Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(16,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, 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("45.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.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: | \(2.65508595026\) |
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: | \( x^{14} - 2 x^{13} + 48 x^{12} - 60 x^{11} + 1605 x^{10} - 1800 x^{9} + 23232 x^{8} - 2346 x^{7} + \cdots + 82944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Root | \(2.13089 - 3.69081i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.31 |
Dual form | 45.4.e.c.16.6 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | \(0.104913\pi\) |
−0.192791 | + | 0.981240i | \(0.561754\pi\) | |||||||
\(3\) | 4.39640 | + | 2.76977i | 0.846088 | + | 0.533043i | ||||
\(4\) | −5.08138 | + | 8.80120i | −0.635172 | + | 1.10015i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.854448 | + | 22.1284i | −0.0581378 | + | 1.50564i | ||||
\(7\) | −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 | ||||||||
\(9\) | 11.6567 | + | 24.3541i | 0.431731 | + | 0.902003i | ||||
\(10\) | 21.3089 | 0.673846 | ||||||||
\(11\) | −20.3573 | − | 35.2599i | −0.557996 | − | 0.966478i | −0.997664 | − | 0.0683175i | \(-0.978237\pi\) |
0.439667 | − | 0.898161i | \(-0.355096\pi\) | |||||||
\(12\) | −46.7171 | + | 24.6194i | −1.12384 | + | 0.592250i | ||||
\(13\) | −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 | ||||
\(15\) | 22.9845 | − | 12.1126i | 0.395638 | − | 0.208497i | ||||
\(16\) | 21.0102 | + | 36.3908i | 0.328285 | + | 0.568606i | ||||
\(17\) | −6.58990 | −0.0940168 | −0.0470084 | − | 0.998894i | \(-0.514969\pi\) | ||||
−0.0470084 | + | 0.998894i | \(0.514969\pi\) | |||||||
\(18\) | −65.0470 | + | 94.9186i | −0.851763 | + | 1.24292i | ||||
\(19\) | 75.3803 | 0.910180 | 0.455090 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455090 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(20\) | 25.4069 | + | 44.0060i | 0.284058 | + | 0.492002i | ||||
\(21\) | 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 | \(-0.742108\pi\) |
0.972045 | + | 0.234793i | \(0.0754414\pi\) | |||||||
\(24\) | −40.5225 | − | 25.5295i | −0.344651 | − | 0.217133i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −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 | 0.775618 | − | 0.631202i | \(-0.217438\pi\) |
−0.934446 | + | 0.356104i | \(0.884105\pi\) | |||||||
\(30\) | 93.6825 | + | 59.0208i | 0.570133 | + | 0.359189i | ||||
\(31\) | −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 | ||||
\(33\) | 8.16291 | − | 211.402i | 0.0430600 | − | 1.11516i | ||||
\(34\) | −14.0423 | − | 24.3221i | −0.0708306 | − | 0.122682i | ||||
\(35\) | −153.820 | −0.742865 | ||||||||
\(36\) | −273.577 | − | 21.1590i | −1.26656 | − | 0.0979582i | ||||
\(37\) | −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 | ||||
\(39\) | −290.606 | + | 153.146i | −1.19318 | + | 0.628794i | ||||
\(40\) | −23.0430 | + | 39.9116i | −0.0910853 | + | 0.157764i | ||||
\(41\) | 78.7700 | − | 136.434i | 0.300044 | − | 0.519692i | −0.676102 | − | 0.736808i | \(-0.736332\pi\) |
0.976146 | + | 0.217117i | \(0.0696653\pi\) | |||||||
\(42\) | 602.695 | − | 317.613i | 2.21423 | − | 1.16688i | ||||
\(43\) | 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 | ||||||||
\(45\) | 134.598 | + | 10.4101i | 0.445882 | + | 0.0344853i | ||||
\(46\) | 265.776 | 0.851882 | ||||||||
\(47\) | −22.2579 | − | 38.5518i | −0.0690777 | − | 0.119646i | 0.829418 | − | 0.558629i | \(-0.188672\pi\) |
−0.898496 | + | 0.438983i | \(0.855339\pi\) | |||||||
\(48\) | −8.42472 | + | 218.182i | −0.0253334 | + | 0.656081i | ||||
\(49\) | −301.710 | + | 522.577i | −0.879620 | + | 1.52355i | ||||
\(50\) | 53.2722 | − | 92.2702i | 0.150677 | − | 0.260980i | ||||
\(51\) | −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 | \(-0.489160\pi\) | ||||
0.0340489 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(54\) | −548.876 | + | 237.135i | −1.38319 | + | 0.597592i | ||||
\(55\) | −203.573 | −0.499087 | ||||||||
\(56\) | 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 | −0.529486 | − | 0.848319i | \(-0.677615\pi\) |
0.999409 | + | 0.0343889i | \(0.0109485\pi\) | |||||||
\(60\) | −10.1877 | + | 263.840i | −0.0219204 | + | 0.567692i | ||||
\(61\) | −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 | ||||||||
\(63\) | 469.546 | − | 685.176i | 0.939004 | − | 1.37022i | ||||
\(64\) | −741.296 | −1.44784 | ||||||||
\(65\) | 158.045 | + | 273.741i | 0.301585 | + | 0.522360i | ||||
\(66\) | 797.638 | − | 420.346i | 1.48761 | − | 0.783955i | ||||
\(67\) | −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 | ||||
\(69\) | 286.675 | − | 151.075i | 0.500169 | − | 0.263583i | ||||
\(70\) | −327.773 | − | 567.719i | −0.559662 | − | 0.969363i | ||||
\(71\) | 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 | \(-0.512981\pi\) | ||||
−0.0407686 | + | 0.999169i | \(0.512981\pi\) | |||||||
\(74\) | −600.973 | − | 1040.92i | −0.944077 | − | 1.63519i | ||||
\(75\) | 5.01227 | − | 129.807i | 0.00771690 | − | 0.199851i | ||||
\(76\) | −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 | 0.927677 | − | 0.373384i | \(-0.121803\pi\) |
−0.787198 | + | 0.616700i | \(0.788469\pi\) | |||||||
\(80\) | 210.102 | 0.293627 | ||||||||
\(81\) | −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 | \(-0.124928\pi\) |
−0.793215 | + | 0.608941i | \(0.791595\pi\) | |||||||
\(84\) | 1374.52 | + | 865.959i | 1.78539 | + | 1.12481i | ||||
\(85\) | −16.4747 | + | 28.5351i | −0.0210228 | + | 0.0364125i | ||||
\(86\) | −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 | \(0.198056\pi\) | |||||||
\(90\) | 248.392 | + | 518.958i | 0.290920 | + | 0.607811i | ||||
\(91\) | 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 | ||||
\(95\) | 188.451 | − | 326.406i | 0.203522 | − | 0.352511i | ||||
\(96\) | −1162.18 | + | 612.458i | −1.23557 | + | 0.651132i | ||||
\(97\) | 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 | ||||||||
\(99\) | 621.422 | − | 906.799i | 0.630862 | − | 0.920573i | ||||
\(100\) | 254.069 | 0.254069 | ||||||||
\(101\) | −553.808 | − | 959.224i | −0.545604 | − | 0.945013i | −0.998569 | − | 0.0534851i | \(-0.982967\pi\) |
0.452965 | − | 0.891528i | \(-0.350366\pi\) | |||||||
\(102\) | 5.63073 | − | 145.824i | 0.00546593 | − | 0.141556i | ||||
\(103\) | −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 | ||||
\(105\) | −676.253 | − | 426.045i | −0.628529 | − | 0.395979i | ||||
\(106\) | 55.9896 | + | 96.9769i | 0.0513037 | + | 0.0888607i | ||||
\(107\) | 490.910 | 0.443533 | 0.221766 | − | 0.975100i | \(-0.428818\pi\) | ||||
0.221766 | + | 0.975100i | \(0.428818\pi\) | |||||||
\(108\) | −1144.15 | − | 850.770i | −1.01941 | − | 0.758013i | ||||
\(109\) | −351.634 | −0.308994 | −0.154497 | − | 0.987993i | \(-0.549376\pi\) | ||||
−0.154497 | + | 0.987993i | \(0.549376\pi\) | |||||||
\(110\) | −433.792 | − | 751.349i | −0.376004 | − | 0.651258i | ||||
\(111\) | −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 | 0.221710 | + | 0.975113i | \(0.428836\pi\) |
−0.955327 | + | 0.295550i | \(0.904497\pi\) | |||||||
\(114\) | −64.4085 | + | 1668.04i | −0.0529159 | + | 1.37041i | ||||
\(115\) | −155.907 | − | 270.039i | −0.126421 | − | 0.218967i | ||||
\(116\) | 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 | ||||
\(120\) | −211.852 | + | 111.644i | −0.161161 | + | 0.0849302i | ||||
\(121\) | −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 | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 3529.40 | + | 272.971i | 2.49543 | + | 0.193001i | ||||
\(127\) | −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 | ||||
\(129\) | −67.7286 | + | 1754.03i | −0.0462262 | + | 1.19716i | ||||
\(130\) | −673.551 | + | 1166.62i | −0.454418 | + | 0.787075i | ||||
\(131\) | −637.562 | + | 1104.29i | −0.425222 | + | 0.736506i | −0.996441 | − | 0.0842915i | \(-0.973137\pi\) |
0.571219 | + | 0.820798i | \(0.306471\pi\) | |||||||
\(132\) | 1819.11 | + | 1146.06i | 1.19950 | + | 0.755692i | ||||
\(133\) | −1159.50 | − | 2008.31i | −0.755948 | − | 1.30934i | ||||
\(134\) | −410.441 | −0.264603 | ||||||||
\(135\) | 562.914 | + | 418.573i | 0.358873 | + | 0.266852i | ||||
\(136\) | 60.7403 | 0.0382973 | ||||||||
\(137\) | −719.712 | − | 1246.58i | −0.448826 | − | 0.777389i | 0.549484 | − | 0.835504i | \(-0.314824\pi\) |
−0.998310 | + | 0.0581150i | \(0.981491\pi\) | |||||||
\(138\) | 1168.46 | + | 736.140i | 0.720768 | + | 0.454090i | ||||
\(139\) | 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 | ||||
\(141\) | 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 | ||||
\(145\) | −248.042 | −0.142060 | ||||||||
\(146\) | −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 | −0.878625 | − | 0.477512i | \(-0.841539\pi\) |
0.852850 | + | 0.522156i | \(0.174872\pi\) | |||||||
\(150\) | 489.774 | − | 258.105i | 0.266599 | − | 0.140495i | ||||
\(151\) | 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 | ||||||||
\(153\) | −76.8166 | − | 160.491i | −0.0405899 | − | 0.0848034i | ||||
\(154\) | −5338.06 | −2.79320 | ||||||||
\(155\) | 257.510 | + | 446.021i | 0.133443 | + | 0.231131i | ||||
\(156\) | 128.809 | − | 3335.87i | 0.0661087 | − | 1.71207i | ||||
\(157\) | −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 | ||||
\(159\) | 115.517 | + | 72.7764i | 0.0576167 | + | 0.0362990i | ||||
\(160\) | 632.048 | + | 1094.74i | 0.312299 | + | 0.540917i | ||||
\(161\) | −1918.52 | −0.939136 | ||||||||
\(162\) | −3069.89 | − | 477.719i | −1.48885 | − | 0.231686i | ||||
\(163\) | −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 | ||||
\(165\) | −894.990 | − | 563.851i | −0.422272 | − | 0.266035i | ||||
\(166\) | −421.359 | + | 729.816i | −0.197011 | + | 0.341233i | ||||
\(167\) | 2020.85 | − | 3500.22i | 0.936396 | − | 1.62189i | 0.164270 | − | 0.986415i | \(-0.447473\pi\) |
0.772126 | − | 0.635470i | \(-0.219194\pi\) | |||||||
\(168\) | −56.8506 | + | 1472.31i | −0.0261078 | + | 0.676137i | ||||
\(169\) | −899.745 | − | 1558.40i | −0.409534 | − | 0.709333i | ||||
\(170\) | −140.423 | −0.0633529 | ||||||||
\(171\) | 878.687 | + | 1835.82i | 0.392953 | + | 0.820985i | ||||
\(172\) | −3433.12 | −1.52194 | ||||||||
\(173\) | 1373.88 | + | 2379.63i | 0.603780 | + | 1.04578i | 0.992243 | + | 0.124314i | \(0.0396730\pi\) |
−0.388463 | + | 0.921465i | \(0.626994\pi\) | |||||||
\(174\) | 971.875 | − | 512.167i | 0.423435 | − | 0.223145i | ||||
\(175\) | −384.549 | + | 666.059i | −0.166110 | + | 0.287710i | ||||
\(176\) | 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 | \(0.701893\pi\) | |||||||
\(180\) | −775.564 | + | 1131.73i | −0.321151 | + | 0.468633i | ||||
\(181\) | 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 | ||||
\(185\) | −705.073 | + | 1221.22i | −0.280206 | + | 0.485330i | ||||
\(186\) | −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 | ||||
\(190\) | 1606.27 | 0.613322 | ||||||||
\(191\) | 373.148 | + | 646.311i | 0.141361 | + | 0.244845i | 0.928010 | − | 0.372557i | \(-0.121519\pi\) |
−0.786648 | + | 0.617402i | \(0.788185\pi\) | |||||||
\(192\) | −3259.04 | − | 2053.22i | −1.22500 | − | 0.771763i | ||||
\(193\) | −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 | ||||
\(195\) | −63.3730 | + | 1641.22i | −0.0232730 | + | 0.602720i | ||||
\(196\) | −3066.20 | − | 5310.82i | −1.11742 | − | 1.93543i | ||||
\(197\) | −3361.02 | −1.21555 | −0.607774 | − | 0.794110i | \(-0.707937\pi\) | ||||
−0.607774 | + | 0.794110i | \(0.707937\pi\) | |||||||
\(198\) | 4671.00 | + | 361.264i | 1.67653 | + | 0.129666i | ||||
\(199\) | 1368.99 | 0.487663 | 0.243831 | − | 0.969818i | \(-0.421596\pi\) | ||||
0.243831 | + | 0.969818i | \(0.421596\pi\) | |||||||
\(200\) | 115.215 | + | 199.558i | 0.0407346 | + | 0.0705544i | ||||
\(201\) | −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 | ||||
\(205\) | −393.850 | − | 682.168i | −0.134184 | − | 0.232413i | ||||
\(206\) | −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 | ||||
\(210\) | 131.431 | − | 3403.78i | 0.0431885 | − | 1.11849i | ||||
\(211\) | −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 | ||||
\(213\) | 4186.10 | + | 2637.28i | 1.34660 | + | 0.848372i | ||||
\(214\) | 1046.07 | + | 1811.85i | 0.334150 | + | 0.578765i | ||||
\(215\) | 1689.07 | 0.535784 | ||||||||
\(216\) | 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 | ||||
\(220\) | 1034.43 | − | 1791.69i | 0.317006 | − | 0.549071i | ||||
\(221\) | 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 | \(-0.257483\pi\) |
−0.971743 | + | 0.236043i | \(0.924149\pi\) | |||||||
\(224\) | 7777.72 | 2.31996 | ||||||||
\(225\) | 381.572 | − | 556.801i | 0.113058 | − | 0.164978i | ||||
\(226\) | −7511.18 | −2.21078 | ||||||||
\(227\) | −2539.37 | − | 4398.32i | −0.742484 | − | 1.28602i | −0.951361 | − | 0.308078i | \(-0.900314\pi\) |
0.208877 | − | 0.977942i | \(-0.433019\pi\) | |||||||
\(228\) | −3521.55 | + | 1855.82i | −1.02290 | + | 0.539055i | ||||
\(229\) | −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 | ||||
\(231\) | −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 | \(-0.448670\pi\) | ||||
0.160561 | + | 0.987026i | \(0.448670\pi\) | |||||||
\(234\) | −3140.56 | − | 6561.48i | −0.877371 | − | 1.83307i | ||||
\(235\) | −222.579 | −0.0617849 | ||||||||
\(236\) | 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 | −0.570347 | − | 0.821404i | \(-0.693191\pi\) |
0.996530 | + | 0.0832330i | \(0.0265246\pi\) | |||||||
\(240\) | 923.694 | + | 581.935i | 0.248434 | + | 0.156516i | ||||
\(241\) | −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 | ||||||||
\(243\) | −3582.83 | + | 1229.72i | −0.945839 | + | 0.324637i | ||||
\(244\) | 8644.39 | 2.26803 | ||||||||
\(245\) | 1508.55 | + | 2612.88i | 0.393378 | + | 0.681351i | ||||
\(246\) | 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 | ||||
\(250\) | −266.361 | − | 461.351i | −0.0673846 | − | 0.116714i | ||||
\(251\) | 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 | ||||
\(255\) | −151.465 | + | 79.8205i | −0.0371966 | + | 0.0196022i | ||||
\(256\) | −543.033 | + | 940.561i | −0.132576 | + | 0.229629i | ||||
\(257\) | −1131.02 | + | 1958.98i | −0.274517 | + | 0.475478i | −0.970013 | − | 0.243052i | \(-0.921851\pi\) |
0.695496 | + | 0.718530i | \(0.255185\pi\) | |||||||
\(258\) | −6618.09 | + | 3487.66i | −1.59699 | + | 0.841598i | ||||
\(259\) | 4338.17 | + | 7513.92i | 1.04077 | + | 1.80267i | ||||
\(260\) | −3212.34 | −0.766233 | ||||||||
\(261\) | 757.166 | − | 1104.88i | 0.179569 | − | 0.262032i | ||||
\(262\) | −5434.30 | −1.28142 | ||||||||
\(263\) | −3640.31 | − | 6305.20i | −0.853503 | − | 1.47831i | −0.878027 | − | 0.478611i | \(-0.841141\pi\) |
0.0245245 | − | 0.999699i | \(-0.492193\pi\) | |||||||
\(264\) | −75.2391 | + | 1948.53i | −0.0175403 | + | 0.454257i | ||||
\(265\) | 65.6881 | − | 113.775i | 0.0152271 | − | 0.0263742i | ||||
\(266\) | 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 | \(0.503852\pi\) | |||||||
\(270\) | −345.365 | + | 2969.54i | −0.0778452 | + | 0.669335i | ||||
\(271\) | 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 | ||||
\(275\) | −508.933 | + | 881.498i | −0.111599 | + | 0.193296i | ||||
\(276\) | −127.067 | + | 3290.75i | −0.0277120 | + | 0.717681i | ||||
\(277\) | −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 | ||||||||
\(279\) | −2772.83 | − | 214.456i | −0.595000 | − | 0.0460184i | ||||
\(280\) | 1417.78 | 0.302603 | ||||||||
\(281\) | −169.861 | − | 294.209i | −0.0360608 | − | 0.0624591i | 0.847432 | − | 0.530904i | \(-0.178148\pi\) |
−0.883493 | + | 0.468445i | \(0.844814\pi\) | |||||||
\(282\) | 872.107 | − | 459.590i | 0.184160 | − | 0.0970504i | ||||
\(283\) | −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 | ||||
\(285\) | 1732.58 | − | 913.048i | 0.360102 | − | 0.189769i | ||||
\(286\) | 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 | ||||||||
\(290\) | −528.550 | − | 915.475i | −0.107026 | − | 0.185374i | ||||
\(291\) | −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 | \(-0.838985\pi\) |
0.857012 | + | 0.515297i | \(0.172318\pi\) | |||||||
\(294\) | −11306.0 | − | 7122.86i | −2.24278 | − | 1.41297i | ||||
\(295\) | −1064.82 | − | 1844.31i | −0.210156 | − | 0.364001i | ||||
\(296\) | 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 | ||||
\(300\) | 1116.99 | + | 703.713i | 0.214965 | + | 0.135430i | ||||
\(301\) | 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 | ||||
\(305\) | −4252.97 | −0.798441 | ||||||||
\(306\) | 428.653 | − | 625.504i | 0.0800800 | − | 0.116855i | ||||
\(307\) | 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 | ||||
\(309\) | −2431.18 | + | 1281.20i | −0.447589 | + | 0.235874i | ||||
\(310\) | −1097.45 | + | 1900.84i | −0.201068 | + | 0.348260i | ||||
\(311\) | −472.662 | + | 818.674i | −0.0861807 | + | 0.149269i | −0.905894 | − | 0.423505i | \(-0.860800\pi\) |
0.819713 | + | 0.572774i | \(0.194133\pi\) | |||||||
\(312\) | 2678.57 | − | 1411.57i | 0.486038 | − | 0.256137i | ||||
\(313\) | −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 | ||||||||
\(315\) | −1793.03 | − | 3746.13i | −0.320718 | − | 0.670066i | ||||
\(316\) | −2004.90 | −0.356913 | ||||||||
\(317\) | 2591.62 | + | 4488.81i | 0.459179 | + | 0.795321i | 0.998918 | − | 0.0465112i | \(-0.0148103\pi\) |
−0.539739 | + | 0.841833i | \(0.681477\pi\) | |||||||
\(318\) | −22.4508 | + | 581.428i | −0.00395906 | + | 0.102531i | ||||
\(319\) | −1009.89 | + | 1749.19i | −0.177251 | + | 0.307008i | ||||
\(320\) | −1853.24 | + | 3209.91i | −0.323748 | + | 0.560748i | ||||
\(321\) | 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 | ||||
\(325\) | 1580.45 | 0.269746 | ||||||||
\(326\) | −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 | ||||
\(330\) | 173.943 | − | 4504.74i | 0.0290158 | − | 0.751448i | ||||
\(331\) | 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 | ||||||||
\(333\) | −3287.54 | − | 6868.56i | −0.541009 | − | 1.13032i | ||||
\(334\) | 17224.8 | 2.82186 | ||||||||
\(335\) | 240.769 | + | 417.024i | 0.0392675 | + | 0.0680133i | ||||
\(336\) | 5942.47 | − | 3131.61i | 0.964846 | − | 0.508463i | ||||
\(337\) | 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 | ||||
\(339\) | −8101.81 | + | 4269.56i | −1.29802 | + | 0.684043i | ||||
\(340\) | −167.429 | − | 289.995i | −0.0267062 | − | 0.0462565i | ||||
\(341\) | 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 | ||||
\(345\) | 62.5159 | − | 1619.03i | 0.00975577 | − | 0.252653i | ||||
\(346\) | −5855.16 | + | 10141.4i | −0.909756 | + | 1.57574i | ||||
\(347\) | 4686.12 | − | 8116.60i | 0.724969 | − | 1.25568i | −0.234018 | − | 0.972232i | \(-0.575187\pi\) |
0.958987 | − | 0.283451i | \(-0.0914792\pi\) | |||||||
\(348\) | 2216.48 | + | 1396.40i | 0.341425 | + | 0.215101i | ||||
\(349\) | 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 | ||||||||
\(351\) | −7117.23 | − | 5292.25i | −1.08231 | − | 0.804784i | ||||
\(352\) | 10293.4 | 1.55864 | ||||||||
\(353\) | 3631.06 | + | 6289.19i | 0.547484 | + | 0.948271i | 0.998446 | + | 0.0557274i | \(0.0177478\pi\) |
−0.450962 | + | 0.892543i | \(0.648919\pi\) | |||||||
\(354\) | 7980.37 | + | 5027.70i | 1.19817 | + | 0.754856i | ||||
\(355\) | 2380.41 | − | 4122.99i | 0.355885 | − | 0.616410i | ||||
\(356\) | −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 | \(0.545546\pi\) | |||||||
\(360\) | −1240.61 | − | 95.9514i | −0.181628 | − | 0.0140475i | ||||
\(361\) | −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 | ||||
\(365\) | −127.139 | + | 220.212i | −0.0182323 | + | 0.0315792i | ||||
\(366\) | 16664.0 | − | 8781.72i | 2.37989 | − | 1.25417i | ||||
\(367\) | −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 | ||||||||
\(369\) | 4240.91 | + | 328.000i | 0.598301 | + | 0.0462737i | ||||
\(370\) | −6009.73 | −0.844409 | ||||||||
\(371\) | −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 | −0.131805 | + | 0.991276i | \(0.542077\pi\) |
−0.792568 | + | 0.609784i | \(0.791256\pi\) | |||||||
\(374\) | −571.729 | + | 990.263i | −0.0790465 | + | 0.136913i | ||||
\(375\) | −549.550 | − | 346.221i | −0.0756764 | − | 0.0476768i | ||||
\(376\) | 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 | \(0.569544\pi\) | |||||||
\(380\) | 1915.18 | + | 3317.19i | 0.258544 | + | 0.447811i | ||||
\(381\) | −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 | \(-0.783432\pi\) |
0.933469 | + | 0.358658i | \(0.116765\pi\) | |||||||
\(384\) | 227.895 | − | 5902.00i | 0.0302858 | − | 0.784336i | ||||
\(385\) | 3131.36 | + | 5423.67i | 0.414516 | + | 0.717963i | ||||
\(386\) | −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 | 0.706129 | − | 0.708083i | \(-0.250440\pi\) |
−0.966282 | + | 0.257484i | \(0.917106\pi\) | |||||||
\(390\) | −6192.48 | + | 3263.37i | −0.804022 | + | 0.423710i | ||||
\(391\) | −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 | ||||
\(395\) | 986.395 | 0.125648 | ||||||||
\(396\) | 4823.24 | + | 10077.1i | 0.612063 | + | 1.27876i | ||||
\(397\) | −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 | ||||
\(399\) | 464.937 | − | 12040.9i | 0.0583358 | − | 1.51077i | ||||
\(400\) | 525.256 | − | 909.769i | 0.0656569 | − | 0.113721i | ||||
\(401\) | −413.811 | + | 716.742i | −0.0515330 | + | 0.0892578i | −0.890641 | − | 0.454707i | \(-0.849744\pi\) |
0.839108 | + | 0.543965i | \(0.183077\pi\) | |||||||
\(402\) | −1804.47 | − | 1136.83i | −0.223877 | − | 0.141044i | ||||
\(403\) | −3255.85 | − | 5639.30i | −0.402445 | − | 0.697056i | ||||
\(404\) | 11256.4 | 1.38621 | ||||||||
\(405\) | 1315.45 | + | 3399.36i | 0.161395 | + | 0.417075i | ||||
\(406\) | −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 | −0.494167 | − | 0.869367i | \(-0.664527\pi\) |
0.999977 | − | 0.00672263i | \(-0.00213989\pi\) | |||||||
\(410\) | 1678.50 | − | 2907.25i | 0.202184 | − | 0.350192i | ||||
\(411\) | 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 | ||||
\(415\) | 988.693 | 0.116947 | ||||||||
\(416\) | −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 | −0.962101 | − | 0.272694i | \(-0.912085\pi\) |
0.717210 | + | 0.696857i | \(0.245419\pi\) | |||||||
\(420\) | 7186.01 | − | 3786.95i | 0.834861 | − | 0.439962i | ||||
\(421\) | −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 | ||||||||
\(423\) | 679.440 | − | 991.459i | 0.0780981 | − | 0.113963i | ||||
\(424\) | −242.184 | −0.0277394 | ||||||||
\(425\) | 82.3737 | + | 142.675i | 0.00940168 | + | 0.0162842i | ||||
\(426\) | −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 | ||||
\(430\) | 3599.22 | + | 6234.03i | 0.403651 | + | 0.699144i | ||||
\(431\) | 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 | \(-0.538951\pi\) | ||||
−0.122062 | + | 0.992522i | \(0.538951\pi\) | |||||||
\(434\) | 6752.39 | + | 11695.5i | 0.746832 | + | 1.29355i | ||||
\(435\) | −1090.49 | − | 687.019i | −0.120196 | − | 0.0757243i | ||||
\(436\) | 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 | 0.546037 | − | 0.837761i | \(-0.316136\pi\) |
−0.998541 | + | 0.0540018i | \(0.982802\pi\) | |||||||
\(440\) | 1876.37 | 0.203301 | ||||||||
\(441\) | −16243.8 | − | 1256.33i | −1.75400 | − | 0.135658i | ||||
\(442\) | 1775.45 | 0.191063 | ||||||||
\(443\) | 5433.41 | + | 9410.93i | 0.582729 | + | 1.00932i | 0.995154 | + | 0.0983247i | \(0.0313484\pi\) |
−0.412426 | + | 0.910991i | \(0.635318\pi\) | |||||||
\(444\) | 13175.6 | − | 6943.39i | 1.40830 | − | 0.742159i | ||||
\(445\) | 3411.36 | − | 5908.65i | 0.363402 | − | 0.629431i | ||||
\(446\) | 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 | \(0.583729\pi\) | |||||||
\(450\) | 2868.13 | + | 221.827i | 0.300456 | + | 0.0232378i | ||||
\(451\) | −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 | ||||
\(455\) | 4862.07 | − | 8421.35i | 0.500961 | − | 0.867690i | ||||
\(456\) | −3054.59 | − | 1924.42i | −0.313694 | − | 0.197630i | ||||
\(457\) | 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 | ||||||||
\(459\) | 106.806 | − | 918.347i | 0.0108612 | − | 0.0933873i | ||||
\(460\) | 3168.89 | 0.321196 | ||||||||
\(461\) | 9114.02 | + | 15785.9i | 0.920786 | + | 1.59485i | 0.798202 | + | 0.602390i | \(0.205785\pi\) |
0.122584 | + | 0.992458i | \(0.460882\pi\) | |||||||
\(462\) | −23468.3 | − | 14785.2i | −2.36329 | − | 1.48890i | ||||
\(463\) | −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 | ||||
\(465\) | −103.257 | + | 2674.13i | −0.0102977 | + | 0.266688i | ||||
\(466\) | 2433.69 | + | 4215.28i | 0.241928 | + | 0.419032i | ||||
\(467\) | 4919.63 | 0.487481 | 0.243740 | − | 0.969841i | \(-0.421626\pi\) | ||||
0.243740 | + | 0.969841i | \(0.421626\pi\) | |||||||
\(468\) | 9805.90 | − | 14309.1i | 0.968542 | − | 1.41333i | ||||
\(469\) | 2962.80 | 0.291704 | ||||||||
\(470\) | −474.291 | − | 821.497i | −0.0465477 | − | 0.0806230i | ||||
\(471\) | −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 | ||||
\(475\) | −942.254 | − | 1632.03i | −0.0910180 | − | 0.157648i | ||||
\(476\) | −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 | 0.736128 | − | 0.676842i | \(-0.236652\pi\) |
−0.954226 | + | 0.299085i | \(0.903319\pi\) | |||||||
\(480\) | −253.440 | + | 6563.55i | −0.0240998 | + | 0.624132i | ||||
\(481\) | 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 | ||||
\(485\) | 7155.79 | 0.669954 | ||||||||
\(486\) | −12173.3 | − | 10603.1i | −1.13620 | − | 0.989646i | ||||
\(487\) | 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 | ||||
\(489\) | −4849.55 | − | 3055.26i | −0.448475 | − | 0.282543i | ||||
\(490\) | −6429.10 | + | 11135.5i | −0.592729 | + | 1.02664i | ||||
\(491\) | −7654.18 | + | 13257.4i | −0.703520 | + | 1.21853i | 0.263703 | + | 0.964604i | \(0.415056\pi\) |
−0.967223 | + | 0.253928i | \(0.918277\pi\) | |||||||
\(492\) | −320.994 | + | 8313.05i | −0.0294137 | + | 0.761751i | ||||
\(493\) | 163.457 | + | 283.116i | 0.0149325 | + | 0.0258639i | ||||
\(494\) | −20309.0 | −1.84968 | ||||||||
\(495\) | −2373.00 | − | 4957.83i | −0.215471 | − | 0.450178i | ||||
\(496\) | −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 | 0.127203 | + | 0.991877i | \(0.459400\pi\) |
−0.922592 | + | 0.385777i | \(0.873933\pi\) | |||||||
\(500\) | 635.172 | − | 1100.15i | 0.0568115 | − | 0.0984005i | ||||
\(501\) | 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 | \(-0.654265\pi\) | ||||
−0.465887 | + | 0.884844i | \(0.654265\pi\) | |||||||
\(504\) | −4327.89 | + | 6315.39i | −0.382499 | + | 0.558155i | ||||
\(505\) | −5538.08 | −0.488003 | ||||||||
\(506\) | −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 | 0.0221524 | + | 0.999755i | \(0.492948\pi\) |
−0.876889 | + | 0.480693i | \(0.840385\pi\) | |||||||
\(510\) | −617.358 | − | 388.941i | −0.0536021 | − | 0.0337698i | ||||
\(511\) | 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 | ||||||||
\(515\) | 1322.19 | + | 2290.09i | 0.113131 | + | 0.195949i | ||||
\(516\) | −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 | ||||
\(520\) | −1456.73 | − | 2523.12i | −0.122849 | − | 0.212781i | ||||
\(521\) | 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 | \(-0.149046\pi\) | ||||
0.892363 | + | 0.451317i | \(0.149046\pi\) | |||||||
\(524\) | −6479.39 | − | 11222.6i | −0.540178 | − | 0.935616i | ||||
\(525\) | −3535.46 | + | 1863.15i | −0.293905 | + | 0.154885i | ||||
\(526\) | 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 | ||||
\(530\) | 559.896 | 0.0458874 | ||||||||
\(531\) | 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 | ||||
\(535\) | 1227.27 | − | 2125.70i | 0.0991770 | − | 0.171780i | ||||
\(536\) | 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 | ||||||||
\(540\) | −6544.32 | + | 2827.39i | −0.521524 | + | 0.225318i | ||||
\(541\) | −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 | ||||
\(545\) | −879.084 | + | 1522.62i | −0.0690933 | + | 0.119673i | ||||
\(546\) | −1661.75 | + | 43035.9i | −0.130250 | + | 3.37320i | ||||
\(547\) | 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 | ||||||||
\(549\) | 12982.5 | − | 18944.5i | 1.00925 | − | 1.47273i | ||||
\(550\) | −4337.92 | −0.336308 | ||||||||
\(551\) | −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 | ||||
\(555\) | −6482.30 | + | 3416.10i | −0.495780 | + | 0.261271i | ||||
\(556\) | 12904.1 | + | 22350.6i | 0.984277 | + | 1.70482i | ||||
\(557\) | 11597.0 | 0.882191 | 0.441096 | − | 0.897460i | \(-0.354590\pi\) | ||||
0.441096 | + | 0.897460i | \(0.354590\pi\) | |||||||
\(558\) | −5117.08 | − | 10691.0i | −0.388214 | − | 0.811084i | ||||
\(559\) | −21355.9 | −1.61584 | ||||||||
\(560\) | −3231.79 | − | 5597.62i | −0.243871 | − | 0.422397i | ||||
\(561\) | −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 | −0.00659429 | − | 0.999978i | \(-0.502099\pi\) |
0.869304 | − | 0.494278i | \(-0.164568\pi\) | |||||||
\(564\) | 1988.95 | + | 1253.05i | 0.148493 | + | 0.0935516i | ||||
\(565\) | 4406.13 | + | 7631.64i | 0.328084 | + | 0.568258i | ||||
\(566\) | −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 | −0.998743 | − | 0.0501179i | \(-0.984040\pi\) |
0.455968 | − | 0.889996i | \(-0.349293\pi\) | |||||||
\(570\) | 7061.81 | + | 4449.00i | 0.518924 | + | 0.326927i | ||||
\(571\) | −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 | ||||
\(573\) | −149.625 | + | 3874.98i | −0.0109087 | + | 0.282512i | ||||
\(574\) | −10327.5 | − | 17887.7i | −0.750975 | − | 1.30073i | ||||
\(575\) | −1559.07 | −0.113074 | ||||||||
\(576\) | −8641.09 | − | 18053.6i | −0.625079 | − | 1.30596i | ||||
\(577\) | −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 | ||||
\(579\) | −496.039 | + | 261.407i | −0.0356040 | + | 0.0187629i | ||||
\(580\) | 1260.39 | − | 2183.07i | 0.0902328 | − | 0.156288i | ||||
\(581\) | 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 | ||||||||
\(585\) | −4824.43 | + | 7039.95i | −0.340967 | + | 0.497549i | ||||
\(586\) | −758.961 | −0.0535023 | ||||||||
\(587\) | −1045.77 | − | 1811.33i | −0.0735326 | − | 0.127362i | 0.826915 | − | 0.562327i | \(-0.190094\pi\) |
−0.900447 | + | 0.434965i | \(0.856761\pi\) | |||||||
\(588\) | 1229.49 | − | 31841.2i | 0.0862303 | − | 2.23318i | ||||
\(589\) | −3882.24 | + | 6724.24i | −0.271587 | + | 0.470403i | ||||
\(590\) | 4538.01 | − | 7860.06i | 0.316656 | − | 0.548464i | ||||
\(591\) | −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 | \(-0.463990\pi\) | ||||
0.112889 | + | 0.993608i | \(0.463990\pi\) | |||||||
\(594\) | 19535.0 | + | 14525.9i | 1.34938 | + | 1.00337i | ||||
\(595\) | 1013.66 | 0.0698417 | ||||||||
\(596\) | −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 | −0.144941 | − | 0.989440i | \(-0.546299\pi\) |
0.929351 | − | 0.369197i | \(-0.120367\pi\) | |||||||
\(600\) | −46.1991 | + | 1196.46i | −0.00314345 | + | 0.0814085i | ||||
\(601\) | 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 | ||||||||
\(603\) | −2592.56 | − | 200.513i | −0.175087 | − | 0.0135415i | ||||
\(604\) | −10855.1 | −0.731274 | ||||||||
\(605\) | 816.702 | + | 1414.57i | 0.0548821 | + | 0.0950586i | ||||
\(606\) | 21699.3 | − | 11435.3i | 1.45457 | − | 0.766544i | ||||
\(607\) | 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 | ||||
\(609\) | −7015.54 | + | 3697.11i | −0.466805 | + | 0.246001i | ||||
\(610\) | −9062.62 | − | 15696.9i | −0.601532 | − | 1.04188i | ||||
\(611\) | 2814.19 | 0.186334 | ||||||||
\(612\) | 1802.85 | + | 139.435i | 0.119078 | + | 0.00920971i | ||||
\(613\) | 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 | ||||
\(615\) | 157.927 | − | 4089.96i | 0.0103548 | − | 0.268168i | ||||
\(616\) | 5772.46 | − | 9998.19i | 0.377563 | − | 0.653958i | ||||
\(617\) | −4313.78 | + | 7471.69i | −0.281469 | + | 0.487519i | −0.971747 | − | 0.236026i | \(-0.924155\pi\) |
0.690278 | + | 0.723544i | \(0.257488\pi\) | |||||||
\(618\) | −9909.25 | − | 6242.91i | −0.644998 | − | 0.406354i | ||||
\(619\) | 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 | ||||||||
\(621\) | 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 | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 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 | ||||||||
\(630\) | 10005.5 | − | 14600.3i | 0.632744 | − | 0.923320i | ||||
\(631\) | 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 | ||||
\(635\) | −3765.31 | + | 6521.71i | −0.235310 | + | 0.407569i | ||||
\(636\) | −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 | ||||
\(640\) | −5683.43 | −0.351027 | ||||||||
\(641\) | 10036.6 | + | 17383.8i | 0.618440 | + | 1.07117i | 0.989770 | + | 0.142669i | \(0.0455685\pi\) |
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(642\) | −419.457 | + | 10863.0i | −0.0257860 | + | 0.667803i | ||||
\(643\) | 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 | ||||
\(645\) | 7425.83 | + | 4678.34i | 0.453321 | + | 0.285596i | ||||
\(646\) | −1058.52 | − | 1833.40i | −0.0644686 | − | 0.111663i | ||||
\(647\) | −11456.8 | −0.696158 | −0.348079 | − | 0.937465i | \(-0.613166\pi\) | ||||
−0.348079 | + | 0.937465i | \(0.613166\pi\) | |||||||
\(648\) | 4214.48 | − | 5233.31i | 0.255494 | − | 0.317259i | ||||
\(649\) | −17341.4 | −1.04886 | ||||||||
\(650\) | 3367.75 | + | 5833.12i | 0.203222 | + | 0.351990i | ||||
\(651\) | 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 | −0.0102660 | + | 0.999947i | \(0.503268\pi\) |
−0.860847 | + | 0.508864i | \(0.830065\pi\) | |||||||
\(654\) | 300.453 | − | 7781.08i | 0.0179643 | − | 0.465236i | ||||
\(655\) | 3187.81 | + | 5521.45i | 0.190165 | + | 0.329376i | ||||
\(656\) | 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 | 0.923180 | − | 0.384368i | \(-0.125581\pi\) |
−0.794462 | + | 0.607314i | \(0.792247\pi\) | |||||||
\(660\) | 9510.35 | − | 5011.85i | 0.560894 | − | 0.295585i | ||||
\(661\) | −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 | ||||
\(663\) | 1915.06 | − | 1009.22i | 0.112179 | − | 0.0591172i | ||||
\(664\) | −911.297 | − | 1578.41i | −0.0532608 | − | 0.0922504i | ||||
\(665\) | −11595.0 | −0.676141 | ||||||||
\(666\) | 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 | ||||
\(670\) | −1026.10 | + | 1777.26i | −0.0591669 | + | 0.102480i | ||||
\(671\) | −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 | 0.999950 | + | 0.00997909i | \(0.00317650\pi\) |
−0.491333 | + | 0.870972i | \(0.663490\pi\) | |||||||
\(674\) | 33456.3 | 1.91200 | ||||||||
\(675\) | 3219.76 | − | 1391.06i | 0.183598 | − | 0.0793212i | ||||
\(676\) | 18287.8 | 1.04050 | ||||||||
\(677\) | −968.667 | − | 1677.78i | −0.0549910 | − | 0.0952472i | 0.837219 | − | 0.546867i | \(-0.184180\pi\) |
−0.892210 | + | 0.451620i | \(0.850846\pi\) | |||||||
\(678\) | −33022.2 | − | 20804.3i | −1.87052 | − | 1.17844i | ||||
\(679\) | 22014.0 | − | 38129.4i | 1.24421 | − | 2.15504i | ||||
\(680\) | 151.851 | − | 263.013i | 0.00856355 | − | 0.0148325i | ||||
\(681\) | 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 | \(-0.518965\pi\) | ||||
−0.0595448 | + | 0.998226i | \(0.518965\pi\) | |||||||
\(684\) | −20622.3 | − | 1594.97i | −1.15280 | − | 0.0891596i | ||||
\(685\) | −7197.12 | −0.401442 | ||||||||
\(686\) | 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 | ||||
\(690\) | 6108.73 | − | 3219.23i | 0.337037 | − | 0.177615i | ||||
\(691\) | −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 | ||||||||
\(693\) | −33717.9 | − | 2607.81i | −1.84825 | − | 0.142947i | ||||
\(694\) | 39942.4 | 2.18472 | ||||||||
\(695\) | −6348.74 | − | 10996.3i | −0.346506 | − | 0.600166i | ||||
\(696\) | −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 | ||||
\(700\) | −3908.08 | − | 6768.99i | −0.211016 | − | 0.365491i | ||||
\(701\) | −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 | ||||
\(705\) | −978.548 | − | 616.493i | −0.0522755 | − | 0.0329340i | ||||
\(706\) | −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 | 0.931206 | + | 0.364492i | \(0.118757\pi\) |
−0.149944 | + | 0.988695i | \(0.547909\pi\) | |||||||
\(710\) | 20289.6 | 1.07247 | ||||||||
\(711\) | −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 | ||||
\(715\) | 6434.72 | − | 11145.3i | 0.336566 | − | 0.582950i | ||||
\(716\) | 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 | \(0.531899\pi\) | |||||||
\(720\) | 2449.10 | + | 5116.84i | 0.126768 | + | 0.264852i | ||||
\(721\) | 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 | ||||
\(725\) | −620.105 | + | 1074.05i | −0.0317657 | + | 0.0550197i | ||||
\(726\) | −6120.86 | − | 3856.19i | −0.312901 | − | 0.197130i | ||||
\(727\) | −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 | ||||||||
\(729\) | −19157.6 | − | 4517.26i | −0.973309 | − | 0.229501i | ||||
\(730\) | −1083.68 | −0.0549436 | ||||||||
\(731\) | −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 | \(-0.757072\pi\) |
0.959938 | + | 0.280214i | \(0.0904054\pi\) | |||||||
\(734\) | 13854.9 | − | 23997.4i | 0.696723 | − | 1.20676i | ||||
\(735\) | −604.901 | + | 15665.6i | −0.0303566 | + | 0.786171i | ||||
\(736\) | 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 | \(0.450529\pi\) | |||||||
\(740\) | −7165.49 | − | 12411.0i | −0.355958 | − | 0.616537i | ||||
\(741\) | −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 | −0.233242 | − | 0.972419i | \(-0.574933\pi\) |
0.958760 | − | 0.284216i | \(-0.0917333\pi\) | |||||||
\(744\) | 4364.33 | − | 2299.95i | 0.215059 | − | 0.113334i | ||||
\(745\) | 234.398 | + | 405.989i | 0.0115271 | + | 0.0199655i | ||||
\(746\) | −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 | ||||
\(750\) | 106.806 | − | 2766.04i | 0.00520001 | − | 0.134669i | ||||
\(751\) | 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 | ||||
\(753\) | 3899.00 | + | 2456.40i | 0.188695 | + | 0.118880i | ||||
\(754\) | 6682.75 | + | 11574.9i | 0.322774 | + | 0.559061i | ||||
\(755\) | 5340.65 | 0.257438 | ||||||||
\(756\) | −5067.23 | + | 43569.4i | −0.243774 | + | 2.09604i | ||||
\(757\) | −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 | ||||
\(759\) | −11162.8 | − | 7032.66i | −0.533840 | − | 0.336324i | ||||
\(760\) | −1736.98 | + | 3008.55i | −0.0829040 | + | 0.143594i | ||||
\(761\) | 11953.0 | − | 20703.3i | 0.569379 | − | 0.986193i | −0.427249 | − | 0.904134i | \(-0.640517\pi\) |
0.996628 | − | 0.0820585i | \(-0.0261494\pi\) | |||||||
\(762\) | 1286.90 | − | 33328.0i | 0.0611806 | − | 1.58445i | ||||
\(763\) | 5408.82 | + | 9368.35i | 0.256635 | + | 0.444504i | ||||
\(764\) | −7584.42 | −0.359155 | ||||||||
\(765\) | −886.987 | − | 68.6012i | −0.0419204 | − | 0.00324220i | ||||
\(766\) | 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 | −0.405609 | − | 0.914047i | \(-0.632941\pi\) |
0.994392 | − | 0.105755i | \(-0.0337261\pi\) | |||||||
\(770\) | −13345.1 | + | 23114.5i | −0.624579 | + | 1.08180i | ||||
\(771\) | −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 | \(-0.387246\pi\) | ||||
0.346865 | + | 0.937915i | \(0.387246\pi\) | |||||||
\(774\) | −38755.8 | − | 2997.45i | −1.79981 | − | 0.139200i | ||||
\(775\) | 2575.10 | 0.119355 | ||||||||
\(776\) | −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 | ||||
\(780\) | −14122.7 | − | 8897.44i | −0.648301 | − | 0.408435i | ||||
\(781\) | −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 | ||||||||
\(785\) | 454.287 | + | 786.848i | 0.0206550 | + | 0.0357756i | ||||
\(786\) | −23891.4 | − | 15051.8i | −1.08419 | − | 0.683052i | ||||
\(787\) | 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 | ||||
\(789\) | 1459.70 | − | 37803.1i | 0.0658640 | − | 1.70573i | ||||
\(790\) | 2101.90 | + | 3640.60i | 0.0946610 | + | 0.163958i | ||||
\(791\) | 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 | ||||
\(795\) | 603.923 | − | 318.260i | 0.0269421 | − | 0.0141982i | ||||
\(796\) | −6956.33 | + | 12048.7i | −0.309750 | + | 0.536502i | ||||
\(797\) | 7086.11 | − | 12273.5i | 0.314935 | − | 0.545483i | −0.664489 | − | 0.747298i | \(-0.731351\pi\) |
0.979424 | + | 0.201815i | \(0.0646840\pi\) | |||||||
\(798\) | 45431.3 | − | 23941.8i | 2.01535 | − | 1.06207i | ||||
\(799\) | 146.677 | + | 254.053i | 0.00649446 | + | 0.0112487i | ||||
\(800\) | 6320.48 | 0.279329 | ||||||||
\(801\) | 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 | ||||
\(805\) | −4796.31 | + | 8307.45i | −0.209997 | + | 0.363726i | ||||
\(806\) | 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 | \(0.651436\pi\) | |||||||
\(810\) | −9743.31 | + | 12098.7i | −0.422648 | + | 0.524821i | ||||
\(811\) | −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 | ||||
\(815\) | −2757.68 | + | 4776.44i | −0.118524 | + | 0.205290i | ||||
\(816\) | 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 | ||||
\(820\) | 8005.20 | 0.340919 | ||||||||
\(821\) | −7400.25 | − | 12817.6i | −0.314580 | − | 0.544869i | 0.664768 | − | 0.747050i | \(-0.268530\pi\) |
−0.979348 | + | 0.202181i | \(0.935197\pi\) | |||||||
\(822\) | 28199.7 | − | 14860.9i | 1.19657 | − | 0.630576i | ||||
\(823\) | −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 | ||||
\(825\) | −4679.02 | + | 2465.79i | −0.197458 | + | 0.104058i | ||||
\(826\) | −27921.4 | − | 48361.3i | −1.17616 | − | 2.03717i | ||||
\(827\) | −29001.3 | −1.21944 | −0.609718 | − | 0.792619i | \(-0.708717\pi\) | ||||
−0.609718 | + | 0.792619i | \(0.708717\pi\) | |||||||
\(828\) | −9673.27 | + | 14115.5i | −0.406002 | + | 0.592450i | ||||
\(829\) | 13221.1 | 0.553904 | 0.276952 | − | 0.960884i | \(-0.410676\pi\) | ||||
0.276952 | + | 0.960884i | \(0.410676\pi\) | |||||||
\(830\) | 2106.80 | + | 3649.08i | 0.0881060 | + | 0.152604i | ||||
\(831\) | 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 | ||||
\(835\) | −10104.3 | − | 17501.1i | −0.418769 | − | 0.725329i | ||||
\(836\) | 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 | 0.865375 | + | 0.501125i | \(0.167080\pi\) |
0.00129985 | + | 0.999999i | \(0.499586\pi\) | |||||||
\(840\) | 6233.15 | + | 3926.94i | 0.256029 | + | 0.161300i | ||||
\(841\) | 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 | ||||
\(845\) | −8997.45 | −0.366298 | ||||||||
\(846\) | 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 | ||||
\(850\) | −351.059 | + | 608.051i | −0.0141661 | + | 0.0245365i | ||||
\(851\) | −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 | \(-0.260203\pi\) |
−0.973725 | + | 0.227729i | \(0.926870\pi\) | |||||||
\(854\) | −111521. | −4.46857 | ||||||||
\(855\) | 10146.0 | + | 784.713i | 0.405833 | + | 0.0313879i | ||||
\(856\) | −4524.80 | −0.180671 | ||||||||
\(857\) | −8056.71 | − | 13954.6i | −0.321134 | − | 0.556220i | 0.659588 | − | 0.751627i | \(-0.270731\pi\) |
−0.980722 | + | 0.195407i | \(0.937397\pi\) | |||||||
\(858\) | −2199.25 | + | 56956.0i | −0.0875074 | + | 2.26625i | ||||
\(859\) | 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 | ||||
\(861\) | −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 | \(-0.826982\pi\) | ||||
−0.855877 | + | 0.517180i | \(0.826982\pi\) | |||||||
\(864\) | −28463.1 | − | 21164.6i | −1.12076 | − | 0.833375i | ||||
\(865\) | 13738.8 | 0.540038 | ||||||||
\(866\) | −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 | ||||
\(870\) | 211.939 | − | 5488.76i | 0.00825908 | − | 0.213892i | ||||
\(871\) | −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 | ||||||||
\(875\) | 1922.75 | + | 3330.29i | 0.0742865 | + | 0.128668i | ||||
\(876\) | 2375.84 | − | 1252.04i | 0.0916348 | − | 0.0482905i | ||||
\(877\) | 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 | ||||
\(879\) | −818.640 | + | 431.414i | −0.0314130 | + | 0.0165543i | ||||
\(880\) | −4277.12 | − | 7408.18i | −0.163843 | − | 0.283784i | ||||
\(881\) | 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 | \(-0.347190\pi\) | ||||
0.461840 | + | 0.886963i | \(0.347190\pi\) | |||||||
\(884\) | 2116.90 | + | 3666.57i | 0.0805418 | + | 0.139502i | ||||
\(885\) | 426.972 | − | 11057.6i | 0.0162175 | − | 0.419999i | ||||
\(886\) | −23156.0 | + | 40107.3i | −0.878036 | + | 1.52080i | ||||
\(887\) | −12599.3 | + | 21822.7i | −0.476939 | + | 0.826082i | −0.999651 | − | 0.0264274i | \(-0.991587\pi\) |
0.522712 | + | 0.852509i | \(0.324920\pi\) | |||||||
\(888\) | 11428.5 | + | 7200.07i | 0.431888 | + | 0.272093i | ||||
\(889\) | 23167.1 | + | 40126.7i | 0.874017 | + | 1.51384i | ||||
\(890\) | 29076.9 | 1.09512 | ||||||||
\(891\) | 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 | ||||
\(895\) | −7095.81 | + | 12290.3i | −0.265013 | + | 0.459016i | ||||
\(896\) | −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 | ||||||||
\(900\) | 2961.61 | + | 6187.61i | 0.109689 | + | 0.229171i | ||||
\(901\) | −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 | ||||
\(905\) | 8605.62 | − | 14905.4i | 0.316089 | − | 0.547482i | ||||
\(906\) | −20925.7 | + | 11027.6i | −0.767338 | + | 0.404379i | ||||
\(907\) | −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 | ||||||||
\(909\) | 16905.4 | − | 24668.9i | 0.616851 | − | 0.900127i | ||||
\(910\) | 41442.1 | 1.50966 | ||||||||
\(911\) | −12416.1 | − | 21505.2i | −0.451550 | − | 0.782108i | 0.546932 | − | 0.837177i | \(-0.315796\pi\) |
−0.998483 | + | 0.0550686i | \(0.982462\pi\) | |||||||
\(912\) | −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 | ||||
\(915\) | −18697.8 | − | 11779.8i | −0.675552 | − | 0.425603i | ||||
\(916\) | −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 | \(0.655224\pi\) | |||||||
\(920\) | 1437.02 | + | 2489.00i | 0.0514970 | + | 0.0891954i | ||||
\(921\) | 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 | ||||
\(925\) | 3525.37 | + | 6106.11i | 0.125312 | + | 0.217046i | ||||
\(926\) | −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 | 0.995165 | − | 0.0982184i | \(-0.0313144\pi\) |
−0.582642 | + | 0.812729i | \(0.697981\pi\) | |||||||
\(930\) | −10089.7 | + | 5317.18i | −0.355759 | + | 0.187481i | ||||
\(931\) | −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 | ||||
\(935\) | 1341.53 | 0.0469226 | ||||||||
\(936\) | 15685.8 | + | 1213.17i | 0.547763 | + | 0.0423650i | ||||
\(937\) | 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 | ||||
\(939\) | 398.082 | − | 10309.5i | 0.0138348 | − | 0.358292i | ||||
\(940\) | 1131.01 | − | 1958.96i | 0.0392441 | − | 0.0679727i | ||||
\(941\) | 3245.07 | − | 5620.62i | 0.112419 | − | 0.194715i | −0.804326 | − | 0.594188i | \(-0.797473\pi\) |
0.916745 | + | 0.399473i | \(0.130807\pi\) | |||||||
\(942\) | −3404.70 | − | 2144.99i | −0.117761 | − | 0.0741906i | ||||
\(943\) | −4912.32 | − | 8508.38i | −0.169636 | − | 0.293819i | ||||
\(944\) | 17897.6 | 0.617074 | ||||||||
\(945\) | 2493.04 | − | 21435.8i | 0.0858185 | − | 0.737891i | ||||
\(946\) | 58616.4 | 2.01457 | ||||||||
\(947\) | −11753.0 | − | 20356.8i | −0.403295 | − | 0.698528i | 0.590826 | − | 0.806799i | \(-0.298802\pi\) |
−0.994121 | + | 0.108271i | \(0.965469\pi\) | |||||||
\(948\) | −8814.34 | − | 5553.11i | −0.301979 | − | 0.190250i | ||||
\(949\) | 1607.50 | − | 2784.26i | 0.0549858 | − | 0.0952382i | ||||
\(950\) | 4015.68 | − | 6955.35i | 0.137143 | − | 0.237538i | ||||
\(951\) | −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 | \(-0.463456\pi\) | ||||
0.114553 | + | 0.993417i | \(0.463456\pi\) | |||||||
\(954\) | −1709.13 | + | 2494.01i | −0.0580032 | + | 0.0846400i | ||||
\(955\) | 3731.48 | 0.126437 | ||||||||
\(956\) | 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 | ||||
\(960\) | −17038.3 | + | 8978.99i | −0.572822 | + | 0.301871i | ||||
\(961\) | 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 | ||||||||
\(965\) | 269.769 | + | 467.253i | 0.00899913 | + | 0.0155870i | ||||
\(966\) | 1639.28 | − | 42453.8i | 0.0545993 | − | 1.41400i | ||||
\(967\) | −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 | ||||
\(969\) | −2183.91 | − | 1375.88i | −0.0724016 | − | 0.0456136i | ||||
\(970\) | 15248.2 | + | 26410.6i | 0.504732 | + | 0.874221i | ||||
\(971\) | −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 | ||||
\(975\) | 6948.27 | + | 4377.47i | 0.228229 | + | 0.143786i | ||||
\(976\) | 17871.2 | − | 30953.8i | 0.586109 | − | 1.01517i | ||||
\(977\) | −3383.98 | + | 5861.22i | −0.110812 | + | 0.191931i | −0.916098 | − | 0.400955i | \(-0.868678\pi\) |
0.805286 | + | 0.592886i | \(0.202012\pi\) | |||||||
\(978\) | 942.517 | − | 24409.2i | 0.0308163 | − | 0.798076i | ||||
\(979\) | −27778.5 | − | 48113.7i | −0.906848 | − | 1.57071i | ||||
\(980\) | −30662.0 | −0.999452 | ||||||||
\(981\) | −4098.90 | − | 8563.71i | −0.133402 | − | 0.278714i | ||||
\(982\) | −65240.8 | −2.12008 | ||||||||
\(983\) | 25037.4 | + | 43366.1i | 0.812381 | + | 1.40708i | 0.911194 | + | 0.411979i | \(0.135162\pi\) |
−0.0988128 | + | 0.995106i | \(0.531504\pi\) | |||||||
\(984\) | −6675.04 | + | 3517.67i | −0.216252 | + | 0.113963i | ||||
\(985\) | −8402.55 | + | 14553.6i | −0.271805 | + | 0.470779i | ||||
\(986\) | −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 | ||||||||
\(990\) | 13241.8 | − | 19322.9i | 0.425104 | − | 0.620324i | ||||
\(991\) | −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 | ||||
\(995\) | 3422.46 | − | 5927.88i | 0.109045 | − | 0.188871i | ||||
\(996\) | −8834.88 | − | 5566.05i | −0.281068 | − | 0.177075i | ||||
\(997\) | 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 | ||||||||
\(999\) | 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 | 45.4.e.c.31.6 | yes | 14 | |
3.2 | odd | 2 | 135.4.e.c.91.2 | 14 | |||
5.2 | odd | 4 | 225.4.k.d.49.3 | 28 | |||
5.3 | odd | 4 | 225.4.k.d.49.12 | 28 | |||
5.4 | even | 2 | 225.4.e.d.76.2 | 14 | |||
9.2 | odd | 6 | 135.4.e.c.46.2 | 14 | |||
9.4 | even | 3 | 405.4.a.m.1.2 | 7 | |||
9.5 | odd | 6 | 405.4.a.n.1.6 | 7 | |||
9.7 | even | 3 | inner | 45.4.e.c.16.6 | ✓ | 14 | |
45.4 | even | 6 | 2025.4.a.bb.1.6 | 7 | |||
45.7 | odd | 12 | 225.4.k.d.124.12 | 28 | |||
45.14 | odd | 6 | 2025.4.a.ba.1.2 | 7 | |||
45.34 | even | 6 | 225.4.e.d.151.2 | 14 | |||
45.43 | odd | 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 | 9.7 | even | 3 | inner | |
45.4.e.c.31.6 | yes | 14 | 1.1 | even | 1 | trivial | |
135.4.e.c.46.2 | 14 | 9.2 | odd | 6 | |||
135.4.e.c.91.2 | 14 | 3.2 | odd | 2 | |||
225.4.e.d.76.2 | 14 | 5.4 | even | 2 | |||
225.4.e.d.151.2 | 14 | 45.34 | even | 6 | |||
225.4.k.d.49.3 | 28 | 5.2 | odd | 4 | |||
225.4.k.d.49.12 | 28 | 5.3 | odd | 4 | |||
225.4.k.d.124.3 | 28 | 45.43 | odd | 12 | |||
225.4.k.d.124.12 | 28 | 45.7 | odd | 12 | |||
405.4.a.m.1.2 | 7 | 9.4 | even | 3 | |||
405.4.a.n.1.6 | 7 | 9.5 | odd | 6 | |||
2025.4.a.ba.1.2 | 7 | 45.14 | odd | 6 | |||
2025.4.a.bb.1.6 | 7 | 45.4 | even | 6 |