Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 163.2 | ||
Root | \(-1.84763 + 3.20018i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.163 |
Dual form | 378.4.g.f.109.2 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −5.04834 | + | 8.74398i | −0.451537 | + | 0.782085i | −0.998482 | − | 0.0550835i | \(-0.982458\pi\) |
0.546945 | + | 0.837169i | \(0.315791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.48778 | − | 17.6885i | −0.296312 | − | 0.955091i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0967 | + | 17.4880i | 0.319285 | + | 0.553018i | ||||
\(11\) | 18.0748 | + | 31.3065i | 0.495433 | + | 0.858116i | 0.999986 | − | 0.00526523i | \(-0.00167598\pi\) |
−0.504553 | + | 0.863381i | \(0.668343\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.01927 | −0.0857495 | −0.0428748 | − | 0.999080i | \(-0.513652\pi\) | ||||
−0.0428748 | + | 0.999080i | \(0.513652\pi\) | |||||||
\(14\) | −36.1252 | − | 8.18341i | −0.689634 | − | 0.156222i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 18.9802 | + | 32.8747i | 0.270787 | + | 0.469017i | 0.969064 | − | 0.246811i | \(-0.0793828\pi\) |
−0.698277 | + | 0.715828i | \(0.746049\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.5163 | + | 49.3917i | −0.344321 | + | 0.596381i | −0.985230 | − | 0.171236i | \(-0.945224\pi\) |
0.640909 | + | 0.767617i | \(0.278557\pi\) | |||||||
\(20\) | 40.3867 | 0.451537 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 72.2993 | 0.700648 | ||||||||
\(23\) | 39.2198 | − | 67.9308i | 0.355561 | − | 0.615850i | −0.631653 | − | 0.775251i | \(-0.717623\pi\) |
0.987214 | + | 0.159402i | \(0.0509565\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.5285 | + | 19.9680i | 0.0922284 | + | 0.159744i | ||||
\(26\) | −4.01927 | + | 6.96157i | −0.0303170 | + | 0.0525107i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −50.2993 | + | 54.3873i | −0.339488 | + | 0.367080i | ||||
\(29\) | 215.332 | 1.37884 | 0.689418 | − | 0.724364i | \(-0.257866\pi\) | ||||
0.689418 | + | 0.724364i | \(0.257866\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 91.1642 | + | 157.901i | 0.528180 | + | 0.914834i | 0.999460 | + | 0.0328507i | \(0.0104586\pi\) |
−0.471281 | + | 0.881983i | \(0.656208\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 75.9208 | 0.382950 | ||||||||
\(35\) | 182.372 | + | 41.3127i | 0.880759 | + | 0.199518i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −156.279 | + | 270.683i | −0.694380 | + | 1.20270i | 0.276010 | + | 0.961155i | \(0.410988\pi\) |
−0.970389 | + | 0.241546i | \(0.922346\pi\) | |||||||
\(38\) | 57.0327 | + | 98.7835i | 0.243472 | + | 0.421705i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.3867 | − | 69.9518i | 0.159642 | − | 0.276509i | ||||
\(41\) | 186.557 | 0.710617 | 0.355308 | − | 0.934749i | \(-0.384376\pi\) | ||||
0.355308 | + | 0.934749i | \(0.384376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 262.266 | 0.930121 | 0.465061 | − | 0.885279i | \(-0.346033\pi\) | ||||
0.465061 | + | 0.885279i | \(0.346033\pi\) | |||||||
\(44\) | 72.2993 | − | 125.226i | 0.247717 | − | 0.429058i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −78.4397 | − | 135.862i | −0.251420 | − | 0.435472i | ||||
\(47\) | −68.9606 | + | 119.443i | −0.214020 | + | 0.370693i | −0.952969 | − | 0.303068i | \(-0.901989\pi\) |
0.738949 | + | 0.673761i | \(0.235322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −282.768 | + | 194.142i | −0.824398 | + | 0.566011i | ||||
\(50\) | 46.1142 | 0.130431 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8.03853 | + | 13.9231i | 0.0214374 | + | 0.0371306i | ||||
\(53\) | 273.767 | + | 474.179i | 0.709526 | + | 1.22893i | 0.965033 | + | 0.262127i | \(0.0844241\pi\) |
−0.255508 | + | 0.966807i | \(0.582243\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −364.991 | −0.894826 | ||||||||
\(56\) | 43.9023 | + | 141.508i | 0.104762 | + | 0.337676i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 215.332 | − | 372.967i | 0.487492 | − | 0.844361i | ||||
\(59\) | 1.86703 | + | 3.23378i | 0.00411976 | + | 0.00713564i | 0.868078 | − | 0.496428i | \(-0.165355\pi\) |
−0.863958 | + | 0.503564i | \(0.832022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.5008 | − | 99.5943i | 0.120692 | − | 0.209045i | −0.799349 | − | 0.600868i | \(-0.794822\pi\) |
0.920041 | + | 0.391822i | \(0.128155\pi\) | |||||||
\(62\) | 364.657 | 0.746959 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 20.2906 | − | 35.1444i | 0.0387191 | − | 0.0670635i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −313.900 | − | 543.690i | −0.572373 | − | 0.991378i | −0.996322 | − | 0.0856924i | \(-0.972690\pi\) |
0.423949 | − | 0.905686i | \(-0.360644\pi\) | |||||||
\(68\) | 75.9208 | − | 131.499i | 0.135393 | − | 0.234508i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 253.928 | − | 274.566i | 0.433574 | − | 0.468812i | ||||
\(71\) | 533.107 | 0.891100 | 0.445550 | − | 0.895257i | \(-0.353008\pi\) | ||||
0.445550 | + | 0.895257i | \(0.353008\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 149.197 | + | 258.417i | 0.239208 | + | 0.414320i | 0.960487 | − | 0.278324i | \(-0.0897789\pi\) |
−0.721279 | + | 0.692644i | \(0.756446\pi\) | |||||||
\(74\) | 312.557 | + | 541.365i | 0.491001 | + | 0.850438i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 228.131 | 0.344321 | ||||||||
\(77\) | 454.576 | − | 491.521i | 0.672775 | − | 0.727454i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 433.508 | − | 750.857i | 0.617385 | − | 1.06934i | −0.372576 | − | 0.928002i | \(-0.621525\pi\) |
0.989961 | − | 0.141340i | \(-0.0451412\pi\) | |||||||
\(80\) | −80.7734 | − | 139.904i | −0.112884 | − | 0.195521i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 186.557 | − | 323.126i | 0.251241 | − | 0.435162i | ||||
\(83\) | −244.224 | −0.322977 | −0.161489 | − | 0.986875i | \(-0.551630\pi\) | ||||
−0.161489 | + | 0.986875i | \(0.551630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −383.274 | −0.489081 | ||||||||
\(86\) | 262.266 | − | 454.258i | 0.328847 | − | 0.569580i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −144.599 | − | 250.452i | −0.175162 | − | 0.303390i | ||||
\(89\) | −223.508 | + | 387.128i | −0.266200 | + | 0.461073i | −0.967877 | − | 0.251423i | \(-0.919102\pi\) |
0.701677 | + | 0.712495i | \(0.252435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 22.0569 | + | 71.0949i | 0.0254087 | + | 0.0818986i | ||||
\(92\) | −313.759 | −0.355561 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 137.921 | + | 238.887i | 0.151335 | + | 0.262120i | ||||
\(95\) | −287.920 | − | 498.692i | −0.310947 | − | 0.538576i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1803.99 | −1.88832 | −0.944162 | − | 0.329481i | \(-0.893126\pi\) | ||||
−0.944162 | + | 0.329481i | \(0.893126\pi\) | |||||||
\(98\) | 53.4948 | + | 683.911i | 0.0551407 | + | 0.704954i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 46.1142 | − | 79.8721i | 0.0461142 | − | 0.0798721i | ||||
\(101\) | 842.134 | + | 1458.62i | 0.829658 | + | 1.43701i | 0.898307 | + | 0.439369i | \(0.144798\pi\) |
−0.0686484 | + | 0.997641i | \(0.521869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −820.532 | + | 1421.20i | −0.784946 | + | 1.35957i | 0.144085 | + | 0.989565i | \(0.453976\pi\) |
−0.929031 | + | 0.370001i | \(0.879357\pi\) | |||||||
\(104\) | 32.1541 | 0.0303170 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1095.07 | 1.00342 | ||||||||
\(107\) | 160.547 | − | 278.076i | 0.145053 | − | 0.251239i | −0.784340 | − | 0.620332i | \(-0.786998\pi\) |
0.929393 | + | 0.369092i | \(0.120331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −280.005 | − | 484.982i | −0.246051 | − | 0.426173i | 0.716376 | − | 0.697715i | \(-0.245800\pi\) |
−0.962427 | + | 0.271542i | \(0.912466\pi\) | |||||||
\(110\) | −364.991 | + | 632.184i | −0.316369 | + | 0.547967i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 289.002 | + | 65.4673i | 0.243822 | + | 0.0552329i | ||||
\(113\) | −1870.65 | −1.55731 | −0.778655 | − | 0.627452i | \(-0.784098\pi\) | ||||
−0.778655 | + | 0.627452i | \(0.784098\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 395.990 | + | 685.875i | 0.321098 | + | 0.556158i | ||||
\(116\) | −430.665 | − | 745.934i | −0.344709 | − | 0.597053i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.46811 | 0.00582623 | ||||||||
\(119\) | 477.346 | − | 516.141i | 0.367716 | − | 0.397602i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.1012 | − | 20.9598i | 0.00909179 | − | 0.0157474i | ||||
\(122\) | −115.002 | − | 199.189i | −0.0853423 | − | 0.147817i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 364.657 | − | 631.604i | 0.264090 | − | 0.457417i | ||||
\(125\) | −1494.88 | −1.06965 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 790.048 | 0.552011 | 0.276006 | − | 0.961156i | \(-0.410989\pi\) | ||||
0.276006 | + | 0.961156i | \(0.410989\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −40.5812 | − | 70.2888i | −0.0273785 | − | 0.0474210i | ||||
\(131\) | 819.041 | − | 1418.62i | 0.546259 | − | 0.946148i | −0.452267 | − | 0.891882i | \(-0.649385\pi\) |
0.998527 | − | 0.0542661i | \(-0.0172819\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1030.16 | + | 233.361i | 0.671625 | + | 0.152143i | ||||
\(134\) | −1255.60 | −0.809457 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −151.842 | − | 262.997i | −0.0957376 | − | 0.165822i | ||||
\(137\) | 994.660 | + | 1722.80i | 0.620289 | + | 1.07437i | 0.989432 | + | 0.144999i | \(0.0463178\pi\) |
−0.369143 | + | 0.929373i | \(0.620349\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −655.628 | −0.400069 | −0.200035 | − | 0.979789i | \(-0.564105\pi\) | ||||
−0.200035 | + | 0.979789i | \(0.564105\pi\) | |||||||
\(140\) | −221.634 | − | 714.382i | −0.133796 | − | 0.431259i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 533.107 | − | 923.368i | 0.315052 | − | 0.545685i | ||||
\(143\) | −72.6475 | − | 125.829i | −0.0424832 | − | 0.0735830i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1087.07 | + | 1882.86i | −0.622596 | + | 1.07837i | ||||
\(146\) | 596.788 | 0.338291 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1250.23 | 0.694380 | ||||||||
\(149\) | 1494.77 | − | 2589.01i | 0.821853 | − | 1.42349i | −0.0824482 | − | 0.996595i | \(-0.526274\pi\) |
0.904301 | − | 0.426895i | \(-0.140393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 547.979 | + | 949.128i | 0.295324 | + | 0.511516i | 0.975060 | − | 0.221940i | \(-0.0712391\pi\) |
−0.679736 | + | 0.733457i | \(0.737906\pi\) | |||||||
\(152\) | 228.131 | − | 395.134i | 0.121736 | − | 0.210853i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −396.763 | − | 1278.87i | −0.207611 | − | 0.669183i | ||||
\(155\) | −1840.91 | −0.953971 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −250.513 | − | 433.901i | −0.127345 | − | 0.220567i | 0.795302 | − | 0.606213i | \(-0.207312\pi\) |
−0.922647 | + | 0.385646i | \(0.873979\pi\) | |||||||
\(158\) | −867.015 | − | 1501.71i | −0.436557 | − | 0.756139i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −323.094 | −0.159642 | ||||||||
\(161\) | −1416.83 | − | 320.952i | −0.693550 | − | 0.157109i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1134.21 | + | 1964.50i | −0.545018 | + | 0.943998i | 0.453588 | + | 0.891211i | \(0.350144\pi\) |
−0.998606 | + | 0.0527870i | \(0.983190\pi\) | |||||||
\(164\) | −373.114 | − | 646.252i | −0.177654 | − | 0.307706i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −244.224 | + | 423.009i | −0.114190 | + | 0.197782i | ||||
\(167\) | −1369.97 | −0.634799 | −0.317400 | − | 0.948292i | \(-0.602810\pi\) | ||||
−0.317400 | + | 0.948292i | \(0.602810\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2180.85 | −0.992647 | ||||||||
\(170\) | −383.274 | + | 663.850i | −0.172916 | + | 0.299500i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −524.532 | − | 908.516i | −0.232530 | − | 0.402754i | ||||
\(173\) | −921.885 | + | 1596.75i | −0.405142 | + | 0.701727i | −0.994338 | − | 0.106264i | \(-0.966111\pi\) |
0.589196 | + | 0.807990i | \(0.299445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 289.939 | − | 313.503i | 0.125242 | − | 0.135421i | ||||
\(176\) | −578.395 | −0.247717 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 447.017 | + | 774.255i | 0.188232 | + | 0.326028i | ||||
\(179\) | −530.785 | − | 919.346i | −0.221635 | − | 0.383884i | 0.733669 | − | 0.679507i | \(-0.237806\pi\) |
−0.955305 | + | 0.295623i | \(0.904473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2441.54 | 1.00264 | 0.501320 | − | 0.865262i | \(-0.332848\pi\) | ||||
0.501320 | + | 0.865262i | \(0.332848\pi\) | |||||||
\(182\) | 145.197 | + | 32.8913i | 0.0591358 | + | 0.0133960i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −313.759 | + | 543.446i | −0.125710 | + | 0.217736i | ||||
\(185\) | −1577.90 | − | 2732.99i | −0.627077 | − | 1.08613i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −686.128 | + | 1188.41i | −0.268314 | + | 0.464733i | ||||
\(188\) | 551.685 | 0.214020 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1151.68 | −0.439746 | ||||||||
\(191\) | −1846.08 | + | 3197.50i | −0.699359 | + | 1.21132i | 0.269331 | + | 0.963048i | \(0.413198\pi\) |
−0.968689 | + | 0.248277i | \(0.920136\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1571.16 | − | 2721.33i | −0.585982 | − | 1.01495i | −0.994752 | − | 0.102313i | \(-0.967376\pi\) |
0.408770 | − | 0.912637i | \(-0.365958\pi\) | |||||||
\(194\) | −1803.99 | + | 3124.60i | −0.667623 | + | 1.15636i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1238.06 | + | 591.255i | 0.451189 | + | 0.215472i | ||||
\(197\) | −2273.51 | −0.822236 | −0.411118 | − | 0.911582i | \(-0.634862\pi\) | ||||
−0.411118 | + | 0.911582i | \(0.634862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1368.26 | + | 2369.89i | 0.487403 | + | 0.844206i | 0.999895 | − | 0.0144854i | \(-0.00461100\pi\) |
−0.512492 | + | 0.858692i | \(0.671278\pi\) | |||||||
\(200\) | −92.2284 | − | 159.744i | −0.0326076 | − | 0.0564781i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3368.54 | 1.17331 | ||||||||
\(203\) | −1181.70 | − | 3808.92i | −0.408566 | − | 1.31691i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −941.803 | + | 1631.25i | −0.320870 | + | 0.555763i | ||||
\(206\) | 1641.06 | + | 2842.41i | 0.555041 | + | 0.961359i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 32.1541 | − | 55.6926i | 0.0107187 | − | 0.0185653i | ||||
\(209\) | −2061.71 | −0.682352 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2915.84 | 0.951349 | 0.475675 | − | 0.879621i | \(-0.342204\pi\) | ||||
0.475675 | + | 0.879621i | \(0.342204\pi\) | |||||||
\(212\) | 1095.07 | − | 1896.72i | 0.354763 | − | 0.614467i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −321.094 | − | 556.151i | −0.102568 | − | 0.177653i | ||||
\(215\) | −1324.01 | + | 2293.25i | −0.419984 | + | 0.727434i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2292.75 | − | 2479.09i | 0.717244 | − | 0.775536i | ||||
\(218\) | −1120.02 | −0.347969 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 729.983 | + | 1264.37i | 0.223707 | + | 0.387471i | ||||
\(221\) | −76.2865 | − | 132.132i | −0.0232198 | − | 0.0402179i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1875.11 | −0.563078 | −0.281539 | − | 0.959550i | \(-0.590845\pi\) | ||||
−0.281539 | + | 0.959550i | \(0.590845\pi\) | |||||||
\(224\) | 402.395 | − | 435.098i | 0.120027 | − | 0.129782i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1870.65 | + | 3240.06i | −0.550592 | + | 0.953654i | ||||
\(227\) | 2019.15 | + | 3497.27i | 0.590377 | + | 1.02256i | 0.994182 | + | 0.107717i | \(0.0343542\pi\) |
−0.403805 | + | 0.914845i | \(0.632312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −686.456 | + | 1188.98i | −0.198089 | + | 0.343099i | −0.947909 | − | 0.318542i | \(-0.896807\pi\) |
0.749820 | + | 0.661642i | \(0.230140\pi\) | |||||||
\(230\) | 1583.96 | 0.454101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1722.66 | −0.487492 | ||||||||
\(233\) | 2087.15 | − | 3615.06i | 0.586841 | − | 1.01644i | −0.407802 | − | 0.913070i | \(-0.633705\pi\) |
0.994643 | − | 0.103368i | \(-0.0329620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −696.273 | − | 1205.98i | −0.193276 | − | 0.334764i | ||||
\(236\) | 7.46811 | − | 12.9351i | 0.00205988 | − | 0.00356782i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −416.637 | − | 1342.93i | −0.113473 | − | 0.365753i | ||||
\(239\) | −5544.70 | −1.50066 | −0.750329 | − | 0.661065i | \(-0.770105\pi\) | ||||
−0.750329 | + | 0.661065i | \(0.770105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2445.07 | − | 4234.98i | −0.653530 | − | 1.13195i | −0.982260 | − | 0.187524i | \(-0.939954\pi\) |
0.328730 | − | 0.944424i | \(-0.393379\pi\) | |||||||
\(242\) | −24.2023 | − | 41.9197i | −0.00642887 | − | 0.0111351i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −460.007 | −0.120692 | ||||||||
\(245\) | −270.060 | − | 3452.61i | −0.0704224 | − | 0.900324i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 114.615 | − | 198.519i | 0.0295253 | − | 0.0511394i | ||||
\(248\) | −729.313 | − | 1263.21i | −0.186740 | − | 0.323443i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1494.88 | + | 2589.22i | −0.378179 | + | 0.655026i | ||||
\(251\) | 7560.15 | 1.90117 | 0.950583 | − | 0.310470i | \(-0.100487\pi\) | ||||
0.950583 | + | 0.310470i | \(0.100487\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2835.57 | 0.704627 | ||||||||
\(254\) | 790.048 | − | 1368.40i | 0.195165 | − | 0.338037i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1616.43 | − | 2799.74i | 0.392335 | − | 0.679545i | −0.600422 | − | 0.799683i | \(-0.705001\pi\) |
0.992757 | + | 0.120139i | \(0.0383340\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5645.60 | + | 1278.89i | 1.35444 | + | 0.306821i | ||||
\(260\) | −162.325 | −0.0387191 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1638.08 | − | 2837.24i | −0.386263 | − | 0.669028i | ||||
\(263\) | 2142.26 | + | 3710.51i | 0.502272 | + | 0.869961i | 0.999997 | + | 0.00262575i | \(0.000835803\pi\) |
−0.497724 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5528.28 | −1.28151 | ||||||||
\(266\) | 1434.35 | − | 1550.93i | 0.330623 | − | 0.357494i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1255.60 | + | 2174.76i | −0.286186 | + | 0.495689i | ||||
\(269\) | 3348.26 | + | 5799.36i | 0.758912 | + | 1.31447i | 0.943406 | + | 0.331640i | \(0.107602\pi\) |
−0.184495 | + | 0.982834i | \(0.559065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3157.89 | − | 5469.63i | 0.707854 | − | 1.22604i | −0.257798 | − | 0.966199i | \(-0.582997\pi\) |
0.965652 | − | 0.259840i | \(-0.0836698\pi\) | |||||||
\(272\) | −607.367 | −0.135393 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3978.64 | 0.877221 | ||||||||
\(275\) | −416.753 | + | 721.837i | −0.0913860 | + | 0.158285i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1377.62 | − | 2386.12i | −0.298821 | − | 0.517573i | 0.677045 | − | 0.735941i | \(-0.263260\pi\) |
−0.975866 | + | 0.218368i | \(0.929927\pi\) | |||||||
\(278\) | −655.628 | + | 1135.58i | −0.141446 | + | 0.244991i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1458.98 | − | 330.501i | −0.311395 | − | 0.0705401i | ||||
\(281\) | 1453.00 | 0.308464 | 0.154232 | − | 0.988035i | \(-0.450710\pi\) | ||||
0.154232 | + | 0.988035i | \(0.450710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2715.92 | − | 4704.11i | −0.570476 | − | 0.988093i | −0.996517 | − | 0.0833890i | \(-0.973426\pi\) |
0.426042 | − | 0.904704i | \(-0.359908\pi\) | |||||||
\(284\) | −1066.21 | − | 1846.74i | −0.222775 | − | 0.385858i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −290.590 | −0.0600803 | ||||||||
\(287\) | −1023.78 | − | 3299.92i | −0.210565 | − | 0.678704i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1736.00 | − | 3006.85i | 0.353349 | − | 0.612018i | ||||
\(290\) | 2174.14 | + | 3765.73i | 0.440242 | + | 0.762521i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 596.788 | − | 1033.67i | 0.119604 | − | 0.207160i | ||||
\(293\) | 6227.21 | 1.24163 | 0.620815 | − | 0.783957i | \(-0.286802\pi\) | ||||
0.620815 | + | 0.783957i | \(0.286802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −37.7015 | −0.00744091 | ||||||||
\(296\) | 1250.23 | − | 2165.46i | 0.245500 | − | 0.425219i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2989.53 | − | 5178.02i | −0.581138 | − | 1.00656i | ||||
\(299\) | −157.635 | + | 273.032i | −0.0304892 | + | 0.0528088i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1439.26 | − | 4639.10i | −0.275606 | − | 0.888350i | ||||
\(302\) | 2191.92 | 0.417651 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −456.261 | − | 790.268i | −0.0860802 | − | 0.149095i | ||||
\(305\) | 580.567 | + | 1005.57i | 0.108994 | + | 0.188783i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8621.61 | 1.60281 | 0.801403 | − | 0.598125i | \(-0.204088\pi\) | ||||
0.801403 | + | 0.598125i | \(0.204088\pi\) | |||||||
\(308\) | −2611.83 | − | 591.655i | −0.483191 | − | 0.109457i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1840.91 | + | 3188.55i | −0.337280 | + | 0.584186i | ||||
\(311\) | 3712.11 | + | 6429.56i | 0.676831 | + | 1.17230i | 0.975930 | + | 0.218083i | \(0.0699804\pi\) |
−0.299100 | + | 0.954222i | \(0.596686\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1633.30 | + | 2828.96i | −0.294951 | + | 0.510870i | −0.974974 | − | 0.222321i | \(-0.928637\pi\) |
0.680022 | + | 0.733191i | \(0.261970\pi\) | |||||||
\(314\) | −1002.05 | −0.180092 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3468.06 | −0.617385 | ||||||||
\(317\) | 2440.25 | − | 4226.63i | 0.432359 | − | 0.748868i | −0.564717 | − | 0.825285i | \(-0.691015\pi\) |
0.997076 | + | 0.0764167i | \(0.0243479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3892.10 | + | 6741.31i | 0.683121 | + | 1.18320i | ||||
\(320\) | −323.094 | + | 559.615i | −0.0564421 | + | 0.0977607i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1972.73 | + | 2133.06i | −0.341416 | + | 0.369164i | ||||
\(323\) | −2164.98 | −0.372950 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −46.3363 | − | 80.2568i | −0.00790854 | − | 0.0136980i | ||||
\(326\) | 2268.41 | + | 3929.01i | 0.385386 | + | 0.667508i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1492.46 | −0.251241 | ||||||||
\(329\) | 2491.22 | + | 564.333i | 0.417463 | + | 0.0945675i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4799.58 | − | 8313.11i | 0.797005 | − | 1.38045i | −0.124554 | − | 0.992213i | \(-0.539750\pi\) |
0.921558 | − | 0.388240i | \(-0.126917\pi\) | |||||||
\(332\) | 488.449 | + | 846.018i | 0.0807443 | + | 0.139853i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1369.97 | + | 2372.86i | −0.224436 | + | 0.388734i | ||||
\(335\) | 6338.69 | 1.03379 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2895.79 | −0.468082 | −0.234041 | − | 0.972227i | \(-0.575195\pi\) | ||||
−0.234041 | + | 0.972227i | \(0.575195\pi\) | |||||||
\(338\) | −2180.85 | + | 3777.34i | −0.350954 | + | 0.607870i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 766.548 | + | 1327.70i | 0.122270 | + | 0.211778i | ||||
\(341\) | −3295.55 | + | 5708.07i | −0.523356 | + | 0.906478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4985.85 | + | 3936.35i | 0.784871 | + | 0.619659i | ||||
\(344\) | −2098.13 | −0.328847 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1843.77 | + | 3193.50i | 0.286479 | + | 0.496196i | ||||
\(347\) | 2678.81 | + | 4639.83i | 0.414426 | + | 0.717807i | 0.995368 | − | 0.0961381i | \(-0.0306490\pi\) |
−0.580942 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6049.21 | −0.927813 | −0.463906 | − | 0.885884i | \(-0.653553\pi\) | ||||
−0.463906 | + | 0.885884i | \(0.653553\pi\) | |||||||
\(350\) | −253.065 | − | 815.692i | −0.0386482 | − | 0.124573i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −578.395 | + | 1001.81i | −0.0875811 | + | 0.151695i | ||||
\(353\) | 3440.28 | + | 5958.74i | 0.518718 | + | 0.898446i | 0.999763 | + | 0.0217505i | \(0.00692394\pi\) |
−0.481045 | + | 0.876696i | \(0.659743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2691.30 | + | 4661.47i | −0.402365 | + | 0.696916i | ||||
\(356\) | 1788.07 | 0.266200 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2123.14 | −0.313440 | ||||||||
\(359\) | 2995.95 | − | 5189.15i | 0.440447 | − | 0.762876i | −0.557276 | − | 0.830328i | \(-0.688153\pi\) |
0.997723 | + | 0.0674511i | \(0.0214867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1803.14 | + | 3123.13i | 0.262886 | + | 0.455333i | ||||
\(362\) | 2441.54 | − | 4228.86i | 0.354487 | − | 0.613989i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 202.166 | − | 218.597i | 0.0291110 | − | 0.0314769i | ||||
\(365\) | −3012.79 | −0.432045 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3285.52 | + | 5690.70i | 0.467311 | + | 0.809406i | 0.999302 | − | 0.0373437i | \(-0.0118896\pi\) |
−0.531992 | + | 0.846749i | \(0.678556\pi\) | |||||||
\(368\) | 627.518 | + | 1086.89i | 0.0888903 | + | 0.153962i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6311.58 | −0.886820 | ||||||||
\(371\) | 6885.16 | − | 7444.74i | 0.963503 | − | 1.04181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1866.81 | − | 3233.41i | 0.259141 | − | 0.448846i | −0.706871 | − | 0.707343i | \(-0.749894\pi\) |
0.966012 | + | 0.258497i | \(0.0832272\pi\) | |||||||
\(374\) | 1372.26 | + | 2376.82i | 0.189726 | + | 0.328616i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 551.685 | − | 955.546i | 0.0756675 | − | 0.131060i | ||||
\(377\) | −865.479 | −0.118235 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8419.14 | 1.14106 | 0.570531 | − | 0.821276i | \(-0.306738\pi\) | ||||
0.570531 | + | 0.821276i | \(0.306738\pi\) | |||||||
\(380\) | −1151.68 | + | 1994.77i | −0.155474 | + | 0.269288i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3692.15 | + | 6395.00i | 0.494521 | + | 0.856536i | ||||
\(383\) | −2665.21 | + | 4616.28i | −0.355577 | + | 0.615877i | −0.987217 | − | 0.159385i | \(-0.949049\pi\) |
0.631640 | + | 0.775262i | \(0.282382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2002.99 | + | 6456.16i | 0.265148 | + | 0.854640i | ||||
\(386\) | −6284.64 | −0.828704 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3607.98 | + | 6249.21i | 0.472081 | + | 0.817668i | ||||
\(389\) | −3905.58 | − | 6764.67i | −0.509051 | − | 0.881703i | −0.999945 | − | 0.0104832i | \(-0.996663\pi\) |
0.490894 | − | 0.871219i | \(-0.336670\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2977.60 | 0.385125 | ||||||||
\(392\) | 2262.15 | − | 1553.13i | 0.291469 | − | 0.200115i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2273.51 | + | 3937.83i | −0.290704 | + | 0.503515i | ||||
\(395\) | 4376.99 | + | 7581.16i | 0.557544 | + | 0.965695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −455.847 | + | 789.550i | −0.0576279 | + | 0.0998145i | −0.893400 | − | 0.449262i | \(-0.851687\pi\) |
0.835772 | + | 0.549076i | \(0.185020\pi\) | |||||||
\(398\) | 5473.03 | 0.689292 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −368.913 | −0.0461142 | ||||||||
\(401\) | −834.008 | + | 1444.54i | −0.103861 | + | 0.179893i | −0.913272 | − | 0.407349i | \(-0.866453\pi\) |
0.809411 | + | 0.587242i | \(0.199786\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −366.413 | − | 634.646i | −0.0452912 | − | 0.0784466i | ||||
\(404\) | 3368.54 | − | 5834.48i | 0.414829 | − | 0.718505i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7778.93 | − | 1762.15i | −0.950892 | − | 0.215405i | ||||
\(407\) | −11298.8 | −1.37608 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4555.24 | − | 7889.90i | −0.550714 | − | 0.953864i | −0.998223 | − | 0.0595852i | \(-0.981022\pi\) |
0.447509 | − | 0.894279i | \(-0.352311\pi\) | |||||||
\(410\) | 1883.61 | + | 3262.50i | 0.226889 | + | 0.392984i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6564.26 | 0.784946 | ||||||||
\(413\) | 46.9551 | − | 50.7713i | 0.00559445 | − | 0.00604913i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1232.93 | − | 2135.49i | 0.145836 | − | 0.252596i | ||||
\(416\) | −64.3083 | − | 111.385i | −0.00757926 | − | 0.0131277i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2061.71 | + | 3570.99i | −0.241248 | + | 0.417853i | ||||
\(419\) | 12626.4 | 1.47217 | 0.736085 | − | 0.676889i | \(-0.236672\pi\) | ||||
0.736085 | + | 0.676889i | \(0.236672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4805.61 | −0.556320 | −0.278160 | − | 0.960535i | \(-0.589725\pi\) | ||||
−0.278160 | + | 0.960535i | \(0.589725\pi\) | |||||||
\(422\) | 2915.84 | − | 5050.38i | 0.336353 | − | 0.582580i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2190.14 | − | 3793.43i | −0.250855 | − | 0.434494i | ||||
\(425\) | −437.628 | + | 757.994i | −0.0499484 | + | 0.0865132i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2077.23 | − | 470.553i | −0.235420 | − | 0.0533294i | ||||
\(428\) | −1284.38 | −0.145053 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2648.02 | + | 4586.50i | 0.296974 | + | 0.514374i | ||||
\(431\) | −3341.06 | − | 5786.89i | −0.373395 | − | 0.646739i | 0.616690 | − | 0.787206i | \(-0.288473\pi\) |
−0.990085 | + | 0.140467i | \(0.955140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8502.27 | −0.943632 | −0.471816 | − | 0.881697i | \(-0.656401\pi\) | ||||
−0.471816 | + | 0.881697i | \(0.656401\pi\) | |||||||
\(434\) | −2001.16 | − | 6450.24i | −0.221333 | − | 0.713414i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1120.02 | + | 1939.93i | −0.123026 | + | 0.213087i | ||||
\(437\) | 2236.81 | + | 3874.27i | 0.244854 | + | 0.424100i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6814.77 | − | 11803.5i | 0.740891 | − | 1.28326i | −0.211199 | − | 0.977443i | \(-0.567737\pi\) |
0.952090 | − | 0.305818i | \(-0.0989299\pi\) | |||||||
\(440\) | 2919.93 | 0.316369 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −305.146 | −0.0328378 | ||||||||
\(443\) | 3427.16 | − | 5936.02i | 0.367561 | − | 0.636634i | −0.621623 | − | 0.783317i | \(-0.713526\pi\) |
0.989184 | + | 0.146683i | \(0.0468597\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2256.69 | − | 3908.70i | −0.240399 | − | 0.416383i | ||||
\(446\) | −1875.11 | + | 3247.78i | −0.199078 | + | 0.344813i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −351.218 | − | 1132.07i | −0.0370391 | − | 0.119386i | ||||
\(449\) | −10372.3 | −1.09019 | −0.545097 | − | 0.838373i | \(-0.683507\pi\) | ||||
−0.545097 | + | 0.838373i | \(0.683507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3371.98 | + | 5840.45i | 0.352063 | + | 0.609791i | ||||
\(452\) | 3741.30 | + | 6480.13i | 0.389328 | + | 0.674335i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8076.59 | 0.834919 | ||||||||
\(455\) | −733.003 | − | 166.047i | −0.0755247 | − | 0.0171085i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3950.40 | − | 6842.30i | 0.404359 | − | 0.700370i | −0.589888 | − | 0.807485i | \(-0.700828\pi\) |
0.994247 | + | 0.107115i | \(0.0341613\pi\) | |||||||
\(458\) | 1372.91 | + | 2377.95i | 0.140070 | + | 0.242608i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1583.96 | − | 2743.50i | 0.160549 | − | 0.278079i | ||||
\(461\) | −11359.7 | −1.14767 | −0.573834 | − | 0.818972i | \(-0.694544\pi\) | ||||
−0.573834 | + | 0.818972i | \(0.694544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7346.85 | 0.737445 | 0.368723 | − | 0.929539i | \(-0.379795\pi\) | ||||
0.368723 | + | 0.929539i | \(0.379795\pi\) | |||||||
\(464\) | −1722.66 | + | 2983.73i | −0.172354 | + | 0.298527i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4174.31 | − | 7230.11i | −0.414959 | − | 0.718731i | ||||
\(467\) | −473.289 | + | 819.760i | −0.0468976 | + | 0.0812291i | −0.888521 | − | 0.458835i | \(-0.848267\pi\) |
0.841624 | + | 0.540064i | \(0.181600\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7894.47 | + | 8536.08i | −0.777256 | + | 0.840426i | ||||
\(470\) | −2785.09 | −0.273333 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.9362 | − | 25.8703i | −0.00145656 | − | 0.00252283i | ||||
\(473\) | 4740.41 | + | 8210.64i | 0.460813 | + | 0.798151i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1315.01 | −0.127025 | ||||||||
\(476\) | −2742.66 | − | 621.292i | −0.264096 | − | 0.0598253i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5544.70 | + | 9603.71i | −0.530562 | + | 0.918961i | ||||
\(479\) | −7657.75 | − | 13263.6i | −0.730462 | − | 1.26520i | −0.956686 | − | 0.291122i | \(-0.905971\pi\) |
0.226224 | − | 0.974075i | \(-0.427362\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 628.125 | − | 1087.95i | 0.0595427 | − | 0.103131i | ||||
\(482\) | −9780.28 | −0.924231 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −96.8094 | −0.00909179 | ||||||||
\(485\) | 9107.15 | − | 15774.1i | 0.852649 | − | 1.47683i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4320.19 | + | 7482.78i | 0.401984 | + | 0.696257i | 0.993965 | − | 0.109695i | \(-0.0349873\pi\) |
−0.591981 | + | 0.805952i | \(0.701654\pi\) | |||||||
\(488\) | −460.007 | + | 796.755i | −0.0426711 | + | 0.0739086i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6250.16 | − | 2984.86i | −0.576232 | − | 0.275188i | ||||
\(491\) | −13425.6 | −1.23399 | −0.616996 | − | 0.786966i | \(-0.711651\pi\) | ||||
−0.616996 | + | 0.786966i | \(0.711651\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4087.05 | + | 7078.99i | 0.373371 | + | 0.646697i | ||||
\(494\) | −229.229 | − | 397.037i | −0.0208776 | − | 0.0361610i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2917.25 | −0.264090 | ||||||||
\(497\) | −2925.57 | − | 9429.88i | −0.264044 | − | 0.851082i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5489.01 | − | 9507.24i | 0.492429 | − | 0.852911i | −0.507533 | − | 0.861632i | \(-0.669443\pi\) |
0.999962 | + | 0.00872085i | \(0.00277597\pi\) | |||||||
\(500\) | 2989.77 | + | 5178.43i | 0.267413 | + | 0.463173i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7560.15 | − | 13094.6i | 0.672164 | − | 1.16422i | ||||
\(503\) | −7829.41 | −0.694028 | −0.347014 | − | 0.937860i | \(-0.612804\pi\) | ||||
−0.347014 | + | 0.937860i | \(0.612804\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17005.5 | −1.49849 | ||||||||
\(506\) | 2835.57 | − | 4911.35i | 0.249123 | − | 0.431494i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1580.10 | − | 2736.81i | −0.138003 | − | 0.239028i | ||||
\(509\) | −9091.90 | + | 15747.6i | −0.791732 | + | 1.37132i | 0.133162 | + | 0.991094i | \(0.457487\pi\) |
−0.924894 | + | 0.380225i | \(0.875847\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3752.25 | − | 4057.21i | 0.324833 | − | 0.351234i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3232.86 | − | 5599.48i | −0.277423 | − | 0.480511i | ||||
\(515\) | −8284.65 | − | 14349.4i | −0.708865 | − | 1.22779i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4985.80 | −0.424130 | ||||||||
\(518\) | 7860.71 | − | 8499.57i | 0.666756 | − | 0.720946i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −162.325 | + | 281.155i | −0.0136893 | + | 0.0237105i | ||||
\(521\) | 11202.3 | + | 19402.9i | 0.941997 | + | 1.63159i | 0.761656 | + | 0.647982i | \(0.224387\pi\) |
0.180341 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2843.67 | + | 4925.38i | −0.237753 | + | 0.411801i | −0.960069 | − | 0.279763i | \(-0.909744\pi\) |
0.722316 | + | 0.691563i | \(0.243078\pi\) | |||||||
\(524\) | −6552.33 | −0.546259 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8569.05 | 0.710320 | ||||||||
\(527\) | −3460.63 | + | 5993.99i | −0.286048 | + | 0.495450i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3007.11 | + | 5208.46i | 0.247153 | + | 0.428081i | ||||
\(530\) | −5528.28 | + | 9575.27i | −0.453082 | + | 0.784761i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1251.93 | − | 4035.30i | −0.102027 | − | 0.328858i | ||||
\(533\) | −749.822 | −0.0609351 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1620.99 | + | 2807.64i | 0.130994 | + | 0.226888i | ||||
\(536\) | 2511.20 | + | 4349.52i | 0.202364 | + | 0.350505i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13393.1 | 1.07326 | ||||||||
\(539\) | −11188.9 | − | 5343.42i | −0.894137 | − | 0.427008i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6508.78 | − | 11273.5i | 0.517254 | − | 0.895910i | −0.482545 | − | 0.875871i | \(-0.660288\pi\) |
0.999799 | − | 0.0200392i | \(-0.00637910\pi\) | |||||||
\(542\) | −6315.79 | − | 10939.3i | −0.500528 | − | 0.866940i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −607.367 | + | 1051.99i | −0.0478688 | + | 0.0829112i | ||||
\(545\) | 5654.23 | 0.444405 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6353.31 | −0.496614 | −0.248307 | − | 0.968681i | \(-0.579874\pi\) | ||||
−0.248307 | + | 0.968681i | \(0.579874\pi\) | |||||||
\(548\) | 3978.64 | − | 6891.21i | 0.310144 | − | 0.537186i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 833.506 | + | 1443.67i | 0.0646197 | + | 0.111925i | ||||
\(551\) | −6140.49 | + | 10635.6i | −0.474762 | + | 0.822311i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15660.6 | − | 3547.57i | −1.20426 | − | 0.272799i | ||||
\(554\) | −5510.50 | −0.422597 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1311.26 | + | 2271.16i | 0.100017 | + | 0.173235i | ||||
\(557\) | −7759.69 | − | 13440.2i | −0.590285 | − | 1.02240i | −0.994194 | − | 0.107604i | \(-0.965682\pi\) |
0.403909 | − | 0.914799i | \(-0.367651\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1054.12 | −0.0797574 | ||||||||
\(560\) | −2031.42 | + | 2196.52i | −0.153292 | + | 0.165750i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1453.00 | − | 2516.66i | 0.109059 | − | 0.188895i | ||||
\(563\) | −9095.49 | − | 15753.9i | −0.680869 | − | 1.17930i | −0.974716 | − | 0.223448i | \(-0.928269\pi\) |
0.293847 | − | 0.955853i | \(-0.405064\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9443.68 | − | 16356.9i | 0.703184 | − | 1.21795i | ||||
\(566\) | −10863.7 | −0.806774 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4264.85 | −0.315052 | ||||||||
\(569\) | 6159.38 | − | 10668.4i | 0.453804 | − | 0.786012i | −0.544814 | − | 0.838557i | \(-0.683400\pi\) |
0.998619 | + | 0.0525449i | \(0.0167333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8694.98 | + | 15060.2i | 0.637257 | + | 1.10376i | 0.986032 | + | 0.166555i | \(0.0532644\pi\) |
−0.348775 | + | 0.937206i | \(0.613402\pi\) | |||||||
\(572\) | −290.590 | + | 503.317i | −0.0212416 | + | 0.0367915i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6739.41 | − | 1526.67i | −0.490065 | − | 0.111014i | ||||
\(575\) | 1808.59 | 0.131171 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1625.45 | − | 2815.37i | −0.117276 | − | 0.203129i | 0.801411 | − | 0.598114i | \(-0.204083\pi\) |
−0.918687 | + | 0.394985i | \(0.870750\pi\) | |||||||
\(578\) | −3472.01 | − | 6013.69i | −0.249855 | − | 0.432762i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8696.57 | 0.622596 | ||||||||
\(581\) | 1340.25 | + | 4319.97i | 0.0957022 | + | 0.308473i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9896.60 | + | 17141.4i | −0.703045 | + | 1.21771i | ||||
\(584\) | −1193.58 | − | 2067.33i | −0.0845728 | − | 0.146484i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6227.21 | − | 10785.8i | 0.438982 | − | 0.760339i | ||||
\(587\) | 6993.54 | 0.491745 | 0.245872 | − | 0.969302i | \(-0.420926\pi\) | ||||
0.245872 | + | 0.969302i | \(0.420926\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10398.7 | −0.727453 | ||||||||
\(590\) | −37.7015 | + | 65.3010i | −0.00263076 | + | 0.00455661i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2500.46 | − | 4330.92i | −0.173595 | − | 0.300675i | ||||
\(593\) | 5001.10 | − | 8662.15i | 0.346324 | − | 0.599851i | −0.639269 | − | 0.768983i | \(-0.720763\pi\) |
0.985593 | + | 0.169132i | \(0.0540963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2103.32 | + | 6779.56i | 0.144921 | + | 0.467117i | ||||
\(596\) | −11958.1 | −0.821853 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 315.270 | + | 546.064i | 0.0215591 | + | 0.0373415i | ||||
\(599\) | 12362.1 | + | 21411.8i | 0.843241 | + | 1.46054i | 0.887140 | + | 0.461500i | \(0.152688\pi\) |
−0.0438997 | + | 0.999036i | \(0.513978\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4825.50 | −0.327515 | −0.163757 | − | 0.986501i | \(-0.552361\pi\) | ||||
−0.163757 | + | 0.986501i | \(0.552361\pi\) | |||||||
\(602\) | −9474.42 | − | 2146.23i | −0.641443 | − | 0.145305i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2191.92 | − | 3796.51i | 0.147662 | − | 0.255758i | ||||
\(605\) | 122.182 | + | 211.625i | 0.00821056 | + | 0.0142211i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12365.1 | + | 21417.0i | −0.826826 | + | 1.43210i | 0.0736896 | + | 0.997281i | \(0.476523\pi\) |
−0.900516 | + | 0.434824i | \(0.856811\pi\) | |||||||
\(608\) | −1825.04 | −0.121736 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2322.27 | 0.154141 | ||||||||
\(611\) | 277.171 | − | 480.074i | 0.0183521 | − | 0.0317868i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3804.29 | + | 6589.22i | 0.250659 | + | 0.434154i | 0.963707 | − | 0.266961i | \(-0.0860195\pi\) |
−0.713049 | + | 0.701115i | \(0.752686\pi\) | |||||||
\(614\) | 8621.61 | − | 14933.1i | 0.566677 | − | 0.981514i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3636.61 | + | 3932.16i | −0.237862 | + | 0.257194i | ||||
\(617\) | −25089.8 | −1.63708 | −0.818538 | − | 0.574452i | \(-0.805215\pi\) | ||||
−0.818538 | + | 0.574452i | \(0.805215\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11452.5 | − | 19836.3i | −0.743642 | − | 1.28803i | −0.950827 | − | 0.309724i | \(-0.899763\pi\) |
0.207185 | − | 0.978302i | \(-0.433570\pi\) | |||||||
\(620\) | 3681.82 | + | 6377.10i | 0.238493 | + | 0.413082i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14848.4 | 0.957183 | ||||||||
\(623\) | 8074.29 | + | 1829.06i | 0.519245 | + | 0.117624i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6105.62 | − | 10575.2i | 0.390760 | − | 0.676815i | ||||
\(626\) | 3266.61 | + | 5657.93i | 0.208562 | + | 0.361240i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1002.05 | + | 1735.60i | −0.0636723 | + | 0.110284i | ||||
\(629\) | −11864.8 | −0.752116 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2253.93 | 0.142199 | 0.0710996 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0710996 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(632\) | −3468.06 | + | 6006.86i | −0.218279 | + | 0.378070i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4880.49 | − | 8453.26i | −0.305724 | − | 0.529530i | ||||
\(635\) | −3988.43 | + | 6908.17i | −0.249254 | + | 0.431720i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1136.52 | − | 780.307i | 0.0706917 | − | 0.0485352i | ||||
\(638\) | 15568.4 | 0.966079 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 646.187 | + | 1119.23i | 0.0399106 | + | 0.0691272i | ||||
\(641\) | 6014.77 | + | 10417.9i | 0.370623 | + | 0.641938i | 0.989661 | − | 0.143423i | \(-0.0458109\pi\) |
−0.619039 | + | 0.785361i | \(0.712478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4738.59 | −0.290625 | −0.145312 | − | 0.989386i | \(-0.546419\pi\) | ||||
−0.145312 | + | 0.989386i | \(0.546419\pi\) | |||||||
\(644\) | 1721.84 | + | 5549.93i | 0.105357 | + | 0.339593i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2164.98 | + | 3749.86i | −0.131858 | + | 0.228384i | ||||
\(647\) | −2869.84 | − | 4970.71i | −0.174382 | − | 0.302038i | 0.765565 | − | 0.643358i | \(-0.222459\pi\) |
−0.939947 | + | 0.341320i | \(0.889126\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −67.4924 | + | 116.900i | −0.00408214 | + | 0.00707047i | ||||
\(650\) | −185.345 | −0.0111844 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9073.65 | 0.545018 | ||||||||
\(653\) | −863.084 | + | 1494.91i | −0.0517230 | + | 0.0895868i | −0.890728 | − | 0.454537i | \(-0.849805\pi\) |
0.839005 | + | 0.544124i | \(0.183138\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8269.59 | + | 14323.4i | 0.493313 | + | 0.854442i | ||||
\(656\) | −1492.46 | + | 2585.01i | −0.0888271 | + | 0.153853i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3468.67 | − | 3750.58i | 0.205506 | − | 0.222208i | ||||
\(659\) | −10987.7 | −0.649501 | −0.324751 | − | 0.945800i | \(-0.605280\pi\) | ||||
−0.324751 | + | 0.945800i | \(0.605280\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16020.4 | − | 27748.1i | −0.942695 | − | 1.63280i | −0.760302 | − | 0.649570i | \(-0.774949\pi\) |
−0.182393 | − | 0.983226i | \(-0.558384\pi\) | |||||||
\(662\) | −9599.15 | − | 16626.2i | −0.563567 | − | 0.976127i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1953.80 | 0.114190 | ||||||||
\(665\) | −7241.09 | + | 7829.60i | −0.422252 | + | 0.456570i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8445.31 | − | 14627.7i | 0.490260 | − | 0.849156i | ||||
\(668\) | 2739.94 | + | 4745.72i | 0.158700 | + | 0.274876i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6338.69 | − | 10978.9i | 0.365500 | − | 0.633065i | ||||
\(671\) | 4157.27 | 0.239180 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13026.7 | −0.746124 | −0.373062 | − | 0.927806i | \(-0.621692\pi\) | ||||
−0.373062 | + | 0.927806i | \(0.621692\pi\) | |||||||
\(674\) | −2895.79 | + | 5015.65i | −0.165492 | + | 0.286641i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4361.69 | + | 7554.67i | 0.248162 | + | 0.429829i | ||||
\(677\) | 2360.39 | − | 4088.32i | 0.133999 | − | 0.232093i | −0.791216 | − | 0.611537i | \(-0.790551\pi\) |
0.925215 | + | 0.379444i | \(0.123885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9899.91 | + | 31909.9i | 0.559534 | + | 1.80352i | ||||
\(680\) | 3066.19 | 0.172916 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6591.11 | + | 11416.1i | 0.370068 | + | 0.640977i | ||||
\(683\) | 5585.00 | + | 9673.51i | 0.312890 | + | 0.541942i | 0.978987 | − | 0.203924i | \(-0.0653694\pi\) |
−0.666096 | + | 0.745866i | \(0.732036\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20085.5 | −1.12033 | ||||||||
\(686\) | 11803.8 | − | 4699.40i | 0.656956 | − | 0.261551i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2098.13 | + | 3634.07i | −0.116265 | + | 0.201377i | ||||
\(689\) | −1100.34 | − | 1905.85i | −0.0608415 | − | 0.105381i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6986.42 | − | 12100.8i | 0.384625 | − | 0.666190i | −0.607092 | − | 0.794632i | \(-0.707664\pi\) |
0.991717 | + | 0.128441i | \(0.0409974\pi\) | |||||||
\(692\) | 7375.08 | 0.405142 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10715.2 | 0.586087 | ||||||||
\(695\) | 3309.83 | − | 5732.79i | 0.180646 | − | 0.312888i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3540.89 | + | 6133.00i | 0.192426 | + | 0.333291i | ||||
\(698\) | −6049.21 | + | 10477.5i | −0.328031 | + | 0.568167i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1665.88 | − | 377.371i | −0.0899493 | − | 0.0203761i | ||||
\(701\) | 9694.83 | 0.522352 | 0.261176 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261176 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8912.99 | − | 15437.7i | −0.478179 | − | 0.828230i | ||||
\(704\) | 1156.79 | + | 2003.62i | 0.0619292 | + | 0.107264i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13761.1 | 0.733578 | ||||||||
\(707\) | 21179.4 | − | 22900.7i | 1.12664 | − | 1.21820i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12712.8 | + | 22019.3i | −0.673399 | + | 1.16636i | 0.303535 | + | 0.952820i | \(0.401833\pi\) |
−0.976934 | + | 0.213541i | \(0.931500\pi\) | |||||||
\(710\) | 5382.61 | + | 9322.95i | 0.284515 | + | 0.492794i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1788.07 | − | 3097.02i | 0.0941160 | − | 0.163014i | ||||
\(713\) | 14301.8 | 0.751200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1467.00 | 0.0767309 | ||||||||
\(716\) | −2123.14 | + | 3677.39i | −0.110818 | + | 0.191942i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5991.91 | − | 10378.3i | −0.311443 | − | 0.539435i | ||||
\(719\) | 8796.40 | − | 15235.8i | 0.456259 | − | 0.790264i | −0.542500 | − | 0.840056i | \(-0.682522\pi\) |
0.998760 | + | 0.0497912i | \(0.0158556\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29641.9 | + | 6714.76i | 1.53110 | + | 0.346839i | ||||
\(722\) | 7212.55 | 0.371778 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4883.07 | − | 8457.73i | −0.250660 | − | 0.434156i | ||||
\(725\) | 2482.47 | + | 4299.76i | 0.127168 | + | 0.220261i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10087.1 | −0.514596 | −0.257298 | − | 0.966332i | \(-0.582832\pi\) | ||||
−0.257298 | + | 0.966332i | \(0.582832\pi\) | |||||||
\(728\) | −176.455 | − | 568.759i | −0.00898332 | − | 0.0289555i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3012.79 | + | 5218.30i | −0.152751 | + | 0.264572i | ||||
\(731\) | 4977.86 | + | 8621.91i | 0.251865 | + | 0.436242i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15904.3 | + | 27547.1i | −0.801417 | + | 1.38810i | 0.117266 | + | 0.993101i | \(0.462587\pi\) |
−0.918683 | + | 0.394995i | \(0.870746\pi\) | |||||||
\(734\) | 13142.1 | 0.660877 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2510.07 | 0.125710 | ||||||||
\(737\) | 11347.4 | − | 19654.2i | 0.567145 | − | 0.982324i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8287.63 | + | 14354.6i | 0.412538 | + | 0.714536i | 0.995166 | − | 0.0982021i | \(-0.0313092\pi\) |
−0.582629 | + | 0.812738i | \(0.697976\pi\) | |||||||
\(740\) | −6311.58 | + | 10932.0i | −0.313538 | + | 0.543064i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6009.51 | − | 19370.2i | −0.297326 | − | 0.958358i | ||||
\(743\) | 11053.4 | 0.545773 | 0.272886 | − | 0.962046i | \(-0.412022\pi\) | ||||
0.272886 | + | 0.962046i | \(0.412022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15092.2 | + | 26140.4i | 0.742194 | + | 1.28552i | ||||
\(746\) | −3733.61 | − | 6466.81i | −0.183240 | − | 0.317382i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5489.02 | 0.268314 | ||||||||
\(749\) | −5799.80 | − | 1313.82i | −0.282937 | − | 0.0640935i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1589.84 | + | 2753.68i | −0.0772490 | + | 0.133799i | −0.902062 | − | 0.431606i | \(-0.857947\pi\) |
0.824813 | + | 0.565405i | \(0.191280\pi\) | |||||||
\(752\) | −1103.37 | − | 1911.09i | −0.0535050 | − | 0.0926733i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −865.479 | + | 1499.05i | −0.0418022 | + | 0.0724036i | ||||
\(755\) | −11065.5 | −0.533399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31130.8 | −1.49467 | −0.747336 | − | 0.664446i | \(-0.768667\pi\) | ||||
−0.747336 | + | 0.664446i | \(0.768667\pi\) | |||||||
\(758\) | 8419.14 | − | 14582.4i | 0.403426 | − | 0.698755i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2303.36 | + | 3989.54i | 0.109936 | + | 0.190416i | ||||
\(761\) | 3915.15 | − | 6781.24i | 0.186497 | − | 0.323022i | −0.757583 | − | 0.652739i | \(-0.773620\pi\) |
0.944080 | + | 0.329717i | \(0.106953\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7042.02 | + | 7614.35i | −0.334126 | + | 0.361282i | ||||
\(764\) | 14768.6 | 0.699359 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5330.42 | + | 9232.56i | 0.251431 | + | 0.435491i | ||||
\(767\) | −7.50408 | − | 12.9974i | −0.000353268 | − | 0.000611878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9389.21 | 0.440291 | 0.220145 | − | 0.975467i | \(-0.429347\pi\) | ||||
0.220145 | + | 0.975467i | \(0.429347\pi\) | |||||||
\(770\) | 13185.4 | + | 2986.88i | 0.617102 | + | 0.139792i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6284.64 | + | 10885.3i | −0.292991 | + | 0.507475i | ||||
\(773\) | 13896.1 | + | 24068.8i | 0.646584 | + | 1.11992i | 0.983933 | + | 0.178537i | \(0.0571363\pi\) |
−0.337349 | + | 0.941380i | \(0.609530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2101.98 | + | 3640.74i | −0.0974263 | + | 0.168747i | ||||
\(776\) | 14431.9 | 0.667623 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15622.3 | −0.719907 | ||||||||
\(779\) | −5319.92 | + | 9214.37i | −0.244680 | + | 0.423798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9635.81 | + | 16689.7i | 0.441481 | + | 0.764667i | ||||
\(782\) | 2977.60 | − | 5157.36i | 0.136162 | − | 0.235840i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −427.958 | − | 5471.29i | −0.0194952 | − | 0.249239i | ||||
\(785\) | 5058.69 | 0.230003 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1413.31 | − | 2447.93i | −0.0640141 | − | 0.110876i | 0.832242 | − | 0.554412i | \(-0.187057\pi\) |
−0.896256 | + | 0.443537i | \(0.853724\pi\) | |||||||
\(788\) | 4547.01 | + | 7875.65i | 0.205559 | + | 0.356039i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 17507.9 | 0.788487 | ||||||||
\(791\) | 10265.7 | + | 33089.1i | 0.461450 | + | 1.48737i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −231.111 | + | 400.296i | −0.0103493 | + | 0.0179255i | ||||
\(794\) | 911.693 | + | 1579.10i | 0.0407491 | + | 0.0705795i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5473.03 | − | 9479.56i | 0.243701 | − | 0.422103i | ||||
\(797\) | 29567.2 | 1.31408 | 0.657041 | − | 0.753855i | \(-0.271808\pi\) | ||||
0.657041 | + | 0.753855i | \(0.271808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5235.54 | −0.231815 | ||||||||
\(800\) | −368.913 | + | 638.977i | −0.0163038 | + | 0.0282391i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1668.02 | + | 2889.09i | 0.0734410 | + | 0.127204i | ||||
\(803\) | −5393.42 | + | 9341.67i | −0.237023 | + | 0.410536i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9959.02 | − | 10768.4i | 0.436036 | − | 0.471474i | ||||
\(806\) | −1465.65 | −0.0640514 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −6737.07 | − | 11669.0i | −0.293328 | − | 0.508060i | ||||
\(809\) | −4385.17 | − | 7595.33i | −0.190574 | − | 0.330084i | 0.754867 | − | 0.655878i | \(-0.227702\pi\) |
−0.945441 | + | 0.325795i | \(0.894368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2017.43 | −0.0873508 | −0.0436754 | − | 0.999046i | \(-0.513907\pi\) | ||||
−0.0436754 | + | 0.999046i | \(0.513907\pi\) | |||||||
\(812\) | −10831.1 | + | 11711.4i | −0.468099 | + | 0.506143i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11298.8 | + | 19570.2i | −0.486516 | + | 0.842671i | ||||
\(815\) | −11451.7 | − | 19835.0i | −0.492192 | − | 0.852501i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7478.87 | + | 12953.8i | −0.320260 | + | 0.554707i | ||||
\(818\) | −18220.9 | −0.778827 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7534.42 | 0.320870 | ||||||||
\(821\) | −22549.5 | + | 39056.9i | −0.958567 | + | 1.66029i | −0.232582 | + | 0.972577i | \(0.574717\pi\) |
−0.725985 | + | 0.687710i | \(0.758616\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14738.3 | + | 25527.5i | 0.624236 | + | 1.08121i | 0.988688 | + | 0.149986i | \(0.0479228\pi\) |
−0.364452 | + | 0.931222i | \(0.618744\pi\) | |||||||
\(824\) | 6564.26 | − | 11369.6i | 0.277520 | − | 0.480679i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.9833 | − | 132.100i | −0.00172638 | − | 0.00556458i | ||||
\(827\) | 20417.9 | 0.858526 | 0.429263 | − | 0.903179i | \(-0.358773\pi\) | ||||
0.429263 | + | 0.903179i | \(0.358773\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9150.67 | − | 15849.4i | −0.383373 | − | 0.664021i | 0.608169 | − | 0.793807i | \(-0.291904\pi\) |
−0.991542 | + | 0.129786i | \(0.958571\pi\) | |||||||
\(830\) | −2465.86 | − | 4270.99i | −0.103122 | − | 0.178612i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −257.233 | −0.0107187 | ||||||||
\(833\) | −11749.3 | − | 5611.07i | −0.488704 | − | 0.233388i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6916.08 | − | 11979.0i | 0.286636 | − | 0.496467i | ||||
\(836\) | 4123.42 | + | 7141.98i | 0.170588 | + | 0.295467i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12626.4 | − | 21869.5i | 0.520491 | − | 0.901516i | ||||
\(839\) | −4380.29 | −0.180244 | −0.0901218 | − | 0.995931i | \(-0.528726\pi\) | ||||
−0.0901218 | + | 0.995931i | \(0.528726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21979.1 | 0.901188 | ||||||||
\(842\) | −4805.61 | + | 8323.55i | −0.196689 | + | 0.340675i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5831.68 | − | 10100.8i | −0.237837 | − | 0.411946i | ||||
\(845\) | 11009.6 | − | 19069.3i | 0.448217 | − | 0.776335i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −437.157 | − | 99.0289i | −0.0177342 | − | 0.00401732i | ||||
\(848\) | −8760.56 | −0.354763 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 875.257 | + | 1515.99i | 0.0353189 | + | 0.0611741i | ||||
\(851\) | 12258.4 | + | 21232.3i | 0.493789 | + | 0.855267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6855.49 | −0.275179 | −0.137589 | − | 0.990489i | \(-0.543935\pi\) | ||||
−0.137589 | + | 0.990489i | \(0.543935\pi\) | |||||||
\(854\) | −2892.25 | + | 3127.31i | −0.115891 | + | 0.125310i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1284.38 | + | 2224.61i | −0.0512840 | + | 0.0888265i | ||||
\(857\) | 8858.08 | + | 15342.7i | 0.353076 | + | 0.611546i | 0.986787 | − | 0.162024i | \(-0.0518023\pi\) |
−0.633710 | + | 0.773570i | \(0.718469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11521.0 | − | 19955.0i | 0.457616 | − | 0.792615i | −0.541218 | − | 0.840882i | \(-0.682037\pi\) |
0.998834 | + | 0.0482676i | \(0.0153700\pi\) | |||||||
\(860\) | 10592.1 | 0.419984 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13364.2 | −0.528060 | ||||||||
\(863\) | −5983.70 | + | 10364.1i | −0.236022 | + | 0.408803i | −0.959569 | − | 0.281472i | \(-0.909177\pi\) |
0.723547 | + | 0.690275i | \(0.242511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9307.97 | − | 16121.9i | −0.365873 | − | 0.633711i | ||||
\(866\) | −8502.27 | + | 14726.4i | −0.333624 | + | 0.577855i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13173.3 | − | 2984.14i | −0.515128 | − | 0.116691i | ||||
\(869\) | 31342.3 | 1.22349 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1261.65 | + | 2185.24i | 0.0490807 | + | 0.0850102i | ||||
\(872\) | 2240.04 | + | 3879.86i | 0.0869922 | + | 0.150675i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8947.25 | 0.346276 | ||||||||
\(875\) | 8203.60 | + | 26442.3i | 0.316951 | + | 1.02162i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21877.6 | − | 37893.1i | 0.842364 | − | 1.45902i | −0.0455264 | − | 0.998963i | \(-0.514497\pi\) |
0.887891 | − | 0.460055i | \(-0.152170\pi\) | |||||||
\(878\) | −13629.5 | − | 23607.1i | −0.523889 | − | 0.907403i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2919.93 | − | 5057.47i | 0.111853 | − | 0.193736i | ||||
\(881\) | −36896.0 | −1.41096 | −0.705482 | − | 0.708728i | \(-0.749269\pi\) | ||||
−0.705482 | + | 0.708728i | \(0.749269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10988.6 | −0.418793 | −0.209397 | − | 0.977831i | \(-0.567150\pi\) | ||||
−0.209397 | + | 0.977831i | \(0.567150\pi\) | |||||||
\(884\) | −305.146 | + | 528.528i | −0.0116099 | + | 0.0201090i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6854.32 | − | 11872.0i | −0.259905 | − | 0.450168i | ||||
\(887\) | 16024.0 | − | 27754.4i | 0.606578 | − | 1.05062i | −0.385222 | − | 0.922824i | \(-0.625875\pi\) |
0.991800 | − | 0.127800i | \(-0.0407915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4335.61 | − | 13974.8i | −0.163568 | − | 0.527221i | ||||
\(890\) | −9026.77 | −0.339975 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3750.21 | + | 6495.56i | 0.140770 | + | 0.243820i | ||||
\(893\) | −3933.01 | − | 6812.17i | −0.147383 | − | 0.255275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10718.3 | 0.400306 | ||||||||
\(896\) | −2312.01 | − | 523.739i | −0.0862042 | − | 0.0195278i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10372.3 | + | 17965.3i | −0.385442 | + | 0.667605i | ||||
\(899\) | 19630.6 | + | 34001.2i | 0.728273 | + | 1.26141i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10392.3 | + | 18000.0i | −0.384260 | + | 0.665558i | ||||
\(902\) | 13487.9 | 0.497893 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14965.2 | 0.550592 | ||||||||
\(905\) | −12325.7 | + | 21348.7i | −0.452729 | + | 0.784150i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26578.9 | − | 46035.9i | −0.973028 | − | 1.68533i | −0.686293 | − | 0.727325i | \(-0.740763\pi\) |
−0.286735 | − | 0.958010i | \(-0.592570\pi\) | |||||||
\(908\) | 8076.59 | − | 13989.1i | 0.295188 | − | 0.511281i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1020.60 | + | 1103.55i | −0.0371788 | + | 0.0402004i | ||||
\(911\) | 42187.2 | 1.53427 | 0.767137 | − | 0.641484i | \(-0.221681\pi\) | ||||
0.767137 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4414.31 | − | 7645.82i | −0.160014 | − | 0.277152i | ||||
\(914\) | −7900.81 | − | 13684.6i | −0.285925 | − | 0.495237i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5491.65 | 0.198089 | ||||||||
\(917\) | −29588.0 | − | 6702.55i | −1.06552 | − | 0.241372i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6003.98 | − | 10399.2i | 0.215509 | − | 0.373273i | −0.737921 | − | 0.674887i | \(-0.764192\pi\) |
0.953430 | + | 0.301614i | \(0.0975256\pi\) | |||||||
\(920\) | −3167.92 | − | 5487.00i | −0.113525 | − | 0.196632i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11359.7 | + | 19675.6i | −0.405762 | + | 0.702800i | ||||
\(923\) | −2142.70 | −0.0764114 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7206.66 | −0.256166 | ||||||||
\(926\) | 7346.85 | − | 12725.1i | 0.260726 | − | 0.451591i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3445.32 | + | 5967.47i | 0.121873 | + | 0.211090i | ||||
\(929\) | 10558.0 | − | 18287.0i | 0.372871 | − | 0.645831i | −0.617135 | − | 0.786857i | \(-0.711707\pi\) |
0.990006 | + | 0.141026i | \(0.0450402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1525.47 | − | 19502.6i | −0.0537008 | − | 0.686544i | ||||
\(932\) | −16697.2 | −0.586841 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 946.578 | + | 1639.52i | 0.0331616 | + | 0.0574376i | ||||
\(935\) | −6927.61 | − | 11999.0i | −0.242307 | − | 0.419688i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9506.74 | 0.331453 | 0.165727 | − | 0.986172i | \(-0.447003\pi\) | ||||
0.165727 | + | 0.986172i | \(0.447003\pi\) | |||||||
\(938\) | 6890.46 | + | 22209.7i | 0.239852 | + | 0.773105i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2785.09 | + | 4823.92i | −0.0966380 | + | 0.167382i | ||||
\(941\) | −26695.9 | − | 46238.6i | −0.924825 | − | 1.60184i | −0.791843 | − | 0.610725i | \(-0.790878\pi\) |
−0.132982 | − | 0.991119i | \(-0.542455\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7316.73 | − | 12673.0i | 0.252668 | − | 0.437633i | ||||
\(944\) | −59.7448 | −0.00205988 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18961.7 | 0.651688 | ||||||||
\(947\) | −2189.61 | + | 3792.52i | −0.0751350 | + | 0.130138i | −0.901145 | − | 0.433518i | \(-0.857272\pi\) |
0.826010 | + | 0.563655i | \(0.190605\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −599.662 | − | 1038.65i | −0.0205120 | − | 0.0355278i | ||||
\(950\) | −1315.01 | + | 2277.66i | −0.0449100 | + | 0.0777863i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3818.77 | + | 4129.13i | −0.130007 | + | 0.140573i | ||||
\(953\) | 57958.4 | 1.97005 | 0.985025 | − | 0.172411i | \(-0.0551557\pi\) | ||||
0.985025 | + | 0.172411i | \(0.0551557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18639.2 | − | 32284.1i | −0.631573 | − | 1.09392i | ||||
\(956\) | 11089.4 | + | 19207.4i | 0.375164 | + | 0.649804i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30631.0 | −1.03303 | ||||||||
\(959\) | 25015.4 | − | 27048.4i | 0.842323 | − | 0.910782i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1726.31 | + | 2990.06i | −0.0579475 | + | 0.100368i | ||||
\(962\) | −1256.25 | − | 2175.89i | −0.0421031 | − | 0.0729247i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9780.28 | + | 16939.9i | −0.326765 | + | 0.565974i | ||||
\(965\) | 31727.0 | 1.05837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17466.6 | 0.580857 | 0.290429 | − | 0.956897i | \(-0.406202\pi\) | ||||
0.290429 | + | 0.956897i | \(0.406202\pi\) | |||||||
\(968\) | −96.8094 | + | 167.679i | −0.00321443 | + | 0.00556756i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18214.3 | − | 31548.1i | −0.602914 | − | 1.04428i | ||||
\(971\) | −15895.2 | + | 27531.3i | −0.525336 | + | 0.909908i | 0.474229 | + | 0.880402i | \(0.342727\pi\) |
−0.999565 | + | 0.0295066i | \(0.990606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3597.94 | + | 11597.1i | 0.118545 | + | 0.382102i | ||||
\(974\) | 17280.7 | 0.568491 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 920.013 | + | 1593.51i | 0.0301731 | + | 0.0522613i | ||||
\(977\) | −29302.2 | − | 50753.0i | −0.959531 | − | 1.66196i | −0.723641 | − | 0.690177i | \(-0.757533\pi\) |
−0.235890 | − | 0.971780i | \(-0.575800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16159.5 | −0.527538 | ||||||||
\(980\) | −11420.1 | + | 7840.74i | −0.372246 | + | 0.255575i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13425.6 | + | 23253.9i | −0.436282 | + | 0.755663i | ||||
\(983\) | −20073.7 | − | 34768.8i | −0.651326 | − | 1.12813i | −0.982801 | − | 0.184665i | \(-0.940880\pi\) |
0.331476 | − | 0.943464i | \(-0.392453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11477.4 | − | 19879.5i | 0.371270 | − | 0.643059i | ||||
\(986\) | 16348.2 | 0.528026 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −916.918 | −0.0295253 | ||||||||
\(989\) | 10286.0 | − | 17815.9i | 0.330715 | − | 0.572815i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21436.6 | − | 37129.4i | −0.687142 | − | 1.19016i | −0.972759 | − | 0.231821i | \(-0.925532\pi\) |
0.285617 | − | 0.958344i | \(-0.407802\pi\) | |||||||
\(992\) | −2917.25 | + | 5052.83i | −0.0933699 | + | 0.161721i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19258.6 | − | 4362.63i | −0.614533 | − | 0.139210i | ||||
\(995\) | −27629.7 | −0.880322 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9752.05 | + | 16891.0i | 0.309780 | + | 0.536554i | 0.978314 | − | 0.207127i | \(-0.0664113\pi\) |
−0.668534 | + | 0.743681i | \(0.733078\pi\) | |||||||
\(998\) | −10978.0 | − | 19014.5i | −0.348200 | − | 0.603099i | ||||
\(999\) | 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 | 378.4.g.f.163.2 | yes | 8 | |
3.2 | odd | 2 | 378.4.g.c.163.3 | yes | 8 | ||
7.4 | even | 3 | inner | 378.4.g.f.109.2 | yes | 8 | |
21.11 | odd | 6 | 378.4.g.c.109.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.c.109.3 | ✓ | 8 | 21.11 | odd | 6 | ||
378.4.g.c.163.3 | yes | 8 | 3.2 | odd | 2 | ||
378.4.g.f.109.2 | yes | 8 | 7.4 | even | 3 | inner | |
378.4.g.f.163.2 | yes | 8 | 1.1 | even | 1 | trivial |