Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(46,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.46");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.e (of order \(3\), degree \(2\), not 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: | \(7.96525785077\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{13} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(2.13089 - 3.69081i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.91 |
Dual form | 135.4.e.c.46.2 |
$q$-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 \(\left(\mathbb{Z}/135\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(82\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | −0.946174 | − | 0.323658i | \(-0.895087\pi\) |
0.192791 | − | 0.981240i | \(-0.438246\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.08138 | + | 8.80120i | −0.635172 | + | 1.10015i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.3820 | − | 26.6423i | −0.830548 | − | 1.43855i | −0.897604 | − | 0.440802i | \(-0.854694\pi\) |
0.0670561 | − | 0.997749i | \(-0.478639\pi\) | |||||||
\(8\) | 9.21718 | 0.407346 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 21.3089 | 0.673846 | ||||||||
\(11\) | 20.3573 | + | 35.2599i | 0.557996 | + | 0.966478i | 0.997664 | + | 0.0683175i | \(0.0217631\pi\) |
−0.439667 | + | 0.898161i | \(0.644904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −31.6089 | + | 54.7482i | −0.674364 | + | 1.16803i | 0.302290 | + | 0.953216i | \(0.402249\pi\) |
−0.976654 | + | 0.214817i | \(0.931085\pi\) | |||||||
\(14\) | −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 | \(0.485031\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 75.3803 | 0.910180 | 0.455090 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455090 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(20\) | −25.4069 | − | 44.0060i | −0.284058 | − | 0.492002i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 86.7584 | − | 150.270i | 0.840770 | − | 1.45626i | ||||
\(23\) | −31.1814 | + | 54.0077i | −0.282686 | + | 0.489626i | −0.972045 | − | 0.234793i | \(-0.924559\pi\) |
0.689360 | + | 0.724419i | \(0.257892\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 269.420 | 2.03222 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 312.646 | 2.11016 | ||||||||
\(29\) | 24.8042 | + | 42.9621i | 0.158828 | + | 0.275099i | 0.934446 | − | 0.356104i | \(-0.115895\pi\) |
−0.775618 | + | 0.631202i | \(0.782562\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −51.5021 | + | 89.2043i | −0.298389 | + | 0.516824i | −0.975767 | − | 0.218810i | \(-0.929783\pi\) |
0.677379 | + | 0.735634i | \(0.263116\pi\) | |||||||
\(32\) | 126.410 | − | 218.948i | 0.698321 | − | 1.20953i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −14.0423 | − | 24.3221i | −0.0708306 | − | 0.122682i | ||||
\(35\) | 153.820 | 0.742865 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −282.029 | −1.25312 | −0.626559 | − | 0.779374i | \(-0.715537\pi\) | ||||
−0.626559 | + | 0.779374i | \(0.715537\pi\) | |||||||
\(38\) | −160.627 | − | 278.214i | −0.685714 | − | 1.18769i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −23.0430 | + | 39.9116i | −0.0910853 | + | 0.157764i | ||||
\(41\) | −78.7700 | + | 136.434i | −0.300044 | + | 0.519692i | −0.976146 | − | 0.217117i | \(-0.930335\pi\) |
0.676102 | + | 0.736808i | \(0.263668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 168.907 | + | 292.555i | 0.599025 | + | 1.03754i | 0.992965 | + | 0.118406i | \(0.0377783\pi\) |
−0.393940 | + | 0.919136i | \(0.628888\pi\) | |||||||
\(44\) | −413.773 | −1.41770 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 265.776 | 0.851882 | ||||||||
\(47\) | 22.2579 | + | 38.5518i | 0.0690777 | + | 0.119646i | 0.898496 | − | 0.438983i | \(-0.144661\pi\) |
−0.829418 | + | 0.558629i | \(0.811328\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −301.710 | + | 522.577i | −0.879620 | + | 1.52355i | ||||
\(50\) | −53.2722 | + | 92.2702i | −0.150677 | + | 0.260980i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −321.234 | − | 556.393i | −0.856675 | − | 1.48380i | ||||
\(53\) | −26.2752 | −0.0680978 | −0.0340489 | − | 0.999420i | \(-0.510840\pi\) | ||||
−0.0340489 | + | 0.999420i | \(0.510840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −203.573 | −0.499087 | ||||||||
\(56\) | −141.778 | − | 245.567i | −0.338320 | − | 0.585988i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 105.710 | − | 183.095i | 0.239317 | − | 0.414509i | ||||
\(59\) | −212.963 | + | 368.863i | −0.469923 | + | 0.813930i | −0.999409 | − | 0.0343889i | \(-0.989052\pi\) |
0.529486 | + | 0.848319i | \(0.322385\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −425.297 | − | 736.637i | −0.892684 | − | 1.54617i | −0.836644 | − | 0.547746i | \(-0.815486\pi\) |
−0.0560400 | − | 0.998429i | \(-0.517847\pi\) | |||||||
\(62\) | 438.981 | 0.899204 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −741.296 | −1.44784 | ||||||||
\(65\) | −158.045 | − | 273.741i | −0.301585 | − | 0.522360i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48.1538 | + | 83.4048i | −0.0878048 | + | 0.152082i | −0.906583 | − | 0.422028i | \(-0.861319\pi\) |
0.818778 | + | 0.574110i | \(0.194652\pi\) | |||||||
\(68\) | −33.4858 | + | 57.9990i | −0.0597168 | + | 0.103433i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −327.773 | − | 567.719i | −0.559662 | − | 0.969363i | ||||
\(71\) | −952.164 | −1.59156 | −0.795782 | − | 0.605583i | \(-0.792940\pi\) | ||||
−0.795782 | + | 0.605583i | \(0.792940\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −50.8558 | −0.0815373 | −0.0407686 | − | 0.999169i | \(-0.512981\pi\) | ||||
−0.0407686 | + | 0.999169i | \(0.512981\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 98.6395 | + | 170.849i | 0.140479 | + | 0.243316i | 0.927677 | − | 0.373384i | \(-0.121803\pi\) |
−0.787198 | + | 0.616700i | \(0.788469\pi\) | |||||||
\(80\) | −210.102 | −0.293627 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 671.400 | 0.904192 | ||||||||
\(83\) | −98.8693 | − | 171.247i | −0.130751 | − | 0.226467i | 0.793215 | − | 0.608941i | \(-0.208405\pi\) |
−0.923966 | + | 0.382474i | \(0.875072\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4747 | + | 28.5351i | −0.0210228 | + | 0.0364125i | ||||
\(86\) | 719.844 | − | 1246.81i | 0.902590 | − | 1.56333i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 187.637 | + | 324.997i | 0.227298 | + | 0.393691i | ||||
\(89\) | −1364.54 | −1.62519 | −0.812593 | − | 0.582832i | \(-0.801944\pi\) | ||||
−0.812593 | + | 0.582832i | \(0.801944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1944.83 | 2.24037 | ||||||||
\(92\) | −316.889 | − | 548.868i | −0.359108 | − | 0.621993i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 94.8583 | − | 164.299i | 0.104084 | − | 0.180279i | ||||
\(95\) | −188.451 | + | 326.406i | −0.203522 | + | 0.352511i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 715.579 | + | 1239.42i | 0.749031 | + | 1.29736i | 0.948288 | + | 0.317413i | \(0.102814\pi\) |
−0.199256 | + | 0.979947i | \(0.563853\pi\) | |||||||
\(98\) | 2571.64 | 2.65076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 254.069 | 0.254069 | ||||||||
\(101\) | 553.808 | + | 959.224i | 0.545604 | + | 0.945013i | 0.998569 | + | 0.0534851i | \(0.0170329\pi\) |
−0.452965 | + | 0.891528i | \(0.649634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −264.437 | + | 458.018i | −0.252969 | + | 0.438154i | −0.964342 | − | 0.264660i | \(-0.914740\pi\) |
0.711373 | + | 0.702814i | \(0.248074\pi\) | |||||||
\(104\) | −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 | \(0.571182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −351.634 | −0.308994 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(110\) | 433.792 | + | 751.349i | 0.376004 | + | 0.651258i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 646.357 | − | 1119.52i | 0.545313 | − | 0.944509i | ||||
\(113\) | 881.226 | − | 1526.33i | 0.733618 | − | 1.27066i | −0.221710 | − | 0.975113i | \(-0.571164\pi\) |
0.955327 | − | 0.295550i | \(-0.0955030\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −155.907 | − | 270.039i | −0.126421 | − | 0.218967i | ||||
\(116\) | −504.158 | −0.403533 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −523.403 | − | 906.561i | −0.379056 | − | 0.656545i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1506.12 | −1.05234 | −0.526169 | − | 0.850380i | \(-0.676372\pi\) | ||||
−0.526169 | + | 0.850380i | \(0.676372\pi\) | |||||||
\(128\) | 568.343 | + | 984.399i | 0.392460 | + | 0.679761i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −673.551 | + | 1166.62i | −0.454418 | + | 0.787075i | ||||
\(131\) | 637.562 | − | 1104.29i | 0.425222 | − | 0.736506i | −0.571219 | − | 0.820798i | \(-0.693529\pi\) |
0.996441 | + | 0.0842915i | \(0.0268627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −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 | 0.998310 | − | 0.0581150i | \(-0.0185090\pi\) |
−0.549484 | + | 0.835504i | \(0.685176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1269.75 | − | 2199.27i | 0.774811 | − | 1.34201i | −0.160090 | − | 0.987102i | \(-0.551178\pi\) |
0.934901 | − | 0.354909i | \(-0.115488\pi\) | |||||||
\(140\) | −781.616 | + | 1353.80i | −0.471847 | + | 0.817263i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2028.96 | + | 3514.25i | 1.19906 | + | 2.07683i | ||||
\(143\) | −2573.89 | −1.50517 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −248.042 | −0.142060 | ||||||||
\(146\) | 108.368 | + | 187.699i | 0.0614288 | + | 0.106398i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1433.10 | − | 2482.20i | 0.795945 | − | 1.37862i | ||||
\(149\) | 46.8796 | − | 81.1979i | 0.0257754 | − | 0.0446442i | −0.852850 | − | 0.522156i | \(-0.825128\pi\) |
0.878625 | + | 0.477512i | \(0.158461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534.065 | + | 925.027i | 0.287825 | + | 0.498527i | 0.973290 | − | 0.229578i | \(-0.0737345\pi\) |
−0.685465 | + | 0.728105i | \(0.740401\pi\) | |||||||
\(152\) | 694.794 | 0.370758 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5338.06 | −2.79320 | ||||||||
\(155\) | −257.510 | − | 446.021i | −0.133443 | − | 0.231131i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −90.8574 | + | 157.370i | −0.0461861 | + | 0.0799966i | −0.888194 | − | 0.459468i | \(-0.848040\pi\) |
0.842008 | + | 0.539465i | \(0.181373\pi\) | |||||||
\(158\) | 420.380 | − | 728.119i | 0.211668 | − | 0.366621i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 632.048 | + | 1094.74i | 0.312299 | + | 0.540917i | ||||
\(161\) | 1918.52 | 0.939136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1103.07 | −0.530056 | −0.265028 | − | 0.964241i | \(-0.585381\pi\) | ||||
−0.265028 | + | 0.964241i | \(0.585381\pi\) | |||||||
\(164\) | −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 | −0.164270 | + | 0.986415i | \(0.552527\pi\) |
−0.772126 | + | 0.635470i | \(0.780806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −899.745 | − | 1558.40i | −0.409534 | − | 0.709333i | ||||
\(170\) | 140.423 | 0.0633529 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3433.12 | −1.52194 | ||||||||
\(173\) | −1373.88 | − | 2379.63i | −0.603780 | − | 1.04578i | −0.992243 | − | 0.124314i | \(-0.960327\pi\) |
0.388463 | − | 0.921465i | \(-0.373006\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −384.549 | + | 666.059i | −0.166110 | + | 0.287710i | ||||
\(176\) | −855.423 | + | 1481.64i | −0.366363 | + | 0.634560i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2907.69 | + | 5036.27i | 1.22439 | + | 2.12070i | ||||
\(179\) | 2838.32 | 1.18517 | 0.592587 | − | 0.805506i | \(-0.298107\pi\) | ||||
0.592587 | + | 0.805506i | \(0.298107\pi\) | |||||||
\(180\) | 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 | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −287.405 | + | 497.799i | −0.115151 | + | 0.199447i | ||||
\(185\) | 705.073 | − | 1221.22i | 0.280206 | − | 0.485330i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 134.153 | + | 232.359i | 0.0524610 | + | 0.0908652i | ||||
\(188\) | −452.403 | −0.175505 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1606.27 | 0.613322 | ||||||||
\(191\) | −373.148 | − | 646.311i | −0.141361 | − | 0.244845i | 0.786648 | − | 0.617402i | \(-0.211815\pi\) |
−0.928010 | + | 0.372557i | \(0.878481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −53.9538 | + | 93.4506i | −0.0201227 | + | 0.0348535i | −0.875911 | − | 0.482472i | \(-0.839739\pi\) |
0.855789 | + | 0.517326i | \(0.173072\pi\) | |||||||
\(194\) | 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 | \(0.292063\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1368.99 | 0.487663 | 0.243831 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243831 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(200\) | −115.215 | − | 199.558i | −0.0407346 | − | 0.0705544i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2360.21 | − | 4088.00i | 0.822097 | − | 1.42391i | ||||
\(203\) | 763.074 | − | 1321.68i | 0.263829 | − | 0.456965i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −393.850 | − | 682.168i | −0.134184 | − | 0.232413i | ||||
\(206\) | 2253.94 | 0.762329 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | −0.994694 | − | 0.102878i | \(-0.967195\pi\) |
0.586442 | + | 0.809991i | \(0.300528\pi\) | |||||||
\(212\) | 133.514 | − | 231.254i | 0.0432538 | − | 0.0749178i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1046.07 | + | 1811.85i | 0.334150 | + | 0.578765i | ||||
\(215\) | −1689.07 | −0.535784 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3168.81 | 0.991305 | ||||||||
\(218\) | 749.292 | + | 1297.81i | 0.232791 | + | 0.403206i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1034.43 | − | 1791.69i | 0.317006 | − | 0.549071i | ||||
\(221\) | −208.299 | + | 360.785i | −0.0634015 | + | 0.109815i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −937.263 | − | 1623.39i | −0.281452 | − | 0.487489i | 0.690291 | − | 0.723532i | \(-0.257483\pi\) |
−0.971743 | + | 0.236043i | \(0.924149\pi\) | |||||||
\(224\) | −7777.72 | −2.31996 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7511.18 | −2.21078 | ||||||||
\(227\) | 2539.37 | + | 4398.32i | 0.742484 | + | 1.28602i | 0.951361 | + | 0.308078i | \(0.0996859\pi\) |
−0.208877 | + | 0.977942i | \(0.566981\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −432.933 | + | 749.861i | −0.124930 | + | 0.216385i | −0.921706 | − | 0.387890i | \(-0.873204\pi\) |
0.796776 | + | 0.604275i | \(0.206537\pi\) | |||||||
\(230\) | −664.441 | + | 1150.85i | −0.190487 | + | 0.329933i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 228.625 | + | 395.990i | 0.0646981 | + | 0.112060i | ||||
\(233\) | −1142.10 | −0.321122 | −0.160561 | − | 0.987026i | \(-0.551330\pi\) | ||||
−0.160561 | + | 0.987026i | \(0.551330\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −222.579 | −0.0617849 | ||||||||
\(236\) | −2164.29 | − | 3748.66i | −0.596964 | − | 1.03397i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −431.998 | + | 748.242i | −0.117657 | + | 0.203787i | ||||
\(239\) | −1574.68 | + | 2727.43i | −0.426183 | + | 0.738171i | −0.996530 | − | 0.0832330i | \(-0.973475\pi\) |
0.570347 | + | 0.821404i | \(0.306809\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2252.18 | − | 3900.90i | −0.601975 | − | 1.04265i | −0.992522 | − | 0.122068i | \(-0.961047\pi\) |
0.390547 | − | 0.920583i | \(-0.372286\pi\) | |||||||
\(242\) | 1392.24 | 0.369821 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8644.39 | 2.26803 | ||||||||
\(245\) | −1508.55 | − | 2612.88i | −0.393378 | − | 0.681351i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2382.69 | + | 4126.94i | −0.613793 | + | 1.06312i | ||||
\(248\) | −474.704 | + | 822.212i | −0.121547 | + | 0.210526i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −266.361 | − | 461.351i | −0.0673846 | − | 0.116714i | ||||
\(251\) | −886.861 | −0.223021 | −0.111510 | − | 0.993763i | \(-0.535569\pi\) | ||||
−0.111510 | + | 0.993763i | \(0.535569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −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 | −0.695496 | − | 0.718530i | \(-0.744815\pi\) |
0.970013 | + | 0.243052i | \(0.0781486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4338.17 | + | 7513.92i | 1.04077 | + | 1.80267i | ||||
\(260\) | 3212.34 | 0.766233 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5434.30 | −1.28142 | ||||||||
\(263\) | 3640.31 | + | 6305.20i | 0.853503 | + | 1.47831i | 0.878027 | + | 0.478611i | \(0.158859\pi\) |
−0.0245245 | + | 0.999699i | \(0.507807\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 65.6881 | − | 113.775i | 0.0152271 | − | 0.0263742i | ||||
\(266\) | −4941.52 | + | 8558.96i | −1.13904 | + | 1.97287i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −489.375 | − | 847.622i | −0.111542 | − | 0.193197i | ||||
\(269\) | 106.781 | 0.0242028 | 0.0121014 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121014 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(270\) | 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 | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3067.25 | − | 5312.64i | 0.676276 | − | 1.17134i | ||||
\(275\) | 508.933 | − | 881.498i | 0.111599 | − | 0.193296i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1645.04 | − | 2849.30i | −0.356827 | − | 0.618042i | 0.630602 | − | 0.776106i | \(-0.282808\pi\) |
−0.987429 | + | 0.158064i | \(0.949475\pi\) | |||||||
\(278\) | −10822.8 | −2.33492 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1417.78 | 0.302603 | ||||||||
\(281\) | 169.861 | + | 294.209i | 0.0360608 | + | 0.0624591i | 0.883493 | − | 0.468445i | \(-0.155186\pi\) |
−0.847432 | + | 0.530904i | \(0.821852\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1299.83 | + | 2251.37i | −0.273028 | + | 0.472898i | −0.969636 | − | 0.244554i | \(-0.921358\pi\) |
0.696608 | + | 0.717452i | \(0.254692\pi\) | |||||||
\(284\) | 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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4869.57 | −0.991161 | ||||||||
\(290\) | 528.550 | + | 915.475i | 0.107026 | + | 0.185374i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 258.418 | − | 447.592i | 0.0517902 | − | 0.0897033i | ||||
\(293\) | 89.0427 | − | 154.227i | 0.0177540 | − | 0.0307509i | −0.857012 | − | 0.515297i | \(-0.827682\pi\) |
0.874766 | + | 0.484546i | \(0.161015\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1064.82 | − | 1844.31i | −0.210156 | − | 0.364001i | ||||
\(296\) | −2599.52 | −0.510452 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1583.76 | + | 2743.15i | 0.298798 | + | 0.517534i | ||||
\(305\) | 4252.97 | 0.798441 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1537.60 | 0.285848 | 0.142924 | − | 0.989734i | \(-0.454349\pi\) | ||||
0.142924 | + | 0.989734i | \(0.454349\pi\) | |||||||
\(308\) | 6364.64 | + | 11023.9i | 1.17746 | + | 2.03943i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1097.45 | + | 1900.84i | −0.201068 | + | 0.348260i | ||||
\(311\) | 472.662 | − | 818.674i | 0.0861807 | − | 0.149269i | −0.819713 | − | 0.572774i | \(-0.805867\pi\) |
0.905894 | + | 0.423505i | \(0.139200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −992.767 | − | 1719.52i | −0.179280 | − | 0.310521i | 0.762354 | − | 0.647160i | \(-0.224043\pi\) |
−0.941634 | + | 0.336638i | \(0.890710\pi\) | |||||||
\(314\) | 774.428 | 0.139183 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2004.90 | −0.356913 | ||||||||
\(317\) | −2591.62 | − | 4488.81i | −0.459179 | − | 0.795321i | 0.539739 | − | 0.841833i | \(-0.318523\pi\) |
−0.998918 | + | 0.0465112i | \(0.985190\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1009.89 | + | 1749.19i | −0.177251 | + | 0.307008i | ||||
\(320\) | 1853.24 | − | 3209.91i | 0.323748 | − | 0.560748i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4088.16 | − | 7080.91i | −0.707529 | − | 1.22548i | ||||
\(323\) | 496.748 | 0.0855722 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1580.45 | 0.269746 | ||||||||
\(326\) | 2350.52 | + | 4071.22i | 0.399336 | + | 0.691670i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | 0.942034 | − | 0.335517i | \(-0.108911\pi\) |
−0.761583 | + | 0.648067i | \(0.775578\pi\) | |||||||
\(332\) | 2009.57 | 0.332197 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17224.8 | 2.82186 | ||||||||
\(335\) | −240.769 | − | 417.024i | −0.0392675 | − | 0.0680133i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3925.16 | − | 6798.57i | 0.634472 | − | 1.09894i | −0.352155 | − | 0.935942i | \(-0.614551\pi\) |
0.986627 | − | 0.162995i | \(-0.0521156\pi\) | |||||||
\(338\) | −3834.52 | + | 6641.58i | −0.617071 | + | 1.06880i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −167.429 | − | 289.995i | −0.0267062 | − | 0.0462565i | ||||
\(341\) | −4193.78 | −0.665999 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | 0.234018 | + | 0.972232i | \(0.424813\pi\) |
−0.958987 | + | 0.283451i | \(0.908521\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 588.952 | + | 1020.10i | 0.0903321 | + | 0.156460i | 0.907651 | − | 0.419726i | \(-0.137874\pi\) |
−0.817319 | + | 0.576186i | \(0.804540\pi\) | |||||||
\(350\) | 3277.73 | 0.500577 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10293.4 | 1.55864 | ||||||||
\(353\) | −3631.06 | − | 6289.19i | −0.547484 | − | 0.948271i | −0.998446 | − | 0.0557274i | \(-0.982252\pi\) |
0.450962 | − | 0.892543i | \(-0.351081\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2380.41 | − | 4122.99i | 0.355885 | − | 0.616410i | ||||
\(356\) | 6933.77 | − | 12009.6i | 1.03227 | − | 1.78795i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6048.15 | − | 10475.7i | −0.892890 | − | 1.54653i | ||||
\(359\) | 1939.95 | 0.285199 | 0.142600 | − | 0.989780i | \(-0.454454\pi\) | ||||
0.142600 | + | 0.989780i | \(0.454454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1176.81 | −0.171572 | ||||||||
\(362\) | −7335.05 | − | 12704.7i | −1.06498 | − | 1.84459i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9882.41 | + | 17116.8i | −1.42302 | + | 2.46474i | ||||
\(365\) | 127.139 | − | 220.212i | 0.0182323 | − | 0.0315792i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3250.97 | − | 5630.85i | −0.462396 | − | 0.800893i | 0.536684 | − | 0.843783i | \(-0.319677\pi\) |
−0.999080 | + | 0.0428901i | \(0.986343\pi\) | |||||||
\(368\) | −2620.51 | −0.371205 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6009.73 | −0.844409 | ||||||||
\(371\) | 404.165 | + | 700.034i | 0.0565585 | + | 0.0979622i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6659.02 | + | 11533.8i | −0.924372 | + | 1.60106i | −0.131805 | + | 0.991276i | \(0.542077\pi\) |
−0.792568 | + | 0.609784i | \(0.791256\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3198.42 | −0.433488 | −0.216744 | − | 0.976228i | \(-0.569544\pi\) | ||||
−0.216744 | + | 0.976228i | \(0.569544\pi\) | |||||||
\(380\) | −1915.18 | − | 3317.19i | −0.258544 | − | 0.447811i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1590.27 | + | 2754.43i | −0.212999 | + | 0.368924i | ||||
\(383\) | −1170.25 | + | 2026.93i | −0.156128 | + | 0.270422i | −0.933469 | − | 0.358658i | \(-0.883235\pi\) |
0.777341 | + | 0.629079i | \(0.216568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3131.36 | + | 5423.67i | 0.414516 | + | 0.717963i | ||||
\(386\) | 459.878 | 0.0606403 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14544.5 | −1.90305 | ||||||||
\(389\) | 1995.97 | + | 3457.12i | 0.260153 | + | 0.450599i | 0.966282 | − | 0.257484i | \(-0.0828936\pi\) |
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −205.482 | + | 355.906i | −0.0265772 | + | 0.0460330i | ||||
\(392\) | −2780.91 | + | 4816.69i | −0.358310 | + | 0.620611i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7161.96 | − | 12404.9i | −0.915773 | − | 1.58616i | ||||
\(395\) | −986.395 | −0.125648 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4960.90 | −0.627155 | −0.313577 | − | 0.949563i | \(-0.601528\pi\) | ||||
−0.313577 | + | 0.949563i | \(0.601528\pi\) | |||||||
\(398\) | −2917.16 | − | 5052.66i | −0.367397 | − | 0.636350i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 525.256 | − | 909.769i | 0.0656569 | − | 0.113721i | ||||
\(401\) | 413.811 | − | 716.742i | 0.0515330 | − | 0.0892578i | −0.839108 | − | 0.543965i | \(-0.816923\pi\) |
0.890641 | + | 0.454707i | \(0.150256\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −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 | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4183.82 | − | 7246.59i | 0.505811 | − | 0.876090i | −0.494167 | − | 0.869367i | \(-0.664527\pi\) |
0.999977 | − | 0.00672263i | \(-0.00213989\pi\) | |||||||
\(410\) | −1678.50 | + | 2907.25i | −0.202184 | + | 0.350192i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2687.41 | − | 4654.73i | −0.321357 | − | 0.556607i | ||||
\(413\) | 13103.2 | 1.56117 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 988.693 | 0.116947 | ||||||||
\(416\) | 7991.34 | + | 13841.4i | 0.941845 | + | 1.63132i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6539.87 | − | 11327.4i | 0.765252 | − | 1.32546i | ||||
\(419\) | 2100.36 | − | 3637.93i | 0.244891 | − | 0.424163i | −0.717210 | − | 0.696857i | \(-0.754581\pi\) |
0.962101 | + | 0.272694i | \(0.0879145\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3469.38 | − | 6009.14i | −0.401632 | − | 0.695648i | 0.592291 | − | 0.805724i | \(-0.298224\pi\) |
−0.993923 | + | 0.110077i | \(0.964890\pi\) | |||||||
\(422\) | 10665.3 | 1.23028 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −242.184 | −0.0277394 | ||||||||
\(425\) | −82.3737 | − | 142.675i | −0.00940168 | − | 0.0162842i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13083.8 | + | 22661.8i | −1.48283 | + | 2.56835i | ||||
\(428\) | 2494.50 | − | 4320.60i | 0.281720 | − | 0.487953i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3599.22 | + | 6234.03i | 0.403651 | + | 0.699144i | ||||
\(431\) | −6827.09 | −0.762991 | −0.381496 | − | 0.924371i | \(-0.624591\pi\) | ||||
−0.381496 | + | 0.924371i | \(0.624591\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2199.59 | −0.244124 | −0.122062 | − | 0.992522i | \(-0.538951\pi\) | ||||
−0.122062 | + | 0.992522i | \(0.538951\pi\) | |||||||
\(434\) | −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 | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4162.16 | − | 7209.07i | −0.452504 | − | 0.783759i | 0.546037 | − | 0.837761i | \(-0.316136\pi\) |
−0.998541 | + | 0.0540018i | \(0.982802\pi\) | |||||||
\(440\) | −1876.37 | −0.203301 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1775.45 | 0.191063 | ||||||||
\(443\) | −5433.41 | − | 9410.93i | −0.582729 | − | 1.00932i | −0.995154 | − | 0.0983247i | \(-0.968652\pi\) |
0.412426 | − | 0.910991i | \(-0.364682\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3411.36 | − | 5908.65i | 0.363402 | − | 0.629431i | ||||
\(446\) | −3994.41 | + | 6918.51i | −0.424082 | + | 0.734532i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11402.6 | + | 19749.9i | 1.20250 | + | 2.08280i | ||||
\(449\) | 4947.73 | 0.520040 | 0.260020 | − | 0.965603i | \(-0.416271\pi\) | ||||
0.260020 | + | 0.965603i | \(0.416271\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6414.18 | −0.669694 | ||||||||
\(452\) | 8955.69 | + | 15511.7i | 0.931947 | + | 1.61418i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10822.2 | − | 18744.7i | 1.11875 | − | 1.93773i | ||||
\(455\) | −4862.07 | + | 8421.35i | −0.500961 | + | 0.867690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7098.85 | + | 12295.6i | 0.726630 | + | 1.25856i | 0.958299 | + | 0.285766i | \(0.0922480\pi\) |
−0.231669 | + | 0.972795i | \(0.574419\pi\) | |||||||
\(458\) | 3690.13 | 0.376481 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3168.89 | 0.321196 | ||||||||
\(461\) | −9114.02 | − | 15785.9i | −0.920786 | − | 1.59485i | −0.798202 | − | 0.602390i | \(-0.794215\pi\) |
−0.122584 | − | 0.992458i | \(-0.539118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2170.59 | + | 3759.58i | −0.217875 | + | 0.377370i | −0.954158 | − | 0.299303i | \(-0.903246\pi\) |
0.736283 | + | 0.676674i | \(0.236579\pi\) | |||||||
\(464\) | −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 | \(0.578374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2962.80 | 0.291704 | ||||||||
\(470\) | 474.291 | + | 821.497i | 0.0465477 | + | 0.0806230i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1962.92 | + | 3399.88i | −0.191421 | + | 0.331551i | ||||
\(473\) | −6876.98 | + | 11911.3i | −0.668508 | + | 1.15789i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −942.254 | − | 1632.03i | −0.0910180 | − | 0.157648i | ||||
\(476\) | 2060.31 | 0.198391 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13421.9 | 1.28432 | ||||||||
\(479\) | 2286.41 | + | 3960.19i | 0.218098 | + | 0.377757i | 0.954226 | − | 0.299085i | \(-0.0966814\pi\) |
−0.736128 | + | 0.676842i | \(0.763348\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8914.64 | − | 15440.6i | 0.845057 | − | 1.46368i | ||||
\(482\) | −9598.31 | + | 16624.8i | −0.907035 | + | 1.57103i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1659.99 | − | 2875.19i | −0.155897 | − | 0.270021i | ||||
\(485\) | −7155.79 | −0.669954 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15751.5 | 1.46564 | 0.732822 | − | 0.680421i | \(-0.238203\pi\) | ||||
0.732822 | + | 0.680421i | \(0.238203\pi\) | |||||||
\(488\) | −3920.04 | − | 6789.72i | −0.363631 | − | 0.629828i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6429.10 | + | 11135.5i | −0.592729 | + | 1.02664i | ||||
\(491\) | 7654.18 | − | 13257.4i | 0.703520 | − | 1.21853i | −0.263703 | − | 0.964604i | \(-0.584944\pi\) |
0.967223 | − | 0.253928i | \(-0.0817227\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 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 | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8866.05 | + | 15356.5i | −0.795389 | + | 1.37765i | 0.127203 | + | 0.991877i | \(0.459400\pi\) |
−0.922592 | + | 0.385777i | \(0.873933\pi\) | |||||||
\(500\) | −635.172 | + | 1100.15i | −0.0568115 | + | 0.0984005i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1889.80 | + | 3273.23i | 0.168020 | + | 0.291019i | ||||
\(503\) | 10511.5 | 0.931775 | 0.465887 | − | 0.884844i | \(-0.345735\pi\) | ||||
0.465887 | + | 0.884844i | \(0.345735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5538.08 | −0.488003 | ||||||||
\(506\) | 5410.49 | + | 9371.25i | 0.475347 | + | 0.823326i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7653.18 | − | 13255.7i | 0.668416 | − | 1.15773i | ||||
\(509\) | 9815.42 | − | 17000.8i | 0.854737 | − | 1.48045i | −0.0221524 | − | 0.999755i | \(-0.507052\pi\) |
0.876889 | − | 0.480693i | \(-0.159615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 782.262 | + | 1354.92i | 0.0677206 | + | 0.117296i | ||||
\(512\) | 13722.1 | 1.18444 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9640.30 | −0.827267 | ||||||||
\(515\) | −1322.19 | − | 2290.09i | −0.113131 | − | 0.195949i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −906.223 | + | 1569.62i | −0.0770902 | + | 0.133524i | ||||
\(518\) | 18488.3 | − | 32022.7i | 1.56820 | − | 2.71621i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1456.73 | − | 2523.12i | −0.122849 | − | 0.212781i | ||||
\(521\) | −88.4336 | −0.00743636 | −0.00371818 | − | 0.999993i | \(-0.501184\pi\) | ||||
−0.00371818 | + | 0.999993i | \(0.501184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21346.4 | 1.78473 | 0.892363 | − | 0.451317i | \(-0.149046\pi\) | ||||
0.892363 | + | 0.451317i | \(0.149046\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4138.94 | + | 7168.86i | 0.340178 | + | 0.589205i | ||||
\(530\) | −559.896 | −0.0458874 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 23567.4 | 1.92063 | ||||||||
\(533\) | −4979.67 | − | 8625.03i | −0.404678 | − | 0.700923i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1227.27 | − | 2125.70i | 0.0991770 | − | 0.171780i | ||||
\(536\) | −443.842 | + | 768.757i | −0.0357669 | + | 0.0619501i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 833.027 | − | 1442.84i | 0.0656539 | − | 0.113716i | ||||
\(545\) | 879.084 | − | 1522.62i | 0.0690933 | − | 0.119673i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8284.80 | + | 14349.7i | 0.647592 | + | 1.12166i | 0.983696 | + | 0.179837i | \(0.0575571\pi\) |
−0.336105 | + | 0.941825i | \(0.609110\pi\) | |||||||
\(548\) | −14628.5 | −1.14033 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4337.92 | −0.336308 | ||||||||
\(551\) | 1869.75 | + | 3238.50i | 0.144562 | + | 0.250389i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.645410\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21355.9 | −1.61584 | ||||||||
\(560\) | 3231.79 | + | 5597.62i | 0.243871 | + | 0.422397i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 723.912 | − | 1253.85i | 0.0543352 | − | 0.0941113i | ||||
\(563\) | −11524.6 | + | 19961.3i | −0.862709 | + | 1.49426i | 0.00659429 | + | 0.999978i | \(0.497901\pi\) |
−0.869304 | + | 0.494278i | \(0.835432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4406.13 | + | 7631.64i | 0.328084 | + | 0.568258i | ||||
\(566\) | 11079.2 | 0.822778 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8776.27 | −0.648317 | ||||||||
\(569\) | 7366.96 | + | 12759.9i | 0.542775 | + | 0.940114i | 0.998743 | + | 0.0501179i | \(0.0159597\pi\) |
−0.455968 | + | 0.889996i | \(0.650707\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7555.94 | + | 13087.3i | −0.553776 | + | 0.959169i | 0.444221 | + | 0.895917i | \(0.353480\pi\) |
−0.997998 | + | 0.0632515i | \(0.979853\pi\) | |||||||
\(572\) | 13078.9 | − | 22653.3i | 0.956043 | − | 1.65591i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10327.5 | − | 17887.7i | −0.750975 | − | 1.30073i | ||||
\(575\) | 1559.07 | 0.113074 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26150.5 | −1.88676 | −0.943380 | − | 0.331715i | \(-0.892373\pi\) | ||||
−0.943380 | + | 0.331715i | \(0.892373\pi\) | |||||||
\(578\) | 10376.5 | + | 17972.7i | 0.746724 | + | 1.29336i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1260.39 | − | 2183.07i | 0.0902328 | − | 0.156288i | ||||
\(581\) | −3041.61 | + | 5268.22i | −0.217190 | + | 0.376184i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | 0.900447 | − | 0.434965i | \(-0.143239\pi\) |
−0.826915 | + | 0.562327i | \(0.809906\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3882.24 | + | 6724.24i | −0.271587 | + | 0.470403i | ||||
\(590\) | −4538.01 | + | 7860.06i | −0.316656 | + | 0.548464i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5925.50 | − | 10263.3i | −0.411379 | − | 0.712530i | ||||
\(593\) | −3260.34 | −0.225778 | −0.112889 | − | 0.993608i | \(-0.536010\pi\) | ||||
−0.112889 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1013.66 | 0.0698417 | ||||||||
\(596\) | 476.426 | + | 825.194i | 0.0327436 | + | 0.0567135i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8400.90 | + | 14550.8i | −0.574479 | + | 0.995026i | ||||
\(599\) | −11499.6 | + | 19917.9i | −0.784410 | + | 1.35864i | 0.144941 | + | 0.989440i | \(0.453701\pi\) |
−0.929351 | + | 0.369197i | \(0.879633\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7146.93 | + | 12378.9i | 0.485074 | + | 0.840173i | 0.999853 | − | 0.0171500i | \(-0.00545928\pi\) |
−0.514779 | + | 0.857323i | \(0.672126\pi\) | |||||||
\(602\) | −44290.5 | −2.99858 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10855.1 | −0.731274 | ||||||||
\(605\) | −816.702 | − | 1414.57i | −0.0548821 | − | 0.0950586i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8217.04 | − | 14232.3i | 0.549455 | − | 0.951685i | −0.448856 | − | 0.893604i | \(-0.648169\pi\) |
0.998312 | − | 0.0580809i | \(-0.0184981\pi\) | |||||||
\(608\) | 9528.80 | − | 16504.4i | 0.635598 | − | 1.10089i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9062.62 | − | 15696.9i | −0.601532 | − | 1.04188i | ||||
\(611\) | −2814.19 | −0.186334 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3674.45 | 0.242104 | 0.121052 | − | 0.992646i | \(-0.461373\pi\) | ||||
0.121052 | + | 0.992646i | \(0.461373\pi\) | |||||||
\(614\) | −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 | −0.690278 | − | 0.723544i | \(-0.742512\pi\) |
0.971747 | + | 0.236026i | \(0.0758450\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 654.905 | + | 1134.33i | 0.0425248 | + | 0.0736551i | 0.886504 | − | 0.462720i | \(-0.153127\pi\) |
−0.843980 | + | 0.536375i | \(0.819793\pi\) | |||||||
\(620\) | 5234.03 | 0.339038 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4028.76 | −0.259708 | ||||||||
\(623\) | 20989.4 | + | 36354.7i | 1.34979 | + | 2.33791i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4230.95 | + | 7328.23i | −0.270132 | + | 0.467883i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11044.9 | + | 19130.3i | −0.691875 | + | 1.19836i | ||||
\(635\) | 3765.31 | − | 6521.71i | 0.235310 | − | 0.407569i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19073.4 | − | 33036.2i | −1.18637 | − | 2.05485i | ||||
\(638\) | 8607.88 | 0.534152 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5683.43 | −0.351027 | ||||||||
\(641\) | −10036.6 | − | 17383.8i | −0.618440 | − | 1.07117i | −0.989770 | − | 0.142669i | \(-0.954431\pi\) |
0.371330 | − | 0.928501i | \(-0.378902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8867.96 | − | 15359.8i | 0.543885 | − | 0.942037i | −0.454791 | − | 0.890598i | \(-0.650286\pi\) |
0.998676 | − | 0.0514386i | \(-0.0163807\pi\) | |||||||
\(644\) | −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 | \(0.386834\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17341.4 | −1.04886 | ||||||||
\(650\) | −3367.75 | − | 5833.12i | −0.203222 | − | 0.351990i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5605.12 | − | 9708.36i | 0.336677 | − | 0.583142i | ||||
\(653\) | 14536.0 | − | 25177.0i | 0.871113 | − | 1.50881i | 0.0102660 | − | 0.999947i | \(-0.496732\pi\) |
0.860847 | − | 0.508864i | \(-0.169935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3187.81 | + | 5521.45i | 0.190165 | + | 0.329376i | ||||
\(656\) | −6619.90 | −0.393999 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5836.43 | −0.345787 | ||||||||
\(659\) | −2177.54 | − | 3771.62i | −0.128718 | − | 0.222946i | 0.794462 | − | 0.607314i | \(-0.207753\pi\) |
−0.923180 | + | 0.384368i | \(0.874419\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13647.7 | + | 23638.5i | −0.803075 | + | 1.39097i | 0.114508 | + | 0.993422i | \(0.463471\pi\) |
−0.917583 | + | 0.397545i | \(0.869862\pi\) | |||||||
\(662\) | 4631.19 | − | 8021.46i | 0.271898 | − | 0.470941i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −911.297 | − | 1578.41i | −0.0532608 | − | 0.0922504i | ||||
\(665\) | 11595.0 | 0.676141 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3093.72 | −0.179594 | ||||||||
\(668\) | −20537.4 | − | 35571.8i | −1.18955 | − | 2.06035i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1026.10 | + | 1777.26i | −0.0591669 | + | 0.102480i | ||||
\(671\) | 17315.8 | − | 29991.9i | 0.996230 | − | 1.72552i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8880.01 | + | 15380.6i | 0.508617 | + | 0.880951i | 0.999950 | + | 0.00997909i | \(0.00317650\pi\) |
−0.491333 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(674\) | −33456.3 | −1.91200 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18287.8 | 1.04050 | ||||||||
\(677\) | 968.667 | + | 1677.78i | 0.0549910 | + | 0.0952472i | 0.892210 | − | 0.451620i | \(-0.149154\pi\) |
−0.837219 | + | 0.546867i | \(0.815820\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22014.0 | − | 38129.4i | 1.24421 | − | 2.15504i | ||||
\(680\) | −151.851 | + | 263.013i | −0.00856355 | + | 0.0148325i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8936.48 | + | 15478.4i | 0.501753 | + | 0.869061i | ||||
\(683\) | 2125.71 | 0.119090 | 0.0595448 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595448 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7197.12 | −0.401442 | ||||||||
\(686\) | −17071.7 | − | 29569.0i | −0.950146 | − | 1.64570i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −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 | 0.610557 | − | 0.791973i | \(-0.290946\pi\) |
−0.991147 | + | 0.132771i | \(0.957612\pi\) | |||||||
\(692\) | 27924.8 | 1.53402 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 39942.4 | 2.18472 | ||||||||
\(695\) | 6348.74 | + | 10996.3i | 0.346506 | + | 0.600166i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −519.086 | + | 899.084i | −0.0282092 | + | 0.0488597i | ||||
\(698\) | 2509.98 | − | 4347.42i | 0.136109 | − | 0.235748i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3908.08 | − | 6768.99i | −0.211016 | − | 0.365491i | ||||
\(701\) | 24464.0 | 1.31810 | 0.659052 | − | 0.752097i | \(-0.270958\pi\) | ||||
0.659052 | + | 0.752097i | \(0.270958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −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 | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14749.1 | + | 25546.2i | 0.781263 | + | 1.35319i | 0.931206 | + | 0.364492i | \(0.118757\pi\) |
−0.149944 | + | 0.988695i | \(0.547909\pi\) | |||||||
\(710\) | −20289.6 | −1.07247 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12577.3 | −0.662012 | ||||||||
\(713\) | −3211.81 | − | 5563.02i | −0.168700 | − | 0.292198i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6434.72 | − | 11145.3i | 0.336566 | − | 0.582950i | ||||
\(716\) | −14422.6 | + | 24980.7i | −0.752790 | + | 1.30387i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4133.81 | − | 7159.98i | −0.214864 | − | 0.372156i | ||||
\(719\) | 3857.66 | 0.200093 | 0.100046 | − | 0.994983i | \(-0.468101\pi\) | ||||
0.100046 | + | 0.994983i | \(0.468101\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16270.2 | 0.840410 | ||||||||
\(722\) | 2507.66 | + | 4343.39i | 0.129260 | + | 0.223884i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17491.4 | + | 30295.9i | −0.897874 | + | 1.55516i | ||||
\(725\) | 620.105 | − | 1074.05i | 0.0317657 | − | 0.0550197i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4372.55 | − | 7573.48i | −0.223066 | − | 0.386361i | 0.732672 | − | 0.680582i | \(-0.238273\pi\) |
−0.955737 | + | 0.294221i | \(0.904940\pi\) | |||||||
\(728\) | 17925.8 | 0.912604 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1083.68 | −0.0549436 | ||||||||
\(731\) | 1113.08 | + | 1927.91i | 0.0563184 | + | 0.0975463i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4709.20 | − | 8156.58i | 0.237296 | − | 0.411010i | −0.722641 | − | 0.691223i | \(-0.757072\pi\) |
0.959938 | + | 0.280214i | \(0.0904054\pi\) | |||||||
\(734\) | −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 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6219.42 | 0.309587 | 0.154794 | − | 0.987947i | \(-0.450529\pi\) | ||||
0.154794 | + | 0.987947i | \(0.450529\pi\) | |||||||
\(740\) | 7165.49 | + | 12411.0i | 0.355958 | + | 0.616537i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1722.46 | − | 2983.39i | 0.0852204 | − | 0.147606i | ||||
\(743\) | −14693.7 | + | 25450.3i | −0.725518 | + | 1.25663i | 0.233242 | + | 0.972419i | \(0.425067\pi\) |
−0.958760 | + | 0.284216i | \(0.908267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 234.398 | + | 405.989i | 0.0115271 | + | 0.0199655i | ||||
\(746\) | 56758.5 | 2.78563 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | −0.473636 | − | 0.880721i | \(-0.657059\pi\) |
0.999544 | − | 0.0301801i | \(-0.00960808\pi\) | |||||||
\(752\) | −935.287 | + | 1619.97i | −0.0453543 | + | 0.0785559i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6682.75 | + | 11574.9i | 0.322774 | + | 0.559061i | ||||
\(755\) | −5340.65 | −0.257438 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13907.2 | −0.667722 | −0.333861 | − | 0.942622i | \(-0.608352\pi\) | ||||
−0.333861 | + | 0.942622i | \(0.608352\pi\) | |||||||
\(758\) | 6815.48 | + | 11804.8i | 0.326582 | + | 0.565657i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1736.98 | + | 3008.55i | −0.0829040 | + | 0.143594i | ||||
\(761\) | −11953.0 | + | 20703.3i | −0.569379 | + | 0.986193i | 0.427249 | + | 0.904134i | \(0.359483\pi\) |
−0.996628 | + | 0.0820585i | \(0.973851\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 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 | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12555.8 | − | 21747.3i | 0.588783 | − | 1.01980i | −0.405609 | − | 0.914047i | \(-0.632941\pi\) |
0.994392 | − | 0.105755i | \(-0.0337261\pi\) | |||||||
\(770\) | 13345.1 | − | 23114.5i | 0.624579 | − | 1.08180i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −548.319 | − | 949.716i | −0.0255627 | − | 0.0442759i | ||||
\(773\) | −14909.4 | −0.693729 | −0.346865 | − | 0.937915i | \(-0.612754\pi\) | ||||
−0.346865 | + | 0.937915i | \(0.612754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2575.10 | 0.119355 | ||||||||
\(776\) | 6595.62 | + | 11424.0i | 0.305115 | + | 0.528474i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −25356.0 | −1.15506 | ||||||||
\(785\) | −454.287 | − | 786.848i | −0.0206550 | − | 0.0357756i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1329.38 | − | 2302.56i | 0.0602128 | − | 0.104292i | −0.834348 | − | 0.551239i | \(-0.814155\pi\) |
0.894560 | + | 0.446947i | \(0.147489\pi\) | |||||||
\(788\) | −17078.6 | + | 29581.0i | −0.772082 | + | 1.33728i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2101.90 | + | 3640.60i | 0.0946610 | + | 0.163958i | ||||
\(791\) | −54220.0 | −2.43722 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | −0.979424 | − | 0.201815i | \(-0.935316\pi\) |
0.664489 | + | 0.747298i | \(0.268649\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 146.677 | + | 254.053i | 0.00649446 | + | 0.0112487i | ||||
\(800\) | −6320.48 | −0.279329 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3527.14 | −0.155296 | ||||||||
\(803\) | −1035.29 | − | 1793.17i | −0.0454975 | − | 0.0788040i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4796.31 | + | 8307.45i | −0.209997 | + | 0.363726i | ||||
\(806\) | −13875.7 | + | 24033.4i | −0.606391 | + | 1.05030i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5104.55 | + | 8841.34i | 0.222249 | + | 0.384947i | ||||
\(809\) | 21077.7 | 0.916012 | 0.458006 | − | 0.888949i | \(-0.348564\pi\) | ||||
0.458006 | + | 0.888949i | \(0.348564\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24468.4 | + | 42380.5i | −1.05358 | + | 1.82486i | ||||
\(815\) | 2757.68 | − | 4776.44i | 0.118524 | − | 0.205290i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12732.3 | + | 22052.9i | 0.545221 | + | 0.944350i | ||||
\(818\) | −35661.0 | −1.52428 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8005.20 | 0.340919 | ||||||||
\(821\) | 7400.25 | + | 12817.6i | 0.314580 | + | 0.544869i | 0.979348 | − | 0.202181i | \(-0.0648029\pi\) |
−0.664768 | + | 0.747050i | \(0.731470\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16588.3 | + | 28731.8i | −0.702591 | + | 1.21692i | 0.264963 | + | 0.964259i | \(0.414640\pi\) |
−0.967554 | + | 0.252665i | \(0.918693\pi\) | |||||||
\(824\) | −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 | \(0.291283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13221.1 | 0.553904 | 0.276952 | − | 0.960884i | \(-0.410676\pi\) | ||||
0.276952 | + | 0.960884i | \(0.410676\pi\) | |||||||
\(830\) | −2106.80 | − | 3649.08i | −0.0881060 | − | 0.152604i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23431.6 | − | 40584.7i | 0.976374 | − | 1.69113i | ||||
\(833\) | −1988.24 | + | 3443.73i | −0.0826991 | + | 0.143239i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10104.3 | − | 17501.1i | −0.418769 | − | 0.725329i | ||||
\(836\) | −31190.3 | −1.29036 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17902.5 | −0.737987 | ||||||||
\(839\) | −21062.0 | − | 36480.4i | −0.866675 | − | 1.50112i | −0.865375 | − | 0.501125i | \(-0.832920\pi\) |
−0.00129985 | − | 0.999999i | \(-0.500414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10964.0 | − | 18990.2i | 0.449547 | − | 0.778638i | ||||
\(842\) | −14785.7 | + | 25609.6i | −0.605166 | + | 1.04818i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12716.4 | − | 22025.4i | −0.518621 | − | 0.898278i | ||||
\(845\) | 8997.45 | 0.366298 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10050.0 | 0.407700 | ||||||||
\(848\) | −552.049 | − | 956.177i | −0.0223555 | − | 0.0387208i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −351.059 | + | 608.051i | −0.0141661 | + | 0.0245365i | ||||
\(851\) | 8794.07 | − | 15231.8i | 0.354238 | − | 0.613559i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7215.84 | − | 12498.2i | −0.289643 | − | 0.501677i | 0.684081 | − | 0.729406i | \(-0.260203\pi\) |
−0.973725 | + | 0.227729i | \(0.926870\pi\) | |||||||
\(854\) | 111521. | 4.46857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4524.80 | −0.180671 | ||||||||
\(857\) | 8056.71 | + | 13954.6i | 0.321134 | + | 0.556220i | 0.980722 | − | 0.195407i | \(-0.0626027\pi\) |
−0.659588 | + | 0.751627i | \(0.729269\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11250.2 | − | 19485.9i | 0.446858 | − | 0.773982i | −0.551321 | − | 0.834293i | \(-0.685876\pi\) |
0.998180 | + | 0.0603115i | \(0.0192094\pi\) | |||||||
\(860\) | 8582.80 | − | 14865.8i | 0.340315 | − | 0.589443i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14547.8 | + | 25197.5i | 0.574825 | + | 0.995626i | ||||
\(863\) | 43396.8 | 1.71175 | 0.855877 | − | 0.517180i | \(-0.173018\pi\) | ||||
0.855877 | + | 0.517180i | \(0.173018\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13738.8 | 0.540038 | ||||||||
\(866\) | 4687.09 | + | 8118.28i | 0.183919 | + | 0.318557i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20034.3 | 0.775366 | ||||||||
\(875\) | −1922.75 | − | 3330.29i | −0.0742865 | − | 0.128668i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1232.77 | − | 2135.21i | 0.0474659 | − | 0.0822133i | −0.841316 | − | 0.540543i | \(-0.818219\pi\) |
0.888782 | + | 0.458330i | \(0.151552\pi\) | |||||||
\(878\) | −17738.2 | + | 30723.5i | −0.681817 | + | 1.18094i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4277.12 | − | 7408.18i | −0.163843 | − | 0.283784i | ||||
\(881\) | −24512.9 | −0.937412 | −0.468706 | − | 0.883354i | \(-0.655280\pi\) | ||||
−0.468706 | + | 0.883354i | \(0.655280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24236.1 | 0.923679 | 0.461840 | − | 0.886963i | \(-0.347190\pi\) | ||||
0.461840 | + | 0.886963i | \(0.347190\pi\) | |||||||
\(884\) | −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 | −0.522712 | − | 0.852509i | \(-0.675080\pi\) |
0.999651 | + | 0.0264274i | \(0.00841308\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23167.1 | + | 40126.7i | 0.874017 | + | 1.51384i | ||||
\(890\) | −29076.9 | −1.09512 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19050.3 | 0.715081 | ||||||||
\(893\) | 1677.81 | + | 2906.05i | 0.0628731 | + | 0.108899i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7095.81 | + | 12290.3i | −0.265013 | + | 0.459016i | ||||
\(896\) | 17484.5 | − | 30284.0i | 0.651914 | − | 1.12915i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8122.42 | − | 14068.5i | 0.298836 | − | 0.517599i | ||||
\(905\) | −8605.62 | + | 14905.4i | −0.316089 | + | 0.547482i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13304.0 | − | 23043.3i | −0.487049 | − | 0.843594i | 0.512840 | − | 0.858484i | \(-0.328593\pi\) |
−0.999889 | + | 0.0148906i | \(0.995260\pi\) | |||||||
\(908\) | −51614.0 | −1.88642 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41442.1 | 1.50966 | ||||||||
\(911\) | 12416.1 | + | 21505.2i | 0.451550 | + | 0.782108i | 0.998483 | − | 0.0550686i | \(-0.0175378\pi\) |
−0.546932 | + | 0.837177i | \(0.684204\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 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 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26107.2 | −0.937102 | −0.468551 | − | 0.883436i | \(-0.655224\pi\) | ||||
−0.468551 | + | 0.883436i | \(0.655224\pi\) | |||||||
\(920\) | −1437.02 | − | 2489.00i | −0.0514970 | − | 0.0891954i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −38841.9 | + | 67276.2i | −1.38741 | + | 2.40306i | ||||
\(923\) | 30096.9 | − | 52129.3i | 1.07329 | − | 1.85900i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3525.37 | + | 6106.11i | 0.125312 | + | 0.217046i | ||||
\(926\) | 18501.2 | 0.656573 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12542.0 | 0.443653 | ||||||||
\(929\) | −11680.8 | − | 20231.7i | −0.412523 | − | 0.714511i | 0.582642 | − | 0.812729i | \(-0.302019\pi\) |
−0.995165 | + | 0.0982184i | \(0.968686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22743.0 | + | 39392.0i | −0.800613 | + | 1.38670i | ||||
\(932\) | 5803.45 | − | 10051.9i | 0.203968 | − | 0.353283i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10483.2 | + | 18157.4i | 0.367260 | + | 0.636112i | ||||
\(935\) | −1341.53 | −0.0469226 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10548.5 | 0.367775 | 0.183888 | − | 0.982947i | \(-0.441132\pi\) | ||||
0.183888 | + | 0.982947i | \(0.441132\pi\) | |||||||
\(938\) | −6313.40 | − | 10935.1i | −0.219765 | − | 0.380644i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1131.01 | − | 1958.96i | 0.0392441 | − | 0.0679727i | ||||
\(941\) | −3245.07 | + | 5620.62i | −0.112419 | + | 0.194715i | −0.916745 | − | 0.399473i | \(-0.869193\pi\) |
0.804326 | + | 0.594188i | \(0.202527\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −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 | 0.994121 | − | 0.108271i | \(-0.0345314\pi\) |
−0.590826 | + | 0.806799i | \(0.701198\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1607.50 | − | 2784.26i | 0.0549858 | − | 0.0952382i | ||||
\(950\) | −4015.68 | + | 6955.35i | −0.137143 | + | 0.237538i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −934.305 | − | 1618.26i | −0.0318078 | − | 0.0550927i | ||||
\(953\) | −6740.26 | −0.229106 | −0.114553 | − | 0.993417i | \(-0.536544\pi\) | ||||
−0.114553 | + | 0.993417i | \(0.536544\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3731.48 | 0.126437 | ||||||||
\(956\) | −16003.1 | − | 27718.2i | −0.541399 | − | 0.937731i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 45776.8 | 1.52943 | ||||||||
\(965\) | −269.769 | − | 467.253i | −0.00899913 | − | 0.0155870i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8391.27 | + | 14534.1i | −0.279054 | + | 0.483336i | −0.971150 | − | 0.238470i | \(-0.923354\pi\) |
0.692096 | + | 0.721806i | \(0.256688\pi\) | |||||||
\(968\) | −1505.54 | + | 2607.67i | −0.0499895 | + | 0.0865844i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15248.2 | + | 26410.6i | 0.504732 | + | 0.874221i | ||||
\(971\) | 46282.7 | 1.52964 | 0.764822 | − | 0.644242i | \(-0.222827\pi\) | ||||
0.764822 | + | 0.644242i | \(0.222827\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −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 | −0.805286 | − | 0.592886i | \(-0.797988\pi\) |
0.916098 | + | 0.400955i | \(0.131322\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27778.5 | − | 48113.7i | −0.906848 | − | 1.57071i | ||||
\(980\) | 30662.0 | 0.999452 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −65240.8 | −2.12008 | ||||||||
\(983\) | −25037.4 | − | 43366.1i | −0.812381 | − | 1.40708i | −0.911194 | − | 0.411979i | \(-0.864838\pi\) |
0.0988128 | − | 0.995106i | \(-0.468496\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8402.55 | + | 14553.6i | −0.271805 | + | 0.470779i | ||||
\(986\) | 696.618 | − | 1206.58i | 0.0224998 | − | 0.0389708i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 62418.7 | − | 108112.i | 1.99175 | − | 3.44981i | ||||
\(995\) | −3422.46 | + | 5927.88i | −0.109045 | + | 0.188871i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30310.0 | + | 52498.5i | 0.962817 | + | 1.66765i | 0.715368 | + | 0.698748i | \(0.246259\pi\) |
0.247449 | + | 0.968901i | \(0.420408\pi\) | |||||||
\(998\) | 75570.3 | 2.39693 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 135.4.e.c.91.2 | 14 | ||
3.2 | odd | 2 | 45.4.e.c.31.6 | yes | 14 | ||
9.2 | odd | 6 | 45.4.e.c.16.6 | ✓ | 14 | ||
9.4 | even | 3 | 405.4.a.n.1.6 | 7 | |||
9.5 | odd | 6 | 405.4.a.m.1.2 | 7 | |||
9.7 | even | 3 | inner | 135.4.e.c.46.2 | 14 | ||
15.2 | even | 4 | 225.4.k.d.49.3 | 28 | |||
15.8 | even | 4 | 225.4.k.d.49.12 | 28 | |||
15.14 | odd | 2 | 225.4.e.d.76.2 | 14 | |||
45.2 | even | 12 | 225.4.k.d.124.12 | 28 | |||
45.4 | even | 6 | 2025.4.a.ba.1.2 | 7 | |||
45.14 | odd | 6 | 2025.4.a.bb.1.6 | 7 | |||
45.29 | odd | 6 | 225.4.e.d.151.2 | 14 | |||
45.38 | even | 12 | 225.4.k.d.124.3 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.c.16.6 | ✓ | 14 | 9.2 | odd | 6 | ||
45.4.e.c.31.6 | yes | 14 | 3.2 | odd | 2 | ||
135.4.e.c.46.2 | 14 | 9.7 | even | 3 | inner | ||
135.4.e.c.91.2 | 14 | 1.1 | even | 1 | trivial | ||
225.4.e.d.76.2 | 14 | 15.14 | odd | 2 | |||
225.4.e.d.151.2 | 14 | 45.29 | odd | 6 | |||
225.4.k.d.49.3 | 28 | 15.2 | even | 4 | |||
225.4.k.d.49.12 | 28 | 15.8 | even | 4 | |||
225.4.k.d.124.3 | 28 | 45.38 | even | 12 | |||
225.4.k.d.124.12 | 28 | 45.2 | even | 12 | |||
405.4.a.m.1.2 | 7 | 9.5 | odd | 6 | |||
405.4.a.n.1.6 | 7 | 9.4 | even | 3 | |||
2025.4.a.ba.1.2 | 7 | 45.4 | even | 6 | |||
2025.4.a.bb.1.6 | 7 | 45.14 | odd | 6 |