Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(47,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.s (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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 59.19 | ||
Character | \(\chi\) | \(=\) | 63.59 |
Dual form | 63.4.s.a.47.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.55689 | + | 2.05357i | 1.25755 | + | 0.726047i | 0.972598 | − | 0.232495i | \(-0.0746889\pi\) |
0.284952 | + | 0.958542i | \(0.408022\pi\) | |||||||
\(3\) | 4.91877 | − | 1.67502i | 0.946618 | − | 0.322358i | ||||
\(4\) | 4.43430 | + | 7.68044i | 0.554288 | + | 0.960055i | ||||
\(5\) | −7.61183 | −0.680823 | −0.340411 | − | 0.940277i | \(-0.610566\pi\) | ||||
−0.340411 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(6\) | 20.9353 | + | 4.14318i | 1.42447 | + | 0.281908i | ||||
\(7\) | 4.76690 | + | 17.8963i | 0.257388 | + | 0.966308i | ||||
\(8\) | 3.56749i | 0.157662i | ||||||||
\(9\) | 21.3886 | − | 16.4781i | 0.792171 | − | 0.610300i | ||||
\(10\) | −27.0744 | − | 15.6314i | −0.856168 | − | 0.494309i | ||||
\(11\) | − | 7.17024i | − | 0.196537i | −0.995160 | − | 0.0982686i | \(-0.968670\pi\) | ||
0.995160 | − | 0.0982686i | \(-0.0313304\pi\) | |||||||
\(12\) | 34.6762 | + | 30.3508i | 0.834180 | + | 0.730126i | ||||
\(13\) | −59.6417 | − | 34.4342i | −1.27243 | − | 0.734640i | −0.296988 | − | 0.954881i | \(-0.595982\pi\) |
−0.975445 | + | 0.220241i | \(0.929316\pi\) | |||||||
\(14\) | −19.7959 | + | 73.4442i | −0.377906 | + | 1.40206i | ||||
\(15\) | −37.4408 | + | 12.7500i | −0.644479 | + | 0.219469i | ||||
\(16\) | 28.1483 | − | 48.7543i | 0.439818 | − | 0.761787i | ||||
\(17\) | 11.4334 | − | 19.8032i | 0.163118 | − | 0.282529i | −0.772867 | − | 0.634568i | \(-0.781178\pi\) |
0.935985 | + | 0.352039i | \(0.114512\pi\) | |||||||
\(18\) | 109.916 | − | 14.6877i | 1.43930 | − | 0.192329i | ||||
\(19\) | −86.1218 | + | 49.7224i | −1.03988 | + | 0.600374i | −0.919799 | − | 0.392390i | \(-0.871648\pi\) |
−0.120079 | + | 0.992764i | \(0.538315\pi\) | |||||||
\(20\) | −33.7532 | − | 58.4622i | −0.377372 | − | 0.653627i | ||||
\(21\) | 53.4239 | + | 80.0430i | 0.555146 | + | 0.831753i | ||||
\(22\) | 14.7246 | − | 25.5037i | 0.142695 | − | 0.247155i | ||||
\(23\) | 122.450i | 1.11011i | 0.831814 | + | 0.555055i | \(0.187303\pi\) | ||||
−0.831814 | + | 0.555055i | \(0.812697\pi\) | |||||||
\(24\) | 5.97563 | + | 17.5477i | 0.0508238 | + | 0.149246i | ||||
\(25\) | −67.0601 | −0.536481 | ||||||||
\(26\) | −141.426 | − | 244.957i | −1.06677 | − | 1.84769i | ||||
\(27\) | 77.6045 | − | 116.878i | 0.553148 | − | 0.833083i | ||||
\(28\) | −116.313 | + | 115.969i | −0.785042 | + | 0.782720i | ||||
\(29\) | 143.427 | − | 82.8076i | 0.918404 | − | 0.530241i | 0.0352788 | − | 0.999378i | \(-0.488768\pi\) |
0.883126 | + | 0.469136i | \(0.155435\pi\) | |||||||
\(30\) | −159.356 | − | 31.5372i | −0.969809 | − | 0.191929i | ||||
\(31\) | −11.9405 | + | 6.89384i | −0.0691798 | + | 0.0399410i | −0.534191 | − | 0.845364i | \(-0.679384\pi\) |
0.465011 | + | 0.885305i | \(0.346050\pi\) | |||||||
\(32\) | 224.957 | − | 129.879i | 1.24273 | − | 0.717488i | ||||
\(33\) | −12.0103 | − | 35.2688i | −0.0633553 | − | 0.186046i | ||||
\(34\) | 81.3346 | − | 46.9585i | 0.410258 | − | 0.236862i | ||||
\(35\) | −36.2848 | − | 136.223i | −0.175236 | − | 0.657884i | ||||
\(36\) | 221.403 | + | 91.2050i | 1.02501 | + | 0.422246i | ||||
\(37\) | 126.544 | + | 219.181i | 0.562263 | + | 0.973868i | 0.997299 | + | 0.0734549i | \(0.0234025\pi\) |
−0.435035 | + | 0.900413i | \(0.643264\pi\) | |||||||
\(38\) | −408.434 | −1.74360 | ||||||||
\(39\) | −351.042 | − | 69.4726i | −1.44133 | − | 0.285244i | ||||
\(40\) | − | 27.1552i | − | 0.107340i | ||||||
\(41\) | 159.598 | − | 276.433i | 0.607929 | − | 1.05296i | −0.383652 | − | 0.923478i | \(-0.625334\pi\) |
0.991581 | − | 0.129486i | \(-0.0413328\pi\) | |||||||
\(42\) | 25.6490 | + | 394.414i | 0.0942316 | + | 1.44903i | ||||
\(43\) | 156.693 | + | 271.399i | 0.555707 | + | 0.962512i | 0.997848 | + | 0.0655670i | \(0.0208856\pi\) |
−0.442141 | + | 0.896945i | \(0.645781\pi\) | |||||||
\(44\) | 55.0706 | − | 31.7950i | 0.188686 | − | 0.108938i | ||||
\(45\) | −162.806 | + | 125.428i | −0.539328 | + | 0.415506i | ||||
\(46\) | −251.459 | + | 435.540i | −0.805992 | + | 1.39602i | ||||
\(47\) | −35.3934 | + | 61.3031i | −0.109844 | + | 0.190255i | −0.915707 | − | 0.401847i | \(-0.868368\pi\) |
0.805863 | + | 0.592102i | \(0.201702\pi\) | |||||||
\(48\) | 56.7906 | − | 286.960i | 0.170771 | − | 0.862899i | ||||
\(49\) | −297.553 | + | 170.620i | −0.867502 | + | 0.497433i | ||||
\(50\) | −238.525 | − | 137.713i | −0.674651 | − | 0.389510i | ||||
\(51\) | 23.0674 | − | 116.559i | 0.0633350 | − | 0.320029i | ||||
\(52\) | − | 610.766i | − | 1.62881i | ||||||
\(53\) | 254.574 | + | 146.979i | 0.659783 | + | 0.380926i | 0.792194 | − | 0.610269i | \(-0.208939\pi\) |
−0.132412 | + | 0.991195i | \(0.542272\pi\) | |||||||
\(54\) | 516.048 | − | 256.357i | 1.30047 | − | 0.646032i | ||||
\(55\) | 54.5786i | 0.133807i | ||||||||
\(56\) | −63.8449 | + | 17.0059i | −0.152351 | + | 0.0405805i | ||||
\(57\) | −340.327 | + | 388.829i | −0.790832 | + | 0.903538i | ||||
\(58\) | 680.205 | 1.53992 | ||||||||
\(59\) | 230.615 | + | 399.437i | 0.508873 | + | 0.881394i | 0.999947 | + | 0.0102763i | \(0.00327112\pi\) |
−0.491074 | + | 0.871118i | \(0.663396\pi\) | |||||||
\(60\) | −263.949 | − | 231.025i | −0.567929 | − | 0.497086i | ||||
\(61\) | 573.665 | + | 331.205i | 1.20410 | + | 0.695189i | 0.961465 | − | 0.274928i | \(-0.0886541\pi\) |
0.242637 | + | 0.970117i | \(0.421987\pi\) | |||||||
\(62\) | −56.6280 | −0.115996 | ||||||||
\(63\) | 396.854 | + | 304.227i | 0.793633 | + | 0.608397i | ||||
\(64\) | 616.491 | 1.20408 | ||||||||
\(65\) | 453.983 | + | 262.107i | 0.866302 | + | 0.500159i | ||||
\(66\) | 29.7076 | − | 150.111i | 0.0554053 | − | 0.279961i | ||||
\(67\) | −359.139 | − | 622.047i | −0.654863 | − | 1.13426i | −0.981928 | − | 0.189254i | \(-0.939393\pi\) |
0.327065 | − | 0.945002i | \(-0.393940\pi\) | |||||||
\(68\) | 202.797 | 0.361657 | ||||||||
\(69\) | 205.106 | + | 602.302i | 0.357853 | + | 1.05085i | ||||
\(70\) | 150.683 | − | 559.045i | 0.257287 | − | 0.954552i | ||||
\(71\) | − | 92.9435i | − | 0.155357i | −0.996978 | − | 0.0776787i | \(-0.975249\pi\) | ||
0.996978 | − | 0.0776787i | \(-0.0247508\pi\) | |||||||
\(72\) | 58.7855 | + | 76.3037i | 0.0962214 | + | 0.124896i | ||||
\(73\) | −882.012 | − | 509.230i | −1.41413 | − | 0.816450i | −0.418358 | − | 0.908282i | \(-0.637394\pi\) |
−0.995774 | + | 0.0918323i | \(0.970728\pi\) | |||||||
\(74\) | 1039.47i | 1.63292i | ||||||||
\(75\) | −329.853 | + | 112.327i | −0.507842 | + | 0.172939i | ||||
\(76\) | −763.780 | − | 440.969i | −1.15278 | − | 0.665560i | ||||
\(77\) | 128.321 | − | 34.1798i | 0.189915 | − | 0.0505864i | ||||
\(78\) | −1105.95 | − | 967.996i | −1.60544 | − | 1.40518i | ||||
\(79\) | −398.113 | + | 689.551i | −0.566977 | + | 0.982033i | 0.429886 | + | 0.902883i | \(0.358554\pi\) |
−0.996863 | + | 0.0791495i | \(0.974780\pi\) | |||||||
\(80\) | −214.260 | + | 371.110i | −0.299438 | + | 0.518641i | ||||
\(81\) | 185.945 | − | 704.887i | 0.255069 | − | 0.966923i | ||||
\(82\) | 1135.35 | − | 655.493i | 1.52900 | − | 0.882770i | ||||
\(83\) | 10.7079 | + | 18.5466i | 0.0141608 | + | 0.0245272i | 0.873019 | − | 0.487686i | \(-0.162159\pi\) |
−0.858858 | + | 0.512213i | \(0.828826\pi\) | |||||||
\(84\) | −377.868 | + | 765.254i | −0.490818 | + | 0.994001i | ||||
\(85\) | −87.0290 | + | 150.739i | −0.111054 | + | 0.192352i | ||||
\(86\) | 1287.12i | 1.61388i | ||||||||
\(87\) | 566.780 | − | 647.555i | 0.698451 | − | 0.797991i | ||||
\(88\) | 25.5798 | 0.0309865 | ||||||||
\(89\) | −339.721 | − | 588.414i | −0.404611 | − | 0.700806i | 0.589665 | − | 0.807648i | \(-0.299260\pi\) |
−0.994276 | + | 0.106841i | \(0.965926\pi\) | |||||||
\(90\) | −836.660 | + | 111.800i | −0.979908 | + | 0.130942i | ||||
\(91\) | 331.937 | − | 1231.51i | 0.382379 | − | 1.41865i | ||||
\(92\) | −940.467 | + | 542.979i | −1.06577 | + | 0.615320i | ||||
\(93\) | −47.1852 | + | 53.9098i | −0.0526116 | + | 0.0601095i | ||||
\(94\) | −251.780 | + | 145.366i | −0.276268 | + | 0.159503i | ||||
\(95\) | 655.544 | − | 378.479i | 0.707973 | − | 0.408748i | ||||
\(96\) | 888.963 | − | 1015.65i | 0.945098 | − | 1.07979i | ||||
\(97\) | −984.068 | + | 568.152i | −1.03007 | + | 0.594713i | −0.917005 | − | 0.398875i | \(-0.869401\pi\) |
−0.113067 | + | 0.993587i | \(0.536067\pi\) | |||||||
\(98\) | −1408.74 | − | 4.17218i | −1.45209 | − | 0.00430054i | ||||
\(99\) | −118.152 | − | 153.361i | −0.119947 | − | 0.155691i | ||||
\(100\) | −297.365 | − | 515.051i | −0.297365 | − | 0.515051i | ||||
\(101\) | −1542.10 | −1.51926 | −0.759629 | − | 0.650357i | \(-0.774619\pi\) | ||||
−0.759629 | + | 0.650357i | \(0.774619\pi\) | |||||||
\(102\) | 321.410 | − | 367.216i | 0.312003 | − | 0.356468i | ||||
\(103\) | − | 418.265i | − | 0.400125i | −0.979783 | − | 0.200062i | \(-0.935885\pi\) | ||
0.979783 | − | 0.200062i | \(-0.0641145\pi\) | |||||||
\(104\) | 122.844 | − | 212.772i | 0.115825 | − | 0.200615i | ||||
\(105\) | −406.654 | − | 609.274i | −0.377956 | − | 0.566276i | ||||
\(106\) | 603.662 | + | 1045.57i | 0.553140 | + | 0.958066i | ||||
\(107\) | 1368.79 | − | 790.270i | 1.23669 | − | 0.714003i | 0.268273 | − | 0.963343i | \(-0.413547\pi\) |
0.968416 | + | 0.249340i | \(0.0802138\pi\) | |||||||
\(108\) | 1241.80 | + | 77.7626i | 1.10641 | + | 0.0692843i | ||||
\(109\) | 234.533 | − | 406.222i | 0.206093 | − | 0.356964i | −0.744387 | − | 0.667748i | \(-0.767258\pi\) |
0.950480 | + | 0.310784i | \(0.100592\pi\) | |||||||
\(110\) | −112.081 | + | 194.130i | −0.0971501 | + | 0.168269i | ||||
\(111\) | 989.574 | + | 866.137i | 0.846182 | + | 0.740631i | ||||
\(112\) | 1006.70 | + | 271.343i | 0.849324 | + | 0.228924i | ||||
\(113\) | −1733.74 | − | 1000.97i | −1.44333 | − | 0.833306i | −0.445259 | − | 0.895402i | \(-0.646888\pi\) |
−0.998070 | + | 0.0620958i | \(0.980222\pi\) | |||||||
\(114\) | −2008.99 | + | 684.136i | −1.65052 | + | 0.562063i | ||||
\(115\) | − | 932.066i | − | 0.755788i | ||||||
\(116\) | 1272.00 | + | 734.388i | 1.01812 | + | 0.587813i | ||||
\(117\) | −1843.06 | + | 246.283i | −1.45634 | + | 0.194606i | ||||
\(118\) | 1894.34i | 1.47786i | ||||||||
\(119\) | 408.906 | + | 110.215i | 0.314994 | + | 0.0849026i | ||||
\(120\) | −45.4855 | − | 133.570i | −0.0346020 | − | 0.101610i | ||||
\(121\) | 1279.59 | 0.961373 | ||||||||
\(122\) | 1360.31 | + | 2356.12i | 1.00948 | + | 1.74847i | ||||
\(123\) | 321.998 | − | 1627.04i | 0.236045 | − | 1.19273i | ||||
\(124\) | −105.895 | − | 61.1388i | −0.0766911 | − | 0.0442776i | ||||
\(125\) | 1461.93 | 1.04607 | ||||||||
\(126\) | 786.813 | + | 1897.07i | 0.556309 | + | 1.34130i | ||||
\(127\) | 522.832 | 0.365306 | 0.182653 | − | 0.983177i | \(-0.441532\pi\) | ||||
0.182653 | + | 0.983177i | \(0.441532\pi\) | |||||||
\(128\) | 393.130 | + | 226.974i | 0.271470 | + | 0.156733i | ||||
\(129\) | 1225.33 | + | 1072.49i | 0.836316 | + | 0.731995i | ||||
\(130\) | 1076.51 | + | 1864.57i | 0.726278 | + | 1.25795i | ||||
\(131\) | 2561.88 | 1.70864 | 0.854321 | − | 0.519746i | \(-0.173973\pi\) | ||||
0.854321 | + | 0.519746i | \(0.173973\pi\) | |||||||
\(132\) | 217.622 | − | 248.637i | 0.143497 | − | 0.163947i | ||||
\(133\) | −1300.38 | − | 1304.24i | −0.847799 | − | 0.850313i | ||||
\(134\) | − | 2950.07i | − | 1.90184i | ||||||
\(135\) | −590.712 | + | 889.658i | −0.376596 | + | 0.567182i | ||||
\(136\) | 70.6479 | + | 40.7886i | 0.0445441 | + | 0.0257176i | ||||
\(137\) | 1.22835i | 0.000766021i | 1.00000 | 0.000383011i | \(0.000121916\pi\) | |||||
−1.00000 | 0.000383011i | \(0.999878\pi\) | ||||||||
\(138\) | −507.331 | + | 2563.52i | −0.312948 | + | 1.58131i | ||||
\(139\) | 1676.23 | + | 967.770i | 1.02285 | + | 0.590541i | 0.914927 | − | 0.403619i | \(-0.132248\pi\) |
0.107920 | + | 0.994160i | \(0.465581\pi\) | |||||||
\(140\) | 885.357 | − | 882.739i | 0.534474 | − | 0.532893i | ||||
\(141\) | −71.4078 | + | 360.821i | −0.0426498 | + | 0.215508i | ||||
\(142\) | 190.866 | − | 330.590i | 0.112797 | − | 0.195370i | ||||
\(143\) | −246.901 | + | 427.645i | −0.144384 | + | 0.250080i | ||||
\(144\) | −201.325 | − | 1506.62i | −0.116507 | − | 0.871885i | ||||
\(145\) | −1091.74 | + | 630.317i | −0.625271 | + | 0.361000i | ||||
\(146\) | −2091.48 | − | 3622.55i | −1.18556 | − | 2.05345i | ||||
\(147\) | −1177.81 | + | 1337.65i | −0.660842 | + | 0.750525i | ||||
\(148\) | −1122.27 | + | 1943.83i | −0.623311 | + | 1.07961i | ||||
\(149\) | − | 2427.95i | − | 1.33494i | −0.744639 | − | 0.667468i | \(-0.767378\pi\) | ||
0.744639 | − | 0.667468i | \(-0.232622\pi\) | |||||||
\(150\) | −1403.92 | − | 277.842i | −0.764199 | − | 0.151238i | ||||
\(151\) | −1396.38 | −0.752552 | −0.376276 | − | 0.926508i | \(-0.622796\pi\) | ||||
−0.376276 | + | 0.926508i | \(0.622796\pi\) | |||||||
\(152\) | −177.384 | − | 307.239i | −0.0946565 | − | 0.163950i | ||||
\(153\) | −81.7749 | − | 611.964i | −0.0432099 | − | 0.323362i | ||||
\(154\) | 526.613 | + | 141.942i | 0.275556 | + | 0.0742726i | ||||
\(155\) | 90.8889 | − | 52.4747i | 0.0470992 | − | 0.0271927i | ||||
\(156\) | −1023.05 | − | 3004.22i | −0.525059 | − | 1.54186i | ||||
\(157\) | −635.157 | + | 366.708i | −0.322873 | + | 0.186411i | −0.652672 | − | 0.757640i | \(-0.726352\pi\) |
0.329799 | + | 0.944051i | \(0.393019\pi\) | |||||||
\(158\) | −2832.08 | + | 1635.10i | −1.42600 | + | 0.823304i | ||||
\(159\) | 1498.38 | + | 296.536i | 0.747356 | + | 0.147905i | ||||
\(160\) | −1712.34 | + | 988.618i | −0.846075 | + | 0.488482i | ||||
\(161\) | −2191.39 | + | 583.705i | −1.07271 | + | 0.285729i | ||||
\(162\) | 2108.92 | − | 2125.35i | 1.02279 | − | 1.03076i | ||||
\(163\) | −1504.67 | − | 2606.16i | −0.723036 | − | 1.25233i | −0.959777 | − | 0.280762i | \(-0.909413\pi\) |
0.236742 | − | 0.971573i | \(-0.423920\pi\) | |||||||
\(164\) | 2830.83 | 1.34787 | ||||||||
\(165\) | 91.4204 | + | 268.460i | 0.0431337 | + | 0.126664i | ||||
\(166\) | 87.9577i | 0.0411256i | ||||||||
\(167\) | 40.1692 | − | 69.5751i | 0.0186131 | − | 0.0322388i | −0.856569 | − | 0.516033i | \(-0.827408\pi\) |
0.875182 | + | 0.483794i | \(0.160742\pi\) | |||||||
\(168\) | −285.553 | + | 190.590i | −0.131136 | + | 0.0875256i | ||||
\(169\) | 1272.92 | + | 2204.77i | 0.579392 | + | 1.00354i | ||||
\(170\) | −619.105 | + | 357.440i | −0.279313 | + | 0.161261i | ||||
\(171\) | −1022.69 | + | 2482.62i | −0.457353 | + | 1.11024i | ||||
\(172\) | −1389.64 | + | 2406.94i | −0.616043 | + | 1.06702i | ||||
\(173\) | −1373.36 | + | 2378.73i | −0.603553 | + | 1.04538i | 0.388725 | + | 0.921354i | \(0.372916\pi\) |
−0.992278 | + | 0.124031i | \(0.960418\pi\) | |||||||
\(174\) | 3345.77 | − | 1139.36i | 1.45772 | − | 0.496405i | ||||
\(175\) | −319.669 | − | 1200.13i | −0.138084 | − | 0.518406i | ||||
\(176\) | −349.580 | − | 201.830i | −0.149719 | − | 0.0864405i | ||||
\(177\) | 1803.41 | + | 1578.45i | 0.765833 | + | 0.670304i | ||||
\(178\) | − | 2790.56i | − | 1.17507i | ||||||
\(179\) | −2491.90 | − | 1438.70i | −1.04052 | − | 0.600745i | −0.120540 | − | 0.992708i | \(-0.538463\pi\) |
−0.919981 | + | 0.391964i | \(0.871796\pi\) | |||||||
\(180\) | −1685.28 | − | 694.237i | −0.697851 | − | 0.287474i | ||||
\(181\) | − | 320.544i | − | 0.131634i | −0.997832 | − | 0.0658172i | \(-0.979035\pi\) | ||
0.997832 | − | 0.0658172i | \(-0.0209654\pi\) | |||||||
\(182\) | 3709.65 | − | 3698.68i | 1.51087 | − | 1.50640i | ||||
\(183\) | 3376.50 | + | 668.223i | 1.36392 | + | 0.269926i | ||||
\(184\) | −436.839 | −0.175023 | ||||||||
\(185\) | −963.232 | − | 1668.37i | −0.382801 | − | 0.663031i | ||||
\(186\) | −278.540 | + | 94.8531i | −0.109804 | + | 0.0373923i | ||||
\(187\) | −141.994 | − | 81.9801i | −0.0555273 | − | 0.0320587i | ||||
\(188\) | −627.780 | −0.243540 | ||||||||
\(189\) | 2461.62 | + | 831.684i | 0.947389 | + | 0.320085i | ||||
\(190\) | 3108.93 | 1.18708 | ||||||||
\(191\) | 818.447 | + | 472.531i | 0.310056 | + | 0.179011i | 0.646952 | − | 0.762531i | \(-0.276044\pi\) |
−0.336895 | + | 0.941542i | \(0.609377\pi\) | |||||||
\(192\) | 3032.38 | − | 1032.63i | 1.13981 | − | 0.388146i | ||||
\(193\) | −393.384 | − | 681.362i | −0.146717 | − | 0.254122i | 0.783295 | − | 0.621650i | \(-0.213537\pi\) |
−0.930012 | + | 0.367528i | \(0.880204\pi\) | |||||||
\(194\) | −4666.96 | −1.72716 | ||||||||
\(195\) | 2672.07 | + | 528.813i | 0.981287 | + | 0.194201i | ||||
\(196\) | −2629.87 | − | 1528.76i | −0.958409 | − | 0.557129i | ||||
\(197\) | 5047.70i | 1.82555i | 0.408462 | + | 0.912775i | \(0.366065\pi\) | ||||
−0.408462 | + | 0.912775i | \(0.633935\pi\) | |||||||
\(198\) | −105.314 | − | 788.123i | −0.0377999 | − | 0.282876i | ||||
\(199\) | 1052.30 | + | 607.546i | 0.374852 | + | 0.216421i | 0.675576 | − | 0.737290i | \(-0.263895\pi\) |
−0.300724 | + | 0.953711i | \(0.597228\pi\) | |||||||
\(200\) | − | 239.236i | − | 0.0845829i | ||||||
\(201\) | −2808.46 | − | 2458.14i | −0.985541 | − | 0.862606i | ||||
\(202\) | −5485.09 | − | 3166.82i | −1.91054 | − | 1.10305i | ||||
\(203\) | 2165.65 | + | 2172.07i | 0.748763 | + | 0.750984i | ||||
\(204\) | 997.510 | − | 339.689i | 0.342351 | − | 0.116583i | ||||
\(205\) | −1214.84 | + | 2104.16i | −0.413892 | + | 0.716882i | ||||
\(206\) | 858.937 | − | 1487.72i | 0.290509 | − | 0.503177i | ||||
\(207\) | 2017.74 | + | 2619.03i | 0.677500 | + | 0.879396i | ||||
\(208\) | −3357.63 | + | 1938.53i | −1.11928 | + | 0.646215i | ||||
\(209\) | 356.522 | + | 617.514i | 0.117996 | + | 0.204375i | ||||
\(210\) | −195.236 | − | 3002.21i | −0.0641550 | − | 0.986534i | ||||
\(211\) | 312.466 | − | 541.206i | 0.101948 | − | 0.176579i | −0.810539 | − | 0.585684i | \(-0.800826\pi\) |
0.912487 | + | 0.409105i | \(0.134159\pi\) | |||||||
\(212\) | 2606.99i | 0.844570i | ||||||||
\(213\) | −155.682 | − | 457.168i | −0.0500807 | − | 0.147064i | ||||
\(214\) | 6491.50 | 2.07360 | ||||||||
\(215\) | −1192.72 | − | 2065.85i | −0.378338 | − | 0.655300i | ||||
\(216\) | 416.963 | + | 276.854i | 0.131346 | + | 0.0872107i | ||||
\(217\) | −180.293 | − | 180.828i | −0.0564014 | − | 0.0565687i | ||||
\(218\) | 1668.41 | − | 963.259i | 0.518345 | − | 0.299267i | ||||
\(219\) | −5191.38 | − | 1027.40i | −1.60183 | − | 0.317009i | ||||
\(220\) | −419.188 | + | 242.018i | −0.128462 | + | 0.0741676i | ||||
\(221\) | −1363.81 | + | 787.399i | −0.415113 | + | 0.239666i | ||||
\(222\) | 1741.13 | + | 5112.91i | 0.526384 | + | 1.54575i | ||||
\(223\) | 2295.49 | − | 1325.30i | 0.689316 | − | 0.397977i | −0.114040 | − | 0.993476i | \(-0.536379\pi\) |
0.803356 | + | 0.595499i | \(0.203046\pi\) | |||||||
\(224\) | 3396.70 | + | 3406.78i | 1.01318 | + | 1.01618i | ||||
\(225\) | −1434.32 | + | 1105.02i | −0.424984 | + | 0.327414i | ||||
\(226\) | −4111.14 | − | 7120.70i | −1.21004 | − | 2.09585i | ||||
\(227\) | 817.772 | 0.239108 | 0.119554 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119554 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(228\) | −4495.49 | − | 889.676i | −1.30579 | − | 0.258422i | ||||
\(229\) | − | 702.979i | − | 0.202857i | −0.994843 | − | 0.101428i | \(-0.967659\pi\) | ||
0.994843 | − | 0.101428i | \(-0.0323412\pi\) | |||||||
\(230\) | 1914.06 | − | 3315.25i | 0.548737 | − | 0.950441i | ||||
\(231\) | 573.928 | − | 383.062i | 0.163470 | − | 0.109107i | ||||
\(232\) | 295.416 | + | 511.675i | 0.0835991 | + | 0.144798i | ||||
\(233\) | −3559.17 | + | 2054.89i | −1.00073 | + | 0.577769i | −0.908463 | − | 0.417966i | \(-0.862743\pi\) |
−0.0922626 | + | 0.995735i | \(0.529410\pi\) | |||||||
\(234\) | −7061.33 | − | 2908.86i | −1.97271 | − | 0.812641i | ||||
\(235\) | 269.408 | − | 466.629i | 0.0747841 | − | 0.129530i | ||||
\(236\) | −2045.23 | + | 3542.45i | −0.564125 | + | 0.977092i | ||||
\(237\) | −803.211 | + | 4058.59i | −0.220144 | + | 1.11238i | ||||
\(238\) | 1228.10 | + | 1231.74i | 0.334478 | + | 0.335470i | ||||
\(239\) | −2082.70 | − | 1202.45i | −0.563677 | − | 0.325439i | 0.190943 | − | 0.981601i | \(-0.438845\pi\) |
−0.754620 | + | 0.656162i | \(0.772179\pi\) | |||||||
\(240\) | −432.280 | + | 2184.29i | −0.116265 | + | 0.587481i | ||||
\(241\) | − | 726.363i | − | 0.194146i | −0.995277 | − | 0.0970729i | \(-0.969052\pi\) | ||
0.995277 | − | 0.0970729i | \(-0.0309480\pi\) | |||||||
\(242\) | 4551.35 | + | 2627.72i | 1.20897 | + | 0.698002i | ||||
\(243\) | −266.080 | − | 3778.64i | −0.0702430 | − | 0.997530i | ||||
\(244\) | 5874.66i | 1.54134i | ||||||||
\(245\) | 2264.92 | − | 1298.73i | 0.590615 | − | 0.338664i | ||||
\(246\) | 4486.55 | − | 5125.95i | 1.16281 | − | 1.32853i | ||||
\(247\) | 6848.60 | 1.76423 | ||||||||
\(248\) | −24.5937 | − | 42.5976i | −0.00629720 | − | 0.0109071i | ||||
\(249\) | 83.7357 | + | 73.2906i | 0.0213114 | + | 0.0186530i | ||||
\(250\) | 5199.92 | + | 3002.17i | 1.31549 | + | 0.759496i | ||||
\(251\) | −529.985 | −0.133276 | −0.0666382 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666382 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(252\) | −576.826 | + | 4397.05i | −0.144193 | + | 1.09916i | ||||
\(253\) | 877.994 | 0.218178 | ||||||||
\(254\) | 1859.66 | + | 1073.67i | 0.459390 | + | 0.265229i | ||||
\(255\) | −175.585 | + | 887.224i | −0.0431199 | + | 0.217883i | ||||
\(256\) | −1533.75 | − | 2656.53i | −0.374450 | − | 0.648567i | ||||
\(257\) | 1948.86 | 0.473021 | 0.236511 | − | 0.971629i | \(-0.423996\pi\) | ||||
0.236511 | + | 0.971629i | \(0.423996\pi\) | |||||||
\(258\) | 2155.95 | + | 6331.03i | 0.520246 | + | 1.52772i | ||||
\(259\) | −3319.30 | + | 3309.48i | −0.796337 | + | 0.793982i | ||||
\(260\) | 4649.05i | 1.10893i | ||||||||
\(261\) | 1703.19 | − | 4134.54i | 0.403927 | − | 0.980543i | ||||
\(262\) | 9112.31 | + | 5260.99i | 2.14870 | + | 1.24055i | ||||
\(263\) | 506.885i | 0.118844i | 0.998233 | + | 0.0594218i | \(0.0189257\pi\) | ||||
−0.998233 | + | 0.0594218i | \(0.981074\pi\) | |||||||
\(264\) | 125.821 | − | 42.8467i | 0.0293324 | − | 0.00998876i | ||||
\(265\) | −1937.78 | − | 1118.78i | −0.449195 | − | 0.259343i | ||||
\(266\) | −1946.96 | − | 7309.45i | −0.448782 | − | 1.68485i | ||||
\(267\) | −2656.62 | − | 2325.23i | −0.608922 | − | 0.532966i | ||||
\(268\) | 3185.06 | − | 5516.69i | 0.725965 | − | 1.25741i | ||||
\(269\) | 3851.69 | − | 6671.33i | 0.873018 | − | 1.51211i | 0.0141598 | − | 0.999900i | \(-0.495493\pi\) |
0.858859 | − | 0.512213i | \(-0.171174\pi\) | |||||||
\(270\) | −3928.07 | + | 1951.34i | −0.885388 | + | 0.439833i | ||||
\(271\) | −4585.66 | + | 2647.53i | −1.02789 | + | 0.593455i | −0.916380 | − | 0.400308i | \(-0.868903\pi\) |
−0.111513 | + | 0.993763i | \(0.535570\pi\) | |||||||
\(272\) | −643.662 | − | 1114.85i | −0.143484 | − | 0.248522i | ||||
\(273\) | −430.081 | − | 6613.51i | −0.0953469 | − | 1.46618i | ||||
\(274\) | −2.52250 | + | 4.36910i | −0.000556167 | + | 0.000963310i | ||||
\(275\) | 480.837i | 0.105438i | ||||||||
\(276\) | −3716.44 | + | 4246.09i | −0.810520 | + | 0.926032i | ||||
\(277\) | 4216.97 | 0.914705 | 0.457353 | − | 0.889285i | \(-0.348798\pi\) | ||||
0.457353 | + | 0.889285i | \(0.348798\pi\) | |||||||
\(278\) | 3974.77 | + | 6884.50i | 0.857521 | + | 1.48527i | ||||
\(279\) | −141.793 | + | 344.206i | −0.0304263 | + | 0.0738605i | ||||
\(280\) | 485.976 | − | 129.446i | 0.103724 | − | 0.0276281i | ||||
\(281\) | −7104.37 | + | 4101.71i | −1.50823 | + | 0.870774i | −0.508271 | + | 0.861197i | \(0.669715\pi\) |
−0.999954 | + | 0.00957745i | \(0.996951\pi\) | |||||||
\(282\) | −994.960 | + | 1136.76i | −0.210103 | + | 0.240046i | ||||
\(283\) | 1358.81 | − | 784.511i | 0.285417 | − | 0.164786i | −0.350456 | − | 0.936579i | \(-0.613973\pi\) |
0.635873 | + | 0.771794i | \(0.280640\pi\) | |||||||
\(284\) | 713.847 | − | 412.140i | 0.149152 | − | 0.0861127i | ||||
\(285\) | 2590.51 | − | 2959.70i | 0.538416 | − | 0.615149i | ||||
\(286\) | −1756.40 | + | 1014.06i | −0.363140 | + | 0.209659i | ||||
\(287\) | 5707.90 | + | 1538.49i | 1.17396 | + | 0.316426i | ||||
\(288\) | 2671.36 | − | 6484.80i | 0.546568 | − | 1.32681i | ||||
\(289\) | 2195.06 | + | 3801.95i | 0.446785 | + | 0.773854i | ||||
\(290\) | −5177.61 | −1.04841 | ||||||||
\(291\) | −3888.74 | + | 4442.95i | −0.783374 | + | 0.895018i | ||||
\(292\) | − | 9032.32i | − | 1.81019i | ||||||
\(293\) | 227.022 | − | 393.213i | 0.0452653 | − | 0.0784019i | −0.842505 | − | 0.538688i | \(-0.818920\pi\) |
0.887770 | + | 0.460287i | \(0.152253\pi\) | |||||||
\(294\) | −6936.27 | + | 2339.15i | −1.37596 | + | 0.464021i | ||||
\(295\) | −1755.40 | − | 3040.45i | −0.346452 | − | 0.600073i | ||||
\(296\) | −781.927 | + | 451.446i | −0.153542 | + | 0.0886478i | ||||
\(297\) | −838.046 | − | 556.443i | −0.163732 | − | 0.108714i | ||||
\(298\) | 4985.97 | − | 8635.94i | 0.969226 | − | 1.67875i | ||||
\(299\) | 4216.45 | − | 7303.11i | 0.815531 | − | 1.41254i | ||||
\(300\) | −2325.39 | − | 2035.32i | −0.447522 | − | 0.391698i | ||||
\(301\) | −4110.10 | + | 4097.95i | −0.787051 | + | 0.784723i | ||||
\(302\) | −4966.75 | − | 2867.56i | −0.946372 | − | 0.546388i | ||||
\(303\) | −7585.25 | + | 2583.06i | −1.43816 | + | 0.489745i | ||||
\(304\) | 5598.41i | 1.05622i | ||||||||
\(305\) | −4366.64 | − | 2521.08i | −0.819780 | − | 0.473300i | ||||
\(306\) | 965.846 | − | 2344.62i | 0.180437 | − | 0.438016i | ||||
\(307\) | 74.2025i | 0.0137947i | 0.999976 | + | 0.00689733i | \(0.00219550\pi\) | ||||
−0.999976 | + | 0.00689733i | \(0.997804\pi\) | |||||||
\(308\) | 831.528 | + | 833.995i | 0.153834 | + | 0.154290i | ||||
\(309\) | −700.603 | − | 2057.35i | −0.128983 | − | 0.378765i | ||||
\(310\) | 431.042 | 0.0789728 | ||||||||
\(311\) | 3212.96 | + | 5565.00i | 0.585820 | + | 1.01467i | 0.994773 | + | 0.102114i | \(0.0325608\pi\) |
−0.408953 | + | 0.912556i | \(0.634106\pi\) | |||||||
\(312\) | 247.843 | − | 1252.34i | 0.0449723 | − | 0.227243i | ||||
\(313\) | 6681.09 | + | 3857.33i | 1.20651 | + | 0.696578i | 0.961995 | − | 0.273067i | \(-0.0880382\pi\) |
0.244514 | + | 0.969646i | \(0.421372\pi\) | |||||||
\(314\) | −3012.24 | −0.541372 | ||||||||
\(315\) | −3020.78 | − | 2315.72i | −0.540323 | − | 0.414210i | ||||
\(316\) | −7061.41 | −1.25707 | ||||||||
\(317\) | −265.053 | − | 153.028i | −0.0469617 | − | 0.0271133i | 0.476335 | − | 0.879264i | \(-0.341965\pi\) |
−0.523297 | + | 0.852150i | \(0.675298\pi\) | |||||||
\(318\) | 4720.63 | + | 4131.79i | 0.832452 | + | 0.728613i | ||||
\(319\) | −593.751 | − | 1028.41i | −0.104212 | − | 0.180501i | ||||
\(320\) | −4692.62 | −0.819767 | ||||||||
\(321\) | 5409.03 | − | 6179.90i | 0.940507 | − | 1.07454i | ||||
\(322\) | −8993.22 | − | 2424.01i | −1.55644 | − | 0.419517i | ||||
\(323\) | 2273.98i | 0.391727i | ||||||||
\(324\) | 6238.38 | − | 1697.54i | 1.06968 | − | 0.291074i | ||||
\(325\) | 3999.58 | + | 2309.16i | 0.682636 | + | 0.394120i | ||||
\(326\) | − | 12359.8i | − | 2.09983i | ||||||
\(327\) | 473.181 | − | 2390.96i | 0.0800213 | − | 0.404344i | ||||
\(328\) | 986.172 | + | 569.367i | 0.166013 | + | 0.0958476i | ||||
\(329\) | −1265.81 | − | 341.184i | −0.212117 | − | 0.0571734i | ||||
\(330\) | −226.129 | + | 1142.62i | −0.0377212 | + | 0.190603i | ||||
\(331\) | 2049.56 | − | 3549.94i | 0.340344 | − | 0.589493i | −0.644152 | − | 0.764897i | \(-0.722790\pi\) |
0.984497 | + | 0.175404i | \(0.0561231\pi\) | |||||||
\(332\) | −94.9642 | + | 164.483i | −0.0156983 | + | 0.0271903i | ||||
\(333\) | 6318.29 | + | 2602.77i | 1.03976 | + | 0.428321i | ||||
\(334\) | 285.755 | − | 164.981i | 0.0468138 | − | 0.0270280i | ||||
\(335\) | 2733.70 | + | 4734.91i | 0.445845 | + | 0.772227i | ||||
\(336\) | 5406.24 | − | 351.571i | 0.877781 | − | 0.0570827i | ||||
\(337\) | −3390.68 | + | 5872.83i | −0.548078 | + | 0.949298i | 0.450329 | + | 0.892863i | \(0.351307\pi\) |
−0.998406 | + | 0.0564355i | \(0.982026\pi\) | |||||||
\(338\) | 10456.2i | 1.68266i | ||||||||
\(339\) | −10204.5 | − | 2019.51i | −1.63490 | − | 0.323554i | ||||
\(340\) | −1543.65 | −0.246224 | ||||||||
\(341\) | 49.4305 | + | 85.6161i | 0.00784989 | + | 0.0135964i | ||||
\(342\) | −8735.83 | + | 6730.21i | −1.38123 | + | 1.06412i | ||||
\(343\) | −4471.86 | − | 4511.77i | −0.703959 | − | 0.710241i | ||||
\(344\) | −968.216 | + | 559.000i | −0.151752 | + | 0.0876141i | ||||
\(345\) | −1561.23 | − | 4584.62i | −0.243634 | − | 0.715442i | ||||
\(346\) | −9769.78 | + | 5640.59i | −1.51800 | + | 0.876416i | ||||
\(347\) | −8450.67 | + | 4878.99i | −1.30736 | + | 0.754807i | −0.981656 | − | 0.190663i | \(-0.938936\pi\) |
−0.325709 | + | 0.945470i | \(0.605603\pi\) | |||||||
\(348\) | 7486.78 | + | 1481.66i | 1.15326 | + | 0.228234i | ||||
\(349\) | −2576.08 | + | 1487.30i | −0.395113 | + | 0.228119i | −0.684373 | − | 0.729132i | \(-0.739924\pi\) |
0.289260 | + | 0.957251i | \(0.406591\pi\) | |||||||
\(350\) | 1327.52 | − | 4925.18i | 0.202739 | − | 0.752176i | ||||
\(351\) | −8653.07 | + | 4298.58i | −1.31586 | + | 0.653679i | ||||
\(352\) | −931.265 | − | 1613.00i | −0.141013 | − | 0.244242i | ||||
\(353\) | 9788.58 | 1.47590 | 0.737951 | − | 0.674854i | \(-0.235793\pi\) | ||||
0.737951 | + | 0.674854i | \(0.235793\pi\) | |||||||
\(354\) | 3173.05 | + | 9317.81i | 0.476401 | + | 1.39897i | ||||
\(355\) | 707.470i | 0.105771i | ||||||||
\(356\) | 3012.85 | − | 5218.41i | 0.448542 | − | 0.776897i | ||||
\(357\) | 2195.93 | − | 142.803i | 0.325548 | − | 0.0211706i | ||||
\(358\) | −5908.94 | − | 10234.6i | −0.872338 | − | 1.51093i | ||||
\(359\) | −3444.96 | + | 1988.95i | −0.506456 | + | 0.292403i | −0.731376 | − | 0.681975i | \(-0.761121\pi\) |
0.224919 | + | 0.974377i | \(0.427788\pi\) | |||||||
\(360\) | −447.465 | − | 580.811i | −0.0655097 | − | 0.0850317i | ||||
\(361\) | 1515.14 | − | 2624.30i | 0.220898 | − | 0.382606i | ||||
\(362\) | 658.259 | − | 1140.14i | 0.0955727 | − | 0.165537i | ||||
\(363\) | 6294.00 | − | 2143.34i | 0.910053 | − | 0.309906i | ||||
\(364\) | 10930.4 | − | 2911.46i | 1.57393 | − | 0.419236i | ||||
\(365\) | 6713.72 | + | 3876.17i | 0.962773 | + | 0.555858i | ||||
\(366\) | 10637.6 | + | 9310.68i | 1.51922 | + | 1.32972i | ||||
\(367\) | − | 3534.28i | − | 0.502692i | −0.967897 | − | 0.251346i | \(-0.919127\pi\) | ||
0.967897 | − | 0.251346i | \(-0.0808732\pi\) | |||||||
\(368\) | 5969.95 | + | 3446.75i | 0.845667 | + | 0.488246i | ||||
\(369\) | −1141.49 | − | 8542.39i | −0.161040 | − | 1.20515i | ||||
\(370\) | − | 7912.26i | − | 1.11173i | ||||||
\(371\) | −1416.84 | + | 5256.56i | −0.198271 | + | 0.735599i | ||||
\(372\) | −623.284 | − | 123.350i | −0.0868704 | − | 0.0171920i | ||||
\(373\) | 4725.85 | 0.656019 | 0.328010 | − | 0.944674i | \(-0.393622\pi\) | ||||
0.328010 | + | 0.944674i | \(0.393622\pi\) | |||||||
\(374\) | −336.704 | − | 583.189i | −0.0465523 | − | 0.0806309i | ||||
\(375\) | 7190.89 | − | 2448.76i | 0.990229 | − | 0.337209i | ||||
\(376\) | −218.698 | − | 126.266i | −0.0299960 | − | 0.0173182i | ||||
\(377\) | −11405.6 | −1.55815 | ||||||||
\(378\) | 7047.78 | + | 8013.32i | 0.958992 | + | 1.09037i | ||||
\(379\) | 5183.61 | 0.702545 | 0.351272 | − | 0.936273i | \(-0.385749\pi\) | ||||
0.351272 | + | 0.936273i | \(0.385749\pi\) | |||||||
\(380\) | 5813.76 | + | 3356.58i | 0.784841 | + | 0.453128i | ||||
\(381\) | 2571.69 | − | 875.755i | 0.345805 | − | 0.117759i | ||||
\(382\) | 1940.75 | + | 3361.48i | 0.259941 | + | 0.450231i | ||||
\(383\) | 6894.41 | 0.919811 | 0.459906 | − | 0.887968i | \(-0.347883\pi\) | ||||
0.459906 | + | 0.887968i | \(0.347883\pi\) | |||||||
\(384\) | 2313.90 | + | 457.931i | 0.307502 | + | 0.0608559i | ||||
\(385\) | −976.754 | + | 260.171i | −0.129299 | + | 0.0344404i | ||||
\(386\) | − | 3231.37i | − | 0.426094i | ||||||
\(387\) | 7823.58 | + | 3222.86i | 1.02764 | + | 0.423326i | ||||
\(388\) | −8727.32 | − | 5038.72i | −1.14191 | − | 0.659284i | ||||
\(389\) | 2814.17i | 0.366797i | 0.983039 | + | 0.183398i | \(0.0587098\pi\) | ||||
−0.983039 | + | 0.183398i | \(0.941290\pi\) | |||||||
\(390\) | 8418.30 | + | 7368.22i | 1.09302 | + | 0.956677i | ||||
\(391\) | 2424.90 | + | 1400.02i | 0.313638 | + | 0.181079i | ||||
\(392\) | −608.684 | − | 1061.52i | −0.0784265 | − | 0.136773i | ||||
\(393\) | 12601.3 | − | 4291.20i | 1.61743 | − | 0.550795i | ||||
\(394\) | −10365.8 | + | 17954.1i | −1.32544 | + | 2.29572i | ||||
\(395\) | 3030.36 | − | 5248.75i | 0.386011 | − | 0.668590i | ||||
\(396\) | 653.962 | − | 1587.51i | 0.0829869 | − | 0.201453i | ||||
\(397\) | −5248.35 | + | 3030.14i | −0.663494 | + | 0.383068i | −0.793607 | − | 0.608431i | \(-0.791799\pi\) |
0.130113 | + | 0.991499i | \(0.458466\pi\) | |||||||
\(398\) | 2495.28 | + | 4321.95i | 0.314264 | + | 0.544320i | ||||
\(399\) | −8580.90 | − | 4237.08i | −1.07665 | − | 0.531627i | ||||
\(400\) | −1887.63 | + | 3269.47i | −0.235954 | + | 0.408684i | ||||
\(401\) | − | 12064.2i | − | 1.50239i | −0.660080 | − | 0.751196i | \(-0.729477\pi\) | ||
0.660080 | − | 0.751196i | \(-0.270523\pi\) | |||||||
\(402\) | −4941.43 | − | 14510.7i | −0.613075 | − | 1.80032i | ||||
\(403\) | 949.535 | 0.117369 | ||||||||
\(404\) | −6838.15 | − | 11844.0i | −0.842106 | − | 1.45857i | ||||
\(405\) | −1415.38 | + | 5365.48i | −0.173656 | + | 0.658303i | ||||
\(406\) | 3242.47 | + | 12173.1i | 0.396357 | + | 1.48804i | ||||
\(407\) | 1571.58 | − | 907.352i | 0.191401 | − | 0.110506i | ||||
\(408\) | 415.822 | + | 82.2929i | 0.0504566 | + | 0.00998555i | ||||
\(409\) | 292.292 | − | 168.755i | 0.0353372 | − | 0.0204019i | −0.482227 | − | 0.876046i | \(-0.660172\pi\) |
0.517565 | + | 0.855644i | \(0.326839\pi\) | |||||||
\(410\) | −8642.07 | + | 4989.50i | −1.04098 | + | 0.601010i | ||||
\(411\) | 2.05751 | + | 6.04196i | 0.000246933 | + | 0.000725129i | ||||
\(412\) | 3212.46 | − | 1854.71i | 0.384142 | − | 0.221784i | ||||
\(413\) | −6049.11 | + | 6031.23i | −0.720720 | + | 0.718589i | ||||
\(414\) | 1798.51 | + | 13459.2i | 0.213507 | + | 1.59778i | ||||
\(415\) | −81.5067 | − | 141.174i | −0.00964098 | − | 0.0166987i | ||||
\(416\) | −17889.1 | −2.10838 | ||||||||
\(417\) | 9866.01 | + | 1952.52i | 1.15861 | + | 0.229294i | ||||
\(418\) | 2928.57i | 0.342682i | ||||||||
\(419\) | 4094.25 | − | 7091.45i | 0.477368 | − | 0.826826i | −0.522295 | − | 0.852765i | \(-0.674924\pi\) |
0.999664 | + | 0.0259386i | \(0.00825744\pi\) | |||||||
\(420\) | 2876.26 | − | 5824.98i | 0.334160 | − | 0.676738i | ||||
\(421\) | 958.165 | + | 1659.59i | 0.110922 | + | 0.192122i | 0.916142 | − | 0.400853i | \(-0.131286\pi\) |
−0.805220 | + | 0.592976i | \(0.797953\pi\) | |||||||
\(422\) | 2222.81 | − | 1283.34i | 0.256409 | − | 0.148038i | ||||
\(423\) | 253.143 | + | 1894.40i | 0.0290975 | + | 0.217752i | ||||
\(424\) | −524.345 | + | 908.193i | −0.0600577 | + | 0.104023i | ||||
\(425\) | −766.724 | + | 1328.01i | −0.0875096 | + | 0.151571i | ||||
\(426\) | 385.082 | − | 1945.80i | 0.0437964 | − | 0.221301i | ||||
\(427\) | −3192.74 | + | 11845.3i | −0.361844 | + | 1.34247i | ||||
\(428\) | 12139.2 | + | 7008.59i | 1.37096 | + | 0.791526i | ||||
\(429\) | −498.135 | + | 2517.05i | −0.0560610 | + | 0.283274i | ||||
\(430\) | − | 9797.31i | − | 1.09876i | ||||||
\(431\) | −8604.78 | − | 4967.97i | −0.961665 | − | 0.555218i | −0.0649800 | − | 0.997887i | \(-0.520698\pi\) |
−0.896685 | + | 0.442669i | \(0.854032\pi\) | |||||||
\(432\) | −3513.89 | − | 7073.48i | −0.391347 | − | 0.787785i | ||||
\(433\) | 4551.00i | 0.505098i | 0.967584 | + | 0.252549i | \(0.0812688\pi\) | ||||
−0.967584 | + | 0.252549i | \(0.918731\pi\) | |||||||
\(434\) | −269.940 | − | 1013.43i | −0.0298561 | − | 0.112088i | ||||
\(435\) | −4314.23 | + | 4929.08i | −0.475521 | + | 0.543290i | ||||
\(436\) | 4159.96 | 0.456940 | ||||||||
\(437\) | −6088.49 | − | 10545.6i | −0.666481 | − | 1.15438i | ||||
\(438\) | −16355.3 | − | 14315.2i | −1.78422 | − | 1.56166i | ||||
\(439\) | −6424.18 | − | 3709.00i | −0.698427 | − | 0.403237i | 0.108335 | − | 0.994114i | \(-0.465448\pi\) |
−0.806761 | + | 0.590878i | \(0.798782\pi\) | |||||||
\(440\) | −194.709 | −0.0210963 | ||||||||
\(441\) | −3552.77 | + | 8552.42i | −0.383627 | + | 0.923488i | ||||
\(442\) | −6467.91 | −0.696035 | ||||||||
\(443\) | −5479.67 | − | 3163.69i | −0.587691 | − | 0.339303i | 0.176493 | − | 0.984302i | \(-0.443525\pi\) |
−0.764184 | + | 0.644999i | \(0.776858\pi\) | |||||||
\(444\) | −2264.24 | + | 11441.1i | −0.242018 | + | 1.22290i | ||||
\(445\) | 2585.90 | + | 4478.91i | 0.275468 | + | 0.477125i | ||||
\(446\) | 10886.4 | 1.15580 | ||||||||
\(447\) | −4066.87 | − | 11942.5i | −0.430327 | − | 1.26367i | ||||
\(448\) | 2938.75 | + | 11032.9i | 0.309917 | + | 1.16352i | ||||
\(449\) | − | 14396.4i | − | 1.51316i | −0.653904 | − | 0.756578i | \(-0.726870\pi\) | ||
0.653904 | − | 0.756578i | \(-0.273130\pi\) | |||||||
\(450\) | −7370.96 | + | 984.960i | −0.772157 | + | 0.103181i | ||||
\(451\) | −1982.09 | − | 1144.36i | −0.206946 | − | 0.119481i | ||||
\(452\) | − | 17754.5i | − | 1.84757i | ||||||
\(453\) | −6868.45 | + | 2338.96i | −0.712380 | + | 0.242591i | ||||
\(454\) | 2908.72 | + | 1679.35i | 0.300690 | + | 0.173603i | ||||
\(455\) | −2526.65 | + | 9374.03i | −0.260332 | + | 0.965849i | ||||
\(456\) | −1387.15 | − | 1214.11i | −0.142454 | − | 0.124685i | ||||
\(457\) | −2573.61 | + | 4457.63i | −0.263432 | + | 0.456278i | −0.967152 | − | 0.254200i | \(-0.918188\pi\) |
0.703719 | + | 0.710478i | \(0.251521\pi\) | |||||||
\(458\) | 1443.62 | − | 2500.42i | 0.147283 | − | 0.255102i | ||||
\(459\) | −1427.28 | − | 2873.13i | −0.145141 | − | 0.292171i | ||||
\(460\) | 7158.68 | − | 4133.06i | 0.725598 | − | 0.418924i | ||||
\(461\) | 446.618 | + | 773.565i | 0.0451217 | + | 0.0781530i | 0.887704 | − | 0.460414i | \(-0.152299\pi\) |
−0.842583 | + | 0.538567i | \(0.818966\pi\) | |||||||
\(462\) | 2828.04 | − | 183.909i | 0.284789 | − | 0.0185200i | ||||
\(463\) | 5520.47 | − | 9561.73i | 0.554121 | − | 0.959765i | −0.443851 | − | 0.896101i | \(-0.646388\pi\) |
0.997971 | − | 0.0636644i | \(-0.0202787\pi\) | |||||||
\(464\) | − | 9323.59i | − | 0.932838i | ||||||
\(465\) | 359.165 | − | 410.352i | 0.0358191 | − | 0.0409239i | ||||
\(466\) | −16879.4 | −1.67795 | ||||||||
\(467\) | 4900.18 | + | 8487.36i | 0.485553 | + | 0.841003i | 0.999862 | − | 0.0166023i | \(-0.00528493\pi\) |
−0.514309 | + | 0.857605i | \(0.671952\pi\) | |||||||
\(468\) | −10064.3 | − | 13063.4i | −0.994061 | − | 1.29029i | ||||
\(469\) | 9420.34 | − | 9392.49i | 0.927486 | − | 0.924744i | ||||
\(470\) | 1916.51 | − | 1106.50i | 0.188089 | − | 0.108593i | ||||
\(471\) | −2509.95 | + | 2867.66i | −0.245546 | + | 0.280541i | ||||
\(472\) | −1424.99 | + | 822.718i | −0.138963 | + | 0.0802302i | ||||
\(473\) | 1946.00 | − | 1123.52i | 0.189169 | − | 0.109217i | ||||
\(474\) | −11191.5 | + | 12786.5i | −1.08448 | + | 1.23904i | ||||
\(475\) | 5775.33 | − | 3334.39i | 0.557875 | − | 0.322089i | ||||
\(476\) | 966.711 | + | 3629.30i | 0.0930864 | + | 0.349472i | ||||
\(477\) | 7866.92 | − | 1051.23i | 0.755139 | − | 0.100907i | ||||
\(478\) | −4938.63 | − | 8553.95i | −0.472568 | − | 0.818512i | ||||
\(479\) | 138.670 | 0.0132275 | 0.00661377 | − | 0.999978i | \(-0.497895\pi\) | ||||
0.00661377 | + | 0.999978i | \(0.497895\pi\) | |||||||
\(480\) | −6766.63 | + | 7730.98i | −0.643444 | + | 0.735145i | ||||
\(481\) | − | 17429.8i | − | 1.65224i | ||||||
\(482\) | 1491.64 | − | 2583.59i | 0.140959 | − | 0.244148i | ||||
\(483\) | −9801.24 | + | 6541.74i | −0.923337 | + | 0.616273i | ||||
\(484\) | 5674.08 | + | 9827.80i | 0.532878 | + | 0.922971i | ||||
\(485\) | 7490.56 | − | 4324.68i | 0.701296 | − | 0.404894i | ||||
\(486\) | 6813.28 | − | 13986.6i | 0.635919 | − | 1.30544i | ||||
\(487\) | −9148.40 | + | 15845.5i | −0.851239 | + | 1.47439i | 0.0288514 | + | 0.999584i | \(0.490815\pi\) |
−0.880091 | + | 0.474806i | \(0.842518\pi\) | |||||||
\(488\) | −1181.57 | + | 2046.55i | −0.109605 | + | 0.189842i | ||||
\(489\) | −11766.5 | − | 10298.8i | −1.08814 | − | 0.952406i | ||||
\(490\) | 10723.1 | + | 31.7579i | 0.988614 | + | 0.00292791i | ||||
\(491\) | 5097.03 | + | 2942.77i | 0.468484 | + | 0.270479i | 0.715605 | − | 0.698505i | \(-0.246151\pi\) |
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(492\) | 13924.2 | − | 4741.70i | 1.27592 | − | 0.434497i | ||||
\(493\) | − | 3787.09i | − | 0.345967i | ||||||
\(494\) | 24359.7 | + | 14064.1i | 2.21861 | + | 1.28092i | ||||
\(495\) | 899.352 | + | 1167.36i | 0.0816623 | + | 0.105998i | ||||
\(496\) | 776.201i | 0.0702670i | ||||||||
\(497\) | 1663.34 | − | 443.053i | 0.150123 | − | 0.0399872i | ||||
\(498\) | 147.331 | + | 432.644i | 0.0132572 | + | 0.0389302i | ||||
\(499\) | 534.725 | 0.0479711 | 0.0239856 | − | 0.999712i | \(-0.492364\pi\) | ||||
0.0239856 | + | 0.999712i | \(0.492364\pi\) | |||||||
\(500\) | 6482.63 | + | 11228.3i | 0.579824 | + | 1.00429i | ||||
\(501\) | 81.0433 | − | 409.508i | 0.00722704 | − | 0.0365179i | ||||
\(502\) | −1885.10 | − | 1088.36i | −0.167602 | − | 0.0967649i | ||||
\(503\) | −10504.5 | −0.931155 | −0.465578 | − | 0.885007i | \(-0.654153\pi\) | ||||
−0.465578 | + | 0.885007i | \(0.654153\pi\) | |||||||
\(504\) | −1085.33 | + | 1415.77i | −0.0959213 | + | 0.125126i | ||||
\(505\) | 11738.2 | 1.03434 | ||||||||
\(506\) | 3122.93 | + | 1803.02i | 0.274369 | + | 0.158407i | ||||
\(507\) | 9954.25 | + | 8712.57i | 0.871960 | + | 0.763193i | ||||
\(508\) | 2318.40 | + | 4015.58i | 0.202485 | + | 0.350714i | ||||
\(509\) | 2817.87 | 0.245383 | 0.122691 | − | 0.992445i | \(-0.460847\pi\) | ||||
0.122691 | + | 0.992445i | \(0.460847\pi\) | |||||||
\(510\) | −2446.51 | + | 2795.18i | −0.212419 | + | 0.242692i | ||||
\(511\) | 4908.85 | − | 18212.2i | 0.424961 | − | 1.57663i | ||||
\(512\) | − | 16230.2i | − | 1.40094i | ||||||
\(513\) | −871.962 | + | 13924.5i | −0.0750449 | + | 1.19840i | ||||
\(514\) | 6931.87 | + | 4002.12i | 0.594848 | + | 0.343435i | ||||
\(515\) | 3183.76i | 0.272414i | ||||||||
\(516\) | −2803.68 | + | 14166.8i | −0.239196 | + | 1.20864i | ||||
\(517\) | 439.558 | + | 253.779i | 0.0373921 | + | 0.0215884i | ||||
\(518\) | −18602.6 | + | 4955.05i | −1.57790 | + | 0.420294i | ||||
\(519\) | −2770.82 | + | 14000.8i | −0.234346 | + | 1.18414i | ||||
\(520\) | −935.065 | + | 1619.58i | −0.0788564 | + | 0.136583i | ||||
\(521\) | −5520.76 | + | 9562.24i | −0.464240 | + | 0.804087i | −0.999167 | − | 0.0408113i | \(-0.987006\pi\) |
0.534927 | + | 0.844898i | \(0.320339\pi\) | |||||||
\(522\) | 14548.6 | − | 11208.5i | 1.21988 | − | 0.939812i | ||||
\(523\) | −4094.57 | + | 2364.00i | −0.342338 | + | 0.197649i | −0.661306 | − | 0.750117i | \(-0.729997\pi\) |
0.318967 | + | 0.947766i | \(0.396664\pi\) | |||||||
\(524\) | 11360.1 | + | 19676.3i | 0.947080 | + | 1.64039i | ||||
\(525\) | −3582.61 | − | 5367.69i | −0.297825 | − | 0.446219i | ||||
\(526\) | −1040.92 | + | 1802.93i | −0.0862860 | + | 0.149452i | ||||
\(527\) | 315.280i | 0.0260604i | ||||||||
\(528\) | −2057.58 | − | 407.202i | −0.169592 | − | 0.0335629i | ||||
\(529\) | −2826.93 | −0.232344 | ||||||||
\(530\) | −4594.97 | − | 7958.72i | −0.376590 | − | 0.652273i | ||||
\(531\) | 11514.5 | + | 4743.30i | 0.941029 | + | 0.387649i | ||||
\(532\) | 4250.83 | − | 15770.9i | 0.346423 | − | 1.28525i | ||||
\(533\) | −19037.5 | + | 10991.3i | −1.54710 | + | 0.893218i | ||||
\(534\) | −4674.25 | − | 13726.1i | −0.378792 | − | 1.11234i | ||||
\(535\) | −10419.0 | + | 6015.40i | −0.841966 | + | 0.486109i | ||||
\(536\) | 2219.15 | − | 1281.23i | 0.178830 | − | 0.103247i | ||||
\(537\) | −14666.9 | − | 2902.64i | −1.17863 | − | 0.233256i | ||||
\(538\) | 27400.1 | − | 15819.5i | 2.19573 | − | 1.26770i | ||||
\(539\) | 1223.38 | + | 2133.53i | 0.0977641 | + | 0.170496i | ||||
\(540\) | −9452.36 | − | 591.915i | −0.753268 | − | 0.0471703i | ||||
\(541\) | 11254.7 | + | 19493.8i | 0.894415 | + | 1.54917i | 0.834527 | + | 0.550967i | \(0.185741\pi\) |
0.0598879 | + | 0.998205i | \(0.480926\pi\) | |||||||
\(542\) | −21747.6 | −1.72350 | ||||||||
\(543\) | −536.917 | − | 1576.68i | −0.0424334 | − | 0.124607i | ||||
\(544\) | − | 5939.84i | − | 0.468140i | ||||||
\(545\) | −1785.22 | + | 3092.10i | −0.140313 | + | 0.243029i | ||||
\(546\) | 12051.6 | − | 24406.7i | 0.944614 | − | 1.91302i | ||||
\(547\) | −1219.31 | − | 2111.91i | −0.0953088 | − | 0.165080i | 0.814429 | − | 0.580264i | \(-0.197051\pi\) |
−0.909737 | + | 0.415184i | \(0.863717\pi\) | |||||||
\(548\) | −9.43426 | + | 5.44687i | −0.000735422 | + | 0.000424596i | ||||
\(549\) | 17727.5 | − | 2368.88i | 1.37813 | − | 0.184155i | ||||
\(550\) | −987.432 | + | 1710.28i | −0.0765532 | + | 0.132594i | ||||
\(551\) | −8234.79 | + | 14263.1i | −0.636686 | + | 1.10277i | ||||
\(552\) | −2148.71 | + | 731.714i | −0.165680 | + | 0.0564200i | ||||
\(553\) | −14238.2 | − | 3837.71i | −1.09488 | − | 0.295110i | ||||
\(554\) | 14999.3 | + | 8659.85i | 1.15029 | + | 0.664119i | ||||
\(555\) | −7532.47 | − | 6592.88i | −0.576100 | − | 0.504238i | ||||
\(556\) | 17165.5i | 1.30932i | ||||||||
\(557\) | 9826.37 | + | 5673.25i | 0.747498 | + | 0.431568i | 0.824789 | − | 0.565440i | \(-0.191294\pi\) |
−0.0772911 | + | 0.997009i | \(0.524627\pi\) | |||||||
\(558\) | −1211.19 | + | 933.121i | −0.0918887 | + | 0.0707924i | ||||
\(559\) | − | 21582.3i | − | 1.63298i | ||||||
\(560\) | −7662.84 | − | 2065.42i | −0.578239 | − | 0.155857i | ||||
\(561\) | −835.753 | − | 165.399i | −0.0628976 | − | 0.0124477i | ||||
\(562\) | −33692.6 | −2.52889 | ||||||||
\(563\) | 8427.86 | + | 14597.5i | 0.630891 | + | 1.09274i | 0.987370 | + | 0.158432i | \(0.0506440\pi\) |
−0.356478 | + | 0.934304i | \(0.616023\pi\) | |||||||
\(564\) | −3087.90 | + | 1051.54i | −0.230539 | + | 0.0785071i | ||||
\(565\) | 13196.9 | + | 7619.23i | 0.982651 | + | 0.567334i | ||||
\(566\) | 6444.19 | 0.478568 | ||||||||
\(567\) | 13501.2 | − | 32.4028i | 0.999997 | − | 0.00239999i | ||||
\(568\) | 331.576 | 0.0244940 | ||||||||
\(569\) | −10320.6 | − | 5958.57i | −0.760387 | − | 0.439009i | 0.0690479 | − | 0.997613i | \(-0.478004\pi\) |
−0.829435 | + | 0.558604i | \(0.811337\pi\) | |||||||
\(570\) | 15292.1 | − | 5207.52i | 1.12371 | − | 0.382665i | ||||
\(571\) | −10204.7 | − | 17675.0i | −0.747902 | − | 1.29540i | −0.948826 | − | 0.315798i | \(-0.897728\pi\) |
0.200924 | − | 0.979607i | \(-0.435606\pi\) | |||||||
\(572\) | −4379.34 | −0.320121 | ||||||||
\(573\) | 4817.25 | + | 953.353i | 0.351210 | + | 0.0695059i | ||||
\(574\) | 17143.0 | + | 17193.8i | 1.24657 | + | 1.25027i | ||||
\(575\) | − | 8211.49i | − | 0.595552i | ||||||
\(576\) | 13185.9 | − | 10158.6i | 0.953839 | − | 0.734852i | ||||
\(577\) | −3374.84 | − | 1948.46i | −0.243495 | − | 0.140582i | 0.373287 | − | 0.927716i | \(-0.378231\pi\) |
−0.616782 | + | 0.787134i | \(0.711564\pi\) | |||||||
\(578\) | 18030.8i | 1.29755i | ||||||||
\(579\) | −3076.26 | − | 2692.53i | −0.220803 | − | 0.193261i | ||||
\(580\) | −9682.23 | − | 5590.04i | −0.693160 | − | 0.400196i | ||||
\(581\) | −280.872 | + | 280.041i | −0.0200560 | + | 0.0199967i | ||||
\(582\) | −22955.7 | + | 7817.26i | −1.63496 | + | 0.556763i | ||||
\(583\) | 1053.87 | − | 1825.36i | 0.0748660 | − | 0.129672i | ||||
\(584\) | 1816.67 | − | 3146.57i | 0.128724 | − | 0.222956i | ||||
\(585\) | 14029.1 | − | 1874.66i | 0.991506 | − | 0.132492i | ||||
\(586\) | 1614.98 | − | 932.410i | 0.113847 | − | 0.0657295i | ||||
\(587\) | 8643.77 | + | 14971.5i | 0.607780 | + | 1.05271i | 0.991606 | + | 0.129300i | \(0.0412730\pi\) |
−0.383826 | + | 0.923406i | \(0.625394\pi\) | |||||||
\(588\) | −15496.5 | − | 3114.53i | −1.08684 | − | 0.218437i | ||||
\(589\) | 685.557 | − | 1187.42i | 0.0479591 | − | 0.0830675i | ||||
\(590\) | − | 14419.4i | − | 1.00616i | ||||||
\(591\) | 8455.00 | + | 24828.5i | 0.588481 | + | 1.72810i | ||||
\(592\) | 14248.0 | 0.989173 | ||||||||
\(593\) | 985.742 | + | 1707.36i | 0.0682623 | + | 0.118234i | 0.898136 | − | 0.439717i | \(-0.144921\pi\) |
−0.829874 | + | 0.557951i | \(0.811588\pi\) | |||||||
\(594\) | −1838.14 | − | 3700.19i | −0.126969 | − | 0.255590i | ||||
\(595\) | −3112.52 | − | 838.939i | −0.214455 | − | 0.0578036i | ||||
\(596\) | 18647.7 | − | 10766.3i | 1.28161 | − | 0.739939i | ||||
\(597\) | 6193.68 | + | 1225.75i | 0.424607 | + | 0.0840314i | ||||
\(598\) | 29994.9 | − | 17317.6i | 2.05114 | − | 1.18423i | ||||
\(599\) | 12120.3 | − | 6997.65i | 0.826747 | − | 0.477323i | −0.0259904 | − | 0.999662i | \(-0.508274\pi\) |
0.852738 | + | 0.522339i | \(0.174941\pi\) | |||||||
\(600\) | −400.726 | − | 1176.75i | −0.0272660 | − | 0.0800676i | ||||
\(601\) | −17296.5 | + | 9986.12i | −1.17394 | + | 0.677774i | −0.954605 | − | 0.297875i | \(-0.903722\pi\) |
−0.219335 | + | 0.975650i | \(0.570389\pi\) | |||||||
\(602\) | −23034.6 | + | 6135.56i | −1.55950 | + | 0.415393i | ||||
\(603\) | −17931.6 | − | 7386.79i | −1.21100 | − | 0.498861i | ||||
\(604\) | −6191.95 | − | 10724.8i | −0.417131 | − | 0.722492i | ||||
\(605\) | −9740.00 | −0.654525 | ||||||||
\(606\) | −32284.4 | − | 6389.21i | −2.16413 | − | 0.428290i | ||||
\(607\) | 12997.8i | 0.869136i | 0.900639 | + | 0.434568i | \(0.143099\pi\) | ||||
−0.900639 | + | 0.434568i | \(0.856901\pi\) | |||||||
\(608\) | −12915.8 | + | 22370.8i | −0.861522 | + | 1.49220i | ||||
\(609\) | 14290.6 | + | 7056.42i | 0.950878 | + | 0.469525i | ||||
\(610\) | −10354.4 | − | 17934.4i | −0.687276 | − | 1.19040i | ||||
\(611\) | 4221.84 | − | 2437.48i | 0.279538 | − | 0.161391i | ||||
\(612\) | 4337.53 | − | 3341.70i | 0.286494 | − | 0.220719i | ||||
\(613\) | −3450.80 | + | 5976.96i | −0.227368 | + | 0.393812i | −0.957027 | − | 0.289998i | \(-0.906345\pi\) |
0.729659 | + | 0.683811i | \(0.239679\pi\) | |||||||
\(614\) | −152.380 | + | 263.930i | −0.0100156 | + | 0.0173475i | ||||
\(615\) | −2450.99 | + | 12384.7i | −0.160705 | + | 0.812034i | ||||
\(616\) | 121.936 | + | 457.783i | 0.00797557 | + | 0.0299425i | ||||
\(617\) | −8207.48 | − | 4738.59i | −0.535528 | − | 0.309187i | 0.207737 | − | 0.978185i | \(-0.433390\pi\) |
−0.743265 | + | 0.668998i | \(0.766724\pi\) | |||||||
\(618\) | 1732.95 | − | 8756.50i | 0.112798 | − | 0.569964i | ||||
\(619\) | − | 15581.4i | − | 1.01174i | −0.862609 | − | 0.505871i | \(-0.831171\pi\) | ||
0.862609 | − | 0.505871i | \(-0.168829\pi\) | |||||||
\(620\) | 806.058 | + | 465.378i | 0.0522130 | + | 0.0301452i | ||||
\(621\) | 14311.7 | + | 9502.65i | 0.924814 | + | 0.614055i | ||||
\(622\) | 26392.1i | 1.70133i | ||||||||
\(623\) | 8911.00 | − | 8884.65i | 0.573053 | − | 0.571358i | ||||
\(624\) | −13268.3 | + | 15159.3i | −0.851215 | + | 0.972527i | ||||
\(625\) | −2745.44 | −0.175708 | ||||||||
\(626\) | 15842.6 | + | 27440.2i | 1.01150 | + | 1.75196i | ||||
\(627\) | 2788.00 | + | 2440.23i | 0.177579 | + | 0.155428i | ||||
\(628\) | −5632.96 | − | 3252.19i | −0.357929 | − | 0.206651i | ||||
\(629\) | 5787.32 | 0.366861 | ||||||||
\(630\) | −5989.09 | − | 14440.2i | −0.378748 | − | 0.913190i | ||||
\(631\) | 7028.73 | 0.443438 | 0.221719 | − | 0.975111i | \(-0.428833\pi\) | ||||
0.221719 | + | 0.975111i | \(0.428833\pi\) | |||||||
\(632\) | −2459.97 | − | 1420.26i | −0.154830 | − | 0.0893910i | ||||
\(633\) | 630.415 | − | 3185.46i | 0.0395841 | − | 0.200017i | ||||
\(634\) | −628.509 | − | 1088.61i | −0.0393711 | − | 0.0681928i | ||||
\(635\) | −3979.71 | −0.248709 | ||||||||
\(636\) | 4366.76 | + | 12823.2i | 0.272254 | + | 0.799485i | ||||
\(637\) | 23621.7 | + | 69.9588i | 1.46927 | + | 0.00435144i | ||||
\(638\) | − | 4877.23i | − | 0.302651i | ||||||
\(639\) | −1531.53 | − | 1987.93i | −0.0948145 | − | 0.123069i | ||||
\(640\) | −2992.44 | − | 1727.69i | −0.184823 | − | 0.106707i | ||||
\(641\) | − | 19240.0i | − | 1.18555i | −0.805369 | − | 0.592773i | \(-0.798033\pi\) | ||
0.805369 | − | 0.592773i | \(-0.201967\pi\) | |||||||
\(642\) | 31930.2 | − | 10873.4i | 1.96290 | − | 0.668441i | ||||
\(643\) | 2402.55 | + | 1387.11i | 0.147352 | + | 0.0850737i | 0.571863 | − | 0.820349i | \(-0.306221\pi\) |
−0.424511 | + | 0.905423i | \(0.639554\pi\) | |||||||
\(644\) | −14200.4 | − | 14242.5i | −0.868905 | − | 0.871482i | ||||
\(645\) | −9327.04 | − | 8163.60i | −0.569383 | − | 0.498359i | ||||
\(646\) | −4669.79 | + | 8088.31i | −0.284412 | + | 0.492616i | ||||
\(647\) | 4830.91 | − | 8367.38i | 0.293544 | − | 0.508432i | −0.681101 | − | 0.732189i | \(-0.738499\pi\) |
0.974645 | + | 0.223757i | \(0.0718321\pi\) | |||||||
\(648\) | 2514.68 | + | 663.358i | 0.152447 | + | 0.0402147i | ||||
\(649\) | 2864.06 | − | 1653.56i | 0.173227 | − | 0.100012i | ||||
\(650\) | 9484.04 | + | 16426.8i | 0.572299 | + | 0.991251i | ||||
\(651\) | −1189.71 | − | 587.456i | −0.0716259 | − | 0.0353675i | ||||
\(652\) | 13344.3 | − | 23113.0i | 0.801540 | − | 1.38831i | ||||
\(653\) | − | 11885.8i | − | 0.712294i | −0.934430 | − | 0.356147i | \(-0.884090\pi\) | ||
0.934430 | − | 0.356147i | \(-0.115910\pi\) | |||||||
\(654\) | 6593.06 | − | 7532.68i | 0.394203 | − | 0.450384i | ||||
\(655\) | −19500.6 | −1.16328 | ||||||||
\(656\) | −8984.86 | − | 15562.2i | −0.534756 | − | 0.926224i | ||||
\(657\) | −27256.1 | + | 3642.16i | −1.61851 | + | 0.216277i | ||||
\(658\) | −3801.71 | − | 3812.99i | −0.225237 | − | 0.225906i | ||||
\(659\) | 20497.2 | − | 11834.1i | 1.21162 | − | 0.699529i | 0.248508 | − | 0.968630i | \(-0.420060\pi\) |
0.963112 | + | 0.269100i | \(0.0867263\pi\) | |||||||
\(660\) | −1656.50 | + | 1892.58i | −0.0976959 | + | 0.111619i | ||||
\(661\) | −8316.03 | + | 4801.26i | −0.489344 | + | 0.282523i | −0.724302 | − | 0.689483i | \(-0.757838\pi\) |
0.234959 | + | 0.972005i | \(0.424505\pi\) | |||||||
\(662\) | 14580.1 | − | 8417.83i | 0.856000 | − | 0.494212i | ||||
\(663\) | −5389.38 | + | 6157.45i | −0.315696 | + | 0.360687i | ||||
\(664\) | −66.1650 | + | 38.2004i | −0.00386702 | + | 0.00223262i | ||||
\(665\) | 9898.27 | + | 9927.63i | 0.577201 | + | 0.578913i | ||||
\(666\) | 17128.5 | + | 22232.8i | 0.996569 | + | 1.29355i | ||||
\(667\) | 10139.8 | + | 17562.6i | 0.588626 | + | 1.01953i | ||||
\(668\) | 712.490 | 0.0412681 | ||||||||
\(669\) | 9071.09 | − | 10363.9i | 0.524228 | − | 0.598939i | ||||
\(670\) | 22455.4i | 1.29482i | ||||||||
\(671\) | 2374.82 | − | 4113.31i | 0.136630 | − | 0.236651i | ||||
\(672\) | 22414.0 | + | 11067.6i | 1.28667 | + | 0.635330i | ||||
\(673\) | −3469.40 | − | 6009.18i | −0.198716 | − | 0.344186i | 0.749397 | − | 0.662121i | \(-0.230344\pi\) |
−0.948112 | + | 0.317936i | \(0.897010\pi\) | |||||||
\(674\) | −24120.6 | + | 13926.0i | −1.37847 | + | 0.795860i | ||||
\(675\) | −5204.16 | + | 7837.87i | −0.296753 | + | 0.446933i | ||||
\(676\) | −11289.1 | + | 19553.2i | −0.642300 | + | 1.11250i | ||||
\(677\) | 4176.49 | − | 7233.90i | 0.237098 | − | 0.410667i | −0.722782 | − | 0.691076i | \(-0.757137\pi\) |
0.959880 | + | 0.280410i | \(0.0904703\pi\) | |||||||
\(678\) | −32149.1 | − | 28138.8i | −1.82106 | − | 1.59390i | ||||
\(679\) | −14858.8 | − | 14902.8i | −0.839804 | − | 0.842295i | ||||
\(680\) | −537.759 | − | 310.476i | −0.0303267 | − | 0.0175091i | ||||
\(681\) | 4022.43 | − | 1369.79i | 0.226344 | − | 0.0770783i | ||||
\(682\) | 406.036i | 0.0227975i | ||||||||
\(683\) | 8631.82 | + | 4983.58i | 0.483583 | + | 0.279197i | 0.721908 | − | 0.691989i | \(-0.243265\pi\) |
−0.238325 | + | 0.971185i | \(0.576598\pi\) | |||||||
\(684\) | −23602.5 | + | 3153.93i | −1.31939 | + | 0.176307i | ||||
\(685\) | − | 9.34998i | − | 0.000521524i | ||||||
\(686\) | −6640.67 | − | 25231.1i | −0.369595 | − | 1.40427i | ||||
\(687\) | −1177.50 | − | 3457.79i | −0.0653924 | − | 0.192028i | ||||
\(688\) | 17642.5 | 0.977639 | ||||||||
\(689\) | −10122.2 | − | 17532.1i | −0.559686 | − | 0.969405i | ||||
\(690\) | 3861.71 | − | 19513.1i | 0.213062 | − | 1.07659i | ||||
\(691\) | 4151.78 | + | 2397.03i | 0.228569 | + | 0.131964i | 0.609912 | − | 0.792469i | \(-0.291205\pi\) |
−0.381343 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(692\) | −24359.6 | −1.33817 | ||||||||
\(693\) | 2181.38 | − | 2845.54i | 0.119573 | − | 0.155978i | ||||
\(694\) | −40077.4 | −2.19210 | ||||||||
\(695\) | −12759.2 | − | 7366.50i | −0.696377 | − | 0.402054i | ||||
\(696\) | 2310.15 | + | 2021.98i | 0.125813 | + | 0.110119i | ||||
\(697\) | −3649.50 | − | 6321.12i | −0.198328 | − | 0.343515i | ||||
\(698\) | −12217.1 | −0.662499 | ||||||||
\(699\) | −14064.8 | + | 16069.2i | −0.761056 | + | 0.869518i | ||||
\(700\) | 7799.98 | − | 7776.92i | 0.421160 | − | 0.419914i | ||||
\(701\) | 13815.7i | 0.744382i | 0.928156 | + | 0.372191i | \(0.121393\pi\) | ||||
−0.928156 | + | 0.372191i | \(0.878607\pi\) | |||||||
\(702\) | −39605.5 | − | 2480.13i | −2.12936 | − | 0.133343i | ||||
\(703\) | −21796.4 | − | 12584.2i | −1.16937 | − | 0.675136i | ||||
\(704\) | − | 4420.39i | − | 0.236647i | ||||||
\(705\) | 543.544 | − | 2746.50i | 0.0290370 | − | 0.146722i | ||||
\(706\) | 34816.9 | + | 20101.5i | 1.85602 | + | 1.07157i | ||||
\(707\) | −7351.05 | − | 27597.9i | −0.391039 | − | 1.46807i | ||||
\(708\) | −4126.36 | + | 20850.3i | −0.219037 | + | 1.10678i | ||||
\(709\) | −67.3023 | + | 116.571i | −0.00356501 | + | 0.00617477i | −0.867802 | − | 0.496909i | \(-0.834468\pi\) |
0.864237 | + | 0.503084i | \(0.167801\pi\) | |||||||
\(710\) | −1452.84 | + | 2516.39i | −0.0767945 | + | 0.133012i | ||||
\(711\) | 2847.42 | + | 21308.7i | 0.150192 | + | 1.12396i | ||||
\(712\) | 2099.16 | − | 1211.95i | 0.110491 | − | 0.0637919i | ||||
\(713\) | −844.149 | − | 1462.11i | −0.0443389 | − | 0.0767972i | ||||
\(714\) | 8103.92 | + | 4001.56i | 0.424764 | + | 0.209740i | ||||
\(715\) | 1879.37 | − | 3255.16i | 0.0982999 | − | 0.170260i | ||||
\(716\) | − | 25518.5i | − | 1.33194i | ||||||
\(717\) | −12258.5 | − | 2426.00i | −0.638494 | − | 0.126361i | ||||
\(718\) | −16337.8 | −0.849192 | ||||||||
\(719\) | −279.689 | − | 484.435i | −0.0145071 | − | 0.0251271i | 0.858681 | − | 0.512511i | \(-0.171285\pi\) |
−0.873188 | + | 0.487384i | \(0.837951\pi\) | |||||||
\(720\) | 1532.45 | + | 11468.1i | 0.0793209 | + | 0.593599i | ||||
\(721\) | 7485.38 | − | 1993.83i | 0.386644 | − | 0.102988i | ||||
\(722\) | 10778.4 | − | 6222.89i | 0.555580 | − | 0.320764i | ||||
\(723\) | −1216.67 | − | 3572.81i | −0.0625844 | − | 0.183782i | ||||
\(724\) | 2461.92 | − | 1421.39i | 0.126376 | − | 0.0729633i | ||||
\(725\) | −9618.23 | + | 5553.09i | −0.492706 | + | 0.284464i | ||||
\(726\) | 26788.5 | + | 5301.56i | 1.36944 | + | 0.271018i | ||||
\(727\) | −6529.04 | + | 3769.54i | −0.333079 | + | 0.192303i | −0.657207 | − | 0.753710i | \(-0.728262\pi\) |
0.324128 | + | 0.946013i | \(0.394929\pi\) | |||||||
\(728\) | 4393.40 | + | 1184.18i | 0.223668 | + | 0.0602868i | ||||
\(729\) | −7638.09 | − | 18140.6i | −0.388055 | − | 0.921636i | ||||
\(730\) | 15920.0 | + | 27574.2i | 0.807157 | + | 1.39804i | ||||
\(731\) | 7166.11 | 0.362583 | ||||||||
\(732\) | 9840.19 | + | 28896.1i | 0.496863 | + | 1.45906i | ||||
\(733\) | 34171.1i | 1.72188i | 0.508708 | + | 0.860939i | \(0.330123\pi\) | ||||
−0.508708 | + | 0.860939i | \(0.669877\pi\) | |||||||
\(734\) | 7257.90 | − | 12571.0i | 0.364978 | − | 0.632161i | ||||
\(735\) | 8965.25 | − | 10181.9i | 0.449916 | − | 0.510975i | ||||
\(736\) | 15903.7 | + | 27545.9i | 0.796490 | + | 1.37956i | ||||
\(737\) | −4460.23 | + | 2575.11i | −0.222923 | + | 0.128705i | ||||
\(738\) | 13482.2 | − | 32728.4i | 0.672476 | − | 1.63245i | ||||
\(739\) | −5524.56 | + | 9568.82i | −0.274999 | + | 0.476312i | −0.970135 | − | 0.242566i | \(-0.922011\pi\) |
0.695136 | + | 0.718878i | \(0.255344\pi\) | |||||||
\(740\) | 8542.53 | − | 14796.1i | 0.424364 | − | 0.735021i | ||||
\(741\) | 33686.7 | − | 11471.6i | 1.67006 | − | 0.568715i | ||||
\(742\) | −15834.3 | + | 15787.4i | −0.783415 | + | 0.781098i | ||||
\(743\) | −5588.14 | − | 3226.32i | −0.275921 | − | 0.159303i | 0.355655 | − | 0.934617i | \(-0.384258\pi\) |
−0.631575 | + | 0.775315i | \(0.717591\pi\) | |||||||
\(744\) | −192.323 | − | 168.333i | −0.00947702 | − | 0.00829487i | ||||
\(745\) | 18481.1i | 0.908854i | ||||||||
\(746\) | 16809.3 | + | 9704.87i | 0.824977 | + | 0.476301i | ||||
\(747\) | 534.640 | + | 220.241i | 0.0261867 | + | 0.0107874i | ||||
\(748\) | − | 1454.10i | − | 0.0710791i | ||||||
\(749\) | 20667.8 | + | 20729.1i | 1.00826 | + | 1.01125i | ||||
\(750\) | 30605.9 | + | 6057.03i | 1.49009 | + | 0.294895i | ||||
\(751\) | −1687.78 | −0.0820081 | −0.0410041 | − | 0.999159i | \(-0.513056\pi\) | ||||
−0.0410041 | + | 0.999159i | \(0.513056\pi\) | |||||||
\(752\) | 1992.53 | + | 3451.16i | 0.0966224 | + | 0.167355i | ||||
\(753\) | −2606.88 | + | 887.737i | −0.126162 | + | 0.0429627i | ||||
\(754\) | −40568.6 | − | 23422.3i | −1.95945 | − | 1.13129i | ||||
\(755\) | 10629.0 | 0.512355 | ||||||||
\(756\) | 4527.87 | + | 22594.3i | 0.217827 | + | 1.08696i | ||||
\(757\) | 10839.9 | 0.520453 | 0.260226 | − | 0.965548i | \(-0.416203\pi\) | ||||
0.260226 | + | 0.965548i | \(0.416203\pi\) | |||||||
\(758\) | 18437.5 | + | 10644.9i | 0.883485 | + | 0.510080i | ||||
\(759\) | 4318.65 | − | 1470.66i | 0.206531 | − | 0.0703314i | ||||
\(760\) | 1350.22 | + | 2338.65i | 0.0644443 | + | 0.111621i | ||||
\(761\) | 9058.83 | 0.431514 | 0.215757 | − | 0.976447i | \(-0.430778\pi\) | ||||
0.215757 | + | 0.976447i | \(0.430778\pi\) | |||||||
\(762\) | 10945.6 | + | 2166.19i | 0.520366 | + | 0.102982i | ||||
\(763\) | 8387.86 | + | 2260.84i | 0.397983 | + | 0.107271i | ||||
\(764\) | 8381.38i | 0.396895i | ||||||||
\(765\) | 622.456 | + | 4658.16i | 0.0294182 | + | 0.220152i | ||||
\(766\) | 24522.6 | + | 14158.2i | 1.15671 | + | 0.667826i | ||||
\(767\) | − | 31764.1i | − | 1.49535i | ||||||
\(768\) | −11993.9 | − | 10497.8i | −0.563532 | − | 0.493238i | ||||
\(769\) | 10991.2 | + | 6345.79i | 0.515415 | + | 0.297575i | 0.735057 | − | 0.678006i | \(-0.237156\pi\) |
−0.219642 | + | 0.975581i | \(0.570489\pi\) | |||||||
\(770\) | −4008.48 | − | 1080.43i | −0.187605 | − | 0.0505665i | ||||
\(771\) | 9585.98 | − | 3264.38i | 0.447770 | − | 0.152482i | ||||
\(772\) | 3488.77 | − | 6042.73i | 0.162647 | − | 0.281713i | ||||
\(773\) | 10423.9 | − | 18054.8i | 0.485023 | − | 0.840085i | −0.514829 | − | 0.857293i | \(-0.672145\pi\) |
0.999852 | + | 0.0172084i | \(0.00547788\pi\) | |||||||
\(774\) | 21209.2 | + | 27529.6i | 0.984948 | + | 1.27847i | ||||
\(775\) | 800.730 | − | 462.302i | 0.0371136 | − | 0.0214276i | ||||
\(776\) | −2026.88 | − | 3510.66i | −0.0937639 | − | 0.162404i | ||||
\(777\) | −10783.4 | + | 21838.5i | −0.497880 | + | 1.00830i | ||||
\(778\) | −5779.09 | + | 10009.7i | −0.266312 | + | 0.461265i | ||||
\(779\) | 31742.5i | 1.45994i | ||||||||
\(780\) | 7787.25 | + | 22867.6i | 0.357472 | + | 1.04973i | ||||
\(781\) | −666.427 | −0.0305335 | ||||||||
\(782\) | 5750.06 | + | 9959.40i | 0.262943 | + | 0.455431i | ||||
\(783\) | 1452.16 | − | 23189.8i | 0.0662785 | − | 1.05841i | ||||
\(784\) | −57.1881 | + | 19309.7i | −0.00260514 | + | 0.879631i | ||||
\(785\) | 4834.71 | − | 2791.32i | 0.219819 | − | 0.126913i | ||||
\(786\) | 53633.6 | + | 10614.3i | 2.43390 | + | 0.481679i | ||||
\(787\) | 4472.89 | − | 2582.42i | 0.202594 | − | 0.116968i | −0.395271 | − | 0.918565i | \(-0.629349\pi\) |
0.597865 | + | 0.801597i | \(0.296016\pi\) | |||||||
\(788\) | −38768.5 | + | 22383.0i | −1.75263 | + | 1.01188i | ||||
\(789\) | 849.043 | + | 2493.25i | 0.0383102 | + | 0.112499i | ||||
\(790\) | 21557.3 | − | 12446.1i | 0.970855 | − | 0.560524i | ||||
\(791\) | 9649.14 | − | 35799.0i | 0.433734 | − | 1.60918i | ||||
\(792\) | 547.116 | − | 421.506i | 0.0245466 | − | 0.0189111i | ||||
\(793\) | −22809.6 | − | 39507.3i | −1.02143 | − | 1.76916i | ||||
\(794\) | −24890.4 | −1.11250 | ||||||||
\(795\) | −11405.4 | − | 2257.18i | −0.508817 | − | 0.100697i | ||||
\(796\) | 10776.2i | 0.479838i | ||||||||
\(797\) | −3686.20 | + | 6384.68i | −0.163829 | + | 0.283760i | −0.936239 | − | 0.351364i | \(-0.885718\pi\) |
0.772410 | + | 0.635125i | \(0.219051\pi\) | |||||||
\(798\) | −21820.2 | − | 32692.3i | −0.967951 | − | 1.45024i | ||||
\(799\) | 809.332 | + | 1401.80i | 0.0358349 | + | 0.0620679i | ||||
\(800\) | −15085.7 | + | 8709.70i | −0.666698 | + | 0.384918i | ||||
\(801\) | −16962.1 | − | 6987.40i | −0.748223 | − | 0.308224i | ||||
\(802\) | 24774.7 | − | 42911.1i | 1.09081 | − | 1.88933i | ||||
\(803\) | −3651.30 | + | 6324.24i | −0.160463 | + | 0.277930i | ||||
\(804\) | 6426.02 | − | 32470.4i | 0.281876 | − | 1.42431i | ||||
\(805\) | 16680.5 | − | 4443.07i | 0.730324 | − | 0.194531i | ||||
\(806\) | 3377.39 | + | 1949.94i | 0.147597 | + | 0.0852154i | ||||
\(807\) | 7770.98 | − | 39266.4i | 0.338973 | − | 1.71282i | ||||
\(808\) | − | 5501.45i | − | 0.239530i | ||||||
\(809\) | −15808.7 | − | 9127.15i | −0.687026 | − | 0.396655i | 0.115471 | − | 0.993311i | \(-0.463162\pi\) |
−0.802497 | + | 0.596656i | \(0.796496\pi\) | |||||||
\(810\) | −16052.7 | + | 16177.8i | −0.696340 | + | 0.701766i | ||||
\(811\) | − | 32302.9i | − | 1.39865i | −0.714802 | − | 0.699327i | \(-0.753483\pi\) | ||
0.714802 | − | 0.699327i | \(-0.246517\pi\) | |||||||
\(812\) | −7079.33 | + | 26264.8i | −0.305955 | + | 1.13511i | ||||
\(813\) | −18121.1 | + | 20703.7i | −0.781717 | + | 0.893124i | ||||
\(814\) | 7453.25 | 0.320929 | ||||||||
\(815\) | 11453.3 | + | 19837.7i | 0.492259 | + | 0.852618i | ||||
\(816\) | −5033.43 | − | 4405.57i | −0.215938 | − | 0.189002i | ||||
\(817\) | −26989.3 | − | 15582.3i | −1.15573 | − | 0.667264i | ||||
\(818\) | 1386.20 | 0.0592510 | ||||||||
\(819\) | −13193.2 | − | 31810.0i | −0.562893 | − | 1.35718i | ||||
\(820\) | −21547.8 | −0.917661 | ||||||||
\(821\) | 15044.6 | + | 8686.02i | 0.639538 | + | 0.369238i | 0.784437 | − | 0.620209i | \(-0.212952\pi\) |
−0.144898 | + | 0.989447i | \(0.546286\pi\) | |||||||
\(822\) | −5.08927 | + | 25.7158i | −0.000215947 | + | 0.00109117i | ||||
\(823\) | 6448.43 | + | 11169.0i | 0.273120 | + | 0.473058i | 0.969659 | − | 0.244461i | \(-0.0786109\pi\) |
−0.696539 | + | 0.717519i | \(0.745278\pi\) | |||||||
\(824\) | 1492.16 | 0.0630847 | ||||||||
\(825\) | 805.412 | + | 2365.13i | 0.0339889 | + | 0.0998098i | ||||
\(826\) | −33901.6 | + | 9030.11i | −1.42807 | + | 0.380385i | ||||
\(827\) | 34437.8i | 1.44803i | 0.689785 | + | 0.724014i | \(0.257705\pi\) | ||||
−0.689785 | + | 0.724014i | \(0.742295\pi\) | |||||||
\(828\) | −11168.0 | + | 27110.7i | −0.468739 | + | 1.13788i | ||||
\(829\) | −37770.2 | − | 21806.6i | −1.58240 | − | 0.913601i | −0.994508 | − | 0.104664i | \(-0.966623\pi\) |
−0.587896 | − | 0.808937i | \(-0.700043\pi\) | |||||||
\(830\) | − | 669.519i | − | 0.0279992i | ||||||
\(831\) | 20742.3 | − | 7063.52i | 0.865876 | − | 0.294863i | ||||
\(832\) | −36768.6 | − | 21228.3i | −1.53212 | − | 0.884568i | ||||
\(833\) | −23.2289 | + | 7843.27i | −0.000966185 | + | 0.326234i | ||||
\(834\) | 31082.7 | + | 27205.5i | 1.29053 | + | 1.12955i | ||||
\(835\) | −305.761 | + | 529.594i | −0.0126722 | + | 0.0219489i | ||||
\(836\) | −3161.85 | + | 5476.49i | −0.130807 | + | 0.226565i | ||||
\(837\) | −120.895 | + | 1930.58i | −0.00499250 | + | 0.0797258i | ||||
\(838\) | 29125.6 | − | 16815.7i | 1.20063 | − | 0.693183i | ||||
\(839\) | −15073.9 | − | 26108.8i | −0.620274 | − | 1.07435i | −0.989434 | − | 0.144981i | \(-0.953688\pi\) |
0.369160 | − | 0.929366i | \(-0.379645\pi\) | |||||||
\(840\) | 2173.58 | − | 1450.74i | 0.0892805 | − | 0.0595894i | ||||
\(841\) | 1519.71 | − | 2632.21i | 0.0623112 | − | 0.107926i | ||||
\(842\) | 7870.64i | 0.322138i | ||||||||
\(843\) | −28074.3 | + | 32075.4i | −1.14701 | + | 1.31048i | ||||
\(844\) | 5542.27 | 0.226034 | ||||||||
\(845\) | −9689.27 | − | 16782.3i | −0.394463 | − | 0.683230i | ||||
\(846\) | −2989.89 | + | 7258.03i | −0.121506 | + | 0.294960i | ||||
\(847\) | 6099.67 | + | 22899.9i | 0.247446 | + | 0.928983i | ||||
\(848\) | 14331.7 | − | 8274.40i | 0.580368 | − | 0.335076i | ||||
\(849\) | 5369.62 | − | 6134.87i | 0.217061 | − | 0.247996i | ||||
\(850\) | −5454.30 | + | 3149.04i | −0.220095 | + | 0.127072i | ||||
\(851\) | −26838.6 | + | 15495.3i | −1.08110 | + | 0.624174i | ||||
\(852\) | 2820.91 | − | 3222.93i | 0.113430 | − | 0.129596i | ||||
\(853\) | −23967.5 | + | 13837.6i | −0.962053 | + | 0.555441i | −0.896804 | − | 0.442428i | \(-0.854117\pi\) |
−0.0652484 | + | 0.997869i | \(0.520784\pi\) | |||||||
\(854\) | −35681.4 | + | 35575.8i | −1.42973 | + | 1.42550i | ||||
\(855\) | 7784.57 | − | 18897.2i | 0.311376 | − | 0.755874i | ||||
\(856\) | 2819.28 | + | 4883.14i | 0.112571 | + | 0.194979i | ||||
\(857\) | 16486.5 | 0.657140 | 0.328570 | − | 0.944480i | \(-0.393433\pi\) | ||||
0.328570 | + | 0.944480i | \(0.393433\pi\) | |||||||
\(858\) | −6940.76 | + | 7929.93i | −0.276170 | + | 0.315528i | ||||
\(859\) | − | 20081.3i | − | 0.797633i | −0.917031 | − | 0.398817i | \(-0.869421\pi\) | ||
0.917031 | − | 0.398817i | \(-0.130579\pi\) | |||||||
\(860\) | 10577.7 | − | 18321.2i | 0.419416 | − | 0.726450i | ||||
\(861\) | 30652.9 | − | 1993.38i | 1.21330 | − | 0.0789014i | ||||
\(862\) | −20404.2 | − | 35341.0i | −0.806228 | − | 1.39643i | ||||
\(863\) | 23674.1 | − | 13668.3i | 0.933808 | − | 0.539134i | 0.0457940 | − | 0.998951i | \(-0.485418\pi\) |
0.888014 | + | 0.459817i | \(0.152085\pi\) | |||||||
\(864\) | 2277.64 | − | 36371.8i | 0.0896838 | − | 1.43217i | ||||
\(865\) | 10453.8 | − | 18106.5i | 0.410913 | − | 0.711721i | ||||
\(866\) | −9345.81 | + | 16187.4i | −0.366725 | + | 0.635186i | ||||
\(867\) | 17165.3 | + | 15024.1i | 0.672393 | + | 0.588520i | ||||
\(868\) | 589.363 | − | 2186.58i | 0.0230464 | − | 0.0855038i | ||||
\(869\) | 4944.25 | + | 2854.56i | 0.193006 | + | 0.111432i | ||||
\(870\) | −25467.5 | + | 8672.60i | −0.992445 | + | 0.337964i | ||||
\(871\) | 49466.6i | 1.92435i | ||||||||
\(872\) | 1449.20 | + | 836.694i | 0.0562798 | + | 0.0324932i | ||||
\(873\) | −11685.8 | + | 28367.6i | −0.453040 | + | 1.09977i | ||||
\(874\) | − | 50012.6i | − | 1.93559i | ||||||
\(875\) | 6968.87 | + | 26163.1i | 0.269246 | + | 1.01083i | ||||
\(876\) | −15129.3 | − | 44427.9i | −0.583530 | − | 1.71356i | ||||
\(877\) | −43336.3 | −1.66860 | −0.834300 | − | 0.551310i | \(-0.814128\pi\) | ||||
−0.834300 | + | 0.551310i | \(0.814128\pi\) | |||||||
\(878\) | −15233.4 | − | 26385.0i | −0.585538 | − | 1.01418i | ||||
\(879\) | 458.027 | − | 2314.39i | 0.0175755 | − | 0.0888082i | ||||
\(880\) | 2660.94 | + | 1536.30i | 0.101932 | + | 0.0588506i | ||||
\(881\) | −48.3703 | −0.00184976 | −0.000924878 | − | 1.00000i | \(-0.500294\pi\) | ||||
−0.000924878 | 1.00000i | \(0.500294\pi\) | ||||||||
\(882\) | −30199.8 | + | 23124.2i | −1.15293 | + | 0.882802i | ||||
\(883\) | 36776.7 | 1.40162 | 0.700812 | − | 0.713346i | \(-0.252821\pi\) | ||||
0.700812 | + | 0.713346i | \(0.252821\pi\) | |||||||
\(884\) | −12095.1 | − | 6983.13i | −0.460185 | − | 0.265688i | ||||
\(885\) | −13727.2 | − | 12014.9i | −0.521396 | − | 0.456358i | ||||
\(886\) | −12993.7 | − | 22505.8i | −0.492700 | − | 0.853382i | ||||
\(887\) | 27950.3 | 1.05804 | 0.529019 | − | 0.848610i | \(-0.322560\pi\) | ||||
0.529019 | + | 0.848610i | \(0.322560\pi\) | |||||||
\(888\) | −3089.94 | + | 3530.30i | −0.116770 | + | 0.133411i | ||||
\(889\) | 2492.29 | + | 9356.75i | 0.0940255 | + | 0.352998i | ||||
\(890\) | 21241.3i | 0.800011i | ||||||||
\(891\) | −5054.21 | − | 1333.27i | −0.190036 | − | 0.0501304i | ||||
\(892\) | 20357.8 | + | 11753.6i | 0.764159 | + | 0.441188i | ||||
\(893\) | − | 7039.37i | − | 0.263789i | ||||||
\(894\) | 10059.4 | − | 50829.8i | 0.376328 | − | 1.90157i | ||||
\(895\) | 18967.9 | + | 10951.1i | 0.708410 | + | 0.409001i | ||||
\(896\) | −2187.97 | + | 8117.53i | −0.0815793 | + | 0.302665i | ||||
\(897\) | 8506.90 | − | 42985.0i | 0.316652 | − | 1.60003i | ||||
\(898\) | 29564.0 | − | 51206.3i | 1.09862 | − | 1.90287i | ||||
\(899\) | −1141.73 | + | 1977.53i | −0.0423567 | + | 0.0733640i | ||||
\(900\) | −14847.3 | − | 6116.22i | −0.549899 | − | 0.226527i | ||||
\(901\) | 5821.30 | − | 3360.93i | 0.215245 | − | 0.124272i | ||||
\(902\) | −4700.04 | − | 8140.71i | −0.173497 | − | 0.300506i | ||||
\(903\) | −13352.5 | + | 27041.4i | −0.492075 | + | 0.996545i | ||||
\(904\) | 3570.97 | − | 6185.09i | 0.131381 | − | 0.227559i | ||||
\(905\) | 2439.92i | 0.0896196i | ||||||||
\(906\) | −29233.5 | − | 5785.43i | −1.07199 | − | 0.212150i | ||||
\(907\) | 21610.8 | 0.791153 | 0.395576 | − | 0.918433i | \(-0.370545\pi\) | ||||
0.395576 | + | 0.918433i | \(0.370545\pi\) | |||||||
\(908\) | 3626.25 | + | 6280.85i | 0.132535 | + | 0.229557i | ||||
\(909\) | −32983.4 | + | 25410.9i | −1.20351 | + | 0.927202i | ||||
\(910\) | −28237.2 | + | 28153.7i | −1.02863 | + | 1.02559i | ||||
\(911\) | −5927.13 | + | 3422.03i | −0.215560 | + | 0.124453i | −0.603892 | − | 0.797066i | \(-0.706384\pi\) |
0.388333 | + | 0.921519i | \(0.373051\pi\) | |||||||
\(912\) | 9377.46 | + | 27537.3i | 0.340481 | + | 0.999837i | ||||
\(913\) | 132.984 | − | 76.7782i | 0.00482050 | − | 0.00278312i | ||||
\(914\) | −18308.1 | + | 10570.2i | −0.662559 | + | 0.382528i | ||||
\(915\) | −25701.3 | − | 5086.40i | −0.928590 | − | 0.183772i | ||||
\(916\) | 5399.19 | − | 3117.22i | 0.194753 | − | 0.112441i | ||||
\(917\) | 12212.2 | + | 45848.0i | 0.439785 | + | 1.65107i | ||||
\(918\) | 823.493 | − | 13150.4i | 0.0296071 | − | 0.472799i | ||||
\(919\) | 14558.6 | + | 25216.3i | 0.522573 | + | 0.905124i | 0.999655 | + | 0.0262648i | \(0.00836130\pi\) |
−0.477082 | + | 0.878859i | \(0.658305\pi\) | |||||||
\(920\) | 3325.14 | 0.119159 | ||||||||
\(921\) | 124.291 | + | 364.985i | 0.00444682 | + | 0.0130583i | ||||
\(922\) | 3668.65i | 0.131042i | ||||||||
\(923\) | −3200.43 | + | 5543.31i | −0.114132 | + | 0.197682i | ||||
\(924\) | 5487.06 | + | 2709.40i | 0.195358 | + | 0.0964640i | ||||
\(925\) | −8486.06 | − | 14698.3i | −0.301643 | − | 0.522461i | ||||
\(926\) | 39271.4 | − | 22673.3i | 1.39367 | − | 0.804635i | ||||
\(927\) | −6892.21 | − | 8946.10i | −0.244196 | − | 0.316967i | ||||
\(928\) | 21510.0 | − | 37256.4i | 0.760883 | − | 1.31789i | ||||
\(929\) | −11238.9 | + | 19466.3i | −0.396917 | + | 0.687480i | −0.993344 | − | 0.115187i | \(-0.963253\pi\) |
0.596427 | + | 0.802667i | \(0.296587\pi\) | |||||||
\(930\) | 2120.20 | − | 722.005i | 0.0747570 | − | 0.0254575i | ||||
\(931\) | 17142.2 | − | 29489.1i | 0.603451 | − | 1.03810i | ||||
\(932\) | −31564.9 | − | 18224.0i | −1.10938 | − | 0.640501i | ||||
\(933\) | 25125.3 | + | 21991.2i | 0.881635 | + | 0.771661i | ||||
\(934\) | 40251.5i | 1.41014i | ||||||||
\(935\) | 1080.83 | + | 624.019i | 0.0378043 | + | 0.0218263i | ||||
\(936\) | −878.613 | − | 6575.12i | −0.0306820 | − | 0.229609i | ||||
\(937\) | 25912.1i | 0.903426i | 0.892163 | + | 0.451713i | \(0.149187\pi\) | ||||
−0.892163 | + | 0.451713i | \(0.850813\pi\) | |||||||
\(938\) | 52795.3 | − | 14062.7i | 1.83777 | − | 0.489513i | ||||
\(939\) | 39323.8 | + | 7782.34i | 1.36665 | + | 0.270466i | ||||
\(940\) | 4778.55 | 0.165808 | ||||||||
\(941\) | −19906.3 | − | 34478.8i | −0.689615 | − | 1.19445i | −0.971962 | − | 0.235136i | \(-0.924446\pi\) |
0.282347 | − | 0.959312i | \(-0.408887\pi\) | |||||||
\(942\) | −14816.5 | + | 5045.57i | −0.512472 | + | 0.174516i | ||||
\(943\) | 33849.1 | + | 19542.8i | 1.16891 | + | 0.674868i | ||||
\(944\) | 25965.7 | 0.895246 | ||||||||
\(945\) | −18737.4 | − | 6330.64i | −0.645004 | − | 0.217921i | ||||
\(946\) | 9228.94 | 0.317187 | ||||||||
\(947\) | −32618.1 | − | 18832.1i | −1.11927 | − | 0.646209i | −0.178053 | − | 0.984021i | \(-0.556980\pi\) |
−0.941213 | + | 0.337812i | \(0.890313\pi\) | |||||||
\(948\) | −34733.5 | + | 11828.0i | −1.18997 | + | 0.405228i | ||||
\(949\) | 35069.8 | + | 60742.7i | 1.19959 | + | 2.07776i | ||||
\(950\) | 27389.6 | 0.935407 | ||||||||
\(951\) | −1560.06 | − | 308.742i | −0.0531950 | − | 0.0105275i | ||||
\(952\) | −393.192 | + | 1458.77i | −0.0133860 | + | 0.0496628i | ||||
\(953\) | 18055.8i | 0.613730i | 0.951753 | + | 0.306865i | \(0.0992801\pi\) | ||||
−0.951753 | + | 0.306865i | \(0.900720\pi\) | |||||||
\(954\) | 30140.5 | + | 12416.1i | 1.02289 | + | 0.421371i | ||||
\(955\) | −6229.88 | − | 3596.82i | −0.211093 | − | 0.121875i | ||||
\(956\) | − | 21328.1i | − | 0.721548i | ||||||
\(957\) | −4643.12 | − | 4063.95i | −0.156835 | − | 0.137271i | ||||
\(958\) | 493.233 | + | 284.768i | 0.0166343 | + | 0.00960381i | ||||
\(959\) | −21.9829 | + | 5.85541i | −0.000740212 | + | 0.000197165i | ||||
\(960\) | −23081.9 | + | 7860.24i | −0.776006 | + | 0.264258i | ||||
\(961\) | −14800.4 | + | 25635.1i | −0.496809 | + | 0.860499i | ||||
\(962\) | 35793.3 | − | 61995.8i | 1.19961 | − | 2.07778i | ||||
\(963\) | 16254.3 | − | 39457.8i | 0.543913 | − | 1.32036i | ||||
\(964\) | 5578.78 | − | 3220.91i | 0.186391 | − | 0.107613i | ||||
\(965\) | 2994.37 | + | 5186.41i | 0.0998884 | + | 0.173012i | ||||
\(966\) | −48295.9 | + | 3140.71i | −1.60859 | + | 0.104607i | ||||
\(967\) | −15995.7 | + | 27705.3i | −0.531940 | + | 0.921348i | 0.467364 | + | 0.884065i | \(0.345204\pi\) |
−0.999305 | + | 0.0372829i | \(0.988130\pi\) | |||||||
\(968\) | 4564.92i | 0.151572i | ||||||||
\(969\) | 3808.97 | + | 11185.2i | 0.126276 | + | 0.370816i | ||||
\(970\) | 35524.1 | 1.17589 | ||||||||
\(971\) | 13431.5 | + | 23264.0i | 0.443910 | + | 0.768874i | 0.997976 | − | 0.0635987i | \(-0.0202578\pi\) |
−0.554066 | + | 0.832473i | \(0.686924\pi\) | |||||||
\(972\) | 27841.7 | − | 18799.2i | 0.918749 | − | 0.620356i | ||||
\(973\) | −9329.07 | + | 34611.5i | −0.307376 | + | 1.14038i | ||||
\(974\) | −65079.7 | + | 37573.8i | −2.14095 | + | 1.23608i | ||||
\(975\) | 23540.9 | + | 4658.84i | 0.773243 | + | 0.153028i | ||||
\(976\) | 32295.4 | − | 18645.8i | 1.05917 | − | 0.611513i | ||||
\(977\) | 25359.6 | − | 14641.4i | 0.830427 | − | 0.479447i | −0.0235720 | − | 0.999722i | \(-0.507504\pi\) |
0.853999 | + | 0.520275i | \(0.174171\pi\) | |||||||
\(978\) | −20702.9 | − | 60794.9i | −0.676897 | − | 1.98774i | ||||
\(979\) | −4219.07 | + | 2435.88i | −0.137734 | + | 0.0795210i | ||||
\(980\) | 20018.2 | + | 11636.7i | 0.652507 | + | 0.379306i | ||||
\(981\) | −1677.44 | − | 12553.2i | −0.0545940 | − | 0.408555i | ||||
\(982\) | 12086.4 | + | 20934.2i | 0.392761 | + | 0.680283i | ||||
\(983\) | 1993.91 | 0.0646958 | 0.0323479 | − | 0.999477i | \(-0.489702\pi\) | ||||
0.0323479 | + | 0.999477i | \(0.489702\pi\) | |||||||
\(984\) | 5804.45 | + | 1148.72i | 0.188048 | + | 0.0372154i | ||||
\(985\) | − | 38422.2i | − | 1.24288i | ||||||
\(986\) | 7777.05 | − | 13470.2i | 0.251188 | − | 0.435071i | ||||
\(987\) | −6797.74 | + | 442.061i | −0.219224 | + | 0.0142563i | ||||
\(988\) | 30368.8 | + | 52600.3i | 0.977894 | + | 1.69376i | ||||
\(989\) | −33232.8 | + | 19187.0i | −1.06849 | + | 0.616896i | ||||
\(990\) | 801.636 | + | 5999.05i | 0.0257350 | + | 0.192588i | ||||
\(991\) | −8752.81 | + | 15160.3i | −0.280567 | + | 0.485957i | −0.971525 | − | 0.236939i | \(-0.923856\pi\) |
0.690957 | + | 0.722896i | \(0.257189\pi\) | |||||||
\(992\) | −1790.73 | + | 3101.64i | −0.0573143 | + | 0.0992713i | ||||
\(993\) | 4135.08 | − | 20894.4i | 0.132148 | − | 0.667738i | ||||
\(994\) | 6826.17 | + | 1839.90i | 0.217820 | + | 0.0587105i | ||||
\(995\) | −8009.93 | − | 4624.53i | −0.255208 | − | 0.147344i | ||||
\(996\) | −191.595 | + | 968.120i | −0.00609529 | + | 0.0307992i | ||||
\(997\) | − | 30841.0i | − | 0.979684i | −0.871811 | − | 0.489842i | \(-0.837054\pi\) | ||
0.871811 | − | 0.489842i | \(-0.162946\pi\) | |||||||
\(998\) | 1901.96 | + | 1098.10i | 0.0603261 | + | 0.0348293i | ||||
\(999\) | 35437.9 | + | 2219.15i | 1.12233 | + | 0.0702812i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.4.s.a.59.19 | yes | 44 | |
3.2 | odd | 2 | 189.4.s.a.17.4 | 44 | |||
7.5 | odd | 6 | 63.4.i.a.5.4 | ✓ | 44 | ||
9.2 | odd | 6 | 63.4.i.a.38.19 | yes | 44 | ||
9.7 | even | 3 | 189.4.i.a.143.4 | 44 | |||
21.5 | even | 6 | 189.4.i.a.152.19 | 44 | |||
63.47 | even | 6 | inner | 63.4.s.a.47.19 | yes | 44 | |
63.61 | odd | 6 | 189.4.s.a.89.4 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.4 | ✓ | 44 | 7.5 | odd | 6 | ||
63.4.i.a.38.19 | yes | 44 | 9.2 | odd | 6 | ||
63.4.s.a.47.19 | yes | 44 | 63.47 | even | 6 | inner | |
63.4.s.a.59.19 | yes | 44 | 1.1 | even | 1 | trivial | |
189.4.i.a.143.4 | 44 | 9.7 | even | 3 | |||
189.4.i.a.152.19 | 44 | 21.5 | even | 6 | |||
189.4.s.a.17.4 | 44 | 3.2 | odd | 2 | |||
189.4.s.a.89.4 | 44 | 63.61 | odd | 6 |