Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 185x^{10} + 12748x^{8} + 405460x^{6} + 5908496x^{4} + 33016000x^{2} + 60840000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.5 | ||
Root | \(5.49484i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.e.99.8 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00000i | − | 0.707107i | ||||||
\(3\) | 4.49484i | 0.865032i | 0.901626 | + | 0.432516i | \(0.142374\pi\) | ||||
−0.901626 | + | 0.432516i | \(0.857626\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | 3.34202 | + | 10.6692i | 0.298919 | + | 0.954278i | ||||
\(6\) | 8.98967 | 0.611670 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000i | 0.353553i | ||||||||
\(9\) | 6.79645 | 0.251720 | ||||||||
\(10\) | 21.3383 | − | 6.68404i | 0.674777 | − | 0.211368i | ||||
\(11\) | 13.9329 | 0.381902 | 0.190951 | − | 0.981600i | \(-0.438843\pi\) | ||||
0.190951 | + | 0.981600i | \(0.438843\pi\) | |||||||
\(12\) | − | 17.9793i | − | 0.432516i | ||||||
\(13\) | − | 78.0096i | − | 1.66431i | −0.554546 | − | 0.832153i | \(-0.687108\pi\) | ||
0.554546 | − | 0.832153i | \(-0.312892\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −47.9561 | + | 15.0218i | −0.825481 | + | 0.258575i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 105.132i | − | 1.49990i | −0.661492 | − | 0.749952i | \(-0.730077\pi\) | ||
0.661492 | − | 0.749952i | \(-0.269923\pi\) | |||||||
\(18\) | − | 13.5929i | − | 0.177993i | ||||||
\(19\) | 152.300 | 1.83895 | 0.919477 | − | 0.393144i | \(-0.128613\pi\) | ||||
0.919477 | + | 0.393144i | \(0.128613\pi\) | |||||||
\(20\) | −13.3681 | − | 42.6766i | −0.149460 | − | 0.477139i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 27.8658i | − | 0.270046i | ||||||
\(23\) | 108.116i | 0.980161i | 0.871677 | + | 0.490081i | \(0.163033\pi\) | ||||
−0.871677 | + | 0.490081i | \(0.836967\pi\) | |||||||
\(24\) | −35.9587 | −0.305835 | ||||||||
\(25\) | −102.662 | + | 71.3130i | −0.821295 | + | 0.570504i | ||||
\(26\) | −156.019 | −1.17684 | ||||||||
\(27\) | 151.909i | 1.08278i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 109.323 | 0.700023 | 0.350012 | − | 0.936745i | \(-0.386178\pi\) | ||||
0.350012 | + | 0.936745i | \(0.386178\pi\) | |||||||
\(30\) | 30.0436 | + | 95.9122i | 0.182840 | + | 0.583703i | ||||
\(31\) | 197.196 | 1.14250 | 0.571249 | − | 0.820777i | \(-0.306459\pi\) | ||||
0.571249 | + | 0.820777i | \(0.306459\pi\) | |||||||
\(32\) | − | 32.0000i | − | 0.176777i | ||||||
\(33\) | 62.6261i | 0.330358i | ||||||||
\(34\) | −210.265 | −1.06059 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −27.1858 | −0.125860 | ||||||||
\(37\) | 254.290i | 1.12986i | 0.825137 | + | 0.564932i | \(0.191098\pi\) | ||||
−0.825137 | + | 0.564932i | \(0.808902\pi\) | |||||||
\(38\) | − | 304.601i | − | 1.30034i | ||||||
\(39\) | 350.641 | 1.43968 | ||||||||
\(40\) | −85.3533 | + | 26.7361i | −0.337388 | + | 0.105684i | ||||
\(41\) | −193.905 | −0.738606 | −0.369303 | − | 0.929309i | \(-0.620404\pi\) | ||||
−0.369303 | + | 0.929309i | \(0.620404\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.5329i | 0.147295i | 0.997284 | + | 0.0736477i | \(0.0234640\pi\) | ||||
−0.997284 | + | 0.0736477i | \(0.976536\pi\) | |||||||
\(44\) | −55.7316 | −0.190951 | ||||||||
\(45\) | 22.7139 | + | 72.5124i | 0.0752440 | + | 0.240211i | ||||
\(46\) | 216.232 | 0.693079 | ||||||||
\(47\) | 109.886i | 0.341032i | 0.985355 | + | 0.170516i | \(0.0545434\pi\) | ||||
−0.985355 | + | 0.170516i | \(0.945457\pi\) | |||||||
\(48\) | 71.9174i | 0.216258i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 142.626 | + | 205.324i | 0.403407 | + | 0.580743i | ||||
\(51\) | 472.553 | 1.29746 | ||||||||
\(52\) | 312.039i | 0.832153i | ||||||||
\(53\) | − | 11.0054i | − | 0.0285228i | −0.999898 | − | 0.0142614i | \(-0.995460\pi\) | ||
0.999898 | − | 0.0142614i | \(-0.00453969\pi\) | |||||||
\(54\) | 303.819 | 0.765639 | ||||||||
\(55\) | 46.5640 | + | 148.652i | 0.114158 | + | 0.364441i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 684.566i | 1.59075i | ||||||||
\(58\) | − | 218.645i | − | 0.494991i | ||||||
\(59\) | 192.141 | 0.423978 | 0.211989 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211989 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(60\) | 191.824 | − | 60.0873i | 0.412741 | − | 0.129287i | ||||
\(61\) | 34.9035 | 0.0732611 | 0.0366306 | − | 0.999329i | \(-0.488338\pi\) | ||||
0.0366306 | + | 0.999329i | \(0.488338\pi\) | |||||||
\(62\) | − | 394.392i | − | 0.807868i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 832.297 | − | 260.710i | 1.58821 | − | 0.497493i | ||||
\(66\) | 125.252 | 0.233598 | ||||||||
\(67\) | 374.830i | 0.683474i | 0.939796 | + | 0.341737i | \(0.111015\pi\) | ||||
−0.939796 | + | 0.341737i | \(0.888985\pi\) | |||||||
\(68\) | 420.530i | 0.749952i | ||||||||
\(69\) | −485.963 | −0.847870 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −575.722 | −0.962333 | −0.481167 | − | 0.876629i | \(-0.659787\pi\) | ||||
−0.481167 | + | 0.876629i | \(0.659787\pi\) | |||||||
\(72\) | 54.3716i | 0.0889966i | ||||||||
\(73\) | 522.161i | 0.837182i | 0.908175 | + | 0.418591i | \(0.137476\pi\) | ||||
−0.908175 | + | 0.418591i | \(0.862524\pi\) | |||||||
\(74\) | 508.580 | 0.798935 | ||||||||
\(75\) | −320.540 | − | 461.448i | −0.493504 | − | 0.710446i | ||||
\(76\) | −609.202 | −0.919477 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 701.281i | − | 1.01801i | ||||||
\(79\) | 456.182 | 0.649676 | 0.324838 | − | 0.945770i | \(-0.394690\pi\) | ||||
0.324838 | + | 0.945770i | \(0.394690\pi\) | |||||||
\(80\) | 53.4723 | + | 170.707i | 0.0747298 | + | 0.238570i | ||||
\(81\) | −499.304 | −0.684917 | ||||||||
\(82\) | 387.810i | 0.522273i | ||||||||
\(83\) | − | 773.057i | − | 1.02234i | −0.859480 | − | 0.511169i | \(-0.829213\pi\) | ||
0.859480 | − | 0.511169i | \(-0.170787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1121.67 | − | 351.355i | 1.43133 | − | 0.448350i | ||||
\(86\) | 83.0657 | 0.104154 | ||||||||
\(87\) | 491.387i | 0.605542i | ||||||||
\(88\) | 111.463i | 0.135023i | ||||||||
\(89\) | 1329.07 | 1.58294 | 0.791470 | − | 0.611208i | \(-0.209316\pi\) | ||||
0.791470 | + | 0.611208i | \(0.209316\pi\) | |||||||
\(90\) | 145.025 | − | 45.4277i | 0.169855 | − | 0.0532056i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 432.463i | − | 0.490081i | ||||||
\(93\) | 886.364i | 0.988297i | ||||||||
\(94\) | 219.772 | 0.241146 | ||||||||
\(95\) | 508.991 | + | 1624.92i | 0.549699 | + | 1.75487i | ||||
\(96\) | 143.835 | 0.152917 | ||||||||
\(97\) | 1038.18i | 1.08671i | 0.839503 | + | 0.543356i | \(0.182847\pi\) | ||||
−0.839503 | + | 0.543356i | \(0.817153\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 94.6942 | 0.0961325 | ||||||||
\(100\) | 410.647 | − | 285.252i | 0.410647 | − | 0.285252i | ||||
\(101\) | 489.559 | 0.482307 | 0.241153 | − | 0.970487i | \(-0.422474\pi\) | ||||
0.241153 | + | 0.970487i | \(0.422474\pi\) | |||||||
\(102\) | − | 945.107i | − | 0.917446i | ||||||
\(103\) | − | 1185.15i | − | 1.13375i | −0.823802 | − | 0.566877i | \(-0.808151\pi\) | ||
0.823802 | − | 0.566877i | \(-0.191849\pi\) | |||||||
\(104\) | 624.077 | 0.588421 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −22.0108 | −0.0201686 | ||||||||
\(107\) | − | 1192.49i | − | 1.07741i | −0.842496 | − | 0.538703i | \(-0.818915\pi\) | ||
0.842496 | − | 0.538703i | \(-0.181085\pi\) | |||||||
\(108\) | − | 607.638i | − | 0.541389i | ||||||
\(109\) | 285.431 | 0.250820 | 0.125410 | − | 0.992105i | \(-0.459975\pi\) | ||||
0.125410 | + | 0.992105i | \(0.459975\pi\) | |||||||
\(110\) | 297.304 | − | 93.1280i | 0.257699 | − | 0.0807218i | ||||
\(111\) | −1142.99 | −0.977369 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 350.019i | 0.291389i | 0.989330 | + | 0.145695i | \(0.0465417\pi\) | ||||
−0.989330 | + | 0.145695i | \(0.953458\pi\) | |||||||
\(114\) | 1369.13 | 1.12483 | ||||||||
\(115\) | −1153.50 | + | 361.325i | −0.935347 | + | 0.292989i | ||||
\(116\) | −437.290 | −0.350012 | ||||||||
\(117\) | − | 530.188i | − | 0.418940i | ||||||
\(118\) | − | 384.283i | − | 0.299798i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −120.175 | − | 383.649i | −0.0914199 | − | 0.291852i | ||||
\(121\) | −1136.87 | −0.854151 | ||||||||
\(122\) | − | 69.8069i | − | 0.0518034i | ||||||
\(123\) | − | 871.570i | − | 0.638917i | ||||||
\(124\) | −788.784 | −0.571249 | ||||||||
\(125\) | −1103.95 | − | 856.986i | −0.789921 | − | 0.613209i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1112.45i | − | 0.777274i | −0.921391 | − | 0.388637i | \(-0.872946\pi\) | ||
0.921391 | − | 0.388637i | \(-0.127054\pi\) | |||||||
\(128\) | 128.000i | 0.0883883i | ||||||||
\(129\) | −186.683 | −0.127415 | ||||||||
\(130\) | −521.419 | − | 1664.59i | −0.351781 | − | 1.12304i | ||||
\(131\) | −605.974 | −0.404154 | −0.202077 | − | 0.979370i | \(-0.564769\pi\) | ||||
−0.202077 | + | 0.979370i | \(0.564769\pi\) | |||||||
\(132\) | − | 250.504i | − | 0.165179i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 749.659 | 0.483289 | ||||||||
\(135\) | −1620.75 | + | 507.684i | −1.03327 | + | 0.323663i | ||||
\(136\) | 841.060 | 0.530296 | ||||||||
\(137\) | 403.891i | 0.251874i | 0.992038 | + | 0.125937i | \(0.0401938\pi\) | ||||
−0.992038 | + | 0.125937i | \(0.959806\pi\) | |||||||
\(138\) | 971.926i | 0.599535i | ||||||||
\(139\) | 525.532 | 0.320683 | 0.160342 | − | 0.987062i | \(-0.448740\pi\) | ||||
0.160342 | + | 0.987062i | \(0.448740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −493.918 | −0.295003 | ||||||||
\(142\) | 1151.44i | 0.680472i | ||||||||
\(143\) | − | 1086.90i | − | 0.635602i | ||||||
\(144\) | 108.743 | 0.0629301 | ||||||||
\(145\) | 365.358 | + | 1166.38i | 0.209250 | + | 0.668017i | ||||
\(146\) | 1044.32 | 0.591977 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1017.16i | − | 0.564932i | ||||||
\(149\) | 2034.87 | 1.11881 | 0.559407 | − | 0.828893i | \(-0.311029\pi\) | ||||
0.559407 | + | 0.828893i | \(0.311029\pi\) | |||||||
\(150\) | −922.896 | + | 641.081i | −0.502361 | + | 0.348960i | ||||
\(151\) | 1748.70 | 0.942430 | 0.471215 | − | 0.882018i | \(-0.343816\pi\) | ||||
0.471215 | + | 0.882018i | \(0.343816\pi\) | |||||||
\(152\) | 1218.40i | 0.650168i | ||||||||
\(153\) | − | 714.527i | − | 0.377556i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 659.033 | + | 2103.91i | 0.341515 | + | 1.09026i | ||||
\(156\) | −1402.56 | −0.719839 | ||||||||
\(157\) | 448.507i | 0.227992i | 0.993481 | + | 0.113996i | \(0.0363651\pi\) | ||||
−0.993481 | + | 0.113996i | \(0.963635\pi\) | |||||||
\(158\) | − | 912.363i | − | 0.459391i | ||||||
\(159\) | 49.4674 | 0.0246731 | ||||||||
\(160\) | 341.413 | − | 106.945i | 0.168694 | − | 0.0528419i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 998.608i | 0.484309i | ||||||||
\(163\) | 911.681i | 0.438088i | 0.975715 | + | 0.219044i | \(0.0702939\pi\) | ||||
−0.975715 | + | 0.219044i | \(0.929706\pi\) | |||||||
\(164\) | 775.619 | 0.369303 | ||||||||
\(165\) | −668.167 | + | 209.297i | −0.315253 | + | 0.0987502i | ||||
\(166\) | −1546.11 | −0.722902 | ||||||||
\(167\) | 1131.12i | 0.524125i | 0.965051 | + | 0.262063i | \(0.0844027\pi\) | ||||
−0.965051 | + | 0.262063i | \(0.915597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3888.51 | −1.76992 | ||||||||
\(170\) | −702.709 | − | 2243.35i | −0.317031 | − | 1.01210i | ||||
\(171\) | 1035.10 | 0.462902 | ||||||||
\(172\) | − | 166.131i | − | 0.0736477i | ||||||
\(173\) | − | 2138.58i | − | 0.939844i | −0.882708 | − | 0.469922i | \(-0.844282\pi\) | ||
0.882708 | − | 0.469922i | \(-0.155718\pi\) | |||||||
\(174\) | 982.773 | 0.428183 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 222.926 | 0.0954756 | ||||||||
\(177\) | 863.644i | 0.366754i | ||||||||
\(178\) | − | 2658.15i | − | 1.11931i | ||||||
\(179\) | −1739.07 | −0.726170 | −0.363085 | − | 0.931756i | \(-0.618276\pi\) | ||||
−0.363085 | + | 0.931756i | \(0.618276\pi\) | |||||||
\(180\) | −90.8554 | − | 290.049i | −0.0376220 | − | 0.120106i | ||||
\(181\) | 2304.17 | 0.946231 | 0.473115 | − | 0.881001i | \(-0.343129\pi\) | ||||
0.473115 | + | 0.881001i | \(0.343129\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 156.885i | 0.0633732i | ||||||||
\(184\) | −864.927 | −0.346539 | ||||||||
\(185\) | −2713.06 | + | 849.841i | −1.07821 | + | 0.337738i | ||||
\(186\) | 1772.73 | 0.698832 | ||||||||
\(187\) | − | 1464.80i | − | 0.572817i | ||||||
\(188\) | − | 439.543i | − | 0.170516i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3249.84 | − | 1017.98i | 1.24088 | − | 0.388696i | ||||
\(191\) | −3611.07 | −1.36800 | −0.684000 | − | 0.729482i | \(-0.739761\pi\) | ||||
−0.684000 | + | 0.729482i | \(0.739761\pi\) | |||||||
\(192\) | − | 287.670i | − | 0.108129i | ||||||
\(193\) | 4340.90i | 1.61899i | 0.587128 | + | 0.809494i | \(0.300259\pi\) | ||||
−0.587128 | + | 0.809494i | \(0.699741\pi\) | |||||||
\(194\) | 2076.36 | 0.768421 | ||||||||
\(195\) | 1171.85 | + | 3741.04i | 0.430347 | + | 1.37385i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 380.943i | 0.137772i | 0.997625 | + | 0.0688859i | \(0.0219444\pi\) | ||||
−0.997625 | + | 0.0688859i | \(0.978056\pi\) | |||||||
\(198\) | − | 189.388i | − | 0.0679760i | ||||||
\(199\) | 3476.70 | 1.23848 | 0.619238 | − | 0.785203i | \(-0.287441\pi\) | ||||
0.619238 | + | 0.785203i | \(0.287441\pi\) | |||||||
\(200\) | −570.504 | − | 821.295i | −0.201704 | − | 0.290372i | ||||
\(201\) | −1684.80 | −0.591226 | ||||||||
\(202\) | − | 979.119i | − | 0.341042i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1890.21 | −0.648732 | ||||||||
\(205\) | −648.033 | − | 2068.80i | −0.220783 | − | 0.704836i | ||||
\(206\) | −2370.31 | −0.801685 | ||||||||
\(207\) | 734.804i | 0.246726i | ||||||||
\(208\) | − | 1248.15i | − | 0.416077i | ||||||
\(209\) | 2121.99 | 0.702301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1693.38 | 0.552497 | 0.276248 | − | 0.961086i | \(-0.410909\pi\) | ||||
0.276248 | + | 0.961086i | \(0.410909\pi\) | |||||||
\(212\) | 44.0216i | 0.0142614i | ||||||||
\(213\) | − | 2587.78i | − | 0.832449i | ||||||
\(214\) | −2384.98 | −0.761841 | ||||||||
\(215\) | −443.121 | + | 138.804i | −0.140561 | + | 0.0440294i | ||||
\(216\) | −1215.28 | −0.382820 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 570.862i | − | 0.177356i | ||||||
\(219\) | −2347.03 | −0.724189 | ||||||||
\(220\) | −186.256 | − | 594.609i | −0.0570790 | − | 0.182221i | ||||
\(221\) | −8201.35 | −2.49630 | ||||||||
\(222\) | 2285.98i | 0.691104i | ||||||||
\(223\) | 260.918i | 0.0783514i | 0.999232 | + | 0.0391757i | \(0.0124732\pi\) | ||||
−0.999232 | + | 0.0391757i | \(0.987527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −697.736 | + | 484.675i | −0.206737 | + | 0.143607i | ||||
\(226\) | 700.038 | 0.206043 | ||||||||
\(227\) | 279.657i | 0.0817688i | 0.999164 | + | 0.0408844i | \(0.0130175\pi\) | ||||
−0.999164 | + | 0.0408844i | \(0.986982\pi\) | |||||||
\(228\) | − | 2738.26i | − | 0.795377i | ||||||
\(229\) | −1722.39 | −0.497024 | −0.248512 | − | 0.968629i | \(-0.579942\pi\) | ||||
−0.248512 | + | 0.968629i | \(0.579942\pi\) | |||||||
\(230\) | 722.650 | + | 2307.01i | 0.207175 | + | 0.661390i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 874.580i | 0.247496i | ||||||||
\(233\) | 6659.62i | 1.87247i | 0.351370 | + | 0.936237i | \(0.385716\pi\) | ||||
−0.351370 | + | 0.936237i | \(0.614284\pi\) | |||||||
\(234\) | −1060.38 | −0.296235 | ||||||||
\(235\) | −1172.39 | + | 367.240i | −0.325439 | + | 0.101941i | ||||
\(236\) | −768.566 | −0.211989 | ||||||||
\(237\) | 2050.46i | 0.561991i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1018.63 | −0.275688 | −0.137844 | − | 0.990454i | \(-0.544017\pi\) | ||||
−0.137844 | + | 0.990454i | \(0.544017\pi\) | |||||||
\(240\) | −767.298 | + | 240.349i | −0.206370 | + | 0.0646436i | ||||
\(241\) | −5853.84 | −1.56464 | −0.782322 | − | 0.622875i | \(-0.785965\pi\) | ||||
−0.782322 | + | 0.622875i | \(0.785965\pi\) | |||||||
\(242\) | 2273.75i | 0.603976i | ||||||||
\(243\) | 1857.27i | 0.490303i | ||||||||
\(244\) | −139.614 | −0.0366306 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1743.14 | −0.451783 | ||||||||
\(247\) | − | 11880.9i | − | 3.06058i | ||||||
\(248\) | 1577.57i | 0.403934i | ||||||||
\(249\) | 3474.77 | 0.884355 | ||||||||
\(250\) | −1713.97 | + | 2207.90i | −0.433604 | + | 0.558558i | ||||
\(251\) | 1101.55 | 0.277008 | 0.138504 | − | 0.990362i | \(-0.455771\pi\) | ||||
0.138504 | + | 0.990362i | \(0.455771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1506.37i | 0.374326i | ||||||||
\(254\) | −2224.90 | −0.549616 | ||||||||
\(255\) | 1579.28 | + | 5041.74i | 0.387837 | + | 1.23814i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | − | 1442.47i | − | 0.350111i | −0.984559 | − | 0.175056i | \(-0.943989\pi\) | ||
0.984559 | − | 0.175056i | \(-0.0560105\pi\) | |||||||
\(258\) | 373.367i | 0.0900961i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3329.19 | + | 1042.84i | −0.794106 | + | 0.248747i | ||||
\(261\) | 743.005 | 0.176210 | ||||||||
\(262\) | 1211.95i | 0.285780i | ||||||||
\(263\) | − | 5430.39i | − | 1.27320i | −0.771194 | − | 0.636601i | \(-0.780340\pi\) | ||
0.771194 | − | 0.636601i | \(-0.219660\pi\) | |||||||
\(264\) | −501.009 | −0.116799 | ||||||||
\(265\) | 117.418 | − | 36.7802i | 0.0272187 | − | 0.00852600i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5973.97i | 1.36929i | ||||||||
\(268\) | − | 1499.32i | − | 0.341737i | ||||||
\(269\) | −5011.89 | −1.13599 | −0.567993 | − | 0.823033i | \(-0.692280\pi\) | ||||
−0.567993 | + | 0.823033i | \(0.692280\pi\) | |||||||
\(270\) | 1015.37 | + | 3241.49i | 0.228864 | + | 0.730633i | ||||
\(271\) | 3317.40 | 0.743607 | 0.371803 | − | 0.928311i | \(-0.378740\pi\) | ||||
0.371803 | + | 0.928311i | \(0.378740\pi\) | |||||||
\(272\) | − | 1682.12i | − | 0.374976i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 807.783 | 0.178102 | ||||||||
\(275\) | −1430.38 | + | 993.597i | −0.313654 | + | 0.217877i | ||||
\(276\) | 1943.85 | 0.423935 | ||||||||
\(277\) | − | 4160.35i | − | 0.902424i | −0.892417 | − | 0.451212i | \(-0.850992\pi\) | ||
0.892417 | − | 0.451212i | \(-0.149008\pi\) | |||||||
\(278\) | − | 1051.06i | − | 0.226757i | ||||||
\(279\) | 1340.23 | 0.287590 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2423.12 | −0.514418 | −0.257209 | − | 0.966356i | \(-0.582803\pi\) | ||||
−0.257209 | + | 0.966356i | \(0.582803\pi\) | |||||||
\(282\) | 987.837i | 0.208599i | ||||||||
\(283\) | − | 8370.14i | − | 1.75814i | −0.476695 | − | 0.879069i | \(-0.658165\pi\) | ||
0.476695 | − | 0.879069i | \(-0.341835\pi\) | |||||||
\(284\) | 2302.89 | 0.481167 | ||||||||
\(285\) | −7303.74 | + | 2287.83i | −1.51802 | + | 0.475507i | ||||
\(286\) | −2173.80 | −0.449439 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 217.486i | − | 0.0444983i | ||||||
\(289\) | −6139.84 | −1.24971 | ||||||||
\(290\) | 2332.76 | − | 730.716i | 0.472360 | − | 0.147962i | ||||
\(291\) | −4666.44 | −0.940040 | ||||||||
\(292\) | − | 2088.64i | − | 0.418591i | ||||||
\(293\) | − | 5292.21i | − | 1.05520i | −0.849492 | − | 0.527601i | \(-0.823092\pi\) | ||
0.849492 | − | 0.527601i | \(-0.176908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 642.140 | + | 2049.99i | 0.126735 | + | 0.404593i | ||||
\(296\) | −2034.32 | −0.399467 | ||||||||
\(297\) | 2116.54i | 0.413515i | ||||||||
\(298\) | − | 4069.75i | − | 0.791121i | ||||||
\(299\) | 8434.08 | 1.63129 | ||||||||
\(300\) | 1282.16 | + | 1845.79i | 0.246752 | + | 0.355223i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 3497.39i | − | 0.666398i | ||||||
\(303\) | 2200.49i | 0.417211i | ||||||||
\(304\) | 2436.81 | 0.459738 | ||||||||
\(305\) | 116.648 | + | 372.390i | 0.0218992 | + | 0.0699115i | ||||
\(306\) | −1429.05 | −0.266973 | ||||||||
\(307\) | 3852.07i | 0.716121i | 0.933698 | + | 0.358061i | \(0.116562\pi\) | ||||
−0.933698 | + | 0.358061i | \(0.883438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5327.07 | 0.980733 | ||||||||
\(310\) | 4207.83 | − | 1318.07i | 0.770931 | − | 0.241487i | ||||
\(311\) | 1092.48 | 0.199192 | 0.0995962 | − | 0.995028i | \(-0.468245\pi\) | ||||
0.0995962 | + | 0.995028i | \(0.468245\pi\) | |||||||
\(312\) | 2805.12i | 0.509003i | ||||||||
\(313\) | 1324.90i | 0.239257i | 0.992819 | + | 0.119629i | \(0.0381704\pi\) | ||||
−0.992819 | + | 0.119629i | \(0.961830\pi\) | |||||||
\(314\) | 897.014 | 0.161215 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1824.73 | −0.324838 | ||||||||
\(317\) | 4985.47i | 0.883319i | 0.897183 | + | 0.441659i | \(0.145610\pi\) | ||||
−0.897183 | + | 0.441659i | \(0.854390\pi\) | |||||||
\(318\) | − | 98.9349i | − | 0.0174465i | ||||||
\(319\) | 1523.18 | 0.267341 | ||||||||
\(320\) | −213.889 | − | 682.826i | −0.0373649 | − | 0.119285i | ||||
\(321\) | 5360.05 | 0.931990 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16011.7i | − | 2.75825i | ||||||
\(324\) | 1997.22 | 0.342458 | ||||||||
\(325\) | 5563.10 | + | 8008.61i | 0.949494 | + | 1.36689i | ||||
\(326\) | 1823.36 | 0.309775 | ||||||||
\(327\) | 1282.97i | 0.216967i | ||||||||
\(328\) | − | 1551.24i | − | 0.261137i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 418.595 | + | 1336.33i | 0.0698269 | + | 0.222918i | ||||
\(331\) | 10041.0 | 1.66738 | 0.833691 | − | 0.552231i | \(-0.186223\pi\) | ||||
0.833691 | + | 0.552231i | \(0.186223\pi\) | |||||||
\(332\) | 3092.23i | 0.511169i | ||||||||
\(333\) | 1728.27i | 0.284410i | ||||||||
\(334\) | 2262.25 | 0.370613 | ||||||||
\(335\) | −3999.12 | + | 1252.69i | −0.652224 | + | 0.204303i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7227.40i | − | 1.16825i | −0.811662 | − | 0.584127i | \(-0.801437\pi\) | ||
0.811662 | − | 0.584127i | \(-0.198563\pi\) | |||||||
\(338\) | 7777.01i | 1.25152i | ||||||||
\(339\) | −1573.28 | −0.252061 | ||||||||
\(340\) | −4486.70 | + | 1405.42i | −0.715663 | + | 0.224175i | ||||
\(341\) | 2747.51 | 0.436323 | ||||||||
\(342\) | − | 2070.20i | − | 0.327321i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −332.263 | −0.0520768 | ||||||||
\(345\) | −1624.10 | − | 5184.81i | −0.253445 | − | 0.809104i | ||||
\(346\) | −4277.16 | −0.664570 | ||||||||
\(347\) | 3425.67i | 0.529970i | 0.964252 | + | 0.264985i | \(0.0853671\pi\) | ||||
−0.964252 | + | 0.264985i | \(0.914633\pi\) | |||||||
\(348\) | − | 1965.55i | − | 0.302771i | ||||||
\(349\) | −7092.03 | −1.08776 | −0.543879 | − | 0.839164i | \(-0.683045\pi\) | ||||
−0.543879 | + | 0.839164i | \(0.683045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11850.4 | 1.80207 | ||||||||
\(352\) | − | 445.853i | − | 0.0675114i | ||||||
\(353\) | − | 11964.8i | − | 1.80402i | −0.431714 | − | 0.902011i | \(-0.642091\pi\) | ||
0.431714 | − | 0.902011i | \(-0.357909\pi\) | |||||||
\(354\) | 1727.29 | 0.259334 | ||||||||
\(355\) | −1924.07 | − | 6142.47i | −0.287660 | − | 0.918334i | ||||
\(356\) | −5316.30 | −0.791470 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3478.14i | 0.513479i | ||||||||
\(359\) | 1556.01 | 0.228755 | 0.114377 | − | 0.993437i | \(-0.463513\pi\) | ||||
0.114377 | + | 0.993437i | \(0.463513\pi\) | |||||||
\(360\) | −580.099 | + | 181.711i | −0.0849275 | + | 0.0266028i | ||||
\(361\) | 16336.4 | 2.38175 | ||||||||
\(362\) | − | 4608.34i | − | 0.669086i | ||||||
\(363\) | − | 5110.06i | − | 0.738867i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5571.02 | + | 1745.07i | −0.798905 | + | 0.250250i | ||||
\(366\) | 313.771 | 0.0448116 | ||||||||
\(367\) | − | 2418.56i | − | 0.343999i | −0.985097 | − | 0.172000i | \(-0.944977\pi\) | ||
0.985097 | − | 0.172000i | \(-0.0550228\pi\) | |||||||
\(368\) | 1729.85i | 0.245040i | ||||||||
\(369\) | −1317.86 | −0.185922 | ||||||||
\(370\) | 1699.68 | + | 5426.12i | 0.238817 | + | 0.762406i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 3545.45i | − | 0.494149i | ||||||
\(373\) | 2737.30i | 0.379979i | 0.981786 | + | 0.189989i | \(0.0608453\pi\) | ||||
−0.981786 | + | 0.189989i | \(0.939155\pi\) | |||||||
\(374\) | −2929.60 | −0.405043 | ||||||||
\(375\) | 3852.01 | − | 4962.06i | 0.530445 | − | 0.683306i | ||||
\(376\) | −879.086 | −0.120573 | ||||||||
\(377\) | − | 8528.21i | − | 1.16505i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3489.69 | −0.472964 | −0.236482 | − | 0.971636i | \(-0.575994\pi\) | ||||
−0.236482 | + | 0.971636i | \(0.575994\pi\) | |||||||
\(380\) | −2035.96 | − | 6499.67i | −0.274849 | − | 0.877437i | ||||
\(381\) | 5000.27 | 0.672367 | ||||||||
\(382\) | 7222.15i | 0.967323i | ||||||||
\(383\) | 180.481i | 0.0240787i | 0.999928 | + | 0.0120394i | \(0.00383234\pi\) | ||||
−0.999928 | + | 0.0120394i | \(0.996168\pi\) | |||||||
\(384\) | −575.339 | −0.0764587 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8681.80 | 1.14480 | ||||||||
\(387\) | 282.276i | 0.0370772i | ||||||||
\(388\) | − | 4152.71i | − | 0.543356i | ||||||
\(389\) | −6220.77 | −0.810811 | −0.405406 | − | 0.914137i | \(-0.632870\pi\) | ||||
−0.405406 | + | 0.914137i | \(0.632870\pi\) | |||||||
\(390\) | 7482.08 | − | 2343.69i | 0.971461 | − | 0.304301i | ||||
\(391\) | 11366.5 | 1.47015 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2723.75i | − | 0.349606i | ||||||
\(394\) | 761.885 | 0.0974194 | ||||||||
\(395\) | 1524.57 | + | 4867.07i | 0.194201 | + | 0.619972i | ||||
\(396\) | −378.777 | −0.0480663 | ||||||||
\(397\) | − | 651.379i | − | 0.0823470i | −0.999152 | − | 0.0411735i | \(-0.986890\pi\) | ||
0.999152 | − | 0.0411735i | \(-0.0131096\pi\) | |||||||
\(398\) | − | 6953.40i | − | 0.875735i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1642.59 | + | 1141.01i | −0.205324 | + | 0.142626i | ||||
\(401\) | 12791.2 | 1.59292 | 0.796460 | − | 0.604692i | \(-0.206704\pi\) | ||||
0.796460 | + | 0.604692i | \(0.206704\pi\) | |||||||
\(402\) | 3369.60i | 0.418060i | ||||||||
\(403\) | − | 15383.2i | − | 1.90147i | ||||||
\(404\) | −1958.24 | −0.241153 | ||||||||
\(405\) | −1668.68 | − | 5327.16i | −0.204735 | − | 0.653601i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3542.99i | 0.431498i | ||||||||
\(408\) | 3780.43i | 0.458723i | ||||||||
\(409\) | 12347.5 | 1.49278 | 0.746389 | − | 0.665510i | \(-0.231786\pi\) | ||||
0.746389 | + | 0.665510i | \(0.231786\pi\) | |||||||
\(410\) | −4137.60 | + | 1296.07i | −0.498394 | + | 0.156117i | ||||
\(411\) | −1815.43 | −0.217879 | ||||||||
\(412\) | 4740.61i | 0.566877i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1469.61 | 0.174462 | ||||||||
\(415\) | 8247.87 | − | 2583.57i | 0.975595 | − | 0.305596i | ||||
\(416\) | −2496.31 | −0.294211 | ||||||||
\(417\) | 2362.18i | 0.277401i | ||||||||
\(418\) | − | 4243.97i | − | 0.496602i | ||||||
\(419\) | −9286.60 | −1.08277 | −0.541385 | − | 0.840775i | \(-0.682100\pi\) | ||||
−0.541385 | + | 0.840775i | \(0.682100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9253.33 | 1.07121 | 0.535605 | − | 0.844469i | \(-0.320084\pi\) | ||||
0.535605 | + | 0.844469i | \(0.320084\pi\) | |||||||
\(422\) | − | 3386.75i | − | 0.390674i | ||||||
\(423\) | 746.833i | 0.0858446i | ||||||||
\(424\) | 88.0432 | 0.0100843 | ||||||||
\(425\) | 7497.32 | + | 10793.1i | 0.855702 | + | 1.23186i | ||||
\(426\) | −5175.55 | −0.588630 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4769.96i | 0.538703i | ||||||||
\(429\) | 4885.44 | 0.549816 | ||||||||
\(430\) | 277.607 | + | 886.241i | 0.0311335 | + | 0.0993915i | ||||
\(431\) | −3385.57 | −0.378369 | −0.189185 | − | 0.981942i | \(-0.560584\pi\) | ||||
−0.189185 | + | 0.981942i | \(0.560584\pi\) | |||||||
\(432\) | 2430.55i | 0.270694i | ||||||||
\(433\) | − | 12073.8i | − | 1.34002i | −0.742352 | − | 0.670010i | \(-0.766290\pi\) | ||
0.742352 | − | 0.670010i | \(-0.233710\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5242.68 | + | 1642.22i | −0.577856 | + | 0.181008i | ||||
\(436\) | −1141.72 | −0.125410 | ||||||||
\(437\) | 16466.1i | 1.80247i | ||||||||
\(438\) | 4694.05i | 0.512079i | ||||||||
\(439\) | −13382.5 | −1.45492 | −0.727462 | − | 0.686148i | \(-0.759300\pi\) | ||||
−0.727462 | + | 0.686148i | \(0.759300\pi\) | |||||||
\(440\) | −1189.22 | + | 372.512i | −0.128849 | + | 0.0403609i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16402.7i | 1.76515i | ||||||||
\(443\) | − | 1205.17i | − | 0.129254i | −0.997909 | − | 0.0646271i | \(-0.979414\pi\) | ||
0.997909 | − | 0.0646271i | \(-0.0205858\pi\) | |||||||
\(444\) | 4571.96 | 0.488684 | ||||||||
\(445\) | 4441.79 | + | 14180.1i | 0.473171 | + | 1.51056i | ||||
\(446\) | 521.836 | 0.0554028 | ||||||||
\(447\) | 9146.42i | 0.967810i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7957.88 | −0.836427 | −0.418214 | − | 0.908349i | \(-0.637344\pi\) | ||||
−0.418214 | + | 0.908349i | \(0.637344\pi\) | |||||||
\(450\) | 969.351 | + | 1395.47i | 0.101546 | + | 0.146185i | ||||
\(451\) | −2701.65 | −0.282075 | ||||||||
\(452\) | − | 1400.08i | − | 0.145695i | ||||||
\(453\) | 7860.10i | 0.815231i | ||||||||
\(454\) | 559.315 | 0.0578193 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5476.53 | −0.562416 | ||||||||
\(457\) | 1697.84i | 0.173789i | 0.996218 | + | 0.0868943i | \(0.0276942\pi\) | ||||
−0.996218 | + | 0.0868943i | \(0.972306\pi\) | |||||||
\(458\) | 3444.77i | 0.351449i | ||||||||
\(459\) | 15970.6 | 1.62406 | ||||||||
\(460\) | 4614.02 | − | 1445.30i | 0.467673 | − | 0.146494i | ||||
\(461\) | −14516.2 | −1.46657 | −0.733283 | − | 0.679924i | \(-0.762013\pi\) | ||||
−0.733283 | + | 0.679924i | \(0.762013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6570.80i | − | 0.659549i | −0.944060 | − | 0.329774i | \(-0.893027\pi\) | ||
0.944060 | − | 0.329774i | \(-0.106973\pi\) | |||||||
\(464\) | 1749.16 | 0.175006 | ||||||||
\(465\) | −9456.75 | + | 2962.24i | −0.943111 | + | 0.295421i | ||||
\(466\) | 13319.2 | 1.32404 | ||||||||
\(467\) | 18664.4i | 1.84943i | 0.380659 | + | 0.924715i | \(0.375697\pi\) | ||||
−0.380659 | + | 0.924715i | \(0.624303\pi\) | |||||||
\(468\) | 2120.75i | 0.209470i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 734.480 | + | 2344.78i | 0.0720831 | + | 0.230120i | ||||
\(471\) | −2015.97 | −0.197220 | ||||||||
\(472\) | 1537.13i | 0.149899i | ||||||||
\(473\) | 578.673i | 0.0562524i | ||||||||
\(474\) | 4100.92 | 0.397387 | ||||||||
\(475\) | −15635.4 | + | 10861.0i | −1.51032 | + | 1.04913i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 74.7976i | − | 0.00717976i | ||||||
\(478\) | 2037.25i | 0.194941i | ||||||||
\(479\) | −5296.28 | −0.505205 | −0.252602 | − | 0.967570i | \(-0.581286\pi\) | ||||
−0.252602 | + | 0.967570i | \(0.581286\pi\) | |||||||
\(480\) | 480.698 | + | 1534.60i | 0.0457100 | + | 0.145926i | ||||
\(481\) | 19837.1 | 1.88044 | ||||||||
\(482\) | 11707.7i | 1.10637i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4547.50 | 0.427075 | ||||||||
\(485\) | −11076.5 | + | 3469.61i | −1.03703 | + | 0.324839i | ||||
\(486\) | 3714.53 | 0.346697 | ||||||||
\(487\) | − | 13257.2i | − | 1.23355i | −0.787138 | − | 0.616777i | \(-0.788438\pi\) | ||
0.787138 | − | 0.616777i | \(-0.211562\pi\) | |||||||
\(488\) | 279.228i | 0.0259017i | ||||||||
\(489\) | −4097.86 | −0.378960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11404.4 | −1.04821 | −0.524107 | − | 0.851653i | \(-0.675601\pi\) | ||||
−0.524107 | + | 0.851653i | \(0.675601\pi\) | |||||||
\(492\) | 3486.28i | 0.319459i | ||||||||
\(493\) | − | 11493.3i | − | 1.04997i | ||||||
\(494\) | −23761.8 | −2.16416 | ||||||||
\(495\) | 316.470 | + | 1010.31i | 0.0287359 | + | 0.0917372i | ||||
\(496\) | 3155.14 | 0.285625 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 6949.53i | − | 0.625333i | ||||||
\(499\) | 18988.6 | 1.70350 | 0.851751 | − | 0.523947i | \(-0.175541\pi\) | ||||
0.851751 | + | 0.523947i | \(0.175541\pi\) | |||||||
\(500\) | 4415.79 | + | 3427.94i | 0.394960 | + | 0.306605i | ||||
\(501\) | −5084.21 | −0.453385 | ||||||||
\(502\) | − | 2203.09i | − | 0.195874i | ||||||
\(503\) | 5173.78i | 0.458623i | 0.973353 | + | 0.229311i | \(0.0736474\pi\) | ||||
−0.973353 | + | 0.229311i | \(0.926353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1636.12 | + | 5223.19i | 0.144171 | + | 0.460255i | ||||
\(506\) | 3012.73 | 0.264688 | ||||||||
\(507\) | − | 17478.2i | − | 1.53103i | ||||||
\(508\) | 4449.79i | 0.388637i | ||||||||
\(509\) | −15987.0 | −1.39216 | −0.696080 | − | 0.717964i | \(-0.745074\pi\) | ||||
−0.696080 | + | 0.717964i | \(0.745074\pi\) | |||||||
\(510\) | 10083.5 | − | 3158.56i | 0.875499 | − | 0.274242i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 512.000i | − | 0.0441942i | ||||||
\(513\) | 23135.9i | 1.99118i | ||||||||
\(514\) | −2884.93 | −0.247566 | ||||||||
\(515\) | 12644.6 | − | 3960.80i | 1.08192 | − | 0.338901i | ||||
\(516\) | 746.734 | 0.0637076 | ||||||||
\(517\) | 1531.03i | 0.130241i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9612.56 | 0.812995 | ||||||||
\(520\) | 2085.68 | + | 6658.38i | 0.175890 | + | 0.561518i | ||||
\(521\) | 6278.45 | 0.527954 | 0.263977 | − | 0.964529i | \(-0.414966\pi\) | ||||
0.263977 | + | 0.964529i | \(0.414966\pi\) | |||||||
\(522\) | − | 1486.01i | − | 0.124599i | ||||||
\(523\) | − | 16580.9i | − | 1.38629i | −0.720797 | − | 0.693147i | \(-0.756224\pi\) | ||
0.720797 | − | 0.693147i | \(-0.243776\pi\) | |||||||
\(524\) | 2423.90 | 0.202077 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10860.8 | −0.900289 | ||||||||
\(527\) | − | 20731.7i | − | 1.71364i | ||||||
\(528\) | 1002.02i | 0.0825894i | ||||||||
\(529\) | 477.968 | 0.0392840 | ||||||||
\(530\) | −73.5605 | − | 234.837i | −0.00602880 | − | 0.0192465i | ||||
\(531\) | 1305.88 | 0.106724 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15126.4i | 1.22927i | ||||||||
\(534\) | 11947.9 | 0.968236 | ||||||||
\(535\) | 12722.9 | − | 3985.32i | 1.02815 | − | 0.322057i | ||||
\(536\) | −2998.64 | −0.241644 | ||||||||
\(537\) | − | 7816.84i | − | 0.628160i | ||||||
\(538\) | 10023.8i | 0.803263i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6482.99 | − | 2030.74i | 0.516636 | − | 0.161832i | ||||
\(541\) | −10593.3 | −0.841851 | −0.420925 | − | 0.907095i | \(-0.638295\pi\) | ||||
−0.420925 | + | 0.907095i | \(0.638295\pi\) | |||||||
\(542\) | − | 6634.79i | − | 0.525809i | ||||||
\(543\) | 10356.9i | 0.818519i | ||||||||
\(544\) | −3364.24 | −0.265148 | ||||||||
\(545\) | 953.915 | + | 3045.31i | 0.0749748 | + | 0.239352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 163.918i | 0.0128129i | 0.999979 | + | 0.00640644i | \(0.00203925\pi\) | ||||
−0.999979 | + | 0.00640644i | \(0.997961\pi\) | |||||||
\(548\) | − | 1615.57i | − | 0.125937i | ||||||
\(549\) | 237.219 | 0.0184413 | ||||||||
\(550\) | 1987.19 | + | 2860.75i | 0.154062 | + | 0.221787i | ||||
\(551\) | 16649.9 | 1.28731 | ||||||||
\(552\) | − | 3887.70i | − | 0.299767i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8320.71 | −0.638110 | ||||||||
\(555\) | −3819.90 | − | 12194.8i | −0.292154 | − | 0.932682i | ||||
\(556\) | −2102.13 | −0.160342 | ||||||||
\(557\) | − | 3673.20i | − | 0.279423i | −0.990192 | − | 0.139712i | \(-0.955382\pi\) | ||
0.990192 | − | 0.139712i | \(-0.0446175\pi\) | |||||||
\(558\) | − | 2680.46i | − | 0.203357i | ||||||
\(559\) | 3239.96 | 0.245145 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6584.03 | 0.495505 | ||||||||
\(562\) | 4846.24i | 0.363748i | ||||||||
\(563\) | − | 10985.5i | − | 0.822353i | −0.911556 | − | 0.411176i | \(-0.865118\pi\) | ||
0.911556 | − | 0.411176i | \(-0.134882\pi\) | |||||||
\(564\) | 1975.67 | 0.147502 | ||||||||
\(565\) | −3734.41 | + | 1169.77i | −0.278067 | + | 0.0871019i | ||||
\(566\) | −16740.3 | −1.24319 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 4605.78i | − | 0.340236i | ||||||
\(569\) | −26436.8 | −1.94778 | −0.973891 | − | 0.227016i | \(-0.927103\pi\) | ||||
−0.973891 | + | 0.227016i | \(0.927103\pi\) | |||||||
\(570\) | 4575.66 | + | 14607.5i | 0.336234 | + | 1.07340i | ||||
\(571\) | −4688.41 | −0.343614 | −0.171807 | − | 0.985131i | \(-0.554961\pi\) | ||||
−0.171807 | + | 0.985131i | \(0.554961\pi\) | |||||||
\(572\) | 4347.60i | 0.317801i | ||||||||
\(573\) | − | 16231.2i | − | 1.18336i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7710.07 | − | 11099.4i | −0.559186 | − | 0.805001i | ||||
\(576\) | −434.973 | −0.0314650 | ||||||||
\(577\) | 21915.1i | 1.58118i | 0.612349 | + | 0.790588i | \(0.290225\pi\) | ||||
−0.612349 | + | 0.790588i | \(0.709775\pi\) | |||||||
\(578\) | 12279.7i | 0.883680i | ||||||||
\(579\) | −19511.6 | −1.40048 | ||||||||
\(580\) | −1461.43 | − | 4665.52i | −0.104625 | − | 0.334009i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 9332.88i | 0.664709i | ||||||||
\(583\) | − | 153.337i | − | 0.0108929i | ||||||
\(584\) | −4177.29 | −0.295989 | ||||||||
\(585\) | 5656.66 | − | 1771.90i | 0.399785 | − | 0.125229i | ||||
\(586\) | −10584.4 | −0.746141 | ||||||||
\(587\) | − | 10705.4i | − | 0.752742i | −0.926469 | − | 0.376371i | \(-0.877172\pi\) | ||
0.926469 | − | 0.376371i | \(-0.122828\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30033.0 | 2.10100 | ||||||||
\(590\) | 4099.97 | − | 1284.28i | 0.286090 | − | 0.0896152i | ||||
\(591\) | −1712.28 | −0.119177 | ||||||||
\(592\) | 4068.64i | 0.282466i | ||||||||
\(593\) | 17638.7i | 1.22148i | 0.791832 | + | 0.610739i | \(0.209128\pi\) | ||||
−0.791832 | + | 0.610739i | \(0.790872\pi\) | |||||||
\(594\) | 4233.08 | 0.292399 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8139.49 | −0.559407 | ||||||||
\(597\) | 15627.2i | 1.07132i | ||||||||
\(598\) | − | 16868.2i | − | 1.15350i | ||||||
\(599\) | −12921.6 | −0.881407 | −0.440703 | − | 0.897653i | \(-0.645271\pi\) | ||||
−0.440703 | + | 0.897653i | \(0.645271\pi\) | |||||||
\(600\) | 3691.58 | − | 2564.32i | 0.251181 | − | 0.174480i | ||||
\(601\) | 25860.7 | 1.75521 | 0.877603 | − | 0.479388i | \(-0.159141\pi\) | ||||
0.877603 | + | 0.479388i | \(0.159141\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2547.51i | 0.172044i | ||||||||
\(604\) | −6994.78 | −0.471215 | ||||||||
\(605\) | −3799.46 | − | 12129.5i | −0.255322 | − | 0.815098i | ||||
\(606\) | 4400.98 | 0.295012 | ||||||||
\(607\) | 6462.68i | 0.432145i | 0.976377 | + | 0.216073i | \(0.0693248\pi\) | ||||
−0.976377 | + | 0.216073i | \(0.930675\pi\) | |||||||
\(608\) | − | 4873.62i | − | 0.325084i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 744.781 | − | 233.296i | 0.0494349 | − | 0.0154850i | ||||
\(611\) | 8572.15 | 0.567581 | ||||||||
\(612\) | 2858.11i | 0.188778i | ||||||||
\(613\) | − | 13103.7i | − | 0.863382i | −0.902022 | − | 0.431691i | \(-0.857917\pi\) | ||
0.902022 | − | 0.431691i | \(-0.142083\pi\) | |||||||
\(614\) | 7704.14 | 0.506374 | ||||||||
\(615\) | 9298.92 | − | 2912.80i | 0.609705 | − | 0.190985i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1840.69i | − | 0.120103i | −0.998195 | − | 0.0600514i | \(-0.980874\pi\) | ||
0.998195 | − | 0.0600514i | \(-0.0191265\pi\) | |||||||
\(618\) | − | 10654.1i | − | 0.693483i | ||||||
\(619\) | −20894.4 | −1.35673 | −0.678365 | − | 0.734725i | \(-0.737311\pi\) | ||||
−0.678365 | + | 0.734725i | \(0.737311\pi\) | |||||||
\(620\) | −2636.13 | − | 8415.66i | −0.170757 | − | 0.545131i | ||||
\(621\) | −16423.8 | −1.06130 | ||||||||
\(622\) | − | 2184.96i | − | 0.140850i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5610.25 | 0.359919 | ||||||||
\(625\) | 5453.90 | − | 14642.3i | 0.349050 | − | 0.937104i | ||||
\(626\) | 2649.79 | 0.169181 | ||||||||
\(627\) | 9537.98i | 0.607512i | ||||||||
\(628\) | − | 1794.03i | − | 0.113996i | ||||||
\(629\) | 26734.1 | 1.69469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11128.4 | −0.702086 | −0.351043 | − | 0.936359i | \(-0.614173\pi\) | ||||
−0.351043 | + | 0.936359i | \(0.614173\pi\) | |||||||
\(632\) | 3649.45i | 0.229695i | ||||||||
\(633\) | 7611.44i | 0.477927i | ||||||||
\(634\) | 9970.95 | 0.624601 | ||||||||
\(635\) | 11868.9 | − | 3717.82i | 0.741736 | − | 0.232342i | ||||
\(636\) | −197.870 | −0.0123366 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 3046.36i | − | 0.189038i | ||||||
\(639\) | −3912.87 | −0.242239 | ||||||||
\(640\) | −1365.65 | + | 427.778i | −0.0843471 | + | 0.0264210i | ||||
\(641\) | −31784.4 | −1.95851 | −0.979257 | − | 0.202620i | \(-0.935054\pi\) | ||||
−0.979257 | + | 0.202620i | \(0.935054\pi\) | |||||||
\(642\) | − | 10720.1i | − | 0.659016i | ||||||
\(643\) | − | 1781.74i | − | 0.109277i | −0.998506 | − | 0.0546384i | \(-0.982599\pi\) | ||
0.998506 | − | 0.0546384i | \(-0.0174006\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −623.899 | − | 1991.75i | −0.0380868 | − | 0.121590i | ||||
\(646\) | −32023.5 | −1.95038 | ||||||||
\(647\) | − | 13936.7i | − | 0.846843i | −0.905933 | − | 0.423422i | \(-0.860829\pi\) | ||
0.905933 | − | 0.423422i | \(-0.139171\pi\) | |||||||
\(648\) | − | 3994.43i | − | 0.242155i | ||||||
\(649\) | 2677.09 | 0.161918 | ||||||||
\(650\) | 16017.2 | − | 11126.2i | 0.966534 | − | 0.671394i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 3646.72i | − | 0.219044i | ||||||
\(653\) | 856.900i | 0.0513523i | 0.999670 | + | 0.0256762i | \(0.00817388\pi\) | ||||
−0.999670 | + | 0.0256762i | \(0.991826\pi\) | |||||||
\(654\) | 2565.93 | 0.153419 | ||||||||
\(655\) | −2025.18 | − | 6465.23i | −0.120809 | − | 0.385676i | ||||
\(656\) | −3102.48 | −0.184651 | ||||||||
\(657\) | 3548.84i | 0.210736i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11560.8 | −0.683374 | −0.341687 | − | 0.939814i | \(-0.610998\pi\) | ||||
−0.341687 | + | 0.939814i | \(0.610998\pi\) | |||||||
\(660\) | 2672.67 | − | 837.190i | 0.157627 | − | 0.0493751i | ||||
\(661\) | 9094.31 | 0.535140 | 0.267570 | − | 0.963538i | \(-0.413779\pi\) | ||||
0.267570 | + | 0.963538i | \(0.413779\pi\) | |||||||
\(662\) | − | 20082.0i | − | 1.17902i | ||||||
\(663\) | − | 36863.7i | − | 2.15938i | ||||||
\(664\) | 6184.46 | 0.361451 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3456.54 | 0.201108 | ||||||||
\(667\) | 11819.5i | 0.686136i | ||||||||
\(668\) | − | 4524.49i | − | 0.262063i | ||||||
\(669\) | −1172.78 | −0.0677765 | ||||||||
\(670\) | 2505.37 | + | 7998.23i | 0.144464 | + | 0.461192i | ||||
\(671\) | 486.306 | 0.0279786 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5216.21i | − | 0.298767i | −0.988779 | − | 0.149384i | \(-0.952271\pi\) | ||
0.988779 | − | 0.149384i | \(-0.0477289\pi\) | |||||||
\(674\) | −14454.8 | −0.826080 | ||||||||
\(675\) | −10833.1 | − | 15595.3i | −0.617729 | − | 0.889279i | ||||
\(676\) | 15554.0 | 0.884958 | ||||||||
\(677\) | − | 5631.52i | − | 0.319700i | −0.987141 | − | 0.159850i | \(-0.948899\pi\) | ||
0.987141 | − | 0.159850i | \(-0.0511010\pi\) | |||||||
\(678\) | 3146.56i | 0.178234i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2810.84 | + | 8973.40i | 0.158516 | + | 0.506050i | ||||
\(681\) | −1257.01 | −0.0707326 | ||||||||
\(682\) | − | 5495.02i | − | 0.308527i | ||||||
\(683\) | − | 20993.9i | − | 1.17615i | −0.808807 | − | 0.588074i | \(-0.799886\pi\) | ||
0.808807 | − | 0.588074i | \(-0.200114\pi\) | |||||||
\(684\) | −4140.41 | −0.231451 | ||||||||
\(685\) | −4309.18 | + | 1349.81i | −0.240358 | + | 0.0752901i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7741.84i | − | 0.429941i | ||||||
\(688\) | 664.526i | 0.0368238i | ||||||||
\(689\) | −858.527 | −0.0474706 | ||||||||
\(690\) | −10369.6 | + | 3248.19i | −0.572123 | + | 0.179212i | ||||
\(691\) | −20881.2 | −1.14958 | −0.574790 | − | 0.818301i | \(-0.694916\pi\) | ||||
−0.574790 | + | 0.818301i | \(0.694916\pi\) | |||||||
\(692\) | 8554.31i | 0.469922i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6851.34 | 0.374746 | ||||||||
\(695\) | 1756.34 | + | 5606.98i | 0.0958584 | + | 0.306021i | ||||
\(696\) | −3931.09 | −0.214092 | ||||||||
\(697\) | 20385.7i | 1.10784i | ||||||||
\(698\) | 14184.1i | 0.769161i | ||||||||
\(699\) | −29933.9 | −1.61975 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14493.3 | −0.780889 | −0.390444 | − | 0.920626i | \(-0.627679\pi\) | ||||
−0.390444 | + | 0.920626i | \(0.627679\pi\) | |||||||
\(702\) | − | 23700.8i | − | 1.27426i | ||||||
\(703\) | 38728.5i | 2.07777i | ||||||||
\(704\) | −891.705 | −0.0477378 | ||||||||
\(705\) | −1650.68 | − | 5269.69i | −0.0881821 | − | 0.281515i | ||||
\(706\) | −23929.5 | −1.27564 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 3454.58i | − | 0.183377i | ||||||
\(709\) | −19466.9 | −1.03116 | −0.515580 | − | 0.856841i | \(-0.672424\pi\) | ||||
−0.515580 | + | 0.856841i | \(0.672424\pi\) | |||||||
\(710\) | −12284.9 | + | 3848.15i | −0.649360 | + | 0.203406i | ||||
\(711\) | 3100.41 | 0.163537 | ||||||||
\(712\) | 10632.6i | 0.559654i | ||||||||
\(713\) | 21320.0i | 1.11983i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11596.3 | − | 3632.44i | 0.606542 | − | 0.189994i | ||||
\(716\) | 6956.29 | 0.363085 | ||||||||
\(717\) | − | 4578.56i | − | 0.238479i | ||||||
\(718\) | − | 3112.01i | − | 0.161754i | ||||||
\(719\) | 31341.8 | 1.62566 | 0.812831 | − | 0.582499i | \(-0.197925\pi\) | ||||
0.812831 | + | 0.582499i | \(0.197925\pi\) | |||||||
\(720\) | 363.422 | + | 1160.20i | 0.0188110 | + | 0.0600528i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 32672.9i | − | 1.68415i | ||||||
\(723\) | − | 26312.1i | − | 1.35347i | ||||||
\(724\) | −9216.69 | −0.473115 | ||||||||
\(725\) | −11223.2 | + | 7796.12i | −0.574925 | + | 0.399366i | ||||
\(726\) | −10220.1 | −0.522458 | ||||||||
\(727\) | 21225.4i | 1.08282i | 0.840760 | + | 0.541408i | \(0.182108\pi\) | ||||
−0.840760 | + | 0.541408i | \(0.817892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21829.3 | −1.10904 | ||||||||
\(730\) | 3490.14 | + | 11142.0i | 0.176953 | + | 0.564911i | ||||
\(731\) | 4366.45 | 0.220929 | ||||||||
\(732\) | − | 627.541i | − | 0.0316866i | ||||||
\(733\) | 10542.1i | 0.531217i | 0.964081 | + | 0.265609i | \(0.0855729\pi\) | ||||
−0.964081 | + | 0.265609i | \(0.914427\pi\) | |||||||
\(734\) | −4837.12 | −0.243244 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3459.71 | 0.173270 | ||||||||
\(737\) | 5222.46i | 0.261020i | ||||||||
\(738\) | 2635.73i | 0.131467i | ||||||||
\(739\) | −13623.8 | −0.678158 | −0.339079 | − | 0.940758i | \(-0.610115\pi\) | ||||
−0.339079 | + | 0.940758i | \(0.610115\pi\) | |||||||
\(740\) | 10852.2 | − | 3399.36i | 0.539103 | − | 0.168869i | ||||
\(741\) | 53402.7 | 2.64750 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8366.07i | − | 0.413084i | −0.978438 | − | 0.206542i | \(-0.933779\pi\) | ||
0.978438 | − | 0.206542i | \(-0.0662210\pi\) | |||||||
\(744\) | −7090.91 | −0.349416 | ||||||||
\(745\) | 6800.58 | + | 21710.4i | 0.334435 | + | 1.06766i | ||||
\(746\) | 5474.60 | 0.268685 | ||||||||
\(747\) | − | 5254.04i | − | 0.257343i | ||||||
\(748\) | 5859.20i | 0.286408i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −9924.13 | − | 7704.02i | −0.483171 | − | 0.375081i | ||||
\(751\) | −4026.96 | −0.195667 | −0.0978334 | − | 0.995203i | \(-0.531191\pi\) | ||||
−0.0978334 | + | 0.995203i | \(0.531191\pi\) | |||||||
\(752\) | 1758.17i | 0.0852579i | ||||||||
\(753\) | 4951.27i | 0.239621i | ||||||||
\(754\) | −17056.4 | −0.823817 | ||||||||
\(755\) | 5844.17 | + | 18657.1i | 0.281710 | + | 0.899340i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7909.33i | − | 0.379748i | −0.981808 | − | 0.189874i | \(-0.939192\pi\) | ||
0.981808 | − | 0.189874i | \(-0.0608080\pi\) | |||||||
\(758\) | 6979.38i | 0.334436i | ||||||||
\(759\) | −6770.87 | −0.323804 | ||||||||
\(760\) | −12999.3 | + | 4071.93i | −0.620442 | + | 0.194348i | ||||
\(761\) | 12265.2 | 0.584247 | 0.292124 | − | 0.956381i | \(-0.405638\pi\) | ||||
0.292124 | + | 0.956381i | \(0.405638\pi\) | |||||||
\(762\) | − | 10000.5i | − | 0.475435i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14444.3 | 0.684000 | ||||||||
\(765\) | 7623.40 | − | 2387.96i | 0.360294 | − | 0.112859i | ||||
\(766\) | 360.962 | 0.0170262 | ||||||||
\(767\) | − | 14988.9i | − | 0.705629i | ||||||
\(768\) | 1150.68i | 0.0540645i | ||||||||
\(769\) | 7111.92 | 0.333501 | 0.166750 | − | 0.985999i | \(-0.446673\pi\) | ||||
0.166750 | + | 0.985999i | \(0.446673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6483.65 | 0.302857 | ||||||||
\(772\) | − | 17363.6i | − | 0.809494i | ||||||
\(773\) | 7131.22i | 0.331814i | 0.986141 | + | 0.165907i | \(0.0530551\pi\) | ||||
−0.986141 | + | 0.165907i | \(0.946945\pi\) | |||||||
\(774\) | 564.552 | 0.0262176 | ||||||||
\(775\) | −20244.5 | + | 14062.6i | −0.938328 | + | 0.651800i | ||||
\(776\) | −8305.43 | −0.384211 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12441.5i | 0.573330i | ||||||||
\(779\) | −29531.8 | −1.35826 | ||||||||
\(780\) | −4687.39 | − | 14964.2i | −0.215174 | − | 0.686927i | ||||
\(781\) | −8021.48 | −0.367517 | ||||||||
\(782\) | − | 22733.0i | − | 1.03955i | ||||||
\(783\) | 16607.1i | 0.757970i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4785.19 | + | 1498.92i | −0.217568 | + | 0.0681512i | ||||
\(786\) | −5447.51 | −0.247209 | ||||||||
\(787\) | 12062.3i | 0.546345i | 0.961965 | + | 0.273172i | \(0.0880729\pi\) | ||||
−0.961965 | + | 0.273172i | \(0.911927\pi\) | |||||||
\(788\) | − | 1523.77i | − | 0.0688859i | ||||||
\(789\) | 24408.7 | 1.10136 | ||||||||
\(790\) | 9734.14 | − | 3049.13i | 0.438386 | − | 0.137321i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 757.553i | 0.0339880i | ||||||||
\(793\) | − | 2722.81i | − | 0.121929i | ||||||
\(794\) | −1302.76 | −0.0582281 | ||||||||
\(795\) | 165.321 | + | 527.776i | 0.00737526 | + | 0.0235450i | ||||
\(796\) | −13906.8 | −0.619238 | ||||||||
\(797\) | − | 15849.5i | − | 0.704415i | −0.935922 | − | 0.352207i | \(-0.885431\pi\) | ||
0.935922 | − | 0.352207i | \(-0.114569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11552.6 | 0.511515 | ||||||||
\(800\) | 2282.02 | + | 3285.18i | 0.100852 | + | 0.145186i | ||||
\(801\) | 9032.98 | 0.398458 | ||||||||
\(802\) | − | 25582.3i | − | 1.12636i | ||||||
\(803\) | 7275.21i | 0.319722i | ||||||||
\(804\) | 6739.19 | 0.295613 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30766.4 | −1.34454 | ||||||||
\(807\) | − | 22527.6i | − | 0.982664i | ||||||
\(808\) | 3916.47i | 0.170521i | ||||||||
\(809\) | 4367.34 | 0.189799 | 0.0948995 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0948995 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(810\) | −10654.3 | + | 3337.37i | −0.462166 | + | 0.144769i | ||||
\(811\) | −284.034 | −0.0122981 | −0.00614907 | − | 0.999981i | \(-0.501957\pi\) | ||||
−0.00614907 | + | 0.999981i | \(0.501957\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14911.2i | 0.643243i | ||||||||
\(814\) | 7085.99 | 0.305115 | ||||||||
\(815\) | −9726.87 | + | 3046.85i | −0.418058 | + | 0.130953i | ||||
\(816\) | 7560.85 | 0.324366 | ||||||||
\(817\) | 6325.47i | 0.270869i | ||||||||
\(818\) | − | 24695.1i | − | 1.05555i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2592.13 | + | 8275.20i | 0.110392 | + | 0.352418i | ||||
\(821\) | −11862.3 | −0.504261 | −0.252131 | − | 0.967693i | \(-0.581131\pi\) | ||||
−0.252131 | + | 0.967693i | \(0.581131\pi\) | |||||||
\(822\) | 3630.85i | 0.154064i | ||||||||
\(823\) | 33092.7i | 1.40163i | 0.713344 | + | 0.700814i | \(0.247180\pi\) | ||||
−0.713344 | + | 0.700814i | \(0.752820\pi\) | |||||||
\(824\) | 9481.23 | 0.400843 | ||||||||
\(825\) | −4466.05 | − | 6429.31i | −0.188470 | − | 0.271321i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38358.2i | 1.61287i | 0.591322 | + | 0.806436i | \(0.298606\pi\) | ||||
−0.591322 | + | 0.806436i | \(0.701394\pi\) | |||||||
\(828\) | − | 2939.21i | − | 0.123363i | ||||||
\(829\) | −44688.0 | −1.87223 | −0.936114 | − | 0.351697i | \(-0.885605\pi\) | ||||
−0.936114 | + | 0.351697i | \(0.885605\pi\) | |||||||
\(830\) | −5167.14 | − | 16495.7i | −0.216089 | − | 0.689850i | ||||
\(831\) | 18700.1 | 0.780625 | ||||||||
\(832\) | 4992.62i | 0.208038i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4724.36 | 0.196152 | ||||||||
\(835\) | −12068.1 | + | 3780.23i | −0.500161 | + | 0.156671i | ||||
\(836\) | −8487.94 | −0.351150 | ||||||||
\(837\) | 29955.9i | 1.23707i | ||||||||
\(838\) | 18573.2i | 0.765633i | ||||||||
\(839\) | −25673.2 | −1.05642 | −0.528211 | − | 0.849113i | \(-0.677137\pi\) | ||||
−0.528211 | + | 0.849113i | \(0.677137\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12437.6 | −0.509967 | ||||||||
\(842\) | − | 18506.7i | − | 0.757460i | ||||||
\(843\) | − | 10891.5i | − | 0.444987i | ||||||
\(844\) | −6773.50 | −0.276248 | ||||||||
\(845\) | −12995.5 | − | 41487.1i | −0.529062 | − | 1.68899i | ||||
\(846\) | 1493.67 | 0.0607013 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 176.086i | − | 0.00713069i | ||||||
\(849\) | 37622.4 | 1.52084 | ||||||||
\(850\) | 21586.2 | − | 14994.6i | 0.871059 | − | 0.605072i | ||||
\(851\) | −27492.8 | −1.10745 | ||||||||
\(852\) | 10351.1i | 0.416224i | ||||||||
\(853\) | − | 1652.74i | − | 0.0663408i | −0.999450 | − | 0.0331704i | \(-0.989440\pi\) | ||
0.999450 | − | 0.0331704i | \(-0.0105604\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3459.33 | + | 11043.7i | 0.138370 | + | 0.441737i | ||||
\(856\) | 9539.92 | 0.380920 | ||||||||
\(857\) | − | 1566.46i | − | 0.0624379i | −0.999513 | − | 0.0312190i | \(-0.990061\pi\) | ||
0.999513 | − | 0.0312190i | \(-0.00993892\pi\) | |||||||
\(858\) | − | 9770.87i | − | 0.388779i | ||||||
\(859\) | −17466.8 | −0.693783 | −0.346892 | − | 0.937905i | \(-0.612763\pi\) | ||||
−0.346892 | + | 0.937905i | \(0.612763\pi\) | |||||||
\(860\) | 1772.48 | − | 555.214i | 0.0702804 | − | 0.0220147i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6771.14i | 0.267547i | ||||||||
\(863\) | − | 42901.9i | − | 1.69224i | −0.532996 | − | 0.846118i | \(-0.678934\pi\) | ||
0.532996 | − | 0.846118i | \(-0.321066\pi\) | |||||||
\(864\) | 4861.10 | 0.191410 | ||||||||
\(865\) | 22816.8 | − | 7147.17i | 0.896873 | − | 0.280937i | ||||
\(866\) | −24147.6 | −0.947537 | ||||||||
\(867\) | − | 27597.6i | − | 1.08104i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6355.93 | 0.248113 | ||||||||
\(870\) | 3284.45 | + | 10485.4i | 0.127992 | + | 0.408606i | ||||
\(871\) | 29240.3 | 1.13751 | ||||||||
\(872\) | 2283.45i | 0.0886781i | ||||||||
\(873\) | 7055.92i | 0.273547i | ||||||||
\(874\) | 32932.2 | 1.27454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9388.11 | 0.362095 | ||||||||
\(877\) | 35156.0i | 1.35363i | 0.736153 | + | 0.676815i | \(0.236640\pi\) | ||||
−0.736153 | + | 0.676815i | \(0.763360\pi\) | |||||||
\(878\) | 26765.0i | 1.02879i | ||||||||
\(879\) | 23787.6 | 0.912783 | ||||||||
\(880\) | 745.024 | + | 2378.44i | 0.0285395 | + | 0.0911103i | ||||
\(881\) | −26203.5 | −1.00206 | −0.501032 | − | 0.865429i | \(-0.667046\pi\) | ||||
−0.501032 | + | 0.865429i | \(0.667046\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12182.9i | 0.464312i | 0.972679 | + | 0.232156i | \(0.0745780\pi\) | ||||
−0.972679 | + | 0.232156i | \(0.925422\pi\) | |||||||
\(884\) | 32805.4 | 1.24815 | ||||||||
\(885\) | −9214.36 | + | 2886.31i | −0.349986 | + | 0.109630i | ||||
\(886\) | −2410.35 | −0.0913965 | ||||||||
\(887\) | − | 22769.7i | − | 0.861931i | −0.902368 | − | 0.430965i | \(-0.858173\pi\) | ||
0.902368 | − | 0.430965i | \(-0.141827\pi\) | |||||||
\(888\) | − | 9143.93i | − | 0.345552i | ||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28360.2 | − | 8883.58i | 1.06813 | − | 0.334582i | ||||
\(891\) | −6956.75 | −0.261571 | ||||||||
\(892\) | − | 1043.67i | − | 0.0391757i | ||||||
\(893\) | 16735.7i | 0.627141i | ||||||||
\(894\) | 18292.8 | 0.684345 | ||||||||
\(895\) | −5812.01 | − | 18554.4i | −0.217066 | − | 0.692968i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37909.8i | 1.41112i | ||||||||
\(898\) | 15915.8i | 0.591443i | ||||||||
\(899\) | 21558.0 | 0.799775 | ||||||||
\(900\) | 2790.94 | − | 1938.70i | 0.103368 | − | 0.0718037i | ||||
\(901\) | −1157.02 | −0.0427814 | ||||||||
\(902\) | 5403.31i | 0.199457i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2800.15 | −0.103022 | ||||||||
\(905\) | 7700.58 | + | 24583.6i | 0.282846 | + | 0.902967i | ||||
\(906\) | 15720.2 | 0.576456 | ||||||||
\(907\) | 28419.0i | 1.04039i | 0.854046 | + | 0.520197i | \(0.174142\pi\) | ||||
−0.854046 | + | 0.520197i | \(0.825858\pi\) | |||||||
\(908\) | − | 1118.63i | − | 0.0408844i | ||||||
\(909\) | 3327.26 | 0.121406 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21021.6 | 0.764519 | 0.382259 | − | 0.924055i | \(-0.375146\pi\) | ||||
0.382259 | + | 0.924055i | \(0.375146\pi\) | |||||||
\(912\) | 10953.1i | 0.397688i | ||||||||
\(913\) | − | 10770.9i | − | 0.390433i | ||||||
\(914\) | 3395.67 | 0.122887 | ||||||||
\(915\) | −1673.83 | + | 524.314i | −0.0604757 | + | 0.0189435i | ||||
\(916\) | 6889.54 | 0.248512 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 31941.2i | − | 1.14839i | ||||||
\(919\) | 24704.5 | 0.886752 | 0.443376 | − | 0.896336i | \(-0.353781\pi\) | ||||
0.443376 | + | 0.896336i | \(0.353781\pi\) | |||||||
\(920\) | −2890.60 | − | 9228.04i | −0.103587 | − | 0.330695i | ||||
\(921\) | −17314.4 | −0.619467 | ||||||||
\(922\) | 29032.4i | 1.03702i | ||||||||
\(923\) | 44911.9i | 1.60162i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18134.2 | − | 26105.9i | −0.644593 | − | 0.927952i | ||||
\(926\) | −13141.6 | −0.466371 | ||||||||
\(927\) | − | 8054.83i | − | 0.285389i | ||||||
\(928\) | − | 3498.32i | − | 0.123748i | ||||||
\(929\) | −17304.1 | −0.611119 | −0.305560 | − | 0.952173i | \(-0.598844\pi\) | ||||
−0.305560 | + | 0.952173i | \(0.598844\pi\) | |||||||
\(930\) | 5924.49 | + | 18913.5i | 0.208894 | + | 0.666880i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 26638.5i | − | 0.936237i | ||||||
\(933\) | 4910.52i | 0.172308i | ||||||||
\(934\) | 37328.7 | 1.30775 | ||||||||
\(935\) | 15628.2 | − | 4895.39i | 0.546627 | − | 0.171226i | ||||
\(936\) | 4241.51 | 0.148118 | ||||||||
\(937\) | − | 31154.0i | − | 1.08619i | −0.839672 | − | 0.543094i | \(-0.817253\pi\) | ||
0.839672 | − | 0.543094i | \(-0.182747\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5955.19 | −0.206965 | ||||||||
\(940\) | 4689.55 | − | 1468.96i | 0.162720 | − | 0.0509704i | ||||
\(941\) | −53006.5 | −1.83631 | −0.918153 | − | 0.396227i | \(-0.870319\pi\) | ||||
−0.918153 | + | 0.396227i | \(0.870319\pi\) | |||||||
\(942\) | 4031.93i | 0.139456i | ||||||||
\(943\) | − | 20964.2i | − | 0.723953i | ||||||
\(944\) | 3074.26 | 0.105994 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1157.35 | 0.0397765 | ||||||||
\(947\) | 54176.8i | 1.85904i | 0.368772 | + | 0.929520i | \(0.379778\pi\) | ||||
−0.368772 | + | 0.929520i | \(0.620222\pi\) | |||||||
\(948\) | − | 8201.85i | − | 0.280995i | ||||||
\(949\) | 40733.6 | 1.39333 | ||||||||
\(950\) | 21722.0 | + | 31270.9i | 0.741848 | + | 1.06796i | ||||
\(951\) | −22408.9 | −0.764099 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6214.74i | 0.211244i | 0.994406 | + | 0.105622i | \(0.0336833\pi\) | ||||
−0.994406 | + | 0.105622i | \(0.966317\pi\) | |||||||
\(954\) | −149.595 | −0.00507686 | ||||||||
\(955\) | −12068.3 | − | 38527.1i | −0.408922 | − | 1.30545i | ||||
\(956\) | 4074.51 | 0.137844 | ||||||||
\(957\) | 6846.44i | 0.231258i | ||||||||
\(958\) | 10592.6i | 0.357234i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3069.19 | − | 961.397i | 0.103185 | − | 0.0323218i | ||||
\(961\) | 9095.25 | 0.305302 | ||||||||
\(962\) | − | 39674.1i | − | 1.32967i | ||||||
\(963\) | − | 8104.70i | − | 0.271205i | ||||||
\(964\) | 23415.4 | 0.782322 | ||||||||
\(965\) | −46313.7 | + | 14507.4i | −1.54497 | + | 0.483947i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45681.3i | − | 1.51914i | −0.650424 | − | 0.759571i | \(-0.725409\pi\) | ||
0.650424 | − | 0.759571i | \(-0.274591\pi\) | |||||||
\(968\) | − | 9095.00i | − | 0.301988i | ||||||
\(969\) | 71970.1 | 2.38598 | ||||||||
\(970\) | 6939.22 | + | 22153.0i | 0.229696 | + | 0.733288i | ||||
\(971\) | 52107.6 | 1.72215 | 0.861077 | − | 0.508474i | \(-0.169790\pi\) | ||||
0.861077 | + | 0.508474i | \(0.169790\pi\) | |||||||
\(972\) | − | 7429.06i | − | 0.245152i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26514.4 | −0.872255 | ||||||||
\(975\) | −35997.4 | + | 25005.2i | −1.18240 | + | 0.821342i | ||||
\(976\) | 558.455 | 0.0183153 | ||||||||
\(977\) | 4174.15i | 0.136687i | 0.997662 | + | 0.0683433i | \(0.0217713\pi\) | ||||
−0.997662 | + | 0.0683433i | \(0.978229\pi\) | |||||||
\(978\) | 8195.71i | 0.267965i | ||||||||
\(979\) | 18517.8 | 0.604528 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1939.92 | 0.0631364 | ||||||||
\(982\) | 22808.8i | 0.741199i | ||||||||
\(983\) | 19717.9i | 0.639781i | 0.947455 | + | 0.319890i | \(0.103646\pi\) | ||||
−0.947455 | + | 0.319890i | \(0.896354\pi\) | |||||||
\(984\) | 6972.56 | 0.225891 | ||||||||
\(985\) | −4064.34 | + | 1273.12i | −0.131473 | + | 0.0411826i | ||||
\(986\) | −22986.7 | −0.742440 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 47523.6i | 1.53029i | ||||||||
\(989\) | −4490.36 | −0.144373 | ||||||||
\(990\) | 2020.61 | − | 632.939i | 0.0648680 | − | 0.0203193i | ||||
\(991\) | 24502.6 | 0.785419 | 0.392710 | − | 0.919663i | \(-0.371538\pi\) | ||||
0.392710 | + | 0.919663i | \(0.371538\pi\) | |||||||
\(992\) | − | 6310.27i | − | 0.201967i | ||||||
\(993\) | 45132.7i | 1.44234i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11619.2 | + | 37093.5i | 0.370204 | + | 1.18185i | ||||
\(996\) | −13899.1 | −0.442177 | ||||||||
\(997\) | − | 22942.8i | − | 0.728791i | −0.931244 | − | 0.364395i | \(-0.881276\pi\) | ||
0.931244 | − | 0.364395i | \(-0.118724\pi\) | |||||||
\(998\) | − | 37977.2i | − | 1.20456i | ||||||
\(999\) | −38629.0 | −1.22339 |
(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 | 490.4.c.e.99.5 | 12 | ||
5.2 | odd | 4 | 2450.4.a.cx.1.5 | 6 | |||
5.3 | odd | 4 | 2450.4.a.cw.1.2 | 6 | |||
5.4 | even | 2 | inner | 490.4.c.e.99.8 | 12 | ||
7.3 | odd | 6 | 70.4.i.a.9.8 | yes | 24 | ||
7.5 | odd | 6 | 70.4.i.a.39.5 | yes | 24 | ||
7.6 | odd | 2 | 490.4.c.f.99.2 | 12 | |||
35.3 | even | 12 | 350.4.e.o.51.2 | 12 | |||
35.12 | even | 12 | 350.4.e.n.151.5 | 12 | |||
35.13 | even | 4 | 2450.4.a.cv.1.5 | 6 | |||
35.17 | even | 12 | 350.4.e.n.51.5 | 12 | |||
35.19 | odd | 6 | 70.4.i.a.39.8 | yes | 24 | ||
35.24 | odd | 6 | 70.4.i.a.9.5 | ✓ | 24 | ||
35.27 | even | 4 | 2450.4.a.cy.1.2 | 6 | |||
35.33 | even | 12 | 350.4.e.o.151.2 | 12 | |||
35.34 | odd | 2 | 490.4.c.f.99.11 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.i.a.9.5 | ✓ | 24 | 35.24 | odd | 6 | ||
70.4.i.a.9.8 | yes | 24 | 7.3 | odd | 6 | ||
70.4.i.a.39.5 | yes | 24 | 7.5 | odd | 6 | ||
70.4.i.a.39.8 | yes | 24 | 35.19 | odd | 6 | ||
350.4.e.n.51.5 | 12 | 35.17 | even | 12 | |||
350.4.e.n.151.5 | 12 | 35.12 | even | 12 | |||
350.4.e.o.51.2 | 12 | 35.3 | even | 12 | |||
350.4.e.o.151.2 | 12 | 35.33 | even | 12 | |||
490.4.c.e.99.5 | 12 | 1.1 | even | 1 | trivial | ||
490.4.c.e.99.8 | 12 | 5.4 | even | 2 | inner | ||
490.4.c.f.99.2 | 12 | 7.6 | odd | 2 | |||
490.4.c.f.99.11 | 12 | 35.34 | odd | 2 | |||
2450.4.a.cv.1.5 | 6 | 35.13 | even | 4 | |||
2450.4.a.cw.1.2 | 6 | 5.3 | odd | 4 | |||
2450.4.a.cx.1.5 | 6 | 5.2 | odd | 4 | |||
2450.4.a.cy.1.2 | 6 | 35.27 | even | 4 |