Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), 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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.2 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.b.146.24 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 5.37572i | − | 1.90061i | −0.311328 | − | 0.950303i | \(-0.600774\pi\) | ||
0.311328 | − | 0.950303i | \(-0.399226\pi\) | |||||||
\(3\) | 2.08523 | + | 4.75939i | 0.401302 | + | 0.915946i | ||||
\(4\) | −20.8984 | −2.61230 | ||||||||
\(5\) | −2.78815 | −0.249380 | −0.124690 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124690 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(6\) | 25.5852 | − | 11.2096i | 1.74085 | − | 0.762717i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 69.3382i | 3.06435i | ||||||||
\(9\) | −18.3036 | + | 19.8488i | −0.677913 | + | 0.735142i | ||||
\(10\) | 14.9883i | 0.473973i | ||||||||
\(11\) | 17.5600i | 0.481322i | 0.970609 | + | 0.240661i | \(0.0773643\pi\) | ||||
−0.970609 | + | 0.240661i | \(0.922636\pi\) | |||||||
\(12\) | −43.5779 | − | 99.4637i | −1.04832 | − | 2.39272i | ||||
\(13\) | 47.8755i | 1.02140i | 0.859758 | + | 0.510702i | \(0.170615\pi\) | ||||
−0.859758 | + | 0.510702i | \(0.829385\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.81394 | − | 13.2699i | −0.100077 | − | 0.228419i | ||||
\(16\) | 205.556 | 3.21181 | ||||||||
\(17\) | 89.4402 | 1.27603 | 0.638013 | − | 0.770026i | \(-0.279757\pi\) | ||||
0.638013 | + | 0.770026i | \(0.279757\pi\) | |||||||
\(18\) | 106.702 | + | 98.3954i | 1.39721 | + | 1.28844i | ||||
\(19\) | 42.2598i | 0.510267i | 0.966906 | + | 0.255133i | \(0.0821194\pi\) | ||||
−0.966906 | + | 0.255133i | \(0.917881\pi\) | |||||||
\(20\) | 58.2680 | 0.651456 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 94.3978 | 0.914804 | ||||||||
\(23\) | 87.6734i | 0.794833i | 0.917638 | + | 0.397417i | \(0.130093\pi\) | ||||
−0.917638 | + | 0.397417i | \(0.869907\pi\) | |||||||
\(24\) | −330.008 | + | 144.586i | −2.80677 | + | 1.22973i | ||||
\(25\) | −117.226 | −0.937810 | ||||||||
\(26\) | 257.365 | 1.94129 | ||||||||
\(27\) | −132.636 | − | 45.7249i | −0.945398 | − | 0.325917i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 40.8422i | − | 0.261524i | −0.991414 | − | 0.130762i | \(-0.958258\pi\) | ||
0.991414 | − | 0.130762i | \(-0.0417424\pi\) | |||||||
\(30\) | −71.3354 | + | 31.2541i | −0.434134 | + | 0.190206i | ||||
\(31\) | 95.6222i | 0.554008i | 0.960869 | + | 0.277004i | \(0.0893416\pi\) | ||||
−0.960869 | + | 0.277004i | \(0.910658\pi\) | |||||||
\(32\) | − | 550.306i | − | 3.04004i | ||||||
\(33\) | −83.5751 | + | 36.6167i | −0.440865 | + | 0.193156i | ||||
\(34\) | − | 480.806i | − | 2.42522i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 382.517 | − | 414.809i | 1.77091 | − | 1.92041i | ||||
\(37\) | −64.5502 | −0.286810 | −0.143405 | − | 0.989664i | \(-0.545805\pi\) | ||||
−0.143405 | + | 0.989664i | \(0.545805\pi\) | |||||||
\(38\) | 227.177 | 0.969815 | ||||||||
\(39\) | −227.858 | + | 99.8313i | −0.935551 | + | 0.409892i | ||||
\(40\) | − | 193.326i | − | 0.764187i | ||||||
\(41\) | −403.003 | −1.53509 | −0.767543 | − | 0.640997i | \(-0.778521\pi\) | ||||
−0.767543 | + | 0.640997i | \(0.778521\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −230.669 | −0.818061 | −0.409031 | − | 0.912521i | \(-0.634133\pi\) | ||||
−0.409031 | + | 0.912521i | \(0.634133\pi\) | |||||||
\(44\) | − | 366.976i | − | 1.25736i | ||||||
\(45\) | 51.0334 | − | 55.3416i | 0.169058 | − | 0.183330i | ||||
\(46\) | 471.308 | 1.51066 | ||||||||
\(47\) | 365.410 | 1.13405 | 0.567027 | − | 0.823699i | \(-0.308094\pi\) | ||||
0.567027 | + | 0.823699i | \(0.308094\pi\) | |||||||
\(48\) | 428.631 | + | 978.321i | 1.28891 | + | 2.94184i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 630.176i | 1.78241i | ||||||||
\(51\) | 186.503 | + | 425.681i | 0.512072 | + | 1.16877i | ||||
\(52\) | − | 1000.52i | − | 2.66822i | ||||||
\(53\) | 598.298i | 1.55061i | 0.631585 | + | 0.775307i | \(0.282405\pi\) | ||||
−0.631585 | + | 0.775307i | \(0.717595\pi\) | |||||||
\(54\) | −245.805 | + | 713.013i | −0.619440 | + | 1.79683i | ||||
\(55\) | − | 48.9601i | − | 0.120032i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −201.131 | + | 88.1213i | −0.467377 | + | 0.204771i | ||||
\(58\) | −219.556 | −0.497054 | ||||||||
\(59\) | 236.679 | 0.522254 | 0.261127 | − | 0.965304i | \(-0.415906\pi\) | ||||
0.261127 | + | 0.965304i | \(0.415906\pi\) | |||||||
\(60\) | 121.502 | + | 277.320i | 0.261431 | + | 0.596698i | ||||
\(61\) | − | 430.942i | − | 0.904532i | −0.891883 | − | 0.452266i | \(-0.850616\pi\) | ||
0.891883 | − | 0.452266i | \(-0.149384\pi\) | |||||||
\(62\) | 514.039 | 1.05295 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1313.84 | −2.56610 | ||||||||
\(65\) | − | 133.484i | − | 0.254718i | ||||||
\(66\) | 196.841 | + | 449.276i | 0.367113 | + | 0.837911i | ||||
\(67\) | −428.035 | −0.780490 | −0.390245 | − | 0.920711i | \(-0.627610\pi\) | ||||
−0.390245 | + | 0.920711i | \(0.627610\pi\) | |||||||
\(68\) | −1869.16 | −3.33336 | ||||||||
\(69\) | −417.272 | + | 182.819i | −0.728024 | + | 0.318968i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 519.586i | − | 0.868500i | −0.900792 | − | 0.434250i | \(-0.857013\pi\) | ||
0.900792 | − | 0.434250i | \(-0.142987\pi\) | |||||||
\(72\) | −1376.28 | − | 1269.14i | −2.25273 | − | 2.07736i | ||||
\(73\) | 764.579i | 1.22585i | 0.790140 | + | 0.612926i | \(0.210008\pi\) | ||||
−0.790140 | + | 0.612926i | \(0.789992\pi\) | |||||||
\(74\) | 347.004i | 0.545113i | ||||||||
\(75\) | −244.443 | − | 557.926i | −0.376345 | − | 0.858983i | ||||
\(76\) | − | 883.162i | − | 1.33297i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 536.665 | + | 1224.90i | 0.779043 | + | 1.77811i | ||||
\(79\) | −227.679 | −0.324252 | −0.162126 | − | 0.986770i | \(-0.551835\pi\) | ||||
−0.162126 | + | 0.986770i | \(0.551835\pi\) | |||||||
\(80\) | −573.121 | −0.800962 | ||||||||
\(81\) | −58.9528 | − | 726.612i | −0.0808680 | − | 0.996725i | ||||
\(82\) | 2166.43i | 2.91759i | ||||||||
\(83\) | 1136.62 | 1.50313 | 0.751565 | − | 0.659659i | \(-0.229299\pi\) | ||||
0.751565 | + | 0.659659i | \(0.229299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −249.373 | −0.318215 | ||||||||
\(86\) | 1240.01i | 1.55481i | ||||||||
\(87\) | 194.384 | − | 85.1652i | 0.239542 | − | 0.104950i | ||||
\(88\) | −1217.58 | −1.47494 | ||||||||
\(89\) | 1130.48 | 1.34641 | 0.673205 | − | 0.739455i | \(-0.264917\pi\) | ||||
0.673205 | + | 0.739455i | \(0.264917\pi\) | |||||||
\(90\) | −297.501 | − | 274.341i | −0.348438 | − | 0.321312i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1832.23i | − | 2.07634i | ||||||
\(93\) | −455.104 | + | 199.394i | −0.507442 | + | 0.222325i | ||||
\(94\) | − | 1964.34i | − | 2.15539i | ||||||
\(95\) | − | 117.827i | − | 0.127250i | ||||||
\(96\) | 2619.12 | − | 1147.51i | 2.78451 | − | 1.21997i | ||||
\(97\) | 1480.50i | 1.54971i | 0.632136 | + | 0.774857i | \(0.282178\pi\) | ||||
−0.632136 | + | 0.774857i | \(0.717822\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −348.546 | − | 321.413i | −0.353840 | − | 0.326295i | ||||
\(100\) | 2449.84 | 2.44984 | ||||||||
\(101\) | −1162.07 | −1.14486 | −0.572429 | − | 0.819954i | \(-0.693999\pi\) | ||||
−0.572429 | + | 0.819954i | \(0.693999\pi\) | |||||||
\(102\) | 2288.34 | − | 1002.59i | 2.22137 | − | 0.973246i | ||||
\(103\) | − | 91.5428i | − | 0.0875726i | −0.999041 | − | 0.0437863i | \(-0.986058\pi\) | ||
0.999041 | − | 0.0437863i | \(-0.0139421\pi\) | |||||||
\(104\) | −3319.60 | −3.12994 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3216.28 | 2.94710 | ||||||||
\(107\) | − | 1499.33i | − | 1.35463i | −0.735693 | − | 0.677315i | \(-0.763143\pi\) | ||
0.735693 | − | 0.677315i | \(-0.236857\pi\) | |||||||
\(108\) | 2771.87 | + | 955.578i | 2.46966 | + | 0.851393i | ||||
\(109\) | 1244.48 | 1.09357 | 0.546785 | − | 0.837273i | \(-0.315851\pi\) | ||||
0.546785 | + | 0.837273i | \(0.315851\pi\) | |||||||
\(110\) | −263.196 | −0.228134 | ||||||||
\(111\) | −134.602 | − | 307.220i | −0.115098 | − | 0.262703i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 470.193i | − | 0.391434i | −0.980660 | − | 0.195717i | \(-0.937297\pi\) | ||
0.980660 | − | 0.195717i | \(-0.0627034\pi\) | |||||||
\(114\) | 473.716 | + | 1081.23i | 0.389189 | + | 0.888298i | ||||
\(115\) | − | 244.447i | − | 0.198216i | ||||||
\(116\) | 853.536i | 0.683179i | ||||||||
\(117\) | −950.272 | − | 876.296i | −0.750878 | − | 0.692424i | ||||
\(118\) | − | 1272.32i | − | 0.992599i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 920.113 | − | 403.128i | 0.699953 | − | 0.306670i | ||||
\(121\) | 1022.65 | 0.768329 | ||||||||
\(122\) | −2316.62 | −1.71916 | ||||||||
\(123\) | −840.353 | − | 1918.05i | −0.616033 | − | 1.40606i | ||||
\(124\) | − | 1998.35i | − | 1.44724i | ||||||
\(125\) | 675.364 | 0.483251 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2329.37 | −1.62754 | −0.813772 | − | 0.581185i | \(-0.802589\pi\) | ||||
−0.813772 | + | 0.581185i | \(0.802589\pi\) | |||||||
\(128\) | 2660.42i | 1.83711i | ||||||||
\(129\) | −480.997 | − | 1097.84i | −0.328290 | − | 0.749300i | ||||
\(130\) | −717.574 | −0.484118 | ||||||||
\(131\) | 588.971 | 0.392814 | 0.196407 | − | 0.980522i | \(-0.437073\pi\) | ||||
0.196407 | + | 0.980522i | \(0.437073\pi\) | |||||||
\(132\) | 1746.59 | − | 765.229i | 1.15167 | − | 0.504581i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2301.00i | 1.48340i | ||||||||
\(135\) | 369.809 | + | 127.488i | 0.235763 | + | 0.0812773i | ||||
\(136\) | 6201.62i | 3.91018i | ||||||||
\(137\) | − | 529.151i | − | 0.329989i | −0.986295 | − | 0.164994i | \(-0.947239\pi\) | ||
0.986295 | − | 0.164994i | \(-0.0527606\pi\) | |||||||
\(138\) | 982.784 | + | 2243.14i | 0.606233 | + | 1.38369i | ||||
\(139\) | − | 1043.90i | − | 0.636997i | −0.947923 | − | 0.318499i | \(-0.896821\pi\) | ||
0.947923 | − | 0.318499i | \(-0.103179\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 761.963 | + | 1739.13i | 0.455098 | + | 1.03873i | ||||
\(142\) | −2793.15 | −1.65068 | ||||||||
\(143\) | −840.694 | −0.491625 | ||||||||
\(144\) | −3762.42 | + | 4080.05i | −2.17733 | + | 2.36114i | ||||
\(145\) | 113.874i | 0.0652189i | ||||||||
\(146\) | 4110.17 | 2.32986 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1349.00 | 0.749235 | ||||||||
\(149\) | − | 2065.04i | − | 1.13540i | −0.823235 | − | 0.567701i | \(-0.807833\pi\) | ||
0.823235 | − | 0.567701i | \(-0.192167\pi\) | |||||||
\(150\) | −2999.25 | + | 1314.06i | −1.63259 | + | 0.715283i | ||||
\(151\) | −540.261 | −0.291164 | −0.145582 | − | 0.989346i | \(-0.546506\pi\) | ||||
−0.145582 | + | 0.989346i | \(0.546506\pi\) | |||||||
\(152\) | −2930.22 | −1.56363 | ||||||||
\(153\) | −1637.08 | + | 1775.28i | −0.865034 | + | 0.938060i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 266.610i | − | 0.138159i | ||||||
\(156\) | 4761.87 | − | 2086.31i | 2.44394 | − | 1.07076i | ||||
\(157\) | − | 658.650i | − | 0.334815i | −0.985888 | − | 0.167408i | \(-0.946460\pi\) | ||
0.985888 | − | 0.167408i | \(-0.0535396\pi\) | |||||||
\(158\) | 1223.94i | 0.616274i | ||||||||
\(159\) | −2847.53 | + | 1247.59i | −1.42028 | + | 0.622265i | ||||
\(160\) | 1534.34i | 0.758125i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3906.07 | + | 316.914i | −1.89438 | + | 0.153698i | ||||
\(163\) | 403.947 | 0.194108 | 0.0970540 | − | 0.995279i | \(-0.469058\pi\) | ||||
0.0970540 | + | 0.995279i | \(0.469058\pi\) | |||||||
\(164\) | 8422.12 | 4.01010 | ||||||||
\(165\) | 233.020 | − | 102.093i | 0.109943 | − | 0.0481692i | ||||
\(166\) | − | 6110.13i | − | 2.85686i | ||||||
\(167\) | 2046.40 | 0.948237 | 0.474118 | − | 0.880461i | \(-0.342767\pi\) | ||||
0.474118 | + | 0.880461i | \(0.342767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −95.0602 | −0.0432682 | ||||||||
\(170\) | 1340.56i | 0.604802i | ||||||||
\(171\) | −838.808 | − | 773.509i | −0.375119 | − | 0.345916i | ||||
\(172\) | 4820.61 | 2.13702 | ||||||||
\(173\) | 705.271 | 0.309947 | 0.154973 | − | 0.987919i | \(-0.450471\pi\) | ||||
0.154973 | + | 0.987919i | \(0.450471\pi\) | |||||||
\(174\) | −457.825 | − | 1044.95i | −0.199469 | − | 0.455274i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3609.57i | 1.54592i | ||||||||
\(177\) | 493.530 | + | 1126.45i | 0.209582 | + | 0.478357i | ||||
\(178\) | − | 6077.14i | − | 2.55900i | ||||||
\(179\) | − | 740.849i | − | 0.309350i | −0.987965 | − | 0.154675i | \(-0.950567\pi\) | ||
0.987965 | − | 0.154675i | \(-0.0494331\pi\) | |||||||
\(180\) | −1066.52 | + | 1156.55i | −0.441630 | + | 0.478912i | ||||
\(181\) | 1339.29i | 0.549993i | 0.961445 | + | 0.274997i | \(0.0886768\pi\) | ||||
−0.961445 | + | 0.274997i | \(0.911323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2051.02 | − | 898.612i | 0.828502 | − | 0.362991i | ||||
\(184\) | −6079.12 | −2.43564 | ||||||||
\(185\) | 179.976 | 0.0715248 | ||||||||
\(186\) | 1071.89 | + | 2446.51i | 0.422552 | + | 0.964446i | ||||
\(187\) | 1570.57i | 0.614180i | ||||||||
\(188\) | −7636.48 | −2.96249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −633.405 | −0.241853 | ||||||||
\(191\) | 1863.68i | 0.706027i | 0.935618 | + | 0.353014i | \(0.114843\pi\) | ||||
−0.935618 | + | 0.353014i | \(0.885157\pi\) | |||||||
\(192\) | −2739.66 | − | 6253.10i | −1.02978 | − | 2.35041i | ||||
\(193\) | 2190.72 | 0.817055 | 0.408528 | − | 0.912746i | \(-0.366042\pi\) | ||||
0.408528 | + | 0.912746i | \(0.366042\pi\) | |||||||
\(194\) | 7958.77 | 2.94539 | ||||||||
\(195\) | 635.304 | − | 278.345i | 0.233308 | − | 0.102219i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1173.24i | 0.424315i | 0.977236 | + | 0.212157i | \(0.0680489\pi\) | ||||
−0.977236 | + | 0.212157i | \(0.931951\pi\) | |||||||
\(198\) | −1727.82 | + | 1873.69i | −0.620157 | + | 0.672511i | ||||
\(199\) | 4835.99i | 1.72268i | 0.508025 | + | 0.861342i | \(0.330376\pi\) | ||||
−0.508025 | + | 0.861342i | \(0.669624\pi\) | |||||||
\(200\) | − | 8128.26i | − | 2.87377i | ||||||
\(201\) | −892.551 | − | 2037.19i | −0.313213 | − | 0.714887i | ||||
\(202\) | 6246.99i | 2.17592i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3897.62 | − | 8896.05i | −1.33769 | − | 3.05318i | ||||
\(205\) | 1123.63 | 0.382820 | ||||||||
\(206\) | −492.109 | −0.166441 | ||||||||
\(207\) | −1740.21 | − | 1604.74i | −0.584315 | − | 0.538828i | ||||
\(208\) | 9841.08i | 3.28056i | ||||||||
\(209\) | −742.083 | −0.245603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2930.01 | 0.955972 | 0.477986 | − | 0.878368i | \(-0.341367\pi\) | ||||
0.477986 | + | 0.878368i | \(0.341367\pi\) | |||||||
\(212\) | − | 12503.5i | − | 4.05067i | ||||||
\(213\) | 2472.91 | − | 1083.46i | 0.795499 | − | 0.348531i | ||||
\(214\) | −8059.97 | −2.57462 | ||||||||
\(215\) | 643.140 | 0.204008 | ||||||||
\(216\) | 3170.48 | − | 9196.72i | 0.998723 | − | 2.89703i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6689.96i | − | 2.07845i | ||||||
\(219\) | −3638.93 | + | 1594.32i | −1.12281 | + | 0.491937i | ||||
\(220\) | 1023.19i | 0.313560i | ||||||||
\(221\) | 4281.99i | 1.30334i | ||||||||
\(222\) | −1651.53 | + | 723.582i | −0.499294 | + | 0.218755i | ||||
\(223\) | − | 4874.38i | − | 1.46373i | −0.681447 | − | 0.731867i | \(-0.738649\pi\) | ||
0.681447 | − | 0.731867i | \(-0.261351\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2145.67 | − | 2326.80i | 0.635753 | − | 0.689423i | ||||
\(226\) | −2527.63 | −0.743962 | ||||||||
\(227\) | 2439.53 | 0.713293 | 0.356647 | − | 0.934239i | \(-0.383920\pi\) | ||||
0.356647 | + | 0.934239i | \(0.383920\pi\) | |||||||
\(228\) | 4203.32 | − | 1841.59i | 1.22093 | − | 0.534924i | ||||
\(229\) | 4723.32i | 1.36299i | 0.731820 | + | 0.681497i | \(0.238671\pi\) | ||||
−0.731820 | + | 0.681497i | \(0.761329\pi\) | |||||||
\(230\) | −1314.08 | −0.376730 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2831.92 | 0.801400 | ||||||||
\(233\) | 1768.83i | 0.497339i | 0.968588 | + | 0.248670i | \(0.0799933\pi\) | ||||
−0.968588 | + | 0.248670i | \(0.920007\pi\) | |||||||
\(234\) | −4710.72 | + | 5108.40i | −1.31602 | + | 1.42712i | ||||
\(235\) | −1018.82 | −0.282810 | ||||||||
\(236\) | −4946.22 | −1.36428 | ||||||||
\(237\) | −474.762 | − | 1083.61i | −0.130123 | − | 0.296997i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1527.40i | 0.413386i | 0.978406 | + | 0.206693i | \(0.0662701\pi\) | ||||
−0.978406 | + | 0.206693i | \(0.933730\pi\) | |||||||
\(240\) | −1195.09 | − | 2727.71i | −0.321428 | − | 0.733637i | ||||
\(241\) | − | 1418.76i | − | 0.379214i | −0.981860 | − | 0.189607i | \(-0.939279\pi\) | ||
0.981860 | − | 0.189607i | \(-0.0607214\pi\) | |||||||
\(242\) | − | 5497.46i | − | 1.46029i | ||||||
\(243\) | 3335.30 | − | 1795.73i | 0.880493 | − | 0.474059i | ||||
\(244\) | 9005.99i | 2.36291i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10310.9 | + | 4517.51i | −2.67236 | + | 1.17084i | ||||
\(247\) | −2023.21 | −0.521189 | ||||||||
\(248\) | −6630.28 | −1.69767 | ||||||||
\(249\) | 2370.10 | + | 5409.60i | 0.603209 | + | 1.37678i | ||||
\(250\) | − | 3630.57i | − | 0.918469i | ||||||
\(251\) | −2152.91 | −0.541396 | −0.270698 | − | 0.962664i | \(-0.587255\pi\) | ||||
−0.270698 | + | 0.962664i | \(0.587255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1539.55 | −0.382571 | ||||||||
\(254\) | 12522.0i | 3.09332i | ||||||||
\(255\) | −520.000 | − | 1186.86i | −0.127701 | − | 0.291468i | ||||
\(256\) | 3790.91 | 0.925515 | ||||||||
\(257\) | 665.100 | 0.161431 | 0.0807156 | − | 0.996737i | \(-0.474279\pi\) | ||||
0.0807156 | + | 0.996737i | \(0.474279\pi\) | |||||||
\(258\) | −5901.70 | + | 2585.70i | −1.42412 | + | 0.623949i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2789.61i | 0.665400i | ||||||||
\(261\) | 810.669 | + | 747.561i | 0.192257 | + | 0.177291i | ||||
\(262\) | − | 3166.14i | − | 0.746584i | ||||||
\(263\) | 5133.87i | 1.20368i | 0.798617 | + | 0.601840i | \(0.205566\pi\) | ||||
−0.798617 | + | 0.601840i | \(0.794434\pi\) | |||||||
\(264\) | −2538.93 | − | 5794.95i | −0.591896 | − | 1.35096i | ||||
\(265\) | − | 1668.15i | − | 0.386692i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2357.31 | + | 5380.40i | 0.540318 | + | 1.23324i | ||||
\(268\) | 8945.26 | 2.03887 | ||||||||
\(269\) | 5975.29 | 1.35435 | 0.677174 | − | 0.735823i | \(-0.263204\pi\) | ||||
0.677174 | + | 0.735823i | \(0.263204\pi\) | |||||||
\(270\) | 685.341 | − | 1987.99i | 0.154476 | − | 0.448093i | ||||
\(271\) | 1496.60i | 0.335469i | 0.985832 | + | 0.167734i | \(0.0536451\pi\) | ||||
−0.985832 | + | 0.167734i | \(0.946355\pi\) | |||||||
\(272\) | 18385.0 | 4.09835 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2844.57 | −0.627178 | ||||||||
\(275\) | − | 2058.49i | − | 0.451389i | ||||||
\(276\) | 8720.32 | − | 3820.62i | 1.90182 | − | 0.833241i | ||||
\(277\) | 6515.07 | 1.41319 | 0.706593 | − | 0.707620i | \(-0.250231\pi\) | ||||
0.706593 | + | 0.707620i | \(0.250231\pi\) | |||||||
\(278\) | −5611.73 | −1.21068 | ||||||||
\(279\) | −1897.99 | − | 1750.24i | −0.407275 | − | 0.375569i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2236.41i | − | 0.474780i | −0.971414 | − | 0.237390i | \(-0.923708\pi\) | ||
0.971414 | − | 0.237390i | \(-0.0762920\pi\) | |||||||
\(282\) | 9349.08 | − | 4096.10i | 1.97422 | − | 0.864962i | ||||
\(283\) | 3959.25i | 0.831636i | 0.909448 | + | 0.415818i | \(0.136505\pi\) | ||||
−0.909448 | + | 0.415818i | \(0.863495\pi\) | |||||||
\(284\) | 10858.5i | 2.26878i | ||||||||
\(285\) | 560.784 | − | 245.696i | 0.116554 | − | 0.0510659i | ||||
\(286\) | 4519.34i | 0.934385i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10922.9 | + | 10072.6i | 2.23486 | + | 2.06088i | ||||
\(289\) | 3086.55 | 0.628241 | ||||||||
\(290\) | 612.156 | 0.123955 | ||||||||
\(291\) | −7046.30 | + | 3087.19i | −1.41945 | + | 0.621904i | ||||
\(292\) | − | 15978.5i | − | 3.20229i | ||||||
\(293\) | −3668.54 | −0.731461 | −0.365731 | − | 0.930721i | \(-0.619181\pi\) | ||||
−0.365731 | + | 0.930721i | \(0.619181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −659.898 | −0.130240 | ||||||||
\(296\) | − | 4475.80i | − | 0.878886i | ||||||
\(297\) | 802.931 | − | 2329.09i | 0.156871 | − | 0.455041i | ||||
\(298\) | −11101.1 | −2.15795 | ||||||||
\(299\) | −4197.40 | −0.811847 | ||||||||
\(300\) | 5108.47 | + | 11659.8i | 0.983126 | + | 2.24392i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2904.29i | 0.553388i | ||||||||
\(303\) | −2423.19 | − | 5530.77i | −0.459434 | − | 1.04863i | ||||
\(304\) | 8686.75i | 1.63888i | ||||||||
\(305\) | 1201.53i | 0.225572i | ||||||||
\(306\) | 9543.43 | + | 8800.50i | 1.78288 | + | 1.64409i | ||||
\(307\) | − | 6704.82i | − | 1.24646i | −0.782037 | − | 0.623231i | \(-0.785819\pi\) | ||
0.782037 | − | 0.623231i | \(-0.214181\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 435.688 | − | 190.888i | 0.0802117 | − | 0.0351431i | ||||
\(310\) | −1433.22 | −0.262585 | ||||||||
\(311\) | −8012.92 | −1.46100 | −0.730500 | − | 0.682913i | \(-0.760713\pi\) | ||||
−0.730500 | + | 0.682913i | \(0.760713\pi\) | |||||||
\(312\) | −6922.12 | − | 15799.3i | −1.25605 | − | 2.86685i | ||||
\(313\) | 177.232i | 0.0320056i | 0.999872 | + | 0.0160028i | \(0.00509407\pi\) | ||||
−0.999872 | + | 0.0160028i | \(0.994906\pi\) | |||||||
\(314\) | −3540.72 | −0.636352 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4758.12 | 0.847042 | ||||||||
\(317\) | 6088.73i | 1.07879i | 0.842052 | + | 0.539396i | \(0.181347\pi\) | ||||
−0.842052 | + | 0.539396i | \(0.818653\pi\) | |||||||
\(318\) | 6706.68 | + | 15307.6i | 1.18268 | + | 2.69939i | ||||
\(319\) | 717.189 | 0.125877 | ||||||||
\(320\) | 3663.20 | 0.639935 | ||||||||
\(321\) | 7135.89 | − | 3126.44i | 1.24077 | − | 0.543616i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3779.73i | 0.651113i | ||||||||
\(324\) | 1232.02 | + | 15185.0i | 0.211252 | + | 2.60374i | ||||
\(325\) | − | 5612.26i | − | 0.957883i | ||||||
\(326\) | − | 2171.51i | − | 0.368923i | ||||||
\(327\) | 2595.02 | + | 5922.95i | 0.438852 | + | 1.00165i | ||||
\(328\) | − | 27943.5i | − | 4.70403i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −548.823 | − | 1252.65i | −0.0915506 | − | 0.208958i | ||||
\(331\) | −10388.3 | −1.72505 | −0.862526 | − | 0.506013i | \(-0.831119\pi\) | ||||
−0.862526 | + | 0.506013i | \(0.831119\pi\) | |||||||
\(332\) | −23753.4 | −3.92662 | ||||||||
\(333\) | 1181.50 | − | 1281.25i | 0.194433 | − | 0.210846i | ||||
\(334\) | − | 11000.9i | − | 1.80222i | ||||||
\(335\) | 1193.43 | 0.194639 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −565.857 | −0.0914664 | −0.0457332 | − | 0.998954i | \(-0.514562\pi\) | ||||
−0.0457332 | + | 0.998954i | \(0.514562\pi\) | |||||||
\(338\) | 511.017i | 0.0822357i | ||||||||
\(339\) | 2237.83 | − | 980.460i | 0.358532 | − | 0.157083i | ||||
\(340\) | 5211.50 | 0.831274 | ||||||||
\(341\) | −1679.13 | −0.266657 | ||||||||
\(342\) | −4158.17 | + | 4509.20i | −0.657450 | + | 0.712952i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 15994.2i | − | 2.50682i | ||||||
\(345\) | 1163.42 | − | 509.727i | 0.181555 | − | 0.0795444i | ||||
\(346\) | − | 3791.34i | − | 0.589086i | ||||||
\(347\) | − | 10179.1i | − | 1.57476i | −0.616465 | − | 0.787382i | \(-0.711436\pi\) | ||
0.616465 | − | 0.787382i | \(-0.288564\pi\) | |||||||
\(348\) | −4062.31 | + | 1779.82i | −0.625755 | + | 0.274161i | ||||
\(349\) | 6924.54i | 1.06207i | 0.847350 | + | 0.531034i | \(0.178196\pi\) | ||||
−0.847350 | + | 0.531034i | \(0.821804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2189.10 | − | 6350.00i | 0.332893 | − | 0.965635i | ||||
\(352\) | 9663.38 | 1.46324 | ||||||||
\(353\) | 2975.74 | 0.448677 | 0.224338 | − | 0.974511i | \(-0.427978\pi\) | ||||
0.224338 | + | 0.974511i | \(0.427978\pi\) | |||||||
\(354\) | 6055.48 | − | 2653.08i | 0.909167 | − | 0.398332i | ||||
\(355\) | 1448.69i | 0.216587i | ||||||||
\(356\) | −23625.2 | −3.51723 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3982.60 | −0.587952 | ||||||||
\(359\) | − | 2753.05i | − | 0.404736i | −0.979310 | − | 0.202368i | \(-0.935136\pi\) | ||
0.979310 | − | 0.202368i | \(-0.0648637\pi\) | |||||||
\(360\) | 3837.29 | + | 3538.56i | 0.561786 | + | 0.518052i | ||||
\(361\) | 5073.11 | 0.739628 | ||||||||
\(362\) | 7199.66 | 1.04532 | ||||||||
\(363\) | 2132.45 | + | 4867.17i | 0.308332 | + | 0.703747i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2131.76i | − | 0.305703i | ||||||
\(366\) | −4830.69 | − | 11025.7i | −0.689902 | − | 1.57466i | ||||
\(367\) | 12658.1i | 1.80040i | 0.435482 | + | 0.900198i | \(0.356578\pi\) | ||||
−0.435482 | + | 0.900198i | \(0.643422\pi\) | |||||||
\(368\) | 18021.8i | 2.55285i | ||||||||
\(369\) | 7376.43 | − | 7999.15i | 1.04065 | − | 1.12851i | ||||
\(370\) | − | 967.501i | − | 0.135940i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9510.94 | − | 4167.02i | 1.32559 | − | 0.580779i | ||||
\(373\) | 10810.6 | 1.50068 | 0.750339 | − | 0.661054i | \(-0.229890\pi\) | ||||
0.750339 | + | 0.661054i | \(0.229890\pi\) | |||||||
\(374\) | 8442.96 | 1.16731 | ||||||||
\(375\) | 1408.29 | + | 3214.32i | 0.193930 | + | 0.442632i | ||||
\(376\) | 25336.9i | 3.47513i | ||||||||
\(377\) | 1955.34 | 0.267122 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5489.38 | 0.743985 | 0.371993 | − | 0.928236i | \(-0.378675\pi\) | ||||
0.371993 | + | 0.928236i | \(0.378675\pi\) | |||||||
\(380\) | 2462.39i | 0.332416i | ||||||||
\(381\) | −4857.26 | − | 11086.4i | −0.653137 | − | 1.49074i | ||||
\(382\) | 10018.6 | 1.34188 | ||||||||
\(383\) | −12465.9 | −1.66313 | −0.831566 | − | 0.555426i | \(-0.812555\pi\) | ||||
−0.831566 | + | 0.555426i | \(0.812555\pi\) | |||||||
\(384\) | −12662.0 | + | 5547.57i | −1.68269 | + | 0.737236i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11776.7i | − | 1.55290i | ||||||
\(387\) | 4222.08 | − | 4578.50i | 0.554574 | − | 0.601391i | ||||
\(388\) | − | 30940.1i | − | 4.04832i | ||||||
\(389\) | − | 7252.37i | − | 0.945269i | −0.881259 | − | 0.472634i | \(-0.843303\pi\) | ||
0.881259 | − | 0.472634i | \(-0.156697\pi\) | |||||||
\(390\) | −1496.31 | − | 3415.22i | −0.194278 | − | 0.443426i | ||||
\(391\) | 7841.52i | 1.01423i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1228.14 | + | 2803.14i | 0.157637 | + | 0.359796i | ||||
\(394\) | 6307.02 | 0.806454 | ||||||||
\(395\) | 634.804 | 0.0808619 | ||||||||
\(396\) | 7284.06 | + | 6717.01i | 0.924337 | + | 0.852380i | ||||
\(397\) | 1114.55i | 0.140900i | 0.997515 | + | 0.0704502i | \(0.0224436\pi\) | ||||
−0.997515 | + | 0.0704502i | \(0.977556\pi\) | |||||||
\(398\) | 25996.9 | 3.27414 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −24096.5 | −3.01207 | ||||||||
\(401\) | 10183.0i | 1.26811i | 0.773287 | + | 0.634056i | \(0.218611\pi\) | ||||
−0.773287 | + | 0.634056i | \(0.781389\pi\) | |||||||
\(402\) | −10951.4 | + | 4798.11i | −1.35872 | + | 0.595293i | ||||
\(403\) | −4577.96 | −0.565867 | ||||||||
\(404\) | 24285.5 | 2.99071 | ||||||||
\(405\) | 164.369 | + | 2025.91i | 0.0201669 | + | 0.248563i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1133.50i | − | 0.138048i | ||||||
\(408\) | −29516.0 | + | 12931.8i | −3.58151 | + | 1.56917i | ||||
\(409\) | 756.556i | 0.0914653i | 0.998954 | + | 0.0457327i | \(0.0145622\pi\) | ||||
−0.998954 | + | 0.0457327i | \(0.985438\pi\) | |||||||
\(410\) | − | 6040.35i | − | 0.727589i | ||||||
\(411\) | 2518.44 | − | 1103.40i | 0.302252 | − | 0.132425i | ||||
\(412\) | 1913.10i | 0.228766i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8626.65 | + | 9354.91i | −1.02410 | + | 1.11055i | ||||
\(415\) | −3169.06 | −0.374851 | ||||||||
\(416\) | 26346.1 | 3.10511 | ||||||||
\(417\) | 4968.34 | − | 2176.77i | 0.583455 | − | 0.255628i | ||||
\(418\) | 3989.23i | 0.466794i | ||||||||
\(419\) | −1348.55 | −0.157234 | −0.0786169 | − | 0.996905i | \(-0.525050\pi\) | ||||
−0.0786169 | + | 0.996905i | \(0.525050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5570.16 | −0.644829 | −0.322415 | − | 0.946599i | \(-0.604495\pi\) | ||||
−0.322415 | + | 0.946599i | \(0.604495\pi\) | |||||||
\(422\) | − | 15750.9i | − | 1.81692i | ||||||
\(423\) | −6688.33 | + | 7252.96i | −0.768789 | + | 0.833690i | ||||
\(424\) | −41484.9 | −4.75161 | ||||||||
\(425\) | −10484.7 | −1.19667 | ||||||||
\(426\) | −5824.36 | − | 13293.7i | −0.662420 | − | 1.51193i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 31333.5i | 3.53870i | ||||||||
\(429\) | −1753.04 | − | 4001.20i | −0.197290 | − | 0.450302i | ||||
\(430\) | − | 3457.34i | − | 0.387739i | ||||||
\(431\) | − | 15192.0i | − | 1.69785i | −0.528514 | − | 0.848924i | \(-0.677251\pi\) | ||
0.528514 | − | 0.848924i | \(-0.322749\pi\) | |||||||
\(432\) | −27264.1 | − | 9399.03i | −3.03644 | − | 1.04678i | ||||
\(433\) | 6207.85i | 0.688984i | 0.938789 | + | 0.344492i | \(0.111949\pi\) | ||||
−0.938789 | + | 0.344492i | \(0.888051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −541.972 | + | 237.454i | −0.0597370 | + | 0.0261725i | ||||
\(436\) | −26007.6 | −2.85673 | ||||||||
\(437\) | −3705.06 | −0.405577 | ||||||||
\(438\) | 8570.63 | + | 19561.9i | 0.934979 | + | 2.13403i | ||||
\(439\) | 1123.90i | 0.122189i | 0.998132 | + | 0.0610945i | \(0.0194591\pi\) | ||||
−0.998132 | + | 0.0610945i | \(0.980541\pi\) | |||||||
\(440\) | 3394.80 | 0.367820 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23018.8 | 2.47713 | ||||||||
\(443\) | − | 8246.58i | − | 0.884440i | −0.896907 | − | 0.442220i | \(-0.854191\pi\) | ||
0.896907 | − | 0.442220i | \(-0.145809\pi\) | |||||||
\(444\) | 2812.96 | + | 6420.40i | 0.300670 | + | 0.686259i | ||||
\(445\) | −3151.95 | −0.335768 | ||||||||
\(446\) | −26203.3 | −2.78198 | ||||||||
\(447\) | 9828.35 | − | 4306.08i | 1.03997 | − | 0.455639i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11803.3i | 1.24060i | 0.784364 | + | 0.620301i | \(0.212989\pi\) | ||||
−0.784364 | + | 0.620301i | \(0.787011\pi\) | |||||||
\(450\) | −12508.3 | − | 11534.5i | −1.31032 | − | 1.20832i | ||||
\(451\) | − | 7076.75i | − | 0.738871i | ||||||
\(452\) | 9826.29i | 1.02254i | ||||||||
\(453\) | −1126.57 | − | 2571.31i | −0.116845 | − | 0.266691i | ||||
\(454\) | − | 13114.3i | − | 1.35569i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6110.18 | − | 13946.1i | −0.627490 | − | 1.43220i | ||||
\(457\) | 16386.5 | 1.67731 | 0.838653 | − | 0.544666i | \(-0.183343\pi\) | ||||
0.838653 | + | 0.544666i | \(0.183343\pi\) | |||||||
\(458\) | 25391.3 | 2.59052 | ||||||||
\(459\) | −11863.0 | − | 4089.65i | −1.20635 | − | 0.415879i | ||||
\(460\) | 5108.55i | 0.517798i | ||||||||
\(461\) | −3268.14 | −0.330179 | −0.165089 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165089 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12241.9 | −1.22879 | −0.614395 | − | 0.788999i | \(-0.710600\pi\) | ||||
−0.614395 | + | 0.788999i | \(0.710600\pi\) | |||||||
\(464\) | − | 8395.35i | − | 0.839966i | ||||||
\(465\) | 1268.90 | − | 555.942i | 0.126546 | − | 0.0554434i | ||||
\(466\) | 9508.75 | 0.945245 | ||||||||
\(467\) | 10989.3 | 1.08892 | 0.544459 | − | 0.838788i | \(-0.316735\pi\) | ||||
0.544459 | + | 0.838788i | \(0.316735\pi\) | |||||||
\(468\) | 19859.2 | + | 18313.2i | 1.96152 | + | 1.80882i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5476.89i | 0.537511i | ||||||||
\(471\) | 3134.78 | − | 1373.44i | 0.306673 | − | 0.134362i | ||||
\(472\) | 16410.9i | 1.60037i | ||||||||
\(473\) | − | 4050.55i | − | 0.393751i | ||||||
\(474\) | −5825.20 | + | 2552.19i | −0.564474 | + | 0.247312i | ||||
\(475\) | − | 4953.96i | − | 0.478533i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11875.5 | − | 10951.0i | −1.13992 | − | 1.05118i | ||||
\(478\) | 8210.87 | 0.785683 | ||||||||
\(479\) | −14237.8 | −1.35812 | −0.679062 | − | 0.734081i | \(-0.737613\pi\) | ||||
−0.679062 | + | 0.734081i | \(0.737613\pi\) | |||||||
\(480\) | −7302.51 | + | 3199.44i | −0.694401 | + | 0.304237i | ||||
\(481\) | − | 3090.37i | − | 0.292950i | ||||||
\(482\) | −7626.88 | −0.720736 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21371.7 | −2.00710 | ||||||||
\(485\) | − | 4127.87i | − | 0.386468i | ||||||
\(486\) | −9653.36 | − | 17929.7i | −0.900998 | − | 1.67347i | ||||
\(487\) | −1229.45 | −0.114398 | −0.0571988 | − | 0.998363i | \(-0.518217\pi\) | ||||
−0.0571988 | + | 0.998363i | \(0.518217\pi\) | |||||||
\(488\) | 29880.7 | 2.77180 | ||||||||
\(489\) | 842.322 | + | 1922.54i | 0.0778960 | + | 0.177792i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4755.37i | 0.437081i | 0.975828 | + | 0.218540i | \(0.0701296\pi\) | ||||
−0.975828 | + | 0.218540i | \(0.929870\pi\) | |||||||
\(492\) | 17562.0 | + | 40084.2i | 1.60926 | + | 3.67304i | ||||
\(493\) | − | 3652.93i | − | 0.333711i | ||||||
\(494\) | 10876.2i | 0.990574i | ||||||||
\(495\) | 971.800 | + | 896.148i | 0.0882407 | + | 0.0813714i | ||||
\(496\) | 19655.7i | 1.77937i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 29080.5 | − | 12741.0i | 2.61672 | − | 1.14646i | ||||
\(499\) | −6041.14 | −0.541961 | −0.270980 | − | 0.962585i | \(-0.587348\pi\) | ||||
−0.270980 | + | 0.962585i | \(0.587348\pi\) | |||||||
\(500\) | −14114.0 | −1.26240 | ||||||||
\(501\) | 4267.22 | + | 9739.65i | 0.380530 | + | 0.868534i | ||||
\(502\) | 11573.5i | 1.02898i | ||||||||
\(503\) | −9730.02 | −0.862505 | −0.431253 | − | 0.902231i | \(-0.641928\pi\) | ||||
−0.431253 | + | 0.902231i | \(0.641928\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3240.04 | 0.285505 | ||||||||
\(506\) | 8276.18i | 0.727117i | ||||||||
\(507\) | −198.222 | − | 452.429i | −0.0173636 | − | 0.0396313i | ||||
\(508\) | 48680.1 | 4.25163 | ||||||||
\(509\) | 3117.41 | 0.271467 | 0.135733 | − | 0.990745i | \(-0.456661\pi\) | ||||
0.135733 | + | 0.990745i | \(0.456661\pi\) | |||||||
\(510\) | −6380.25 | + | 2795.37i | −0.553965 | + | 0.242708i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 904.452i | 0.0780694i | ||||||||
\(513\) | 1932.33 | − | 5605.16i | 0.166305 | − | 0.482405i | ||||
\(514\) | − | 3575.39i | − | 0.306817i | ||||||
\(515\) | 255.235i | 0.0218389i | ||||||||
\(516\) | 10052.1 | + | 22943.2i | 0.857592 | + | 1.95740i | ||||
\(517\) | 6416.61i | 0.545845i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1470.65 | + | 3356.66i | 0.124382 | + | 0.283894i | ||||
\(520\) | 9255.55 | 0.780544 | ||||||||
\(521\) | 6598.64 | 0.554879 | 0.277439 | − | 0.960743i | \(-0.410514\pi\) | ||||
0.277439 | + | 0.960743i | \(0.410514\pi\) | |||||||
\(522\) | 4018.68 | − | 4357.93i | 0.336959 | − | 0.365405i | ||||
\(523\) | − | 20339.3i | − | 1.70052i | −0.526360 | − | 0.850262i | \(-0.676444\pi\) | ||
0.526360 | − | 0.850262i | \(-0.323556\pi\) | |||||||
\(524\) | −12308.5 | −1.02615 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27598.3 | 2.28772 | ||||||||
\(527\) | 8552.47i | 0.706929i | ||||||||
\(528\) | −17179.3 | + | 7526.77i | −1.41598 | + | 0.620380i | ||||
\(529\) | 4480.38 | 0.368240 | ||||||||
\(530\) | −8967.49 | −0.734949 | ||||||||
\(531\) | −4332.09 | + | 4697.81i | −0.354043 | + | 0.383931i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19294.0i | − | 1.56794i | ||||||
\(534\) | 28923.5 | − | 12672.2i | 2.34390 | − | 1.02693i | ||||
\(535\) | 4180.35i | 0.337818i | ||||||||
\(536\) | − | 29679.2i | − | 2.39169i | ||||||
\(537\) | 3525.99 | − | 1544.84i | 0.283348 | − | 0.124143i | ||||
\(538\) | − | 32121.5i | − | 2.57408i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7728.41 | − | 2664.30i | −0.615885 | − | 0.212321i | ||||
\(541\) | −14425.4 | −1.14639 | −0.573193 | − | 0.819420i | \(-0.694295\pi\) | ||||
−0.573193 | + | 0.819420i | \(0.694295\pi\) | |||||||
\(542\) | 8045.31 | 0.637594 | ||||||||
\(543\) | −6374.22 | + | 2792.73i | −0.503764 | + | 0.220714i | ||||
\(544\) | − | 49219.4i | − | 3.87917i | ||||||
\(545\) | −3469.79 | −0.272715 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4720.80 | −0.369007 | −0.184503 | − | 0.982832i | \(-0.559068\pi\) | ||||
−0.184503 | + | 0.982832i | \(0.559068\pi\) | |||||||
\(548\) | 11058.4i | 0.862030i | ||||||||
\(549\) | 8553.69 | + | 7887.81i | 0.664960 | + | 0.613194i | ||||
\(550\) | −11065.9 | −0.857912 | ||||||||
\(551\) | 1725.98 | 0.133447 | ||||||||
\(552\) | −12676.3 | − | 28932.9i | −0.977429 | − | 2.23092i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 35023.2i | − | 2.68591i | ||||||
\(555\) | 375.291 | + | 856.576i | 0.0287031 | + | 0.0655128i | ||||
\(556\) | 21815.9i | 1.66403i | ||||||||
\(557\) | 5248.72i | 0.399273i | 0.979870 | + | 0.199637i | \(0.0639762\pi\) | ||||
−0.979870 | + | 0.199637i | \(0.936024\pi\) | |||||||
\(558\) | −9408.78 | + | 10203.1i | −0.713809 | + | 0.774069i | ||||
\(559\) | − | 11043.4i | − | 0.835572i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7474.97 | + | 3275.00i | −0.562555 | + | 0.246472i | ||||
\(562\) | −12022.3 | −0.902370 | ||||||||
\(563\) | 15779.6 | 1.18122 | 0.590612 | − | 0.806955i | \(-0.298886\pi\) | ||||
0.590612 | + | 0.806955i | \(0.298886\pi\) | |||||||
\(564\) | −15923.8 | − | 36345.0i | −1.18885 | − | 2.71348i | ||||
\(565\) | 1310.97i | 0.0976159i | ||||||||
\(566\) | 21283.8 | 1.58061 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 36027.2 | 2.66139 | ||||||||
\(569\) | 2878.32i | 0.212066i | 0.994363 | + | 0.106033i | \(0.0338149\pi\) | ||||
−0.994363 | + | 0.106033i | \(0.966185\pi\) | |||||||
\(570\) | −1320.79 | − | 3014.62i | −0.0970560 | − | 0.221524i | ||||
\(571\) | −8287.48 | −0.607391 | −0.303696 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303696 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(572\) | 17569.2 | 1.28427 | ||||||||
\(573\) | −8869.99 | + | 3886.20i | −0.646683 | + | 0.283330i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10277.6i | − | 0.745402i | ||||||
\(576\) | 24048.1 | − | 26078.3i | 1.73959 | − | 1.88645i | ||||
\(577\) | 3726.07i | 0.268836i | 0.990925 | + | 0.134418i | \(0.0429165\pi\) | ||||
−0.990925 | + | 0.134418i | \(0.957083\pi\) | |||||||
\(578\) | − | 16592.4i | − | 1.19404i | ||||||
\(579\) | 4568.16 | + | 10426.5i | 0.327886 | + | 0.748378i | ||||
\(580\) | − | 2379.79i | − | 0.170371i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 16595.9 | + | 37878.9i | 1.18199 | + | 2.69782i | ||||
\(583\) | −10506.1 | −0.746345 | ||||||||
\(584\) | −53014.6 | −3.75644 | ||||||||
\(585\) | 2649.51 | + | 2443.25i | 0.187254 | + | 0.172677i | ||||
\(586\) | 19721.0i | 1.39022i | ||||||||
\(587\) | 10108.9 | 0.710799 | 0.355399 | − | 0.934715i | \(-0.384345\pi\) | ||||
0.355399 | + | 0.934715i | \(0.384345\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4040.98 | −0.282692 | ||||||||
\(590\) | 3547.43i | 0.247534i | ||||||||
\(591\) | −5583.92 | + | 2446.47i | −0.388649 | + | 0.170278i | ||||
\(592\) | −13268.7 | −0.921181 | ||||||||
\(593\) | 7119.62 | 0.493032 | 0.246516 | − | 0.969139i | \(-0.420714\pi\) | ||||
0.246516 | + | 0.969139i | \(0.420714\pi\) | |||||||
\(594\) | −12520.5 | − | 4316.33i | −0.864854 | − | 0.298150i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 43156.1i | 2.96601i | ||||||||
\(597\) | −23016.4 | + | 10084.1i | −1.57789 | + | 0.691317i | ||||
\(598\) | 22564.1i | 1.54300i | ||||||||
\(599\) | 25732.9i | 1.75529i | 0.479311 | + | 0.877645i | \(0.340887\pi\) | ||||
−0.479311 | + | 0.877645i | \(0.659113\pi\) | |||||||
\(600\) | 38685.6 | − | 16949.3i | 2.63222 | − | 1.15325i | ||||
\(601\) | 13381.0i | 0.908193i | 0.890952 | + | 0.454097i | \(0.150038\pi\) | ||||
−0.890952 | + | 0.454097i | \(0.849962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7834.61 | − | 8496.01i | 0.529105 | − | 0.573771i | ||||
\(604\) | 11290.6 | 0.760608 | ||||||||
\(605\) | −2851.29 | −0.191606 | ||||||||
\(606\) | −29731.9 | + | 13026.4i | −1.99303 | + | 0.873203i | ||||
\(607\) | − | 1107.28i | − | 0.0740412i | −0.999315 | − | 0.0370206i | \(-0.988213\pi\) | ||
0.999315 | − | 0.0370206i | \(-0.0117867\pi\) | |||||||
\(608\) | 23255.8 | 1.55123 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6459.10 | 0.428724 | ||||||||
\(611\) | 17494.2i | 1.15833i | ||||||||
\(612\) | 34212.4 | − | 37100.6i | 2.25973 | − | 2.45049i | ||||
\(613\) | −13454.7 | −0.886509 | −0.443255 | − | 0.896396i | \(-0.646176\pi\) | ||||
−0.443255 | + | 0.896396i | \(0.646176\pi\) | |||||||
\(614\) | −36043.2 | −2.36903 | ||||||||
\(615\) | 2343.03 | + | 5347.82i | 0.153626 | + | 0.350642i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1025.37i | − | 0.0669043i | −0.999440 | − | 0.0334521i | \(-0.989350\pi\) | ||
0.999440 | − | 0.0334521i | \(-0.0106501\pi\) | |||||||
\(618\) | −1026.16 | − | 2342.14i | −0.0667931 | − | 0.152451i | ||||
\(619\) | 165.513i | 0.0107472i | 0.999986 | + | 0.00537360i | \(0.00171048\pi\) | ||||
−0.999986 | + | 0.00537360i | \(0.998290\pi\) | |||||||
\(620\) | 5571.71i | 0.360912i | ||||||||
\(621\) | 4008.86 | − | 11628.6i | 0.259050 | − | 0.751434i | ||||
\(622\) | 43075.2i | 2.77678i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −46837.6 | + | 20520.9i | −3.00481 | + | 1.31650i | ||||
\(625\) | 12770.3 | 0.817296 | ||||||||
\(626\) | 952.751 | 0.0608300 | ||||||||
\(627\) | −1547.41 | − | 3531.87i | −0.0985610 | − | 0.224959i | ||||
\(628\) | 13764.7i | 0.874638i | ||||||||
\(629\) | −5773.38 | −0.365977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8462.41 | −0.533888 | −0.266944 | − | 0.963712i | \(-0.586014\pi\) | ||||
−0.266944 | + | 0.963712i | \(0.586014\pi\) | |||||||
\(632\) | − | 15786.8i | − | 0.993619i | ||||||
\(633\) | 6109.73 | + | 13945.1i | 0.383634 | + | 0.875618i | ||||
\(634\) | 32731.3 | 2.05036 | ||||||||
\(635\) | 6494.64 | 0.405877 | ||||||||
\(636\) | 59508.9 | − | 26072.6i | 3.71019 | − | 1.62554i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 3855.41i | − | 0.239243i | ||||||
\(639\) | 10313.2 | + | 9510.32i | 0.638471 | + | 0.588768i | ||||
\(640\) | − | 7417.65i | − | 0.458138i | ||||||
\(641\) | 25724.2i | 1.58510i | 0.609810 | + | 0.792548i | \(0.291246\pi\) | ||||
−0.609810 | + | 0.792548i | \(0.708754\pi\) | |||||||
\(642\) | −16806.9 | − | 38360.5i | −1.03320 | − | 2.35821i | ||||
\(643\) | − | 13662.8i | − | 0.837961i | −0.907995 | − | 0.418980i | \(-0.862388\pi\) | ||
0.907995 | − | 0.418980i | \(-0.137612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1341.09 | + | 3060.95i | 0.0818690 | + | 0.186860i | ||||
\(646\) | 20318.8 | 1.23751 | ||||||||
\(647\) | 26101.8 | 1.58604 | 0.793021 | − | 0.609194i | \(-0.208507\pi\) | ||||
0.793021 | + | 0.609194i | \(0.208507\pi\) | |||||||
\(648\) | 50382.0 | − | 4087.68i | 3.05431 | − | 0.247808i | ||||
\(649\) | 4156.09i | 0.251373i | ||||||||
\(650\) | −30169.9 | −1.82056 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8441.85 | −0.507068 | ||||||||
\(653\) | − | 22257.9i | − | 1.33387i | −0.745114 | − | 0.666937i | \(-0.767605\pi\) | ||
0.745114 | − | 0.666937i | \(-0.232395\pi\) | |||||||
\(654\) | 31840.1 | − | 13950.1i | 1.90374 | − | 0.834085i | ||||
\(655\) | −1642.14 | −0.0979599 | ||||||||
\(656\) | −82839.7 | −4.93041 | ||||||||
\(657\) | −15176.0 | − | 13994.6i | −0.901176 | − | 0.831021i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1866.04i | 0.110304i | 0.998478 | + | 0.0551521i | \(0.0175644\pi\) | ||||
−0.998478 | + | 0.0551521i | \(0.982436\pi\) | |||||||
\(660\) | −4869.75 | + | 2133.58i | −0.287204 | + | 0.125832i | ||||
\(661\) | − | 15987.1i | − | 0.940737i | −0.882470 | − | 0.470369i | \(-0.844121\pi\) | ||
0.882470 | − | 0.470369i | \(-0.155879\pi\) | |||||||
\(662\) | 55844.6i | 3.27864i | ||||||||
\(663\) | −20379.7 | + | 8928.93i | −1.19379 | + | 0.523033i | ||||
\(664\) | 78810.9i | 4.60611i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6887.63 | − | 6351.44i | −0.400736 | − | 0.369539i | ||||
\(667\) | 3580.77 | 0.207868 | ||||||||
\(668\) | −42766.6 | −2.47708 | ||||||||
\(669\) | 23199.1 | − | 10164.2i | 1.34070 | − | 0.587400i | ||||
\(670\) | − | 6415.54i | − | 0.369931i | ||||||
\(671\) | 7567.35 | 0.435372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28696.0 | 1.64361 | 0.821805 | − | 0.569768i | \(-0.192967\pi\) | ||||
0.821805 | + | 0.569768i | \(0.192967\pi\) | |||||||
\(674\) | 3041.89i | 0.173842i | ||||||||
\(675\) | 15548.4 | + | 5360.16i | 0.886604 | + | 0.305648i | ||||
\(676\) | 1986.60 | 0.113029 | ||||||||
\(677\) | 3352.98 | 0.190348 | 0.0951740 | − | 0.995461i | \(-0.469659\pi\) | ||||
0.0951740 | + | 0.995461i | \(0.469659\pi\) | |||||||
\(678\) | −5270.68 | − | 12030.0i | −0.298554 | − | 0.681429i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 17291.1i | − | 0.975122i | ||||||
\(681\) | 5086.98 | + | 11610.7i | 0.286246 | + | 0.653338i | ||||
\(682\) | 9026.53i | 0.506809i | ||||||||
\(683\) | − | 12564.9i | − | 0.703925i | −0.936014 | − | 0.351963i | \(-0.885514\pi\) | ||
0.936014 | − | 0.351963i | \(-0.114486\pi\) | |||||||
\(684\) | 17529.7 | + | 16165.1i | 0.979922 | + | 0.903637i | ||||
\(685\) | 1475.36i | 0.0822926i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22480.1 | + | 9849.20i | −1.24843 | + | 0.546973i | ||||
\(688\) | −47415.3 | −2.62746 | ||||||||
\(689\) | −28643.8 | −1.58380 | ||||||||
\(690\) | −2740.15 | − | 6254.22i | −0.151182 | − | 0.345064i | ||||
\(691\) | − | 12429.0i | − | 0.684255i | −0.939654 | − | 0.342127i | \(-0.888853\pi\) | ||
0.939654 | − | 0.342127i | \(-0.111147\pi\) | |||||||
\(692\) | −14739.0 | −0.809673 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54720.1 | −2.99301 | ||||||||
\(695\) | 2910.56i | 0.158854i | ||||||||
\(696\) | 5905.20 | + | 13478.2i | 0.321604 | + | 0.734039i | ||||
\(697\) | −36044.7 | −1.95881 | ||||||||
\(698\) | 37224.4 | 2.01857 | ||||||||
\(699\) | −8418.57 | + | 3688.42i | −0.455536 | + | 0.199583i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28195.4i | 1.51915i | 0.650420 | + | 0.759575i | \(0.274593\pi\) | ||||
−0.650420 | + | 0.759575i | \(0.725407\pi\) | |||||||
\(702\) | −34135.8 | − | 11768.0i | −1.83529 | − | 0.632699i | ||||
\(703\) | − | 2727.88i | − | 0.146350i | ||||||
\(704\) | − | 23071.1i | − | 1.23512i | ||||||
\(705\) | −2124.47 | − | 4848.96i | −0.113492 | − | 0.259039i | ||||
\(706\) | − | 15996.8i | − | 0.852757i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −10314.0 | − | 23541.0i | −0.547491 | − | 1.24961i | ||||
\(709\) | −15169.6 | −0.803535 | −0.401767 | − | 0.915742i | \(-0.631604\pi\) | ||||
−0.401767 | + | 0.915742i | \(0.631604\pi\) | |||||||
\(710\) | 7787.73 | 0.411646 | ||||||||
\(711\) | 4167.35 | − | 4519.16i | 0.219814 | − | 0.238371i | ||||
\(712\) | 78385.4i | 4.12587i | ||||||||
\(713\) | −8383.52 | −0.440344 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2343.99 | 0.122602 | ||||||||
\(716\) | 15482.6i | 0.808115i | ||||||||
\(717\) | −7269.49 | + | 3184.98i | −0.378639 | + | 0.165893i | ||||
\(718\) | −14799.6 | −0.769243 | ||||||||
\(719\) | 10512.1 | 0.545250 | 0.272625 | − | 0.962120i | \(-0.412108\pi\) | ||||
0.272625 | + | 0.962120i | \(0.412108\pi\) | |||||||
\(720\) | 10490.2 | − | 11375.8i | 0.542982 | − | 0.588821i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 27271.6i | − | 1.40574i | ||||||
\(723\) | 6752.45 | − | 2958.44i | 0.347339 | − | 0.152179i | ||||
\(724\) | − | 27989.1i | − | 1.43675i | ||||||
\(725\) | 4787.77i | 0.245260i | ||||||||
\(726\) | 26164.6 | − | 11463.5i | 1.33755 | − | 0.586018i | ||||
\(727\) | − | 14866.0i | − | 0.758390i | −0.925317 | − | 0.379195i | \(-0.876201\pi\) | ||
0.925317 | − | 0.379195i | \(-0.123799\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15501.5 | + | 12129.5i | 0.787556 | + | 0.616243i | ||||
\(730\) | −11459.8 | −0.581021 | ||||||||
\(731\) | −20631.0 | −1.04387 | ||||||||
\(732\) | −42863.1 | + | 18779.5i | −2.16430 | + | 0.948241i | ||||
\(733\) | 27332.1i | 1.37726i | 0.725111 | + | 0.688632i | \(0.241789\pi\) | ||||
−0.725111 | + | 0.688632i | \(0.758211\pi\) | |||||||
\(734\) | 68046.2 | 3.42184 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 48247.2 | 2.41632 | ||||||||
\(737\) | − | 7516.31i | − | 0.375667i | ||||||
\(738\) | −43001.2 | − | 39653.6i | −2.14485 | − | 1.97787i | ||||
\(739\) | 17041.0 | 0.848257 | 0.424128 | − | 0.905602i | \(-0.360581\pi\) | ||||
0.424128 | + | 0.905602i | \(0.360581\pi\) | |||||||
\(740\) | −3761.21 | −0.186844 | ||||||||
\(741\) | −4218.85 | − | 9629.24i | −0.209154 | − | 0.477381i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 31844.1i | − | 1.57234i | −0.618012 | − | 0.786169i | \(-0.712062\pi\) | ||
0.618012 | − | 0.786169i | \(-0.287938\pi\) | |||||||
\(744\) | −13825.6 | − | 31556.1i | −0.681280 | − | 1.55498i | ||||
\(745\) | 5757.66i | 0.283147i | ||||||||
\(746\) | − | 58114.9i | − | 2.85219i | ||||||
\(747\) | −20804.2 | + | 22560.5i | −1.01899 | + | 1.10501i | ||||
\(748\) | − | 32822.4i | − | 1.60442i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17279.3 | − | 7570.56i | 0.841268 | − | 0.368584i | ||||
\(751\) | 14506.4 | 0.704854 | 0.352427 | − | 0.935839i | \(-0.385356\pi\) | ||||
0.352427 | + | 0.935839i | \(0.385356\pi\) | |||||||
\(752\) | 75112.1 | 3.64236 | ||||||||
\(753\) | −4489.31 | − | 10246.5i | −0.217264 | − | 0.495890i | ||||
\(754\) | − | 10511.4i | − | 0.507693i | ||||||
\(755\) | 1506.33 | 0.0726106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1811.69 | −0.0869843 | −0.0434921 | − | 0.999054i | \(-0.513848\pi\) | ||||
−0.0434921 | + | 0.999054i | \(0.513848\pi\) | |||||||
\(758\) | − | 29509.4i | − | 1.41402i | ||||||
\(759\) | −3210.31 | − | 7327.31i | −0.153527 | − | 0.350414i | ||||
\(760\) | 8169.91 | 0.389939 | ||||||||
\(761\) | 12464.2 | 0.593726 | 0.296863 | − | 0.954920i | \(-0.404060\pi\) | ||||
0.296863 | + | 0.954920i | \(0.404060\pi\) | |||||||
\(762\) | −59597.3 | + | 26111.3i | −2.83331 | + | 1.24136i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 38947.9i | − | 1.84435i | ||||||
\(765\) | 4564.44 | − | 4949.76i | 0.215722 | − | 0.233933i | ||||
\(766\) | 67013.4i | 3.16096i | ||||||||
\(767\) | 11331.1i | 0.533433i | ||||||||
\(768\) | 7904.91 | + | 18042.4i | 0.371411 | + | 0.847721i | ||||
\(769\) | − | 216.728i | − | 0.0101631i | −0.999987 | − | 0.00508155i | \(-0.998382\pi\) | ||
0.999987 | − | 0.00508155i | \(-0.00161751\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1386.88 | + | 3165.47i | 0.0647827 | + | 0.147862i | ||||
\(772\) | −45782.6 | −2.13439 | ||||||||
\(773\) | 32130.7 | 1.49503 | 0.747517 | − | 0.664243i | \(-0.231246\pi\) | ||||
0.747517 | + | 0.664243i | \(0.231246\pi\) | |||||||
\(774\) | −24612.8 | − | 22696.7i | −1.14301 | − | 1.05403i | ||||
\(775\) | − | 11209.4i | − | 0.519554i | ||||||
\(776\) | −102655. | −4.74886 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38986.7 | −1.79658 | ||||||||
\(779\) | − | 17030.8i | − | 0.783303i | ||||||
\(780\) | −13276.8 | + | 5816.96i | −0.609470 | + | 0.267027i | ||||
\(781\) | 9123.94 | 0.418029 | ||||||||
\(782\) | 42153.9 | 1.92765 | ||||||||
\(783\) | −1867.50 | + | 5417.13i | −0.0852352 | + | 0.247244i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1836.42i | 0.0834963i | ||||||||
\(786\) | 15068.9 | − | 6602.13i | 0.683830 | − | 0.299606i | ||||
\(787\) | − | 40574.9i | − | 1.83779i | −0.394507 | − | 0.918893i | \(-0.629084\pi\) | ||
0.394507 | − | 0.918893i | \(-0.370916\pi\) | |||||||
\(788\) | − | 24518.9i | − | 1.10844i | ||||||
\(789\) | −24434.1 | + | 10705.3i | −1.10251 | + | 0.483040i | ||||
\(790\) | − | 3412.53i | − | 0.153686i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22286.2 | − | 24167.6i | 0.999880 | − | 1.08429i | ||||
\(793\) | 20631.5 | 0.923893 | ||||||||
\(794\) | 5991.49 | 0.267796 | ||||||||
\(795\) | 7939.36 | − | 3478.46i | 0.354189 | − | 0.155180i | ||||
\(796\) | − | 101064.i | − | 4.50017i | ||||||
\(797\) | 28873.3 | 1.28324 | 0.641622 | − | 0.767021i | \(-0.278262\pi\) | ||||
0.641622 | + | 0.767021i | \(0.278262\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32682.3 | 1.44708 | ||||||||
\(800\) | 64510.2i | 2.85098i | ||||||||
\(801\) | −20691.9 | + | 22438.7i | −0.912749 | + | 0.989803i | ||||
\(802\) | 54740.8 | 2.41018 | ||||||||
\(803\) | −13426.0 | −0.590030 | ||||||||
\(804\) | 18652.9 | + | 42574.0i | 0.818205 | + | 1.86750i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24609.8i | 1.07549i | ||||||||
\(807\) | 12459.8 | + | 28438.7i | 0.543503 | + | 1.24051i | ||||
\(808\) | − | 80576.2i | − | 3.50824i | ||||||
\(809\) | − | 30282.2i | − | 1.31603i | −0.753007 | − | 0.658013i | \(-0.771397\pi\) | ||
0.753007 | − | 0.658013i | \(-0.228603\pi\) | |||||||
\(810\) | 10890.7 | − | 883.605i | 0.472421 | − | 0.0383293i | ||||
\(811\) | 4448.04i | 0.192592i | 0.995353 | + | 0.0962959i | \(0.0306995\pi\) | ||||
−0.995353 | + | 0.0962959i | \(0.969301\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7122.91 | + | 3120.75i | −0.307271 | + | 0.134624i | ||||
\(814\) | −6093.40 | −0.262375 | ||||||||
\(815\) | −1126.27 | −0.0484067 | ||||||||
\(816\) | 38336.8 | + | 87501.2i | 1.64468 | + | 3.75387i | ||||
\(817\) | − | 9748.01i | − | 0.417429i | ||||||
\(818\) | 4067.04 | 0.173839 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23482.2 | −1.00004 | ||||||||
\(821\) | − | 1136.44i | − | 0.0483093i | −0.999708 | − | 0.0241547i | \(-0.992311\pi\) | ||
0.999708 | − | 0.0241547i | \(-0.00768941\pi\) | |||||||
\(822\) | −5931.58 | − | 13538.4i | −0.251688 | − | 0.574461i | ||||
\(823\) | 42010.7 | 1.77934 | 0.889672 | − | 0.456600i | \(-0.150933\pi\) | ||||
0.889672 | + | 0.456600i | \(0.150933\pi\) | |||||||
\(824\) | 6347.41 | 0.268353 | ||||||||
\(825\) | 9797.19 | − | 4292.43i | 0.413448 | − | 0.181143i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18205.4i | 0.765494i | 0.923853 | + | 0.382747i | \(0.125022\pi\) | ||||
−0.923853 | + | 0.382747i | \(0.874978\pi\) | |||||||
\(828\) | 36367.7 | + | 33536.6i | 1.52641 | + | 1.40758i | ||||
\(829\) | − | 3278.77i | − | 0.137366i | −0.997639 | − | 0.0686829i | \(-0.978120\pi\) | ||
0.997639 | − | 0.0686829i | \(-0.0218797\pi\) | |||||||
\(830\) | 17036.0i | 0.712443i | ||||||||
\(831\) | 13585.4 | + | 31007.8i | 0.567115 | + | 1.29440i | ||||
\(832\) | − | 62900.9i | − | 2.62103i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −11701.7 | − | 26708.4i | −0.485849 | − | 1.10892i | ||||
\(835\) | −5705.69 | −0.236471 | ||||||||
\(836\) | 15508.4 | 0.641588 | ||||||||
\(837\) | 4372.32 | − | 12682.9i | 0.180561 | − | 0.523759i | ||||
\(838\) | 7249.43i | 0.298839i | ||||||||
\(839\) | 13743.0 | 0.565507 | 0.282754 | − | 0.959193i | \(-0.408752\pi\) | ||||
0.282754 | + | 0.959193i | \(0.408752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22720.9 | 0.931605 | ||||||||
\(842\) | 29943.7i | 1.22557i | ||||||||
\(843\) | 10644.0 | − | 4663.43i | 0.434873 | − | 0.190530i | ||||
\(844\) | −61232.5 | −2.49728 | ||||||||
\(845\) | 265.042 | 0.0107902 | ||||||||
\(846\) | 38989.9 | + | 35954.6i | 1.58452 | + | 1.46117i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 122984.i | 4.98028i | ||||||||
\(849\) | −18843.6 | + | 8255.94i | −0.761734 | + | 0.333738i | ||||
\(850\) | 56363.0i | 2.27439i | ||||||||
\(851\) | − | 5659.33i | − | 0.227967i | ||||||
\(852\) | −51680.0 | + | 22642.5i | −2.07808 | + | 0.910468i | ||||
\(853\) | 23952.0i | 0.961431i | 0.876877 | + | 0.480715i | \(0.159623\pi\) | ||||
−0.876877 | + | 0.480715i | \(0.840377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2338.73 | + | 2156.66i | 0.0935471 | + | 0.0862647i | ||||
\(856\) | 103961. | 4.15105 | ||||||||
\(857\) | −34665.8 | −1.38175 | −0.690876 | − | 0.722973i | \(-0.742775\pi\) | ||||
−0.690876 | + | 0.722973i | \(0.742775\pi\) | |||||||
\(858\) | −21509.3 | + | 9423.85i | −0.855846 | + | 0.374971i | ||||
\(859\) | − | 17822.0i | − | 0.707891i | −0.935266 | − | 0.353946i | \(-0.884840\pi\) | ||
0.935266 | − | 0.353946i | \(-0.115160\pi\) | |||||||
\(860\) | −13440.6 | −0.532931 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −81668.0 | −3.22694 | ||||||||
\(863\) | − | 48219.7i | − | 1.90199i | −0.309205 | − | 0.950995i | \(-0.600063\pi\) | ||
0.309205 | − | 0.950995i | \(-0.399937\pi\) | |||||||
\(864\) | −25162.7 | + | 72990.2i | −0.990801 | + | 2.87405i | ||||
\(865\) | −1966.40 | −0.0772945 | ||||||||
\(866\) | 33371.7 | 1.30949 | ||||||||
\(867\) | 6436.15 | + | 14690.1i | 0.252114 | + | 0.575434i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 3998.05i | − | 0.156070i | ||||||
\(870\) | 1276.49 | + | 2913.49i | 0.0497436 | + | 0.113536i | ||||
\(871\) | − | 20492.4i | − | 0.797197i | ||||||
\(872\) | 86289.8i | 3.35108i | ||||||||
\(873\) | −29386.3 | − | 27098.6i | −1.13926 | − | 1.05057i | ||||
\(874\) | 19917.4i | 0.770842i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 76047.9 | − | 33318.8i | 2.93313 | − | 1.28509i | ||||
\(877\) | −44764.3 | −1.72358 | −0.861791 | − | 0.507264i | \(-0.830657\pi\) | ||||
−0.861791 | + | 0.507264i | \(0.830657\pi\) | |||||||
\(878\) | 6041.79 | 0.232233 | ||||||||
\(879\) | −7649.73 | − | 17460.0i | −0.293537 | − | 0.669979i | ||||
\(880\) | − | 10064.0i | − | 0.385521i | ||||||
\(881\) | 40193.4 | 1.53706 | 0.768530 | − | 0.639814i | \(-0.220989\pi\) | ||||
0.768530 | + | 0.639814i | \(0.220989\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2601.94 | 0.0991646 | 0.0495823 | − | 0.998770i | \(-0.484211\pi\) | ||||
0.0495823 | + | 0.998770i | \(0.484211\pi\) | |||||||
\(884\) | − | 89486.7i | − | 3.40471i | ||||||
\(885\) | −1376.04 | − | 3140.71i | −0.0522655 | − | 0.119293i | ||||
\(886\) | −44331.3 | −1.68097 | ||||||||
\(887\) | −7890.46 | −0.298688 | −0.149344 | − | 0.988785i | \(-0.547716\pi\) | ||||
−0.149344 | + | 0.988785i | \(0.547716\pi\) | |||||||
\(888\) | 21302.1 | − | 9333.05i | 0.805012 | − | 0.352699i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 16944.0i | 0.638162i | ||||||||
\(891\) | 12759.3 | − | 1035.21i | 0.479746 | − | 0.0389236i | ||||
\(892\) | 101867.i | 3.82371i | ||||||||
\(893\) | 15442.2i | 0.578670i | ||||||||
\(894\) | −23148.3 | − | 52834.5i | −0.865991 | − | 1.97657i | ||||
\(895\) | 2065.60i | 0.0771458i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8752.54 | − | 19977.1i | −0.325796 | − | 0.743607i | ||||
\(898\) | 63451.0 | 2.35789 | ||||||||
\(899\) | 3905.42 | 0.144887 | ||||||||
\(900\) | −44841.0 | + | 48626.5i | −1.66078 | + | 1.80098i | ||||
\(901\) | 53511.9i | 1.97862i | ||||||||
\(902\) | −38042.6 | −1.40430 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32602.4 | 1.19949 | ||||||||
\(905\) | − | 3734.15i | − | 0.137157i | ||||||
\(906\) | −13822.7 | + | 6056.11i | −0.506874 | + | 0.222076i | ||||
\(907\) | 6554.14 | 0.239941 | 0.119971 | − | 0.992777i | \(-0.461720\pi\) | ||||
0.119971 | + | 0.992777i | \(0.461720\pi\) | |||||||
\(908\) | −50982.3 | −1.86334 | ||||||||
\(909\) | 21270.2 | − | 23065.8i | 0.776114 | − | 0.841634i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15918.4i | 0.578926i | 0.957189 | + | 0.289463i | \(0.0934767\pi\) | ||||
−0.957189 | + | 0.289463i | \(0.906523\pi\) | |||||||
\(912\) | −41343.7 | + | 18113.9i | −1.50112 | + | 0.657686i | ||||
\(913\) | 19959.0i | 0.723490i | ||||||||
\(914\) | − | 88089.4i | − | 3.18790i | ||||||
\(915\) | −5718.56 | + | 2505.47i | −0.206612 | + | 0.0905227i | ||||
\(916\) | − | 98709.8i | − | 3.56055i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −21984.8 | + | 63772.0i | −0.790421 | + | 2.29280i | ||||
\(919\) | −17041.1 | −0.611681 | −0.305840 | − | 0.952083i | \(-0.598937\pi\) | ||||
−0.305840 | + | 0.952083i | \(0.598937\pi\) | |||||||
\(920\) | 16949.5 | 0.607401 | ||||||||
\(921\) | 31910.9 | − | 13981.1i | 1.14169 | − | 0.500208i | ||||
\(922\) | 17568.6i | 0.627539i | ||||||||
\(923\) | 24875.4 | 0.887091 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7566.97 | 0.268974 | ||||||||
\(926\) | 65809.1i | 2.33544i | ||||||||
\(927\) | 1817.02 | + | 1675.57i | 0.0643783 | + | 0.0593666i | ||||
\(928\) | −22475.7 | −0.795043 | ||||||||
\(929\) | 13404.8 | 0.473411 | 0.236705 | − | 0.971581i | \(-0.423932\pi\) | ||||
0.236705 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(930\) | −2988.59 | − | 6821.25i | −0.105376 | − | 0.240514i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 36965.8i | − | 1.29920i | ||||||
\(933\) | −16708.8 | − | 38136.6i | −0.586303 | − | 1.33820i | ||||
\(934\) | − | 59075.5i | − | 2.06960i | ||||||
\(935\) | − | 4379.00i | − | 0.153164i | ||||||
\(936\) | 60760.8 | − | 65890.2i | 2.12183 | − | 2.30095i | ||||
\(937\) | − | 36713.4i | − | 1.28002i | −0.768368 | − | 0.640008i | \(-0.778931\pi\) | ||
0.768368 | − | 0.640008i | \(-0.221069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −843.517 | + | 369.569i | −0.0293154 | + | 0.0128439i | ||||
\(940\) | 21291.7 | 0.738785 | ||||||||
\(941\) | 1664.85 | 0.0576755 | 0.0288378 | − | 0.999584i | \(-0.490819\pi\) | ||||
0.0288378 | + | 0.999584i | \(0.490819\pi\) | |||||||
\(942\) | −7383.21 | − | 16851.7i | −0.255369 | − | 0.582864i | ||||
\(943\) | − | 35332.7i | − | 1.22014i | ||||||
\(944\) | 48650.8 | 1.67738 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21774.6 | −0.748366 | ||||||||
\(947\) | 15367.2i | 0.527316i | 0.964616 | + | 0.263658i | \(0.0849290\pi\) | ||||
−0.964616 | + | 0.263658i | \(0.915071\pi\) | |||||||
\(948\) | 9921.77 | + | 22645.8i | 0.339920 | + | 0.775845i | ||||
\(949\) | −36604.6 | −1.25209 | ||||||||
\(950\) | −26631.1 | −0.909502 | ||||||||
\(951\) | −28978.7 | + | 12696.4i | −0.988115 | + | 0.432922i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1033.81i | 0.0351398i | 0.999846 | + | 0.0175699i | \(0.00559296\pi\) | ||||
−0.999846 | + | 0.0175699i | \(0.994407\pi\) | |||||||
\(954\) | −58869.7 | + | 63839.5i | −1.99788 | + | 2.16654i | ||||
\(955\) | − | 5196.23i | − | 0.176069i | ||||||
\(956\) | − | 31920.2i | − | 1.07989i | ||||||
\(957\) | 1495.50 | + | 3413.39i | 0.0505149 | + | 0.115297i | ||||
\(958\) | 76538.5i | 2.58126i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 7638.61 | + | 17434.6i | 0.256807 | + | 0.586145i | ||||
\(961\) | 20647.4 | 0.693075 | ||||||||
\(962\) | −16613.0 | −0.556782 | ||||||||
\(963\) | 29759.9 | + | 27443.2i | 0.995846 | + | 0.918321i | ||||
\(964\) | 29649.9i | 0.990621i | ||||||||
\(965\) | −6108.07 | −0.203757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16347.0 | 0.543623 | 0.271811 | − | 0.962351i | \(-0.412377\pi\) | ||||
0.271811 | + | 0.962351i | \(0.412377\pi\) | |||||||
\(968\) | 70908.4i | 2.35442i | ||||||||
\(969\) | −17989.2 | + | 7881.59i | −0.596384 | + | 0.261293i | ||||
\(970\) | −22190.3 | −0.734523 | ||||||||
\(971\) | 52204.0 | 1.72534 | 0.862670 | − | 0.505766i | \(-0.168790\pi\) | ||||
0.862670 | + | 0.505766i | \(0.168790\pi\) | |||||||
\(972\) | −69702.5 | + | 37527.9i | −2.30011 | + | 1.23838i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6609.17i | 0.217425i | ||||||||
\(975\) | 26710.9 | − | 11702.8i | 0.877369 | − | 0.384401i | ||||
\(976\) | − | 88582.6i | − | 2.90519i | ||||||
\(977\) | − | 1257.19i | − | 0.0411680i | −0.999788 | − | 0.0205840i | \(-0.993447\pi\) | ||
0.999788 | − | 0.0205840i | \(-0.00655256\pi\) | |||||||
\(978\) | 10335.1 | − | 4528.09i | 0.337913 | − | 0.148049i | ||||
\(979\) | 19851.2i | 0.648058i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −22778.5 | + | 24701.4i | −0.741346 | + | 0.803930i | ||||
\(982\) | 25563.5 | 0.830718 | ||||||||
\(983\) | −14001.0 | −0.454285 | −0.227143 | − | 0.973861i | \(-0.572938\pi\) | ||||
−0.227143 | + | 0.973861i | \(0.572938\pi\) | |||||||
\(984\) | 132994. | − | 58268.6i | 4.30864 | − | 1.88774i | ||||
\(985\) | − | 3271.18i | − | 0.105816i | ||||||
\(986\) | −19637.1 | −0.634254 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 42281.8 | 1.36150 | ||||||||
\(989\) | − | 20223.5i | − | 0.650222i | ||||||
\(990\) | 4817.44 | − | 5224.13i | 0.154655 | − | 0.167711i | ||||
\(991\) | 37981.7 | 1.21749 | 0.608743 | − | 0.793368i | \(-0.291674\pi\) | ||||
0.608743 | + | 0.793368i | \(0.291674\pi\) | |||||||
\(992\) | 52621.5 | 1.68421 | ||||||||
\(993\) | −21662.0 | − | 49442.0i | −0.692267 | − | 1.58005i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 13483.5i | − | 0.429603i | ||||||
\(996\) | −49531.3 | − | 113052.i | −1.57576 | − | 3.59657i | ||||
\(997\) | − | 29489.2i | − | 0.936743i | −0.883532 | − | 0.468371i | \(-0.844841\pi\) | ||
0.883532 | − | 0.468371i | \(-0.155159\pi\) | |||||||
\(998\) | 32475.5i | 1.03005i | ||||||||
\(999\) | 8561.66 | + | 2951.55i | 0.271150 | + | 0.0934765i |
(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 | 147.4.c.b.146.2 | yes | 24 | |
3.2 | odd | 2 | inner | 147.4.c.b.146.23 | yes | 24 | |
7.2 | even | 3 | 147.4.g.e.80.1 | 48 | |||
7.3 | odd | 6 | 147.4.g.e.68.23 | 48 | |||
7.4 | even | 3 | 147.4.g.e.68.24 | 48 | |||
7.5 | odd | 6 | 147.4.g.e.80.2 | 48 | |||
7.6 | odd | 2 | inner | 147.4.c.b.146.1 | ✓ | 24 | |
21.2 | odd | 6 | 147.4.g.e.80.23 | 48 | |||
21.5 | even | 6 | 147.4.g.e.80.24 | 48 | |||
21.11 | odd | 6 | 147.4.g.e.68.2 | 48 | |||
21.17 | even | 6 | 147.4.g.e.68.1 | 48 | |||
21.20 | even | 2 | inner | 147.4.c.b.146.24 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.c.b.146.1 | ✓ | 24 | 7.6 | odd | 2 | inner | |
147.4.c.b.146.2 | yes | 24 | 1.1 | even | 1 | trivial | |
147.4.c.b.146.23 | yes | 24 | 3.2 | odd | 2 | inner | |
147.4.c.b.146.24 | yes | 24 | 21.20 | even | 2 | inner | |
147.4.g.e.68.1 | 48 | 21.17 | even | 6 | |||
147.4.g.e.68.2 | 48 | 21.11 | odd | 6 | |||
147.4.g.e.68.23 | 48 | 7.3 | odd | 6 | |||
147.4.g.e.68.24 | 48 | 7.4 | even | 3 | |||
147.4.g.e.80.1 | 48 | 7.2 | even | 3 | |||
147.4.g.e.80.2 | 48 | 7.5 | odd | 6 | |||
147.4.g.e.80.23 | 48 | 21.2 | odd | 6 | |||
147.4.g.e.80.24 | 48 | 21.5 | even | 6 |