Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,5,Mod(3,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.d (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: | \(0.723589741587\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 22x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 3.1 | ||
Root | \(-2.34521 - 4.06202i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.3 |
Dual form | 7.5.d.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.34521 | − | 5.79407i | −0.836302 | − | 1.44852i | −0.892966 | − | 0.450124i | \(-0.851380\pi\) |
0.0566640 | − | 0.998393i | \(-0.481954\pi\) | |||||||
\(3\) | 8.53562 | + | 4.92804i | 0.948403 | + | 0.547561i | 0.892584 | − | 0.450880i | \(-0.148890\pi\) |
0.0558183 | + | 0.998441i | \(0.482223\pi\) | |||||||
\(4\) | −14.3808 | + | 24.9083i | −0.898802 | + | 1.55677i | ||||
\(5\) | 6.57125 | − | 3.79391i | 0.262850 | − | 0.151756i | −0.362784 | − | 0.931873i | \(-0.618174\pi\) |
0.625634 | + | 0.780117i | \(0.284840\pi\) | |||||||
\(6\) | − | 65.9413i | − | 1.83170i | ||||||
\(7\) | −32.8329 | + | 36.3731i | −0.670059 | + | 0.742307i | ||||
\(8\) | 85.3808 | 1.33408 | ||||||||
\(9\) | 8.07125 | + | 13.9798i | 0.0996450 | + | 0.172590i | ||||
\(10\) | −43.9644 | − | 25.3828i | −0.439644 | − | 0.253828i | ||||
\(11\) | 25.3685 | − | 43.9396i | 0.209657 | − | 0.363137i | −0.741949 | − | 0.670456i | \(-0.766098\pi\) |
0.951607 | + | 0.307319i | \(0.0994318\pi\) | |||||||
\(12\) | −245.499 | + | 141.739i | −1.70485 | + | 0.984297i | ||||
\(13\) | − | 7.50702i | − | 0.0444202i | −0.999753 | − | 0.0222101i | \(-0.992930\pi\) | ||
0.999753 | − | 0.0222101i | \(-0.00707028\pi\) | |||||||
\(14\) | 320.581 | + | 68.5607i | 1.63562 | + | 0.349800i | ||||
\(15\) | 74.7863 | 0.332383 | ||||||||
\(16\) | −55.5233 | − | 96.1692i | −0.216888 | − | 0.375661i | ||||
\(17\) | −300.711 | − | 173.616i | −1.04052 | − | 0.600746i | −0.120542 | − | 0.992708i | \(-0.538463\pi\) |
−0.919981 | + | 0.391962i | \(0.871796\pi\) | |||||||
\(18\) | 54.0000 | − | 93.5307i | 0.166667 | − | 0.288675i | ||||
\(19\) | 420.818 | − | 242.959i | 1.16570 | − | 0.673018i | 0.213037 | − | 0.977044i | \(-0.431664\pi\) |
0.952664 | + | 0.304026i | \(0.0983311\pi\) | |||||||
\(20\) | 218.238i | 0.545596i | ||||||||
\(21\) | −459.497 | + | 148.665i | −1.04194 | + | 0.337108i | ||||
\(22\) | −339.452 | −0.701347 | ||||||||
\(23\) | 168.654 | + | 292.116i | 0.318816 | + | 0.552205i | 0.980241 | − | 0.197806i | \(-0.0633816\pi\) |
−0.661425 | + | 0.750011i | \(0.730048\pi\) | |||||||
\(24\) | 728.779 | + | 420.761i | 1.26524 | + | 0.730487i | ||||
\(25\) | −283.712 | + | 491.404i | −0.453940 | + | 0.786247i | ||||
\(26\) | −43.4962 | + | 25.1125i | −0.0643435 | + | 0.0371487i | ||||
\(27\) | − | 639.241i | − | 0.876874i | ||||||
\(28\) | −433.828 | − | 1340.89i | −0.553352 | − | 1.71032i | ||||
\(29\) | −215.671 | −0.256446 | −0.128223 | − | 0.991745i | \(-0.540927\pi\) | ||||
−0.128223 | + | 0.991745i | \(0.540927\pi\) | |||||||
\(30\) | −250.176 | − | 433.317i | −0.277973 | − | 0.481463i | ||||
\(31\) | 1108.53 | + | 640.012i | 1.15352 | + | 0.665985i | 0.949743 | − | 0.313032i | \(-0.101345\pi\) |
0.203778 | + | 0.979017i | \(0.434678\pi\) | |||||||
\(32\) | 311.573 | − | 539.659i | 0.304270 | − | 0.527011i | ||||
\(33\) | 433.073 | − | 250.035i | 0.397679 | − | 0.229600i | ||||
\(34\) | 2323.12i | 2.00962i | ||||||||
\(35\) | −77.7570 | + | 363.582i | −0.0634751 | + | 0.296801i | ||||
\(36\) | −464.285 | −0.358245 | ||||||||
\(37\) | 176.402 | + | 305.537i | 0.128854 | + | 0.223182i | 0.923233 | − | 0.384241i | \(-0.125537\pi\) |
−0.794379 | + | 0.607423i | \(0.792203\pi\) | |||||||
\(38\) | −2815.45 | − | 1625.50i | −1.94976 | − | 1.12569i | ||||
\(39\) | 36.9949 | − | 64.0771i | 0.0243228 | − | 0.0421283i | ||||
\(40\) | 561.059 | − | 323.927i | 0.350662 | − | 0.202455i | ||||
\(41\) | − | 1040.97i | − | 0.619255i | −0.950858 | − | 0.309627i | \(-0.899796\pi\) | ||
0.950858 | − | 0.309627i | \(-0.100204\pi\) | |||||||
\(42\) | 2398.49 | + | 2165.05i | 1.35969 | + | 1.22735i | ||||
\(43\) | −1023.65 | −0.553621 | −0.276811 | − | 0.960925i | \(-0.589277\pi\) | ||||
−0.276811 | + | 0.960925i | \(0.589277\pi\) | |||||||
\(44\) | 729.641 | + | 1263.78i | 0.376881 | + | 0.652777i | ||||
\(45\) | 106.076 | + | 61.2432i | 0.0523834 | + | 0.0302436i | ||||
\(46\) | 1128.36 | − | 1954.38i | 0.533252 | − | 0.923620i | ||||
\(47\) | −1701.16 | + | 982.166i | −0.770105 | + | 0.444620i | −0.832912 | − | 0.553405i | \(-0.813328\pi\) |
0.0628072 | + | 0.998026i | \(0.479995\pi\) | |||||||
\(48\) | − | 1094.49i | − | 0.475037i | ||||||
\(49\) | −245.000 | − | 2388.47i | −0.102041 | − | 0.994780i | ||||
\(50\) | 3796.31 | 1.51852 | ||||||||
\(51\) | −1711.17 | − | 2963.84i | −0.657890 | − | 1.13950i | ||||
\(52\) | 186.987 | + | 107.957i | 0.0691521 | + | 0.0399250i | ||||
\(53\) | −1924.87 | + | 3333.97i | −0.685251 | + | 1.18689i | 0.288107 | + | 0.957598i | \(0.406974\pi\) |
−0.973358 | + | 0.229292i | \(0.926359\pi\) | |||||||
\(54\) | −3703.81 | + | 2138.40i | −1.27017 | + | 0.733332i | ||||
\(55\) | − | 384.984i | − | 0.127267i | ||||||
\(56\) | −2803.30 | + | 3105.56i | −0.893910 | + | 0.990294i | ||||
\(57\) | 4789.26 | 1.47407 | ||||||||
\(58\) | 721.464 | + | 1249.61i | 0.214466 | + | 0.371466i | ||||
\(59\) | 3790.50 | + | 2188.44i | 1.08891 | + | 0.628682i | 0.933286 | − | 0.359134i | \(-0.116928\pi\) |
0.155624 | + | 0.987816i | \(0.450261\pi\) | |||||||
\(60\) | −1075.49 | + | 1862.80i | −0.298747 | + | 0.517445i | ||||
\(61\) | 1618.05 | − | 934.181i | 0.434843 | − | 0.251057i | −0.266565 | − | 0.963817i | \(-0.585889\pi\) |
0.701408 | + | 0.712760i | \(0.252555\pi\) | |||||||
\(62\) | − | 8563.89i | − | 2.22786i | ||||||
\(63\) | −773.491 | − | 165.422i | −0.194883 | − | 0.0416785i | ||||
\(64\) | −5945.85 | −1.45162 | ||||||||
\(65\) | −28.4810 | − | 49.3305i | −0.00674106 | − | 0.0116759i | ||||
\(66\) | −2897.44 | − | 1672.83i | −0.665160 | − | 0.384030i | ||||
\(67\) | −223.966 | + | 387.920i | −0.0498921 | + | 0.0864157i | −0.889893 | − | 0.456169i | \(-0.849221\pi\) |
0.840001 | + | 0.542585i | \(0.182554\pi\) | |||||||
\(68\) | 8648.95 | − | 4993.48i | 1.87045 | − | 1.07990i | ||||
\(69\) | 3324.53i | 0.698284i | ||||||||
\(70\) | 2366.73 | − | 765.727i | 0.483006 | − | 0.156271i | ||||
\(71\) | −1485.68 | −0.294720 | −0.147360 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147360 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(72\) | 689.130 | + | 1193.61i | 0.132934 | + | 0.230248i | ||||
\(73\) | −610.190 | − | 352.293i | −0.114504 | − | 0.0661087i | 0.441654 | − | 0.897185i | \(-0.354392\pi\) |
−0.556158 | + | 0.831077i | \(0.687725\pi\) | |||||||
\(74\) | 1180.20 | − | 2044.17i | 0.215522 | − | 0.373296i | ||||
\(75\) | −4843.33 | + | 2796.30i | −0.861036 | + | 0.497119i | ||||
\(76\) | 13975.8i | 2.41964i | ||||||||
\(77\) | 765.295 | + | 2365.40i | 0.129077 | + | 0.398954i | ||||
\(78\) | −495.023 | −0.0813647 | ||||||||
\(79\) | −2850.67 | − | 4937.50i | −0.456765 | − | 0.791140i | 0.542023 | − | 0.840364i | \(-0.317659\pi\) |
−0.998788 | + | 0.0492240i | \(0.984325\pi\) | |||||||
\(80\) | −729.715 | − | 421.301i | −0.114018 | − | 0.0658283i | ||||
\(81\) | 3803.98 | − | 6588.69i | 0.579787 | − | 1.00422i | ||||
\(82\) | −6031.44 | + | 3482.25i | −0.897001 | + | 0.517884i | ||||
\(83\) | 4028.74i | 0.584808i | 0.956295 | + | 0.292404i | \(0.0944552\pi\) | ||||
−0.956295 | + | 0.292404i | \(0.905545\pi\) | |||||||
\(84\) | 2904.96 | − | 13583.2i | 0.411701 | − | 1.92506i | ||||
\(85\) | −2634.73 | −0.364669 | ||||||||
\(86\) | 3424.31 | + | 5931.07i | 0.462994 | + | 0.801930i | ||||
\(87\) | −1840.89 | − | 1062.84i | −0.243214 | − | 0.140420i | ||||
\(88\) | 2165.99 | − | 3751.60i | 0.279699 | − | 0.484452i | ||||
\(89\) | 5852.11 | − | 3378.71i | 0.738809 | − | 0.426552i | −0.0828272 | − | 0.996564i | \(-0.526395\pi\) |
0.821636 | + | 0.570012i | \(0.193062\pi\) | |||||||
\(90\) | − | 819.485i | − | 0.101171i | ||||||
\(91\) | 273.053 | + | 246.477i | 0.0329735 | + | 0.0297642i | ||||
\(92\) | −9701.51 | −1.14621 | ||||||||
\(93\) | 6308.01 | + | 10925.8i | 0.729335 | + | 1.26324i | ||||
\(94\) | 11381.5 | + | 6571.10i | 1.28808 | + | 0.743674i | ||||
\(95\) | 1843.53 | − | 3193.09i | 0.204270 | − | 0.353805i | ||||
\(96\) | 5318.93 | − | 3070.89i | 0.577141 | − | 0.333213i | ||||
\(97\) | − | 11538.2i | − | 1.22630i | −0.789968 | − | 0.613148i | \(-0.789903\pi\) | ||
0.789968 | − | 0.613148i | \(-0.210097\pi\) | |||||||
\(98\) | −13019.4 | + | 9409.47i | −1.35562 | + | 0.979745i | ||||
\(99\) | 819.023 | 0.0835652 | ||||||||
\(100\) | −8160.04 | − | 14133.6i | −0.816004 | − | 1.41336i | ||||
\(101\) | −14199.7 | − | 8198.21i | −1.39199 | − | 0.803667i | −0.398457 | − | 0.917187i | \(-0.630454\pi\) |
−0.993536 | + | 0.113520i | \(0.963788\pi\) | |||||||
\(102\) | −11448.5 | + | 19829.3i | −1.10039 | + | 1.90593i | ||||
\(103\) | 2405.70 | − | 1388.93i | 0.226760 | − | 0.130920i | −0.382316 | − | 0.924032i | \(-0.624874\pi\) |
0.609077 | + | 0.793111i | \(0.291540\pi\) | |||||||
\(104\) | − | 640.956i | − | 0.0592599i | ||||||
\(105\) | −2455.45 | + | 2720.21i | −0.222717 | + | 0.246731i | ||||
\(106\) | 25756.4 | 2.29231 | ||||||||
\(107\) | 3526.64 | + | 6108.32i | 0.308030 | + | 0.533524i | 0.977931 | − | 0.208926i | \(-0.0669968\pi\) |
−0.669901 | + | 0.742450i | \(0.733663\pi\) | |||||||
\(108\) | 15922.4 | + | 9192.82i | 1.36509 | + | 0.788136i | ||||
\(109\) | −5484.31 | + | 9499.10i | −0.461603 | + | 0.799520i | −0.999041 | − | 0.0437831i | \(-0.986059\pi\) |
0.537438 | + | 0.843303i | \(0.319392\pi\) | |||||||
\(110\) | −2230.62 | + | 1287.85i | −0.184349 | + | 0.106434i | ||||
\(111\) | 3477.26i | 0.282222i | ||||||||
\(112\) | 5320.96 | + | 1137.96i | 0.424184 | + | 0.0907176i | ||||
\(113\) | −12985.5 | −1.01696 | −0.508478 | − | 0.861075i | \(-0.669792\pi\) | ||||
−0.508478 | + | 0.861075i | \(0.669792\pi\) | |||||||
\(114\) | −16021.1 | − | 27749.3i | −1.23277 | − | 2.13522i | ||||
\(115\) | 2216.53 | + | 1279.71i | 0.167601 | + | 0.0967647i | ||||
\(116\) | 3101.53 | − | 5372.00i | 0.230494 | − | 0.399227i | ||||
\(117\) | 104.947 | − | 60.5910i | 0.00766650 | − | 0.00442626i | ||||
\(118\) | − | 29283.2i | − | 2.10307i | ||||||
\(119\) | 16188.2 | − | 5237.48i | 1.14315 | − | 0.369852i | ||||
\(120\) | 6385.31 | 0.443425 | ||||||||
\(121\) | 6033.37 | + | 10450.1i | 0.412088 | + | 0.713757i | ||||
\(122\) | −10825.4 | − | 6250.06i | −0.727320 | − | 0.419918i | ||||
\(123\) | 5129.93 | − | 8885.30i | 0.339079 | − | 0.587303i | ||||
\(124\) | −31883.3 | + | 18407.8i | −2.07357 | + | 1.19718i | ||||
\(125\) | 9047.91i | 0.579066i | ||||||||
\(126\) | 1629.02 | + | 5035.03i | 0.102609 | + | 0.317147i | ||||
\(127\) | 14948.9 | 0.926836 | 0.463418 | − | 0.886140i | \(-0.346623\pi\) | ||||
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(128\) | 14904.9 | + | 25816.1i | 0.909725 | + | 1.57569i | ||||
\(129\) | −8737.45 | − | 5044.57i | −0.525056 | − | 0.303141i | ||||
\(130\) | −190.549 | + | 330.041i | −0.0112751 | + | 0.0195291i | ||||
\(131\) | −2880.21 | + | 1662.89i | −0.167834 | + | 0.0968993i | −0.581564 | − | 0.813500i | \(-0.697559\pi\) |
0.413730 | + | 0.910400i | \(0.364226\pi\) | |||||||
\(132\) | 14382.8i | 0.825460i | ||||||||
\(133\) | −4979.50 | + | 23283.5i | −0.281503 | + | 1.31627i | ||||
\(134\) | 2996.85 | 0.166899 | ||||||||
\(135\) | −2425.23 | − | 4200.61i | −0.133071 | − | 0.230486i | ||||
\(136\) | −25675.0 | − | 14823.5i | −1.38814 | − | 0.801441i | ||||
\(137\) | 17514.5 | − | 30336.0i | 0.933162 | − | 1.61628i | 0.155283 | − | 0.987870i | \(-0.450371\pi\) |
0.777879 | − | 0.628414i | \(-0.216296\pi\) | |||||||
\(138\) | 19262.5 | − | 11121.2i | 1.01148 | − | 0.583976i | ||||
\(139\) | 5437.55i | 0.281432i | 0.990050 | + | 0.140716i | \(0.0449405\pi\) | ||||
−0.990050 | + | 0.140716i | \(0.955060\pi\) | |||||||
\(140\) | −7938.00 | − | 7165.40i | −0.405000 | − | 0.365582i | ||||
\(141\) | −19360.6 | −0.973826 | ||||||||
\(142\) | 4969.91 | + | 8608.14i | 0.246475 | + | 0.426906i | ||||
\(143\) | −329.855 | − | 190.442i | −0.0161306 | − | 0.00931303i | ||||
\(144\) | 896.285 | − | 1552.41i | 0.0432236 | − | 0.0748655i | ||||
\(145\) | −1417.23 | + | 818.236i | −0.0674067 | + | 0.0389173i | ||||
\(146\) | 4713.98i | 0.221147i | ||||||||
\(147\) | 9679.25 | − | 21594.4i | 0.447927 | − | 0.999326i | ||||
\(148\) | −10147.2 | −0.463258 | ||||||||
\(149\) | −11297.9 | − | 19568.5i | −0.508891 | − | 0.881424i | −0.999947 | − | 0.0102966i | \(-0.996722\pi\) |
0.491056 | − | 0.871128i | \(-0.336611\pi\) | |||||||
\(150\) | 32403.9 | + | 18708.4i | 1.44017 | + | 0.831484i | ||||
\(151\) | −15871.4 | + | 27490.1i | −0.696085 | + | 1.20565i | 0.273728 | + | 0.961807i | \(0.411743\pi\) |
−0.969814 | + | 0.243848i | \(0.921590\pi\) | |||||||
\(152\) | 35929.8 | − | 20744.1i | 1.55513 | − | 0.897857i | ||||
\(153\) | − | 5605.18i | − | 0.239446i | ||||||
\(154\) | 11145.2 | − | 12346.9i | 0.469944 | − | 0.520615i | ||||
\(155\) | 9712.59 | 0.404270 | ||||||||
\(156\) | 1064.04 | + | 1842.96i | 0.0437227 | + | 0.0757299i | ||||
\(157\) | 18523.5 | + | 10694.6i | 0.751492 | + | 0.433874i | 0.826233 | − | 0.563329i | \(-0.190480\pi\) |
−0.0747405 | + | 0.997203i | \(0.523813\pi\) | |||||||
\(158\) | −19072.2 | + | 33033.9i | −0.763986 | + | 1.32326i | ||||
\(159\) | −32859.9 | + | 18971.7i | −1.29979 | + | 0.750433i | ||||
\(160\) | − | 4728.31i | − | 0.184700i | ||||||
\(161\) | −16162.6 | − | 3456.59i | −0.623531 | − | 0.133351i | ||||
\(162\) | −50900.4 | −1.93951 | ||||||||
\(163\) | −21528.6 | − | 37288.6i | −0.810290 | − | 1.40346i | −0.912661 | − | 0.408717i | \(-0.865976\pi\) |
0.102371 | − | 0.994746i | \(-0.467357\pi\) | |||||||
\(164\) | 25928.7 | + | 14970.0i | 0.964037 | + | 0.556587i | ||||
\(165\) | 1897.22 | − | 3286.08i | 0.0696866 | − | 0.120701i | ||||
\(166\) | 23342.8 | − | 13477.0i | 0.847104 | − | 0.489076i | ||||
\(167\) | 24861.8i | 0.891457i | 0.895168 | + | 0.445728i | \(0.147055\pi\) | ||||
−0.895168 | + | 0.445728i | \(0.852945\pi\) | |||||||
\(168\) | −39232.3 | + | 12693.1i | −1.39003 | + | 0.449728i | ||||
\(169\) | 28504.6 | 0.998027 | ||||||||
\(170\) | 8813.72 | + | 15265.8i | 0.304973 | + | 0.528229i | ||||
\(171\) | 6793.05 | + | 3921.97i | 0.232313 | + | 0.134126i | ||||
\(172\) | 14720.9 | − | 25497.3i | 0.497596 | − | 0.861861i | ||||
\(173\) | 32456.1 | − | 18738.5i | 1.08444 | − | 0.626099i | 0.152346 | − | 0.988327i | \(-0.451317\pi\) |
0.932089 | + | 0.362228i | \(0.117984\pi\) | |||||||
\(174\) | 14221.6i | 0.469733i | ||||||||
\(175\) | −8558.78 | − | 26453.7i | −0.279470 | − | 0.863795i | ||||
\(176\) | −5634.18 | −0.181889 | ||||||||
\(177\) | 21569.5 | + | 37359.5i | 0.688483 | + | 1.19249i | ||||
\(178\) | −39153.0 | − | 22605.0i | −1.23573 | − | 0.713452i | ||||
\(179\) | −11768.6 | + | 20383.8i | −0.367298 | + | 0.636178i | −0.989142 | − | 0.146963i | \(-0.953050\pi\) |
0.621844 | + | 0.783141i | \(0.286384\pi\) | |||||||
\(180\) | −3050.93 | + | 1761.46i | −0.0941646 | + | 0.0543659i | ||||
\(181\) | − | 9211.05i | − | 0.281159i | −0.990069 | − | 0.140580i | \(-0.955103\pi\) | ||
0.990069 | − | 0.140580i | \(-0.0448966\pi\) | |||||||
\(182\) | 514.687 | − | 2406.61i | 0.0155382 | − | 0.0726545i | ||||
\(183\) | 18414.8 | 0.549875 | ||||||||
\(184\) | 14399.8 | + | 24941.1i | 0.425324 | + | 0.736683i | ||||
\(185\) | 2318.36 | + | 1338.50i | 0.0677387 | + | 0.0391090i | ||||
\(186\) | 42203.2 | − | 73098.2i | 1.21989 | − | 2.11291i | ||||
\(187\) | −15257.2 | + | 8808.75i | −0.436307 | + | 0.251902i | ||||
\(188\) | − | 56497.5i | − | 1.59850i | ||||||
\(189\) | 23251.2 | + | 20988.2i | 0.650910 | + | 0.587558i | ||||
\(190\) | −24668.0 | −0.683324 | ||||||||
\(191\) | −6033.47 | − | 10450.3i | −0.165387 | − | 0.286458i | 0.771406 | − | 0.636343i | \(-0.219554\pi\) |
−0.936793 | + | 0.349885i | \(0.886221\pi\) | |||||||
\(192\) | −50751.5 | − | 29301.4i | −1.37672 | − | 0.794851i | ||||
\(193\) | −4276.53 | + | 7407.17i | −0.114809 | + | 0.198856i | −0.917704 | − | 0.397266i | \(-0.869959\pi\) |
0.802894 | + | 0.596122i | \(0.203292\pi\) | |||||||
\(194\) | −66853.2 | + | 38597.7i | −1.77631 | + | 1.02555i | ||||
\(195\) | − | 561.422i | − | 0.0147645i | ||||||
\(196\) | 63016.0 | + | 28245.6i | 1.64036 | + | 0.735256i | ||||
\(197\) | −15909.4 | −0.409942 | −0.204971 | − | 0.978768i | \(-0.565710\pi\) | ||||
−0.204971 | + | 0.978768i | \(0.565710\pi\) | |||||||
\(198\) | −2739.80 | − | 4745.48i | −0.0698858 | − | 0.121046i | ||||
\(199\) | 23829.4 | + | 13757.9i | 0.601737 | + | 0.347413i | 0.769725 | − | 0.638376i | \(-0.220393\pi\) |
−0.167988 | + | 0.985789i | \(0.553727\pi\) | |||||||
\(200\) | −24223.6 | + | 41956.5i | −0.605590 | + | 1.04891i | ||||
\(201\) | −3823.37 | + | 2207.43i | −0.0946356 | + | 0.0546379i | ||||
\(202\) | 109699.i | 2.68843i | ||||||||
\(203\) | 7081.10 | − | 7844.61i | 0.171834 | − | 0.190362i | ||||
\(204\) | 98432.3 | 2.36525 | ||||||||
\(205\) | −3949.34 | − | 6840.45i | −0.0939759 | − | 0.162771i | ||||
\(206\) | −16095.1 | − | 9292.53i | −0.379280 | − | 0.218978i | ||||
\(207\) | −2722.49 | + | 4715.49i | −0.0635368 | + | 0.110049i | ||||
\(208\) | −721.944 | + | 416.815i | −0.0166869 | + | 0.00963421i | ||||
\(209\) | − | 24654.1i | − | 0.564412i | ||||||
\(210\) | 23975.1 | + | 5127.40i | 0.543652 | + | 0.116268i | ||||
\(211\) | −50656.9 | −1.13782 | −0.568910 | − | 0.822400i | \(-0.692635\pi\) | ||||
−0.568910 | + | 0.822400i | \(0.692635\pi\) | |||||||
\(212\) | −55362.5 | − | 95890.6i | −1.23181 | − | 2.13356i | ||||
\(213\) | −12681.2 | − | 7321.50i | −0.279513 | − | 0.161377i | ||||
\(214\) | 23594.7 | − | 40867.2i | 0.515213 | − | 0.892375i | ||||
\(215\) | −6726.63 | + | 3883.62i | −0.145519 | + | 0.0840156i | ||||
\(216\) | − | 54579.0i | − | 1.16982i | ||||||
\(217\) | −59675.6 | + | 19307.3i | −1.26729 | + | 0.410017i | ||||
\(218\) | 73384.6 | 1.54416 | ||||||||
\(219\) | −3472.23 | − | 6014.08i | −0.0723970 | − | 0.125395i | ||||
\(220\) | 9589.31 | + | 5536.39i | 0.198126 | + | 0.114388i | ||||
\(221\) | −1303.34 | + | 2257.44i | −0.0266853 | + | 0.0462203i | ||||
\(222\) | 20147.5 | − | 11632.2i | 0.408804 | − | 0.236023i | ||||
\(223\) | − | 82476.6i | − | 1.65852i | −0.558862 | − | 0.829261i | \(-0.688762\pi\) | ||
0.558862 | − | 0.829261i | \(-0.311238\pi\) | |||||||
\(224\) | 9399.24 | + | 29051.4i | 0.187325 | + | 0.578991i | ||||
\(225\) | −9159.65 | −0.180931 | ||||||||
\(226\) | 43439.3 | + | 75239.0i | 0.850483 | + | 1.47308i | ||||
\(227\) | 28408.6 | + | 16401.7i | 0.551314 | + | 0.318301i | 0.749652 | − | 0.661833i | \(-0.230221\pi\) |
−0.198338 | + | 0.980134i | \(0.563554\pi\) | |||||||
\(228\) | −68873.5 | + | 119292.i | −1.32490 | + | 2.29479i | ||||
\(229\) | 89549.0 | − | 51701.1i | 1.70761 | − | 0.985892i | 0.770115 | − | 0.637905i | \(-0.220199\pi\) |
0.937500 | − | 0.347986i | \(-0.113134\pi\) | |||||||
\(230\) | − | 17123.6i | − | 0.323698i | ||||||
\(231\) | −5124.51 | + | 23961.5i | −0.0960347 | + | 0.449046i | ||||
\(232\) | −18414.2 | −0.342118 | ||||||||
\(233\) | 35601.4 | + | 61663.5i | 0.655776 | + | 1.13584i | 0.981699 | + | 0.190441i | \(0.0609919\pi\) |
−0.325922 | + | 0.945397i | \(0.605675\pi\) | |||||||
\(234\) | −702.137 | − | 405.379i | −0.0128230 | − | 0.00740337i | ||||
\(235\) | −7452.50 | + | 12908.1i | −0.134948 | + | 0.233737i | ||||
\(236\) | −109021. | + | 62943.3i | −1.95743 | + | 1.13012i | ||||
\(237\) | − | 56192.9i | − | 1.00043i | ||||||
\(238\) | −84499.1 | − | 76274.9i | −1.49176 | − | 1.34657i | ||||
\(239\) | 8170.08 | 0.143031 | 0.0715156 | − | 0.997439i | \(-0.477216\pi\) | ||||
0.0715156 | + | 0.997439i | \(0.477216\pi\) | |||||||
\(240\) | −4152.38 | − | 7192.14i | −0.0720900 | − | 0.124863i | ||||
\(241\) | −3341.65 | − | 1929.30i | −0.0575343 | − | 0.0332174i | 0.470957 | − | 0.882156i | \(-0.343909\pi\) |
−0.528491 | + | 0.848939i | \(0.677242\pi\) | |||||||
\(242\) | 40365.8 | − | 69915.6i | 0.689259 | − | 1.19383i | ||||
\(243\) | 20097.2 | − | 11603.1i | 0.340347 | − | 0.196500i | ||||
\(244\) | 53737.2i | 0.902600i | ||||||||
\(245\) | −10671.6 | − | 14765.7i | −0.177786 | − | 0.245993i | ||||
\(246\) | −68642.7 | −1.13429 | ||||||||
\(247\) | −1823.90 | − | 3159.09i | −0.0298956 | − | 0.0517807i | ||||
\(248\) | 94647.5 | + | 54644.7i | 1.53888 | + | 0.888475i | ||||
\(249\) | −19853.8 | + | 34387.8i | −0.320218 | + | 0.554633i | ||||
\(250\) | 52424.2 | − | 30267.1i | 0.838788 | − | 0.484274i | ||||
\(251\) | 93998.6i | 1.49202i | 0.665936 | + | 0.746008i | \(0.268032\pi\) | ||||
−0.665936 | + | 0.746008i | \(0.731968\pi\) | |||||||
\(252\) | 15243.8 | − | 16887.5i | 0.240045 | − | 0.265928i | ||||
\(253\) | 17114.0 | 0.267368 | ||||||||
\(254\) | −50007.3 | − | 86615.2i | −0.775115 | − | 1.34254i | ||||
\(255\) | −22489.1 | − | 12984.1i | −0.345853 | − | 0.199678i | ||||
\(256\) | 52153.4 | − | 90332.4i | 0.795798 | − | 1.37836i | ||||
\(257\) | −46558.9 | + | 26880.8i | −0.704915 | + | 0.406983i | −0.809175 | − | 0.587567i | \(-0.800086\pi\) |
0.104260 | + | 0.994550i | \(0.466752\pi\) | |||||||
\(258\) | 67500.6i | 1.01407i | ||||||||
\(259\) | −16905.1 | − | 3615.39i | −0.252010 | − | 0.0538958i | ||||
\(260\) | 1638.32 | 0.0242355 | ||||||||
\(261\) | −1740.73 | − | 3015.04i | −0.0255535 | − | 0.0442600i | ||||
\(262\) | 19269.8 | + | 11125.4i | 0.280721 | + | 0.162074i | ||||
\(263\) | 25434.8 | − | 44054.3i | 0.367719 | − | 0.636909i | −0.621489 | − | 0.783423i | \(-0.713472\pi\) |
0.989209 | + | 0.146514i | \(0.0468054\pi\) | |||||||
\(264\) | 36976.1 | − | 21348.2i | 0.530534 | − | 0.306304i | ||||
\(265\) | 29211.2i | 0.415965i | ||||||||
\(266\) | 151564. | − | 49036.6i | 2.14206 | − | 0.693038i | ||||
\(267\) | 66601.8 | 0.934251 | ||||||||
\(268\) | −6441.62 | − | 11157.2i | −0.0896862 | − | 0.155341i | ||||
\(269\) | −102004. | − | 58892.1i | −1.40965 | − | 0.813865i | −0.414300 | − | 0.910140i | \(-0.635974\pi\) |
−0.995355 | + | 0.0962757i | \(0.969307\pi\) | |||||||
\(270\) | −16225.8 | + | 28103.8i | −0.222576 | + | 0.385512i | ||||
\(271\) | 593.717 | − | 342.782i | 0.00808427 | − | 0.00466745i | −0.495952 | − | 0.868350i | \(-0.665181\pi\) |
0.504037 | + | 0.863682i | \(0.331848\pi\) | |||||||
\(272\) | 38558.9i | 0.521179i | ||||||||
\(273\) | 1116.03 | + | 3449.46i | 0.0149744 | + | 0.0462834i | ||||
\(274\) | −234359. | −3.12162 | ||||||||
\(275\) | 14394.7 | + | 24932.4i | 0.190344 | + | 0.329685i | ||||
\(276\) | −82808.5 | − | 47809.5i | −1.08707 | − | 0.627619i | ||||
\(277\) | −18426.9 | + | 31916.3i | −0.240156 | + | 0.415962i | −0.960758 | − | 0.277386i | \(-0.910532\pi\) |
0.720603 | + | 0.693348i | \(0.243865\pi\) | |||||||
\(278\) | 31505.6 | − | 18189.7i | 0.407660 | − | 0.235362i | ||||
\(279\) | 20662.8i | 0.265448i | ||||||||
\(280\) | −6638.96 | + | 31042.9i | −0.0846806 | + | 0.395955i | ||||
\(281\) | −53123.9 | −0.672787 | −0.336393 | − | 0.941722i | \(-0.609207\pi\) | ||||
−0.336393 | + | 0.941722i | \(0.609207\pi\) | |||||||
\(282\) | 64765.3 | + | 112177.i | 0.814413 | + | 1.41060i | ||||
\(283\) | 74715.1 | + | 43136.8i | 0.932901 | + | 0.538611i | 0.887728 | − | 0.460368i | \(-0.152283\pi\) |
0.0451732 | + | 0.998979i | \(0.485616\pi\) | |||||||
\(284\) | 21365.3 | − | 37005.8i | 0.264894 | − | 0.458811i | ||||
\(285\) | 31471.4 | − | 18170.0i | 0.387460 | − | 0.223700i | ||||
\(286\) | 2548.27i | 0.0311540i | ||||||||
\(287\) | 37863.2 | + | 34178.0i | 0.459677 | + | 0.414937i | ||||
\(288\) | 10059.1 | 0.121276 | ||||||||
\(289\) | 18524.3 | + | 32085.1i | 0.221792 | + | 0.384156i | ||||
\(290\) | 9481.84 | + | 5474.34i | 0.112745 | + | 0.0650932i | ||||
\(291\) | 56860.8 | − | 98485.8i | 0.671471 | − | 1.16302i | ||||
\(292\) | 17550.1 | − | 10132.5i | 0.205832 | − | 0.118837i | ||||
\(293\) | 54510.6i | 0.634959i | 0.948265 | + | 0.317480i | \(0.102836\pi\) | ||||
−0.948265 | + | 0.317480i | \(0.897164\pi\) | |||||||
\(294\) | −157499. | + | 16155.6i | −1.82214 | + | 0.186909i | ||||
\(295\) | 33211.0 | 0.381626 | ||||||||
\(296\) | 15061.3 | + | 26087.0i | 0.171901 | + | 0.297742i | ||||
\(297\) | −28088.0 | − | 16216.6i | −0.318426 | − | 0.183843i | ||||
\(298\) | −75587.5 | + | 130921.i | −0.851173 | + | 1.47427i | ||||
\(299\) | 2192.92 | − | 1266.09i | 0.0245291 | − | 0.0141619i | ||||
\(300\) | − | 160852.i | − | 1.78725i | ||||||
\(301\) | 33609.3 | − | 37233.1i | 0.370959 | − | 0.410957i | ||||
\(302\) | 212373. | 2.32855 | ||||||||
\(303\) | −80802.3 | − | 139954.i | −0.880113 | − | 1.52440i | ||||
\(304\) | −46730.4 | − | 26979.8i | −0.505653 | − | 0.291939i | ||||
\(305\) | 7088.40 | − | 12277.5i | 0.0761989 | − | 0.131980i | ||||
\(306\) | −32476.8 | + | 18750.5i | −0.346841 | + | 0.200249i | ||||
\(307\) | − | 62508.0i | − | 0.663222i | −0.943416 | − | 0.331611i | \(-0.892408\pi\) | ||
0.943416 | − | 0.331611i | \(-0.107592\pi\) | |||||||
\(308\) | −69923.6 | − | 14954.1i | −0.737094 | − | 0.157638i | ||||
\(309\) | 27378.9 | 0.286747 | ||||||||
\(310\) | −32490.6 | − | 56275.4i | −0.338092 | − | 0.585593i | ||||
\(311\) | 87021.0 | + | 50241.6i | 0.899712 | + | 0.519449i | 0.877107 | − | 0.480296i | \(-0.159471\pi\) |
0.0226052 | + | 0.999744i | \(0.492804\pi\) | |||||||
\(312\) | 3158.66 | − | 5470.96i | 0.0324484 | − | 0.0562023i | ||||
\(313\) | −141974. | + | 81968.7i | −1.44917 | + | 0.836680i | −0.998432 | − | 0.0559755i | \(-0.982173\pi\) |
−0.450740 | + | 0.892655i | \(0.648840\pi\) | |||||||
\(314\) | − | 143102.i | − | 1.45140i | ||||||
\(315\) | −5710.40 | + | 1847.53i | −0.0575500 | + | 0.0186196i | ||||
\(316\) | 163980. | 1.64216 | ||||||||
\(317\) | −60956.2 | − | 105579.i | −0.606596 | − | 1.05066i | −0.991797 | − | 0.127822i | \(-0.959201\pi\) |
0.385201 | − | 0.922833i | \(-0.374132\pi\) | |||||||
\(318\) | 219847. | + | 126929.i | 2.17403 | + | 1.25518i | ||||
\(319\) | −5471.25 | + | 9476.49i | −0.0537657 | + | 0.0931250i | ||||
\(320\) | −39071.6 | + | 22558.0i | −0.381559 | + | 0.220293i | ||||
\(321\) | 69517.8i | 0.674661i | ||||||||
\(322\) | 34039.4 | + | 105210.i | 0.328299 | + | 1.01472i | ||||
\(323\) | −168726. | −1.61725 | ||||||||
\(324\) | 109409. | + | 189502.i | 1.04223 | + | 1.80519i | ||||
\(325\) | 3688.98 | + | 2129.83i | 0.0349253 | + | 0.0201641i | ||||
\(326\) | −144035. | + | 249476.i | −1.35529 | + | 2.34744i | ||||
\(327\) | −93624.0 | + | 54053.8i | −0.875572 | + | 0.505511i | ||||
\(328\) | − | 88878.6i | − | 0.826132i | ||||||
\(329\) | 20129.7 | − | 94123.8i | 0.185971 | − | 0.869577i | ||||
\(330\) | −25386.4 | −0.233116 | ||||||||
\(331\) | 22437.7 | + | 38863.2i | 0.204796 | + | 0.354717i | 0.950068 | − | 0.312044i | \(-0.101014\pi\) |
−0.745272 | + | 0.666761i | \(0.767680\pi\) | |||||||
\(332\) | −100349. | − | 57936.7i | −0.910412 | − | 0.525626i | ||||
\(333\) | −2847.56 | + | 4932.12i | −0.0256794 | + | 0.0444780i | ||||
\(334\) | 144051. | − | 83168.0i | 1.29129 | − | 0.745527i | ||||
\(335\) | 3398.82i | 0.0302858i | ||||||||
\(336\) | 39809.8 | + | 35935.2i | 0.352624 | + | 0.318303i | ||||
\(337\) | 128343. | 1.13009 | 0.565045 | − | 0.825060i | \(-0.308859\pi\) | ||||
0.565045 | + | 0.825060i | \(0.308859\pi\) | |||||||
\(338\) | −95354.0 | − | 165158.i | −0.834652 | − | 1.44566i | ||||
\(339\) | −110840. | − | 63993.2i | −0.964485 | − | 0.556845i | ||||
\(340\) | 37889.6 | − | 65626.7i | 0.327765 | − | 0.567705i | ||||
\(341\) | 56243.7 | − | 32472.3i | 0.483688 | − | 0.279257i | ||||
\(342\) | − | 52479.2i | − | 0.448679i | ||||||
\(343\) | 94919.9 | + | 69508.9i | 0.806806 | + | 0.590816i | ||||
\(344\) | −87399.7 | −0.738572 | ||||||||
\(345\) | 12613.0 | + | 21846.3i | 0.105969 | + | 0.183544i | ||||
\(346\) | −217145. | − | 125368.i | −1.81383 | − | 1.04722i | ||||
\(347\) | −6153.32 | + | 10657.9i | −0.0511035 | + | 0.0885138i | −0.890446 | − | 0.455090i | \(-0.849607\pi\) |
0.839342 | + | 0.543604i | \(0.182940\pi\) | |||||||
\(348\) | 52946.9 | − | 30568.9i | 0.437202 | − | 0.252419i | ||||
\(349\) | − | 8868.22i | − | 0.0728091i | −0.999337 | − | 0.0364046i | \(-0.988410\pi\) | ||
0.999337 | − | 0.0364046i | \(-0.0115905\pi\) | |||||||
\(350\) | −124644. | + | 138083.i | −1.01750 | + | 1.12721i | ||||
\(351\) | −4798.80 | −0.0389510 | ||||||||
\(352\) | −15808.3 | − | 27380.7i | −0.127585 | − | 0.220983i | ||||
\(353\) | 94106.1 | + | 54332.2i | 0.755211 | + | 0.436021i | 0.827574 | − | 0.561357i | \(-0.189721\pi\) |
−0.0723626 | + | 0.997378i | \(0.523054\pi\) | |||||||
\(354\) | 144309. | − | 249950.i | 1.15156 | − | 1.99456i | ||||
\(355\) | −9762.78 | + | 5636.54i | −0.0774670 | + | 0.0447256i | ||||
\(356\) | 194355.i | 1.53354i | ||||||||
\(357\) | 163987. | + | 35070.8i | 1.28668 | + | 0.275175i | ||||
\(358\) | 157473. | 1.22869 | ||||||||
\(359\) | 114037. | + | 197517.i | 0.884821 | + | 1.53256i | 0.845918 | + | 0.533313i | \(0.179053\pi\) |
0.0389030 | + | 0.999243i | \(0.487614\pi\) | |||||||
\(360\) | 9056.88 | + | 5228.99i | 0.0698834 | + | 0.0403472i | ||||
\(361\) | 52898.1 | − | 91622.1i | 0.405906 | − | 0.703050i | ||||
\(362\) | −53369.5 | + | 30812.9i | −0.407264 | + | 0.235134i | ||||
\(363\) | 118931.i | 0.902572i | ||||||||
\(364\) | −10066.1 | + | 3256.75i | −0.0759726 | + | 0.0245800i | ||||
\(365\) | −5346.28 | −0.0401297 | ||||||||
\(366\) | −61601.2 | − | 106696.i | −0.459861 | − | 0.796503i | ||||
\(367\) | −207527. | − | 119816.i | −1.54079 | − | 0.889576i | −0.998789 | − | 0.0491977i | \(-0.984334\pi\) |
−0.542001 | − | 0.840378i | \(-0.682333\pi\) | |||||||
\(368\) | 18728.4 | − | 32438.6i | 0.138295 | − | 0.239533i | ||||
\(369\) | 14552.5 | − | 8401.90i | 0.106877 | − | 0.0617056i | ||||
\(370\) | − | 17910.3i | − | 0.130828i | ||||||
\(371\) | −58067.7 | − | 179478.i | −0.421878 | − | 1.30395i | ||||
\(372\) | −362858. | −2.62211 | ||||||||
\(373\) | 10718.0 | + | 18564.1i | 0.0770363 | + | 0.133431i | 0.901970 | − | 0.431799i | \(-0.142121\pi\) |
−0.824934 | + | 0.565230i | \(0.808788\pi\) | |||||||
\(374\) | 102077. | + | 58934.2i | 0.729768 | + | 0.421332i | ||||
\(375\) | −44588.5 | + | 77229.5i | −0.317074 | + | 0.549188i | ||||
\(376\) | −145247. | + | 83858.2i | −1.02738 | + | 0.593157i | ||||
\(377\) | 1619.05i | 0.0113914i | ||||||||
\(378\) | 43826.8 | − | 204929.i | 0.306730 | − | 1.43423i | ||||
\(379\) | −42375.1 | −0.295007 | −0.147504 | − | 0.989062i | \(-0.547124\pi\) | ||||
−0.147504 | + | 0.989062i | \(0.547124\pi\) | |||||||
\(380\) | 53023.1 | + | 91838.7i | 0.367196 | + | 0.636002i | ||||
\(381\) | 127599. | + | 73669.1i | 0.879014 | + | 0.507499i | ||||
\(382\) | −40366.4 | + | 69916.7i | −0.276626 | + | 0.479131i | ||||
\(383\) | 24769.1 | − | 14300.4i | 0.168854 | − | 0.0974882i | −0.413191 | − | 0.910644i | \(-0.635586\pi\) |
0.582046 | + | 0.813156i | \(0.302253\pi\) | |||||||
\(384\) | 293809.i | 1.99252i | ||||||||
\(385\) | 14003.0 | + | 12640.1i | 0.0944715 | + | 0.0852767i | ||||
\(386\) | 57223.6 | 0.384061 | ||||||||
\(387\) | −8262.10 | − | 14310.4i | −0.0551656 | − | 0.0955496i | ||||
\(388\) | 287398. | + | 165929.i | 1.90906 | + | 1.10220i | ||||
\(389\) | 21801.6 | − | 37761.5i | 0.144075 | − | 0.249546i | −0.784952 | − | 0.619556i | \(-0.787313\pi\) |
0.929028 | + | 0.370010i | \(0.120646\pi\) | |||||||
\(390\) | −3252.92 | + | 1878.07i | −0.0213867 | + | 0.0123476i | ||||
\(391\) | − | 117124.i | − | 0.766110i | ||||||
\(392\) | −20918.3 | − | 203929.i | −0.136130 | − | 1.32711i | ||||
\(393\) | −32779.2 | −0.212233 | ||||||||
\(394\) | 53220.3 | + | 92180.3i | 0.342835 | + | 0.593808i | ||||
\(395\) | −37464.9 | − | 21630.4i | −0.240121 | − | 0.138634i | ||||
\(396\) | −11778.2 | + | 20400.5i | −0.0751086 | + | 0.130092i | ||||
\(397\) | −145187. | + | 83823.6i | −0.921183 | + | 0.531845i | −0.884012 | − | 0.467463i | \(-0.845168\pi\) |
−0.0371710 | + | 0.999309i | \(0.511835\pi\) | |||||||
\(398\) | − | 184092.i | − | 1.16217i | ||||||
\(399\) | −157245. | + | 174200.i | −0.987716 | + | 1.09421i | ||||
\(400\) | 63010.6 | 0.393817 | ||||||||
\(401\) | −62660.0 | − | 108530.i | −0.389674 | − | 0.674936i | 0.602731 | − | 0.797944i | \(-0.294079\pi\) |
−0.992406 | + | 0.123008i | \(0.960746\pi\) | |||||||
\(402\) | 25580.0 | + | 14768.6i | 0.158288 | + | 0.0913875i | ||||
\(403\) | 4804.58 | − | 8321.78i | 0.0295832 | − | 0.0512396i | ||||
\(404\) | 408408. | − | 235794.i | 2.50225 | − | 1.44468i | ||||
\(405\) | − | 57727.9i | − | 0.351946i | ||||||
\(406\) | −69140.0 | − | 14786.5i | −0.419447 | − | 0.0897046i | ||||
\(407\) | 17900.2 | 0.108061 | ||||||||
\(408\) | −146101. | − | 253055.i | −0.877675 | − | 1.52018i | ||||
\(409\) | −62991.3 | − | 36368.0i | −0.376560 | − | 0.217407i | 0.299761 | − | 0.954014i | \(-0.403093\pi\) |
−0.676320 | + | 0.736608i | \(0.736427\pi\) | |||||||
\(410\) | −26422.7 | + | 45765.5i | −0.157184 | + | 0.272251i | ||||
\(411\) | 298995. | − | 172625.i | 1.77003 | − | 1.02193i | ||||
\(412\) | 79896.0i | 0.470685i | ||||||||
\(413\) | −204053. | + | 66019.0i | −1.19631 | + | 0.387051i | ||||
\(414\) | 36429.2 | 0.212544 | ||||||||
\(415\) | 15284.7 | + | 26473.9i | 0.0887484 | + | 0.153717i | ||||
\(416\) | −4051.23 | − | 2338.98i | −0.0234100 | − | 0.0135157i | ||||
\(417\) | −26796.5 | + | 46412.9i | −0.154101 | + | 0.266911i | ||||
\(418\) | −142848. | + | 82473.1i | −0.817561 | + | 0.472019i | ||||
\(419\) | − | 48455.0i | − | 0.276001i | −0.990432 | − | 0.138000i | \(-0.955932\pi\) | ||
0.990432 | − | 0.138000i | \(-0.0440675\pi\) | |||||||
\(420\) | −32444.4 | − | 100280.i | −0.183925 | − | 0.568481i | ||||
\(421\) | −67350.5 | −0.379994 | −0.189997 | − | 0.981785i | \(-0.560848\pi\) | ||||
−0.189997 | + | 0.981785i | \(0.560848\pi\) | |||||||
\(422\) | 169458. | + | 293510.i | 0.951561 | + | 1.64815i | ||||
\(423\) | −27461.0 | − | 15854.6i | −0.153474 | − | 0.0886084i | ||||
\(424\) | −164347. | + | 284657.i | −0.914177 | + | 1.58340i | ||||
\(425\) | 170631. | − | 98513.9i | 0.944670 | − | 0.545406i | ||||
\(426\) | 97967.8i | 0.539839i | ||||||||
\(427\) | −19146.2 | + | 89525.3i | −0.105009 | + | 0.491010i | ||||
\(428\) | −202864. | −1.10743 | ||||||||
\(429\) | −1877.01 | − | 3251.08i | −0.0101989 | − | 0.0176650i | ||||
\(430\) | 45003.9 | + | 25983.0i | 0.243396 | + | 0.140525i | ||||
\(431\) | 60765.0 | − | 105248.i | 0.327114 | − | 0.566578i | −0.654824 | − | 0.755781i | \(-0.727257\pi\) |
0.981938 | + | 0.189204i | \(0.0605906\pi\) | |||||||
\(432\) | −61475.3 | + | 35492.8i | −0.329407 | + | 0.190184i | ||||
\(433\) | 21137.1i | 0.112738i | 0.998410 | + | 0.0563689i | \(0.0179523\pi\) | ||||
−0.998410 | + | 0.0563689i | \(0.982048\pi\) | |||||||
\(434\) | 311495. | + | 281177.i | 1.65376 | + | 1.49280i | ||||
\(435\) | −16129.2 | −0.0852383 | ||||||||
\(436\) | −157738. | − | 273210.i | −0.829780 | − | 1.43722i | ||||
\(437\) | 141945. | + | 81951.9i | 0.743288 | + | 0.429137i | ||||
\(438\) | −23230.7 | + | 40236.7i | −0.121092 | + | 0.209737i | ||||
\(439\) | 15020.7 | − | 8672.20i | 0.0779400 | − | 0.0449987i | −0.460523 | − | 0.887648i | \(-0.652338\pi\) |
0.538464 | + | 0.842649i | \(0.319005\pi\) | |||||||
\(440\) | − | 32870.2i | − | 0.169784i | ||||||
\(441\) | 31412.9 | − | 22703.0i | 0.161522 | − | 0.116736i | ||||
\(442\) | 17439.7 | 0.0892678 | ||||||||
\(443\) | 94338.1 | + | 163398.i | 0.480706 | + | 0.832607i | 0.999755 | − | 0.0221372i | \(-0.00704707\pi\) |
−0.519049 | + | 0.854745i | \(0.673714\pi\) | |||||||
\(444\) | −86612.7 | − | 50005.9i | −0.439355 | − | 0.253662i | ||||
\(445\) | 25637.1 | − | 44404.7i | 0.129464 | − | 0.224238i | ||||
\(446\) | −477875. | + | 275901.i | −2.40240 | + | 1.38702i | ||||
\(447\) | − | 222706.i | − | 1.11459i | ||||||
\(448\) | 195219. | − | 216269.i | 0.972673 | − | 1.07755i | ||||
\(449\) | 64161.0 | 0.318257 | 0.159129 | − | 0.987258i | \(-0.449132\pi\) | ||||
0.159129 | + | 0.987258i | \(0.449132\pi\) | |||||||
\(450\) | 30640.9 | + | 53071.7i | 0.151313 | + | 0.262082i | ||||
\(451\) | −45739.7 | − | 26407.8i | −0.224874 | − | 0.129831i | ||||
\(452\) | 186743. | − | 323448.i | 0.914043 | − | 1.58317i | ||||
\(453\) | −270945. | + | 156430.i | −1.32034 | + | 0.762297i | ||||
\(454\) | − | 219469.i | − | 1.06478i | ||||||
\(455\) | 2729.41 | + | 583.723i | 0.0131840 | + | 0.00281958i | ||||
\(456\) | 408911. | 1.96652 | ||||||||
\(457\) | −127623. | − | 221050.i | −0.611078 | − | 1.05842i | −0.991059 | − | 0.133424i | \(-0.957403\pi\) |
0.379981 | − | 0.924994i | \(-0.375930\pi\) | |||||||
\(458\) | −599120. | − | 345902.i | −2.85616 | − | 1.64901i | ||||
\(459\) | −110982. | + | 192227.i | −0.526779 | + | 0.912408i | ||||
\(460\) | −63751.0 | + | 36806.7i | −0.301281 | + | 0.173945i | ||||
\(461\) | 301500.i | 1.41868i | 0.704865 | + | 0.709341i | \(0.251008\pi\) | ||||
−0.704865 | + | 0.709341i | \(0.748992\pi\) | |||||||
\(462\) | 155977. | − | 50464.6i | 0.730765 | − | 0.236430i | ||||
\(463\) | 297623. | 1.38837 | 0.694183 | − | 0.719798i | \(-0.255766\pi\) | ||||
0.694183 | + | 0.719798i | \(0.255766\pi\) | |||||||
\(464\) | 11974.8 | + | 20740.9i | 0.0556200 | + | 0.0963367i | ||||
\(465\) | 82903.0 | + | 47864.1i | 0.383411 | + | 0.221362i | ||||
\(466\) | 238188. | − | 412555.i | 1.09685 | − | 1.89981i | ||||
\(467\) | 219771. | − | 126885.i | 1.00771 | − | 0.581803i | 0.0971917 | − | 0.995266i | \(-0.469014\pi\) |
0.910521 | + | 0.413462i | \(0.135681\pi\) | |||||||
\(468\) | 3485.40i | 0.0159133i | ||||||||
\(469\) | −6756.39 | − | 20882.9i | −0.0307163 | − | 0.0949389i | ||||
\(470\) | 99720.7 | 0.451429 | ||||||||
\(471\) | 105407. | + | 182570.i | 0.475145 | + | 0.822975i | ||||
\(472\) | 323636. | + | 186851.i | 1.45269 | + | 0.838710i | ||||
\(473\) | −25968.4 | + | 44978.6i | −0.116071 | + | 0.201040i | ||||
\(474\) | −325585. | + | 187977.i | −1.44913 | + | 0.836657i | ||||
\(475\) | 275722.i | 1.22204i | ||||||||
\(476\) | −102342. | + | 478539.i | −0.451691 | + | 2.11205i | ||||
\(477\) | −62144.4 | −0.273128 | ||||||||
\(478\) | −27330.6 | − | 47338.0i | −0.119617 | − | 0.207183i | ||||
\(479\) | −162787. | − | 93985.3i | −0.709496 | − | 0.409627i | 0.101379 | − | 0.994848i | \(-0.467675\pi\) |
−0.810874 | + | 0.585220i | \(0.801008\pi\) | |||||||
\(480\) | 23301.3 | − | 40359.1i | 0.101134 | − | 0.175170i | ||||
\(481\) | 2293.67 | − | 1324.25i | 0.00991381 | − | 0.00572374i | ||||
\(482\) | 25815.7i | 0.111119i | ||||||||
\(483\) | −120923. | − | 109154.i | −0.518341 | − | 0.467892i | ||||
\(484\) | −347060. | −1.48154 | ||||||||
\(485\) | −43775.0 | − | 75820.4i | −0.186098 | − | 0.322332i | ||||
\(486\) | −134458. | − | 77629.6i | −0.569266 | − | 0.328666i | ||||
\(487\) | −91840.8 | + | 159073.i | −0.387238 | + | 0.670716i | −0.992077 | − | 0.125632i | \(-0.959904\pi\) |
0.604839 | + | 0.796348i | \(0.293237\pi\) | |||||||
\(488\) | 138150. | − | 79761.2i | 0.580113 | − | 0.334928i | ||||
\(489\) | − | 424375.i | − | 1.77473i | ||||||
\(490\) | −49854.8 | + | 111226.i | −0.207642 | + | 0.463250i | ||||
\(491\) | −135410. | −0.561681 | −0.280840 | − | 0.959755i | \(-0.590613\pi\) | ||||
−0.280840 | + | 0.959755i | \(0.590613\pi\) | |||||||
\(492\) | 147545. | + | 255556.i | 0.609530 | + | 1.05574i | ||||
\(493\) | 64854.7 | + | 37443.9i | 0.266838 | + | 0.154059i | ||||
\(494\) | −12202.7 | + | 21135.6i | −0.0500035 | + | 0.0866086i | ||||
\(495\) | 5382.00 | − | 3107.30i | 0.0219651 | − | 0.0126816i | ||||
\(496\) | − | 142142.i | − | 0.577777i | ||||||
\(497\) | 48779.2 | − | 54038.8i | 0.197480 | − | 0.218772i | ||||
\(498\) | 265661. | 1.07119 | ||||||||
\(499\) | 89910.7 | + | 155730.i | 0.361086 | + | 0.625419i | 0.988140 | − | 0.153557i | \(-0.0490728\pi\) |
−0.627054 | + | 0.778976i | \(0.715739\pi\) | |||||||
\(500\) | −225368. | − | 130116.i | −0.901473 | − | 0.520466i | ||||
\(501\) | −122520. | + | 212211.i | −0.488127 | + | 0.845460i | ||||
\(502\) | 544634. | − | 314445.i | 2.16121 | − | 1.24778i | ||||
\(503\) | − | 372946.i | − | 1.47404i | −0.675869 | − | 0.737022i | \(-0.736231\pi\) | ||
0.675869 | − | 0.737022i | \(-0.263769\pi\) | |||||||
\(504\) | −66041.3 | − | 14123.9i | −0.259989 | − | 0.0556022i | ||||
\(505\) | −124413. | −0.487847 | ||||||||
\(506\) | −57249.8 | − | 99159.5i | −0.223601 | − | 0.387288i | ||||
\(507\) | 243305. | + | 140472.i | 0.946531 | + | 0.546480i | ||||
\(508\) | −214978. | + | 372353.i | −0.833042 | + | 1.44287i | ||||
\(509\) | −268892. | + | 155245.i | −1.03787 | + | 0.599213i | −0.919228 | − | 0.393725i | \(-0.871186\pi\) |
−0.118638 | + | 0.992938i | \(0.537853\pi\) | |||||||
\(510\) | 173738.i | 0.667965i | ||||||||
\(511\) | 32848.3 | − | 10627.7i | 0.125797 | − | 0.0407001i | ||||
\(512\) | −220898. | −0.842660 | ||||||||
\(513\) | −155310. | − | 269004.i | −0.590152 | − | 1.02217i | ||||
\(514\) | 311499. | + | 179844.i | 1.17904 | + | 0.680721i | ||||
\(515\) | 10539.0 | − | 18254.0i | 0.0397360 | − | 0.0688247i | ||||
\(516\) | 251304. | − | 145090.i | 0.943842 | − | 0.544928i | ||||
\(517\) | 99664.5i | 0.372872i | ||||||||
\(518\) | 35603.2 | + | 110043.i | 0.132687 | + | 0.410114i | ||||
\(519\) | 369377. | 1.37131 | ||||||||
\(520\) | −2431.73 | − | 4211.88i | −0.00899308 | − | 0.0155765i | ||||
\(521\) | 374408. | + | 216164.i | 1.37933 | + | 0.796359i | 0.992079 | − | 0.125614i | \(-0.0400901\pi\) |
0.387255 | + | 0.921973i | \(0.373423\pi\) | |||||||
\(522\) | −11646.2 | + | 20171.9i | −0.0427410 | + | 0.0740295i | ||||
\(523\) | 122106. | − | 70497.7i | 0.446408 | − | 0.257734i | −0.259904 | − | 0.965634i | \(-0.583691\pi\) |
0.706312 | + | 0.707901i | \(0.250358\pi\) | |||||||
\(524\) | − | 95654.9i | − | 0.348373i | ||||||
\(525\) | 57310.6 | − | 267977.i | 0.207930 | − | 0.972253i | ||||
\(526\) | −340339. | −1.23010 | ||||||||
\(527\) | −222232. | − | 384917.i | −0.800176 | − | 1.38595i | ||||
\(528\) | −48091.3 | − | 27765.5i | −0.172504 | − | 0.0995950i | ||||
\(529\) | 83032.5 | − | 143816.i | 0.296713 | − | 0.513922i | ||||
\(530\) | 169251. | − | 97717.4i | 0.602533 | − | 0.347873i | ||||
\(531\) | 70653.9i | 0.250580i | ||||||||
\(532\) | −508344. | − | 458867.i | −1.79612 | − | 1.62130i | ||||
\(533\) | −7814.56 | −0.0275074 | ||||||||
\(534\) | −222797. | − | 385896.i | −0.781316 | − | 1.35328i | ||||
\(535\) | 46348.9 | + | 26759.5i | 0.161932 | + | 0.0934912i | ||||
\(536\) | −19122.4 | + | 33120.9i | −0.0665598 | + | 0.115285i | ||||
\(537\) | −200904. | + | 115992.i | −0.696692 | + | 0.402235i | ||||
\(538\) | 788025.i | 2.72255i | ||||||||
\(539\) | −111164. | − | 49826.7i | −0.382635 | − | 0.171508i | ||||
\(540\) | 139507. | 0.478419 | ||||||||
\(541\) | 36434.9 | + | 63107.0i | 0.124487 | + | 0.215617i | 0.921532 | − | 0.388302i | \(-0.126938\pi\) |
−0.797046 | + | 0.603919i | \(0.793605\pi\) | |||||||
\(542\) | −3972.21 | − | 2293.36i | −0.0135218 | − | 0.00780680i | ||||
\(543\) | 45392.5 | − | 78622.1i | 0.153952 | − | 0.266652i | ||||
\(544\) | −187387. | + | 108188.i | −0.633200 | + | 0.365578i | ||||
\(545\) | 83227.9i | 0.280205i | ||||||||
\(546\) | 16253.0 | − | 18005.5i | 0.0545192 | − | 0.0603976i | ||||
\(547\) | −422856. | −1.41325 | −0.706623 | − | 0.707590i | \(-0.749782\pi\) | ||||
−0.706623 | + | 0.707590i | \(0.749782\pi\) | |||||||
\(548\) | 503747. | + | 872515.i | 1.67746 | + | 2.90544i | ||||
\(549\) | 26119.4 | + | 15080.0i | 0.0866598 | + | 0.0500331i | ||||
\(550\) | 96306.8 | − | 166808.i | 0.318370 | − | 0.551432i | ||||
\(551\) | −90758.2 | + | 52399.3i | −0.298939 | + | 0.172593i | ||||
\(552\) | 283851.i | 0.931563i | ||||||||
\(553\) | 273188. | + | 58425.0i | 0.893328 | + | 0.191051i | ||||
\(554\) | 246567. | 0.803371 | ||||||||
\(555\) | 13192.4 | + | 22849.9i | 0.0428290 | + | 0.0741821i | ||||
\(556\) | −135440. | − | 78196.5i | −0.438125 | − | 0.252952i | ||||
\(557\) | −139947. | + | 242396.i | −0.451080 | + | 0.781294i | −0.998453 | − | 0.0555948i | \(-0.982295\pi\) |
0.547373 | + | 0.836889i | \(0.315628\pi\) | |||||||
\(558\) | 119722. | − | 69121.3i | 0.384507 | − | 0.221995i | ||||
\(559\) | 7684.53i | 0.0245920i | ||||||||
\(560\) | 39282.7 | − | 12709.4i | 0.125264 | − | 0.0405275i | ||||
\(561\) | −173640. | −0.551726 | ||||||||
\(562\) | 177711. | + | 307804.i | 0.562653 | + | 0.974543i | ||||
\(563\) | −93652.7 | − | 54070.4i | −0.295463 | − | 0.170586i | 0.344940 | − | 0.938625i | \(-0.387899\pi\) |
−0.640403 | + | 0.768039i | \(0.721233\pi\) | |||||||
\(564\) | 278422. | − | 482241.i | 0.875277 | − | 1.51602i | ||||
\(565\) | −85331.1 | + | 49265.9i | −0.267307 | + | 0.154330i | ||||
\(566\) | − | 577206.i | − | 1.80176i | ||||||
\(567\) | 114755. | + | 354688.i | 0.356949 | + | 1.10327i | ||||
\(568\) | −126849. | −0.393178 | ||||||||
\(569\) | 7795.85 | + | 13502.8i | 0.0240790 | + | 0.0417061i | 0.877814 | − | 0.479002i | \(-0.159001\pi\) |
−0.853735 | + | 0.520708i | \(0.825668\pi\) | |||||||
\(570\) | −210557. | − | 121565.i | −0.648067 | − | 0.374161i | ||||
\(571\) | 246603. | − | 427128.i | 0.756355 | − | 1.31004i | −0.188343 | − | 0.982103i | \(-0.560312\pi\) |
0.944698 | − | 0.327942i | \(-0.106355\pi\) | |||||||
\(572\) | 9487.19 | − | 5477.43i | 0.0289965 | − | 0.0167411i | ||||
\(573\) | − | 118933.i | − | 0.362237i | ||||||
\(574\) | 71369.4 | − | 333714.i | 0.216615 | − | 1.01286i | ||||
\(575\) | −191396. | −0.578893 | ||||||||
\(576\) | −47990.4 | − | 83121.8i | −0.144647 | − | 0.250536i | ||||
\(577\) | −280469. | − | 161929.i | −0.842429 | − | 0.486377i | 0.0156601 | − | 0.999877i | \(-0.495015\pi\) |
−0.858089 | + | 0.513501i | \(0.828348\pi\) | |||||||
\(578\) | 123935. | − | 214662.i | 0.370971 | − | 0.642540i | ||||
\(579\) | −73005.7 | + | 42149.9i | −0.217771 | + | 0.125730i | ||||
\(580\) | − | 47067.7i | − | 0.139916i | ||||||
\(581\) | −146538. | − | 132275.i | −0.434107 | − | 0.391856i | ||||
\(582\) | −760845. | −2.24621 | ||||||||
\(583\) | 97662.3 | + | 169156.i | 0.287336 | + | 0.497680i | ||||
\(584\) | −52098.5 | − | 30079.1i | −0.152756 | − | 0.0881940i | ||||
\(585\) | 459.754 | − | 796.317i | 0.00134343 | − | 0.00232688i | ||||
\(586\) | 315838. | − | 182349.i | 0.919749 | − | 0.531018i | ||||
\(587\) | 318676.i | 0.924854i | 0.886657 | + | 0.462427i | \(0.153021\pi\) | ||||
−0.886657 | + | 0.462427i | \(0.846979\pi\) | |||||||
\(588\) | 398686. | + | 551640.i | 1.15312 | + | 1.59551i | ||||
\(589\) | 621988. | 1.79288 | ||||||||
\(590\) | −111098. | − | 192427.i | −0.319155 | − | 0.552793i | ||||
\(591\) | −135797. | − | 78402.3i | −0.388790 | − | 0.224468i | ||||
\(592\) | 19588.8 | − | 33928.8i | 0.0558939 | − | 0.0968111i | ||||
\(593\) | 497448. | − | 287202.i | 1.41461 | − | 0.816728i | 0.418796 | − | 0.908080i | \(-0.362452\pi\) |
0.995819 | + | 0.0913521i | \(0.0291189\pi\) | |||||||
\(594\) | 216992.i | 0.614993i | ||||||||
\(595\) | 86505.9 | − | 95833.2i | 0.244350 | − | 0.270696i | ||||
\(596\) | 649892. | 1.82957 | ||||||||
\(597\) | 135599. | + | 234865.i | 0.380459 | + | 0.658975i | ||||
\(598\) | −14671.6 | − | 8470.64i | −0.0410274 | − | 0.0236872i | ||||
\(599\) | −158653. | + | 274795.i | −0.442176 | + | 0.765871i | −0.997851 | − | 0.0655285i | \(-0.979127\pi\) |
0.555675 | + | 0.831400i | \(0.312460\pi\) | |||||||
\(600\) | −413527. | + | 238750.i | −1.14869 | + | 0.663195i | ||||
\(601\) | 540394.i | 1.49610i | 0.663640 | + | 0.748052i | \(0.269011\pi\) | ||||
−0.663640 | + | 0.748052i | \(0.730989\pi\) | |||||||
\(602\) | −328161. | − | 70181.9i | −0.905512 | − | 0.193656i | ||||
\(603\) | −7230.73 | −0.0198860 | ||||||||
\(604\) | −456489. | − | 790662.i | −1.25129 | − | 2.16729i | ||||
\(605\) | 79293.6 | + | 45780.2i | 0.216634 | + | 0.125074i | ||||
\(606\) | −540601. | + | 936348.i | −1.47208 | + | 2.54972i | ||||
\(607\) | −295743. | + | 170747.i | −0.802669 | + | 0.463421i | −0.844404 | − | 0.535707i | \(-0.820045\pi\) |
0.0417345 | + | 0.999129i | \(0.486712\pi\) | |||||||
\(608\) | − | 302798.i | − | 0.819117i | ||||||
\(609\) | 99100.2 | − | 32062.7i | 0.267202 | − | 0.0864500i | ||||
\(610\) | −94848.7 | −0.254901 | ||||||||
\(611\) | 7373.14 | + | 12770.7i | 0.0197501 | + | 0.0342082i | ||||
\(612\) | 139616. | + | 80607.2i | 0.372762 | + | 0.215214i | ||||
\(613\) | 190344. | − | 329686.i | 0.506545 | − | 0.877362i | −0.493426 | − | 0.869788i | \(-0.664256\pi\) |
0.999971 | − | 0.00757447i | \(-0.00241105\pi\) | |||||||
\(614\) | −362176. | + | 209102.i | −0.960689 | + | 0.554654i | ||||
\(615\) | − | 77850.0i | − | 0.205830i | ||||||
\(616\) | 65341.5 | + | 201959.i | 0.172198 | + | 0.532234i | ||||
\(617\) | 658048. | 1.72857 | 0.864286 | − | 0.503001i | \(-0.167771\pi\) | ||||
0.864286 | + | 0.503001i | \(0.167771\pi\) | |||||||
\(618\) | −91588.0 | − | 158635.i | −0.239807 | − | 0.415358i | ||||
\(619\) | −53221.2 | − | 30727.3i | −0.138900 | − | 0.0801942i | 0.428939 | − | 0.903333i | \(-0.358887\pi\) |
−0.567840 | + | 0.823139i | \(0.692221\pi\) | |||||||
\(620\) | −139675. | + | 241924.i | −0.363359 | + | 0.629356i | ||||
\(621\) | 186733. | − | 107810.i | 0.484214 | − | 0.279561i | ||||
\(622\) | − | 672275.i | − | 1.73766i | ||||||
\(623\) | −69247.4 | + | 323792.i | −0.178413 | + | 0.834238i | ||||
\(624\) | −8216.32 | −0.0211013 | ||||||||
\(625\) | −142993. | − | 247672.i | −0.366063 | − | 0.634040i | ||||
\(626\) | 949865. | + | 548405.i | 2.42389 | + | 1.39943i | ||||
\(627\) | 121496. | − | 210438.i | 0.309050 | − | 0.535290i | ||||
\(628\) | −532768. | + | 307594.i | −1.35089 | + | 0.779934i | ||||
\(629\) | − | 122504.i | − | 0.309635i | ||||||
\(630\) | 29807.2 | + | 26906.1i | 0.0751000 | + | 0.0677906i | ||||
\(631\) | −253942. | −0.637786 | −0.318893 | − | 0.947791i | \(-0.603311\pi\) | ||||
−0.318893 | + | 0.947791i | \(0.603311\pi\) | |||||||
\(632\) | −243392. | − | 421568.i | −0.609358 | − | 1.05544i | ||||
\(633\) | −432388. | − | 249639.i | −1.07911 | − | 0.623025i | ||||
\(634\) | −407822. | + | 706369.i | −1.01459 | + | 1.75733i | ||||
\(635\) | 98233.2 | − | 56715.0i | 0.243619 | − | 0.140653i | ||||
\(636\) | − | 1.09132e6i | − | 2.69796i | ||||||
\(637\) | −17930.3 | + | 1839.22i | −0.0441884 | + | 0.00453268i | ||||
\(638\) | 73209.9 | 0.179858 | ||||||||
\(639\) | −11991.3 | − | 20769.5i | −0.0293673 | − | 0.0508657i | ||||
\(640\) | 195888. | + | 113096.i | 0.478242 | + | 0.276113i | ||||
\(641\) | −223890. | + | 387789.i | −0.544903 | + | 0.943800i | 0.453710 | + | 0.891149i | \(0.350100\pi\) |
−0.998613 | + | 0.0526504i | \(0.983233\pi\) | |||||||
\(642\) | 402791. | − | 232551.i | 0.977259 | − | 0.564221i | ||||
\(643\) | − | 229530.i | − | 0.555160i | −0.960702 | − | 0.277580i | \(-0.910468\pi\) | ||
0.960702 | − | 0.277580i | \(-0.0895324\pi\) | |||||||
\(644\) | 318529. | − | 352874.i | 0.768028 | − | 0.850839i | ||||
\(645\) | −76554.6 | −0.184014 | ||||||||
\(646\) | 564424. | + | 977612.i | 1.35251 | + | 2.34262i | ||||
\(647\) | −273365. | − | 157828.i | −0.653033 | − | 0.377029i | 0.136584 | − | 0.990628i | \(-0.456388\pi\) |
−0.789617 | + | 0.613600i | \(0.789721\pi\) | |||||||
\(648\) | 324787. | − | 562548.i | 0.773479 | − | 1.33971i | ||||
\(649\) | 192319. | − | 111035.i | 0.456596 | − | 0.263616i | ||||
\(650\) | − | 28499.0i | − | 0.0674532i | ||||||
\(651\) | −604515. | − | 129284.i | −1.42641 | − | 0.305058i | ||||
\(652\) | 1.23840e6 | 2.91316 | ||||||||
\(653\) | 303655. | + | 525945.i | 0.712121 | + | 1.23343i | 0.964060 | + | 0.265686i | \(0.0855984\pi\) |
−0.251939 | + | 0.967743i | \(0.581068\pi\) | |||||||
\(654\) | 626383. | + | 361643.i | 1.46448 | + | 0.845520i | ||||
\(655\) | −12617.7 | + | 21854.5i | −0.0294102 | + | 0.0509399i | ||||
\(656\) | −100109. | + | 57797.9i | −0.232630 | + | 0.134309i | ||||
\(657\) | − | 11373.8i | − | 0.0263496i | ||||||
\(658\) | −612698. | + | 198231.i | −1.41512 | + | 0.457846i | ||||
\(659\) | −780948. | −1.79826 | −0.899128 | − | 0.437686i | \(-0.855798\pi\) | ||||
−0.899128 | + | 0.437686i | \(0.855798\pi\) | |||||||
\(660\) | 54567.1 | + | 94513.1i | 0.125269 | + | 0.216972i | ||||
\(661\) | −503807. | − | 290873.i | −1.15309 | − | 0.665734i | −0.203448 | − | 0.979086i | \(-0.565215\pi\) |
−0.949637 | + | 0.313351i | \(0.898548\pi\) | |||||||
\(662\) | 150117. | − | 260011.i | 0.342543 | − | 0.593301i | ||||
\(663\) | −22249.6 | + | 12845.8i | −0.0506168 | + | 0.0292236i | ||||
\(664\) | 343977.i | 0.780178i | ||||||||
\(665\) | 55614.0 | + | 171893.i | 0.125760 | + | 0.388701i | ||||
\(666\) | 38102.7 | 0.0859029 | ||||||||
\(667\) | −36373.7 | − | 63001.0i | −0.0817589 | − | 0.141611i | ||||
\(668\) | −619267. | − | 357534.i | −1.38779 | − | 0.801243i | ||||
\(669\) | 406448. | − | 703989.i | 0.908141 | − | 1.57295i | ||||
\(670\) | 19693.0 | − | 11369.8i | 0.0438695 | − | 0.0253281i | ||||
\(671\) | − | 94795.3i | − | 0.210543i | ||||||
\(672\) | −62938.4 | + | 294292.i | −0.139373 | + | 0.651688i | ||||
\(673\) | −566904. | −1.25164 | −0.625820 | − | 0.779968i | \(-0.715235\pi\) | ||||
−0.625820 | + | 0.779968i | \(0.715235\pi\) | |||||||
\(674\) | −429335. | − | 743630.i | −0.945097 | − | 1.63696i | ||||
\(675\) | 314126. | + | 181361.i | 0.689440 | + | 0.398048i | ||||
\(676\) | −409920. | + | 710003.i | −0.897028 | + | 1.55370i | ||||
\(677\) | −290467. | + | 167701.i | −0.633753 | + | 0.365897i | −0.782204 | − | 0.623022i | \(-0.785905\pi\) |
0.148451 | + | 0.988920i | \(0.452571\pi\) | |||||||
\(678\) | 856283.i | 1.86276i | ||||||||
\(679\) | 419680. | + | 378833.i | 0.910288 | + | 0.821691i | ||||
\(680\) | −224955. | −0.486495 | ||||||||
\(681\) | 161657. | + | 279998.i | 0.348578 | + | 0.603755i | ||||
\(682\) | −376294. | − | 217253.i | −0.809018 | − | 0.467087i | ||||
\(683\) | 320814. | − | 555666.i | 0.687720 | − | 1.19117i | −0.284854 | − | 0.958571i | \(-0.591945\pi\) |
0.972574 | − | 0.232595i | \(-0.0747217\pi\) | |||||||
\(684\) | −195380. | + | 112802.i | −0.417606 | + | 0.241105i | ||||
\(685\) | − | 265794.i | − | 0.566454i | ||||||
\(686\) | 85212.7 | − | 782495.i | 0.181074 | − | 1.66277i | ||||
\(687\) | 1.01914e6 | 2.15934 | ||||||||
\(688\) | 56836.2 | + | 98443.2i | 0.120074 | + | 0.207974i | ||||
\(689\) | 25028.2 | + | 14450.0i | 0.0527219 | + | 0.0304390i | ||||
\(690\) | 84386.0 | − | 146161.i | 0.177244 | − | 0.306996i | ||||
\(691\) | 277213. | − | 160049.i | 0.580573 | − | 0.335194i | −0.180788 | − | 0.983522i | \(-0.557865\pi\) |
0.761361 | + | 0.648328i | \(0.224531\pi\) | |||||||
\(692\) | 1.07790e6i | 2.25096i | ||||||||
\(693\) | −26890.9 | + | 29790.4i | −0.0559937 | + | 0.0620311i | ||||
\(694\) | 82336.5 | 0.170952 | ||||||||
\(695\) | 20629.6 | + | 35731.5i | 0.0427092 | + | 0.0739744i | ||||
\(696\) | −157176. | − | 90745.8i | −0.324466 | − | 0.187330i | ||||
\(697\) | −180728. | + | 313030.i | −0.372015 | + | 0.644349i | ||||
\(698\) | −51383.1 | + | 29666.0i | −0.105465 | + | 0.0608904i | ||||
\(699\) | 701782.i | 1.43631i | ||||||||
\(700\) | 782001. | + | 167242.i | 1.59592 | + | 0.341310i | ||||
\(701\) | −403113. | −0.820333 | −0.410167 | − | 0.912011i | \(-0.634529\pi\) | ||||
−0.410167 | + | 0.912011i | \(0.634529\pi\) | |||||||
\(702\) | 16053.0 | + | 27804.6i | 0.0325748 | + | 0.0564211i | ||||
\(703\) | 148466. | + | 85716.9i | 0.300411 | + | 0.173443i | ||||
\(704\) | −150837. | + | 261258.i | −0.304343 | + | 0.527138i | ||||
\(705\) | −127224. | + | 73452.5i | −0.255970 | + | 0.147784i | ||||
\(706\) | − | 727010.i | − | 1.45858i | ||||||
\(707\) | 764412. | − | 247316.i | 1.52929 | − | 0.494782i | ||||
\(708\) | −1.24075e6 | −2.47524 | ||||||||
\(709\) | −59075.5 | − | 102322.i | −0.117521 | − | 0.203552i | 0.801264 | − | 0.598311i | \(-0.204161\pi\) |
−0.918785 | + | 0.394759i | \(0.870828\pi\) | |||||||
\(710\) | 65317.0 | + | 37710.8i | 0.129572 | + | 0.0748082i | ||||
\(711\) | 46016.9 | − | 79703.6i | 0.0910286 | − | 0.157666i | ||||
\(712\) | 499658. | − | 288477.i | 0.985627 | − | 0.569052i | ||||
\(713\) | 431761.i | 0.849306i | ||||||||
\(714\) | −345366. | − | 1.06747e6i | −0.677460 | − | 2.09391i | ||||
\(715\) | −2890.08 | −0.00565325 | ||||||||
\(716\) | −338484. | − | 586271.i | −0.660256 | − | 1.14360i | ||||
\(717\) | 69736.7 | + | 40262.5i | 0.135651 | + | 0.0783182i | ||||
\(718\) | 762953. | − | 1.32147e6i | 1.47996 | − | 2.56336i | ||||
\(719\) | −274033. | + | 158213.i | −0.530085 | + | 0.306045i | −0.741051 | − | 0.671448i | \(-0.765672\pi\) |
0.210966 | + | 0.977493i | \(0.432339\pi\) | |||||||
\(720\) | − | 13601.7i | − | 0.0262379i | ||||||
\(721\) | −28466.4 | + | 133105.i | −0.0547599 | + | 0.256050i | ||||
\(722\) | −707820. | −1.35784 | ||||||||
\(723\) | −19015.4 | − | 32935.6i | −0.0363771 | − | 0.0630070i | ||||
\(724\) | 229432. | + | 132463.i | 0.437700 | + | 0.252706i | ||||
\(725\) | 61188.5 | − | 105982.i | 0.116411 | − | 0.201630i | ||||
\(726\) | 689094. | − | 397849.i | 1.30739 | − | 0.754822i | ||||
\(727\) | − | 773616.i | − | 1.46371i | −0.681458 | − | 0.731857i | \(-0.738654\pi\) | ||
0.681458 | − | 0.731857i | \(-0.261346\pi\) | |||||||
\(728\) | 23313.5 | + | 21044.4i | 0.0439891 | + | 0.0397077i | ||||
\(729\) | −387523. | −0.729192 | ||||||||
\(730\) | 17884.4 | + | 30976.7i | 0.0335605 | + | 0.0581285i | ||||
\(731\) | 307822. | + | 177721.i | 0.576056 | + | 0.332586i | ||||
\(732\) | −264819. | + | 458681.i | −0.494228 | + | 0.856029i | ||||
\(733\) | 144928. | − | 83674.1i | 0.269739 | − | 0.155734i | −0.359030 | − | 0.933326i | \(-0.616892\pi\) |
0.628769 | + | 0.777592i | \(0.283559\pi\) | |||||||
\(734\) | 1.60324e6i | 2.97582i | ||||||||
\(735\) | −18322.6 | − | 178625.i | −0.0339167 | − | 0.330648i | ||||
\(736\) | 210191. | 0.388024 | ||||||||
\(737\) | 11363.4 | + | 19681.9i | 0.0209205 | + | 0.0362353i | ||||
\(738\) | −97362.4 | − | 56212.2i | −0.178763 | − | 0.103209i | ||||
\(739\) | −327676. | + | 567552.i | −0.600007 | + | 1.03924i | 0.392813 | + | 0.919618i | \(0.371502\pi\) |
−0.992819 | + | 0.119623i | \(0.961831\pi\) | |||||||
\(740\) | −66679.8 | + | 38497.6i | −0.121767 | + | 0.0703024i | ||||
\(741\) | − | 35953.1i | − | 0.0654786i | ||||||
\(742\) | −845657. | + | 936838.i | −1.53598 | + | 1.70160i | ||||
\(743\) | 322777. | 0.584690 | 0.292345 | − | 0.956313i | \(-0.405565\pi\) | ||||
0.292345 | + | 0.956313i | \(0.405565\pi\) | |||||||
\(744\) | 538583. | + | 932854.i | 0.972987 | + | 1.68526i | ||||
\(745\) | −148482. | − | 85726.3i | −0.267524 | − | 0.154455i | ||||
\(746\) | 71707.8 | − | 124202.i | 0.128851 | − | 0.223177i | ||||
\(747\) | −56321.0 | + | 32517.0i | −0.100932 | + | 0.0582732i | ||||
\(748\) | − | 506709.i | − | 0.905639i | ||||||
\(749\) | −337968. | − | 72279.2i | −0.602438 | − | 0.128840i | ||||
\(750\) | 596631. | 1.06068 | ||||||||
\(751\) | −2637.27 | − | 4567.89i | −0.00467601 | − | 0.00809908i | 0.863678 | − | 0.504044i | \(-0.168155\pi\) |
−0.868354 | + | 0.495945i | \(0.834822\pi\) | |||||||
\(752\) | 188908. | + | 109066.i | 0.334053 | + | 0.192866i | ||||
\(753\) | −463229. | + | 802336.i | −0.816970 | + | 1.41503i | ||||
\(754\) | 9380.86 | − | 5416.04i | 0.0165006 | − | 0.00952663i | ||||
\(755\) | 240859.i | 0.422542i | ||||||||
\(756\) | −857151. | + | 277321.i | −1.49973 | + | 0.485220i | ||||
\(757\) | 469746. | 0.819732 | 0.409866 | − | 0.912146i | \(-0.365576\pi\) | ||||
0.409866 | + | 0.912146i | \(0.365576\pi\) | |||||||
\(758\) | 141754. | + | 245524.i | 0.246715 | + | 0.427323i | ||||
\(759\) | 146078. | + | 84338.4i | 0.253573 | + | 0.146400i | ||||
\(760\) | 157402. | − | 272629.i | 0.272511 | − | 0.472003i | ||||
\(761\) | 104873. | − | 60548.6i | 0.181090 | − | 0.104553i | −0.406715 | − | 0.913555i | \(-0.633326\pi\) |
0.587805 | + | 0.809003i | \(0.299992\pi\) | |||||||
\(762\) | − | 985753.i | − | 1.69769i | ||||||
\(763\) | −165446. | − | 511364.i | −0.284188 | − | 0.878378i | ||||
\(764\) | 347065. | 0.594599 | ||||||||
\(765\) | −21265.6 | − | 36833.0i | −0.0363374 | − | 0.0629382i | ||||
\(766\) | −165716. | − | 95675.9i | −0.282427 | − | 0.163059i | ||||
\(767\) | 16428.7 | − | 28455.3i | 0.0279262 | − | 0.0483696i | ||||
\(768\) | 890324. | − | 514029.i | 1.50947 | − | 0.871495i | ||||
\(769\) | − | 268249.i | − | 0.453613i | −0.973940 | − | 0.226807i | \(-0.927171\pi\) | ||
0.973940 | − | 0.226807i | \(-0.0728285\pi\) | |||||||
\(770\) | 26394.8 | − | 123419.i | 0.0445181 | − | 0.208161i | ||||
\(771\) | −529879. | −0.891391 | ||||||||
\(772\) | −123000. | − | 213043.i | −0.206382 | − | 0.357464i | ||||
\(773\) | −209245. | − | 120807.i | −0.350183 | − | 0.202178i | 0.314583 | − | 0.949230i | \(-0.398135\pi\) |
−0.664766 | + | 0.747052i | \(0.731469\pi\) | |||||||
\(774\) | −55276.9 | + | 95742.3i | −0.0922702 | + | 0.159817i | ||||
\(775\) | −629009. | + | 363159.i | −1.04726 | + | 0.604635i | ||||
\(776\) | − | 985142.i | − | 1.63597i | ||||||
\(777\) | −126479. | − | 114169.i | −0.209496 | − | 0.189106i | ||||
\(778\) | −291724. | −0.481962 | ||||||||
\(779\) | −252913. | − | 438058.i | −0.416769 | − | 0.721866i | ||||
\(780\) | 13984.1 | + | 8073.71i | 0.0229850 | + | 0.0132704i | ||||
\(781\) | −37689.6 | + | 65280.2i | −0.0617901 | + | 0.107024i | ||||
\(782\) | −678622. | + | 391803.i | −1.10972 | + | 0.640699i | ||||
\(783\) | 137866.i | 0.224871i | ||||||||
\(784\) | −216094. | + | 156177.i | −0.351569 | + | 0.254089i | ||||
\(785\) | 162297. | 0.263373 | ||||||||
\(786\) | 109653. | + | 189925.i | 0.177491 | + | 0.307423i | ||||
\(787\) | 974603. | + | 562687.i | 1.57354 | + | 0.908484i | 0.995730 | + | 0.0923139i | \(0.0294263\pi\) |
0.577811 | + | 0.816170i | \(0.303907\pi\) | |||||||
\(788\) | 228791. | − | 396277.i | 0.368456 | − | 0.638185i | ||||
\(789\) | 434203. | − | 250687.i | 0.697492 | − | 0.402697i | ||||
\(790\) | 289432.i | 0.463759i | ||||||||
\(791\) | 426353. | − | 472323.i | 0.681422 | − | 0.754895i | ||||
\(792\) | 69928.9 | 0.111482 | ||||||||
\(793\) | −7012.92 | − | 12146.7i | −0.0111520 | − | 0.0193158i | ||||
\(794\) | 971360. | + | 560815.i | 1.54077 | + | 0.889567i | ||||
\(795\) | −143954. | + | 249335.i | −0.227766 | + | 0.394502i | ||||
\(796\) | −685373. | + | 395700.i | −1.08169 | + | 0.624511i | ||||
\(797\) | − | 875198.i | − | 1.37781i | −0.724851 | − | 0.688905i | \(-0.758092\pi\) | ||
0.724851 | − | 0.688905i | \(-0.241908\pi\) | |||||||
\(798\) | 1.53535e6 | + | 328355.i | 2.41102 | + | 0.515630i | ||||
\(799\) | 682078. | 1.06842 | ||||||||
\(800\) | 176794. | + | 306216.i | 0.276241 | + | 0.478463i | ||||
\(801\) | 94467.6 | + | 54540.9i | 0.147237 | + | 0.0850075i | ||||
\(802\) | −419222. | + | 726113.i | −0.651771 | + | 1.12890i | ||||
\(803\) | −30959.2 | + | 17874.3i | −0.0480130 | + | 0.0277203i | ||||
\(804\) | − | 126978.i | − | 0.196435i | ||||||
\(805\) | −119322. | + | 38605.2i | −0.184132 | + | 0.0595737i | ||||
\(806\) | −64289.3 | −0.0989620 | ||||||||
\(807\) | −580445. | − | 1.00536e6i | −0.891280 | − | 1.54374i | ||||
\(808\) | −1.21238e6 | − | 699970.i | −1.85702 | − | 1.07215i | ||||
\(809\) | 272358. | − | 471738.i | 0.416144 | − | 0.720782i | −0.579404 | − | 0.815040i | \(-0.696715\pi\) |
0.995548 | + | 0.0942585i | \(0.0300480\pi\) | |||||||
\(810\) | −334479. | + | 193112.i | −0.509799 | + | 0.294333i | ||||
\(811\) | 786948.i | 1.19648i | 0.801318 | + | 0.598238i | \(0.204132\pi\) | ||||
−0.801318 | + | 0.598238i | \(0.795868\pi\) | |||||||
\(812\) | 93564.0 | + | 289191.i | 0.141905 | + | 0.438603i | ||||
\(813\) | 6756.99 | 0.0102229 | ||||||||
\(814\) | −59879.9 | − | 103715.i | −0.0903717 | − | 0.156528i | ||||
\(815\) | −282939. | − | 163355.i | −0.425969 | − | 0.245933i | ||||
\(816\) | −190020. | + | 329124.i | −0.285377 | + | 0.494287i | ||||
\(817\) | −430769. | + | 248704.i | −0.645357 | + | 0.372597i | ||||
\(818\) | 486635.i | 0.727271i | ||||||||
\(819\) | −1241.82 | + | 5806.61i | −0.00185137 | + | 0.00865675i | ||||
\(820\) | 227179. | 0.337863 | ||||||||
\(821\) | −287810. | − | 498502.i | −0.426992 | − | 0.739572i | 0.569612 | − | 0.821914i | \(-0.307093\pi\) |
−0.996604 | + | 0.0823419i | \(0.973760\pi\) | |||||||
\(822\) | −2.00040e6 | − | 1.15493e6i | −2.96055 | − | 1.70928i | ||||
\(823\) | −217990. | + | 377569.i | −0.321837 | + | 0.557438i | −0.980867 | − | 0.194678i | \(-0.937634\pi\) |
0.659030 | + | 0.752117i | \(0.270967\pi\) | |||||||
\(824\) | 205401. | − | 118588.i | 0.302516 | − | 0.174657i | ||||
\(825\) | 283752.i | 0.416899i | ||||||||
\(826\) | 1.06512e6 | + | 961452.i | 1.56113 | + | 1.40918i | ||||
\(827\) | 567533. | 0.829813 | 0.414907 | − | 0.909864i | \(-0.363814\pi\) | ||||
0.414907 | + | 0.909864i | \(0.363814\pi\) | |||||||
\(828\) | −78303.3 | − | 135625.i | −0.114214 | − | 0.197824i | ||||
\(829\) | 451387. | + | 260608.i | 0.656810 | + | 0.379209i | 0.791060 | − | 0.611738i | \(-0.209529\pi\) |
−0.134250 | + | 0.990947i | \(0.542863\pi\) | |||||||
\(830\) | 102261. | − | 177121.i | 0.148441 | − | 0.257107i | ||||
\(831\) | −314570. | + | 181617.i | −0.455529 | + | 0.263000i | ||||
\(832\) | 44635.6i | 0.0644814i | ||||||||
\(833\) | −341001. | + | 760775.i | −0.491435 | + | 1.09639i | ||||
\(834\) | 358559. | 0.515500 | ||||||||
\(835\) | 94323.6 | + | 163373.i | 0.135284 | + | 0.234319i | ||||
\(836\) | 614092. | + | 354546.i | 0.878661 | + | 0.507295i | ||||
\(837\) | 409122. | − | 708620.i | 0.583985 | − | 1.01149i | ||||
\(838\) | −280752. | + | 162092.i | −0.399792 | + | 0.230820i | ||||
\(839\) | − | 426309.i | − | 0.605620i | −0.953051 | − | 0.302810i | \(-0.902075\pi\) | ||
0.953051 | − | 0.302810i | \(-0.0979247\pi\) | |||||||
\(840\) | −209648. | + | 232253.i | −0.297121 | + | 0.329157i | ||||
\(841\) | −660767. | −0.934236 | ||||||||
\(842\) | 225301. | + | 390234.i | 0.317790 | + | 0.550428i | ||||
\(843\) | −453446. | − | 261797.i | −0.638073 | − | 0.368391i | ||||
\(844\) | 728488. | − | 1.26178e6i | 1.02267 | − | 1.77132i | ||||
\(845\) | 187311. | − | 108144.i | 0.262331 | − | 0.151457i | ||||
\(846\) | 212148.i | 0.296413i | ||||||||
\(847\) | −578196. | − | 123655.i | −0.805950 | − | 0.172364i | ||||
\(848\) | 427501. | 0.594491 | ||||||||
\(849\) | 425160. | + | 736399.i | 0.589844 | + | 1.02164i | ||||
\(850\) | −1.14159e6 | − | 659099.i | −1.58006 | − | 0.912247i | ||||
\(851\) | −59501.5 | + | 103060.i | −0.0821616 | + | 0.142308i | ||||
\(852\) | 364733. | − | 210579.i | 0.502453 | − | 0.290092i | ||||
\(853\) | 200874.i | 0.276074i | 0.990427 | + | 0.138037i | \(0.0440793\pi\) | ||||
−0.990427 | + | 0.138037i | \(0.955921\pi\) | |||||||
\(854\) | 582764. | − | 188546.i | 0.799056 | − | 0.258525i | ||||
\(855\) | 59518.4 | 0.0814178 | ||||||||
\(856\) | 301108. | + | 521534.i | 0.410936 | + | 0.711762i | ||||
\(857\) | 580831. | + | 335343.i | 0.790839 | + | 0.456591i | 0.840258 | − | 0.542187i | \(-0.182404\pi\) |
−0.0494189 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(858\) | −12558.0 | + | 21751.1i | −0.0170587 | + | 0.0295465i | ||||
\(859\) | 670028. | − | 386841.i | 0.908044 | − | 0.524259i | 0.0282427 | − | 0.999601i | \(-0.491009\pi\) |
0.879801 | + | 0.475342i | \(0.157676\pi\) | |||||||
\(860\) | − | 223399.i | − | 0.302053i | ||||||
\(861\) | 154755. | + | 478322.i | 0.208756 | + | 0.645229i | ||||
\(862\) | −813086. | −1.09426 | ||||||||
\(863\) | −8329.28 | − | 14426.7i | −0.0111837 | − | 0.0193707i | 0.860379 | − | 0.509654i | \(-0.170227\pi\) |
−0.871563 | + | 0.490283i | \(0.836893\pi\) | |||||||
\(864\) | −344973. | − | 199170.i | −0.462123 | − | 0.266807i | ||||
\(865\) | 142185. | − | 246271.i | 0.190029 | − | 0.329140i | ||||
\(866\) | 122470. | − | 70707.9i | 0.163303 | − | 0.0942828i | ||||
\(867\) | 365155.i | 0.485779i | ||||||||
\(868\) | 377272. | − | 1.76407e6i | 0.500743 | − | 2.34141i | ||||
\(869\) | −289269. | −0.383056 | ||||||||
\(870\) | 53955.6 | + | 93453.8i | 0.0712850 | + | 0.123469i | ||||
\(871\) | 2912.12 | + | 1681.31i | 0.00383860 | + | 0.00221622i | ||||
\(872\) | −468255. | + | 811041.i | −0.615814 | + | 1.06662i | ||||
\(873\) | 161302. | − | 93127.8i | 0.211647 | − | 0.122194i | ||||
\(874\) | − | 1.09658e6i | − | 1.43555i | ||||||
\(875\) | −329100. | − | 297069.i | −0.429845 | − | 0.388009i | ||||
\(876\) | 199734. | 0.260282 | ||||||||
\(877\) | 243088. | + | 421040.i | 0.316056 | + | 0.547425i | 0.979661 | − | 0.200658i | \(-0.0643080\pi\) |
−0.663606 | + | 0.748083i | \(0.730975\pi\) | |||||||
\(878\) | −100495. | − | 58020.6i | −0.130363 | − | 0.0752650i | ||||
\(879\) | −268631. | + | 465282.i | −0.347679 | + | 0.602197i | ||||
\(880\) | −37023.6 | + | 21375.6i | −0.0478094 | + | 0.0276028i | ||||
\(881\) | − | 867783.i | − | 1.11805i | −0.829152 | − | 0.559023i | \(-0.811176\pi\) | ||
0.829152 | − | 0.559023i | \(-0.188824\pi\) | |||||||
\(882\) | −236625. | − | 106062.i | −0.304175 | − | 0.136340i | ||||
\(883\) | 103207. | 0.132369 | 0.0661845 | − | 0.997807i | \(-0.478917\pi\) | ||||
0.0661845 | + | 0.997807i | \(0.478917\pi\) | |||||||
\(884\) | −37486.1 | − | 64927.9i | −0.0479696 | − | 0.0830858i | ||||
\(885\) | 283477. | + | 163665.i | 0.361936 | + | 0.208964i | ||||
\(886\) | 631161. | − | 1.09320e6i | 0.804031 | − | 1.39262i | ||||
\(887\) | −752733. | + | 434591.i | −0.956740 | + | 0.552374i | −0.895168 | − | 0.445729i | \(-0.852945\pi\) |
−0.0615718 | + | 0.998103i | \(0.519611\pi\) | |||||||
\(888\) | 296891.i | 0.376506i | ||||||||
\(889\) | −490817. | + | 543739.i | −0.621035 | + | 0.687997i | ||||
\(890\) | −343046. | −0.433084 | ||||||||
\(891\) | −193003. | − | 334291.i | −0.243113 | − | 0.421084i | ||||
\(892\) | 2.05435e6 | + | 1.18608e6i | 2.58194 | + | 1.49068i | ||||
\(893\) | −477253. | + | 826627.i | −0.598475 | + | 1.03659i | ||||
\(894\) | −1.29037e6 | + | 744997.i | −1.61451 | + | 0.932137i | ||||
\(895\) | 178596.i | 0.222959i | ||||||||
\(896\) | −1.42838e6 | − | 305480.i | −1.77922 | − | 0.380510i | ||||
\(897\) | 24957.3 | 0.0310179 | ||||||||
\(898\) | −214632. | − | 371753.i | −0.266159 | − | 0.461001i | ||||
\(899\) | −239078. | − | 138032.i | −0.295815 | − | 0.170789i | ||||
\(900\) | 131723. | − | 228152.i | 0.162622 | − | 0.281669i | ||||
\(901\) | 1.15766e6 | − | 668376.i | 1.42604 | − | 0.823324i | ||||
\(902\) | 353358.i | 0.434313i | ||||||||
\(903\) | 470363. | − | 152180.i | 0.576842 | − | 0.186630i | ||||
\(904\) | −1.10871e6 | −1.35670 | ||||||||
\(905\) | −34945.9 | − | 60528.1i | −0.0426677 | − | 0.0739027i | ||||
\(906\) | 1.81274e6 | + | 1.04658e6i | 2.20840 | + | 1.27502i | ||||
\(907\) | −270302. | + | 468177.i | −0.328575 | + | 0.569109i | −0.982229 | − | 0.187685i | \(-0.939902\pi\) |
0.653654 | + | 0.756793i | \(0.273235\pi\) | |||||||
\(908\) | −817080. | + | 471741.i | −0.991044 | + | 0.572179i | ||||
\(909\) | − | 264679.i | − | 0.320326i | ||||||
\(910\) | −5748.32 | − | 17767.1i | −0.00694158 | − | 0.0214552i | ||||
\(911\) | 1.10640e6 | 1.33314 | 0.666572 | − | 0.745441i | \(-0.267761\pi\) | ||||
0.666572 | + | 0.745441i | \(0.267761\pi\) | |||||||
\(912\) | −265916. | − | 460579.i | −0.319708 | − | 0.553751i | ||||
\(913\) | 177021. | + | 102203.i | 0.212365 | + | 0.122609i | ||||
\(914\) | −853851. | + | 1.47891e6i | −1.02209 | + | 1.77031i | ||||
\(915\) | 121008. | − | 69863.9i | 0.144534 | − | 0.0834470i | ||||
\(916\) | 2.97402e6i | 3.54449i | ||||||||
\(917\) | 34081.2 | − | 159359.i | 0.0405300 | − | 0.189513i | ||||
\(918\) | 1.48504e6 | 1.76219 | ||||||||
\(919\) | −40794.0 | − | 70657.3i | −0.0483020 | − | 0.0836616i | 0.840864 | − | 0.541247i | \(-0.182048\pi\) |
−0.889166 | + | 0.457586i | \(0.848714\pi\) | |||||||
\(920\) | 189249. | + | 109263.i | 0.223593 | + | 0.129091i | ||||
\(921\) | 308042. | − | 533545.i | 0.363154 | − | 0.629002i | ||||
\(922\) | 1.74691e6 | − | 1.00858e6i | 2.05499 | − | 1.18645i | ||||
\(923\) | 11153.0i | 0.0130915i | ||||||||
\(924\) | −523147. | − | 472230.i | −0.612745 | − | 0.553107i | ||||
\(925\) | −200189. | −0.233969 | ||||||||
\(926\) | −995610. | − | 1.72445e6i | −1.16109 | − | 2.01107i | ||||
\(927\) | 38834.0 | + | 22420.8i | 0.0451911 | + | 0.0260911i | ||||
\(928\) | −67197.1 | + | 116389.i | −0.0780288 | + | 0.135150i | ||||
\(929\) | 949898. | − | 548424.i | 1.10064 | − | 0.635455i | 0.164252 | − | 0.986418i | \(-0.447479\pi\) |
0.936389 | + | 0.350963i | \(0.114146\pi\) | |||||||
\(930\) | − | 640461.i | − | 0.740503i | ||||||
\(931\) | −683401. | − | 945585.i | −0.788454 | − | 1.09094i | ||||
\(932\) | −2.04791e6 | −2.35765 | ||||||||
\(933\) | 495186. | + | 857687.i | 0.568859 | + | 0.985293i | ||||
\(934\) | −1.47036e6 | − | 848913.i | −1.68550 | − | 0.973126i | ||||
\(935\) | −66839.2 | + | 115769.i | −0.0764554 | + | 0.132425i | ||||
\(936\) | 8960.44 | − | 5173.31i | 0.0102277 | − | 0.00590496i | ||||
\(937\) | − | 280065.i | − | 0.318992i | −0.987199 | − | 0.159496i | \(-0.949013\pi\) | ||
0.987199 | − | 0.159496i | \(-0.0509869\pi\) | |||||||
\(938\) | −98395.2 | + | 109005.i | −0.111833 | + | 0.123891i | ||||
\(939\) | −1.61578e6 | −1.83253 | ||||||||
\(940\) | −214346. | − | 371259.i | −0.242583 | − | 0.420166i | ||||
\(941\) | −1.04479e6 | − | 603208.i | −1.17991 | − | 0.681221i | −0.223916 | − | 0.974608i | \(-0.571884\pi\) |
−0.955994 | + | 0.293387i | \(0.905217\pi\) | |||||||
\(942\) | 705214. | − | 1.22147e6i | 0.794729 | − | 1.37651i | ||||
\(943\) | 304084. | − | 175563.i | 0.341955 | − | 0.197428i | ||||
\(944\) | − | 486039.i | − | 0.545415i | ||||||
\(945\) | 232416. | + | 49705.5i | 0.260257 | + | 0.0556597i | ||||
\(946\) | 347479. | 0.388281 | ||||||||
\(947\) | 484847. | + | 839780.i | 0.540636 | + | 0.936409i | 0.998868 | + | 0.0475763i | \(0.0151497\pi\) |
−0.458232 | + | 0.888833i | \(0.651517\pi\) | |||||||
\(948\) | 1.39967e6 | + | 808100.i | 1.55743 | + | 0.899184i | ||||
\(949\) | −2644.67 | + | 4580.71i | −0.00293656 | + | 0.00508628i | ||||
\(950\) | 1.59756e6 | − | 922349.i | 1.77014 | − | 1.02199i | ||||
\(951\) | − | 1.20158e6i | − | 1.32859i | ||||||
\(952\) | 1.38216e6 | − | 447180.i | 1.52505 | − | 0.493411i | ||||
\(953\) | 566973. | 0.624275 | 0.312138 | − | 0.950037i | \(-0.398955\pi\) | ||||
0.312138 | + | 0.950037i | \(0.398955\pi\) | |||||||
\(954\) | 207886. | + | 360069.i | 0.228417 | + | 0.395630i | ||||
\(955\) | −79294.9 | − | 45780.9i | −0.0869437 | − | 0.0501970i | ||||
\(956\) | −117493. | + | 203503.i | −0.128557 | + | 0.222667i | ||||
\(957\) | −93401.1 | + | 53925.2i | −0.101983 | + | 0.0588800i | ||||
\(958\) | 1.25760e6i | 1.37029i | ||||||||
\(959\) | 528362. | + | 1.63308e6i | 0.574506 | + | 1.77570i | ||||
\(960\) | −444668. | −0.482495 | ||||||||
\(961\) | 357470. | + | 619156.i | 0.387073 | + | 0.670430i | ||||
\(962\) | −15345.6 | − | 8859.78i | −0.0165819 | − | 0.00957355i | ||||
\(963\) | −56928.8 | + | 98603.5i | −0.0613874 | + | 0.106326i | ||||
\(964\) | 96111.4 | − | 55489.9i | 0.103424 | − | 0.0597118i | ||||
\(965\) | 64899.1i | 0.0696922i | ||||||||
\(966\) | −227932. | + | 1.06578e6i | −0.244259 | + | 1.14212i | ||||
\(967\) | −1.18372e6 | −1.26590 | −0.632948 | − | 0.774195i | \(-0.718155\pi\) | ||||
−0.632948 | + | 0.774195i | \(0.718155\pi\) | |||||||
\(968\) | 515135. | + | 892239.i | 0.549756 | + | 0.952205i | ||||
\(969\) | −1.44018e6 | − | 831491.i | −1.53381 | − | 0.885543i | ||||
\(970\) | −292873. | + | 507270.i | −0.311269 | + | 0.539133i | ||||
\(971\) | −995192. | + | 574574.i | −1.05552 | + | 0.609408i | −0.924191 | − | 0.381931i | \(-0.875259\pi\) |
−0.131334 | + | 0.991338i | \(0.541926\pi\) | |||||||
\(972\) | 667449.i | 0.706457i | ||||||||
\(973\) | −197780. | − | 178531.i | −0.208909 | − | 0.188576i | ||||
\(974\) | 1.22891e6 | 1.29539 | ||||||||
\(975\) | 20991.8 | + | 36358.9i | 0.0220821 | + | 0.0382474i | ||||
\(976\) | −179679. | − | 103738.i | −0.188624 | − | 0.108902i | ||||
\(977\) | 505838. | − | 876138.i | 0.529935 | − | 0.917875i | −0.469455 | − | 0.882956i | \(-0.655550\pi\) |
0.999390 | − | 0.0349182i | \(-0.0111171\pi\) | |||||||
\(978\) | −2.45886e6 | + | 1.41962e6i | −2.57073 | + | 1.48421i | ||||
\(979\) | − | 342852.i | − | 0.357719i | ||||||
\(980\) | 521255. | − | 53468.4i | 0.542748 | − | 0.0556731i | ||||
\(981\) | −177061. | −0.183986 | ||||||||
\(982\) | 452976. | + | 784578.i | 0.469735 | + | 0.813604i | ||||
\(983\) | −572273. | − | 330402.i | −0.592238 | − | 0.341929i | 0.173744 | − | 0.984791i | \(-0.444414\pi\) |
−0.765982 | + | 0.642862i | \(0.777747\pi\) | |||||||
\(984\) | 437998. | − | 758634.i | 0.452357 | − | 0.783506i | ||||
\(985\) | −104545. | + | 60358.9i | −0.107753 | + | 0.0622113i | ||||
\(986\) | − | 501030.i | − | 0.515359i | ||||||
\(987\) | 635666. | − | 704206.i | 0.652521 | − | 0.722878i | ||||
\(988\) | 104917. | 0.107481 | ||||||||
\(989\) | −172641. | − | 299024.i | −0.176503 | − | 0.305712i | ||||
\(990\) | −36007.8 | − | 20789.1i | −0.0367389 | − | 0.0212112i | ||||
\(991\) | −20806.4 | + | 36037.7i | −0.0211860 | + | 0.0366953i | −0.876424 | − | 0.481540i | \(-0.840078\pi\) |
0.855238 | + | 0.518235i | \(0.173411\pi\) | |||||||
\(992\) | 690777. | − | 398820.i | 0.701963 | − | 0.405279i | ||||
\(993\) | 442295.i | 0.448553i | ||||||||
\(994\) | −476281. | − | 101859.i | −0.482048 | − | 0.103093i | ||||
\(995\) | 208785. | 0.210889 | ||||||||
\(996\) | −571029. | − | 989051.i | −0.575625 | − | 0.997011i | ||||
\(997\) | 345563. | + | 199511.i | 0.347646 | + | 0.200713i | 0.663648 | − | 0.748045i | \(-0.269007\pi\) |
−0.316002 | + | 0.948758i | \(0.602341\pi\) | |||||||
\(998\) | 601540. | − | 1.04190e6i | 0.603953 | − | 1.04608i | ||||
\(999\) | 195312. | − | 112763.i | 0.195703 | − | 0.112989i |
(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 | 7.5.d.a.3.1 | ✓ | 4 | |
3.2 | odd | 2 | 63.5.m.d.10.2 | 4 | |||
4.3 | odd | 2 | 112.5.s.a.17.1 | 4 | |||
5.2 | odd | 4 | 175.5.j.a.24.4 | 8 | |||
5.3 | odd | 4 | 175.5.j.a.24.1 | 8 | |||
5.4 | even | 2 | 175.5.i.a.101.2 | 4 | |||
7.2 | even | 3 | 49.5.d.b.19.1 | 4 | |||
7.3 | odd | 6 | 49.5.b.a.48.4 | 4 | |||
7.4 | even | 3 | 49.5.b.a.48.3 | 4 | |||
7.5 | odd | 6 | inner | 7.5.d.a.5.1 | yes | 4 | |
7.6 | odd | 2 | 49.5.d.b.31.1 | 4 | |||
21.5 | even | 6 | 63.5.m.d.19.2 | 4 | |||
21.11 | odd | 6 | 441.5.d.d.244.1 | 4 | |||
21.17 | even | 6 | 441.5.d.d.244.2 | 4 | |||
28.3 | even | 6 | 784.5.c.c.97.1 | 4 | |||
28.11 | odd | 6 | 784.5.c.c.97.4 | 4 | |||
28.19 | even | 6 | 112.5.s.a.33.1 | 4 | |||
35.12 | even | 12 | 175.5.j.a.124.1 | 8 | |||
35.19 | odd | 6 | 175.5.i.a.26.2 | 4 | |||
35.33 | even | 12 | 175.5.j.a.124.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.5.d.a.3.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7.5.d.a.5.1 | yes | 4 | 7.5 | odd | 6 | inner | |
49.5.b.a.48.3 | 4 | 7.4 | even | 3 | |||
49.5.b.a.48.4 | 4 | 7.3 | odd | 6 | |||
49.5.d.b.19.1 | 4 | 7.2 | even | 3 | |||
49.5.d.b.31.1 | 4 | 7.6 | odd | 2 | |||
63.5.m.d.10.2 | 4 | 3.2 | odd | 2 | |||
63.5.m.d.19.2 | 4 | 21.5 | even | 6 | |||
112.5.s.a.17.1 | 4 | 4.3 | odd | 2 | |||
112.5.s.a.33.1 | 4 | 28.19 | even | 6 | |||
175.5.i.a.26.2 | 4 | 35.19 | odd | 6 | |||
175.5.i.a.101.2 | 4 | 5.4 | even | 2 | |||
175.5.j.a.24.1 | 8 | 5.3 | odd | 4 | |||
175.5.j.a.24.4 | 8 | 5.2 | odd | 4 | |||
175.5.j.a.124.1 | 8 | 35.12 | even | 12 | |||
175.5.j.a.124.4 | 8 | 35.33 | even | 12 | |||
441.5.d.d.244.1 | 4 | 21.11 | odd | 6 | |||
441.5.d.d.244.2 | 4 | 21.17 | even | 6 | |||
784.5.c.c.97.1 | 4 | 28.3 | even | 6 | |||
784.5.c.c.97.4 | 4 | 28.11 | odd | 6 |