Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (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: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 230x^{12} - 96x^{10} + 25551x^{8} - 7776x^{6} - 1509030x^{4} + 1062882x^{2} + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{8} \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.6 | ||
Root | \(0.173499 + 2.99498i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.b.809.5 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 3.56108 | + | 3.50980i | 0.712217 | + | 0.701960i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.17976i | 0.454251i | 0.973865 | + | 0.227126i | \(0.0729328\pi\) | ||||
−0.973865 | + | 0.227126i | \(0.927067\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.03613 | − | 4.96360i | −0.503613 | − | 0.496360i | ||||
\(11\) | − | 15.6543i | − | 1.42312i | −0.702624 | − | 0.711561i | \(-0.747989\pi\) | ||
0.702624 | − | 0.711561i | \(-0.252011\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.33596i | − | 0.102766i | −0.998679 | − | 0.0513830i | \(-0.983637\pi\) | ||
0.998679 | − | 0.0513830i | \(-0.0163629\pi\) | |||||||
\(14\) | − | 4.49686i | − | 0.321204i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −23.4761 | −1.38094 | −0.690472 | − | 0.723359i | \(-0.742597\pi\) | ||||
−0.690472 | + | 0.723359i | \(0.742597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.3447 | −1.22867 | −0.614334 | − | 0.789046i | \(-0.710575\pi\) | ||||
−0.614334 | + | 0.789046i | \(0.710575\pi\) | |||||||
\(20\) | 7.12217 | + | 7.01960i | 0.356108 | + | 0.350980i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 22.1386i | 1.00630i | ||||||||
\(23\) | −28.6849 | −1.24717 | −0.623584 | − | 0.781756i | \(-0.714324\pi\) | ||||
−0.623584 | + | 0.781756i | \(0.714324\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.362627 | + | 24.9974i | 0.0145051 | + | 0.999895i | ||||
\(26\) | 1.88933i | 0.0726665i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.35952i | 0.227126i | ||||||||
\(29\) | − | 33.1593i | − | 1.14342i | −0.820454 | − | 0.571712i | \(-0.806279\pi\) | ||
0.820454 | − | 0.571712i | \(-0.193721\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.5472 | 0.598296 | 0.299148 | − | 0.954207i | \(-0.403298\pi\) | ||||
0.299148 | + | 0.954207i | \(0.403298\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 33.2002 | 0.976475 | ||||||||
\(35\) | −11.1603 | + | 11.3234i | −0.318866 | + | 0.323525i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.95544i | − | 0.106904i | −0.998570 | − | 0.0534519i | \(-0.982978\pi\) | ||
0.998570 | − | 0.0534519i | \(-0.0170224\pi\) | |||||||
\(38\) | 33.0144 | 0.868799 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.0723 | − | 9.92721i | −0.251807 | − | 0.248180i | ||||
\(41\) | − | 60.3301i | − | 1.47147i | −0.677272 | − | 0.735733i | \(-0.736838\pi\) | ||
0.677272 | − | 0.735733i | \(-0.263162\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.83257i | − | 0.0658738i | −0.999457 | − | 0.0329369i | \(-0.989514\pi\) | ||
0.999457 | − | 0.0329369i | \(-0.0104860\pi\) | |||||||
\(44\) | − | 31.3087i | − | 0.711561i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 40.5665 | 0.881881 | ||||||||
\(47\) | −71.6735 | −1.52497 | −0.762485 | − | 0.647006i | \(-0.776021\pi\) | ||||
−0.762485 | + | 0.647006i | \(0.776021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 38.8891 | 0.793656 | ||||||||
\(50\) | −0.512832 | − | 35.3516i | −0.0102566 | − | 0.707032i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.67192i | − | 0.0513830i | ||||||
\(53\) | 14.3465 | 0.270689 | 0.135345 | − | 0.990799i | \(-0.456786\pi\) | ||||
0.135345 | + | 0.990799i | \(0.456786\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 54.9436 | − | 55.7464i | 0.998974 | − | 1.01357i | ||||
\(56\) | − | 8.99372i | − | 0.160602i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 46.8943i | 0.808523i | ||||||||
\(59\) | 72.3760i | 1.22671i | 0.789807 | + | 0.613356i | \(0.210181\pi\) | ||||
−0.789807 | + | 0.613356i | \(0.789819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2385 | 0.184237 | 0.0921186 | − | 0.995748i | \(-0.470636\pi\) | ||||
0.0921186 | + | 0.995748i | \(0.470636\pi\) | |||||||
\(62\) | −26.2296 | −0.423059 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 4.68894 | − | 4.75746i | 0.0721376 | − | 0.0731917i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.35443i | 0.0500661i | 0.999687 | + | 0.0250330i | \(0.00796909\pi\) | ||||
−0.999687 | + | 0.0250330i | \(0.992031\pi\) | |||||||
\(68\) | −46.9521 | −0.690472 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.7831 | − | 16.0137i | 0.225472 | − | 0.228767i | ||||
\(71\) | − | 40.0554i | − | 0.564160i | −0.959391 | − | 0.282080i | \(-0.908976\pi\) | ||
0.959391 | − | 0.282080i | \(-0.0910244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 86.6579i | 1.18709i | 0.804799 | + | 0.593547i | \(0.202273\pi\) | ||||
−0.804799 | + | 0.593547i | \(0.797727\pi\) | |||||||
\(74\) | 5.59384i | 0.0755925i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −46.6894 | −0.614334 | ||||||||
\(77\) | 49.7770 | 0.646455 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −90.5804 | −1.14659 | −0.573294 | − | 0.819350i | \(-0.694335\pi\) | ||||
−0.573294 | + | 0.819350i | \(0.694335\pi\) | |||||||
\(80\) | 14.2443 | + | 14.0392i | 0.178054 | + | 0.175490i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 85.3196i | 1.04048i | ||||||||
\(83\) | −102.892 | −1.23967 | −0.619833 | − | 0.784734i | \(-0.712800\pi\) | ||||
−0.619833 | + | 0.784734i | \(0.712800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −83.6002 | − | 82.3962i | −0.983531 | − | 0.969367i | ||||
\(86\) | 4.00586i | 0.0465798i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 44.2772i | 0.503150i | ||||||||
\(89\) | − | 144.459i | − | 1.62313i | −0.584259 | − | 0.811567i | \(-0.698615\pi\) | ||
0.584259 | − | 0.811567i | \(-0.301385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.24802 | 0.0466816 | ||||||||
\(92\) | −57.3697 | −0.623584 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 101.362 | 1.07832 | ||||||||
\(95\) | −83.1323 | − | 81.9351i | −0.875077 | − | 0.862475i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 74.8437i | − | 0.771584i | −0.922586 | − | 0.385792i | \(-0.873928\pi\) | ||
0.922586 | − | 0.385792i | \(-0.126072\pi\) | |||||||
\(98\) | −54.9975 | −0.561199 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.725253 | + | 49.9947i | 0.00725253 | + | 0.499947i | ||||
\(101\) | 16.9570i | 0.167891i | 0.996470 | + | 0.0839455i | \(0.0267522\pi\) | ||||
−0.996470 | + | 0.0839455i | \(0.973248\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 105.653i | − | 1.02576i | −0.858461 | − | 0.512879i | \(-0.828579\pi\) | ||
0.858461 | − | 0.512879i | \(-0.171421\pi\) | |||||||
\(104\) | 3.77866i | 0.0363333i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.2891 | −0.191406 | ||||||||
\(107\) | 58.8159 | 0.549681 | 0.274840 | − | 0.961490i | \(-0.411375\pi\) | ||||
0.274840 | + | 0.961490i | \(0.411375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −184.365 | −1.69142 | −0.845710 | − | 0.533643i | \(-0.820823\pi\) | ||||
−0.845710 | + | 0.533643i | \(0.820823\pi\) | |||||||
\(110\) | −77.7020 | + | 78.8373i | −0.706382 | + | 0.716703i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.7190i | 0.113563i | ||||||||
\(113\) | 17.1551 | 0.151815 | 0.0759073 | − | 0.997115i | \(-0.475815\pi\) | ||||
0.0759073 | + | 0.997115i | \(0.475815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −102.149 | − | 100.678i | −0.888254 | − | 0.875461i | ||||
\(116\) | − | 66.3186i | − | 0.571712i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 102.355i | − | 0.867416i | ||||||
\(119\) | − | 74.6482i | − | 0.627296i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124.058 | −1.02528 | ||||||||
\(122\) | −15.8936 | −0.130275 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 37.0943 | 0.299148 | ||||||||
\(125\) | −86.4444 | + | 90.2905i | −0.691555 | + | 0.722324i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.8557i | 0.140596i | 0.997526 | + | 0.0702979i | \(0.0223950\pi\) | ||||
−0.997526 | + | 0.0702979i | \(0.977605\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.63117 | + | 6.72806i | −0.0510090 | + | 0.0517543i | ||||
\(131\) | − | 212.823i | − | 1.62460i | −0.583239 | − | 0.812301i | \(-0.698215\pi\) | ||
0.583239 | − | 0.812301i | \(-0.301785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 74.2305i | − | 0.558124i | ||||||
\(134\) | − | 4.74387i | − | 0.0354020i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 66.4003 | 0.488238 | ||||||||
\(137\) | 197.548 | 1.44195 | 0.720977 | − | 0.692959i | \(-0.243693\pi\) | ||||
0.720977 | + | 0.692959i | \(0.243693\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −51.5742 | −0.371037 | −0.185519 | − | 0.982641i | \(-0.559396\pi\) | ||||
−0.185519 | + | 0.982641i | \(0.559396\pi\) | |||||||
\(140\) | −22.3206 | + | 22.6468i | −0.159433 | + | 0.161763i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 56.6469i | 0.398922i | ||||||||
\(143\) | −20.9135 | −0.146249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 116.382 | − | 118.083i | 0.802638 | − | 0.814366i | ||||
\(146\) | − | 122.553i | − | 0.839403i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 7.91089i | − | 0.0534519i | ||||||
\(149\) | 225.983i | 1.51666i | 0.651868 | + | 0.758332i | \(0.273985\pi\) | ||||
−0.651868 | + | 0.758332i | \(0.726015\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −53.6516 | −0.355308 | −0.177654 | − | 0.984093i | \(-0.556851\pi\) | ||||
−0.177654 | + | 0.984093i | \(0.556851\pi\) | |||||||
\(152\) | 66.0287 | 0.434400 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −70.3954 | −0.457113 | ||||||||
\(155\) | 66.0480 | + | 65.0968i | 0.426116 | + | 0.419979i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 153.382i | 0.976953i | 0.872577 | + | 0.488477i | \(0.162447\pi\) | ||||
−0.872577 | + | 0.488477i | \(0.837553\pi\) | |||||||
\(158\) | 128.100 | 0.810760 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20.1445 | − | 19.8544i | −0.125903 | − | 0.124090i | ||||
\(161\) | − | 91.2109i | − | 0.566528i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 272.064i | − | 1.66910i | −0.550929 | − | 0.834552i | \(-0.685727\pi\) | ||
0.550929 | − | 0.834552i | \(-0.314273\pi\) | |||||||
\(164\) | − | 120.660i | − | 0.735733i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 145.512 | 0.876576 | ||||||||
\(167\) | −160.173 | −0.959122 | −0.479561 | − | 0.877508i | \(-0.659204\pi\) | ||||
−0.479561 | + | 0.877508i | \(0.659204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 167.215 | 0.989439 | ||||||||
\(170\) | 118.228 | + | 116.526i | 0.695462 | + | 0.685446i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 5.66514i | − | 0.0329369i | ||||||
\(173\) | −30.4179 | −0.175826 | −0.0879130 | − | 0.996128i | \(-0.528020\pi\) | ||||
−0.0879130 | + | 0.996128i | \(0.528020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −79.4856 | + | 1.15307i | −0.454204 | + | 0.00658895i | ||||
\(176\) | − | 62.6174i | − | 0.355781i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 204.296i | 1.14773i | ||||||||
\(179\) | 261.709i | 1.46206i | 0.682344 | + | 0.731031i | \(0.260961\pi\) | ||||
−0.682344 | + | 0.731031i | \(0.739039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −158.159 | −0.873806 | −0.436903 | − | 0.899509i | \(-0.643925\pi\) | ||||
−0.436903 | + | 0.899509i | \(0.643925\pi\) | |||||||
\(182\) | −6.00761 | −0.0330089 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 81.1330 | 0.440940 | ||||||||
\(185\) | 13.8828 | − | 14.0857i | 0.0750422 | − | 0.0761387i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 367.502i | 1.96525i | ||||||||
\(188\) | −143.347 | −0.762485 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 117.567 | + | 115.874i | 0.618773 | + | 0.609862i | ||||
\(191\) | − | 123.681i | − | 0.647542i | −0.946135 | − | 0.323771i | \(-0.895049\pi\) | ||
0.946135 | − | 0.323771i | \(-0.104951\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 44.7888i | 0.232066i | 0.993245 | + | 0.116033i | \(0.0370179\pi\) | ||||
−0.993245 | + | 0.116033i | \(0.962982\pi\) | |||||||
\(194\) | 105.845i | 0.545592i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 77.7783 | 0.396828 | ||||||||
\(197\) | −203.271 | −1.03183 | −0.515917 | − | 0.856638i | \(-0.672549\pi\) | ||||
−0.515917 | + | 0.856638i | \(0.672549\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −77.5958 | −0.389929 | −0.194964 | − | 0.980810i | \(-0.562459\pi\) | ||||
−0.194964 | + | 0.980810i | \(0.562459\pi\) | |||||||
\(200\) | −1.02566 | − | 70.7032i | −0.00512832 | − | 0.353516i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 23.9808i | − | 0.118717i | ||||||
\(203\) | 105.439 | 0.519402 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 211.746 | − | 214.840i | 1.03291 | − | 1.04800i | ||||
\(206\) | 149.416i | 0.725320i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.34383i | − | 0.0256915i | ||||||
\(209\) | 365.446i | 1.74854i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −132.330 | −0.627157 | −0.313578 | − | 0.949562i | \(-0.601528\pi\) | ||||
−0.313578 | + | 0.949562i | \(0.601528\pi\) | |||||||
\(212\) | 28.6931 | 0.135345 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −83.1782 | −0.388683 | ||||||||
\(215\) | 9.94176 | − | 10.0870i | 0.0462407 | − | 0.0469164i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 58.9755i | 0.271777i | ||||||||
\(218\) | 260.731 | 1.19601 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 109.887 | − | 111.493i | 0.499487 | − | 0.506786i | ||||
\(221\) | 31.3630i | 0.141914i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 349.183i | − | 1.56584i | −0.622122 | − | 0.782921i | \(-0.713729\pi\) | ||
0.622122 | − | 0.782921i | \(-0.286271\pi\) | |||||||
\(224\) | − | 17.9874i | − | 0.0803010i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −24.2609 | −0.107349 | ||||||||
\(227\) | 218.334 | 0.961825 | 0.480912 | − | 0.876769i | \(-0.340306\pi\) | ||||
0.480912 | + | 0.876769i | \(0.340306\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 380.456 | 1.66138 | 0.830690 | − | 0.556735i | \(-0.187946\pi\) | ||||
0.830690 | + | 0.556735i | \(0.187946\pi\) | |||||||
\(230\) | 144.461 | + | 142.380i | 0.628090 | + | 0.619045i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 93.7887i | 0.404261i | ||||||||
\(233\) | 232.991 | 0.999963 | 0.499981 | − | 0.866036i | \(-0.333340\pi\) | ||||
0.499981 | + | 0.866036i | \(0.333340\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −255.235 | − | 251.560i | −1.08611 | − | 1.07047i | ||||
\(236\) | 144.752i | 0.613356i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 105.568i | 0.443565i | ||||||||
\(239\) | 157.493i | 0.658965i | 0.944162 | + | 0.329482i | \(0.106874\pi\) | ||||
−0.944162 | + | 0.329482i | \(0.893126\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −115.151 | −0.477806 | −0.238903 | − | 0.971043i | \(-0.576788\pi\) | ||||
−0.238903 | + | 0.971043i | \(0.576788\pi\) | |||||||
\(242\) | 175.445 | 0.724980 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.4769 | 0.0921186 | ||||||||
\(245\) | 138.487 | + | 136.493i | 0.565255 | + | 0.557114i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.1875i | 0.126265i | ||||||||
\(248\) | −52.4593 | −0.211529 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 122.251 | − | 127.690i | 0.489003 | − | 0.510760i | ||||
\(251\) | 157.563i | 0.627740i | 0.949466 | + | 0.313870i | \(0.101626\pi\) | ||||
−0.949466 | + | 0.313870i | \(0.898374\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 449.043i | 1.77487i | ||||||||
\(254\) | − | 25.2517i | − | 0.0994162i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 20.1945 | 0.0785777 | 0.0392889 | − | 0.999228i | \(-0.487491\pi\) | ||||
0.0392889 | + | 0.999228i | \(0.487491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5774 | 0.0485612 | ||||||||
\(260\) | 9.37789 | − | 9.51491i | 0.0360688 | − | 0.0365958i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 300.977i | 1.14877i | ||||||||
\(263\) | −101.679 | −0.386614 | −0.193307 | − | 0.981138i | \(-0.561921\pi\) | ||||
−0.193307 | + | 0.981138i | \(0.561921\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 51.0892 | + | 50.3534i | 0.192789 | + | 0.190013i | ||||
\(266\) | 104.978i | 0.394653i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.70885i | 0.0250330i | ||||||||
\(269\) | − | 83.9984i | − | 0.312262i | −0.987736 | − | 0.156131i | \(-0.950098\pi\) | ||
0.987736 | − | 0.156131i | \(-0.0499022\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 349.591 | 1.29000 | 0.645001 | − | 0.764182i | \(-0.276857\pi\) | ||||
0.645001 | + | 0.764182i | \(0.276857\pi\) | |||||||
\(272\) | −93.9042 | −0.345236 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −279.375 | −1.01962 | ||||||||
\(275\) | 391.317 | − | 5.67668i | 1.42297 | − | 0.0206425i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 326.401i | 1.17834i | 0.808008 | + | 0.589172i | \(0.200546\pi\) | ||||
−0.808008 | + | 0.589172i | \(0.799454\pi\) | |||||||
\(278\) | 72.9369 | 0.262363 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 31.5661 | − | 32.0274i | 0.112736 | − | 0.114383i | ||||
\(281\) | − | 108.743i | − | 0.386986i | −0.981102 | − | 0.193493i | \(-0.938018\pi\) | ||
0.981102 | − | 0.193493i | \(-0.0619816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 380.702i | − | 1.34524i | −0.739990 | − | 0.672618i | \(-0.765170\pi\) | ||
0.739990 | − | 0.672618i | \(-0.234830\pi\) | |||||||
\(284\) | − | 80.1108i | − | 0.282080i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 29.5762 | 0.103413 | ||||||||
\(287\) | 191.835 | 0.668415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 262.125 | 0.907007 | ||||||||
\(290\) | −164.590 | + | 166.995i | −0.567550 | + | 0.575843i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 173.316i | 0.593547i | ||||||||
\(293\) | 101.317 | 0.345790 | 0.172895 | − | 0.984940i | \(-0.444688\pi\) | ||||
0.172895 | + | 0.984940i | \(0.444688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −254.025 | + | 257.737i | −0.861102 | + | 0.873685i | ||||
\(296\) | 11.1877i | 0.0377962i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 319.588i | − | 1.07244i | ||||||
\(299\) | 38.3218i | 0.128166i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.00690 | 0.0299232 | ||||||||
\(302\) | 75.8748 | 0.251241 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −93.3787 | −0.307167 | ||||||||
\(305\) | 40.0211 | + | 39.4448i | 0.131217 | + | 0.129327i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 115.566i | 0.376436i | 0.982127 | + | 0.188218i | \(0.0602711\pi\) | ||||
−0.982127 | + | 0.188218i | \(0.939729\pi\) | |||||||
\(308\) | 99.5541 | 0.323228 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −93.4060 | − | 92.0608i | −0.301310 | − | 0.296970i | ||||
\(311\) | 338.675i | 1.08899i | 0.838765 | + | 0.544494i | \(0.183278\pi\) | ||||
−0.838765 | + | 0.544494i | \(0.816722\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 267.167i | − | 0.853569i | −0.904353 | − | 0.426785i | \(-0.859646\pi\) | ||
0.904353 | − | 0.426785i | \(-0.140354\pi\) | |||||||
\(314\) | − | 216.914i | − | 0.690810i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −181.161 | −0.573294 | ||||||||
\(317\) | −293.696 | −0.926485 | −0.463243 | − | 0.886231i | \(-0.653314\pi\) | ||||
−0.463243 | + | 0.886231i | \(0.653314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −519.087 | −1.62723 | ||||||||
\(320\) | 28.4887 | + | 28.0784i | 0.0890271 | + | 0.0877450i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 128.992i | 0.400595i | ||||||||
\(323\) | 548.041 | 1.69672 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.3954 | − | 0.484454i | 0.102755 | − | 0.00149063i | ||||
\(326\) | 384.757i | 1.18023i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 170.639i | 0.520242i | ||||||||
\(329\) | − | 227.905i | − | 0.692719i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −47.2025 | −0.142606 | −0.0713028 | − | 0.997455i | \(-0.522716\pi\) | ||||
−0.0713028 | + | 0.997455i | \(0.522716\pi\) | |||||||
\(332\) | −205.785 | −0.619833 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 226.519 | 0.678202 | ||||||||
\(335\) | −11.7734 | + | 11.9454i | −0.0351444 | + | 0.0356579i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 468.253i | 1.38947i | 0.719264 | + | 0.694737i | \(0.244479\pi\) | ||||
−0.719264 | + | 0.694737i | \(0.755521\pi\) | |||||||
\(338\) | −236.478 | −0.699639 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −167.200 | − | 164.792i | −0.491766 | − | 0.484684i | ||||
\(341\) | − | 290.344i | − | 0.851448i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 279.466i | 0.814770i | ||||||||
\(344\) | 8.01172i | 0.0232899i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 43.0174 | 0.124328 | ||||||||
\(347\) | 57.0054 | 0.164281 | 0.0821404 | − | 0.996621i | \(-0.473824\pi\) | ||||
0.0821404 | + | 0.996621i | \(0.473824\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −179.131 | −0.513268 | −0.256634 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256634 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(350\) | 112.410 | − | 1.63068i | 0.321170 | − | 0.00465909i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 88.5543i | 0.251575i | ||||||||
\(353\) | 22.8170 | 0.0646375 | 0.0323188 | − | 0.999478i | \(-0.489711\pi\) | ||||
0.0323188 | + | 0.999478i | \(0.489711\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 140.586 | − | 142.641i | 0.396018 | − | 0.401804i | ||||
\(356\) | − | 288.918i | − | 0.811567i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 370.113i | − | 1.03383i | ||||||
\(359\) | 598.539i | 1.66724i | 0.552339 | + | 0.833619i | \(0.313735\pi\) | ||||
−0.552339 | + | 0.833619i | \(0.686265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 183.974 | 0.509623 | ||||||||
\(362\) | 223.670 | 0.617874 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.49605 | 0.0233408 | ||||||||
\(365\) | −304.152 | + | 308.596i | −0.833293 | + | 0.845469i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.7000i | 0.0509536i | 0.999675 | + | 0.0254768i | \(0.00811039\pi\) | ||||
−0.999675 | + | 0.0254768i | \(0.991890\pi\) | |||||||
\(368\) | −114.739 | −0.311792 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −19.6333 | + | 19.9201i | −0.0530629 | + | 0.0538382i | ||||
\(371\) | 45.6185i | 0.122961i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 288.883i | − | 0.774485i | −0.921978 | − | 0.387243i | \(-0.873428\pi\) | ||
0.921978 | − | 0.387243i | \(-0.126572\pi\) | |||||||
\(374\) | − | 519.727i | − | 1.38964i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 202.723 | 0.539158 | ||||||||
\(377\) | −44.2994 | −0.117505 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 427.427 | 1.12778 | 0.563888 | − | 0.825852i | \(-0.309305\pi\) | ||||
0.563888 | + | 0.825852i | \(0.309305\pi\) | |||||||
\(380\) | −166.265 | − | 163.870i | −0.437539 | − | 0.431237i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 174.911i | 0.457881i | ||||||||
\(383\) | −178.280 | −0.465484 | −0.232742 | − | 0.972539i | \(-0.574770\pi\) | ||||
−0.232742 | + | 0.972539i | \(0.574770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 177.260 | + | 174.707i | 0.460416 | + | 0.453785i | ||||
\(386\) | − | 63.3409i | − | 0.164096i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 149.687i | − | 0.385792i | ||||||
\(389\) | 368.910i | 0.948356i | 0.880429 | + | 0.474178i | \(0.157255\pi\) | ||||
−0.880429 | + | 0.474178i | \(0.842745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 673.407 | 1.72227 | ||||||||
\(392\) | −109.995 | −0.280600 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 287.469 | 0.729617 | ||||||||
\(395\) | −322.564 | − | 317.919i | −0.816619 | − | 0.804859i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 520.661i | 1.31149i | 0.754983 | + | 0.655745i | \(0.227645\pi\) | ||||
−0.754983 | + | 0.655745i | \(0.772355\pi\) | |||||||
\(398\) | 109.737 | 0.275721 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.45051 | + | 99.9895i | 0.00362627 | + | 0.249974i | ||||
\(401\) | 0.323245i | 0.000806096i | 1.00000 | 0.000403048i | \(0.000128294\pi\) | |||||
−1.00000 | 0.000403048i | \(0.999872\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 24.7782i | − | 0.0614844i | ||||||
\(404\) | 33.9140i | 0.0839455i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −149.113 | −0.367273 | ||||||||
\(407\) | −61.9199 | −0.152137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.52823 | 0.0232964 | 0.0116482 | − | 0.999932i | \(-0.496292\pi\) | ||||
0.0116482 | + | 0.999932i | \(0.496292\pi\) | |||||||
\(410\) | −299.455 | + | 303.830i | −0.730377 | + | 0.741050i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 211.306i | − | 0.512879i | ||||||
\(413\) | −230.138 | −0.557236 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −366.408 | − | 361.131i | −0.882911 | − | 0.870196i | ||||
\(416\) | 7.55732i | 0.0181666i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 516.818i | − | 1.23641i | ||||||
\(419\) | − | 390.835i | − | 0.932780i | −0.884579 | − | 0.466390i | \(-0.845554\pi\) | ||
0.884579 | − | 0.466390i | \(-0.154446\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 427.682 | 1.01587 | 0.507935 | − | 0.861395i | \(-0.330409\pi\) | ||||
0.507935 | + | 0.861395i | \(0.330409\pi\) | |||||||
\(422\) | 187.143 | 0.443467 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −40.5781 | −0.0957031 | ||||||||
\(425\) | −8.51304 | − | 586.840i | −0.0200307 | − | 1.38080i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 35.7356i | 0.0836900i | ||||||||
\(428\) | 117.632 | 0.274840 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0598 | + | 14.2652i | −0.0326971 | + | 0.0331749i | ||||
\(431\) | − | 396.306i | − | 0.919503i | −0.888048 | − | 0.459752i | \(-0.847938\pi\) | ||
0.888048 | − | 0.459752i | \(-0.152062\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 700.722i | − | 1.61830i | −0.587606 | − | 0.809148i | \(-0.699929\pi\) | ||
0.587606 | − | 0.809148i | \(-0.300071\pi\) | |||||||
\(434\) | − | 83.4040i | − | 0.192175i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −368.730 | −0.845710 | ||||||||
\(437\) | 669.639 | 1.53235 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −95.1798 | −0.216811 | −0.108405 | − | 0.994107i | \(-0.534574\pi\) | ||||
−0.108405 | + | 0.994107i | \(0.534574\pi\) | |||||||
\(440\) | −155.404 | + | 157.675i | −0.353191 | + | 0.358352i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 44.3540i | − | 0.100348i | ||||||
\(443\) | −237.685 | −0.536536 | −0.268268 | − | 0.963344i | \(-0.586451\pi\) | ||||
−0.268268 | + | 0.963344i | \(0.586451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 507.022 | − | 514.430i | 1.13937 | − | 1.15602i | ||||
\(446\) | 493.819i | 1.10722i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 25.4381i | 0.0567814i | ||||||||
\(449\) | 574.978i | 1.28057i | 0.768136 | + | 0.640287i | \(0.221185\pi\) | ||||
−0.768136 | + | 0.640287i | \(0.778815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −944.428 | −2.09408 | ||||||||
\(452\) | 34.3101 | 0.0759073 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −308.771 | −0.680113 | ||||||||
\(455\) | 15.1276 | + | 14.9097i | 0.0332474 | + | 0.0327686i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 552.639i | 1.20927i | 0.796501 | + | 0.604637i | \(0.206682\pi\) | ||||
−0.796501 | + | 0.604637i | \(0.793318\pi\) | |||||||
\(458\) | −538.046 | −1.17477 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −204.298 | − | 201.356i | −0.444127 | − | 0.437731i | ||||
\(461\) | − | 753.521i | − | 1.63454i | −0.576258 | − | 0.817268i | \(-0.695488\pi\) | ||
0.576258 | − | 0.817268i | \(-0.304512\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 393.957i | 0.850878i | 0.904987 | + | 0.425439i | \(0.139880\pi\) | ||||
−0.904987 | + | 0.425439i | \(0.860120\pi\) | |||||||
\(464\) | − | 132.637i | − | 0.285856i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −329.499 | −0.707080 | ||||||||
\(467\) | 144.091 | 0.308546 | 0.154273 | − | 0.988028i | \(-0.450696\pi\) | ||||
0.154273 | + | 0.988028i | \(0.450696\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6663 | −0.0227426 | ||||||||
\(470\) | 360.957 | + | 355.759i | 0.767995 | + | 0.756934i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 204.710i | − | 0.433708i | ||||||
\(473\) | −44.3421 | −0.0937464 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.46540 | − | 583.556i | −0.0178219 | − | 1.22854i | ||||
\(476\) | − | 149.296i | − | 0.313648i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 222.728i | − | 0.465959i | ||||||
\(479\) | − | 160.218i | − | 0.334484i | −0.985916 | − | 0.167242i | \(-0.946514\pi\) | ||
0.985916 | − | 0.167242i | \(-0.0534861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.28431 | −0.0109861 | ||||||||
\(482\) | 162.848 | 0.337860 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −248.117 | −0.512638 | ||||||||
\(485\) | 262.686 | − | 266.524i | 0.541621 | − | 0.549535i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 184.489i | 0.378827i | 0.981897 | + | 0.189414i | \(0.0606587\pi\) | ||||
−0.981897 | + | 0.189414i | \(0.939341\pi\) | |||||||
\(488\) | −31.7872 | −0.0651377 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −195.851 | − | 193.030i | −0.399696 | − | 0.393939i | ||||
\(491\) | 83.3423i | 0.169740i | 0.996392 | + | 0.0848700i | \(0.0270475\pi\) | ||||
−0.996392 | + | 0.0848700i | \(0.972953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 778.449i | 1.57900i | ||||||||
\(494\) | − | 44.1058i | − | 0.0892830i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 74.1886 | 0.149574 | ||||||||
\(497\) | 127.366 | 0.256271 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −402.812 | −0.807238 | −0.403619 | − | 0.914927i | \(-0.632248\pi\) | ||||
−0.403619 | + | 0.914927i | \(0.632248\pi\) | |||||||
\(500\) | −172.889 | + | 180.581i | −0.345778 | + | 0.361162i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 222.827i | − | 0.443879i | ||||||
\(503\) | −743.290 | −1.47771 | −0.738857 | − | 0.673862i | \(-0.764634\pi\) | ||||
−0.738857 | + | 0.673862i | \(0.764634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.5156 | + | 60.3852i | −0.117853 | + | 0.119575i | ||||
\(506\) | − | 635.042i | − | 1.25502i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 35.7113i | 0.0702979i | ||||||||
\(509\) | 97.6240i | 0.191796i | 0.995391 | + | 0.0958978i | \(0.0305722\pi\) | ||||
−0.995391 | + | 0.0958978i | \(0.969428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −275.551 | −0.539239 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −28.5593 | −0.0555628 | ||||||||
\(515\) | 370.821 | − | 376.239i | 0.720040 | − | 0.730562i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1122.00i | 2.17022i | ||||||||
\(518\) | −17.7871 | −0.0343380 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −13.2623 | + | 13.4561i | −0.0255045 | + | 0.0258772i | ||||
\(521\) | 630.912i | 1.21096i | 0.795859 | + | 0.605482i | \(0.207019\pi\) | ||||
−0.795859 | + | 0.605482i | \(0.792981\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 441.750i | − | 0.844647i | −0.906445 | − | 0.422323i | \(-0.861215\pi\) | ||
0.906445 | − | 0.422323i | \(-0.138785\pi\) | |||||||
\(524\) | − | 425.646i | − | 0.812301i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 143.797 | 0.273377 | ||||||||
\(527\) | −435.414 | −0.826213 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 293.821 | 0.555427 | ||||||||
\(530\) | −72.2510 | − | 71.2105i | −0.136323 | − | 0.134359i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 148.461i | − | 0.279062i | ||||||
\(533\) | −80.5985 | −0.151217 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 209.448 | + | 206.432i | 0.391492 | + | 0.385854i | ||||
\(536\) | − | 9.48775i | − | 0.0177010i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 118.792i | 0.220802i | ||||||||
\(539\) | − | 608.784i | − | 1.12947i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 365.131 | 0.674919 | 0.337459 | − | 0.941340i | \(-0.390432\pi\) | ||||
0.337459 | + | 0.941340i | \(0.390432\pi\) | |||||||
\(542\) | −494.396 | −0.912169 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 132.801 | 0.244119 | ||||||||
\(545\) | −656.538 | − | 647.083i | −1.20466 | − | 1.18731i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 364.069i | − | 0.665574i | −0.943002 | − | 0.332787i | \(-0.892011\pi\) | ||
0.943002 | − | 0.332787i | \(-0.107989\pi\) | |||||||
\(548\) | 395.095 | 0.720977 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −553.406 | + | 8.02804i | −1.00619 | + | 0.0145964i | ||||
\(551\) | 774.093i | 1.40489i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 288.024i | − | 0.520839i | ||||||
\(554\) | − | 461.601i | − | 0.833215i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −103.148 | −0.185519 | ||||||||
\(557\) | −901.292 | −1.61812 | −0.809059 | − | 0.587728i | \(-0.800023\pi\) | ||||
−0.809059 | + | 0.587728i | \(0.800023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.78420 | −0.00676958 | ||||||||
\(560\) | −44.6413 | + | 45.2935i | −0.0797165 | + | 0.0808813i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 153.786i | 0.273640i | ||||||||
\(563\) | 81.6432 | 0.145015 | 0.0725073 | − | 0.997368i | \(-0.476900\pi\) | ||||
0.0725073 | + | 0.997368i | \(0.476900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.0906 | + | 60.2108i | 0.108125 | + | 0.106568i | ||||
\(566\) | 538.394i | 0.951225i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 113.294i | 0.199461i | ||||||||
\(569\) | 99.5184i | 0.174900i | 0.996169 | + | 0.0874502i | \(0.0278719\pi\) | ||||
−0.996169 | + | 0.0874502i | \(0.972128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −402.277 | −0.704514 | −0.352257 | − | 0.935903i | \(-0.614586\pi\) | ||||
−0.352257 | + | 0.935903i | \(0.614586\pi\) | |||||||
\(572\) | −41.8271 | −0.0731243 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −271.296 | −0.472641 | ||||||||
\(575\) | −10.4019 | − | 717.046i | −0.0180903 | − | 1.24704i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 278.698i | 0.483012i | 0.970399 | + | 0.241506i | \(0.0776414\pi\) | ||||
−0.970399 | + | 0.241506i | \(0.922359\pi\) | |||||||
\(578\) | −370.701 | −0.641351 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 232.765 | − | 236.166i | 0.401319 | − | 0.407183i | ||||
\(581\) | − | 327.173i | − | 0.563120i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 224.585i | − | 0.385224i | ||||||
\(584\) | − | 245.106i | − | 0.419701i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −143.283 | −0.244511 | ||||||||
\(587\) | −325.927 | −0.555243 | −0.277621 | − | 0.960691i | \(-0.589546\pi\) | ||||
−0.277621 | + | 0.960691i | \(0.589546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −432.978 | −0.735106 | ||||||||
\(590\) | 359.246 | − | 364.495i | 0.608891 | − | 0.617788i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 15.8218i | − | 0.0267260i | ||||||
\(593\) | 113.167 | 0.190838 | 0.0954190 | − | 0.995437i | \(-0.469581\pi\) | ||||
0.0954190 | + | 0.995437i | \(0.469581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 262.000 | − | 265.828i | 0.440336 | − | 0.446770i | ||||
\(596\) | 451.966i | 0.758332i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 54.1952i | − | 0.0906273i | ||||||
\(599\) | − | 283.109i | − | 0.472636i | −0.971676 | − | 0.236318i | \(-0.924059\pi\) | ||
0.971676 | − | 0.236318i | \(-0.0759407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 523.593 | 0.871203 | 0.435601 | − | 0.900140i | \(-0.356536\pi\) | ||||
0.435601 | + | 0.900140i | \(0.356536\pi\) | |||||||
\(602\) | −12.7377 | −0.0211589 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −107.303 | −0.177654 | ||||||||
\(605\) | −441.782 | − | 435.420i | −0.730219 | − | 0.719703i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1018.05i | − | 1.67718i | −0.544761 | − | 0.838591i | \(-0.683380\pi\) | ||
0.544761 | − | 0.838591i | \(-0.316620\pi\) | |||||||
\(608\) | 132.057 | 0.217200 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −56.5984 | − | 55.7833i | −0.0927843 | − | 0.0914481i | ||||
\(611\) | 95.7528i | 0.156715i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 537.130i | 0.876231i | 0.898919 | + | 0.438116i | \(0.144354\pi\) | ||||
−0.898919 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(614\) | − | 163.435i | − | 0.266180i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −140.791 | −0.228556 | ||||||||
\(617\) | −1136.98 | −1.84275 | −0.921375 | − | 0.388676i | \(-0.872933\pi\) | ||||
−0.921375 | + | 0.388676i | \(0.872933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −234.742 | −0.379228 | −0.189614 | − | 0.981859i | \(-0.560724\pi\) | ||||
−0.189614 | + | 0.981859i | \(0.560724\pi\) | |||||||
\(620\) | 132.096 | + | 130.194i | 0.213058 | + | 0.209990i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 478.959i | − | 0.770031i | ||||||
\(623\) | 459.345 | 0.737311 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −624.737 | + | 18.1294i | −0.999579 | + | 0.0290071i | ||||
\(626\) | 377.832i | 0.603565i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 306.763i | 0.488477i | ||||||||
\(629\) | 92.8582i | 0.147628i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 131.866 | 0.208980 | 0.104490 | − | 0.994526i | \(-0.466679\pi\) | ||||
0.104490 | + | 0.994526i | \(0.466679\pi\) | |||||||
\(632\) | 256.200 | 0.405380 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 415.349 | 0.655124 | ||||||||
\(635\) | −62.6698 | + | 63.5855i | −0.0986925 | + | 0.100135i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 51.9542i | − | 0.0815608i | ||||||
\(638\) | 734.100 | 1.15063 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40.2891 | − | 39.7088i | −0.0629517 | − | 0.0620451i | ||||
\(641\) | 536.826i | 0.837483i | 0.908106 | + | 0.418741i | \(0.137529\pi\) | ||||
−0.908106 | + | 0.418741i | \(0.862471\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 585.189i | 0.910092i | 0.890468 | + | 0.455046i | \(0.150377\pi\) | ||||
−0.890468 | + | 0.455046i | \(0.849623\pi\) | |||||||
\(644\) | − | 182.422i | − | 0.283264i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −775.047 | −1.19976 | ||||||||
\(647\) | 375.007 | 0.579609 | 0.289805 | − | 0.957086i | \(-0.406410\pi\) | ||||
0.289805 | + | 0.957086i | \(0.406410\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1133.00 | 1.74576 | ||||||||
\(650\) | −47.2283 | + | 0.685121i | −0.0726589 | + | 0.00105403i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 544.128i | − | 0.834552i | ||||||
\(653\) | −453.112 | −0.693892 | −0.346946 | − | 0.937885i | \(-0.612781\pi\) | ||||
−0.346946 | + | 0.937885i | \(0.612781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 746.965 | − | 757.880i | 1.14040 | − | 1.15707i | ||||
\(656\) | − | 241.320i | − | 0.367866i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 322.306i | 0.489826i | ||||||||
\(659\) | 347.194i | 0.526850i | 0.964680 | + | 0.263425i | \(0.0848521\pi\) | ||||
−0.964680 | + | 0.263425i | \(0.915148\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 946.578 | 1.43204 | 0.716020 | − | 0.698080i | \(-0.245962\pi\) | ||||
0.716020 | + | 0.698080i | \(0.245962\pi\) | |||||||
\(662\) | 66.7544 | 0.100837 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 291.023 | 0.438288 | ||||||||
\(665\) | 260.534 | − | 264.341i | 0.391780 | − | 0.397505i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 951.170i | 1.42604i | ||||||||
\(668\) | −320.347 | −0.479561 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 16.6500 | − | 16.8933i | 0.0248508 | − | 0.0252139i | ||||
\(671\) | − | 175.931i | − | 0.262192i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 208.778i | 0.310220i | 0.987897 | + | 0.155110i | \(0.0495732\pi\) | ||||
−0.987897 | + | 0.155110i | \(0.950427\pi\) | |||||||
\(674\) | − | 662.210i | − | 0.982507i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 334.430 | 0.494720 | ||||||||
\(677\) | −416.186 | −0.614751 | −0.307375 | − | 0.951588i | \(-0.599451\pi\) | ||||
−0.307375 | + | 0.951588i | \(0.599451\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 237.985 | 0.350493 | ||||||||
\(680\) | 236.457 | + | 233.052i | 0.347731 | + | 0.342723i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 410.608i | 0.602064i | ||||||||
\(683\) | −883.982 | −1.29426 | −0.647132 | − | 0.762378i | \(-0.724032\pi\) | ||||
−0.647132 | + | 0.762378i | \(0.724032\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 703.484 | + | 693.352i | 1.02698 | + | 1.01219i | ||||
\(686\) | − | 395.225i | − | 0.576130i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 11.3303i | − | 0.0164684i | ||||||
\(689\) | − | 19.1664i | − | 0.0278176i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 370.080 | 0.535571 | 0.267786 | − | 0.963479i | \(-0.413708\pi\) | ||||
0.267786 | + | 0.963479i | \(0.413708\pi\) | |||||||
\(692\) | −60.8358 | −0.0879130 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80.6178 | −0.116164 | ||||||||
\(695\) | −183.660 | − | 181.015i | −0.264259 | − | 0.260453i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1416.31i | 2.03201i | ||||||||
\(698\) | 253.329 | 0.362935 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −158.971 | + | 2.30613i | −0.227102 | + | 0.00329447i | ||||
\(701\) | − | 820.094i | − | 1.16989i | −0.811073 | − | 0.584946i | \(-0.801116\pi\) | ||
0.811073 | − | 0.584946i | \(-0.198884\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 92.3386i | 0.131349i | ||||||||
\(704\) | − | 125.235i | − | 0.177890i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.2682 | −0.0457056 | ||||||||
\(707\) | −53.9191 | −0.0762647 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −280.410 | −0.395500 | −0.197750 | − | 0.980252i | \(-0.563363\pi\) | ||||
−0.197750 | + | 0.980252i | \(0.563363\pi\) | |||||||
\(710\) | −198.819 | + | 201.724i | −0.280027 | + | 0.284119i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 408.592i | 0.573865i | ||||||||
\(713\) | −532.023 | −0.746175 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −74.4749 | − | 73.4023i | −0.104161 | − | 0.102661i | ||||
\(716\) | 523.418i | 0.731031i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 846.462i | − | 1.17892i | ||||||
\(719\) | − | 144.017i | − | 0.200302i | −0.994972 | − | 0.100151i | \(-0.968067\pi\) | ||
0.994972 | − | 0.100151i | \(-0.0319327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 335.951 | 0.465952 | ||||||||
\(722\) | −260.179 | −0.360358 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −316.318 | −0.436903 | ||||||||
\(725\) | 828.895 | − | 12.0244i | 1.14330 | − | 0.0165854i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 567.714i | 0.780900i | 0.920624 | + | 0.390450i | \(0.127681\pi\) | ||||
−0.920624 | + | 0.390450i | \(0.872319\pi\) | |||||||
\(728\) | −12.0152 | −0.0165044 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 430.136 | − | 436.421i | 0.589227 | − | 0.597837i | ||||
\(731\) | 66.4976i | 0.0909680i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 135.891i | 0.185390i | 0.995695 | + | 0.0926949i | \(0.0295481\pi\) | ||||
−0.995695 | + | 0.0926949i | \(0.970452\pi\) | |||||||
\(734\) | − | 26.4457i | − | 0.0360296i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 162.266 | 0.220470 | ||||||||
\(737\) | 52.5113 | 0.0712501 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −799.789 | −1.08226 | −0.541129 | − | 0.840939i | \(-0.682003\pi\) | ||||
−0.541129 | + | 0.840939i | \(0.682003\pi\) | |||||||
\(740\) | 27.7656 | − | 28.1713i | 0.0375211 | − | 0.0380694i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 64.5143i | − | 0.0869465i | ||||||
\(743\) | 642.938 | 0.865327 | 0.432663 | − | 0.901556i | \(-0.357574\pi\) | ||||
0.432663 | + | 0.901556i | \(0.357574\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −793.155 | + | 804.744i | −1.06464 | + | 1.08019i | ||||
\(746\) | 408.542i | 0.547644i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 735.004i | 0.982626i | ||||||||
\(749\) | 187.020i | 0.249693i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −804.131 | −1.07075 | −0.535374 | − | 0.844615i | \(-0.679829\pi\) | ||||
−0.535374 | + | 0.844615i | \(0.679829\pi\) | |||||||
\(752\) | −286.694 | −0.381242 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 62.6488 | 0.0830887 | ||||||||
\(755\) | −191.058 | − | 188.306i | −0.253057 | − | 0.249412i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 998.545i | − | 1.31908i | −0.751668 | − | 0.659541i | \(-0.770751\pi\) | ||
0.751668 | − | 0.659541i | \(-0.229249\pi\) | |||||||
\(758\) | −604.473 | −0.797458 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 235.134 | + | 231.748i | 0.309387 | + | 0.304931i | ||||
\(761\) | − | 436.073i | − | 0.573027i | −0.958076 | − | 0.286513i | \(-0.907504\pi\) | ||
0.958076 | − | 0.286513i | \(-0.0924963\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 586.236i | − | 0.768330i | ||||||
\(764\) | − | 247.361i | − | 0.323771i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 252.126 | 0.329147 | ||||||||
\(767\) | 96.6913 | 0.126064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1432.72 | 1.86310 | 0.931551 | − | 0.363612i | \(-0.118456\pi\) | ||||
0.931551 | + | 0.363612i | \(0.118456\pi\) | |||||||
\(770\) | −250.684 | − | 247.074i | −0.325563 | − | 0.320875i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 89.5776i | 0.116033i | ||||||||
\(773\) | 1341.08 | 1.73490 | 0.867449 | − | 0.497526i | \(-0.165758\pi\) | ||||
0.867449 | + | 0.497526i | \(0.165758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.72570 | + | 463.630i | 0.00867832 | + | 0.598233i | ||||
\(776\) | 211.690i | 0.272796i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 521.718i | − | 0.670589i | ||||||
\(779\) | 1408.39i | 1.80794i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −627.041 | −0.802869 | ||||||||
\(782\) | −952.342 | −1.21783 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 155.557 | 0.198414 | ||||||||
\(785\) | −538.339 | + | 546.205i | −0.685782 | + | 0.695803i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1048.34i | − | 1.33207i | −0.745921 | − | 0.666034i | \(-0.767991\pi\) | ||
0.745921 | − | 0.666034i | \(-0.232009\pi\) | |||||||
\(788\) | −406.543 | −0.515917 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 456.175 | + | 449.606i | 0.577437 | + | 0.569121i | ||||
\(791\) | 54.5489i | 0.0689620i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.0141i | − | 0.0189333i | ||||||
\(794\) | − | 736.326i | − | 0.927363i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −155.192 | −0.194964 | ||||||||
\(797\) | 1327.16 | 1.66519 | 0.832594 | − | 0.553883i | \(-0.186855\pi\) | ||||
0.832594 | + | 0.553883i | \(0.186855\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1682.61 | 2.10590 | ||||||||
\(800\) | −2.05133 | − | 141.406i | −0.00256416 | − | 0.176758i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 0.457137i | − | 0.000569996i | ||||||
\(803\) | 1356.57 | 1.68938 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 320.132 | − | 324.810i | 0.397680 | − | 0.403490i | ||||
\(806\) | 35.0417i | 0.0434761i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 47.9616i | − | 0.0593584i | ||||||
\(809\) | 976.178i | 1.20665i | 0.797496 | + | 0.603324i | \(0.206157\pi\) | ||||
−0.797496 | + | 0.603324i | \(0.793843\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −289.065 | −0.356431 | −0.178215 | − | 0.983991i | \(-0.557032\pi\) | ||||
−0.178215 | + | 0.983991i | \(0.557032\pi\) | |||||||
\(812\) | 210.877 | 0.259701 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 87.5679 | 0.107577 | ||||||||
\(815\) | 954.890 | − | 968.842i | 1.17164 | − | 1.18876i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.1255i | 0.0809369i | ||||||||
\(818\) | −13.4750 | −0.0164731 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 423.493 | − | 429.681i | 0.516455 | − | 0.524001i | ||||
\(821\) | − | 238.422i | − | 0.290405i | −0.989402 | − | 0.145202i | \(-0.953617\pi\) | ||
0.989402 | − | 0.145202i | \(-0.0463833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 421.581i | 0.512249i | 0.966644 | + | 0.256125i | \(0.0824458\pi\) | ||||
−0.966644 | + | 0.256125i | \(0.917554\pi\) | |||||||
\(824\) | 298.832i | 0.362660i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 325.465 | 0.394025 | ||||||||
\(827\) | 944.973 | 1.14265 | 0.571326 | − | 0.820723i | \(-0.306429\pi\) | ||||
0.571326 | + | 0.820723i | \(0.306429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −609.872 | −0.735672 | −0.367836 | − | 0.929891i | \(-0.619901\pi\) | ||||
−0.367836 | + | 0.929891i | \(0.619901\pi\) | |||||||
\(830\) | 518.179 | + | 510.717i | 0.624312 | + | 0.615321i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 10.6877i | − | 0.0128457i | ||||||
\(833\) | −912.963 | −1.09599 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −570.391 | − | 562.176i | −0.683103 | − | 0.673265i | ||||
\(836\) | 730.891i | 0.874272i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 552.724i | 0.659575i | ||||||||
\(839\) | 66.6016i | 0.0793821i | 0.999212 | + | 0.0396911i | \(0.0126374\pi\) | ||||
−0.999212 | + | 0.0396911i | \(0.987363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −258.539 | −0.307418 | ||||||||
\(842\) | −604.833 | −0.718329 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −264.660 | −0.313578 | ||||||||
\(845\) | 595.467 | + | 586.892i | 0.704695 | + | 0.694546i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 394.476i | − | 0.465733i | ||||||
\(848\) | 57.3861 | 0.0676723 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0393 | + | 829.916i | 0.0141638 | + | 0.976372i | ||||
\(851\) | 113.461i | 0.133327i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 361.920i | 0.424291i | 0.977238 | + | 0.212145i | \(0.0680451\pi\) | ||||
−0.977238 | + | 0.212145i | \(0.931955\pi\) | |||||||
\(854\) | − | 50.5378i | − | 0.0591778i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −166.356 | −0.194342 | ||||||||
\(857\) | 1035.43 | 1.20821 | 0.604103 | − | 0.796906i | \(-0.293532\pi\) | ||||
0.604103 | + | 0.796906i | \(0.293532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 251.841 | 0.293180 | 0.146590 | − | 0.989197i | \(-0.453170\pi\) | ||||
0.146590 | + | 0.989197i | \(0.453170\pi\) | |||||||
\(860\) | 19.8835 | − | 20.1740i | 0.0231204 | − | 0.0234582i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 560.461i | 0.650187i | ||||||||
\(863\) | −872.334 | −1.01082 | −0.505408 | − | 0.862881i | \(-0.668658\pi\) | ||||
−0.505408 | + | 0.862881i | \(0.668658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −108.321 | − | 106.761i | −0.125226 | − | 0.123423i | ||||
\(866\) | 990.970i | 1.14431i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 117.951i | 0.135888i | ||||||||
\(869\) | 1417.98i | 1.63173i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.48137 | 0.00514509 | ||||||||
\(872\) | 521.462 | 0.598007 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −947.012 | −1.08354 | ||||||||
\(875\) | −287.102 | − | 274.872i | −0.328116 | − | 0.314140i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1468.28i | − | 1.67421i | −0.547044 | − | 0.837104i | \(-0.684247\pi\) | ||
0.547044 | − | 0.837104i | \(-0.315753\pi\) | |||||||
\(878\) | 134.605 | 0.153308 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 219.774 | − | 222.986i | 0.249744 | − | 0.253393i | ||||
\(881\) | 727.513i | 0.825781i | 0.910781 | + | 0.412891i | \(0.135481\pi\) | ||||
−0.910781 | + | 0.412891i | \(0.864519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 384.077i | − | 0.434968i | −0.976064 | − | 0.217484i | \(-0.930215\pi\) | ||
0.976064 | − | 0.217484i | \(-0.0697850\pi\) | |||||||
\(884\) | 62.7260i | 0.0709571i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 336.138 | 0.379388 | ||||||||
\(887\) | −464.833 | −0.524051 | −0.262026 | − | 0.965061i | \(-0.584391\pi\) | ||||
−0.262026 | + | 0.965061i | \(0.584391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −56.7767 | −0.0638658 | ||||||||
\(890\) | −717.037 | + | 727.514i | −0.805660 | + | 0.817432i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 698.365i | − | 0.782921i | ||||||
\(893\) | 1673.20 | 1.87368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −918.546 | + | 931.968i | −1.02631 | + | 1.04131i | ||||
\(896\) | − | 35.9749i | − | 0.0401505i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 813.141i | − | 0.905503i | ||||||
\(899\) | − | 615.011i | − | 0.684105i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −336.800 | −0.373807 | ||||||||
\(902\) | 1335.62 | 1.48073 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48.5218 | −0.0536746 | ||||||||
\(905\) | −563.217 | − | 555.106i | −0.622339 | − | 0.613376i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 246.427i | − | 0.271695i | −0.990730 | − | 0.135847i | \(-0.956624\pi\) | ||
0.990730 | − | 0.135847i | \(-0.0433757\pi\) | |||||||
\(908\) | 436.668 | 0.480912 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −21.3936 | − | 21.0855i | −0.0235095 | − | 0.0231709i | ||||
\(911\) | − | 144.890i | − | 0.159045i | −0.996833 | − | 0.0795224i | \(-0.974660\pi\) | ||
0.996833 | − | 0.0795224i | \(-0.0253395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1610.71i | 1.76420i | ||||||||
\(914\) | − | 781.549i | − | 0.855086i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 760.912 | 0.830690 | ||||||||
\(917\) | 676.725 | 0.737977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1421.82 | −1.54714 | −0.773569 | − | 0.633712i | \(-0.781530\pi\) | ||||
−0.773569 | + | 0.633712i | \(0.781530\pi\) | |||||||
\(920\) | 288.921 | + | 284.761i | 0.314045 | + | 0.309522i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1065.64i | 1.15579i | ||||||||
\(923\) | −53.5123 | −0.0579765 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 98.8757 | − | 1.43435i | 0.106893 | − | 0.00155065i | ||||
\(926\) | − | 557.139i | − | 0.601662i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 187.577i | 0.202131i | ||||||||
\(929\) | − | 547.295i | − | 0.589123i | −0.955632 | − | 0.294562i | \(-0.904826\pi\) | ||
0.955632 | − | 0.294562i | \(-0.0951736\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −907.854 | −0.975139 | ||||||||
\(932\) | 465.983 | 0.499981 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −203.776 | −0.218175 | ||||||||
\(935\) | −1289.86 | + | 1308.71i | −1.37953 | + | 1.39969i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1384.47i | − | 1.47756i | −0.673948 | − | 0.738779i | \(-0.735403\pi\) | ||
0.673948 | − | 0.738779i | \(-0.264597\pi\) | |||||||
\(938\) | 15.0844 | 0.0160814 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −510.471 | − | 503.119i | −0.543054 | − | 0.535233i | ||||
\(941\) | 701.042i | 0.744996i | 0.928033 | + | 0.372498i | \(0.121499\pi\) | ||||
−0.928033 | + | 0.372498i | \(0.878501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1730.56i | 1.83516i | ||||||||
\(944\) | 289.504i | 0.306678i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 62.7091 | 0.0662887 | ||||||||
\(947\) | 655.997 | 0.692711 | 0.346355 | − | 0.938103i | \(-0.387419\pi\) | ||||
0.346355 | + | 0.938103i | \(0.387419\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 115.771 | 0.121993 | ||||||||
\(950\) | 11.9719 | + | 825.272i | 0.0126020 | + | 0.868708i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 211.137i | 0.221783i | ||||||||
\(953\) | 290.181 | 0.304492 | 0.152246 | − | 0.988343i | \(-0.451349\pi\) | ||||
0.152246 | + | 0.988343i | \(0.451349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 434.094 | − | 440.437i | 0.454548 | − | 0.461190i | ||||
\(956\) | 314.985i | 0.329482i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 226.582i | 0.236516i | ||||||||
\(959\) | 628.154i | 0.655009i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −617.003 | −0.642042 | ||||||||
\(962\) | 7.47314 | 0.00776834 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −230.302 | −0.238903 | ||||||||
\(965\) | −157.200 | + | 159.497i | −0.162901 | + | 0.165281i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1037.15i | − | 1.07254i | −0.844047 | − | 0.536270i | \(-0.819833\pi\) | ||
0.844047 | − | 0.536270i | \(-0.180167\pi\) | |||||||
\(968\) | 350.890 | 0.362490 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −371.494 | + | 376.923i | −0.382984 | + | 0.388580i | ||||
\(971\) | 1762.50i | 1.81514i | 0.419901 | + | 0.907570i | \(0.362065\pi\) | ||||
−0.419901 | + | 0.907570i | \(0.637935\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 163.993i | − | 0.168544i | ||||||
\(974\) | − | 260.907i | − | 0.267871i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 44.9539 | 0.0460593 | ||||||||
\(977\) | 1771.34 | 1.81304 | 0.906519 | − | 0.422165i | \(-0.138730\pi\) | ||||
0.906519 | + | 0.422165i | \(0.138730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2261.41 | −2.30992 | ||||||||
\(980\) | 276.975 | + | 272.986i | 0.282627 | + | 0.278557i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 117.864i | − | 0.120024i | ||||||
\(983\) | −1525.11 | −1.55149 | −0.775745 | − | 0.631047i | \(-0.782626\pi\) | ||||
−0.775745 | + | 0.631047i | \(0.782626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −723.867 | − | 713.442i | −0.734890 | − | 0.724306i | ||||
\(986\) | − | 1100.89i | − | 1.11652i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 62.3750i | 0.0631326i | ||||||||
\(989\) | 81.2519i | 0.0821556i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −296.858 | −0.299554 | −0.149777 | − | 0.988720i | \(-0.547856\pi\) | ||||
−0.149777 | + | 0.988720i | \(0.547856\pi\) | |||||||
\(992\) | −104.919 | −0.105765 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −180.123 | −0.181211 | ||||||||
\(995\) | −276.325 | − | 272.346i | −0.277714 | − | 0.273714i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1318.45i | − | 1.32242i | −0.750203 | − | 0.661208i | \(-0.770044\pi\) | ||
0.750203 | − | 0.661208i | \(-0.229956\pi\) | |||||||
\(998\) | 569.662 | 0.570803 | ||||||||
\(999\) | 0 | 0 |
(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 | 810.3.b.b.809.6 | 16 | ||
3.2 | odd | 2 | inner | 810.3.b.b.809.11 | 16 | ||
5.4 | even | 2 | inner | 810.3.b.b.809.12 | 16 | ||
9.2 | odd | 6 | 90.3.j.b.59.1 | yes | 16 | ||
9.4 | even | 3 | 90.3.j.b.29.8 | yes | 16 | ||
9.5 | odd | 6 | 270.3.j.b.89.3 | 16 | |||
9.7 | even | 3 | 270.3.j.b.179.5 | 16 | |||
15.14 | odd | 2 | inner | 810.3.b.b.809.5 | 16 | ||
45.2 | even | 12 | 450.3.i.e.401.7 | 16 | |||
45.4 | even | 6 | 90.3.j.b.29.1 | ✓ | 16 | ||
45.7 | odd | 12 | 1350.3.i.e.1151.3 | 16 | |||
45.13 | odd | 12 | 450.3.i.e.101.2 | 16 | |||
45.14 | odd | 6 | 270.3.j.b.89.5 | 16 | |||
45.22 | odd | 12 | 450.3.i.e.101.7 | 16 | |||
45.23 | even | 12 | 1350.3.i.e.251.6 | 16 | |||
45.29 | odd | 6 | 90.3.j.b.59.8 | yes | 16 | ||
45.32 | even | 12 | 1350.3.i.e.251.3 | 16 | |||
45.34 | even | 6 | 270.3.j.b.179.3 | 16 | |||
45.38 | even | 12 | 450.3.i.e.401.2 | 16 | |||
45.43 | odd | 12 | 1350.3.i.e.1151.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.3.j.b.29.1 | ✓ | 16 | 45.4 | even | 6 | ||
90.3.j.b.29.8 | yes | 16 | 9.4 | even | 3 | ||
90.3.j.b.59.1 | yes | 16 | 9.2 | odd | 6 | ||
90.3.j.b.59.8 | yes | 16 | 45.29 | odd | 6 | ||
270.3.j.b.89.3 | 16 | 9.5 | odd | 6 | |||
270.3.j.b.89.5 | 16 | 45.14 | odd | 6 | |||
270.3.j.b.179.3 | 16 | 45.34 | even | 6 | |||
270.3.j.b.179.5 | 16 | 9.7 | even | 3 | |||
450.3.i.e.101.2 | 16 | 45.13 | odd | 12 | |||
450.3.i.e.101.7 | 16 | 45.22 | odd | 12 | |||
450.3.i.e.401.2 | 16 | 45.38 | even | 12 | |||
450.3.i.e.401.7 | 16 | 45.2 | even | 12 | |||
810.3.b.b.809.5 | 16 | 15.14 | odd | 2 | inner | ||
810.3.b.b.809.6 | 16 | 1.1 | even | 1 | trivial | ||
810.3.b.b.809.11 | 16 | 3.2 | odd | 2 | inner | ||
810.3.b.b.809.12 | 16 | 5.4 | even | 2 | inner | ||
1350.3.i.e.251.3 | 16 | 45.32 | even | 12 | |||
1350.3.i.e.251.6 | 16 | 45.23 | even | 12 | |||
1350.3.i.e.1151.3 | 16 | 45.7 | odd | 12 | |||
1350.3.i.e.1151.6 | 16 | 45.43 | odd | 12 |