Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\), 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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 36x^{14} + 562x^{12} - 3672x^{10} + 16413x^{8} - 6588x^{6} + 43024x^{4} + 499896x^{2} + 532900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{8}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 32.7 | ||
Root | \(-3.99991 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.32 |
Dual form | 75.4.e.d.68.7 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.39887 | − | 3.39887i | 1.20168 | − | 1.20168i | 0.228029 | − | 0.973654i | \(-0.426772\pi\) |
0.973654 | − | 0.228029i | \(-0.0732281\pi\) | |||||||
\(3\) | −5.15843 | − | 0.624963i | −0.992741 | − | 0.120274i | ||||
\(4\) | − | 15.1047i | − | 1.88809i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −19.6570 | + | 15.4087i | −1.33749 | + | 1.04843i | ||||
\(7\) | −19.7241 | − | 19.7241i | −1.06500 | − | 1.06500i | −0.997735 | − | 0.0672681i | \(-0.978572\pi\) |
−0.0672681 | − | 0.997735i | \(-0.521428\pi\) | |||||||
\(8\) | −24.1479 | − | 24.1479i | −1.06720 | − | 1.06720i | ||||
\(9\) | 26.2188 | + | 6.44766i | 0.971068 | + | 0.238802i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.19707i | 0.252093i | 0.992024 | + | 0.126046i | \(0.0402288\pi\) | ||||
−0.992024 | + | 0.126046i | \(0.959771\pi\) | |||||||
\(12\) | −9.43987 | + | 77.9165i | −0.227088 | + | 1.87438i | ||||
\(13\) | 22.4300 | − | 22.4300i | 0.478537 | − | 0.478537i | −0.426127 | − | 0.904663i | \(-0.640122\pi\) |
0.904663 | + | 0.426127i | \(0.140122\pi\) | |||||||
\(14\) | −134.080 | −2.55959 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −43.3141 | −0.676782 | ||||||||
\(17\) | 50.6273 | − | 50.6273i | 0.722290 | − | 0.722290i | −0.246782 | − | 0.969071i | \(-0.579373\pi\) |
0.969071 | + | 0.246782i | \(0.0793730\pi\) | |||||||
\(18\) | 111.029 | − | 67.1998i | 1.45388 | − | 0.879952i | ||||
\(19\) | − | 16.5813i | − | 0.200211i | −0.994977 | − | 0.100105i | \(-0.968082\pi\) | ||
0.994977 | − | 0.100105i | \(-0.0319180\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 89.4187 | + | 114.072i | 0.929180 | + | 1.18536i | ||||
\(22\) | 31.2597 | + | 31.2597i | 0.302936 | + | 0.302936i | ||||
\(23\) | 48.2959 | + | 48.2959i | 0.437843 | + | 0.437843i | 0.891285 | − | 0.453443i | \(-0.149804\pi\) |
−0.453443 | + | 0.891285i | \(0.649804\pi\) | |||||||
\(24\) | 109.474 | + | 139.657i | 0.931094 | + | 1.18781i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 152.474i | − | 1.15010i | ||||||
\(27\) | −131.219 | − | 49.6456i | −0.935297 | − | 0.353863i | ||||
\(28\) | −297.927 | + | 297.927i | −2.01082 | + | 2.01082i | ||||
\(29\) | 203.298 | 1.30178 | 0.650889 | − | 0.759173i | \(-0.274396\pi\) | ||||
0.650889 | + | 0.759173i | \(0.274396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −27.4766 | −0.159192 | −0.0795958 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795958 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(32\) | 45.9644 | − | 45.9644i | 0.253920 | − | 0.253920i | ||||
\(33\) | 5.74783 | − | 47.4425i | 0.0303203 | − | 0.250263i | ||||
\(34\) | − | 344.152i | − | 1.73593i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 97.3898 | − | 396.027i | 0.450879 | − | 1.83346i | ||||
\(37\) | −130.592 | − | 130.592i | −0.580250 | − | 0.580250i | 0.354722 | − | 0.934972i | \(-0.384575\pi\) |
−0.934972 | + | 0.354722i | \(0.884575\pi\) | |||||||
\(38\) | −56.3576 | − | 56.3576i | −0.240590 | − | 0.240590i | ||||
\(39\) | −129.722 | + | 101.686i | −0.532618 | + | 0.417507i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.19707i | − | 0.0350327i | −0.999847 | − | 0.0175164i | \(-0.994424\pi\) | ||
0.999847 | − | 0.0175164i | \(-0.00557592\pi\) | |||||||
\(42\) | 691.641 | + | 83.7948i | 2.54101 | + | 0.307853i | ||||
\(43\) | −63.3021 | + | 63.3021i | −0.224499 | + | 0.224499i | −0.810390 | − | 0.585891i | \(-0.800745\pi\) |
0.585891 | + | 0.810390i | \(0.300745\pi\) | |||||||
\(44\) | 138.919 | 0.475973 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 328.303 | 1.05230 | ||||||||
\(47\) | −383.520 | + | 383.520i | −1.19026 | + | 1.19026i | −0.213265 | + | 0.976994i | \(0.568410\pi\) |
−0.976994 | + | 0.213265i | \(0.931590\pi\) | |||||||
\(48\) | 223.433 | + | 27.0697i | 0.671869 | + | 0.0813994i | ||||
\(49\) | 435.083i | 1.26846i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −292.798 | + | 229.517i | −0.803919 | + | 0.630173i | ||||
\(52\) | −338.799 | − | 338.799i | −0.903518 | − | 0.903518i | ||||
\(53\) | 441.142 | + | 441.142i | 1.14331 | + | 1.14331i | 0.987840 | + | 0.155471i | \(0.0496895\pi\) |
0.155471 | + | 0.987840i | \(0.450310\pi\) | |||||||
\(54\) | −614.735 | + | 277.256i | −1.54916 | + | 0.698700i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 952.594i | 2.27314i | ||||||||
\(57\) | −10.3627 | + | 85.5333i | −0.0240802 | + | 0.198757i | ||||
\(58\) | 690.986 | − | 690.986i | 1.56433 | − | 1.56433i | ||||
\(59\) | 314.626 | 0.694251 | 0.347126 | − | 0.937819i | \(-0.387158\pi\) | ||||
0.347126 | + | 0.937819i | \(0.387158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −431.664 | −0.906048 | −0.453024 | − | 0.891498i | \(-0.649655\pi\) | ||||
−0.453024 | + | 0.891498i | \(0.649655\pi\) | |||||||
\(62\) | −93.3894 | + | 93.3894i | −0.191298 | + | 0.191298i | ||||
\(63\) | −389.969 | − | 644.318i | −0.779866 | − | 1.28852i | ||||
\(64\) | − | 658.967i | − | 1.28705i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −141.715 | − | 180.787i | −0.264301 | − | 0.337172i | ||||
\(67\) | 649.685 | + | 649.685i | 1.18465 | + | 1.18465i | 0.978525 | + | 0.206126i | \(0.0660858\pi\) |
0.206126 | + | 0.978525i | \(0.433914\pi\) | |||||||
\(68\) | −764.709 | − | 764.709i | −1.36374 | − | 1.36374i | ||||
\(69\) | −218.948 | − | 279.314i | −0.382003 | − | 0.487326i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 722.186i | − | 1.20715i | −0.797306 | − | 0.603575i | \(-0.793742\pi\) | ||
0.797306 | − | 0.603575i | \(-0.206258\pi\) | |||||||
\(72\) | −477.433 | − | 788.828i | −0.781473 | − | 1.29117i | ||||
\(73\) | −662.432 | + | 662.432i | −1.06208 | + | 1.06208i | −0.0641383 | + | 0.997941i | \(0.520430\pi\) |
−0.997941 | + | 0.0641383i | \(0.979570\pi\) | |||||||
\(74\) | −887.733 | −1.39455 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −250.455 | −0.378015 | ||||||||
\(77\) | 181.404 | − | 181.404i | 0.268480 | − | 0.268480i | ||||
\(78\) | −95.2905 | + | 786.526i | −0.138327 | + | 1.14175i | ||||
\(79\) | − | 206.816i | − | 0.294539i | −0.989096 | − | 0.147269i | \(-0.952952\pi\) | ||
0.989096 | − | 0.147269i | \(-0.0470484\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 645.855 | + | 338.100i | 0.885947 | + | 0.463786i | ||||
\(82\) | −31.2597 | − | 31.2597i | −0.0420982 | − | 0.0420982i | ||||
\(83\) | −544.335 | − | 544.335i | −0.719862 | − | 0.719862i | 0.248715 | − | 0.968577i | \(-0.419992\pi\) |
−0.968577 | + | 0.248715i | \(0.919992\pi\) | |||||||
\(84\) | 1723.03 | − | 1350.64i | 2.23807 | − | 1.75437i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 430.312i | 0.539555i | ||||||||
\(87\) | −1048.70 | − | 127.054i | −1.29233 | − | 0.156570i | ||||
\(88\) | 222.090 | − | 222.090i | 0.269033 | − | 0.269033i | ||||
\(89\) | 563.910 | 0.671622 | 0.335811 | − | 0.941929i | \(-0.390990\pi\) | ||||
0.335811 | + | 0.941929i | \(0.390990\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −884.827 | −1.01929 | ||||||||
\(92\) | 729.494 | − | 729.494i | 0.826685 | − | 0.826685i | ||||
\(93\) | 141.736 | + | 17.1718i | 0.158036 | + | 0.0191466i | ||||
\(94\) | 2607.07i | 2.86063i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −265.830 | + | 208.378i | −0.282617 | + | 0.221537i | ||||
\(97\) | 66.0080 | + | 66.0080i | 0.0690938 | + | 0.0690938i | 0.740809 | − | 0.671715i | \(-0.234442\pi\) |
−0.671715 | + | 0.740809i | \(0.734442\pi\) | |||||||
\(98\) | 1478.79 | + | 1478.79i | 1.52429 | + | 1.52429i | ||||
\(99\) | −59.2996 | + | 241.137i | −0.0602003 | + | 0.244799i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1108.46i | − | 1.09204i | −0.837772 | − | 0.546021i | \(-0.816142\pi\) | ||
0.837772 | − | 0.546021i | \(-0.183858\pi\) | |||||||
\(102\) | −215.082 | + | 1775.28i | −0.208787 | + | 1.72332i | ||||
\(103\) | 823.002 | − | 823.002i | 0.787308 | − | 0.787308i | −0.193744 | − | 0.981052i | \(-0.562063\pi\) |
0.981052 | + | 0.193744i | \(0.0620630\pi\) | |||||||
\(104\) | −1083.28 | −1.02139 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2998.77 | 2.74780 | ||||||||
\(107\) | 918.923 | − | 918.923i | 0.830239 | − | 0.830239i | −0.157310 | − | 0.987549i | \(-0.550282\pi\) |
0.987549 | + | 0.157310i | \(0.0502822\pi\) | |||||||
\(108\) | −749.881 | + | 1982.02i | −0.668124 | + | 1.76592i | ||||
\(109\) | 4.75472i | 0.00417816i | 0.999998 | + | 0.00208908i | \(0.000664976\pi\) | ||||
−0.999998 | + | 0.00208908i | \(0.999335\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 592.036 | + | 755.267i | 0.506248 | + | 0.645826i | ||||
\(112\) | 854.332 | + | 854.332i | 0.720775 | + | 0.720775i | ||||
\(113\) | 791.114 | + | 791.114i | 0.658600 | + | 0.658600i | 0.955049 | − | 0.296449i | \(-0.0958025\pi\) |
−0.296449 | + | 0.955049i | \(0.595802\pi\) | |||||||
\(114\) | 255.495 | + | 325.938i | 0.209906 | + | 0.267780i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 3070.76i | − | 2.45787i | ||||||
\(117\) | 732.711 | − | 443.469i | 0.578967 | − | 0.350416i | ||||
\(118\) | 1069.37 | − | 1069.37i | 0.834270 | − | 0.834270i | ||||
\(119\) | −1997.16 | −1.53848 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1246.41 | 0.936449 | ||||||||
\(122\) | −1467.17 | + | 1467.17i | −1.08878 | + | 1.08878i | ||||
\(123\) | −5.74783 | + | 47.4425i | −0.00421353 | + | 0.0347784i | ||||
\(124\) | 415.025i | 0.300567i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3515.41 | − | 864.500i | −2.48554 | − | 0.611236i | ||||
\(127\) | 9.96644 | + | 9.96644i | 0.00696361 | + | 0.00696361i | 0.710580 | − | 0.703616i | \(-0.248433\pi\) |
−0.703616 | + | 0.710580i | \(0.748433\pi\) | |||||||
\(128\) | −1872.03 | − | 1872.03i | −1.29270 | − | 1.29270i | ||||
\(129\) | 366.101 | − | 286.978i | 0.249871 | − | 0.195868i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2663.20i | 1.77622i | 0.459631 | + | 0.888110i | \(0.347982\pi\) | ||||
−0.459631 | + | 0.888110i | \(0.652018\pi\) | |||||||
\(132\) | −716.604 | − | 86.8192i | −0.472518 | − | 0.0572473i | ||||
\(133\) | −327.051 | + | 327.051i | −0.213225 | + | 0.213225i | ||||
\(134\) | 4416.39 | 2.84715 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2445.09 | −1.54165 | ||||||||
\(137\) | 351.396 | − | 351.396i | 0.219137 | − | 0.219137i | −0.588998 | − | 0.808135i | \(-0.700477\pi\) |
0.808135 | + | 0.588998i | \(0.200477\pi\) | |||||||
\(138\) | −1693.53 | − | 205.177i | −1.04466 | − | 0.126564i | ||||
\(139\) | − | 1738.04i | − | 1.06057i | −0.847820 | − | 0.530283i | \(-0.822086\pi\) | ||
0.847820 | − | 0.530283i | \(-0.177914\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2218.05 | − | 1738.68i | 1.32478 | − | 1.03846i | ||||
\(142\) | −2454.62 | − | 2454.62i | −1.45061 | − | 1.45061i | ||||
\(143\) | 206.291 | + | 206.291i | 0.120636 | + | 0.120636i | ||||
\(144\) | −1135.64 | − | 279.274i | −0.657202 | − | 0.161617i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4503.04i | 2.55257i | ||||||||
\(147\) | 271.911 | − | 2244.34i | 0.152563 | − | 1.25925i | ||||
\(148\) | −1972.55 | + | 1972.55i | −1.09556 | + | 1.09556i | ||||
\(149\) | −183.941 | −0.101135 | −0.0505674 | − | 0.998721i | \(-0.516103\pi\) | ||||
−0.0505674 | + | 0.998721i | \(0.516103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −805.273 | −0.433988 | −0.216994 | − | 0.976173i | \(-0.569625\pi\) | ||||
−0.216994 | + | 0.976173i | \(0.569625\pi\) | |||||||
\(152\) | −400.403 | + | 400.403i | −0.213664 | + | 0.213664i | ||||
\(153\) | 1653.82 | − | 1000.96i | 0.873877 | − | 0.528908i | ||||
\(154\) | − | 1233.14i | − | 0.645255i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1535.93 | + | 1959.41i | 0.788289 | + | 1.00563i | ||||
\(157\) | 1626.56 | + | 1626.56i | 0.826840 | + | 0.826840i | 0.987078 | − | 0.160239i | \(-0.0512264\pi\) |
−0.160239 | + | 0.987078i | \(0.551226\pi\) | |||||||
\(158\) | −702.940 | − | 702.940i | −0.353942 | − | 0.353942i | ||||
\(159\) | −1999.90 | − | 2551.30i | −0.997501 | − | 1.27252i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1905.19i | − | 0.932608i | ||||||
\(162\) | 3344.34 | − | 1046.02i | 1.62195 | − | 0.507304i | ||||
\(163\) | 395.910 | − | 395.910i | 0.190246 | − | 0.190246i | −0.605556 | − | 0.795802i | \(-0.707049\pi\) |
0.795802 | + | 0.605556i | \(0.207049\pi\) | |||||||
\(164\) | −138.919 | −0.0661448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3700.25 | −1.73009 | ||||||||
\(167\) | −875.168 | + | 875.168i | −0.405524 | + | 0.405524i | −0.880174 | − | 0.474650i | \(-0.842574\pi\) |
0.474650 | + | 0.880174i | \(0.342574\pi\) | |||||||
\(168\) | 595.336 | − | 4913.89i | 0.273400 | − | 2.25664i | ||||
\(169\) | 1190.79i | 0.542005i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 106.910 | − | 434.741i | 0.0478107 | − | 0.194418i | ||||
\(172\) | 956.158 | + | 956.158i | 0.423874 | + | 0.423874i | ||||
\(173\) | −1048.43 | − | 1048.43i | −0.460753 | − | 0.460753i | 0.438149 | − | 0.898902i | \(-0.355634\pi\) |
−0.898902 | + | 0.438149i | \(0.855634\pi\) | |||||||
\(174\) | −3996.24 | + | 3132.56i | −1.74112 | + | 1.36482i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 398.363i | − | 0.170612i | ||||||
\(177\) | −1622.98 | − | 196.630i | −0.689212 | − | 0.0835005i | ||||
\(178\) | 1916.66 | − | 1916.66i | 0.807077 | − | 0.807077i | ||||
\(179\) | −210.570 | −0.0879259 | −0.0439629 | − | 0.999033i | \(-0.513998\pi\) | ||||
−0.0439629 | + | 0.999033i | \(0.513998\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −128.633 | −0.0528244 | −0.0264122 | − | 0.999651i | \(-0.508408\pi\) | ||||
−0.0264122 | + | 0.999651i | \(0.508408\pi\) | |||||||
\(182\) | −3007.41 | + | 3007.41i | −1.22486 | + | 1.22486i | ||||
\(183\) | 2226.71 | + | 269.774i | 0.899471 | + | 0.108974i | ||||
\(184\) | − | 2332.49i | − | 0.934530i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 540.108 | − | 423.378i | 0.212917 | − | 0.166901i | ||||
\(187\) | 465.623 | + | 465.623i | 0.182084 | + | 0.182084i | ||||
\(188\) | 5792.96 | + | 5792.96i | 2.24731 | + | 2.24731i | ||||
\(189\) | 1608.96 | + | 3567.39i | 0.619229 | + | 1.37296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4291.51i | 1.62577i | 0.582421 | + | 0.812887i | \(0.302106\pi\) | ||||
−0.582421 | + | 0.812887i | \(0.697894\pi\) | |||||||
\(192\) | −411.830 | + | 3399.24i | −0.154798 | + | 1.27770i | ||||
\(193\) | −3567.00 | + | 3567.00i | −1.33035 | + | 1.33035i | −0.425303 | + | 0.905051i | \(0.639832\pi\) |
−0.905051 | + | 0.425303i | \(0.860168\pi\) | |||||||
\(194\) | 448.706 | 0.166058 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6571.79 | 2.39497 | ||||||||
\(197\) | −421.067 | + | 421.067i | −0.152283 | + | 0.152283i | −0.779137 | − | 0.626854i | \(-0.784342\pi\) |
0.626854 | + | 0.779137i | \(0.284342\pi\) | |||||||
\(198\) | 618.041 | + | 1021.14i | 0.221830 | + | 0.366513i | ||||
\(199\) | 3024.07i | 1.07724i | 0.842549 | + | 0.538619i | \(0.181054\pi\) | ||||
−0.842549 | + | 0.538619i | \(0.818946\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2945.33 | − | 3757.39i | −1.03357 | − | 1.31853i | ||||
\(202\) | −3767.53 | − | 3767.53i | −1.31229 | − | 1.31229i | ||||
\(203\) | −4009.88 | − | 4009.88i | −1.38640 | − | 1.38640i | ||||
\(204\) | 3466.79 | + | 4422.62i | 1.18982 | + | 1.51787i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 5594.56i | − | 1.89219i | ||||||
\(207\) | 954.867 | + | 1577.66i | 0.320617 | + | 0.529733i | ||||
\(208\) | −971.537 | + | 971.537i | −0.323865 | + | 0.323865i | ||||
\(209\) | 152.499 | 0.0504717 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2881.37 | −0.940104 | −0.470052 | − | 0.882639i | \(-0.655765\pi\) | ||||
−0.470052 | + | 0.882639i | \(0.655765\pi\) | |||||||
\(212\) | 6663.31 | − | 6663.31i | 2.15867 | − | 2.15867i | ||||
\(213\) | −451.339 | + | 3725.35i | −0.145189 | + | 1.19839i | ||||
\(214\) | − | 6246.60i | − | 1.99537i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1969.82 | + | 4367.50i | 0.620505 | + | 1.37579i | ||||
\(217\) | 541.951 | + | 541.951i | 0.169539 | + | 0.169539i | ||||
\(218\) | 16.1607 | + | 16.1607i | 0.00502083 | + | 0.00502083i | ||||
\(219\) | 3831.11 | − | 3003.11i | 1.18211 | − | 0.926629i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2271.15i | − | 0.691284i | ||||||
\(222\) | 4579.31 | + | 554.800i | 1.38443 | + | 0.167729i | ||||
\(223\) | 1334.90 | − | 1334.90i | 0.400858 | − | 0.400858i | −0.477677 | − | 0.878535i | \(-0.658521\pi\) |
0.878535 | + | 0.477677i | \(0.158521\pi\) | |||||||
\(224\) | −1813.22 | −0.540851 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5377.79 | 1.58286 | ||||||||
\(227\) | 337.339 | − | 337.339i | 0.0986342 | − | 0.0986342i | −0.656068 | − | 0.754702i | \(-0.727781\pi\) |
0.754702 | + | 0.656068i | \(0.227781\pi\) | |||||||
\(228\) | 1291.95 | + | 156.525i | 0.375271 | + | 0.0454654i | ||||
\(229\) | − | 4575.71i | − | 1.32040i | −0.751090 | − | 0.660200i | \(-0.770471\pi\) | ||
0.751090 | − | 0.660200i | \(-0.229529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1049.13 | + | 822.391i | −0.298822 | + | 0.234240i | ||||
\(232\) | −4909.24 | − | 4909.24i | −1.38926 | − | 1.38926i | ||||
\(233\) | 529.682 | + | 529.682i | 0.148930 | + | 0.148930i | 0.777640 | − | 0.628710i | \(-0.216417\pi\) |
−0.628710 | + | 0.777640i | \(0.716417\pi\) | |||||||
\(234\) | 983.099 | − | 3997.69i | 0.274646 | − | 1.11682i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 4752.33i | − | 1.31081i | ||||||
\(237\) | −129.252 | + | 1066.84i | −0.0354254 | + | 0.292401i | ||||
\(238\) | −6788.09 | + | 6788.09i | −1.84877 | + | 1.84877i | ||||
\(239\) | −871.265 | −0.235805 | −0.117903 | − | 0.993025i | \(-0.537617\pi\) | ||||
−0.117903 | + | 0.993025i | \(0.537617\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 42.9221 | 0.0114724 | 0.00573622 | − | 0.999984i | \(-0.498174\pi\) | ||||
0.00573622 | + | 0.999984i | \(0.498174\pi\) | |||||||
\(242\) | 4236.40 | − | 4236.40i | 1.12532 | − | 1.12532i | ||||
\(243\) | −3120.30 | − | 2147.70i | −0.823734 | − | 0.566976i | ||||
\(244\) | 6520.15i | 1.71070i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 141.715 | + | 180.787i | 0.0367293 | + | 0.0468560i | ||||
\(247\) | −371.918 | − | 371.918i | −0.0958081 | − | 0.0958081i | ||||
\(248\) | 663.502 | + | 663.502i | 0.169889 | + | 0.169889i | ||||
\(249\) | 2467.73 | + | 3148.10i | 0.628055 | + | 0.801217i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 50.7994i | − | 0.0127746i | −0.999980 | − | 0.00638731i | \(-0.997967\pi\) | ||
0.999980 | − | 0.00638731i | \(-0.00203316\pi\) | |||||||
\(252\) | −9732.23 | + | 5890.37i | −2.43283 | + | 1.47245i | ||||
\(253\) | −444.181 | + | 444.181i | −0.110377 | + | 0.110377i | ||||
\(254\) | 67.7493 | 0.0167361 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7453.85 | −1.81979 | ||||||||
\(257\) | −4271.29 | + | 4271.29i | −1.03671 | + | 1.03671i | −0.0374152 | + | 0.999300i | \(0.511912\pi\) |
−0.999300 | + | 0.0374152i | \(0.988088\pi\) | |||||||
\(258\) | 268.929 | − | 2219.73i | 0.0648945 | − | 0.535638i | ||||
\(259\) | 5151.64i | 1.23593i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5330.25 | + | 1310.80i | 1.26412 | + | 0.310867i | ||||
\(262\) | 9051.88 | + | 9051.88i | 2.13445 | + | 2.13445i | ||||
\(263\) | 1151.74 | + | 1151.74i | 0.270036 | + | 0.270036i | 0.829114 | − | 0.559079i | \(-0.188845\pi\) |
−0.559079 | + | 0.829114i | \(0.688845\pi\) | |||||||
\(264\) | −1284.44 | + | 1006.84i | −0.299438 | + | 0.234722i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2223.21i | 0.512458i | ||||||||
\(267\) | −2908.89 | − | 352.423i | −0.666746 | − | 0.0807787i | ||||
\(268\) | 9813.29 | − | 9813.29i | 2.23672 | − | 2.23672i | ||||
\(269\) | −1684.46 | −0.381796 | −0.190898 | − | 0.981610i | \(-0.561140\pi\) | ||||
−0.190898 | + | 0.981610i | \(0.561140\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3308.36 | −0.741581 | −0.370791 | − | 0.928717i | \(-0.620913\pi\) | ||||
−0.370791 | + | 0.928717i | \(0.620913\pi\) | |||||||
\(272\) | −2192.87 | + | 2192.87i | −0.488833 | + | 0.488833i | ||||
\(273\) | 4564.32 | + | 552.984i | 1.01189 | + | 0.122594i | ||||
\(274\) | − | 2388.70i | − | 0.526666i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4218.95 | + | 3307.14i | −0.920112 | + | 0.721255i | ||||
\(277\) | −2178.55 | − | 2178.55i | −0.472550 | − | 0.472550i | 0.430189 | − | 0.902739i | \(-0.358447\pi\) |
−0.902739 | + | 0.430189i | \(0.858447\pi\) | |||||||
\(278\) | −5907.39 | − | 5907.39i | −1.27447 | − | 1.27447i | ||||
\(279\) | −720.404 | − | 177.159i | −0.154586 | − | 0.0380153i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4972.10i | 1.05555i | 0.849383 | + | 0.527776i | \(0.176974\pi\) | ||||
−0.849383 | + | 0.527776i | \(0.823026\pi\) | |||||||
\(282\) | 1629.32 | − | 13448.4i | 0.344060 | − | 2.83986i | ||||
\(283\) | 3325.61 | − | 3325.61i | 0.698542 | − | 0.698542i | −0.265554 | − | 0.964096i | \(-0.585555\pi\) |
0.964096 | + | 0.265554i | \(0.0855550\pi\) | |||||||
\(284\) | −10908.4 | −2.27920 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1402.31 | 0.289932 | ||||||||
\(287\) | −181.404 | + | 181.404i | −0.0373100 | + | 0.0373100i | ||||
\(288\) | 1501.50 | − | 908.771i | 0.307210 | − | 0.185937i | ||||
\(289\) | − | 213.245i | − | 0.0434043i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −299.245 | − | 381.750i | −0.0602820 | − | 0.0769024i | ||||
\(292\) | 10005.8 | + | 10005.8i | 2.00530 | + | 2.00530i | ||||
\(293\) | 3473.24 | + | 3473.24i | 0.692521 | + | 0.692521i | 0.962786 | − | 0.270265i | \(-0.0871114\pi\) |
−0.270265 | + | 0.962786i | \(0.587111\pi\) | |||||||
\(294\) | −6704.06 | − | 8552.43i | −1.32989 | − | 1.69656i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6307.07i | 1.23848i | ||||||||
\(297\) | 456.594 | − | 1206.83i | 0.0892063 | − | 0.235782i | ||||
\(298\) | −625.194 | + | 625.194i | −0.121532 | + | 0.121532i | ||||
\(299\) | 2166.56 | 0.419048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2497.16 | 0.478185 | ||||||||
\(302\) | −2737.02 | + | 2737.02i | −0.521516 | + | 0.521516i | ||||
\(303\) | −692.748 | + | 5717.93i | −0.131344 | + | 1.08411i | ||||
\(304\) | 718.201i | 0.135499i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2218.97 | − | 9023.26i | 0.414543 | − | 1.68570i | ||||
\(307\) | −4105.90 | − | 4105.90i | −0.763310 | − | 0.763310i | 0.213609 | − | 0.976919i | \(-0.431478\pi\) |
−0.976919 | + | 0.213609i | \(0.931478\pi\) | |||||||
\(308\) | −2740.05 | − | 2740.05i | −0.506913 | − | 0.506913i | ||||
\(309\) | −4759.74 | + | 3731.05i | −0.876286 | + | 0.686900i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3937.21i | 0.717874i | 0.933362 | + | 0.358937i | \(0.116861\pi\) | ||||
−0.933362 | + | 0.358937i | \(0.883139\pi\) | |||||||
\(312\) | 5588.02 | + | 677.009i | 1.01397 | + | 0.122846i | ||||
\(313\) | 160.559 | − | 160.559i | 0.0289946 | − | 0.0289946i | −0.692461 | − | 0.721455i | \(-0.743473\pi\) |
0.721455 | + | 0.692461i | \(0.243473\pi\) | |||||||
\(314\) | 11057.0 | 1.98720 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3123.88 | −0.556115 | ||||||||
\(317\) | 6408.72 | − | 6408.72i | 1.13549 | − | 1.13549i | 0.146239 | − | 0.989249i | \(-0.453283\pi\) |
0.989249 | − | 0.146239i | \(-0.0467169\pi\) | |||||||
\(318\) | −15469.0 | − | 1874.12i | −2.72785 | − | 0.330489i | ||||
\(319\) | 1869.75i | 0.328169i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5314.49 | + | 4165.91i | −0.924069 | + | 0.724356i | ||||
\(322\) | −6475.49 | − | 6475.49i | −1.12070 | − | 1.12070i | ||||
\(323\) | −839.464 | − | 839.464i | −0.144610 | − | 0.144610i | ||||
\(324\) | 5106.90 | − | 9755.44i | 0.875668 | − | 1.67274i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 2691.30i | − | 0.457231i | ||||||
\(327\) | 2.97153 | − | 24.5269i | 0.000502525 | − | 0.00414783i | ||||
\(328\) | −222.090 | + | 222.090i | −0.0373868 | + | 0.0373868i | ||||
\(329\) | 15129.2 | 2.53526 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8806.84 | 1.46244 | 0.731220 | − | 0.682142i | \(-0.238951\pi\) | ||||
0.731220 | + | 0.682142i | \(0.238951\pi\) | |||||||
\(332\) | −8222.01 | + | 8222.01i | −1.35916 | + | 1.35916i | ||||
\(333\) | −2581.96 | − | 4265.99i | −0.424897 | − | 0.702027i | ||||
\(334\) | 5949.17i | 0.974623i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3873.09 | − | 4940.94i | −0.628852 | − | 0.802233i | ||||
\(337\) | −5690.38 | − | 5690.38i | −0.919806 | − | 0.919806i | 0.0772088 | − | 0.997015i | \(-0.475399\pi\) |
−0.997015 | + | 0.0772088i | \(0.975399\pi\) | |||||||
\(338\) | 4047.33 | + | 4047.33i | 0.651319 | + | 0.651319i | ||||
\(339\) | −3586.49 | − | 4575.33i | −0.574606 | − | 0.733031i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 252.704i | − | 0.0401311i | ||||||
\(342\) | −1114.26 | − | 1841.01i | −0.176176 | − | 0.291082i | ||||
\(343\) | 1816.25 | − | 1816.25i | 0.285914 | − | 0.285914i | ||||
\(344\) | 3057.23 | 0.479171 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7126.93 | −1.10736 | ||||||||
\(347\) | −4974.95 | + | 4974.95i | −0.769652 | + | 0.769652i | −0.978045 | − | 0.208393i | \(-0.933177\pi\) |
0.208393 | + | 0.978045i | \(0.433177\pi\) | |||||||
\(348\) | −1919.11 | + | 15840.3i | −0.295618 | + | 2.44003i | ||||
\(349\) | − | 6686.71i | − | 1.02559i | −0.858511 | − | 0.512795i | \(-0.828610\pi\) | ||
0.858511 | − | 0.512795i | \(-0.171390\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4056.79 | + | 1829.69i | −0.616910 | + | 0.278238i | ||||
\(352\) | 422.738 | + | 422.738i | 0.0640114 | + | 0.0640114i | ||||
\(353\) | 2025.97 | + | 2025.97i | 0.305472 | + | 0.305472i | 0.843150 | − | 0.537678i | \(-0.180698\pi\) |
−0.537678 | + | 0.843150i | \(0.680698\pi\) | |||||||
\(354\) | −6184.61 | + | 4847.98i | −0.928555 | + | 0.727873i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8517.68i | − | 1.26808i | ||||||
\(357\) | 10302.2 | + | 1248.15i | 1.52731 | + | 0.185040i | ||||
\(358\) | −715.700 | + | 715.700i | −0.105659 | + | 0.105659i | ||||
\(359\) | −7178.33 | −1.05531 | −0.527657 | − | 0.849458i | \(-0.676929\pi\) | ||||
−0.527657 | + | 0.849458i | \(0.676929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6584.06 | 0.959916 | ||||||||
\(362\) | −437.207 | + | 437.207i | −0.0634782 | + | 0.0634782i | ||||
\(363\) | −6429.54 | − | 778.962i | −0.929651 | − | 0.112631i | ||||
\(364\) | 13365.0i | 1.92450i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8485.23 | − | 6651.38i | 1.21183 | − | 0.949926i | ||||
\(367\) | 5129.64 | + | 5129.64i | 0.729605 | + | 0.729605i | 0.970541 | − | 0.240936i | \(-0.0774545\pi\) |
−0.240936 | + | 0.970541i | \(0.577454\pi\) | |||||||
\(368\) | −2091.89 | − | 2091.89i | −0.296324 | − | 0.296324i | ||||
\(369\) | 59.2996 | − | 241.137i | 0.00836589 | − | 0.0340192i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 17402.3i | − | 2.43526i | ||||||
\(372\) | 259.375 | − | 2140.88i | 0.0361505 | − | 0.298385i | ||||
\(373\) | 1332.77 | − | 1332.77i | 0.185009 | − | 0.185009i | −0.608525 | − | 0.793534i | \(-0.708239\pi\) |
0.793534 | + | 0.608525i | \(0.208239\pi\) | |||||||
\(374\) | 3165.19 | 0.437615 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18522.4 | 2.54049 | ||||||||
\(377\) | 4559.99 | − | 4559.99i | 0.622949 | − | 0.622949i | ||||
\(378\) | 17593.7 | + | 6656.47i | 2.39398 | + | 0.905745i | ||||
\(379\) | − | 5792.28i | − | 0.785039i | −0.919744 | − | 0.392519i | \(-0.871604\pi\) | ||
0.919744 | − | 0.392519i | \(-0.128396\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.1825 | − | 57.6399i | −0.00607552 | − | 0.00775060i | ||||
\(382\) | 14586.3 | + | 14586.3i | 1.95367 | + | 1.95367i | ||||
\(383\) | 5023.31 | + | 5023.31i | 0.670181 | + | 0.670181i | 0.957758 | − | 0.287577i | \(-0.0928496\pi\) |
−0.287577 | + | 0.957758i | \(0.592850\pi\) | |||||||
\(384\) | 8486.79 | + | 10826.7i | 1.12784 | + | 1.43880i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24247.6i | 3.19733i | ||||||||
\(387\) | −2067.86 | + | 1251.56i | −0.271615 | + | 0.164393i | ||||
\(388\) | 997.030 | − | 997.030i | 0.130455 | − | 0.130455i | ||||
\(389\) | −10198.8 | −1.32931 | −0.664654 | − | 0.747151i | \(-0.731421\pi\) | ||||
−0.664654 | + | 0.747151i | \(0.731421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4890.18 | 0.632498 | ||||||||
\(392\) | 10506.3 | − | 10506.3i | 1.35370 | − | 1.35370i | ||||
\(393\) | 1664.40 | − | 13737.9i | 0.213633 | − | 1.76333i | ||||
\(394\) | 2862.31i | 0.365993i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3642.29 | + | 895.701i | 0.462202 | + | 0.113663i | ||||
\(397\) | 90.2345 | + | 90.2345i | 0.0114074 | + | 0.0114074i | 0.712787 | − | 0.701380i | \(-0.247432\pi\) |
−0.701380 | + | 0.712787i | \(0.747432\pi\) | |||||||
\(398\) | 10278.4 | + | 10278.4i | 1.29450 | + | 1.29450i | ||||
\(399\) | 1891.46 | − | 1482.67i | 0.237322 | − | 0.186032i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 597.810i | 0.0744469i | 0.999307 | + | 0.0372234i | \(0.0118513\pi\) | ||||
−0.999307 | + | 0.0372234i | \(0.988149\pi\) | |||||||
\(402\) | −22781.7 | − | 2760.08i | −2.82648 | − | 0.342439i | ||||
\(403\) | −616.301 | + | 616.301i | −0.0761790 | + | 0.0761790i | ||||
\(404\) | −16743.0 | −2.06187 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −27258.2 | −3.33202 | ||||||||
\(407\) | 1201.07 | − | 1201.07i | 0.146277 | − | 0.146277i | ||||
\(408\) | 12612.8 | + | 1528.09i | 1.53046 | + | 0.185421i | ||||
\(409\) | 10819.0i | 1.30799i | 0.756500 | + | 0.653994i | \(0.226908\pi\) | ||||
−0.756500 | + | 0.653994i | \(0.773092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2032.26 | + | 1593.04i | −0.243903 | + | 0.191190i | ||||
\(412\) | −12431.2 | − | 12431.2i | −1.48651 | − | 1.48651i | ||||
\(413\) | −6205.73 | − | 6205.73i | −0.739380 | − | 0.739380i | ||||
\(414\) | 8607.73 | + | 2116.79i | 1.02185 | + | 0.251291i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 2061.97i | − | 0.243020i | ||||||
\(417\) | −1086.21 | + | 8965.57i | −0.127559 | + | 1.05287i | ||||
\(418\) | 518.325 | − | 518.325i | 0.0606510 | − | 0.0606510i | ||||
\(419\) | 10849.8 | 1.26503 | 0.632514 | − | 0.774549i | \(-0.282023\pi\) | ||||
0.632514 | + | 0.774549i | \(0.282023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12341.0 | −1.42865 | −0.714324 | − | 0.699815i | \(-0.753266\pi\) | ||||
−0.714324 | + | 0.699815i | \(0.753266\pi\) | |||||||
\(422\) | −9793.43 | + | 9793.43i | −1.12971 | + | 1.12971i | ||||
\(423\) | −12528.3 | + | 7582.65i | −1.44006 | + | 0.871587i | ||||
\(424\) | − | 21305.3i | − | 2.44028i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 11127.9 | + | 14196.0i | 1.26561 | + | 1.61455i | ||||
\(427\) | 8514.20 | + | 8514.20i | 0.964944 | + | 0.964944i | ||||
\(428\) | −13880.0 | − | 13880.0i | −1.56756 | − | 1.56756i | ||||
\(429\) | −935.213 | − | 1193.06i | −0.105251 | − | 0.134269i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10648.0i | − | 1.19001i | −0.803721 | − | 0.595006i | \(-0.797150\pi\) | ||
0.803721 | − | 0.595006i | \(-0.202850\pi\) | |||||||
\(432\) | 5683.61 | + | 2150.35i | 0.632993 | + | 0.239488i | ||||
\(433\) | −10825.2 | + | 10825.2i | −1.20144 | + | 1.20144i | −0.227716 | + | 0.973728i | \(0.573126\pi\) |
−0.973728 | + | 0.227716i | \(0.926874\pi\) | |||||||
\(434\) | 3684.05 | 0.407465 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 71.8186 | 0.00788873 | ||||||||
\(437\) | 800.806 | − | 800.806i | 0.0876607 | − | 0.0876607i | ||||
\(438\) | 2814.24 | − | 23228.7i | 0.307008 | − | 2.53404i | ||||
\(439\) | 1560.21i | 0.169623i | 0.996397 | + | 0.0848117i | \(0.0270289\pi\) | ||||
−0.996397 | + | 0.0848117i | \(0.972971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2805.26 | + | 11407.4i | −0.302912 | + | 1.23176i | ||||
\(442\) | −7719.34 | − | 7719.34i | −0.830705 | − | 0.830705i | ||||
\(443\) | 2588.92 | + | 2588.92i | 0.277660 | + | 0.277660i | 0.832174 | − | 0.554514i | \(-0.187096\pi\) |
−0.554514 | + | 0.832174i | \(0.687096\pi\) | |||||||
\(444\) | 11408.1 | − | 8942.52i | 1.21938 | − | 0.955840i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 9074.30i | − | 0.963409i | ||||||
\(447\) | 948.850 | + | 114.957i | 0.100401 | + | 0.0121639i | ||||
\(448\) | −12997.6 | + | 12997.6i | −1.37071 | + | 1.37071i | ||||
\(449\) | −14291.3 | −1.50211 | −0.751057 | − | 0.660238i | \(-0.770456\pi\) | ||||
−0.751057 | + | 0.660238i | \(0.770456\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 84.5862 | 0.00883150 | ||||||||
\(452\) | 11949.5 | − | 11949.5i | 1.24349 | − | 1.24349i | ||||
\(453\) | 4153.95 | + | 503.266i | 0.430838 | + | 0.0521976i | ||||
\(454\) | − | 2293.14i | − | 0.237054i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2315.69 | − | 1815.21i | 0.237812 | − | 0.186415i | ||||
\(457\) | −7928.59 | − | 7928.59i | −0.811562 | − | 0.811562i | 0.173306 | − | 0.984868i | \(-0.444555\pi\) |
−0.984868 | + | 0.173306i | \(0.944555\pi\) | |||||||
\(458\) | −15552.3 | − | 15552.3i | −1.58670 | − | 1.58670i | ||||
\(459\) | −9156.66 | + | 4129.82i | −0.931147 | + | 0.419964i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 10685.6i | − | 1.07957i | −0.841804 | − | 0.539783i | \(-0.818506\pi\) | ||
0.841804 | − | 0.539783i | \(-0.181494\pi\) | |||||||
\(462\) | −770.667 | + | 6361.07i | −0.0776075 | + | 0.640571i | ||||
\(463\) | 9059.56 | − | 9059.56i | 0.909360 | − | 0.909360i | −0.0868606 | − | 0.996220i | \(-0.527683\pi\) |
0.996220 | + | 0.0868606i | \(0.0276835\pi\) | |||||||
\(464\) | −8805.68 | −0.881020 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3600.65 | 0.357933 | ||||||||
\(467\) | 9692.99 | − | 9692.99i | 0.960467 | − | 0.960467i | −0.0387806 | − | 0.999248i | \(-0.512347\pi\) |
0.999248 | + | 0.0387806i | \(0.0123473\pi\) | |||||||
\(468\) | −6698.46 | − | 11067.4i | −0.661616 | − | 1.09314i | ||||
\(469\) | − | 25628.9i | − | 2.52332i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7373.97 | − | 9407.05i | −0.721390 | − | 0.920285i | ||||
\(472\) | −7597.57 | − | 7597.57i | −0.740904 | − | 0.740904i | ||||
\(473\) | −582.194 | − | 582.194i | −0.0565947 | − | 0.0565947i | ||||
\(474\) | 3186.76 | + | 4065.38i | 0.308803 | + | 0.393943i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 30166.5i | 2.90478i | ||||||||
\(477\) | 8721.90 | + | 14410.6i | 0.837208 | + | 1.38326i | ||||
\(478\) | −2961.32 | + | 2961.32i | −0.283363 | + | 0.283363i | ||||
\(479\) | 5193.79 | 0.495428 | 0.247714 | − | 0.968833i | \(-0.420321\pi\) | ||||
0.247714 | + | 0.968833i | \(0.420321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5858.38 | −0.555341 | ||||||||
\(482\) | 145.887 | − | 145.887i | 0.0137862 | − | 0.0137862i | ||||
\(483\) | −1190.67 | + | 9827.78i | −0.112169 | + | 0.925838i | ||||
\(484\) | − | 18826.7i | − | 1.76810i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17905.3 | + | 3305.74i | −1.67119 | + | 0.308542i | ||||
\(487\) | 1020.47 | + | 1020.47i | 0.0949523 | + | 0.0949523i | 0.752987 | − | 0.658035i | \(-0.228612\pi\) |
−0.658035 | + | 0.752987i | \(0.728612\pi\) | |||||||
\(488\) | 10423.8 | + | 10423.8i | 0.966932 | + | 0.966932i | ||||
\(489\) | −2289.70 | + | 1794.85i | −0.211746 | + | 0.165983i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7350.62i | 0.675619i | 0.941215 | + | 0.337809i | \(0.109686\pi\) | ||||
−0.941215 | + | 0.337809i | \(0.890314\pi\) | |||||||
\(492\) | 716.604 | + | 86.8192i | 0.0656646 | + | 0.00795551i | ||||
\(493\) | 10292.4 | − | 10292.4i | 0.940261 | − | 0.940261i | ||||
\(494\) | −2528.21 | −0.230262 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1190.12 | 0.107738 | ||||||||
\(497\) | −14244.5 | + | 14244.5i | −1.28562 | + | 1.28562i | ||||
\(498\) | 19087.5 | + | 2312.52i | 1.71753 | + | 0.208085i | ||||
\(499\) | 15309.0i | 1.37339i | 0.726944 | + | 0.686697i | \(0.240940\pi\) | ||||
−0.726944 | + | 0.686697i | \(0.759060\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5061.44 | − | 3967.55i | 0.451354 | − | 0.353806i | ||||
\(502\) | −172.661 | − | 172.661i | −0.0153511 | − | 0.0153511i | ||||
\(503\) | −738.534 | − | 738.534i | −0.0654664 | − | 0.0654664i | 0.673616 | − | 0.739082i | \(-0.264740\pi\) |
−0.739082 | + | 0.673616i | \(0.764740\pi\) | |||||||
\(504\) | −6142.00 | + | 24975.9i | −0.542830 | + | 2.20737i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3019.43i | 0.265277i | ||||||||
\(507\) | 744.197 | − | 6142.59i | 0.0651892 | − | 0.538071i | ||||
\(508\) | 150.540 | − | 150.540i | 0.0131479 | − | 0.0131479i | ||||
\(509\) | −4477.48 | −0.389903 | −0.194952 | − | 0.980813i | \(-0.562455\pi\) | ||||
−0.194952 | + | 0.980813i | \(0.562455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26131.8 | 2.26224 | ||||||||
\(512\) | −10358.5 | + | 10358.5i | −0.894109 | + | 0.894109i | ||||
\(513\) | −823.186 | + | 2175.77i | −0.0708471 | + | 0.187256i | ||||
\(514\) | 29035.2i | 2.49161i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4334.71 | − | 5529.84i | −0.369816 | − | 0.471778i | ||||
\(517\) | −3527.27 | − | 3527.27i | −0.300056 | − | 0.300056i | ||||
\(518\) | 17509.8 | + | 17509.8i | 1.48520 | + | 1.48520i | ||||
\(519\) | 4753.00 | + | 6063.46i | 0.401992 | + | 0.512825i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14580.8i | 1.22610i | 0.790045 | + | 0.613049i | \(0.210057\pi\) | ||||
−0.790045 | + | 0.613049i | \(0.789943\pi\) | |||||||
\(522\) | 22572.1 | − | 13661.6i | 1.89263 | − | 1.14550i | ||||
\(523\) | 2457.46 | − | 2457.46i | 0.205463 | − | 0.205463i | −0.596873 | − | 0.802336i | \(-0.703590\pi\) |
0.802336 | + | 0.596873i | \(0.203590\pi\) | |||||||
\(524\) | 40226.8 | 3.35366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7829.24 | 0.648994 | ||||||||
\(527\) | −1391.06 | + | 1391.06i | −0.114982 | + | 0.114982i | ||||
\(528\) | −248.962 | + | 2054.93i | −0.0205202 | + | 0.169373i | ||||
\(529\) | − | 7502.02i | − | 0.616587i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8249.13 | + | 2028.60i | 0.674165 | + | 0.165789i | ||||
\(532\) | 4940.00 | + | 4940.00i | 0.402587 | + | 0.402587i | ||||
\(533\) | −206.291 | − | 206.291i | −0.0167644 | − | 0.0167644i | ||||
\(534\) | −11084.8 | + | 8689.11i | −0.898288 | + | 0.704147i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 31377.1i | − | 2.52852i | ||||||
\(537\) | 1086.21 | + | 131.598i | 0.0872876 | + | 0.0105752i | ||||
\(538\) | −5725.26 | + | 5725.26i | −0.458798 | + | 0.458798i | ||||
\(539\) | −4001.49 | −0.319770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 375.804 | 0.0298652 | 0.0149326 | − | 0.999889i | \(-0.495247\pi\) | ||||
0.0149326 | + | 0.999889i | \(0.495247\pi\) | |||||||
\(542\) | −11244.7 | + | 11244.7i | −0.891146 | + | 0.891146i | ||||
\(543\) | 663.545 | + | 80.3909i | 0.0524409 | + | 0.00635341i | ||||
\(544\) | − | 4654.11i | − | 0.366808i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 17393.1 | − | 13634.0i | 1.36329 | − | 1.06865i | ||||
\(547\) | 3656.92 | + | 3656.92i | 0.285848 | + | 0.285848i | 0.835436 | − | 0.549588i | \(-0.185215\pi\) |
−0.549588 | + | 0.835436i | \(0.685215\pi\) | |||||||
\(548\) | −5307.72 | − | 5307.72i | −0.413749 | − | 0.413749i | ||||
\(549\) | −11317.7 | − | 2783.22i | −0.879834 | − | 0.216366i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3370.94i | − | 0.260630i | ||||||
\(552\) | −1457.72 | + | 12032.0i | −0.112400 | + | 0.927746i | ||||
\(553\) | −4079.26 | + | 4079.26i | −0.313685 | + | 0.313685i | ||||
\(554\) | −14809.2 | −1.13571 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −26252.6 | −2.00244 | ||||||||
\(557\) | 4512.51 | − | 4512.51i | 0.343270 | − | 0.343270i | −0.514325 | − | 0.857595i | \(-0.671958\pi\) |
0.857595 | + | 0.514325i | \(0.171958\pi\) | |||||||
\(558\) | −3050.70 | + | 1846.42i | −0.231446 | + | 0.140081i | ||||
\(559\) | 2839.74i | 0.214862i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2110.89 | − | 2692.88i | −0.158862 | − | 0.202662i | ||||
\(562\) | 16899.5 | + | 16899.5i | 1.26844 | + | 1.26844i | ||||
\(563\) | 15527.9 | + | 15527.9i | 1.16238 | + | 1.16238i | 0.983953 | + | 0.178430i | \(0.0571017\pi\) |
0.178430 | + | 0.983953i | \(0.442898\pi\) | |||||||
\(564\) | −26262.2 | − | 33502.9i | −1.96070 | − | 2.50129i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 22606.7i | − | 1.67885i | ||||||
\(567\) | −6070.20 | − | 19407.7i | −0.449603 | − | 1.43747i | ||||
\(568\) | −17439.3 | + | 17439.3i | −1.28827 | + | 1.28827i | ||||
\(569\) | 12965.1 | 0.955230 | 0.477615 | − | 0.878569i | \(-0.341501\pi\) | ||||
0.477615 | + | 0.878569i | \(0.341501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6452.24 | −0.472886 | −0.236443 | − | 0.971645i | \(-0.575982\pi\) | ||||
−0.236443 | + | 0.971645i | \(0.575982\pi\) | |||||||
\(572\) | 3115.96 | − | 3115.96i | 0.227771 | − | 0.227771i | ||||
\(573\) | 2682.04 | − | 22137.5i | 0.195539 | − | 1.61397i | ||||
\(574\) | 1233.14i | 0.0896695i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4248.79 | − | 17277.4i | 0.307349 | − | 1.24981i | ||||
\(577\) | −11704.9 | − | 11704.9i | −0.844508 | − | 0.844508i | 0.144934 | − | 0.989441i | \(-0.453703\pi\) |
−0.989441 | + | 0.144934i | \(0.953703\pi\) | |||||||
\(578\) | −724.794 | − | 724.794i | −0.0521582 | − | 0.0521582i | ||||
\(579\) | 20629.4 | − | 16170.9i | 1.48070 | − | 1.16069i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 21473.1i | 1.53331i | ||||||||
\(582\) | −2314.62 | − | 280.424i | −0.164852 | − | 0.0199725i | ||||
\(583\) | −4057.22 | + | 4057.22i | −0.288221 | + | 0.288221i | ||||
\(584\) | 31992.7 | 2.26690 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23610.2 | 1.66438 | ||||||||
\(587\) | 6441.65 | − | 6441.65i | 0.452939 | − | 0.452939i | −0.443390 | − | 0.896329i | \(-0.646224\pi\) |
0.896329 | + | 0.443390i | \(0.146224\pi\) | |||||||
\(588\) | −33900.1 | − | 4107.12i | −2.37758 | − | 0.288053i | ||||
\(589\) | 455.596i | 0.0318718i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2435.20 | − | 1908.90i | 0.169494 | − | 0.132862i | ||||
\(592\) | 5656.48 | + | 5656.48i | 0.392703 | + | 0.392703i | ||||
\(593\) | −12555.8 | − | 12555.8i | −0.869487 | − | 0.869487i | 0.122928 | − | 0.992416i | \(-0.460772\pi\) |
−0.992416 | + | 0.122928i | \(0.960772\pi\) | |||||||
\(594\) | −2549.95 | − | 5653.76i | −0.176137 | − | 0.390533i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2778.38i | 0.190951i | ||||||||
\(597\) | 1889.93 | − | 15599.4i | 0.129564 | − | 1.06942i | ||||
\(598\) | 7363.85 | − | 7363.85i | 0.503563 | − | 0.503563i | ||||
\(599\) | 24700.6 | 1.68487 | 0.842437 | − | 0.538795i | \(-0.181120\pi\) | ||||
0.842437 | + | 0.538795i | \(0.181120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22487.6 | −1.52627 | −0.763135 | − | 0.646239i | \(-0.776341\pi\) | ||||
−0.763135 | + | 0.646239i | \(0.776341\pi\) | |||||||
\(602\) | 8487.52 | − | 8487.52i | 0.574627 | − | 0.574627i | ||||
\(603\) | 12845.0 | + | 21222.9i | 0.867480 | + | 1.43327i | ||||
\(604\) | 12163.4i | 0.819407i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17080.0 | + | 21789.1i | 1.14493 | + | 1.46060i | ||||
\(607\) | −13817.0 | − | 13817.0i | −0.923912 | − | 0.923912i | 0.0733910 | − | 0.997303i | \(-0.476618\pi\) |
−0.997303 | + | 0.0733910i | \(0.976618\pi\) | |||||||
\(608\) | −762.148 | − | 762.148i | −0.0508375 | − | 0.0508375i | ||||
\(609\) | 18178.7 | + | 23190.7i | 1.20959 | + | 1.54308i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17204.8i | 1.13917i | ||||||||
\(612\) | −15119.2 | − | 24980.4i | −0.998624 | − | 1.64995i | ||||
\(613\) | −7861.86 | + | 7861.86i | −0.518005 | + | 0.518005i | −0.916967 | − | 0.398962i | \(-0.869371\pi\) |
0.398962 | + | 0.916967i | \(0.369371\pi\) | |||||||
\(614\) | −27910.9 | −1.83451 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8761.08 | −0.573042 | ||||||||
\(617\) | −17057.5 | + | 17057.5i | −1.11298 | + | 1.11298i | −0.120233 | + | 0.992746i | \(0.538364\pi\) |
−0.992746 | + | 0.120233i | \(0.961636\pi\) | |||||||
\(618\) | −3496.39 | + | 28859.1i | −0.227582 | + | 1.87845i | ||||
\(619\) | 24671.5i | 1.60199i | 0.598671 | + | 0.800995i | \(0.295696\pi\) | ||||
−0.598671 | + | 0.800995i | \(0.704304\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3939.64 | − | 8734.99i | −0.254577 | − | 0.564450i | ||||
\(622\) | 13382.1 | + | 13382.1i | 0.862657 | + | 0.862657i | ||||
\(623\) | −11122.6 | − | 11122.6i | −0.715279 | − | 0.715279i | ||||
\(624\) | 5618.78 | − | 4404.43i | 0.360467 | − | 0.282561i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 1091.44i | − | 0.0696847i | ||||||
\(627\) | −786.656 | − | 95.3062i | −0.0501053 | − | 0.00607044i | ||||
\(628\) | 24568.7 | − | 24568.7i | 1.56114 | − | 1.56114i | ||||
\(629\) | −13223.1 | −0.838216 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13039.4 | 0.822648 | 0.411324 | − | 0.911489i | \(-0.365066\pi\) | ||||
0.411324 | + | 0.911489i | \(0.365066\pi\) | |||||||
\(632\) | −4994.17 | + | 4994.17i | −0.314331 | + | 0.314331i | ||||
\(633\) | 14863.4 | + | 1800.75i | 0.933280 | + | 0.113070i | ||||
\(634\) | − | 43564.9i | − | 2.72900i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −38536.6 | + | 30207.9i | −2.40263 | + | 1.88337i | ||||
\(637\) | 9758.93 | + | 9758.93i | 0.607006 | + | 0.607006i | ||||
\(638\) | 6355.05 | + | 6355.05i | 0.394355 | + | 0.394355i | ||||
\(639\) | 4656.41 | − | 18934.9i | 0.288270 | − | 1.17223i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7413.70i | 0.456823i | 0.973565 | + | 0.228412i | \(0.0733532\pi\) | ||||
−0.973565 | + | 0.228412i | \(0.926647\pi\) | |||||||
\(642\) | −3903.90 | + | 32222.7i | −0.239991 | + | 1.98088i | ||||
\(643\) | −3856.84 | + | 3856.84i | −0.236546 | + | 0.236546i | −0.815418 | − | 0.578872i | \(-0.803493\pi\) |
0.578872 | + | 0.815418i | \(0.303493\pi\) | |||||||
\(644\) | −28777.3 | −1.76084 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5706.46 | −0.347551 | ||||||||
\(647\) | 762.540 | − | 762.540i | 0.0463347 | − | 0.0463347i | −0.683560 | − | 0.729894i | \(-0.739569\pi\) |
0.729894 | + | 0.683560i | \(0.239569\pi\) | |||||||
\(648\) | −7431.65 | − | 23760.5i | −0.450529 | − | 1.44043i | ||||
\(649\) | 2893.64i | 0.175016i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2456.92 | − | 3134.32i | −0.147918 | − | 0.188700i | ||||
\(652\) | −5980.10 | − | 5980.10i | −0.359200 | − | 0.359200i | ||||
\(653\) | −18549.1 | − | 18549.1i | −1.11161 | − | 1.11161i | −0.992933 | − | 0.118679i | \(-0.962134\pi\) |
−0.118679 | − | 0.992933i | \(-0.537866\pi\) | |||||||
\(654\) | −73.2641 | − | 93.4637i | −0.00438051 | − | 0.00558826i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 398.363i | 0.0237095i | ||||||||
\(657\) | −21639.3 | + | 13097.1i | −1.28498 | + | 0.777725i | ||||
\(658\) | 51422.3 | − | 51422.3i | 3.04658 | − | 3.04658i | ||||
\(659\) | −27210.3 | −1.60844 | −0.804222 | − | 0.594329i | \(-0.797418\pi\) | ||||
−0.804222 | + | 0.594329i | \(0.797418\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17912.8 | 1.05405 | 0.527026 | − | 0.849849i | \(-0.323307\pi\) | ||||
0.527026 | + | 0.849849i | \(0.323307\pi\) | |||||||
\(662\) | 29933.3 | − | 29933.3i | 1.75739 | − | 1.75739i | ||||
\(663\) | −1419.38 | + | 11715.5i | −0.0831436 | + | 0.686266i | ||||
\(664\) | 26289.1i | 1.53647i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −23275.3 | − | 5723.80i | −1.35421 | − | 0.333022i | ||||
\(667\) | 9818.47 | + | 9818.47i | 0.569974 | + | 0.569974i | ||||
\(668\) | 13219.1 | + | 13219.1i | 0.765664 | + | 0.765664i | ||||
\(669\) | −7720.24 | + | 6051.72i | −0.446161 | + | 0.349735i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3970.05i | − | 0.228408i | ||||||
\(672\) | 9353.36 | + | 1133.19i | 0.536925 | + | 0.0650504i | ||||
\(673\) | 13447.5 | − | 13447.5i | 0.770225 | − | 0.770225i | −0.207921 | − | 0.978146i | \(-0.566670\pi\) |
0.978146 | + | 0.207921i | \(0.0666696\pi\) | |||||||
\(674\) | −38681.8 | −2.21063 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17986.4 | 1.02335 | ||||||||
\(677\) | 14818.2 | − | 14818.2i | 0.841228 | − | 0.841228i | −0.147791 | − | 0.989019i | \(-0.547216\pi\) |
0.989019 | + | 0.147791i | \(0.0472163\pi\) | |||||||
\(678\) | −27741.0 | − | 3360.92i | −1.57137 | − | 0.190377i | ||||
\(679\) | − | 2603.90i | − | 0.147170i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1950.96 | + | 1529.32i | −0.109781 | + | 0.0860550i | ||||
\(682\) | −858.909 | − | 858.909i | −0.0482248 | − | 0.0482248i | ||||
\(683\) | 10932.8 | + | 10932.8i | 0.612493 | + | 0.612493i | 0.943595 | − | 0.331102i | \(-0.107421\pi\) |
−0.331102 | + | 0.943595i | \(0.607421\pi\) | |||||||
\(684\) | −6566.63 | − | 1614.85i | −0.367078 | − | 0.0902707i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 12346.4i | − | 0.687156i | ||||||
\(687\) | −2859.65 | + | 23603.5i | −0.158810 | + | 1.31082i | ||||
\(688\) | 2741.87 | − | 2741.87i | 0.151937 | − | 0.151937i | ||||
\(689\) | 19789.7 | 1.09423 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6859.09 | −0.377615 | −0.188807 | − | 0.982014i | \(-0.560462\pi\) | ||||
−0.188807 | + | 0.982014i | \(0.560462\pi\) | |||||||
\(692\) | −15836.1 | + | 15836.1i | −0.869942 | + | 0.869942i | ||||
\(693\) | 5925.84 | − | 3586.58i | 0.324826 | − | 0.196599i | ||||
\(694\) | 33818.4i | 1.84976i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 22255.9 | + | 28392.1i | 1.21208 | + | 1.54626i | ||||
\(697\) | −465.623 | − | 465.623i | −0.0253038 | − | 0.0253038i | ||||
\(698\) | −22727.3 | − | 22727.3i | −1.23244 | − | 1.23244i | ||||
\(699\) | −2401.30 | − | 3063.36i | −0.129936 | − | 0.165761i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 26912.7i | − | 1.45004i | −0.688727 | − | 0.725021i | \(-0.741830\pi\) | ||
0.688727 | − | 0.725021i | \(-0.258170\pi\) | |||||||
\(702\) | −7569.65 | + | 20007.4i | −0.406977 | + | 1.07568i | ||||
\(703\) | −2165.38 | + | 2165.38i | −0.116172 | + | 0.116172i | ||||
\(704\) | 6060.57 | 0.324455 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13772.1 | 0.734162 | ||||||||
\(707\) | −21863.5 | + | 21863.5i | −1.16303 | + | 1.16303i | ||||
\(708\) | −2970.03 | + | 24514.6i | −0.157656 | + | 1.30129i | ||||
\(709\) | − | 12724.4i | − | 0.674011i | −0.941503 | − | 0.337005i | \(-0.890586\pi\) | ||
0.941503 | − | 0.337005i | \(-0.109414\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1333.48 | − | 5422.46i | 0.0703365 | − | 0.286017i | ||||
\(712\) | −13617.3 | − | 13617.3i | −0.716753 | − | 0.716753i | ||||
\(713\) | −1327.00 | − | 1327.00i | −0.0697009 | − | 0.0697009i | ||||
\(714\) | 39258.2 | − | 30773.6i | 2.05771 | − | 1.61299i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3180.59i | 0.166012i | ||||||||
\(717\) | 4494.36 | + | 544.508i | 0.234093 | + | 0.0283613i | ||||
\(718\) | −24398.2 | + | 24398.2i | −1.26815 | + | 1.26815i | ||||
\(719\) | −1776.43 | −0.0921413 | −0.0460707 | − | 0.998938i | \(-0.514670\pi\) | ||||
−0.0460707 | + | 0.998938i | \(0.514670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32466.0 | −1.67697 | ||||||||
\(722\) | 22378.4 | − | 22378.4i | 1.15351 | − | 1.15351i | ||||
\(723\) | −221.411 | − | 26.8247i | −0.0113892 | − | 0.00137984i | ||||
\(724\) | 1942.96i | 0.0997370i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −24500.8 | + | 19205.6i | −1.25249 | + | 0.981800i | ||||
\(727\) | 11790.0 | + | 11790.0i | 0.601465 | + | 0.601465i | 0.940701 | − | 0.339236i | \(-0.110169\pi\) |
−0.339236 | + | 0.940701i | \(0.610169\pi\) | |||||||
\(728\) | 21366.7 | + | 21366.7i | 1.08778 | + | 1.08778i | ||||
\(729\) | 14753.6 | + | 13028.9i | 0.749562 | + | 0.661934i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6409.63i | 0.324307i | ||||||||
\(732\) | 4074.85 | − | 33633.7i | 0.205753 | − | 1.69828i | ||||
\(733\) | −22491.0 | + | 22491.0i | −1.13332 | + | 1.13332i | −0.143696 | + | 0.989622i | \(0.545899\pi\) |
−0.989622 | + | 0.143696i | \(0.954101\pi\) | |||||||
\(734\) | 34870.0 | 1.75351 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4439.78 | 0.222354 | ||||||||
\(737\) | −5975.20 | + | 5975.20i | −0.298642 | + | 0.298642i | ||||
\(738\) | −618.041 | − | 1021.14i | −0.0308271 | − | 0.0509334i | ||||
\(739\) | 9723.29i | 0.484002i | 0.970276 | + | 0.242001i | \(0.0778037\pi\) | ||||
−0.970276 | + | 0.242001i | \(0.922196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1686.08 | + | 2150.95i | 0.0835894 | + | 0.106636i | ||||
\(742\) | −59148.2 | − | 59148.2i | −2.92641 | − | 2.92641i | ||||
\(743\) | −3640.61 | − | 3640.61i | −0.179759 | − | 0.179759i | 0.611492 | − | 0.791251i | \(-0.290570\pi\) |
−0.791251 | + | 0.611492i | \(0.790570\pi\) | |||||||
\(744\) | −3007.97 | − | 3837.30i | −0.148222 | − | 0.189089i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 9059.85i | − | 0.444645i | ||||||
\(747\) | −10762.1 | − | 17781.5i | −0.527130 | − | 0.870939i | ||||
\(748\) | 7033.09 | − | 7033.09i | 0.343790 | − | 0.343790i | ||||
\(749\) | −36249.9 | −1.76841 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39901.6 | −1.93879 | −0.969395 | − | 0.245508i | \(-0.921045\pi\) | ||||
−0.969395 | + | 0.245508i | \(0.921045\pi\) | |||||||
\(752\) | 16611.8 | − | 16611.8i | 0.805546 | − | 0.805546i | ||||
\(753\) | −31.7477 | + | 262.045i | −0.00153646 | + | 0.0126819i | ||||
\(754\) | − | 30997.7i | − | 1.49717i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 53884.3 | − | 24302.8i | 2.59227 | − | 1.16916i | ||||
\(757\) | 19152.6 | + | 19152.6i | 0.919568 | + | 0.919568i | 0.996998 | − | 0.0774296i | \(-0.0246713\pi\) |
−0.0774296 | + | 0.996998i | \(0.524671\pi\) | |||||||
\(758\) | −19687.2 | − | 19687.2i | −0.943368 | − | 0.943368i | ||||
\(759\) | 2568.87 | − | 2013.68i | 0.122851 | − | 0.0963003i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28330.4i | 1.34951i | 0.738043 | + | 0.674753i | \(0.235750\pi\) | ||||
−0.738043 | + | 0.674753i | \(0.764250\pi\) | |||||||
\(762\) | −349.480 | − | 42.3408i | −0.0166146 | − | 0.00201292i | ||||
\(763\) | 93.7828 | − | 93.7828i | 0.00444976 | − | 0.00444976i | ||||
\(764\) | 64821.9 | 3.06960 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34147.2 | 1.61069 | ||||||||
\(767\) | 7057.08 | − | 7057.08i | 0.332225 | − | 0.332225i | ||||
\(768\) | 38450.2 | + | 4658.38i | 1.80658 | + | 0.218874i | ||||
\(769\) | − | 12352.6i | − | 0.579256i | −0.957139 | − | 0.289628i | \(-0.906468\pi\) | ||
0.957139 | − | 0.289628i | \(-0.0935316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24702.6 | − | 19363.8i | 1.15388 | − | 0.904499i | ||||
\(772\) | 53878.4 | + | 53878.4i | 2.51182 | + | 2.51182i | ||||
\(773\) | 12713.0 | + | 12713.0i | 0.591532 | + | 0.591532i | 0.938045 | − | 0.346513i | \(-0.112634\pi\) |
−0.346513 | + | 0.938045i | \(0.612634\pi\) | |||||||
\(774\) | −2774.50 | + | 11282.3i | −0.128847 | + | 0.523944i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 3187.91i | − | 0.147474i | ||||||
\(777\) | 3219.58 | − | 26574.4i | 0.148651 | − | 1.22696i | ||||
\(778\) | −34664.5 | + | 34664.5i | −1.59741 | + | 1.59741i | ||||
\(779\) | −152.499 | −0.00701392 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6642.00 | 0.304314 | ||||||||
\(782\) | 16621.1 | − | 16621.1i | 0.760063 | − | 0.760063i | ||||
\(783\) | −26676.5 | − | 10092.9i | −1.21755 | − | 0.460651i | ||||
\(784\) | − | 18845.2i | − | 0.858473i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −41036.4 | − | 52350.6i | −1.86224 | − | 2.37568i | ||||
\(787\) | 11888.6 | + | 11888.6i | 0.538481 | + | 0.538481i | 0.923083 | − | 0.384602i | \(-0.125661\pi\) |
−0.384602 | + | 0.923083i | \(0.625661\pi\) | |||||||
\(788\) | 6360.09 | + | 6360.09i | 0.287524 | + | 0.287524i | ||||
\(789\) | −5221.38 | − | 6660.97i | −0.235597 | − | 0.300554i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 31208.1i | − | 1.40282i | ||||||
\(792\) | 7254.91 | − | 4390.99i | 0.325495 | − | 0.197004i | ||||
\(793\) | −9682.25 | + | 9682.25i | −0.433577 | + | 0.433577i | ||||
\(794\) | 613.391 | 0.0274162 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45677.6 | 2.03392 | ||||||||
\(797\) | −8060.57 | + | 8060.57i | −0.358243 | + | 0.358243i | −0.863165 | − | 0.504922i | \(-0.831521\pi\) |
0.504922 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(798\) | 1389.42 | − | 11468.3i | 0.0616354 | − | 0.508737i | ||||
\(799\) | 38833.2i | 1.71942i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14785.1 | + | 3635.90i | 0.652191 | + | 0.160385i | ||||
\(802\) | 2031.88 | + | 2031.88i | 0.0894616 | + | 0.0894616i | ||||
\(803\) | −6092.44 | − | 6092.44i | −0.267743 | − | 0.267743i | ||||
\(804\) | −56754.1 | + | 44488.2i | −2.48951 | + | 1.95147i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4189.46i | 0.183086i | ||||||||
\(807\) | 8689.16 | + | 1052.72i | 0.379025 | + | 0.0459202i | ||||
\(808\) | −26767.1 | + | 26767.1i | −1.16542 | + | 1.16542i | ||||
\(809\) | 13824.2 | 0.600782 | 0.300391 | − | 0.953816i | \(-0.402883\pi\) | ||||
0.300391 | + | 0.953816i | \(0.402883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20584.0 | −0.891249 | −0.445625 | − | 0.895220i | \(-0.647018\pi\) | ||||
−0.445625 | + | 0.895220i | \(0.647018\pi\) | |||||||
\(812\) | −60568.1 | + | 60568.1i | −2.61764 | + | 2.61764i | ||||
\(813\) | 17065.9 | + | 2067.60i | 0.736198 | + | 0.0891931i | ||||
\(814\) | − | 8164.55i | − | 0.351557i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12682.3 | − | 9941.32i | 0.544078 | − | 0.426490i | ||||
\(817\) | 1049.63 | + | 1049.63i | 0.0449472 | + | 0.0449472i | ||||
\(818\) | 36772.6 | + | 36772.6i | 1.57179 | + | 1.57179i | ||||
\(819\) | −23199.1 | − | 5705.06i | −0.989796 | − | 0.243408i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7269.14i | 0.309007i | 0.987992 | + | 0.154503i | \(0.0493778\pi\) | ||||
−0.987992 | + | 0.154503i | \(0.950622\pi\) | |||||||
\(822\) | −1492.85 | + | 12321.9i | −0.0633443 | + | 0.522843i | ||||
\(823\) | 22295.9 | − | 22295.9i | 0.944334 | − | 0.944334i | −0.0541961 | − | 0.998530i | \(-0.517260\pi\) |
0.998530 | + | 0.0541961i | \(0.0172596\pi\) | |||||||
\(824\) | −39747.6 | −1.68043 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42185.0 | −1.77700 | ||||||||
\(827\) | −4878.42 | + | 4878.42i | −0.205126 | + | 0.205126i | −0.802192 | − | 0.597066i | \(-0.796333\pi\) |
0.597066 | + | 0.802192i | \(0.296333\pi\) | |||||||
\(828\) | 23830.0 | − | 14423.0i | 1.00018 | − | 0.605353i | ||||
\(829\) | − | 28818.4i | − | 1.20736i | −0.797225 | − | 0.603682i | \(-0.793700\pi\) | ||
0.797225 | − | 0.603682i | \(-0.206300\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9876.38 | + | 12599.4i | 0.412284 | + | 0.525955i | ||||
\(832\) | −14780.7 | − | 14780.7i | −0.615898 | − | 0.615898i | ||||
\(833\) | 22027.1 | + | 22027.1i | 0.916197 | + | 0.916197i | ||||
\(834\) | 26780.9 | + | 34164.7i | 1.11193 | + | 1.41850i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2303.45i | − | 0.0952948i | ||||||
\(837\) | 3605.44 | + | 1364.09i | 0.148891 | + | 0.0563320i | ||||
\(838\) | 36877.1 | − | 36877.1i | 1.52016 | − | 1.52016i | ||||
\(839\) | 19129.2 | 0.787144 | 0.393572 | − | 0.919294i | \(-0.371239\pi\) | ||||
0.393572 | + | 0.919294i | \(0.371239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16941.2 | 0.694627 | ||||||||
\(842\) | −41945.3 | + | 41945.3i | −1.71678 | + | 1.71678i | ||||
\(843\) | 3107.38 | − | 25648.2i | 0.126956 | − | 1.04789i | ||||
\(844\) | 43522.3i | 1.77500i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16809.5 | + | 68354.5i | −0.683125 | + | 2.77787i | ||||
\(847\) | −24584.4 | − | 24584.4i | −0.997321 | − | 0.997321i | ||||
\(848\) | −19107.6 | − | 19107.6i | −0.773773 | − | 0.773773i | ||||
\(849\) | −19233.3 | + | 15076.6i | −0.777487 | + | 0.609454i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 12614.1i | − | 0.508116i | ||||||
\(852\) | 56270.2 | + | 6817.34i | 2.26266 | + | 0.274129i | ||||
\(853\) | −415.608 | + | 415.608i | −0.0166825 | + | 0.0166825i | −0.715399 | − | 0.698716i | \(-0.753755\pi\) |
0.698716 | + | 0.715399i | \(0.253755\pi\) | |||||||
\(854\) | 57877.4 | 2.31911 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44380.2 | −1.77206 | ||||||||
\(857\) | 21659.9 | − | 21659.9i | 0.863347 | − | 0.863347i | −0.128378 | − | 0.991725i | \(-0.540977\pi\) |
0.991725 | + | 0.128378i | \(0.0409771\pi\) | |||||||
\(858\) | −7233.74 | − | 876.393i | −0.287827 | − | 0.0348713i | ||||
\(859\) | − | 20261.0i | − | 0.804769i | −0.915471 | − | 0.402384i | \(-0.868182\pi\) | ||
0.915471 | − | 0.402384i | \(-0.131818\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1049.13 | − | 822.391i | 0.0415265 | − | 0.0325517i | ||||
\(862\) | −36191.2 | − | 36191.2i | −1.43002 | − | 1.43002i | ||||
\(863\) | −23444.8 | − | 23444.8i | −0.924762 | − | 0.924762i | 0.0725989 | − | 0.997361i | \(-0.476871\pi\) |
−0.997361 | + | 0.0725989i | \(0.976871\pi\) | |||||||
\(864\) | −8313.32 | + | 3749.46i | −0.327344 | + | 0.147638i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 73586.9i | 2.88751i | ||||||||
\(867\) | −133.270 | + | 1100.01i | −0.00522041 | + | 0.0430892i | ||||
\(868\) | 8186.01 | − | 8186.01i | 0.320105 | − | 0.320105i | ||||
\(869\) | 1902.10 | 0.0742512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29144.9 | 1.13380 | ||||||||
\(872\) | 114.817 | − | 114.817i | 0.00445893 | − | 0.00445893i | ||||
\(873\) | 1305.06 | + | 2156.25i | 0.0505950 | + | 0.0835945i | ||||
\(874\) | − | 5443.68i | − | 0.210681i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −45361.1 | − | 57867.6i | −1.74955 | − | 2.23193i | ||||
\(877\) | 11791.4 | + | 11791.4i | 0.454012 | + | 0.454012i | 0.896684 | − | 0.442672i | \(-0.145969\pi\) |
−0.442672 | + | 0.896684i | \(0.645969\pi\) | |||||||
\(878\) | 5302.95 | + | 5302.95i | 0.203834 | + | 0.203834i | ||||
\(879\) | −15745.8 | − | 20087.1i | −0.604201 | − | 0.770786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30662.9i | − | 1.17260i | −0.810095 | − | 0.586299i | \(-0.800584\pi\) | ||
0.810095 | − | 0.586299i | \(-0.199416\pi\) | |||||||
\(882\) | 29237.5 | + | 48306.9i | 1.11619 | + | 1.84419i | ||||
\(883\) | −1717.16 | + | 1717.16i | −0.0654439 | + | 0.0654439i | −0.739071 | − | 0.673627i | \(-0.764735\pi\) |
0.673627 | + | 0.739071i | \(0.264735\pi\) | |||||||
\(884\) | −34304.9 | −1.30520 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17598.8 | 0.667318 | ||||||||
\(887\) | 13438.0 | − | 13438.0i | 0.508687 | − | 0.508687i | −0.405436 | − | 0.914123i | \(-0.632880\pi\) |
0.914123 | + | 0.405436i | \(0.132880\pi\) | |||||||
\(888\) | 3941.68 | − | 32534.6i | 0.148957 | − | 1.22949i | ||||
\(889\) | − | 393.159i | − | 0.0148325i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3109.53 | + | 5939.98i | −0.116917 | + | 0.223341i | ||||
\(892\) | −20163.2 | − | 20163.2i | −0.756854 | − | 0.756854i | ||||
\(893\) | 6359.25 | + | 6359.25i | 0.238303 | + | 0.238303i | ||||
\(894\) | 3615.74 | − | 2834.30i | 0.135267 | − | 0.106033i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 73848.4i | 2.75346i | ||||||||
\(897\) | −11176.0 | − | 1354.02i | −0.416006 | − | 0.0504006i | ||||
\(898\) | −48574.4 | + | 48574.4i | −1.80506 | + | 1.80506i | ||||
\(899\) | −5585.94 | −0.207232 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44667.6 | 1.65160 | ||||||||
\(902\) | 287.498 | − | 287.498i | 0.0106127 | − | 0.0106127i | ||||
\(903\) | −12881.4 | − | 1560.63i | −0.474714 | − | 0.0575133i | ||||
\(904\) | − | 38207.5i | − | 1.40571i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 15829.3 | − | 12408.2i | 0.580455 | − | 0.455006i | ||||
\(907\) | 14586.4 | + | 14586.4i | 0.533994 | + | 0.533994i | 0.921759 | − | 0.387764i | \(-0.126753\pi\) |
−0.387764 | + | 0.921759i | \(0.626753\pi\) | |||||||
\(908\) | −5095.40 | − | 5095.40i | −0.186230 | − | 0.186230i | ||||
\(909\) | 7146.99 | − | 29062.6i | 0.260782 | − | 1.06045i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27679.6i | 1.00666i | 0.864095 | + | 0.503329i | \(0.167892\pi\) | ||||
−0.864095 | + | 0.503329i | \(0.832108\pi\) | |||||||
\(912\) | 448.849 | − | 3704.79i | 0.0162970 | − | 0.134515i | ||||
\(913\) | 5006.29 | − | 5006.29i | 0.181472 | − | 0.181472i | ||||
\(914\) | −53896.6 | −1.95048 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −69114.7 | −2.49303 | ||||||||
\(917\) | 52529.3 | − | 52529.3i | 1.89168 | − | 1.89168i | ||||
\(918\) | −17085.6 | + | 45159.1i | −0.614280 | + | 1.62361i | ||||
\(919\) | − | 44894.9i | − | 1.61147i | −0.592273 | − | 0.805737i | \(-0.701769\pi\) | ||
0.592273 | − | 0.805737i | \(-0.298231\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18614.0 | + | 23746.1i | 0.665963 | + | 0.849576i | ||||
\(922\) | −36319.1 | − | 36319.1i | −1.29730 | − | 1.29730i | ||||
\(923\) | −16198.7 | − | 16198.7i | −0.577666 | − | 0.577666i | ||||
\(924\) | 12422.0 | + | 15846.8i | 0.442264 | + | 0.564201i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 61584.6i | − | 2.18553i | ||||||
\(927\) | 26884.6 | − | 16271.7i | 0.952541 | − | 0.576519i | ||||
\(928\) | 9344.50 | − | 9344.50i | 0.330548 | − | 0.330548i | ||||
\(929\) | 29033.0 | 1.02534 | 0.512670 | − | 0.858586i | \(-0.328656\pi\) | ||||
0.512670 | + | 0.858586i | \(0.328656\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7214.22 | 0.253960 | ||||||||
\(932\) | 8000.68 | − | 8000.68i | 0.281192 | − | 0.281192i | ||||
\(933\) | 2460.61 | − | 20309.8i | 0.0863416 | − | 0.712662i | ||||
\(934\) | − | 65890.5i | − | 2.30835i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −28402.3 | − | 6984.61i | −0.991836 | − | 0.243909i | ||||
\(937\) | −35681.0 | − | 35681.0i | −1.24402 | − | 1.24402i | −0.958318 | − | 0.285703i | \(-0.907773\pi\) |
−0.285703 | − | 0.958318i | \(-0.592227\pi\) | |||||||
\(938\) | −87109.6 | − | 87109.6i | −3.03223 | − | 3.03223i | ||||
\(939\) | −928.574 | + | 727.888i | −0.0322714 | + | 0.0252968i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28986.4i | − | 1.00418i | −0.864816 | − | 0.502089i | \(-0.832565\pi\) | ||
0.864816 | − | 0.502089i | \(-0.167435\pi\) | |||||||
\(942\) | −57036.6 | − | 6910.19i | −1.97277 | − | 0.239009i | ||||
\(943\) | 444.181 | − | 444.181i | 0.0153388 | − | 0.0153388i | ||||
\(944\) | −13627.7 | −0.469857 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3957.61 | −0.136018 | ||||||||
\(947\) | −10086.1 | + | 10086.1i | −0.346099 | + | 0.346099i | −0.858654 | − | 0.512555i | \(-0.828699\pi\) |
0.512555 | + | 0.858654i | \(0.328699\pi\) | |||||||
\(948\) | 16114.3 | + | 1952.31i | 0.552078 | + | 0.0668862i | ||||
\(949\) | 29716.8i | 1.01649i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −37064.2 | + | 29053.8i | −1.26382 | + | 0.990676i | ||||
\(952\) | 48227.3 | + | 48227.3i | 1.64186 | + | 1.64186i | ||||
\(953\) | 35251.1 | + | 35251.1i | 1.19821 | + | 1.19821i | 0.974702 | + | 0.223509i | \(0.0717513\pi\) |
0.223509 | + | 0.974702i | \(0.428249\pi\) | |||||||
\(954\) | 78624.3 | + | 19335.1i | 2.66830 | + | 0.656180i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13160.2i | 0.445220i | ||||||||
\(957\) | 1168.52 | − | 9644.98i | 0.0394703 | − | 0.325787i | ||||
\(958\) | 17653.0 | − | 17653.0i | 0.595348 | − | 0.595348i | ||||
\(959\) | −13861.9 | −0.466763 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29036.0 | −0.974658 | ||||||||
\(962\) | −19911.9 | + | 19911.9i | −0.667344 | + | 0.667344i | ||||
\(963\) | 30018.0 | − | 18168.2i | 1.00448 | − | 0.607956i | ||||
\(964\) | − | 648.325i | − | 0.0216610i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 29356.5 | + | 37450.3i | 0.977773 | + | 1.24735i | ||||
\(967\) | 29437.7 | + | 29437.7i | 0.978958 | + | 0.978958i | 0.999783 | − | 0.0208251i | \(-0.00662933\pi\) |
−0.0208251 | + | 0.999783i | \(0.506629\pi\) | |||||||
\(968\) | −30098.3 | − | 30098.3i | −0.999377 | − | 0.999377i | ||||
\(969\) | 3805.68 | + | 4854.95i | 0.126167 | + | 0.160953i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14117.9i | − | 0.466595i | −0.972405 | − | 0.233298i | \(-0.925048\pi\) | ||
0.972405 | − | 0.233298i | \(-0.0749516\pi\) | |||||||
\(972\) | −32440.4 | + | 47131.2i | −1.07050 | + | 1.55528i | ||||
\(973\) | −34281.4 | + | 34281.4i | −1.12951 | + | 1.12951i | ||||
\(974\) | 6936.87 | 0.228205 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18697.1 | 0.613197 | ||||||||
\(977\) | −18396.9 | + | 18396.9i | −0.602423 | + | 0.602423i | −0.940955 | − | 0.338532i | \(-0.890070\pi\) |
0.338532 | + | 0.940955i | \(0.390070\pi\) | |||||||
\(978\) | −1681.96 | + | 13882.9i | −0.0549930 | + | 0.453911i | ||||
\(979\) | 5186.32i | 0.169311i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.6568 | + | 124.663i | −0.000997754 | + | 0.00405728i | ||||
\(982\) | 24983.8 | + | 24983.8i | 0.811880 | + | 0.811880i | ||||
\(983\) | 37328.5 | + | 37328.5i | 1.21119 | + | 1.21119i | 0.970637 | + | 0.240549i | \(0.0773274\pi\) |
0.240549 | + | 0.970637i | \(0.422673\pi\) | |||||||
\(984\) | 1284.44 | − | 1006.84i | 0.0416121 | − | 0.0326188i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 69965.5i | − | 2.25979i | ||||||
\(987\) | −78043.0 | − | 9455.20i | −2.51686 | − | 0.304926i | ||||
\(988\) | −5617.71 | + | 5617.71i | −0.180894 | + | 0.180894i | ||||
\(989\) | −6114.46 | −0.196591 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26565.6 | −0.851547 | −0.425773 | − | 0.904830i | \(-0.639998\pi\) | ||||
−0.425773 | + | 0.904830i | \(0.639998\pi\) | |||||||
\(992\) | −1262.95 | + | 1262.95i | −0.0404219 | + | 0.0404219i | ||||
\(993\) | −45429.5 | − | 5503.95i | −1.45182 | − | 0.175894i | ||||
\(994\) | 96830.4i | 3.08981i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 47551.1 | − | 37274.2i | 1.51277 | − | 1.18582i | ||||
\(997\) | 3172.34 | + | 3172.34i | 0.100771 | + | 0.100771i | 0.755695 | − | 0.654924i | \(-0.227299\pi\) |
−0.654924 | + | 0.755695i | \(0.727299\pi\) | |||||||
\(998\) | 52033.3 | + | 52033.3i | 1.65039 | + | 1.65039i | ||||
\(999\) | 10652.8 | + | 23619.5i | 0.337377 | + | 0.748035i |
(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 | 75.4.e.d.32.7 | yes | 16 | |
3.2 | odd | 2 | inner | 75.4.e.d.32.1 | ✓ | 16 | |
5.2 | odd | 4 | inner | 75.4.e.d.68.8 | yes | 16 | |
5.3 | odd | 4 | inner | 75.4.e.d.68.1 | yes | 16 | |
5.4 | even | 2 | inner | 75.4.e.d.32.2 | yes | 16 | |
15.2 | even | 4 | inner | 75.4.e.d.68.2 | yes | 16 | |
15.8 | even | 4 | inner | 75.4.e.d.68.7 | yes | 16 | |
15.14 | odd | 2 | inner | 75.4.e.d.32.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.e.d.32.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
75.4.e.d.32.2 | yes | 16 | 5.4 | even | 2 | inner | |
75.4.e.d.32.7 | yes | 16 | 1.1 | even | 1 | trivial | |
75.4.e.d.32.8 | yes | 16 | 15.14 | odd | 2 | inner | |
75.4.e.d.68.1 | yes | 16 | 5.3 | odd | 4 | inner | |
75.4.e.d.68.2 | yes | 16 | 15.2 | even | 4 | inner | |
75.4.e.d.68.7 | yes | 16 | 15.8 | even | 4 | inner | |
75.4.e.d.68.8 | yes | 16 | 5.2 | odd | 4 | inner |