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 | 109.3 | ||
Root | \(-1.84763 + 3.20018i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.109 |
Dual form | 378.4.g.c.163.3 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.0175425\pi\) |
−0.546945 | + | 0.837169i | \(0.684209\pi\) | |||||||
\(6\) | 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 | \(-0.998324\pi\) |
0.504553 | + | 0.863381i | \(0.331657\pi\) | |||||||
\(12\) | 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 | \(-0.920617\pi\) |
0.698277 | + | 0.715828i | \(0.253951\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −28.5163 | − | 49.3917i | −0.344321 | − | 0.596381i | 0.640909 | − | 0.767617i | \(-0.278557\pi\) |
−0.985230 | + | 0.171236i | \(0.945224\pi\) | |||||||
\(20\) | −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 | \(-0.282377\pi\) |
−0.987214 | + | 0.159402i | \(0.949044\pi\) | |||||||
\(24\) | 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 | \(-0.742134\pi\) | ||||
−0.689418 | + | 0.724364i | \(0.742134\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 91.1642 | − | 157.901i | 0.528180 | − | 0.914834i | −0.471281 | − | 0.881983i | \(-0.656208\pi\) |
0.999460 | − | 0.0328507i | \(-0.0104586\pi\) | |||||||
\(32\) | −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 | −0.970389 | − | 0.241546i | \(-0.922346\pi\) |
0.276010 | − | 0.961155i | \(-0.410988\pi\) | |||||||
\(38\) | −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 | \(-0.615624\pi\) | ||||
−0.355308 | + | 0.934749i | \(0.615624\pi\) | |||||||
\(42\) | 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 | \(-0.0980109\pi\) |
−0.738949 | + | 0.673761i | \(0.764678\pi\) | |||||||
\(48\) | 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 | 0.255508 | + | 0.966807i | \(0.417757\pi\) |
−0.965033 | + | 0.262127i | \(0.915576\pi\) | |||||||
\(54\) | 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 | \(-0.834645\pi\) |
0.863958 | + | 0.503564i | \(0.167978\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 57.5008 | + | 99.5943i | 0.120692 | + | 0.209045i | 0.920041 | − | 0.391822i | \(-0.128155\pi\) |
−0.799349 | + | 0.600868i | \(0.794822\pi\) | |||||||
\(62\) | −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 | 0.423949 | + | 0.905686i | \(0.360644\pi\) |
−0.996322 | + | 0.0856924i | \(0.972690\pi\) | |||||||
\(68\) | −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 | \(-0.646992\pi\) | ||||
−0.445550 | + | 0.895257i | \(0.646992\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 149.197 | − | 258.417i | 0.239208 | − | 0.414320i | −0.721279 | − | 0.692644i | \(-0.756446\pi\) |
0.960487 | + | 0.278324i | \(0.0897789\pi\) | |||||||
\(74\) | −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 | 0.989961 | + | 0.141340i | \(0.0451412\pi\) |
−0.372576 | + | 0.928002i | \(0.621525\pi\) | |||||||
\(80\) | 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 | \(-0.448370\pi\) | ||||
0.161489 | + | 0.986875i | \(0.448370\pi\) | |||||||
\(84\) | 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 | \(-0.0808984\pi\) |
−0.701677 | + | 0.712495i | \(0.747565\pi\) | |||||||
\(90\) | 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 | 0.0686484 | + | 0.997641i | \(0.478131\pi\) |
−0.898307 | + | 0.439369i | \(0.855202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −820.532 | − | 1421.20i | −0.784946 | − | 1.35957i | −0.929031 | − | 0.370001i | \(-0.879357\pi\) |
0.144085 | − | 0.989565i | \(-0.453976\pi\) | |||||||
\(104\) | −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 | \(-0.213002\pi\) |
−0.929393 | + | 0.369092i | \(0.879669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −280.005 | + | 484.982i | −0.246051 | + | 0.426173i | −0.962427 | − | 0.271542i | \(-0.912466\pi\) |
0.716376 | + | 0.697715i | \(0.245800\pi\) | |||||||
\(110\) | 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 | \(-0.215902\pi\) | ||||
0.778655 | + | 0.627452i | \(0.215902\pi\) | |||||||
\(114\) | 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 | −0.998527 | − | 0.0542661i | \(-0.982718\pi\) |
0.452267 | − | 0.891882i | \(-0.350615\pi\) | |||||||
\(132\) | 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 | 0.369143 | + | 0.929373i | \(0.379651\pi\) |
−0.989432 | + | 0.144999i | \(0.953682\pi\) | |||||||
\(138\) | 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 | −0.904301 | − | 0.426895i | \(-0.859607\pi\) |
0.0824482 | − | 0.996595i | \(-0.473726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 547.979 | − | 949.128i | 0.295324 | − | 0.511516i | −0.679736 | − | 0.733457i | \(-0.737906\pi\) |
0.975060 | + | 0.221940i | \(0.0712391\pi\) | |||||||
\(152\) | −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 | −0.922647 | − | 0.385646i | \(-0.873979\pi\) |
0.795302 | + | 0.606213i | \(0.207312\pi\) | |||||||
\(158\) | 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 | −0.998606 | − | 0.0527870i | \(-0.983190\pi\) |
0.453588 | − | 0.891211i | \(-0.350144\pi\) | |||||||
\(164\) | 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 | \(-0.397190\pi\) | ||||
0.317400 | + | 0.948292i | \(0.397190\pi\) | |||||||
\(168\) | 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 | \(-0.0338887\pi\) |
−0.589196 | + | 0.807990i | \(0.700555\pi\) | |||||||
\(174\) | 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 | \(-0.762194\pi\) |
0.955305 | + | 0.295623i | \(0.0955272\pi\) | |||||||
\(180\) | 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 | 0.968689 | + | 0.248277i | \(0.0798642\pi\) |
−0.269331 | + | 0.963048i | \(0.586802\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1571.16 | + | 2721.33i | −0.585982 | + | 1.01495i | 0.408770 | + | 0.912637i | \(0.365958\pi\) |
−0.994752 | + | 0.102313i | \(0.967376\pi\) | |||||||
\(194\) | 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 | \(-0.365138\pi\) | ||||
0.411118 | + | 0.911582i | \(0.365138\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1368.26 | − | 2369.89i | 0.487403 | − | 0.844206i | −0.512492 | − | 0.858692i | \(-0.671278\pi\) |
0.999895 | + | 0.0144854i | \(0.00461100\pi\) | |||||||
\(200\) | 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 | 0.403805 | + | 0.914845i | \(0.367688\pi\) |
−0.994182 | + | 0.107717i | \(0.965646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −686.456 | − | 1188.98i | −0.198089 | − | 0.343099i | 0.749820 | − | 0.661642i | \(-0.230140\pi\) |
−0.947909 | + | 0.318542i | \(0.896807\pi\) | |||||||
\(230\) | −1583.96 | −0.454101 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1722.66 | −0.487492 | ||||||||
\(233\) | −2087.15 | − | 3615.06i | −0.586841 | − | 1.01644i | −0.994643 | − | 0.103368i | \(-0.967038\pi\) |
0.407802 | − | 0.913070i | \(-0.366295\pi\) | |||||||
\(234\) | 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 | \(-0.229895\pi\) | ||||
0.750329 | + | 0.661065i | \(0.229895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2445.07 | + | 4234.98i | −0.653530 | + | 1.13195i | 0.328730 | + | 0.944424i | \(0.393379\pi\) |
−0.982260 | + | 0.187524i | \(0.939954\pi\) | |||||||
\(242\) | 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 | \(-0.899513\pi\) | ||||
−0.950583 | + | 0.310470i | \(0.899513\pi\) | |||||||
\(252\) | 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 | \(-0.294999\pi\) |
−0.992757 | + | 0.120139i | \(0.961666\pi\) | |||||||
\(258\) | 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 | 0.497724 | + | 0.867335i | \(0.334169\pi\) |
−0.999997 | + | 0.00262575i | \(0.999164\pi\) | |||||||
\(264\) | 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 | 0.184495 | + | 0.982834i | \(0.440935\pi\) |
−0.943406 | + | 0.331640i | \(0.892398\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3157.89 | + | 5469.63i | 0.707854 | + | 1.22604i | 0.965652 | + | 0.259840i | \(0.0836698\pi\) |
−0.257798 | + | 0.966199i | \(0.582997\pi\) | |||||||
\(272\) | 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 | −0.975866 | − | 0.218368i | \(-0.929927\pi\) |
0.677045 | + | 0.735941i | \(0.263260\pi\) | |||||||
\(278\) | 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 | \(-0.549290\pi\) | ||||
−0.154232 | + | 0.988035i | \(0.549290\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2715.92 | + | 4704.11i | −0.570476 | + | 0.988093i | 0.426042 | + | 0.904704i | \(0.359908\pi\) |
−0.996517 | + | 0.0833890i | \(0.973426\pi\) | |||||||
\(284\) | 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 | \(-0.713198\pi\) | ||||
−0.620815 | + | 0.783957i | \(0.713198\pi\) | |||||||
\(294\) | 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 | 0.299100 | + | 0.954222i | \(0.403314\pi\) |
−0.975930 | + | 0.218083i | \(0.930020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1633.30 | − | 2828.96i | −0.294951 | − | 0.510870i | 0.680022 | − | 0.733191i | \(-0.261970\pi\) |
−0.974974 | + | 0.222321i | \(0.928637\pi\) | |||||||
\(314\) | 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 | \(-0.308985\pi\) |
−0.997076 | + | 0.0764167i | \(0.975652\pi\) | |||||||
\(318\) | 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 | 0.921558 | + | 0.388240i | \(0.126917\pi\) |
−0.124554 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(332\) | −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 | \(-0.969351\pi\) |
0.580942 | + | 0.813945i | \(0.302684\pi\) | |||||||
\(348\) | 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 | 0.481045 | + | 0.876696i | \(0.340257\pi\) |
−0.999763 | + | 0.0217505i | \(0.993076\pi\) | |||||||
\(354\) | 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 | \(-0.311847\pi\) |
−0.997723 | + | 0.0674511i | \(0.978513\pi\) | |||||||
\(360\) | 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 | −0.531992 | − | 0.846749i | \(-0.678556\pi\) |
0.999302 | + | 0.0373437i | \(0.0118896\pi\) | |||||||
\(368\) | −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 | 0.966012 | − | 0.258497i | \(-0.0832272\pi\) |
−0.706871 | + | 0.707343i | \(0.749894\pi\) | |||||||
\(374\) | −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 | \(-0.0509511\pi\) |
−0.631640 | + | 0.775262i | \(0.717618\pi\) | |||||||
\(384\) | 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 | −0.490894 | − | 0.871219i | \(-0.663330\pi\) |
0.999945 | − | 0.0104832i | \(-0.00333696\pi\) | |||||||
\(390\) | 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 | 0.835772 | − | 0.549076i | \(-0.185020\pi\) |
−0.893400 | + | 0.449262i | \(0.851687\pi\) | |||||||
\(398\) | −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 | \(-0.133547\pi\) |
−0.809411 | + | 0.587242i | \(0.800214\pi\) | |||||||
\(402\) | 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 | 0.447509 | + | 0.894279i | \(0.352311\pi\) |
−0.998223 | + | 0.0595852i | \(0.981022\pi\) | |||||||
\(410\) | −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 | \(-0.763328\pi\) | ||||
−0.736085 | + | 0.676889i | \(0.763328\pi\) | |||||||
\(420\) | 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 | \(-0.711527\pi\) |
0.990085 | + | 0.140467i | \(0.0448603\pi\) | |||||||
\(432\) | 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 | 0.952090 | + | 0.305818i | \(0.0989299\pi\) |
−0.211199 | + | 0.977443i | \(0.567737\pi\) | |||||||
\(440\) | −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 | \(-0.286474\pi\) |
−0.989184 | + | 0.146683i | \(0.953140\pi\) | |||||||
\(444\) | 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 | \(-0.316493\pi\) | ||||
0.545097 | + | 0.838373i | \(0.316493\pi\) | |||||||
\(450\) | 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 | 0.994247 | − | 0.107115i | \(-0.0341613\pi\) |
−0.589888 | + | 0.807485i | \(0.700828\pi\) | |||||||
\(458\) | −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 | \(-0.305456\pi\) | ||||
0.573834 | + | 0.818972i | \(0.305456\pi\) | |||||||
\(462\) | 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 | \(-0.151733\pi\) |
−0.841624 | + | 0.540064i | \(0.818400\pi\) | |||||||
\(468\) | 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 | −0.226224 | − | 0.974075i | \(-0.572638\pi\) |
0.956686 | − | 0.291122i | \(-0.0940287\pi\) | |||||||
\(480\) | 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 | −0.591981 | − | 0.805952i | \(-0.701654\pi\) |
0.993965 | + | 0.109695i | \(0.0349873\pi\) | |||||||
\(488\) | 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 | \(-0.288349\pi\) | ||||
0.616996 | + | 0.786966i | \(0.288349\pi\) | |||||||
\(492\) | 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 | 0.999962 | − | 0.00872085i | \(-0.00277597\pi\) |
−0.507533 | + | 0.861632i | \(0.669443\pi\) | |||||||
\(500\) | −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 | \(-0.387196\pi\) | ||||
0.347014 | + | 0.937860i | \(0.387196\pi\) | |||||||
\(504\) | 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 | 0.924894 | + | 0.380225i | \(0.124153\pi\) |
−0.133162 | + | 0.991094i | \(0.542513\pi\) | |||||||
\(510\) | 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 | −0.180341 | + | 0.983604i | \(0.557720\pi\) |
−0.761656 | + | 0.647982i | \(0.775613\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2843.67 | − | 4925.38i | −0.237753 | − | 0.411801i | 0.722316 | − | 0.691563i | \(-0.243078\pi\) |
−0.960069 | + | 0.279763i | \(0.909744\pi\) | |||||||
\(524\) | 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 | 0.999799 | + | 0.0200392i | \(0.00637910\pi\) |
−0.482545 | + | 0.875871i | \(0.660288\pi\) | |||||||
\(542\) | 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 | −0.403909 | − | 0.914799i | \(-0.632349\pi\) |
0.994194 | − | 0.107604i | \(-0.0343179\pi\) | |||||||
\(558\) | 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 | −0.293847 | − | 0.955853i | \(-0.594936\pi\) |
0.974716 | − | 0.223448i | \(-0.0717311\pi\) | |||||||
\(564\) | 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 | \(-0.316600\pi\) |
−0.998619 | + | 0.0525449i | \(0.983267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8694.98 | − | 15060.2i | 0.637257 | − | 1.10376i | −0.348775 | − | 0.937206i | \(-0.613402\pi\) |
0.986032 | − | 0.166555i | \(-0.0532644\pi\) | |||||||
\(572\) | 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 | −0.918687 | − | 0.394985i | \(-0.870750\pi\) |
0.801411 | + | 0.598114i | \(0.204083\pi\) | |||||||
\(578\) | 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 | \(-0.579074\pi\) | ||||
−0.245872 | + | 0.969302i | \(0.579074\pi\) | |||||||
\(588\) | 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 | \(-0.279237\pi\) |
−0.985593 | + | 0.169132i | \(0.945904\pi\) | |||||||
\(594\) | 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 | 0.0438997 | + | 0.999036i | \(0.486022\pi\) |
−0.887140 | + | 0.461500i | \(0.847312\pi\) | |||||||
\(600\) | 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 | −0.900516 | − | 0.434824i | \(-0.856811\pi\) |
0.0736896 | − | 0.997281i | \(-0.476523\pi\) | |||||||
\(608\) | 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 | −0.713049 | − | 0.701115i | \(-0.752686\pi\) |
0.963707 | + | 0.266961i | \(0.0860195\pi\) | |||||||
\(614\) | −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 | \(-0.194785\pi\) | ||||
0.818538 | + | 0.574452i | \(0.194785\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11452.5 | + | 19836.3i | −0.743642 | + | 1.28803i | 0.207185 | + | 0.978302i | \(0.433570\pi\) |
−0.950827 | + | 0.309724i | \(0.899763\pi\) | |||||||
\(620\) | −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 | \(-0.954189\pi\) |
0.619039 | + | 0.785361i | \(0.287522\pi\) | |||||||
\(642\) | 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 | \(-0.777541\pi\) |
0.939947 | + | 0.341320i | \(0.110874\pi\) | |||||||
\(648\) | 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 | \(-0.150195\pi\) |
−0.839005 | + | 0.544124i | \(0.816862\pi\) | |||||||
\(654\) | 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 | \(-0.394720\pi\) | ||||
0.324751 | + | 0.945800i | \(0.394720\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16020.4 | + | 27748.1i | −0.942695 | + | 1.63280i | −0.182393 | + | 0.983226i | \(0.558384\pi\) |
−0.760302 | + | 0.649570i | \(0.774949\pi\) | |||||||
\(662\) | 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 | \(-0.209449\pi\) |
−0.925215 | + | 0.379444i | \(0.876115\pi\) | |||||||
\(678\) | 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 | \(-0.934631\pi\) |
0.666096 | + | 0.745866i | \(0.267964\pi\) | |||||||
\(684\) | 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 | 0.991717 | − | 0.128441i | \(-0.0409974\pi\) |
−0.607092 | + | 0.794632i | \(0.707664\pi\) | |||||||
\(692\) | −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 | \(-0.584110\pi\) | ||||
−0.261176 | + | 0.965291i | \(0.584110\pi\) | |||||||
\(702\) | 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 | −0.976934 | − | 0.213541i | \(-0.931500\pi\) |
0.303535 | − | 0.952820i | \(-0.401833\pi\) | |||||||
\(710\) | −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 | \(-0.317478\pi\) |
−0.998760 | + | 0.0497912i | \(0.984144\pi\) | |||||||
\(720\) | 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 | −0.918683 | − | 0.394995i | \(-0.870746\pi\) |
0.117266 | − | 0.993101i | \(-0.462587\pi\) | |||||||
\(734\) | −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 | −0.582629 | − | 0.812738i | \(-0.697976\pi\) |
0.995166 | + | 0.0982021i | \(0.0313092\pi\) | |||||||
\(740\) | 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 | \(-0.587978\pi\) | ||||
−0.272886 | + | 0.962046i | \(0.587978\pi\) | |||||||
\(744\) | 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 | 0.824813 | − | 0.565405i | \(-0.191280\pi\) |
−0.902062 | + | 0.431606i | \(0.857947\pi\) | |||||||
\(752\) | 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 | \(-0.226380\pi\) |
−0.944080 | + | 0.329717i | \(0.893047\pi\) | |||||||
\(762\) | 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 | 0.337349 | + | 0.941380i | \(0.390470\pi\) |
−0.983933 | + | 0.178537i | \(0.942864\pi\) | |||||||
\(774\) | 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 | −0.896256 | − | 0.443537i | \(-0.853724\pi\) |
0.832242 | + | 0.554412i | \(0.187057\pi\) | |||||||
\(788\) | −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 | \(-0.728192\pi\) | ||||
−0.657041 | + | 0.753855i | \(0.728192\pi\) | |||||||
\(798\) | 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 | \(-0.772298\pi\) |
0.945441 | + | 0.325795i | \(0.105632\pi\) | |||||||
\(810\) | 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 | 0.725985 | + | 0.687710i | \(0.241384\pi\) |
0.232582 | + | 0.972577i | \(0.425283\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14738.3 | − | 25527.5i | 0.624236 | − | 1.08121i | −0.364452 | − | 0.931222i | \(-0.618744\pi\) |
0.988688 | − | 0.149986i | \(-0.0479228\pi\) | |||||||
\(824\) | −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 | \(-0.641227\pi\) | ||||
−0.429263 | + | 0.903179i | \(0.641227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9150.67 | + | 15849.4i | −0.383373 | + | 0.664021i | −0.991542 | − | 0.129786i | \(-0.958571\pi\) |
0.608169 | + | 0.793807i | \(0.291904\pi\) | |||||||
\(830\) | 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 | \(-0.471274\pi\) | ||||
0.0901218 | + | 0.995931i | \(0.471274\pi\) | |||||||
\(840\) | 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 | \(-0.948198\pi\) |
0.633710 | + | 0.773570i | \(0.281531\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11521.0 | + | 19955.0i | 0.457616 | + | 0.792615i | 0.998834 | − | 0.0482676i | \(-0.0153700\pi\) |
−0.541218 | + | 0.840882i | \(0.682037\pi\) | |||||||
\(860\) | −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 | \(-0.0908228\pi\) |
−0.723547 | + | 0.690275i | \(0.757489\pi\) | |||||||
\(864\) | 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 | 0.887891 | + | 0.460055i | \(0.152170\pi\) |
−0.0455264 | + | 0.998963i | \(0.514497\pi\) | |||||||
\(878\) | 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 | \(-0.250731\pi\) | ||||
0.705482 | + | 0.708728i | \(0.250731\pi\) | |||||||
\(882\) | 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 | −0.991800 | − | 0.127800i | \(-0.959209\pi\) |
0.385222 | − | 0.922824i | \(-0.374125\pi\) | |||||||
\(888\) | 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 | −0.286735 | + | 0.958010i | \(0.592570\pi\) |
−0.686293 | + | 0.727325i | \(0.740763\pi\) | |||||||
\(908\) | −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 | \(-0.778319\pi\) | ||||
−0.767137 | + | 0.641484i | \(0.778319\pi\) | |||||||
\(912\) | 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 | 0.953430 | − | 0.301614i | \(-0.0975256\pi\) |
−0.737921 | + | 0.674887i | \(0.764192\pi\) | |||||||
\(920\) | 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 | \(-0.288293\pi\) |
−0.990006 | + | 0.141026i | \(0.954960\pi\) | |||||||
\(930\) | 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 | 0.132982 | − | 0.991119i | \(-0.457545\pi\) |
0.791843 | − | 0.610725i | \(-0.209122\pi\) | |||||||
\(942\) | 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 | \(-0.142728\pi\) |
−0.826010 | + | 0.563655i | \(0.809395\pi\) | |||||||
\(948\) | 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 | \(-0.944844\pi\) | ||||
−0.985025 | + | 0.172411i | \(0.944844\pi\) | |||||||
\(954\) | 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 | 0.999565 | + | 0.0295066i | \(0.00939360\pi\) |
−0.474229 | + | 0.880402i | \(0.657273\pi\) | |||||||
\(972\) | 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 | 0.235890 | − | 0.971780i | \(-0.424200\pi\) |
0.723641 | − | 0.690177i | \(-0.242467\pi\) | |||||||
\(978\) | 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 | −0.331476 | − | 0.943464i | \(-0.607547\pi\) |
0.982801 | − | 0.184665i | \(-0.0591202\pi\) | |||||||
\(984\) | 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 | 0.285617 | + | 0.958344i | \(0.407802\pi\) |
−0.972759 | + | 0.231821i | \(0.925532\pi\) | |||||||
\(992\) | 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 | −0.668534 | − | 0.743681i | \(-0.733078\pi\) |
0.978314 | + | 0.207127i | \(0.0664113\pi\) | |||||||
\(998\) | 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.c.109.3 | ✓ | 8 | |
3.2 | odd | 2 | 378.4.g.f.109.2 | yes | 8 | ||
7.2 | even | 3 | inner | 378.4.g.c.163.3 | yes | 8 | |
21.2 | odd | 6 | 378.4.g.f.163.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.c.109.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
378.4.g.c.163.3 | yes | 8 | 7.2 | even | 3 | inner | |
378.4.g.f.109.2 | yes | 8 | 3.2 | odd | 2 | ||
378.4.g.f.163.2 | yes | 8 | 21.2 | odd | 6 |