Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(109,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.g (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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 18x^{6} + 9x^{5} + 283x^{4} - 48x^{3} + 186x^{2} + 40x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(-0.338925 - 0.587036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.109 |
Dual form | 378.4.g.f.163.1 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −8.05411 | − | 13.9501i | −0.720381 | − | 1.24774i | −0.960847 | − | 0.277080i | \(-0.910633\pi\) |
0.240466 | − | 0.970658i | \(-0.422700\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.77345 | − | 17.2372i | 0.365732 | − | 0.930720i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 16.1082 | − | 27.9003i | 0.509387 | − | 0.882283i | ||||
\(11\) | −6.04111 | + | 10.4635i | −0.165588 | + | 0.286806i | −0.936864 | − | 0.349694i | \(-0.886285\pi\) |
0.771276 | + | 0.636501i | \(0.219619\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −39.7518 | −0.848089 | −0.424045 | − | 0.905641i | \(-0.639390\pi\) | ||||
−0.424045 | + | 0.905641i | \(0.639390\pi\) | |||||||
\(14\) | 36.6291 | − | 5.50523i | 0.699253 | − | 0.105095i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | −62.7914 | + | 108.758i | −0.895833 | + | 1.55163i | −0.0630630 | + | 0.998010i | \(0.520087\pi\) |
−0.832770 | + | 0.553619i | \(0.813246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 62.5108 | + | 108.272i | 0.754787 | + | 1.30733i | 0.945480 | + | 0.325680i | \(0.105593\pi\) |
−0.190693 | + | 0.981650i | \(0.561073\pi\) | |||||||
\(20\) | 64.4329 | 0.720381 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.1645 | −0.234176 | ||||||||
\(23\) | 24.1212 | + | 41.7792i | 0.218679 | + | 0.378763i | 0.954404 | − | 0.298517i | \(-0.0964919\pi\) |
−0.735725 | + | 0.677280i | \(0.763159\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67.2373 | + | 116.458i | −0.537899 | + | 0.931668i | ||||
\(26\) | −39.7518 | − | 68.8521i | −0.299845 | − | 0.519346i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 46.1645 | + | 57.9383i | 0.311581 | + | 0.391047i | ||||
\(29\) | −93.0461 | −0.595801 | −0.297900 | − | 0.954597i | \(-0.596286\pi\) | ||||
−0.297900 | + | 0.954597i | \(0.596286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.3809 | + | 19.7123i | −0.0659379 | + | 0.114208i | −0.897110 | − | 0.441808i | \(-0.854337\pi\) |
0.831172 | + | 0.556016i | \(0.187671\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −251.166 | −1.26690 | ||||||||
\(35\) | −295.015 | + | 44.3397i | −1.42476 | + | 0.214137i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 200.361 | + | 347.035i | 0.890245 | + | 1.54195i | 0.839581 | + | 0.543234i | \(0.182800\pi\) |
0.0506642 | + | 0.998716i | \(0.483866\pi\) | |||||||
\(38\) | −125.022 | + | 216.544i | −0.533715 | + | 0.924422i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 64.4329 | + | 111.601i | 0.254693 | + | 0.441142i | ||||
\(41\) | −354.070 | −1.34870 | −0.674348 | − | 0.738414i | \(-0.735575\pi\) | ||||
−0.674348 | + | 0.738414i | \(0.735575\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 225.918 | 0.801212 | 0.400606 | − | 0.916250i | \(-0.368800\pi\) | ||||
0.400606 | + | 0.916250i | \(0.368800\pi\) | |||||||
\(44\) | −24.1645 | − | 41.8541i | −0.0827938 | − | 0.143403i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.2424 | + | 83.5583i | −0.154630 | + | 0.267826i | ||||
\(47\) | −124.107 | − | 214.960i | −0.385169 | − | 0.667132i | 0.606624 | − | 0.794989i | \(-0.292523\pi\) |
−0.991793 | + | 0.127857i | \(0.959190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −251.241 | − | 233.510i | −0.732481 | − | 0.680788i | ||||
\(50\) | −268.949 | −0.760704 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 79.5036 | − | 137.704i | 0.212022 | − | 0.367233i | ||||
\(53\) | −167.460 | + | 290.050i | −0.434008 | + | 0.751724i | −0.997214 | − | 0.0745926i | \(-0.976234\pi\) |
0.563206 | + | 0.826316i | \(0.309568\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 194.623 | 0.477145 | ||||||||
\(56\) | −54.1876 | + | 137.897i | −0.129306 | + | 0.329059i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −93.0461 | − | 161.161i | −0.210647 | − | 0.364852i | ||||
\(59\) | 91.4364 | − | 158.373i | 0.201763 | − | 0.349464i | −0.747334 | − | 0.664449i | \(-0.768666\pi\) |
0.949097 | + | 0.314985i | \(0.102000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −304.912 | − | 528.123i | −0.639999 | − | 1.10851i | −0.985432 | − | 0.170068i | \(-0.945601\pi\) |
0.345433 | − | 0.938443i | \(-0.387732\pi\) | |||||||
\(62\) | −45.5237 | −0.0932502 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 320.165 | + | 554.542i | 0.610948 | + | 1.05819i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −59.1898 | + | 102.520i | −0.107928 | + | 0.186937i | −0.914931 | − | 0.403611i | \(-0.867755\pi\) |
0.807003 | + | 0.590548i | \(0.201088\pi\) | |||||||
\(68\) | −251.166 | − | 435.032i | −0.447917 | − | 0.775814i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −371.814 | − | 466.641i | −0.634860 | − | 0.796775i | ||||
\(71\) | −81.4905 | −0.136213 | −0.0681066 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681066 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 489.415 | − | 847.692i | 0.784681 | − | 1.35911i | −0.144508 | − | 0.989504i | \(-0.546160\pi\) |
0.929189 | − | 0.369604i | \(-0.120507\pi\) | |||||||
\(74\) | −400.721 | + | 694.069i | −0.629498 | + | 1.09032i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −500.086 | −0.754787 | ||||||||
\(77\) | 139.442 | + | 175.006i | 0.206376 | + | 0.259010i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 346.714 | + | 600.527i | 0.493777 | + | 0.855247i | 0.999974 | − | 0.00717076i | \(-0.00228254\pi\) |
−0.506197 | + | 0.862418i | \(0.668949\pi\) | |||||||
\(80\) | −128.866 | + | 223.202i | −0.180095 | + | 0.311934i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −354.070 | − | 613.268i | −0.476836 | − | 0.825904i | ||||
\(83\) | −1409.05 | −1.86341 | −0.931707 | − | 0.363212i | \(-0.881680\pi\) | ||||
−0.931707 | + | 0.363212i | \(0.881680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2022.92 | 2.58137 | ||||||||
\(86\) | 225.918 | + | 391.301i | 0.283271 | + | 0.490640i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 48.3289 | − | 83.7081i | 0.0585441 | − | 0.101401i | ||||
\(89\) | 605.706 | + | 1049.11i | 0.721401 | + | 1.24950i | 0.960438 | + | 0.278493i | \(0.0898348\pi\) |
−0.239037 | + | 0.971010i | \(0.576832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −269.256 | + | 685.209i | −0.310173 | + | 0.789334i | ||||
\(92\) | −192.970 | −0.218679 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 248.215 | − | 429.921i | 0.272355 | − | 0.471733i | ||||
\(95\) | 1006.94 | − | 1744.07i | 1.08747 | − | 1.88355i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1336.50 | −1.39898 | −0.699492 | − | 0.714641i | \(-0.746590\pi\) | ||||
−0.699492 | + | 0.714641i | \(0.746590\pi\) | |||||||
\(98\) | 153.211 | − | 668.672i | 0.157925 | − | 0.689246i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −268.949 | − | 465.834i | −0.268949 | − | 0.465834i | ||||
\(101\) | −103.208 | + | 178.762i | −0.101679 | + | 0.176114i | −0.912377 | − | 0.409352i | \(-0.865755\pi\) |
0.810697 | + | 0.585465i | \(0.199088\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 344.223 | + | 596.212i | 0.329294 | + | 0.570354i | 0.982372 | − | 0.186936i | \(-0.0598559\pi\) |
−0.653078 | + | 0.757291i | \(0.726523\pi\) | |||||||
\(104\) | 318.014 | 0.299845 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −669.841 | −0.613780 | ||||||||
\(107\) | −226.713 | − | 392.678i | −0.204833 | − | 0.354781i | 0.745247 | − | 0.666789i | \(-0.232332\pi\) |
−0.950079 | + | 0.312008i | \(0.898998\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −685.492 | + | 1187.31i | −0.602369 | + | 1.04333i | 0.390093 | + | 0.920776i | \(0.372443\pi\) |
−0.992461 | + | 0.122558i | \(0.960890\pi\) | |||||||
\(110\) | 194.623 | + | 337.097i | 0.168696 | + | 0.292191i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −293.033 | + | 44.0418i | −0.247223 | + | 0.0371568i | ||||
\(113\) | −1807.69 | −1.50489 | −0.752446 | − | 0.658654i | \(-0.771126\pi\) | ||||
−0.752446 | + | 0.658654i | \(0.771126\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 388.550 | − | 672.988i | 0.315065 | − | 0.545708i | ||||
\(116\) | 186.092 | − | 322.321i | 0.148950 | − | 0.257989i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 365.746 | 0.285336 | ||||||||
\(119\) | 1449.37 | + | 1819.01i | 1.11650 | + | 1.40125i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 592.510 | + | 1026.26i | 0.445161 | + | 0.771042i | ||||
\(122\) | 609.824 | − | 1056.25i | 0.452548 | − | 0.783836i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −45.5237 | − | 78.8493i | −0.0329689 | − | 0.0571039i | ||||
\(125\) | 152.620 | 0.109206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −196.476 | −0.137279 | −0.0686394 | − | 0.997642i | \(-0.521866\pi\) | ||||
−0.0686394 | + | 0.997642i | \(0.521866\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −640.330 | + | 1109.08i | −0.432005 | + | 0.748255i | ||||
\(131\) | −753.242 | − | 1304.65i | −0.502374 | − | 0.870138i | −0.999996 | − | 0.00274396i | \(-0.999127\pi\) |
0.497622 | − | 0.867394i | \(-0.334207\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2289.71 | − | 344.136i | 1.49281 | − | 0.224364i | ||||
\(134\) | −236.759 | −0.152634 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 502.332 | − | 870.064i | 0.316725 | − | 0.548583i | ||||
\(137\) | 157.673 | − | 273.097i | 0.0983277 | − | 0.170309i | −0.812665 | − | 0.582731i | \(-0.801984\pi\) |
0.910993 | + | 0.412423i | \(0.135317\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −324.501 | −0.198013 | −0.0990064 | − | 0.995087i | \(-0.531566\pi\) | ||||
−0.0990064 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(140\) | 436.433 | − | 1110.64i | 0.263466 | − | 0.670474i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −81.4905 | − | 141.146i | −0.0481587 | − | 0.0834132i | ||||
\(143\) | 240.145 | − | 415.943i | 0.140433 | − | 0.243237i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 749.403 | + | 1298.00i | 0.429204 | + | 0.743403i | ||||
\(146\) | 1957.66 | 1.10971 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1602.88 | −0.890245 | ||||||||
\(149\) | −638.745 | − | 1106.34i | −0.351195 | − | 0.608287i | 0.635264 | − | 0.772295i | \(-0.280891\pi\) |
−0.986459 | + | 0.164008i | \(0.947558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −258.424 | + | 447.604i | −0.139273 | + | 0.241228i | −0.927222 | − | 0.374513i | \(-0.877810\pi\) |
0.787948 | + | 0.615741i | \(0.211143\pi\) | |||||||
\(152\) | −500.086 | − | 866.175i | −0.266858 | − | 0.462211i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −163.677 | + | 416.527i | −0.0856457 | + | 0.217953i | ||||
\(155\) | 366.653 | 0.190002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 649.320 | − | 1124.66i | 0.330073 | − | 0.571702i | −0.652453 | − | 0.757829i | \(-0.726260\pi\) |
0.982526 | + | 0.186127i | \(0.0595935\pi\) | |||||||
\(158\) | −693.428 | + | 1201.05i | −0.349153 | + | 0.604751i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −515.463 | −0.254693 | ||||||||
\(161\) | 883.539 | − | 132.793i | 0.432501 | − | 0.0650034i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1487.02 | − | 2575.60i | −0.714556 | − | 1.23765i | −0.963130 | − | 0.269035i | \(-0.913295\pi\) |
0.248574 | − | 0.968613i | \(-0.420038\pi\) | |||||||
\(164\) | 708.141 | − | 1226.54i | 0.337174 | − | 0.584002i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1409.05 | − | 2440.55i | −0.658816 | − | 1.14110i | ||||
\(167\) | 3607.22 | 1.67147 | 0.835733 | − | 0.549135i | \(-0.185043\pi\) | ||||
0.835733 | + | 0.549135i | \(0.185043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −616.796 | −0.280745 | ||||||||
\(170\) | 2022.92 | + | 3503.79i | 0.912651 | + | 1.58076i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −451.835 | + | 782.602i | −0.200303 | + | 0.346935i | ||||
\(173\) | 1263.21 | + | 2187.94i | 0.555143 | + | 0.961536i | 0.997892 | + | 0.0648904i | \(0.0206698\pi\) |
−0.442749 | + | 0.896645i | \(0.645997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1551.99 | + | 1947.81i | 0.670396 | + | 0.841374i | ||||
\(176\) | 193.316 | 0.0827938 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1211.41 | + | 2098.23i | −0.510108 | + | 0.883532i | ||||
\(179\) | 711.221 | − | 1231.87i | 0.296979 | − | 0.514382i | −0.678465 | − | 0.734633i | \(-0.737354\pi\) |
0.975443 | + | 0.220251i | \(0.0706877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2494.29 | 1.02431 | 0.512153 | − | 0.858894i | \(-0.328848\pi\) | ||||
0.512153 | + | 0.858894i | \(0.328848\pi\) | |||||||
\(182\) | −1456.07 | + | 218.843i | −0.593029 | + | 0.0891302i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −192.970 | − | 334.233i | −0.0773148 | − | 0.133913i | ||||
\(185\) | 3227.45 | − | 5590.11i | 1.28263 | − | 2.22158i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −758.661 | − | 1314.04i | −0.296678 | − | 0.513861i | ||||
\(188\) | 992.859 | 0.385169 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4027.75 | 1.53791 | ||||||||
\(191\) | 1846.91 | + | 3198.94i | 0.699674 | + | 1.21187i | 0.968580 | + | 0.248704i | \(0.0800047\pi\) |
−0.268906 | + | 0.963167i | \(0.586662\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 38.5601 | − | 66.7881i | 0.0143815 | − | 0.0249094i | −0.858745 | − | 0.512403i | \(-0.828755\pi\) |
0.873127 | + | 0.487494i | \(0.162089\pi\) | |||||||
\(194\) | −1336.50 | − | 2314.89i | −0.494615 | − | 0.856699i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1311.38 | − | 403.304i | 0.477910 | − | 0.146977i | ||||
\(197\) | 1259.96 | 0.455679 | 0.227839 | − | 0.973699i | \(-0.426834\pi\) | ||||
0.227839 | + | 0.973699i | \(0.426834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2725.37 | + | 4720.48i | −0.970837 | + | 1.68154i | −0.277796 | + | 0.960640i | \(0.589604\pi\) |
−0.693041 | + | 0.720898i | \(0.743729\pi\) | |||||||
\(200\) | 537.899 | − | 931.668i | 0.190176 | − | 0.329394i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −412.833 | −0.143796 | ||||||||
\(203\) | −630.242 | + | 1603.85i | −0.217903 | + | 0.554524i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2851.72 | + | 4939.33i | 0.971575 | + | 1.68282i | ||||
\(206\) | −688.446 | + | 1192.42i | −0.232846 | + | 0.403301i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 318.014 | + | 550.817i | 0.106011 | + | 0.183617i | ||||
\(209\) | −1510.54 | −0.499934 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 326.412 | 0.106498 | 0.0532492 | − | 0.998581i | \(-0.483042\pi\) | ||||
0.0532492 | + | 0.998581i | \(0.483042\pi\) | |||||||
\(212\) | −669.841 | − | 1160.20i | −0.217004 | − | 0.375862i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 453.425 | − | 785.355i | 0.144839 | − | 0.250868i | ||||
\(215\) | −1819.57 | − | 3151.58i | −0.577178 | − | 0.999702i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 262.697 | + | 329.695i | 0.0821799 | + | 0.103139i | ||||
\(218\) | −2741.97 | −0.851878 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −389.246 | + | 674.195i | −0.119286 | + | 0.206610i | ||||
\(221\) | 2496.07 | − | 4323.32i | 0.759746 | − | 1.31592i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3095.25 | −0.929477 | −0.464738 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464738 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(224\) | −369.316 | − | 463.506i | −0.110160 | − | 0.138256i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1807.69 | − | 3131.01i | −0.532060 | − | 0.921555i | ||||
\(227\) | −313.357 | + | 542.750i | −0.0916221 | + | 0.158694i | −0.908194 | − | 0.418550i | \(-0.862539\pi\) |
0.816572 | + | 0.577244i | \(0.195872\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3333.25 | − | 5773.36i | −0.961867 | − | 1.66600i | −0.717808 | − | 0.696241i | \(-0.754854\pi\) |
−0.244059 | − | 0.969760i | \(-0.578479\pi\) | |||||||
\(230\) | 1554.20 | 0.445569 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 744.369 | 0.210647 | ||||||||
\(233\) | 1750.26 | + | 3031.53i | 0.492117 | + | 0.852371i | 0.999959 | − | 0.00907927i | \(-0.00289006\pi\) |
−0.507842 | + | 0.861450i | \(0.669557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1999.15 | + | 3462.63i | −0.554937 | + | 0.961179i | ||||
\(236\) | 365.746 | + | 633.490i | 0.100881 | + | 0.174732i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1701.26 | + | 4329.39i | −0.463345 | + | 1.17913i | ||||
\(239\) | 119.098 | 0.0322335 | 0.0161168 | − | 0.999870i | \(-0.494870\pi\) | ||||
0.0161168 | + | 0.999870i | \(0.494870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −635.903 | + | 1101.42i | −0.169967 | + | 0.294392i | −0.938408 | − | 0.345529i | \(-0.887699\pi\) |
0.768441 | + | 0.639921i | \(0.221033\pi\) | |||||||
\(242\) | −1185.02 | + | 2052.51i | −0.314777 | + | 0.545209i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2439.29 | 0.639999 | ||||||||
\(245\) | −1233.98 | + | 5385.56i | −0.321779 | + | 1.40437i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2484.91 | − | 4304.00i | −0.640127 | − | 1.10873i | ||||
\(248\) | 91.0474 | − | 157.699i | 0.0233126 | − | 0.0403785i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 152.620 | + | 264.346i | 0.0386102 | + | 0.0668748i | ||||
\(251\) | −330.354 | −0.0830749 | −0.0415374 | − | 0.999137i | \(-0.513226\pi\) | ||||
−0.0415374 | + | 0.999137i | \(0.513226\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −582.876 | −0.144842 | ||||||||
\(254\) | −196.476 | − | 340.306i | −0.0485354 | − | 0.0840658i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1260.40 | − | 2183.08i | −0.305921 | − | 0.529870i | 0.671545 | − | 0.740964i | \(-0.265631\pi\) |
−0.977466 | + | 0.211093i | \(0.932298\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7339.03 | − | 1103.03i | 1.76072 | − | 0.264629i | ||||
\(260\) | −2561.32 | −0.610948 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1506.48 | − | 2609.31i | 0.355232 | − | 0.615281i | ||||
\(263\) | −713.729 | + | 1236.21i | −0.167340 | + | 0.289841i | −0.937484 | − | 0.348029i | \(-0.886851\pi\) |
0.770144 | + | 0.637870i | \(0.220184\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5394.97 | 1.25061 | ||||||||
\(266\) | 2885.78 | + | 3621.77i | 0.665182 | + | 0.834830i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −236.759 | − | 410.079i | −0.0539641 | − | 0.0934686i | ||||
\(269\) | 4094.93 | − | 7092.63i | 0.928151 | − | 1.60760i | 0.141737 | − | 0.989904i | \(-0.454731\pi\) |
0.786414 | − | 0.617700i | \(-0.211935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3197.35 | − | 5537.98i | −0.716699 | − | 1.24136i | −0.962301 | − | 0.271988i | \(-0.912319\pi\) |
0.245602 | − | 0.969371i | \(-0.421014\pi\) | |||||||
\(272\) | 2009.33 | 0.447917 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 630.691 | 0.139056 | ||||||||
\(275\) | −812.377 | − | 1407.08i | −0.178139 | − | 0.308545i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3319.70 | − | 5749.90i | 0.720078 | − | 1.24721i | −0.240890 | − | 0.970553i | \(-0.577439\pi\) |
0.960968 | − | 0.276660i | \(-0.0892275\pi\) | |||||||
\(278\) | −324.501 | − | 562.052i | −0.0700081 | − | 0.121258i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2360.12 | − | 354.718i | 0.503729 | − | 0.0757087i | ||||
\(281\) | −4929.95 | −1.04661 | −0.523303 | − | 0.852147i | \(-0.675300\pi\) | ||||
−0.523303 | + | 0.852147i | \(0.675300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1391.39 | + | 2409.96i | −0.292261 | + | 0.506210i | −0.974344 | − | 0.225064i | \(-0.927741\pi\) |
0.682083 | + | 0.731274i | \(0.261074\pi\) | |||||||
\(284\) | 162.981 | − | 282.291i | 0.0340533 | − | 0.0589821i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 960.580 | 0.198602 | ||||||||
\(287\) | −2398.28 | + | 6103.18i | −0.493261 | + | 1.25526i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5429.03 | − | 9403.36i | −1.10503 | − | 1.91397i | ||||
\(290\) | −1498.81 | + | 2596.01i | −0.303493 | + | 0.525665i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1957.66 | + | 3390.77i | 0.392341 | + | 0.679554i | ||||
\(293\) | −1639.57 | −0.326910 | −0.163455 | − | 0.986551i | \(-0.552264\pi\) | ||||
−0.163455 | + | 0.986551i | \(0.552264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2945.76 | −0.581385 | ||||||||
\(296\) | −1602.88 | − | 2776.28i | −0.314749 | − | 0.545162i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1277.49 | − | 2212.68i | 0.248332 | − | 0.430124i | ||||
\(299\) | −958.861 | − | 1660.80i | −0.185459 | − | 0.321225i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1530.24 | − | 3894.18i | 0.293029 | − | 0.745705i | ||||
\(302\) | −1033.70 | −0.196962 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1000.17 | − | 1732.35i | 0.188697 | − | 0.326832i | ||||
\(305\) | −4911.59 | + | 8507.12i | −0.922087 | + | 1.59710i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10332.5 | −1.92087 | −0.960436 | − | 0.278502i | \(-0.910162\pi\) | ||||
−0.960436 | + | 0.278502i | \(0.910162\pi\) | |||||||
\(308\) | −885.123 | + | 133.031i | −0.163749 | + | 0.0246108i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 366.653 | + | 635.061i | 0.0671757 | + | 0.116352i | ||||
\(311\) | −4626.39 | + | 8013.14i | −0.843532 | + | 1.46104i | 0.0433584 | + | 0.999060i | \(0.486194\pi\) |
−0.886890 | + | 0.461980i | \(0.847139\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1238.89 | + | 2145.82i | 0.223726 | + | 0.387504i | 0.955936 | − | 0.293574i | \(-0.0948447\pi\) |
−0.732211 | + | 0.681078i | \(0.761511\pi\) | |||||||
\(314\) | 2597.28 | 0.466793 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2773.71 | −0.493777 | ||||||||
\(317\) | −1441.61 | − | 2496.94i | −0.255422 | − | 0.442404i | 0.709588 | − | 0.704617i | \(-0.248881\pi\) |
−0.965010 | + | 0.262213i | \(0.915548\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 562.102 | − | 973.589i | 0.0986573 | − | 0.170879i | ||||
\(320\) | −515.463 | − | 892.808i | −0.0900477 | − | 0.155967i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1113.54 | + | 1397.54i | 0.192718 | + | 0.241869i | ||||
\(323\) | −15700.6 | −2.70465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2672.80 | − | 4629.43i | 0.456186 | − | 0.790137i | ||||
\(326\) | 2974.05 | − | 5151.20i | 0.505267 | − | 0.875149i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2832.56 | 0.476836 | ||||||||
\(329\) | −4545.95 | + | 683.240i | −0.761782 | + | 0.114493i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 248.565 | + | 430.528i | 0.0412761 | + | 0.0714923i | 0.885925 | − | 0.463828i | \(-0.153524\pi\) |
−0.844649 | + | 0.535320i | \(0.820191\pi\) | |||||||
\(332\) | 2818.10 | − | 4881.09i | 0.465853 | − | 0.806882i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3607.22 | + | 6247.89i | 0.590953 | + | 1.02356i | ||||
\(335\) | 1906.89 | 0.310998 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6711.07 | 1.08479 | 0.542397 | − | 0.840123i | \(-0.317517\pi\) | ||||
0.542397 | + | 0.840123i | \(0.317517\pi\) | |||||||
\(338\) | −616.796 | − | 1068.32i | −0.0992583 | − | 0.171920i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4045.83 | + | 7007.59i | −0.645341 | + | 1.11776i | ||||
\(341\) | −137.507 | − | 238.169i | −0.0218370 | − | 0.0378228i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5726.82 | + | 2749.02i | −0.901514 | + | 0.432749i | ||||
\(344\) | −1807.34 | −0.283271 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2526.41 | + | 4375.87i | −0.392545 | + | 0.679908i | ||||
\(347\) | 80.8131 | − | 139.972i | 0.0125022 | − | 0.0216545i | −0.859707 | − | 0.510788i | \(-0.829354\pi\) |
0.872209 | + | 0.489134i | \(0.162687\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3970.85 | −0.609040 | −0.304520 | − | 0.952506i | \(-0.598496\pi\) | ||||
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(350\) | −1821.71 | + | 4635.93i | −0.278213 | + | 0.708002i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 193.316 | + | 334.833i | 0.0292720 | + | 0.0507007i | ||||
\(353\) | 5777.83 | − | 10007.5i | 0.871169 | − | 1.50891i | 0.0103815 | − | 0.999946i | \(-0.496695\pi\) |
0.860788 | − | 0.508964i | \(-0.169971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 656.333 | + | 1136.80i | 0.0981255 | + | 0.169958i | ||||
\(356\) | −4845.65 | −0.721401 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2844.88 | 0.419991 | ||||||||
\(359\) | 4270.56 | + | 7396.82i | 0.627831 | + | 1.08744i | 0.987986 | + | 0.154543i | \(0.0493904\pi\) |
−0.360155 | + | 0.932892i | \(0.617276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4385.70 | + | 7596.25i | −0.639407 | + | 1.10749i | ||||
\(362\) | 2494.29 | + | 4320.24i | 0.362147 | + | 0.627257i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1835.12 | − | 2303.15i | −0.264248 | − | 0.331642i | ||||
\(365\) | −15767.2 | −2.26108 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1901.32 | + | 3293.18i | −0.270431 | + | 0.468400i | −0.968972 | − | 0.247170i | \(-0.920499\pi\) |
0.698541 | + | 0.715570i | \(0.253833\pi\) | |||||||
\(368\) | 385.939 | − | 668.467i | 0.0546698 | − | 0.0946908i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12909.8 | 1.81392 | ||||||||
\(371\) | 3865.35 | + | 4851.18i | 0.540914 | + | 0.678869i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4296.45 | + | 7441.66i | 0.596412 | + | 1.03302i | 0.993346 | + | 0.115168i | \(0.0367407\pi\) |
−0.396934 | + | 0.917847i | \(0.629926\pi\) | |||||||
\(374\) | 1517.32 | − | 2628.08i | 0.209783 | − | 0.363355i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 992.859 | + | 1719.68i | 0.136178 | + | 0.235867i | ||||
\(377\) | 3698.75 | 0.505292 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9415.95 | −1.27616 | −0.638080 | − | 0.769970i | \(-0.720271\pi\) | ||||
−0.638080 | + | 0.769970i | \(0.720271\pi\) | |||||||
\(380\) | 4027.75 | + | 6976.27i | 0.543735 | + | 0.941776i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3693.82 | + | 6397.88i | −0.494744 | + | 0.856922i | ||||
\(383\) | 4618.37 | + | 7999.25i | 0.616156 | + | 1.06721i | 0.990181 | + | 0.139795i | \(0.0446442\pi\) |
−0.374025 | + | 0.927419i | \(0.622022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1318.27 | − | 3354.76i | 0.174507 | − | 0.444089i | ||||
\(386\) | 154.241 | 0.0203384 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2673.01 | − | 4629.78i | 0.349746 | − | 0.605777i | ||||
\(389\) | −1003.96 | + | 1738.90i | −0.130855 | + | 0.226648i | −0.924006 | − | 0.382377i | \(-0.875106\pi\) |
0.793151 | + | 0.609025i | \(0.208439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6058.42 | −0.783600 | ||||||||
\(392\) | 2009.93 | + | 1868.08i | 0.258971 | + | 0.240695i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1259.96 | + | 2182.32i | 0.161107 | + | 0.279045i | ||||
\(395\) | 5584.95 | − | 9673.41i | 0.711416 | − | 1.23221i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −635.532 | − | 1100.77i | −0.0803437 | − | 0.139159i | 0.823054 | − | 0.567963i | \(-0.192268\pi\) |
−0.903398 | + | 0.428804i | \(0.858935\pi\) | |||||||
\(398\) | −10901.5 | −1.37297 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2151.59 | 0.268949 | ||||||||
\(401\) | 7512.71 | + | 13012.4i | 0.935578 | + | 1.62047i | 0.773600 | + | 0.633674i | \(0.218454\pi\) |
0.161978 | + | 0.986794i | \(0.448213\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 452.412 | − | 783.600i | 0.0559212 | − | 0.0968583i | ||||
\(404\) | −412.833 | − | 715.048i | −0.0508396 | − | 0.0880568i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3408.20 | + | 512.240i | −0.416616 | + | 0.0626159i | ||||
\(407\) | −4841.61 | −0.589655 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −239.226 | + | 414.352i | −0.0289217 | + | 0.0500939i | −0.880124 | − | 0.474744i | \(-0.842541\pi\) |
0.851202 | + | 0.524838i | \(0.175874\pi\) | |||||||
\(410\) | −5703.44 | + | 9878.66i | −0.687007 | + | 1.18993i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2753.78 | −0.329294 | ||||||||
\(413\) | −2110.56 | − | 2648.83i | −0.251462 | − | 0.315595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11348.6 | + | 19656.4i | 1.34237 | + | 2.32505i | ||||
\(416\) | −636.028 | + | 1101.63i | −0.0749612 | + | 0.129837i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1510.54 | − | 2616.33i | −0.176753 | − | 0.306146i | ||||
\(419\) | 11608.0 | 1.35343 | 0.676715 | − | 0.736245i | \(-0.263403\pi\) | ||||
0.676715 | + | 0.736245i | \(0.263403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3833.92 | −0.443833 | −0.221917 | − | 0.975066i | \(-0.571231\pi\) | ||||
−0.221917 | + | 0.975066i | \(0.571231\pi\) | |||||||
\(422\) | 326.412 | + | 565.363i | 0.0376529 | + | 0.0652167i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1339.68 | − | 2320.40i | 0.153445 | − | 0.265775i | ||||
\(425\) | −8443.86 | − | 14625.2i | −0.963735 | − | 1.66924i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11168.7 | + | 1678.61i | −1.26578 | + | 0.190243i | ||||
\(428\) | 1813.70 | 0.204833 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3639.13 | − | 6303.16i | 0.408127 | − | 0.706896i | ||||
\(431\) | 499.024 | − | 864.334i | 0.0557706 | − | 0.0965975i | −0.836792 | − | 0.547521i | \(-0.815572\pi\) |
0.892563 | + | 0.450923i | \(0.148905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1298.17 | 0.144079 | 0.0720396 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720396 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(434\) | −308.352 | + | 784.700i | −0.0341046 | + | 0.0867899i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2741.97 | − | 4749.23i | −0.301184 | − | 0.521667i | ||||
\(437\) | −3015.67 | + | 5223.30i | −0.330112 | + | 0.571772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 966.704 | + | 1674.38i | 0.105099 | + | 0.182036i | 0.913778 | − | 0.406213i | \(-0.133151\pi\) |
−0.808680 | + | 0.588249i | \(0.799818\pi\) | |||||||
\(440\) | −1556.99 | −0.168696 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9984.29 | 1.07444 | ||||||||
\(443\) | −7267.01 | − | 12586.8i | −0.779382 | − | 1.34993i | −0.932299 | − | 0.361690i | \(-0.882200\pi\) |
0.152917 | − | 0.988239i | \(-0.451133\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9756.84 | − | 16899.3i | 1.03937 | − | 1.80024i | ||||
\(446\) | −3095.25 | − | 5361.13i | −0.328620 | − | 0.569186i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 433.500 | − | 1103.18i | 0.0457165 | − | 0.116340i | ||||
\(449\) | 4799.65 | 0.504476 | 0.252238 | − | 0.967665i | \(-0.418833\pi\) | ||||
0.252238 | + | 0.967665i | \(0.418833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2138.98 | − | 3704.82i | 0.223327 | − | 0.386814i | ||||
\(452\) | 3615.37 | − | 6262.01i | 0.376223 | − | 0.651638i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1253.43 | −0.129573 | ||||||||
\(455\) | 11727.4 | − | 1762.58i | 1.20832 | − | 0.181607i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2367.14 | − | 4100.00i | −0.242297 | − | 0.419671i | 0.719071 | − | 0.694937i | \(-0.244568\pi\) |
−0.961368 | + | 0.275265i | \(0.911234\pi\) | |||||||
\(458\) | 6666.50 | − | 11546.7i | 0.680142 | − | 1.17804i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1554.20 | + | 2691.95i | 0.157532 | + | 0.272854i | ||||
\(461\) | 8137.41 | 0.822119 | 0.411060 | − | 0.911608i | \(-0.365159\pi\) | ||||
0.411060 | + | 0.911608i | \(0.365159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8671.77 | 0.870435 | 0.435218 | − | 0.900325i | \(-0.356671\pi\) | ||||
0.435218 | + | 0.900325i | \(0.356671\pi\) | |||||||
\(464\) | 744.369 | + | 1289.28i | 0.0744751 | + | 0.128995i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3500.51 | + | 6063.07i | −0.347979 | + | 0.602717i | ||||
\(467\) | −7794.04 | − | 13499.7i | −0.772303 | − | 1.33767i | −0.936298 | − | 0.351206i | \(-0.885772\pi\) |
0.163995 | − | 0.986461i | \(-0.447562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1366.23 | + | 1714.68i | 0.134513 | + | 0.168820i | ||||
\(470\) | −7996.60 | −0.784799 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −731.492 | + | 1266.98i | −0.0713340 | + | 0.123554i | ||||
\(473\) | −1364.79 | + | 2363.89i | −0.132671 | + | 0.229793i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16812.2 | −1.62400 | ||||||||
\(476\) | −9199.98 | + | 1382.73i | −0.885883 | + | 0.133145i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 119.098 | + | 206.284i | 0.0113963 | + | 0.0197389i | ||||
\(479\) | 4767.04 | − | 8256.76i | 0.454722 | − | 0.787601i | −0.543951 | − | 0.839117i | \(-0.683072\pi\) |
0.998672 | + | 0.0515163i | \(0.0164054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7964.69 | − | 13795.2i | −0.755007 | − | 1.30771i | ||||
\(482\) | −2543.61 | −0.240370 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4740.08 | −0.445161 | ||||||||
\(485\) | 10764.3 | + | 18644.4i | 1.00780 | + | 1.74556i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4398.55 | − | 7618.51i | 0.409276 | − | 0.708887i | −0.585533 | − | 0.810649i | \(-0.699115\pi\) |
0.994809 | + | 0.101762i | \(0.0324480\pi\) | |||||||
\(488\) | 2439.29 | + | 4224.98i | 0.226274 | + | 0.391918i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10562.0 | + | 3248.25i | −0.973764 | + | 0.299471i | ||||
\(491\) | −15749.6 | −1.44760 | −0.723799 | − | 0.690010i | \(-0.757606\pi\) | ||||
−0.723799 | + | 0.690010i | \(0.757606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5842.50 | − | 10119.5i | 0.533738 | − | 0.924461i | ||||
\(494\) | 4969.83 | − | 8608.00i | 0.452638 | − | 0.783992i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 364.190 | 0.0329689 | ||||||||
\(497\) | −551.971 | + | 1404.67i | −0.0498175 | + | 0.126776i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6490.60 | + | 11242.0i | 0.582283 | + | 1.00854i | 0.995208 | + | 0.0977783i | \(0.0311736\pi\) |
−0.412926 | + | 0.910765i | \(0.635493\pi\) | |||||||
\(500\) | −305.240 | + | 528.692i | −0.0273015 | + | 0.0472876i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −330.354 | − | 572.191i | −0.0293714 | − | 0.0508727i | ||||
\(503\) | 13047.4 | 1.15657 | 0.578284 | − | 0.815836i | \(-0.303723\pi\) | ||||
0.578284 | + | 0.815836i | \(0.303723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3325.00 | 0.292991 | ||||||||
\(506\) | −582.876 | − | 1009.57i | −0.0512095 | − | 0.0886974i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 392.952 | − | 680.612i | 0.0343197 | − | 0.0594435i | ||||
\(509\) | 381.720 | + | 661.159i | 0.0332406 | + | 0.0575744i | 0.882167 | − | 0.470937i | \(-0.156084\pi\) |
−0.848927 | + | 0.528511i | \(0.822751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11296.8 | − | 14177.9i | −0.977967 | − | 1.22739i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2520.80 | − | 4366.15i | 0.216319 | − | 0.374675i | ||||
\(515\) | 5544.82 | − | 9603.91i | 0.474435 | − | 0.821745i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2998.99 | 0.255117 | ||||||||
\(518\) | 9249.54 | + | 11608.5i | 0.784559 | + | 0.984653i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2561.32 | − | 4436.34i | −0.216003 | − | 0.374127i | ||||
\(521\) | 1015.38 | − | 1758.68i | 0.0853829 | − | 0.147887i | −0.820171 | − | 0.572118i | \(-0.806122\pi\) |
0.905554 | + | 0.424230i | \(0.139455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6482.87 | + | 11228.7i | 0.542019 | + | 0.938805i | 0.998788 | + | 0.0492192i | \(0.0156733\pi\) |
−0.456769 | + | 0.889585i | \(0.650993\pi\) | |||||||
\(524\) | 6025.94 | 0.502374 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2854.91 | −0.236654 | ||||||||
\(527\) | −1429.25 | − | 2475.53i | −0.118139 | − | 0.204622i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4919.83 | − | 8521.40i | 0.404359 | − | 0.700370i | ||||
\(530\) | 5394.97 | + | 9344.36i | 0.442156 | + | 0.765836i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3387.31 | + | 8620.08i | −0.276050 | + | 0.702496i | ||||
\(533\) | 14074.9 | 1.14381 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3651.93 | + | 6325.34i | −0.295116 | + | 0.511155i | ||||
\(536\) | 473.519 | − | 820.158i | 0.0381584 | − | 0.0660923i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16379.7 | 1.31260 | ||||||||
\(539\) | 3961.11 | − | 1218.20i | 0.316544 | − | 0.0973500i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7812.43 | + | 13531.5i | 0.620855 | + | 1.07535i | 0.989327 | + | 0.145714i | \(0.0465479\pi\) |
−0.368471 | + | 0.929639i | \(0.620119\pi\) | |||||||
\(542\) | 6394.70 | − | 11076.0i | 0.506782 | − | 0.877773i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2009.33 | + | 3480.26i | 0.158362 | + | 0.274292i | ||||
\(545\) | 22084.1 | 1.73574 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14437.8 | −1.12855 | −0.564273 | − | 0.825588i | \(-0.690843\pi\) | ||||
−0.564273 | + | 0.825588i | \(0.690843\pi\) | |||||||
\(548\) | 630.691 | + | 1092.39i | 0.0491639 | + | 0.0851543i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1624.75 | − | 2814.16i | 0.125963 | − | 0.218175i | ||||
\(551\) | −5816.38 | − | 10074.3i | −0.449703 | − | 0.778908i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12699.8 | − | 1908.74i | 0.976586 | − | 0.146777i | ||||
\(554\) | 13278.8 | 1.01834 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 649.001 | − | 1124.10i | 0.0495032 | − | 0.0857421i | ||||
\(557\) | 8242.53 | − | 14276.5i | 0.627015 | − | 1.08602i | −0.361133 | − | 0.932514i | \(-0.617610\pi\) |
0.988148 | − | 0.153507i | \(-0.0490567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8980.63 | −0.679499 | ||||||||
\(560\) | 2974.51 | + | 3733.13i | 0.224457 | + | 0.281703i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4929.95 | − | 8538.92i | −0.370031 | − | 0.640912i | ||||
\(563\) | −8366.91 | + | 14491.9i | −0.626329 | + | 1.08483i | 0.361954 | + | 0.932196i | \(0.382110\pi\) |
−0.988282 | + | 0.152637i | \(0.951223\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14559.3 | + | 25217.5i | 1.08410 | + | 1.87771i | ||||
\(566\) | −5565.57 | −0.413319 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 651.924 | 0.0481587 | ||||||||
\(569\) | 7508.37 | + | 13004.9i | 0.553194 | + | 0.958160i | 0.998042 | + | 0.0625539i | \(0.0199245\pi\) |
−0.444848 | + | 0.895606i | \(0.646742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3236.25 | + | 5605.35i | −0.237186 | + | 0.410817i | −0.959906 | − | 0.280323i | \(-0.909558\pi\) |
0.722720 | + | 0.691141i | \(0.242892\pi\) | |||||||
\(572\) | 960.580 | + | 1663.77i | 0.0702166 | + | 0.121619i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12969.3 | + | 1949.24i | −0.943080 | + | 0.141742i | ||||
\(575\) | −6487.38 | −0.470509 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4955.10 | + | 8582.48i | −0.357510 | + | 0.619226i | −0.987544 | − | 0.157342i | \(-0.949708\pi\) |
0.630034 | + | 0.776567i | \(0.283041\pi\) | |||||||
\(578\) | 10858.1 | − | 18806.7i | 0.781377 | − | 1.35338i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5995.23 | −0.429204 | ||||||||
\(581\) | −9544.12 | + | 24288.0i | −0.681509 | + | 1.73432i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2023.29 | − | 3504.45i | −0.143733 | − | 0.248952i | ||||
\(584\) | −3915.32 | + | 6781.54i | −0.277427 | + | 0.480517i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1639.57 | − | 2839.81i | −0.115580 | − | 0.200191i | ||||
\(587\) | −1112.26 | −0.0782079 | −0.0391039 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391039 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2845.72 | −0.199076 | ||||||||
\(590\) | −2945.76 | − | 5102.20i | −0.205551 | − | 0.356024i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3205.77 | − | 5552.56i | 0.222561 | − | 0.385488i | ||||
\(593\) | 379.191 | + | 656.778i | 0.0262589 | + | 0.0454817i | 0.878856 | − | 0.477087i | \(-0.158307\pi\) |
−0.852597 | + | 0.522568i | \(0.824974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13702.1 | − | 34869.4i | 0.944087 | − | 2.40253i | ||||
\(596\) | 5109.96 | 0.351195 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1917.72 | − | 3321.59i | 0.131140 | − | 0.227140i | ||||
\(599\) | 8957.35 | − | 15514.6i | 0.610997 | − | 1.05828i | −0.380076 | − | 0.924955i | \(-0.624102\pi\) |
0.991073 | − | 0.133323i | \(-0.0425646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19337.1 | 1.31244 | 0.656221 | − | 0.754569i | \(-0.272154\pi\) | ||||
0.656221 | + | 0.754569i | \(0.272154\pi\) | |||||||
\(602\) | 8275.17 | − | 1243.73i | 0.560250 | − | 0.0842037i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1033.70 | − | 1790.42i | −0.0696366 | − | 0.120614i | ||||
\(605\) | 9544.28 | − | 16531.2i | 0.641372 | − | 1.11089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −787.211 | − | 1363.49i | −0.0526391 | − | 0.0911736i | 0.838505 | − | 0.544894i | \(-0.183430\pi\) |
−0.891144 | + | 0.453720i | \(0.850097\pi\) | |||||||
\(608\) | 4000.69 | 0.266858 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19646.3 | −1.30403 | ||||||||
\(611\) | 4933.49 | + | 8545.06i | 0.326657 | + | 0.565787i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2597.21 | − | 4498.49i | 0.171126 | − | 0.296399i | −0.767688 | − | 0.640824i | \(-0.778593\pi\) |
0.938814 | + | 0.344425i | \(0.111926\pi\) | |||||||
\(614\) | −10332.5 | − | 17896.4i | −0.679131 | − | 1.17629i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1115.54 | − | 1400.05i | −0.0729649 | − | 0.0915739i | ||||
\(617\) | −1699.80 | −0.110910 | −0.0554550 | − | 0.998461i | \(-0.517661\pi\) | ||||
−0.0554550 | + | 0.998461i | \(0.517661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6362.04 | − | 11019.4i | 0.413105 | − | 0.715518i | −0.582123 | − | 0.813101i | \(-0.697778\pi\) |
0.995227 | + | 0.0975825i | \(0.0311110\pi\) | |||||||
\(620\) | −733.305 | + | 1270.12i | −0.0475004 | + | 0.0822731i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18505.6 | −1.19293 | ||||||||
\(623\) | 22186.5 | − | 3334.55i | 1.42678 | − | 0.214440i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7175.45 | + | 12428.2i | 0.459229 | + | 0.795407i | ||||
\(626\) | −2477.78 | + | 4291.63i | −0.158198 | + | 0.274007i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2597.28 | + | 4498.62i | 0.165036 | + | 0.285851i | ||||
\(629\) | −50323.7 | −3.19004 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14921.6 | −0.941392 | −0.470696 | − | 0.882295i | \(-0.655997\pi\) | ||||
−0.470696 | + | 0.882295i | \(0.655997\pi\) | |||||||
\(632\) | −2773.71 | − | 4804.21i | −0.174577 | − | 0.302375i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2883.22 | − | 4993.88i | 0.180611 | − | 0.312827i | ||||
\(635\) | 1582.44 | + | 2740.86i | 0.0988931 | + | 0.171288i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9987.27 | + | 9282.45i | 0.621209 | + | 0.577369i | ||||
\(638\) | 2248.41 | 0.139522 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1030.93 | − | 1785.62i | 0.0636733 | − | 0.110285i | ||||
\(641\) | −13483.7 | + | 23354.5i | −0.830850 | + | 1.43907i | 0.0665155 | + | 0.997785i | \(0.478812\pi\) |
−0.897365 | + | 0.441289i | \(0.854522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12146.2 | 0.744947 | 0.372473 | − | 0.928043i | \(-0.378510\pi\) | ||||
0.372473 | + | 0.928043i | \(0.378510\pi\) | |||||||
\(644\) | −1307.07 | + | 3326.25i | −0.0799779 | + | 0.203529i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15700.6 | − | 27194.2i | −0.956239 | − | 1.65626i | ||||
\(647\) | 13575.9 | − | 23514.1i | 0.824919 | − | 1.42880i | −0.0770625 | − | 0.997026i | \(-0.524554\pi\) |
0.901981 | − | 0.431775i | \(-0.142113\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1104.76 | + | 1913.49i | 0.0668189 | + | 0.115734i | ||||
\(650\) | 10691.2 | 0.645144 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11896.2 | 0.714556 | ||||||||
\(653\) | 6320.52 | + | 10947.5i | 0.378776 | + | 0.656060i | 0.990884 | − | 0.134714i | \(-0.0430117\pi\) |
−0.612108 | + | 0.790774i | \(0.709678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12133.4 | + | 21015.6i | −0.723802 | + | 1.25366i | ||||
\(656\) | 2832.56 | + | 4906.14i | 0.168587 | + | 0.292001i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5729.35 | − | 7190.57i | −0.339443 | − | 0.426015i | ||||
\(659\) | −11360.0 | −0.671506 | −0.335753 | − | 0.941950i | \(-0.608991\pi\) | ||||
−0.335753 | + | 0.941950i | \(0.608991\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2078.99 | + | 3600.91i | −0.122335 | + | 0.211890i | −0.920688 | − | 0.390300i | \(-0.872371\pi\) |
0.798353 | + | 0.602189i | \(0.205705\pi\) | |||||||
\(662\) | −497.131 | + | 861.056i | −0.0291866 | + | 0.0505527i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 11272.4 | 0.658816 | ||||||||
\(665\) | −23242.4 | − | 29170.1i | −1.35534 | − | 1.70100i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2244.38 | − | 3887.39i | −0.130289 | − | 0.225668i | ||||
\(668\) | −7214.44 | + | 12495.8i | −0.417867 | + | 0.723766i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1906.89 | + | 3302.82i | 0.109954 | + | 0.190447i | ||||
\(671\) | 7368.03 | 0.423904 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8753.81 | 0.501389 | 0.250694 | − | 0.968066i | \(-0.419341\pi\) | ||||
0.250694 | + | 0.968066i | \(0.419341\pi\) | |||||||
\(674\) | 6711.07 | + | 11623.9i | 0.383532 | + | 0.664297i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1233.59 | − | 2136.65i | 0.0701862 | − | 0.121566i | ||||
\(677\) | −5802.61 | − | 10050.4i | −0.329413 | − | 0.570560i | 0.652983 | − | 0.757373i | \(-0.273517\pi\) |
−0.982395 | + | 0.186813i | \(0.940184\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9052.73 | + | 23037.6i | −0.511652 | + | 1.30206i | ||||
\(680\) | −16183.3 | −0.912651 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 275.014 | − | 476.338i | 0.0154411 | − | 0.0267448i | ||||
\(683\) | −9199.15 | + | 15933.4i | −0.515367 | + | 0.892642i | 0.484474 | + | 0.874806i | \(0.339011\pi\) |
−0.999841 | + | 0.0178364i | \(0.994322\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5079.66 | −0.283334 | ||||||||
\(686\) | −10488.3 | − | 7170.13i | −0.583737 | − | 0.399063i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1807.34 | − | 3130.41i | −0.100152 | − | 0.173468i | ||||
\(689\) | 6656.84 | − | 11530.0i | 0.368077 | − | 0.637529i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7919 | + | 36.0127i | 0.00114466 | + | 0.00198261i | 0.866597 | − | 0.499008i | \(-0.166302\pi\) |
−0.865453 | + | 0.500991i | \(0.832969\pi\) | |||||||
\(692\) | −10105.6 | −0.555143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 323.252 | 0.0176808 | ||||||||
\(695\) | 2613.56 | + | 4526.83i | 0.142645 | + | 0.247068i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22232.6 | − | 38508.0i | 1.20821 | − | 2.09267i | ||||
\(698\) | −3970.85 | − | 6877.72i | −0.215328 | − | 0.372959i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9851.38 | + | 1480.63i | −0.531924 | + | 0.0799464i | ||||
\(701\) | 29655.0 | 1.59779 | 0.798896 | − | 0.601469i | \(-0.205418\pi\) | ||||
0.798896 | + | 0.601469i | \(0.205418\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25049.4 | + | 43386.8i | −1.34389 | + | 2.32769i | ||||
\(704\) | −386.631 | + | 669.665i | −0.0206985 | + | 0.0358508i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23111.3 | 1.23202 | ||||||||
\(707\) | 2382.28 | + | 2989.85i | 0.126725 | + | 0.159045i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4375.23 | + | 7578.13i | 0.231757 | + | 0.401414i | 0.958325 | − | 0.285680i | \(-0.0922194\pi\) |
−0.726569 | + | 0.687094i | \(0.758886\pi\) | |||||||
\(710\) | −1312.67 | + | 2273.60i | −0.0693852 | + | 0.120179i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4845.65 | − | 8392.91i | −0.255054 | − | 0.441766i | ||||
\(713\) | −1098.09 | −0.0576769 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7736.62 | −0.404662 | ||||||||
\(716\) | 2844.88 | + | 4927.48i | 0.148489 | + | 0.257191i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8541.11 | + | 14793.6i | −0.443944 | + | 0.768933i | ||||
\(719\) | 9541.72 | + | 16526.8i | 0.494918 | + | 0.857224i | 0.999983 | − | 0.00585789i | \(-0.00186464\pi\) |
−0.505065 | + | 0.863082i | \(0.668531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12608.6 | − | 1895.03i | 0.651274 | − | 0.0978842i | ||||
\(722\) | −17542.8 | −0.904259 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4988.59 | + | 8640.49i | −0.256076 | + | 0.443537i | ||||
\(725\) | 6256.17 | − | 10836.0i | 0.320480 | − | 0.555088i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15050.9 | 0.767821 | 0.383910 | − | 0.923370i | \(-0.374577\pi\) | ||||
0.383910 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(728\) | 2154.05 | − | 5481.67i | 0.109663 | − | 0.279072i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15767.2 | − | 27309.6i | −0.799412 | − | 1.38462i | ||||
\(731\) | −14185.7 | + | 24570.4i | −0.717752 | + | 1.24318i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5279.02 | − | 9143.53i | −0.266010 | − | 0.460742i | 0.701818 | − | 0.712356i | \(-0.252372\pi\) |
−0.967828 | + | 0.251614i | \(0.919039\pi\) | |||||||
\(734\) | −7605.28 | −0.382447 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1543.76 | 0.0773148 | ||||||||
\(737\) | −715.145 | − | 1238.67i | −0.0357432 | − | 0.0619090i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16623.4 | − | 28792.5i | 0.827470 | − | 1.43322i | −0.0725462 | − | 0.997365i | \(-0.523112\pi\) |
0.900017 | − | 0.435856i | \(-0.143554\pi\) | |||||||
\(740\) | 12909.8 | + | 22360.4i | 0.641316 | + | 1.11079i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4537.13 | + | 11546.2i | −0.224479 | + | 0.571258i | ||||
\(743\) | −32799.7 | −1.61952 | −0.809761 | − | 0.586760i | \(-0.800403\pi\) | ||||
−0.809761 | + | 0.586760i | \(0.800403\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10289.0 | + | 17821.1i | −0.505988 | + | 0.876397i | ||||
\(746\) | −8592.89 | + | 14883.3i | −0.421727 | + | 0.730452i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6069.29 | 0.296678 | ||||||||
\(749\) | −8304.28 | + | 1248.10i | −0.405116 | + | 0.0608875i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12113.3 | + | 20980.8i | 0.588574 | + | 1.01944i | 0.994419 | + | 0.105499i | \(0.0336439\pi\) |
−0.405845 | + | 0.913942i | \(0.633023\pi\) | |||||||
\(752\) | −1985.72 | + | 3439.37i | −0.0962922 | + | 0.166783i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3698.75 | + | 6406.42i | 0.178648 | + | 0.309427i | ||||
\(755\) | 8325.51 | 0.401319 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3116.97 | −0.149654 | −0.0748271 | − | 0.997197i | \(-0.523840\pi\) | ||||
−0.0748271 | + | 0.997197i | \(0.523840\pi\) | |||||||
\(758\) | −9415.95 | − | 16308.9i | −0.451191 | − | 0.781485i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8055.50 | + | 13952.5i | −0.384478 | + | 0.665936i | ||||
\(761\) | 4355.33 | + | 7543.65i | 0.207464 | + | 0.359339i | 0.950915 | − | 0.309452i | \(-0.100146\pi\) |
−0.743451 | + | 0.668791i | \(0.766812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15822.7 | + | 19858.1i | 0.750746 | + | 0.942217i | ||||
\(764\) | −14775.3 | −0.699674 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9236.74 | + | 15998.5i | −0.435688 | + | 0.754634i | ||||
\(767\) | −3634.76 | + | 6295.59i | −0.171113 | + | 0.296376i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14498.2 | −0.679868 | −0.339934 | − | 0.940449i | \(-0.610405\pi\) | ||||
−0.339934 | + | 0.940449i | \(0.610405\pi\) | |||||||
\(770\) | 7128.88 | − | 1071.45i | 0.333645 | − | 0.0501457i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 154.241 | + | 267.153i | 0.00719073 | + | 0.0124547i | ||||
\(773\) | 7418.91 | − | 12849.9i | 0.345200 | − | 0.597904i | −0.640190 | − | 0.768217i | \(-0.721144\pi\) |
0.985390 | + | 0.170312i | \(0.0544777\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1530.45 | − | 2650.81i | −0.0709358 | − | 0.122864i | ||||
\(776\) | 10692.0 | 0.494615 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4015.82 | −0.185057 | ||||||||
\(779\) | −22133.2 | − | 38335.9i | −1.01798 | − | 1.76319i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 492.293 | − | 852.677i | 0.0225552 | − | 0.0390668i | ||||
\(782\) | −6058.42 | − | 10493.5i | −0.277044 | − | 0.479855i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1225.69 | + | 5349.38i | −0.0558348 | + | 0.243685i | ||||
\(785\) | −20918.8 | −0.951112 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22013.0 | + | 38127.6i | −0.997050 | + | 1.72694i | −0.432059 | + | 0.901845i | \(0.642213\pi\) |
−0.564991 | + | 0.825097i | \(0.691120\pi\) | |||||||
\(788\) | −2519.93 | + | 4364.64i | −0.113920 | + | 0.197315i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22339.8 | 1.00609 | ||||||||
\(791\) | −12244.3 | + | 31159.4i | −0.550387 | + | 1.40063i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12120.8 | + | 20993.8i | 0.542776 | + | 0.940116i | ||||
\(794\) | 1271.06 | − | 2201.55i | 0.0568116 | − | 0.0984005i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10901.5 | − | 18881.9i | −0.485418 | − | 0.840769i | ||||
\(797\) | −14499.6 | −0.644419 | −0.322209 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322209 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31171.5 | 1.38019 | ||||||||
\(800\) | 2151.59 | + | 3726.67i | 0.0950880 | + | 0.164697i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −15025.4 | + | 26024.8i | −0.661553 | + | 1.14584i | ||||
\(803\) | 5913.23 | + | 10242.0i | 0.259867 | + | 0.450103i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8968.59 | − | 11255.9i | −0.392673 | − | 0.492820i | ||||
\(806\) | 1809.65 | 0.0790845 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 825.666 | − | 1430.10i | 0.0359490 | − | 0.0622656i | ||||
\(809\) | −8965.81 | + | 15529.2i | −0.389643 | + | 0.674881i | −0.992401 | − | 0.123042i | \(-0.960735\pi\) |
0.602758 | + | 0.797924i | \(0.294068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7961.18 | 0.344704 | 0.172352 | − | 0.985035i | \(-0.444863\pi\) | ||||
0.172352 | + | 0.985035i | \(0.444863\pi\) | |||||||
\(812\) | −4295.42 | − | 5390.93i | −0.185640 | − | 0.232986i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4841.61 | − | 8385.91i | −0.208474 | − | 0.361088i | ||||
\(815\) | −23953.3 | + | 41488.3i | −1.02951 | + | 1.78316i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14122.3 | + | 24460.5i | 0.604745 | + | 1.04745i | ||||
\(818\) | −956.906 | −0.0409015 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −22813.8 | −0.971575 | ||||||||
\(821\) | −3354.32 | − | 5809.86i | −0.142590 | − | 0.246974i | 0.785881 | − | 0.618378i | \(-0.212210\pi\) |
−0.928471 | + | 0.371404i | \(0.878877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 279.982 | − | 484.944i | 0.0118585 | − | 0.0205396i | −0.860035 | − | 0.510235i | \(-0.829559\pi\) |
0.871894 | + | 0.489695i | \(0.162892\pi\) | |||||||
\(824\) | −2753.78 | − | 4769.70i | −0.116423 | − | 0.201651i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2477.36 | − | 6304.43i | 0.104356 | − | 0.265568i | ||||
\(827\) | 41169.0 | 1.73106 | 0.865530 | − | 0.500858i | \(-0.166982\pi\) | ||||
0.865530 | + | 0.500858i | \(0.166982\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2086.87 | − | 3614.57i | 0.0874308 | − | 0.151435i | −0.818994 | − | 0.573803i | \(-0.805468\pi\) |
0.906424 | + | 0.422368i | \(0.138801\pi\) | |||||||
\(830\) | −22697.3 | + | 39312.8i | −0.949198 | + | 1.64406i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2544.11 | −0.106011 | ||||||||
\(833\) | 41171.9 | − | 12662.0i | 1.71251 | − | 0.526666i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29052.9 | − | 50321.2i | −1.20409 | − | 2.08555i | ||||
\(836\) | 3021.08 | − | 5232.66i | 0.124983 | − | 0.216478i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11608.0 | + | 20105.6i | 0.478510 | + | 0.828803i | ||||
\(839\) | −9010.93 | −0.370789 | −0.185394 | − | 0.982664i | \(-0.559356\pi\) | ||||
−0.185394 | + | 0.982664i | \(0.559356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15731.4 | −0.645021 | ||||||||
\(842\) | −3833.92 | − | 6640.55i | −0.156919 | − | 0.271791i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −652.825 | + | 1130.73i | −0.0266246 | + | 0.0461152i | ||||
\(845\) | 4967.75 | + | 8604.39i | 0.202243 | + | 0.350296i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21703.1 | − | 3261.90i | 0.880434 | − | 0.132326i | ||||
\(848\) | 5358.73 | 0.217004 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16887.7 | − | 29250.4i | 0.681463 | − | 1.18033i | ||||
\(851\) | −9665.88 | + | 16741.8i | −0.389356 | + | 0.674385i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24474.7 | −0.982411 | −0.491205 | − | 0.871044i | \(-0.663444\pi\) | ||||
−0.491205 | + | 0.871044i | \(0.663444\pi\) | |||||||
\(854\) | −14076.1 | − | 17666.1i | −0.564021 | − | 0.707869i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1813.70 | + | 3141.42i | 0.0724194 | + | 0.125434i | ||||
\(857\) | −14742.4 | + | 25534.5i | −0.587619 | + | 1.01779i | 0.406925 | + | 0.913462i | \(0.366601\pi\) |
−0.994543 | + | 0.104324i | \(0.966732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3986.84 | − | 6905.41i | −0.158358 | − | 0.274284i | 0.775919 | − | 0.630833i | \(-0.217287\pi\) |
−0.934277 | + | 0.356549i | \(0.883953\pi\) | |||||||
\(860\) | 14556.5 | 0.577178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1996.09 | 0.0788715 | ||||||||
\(863\) | −13792.0 | − | 23888.4i | −0.544015 | − | 0.942261i | −0.998668 | − | 0.0515928i | \(-0.983570\pi\) |
0.454653 | − | 0.890668i | \(-0.349763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20348.0 | − | 35243.7i | 0.799829 | − | 1.38535i | ||||
\(866\) | 1298.17 | + | 2248.50i | 0.0509397 | + | 0.0882301i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1667.49 | + | 250.618i | −0.0652055 | + | 0.00980017i | ||||
\(869\) | −8378.16 | −0.327054 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2352.90 | − | 4075.34i | 0.0915327 | − | 0.158539i | ||||
\(872\) | 5483.93 | − | 9498.45i | 0.212970 | − | 0.368874i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12062.7 | −0.466849 | ||||||||
\(875\) | 1033.76 | − | 2630.74i | 0.0399401 | − | 0.101640i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7078.94 | − | 12261.1i | −0.272564 | − | 0.472095i | 0.696954 | − | 0.717116i | \(-0.254538\pi\) |
−0.969518 | + | 0.245021i | \(0.921205\pi\) | |||||||
\(878\) | −1933.41 | + | 3348.76i | −0.0743159 | + | 0.128719i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1556.99 | − | 2696.78i | −0.0596431 | − | 0.103305i | ||||
\(881\) | −31107.6 | −1.18960 | −0.594802 | − | 0.803873i | \(-0.702769\pi\) | ||||
−0.594802 | + | 0.803873i | \(0.702769\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9141.04 | 0.348381 | 0.174190 | − | 0.984712i | \(-0.444269\pi\) | ||||
0.174190 | + | 0.984712i | \(0.444269\pi\) | |||||||
\(884\) | 9984.29 | + | 17293.3i | 0.379873 | + | 0.657960i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14534.0 | − | 25173.7i | 0.551106 | − | 0.954544i | ||||
\(887\) | −17902.3 | − | 31007.8i | −0.677680 | − | 1.17378i | −0.975678 | − | 0.219209i | \(-0.929652\pi\) |
0.297998 | − | 0.954567i | \(-0.403681\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1330.82 | + | 3386.69i | −0.0502072 | + | 0.127768i | ||||
\(890\) | 39027.4 | 1.46989 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6190.50 | − | 10722.3i | 0.232369 | − | 0.402475i | ||||
\(893\) | 15516.1 | − | 26874.7i | 0.581441 | − | 1.00709i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22913.0 | −0.855751 | ||||||||
\(896\) | 2344.26 | − | 352.335i | 0.0874066 | − | 0.0131369i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4799.65 | + | 8313.24i | 0.178359 | + | 0.308927i | ||||
\(899\) | 1058.95 | − | 1834.16i | 0.0392858 | − | 0.0680451i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21030.1 | − | 36425.3i | −0.777597 | − | 1.34684i | ||||
\(902\) | 8555.92 | 0.315833 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14461.5 | 0.532060 | ||||||||
\(905\) | −20089.3 | − | 34795.7i | −0.737891 | − | 1.27806i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11155.9 | − | 19322.6i | 0.408407 | − | 0.707382i | −0.586304 | − | 0.810091i | \(-0.699418\pi\) |
0.994711 | + | 0.102709i | \(0.0327511\pi\) | |||||||
\(908\) | −1253.43 | − | 2171.00i | −0.0458110 | − | 0.0793470i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 14780.2 | + | 18549.8i | 0.538418 | + | 0.675737i | ||||
\(911\) | −11553.9 | −0.420195 | −0.210097 | − | 0.977680i | \(-0.567378\pi\) | ||||
−0.210097 | + | 0.977680i | \(0.567378\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8512.23 | − | 14743.6i | 0.308558 | − | 0.534439i | ||||
\(914\) | 4734.27 | − | 8200.00i | 0.171330 | − | 0.296753i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26666.0 | 0.961867 | ||||||||
\(917\) | −27590.6 | + | 4146.77i | −0.993589 | + | 0.149333i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13687.1 | + | 23706.8i | 0.491291 | + | 0.850942i | 0.999950 | − | 0.0100269i | \(-0.00319171\pi\) |
−0.508658 | + | 0.860968i | \(0.669858\pi\) | |||||||
\(920\) | −3108.40 | + | 5383.90i | −0.111392 | + | 0.192937i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8137.41 | + | 14094.4i | 0.290663 | + | 0.503443i | ||||
\(923\) | 3239.39 | 0.115521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53886.8 | −1.91545 | ||||||||
\(926\) | 8671.77 | + | 15020.0i | 0.307745 | + | 0.533031i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1488.74 | + | 2578.57i | −0.0526618 | + | 0.0912130i | ||||
\(929\) | 18587.1 | + | 32193.7i | 0.656428 | + | 1.13697i | 0.981534 | + | 0.191289i | \(0.0612669\pi\) |
−0.325105 | + | 0.945678i | \(0.605400\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9577.32 | − | 41799.2i | 0.337147 | − | 1.47144i | ||||
\(932\) | −14002.1 | −0.492117 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15588.1 | − | 26999.4i | 0.546100 | − | 0.945874i | ||||
\(935\) | −12220.7 | + | 21166.8i | −0.427442 | + | 0.740352i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 603.266 | 0.0210329 | 0.0105165 | − | 0.999945i | \(-0.496652\pi\) | ||||
0.0105165 | + | 0.999945i | \(0.496652\pi\) | |||||||
\(938\) | −1603.68 | + | 4081.06i | −0.0558229 | + | 0.142059i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7996.60 | − | 13850.5i | −0.277468 | − | 0.480589i | ||||
\(941\) | −8075.89 | + | 13987.9i | −0.279773 | + | 0.484581i | −0.971328 | − | 0.237742i | \(-0.923593\pi\) |
0.691555 | + | 0.722324i | \(0.256926\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8540.61 | − | 14792.8i | −0.294932 | − | 0.510837i | ||||
\(944\) | −2925.97 | −0.100881 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5459.18 | −0.187625 | ||||||||
\(947\) | 8506.64 | + | 14733.9i | 0.291899 | + | 0.505585i | 0.974259 | − | 0.225432i | \(-0.0723794\pi\) |
−0.682359 | + | 0.731017i | \(0.739046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19455.1 | + | 33697.3i | −0.665480 | + | 1.15264i | ||||
\(950\) | −16812.2 | − | 29119.6i | −0.574169 | − | 0.994491i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11594.9 | − | 14552.1i | −0.394742 | − | 0.495417i | ||||
\(953\) | −5233.67 | −0.177896 | −0.0889482 | − | 0.996036i | \(-0.528351\pi\) | ||||
−0.0889482 | + | 0.996036i | \(0.528351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29750.4 | − | 51529.2i | 1.00806 | − | 1.74602i | ||||
\(956\) | −238.196 | + | 412.568i | −0.00805838 | + | 0.0139575i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19068.2 | 0.643074 | ||||||||
\(959\) | −3639.44 | − | 4567.65i | −0.122548 | − | 0.153803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14636.4 | + | 25351.1i | 0.491304 | + | 0.850964i | ||||
\(962\) | 15929.4 | − | 27590.5i | 0.533871 | − | 0.924691i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2543.61 | − | 4405.66i | −0.0849836 | − | 0.147196i | ||||
\(965\) | −1242.27 | −0.0414405 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16834.4 | 0.559832 | 0.279916 | − | 0.960024i | \(-0.409693\pi\) | ||||
0.279916 | + | 0.960024i | \(0.409693\pi\) | |||||||
\(968\) | −4740.08 | − | 8210.06i | −0.157388 | − | 0.272605i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −21528.7 | + | 37288.8i | −0.712623 | + | 1.23430i | ||||
\(971\) | 26609.2 | + | 46088.5i | 0.879434 | + | 1.52322i | 0.851963 | + | 0.523602i | \(0.175412\pi\) |
0.0274708 | + | 0.999623i | \(0.491255\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2197.99 | + | 5593.48i | −0.0724196 | + | 0.184295i | ||||
\(974\) | 17594.2 | 0.578803 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4878.59 | + | 8449.96i | −0.160000 | + | 0.277128i | ||||
\(977\) | 27579.9 | − | 47769.9i | 0.903133 | − | 1.56427i | 0.0797279 | − | 0.996817i | \(-0.474595\pi\) |
0.823405 | − | 0.567455i | \(-0.192072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14636.6 | −0.477821 | ||||||||
\(980\) | −16188.2 | − | 15045.7i | −0.527665 | − | 0.490427i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −15749.6 | − | 27279.2i | −0.511804 | − | 0.886470i | ||||
\(983\) | −25566.4 | + | 44282.2i | −0.829542 | + | 1.43681i | 0.0688555 | + | 0.997627i | \(0.478065\pi\) |
−0.898398 | + | 0.439183i | \(0.855268\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10147.9 | − | 17576.6i | −0.328262 | − | 0.568567i | ||||
\(986\) | 23370.0 | 0.754820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19879.3 | 0.640127 | ||||||||
\(989\) | 5449.41 | + | 9438.65i | 0.175208 | + | 0.303470i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18879.1 | + | 32699.6i | −0.605161 | + | 1.04817i | 0.386865 | + | 0.922136i | \(0.373558\pi\) |
−0.992026 | + | 0.126033i | \(0.959776\pi\) | |||||||
\(992\) | 364.190 | + | 630.795i | 0.0116563 | + | 0.0201893i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2984.92 | + | 448.624i | −0.0952475 | + | 0.0143154i | ||||
\(995\) | 87801.8 | 2.79749 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12028.9 | − | 20834.6i | 0.382105 | − | 0.661825i | −0.609258 | − | 0.792972i | \(-0.708533\pi\) |
0.991363 | + | 0.131147i | \(0.0418660\pi\) | |||||||
\(998\) | −12981.2 | + | 22484.1i | −0.411736 | + | 0.713148i | ||||
\(999\) | 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 | 378.4.g.f.109.1 | yes | 8 | |
3.2 | odd | 2 | 378.4.g.c.109.4 | ✓ | 8 | ||
7.2 | even | 3 | inner | 378.4.g.f.163.1 | yes | 8 | |
21.2 | odd | 6 | 378.4.g.c.163.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.4.g.c.109.4 | ✓ | 8 | 3.2 | odd | 2 | ||
378.4.g.c.163.4 | yes | 8 | 21.2 | odd | 6 | ||
378.4.g.f.109.1 | yes | 8 | 1.1 | even | 1 | trivial | |
378.4.g.f.163.1 | yes | 8 | 7.2 | even | 3 | inner |