Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (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: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 84 x^{8} - 140 x^{7} + 6309 x^{6} - 5214 x^{5} + 67648 x^{4} + 164178 x^{3} + 511389 x^{2} + \cdots + 443556 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 47.1 | ||
Root | \(-4.57142 - 7.91792i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.4.c.b.63.1 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||
\(3\) | −5.07142 | − | 8.78395i | −0.975994 | − | 1.69047i | −0.676614 | − | 0.736338i | \(-0.736553\pi\) |
−0.299381 | − | 0.954134i | \(-0.596780\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 3.82762 | + | 6.62963i | 0.342353 | + | 0.592973i | 0.984869 | − | 0.173299i | \(-0.0554428\pi\) |
−0.642516 | + | 0.766272i | \(0.722110\pi\) | |||||||
\(6\) | 20.2857 | 1.38026 | ||||||||
\(7\) | −2.78651 | − | 4.82638i | −0.150457 | − | 0.260600i | 0.780938 | − | 0.624608i | \(-0.214741\pi\) |
−0.931396 | + | 0.364008i | \(0.881408\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −37.9385 | + | 65.7114i | −1.40513 | + | 2.43376i | ||||
\(10\) | −15.3105 | −0.484160 | ||||||||
\(11\) | −66.0355 | −1.81004 | −0.905020 | − | 0.425369i | \(-0.860144\pi\) | ||||
−0.905020 | + | 0.425369i | \(0.860144\pi\) | |||||||
\(12\) | −20.2857 | + | 35.1358i | −0.487997 | + | 0.845236i | ||||
\(13\) | 28.6948 | + | 49.7008i | 0.612192 | + | 1.06035i | 0.990870 | + | 0.134819i | \(0.0430454\pi\) |
−0.378678 | + | 0.925528i | \(0.623621\pi\) | |||||||
\(14\) | 11.1460 | 0.212779 | ||||||||
\(15\) | 38.8229 | − | 67.2433i | 0.668269 | − | 1.15748i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.639621 | + | 1.10786i | −0.00912535 | + | 0.0158056i | −0.870552 | − | 0.492076i | \(-0.836238\pi\) |
0.861427 | + | 0.507882i | \(0.169571\pi\) | |||||||
\(18\) | −75.8770 | − | 131.423i | −0.993577 | − | 1.72093i | ||||
\(19\) | 16.1071 | + | 27.8984i | 0.194486 | + | 0.336859i | 0.946732 | − | 0.322023i | \(-0.104363\pi\) |
−0.752246 | + | 0.658882i | \(0.771030\pi\) | |||||||
\(20\) | 15.3105 | − | 26.5185i | 0.171176 | − | 0.296486i | ||||
\(21\) | −28.2631 | + | 48.9531i | −0.293691 | + | 0.508688i | ||||
\(22\) | 66.0355 | − | 114.377i | 0.639946 | − | 1.10842i | ||||
\(23\) | −143.964 | −1.30516 | −0.652578 | − | 0.757721i | \(-0.726313\pi\) | ||||
−0.652578 | + | 0.757721i | \(0.726313\pi\) | |||||||
\(24\) | −40.5713 | − | 70.2716i | −0.345066 | − | 0.597672i | ||||
\(25\) | 33.1986 | − | 57.5017i | 0.265589 | − | 0.460014i | ||||
\(26\) | −114.779 | −0.865770 | ||||||||
\(27\) | 495.752 | 3.53361 | ||||||||
\(28\) | −11.1460 | + | 19.3055i | −0.0752287 | + | 0.130300i | ||||
\(29\) | −102.082 | −0.653662 | −0.326831 | − | 0.945083i | \(-0.605981\pi\) | ||||
−0.326831 | + | 0.945083i | \(0.605981\pi\) | |||||||
\(30\) | 77.6458 | + | 134.487i | 0.472538 | + | 0.818459i | ||||
\(31\) | −87.0826 | −0.504532 | −0.252266 | − | 0.967658i | \(-0.581176\pi\) | ||||
−0.252266 | + | 0.967658i | \(0.581176\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 334.893 | + | 580.052i | 1.76659 | + | 3.05982i | ||||
\(34\) | −1.27924 | − | 2.21571i | −0.00645259 | − | 0.0111762i | ||||
\(35\) | 21.3314 | − | 36.9471i | 0.103019 | − | 0.178434i | ||||
\(36\) | 303.508 | 1.40513 | ||||||||
\(37\) | −171.144 | − | 146.160i | −0.760431 | − | 0.649418i | ||||
\(38\) | −64.4285 | −0.275044 | ||||||||
\(39\) | 291.046 | − | 504.107i | 1.19499 | − | 2.06979i | ||||
\(40\) | 30.6210 | + | 53.0371i | 0.121040 | + | 0.209647i | ||||
\(41\) | −31.8414 | − | 55.1509i | −0.121288 | − | 0.210076i | 0.798988 | − | 0.601347i | \(-0.205369\pi\) |
−0.920276 | + | 0.391271i | \(0.872036\pi\) | |||||||
\(42\) | −56.5262 | − | 97.9063i | −0.207671 | − | 0.359697i | ||||
\(43\) | −310.394 | −1.10080 | −0.550402 | − | 0.834900i | \(-0.685526\pi\) | ||||
−0.550402 | + | 0.834900i | \(0.685526\pi\) | |||||||
\(44\) | 132.071 | + | 228.754i | 0.452510 | + | 0.783770i | ||||
\(45\) | −580.857 | −1.92420 | ||||||||
\(46\) | 143.964 | − | 249.353i | 0.461442 | − | 0.799242i | ||||
\(47\) | −52.7493 | −0.163708 | −0.0818540 | − | 0.996644i | \(-0.526084\pi\) | ||||
−0.0818540 | + | 0.996644i | \(0.526084\pi\) | |||||||
\(48\) | 162.285 | 0.487997 | ||||||||
\(49\) | 155.971 | − | 270.149i | 0.454725 | − | 0.787607i | ||||
\(50\) | 66.3973 | + | 115.003i | 0.187800 | + | 0.325279i | ||||
\(51\) | 12.9751 | 0.0356251 | ||||||||
\(52\) | 114.779 | − | 198.803i | 0.306096 | − | 0.530174i | ||||
\(53\) | −222.423 | + | 385.248i | −0.576456 | + | 0.998451i | 0.419426 | + | 0.907790i | \(0.362231\pi\) |
−0.995882 | + | 0.0906615i | \(0.971102\pi\) | |||||||
\(54\) | −495.752 | + | 858.667i | −1.24932 | + | 2.16388i | ||||
\(55\) | −252.759 | − | 437.791i | −0.619672 | − | 1.07330i | ||||
\(56\) | −22.2921 | − | 38.6110i | −0.0531947 | − | 0.0921360i | ||||
\(57\) | 163.372 | − | 282.969i | 0.379634 | − | 0.657546i | ||||
\(58\) | 102.082 | − | 176.812i | 0.231104 | − | 0.400285i | ||||
\(59\) | −9.36865 | + | 16.2270i | −0.0206728 | + | 0.0358063i | −0.876177 | − | 0.481990i | \(-0.839914\pi\) |
0.855504 | + | 0.517796i | \(0.173247\pi\) | |||||||
\(60\) | −310.583 | −0.668269 | ||||||||
\(61\) | −377.129 | − | 653.206i | −0.791581 | − | 1.37106i | −0.924988 | − | 0.379996i | \(-0.875925\pi\) |
0.133407 | − | 0.991061i | \(-0.457408\pi\) | |||||||
\(62\) | 87.0826 | − | 150.832i | 0.178379 | − | 0.308962i | ||||
\(63\) | 422.864 | 0.845649 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −219.665 | + | 380.472i | −0.419171 | + | 0.726026i | ||||
\(66\) | −1339.57 | −2.49833 | ||||||||
\(67\) | 365.141 | + | 632.443i | 0.665808 | + | 1.15321i | 0.979066 | + | 0.203545i | \(0.0652462\pi\) |
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(68\) | 5.11697 | 0.00912535 | ||||||||
\(69\) | 730.102 | + | 1264.57i | 1.27383 | + | 2.20633i | ||||
\(70\) | 42.6628 | + | 73.8942i | 0.0728455 | + | 0.126172i | ||||
\(71\) | 112.895 | + | 195.540i | 0.188706 | + | 0.326849i | 0.944819 | − | 0.327592i | \(-0.106237\pi\) |
−0.756113 | + | 0.654441i | \(0.772904\pi\) | |||||||
\(72\) | −303.508 | + | 525.692i | −0.496789 | + | 0.860463i | ||||
\(73\) | 278.367 | 0.446307 | 0.223153 | − | 0.974783i | \(-0.428365\pi\) | ||||
0.223153 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(74\) | 424.300 | − | 150.271i | 0.666539 | − | 0.236063i | ||||
\(75\) | −673.456 | −1.03685 | ||||||||
\(76\) | 64.4285 | − | 111.593i | 0.0972429 | − | 0.168430i | ||||
\(77\) | 184.009 | + | 318.712i | 0.272334 | + | 0.471696i | ||||
\(78\) | 582.092 | + | 1008.21i | 0.844987 | + | 1.46356i | ||||
\(79\) | 147.223 | + | 254.998i | 0.209670 | + | 0.363159i | 0.951611 | − | 0.307307i | \(-0.0994277\pi\) |
−0.741941 | + | 0.670466i | \(0.766094\pi\) | |||||||
\(80\) | −122.484 | −0.171176 | ||||||||
\(81\) | −1489.82 | − | 2580.45i | −2.04365 | − | 3.53971i | ||||
\(82\) | 127.366 | 0.171527 | ||||||||
\(83\) | −299.816 | + | 519.296i | −0.396494 | + | 0.686749i | −0.993291 | − | 0.115644i | \(-0.963107\pi\) |
0.596796 | + | 0.802393i | \(0.296440\pi\) | |||||||
\(84\) | 226.105 | 0.293691 | ||||||||
\(85\) | −9.79291 | −0.0124964 | ||||||||
\(86\) | 310.394 | − | 537.618i | 0.389193 | − | 0.674102i | ||||
\(87\) | 517.702 | + | 896.686i | 0.637971 | + | 1.10500i | ||||
\(88\) | −528.284 | −0.639946 | ||||||||
\(89\) | 475.980 | − | 824.422i | 0.566896 | − | 0.981894i | −0.429974 | − | 0.902841i | \(-0.641477\pi\) |
0.996870 | − | 0.0790522i | \(-0.0251894\pi\) | |||||||
\(90\) | 580.857 | − | 1006.07i | 0.680308 | − | 1.17833i | ||||
\(91\) | 159.917 | − | 276.984i | 0.184218 | − | 0.319074i | ||||
\(92\) | 287.928 | + | 498.706i | 0.326289 | + | 0.565149i | ||||
\(93\) | 441.632 | + | 764.929i | 0.492421 | + | 0.852898i | ||||
\(94\) | 52.7493 | − | 91.3644i | 0.0578795 | − | 0.100250i | ||||
\(95\) | −123.304 | + | 213.569i | −0.133166 | + | 0.230649i | ||||
\(96\) | −162.285 | + | 281.086i | −0.172533 | + | 0.298836i | ||||
\(97\) | −474.578 | −0.496764 | −0.248382 | − | 0.968662i | \(-0.579899\pi\) | ||||
−0.248382 | + | 0.968662i | \(0.579899\pi\) | |||||||
\(98\) | 311.941 | + | 540.298i | 0.321539 | + | 0.556922i | ||||
\(99\) | 2505.29 | − | 4339.29i | 2.54334 | − | 4.40520i | ||||
\(100\) | −265.589 | −0.265589 | ||||||||
\(101\) | −1902.70 | −1.87452 | −0.937258 | − | 0.348636i | \(-0.886645\pi\) | ||||
−0.937258 | + | 0.348636i | \(0.886645\pi\) | |||||||
\(102\) | −12.9751 | + | 22.4736i | −0.0125954 | + | 0.0218159i | ||||
\(103\) | 1064.63 | 1.01845 | 0.509227 | − | 0.860632i | \(-0.329931\pi\) | ||||
0.509227 | + | 0.860632i | \(0.329931\pi\) | |||||||
\(104\) | 229.558 | + | 397.606i | 0.216443 | + | 0.374890i | ||||
\(105\) | −432.722 | −0.402184 | ||||||||
\(106\) | −444.846 | − | 770.496i | −0.407616 | − | 0.706012i | ||||
\(107\) | 412.713 | + | 714.841i | 0.372883 | + | 0.645853i | 0.990008 | − | 0.141013i | \(-0.0450358\pi\) |
−0.617124 | + | 0.786866i | \(0.711702\pi\) | |||||||
\(108\) | −991.503 | − | 1717.33i | −0.883402 | − | 1.53010i | ||||
\(109\) | 214.188 | − | 370.984i | 0.188215 | − | 0.325999i | −0.756440 | − | 0.654063i | \(-0.773063\pi\) |
0.944655 | + | 0.328065i | \(0.106396\pi\) | |||||||
\(110\) | 1011.03 | 0.876349 | ||||||||
\(111\) | −415.914 | + | 2244.56i | −0.355647 | + | 1.91932i | ||||
\(112\) | 89.1683 | 0.0752287 | ||||||||
\(113\) | −499.424 | + | 865.028i | −0.415769 | + | 0.720133i | −0.995509 | − | 0.0946687i | \(-0.969821\pi\) |
0.579740 | + | 0.814802i | \(0.303154\pi\) | |||||||
\(114\) | 326.744 | + | 565.937i | 0.268442 | + | 0.464955i | ||||
\(115\) | −551.040 | − | 954.429i | −0.446824 | − | 0.773922i | ||||
\(116\) | 204.165 | + | 353.623i | 0.163416 | + | 0.283044i | ||||
\(117\) | −4354.55 | −3.44084 | ||||||||
\(118\) | −18.7373 | − | 32.4539i | −0.0146179 | − | 0.0253189i | ||||
\(119\) | 7.12924 | 0.00549190 | ||||||||
\(120\) | 310.583 | − | 537.946i | 0.236269 | − | 0.409229i | ||||
\(121\) | 3029.68 | 2.27625 | ||||||||
\(122\) | 1508.52 | 1.11946 | ||||||||
\(123\) | −322.962 | + | 559.387i | −0.236752 | + | 0.410067i | ||||
\(124\) | 174.165 | + | 301.663i | 0.126133 | + | 0.218469i | ||||
\(125\) | 1465.19 | 1.04841 | ||||||||
\(126\) | −422.864 | + | 732.422i | −0.298982 | + | 0.517852i | ||||
\(127\) | 52.6827 | − | 91.2491i | 0.0368097 | − | 0.0637563i | −0.847034 | − | 0.531539i | \(-0.821614\pi\) |
0.883843 | + | 0.467783i | \(0.154947\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 1574.14 | + | 2726.48i | 1.07438 | + | 1.86088i | ||||
\(130\) | −439.331 | − | 760.943i | −0.296399 | − | 0.513378i | ||||
\(131\) | −205.903 | + | 356.635i | −0.137327 | + | 0.237858i | −0.926484 | − | 0.376334i | \(-0.877185\pi\) |
0.789157 | + | 0.614192i | \(0.210518\pi\) | |||||||
\(132\) | 1339.57 | − | 2320.21i | 0.883295 | − | 1.52991i | ||||
\(133\) | 89.7654 | − | 155.478i | 0.0585237 | − | 0.101366i | ||||
\(134\) | −1460.57 | −0.941594 | ||||||||
\(135\) | 1897.55 | + | 3286.65i | 1.20974 | + | 2.09533i | ||||
\(136\) | −5.11697 | + | 8.86285i | −0.00322630 | + | 0.00558811i | ||||
\(137\) | 2489.23 | 1.55233 | 0.776167 | − | 0.630528i | \(-0.217162\pi\) | ||||
0.776167 | + | 0.630528i | \(0.217162\pi\) | |||||||
\(138\) | −2920.41 | −1.80146 | ||||||||
\(139\) | −629.928 | + | 1091.07i | −0.384387 | + | 0.665778i | −0.991684 | − | 0.128697i | \(-0.958921\pi\) |
0.607297 | + | 0.794475i | \(0.292254\pi\) | |||||||
\(140\) | −170.651 | −0.103019 | ||||||||
\(141\) | 267.514 | + | 463.347i | 0.159778 | + | 0.276744i | ||||
\(142\) | −451.579 | −0.266871 | ||||||||
\(143\) | −1894.87 | − | 3282.02i | −1.10809 | − | 1.91927i | ||||
\(144\) | −607.016 | − | 1051.38i | −0.351283 | − | 0.608439i | ||||
\(145\) | −390.732 | − | 676.768i | −0.223783 | − | 0.387604i | ||||
\(146\) | −278.367 | + | 482.146i | −0.157793 | + | 0.273306i | ||||
\(147\) | −3163.97 | −1.77524 | ||||||||
\(148\) | −164.023 | + | 885.181i | −0.0910986 | + | 0.491631i | ||||
\(149\) | −581.828 | −0.319901 | −0.159950 | − | 0.987125i | \(-0.551133\pi\) | ||||
−0.159950 | + | 0.987125i | \(0.551133\pi\) | |||||||
\(150\) | 673.456 | − | 1166.46i | 0.366583 | − | 0.634941i | ||||
\(151\) | −956.805 | − | 1657.23i | −0.515653 | − | 0.893138i | −0.999835 | − | 0.0181702i | \(-0.994216\pi\) |
0.484182 | − | 0.874968i | \(-0.339117\pi\) | |||||||
\(152\) | 128.857 | + | 223.187i | 0.0687611 | + | 0.119098i | ||||
\(153\) | −48.5325 | − | 84.0608i | −0.0256446 | − | 0.0444178i | ||||
\(154\) | −736.034 | −0.385138 | ||||||||
\(155\) | −333.319 | − | 577.326i | −0.172728 | − | 0.299174i | ||||
\(156\) | −2328.37 | −1.19499 | ||||||||
\(157\) | −1074.60 | + | 1861.26i | −0.546257 | + | 0.946145i | 0.452270 | + | 0.891881i | \(0.350615\pi\) |
−0.998527 | + | 0.0542637i | \(0.982719\pi\) | |||||||
\(158\) | −588.893 | −0.296518 | ||||||||
\(159\) | 4512.00 | 2.25047 | ||||||||
\(160\) | 122.484 | − | 212.148i | 0.0605200 | − | 0.104824i | ||||
\(161\) | 401.158 | + | 694.825i | 0.196370 | + | 0.340124i | ||||
\(162\) | 5959.29 | 2.89016 | ||||||||
\(163\) | 1813.31 | − | 3140.74i | 0.871344 | − | 1.50921i | 0.0107365 | − | 0.999942i | \(-0.496582\pi\) |
0.860607 | − | 0.509269i | \(-0.170084\pi\) | |||||||
\(164\) | −127.366 | + | 220.604i | −0.0606438 | + | 0.105038i | ||||
\(165\) | −2563.69 | + | 4440.44i | −1.20959 | + | 2.09508i | ||||
\(166\) | −599.631 | − | 1038.59i | −0.280364 | − | 0.485605i | ||||
\(167\) | −751.637 | − | 1301.87i | −0.348284 | − | 0.603245i | 0.637661 | − | 0.770317i | \(-0.279902\pi\) |
−0.985945 | + | 0.167072i | \(0.946569\pi\) | |||||||
\(168\) | −226.105 | + | 391.625i | −0.103836 | + | 0.179848i | ||||
\(169\) | −548.280 | + | 949.648i | −0.249558 | + | 0.432248i | ||||
\(170\) | 9.79291 | − | 16.9618i | 0.00441813 | − | 0.00765242i | ||||
\(171\) | −2444.32 | −1.09311 | ||||||||
\(172\) | 620.787 | + | 1075.24i | 0.275201 | + | 0.476662i | ||||
\(173\) | 1061.60 | − | 1838.75i | 0.466543 | − | 0.808077i | −0.532726 | − | 0.846288i | \(-0.678833\pi\) |
0.999270 | + | 0.0382108i | \(0.0121658\pi\) | |||||||
\(174\) | −2070.81 | −0.902227 | ||||||||
\(175\) | −370.033 | −0.159839 | ||||||||
\(176\) | 528.284 | − | 915.014i | 0.226255 | − | 0.391885i | ||||
\(177\) | 190.049 | 0.0807061 | ||||||||
\(178\) | 951.960 | + | 1648.84i | 0.400856 | + | 0.694304i | ||||
\(179\) | −2098.15 | −0.876106 | −0.438053 | − | 0.898949i | \(-0.644332\pi\) | ||||
−0.438053 | + | 0.898949i | \(0.644332\pi\) | |||||||
\(180\) | 1161.71 | + | 2012.15i | 0.481050 | + | 0.833204i | ||||
\(181\) | 397.353 | + | 688.235i | 0.163177 | + | 0.282630i | 0.936006 | − | 0.351983i | \(-0.114493\pi\) |
−0.772830 | + | 0.634614i | \(0.781159\pi\) | |||||||
\(182\) | 319.833 | + | 553.967i | 0.130262 | + | 0.225620i | ||||
\(183\) | −3825.16 | + | 6625.36i | −1.54516 | + | 2.67629i | ||||
\(184\) | −1151.71 | −0.461442 | ||||||||
\(185\) | 313.909 | − | 1694.07i | 0.124751 | − | 0.673245i | ||||
\(186\) | −1766.53 | −0.696388 | ||||||||
\(187\) | 42.2377 | − | 73.1578i | 0.0165172 | − | 0.0286087i | ||||
\(188\) | 105.499 | + | 182.729i | 0.0409270 | + | 0.0708876i | ||||
\(189\) | −1381.42 | − | 2392.68i | −0.531658 | − | 0.920858i | ||||
\(190\) | −246.608 | − | 427.138i | −0.0941622 | − | 0.163094i | ||||
\(191\) | 2581.88 | 0.978106 | 0.489053 | − | 0.872254i | \(-0.337342\pi\) | ||||
0.489053 | + | 0.872254i | \(0.337342\pi\) | |||||||
\(192\) | −324.571 | − | 562.173i | −0.121999 | − | 0.211309i | ||||
\(193\) | −3743.65 | −1.39624 | −0.698119 | − | 0.715982i | \(-0.745979\pi\) | ||||
−0.698119 | + | 0.715982i | \(0.745979\pi\) | |||||||
\(194\) | 474.578 | − | 821.994i | 0.175633 | − | 0.304205i | ||||
\(195\) | 4456.06 | 1.63644 | ||||||||
\(196\) | −1247.77 | −0.454725 | ||||||||
\(197\) | −1140.45 | + | 1975.31i | −0.412455 | + | 0.714392i | −0.995158 | − | 0.0982929i | \(-0.968662\pi\) |
0.582703 | + | 0.812685i | \(0.301995\pi\) | |||||||
\(198\) | 5010.57 | + | 8678.57i | 1.79841 | + | 3.11495i | ||||
\(199\) | −1268.83 | −0.451985 | −0.225992 | − | 0.974129i | \(-0.572562\pi\) | ||||
−0.225992 | + | 0.974129i | \(0.572562\pi\) | |||||||
\(200\) | 265.589 | − | 460.014i | 0.0938999 | − | 0.162639i | ||||
\(201\) | 3703.57 | − | 6414.77i | 1.29965 | − | 2.25106i | ||||
\(202\) | 1902.70 | − | 3295.58i | 0.662742 | − | 1.14790i | ||||
\(203\) | 284.453 | + | 492.688i | 0.0983483 | + | 0.170344i | ||||
\(204\) | −25.9503 | − | 44.9472i | −0.00890629 | − | 0.0154261i | ||||
\(205\) | 243.754 | − | 422.194i | 0.0830463 | − | 0.143840i | ||||
\(206\) | −1064.63 | + | 1843.99i | −0.360078 | + | 0.623674i | ||||
\(207\) | 5461.78 | − | 9460.09i | 1.83391 | − | 3.17643i | ||||
\(208\) | −918.233 | −0.306096 | ||||||||
\(209\) | −1063.64 | − | 1842.28i | −0.352027 | − | 0.609729i | ||||
\(210\) | 432.722 | − | 749.496i | 0.142194 | − | 0.246286i | ||||
\(211\) | −374.691 | −0.122250 | −0.0611251 | − | 0.998130i | \(-0.519469\pi\) | ||||
−0.0611251 | + | 0.998130i | \(0.519469\pi\) | |||||||
\(212\) | 1779.39 | 0.576456 | ||||||||
\(213\) | 1145.07 | − | 1983.33i | 0.368353 | − | 0.638006i | ||||
\(214\) | −1650.85 | −0.527337 | ||||||||
\(215\) | −1188.07 | − | 2057.80i | −0.376864 | − | 0.652747i | ||||
\(216\) | 3966.01 | 1.24932 | ||||||||
\(217\) | 242.657 | + | 420.294i | 0.0759106 | + | 0.131481i | ||||
\(218\) | 428.376 | + | 741.969i | 0.133088 | + | 0.230516i | ||||
\(219\) | −1411.72 | − | 2445.16i | −0.435593 | − | 0.754469i | ||||
\(220\) | −1011.03 | + | 1751.16i | −0.309836 | + | 0.536652i | ||||
\(221\) | −73.4151 | −0.0223459 | ||||||||
\(222\) | −3471.78 | − | 2964.94i | −1.04960 | − | 0.896369i | ||||
\(223\) | 4441.53 | 1.33375 | 0.666876 | − | 0.745169i | \(-0.267631\pi\) | ||||
0.666876 | + | 0.745169i | \(0.267631\pi\) | |||||||
\(224\) | −89.1683 | + | 154.444i | −0.0265974 | + | 0.0460680i | ||||
\(225\) | 2519.01 | + | 4363.06i | 0.746374 | + | 1.29276i | ||||
\(226\) | −998.849 | − | 1730.06i | −0.293993 | − | 0.509211i | ||||
\(227\) | −304.105 | − | 526.725i | −0.0889170 | − | 0.154009i | 0.818137 | − | 0.575024i | \(-0.195007\pi\) |
−0.907054 | + | 0.421015i | \(0.861674\pi\) | |||||||
\(228\) | −1306.98 | −0.379634 | ||||||||
\(229\) | −283.788 | − | 491.535i | −0.0818918 | − | 0.141841i | 0.822171 | − | 0.569241i | \(-0.192763\pi\) |
−0.904063 | + | 0.427400i | \(0.859430\pi\) | |||||||
\(230\) | 2204.16 | 0.631904 | ||||||||
\(231\) | 1866.37 | − | 3232.64i | 0.531593 | − | 0.920746i | ||||
\(232\) | −816.658 | −0.231104 | ||||||||
\(233\) | 623.588 | 0.175333 | 0.0876666 | − | 0.996150i | \(-0.472059\pi\) | ||||
0.0876666 | + | 0.996150i | \(0.472059\pi\) | |||||||
\(234\) | 4354.55 | − | 7542.30i | 1.21652 | − | 2.10707i | ||||
\(235\) | −201.904 | − | 349.708i | −0.0560459 | − | 0.0970743i | ||||
\(236\) | 74.9492 | 0.0206728 | ||||||||
\(237\) | 1493.26 | − | 2586.40i | 0.409273 | − | 0.708882i | ||||
\(238\) | −7.12924 | + | 12.3482i | −0.00194168 | + | 0.00336309i | ||||
\(239\) | −2547.73 | + | 4412.80i | −0.689535 | + | 1.19431i | 0.282453 | + | 0.959281i | \(0.408852\pi\) |
−0.971988 | + | 0.235029i | \(0.924482\pi\) | |||||||
\(240\) | 621.167 | + | 1075.89i | 0.167067 | + | 0.289369i | ||||
\(241\) | 2241.00 | + | 3881.53i | 0.598986 | + | 1.03747i | 0.992971 | + | 0.118358i | \(0.0377630\pi\) |
−0.393985 | + | 0.919117i | \(0.628904\pi\) | |||||||
\(242\) | −3029.68 | + | 5247.56i | −0.804774 | + | 1.39391i | ||||
\(243\) | −8418.37 | + | 14581.0i | −2.22238 | + | 3.84928i | ||||
\(244\) | −1508.52 | + | 2612.83i | −0.395790 | + | 0.685529i | ||||
\(245\) | 2387.99 | 0.622706 | ||||||||
\(246\) | −645.924 | − | 1118.77i | −0.167409 | − | 0.289961i | ||||
\(247\) | −924.381 | + | 1601.07i | −0.238125 | + | 0.412445i | ||||
\(248\) | −696.661 | −0.178379 | ||||||||
\(249\) | 6081.96 | 1.54791 | ||||||||
\(250\) | −1465.19 | + | 2537.79i | −0.370668 | + | 0.642015i | ||||
\(251\) | −3367.41 | −0.846808 | −0.423404 | − | 0.905941i | \(-0.639165\pi\) | ||||
−0.423404 | + | 0.905941i | \(0.639165\pi\) | |||||||
\(252\) | −845.729 | − | 1464.84i | −0.211412 | − | 0.366177i | ||||
\(253\) | 9506.74 | 2.36238 | ||||||||
\(254\) | 105.365 | + | 182.498i | 0.0260284 | + | 0.0450825i | ||||
\(255\) | 49.6639 | + | 86.0204i | 0.0121964 | + | 0.0211247i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 969.585 | − | 1679.37i | 0.235335 | − | 0.407612i | −0.724035 | − | 0.689763i | \(-0.757715\pi\) |
0.959370 | + | 0.282151i | \(0.0910480\pi\) | |||||||
\(258\) | −6296.54 | −1.51940 | ||||||||
\(259\) | −228.526 | + | 1233.28i | −0.0548258 | + | 0.295878i | ||||
\(260\) | 1757.32 | 0.419171 | ||||||||
\(261\) | 3872.85 | − | 6707.97i | 0.918481 | − | 1.59085i | ||||
\(262\) | −411.807 | − | 713.270i | −0.0971050 | − | 0.168191i | ||||
\(263\) | −891.665 | − | 1544.41i | −0.209059 | − | 0.362100i | 0.742360 | − | 0.670002i | \(-0.233707\pi\) |
−0.951418 | + | 0.307901i | \(0.900373\pi\) | |||||||
\(264\) | 2679.15 | + | 4640.42i | 0.624584 | + | 1.08181i | ||||
\(265\) | −3405.41 | −0.789405 | ||||||||
\(266\) | 179.531 | + | 310.956i | 0.0413825 | + | 0.0716766i | ||||
\(267\) | −9655.57 | −2.21315 | ||||||||
\(268\) | 1460.57 | − | 2529.77i | 0.332904 | − | 0.576606i | ||||
\(269\) | −7323.39 | −1.65991 | −0.829953 | − | 0.557833i | \(-0.811633\pi\) | ||||
−0.829953 | + | 0.557833i | \(0.811633\pi\) | |||||||
\(270\) | −7590.20 | −1.71083 | ||||||||
\(271\) | −2741.77 | + | 4748.88i | −0.614578 | + | 1.06448i | 0.375881 | + | 0.926668i | \(0.377340\pi\) |
−0.990458 | + | 0.137812i | \(0.955993\pi\) | |||||||
\(272\) | −10.2339 | − | 17.7257i | −0.00228134 | − | 0.00395139i | ||||
\(273\) | −3244.01 | −0.719182 | ||||||||
\(274\) | −2489.23 | + | 4311.48i | −0.548833 | + | 0.950606i | ||||
\(275\) | −2192.29 | + | 3797.15i | −0.480727 | + | 0.832643i | ||||
\(276\) | 2920.41 | − | 5058.29i | 0.636913 | − | 1.10316i | ||||
\(277\) | 802.216 | + | 1389.48i | 0.174009 | + | 0.301392i | 0.939818 | − | 0.341676i | \(-0.110995\pi\) |
−0.765809 | + | 0.643068i | \(0.777661\pi\) | |||||||
\(278\) | −1259.86 | − | 2182.13i | −0.271803 | − | 0.470776i | ||||
\(279\) | 3303.79 | − | 5722.32i | 0.708934 | − | 1.22791i | ||||
\(280\) | 170.651 | − | 295.577i | 0.0364227 | − | 0.0630860i | ||||
\(281\) | 4000.65 | − | 6929.32i | 0.849319 | − | 1.47106i | −0.0324988 | − | 0.999472i | \(-0.510347\pi\) |
0.881817 | − | 0.471591i | \(-0.156320\pi\) | |||||||
\(282\) | −1070.05 | −0.225960 | ||||||||
\(283\) | −542.053 | − | 938.863i | −0.113858 | − | 0.197207i | 0.803465 | − | 0.595352i | \(-0.202987\pi\) |
−0.917322 | + | 0.398145i | \(0.869654\pi\) | |||||||
\(284\) | 451.579 | − | 782.159i | 0.0943532 | − | 0.163425i | ||||
\(285\) | 2501.30 | 0.519875 | ||||||||
\(286\) | 7579.49 | 1.56708 | ||||||||
\(287\) | −177.453 | + | 307.357i | −0.0364972 | + | 0.0632151i | ||||
\(288\) | 2428.07 | 0.496789 | ||||||||
\(289\) | 2455.68 | + | 4253.37i | 0.499833 | + | 0.865737i | ||||
\(290\) | 1562.93 | 0.316477 | ||||||||
\(291\) | 2406.78 | + | 4168.67i | 0.484839 | + | 0.839766i | ||||
\(292\) | −556.734 | − | 964.292i | −0.111577 | − | 0.193257i | ||||
\(293\) | 1699.01 | + | 2942.77i | 0.338762 | + | 0.586753i | 0.984200 | − | 0.177060i | \(-0.0566586\pi\) |
−0.645438 | + | 0.763812i | \(0.723325\pi\) | |||||||
\(294\) | 3163.97 | − | 5480.16i | 0.627641 | − | 1.08711i | ||||
\(295\) | −143.439 | −0.0283095 | ||||||||
\(296\) | −1369.15 | − | 1169.28i | −0.268853 | − | 0.229604i | ||||
\(297\) | −32737.2 | −6.39597 | ||||||||
\(298\) | 581.828 | − | 1007.76i | 0.113102 | − | 0.195898i | ||||
\(299\) | −4131.02 | − | 7155.13i | −0.799006 | − | 1.38392i | ||||
\(300\) | 1346.91 | + | 2332.92i | 0.259213 | + | 0.448971i | ||||
\(301\) | 864.915 | + | 1498.08i | 0.165624 | + | 0.286870i | ||||
\(302\) | 3827.22 | 0.729244 | ||||||||
\(303\) | 9649.41 | + | 16713.3i | 1.82952 | + | 3.16882i | ||||
\(304\) | −515.428 | −0.0972429 | ||||||||
\(305\) | 2887.01 | − | 5000.45i | 0.542000 | − | 0.938771i | ||||
\(306\) | 194.130 | 0.0362669 | ||||||||
\(307\) | −4586.37 | −0.852632 | −0.426316 | − | 0.904574i | \(-0.640189\pi\) | ||||
−0.426316 | + | 0.904574i | \(0.640189\pi\) | |||||||
\(308\) | 736.034 | − | 1274.85i | 0.136167 | − | 0.235848i | ||||
\(309\) | −5399.17 | − | 9351.63i | −0.994006 | − | 1.72167i | ||||
\(310\) | 1333.28 | 0.244274 | ||||||||
\(311\) | 79.8898 | − | 138.373i | 0.0145664 | − | 0.0252297i | −0.858650 | − | 0.512562i | \(-0.828697\pi\) |
0.873217 | + | 0.487332i | \(0.162030\pi\) | |||||||
\(312\) | 2328.37 | − | 4032.85i | 0.422494 | − | 0.731780i | ||||
\(313\) | −2340.42 | + | 4053.73i | −0.422647 | + | 0.732047i | −0.996197 | − | 0.0871238i | \(-0.972232\pi\) |
0.573550 | + | 0.819170i | \(0.305566\pi\) | |||||||
\(314\) | −2149.20 | − | 3722.52i | −0.386262 | − | 0.669026i | ||||
\(315\) | 1618.56 | + | 2803.44i | 0.289510 | + | 0.501447i | ||||
\(316\) | 588.893 | − | 1019.99i | 0.104835 | − | 0.181579i | ||||
\(317\) | 120.064 | − | 207.957i | 0.0212727 | − | 0.0368455i | −0.855193 | − | 0.518310i | \(-0.826562\pi\) |
0.876466 | + | 0.481464i | \(0.159895\pi\) | |||||||
\(318\) | −4512.00 | + | 7815.02i | −0.795662 | + | 1.37813i | ||||
\(319\) | 6741.05 | 1.18315 | ||||||||
\(320\) | 244.968 | + | 424.297i | 0.0427941 | + | 0.0741216i | ||||
\(321\) | 4186.08 | − | 7250.51i | 0.727864 | − | 1.26070i | ||||
\(322\) | −1604.63 | −0.277710 | ||||||||
\(323\) | −41.2098 | −0.00709900 | ||||||||
\(324\) | −5959.29 | + | 10321.8i | −1.02183 | + | 1.76985i | ||||
\(325\) | 3810.51 | 0.650366 | ||||||||
\(326\) | 3626.61 | + | 6281.47i | 0.616133 | + | 1.06717i | ||||
\(327\) | −4344.94 | −0.734789 | ||||||||
\(328\) | −254.731 | − | 441.207i | −0.0428816 | − | 0.0742732i | ||||
\(329\) | 146.986 | + | 254.588i | 0.0246311 | + | 0.0426623i | ||||
\(330\) | −5127.38 | − | 8880.88i | −0.855312 | − | 1.48144i | ||||
\(331\) | 555.284 | − | 961.781i | 0.0922090 | − | 0.159711i | −0.816231 | − | 0.577725i | \(-0.803941\pi\) |
0.908440 | + | 0.418014i | \(0.137274\pi\) | |||||||
\(332\) | 2398.52 | 0.396494 | ||||||||
\(333\) | 16097.3 | − | 5701.07i | 2.64903 | − | 0.938188i | ||||
\(334\) | 3006.55 | 0.492548 | ||||||||
\(335\) | −2795.25 | + | 4841.51i | −0.455882 | + | 0.789611i | ||||
\(336\) | −452.210 | − | 783.250i | −0.0734228 | − | 0.127172i | ||||
\(337\) | 3344.14 | + | 5792.22i | 0.540554 | + | 0.936268i | 0.998872 | + | 0.0474793i | \(0.0151188\pi\) |
−0.458318 | + | 0.888788i | \(0.651548\pi\) | |||||||
\(338\) | −1096.56 | − | 1899.30i | −0.176464 | − | 0.305645i | ||||
\(339\) | 10131.2 | 1.62315 | ||||||||
\(340\) | 19.5858 | + | 33.9236i | 0.00312409 | + | 0.00541108i | ||||
\(341\) | 5750.54 | 0.913224 | ||||||||
\(342\) | 2444.32 | − | 4233.69i | 0.386473 | − | 0.669391i | ||||
\(343\) | −3650.00 | −0.574582 | ||||||||
\(344\) | −2483.15 | −0.389193 | ||||||||
\(345\) | −5589.11 | + | 9680.62i | −0.872195 | + | 1.51069i | ||||
\(346\) | 2123.20 | + | 3677.49i | 0.329896 | + | 0.571397i | ||||
\(347\) | 9335.65 | 1.44428 | 0.722138 | − | 0.691749i | \(-0.243159\pi\) | ||||
0.722138 | + | 0.691749i | \(0.243159\pi\) | |||||||
\(348\) | 2070.81 | − | 3586.74i | 0.318985 | − | 0.552499i | ||||
\(349\) | 2559.19 | − | 4432.64i | 0.392522 | − | 0.679868i | −0.600259 | − | 0.799805i | \(-0.704936\pi\) |
0.992781 | + | 0.119937i | \(0.0382693\pi\) | |||||||
\(350\) | 370.033 | − | 640.917i | 0.0565118 | − | 0.0978812i | ||||
\(351\) | 14225.5 | + | 24639.2i | 2.16325 | + | 3.74685i | ||||
\(352\) | 1056.57 | + | 1830.03i | 0.159986 | + | 0.277105i | ||||
\(353\) | −5602.00 | + | 9702.95i | −0.844658 | + | 1.46299i | 0.0412594 | + | 0.999148i | \(0.486863\pi\) |
−0.885918 | + | 0.463843i | \(0.846470\pi\) | |||||||
\(354\) | −190.049 | + | 329.175i | −0.0285339 | + | 0.0494222i | ||||
\(355\) | −864.238 | + | 1496.90i | −0.129208 | + | 0.223795i | ||||
\(356\) | −3807.84 | −0.566896 | ||||||||
\(357\) | −36.1554 | − | 62.6229i | −0.00536007 | − | 0.00928391i | ||||
\(358\) | 2098.15 | − | 3634.10i | 0.309750 | − | 0.536503i | ||||
\(359\) | −8468.69 | −1.24502 | −0.622508 | − | 0.782614i | \(-0.713886\pi\) | ||||
−0.622508 | + | 0.782614i | \(0.713886\pi\) | |||||||
\(360\) | −4646.86 | −0.680308 | ||||||||
\(361\) | 2910.62 | − | 5041.34i | 0.424351 | − | 0.734997i | ||||
\(362\) | −1589.41 | −0.230767 | ||||||||
\(363\) | −15364.8 | − | 26612.6i | −2.22160 | − | 3.84793i | ||||
\(364\) | −1279.33 | −0.184218 | ||||||||
\(365\) | 1065.48 | + | 1845.47i | 0.152794 | + | 0.264648i | ||||
\(366\) | −7650.31 | − | 13250.7i | −1.09259 | − | 1.89242i | ||||
\(367\) | −1651.97 | − | 2861.29i | −0.234965 | − | 0.406971i | 0.724298 | − | 0.689487i | \(-0.242164\pi\) |
−0.959262 | + | 0.282517i | \(0.908831\pi\) | |||||||
\(368\) | 1151.71 | − | 1994.83i | 0.163145 | − | 0.282575i | ||||
\(369\) | 4832.06 | 0.681700 | ||||||||
\(370\) | 2620.30 | + | 2237.77i | 0.368170 | + | 0.314422i | ||||
\(371\) | 2479.14 | 0.346928 | ||||||||
\(372\) | 1766.53 | − | 3059.72i | 0.246210 | − | 0.426449i | ||||
\(373\) | 3835.22 | + | 6642.79i | 0.532386 | + | 0.922120i | 0.999285 | + | 0.0378092i | \(0.0120379\pi\) |
−0.466899 | + | 0.884311i | \(0.654629\pi\) | |||||||
\(374\) | 84.4753 | + | 146.316i | 0.0116795 | + | 0.0202294i | ||||
\(375\) | −7430.60 | − | 12870.2i | −1.02324 | − | 1.77230i | ||||
\(376\) | −421.994 | −0.0578795 | ||||||||
\(377\) | −2929.23 | − | 5073.57i | −0.400167 | − | 0.693109i | ||||
\(378\) | 5525.67 | 0.751877 | ||||||||
\(379\) | −1198.43 | + | 2075.74i | −0.162425 | + | 0.281329i | −0.935738 | − | 0.352696i | \(-0.885265\pi\) |
0.773313 | + | 0.634025i | \(0.218598\pi\) | |||||||
\(380\) | 986.432 | 0.133166 | ||||||||
\(381\) | −1068.70 | −0.143704 | ||||||||
\(382\) | −2581.88 | + | 4471.95i | −0.345813 | + | 0.598965i | ||||
\(383\) | 2086.38 | + | 3613.72i | 0.278353 | + | 0.482121i | 0.970976 | − | 0.239179i | \(-0.0768782\pi\) |
−0.692623 | + | 0.721300i | \(0.743545\pi\) | |||||||
\(384\) | 1298.28 | 0.172533 | ||||||||
\(385\) | −1408.63 | + | 2439.82i | −0.186469 | + | 0.322973i | ||||
\(386\) | 3743.65 | − | 6484.19i | 0.493644 | − | 0.855017i | ||||
\(387\) | 11775.9 | − | 20396.4i | 1.54677 | − | 2.67909i | ||||
\(388\) | 949.157 | + | 1643.99i | 0.124191 | + | 0.215105i | ||||
\(389\) | −1517.48 | − | 2628.34i | −0.197787 | − | 0.342577i | 0.750024 | − | 0.661411i | \(-0.230042\pi\) |
−0.947811 | + | 0.318834i | \(0.896709\pi\) | |||||||
\(390\) | −4456.06 | + | 7718.12i | −0.578567 | + | 1.00211i | ||||
\(391\) | 92.0825 | − | 159.492i | 0.0119100 | − | 0.0206287i | ||||
\(392\) | 1247.77 | − | 2161.19i | 0.160770 | − | 0.278461i | ||||
\(393\) | 4176.89 | 0.536122 | ||||||||
\(394\) | −2280.90 | − | 3950.63i | −0.291649 | − | 0.505152i | ||||
\(395\) | −1127.03 | + | 1952.07i | −0.143562 | + | 0.248657i | ||||
\(396\) | −20042.3 | −2.54334 | ||||||||
\(397\) | 7533.84 | 0.952425 | 0.476212 | − | 0.879330i | \(-0.342009\pi\) | ||||
0.476212 | + | 0.879330i | \(0.342009\pi\) | |||||||
\(398\) | 1268.83 | − | 2197.68i | 0.159801 | − | 0.276783i | ||||
\(399\) | −1820.95 | −0.228475 | ||||||||
\(400\) | 531.178 | + | 920.027i | 0.0663973 | + | 0.115003i | ||||
\(401\) | −7767.41 | −0.967297 | −0.483649 | − | 0.875262i | \(-0.660689\pi\) | ||||
−0.483649 | + | 0.875262i | \(0.660689\pi\) | |||||||
\(402\) | 7407.13 | + | 12829.5i | 0.918991 | + | 1.59174i | ||||
\(403\) | −2498.82 | − | 4328.08i | −0.308871 | − | 0.534980i | ||||
\(404\) | 3805.41 | + | 6591.16i | 0.468629 | + | 0.811690i | ||||
\(405\) | 11405.0 | − | 19754.0i | 1.39930 | − | 2.42366i | ||||
\(406\) | −1137.81 | −0.139086 | ||||||||
\(407\) | 11301.6 | + | 9651.71i | 1.37641 | + | 1.17547i | ||||
\(408\) | 103.801 | 0.0125954 | ||||||||
\(409\) | −6555.40 | + | 11354.3i | −0.792528 | + | 1.37270i | 0.131870 | + | 0.991267i | \(0.457902\pi\) |
−0.924397 | + | 0.381431i | \(0.875431\pi\) | |||||||
\(410\) | 487.507 | + | 844.387i | 0.0587226 | + | 0.101711i | ||||
\(411\) | −12623.9 | − | 21865.3i | −1.51507 | − | 2.62418i | ||||
\(412\) | −2129.25 | − | 3687.98i | −0.254614 | − | 0.441004i | ||||
\(413\) | 104.423 | 0.0124415 | ||||||||
\(414\) | 10923.6 | + | 18920.2i | 1.29677 | + | 2.24608i | ||||
\(415\) | −4590.32 | −0.542964 | ||||||||
\(416\) | 918.233 | − | 1590.43i | 0.108221 | − | 0.187445i | ||||
\(417\) | 12778.5 | 1.50064 | ||||||||
\(418\) | 4254.57 | 0.497841 | ||||||||
\(419\) | 412.834 | − | 715.049i | 0.0481342 | − | 0.0833709i | −0.840954 | − | 0.541106i | \(-0.818006\pi\) |
0.889089 | + | 0.457735i | \(0.151339\pi\) | |||||||
\(420\) | 865.444 | + | 1498.99i | 0.100546 | + | 0.174151i | ||||
\(421\) | −15471.7 | −1.79108 | −0.895539 | − | 0.444984i | \(-0.853210\pi\) | ||||
−0.895539 | + | 0.444984i | \(0.853210\pi\) | |||||||
\(422\) | 374.691 | − | 648.984i | 0.0432220 | − | 0.0748627i | ||||
\(423\) | 2001.23 | − | 3466.23i | 0.230031 | − | 0.398425i | ||||
\(424\) | −1779.39 | + | 3081.99i | −0.203808 | + | 0.353006i | ||||
\(425\) | 42.4691 | + | 73.5586i | 0.00484718 | + | 0.00839557i | ||||
\(426\) | 2290.15 | + | 3966.65i | 0.260465 | + | 0.451138i | ||||
\(427\) | −2101.75 | + | 3640.33i | −0.238198 | + | 0.412572i | ||||
\(428\) | 1650.85 | − | 2859.36i | 0.186442 | − | 0.322926i | ||||
\(429\) | −19219.4 | + | 33288.9i | −2.16298 | + | 3.74640i | ||||
\(430\) | 4752.28 | 0.532966 | ||||||||
\(431\) | −3312.02 | − | 5736.58i | −0.370149 | − | 0.641117i | 0.619439 | − | 0.785045i | \(-0.287360\pi\) |
−0.989588 | + | 0.143928i | \(0.954027\pi\) | |||||||
\(432\) | −3966.01 | + | 6869.33i | −0.441701 | + | 0.765049i | ||||
\(433\) | −10701.0 | −1.18766 | −0.593832 | − | 0.804589i | \(-0.702386\pi\) | ||||
−0.593832 | + | 0.804589i | \(0.702386\pi\) | |||||||
\(434\) | −970.627 | −0.107354 | ||||||||
\(435\) | −3963.13 | + | 6864.35i | −0.436822 | + | 0.756598i | ||||
\(436\) | −1713.50 | −0.188215 | ||||||||
\(437\) | −2318.85 | − | 4016.36i | −0.253834 | − | 0.439654i | ||||
\(438\) | 5646.86 | 0.616022 | ||||||||
\(439\) | −4582.14 | − | 7936.49i | −0.498163 | − | 0.862843i | 0.501835 | − | 0.864963i | \(-0.332658\pi\) |
−0.999998 | + | 0.00212020i | \(0.999325\pi\) | |||||||
\(440\) | −2022.07 | − | 3502.33i | −0.219087 | − | 0.379470i | ||||
\(441\) | 11834.6 | + | 20498.1i | 1.27790 | + | 2.21338i | ||||
\(442\) | 73.4151 | − | 127.159i | 0.00790045 | − | 0.0136840i | ||||
\(443\) | −9742.85 | −1.04491 | −0.522457 | − | 0.852666i | \(-0.674984\pi\) | ||||
−0.522457 | + | 0.852666i | \(0.674984\pi\) | |||||||
\(444\) | 8607.21 | − | 3048.35i | 0.920000 | − | 0.325830i | ||||
\(445\) | 7287.49 | 0.776315 | ||||||||
\(446\) | −4441.53 | + | 7692.95i | −0.471552 | + | 0.816753i | ||||
\(447\) | 2950.69 | + | 5110.75i | 0.312221 | + | 0.540783i | ||||
\(448\) | −178.337 | − | 308.888i | −0.0188072 | − | 0.0325750i | ||||
\(449\) | −2373.10 | − | 4110.33i | −0.249429 | − | 0.432023i | 0.713939 | − | 0.700208i | \(-0.246910\pi\) |
−0.963367 | + | 0.268185i | \(0.913576\pi\) | |||||||
\(450\) | −10076.1 | −1.05553 | ||||||||
\(451\) | 2102.66 | + | 3641.92i | 0.219535 | + | 0.380246i | ||||
\(452\) | 3995.39 | 0.415769 | ||||||||
\(453\) | −9704.71 | + | 16809.0i | −1.00655 | + | 1.74339i | ||||
\(454\) | 1216.42 | 0.125748 | ||||||||
\(455\) | 2448.40 | 0.252270 | ||||||||
\(456\) | 1306.98 | − | 2263.75i | 0.134221 | − | 0.232477i | ||||
\(457\) | −3103.33 | − | 5375.12i | −0.317653 | − | 0.550192i | 0.662345 | − | 0.749199i | \(-0.269561\pi\) |
−0.979998 | + | 0.199008i | \(0.936228\pi\) | |||||||
\(458\) | 1135.15 | 0.115812 | ||||||||
\(459\) | −317.093 | + | 549.221i | −0.0322454 | + | 0.0558507i | ||||
\(460\) | −2204.16 | + | 3817.72i | −0.223412 | + | 0.386961i | ||||
\(461\) | −1497.80 | + | 2594.26i | −0.151322 | + | 0.262097i | −0.931714 | − | 0.363194i | \(-0.881686\pi\) |
0.780392 | + | 0.625291i | \(0.215020\pi\) | |||||||
\(462\) | 3732.73 | + | 6465.29i | 0.375893 | + | 0.651066i | ||||
\(463\) | −2249.67 | − | 3896.55i | −0.225813 | − | 0.391119i | 0.730750 | − | 0.682645i | \(-0.239170\pi\) |
−0.956563 | + | 0.291526i | \(0.905837\pi\) | |||||||
\(464\) | 816.658 | − | 1414.49i | 0.0817078 | − | 0.141522i | ||||
\(465\) | −3380.80 | + | 5855.72i | −0.337163 | + | 0.583984i | ||||
\(466\) | −623.588 | + | 1080.09i | −0.0619896 | + | 0.107369i | ||||
\(467\) | 347.289 | 0.0344125 | 0.0172062 | − | 0.999852i | \(-0.494523\pi\) | ||||
0.0172062 | + | 0.999852i | \(0.494523\pi\) | |||||||
\(468\) | 8709.10 | + | 15084.6i | 0.860210 | + | 1.48993i | ||||
\(469\) | 2034.94 | − | 3524.62i | 0.200351 | − | 0.347019i | ||||
\(470\) | 807.617 | 0.0792608 | ||||||||
\(471\) | 21799.0 | 2.13258 | ||||||||
\(472\) | −74.9492 | + | 129.816i | −0.00730893 | + | 0.0126594i | ||||
\(473\) | 20497.0 | 1.99250 | ||||||||
\(474\) | 2986.52 | + | 5172.81i | 0.289400 | + | 0.501255i | ||||
\(475\) | 2138.94 | 0.206613 | ||||||||
\(476\) | −14.2585 | − | 24.6964i | −0.00137298 | − | 0.00237806i | ||||
\(477\) | −16876.8 | − | 29231.5i | −1.61999 | − | 2.80591i | ||||
\(478\) | −5095.46 | − | 8825.59i | −0.487575 | − | 0.844504i | ||||
\(479\) | 6447.17 | − | 11166.8i | 0.614987 | − | 1.06519i | −0.375400 | − | 0.926863i | \(-0.622495\pi\) |
0.990387 | − | 0.138325i | \(-0.0441720\pi\) | |||||||
\(480\) | −2484.67 | −0.236269 | ||||||||
\(481\) | 2353.30 | − | 12700.0i | 0.223079 | − | 1.20389i | ||||
\(482\) | −8964.01 | −0.847095 | ||||||||
\(483\) | 4068.87 | − | 7047.50i | 0.383313 | − | 0.663917i | ||||
\(484\) | −6059.36 | − | 10495.1i | −0.569061 | − | 0.985643i | ||||
\(485\) | −1816.51 | − | 3146.28i | −0.170069 | − | 0.294568i | ||||
\(486\) | −16836.7 | − | 29162.1i | −1.57146 | − | 2.72185i | ||||
\(487\) | −3481.17 | −0.323916 | −0.161958 | − | 0.986798i | \(-0.551781\pi\) | ||||
−0.161958 | + | 0.986798i | \(0.551781\pi\) | |||||||
\(488\) | −3017.03 | − | 5225.65i | −0.279866 | − | 0.484742i | ||||
\(489\) | −36784.1 | −3.40171 | ||||||||
\(490\) | −2387.99 | + | 4136.12i | −0.220160 | + | 0.381328i | ||||
\(491\) | 7626.23 | 0.700951 | 0.350475 | − | 0.936572i | \(-0.386020\pi\) | ||||
0.350475 | + | 0.936572i | \(0.386020\pi\) | |||||||
\(492\) | 2583.70 | 0.236752 | ||||||||
\(493\) | 65.2940 | − | 113.092i | 0.00596489 | − | 0.0103315i | ||||
\(494\) | −1848.76 | − | 3202.15i | −0.168380 | − | 0.291643i | ||||
\(495\) | 38357.2 | 3.48288 | ||||||||
\(496\) | 696.661 | − | 1206.65i | 0.0630665 | − | 0.109234i | ||||
\(497\) | 629.165 | − | 1089.75i | 0.0567846 | − | 0.0983537i | ||||
\(498\) | −6081.96 | + | 10534.3i | −0.547267 | + | 0.947895i | ||||
\(499\) | −953.422 | − | 1651.38i | −0.0855331 | − | 0.148148i | 0.820085 | − | 0.572242i | \(-0.193926\pi\) |
−0.905618 | + | 0.424094i | \(0.860593\pi\) | |||||||
\(500\) | −2930.38 | − | 5075.58i | −0.262102 | − | 0.453973i | ||||
\(501\) | −7623.73 | + | 13204.7i | −0.679846 | + | 1.17753i | ||||
\(502\) | 3367.41 | − | 5832.52i | 0.299392 | − | 0.518562i | ||||
\(503\) | −2752.07 | + | 4766.72i | −0.243954 | + | 0.422540i | −0.961837 | − | 0.273623i | \(-0.911778\pi\) |
0.717883 | + | 0.696163i | \(0.245111\pi\) | |||||||
\(504\) | 3382.91 | 0.298982 | ||||||||
\(505\) | −7282.83 | − | 12614.2i | −0.641746 | − | 1.11154i | ||||
\(506\) | −9506.74 | + | 16466.2i | −0.835229 | + | 1.44666i | ||||
\(507\) | 11122.2 | 0.974270 | ||||||||
\(508\) | −421.461 | −0.0368097 | ||||||||
\(509\) | −2534.42 | + | 4389.75i | −0.220700 | + | 0.382264i | −0.955021 | − | 0.296539i | \(-0.904168\pi\) |
0.734321 | + | 0.678803i | \(0.237501\pi\) | |||||||
\(510\) | −198.656 | −0.0172483 | ||||||||
\(511\) | −775.673 | − | 1343.50i | −0.0671502 | − | 0.116308i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 7985.14 | + | 13830.7i | 0.687237 | + | 1.19033i | ||||
\(514\) | 1939.17 | + | 3358.74i | 0.166407 | + | 0.288225i | ||||
\(515\) | 4074.99 | + | 7058.09i | 0.348671 | + | 0.603916i | ||||
\(516\) | 6296.54 | − | 10905.9i | 0.537190 | − | 0.930440i | ||||
\(517\) | 3483.32 | 0.296318 | ||||||||
\(518\) | −1907.58 | − | 1629.10i | −0.161804 | − | 0.138183i | ||||
\(519\) | −21535.3 | −1.82137 | ||||||||
\(520\) | −1757.32 | + | 3043.77i | −0.148199 | + | 0.256689i | ||||
\(521\) | −3712.40 | − | 6430.06i | −0.312175 | − | 0.540703i | 0.666658 | − | 0.745364i | \(-0.267724\pi\) |
−0.978833 | + | 0.204661i | \(0.934391\pi\) | |||||||
\(522\) | 7745.70 | + | 13415.9i | 0.649464 | + | 1.12490i | ||||
\(523\) | 5386.00 | + | 9328.82i | 0.450312 | + | 0.779963i | 0.998405 | − | 0.0564539i | \(-0.0179794\pi\) |
−0.548093 | + | 0.836417i | \(0.684646\pi\) | |||||||
\(524\) | 1647.23 | 0.137327 | ||||||||
\(525\) | 1876.59 | + | 3250.35i | 0.156002 | + | 0.270204i | ||||
\(526\) | 3566.66 | 0.295654 | ||||||||
\(527\) | 55.6999 | − | 96.4750i | 0.00460403 | − | 0.00797442i | ||||
\(528\) | −10716.6 | −0.883295 | ||||||||
\(529\) | 8558.67 | 0.703433 | ||||||||
\(530\) | 3405.41 | − | 5898.34i | 0.279097 | − | 0.483410i | ||||
\(531\) | −710.865 | − | 1231.25i | −0.0580959 | − | 0.100625i | ||||
\(532\) | −718.123 | −0.0585237 | ||||||||
\(533\) | 1827.36 | − | 3165.09i | 0.148503 | − | 0.257214i | ||||
\(534\) | 9655.57 | − | 16723.9i | 0.782467 | − | 1.35527i | ||||
\(535\) | −3159.42 | + | 5472.28i | −0.255315 | + | 0.442219i | ||||
\(536\) | 2921.13 | + | 5059.55i | 0.235399 | + | 0.407722i | ||||
\(537\) | 10640.6 | + | 18430.0i | 0.855074 | + | 1.48103i | ||||
\(538\) | 7323.39 | − | 12684.5i | 0.586865 | − | 1.01648i | ||||
\(539\) | −10299.6 | + | 17839.4i | −0.823071 | + | 1.42560i | ||||
\(540\) | 7590.20 | − | 13146.6i | 0.604870 | − | 1.04767i | ||||
\(541\) | −14956.2 | −1.18857 | −0.594287 | − | 0.804253i | \(-0.702566\pi\) | ||||
−0.594287 | + | 0.804253i | \(0.702566\pi\) | |||||||
\(542\) | −5483.54 | − | 9497.77i | −0.434572 | − | 0.752701i | ||||
\(543\) | 4030.28 | − | 6980.65i | 0.318519 | − | 0.551691i | ||||
\(544\) | 40.9357 | 0.00322630 | ||||||||
\(545\) | 3279.32 | 0.257744 | ||||||||
\(546\) | 3244.01 | − | 5618.80i | 0.254269 | − | 0.440407i | ||||
\(547\) | −3223.61 | −0.251977 | −0.125989 | − | 0.992032i | \(-0.540210\pi\) | ||||
−0.125989 | + | 0.992032i | \(0.540210\pi\) | |||||||
\(548\) | −4978.47 | − | 8622.96i | −0.388083 | − | 0.672180i | ||||
\(549\) | 57230.8 | 4.44909 | ||||||||
\(550\) | −4384.57 | − | 7594.30i | −0.339925 | − | 0.588768i | ||||
\(551\) | −1644.25 | − | 2847.93i | −0.127128 | − | 0.220192i | ||||
\(552\) | 5840.81 | + | 10116.6i | 0.450365 | + | 0.780055i | ||||
\(553\) | 820.479 | − | 1421.11i | 0.0630928 | − | 0.109280i | ||||
\(554\) | −3208.86 | −0.246086 | ||||||||
\(555\) | −16472.6 | + | 5833.97i | −1.25986 | + | 0.446195i | ||||
\(556\) | 5039.42 | 0.384387 | ||||||||
\(557\) | −1157.96 | + | 2005.64i | −0.0880867 | + | 0.152571i | −0.906702 | − | 0.421771i | \(-0.861409\pi\) |
0.818616 | + | 0.574342i | \(0.194742\pi\) | |||||||
\(558\) | 6607.57 | + | 11444.6i | 0.501292 | + | 0.868263i | ||||
\(559\) | −8906.68 | − | 15426.8i | −0.673904 | − | 1.16724i | ||||
\(560\) | 341.303 | + | 591.154i | 0.0257548 | + | 0.0446086i | ||||
\(561\) | −856.819 | −0.0644829 | ||||||||
\(562\) | 8001.29 | + | 13858.6i | 0.600559 | + | 1.04020i | ||||
\(563\) | 26311.1 | 1.96959 | 0.984797 | − | 0.173709i | \(-0.0555752\pi\) | ||||
0.984797 | + | 0.173709i | \(0.0555752\pi\) | |||||||
\(564\) | 1070.05 | − | 1853.39i | 0.0798890 | − | 0.138372i | ||||
\(565\) | −7646.43 | −0.569359 | ||||||||
\(566\) | 2168.21 | 0.161019 | ||||||||
\(567\) | −8302.81 | + | 14380.9i | −0.614965 | + | 1.06515i | ||||
\(568\) | 903.159 | + | 1564.32i | 0.0667178 | + | 0.115559i | ||||
\(569\) | −5859.06 | −0.431678 | −0.215839 | − | 0.976429i | \(-0.569249\pi\) | ||||
−0.215839 | + | 0.976429i | \(0.569249\pi\) | |||||||
\(570\) | −2501.30 | + | 4332.39i | −0.183804 | + | 0.318357i | ||||
\(571\) | −2511.54 | + | 4350.12i | −0.184071 | + | 0.318821i | −0.943263 | − | 0.332046i | \(-0.892261\pi\) |
0.759192 | + | 0.650867i | \(0.225594\pi\) | |||||||
\(572\) | −7579.49 | + | 13128.1i | −0.554046 | + | 0.959636i | ||||
\(573\) | −13093.8 | − | 22679.1i | −0.954626 | − | 1.65346i | ||||
\(574\) | −354.906 | − | 614.715i | −0.0258074 | − | 0.0446998i | ||||
\(575\) | −4779.41 | + | 8278.18i | −0.346635 | + | 0.600390i | ||||
\(576\) | −2428.07 | + | 4205.53i | −0.175641 | + | 0.304220i | ||||
\(577\) | 6427.65 | − | 11133.0i | 0.463755 | − | 0.803247i | −0.535389 | − | 0.844605i | \(-0.679835\pi\) |
0.999144 | + | 0.0413580i | \(0.0131684\pi\) | |||||||
\(578\) | −9822.73 | −0.706871 | ||||||||
\(579\) | 18985.6 | + | 32884.0i | 1.36272 | + | 2.36030i | ||||
\(580\) | −1562.93 | + | 2707.07i | −0.111892 | + | 0.193802i | ||||
\(581\) | 3341.76 | 0.238622 | ||||||||
\(582\) | −9627.14 | −0.685666 | ||||||||
\(583\) | 14687.8 | − | 25440.0i | 1.04341 | − | 1.80724i | ||||
\(584\) | 2226.94 | 0.157793 | ||||||||
\(585\) | −16667.6 | − | 28869.1i | −1.17798 | − | 2.04032i | ||||
\(586\) | −6796.04 | −0.479082 | ||||||||
\(587\) | −3731.02 | − | 6462.32i | −0.262344 | − | 0.454393i | 0.704520 | − | 0.709684i | \(-0.251162\pi\) |
−0.966864 | + | 0.255291i | \(0.917829\pi\) | |||||||
\(588\) | 6327.94 | + | 10960.3i | 0.443809 | + | 0.768700i | ||||
\(589\) | −1402.65 | − | 2429.46i | −0.0981244 | − | 0.169956i | ||||
\(590\) | 143.439 | − | 248.443i | 0.0100089 | − | 0.0173360i | ||||
\(591\) | 23134.7 | 1.61021 | ||||||||
\(592\) | 3394.40 | − | 1202.17i | 0.235657 | − | 0.0834609i | ||||
\(593\) | 10116.4 | 0.700556 | 0.350278 | − | 0.936646i | \(-0.386087\pi\) | ||||
0.350278 | + | 0.936646i | \(0.386087\pi\) | |||||||
\(594\) | 32737.2 | − | 56702.5i | 2.26132 | − | 3.91672i | ||||
\(595\) | 27.2880 | + | 47.2643i | 0.00188017 | + | 0.00325655i | ||||
\(596\) | 1163.66 | + | 2015.51i | 0.0799752 | + | 0.138521i | ||||
\(597\) | 6434.76 | + | 11145.3i | 0.441135 | + | 0.764067i | ||||
\(598\) | 16524.1 | 1.12997 | ||||||||
\(599\) | 12409.6 | + | 21494.1i | 0.846483 | + | 1.46615i | 0.884327 | + | 0.466867i | \(0.154617\pi\) |
−0.0378447 | + | 0.999284i | \(0.512049\pi\) | |||||||
\(600\) | −5387.65 | −0.366583 | ||||||||
\(601\) | −422.361 | + | 731.551i | −0.0286663 | + | 0.0496515i | −0.880003 | − | 0.474969i | \(-0.842459\pi\) |
0.851336 | + | 0.524620i | \(0.175793\pi\) | |||||||
\(602\) | −3459.66 | −0.234228 | ||||||||
\(603\) | −55411.7 | −3.74219 | ||||||||
\(604\) | −3827.22 | + | 6628.94i | −0.257827 | + | 0.446569i | ||||
\(605\) | 11596.5 | + | 20085.7i | 0.779279 | + | 1.34975i | ||||
\(606\) | −38597.6 | −2.58733 | ||||||||
\(607\) | 4851.67 | − | 8403.34i | 0.324421 | − | 0.561913i | −0.656974 | − | 0.753913i | \(-0.728164\pi\) |
0.981395 | + | 0.192000i | \(0.0614973\pi\) | |||||||
\(608\) | 515.428 | − | 892.748i | 0.0343806 | − | 0.0595489i | ||||
\(609\) | 2885.16 | − | 4997.25i | 0.191975 | − | 0.332510i | ||||
\(610\) | 5774.03 | + | 10000.9i | 0.383252 | + | 0.663811i | ||||
\(611\) | −1513.63 | − | 2621.68i | −0.100221 | − | 0.173587i | ||||
\(612\) | −194.130 | + | 336.243i | −0.0128223 | + | 0.0222089i | ||||
\(613\) | −6379.84 | + | 11050.2i | −0.420358 | + | 0.728081i | −0.995974 | − | 0.0896387i | \(-0.971429\pi\) |
0.575617 | + | 0.817720i | \(0.304762\pi\) | |||||||
\(614\) | 4586.37 | − | 7943.83i | 0.301451 | − | 0.522128i | ||||
\(615\) | −4944.70 | −0.324211 | ||||||||
\(616\) | 1472.07 | + | 2549.70i | 0.0962846 | + | 0.166770i | ||||
\(617\) | 6474.12 | − | 11213.5i | 0.422429 | − | 0.731668i | −0.573748 | − | 0.819032i | \(-0.694511\pi\) |
0.996176 | + | 0.0873643i | \(0.0278444\pi\) | |||||||
\(618\) | 21596.7 | 1.40574 | ||||||||
\(619\) | 4029.47 | 0.261645 | 0.130822 | − | 0.991406i | \(-0.458238\pi\) | ||||
0.130822 | + | 0.991406i | \(0.458238\pi\) | |||||||
\(620\) | −1333.28 | + | 2309.30i | −0.0863640 | + | 0.149587i | ||||
\(621\) | −71370.4 | −4.61191 | ||||||||
\(622\) | 159.780 | + | 276.746i | 0.0103000 | + | 0.0178401i | ||||
\(623\) | −5305.29 | −0.341175 | ||||||||
\(624\) | 4656.74 | + | 8065.71i | 0.298748 | + | 0.517447i | ||||
\(625\) | 1458.37 | + | 2525.98i | 0.0933359 | + | 0.161662i | ||||
\(626\) | −4680.85 | − | 8107.47i | −0.298857 | − | 0.517635i | ||||
\(627\) | −10788.3 | + | 18686.0i | −0.687153 | + | 1.19018i | ||||
\(628\) | 8596.79 | 0.546257 | ||||||||
\(629\) | 271.391 | − | 96.1166i | 0.0172036 | − | 0.00609288i | ||||
\(630\) | −6474.26 | −0.409430 | ||||||||
\(631\) | 14151.6 | − | 24511.3i | 0.892816 | − | 1.54640i | 0.0563319 | − | 0.998412i | \(-0.482059\pi\) |
0.836484 | − | 0.547991i | \(-0.184607\pi\) | |||||||
\(632\) | 1177.79 | + | 2039.99i | 0.0741295 | + | 0.128396i | ||||
\(633\) | 1900.22 | + | 3291.27i | 0.119316 | + | 0.206661i | ||||
\(634\) | 240.128 | + | 415.913i | 0.0150421 | + | 0.0260537i | ||||
\(635\) | 806.597 | 0.0504076 | ||||||||
\(636\) | −9024.00 | − | 15630.0i | −0.562618 | − | 0.974483i | ||||
\(637\) | 17902.2 | 1.11352 | ||||||||
\(638\) | −6741.05 | + | 11675.8i | −0.418308 | + | 0.724531i | ||||
\(639\) | −17132.3 | −1.06063 | ||||||||
\(640\) | −979.871 | −0.0605200 | ||||||||
\(641\) | 9320.92 | − | 16144.3i | 0.574343 | − | 0.994792i | −0.421769 | − | 0.906703i | \(-0.638591\pi\) |
0.996113 | − | 0.0880887i | \(-0.0280759\pi\) | |||||||
\(642\) | 8372.17 | + | 14501.0i | 0.514678 | + | 0.891448i | ||||
\(643\) | −19547.8 | −1.19890 | −0.599448 | − | 0.800413i | \(-0.704613\pi\) | ||||
−0.599448 | + | 0.800413i | \(0.704613\pi\) | |||||||
\(644\) | 1604.63 | − | 2779.30i | 0.0981852 | − | 0.170062i | ||||
\(645\) | −12050.4 | + | 20871.9i | −0.735633 | + | 1.27415i | ||||
\(646\) | 41.2098 | − | 71.3775i | 0.00250988 | − | 0.00434723i | ||||
\(647\) | −2594.18 | − | 4493.24i | −0.157631 | − | 0.273026i | 0.776383 | − | 0.630262i | \(-0.217052\pi\) |
−0.934014 | + | 0.357236i | \(0.883719\pi\) | |||||||
\(648\) | −11918.6 | − | 20643.6i | −0.722540 | − | 1.25148i | ||||
\(649\) | 618.663 | − | 1071.56i | 0.0374186 | − | 0.0648108i | ||||
\(650\) | −3810.51 | + | 6599.99i | −0.229939 | + | 0.398266i | ||||
\(651\) | 2461.23 | − | 4262.97i | 0.148177 | − | 0.256650i | ||||
\(652\) | −14506.4 | −0.871344 | ||||||||
\(653\) | −10445.6 | − | 18092.3i | −0.625983 | − | 1.08423i | −0.988350 | − | 0.152199i | \(-0.951365\pi\) |
0.362367 | − | 0.932035i | \(-0.381969\pi\) | |||||||
\(654\) | 4344.94 | − | 7525.66i | 0.259787 | − | 0.449964i | ||||
\(655\) | −3152.48 | −0.188057 | ||||||||
\(656\) | 1018.92 | 0.0606438 | ||||||||
\(657\) | −10560.8 | + | 18291.9i | −0.627119 | + | 1.08620i | ||||
\(658\) | −587.946 | −0.0348336 | ||||||||
\(659\) | 14711.7 | + | 25481.5i | 0.869632 | + | 1.50625i | 0.862373 | + | 0.506274i | \(0.168977\pi\) |
0.00725932 | + | 0.999974i | \(0.497689\pi\) | |||||||
\(660\) | 20509.5 | 1.20959 | ||||||||
\(661\) | 6298.21 | + | 10908.8i | 0.370608 | + | 0.641912i | 0.989659 | − | 0.143439i | \(-0.0458160\pi\) |
−0.619051 | + | 0.785351i | \(0.712483\pi\) | |||||||
\(662\) | 1110.57 | + | 1923.56i | 0.0652016 | + | 0.112933i | ||||
\(663\) | 372.319 | + | 644.875i | 0.0218094 | + | 0.0377750i | ||||
\(664\) | −2398.52 | + | 4154.37i | −0.140182 | + | 0.242802i | ||||
\(665\) | 1374.35 | 0.0801430 | ||||||||
\(666\) | −6222.78 | + | 33582.4i | −0.362054 | + | 1.95389i | ||||
\(667\) | 14696.2 | 0.853131 | ||||||||
\(668\) | −3006.55 | + | 5207.49i | −0.174142 | + | 0.301623i | ||||
\(669\) | −22524.8 | − | 39014.1i | −1.30173 | − | 2.25467i | ||||
\(670\) | −5590.49 | − | 9683.01i | −0.322357 | − | 0.558339i | ||||
\(671\) | 24903.9 | + | 43134.8i | 1.43279 | + | 2.48167i | ||||
\(672\) | 1808.84 | 0.103836 | ||||||||
\(673\) | 4361.15 | + | 7553.74i | 0.249792 | + | 0.432653i | 0.963468 | − | 0.267823i | \(-0.0863044\pi\) |
−0.713676 | + | 0.700476i | \(0.752971\pi\) | |||||||
\(674\) | −13376.6 | −0.764459 | ||||||||
\(675\) | 16458.3 | − | 28506.6i | 0.938488 | − | 1.62551i | ||||
\(676\) | 4386.24 | 0.249558 | ||||||||
\(677\) | 22035.2 | 1.25093 | 0.625466 | − | 0.780252i | \(-0.284909\pi\) | ||||
0.625466 | + | 0.780252i | \(0.284909\pi\) | |||||||
\(678\) | −10131.2 | + | 17547.7i | −0.573871 | + | 0.993974i | ||||
\(679\) | 1322.42 | + | 2290.49i | 0.0747419 | + | 0.129457i | ||||
\(680\) | −78.3433 | −0.00441813 | ||||||||
\(681\) | −3084.49 | + | 5342.49i | −0.173565 | + | 0.300623i | ||||
\(682\) | −5750.54 | + | 9960.23i | −0.322873 | + | 0.559233i | ||||
\(683\) | 6168.99 | − | 10685.0i | 0.345607 | − | 0.598610i | −0.639857 | − | 0.768494i | \(-0.721006\pi\) |
0.985464 | + | 0.169885i | \(0.0543396\pi\) | |||||||
\(684\) | 4888.65 | + | 8467.38i | 0.273278 | + | 0.473331i | ||||
\(685\) | 9527.85 | + | 16502.7i | 0.531446 | + | 0.920491i | ||||
\(686\) | 3650.00 | − | 6321.99i | 0.203145 | − | 0.351858i | ||||
\(687\) | −2878.41 | + | 4985.55i | −0.159852 | + | 0.276872i | ||||
\(688\) | 2483.15 | − | 4300.94i | 0.137601 | − | 0.238331i | ||||
\(689\) | −25529.5 | −1.41161 | ||||||||
\(690\) | −11178.2 | − | 19361.2i | −0.616735 | − | 1.06822i | ||||
\(691\) | 6534.28 | − | 11317.7i | 0.359733 | − | 0.623076i | −0.628183 | − | 0.778066i | \(-0.716201\pi\) |
0.987916 | + | 0.154990i | \(0.0495344\pi\) | |||||||
\(692\) | −8492.80 | −0.466543 | ||||||||
\(693\) | −27924.0 | −1.53066 | ||||||||
\(694\) | −9335.65 | + | 16169.8i | −0.510629 | + | 0.884435i | ||||
\(695\) | −9644.50 | −0.526384 | ||||||||
\(696\) | 4141.61 | + | 7173.48i | 0.225557 | + | 0.390676i | ||||
\(697\) | 81.4657 | 0.00442717 | ||||||||
\(698\) | 5118.38 | + | 8865.29i | 0.277555 | + | 0.480739i | ||||
\(699\) | −3162.48 | − | 5477.57i | −0.171124 | − | 0.296396i | ||||
\(700\) | 740.067 | + | 1281.83i | 0.0399598 | + | 0.0692125i | ||||
\(701\) | −13286.6 | + | 23013.1i | −0.715874 | + | 1.23993i | 0.246747 | + | 0.969080i | \(0.420638\pi\) |
−0.962621 | + | 0.270851i | \(0.912695\pi\) | |||||||
\(702\) | −56901.9 | −3.05929 | ||||||||
\(703\) | 1320.97 | − | 7128.86i | 0.0708695 | − | 0.382461i | ||||
\(704\) | −4226.27 | −0.226255 | ||||||||
\(705\) | −2047.88 | + | 3547.03i | −0.109401 | + | 0.189488i | ||||
\(706\) | −11204.0 | − | 19405.9i | −0.597264 | − | 1.03449i | ||||
\(707\) | 5301.91 | + | 9183.17i | 0.282035 | + | 0.488499i | ||||
\(708\) | −380.098 | − | 658.350i | −0.0201765 | − | 0.0349467i | ||||
\(709\) | −21634.3 | −1.14597 | −0.572985 | − | 0.819566i | \(-0.694215\pi\) | ||||
−0.572985 | + | 0.819566i | \(0.694215\pi\) | |||||||
\(710\) | −1728.48 | − | 2993.81i | −0.0913641 | − | 0.158247i | ||||
\(711\) | −22341.7 | −1.17845 | ||||||||
\(712\) | 3807.84 | − | 6595.37i | 0.200428 | − | 0.347152i | ||||
\(713\) | 12536.8 | 0.658493 | ||||||||
\(714\) | 144.621 | 0.00758028 | ||||||||
\(715\) | 14505.7 | − | 25124.6i | 0.758717 | − | 1.31414i | ||||
\(716\) | 4196.30 | + | 7268.20i | 0.219026 | + | 0.379365i | ||||
\(717\) | 51682.4 | 2.69193 | ||||||||
\(718\) | 8468.69 | − | 14668.2i | 0.440179 | − | 0.762413i | ||||
\(719\) | −16443.9 | + | 28481.7i | −0.852928 | + | 1.47731i | 0.0256263 | + | 0.999672i | \(0.491842\pi\) |
−0.878554 | + | 0.477643i | \(0.841491\pi\) | |||||||
\(720\) | 4646.86 | − | 8048.59i | 0.240525 | − | 0.416602i | ||||
\(721\) | −2966.59 | − | 5138.29i | −0.153234 | − | 0.265409i | ||||
\(722\) | 5821.24 | + | 10082.7i | 0.300061 | + | 0.519721i | ||||
\(723\) | 22730.1 | − | 39369.7i | 1.16921 | − | 2.02514i | ||||
\(724\) | 1589.41 | − | 2752.94i | 0.0815884 | − | 0.141315i | ||||
\(725\) | −3388.99 | + | 5869.91i | −0.173606 | + | 0.300694i | ||||
\(726\) | 61459.1 | 3.14182 | ||||||||
\(727\) | 3719.49 | + | 6442.34i | 0.189750 | + | 0.328657i | 0.945167 | − | 0.326588i | \(-0.105899\pi\) |
−0.755417 | + | 0.655245i | \(0.772566\pi\) | |||||||
\(728\) | 1279.33 | − | 2215.87i | 0.0651308 | − | 0.112810i | ||||
\(729\) | 90321.8 | 4.58882 | ||||||||
\(730\) | −4261.94 | −0.216084 | ||||||||
\(731\) | 198.534 | − | 343.872i | 0.0100452 | − | 0.0173988i | ||||
\(732\) | 30601.2 | 1.54516 | ||||||||
\(733\) | 6600.82 | + | 11433.0i | 0.332615 | + | 0.576106i | 0.983024 | − | 0.183478i | \(-0.0587356\pi\) |
−0.650409 | + | 0.759585i | \(0.725402\pi\) | |||||||
\(734\) | 6607.87 | 0.332290 | ||||||||
\(735\) | −12110.5 | − | 20976.0i | −0.607757 | − | 1.05267i | ||||
\(736\) | 2303.43 | + | 3989.65i | 0.115361 | + | 0.199810i | ||||
\(737\) | −24112.3 | − | 41763.7i | −1.20514 | − | 2.08736i | ||||
\(738\) | −4832.06 | + | 8369.38i | −0.241017 | + | 0.417454i | ||||
\(739\) | 1703.34 | 0.0847882 | 0.0423941 | − | 0.999101i | \(-0.486501\pi\) | ||||
0.0423941 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(740\) | −6496.24 | + | 2300.72i | −0.322712 | + | 0.114292i | ||||
\(741\) | 18751.7 | 0.929636 | ||||||||
\(742\) | −2479.14 | + | 4293.99i | −0.122658 | + | 0.212449i | ||||
\(743\) | 6366.22 | + | 11026.6i | 0.314339 | + | 0.544451i | 0.979297 | − | 0.202430i | \(-0.0648838\pi\) |
−0.664958 | + | 0.746881i | \(0.731550\pi\) | |||||||
\(744\) | 3533.06 | + | 6119.43i | 0.174097 | + | 0.301545i | ||||
\(745\) | −2227.02 | − | 3857.31i | −0.109519 | − | 0.189692i | ||||
\(746\) | −15340.9 | −0.752908 | ||||||||
\(747\) | −22749.1 | − | 39402.6i | −1.11425 | − | 1.92994i | ||||
\(748\) | −337.901 | −0.0165172 | ||||||||
\(749\) | 2300.06 | − | 3983.82i | 0.112206 | − | 0.194347i | ||||
\(750\) | 29722.4 | 1.44708 | ||||||||
\(751\) | 26358.6 | 1.28074 | 0.640372 | − | 0.768065i | \(-0.278780\pi\) | ||||
0.640372 | + | 0.768065i | \(0.278780\pi\) | |||||||
\(752\) | 421.994 | − | 730.915i | 0.0204635 | − | 0.0354438i | ||||
\(753\) | 17077.5 | + | 29579.1i | 0.826480 | + | 1.43151i | ||||
\(754\) | 11716.9 | 0.565921 | ||||||||
\(755\) | 7324.57 | − | 12686.5i | 0.353071 | − | 0.611537i | ||||
\(756\) | −5525.67 | + | 9570.74i | −0.265829 | + | 0.460429i | ||||
\(757\) | −10166.8 | + | 17609.5i | −0.488138 | + | 0.845479i | −0.999907 | − | 0.0136438i | \(-0.995657\pi\) |
0.511769 | + | 0.859123i | \(0.328990\pi\) | |||||||
\(758\) | −2396.86 | − | 4151.48i | −0.114852 | − | 0.198930i | ||||
\(759\) | −48212.6 | − | 83506.7i | −2.30567 | − | 3.99355i | ||||
\(760\) | −986.432 | + | 1708.55i | −0.0470811 | + | 0.0815469i | ||||
\(761\) | 3852.56 | − | 6672.83i | 0.183515 | − | 0.317858i | −0.759560 | − | 0.650437i | \(-0.774586\pi\) |
0.943075 | + | 0.332580i | \(0.107919\pi\) | |||||||
\(762\) | 1068.70 | − | 1851.05i | 0.0508071 | − | 0.0880005i | ||||
\(763\) | −2387.35 | −0.113274 | ||||||||
\(764\) | −5163.76 | − | 8943.89i | −0.244527 | − | 0.423532i | ||||
\(765\) | 371.528 | − | 643.506i | 0.0175590 | − | 0.0304131i | ||||
\(766\) | −8345.52 | −0.393650 | ||||||||
\(767\) | −1075.32 | −0.0506228 | ||||||||
\(768\) | −1298.28 | + | 2248.69i | −0.0609997 | + | 0.105654i | ||||
\(769\) | −3439.80 | −0.161303 | −0.0806517 | − | 0.996742i | \(-0.525700\pi\) | ||||
−0.0806517 | + | 0.996742i | \(0.525700\pi\) | |||||||
\(770\) | −2817.26 | − | 4879.64i | −0.131853 | − | 0.228376i | ||||
\(771\) | −19668.7 | −0.918742 | ||||||||
\(772\) | 7487.30 | + | 12968.4i | 0.349059 | + | 0.604588i | ||||
\(773\) | −3727.30 | − | 6455.88i | −0.173430 | − | 0.300390i | 0.766187 | − | 0.642618i | \(-0.222152\pi\) |
−0.939617 | + | 0.342228i | \(0.888819\pi\) | |||||||
\(774\) | 23551.8 | + | 40792.8i | 1.09373 | + | 1.89440i | ||||
\(775\) | −2891.02 | + | 5007.40i | −0.133998 | + | 0.232092i | ||||
\(776\) | −3796.63 | −0.175633 | ||||||||
\(777\) | 11992.0 | − | 4247.13i | 0.553683 | − | 0.196094i | ||||
\(778\) | 6069.90 | 0.279713 | ||||||||
\(779\) | 1025.75 | − | 1776.65i | 0.0471774 | − | 0.0817137i | ||||
\(780\) | −8912.12 | − | 15436.2i | −0.409109 | − | 0.708598i | ||||
\(781\) | −7455.06 | − | 12912.6i | −0.341566 | − | 0.591610i | ||||
\(782\) | 184.165 | + | 318.983i | 0.00842164 | + | 0.0145867i | ||||
\(783\) | −50607.4 | −2.30979 | ||||||||
\(784\) | 2495.53 | + | 4322.39i | 0.113681 | + | 0.196902i | ||||
\(785\) | −16452.6 | −0.748051 | ||||||||
\(786\) | −4176.89 | + | 7234.58i | −0.189548 | + | 0.328306i | ||||
\(787\) | −40189.9 | −1.82035 | −0.910174 | − | 0.414227i | \(-0.864052\pi\) | ||||
−0.910174 | + | 0.414227i | \(0.864052\pi\) | |||||||
\(788\) | 9123.58 | 0.412455 | ||||||||
\(789\) | −9044.01 | + | 15664.7i | −0.408080 | + | 0.706815i | ||||
\(790\) | −2254.06 | − | 3904.15i | −0.101514 | − | 0.175827i | ||||
\(791\) | 5566.60 | 0.250222 | ||||||||
\(792\) | 20042.3 | − | 34714.3i | 0.899207 | − | 1.55747i | ||||
\(793\) | 21643.3 | − | 37487.2i | 0.969199 | − | 1.67870i | ||||
\(794\) | −7533.84 | + | 13049.0i | −0.336733 | + | 0.583239i | ||||
\(795\) | 17270.2 | + | 29912.9i | 0.770455 | + | 1.33447i | ||||
\(796\) | 2537.66 | + | 4395.35i | 0.112996 | + | 0.195715i | ||||
\(797\) | 9269.22 | − | 16054.8i | 0.411960 | − | 0.713536i | −0.583144 | − | 0.812369i | \(-0.698178\pi\) |
0.995104 | + | 0.0988326i | \(0.0315108\pi\) | |||||||
\(798\) | 1820.95 | − | 3153.98i | 0.0807781 | − | 0.139912i | ||||
\(799\) | 33.7395 | − | 58.4386i | 0.00149389 | − | 0.00258750i | ||||
\(800\) | −2124.71 | −0.0938999 | ||||||||
\(801\) | 36116.0 | + | 62554.7i | 1.59313 | + | 2.75938i | ||||
\(802\) | 7767.41 | − | 13453.6i | 0.341991 | − | 0.592346i | ||||
\(803\) | −18382.1 | −0.807833 | ||||||||
\(804\) | −29628.5 | −1.29965 | ||||||||
\(805\) | −3070.96 | + | 5319.06i | −0.134456 | + | 0.232885i | ||||
\(806\) | 9995.26 | 0.436809 | ||||||||
\(807\) | 37139.9 | + | 64328.3i | 1.62006 | + | 2.80602i | ||||
\(808\) | −15221.6 | −0.662742 | ||||||||
\(809\) | −17392.0 | − | 30123.8i | −0.755835 | − | 1.30914i | −0.944958 | − | 0.327191i | \(-0.893898\pi\) |
0.189124 | − | 0.981953i | \(-0.439435\pi\) | |||||||
\(810\) | 22809.9 | + | 39507.9i | 0.989455 | + | 1.71379i | ||||
\(811\) | 3880.99 | + | 6722.07i | 0.168039 | + | 0.291053i | 0.937730 | − | 0.347364i | \(-0.112923\pi\) |
−0.769691 | + | 0.638416i | \(0.779590\pi\) | |||||||
\(812\) | 1137.81 | − | 1970.75i | 0.0491742 | − | 0.0851722i | ||||
\(813\) | 55618.6 | 2.39930 | ||||||||
\(814\) | −28018.9 | + | 9923.23i | −1.20646 | + | 0.427284i | ||||
\(815\) | 27762.6 | 1.19323 | ||||||||
\(816\) | −103.801 | + | 179.789i | −0.00445314 | + | 0.00771307i | ||||
\(817\) | −4999.55 | − | 8659.48i | −0.214091 | − | 0.370816i | ||||
\(818\) | −13110.8 | − | 22708.6i | −0.560402 | − | 0.970644i | ||||
\(819\) | 12134.0 | + | 21016.7i | 0.517700 | + | 0.896682i | ||||
\(820\) | −1950.03 | −0.0830463 | ||||||||
\(821\) | 4049.75 | + | 7014.37i | 0.172152 | + | 0.298177i | 0.939172 | − | 0.343447i | \(-0.111594\pi\) |
−0.767020 | + | 0.641624i | \(0.778261\pi\) | |||||||
\(822\) | 50495.8 | 2.14263 | ||||||||
\(823\) | −11072.3 | + | 19177.8i | −0.468964 | + | 0.812269i | −0.999371 | − | 0.0354741i | \(-0.988706\pi\) |
0.530407 | + | 0.847743i | \(0.322039\pi\) | |||||||
\(824\) | 8517.02 | 0.360078 | ||||||||
\(825\) | 44472.0 | 1.87675 | ||||||||
\(826\) | −104.423 | + | 180.866i | −0.00439873 | + | 0.00761883i | ||||
\(827\) | −17546.5 | − | 30391.4i | −0.737788 | − | 1.27789i | −0.953489 | − | 0.301428i | \(-0.902537\pi\) |
0.215701 | − | 0.976460i | \(-0.430796\pi\) | |||||||
\(828\) | −43694.3 | −1.83391 | ||||||||
\(829\) | −18819.2 | + | 32595.9i | −0.788443 | + | 1.36562i | 0.138478 | + | 0.990366i | \(0.455779\pi\) |
−0.926921 | + | 0.375257i | \(0.877554\pi\) | |||||||
\(830\) | 4590.32 | − | 7950.67i | 0.191967 | − | 0.332496i | ||||
\(831\) | 8136.74 | − | 14093.2i | 0.339663 | − | 0.588314i | ||||
\(832\) | 1836.47 | + | 3180.85i | 0.0765240 | + | 0.132543i | ||||
\(833\) | 199.524 | + | 345.586i | 0.00829905 | + | 0.0143744i | ||||
\(834\) | −12778.5 | + | 22133.0i | −0.530556 | + | 0.918950i | ||||
\(835\) | 5753.96 | − | 9966.16i | 0.238472 | − | 0.413046i | ||||
\(836\) | −4254.57 | + | 7369.13i | −0.176014 | + | 0.304864i | ||||
\(837\) | −43171.3 | −1.78282 | ||||||||
\(838\) | 825.667 | + | 1430.10i | 0.0340360 | + | 0.0589522i | ||||
\(839\) | −11589.2 | + | 20073.0i | −0.476880 | + | 0.825981i | −0.999649 | − | 0.0264939i | \(-0.991566\pi\) |
0.522769 | + | 0.852474i | \(0.324899\pi\) | |||||||
\(840\) | −3461.78 | −0.142194 | ||||||||
\(841\) | −13968.2 | −0.572726 | ||||||||
\(842\) | 15471.7 | − | 26797.7i | 0.633242 | − | 1.09681i | ||||
\(843\) | −81155.8 | −3.31572 | ||||||||
\(844\) | 749.383 | + | 1297.97i | 0.0305626 | + | 0.0529359i | ||||
\(845\) | −8394.43 | −0.341748 | ||||||||
\(846\) | 4002.46 | + | 6932.46i | 0.162656 | + | 0.281729i | ||||
\(847\) | −8442.24 | − | 14622.4i | −0.342478 | − | 0.593189i | ||||
\(848\) | −3558.77 | − | 6163.97i | −0.144114 | − | 0.249613i | ||||
\(849\) | −5497.95 | + | 9522.73i | −0.222249 | + | 0.384946i | ||||
\(850\) | −169.876 | −0.00685495 | ||||||||
\(851\) | 24638.6 | + | 21041.7i | 0.992482 | + | 0.847592i | ||||
\(852\) | −9160.59 | −0.368353 | ||||||||
\(853\) | −7673.62 | + | 13291.1i | −0.308019 | + | 0.533504i | −0.977929 | − | 0.208938i | \(-0.932999\pi\) |
0.669910 | + | 0.742442i | \(0.266333\pi\) | |||||||
\(854\) | −4203.49 | − | 7280.67i | −0.168432 | − | 0.291732i | ||||
\(855\) | −9355.94 | − | 16205.0i | −0.374230 | − | 0.648185i | ||||
\(856\) | 3301.71 | + | 5718.73i | 0.131834 | + | 0.228343i | ||||
\(857\) | −18784.0 | −0.748716 | −0.374358 | − | 0.927284i | \(-0.622137\pi\) | ||||
−0.374358 | + | 0.927284i | \(0.622137\pi\) | |||||||
\(858\) | −38438.7 | − | 66577.9i | −1.52946 | − | 2.64910i | ||||
\(859\) | 18605.9 | 0.739027 | 0.369514 | − | 0.929225i | \(-0.379524\pi\) | ||||
0.369514 | + | 0.929225i | \(0.379524\pi\) | |||||||
\(860\) | −4752.28 | + | 8231.19i | −0.188432 | + | 0.326373i | ||||
\(861\) | 3599.75 | 0.142484 | ||||||||
\(862\) | 13248.1 | 0.523470 | ||||||||
\(863\) | 1000.60 | − | 1733.09i | 0.0394679 | − | 0.0683604i | −0.845617 | − | 0.533791i | \(-0.820767\pi\) |
0.885085 | + | 0.465430i | \(0.154100\pi\) | |||||||
\(864\) | −7932.02 | − | 13738.7i | −0.312330 | − | 0.540971i | ||||
\(865\) | 16253.6 | 0.638890 | ||||||||
\(866\) | 10701.0 | − | 18534.7i | 0.419903 | − | 0.727293i | ||||
\(867\) | 24907.6 | − | 43141.2i | 0.975669 | − | 1.68991i | ||||
\(868\) | 970.627 | − | 1681.17i | 0.0379553 | − | 0.0657405i | ||||
\(869\) | −9721.96 | − | 16838.9i | −0.379511 | − | 0.657332i | ||||
\(870\) | −7926.26 | − | 13728.7i | −0.308880 | − | 0.534996i | ||||
\(871\) | −20955.3 | + | 36295.6i | −0.815204 | + | 1.41198i | ||||
\(872\) | 1713.50 | − | 2967.87i | 0.0665442 | − | 0.115258i | ||||
\(873\) | 18004.8 | − | 31185.2i | 0.698018 | − | 1.20900i | ||||
\(874\) | 9275.40 | 0.358976 | ||||||||
\(875\) | −4082.77 | − | 7071.57i | −0.157741 | − | 0.273215i | ||||
\(876\) | −5646.86 | + | 9780.65i | −0.217797 | + | 0.377235i | ||||
\(877\) | −46025.9 | −1.77216 | −0.886081 | − | 0.463531i | \(-0.846582\pi\) | ||||
−0.886081 | + | 0.463531i | \(0.846582\pi\) | |||||||
\(878\) | 18328.5 | 0.704508 | ||||||||
\(879\) | 17232.8 | − | 29848.0i | 0.661259 | − | 1.14533i | ||||
\(880\) | 8088.28 | 0.309836 | ||||||||
\(881\) | −18008.9 | − | 31192.4i | −0.688691 | − | 1.19285i | −0.972262 | − | 0.233896i | \(-0.924853\pi\) |
0.283571 | − | 0.958951i | \(-0.408481\pi\) | |||||||
\(882\) | −47338.4 | −1.80722 | ||||||||
\(883\) | 16128.4 | + | 27935.2i | 0.614682 | + | 1.06466i | 0.990440 | + | 0.137943i | \(0.0440490\pi\) |
−0.375758 | + | 0.926718i | \(0.622618\pi\) | |||||||
\(884\) | 146.830 | + | 254.317i | 0.00558647 | + | 0.00967604i | ||||
\(885\) | 727.436 | + | 1259.96i | 0.0276299 | + | 0.0478565i | ||||
\(886\) | 9742.85 | − | 16875.1i | 0.369433 | − | 0.639876i | ||||
\(887\) | −15291.0 | −0.578830 | −0.289415 | − | 0.957204i | \(-0.593461\pi\) | ||||
−0.289415 | + | 0.957204i | \(0.593461\pi\) | |||||||
\(888\) | −3327.31 | + | 17956.5i | −0.125740 | + | 0.678581i | ||||
\(889\) | −587.203 | −0.0221532 | ||||||||
\(890\) | −7287.49 | + | 12622.3i | −0.274469 | + | 0.475394i | ||||
\(891\) | 98381.1 | + | 170401.i | 3.69909 | + | 6.40701i | ||||
\(892\) | −8883.05 | − | 15385.9i | −0.333438 | − | 0.577531i | ||||
\(893\) | −849.640 | − | 1471.62i | −0.0318389 | − | 0.0551465i | ||||
\(894\) | −11802.8 | −0.441548 | ||||||||
\(895\) | −8030.92 | − | 13910.0i | −0.299937 | − | 0.519507i | ||||
\(896\) | 713.347 | 0.0265974 | ||||||||
\(897\) | −41900.2 | + | 72573.3i | −1.55965 | + | 2.70140i | ||||
\(898\) | 9492.40 | 0.352746 | ||||||||
\(899\) | 8889.59 | 0.329794 | ||||||||
\(900\) | 10076.1 | − | 17452.2i | 0.373187 | − | 0.646379i | ||||
\(901\) | −284.533 | − | 492.826i | −0.0105207 | − | 0.0182224i | ||||
\(902\) | −8410.65 | −0.310470 | ||||||||
\(903\) | 8772.69 | − | 15194.7i | 0.323297 | − | 0.559966i | ||||
\(904\) | −3995.39 | + | 6920.23i | −0.146997 | + | 0.254605i | ||||
\(905\) | −3041.83 | + | 5268.61i | −0.111728 | + | 0.193519i | ||||
\(906\) | −19409.4 | − | 33618.1i | −0.711738 | − | 1.23277i | ||||
\(907\) | 5405.95 | + | 9363.38i | 0.197907 | + | 0.342785i | 0.947850 | − | 0.318718i | \(-0.103252\pi\) |
−0.749943 | + | 0.661503i | \(0.769919\pi\) | |||||||
\(908\) | −1216.42 | + | 2106.90i | −0.0444585 | + | 0.0770044i | ||||
\(909\) | 72185.8 | − | 125029.i | 2.63394 | − | 4.56212i | ||||
\(910\) | −2448.40 | + | 4240.75i | −0.0891909 | + | 0.154483i | ||||
\(911\) | 3217.52 | 0.117015 | 0.0585077 | − | 0.998287i | \(-0.481366\pi\) | ||||
0.0585077 | + | 0.998287i | \(0.481366\pi\) | |||||||
\(912\) | 2613.95 | + | 4527.50i | 0.0949085 | + | 0.164386i | ||||
\(913\) | 19798.5 | − | 34291.9i | 0.717671 | − | 1.24304i | ||||
\(914\) | 12413.3 | 0.449230 | ||||||||
\(915\) | −58565.0 | −2.11595 | ||||||||
\(916\) | −1135.15 | + | 1966.14i | −0.0409459 | + | 0.0709204i | ||||
\(917\) | 2295.01 | 0.0826476 | ||||||||
\(918\) | −634.186 | − | 1098.44i | −0.0228009 | − | 0.0394924i | ||||
\(919\) | −8273.90 | −0.296987 | −0.148493 | − | 0.988913i | \(-0.547442\pi\) | ||||
−0.148493 | + | 0.988913i | \(0.547442\pi\) | |||||||
\(920\) | −4408.32 | − | 7635.44i | −0.157976 | − | 0.273623i | ||||
\(921\) | 23259.4 | + | 40286.5i | 0.832164 | + | 1.44135i | ||||
\(922\) | −2995.59 | − | 5188.52i | −0.107001 | − | 0.185331i | ||||
\(923\) | −6478.98 | + | 11221.9i | −0.231049 | + | 0.400189i | ||||
\(924\) | −14930.9 | −0.531593 | ||||||||
\(925\) | −14086.2 | + | 4988.80i | −0.500704 | + | 0.177330i | ||||
\(926\) | 8998.70 | 0.319347 | ||||||||
\(927\) | −40390.4 | + | 69958.2i | −1.43106 | + | 2.47867i | ||||
\(928\) | 1633.32 | + | 2828.99i | 0.0577761 | + | 0.100071i | ||||
\(929\) | 17450.4 | + | 30225.0i | 0.616285 | + | 1.06744i | 0.990158 | + | 0.139957i | \(0.0446965\pi\) |
−0.373872 | + | 0.927480i | \(0.621970\pi\) | |||||||
\(930\) | −6761.60 | − | 11711.4i | −0.238410 | − | 0.412939i | ||||
\(931\) | 10049.0 | 0.353750 | ||||||||
\(932\) | −1247.18 | − | 2160.17i | −0.0438333 | − | 0.0759215i | ||||
\(933\) | −1620.62 | −0.0568667 | ||||||||
\(934\) | −347.289 | + | 601.522i | −0.0121666 | + | 0.0210732i | ||||
\(935\) | 646.679 | 0.0226189 | ||||||||
\(936\) | −34836.4 | −1.21652 | ||||||||
\(937\) | 2819.43 | − | 4883.39i | 0.0982995 | − | 0.170260i | −0.812681 | − | 0.582708i | \(-0.801993\pi\) |
0.910981 | + | 0.412449i | \(0.135326\pi\) | |||||||
\(938\) | 4069.88 | + | 7049.24i | 0.141670 | + | 0.245379i | ||||
\(939\) | 47477.1 | 1.65001 | ||||||||
\(940\) | −807.617 | + | 1398.83i | −0.0280229 | + | 0.0485372i | ||||
\(941\) | −6372.23 | + | 11037.0i | −0.220753 | + | 0.382356i | −0.955037 | − | 0.296487i | \(-0.904185\pi\) |
0.734284 | + | 0.678843i | \(0.237518\pi\) | |||||||
\(942\) | −21799.0 | + | 37756.9i | −0.753979 | + | 1.30593i | ||||
\(943\) | 4584.02 | + | 7939.75i | 0.158299 | + | 0.274182i | ||||
\(944\) | −149.898 | − | 259.632i | −0.00516819 | − | 0.00895157i | ||||
\(945\) | 10575.1 | − | 18316.6i | 0.364029 | − | 0.630517i | ||||
\(946\) | −20497.0 | + | 35501.8i | −0.704455 | + | 1.22015i | ||||
\(947\) | −16530.6 | + | 28631.8i | −0.567234 | + | 0.982479i | 0.429604 | + | 0.903018i | \(0.358653\pi\) |
−0.996838 | + | 0.0794610i | \(0.974680\pi\) | |||||||
\(948\) | −11946.1 | −0.409273 | ||||||||
\(949\) | 7987.68 | + | 13835.1i | 0.273226 | + | 0.473241i | ||||
\(950\) | −2138.94 | + | 3704.75i | −0.0730488 | + | 0.126524i | ||||
\(951\) | −2435.57 | −0.0830483 | ||||||||
\(952\) | 57.0339 | 0.00194168 | ||||||||
\(953\) | 8109.66 | − | 14046.4i | 0.275654 | − | 0.477446i | −0.694646 | − | 0.719351i | \(-0.744439\pi\) |
0.970300 | + | 0.241906i | \(0.0777724\pi\) | |||||||
\(954\) | 67507.2 | 2.29101 | ||||||||
\(955\) | 9882.46 | + | 17116.9i | 0.334857 | + | 0.579990i | ||||
\(956\) | 20381.8 | 0.689535 | ||||||||
\(957\) | −34186.7 | − | 59213.0i | −1.15475 | − | 2.00009i | ||||
\(958\) | 12894.3 | + | 22333.6i | 0.434861 | + | 0.753202i | ||||
\(959\) | −6936.28 | − | 12014.0i | −0.233560 | − | 0.404538i | ||||
\(960\) | 2484.67 | − | 4303.57i | 0.0835336 | − | 0.144684i | ||||
\(961\) | −22207.6 | −0.745447 | ||||||||
\(962\) | 19643.8 | + | 16776.1i | 0.658359 | + | 0.562247i | ||||
\(963\) | −62630.9 | −2.09580 | ||||||||
\(964\) | 8964.01 | − | 15526.1i | 0.299493 | − | 0.518737i | ||||
\(965\) | −14329.3 | − | 24819.0i | −0.478006 | − | 0.827930i | ||||
\(966\) | 8137.75 | + | 14095.0i | 0.271043 | + | 0.469461i | ||||
\(967\) | 16987.9 | + | 29423.9i | 0.564936 | + | 0.978498i | 0.997056 | + | 0.0766814i | \(0.0244324\pi\) |
−0.432120 | + | 0.901816i | \(0.642234\pi\) | |||||||
\(968\) | 24237.5 | 0.804774 | ||||||||
\(969\) | 208.992 | + | 361.985i | 0.00692859 | + | 0.0120007i | ||||
\(970\) | 7266.02 | 0.240513 | ||||||||
\(971\) | 2319.35 | − | 4017.23i | 0.0766544 | − | 0.132769i | −0.825150 | − | 0.564914i | \(-0.808910\pi\) |
0.901805 | + | 0.432144i | \(0.142243\pi\) | |||||||
\(972\) | 67347.0 | 2.22238 | ||||||||
\(973\) | 7021.21 | 0.231336 | ||||||||
\(974\) | 3481.17 | − | 6029.57i | 0.114522 | − | 0.198357i | ||||
\(975\) | −19324.7 | − | 33471.3i | −0.634754 | − | 1.09943i | ||||
\(976\) | 12068.1 | 0.395790 | ||||||||
\(977\) | 568.759 | − | 985.119i | 0.0186246 | − | 0.0322587i | −0.856563 | − | 0.516043i | \(-0.827405\pi\) |
0.875187 | + | 0.483784i | \(0.160738\pi\) | |||||||
\(978\) | 36784.1 | − | 63711.9i | 1.20268 | − | 2.08311i | ||||
\(979\) | −31431.6 | + | 54441.1i | −1.02611 | + | 1.77727i | ||||
\(980\) | −4775.97 | − | 8272.23i | −0.155676 | − | 0.269640i | ||||
\(981\) | 16251.9 | + | 28149.2i | 0.528934 | + | 0.916141i | ||||
\(982\) | −7626.23 | + | 13209.0i | −0.247824 | + | 0.429243i | ||||
\(983\) | 5064.21 | − | 8771.47i | 0.164317 | − | 0.284605i | −0.772096 | − | 0.635506i | \(-0.780791\pi\) |
0.936412 | + | 0.350901i | \(0.114125\pi\) | |||||||
\(984\) | −2583.70 | + | 4475.09i | −0.0837045 | + | 0.144980i | ||||
\(985\) | −17460.8 | −0.564820 | ||||||||
\(986\) | 130.588 | + | 226.185i | 0.00421782 | + | 0.00730547i | ||||
\(987\) | 1490.86 | − | 2582.24i | 0.0480796 | − | 0.0832763i | ||||
\(988\) | 7395.05 | 0.238125 | ||||||||
\(989\) | 44685.5 | 1.43672 | ||||||||
\(990\) | −38357.2 | + | 66436.6i | −1.23138 | + | 2.13282i | ||||
\(991\) | 17617.6 | 0.564725 | 0.282362 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282362 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(992\) | 1393.32 | + | 2413.30i | 0.0445948 | + | 0.0772404i | ||||
\(993\) | −11264.3 | −0.359982 | ||||||||
\(994\) | 1258.33 | + | 2179.49i | 0.0401527 | + | 0.0695466i | ||||
\(995\) | −4856.60 | − | 8411.88i | −0.154738 | − | 0.268014i | ||||
\(996\) | −12163.9 | − | 21068.5i | −0.386976 | − | 0.670263i | ||||
\(997\) | −10223.8 | + | 17708.2i | −0.324767 | + | 0.562512i | −0.981465 | − | 0.191641i | \(-0.938619\pi\) |
0.656699 | + | 0.754153i | \(0.271952\pi\) | |||||||
\(998\) | 3813.69 | 0.120962 | ||||||||
\(999\) | −84845.1 | − | 72458.8i | −2.68707 | − | 2.29479i |
(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 | 74.4.c.b.47.1 | ✓ | 10 | |
3.2 | odd | 2 | 666.4.f.d.343.1 | 10 | |||
37.26 | even | 3 | inner | 74.4.c.b.63.1 | yes | 10 | |
111.26 | odd | 6 | 666.4.f.d.433.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.c.b.47.1 | ✓ | 10 | 1.1 | even | 1 | trivial | |
74.4.c.b.63.1 | yes | 10 | 37.26 | even | 3 | inner | |
666.4.f.d.343.1 | 10 | 3.2 | odd | 2 | |||
666.4.f.d.433.1 | 10 | 111.26 | odd | 6 |