138623i | \(0.0442675\pi\) |
−0.375122 | + | 0.926975i | \(0.622399\pi\) | |||||||
\(444\) | −7708.58 | + | 13351.6i | −0.823948 | + | 1.42712i | ||||
\(445\) | 1184.62 | − | 2051.83i | 0.126195 | − | 0.218575i | ||||
\(446\) | 14295.9 | + | 24761.3i | 1.51778 | + | 2.62888i | ||||
\(447\) | −2599.97 | −0.275111 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1963.80 | 0.206409 | 0.103204 | − | 0.994660i | \(-0.467090\pi\) | ||||
0.103204 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(450\) | −834.413 | − | 1445.25i | −0.0874102 | − | 0.151399i | ||||
\(451\) | 2507.05 | − | 4342.34i | 0.261757 | − | 0.453376i | ||||
\(452\) | 3923.71 | − | 6796.06i | 0.408309 | − | 0.707212i | ||||
\(453\) | −4102.01 | − | 7104.89i | −0.425451 | − | 0.736903i | ||||
\(454\) | 20709.3 | 2.14083 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3640.20 | −0.373833 | ||||||||
\(457\) | −2794.93 | − | 4840.96i | −0.286086 | − | 0.495515i | 0.686786 | − | 0.726860i | \(-0.259021\pi\) |
−0.972872 | + | 0.231344i | \(0.925688\pi\) | |||||||
\(458\) | 17266.1 | − | 29905.8i | 1.76156 | − | 3.05111i | ||||
\(459\) | −6900.16 | + | 11951.4i | −0.701682 | + | 1.21535i | ||||
\(460\) | 5.84577 | + | 10.1252i | 0.000592523 | + | 0.00102628i | ||||
\(461\) | 18790.9 | 1.89844 | 0.949219 | − | 0.314618i | \(-0.101876\pi\) | ||||
0.949219 | + | 0.314618i | \(0.101876\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7892.22 | −0.792187 | −0.396094 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396094 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(464\) | −24843.7 | − | 43030.6i | −2.48565 | − | 4.30527i | ||||
\(465\) | −1542.24 | + | 2671.25i | −0.153806 | + | 0.266400i | ||||
\(466\) | 4910.89 | − | 8505.91i | 0.488182 | − | 0.845556i | ||||
\(467\) | 192.755 | + | 333.862i | 0.0190999 | + | 0.0330820i | 0.875417 | − | 0.483368i | \(-0.160587\pi\) |
−0.856317 | + | 0.516450i | \(0.827253\pi\) | |||||||
\(468\) | 18708.9 | 1.84790 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7187.95 | 0.705437 | ||||||||
\(471\) | 5429.71 | + | 9404.53i | 0.531184 | + | 0.920038i | ||||
\(472\) | −9586.58 | + | 16604.4i | −0.934869 | + | 1.61924i | ||||
\(473\) | −142.525 | + | 246.861i | −0.0138548 | + | 0.0239972i | ||||
\(474\) | −4166.43 | − | 7216.47i | −0.403735 | − | 0.699290i | ||||
\(475\) | −295.696 | −0.0285631 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4271.67 | −0.410035 | ||||||||
\(478\) | 9710.15 | + | 16818.5i | 0.929146 | + | 1.60933i | ||||
\(479\) | 847.229 | − | 1467.44i | 0.0808160 | − | 0.139977i | −0.822785 | − | 0.568353i | \(-0.807581\pi\) |
0.903601 | + | 0.428376i | \(0.140914\pi\) | |||||||
\(480\) | −7708.27 | + | 13351.1i | −0.732985 | + | 1.26957i | ||||
\(481\) | −6128.34 | − | 10614.6i | −0.580932 | − | 1.00620i | ||||
\(482\) | 2002.64 | 0.189248 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3126.91 | −0.293662 | ||||||||
\(485\) | 2097.51 | + | 3633.00i | 0.196378 | + | 0.340136i | ||||
\(486\) | −8516.41 | + | 14750.9i | −0.794881 | + | 1.37677i | ||||
\(487\) | −7855.58 | + | 13606.3i | −0.730945 | + | 1.26603i | 0.225534 | + | 0.974235i | \(0.427587\pi\) |
−0.956480 | + | 0.291799i | \(0.905746\pi\) | |||||||
\(488\) | −31020.1 | − | 53728.4i | −2.87749 | − | 4.98395i | ||||
\(489\) | 5189.99 | 0.479958 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2716.34 | −0.249667 | −0.124834 | − | 0.992178i | \(-0.539840\pi\) | ||||
−0.124834 | + | 0.992178i | \(0.539840\pi\) | |||||||
\(492\) | −6293.44 | − | 10900.6i | −0.576687 | − | 0.998852i | ||||
\(493\) | −8725.75 | + | 15113.4i | −0.797136 | + | 1.38068i | ||||
\(494\) | 2248.19 | − | 3893.98i | 0.204759 | − | 0.354653i | ||||
\(495\) | 1044.04 | + | 1808.32i | 0.0947999 | + | 0.164198i | ||||
\(496\) | −41601.2 | −3.76603 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −10506.0 | −0.945355 | ||||||||
\(499\) | −2147.67 | − | 3719.87i | −0.192671 | − | 0.333716i | 0.753463 | − | 0.657490i | \(-0.228382\pi\) |
−0.946135 | + | 0.323774i | \(0.895048\pi\) | |||||||
\(500\) | −1403.00 | + | 2430.07i | −0.125488 | + | 0.217352i | ||||
\(501\) | −2801.17 | + | 4851.77i | −0.249795 | + | 0.432657i | ||||
\(502\) | 14716.0 | + | 25488.9i | 1.30838 | + | 2.26619i | ||||
\(503\) | −6515.26 | −0.577537 | −0.288769 | − | 0.957399i | \(-0.593246\pi\) | ||||
−0.288769 | + | 0.957399i | \(0.593246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4437.20 | −0.390996 | ||||||||
\(506\) | −9.92105 | − | 17.1838i | −0.000871629 | − | 0.00150971i | ||||
\(507\) | 4920.67 | − | 8522.85i | 0.431035 | − | 0.746574i | ||||
\(508\) | −13286.8 | + | 23013.3i | −1.16044 | + | 2.00994i | ||||
\(509\) | 7195.88 | + | 12463.6i | 0.626624 | + | 1.08535i | 0.988224 | + | 0.153012i | \(0.0488973\pi\) |
−0.361600 | + | 0.932333i | \(0.617769\pi\) | |||||||
\(510\) | 9738.48 | 0.845544 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −41890.2 | −3.61583 | ||||||||
\(513\) | 892.594 | + | 1546.02i | 0.0768207 | + | 0.133057i | ||||
\(514\) | 6728.56 | − | 11654.2i | 0.577401 | − | 1.00009i | ||||
\(515\) | 1547.72 | − | 2680.73i | 0.132428 | − | 0.229373i | ||||
\(516\) | 357.781 | + | 619.695i | 0.0305241 | + | 0.0528692i | ||||
\(517\) | −8993.73 | −0.765075 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7640.32 | −0.646191 | ||||||||
\(520\) | −13731.1 | − | 23783.0i | −1.15798 | − | 2.00568i | ||||
\(521\) | 1456.68 | − | 2523.05i | 0.122492 | − | 0.212163i | −0.798258 | − | 0.602316i | \(-0.794245\pi\) |
0.920750 | + | 0.390153i | \(0.127578\pi\) | |||||||
\(522\) | −6370.35 | + | 11033.8i | −0.534143 | + | 0.925163i | ||||
\(523\) | 8435.11 | + | 14610.0i | 0.705242 | + | 1.22151i | 0.966604 | + | 0.256274i | \(0.0824949\pi\) |
−0.261362 | + | 0.965241i | \(0.584172\pi\) | |||||||
\(524\) | −5013.93 | −0.418005 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8421.82 | −0.698115 | ||||||||
\(527\) | 7305.71 | + | 12653.9i | 0.603874 | + | 1.04594i | ||||
\(528\) | 17346.4 | − | 30044.9i | 1.42975 | − | 2.47639i | ||||
\(529\) | 6083.49 | − | 10536.9i | 0.500000 | − | 0.866025i | ||||
\(530\) | 4871.09 | + | 8436.98i | 0.399220 | + | 0.691470i | ||||
\(531\) | 2909.35 | 0.237769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10006.6 | 0.813197 | ||||||||
\(534\) | 5046.86 | + | 8741.43i | 0.408987 | + | 0.708387i | ||||
\(535\) | 5378.25 | − | 9315.40i | 0.434620 | − | 0.752785i | ||||
\(536\) | 6056.80 | − | 10490.7i | 0.488086 | − | 0.845390i | ||||
\(537\) | −8413.07 | − | 14571.9i | −0.676072 | − | 1.17099i | ||||
\(538\) | −41738.6 | −3.34476 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 16940.5 | 1.35001 | ||||||||
\(541\) | 1114.79 | + | 1930.88i | 0.0885929 | + | 0.153447i | 0.906917 | − | 0.421310i | \(-0.138430\pi\) |
−0.818324 | + | 0.574758i | \(0.805096\pi\) | |||||||
\(542\) | −11815.9 | + | 20465.7i | −0.936412 | + | 1.62191i | ||||
\(543\) | 729.465 | − | 1263.47i | 0.0576507 | − | 0.0998539i | ||||
\(544\) | 36514.5 | + | 63245.0i | 2.87785 | + | 4.98457i | ||||
\(545\) | −2035.38 | −0.159975 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1218.73 | −0.0952639 | −0.0476319 | − | 0.998865i | \(-0.515167\pi\) | ||||
−0.0476319 | + | 0.998865i | \(0.515167\pi\) | |||||||
\(548\) | −22859.5 | − | 39593.9i | −1.78195 | − | 3.08643i | ||||
\(549\) | −4707.02 | + | 8152.80i | −0.365921 | + | 0.633794i | ||||
\(550\) | 2381.08 | − | 4124.15i | 0.184599 | − | 0.319735i | ||||
\(551\) | 1128.75 | + | 1955.05i | 0.0872710 | + | 0.151158i | ||||
\(552\) | −32.0585 | −0.00247192 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 22118.3 | 1.69624 | ||||||||
\(555\) | −1716.98 | − | 2973.90i | −0.131319 | − | 0.227451i | ||||
\(556\) | 30158.9 | − | 52236.8i | 2.30040 | − | 3.98442i | ||||
\(557\) | 11367.3 | − | 19688.7i | 0.864714 | − | 1.49773i | −0.00261590 | − | 0.999997i | \(-0.500833\pi\) |
0.867330 | − | 0.497733i | \(-0.165834\pi\) | |||||||
\(558\) | 5333.63 | + | 9238.12i | 0.404643 | + | 0.700862i | ||||
\(559\) | −568.873 | −0.0430425 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12185.0 | −0.917026 | ||||||||
\(562\) | 19134.8 | + | 33142.4i | 1.43621 | + | 2.48759i | ||||
\(563\) | 2151.06 | − | 3725.74i | 0.161023 | − | 0.278901i | −0.774213 | − | 0.632926i | \(-0.781854\pi\) |
0.935236 | + | 0.354025i | \(0.115187\pi\) | |||||||
\(564\) | −11288.5 | + | 19552.2i | −0.842784 | + | 1.45975i | ||||
\(565\) | 873.954 | + | 1513.73i | 0.0650752 | + | 0.112714i | ||||
\(566\) | −14714.4 | −1.09275 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24829.9 | 1.83422 | ||||||||
\(569\) | −7433.46 | − | 12875.1i | −0.547675 | − | 0.948601i | −0.998433 | − | 0.0559547i | \(-0.982180\pi\) |
0.450759 | − | 0.892646i | \(-0.351154\pi\) | |||||||
\(570\) | 629.878 | − | 1090.98i | 0.0462854 | − | 0.0801686i | ||||
\(571\) | −8257.24 | + | 14302.0i | −0.605174 | + | 1.04819i | 0.386850 | + | 0.922143i | \(0.373563\pi\) |
−0.992024 | + | 0.126050i | \(0.959770\pi\) | |||||||
\(572\) | 26693.8 | + | 46235.1i | 1.95127 | + | 3.37969i | ||||
\(573\) | 9365.10 | 0.682780 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.60414 | −0.000188870 | ||||||||
\(576\) | 14060.7 | + | 24353.8i | 1.01712 | + | 1.76171i | ||||
\(577\) | 933.984 | − | 1617.71i | 0.0673870 | − | 0.116718i | −0.830363 | − | 0.557222i | \(-0.811867\pi\) |
0.897750 | + | 0.440505i | \(0.145200\pi\) | |||||||
\(578\) | 9511.00 | − | 16473.5i | 0.684438 | − | 1.18548i | ||||
\(579\) | −1202.36 | − | 2082.55i | −0.0863014 | − | 0.149478i | ||||
\(580\) | 21422.5 | 1.53366 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −17872.1 | −1.27289 | ||||||||
\(583\) | −6094.82 | − | 10556.5i | −0.432970 | − | 0.749927i | ||||
\(584\) | −25507.2 | + | 44179.7i | −1.80735 | + | 3.13043i | ||||
\(585\) | −2083.58 | + | 3608.86i | −0.147257 | + | 0.255056i | ||||
\(586\) | −16385.9 | − | 28381.2i | −1.15511 | − | 2.00071i | ||||
\(587\) | −3926.15 | −0.276064 | −0.138032 | − | 0.990428i | \(-0.544078\pi\) | ||||
−0.138032 | + | 0.990428i | \(0.544078\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1890.11 | 0.132225 | ||||||||
\(590\) | −3317.61 | − | 5746.26i | −0.231498 | − | 0.400966i | ||||
\(591\) | 5486.17 | − | 9502.33i | 0.381846 | − | 0.661377i | ||||
\(592\) | 23157.3 | − | 40109.7i | 1.60770 | − | 2.78463i | ||||
\(593\) | −3777.09 | − | 6542.11i | −0.261562 | − | 0.453039i | 0.705095 | − | 0.709113i | \(-0.250904\pi\) |
−0.966657 | + | 0.256074i | \(0.917571\pi\) | |||||||
\(594\) | −28750.3 | −1.98593 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15118.8 | 1.03907 | ||||||||
\(597\) | 1674.18 | + | 2899.77i | 0.114773 | + | 0.198793i | ||||
\(598\) | 19.7994 | − | 34.2935i | 0.00135394 | − | 0.00234509i | ||||
\(599\) | −14105.5 | + | 24431.4i | −0.962160 | + | 1.66651i | −0.245099 | + | 0.969498i | \(0.578821\pi\) |
−0.717060 | + | 0.697011i | \(0.754513\pi\) | |||||||
\(600\) | −3847.07 | − | 6663.32i | −0.261760 | − | 0.453381i | ||||
\(601\) | 23181.4 | 1.57336 | 0.786679 | − | 0.617363i | \(-0.211799\pi\) | ||||
0.786679 | + | 0.617363i | \(0.211799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1838.13 | −0.124137 | ||||||||
\(604\) | 23853.0 | + | 41314.7i | 1.60690 | + | 2.78323i | ||||
\(605\) | 348.239 | − | 603.167i | 0.0234015 | − | 0.0405326i | ||||
\(606\) | 9451.92 | − | 16371.2i | 0.633594 | − | 1.09742i | ||||
\(607\) | −12431.8 | − | 21532.5i | −0.831287 | − | 1.43983i | −0.897018 | − | 0.441994i | \(-0.854271\pi\) |
0.0657313 | − | 0.997837i | \(-0.479062\pi\) | |||||||
\(608\) | 9446.93 | 0.630137 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 21470.1 | 1.42508 | ||||||||
\(611\) | −8974.36 | − | 15544.1i | −0.594213 | − | 1.02921i | ||||
\(612\) | 12415.1 | − | 21503.6i | 0.820017 | − | 1.42031i | ||||
\(613\) | 6396.36 | − | 11078.8i | 0.421446 | − | 0.729966i | −0.574635 | − | 0.818410i | \(-0.694856\pi\) |
0.996081 | + | 0.0884435i | \(0.0281893\pi\) | |||||||
\(614\) | −28642.5 | − | 49610.3i | −1.88260 | − | 3.26076i | ||||
\(615\) | 2803.56 | 0.183822 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19793.3 | 1.29149 | 0.645744 | − | 0.763554i | \(-0.276547\pi\) | ||||
0.645744 | + | 0.763554i | \(0.276547\pi\) | |||||||
\(618\) | 6593.76 | + | 11420.7i | 0.429191 | + | 0.743380i | ||||
\(619\) | −10475.8 | + | 18144.7i | −0.680226 | + | 1.17819i | 0.294686 | + | 0.955594i | \(0.404785\pi\) |
−0.974912 | + | 0.222592i | \(0.928548\pi\) | |||||||
\(620\) | 8968.10 | − | 15533.2i | 0.580915 | − | 1.00617i | ||||
\(621\) | 7.86091 | + | 13.6155i | 0.000507967 | + | 0.000879824i | ||||
\(622\) | 23399.2 | 1.50840 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 69236.3 | 4.44178 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 783.284 | − | 1356.69i | 0.0500101 | − | 0.0866200i | ||||
\(627\) | −788.117 | + | 1365.06i | −0.0501984 | + | 0.0869461i | ||||
\(628\) | −31573.5 | − | 54687.0i | −2.00624 | − | 3.47492i | ||||
\(629\) | −16266.9 | −1.03117 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23273.5 | 1.46831 | 0.734156 | − | 0.678981i | \(-0.237578\pi\) | ||||
0.734156 | + | 0.678981i | \(0.237578\pi\) | |||||||
\(632\) | 15593.4 | + | 27008.6i | 0.981446 | + | 1.69991i | ||||
\(633\) | −11534.7 | + | 19978.7i | −0.724270 | + | 1.25447i | ||||
\(634\) | 4799.24 | − | 8312.52i | 0.300634 | − | 0.520713i | ||||
\(635\) | −2959.45 | − | 5125.91i | −0.184948 | − | 0.320340i | ||||
\(636\) | −30599.6 | −1.90779 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −36356.8 | −2.25608 | ||||||||
\(639\) | −1883.86 | − | 3262.94i | −0.116626 | − | 0.202003i | ||||
\(640\) | 16093.4 | − | 27874.6i | 0.993981 | − | 1.72163i | ||||
\(641\) | 11058.9 | − | 19154.5i | 0.681434 | − | 1.18028i | −0.293110 | − | 0.956079i | \(-0.594690\pi\) |
0.974543 | − | 0.224199i | \(-0.0719765\pi\) | |||||||
\(642\) | 22913.0 | + | 39686.5i | 1.40857 | + | 2.43972i | ||||
\(643\) | −20269.9 | −1.24318 | −0.621591 | − | 0.783342i | \(-0.713513\pi\) | ||||
−0.621591 | + | 0.783342i | \(0.713513\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −159.382 | −0.00972969 | ||||||||
\(646\) | −2983.77 | − | 5168.04i | −0.181726 | − | 0.314758i | ||||
\(647\) | −1572.62 | + | 2723.87i | −0.0955583 | + | 0.165512i | −0.909841 | − | 0.414956i | \(-0.863797\pi\) |
0.814283 | + | 0.580468i | \(0.197130\pi\) | |||||||
\(648\) | −10205.6 | + | 17676.6i | −0.618695 | + | 1.07161i | ||||
\(649\) | 4151.06 | + | 7189.85i | 0.251069 | + | 0.434864i | ||||
\(650\) | 9503.81 | 0.573493 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30179.6 | −1.81277 | ||||||||
\(653\) | 2976.67 | + | 5155.75i | 0.178386 | + | 0.308974i | 0.941328 | − | 0.337493i | \(-0.109579\pi\) |
−0.762942 | + | 0.646467i | \(0.776246\pi\) | |||||||
\(654\) | 4335.68 | − | 7509.61i | 0.259233 | − | 0.449005i | ||||
\(655\) | 558.393 | − | 967.165i | 0.0333102 | − | 0.0576950i | ||||
\(656\) | 18906.1 | + | 32746.4i | 1.12524 | + | 1.94898i | ||||
\(657\) | 7740.96 | 0.459671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26277.5 | 1.55330 | 0.776652 | − | 0.629930i | \(-0.216916\pi\) | ||||
0.776652 | + | 0.629930i | \(0.216916\pi\) | |||||||
\(660\) | 7478.83 | + | 12953.7i | 0.441081 | + | 0.763974i | ||||
\(661\) | −12002.2 | + | 20788.4i | −0.706248 | + | 1.22326i | 0.259991 | + | 0.965611i | \(0.416280\pi\) |
−0.966239 | + | 0.257647i | \(0.917053\pi\) | |||||||
\(662\) | 15469.5 | − | 26794.0i | 0.908218 | − | 1.57308i | ||||
\(663\) | −12158.8 | − | 21059.6i | −0.712229 | − | 1.23362i | ||||
\(664\) | 39320.3 | 2.29808 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −11875.9 | −0.690962 | ||||||||
\(667\) | 9.94068 | + | 17.2178i | 0.000577068 | + | 0.000999512i | ||||
\(668\) | 16288.7 | − | 28212.9i | 0.943457 | − | 1.63412i | ||||
\(669\) | 10001.5 | − | 17323.1i | 0.577996 | − | 1.00112i | ||||
\(670\) | 2096.06 | + | 3630.49i | 0.120863 | + | 0.209340i | ||||
\(671\) | −26863.9 | −1.54556 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9205.36 | 0.527252 | 0.263626 | − | 0.964625i | \(-0.415082\pi\) | ||||
0.263626 | + | 0.964625i | \(0.415082\pi\) | |||||||
\(674\) | −26010.2 | − | 45050.9i | −1.48646 | − | 2.57463i | ||||
\(675\) | −1886.64 | + | 3267.76i | −0.107580 | + | 0.186335i | ||||
\(676\) | −28613.5 | + | 49560.1i | −1.62799 | + | 2.81976i | ||||
\(677\) | −9386.57 | − | 16258.0i | −0.532873 | − | 0.922964i | −0.999263 | − | 0.0383843i | \(-0.987779\pi\) |
0.466390 | − | 0.884579i | \(-0.345554\pi\) | |||||||
\(678\) | −7446.62 | −0.421808 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −36447.6 | −2.05544 | ||||||||
\(681\) | −7244.14 | − | 12547.2i | −0.407630 | − | 0.706036i | ||||
\(682\) | −15220.0 | + | 26361.9i | −0.854554 | + | 1.48013i | ||||
\(683\) | 5111.12 | − | 8852.73i | 0.286342 | − | 0.495959i | −0.686592 | − | 0.727043i | \(-0.740894\pi\) |
0.972934 | + | 0.231084i | \(0.0742272\pi\) | |||||||
\(684\) | −1606.00 | − | 2781.67i | −0.0897761 | − | 0.155497i | ||||
\(685\) | 10183.3 | 0.568006 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24158.9 | −1.34166 | ||||||||
\(688\) | −1074.81 | − | 1861.63i | −0.0595592 | − | 0.103160i | ||||
\(689\) | 12163.4 | − | 21067.6i | 0.672552 | − | 1.16489i | ||||
\(690\) | 5.54721 | − | 9.60805i | 0.000306056 | − | 0.000530105i | ||||
\(691\) | 11177.6 | + | 19360.1i | 0.615361 | + | 1.06584i | 0.990321 | + | 0.138795i | \(0.0443229\pi\) |
−0.374961 | + | 0.927041i | \(0.622344\pi\) | |||||||
\(692\) | 44428.2 | 2.44062 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −64197.3 | −3.51138 | ||||||||
\(695\) | 6717.50 | + | 11635.1i | 0.366632 | + | 0.635026i | ||||
\(696\) | −29370.5 | + | 50871.3i | −1.59955 | + | 2.77050i | ||||
\(697\) | 6640.32 | − | 11501.4i | 0.360861 | − | 0.625029i | ||||
\(698\) | 3633.85 | + | 6294.01i | 0.197053 | + | 0.341307i | ||||
\(699\) | −6871.35 | −0.371814 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16217.3 | 0.873779 | 0.436890 | − | 0.899515i | \(-0.356080\pi\) | ||||
0.436890 | + | 0.899515i | \(0.356080\pi\) | |||||||
\(702\) | −28688.4 | − | 49689.8i | −1.54241 | − | 2.67154i | ||||
\(703\) | −1052.13 | + | 1822.34i | −0.0564465 | + | 0.0977682i | ||||
\(704\) | −40123.5 | + | 69496.0i | −2.14803 | + | 3.72050i | ||||
\(705\) | −2514.36 | − | 4354.99i | −0.134321 | − | 0.232650i | ||||
\(706\) | 32273.7 | 1.72045 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20840.8 | 1.10628 | ||||||||
\(709\) | −1961.46 | − | 3397.35i | −0.103899 | − | 0.179958i | 0.809389 | − | 0.587273i | \(-0.199798\pi\) |
−0.913288 | + | 0.407315i | \(0.866465\pi\) | |||||||
\(710\) | −4296.41 | + | 7441.61i | −0.227101 | + | 0.393350i | ||||
\(711\) | 2366.16 | − | 4098.32i | 0.124807 | − | 0.216173i | ||||
\(712\) | −18888.6 | − | 32716.0i | −0.994212 | − | 1.72203i | ||||
\(713\) | 16.6458 | 0.000874322 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11891.4 | −0.621976 | ||||||||
\(716\) | 48921.7 | + | 84734.9i | 2.55348 | + | 4.42275i | ||||
\(717\) | 6793.25 | − | 11766.3i | 0.353833 | − | 0.612857i | ||||
\(718\) | −34272.2 | + | 59361.1i | −1.78137 | + | 3.08543i | ||||
\(719\) | 11954.3 | + | 20705.4i | 0.620055 | + | 1.07397i | 0.989475 | + | 0.144705i | \(0.0462232\pi\) |
−0.369420 | + | 0.929263i | \(0.620444\pi\) | |||||||
\(720\) | −15746.6 | −0.815055 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 37075.8 | 1.91111 | ||||||||
\(723\) | −700.527 | − | 1213.35i | −0.0360344 | − | 0.0624134i | ||||
\(724\) | −4241.81 | + | 7347.03i | −0.217743 | + | 0.377141i | ||||
\(725\) | −2385.79 | + | 4132.31i | −0.122215 | + | 0.211683i | ||||
\(726\) | 1483.60 | + | 2569.68i | 0.0758426 | + | 0.131363i | ||||
\(727\) | 26906.4 | 1.37263 | 0.686315 | − | 0.727305i | \(-0.259227\pi\) | ||||
0.686315 | + | 0.727305i | \(0.259227\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18828.9 | 0.956605 | ||||||||
\(730\) | −8827.21 | − | 15289.2i | −0.447547 | − | 0.775175i | ||||
\(731\) | −377.501 | + | 653.850i | −0.0191004 | + | 0.0330828i | ||||
\(732\) | −33718.2 | + | 58401.6i | −1.70254 | + | 2.94889i | ||||
\(733\) | 13818.7 | + | 23934.7i | 0.696325 | + | 1.20607i | 0.969732 | + | 0.244172i | \(0.0785162\pi\) |
−0.273407 | + | 0.961899i | \(0.588150\pi\) | |||||||
\(734\) | −36367.7 | −1.82882 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 83.1973 | 0.00416670 | ||||||||
\(737\) | −2622.64 | − | 4542.55i | −0.131080 | − | 0.227038i | ||||
\(738\) | 4847.85 | − | 8396.73i | 0.241805 | − | 0.418818i | ||||
\(739\) | 7019.44 | − | 12158.0i | 0.349410 | − | 0.605197i | −0.636734 | − | 0.771083i | \(-0.719715\pi\) |
0.986145 | + | 0.165887i | \(0.0530486\pi\) | |||||||
\(740\) | 9984.19 | + | 17293.1i | 0.495981 | + | 0.859065i | ||||
\(741\) | −3145.68 | −0.155951 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17698.7 | 0.873893 | 0.436946 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436946 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(744\) | 24590.7 | + | 42592.4i | 1.21175 | + | 2.09881i | ||||
\(745\) | −1683.75 | + | 2916.34i | −0.0828025 | + | 0.143418i | ||||
\(746\) | 949.859 | − | 1645.20i | 0.0466177 | − | 0.0807442i | ||||
\(747\) | −2983.25 | − | 5167.14i | −0.146120 | − | 0.253087i | ||||
\(748\) | 70855.4 | 3.46354 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2662.69 | 0.129637 | ||||||||
\(751\) | −8599.83 | − | 14895.3i | −0.417859 | − | 0.723754i | 0.577865 | − | 0.816133i | \(-0.303886\pi\) |
−0.995724 | + | 0.0923791i | \(0.970553\pi\) | |||||||
\(752\) | 33911.7 | − | 58736.8i | 1.64446 | − | 2.84829i | ||||
\(753\) | 10295.4 | − | 17832.1i | 0.498253 | − | 0.862999i | ||||
\(754\) | −36278.6 | − | 62836.3i | −1.75224 | − | 3.03496i | ||||
\(755\) | −10625.9 | −0.512206 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19200.7 | −0.921879 | −0.460939 | − | 0.887432i | \(-0.652487\pi\) | ||||
−0.460939 | + | 0.887432i | \(0.652487\pi\) | |||||||
\(758\) | 14460.5 | + | 25046.3i | 0.692914 | + | 1.20016i | ||||
\(759\) | −6.94080 | + | 12.0218i | −0.000331930 | + | 0.000574920i | ||||
\(760\) | −2357.40 | + | 4083.14i | −0.112516 | + | 0.194883i | ||||
\(761\) | −13959.4 | − | 24178.3i | −0.664949 | − | 1.15173i | −0.979299 | − | 0.202419i | \(-0.935120\pi\) |
0.314350 | − | 0.949307i | \(-0.398213\pi\) | |||||||
\(762\) | 25216.3 | 1.19881 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −54457.7 | −2.57881 | ||||||||
\(765\) | 2765.30 | + | 4789.64i | 0.130692 | + | 0.226366i | ||||
\(766\) | −20961.1 | + | 36305.6i | −0.988712 | + | 1.71250i | ||||
\(767\) | −8284.25 | + | 14348.7i | −0.389996 | + | 0.675493i | ||||
\(768\) | 32667.7 | + | 56582.1i | 1.53489 | + | 2.65850i | ||||
\(769\) | 7436.29 | 0.348712 | 0.174356 | − | 0.984683i | \(-0.444216\pi\) | ||||
0.174356 | + | 0.984683i | \(0.444216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9414.64 | −0.439766 | ||||||||
\(772\) | 6991.70 | + | 12110.0i | 0.325954 | + | 0.564569i | ||||
\(773\) | 2494.92 | − | 4321.33i | 0.116088 | − | 0.201070i | −0.802126 | − | 0.597155i | \(-0.796298\pi\) |
0.918214 | + | 0.396084i | \(0.129631\pi\) | |||||||
\(774\) | −275.600 | + | 477.352i | −0.0127987 | + | 0.0221681i | ||||
\(775\) | 1997.52 | + | 3459.81i | 0.0925847 | + | 0.160361i | ||||
\(776\) | 66888.7 | 3.09429 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −17115.9 | −0.788731 | ||||||||
\(779\) | −858.981 | − | 1487.80i | −0.0395073 | − | 0.0684287i | ||||
\(780\) | −14925.5 | + | 25851.7i | −0.685150 | + | 1.18672i | ||||
\(781\) | 5375.77 | − | 9311.11i | 0.246300 | − | 0.426604i | ||||
\(782\) | −26.2775 | − | 45.5139i | −0.00120164 | − | 0.00208130i | ||||
\(783\) | 28807.2 | 1.31480 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14065.2 | 0.639500 | ||||||||
\(786\) | 2378.92 | + | 4120.42i | 0.107956 | + | 0.186985i | ||||
\(787\) | −1435.35 | + | 2486.09i | −0.0650122 | + | 0.112604i | −0.896699 | − | 0.442640i | \(-0.854042\pi\) |
0.831687 | + | 0.555244i | \(0.187375\pi\) | |||||||
\(788\) | −31901.9 | + | 55255.7i | −1.44221 | + | 2.49797i | ||||
\(789\) | 2945.96 | + | 5102.56i | 0.132927 | + | 0.230236i | ||||
\(790\) | −10792.8 | −0.486063 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 33293.9 | 1.49374 | ||||||||
\(793\) | −26806.1 | − | 46429.4i | −1.20039 | − | 2.07914i | ||||
\(794\) | 8089.50 | − | 14011.4i | 0.361569 | − | 0.626256i | ||||
\(795\) | 3407.83 | − | 5902.54i | 0.152029 | − | 0.263322i | ||||
\(796\) | −9735.31 | − | 16862.0i | −0.433491 | − | 0.750828i | ||||
\(797\) | −4676.61 | −0.207847 | −0.103923 | − | 0.994585i | \(-0.533140\pi\) | ||||
−0.103923 | + | 0.994585i | \(0.533140\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23821.3 | −1.05474 | ||||||||
\(800\) | 9983.79 | + | 17292.4i | 0.441225 | + | 0.764225i | ||||
\(801\) | −2866.17 | + | 4964.35i | −0.126431 | + | 0.218985i | ||||
\(802\) | 246.205 | − | 426.440i | 0.0108402 | − | 0.0187757i | ||||
\(803\) | 11044.8 | + | 19130.2i | 0.485383 | + | 0.840708i | ||||
\(804\) | −13167.2 | −0.577578 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −60749.1 | −2.65483 | ||||||||
\(807\) | 14600.2 | + | 25288.3i | 0.636868 | + | 1.10309i | ||||
\(808\) | −35375.1 | + | 61271.4i | −1.54021 | + | 2.66772i | ||||
\(809\) | 7688.45 | − | 13316.8i | 0.334131 | − | 0.578731i | −0.649187 | − | 0.760629i | \(-0.724891\pi\) |
0.983317 | + | 0.181898i | \(0.0582240\pi\) | |||||||
\(810\) | −3531.83 | − | 6117.32i | −0.153205 | − | 0.265359i | ||||
\(811\) | −36422.9 | −1.57704 | −0.788522 | − | 0.615007i | \(-0.789153\pi\) | ||||
−0.788522 | + | 0.615007i | \(0.789153\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16532.8 | 0.713200 | ||||||||
\(814\) | −16944.5 | − | 29348.7i | −0.729612 | − | 1.26372i | ||||
\(815\) | 3361.05 | − | 5821.51i | 0.144457 | − | 0.250207i | ||||
\(816\) | 45944.8 | − | 79578.6i | 1.97106 | − | 3.41398i | ||||
\(817\) | 48.8329 | + | 84.5811i | 0.00209112 | + | 0.00362193i | ||||
\(818\) | 813.285 | 0.0347627 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16302.6 | −0.694282 | ||||||||
\(821\) | 12739.5 | + | 22065.5i | 0.541550 | + | 0.937991i | 0.998815 | + | 0.0486612i | \(0.0154955\pi\) |
−0.457266 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(822\) | −21692.0 | + | 37571.7i | −0.920433 | + | 1.59424i | ||||
\(823\) | 8966.65 | − | 15530.7i | 0.379779 | − | 0.657796i | −0.611251 | − | 0.791437i | \(-0.709334\pi\) |
0.991030 | + | 0.133641i | \(0.0426668\pi\) | |||||||
\(824\) | −24678.0 | − | 42743.6i | −1.04333 | − | 1.80709i | ||||
\(825\) | −3331.62 | −0.140597 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13021.6 | 0.547529 | 0.273764 | − | 0.961797i | \(-0.411731\pi\) | ||||
0.273764 | + | 0.961797i | \(0.411731\pi\) | |||||||
\(828\) | −14.1437 | − | 24.4976i | −0.000593633 | − | 0.00102820i | ||||
\(829\) | −5698.80 | + | 9870.61i | −0.238754 | + | 0.413535i | −0.960357 | − | 0.278773i | \(-0.910072\pi\) |
0.721603 | + | 0.692307i | \(0.243406\pi\) | |||||||
\(830\) | −6803.74 | + | 11784.4i | −0.284532 | + | 0.492823i | ||||
\(831\) | −7737.01 | − | 13400.9i | −0.322977 | − | 0.559412i | ||||
\(832\) | −160149. | −6.67326 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −57237.2 | −2.37646 | ||||||||
\(835\) | 3628.09 | + | 6284.04i | 0.150366 | + | 0.260441i | ||||
\(836\) | 4582.87 | − | 7937.77i | 0.189596 | − | 0.328389i | ||||
\(837\) | 12059.5 | − | 20887.7i | 0.498015 | − | 0.862588i | ||||
\(838\) | 10433.6 | + | 18071.5i | 0.430098 | + | 0.744952i | ||||
\(839\) | 37681.2 | 1.55053 | 0.775267 | − | 0.631633i | \(-0.217615\pi\) | ||||
0.775267 | + | 0.631633i | \(0.217615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12039.8 | 0.493656 | ||||||||
\(842\) | −30070.8 | − | 52084.2i | −1.23077 | − | 2.13176i | ||||
\(843\) | 13386.7 | − | 23186.5i | 0.546932 | − | 0.947315i | ||||
\(844\) | 67073.9 | − | 116175.i | 2.73552 | − | 4.73806i | ||||
\(845\) | −6373.28 | − | 11038.8i | −0.259465 | − | 0.449406i | ||||
\(846\) | −17391.1 | −0.706758 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 91924.4 | 3.72252 | ||||||||
\(849\) | 5147.13 | + | 8915.09i | 0.208067 | + | 0.360383i | ||||
\(850\) | 6306.67 | − | 10923.5i | 0.254491 | − | 0.440791i | ||||
\(851\) | −9.26591 | + | 16.0490i | −0.000373245 | + | 0.000646479i | ||||
\(852\) | −13494.8 | − | 23373.7i | −0.542634 | − | 0.939869i | ||||
\(853\) | −21771.6 | −0.873911 | −0.436956 | − | 0.899483i | \(-0.643943\pi\) | ||||
−0.436956 | + | 0.899483i | \(0.643943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 715.429 | 0.0286166 | ||||||||
\(856\) | −85754.9 | − | 148532.i | −3.42412 | − | 5.93074i | ||||
\(857\) | 14930.1 | − | 25859.7i | 0.595103 | − | 1.03075i | −0.398429 | − | 0.917199i | \(-0.630445\pi\) |
0.993532 | − | 0.113550i | \(-0.0362221\pi\) | |||||||
\(858\) | 25330.5 | − | 43873.7i | 1.00789 | − | 1.74571i | ||||
\(859\) | 9265.32 | + | 16048.0i | 0.368019 | + | 0.637428i | 0.989256 | − | 0.146195i | \(-0.0467027\pi\) |
−0.621236 | + | 0.783623i | \(0.713369\pi\) | |||||||
\(860\) | 926.799 | 0.0367484 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 62261.4 | 2.46013 | ||||||||
\(863\) | 10648.2 | + | 18443.3i | 0.420012 | + | 0.727482i | 0.995940 | − | 0.0900182i | \(-0.0286925\pi\) |
−0.575928 | + | 0.817500i | \(0.695359\pi\) | |||||||
\(864\) | 60274.6 | − | 104399.i | 2.37336 | − | 4.11078i | ||||
\(865\) | −4947.90 | + | 8570.01i | −0.194490 | + | 0.336866i | ||||
\(866\) | 24572.1 | + | 42560.1i | 0.964195 | + | 1.67003i | ||||
\(867\) | −13307.8 | −0.521290 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13504.2 | 0.527155 | ||||||||
\(870\) | −10164.2 | − | 17604.9i | −0.396090 | − | 0.686049i | ||||
\(871\) | 5233.99 | − | 9065.54i | 0.203613 | − | 0.352668i | ||||
\(872\) | −16226.9 | + | 28105.7i | −0.630173 | + | 1.09149i | ||||
\(873\) | −5074.88 | − | 8789.96i | −0.196745 | − | 0.340773i | ||||
\(874\) | −6.79843 | −0.000263112 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 55451.5 | 2.13874 | ||||||||
\(877\) | 9396.72 | + | 16275.6i | 0.361807 | + | 0.626668i | 0.988258 | − | 0.152793i | \(-0.0488266\pi\) |
−0.626451 | + | 0.779460i | \(0.715493\pi\) | |||||||
\(878\) | −22484.3 | + | 38944.0i | −0.864248 | + | 1.49692i | ||||
\(879\) | −11463.6 | + | 19855.6i | −0.439885 | + | 0.761902i | ||||
\(880\) | −22467.2 | − | 38914.3i | −0.860646 | − | 1.49068i | ||||
\(881\) | −1638.62 | −0.0626634 | −0.0313317 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313317 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35424.1 | −1.35008 | −0.675038 | − | 0.737783i | \(-0.735873\pi\) | ||||
−0.675038 | + | 0.737783i | \(0.735873\pi\) | |||||||
\(884\) | 70702.8 | + | 122461.i | 2.69004 | + | 4.65928i | ||||
\(885\) | −2321.01 | + | 4020.10i | −0.0881580 | + | 0.152694i | ||||
\(886\) | −31653.2 | + | 54825.0i | −1.20024 | + | 2.07887i | ||||
\(887\) | −2565.71 | − | 4443.93i | −0.0971229 | − | 0.168222i | 0.813370 | − | 0.581747i | \(-0.197631\pi\) |
−0.910493 | + | 0.413525i | \(0.864297\pi\) | |||||||
\(888\) | −54753.8 | −2.06916 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 13073.5 | 0.492386 | ||||||||
\(891\) | 4419.11 | + | 7654.13i | 0.166157 | + | 0.287792i | ||||
\(892\) | −58158.2 | + | 100733.i | −2.18305 | + | 3.78115i | ||||
\(893\) | −1540.74 | + | 2668.65i | −0.0577369 | + | 0.100003i | ||||
\(894\) | −7173.30 | − | 12424.5i | −0.268357 | − | 0.464807i | ||||
\(895\) | −21793.3 | −0.813933 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.7034 | −0.00103120 | ||||||||
\(898\) | 5418.10 | + | 9384.43i | 0.201341 | + | 0.348733i | ||||
\(899\) | 15250.2 | − | 26414.0i | 0.565763 | − | 0.979931i | ||||
\(900\) | 3394.53 | − | 5879.50i | 0.125723 | − | 0.217759i | ||||
\(901\) | −16143.1 | − | 27960.7i | −0.596898 | − | 1.03386i | ||||
\(902\) | 27667.7 | 1.02132 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27870.0 | 1.02538 | ||||||||
\(905\) | −944.807 | − | 1636.45i | −0.0347032 | − | 0.0601078i | ||||
\(906\) | 22634.8 | − | 39204.6i | 0.830011 | − | 1.43762i | ||||
\(907\) | 9967.28 | − | 17263.8i | 0.364893 | − | 0.632014i | −0.623866 | − | 0.781532i | \(-0.714439\pi\) |
0.988759 | + | 0.149518i | \(0.0477721\pi\) | |||||||
\(908\) | 42124.4 | + | 72961.6i | 1.53959 | + | 2.66665i | ||||
\(909\) | 10735.7 | 0.391728 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48387.4 | 1.75976 | 0.879882 | − | 0.475193i | \(-0.157622\pi\) | ||||
0.879882 | + | 0.475193i | \(0.157622\pi\) | |||||||
\(912\) | −5943.34 | − | 10294.2i | −0.215794 | − | 0.373765i | ||||
\(913\) | 8512.99 | − | 14744.9i | 0.308586 | − | 0.534486i | ||||
\(914\) | 15422.3 | − | 26712.3i | 0.558124 | − | 0.966700i | ||||
\(915\) | −7510.28 | − | 13008.2i | −0.271347 | − | 0.469986i | ||||
\(916\) | 140483. | 5.06735 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −76149.8 | −2.73782 | ||||||||
\(919\) | 7215.87 | + | 12498.2i | 0.259009 | + | 0.448617i | 0.965977 | − | 0.258629i | \(-0.0832706\pi\) |
−0.706968 | + | 0.707246i | \(0.749937\pi\) | |||||||
\(920\) | −20.7612 | + | 35.9594i | −0.000743996 | + | 0.00128864i | ||||
\(921\) | −20038.4 | + | 34707.5i | −0.716924 | + | 1.24175i | ||||
\(922\) | 51843.8 | + | 89796.2i | 1.85183 | + | 3.20746i | ||||
\(923\) | 21456.8 | 0.765177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4447.69 | −0.158096 | ||||||||
\(926\) | −21774.5 | − | 37714.6i | −0.772738 | − | 1.33842i | ||||
\(927\) | −3744.67 | + | 6485.96i | −0.132676 | + | 0.229802i | ||||
\(928\) | 76221.5 | − | 132020.i | 2.69622 | − | 4.66999i | ||||
\(929\) | 2774.91 | + | 4806.28i | 0.0979998 | + | 0.169741i | 0.910857 | − | 0.412723i | \(-0.135422\pi\) |
−0.812857 | + | 0.582464i | \(0.802089\pi\) | |||||||
\(930\) | −17020.1 | −0.600120 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39956.7 | 1.40432 | ||||||||
\(933\) | −8185.08 | − | 14177.0i | −0.287211 | − | 0.497463i | ||||
\(934\) | −1063.62 | + | 1842.24i | −0.0372620 | + | 0.0645396i | ||||
\(935\) | −7891.05 | + | 13667.7i | −0.276005 | + | 0.478055i | ||||
\(936\) | 33222.2 | + | 57542.5i | 1.16015 | + | 2.00944i | ||||
\(937\) | −26231.9 | −0.914576 | −0.457288 | − | 0.889319i | \(-0.651179\pi\) | ||||
−0.457288 | + | 0.889319i | \(0.651179\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1095.98 | −0.0380893 | ||||||||
\(940\) | 14620.9 | + | 25324.1i | 0.507320 | + | 0.878704i | ||||
\(941\) | 1418.40 | − | 2456.74i | 0.0491376 | − | 0.0851089i | −0.840410 | − | 0.541950i | \(-0.817686\pi\) |
0.889548 | + | 0.456842i | \(0.151019\pi\) | |||||||
\(942\) | −29961.0 | + | 51893.9i | −1.03629 | + | 1.79490i | ||||
\(943\) | −7.56488 | − | 13.1028i | −0.000261237 | − | 0.000452476i | ||||
\(944\) | −62607.9 | −2.15860 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1572.90 | −0.0540586 | ||||||||
\(947\) | 20136.4 | + | 34877.3i | 0.690967 | + | 1.19679i | 0.971521 | + | 0.236952i | \(0.0761486\pi\) |
−0.280554 | + | 0.959838i | \(0.590518\pi\) | |||||||
\(948\) | 16949.7 | − | 29357.8i | 0.580698 | − | 1.00580i | ||||
\(949\) | −22042.0 | + | 38177.9i | −0.753967 | + | 1.30591i | ||||
\(950\) | −815.821 | − | 1413.04i | −0.0278618 | − | 0.0482581i | ||||
\(951\) | −6715.12 | −0.228972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17770.1 | 0.604019 | 0.302010 | − | 0.953305i | \(-0.402343\pi\) | ||||
0.302010 | + | 0.953305i | \(0.402343\pi\) | |||||||
\(954\) | −11785.5 | − | 20413.1i | −0.399968 | − | 0.692765i | ||||
\(955\) | 6064.87 | − | 10504.7i | 0.205502 | − | 0.355940i | ||||
\(956\) | −39502.5 | + | 68420.3i | −1.33640 | + | 2.31472i | ||||
\(957\) | 12717.7 | + | 22027.7i | 0.429576 | + | 0.744047i | ||||
\(958\) | 9349.97 | 0.315328 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −44869.0 | −1.50848 | ||||||||
\(961\) | 2127.18 | + | 3684.38i | 0.0714033 | + | 0.123674i | ||||
\(962\) | 33816.0 | − | 58571.0i | 1.13334 | − | 1.96300i | ||||
\(963\) | −13012.5 | + | 22538.4i | −0.435434 | + | 0.754194i | ||||
\(964\) | 4073.54 | + | 7055.57i | 0.136099 | + | 0.235731i | ||||
\(965\) | −3114.61 | −0.103899 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3530.14 | −0.117396 | −0.0586978 | − | 0.998276i | \(-0.518695\pi\) | ||||
−0.0586978 | + | 0.998276i | \(0.518695\pi\) | |||||||
\(968\) | −5552.59 | − | 9617.37i | −0.184367 | − | 0.319333i | ||||
\(969\) | −2087.45 | + | 3615.58i | −0.0692040 | + | 0.119865i | ||||
\(970\) | −11574.0 | + | 20046.8i | −0.383113 | + | 0.663571i | ||||
\(971\) | 8825.36 | + | 15286.0i | 0.291678 | + | 0.505201i | 0.974207 | − | 0.225658i | \(-0.0724532\pi\) |
−0.682529 | + | 0.730859i | \(0.739120\pi\) | |||||||
\(972\) | −69292.3 | −2.28658 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −86693.8 | −2.85200 | ||||||||
\(975\) | −3324.45 | − | 5758.11i | −0.109197 | − | 0.189136i | ||||
\(976\) | 101293. | − | 175444.i | 3.32204 | − | 5.75393i | ||||
\(977\) | 7238.82 | − | 12538.0i | 0.237042 | − | 0.410569i | −0.722822 | − | 0.691034i | \(-0.757155\pi\) |
0.959864 | + | 0.280465i | \(0.0904886\pi\) | |||||||
\(978\) | 14319.1 | + | 24801.4i | 0.468175 | + | 0.810902i | ||||
\(979\) | −16357.8 | −0.534012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4924.56 | 0.160274 | ||||||||
\(982\) | −7494.34 | − | 12980.6i | −0.243538 | − | 0.421820i | ||||
\(983\) | −4382.05 | + | 7589.93i | −0.142183 | + | 0.246268i | −0.928318 | − | 0.371786i | \(-0.878745\pi\) |
0.786136 | + | 0.618054i | \(0.212079\pi\) | |||||||
\(984\) | 22351.1 | − | 38713.2i | 0.724112 | − | 1.25420i | ||||
\(985\) | −7105.72 | − | 12307.5i | −0.229855 | − | 0.398120i | ||||
\(986\) | −96296.9 | −3.11026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18292.0 | 0.589015 | ||||||||
\(989\) | 0.430062 | + | 0.744889i | 1.38273e−5 | + | 2.39495e-5i | ||||
\(990\) | −5760.97 | + | 9978.29i | −0.184945 | + | 0.320334i | ||||
\(991\) | −16812.1 | + | 29119.3i | −0.538903 | + | 0.933407i | 0.460061 | + | 0.887887i | \(0.347828\pi\) |
−0.998963 | + | 0.0455192i | \(0.985506\pi\) | |||||||
\(992\) | −63817.1 | − | 110535.i | −2.04254 | − | 3.53778i | ||||
\(993\) | −21645.1 | −0.691727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4336.82 | 0.138177 | ||||||||
\(996\) | −21370.1 | − | 37014.2i | −0.679858 | − | 1.17755i | ||||
\(997\) | 8315.63 | − | 14403.1i | 0.264151 | − | 0.457523i | −0.703190 | − | 0.711002i | \(-0.748242\pi\) |
0.967341 | + | 0.253479i | \(0.0815749\pi\) | |||||||
\(998\) | 11850.8 | − | 20526.2i | 0.375882 | − | 0.651046i | ||||
\(999\) | 13425.9 | + | 23254.3i | 0.425202 | + | 0.736471i |
(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 | 245.4.e.q.116.6 | 12 | ||
7.2 | even | 3 | inner | 245.4.e.q.226.6 | 12 | ||
7.3 | odd | 6 | 245.4.a.p.1.1 | yes | 6 | ||
7.4 | even | 3 | 245.4.a.o.1.1 | ✓ | 6 | ||
7.5 | odd | 6 | 245.4.e.p.226.6 | 12 | |||
7.6 | odd | 2 | 245.4.e.p.116.6 | 12 | |||
21.11 | odd | 6 | 2205.4.a.bz.1.6 | 6 | |||
21.17 | even | 6 | 2205.4.a.ca.1.6 | 6 | |||
35.4 | even | 6 | 1225.4.a.bj.1.6 | 6 | |||
35.24 | odd | 6 | 1225.4.a.bi.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.1 | ✓ | 6 | 7.4 | even | 3 | ||
245.4.a.p.1.1 | yes | 6 | 7.3 | odd | 6 | ||
245.4.e.p.116.6 | 12 | 7.6 | odd | 2 | |||
245.4.e.p.226.6 | 12 | 7.5 | odd | 6 | |||
245.4.e.q.116.6 | 12 | 1.1 | even | 1 | trivial | ||
245.4.e.q.226.6 | 12 | 7.2 | even | 3 | inner | ||
1225.4.a.bi.1.6 | 6 | 35.24 | odd | 6 | |||
1225.4.a.bj.1.6 | 6 | 35.4 | even | 6 | |||
2205.4.a.bz.1.6 | 6 | 21.11 | odd | 6 | |||
2205.4.a.ca.1.6 | 6 | 21.17 | even | 6 |