Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [26,4,Mod(17,26)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(26, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("26.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.e (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.53404966015\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 122x^{6} + 5305x^{4} + 97056x^{2} + 627264 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.3 | ||
Root | \(-6.87513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 26.23 |
Dual form | 26.4.e.a.17.3 |
$q$-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 \(\left(\mathbb{Z}/26\mathbb{Z}\right)^\times\).
\(n\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.00000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −3.93757 | − | 6.82006i | −0.757785 | − | 1.31252i | −0.943978 | − | 0.330009i | \(-0.892948\pi\) |
0.186193 | − | 0.982513i | \(-0.440385\pi\) | |||||||
\(4\) | 2.00000 | − | 3.46410i | 0.250000 | − | 0.433013i | ||||
\(5\) | 3.30629i | 0.295723i | 0.989008 | + | 0.147862i | \(0.0472390\pi\) | ||||
−0.989008 | + | 0.147862i | \(0.952761\pi\) | |||||||
\(6\) | −13.6401 | − | 7.87513i | −0.928093 | − | 0.535835i | ||||
\(7\) | 27.1849 | + | 15.6952i | 1.46785 | + | 0.847461i | 0.999352 | − | 0.0360059i | \(-0.0114635\pi\) |
0.468494 | + | 0.883467i | \(0.344797\pi\) | |||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | −17.5089 | + | 30.3262i | −0.648476 | + | 1.12319i | ||||
\(10\) | 3.30629 | + | 5.72666i | 0.104554 | + | 0.181093i | ||||
\(11\) | 13.5192 | − | 7.80533i | 0.370564 | − | 0.213945i | −0.303141 | − | 0.952946i | \(-0.598035\pi\) |
0.673705 | + | 0.739001i | \(0.264702\pi\) | |||||||
\(12\) | −31.5005 | −0.757785 | ||||||||
\(13\) | −45.2497 | − | 12.2255i | −0.965386 | − | 0.260826i | ||||
\(14\) | 62.7808 | 1.19849 | ||||||||
\(15\) | 22.5491 | − | 13.0187i | 0.388143 | − | 0.224095i | ||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −53.8638 | + | 93.2949i | −0.768465 | + | 1.33102i | 0.169930 | + | 0.985456i | \(0.445646\pi\) |
−0.938395 | + | 0.345564i | \(0.887688\pi\) | |||||||
\(18\) | 70.0354i | 0.917083i | ||||||||
\(19\) | 52.6358 | + | 30.3893i | 0.635551 | + | 0.366936i | 0.782899 | − | 0.622149i | \(-0.213740\pi\) |
−0.147347 | + | 0.989085i | \(0.547074\pi\) | |||||||
\(20\) | 11.4533 | + | 6.61258i | 0.128052 | + | 0.0739308i | ||||
\(21\) | − | 247.203i | − | 2.56877i | ||||||
\(22\) | 15.6107 | − | 27.0385i | 0.151282 | − | 0.262028i | ||||
\(23\) | −62.1540 | − | 107.654i | −0.563479 | − | 0.975974i | −0.997189 | − | 0.0749214i | \(-0.976129\pi\) |
0.433711 | − | 0.901052i | \(-0.357204\pi\) | |||||||
\(24\) | −54.5605 | + | 31.5005i | −0.464047 | + | 0.267917i | ||||
\(25\) | 114.068 | 0.912548 | ||||||||
\(26\) | −90.6003 | + | 24.0746i | −0.683392 | + | 0.181593i | ||||
\(27\) | 63.1404 | 0.450051 | ||||||||
\(28\) | 108.740 | − | 62.7808i | 0.733923 | − | 0.423730i | ||||
\(29\) | −29.1001 | − | 50.4028i | −0.186336 | − | 0.322744i | 0.757690 | − | 0.652615i | \(-0.226328\pi\) |
−0.944026 | + | 0.329871i | \(0.892995\pi\) | |||||||
\(30\) | 26.0375 | − | 45.0982i | 0.158459 | − | 0.274459i | ||||
\(31\) | 200.934i | 1.16416i | 0.813133 | + | 0.582078i | \(0.197760\pi\) | ||||
−0.813133 | + | 0.582078i | \(0.802240\pi\) | |||||||
\(32\) | −27.7128 | − | 16.0000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −106.466 | − | 61.4680i | −0.561615 | − | 0.324249i | ||||
\(34\) | 215.455i | 1.08677i | ||||||||
\(35\) | −51.8928 | + | 89.8810i | −0.250614 | + | 0.434076i | ||||
\(36\) | 70.0354 | + | 121.305i | 0.324238 | + | 0.561597i | ||||
\(37\) | −90.9447 | + | 52.5069i | −0.404087 | + | 0.233300i | −0.688246 | − | 0.725478i | \(-0.741619\pi\) |
0.284159 | + | 0.958777i | \(0.408286\pi\) | |||||||
\(38\) | 121.557 | 0.518926 | ||||||||
\(39\) | 94.7953 | + | 356.745i | 0.389215 | + | 1.46474i | ||||
\(40\) | 26.4503 | 0.104554 | ||||||||
\(41\) | −191.461 | + | 110.540i | −0.729298 | + | 0.421060i | −0.818165 | − | 0.574983i | \(-0.805009\pi\) |
0.0888675 | + | 0.996043i | \(0.471675\pi\) | |||||||
\(42\) | −247.203 | − | 428.169i | −0.908198 | − | 1.57305i | ||||
\(43\) | 56.0339 | − | 97.0535i | 0.198723 | − | 0.344198i | −0.749392 | − | 0.662127i | \(-0.769654\pi\) |
0.948115 | + | 0.317929i | \(0.102987\pi\) | |||||||
\(44\) | − | 62.4426i | − | 0.213945i | ||||||
\(45\) | −100.267 | − | 57.8893i | −0.332154 | − | 0.191769i | ||||
\(46\) | −215.308 | − | 124.308i | −0.690117 | − | 0.398440i | ||||
\(47\) | − | 512.102i | − | 1.58931i | −0.607058 | − | 0.794657i | \(-0.707651\pi\) | ||
0.607058 | − | 0.794657i | \(-0.292349\pi\) | |||||||
\(48\) | −63.0011 | + | 109.121i | −0.189446 | + | 0.328130i | ||||
\(49\) | 321.178 | + | 556.297i | 0.936380 | + | 1.62186i | ||||
\(50\) | 197.572 | − | 114.068i | 0.558819 | − | 0.322634i | ||||
\(51\) | 848.370 | 2.32932 | ||||||||
\(52\) | −132.850 | + | 132.299i | −0.354287 | + | 0.352818i | ||||
\(53\) | −221.755 | −0.574724 | −0.287362 | − | 0.957822i | \(-0.592778\pi\) | ||||
−0.287362 | + | 0.957822i | \(0.592778\pi\) | |||||||
\(54\) | 109.362 | − | 63.1404i | 0.275599 | − | 0.159117i | ||||
\(55\) | 25.8067 | + | 44.6985i | 0.0632686 | + | 0.109584i | ||||
\(56\) | 125.562 | − | 217.479i | 0.299623 | − | 0.518962i | ||||
\(57\) | − | 478.639i | − | 1.11223i | ||||||
\(58\) | −100.806 | − | 58.2002i | −0.228214 | − | 0.131760i | ||||
\(59\) | −482.310 | − | 278.462i | −1.06426 | − | 0.614452i | −0.137654 | − | 0.990480i | \(-0.543956\pi\) |
−0.926608 | + | 0.376028i | \(0.877290\pi\) | |||||||
\(60\) | − | 104.150i | − | 0.224095i | ||||||
\(61\) | 229.105 | − | 396.821i | 0.480882 | − | 0.832913i | −0.518877 | − | 0.854849i | \(-0.673650\pi\) |
0.999759 | + | 0.0219361i | \(0.00698304\pi\) | |||||||
\(62\) | 200.934 | + | 348.028i | 0.411591 | + | 0.712897i | ||||
\(63\) | −951.952 | + | 549.610i | −1.90372 | + | 1.09912i | ||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 40.4209 | − | 149.609i | 0.0771323 | − | 0.285487i | ||||
\(66\) | −245.872 | −0.458557 | ||||||||
\(67\) | 458.769 | − | 264.870i | 0.836530 | − | 0.482971i | −0.0195533 | − | 0.999809i | \(-0.506224\pi\) |
0.856083 | + | 0.516838i | \(0.172891\pi\) | |||||||
\(68\) | 215.455 | + | 373.180i | 0.384232 | + | 0.665510i | ||||
\(69\) | −489.471 | + | 847.789i | −0.853991 | + | 1.47916i | ||||
\(70\) | 207.571i | 0.354422i | ||||||||
\(71\) | 58.5007 | + | 33.7754i | 0.0977854 | + | 0.0564564i | 0.548095 | − | 0.836416i | \(-0.315353\pi\) |
−0.450310 | + | 0.892872i | \(0.648686\pi\) | |||||||
\(72\) | 242.610 | + | 140.071i | 0.397109 | + | 0.229271i | ||||
\(73\) | 104.504i | 0.167552i | 0.996485 | + | 0.0837759i | \(0.0266980\pi\) | ||||
−0.996485 | + | 0.0837759i | \(0.973302\pi\) | |||||||
\(74\) | −105.014 | + | 181.889i | −0.164968 | + | 0.285732i | ||||
\(75\) | −449.152 | − | 777.954i | −0.691515 | − | 1.19774i | ||||
\(76\) | 210.543 | − | 121.557i | 0.317776 | − | 0.183468i | ||||
\(77\) | 490.025 | 0.725240 | ||||||||
\(78\) | 520.935 | + | 523.105i | 0.756209 | + | 0.759358i | ||||
\(79\) | 611.085 | 0.870284 | 0.435142 | − | 0.900362i | \(-0.356698\pi\) | ||||
0.435142 | + | 0.900362i | \(0.356698\pi\) | |||||||
\(80\) | 45.8133 | − | 26.4503i | 0.0640260 | − | 0.0369654i | ||||
\(81\) | 224.119 | + | 388.186i | 0.307434 | + | 0.532491i | ||||
\(82\) | −221.080 | + | 382.922i | −0.297735 | + | 0.515691i | ||||
\(83\) | 491.565i | 0.650075i | 0.945701 | + | 0.325038i | \(0.105377\pi\) | ||||
−0.945701 | + | 0.325038i | \(0.894623\pi\) | |||||||
\(84\) | −856.338 | − | 494.407i | −1.11231 | − | 0.642193i | ||||
\(85\) | −308.460 | − | 178.089i | −0.393614 | − | 0.227253i | ||||
\(86\) | − | 224.136i | − | 0.281037i | ||||||
\(87\) | −229.167 | + | 396.929i | −0.282406 | + | 0.489141i | ||||
\(88\) | −62.4426 | − | 108.154i | −0.0756410 | − | 0.131014i | ||||
\(89\) | 326.626 | − | 188.578i | 0.389014 | − | 0.224598i | −0.292719 | − | 0.956199i | \(-0.594560\pi\) |
0.681733 | + | 0.731601i | \(0.261227\pi\) | |||||||
\(90\) | −231.557 | −0.271203 | ||||||||
\(91\) | −1038.23 | − | 1042.55i | −1.19600 | − | 1.20098i | ||||
\(92\) | −497.232 | −0.563479 | ||||||||
\(93\) | 1370.38 | − | 791.191i | 1.52798 | − | 0.882179i | ||||
\(94\) | −512.102 | − | 886.987i | −0.561908 | − | 0.973252i | ||||
\(95\) | −100.476 | + | 174.029i | −0.108511 | + | 0.187947i | ||||
\(96\) | 252.004i | 0.267917i | ||||||||
\(97\) | −496.503 | − | 286.656i | −0.519713 | − | 0.300057i | 0.217104 | − | 0.976148i | \(-0.430339\pi\) |
−0.736817 | + | 0.676092i | \(0.763672\pi\) | |||||||
\(98\) | 1112.59 | + | 642.357i | 1.14683 | + | 0.662121i | ||||
\(99\) | 546.649i | 0.554953i | ||||||||
\(100\) | 228.137 | − | 395.145i | 0.228137 | − | 0.395145i | ||||
\(101\) | 477.751 | + | 827.489i | 0.470673 | + | 0.815230i | 0.999437 | − | 0.0335385i | \(-0.0106776\pi\) |
−0.528764 | + | 0.848769i | \(0.677344\pi\) | |||||||
\(102\) | 1469.42 | − | 848.370i | 1.42641 | − | 0.823540i | ||||
\(103\) | −1478.96 | −1.41481 | −0.707407 | − | 0.706806i | \(-0.750135\pi\) | ||||
−0.707407 | + | 0.706806i | \(0.750135\pi\) | |||||||
\(104\) | −97.8037 | + | 361.998i | −0.0922158 | + | 0.341315i | ||||
\(105\) | 817.326 | 0.759646 | ||||||||
\(106\) | −384.091 | + | 221.755i | −0.351945 | + | 0.203196i | ||||
\(107\) | −106.558 | − | 184.564i | −0.0962741 | − | 0.166752i | 0.813866 | − | 0.581053i | \(-0.197359\pi\) |
−0.910140 | + | 0.414302i | \(0.864026\pi\) | |||||||
\(108\) | 126.281 | − | 218.725i | 0.112513 | − | 0.194878i | ||||
\(109\) | 84.4197i | 0.0741829i | 0.999312 | + | 0.0370915i | \(0.0118093\pi\) | ||||
−0.999312 | + | 0.0370915i | \(0.988191\pi\) | |||||||
\(110\) | 89.3969 | + | 51.6133i | 0.0774878 | + | 0.0447376i | ||||
\(111\) | 716.201 | + | 413.499i | 0.612422 | + | 0.353582i | ||||
\(112\) | − | 502.246i | − | 0.423730i | ||||||
\(113\) | 393.209 | − | 681.058i | 0.327345 | − | 0.566979i | −0.654639 | − | 0.755942i | \(-0.727179\pi\) |
0.981984 | + | 0.188963i | \(0.0605127\pi\) | |||||||
\(114\) | −478.639 | − | 829.027i | −0.393234 | − | 0.681101i | ||||
\(115\) | 355.935 | − | 205.499i | 0.288618 | − | 0.166634i | ||||
\(116\) | −232.801 | −0.186336 | ||||||||
\(117\) | 1163.02 | − | 1158.20i | 0.918987 | − | 0.915176i | ||||
\(118\) | −1113.85 | −0.868966 | ||||||||
\(119\) | −2928.56 | + | 1690.81i | −2.25598 | + | 1.30249i | ||||
\(120\) | −104.150 | − | 180.393i | −0.0792294 | − | 0.137229i | ||||
\(121\) | −543.654 | + | 941.636i | −0.408455 | + | 0.707465i | ||||
\(122\) | − | 916.418i | − | 0.680070i | ||||||
\(123\) | 1507.78 | + | 870.518i | 1.10530 | + | 0.638146i | ||||
\(124\) | 696.056 | + | 401.868i | 0.504094 | + | 0.291039i | ||||
\(125\) | 790.429i | 0.565585i | ||||||||
\(126\) | −1099.22 | + | 1903.90i | −0.777192 | + | 1.34614i | ||||
\(127\) | −366.227 | − | 634.324i | −0.255885 | − | 0.443206i | 0.709250 | − | 0.704957i | \(-0.249034\pi\) |
−0.965136 | + | 0.261750i | \(0.915700\pi\) | |||||||
\(128\) | −110.851 | + | 64.0000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −882.549 | −0.602357 | ||||||||
\(130\) | −79.5975 | − | 299.551i | −0.0537013 | − | 0.202095i | ||||
\(131\) | 1862.41 | 1.24213 | 0.621066 | − | 0.783758i | \(-0.286700\pi\) | ||||
0.621066 | + | 0.783758i | \(0.286700\pi\) | |||||||
\(132\) | −425.863 | + | 245.872i | −0.280808 | + | 0.162124i | ||||
\(133\) | 953.932 | + | 1652.26i | 0.621927 | + | 1.07721i | ||||
\(134\) | 529.740 | − | 917.537i | 0.341512 | − | 0.591516i | ||||
\(135\) | 208.760i | 0.133091i | ||||||||
\(136\) | 746.359 | + | 430.911i | 0.470587 | + | 0.271693i | ||||
\(137\) | −768.559 | − | 443.728i | −0.479288 | − | 0.276717i | 0.240832 | − | 0.970567i | \(-0.422580\pi\) |
−0.720120 | + | 0.693850i | \(0.755913\pi\) | |||||||
\(138\) | 1957.88i | 1.20773i | ||||||||
\(139\) | 726.060 | − | 1257.57i | 0.443047 | − | 0.767381i | −0.554867 | − | 0.831939i | \(-0.687231\pi\) |
0.997914 | + | 0.0645588i | \(0.0205640\pi\) | |||||||
\(140\) | 207.571 | + | 359.524i | 0.125307 | + | 0.217038i | ||||
\(141\) | −3492.57 | + | 2016.44i | −2.08601 | + | 1.20436i | ||||
\(142\) | 135.102 | 0.0798414 | ||||||||
\(143\) | −707.165 | + | 187.910i | −0.413539 | + | 0.109887i | ||||
\(144\) | 560.283 | 0.324238 | ||||||||
\(145\) | 166.646 | − | 96.2133i | 0.0954429 | − | 0.0551040i | ||||
\(146\) | 104.504 | + | 181.007i | 0.0592385 | + | 0.102604i | ||||
\(147\) | 2529.32 | − | 4380.91i | 1.41915 | − | 2.45804i | ||||
\(148\) | 420.055i | 0.233300i | ||||||||
\(149\) | 1336.02 | + | 771.351i | 0.734570 | + | 0.424104i | 0.820092 | − | 0.572232i | \(-0.193922\pi\) |
−0.0855217 | + | 0.996336i | \(0.527256\pi\) | |||||||
\(150\) | −1555.91 | − | 898.304i | −0.846929 | − | 0.488975i | ||||
\(151\) | − | 1623.81i | − | 0.875125i | −0.899188 | − | 0.437562i | \(-0.855842\pi\) | ||
0.899188 | − | 0.437562i | \(-0.144158\pi\) | |||||||
\(152\) | 243.114 | − | 421.086i | 0.129731 | − | 0.224701i | ||||
\(153\) | −1886.19 | − | 3266.97i | −0.996662 | − | 1.72627i | ||||
\(154\) | 848.748 | − | 490.025i | 0.444117 | − | 0.256411i | ||||
\(155\) | −664.346 | −0.344268 | ||||||||
\(156\) | 1425.39 | + | 385.109i | 0.731555 | + | 0.197650i | ||||
\(157\) | −2795.18 | −1.42089 | −0.710445 | − | 0.703753i | \(-0.751506\pi\) | ||||
−0.710445 | + | 0.703753i | \(0.751506\pi\) | |||||||
\(158\) | 1058.43 | − | 611.085i | 0.532938 | − | 0.307692i | ||||
\(159\) | 873.174 | + | 1512.38i | 0.435517 | + | 0.754338i | ||||
\(160\) | 52.9006 | − | 91.6265i | 0.0261385 | − | 0.0452732i | ||||
\(161\) | − | 3902.08i | − | 1.91010i | ||||||
\(162\) | 776.372 | + | 448.239i | 0.376528 | + | 0.217389i | ||||
\(163\) | 250.884 | + | 144.848i | 0.120557 | + | 0.0696036i | 0.559066 | − | 0.829123i | \(-0.311160\pi\) |
−0.438509 | + | 0.898727i | \(0.644493\pi\) | |||||||
\(164\) | 884.321i | 0.421060i | ||||||||
\(165\) | 203.231 | − | 352.006i | 0.0958879 | − | 0.166083i | ||||
\(166\) | 491.565 | + | 851.415i | 0.229836 | + | 0.398088i | ||||
\(167\) | 2016.21 | − | 1164.06i | 0.934246 | − | 0.539387i | 0.0460940 | − | 0.998937i | \(-0.485323\pi\) |
0.888152 | + | 0.459550i | \(0.151989\pi\) | |||||||
\(168\) | −1977.63 | −0.908198 | ||||||||
\(169\) | 1898.08 | + | 1106.40i | 0.863940 | + | 0.503595i | ||||
\(170\) | −712.357 | −0.321384 | ||||||||
\(171\) | −1843.18 | + | 1064.16i | −0.824280 | + | 0.475898i | ||||
\(172\) | −224.136 | − | 388.214i | −0.0993615 | − | 0.172099i | ||||
\(173\) | 531.941 | − | 921.349i | 0.233773 | − | 0.404907i | −0.725142 | − | 0.688599i | \(-0.758226\pi\) |
0.958915 | + | 0.283692i | \(0.0915594\pi\) | |||||||
\(174\) | 916.668i | 0.399382i | ||||||||
\(175\) | 3100.94 | + | 1790.33i | 1.33948 | + | 0.773349i | ||||
\(176\) | −216.308 | − | 124.885i | −0.0926409 | − | 0.0534863i | ||||
\(177\) | 4385.85i | 1.86249i | ||||||||
\(178\) | 377.155 | − | 653.252i | 0.158814 | − | 0.275075i | ||||
\(179\) | 1235.50 | + | 2139.95i | 0.515898 | + | 0.893561i | 0.999830 | + | 0.0184553i | \(0.00587483\pi\) |
−0.483932 | + | 0.875106i | \(0.660792\pi\) | |||||||
\(180\) | −401.069 | + | 231.557i | −0.166077 | + | 0.0958847i | ||||
\(181\) | −2196.50 | −0.902014 | −0.451007 | − | 0.892520i | \(-0.648935\pi\) | ||||
−0.451007 | + | 0.892520i | \(0.648935\pi\) | |||||||
\(182\) | −2840.81 | − | 767.524i | −1.15701 | − | 0.312597i | ||||
\(183\) | −3608.46 | −1.45762 | ||||||||
\(184\) | −861.231 | + | 497.232i | −0.345059 | + | 0.199220i | ||||
\(185\) | −173.603 | − | 300.689i | −0.0689921 | − | 0.119498i | ||||
\(186\) | 1582.38 | − | 2740.77i | 0.623795 | − | 1.08044i | ||||
\(187\) | 1681.70i | 0.657637i | ||||||||
\(188\) | −1773.97 | − | 1024.20i | −0.688193 | − | 0.397329i | ||||
\(189\) | 1716.47 | + | 991.002i | 0.660606 | + | 0.381401i | ||||
\(190\) | 401.903i | 0.153458i | ||||||||
\(191\) | −1025.60 | + | 1776.39i | −0.388534 | + | 0.672960i | −0.992253 | − | 0.124237i | \(-0.960352\pi\) |
0.603719 | + | 0.797197i | \(0.293685\pi\) | |||||||
\(192\) | 252.004 | + | 436.484i | 0.0947231 | + | 0.164065i | ||||
\(193\) | 3250.32 | − | 1876.57i | 1.21224 | − | 0.699889i | 0.248996 | − | 0.968505i | \(-0.419899\pi\) |
0.963247 | + | 0.268616i | \(0.0865661\pi\) | |||||||
\(194\) | −1146.62 | −0.424344 | ||||||||
\(195\) | −1179.50 | + | 313.421i | −0.433158 | + | 0.115100i | ||||
\(196\) | 2569.43 | 0.936380 | ||||||||
\(197\) | −646.501 | + | 373.258i | −0.233814 | + | 0.134992i | −0.612330 | − | 0.790602i | \(-0.709768\pi\) |
0.378516 | + | 0.925595i | \(0.376434\pi\) | |||||||
\(198\) | 546.649 | + | 946.825i | 0.196205 | + | 0.339838i | ||||
\(199\) | −1328.65 | + | 2301.28i | −0.473293 | + | 0.819767i | −0.999533 | − | 0.0305691i | \(-0.990268\pi\) |
0.526240 | + | 0.850336i | \(0.323601\pi\) | |||||||
\(200\) | − | 912.548i | − | 0.322634i | ||||||
\(201\) | −3612.86 | − | 2085.89i | −1.26782 | − | 0.731976i | ||||
\(202\) | 1654.98 | + | 955.502i | 0.576455 | + | 0.332816i | ||||
\(203\) | − | 1826.93i | − | 0.631651i | ||||||
\(204\) | 1696.74 | − | 2938.84i | 0.582331 | − | 1.00863i | ||||
\(205\) | −365.477 | − | 633.026i | −0.124517 | − | 0.215670i | ||||
\(206\) | −2561.63 | + | 1478.96i | −0.866394 | + | 0.500213i | ||||
\(207\) | 4352.98 | 1.46161 | ||||||||
\(208\) | 192.597 | + | 724.802i | 0.0642028 | + | 0.241615i | ||||
\(209\) | 948.794 | 0.314016 | ||||||||
\(210\) | 1415.65 | − | 817.326i | 0.465186 | − | 0.268575i | ||||
\(211\) | 753.671 | + | 1305.40i | 0.245900 | + | 0.425911i | 0.962384 | − | 0.271692i | \(-0.0875832\pi\) |
−0.716484 | + | 0.697603i | \(0.754250\pi\) | |||||||
\(212\) | −443.510 | + | 768.181i | −0.143681 | + | 0.248863i | ||||
\(213\) | − | 531.972i | − | 0.171127i | ||||||
\(214\) | −369.127 | − | 213.116i | −0.117911 | − | 0.0680761i | ||||
\(215\) | 320.887 | + | 185.264i | 0.101787 | + | 0.0587670i | ||||
\(216\) | − | 505.124i | − | 0.159117i | ||||||
\(217\) | −3153.70 | + | 5462.37i | −0.986576 | + | 1.70880i | ||||
\(218\) | 84.4197 | + | 146.219i | 0.0262276 | + | 0.0454276i | ||||
\(219\) | 712.725 | − | 411.492i | 0.219916 | − | 0.126968i | ||||
\(220\) | 206.453 | 0.0632686 | ||||||||
\(221\) | 3577.90 | − | 3563.06i | 1.08903 | − | 1.08451i | ||||
\(222\) | 1654.00 | 0.500040 | ||||||||
\(223\) | 1713.91 | − | 989.529i | 0.514673 | − | 0.297147i | −0.220079 | − | 0.975482i | \(-0.570632\pi\) |
0.734753 | + | 0.678335i | \(0.237298\pi\) | |||||||
\(224\) | −502.246 | − | 869.916i | −0.149811 | − | 0.259481i | ||||
\(225\) | −1997.21 | + | 3459.27i | −0.591765 | + | 1.02497i | ||||
\(226\) | − | 1572.84i | − | 0.462936i | ||||||
\(227\) | −1828.00 | − | 1055.39i | −0.534486 | − | 0.308586i | 0.208355 | − | 0.978053i | \(-0.433189\pi\) |
−0.742841 | + | 0.669467i | \(0.766522\pi\) | |||||||
\(228\) | −1658.05 | − | 957.278i | −0.481611 | − | 0.278058i | ||||
\(229\) | − | 5326.76i | − | 1.53713i | −0.639774 | − | 0.768563i | \(-0.720972\pi\) | ||
0.639774 | − | 0.768563i | \(-0.279028\pi\) | |||||||
\(230\) | 410.998 | − | 711.870i | 0.117828 | − | 0.204084i | ||||
\(231\) | −1929.50 | − | 3342.00i | −0.549576 | − | 0.951894i | ||||
\(232\) | −403.223 | + | 232.801i | −0.114107 | + | 0.0658798i | ||||
\(233\) | 148.949 | 0.0418797 | 0.0209398 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209398 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(234\) | 856.216 | − | 3169.08i | 0.239199 | − | 0.885339i | ||||
\(235\) | 1693.16 | 0.469997 | ||||||||
\(236\) | −1929.24 | + | 1113.85i | −0.532131 | + | 0.307226i | ||||
\(237\) | −2406.19 | − | 4167.64i | −0.659488 | − | 1.14227i | ||||
\(238\) | −3381.61 | + | 5857.13i | −0.920998 | + | 1.59522i | ||||
\(239\) | 3081.18i | 0.833912i | 0.908927 | + | 0.416956i | \(0.136903\pi\) | ||||
−0.908927 | + | 0.416956i | \(0.863097\pi\) | |||||||
\(240\) | −360.785 | − | 208.300i | −0.0970358 | − | 0.0560237i | ||||
\(241\) | 2225.94 | + | 1285.15i | 0.594960 | + | 0.343500i | 0.767056 | − | 0.641580i | \(-0.221721\pi\) |
−0.172096 | + | 0.985080i | \(0.555054\pi\) | |||||||
\(242\) | 2174.61i | 0.577643i | ||||||||
\(243\) | 2617.36 | − | 4533.41i | 0.690963 | − | 1.19678i | ||||
\(244\) | −916.418 | − | 1587.28i | −0.240441 | − | 0.416456i | ||||
\(245\) | −1839.28 | + | 1061.91i | −0.479621 | + | 0.276909i | ||||
\(246\) | 3482.07 | 0.902475 | ||||||||
\(247\) | −2010.23 | − | 2018.60i | −0.517846 | − | 0.520003i | ||||
\(248\) | 1607.47 | 0.411591 | ||||||||
\(249\) | 3352.50 | − | 1935.57i | 0.853238 | − | 0.492617i | ||||
\(250\) | 790.429 | + | 1369.06i | 0.199965 | + | 0.346349i | ||||
\(251\) | −1021.88 | + | 1769.95i | −0.256974 | + | 0.445093i | −0.965430 | − | 0.260663i | \(-0.916059\pi\) |
0.708456 | + | 0.705755i | \(0.249392\pi\) | |||||||
\(252\) | 4396.88i | 1.09912i | ||||||||
\(253\) | −1680.55 | − | 970.265i | −0.417609 | − | 0.241107i | ||||
\(254\) | −1268.65 | − | 732.455i | −0.313394 | − | 0.180938i | ||||
\(255\) | 2804.95i | 0.688836i | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 3859.47 | + | 6684.79i | 0.936758 | + | 1.62251i | 0.771468 | + | 0.636268i | \(0.219523\pi\) |
0.165290 | + | 0.986245i | \(0.447144\pi\) | |||||||
\(258\) | −1528.62 | + | 882.549i | −0.368867 | + | 0.212965i | ||||
\(259\) | −3296.43 | −0.790849 | ||||||||
\(260\) | −437.418 | − | 439.239i | −0.104336 | − | 0.104771i | ||||
\(261\) | 2038.04 | 0.483338 | ||||||||
\(262\) | 3225.78 | − | 1862.41i | 0.760647 | − | 0.439160i | ||||
\(263\) | −742.261 | − | 1285.63i | −0.174030 | − | 0.301428i | 0.765795 | − | 0.643084i | \(-0.222345\pi\) |
−0.939825 | + | 0.341656i | \(0.889012\pi\) | |||||||
\(264\) | −491.744 | + | 851.726i | −0.114639 | + | 0.198561i | ||||
\(265\) | − | 733.185i | − | 0.169959i | ||||||
\(266\) | 3304.52 | + | 1907.86i | 0.761702 | + | 0.439769i | ||||
\(267\) | −2572.22 | − | 1485.07i | −0.589578 | − | 0.340393i | ||||
\(268\) | − | 2118.96i | − | 0.482971i | ||||||
\(269\) | 1133.27 | − | 1962.88i | 0.256865 | − | 0.444904i | −0.708535 | − | 0.705675i | \(-0.750644\pi\) |
0.965400 | + | 0.260772i | \(0.0839770\pi\) | |||||||
\(270\) | 208.760 | + | 361.584i | 0.0470547 | + | 0.0815011i | ||||
\(271\) | 4561.73 | − | 2633.72i | 1.02253 | − | 0.590357i | 0.107693 | − | 0.994184i | \(-0.465654\pi\) |
0.914835 | + | 0.403827i | \(0.132320\pi\) | |||||||
\(272\) | 1723.64 | 0.384232 | ||||||||
\(273\) | −3022.18 | + | 11185.9i | −0.670002 | + | 2.47986i | ||||
\(274\) | −1774.91 | −0.391337 | ||||||||
\(275\) | 1542.12 | − | 890.342i | 0.338157 | − | 0.195235i | ||||
\(276\) | 1957.88 | + | 3391.15i | 0.426996 | + | 0.739578i | ||||
\(277\) | −2407.72 | + | 4170.29i | −0.522260 | + | 0.904580i | 0.477405 | + | 0.878683i | \(0.341577\pi\) |
−0.999665 | + | 0.0258968i | \(0.991756\pi\) | |||||||
\(278\) | − | 2904.24i | − | 0.626564i | ||||||
\(279\) | −6093.57 | − | 3518.12i | −1.30757 | − | 0.754927i | ||||
\(280\) | 719.048 | + | 415.143i | 0.153469 | + | 0.0886054i | ||||
\(281\) | − | 1983.72i | − | 0.421134i | −0.977579 | − | 0.210567i | \(-0.932469\pi\) | ||
0.977579 | − | 0.210567i | \(-0.0675310\pi\) | |||||||
\(282\) | −4032.87 | + | 6985.14i | −0.851610 | + | 1.47503i | ||||
\(283\) | −413.551 | − | 716.291i | −0.0868658 | − | 0.150456i | 0.819319 | − | 0.573338i | \(-0.194352\pi\) |
−0.906185 | + | 0.422882i | \(0.861018\pi\) | |||||||
\(284\) | 234.003 | − | 135.102i | 0.0488927 | − | 0.0282282i | ||||
\(285\) | 1582.52 | 0.328913 | ||||||||
\(286\) | −1036.94 | + | 1032.64i | −0.214389 | + | 0.213500i | ||||
\(287\) | −6939.80 | −1.42733 | ||||||||
\(288\) | 970.439 | − | 560.283i | 0.198554 | − | 0.114635i | ||||
\(289\) | −3346.13 | − | 5795.66i | −0.681076 | − | 1.17966i | ||||
\(290\) | 192.427 | − | 333.292i | 0.0389644 | − | 0.0674883i | ||||
\(291\) | 4514.91i | 0.909514i | ||||||||
\(292\) | 362.013 | + | 209.008i | 0.0725521 | + | 0.0418880i | ||||
\(293\) | −1027.62 | − | 593.298i | −0.204895 | − | 0.118296i | 0.394041 | − | 0.919093i | \(-0.371077\pi\) |
−0.598937 | + | 0.800796i | \(0.704410\pi\) | |||||||
\(294\) | − | 10117.3i | − | 2.00698i | ||||||
\(295\) | 920.676 | − | 1594.66i | 0.181708 | − | 0.314727i | ||||
\(296\) | 420.055 | + | 727.557i | 0.0824839 | + | 0.142866i | ||||
\(297\) | 853.610 | − | 492.832i | 0.166773 | − | 0.0962863i | ||||
\(298\) | 3085.40 | 0.599774 | ||||||||
\(299\) | 1496.33 | + | 5631.17i | 0.289415 | + | 1.08916i | ||||
\(300\) | −3593.22 | −0.691515 | ||||||||
\(301\) | 3046.55 | − | 1758.93i | 0.583389 | − | 0.336820i | ||||
\(302\) | −1623.81 | − | 2812.52i | −0.309403 | − | 0.535902i | ||||
\(303\) | 3762.35 | − | 6516.59i | 0.713339 | − | 1.23554i | ||||
\(304\) | − | 972.457i | − | 0.183468i | ||||||
\(305\) | 1312.00 | + | 757.485i | 0.246312 | + | 0.142208i | ||||
\(306\) | −6533.95 | − | 3772.38i | −1.22066 | − | 0.704746i | ||||
\(307\) | 6191.17i | 1.15097i | 0.817811 | + | 0.575486i | \(0.195187\pi\) | ||||
−0.817811 | + | 0.575486i | \(0.804813\pi\) | |||||||
\(308\) | 980.050 | − | 1697.50i | 0.181310 | − | 0.314038i | ||||
\(309\) | 5823.49 | + | 10086.6i | 1.07213 | + | 1.85698i | ||||
\(310\) | −1150.68 | + | 664.346i | −0.210820 | + | 0.121717i | ||||
\(311\) | 10609.3 | 1.93440 | 0.967198 | − | 0.254024i | \(-0.0817541\pi\) | ||||
0.967198 | + | 0.254024i | \(0.0817541\pi\) | |||||||
\(312\) | 2853.96 | − | 758.363i | 0.517864 | − | 0.137608i | ||||
\(313\) | 9833.23 | 1.77574 | 0.887871 | − | 0.460093i | \(-0.152184\pi\) | ||||
0.887871 | + | 0.460093i | \(0.152184\pi\) | |||||||
\(314\) | −4841.39 | + | 2795.18i | −0.870114 | + | 0.502360i | ||||
\(315\) | −1817.17 | − | 3147.43i | −0.325034 | − | 0.562976i | ||||
\(316\) | 1222.17 | − | 2116.86i | 0.217571 | − | 0.376844i | ||||
\(317\) | − | 4674.74i | − | 0.828263i | −0.910217 | − | 0.414131i | \(-0.864085\pi\) | ||
0.910217 | − | 0.414131i | \(-0.135915\pi\) | |||||||
\(318\) | 3024.77 | + | 1746.35i | 0.533398 | + | 0.307957i | ||||
\(319\) | −786.822 | − | 454.272i | −0.138099 | − | 0.0797314i | ||||
\(320\) | − | 211.602i | − | 0.0369654i | ||||||
\(321\) | −839.157 | + | 1453.46i | −0.145910 | + | 0.252724i | ||||
\(322\) | −3902.08 | − | 6758.60i | −0.675324 | − | 1.16970i | ||||
\(323\) | −5670.33 | + | 3273.77i | −0.976798 | + | 0.563954i | ||||
\(324\) | 1792.95 | 0.307434 | ||||||||
\(325\) | −5161.57 | − | 1394.54i | −0.880961 | − | 0.238016i | ||||
\(326\) | 579.393 | 0.0984344 | ||||||||
\(327\) | 575.748 | − | 332.408i | 0.0973667 | − | 0.0562147i | ||||
\(328\) | 884.321 | + | 1531.69i | 0.148867 | + | 0.257846i | ||||
\(329\) | 8037.54 | − | 13921.4i | 1.34688 | − | 2.33287i | ||||
\(330\) | − | 812.924i | − | 0.135606i | ||||||
\(331\) | −9018.24 | − | 5206.68i | −1.49755 | − | 0.864608i | −0.497549 | − | 0.867436i | \(-0.665767\pi\) |
−0.999996 | + | 0.00282772i | \(0.999100\pi\) | |||||||
\(332\) | 1702.83 | + | 983.130i | 0.281491 | + | 0.162519i | ||||
\(333\) | − | 3677.34i | − | 0.605157i | ||||||
\(334\) | 2328.12 | − | 4032.42i | 0.381404 | − | 0.660612i | ||||
\(335\) | 875.737 | + | 1516.82i | 0.142826 | + | 0.247381i | ||||
\(336\) | −3425.35 | + | 1977.63i | −0.556156 | + | 0.321097i | ||||
\(337\) | −4873.47 | −0.787759 | −0.393879 | − | 0.919162i | \(-0.628867\pi\) | ||||
−0.393879 | + | 0.919162i | \(0.628867\pi\) | |||||||
\(338\) | 4393.96 | + | 18.2620i | 0.707101 | + | 0.00293882i | ||||
\(339\) | −6193.15 | −0.992229 | ||||||||
\(340\) | −1233.84 | + | 712.357i | −0.196807 | + | 0.113626i | ||||
\(341\) | 1568.36 | + | 2716.47i | 0.249065 | + | 0.431394i | ||||
\(342\) | −2128.33 | + | 3686.37i | −0.336511 | + | 0.582854i | ||||
\(343\) | 9396.92i | 1.47926i | ||||||||
\(344\) | −776.428 | − | 448.271i | −0.121692 | − | 0.0702592i | ||||
\(345\) | −2803.03 | − | 1618.33i | −0.437421 | − | 0.252545i | ||||
\(346\) | − | 2127.77i | − | 0.330605i | ||||||
\(347\) | −6060.84 | + | 10497.7i | −0.937645 | + | 1.62405i | −0.167798 | + | 0.985821i | \(0.553666\pi\) |
−0.769847 | + | 0.638228i | \(0.779668\pi\) | |||||||
\(348\) | 916.668 | + | 1587.72i | 0.141203 | + | 0.244570i | ||||
\(349\) | −7683.52 | + | 4436.08i | −1.17848 | + | 0.680396i | −0.955663 | − | 0.294464i | \(-0.904859\pi\) |
−0.222818 | + | 0.974860i | \(0.571526\pi\) | |||||||
\(350\) | 7161.31 | 1.09368 | ||||||||
\(351\) | −2857.09 | − | 771.921i | −0.434473 | − | 0.117385i | ||||
\(352\) | −499.541 | −0.0756410 | ||||||||
\(353\) | −3933.22 | + | 2270.84i | −0.593043 | + | 0.342393i | −0.766300 | − | 0.642483i | \(-0.777904\pi\) |
0.173257 | + | 0.984877i | \(0.444571\pi\) | |||||||
\(354\) | 4385.85 | + | 7596.52i | 0.658490 | + | 1.14054i | ||||
\(355\) | −111.671 | + | 193.420i | −0.0166955 | + | 0.0289174i | ||||
\(356\) | − | 1508.62i | − | 0.224598i | ||||||
\(357\) | 23062.8 | + | 13315.3i | 3.41909 | + | 1.97401i | ||||
\(358\) | 4279.90 | + | 2471.00i | 0.631843 | + | 0.364795i | ||||
\(359\) | − | 1398.34i | − | 0.205576i | −0.994703 | − | 0.102788i | \(-0.967224\pi\) | ||
0.994703 | − | 0.102788i | \(-0.0327763\pi\) | |||||||
\(360\) | −463.114 | + | 802.138i | −0.0678007 | + | 0.117434i | ||||
\(361\) | −1582.48 | − | 2740.94i | −0.230716 | − | 0.399612i | ||||
\(362\) | −3804.45 | + | 2196.50i | −0.552368 | + | 0.318910i | ||||
\(363\) | 8562.69 | 1.23808 | ||||||||
\(364\) | −5687.96 | + | 1511.42i | −0.819038 | + | 0.217637i | ||||
\(365\) | −345.521 | −0.0495490 | ||||||||
\(366\) | −6250.03 | + | 3608.46i | −0.892607 | + | 0.515347i | ||||
\(367\) | −2019.26 | − | 3497.46i | −0.287205 | − | 0.497454i | 0.685936 | − | 0.727662i | \(-0.259393\pi\) |
−0.973142 | + | 0.230207i | \(0.926060\pi\) | |||||||
\(368\) | −994.464 | + | 1722.46i | −0.140870 | + | 0.243993i | ||||
\(369\) | − | 7741.72i | − | 1.09219i | ||||||
\(370\) | −601.378 | − | 347.206i | −0.0844978 | − | 0.0487848i | ||||
\(371\) | −6028.38 | − | 3480.49i | −0.843606 | − | 0.487056i | ||||
\(372\) | − | 6329.53i | − | 0.882179i | ||||||
\(373\) | −315.134 | + | 545.828i | −0.0437454 | + | 0.0757692i | −0.887069 | − | 0.461637i | \(-0.847262\pi\) |
0.843324 | + | 0.537406i | \(0.180596\pi\) | |||||||
\(374\) | 1681.70 | + | 2912.79i | 0.232510 | + | 0.402719i | ||||
\(375\) | 5390.78 | − | 3112.37i | 0.742343 | − | 0.428592i | ||||
\(376\) | −4096.82 | −0.561908 | ||||||||
\(377\) | 700.573 | + | 2636.48i | 0.0957065 | + | 0.360174i | ||||
\(378\) | 3964.01 | 0.539382 | ||||||||
\(379\) | 4259.91 | − | 2459.46i | 0.577353 | − | 0.333335i | −0.182728 | − | 0.983164i | \(-0.558493\pi\) |
0.760081 | + | 0.649828i | \(0.225159\pi\) | |||||||
\(380\) | 401.903 | + | 696.116i | 0.0542557 | + | 0.0939737i | ||||
\(381\) | −2884.09 | + | 4995.39i | −0.387812 | + | 0.671710i | ||||
\(382\) | 4102.41i | 0.549470i | ||||||||
\(383\) | −8681.96 | − | 5012.53i | −1.15830 | − | 0.668742i | −0.207401 | − | 0.978256i | \(-0.566500\pi\) |
−0.950895 | + | 0.309514i | \(0.899834\pi\) | |||||||
\(384\) | 872.968 | + | 504.008i | 0.116012 | + | 0.0669794i | ||||
\(385\) | 1620.16i | 0.214471i | ||||||||
\(386\) | 3753.14 | − | 6500.63i | 0.494896 | − | 0.857185i | ||||
\(387\) | 1962.18 | + | 3398.59i | 0.257734 | + | 0.446409i | ||||
\(388\) | −1986.01 | + | 1146.62i | −0.259857 | + | 0.150028i | ||||
\(389\) | −13329.5 | −1.73735 | −0.868676 | − | 0.495380i | \(-0.835029\pi\) | ||||
−0.868676 | + | 0.495380i | \(0.835029\pi\) | |||||||
\(390\) | −1729.53 | + | 1722.36i | −0.224560 | + | 0.223629i | ||||
\(391\) | 13391.4 | 1.73205 | ||||||||
\(392\) | 4450.38 | − | 2569.43i | 0.573413 | − | 0.331060i | ||||
\(393\) | −7333.35 | − | 12701.7i | −0.941269 | − | 1.63033i | ||||
\(394\) | −746.515 | + | 1293.00i | −0.0954540 | + | 0.165331i | ||||
\(395\) | 2020.42i | 0.257363i | ||||||||
\(396\) | 1893.65 | + | 1093.30i | 0.240302 | + | 0.138738i | ||||
\(397\) | 401.196 | + | 231.631i | 0.0507191 | + | 0.0292827i | 0.525145 | − | 0.851013i | \(-0.324011\pi\) |
−0.474426 | + | 0.880295i | \(0.657344\pi\) | |||||||
\(398\) | 5314.59i | 0.669337i | ||||||||
\(399\) | 7512.34 | − | 13011.7i | 0.942574 | − | 1.63259i | ||||
\(400\) | −912.548 | − | 1580.58i | −0.114068 | − | 0.197572i | ||||
\(401\) | 12170.0 | − | 7026.32i | 1.51556 | − | 0.875007i | 0.515723 | − | 0.856755i | \(-0.327523\pi\) |
0.999833 | − | 0.0182521i | \(-0.00581015\pi\) | |||||||
\(402\) | −8343.55 | −1.03517 | ||||||||
\(403\) | 2456.51 | − | 9092.21i | 0.303642 | − | 1.12386i | ||||
\(404\) | 3822.01 | 0.470673 | ||||||||
\(405\) | −1283.45 | + | 741.003i | −0.157470 | + | 0.0909154i | ||||
\(406\) | −1826.93 | − | 3164.33i | −0.223322 | − | 0.386805i | ||||
\(407\) | −819.668 | + | 1419.71i | −0.0998266 | + | 0.172905i | ||||
\(408\) | − | 6786.96i | − | 0.823540i | ||||||
\(409\) | −3844.75 | − | 2219.77i | −0.464819 | − | 0.268363i | 0.249250 | − | 0.968439i | \(-0.419816\pi\) |
−0.714068 | + | 0.700076i | \(0.753149\pi\) | |||||||
\(410\) | −1266.05 | − | 730.955i | −0.152502 | − | 0.0880471i | ||||
\(411\) | 6988.83i | 0.838768i | ||||||||
\(412\) | −2957.91 | + | 5123.26i | −0.353704 | + | 0.612633i | ||||
\(413\) | −8741.03 | − | 15139.9i | −1.04145 | − | 1.80384i | ||||
\(414\) | 7539.58 | − | 4352.98i | 0.895049 | − | 0.516757i | ||||
\(415\) | −1625.25 | −0.192242 | ||||||||
\(416\) | 1058.39 | + | 1062.80i | 0.124740 | + | 0.125259i | ||||
\(417\) | −11435.6 | −1.34294 | ||||||||
\(418\) | 1643.36 | − | 948.794i | 0.192295 | − | 0.111022i | ||||
\(419\) | 6839.51 | + | 11846.4i | 0.797451 | + | 1.38123i | 0.921271 | + | 0.388921i | \(0.127152\pi\) |
−0.123820 | + | 0.992305i | \(0.539514\pi\) | |||||||
\(420\) | 1634.65 | − | 2831.30i | 0.189911 | − | 0.328936i | ||||
\(421\) | 11133.2i | 1.28884i | 0.764673 | + | 0.644419i | \(0.222901\pi\) | ||||
−0.764673 | + | 0.644419i | \(0.777099\pi\) | |||||||
\(422\) | 2610.79 | + | 1507.34i | 0.301165 | + | 0.173877i | ||||
\(423\) | 15530.1 | + | 8966.32i | 1.78511 | + | 1.03063i | ||||
\(424\) | 1774.04i | 0.203196i | ||||||||
\(425\) | −6144.17 | + | 10642.0i | −0.701261 | + | 1.21462i | ||||
\(426\) | −531.972 | − | 921.402i | −0.0605026 | − | 0.104794i | ||||
\(427\) | 12456.4 | − | 7191.68i | 1.41172 | − | 0.815058i | ||||
\(428\) | −852.463 | −0.0962741 | ||||||||
\(429\) | 4066.07 | + | 4083.00i | 0.457603 | + | 0.459509i | ||||
\(430\) | 741.057 | 0.0831091 | ||||||||
\(431\) | −1259.28 | + | 727.043i | −0.140736 | + | 0.0812539i | −0.568715 | − | 0.822535i | \(-0.692559\pi\) |
0.427979 | + | 0.903789i | \(0.359226\pi\) | |||||||
\(432\) | −505.124 | − | 874.900i | −0.0562564 | − | 0.0974390i | ||||
\(433\) | −3844.28 | + | 6658.49i | −0.426662 | + | 0.738999i | −0.996574 | − | 0.0827060i | \(-0.973644\pi\) |
0.569912 | + | 0.821705i | \(0.306977\pi\) | |||||||
\(434\) | 12614.8i | 1.39523i | ||||||||
\(435\) | −1312.36 | − | 757.692i | −0.144650 | − | 0.0835139i | ||||
\(436\) | 292.438 | + | 168.839i | 0.0321222 | + | 0.0185457i | ||||
\(437\) | − | 7555.26i | − | 0.827042i | ||||||
\(438\) | 822.984 | − | 1425.45i | 0.0897801 | − | 0.155504i | ||||
\(439\) | −4320.81 | − | 7483.86i | −0.469751 | − | 0.813633i | 0.529651 | − | 0.848216i | \(-0.322323\pi\) |
−0.999402 | + | 0.0345828i | \(0.988990\pi\) | |||||||
\(440\) | 357.588 | − | 206.453i | 0.0387439 | − | 0.0223688i | ||||
\(441\) | −22493.9 | −2.42888 | ||||||||
\(442\) | 2634.04 | − | 9749.30i | 0.283458 | − | 1.04916i | ||||
\(443\) | −13563.6 | −1.45469 | −0.727346 | − | 0.686271i | \(-0.759246\pi\) | ||||
−0.727346 | + | 0.686271i | \(0.759246\pi\) | |||||||
\(444\) | 2864.80 | − | 1654.00i | 0.306211 | − | 0.176791i | ||||
\(445\) | 623.492 | + | 1079.92i | 0.0664187 | + | 0.115041i | ||||
\(446\) | 1979.06 | − | 3427.83i | 0.210115 | − | 0.363929i | ||||
\(447\) | − | 12149.0i | − | 1.28552i | ||||||
\(448\) | −1739.83 | − | 1004.49i | −0.183481 | − | 0.105933i | ||||
\(449\) | 16278.9 | + | 9398.65i | 1.71103 | + | 0.987862i | 0.933181 | + | 0.359406i | \(0.117021\pi\) |
0.777845 | + | 0.628456i | \(0.216313\pi\) | |||||||
\(450\) | 7988.83i | 0.836882i | ||||||||
\(451\) | −1725.60 | + | 2988.84i | −0.180168 | + | 0.312059i | ||||
\(452\) | −1572.84 | − | 2724.23i | −0.163673 | − | 0.283489i | ||||
\(453\) | −11074.5 | + | 6393.86i | −1.14862 | + | 0.663156i | ||||
\(454\) | −4221.58 | −0.436406 | ||||||||
\(455\) | 3446.97 | − | 3432.68i | 0.355157 | − | 0.353684i | ||||
\(456\) | −3829.11 | −0.393234 | ||||||||
\(457\) | 6257.55 | − | 3612.80i | 0.640516 | − | 0.369802i | −0.144297 | − | 0.989534i | \(-0.546092\pi\) |
0.784813 | + | 0.619732i | \(0.212759\pi\) | |||||||
\(458\) | −5326.76 | − | 9226.21i | −0.543456 | − | 0.941294i | ||||
\(459\) | −3400.99 | + | 5890.68i | −0.345849 | + | 0.599027i | ||||
\(460\) | − | 1643.99i | − | 0.166634i | ||||||
\(461\) | 1987.84 | + | 1147.68i | 0.200831 | + | 0.115950i | 0.597043 | − | 0.802209i | \(-0.296342\pi\) |
−0.396212 | + | 0.918159i | \(0.629676\pi\) | |||||||
\(462\) | −6684.00 | − | 3859.01i | −0.673091 | − | 0.388609i | ||||
\(463\) | 9457.75i | 0.949328i | 0.880167 | + | 0.474664i | \(0.157430\pi\) | ||||
−0.880167 | + | 0.474664i | \(0.842570\pi\) | |||||||
\(464\) | −465.601 | + | 806.445i | −0.0465841 | + | 0.0806859i | ||||
\(465\) | 2615.91 | + | 4530.88i | 0.260881 | + | 0.451859i | ||||
\(466\) | 257.987 | − | 148.949i | 0.0256460 | − | 0.0148067i | ||||
\(467\) | 13310.9 | 1.31896 | 0.659481 | − | 0.751721i | \(-0.270776\pi\) | ||||
0.659481 | + | 0.751721i | \(0.270776\pi\) | |||||||
\(468\) | −1686.07 | − | 6345.23i | −0.166536 | − | 0.626727i | ||||
\(469\) | 16628.8 | 1.63720 | ||||||||
\(470\) | 2932.63 | − | 1693.16i | 0.287813 | − | 0.166169i | ||||
\(471\) | 11006.2 | + | 19063.3i | 1.07673 | + | 1.86495i | ||||
\(472\) | −2227.70 | + | 3858.48i | −0.217242 | + | 0.376273i | ||||
\(473\) | − | 1749.45i | − | 0.170063i | ||||||
\(474\) | −8335.27 | − | 4812.37i | −0.807704 | − | 0.466328i | ||||
\(475\) | 6004.08 | + | 3466.46i | 0.579971 | + | 0.334846i | ||||
\(476\) | 13526.5i | 1.30249i | ||||||||
\(477\) | 3882.67 | − | 6724.99i | 0.372695 | − | 0.645526i | ||||
\(478\) | 3081.18 | + | 5336.76i | 0.294833 | + | 0.510665i | ||||
\(479\) | −6901.57 | + | 3984.62i | −0.658332 | + | 0.380088i | −0.791641 | − | 0.610987i | \(-0.790773\pi\) |
0.133309 | + | 0.991074i | \(0.457440\pi\) | |||||||
\(480\) | −833.198 | −0.0792294 | ||||||||
\(481\) | 4757.14 | − | 1264.08i | 0.450950 | − | 0.119828i | ||||
\(482\) | 5140.59 | 0.485783 | ||||||||
\(483\) | −26612.4 | + | 15364.7i | −2.50705 | + | 1.44745i | ||||
\(484\) | 2174.61 | + | 3766.54i | 0.204228 | + | 0.353732i | ||||
\(485\) | 947.767 | − | 1641.58i | 0.0887338 | − | 0.153691i | ||||
\(486\) | − | 10469.5i | − | 0.977169i | ||||||
\(487\) | −1225.83 | − | 707.734i | −0.114061 | − | 0.0658532i | 0.441884 | − | 0.897072i | \(-0.354310\pi\) |
−0.555945 | + | 0.831219i | \(0.687644\pi\) | |||||||
\(488\) | −3174.57 | − | 1832.84i | −0.294479 | − | 0.170018i | ||||
\(489\) | − | 2281.40i | − | 0.210978i | ||||||
\(490\) | −2123.82 | + | 3678.56i | −0.195805 | + | 0.339143i | ||||
\(491\) | −1600.46 | − | 2772.07i | −0.147103 | − | 0.254790i | 0.783053 | − | 0.621956i | \(-0.213662\pi\) |
−0.930156 | + | 0.367166i | \(0.880328\pi\) | |||||||
\(492\) | 6031.13 | − | 3482.07i | 0.552651 | − | 0.319073i | ||||
\(493\) | 6269.77 | 0.572771 | ||||||||
\(494\) | −5500.43 | − | 1486.09i | −0.500963 | − | 0.135349i | ||||
\(495\) | −1807.38 | −0.164113 | ||||||||
\(496\) | 2784.22 | − | 1607.47i | 0.252047 | − | 0.145519i | ||||
\(497\) | 1060.22 | + | 1836.36i | 0.0956892 | + | 0.165739i | ||||
\(498\) | 3871.14 | − | 6705.01i | 0.348333 | − | 0.603330i | ||||
\(499\) | − | 1480.51i | − | 0.132819i | −0.997792 | − | 0.0664097i | \(-0.978846\pi\) | ||
0.997792 | − | 0.0664097i | \(-0.0211544\pi\) | |||||||
\(500\) | 2738.13 | + | 1580.86i | 0.244905 | + | 0.141396i | ||||
\(501\) | −15877.9 | − | 9167.12i | −1.41591 | − | 0.817479i | ||||
\(502\) | 4087.52i | 0.363417i | ||||||||
\(503\) | 10129.6 | − | 17545.1i | 0.897929 | − | 1.55526i | 0.0677919 | − | 0.997699i | \(-0.478405\pi\) |
0.830137 | − | 0.557559i | \(-0.188262\pi\) | |||||||
\(504\) | 4396.88 | + | 7615.61i | 0.388596 | + | 0.673068i | ||||
\(505\) | −2735.92 | + | 1579.58i | −0.241083 | + | 0.139189i | ||||
\(506\) | −3881.06 | −0.340977 | ||||||||
\(507\) | 71.9077 | − | 17301.5i | 0.00629889 | − | 1.51556i | ||||
\(508\) | −2929.82 | −0.255885 | ||||||||
\(509\) | −6122.14 | + | 3534.62i | −0.533122 | + | 0.307798i | −0.742287 | − | 0.670082i | \(-0.766259\pi\) |
0.209165 | + | 0.977880i | \(0.432925\pi\) | |||||||
\(510\) | 2804.95 | + | 4858.32i | 0.243540 | + | 0.421824i | ||||
\(511\) | −1640.21 | + | 2840.93i | −0.141994 | + | 0.245940i | ||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 3323.45 | + | 1918.79i | 0.286031 | + | 0.165140i | ||||
\(514\) | 13369.6 | + | 7718.93i | 1.14729 | + | 0.662388i | ||||
\(515\) | − | 4889.86i | − | 0.418394i | ||||||
\(516\) | −1765.10 | + | 3057.24i | −0.150589 | + | 0.260828i | ||||
\(517\) | −3997.13 | − | 6923.23i | −0.340026 | − | 0.588942i | ||||
\(518\) | −5709.58 | + | 3296.43i | −0.484294 | + | 0.279607i | ||||
\(519\) | −8378.22 | −0.708599 | ||||||||
\(520\) | −1196.87 | − | 323.367i | −0.100935 | − | 0.0272704i | ||||
\(521\) | −13874.4 | −1.16670 | −0.583348 | − | 0.812223i | \(-0.698257\pi\) | ||||
−0.583348 | + | 0.812223i | \(0.698257\pi\) | |||||||
\(522\) | 3529.98 | − | 2038.04i | 0.295983 | − | 0.170886i | ||||
\(523\) | 8176.89 | + | 14162.8i | 0.683653 | + | 1.18412i | 0.973858 | + | 0.227158i | \(0.0729432\pi\) |
−0.290205 | + | 0.956965i | \(0.593723\pi\) | |||||||
\(524\) | 3724.82 | − | 6451.57i | 0.310533 | − | 0.537859i | ||||
\(525\) | − | 28198.1i | − | 2.34413i | ||||||
\(526\) | −2571.27 | − | 1484.52i | −0.213142 | − | 0.123057i | ||||
\(527\) | −18746.1 | − | 10823.1i | −1.54951 | − | 0.894613i | ||||
\(528\) | 1966.98i | 0.162124i | ||||||||
\(529\) | −1642.74 | + | 2845.31i | −0.135016 | + | 0.233855i | ||||
\(530\) | −733.185 | − | 1269.91i | −0.0600897 | − | 0.104078i | ||||
\(531\) | 16889.4 | − | 9751.10i | 1.38030 | − | 0.796915i | ||||
\(532\) | 7631.45 | 0.621927 | ||||||||
\(533\) | 10015.0 | − | 2661.21i | 0.813877 | − | 0.216266i | ||||
\(534\) | −5940.29 | −0.481389 | ||||||||
\(535\) | 610.220 | − | 352.311i | 0.0493124 | − | 0.0284705i | ||||
\(536\) | −2118.96 | − | 3670.15i | −0.170756 | − | 0.295758i | ||||
\(537\) | 9729.73 | − | 16852.4i | 0.781879 | − | 1.35425i | ||||
\(538\) | − | 4533.08i | − | 0.363262i | ||||||
\(539\) | 8684.17 | + | 5013.81i | 0.693977 | + | 0.400668i | ||||
\(540\) | 723.167 | + | 417.521i | 0.0576300 | + | 0.0332727i | ||||
\(541\) | − | 2609.54i | − | 0.207381i | −0.994610 | − | 0.103690i | \(-0.966935\pi\) | ||
0.994610 | − | 0.103690i | \(-0.0330651\pi\) | |||||||
\(542\) | 5267.43 | − | 9123.46i | 0.417446 | − | 0.723037i | ||||
\(543\) | 8648.86 | + | 14980.3i | 0.683533 | + | 1.18391i | ||||
\(544\) | 2985.44 | − | 1723.64i | 0.235293 | − | 0.135847i | ||||
\(545\) | −279.116 | −0.0219376 | ||||||||
\(546\) | 5951.32 | + | 22396.7i | 0.466471 | + | 1.75548i | ||||
\(547\) | −22168.6 | −1.73284 | −0.866419 | − | 0.499318i | \(-0.833584\pi\) | ||||
−0.866419 | + | 0.499318i | \(0.833584\pi\) | |||||||
\(548\) | −3074.24 | + | 1774.91i | −0.239644 | + | 0.138358i | ||||
\(549\) | 8022.71 | + | 13895.7i | 0.623681 | + | 1.08025i | ||||
\(550\) | 1780.68 | − | 3084.24i | 0.138052 | − | 0.239113i | ||||
\(551\) | − | 3537.32i | − | 0.273494i | ||||||
\(552\) | 6782.31 | + | 3915.77i | 0.522961 | + | 0.301931i | ||||
\(553\) | 16612.3 | + | 9591.09i | 1.27744 | + | 0.737531i | ||||
\(554\) | 9630.88i | 0.738587i | ||||||||
\(555\) | −1367.15 | + | 2367.97i | −0.104562 | + | 0.181107i | ||||
\(556\) | −2904.24 | − | 5030.29i | −0.221524 | − | 0.383690i | ||||
\(557\) | −18090.3 | + | 10444.4i | −1.37614 | + | 0.794514i | −0.991692 | − | 0.128634i | \(-0.958941\pi\) |
−0.384446 | + | 0.923147i | \(0.625608\pi\) | |||||||
\(558\) | −14072.5 | −1.06763 | ||||||||
\(559\) | −3722.04 | + | 3706.61i | −0.281620 | + | 0.280452i | ||||
\(560\) | 1660.57 | 0.125307 | ||||||||
\(561\) | 11469.3 | − | 6621.81i | 0.863163 | − | 0.498347i | ||||
\(562\) | −1983.72 | − | 3435.90i | −0.148893 | − | 0.257891i | ||||
\(563\) | 6340.33 | − | 10981.8i | 0.474623 | − | 0.822071i | −0.524955 | − | 0.851130i | \(-0.675918\pi\) |
0.999578 | + | 0.0290588i | \(0.00925100\pi\) | |||||||
\(564\) | 16131.5i | 1.20436i | ||||||||
\(565\) | 2251.77 | + | 1300.06i | 0.167669 | + | 0.0968036i | ||||
\(566\) | −1432.58 | − | 827.101i | −0.106388 | − | 0.0614234i | ||||
\(567\) | 14070.4i | 1.04215i | ||||||||
\(568\) | 270.203 | − | 468.006i | 0.0199604 | − | 0.0345723i | ||||
\(569\) | −316.343 | − | 547.922i | −0.0233072 | − | 0.0403692i | 0.854137 | − | 0.520049i | \(-0.174086\pi\) |
−0.877444 | + | 0.479680i | \(0.840753\pi\) | |||||||
\(570\) | 2741.00 | − | 1582.52i | 0.201418 | − | 0.116288i | ||||
\(571\) | −8050.66 | −0.590034 | −0.295017 | − | 0.955492i | \(-0.595325\pi\) | ||||
−0.295017 | + | 0.955492i | \(0.595325\pi\) | |||||||
\(572\) | −763.391 | + | 2825.51i | −0.0558024 | + | 0.206540i | ||||
\(573\) | 16153.5 | 1.17770 | ||||||||
\(574\) | −12020.1 | + | 6939.80i | −0.874057 | + | 0.504637i | ||||
\(575\) | −7089.81 | − | 12279.9i | −0.514201 | − | 0.890622i | ||||
\(576\) | 1120.57 | − | 1940.88i | 0.0810595 | − | 0.140399i | ||||
\(577\) | 14173.9i | 1.02265i | 0.859389 | + | 0.511323i | \(0.170844\pi\) | ||||
−0.859389 | + | 0.511323i | \(0.829156\pi\) | |||||||
\(578\) | −11591.3 | − | 6692.26i | −0.834145 | − | 0.481594i | ||||
\(579\) | −25596.7 | − | 14778.2i | −1.83724 | − | 1.06073i | ||||
\(580\) | − | 769.706i | − | 0.0551040i | ||||||
\(581\) | −7715.21 | + | 13363.1i | −0.550913 | + | 0.954210i | ||||
\(582\) | 4514.91 | + | 7820.05i | 0.321562 | + | 0.556961i | ||||
\(583\) | −2997.96 | + | 1730.87i | −0.212972 | + | 0.122959i | ||||
\(584\) | 836.033 | 0.0592385 | ||||||||
\(585\) | 3829.34 | + | 3845.29i | 0.270639 | + | 0.271766i | ||||
\(586\) | −2373.19 | −0.167296 | ||||||||
\(587\) | 11411.7 | − | 6588.56i | 0.802406 | − | 0.463269i | −0.0419057 | − | 0.999122i | \(-0.513343\pi\) |
0.844312 | + | 0.535852i | \(0.180010\pi\) | |||||||
\(588\) | −10117.3 | − | 17523.7i | −0.709575 | − | 1.22902i | ||||
\(589\) | −6106.24 | + | 10576.3i | −0.427170 | + | 0.739881i | ||||
\(590\) | − | 3682.70i | − | 0.256974i | ||||||
\(591\) | 5091.28 | + | 2939.45i | 0.354361 | + | 0.204590i | ||||
\(592\) | 1455.11 | + | 840.111i | 0.101022 | + | 0.0583249i | ||||
\(593\) | 20637.4i | 1.42913i | 0.699568 | + | 0.714566i | \(0.253376\pi\) | ||||
−0.699568 | + | 0.714566i | \(0.746624\pi\) | |||||||
\(594\) | 985.664 | − | 1707.22i | 0.0680847 | − | 0.117926i | ||||
\(595\) | −5590.30 | − | 9682.68i | −0.385176 | − | 0.667145i | ||||
\(596\) | 5344.08 | − | 3085.40i | 0.367285 | − | 0.212052i | ||||
\(597\) | 20926.5 | 1.43462 | ||||||||
\(598\) | 8222.90 | + | 8257.14i | 0.562306 | + | 0.564648i | ||||
\(599\) | 286.244 | 0.0195252 | 0.00976262 | − | 0.999952i | \(-0.496892\pi\) | ||||
0.00976262 | + | 0.999952i | \(0.496892\pi\) | |||||||
\(600\) | −6223.63 | + | 3593.22i | −0.423465 | + | 0.244487i | ||||
\(601\) | −10160.8 | − | 17599.1i | −0.689633 | − | 1.19448i | −0.971957 | − | 0.235160i | \(-0.924439\pi\) |
0.282324 | − | 0.959319i | \(-0.408895\pi\) | |||||||
\(602\) | 3517.85 | − | 6093.10i | 0.238168 | − | 0.412518i | ||||
\(603\) | 18550.3i | 1.25278i | ||||||||
\(604\) | −5625.04 | − | 3247.62i | −0.378940 | − | 0.218781i | ||||
\(605\) | −3113.32 | − | 1797.48i | −0.209214 | − | 0.120790i | ||||
\(606\) | − | 15049.4i | − | 1.00881i | ||||||
\(607\) | −2454.43 | + | 4251.19i | −0.164122 | + | 0.284268i | −0.936343 | − | 0.351086i | \(-0.885812\pi\) |
0.772221 | + | 0.635354i | \(0.219146\pi\) | |||||||
\(608\) | −972.457 | − | 1684.35i | −0.0648657 | − | 0.112351i | ||||
\(609\) | −12459.8 | + | 7193.64i | −0.829055 | + | 0.478655i | ||||
\(610\) | 3029.94 | 0.201113 | ||||||||
\(611\) | −6260.69 | + | 23172.5i | −0.414534 | + | 1.53430i | ||||
\(612\) | −15089.5 | −0.996662 | ||||||||
\(613\) | −7008.38 | + | 4046.29i | −0.461771 | + | 0.266604i | −0.712789 | − | 0.701379i | \(-0.752568\pi\) |
0.251018 | + | 0.967983i | \(0.419235\pi\) | |||||||
\(614\) | 6191.17 | + | 10723.4i | 0.406930 | + | 0.704824i | ||||
\(615\) | −2878.18 | + | 4985.16i | −0.188715 | + | 0.326863i | ||||
\(616\) | − | 3920.20i | − | 0.256411i | ||||||
\(617\) | 19404.8 | + | 11203.4i | 1.26614 | + | 0.731006i | 0.974255 | − | 0.225448i | \(-0.0723847\pi\) |
0.291884 | + | 0.956454i | \(0.405718\pi\) | |||||||
\(618\) | 20173.2 | + | 11647.0i | 1.31308 | + | 0.758107i | ||||
\(619\) | − | 29226.6i | − | 1.89777i | −0.315627 | − | 0.948883i | \(-0.602215\pi\) | ||
0.315627 | − | 0.948883i | \(-0.397785\pi\) | |||||||
\(620\) | −1328.69 | + | 2301.36i | −0.0860670 | + | 0.149072i | ||||
\(621\) | −3924.43 | − | 6797.32i | −0.253594 | − | 0.439238i | ||||
\(622\) | 18375.8 | − | 10609.3i | 1.18457 | − | 0.683912i | ||||
\(623\) | 11839.0 | 0.761351 | ||||||||
\(624\) | 4184.84 | − | 4167.48i | 0.268474 | − | 0.267360i | ||||
\(625\) | 11645.2 | 0.745291 | ||||||||
\(626\) | 17031.7 | − | 9833.23i | 1.08742 | − | 0.627819i | ||||
\(627\) | −3735.94 | − | 6470.83i | −0.237957 | − | 0.412153i | ||||
\(628\) | −5590.36 | + | 9682.79i | −0.355222 | + | 0.615263i | ||||
\(629\) | − | 11312.9i | − | 0.717130i | ||||||
\(630\) | −6294.85 | − | 3634.34i | −0.398084 | − | 0.229834i | ||||
\(631\) | 5473.32 | + | 3160.03i | 0.345308 | + | 0.199364i | 0.662617 | − | 0.748958i | \(-0.269446\pi\) |
−0.317309 | + | 0.948322i | \(0.602779\pi\) | |||||||
\(632\) | − | 4888.68i | − | 0.307692i | ||||||
\(633\) | 5935.26 | − | 10280.2i | 0.372678 | − | 0.645498i | ||||
\(634\) | −4674.74 | − | 8096.88i | −0.292835 | − | 0.507205i | ||||
\(635\) | 2097.26 | − | 1210.85i | 0.131066 | − | 0.0756712i | ||||
\(636\) | 6985.40 | 0.435517 | ||||||||
\(637\) | −7732.24 | − | 29098.9i | −0.480946 | − | 1.80995i | ||||
\(638\) | −1817.09 | −0.112757 | ||||||||
\(639\) | −2048.56 | + | 1182.74i | −0.126823 | + | 0.0732212i | ||||
\(640\) | −211.602 | − | 366.506i | −0.0130692 | − | 0.0226366i | ||||
\(641\) | −4201.52 | + | 7277.24i | −0.258892 | + | 0.448415i | −0.965945 | − | 0.258746i | \(-0.916691\pi\) |
0.707053 | + | 0.707160i | \(0.250024\pi\) | |||||||
\(642\) | 3356.63i | 0.206348i | ||||||||
\(643\) | −271.587 | − | 156.801i | −0.0166568 | − | 0.00961684i | 0.491648 | − | 0.870794i | \(-0.336395\pi\) |
−0.508305 | + | 0.861177i | \(0.669728\pi\) | |||||||
\(644\) | −13517.2 | − | 7804.15i | −0.827099 | − | 0.477526i | ||||
\(645\) | − | 2917.96i | − | 0.178131i | ||||||
\(646\) | −6547.54 | + | 11340.7i | −0.398776 | + | 0.690700i | ||||
\(647\) | −4037.44 | − | 6993.04i | −0.245329 | − | 0.424923i | 0.716895 | − | 0.697181i | \(-0.245563\pi\) |
−0.962224 | + | 0.272259i | \(0.912229\pi\) | |||||||
\(648\) | 3105.49 | − | 1792.95i | 0.188264 | − | 0.108694i | ||||
\(649\) | −8693.95 | −0.525836 | ||||||||
\(650\) | −10334.6 | + | 2746.15i | −0.623627 | + | 0.165712i | ||||
\(651\) | 49671.6 | 2.99045 | ||||||||
\(652\) | 1003.54 | − | 579.393i | 0.0602785 | − | 0.0348018i | ||||
\(653\) | 9083.36 | + | 15732.8i | 0.544348 | + | 0.942839i | 0.998648 | + | 0.0519898i | \(0.0165563\pi\) |
−0.454299 | + | 0.890849i | \(0.650110\pi\) | |||||||
\(654\) | 664.816 | − | 1151.50i | 0.0397498 | − | 0.0688487i | ||||
\(655\) | 6157.66i | 0.367327i | ||||||||
\(656\) | 3063.38 | + | 1768.64i | 0.182324 | + | 0.105265i | ||||
\(657\) | −3169.22 | − | 1829.75i | −0.188193 | − | 0.108653i | ||||
\(658\) | − | 32150.2i | − | 1.90478i | ||||||
\(659\) | 9822.68 | − | 17013.4i | 0.580633 | − | 1.00569i | −0.414771 | − | 0.909926i | \(-0.636138\pi\) |
0.995404 | − | 0.0957607i | \(-0.0305284\pi\) | |||||||
\(660\) | −812.924 | − | 1408.03i | −0.0479440 | − | 0.0830414i | ||||
\(661\) | −9515.27 | + | 5493.64i | −0.559911 | + | 0.323265i | −0.753110 | − | 0.657895i | \(-0.771447\pi\) |
0.193199 | + | 0.981160i | \(0.438114\pi\) | |||||||
\(662\) | −20826.7 | −1.22274 | ||||||||
\(663\) | −38388.5 | − | 10371.7i | −2.24870 | − | 0.607548i | ||||
\(664\) | 3932.52 | 0.229836 | ||||||||
\(665\) | −5462.84 | + | 3153.97i | −0.318556 | + | 0.183918i | ||||
\(666\) | −3677.34 | − | 6369.35i | −0.213955 | − | 0.370581i | ||||
\(667\) | −3617.37 | + | 6265.48i | −0.209993 | + | 0.363718i | ||||
\(668\) | − | 9312.48i | − | 0.539387i | ||||||
\(669\) | −13497.3 | − | 7792.67i | −0.780023 | − | 0.450347i | ||||
\(670\) | 3033.64 | + | 1751.47i | 0.174925 | + | 0.100993i | ||||
\(671\) | − | 7152.95i | − | 0.411530i | ||||||
\(672\) | −3955.26 | + | 6850.70i | −0.227050 | + | 0.393261i | ||||
\(673\) | 17128.5 | + | 29667.5i | 0.981065 | + | 1.69925i | 0.658264 | + | 0.752787i | \(0.271291\pi\) |
0.322801 | + | 0.946467i | \(0.395376\pi\) | |||||||
\(674\) | −8441.09 | + | 4873.47i | −0.482402 | + | 0.278515i | ||||
\(675\) | 7202.33 | 0.410693 | ||||||||
\(676\) | 7628.83 | − | 4362.33i | 0.434048 | − | 0.248198i | ||||
\(677\) | 25142.1 | 1.42731 | 0.713656 | − | 0.700497i | \(-0.247038\pi\) | ||||
0.713656 | + | 0.700497i | \(0.247038\pi\) | |||||||
\(678\) | −10726.8 | + | 6193.15i | −0.607614 | + | 0.350806i | ||||
\(679\) | −8998.24 | − | 15585.4i | −0.508573 | − | 0.880874i | ||||
\(680\) | −1424.71 | + | 2467.68i | −0.0803461 | + | 0.139163i | ||||
\(681\) | 16622.7i | 0.935367i | ||||||||
\(682\) | 5432.95 | + | 3136.71i | 0.305041 | + | 0.176116i | ||||
\(683\) | 8664.54 | + | 5002.48i | 0.485416 | + | 0.280255i | 0.722671 | − | 0.691192i | \(-0.242914\pi\) |
−0.237255 | + | 0.971448i | \(0.576248\pi\) | |||||||
\(684\) | 8513.30i | 0.475898i | ||||||||
\(685\) | 1467.09 | − | 2541.08i | 0.0818317 | − | 0.141737i | ||||
\(686\) | 9396.92 | + | 16275.9i | 0.522997 | + | 0.905858i | ||||
\(687\) | −36328.8 | + | 20974.5i | −2.01751 | + | 1.16481i | ||||
\(688\) | −1793.08 | −0.0993615 | ||||||||
\(689\) | 10034.3 | + | 2711.06i | 0.554831 | + | 0.149903i | ||||
\(690\) | −6473.33 | −0.357153 | ||||||||
\(691\) | 6354.19 | − | 3668.59i | 0.349819 | − | 0.201968i | −0.314787 | − | 0.949162i | \(-0.601933\pi\) |
0.664605 | + | 0.747195i | \(0.268600\pi\) | |||||||
\(692\) | −2127.77 | − | 3685.40i | −0.116887 | − | 0.202453i | ||||
\(693\) | −8579.77 | + | 14860.6i | −0.470301 | + | 0.814585i | ||||
\(694\) | 24243.4i | 1.32603i | ||||||||
\(695\) | 4157.90 | + | 2400.56i | 0.226932 | + | 0.131019i | ||||
\(696\) | 3175.43 | + | 1833.34i | 0.172937 | + | 0.0998454i | ||||
\(697\) | − | 23816.5i | − | 1.29428i | ||||||
\(698\) | −8872.17 | + | 15367.0i | −0.481113 | + | 0.833311i | ||||
\(699\) | −586.496 | − | 1015.84i | −0.0317358 | − | 0.0549680i | ||||
\(700\) | 12403.7 | − | 7161.31i | 0.669739 | − | 0.386674i | ||||
\(701\) | 7785.35 | 0.419470 | 0.209735 | − | 0.977758i | \(-0.432740\pi\) | ||||
0.209735 | + | 0.977758i | \(0.432740\pi\) | |||||||
\(702\) | −5720.54 | + | 1520.08i | −0.307561 | + | 0.0817261i | ||||
\(703\) | −6382.59 | −0.342424 | ||||||||
\(704\) | −865.231 | + | 499.541i | −0.0463205 | + | 0.0267431i | ||||
\(705\) | −6666.92 | − | 11547.4i | −0.356157 | − | 0.616882i | ||||
\(706\) | −4541.69 | + | 7866.44i | −0.242109 | + | 0.419345i | ||||
\(707\) | 29993.6i | 1.59551i | ||||||||
\(708\) | 15193.0 | + | 8771.70i | 0.806482 | + | 0.465622i | ||||
\(709\) | 517.039 | + | 298.513i | 0.0273876 | + | 0.0158122i | 0.513631 | − | 0.858011i | \(-0.328300\pi\) |
−0.486244 | + | 0.873823i | \(0.661633\pi\) | |||||||
\(710\) | 446.685i | 0.0236110i | ||||||||
\(711\) | −10699.4 | + | 18531.9i | −0.564358 | + | 0.977497i | ||||
\(712\) | −1508.62 | − | 2613.01i | −0.0794072 | − | 0.137537i | ||||
\(713\) | 21631.3 | − | 12488.9i | 1.13618 | − | 0.655977i | ||||
\(714\) | 53261.3 | 2.79167 | ||||||||
\(715\) | −621.285 | − | 2338.09i | −0.0324962 | − | 0.122293i | ||||
\(716\) | 9884.01 | 0.515898 | ||||||||
\(717\) | 21013.9 | − | 12132.4i | 1.09453 | − | 0.631926i | ||||
\(718\) | −1398.34 | − | 2422.00i | −0.0726820 | − | 0.125889i | ||||
\(719\) | −6006.81 | + | 10404.1i | −0.311566 | + | 0.539648i | −0.978702 | − | 0.205288i | \(-0.934187\pi\) |
0.667135 | + | 0.744936i | \(0.267520\pi\) | |||||||
\(720\) | 1852.46i | 0.0958847i | ||||||||
\(721\) | −40205.3 | − | 23212.5i | −2.07673 | − | 1.19900i | ||||
\(722\) | −5481.88 | − | 3164.97i | −0.282569 | − | 0.163141i | ||||
\(723\) | − | 20241.4i | − | 1.04120i | ||||||
\(724\) | −4393.00 | + | 7608.90i | −0.225503 | + | 0.390583i | ||||
\(725\) | −3319.40 | − | 5749.37i | −0.170041 | − | 0.294519i | ||||
\(726\) | 14831.0 | − | 8562.69i | 0.758169 | − | 0.437729i | ||||
\(727\) | −1137.34 | −0.0580216 | −0.0290108 | − | 0.999579i | \(-0.509236\pi\) | ||||
−0.0290108 | + | 0.999579i | \(0.509236\pi\) | |||||||
\(728\) | −8340.41 | + | 8305.82i | −0.424610 | + | 0.422849i | ||||
\(729\) | −29121.7 | −1.47954 | ||||||||
\(730\) | −598.460 | + | 345.521i | −0.0303424 | + | 0.0175182i | ||||
\(731\) | 6036.40 | + | 10455.4i | 0.305423 | + | 0.529009i | ||||
\(732\) | −7216.91 | + | 12500.1i | −0.364405 | + | 0.631169i | ||||
\(733\) | − | 24930.1i | − | 1.25623i | −0.778122 | − | 0.628113i | \(-0.783828\pi\) | ||
0.778122 | − | 0.628113i | \(-0.216172\pi\) | |||||||
\(734\) | −6994.91 | − | 4038.51i | −0.351753 | − | 0.203085i | ||||
\(735\) | 14484.6 | + | 8362.67i | 0.726899 | + | 0.419676i | ||||
\(736\) | 3977.86i | 0.199220i | ||||||||
\(737\) | 4134.80 | − | 7161.68i | 0.206658 | − | 0.357943i | ||||
\(738\) | −7741.72 | − | 13409.1i | −0.386147 | − | 0.668827i | ||||
\(739\) | −9626.47 | + | 5557.84i | −0.479182 | + | 0.276656i | −0.720075 | − | 0.693896i | \(-0.755893\pi\) |
0.240894 | + | 0.970552i | \(0.422560\pi\) | |||||||
\(740\) | −1388.82 | −0.0689921 | ||||||||
\(741\) | −5851.59 | + | 21658.3i | −0.290099 | + | 1.07373i | ||||
\(742\) | −13921.9 | −0.688802 | ||||||||
\(743\) | 10675.7 | − | 6163.62i | 0.527125 | − | 0.304336i | −0.212720 | − | 0.977113i | \(-0.568232\pi\) |
0.739845 | + | 0.672777i | \(0.234899\pi\) | |||||||
\(744\) | −6329.53 | − | 10963.1i | −0.311898 | − | 0.540222i | ||||
\(745\) | −2550.31 | + | 4417.26i | −0.125418 | + | 0.217230i | ||||
\(746\) | 1260.54i | 0.0618653i | ||||||||
\(747\) | −14907.3 | − | 8606.73i | −0.730160 | − | 0.421558i | ||||
\(748\) | 5825.58 | + | 3363.40i | 0.284765 | + | 0.164409i | ||||
\(749\) | − | 6689.78i | − | 0.326354i | ||||||
\(750\) | 6224.73 | − | 10781.6i | 0.303060 | − | 0.524916i | ||||
\(751\) | −6902.03 | − | 11954.7i | −0.335364 | − | 0.580868i | 0.648190 | − | 0.761478i | \(-0.275526\pi\) |
−0.983555 | + | 0.180610i | \(0.942193\pi\) | |||||||
\(752\) | −7095.90 | + | 4096.82i | −0.344097 | + | 0.198664i | ||||
\(753\) | 16094.9 | 0.778925 | ||||||||
\(754\) | 3849.90 | + | 3865.94i | 0.185949 | + | 0.186723i | ||||
\(755\) | 5368.78 | 0.258795 | ||||||||
\(756\) | 6865.86 | − | 3964.01i | 0.330303 | − | 0.190700i | ||||
\(757\) | −450.515 | − | 780.315i | −0.0216304 | − | 0.0374650i | 0.855008 | − | 0.518616i | \(-0.173552\pi\) |
−0.876638 | + | 0.481151i | \(0.840219\pi\) | |||||||
\(758\) | 4918.92 | − | 8519.82i | 0.235704 | − | 0.408250i | ||||
\(759\) | 15281.9i | 0.730829i | ||||||||
\(760\) | 1392.23 | + | 803.806i | 0.0664494 | + | 0.0383646i | ||||
\(761\) | −25742.3 | − | 14862.3i | −1.22623 | − | 0.707962i | −0.259987 | − | 0.965612i | \(-0.583718\pi\) |
−0.966238 | + | 0.257650i | \(0.917052\pi\) | |||||||
\(762\) | 11536.4i | 0.548449i | ||||||||
\(763\) | −1324.98 | + | 2294.94i | −0.0628671 | + | 0.108889i | ||||
\(764\) | 4102.41 | + | 7105.58i | 0.194267 | + | 0.336480i | ||||
\(765\) | 10801.6 | − | 6236.28i | 0.510498 | − | 0.294736i | ||||
\(766\) | −20050.1 | −0.945745 | ||||||||
\(767\) | 18420.1 | + | 18496.8i | 0.867159 | + | 0.870770i | ||||
\(768\) | 2016.03 | 0.0947231 | ||||||||
\(769\) | 22531.8 | − | 13008.7i | 1.05659 | − | 0.610021i | 0.132101 | − | 0.991236i | \(-0.457828\pi\) |
0.924486 | + | 0.381215i | \(0.124494\pi\) | |||||||
\(770\) | 1620.16 | + | 2806.20i | 0.0758268 | + | 0.131336i | ||||
\(771\) | 30393.8 | − | 52643.6i | 1.41972 | − | 2.45903i | ||||
\(772\) | − | 15012.6i | − | 0.699889i | ||||||
\(773\) | −3392.26 | − | 1958.52i | −0.157841 | − | 0.0911296i | 0.418999 | − | 0.907987i | \(-0.362381\pi\) |
−0.576840 | + | 0.816857i | \(0.695714\pi\) | |||||||
\(774\) | 6797.18 | + | 3924.36i | 0.315659 | + | 0.182246i | ||||
\(775\) | 22920.2i | 1.06235i | ||||||||
\(776\) | −2293.25 | + | 3972.02i | −0.106086 | + | 0.183746i | ||||
\(777\) | 12979.9 | + | 22481.8i | 0.599294 | + | 1.03801i | ||||
\(778\) | −23087.3 | + | 13329.5i | −1.06391 | + | 0.614247i | ||||
\(779\) | −13436.9 | −0.618008 | ||||||||
\(780\) | −1273.28 | + | 4712.75i | −0.0584497 | + | 0.216338i | ||||
\(781\) | 1054.51 | 0.0483143 | ||||||||
\(782\) | 23194.6 | − | 13391.4i | 1.06066 | − | 0.612374i | ||||
\(783\) | −1837.39 | − | 3182.46i | −0.0838609 | − | 0.145251i | ||||
\(784\) | 5138.85 | − | 8900.76i | 0.234095 | − | 0.405464i | ||||
\(785\) | − | 9241.67i | − | 0.420190i | ||||||
\(786\) | −25403.5 | − | 14666.7i | −1.15281 | − | 0.665578i | ||||
\(787\) | −1556.50 | − | 898.643i | −0.0704995 | − | 0.0407029i | 0.464336 | − | 0.885659i | \(-0.346293\pi\) |
−0.534835 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(788\) | 2986.06i | 0.134992i | ||||||||
\(789\) | −5845.40 | + | 10124.5i | −0.263754 | + | 0.456835i | ||||
\(790\) | 2020.42 | + | 3499.47i | 0.0909916 | + | 0.157602i | ||||
\(791\) | 21378.7 | − | 12343.0i | 0.960984 | − | 0.554825i | ||||
\(792\) | 4373.20 | 0.196205 | ||||||||
\(793\) | −15218.2 | + | 15155.1i | −0.681482 | + | 0.678656i | ||||
\(794\) | 926.524 | 0.0414120 | ||||||||
\(795\) | −5000.37 | + | 2886.97i | −0.223075 | + | 0.128793i | ||||
\(796\) | 5314.59 | + | 9205.13i | 0.236646 | + | 0.409883i | ||||
\(797\) | −17645.3 | + | 30562.5i | −0.784226 | + | 1.35832i | 0.145234 | + | 0.989397i | \(0.453607\pi\) |
−0.929460 | + | 0.368923i | \(0.879727\pi\) | |||||||
\(798\) | − | 30049.3i | − | 1.33300i | ||||||
\(799\) | 47776.5 | + | 27583.8i | 2.11541 | + | 1.22133i | ||||
\(800\) | −3161.16 | − | 1825.10i | −0.139705 | − | 0.0806586i | ||||
\(801\) | 13207.1i | 0.582584i | ||||||||
\(802\) | 14052.6 | − | 24339.9i | 0.618724 | − | 1.07166i | ||||
\(803\) | 815.690 | + | 1412.82i | 0.0358469 | + | 0.0620887i | ||||
\(804\) | −14451.5 | + | 8343.55i | −0.633910 | + | 0.365988i | ||||
\(805\) | 12901.4 | 0.564862 | ||||||||
\(806\) | −4837.41 | − | 18204.7i | −0.211402 | − | 0.795574i | ||||
\(807\) | −17849.3 | −0.778594 | ||||||||
\(808\) | 6619.92 | − | 3822.01i | 0.288227 | − | 0.166408i | ||||
\(809\) | −9348.92 | − | 16192.8i | −0.406292 | − | 0.703719i | 0.588178 | − | 0.808731i | \(-0.299845\pi\) |
−0.994471 | + | 0.105012i | \(0.966512\pi\) | |||||||
\(810\) | −1482.01 | + | 2566.91i | −0.0642869 | + | 0.111348i | ||||
\(811\) | − | 22245.0i | − | 0.963165i | −0.876401 | − | 0.481582i | \(-0.840062\pi\) | ||
0.876401 | − | 0.481582i | \(-0.159938\pi\) | |||||||
\(812\) | −6328.66 | − | 3653.85i | −0.273513 | − | 0.157913i | ||||
\(813\) | −35924.2 | − | 20740.9i | −1.54971 | − | 0.894728i | ||||
\(814\) | 3278.67i | 0.141176i | ||||||||
\(815\) | −478.910 | + | 829.496i | −0.0205834 | + | 0.0356515i | ||||
\(816\) | −6786.96 | − | 11755.4i | −0.291166 | − | 0.504313i | ||||
\(817\) | 5898.78 | − | 3405.66i | 0.252597 | − | 0.145837i | ||||
\(818\) | −8879.08 | −0.379523 | ||||||||
\(819\) | 49794.8 | − | 13231.6i | 2.12451 | − | 0.564531i | ||||
\(820\) | −2923.82 | −0.124517 | ||||||||
\(821\) | −34027.2 | + | 19645.6i | −1.44648 | + | 0.835123i | −0.998269 | − | 0.0588066i | \(-0.981270\pi\) |
−0.448207 | + | 0.893930i | \(0.647937\pi\) | |||||||
\(822\) | 6988.83 | + | 12105.0i | 0.296549 | + | 0.513638i | ||||
\(823\) | 15.7571 | − | 27.2921i | 0.000667386 | − | 0.00115595i | −0.865692 | − | 0.500578i | \(-0.833121\pi\) |
0.866359 | + | 0.499422i | \(0.166454\pi\) | |||||||
\(824\) | 11831.7i | 0.500213i | ||||||||
\(825\) | −12144.4 | − | 7011.56i | −0.512501 | − | 0.295892i | ||||
\(826\) | −30279.8 | − | 17482.1i | −1.27551 | − | 0.736415i | ||||
\(827\) | − | 30870.8i | − | 1.29805i | −0.760769 | − | 0.649023i | \(-0.775178\pi\) | ||
0.760769 | − | 0.649023i | \(-0.224822\pi\) | |||||||
\(828\) | 8705.96 | − | 15079.2i | 0.365402 | − | 0.632895i | ||||
\(829\) | 19332.5 | + | 33484.9i | 0.809946 | + | 1.40287i | 0.912901 | + | 0.408181i | \(0.133837\pi\) |
−0.102955 | + | 0.994686i | \(0.532830\pi\) | |||||||
\(830\) | −2815.02 | + | 1625.25i | −0.117724 | + | 0.0679680i | ||||
\(831\) | 37922.2 | 1.58304 | ||||||||
\(832\) | 2895.98 | + | 782.430i | 0.120673 | + | 0.0326032i | ||||
\(833\) | −69199.6 | −2.87830 | ||||||||
\(834\) | −19807.1 | + | 11435.6i | −0.822378 | + | 0.474800i | ||||
\(835\) | 3848.72 | + | 6666.17i | 0.159509 | + | 0.276278i | ||||
\(836\) | 1897.59 | − | 3286.72i | 0.0785041 | − | 0.135973i | ||||
\(837\) | 12687.1i | 0.523930i | ||||||||
\(838\) | 23692.8 | + | 13679.0i | 0.976674 | + | 0.563883i | ||||
\(839\) | 8566.99 | + | 4946.15i | 0.352521 | + | 0.203528i | 0.665795 | − | 0.746135i | \(-0.268092\pi\) |
−0.313274 | + | 0.949663i | \(0.601426\pi\) | |||||||
\(840\) | − | 6538.61i | − | 0.268575i | ||||||
\(841\) | 10500.9 | − | 18188.0i | 0.430558 | − | 0.745748i | ||||
\(842\) | 11133.2 | + | 19283.3i | 0.455673 | + | 0.789248i | ||||
\(843\) | −13529.1 | + | 7811.02i | −0.552748 | + | 0.319129i | ||||
\(844\) | 6029.37 | 0.245900 | ||||||||
\(845\) | −3658.07 | + | 6275.58i | −0.148925 | + | 0.255487i | ||||
\(846\) | 35865.3 | 1.45753 | ||||||||
\(847\) | −29558.3 | + | 17065.5i | −1.19910 | + | 0.692299i | ||||
\(848\) | 1774.04 | + | 3072.73i | 0.0718405 | + | 0.124431i | ||||
\(849\) | −3256.77 | + | 5640.88i | −0.131651 | + | 0.228027i | ||||
\(850\) | 24576.7i | 0.991733i | ||||||||
\(851\) | 11305.1 | + | 6527.03i | 0.455388 | + | 0.262919i | ||||
\(852\) | −1842.80 | − | 1063.94i | −0.0741003 | − | 0.0427818i | ||||
\(853\) | 35366.0i | 1.41959i | 0.704409 | + | 0.709794i | \(0.251212\pi\) | ||||
−0.704409 | + | 0.709794i | \(0.748788\pi\) | |||||||
\(854\) | 14383.4 | − | 24912.7i | 0.576333 | − | 0.998238i | ||||
\(855\) | −3518.43 | − | 6094.10i | −0.140734 | − | 0.243759i | ||||
\(856\) | −1476.51 | + | 852.463i | −0.0589556 | + | 0.0340381i | ||||
\(857\) | −760.177 | −0.0303001 | −0.0151500 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151500 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(858\) | 11125.6 | + | 3005.90i | 0.442684 | + | 0.119603i | ||||
\(859\) | 27332.4 | 1.08565 | 0.542823 | − | 0.839847i | \(-0.317355\pi\) | ||||
0.542823 | + | 0.839847i | \(0.317355\pi\) | |||||||
\(860\) | 1283.55 | − | 741.057i | 0.0508937 | − | 0.0293835i | ||||
\(861\) | 27325.9 | + | 47329.9i | 1.08161 | + | 1.87340i | ||||
\(862\) | −1454.09 | + | 2518.55i | −0.0574552 | + | 0.0995153i | ||||
\(863\) | − | 35583.9i | − | 1.40358i | −0.712384 | − | 0.701790i | \(-0.752385\pi\) | ||
0.712384 | − | 0.701790i | \(-0.247615\pi\) | |||||||
\(864\) | −1749.80 | − | 1010.25i | −0.0688997 | − | 0.0397793i | ||||
\(865\) | 3046.25 | + | 1758.75i | 0.119740 | + | 0.0691322i | ||||
\(866\) | 15377.1i | 0.603391i | ||||||||
\(867\) | −26351.2 | + | 45641.6i | −1.03222 | + | 1.78786i | ||||
\(868\) | 12614.8 | + | 21849.5i | 0.493288 | + | 0.854400i | ||||
\(869\) | 8261.39 | − | 4769.72i | 0.322496 | − | 0.186193i | ||||
\(870\) | −3030.77 | −0.118107 | ||||||||
\(871\) | −23997.3 | + | 6376.64i | −0.933545 | + | 0.248065i | ||||
\(872\) | 675.358 | 0.0262276 | ||||||||
\(873\) | 17386.4 | − | 10038.0i | 0.674043 | − | 0.389159i | ||||
\(874\) | −7555.26 | − | 13086.1i | −0.292403 | − | 0.506458i | ||||
\(875\) | −12405.9 | + | 21487.7i | −0.479311 | + | 0.830191i | ||||
\(876\) | − | 3291.94i | − | 0.126968i | ||||||
\(877\) | −2983.50 | − | 1722.52i | −0.114875 | − | 0.0663232i | 0.441462 | − | 0.897280i | \(-0.354460\pi\) |
−0.556337 | + | 0.830957i | \(0.687793\pi\) | |||||||
\(878\) | −14967.7 | − | 8641.61i | −0.575325 | − | 0.332164i | ||||
\(879\) | 9344.60i | 0.358573i | ||||||||
\(880\) | 412.907 | − | 715.175i | 0.0158171 | − | 0.0273961i | ||||
\(881\) | −10148.1 | − | 17577.0i | −0.388079 | − | 0.672173i | 0.604112 | − | 0.796899i | \(-0.293528\pi\) |
−0.992191 | + | 0.124727i | \(0.960195\pi\) | |||||||
\(882\) | −38960.5 | + | 22493.9i | −1.48738 | + | 0.858739i | ||||
\(883\) | −2952.08 | −0.112509 | −0.0562545 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562545 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(884\) | −5187.00 | − | 19520.3i | −0.197350 | − | 0.742692i | ||||
\(885\) | −14500.9 | −0.550782 | ||||||||
\(886\) | −23492.9 | + | 13563.6i | −0.890813 | + | 0.514311i | ||||
\(887\) | −12377.2 | − | 21438.0i | −0.468531 | − | 0.811520i | 0.530822 | − | 0.847483i | \(-0.321883\pi\) |
−0.999353 | + | 0.0359637i | \(0.988550\pi\) | |||||||
\(888\) | 3307.99 | − | 5729.61i | 0.125010 | − | 0.216524i | ||||
\(889\) | − | 22992.0i | − | 0.867411i | ||||||
\(890\) | 2159.84 | + | 1246.98i | 0.0813460 | + | 0.0469651i | ||||
\(891\) | 6059.84 | + | 3498.65i | 0.227848 | + | 0.131548i | ||||
\(892\) | − | 7916.23i | − | 0.297147i | ||||||
\(893\) | 15562.4 | − | 26954.9i | 0.583176 | − | 1.01009i | ||||
\(894\) | −12149.0 | − | 21042.7i | −0.454500 | − | 0.787216i | ||||
\(895\) | −7075.29 | + | 4084.92i | −0.264247 | + | 0.152563i | ||||
\(896\) | −4017.97 | −0.149811 | ||||||||
\(897\) | 32513.0 | − | 32378.2i | 1.21023 | − | 1.20521i | ||||
\(898\) | 37594.6 | 1.39705 | ||||||||
\(899\) | 10127.6 | − | 5847.20i | 0.375724 | − | 0.216924i | ||||
\(900\) | 7988.83 | + | 13837.1i | 0.295883 | + | 0.512484i | ||||
\(901\) | 11944.6 | − | 20688.6i | 0.441655 | − | 0.764969i | ||||
\(902\) | 6902.42i | 0.254795i | ||||||||
\(903\) | −23992.0 | − | 13851.8i | −0.884167 | − | 0.510474i | ||||
\(904\) | −5448.47 | − | 3145.67i | −0.200457 | − | 0.115734i | ||||
\(905\) | − | 7262.26i | − | 0.266747i | ||||||
\(906\) | −12787.7 | + | 22149.0i | −0.468922 | + | 0.812197i | ||||
\(907\) | 12103.5 | + | 20963.9i | 0.443099 | + | 0.767469i | 0.997918 | − | 0.0645018i | \(-0.0205458\pi\) |
−0.554819 | + | 0.831971i | \(0.687212\pi\) | |||||||
\(908\) | −7311.99 | + | 4221.58i | −0.267243 | + | 0.154293i | ||||
\(909\) | −33459.5 | −1.22088 | ||||||||
\(910\) | 2537.66 | − | 9392.55i | 0.0924423 | − | 0.342154i | ||||
\(911\) | −21027.3 | −0.764725 | −0.382363 | − | 0.924012i | \(-0.624889\pi\) | ||||
−0.382363 | + | 0.924012i | \(0.624889\pi\) | |||||||
\(912\) | −6632.22 | + | 3829.11i | −0.240806 | + | 0.139029i | ||||
\(913\) | 3836.83 | + | 6645.58i | 0.139080 | + | 0.240894i | ||||
\(914\) | 7225.60 | − | 12515.1i | 0.261490 | − | 0.452913i | ||||
\(915\) | − | 11930.6i | − | 0.431053i | ||||||
\(916\) | −18452.4 | − | 10653.5i | −0.665595 | − | 0.384282i | ||||
\(917\) | 50629.3 | + | 29230.9i | 1.82326 | + | 1.05266i | ||||
\(918\) | 13603.9i | 0.489104i | ||||||||
\(919\) | 3949.78 | − | 6841.22i | 0.141775 | − | 0.245561i | −0.786390 | − | 0.617730i | \(-0.788052\pi\) |
0.928165 | + | 0.372169i | \(0.121386\pi\) | |||||||
\(920\) | −1643.99 | − | 2847.48i | −0.0589139 | − | 0.102042i | ||||
\(921\) | 42224.2 | − | 24378.1i | 1.51068 | − | 0.872190i | ||||
\(922\) | 4590.72 | 0.163977 | ||||||||
\(923\) | −2234.22 | − | 2243.53i | −0.0796753 | − | 0.0800072i | ||||
\(924\) | −15436.0 | −0.549576 | ||||||||
\(925\) | −10373.9 | + | 5989.38i | −0.368748 | + | 0.212897i | ||||
\(926\) | 9457.75 | + | 16381.3i | 0.335638 | + | 0.581342i | ||||
\(927\) | 25894.8 | − | 44851.2i | 0.917473 | − | 1.58911i | ||||
\(928\) | 1862.41i | 0.0658798i | ||||||||
\(929\) | 4706.55 | + | 2717.33i | 0.166218 | + | 0.0959662i | 0.580801 | − | 0.814045i | \(-0.302739\pi\) |
−0.414583 | + | 0.910011i | \(0.636073\pi\) | |||||||
\(930\) | 9061.76 | + | 5231.81i | 0.319513 | + | 0.184471i | ||||
\(931\) | 39041.5i | 1.37437i | ||||||||
\(932\) | 297.898 | − | 515.974i | 0.0104699 | − | 0.0181344i | ||||
\(933\) | −41774.7 | − | 72356.0i | −1.46586 | − | 2.53894i | ||||
\(934\) | 23055.2 | − | 13310.9i | 0.807696 | − | 0.466323i | ||||
\(935\) | −5560.19 | −0.194479 | ||||||||
\(936\) | −9265.59 | − | 9304.18i | −0.323563 | − | 0.324911i | ||||
\(937\) | 8130.03 | 0.283454 | 0.141727 | − | 0.989906i | \(-0.454734\pi\) | ||||
0.141727 | + | 0.989906i | \(0.454734\pi\) | |||||||
\(938\) | 28801.8 | − | 16628.8i | 1.00257 | − | 0.578836i | ||||
\(939\) | −38719.0 | − | 67063.3i | −1.34563 | − | 2.33070i | ||||
\(940\) | 3386.31 | − | 5865.27i | 0.117499 | − | 0.203515i | ||||
\(941\) | − | 5409.95i | − | 0.187417i | −0.995600 | − | 0.0937084i | \(-0.970128\pi\) | ||
0.995600 | − | 0.0937084i | \(-0.0298721\pi\) | |||||||
\(942\) | 38126.6 | + | 22012.4i | 1.31872 | + | 0.761362i | ||||
\(943\) | 23800.2 | + | 13741.0i | 0.821887 | + | 0.474517i | ||||
\(944\) | 8910.79i | 0.307226i | ||||||||
\(945\) | −3276.54 | + | 5675.13i | −0.112789 | + | 0.195357i | ||||
\(946\) | −1749.45 | − | 3030.14i | −0.0601264 | − | 0.104142i | ||||
\(947\) | 32164.9 | − | 18570.4i | 1.10372 | − | 0.637231i | 0.166522 | − | 0.986038i | \(-0.446746\pi\) |
0.937195 | + | 0.348807i | \(0.113413\pi\) | |||||||
\(948\) | −19249.5 | −0.659488 | ||||||||
\(949\) | 1277.61 | − | 4728.79i | 0.0437018 | − | 0.161752i | ||||
\(950\) | 13865.8 | 0.473544 | ||||||||
\(951\) | −31882.0 | + | 18407.1i | −1.08711 | + | 0.627645i | ||||
\(952\) | 13526.5 | + | 23428.5i | 0.460499 | + | 0.797608i | ||||
\(953\) | −1770.71 | + | 3066.97i | −0.0601879 | + | 0.104249i | −0.894549 | − | 0.446969i | \(-0.852503\pi\) |
0.834361 | + | 0.551218i | \(0.185837\pi\) | |||||||
\(954\) | − | 15530.7i | − | 0.527070i | ||||||
\(955\) | −5873.27 | − | 3390.93i | −0.199010 | − | 0.114899i | ||||
\(956\) | 10673.5 | + | 6162.36i | 0.361095 | + | 0.208478i | ||||
\(957\) | 7154.90i | 0.241677i | ||||||||
\(958\) | −7969.25 | + | 13803.1i | −0.268763 | + | 0.465511i | ||||
\(959\) | −13928.8 | − | 24125.4i | −0.469014 | − | 0.812356i | ||||
\(960\) | −1443.14 | + | 833.198i | −0.0485179 | + | 0.0280118i | ||||
\(961\) | −10583.5 | −0.355258 | ||||||||
\(962\) | 6975.53 | − | 6946.60i | 0.233784 | − | 0.232814i | ||||
\(963\) | 7462.82 | 0.249726 | ||||||||
\(964\) | 8903.76 | − | 5140.59i | 0.297480 | − | 0.171750i | ||||
\(965\) | 6204.48 | + | 10746.5i | 0.206974 | + | 0.358489i | ||||
\(966\) | −30729.4 | + | 53224.8i | −1.02350 | + | 1.77275i | ||||
\(967\) | 48102.4i | 1.59966i | 0.600229 | + | 0.799828i | \(0.295076\pi\) | ||||
−0.600229 | + | 0.799828i | \(0.704924\pi\) | |||||||
\(968\) | 7533.09 | + | 4349.23i | 0.250127 | + | 0.144411i | ||||
\(969\) | 44654.6 | + | 25781.4i | 1.48041 | + | 0.854712i | ||||
\(970\) | − | 3791.07i | − | 0.125488i | ||||||
\(971\) | −17539.6 | + | 30379.5i | −0.579683 | + | 1.00404i | 0.415833 | + | 0.909441i | \(0.363490\pi\) |
−0.995515 | + | 0.0945990i | \(0.969843\pi\) | |||||||
\(972\) | −10469.5 | − | 18133.6i | −0.345482 | − | 0.598392i | ||||
\(973\) | 39475.7 | − | 22791.3i | 1.30065 | − | 0.750931i | ||||
\(974\) | −2830.94 | −0.0931305 | ||||||||
\(975\) | 10813.2 | + | 40693.3i | 0.355178 | + | 1.33665i | ||||
\(976\) | −7331.35 | −0.240441 | ||||||||
\(977\) | −36950.2 | + | 21333.2i | −1.20997 | + | 0.698577i | −0.962753 | − | 0.270383i | \(-0.912850\pi\) |
−0.247217 | + | 0.968960i | \(0.579516\pi\) | |||||||
\(978\) | −2281.40 | − | 3951.50i | −0.0745921 | − | 0.129197i | ||||
\(979\) | 2943.82 | − | 5098.85i | 0.0961031 | − | 0.166455i | ||||
\(980\) | 8495.26i | 0.276909i | ||||||||
\(981\) | −2560.13 | − | 1478.09i | −0.0833218 | − | 0.0481059i | ||||
\(982\) | −5544.15 | − | 3200.91i | −0.180164 | − | 0.104018i | ||||
\(983\) | − | 32297.0i | − | 1.04793i | −0.851740 | − | 0.523964i | \(-0.824453\pi\) | ||
0.851740 | − | 0.523964i | \(-0.175547\pi\) | |||||||
\(984\) | 6964.15 | − | 12062.3i | 0.225619 | − | 0.390783i | ||||
\(985\) | −1234.10 | − | 2137.52i | −0.0399204 | − | 0.0691442i | ||||
\(986\) | 10859.6 | − | 6269.77i | 0.350749 | − | 0.202505i | ||||
\(987\) | −126593. | −4.08259 | ||||||||
\(988\) | −11013.1 | + | 2926.44i | −0.354629 | + | 0.0942332i | ||||
\(989\) | −13930.9 | −0.447905 | ||||||||
\(990\) | −3130.47 | + | 1807.38i | −0.100498 | + | 0.0580225i | ||||
\(991\) | 5674.60 | + | 9828.69i | 0.181897 | + | 0.315054i | 0.942526 | − | 0.334132i | \(-0.108443\pi\) |
−0.760630 | + | 0.649186i | \(0.775110\pi\) | |||||||
\(992\) | 3214.94 | − | 5568.45i | 0.102898 | − | 0.178224i | ||||
\(993\) | 82006.7i | 2.62075i | ||||||||
\(994\) | 3672.72 | + | 2120.45i | 0.117195 | + | 0.0676625i | ||||
\(995\) | −7608.70 | − | 4392.89i | −0.242424 | − | 0.139964i | ||||
\(996\) | − | 15484.6i | − | 0.492617i | ||||||
\(997\) | 15268.2 | − | 26445.3i | 0.485003 | − | 0.840050i | −0.514848 | − | 0.857281i | \(-0.672152\pi\) |
0.999852 | + | 0.0172310i | \(0.00548508\pi\) | |||||||
\(998\) | −1480.51 | − | 2564.32i | −0.0469588 | − | 0.0813349i | ||||
\(999\) | −5742.29 | + | 3315.31i | −0.181860 | + | 0.104997i |
(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 | 26.4.e.a.23.3 | yes | 8 | |
3.2 | odd | 2 | 234.4.l.b.127.1 | 8 | |||
4.3 | odd | 2 | 208.4.w.d.49.4 | 8 | |||
13.2 | odd | 12 | 338.4.a.m.1.4 | 4 | |||
13.3 | even | 3 | 338.4.b.g.337.8 | 8 | |||
13.4 | even | 6 | inner | 26.4.e.a.17.3 | ✓ | 8 | |
13.5 | odd | 4 | 338.4.c.m.315.1 | 8 | |||
13.6 | odd | 12 | 338.4.c.m.191.1 | 8 | |||
13.7 | odd | 12 | 338.4.c.n.191.1 | 8 | |||
13.8 | odd | 4 | 338.4.c.n.315.1 | 8 | |||
13.9 | even | 3 | 338.4.e.e.147.1 | 8 | |||
13.10 | even | 6 | 338.4.b.g.337.4 | 8 | |||
13.11 | odd | 12 | 338.4.a.l.1.4 | 4 | |||
13.12 | even | 2 | 338.4.e.e.23.1 | 8 | |||
39.17 | odd | 6 | 234.4.l.b.199.2 | 8 | |||
52.43 | odd | 6 | 208.4.w.d.17.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
26.4.e.a.17.3 | ✓ | 8 | 13.4 | even | 6 | inner | |
26.4.e.a.23.3 | yes | 8 | 1.1 | even | 1 | trivial | |
208.4.w.d.17.4 | 8 | 52.43 | odd | 6 | |||
208.4.w.d.49.4 | 8 | 4.3 | odd | 2 | |||
234.4.l.b.127.1 | 8 | 3.2 | odd | 2 | |||
234.4.l.b.199.2 | 8 | 39.17 | odd | 6 | |||
338.4.a.l.1.4 | 4 | 13.11 | odd | 12 | |||
338.4.a.m.1.4 | 4 | 13.2 | odd | 12 | |||
338.4.b.g.337.4 | 8 | 13.10 | even | 6 | |||
338.4.b.g.337.8 | 8 | 13.3 | even | 3 | |||
338.4.c.m.191.1 | 8 | 13.6 | odd | 12 | |||
338.4.c.m.315.1 | 8 | 13.5 | odd | 4 | |||
338.4.c.n.191.1 | 8 | 13.7 | odd | 12 | |||
338.4.c.n.315.1 | 8 | 13.8 | odd | 4 | |||
338.4.e.e.23.1 | 8 | 13.12 | even | 2 | |||
338.4.e.e.147.1 | 8 | 13.9 | even | 3 |