Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,4,Mod(11,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.e (of order \(6\), 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: | \(2.18307067021\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 82 x^{14} + 2679 x^{12} + 44392 x^{10} + 392767 x^{8} + 1779258 x^{6} + 3438825 x^{4} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.4 | ||
Root | \(-0.575927i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.27 |
Dual form | 37.4.e.a.11.4 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.498768 | − | 0.287964i | −0.176341 | − | 0.101811i | 0.409231 | − | 0.912431i | \(-0.365797\pi\) |
−0.585572 | + | 0.810620i | \(0.699130\pi\) | |||||||
\(3\) | −1.51417 | − | 2.62262i | −0.291402 | − | 0.504723i | 0.682740 | − | 0.730662i | \(-0.260788\pi\) |
−0.974141 | + | 0.225939i | \(0.927455\pi\) | |||||||
\(4\) | −3.83415 | − | 6.64095i | −0.479269 | − | 0.830119i | ||||
\(5\) | −6.67348 | + | 3.85293i | −0.596894 | + | 0.344617i | −0.767819 | − | 0.640667i | \(-0.778658\pi\) |
0.170925 | + | 0.985284i | \(0.445324\pi\) | |||||||
\(6\) | 1.74410i | 0.118671i | ||||||||
\(7\) | −10.3028 | − | 17.8450i | −0.556298 | − | 0.963537i | −0.997801 | − | 0.0662770i | \(-0.978888\pi\) |
0.441503 | − | 0.897260i | \(-0.354445\pi\) | |||||||
\(8\) | 9.02381i | 0.398800i | ||||||||
\(9\) | 8.91459 | − | 15.4405i | 0.330170 | − | 0.571871i | ||||
\(10\) | 4.43802 | 0.140343 | ||||||||
\(11\) | 20.9419 | 0.574021 | 0.287010 | − | 0.957927i | \(-0.407339\pi\) | ||||
0.287010 | + | 0.957927i | \(0.407339\pi\) | |||||||
\(12\) | −11.6111 | + | 20.1110i | −0.279320 | + | 0.483796i | ||||
\(13\) | −4.26314 | + | 2.46133i | −0.0909525 | + | 0.0525114i | −0.544786 | − | 0.838575i | \(-0.683389\pi\) |
0.453834 | + | 0.891086i | \(0.350056\pi\) | |||||||
\(14\) | 11.8673i | 0.226548i | ||||||||
\(15\) | 20.2095 | + | 11.6680i | 0.347872 | + | 0.200844i | ||||
\(16\) | −28.0747 | + | 48.6268i | −0.438667 | + | 0.759794i | ||||
\(17\) | 42.2040 | + | 24.3665i | 0.602116 | + | 0.347632i | 0.769873 | − | 0.638197i | \(-0.220319\pi\) |
−0.167758 | + | 0.985828i | \(0.553653\pi\) | |||||||
\(18\) | −8.89262 | + | 5.13416i | −0.116445 | + | 0.0672296i | ||||
\(19\) | 62.6916 | − | 36.1950i | 0.756971 | − | 0.437037i | −0.0712365 | − | 0.997459i | \(-0.522694\pi\) |
0.828207 | + | 0.560422i | \(0.189361\pi\) | |||||||
\(20\) | 51.1743 | + | 29.5455i | 0.572146 | + | 0.330328i | ||||
\(21\) | −31.2003 | + | 54.0405i | −0.324213 | + | 0.561553i | ||||
\(22\) | −10.4452 | − | 6.03052i | −0.101223 | − | 0.0584414i | ||||
\(23\) | − | 149.439i | − | 1.35479i | −0.735617 | − | 0.677397i | \(-0.763108\pi\) | ||
0.735617 | − | 0.677397i | \(-0.236892\pi\) | |||||||
\(24\) | 23.6660 | − | 13.6636i | 0.201283 | − | 0.116211i | ||||
\(25\) | −32.8098 | + | 56.8283i | −0.262479 | + | 0.454626i | ||||
\(26\) | 2.83509 | 0.0213849 | ||||||||
\(27\) | −135.758 | −0.967652 | ||||||||
\(28\) | −79.0049 | + | 136.841i | −0.533233 | + | 0.923587i | ||||
\(29\) | − | 132.515i | − | 0.848532i | −0.905538 | − | 0.424266i | \(-0.860532\pi\) | ||
0.905538 | − | 0.424266i | \(-0.139468\pi\) | |||||||
\(30\) | −6.71991 | − | 11.6392i | −0.0408960 | − | 0.0708340i | ||||
\(31\) | − | 133.601i | − | 0.774049i | −0.922069 | − | 0.387024i | \(-0.873503\pi\) | ||
0.922069 | − | 0.387024i | \(-0.126497\pi\) | |||||||
\(32\) | 90.5243 | − | 52.2642i | 0.500081 | − | 0.288722i | ||||
\(33\) | −31.7096 | − | 54.9226i | −0.167271 | − | 0.289721i | ||||
\(34\) | −14.0333 | − | 24.3064i | −0.0707851 | − | 0.122603i | ||||
\(35\) | 137.511 | + | 79.3919i | 0.664102 | + | 0.383419i | ||||
\(36\) | −136.720 | −0.632961 | ||||||||
\(37\) | −138.484 | − | 177.412i | −0.615315 | − | 0.788282i | ||||
\(38\) | −41.6914 | −0.177980 | ||||||||
\(39\) | 12.9102 | + | 7.45372i | 0.0530074 | + | 0.0306039i | ||||
\(40\) | −34.7681 | − | 60.2202i | −0.137433 | − | 0.238041i | ||||
\(41\) | 54.2927 | + | 94.0377i | 0.206807 | + | 0.358201i | 0.950707 | − | 0.310091i | \(-0.100359\pi\) |
−0.743900 | + | 0.668291i | \(0.767026\pi\) | |||||||
\(42\) | 31.1234 | − | 17.9691i | 0.114344 | − | 0.0660165i | ||||
\(43\) | 331.680i | 1.17630i | 0.808754 | + | 0.588148i | \(0.200143\pi\) | ||||
−0.808754 | + | 0.588148i | \(0.799857\pi\) | |||||||
\(44\) | −80.2946 | − | 139.074i | −0.275111 | − | 0.476505i | ||||
\(45\) | 137.389i | 0.455129i | ||||||||
\(46\) | −43.0331 | + | 74.5356i | −0.137932 | + | 0.238906i | ||||
\(47\) | 491.766 | 1.52620 | 0.763101 | − | 0.646280i | \(-0.223676\pi\) | ||||
0.763101 | + | 0.646280i | \(0.223676\pi\) | |||||||
\(48\) | 170.039 | 0.511314 | ||||||||
\(49\) | −40.7948 | + | 70.6587i | −0.118935 | + | 0.206002i | ||||
\(50\) | 32.7290 | − | 18.8961i | 0.0925715 | − | 0.0534462i | ||||
\(51\) | − | 147.580i | − | 0.405202i | ||||||
\(52\) | 32.6911 | + | 18.8742i | 0.0871815 | + | 0.0503342i | ||||
\(53\) | −165.865 | + | 287.286i | −0.429874 | + | 0.744563i | −0.996862 | − | 0.0791632i | \(-0.974775\pi\) |
0.566988 | + | 0.823726i | \(0.308109\pi\) | |||||||
\(54\) | 67.7116 | + | 39.0933i | 0.170637 | + | 0.0985172i | ||||
\(55\) | −139.755 | + | 80.6878i | −0.342629 | + | 0.197817i | ||||
\(56\) | 161.029 | − | 92.9704i | 0.384258 | − | 0.221852i | ||||
\(57\) | −189.851 | − | 109.611i | −0.441165 | − | 0.254707i | ||||
\(58\) | −38.1596 | + | 66.0943i | −0.0863896 | + | 0.149631i | ||||
\(59\) | 633.562 | + | 365.787i | 1.39801 | + | 0.807143i | 0.994184 | − | 0.107691i | \(-0.0343457\pi\) |
0.403829 | + | 0.914834i | \(0.367679\pi\) | |||||||
\(60\) | − | 178.947i | − | 0.385033i | ||||||
\(61\) | −191.768 | + | 110.717i | −0.402515 | + | 0.232392i | −0.687569 | − | 0.726119i | \(-0.741322\pi\) |
0.285054 | + | 0.958512i | \(0.407989\pi\) | |||||||
\(62\) | −38.4723 | + | 66.6361i | −0.0788063 | + | 0.136497i | ||||
\(63\) | −367.381 | −0.734692 | ||||||||
\(64\) | 388.994 | 0.759755 | ||||||||
\(65\) | 18.9666 | − | 32.8512i | 0.0361926 | − | 0.0626875i | ||||
\(66\) | 36.5249i | 0.0681197i | ||||||||
\(67\) | −153.422 | − | 265.735i | −0.279754 | − | 0.484548i | 0.691570 | − | 0.722310i | \(-0.256920\pi\) |
−0.971323 | + | 0.237762i | \(0.923586\pi\) | |||||||
\(68\) | − | 373.699i | − | 0.666437i | ||||||
\(69\) | −391.922 | + | 226.276i | −0.683796 | + | 0.394790i | ||||
\(70\) | −45.7240 | − | 79.1962i | −0.0780723 | − | 0.135225i | ||||
\(71\) | −15.5789 | − | 26.9835i | −0.0260405 | − | 0.0451035i | 0.852711 | − | 0.522382i | \(-0.174957\pi\) |
−0.878752 | + | 0.477279i | \(0.841623\pi\) | |||||||
\(72\) | 139.332 | + | 80.4436i | 0.228062 | + | 0.131672i | ||||
\(73\) | −543.061 | −0.870692 | −0.435346 | − | 0.900263i | \(-0.643374\pi\) | ||||
−0.435346 | + | 0.900263i | \(0.643374\pi\) | |||||||
\(74\) | 17.9831 | + | 128.366i | 0.0282498 | + | 0.201652i | ||||
\(75\) | 198.718 | 0.305947 | ||||||||
\(76\) | −480.738 | − | 277.554i | −0.725585 | − | 0.418917i | ||||
\(77\) | −215.760 | − | 373.708i | −0.319327 | − | 0.553090i | ||||
\(78\) | −4.29280 | − | 7.43535i | −0.00623159 | − | 0.0107934i | ||||
\(79\) | 1143.97 | − | 660.473i | 1.62920 | − | 0.940620i | 0.644870 | − | 0.764292i | \(-0.276912\pi\) |
0.984332 | − | 0.176327i | \(-0.0564217\pi\) | |||||||
\(80\) | − | 432.680i | − | 0.604688i | ||||||
\(81\) | −35.1339 | − | 60.8536i | −0.0481946 | − | 0.0834755i | ||||
\(82\) | − | 62.5373i | − | 0.0842206i | ||||||
\(83\) | −159.240 | + | 275.813i | −0.210589 | + | 0.364751i | −0.951899 | − | 0.306412i | \(-0.900872\pi\) |
0.741310 | + | 0.671163i | \(0.234205\pi\) | |||||||
\(84\) | 478.507 | 0.621540 | ||||||||
\(85\) | −375.530 | −0.479199 | ||||||||
\(86\) | 95.5118 | − | 165.431i | 0.119759 | − | 0.207429i | ||||
\(87\) | −347.536 | + | 200.650i | −0.428274 | + | 0.247264i | ||||
\(88\) | 188.976i | 0.228919i | ||||||||
\(89\) | −178.806 | − | 103.234i | −0.212960 | − | 0.122953i | 0.389726 | − | 0.920931i | \(-0.372570\pi\) |
−0.602686 | + | 0.797978i | \(0.705903\pi\) | |||||||
\(90\) | 39.5631 | − | 68.5254i | 0.0463369 | − | 0.0802579i | ||||
\(91\) | 87.8444 | + | 50.7170i | 0.101193 | + | 0.0584240i | ||||
\(92\) | −992.420 | + | 572.974i | −1.12464 | + | 0.649312i | ||||
\(93\) | −350.385 | + | 202.295i | −0.390680 | + | 0.225559i | ||||
\(94\) | −245.277 | − | 141.611i | −0.269132 | − | 0.155383i | ||||
\(95\) | −278.914 | + | 483.093i | −0.301221 | + | 0.521729i | ||||
\(96\) | −274.138 | − | 158.274i | −0.291449 | − | 0.168268i | ||||
\(97\) | 835.414i | 0.874468i | 0.899348 | + | 0.437234i | \(0.144042\pi\) | ||||
−0.899348 | + | 0.437234i | \(0.855958\pi\) | |||||||
\(98\) | 40.6943 | − | 23.4949i | 0.0419464 | − | 0.0242178i | ||||
\(99\) | 186.689 | − | 323.354i | 0.189524 | − | 0.328266i | ||||
\(100\) | 503.192 | 0.503192 | ||||||||
\(101\) | 1640.78 | 1.61647 | 0.808234 | − | 0.588861i | \(-0.200424\pi\) | ||||
0.808234 | + | 0.588861i | \(0.200424\pi\) | |||||||
\(102\) | −42.4976 | + | 73.6080i | −0.0412538 | + | 0.0714537i | ||||
\(103\) | − | 1137.38i | − | 1.08806i | −0.839067 | − | 0.544028i | \(-0.816899\pi\) | ||
0.839067 | − | 0.544028i | \(-0.183101\pi\) | |||||||
\(104\) | −22.2105 | − | 38.4698i | −0.0209416 | − | 0.0362718i | ||||
\(105\) | − | 480.851i | − | 0.446916i | ||||||
\(106\) | 165.456 | − | 95.5262i | 0.151609 | − | 0.0875313i | ||||
\(107\) | 525.866 | + | 910.827i | 0.475116 | + | 0.822925i | 0.999594 | − | 0.0284994i | \(-0.00907286\pi\) |
−0.524478 | + | 0.851424i | \(0.675740\pi\) | |||||||
\(108\) | 520.516 | + | 901.561i | 0.463766 | + | 0.803266i | ||||
\(109\) | 1384.54 | + | 799.363i | 1.21665 | + | 0.702432i | 0.964199 | − | 0.265179i | \(-0.0854310\pi\) |
0.252448 | + | 0.967610i | \(0.418764\pi\) | |||||||
\(110\) | 92.9407 | 0.0805595 | ||||||||
\(111\) | −255.596 | + | 631.823i | −0.218560 | + | 0.540270i | ||||
\(112\) | 1156.99 | 0.976119 | ||||||||
\(113\) | −720.246 | − | 415.834i | −0.599602 | − | 0.346180i | 0.169283 | − | 0.985567i | \(-0.445855\pi\) |
−0.768885 | + | 0.639387i | \(0.779188\pi\) | |||||||
\(114\) | 63.1278 | + | 109.341i | 0.0518637 | + | 0.0898305i | ||||
\(115\) | 575.780 | + | 997.281i | 0.466885 | + | 0.808669i | ||||
\(116\) | −880.026 | + | 508.083i | −0.704383 | + | 0.406675i | ||||
\(117\) | 87.7668i | 0.0693508i | ||||||||
\(118\) | −210.667 | − | 364.886i | −0.164351 | − | 0.284665i | ||||
\(119\) | − | 1004.17i | − | 0.773547i | ||||||
\(120\) | −105.290 | + | 182.367i | −0.0800965 | + | 0.138731i | ||||
\(121\) | −892.436 | −0.670500 | ||||||||
\(122\) | 127.530 | 0.0946399 | ||||||||
\(123\) | 164.416 | − | 284.778i | 0.120528 | − | 0.208761i | ||||
\(124\) | −887.240 | + | 512.248i | −0.642552 | + | 0.370978i | ||||
\(125\) | − | 1468.89i | − | 1.05105i | ||||||
\(126\) | 183.238 | + | 105.792i | 0.129556 | + | 0.0747994i | ||||
\(127\) | −551.355 | + | 954.976i | −0.385235 | + | 0.667247i | −0.991802 | − | 0.127786i | \(-0.959213\pi\) |
0.606566 | + | 0.795033i | \(0.292546\pi\) | |||||||
\(128\) | −918.212 | − | 530.130i | −0.634057 | − | 0.366073i | ||||
\(129\) | 869.869 | − | 502.219i | 0.593703 | − | 0.342775i | ||||
\(130\) | −18.9199 | + | 10.9234i | −0.0127645 | + | 0.00736959i | ||||
\(131\) | 60.2528 | + | 34.7870i | 0.0401856 | + | 0.0232012i | 0.519958 | − | 0.854192i | \(-0.325948\pi\) |
−0.479773 | + | 0.877393i | \(0.659281\pi\) | |||||||
\(132\) | −243.159 | + | 421.164i | −0.160335 | + | 0.277709i | ||||
\(133\) | −1291.80 | − | 745.819i | −0.842203 | − | 0.486246i | ||||
\(134\) | 176.720i | 0.113928i | ||||||||
\(135\) | 905.976 | − | 523.066i | 0.577585 | − | 0.333469i | ||||
\(136\) | −219.878 | + | 380.841i | −0.138635 | + | 0.240124i | ||||
\(137\) | −2788.85 | −1.73918 | −0.869588 | − | 0.493778i | \(-0.835616\pi\) | ||||
−0.869588 | + | 0.493778i | \(0.835616\pi\) | |||||||
\(138\) | 260.638 | 0.160775 | ||||||||
\(139\) | 1165.16 | − | 2018.12i | 0.710990 | − | 1.23147i | −0.253496 | − | 0.967337i | \(-0.581580\pi\) |
0.964486 | − | 0.264134i | \(-0.0850863\pi\) | |||||||
\(140\) | − | 1217.60i | − | 0.735044i | ||||||
\(141\) | −744.616 | − | 1289.71i | −0.444738 | − | 0.770308i | ||||
\(142\) | 17.9447i | 0.0106048i | ||||||||
\(143\) | −89.2784 | + | 51.5449i | −0.0522086 | + | 0.0301427i | ||||
\(144\) | 500.549 | + | 866.976i | 0.289670 | + | 0.501722i | ||||
\(145\) | 510.572 | + | 884.336i | 0.292419 | + | 0.506484i | ||||
\(146\) | 270.861 | + | 156.382i | 0.153539 | + | 0.0886456i | ||||
\(147\) | 247.081 | 0.138632 | ||||||||
\(148\) | −647.218 | + | 1599.89i | −0.359466 | + | 0.888583i | ||||
\(149\) | 1494.69 | 0.821809 | 0.410904 | − | 0.911678i | \(-0.365213\pi\) | ||||
0.410904 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(150\) | −99.1143 | − | 57.2237i | −0.0539510 | − | 0.0311486i | ||||
\(151\) | −1536.43 | − | 2661.18i | −0.828033 | − | 1.43419i | −0.899579 | − | 0.436757i | \(-0.856127\pi\) |
0.0715468 | − | 0.997437i | \(-0.477206\pi\) | |||||||
\(152\) | 326.617 | + | 565.717i | 0.174290 | + | 0.301880i | ||||
\(153\) | 752.462 | − | 434.434i | 0.397601 | − | 0.229555i | ||||
\(154\) | 248.524i | 0.130043i | ||||||||
\(155\) | 514.757 | + | 891.585i | 0.266750 | + | 0.462025i | ||||
\(156\) | − | 114.315i | − | 0.0586699i | ||||||
\(157\) | 1239.86 | − | 2147.49i | 0.630263 | − | 1.09165i | −0.357234 | − | 0.934015i | \(-0.616280\pi\) |
0.987498 | − | 0.157633i | \(-0.0503864\pi\) | |||||||
\(158\) | −760.769 | −0.383060 | ||||||||
\(159\) | 1004.59 | 0.501064 | ||||||||
\(160\) | −402.741 | + | 697.568i | −0.198997 | + | 0.344672i | ||||
\(161\) | −2666.74 | + | 1539.64i | −1.30539 | + | 0.753670i | ||||
\(162\) | 40.4691i | 0.0196269i | ||||||||
\(163\) | 430.043 | + | 248.286i | 0.206648 | + | 0.119308i | 0.599753 | − | 0.800186i | \(-0.295266\pi\) |
−0.393105 | + | 0.919494i | \(0.628599\pi\) | |||||||
\(164\) | 416.333 | − | 721.110i | 0.198233 | − | 0.343349i | ||||
\(165\) | 423.226 | + | 244.350i | 0.199686 | + | 0.115289i | ||||
\(166\) | 158.848 | − | 91.7109i | 0.0742711 | − | 0.0428804i | ||||
\(167\) | −1294.14 | + | 747.174i | −0.599664 | + | 0.346216i | −0.768909 | − | 0.639358i | \(-0.779200\pi\) |
0.169245 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(168\) | −487.651 | − | 281.546i | −0.223947 | − | 0.129296i | ||||
\(169\) | −1086.38 | + | 1881.67i | −0.494485 | + | 0.856473i | ||||
\(170\) | 187.302 | + | 108.139i | 0.0845024 | + | 0.0487875i | ||||
\(171\) | − | 1290.66i | − | 0.577186i | ||||||
\(172\) | 2202.67 | − | 1271.71i | 0.976465 | − | 0.563762i | ||||
\(173\) | −1921.68 | + | 3328.45i | −0.844525 | + | 1.46276i | 0.0415088 | + | 0.999138i | \(0.486784\pi\) |
−0.886033 | + | 0.463621i | \(0.846550\pi\) | |||||||
\(174\) | 231.120 | 0.100696 | ||||||||
\(175\) | 1352.13 | 0.584065 | ||||||||
\(176\) | −587.938 | + | 1018.34i | −0.251804 | + | 0.436137i | ||||
\(177\) | − | 2215.45i | − | 0.940812i | ||||||
\(178\) | 59.4553 | + | 102.980i | 0.0250357 | + | 0.0433632i | ||||
\(179\) | 520.251i | 0.217237i | 0.994084 | + | 0.108618i | \(0.0346426\pi\) | ||||
−0.994084 | + | 0.108618i | \(0.965357\pi\) | |||||||
\(180\) | 912.395 | − | 526.772i | 0.377811 | − | 0.218129i | ||||
\(181\) | 2191.24 | + | 3795.34i | 0.899855 | + | 1.55859i | 0.827678 | + | 0.561203i | \(0.189661\pi\) |
0.0721768 | + | 0.997392i | \(0.477005\pi\) | |||||||
\(182\) | −29.2093 | − | 50.5920i | −0.0118964 | − | 0.0206051i | ||||
\(183\) | 580.739 | + | 335.290i | 0.234587 | + | 0.135439i | ||||
\(184\) | 1348.51 | 0.540292 | ||||||||
\(185\) | 1607.73 | + | 650.388i | 0.638933 | + | 0.258473i | ||||
\(186\) | 233.014 | 0.0918572 | ||||||||
\(187\) | 883.832 | + | 510.281i | 0.345627 | + | 0.199548i | ||||
\(188\) | −1885.51 | − | 3265.79i | −0.731461 | − | 1.26693i | ||||
\(189\) | 1398.68 | + | 2422.59i | 0.538303 | + | 0.932368i | ||||
\(190\) | 278.227 | − | 160.634i | 0.106235 | − | 0.0613349i | ||||
\(191\) | 3872.71i | 1.46712i | 0.679626 | + | 0.733558i | \(0.262142\pi\) | ||||
−0.679626 | + | 0.733558i | \(0.737858\pi\) | |||||||
\(192\) | −589.003 | − | 1020.18i | −0.221394 | − | 0.383465i | ||||
\(193\) | − | 1486.91i | − | 0.554559i | −0.960789 | − | 0.277280i | \(-0.910567\pi\) | ||
0.960789 | − | 0.277280i | \(-0.0894328\pi\) | |||||||
\(194\) | 240.569 | − | 416.677i | 0.0890301 | − | 0.154205i | ||||
\(195\) | −114.875 | −0.0421864 | ||||||||
\(196\) | 625.655 | 0.228008 | ||||||||
\(197\) | 1075.51 | − | 1862.85i | 0.388971 | − | 0.673717i | −0.603341 | − | 0.797484i | \(-0.706164\pi\) |
0.992311 | + | 0.123767i | \(0.0394974\pi\) | |||||||
\(198\) | −186.229 | + | 107.519i | −0.0668419 | + | 0.0385912i | ||||
\(199\) | − | 2274.75i | − | 0.810316i | −0.914247 | − | 0.405158i | \(-0.867216\pi\) | ||
0.914247 | − | 0.405158i | \(-0.132784\pi\) | |||||||
\(200\) | −512.807 | − | 296.070i | −0.181305 | − | 0.104676i | ||||
\(201\) | −464.614 | + | 804.735i | −0.163042 | + | 0.282396i | ||||
\(202\) | −818.366 | − | 472.484i | −0.285050 | − | 0.164574i | ||||
\(203\) | −2364.73 | + | 1365.28i | −0.817592 | + | 0.472037i | ||||
\(204\) | −980.069 | + | 565.843i | −0.336366 | + | 0.194201i | ||||
\(205\) | −724.642 | − | 418.372i | −0.246884 | − | 0.142538i | ||||
\(206\) | −327.525 | + | 567.290i | −0.110776 | + | 0.191869i | ||||
\(207\) | −2307.42 | − | 1332.19i | −0.774768 | − | 0.447313i | ||||
\(208\) | − | 276.404i | − | 0.0921402i | ||||||
\(209\) | 1312.88 | − | 757.993i | 0.434517 | − | 0.250868i | ||||
\(210\) | −138.468 | + | 239.833i | −0.0455008 | + | 0.0788097i | ||||
\(211\) | −2315.52 | −0.755483 | −0.377741 | − | 0.925911i | \(-0.623299\pi\) | ||||
−0.377741 | + | 0.925911i | \(0.623299\pi\) | |||||||
\(212\) | 2543.81 | 0.824101 | ||||||||
\(213\) | −47.1782 | + | 81.7151i | −0.0151765 | + | 0.0262865i | ||||
\(214\) | − | 605.721i | − | 0.193487i | ||||||
\(215\) | −1277.94 | − | 2213.46i | −0.405371 | − | 0.702123i | ||||
\(216\) | − | 1225.05i | − | 0.385899i | ||||||
\(217\) | −2384.11 | + | 1376.47i | −0.745824 | + | 0.430602i | ||||
\(218\) | −460.375 | − | 797.393i | −0.143030 | − | 0.247735i | ||||
\(219\) | 822.286 | + | 1424.24i | 0.253721 | + | 0.439458i | ||||
\(220\) | 1071.69 | + | 618.739i | 0.328423 | + | 0.189615i | ||||
\(221\) | −239.895 | −0.0730186 | ||||||||
\(222\) | 309.425 | − | 241.530i | 0.0935462 | − | 0.0730201i | ||||
\(223\) | −1347.61 | −0.404676 | −0.202338 | − | 0.979316i | \(-0.564854\pi\) | ||||
−0.202338 | + | 0.979316i | \(0.564854\pi\) | |||||||
\(224\) | −1865.31 | − | 1076.93i | −0.556388 | − | 0.321231i | ||||
\(225\) | 584.972 | + | 1013.20i | 0.173325 | + | 0.300208i | ||||
\(226\) | 239.490 | + | 414.809i | 0.0704896 | + | 0.122092i | ||||
\(227\) | 4137.73 | − | 2388.92i | 1.20983 | − | 0.698495i | 0.247107 | − | 0.968988i | \(-0.420520\pi\) |
0.962722 | + | 0.270493i | \(0.0871868\pi\) | |||||||
\(228\) | 1681.06i | 0.488292i | ||||||||
\(229\) | −1127.51 | − | 1952.91i | −0.325364 | − | 0.563546i | 0.656222 | − | 0.754568i | \(-0.272153\pi\) |
−0.981586 | + | 0.191021i | \(0.938820\pi\) | |||||||
\(230\) | − | 663.215i | − | 0.190135i | ||||||
\(231\) | −653.394 | + | 1131.71i | −0.186105 | + | 0.322343i | ||||
\(232\) | 1195.79 | 0.338395 | ||||||||
\(233\) | 5884.25 | 1.65446 | 0.827232 | − | 0.561861i | \(-0.189914\pi\) | ||||
0.827232 | + | 0.561861i | \(0.189914\pi\) | |||||||
\(234\) | 25.2737 | − | 43.7753i | 0.00706065 | − | 0.0122294i | ||||
\(235\) | −3281.79 | + | 1894.74i | −0.910980 | + | 0.525955i | ||||
\(236\) | − | 5609.94i | − | 1.54736i | ||||||
\(237\) | −3464.33 | − | 2000.13i | −0.949504 | − | 0.548196i | ||||
\(238\) | −289.165 | + | 500.848i | −0.0787553 | + | 0.136408i | ||||
\(239\) | −5209.39 | − | 3007.64i | −1.40990 | − | 0.814009i | −0.414526 | − | 0.910038i | \(-0.636053\pi\) |
−0.995379 | + | 0.0960288i | \(0.969386\pi\) | |||||||
\(240\) | −1134.75 | + | 655.150i | −0.305200 | + | 0.176207i | ||||
\(241\) | 3226.18 | − | 1862.63i | 0.862309 | − | 0.497854i | −0.00247597 | − | 0.999997i | \(-0.500788\pi\) |
0.864785 | + | 0.502143i | \(0.167455\pi\) | |||||||
\(242\) | 445.118 | + | 256.989i | 0.118237 | + | 0.0682640i | ||||
\(243\) | −1939.13 | + | 3358.67i | −0.511914 | + | 0.886661i | ||||
\(244\) | 1470.54 | + | 849.015i | 0.385826 | + | 0.222757i | ||||
\(245\) | − | 628.719i | − | 0.163949i | ||||||
\(246\) | −164.011 | + | 94.6920i | −0.0425080 | + | 0.0245420i | ||||
\(247\) | −178.175 | + | 308.609i | −0.0458989 | + | 0.0794992i | ||||
\(248\) | 1205.59 | 0.308690 | ||||||||
\(249\) | 964.467 | 0.245464 | ||||||||
\(250\) | −422.987 | + | 732.635i | −0.107008 | + | 0.185344i | ||||
\(251\) | 3657.74i | 0.919818i | 0.887966 | + | 0.459909i | \(0.152118\pi\) | ||||
−0.887966 | + | 0.459909i | \(0.847882\pi\) | |||||||
\(252\) | 1408.59 | + | 2439.76i | 0.352115 | + | 0.609882i | ||||
\(253\) | − | 3129.55i | − | 0.777680i | ||||||
\(254\) | 549.997 | − | 317.541i | 0.135866 | − | 0.0784420i | ||||
\(255\) | 568.615 | + | 984.870i | 0.139639 | + | 0.241862i | ||||
\(256\) | −1250.66 | − | 2166.21i | −0.305337 | − | 0.528860i | ||||
\(257\) | 4654.55 | + | 2687.31i | 1.12974 | + | 0.652255i | 0.943869 | − | 0.330319i | \(-0.107156\pi\) |
0.185870 | + | 0.982574i | \(0.440490\pi\) | |||||||
\(258\) | −578.483 | −0.139592 | ||||||||
\(259\) | −1739.14 | + | 4299.08i | −0.417240 | + | 1.03140i | ||||
\(260\) | −290.884 | −0.0693841 | ||||||||
\(261\) | −2046.10 | − | 1181.32i | −0.485251 | − | 0.280160i | ||||
\(262\) | −20.0348 | − | 34.7013i | −0.00472425 | − | 0.00818264i | ||||
\(263\) | 727.394 | + | 1259.88i | 0.170544 | + | 0.295391i | 0.938610 | − | 0.344980i | \(-0.112114\pi\) |
−0.768066 | + | 0.640370i | \(0.778781\pi\) | |||||||
\(264\) | 495.611 | − | 286.141i | 0.115541 | − | 0.0667075i | ||||
\(265\) | − | 2556.27i | − | 0.592567i | ||||||
\(266\) | 429.538 | + | 743.981i | 0.0990099 | + | 0.171490i | ||||
\(267\) | 625.254i | 0.143314i | ||||||||
\(268\) | −1176.49 | + | 2037.74i | −0.268155 | + | 0.464458i | ||||
\(269\) | 8297.07 | 1.88060 | 0.940299 | − | 0.340349i | \(-0.110545\pi\) | ||||
0.940299 | + | 0.340349i | \(0.110545\pi\) | |||||||
\(270\) | −602.496 | −0.135803 | ||||||||
\(271\) | −47.7760 | + | 82.7505i | −0.0107092 | + | 0.0185488i | −0.871330 | − | 0.490697i | \(-0.836742\pi\) |
0.860621 | + | 0.509246i | \(0.170076\pi\) | |||||||
\(272\) | −2369.73 | + | 1368.16i | −0.528257 | + | 0.304989i | ||||
\(273\) | − | 307.176i | − | 0.0680995i | ||||||
\(274\) | 1390.99 | + | 803.086i | 0.306688 | + | 0.177067i | ||||
\(275\) | −687.101 | + | 1190.09i | −0.150668 | + | 0.260965i | ||||
\(276\) | 3005.38 | + | 1735.16i | 0.655444 | + | 0.378421i | ||||
\(277\) | −4320.43 | + | 2494.40i | −0.937146 | + | 0.541061i | −0.889064 | − | 0.457782i | \(-0.848644\pi\) |
−0.0480814 | + | 0.998843i | \(0.515311\pi\) | |||||||
\(278\) | −1162.29 | + | 671.048i | −0.250753 | + | 0.144773i | ||||
\(279\) | −2062.88 | − | 1191.00i | −0.442656 | − | 0.255568i | ||||
\(280\) | −716.417 | + | 1240.87i | −0.152908 | + | 0.264844i | ||||
\(281\) | 2815.02 | + | 1625.25i | 0.597616 | + | 0.345034i | 0.768103 | − | 0.640326i | \(-0.221201\pi\) |
−0.170487 | + | 0.985360i | \(0.554534\pi\) | |||||||
\(282\) | 857.690i | 0.181116i | ||||||||
\(283\) | 4903.76 | − | 2831.19i | 1.03003 | − | 0.594688i | 0.113036 | − | 0.993591i | \(-0.463942\pi\) |
0.916993 | + | 0.398903i | \(0.130609\pi\) | |||||||
\(284\) | −119.464 | + | 206.918i | −0.0249609 | + | 0.0432335i | ||||
\(285\) | 1689.29 | 0.351105 | ||||||||
\(286\) | 59.3722 | 0.0122754 | ||||||||
\(287\) | 1118.73 | − | 1937.70i | 0.230093 | − | 0.398533i | ||||
\(288\) | − | 1863.66i | − | 0.381309i | ||||||
\(289\) | −1269.05 | − | 2198.06i | −0.258305 | − | 0.447397i | ||||
\(290\) | − | 588.105i | − | 0.119085i | ||||||
\(291\) | 2190.97 | − | 1264.96i | 0.441364 | − | 0.254821i | ||||
\(292\) | 2082.18 | + | 3606.44i | 0.417296 | + | 0.722777i | ||||
\(293\) | 1307.89 | + | 2265.33i | 0.260777 | + | 0.451680i | 0.966449 | − | 0.256860i | \(-0.0826878\pi\) |
−0.705671 | + | 0.708539i | \(0.749354\pi\) | |||||||
\(294\) | −123.236 | − | 71.1503i | −0.0244465 | − | 0.0141142i | ||||
\(295\) | −5637.42 | −1.11262 | ||||||||
\(296\) | 1600.94 | − | 1249.65i | 0.314367 | − | 0.245387i | ||||
\(297\) | −2843.03 | −0.555452 | ||||||||
\(298\) | −745.502 | − | 430.416i | −0.144919 | − | 0.0836688i | ||||
\(299\) | 367.819 | + | 637.081i | 0.0711422 | + | 0.123222i | ||||
\(300\) | −761.916 | − | 1319.68i | −0.146631 | − | 0.253972i | ||||
\(301\) | 5918.81 | − | 3417.23i | 1.13340 | − | 0.654371i | ||||
\(302\) | 1769.74i | 0.337210i | ||||||||
\(303\) | −2484.41 | − | 4303.12i | −0.471042 | − | 0.815868i | ||||
\(304\) | 4064.66i | 0.766855i | ||||||||
\(305\) | 853.174 | − | 1477.74i | 0.160172 | − | 0.277427i | ||||
\(306\) | −500.405 | −0.0934845 | ||||||||
\(307\) | −3928.33 | −0.730299 | −0.365149 | − | 0.930949i | \(-0.618982\pi\) | ||||
−0.365149 | + | 0.930949i | \(0.618982\pi\) | |||||||
\(308\) | −1654.52 | + | 2865.71i | −0.306087 | + | 0.530158i | ||||
\(309\) | −2982.92 | + | 1722.19i | −0.549166 | + | 0.317061i | ||||
\(310\) | − | 592.925i | − | 0.108632i | ||||||
\(311\) | −1603.67 | − | 925.878i | −0.292398 | − | 0.168816i | 0.346625 | − | 0.938004i | \(-0.387328\pi\) |
−0.639023 | + | 0.769188i | \(0.720661\pi\) | |||||||
\(312\) | −67.2609 | + | 116.499i | −0.0122048 | + | 0.0211393i | ||||
\(313\) | 4822.74 | + | 2784.41i | 0.870918 | + | 0.502825i | 0.867653 | − | 0.497170i | \(-0.165627\pi\) |
0.00326481 | + | 0.999995i | \(0.498961\pi\) | |||||||
\(314\) | −1236.80 | + | 714.068i | −0.222283 | + | 0.128335i | ||||
\(315\) | 2451.71 | − | 1415.49i | 0.438533 | − | 0.253187i | ||||
\(316\) | −8772.33 | − | 5064.71i | −1.56165 | − | 0.901620i | ||||
\(317\) | −269.865 | + | 467.420i | −0.0478143 | + | 0.0828168i | −0.888942 | − | 0.458020i | \(-0.848559\pi\) |
0.841128 | + | 0.540837i | \(0.181892\pi\) | |||||||
\(318\) | −501.057 | − | 289.285i | −0.0883581 | − | 0.0510136i | ||||
\(319\) | − | 2775.12i | − | 0.487075i | ||||||
\(320\) | −2595.94 | + | 1498.77i | −0.453493 | + | 0.261824i | ||||
\(321\) | 1592.50 | − | 2758.29i | 0.276899 | − | 0.479603i | ||||
\(322\) | 1773.45 | 0.306926 | ||||||||
\(323\) | 3527.78 | 0.607712 | ||||||||
\(324\) | −269.417 | + | 466.644i | −0.0461964 | + | 0.0800145i | ||||
\(325\) | − | 323.023i | − | 0.0551325i | ||||||
\(326\) | −142.995 | − | 247.674i | −0.0242937 | − | 0.0420779i | ||||
\(327\) | − | 4841.48i | − | 0.818759i | ||||||
\(328\) | −848.578 | + | 489.927i | −0.142850 | + | 0.0824747i | ||||
\(329\) | −5066.56 | − | 8775.54i | −0.849023 | − | 1.47055i | ||||
\(330\) | −140.728 | − | 243.748i | −0.0234752 | − | 0.0406602i | ||||
\(331\) | 327.715 | + | 189.206i | 0.0544195 | + | 0.0314191i | 0.526963 | − | 0.849888i | \(-0.323331\pi\) |
−0.472543 | + | 0.881307i | \(0.656664\pi\) | |||||||
\(332\) | 2442.21 | 0.403716 | ||||||||
\(333\) | −3973.87 | + | 556.708i | −0.653954 | + | 0.0916138i | ||||
\(334\) | 860.637 | 0.140994 | ||||||||
\(335\) | 2047.72 | + | 1182.25i | 0.333967 | + | 0.192816i | ||||
\(336\) | −1751.88 | − | 3034.34i | −0.284443 | − | 0.492669i | ||||
\(337\) | −819.020 | − | 1418.58i | −0.132388 | − | 0.229303i | 0.792208 | − | 0.610251i | \(-0.208931\pi\) |
−0.924597 | + | 0.380947i | \(0.875598\pi\) | |||||||
\(338\) | 1083.71 | − | 625.678i | 0.174396 | − | 0.100688i | ||||
\(339\) | 2518.57i | 0.403510i | ||||||||
\(340\) | 1439.84 | + | 2493.87i | 0.229665 | + | 0.397792i | ||||
\(341\) | − | 2797.87i | − | 0.444320i | ||||||
\(342\) | −371.662 | + | 643.737i | −0.0587637 | + | 0.101782i | ||||
\(343\) | −5386.51 | −0.847942 | ||||||||
\(344\) | −2993.02 | −0.469106 | ||||||||
\(345\) | 1743.66 | − | 3020.10i | 0.272102 | − | 0.471295i | ||||
\(346\) | 1916.95 | − | 1106.75i | 0.297849 | − | 0.171963i | ||||
\(347\) | − | 21.6121i | − | 0.00334351i | −0.999999 | − | 0.00167175i | \(-0.999468\pi\) | ||
0.999999 | − | 0.00167175i | \(-0.000532136\pi\) | |||||||
\(348\) | 2665.01 | + | 1538.65i | 0.410517 | + | 0.237012i | ||||
\(349\) | −5020.49 | + | 8695.75i | −0.770031 | + | 1.33373i | 0.167515 | + | 0.985870i | \(0.446426\pi\) |
−0.937545 | + | 0.347863i | \(0.886907\pi\) | |||||||
\(350\) | −674.399 | − | 389.364i | −0.102995 | − | 0.0594640i | ||||
\(351\) | 578.755 | − | 334.144i | 0.0880104 | − | 0.0508128i | ||||
\(352\) | 1895.75 | − | 1094.51i | 0.287057 | − | 0.165732i | ||||
\(353\) | 5081.22 | + | 2933.64i | 0.766135 | + | 0.442328i | 0.831494 | − | 0.555533i | \(-0.187486\pi\) |
−0.0653588 | + | 0.997862i | \(0.520819\pi\) | |||||||
\(354\) | −637.970 | + | 1105.00i | −0.0957846 | + | 0.165904i | ||||
\(355\) | 207.931 | + | 120.049i | 0.0310869 | + | 0.0179480i | ||||
\(356\) | 1583.26i | 0.235710i | ||||||||
\(357\) | −2633.55 | + | 1520.48i | −0.390427 | + | 0.225413i | ||||
\(358\) | 149.813 | − | 259.484i | 0.0221170 | − | 0.0383077i | ||||
\(359\) | −7869.97 | −1.15699 | −0.578497 | − | 0.815684i | \(-0.696361\pi\) | ||||
−0.578497 | + | 0.815684i | \(0.696361\pi\) | |||||||
\(360\) | −1239.77 | −0.181505 | ||||||||
\(361\) | −809.342 | + | 1401.82i | −0.117997 | + | 0.204377i | ||||
\(362\) | − | 2523.99i | − | 0.366459i | ||||||
\(363\) | 1351.30 | + | 2340.52i | 0.195385 | + | 0.338417i | ||||
\(364\) | − | 777.827i | − | 0.112003i | ||||||
\(365\) | 3624.10 | − | 2092.38i | 0.519710 | − | 0.300055i | ||||
\(366\) | −193.102 | − | 334.463i | −0.0275782 | − | 0.0477669i | ||||
\(367\) | 2166.86 | + | 3753.11i | 0.308199 | + | 0.533817i | 0.977969 | − | 0.208752i | \(-0.0669402\pi\) |
−0.669769 | + | 0.742569i | \(0.733607\pi\) | |||||||
\(368\) | 7266.76 | + | 4195.47i | 1.02936 | + | 0.594304i | ||||
\(369\) | 1935.99 | 0.273126 | ||||||||
\(370\) | −614.595 | − | 787.360i | −0.0863548 | − | 0.110629i | ||||
\(371\) | 6835.48 | 0.956552 | ||||||||
\(372\) | 2686.86 | + | 1551.26i | 0.374482 | + | 0.216207i | ||||
\(373\) | 386.908 | + | 670.144i | 0.0537087 | + | 0.0930262i | 0.891630 | − | 0.452765i | \(-0.149562\pi\) |
−0.837921 | + | 0.545791i | \(0.816229\pi\) | |||||||
\(374\) | −293.885 | − | 509.023i | −0.0406321 | − | 0.0703769i | ||||
\(375\) | −3852.33 | + | 2224.14i | −0.530490 | + | 0.306278i | ||||
\(376\) | 4437.60i | 0.608649i | ||||||||
\(377\) | 326.163 | + | 564.931i | 0.0445577 | + | 0.0771761i | ||||
\(378\) | − | 1611.08i | − | 0.219220i | ||||||
\(379\) | 1345.27 | − | 2330.08i | 0.182327 | − | 0.315800i | −0.760346 | − | 0.649519i | \(-0.774970\pi\) |
0.942673 | + | 0.333719i | \(0.108304\pi\) | |||||||
\(380\) | 4277.60 | 0.577463 | ||||||||
\(381\) | 3339.38 | 0.449033 | ||||||||
\(382\) | 1115.20 | − | 1931.58i | 0.149368 | − | 0.258713i | ||||
\(383\) | 5215.23 | − | 3011.02i | 0.695786 | − | 0.401712i | −0.109990 | − | 0.993933i | \(-0.535082\pi\) |
0.805776 | + | 0.592220i | \(0.201749\pi\) | |||||||
\(384\) | 3210.82i | 0.426697i | ||||||||
\(385\) | 2879.74 | + | 1662.62i | 0.381208 | + | 0.220091i | ||||
\(386\) | −428.175 | + | 741.621i | −0.0564600 | + | 0.0977915i | ||||
\(387\) | 5121.31 | + | 2956.79i | 0.672690 | + | 0.388378i | ||||
\(388\) | 5547.94 | − | 3203.10i | 0.725912 | − | 0.419106i | ||||
\(389\) | −6580.66 | + | 3799.35i | −0.857719 | + | 0.495204i | −0.863248 | − | 0.504780i | \(-0.831573\pi\) |
0.00552873 | + | 0.999985i | \(0.498240\pi\) | |||||||
\(390\) | 57.2958 | + | 33.0797i | 0.00743919 | + | 0.00429502i | ||||
\(391\) | 3641.31 | − | 6306.94i | 0.470970 | − | 0.815743i | ||||
\(392\) | −637.611 | − | 368.125i | −0.0821536 | − | 0.0474314i | ||||
\(393\) | − | 210.693i | − | 0.0270434i | ||||||
\(394\) | −1072.86 | + | 619.418i | −0.137183 | + | 0.0792027i | ||||
\(395\) | −5089.51 | + | 8815.29i | −0.648307 | + | 1.12290i | ||||
\(396\) | −2863.17 | −0.363333 | ||||||||
\(397\) | −3543.61 | −0.447981 | −0.223991 | − | 0.974591i | \(-0.571908\pi\) | ||||
−0.223991 | + | 0.974591i | \(0.571908\pi\) | |||||||
\(398\) | −655.046 | + | 1134.57i | −0.0824987 | + | 0.142892i | ||||
\(399\) | 4517.18i | 0.566772i | ||||||||
\(400\) | −1842.25 | − | 3190.87i | −0.230281 | − | 0.398859i | ||||
\(401\) | 8806.53i | 1.09670i | 0.836249 | + | 0.548350i | \(0.184744\pi\) | ||||
−0.836249 | + | 0.548350i | \(0.815256\pi\) | |||||||
\(402\) | 463.469 | − | 267.584i | 0.0575019 | − | 0.0331987i | ||||
\(403\) | 328.836 | + | 569.561i | 0.0406464 | + | 0.0704017i | ||||
\(404\) | −6290.99 | − | 10896.3i | −0.774723 | − | 1.34186i | ||||
\(405\) | 468.930 | + | 270.737i | 0.0575341 | + | 0.0332173i | ||||
\(406\) | 1572.60 | 0.192233 | ||||||||
\(407\) | −2900.12 | − | 3715.36i | −0.353203 | − | 0.452490i | ||||
\(408\) | 1331.73 | 0.161594 | ||||||||
\(409\) | −2211.68 | − | 1276.91i | −0.267385 | − | 0.154375i | 0.360314 | − | 0.932831i | \(-0.382670\pi\) |
−0.627699 | + | 0.778456i | \(0.716003\pi\) | |||||||
\(410\) | 240.952 | + | 417.341i | 0.0290238 | + | 0.0502708i | ||||
\(411\) | 4222.78 | + | 7314.07i | 0.506799 | + | 0.877802i | ||||
\(412\) | −7553.30 | + | 4360.90i | −0.903215 | + | 0.521471i | ||||
\(413\) | − | 15074.5i | − | 1.79605i | ||||||
\(414\) | 767.246 | + | 1328.91i | 0.0910823 | + | 0.157759i | ||||
\(415\) | − | 2454.17i | − | 0.290290i | ||||||
\(416\) | −257.279 | + | 445.619i | −0.0303224 | + | 0.0525199i | ||||
\(417\) | −7056.99 | −0.828735 | ||||||||
\(418\) | −873.098 | −0.102164 | ||||||||
\(419\) | −2675.34 | + | 4633.82i | −0.311930 | + | 0.540279i | −0.978780 | − | 0.204913i | \(-0.934309\pi\) |
0.666850 | + | 0.745192i | \(0.267642\pi\) | |||||||
\(420\) | −3193.30 | + | 1843.66i | −0.370994 | + | 0.214193i | ||||
\(421\) | 11971.9i | 1.38593i | 0.720973 | + | 0.692963i | \(0.243695\pi\) | ||||
−0.720973 | + | 0.692963i | \(0.756305\pi\) | |||||||
\(422\) | 1154.91 | + | 666.785i | 0.133223 | + | 0.0769161i | ||||
\(423\) | 4383.89 | − | 7593.13i | 0.503906 | − | 0.872791i | ||||
\(424\) | −2592.42 | − | 1496.73i | −0.296931 | − | 0.171433i | ||||
\(425\) | −2769.41 | + | 1598.92i | −0.316085 | + | 0.182492i | ||||
\(426\) | 47.0619 | − | 27.1712i | 0.00535249 | − | 0.00309026i | ||||
\(427\) | 3951.49 | + | 2281.40i | 0.447837 | + | 0.258559i | ||||
\(428\) | 4032.50 | − | 6984.50i | 0.455417 | − | 0.788805i | ||||
\(429\) | 270.365 | + | 156.095i | 0.0304274 | + | 0.0175672i | ||||
\(430\) | 1472.00i | 0.165084i | ||||||||
\(431\) | −1549.71 | + | 894.723i | −0.173194 | + | 0.0999937i | −0.584091 | − | 0.811688i | \(-0.698549\pi\) |
0.410897 | + | 0.911682i | \(0.365216\pi\) | |||||||
\(432\) | 3811.36 | − | 6601.47i | 0.424477 | − | 0.735216i | ||||
\(433\) | 1286.89 | 0.142826 | 0.0714132 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714132 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(434\) | 1585.49 | 0.175359 | ||||||||
\(435\) | 1546.18 | − | 2678.07i | 0.170423 | − | 0.295180i | ||||
\(436\) | − | 12259.5i | − | 1.34662i | ||||||
\(437\) | −5408.96 | − | 9368.60i | −0.592096 | − | 1.02554i | ||||
\(438\) | − | 947.154i | − | 0.103326i | ||||||
\(439\) | 1813.82 | − | 1047.21i | 0.197196 | − | 0.113851i | −0.398151 | − | 0.917320i | \(-0.630348\pi\) |
0.595347 | + | 0.803469i | \(0.297015\pi\) | |||||||
\(440\) | −728.112 | − | 1261.13i | −0.0788895 | − | 0.136641i | ||||
\(441\) | 727.339 | + | 1259.79i | 0.0785378 | + | 0.136031i | ||||
\(442\) | 119.652 | + | 69.0811i | 0.0128762 | + | 0.00743406i | ||||
\(443\) | −3464.97 | −0.371615 | −0.185808 | − | 0.982586i | \(-0.559490\pi\) | ||||
−0.185808 | + | 0.982586i | \(0.559490\pi\) | |||||||
\(444\) | 5175.90 | − | 725.102i | 0.553237 | − | 0.0775041i | ||||
\(445\) | 1591.01 | 0.169486 | ||||||||
\(446\) | 672.145 | + | 388.063i | 0.0713609 | + | 0.0412002i | ||||
\(447\) | −2263.21 | − | 3919.99i | −0.239476 | − | 0.414785i | ||||
\(448\) | −4007.73 | − | 6941.59i | −0.422650 | − | 0.732052i | ||||
\(449\) | −10634.1 | + | 6139.61i | −1.11772 | + | 0.645314i | −0.940817 | − | 0.338914i | \(-0.889940\pi\) |
−0.176900 | + | 0.984229i | \(0.556607\pi\) | |||||||
\(450\) | − | 673.803i | − | 0.0705853i | ||||||
\(451\) | 1136.99 | + | 1969.33i | 0.118712 | + | 0.205615i | ||||
\(452\) | 6377.49i | 0.663654i | ||||||||
\(453\) | −4652.83 | + | 8058.93i | −0.482580 | + | 0.835854i | ||||
\(454\) | −2751.69 | −0.284457 | ||||||||
\(455\) | −781.637 | −0.0805356 | ||||||||
\(456\) | 989.106 | − | 1713.18i | 0.101577 | − | 0.175937i | ||||
\(457\) | 10609.4 | − | 6125.36i | 1.08597 | − | 0.626985i | 0.153470 | − | 0.988153i | \(-0.450955\pi\) |
0.932501 | + | 0.361168i | \(0.117622\pi\) | |||||||
\(458\) | 1298.73i | 0.132502i | ||||||||
\(459\) | −5729.52 | − | 3307.94i | −0.582638 | − | 0.336386i | ||||
\(460\) | 4415.26 | − | 7647.45i | 0.447527 | − | 0.775140i | ||||
\(461\) | −1689.85 | − | 975.635i | −0.170725 | − | 0.0985680i | 0.412203 | − | 0.911092i | \(-0.364760\pi\) |
−0.582928 | + | 0.812524i | \(0.698093\pi\) | |||||||
\(462\) | 651.784 | − | 376.308i | 0.0656358 | − | 0.0378949i | ||||
\(463\) | 9035.95 | − | 5216.91i | 0.906989 | − | 0.523650i | 0.0275280 | − | 0.999621i | \(-0.491236\pi\) |
0.879461 | + | 0.475971i | \(0.157903\pi\) | |||||||
\(464\) | 6443.79 | + | 3720.32i | 0.644710 | + | 0.372223i | ||||
\(465\) | 1558.86 | − | 2700.02i | 0.155463 | − | 0.269270i | ||||
\(466\) | −2934.87 | − | 1694.45i | −0.291750 | − | 0.168442i | ||||
\(467\) | 1190.11i | 0.117927i | 0.998260 | + | 0.0589635i | \(0.0187796\pi\) | ||||
−0.998260 | + | 0.0589635i | \(0.981220\pi\) | |||||||
\(468\) | 582.855 | − | 336.512i | 0.0575694 | − | 0.0332377i | ||||
\(469\) | −3161.35 | + | 5475.63i | −0.311253 | + | 0.539106i | ||||
\(470\) | 2182.47 | 0.214191 | ||||||||
\(471\) | −7509.40 | −0.734639 | ||||||||
\(472\) | −3300.80 | + | 5717.15i | −0.321889 | + | 0.557527i | ||||
\(473\) | 6946.02i | 0.675218i | ||||||||
\(474\) | 1151.93 | + | 1995.20i | 0.111624 | + | 0.193339i | ||||
\(475\) | 4750.21i | 0.458851i | ||||||||
\(476\) | −6668.64 | + | 3850.14i | −0.642136 | + | 0.370737i | ||||
\(477\) | 2957.24 | + | 5122.08i | 0.283863 | + | 0.491665i | ||||
\(478\) | 1732.18 | + | 3000.23i | 0.165749 | + | 0.287086i | ||||
\(479\) | −17006.1 | − | 9818.50i | −1.62219 | − | 0.936574i | −0.986332 | − | 0.164771i | \(-0.947311\pi\) |
−0.635862 | − | 0.771803i | \(-0.719355\pi\) | |||||||
\(480\) | 2439.27 | 0.231952 | ||||||||
\(481\) | 1027.05 | + | 415.480i | 0.0973582 | + | 0.0393851i | ||||
\(482\) | −2145.49 | −0.202747 | ||||||||
\(483\) | 8075.78 | + | 4662.56i | 0.760789 | + | 0.439241i | ||||
\(484\) | 3421.74 | + | 5926.62i | 0.321350 | + | 0.556595i | ||||
\(485\) | −3218.79 | − | 5575.11i | −0.301356 | − | 0.521965i | ||||
\(486\) | 1934.35 | − | 1116.80i | 0.180543 | − | 0.104236i | ||||
\(487\) | − | 3344.98i | − | 0.311243i | −0.987817 | − | 0.155622i | \(-0.950262\pi\) | ||
0.987817 | − | 0.155622i | \(-0.0497381\pi\) | |||||||
\(488\) | −999.093 | − | 1730.48i | −0.0926779 | − | 0.160523i | ||||
\(489\) | − | 1503.78i | − | 0.139066i | ||||||
\(490\) | −181.048 | + | 313.585i | −0.0166917 | + | 0.0289109i | ||||
\(491\) | −9263.52 | −0.851440 | −0.425720 | − | 0.904855i | \(-0.639979\pi\) | ||||
−0.425720 | + | 0.904855i | \(0.639979\pi\) | |||||||
\(492\) | −2521.59 | −0.231061 | ||||||||
\(493\) | 3228.93 | − | 5592.66i | 0.294977 | − | 0.510915i | ||||
\(494\) | 177.736 | − | 102.616i | 0.0161877 | − | 0.00934599i | ||||
\(495\) | 2877.20i | 0.261253i | ||||||||
\(496\) | 6496.61 | + | 3750.82i | 0.588117 | + | 0.339550i | ||||
\(497\) | −321.013 | + | 556.010i | −0.0289726 | + | 0.0501820i | ||||
\(498\) | −481.045 | − | 277.731i | −0.0432854 | − | 0.0249909i | ||||
\(499\) | 12839.2 | − | 7412.71i | 1.15183 | − | 0.665007i | 0.202494 | − | 0.979283i | \(-0.435095\pi\) |
0.949332 | + | 0.314276i | \(0.101762\pi\) | |||||||
\(500\) | −9754.82 | + | 5631.95i | −0.872498 | + | 0.503737i | ||||
\(501\) | 3919.10 | + | 2262.69i | 0.349486 | + | 0.201776i | ||||
\(502\) | 1053.30 | − | 1824.36i | 0.0936472 | − | 0.162202i | ||||
\(503\) | 5575.51 | + | 3219.02i | 0.494234 | + | 0.285346i | 0.726329 | − | 0.687347i | \(-0.241225\pi\) |
−0.232095 | + | 0.972693i | \(0.574558\pi\) | |||||||
\(504\) | − | 3315.17i | − | 0.292995i | ||||||
\(505\) | −10949.7 | + | 6321.80i | −0.964860 | + | 0.557062i | ||||
\(506\) | −901.197 | + | 1560.92i | −0.0791761 | + | 0.137137i | ||||
\(507\) | 6579.87 | 0.576375 | ||||||||
\(508\) | 8455.93 | 0.738526 | ||||||||
\(509\) | 4346.88 | − | 7529.02i | 0.378531 | − | 0.655635i | −0.612318 | − | 0.790612i | \(-0.709763\pi\) |
0.990849 | + | 0.134977i | \(0.0430961\pi\) | |||||||
\(510\) | − | 654.962i | − | 0.0568670i | ||||||
\(511\) | 5595.04 | + | 9690.90i | 0.484364 | + | 0.838943i | ||||
\(512\) | 9922.66i | 0.856492i | ||||||||
\(513\) | −8510.87 | + | 4913.76i | −0.732484 | + | 0.422900i | ||||
\(514\) | −1547.69 | − | 2680.68i | −0.132813 | − | 0.230039i | ||||
\(515\) | 4382.26 | + | 7590.30i | 0.374962 | + | 0.649453i | ||||
\(516\) | −6670.42 | − | 3851.17i | −0.569087 | − | 0.328563i | ||||
\(517\) | 10298.5 | 0.876071 | ||||||||
\(518\) | 2105.41 | − | 1643.43i | 0.178584 | − | 0.139398i | ||||
\(519\) | 11639.0 | 0.984384 | ||||||||
\(520\) | 296.443 | + | 171.151i | 0.0249998 | + | 0.0144336i | ||||
\(521\) | 9044.83 | + | 15666.1i | 0.760578 | + | 1.31736i | 0.942553 | + | 0.334056i | \(0.108418\pi\) |
−0.181975 | + | 0.983303i | \(0.558249\pi\) | |||||||
\(522\) | 680.354 | + | 1178.41i | 0.0570465 | + | 0.0988074i | ||||
\(523\) | 8418.02 | − | 4860.15i | 0.703814 | − | 0.406347i | −0.104953 | − | 0.994477i | \(-0.533469\pi\) |
0.808766 | + | 0.588130i | \(0.200136\pi\) | |||||||
\(524\) | − | 533.515i | − | 0.0444784i | ||||||
\(525\) | −2047.35 | − | 3546.12i | −0.170198 | − | 0.294791i | ||||
\(526\) | − | 837.853i | − | 0.0694527i | ||||||
\(527\) | 3255.39 | − | 5638.51i | 0.269084 | − | 0.466067i | ||||
\(528\) | 3560.95 | 0.293505 | ||||||||
\(529\) | −10165.2 | −0.835469 | ||||||||
\(530\) | −736.112 | + | 1274.98i | −0.0603295 | + | 0.104494i | ||||
\(531\) | 11295.9 | − | 6521.69i | 0.923164 | − | 0.532989i | ||||
\(532\) | 11438.3i | 0.932171i | ||||||||
\(533\) | −462.915 | − | 267.264i | −0.0376193 | − | 0.0217195i | ||||
\(534\) | 180.051 | − | 311.857i | 0.0145909 | − | 0.0252722i | ||||
\(535\) | −7018.71 | − | 4052.25i | −0.567187 | − | 0.327466i | ||||
\(536\) | 2397.94 | − | 1384.45i | 0.193238 | − | 0.111566i | ||||
\(537\) | 1364.42 | − | 787.747i | 0.109644 | − | 0.0633031i | ||||
\(538\) | −4138.31 | − | 2389.25i | −0.331627 | − | 0.191465i | ||||
\(539\) | −854.323 | + | 1479.73i | −0.0682714 | + | 0.118250i | ||||
\(540\) | −6947.31 | − | 4011.03i | −0.553638 | − | 0.319643i | ||||
\(541\) | 10361.6i | 0.823439i | 0.911311 | + | 0.411720i | \(0.135072\pi\) | ||||
−0.911311 | + | 0.411720i | \(0.864928\pi\) | |||||||
\(542\) | 47.6583 | − | 27.5155i | 0.00377693 | − | 0.00218061i | ||||
\(543\) | 6635.82 | − | 11493.6i | 0.524439 | − | 0.908354i | ||||
\(544\) | 5093.98 | 0.401475 | ||||||||
\(545\) | −12319.6 | −0.968279 | ||||||||
\(546\) | −88.4556 | + | 153.210i | −0.00693324 | + | 0.0120087i | ||||
\(547\) | 12850.4i | 1.00446i | 0.864733 | + | 0.502232i | \(0.167488\pi\) | ||||
−0.864733 | + | 0.502232i | \(0.832512\pi\) | |||||||
\(548\) | 10692.9 | + | 18520.6i | 0.833534 | + | 1.44372i | ||||
\(549\) | 3948.00i | 0.306916i | ||||||||
\(550\) | 685.408 | − | 395.720i | 0.0531380 | − | 0.0306792i | ||||
\(551\) | −4796.39 | − | 8307.59i | −0.370840 | − | 0.642314i | ||||
\(552\) | −2041.88 | − | 3536.63i | −0.157442 | − | 0.272698i | ||||
\(553\) | −23572.2 | − | 13609.4i | −1.81264 | − | 1.04653i | ||||
\(554\) | 2873.19 | 0.220343 | ||||||||
\(555\) | −728.654 | − | 5201.25i | −0.0557290 | − | 0.397803i | ||||
\(556\) | −17869.6 | −1.36302 | ||||||||
\(557\) | −19662.7 | − | 11352.2i | −1.49575 | − | 0.863573i | −0.495764 | − | 0.868457i | \(-0.665112\pi\) |
−0.999988 | + | 0.00488411i | \(0.998445\pi\) | |||||||
\(558\) | 685.931 | + | 1188.07i | 0.0520390 | + | 0.0901342i | ||||
\(559\) | −816.372 | − | 1414.00i | −0.0617690 | − | 0.106987i | ||||
\(560\) | −7721.15 | + | 4457.81i | −0.582639 | + | 0.336387i | ||||
\(561\) | − | 3090.60i | − | 0.232594i | ||||||
\(562\) | −936.027 | − | 1621.25i | −0.0702561 | − | 0.121687i | ||||
\(563\) | 14518.8i | 1.08685i | 0.839458 | + | 0.543425i | \(0.182873\pi\) | ||||
−0.839458 | + | 0.543425i | \(0.817127\pi\) | |||||||
\(564\) | −5709.95 | + | 9889.92i | −0.426298 | + | 0.738370i | ||||
\(565\) | 6408.72 | 0.477198 | ||||||||
\(566\) | −3261.12 | −0.242182 | ||||||||
\(567\) | −723.954 | + | 1253.92i | −0.0536211 | + | 0.0928745i | ||||
\(568\) | 243.494 | − | 140.581i | 0.0179873 | − | 0.0103850i | ||||
\(569\) | − | 23900.1i | − | 1.76088i | −0.474154 | − | 0.880442i | \(-0.657246\pi\) | ||
0.474154 | − | 0.880442i | \(-0.342754\pi\) | |||||||
\(570\) | −842.563 | − | 486.454i | −0.0619142 | − | 0.0357462i | ||||
\(571\) | 10728.0 | − | 18581.5i | 0.786259 | − | 1.36184i | −0.141985 | − | 0.989869i | \(-0.545349\pi\) |
0.928244 | − | 0.371972i | \(-0.121318\pi\) | |||||||
\(572\) | 684.614 | + | 395.262i | 0.0500440 | + | 0.0288929i | ||||
\(573\) | 10156.6 | − | 5863.93i | 0.740487 | − | 0.427520i | ||||
\(574\) | −1115.98 | + | 644.309i | −0.0811497 | + | 0.0468518i | ||||
\(575\) | 8492.39 | + | 4903.08i | 0.615925 | + | 0.355605i | ||||
\(576\) | 3467.73 | − | 6006.28i | 0.250848 | − | 0.434482i | ||||
\(577\) | 2947.68 | + | 1701.84i | 0.212675 | + | 0.122788i | 0.602554 | − | 0.798078i | \(-0.294150\pi\) |
−0.389879 | + | 0.920866i | \(0.627483\pi\) | |||||||
\(578\) | 1461.76i | 0.105193i | ||||||||
\(579\) | −3899.59 | + | 2251.43i | −0.279899 | + | 0.161599i | ||||
\(580\) | 3915.22 | − | 6781.36i | 0.280294 | − | 0.485484i | ||||
\(581\) | 6562.48 | 0.468602 | ||||||||
\(582\) | −1457.05 | −0.103774 | ||||||||
\(583\) | −3473.53 | + | 6016.33i | −0.246756 | + | 0.427395i | ||||
\(584\) | − | 4900.48i | − | 0.347232i | ||||||
\(585\) | −338.160 | − | 585.710i | −0.0238995 | − | 0.0413951i | ||||
\(586\) | − | 1506.50i | − | 0.106200i | ||||||
\(587\) | 13412.7 | − | 7743.81i | 0.943101 | − | 0.544499i | 0.0521698 | − | 0.998638i | \(-0.483386\pi\) |
0.890931 | + | 0.454139i | \(0.150053\pi\) | |||||||
\(588\) | −947.346 | − | 1640.85i | −0.0664420 | − | 0.115081i | ||||
\(589\) | −4835.70 | − | 8375.68i | −0.338288 | − | 0.585932i | ||||
\(590\) | 2811.76 | + | 1623.37i | 0.196201 | + | 0.113277i | ||||
\(591\) | −6514.04 | −0.453387 | ||||||||
\(592\) | 12514.9 | − | 1753.24i | 0.868850 | − | 0.121719i | ||||
\(593\) | −19322.0 | −1.33804 | −0.669022 | − | 0.743243i | \(-0.733287\pi\) | ||||
−0.669022 | + | 0.743243i | \(0.733287\pi\) | |||||||
\(594\) | 1418.01 | + | 818.690i | 0.0979491 | + | 0.0565509i | ||||
\(595\) | 3869.00 | + | 6701.31i | 0.266577 | + | 0.461726i | ||||
\(596\) | −5730.86 | − | 9926.14i | −0.393868 | − | 0.682199i | ||||
\(597\) | −5965.80 | + | 3444.36i | −0.408985 | + | 0.236128i | ||||
\(598\) | − | 423.674i | − | 0.0289721i | ||||||
\(599\) | 9728.21 | + | 16849.7i | 0.663579 | + | 1.14935i | 0.979669 | + | 0.200623i | \(0.0642966\pi\) |
−0.316090 | + | 0.948729i | \(0.602370\pi\) | |||||||
\(600\) | 1793.20i | 0.122012i | ||||||||
\(601\) | 6618.69 | − | 11463.9i | 0.449221 | − | 0.778074i | −0.549114 | − | 0.835747i | \(-0.685035\pi\) |
0.998336 | + | 0.0576730i | \(0.0183681\pi\) | |||||||
\(602\) | −3936.15 | −0.266488 | ||||||||
\(603\) | −5470.79 | −0.369466 | ||||||||
\(604\) | −11781.8 | + | 20406.7i | −0.793701 | + | 1.37473i | ||||
\(605\) | 5955.65 | − | 3438.49i | 0.400217 | − | 0.231066i | ||||
\(606\) | 2861.68i | 0.191828i | ||||||||
\(607\) | −14603.1 | − | 8431.12i | −0.976479 | − | 0.563770i | −0.0752734 | − | 0.997163i | \(-0.523983\pi\) |
−0.901205 | + | 0.433393i | \(0.857316\pi\) | |||||||
\(608\) | 3783.41 | − | 6553.06i | 0.252364 | − | 0.437108i | ||||
\(609\) | 7161.18 | + | 4134.51i | 0.476496 | + | 0.275105i | ||||
\(610\) | −851.071 | + | 491.366i | −0.0564899 | + | 0.0326145i | ||||
\(611\) | −2096.47 | + | 1210.40i | −0.138812 | + | 0.0801430i | ||||
\(612\) | −5770.11 | − | 3331.38i | −0.381116 | − | 0.220037i | ||||
\(613\) | −1709.65 | + | 2961.20i | −0.112646 | + | 0.195109i | −0.916836 | − | 0.399263i | \(-0.869266\pi\) |
0.804190 | + | 0.594372i | \(0.202599\pi\) | |||||||
\(614\) | 1959.33 | + | 1131.22i | 0.128782 | + | 0.0743521i | ||||
\(615\) | 2533.94i | 0.166144i | ||||||||
\(616\) | 3372.27 | − | 1946.98i | 0.220572 | − | 0.127347i | ||||
\(617\) | 11718.5 | − | 20297.0i | 0.764614 | − | 1.32435i | −0.175836 | − | 0.984419i | \(-0.556263\pi\) |
0.940450 | − | 0.339931i | \(-0.110404\pi\) | |||||||
\(618\) | 1983.71 | 0.129121 | ||||||||
\(619\) | −29510.7 | −1.91621 | −0.958106 | − | 0.286413i | \(-0.907537\pi\) | ||||
−0.958106 | + | 0.286413i | \(0.907537\pi\) | |||||||
\(620\) | 3947.32 | − | 6836.95i | 0.255690 | − | 0.442869i | ||||
\(621\) | 20287.6i | 1.31097i | ||||||||
\(622\) | 533.239 | + | 923.596i | 0.0343745 | + | 0.0595383i | ||||
\(623\) | 4254.39i | 0.273593i | ||||||||
\(624\) | −724.901 | + | 418.522i | −0.0465052 | + | 0.0268498i | ||||
\(625\) | 1558.30 | + | 2699.06i | 0.0997315 | + | 0.172740i | ||||
\(626\) | −1603.62 | − | 2777.55i | −0.102386 | − | 0.177337i | ||||
\(627\) | −3975.85 | − | 2295.46i | −0.253238 | − | 0.146207i | ||||
\(628\) | −19015.2 | −1.20826 | ||||||||
\(629\) | −1521.66 | − | 10861.9i | −0.0964589 | − | 0.688540i | ||||
\(630\) | −1630.44 | −0.103109 | ||||||||
\(631\) | 19364.3 | + | 11180.0i | 1.22168 | + | 0.705339i | 0.965276 | − | 0.261231i | \(-0.0841283\pi\) |
0.256406 | + | 0.966569i | \(0.417462\pi\) | |||||||
\(632\) | 5959.98 | + | 10323.0i | 0.375119 | + | 0.649725i | ||||
\(633\) | 3506.08 | + | 6072.71i | 0.220149 | + | 0.381309i | ||||
\(634\) | 269.200 | − | 155.423i | 0.0168633 | − | 0.00973600i | ||||
\(635\) | − | 8497.34i | − | 0.531034i | ||||||
\(636\) | −3851.75 | − | 6671.43i | −0.240144 | − | 0.415942i | ||||
\(637\) | − | 401.637i | − | 0.0249819i | ||||||
\(638\) | −799.135 | + | 1384.14i | −0.0495894 | + | 0.0858914i | ||||
\(639\) | −555.519 | −0.0343912 | ||||||||
\(640\) | 8170.22 | 0.504619 | ||||||||
\(641\) | 7458.34 | − | 12918.2i | 0.459573 | − | 0.796005i | −0.539365 | − | 0.842072i | \(-0.681336\pi\) |
0.998938 | + | 0.0460676i | \(0.0146690\pi\) | |||||||
\(642\) | −1588.57 | + | 917.164i | −0.0976574 | + | 0.0563825i | ||||
\(643\) | 15243.2i | 0.934888i | 0.884023 | + | 0.467444i | \(0.154825\pi\) | ||||
−0.884023 | + | 0.467444i | \(0.845175\pi\) | |||||||
\(644\) | 20449.4 | + | 11806.5i | 1.25127 | + | 0.722422i | ||||
\(645\) | −3870.03 | + | 6703.09i | −0.236252 | + | 0.409200i | ||||
\(646\) | −1759.54 | − | 1015.87i | −0.107165 | − | 0.0618715i | ||||
\(647\) | 14501.0 | − | 8372.13i | 0.881131 | − | 0.508721i | 0.0100996 | − | 0.999949i | \(-0.496785\pi\) |
0.871031 | + | 0.491228i | \(0.163452\pi\) | |||||||
\(648\) | 549.132 | − | 317.041i | 0.0332900 | − | 0.0192200i | ||||
\(649\) | 13268.0 | + | 7660.29i | 0.802489 | + | 0.463317i | ||||
\(650\) | −93.0188 | + | 161.113i | −0.00561307 | + | 0.00972213i | ||||
\(651\) | 7219.88 | + | 4168.40i | 0.434669 | + | 0.250956i | ||||
\(652\) | − | 3807.86i | − | 0.228723i | ||||||
\(653\) | −5192.95 | + | 2998.15i | −0.311203 | + | 0.179673i | −0.647465 | − | 0.762095i | \(-0.724171\pi\) |
0.336262 | + | 0.941769i | \(0.390837\pi\) | |||||||
\(654\) | −1394.17 | + | 2414.77i | −0.0833583 | + | 0.144381i | ||||
\(655\) | −536.128 | −0.0319821 | ||||||||
\(656\) | −6097.00 | −0.362878 | ||||||||
\(657\) | −4841.17 | + | 8385.15i | −0.287476 | + | 0.497924i | ||||
\(658\) | 5835.94i | 0.345758i | ||||||||
\(659\) | 5174.58 | + | 8962.64i | 0.305877 | + | 0.529795i | 0.977456 | − | 0.211138i | \(-0.0677170\pi\) |
−0.671579 | + | 0.740933i | \(0.734384\pi\) | |||||||
\(660\) | − | 3747.50i | − | 0.221017i | ||||||
\(661\) | −14553.4 | + | 8402.40i | −0.856370 | + | 0.494426i | −0.862795 | − | 0.505554i | \(-0.831288\pi\) |
0.00642473 | + | 0.999979i | \(0.497955\pi\) | |||||||
\(662\) | −108.969 | − | 188.740i | −0.00639759 | − | 0.0110810i | ||||
\(663\) | 363.242 | + | 629.153i | 0.0212777 | + | 0.0368541i | ||||
\(664\) | −2488.88 | − | 1436.96i | −0.145463 | − | 0.0839829i | ||||
\(665\) | 11494.4 | 0.670274 | ||||||||
\(666\) | 2142.35 | + | 866.663i | 0.124646 | + | 0.0504242i | ||||
\(667\) | −19803.0 | −1.14959 | ||||||||
\(668\) | 9923.89 | + | 5729.56i | 0.574801 | + | 0.331861i | ||||
\(669\) | 2040.51 | + | 3534.26i | 0.117923 | + | 0.204249i | ||||
\(670\) | −680.891 | − | 1179.34i | −0.0392614 | − | 0.0680027i | ||||
\(671\) | −4016.00 | + | 2318.64i | −0.231052 | + | 0.133398i | ||||
\(672\) | 6522.64i | 0.374429i | ||||||||
\(673\) | 11413.2 | + | 19768.2i | 0.653709 | + | 1.13226i | 0.982216 | + | 0.187755i | \(0.0601211\pi\) |
−0.328507 | + | 0.944501i | \(0.606546\pi\) | |||||||
\(674\) | 943.393i | 0.0539141i | ||||||||
\(675\) | 4454.19 | − | 7714.88i | 0.253988 | − | 0.439920i | ||||
\(676\) | 16661.4 | 0.947966 | ||||||||
\(677\) | 9732.15 | 0.552492 | 0.276246 | − | 0.961087i | \(-0.410910\pi\) | ||||
0.276246 | + | 0.961087i | \(0.410910\pi\) | |||||||
\(678\) | 725.257 | − | 1256.18i | 0.0410816 | − | 0.0711554i | ||||
\(679\) | 14907.9 | − | 8607.09i | 0.842582 | − | 0.486465i | ||||
\(680\) | − | 3388.71i | − | 0.191104i | ||||||
\(681\) | −12530.4 | − | 7234.46i | −0.705092 | − | 0.407085i | ||||
\(682\) | −805.685 | + | 1395.49i | −0.0452365 | + | 0.0783519i | ||||
\(683\) | 3589.75 | + | 2072.54i | 0.201110 | + | 0.116111i | 0.597173 | − | 0.802112i | \(-0.296291\pi\) |
−0.396063 | + | 0.918223i | \(0.629624\pi\) | |||||||
\(684\) | −8571.17 | + | 4948.57i | −0.479133 | + | 0.276628i | ||||
\(685\) | 18611.3 | − | 10745.2i | 1.03810 | − | 0.599349i | ||||
\(686\) | 2686.62 | + | 1551.12i | 0.149527 | + | 0.0863295i | ||||
\(687\) | −3414.49 | + | 5914.07i | −0.189623 | + | 0.328437i | ||||
\(688\) | −16128.5 | − | 9311.81i | −0.893742 | − | 0.516002i | ||||
\(689\) | − | 1632.99i | − | 0.0902931i | ||||||
\(690\) | −1739.36 | + | 1004.22i | −0.0959656 | + | 0.0554058i | ||||
\(691\) | 2868.74 | − | 4968.80i | 0.157933 | − | 0.273549i | −0.776190 | − | 0.630499i | \(-0.782850\pi\) |
0.934123 | + | 0.356950i | \(0.116184\pi\) | |||||||
\(692\) | 29472.1 | 1.61902 | ||||||||
\(693\) | −7693.66 | −0.421729 | ||||||||
\(694\) | −6.22349 | + | 10.7794i | −0.000340404 | + | 0.000589597i | ||||
\(695\) | 17957.1i | 0.980076i | ||||||||
\(696\) | −1810.63 | − | 3136.10i | −0.0986088 | − | 0.170795i | ||||
\(697\) | 5291.69i | 0.287571i | ||||||||
\(698\) | 5008.12 | − | 2891.44i | 0.271576 | − | 0.156795i | ||||
\(699\) | −8909.74 | − | 15432.1i | −0.482113 | − | 0.835045i | ||||
\(700\) | −5184.28 | − | 8979.43i | −0.279925 | − | 0.484844i | ||||
\(701\) | −8837.88 | − | 5102.55i | −0.476180 | − | 0.274923i | 0.242643 | − | 0.970116i | \(-0.421986\pi\) |
−0.718823 | + | 0.695193i | \(0.755319\pi\) | |||||||
\(702\) | −384.886 | −0.0206931 | ||||||||
\(703\) | −15103.2 | − | 6109.84i | −0.810283 | − | 0.327791i | ||||
\(704\) | 8146.29 | 0.436115 | ||||||||
\(705\) | 9938.36 | + | 5737.91i | 0.530922 | + | 0.306528i | ||||
\(706\) | −1689.56 | − | 2926.41i | −0.0900674 | − | 0.156001i | ||||
\(707\) | −16904.6 | − | 29279.6i | −0.899238 | − | 1.55753i | ||||
\(708\) | −14712.7 | + | 8494.39i | −0.780986 | + | 0.450902i | ||||
\(709\) | 4631.86i | 0.245350i | 0.992447 | + | 0.122675i | \(0.0391473\pi\) | ||||
−0.992447 | + | 0.122675i | \(0.960853\pi\) | |||||||
\(710\) | −69.1396 | − | 119.753i | −0.00365459 | − | 0.00632994i | ||||
\(711\) | − | 23551.4i | − | 1.24226i | ||||||
\(712\) | 931.564 | − | 1613.52i | 0.0490335 | − | 0.0849284i | ||||
\(713\) | −19965.3 | −1.04868 | ||||||||
\(714\) | 1751.38 | 0.0917977 | ||||||||
\(715\) | 397.198 | − | 687.967i | 0.0207753 | − | 0.0359839i | ||||
\(716\) | 3454.96 | − | 1994.72i | 0.180332 | − | 0.104115i | ||||
\(717\) | 18216.3i | 0.948814i | ||||||||
\(718\) | 3925.29 | + | 2266.27i | 0.204026 | + | 0.117794i | ||||
\(719\) | −14628.7 | + | 25337.7i | −0.758776 | + | 1.31424i | 0.184699 | + | 0.982795i | \(0.440869\pi\) |
−0.943475 | + | 0.331443i | \(0.892465\pi\) | |||||||
\(720\) | −6680.80 | − | 3857.16i | −0.345804 | − | 0.199650i | ||||
\(721\) | −20296.5 | + | 11718.2i | −1.04838 | + | 0.605283i | ||||
\(722\) | 807.348 | − | 466.122i | 0.0416155 | − | 0.0240267i | ||||
\(723\) | −9769.95 | − | 5640.68i | −0.502557 | − | 0.290151i | ||||
\(724\) | 16803.1 | − | 29103.9i | 0.862546 | − | 1.49397i | ||||
\(725\) | 7530.61 | + | 4347.80i | 0.385765 | + | 0.222722i | ||||
\(726\) | − | 1556.50i | − | 0.0795690i | ||||||
\(727\) | −14581.6 | + | 8418.67i | −0.743880 | + | 0.429479i | −0.823478 | − | 0.567348i | \(-0.807969\pi\) |
0.0795985 | + | 0.996827i | \(0.474636\pi\) | |||||||
\(728\) | −457.661 | + | 792.692i | −0.0232995 | + | 0.0403559i | ||||
\(729\) | 9847.43 | 0.500301 | ||||||||
\(730\) | −2410.12 | −0.122195 | ||||||||
\(731\) | −8081.87 | + | 13998.2i | −0.408918 | + | 0.708266i | ||||
\(732\) | − | 5142.21i | − | 0.259647i | ||||||
\(733\) | 1186.20 | + | 2054.55i | 0.0597724 | + | 0.103529i | 0.894363 | − | 0.447342i | \(-0.147629\pi\) |
−0.834591 | + | 0.550870i | \(0.814296\pi\) | |||||||
\(734\) | − | 2495.91i | − | 0.125512i | ||||||
\(735\) | −1648.89 | + | 951.986i | −0.0827485 | + | 0.0477749i | ||||
\(736\) | −7810.34 | − | 13527.9i | −0.391159 | − | 0.677507i | ||||
\(737\) | −3212.96 | − | 5565.01i | −0.160585 | − | 0.278141i | ||||
\(738\) | −965.609 | − | 557.495i | −0.0481634 | − | 0.0278071i | ||||
\(739\) | 10708.3 | 0.533031 | 0.266516 | − | 0.963831i | \(-0.414128\pi\) | ||||
0.266516 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(740\) | −1845.09 | − | 13170.5i | −0.0916577 | − | 0.654268i | ||||
\(741\) | 1079.15 | 0.0535001 | ||||||||
\(742\) | −3409.32 | − | 1968.37i | −0.168679 | − | 0.0973870i | ||||
\(743\) | −6405.33 | − | 11094.4i | −0.316270 | − | 0.547796i | 0.663437 | − | 0.748233i | \(-0.269097\pi\) |
−0.979707 | + | 0.200437i | \(0.935764\pi\) | |||||||
\(744\) | −1825.47 | − | 3161.81i | −0.0899529 | − | 0.155803i | ||||
\(745\) | −9974.75 | + | 5758.93i | −0.490533 | + | 0.283209i | ||||
\(746\) | − | 445.662i | − | 0.0218724i | ||||||
\(747\) | 2839.13 | + | 4917.51i | 0.139061 | + | 0.240860i | ||||
\(748\) | − | 7825.98i | − | 0.382548i | ||||||
\(749\) | 10835.8 | − | 18768.1i | 0.528612 | − | 0.915583i | ||||
\(750\) | 2561.89 | 0.124729 | ||||||||
\(751\) | 9312.36 | 0.452480 | 0.226240 | − | 0.974072i | \(-0.427357\pi\) | ||||
0.226240 | + | 0.974072i | \(0.427357\pi\) | |||||||
\(752\) | −13806.2 | + | 23913.0i | −0.669494 | + | 1.15960i | ||||
\(753\) | 9592.84 | − | 5538.43i | 0.464253 | − | 0.268037i | ||||
\(754\) | − | 375.692i | − | 0.0181458i | ||||||
\(755\) | 20506.7 | + | 11839.5i | 0.988495 | + | 0.570708i | ||||
\(756\) | 10725.5 | − | 18577.2i | 0.515984 | − | 0.893711i | ||||
\(757\) | 5004.09 | + | 2889.11i | 0.240260 | + | 0.138714i | 0.615296 | − | 0.788296i | \(-0.289036\pi\) |
−0.375036 | + | 0.927010i | \(0.622370\pi\) | |||||||
\(758\) | −1341.96 | + | 774.778i | −0.0643035 | + | 0.0371256i | ||||
\(759\) | −8207.61 | + | 4738.66i | −0.392513 | + | 0.226617i | ||||
\(760\) | −4359.34 | − | 2516.87i | −0.208066 | − | 0.120127i | ||||
\(761\) | −6471.11 | + | 11208.3i | −0.308249 | + | 0.533903i | −0.977979 | − | 0.208701i | \(-0.933076\pi\) |
0.669730 | + | 0.742604i | \(0.266410\pi\) | |||||||
\(762\) | −1665.57 | − | 961.620i | −0.0791830 | − | 0.0457163i | ||||
\(763\) | − | 32942.6i | − | 1.56305i | ||||||
\(764\) | 25718.5 | − | 14848.6i | 1.21788 | − | 0.703144i | ||||
\(765\) | −3347.69 | + | 5798.37i | −0.158217 | + | 0.274040i | ||||
\(766\) | −3468.26 | −0.163594 | ||||||||
\(767\) | −3601.29 | −0.169537 | ||||||||
\(768\) | −3787.42 | + | 6560.01i | −0.177952 | + | 0.308221i | ||||
\(769\) | 17609.9i | 0.825787i | 0.910779 | + | 0.412893i | \(0.135482\pi\) | ||||
−0.910779 | + | 0.412893i | \(0.864518\pi\) | |||||||
\(770\) | −957.548 | − | 1658.52i | −0.0448151 | − | 0.0776221i | ||||
\(771\) | − | 16276.1i | − | 0.760273i | ||||||
\(772\) | −9874.47 | + | 5701.03i | −0.460350 | + | 0.265783i | ||||
\(773\) | −7548.50 | − | 13074.4i | −0.351230 | − | 0.608348i | 0.635235 | − | 0.772319i | \(-0.280903\pi\) |
−0.986465 | + | 0.163971i | \(0.947570\pi\) | |||||||
\(774\) | −1702.90 | − | 2949.50i | −0.0790819 | − | 0.136974i | ||||
\(775\) | 7592.33 | + | 4383.44i | 0.351903 | + | 0.203171i | ||||
\(776\) | −7538.61 | −0.348738 | ||||||||
\(777\) | 13908.2 | − | 1948.43i | 0.642154 | − | 0.0899607i | ||||
\(778\) | 4376.30 | 0.201668 | ||||||||
\(779\) | 6807.39 | + | 3930.25i | 0.313094 | + | 0.180765i | ||||
\(780\) | 440.447 | + | 762.877i | 0.0202186 | + | 0.0350197i | ||||
\(781\) | −326.253 | − | 565.086i | −0.0149478 | − | 0.0258904i | ||||
\(782\) | −3632.34 | + | 2097.13i | −0.166103 | + | 0.0958993i | ||||
\(783\) | 17990.0i | 0.821084i | ||||||||
\(784\) | −2290.61 | − | 3967.45i | −0.104346 | − | 0.180733i | ||||
\(785\) | 19108.3i | 0.868797i | ||||||||
\(786\) | −60.6721 | + | 105.087i | −0.00275331 | + | 0.00476887i | ||||
\(787\) | −22809.7 | −1.03314 | −0.516568 | − | 0.856246i | \(-0.672791\pi\) | ||||
−0.516568 | + | 0.856246i | \(0.672791\pi\) | |||||||
\(788\) | −16494.8 | −0.745687 | ||||||||
\(789\) | 2202.79 | − | 3815.35i | 0.0993936 | − | 0.172155i | ||||
\(790\) | 5076.97 | − | 2931.19i | 0.228646 | − | 0.132009i | ||||
\(791\) | 17137.0i | 0.770318i | ||||||||
\(792\) | 2917.89 | + | 1684.64i | 0.130912 | + | 0.0755823i | ||||
\(793\) | 545.023 | − | 944.008i | 0.0244065 | − | 0.0422733i | ||||
\(794\) | 1767.44 | + | 1020.43i | 0.0789975 | + | 0.0456092i | ||||
\(795\) | −6704.10 | + | 3870.61i | −0.299082 | + | 0.172675i | ||||
\(796\) | −15106.5 | + | 8721.75i | −0.672658 | + | 0.388360i | ||||
\(797\) | 16475.4 | + | 9512.05i | 0.732230 | + | 0.422753i | 0.819237 | − | 0.573455i | \(-0.194397\pi\) |
−0.0870076 | + | 0.996208i | \(0.527730\pi\) | |||||||
\(798\) | 1300.78 | − | 2253.02i | 0.0577033 | − | 0.0999451i | ||||
\(799\) | 20754.5 | + | 11982.6i | 0.918950 | + | 0.530556i | ||||
\(800\) | 6859.12i | 0.303133i | ||||||||
\(801\) | −3187.97 | + | 1840.58i | −0.140626 | + | 0.0811905i | ||||
\(802\) | 2535.96 | − | 4392.41i | 0.111656 | − | 0.193393i | ||||
\(803\) | −11372.7 | −0.499795 | ||||||||
\(804\) | 7125.61 | 0.312563 | ||||||||
\(805\) | 11864.3 | − | 20549.5i | 0.519455 | − | 0.899722i | ||||
\(806\) | − | 378.772i | − | 0.0165529i | ||||||
\(807\) | −12563.1 | − | 21760.0i | −0.548010 | − | 0.949181i | ||||
\(808\) | 14806.0i | 0.644647i | ||||||||
\(809\) | 34849.9 | − | 20120.6i | 1.51453 | − | 0.874415i | 0.514676 | − | 0.857385i | \(-0.327912\pi\) |
0.999855 | − | 0.0170306i | \(-0.00542126\pi\) | |||||||
\(810\) | −155.925 | − | 270.070i | −0.00676375 | − | 0.0117152i | ||||
\(811\) | −2858.32 | − | 4950.76i | −0.123760 | − | 0.214358i | 0.797488 | − | 0.603335i | \(-0.206162\pi\) |
−0.921248 | + | 0.388977i | \(0.872829\pi\) | |||||||
\(812\) | 18133.4 | + | 10469.3i | 0.783694 | + | 0.452466i | ||||
\(813\) | 289.364 | 0.0124827 | ||||||||
\(814\) | 376.600 | + | 2688.23i | 0.0162160 | + | 0.115752i | ||||
\(815\) | −3826.51 | −0.164462 | ||||||||
\(816\) | 7176.33 | + | 4143.26i | 0.307870 | + | 0.177749i | ||||
\(817\) | 12005.2 | + | 20793.5i | 0.514085 | + | 0.890421i | ||||
\(818\) | 735.409 | + | 1273.77i | 0.0314339 | + | 0.0544452i | ||||
\(819\) | 1566.19 | − | 904.243i | 0.0668221 | − | 0.0385797i | ||||
\(820\) | 6416.41i | 0.273257i | ||||||||
\(821\) | 8080.48 | + | 13995.8i | 0.343496 | + | 0.594953i | 0.985079 | − | 0.172100i | \(-0.0550553\pi\) |
−0.641583 | + | 0.767054i | \(0.721722\pi\) | |||||||
\(822\) | − | 4864.03i | − | 0.206390i | ||||||
\(823\) | −12483.5 | + | 21622.1i | −0.528734 | + | 0.915795i | 0.470704 | + | 0.882291i | \(0.344000\pi\) |
−0.999439 | + | 0.0335039i | \(0.989333\pi\) | |||||||
\(824\) | 10263.5 | 0.433916 | ||||||||
\(825\) | 4161.54 | 0.175620 | ||||||||
\(826\) | −4340.91 | + | 7518.69i | −0.182857 | + | 0.316717i | ||||
\(827\) | 7820.05 | − | 4514.91i | 0.328815 | − | 0.189841i | −0.326500 | − | 0.945197i | \(-0.605869\pi\) |
0.655315 | + | 0.755356i | \(0.272536\pi\) | |||||||
\(828\) | 20431.3i | 0.857533i | ||||||||
\(829\) | −15760.9 | − | 9099.54i | −0.660310 | − | 0.381230i | 0.132085 | − | 0.991238i | \(-0.457833\pi\) |
−0.792395 | + | 0.610008i | \(0.791166\pi\) | |||||||
\(830\) | −706.712 | + | 1224.06i | −0.0295546 | + | 0.0511901i | ||||
\(831\) | 13083.7 | + | 7553.88i | 0.546172 | + | 0.315332i | ||||
\(832\) | −1658.34 | + | 957.442i | −0.0691016 | + | 0.0398958i | ||||
\(833\) | −3443.41 | + | 1988.05i | −0.143226 | + | 0.0826914i | ||||
\(834\) | 3519.80 | + | 2032.16i | 0.146140 | + | 0.0843740i | ||||
\(835\) | 5757.63 | − | 9972.50i | 0.238624 | − | 0.413308i | ||||
\(836\) | −10067.6 | − | 5812.53i | −0.416501 | − | 0.240467i | ||||
\(837\) | 18137.4i | 0.749010i | ||||||||
\(838\) | 2668.74 | − | 1540.80i | 0.110012 | − | 0.0635156i | ||||
\(839\) | −1402.20 | + | 2428.68i | −0.0576988 | + | 0.0999372i | −0.893432 | − | 0.449198i | \(-0.851710\pi\) |
0.835733 | + | 0.549136i | \(0.185043\pi\) | |||||||
\(840\) | 4339.10 | 0.178230 | ||||||||
\(841\) | 6828.74 | 0.279993 | ||||||||
\(842\) | 3447.47 | − | 5971.20i | 0.141102 | − | 0.244396i | ||||
\(843\) | − | 9843.62i | − | 0.402173i | ||||||
\(844\) | 8878.05 | + | 15377.2i | 0.362080 | + | 0.627140i | ||||
\(845\) | − | 16743.1i | − | 0.681631i | ||||||
\(846\) | −4373.09 | + | 2524.81i | −0.177719 | + | 0.102606i | ||||
\(847\) | 9194.57 | + | 15925.5i | 0.372998 | + | 0.646052i | ||||
\(848\) | −9313.22 | − | 16131.0i | −0.377143 | − | 0.653231i | ||||
\(849\) | −14850.2 | − | 8573.79i | −0.600305 | − | 0.346586i | ||||
\(850\) | 1841.72 | 0.0743183 | ||||||||
\(851\) | −26512.4 | + | 20695.0i | −1.06796 | + | 0.833625i | ||||
\(852\) | 723.554 | 0.0290945 | ||||||||
\(853\) | −9249.67 | − | 5340.30i | −0.371281 | − | 0.214359i | 0.302737 | − | 0.953074i | \(-0.402100\pi\) |
−0.674018 | + | 0.738715i | \(0.735433\pi\) | |||||||
\(854\) | −1313.92 | − | 2275.77i | −0.0526480 | − | 0.0911890i | ||||
\(855\) | 4972.81 | + | 8613.15i | 0.198908 | + | 0.344519i | ||||
\(856\) | −8219.13 | + | 4745.31i | −0.328182 | + | 0.189476i | ||||
\(857\) | − | 46362.1i | − | 1.84796i | −0.382446 | − | 0.923978i | \(-0.624918\pi\) | ||
0.382446 | − | 0.923978i | \(-0.375082\pi\) | |||||||
\(858\) | −89.8995 | − | 155.711i | −0.00357706 | − | 0.00619565i | ||||
\(859\) | − | 7813.32i | − | 0.310346i | −0.987887 | − | 0.155173i | \(-0.950407\pi\) | ||
0.987887 | − | 0.155173i | \(-0.0495935\pi\) | |||||||
\(860\) | −9799.64 | + | 16973.5i | −0.388564 | + | 0.673012i | ||||
\(861\) | −6775.79 | −0.268198 | ||||||||
\(862\) | 1030.59 | 0.0407217 | ||||||||
\(863\) | 12022.4 | − | 20823.5i | 0.474216 | − | 0.821366i | −0.525348 | − | 0.850887i | \(-0.676065\pi\) |
0.999564 | + | 0.0295214i | \(0.00939831\pi\) | |||||||
\(864\) | −12289.4 | + | 7095.28i | −0.483904 | + | 0.279382i | ||||
\(865\) | − | 29616.4i | − | 1.16415i | ||||||
\(866\) | −641.858 | − | 370.577i | −0.0251862 | − | 0.0145412i | ||||
\(867\) | −3843.11 | + | 6656.46i | −0.150541 | + | 0.260744i | ||||
\(868\) | 18282.1 | + | 10555.2i | 0.714901 | + | 0.412749i | ||||
\(869\) | 23957.0 | − | 13831.6i | 0.935195 | − | 0.539935i | ||||
\(870\) | −1542.37 | + | 890.489i | −0.0601050 | + | 0.0347016i | ||||
\(871\) | 1308.12 | + | 755.244i | 0.0508886 | + | 0.0293806i | ||||
\(872\) | −7213.29 | + | 12493.8i | −0.280130 | + | 0.485199i | ||||
\(873\) | 12899.2 | + | 7447.37i | 0.500083 | + | 0.288723i | ||||
\(874\) | 6230.34i | 0.241126i | ||||||||
\(875\) | −26212.3 | + | 15133.7i | −1.01273 | + | 0.584698i | ||||
\(876\) | 6305.54 | − | 10921.5i | 0.243201 | − | 0.421237i | ||||
\(877\) | −28699.1 | −1.10502 | −0.552508 | − | 0.833508i | \(-0.686329\pi\) | ||||
−0.552508 | + | 0.833508i | \(0.686329\pi\) | |||||||
\(878\) | −1206.23 | −0.0463649 | ||||||||
\(879\) | 3960.73 | − | 6860.19i | 0.151982 | − | 0.263241i | ||||
\(880\) | − | 9061.15i | − | 0.347104i | ||||||
\(881\) | 5522.34 | + | 9564.97i | 0.211183 | + | 0.365780i | 0.952085 | − | 0.305833i | \(-0.0989350\pi\) |
−0.740902 | + | 0.671613i | \(0.765602\pi\) | |||||||
\(882\) | − | 837.789i | − | 0.0319839i | ||||||
\(883\) | −3022.84 | + | 1745.24i | −0.115206 | + | 0.0665141i | −0.556496 | − | 0.830851i | \(-0.687854\pi\) |
0.441290 | + | 0.897365i | \(0.354521\pi\) | |||||||
\(884\) | 919.795 | + | 1593.13i | 0.0349955 | + | 0.0606141i | ||||
\(885\) | 8536.00 | + | 14784.8i | 0.324220 | + | 0.561565i | ||||
\(886\) | 1728.21 | + | 997.785i | 0.0655310 | + | 0.0378344i | ||||
\(887\) | −12623.4 | −0.477849 | −0.238924 | − | 0.971038i | \(-0.576795\pi\) | ||||
−0.238924 | + | 0.971038i | \(0.576795\pi\) | |||||||
\(888\) | −5701.45 | − | 2306.45i | −0.215459 | − | 0.0871616i | ||||
\(889\) | 22722.0 | 0.857223 | ||||||||
\(890\) | −793.547 | − | 458.154i | −0.0298874 | − | 0.0172555i | ||||
\(891\) | −735.771 | − | 1274.39i | −0.0276647 | − | 0.0479167i | ||||
\(892\) | 5166.94 | + | 8949.41i | 0.193949 | + | 0.335929i | ||||
\(893\) | 30829.6 | − | 17799.5i | 1.15529 | − | 0.667007i | ||||
\(894\) | 2606.89i | 0.0975249i | ||||||||
\(895\) | −2004.49 | − | 3471.88i | −0.0748634 | − | 0.129667i | ||||
\(896\) | 21847.3i | 0.814583i | ||||||||
\(897\) | 1113.88 | − | 1929.30i | 0.0414619 | − | 0.0718142i | ||||
\(898\) | 7071.94 | 0.262799 | ||||||||
\(899\) | −17704.2 | −0.656805 | ||||||||
\(900\) | 4485.75 | − | 7769.54i | 0.166139 | − | 0.287761i | ||||
\(901\) | −14000.3 | + | 8083.09i | −0.517667 | + | 0.298875i | ||||
\(902\) | − | 1309.65i | − | 0.0483444i | ||||||
\(903\) | −17924.1 | − | 10348.5i | −0.660552 | − | 0.381370i | ||||
\(904\) | 3752.41 | − | 6499.36i | 0.138057 | − | 0.239121i | ||||
\(905\) | −29246.4 | − | 16885.4i | −1.07424 | − | 0.620210i | ||||
\(906\) | 4641.36 | − | 2679.69i | 0.170197 | − | 0.0982635i | ||||
\(907\) | 32184.1 | − | 18581.5i | 1.17823 | − | 0.680252i | 0.222627 | − | 0.974904i | \(-0.428537\pi\) |
0.955605 | + | 0.294652i | \(0.0952036\pi\) | |||||||
\(908\) | −31729.4 | − | 18319.0i | −1.15967 | − | 0.669534i | ||||
\(909\) | 14626.8 | − | 25334.4i | 0.533709 | − | 0.924412i | ||||
\(910\) | 389.855 | + | 225.083i | 0.0142017 | + | 0.00819938i | ||||
\(911\) | − | 4423.83i | − | 0.160887i | −0.996759 | − | 0.0804436i | \(-0.974366\pi\) | ||
0.996759 | − | 0.0804436i | \(-0.0256337\pi\) | |||||||
\(912\) | 10660.0 | − | 6154.57i | 0.387049 | − | 0.223463i | ||||
\(913\) | −3334.80 | + | 5776.05i | −0.120883 | + | 0.209375i | ||||
\(914\) | −7055.53 | −0.255335 | ||||||||
\(915\) | −5167.39 | −0.186698 | ||||||||
\(916\) | −8646.13 | + | 14975.5i | −0.311873 | + | 0.540181i | ||||
\(917\) | − | 1433.61i | − | 0.0516271i | ||||||
\(918\) | 1905.13 | + | 3299.79i | 0.0684954 | + | 0.118637i | ||||
\(919\) | − | 6523.46i | − | 0.234156i | −0.993123 | − | 0.117078i | \(-0.962647\pi\) | ||
0.993123 | − | 0.117078i | \(-0.0373527\pi\) | |||||||
\(920\) | −8999.27 | + | 5195.73i | −0.322497 | + | 0.186194i | ||||
\(921\) | 5948.15 | + | 10302.5i | 0.212810 | + | 0.368598i | ||||
\(922\) | 561.895 | + | 973.230i | 0.0200705 | + | 0.0347632i | ||||
\(923\) | 132.830 | + | 76.6896i | 0.00473690 | + | 0.00273485i | ||||
\(924\) | 10020.9 | 0.356777 | ||||||||
\(925\) | 14625.7 | − | 2048.94i | 0.519880 | − | 0.0728311i | ||||
\(926\) | −6009.12 | −0.213253 | ||||||||
\(927\) | −17561.8 | − | 10139.3i | −0.622228 | − | 0.359243i | ||||
\(928\) | −6925.80 | − | 11995.8i | −0.244990 | − | 0.424335i | ||||
\(929\) | −1098.12 | − | 1902.00i | −0.0387816 | − | 0.0671717i | 0.845983 | − | 0.533210i | \(-0.179014\pi\) |
−0.884765 | + | 0.466038i | \(0.845681\pi\) | |||||||
\(930\) | −1555.02 | + | 897.789i | −0.0548290 | + | 0.0316555i | ||||
\(931\) | 5906.28i | 0.207917i | ||||||||
\(932\) | −22561.1 | − | 39077.0i | −0.792933 | − | 1.37340i | ||||
\(933\) | 5607.74i | 0.196773i | ||||||||
\(934\) | 342.710 | − | 593.591i | 0.0120062 | − | 0.0207954i | ||||
\(935\) | −7864.31 | −0.275070 | ||||||||
\(936\) | −791.991 | −0.0276571 | ||||||||
\(937\) | 9903.16 | − | 17152.8i | 0.345274 | − | 0.598033i | −0.640129 | − | 0.768267i | \(-0.721119\pi\) |
0.985404 | + | 0.170234i | \(0.0544525\pi\) | |||||||
\(938\) | 3153.56 | − | 1820.71i | 0.109773 | − | 0.0633777i | ||||
\(939\) | − | 16864.3i | − | 0.586096i | ||||||
\(940\) | 25165.8 | + | 14529.5i | 0.873209 | + | 0.504148i | ||||
\(941\) | −5195.05 | + | 8998.09i | −0.179972 | + | 0.311721i | −0.941871 | − | 0.335975i | \(-0.890934\pi\) |
0.761899 | + | 0.647696i | \(0.224267\pi\) | |||||||
\(942\) | 3745.45 | + | 2162.44i | 0.129547 | + | 0.0747940i | ||||
\(943\) | 14052.9 | − | 8113.47i | 0.485288 | − | 0.280181i | ||||
\(944\) | −35574.1 | + | 20538.7i | −1.22653 | + | 0.708135i | ||||
\(945\) | −18668.2 | − | 10778.1i | −0.642619 | − | 0.371017i | ||||
\(946\) | 2000.20 | − | 3464.45i | 0.0687443 | − | 0.119069i | ||||
\(947\) | −44689.4 | − | 25801.4i | −1.53348 | − | 0.885358i | −0.999197 | − | 0.0400547i | \(-0.987247\pi\) |
−0.534287 | − | 0.845303i | \(-0.679420\pi\) | |||||||
\(948\) | 30675.3i | 1.05093i | ||||||||
\(949\) | 2315.15 | − | 1336.65i | 0.0791916 | − | 0.0457213i | ||||
\(950\) | 1367.89 | − | 2369.25i | 0.0467159 | − | 0.0809144i | ||||
\(951\) | 1634.48 | 0.0557327 | ||||||||
\(952\) | 9061.44 | 0.308491 | ||||||||
\(953\) | 3275.82 | − | 5673.88i | 0.111347 | − | 0.192859i | −0.804966 | − | 0.593321i | \(-0.797817\pi\) |
0.916314 | + | 0.400461i | \(0.131150\pi\) | |||||||
\(954\) | − | 3406.31i | − | 0.115601i | ||||||
\(955\) | −14921.3 | − | 25844.4i | −0.505593 | − | 0.875713i | ||||
\(956\) | 46127.0i | 1.56052i | ||||||||
\(957\) | −7278.08 | + | 4202.00i | −0.245838 | + | 0.141935i | ||||
\(958\) | 5654.75 | + | 9794.31i | 0.190706 | + | 0.330313i | ||||
\(959\) | 28732.9 | + | 49766.8i | 0.967501 | + | 1.67576i | ||||
\(960\) | 7861.39 | + | 4538.78i | 0.264297 | + | 0.152592i | ||||
\(961\) | 11941.7 | 0.400849 | ||||||||
\(962\) | −392.615 | − | 502.980i | −0.0131584 | − | 0.0168573i | ||||
\(963\) | 18751.5 | 0.627476 | ||||||||
\(964\) | −24739.3 | − | 14283.3i | −0.826556 | − | 0.477212i | ||||
\(965\) | 5728.95 | + | 9922.84i | 0.191110 | + | 0.331013i | ||||
\(966\) | −2685.29 | − | 4651.07i | −0.0894388 | − | 0.154913i | ||||
\(967\) | 14762.6 | − | 8523.18i | 0.490933 | − | 0.283441i | −0.234028 | − | 0.972230i | \(-0.575191\pi\) |
0.724962 | + | 0.688789i | \(0.241857\pi\) | |||||||
\(968\) | − | 8053.17i | − | 0.267395i | ||||||
\(969\) | −5341.65 | − | 9252.01i | −0.177088 | − | 0.306726i | ||||
\(970\) | 3707.58i | 0.122725i | ||||||||
\(971\) | −12817.2 | + | 22200.0i | −0.423607 | + | 0.733709i | −0.996289 | − | 0.0860682i | \(-0.972570\pi\) |
0.572682 | + | 0.819778i | \(0.305903\pi\) | |||||||
\(972\) | 29739.7 | 0.981378 | ||||||||
\(973\) | −48017.6 | −1.58209 | ||||||||
\(974\) | −963.233 | + | 1668.37i | −0.0316879 | + | 0.0548850i | ||||
\(975\) | −847.164 | + | 489.110i | −0.0278266 | + | 0.0160657i | ||||
\(976\) | − | 12433.4i | − | 0.407771i | ||||||
\(977\) | 6212.56 | + | 3586.83i | 0.203437 | + | 0.117454i | 0.598257 | − | 0.801304i | \(-0.295860\pi\) |
−0.394821 | + | 0.918758i | \(0.629193\pi\) | |||||||
\(978\) | −433.035 | + | 750.039i | −0.0141584 | + | 0.0245231i | ||||
\(979\) | −3744.55 | − | 2161.92i | −0.122244 | − | 0.0705773i | ||||
\(980\) | −4175.29 | + | 2410.61i | −0.136097 | + | 0.0785755i | ||||
\(981\) | 24685.2 | − | 14252.0i | 0.803401 | − | 0.463844i | ||||
\(982\) | 4620.35 | + | 2667.56i | 0.150144 | + | 0.0866856i | ||||
\(983\) | −16315.7 | + | 28259.7i | −0.529390 | + | 0.916931i | 0.470022 | + | 0.882655i | \(0.344246\pi\) |
−0.999412 | + | 0.0342764i | \(0.989087\pi\) | |||||||
\(984\) | 2569.78 | + | 1483.66i | 0.0832536 | + | 0.0480665i | ||||
\(985\) | 16575.5i | 0.536183i | ||||||||
\(986\) | −3220.97 | + | 1859.63i | −0.104033 | + | 0.0600635i | ||||
\(987\) | −15343.2 | + | 26575.3i | −0.494814 | + | 0.857042i | ||||
\(988\) | 2732.61 | 0.0879917 | ||||||||
\(989\) | 49566.1 | 1.59364 | ||||||||
\(990\) | 828.528 | − | 1435.05i | 0.0265983 | − | 0.0460697i | ||||
\(991\) | − | 38672.1i | − | 1.23962i | −0.784754 | − | 0.619808i | \(-0.787211\pi\) | ||
0.784754 | − | 0.619808i | \(-0.212789\pi\) | |||||||
\(992\) | −6982.57 | − | 12094.2i | −0.223485 | − | 0.387087i | ||||
\(993\) | − | 1145.96i | − | 0.0366223i | ||||||
\(994\) | 320.222 | − | 184.880i | 0.0102181 | − | 0.00589943i | ||||
\(995\) | 8764.47 | + | 15180.5i | 0.279249 | + | 0.483673i | ||||
\(996\) | −3697.91 | − | 6404.98i | −0.117643 | − | 0.203764i | ||||
\(997\) | 26081.5 | + | 15058.2i | 0.828496 | + | 0.478333i | 0.853338 | − | 0.521359i | \(-0.174575\pi\) |
−0.0248413 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(998\) | −8538.37 | −0.270819 | ||||||||
\(999\) | 18800.3 | + | 24085.1i | 0.595410 | + | 0.762782i |
(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 | 37.4.e.a.27.4 | yes | 16 | |
3.2 | odd | 2 | 333.4.s.c.64.5 | 16 | |||
37.11 | even | 6 | inner | 37.4.e.a.11.4 | ✓ | 16 | |
37.14 | odd | 12 | 1369.4.a.g.1.7 | 16 | |||
37.23 | odd | 12 | 1369.4.a.g.1.10 | 16 | |||
111.11 | odd | 6 | 333.4.s.c.307.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.4.e.a.11.4 | ✓ | 16 | 37.11 | even | 6 | inner | |
37.4.e.a.27.4 | yes | 16 | 1.1 | even | 1 | trivial | |
333.4.s.c.64.5 | 16 | 3.2 | odd | 2 | |||
333.4.s.c.307.5 | 16 | 111.11 | odd | 6 | |||
1369.4.a.g.1.7 | 16 | 37.14 | odd | 12 | |||
1369.4.a.g.1.10 | 16 | 37.23 | odd | 12 |