Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + 209529 x^{6} - 55412 x^{5} + 765088 x^{4} + 276096 x^{3} + 1572480 x^{2} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(2.13089 + 3.69081i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.d.76.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.13089 | + | 3.69081i | −0.753383 | + | 1.30490i | 0.192791 | + | 0.981240i | \(0.438246\pi\) |
−0.946174 | + | 0.323658i | \(0.895087\pi\) | |||||||
\(3\) | −4.39640 | + | 2.76977i | −0.846088 | + | 0.533043i | ||||
\(4\) | −5.08138 | − | 8.80120i | −0.635172 | − | 1.10015i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.854448 | − | 22.1284i | −0.0581378 | − | 1.50564i | ||||
\(7\) | 15.3820 | − | 26.6423i | 0.830548 | − | 1.43855i | −0.0670561 | − | 0.997749i | \(-0.521361\pi\) |
0.897604 | − | 0.440802i | \(-0.145306\pi\) | |||||||
\(8\) | 9.21718 | 0.407346 | ||||||||
\(9\) | 11.6567 | − | 24.3541i | 0.431731 | − | 0.902003i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.3573 | + | 35.2599i | −0.557996 | + | 0.966478i | 0.439667 | + | 0.898161i | \(0.355096\pi\) |
−0.997664 | + | 0.0683175i | \(0.978237\pi\) | |||||||
\(12\) | 46.7171 | + | 24.6194i | 1.12384 | + | 0.592250i | ||||
\(13\) | 31.6089 | + | 54.7482i | 0.674364 | + | 1.16803i | 0.976654 | + | 0.214817i | \(0.0689155\pi\) |
−0.302290 | + | 0.953216i | \(0.597751\pi\) | |||||||
\(14\) | 65.5545 | + | 113.544i | 1.25144 | + | 2.16756i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 21.0102 | − | 36.3908i | 0.328285 | − | 0.568606i | ||||
\(17\) | 6.58990 | 0.0940168 | 0.0470084 | − | 0.998894i | \(-0.485031\pi\) | ||||
0.0470084 | + | 0.998894i | \(0.485031\pi\) | |||||||
\(18\) | 65.0470 | + | 94.9186i | 0.851763 | + | 1.24292i | ||||
\(19\) | 75.3803 | 0.910180 | 0.455090 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455090 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.16789 | + | 159.735i | 0.0640926 | + | 1.65986i | ||||
\(22\) | −86.7584 | − | 150.270i | −0.840770 | − | 1.45626i | ||||
\(23\) | −31.1814 | − | 54.0077i | −0.282686 | − | 0.489626i | 0.689360 | − | 0.724419i | \(-0.257892\pi\) |
−0.972045 | + | 0.234793i | \(0.924559\pi\) | |||||||
\(24\) | −40.5225 | + | 25.5295i | −0.344651 | + | 0.217133i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −269.420 | −2.03222 | ||||||||
\(27\) | 16.2075 | + | 139.357i | 0.115524 | + | 0.993305i | ||||
\(28\) | −312.646 | −2.11016 | ||||||||
\(29\) | −24.8042 | + | 42.9621i | −0.158828 | + | 0.275099i | −0.934446 | − | 0.356104i | \(-0.884105\pi\) |
0.775618 | + | 0.631202i | \(0.217438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.5021 | − | 89.2043i | −0.298389 | − | 0.516824i | 0.677379 | − | 0.735634i | \(-0.263116\pi\) |
−0.975767 | + | 0.218810i | \(0.929783\pi\) | |||||||
\(32\) | 126.410 | + | 218.948i | 0.698321 | + | 1.20953i | ||||
\(33\) | −8.16291 | − | 211.402i | −0.0430600 | − | 1.11516i | ||||
\(34\) | −14.0423 | + | 24.3221i | −0.0708306 | + | 0.122682i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −273.577 | + | 21.1590i | −1.26656 | + | 0.0979582i | ||||
\(37\) | 282.029 | 1.25312 | 0.626559 | − | 0.779374i | \(-0.284463\pi\) | ||||
0.626559 | + | 0.779374i | \(0.284463\pi\) | |||||||
\(38\) | −160.627 | + | 278.214i | −0.685714 | + | 1.18769i | ||||
\(39\) | −290.606 | − | 153.146i | −1.19318 | − | 0.628794i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 78.7700 | + | 136.434i | 0.300044 | + | 0.519692i | 0.976146 | − | 0.217117i | \(-0.0696653\pi\) |
−0.676102 | + | 0.736808i | \(0.736332\pi\) | |||||||
\(42\) | −602.695 | − | 317.613i | −2.21423 | − | 1.16688i | ||||
\(43\) | −168.907 | + | 292.555i | −0.599025 | + | 1.03754i | 0.393940 | + | 0.919136i | \(0.371112\pi\) |
−0.992965 | + | 0.118406i | \(0.962222\pi\) | |||||||
\(44\) | 413.773 | 1.41770 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 265.776 | 0.851882 | ||||||||
\(47\) | 22.2579 | − | 38.5518i | 0.0690777 | − | 0.119646i | −0.829418 | − | 0.558629i | \(-0.811328\pi\) |
0.898496 | + | 0.438983i | \(0.144661\pi\) | |||||||
\(48\) | 8.42472 | + | 218.182i | 0.0253334 | + | 0.656081i | ||||
\(49\) | −301.710 | − | 522.577i | −0.879620 | − | 1.52355i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28.9719 | + | 18.2525i | −0.0795465 | + | 0.0501150i | ||||
\(52\) | 321.234 | − | 556.393i | 0.856675 | − | 1.48380i | ||||
\(53\) | −26.2752 | −0.0680978 | −0.0340489 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340489 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(54\) | −548.876 | − | 237.135i | −1.38319 | − | 0.597592i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 141.778 | − | 245.567i | 0.338320 | − | 0.585988i | ||||
\(57\) | −331.402 | + | 208.786i | −0.770093 | + | 0.485165i | ||||
\(58\) | −105.710 | − | 183.095i | −0.239317 | − | 0.414509i | ||||
\(59\) | 212.963 | + | 368.863i | 0.469923 | + | 0.813930i | 0.999409 | − | 0.0343889i | \(-0.0109485\pi\) |
−0.529486 | + | 0.848319i | \(0.677615\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −425.297 | + | 736.637i | −0.892684 | + | 1.54617i | −0.0560400 | + | 0.998429i | \(0.517847\pi\) |
−0.836644 | + | 0.547746i | \(0.815486\pi\) | |||||||
\(62\) | 438.981 | 0.899204 | ||||||||
\(63\) | −469.546 | − | 685.176i | −0.939004 | − | 1.37022i | ||||
\(64\) | −741.296 | −1.44784 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 797.638 | + | 420.346i | 1.48761 | + | 0.783955i | ||||
\(67\) | 48.1538 | + | 83.4048i | 0.0878048 | + | 0.152082i | 0.906583 | − | 0.422028i | \(-0.138681\pi\) |
−0.818778 | + | 0.574110i | \(0.805348\pi\) | |||||||
\(68\) | −33.4858 | − | 57.9990i | −0.0597168 | − | 0.103433i | ||||
\(69\) | 286.675 | + | 151.075i | 0.500169 | + | 0.263583i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 952.164 | 1.59156 | 0.795782 | − | 0.605583i | \(-0.207060\pi\) | ||||
0.795782 | + | 0.605583i | \(0.207060\pi\) | |||||||
\(72\) | 107.442 | − | 224.476i | 0.175864 | − | 0.367427i | ||||
\(73\) | 50.8558 | 0.0815373 | 0.0407686 | − | 0.999169i | \(-0.487019\pi\) | ||||
0.0407686 | + | 0.999169i | \(0.487019\pi\) | |||||||
\(74\) | −600.973 | + | 1040.92i | −0.944077 | + | 1.63519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −383.036 | − | 663.437i | −0.578121 | − | 1.00134i | ||||
\(77\) | 626.271 | + | 1084.73i | 0.926886 | + | 1.60541i | ||||
\(78\) | 1184.48 | − | 746.233i | 1.71944 | − | 1.08326i | ||||
\(79\) | 98.6395 | − | 170.849i | 0.140479 | − | 0.243316i | −0.787198 | − | 0.616700i | \(-0.788469\pi\) |
0.927677 | + | 0.373384i | \(0.121803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −457.241 | − | 567.778i | −0.627217 | − | 0.778844i | ||||
\(82\) | −671.400 | −0.904192 | ||||||||
\(83\) | −98.8693 | + | 171.247i | −0.130751 | + | 0.226467i | −0.923966 | − | 0.382474i | \(-0.875072\pi\) |
0.793215 | + | 0.608941i | \(0.208405\pi\) | |||||||
\(84\) | 1374.52 | − | 865.959i | 1.78539 | − | 1.12481i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −719.844 | − | 1246.81i | −0.902590 | − | 1.56333i | ||||
\(87\) | −9.94603 | − | 257.581i | −0.0122566 | − | 0.317420i | ||||
\(88\) | −187.637 | + | 324.997i | −0.227298 | + | 0.393691i | ||||
\(89\) | 1364.54 | 1.62519 | 0.812593 | − | 0.582832i | \(-0.198056\pi\) | ||||
0.812593 | + | 0.582832i | \(0.198056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1944.83 | 2.24037 | ||||||||
\(92\) | −316.889 | + | 548.868i | −0.359108 | + | 0.621993i | ||||
\(93\) | 473.499 | + | 249.529i | 0.527953 | + | 0.278225i | ||||
\(94\) | 94.8583 | + | 164.299i | 0.104084 | + | 0.180279i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1162.18 | − | 612.458i | −1.23557 | − | 0.651132i | ||||
\(97\) | −715.579 | + | 1239.42i | −0.749031 | + | 1.29736i | 0.199256 | + | 0.979947i | \(0.436147\pi\) |
−0.948288 | + | 0.317413i | \(0.897186\pi\) | |||||||
\(98\) | 2571.64 | 2.65076 | ||||||||
\(99\) | 621.422 | + | 906.799i | 0.630862 | + | 0.920573i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −553.808 | + | 959.224i | −0.545604 | + | 0.945013i | 0.452965 | + | 0.891528i | \(0.350366\pi\) |
−0.998569 | + | 0.0534851i | \(0.982967\pi\) | |||||||
\(102\) | −5.63073 | − | 145.824i | −0.00546593 | − | 0.141556i | ||||
\(103\) | 264.437 | + | 458.018i | 0.252969 | + | 0.438154i | 0.964342 | − | 0.264660i | \(-0.0852597\pi\) |
−0.711373 | + | 0.702814i | \(0.751926\pi\) | |||||||
\(104\) | 291.345 | + | 504.624i | 0.274699 | + | 0.475793i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 55.9896 | − | 96.9769i | 0.0513037 | − | 0.0888607i | ||||
\(107\) | −490.910 | −0.443533 | −0.221766 | − | 0.975100i | \(-0.571182\pi\) | ||||
−0.221766 | + | 0.975100i | \(0.571182\pi\) | |||||||
\(108\) | 1144.15 | − | 850.770i | 1.01941 | − | 0.758013i | ||||
\(109\) | −351.634 | −0.308994 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1239.91 | + | 781.157i | −1.06025 | + | 0.667965i | ||||
\(112\) | −646.357 | − | 1119.52i | −0.545313 | − | 0.944509i | ||||
\(113\) | 881.226 | + | 1526.33i | 0.733618 | + | 1.27066i | 0.955327 | + | 0.295550i | \(0.0955030\pi\) |
−0.221710 | + | 0.975113i | \(0.571164\pi\) | |||||||
\(114\) | −64.4085 | − | 1668.04i | −0.0529159 | − | 1.37041i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 504.158 | 0.403533 | ||||||||
\(117\) | 1701.80 | − | 131.620i | 1.34471 | − | 0.104002i | ||||
\(118\) | −1815.20 | −1.41613 | ||||||||
\(119\) | 101.366 | − | 175.570i | 0.0780854 | − | 0.135248i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −163.340 | − | 282.914i | −0.122720 | − | 0.212557i | ||||
\(122\) | −1812.52 | − | 3139.38i | −1.34507 | − | 2.32972i | ||||
\(123\) | −724.195 | − | 381.642i | −0.530882 | − | 0.279769i | ||||
\(124\) | −523.403 | + | 906.561i | −0.379056 | + | 0.656545i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3529.40 | − | 272.971i | 2.49543 | − | 0.193001i | ||||
\(127\) | 1506.12 | 1.05234 | 0.526169 | − | 0.850380i | \(-0.323628\pi\) | ||||
0.526169 | + | 0.850380i | \(0.323628\pi\) | |||||||
\(128\) | 568.343 | − | 984.399i | 0.392460 | − | 0.679761i | ||||
\(129\) | −67.7286 | − | 1754.03i | −0.0462262 | − | 1.19716i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −637.562 | − | 1104.29i | −0.425222 | − | 0.736506i | 0.571219 | − | 0.820798i | \(-0.306471\pi\) |
−0.996441 | + | 0.0842915i | \(0.973137\pi\) | |||||||
\(132\) | −1819.11 | + | 1146.06i | −1.19950 | + | 0.755692i | ||||
\(133\) | 1159.50 | − | 2008.31i | 0.755948 | − | 1.30934i | ||||
\(134\) | −410.441 | −0.264603 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 60.7403 | 0.0382973 | ||||||||
\(137\) | 719.712 | − | 1246.58i | 0.448826 | − | 0.777389i | −0.549484 | − | 0.835504i | \(-0.685176\pi\) |
0.998310 | + | 0.0581150i | \(0.0185090\pi\) | |||||||
\(138\) | −1168.46 | + | 736.140i | −0.720768 | + | 0.454090i | ||||
\(139\) | 1269.75 | + | 2199.27i | 0.774811 | + | 1.34201i | 0.934901 | + | 0.354909i | \(0.115488\pi\) |
−0.160090 | + | 0.987102i | \(0.551178\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.92502 | + | 231.139i | 0.00533065 | + | 0.138052i | ||||
\(142\) | −2028.96 | + | 3514.25i | −1.19906 | + | 2.07683i | ||||
\(143\) | −2573.89 | −1.50517 | ||||||||
\(144\) | −641.353 | − | 935.882i | −0.371153 | − | 0.541598i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −108.368 | + | 187.699i | −0.0614288 | + | 0.106398i | ||||
\(147\) | 2773.86 | + | 1461.79i | 1.55635 | + | 0.820180i | ||||
\(148\) | −1433.10 | − | 2482.20i | −0.795945 | − | 1.37862i | ||||
\(149\) | −46.8796 | − | 81.1979i | −0.0257754 | − | 0.0446442i | 0.852850 | − | 0.522156i | \(-0.174872\pi\) |
−0.878625 | + | 0.477512i | \(0.841539\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534.065 | − | 925.027i | 0.287825 | − | 0.498527i | −0.685465 | − | 0.728105i | \(-0.740401\pi\) |
0.973290 | + | 0.229578i | \(0.0737345\pi\) | |||||||
\(152\) | 694.794 | 0.370758 | ||||||||
\(153\) | 76.8166 | − | 160.491i | 0.0405899 | − | 0.0848034i | ||||
\(154\) | −5338.06 | −2.79320 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 128.809 | + | 3335.87i | 0.0661087 | + | 1.71207i | ||||
\(157\) | 90.8574 | + | 157.370i | 0.0461861 | + | 0.0799966i | 0.888194 | − | 0.459468i | \(-0.151960\pi\) |
−0.842008 | + | 0.539465i | \(0.818627\pi\) | |||||||
\(158\) | 420.380 | + | 728.119i | 0.211668 | + | 0.366621i | ||||
\(159\) | 115.517 | − | 72.7764i | 0.0576167 | − | 0.0362990i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1918.52 | −0.939136 | ||||||||
\(162\) | 3069.89 | − | 477.719i | 1.48885 | − | 0.231686i | ||||
\(163\) | 1103.07 | 0.530056 | 0.265028 | − | 0.964241i | \(-0.414619\pi\) | ||||
0.265028 | + | 0.964241i | \(0.414619\pi\) | |||||||
\(164\) | 800.520 | − | 1386.54i | 0.381159 | − | 0.660187i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −421.359 | − | 729.816i | −0.197011 | − | 0.341233i | ||||
\(167\) | −2020.85 | − | 3500.22i | −0.936396 | − | 1.62189i | −0.772126 | − | 0.635470i | \(-0.780806\pi\) |
−0.164270 | − | 0.986415i | \(-0.552527\pi\) | |||||||
\(168\) | 56.8506 | + | 1472.31i | 0.0261078 | + | 0.676137i | ||||
\(169\) | −899.745 | + | 1558.40i | −0.409534 | + | 0.709333i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 878.687 | − | 1835.82i | 0.392953 | − | 0.820985i | ||||
\(172\) | 3433.12 | 1.52194 | ||||||||
\(173\) | −1373.88 | + | 2379.63i | −0.603780 | + | 1.04578i | 0.388463 | + | 0.921465i | \(0.373006\pi\) |
−0.992243 | + | 0.124314i | \(0.960327\pi\) | |||||||
\(174\) | 971.875 | + | 512.167i | 0.423435 | + | 0.223145i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 855.423 | + | 1481.64i | 0.366363 | + | 0.634560i | ||||
\(177\) | −1957.94 | − | 1031.81i | −0.831456 | − | 0.438168i | ||||
\(178\) | −2907.69 | + | 5036.27i | −1.22439 | + | 2.12070i | ||||
\(179\) | −2838.32 | −1.18517 | −0.592587 | − | 0.805506i | \(-0.701893\pi\) | ||||
−0.592587 | + | 0.805506i | \(0.701893\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3442.25 | 1.41359 | 0.706796 | − | 0.707417i | \(-0.250140\pi\) | ||||
0.706796 | + | 0.707417i | \(0.250140\pi\) | |||||||
\(182\) | −4144.21 | + | 7177.99i | −1.68785 | + | 2.92345i | ||||
\(183\) | −170.537 | − | 4416.53i | −0.0688876 | − | 1.78404i | ||||
\(184\) | −287.405 | − | 497.799i | −0.115151 | − | 0.199447i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1929.94 | + | 1215.88i | −0.760806 | + | 0.479314i | ||||
\(187\) | −134.153 | + | 232.359i | −0.0524610 | + | 0.0908652i | ||||
\(188\) | −452.403 | −0.175505 | ||||||||
\(189\) | 3962.10 | + | 1711.77i | 1.52487 | + | 0.658801i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 373.148 | − | 646.311i | 0.141361 | − | 0.244845i | −0.786648 | − | 0.617402i | \(-0.788185\pi\) |
0.928010 | + | 0.372557i | \(0.121519\pi\) | |||||||
\(192\) | 3259.04 | − | 2053.22i | 1.22500 | − | 0.771763i | ||||
\(193\) | 53.9538 | + | 93.4506i | 0.0201227 | + | 0.0348535i | 0.875911 | − | 0.482472i | \(-0.160261\pi\) |
−0.855789 | + | 0.517326i | \(0.826928\pi\) | |||||||
\(194\) | −3049.64 | − | 5282.13i | −1.12861 | − | 1.95482i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3066.20 | + | 5310.82i | −1.11742 | + | 1.93543i | ||||
\(197\) | 3361.02 | 1.21555 | 0.607774 | − | 0.794110i | \(-0.292063\pi\) | ||||
0.607774 | + | 0.794110i | \(0.292063\pi\) | |||||||
\(198\) | −4671.00 | + | 361.264i | −1.67653 | + | 0.129666i | ||||
\(199\) | 1368.99 | 0.487663 | 0.243831 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243831 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −442.716 | − | 233.306i | −0.155357 | − | 0.0818714i | ||||
\(202\) | −2360.21 | − | 4088.00i | −0.822097 | − | 1.42391i | ||||
\(203\) | 763.074 | + | 1321.68i | 0.263829 | + | 0.456965i | ||||
\(204\) | 307.861 | + | 162.239i | 0.105660 | + | 0.0556815i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2253.94 | −0.762329 | ||||||||
\(207\) | −1678.78 | + | 129.840i | −0.563688 | + | 0.0435966i | ||||
\(208\) | 2656.44 | 0.885534 | ||||||||
\(209\) | −1534.54 | + | 2657.90i | −0.507877 | + | 0.879669i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1251.27 | − | 2167.27i | −0.408252 | − | 0.707114i | 0.586442 | − | 0.809991i | \(-0.300528\pi\) |
−0.994694 | + | 0.102878i | \(0.967195\pi\) | |||||||
\(212\) | 133.514 | + | 231.254i | 0.0432538 | + | 0.0749178i | ||||
\(213\) | −4186.10 | + | 2637.28i | −1.34660 | + | 0.848372i | ||||
\(214\) | 1046.07 | − | 1811.85i | 0.334150 | − | 0.578765i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 149.388 | + | 1284.48i | 0.0470581 | + | 0.404619i | ||||
\(217\) | −3168.81 | −0.991305 | ||||||||
\(218\) | 749.292 | − | 1297.81i | 0.232791 | − | 0.403206i | ||||
\(219\) | −223.583 | + | 140.859i | −0.0689877 | + | 0.0434629i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 208.299 | + | 360.785i | 0.0634015 | + | 0.109815i | ||||
\(222\) | −240.979 | − | 6240.85i | −0.0728535 | − | 1.88675i | ||||
\(223\) | 937.263 | − | 1623.39i | 0.281452 | − | 0.487489i | −0.690291 | − | 0.723532i | \(-0.742517\pi\) |
0.971743 | + | 0.236043i | \(0.0758507\pi\) | |||||||
\(224\) | 7777.72 | 2.31996 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7511.18 | −2.21078 | ||||||||
\(227\) | 2539.37 | − | 4398.32i | 0.742484 | − | 1.28602i | −0.208877 | − | 0.977942i | \(-0.566981\pi\) |
0.951361 | − | 0.308078i | \(-0.0996859\pi\) | |||||||
\(228\) | 3521.55 | + | 1855.82i | 1.02290 | + | 0.539055i | ||||
\(229\) | −432.933 | − | 749.861i | −0.124930 | − | 0.216385i | 0.796776 | − | 0.604275i | \(-0.206537\pi\) |
−0.921706 | + | 0.387890i | \(0.873204\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5757.80 | − | 3034.30i | −1.63998 | − | 0.864252i | ||||
\(232\) | −228.625 | + | 395.990i | −0.0646981 | + | 0.112060i | ||||
\(233\) | −1142.10 | −0.321122 | −0.160561 | − | 0.987026i | \(-0.551330\pi\) | ||||
−0.160561 | + | 0.987026i | \(0.551330\pi\) | |||||||
\(234\) | −3140.56 | + | 6561.48i | −0.877371 | + | 1.83307i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2164.29 | − | 3748.66i | 0.596964 | − | 1.03397i | ||||
\(237\) | 39.5527 | + | 1024.33i | 0.0108406 | + | 0.280748i | ||||
\(238\) | 431.998 | + | 748.242i | 0.117657 | + | 0.203787i | ||||
\(239\) | 1574.68 | + | 2727.43i | 0.426183 | + | 0.738171i | 0.996530 | − | 0.0832330i | \(-0.0265246\pi\) |
−0.570347 | + | 0.821404i | \(0.693191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2252.18 | + | 3900.90i | −0.601975 | + | 1.04265i | 0.390547 | + | 0.920583i | \(0.372286\pi\) |
−0.992522 | + | 0.122068i | \(0.961047\pi\) | |||||||
\(242\) | 1392.24 | 0.369821 | ||||||||
\(243\) | 3582.83 | + | 1229.72i | 0.945839 | + | 0.324637i | ||||
\(244\) | 8644.39 | 2.26803 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2951.75 | − | 1859.63i | 0.765027 | − | 0.481973i | ||||
\(247\) | 2382.69 | + | 4126.94i | 0.613793 | + | 1.06312i | ||||
\(248\) | −474.704 | − | 822.212i | −0.121547 | − | 0.210526i | ||||
\(249\) | −39.6448 | − | 1026.72i | −0.0100899 | − | 0.261307i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 886.861 | 0.223021 | 0.111510 | − | 0.993763i | \(-0.464431\pi\) | ||||
0.111510 | + | 0.993763i | \(0.464431\pi\) | |||||||
\(252\) | −3644.43 | + | 7614.21i | −0.911023 | + | 1.90337i | ||||
\(253\) | 2539.08 | 0.630950 | ||||||||
\(254\) | −3209.38 | + | 5558.81i | −0.792813 | + | 1.37319i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −543.033 | − | 940.561i | −0.132576 | − | 0.229629i | ||||
\(257\) | 1131.02 | + | 1958.98i | 0.274517 | + | 0.475478i | 0.970013 | − | 0.243052i | \(-0.0781486\pi\) |
−0.695496 | + | 0.718530i | \(0.744815\pi\) | |||||||
\(258\) | 6618.09 | + | 3487.66i | 1.59699 | + | 0.841598i | ||||
\(259\) | 4338.17 | − | 7513.92i | 1.04077 | − | 1.80267i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 757.166 | + | 1104.88i | 0.179569 | + | 0.262032i | ||||
\(262\) | 5434.30 | 1.28142 | ||||||||
\(263\) | 3640.31 | − | 6305.20i | 0.853503 | − | 1.47831i | −0.0245245 | − | 0.999699i | \(-0.507807\pi\) |
0.878027 | − | 0.478611i | \(-0.158859\pi\) | |||||||
\(264\) | −75.2391 | − | 1948.53i | −0.0175403 | − | 0.454257i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4941.52 | + | 8558.96i | 1.13904 | + | 1.97287i | ||||
\(267\) | −5999.09 | + | 3779.48i | −1.37505 | + | 0.866293i | ||||
\(268\) | 489.375 | − | 847.622i | 0.111542 | − | 0.193197i | ||||
\(269\) | −106.781 | −0.0242028 | −0.0121014 | − | 0.999927i | \(-0.503852\pi\) | ||||
−0.0121014 | + | 0.999927i | \(0.503852\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5908.85 | 1.32449 | 0.662246 | − | 0.749287i | \(-0.269603\pi\) | ||||
0.662246 | + | 0.749287i | \(0.269603\pi\) | |||||||
\(272\) | 138.455 | − | 239.811i | 0.0308643 | − | 0.0534585i | ||||
\(273\) | −8550.25 | + | 5386.73i | −1.89555 | + | 1.19421i | ||||
\(274\) | 3067.25 | + | 5312.64i | 0.676276 | + | 1.17134i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −127.067 | − | 3290.75i | −0.0277120 | − | 0.717681i | ||||
\(277\) | 1645.04 | − | 2849.30i | 0.356827 | − | 0.618042i | −0.630602 | − | 0.776106i | \(-0.717192\pi\) |
0.987429 | + | 0.158064i | \(0.0505254\pi\) | |||||||
\(278\) | −10822.8 | −2.33492 | ||||||||
\(279\) | −2772.83 | + | 214.456i | −0.595000 | + | 0.0460184i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −169.861 | + | 294.209i | −0.0360608 | + | 0.0624591i | −0.883493 | − | 0.468445i | \(-0.844814\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(282\) | −872.107 | − | 459.590i | −0.184160 | − | 0.0970504i | ||||
\(283\) | 1299.83 | + | 2251.37i | 0.273028 | + | 0.472898i | 0.969636 | − | 0.244554i | \(-0.0786415\pi\) |
−0.696608 | + | 0.717452i | \(0.745308\pi\) | |||||||
\(284\) | −4838.30 | − | 8380.19i | −1.01092 | − | 1.75096i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5484.67 | − | 9499.73i | 1.13397 | − | 1.96409i | ||||
\(287\) | 4846.55 | 0.996804 | ||||||||
\(288\) | 6805.80 | − | 526.373i | 1.39248 | − | 0.107697i | ||||
\(289\) | −4869.57 | −0.991161 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −286.934 | − | 7430.98i | −0.0578020 | − | 1.49695i | ||||
\(292\) | −258.418 | − | 447.592i | −0.0517902 | − | 0.0897033i | ||||
\(293\) | 89.0427 | + | 154.227i | 0.0177540 | + | 0.0307509i | 0.874766 | − | 0.484546i | \(-0.161015\pi\) |
−0.857012 | + | 0.515297i | \(0.827682\pi\) | |||||||
\(294\) | −11306.0 | + | 7122.86i | −2.24278 | + | 1.41297i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2599.52 | 0.510452 | ||||||||
\(297\) | −5243.65 | − | 2265.45i | −1.02447 | − | 0.442609i | ||||
\(298\) | 399.581 | 0.0776749 | ||||||||
\(299\) | 1971.22 | − | 3414.25i | 0.381266 | − | 0.660372i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5196.24 | + | 9000.16i | 0.995038 | + | 1.72346i | ||||
\(302\) | 2276.07 | + | 3942.26i | 0.433685 | + | 0.751164i | ||||
\(303\) | −222.067 | − | 5751.06i | −0.0421037 | − | 1.09039i | ||||
\(304\) | 1583.76 | − | 2743.15i | 0.298798 | − | 0.517534i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 428.653 | + | 625.504i | 0.0800800 | + | 0.116855i | ||||
\(307\) | −1537.60 | −0.285848 | −0.142924 | − | 0.989734i | \(-0.545651\pi\) | ||||
−0.142924 | + | 0.989734i | \(0.545651\pi\) | |||||||
\(308\) | 6364.64 | − | 11023.9i | 1.17746 | − | 2.03943i | ||||
\(309\) | −2431.18 | − | 1281.20i | −0.447589 | − | 0.235874i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −472.662 | − | 818.674i | −0.0861807 | − | 0.149269i | 0.819713 | − | 0.572774i | \(-0.194133\pi\) |
−0.905894 | + | 0.423505i | \(0.860800\pi\) | |||||||
\(312\) | −2678.57 | − | 1411.57i | −0.486038 | − | 0.256137i | ||||
\(313\) | 992.767 | − | 1719.52i | 0.179280 | − | 0.310521i | −0.762354 | − | 0.647160i | \(-0.775957\pi\) |
0.941634 | + | 0.336638i | \(0.109290\pi\) | |||||||
\(314\) | −774.428 | −0.139183 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2004.90 | −0.356913 | ||||||||
\(317\) | −2591.62 | + | 4488.81i | −0.459179 | + | 0.795321i | −0.998918 | − | 0.0465112i | \(-0.985190\pi\) |
0.539739 | + | 0.841833i | \(0.318523\pi\) | |||||||
\(318\) | 22.4508 | + | 581.428i | 0.00395906 | + | 0.102531i | ||||
\(319\) | −1009.89 | − | 1749.19i | −0.177251 | − | 0.307008i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2158.24 | − | 1359.71i | 0.375268 | − | 0.236422i | ||||
\(322\) | 4088.16 | − | 7080.91i | 0.707529 | − | 1.22548i | ||||
\(323\) | 496.748 | 0.0855722 | ||||||||
\(324\) | −2673.71 | + | 6909.37i | −0.458455 | + | 1.18473i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2350.52 | + | 4071.22i | −0.399336 | + | 0.691670i | ||||
\(327\) | 1545.92 | − | 973.945i | 0.261437 | − | 0.164707i | ||||
\(328\) | 726.037 | + | 1257.53i | 0.122222 | + | 0.211694i | ||||
\(329\) | −684.741 | − | 1186.01i | −0.114745 | − | 0.198744i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1086.68 | − | 1882.19i | 0.180451 | − | 0.312551i | −0.761583 | − | 0.648067i | \(-0.775578\pi\) |
0.942034 | + | 0.335517i | \(0.108911\pi\) | |||||||
\(332\) | 2009.57 | 0.332197 | ||||||||
\(333\) | 3287.54 | − | 6868.56i | 0.541009 | − | 1.13032i | ||||
\(334\) | 17224.8 | 2.82186 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5942.47 | + | 3131.61i | 0.964846 | + | 0.508463i | ||||
\(337\) | −3925.16 | − | 6798.57i | −0.634472 | − | 1.09894i | −0.986627 | − | 0.162995i | \(-0.947884\pi\) |
0.352155 | − | 0.935942i | \(-0.385449\pi\) | |||||||
\(338\) | −3834.52 | − | 6641.58i | −0.617071 | − | 1.06880i | ||||
\(339\) | −8101.81 | − | 4269.56i | −1.29802 | − | 0.684043i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4193.78 | 0.665999 | ||||||||
\(342\) | 4903.26 | + | 7154.99i | 0.775257 | + | 1.13128i | ||||
\(343\) | −8011.53 | −1.26117 | ||||||||
\(344\) | −1556.85 | + | 2696.54i | −0.244010 | + | 0.422638i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5855.16 | − | 10141.4i | −0.909756 | − | 1.57574i | ||||
\(347\) | −4686.12 | − | 8116.60i | −0.724969 | − | 1.25568i | −0.958987 | − | 0.283451i | \(-0.908521\pi\) |
0.234018 | − | 0.972232i | \(-0.424813\pi\) | |||||||
\(348\) | −2216.48 | + | 1396.40i | −0.341425 | + | 0.215101i | ||||
\(349\) | 588.952 | − | 1020.10i | 0.0903321 | − | 0.156460i | −0.817319 | − | 0.576186i | \(-0.804540\pi\) |
0.907651 | + | 0.419726i | \(0.137874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7117.23 | + | 5292.25i | −1.08231 | + | 0.804784i | ||||
\(352\) | −10293.4 | −1.55864 | ||||||||
\(353\) | −3631.06 | + | 6289.19i | −0.547484 | + | 0.948271i | 0.450962 | + | 0.892543i | \(0.351081\pi\) |
−0.998446 | + | 0.0557274i | \(0.982252\pi\) | |||||||
\(354\) | 7980.37 | − | 5027.70i | 1.19817 | − | 0.754856i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6933.77 | − | 12009.6i | −1.03227 | − | 1.78795i | ||||
\(357\) | 40.6458 | + | 1052.64i | 0.00602578 | + | 0.156055i | ||||
\(358\) | 6048.15 | − | 10475.7i | 0.892890 | − | 1.54653i | ||||
\(359\) | −1939.95 | −0.285199 | −0.142600 | − | 0.989780i | \(-0.545546\pi\) | ||||
−0.142600 | + | 0.989780i | \(0.545546\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1176.81 | −0.171572 | ||||||||
\(362\) | −7335.05 | + | 12704.7i | −1.06498 | + | 1.84459i | ||||
\(363\) | 1501.72 | + | 791.388i | 0.217134 | + | 0.114427i | ||||
\(364\) | −9882.41 | − | 17116.8i | −1.42302 | − | 2.46474i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16664.0 | + | 8781.72i | 2.37989 | + | 1.25417i | ||||
\(367\) | 3250.97 | − | 5630.85i | 0.462396 | − | 0.800893i | −0.536684 | − | 0.843783i | \(-0.680323\pi\) |
0.999080 | + | 0.0428901i | \(0.0136565\pi\) | |||||||
\(368\) | −2620.51 | −0.371205 | ||||||||
\(369\) | 4240.91 | − | 328.000i | 0.598301 | − | 0.0462737i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −404.165 | + | 700.034i | −0.0565585 | + | 0.0979622i | ||||
\(372\) | −209.875 | − | 5435.32i | −0.0292514 | − | 0.757548i | ||||
\(373\) | 6659.02 | + | 11533.8i | 0.924372 | + | 1.60106i | 0.792568 | + | 0.609784i | \(0.208744\pi\) |
0.131805 | + | 0.991276i | \(0.457923\pi\) | |||||||
\(374\) | −571.729 | − | 990.263i | −0.0790465 | − | 0.136913i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 205.155 | − | 355.339i | 0.0281385 | − | 0.0487373i | ||||
\(377\) | −3136.13 | −0.428432 | ||||||||
\(378\) | −14760.6 | + | 10975.7i | −2.00848 | + | 1.49347i | ||||
\(379\) | −3198.42 | −0.433488 | −0.216744 | − | 0.976228i | \(-0.569544\pi\) | ||||
−0.216744 | + | 0.976228i | \(0.569544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6621.53 | + | 4171.62i | −0.890370 | + | 0.560941i | ||||
\(382\) | 1590.27 | + | 2754.43i | 0.212999 | + | 0.368924i | ||||
\(383\) | −1170.25 | − | 2026.93i | −0.156128 | − | 0.270422i | 0.777341 | − | 0.629079i | \(-0.216568\pi\) |
−0.933469 | + | 0.358658i | \(0.883235\pi\) | |||||||
\(384\) | 227.895 | + | 5902.00i | 0.0302858 | + | 0.784336i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −459.878 | −0.0606403 | ||||||||
\(387\) | 5156.01 | + | 7523.81i | 0.677248 | + | 0.988261i | ||||
\(388\) | 14544.5 | 1.90305 | ||||||||
\(389\) | −1995.97 | + | 3457.12i | −0.260153 | + | 0.450599i | −0.966282 | − | 0.257484i | \(-0.917106\pi\) |
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −205.482 | − | 355.906i | −0.0265772 | − | 0.0460330i | ||||
\(392\) | −2780.91 | − | 4816.69i | −0.358310 | − | 0.620611i | ||||
\(393\) | 5861.61 | + | 3089.00i | 0.752365 | + | 0.396488i | ||||
\(394\) | −7161.96 | + | 12404.9i | −0.915773 | + | 1.58616i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4823.24 | − | 10077.1i | 0.612063 | − | 1.27876i | ||||
\(397\) | 4960.90 | 0.627155 | 0.313577 | − | 0.949563i | \(-0.398472\pi\) | ||||
0.313577 | + | 0.949563i | \(0.398472\pi\) | |||||||
\(398\) | −2917.16 | + | 5052.66i | −0.367397 | + | 0.636350i | ||||
\(399\) | 464.937 | + | 12040.9i | 0.0583358 | + | 1.51077i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −413.811 | − | 716.742i | −0.0515330 | − | 0.0892578i | 0.839108 | − | 0.543965i | \(-0.183077\pi\) |
−0.890641 | + | 0.454707i | \(0.849744\pi\) | |||||||
\(402\) | 1804.47 | − | 1136.83i | 0.223877 | − | 0.141044i | ||||
\(403\) | 3255.85 | − | 5639.30i | 0.402445 | − | 0.697056i | ||||
\(404\) | 11256.4 | 1.38621 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6504.11 | −0.795058 | ||||||||
\(407\) | −5741.36 | + | 9944.33i | −0.699235 | + | 1.21111i | ||||
\(408\) | −267.039 | + | 168.237i | −0.0324029 | + | 0.0204141i | ||||
\(409\) | 4183.82 | + | 7246.59i | 0.505811 | + | 0.876090i | 0.999977 | + | 0.00672263i | \(0.00213989\pi\) |
−0.494167 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 288.592 | + | 7473.90i | 0.0346354 | + | 0.896983i | ||||
\(412\) | 2687.41 | − | 4654.73i | 0.321357 | − | 0.556607i | ||||
\(413\) | 13103.2 | 1.56117 | ||||||||
\(414\) | 3098.08 | − | 6472.74i | 0.367784 | − | 0.768400i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7991.34 | + | 13841.4i | −0.941845 | + | 1.63132i | ||||
\(417\) | −11673.8 | − | 6151.96i | −1.37091 | − | 0.722453i | ||||
\(418\) | −6539.87 | − | 11327.4i | −0.765252 | − | 1.32546i | ||||
\(419\) | −2100.36 | − | 3637.93i | −0.244891 | − | 0.424163i | 0.717210 | − | 0.696857i | \(-0.245419\pi\) |
−0.962101 | + | 0.272694i | \(0.912085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3469.38 | + | 6009.14i | −0.401632 | + | 0.695648i | −0.993923 | − | 0.110077i | \(-0.964890\pi\) |
0.592291 | + | 0.805724i | \(0.298224\pi\) | |||||||
\(422\) | 10665.3 | 1.23028 | ||||||||
\(423\) | −679.440 | − | 991.459i | −0.0780981 | − | 0.113963i | ||||
\(424\) | −242.184 | −0.0277394 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −813.575 | − | 21069.8i | −0.0925301 | − | 2.39633i | ||||
\(427\) | 13083.8 | + | 22661.8i | 1.48283 | + | 2.56835i | ||||
\(428\) | 2494.50 | + | 4320.60i | 0.281720 | + | 0.487953i | ||||
\(429\) | 11315.9 | − | 7129.09i | 1.27351 | − | 0.802321i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6827.09 | 0.762991 | 0.381496 | − | 0.924371i | \(-0.375409\pi\) | ||||
0.381496 | + | 0.924371i | \(0.375409\pi\) | |||||||
\(432\) | 5411.83 | + | 2338.11i | 0.602724 | + | 0.260399i | ||||
\(433\) | 2199.59 | 0.244124 | 0.122062 | − | 0.992522i | \(-0.461049\pi\) | ||||
0.122062 | + | 0.992522i | \(0.461049\pi\) | |||||||
\(434\) | 6752.39 | − | 11695.5i | 0.746832 | − | 1.29355i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1786.78 | + | 3094.80i | 0.196265 | + | 0.339940i | ||||
\(437\) | −2350.46 | − | 4071.12i | −0.257295 | − | 0.445648i | ||||
\(438\) | −43.4536 | − | 1125.36i | −0.00474040 | − | 0.122766i | ||||
\(439\) | −4162.16 | + | 7209.07i | −0.452504 | + | 0.783759i | −0.998541 | − | 0.0540018i | \(-0.982802\pi\) |
0.546037 | + | 0.837761i | \(0.316136\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16243.8 | + | 1256.33i | −1.75400 | + | 0.135658i | ||||
\(442\) | −1775.45 | −0.191063 | ||||||||
\(443\) | −5433.41 | + | 9410.93i | −0.582729 | + | 1.00932i | 0.412426 | + | 0.910991i | \(0.364682\pi\) |
−0.995154 | + | 0.0983247i | \(0.968652\pi\) | |||||||
\(444\) | 13175.6 | + | 6943.39i | 1.40830 | + | 0.742159i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3994.41 | + | 6918.51i | 0.424082 | + | 0.734532i | ||||
\(447\) | 431.001 | + | 227.133i | 0.0456055 | + | 0.0240336i | ||||
\(448\) | −11402.6 | + | 19749.9i | −1.20250 | + | 2.08280i | ||||
\(449\) | −4947.73 | −0.520040 | −0.260020 | − | 0.965603i | \(-0.583729\pi\) | ||||
−0.260020 | + | 0.965603i | \(0.583729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6414.18 | −0.669694 | ||||||||
\(452\) | 8955.69 | − | 15511.7i | 0.931947 | − | 1.61418i | ||||
\(453\) | 214.150 | + | 5546.03i | 0.0222112 | + | 0.575221i | ||||
\(454\) | 10822.2 | + | 18744.7i | 1.11875 | + | 1.93773i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3054.59 | + | 1924.42i | −0.313694 | + | 0.197630i | ||||
\(457\) | −7098.85 | + | 12295.6i | −0.726630 | + | 1.25856i | 0.231669 | + | 0.972795i | \(0.425581\pi\) |
−0.958299 | + | 0.285766i | \(0.907752\pi\) | |||||||
\(458\) | 3690.13 | 0.376481 | ||||||||
\(459\) | 106.806 | + | 918.347i | 0.0108612 | + | 0.0933873i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9114.02 | − | 15785.9i | 0.920786 | − | 1.59485i | 0.122584 | − | 0.992458i | \(-0.460882\pi\) |
0.798202 | − | 0.602390i | \(-0.205785\pi\) | |||||||
\(462\) | 23468.3 | − | 14785.2i | 2.36329 | − | 1.48890i | ||||
\(463\) | 2170.59 | + | 3759.58i | 0.217875 | + | 0.377370i | 0.954158 | − | 0.299303i | \(-0.0967542\pi\) |
−0.736283 | + | 0.676674i | \(0.763421\pi\) | |||||||
\(464\) | 1042.28 | + | 1805.29i | 0.104282 | + | 0.180621i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2433.69 | − | 4215.28i | 0.241928 | − | 0.419032i | ||||
\(467\) | −4919.63 | −0.487481 | −0.243740 | − | 0.969841i | \(-0.578374\pi\) | ||||
−0.243740 | + | 0.969841i | \(0.578374\pi\) | |||||||
\(468\) | −9805.90 | − | 14309.1i | −0.968542 | − | 1.41333i | ||||
\(469\) | 2962.80 | 0.291704 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −835.324 | − | 440.206i | −0.0817191 | − | 0.0430650i | ||||
\(472\) | 1962.92 | + | 3399.88i | 0.191421 | + | 0.331551i | ||||
\(473\) | −6876.98 | − | 11911.3i | −0.668508 | − | 1.15789i | ||||
\(474\) | −3864.88 | − | 2036.75i | −0.374515 | − | 0.197365i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2060.31 | −0.198391 | ||||||||
\(477\) | −306.283 | + | 639.909i | −0.0293999 | + | 0.0614244i | ||||
\(478\) | −13421.9 | −1.28432 | ||||||||
\(479\) | −2286.41 | + | 3960.19i | −0.218098 | + | 0.377757i | −0.954226 | − | 0.299085i | \(-0.903319\pi\) |
0.736128 | + | 0.676842i | \(0.236652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8914.64 | + | 15440.6i | 0.845057 | + | 1.46368i | ||||
\(482\) | −9598.31 | − | 16624.8i | −0.907035 | − | 1.57103i | ||||
\(483\) | 8434.61 | − | 5313.87i | 0.794592 | − | 0.500600i | ||||
\(484\) | −1659.99 | + | 2875.19i | −0.155897 | + | 0.270021i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −12173.3 | + | 10603.1i | −1.13620 | + | 0.989646i | ||||
\(487\) | −15751.5 | −1.46564 | −0.732822 | − | 0.680421i | \(-0.761797\pi\) | ||||
−0.732822 | + | 0.680421i | \(0.761797\pi\) | |||||||
\(488\) | −3920.04 | + | 6789.72i | −0.363631 | + | 0.629828i | ||||
\(489\) | −4849.55 | + | 3055.26i | −0.448475 | + | 0.282543i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7654.18 | − | 13257.4i | −0.703520 | − | 1.21853i | −0.967223 | − | 0.253928i | \(-0.918277\pi\) |
0.263703 | − | 0.964604i | \(-0.415056\pi\) | |||||||
\(492\) | 320.994 | + | 8313.05i | 0.0294137 | + | 0.761751i | ||||
\(493\) | −163.457 | + | 283.116i | −0.0149325 | + | 0.0258639i | ||||
\(494\) | −20309.0 | −1.84968 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4328.28 | −0.391826 | ||||||||
\(497\) | 14646.2 | − | 25367.9i | 1.32187 | − | 2.28955i | ||||
\(498\) | 3873.89 | + | 2041.49i | 0.348580 | + | 0.183698i | ||||
\(499\) | −8866.05 | − | 15356.5i | −0.795389 | − | 1.37765i | −0.922592 | − | 0.385777i | \(-0.873933\pi\) |
0.127203 | − | 0.991877i | \(-0.459400\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18579.3 | + | 9791.07i | 1.65681 | + | 0.873119i | ||||
\(502\) | −1889.80 | + | 3273.23i | −0.168020 | + | 0.291019i | ||||
\(503\) | 10511.5 | 0.931775 | 0.465887 | − | 0.884844i | \(-0.345735\pi\) | ||||
0.465887 | + | 0.884844i | \(0.345735\pi\) | |||||||
\(504\) | −4327.89 | − | 6315.39i | −0.382499 | − | 0.558155i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5410.49 | + | 9371.25i | −0.475347 | + | 0.823326i | ||||
\(507\) | −360.782 | − | 9343.47i | −0.0316033 | − | 0.818457i | ||||
\(508\) | −7653.18 | − | 13255.7i | −0.668416 | − | 1.15773i | ||||
\(509\) | −9815.42 | − | 17000.8i | −0.854737 | − | 1.48045i | −0.876889 | − | 0.480693i | \(-0.840385\pi\) |
0.0221524 | − | 0.999755i | \(-0.492948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 782.262 | − | 1354.92i | 0.0677206 | − | 0.117296i | ||||
\(512\) | 13722.1 | 1.18444 | ||||||||
\(513\) | 1221.73 | + | 10504.8i | 0.105147 | + | 0.904086i | ||||
\(514\) | −9640.30 | −0.827267 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15093.4 | + | 9508.96i | −1.28769 | + | 0.811257i | ||||
\(517\) | 906.223 | + | 1569.62i | 0.0770902 | + | 0.133524i | ||||
\(518\) | 18488.3 | + | 32022.7i | 1.56820 | + | 2.71621i | ||||
\(519\) | −550.900 | − | 14267.1i | −0.0465931 | − | 1.20666i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 88.4336 | 0.00743636 | 0.00371818 | − | 0.999993i | \(-0.498816\pi\) | ||||
0.00371818 | + | 0.999993i | \(0.498816\pi\) | |||||||
\(522\) | −5691.34 | + | 440.179i | −0.477209 | + | 0.0369082i | ||||
\(523\) | −21346.4 | −1.78473 | −0.892363 | − | 0.451317i | \(-0.850954\pi\) | ||||
−0.892363 | + | 0.451317i | \(0.850954\pi\) | |||||||
\(524\) | −6479.39 | + | 11222.6i | −0.540178 | + | 0.935616i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15514.2 | + | 26871.4i | 1.28603 | + | 2.22747i | ||||
\(527\) | −339.394 | − | 587.847i | −0.0280535 | − | 0.0485902i | ||||
\(528\) | −7864.58 | − | 4144.55i | −0.648224 | − | 0.341606i | ||||
\(529\) | 4138.94 | − | 7168.86i | 0.340178 | − | 0.589205i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11465.8 | − | 886.783i | 0.937047 | − | 0.0724729i | ||||
\(532\) | −23567.4 | −1.92063 | ||||||||
\(533\) | −4979.67 | + | 8625.03i | −0.404678 | + | 0.700923i | ||||
\(534\) | −1165.93 | − | 30195.1i | −0.0944847 | − | 2.44695i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 443.842 | + | 768.757i | 0.0357669 | + | 0.0619501i | ||||
\(537\) | 12478.4 | − | 7861.51i | 1.00276 | − | 0.631749i | ||||
\(538\) | 227.538 | − | 394.108i | 0.0182340 | − | 0.0315821i | ||||
\(539\) | 24568.0 | 1.96330 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14432.6 | −1.14696 | −0.573480 | − | 0.819220i | \(-0.694407\pi\) | ||||
−0.573480 | + | 0.819220i | \(0.694407\pi\) | |||||||
\(542\) | −12591.1 | + | 21808.4i | −0.997850 | + | 1.72833i | ||||
\(543\) | −15133.5 | + | 9534.24i | −1.19602 | + | 0.753505i | ||||
\(544\) | 833.027 | + | 1442.84i | 0.0656539 | + | 0.113716i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1661.75 | − | 43035.9i | −0.130250 | − | 3.37320i | ||||
\(547\) | −8284.80 | + | 14349.7i | −0.647592 | + | 1.12166i | 0.336105 | + | 0.941825i | \(0.390890\pi\) |
−0.983696 | + | 0.179837i | \(0.942443\pi\) | |||||||
\(548\) | −14628.5 | −1.14033 | ||||||||
\(549\) | 12982.5 | + | 18944.5i | 1.00925 | + | 1.47273i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1869.75 | + | 3238.50i | −0.144562 | + | 0.250389i | ||||
\(552\) | 2642.34 | + | 1392.48i | 0.203742 | + | 0.107369i | ||||
\(553\) | −3034.54 | − | 5255.98i | −0.233349 | − | 0.404172i | ||||
\(554\) | 7010.80 | + | 12143.1i | 0.537654 | + | 0.931245i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12904.1 | − | 22350.6i | 0.984277 | − | 1.70482i | ||||
\(557\) | −11597.0 | −0.882191 | −0.441096 | − | 0.897460i | \(-0.645410\pi\) | ||||
−0.441096 | + | 0.897460i | \(0.645410\pi\) | |||||||
\(558\) | 5117.08 | − | 10691.0i | 0.388214 | − | 0.811084i | ||||
\(559\) | −21355.9 | −1.61584 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −53.7928 | − | 1393.12i | −0.00404836 | − | 0.104844i | ||||
\(562\) | −723.912 | − | 1253.85i | −0.0543352 | − | 0.0941113i | ||||
\(563\) | −11524.6 | − | 19961.3i | −0.862709 | − | 1.49426i | −0.869304 | − | 0.494278i | \(-0.835432\pi\) |
0.00659429 | − | 0.999978i | \(-0.497901\pi\) | |||||||
\(564\) | 1988.95 | − | 1253.05i | 0.148493 | − | 0.0935516i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11079.2 | −0.822778 | ||||||||
\(567\) | −22160.2 | + | 3448.45i | −1.64134 | + | 0.255417i | ||||
\(568\) | 8776.27 | 0.648317 | ||||||||
\(569\) | −7366.96 | + | 12759.9i | −0.542775 | + | 0.940114i | 0.455968 | + | 0.889996i | \(0.349293\pi\) |
−0.998743 | + | 0.0501179i | \(0.984040\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7555.94 | − | 13087.3i | −0.553776 | − | 0.959169i | −0.997998 | − | 0.0632515i | \(-0.979853\pi\) |
0.444221 | − | 0.895917i | \(-0.353480\pi\) | |||||||
\(572\) | 13078.9 | + | 22653.3i | 0.956043 | + | 1.65591i | ||||
\(573\) | 149.625 | + | 3874.98i | 0.0109087 | + | 0.282512i | ||||
\(574\) | −10327.5 | + | 17887.7i | −0.750975 | + | 1.30073i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8641.09 | + | 18053.6i | −0.625079 | + | 1.30596i | ||||
\(577\) | 26150.5 | 1.88676 | 0.943380 | − | 0.331715i | \(-0.107627\pi\) | ||||
0.943380 | + | 0.331715i | \(0.107627\pi\) | |||||||
\(578\) | 10376.5 | − | 17972.7i | 0.746724 | − | 1.29336i | ||||
\(579\) | −496.039 | − | 261.407i | −0.0356040 | − | 0.0187629i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3041.61 | + | 5268.22i | 0.217190 | + | 0.376184i | ||||
\(582\) | 28037.7 | + | 14775.6i | 1.99691 | + | 1.05235i | ||||
\(583\) | 534.894 | − | 926.463i | 0.0379983 | − | 0.0658150i | ||||
\(584\) | 468.747 | 0.0332139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −758.961 | −0.0535023 | ||||||||
\(587\) | 1045.77 | − | 1811.33i | 0.0735326 | − | 0.127362i | −0.826915 | − | 0.562327i | \(-0.809906\pi\) |
0.900447 | + | 0.434965i | \(0.143239\pi\) | |||||||
\(588\) | −1229.49 | − | 31841.2i | −0.0862303 | − | 2.23318i | ||||
\(589\) | −3882.24 | − | 6724.24i | −0.271587 | − | 0.470403i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14776.4 | + | 9309.26i | −1.02846 | + | 0.647939i | ||||
\(592\) | 5925.50 | − | 10263.3i | 0.411379 | − | 0.712530i | ||||
\(593\) | −3260.34 | −0.225778 | −0.112889 | − | 0.993608i | \(-0.536010\pi\) | ||||
−0.112889 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(594\) | 19535.0 | − | 14525.9i | 1.34938 | − | 1.00337i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −476.426 | + | 825.194i | −0.0327436 | + | 0.0567135i | ||||
\(597\) | −6018.61 | + | 3791.78i | −0.412606 | + | 0.259945i | ||||
\(598\) | 8400.90 | + | 14550.8i | 0.574479 | + | 0.995026i | ||||
\(599\) | 11499.6 | + | 19917.9i | 0.784410 | + | 1.35864i | 0.929351 | + | 0.369197i | \(0.120367\pi\) |
−0.144941 | + | 0.989440i | \(0.546299\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7146.93 | − | 12378.9i | 0.485074 | − | 0.840173i | −0.514779 | − | 0.857323i | \(-0.672126\pi\) |
0.999853 | + | 0.0171500i | \(0.00545928\pi\) | |||||||
\(602\) | −44290.5 | −2.99858 | ||||||||
\(603\) | 2592.56 | − | 200.513i | 0.175087 | − | 0.0135415i | ||||
\(604\) | −10855.1 | −0.731274 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 21699.3 | + | 11435.3i | 1.45457 | + | 0.766544i | ||||
\(607\) | −8217.04 | − | 14232.3i | −0.549455 | − | 0.951685i | −0.998312 | − | 0.0580809i | \(-0.981502\pi\) |
0.448856 | − | 0.893604i | \(-0.351831\pi\) | |||||||
\(608\) | 9528.80 | + | 16504.4i | 0.635598 | + | 1.10089i | ||||
\(609\) | −7015.54 | − | 3697.11i | −0.466805 | − | 0.246001i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2814.19 | 0.186334 | ||||||||
\(612\) | −1802.85 | + | 139.435i | −0.119078 | + | 0.00920971i | ||||
\(613\) | −3674.45 | −0.242104 | −0.121052 | − | 0.992646i | \(-0.538627\pi\) | ||||
−0.121052 | + | 0.992646i | \(0.538627\pi\) | |||||||
\(614\) | 3276.45 | − | 5674.99i | 0.215353 | − | 0.373003i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5772.46 | + | 9998.19i | 0.377563 | + | 0.653958i | ||||
\(617\) | 4313.78 | + | 7471.69i | 0.281469 | + | 0.487519i | 0.971747 | − | 0.236026i | \(-0.0758450\pi\) |
−0.690278 | + | 0.723544i | \(0.742512\pi\) | |||||||
\(618\) | 9909.25 | − | 6242.91i | 0.644998 | − | 0.406354i | ||||
\(619\) | 654.905 | − | 1134.33i | 0.0425248 | − | 0.0736551i | −0.843980 | − | 0.536375i | \(-0.819793\pi\) |
0.886504 | + | 0.462720i | \(0.153127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7020.97 | − | 5220.67i | 0.453691 | − | 0.337356i | ||||
\(622\) | 4028.76 | 0.259708 | ||||||||
\(623\) | 20989.4 | − | 36354.7i | 1.34979 | − | 2.33791i | ||||
\(624\) | −11678.8 | + | 7357.73i | −0.749240 | + | 0.472027i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4230.95 | + | 7328.23i | 0.270132 | + | 0.467883i | ||||
\(627\) | −615.323 | − | 15935.5i | −0.0391924 | − | 1.01500i | ||||
\(628\) | 923.362 | − | 1599.31i | 0.0586722 | − | 0.101623i | ||||
\(629\) | 1858.54 | 0.117814 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14447.2 | 0.911463 | 0.455731 | − | 0.890117i | \(-0.349378\pi\) | ||||
0.455731 | + | 0.890117i | \(0.349378\pi\) | |||||||
\(632\) | 909.179 | − | 1574.74i | 0.0572234 | − | 0.0991138i | ||||
\(633\) | 11503.9 | + | 6062.45i | 0.722339 | + | 0.380665i | ||||
\(634\) | −11044.9 | − | 19130.3i | −0.691875 | − | 1.19836i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1227.50 | − | 646.881i | −0.0765310 | − | 0.0403309i | ||||
\(637\) | 19073.4 | − | 33036.2i | 1.18637 | − | 2.05485i | ||||
\(638\) | 8607.88 | 0.534152 | ||||||||
\(639\) | 11099.1 | − | 23189.1i | 0.687127 | − | 1.43560i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10036.6 | − | 17383.8i | 0.618440 | − | 1.07117i | −0.371330 | − | 0.928501i | \(-0.621098\pi\) |
0.989770 | − | 0.142669i | \(-0.0455685\pi\) | |||||||
\(642\) | 419.457 | + | 10863.0i | 0.0257860 | + | 0.667803i | ||||
\(643\) | −8867.96 | − | 15359.8i | −0.543885 | − | 0.942037i | −0.998676 | − | 0.0514386i | \(-0.983619\pi\) |
0.454791 | − | 0.890598i | \(-0.349714\pi\) | |||||||
\(644\) | 9748.75 | + | 16885.3i | 0.596513 | + | 1.03319i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1058.52 | + | 1833.40i | −0.0644686 | + | 0.111663i | ||||
\(647\) | 11456.8 | 0.696158 | 0.348079 | − | 0.937465i | \(-0.386834\pi\) | ||||
0.348079 | + | 0.937465i | \(0.386834\pi\) | |||||||
\(648\) | −4214.48 | − | 5233.31i | −0.255494 | − | 0.317259i | ||||
\(649\) | −17341.4 | −1.04886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13931.4 | − | 8776.89i | 0.838731 | − | 0.528408i | ||||
\(652\) | −5605.12 | − | 9708.36i | −0.336677 | − | 0.583142i | ||||
\(653\) | 14536.0 | + | 25177.0i | 0.871113 | + | 1.50881i | 0.860847 | + | 0.508864i | \(0.169935\pi\) |
0.0102660 | + | 0.999947i | \(0.496732\pi\) | |||||||
\(654\) | 300.453 | + | 7781.08i | 0.0179643 | + | 0.465236i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6619.90 | 0.393999 | ||||||||
\(657\) | 592.812 | − | 1238.55i | 0.0352021 | − | 0.0735468i | ||||
\(658\) | 5836.43 | 0.345787 | ||||||||
\(659\) | 2177.54 | − | 3771.62i | 0.128718 | − | 0.222946i | −0.794462 | − | 0.607314i | \(-0.792247\pi\) |
0.923180 | + | 0.384368i | \(0.125581\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13647.7 | − | 23638.5i | −0.803075 | − | 1.39097i | −0.917583 | − | 0.397545i | \(-0.869862\pi\) |
0.114508 | − | 0.993422i | \(-0.463471\pi\) | |||||||
\(662\) | 4631.19 | + | 8021.46i | 0.271898 | + | 0.470941i | ||||
\(663\) | −1915.06 | − | 1009.22i | −0.112179 | − | 0.0591172i | ||||
\(664\) | −911.297 | + | 1578.41i | −0.0532608 | + | 0.0922504i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18345.2 | + | 26769.8i | 1.06736 | + | 1.55752i | ||||
\(667\) | 3093.72 | 0.179594 | ||||||||
\(668\) | −20537.4 | + | 35571.8i | −1.18955 | + | 2.06035i | ||||
\(669\) | 375.825 | + | 9733.06i | 0.0217194 | + | 0.562484i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17315.8 | − | 29991.9i | −0.996230 | − | 1.72552i | ||||
\(672\) | −34194.0 | + | 21542.5i | −1.96289 | + | 1.23664i | ||||
\(673\) | −8880.01 | + | 15380.6i | −0.508617 | + | 0.880951i | 0.491333 | + | 0.870972i | \(0.336510\pi\) |
−0.999950 | + | 0.00997909i | \(0.996824\pi\) | |||||||
\(674\) | 33456.3 | 1.91200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18287.8 | 1.04050 | ||||||||
\(677\) | 968.667 | − | 1677.78i | 0.0549910 | − | 0.0952472i | −0.837219 | − | 0.546867i | \(-0.815820\pi\) |
0.892210 | + | 0.451620i | \(0.149154\pi\) | |||||||
\(678\) | 33022.2 | − | 20804.3i | 1.87052 | − | 1.17844i | ||||
\(679\) | 22014.0 | + | 38129.4i | 1.24421 | + | 2.15504i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1018.24 | + | 26370.3i | 0.0572968 | + | 1.48386i | ||||
\(682\) | −8936.48 | + | 15478.4i | −0.501753 | + | 0.869061i | ||||
\(683\) | 2125.71 | 0.119090 | 0.0595448 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595448 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(684\) | −20622.3 | + | 1594.97i | −1.15280 | + | 0.0891596i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17071.7 | − | 29569.0i | 0.950146 | − | 1.64570i | ||||
\(687\) | 3980.29 | + | 2097.57i | 0.221045 | + | 0.116488i | ||||
\(688\) | 7097.55 | + | 12293.3i | 0.393301 | + | 0.681218i | ||||
\(689\) | −830.532 | − | 1438.52i | −0.0459227 | − | 0.0795405i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6913.13 | + | 11973.9i | −0.380590 | + | 0.659201i | −0.991147 | − | 0.132771i | \(-0.957612\pi\) |
0.610557 | + | 0.791973i | \(0.290946\pi\) | |||||||
\(692\) | 27924.8 | 1.53402 | ||||||||
\(693\) | 33717.9 | − | 2607.81i | 1.84825 | − | 0.142947i | ||||
\(694\) | 39942.4 | 2.18472 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −91.6744 | − | 2374.17i | −0.00499268 | − | 0.129300i | ||||
\(697\) | 519.086 | + | 899.084i | 0.0282092 | + | 0.0488597i | ||||
\(698\) | 2509.98 | + | 4347.42i | 0.136109 | + | 0.235748i | ||||
\(699\) | 5021.14 | − | 3163.36i | 0.271698 | − | 0.171172i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24464.0 | −1.31810 | −0.659052 | − | 0.752097i | \(-0.729042\pi\) | ||||
−0.659052 | + | 0.752097i | \(0.729042\pi\) | |||||||
\(702\) | −4366.64 | − | 37545.5i | −0.234769 | − | 2.01861i | ||||
\(703\) | 21259.5 | 1.14056 | ||||||||
\(704\) | 15090.8 | − | 26138.0i | 0.807892 | − | 1.39931i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15474.8 | − | 26803.1i | −0.824931 | − | 1.42882i | ||||
\(707\) | 17037.3 | + | 29509.5i | 0.906300 | + | 1.56976i | ||||
\(708\) | 867.842 | + | 22475.2i | 0.0460671 | + | 1.19304i | ||||
\(709\) | 14749.1 | − | 25546.2i | 0.781263 | − | 1.35319i | −0.149944 | − | 0.988695i | \(-0.547909\pi\) |
0.931206 | − | 0.364492i | \(-0.118757\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3011.05 | − | 4393.81i | −0.158823 | − | 0.231759i | ||||
\(712\) | 12577.3 | 0.662012 | ||||||||
\(713\) | −3211.81 | + | 5563.02i | −0.168700 | + | 0.292198i | ||||
\(714\) | −3971.70 | − | 2093.04i | −0.208175 | − | 0.109706i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14422.6 | + | 24980.7i | 0.752790 | + | 1.30387i | ||||
\(717\) | −14477.3 | − | 7629.38i | −0.754065 | − | 0.397384i | ||||
\(718\) | 4133.81 | − | 7159.98i | 0.214864 | − | 0.372156i | ||||
\(719\) | −3857.66 | −0.200093 | −0.100046 | − | 0.994983i | \(-0.531899\pi\) | ||||
−0.100046 | + | 0.994983i | \(0.531899\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16270.2 | 0.840410 | ||||||||
\(722\) | 2507.66 | − | 4343.39i | 0.129260 | − | 0.223884i | ||||
\(723\) | −903.085 | − | 23387.9i | −0.0464538 | − | 1.20305i | ||||
\(724\) | −17491.4 | − | 30295.9i | −0.897874 | − | 1.55516i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6120.86 | + | 3856.19i | −0.312901 | + | 0.197130i | ||||
\(727\) | 4372.55 | − | 7573.48i | 0.223066 | − | 0.386361i | −0.732672 | − | 0.680582i | \(-0.761727\pi\) |
0.955737 | + | 0.294221i | \(0.0950602\pi\) | |||||||
\(728\) | 17925.8 | 0.912604 | ||||||||
\(729\) | −19157.6 | + | 4517.26i | −0.973309 | + | 0.229501i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1113.08 | + | 1927.91i | −0.0563184 | + | 0.0975463i | ||||
\(732\) | −38004.2 | + | 23943.0i | −1.91896 | + | 1.20896i | ||||
\(733\) | −4709.20 | − | 8156.58i | −0.237296 | − | 0.411010i | 0.722641 | − | 0.691223i | \(-0.242928\pi\) |
−0.959938 | + | 0.280214i | \(0.909595\pi\) | |||||||
\(734\) | 13854.9 | + | 23997.4i | 0.696723 | + | 1.20676i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7883.26 | − | 13654.2i | 0.394811 | − | 0.683832i | ||||
\(737\) | −3921.13 | −0.195979 | ||||||||
\(738\) | −7826.33 | + | 16351.3i | −0.390368 | + | 0.815584i | ||||
\(739\) | 6219.42 | 0.309587 | 0.154794 | − | 0.987947i | \(-0.450529\pi\) | ||||
0.154794 | + | 0.987947i | \(0.450529\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21905.9 | − | 11544.2i | −1.08601 | − | 0.572316i | ||||
\(742\) | −1722.46 | − | 2983.39i | −0.0852204 | − | 0.147606i | ||||
\(743\) | −14693.7 | − | 25450.3i | −0.725518 | − | 1.25663i | −0.958760 | − | 0.284216i | \(-0.908267\pi\) |
0.233242 | − | 0.972419i | \(-0.425067\pi\) | |||||||
\(744\) | 4364.33 | + | 2299.95i | 0.215059 | + | 0.113334i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −56758.5 | −2.78563 | ||||||||
\(747\) | 3018.06 | + | 4404.05i | 0.147825 | + | 0.215710i | ||||
\(748\) | 2726.72 | 0.133287 | ||||||||
\(749\) | −7551.15 | + | 13079.0i | −0.368375 | + | 0.638045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10823.6 | + | 18747.0i | 0.525909 | + | 0.910901i | 0.999544 | + | 0.0301801i | \(0.00960808\pi\) |
−0.473636 | + | 0.880721i | \(0.657059\pi\) | |||||||
\(752\) | −935.287 | − | 1619.97i | −0.0453543 | − | 0.0785559i | ||||
\(753\) | −3899.00 | + | 2456.40i | −0.188695 | + | 0.118880i | ||||
\(754\) | 6682.75 | − | 11574.9i | 0.322774 | − | 0.559061i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5067.23 | − | 43569.4i | −0.243774 | − | 2.09604i | ||||
\(757\) | 13907.2 | 0.667722 | 0.333861 | − | 0.942622i | \(-0.391648\pi\) | ||||
0.333861 | + | 0.942622i | \(0.391648\pi\) | |||||||
\(758\) | 6815.48 | − | 11804.8i | 0.326582 | − | 0.565657i | ||||
\(759\) | −11162.8 | + | 7032.66i | −0.533840 | + | 0.336324i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11953.0 | + | 20703.3i | 0.569379 | + | 0.986193i | 0.996628 | + | 0.0820585i | \(0.0261494\pi\) |
−0.427249 | + | 0.904134i | \(0.640517\pi\) | |||||||
\(762\) | −1286.90 | − | 33328.0i | −0.0611806 | − | 1.58445i | ||||
\(763\) | −5408.82 | + | 9368.35i | −0.256635 | + | 0.444504i | ||||
\(764\) | −7584.42 | −0.359155 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9974.70 | 0.470497 | ||||||||
\(767\) | −13463.1 | + | 23318.7i | −0.633798 | + | 1.09777i | ||||
\(768\) | 4992.53 | + | 2631.01i | 0.234573 | + | 0.123618i | ||||
\(769\) | 12555.8 | + | 21747.3i | 0.588783 | + | 1.01980i | 0.994392 | + | 0.105755i | \(0.0337261\pi\) |
−0.405609 | + | 0.914047i | \(0.632941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10398.3 | − | 5479.81i | −0.485716 | − | 0.255967i | ||||
\(772\) | 548.319 | − | 949.716i | 0.0255627 | − | 0.0442759i | ||||
\(773\) | −14909.4 | −0.693729 | −0.346865 | − | 0.937915i | \(-0.612754\pi\) | ||||
−0.346865 | + | 0.937915i | \(0.612754\pi\) | |||||||
\(774\) | −38755.8 | + | 2997.45i | −1.79981 | + | 0.139200i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6595.62 | + | 11424.0i | −0.305115 | + | 0.528474i | ||||
\(777\) | 1739.53 | + | 45050.0i | 0.0803155 | + | 2.08000i | ||||
\(778\) | −8506.37 | − | 14733.5i | −0.391990 | − | 0.678947i | ||||
\(779\) | 5937.70 | + | 10284.4i | 0.273094 | + | 0.473013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19383.5 | + | 33573.2i | −0.888087 | + | 1.53821i | ||||
\(782\) | 1751.44 | 0.0800912 | ||||||||
\(783\) | −6389.08 | − | 2760.32i | −0.291605 | − | 0.125984i | ||||
\(784\) | −25356.0 | −1.15506 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −23891.4 | + | 15051.8i | −1.08419 | + | 0.683052i | ||||
\(787\) | −1329.38 | − | 2302.56i | −0.0602128 | − | 0.104292i | 0.834348 | − | 0.551239i | \(-0.185845\pi\) |
−0.894560 | + | 0.446947i | \(0.852511\pi\) | |||||||
\(788\) | −17078.6 | − | 29581.0i | −0.772082 | − | 1.33728i | ||||
\(789\) | 1459.70 | + | 37803.1i | 0.0658640 | + | 1.70573i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54220.0 | 2.43722 | ||||||||
\(792\) | 5727.76 | + | 8358.13i | 0.256979 | + | 0.374991i | ||||
\(793\) | −53772.7 | −2.40798 | ||||||||
\(794\) | −10571.1 | + | 18309.7i | −0.472488 | + | 0.818373i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6956.33 | − | 12048.7i | −0.309750 | − | 0.536502i | ||||
\(797\) | −7086.11 | − | 12273.5i | −0.314935 | − | 0.545483i | 0.664489 | − | 0.747298i | \(-0.268649\pi\) |
−0.979424 | + | 0.201815i | \(0.935316\pi\) | |||||||
\(798\) | −45431.3 | − | 23941.8i | −2.01535 | − | 1.06207i | ||||
\(799\) | 146.677 | − | 254.053i | 0.00649446 | − | 0.0112487i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15906.1 | − | 33232.2i | 0.701642 | − | 1.46592i | ||||
\(802\) | 3527.14 | 0.155296 | ||||||||
\(803\) | −1035.29 | + | 1793.17i | −0.0454975 | + | 0.0788040i | ||||
\(804\) | 196.231 | + | 5081.95i | 0.00860761 | + | 0.222918i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13875.7 | + | 24033.4i | 0.606391 | + | 1.05030i | ||||
\(807\) | 469.452 | − | 295.759i | 0.0204777 | − | 0.0129011i | ||||
\(808\) | −5104.55 | + | 8841.34i | −0.222249 | + | 0.384947i | ||||
\(809\) | −21077.7 | −0.916012 | −0.458006 | − | 0.888949i | \(-0.651436\pi\) | ||||
−0.458006 | + | 0.888949i | \(0.651436\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11937.4 | −0.516868 | −0.258434 | − | 0.966029i | \(-0.583206\pi\) | ||||
−0.258434 | + | 0.966029i | \(0.583206\pi\) | |||||||
\(812\) | 7754.94 | − | 13431.9i | 0.335154 | − | 0.580503i | ||||
\(813\) | −25977.7 | + | 16366.2i | −1.12064 | + | 0.706011i | ||||
\(814\) | −24468.4 | − | 42380.5i | −1.05358 | − | 1.82486i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 55.5180 | + | 1437.80i | 0.00238176 | + | 0.0616826i | ||||
\(817\) | −12732.3 | + | 22052.9i | −0.545221 | + | 0.944350i | ||||
\(818\) | −35661.0 | −1.52428 | ||||||||
\(819\) | 22670.3 | − | 47364.5i | 0.967235 | − | 2.02082i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7400.25 | + | 12817.6i | −0.314580 | + | 0.544869i | −0.979348 | − | 0.202181i | \(-0.935197\pi\) |
0.664768 | + | 0.747050i | \(0.268530\pi\) | |||||||
\(822\) | −28199.7 | − | 14860.9i | −1.19657 | − | 0.630576i | ||||
\(823\) | 16588.3 | + | 28731.8i | 0.702591 | + | 1.21692i | 0.967554 | + | 0.252665i | \(0.0813071\pi\) |
−0.264963 | + | 0.964259i | \(0.585360\pi\) | |||||||
\(824\) | 2437.37 | + | 4221.64i | 0.103046 | + | 0.178480i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27921.4 | + | 48361.3i | −1.17616 | + | 2.03717i | ||||
\(827\) | 29001.3 | 1.21944 | 0.609718 | − | 0.792619i | \(-0.291283\pi\) | ||||
0.609718 | + | 0.792619i | \(0.291283\pi\) | |||||||
\(828\) | 9673.27 | + | 14115.5i | 0.406002 | + | 0.592450i | ||||
\(829\) | 13221.1 | 0.553904 | 0.276952 | − | 0.960884i | \(-0.410676\pi\) | ||||
0.276952 | + | 0.960884i | \(0.410676\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 659.632 | + | 17083.0i | 0.0275360 | + | 0.713122i | ||||
\(832\) | −23431.6 | − | 40584.7i | −0.976374 | − | 1.69113i | ||||
\(833\) | −1988.24 | − | 3443.73i | −0.0826991 | − | 0.143239i | ||||
\(834\) | 47581.3 | − | 29976.6i | 1.97555 | − | 1.24461i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 31190.3 | 1.29036 | ||||||||
\(837\) | 11596.5 | − | 8622.95i | 0.478893 | − | 0.356096i | ||||
\(838\) | 17902.5 | 0.737987 | ||||||||
\(839\) | 21062.0 | − | 36480.4i | 0.866675 | − | 1.50112i | 0.00129985 | − | 0.999999i | \(-0.499586\pi\) |
0.865375 | − | 0.501125i | \(-0.167080\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10964.0 | + | 18990.2i | 0.449547 | + | 0.778638i | ||||
\(842\) | −14785.7 | − | 25609.6i | −0.605166 | − | 1.04818i | ||||
\(843\) | −68.1114 | − | 1763.94i | −0.00278278 | − | 0.0720679i | ||||
\(844\) | −12716.4 | + | 22025.4i | −0.518621 | + | 0.898278i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5107.10 | − | 394.992i | 0.207548 | − | 0.0160521i | ||||
\(847\) | −10050.0 | −0.407700 | ||||||||
\(848\) | −552.049 | + | 956.177i | −0.0223555 | + | 0.0387208i | ||||
\(849\) | −11950.4 | − | 6297.71i | −0.483081 | − | 0.254578i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8794.07 | − | 15231.8i | −0.354238 | − | 0.613559i | ||||
\(852\) | 44482.4 | + | 23441.7i | 1.78866 | + | 0.942605i | ||||
\(853\) | 7215.84 | − | 12498.2i | 0.289643 | − | 0.501677i | −0.684081 | − | 0.729406i | \(-0.739797\pi\) |
0.973725 | + | 0.227729i | \(0.0731300\pi\) | |||||||
\(854\) | −111521. | −4.46857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4524.80 | −0.180671 | ||||||||
\(857\) | 8056.71 | − | 13954.6i | 0.321134 | − | 0.556220i | −0.659588 | − | 0.751627i | \(-0.729269\pi\) |
0.980722 | + | 0.195407i | \(0.0626027\pi\) | |||||||
\(858\) | 2199.25 | + | 56956.0i | 0.0875074 | + | 2.26625i | ||||
\(859\) | 11250.2 | + | 19485.9i | 0.446858 | + | 0.773982i | 0.998180 | − | 0.0603115i | \(-0.0192094\pi\) |
−0.551321 | + | 0.834293i | \(0.685876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −21307.4 | + | 13423.8i | −0.843384 | + | 0.531339i | ||||
\(862\) | −14547.8 | + | 25197.5i | −0.574825 | + | 0.995626i | ||||
\(863\) | 43396.8 | 1.71175 | 0.855877 | − | 0.517180i | \(-0.173018\pi\) | ||||
0.855877 | + | 0.517180i | \(0.173018\pi\) | |||||||
\(864\) | −28463.1 | + | 21164.6i | −1.12076 | + | 0.833375i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4687.09 | + | 8118.28i | −0.183919 | + | 0.318557i | ||||
\(867\) | 21408.6 | − | 13487.6i | 0.838610 | − | 0.528331i | ||||
\(868\) | 16101.9 | + | 27889.4i | 0.629649 | + | 1.09058i | ||||
\(869\) | 4016.07 | + | 6956.04i | 0.156773 | + | 0.271539i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3044.18 | + | 5272.67i | −0.118425 | + | 0.205118i | ||||
\(872\) | −3241.07 | −0.125868 | ||||||||
\(873\) | 21843.6 | + | 31874.8i | 0.846842 | + | 1.23574i | ||||
\(874\) | 20034.3 | 0.775366 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2375.84 | + | 1252.04i | 0.0916348 | + | 0.0482905i | ||||
\(877\) | −1232.77 | − | 2135.21i | −0.0474659 | − | 0.0822133i | 0.841316 | − | 0.540543i | \(-0.181781\pi\) |
−0.888782 | + | 0.458330i | \(0.848448\pi\) | |||||||
\(878\) | −17738.2 | − | 30723.5i | −0.681817 | − | 1.18094i | ||||
\(879\) | −818.640 | − | 431.414i | −0.0314130 | − | 0.0165543i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24512.9 | 0.937412 | 0.468706 | − | 0.883354i | \(-0.344720\pi\) | ||||
0.468706 | + | 0.883354i | \(0.344720\pi\) | |||||||
\(882\) | 29976.9 | − | 62629.9i | 1.14442 | − | 2.39100i | ||||
\(883\) | −24236.1 | −0.923679 | −0.461840 | − | 0.886963i | \(-0.652810\pi\) | ||||
−0.461840 | + | 0.886963i | \(0.652810\pi\) | |||||||
\(884\) | 2116.90 | − | 3666.57i | 0.0805418 | − | 0.139502i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23156.0 | − | 40107.3i | −0.878036 | − | 1.52080i | ||||
\(887\) | 12599.3 | + | 21822.7i | 0.476939 | + | 0.826082i | 0.999651 | − | 0.0264274i | \(-0.00841308\pi\) |
−0.522712 | + | 0.852509i | \(0.675080\pi\) | |||||||
\(888\) | −11428.5 | + | 7200.07i | −0.431888 | + | 0.272093i | ||||
\(889\) | 23167.1 | − | 40126.7i | 0.874017 | − | 1.51384i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 29328.0 | − | 4563.86i | 1.10272 | − | 0.171599i | ||||
\(892\) | −19050.3 | −0.715081 | ||||||||
\(893\) | 1677.81 | − | 2906.05i | 0.0628731 | − | 0.108899i | ||||
\(894\) | −1756.72 | + | 1106.75i | −0.0657198 | + | 0.0414040i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −17484.5 | − | 30284.0i | −0.651914 | − | 1.12915i | ||||
\(897\) | 790.423 | + | 20470.3i | 0.0294219 | + | 0.761964i | ||||
\(898\) | 10543.1 | − | 18261.1i | 0.391789 | − | 0.678599i | ||||
\(899\) | 5109.87 | 0.189570 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −173.151 | −0.00640233 | ||||||||
\(902\) | 13667.9 | − | 23673.5i | 0.504536 | − | 0.873882i | ||||
\(903\) | −47773.2 | − | 25175.9i | −1.76057 | − | 0.927798i | ||||
\(904\) | 8122.42 | + | 14068.5i | 0.298836 | + | 0.517599i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −20925.7 | − | 11027.6i | −0.767338 | − | 0.404379i | ||||
\(907\) | 13304.0 | − | 23043.3i | 0.487049 | − | 0.843594i | −0.512840 | − | 0.858484i | \(-0.671407\pi\) |
0.999889 | + | 0.0148906i | \(0.00473999\pi\) | |||||||
\(908\) | −51614.0 | −1.88642 | ||||||||
\(909\) | 16905.4 | + | 24668.9i | 0.616851 | + | 0.900127i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12416.1 | + | 21505.2i | −0.451550 | + | 0.782108i | −0.998483 | − | 0.0550686i | \(-0.982462\pi\) |
0.546932 | + | 0.837177i | \(0.315796\pi\) | |||||||
\(912\) | 635.058 | + | 16446.6i | 0.0230580 | + | 0.597151i | ||||
\(913\) | −4025.43 | − | 6972.25i | −0.145917 | − | 0.252736i | ||||
\(914\) | −30253.7 | − | 52401.0i | −1.09486 | − | 1.89636i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4399.79 | + | 7620.66i | −0.158704 | + | 0.274884i | ||||
\(917\) | −39227.8 | −1.41267 | ||||||||
\(918\) | −3617.03 | − | 1562.70i | −0.130043 | − | 0.0561837i | ||||
\(919\) | −26107.2 | −0.937102 | −0.468551 | − | 0.883436i | \(-0.655224\pi\) | ||||
−0.468551 | + | 0.883436i | \(0.655224\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6759.91 | − | 4258.80i | 0.241853 | − | 0.152369i | ||||
\(922\) | 38841.9 | + | 67276.2i | 1.38741 | + | 2.40306i | ||||
\(923\) | 30096.9 | + | 52129.3i | 1.07329 | + | 1.85900i | ||||
\(924\) | 2552.11 | + | 66094.0i | 0.0908637 | + | 2.35317i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18501.2 | −0.656573 | ||||||||
\(927\) | 14237.1 | − | 1101.12i | 0.504431 | − | 0.0390136i | ||||
\(928\) | −12542.0 | −0.443653 | ||||||||
\(929\) | 11680.8 | − | 20231.7i | 0.412523 | − | 0.714511i | −0.582642 | − | 0.812729i | \(-0.697981\pi\) |
0.995165 | + | 0.0982184i | \(0.0313144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22743.0 | − | 39392.0i | −0.800613 | − | 1.38670i | ||||
\(932\) | 5803.45 | + | 10051.9i | 0.203968 | + | 0.353283i | ||||
\(933\) | 4345.55 | + | 2290.06i | 0.152483 | + | 0.0803570i | ||||
\(934\) | 10483.2 | − | 18157.4i | 0.367260 | − | 0.636112i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 15685.8 | − | 1213.17i | 0.547763 | − | 0.0423650i | ||||
\(937\) | −10548.5 | −0.367775 | −0.183888 | − | 0.982947i | \(-0.558868\pi\) | ||||
−0.183888 | + | 0.982947i | \(0.558868\pi\) | |||||||
\(938\) | −6313.40 | + | 10935.1i | −0.219765 | + | 0.380644i | ||||
\(939\) | 398.082 | + | 10309.5i | 0.0138348 | + | 0.358292i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3245.07 | + | 5620.62i | 0.112419 | + | 0.194715i | 0.916745 | − | 0.399473i | \(-0.130807\pi\) |
−0.804326 | + | 0.594188i | \(0.797473\pi\) | |||||||
\(942\) | 3404.70 | − | 2144.99i | 0.117761 | − | 0.0741906i | ||||
\(943\) | 4912.32 | − | 8508.38i | 0.169636 | − | 0.293819i | ||||
\(944\) | 17897.6 | 0.617074 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 58616.4 | 2.01457 | ||||||||
\(947\) | 11753.0 | − | 20356.8i | 0.403295 | − | 0.698528i | −0.590826 | − | 0.806799i | \(-0.701198\pi\) |
0.994121 | + | 0.108271i | \(0.0345314\pi\) | |||||||
\(948\) | 8814.34 | − | 5553.11i | 0.301979 | − | 0.190250i | ||||
\(949\) | 1607.50 | + | 2784.26i | 0.0549858 | + | 0.0952382i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1039.19 | − | 26912.8i | −0.0354344 | − | 0.917674i | ||||
\(952\) | 934.305 | − | 1618.26i | 0.0318078 | − | 0.0550927i | ||||
\(953\) | −6740.26 | −0.229106 | −0.114553 | − | 0.993417i | \(-0.536544\pi\) | ||||
−0.114553 | + | 0.993417i | \(0.536544\pi\) | |||||||
\(954\) | −1709.13 | − | 2494.01i | −0.0580032 | − | 0.0846400i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 16003.1 | − | 27718.2i | 0.541399 | − | 0.937731i | ||||
\(957\) | 9284.74 | + | 4892.95i | 0.313619 | + | 0.165274i | ||||
\(958\) | −9744.19 | − | 16877.4i | −0.328623 | − | 0.569191i | ||||
\(959\) | −22141.2 | − | 38349.6i | −0.745543 | − | 1.29132i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9590.57 | − | 16611.4i | 0.321928 | − | 0.557596i | ||||
\(962\) | −75984.4 | −2.54661 | ||||||||
\(963\) | −5722.40 | + | 11955.6i | −0.191487 | + | 0.400068i | ||||
\(964\) | 45776.8 | 1.52943 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1639.28 | + | 42453.8i | 0.0545993 | + | 1.41400i | ||||
\(967\) | 8391.27 | + | 14534.1i | 0.279054 | + | 0.483336i | 0.971150 | − | 0.238470i | \(-0.0766458\pi\) |
−0.692096 | + | 0.721806i | \(0.743312\pi\) | |||||||
\(968\) | −1505.54 | − | 2607.67i | −0.0499895 | − | 0.0865844i | ||||
\(969\) | −2183.91 | + | 1375.88i | −0.0724016 | + | 0.0456136i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46282.7 | −1.52964 | −0.764822 | − | 0.644242i | \(-0.777173\pi\) | ||||
−0.764822 | + | 0.644242i | \(0.777173\pi\) | |||||||
\(972\) | −7382.66 | − | 37781.9i | −0.243620 | − | 1.24677i | ||||
\(973\) | 78124.9 | 2.57407 | ||||||||
\(974\) | 33564.7 | − | 58135.8i | 1.10419 | − | 1.91252i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 17871.2 | + | 30953.8i | 0.586109 | + | 1.01517i | ||||
\(977\) | 3383.98 | + | 5861.22i | 0.110812 | + | 0.191931i | 0.916098 | − | 0.400955i | \(-0.131322\pi\) |
−0.805286 | + | 0.592886i | \(0.797988\pi\) | |||||||
\(978\) | −942.517 | − | 24409.2i | −0.0308163 | − | 0.798076i | ||||
\(979\) | −27778.5 | + | 48113.7i | −0.906848 | + | 1.57071i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4098.90 | + | 8563.71i | −0.133402 | + | 0.278714i | ||||
\(982\) | 65240.8 | 2.12008 | ||||||||
\(983\) | −25037.4 | + | 43366.1i | −0.812381 | + | 1.40708i | 0.0988128 | + | 0.995106i | \(0.468496\pi\) |
−0.911194 | + | 0.411979i | \(0.864838\pi\) | |||||||
\(984\) | −6675.04 | − | 3517.67i | −0.216252 | − | 0.113963i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −696.618 | − | 1206.58i | −0.0224998 | − | 0.0389708i | ||||
\(987\) | 6295.36 | + | 3317.58i | 0.203023 | + | 0.106991i | ||||
\(988\) | 24214.7 | − | 41941.0i | 0.779728 | − | 1.35053i | ||||
\(989\) | 21067.0 | 0.677343 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2658.60 | −0.0852200 | −0.0426100 | − | 0.999092i | \(-0.513567\pi\) | ||||
−0.0426100 | + | 0.999092i | \(0.513567\pi\) | |||||||
\(992\) | 13020.7 | − | 22552.6i | 0.416742 | − | 0.721819i | ||||
\(993\) | 435.739 | + | 11284.7i | 0.0139252 | + | 0.360634i | ||||
\(994\) | 62418.7 | + | 108112.i | 1.99175 | + | 3.44981i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8834.88 | + | 5566.05i | −0.281068 | + | 0.177075i | ||||
\(997\) | −30310.0 | + | 52498.5i | −0.962817 | + | 1.66765i | −0.247449 | + | 0.968901i | \(0.579592\pi\) |
−0.715368 | + | 0.698748i | \(0.753741\pi\) | |||||||
\(998\) | 75570.3 | 2.39693 | ||||||||
\(999\) | 4571.00 | + | 39302.7i | 0.144765 | + | 1.24473i |
(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 | 225.4.e.d.151.2 | 14 | ||
5.2 | odd | 4 | 225.4.k.d.124.3 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.124.12 | 28 | |||
5.4 | even | 2 | 45.4.e.c.16.6 | ✓ | 14 | ||
9.2 | odd | 6 | 2025.4.a.ba.1.2 | 7 | |||
9.4 | even | 3 | inner | 225.4.e.d.76.2 | 14 | ||
9.7 | even | 3 | 2025.4.a.bb.1.6 | 7 | |||
15.14 | odd | 2 | 135.4.e.c.46.2 | 14 | |||
45.4 | even | 6 | 45.4.e.c.31.6 | yes | 14 | ||
45.13 | odd | 12 | 225.4.k.d.49.3 | 28 | |||
45.14 | odd | 6 | 135.4.e.c.91.2 | 14 | |||
45.22 | odd | 12 | 225.4.k.d.49.12 | 28 | |||
45.29 | odd | 6 | 405.4.a.n.1.6 | 7 | |||
45.34 | even | 6 | 405.4.a.m.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.6 | ✓ | 14 | 5.4 | even | 2 | ||
45.4.e.c.31.6 | yes | 14 | 45.4 | even | 6 | ||
135.4.e.c.46.2 | 14 | 15.14 | odd | 2 | |||
135.4.e.c.91.2 | 14 | 45.14 | odd | 6 | |||
225.4.e.d.76.2 | 14 | 9.4 | even | 3 | inner | ||
225.4.e.d.151.2 | 14 | 1.1 | even | 1 | trivial | ||
225.4.k.d.49.3 | 28 | 45.13 | odd | 12 | |||
225.4.k.d.49.12 | 28 | 45.22 | odd | 12 | |||
225.4.k.d.124.3 | 28 | 5.2 | odd | 4 | |||
225.4.k.d.124.12 | 28 | 5.3 | odd | 4 | |||
405.4.a.m.1.2 | 7 | 45.34 | even | 6 | |||
405.4.a.n.1.6 | 7 | 45.29 | odd | 6 | |||
2025.4.a.ba.1.2 | 7 | 9.2 | odd | 6 | |||
2025.4.a.bb.1.6 | 7 | 9.7 | even | 3 |