Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,4,Mod(13,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.j (of order \(4\), 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: | \(2.83209168028\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.10 | ||
Character | \(\chi\) | \(=\) | 48.13 |
Dual form | 48.4.j.a.37.10 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.07099 | + | 1.92640i | 0.732204 | + | 0.681085i | ||||
\(3\) | 2.12132 | + | 2.12132i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0.577966 | + | 7.97909i | 0.0722457 | + | 0.997387i | ||||
\(5\) | 0.644922 | − | 0.644922i | 0.0576835 | − | 0.0576835i | −0.677677 | − | 0.735360i | \(-0.737013\pi\) |
0.735360 | + | 0.677677i | \(0.237013\pi\) | |||||||
\(6\) | 0.306713 | + | 8.47974i | 0.0208692 | + | 0.576973i | ||||
\(7\) | − | 7.13926i | − | 0.385484i | −0.981249 | − | 0.192742i | \(-0.938262\pi\) | ||
0.981249 | − | 0.192742i | \(-0.0617380\pi\) | |||||||
\(8\) | −14.1740 | + | 17.6380i | −0.626407 | + | 0.779496i | ||||
\(9\) | 9.00000i | 0.333333i | ||||||||
\(10\) | 2.57800 | − | 0.0932465i | 0.0815235 | − | 0.00294871i | ||||
\(11\) | 25.4455 | − | 25.4455i | 0.697464 | − | 0.697464i | −0.266399 | − | 0.963863i | \(-0.585834\pi\) |
0.963863 | + | 0.266399i | \(0.0858338\pi\) | |||||||
\(12\) | −15.7002 | + | 18.1523i | −0.377687 | + | 0.436676i | ||||
\(13\) | −14.6030 | − | 14.6030i | −0.311549 | − | 0.311549i | 0.533961 | − | 0.845509i | \(-0.320703\pi\) |
−0.845509 | + | 0.533961i | \(0.820703\pi\) | |||||||
\(14\) | 13.7531 | − | 14.7853i | 0.262547 | − | 0.282253i | ||||
\(15\) | 2.73617 | 0.0470984 | ||||||||
\(16\) | −63.3319 | + | 9.22328i | −0.989561 | + | 0.144114i | ||||
\(17\) | 71.4024 | 1.01868 | 0.509342 | − | 0.860564i | \(-0.329889\pi\) | ||||
0.509342 | + | 0.860564i | \(0.329889\pi\) | |||||||
\(18\) | −17.3376 | + | 18.6389i | −0.227028 | + | 0.244068i | ||||
\(19\) | −43.6238 | − | 43.6238i | −0.526736 | − | 0.526736i | 0.392861 | − | 0.919598i | \(-0.371485\pi\) |
−0.919598 | + | 0.392861i | \(0.871485\pi\) | |||||||
\(20\) | 5.51863 | + | 4.77315i | 0.0617002 | + | 0.0533654i | ||||
\(21\) | 15.1447 | − | 15.1447i | 0.157373 | − | 0.157373i | ||||
\(22\) | 101.715 | − | 3.67906i | 0.985719 | − | 0.0356536i | ||||
\(23\) | − | 211.845i | − | 1.92056i | −0.279045 | − | 0.960278i | \(-0.590018\pi\) | ||
0.279045 | − | 0.960278i | \(-0.409982\pi\) | |||||||
\(24\) | −67.4834 | + | 7.34829i | −0.573958 | + | 0.0624985i | ||||
\(25\) | 124.168i | 0.993345i | ||||||||
\(26\) | −2.11138 | − | 58.3737i | −0.0159260 | − | 0.440309i | ||||
\(27\) | −19.0919 | + | 19.0919i | −0.136083 | + | 0.136083i | ||||
\(28\) | 56.9649 | − | 4.12625i | 0.384477 | − | 0.0278496i | ||||
\(29\) | 5.84463 | + | 5.84463i | 0.0374248 | + | 0.0374248i | 0.725572 | − | 0.688147i | \(-0.241575\pi\) |
−0.688147 | + | 0.725572i | \(0.741575\pi\) | |||||||
\(30\) | 5.66657 | + | 5.27096i | 0.0344856 | + | 0.0320780i | ||||
\(31\) | −107.807 | −0.624604 | −0.312302 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312302 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(32\) | −148.927 | − | 102.901i | −0.822715 | − | 0.568455i | ||||
\(33\) | 107.956 | 0.569477 | ||||||||
\(34\) | 147.873 | + | 137.550i | 0.745884 | + | 0.693811i | ||||
\(35\) | −4.60426 | − | 4.60426i | −0.0222361 | − | 0.0222361i | ||||
\(36\) | −71.8119 | + | 5.20169i | −0.332462 | + | 0.0240819i | ||||
\(37\) | −184.865 | + | 184.865i | −0.821395 | + | 0.821395i | −0.986308 | − | 0.164913i | \(-0.947266\pi\) |
0.164913 | + | 0.986308i | \(0.447266\pi\) | |||||||
\(38\) | −6.30739 | − | 174.381i | −0.0269261 | − | 0.744431i | ||||
\(39\) | − | 61.9551i | − | 0.254379i | ||||||
\(40\) | 2.23402 | + | 20.5162i | 0.00883073 | + | 0.0810975i | ||||
\(41\) | 360.146i | 1.37184i | 0.727679 | + | 0.685918i | \(0.240599\pi\) | ||||
−0.727679 | + | 0.685918i | \(0.759401\pi\) | |||||||
\(42\) | 60.5391 | − | 2.18970i | 0.222414 | − | 0.00804473i | ||||
\(43\) | −312.475 | + | 312.475i | −1.10818 | + | 1.10818i | −0.114795 | + | 0.993389i | \(0.536621\pi\) |
−0.993389 | + | 0.114795i | \(0.963379\pi\) | |||||||
\(44\) | 217.739 | + | 188.325i | 0.746030 | + | 0.645253i | ||||
\(45\) | 5.80429 | + | 5.80429i | 0.0192278 | + | 0.0192278i | ||||
\(46\) | 408.099 | − | 438.729i | 1.30806 | − | 1.40624i | ||||
\(47\) | 343.892 | 1.06727 | 0.533636 | − | 0.845715i | \(-0.320825\pi\) | ||||
0.533636 | + | 0.845715i | \(0.320825\pi\) | |||||||
\(48\) | −153.913 | − | 114.782i | −0.462821 | − | 0.345152i | ||||
\(49\) | 292.031 | 0.851402 | ||||||||
\(50\) | −239.198 | + | 257.150i | −0.676553 | + | 0.727331i | ||||
\(51\) | 151.467 | + | 151.467i | 0.415876 | + | 0.415876i | ||||
\(52\) | 108.078 | − | 124.958i | 0.288227 | − | 0.333243i | ||||
\(53\) | −249.900 | + | 249.900i | −0.647667 | + | 0.647667i | −0.952429 | − | 0.304762i | \(-0.901423\pi\) |
0.304762 | + | 0.952429i | \(0.401423\pi\) | |||||||
\(54\) | −76.3176 | + | 2.76042i | −0.192324 | + | 0.00695639i | ||||
\(55\) | − | 32.8207i | − | 0.0804644i | ||||||
\(56\) | 125.922 | + | 101.192i | 0.300483 | + | 0.241470i | ||||
\(57\) | − | 185.080i | − | 0.430078i | ||||||
\(58\) | 0.845051 | + | 23.3632i | 0.00191311 | + | 0.0528921i | ||||
\(59\) | −152.755 | + | 152.755i | −0.337067 | + | 0.337067i | −0.855262 | − | 0.518195i | \(-0.826604\pi\) |
0.518195 | + | 0.855262i | \(0.326604\pi\) | |||||||
\(60\) | 1.58141 | + | 21.8322i | 0.00340266 | + | 0.0469753i | ||||
\(61\) | −525.985 | − | 525.985i | −1.10402 | − | 1.10402i | −0.993920 | − | 0.110104i | \(-0.964882\pi\) |
−0.110104 | − | 0.993920i | \(-0.535118\pi\) | |||||||
\(62\) | −223.267 | − | 207.680i | −0.457338 | − | 0.425409i | ||||
\(63\) | 64.2534 | 0.128495 | ||||||||
\(64\) | −110.197 | − | 500.001i | −0.215229 | − | 0.976564i | ||||
\(65\) | −18.8355 | −0.0359425 | ||||||||
\(66\) | 223.576 | + | 207.967i | 0.416973 | + | 0.387862i | ||||
\(67\) | −35.3052 | − | 35.3052i | −0.0643764 | − | 0.0643764i | 0.674186 | − | 0.738562i | \(-0.264495\pi\) |
−0.738562 | + | 0.674186i | \(0.764495\pi\) | |||||||
\(68\) | 41.2681 | + | 569.727i | 0.0735955 | + | 1.01602i | ||||
\(69\) | 449.392 | − | 449.392i | 0.784064 | − | 0.784064i | ||||
\(70\) | −0.665712 | − | 18.4050i | −0.00113668 | − | 0.0314260i | ||||
\(71\) | − | 784.715i | − | 1.31167i | −0.754905 | − | 0.655834i | \(-0.772317\pi\) | ||
0.754905 | − | 0.655834i | \(-0.227683\pi\) | |||||||
\(72\) | −158.742 | − | 127.566i | −0.259832 | − | 0.208802i | ||||
\(73\) | − | 800.215i | − | 1.28299i | −0.767128 | − | 0.641494i | \(-0.778315\pi\) | ||
0.767128 | − | 0.641494i | \(-0.221685\pi\) | |||||||
\(74\) | −738.977 | + | 26.7289i | −1.16087 | + | 0.0419888i | ||||
\(75\) | −263.400 | + | 263.400i | −0.405531 | + | 0.405531i | ||||
\(76\) | 322.866 | − | 373.292i | 0.487306 | − | 0.563414i | ||||
\(77\) | −181.662 | − | 181.662i | −0.268861 | − | 0.268861i | ||||
\(78\) | 119.350 | − | 128.308i | 0.173253 | − | 0.186257i | ||||
\(79\) | 548.062 | 0.780530 | 0.390265 | − | 0.920703i | \(-0.372383\pi\) | ||||
0.390265 | + | 0.920703i | \(0.372383\pi\) | |||||||
\(80\) | −34.8958 | + | 46.7924i | −0.0487684 | + | 0.0653944i | ||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | −693.784 | + | 745.856i | −0.934337 | + | 1.00446i | ||||
\(83\) | 464.431 | + | 464.431i | 0.614191 | + | 0.614191i | 0.944035 | − | 0.329844i | \(-0.106996\pi\) |
−0.329844 | + | 0.944035i | \(0.606996\pi\) | |||||||
\(84\) | 129.594 | + | 112.088i | 0.168331 | + | 0.145592i | ||||
\(85\) | 46.0489 | − | 46.0489i | 0.0587613 | − | 0.0587613i | ||||
\(86\) | −1249.08 | + | 45.1794i | −1.56619 | + | 0.0566491i | ||||
\(87\) | 24.7967i | 0.0305573i | ||||||||
\(88\) | 88.1436 | + | 809.471i | 0.106774 | + | 0.980567i | ||||
\(89\) | 302.977i | 0.360849i | 0.983589 | + | 0.180424i | \(0.0577471\pi\) | ||||
−0.983589 | + | 0.180424i | \(0.942253\pi\) | |||||||
\(90\) | 0.839219 | + | 23.2020i | 0.000982905 | + | 0.0271745i | ||||
\(91\) | −104.254 | + | 104.254i | −0.120097 | + | 0.120097i | ||||
\(92\) | 1690.33 | − | 122.439i | 1.91554 | − | 0.138752i | ||||
\(93\) | −228.693 | − | 228.693i | −0.254994 | − | 0.254994i | ||||
\(94\) | 712.195 | + | 662.473i | 0.781460 | + | 0.726903i | ||||
\(95\) | −56.2679 | −0.0607680 | ||||||||
\(96\) | −97.6357 | − | 534.209i | −0.103801 | − | 0.567942i | ||||
\(97\) | 1567.24 | 1.64050 | 0.820252 | − | 0.572002i | \(-0.193833\pi\) | ||||
0.820252 | + | 0.572002i | \(0.193833\pi\) | |||||||
\(98\) | 604.792 | + | 562.568i | 0.623400 | + | 0.579877i | ||||
\(99\) | 229.009 | + | 229.009i | 0.232488 | + | 0.232488i | ||||
\(100\) | −990.749 | + | 71.7649i | −0.990749 | + | 0.0717649i | ||||
\(101\) | 59.6129 | − | 59.6129i | 0.0587297 | − | 0.0587297i | −0.677132 | − | 0.735862i | \(-0.736777\pi\) |
0.735862 | + | 0.677132i | \(0.236777\pi\) | |||||||
\(102\) | 21.9000 | + | 605.474i | 0.0212591 | + | 0.587753i | ||||
\(103\) | 1762.59i | 1.68615i | 0.537795 | + | 0.843076i | \(0.319257\pi\) | ||||
−0.537795 | + | 0.843076i | \(0.680743\pi\) | |||||||
\(104\) | 464.549 | − | 50.5849i | 0.438007 | − | 0.0476948i | ||||
\(105\) | − | 19.5342i | − | 0.0181557i | ||||||
\(106\) | −998.945 | + | 36.1319i | −0.915341 | + | 0.0331080i | ||||
\(107\) | 656.579 | − | 656.579i | 0.593214 | − | 0.593214i | −0.345284 | − | 0.938498i | \(-0.612218\pi\) |
0.938498 | + | 0.345284i | \(0.112218\pi\) | |||||||
\(108\) | −163.370 | − | 141.301i | −0.145559 | − | 0.125896i | ||||
\(109\) | −327.776 | − | 327.776i | −0.288030 | − | 0.288030i | 0.548271 | − | 0.836301i | \(-0.315286\pi\) |
−0.836301 | + | 0.548271i | \(0.815286\pi\) | |||||||
\(110\) | 63.2258 | − | 67.9712i | 0.0548031 | − | 0.0589164i | ||||
\(111\) | −784.316 | −0.670667 | ||||||||
\(112\) | 65.8475 | + | 452.143i | 0.0555536 | + | 0.381460i | ||||
\(113\) | −1349.18 | −1.12319 | −0.561593 | − | 0.827414i | \(-0.689811\pi\) | ||||
−0.561593 | + | 0.827414i | \(0.689811\pi\) | |||||||
\(114\) | 356.539 | − | 383.299i | 0.292920 | − | 0.314905i | ||||
\(115\) | −136.624 | − | 136.624i | −0.110784 | − | 0.110784i | ||||
\(116\) | −43.2569 | + | 50.0128i | −0.0346233 | + | 0.0400308i | ||||
\(117\) | 131.427 | − | 131.427i | 0.103850 | − | 0.103850i | ||||
\(118\) | −610.620 | + | 22.0862i | −0.476374 | + | 0.0172305i | ||||
\(119\) | − | 509.761i | − | 0.392686i | ||||||
\(120\) | −38.7824 | + | 48.2605i | −0.0295028 | + | 0.0367130i | ||||
\(121\) | 36.0534i | 0.0270875i | ||||||||
\(122\) | −76.0500 | − | 2102.56i | −0.0564364 | − | 1.56031i | ||||
\(123\) | −763.984 | + | 763.984i | −0.560050 | + | 0.560050i | ||||
\(124\) | −62.3088 | − | 860.203i | −0.0451250 | − | 0.622972i | ||||
\(125\) | 160.694 | + | 160.694i | 0.114983 | + | 0.114983i | ||||
\(126\) | 133.068 | + | 123.778i | 0.0940843 | + | 0.0875158i | ||||
\(127\) | 52.2111 | 0.0364802 | 0.0182401 | − | 0.999834i | \(-0.494194\pi\) | ||||
0.0182401 | + | 0.999834i | \(0.494194\pi\) | |||||||
\(128\) | 734.984 | − | 1247.78i | 0.507532 | − | 0.861633i | ||||
\(129\) | −1325.72 | −0.904829 | ||||||||
\(130\) | −39.0081 | − | 36.2848i | −0.0263172 | − | 0.0244799i | ||||
\(131\) | −387.958 | − | 387.958i | −0.258749 | − | 0.258749i | 0.565796 | − | 0.824545i | \(-0.308569\pi\) |
−0.824545 | + | 0.565796i | \(0.808569\pi\) | |||||||
\(132\) | 62.3949 | + | 861.392i | 0.0411423 | + | 0.567989i | ||||
\(133\) | −311.442 | + | 311.442i | −0.203048 | + | 0.203048i | ||||
\(134\) | −5.10463 | − | 141.128i | −0.00329084 | − | 0.0909824i | ||||
\(135\) | 24.6255i | 0.0156995i | ||||||||
\(136\) | −1012.06 | + | 1259.39i | −0.638111 | + | 0.794060i | ||||
\(137\) | 795.048i | 0.495807i | 0.968785 | + | 0.247903i | \(0.0797415\pi\) | ||||
−0.968785 | + | 0.247903i | \(0.920258\pi\) | |||||||
\(138\) | 1796.39 | − | 64.9757i | 1.10811 | − | 0.0400804i | ||||
\(139\) | 1708.70 | − | 1708.70i | 1.04266 | − | 1.04266i | 0.0436142 | − | 0.999048i | \(-0.486113\pi\) |
0.999048 | − | 0.0436142i | \(-0.0138872\pi\) | |||||||
\(140\) | 34.0768 | − | 39.3990i | 0.0205715 | − | 0.0237844i | ||||
\(141\) | 729.504 | + | 729.504i | 0.435712 | + | 0.435712i | ||||
\(142\) | 1511.67 | − | 1625.13i | 0.893358 | − | 0.960409i | ||||
\(143\) | −743.160 | −0.434588 | ||||||||
\(144\) | −83.0096 | − | 569.987i | −0.0480379 | − | 0.329854i | ||||
\(145\) | 7.53865 | 0.00431759 | ||||||||
\(146\) | 1541.53 | − | 1657.23i | 0.873824 | − | 0.939409i | ||||
\(147\) | 619.491 | + | 619.491i | 0.347583 | + | 0.347583i | ||||
\(148\) | −1581.90 | − | 1368.21i | −0.878591 | − | 0.759907i | ||||
\(149\) | −69.6301 | + | 69.6301i | −0.0382840 | + | 0.0382840i | −0.725990 | − | 0.687706i | \(-0.758618\pi\) |
0.687706 | + | 0.725990i | \(0.258618\pi\) | |||||||
\(150\) | −1052.91 | + | 38.0840i | −0.573133 | + | 0.0207303i | ||||
\(151\) | 1567.48i | 0.844768i | 0.906417 | + | 0.422384i | \(0.138807\pi\) | ||||
−0.906417 | + | 0.422384i | \(0.861193\pi\) | |||||||
\(152\) | 1387.76 | − | 151.114i | 0.740540 | − | 0.0806377i | ||||
\(153\) | 642.622i | 0.339561i | ||||||||
\(154\) | −26.2658 | − | 726.174i | −0.0137439 | − | 0.379979i | ||||
\(155\) | −69.5271 | + | 69.5271i | −0.0360294 | + | 0.0360294i | ||||
\(156\) | 494.346 | − | 35.8079i | 0.253714 | − | 0.0183778i | ||||
\(157\) | 1738.35 | + | 1738.35i | 0.883667 | + | 0.883667i | 0.993905 | − | 0.110238i | \(-0.0351614\pi\) |
−0.110238 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(158\) | 1135.03 | + | 1055.79i | 0.571507 | + | 0.531607i | ||||
\(159\) | −1060.23 | −0.528818 | ||||||||
\(160\) | −162.410 | + | 29.6831i | −0.0802476 | + | 0.0146666i | ||||
\(161\) | −1512.42 | −0.740344 | ||||||||
\(162\) | −167.750 | − | 156.038i | −0.0813560 | − | 0.0756761i | ||||
\(163\) | −2685.71 | − | 2685.71i | −1.29056 | − | 1.29056i | −0.934442 | − | 0.356116i | \(-0.884101\pi\) |
−0.356116 | − | 0.934442i | \(-0.615899\pi\) | |||||||
\(164\) | −2873.64 | + | 208.152i | −1.36825 | + | 0.0991093i | ||||
\(165\) | 69.6232 | − | 69.6232i | 0.0328495 | − | 0.0328495i | ||||
\(166\) | 67.1501 | + | 1856.51i | 0.0313967 | + | 0.868030i | ||||
\(167\) | 27.5126i | 0.0127484i | 0.999980 | + | 0.00637422i | \(0.00202899\pi\) | ||||
−0.999980 | + | 0.00637422i | \(0.997971\pi\) | |||||||
\(168\) | 52.4614 | + | 481.781i | 0.0240922 | + | 0.221251i | ||||
\(169\) | − | 1770.51i | − | 0.805875i | ||||||
\(170\) | 184.075 | − | 6.65803i | 0.0830467 | − | 0.00300381i | ||||
\(171\) | 392.614 | − | 392.614i | 0.175579 | − | 0.175579i | ||||
\(172\) | −2673.86 | − | 2312.67i | −1.18535 | − | 1.02523i | ||||
\(173\) | 3044.87 | + | 3044.87i | 1.33813 | + | 1.33813i | 0.897867 | + | 0.440267i | \(0.145116\pi\) |
0.440267 | + | 0.897867i | \(0.354884\pi\) | |||||||
\(174\) | −47.7683 | + | 51.3535i | −0.0208121 | + | 0.0223741i | ||||
\(175\) | 886.469 | 0.382919 | ||||||||
\(176\) | −1376.82 | + | 1846.20i | −0.589669 | + | 0.790698i | ||||
\(177\) | −648.083 | −0.275214 | ||||||||
\(178\) | −583.656 | + | 627.462i | −0.245769 | + | 0.264215i | ||||
\(179\) | −365.808 | − | 365.808i | −0.152747 | − | 0.152747i | 0.626597 | − | 0.779344i | \(-0.284447\pi\) |
−0.779344 | + | 0.626597i | \(0.784447\pi\) | |||||||
\(180\) | −42.9583 | + | 49.6677i | −0.0177885 | + | 0.0205667i | ||||
\(181\) | −1737.10 | + | 1737.10i | −0.713359 | + | 0.713359i | −0.967236 | − | 0.253877i | \(-0.918294\pi\) |
0.253877 | + | 0.967236i | \(0.418294\pi\) | |||||||
\(182\) | −416.745 | + | 15.0737i | −0.169732 | + | 0.00613922i | ||||
\(183\) | − | 2231.56i | − | 0.901432i | ||||||
\(184\) | 3736.52 | + | 3002.69i | 1.49707 | + | 1.20305i | ||||
\(185\) | 238.447i | 0.0947620i | ||||||||
\(186\) | −33.0658 | − | 914.176i | −0.0130350 | − | 0.360380i | ||||
\(187\) | 1816.87 | − | 1816.87i | 0.710495 | − | 0.710495i | ||||
\(188\) | 198.757 | + | 2743.94i | 0.0771057 | + | 1.06448i | ||||
\(189\) | 136.302 | + | 136.302i | 0.0524577 | + | 0.0524577i | ||||
\(190\) | −116.530 | − | 108.394i | −0.0444946 | − | 0.0413882i | ||||
\(191\) | −1709.44 | −0.647595 | −0.323798 | − | 0.946126i | \(-0.604960\pi\) | ||||
−0.323798 | + | 0.946126i | \(0.604960\pi\) | |||||||
\(192\) | 826.898 | − | 1294.42i | 0.310814 | − | 0.486547i | ||||
\(193\) | 2404.54 | 0.896800 | 0.448400 | − | 0.893833i | \(-0.351994\pi\) | ||||
0.448400 | + | 0.893833i | \(0.351994\pi\) | |||||||
\(194\) | 3245.73 | + | 3019.13i | 1.20118 | + | 1.11732i | ||||
\(195\) | −39.9562 | − | 39.9562i | −0.0146735 | − | 0.0146735i | ||||
\(196\) | 168.784 | + | 2330.14i | 0.0615101 | + | 0.849177i | ||||
\(197\) | 2772.54 | − | 2772.54i | 1.00272 | − | 1.00272i | 0.00271983 | − | 0.999996i | \(-0.499134\pi\) |
0.999996 | − | 0.00271983i | \(-0.000865750\pi\) | |||||||
\(198\) | 33.1115 | + | 915.439i | 0.0118845 | + | 0.328573i | ||||
\(199\) | 1506.90i | 0.536790i | 0.963309 | + | 0.268395i | \(0.0864932\pi\) | ||||
−0.963309 | + | 0.268395i | \(0.913507\pi\) | |||||||
\(200\) | −2190.08 | − | 1759.96i | −0.774309 | − | 0.622238i | ||||
\(201\) | − | 149.787i | − | 0.0525631i | ||||||
\(202\) | 238.296 | − | 8.61918i | 0.0830021 | − | 0.00300219i | ||||
\(203\) | 41.7263 | − | 41.7263i | 0.0144267 | − | 0.0144267i | ||||
\(204\) | −1121.03 | + | 1296.12i | −0.384744 | + | 0.444834i | ||||
\(205\) | 232.266 | + | 232.266i | 0.0791324 | + | 0.0791324i | ||||
\(206\) | −3395.46 | + | 3650.31i | −1.14841 | + | 1.23461i | ||||
\(207\) | 1906.61 | 0.640185 | ||||||||
\(208\) | 1059.52 | + | 790.147i | 0.353195 | + | 0.263398i | ||||
\(209\) | −2220.06 | −0.734760 | ||||||||
\(210\) | 37.6308 | − | 40.4551i | 0.0123656 | − | 0.0132937i | ||||
\(211\) | −1965.22 | − | 1965.22i | −0.641190 | − | 0.641190i | 0.309658 | − | 0.950848i | \(-0.399785\pi\) |
−0.950848 | + | 0.309658i | \(0.899785\pi\) | |||||||
\(212\) | −2138.41 | − | 1849.54i | −0.692766 | − | 0.599183i | ||||
\(213\) | 1664.63 | − | 1664.63i | 0.535487 | − | 0.535487i | ||||
\(214\) | 2624.60 | − | 94.9320i | 0.838383 | − | 0.0303244i | ||||
\(215\) | 403.043i | 0.127848i | ||||||||
\(216\) | −66.1346 | − | 607.350i | −0.0208328 | − | 0.191319i | ||||
\(217\) | 769.663i | 0.240775i | ||||||||
\(218\) | −47.3918 | − | 1310.25i | −0.0147238 | − | 0.407070i | ||||
\(219\) | 1697.51 | − | 1697.51i | 0.523778 | − | 0.523778i | ||||
\(220\) | 261.879 | − | 18.9692i | 0.0802541 | − | 0.00581321i | ||||
\(221\) | −1042.69 | − | 1042.69i | −0.317370 | − | 0.317370i | ||||
\(222\) | −1624.31 | − | 1510.91i | −0.491065 | − | 0.456781i | ||||
\(223\) | 85.7869 | 0.0257610 | 0.0128805 | − | 0.999917i | \(-0.495900\pi\) | ||||
0.0128805 | + | 0.999917i | \(0.495900\pi\) | |||||||
\(224\) | −734.640 | + | 1063.23i | −0.219130 | + | 0.317143i | ||||
\(225\) | −1117.51 | −0.331115 | ||||||||
\(226\) | −2794.13 | − | 2599.06i | −0.822402 | − | 0.764986i | ||||
\(227\) | 2526.02 | + | 2526.02i | 0.738582 | + | 0.738582i | 0.972304 | − | 0.233722i | \(-0.0750905\pi\) |
−0.233722 | + | 0.972304i | \(0.575090\pi\) | |||||||
\(228\) | 1476.77 | − | 106.970i | 0.428955 | − | 0.0310713i | ||||
\(229\) | −1116.65 | + | 1116.65i | −0.322227 | + | 0.322227i | −0.849621 | − | 0.527394i | \(-0.823169\pi\) |
0.527394 | + | 0.849621i | \(0.323169\pi\) | |||||||
\(230\) | −19.7538 | − | 546.137i | −0.00566317 | − | 0.156570i | ||||
\(231\) | − | 770.727i | − | 0.219524i | ||||||
\(232\) | −185.929 | + | 20.2459i | −0.0526157 | + | 0.00572934i | ||||
\(233\) | − | 5754.25i | − | 1.61791i | −0.587869 | − | 0.808956i | \(-0.700033\pi\) | ||
0.587869 | − | 0.808956i | \(-0.299967\pi\) | |||||||
\(234\) | 525.363 | − | 19.0024i | 0.146770 | − | 0.00530867i | ||||
\(235\) | 221.783 | − | 221.783i | 0.0615640 | − | 0.0615640i | ||||
\(236\) | −1307.13 | − | 1130.56i | −0.360538 | − | 0.311835i | ||||
\(237\) | 1162.62 | + | 1162.62i | 0.318650 | + | 0.318650i | ||||
\(238\) | 982.003 | − | 1055.71i | 0.267453 | − | 0.287527i | ||||
\(239\) | −641.784 | −0.173697 | −0.0868484 | − | 0.996222i | \(-0.527680\pi\) | ||||
−0.0868484 | + | 0.996222i | \(0.527680\pi\) | |||||||
\(240\) | −173.287 | + | 25.2365i | −0.0466068 | + | 0.00678753i | ||||
\(241\) | −2887.45 | −0.771771 | −0.385885 | − | 0.922547i | \(-0.626104\pi\) | ||||
−0.385885 | + | 0.922547i | \(0.626104\pi\) | |||||||
\(242\) | −69.4533 | + | 74.6661i | −0.0184489 | + | 0.0198335i | ||||
\(243\) | −171.827 | − | 171.827i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 3892.88 | − | 4500.88i | 1.02138 | − | 1.18090i | ||||
\(245\) | 188.337 | − | 188.337i | 0.0491119 | − | 0.0491119i | ||||
\(246\) | −3053.94 | + | 110.461i | −0.791512 | + | 0.0286291i | ||||
\(247\) | 1274.07i | 0.328208i | ||||||||
\(248\) | 1528.05 | − | 1901.50i | 0.391256 | − | 0.486877i | ||||
\(249\) | 1970.41i | 0.501485i | ||||||||
\(250\) | 23.2341 | + | 642.356i | 0.00587781 | + | 0.162505i | ||||
\(251\) | −2367.55 | + | 2367.55i | −0.595372 | + | 0.595372i | −0.939077 | − | 0.343706i | \(-0.888318\pi\) |
0.343706 | + | 0.939077i | \(0.388318\pi\) | |||||||
\(252\) | 37.1362 | + | 512.684i | 0.00928319 | + | 0.128159i | ||||
\(253\) | −5390.51 | − | 5390.51i | −1.33952 | − | 1.33952i | ||||
\(254\) | 108.129 | + | 100.580i | 0.0267110 | + | 0.0248462i | ||||
\(255\) | 195.369 | 0.0479784 | ||||||||
\(256\) | 3925.86 | − | 1168.26i | 0.958462 | − | 0.285219i | ||||
\(257\) | 5112.43 | 1.24087 | 0.620437 | − | 0.784256i | \(-0.286955\pi\) | ||||
0.620437 | + | 0.784256i | \(0.286955\pi\) | |||||||
\(258\) | −2745.54 | − | 2553.86i | −0.662519 | − | 0.616266i | ||||
\(259\) | 1319.80 | + | 1319.80i | 0.316635 | + | 0.316635i | ||||
\(260\) | −10.8863 | − | 150.291i | −0.00259669 | − | 0.0358486i | ||||
\(261\) | −52.6017 | + | 52.6017i | −0.0124749 | + | 0.0124749i | ||||
\(262\) | −56.0933 | − | 1550.82i | −0.0132269 | − | 0.365687i | ||||
\(263\) | 5496.36i | 1.28867i | 0.764744 | + | 0.644334i | \(0.222866\pi\) | ||||
−0.764744 | + | 0.644334i | \(0.777134\pi\) | |||||||
\(264\) | −1530.17 | + | 1904.13i | −0.356724 | + | 0.443905i | ||||
\(265\) | 322.331i | 0.0747194i | ||||||||
\(266\) | −1244.95 | + | 45.0301i | −0.286966 | + | 0.0103796i | ||||
\(267\) | −642.712 | + | 642.712i | −0.147316 | + | 0.147316i | ||||
\(268\) | 261.298 | − | 302.109i | 0.0595572 | − | 0.0688591i | ||||
\(269\) | −2474.35 | − | 2474.35i | −0.560831 | − | 0.560831i | 0.368712 | − | 0.929544i | \(-0.379799\pi\) |
−0.929544 | + | 0.368712i | \(0.879799\pi\) | |||||||
\(270\) | −47.4386 | + | 50.9991i | −0.0106927 | + | 0.0114952i | ||||
\(271\) | −1718.58 | −0.385226 | −0.192613 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192613 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(272\) | −4522.05 | + | 658.565i | −1.00805 | + | 0.146806i | ||||
\(273\) | −442.314 | −0.0980589 | ||||||||
\(274\) | −1531.58 | + | 1646.53i | −0.337687 | + | 0.363032i | ||||
\(275\) | 3159.52 | + | 3159.52i | 0.692823 | + | 0.692823i | ||||
\(276\) | 3845.47 | + | 3326.01i | 0.838660 | + | 0.725370i | ||||
\(277\) | −4722.69 | + | 4722.69i | −1.02440 | + | 1.02440i | −0.0247055 | + | 0.999695i | \(0.507865\pi\) |
−0.999695 | + | 0.0247055i | \(0.992135\pi\) | |||||||
\(278\) | 6830.34 | − | 247.054i | 1.47358 | − | 0.0532997i | ||||
\(279\) | − | 970.264i | − | 0.208201i | ||||||
\(280\) | 146.471 | − | 15.9492i | 0.0312618 | − | 0.00340411i | ||||
\(281\) | 2543.21i | 0.539911i | 0.962873 | + | 0.269955i | \(0.0870090\pi\) | ||||
−0.962873 | + | 0.269955i | \(0.912991\pi\) | |||||||
\(282\) | 105.476 | + | 2916.11i | 0.0222731 | + | 0.615787i | ||||
\(283\) | −3206.82 | + | 3206.82i | −0.673589 | + | 0.673589i | −0.958542 | − | 0.284952i | \(-0.908022\pi\) |
0.284952 | + | 0.958542i | \(0.408022\pi\) | |||||||
\(284\) | 6261.31 | − | 453.538i | 1.30824 | − | 0.0947624i | ||||
\(285\) | −119.362 | − | 119.362i | −0.0248084 | − | 0.0248084i | ||||
\(286\) | −1539.07 | − | 1431.62i | −0.318207 | − | 0.295992i | ||||
\(287\) | 2571.17 | 0.528821 | ||||||||
\(288\) | 926.112 | − | 1340.35i | 0.189485 | − | 0.274238i | ||||
\(289\) | 185.302 | 0.0377167 | ||||||||
\(290\) | 15.6124 | + | 14.5225i | 0.00316136 | + | 0.00294065i | ||||
\(291\) | 3324.61 | + | 3324.61i | 0.669733 | + | 0.669733i | ||||
\(292\) | 6384.99 | − | 462.497i | 1.27964 | − | 0.0926903i | ||||
\(293\) | 5911.40 | − | 5911.40i | 1.17866 | − | 1.17866i | 0.198575 | − | 0.980086i | \(-0.436369\pi\) |
0.980086 | − | 0.198575i | \(-0.0636313\pi\) | |||||||
\(294\) | 89.5697 | + | 2476.35i | 0.0177681 | + | 0.491236i | ||||
\(295\) | 197.030i | 0.0388865i | ||||||||
\(296\) | −640.376 | − | 5880.92i | −0.125747 | − | 1.15480i | ||||
\(297\) | 971.605i | 0.189826i | ||||||||
\(298\) | −278.338 | + | 10.0675i | −0.0541064 | + | 0.00195703i | ||||
\(299\) | −3093.57 | + | 3093.57i | −0.598347 | + | 0.598347i | ||||
\(300\) | −2253.93 | − | 1949.46i | −0.433770 | − | 0.375174i | ||||
\(301\) | 2230.84 | + | 2230.84i | 0.427187 | + | 0.427187i | ||||
\(302\) | −3019.60 | + | 3246.23i | −0.575359 | + | 0.618542i | ||||
\(303\) | 252.916 | 0.0479526 | ||||||||
\(304\) | 3165.14 | + | 2360.43i | 0.597148 | + | 0.445328i | ||||
\(305\) | −678.438 | −0.127368 | ||||||||
\(306\) | −1237.95 | + | 1330.86i | −0.231270 | + | 0.248628i | ||||
\(307\) | 1162.25 | + | 1162.25i | 0.216068 | + | 0.216068i | 0.806839 | − | 0.590771i | \(-0.201176\pi\) |
−0.590771 | + | 0.806839i | \(0.701176\pi\) | |||||||
\(308\) | 1344.50 | − | 1554.49i | 0.248735 | − | 0.287583i | ||||
\(309\) | −3739.03 | + | 3739.03i | −0.688368 | + | 0.688368i | ||||
\(310\) | −277.927 | + | 10.0526i | −0.0509199 | + | 0.00184178i | ||||
\(311\) | − | 2357.28i | − | 0.429805i | −0.976636 | − | 0.214902i | \(-0.931057\pi\) | ||
0.976636 | − | 0.214902i | \(-0.0689433\pi\) | |||||||
\(312\) | 1092.76 | + | 878.150i | 0.198287 | + | 0.159344i | ||||
\(313\) | 3785.95i | 0.683689i | 0.939757 | + | 0.341844i | \(0.111052\pi\) | ||||
−0.939757 | + | 0.341844i | \(0.888948\pi\) | |||||||
\(314\) | 251.341 | + | 6948.87i | 0.0451720 | + | 1.24888i | ||||
\(315\) | 41.4384 | − | 41.4384i | 0.00741203 | − | 0.00741203i | ||||
\(316\) | 316.761 | + | 4373.04i | 0.0563899 | + | 0.778490i | ||||
\(317\) | −3135.51 | − | 3135.51i | −0.555545 | − | 0.555545i | 0.372491 | − | 0.928036i | \(-0.378504\pi\) |
−0.928036 | + | 0.372491i | \(0.878504\pi\) | |||||||
\(318\) | −2195.73 | − | 2042.44i | −0.387203 | − | 0.360170i | ||||
\(319\) | 297.439 | 0.0522050 | ||||||||
\(320\) | −393.530 | − | 251.393i | −0.0687468 | − | 0.0439165i | ||||
\(321\) | 2785.63 | 0.484357 | ||||||||
\(322\) | −3132.20 | − | 2913.52i | −0.542083 | − | 0.504237i | ||||
\(323\) | −3114.85 | − | 3114.85i | −0.536578 | − | 0.536578i | ||||
\(324\) | −46.8152 | − | 646.307i | −0.00802730 | − | 0.110821i | ||||
\(325\) | 1813.22 | − | 1813.22i | 0.309476 | − | 0.309476i | ||||
\(326\) | −388.316 | − | 10735.8i | −0.0659718 | − | 1.82393i | ||||
\(327\) | − | 1390.64i | − | 0.235176i | ||||||
\(328\) | −6352.24 | − | 5104.69i | −1.06934 | − | 0.859328i | ||||
\(329\) | − | 2455.13i | − | 0.411416i | ||||||
\(330\) | 278.311 | − | 10.0665i | 0.0464258 | − | 0.00167923i | ||||
\(331\) | −1734.12 | + | 1734.12i | −0.287963 | + | 0.287963i | −0.836274 | − | 0.548312i | \(-0.815271\pi\) |
0.548312 | + | 0.836274i | \(0.315271\pi\) | |||||||
\(332\) | −3437.31 | + | 3974.16i | −0.568214 | + | 0.656959i | ||||
\(333\) | −1663.79 | − | 1663.79i | −0.273798 | − | 0.273798i | ||||
\(334\) | −53.0003 | + | 56.9783i | −0.00868278 | + | 0.00933446i | ||||
\(335\) | −45.5382 | −0.00742691 | ||||||||
\(336\) | −819.457 | + | 1098.82i | −0.133051 | + | 0.178410i | ||||
\(337\) | 5828.89 | 0.942196 | 0.471098 | − | 0.882081i | \(-0.343858\pi\) | ||||
0.471098 | + | 0.882081i | \(0.343858\pi\) | |||||||
\(338\) | 3410.70 | − | 3666.69i | 0.548869 | − | 0.590065i | ||||
\(339\) | −2862.04 | − | 2862.04i | −0.458539 | − | 0.458539i | ||||
\(340\) | 394.044 | + | 340.814i | 0.0628530 | + | 0.0543625i | ||||
\(341\) | −2743.21 | + | 2743.21i | −0.435639 | + | 0.435639i | ||||
\(342\) | 1569.43 | − | 56.7665i | 0.248144 | − | 0.00897538i | ||||
\(343\) | − | 4533.65i | − | 0.713686i | ||||||
\(344\) | −1082.42 | − | 9940.43i | −0.169651 | − | 1.55800i | ||||
\(345\) | − | 579.645i | − | 0.0904551i | ||||||
\(346\) | 440.245 | + | 12171.5i | 0.0684038 | + | 1.89117i | ||||
\(347\) | −716.234 | + | 716.234i | −0.110805 | + | 0.110805i | −0.760336 | − | 0.649530i | \(-0.774966\pi\) |
0.649530 | + | 0.760336i | \(0.274966\pi\) | |||||||
\(348\) | −197.855 | + | 14.3316i | −0.0304774 | + | 0.00220763i | ||||
\(349\) | −4388.39 | − | 4388.39i | −0.673081 | − | 0.673081i | 0.285344 | − | 0.958425i | \(-0.407892\pi\) |
−0.958425 | + | 0.285344i | \(0.907892\pi\) | |||||||
\(350\) | 1835.87 | + | 1707.69i | 0.280375 | + | 0.260800i | ||||
\(351\) | 557.596 | 0.0847928 | ||||||||
\(352\) | −6407.90 | + | 1171.15i | −0.970291 | + | 0.177337i | ||||
\(353\) | 9348.76 | 1.40959 | 0.704794 | − | 0.709412i | \(-0.251040\pi\) | ||||
0.704794 | + | 0.709412i | \(0.251040\pi\) | |||||||
\(354\) | −1342.17 | − | 1248.47i | −0.201513 | − | 0.187444i | ||||
\(355\) | −506.079 | − | 506.079i | −0.0756617 | − | 0.0756617i | ||||
\(356\) | −2417.49 | + | 175.110i | −0.359906 | + | 0.0260698i | ||||
\(357\) | 1081.37 | − | 1081.37i | 0.160314 | − | 0.160314i | ||||
\(358\) | −52.8906 | − | 1462.27i | −0.00780826 | − | 0.215876i | ||||
\(359\) | − | 12531.1i | − | 1.84224i | −0.389275 | − | 0.921122i | \(-0.627274\pi\) | ||
0.389275 | − | 0.921122i | \(-0.372726\pi\) | |||||||
\(360\) | −184.646 | + | 20.1062i | −0.0270325 | + | 0.00294358i | ||||
\(361\) | − | 3052.92i | − | 0.445097i | ||||||
\(362\) | −6943.88 | + | 251.161i | −1.00818 | + | 0.0364661i | ||||
\(363\) | −76.4808 | + | 76.4808i | −0.0110584 | + | 0.0110584i | ||||
\(364\) | −892.112 | − | 771.601i | −0.128460 | − | 0.111107i | ||||
\(365\) | −516.076 | − | 516.076i | −0.0740073 | − | 0.0740073i | ||||
\(366\) | 4298.89 | − | 4621.54i | 0.613952 | − | 0.660032i | ||||
\(367\) | 9276.83 | 1.31947 | 0.659736 | − | 0.751497i | \(-0.270668\pi\) | ||||
0.659736 | + | 0.751497i | \(0.270668\pi\) | |||||||
\(368\) | 1953.91 | + | 13416.6i | 0.276779 | + | 1.90051i | ||||
\(369\) | −3241.31 | −0.457279 | ||||||||
\(370\) | −459.344 | + | 493.820i | −0.0645410 | + | 0.0693851i | ||||
\(371\) | 1784.10 | + | 1784.10i | 0.249665 | + | 0.249665i | ||||
\(372\) | 1692.59 | − | 1956.94i | 0.235905 | − | 0.272749i | ||||
\(373\) | 1765.32 | − | 1765.32i | 0.245053 | − | 0.245053i | −0.573884 | − | 0.818937i | \(-0.694564\pi\) |
0.818937 | + | 0.573884i | \(0.194564\pi\) | |||||||
\(374\) | 7262.73 | − | 262.694i | 1.00414 | − | 0.0363197i | ||||
\(375\) | 681.766i | 0.0938834i | ||||||||
\(376\) | −4874.31 | + | 6065.55i | −0.668546 | + | 0.831934i | ||||
\(377\) | − | 170.698i | − | 0.0233193i | ||||||
\(378\) | 19.7073 | + | 544.852i | 0.00268158 | + | 0.0741380i | ||||
\(379\) | 2909.05 | − | 2909.05i | 0.394269 | − | 0.394269i | −0.481937 | − | 0.876206i | \(-0.660067\pi\) |
0.876206 | + | 0.481937i | \(0.160067\pi\) | |||||||
\(380\) | −32.5209 | − | 448.967i | −0.00439023 | − | 0.0606092i | ||||
\(381\) | 110.757 | + | 110.757i | 0.0148930 | + | 0.0148930i | ||||
\(382\) | −3540.22 | − | 3293.06i | −0.474172 | − | 0.441067i | ||||
\(383\) | 1520.26 | 0.202824 | 0.101412 | − | 0.994845i | \(-0.467664\pi\) | ||||
0.101412 | + | 0.994845i | \(0.467664\pi\) | |||||||
\(384\) | 4206.07 | − | 1087.80i | 0.558959 | − | 0.144561i | ||||
\(385\) | −234.316 | −0.0310177 | ||||||||
\(386\) | 4979.77 | + | 4632.10i | 0.656641 | + | 0.610798i | ||||
\(387\) | −2812.27 | − | 2812.27i | −0.369395 | − | 0.369395i | ||||
\(388\) | 905.810 | + | 12505.1i | 0.118519 | + | 1.63622i | ||||
\(389\) | −8093.35 | + | 8093.35i | −1.05488 | + | 1.05488i | −0.0564785 | + | 0.998404i | \(0.517987\pi\) |
−0.998404 | + | 0.0564785i | \(0.982013\pi\) | |||||||
\(390\) | −5.77710 | − | 159.720i | −0.000750090 | − | 0.0207378i | ||||
\(391\) | − | 15126.3i | − | 1.95644i | ||||||
\(392\) | −4139.24 | + | 5150.84i | −0.533324 | + | 0.663665i | ||||
\(393\) | − | 1645.97i | − | 0.211267i | ||||||
\(394\) | 11082.9 | − | 400.870i | 1.41713 | − | 0.0512577i | ||||
\(395\) | 353.457 | − | 353.457i | 0.0450237 | − | 0.0450237i | ||||
\(396\) | −1694.93 | + | 1959.65i | −0.215084 | + | 0.248677i | ||||
\(397\) | 8897.26 | + | 8897.26i | 1.12479 | + | 1.12479i | 0.991012 | + | 0.133776i | \(0.0427101\pi\) |
0.133776 | + | 0.991012i | \(0.457290\pi\) | |||||||
\(398\) | −2902.89 | + | 3120.76i | −0.365600 | + | 0.393040i | ||||
\(399\) | −1321.34 | −0.165788 | ||||||||
\(400\) | −1145.24 | − | 7863.81i | −0.143155 | − | 0.982976i | ||||
\(401\) | −4199.74 | −0.523004 | −0.261502 | − | 0.965203i | \(-0.584218\pi\) | ||||
−0.261502 | + | 0.965203i | \(0.584218\pi\) | |||||||
\(402\) | 288.550 | − | 310.207i | 0.0357999 | − | 0.0384869i | ||||
\(403\) | 1574.30 | + | 1574.30i | 0.194595 | + | 0.194595i | ||||
\(404\) | 510.111 | + | 441.203i | 0.0628192 | + | 0.0543333i | ||||
\(405\) | −52.2386 | + | 52.2386i | −0.00640928 | + | 0.00640928i | ||||
\(406\) | 166.796 | − | 6.03304i | 0.0203891 | − | 0.000737475i | ||||
\(407\) | 9407.97i | 1.14579i | ||||||||
\(408\) | −4818.47 | + | 524.685i | −0.584681 | + | 0.0636662i | ||||
\(409\) | 7881.87i | 0.952894i | 0.879203 | + | 0.476447i | \(0.158076\pi\) | ||||
−0.879203 | + | 0.476447i | \(0.841924\pi\) | |||||||
\(410\) | 33.5823 | + | 928.455i | 0.00404515 | + | 0.111837i | ||||
\(411\) | −1686.55 | + | 1686.55i | −0.202412 | + | 0.202412i | ||||
\(412\) | −14063.9 | + | 1018.72i | −1.68174 | + | 0.121817i | ||||
\(413\) | 1090.56 | + | 1090.56i | 0.129934 | + | 0.129934i | ||||
\(414\) | 3948.56 | + | 3672.89i | 0.468746 | + | 0.436021i | ||||
\(415\) | 599.043 | 0.0708575 | ||||||||
\(416\) | 672.115 | + | 3677.44i | 0.0792143 | + | 0.433417i | ||||
\(417\) | 7249.40 | 0.851331 | ||||||||
\(418\) | −4597.71 | − | 4276.72i | −0.537994 | − | 0.500434i | ||||
\(419\) | −5502.69 | − | 5502.69i | −0.641585 | − | 0.641585i | 0.309360 | − | 0.950945i | \(-0.399885\pi\) |
−0.950945 | + | 0.309360i | \(0.899885\pi\) | |||||||
\(420\) | 155.866 | − | 11.2901i | 0.0181082 | − | 0.00131167i | ||||
\(421\) | 11302.2 | − | 11302.2i | 1.30840 | − | 1.30840i | 0.385823 | − | 0.922573i | \(-0.373918\pi\) |
0.922573 | − | 0.385823i | \(-0.126082\pi\) | |||||||
\(422\) | −284.142 | − | 7855.73i | −0.0327769 | − | 0.906187i | ||||
\(423\) | 3095.02i | 0.355757i | ||||||||
\(424\) | −865.656 | − | 7949.79i | −0.0991509 | − | 0.910557i | ||||
\(425\) | 8865.90i | 1.01190i | ||||||||
\(426\) | 6654.17 | − | 240.682i | 0.756798 | − | 0.0273734i | ||||
\(427\) | −3755.14 | + | 3755.14i | −0.425584 | + | 0.425584i | ||||
\(428\) | 5618.38 | + | 4859.42i | 0.634521 | + | 0.548806i | ||||
\(429\) | −1576.48 | − | 1576.48i | −0.177420 | − | 0.177420i | ||||
\(430\) | −776.423 | + | 834.697i | −0.0870754 | + | 0.0936108i | ||||
\(431\) | −5428.20 | −0.606652 | −0.303326 | − | 0.952887i | \(-0.598097\pi\) | ||||
−0.303326 | + | 0.952887i | \(0.598097\pi\) | |||||||
\(432\) | 1033.04 | − | 1385.22i | 0.115051 | − | 0.154274i | ||||
\(433\) | −5143.78 | −0.570888 | −0.285444 | − | 0.958395i | \(-0.592141\pi\) | ||||
−0.285444 | + | 0.958395i | \(0.592141\pi\) | |||||||
\(434\) | −1482.68 | + | 1593.96i | −0.163988 | + | 0.176296i | ||||
\(435\) | 15.9919 | + | 15.9919i | 0.00176265 | + | 0.00176265i | ||||
\(436\) | 2425.92 | − | 2804.80i | 0.266469 | − | 0.308086i | ||||
\(437\) | −9241.50 | + | 9241.50i | −1.01163 | + | 1.01163i | ||||
\(438\) | 6785.61 | − | 245.436i | 0.740249 | − | 0.0267749i | ||||
\(439\) | − | 2183.50i | − | 0.237386i | −0.992931 | − | 0.118693i | \(-0.962130\pi\) | ||
0.992931 | − | 0.118693i | \(-0.0378705\pi\) | |||||||
\(440\) | 578.891 | + | 465.200i | 0.0627217 | + | 0.0504035i | ||||
\(441\) | 2628.28i | 0.283801i | ||||||||
\(442\) | −150.758 | − | 4168.02i | −0.0162236 | − | 0.448535i | ||||
\(443\) | 561.821 | − | 561.821i | 0.0602549 | − | 0.0602549i | −0.676337 | − | 0.736592i | \(-0.736434\pi\) |
0.736592 | + | 0.676337i | \(0.236434\pi\) | |||||||
\(444\) | −453.308 | − | 6258.13i | −0.0484528 | − | 0.668914i | ||||
\(445\) | 195.397 | + | 195.397i | 0.0208150 | + | 0.0208150i | ||||
\(446\) | 177.663 | + | 165.260i | 0.0188623 | + | 0.0175455i | ||||
\(447\) | −295.415 | −0.0312588 | ||||||||
\(448\) | −3569.64 | + | 786.726i | −0.376450 | + | 0.0829672i | ||||
\(449\) | −2639.02 | −0.277378 | −0.138689 | − | 0.990336i | \(-0.544289\pi\) | ||||
−0.138689 | + | 0.990336i | \(0.544289\pi\) | |||||||
\(450\) | −2314.35 | − | 2152.78i | −0.242444 | − | 0.225518i | ||||
\(451\) | 9164.08 | + | 9164.08i | 0.956807 | + | 0.956807i | ||||
\(452\) | −779.779 | − | 10765.2i | −0.0811454 | − | 1.12025i | ||||
\(453\) | −3325.13 | + | 3325.13i | −0.344875 | + | 0.344875i | ||||
\(454\) | 365.227 | + | 10097.5i | 0.0377554 | + | 1.04383i | ||||
\(455\) | 134.472i | 0.0138552i | ||||||||
\(456\) | 3264.44 | + | 2623.32i | 0.335245 | + | 0.269404i | ||||
\(457\) | − | 5546.69i | − | 0.567753i | −0.958861 | − | 0.283876i | \(-0.908379\pi\) | ||
0.958861 | − | 0.283876i | \(-0.0916205\pi\) | |||||||
\(458\) | −4463.66 | + | 161.451i | −0.455400 | + | 0.0164719i | ||||
\(459\) | −1363.21 | + | 1363.21i | −0.138625 | + | 0.138625i | ||||
\(460\) | 1011.17 | − | 1169.10i | 0.102491 | − | 0.118499i | ||||
\(461\) | 8475.23 | + | 8475.23i | 0.856249 | + | 0.856249i | 0.990894 | − | 0.134645i | \(-0.0429894\pi\) |
−0.134645 | + | 0.990894i | \(0.542989\pi\) | |||||||
\(462\) | 1484.73 | − | 1596.16i | 0.149515 | − | 0.160737i | ||||
\(463\) | −16410.6 | −1.64722 | −0.823612 | − | 0.567154i | \(-0.808044\pi\) | ||||
−0.823612 | + | 0.567154i | \(0.808044\pi\) | |||||||
\(464\) | −424.058 | − | 316.245i | −0.0424276 | − | 0.0316407i | ||||
\(465\) | −294.979 | −0.0294179 | ||||||||
\(466\) | 11085.0 | − | 11917.0i | 1.10194 | − | 1.18464i | ||||
\(467\) | −6689.53 | − | 6689.53i | −0.662858 | − | 0.662858i | 0.293195 | − | 0.956053i | \(-0.405281\pi\) |
−0.956053 | + | 0.293195i | \(0.905281\pi\) | |||||||
\(468\) | 1124.63 | + | 972.706i | 0.111081 | + | 0.0960755i | ||||
\(469\) | −252.053 | + | 252.053i | −0.0248161 | + | 0.0248161i | ||||
\(470\) | 886.553 | − | 32.0667i | 0.0870077 | − | 0.00314708i | ||||
\(471\) | 7375.21i | 0.721511i | ||||||||
\(472\) | −529.145 | − | 4859.43i | −0.0516014 | − | 0.473884i | ||||
\(473\) | 15902.1i | 1.54584i | ||||||||
\(474\) | 168.098 | + | 4647.42i | 0.0162890 | + | 0.450344i | ||||
\(475\) | 5416.69 | − | 5416.69i | 0.523231 | − | 0.523231i | ||||
\(476\) | 4067.43 | − | 294.624i | 0.391660 | − | 0.0283699i | ||||
\(477\) | −2249.10 | − | 2249.10i | −0.215889 | − | 0.215889i | ||||
\(478\) | −1329.13 | − | 1236.33i | −0.127182 | − | 0.118302i | ||||
\(479\) | 7188.55 | 0.685707 | 0.342853 | − | 0.939389i | \(-0.388607\pi\) | ||||
0.342853 | + | 0.939389i | \(0.388607\pi\) | |||||||
\(480\) | −407.490 | − | 281.555i | −0.0387485 | − | 0.0267733i | ||||
\(481\) | 5399.16 | 0.511810 | ||||||||
\(482\) | −5979.86 | − | 5562.38i | −0.565094 | − | 0.525642i | ||||
\(483\) | −3208.33 | − | 3208.33i | −0.302244 | − | 0.302244i | ||||
\(484\) | −287.674 | + | 20.8376i | −0.0270167 | + | 0.00195695i | ||||
\(485\) | 1010.75 | − | 1010.75i | 0.0946301 | − | 0.0946301i | ||||
\(486\) | −24.8437 | − | 686.859i | −0.00231880 | − | 0.0641081i | ||||
\(487\) | 11181.6i | 1.04042i | 0.854038 | + | 0.520210i | \(0.174146\pi\) | ||||
−0.854038 | + | 0.520210i | \(0.825854\pi\) | |||||||
\(488\) | 16732.6 | − | 1822.02i | 1.55215 | − | 0.169014i | ||||
\(489\) | − | 11394.5i | − | 1.05374i | ||||||
\(490\) | 752.856 | − | 27.2309i | 0.0694093 | − | 0.00251054i | ||||
\(491\) | 11679.8 | − | 11679.8i | 1.07353 | − | 1.07353i | 0.0764529 | − | 0.997073i | \(-0.475641\pi\) |
0.997073 | − | 0.0764529i | \(-0.0243595\pi\) | |||||||
\(492\) | −6537.46 | − | 5654.35i | −0.599048 | − | 0.518125i | ||||
\(493\) | 417.321 | + | 417.321i | 0.0381241 | + | 0.0381241i | ||||
\(494\) | −2454.38 | + | 2638.59i | −0.223538 | + | 0.240315i | ||||
\(495\) | 295.386 | 0.0268215 | ||||||||
\(496\) | 6827.63 | − | 994.336i | 0.618084 | − | 0.0900141i | ||||
\(497\) | −5602.28 | −0.505627 | ||||||||
\(498\) | −3795.80 | + | 4080.70i | −0.341554 | + | 0.367189i | ||||
\(499\) | −2094.26 | − | 2094.26i | −0.187880 | − | 0.187880i | 0.606899 | − | 0.794779i | \(-0.292413\pi\) |
−0.794779 | + | 0.606899i | \(0.792413\pi\) | |||||||
\(500\) | −1189.32 | + | 1375.07i | −0.106376 | + | 0.122990i | ||||
\(501\) | −58.3631 | + | 58.3631i | −0.00520453 | + | 0.00520453i | ||||
\(502\) | −9464.00 | + | 342.314i | −0.841433 | + | 0.0304347i | ||||
\(503\) | 4293.63i | 0.380604i | 0.981726 | + | 0.190302i | \(0.0609466\pi\) | ||||
−0.981726 | + | 0.190302i | \(0.939053\pi\) | |||||||
\(504\) | −910.725 | + | 1133.30i | −0.0804899 | + | 0.100161i | ||||
\(505\) | − | 76.8912i | − | 0.00677548i | ||||||
\(506\) | −779.391 | − | 21547.9i | −0.0684746 | − | 1.89313i | ||||
\(507\) | 3755.81 | − | 3755.81i | 0.328997 | − | 0.328997i | ||||
\(508\) | 30.1762 | + | 416.598i | 0.00263554 | + | 0.0363849i | ||||
\(509\) | −9115.13 | − | 9115.13i | −0.793755 | − | 0.793755i | 0.188348 | − | 0.982102i | \(-0.439687\pi\) |
−0.982102 | + | 0.188348i | \(0.939687\pi\) | |||||||
\(510\) | 404.607 | + | 376.359i | 0.0351300 | + | 0.0326774i | ||||
\(511\) | −5712.95 | −0.494571 | ||||||||
\(512\) | 10380.9 | + | 5143.34i | 0.896048 | + | 0.443956i | ||||
\(513\) | 1665.72 | 0.143359 | ||||||||
\(514\) | 10587.8 | + | 9848.59i | 0.908574 | + | 0.845142i | ||||
\(515\) | 1136.73 | + | 1136.73i | 0.0972631 | + | 0.0972631i | ||||
\(516\) | −766.219 | − | 10578.0i | −0.0653700 | − | 0.902464i | ||||
\(517\) | 8750.49 | − | 8750.49i | 0.744383 | − | 0.744383i | ||||
\(518\) | 190.825 | + | 5275.75i | 0.0161860 | + | 0.447497i | ||||
\(519\) | 12918.3i | 1.09258i | ||||||||
\(520\) | 266.974 | − | 332.221i | 0.0225146 | − | 0.0280170i | ||||
\(521\) | − | 23150.3i | − | 1.94671i | −0.229309 | − | 0.973354i | \(-0.573647\pi\) | ||
0.229309 | − | 0.973354i | \(-0.426353\pi\) | |||||||
\(522\) | −210.269 | + | 7.60546i | −0.0176307 | + | 0.000637705i | ||||
\(523\) | −8510.52 | + | 8510.52i | −0.711547 | + | 0.711547i | −0.966859 | − | 0.255312i | \(-0.917822\pi\) |
0.255312 | + | 0.966859i | \(0.417822\pi\) | |||||||
\(524\) | 2871.33 | − | 3319.78i | 0.239379 | − | 0.276766i | ||||
\(525\) | 1880.49 | + | 1880.49i | 0.156326 | + | 0.156326i | ||||
\(526\) | −10588.2 | + | 11382.9i | −0.877693 | + | 0.943569i | ||||
\(527\) | −7697.69 | −0.636274 | ||||||||
\(528\) | −6837.07 | + | 995.710i | −0.563532 | + | 0.0820695i | ||||
\(529\) | −32711.4 | −2.68854 | ||||||||
\(530\) | −620.939 | + | 667.543i | −0.0508903 | + | 0.0547099i | ||||
\(531\) | −1374.79 | − | 1374.79i | −0.112356 | − | 0.112356i | ||||
\(532\) | −2665.03 | − | 2305.02i | −0.217187 | − | 0.187849i | ||||
\(533\) | 5259.19 | − | 5259.19i | 0.427394 | − | 0.427394i | ||||
\(534\) | −2569.17 | + | 92.9271i | −0.208200 | + | 0.00753061i | ||||
\(535\) | − | 846.884i | − | 0.0684373i | ||||||
\(536\) | 1123.13 | − | 122.298i | 0.0905069 | − | 0.00985533i | ||||
\(537\) | − | 1551.99i | − | 0.124718i | ||||||
\(538\) | −357.756 | − | 9890.92i | −0.0286690 | − | 0.792617i | ||||
\(539\) | 7430.87 | − | 7430.87i | 0.593822 | − | 0.593822i | ||||
\(540\) | −196.489 | + | 14.2327i | −0.0156584 | + | 0.00113422i | ||||
\(541\) | 3403.84 | + | 3403.84i | 0.270504 | + | 0.270504i | 0.829303 | − | 0.558799i | \(-0.188738\pi\) |
−0.558799 | + | 0.829303i | \(0.688738\pi\) | |||||||
\(542\) | −3559.15 | − | 3310.67i | −0.282064 | − | 0.262372i | ||||
\(543\) | −7369.91 | −0.582455 | ||||||||
\(544\) | −10633.8 | − | 7347.40i | −0.838086 | − | 0.579076i | ||||
\(545\) | −422.780 | −0.0332292 | ||||||||
\(546\) | −916.026 | − | 852.074i | −0.0717991 | − | 0.0667864i | ||||
\(547\) | 15672.4 | + | 15672.4i | 1.22505 | + | 1.22505i | 0.965814 | + | 0.259237i | \(0.0834710\pi\) |
0.259237 | + | 0.965814i | \(0.416529\pi\) | |||||||
\(548\) | −6343.76 | + | 459.510i | −0.494511 | + | 0.0358199i | ||||
\(549\) | 4733.86 | − | 4733.86i | 0.368008 | − | 0.368008i | ||||
\(550\) | 456.822 | + | 12629.8i | 0.0354163 | + | 0.979159i | ||||
\(551\) | − | 509.930i | − | 0.0394261i | ||||||
\(552\) | 1556.70 | + | 14296.0i | 0.120032 | + | 1.10232i | ||||
\(553\) | − | 3912.76i | − | 0.300882i | ||||||
\(554\) | −18878.4 | + | 682.834i | −1.44777 | + | 0.0523661i | ||||
\(555\) | −505.822 | + | 505.822i | −0.0386864 | + | 0.0386864i | ||||
\(556\) | 14621.5 | + | 12646.3i | 1.11527 | + | 0.964610i | ||||
\(557\) | 6285.58 | + | 6285.58i | 0.478149 | + | 0.478149i | 0.904539 | − | 0.426391i | \(-0.140215\pi\) |
−0.426391 | + | 0.904539i | \(0.640215\pi\) | |||||||
\(558\) | 1869.12 | − | 2009.40i | 0.141803 | − | 0.152446i | ||||
\(559\) | 9126.11 | 0.690507 | ||||||||
\(560\) | 334.063 | + | 249.130i | 0.0252085 | + | 0.0187994i | ||||
\(561\) | 7708.32 | 0.580117 | ||||||||
\(562\) | −4899.23 | + | 5266.94i | −0.367725 | + | 0.395325i | ||||
\(563\) | −1763.14 | − | 1763.14i | −0.131985 | − | 0.131985i | 0.638028 | − | 0.770013i | \(-0.279750\pi\) |
−0.770013 | + | 0.638028i | \(0.779750\pi\) | |||||||
\(564\) | −5399.15 | + | 6242.41i | −0.403095 | + | 0.466051i | ||||
\(565\) | −870.114 | + | 870.114i | −0.0647894 | + | 0.0647894i | ||||
\(566\) | −12818.9 | + | 463.661i | −0.951977 | + | 0.0344331i | ||||
\(567\) | 578.280i | 0.0428316i | ||||||||
\(568\) | 13840.8 | + | 11122.5i | 1.02244 | + | 0.821639i | ||||
\(569\) | 1150.05i | 0.0847323i | 0.999102 | + | 0.0423662i | \(0.0134896\pi\) | ||||
−0.999102 | + | 0.0423662i | \(0.986510\pi\) | |||||||
\(570\) | −17.2581 | − | 477.137i | −0.00126818 | − | 0.0350615i | ||||
\(571\) | −4853.30 | + | 4853.30i | −0.355699 | + | 0.355699i | −0.862225 | − | 0.506526i | \(-0.830930\pi\) |
0.506526 | + | 0.862225i | \(0.330930\pi\) | |||||||
\(572\) | −429.521 | − | 5929.74i | −0.0313971 | − | 0.433453i | ||||
\(573\) | −3626.27 | − | 3626.27i | −0.264380 | − | 0.264380i | ||||
\(574\) | 5324.87 | + | 4953.11i | 0.387205 | + | 0.360172i | ||||
\(575\) | 26304.4 | 1.90778 | ||||||||
\(576\) | 4500.01 | − | 991.774i | 0.325521 | − | 0.0717429i | ||||
\(577\) | −5152.84 | −0.371777 | −0.185889 | − | 0.982571i | \(-0.559516\pi\) | ||||
−0.185889 | + | 0.982571i | \(0.559516\pi\) | |||||||
\(578\) | 383.759 | + | 356.967i | 0.0276164 | + | 0.0256883i | ||||
\(579\) | 5100.80 | + | 5100.80i | 0.366117 | + | 0.366117i | ||||
\(580\) | 4.35708 | + | 60.1516i | 0.000311928 | + | 0.00430631i | ||||
\(581\) | 3315.69 | − | 3315.69i | 0.236761 | − | 0.236761i | ||||
\(582\) | 480.692 | + | 13289.8i | 0.0342360 | + | 0.946527i | ||||
\(583\) | 12717.6i | 0.903449i | ||||||||
\(584\) | 14114.2 | + | 11342.2i | 1.00008 | + | 0.803672i | ||||
\(585\) | − | 169.520i | − | 0.0119808i | ||||||
\(586\) | 23630.1 | − | 854.705i | 1.66579 | − | 0.0602517i | ||||
\(587\) | 12549.2 | − | 12549.2i | 0.882387 | − | 0.882387i | −0.111390 | − | 0.993777i | \(-0.535530\pi\) |
0.993777 | + | 0.111390i | \(0.0355302\pi\) | |||||||
\(588\) | −4584.93 | + | 5301.02i | −0.321564 | + | 0.371787i | ||||
\(589\) | 4702.96 | + | 4702.96i | 0.329002 | + | 0.329002i | ||||
\(590\) | −379.558 | + | 408.046i | −0.0264850 | + | 0.0284728i | ||||
\(591\) | 11762.9 | 0.818714 | ||||||||
\(592\) | 10002.8 | − | 13412.9i | 0.694447 | − | 0.931195i | ||||
\(593\) | −1116.75 | −0.0773347 | −0.0386674 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386674 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(594\) | −1871.70 | + | 2012.18i | −0.129287 | + | 0.138991i | ||||
\(595\) | −328.756 | − | 328.756i | −0.0226515 | − | 0.0226515i | ||||
\(596\) | −595.829 | − | 515.341i | −0.0409498 | − | 0.0354181i | ||||
\(597\) | −3196.61 | + | 3196.61i | −0.219143 | + | 0.219143i | ||||
\(598\) | −12366.2 | + | 447.286i | −0.845637 | + | 0.0305868i | ||||
\(599\) | 15827.4i | 1.07962i | 0.841788 | + | 0.539808i | \(0.181503\pi\) | ||||
−0.841788 | + | 0.539808i | \(0.818497\pi\) | |||||||
\(600\) | −912.423 | − | 8379.28i | −0.0620825 | − | 0.570138i | ||||
\(601\) | − | 12216.9i | − | 0.829180i | −0.910008 | − | 0.414590i | \(-0.863925\pi\) | ||
0.910008 | − | 0.414590i | \(-0.136075\pi\) | |||||||
\(602\) | 322.548 | + | 8917.52i | 0.0218373 | + | 0.603739i | ||||
\(603\) | 317.747 | − | 317.747i | 0.0214588 | − | 0.0214588i | ||||
\(604\) | −12507.1 | + | 905.951i | −0.842560 | + | 0.0610308i | ||||
\(605\) | 23.2516 | + | 23.2516i | 0.00156250 | + | 0.00156250i | ||||
\(606\) | 523.785 | + | 487.217i | 0.0351111 | + | 0.0326598i | ||||
\(607\) | −24175.5 | −1.61656 | −0.808282 | − | 0.588795i | \(-0.799602\pi\) | ||||
−0.808282 | + | 0.588795i | \(0.799602\pi\) | |||||||
\(608\) | 2007.83 | + | 10985.7i | 0.133928 | + | 0.732780i | ||||
\(609\) | 177.030 | 0.0117793 | ||||||||
\(610\) | −1405.04 | − | 1306.94i | −0.0932594 | − | 0.0867485i | ||||
\(611\) | −5021.84 | − | 5021.84i | −0.332507 | − | 0.332507i | ||||
\(612\) | −5127.54 | + | 371.413i | −0.338674 | + | 0.0245318i | ||||
\(613\) | 12893.7 | − | 12893.7i | 0.849544 | − | 0.849544i | −0.140532 | − | 0.990076i | \(-0.544881\pi\) |
0.990076 | + | 0.140532i | \(0.0448812\pi\) | |||||||
\(614\) | 168.044 | + | 4645.95i | 0.0110451 | + | 0.305367i | ||||
\(615\) | 985.420i | 0.0646113i | ||||||||
\(616\) | 5779.03 | − | 629.280i | 0.377993 | − | 0.0411598i | ||||
\(617\) | − | 13762.7i | − | 0.897998i | −0.893532 | − | 0.448999i | \(-0.851781\pi\) | ||
0.893532 | − | 0.448999i | \(-0.148219\pi\) | |||||||
\(618\) | −14946.3 | + | 540.610i | −0.972864 | + | 0.0351886i | ||||
\(619\) | −326.797 | + | 326.797i | −0.0212199 | + | 0.0212199i | −0.717637 | − | 0.696417i | \(-0.754776\pi\) |
0.696417 | + | 0.717637i | \(0.254776\pi\) | |||||||
\(620\) | −594.948 | − | 514.579i | −0.0385382 | − | 0.0333323i | ||||
\(621\) | 4044.52 | + | 4044.52i | 0.261355 | + | 0.261355i | ||||
\(622\) | 4541.07 | − | 4881.90i | 0.292734 | − | 0.314705i | ||||
\(623\) | 2163.04 | 0.139101 | ||||||||
\(624\) | 571.430 | + | 3923.74i | 0.0366595 | + | 0.251723i | ||||
\(625\) | −15313.7 | −0.980080 | ||||||||
\(626\) | −7293.25 | + | 7840.65i | −0.465650 | + | 0.500600i | ||||
\(627\) | −4709.46 | − | 4709.46i | −0.299964 | − | 0.299964i | ||||
\(628\) | −12865.8 | + | 14875.2i | −0.817517 | + | 0.945199i | ||||
\(629\) | −13199.8 | + | 13199.8i | −0.836742 | + | 0.836742i | ||||
\(630\) | 165.645 | − | 5.99140i | 0.0104753 | − | 0.000378894i | ||||
\(631\) | − | 12260.2i | − | 0.773487i | −0.922187 | − | 0.386744i | \(-0.873600\pi\) | ||
0.922187 | − | 0.386744i | \(-0.126400\pi\) | |||||||
\(632\) | −7768.22 | + | 9666.72i | −0.488929 | + | 0.608420i | ||||
\(633\) | − | 8337.71i | − | 0.523529i | ||||||
\(634\) | −453.350 | − | 12533.8i | −0.0283988 | − | 0.785146i | ||||
\(635\) | 33.6721 | − | 33.6721i | 0.00210431 | − | 0.00210431i | ||||
\(636\) | −612.779 | − | 8459.71i | −0.0382048 | − | 0.527436i | ||||
\(637\) | −4264.52 | − | 4264.52i | −0.265253 | − | 0.265253i | ||||
\(638\) | 615.992 | + | 572.986i | 0.0382247 | + | 0.0355560i | ||||
\(639\) | 7062.43 | 0.437223 | ||||||||
\(640\) | −330.712 | − | 1278.73i | −0.0204258 | − | 0.0789783i | ||||
\(641\) | 10329.4 | 0.636485 | 0.318242 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318242 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(642\) | 5769.00 | + | 5366.23i | 0.354648 | + | 0.329888i | ||||
\(643\) | −19299.9 | − | 19299.9i | −1.18369 | − | 1.18369i | −0.978781 | − | 0.204911i | \(-0.934309\pi\) |
−0.204911 | − | 0.978781i | \(-0.565691\pi\) | |||||||
\(644\) | −874.126 | − | 12067.7i | −0.0534866 | − | 0.738409i | ||||
\(645\) | −854.984 | + | 854.984i | −0.0521937 | + | 0.0521937i | ||||
\(646\) | −450.363 | − | 12451.2i | −0.0274292 | − | 0.758340i | ||||
\(647\) | − | 8657.07i | − | 0.526035i | −0.964791 | − | 0.263017i | \(-0.915282\pi\) | ||
0.964791 | − | 0.263017i | \(-0.0847177\pi\) | |||||||
\(648\) | 1148.09 | − | 1428.68i | 0.0696008 | − | 0.0866107i | ||||
\(649\) | 7773.84i | 0.470185i | ||||||||
\(650\) | 7248.15 | − | 262.167i | 0.437378 | − | 0.0158200i | ||||
\(651\) | −1632.70 | + | 1632.70i | −0.0982960 | + | 0.0982960i | ||||
\(652\) | 19877.3 | − | 22981.8i | 1.19395 | − | 1.38042i | ||||
\(653\) | 5966.31 | + | 5966.31i | 0.357549 | + | 0.357549i | 0.862909 | − | 0.505360i | \(-0.168640\pi\) |
−0.505360 | + | 0.862909i | \(0.668640\pi\) | |||||||
\(654\) | 2678.92 | − | 2879.99i | 0.160175 | − | 0.172197i | ||||
\(655\) | −500.405 | −0.0298511 | ||||||||
\(656\) | −3321.72 | − | 22808.7i | −0.197701 | − | 1.35752i | ||||
\(657\) | 7201.94 | 0.427663 | ||||||||
\(658\) | 4729.57 | − | 5084.55i | 0.280209 | − | 0.301240i | ||||
\(659\) | 7127.52 | + | 7127.52i | 0.421318 | + | 0.421318i | 0.885657 | − | 0.464339i | \(-0.153708\pi\) |
−0.464339 | + | 0.885657i | \(0.653708\pi\) | |||||||
\(660\) | 595.770 | + | 515.290i | 0.0351368 | + | 0.0303904i | ||||
\(661\) | 2386.19 | − | 2386.19i | 0.140412 | − | 0.140412i | −0.633407 | − | 0.773819i | \(-0.718344\pi\) |
0.773819 | + | 0.633407i | \(0.218344\pi\) | |||||||
\(662\) | −6931.93 | + | 250.729i | −0.406974 | + | 0.0147203i | ||||
\(663\) | − | 4423.75i | − | 0.259131i | ||||||
\(664\) | −14774.4 | + | 1608.80i | −0.863494 | + | 0.0940261i | ||||
\(665\) | 401.711i | 0.0234251i | ||||||||
\(666\) | −240.560 | − | 6650.79i | −0.0139963 | − | 0.386956i | ||||
\(667\) | 1238.16 | − | 1238.16i | 0.0718765 | − | 0.0718765i | ||||
\(668\) | −219.526 | + | 15.9013i | −0.0127151 | + | 0.000921020i | ||||
\(669\) | 181.981 | + | 181.981i | 0.0105169 | + | 0.0105169i | ||||
\(670\) | −94.3089 | − | 87.7247i | −0.00543802 | − | 0.00505836i | ||||
\(671\) | −26767.9 | −1.54003 | ||||||||
\(672\) | −3813.86 | + | 697.047i | −0.218933 | + | 0.0400137i | ||||
\(673\) | −3709.39 | −0.212461 | −0.106231 | − | 0.994342i | \(-0.533878\pi\) | ||||
−0.106231 | + | 0.994342i | \(0.533878\pi\) | |||||||
\(674\) | 12071.6 | + | 11228.8i | 0.689880 | + | 0.641716i | ||||
\(675\) | −2370.60 | − | 2370.60i | −0.135177 | − | 0.135177i | ||||
\(676\) | 14127.0 | − | 1023.29i | 0.803769 | − | 0.0582210i | ||||
\(677\) | −1602.20 | + | 1602.20i | −0.0909564 | + | 0.0909564i | −0.751121 | − | 0.660165i | \(-0.770487\pi\) |
0.660165 | + | 0.751121i | \(0.270487\pi\) | |||||||
\(678\) | −413.811 | − | 11440.7i | −0.0234400 | − | 0.648048i | ||||
\(679\) | − | 11188.9i | − | 0.632388i | ||||||
\(680\) | 159.514 | + | 1464.91i | 0.00899572 | + | 0.0826127i | ||||
\(681\) | 10717.0i | 0.603050i | ||||||||
\(682\) | −10965.7 | + | 396.629i | −0.615684 | + | 0.0222694i | ||||
\(683\) | −15495.9 | + | 15495.9i | −0.868130 | + | 0.868130i | −0.992265 | − | 0.124135i | \(-0.960384\pi\) |
0.124135 | + | 0.992265i | \(0.460384\pi\) | |||||||
\(684\) | 3359.63 | + | 2905.79i | 0.187805 | + | 0.162435i | ||||
\(685\) | 512.743 | + | 512.743i | 0.0285999 | + | 0.0285999i | ||||
\(686\) | 8733.63 | − | 9389.13i | 0.486081 | − | 0.522564i | ||||
\(687\) | −4737.52 | −0.263097 | ||||||||
\(688\) | 16907.6 | − | 22671.7i | 0.936912 | − | 1.25632i | ||||
\(689\) | 7298.55 | 0.403560 | ||||||||
\(690\) | 1116.63 | − | 1200.44i | 0.0616077 | − | 0.0662316i | ||||
\(691\) | 6337.43 | + | 6337.43i | 0.348896 | + | 0.348896i | 0.859698 | − | 0.510802i | \(-0.170652\pi\) |
−0.510802 | + | 0.859698i | \(0.670652\pi\) | |||||||
\(692\) | −22535.5 | + | 26055.1i | −1.23796 | + | 1.43131i | ||||
\(693\) | 1634.96 | − | 1634.96i | 0.0896204 | − | 0.0896204i | ||||
\(694\) | −2863.06 | + | 103.557i | −0.156600 | + | 0.00566424i | ||||
\(695\) | − | 2203.96i | − | 0.120289i | ||||||
\(696\) | −437.363 | − | 351.467i | −0.0238193 | − | 0.0191413i | ||||
\(697\) | 25715.3i | 1.39747i | ||||||||
\(698\) | −634.499 | − | 17542.1i | −0.0344071 | − | 0.951258i | ||||
\(699\) | 12206.6 | − | 12206.6i | 0.660510 | − | 0.660510i | ||||
\(700\) | 512.349 | + | 7073.22i | 0.0276642 | + | 0.381918i | ||||
\(701\) | −952.656 | − | 952.656i | −0.0513285 | − | 0.0513285i | 0.680977 | − | 0.732305i | \(-0.261556\pi\) |
−0.732305 | + | 0.680977i | \(0.761556\pi\) | |||||||
\(702\) | 1154.77 | + | 1074.15i | 0.0620857 | + | 0.0577512i | ||||
\(703\) | 16129.0 | 0.865318 | ||||||||
\(704\) | −15526.8 | − | 9918.74i | −0.831233 | − | 0.531004i | ||||
\(705\) | 940.946 | 0.0502668 | ||||||||
\(706\) | 19361.1 | + | 18009.5i | 1.03211 | + | 0.960049i | ||||
\(707\) | −425.592 | − | 425.592i | −0.0226394 | − | 0.0226394i | ||||
\(708\) | −374.570 | − | 5171.12i | −0.0198830 | − | 0.274495i | ||||
\(709\) | −20781.1 | + | 20781.1i | −1.10078 | + | 1.10078i | −0.106461 | + | 0.994317i | \(0.533952\pi\) |
−0.994317 | + | 0.106461i | \(0.966048\pi\) | |||||||
\(710\) | −73.1719 | − | 2022.99i | −0.00386774 | − | 0.106932i | ||||
\(711\) | 4932.56i | 0.260177i | ||||||||
\(712\) | −5343.91 | − | 4294.39i | −0.281280 | − | 0.226038i | ||||
\(713\) | 22838.4i | 1.19959i | ||||||||
\(714\) | 4322.64 | − | 156.350i | 0.226569 | − | 0.00819504i | ||||
\(715\) | −479.280 | + | 479.280i | −0.0250686 | + | 0.0250686i | ||||
\(716\) | 2707.39 | − | 3130.24i | 0.141313 | − | 0.163383i | ||||
\(717\) | −1361.43 | − | 1361.43i | −0.0709114 | − | 0.0709114i | ||||
\(718\) | 24139.9 | − | 25951.7i | 1.25472 | − | 1.34890i | ||||
\(719\) | −1927.96 | −0.100001 | −0.0500006 | − | 0.998749i | \(-0.515922\pi\) | ||||
−0.0500006 | + | 0.998749i | \(0.515922\pi\) | |||||||
\(720\) | −421.132 | − | 314.062i | −0.0217981 | − | 0.0162561i | ||||
\(721\) | 12583.6 | 0.649984 | ||||||||
\(722\) | 5881.15 | − | 6322.56i | 0.303149 | − | 0.325902i | ||||
\(723\) | −6125.20 | − | 6125.20i | −0.315074 | − | 0.315074i | ||||
\(724\) | −14864.5 | − | 12856.5i | −0.763032 | − | 0.659958i | ||||
\(725\) | −725.717 | + | 725.717i | −0.0371758 | + | 0.0371758i | ||||
\(726\) | −305.723 | + | 11.0580i | −0.0156287 | + | 0.000565293i | ||||
\(727\) | − | 5482.27i | − | 0.279678i | −0.990174 | − | 0.139839i | \(-0.955341\pi\) | ||
0.990174 | − | 0.139839i | \(-0.0446585\pi\) | |||||||
\(728\) | −361.139 | − | 3316.54i | −0.0183856 | − | 0.168845i | ||||
\(729\) | − | 729.000i | − | 0.0370370i | ||||||
\(730\) | −74.6173 | − | 2062.95i | −0.00378316 | − | 0.104594i | ||||
\(731\) | −22311.4 | + | 22311.4i | −1.12889 | + | 1.12889i | ||||
\(732\) | 17805.9 | − | 1289.77i | 0.899076 | − | 0.0651246i | ||||
\(733\) | 15048.8 | + | 15048.8i | 0.758311 | + | 0.758311i | 0.976015 | − | 0.217704i | \(-0.0698568\pi\) |
−0.217704 | + | 0.976015i | \(0.569857\pi\) | |||||||
\(734\) | 19212.2 | + | 17870.9i | 0.966123 | + | 0.898673i | ||||
\(735\) | 799.046 | 0.0400997 | ||||||||
\(736\) | −21799.2 | + | 31549.5i | −1.09175 | + | 1.58007i | ||||
\(737\) | −1796.72 | −0.0898004 | ||||||||
\(738\) | −6712.71 | − | 6244.06i | −0.334821 | − | 0.311446i | ||||
\(739\) | 12622.3 | + | 12622.3i | 0.628306 | + | 0.628306i | 0.947642 | − | 0.319335i | \(-0.103460\pi\) |
−0.319335 | + | 0.947642i | \(0.603460\pi\) | |||||||
\(740\) | −1902.59 | + | 137.814i | −0.0945144 | + | 0.00684615i | ||||
\(741\) | −2702.72 | + | 2702.72i | −0.133990 | + | 0.133990i | ||||
\(742\) | 257.956 | + | 7131.73i | 0.0127626 | + | 0.352849i | ||||
\(743\) | 2335.45i | 0.115315i | 0.998336 | + | 0.0576576i | \(0.0183632\pi\) | ||||
−0.998336 | + | 0.0576576i | \(0.981637\pi\) | |||||||
\(744\) | 7275.19 | − | 792.198i | 0.358496 | − | 0.0390368i | ||||
\(745\) | 89.8119i | 0.00441672i | ||||||||
\(746\) | 7056.67 | − | 255.241i | 0.346331 | − | 0.0125268i | ||||
\(747\) | −4179.88 | + | 4179.88i | −0.204730 | + | 0.204730i | ||||
\(748\) | 15547.1 | + | 13446.9i | 0.759969 | + | 0.657309i | ||||
\(749\) | −4687.49 | − | 4687.49i | −0.228674 | − | 0.228674i | ||||
\(750\) | −1313.36 | + | 1411.93i | −0.0639426 | + | 0.0687418i | ||||
\(751\) | −3513.73 | −0.170729 | −0.0853647 | − | 0.996350i | \(-0.527206\pi\) | ||||
−0.0853647 | + | 0.996350i | \(0.527206\pi\) | |||||||
\(752\) | −21779.3 | + | 3171.81i | −1.05613 | + | 0.153809i | ||||
\(753\) | −10044.7 | −0.486119 | ||||||||
\(754\) | 328.832 | − | 353.513i | 0.0158825 | − | 0.0170745i | ||||
\(755\) | 1010.90 | + | 1010.90i | 0.0487292 | + | 0.0487292i | ||||
\(756\) | −1008.79 | + | 1166.34i | −0.0485308 | + | 0.0561105i | ||||
\(757\) | −10416.0 | + | 10416.0i | −0.500102 | + | 0.500102i | −0.911470 | − | 0.411368i | \(-0.865051\pi\) |
0.411368 | + | 0.911470i | \(0.365051\pi\) | |||||||
\(758\) | 11628.6 | − | 420.607i | 0.557215 | − | 0.0201545i | ||||
\(759\) | − | 22870.0i | − | 1.09371i | ||||||
\(760\) | 797.539 | − | 992.452i | 0.0380655 | − | 0.0473685i | ||||
\(761\) | 17937.9i | 0.854464i | 0.904142 | + | 0.427232i | \(0.140511\pi\) | ||||
−0.904142 | + | 0.427232i | \(0.859489\pi\) | |||||||
\(762\) | 16.0138 | + | 442.737i | 0.000761312 | + | 0.0210481i | ||||
\(763\) | −2340.08 | + | 2340.08i | −0.111031 | + | 0.111031i | ||||
\(764\) | −987.997 | − | 13639.8i | −0.0467860 | − | 0.645903i | ||||
\(765\) | 414.440 | + | 414.440i | 0.0195871 | + | 0.0195871i | ||||
\(766\) | 3148.43 | + | 2928.62i | 0.148508 | + | 0.138140i | ||||
\(767\) | 4461.34 | 0.210026 | ||||||||
\(768\) | 10806.3 | + | 5849.76i | 0.507731 | + | 0.274851i | ||||
\(769\) | 32224.0 | 1.51109 | 0.755544 | − | 0.655097i | \(-0.227372\pi\) | ||||
0.755544 | + | 0.655097i | \(0.227372\pi\) | |||||||
\(770\) | −485.264 | − | 451.386i | −0.0227113 | − | 0.0211257i | ||||
\(771\) | 10845.1 | + | 10845.1i | 0.506585 | + | 0.506585i | ||||
\(772\) | 1389.74 | + | 19186.0i | 0.0647900 | + | 0.894457i | ||||
\(773\) | 13719.5 | − | 13719.5i | 0.638365 | − | 0.638365i | −0.311787 | − | 0.950152i | \(-0.600928\pi\) |
0.950152 | + | 0.311787i | \(0.100928\pi\) | |||||||
\(774\) | −406.615 | − | 11241.7i | −0.0188830 | − | 0.522062i | ||||
\(775\) | − | 13386.2i | − | 0.620448i | ||||||
\(776\) | −22214.0 | + | 27642.9i | −1.02762 | + | 1.27877i | ||||
\(777\) | 5599.44i | 0.258531i | ||||||||
\(778\) | −32352.2 | + | 1170.18i | −1.49085 | + | 0.0539243i | ||||
\(779\) | 15710.9 | − | 15710.9i | 0.722596 | − | 0.722596i | ||||
\(780\) | 295.721 | − | 341.908i | 0.0135750 | − | 0.0156952i | ||||
\(781\) | −19967.5 | − | 19967.5i | −0.914842 | − | 0.914842i | ||||
\(782\) | 29139.2 | − | 31326.3i | 1.33250 | − | 1.43251i | ||||
\(783\) | −223.170 | −0.0101858 | ||||||||
\(784\) | −18494.9 | + | 2693.48i | −0.842514 | + | 0.122699i | ||||
\(785\) | 2242.20 | 0.101946 | ||||||||
\(786\) | 3170.79 | − | 3408.77i | 0.143891 | − | 0.154691i | ||||
\(787\) | −9919.72 | − | 9919.72i | −0.449301 | − | 0.449301i | 0.445821 | − | 0.895122i | \(-0.352912\pi\) |
−0.895122 | + | 0.445821i | \(0.852912\pi\) | |||||||
\(788\) | 23724.8 | + | 20519.9i | 1.07254 | + | 0.927654i | ||||
\(789\) | −11659.5 | + | 11659.5i | −0.526097 | + | 0.526097i | ||||
\(790\) | 1412.90 | − | 51.1049i | 0.0636315 | − | 0.00230156i | ||||
\(791\) | 9632.14i | 0.432970i | ||||||||
\(792\) | −7285.24 | + | 793.292i | −0.326856 | + | 0.0355914i | ||||
\(793\) | 15361.9i | 0.687915i | ||||||||
\(794\) | 1286.42 | + | 35565.8i | 0.0574978 | + | 1.58965i | ||||
\(795\) | −683.768 | + | 683.768i | −0.0305041 | + | 0.0305041i | ||||
\(796\) | −12023.7 | + | 870.935i | −0.535387 | + | 0.0387807i | ||||
\(797\) | −20018.0 | − | 20018.0i | −0.889679 | − | 0.889679i | 0.104813 | − | 0.994492i | \(-0.466576\pi\) |
−0.994492 | + | 0.104813i | \(0.966576\pi\) | |||||||
\(798\) | −2736.47 | − | 2545.42i | −0.121391 | − | 0.112916i | ||||
\(799\) | 24554.7 | 1.08721 | ||||||||
\(800\) | 12777.1 | − | 18492.0i | 0.564672 | − | 0.817240i | ||||
\(801\) | −2726.80 | −0.120283 | ||||||||
\(802\) | −8697.59 | − | 8090.37i | −0.382946 | − | 0.356211i | ||||
\(803\) | −20361.9 | − | 20361.9i | −0.894838 | − | 0.894838i | ||||
\(804\) | 1195.17 | − | 86.5719i | 0.0524257 | − | 0.00379746i | ||||
\(805\) | −975.392 | + | 975.392i | −0.0427056 | + | 0.0427056i | ||||
\(806\) | 227.622 | + | 6293.10i | 0.00994745 | + | 0.275019i | ||||
\(807\) | − | 10497.8i | − | 0.457917i | ||||||
\(808\) | 206.500 | + | 1896.40i | 0.00899089 | + | 0.0825683i | ||||
\(809\) | − | 9967.99i | − | 0.433196i | −0.976261 | − | 0.216598i | \(-0.930504\pi\) | ||
0.976261 | − | 0.216598i | \(-0.0694961\pi\) | |||||||
\(810\) | −208.818 | + | 7.55297i | −0.00905817 | + | 0.000327635i | ||||
\(811\) | 16080.2 | − | 16080.2i | 0.696243 | − | 0.696243i | −0.267355 | − | 0.963598i | \(-0.586150\pi\) |
0.963598 | + | 0.267355i | \(0.0861498\pi\) | |||||||
\(812\) | 357.055 | + | 308.822i | 0.0154312 | + | 0.0133467i | ||||
\(813\) | −3645.66 | − | 3645.66i | −0.157268 | − | 0.157268i | ||||
\(814\) | −18123.5 | + | 19483.8i | −0.780379 | + | 0.838950i | ||||
\(815\) | −3464.14 | −0.148888 | ||||||||
\(816\) | −10989.7 | − | 8195.69i | −0.471468 | − | 0.351601i | ||||
\(817\) | 27262.7 | 1.16744 | ||||||||
\(818\) | −15183.6 | + | 16323.3i | −0.649002 | + | 0.697713i | ||||
\(819\) | −938.290 | − | 938.290i | −0.0400324 | − | 0.0400324i | ||||
\(820\) | −1719.03 | + | 1987.51i | −0.0732086 | + | 0.0846426i | ||||
\(821\) | 8235.64 | − | 8235.64i | 0.350092 | − | 0.350092i | −0.510051 | − | 0.860144i | \(-0.670374\pi\) |
0.860144 | + | 0.510051i | \(0.170374\pi\) | |||||||
\(822\) | −6741.79 | + | 243.851i | −0.286067 | + | 0.0103471i | ||||
\(823\) | − | 21762.8i | − | 0.921752i | −0.887464 | − | 0.460876i | \(-0.847535\pi\) | ||
0.887464 | − | 0.460876i | \(-0.152465\pi\) | |||||||
\(824\) | −31088.6 | − | 24983.0i | −1.31435 | − | 1.05622i | ||||
\(825\) | 13404.7i | 0.565687i | ||||||||
\(826\) | 157.679 | + | 4359.37i | 0.00664208 | + | 0.183634i | ||||
\(827\) | −30211.4 | + | 30211.4i | −1.27032 | + | 1.27032i | −0.324396 | + | 0.945921i | \(0.605161\pi\) |
−0.945921 | + | 0.324396i | \(0.894839\pi\) | |||||||
\(828\) | 1101.95 | + | 15213.0i | 0.0462506 | + | 0.638512i | ||||
\(829\) | −16821.1 | − | 16821.1i | −0.704729 | − | 0.704729i | 0.260692 | − | 0.965422i | \(-0.416049\pi\) |
−0.965422 | + | 0.260692i | \(0.916049\pi\) | |||||||
\(830\) | 1240.61 | + | 1154.00i | 0.0518821 | + | 0.0482600i | ||||
\(831\) | −20036.7 | −0.836419 | ||||||||
\(832\) | −5692.29 | + | 8910.70i | −0.237193 | + | 0.371302i | ||||
\(833\) | 20851.7 | 0.867310 | ||||||||
\(834\) | 15013.4 | + | 13965.3i | 0.623348 | + | 0.579829i | ||||
\(835\) | 17.7435 | + | 17.7435i | 0.000735375 | + | 0.000735375i | ||||
\(836\) | −1283.12 | − | 17714.1i | −0.0530832 | − | 0.732840i | ||||
\(837\) | 2058.24 | − | 2058.24i | 0.0849979 | − | 0.0849979i | ||||
\(838\) | −795.612 | − | 21996.4i | −0.0327971 | − | 0.906746i | ||||
\(839\) | − | 21686.9i | − | 0.892389i | −0.894936 | − | 0.446194i | \(-0.852779\pi\) | ||
0.894936 | − | 0.446194i | \(-0.147221\pi\) | |||||||
\(840\) | 344.545 | + | 276.878i | 0.0141523 | + | 0.0113728i | ||||
\(841\) | − | 24320.7i | − | 0.997199i | ||||||
\(842\) | 45179.2 | − | 1634.14i | 1.84914 | − | 0.0668837i | ||||
\(843\) | −5394.95 | + | 5394.95i | −0.220418 | + | 0.220418i | ||||
\(844\) | 14544.8 | − | 16816.5i | 0.593191 | − | 0.685838i | ||||
\(845\) | −1141.84 | − | 1141.84i | −0.0464857 | − | 0.0464857i | ||||
\(846\) | −5962.25 | + | 6409.75i | −0.242301 | + | 0.260487i | ||||
\(847\) | 257.395 | 0.0104418 | ||||||||
\(848\) | 13521.7 | − | 18131.5i | 0.547568 | − | 0.734244i | ||||
\(849\) | −13605.4 | −0.549983 | ||||||||
\(850\) | −17079.3 | + | 18361.2i | −0.689193 | + | 0.740921i | ||||
\(851\) | 39162.8 | + | 39162.8i | 1.57754 | + | 1.57754i | ||||
\(852\) | 14244.3 | + | 12320.2i | 0.572774 | + | 0.495401i | ||||
\(853\) | 12612.5 | − | 12612.5i | 0.506266 | − | 0.506266i | −0.407112 | − | 0.913378i | \(-0.633464\pi\) |
0.913378 | + | 0.407112i | \(0.133464\pi\) | |||||||
\(854\) | −15010.8 | + | 542.941i | −0.601473 | + | 0.0217553i | ||||
\(855\) | − | 506.411i | − | 0.0202560i | ||||||
\(856\) | 2274.40 | + | 20887.1i | 0.0908147 | + | 0.834001i | ||||
\(857\) | − | 46080.3i | − | 1.83672i | −0.395741 | − | 0.918362i | \(-0.629512\pi\) | ||
0.395741 | − | 0.918362i | \(-0.370488\pi\) | |||||||
\(858\) | −227.937 | − | 6301.80i | −0.00906950 | − | 0.250746i | ||||
\(859\) | 8935.85 | − | 8935.85i | 0.354933 | − | 0.354933i | −0.507008 | − | 0.861941i | \(-0.669249\pi\) |
0.861941 | + | 0.507008i | \(0.169249\pi\) | |||||||
\(860\) | −3215.92 | + | 232.945i | −0.127514 | + | 0.00923647i | ||||
\(861\) | 5454.28 | + | 5454.28i | 0.215890 | + | 0.215890i | ||||
\(862\) | −11241.7 | − | 10456.9i | −0.444193 | − | 0.413182i | ||||
\(863\) | 19360.8 | 0.763674 | 0.381837 | − | 0.924230i | \(-0.375292\pi\) | ||||
0.381837 | + | 0.924230i | \(0.375292\pi\) | |||||||
\(864\) | 4807.88 | − | 878.722i | 0.189314 | − | 0.0346004i | ||||
\(865\) | 3927.40 | 0.154377 | ||||||||
\(866\) | −10652.7 | − | 9908.98i | −0.418006 | − | 0.388823i | ||||
\(867\) | 393.086 | + | 393.086i | 0.0153978 | + | 0.0153978i | ||||
\(868\) | −6141.22 | + | 444.839i | −0.240146 | + | 0.0173950i | ||||
\(869\) | 13945.7 | − | 13945.7i | 0.544391 | − | 0.544391i | ||||
\(870\) | 2.31220 | + | 63.9258i | 9.01046e−5 | + | 0.00249114i | ||||
\(871\) | 1031.12i | 0.0401128i | ||||||||
\(872\) | 10427.2 | − | 1135.42i | 0.404943 | − | 0.0440943i | ||||
\(873\) | 14105.1i | 0.546835i | ||||||||
\(874\) | −36941.8 | + | 1336.19i | −1.42972 | + | 0.0517132i | ||||
\(875\) | 1147.24 | − | 1147.24i | 0.0443242 | − | 0.0443242i | ||||
\(876\) | 14525.7 | + | 12563.5i | 0.560250 | + | 0.484568i | ||||
\(877\) | 19139.4 | + | 19139.4i | 0.736933 | + | 0.736933i | 0.971983 | − | 0.235050i | \(-0.0755254\pi\) |
−0.235050 | + | 0.971983i | \(0.575525\pi\) | |||||||
\(878\) | 4206.29 | − | 4521.99i | 0.161680 | − | 0.173815i | ||||
\(879\) | 25079.9 | 0.962372 | ||||||||
\(880\) | 302.715 | + | 2078.60i | 0.0115960 | + | 0.0796244i | ||||
\(881\) | 4836.79 | 0.184967 | 0.0924833 | − | 0.995714i | \(-0.470520\pi\) | ||||
0.0924833 | + | 0.995714i | \(0.470520\pi\) | |||||||
\(882\) | −5063.12 | + | 5443.13i | −0.193292 | + | 0.207800i | ||||
\(883\) | −7730.89 | − | 7730.89i | −0.294638 | − | 0.294638i | 0.544271 | − | 0.838909i | \(-0.316806\pi\) |
−0.838909 | + | 0.544271i | \(0.816806\pi\) | |||||||
\(884\) | 7717.06 | − | 8922.34i | 0.293612 | − | 0.339469i | ||||
\(885\) | −417.963 | + | 417.963i | −0.0158753 | + | 0.0158753i | ||||
\(886\) | 2245.81 | − | 81.2314i | 0.0851576 | − | 0.00308016i | ||||
\(887\) | − | 12163.5i | − | 0.460442i | −0.973138 | − | 0.230221i | \(-0.926055\pi\) | ||
0.973138 | − | 0.230221i | \(-0.0739448\pi\) | |||||||
\(888\) | 11116.9 | − | 13833.8i | 0.420110 | − | 0.522782i | ||||
\(889\) | − | 372.749i | − | 0.0140625i | ||||||
\(890\) | 28.2516 | + | 781.076i | 0.00106404 | + | 0.0294177i | ||||
\(891\) | −2061.09 | + | 2061.09i | −0.0774960 | + | 0.0774960i | ||||
\(892\) | 49.5818 | + | 684.501i | 0.00186112 | + | 0.0256937i | ||||
\(893\) | −15001.9 | − | 15001.9i | −0.562171 | − | 0.562171i | ||||
\(894\) | −611.801 | − | 569.088i | −0.0228878 | − | 0.0212899i | ||||
\(895\) | −471.835 | −0.0176220 | ||||||||
\(896\) | −8908.22 | − | 5247.25i | −0.332146 | − | 0.195645i | ||||
\(897\) | −13124.9 | −0.488548 | ||||||||
\(898\) | −5465.37 | − | 5083.80i | −0.203098 | − | 0.188918i | ||||
\(899\) | −630.093 | − | 630.093i | −0.0233757 | − | 0.0233757i | ||||
\(900\) | −645.884 | − | 8916.75i | −0.0239216 | − | 0.330250i | ||||
\(901\) | −17843.4 | + | 17843.4i | −0.659768 | + | 0.659768i | ||||
\(902\) | 1325.00 | + | 36632.4i | 0.0489108 | + | 1.35224i | ||||
\(903\) | 9464.65i | 0.348797i | ||||||||
\(904\) | 19123.2 | − | 23796.8i | 0.703572 | − | 0.875519i | ||||
\(905\) | 2240.59i | 0.0822981i | ||||||||
\(906\) | −13291.8 | + | 480.767i | −0.487408 | + | 0.0176296i | ||||
\(907\) | −8264.83 | + | 8264.83i | −0.302568 | + | 0.302568i | −0.842018 | − | 0.539450i | \(-0.818632\pi\) |
0.539450 | + | 0.842018i | \(0.318632\pi\) | |||||||
\(908\) | −18695.4 | + | 21615.3i | −0.683292 | + | 0.790011i | ||||
\(909\) | 536.516 | + | 536.516i | 0.0195766 | + | 0.0195766i | ||||
\(910\) | −259.047 | + | 278.489i | −0.00943661 | + | 0.0101449i | ||||
\(911\) | −41364.8 | −1.50437 | −0.752183 | − | 0.658955i | \(-0.770999\pi\) | ||||
−0.752183 | + | 0.658955i | \(0.770999\pi\) | |||||||
\(912\) | 1707.05 | + | 11721.5i | 0.0619803 | + | 0.425589i | ||||
\(913\) | 23635.3 | 0.856753 | ||||||||
\(914\) | 10685.1 | − | 11487.1i | 0.386688 | − | 0.415711i | ||||
\(915\) | −1439.18 | − | 1439.18i | −0.0519978 | − | 0.0519978i | ||||
\(916\) | −9555.20 | − | 8264.44i | −0.344665 | − | 0.298106i | ||||
\(917\) | −2769.74 | + | 2769.74i | −0.0997434 | + | 0.0997434i | ||||
\(918\) | −5449.26 | + | 197.100i | −0.195918 | + | 0.00708636i | ||||
\(919\) | 36966.7i | 1.32690i | 0.748221 | + | 0.663449i | \(0.230908\pi\) | ||||
−0.748221 | + | 0.663449i | \(0.769092\pi\) | |||||||
\(920\) | 4346.26 | − | 473.266i | 0.155752 | − | 0.0169599i | ||||
\(921\) | 4930.99i | 0.176419i | ||||||||
\(922\) | 1225.40 | + | 33878.8i | 0.0437704 | + | 1.21013i | ||||
\(923\) | −11459.2 | + | 11459.2i | −0.408649 | + | 0.408649i | ||||
\(924\) | 6149.70 | − | 445.454i | 0.218951 | − | 0.0158597i | ||||
\(925\) | −22954.4 | − | 22954.4i | −0.815929 | − | 0.815929i | ||||
\(926\) | −33986.1 | − | 31613.3i | −1.20610 | − | 1.12190i | ||||
\(927\) | −15863.3 | −0.562050 | ||||||||
\(928\) | −269.004 | − | 1471.84i | −0.00951563 | − | 0.0520643i | ||||
\(929\) | −18882.5 | −0.666862 | −0.333431 | − | 0.942774i | \(-0.608206\pi\) | ||||
−0.333431 | + | 0.942774i | \(0.608206\pi\) | |||||||
\(930\) | −610.897 | − | 568.247i | −0.0215399 | − | 0.0200361i | ||||
\(931\) | −12739.5 | − | 12739.5i | −0.448464 | − | 0.448464i | ||||
\(932\) | 45913.7 | − | 3325.76i | 1.61368 | − | 0.116887i | ||||
\(933\) | 5000.55 | − | 5000.55i | 0.175467 | − | 0.175467i | ||||
\(934\) | −967.211 | − | 26740.6i | −0.0338845 | − | 0.936810i | ||||
\(935\) | − | 2343.48i | − | 0.0819678i | ||||||
\(936\) | 455.264 | + | 4180.94i | 0.0158983 | + | 0.146002i | ||||
\(937\) | − | 8581.23i | − | 0.299185i | −0.988748 | − | 0.149593i | \(-0.952204\pi\) | ||
0.988748 | − | 0.149593i | \(-0.0477962\pi\) | |||||||
\(938\) | −1007.55 | + | 36.4433i | −0.0350723 | + | 0.00126857i | ||||
\(939\) | −8031.21 | + | 8031.21i | −0.279115 | + | 0.279115i | ||||
\(940\) | 1897.81 | + | 1641.45i | 0.0658508 | + | 0.0569554i | ||||
\(941\) | −5618.83 | − | 5618.83i | −0.194653 | − | 0.194653i | 0.603050 | − | 0.797703i | \(-0.293952\pi\) |
−0.797703 | + | 0.603050i | \(0.793952\pi\) | |||||||
\(942\) | −14207.6 | + | 15274.0i | −0.491411 | + | 0.528293i | ||||
\(943\) | 76295.1 | 2.63469 | ||||||||
\(944\) | 8265.35 | − | 11083.1i | 0.284973 | − | 0.382125i | ||||
\(945\) | 175.808 | 0.00605189 | ||||||||
\(946\) | −30633.9 | + | 32933.1i | −1.05285 | + | 1.13187i | ||||
\(947\) | 18722.7 | + | 18722.7i | 0.642456 | + | 0.642456i | 0.951159 | − | 0.308702i | \(-0.0998947\pi\) |
−0.308702 | + | 0.951159i | \(0.599895\pi\) | |||||||
\(948\) | −8604.67 | + | 9948.57i | −0.294796 | + | 0.340838i | ||||
\(949\) | −11685.5 | + | 11685.5i | −0.399713 | + | 0.399713i | ||||
\(950\) | 21652.6 | − | 783.177i | 0.739477 | − | 0.0267470i | ||||
\(951\) | − | 13302.8i | − | 0.453600i | ||||||
\(952\) | 8991.15 | + | 7225.33i | 0.306098 | + | 0.245981i | ||||
\(953\) | − | 17197.8i | − | 0.584565i | −0.956332 | − | 0.292282i | \(-0.905585\pi\) | ||
0.956332 | − | 0.292282i | \(-0.0944147\pi\) | |||||||
\(954\) | −325.188 | − | 8990.51i | −0.0110360 | − | 0.305114i | ||||
\(955\) | −1102.45 | + | 1102.45i | −0.0373556 | + | 0.0373556i | ||||
\(956\) | −370.929 | − | 5120.85i | −0.0125488 | − | 0.173243i | ||||
\(957\) | 630.963 | + | 630.963i | 0.0213126 | + | 0.0213126i | ||||
\(958\) | 14887.4 | + | 13848.0i | 0.502077 | + | 0.467025i | ||||
\(959\) | 5676.06 | 0.191126 | ||||||||
\(960\) | −301.518 | − | 1368.09i | −0.0101369 | − | 0.0459946i | ||||
\(961\) | −18168.6 | −0.609870 | ||||||||
\(962\) | 11181.6 | + | 10400.9i | 0.374749 | + | 0.348586i | ||||
\(963\) | 5909.21 | + | 5909.21i | 0.197738 | + | 0.197738i | ||||
\(964\) | −1668.84 | − | 23039.2i | −0.0557571 | − | 0.769754i | ||||
\(965\) | 1550.74 | − | 1550.74i | 0.0517306 | − | 0.0517306i | ||||
\(966\) | −463.879 | − | 12824.9i | −0.0154504 | − | 0.427158i | ||||
\(967\) | 58259.3i | 1.93743i | 0.248182 | + | 0.968713i | \(0.420167\pi\) | ||||
−0.248182 | + | 0.968713i | \(0.579833\pi\) | |||||||
\(968\) | −635.909 | − | 511.020i | −0.0211146 | − | 0.0169678i | ||||
\(969\) | − | 13215.2i | − | 0.438114i | ||||||
\(970\) | 4040.34 | − | 146.140i | 0.133740 | − | 0.00483738i | ||||
\(971\) | −19203.8 | + | 19203.8i | −0.634685 | + | 0.634685i | −0.949239 | − | 0.314555i | \(-0.898145\pi\) |
0.314555 | + | 0.949239i | \(0.398145\pi\) | |||||||
\(972\) | 1271.71 | − | 1470.33i | 0.0419653 | − | 0.0485195i | ||||
\(973\) | −12198.9 | − | 12198.9i | −0.401930 | − | 0.401930i | ||||
\(974\) | −21540.2 | + | 23156.9i | −0.708615 | + | 0.761800i | ||||
\(975\) | 7692.86 | 0.252686 | ||||||||
\(976\) | 38162.9 | + | 28460.3i | 1.25160 | + | 0.933394i | ||||
\(977\) | −16691.4 | −0.546578 | −0.273289 | − | 0.961932i | \(-0.588112\pi\) | ||||
−0.273289 | + | 0.961932i | \(0.588112\pi\) | |||||||
\(978\) | 21950.4 | − | 23597.8i | 0.717684 | − | 0.771550i | ||||
\(979\) | 7709.41 | + | 7709.41i | 0.251679 | + | 0.251679i | ||||
\(980\) | 1611.61 | + | 1393.91i | 0.0525317 | + | 0.0454354i | ||||
\(981\) | 2949.99 | − | 2949.99i | 0.0960101 | − | 0.0960101i | ||||
\(982\) | 46688.6 | − | 1688.73i | 1.51720 | − | 0.0548774i | ||||
\(983\) | 36043.6i | 1.16949i | 0.811216 | + | 0.584747i | \(0.198806\pi\) | ||||
−0.811216 | + | 0.584747i | \(0.801194\pi\) | |||||||
\(984\) | −2646.45 | − | 24303.8i | −0.0857376 | − | 0.787376i | ||||
\(985\) | − | 3576.14i | − | 0.115680i | ||||||
\(986\) | 60.3387 | + | 1668.19i | 0.00194886 | + | 0.0538804i | ||||
\(987\) | 5208.12 | − | 5208.12i | 0.167960 | − | 0.167960i | ||||
\(988\) | −10166.0 | + | 736.371i | −0.327351 | + | 0.0237116i | ||||
\(989\) | 66196.3 | + | 66196.3i | 2.12833 | + | 2.12833i | ||||
\(990\) | 611.741 | + | 569.032i | 0.0196388 | + | 0.0182677i | ||||
\(991\) | −48948.9 | −1.56904 | −0.784518 | − | 0.620107i | \(-0.787089\pi\) | ||||
−0.784518 | + | 0.620107i | \(0.787089\pi\) | |||||||
\(992\) | 16055.4 | + | 11093.5i | 0.513871 | + | 0.355059i | ||||
\(993\) | −7357.23 | −0.235120 | ||||||||
\(994\) | −11602.3 | − | 10792.2i | −0.370222 | − | 0.344375i | ||||
\(995\) | 971.831 | + | 971.831i | 0.0309639 | + | 0.0309639i | ||||
\(996\) | −15722.1 | + | 1138.83i | −0.500175 | + | 0.0362301i | ||||
\(997\) | −22542.1 | + | 22542.1i | −0.716062 | + | 0.716062i | −0.967796 | − | 0.251734i | \(-0.918999\pi\) |
0.251734 | + | 0.967796i | \(0.418999\pi\) | |||||||
\(998\) | −302.800 | − | 8371.56i | −0.00960418 | − | 0.265528i | ||||
\(999\) | − | 7058.84i | − | 0.223556i |
(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 | 48.4.j.a.13.10 | ✓ | 24 | |
3.2 | odd | 2 | 144.4.k.b.109.3 | 24 | |||
4.3 | odd | 2 | 192.4.j.a.145.3 | 24 | |||
8.3 | odd | 2 | 384.4.j.a.289.9 | 24 | |||
8.5 | even | 2 | 384.4.j.b.289.4 | 24 | |||
12.11 | even | 2 | 576.4.k.b.145.7 | 24 | |||
16.3 | odd | 4 | 384.4.j.a.97.9 | 24 | |||
16.5 | even | 4 | inner | 48.4.j.a.37.10 | yes | 24 | |
16.11 | odd | 4 | 192.4.j.a.49.3 | 24 | |||
16.13 | even | 4 | 384.4.j.b.97.4 | 24 | |||
48.5 | odd | 4 | 144.4.k.b.37.3 | 24 | |||
48.11 | even | 4 | 576.4.k.b.433.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.4.j.a.13.10 | ✓ | 24 | 1.1 | even | 1 | trivial | |
48.4.j.a.37.10 | yes | 24 | 16.5 | even | 4 | inner | |
144.4.k.b.37.3 | 24 | 48.5 | odd | 4 | |||
144.4.k.b.109.3 | 24 | 3.2 | odd | 2 | |||
192.4.j.a.49.3 | 24 | 16.11 | odd | 4 | |||
192.4.j.a.145.3 | 24 | 4.3 | odd | 2 | |||
384.4.j.a.97.9 | 24 | 16.3 | odd | 4 | |||
384.4.j.a.289.9 | 24 | 8.3 | odd | 2 | |||
384.4.j.b.97.4 | 24 | 16.13 | even | 4 | |||
384.4.j.b.289.4 | 24 | 8.5 | even | 2 | |||
576.4.k.b.145.7 | 24 | 12.11 | even | 2 | |||
576.4.k.b.433.7 | 24 | 48.11 | even | 4 |