Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [28,4,Mod(3,28)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(28, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("28.3");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 28 = 2^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 28.f (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: | \(1.65205348016\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 24 x^{17} + 28 x^{16} + 56 x^{15} - 192 x^{14} + 352 x^{13} - 448 x^{12} + \cdots + 1073741824 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.6 | ||
Root | \(2.19431 + 1.78465i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 28.19 |
Dual form | 28.4.f.a.3.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/28\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.448398 | − | 2.79266i | 0.158533 | − | 0.987354i | ||||
\(3\) | −2.11164 | − | 3.65747i | −0.406386 | − | 0.703881i | 0.588096 | − | 0.808791i | \(-0.299878\pi\) |
−0.994482 | + | 0.104910i | \(0.966544\pi\) | |||||||
\(4\) | −7.59788 | − | 2.50445i | −0.949735 | − | 0.313056i | ||||
\(5\) | 1.03358 | + | 0.596737i | 0.0924461 | + | 0.0533738i | 0.545510 | − | 0.838104i | \(-0.316336\pi\) |
−0.453064 | + | 0.891478i | \(0.649669\pi\) | |||||||
\(6\) | −11.1609 | + | 4.25709i | −0.759405 | + | 0.289658i | ||||
\(7\) | 16.7651 | − | 7.86959i | 0.905232 | − | 0.424918i | ||||
\(8\) | −10.4009 | + | 20.0953i | −0.459661 | + | 0.888095i | ||||
\(9\) | 4.58193 | − | 7.93614i | 0.169701 | − | 0.293931i | ||||
\(10\) | 2.12994 | − | 2.61886i | 0.0673546 | − | 0.0828155i | ||||
\(11\) | 29.6160 | − | 17.0988i | 0.811778 | − | 0.468680i | −0.0357948 | − | 0.999359i | \(-0.511396\pi\) |
0.847573 | + | 0.530679i | \(0.178063\pi\) | |||||||
\(12\) | 6.88406 | + | 33.0775i | 0.165605 | + | 0.795721i | ||||
\(13\) | 56.1127i | 1.19714i | 0.801069 | + | 0.598572i | \(0.204265\pi\) | ||||
−0.801069 | + | 0.598572i | \(0.795735\pi\) | |||||||
\(14\) | −14.4596 | − | 50.3480i | −0.276036 | − | 0.961147i | ||||
\(15\) | − | 5.04038i | − | 0.0867614i | ||||||
\(16\) | 51.4555 | + | 38.0570i | 0.803992 | + | 0.594640i | ||||
\(17\) | 19.4520 | − | 11.2306i | 0.277518 | − | 0.160225i | −0.354781 | − | 0.934949i | \(-0.615445\pi\) |
0.632299 | + | 0.774724i | \(0.282111\pi\) | |||||||
\(18\) | −20.1084 | − | 16.3543i | −0.263311 | − | 0.214153i | ||||
\(19\) | −53.4022 | + | 92.4953i | −0.644806 | + | 1.11684i | 0.339541 | + | 0.940591i | \(0.389728\pi\) |
−0.984346 | + | 0.176245i | \(0.943605\pi\) | |||||||
\(20\) | −6.35851 | − | 7.12248i | −0.0710903 | − | 0.0796317i | ||||
\(21\) | −64.1848 | − | 44.7002i | −0.666965 | − | 0.464495i | ||||
\(22\) | −34.4714 | − | 90.3744i | −0.334060 | − | 0.875813i | ||||
\(23\) | −51.2640 | − | 29.5973i | −0.464752 | − | 0.268325i | 0.249288 | − | 0.968429i | \(-0.419803\pi\) |
−0.714040 | + | 0.700105i | \(0.753137\pi\) | |||||||
\(24\) | 95.4610 | − | 4.39292i | 0.811912 | − | 0.0373625i | ||||
\(25\) | −61.7878 | − | 107.020i | −0.494302 | − | 0.856157i | ||||
\(26\) | 156.704 | + | 25.1609i | 1.18200 | + | 0.189786i | ||||
\(27\) | −152.730 | −1.08863 | ||||||||
\(28\) | −147.088 | + | 17.8049i | −0.992753 | + | 0.120172i | ||||
\(29\) | 211.906 | 1.35689 | 0.678447 | − | 0.734649i | \(-0.262653\pi\) | ||||
0.678447 | + | 0.734649i | \(0.262653\pi\) | |||||||
\(30\) | −14.0761 | − | 2.26010i | −0.0856642 | − | 0.0137545i | ||||
\(31\) | 54.1933 | + | 93.8656i | 0.313981 | + | 0.543831i | 0.979220 | − | 0.202799i | \(-0.0650039\pi\) |
−0.665239 | + | 0.746630i | \(0.731671\pi\) | |||||||
\(32\) | 129.353 | − | 126.633i | 0.714579 | − | 0.699555i | ||||
\(33\) | −125.077 | − | 72.2131i | −0.659790 | − | 0.380930i | ||||
\(34\) | −22.6411 | − | 59.3587i | −0.114203 | − | 0.299410i | ||||
\(35\) | 22.0242 | + | 1.87053i | 0.106365 | + | 0.00903362i | ||||
\(36\) | −54.6886 | + | 48.8226i | −0.253188 | + | 0.226031i | ||||
\(37\) | −81.0013 | + | 140.298i | −0.359906 | + | 0.623376i | −0.987945 | − | 0.154806i | \(-0.950525\pi\) |
0.628038 | + | 0.778182i | \(0.283858\pi\) | |||||||
\(38\) | 234.362 | + | 190.609i | 1.00049 | + | 0.813706i | ||||
\(39\) | 205.231 | − | 118.490i | 0.842646 | − | 0.486502i | ||||
\(40\) | −22.7418 | + | 14.5634i | −0.0898948 | + | 0.0575671i | ||||
\(41\) | 414.943i | 1.58056i | 0.612743 | + | 0.790282i | \(0.290066\pi\) | ||||
−0.612743 | + | 0.790282i | \(0.709934\pi\) | |||||||
\(42\) | −153.613 | + | 159.203i | −0.564356 | + | 0.584893i | ||||
\(43\) | 258.254i | 0.915892i | 0.888980 | + | 0.457946i | \(0.151415\pi\) | ||||
−0.888980 | + | 0.457946i | \(0.848585\pi\) | |||||||
\(44\) | −267.842 | + | 55.7430i | −0.917697 | + | 0.190990i | ||||
\(45\) | 9.47158 | − | 5.46842i | 0.0313765 | − | 0.0181152i | ||||
\(46\) | −105.642 | + | 129.892i | −0.338610 | + | 0.416336i | ||||
\(47\) | 304.267 | − | 527.006i | 0.944295 | − | 1.63557i | 0.187139 | − | 0.982333i | \(-0.440078\pi\) |
0.757156 | − | 0.653234i | \(-0.226588\pi\) | |||||||
\(48\) | 30.5366 | − | 268.560i | 0.0918247 | − | 0.807568i | ||||
\(49\) | 219.139 | − | 263.870i | 0.638889 | − | 0.769299i | ||||
\(50\) | −326.575 | + | 124.565i | −0.923693 | + | 0.352322i | ||||
\(51\) | −82.1515 | − | 47.4302i | −0.225559 | − | 0.130227i | ||||
\(52\) | 140.531 | − | 426.338i | 0.374773 | − | 1.13697i | ||||
\(53\) | −112.165 | − | 194.275i | −0.290698 | − | 0.503503i | 0.683277 | − | 0.730159i | \(-0.260554\pi\) |
−0.973975 | + | 0.226656i | \(0.927221\pi\) | |||||||
\(54\) | −68.4840 | + | 426.524i | −0.172583 | + | 1.07486i | ||||
\(55\) | 40.8140 | 0.100061 | ||||||||
\(56\) | −16.2313 | + | 418.751i | −0.0387321 | + | 0.999250i | ||||
\(57\) | 451.065 | 1.04816 | ||||||||
\(58\) | 95.0183 | − | 591.781i | 0.215112 | − | 1.33974i | ||||
\(59\) | −42.9260 | − | 74.3501i | −0.0947203 | − | 0.164060i | 0.814772 | − | 0.579782i | \(-0.196862\pi\) |
−0.909492 | + | 0.415722i | \(0.863529\pi\) | |||||||
\(60\) | −12.6234 | + | 38.2962i | −0.0271612 | + | 0.0824003i | ||||
\(61\) | −312.035 | − | 180.154i | −0.654951 | − | 0.378136i | 0.135399 | − | 0.990791i | \(-0.456768\pi\) |
−0.790351 | + | 0.612655i | \(0.790102\pi\) | |||||||
\(62\) | 286.435 | − | 109.254i | 0.586730 | − | 0.223795i | ||||
\(63\) | 14.3625 | − | 169.108i | 0.0287223 | − | 0.338185i | ||||
\(64\) | −295.641 | − | 418.020i | −0.577424 | − | 0.816445i | ||||
\(65\) | −33.4846 | + | 57.9969i | −0.0638961 | + | 0.110671i | ||||
\(66\) | −257.751 | + | 316.916i | −0.480711 | + | 0.591056i | ||||
\(67\) | −580.112 | + | 334.928i | −1.05779 | + | 0.610715i | −0.924820 | − | 0.380405i | \(-0.875785\pi\) |
−0.132970 | + | 0.991120i | \(0.542451\pi\) | |||||||
\(68\) | −175.921 | + | 36.6124i | −0.313728 | + | 0.0652928i | ||||
\(69\) | 249.996i | 0.436173i | ||||||||
\(70\) | 15.0993 | − | 60.6672i | 0.0257817 | − | 0.103587i | ||||
\(71\) | 133.439i | 0.223047i | 0.993762 | + | 0.111523i | \(0.0355730\pi\) | ||||
−0.993762 | + | 0.111523i | \(0.964427\pi\) | |||||||
\(72\) | 111.823 | + | 174.619i | 0.183034 | + | 0.285819i | ||||
\(73\) | −675.475 | + | 389.985i | −1.08299 | + | 0.625265i | −0.931702 | − | 0.363225i | \(-0.881676\pi\) |
−0.151289 | + | 0.988490i | \(0.548342\pi\) | |||||||
\(74\) | 355.485 | + | 289.119i | 0.558436 | + | 0.454181i | ||||
\(75\) | −260.947 | + | 451.974i | −0.401755 | + | 0.695860i | ||||
\(76\) | 637.393 | − | 569.025i | 0.962026 | − | 0.858838i | ||||
\(77\) | 361.955 | − | 519.730i | 0.535697 | − | 0.769204i | ||||
\(78\) | −238.877 | − | 626.270i | −0.346763 | − | 0.909117i | ||||
\(79\) | 729.310 | + | 421.067i | 1.03866 | + | 0.599668i | 0.919452 | − | 0.393202i | \(-0.128633\pi\) |
0.119203 | + | 0.992870i | \(0.461966\pi\) | |||||||
\(80\) | 30.4733 | + | 70.0403i | 0.0425878 | + | 0.0978843i | ||||
\(81\) | 198.800 | + | 344.331i | 0.272702 | + | 0.472333i | ||||
\(82\) | 1158.79 | + | 186.060i | 1.56058 | + | 0.250571i | ||||
\(83\) | −432.711 | −0.572243 | −0.286122 | − | 0.958193i | \(-0.592366\pi\) | ||||
−0.286122 | + | 0.958193i | \(0.592366\pi\) | |||||||
\(84\) | 375.719 | + | 500.374i | 0.488027 | + | 0.649944i | ||||
\(85\) | 26.8070 | 0.0342073 | ||||||||
\(86\) | 721.215 | + | 115.801i | 0.904309 | + | 0.145199i | ||||
\(87\) | −447.470 | − | 775.040i | −0.551423 | − | 0.955092i | ||||
\(88\) | 35.5712 | + | 772.986i | 0.0430898 | + | 0.936370i | ||||
\(89\) | −439.022 | − | 253.470i | −0.522879 | − | 0.301884i | 0.215233 | − | 0.976563i | \(-0.430949\pi\) |
−0.738112 | + | 0.674678i | \(0.764282\pi\) | |||||||
\(90\) | −11.0244 | − | 28.9029i | −0.0129119 | − | 0.0338515i | ||||
\(91\) | 441.584 | + | 940.737i | 0.508688 | + | 1.08369i | ||||
\(92\) | 315.373 | + | 353.265i | 0.357390 | + | 0.400330i | ||||
\(93\) | 228.874 | − | 396.421i | 0.255195 | − | 0.442010i | ||||
\(94\) | −1335.31 | − | 1086.02i | −1.46518 | − | 1.19164i | ||||
\(95\) | −110.391 | + | 63.7342i | −0.119220 | + | 0.0688315i | ||||
\(96\) | −736.303 | − | 205.700i | −0.782798 | − | 0.218689i | ||||
\(97\) | − | 372.919i | − | 0.390352i | −0.980768 | − | 0.195176i | \(-0.937472\pi\) | ||
0.980768 | − | 0.195176i | \(-0.0625278\pi\) | |||||||
\(98\) | −638.636 | − | 730.299i | −0.658285 | − | 0.752769i | ||||
\(99\) | − | 313.382i | − | 0.318143i | ||||||
\(100\) | 201.431 | + | 967.866i | 0.201431 | + | 0.967866i | ||||
\(101\) | −426.861 | + | 246.449i | −0.420538 | + | 0.242798i | −0.695307 | − | 0.718713i | \(-0.744732\pi\) |
0.274770 | + | 0.961510i | \(0.411398\pi\) | |||||||
\(102\) | −169.293 | + | 208.153i | −0.164338 | + | 0.202061i | ||||
\(103\) | 253.633 | − | 439.305i | 0.242633 | − | 0.420252i | −0.718831 | − | 0.695185i | \(-0.755322\pi\) |
0.961463 | + | 0.274933i | \(0.0886557\pi\) | |||||||
\(104\) | −1127.60 | − | 583.625i | −1.06318 | − | 0.550280i | ||||
\(105\) | −39.6658 | − | 84.5026i | −0.0368665 | − | 0.0785392i | ||||
\(106\) | −592.837 | + | 226.125i | −0.543221 | + | 0.207200i | ||||
\(107\) | −928.131 | − | 535.857i | −0.838559 | − | 0.484142i | 0.0182153 | − | 0.999834i | \(-0.494202\pi\) |
−0.856774 | + | 0.515692i | \(0.827535\pi\) | |||||||
\(108\) | 1160.43 | + | 382.505i | 1.03391 | + | 0.340801i | ||||
\(109\) | 398.763 | + | 690.678i | 0.350409 | + | 0.606926i | 0.986321 | − | 0.164835i | \(-0.0527093\pi\) |
−0.635912 | + | 0.771761i | \(0.719376\pi\) | |||||||
\(110\) | 18.3009 | − | 113.979i | 0.0158629 | − | 0.0987956i | ||||
\(111\) | 684.183 | 0.585043 | ||||||||
\(112\) | 1162.15 | + | 233.096i | 0.980473 | + | 0.196656i | ||||
\(113\) | 592.933 | 0.493615 | 0.246807 | − | 0.969065i | \(-0.420618\pi\) | ||||
0.246807 | + | 0.969065i | \(0.420618\pi\) | |||||||
\(114\) | 202.257 | − | 1259.67i | 0.166168 | − | 1.03490i | ||||
\(115\) | −35.3236 | − | 61.1823i | −0.0286430 | − | 0.0496111i | ||||
\(116\) | −1610.04 | − | 530.707i | −1.28869 | − | 0.424784i | ||||
\(117\) | 445.319 | + | 257.105i | 0.351878 | + | 0.203157i | ||||
\(118\) | −226.882 | + | 86.5393i | −0.177002 | + | 0.0675135i | ||||
\(119\) | 237.735 | − | 341.363i | 0.183136 | − | 0.262964i | ||||
\(120\) | 101.288 | + | 52.4247i | 0.0770523 | + | 0.0398808i | ||||
\(121\) | −80.7617 | + | 139.883i | −0.0606775 | + | 0.105096i | ||||
\(122\) | −643.024 | + | 790.627i | −0.477186 | + | 0.586722i | ||||
\(123\) | 1517.64 | − | 876.210i | 1.11253 | − | 0.642319i | ||||
\(124\) | −176.673 | − | 848.904i | −0.127949 | − | 0.614789i | ||||
\(125\) | − | 296.669i | − | 0.212279i | ||||||
\(126\) | −465.822 | − | 115.937i | −0.329355 | − | 0.0819724i | ||||
\(127\) | − | 510.787i | − | 0.356890i | −0.983950 | − | 0.178445i | \(-0.942893\pi\) | ||
0.983950 | − | 0.178445i | \(-0.0571066\pi\) | |||||||
\(128\) | −1299.95 | + | 638.185i | −0.897660 | + | 0.440688i | ||||
\(129\) | 944.556 | − | 545.340i | 0.644679 | − | 0.372205i | ||||
\(130\) | 146.951 | + | 119.517i | 0.0991421 | + | 0.0806331i | ||||
\(131\) | −314.812 | + | 545.270i | −0.209963 | + | 0.363667i | −0.951703 | − | 0.307021i | \(-0.900668\pi\) |
0.741739 | + | 0.670688i | \(0.234001\pi\) | |||||||
\(132\) | 769.464 | + | 861.915i | 0.507373 | + | 0.568334i | ||||
\(133\) | −167.394 | + | 1970.95i | −0.109135 | + | 1.28499i | ||||
\(134\) | 675.217 | + | 1770.23i | 0.435298 | + | 1.14123i | ||||
\(135\) | −157.859 | − | 91.1399i | −0.100639 | − | 0.0581042i | ||||
\(136\) | 23.3635 | + | 507.703i | 0.0147309 | + | 0.320112i | ||||
\(137\) | −491.951 | − | 852.084i | −0.306790 | − | 0.531375i | 0.670868 | − | 0.741576i | \(-0.265922\pi\) |
−0.977658 | + | 0.210201i | \(0.932588\pi\) | |||||||
\(138\) | 698.152 | + | 112.098i | 0.430657 | + | 0.0691477i | ||||
\(139\) | 1920.76 | 1.17206 | 0.586032 | − | 0.810288i | \(-0.300689\pi\) | ||||
0.586032 | + | 0.810288i | \(0.300689\pi\) | |||||||
\(140\) | −162.652 | − | 69.3704i | −0.0981902 | − | 0.0418776i | ||||
\(141\) | −2570.01 | −1.53499 | ||||||||
\(142\) | 372.650 | + | 59.8339i | 0.220226 | + | 0.0353602i | ||||
\(143\) | 959.461 | + | 1661.83i | 0.561078 | + | 0.971815i | ||||
\(144\) | 537.791 | − | 233.984i | 0.311222 | − | 0.135407i | ||||
\(145\) | 219.022 | + | 126.452i | 0.125440 | + | 0.0724226i | ||||
\(146\) | 786.214 | + | 2061.24i | 0.445668 | + | 1.16842i | ||||
\(147\) | −1427.84 | − | 244.297i | −0.801130 | − | 0.137070i | ||||
\(148\) | 966.808 | − | 863.107i | 0.536967 | − | 0.479371i | ||||
\(149\) | 44.5907 | − | 77.2334i | 0.0245169 | − | 0.0424645i | −0.853507 | − | 0.521082i | \(-0.825529\pi\) |
0.878024 | + | 0.478617i | \(0.158862\pi\) | |||||||
\(150\) | 1145.20 | + | 931.402i | 0.623369 | + | 0.506991i | ||||
\(151\) | −1878.47 | + | 1084.53i | −1.01237 | + | 0.584491i | −0.911884 | − | 0.410448i | \(-0.865372\pi\) |
−0.100484 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(152\) | −1303.29 | − | 2035.17i | −0.695464 | − | 1.08601i | ||||
\(153\) | − | 205.832i | − | 0.108762i | ||||||
\(154\) | −1289.13 | − | 1243.86i | −0.674551 | − | 0.650866i | ||||
\(155\) | 129.357i | 0.0670334i | ||||||||
\(156\) | −1856.07 | + | 386.283i | −0.952593 | + | 0.198253i | ||||
\(157\) | 2158.33 | − | 1246.11i | 1.09716 | − | 0.633444i | 0.161685 | − | 0.986842i | \(-0.448307\pi\) |
0.935473 | + | 0.353398i | \(0.114974\pi\) | |||||||
\(158\) | 1502.92 | − | 1847.91i | 0.756745 | − | 0.930453i | ||||
\(159\) | −473.703 | + | 820.477i | −0.236271 | + | 0.409233i | ||||
\(160\) | 209.263 | − | 53.6956i | 0.103398 | − | 0.0265313i | ||||
\(161\) | −1092.37 | − | 92.7754i | −0.534724 | − | 0.0454144i | ||||
\(162\) | 1050.74 | − | 400.782i | 0.509592 | − | 0.194373i | ||||
\(163\) | −998.625 | − | 576.557i | −0.479867 | − | 0.277051i | 0.240494 | − | 0.970651i | \(-0.422691\pi\) |
−0.720361 | + | 0.693599i | \(0.756024\pi\) | |||||||
\(164\) | 1039.20 | − | 3152.68i | 0.494805 | − | 1.50112i | ||||
\(165\) | −86.1845 | − | 149.276i | −0.0406634 | − | 0.0704310i | ||||
\(166\) | −194.027 | + | 1208.41i | −0.0907193 | + | 0.565007i | ||||
\(167\) | −3471.09 | −1.60839 | −0.804194 | − | 0.594367i | \(-0.797403\pi\) | ||||
−0.804194 | + | 0.594367i | \(0.797403\pi\) | |||||||
\(168\) | 1565.85 | − | 824.887i | 0.719093 | − | 0.378818i | ||||
\(169\) | −951.638 | −0.433153 | ||||||||
\(170\) | 12.0202 | − | 74.8627i | 0.00542298 | − | 0.0337747i | ||||
\(171\) | 489.371 | + | 847.615i | 0.218849 | + | 0.379057i | ||||
\(172\) | 646.783 | − | 1962.18i | 0.286725 | − | 0.869854i | ||||
\(173\) | 2483.27 | + | 1433.72i | 1.09133 | + | 0.630079i | 0.933930 | − | 0.357456i | \(-0.116356\pi\) |
0.157399 | + | 0.987535i | \(0.449689\pi\) | |||||||
\(174\) | −2365.07 | + | 902.103i | −1.03043 | + | 0.393036i | ||||
\(175\) | −1878.08 | − | 1307.95i | −0.811255 | − | 0.564982i | ||||
\(176\) | 2174.63 | + | 247.267i | 0.931359 | + | 0.105900i | ||||
\(177\) | −181.289 | + | 314.002i | −0.0769859 | + | 0.133344i | ||||
\(178\) | −904.711 | + | 1112.38i | −0.380960 | + | 0.468408i | ||||
\(179\) | 1478.02 | − | 853.337i | 0.617166 | − | 0.356321i | −0.158599 | − | 0.987343i | \(-0.550698\pi\) |
0.775765 | + | 0.631022i | \(0.217364\pi\) | |||||||
\(180\) | −85.6593 | + | 17.8273i | −0.0354704 | + | 0.00738206i | ||||
\(181\) | − | 4153.44i | − | 1.70565i | −0.522197 | − | 0.852825i | \(-0.674887\pi\) | ||
0.522197 | − | 0.852825i | \(-0.325113\pi\) | |||||||
\(182\) | 2825.16 | − | 811.369i | 1.15063 | − | 0.330454i | ||||
\(183\) | 1521.68i | 0.614677i | ||||||||
\(184\) | 1127.96 | − | 722.326i | 0.451926 | − | 0.289405i | ||||
\(185\) | −167.443 | + | 96.6730i | −0.0665439 | + | 0.0384192i | ||||
\(186\) | −1004.44 | − | 816.921i | −0.395964 | − | 0.322041i | ||||
\(187\) | 384.061 | − | 665.213i | 0.150189 | − | 0.260135i | ||||
\(188\) | −3631.64 | + | 3242.10i | −1.40885 | + | 1.25774i | ||||
\(189\) | −2560.54 | + | 1201.93i | −0.985461 | + | 0.462578i | ||||
\(190\) | 128.489 | + | 336.862i | 0.0490608 | + | 0.128624i | ||||
\(191\) | 3079.88 | + | 1778.17i | 1.16677 | + | 0.673633i | 0.952916 | − | 0.303233i | \(-0.0980661\pi\) |
0.213851 | + | 0.976866i | \(0.431399\pi\) | |||||||
\(192\) | −904.607 | + | 1964.01i | −0.340023 | + | 0.738229i | ||||
\(193\) | −380.619 | − | 659.252i | −0.141956 | − | 0.245876i | 0.786277 | − | 0.617874i | \(-0.212006\pi\) |
−0.928233 | + | 0.371999i | \(0.878673\pi\) | |||||||
\(194\) | −1041.43 | − | 167.216i | −0.385416 | − | 0.0618836i | ||||
\(195\) | 282.830 | 0.103866 | ||||||||
\(196\) | −2325.84 | + | 1456.03i | −0.847609 | + | 0.530622i | ||||
\(197\) | −954.802 | −0.345314 | −0.172657 | − | 0.984982i | \(-0.555235\pi\) | ||||
−0.172657 | + | 0.984982i | \(0.555235\pi\) | |||||||
\(198\) | −875.170 | − | 140.520i | −0.314119 | − | 0.0504360i | ||||
\(199\) | 137.500 | + | 238.157i | 0.0489805 | + | 0.0848367i | 0.889476 | − | 0.456982i | \(-0.151069\pi\) |
−0.840496 | + | 0.541818i | \(0.817736\pi\) | |||||||
\(200\) | 2793.24 | − | 128.539i | 0.987560 | − | 0.0454455i | ||||
\(201\) | 2449.98 | + | 1414.49i | 0.859742 | + | 0.496372i | ||||
\(202\) | 496.843 | + | 1302.59i | 0.173058 | + | 0.453711i | ||||
\(203\) | 3552.63 | − | 1667.61i | 1.22830 | − | 0.576569i | ||||
\(204\) | 505.391 | + | 566.113i | 0.173453 | + | 0.194293i | ||||
\(205\) | −247.612 | + | 428.876i | −0.0843607 | + | 0.146117i | ||||
\(206\) | −1113.10 | − | 905.293i | −0.376472 | − | 0.306188i | ||||
\(207\) | −469.777 | + | 271.226i | −0.157738 | + | 0.0910700i | ||||
\(208\) | −2135.48 | + | 2887.31i | −0.711869 | + | 0.962494i | ||||
\(209\) | 3652.46i | 1.20883i | ||||||||
\(210\) | −253.773 | + | 72.8821i | −0.0833905 | + | 0.0239492i | ||||
\(211\) | − | 5361.25i | − | 1.74921i | −0.484835 | − | 0.874605i | \(-0.661121\pi\) | ||
0.484835 | − | 0.874605i | \(-0.338879\pi\) | |||||||
\(212\) | 365.662 | + | 1756.99i | 0.118461 | + | 0.569199i | ||||
\(213\) | 488.050 | − | 281.776i | 0.156998 | − | 0.0906430i | ||||
\(214\) | −1912.64 | + | 2351.67i | −0.610959 | + | 0.751202i | ||||
\(215\) | −154.110 | + | 266.926i | −0.0488846 | + | 0.0846707i | ||||
\(216\) | 1588.54 | − | 3069.16i | 0.500400 | − | 0.966805i | ||||
\(217\) | 1647.24 | + | 1147.19i | 0.515309 | + | 0.358877i | ||||
\(218\) | 2107.63 | − | 803.910i | 0.654802 | − | 0.249760i | ||||
\(219\) | 2852.72 | + | 1647.02i | 0.880224 | + | 0.508198i | ||||
\(220\) | −310.100 | − | 102.216i | −0.0950314 | − | 0.0313247i | ||||
\(221\) | 630.182 | + | 1091.51i | 0.191813 | + | 0.332229i | ||||
\(222\) | 306.787 | − | 1910.69i | 0.0927485 | − | 0.577645i | ||||
\(223\) | 2056.85 | 0.617653 | 0.308826 | − | 0.951118i | \(-0.400064\pi\) | ||||
0.308826 | + | 0.951118i | \(0.400064\pi\) | |||||||
\(224\) | 1172.06 | − | 3140.97i | 0.349606 | − | 0.936897i | ||||
\(225\) | −1132.43 | −0.335535 | ||||||||
\(226\) | 265.870 | − | 1655.86i | 0.0782541 | − | 0.487373i | ||||
\(227\) | −1283.13 | − | 2222.44i | −0.375173 | − | 0.649818i | 0.615180 | − | 0.788387i | \(-0.289083\pi\) |
−0.990353 | + | 0.138568i | \(0.955750\pi\) | |||||||
\(228\) | −3427.14 | − | 1129.67i | −0.995473 | − | 0.328132i | ||||
\(229\) | 804.017 | + | 464.200i | 0.232013 | + | 0.133953i | 0.611500 | − | 0.791244i | \(-0.290566\pi\) |
−0.379487 | + | 0.925197i | \(0.623900\pi\) | |||||||
\(230\) | −186.700 | + | 71.2128i | −0.0535246 | + | 0.0204158i | ||||
\(231\) | −2665.22 | − | 226.358i | −0.759127 | − | 0.0644731i | ||||
\(232\) | −2204.02 | + | 4258.31i | −0.623711 | + | 1.20505i | ||||
\(233\) | 1097.14 | − | 1900.31i | 0.308481 | − | 0.534305i | −0.669549 | − | 0.742768i | \(-0.733513\pi\) |
0.978030 | + | 0.208463i | \(0.0668459\pi\) | |||||||
\(234\) | 917.686 | − | 1128.34i | 0.256372 | − | 0.315221i | ||||
\(235\) | 628.968 | − | 363.135i | 0.174593 | − | 0.100801i | ||||
\(236\) | 139.941 | + | 672.409i | 0.0385991 | + | 0.185466i | ||||
\(237\) | − | 3556.57i | − | 0.974786i | ||||||
\(238\) | −846.709 | − | 816.980i | −0.230605 | − | 0.222508i | ||||
\(239\) | 2314.74i | 0.626479i | 0.949674 | + | 0.313239i | \(0.101414\pi\) | ||||
−0.949674 | + | 0.313239i | \(0.898586\pi\) | |||||||
\(240\) | 191.822 | − | 259.355i | 0.0515918 | − | 0.0697555i | ||||
\(241\) | 228.740 | − | 132.063i | 0.0611388 | − | 0.0352985i | −0.469119 | − | 0.883135i | \(-0.655428\pi\) |
0.530258 | + | 0.847836i | \(0.322095\pi\) | |||||||
\(242\) | 354.433 | + | 288.263i | 0.0941480 | + | 0.0765714i | ||||
\(243\) | −1222.27 | + | 2117.04i | −0.322670 | + | 0.558881i | ||||
\(244\) | 1919.62 | + | 2150.26i | 0.503652 | + | 0.564166i | ||||
\(245\) | 383.958 | − | 141.962i | 0.100123 | − | 0.0370188i | ||||
\(246\) | −1766.45 | − | 4631.14i | −0.457824 | − | 1.20029i | ||||
\(247\) | −5190.17 | − | 2996.54i | −1.33701 | − | 0.771925i | ||||
\(248\) | −2449.92 | + | 112.740i | −0.627298 | + | 0.0288670i | ||||
\(249\) | 913.731 | + | 1582.63i | 0.232552 | + | 0.402791i | ||||
\(250\) | −828.494 | − | 133.026i | −0.209594 | − | 0.0336531i | ||||
\(251\) | 2249.39 | 0.565659 | 0.282830 | − | 0.959170i | \(-0.408727\pi\) | ||||
0.282830 | + | 0.959170i | \(0.408727\pi\) | |||||||
\(252\) | −532.647 | + | 1248.90i | −0.133149 | + | 0.312194i | ||||
\(253\) | −2024.31 | −0.503034 | ||||||||
\(254\) | −1426.45 | − | 229.036i | −0.352377 | − | 0.0565787i | ||||
\(255\) | −56.6067 | − | 98.0457i | −0.0139014 | − | 0.0240779i | ||||
\(256\) | 1199.34 | + | 3916.48i | 0.292807 | + | 0.956172i | ||||
\(257\) | −6237.24 | − | 3601.07i | −1.51388 | − | 0.874042i | −0.999868 | − | 0.0162619i | \(-0.994823\pi\) |
−0.514017 | − | 0.857780i | \(-0.671843\pi\) | |||||||
\(258\) | −1099.41 | − | 2882.35i | −0.265296 | − | 0.695533i | ||||
\(259\) | −253.906 | + | 2989.57i | −0.0609149 | + | 0.717231i | ||||
\(260\) | 399.662 | − | 356.793i | 0.0953307 | − | 0.0851053i | ||||
\(261\) | 970.939 | − | 1681.72i | 0.230267 | − | 0.398834i | ||||
\(262\) | 1381.59 | + | 1123.66i | 0.325782 | + | 0.264961i | ||||
\(263\) | −3065.98 | + | 1770.14i | −0.718845 | + | 0.415026i | −0.814328 | − | 0.580406i | \(-0.802894\pi\) |
0.0954822 | + | 0.995431i | \(0.469561\pi\) | |||||||
\(264\) | 2752.06 | − | 1762.37i | 0.641582 | − | 0.410857i | ||||
\(265\) | − | 267.731i | − | 0.0620626i | ||||||
\(266\) | 5429.13 | + | 1351.24i | 1.25143 | + | 0.311467i | ||||
\(267\) | 2140.95i | 0.490726i | ||||||||
\(268\) | 5246.43 | − | 1091.88i | 1.19581 | − | 0.248870i | ||||
\(269\) | −3374.92 | + | 1948.51i | −0.764954 | + | 0.441646i | −0.831071 | − | 0.556166i | \(-0.812272\pi\) |
0.0661178 | + | 0.997812i | \(0.478939\pi\) | |||||||
\(270\) | −325.306 | + | 399.979i | −0.0733241 | + | 0.0901553i | ||||
\(271\) | 546.539 | − | 946.634i | 0.122509 | − | 0.212192i | −0.798248 | − | 0.602329i | \(-0.794239\pi\) |
0.920756 | + | 0.390138i | \(0.127573\pi\) | |||||||
\(272\) | 1428.32 | + | 162.407i | 0.318399 | + | 0.0362036i | ||||
\(273\) | 2508.25 | − | 3601.58i | 0.556067 | − | 0.798453i | ||||
\(274\) | −2600.17 | + | 991.777i | −0.573292 | + | 0.218670i | ||||
\(275\) | −3659.82 | − | 2113.00i | −0.802528 | − | 0.463340i | ||||
\(276\) | 626.101 | − | 1899.44i | 0.136546 | − | 0.414249i | ||||
\(277\) | 443.394 | + | 767.981i | 0.0961768 | + | 0.166583i | 0.910099 | − | 0.414391i | \(-0.136005\pi\) |
−0.813922 | + | 0.580974i | \(0.802672\pi\) | |||||||
\(278\) | 861.266 | − | 5364.03i | 0.185810 | − | 1.15724i | ||||
\(279\) | 993.241 | 0.213132 | ||||||||
\(280\) | −266.661 | + | 423.127i | −0.0569144 | + | 0.0903095i | ||||
\(281\) | 7748.61 | 1.64499 | 0.822497 | − | 0.568769i | \(-0.192580\pi\) | ||||
0.822497 | + | 0.568769i | \(0.192580\pi\) | |||||||
\(282\) | −1152.39 | + | 7177.16i | −0.243347 | + | 1.51558i | ||||
\(283\) | 453.400 | + | 785.312i | 0.0952362 | + | 0.164954i | 0.909707 | − | 0.415250i | \(-0.136306\pi\) |
−0.814471 | + | 0.580204i | \(0.802973\pi\) | |||||||
\(284\) | 334.191 | − | 1013.85i | 0.0698260 | − | 0.211835i | ||||
\(285\) | 466.212 | + | 269.168i | 0.0968983 | + | 0.0559442i | ||||
\(286\) | 5071.16 | − | 1934.28i | 1.04847 | − | 0.399918i | ||||
\(287\) | 3265.43 | + | 6956.57i | 0.671611 | + | 1.43078i | ||||
\(288\) | −412.292 | − | 1606.78i | −0.0843560 | − | 0.328752i | ||||
\(289\) | −2204.25 | + | 3817.87i | −0.448656 | + | 0.777094i | ||||
\(290\) | 451.347 | − | 554.951i | 0.0913930 | − | 0.112372i | ||||
\(291\) | −1363.94 | + | 787.471i | −0.274761 | + | 0.158634i | ||||
\(292\) | 6108.87 | − | 1271.37i | 1.22430 | − | 0.254799i | ||||
\(293\) | 2063.79i | 0.411495i | 0.978605 | + | 0.205748i | \(0.0659626\pi\) | ||||
−0.978605 | + | 0.205748i | \(0.934037\pi\) | |||||||
\(294\) | −1322.48 | + | 3877.92i | −0.262342 | + | 0.769269i | ||||
\(295\) | − | 102.462i | − | 0.0202223i | ||||||
\(296\) | −1976.85 | − | 3086.98i | −0.388182 | − | 0.606173i | ||||
\(297\) | −4523.26 | + | 2611.51i | −0.883725 | + | 0.510219i | ||||
\(298\) | −195.692 | − | 159.158i | −0.0380407 | − | 0.0309389i | ||||
\(299\) | 1660.79 | − | 2876.56i | 0.321223 | − | 0.556375i | ||||
\(300\) | 3114.59 | − | 2780.52i | 0.599404 | − | 0.535111i | ||||
\(301\) | 2032.35 | + | 4329.66i | 0.389179 | + | 0.829095i | ||||
\(302\) | 2186.43 | + | 5732.22i | 0.416606 | + | 1.09223i | ||||
\(303\) | 1802.76 | + | 1040.82i | 0.341801 | + | 0.197339i | ||||
\(304\) | −6267.93 | + | 2727.07i | −1.18253 | + | 0.514500i | ||||
\(305\) | −215.009 | − | 372.406i | −0.0403651 | − | 0.0699145i | ||||
\(306\) | −574.819 | − | 92.2948i | −0.107386 | − | 0.0172423i | ||||
\(307\) | −4283.78 | −0.796379 | −0.398189 | − | 0.917303i | \(-0.630361\pi\) | ||||
−0.398189 | + | 0.917303i | \(0.630361\pi\) | |||||||
\(308\) | −4051.73 | + | 3042.34i | −0.749573 | + | 0.562836i | ||||
\(309\) | −2142.33 | −0.394410 | ||||||||
\(310\) | 361.249 | + | 58.0033i | 0.0661857 | + | 0.0106270i | ||||
\(311\) | −1950.58 | − | 3378.51i | −0.355650 | − | 0.616005i | 0.631579 | − | 0.775312i | \(-0.282407\pi\) |
−0.987229 | + | 0.159307i | \(0.949074\pi\) | |||||||
\(312\) | 246.499 | + | 5356.58i | 0.0447283 | + | 0.971976i | ||||
\(313\) | −8158.28 | − | 4710.19i | −1.47327 | − | 0.850593i | −0.473722 | − | 0.880674i | \(-0.657090\pi\) |
−0.999547 | + | 0.0300815i | \(0.990423\pi\) | |||||||
\(314\) | −2512.18 | − | 6586.24i | −0.451498 | − | 1.18370i | ||||
\(315\) | 115.758 | − | 166.216i | 0.0207055 | − | 0.0297309i | ||||
\(316\) | −4486.67 | − | 5025.73i | −0.798717 | − | 0.894682i | ||||
\(317\) | 460.618 | − | 797.814i | 0.0816116 | − | 0.141355i | −0.822331 | − | 0.569010i | \(-0.807327\pi\) |
0.903942 | + | 0.427654i | \(0.140660\pi\) | |||||||
\(318\) | 2078.90 | + | 1690.79i | 0.366601 | + | 0.298160i | ||||
\(319\) | 6275.81 | − | 3623.34i | 1.10150 | − | 0.635950i | ||||
\(320\) | −56.1205 | − | 608.476i | −0.00980385 | − | 0.106296i | ||||
\(321\) | 4526.15i | 0.786994i | ||||||||
\(322\) | −748.905 | + | 3009.01i | −0.129611 | + | 0.520762i | ||||
\(323\) | 2398.96i | 0.413257i | ||||||||
\(324\) | −648.096 | − | 3114.07i | −0.111128 | − | 0.533962i | ||||
\(325\) | 6005.16 | − | 3467.08i | 1.02494 | − | 0.591751i | ||||
\(326\) | −2057.91 | + | 2530.29i | −0.349622 | + | 0.429877i | ||||
\(327\) | 1684.09 | − | 2916.93i | 0.284802 | − | 0.493292i | ||||
\(328\) | −8338.39 | − | 4315.79i | −1.40369 | − | 0.726524i | ||||
\(329\) | 953.751 | − | 11229.8i | 0.159824 | − | 1.88182i | ||||
\(330\) | −455.522 | + | 173.749i | −0.0759868 | + | 0.0289835i | ||||
\(331\) | 2745.37 | + | 1585.04i | 0.455889 | + | 0.263208i | 0.710314 | − | 0.703885i | \(-0.248553\pi\) |
−0.254425 | + | 0.967092i | \(0.581886\pi\) | |||||||
\(332\) | 3287.69 | + | 1083.70i | 0.543480 | + | 0.179144i | ||||
\(333\) | 742.286 | + | 1285.68i | 0.122153 | + | 0.211576i | ||||
\(334\) | −1556.43 | + | 9693.56i | −0.254982 | + | 1.58805i | ||||
\(335\) | −799.455 | −0.130385 | ||||||||
\(336\) | −1601.51 | − | 4742.75i | −0.260028 | − | 0.770054i | ||||
\(337\) | 11402.9 | 1.84320 | 0.921598 | − | 0.388145i | \(-0.126884\pi\) | ||||
0.921598 | + | 0.388145i | \(0.126884\pi\) | |||||||
\(338\) | −426.713 | + | 2657.60i | −0.0686690 | + | 0.427675i | ||||
\(339\) | −1252.06 | − | 2168.64i | −0.200598 | − | 0.347446i | ||||
\(340\) | −203.676 | − | 67.1366i | −0.0324879 | − | 0.0107088i | ||||
\(341\) | 3209.98 | + | 1853.28i | 0.509766 | + | 0.294313i | ||||
\(342\) | 2586.53 | − | 986.576i | 0.408958 | − | 0.155988i | ||||
\(343\) | 1597.35 | − | 6148.34i | 0.251454 | − | 0.967869i | ||||
\(344\) | −5189.69 | − | 2686.08i | −0.813399 | − | 0.421000i | ||||
\(345\) | −149.182 | + | 258.390i | −0.0232802 | + | 0.0403225i | ||||
\(346\) | 5117.38 | − | 6292.06i | 0.795122 | − | 0.977639i | ||||
\(347\) | −1629.30 | + | 940.675i | −0.252061 | + | 0.145528i | −0.620708 | − | 0.784042i | \(-0.713155\pi\) |
0.368647 | + | 0.929570i | \(0.379821\pi\) | |||||||
\(348\) | 1458.77 | + | 7009.32i | 0.224708 | + | 1.07971i | ||||
\(349\) | 827.050i | 0.126851i | 0.997987 | + | 0.0634255i | \(0.0202025\pi\) | ||||
−0.997987 | + | 0.0634255i | \(0.979797\pi\) | |||||||
\(350\) | −4494.79 | + | 4658.36i | −0.686448 | + | 0.711427i | ||||
\(351\) | − | 8570.11i | − | 1.30324i | ||||||
\(352\) | 1665.64 | − | 5962.14i | 0.252212 | − | 0.902792i | ||||
\(353\) | −7054.69 | + | 4073.03i | −1.06369 | + | 0.614123i | −0.926451 | − | 0.376415i | \(-0.877157\pi\) |
−0.137241 | + | 0.990538i | \(0.543823\pi\) | |||||||
\(354\) | 795.609 | + | 647.076i | 0.119452 | + | 0.0971517i | ||||
\(355\) | −79.6281 | + | 137.920i | −0.0119048 | + | 0.0206198i | ||||
\(356\) | 2700.84 | + | 3025.34i | 0.402090 | + | 0.450401i | ||||
\(357\) | −1750.54 | − | 148.674i | −0.259519 | − | 0.0220411i | ||||
\(358\) | −1720.34 | − | 4510.25i | −0.253974 | − | 0.665849i | ||||
\(359\) | 2220.38 | + | 1281.94i | 0.326427 | + | 0.188463i | 0.654254 | − | 0.756275i | \(-0.272983\pi\) |
−0.327827 | + | 0.944738i | \(0.606316\pi\) | |||||||
\(360\) | 11.3761 | + | 247.211i | 0.00166549 | + | 0.0361921i | ||||
\(361\) | −2274.09 | − | 3938.84i | −0.331549 | − | 0.574259i | ||||
\(362\) | −11599.1 | − | 1862.40i | −1.68408 | − | 0.270401i | ||||
\(363\) | 682.159 | 0.0986338 | ||||||||
\(364\) | −999.079 | − | 8253.53i | −0.143863 | − | 1.18847i | ||||
\(365\) | −930.875 | −0.133491 | ||||||||
\(366\) | 4249.53 | + | 682.319i | 0.606903 | + | 0.0974464i | ||||
\(367\) | 2738.05 | + | 4742.45i | 0.389442 | + | 0.674533i | 0.992375 | − | 0.123259i | \(-0.0393345\pi\) |
−0.602933 | + | 0.797792i | \(0.706001\pi\) | |||||||
\(368\) | −1511.43 | − | 3473.90i | −0.214100 | − | 0.492091i | ||||
\(369\) | 3293.04 | + | 1901.24i | 0.464577 | + | 0.268224i | ||||
\(370\) | 194.894 | + | 510.958i | 0.0273839 | + | 0.0717931i | ||||
\(371\) | −3409.32 | − | 2374.35i | −0.477097 | − | 0.332264i | ||||
\(372\) | −2731.77 | + | 2438.76i | −0.380741 | + | 0.339902i | ||||
\(373\) | −1993.55 | + | 3452.93i | −0.276735 | + | 0.479319i | −0.970571 | − | 0.240814i | \(-0.922586\pi\) |
0.693836 | + | 0.720133i | \(0.255919\pi\) | |||||||
\(374\) | −1685.50 | − | 1370.83i | −0.233035 | − | 0.189529i | ||||
\(375\) | −1085.06 | + | 626.458i | −0.149419 | + | 0.0862671i | ||||
\(376\) | 7425.67 | + | 11595.7i | 1.01848 | + | 1.59043i | ||||
\(377\) | 11890.6i | 1.62440i | ||||||||
\(378\) | 2208.42 | + | 7689.66i | 0.300500 | + | 1.04633i | ||||
\(379\) | 12140.4i | 1.64542i | 0.568464 | + | 0.822708i | \(0.307538\pi\) | ||||
−0.568464 | + | 0.822708i | \(0.692462\pi\) | |||||||
\(380\) | 998.355 | − | 207.777i | 0.134775 | − | 0.0280492i | ||||
\(381\) | −1868.19 | + | 1078.60i | −0.251208 | + | 0.145035i | ||||
\(382\) | 6346.84 | − | 7803.73i | 0.850085 | − | 1.04522i | ||||
\(383\) | 8.80269 | − | 15.2467i | 0.00117440 | − | 0.00203413i | −0.865438 | − | 0.501017i | \(-0.832960\pi\) |
0.866612 | + | 0.498983i | \(0.166293\pi\) | |||||||
\(384\) | 5079.17 | + | 3406.91i | 0.674988 | + | 0.452756i | ||||
\(385\) | 684.251 | − | 321.189i | 0.0905784 | − | 0.0425177i | ||||
\(386\) | −2011.73 | + | 767.332i | −0.265271 | + | 0.101182i | ||||
\(387\) | 2049.54 | + | 1183.30i | 0.269209 | + | 0.155428i | ||||
\(388\) | −933.955 | + | 2833.39i | −0.122202 | + | 0.370731i | ||||
\(389\) | −2946.39 | − | 5103.30i | −0.384031 | − | 0.665161i | 0.607603 | − | 0.794241i | \(-0.292131\pi\) |
−0.991634 | + | 0.129080i | \(0.958798\pi\) | |||||||
\(390\) | 126.820 | − | 789.846i | 0.0164661 | − | 0.102552i | ||||
\(391\) | −1329.59 | −0.171969 | ||||||||
\(392\) | 3023.28 | + | 7148.15i | 0.389538 | + | 0.921010i | ||||
\(393\) | 2659.08 | 0.341305 | ||||||||
\(394\) | −428.132 | + | 2666.44i | −0.0547435 | + | 0.340947i | ||||
\(395\) | 502.533 | + | 870.413i | 0.0640131 | + | 0.110874i | ||||
\(396\) | −784.850 | + | 2381.04i | −0.0995964 | + | 0.302151i | ||||
\(397\) | −3729.04 | − | 2152.96i | −0.471423 | − | 0.272176i | 0.245412 | − | 0.969419i | \(-0.421077\pi\) |
−0.716835 | + | 0.697242i | \(0.754410\pi\) | |||||||
\(398\) | 726.746 | − | 277.201i | 0.0915288 | − | 0.0349117i | ||||
\(399\) | 7562.17 | − | 3549.70i | 0.948827 | − | 0.445382i | ||||
\(400\) | 893.519 | − | 7858.20i | 0.111690 | − | 0.982275i | ||||
\(401\) | 763.591 | − | 1322.58i | 0.0950921 | − | 0.164704i | −0.814555 | − | 0.580086i | \(-0.803019\pi\) |
0.909647 | + | 0.415382i | \(0.136352\pi\) | |||||||
\(402\) | 5048.77 | − | 6207.69i | 0.626392 | − | 0.770178i | ||||
\(403\) | −5267.05 | + | 3040.94i | −0.651044 | + | 0.375880i | ||||
\(404\) | 3860.46 | − | 803.435i | 0.475408 | − | 0.0989415i | ||||
\(405\) | 474.524i | 0.0582205i | ||||||||
\(406\) | −3064.08 | − | 10669.0i | −0.374551 | − | 1.30418i | ||||
\(407\) | 5540.10i | 0.674724i | ||||||||
\(408\) | 1807.58 | − | 1157.54i | 0.219334 | − | 0.140458i | ||||
\(409\) | 6137.85 | − | 3543.69i | 0.742047 | − | 0.428421i | −0.0807660 | − | 0.996733i | \(-0.525737\pi\) |
0.822813 | + | 0.568312i | \(0.192403\pi\) | |||||||
\(410\) | 1086.68 | + | 883.802i | 0.130895 | + | 0.106458i | ||||
\(411\) | −2077.65 | + | 3598.59i | −0.249350 | + | 0.431887i | ||||
\(412\) | −3027.29 | + | 2702.57i | −0.361999 | + | 0.323171i | ||||
\(413\) | −1304.77 | − | 908.678i | −0.155456 | − | 0.108264i | ||||
\(414\) | 546.794 | + | 1433.54i | 0.0649117 | + | 0.170181i | ||||
\(415\) | −447.241 | − | 258.215i | −0.0529017 | − | 0.0305428i | ||||
\(416\) | 7105.72 | + | 7258.33i | 0.837468 | + | 0.855454i | ||||
\(417\) | −4055.96 | − | 7025.13i | −0.476310 | − | 0.824993i | ||||
\(418\) | 10200.1 | + | 1637.76i | 1.19354 | + | 0.191639i | ||||
\(419\) | −16580.0 | −1.93314 | −0.966569 | − | 0.256406i | \(-0.917462\pi\) | ||||
−0.966569 | + | 0.256406i | \(0.917462\pi\) | |||||||
\(420\) | 89.7433 | + | 741.382i | 0.0104262 | + | 0.0861327i | ||||
\(421\) | −6613.72 | −0.765637 | −0.382818 | − | 0.923824i | \(-0.625046\pi\) | ||||
−0.382818 | + | 0.923824i | \(0.625046\pi\) | |||||||
\(422\) | −14972.1 | − | 2403.97i | −1.72709 | − | 0.277307i | ||||
\(423\) | −2788.26 | − | 4829.41i | −0.320496 | − | 0.555116i | ||||
\(424\) | 5070.62 | − | 233.340i | 0.580781 | − | 0.0267263i | ||||
\(425\) | −2403.80 | − | 1387.83i | −0.274356 | − | 0.158400i | ||||
\(426\) | −568.062 | − | 1489.30i | −0.0646073 | − | 0.169383i | ||||
\(427\) | −6649.05 | − | 564.708i | −0.753560 | − | 0.0640003i | ||||
\(428\) | 5709.80 | + | 6395.83i | 0.644845 | + | 0.722322i | ||||
\(429\) | 4052.07 | − | 7018.40i | 0.456028 | − | 0.789864i | ||||
\(430\) | 676.330 | + | 550.065i | 0.0758501 | + | 0.0616895i | ||||
\(431\) | 9840.60 | − | 5681.47i | 1.09978 | − | 0.634958i | 0.163617 | − | 0.986524i | \(-0.447684\pi\) |
0.936163 | + | 0.351566i | \(0.114351\pi\) | |||||||
\(432\) | −7858.81 | − | 5812.45i | −0.875248 | − | 0.647342i | ||||
\(433\) | 5830.20i | 0.647071i | 0.946216 | + | 0.323535i | \(0.104871\pi\) | ||||
−0.946216 | + | 0.323535i | \(0.895129\pi\) | |||||||
\(434\) | 3942.33 | − | 4085.79i | 0.436032 | − | 0.451899i | ||||
\(435\) | − | 1068.09i | − | 0.117726i | ||||||
\(436\) | −1299.99 | − | 6246.37i | −0.142794 | − | 0.686116i | ||||
\(437\) | 5475.23 | − | 3161.12i | 0.599349 | − | 0.346034i | ||||
\(438\) | 5878.72 | − | 7228.15i | 0.641315 | − | 0.788526i | ||||
\(439\) | −3140.33 | + | 5439.20i | −0.341411 | + | 0.591342i | −0.984695 | − | 0.174286i | \(-0.944238\pi\) |
0.643284 | + | 0.765628i | \(0.277572\pi\) | |||||||
\(440\) | −424.504 | + | 820.168i | −0.0459941 | + | 0.0888636i | ||||
\(441\) | −1090.03 | − | 2948.15i | −0.117701 | − | 0.318340i | ||||
\(442\) | 3330.78 | − | 1270.45i | 0.358436 | − | 0.136718i | ||||
\(443\) | −4211.87 | − | 2431.72i | −0.451720 | − | 0.260801i | 0.256836 | − | 0.966455i | \(-0.417320\pi\) |
−0.708556 | + | 0.705654i | \(0.750653\pi\) | |||||||
\(444\) | −5198.34 | − | 1713.50i | −0.555636 | − | 0.183151i | ||||
\(445\) | −302.509 | − | 523.962i | −0.0322254 | − | 0.0558161i | ||||
\(446\) | 922.286 | − | 5744.07i | 0.0979182 | − | 0.609842i | ||||
\(447\) | −376.639 | −0.0398533 | ||||||||
\(448\) | −8246.10 | − | 4681.58i | −0.869624 | − | 0.493714i | ||||
\(449\) | 6326.57 | 0.664965 | 0.332483 | − | 0.943109i | \(-0.392114\pi\) | ||||
0.332483 | + | 0.943109i | \(0.392114\pi\) | |||||||
\(450\) | −507.780 | + | 3162.49i | −0.0531933 | + | 0.331292i | ||||
\(451\) | 7095.02 | + | 12288.9i | 0.740780 | + | 1.28307i | ||||
\(452\) | −4505.04 | − | 1484.97i | −0.468803 | − | 0.154529i | ||||
\(453\) | 7933.31 | + | 4580.30i | 0.822824 | + | 0.475058i | ||||
\(454\) | −6781.88 | + | 2586.80i | −0.701078 | + | 0.267411i | ||||
\(455\) | −104.960 | + | 1235.84i | −0.0108145 | + | 0.127334i | ||||
\(456\) | −4691.50 | + | 9064.29i | −0.481798 | + | 0.930865i | ||||
\(457\) | −8550.00 | + | 14809.0i | −0.875168 | + | 1.51584i | −0.0185851 | + | 0.999827i | \(0.505916\pi\) |
−0.856583 | + | 0.516009i | \(0.827417\pi\) | |||||||
\(458\) | 1656.87 | − | 2037.20i | 0.169040 | − | 0.207843i | ||||
\(459\) | −2970.92 | + | 1715.26i | −0.302114 | + | 0.174426i | ||||
\(460\) | 115.157 | + | 553.322i | 0.0116722 | + | 0.0560843i | ||||
\(461\) | − | 15378.2i | − | 1.55365i | −0.629717 | − | 0.776825i | \(-0.716829\pi\) | ||
0.629717 | − | 0.776825i | \(-0.283171\pi\) | |||||||
\(462\) | −1827.22 | + | 7341.54i | −0.184004 | + | 0.739306i | ||||
\(463\) | − | 2225.59i | − | 0.223395i | −0.993742 | − | 0.111697i | \(-0.964371\pi\) | ||
0.993742 | − | 0.111697i | \(-0.0356287\pi\) | |||||||
\(464\) | 10903.7 | + | 8064.50i | 1.09093 | + | 0.806864i | ||||
\(465\) | 473.118 | − | 273.155i | 0.0471835 | − | 0.0272414i | ||||
\(466\) | −4814.95 | − | 3916.04i | −0.478644 | − | 0.389285i | ||||
\(467\) | 6133.89 | − | 10624.2i | 0.607800 | − | 1.05274i | −0.383802 | − | 0.923415i | \(-0.625385\pi\) |
0.991602 | − | 0.129325i | \(-0.0412812\pi\) | |||||||
\(468\) | −2739.57 | − | 3068.73i | −0.270591 | − | 0.303103i | ||||
\(469\) | −7089.90 | + | 10180.4i | −0.698041 | + | 1.00231i | ||||
\(470\) | −732.083 | − | 1919.32i | −0.0718478 | − | 0.188365i | ||||
\(471\) | −9115.26 | − | 5262.70i | −0.891738 | − | 0.514845i | ||||
\(472\) | 1940.56 | − | 89.3004i | 0.189240 | − | 0.00870844i | ||||
\(473\) | 4415.83 | + | 7648.45i | 0.429261 | + | 0.743501i | ||||
\(474\) | −9932.29 | − | 1594.76i | −0.962458 | − | 0.154535i | ||||
\(475\) | 13198.4 | 1.27492 | ||||||||
\(476\) | −2661.21 | + | 1998.24i | −0.256253 | + | 0.192414i | ||||
\(477\) | −2055.72 | −0.197327 | ||||||||
\(478\) | 6464.29 | + | 1037.93i | 0.618556 | + | 0.0993174i | ||||
\(479\) | −1770.66 | − | 3066.87i | −0.168901 | − | 0.292545i | 0.769133 | − | 0.639089i | \(-0.220688\pi\) |
−0.938034 | + | 0.346544i | \(0.887355\pi\) | |||||||
\(480\) | −638.278 | − | 651.987i | −0.0606943 | − | 0.0619979i | ||||
\(481\) | −7872.53 | − | 4545.21i | −0.746271 | − | 0.430860i | ||||
\(482\) | −266.241 | − | 698.010i | −0.0251596 | − | 0.0659616i | ||||
\(483\) | 1967.36 | + | 4191.21i | 0.185338 | + | 0.394838i | ||||
\(484\) | 963.948 | − | 860.554i | 0.0905286 | − | 0.0808183i | ||||
\(485\) | 222.534 | − | 385.441i | 0.0208346 | − | 0.0360865i | ||||
\(486\) | 5364.10 | + | 4362.66i | 0.500659 | + | 0.407190i | ||||
\(487\) | 12479.1 | − | 7204.80i | 1.16115 | − | 0.670392i | 0.209573 | − | 0.977793i | \(-0.432793\pi\) |
0.951580 | + | 0.307401i | \(0.0994594\pi\) | |||||||
\(488\) | 6865.70 | − | 4396.67i | 0.636876 | − | 0.407844i | ||||
\(489\) | 4869.92i | 0.450359i | ||||||||
\(490\) | −224.284 | − | 1135.92i | −0.0206778 | − | 0.104726i | ||||
\(491\) | − | 12333.7i | − | 1.13363i | −0.823846 | − | 0.566814i | \(-0.808176\pi\) | ||
0.823846 | − | 0.566814i | \(-0.191824\pi\) | |||||||
\(492\) | −13725.3 | + | 2856.49i | −1.25769 | + | 0.261749i | ||||
\(493\) | 4122.00 | − | 2379.84i | 0.376563 | − | 0.217409i | ||||
\(494\) | −10695.6 | + | 13150.7i | −0.974124 | + | 1.19773i | ||||
\(495\) | 187.007 | − | 323.906i | 0.0169805 | − | 0.0294111i | ||||
\(496\) | −783.694 | + | 6892.33i | −0.0709454 | + | 0.623941i | ||||
\(497\) | 1050.11 | + | 2237.12i | 0.0947766 | + | 0.201909i | ||||
\(498\) | 4829.46 | − | 1842.09i | 0.434564 | − | 0.165755i | ||||
\(499\) | 3342.44 | + | 1929.76i | 0.299856 | + | 0.173122i | 0.642378 | − | 0.766388i | \(-0.277948\pi\) |
−0.342522 | + | 0.939510i | \(0.611281\pi\) | |||||||
\(500\) | −742.991 | + | 2254.05i | −0.0664551 | + | 0.201609i | ||||
\(501\) | 7329.69 | + | 12695.4i | 0.653626 | + | 1.13211i | ||||
\(502\) | 1008.62 | − | 6281.79i | 0.0896755 | − | 0.558506i | ||||
\(503\) | 21123.7 | 1.87248 | 0.936242 | − | 0.351355i | \(-0.114279\pi\) | ||||
0.936242 | + | 0.351355i | \(0.114279\pi\) | |||||||
\(504\) | 3248.90 | + | 2047.50i | 0.287138 | + | 0.180959i | ||||
\(505\) | −588.260 | −0.0518361 | ||||||||
\(506\) | −907.699 | + | 5653.22i | −0.0797473 | + | 0.496672i | ||||
\(507\) | 2009.52 | + | 3480.59i | 0.176027 | + | 0.304888i | ||||
\(508\) | −1279.24 | + | 3880.90i | −0.111726 | + | 0.338951i | ||||
\(509\) | 15427.0 | + | 8906.80i | 1.34340 | + | 0.775613i | 0.987305 | − | 0.158837i | \(-0.0507743\pi\) |
0.356096 | + | 0.934449i | \(0.384108\pi\) | |||||||
\(510\) | −299.190 | + | 114.120i | −0.0259772 | + | 0.00990844i | ||||
\(511\) | −8255.39 | + | 11853.9i | −0.714671 | + | 1.02619i | ||||
\(512\) | 11475.2 | − | 1593.19i | 0.990499 | − | 0.137519i | ||||
\(513\) | 8156.14 | − | 14126.8i | 0.701954 | − | 1.21582i | ||||
\(514\) | −12853.3 | + | 15803.8i | −1.10299 | + | 1.35618i | ||||
\(515\) | 524.299 | − | 302.704i | 0.0448609 | − | 0.0259005i | ||||
\(516\) | −8542.40 | + | 1777.84i | −0.728795 | + | 0.151676i | ||||
\(517\) | − | 20810.4i | − | 1.77029i | ||||||
\(518\) | 8234.99 | + | 2049.59i | 0.698504 | + | 0.173849i | ||||
\(519\) | − | 12110.0i | − | 1.02422i | ||||||
\(520\) | −817.194 | − | 1276.10i | −0.0689160 | − | 0.107617i | ||||
\(521\) | −6584.35 | + | 3801.48i | −0.553677 | + | 0.319665i | −0.750604 | − | 0.660753i | \(-0.770237\pi\) |
0.196927 | + | 0.980418i | \(0.436904\pi\) | |||||||
\(522\) | −4261.09 | − | 3465.58i | −0.357285 | − | 0.290583i | ||||
\(523\) | −866.244 | + | 1500.38i | −0.0724248 | + | 0.125443i | −0.899964 | − | 0.435965i | \(-0.856407\pi\) |
0.827539 | + | 0.561409i | \(0.189740\pi\) | |||||||
\(524\) | 3757.50 | − | 3354.46i | 0.313258 | − | 0.279657i | ||||
\(525\) | −817.963 | + | 9630.96i | −0.0679978 | + | 0.800628i | ||||
\(526\) | 3568.63 | + | 9355.96i | 0.295816 | + | 0.775550i | ||||
\(527\) | 2108.34 | + | 1217.25i | 0.174271 | + | 0.100615i | ||||
\(528\) | −3687.68 | − | 8475.80i | −0.303950 | − | 0.698602i | ||||
\(529\) | −4331.50 | − | 7502.38i | −0.356004 | − | 0.616617i | ||||
\(530\) | −747.681 | − | 120.050i | −0.0612777 | − | 0.00983895i | ||||
\(531\) | −786.737 | −0.0642966 | ||||||||
\(532\) | 6207.98 | − | 14555.8i | 0.505921 | − | 1.18623i | ||||
\(533\) | −23283.6 | −1.89216 | ||||||||
\(534\) | 5978.94 | + | 959.997i | 0.484520 | + | 0.0777962i | ||||
\(535\) | −639.531 | − | 1107.70i | −0.0516810 | − | 0.0895141i | ||||
\(536\) | −696.761 | − | 15141.1i | −0.0561483 | − | 1.22014i | ||||
\(537\) | −6242.11 | − | 3603.88i | −0.501615 | − | 0.289607i | ||||
\(538\) | 3928.22 | + | 10298.7i | 0.314791 | + | 0.825295i | ||||
\(539\) | 1978.17 | − | 11561.8i | 0.158081 | − | 0.923935i | ||||
\(540\) | 971.137 | + | 1087.82i | 0.0773909 | + | 0.0866894i | ||||
\(541\) | −2721.01 | + | 4712.93i | −0.216239 | + | 0.374537i | −0.953655 | − | 0.300902i | \(-0.902712\pi\) |
0.737416 | + | 0.675439i | \(0.236046\pi\) | |||||||
\(542\) | −2398.56 | − | 1950.77i | −0.190086 | − | 0.154599i | ||||
\(543\) | −15191.1 | + | 8770.58i | −1.20057 | + | 0.693152i | ||||
\(544\) | 1094.00 | − | 3915.98i | 0.0862224 | − | 0.308633i | ||||
\(545\) | 951.827i | 0.0748106i | ||||||||
\(546\) | −8933.29 | − | 8619.63i | −0.700201 | − | 0.675615i | ||||
\(547\) | 4559.51i | 0.356399i | 0.983994 | + | 0.178200i | \(0.0570273\pi\) | ||||
−0.983994 | + | 0.178200i | \(0.942973\pi\) | |||||||
\(548\) | 1603.78 | + | 7706.09i | 0.125019 | + | 0.600708i | ||||
\(549\) | −2859.45 | + | 1650.90i | −0.222292 | + | 0.128340i | ||||
\(550\) | −7541.93 | + | 9273.15i | −0.584707 | + | 0.718924i | ||||
\(551\) | −11316.2 | + | 19600.3i | −0.874933 | + | 1.51543i | ||||
\(552\) | −5023.73 | − | 2600.19i | −0.387363 | − | 0.200492i | ||||
\(553\) | 15540.6 | + | 1319.87i | 1.19503 | + | 0.101495i | ||||
\(554\) | 2343.53 | − | 893.886i | 0.179724 | − | 0.0685516i | ||||
\(555\) | 707.158 | + | 408.278i | 0.0540850 | + | 0.0312260i | ||||
\(556\) | −14593.7 | − | 4810.44i | −1.11315 | − | 0.366921i | ||||
\(557\) | 6808.62 | + | 11792.9i | 0.517936 | + | 0.897092i | 0.999783 | + | 0.0208366i | \(0.00663298\pi\) |
−0.481846 | + | 0.876256i | \(0.660034\pi\) | |||||||
\(558\) | 445.368 | − | 2773.78i | 0.0337884 | − | 0.210437i | ||||
\(559\) | −14491.3 | −1.09645 | ||||||||
\(560\) | 1062.08 | + | 934.422i | 0.0801446 | + | 0.0705116i | ||||
\(561\) | −3244.00 | −0.244138 | ||||||||
\(562\) | 3474.46 | − | 21639.2i | 0.260786 | − | 1.62419i | ||||
\(563\) | −10859.4 | − | 18809.0i | −0.812912 | − | 1.40800i | −0.910818 | − | 0.412809i | \(-0.864548\pi\) |
0.0979055 | − | 0.995196i | \(-0.468786\pi\) | |||||||
\(564\) | 19526.6 | + | 6436.45i | 1.45784 | + | 0.480538i | ||||
\(565\) | 612.844 | + | 353.825i | 0.0456328 | + | 0.0263461i | ||||
\(566\) | 2396.41 | − | 914.059i | 0.177966 | − | 0.0678812i | ||||
\(567\) | 6042.64 | + | 4208.28i | 0.447561 | + | 0.311695i | ||||
\(568\) | −2681.50 | − | 1387.89i | −0.198086 | − | 0.102526i | ||||
\(569\) | 8176.19 | − | 14161.6i | 0.602397 | − | 1.04338i | −0.390060 | − | 0.920789i | \(-0.627546\pi\) |
0.992457 | − | 0.122592i | \(-0.0391208\pi\) | |||||||
\(570\) | 960.742 | − | 1181.28i | 0.0705983 | − | 0.0868039i | ||||
\(571\) | −8594.29 | + | 4961.91i | −0.629877 | + | 0.363660i | −0.780704 | − | 0.624901i | \(-0.785140\pi\) |
0.150828 | + | 0.988560i | \(0.451806\pi\) | |||||||
\(572\) | −3127.89 | − | 15029.3i | −0.228643 | − | 1.09862i | ||||
\(573\) | − | 15019.4i | − | 1.09502i | ||||||
\(574\) | 20891.5 | − | 5999.92i | 1.51916 | − | 0.436292i | ||||
\(575\) | 7315.01i | 0.530534i | ||||||||
\(576\) | −4672.07 | + | 430.911i | −0.337968 | + | 0.0311712i | ||||
\(577\) | 6086.87 | − | 3514.26i | 0.439168 | − | 0.253554i | −0.264077 | − | 0.964502i | \(-0.585067\pi\) |
0.703245 | + | 0.710948i | \(0.251734\pi\) | |||||||
\(578\) | 9673.61 | + | 7867.63i | 0.696141 | + | 0.566177i | ||||
\(579\) | −1607.46 | + | 2784.21i | −0.115378 | + | 0.199841i | ||||
\(580\) | −1347.41 | − | 1509.30i | −0.0964621 | − | 0.108052i | ||||
\(581\) | −7254.46 | + | 3405.26i | −0.518013 | + | 0.243157i | ||||
\(582\) | 1587.55 | + | 4162.12i | 0.113069 | + | 0.296435i | ||||
\(583\) | −6643.73 | − | 3835.76i | −0.471964 | − | 0.272489i | ||||
\(584\) | −811.299 | − | 17630.1i | −0.0574860 | − | 1.24921i | ||||
\(585\) | 306.848 | + | 531.476i | 0.0216865 | + | 0.0375621i | ||||
\(586\) | 5763.47 | + | 925.402i | 0.406292 | + | 0.0652355i | ||||
\(587\) | 8277.57 | 0.582030 | 0.291015 | − | 0.956718i | \(-0.406007\pi\) | ||||
0.291015 | + | 0.956718i | \(0.406007\pi\) | |||||||
\(588\) | 10236.7 | + | 5432.08i | 0.717951 | + | 0.380978i | ||||
\(589\) | −11576.2 | −0.809827 | ||||||||
\(590\) | −286.142 | − | 45.9439i | −0.0199666 | − | 0.00320590i | ||||
\(591\) | 2016.20 | + | 3492.16i | 0.140331 | + | 0.243060i | ||||
\(592\) | −9507.30 | + | 4136.46i | −0.660046 | + | 0.287175i | ||||
\(593\) | 10422.0 | + | 6017.16i | 0.721722 | + | 0.416687i | 0.815386 | − | 0.578917i | \(-0.196525\pi\) |
−0.0936639 | + | 0.995604i | \(0.529858\pi\) | |||||||
\(594\) | 5264.82 | + | 13802.9i | 0.363667 | + | 0.953435i | ||||
\(595\) | 449.422 | − | 210.960i | 0.0309656 | − | 0.0145353i | ||||
\(596\) | −532.222 | + | 475.135i | −0.0365783 | + | 0.0326549i | ||||
\(597\) | 580.702 | − | 1005.80i | 0.0398099 | − | 0.0689528i | ||||
\(598\) | −7288.57 | − | 5927.85i | −0.498414 | − | 0.405364i | ||||
\(599\) | −17523.6 | + | 10117.3i | −1.19532 | + | 0.690118i | −0.959508 | − | 0.281681i | \(-0.909108\pi\) |
−0.235811 | + | 0.971799i | \(0.575775\pi\) | |||||||
\(600\) | −6368.45 | − | 9944.77i | −0.433318 | − | 0.676656i | ||||
\(601\) | − | 11846.7i | − | 0.804052i | −0.915628 | − | 0.402026i | \(-0.868306\pi\) | ||
0.915628 | − | 0.402026i | \(-0.131694\pi\) | |||||||
\(602\) | 13002.6 | − | 3734.26i | 0.880307 | − | 0.252819i | ||||
\(603\) | 6138.47i | 0.414557i | ||||||||
\(604\) | 16988.5 | − | 3535.64i | 1.14446 | − | 0.238184i | ||||
\(605\) | −166.947 | + | 96.3871i | −0.0112188 | + | 0.00647718i | ||||
\(606\) | 3715.01 | − | 4567.78i | 0.249030 | − | 0.306194i | ||||
\(607\) | 7756.88 | − | 13435.3i | 0.518686 | − | 0.898390i | −0.481079 | − | 0.876678i | \(-0.659755\pi\) |
0.999764 | − | 0.0217125i | \(-0.00691185\pi\) | |||||||
\(608\) | 4805.24 | + | 18727.0i | 0.320523 | + | 1.24914i | ||||
\(609\) | −13601.1 | − | 9472.24i | −0.905001 | − | 0.630270i | ||||
\(610\) | −1136.41 | + | 433.460i | −0.0754295 | + | 0.0287709i | ||||
\(611\) | 29571.7 | + | 17073.2i | 1.95801 | + | 1.13046i | ||||
\(612\) | −515.496 | + | 1563.89i | −0.0340485 | + | 0.103295i | ||||
\(613\) | 1721.81 | + | 2982.27i | 0.113447 | + | 0.196497i | 0.917158 | − | 0.398524i | \(-0.130477\pi\) |
−0.803711 | + | 0.595020i | \(0.797144\pi\) | |||||||
\(614\) | −1920.84 | + | 11963.1i | −0.126252 | + | 0.786308i | ||||
\(615\) | 2091.47 | 0.137132 | ||||||||
\(616\) | 6679.44 | + | 12679.3i | 0.436887 | + | 0.829322i | ||||
\(617\) | −7010.85 | −0.457449 | −0.228725 | − | 0.973491i | \(-0.573456\pi\) | ||||
−0.228725 | + | 0.973491i | \(0.573456\pi\) | |||||||
\(618\) | −960.616 | + | 5982.78i | −0.0625269 | + | 0.389422i | ||||
\(619\) | −7448.93 | − | 12901.9i | −0.483680 | − | 0.837758i | 0.516144 | − | 0.856502i | \(-0.327367\pi\) |
−0.999824 | + | 0.0187433i | \(0.994033\pi\) | |||||||
\(620\) | 323.967 | − | 982.836i | 0.0209852 | − | 0.0636640i | ||||
\(621\) | 7829.57 | + | 4520.40i | 0.505942 | + | 0.292106i | ||||
\(622\) | −10309.6 | + | 3932.39i | −0.664597 | + | 0.253496i | ||||
\(623\) | −9354.96 | − | 794.523i | −0.601603 | − | 0.0510945i | ||||
\(624\) | 15069.6 | + | 1713.49i | 0.966775 | + | 0.109927i | ||||
\(625\) | −7546.44 | + | 13070.8i | −0.482972 | + | 0.836533i | ||||
\(626\) | −16812.1 | + | 20671.3i | −1.07340 | + | 1.31979i | ||||
\(627\) | 13358.8 | − | 7712.68i | 0.850873 | − | 0.491252i | ||||
\(628\) | −19519.6 | + | 4062.39i | −1.24031 | + | 0.258132i | ||||
\(629\) | 3638.79i | 0.230664i | ||||||||
\(630\) | −412.280 | − | 397.804i | −0.0260724 | − | 0.0251570i | ||||
\(631\) | 3172.41i | 0.200145i | 0.994980 | + | 0.100073i | \(0.0319075\pi\) | ||||
−0.994980 | + | 0.100073i | \(0.968093\pi\) | |||||||
\(632\) | −16047.0 | + | 10276.2i | −1.00999 | + | 0.646780i | ||||
\(633\) | −19608.6 | + | 11321.0i | −1.23124 | + | 0.710854i | ||||
\(634\) | −2021.48 | − | 1644.09i | −0.126630 | − | 0.102989i | ||||
\(635\) | 304.806 | − | 527.939i | 0.0190486 | − | 0.0329931i | ||||
\(636\) | 5653.98 | − | 5047.52i | 0.352507 | − | 0.314697i | ||||
\(637\) | 14806.4 | + | 12296.5i | 0.920961 | + | 0.764842i | ||||
\(638\) | −7304.68 | − | 19150.9i | −0.453284 | − | 1.18839i | ||||
\(639\) | 1058.99 | + | 611.409i | 0.0655604 | + | 0.0378513i | ||||
\(640\) | −1724.43 | − | 116.114i | −0.106506 | − | 0.00717160i | ||||
\(641\) | 880.382 | + | 1524.87i | 0.0542480 | + | 0.0939603i | 0.891874 | − | 0.452284i | \(-0.149391\pi\) |
−0.837626 | + | 0.546244i | \(0.816057\pi\) | |||||||
\(642\) | 12640.0 | + | 2029.52i | 0.777041 | + | 0.124764i | ||||
\(643\) | 11358.8 | 0.696651 | 0.348325 | − | 0.937374i | \(-0.386750\pi\) | ||||
0.348325 | + | 0.937374i | \(0.386750\pi\) | |||||||
\(644\) | 8067.32 | + | 3440.67i | 0.493629 | + | 0.210530i | ||||
\(645\) | 1301.70 | 0.0794641 | ||||||||
\(646\) | 6699.49 | + | 1075.69i | 0.408031 | + | 0.0655147i | ||||
\(647\) | 11317.1 | + | 19601.8i | 0.687667 | + | 1.19107i | 0.972591 | + | 0.232523i | \(0.0746982\pi\) |
−0.284924 | + | 0.958550i | \(0.591968\pi\) | |||||||
\(648\) | −8987.13 | + | 413.569i | −0.544827 | + | 0.0250718i | ||||
\(649\) | −2542.60 | − | 1467.97i | −0.153784 | − | 0.0887870i | ||||
\(650\) | −6989.67 | − | 18325.0i | −0.421781 | − | 1.10579i | ||||
\(651\) | 717.425 | − | 8447.19i | 0.0431922 | − | 0.508559i | ||||
\(652\) | 6143.48 | + | 6881.61i | 0.369014 | + | 0.413351i | ||||
\(653\) | 6027.89 | − | 10440.6i | 0.361240 | − | 0.625686i | −0.626925 | − | 0.779079i | \(-0.715687\pi\) |
0.988165 | + | 0.153393i | \(0.0490202\pi\) | |||||||
\(654\) | −7390.84 | − | 6011.03i | −0.441903 | − | 0.359404i | ||||
\(655\) | −650.765 | + | 375.720i | −0.0388206 | + | 0.0224131i | ||||
\(656\) | −15791.5 | + | 21351.1i | −0.939867 | + | 1.27076i | ||||
\(657\) | 7147.55i | 0.424433i | ||||||||
\(658\) | −30933.3 | − | 7698.91i | −1.83268 | − | 0.456132i | ||||
\(659\) | − | 28180.2i | − | 1.66577i | −0.553443 | − | 0.832887i | \(-0.686686\pi\) | ||
0.553443 | − | 0.832887i | \(-0.313314\pi\) | |||||||
\(660\) | 280.966 | + | 1350.02i | 0.0165706 | + | 0.0796207i | ||||
\(661\) | 12273.4 | − | 7086.03i | 0.722207 | − | 0.416966i | −0.0933574 | − | 0.995633i | \(-0.529760\pi\) |
0.815564 | + | 0.578666i | \(0.196427\pi\) | |||||||
\(662\) | 5657.50 | − | 6956.16i | 0.332152 | − | 0.408397i | ||||
\(663\) | 2661.44 | − | 4609.74i | 0.155900 | − | 0.270027i | ||||
\(664\) | 4500.60 | − | 8695.45i | 0.263038 | − | 0.508206i | ||||
\(665\) | −1349.15 | + | 1937.24i | −0.0786736 | + | 0.112967i | ||||
\(666\) | 3923.30 | − | 1496.46i | 0.228265 | − | 0.0870668i | ||||
\(667\) | −10863.2 | − | 6271.84i | −0.630619 | − | 0.364088i | ||||
\(668\) | 26372.9 | + | 8693.15i | 1.52754 | + | 0.503515i | ||||
\(669\) | −4343.32 | − | 7522.85i | −0.251005 | − | 0.434754i | ||||
\(670\) | −358.474 | + | 2232.61i | −0.0206703 | + | 0.128736i | ||||
\(671\) | −12321.7 | −0.708900 | ||||||||
\(672\) | −13963.0 | + | 2345.82i | −0.801539 | + | 0.134660i | ||||
\(673\) | 20823.6 | 1.19271 | 0.596353 | − | 0.802722i | \(-0.296616\pi\) | ||||
0.596353 | + | 0.802722i | \(0.296616\pi\) | |||||||
\(674\) | 5113.06 | − | 31844.5i | 0.292207 | − | 1.81989i | ||||
\(675\) | 9436.87 | + | 16345.1i | 0.538112 | + | 0.932037i | ||||
\(676\) | 7230.43 | + | 2383.33i | 0.411381 | + | 0.135601i | ||||
\(677\) | 7961.97 | + | 4596.84i | 0.451999 | + | 0.260962i | 0.708674 | − | 0.705536i | \(-0.249294\pi\) |
−0.256675 | + | 0.966498i | \(0.582627\pi\) | |||||||
\(678\) | −6617.69 | + | 2524.17i | −0.374854 | + | 0.142980i | ||||
\(679\) | −2934.72 | − | 6252.03i | −0.165868 | − | 0.353359i | ||||
\(680\) | −278.818 | + | 538.693i | −0.0157238 | + | 0.0303793i | ||||
\(681\) | −5419.02 | + | 9386.01i | −0.304930 | + | 0.528154i | ||||
\(682\) | 6614.93 | − | 8133.37i | 0.371406 | − | 0.456661i | ||||
\(683\) | 6425.91 | − | 3710.00i | 0.360001 | − | 0.207847i | −0.309080 | − | 0.951036i | \(-0.600021\pi\) |
0.669081 | + | 0.743189i | \(0.266688\pi\) | |||||||
\(684\) | −1595.37 | − | 7665.68i | −0.0891822 | − | 0.428516i | ||||
\(685\) | − | 1174.26i | − | 0.0654981i | ||||||
\(686\) | −16454.0 | − | 7217.75i | −0.915766 | − | 0.401713i | ||||
\(687\) | − | 3920.89i | − | 0.217746i | ||||||
\(688\) | −9828.36 | + | 13288.6i | −0.544626 | + | 0.736370i | ||||
\(689\) | 10901.3 | − | 6293.86i | 0.602766 | − | 0.348007i | ||||
\(690\) | 654.703 | + | 532.475i | 0.0361219 | + | 0.0293782i | ||||
\(691\) | 13698.2 | − | 23726.1i | 0.754133 | − | 1.30620i | −0.191672 | − | 0.981459i | \(-0.561391\pi\) |
0.945804 | − | 0.324737i | \(-0.105276\pi\) | |||||||
\(692\) | −15276.9 | − | 17112.4i | −0.839223 | − | 0.940054i | ||||
\(693\) | −2466.19 | − | 5253.90i | −0.135185 | − | 0.287993i | ||||
\(694\) | 1896.41 | + | 4971.87i | 0.103727 | + | 0.271944i | ||||
\(695\) | 1985.26 | + | 1146.19i | 0.108353 | + | 0.0625575i | ||||
\(696\) | 20228.8 | − | 930.885i | 1.10168 | − | 0.0506970i | ||||
\(697\) | 4660.07 | + | 8071.48i | 0.253246 | + | 0.438636i | ||||
\(698\) | 2309.67 | + | 370.848i | 0.125247 | + | 0.0201100i | ||||
\(699\) | −9267.08 | −0.501450 | ||||||||
\(700\) | 10993.7 | + | 14641.2i | 0.593606 | + | 0.790551i | ||||
\(701\) | −14947.5 | −0.805362 | −0.402681 | − | 0.915340i | \(-0.631922\pi\) | ||||
−0.402681 | + | 0.915340i | \(0.631922\pi\) | |||||||
\(702\) | −23933.4 | − | 3842.82i | −1.28676 | − | 0.206607i | ||||
\(703\) | −8651.30 | − | 14984.5i | −0.464139 | − | 0.803913i | ||||
\(704\) | −15903.3 | − | 7324.96i | −0.851392 | − | 0.392145i | ||||
\(705\) | −2656.31 | − | 1533.62i | −0.141904 | − | 0.0819284i | ||||
\(706\) | 8211.26 | + | 21527.7i | 0.437726 | + | 1.14760i | ||||
\(707\) | −5216.94 | + | 7490.97i | −0.277515 | + | 0.398482i | ||||
\(708\) | 2163.81 | − | 1931.72i | 0.114860 | − | 0.102540i | ||||
\(709\) | −1150.36 | + | 1992.49i | −0.0609348 | + | 0.105542i | −0.894884 | − | 0.446300i | \(-0.852742\pi\) |
0.833949 | + | 0.551842i | \(0.186075\pi\) | |||||||
\(710\) | 349.458 | + | 284.217i | 0.0184717 | + | 0.0150232i | ||||
\(711\) | 6683.30 | − | 3858.60i | 0.352522 | − | 0.203529i | ||||
\(712\) | 9659.78 | − | 6185.95i | 0.508449 | − | 0.325602i | ||||
\(713\) | − | 6415.91i | − | 0.336995i | ||||||
\(714\) | −1200.13 | + | 4821.98i | −0.0629046 | + | 0.252743i | ||||
\(715\) | 2290.18i | 0.119787i | ||||||||
\(716\) | −13367.0 | + | 2781.92i | −0.697692 | + | 0.145203i | ||||
\(717\) | 8466.11 | − | 4887.91i | 0.440966 | − | 0.254592i | ||||
\(718\) | 4575.63 | − | 5625.95i | 0.237829 | − | 0.292421i | ||||
\(719\) | −14069.6 | + | 24369.3i | −0.729775 | + | 1.26401i | 0.227202 | + | 0.973848i | \(0.427042\pi\) |
−0.956978 | + | 0.290161i | \(0.906291\pi\) | |||||||
\(720\) | 695.477 | + | 79.0793i | 0.0359984 | + | 0.00409321i | ||||
\(721\) | 795.034 | − | 9360.99i | 0.0410661 | − | 0.483525i | ||||
\(722\) | −12019.5 | + | 4584.59i | −0.619558 | + | 0.236317i | ||||
\(723\) | −966.034 | − | 557.740i | −0.0496918 | − | 0.0286896i | ||||
\(724\) | −10402.1 | + | 31557.3i | −0.533964 | + | 1.61992i | ||||
\(725\) | −13093.2 | − | 22678.1i | −0.670716 | − | 1.16171i | ||||
\(726\) | 305.879 | − | 1905.04i | 0.0156367 | − | 0.0973865i | ||||
\(727\) | 9987.58 | 0.509517 | 0.254758 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254758 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(728\) | −23497.3 | − | 910.782i | −1.19625 | − | 0.0463679i | ||||
\(729\) | 21059.2 | 1.06992 | ||||||||
\(730\) | −417.403 | + | 2599.62i | −0.0211627 | + | 0.131803i | ||||
\(731\) | 2900.36 | + | 5023.57i | 0.146749 | + | 0.254177i | ||||
\(732\) | 3810.97 | − | 11561.5i | 0.192428 | − | 0.583780i | ||||
\(733\) | −25711.7 | − | 14844.7i | −1.29561 | − | 0.748022i | −0.315969 | − | 0.948770i | \(-0.602330\pi\) |
−0.979643 | + | 0.200748i | \(0.935663\pi\) | |||||||
\(734\) | 14471.8 | − | 5519.94i | 0.727742 | − | 0.277581i | ||||
\(735\) | −1330.00 | − | 1104.54i | −0.0667454 | − | 0.0554309i | ||||
\(736\) | −10379.1 | + | 2663.23i | −0.519809 | + | 0.133380i | ||||
\(737\) | −11453.7 | + | 19838.4i | −0.572461 | + | 0.991531i | ||||
\(738\) | 6786.11 | − | 8343.83i | 0.338483 | − | 0.416180i | ||||
\(739\) | 11937.0 | − | 6891.81i | 0.594193 | − | 0.343057i | −0.172561 | − | 0.984999i | \(-0.555204\pi\) |
0.766754 | + | 0.641942i | \(0.221871\pi\) | |||||||
\(740\) | 1514.32 | − | 315.159i | 0.0752264 | − | 0.0156560i | ||||
\(741\) | 25310.5i | 1.25480i | ||||||||
\(742\) | −8159.48 | + | 8456.40i | −0.403698 | + | 0.418388i | ||||
\(743\) | 33130.8i | 1.63587i | 0.575311 | + | 0.817935i | \(0.304881\pi\) | ||||
−0.575311 | + | 0.817935i | \(0.695119\pi\) | |||||||
\(744\) | 5585.69 | + | 8722.44i | 0.275244 | + | 0.429812i | ||||
\(745\) | 92.1761 | − | 53.2179i | 0.00453298 | − | 0.00261712i | ||||
\(746\) | 8748.95 | + | 7115.60i | 0.429386 | + | 0.349223i | ||||
\(747\) | −1982.65 | + | 3434.06i | −0.0971105 | + | 0.168200i | ||||
\(748\) | −4584.04 | + | 4092.35i | −0.224076 | + | 0.200042i | ||||
\(749\) | −19777.2 | − | 1679.69i | −0.964811 | − | 0.0819420i | ||||
\(750\) | 1262.95 | + | 3311.10i | 0.0614883 | + | 0.161206i | ||||
\(751\) | −14825.3 | − | 8559.37i | −0.720348 | − | 0.415893i | 0.0945328 | − | 0.995522i | \(-0.469864\pi\) |
−0.814881 | + | 0.579629i | \(0.803198\pi\) | |||||||
\(752\) | 35712.4 | − | 15537.9i | 1.73178 | − | 0.753468i | ||||
\(753\) | −4749.91 | − | 8227.09i | −0.229876 | − | 0.398157i | ||||
\(754\) | 33206.4 | + | 5331.73i | 1.60386 | + | 0.257520i | ||||
\(755\) | −2588.73 | −0.124786 | ||||||||
\(756\) | 22464.9 | − | 2719.34i | 1.08074 | − | 0.130822i | ||||
\(757\) | 21689.4 | 1.04137 | 0.520683 | − | 0.853750i | \(-0.325677\pi\) | ||||
0.520683 | + | 0.853750i | \(0.325677\pi\) | |||||||
\(758\) | 33904.1 | + | 5443.75i | 1.62461 | + | 0.260852i | ||||
\(759\) | 4274.63 | + | 7403.87i | 0.204426 | + | 0.354076i | ||||
\(760\) | −132.588 | − | 2881.23i | −0.00632827 | − | 0.137517i | ||||
\(761\) | −8593.87 | − | 4961.67i | −0.409366 | − | 0.236347i | 0.281151 | − | 0.959663i | \(-0.409284\pi\) |
−0.690517 | + | 0.723316i | \(0.742617\pi\) | |||||||
\(762\) | 2174.47 | + | 5700.86i | 0.103376 | + | 0.271024i | ||||
\(763\) | 12120.7 | + | 8441.20i | 0.575095 | + | 0.400514i | ||||
\(764\) | −18947.2 | − | 21223.7i | −0.897234 | − | 1.00504i | ||||
\(765\) | 122.828 | − | 212.744i | 0.00580503 | − | 0.0100546i | ||||
\(766\) | −38.6317 | − | 31.4195i | −0.00182222 | − | 0.00148203i | ||||
\(767\) | 4171.99 | − | 2408.70i | 0.196404 | − | 0.113394i | ||||
\(768\) | 11791.8 | − | 12656.7i | 0.554038 | − | 0.594676i | ||||
\(769\) | 39574.3i | 1.85577i | 0.372869 | + | 0.927884i | \(0.378374\pi\) | ||||
−0.372869 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(770\) | −590.155 | − | 2054.90i | −0.0276204 | − | 0.0961734i | ||||
\(771\) | 30416.7i | 1.42079i | ||||||||
\(772\) | 1240.84 | + | 5962.16i | 0.0578481 | + | 0.277957i | ||||
\(773\) | −2247.09 | + | 1297.36i | −0.104557 | + | 0.0603658i | −0.551366 | − | 0.834263i | \(-0.685893\pi\) |
0.446810 | + | 0.894629i | \(0.352560\pi\) | |||||||
\(774\) | 4223.57 | − | 5193.07i | 0.196141 | − | 0.241164i | ||||
\(775\) | 6696.97 | − | 11599.5i | 0.310403 | − | 0.537634i | ||||
\(776\) | 7493.91 | + | 3878.70i | 0.346670 | + | 0.179430i | ||||
\(777\) | 11470.4 | − | 5384.25i | 0.529600 | − | 0.248596i | ||||
\(778\) | −15572.9 | + | 5939.96i | −0.717631 | + | 0.273725i | ||||
\(779\) | −38380.3 | − | 22158.9i | −1.76523 | − | 1.01916i | ||||
\(780\) | −2148.90 | − | 708.331i | −0.0986450 | − | 0.0325158i | ||||
\(781\) | 2281.65 | + | 3951.93i | 0.104538 | + | 0.181064i | ||||
\(782\) | −596.184 | + | 3713.08i | −0.0272628 | + | 0.169795i | ||||
\(783\) | −32364.5 | −1.47715 | ||||||||
\(784\) | 21318.0 | − | 5237.78i | 0.971118 | − | 0.238601i | ||||
\(785\) | 2974.41 | 0.135237 | ||||||||
\(786\) | 1192.33 | − | 7425.89i | 0.0541080 | − | 0.336988i | ||||
\(787\) | 8417.03 | + | 14578.7i | 0.381239 | + | 0.660325i | 0.991240 | − | 0.132076i | \(-0.0421643\pi\) |
−0.610001 | + | 0.792401i | \(0.708831\pi\) | |||||||
\(788\) | 7254.47 | + | 2391.25i | 0.327956 | + | 0.108102i | ||||
\(789\) | 12948.5 | + | 7475.82i | 0.584257 | + | 0.337321i | ||||
\(790\) | 2656.10 | − | 1013.11i | 0.119620 | − | 0.0456264i | ||||
\(791\) | 9940.61 | − | 4666.15i | 0.446836 | − | 0.209746i | ||||
\(792\) | 6297.51 | + | 3259.47i | 0.282541 | + | 0.146238i | ||||
\(793\) | 10108.9 | − | 17509.2i | 0.452684 | − | 0.784071i | ||||
\(794\) | −7684.58 | + | 9448.54i | −0.343470 | + | 0.422313i | ||||
\(795\) | −979.219 | + | 565.352i | −0.0436847 | + | 0.0252214i | ||||
\(796\) | −448.257 | − | 2153.85i | −0.0199598 | − | 0.0959060i | ||||
\(797\) | 1595.10i | 0.0708927i | 0.999372 | + | 0.0354464i | \(0.0112853\pi\) | ||||
−0.999372 | + | 0.0354464i | \(0.988715\pi\) | |||||||
\(798\) | −6522.24 | − | 22710.2i | −0.289329 | − | 1.00744i | ||||
\(799\) | − | 13668.4i | − | 0.605200i | ||||||
\(800\) | −21544.6 | − | 6018.90i | −0.952147 | − | 0.266000i | ||||
\(801\) | −4023.14 | + | 2322.76i | −0.177467 | + | 0.102460i | ||||
\(802\) | −3351.12 | − | 2725.49i | −0.147546 | − | 0.120001i | ||||
\(803\) | −13336.6 | + | 23099.6i | −0.586099 | + | 1.01515i | ||||
\(804\) | −15072.1 | − | 16883.0i | −0.661134 | − | 0.740569i | ||||
\(805\) | −1073.68 | − | 747.747i | −0.0470092 | − | 0.0327386i | ||||
\(806\) | 6130.55 | + | 16072.6i | 0.267915 | + | 0.702400i | ||||
\(807\) | 14253.2 | + | 8229.12i | 0.621732 | + | 0.358957i | ||||
\(808\) | −512.695 | − | 11141.2i | −0.0223225 | − | 0.485082i | ||||
\(809\) | −10018.8 | − | 17353.0i | −0.435403 | − | 0.754140i | 0.561926 | − | 0.827188i | \(-0.310061\pi\) |
−0.997328 | + | 0.0730482i | \(0.976727\pi\) | |||||||
\(810\) | 1325.18 | + | 212.776i | 0.0574842 | + | 0.00922985i | ||||
\(811\) | −16147.8 | −0.699167 | −0.349583 | − | 0.936905i | \(-0.613677\pi\) | ||||
−0.349583 | + | 0.936905i | \(0.613677\pi\) | |||||||
\(812\) | −31168.9 | + | 3772.96i | −1.34706 | + | 0.163060i | ||||
\(813\) | −4616.38 | −0.199143 | ||||||||
\(814\) | 15471.6 | + | 2484.17i | 0.666192 | + | 0.106966i | ||||
\(815\) | −688.105 | − | 1191.83i | −0.0295746 | − | 0.0512247i | ||||
\(816\) | −2422.10 | − | 5566.98i | −0.103910 | − | 0.238827i | ||||
\(817\) | −23887.3 | − | 13791.3i | −1.02290 | − | 0.590572i | ||||
\(818\) | −7144.11 | − | 18729.9i | −0.305364 | − | 0.800582i | ||||
\(819\) | 9489.13 | + | 805.918i | 0.404856 | + | 0.0343847i | ||||
\(820\) | 2955.42 | − | 2638.42i | 0.125863 | − | 0.112363i | ||||
\(821\) | 7626.13 | − | 13208.9i | 0.324183 | − | 0.561501i | −0.657164 | − | 0.753748i | \(-0.728244\pi\) |
0.981347 | + | 0.192247i | \(0.0615774\pi\) | |||||||
\(822\) | 9118.02 | + | 7415.76i | 0.386895 | + | 0.314665i | ||||
\(823\) | 1161.51 | − | 670.600i | 0.0491954 | − | 0.0284030i | −0.475201 | − | 0.879878i | \(-0.657625\pi\) |
0.524396 | + | 0.851475i | \(0.324291\pi\) | |||||||
\(824\) | 6189.94 | + | 9666.00i | 0.261695 | + | 0.408654i | ||||
\(825\) | 17847.6i | 0.753179i | ||||||||
\(826\) | −3122.68 | + | 3236.31i | −0.131540 | + | 0.136327i | ||||
\(827\) | − | 12566.7i | − | 0.528400i | −0.964468 | − | 0.264200i | \(-0.914892\pi\) | ||
0.964468 | − | 0.264200i | \(-0.0851079\pi\) | |||||||
\(828\) | 4248.58 | − | 884.210i | 0.178319 | − | 0.0371116i | ||||
\(829\) | −11202.2 | + | 6467.57i | −0.469321 | + | 0.270963i | −0.715955 | − | 0.698146i | \(-0.754009\pi\) |
0.246634 | + | 0.969109i | \(0.420675\pi\) | |||||||
\(830\) | −921.648 | + | 1133.21i | −0.0385432 | + | 0.0473907i | ||||
\(831\) | 1872.58 | − | 3243.40i | 0.0781697 | − | 0.135394i | ||||
\(832\) | 23456.2 | − | 16589.2i | 0.977402 | − | 0.691259i | ||||
\(833\) | 1299.28 | − | 7593.87i | 0.0540423 | − | 0.315861i | ||||
\(834\) | −21437.5 | + | 8176.85i | −0.890071 | + | 0.339498i | ||||
\(835\) | −3587.64 | − | 2071.33i | −0.148689 | − | 0.0858458i | ||||
\(836\) | 9147.38 | − | 27750.9i | 0.378432 | − | 1.14807i | ||||
\(837\) | −8276.96 | − | 14336.1i | −0.341809 | − | 0.592030i | ||||
\(838\) | −7434.44 | + | 46302.2i | −0.306466 | + | 1.90869i | ||||
\(839\) | 15886.4 | 0.653706 | 0.326853 | − | 0.945075i | \(-0.394012\pi\) | ||||
0.326853 | + | 0.945075i | \(0.394012\pi\) | |||||||
\(840\) | 2110.67 | + | 81.8119i | 0.0866963 | + | 0.00336045i | ||||
\(841\) | 20515.1 | 0.841163 | ||||||||
\(842\) | −2965.58 | + | 18469.9i | −0.121378 | + | 0.755954i | ||||
\(843\) | −16362.3 | − | 28340.3i | −0.668502 | − | 1.15788i | ||||
\(844\) | −13427.0 | + | 40734.1i | −0.547601 | + | 1.66129i | ||||
\(845\) | −983.593 | − | 567.878i | −0.0400433 | − | 0.0231190i | ||||
\(846\) | −14737.1 | + | 5621.16i | −0.598905 | + | 0.228439i | ||||
\(847\) | −253.155 | + | 2980.73i | −0.0102698 | + | 0.120920i | ||||
\(848\) | 1622.02 | − | 14265.1i | 0.0656845 | − | 0.577673i | ||||
\(849\) | 1914.84 | − | 3316.60i | 0.0774053 | − | 0.134070i | ||||
\(850\) | −4953.60 | + | 6090.68i | −0.199891 | + | 0.245775i | ||||
\(851\) | 8304.91 | − | 4794.84i | 0.334534 | − | 0.193143i | ||||
\(852\) | −4413.83 | + | 918.603i | −0.177483 | + | 0.0369376i | ||||
\(853\) | 2788.43i | 0.111928i | 0.998433 | + | 0.0559638i | \(0.0178231\pi\) | ||||
−0.998433 | + | 0.0559638i | \(0.982177\pi\) | |||||||
\(854\) | −4558.46 | + | 18315.3i | −0.182655 | + | 0.733884i | ||||
\(855\) | 1168.10i | 0.0467232i | ||||||||
\(856\) | 20421.6 | − | 13077.6i | 0.815417 | − | 0.522178i | ||||
\(857\) | −5676.87 | + | 3277.55i | −0.226276 | + | 0.130640i | −0.608853 | − | 0.793283i | \(-0.708370\pi\) |
0.382577 | + | 0.923924i | \(0.375037\pi\) | |||||||
\(858\) | −17783.0 | − | 14463.1i | −0.707579 | − | 0.575480i | ||||
\(859\) | −10190.7 | + | 17650.9i | −0.404777 | + | 0.701095i | −0.994296 | − | 0.106660i | \(-0.965984\pi\) |
0.589518 | + | 0.807755i | \(0.299318\pi\) | |||||||
\(860\) | 1839.41 | − | 1642.11i | 0.0729341 | − | 0.0651111i | ||||
\(861\) | 18548.0 | − | 26633.0i | 0.734164 | − | 1.05418i | ||||
\(862\) | −11453.9 | − | 30029.0i | −0.452577 | − | 1.18653i | ||||
\(863\) | 29681.7 | + | 17136.7i | 1.17077 | + | 0.675945i | 0.953862 | − | 0.300246i | \(-0.0970689\pi\) |
0.216910 | + | 0.976192i | \(0.430402\pi\) | |||||||
\(864\) | −19756.1 | + | 19340.7i | −0.777911 | + | 0.761555i | ||||
\(865\) | 1711.11 | + | 2963.72i | 0.0672594 | + | 0.116497i | ||||
\(866\) | 16281.8 | + | 2614.25i | 0.638888 | + | 0.102582i | ||||
\(867\) | 18618.3 | 0.729309 | ||||||||
\(868\) | −9642.47 | − | 12841.6i | −0.377059 | − | 0.502158i | ||||
\(869\) | 28799.0 | 1.12421 | ||||||||
\(870\) | −2982.80 | − | 478.928i | −0.116237 | − | 0.0186634i | ||||
\(871\) | −18793.7 | − | 32551.7i | −0.731114 | − | 1.26633i | ||||
\(872\) | −18026.9 | + | 829.560i | −0.700077 | + | 0.0322161i | ||||
\(873\) | −2959.54 | − | 1708.69i | −0.114737 | − | 0.0662433i | ||||
\(874\) | −6372.85 | − | 16707.9i | −0.246642 | − | 0.646627i | ||||
\(875\) | −2334.66 | − | 4973.69i | −0.0902011 | − | 0.192162i | ||||
\(876\) | −17549.8 | − | 19658.3i | −0.676885 | − | 0.758212i | ||||
\(877\) | −17002.8 | + | 29449.7i | −0.654669 | + | 1.13392i | 0.327308 | + | 0.944918i | \(0.393858\pi\) |
−0.981977 | + | 0.189002i | \(0.939475\pi\) | |||||||
\(878\) | 13781.7 | + | 11208.8i | 0.529738 | + | 0.430841i | ||||
\(879\) | 7548.27 | − | 4358.00i | 0.289644 | − | 0.167226i | ||||
\(880\) | 2100.10 | + | 1553.26i | 0.0804483 | + | 0.0595003i | ||||
\(881\) | − | 3501.55i | − | 0.133905i | −0.997756 | − | 0.0669525i | \(-0.978672\pi\) | ||
0.997756 | − | 0.0669525i | \(-0.0213276\pi\) | |||||||
\(882\) | −8721.94 | + | 1722.12i | −0.332974 | + | 0.0657448i | ||||
\(883\) | − | 19090.8i | − | 0.727583i | −0.931480 | − | 0.363791i | \(-0.881482\pi\) | ||
0.931480 | − | 0.363791i | \(-0.118518\pi\) | |||||||
\(884\) | −2054.42 | − | 9871.39i | −0.0781649 | − | 0.375578i | ||||
\(885\) | −374.753 | + | 216.364i | −0.0142341 | + | 0.00821806i | ||||
\(886\) | −8679.57 | + | 10671.9i | −0.329115 | + | 0.404662i | ||||
\(887\) | 18192.2 | − | 31509.9i | 0.688653 | − | 1.19278i | −0.283621 | − | 0.958937i | \(-0.591536\pi\) |
0.972274 | − | 0.233845i | \(-0.0751310\pi\) | |||||||
\(888\) | −7116.15 | + | 13748.9i | −0.268922 | + | 0.519574i | ||||
\(889\) | −4019.69 | − | 8563.41i | −0.151649 | − | 0.323068i | ||||
\(890\) | −1598.89 | + | 609.862i | −0.0602190 | + | 0.0229692i | ||||
\(891\) | 11775.3 | + | 6798.47i | 0.442746 | + | 0.255620i | ||||
\(892\) | −15627.7 | − | 5151.26i | −0.586606 | − | 0.193360i | ||||
\(893\) | 32497.0 | + | 56286.5i | 1.21777 | + | 2.10925i | ||||
\(894\) | −168.884 | + | 1051.82i | −0.00631805 | + | 0.0393493i | ||||
\(895\) | 2036.87 | 0.0760728 | ||||||||
\(896\) | −16771.6 | + | 20929.3i | −0.625334 | + | 0.780357i | ||||
\(897\) | −14027.9 | −0.522162 | ||||||||
\(898\) | 2836.82 | − | 17668.0i | 0.105419 | − | 0.656556i | ||||
\(899\) | 11483.9 | + | 19890.7i | 0.426039 | + | 0.737921i | ||||
\(900\) | 8604.07 | + | 2836.11i | 0.318669 | + | 0.105041i | ||||
\(901\) | −4363.66 | − | 2519.36i | −0.161348 | − | 0.0931543i | ||||
\(902\) | 37500.2 | − | 14303.6i | 1.38428 | − | 0.528003i | ||||
\(903\) | 11544.0 | − | 16576.0i | 0.425427 | − | 0.610868i | ||||
\(904\) | −6167.06 | + | 11915.2i | −0.226895 | + | 0.438377i | ||||
\(905\) | 2478.51 | − | 4292.91i | 0.0910370 | − | 0.157681i | ||||
\(906\) | 16348.5 | − | 20101.2i | 0.599494 | − | 0.737106i | ||||
\(907\) | −25756.4 | + | 14870.5i | −0.942918 | + | 0.544394i | −0.890874 | − | 0.454251i | \(-0.849907\pi\) |
−0.0520440 | + | 0.998645i | \(0.516574\pi\) | |||||||
\(908\) | 4183.06 | + | 20099.4i | 0.152885 | + | 0.734605i | ||||
\(909\) | 4516.85i | 0.164812i | ||||||||
\(910\) | 3404.20 | + | 847.265i | 0.124009 | + | 0.0308644i | ||||
\(911\) | − | 29434.3i | − | 1.07047i | −0.844702 | − | 0.535236i | \(-0.820223\pi\) | ||
0.844702 | − | 0.535236i | \(-0.179777\pi\) | |||||||
\(912\) | 23209.8 | + | 17166.2i | 0.842712 | + | 0.623277i | ||||
\(913\) | −12815.2 | + | 7398.84i | −0.464535 | + | 0.268199i | ||||
\(914\) | 37522.7 | + | 30517.6i | 1.35792 | + | 1.10441i | ||||
\(915\) | −908.043 | + | 1572.78i | −0.0328076 | + | 0.0568245i | ||||
\(916\) | −4946.26 | − | 5540.55i | −0.178416 | − | 0.199853i | ||||
\(917\) | −986.805 | + | 11619.0i | −0.0355367 | + | 0.418421i | ||||
\(918\) | 3457.98 | + | 9065.87i | 0.124325 | + | 0.325946i | ||||
\(919\) | 38082.9 | + | 21987.2i | 1.36696 | + | 0.789216i | 0.990539 | − | 0.137231i | \(-0.0438203\pi\) |
0.376424 | + | 0.926448i | \(0.377154\pi\) | |||||||
\(920\) | 1596.87 | − | 73.4849i | 0.0572254 | − | 0.00263340i | ||||
\(921\) | 9045.81 | + | 15667.8i | 0.323637 | + | 0.560556i | ||||
\(922\) | −42946.0 | − | 6895.54i | −1.53400 | − | 0.246304i | ||||
\(923\) | −7487.63 | −0.267019 | ||||||||
\(924\) | 19683.1 | + | 8394.73i | 0.700786 | + | 0.298881i | ||||
\(925\) | 20019.6 | 0.711611 | ||||||||
\(926\) | −6215.30 | − | 997.950i | −0.220570 | − | 0.0354154i | ||||
\(927\) | −2324.26 | − | 4025.73i | −0.0823502 | − | 0.142635i | ||||
\(928\) | 27410.6 | − | 26834.3i | 0.969608 | − | 0.949222i | ||||
\(929\) | 23203.6 | + | 13396.6i | 0.819466 | + | 0.473119i | 0.850232 | − | 0.526408i | \(-0.176461\pi\) |
−0.0307661 | + | 0.999527i | \(0.509795\pi\) | |||||||
\(930\) | −550.683 | − | 1443.74i | −0.0194168 | − | 0.0509055i | ||||
\(931\) | 12704.2 | + | 34360.6i | 0.447222 | + | 1.20958i | ||||
\(932\) | −13095.2 | + | 11690.6i | −0.460243 | + | 0.410876i | ||||
\(933\) | −8237.86 | + | 14268.4i | −0.289063 | + | 0.500671i | ||||
\(934\) | −26919.4 | − | 21893.7i | −0.943071 | − | 0.767008i | ||||
\(935\) | 793.915 | − | 458.367i | 0.0277688 | − | 0.0160323i | ||||
\(936\) | −9798.33 | + | 6274.67i | −0.342167 | + | 0.219118i | ||||
\(937\) | − | 26439.9i | − | 0.921831i | −0.887444 | − | 0.460915i | \(-0.847521\pi\) | ||
0.887444 | − | 0.460915i | \(-0.152479\pi\) | |||||||
\(938\) | 25251.1 | + | 24364.5i | 0.878975 | + | 0.848113i | ||||
\(939\) | 39784.9i | 1.38267i | ||||||||
\(940\) | −5688.27 | + | 1183.84i | −0.197373 | + | 0.0410771i | ||||
\(941\) | −33418.7 | + | 19294.3i | −1.15773 | + | 0.668413i | −0.950758 | − | 0.309935i | \(-0.899693\pi\) |
−0.206967 | + | 0.978348i | \(0.566359\pi\) | |||||||
\(942\) | −18784.2 | + | 23096.0i | −0.649704 | + | 0.798841i | ||||
\(943\) | 12281.2 | − | 21271.6i | 0.424104 | − | 0.734570i | ||||
\(944\) | 620.757 | − | 5459.36i | 0.0214025 | − | 0.188228i | ||||
\(945\) | −3363.76 | − | 285.686i | −0.115792 | − | 0.00983425i | ||||
\(946\) | 23339.6 | − | 8902.36i | 0.802150 | − | 0.305963i | ||||
\(947\) | −24197.7 | − | 13970.6i | −0.830328 | − | 0.479390i | 0.0236370 | − | 0.999721i | \(-0.492475\pi\) |
−0.853965 | + | 0.520331i | \(0.825809\pi\) | |||||||
\(948\) | −8907.25 | + | 27022.4i | −0.305162 | + | 0.925788i | ||||
\(949\) | −21883.1 | − | 37902.7i | −0.748532 | − | 1.29650i | ||||
\(950\) | 5918.15 | − | 36858.7i | 0.202116 | − | 1.25879i | ||||
\(951\) | −3890.64 | −0.132663 | ||||||||
\(952\) | 4387.11 | + | 8327.85i | 0.149356 | + | 0.283516i | ||||
\(953\) | −27352.6 | −0.929735 | −0.464867 | − | 0.885380i | \(-0.653898\pi\) | ||||
−0.464867 | + | 0.885380i | \(0.653898\pi\) | |||||||
\(954\) | −921.783 | + | 5740.93i | −0.0312828 | + | 0.194832i | ||||
\(955\) | 2122.20 | + | 3675.76i | 0.0719087 | + | 0.124550i | ||||
\(956\) | 5797.15 | − | 17587.1i | 0.196123 | − | 0.594989i | ||||
\(957\) | −26504.5 | − | 15302.4i | −0.895266 | − | 0.516882i | ||||
\(958\) | −9358.68 | + | 3569.66i | −0.315621 | + | 0.120387i | ||||
\(959\) | −14953.2 | − | 10413.8i | −0.503507 | − | 0.350657i | ||||
\(960\) | −2106.98 | + | 1490.14i | −0.0708359 | + | 0.0500981i | ||||
\(961\) | 9021.67 | − | 15626.0i | 0.302832 | − | 0.524520i | ||||
\(962\) | −16223.2 | + | 19947.2i | −0.543719 | + | 0.668528i | ||||
\(963\) | −8505.27 | + | 4910.52i | −0.284609 | + | 0.164319i | ||||
\(964\) | −2068.68 | + | 430.532i | −0.0691160 | + | 0.0143844i | ||||
\(965\) | − | 908.519i | − | 0.0303070i | ||||||
\(966\) | 12586.8 | − | 3614.84i | 0.419227 | − | 0.120399i | ||||
\(967\) | 35591.9i | 1.18362i | 0.806078 | + | 0.591810i | \(0.201586\pi\) | ||||
−0.806078 | + | 0.591810i | \(0.798414\pi\) | |||||||
\(968\) | −1971.00 | − | 3077.85i | −0.0654445 | − | 0.102196i | ||||
\(969\) | 8774.14 | − | 5065.75i | 0.290883 | − | 0.167942i | ||||
\(970\) | −976.621 | − | 794.294i | −0.0323272 | − | 0.0262920i | ||||
\(971\) | 11608.1 | − | 20105.8i | 0.383646 | − | 0.664495i | −0.607934 | − | 0.793987i | \(-0.708002\pi\) |
0.991580 | + | 0.129493i | \(0.0413349\pi\) | |||||||
\(972\) | 14588.7 | − | 13023.9i | 0.481412 | − | 0.429775i | ||||
\(973\) | 32201.8 | − | 15115.6i | 1.06099 | − | 0.498031i | ||||
\(974\) | −14524.9 | − | 38080.4i | −0.477833 | − | 1.25275i | ||||
\(975\) | −25361.5 | − | 14642.5i | −0.833044 | − | 0.480958i | ||||
\(976\) | −9199.83 | − | 21145.0i | −0.301721 | − | 0.693479i | ||||
\(977\) | −8293.68 | − | 14365.1i | −0.271585 | − | 0.470398i | 0.697683 | − | 0.716406i | \(-0.254214\pi\) |
−0.969268 | + | 0.246008i | \(0.920881\pi\) | |||||||
\(978\) | 13600.0 | + | 2183.67i | 0.444664 | + | 0.0713967i | ||||
\(979\) | −17336.1 | −0.565949 | ||||||||
\(980\) | −3272.80 | + | 117.005i | −0.106679 | + | 0.00381385i | ||||
\(981\) | 7308.43 | 0.237859 | ||||||||
\(982\) | −34443.7 | − | 5530.40i | −1.11929 | − | 0.179717i | ||||
\(983\) | 12644.5 | + | 21900.9i | 0.410271 | + | 0.710611i | 0.994919 | − | 0.100676i | \(-0.0321007\pi\) |
−0.584648 | + | 0.811287i | \(0.698767\pi\) | |||||||
\(984\) | 1822.81 | + | 39610.8i | 0.0590539 | + | 1.28328i | ||||
\(985\) | −986.863 | − | 569.766i | −0.0319229 | − | 0.0184307i | ||||
\(986\) | −4797.78 | − | 12578.5i | −0.154962 | − | 0.406267i | ||||
\(987\) | −43086.6 | + | 20224.9i | −1.38952 | + | 0.652246i | ||||
\(988\) | 31929.6 | + | 35765.9i | 1.02815 | + | 1.15168i | ||||
\(989\) | 7643.62 | − | 13239.1i | 0.245756 | − | 0.425662i | ||||
\(990\) | −820.704 | − | 667.485i | −0.0263472 | − | 0.0214284i | ||||
\(991\) | −39133.0 | + | 22593.5i | −1.25439 | + | 0.724223i | −0.971979 | − | 0.235069i | \(-0.924468\pi\) |
−0.282413 | + | 0.959293i | \(0.591135\pi\) | |||||||
\(992\) | 18896.5 | + | 5279.10i | 0.604804 | + | 0.168963i | ||||
\(993\) | − | 13388.2i | − | 0.427855i | ||||||
\(994\) | 6718.39 | − | 1929.48i | 0.214381 | − | 0.0615688i | ||||
\(995\) | 328.205i | 0.0104571i | ||||||||
\(996\) | −2978.81 | − | 14313.0i | −0.0947662 | − | 0.455346i | ||||
\(997\) | 6968.90 | − | 4023.50i | 0.221371 | − | 0.127809i | −0.385214 | − | 0.922827i | \(-0.625872\pi\) |
0.606585 | + | 0.795019i | \(0.292539\pi\) | |||||||
\(998\) | 6887.89 | − | 8468.98i | 0.218469 | − | 0.268618i | ||||
\(999\) | 12371.4 | − | 21427.8i | 0.391804 | − | 0.678625i |
(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 | 28.4.f.a.19.6 | yes | 20 | |
4.3 | odd | 2 | inner | 28.4.f.a.19.8 | yes | 20 | |
7.2 | even | 3 | 196.4.d.b.195.4 | 20 | |||
7.3 | odd | 6 | inner | 28.4.f.a.3.8 | yes | 20 | |
7.4 | even | 3 | 196.4.f.d.31.8 | 20 | |||
7.5 | odd | 6 | 196.4.d.b.195.3 | 20 | |||
7.6 | odd | 2 | 196.4.f.d.19.6 | 20 | |||
8.3 | odd | 2 | 448.4.p.h.383.3 | 20 | |||
8.5 | even | 2 | 448.4.p.h.383.8 | 20 | |||
28.3 | even | 6 | inner | 28.4.f.a.3.6 | ✓ | 20 | |
28.11 | odd | 6 | 196.4.f.d.31.6 | 20 | |||
28.19 | even | 6 | 196.4.d.b.195.2 | 20 | |||
28.23 | odd | 6 | 196.4.d.b.195.1 | 20 | |||
28.27 | even | 2 | 196.4.f.d.19.8 | 20 | |||
56.3 | even | 6 | 448.4.p.h.255.8 | 20 | |||
56.45 | odd | 6 | 448.4.p.h.255.3 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.4.f.a.3.6 | ✓ | 20 | 28.3 | even | 6 | inner | |
28.4.f.a.3.8 | yes | 20 | 7.3 | odd | 6 | inner | |
28.4.f.a.19.6 | yes | 20 | 1.1 | even | 1 | trivial | |
28.4.f.a.19.8 | yes | 20 | 4.3 | odd | 2 | inner | |
196.4.d.b.195.1 | 20 | 28.23 | odd | 6 | |||
196.4.d.b.195.2 | 20 | 28.19 | even | 6 | |||
196.4.d.b.195.3 | 20 | 7.5 | odd | 6 | |||
196.4.d.b.195.4 | 20 | 7.2 | even | 3 | |||
196.4.f.d.19.6 | 20 | 7.6 | odd | 2 | |||
196.4.f.d.19.8 | 20 | 28.27 | even | 2 | |||
196.4.f.d.31.6 | 20 | 28.11 | odd | 6 | |||
196.4.f.d.31.8 | 20 | 7.4 | even | 3 | |||
448.4.p.h.255.3 | 20 | 56.45 | odd | 6 | |||
448.4.p.h.255.8 | 20 | 56.3 | even | 6 | |||
448.4.p.h.383.3 | 20 | 8.3 | odd | 2 | |||
448.4.p.h.383.8 | 20 | 8.5 | even | 2 |