Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(27,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.27");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.f (of order \(6\), 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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 27.11 | ||
Character | \(\chi\) | \(=\) | 76.27 |
Dual form | 76.4.f.a.31.11 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.06422 | + | 2.62058i | −0.376258 | + | 0.926515i | ||||
\(3\) | 1.31663 | − | 2.28047i | 0.253386 | − | 0.438877i | −0.711070 | − | 0.703121i | \(-0.751789\pi\) |
0.964456 | + | 0.264244i | \(0.0851225\pi\) | |||||||
\(4\) | −5.73488 | − | 5.57774i | −0.716860 | − | 0.697217i | ||||
\(5\) | 1.30962 | − | 2.26832i | 0.117136 | − | 0.202885i | −0.801496 | − | 0.598000i | \(-0.795962\pi\) |
0.918631 | + | 0.395116i | \(0.129295\pi\) | |||||||
\(6\) | 4.57498 | + | 5.87726i | 0.311288 | + | 0.399897i | ||||
\(7\) | 35.2043i | 1.90085i | 0.310946 | + | 0.950427i | \(0.399354\pi\) | ||||
−0.310946 | + | 0.950427i | \(0.600646\pi\) | |||||||
\(8\) | 20.7201 | − | 9.09277i | 0.915707 | − | 0.401848i | ||||
\(9\) | 10.0330 | + | 17.3776i | 0.371591 | + | 0.643615i | ||||
\(10\) | 4.55060 | + | 5.84595i | 0.143903 | + | 0.184865i | ||||
\(11\) | 32.2909i | 0.885098i | 0.896744 | + | 0.442549i | \(0.145926\pi\) | ||||
−0.896744 | + | 0.442549i | \(0.854074\pi\) | |||||||
\(12\) | −20.2706 | + | 5.73440i | −0.487635 | + | 0.137948i | ||||
\(13\) | 26.0944 | − | 15.0656i | 0.556715 | − | 0.321419i | −0.195111 | − | 0.980781i | \(-0.562507\pi\) |
0.751826 | + | 0.659362i | \(0.229173\pi\) | |||||||
\(14\) | −92.2557 | − | 37.4651i | −1.76117 | − | 0.715212i | ||||
\(15\) | −3.44856 | − | 5.97309i | −0.0593610 | − | 0.102816i | ||||
\(16\) | 1.77765 | + | 63.9753i | 0.0277757 | + | 0.999614i | ||||
\(17\) | −20.9363 | + | 36.2627i | −0.298694 | + | 0.517353i | −0.975837 | − | 0.218498i | \(-0.929884\pi\) |
0.677143 | + | 0.735851i | \(0.263218\pi\) | |||||||
\(18\) | −56.2167 | + | 7.79862i | −0.736133 | + | 0.102120i | ||||
\(19\) | −30.4503 | − | 77.0180i | −0.367672 | − | 0.929955i | ||||
\(20\) | −20.1626 | + | 5.70385i | −0.225425 | + | 0.0637710i | ||||
\(21\) | 80.2825 | + | 46.3511i | 0.834242 | + | 0.481650i | ||||
\(22\) | −84.6210 | − | 34.3646i | −0.820057 | − | 0.333025i | ||||
\(23\) | 8.26291 | − | 4.77060i | 0.0749103 | − | 0.0432495i | −0.462077 | − | 0.886840i | \(-0.652896\pi\) |
0.536987 | + | 0.843590i | \(0.319562\pi\) | |||||||
\(24\) | 6.54489 | − | 59.2234i | 0.0556654 | − | 0.503705i | ||||
\(25\) | 59.0698 | + | 102.312i | 0.472558 | + | 0.818495i | ||||
\(26\) | 11.7105 | + | 84.4156i | 0.0883314 | + | 0.636741i | ||||
\(27\) | 123.937 | 0.883395 | ||||||||
\(28\) | 196.361 | − | 201.893i | 1.32531 | − | 1.36265i | ||||
\(29\) | 86.5617 | − | 49.9764i | 0.554280 | − | 0.320014i | −0.196567 | − | 0.980490i | \(-0.562979\pi\) |
0.750846 | + | 0.660477i | \(0.229646\pi\) | |||||||
\(30\) | 19.3230 | − | 2.68057i | 0.117596 | − | 0.0163134i | ||||
\(31\) | −206.646 | −1.19725 | −0.598624 | − | 0.801030i | \(-0.704286\pi\) | ||||
−0.598624 | + | 0.801030i | \(0.704286\pi\) | |||||||
\(32\) | −169.544 | − | 63.4252i | −0.936608 | − | 0.350378i | ||||
\(33\) | 73.6386 | + | 42.5153i | 0.388449 | + | 0.224271i | ||||
\(34\) | −72.7486 | − | 93.4567i | −0.366949 | − | 0.471403i | ||||
\(35\) | 79.8548 | + | 46.1042i | 0.385655 | + | 0.222658i | ||||
\(36\) | 39.3899 | − | 155.620i | 0.182361 | − | 0.720462i | ||||
\(37\) | − | 331.881i | − | 1.47462i | −0.675554 | − | 0.737311i | \(-0.736095\pi\) | ||
0.675554 | − | 0.737311i | \(-0.263905\pi\) | |||||||
\(38\) | 234.238 | + | 2.16660i | 0.999957 | + | 0.00924917i | ||||
\(39\) | − | 79.3435i | − | 0.325772i | ||||||
\(40\) | 6.51002 | − | 58.9079i | 0.0257331 | − | 0.232854i | ||||
\(41\) | 381.777 | + | 220.419i | 1.45423 | + | 0.839602i | 0.998718 | − | 0.0506255i | \(-0.0161215\pi\) |
0.455516 | + | 0.890228i | \(0.349455\pi\) | |||||||
\(42\) | −206.905 | + | 161.059i | −0.760146 | + | 0.591713i | ||||
\(43\) | −171.539 | − | 99.0381i | −0.608359 | − | 0.351237i | 0.163964 | − | 0.986466i | \(-0.447572\pi\) |
−0.772323 | + | 0.635230i | \(0.780905\pi\) | |||||||
\(44\) | 180.110 | − | 185.185i | 0.617106 | − | 0.634491i | ||||
\(45\) | 52.5573 | 0.174106 | ||||||||
\(46\) | 3.70818 | + | 26.7306i | 0.0118857 | + | 0.0856785i | ||||
\(47\) | 307.009 | − | 177.252i | 0.952806 | − | 0.550103i | 0.0588545 | − | 0.998267i | \(-0.481255\pi\) |
0.893951 | + | 0.448164i | \(0.147922\pi\) | |||||||
\(48\) | 148.234 | + | 80.1780i | 0.445746 | + | 0.241098i | ||||
\(49\) | −896.345 | −2.61325 | ||||||||
\(50\) | −330.980 | + | 45.9149i | −0.936152 | + | 0.129867i | ||||
\(51\) | 55.1307 | + | 95.4893i | 0.151370 | + | 0.262180i | ||||
\(52\) | −233.680 | − | 59.1484i | −0.623185 | − | 0.157739i | ||||
\(53\) | −222.337 | + | 128.366i | −0.576232 | + | 0.332687i | −0.759634 | − | 0.650350i | \(-0.774622\pi\) |
0.183403 | + | 0.983038i | \(0.441289\pi\) | |||||||
\(54\) | −131.896 | + | 324.787i | −0.332385 | + | 0.818479i | ||||
\(55\) | 73.2462 | + | 42.2887i | 0.179573 | + | 0.103677i | ||||
\(56\) | 320.105 | + | 729.436i | 0.763854 | + | 1.74063i | ||||
\(57\) | −215.729 | − | 31.9633i | −0.501299 | − | 0.0742745i | ||||
\(58\) | 38.8467 | + | 280.028i | 0.0879451 | + | 0.633956i | ||||
\(59\) | −98.1433 | + | 169.989i | −0.216562 | + | 0.375097i | −0.953755 | − | 0.300586i | \(-0.902818\pi\) |
0.737193 | + | 0.675683i | \(0.236151\pi\) | |||||||
\(60\) | −13.5392 | + | 53.4901i | −0.0291318 | + | 0.115092i | ||||
\(61\) | −91.8624 | − | 159.110i | −0.192816 | − | 0.333967i | 0.753366 | − | 0.657601i | \(-0.228429\pi\) |
−0.946182 | + | 0.323634i | \(0.895095\pi\) | |||||||
\(62\) | 219.916 | − | 541.532i | 0.450474 | − | 1.10927i | ||||
\(63\) | −611.767 | + | 353.204i | −1.22342 | + | 0.706341i | ||||
\(64\) | 346.643 | − | 376.806i | 0.677037 | − | 0.735949i | ||||
\(65\) | − | 78.9207i | − | 0.150599i | ||||||
\(66\) | −189.782 | + | 147.730i | −0.353948 | + | 0.275520i | ||||
\(67\) | 244.352 | + | 423.230i | 0.445557 | + | 0.771728i | 0.998091 | − | 0.0617627i | \(-0.0196722\pi\) |
−0.552534 | + | 0.833491i | \(0.686339\pi\) | |||||||
\(68\) | 322.331 | − | 91.1851i | 0.574829 | − | 0.162615i | ||||
\(69\) | − | 25.1245i | − | 0.0438352i | ||||||
\(70\) | −205.803 | + | 160.201i | −0.351402 | + | 0.273538i | ||||
\(71\) | −8.58821 | + | 14.8752i | −0.0143554 | + | 0.0248643i | −0.873114 | − | 0.487516i | \(-0.837903\pi\) |
0.858758 | + | 0.512381i | \(0.171236\pi\) | |||||||
\(72\) | 365.894 | + | 268.838i | 0.598904 | + | 0.440039i | ||||
\(73\) | 446.746 | − | 773.787i | 0.716270 | − | 1.24062i | −0.246198 | − | 0.969220i | \(-0.579181\pi\) |
0.962468 | − | 0.271396i | \(-0.0874853\pi\) | |||||||
\(74\) | 869.722 | + | 353.194i | 1.36626 | + | 0.554838i | ||||
\(75\) | 311.093 | 0.478958 | ||||||||
\(76\) | −254.958 | + | 611.533i | −0.384811 | + | 0.922995i | ||||
\(77\) | −1136.78 | −1.68244 | ||||||||
\(78\) | 207.926 | + | 84.4388i | 0.301833 | + | 0.122574i | ||||
\(79\) | 238.810 | − | 413.631i | 0.340104 | − | 0.589078i | −0.644348 | − | 0.764733i | \(-0.722871\pi\) |
0.984452 | + | 0.175655i | \(0.0562043\pi\) | |||||||
\(80\) | 147.445 | + | 79.7508i | 0.206060 | + | 0.111455i | ||||
\(81\) | −107.711 | + | 186.561i | −0.147751 | + | 0.255913i | ||||
\(82\) | −983.920 | + | 765.903i | −1.32507 | + | 1.03146i | ||||
\(83\) | − | 1052.05i | − | 1.39129i | −0.718385 | − | 0.695645i | \(-0.755119\pi\) | ||
0.718385 | − | 0.695645i | \(-0.244881\pi\) | |||||||
\(84\) | −201.876 | − | 713.613i | −0.262220 | − | 0.926923i | ||||
\(85\) | 54.8370 | + | 94.9805i | 0.0699754 | + | 0.121201i | ||||
\(86\) | 442.092 | − | 344.134i | 0.554326 | − | 0.431499i | ||||
\(87\) | − | 263.202i | − | 0.324348i | ||||||
\(88\) | 293.614 | + | 669.071i | 0.355675 | + | 0.810491i | ||||
\(89\) | 913.712 | − | 527.532i | 1.08824 | − | 0.628295i | 0.155132 | − | 0.987894i | \(-0.450420\pi\) |
0.933107 | + | 0.359599i | \(0.117086\pi\) | |||||||
\(90\) | −55.9325 | + | 137.731i | −0.0655089 | + | 0.161312i | ||||
\(91\) | 530.375 | + | 918.636i | 0.610971 | + | 1.05823i | ||||
\(92\) | −73.9959 | − | 18.7296i | −0.0838545 | − | 0.0212250i | ||||
\(93\) | −272.077 | + | 471.250i | −0.303366 | + | 0.525445i | ||||
\(94\) | 137.778 | + | 993.176i | 0.151177 | + | 1.08977i | ||||
\(95\) | −214.580 | − | 31.7930i | −0.231741 | − | 0.0343357i | ||||
\(96\) | −367.867 | + | 303.133i | −0.391096 | + | 0.322275i | ||||
\(97\) | −539.875 | − | 311.697i | −0.565114 | − | 0.326269i | 0.190082 | − | 0.981768i | \(-0.439125\pi\) |
−0.755195 | + | 0.655500i | \(0.772458\pi\) | |||||||
\(98\) | 953.906 | − | 2348.94i | 0.983256 | − | 2.42121i | ||||
\(99\) | −561.139 | + | 323.974i | −0.569663 | + | 0.328895i | ||||
\(100\) | 231.911 | − | 916.222i | 0.231911 | − | 0.916222i | ||||
\(101\) | 357.544 | + | 619.284i | 0.352247 | + | 0.610110i | 0.986643 | − | 0.162899i | \(-0.0520844\pi\) |
−0.634396 | + | 0.773008i | \(0.718751\pi\) | |||||||
\(102\) | −308.908 | + | 42.8531i | −0.299868 | + | 0.0415989i | ||||
\(103\) | −679.001 | −0.649553 | −0.324776 | − | 0.945791i | \(-0.605289\pi\) | ||||
−0.324776 | + | 0.945791i | \(0.605289\pi\) | |||||||
\(104\) | 403.690 | − | 549.431i | 0.380626 | − | 0.518040i | ||||
\(105\) | 210.279 | − | 121.404i | 0.195439 | − | 0.112837i | ||||
\(106\) | −99.7789 | − | 719.260i | −0.0914281 | − | 0.659064i | ||||
\(107\) | 994.602 | 0.898615 | 0.449308 | − | 0.893377i | \(-0.351671\pi\) | ||||
0.449308 | + | 0.893377i | \(0.351671\pi\) | |||||||
\(108\) | −710.763 | − | 691.288i | −0.633271 | − | 0.615919i | ||||
\(109\) | −61.9040 | − | 35.7403i | −0.0543975 | − | 0.0314064i | 0.472555 | − | 0.881301i | \(-0.343332\pi\) |
−0.526952 | + | 0.849895i | \(0.676665\pi\) | |||||||
\(110\) | −188.771 | + | 146.943i | −0.163624 | + | 0.127368i | ||||
\(111\) | −756.847 | − | 436.966i | −0.647177 | − | 0.373648i | ||||
\(112\) | −2252.21 | + | 62.5808i | −1.90012 | + | 0.0527976i | ||||
\(113\) | 942.349i | 0.784502i | 0.919858 | + | 0.392251i | \(0.128304\pi\) | ||||
−0.919858 | + | 0.392251i | \(0.871696\pi\) | |||||||
\(114\) | 313.346 | − | 531.320i | 0.257434 | − | 0.436515i | ||||
\(115\) | − | 24.9906i | − | 0.0202642i | ||||||
\(116\) | −775.177 | − | 196.210i | −0.620460 | − | 0.157049i | ||||
\(117\) | 523.609 | + | 302.306i | 0.413741 | + | 0.238873i | ||||
\(118\) | −341.024 | − | 438.098i | −0.266049 | − | 0.341781i | ||||
\(119\) | −1276.60 | − | 737.048i | −0.983413 | − | 0.567774i | ||||
\(120\) | −125.766 | − | 92.4058i | −0.0956738 | − | 0.0702955i | ||||
\(121\) | 288.296 | 0.216601 | ||||||||
\(122\) | 514.723 | − | 71.4046i | 0.381974 | − | 0.0529891i | ||||
\(123\) | 1005.32 | − | 580.421i | 0.736964 | − | 0.425487i | ||||
\(124\) | 1185.09 | + | 1152.62i | 0.858259 | + | 0.834743i | ||||
\(125\) | 636.839 | 0.455685 | ||||||||
\(126\) | −274.545 | − | 1979.07i | −0.194114 | − | 1.39928i | ||||
\(127\) | −360.705 | − | 624.760i | −0.252027 | − | 0.436523i | 0.712057 | − | 0.702122i | \(-0.247764\pi\) |
−0.964084 | + | 0.265598i | \(0.914430\pi\) | |||||||
\(128\) | 618.546 | + | 1309.41i | 0.427127 | + | 0.904192i | ||||
\(129\) | −451.707 | + | 260.793i | −0.308299 | + | 0.177997i | ||||
\(130\) | 206.818 | + | 83.9889i | 0.139532 | + | 0.0566640i | ||||
\(131\) | 1366.91 | + | 789.184i | 0.911658 | + | 0.526346i | 0.880964 | − | 0.473183i | \(-0.156895\pi\) |
0.0306936 | + | 0.999529i | \(0.490228\pi\) | |||||||
\(132\) | −185.169 | − | 654.557i | −0.122098 | − | 0.431605i | ||||
\(133\) | 2711.37 | − | 1071.98i | 1.76771 | − | 0.698892i | ||||
\(134\) | −1369.15 | + | 189.935i | −0.882662 | + | 0.122447i | ||||
\(135\) | 162.310 | − | 281.129i | 0.103477 | − | 0.179228i | ||||
\(136\) | −104.073 | + | 941.735i | −0.0656190 | + | 0.593773i | ||||
\(137\) | 1257.28 | + | 2177.67i | 0.784064 | + | 1.35804i | 0.929557 | + | 0.368679i | \(0.120190\pi\) |
−0.145493 | + | 0.989359i | \(0.546477\pi\) | |||||||
\(138\) | 65.8407 | + | 26.7379i | 0.0406140 | + | 0.0164934i | ||||
\(139\) | 563.163 | − | 325.142i | 0.343647 | − | 0.198404i | −0.318237 | − | 0.948011i | \(-0.603091\pi\) |
0.661883 | + | 0.749607i | \(0.269757\pi\) | |||||||
\(140\) | −200.800 | − | 709.811i | −0.121219 | − | 0.428500i | ||||
\(141\) | − | 933.501i | − | 0.557553i | ||||||
\(142\) | −29.8420 | − | 38.3366i | −0.0176358 | − | 0.0226559i | ||||
\(143\) | 486.483 | + | 842.613i | 0.284488 | + | 0.492747i | ||||
\(144\) | −1093.90 | + | 672.753i | −0.633045 | + | 0.389325i | ||||
\(145\) | − | 261.800i | − | 0.149940i | ||||||
\(146\) | 1552.34 | + | 1994.21i | 0.879946 | + | 1.13043i | ||||
\(147\) | −1180.16 | + | 2044.09i | −0.662160 | + | 1.14690i | ||||
\(148\) | −1851.15 | + | 1903.30i | −1.02813 | + | 1.05710i | ||||
\(149\) | −582.601 | + | 1009.09i | −0.320326 | + | 0.554821i | −0.980555 | − | 0.196243i | \(-0.937126\pi\) |
0.660229 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(150\) | −331.071 | + | 815.243i | −0.180212 | + | 0.443762i | ||||
\(151\) | −530.292 | −0.285792 | −0.142896 | − | 0.989738i | \(-0.545641\pi\) | ||||
−0.142896 | + | 0.989738i | \(0.545641\pi\) | |||||||
\(152\) | −1331.24 | − | 1318.94i | −0.710380 | − | 0.703818i | ||||
\(153\) | −840.212 | −0.443968 | ||||||||
\(154\) | 1209.78 | − | 2979.02i | 0.633033 | − | 1.55881i | ||||
\(155\) | −270.627 | + | 468.740i | −0.140241 | + | 0.242904i | ||||
\(156\) | −442.557 | + | 455.025i | −0.227134 | + | 0.233533i | ||||
\(157\) | 830.276 | − | 1438.08i | 0.422059 | − | 0.731027i | −0.574082 | − | 0.818798i | \(-0.694641\pi\) |
0.996141 | + | 0.0877705i | \(0.0279742\pi\) | |||||||
\(158\) | 829.808 | + | 1066.02i | 0.417822 | + | 0.536757i | ||||
\(159\) | 676.043i | 0.337193i | ||||||||
\(160\) | −365.907 | + | 301.518i | −0.180797 | + | 0.148982i | ||||
\(161\) | 167.946 | + | 290.890i | 0.0822110 | + | 0.142394i | ||||
\(162\) | −374.269 | − | 480.806i | −0.181515 | − | 0.233183i | ||||
\(163\) | 1891.17i | 0.908759i | 0.890808 | + | 0.454380i | \(0.150139\pi\) | ||||
−0.890808 | + | 0.454380i | \(0.849861\pi\) | |||||||
\(164\) | −960.005 | − | 3393.53i | −0.457096 | − | 1.61579i | ||||
\(165\) | 192.877 | − | 111.357i | 0.0910026 | − | 0.0525404i | ||||
\(166\) | 2756.97 | + | 1119.61i | 1.28905 | + | 0.523484i | ||||
\(167\) | −565.274 | − | 979.083i | −0.261929 | − | 0.453675i | 0.704825 | − | 0.709381i | \(-0.251025\pi\) |
−0.966755 | + | 0.255706i | \(0.917692\pi\) | |||||||
\(168\) | 2084.92 | + | 230.408i | 0.957470 | + | 0.105812i | ||||
\(169\) | −644.554 | + | 1116.40i | −0.293379 | + | 0.508148i | ||||
\(170\) | −307.263 | + | 42.6248i | −0.138623 | + | 0.0192304i | ||||
\(171\) | 1032.88 | − | 1301.87i | 0.461909 | − | 0.582203i | ||||
\(172\) | 431.347 | + | 1524.77i | 0.191220 | + | 0.675946i | ||||
\(173\) | −1814.27 | − | 1047.47i | −0.797321 | − | 0.460334i | 0.0452123 | − | 0.998977i | \(-0.485604\pi\) |
−0.842534 | + | 0.538644i | \(0.818937\pi\) | |||||||
\(174\) | 689.742 | + | 280.105i | 0.300513 | + | 0.122038i | ||||
\(175\) | −3601.82 | + | 2079.51i | −1.55584 | + | 0.898265i | ||||
\(176\) | −2065.82 | + | 57.4018i | −0.884757 | + | 0.0245842i | ||||
\(177\) | 258.437 | + | 447.626i | 0.109748 | + | 0.190088i | ||||
\(178\) | 410.050 | + | 2955.86i | 0.172666 | + | 1.24467i | ||||
\(179\) | 4391.92 | 1.83390 | 0.916949 | − | 0.399005i | \(-0.130644\pi\) | ||||
0.916949 | + | 0.399005i | \(0.130644\pi\) | |||||||
\(180\) | −301.410 | − | 293.151i | −0.124810 | − | 0.121390i | ||||
\(181\) | 1382.34 | − | 798.092i | 0.567669 | − | 0.327744i | −0.188549 | − | 0.982064i | \(-0.560378\pi\) |
0.756218 | + | 0.654320i | \(0.227045\pi\) | |||||||
\(182\) | −2971.79 | + | 412.260i | −1.21035 | + | 0.167905i | ||||
\(183\) | −483.796 | −0.195427 | ||||||||
\(184\) | 127.830 | − | 173.980i | 0.0512161 | − | 0.0697063i | ||||
\(185\) | −752.814 | − | 434.637i | −0.299178 | − | 0.172731i | ||||
\(186\) | −945.400 | − | 1214.51i | −0.372689 | − | 0.478776i | ||||
\(187\) | −1170.96 | − | 676.052i | −0.457908 | − | 0.264374i | ||||
\(188\) | −2749.32 | − | 695.899i | −1.06657 | − | 0.269966i | ||||
\(189\) | 4363.12i | 1.67921i | ||||||||
\(190\) | 311.676 | − | 528.489i | 0.119007 | − | 0.201793i | ||||
\(191\) | − | 3703.48i | − | 1.40301i | −0.712666 | − | 0.701504i | \(-0.752512\pi\) | ||
0.712666 | − | 0.701504i | \(-0.247488\pi\) | |||||||
\(192\) | −402.894 | − | 1286.62i | −0.151439 | − | 0.483615i | ||||
\(193\) | −3959.29 | − | 2285.90i | −1.47666 | − | 0.852551i | −0.477009 | − | 0.878898i | \(-0.658279\pi\) |
−0.999653 | + | 0.0263470i | \(0.991613\pi\) | |||||||
\(194\) | 1391.37 | − | 1083.07i | 0.514921 | − | 0.400825i | ||||
\(195\) | −179.977 | − | 103.910i | −0.0660943 | − | 0.0381596i | ||||
\(196\) | 5140.43 | + | 4999.58i | 1.87333 | + | 1.82200i | ||||
\(197\) | −4968.15 | −1.79678 | −0.898391 | − | 0.439196i | \(-0.855263\pi\) | ||||
−0.898391 | + | 0.439196i | \(0.855263\pi\) | |||||||
\(198\) | −251.825 | − | 1815.29i | −0.0903858 | − | 0.651550i | ||||
\(199\) | 1176.93 | − | 679.500i | 0.419247 | − | 0.242053i | −0.275508 | − | 0.961299i | \(-0.588846\pi\) |
0.694755 | + | 0.719246i | \(0.255513\pi\) | |||||||
\(200\) | 2154.23 | + | 1582.80i | 0.761635 | + | 0.559605i | ||||
\(201\) | 1286.89 | 0.451592 | ||||||||
\(202\) | −2003.39 | + | 277.919i | −0.697811 | + | 0.0968034i | ||||
\(203\) | 1759.39 | + | 3047.35i | 0.608299 | + | 1.05361i | ||||
\(204\) | 216.446 | − | 855.124i | 0.0742856 | − | 0.293484i | ||||
\(205\) | 999.963 | − | 577.329i | 0.340685 | − | 0.196695i | ||||
\(206\) | 722.605 | − | 1779.38i | 0.244400 | − | 0.601820i | ||||
\(207\) | 165.803 | + | 95.7264i | 0.0556720 | + | 0.0321423i | ||||
\(208\) | 1010.21 | + | 1642.62i | 0.336758 | + | 0.547572i | ||||
\(209\) | 2486.98 | − | 983.269i | 0.823102 | − | 0.325426i | ||||
\(210\) | 94.3675 | + | 680.252i | 0.0310094 | + | 0.223533i | ||||
\(211\) | 847.638 | − | 1468.15i | 0.276558 | − | 0.479013i | −0.693969 | − | 0.720005i | \(-0.744139\pi\) |
0.970527 | + | 0.240992i | \(0.0774728\pi\) | |||||||
\(212\) | 1991.07 | + | 503.972i | 0.645033 | + | 0.163268i | ||||
\(213\) | 22.6150 | + | 39.1704i | 0.00727491 | + | 0.0126005i | ||||
\(214\) | −1058.47 | + | 2606.43i | −0.338111 | + | 0.832580i | ||||
\(215\) | −449.301 | + | 259.404i | −0.142521 | + | 0.0822846i | ||||
\(216\) | 2567.98 | − | 1126.93i | 0.808931 | − | 0.354990i | ||||
\(217\) | − | 7274.83i | − | 2.27580i | ||||||
\(218\) | 159.540 | − | 124.189i | 0.0495660 | − | 0.0385832i | ||||
\(219\) | −1176.40 | − | 2037.58i | −0.362985 | − | 0.628709i | ||||
\(220\) | −184.183 | − | 651.069i | −0.0564436 | − | 0.199523i | ||||
\(221\) | 1261.67i | 0.384024i | ||||||||
\(222\) | 1950.55 | − | 1518.35i | 0.589696 | − | 0.459031i | ||||
\(223\) | 1675.00 | − | 2901.19i | 0.502988 | − | 0.871201i | −0.497006 | − | 0.867747i | \(-0.665567\pi\) |
0.999994 | − | 0.00345375i | \(-0.00109936\pi\) | |||||||
\(224\) | 2232.84 | − | 5968.69i | 0.666018 | − | 1.78036i | ||||
\(225\) | −1185.29 | + | 2052.98i | −0.351197 | + | 0.608291i | ||||
\(226\) | −2469.50 | − | 1002.86i | −0.726853 | − | 0.295175i | ||||
\(227\) | −5033.12 | −1.47163 | −0.735815 | − | 0.677183i | \(-0.763201\pi\) | ||||
−0.735815 | + | 0.677183i | \(0.763201\pi\) | |||||||
\(228\) | 1058.90 | + | 1386.59i | 0.307576 | + | 0.402759i | ||||
\(229\) | −1770.13 | −0.510801 | −0.255401 | − | 0.966835i | \(-0.582207\pi\) | ||||
−0.255401 | + | 0.966835i | \(0.582207\pi\) | |||||||
\(230\) | 65.4899 | + | 26.5955i | 0.0187751 | + | 0.00762458i | ||||
\(231\) | −1496.72 | + | 2592.40i | −0.426307 | + | 0.738386i | ||||
\(232\) | 1339.14 | − | 1822.60i | 0.378961 | − | 0.515774i | ||||
\(233\) | 680.871 | − | 1179.30i | 0.191439 | − | 0.331582i | −0.754288 | − | 0.656543i | \(-0.772018\pi\) |
0.945727 | + | 0.324961i | \(0.105351\pi\) | |||||||
\(234\) | −1349.45 | + | 1050.44i | −0.376993 | + | 0.293459i | ||||
\(235\) | − | 928.527i | − | 0.257747i | ||||||
\(236\) | 1510.99 | − | 427.449i | 0.416769 | − | 0.117901i | ||||
\(237\) | −628.850 | − | 1089.20i | −0.172355 | − | 0.298528i | ||||
\(238\) | 3290.08 | − | 2561.06i | 0.896068 | − | 0.697517i | ||||
\(239\) | − | 2877.90i | − | 0.778896i | −0.921048 | − | 0.389448i | \(-0.872666\pi\) | ||
0.921048 | − | 0.389448i | \(-0.127334\pi\) | |||||||
\(240\) | 376.000 | − | 231.241i | 0.101128 | − | 0.0621939i | ||||
\(241\) | −1361.52 | + | 786.072i | −0.363913 | + | 0.210105i | −0.670796 | − | 0.741642i | \(-0.734047\pi\) |
0.306883 | + | 0.951747i | \(0.400714\pi\) | |||||||
\(242\) | −306.809 | + | 755.501i | −0.0814978 | + | 0.200684i | ||||
\(243\) | 1956.78 | + | 3389.24i | 0.516574 | + | 0.894732i | ||||
\(244\) | −360.656 | + | 1424.86i | −0.0946257 | + | 0.373842i | ||||
\(245\) | −1173.87 | + | 2033.20i | −0.306105 | + | 0.530189i | ||||
\(246\) | 451.161 | + | 3252.22i | 0.116931 | + | 0.842901i | ||||
\(247\) | −1954.91 | − | 1550.99i | −0.503594 | − | 0.399543i | ||||
\(248\) | −4281.72 | + | 1878.98i | −1.09633 | + | 0.481111i | ||||
\(249\) | −2399.16 | − | 1385.16i | −0.610606 | − | 0.352533i | ||||
\(250\) | −677.736 | + | 1668.89i | −0.171455 | + | 0.422199i | ||||
\(251\) | 962.349 | − | 555.612i | 0.242004 | − | 0.139721i | −0.374094 | − | 0.927391i | \(-0.622046\pi\) |
0.616097 | + | 0.787670i | \(0.288713\pi\) | |||||||
\(252\) | 5478.49 | + | 1386.70i | 1.36949 | + | 0.346641i | ||||
\(253\) | 154.047 | + | 266.817i | 0.0382800 | + | 0.0663030i | ||||
\(254\) | 2021.10 | − | 280.376i | 0.499273 | − | 0.0692612i | ||||
\(255\) | 288.801 | 0.0709231 | ||||||||
\(256\) | −4089.68 | + | 227.451i | −0.998457 | + | 0.0555300i | ||||
\(257\) | 4845.44 | − | 2797.52i | 1.17607 | − | 0.679005i | 0.220969 | − | 0.975281i | \(-0.429078\pi\) |
0.955102 | + | 0.296276i | \(0.0957447\pi\) | |||||||
\(258\) | −202.714 | − | 1461.28i | −0.0489165 | − | 0.352617i | ||||
\(259\) | 11683.7 | 2.80304 | ||||||||
\(260\) | −440.199 | + | 452.601i | −0.105000 | + | 0.107958i | ||||
\(261\) | 1736.94 | + | 1002.82i | 0.411931 | + | 0.237828i | ||||
\(262\) | −3522.81 | + | 2742.22i | −0.830686 | + | 0.646623i | ||||
\(263\) | −5240.50 | − | 3025.60i | −1.22868 | − | 0.709379i | −0.261927 | − | 0.965088i | \(-0.584358\pi\) |
−0.966754 | + | 0.255708i | \(0.917691\pi\) | |||||||
\(264\) | 1912.38 | + | 211.340i | 0.445829 | + | 0.0492693i | ||||
\(265\) | 672.441i | 0.155878i | ||||||||
\(266\) | −76.2736 | + | 8246.18i | −0.0175813 | + | 1.90077i | ||||
\(267\) | − | 2778.26i | − | 0.636804i | ||||||
\(268\) | 959.338 | − | 3790.10i | 0.218660 | − | 0.863871i | ||||
\(269\) | 3245.72 | + | 1873.92i | 0.735670 | + | 0.424739i | 0.820493 | − | 0.571657i | \(-0.193699\pi\) |
−0.0848231 | + | 0.996396i | \(0.527033\pi\) | |||||||
\(270\) | 563.988 | + | 724.529i | 0.127123 | + | 0.163309i | ||||
\(271\) | 4068.47 | + | 2348.93i | 0.911963 | + | 0.526522i | 0.881062 | − | 0.473000i | \(-0.156829\pi\) |
0.0309007 | + | 0.999522i | \(0.490162\pi\) | |||||||
\(272\) | −2357.14 | − | 1274.94i | −0.525450 | − | 0.284209i | ||||
\(273\) | 2793.23 | 0.619246 | ||||||||
\(274\) | −7044.79 | + | 977.283i | −1.55325 | + | 0.215474i | ||||
\(275\) | −3303.75 | + | 1907.42i | −0.724449 | + | 0.418261i | ||||
\(276\) | −140.138 | + | 144.086i | −0.0305627 | + | 0.0314237i | ||||
\(277\) | −7421.52 | −1.60981 | −0.804903 | − | 0.593407i | \(-0.797783\pi\) | ||||
−0.804903 | + | 0.593407i | \(0.797783\pi\) | |||||||
\(278\) | 252.733 | + | 1821.84i | 0.0545249 | + | 0.393045i | ||||
\(279\) | −2073.27 | − | 3591.01i | −0.444887 | − | 0.770567i | ||||
\(280\) | 2073.81 | + | 229.181i | 0.442621 | + | 0.0489149i | ||||
\(281\) | −2727.82 | + | 1574.91i | −0.579104 | + | 0.334346i | −0.760777 | − | 0.649013i | \(-0.775182\pi\) |
0.181673 | + | 0.983359i | \(0.441849\pi\) | |||||||
\(282\) | 2446.31 | + | 993.449i | 0.516581 | + | 0.209784i | ||||
\(283\) | 1610.91 | + | 930.058i | 0.338369 | + | 0.195358i | 0.659551 | − | 0.751660i | \(-0.270747\pi\) |
−0.321181 | + | 0.947018i | \(0.604080\pi\) | |||||||
\(284\) | 132.222 | − | 37.4048i | 0.0276266 | − | 0.00781537i | ||||
\(285\) | −355.026 | + | 447.484i | −0.0737892 | + | 0.0930058i | ||||
\(286\) | −2725.86 | + | 378.143i | −0.563578 | + | 0.0781820i | ||||
\(287\) | −7759.71 | + | 13440.2i | −1.59596 | + | 2.76429i | ||||
\(288\) | −598.852 | − | 3582.62i | −0.122527 | − | 0.733013i | ||||
\(289\) | 1579.84 | + | 2736.37i | 0.321564 | + | 0.556965i | ||||
\(290\) | 686.068 | + | 278.612i | 0.138922 | + | 0.0564161i | ||||
\(291\) | −1421.63 | + | 820.780i | −0.286384 | + | 0.165344i | ||||
\(292\) | −6878.02 | + | 1945.74i | −1.37844 | + | 0.389952i | ||||
\(293\) | 4299.64i | 0.857295i | 0.903472 | + | 0.428648i | \(0.141010\pi\) | ||||
−0.903472 | + | 0.428648i | \(0.858990\pi\) | |||||||
\(294\) | −4100.75 | − | 5268.05i | −0.813472 | − | 1.04503i | ||||
\(295\) | 257.060 | + | 445.241i | 0.0507343 | + | 0.0878744i | ||||
\(296\) | −3017.72 | − | 6876.61i | −0.592573 | − | 1.35032i | ||||
\(297\) | 4002.04i | 0.781892i | ||||||||
\(298\) | −2024.40 | − | 2600.65i | −0.393524 | − | 0.505542i | ||||
\(299\) | 143.744 | − | 248.972i | 0.0278024 | − | 0.0481552i | ||||
\(300\) | −1784.08 | − | 1735.19i | −0.343346 | − | 0.333938i | ||||
\(301\) | 3486.57 | − | 6038.92i | 0.667650 | − | 1.15640i | ||||
\(302\) | 564.347 | − | 1389.67i | 0.107531 | − | 0.264790i | ||||
\(303\) | 1883.01 | 0.357018 | ||||||||
\(304\) | 4873.12 | − | 2084.98i | 0.919384 | − | 0.393361i | ||||
\(305\) | −481.218 | −0.0903425 | ||||||||
\(306\) | 894.169 | − | 2201.84i | 0.167047 | − | 0.411343i | ||||
\(307\) | −2637.34 | + | 4568.01i | −0.490297 | + | 0.849219i | −0.999938 | − | 0.0111684i | \(-0.996445\pi\) |
0.509641 | + | 0.860387i | \(0.329778\pi\) | |||||||
\(308\) | 6519.30 | + | 6340.67i | 1.20608 | + | 1.17303i | ||||
\(309\) | −893.994 | + | 1548.44i | −0.164587 | + | 0.285074i | ||||
\(310\) | −940.363 | − | 1208.04i | −0.172287 | − | 0.221329i | ||||
\(311\) | 865.219i | 0.157756i | 0.996884 | + | 0.0788779i | \(0.0251337\pi\) | ||||
−0.996884 | + | 0.0788779i | \(0.974866\pi\) | |||||||
\(312\) | −721.452 | − | 1644.00i | −0.130911 | − | 0.298312i | ||||
\(313\) | −2558.85 | − | 4432.06i | −0.462092 | − | 0.800366i | 0.536973 | − | 0.843599i | \(-0.319568\pi\) |
−0.999065 | + | 0.0432330i | \(0.986234\pi\) | |||||||
\(314\) | 2885.01 | + | 3706.24i | 0.518505 | + | 0.666099i | ||||
\(315\) | 1850.25i | 0.330951i | ||||||||
\(316\) | −3676.67 | + | 1040.10i | −0.654522 | + | 0.185160i | ||||
\(317\) | 3454.18 | − | 1994.27i | 0.612006 | − | 0.353342i | −0.161744 | − | 0.986833i | \(-0.551712\pi\) |
0.773750 | + | 0.633491i | \(0.218379\pi\) | |||||||
\(318\) | −1771.62 | − | 719.458i | −0.312414 | − | 0.126872i | ||||
\(319\) | 1613.79 | + | 2795.16i | 0.283244 | + | 0.490592i | ||||
\(320\) | −400.748 | − | 1279.77i | −0.0700077 | − | 0.223566i | ||||
\(321\) | 1309.52 | − | 2268.16i | 0.227696 | − | 0.394382i | ||||
\(322\) | −941.032 | + | 130.544i | −0.162862 | + | 0.0225930i | ||||
\(323\) | 3430.40 | + | 508.262i | 0.590937 | + | 0.0875555i | ||||
\(324\) | 1658.29 | − | 469.119i | 0.284344 | − | 0.0804388i | ||||
\(325\) | 3082.78 | + | 1779.85i | 0.526160 | + | 0.303779i | ||||
\(326\) | −4955.96 | − | 2012.62i | −0.841979 | − | 0.341928i | ||||
\(327\) | −163.009 | + | 94.1136i | −0.0275671 | + | 0.0159159i | ||||
\(328\) | 9914.67 | + | 1095.69i | 1.66904 | + | 0.184449i | ||||
\(329\) | 6240.03 | + | 10808.0i | 1.04567 | + | 1.81115i | ||||
\(330\) | 86.5580 | + | 623.957i | 0.0144390 | + | 0.104084i | ||||
\(331\) | 789.560 | 0.131112 | 0.0655561 | − | 0.997849i | \(-0.479118\pi\) | ||||
0.0655561 | + | 0.997849i | \(0.479118\pi\) | |||||||
\(332\) | −5868.04 | + | 6033.36i | −0.970032 | + | 0.997360i | ||||
\(333\) | 5767.31 | − | 3329.76i | 0.949088 | − | 0.547956i | ||||
\(334\) | 3167.34 | − | 439.387i | 0.518890 | − | 0.0719826i | ||||
\(335\) | 1280.03 | 0.208763 | ||||||||
\(336\) | −2822.61 | + | 5218.49i | −0.458292 | + | 0.847298i | ||||
\(337\) | 6646.23 | + | 3837.20i | 1.07431 | + | 0.620255i | 0.929356 | − | 0.369184i | \(-0.120363\pi\) |
0.144956 | + | 0.989438i | \(0.453696\pi\) | |||||||
\(338\) | −2239.67 | − | 2877.20i | −0.360420 | − | 0.463015i | ||||
\(339\) | 2149.00 | + | 1240.73i | 0.344300 | + | 0.198782i | ||||
\(340\) | 215.293 | − | 850.568i | 0.0343409 | − | 0.135672i | ||||
\(341\) | − | 6672.79i | − | 1.05968i | ||||||
\(342\) | 2312.45 | + | 4092.23i | 0.365622 | + | 0.647024i | ||||
\(343\) | − | 19480.1i | − | 3.06655i | ||||||
\(344\) | −4454.83 | − | 492.312i | −0.698222 | − | 0.0771618i | ||||
\(345\) | −56.9904 | − | 32.9034i | −0.00889350 | − | 0.00513467i | ||||
\(346\) | 4675.76 | − | 3639.71i | 0.726505 | − | 0.565526i | ||||
\(347\) | −5062.84 | − | 2923.03i | −0.783249 | − | 0.452209i | 0.0543316 | − | 0.998523i | \(-0.482697\pi\) |
−0.837580 | + | 0.546314i | \(0.816031\pi\) | |||||||
\(348\) | −1468.07 | + | 1509.43i | −0.226141 | + | 0.232512i | ||||
\(349\) | 9466.31 | 1.45192 | 0.725960 | − | 0.687737i | \(-0.241396\pi\) | ||||
0.725960 | + | 0.687737i | \(0.241396\pi\) | |||||||
\(350\) | −1616.40 | − | 11651.9i | −0.246858 | − | 1.77949i | ||||
\(351\) | 3234.06 | − | 1867.19i | 0.491799 | − | 0.283940i | ||||
\(352\) | 2048.06 | − | 5474.74i | 0.310119 | − | 0.828991i | ||||
\(353\) | −5771.85 | −0.870268 | −0.435134 | − | 0.900366i | \(-0.643299\pi\) | ||||
−0.435134 | + | 0.900366i | \(0.643299\pi\) | |||||||
\(354\) | −1448.07 | + | 200.883i | −0.217413 | + | 0.0301605i | ||||
\(355\) | 22.4945 | + | 38.9617i | 0.00336306 | + | 0.00582499i | ||||
\(356\) | −8182.46 | − | 2071.12i | −1.21817 | − | 0.308340i | ||||
\(357\) | −3361.63 | + | 1940.84i | −0.498366 | + | 0.287732i | ||||
\(358\) | −4673.96 | + | 11509.4i | −0.690019 | + | 1.69913i | ||||
\(359\) | 7761.75 | + | 4481.25i | 1.14108 | + | 0.658805i | 0.946699 | − | 0.322120i | \(-0.104395\pi\) |
0.194386 | + | 0.980925i | \(0.437729\pi\) | |||||||
\(360\) | 1088.99 | − | 477.892i | 0.159430 | − | 0.0699642i | ||||
\(361\) | −5004.56 | + | 4690.44i | −0.729634 | + | 0.683838i | ||||
\(362\) | 620.356 | + | 4471.86i | 0.0900696 | + | 0.649271i | ||||
\(363\) | 379.579 | − | 657.450i | 0.0548835 | − | 0.0950611i | ||||
\(364\) | 2082.28 | − | 8226.56i | 0.299838 | − | 1.18459i | ||||
\(365\) | −1170.13 | − | 2026.73i | −0.167801 | − | 0.290641i | ||||
\(366\) | 514.864 | − | 1267.82i | 0.0735311 | − | 0.181066i | ||||
\(367\) | −1725.56 | + | 996.250i | −0.245431 | + | 0.141700i | −0.617671 | − | 0.786437i | \(-0.711923\pi\) |
0.372239 | + | 0.928137i | \(0.378590\pi\) | |||||||
\(368\) | 319.889 | + | 520.142i | 0.0453135 | + | 0.0736801i | ||||
\(369\) | 8845.83i | 1.24796i | ||||||||
\(370\) | 1940.16 | − | 1510.26i | 0.272606 | − | 0.212202i | ||||
\(371\) | −4519.04 | − | 7827.21i | −0.632391 | − | 1.09533i | ||||
\(372\) | 4188.84 | − | 1184.99i | 0.583820 | − | 0.165158i | ||||
\(373\) | − | 12354.7i | − | 1.71502i | −0.514468 | − | 0.857510i | \(-0.672011\pi\) | ||
0.514468 | − | 0.857510i | \(-0.327989\pi\) | |||||||
\(374\) | 3017.80 | − | 2349.12i | 0.417238 | − | 0.324786i | ||||
\(375\) | 838.483 | − | 1452.29i | 0.115464 | − | 0.199990i | ||||
\(376\) | 4749.54 | − | 6464.23i | 0.651433 | − | 0.886615i | ||||
\(377\) | 1505.85 | − | 2608.21i | 0.205717 | − | 0.356312i | ||||
\(378\) | −11433.9 | − | 4643.31i | −1.55581 | − | 0.631815i | ||||
\(379\) | −11795.3 | −1.59863 | −0.799316 | − | 0.600910i | \(-0.794805\pi\) | ||||
−0.799316 | + | 0.600910i | \(0.794805\pi\) | |||||||
\(380\) | 1053.26 | + | 1379.20i | 0.142187 | + | 0.186188i | ||||
\(381\) | −1899.66 | −0.255440 | ||||||||
\(382\) | 9705.27 | + | 3941.31i | 1.29991 | + | 0.527893i | ||||
\(383\) | −5261.84 | + | 9113.78i | −0.702004 | + | 1.21591i | 0.265758 | + | 0.964040i | \(0.414378\pi\) |
−0.967762 | + | 0.251867i | \(0.918956\pi\) | |||||||
\(384\) | 3800.47 | + | 313.433i | 0.505057 | + | 0.0416531i | ||||
\(385\) | −1488.75 | + | 2578.58i | −0.197074 | + | 0.341342i | ||||
\(386\) | 10203.9 | − | 7942.94i | 1.34551 | − | 1.04737i | ||||
\(387\) | − | 3974.58i | − | 0.522066i | ||||||
\(388\) | 1357.55 | + | 4798.83i | 0.177627 | + | 0.627896i | ||||
\(389\) | −150.379 | − | 260.463i | −0.0196003 | − | 0.0339486i | 0.856059 | − | 0.516878i | \(-0.172906\pi\) |
−0.875659 | + | 0.482930i | \(0.839573\pi\) | |||||||
\(390\) | 463.838 | − | 361.060i | 0.0602239 | − | 0.0468795i | ||||
\(391\) | 399.514i | 0.0516734i | ||||||||
\(392\) | −18572.3 | + | 8150.26i | −2.39297 | + | 1.05013i | ||||
\(393\) | 3599.42 | − | 2078.13i | 0.462002 | − | 0.266737i | ||||
\(394\) | 5287.20 | − | 13019.4i | 0.676054 | − | 1.66475i | ||||
\(395\) | −625.499 | − | 1083.40i | −0.0796767 | − | 0.138004i | ||||
\(396\) | 5025.11 | + | 1271.94i | 0.637679 | + | 0.161407i | ||||
\(397\) | −4136.07 | + | 7163.89i | −0.522881 | + | 0.905656i | 0.476765 | + | 0.879031i | \(0.341809\pi\) |
−0.999645 | + | 0.0266250i | \(0.991524\pi\) | |||||||
\(398\) | 528.175 | + | 3807.37i | 0.0665201 | + | 0.479513i | ||||
\(399\) | 1125.25 | − | 7594.61i | 0.141185 | − | 0.952897i | ||||
\(400\) | −6440.43 | + | 3960.88i | −0.805054 | + | 0.495110i | ||||
\(401\) | −6050.65 | − | 3493.35i | −0.753504 | − | 0.435036i | 0.0734544 | − | 0.997299i | \(-0.476598\pi\) |
−0.826959 | + | 0.562263i | \(0.809931\pi\) | |||||||
\(402\) | −1369.53 | + | 3372.39i | −0.169915 | + | 0.418406i | ||||
\(403\) | −5392.31 | + | 3113.25i | −0.666526 | + | 0.384819i | ||||
\(404\) | 1403.74 | − | 5545.81i | 0.172867 | − | 0.682956i | ||||
\(405\) | 282.120 | + | 488.646i | 0.0346139 | + | 0.0599531i | ||||
\(406\) | −9858.19 | + | 1367.57i | −1.20506 | + | 0.167171i | ||||
\(407\) | 10716.8 | 1.30518 | ||||||||
\(408\) | 2010.58 | + | 1477.25i | 0.243966 | + | 0.179252i | ||||
\(409\) | −7871.14 | + | 4544.41i | −0.951597 | + | 0.549405i | −0.893577 | − | 0.448911i | \(-0.851812\pi\) |
−0.0580201 | + | 0.998315i | \(0.518479\pi\) | |||||||
\(410\) | 448.758 | + | 3234.89i | 0.0540550 | + | 0.389658i | ||||
\(411\) | 6621.50 | 0.794682 | ||||||||
\(412\) | 3893.99 | + | 3787.29i | 0.465638 | + | 0.452880i | ||||
\(413\) | −5984.35 | − | 3455.07i | −0.713004 | − | 0.411653i | ||||
\(414\) | −427.309 | + | 332.626i | −0.0507273 | + | 0.0394872i | ||||
\(415\) | −2386.38 | − | 1377.78i | −0.282272 | − | 0.162970i | ||||
\(416\) | −5379.70 | + | 899.244i | −0.634042 | + | 0.105983i | ||||
\(417\) | − | 1712.37i | − | 0.201091i | ||||||
\(418\) | −69.9615 | + | 7563.75i | −0.00818643 | + | 0.885061i | ||||
\(419\) | − | 1933.94i | − | 0.225488i | −0.993624 | − | 0.112744i | \(-0.964036\pi\) | ||
0.993624 | − | 0.112744i | \(-0.0359640\pi\) | |||||||
\(420\) | −1883.08 | − | 476.640i | −0.218774 | − | 0.0553753i | ||||
\(421\) | −1824.93 | − | 1053.62i | −0.211263 | − | 0.121973i | 0.390635 | − | 0.920545i | \(-0.372255\pi\) |
−0.601898 | + | 0.798573i | \(0.705589\pi\) | |||||||
\(422\) | 2945.34 | + | 3783.74i | 0.339755 | + | 0.436468i | ||||
\(423\) | 6160.42 | + | 3556.72i | 0.708109 | + | 0.408827i | ||||
\(424\) | −3439.63 | + | 4681.41i | −0.393969 | + | 0.536201i | ||||
\(425\) | −4946.81 | −0.564601 | ||||||||
\(426\) | −126.716 | + | 17.5786i | −0.0144118 | + | 0.00199927i | ||||
\(427\) | 5601.37 | − | 3233.95i | 0.634823 | − | 0.366515i | ||||
\(428\) | −5703.92 | − | 5547.63i | −0.644181 | − | 0.626530i | ||||
\(429\) | 2562.07 | 0.288341 | ||||||||
\(430\) | −201.634 | − | 1453.49i | −0.0226132 | − | 0.163008i | ||||
\(431\) | −1149.65 | − | 1991.26i | −0.128485 | − | 0.222542i | 0.794605 | − | 0.607127i | \(-0.207678\pi\) |
−0.923090 | + | 0.384585i | \(0.874345\pi\) | |||||||
\(432\) | 220.316 | + | 7928.90i | 0.0245369 | + | 0.883055i | ||||
\(433\) | 5450.07 | − | 3146.60i | 0.604881 | − | 0.349228i | −0.166078 | − | 0.986113i | \(-0.553110\pi\) |
0.770960 | + | 0.636884i | \(0.219777\pi\) | |||||||
\(434\) | 19064.3 | + | 7742.01i | 2.10856 | + | 0.856287i | ||||
\(435\) | −597.027 | − | 344.694i | −0.0658052 | − | 0.0379927i | ||||
\(436\) | 155.662 | + | 550.251i | 0.0170983 | + | 0.0604409i | ||||
\(437\) | −619.030 | − | 491.127i | −0.0677625 | − | 0.0537616i | ||||
\(438\) | 6591.60 | − | 914.415i | 0.719084 | − | 0.0997544i | ||||
\(439\) | −4743.84 | + | 8216.58i | −0.515743 | + | 0.893293i | 0.484090 | + | 0.875018i | \(0.339151\pi\) |
−0.999833 | + | 0.0182751i | \(0.994183\pi\) | |||||||
\(440\) | 1902.19 | + | 210.214i | 0.206098 | + | 0.0227763i | ||||
\(441\) | −8992.99 | − | 15576.3i | −0.971061 | − | 1.68193i | ||||
\(442\) | −3306.31 | − | 1342.70i | −0.355804 | − | 0.144492i | ||||
\(443\) | 5958.12 | − | 3439.92i | 0.639004 | − | 0.368929i | −0.145227 | − | 0.989398i | \(-0.546391\pi\) |
0.784231 | + | 0.620469i | \(0.213058\pi\) | |||||||
\(444\) | 1903.14 | + | 6727.44i | 0.203421 | + | 0.719077i | ||||
\(445\) | − | 2763.46i | − | 0.294383i | ||||||
\(446\) | 5820.22 | + | 7476.97i | 0.617927 | + | 0.793822i | ||||
\(447\) | 1534.14 | + | 2657.21i | 0.162332 | + | 0.281167i | ||||
\(448\) | 13265.2 | + | 12203.3i | 1.39893 | + | 1.28695i | ||||
\(449\) | − | 787.148i | − | 0.0827346i | −0.999144 | − | 0.0413673i | \(-0.986829\pi\) | ||
0.999144 | − | 0.0413673i | \(-0.0131714\pi\) | |||||||
\(450\) | −4118.60 | − | 5290.97i | −0.431450 | − | 0.554264i | ||||
\(451\) | −7117.54 | + | 12327.9i | −0.743131 | + | 1.28714i | ||||
\(452\) | 5256.18 | − | 5404.25i | 0.546968 | − | 0.562378i | ||||
\(453\) | −698.199 | + | 1209.32i | −0.0724156 | + | 0.125427i | ||||
\(454\) | 5356.34 | − | 13189.7i | 0.553712 | − | 1.36349i | ||||
\(455\) | 2778.35 | 0.286266 | ||||||||
\(456\) | −4760.56 | + | 1299.30i | −0.488890 | + | 0.133432i | ||||
\(457\) | 11290.7 | 1.15570 | 0.577850 | − | 0.816143i | \(-0.303892\pi\) | ||||
0.577850 | + | 0.816143i | \(0.303892\pi\) | |||||||
\(458\) | 1883.81 | − | 4638.77i | 0.192193 | − | 0.473265i | ||||
\(459\) | −2594.78 | + | 4494.29i | −0.263865 | + | 0.457027i | ||||
\(460\) | −139.391 | + | 143.318i | −0.0141286 | + | 0.0145266i | ||||
\(461\) | −1771.81 | + | 3068.86i | −0.179005 | + | 0.310045i | −0.941540 | − | 0.336901i | \(-0.890621\pi\) |
0.762535 | + | 0.646947i | \(0.223954\pi\) | |||||||
\(462\) | −5200.74 | − | 6681.15i | −0.523724 | − | 0.672804i | ||||
\(463\) | 10852.7i | 1.08934i | 0.838649 | + | 0.544672i | \(0.183346\pi\) | ||||
−0.838649 | + | 0.544672i | \(0.816654\pi\) | |||||||
\(464\) | 3351.13 | + | 5448.97i | 0.335286 | + | 0.545177i | ||||
\(465\) | 712.632 | + | 1234.31i | 0.0710699 | + | 0.123097i | ||||
\(466\) | 2365.86 | + | 3039.31i | 0.235185 | + | 0.302132i | ||||
\(467\) | 13532.0i | 1.34087i | 0.741970 | + | 0.670433i | \(0.233892\pi\) | ||||
−0.741970 | + | 0.670433i | \(0.766108\pi\) | |||||||
\(468\) | −1316.65 | − | 4654.24i | −0.130047 | − | 0.459706i | ||||
\(469\) | −14899.5 | + | 8602.25i | −1.46694 | + | 0.846940i | ||||
\(470\) | 2433.28 | + | 988.156i | 0.238806 | + | 0.0969792i | ||||
\(471\) | −2186.34 | − | 3786.84i | −0.213887 | − | 0.370464i | ||||
\(472\) | −487.864 | + | 4414.58i | −0.0475757 | + | 0.430503i | ||||
\(473\) | 3198.03 | − | 5539.16i | 0.310879 | − | 0.538458i | ||||
\(474\) | 3523.57 | − | 488.804i | 0.341441 | − | 0.0473661i | ||||
\(475\) | 6081.17 | − | 7664.87i | 0.587417 | − | 0.740396i | ||||
\(476\) | 3210.11 | + | 11347.4i | 0.309107 | + | 1.09267i | ||||
\(477\) | −4461.39 | − | 2575.78i | −0.428245 | − | 0.247248i | ||||
\(478\) | 7541.78 | + | 3062.72i | 0.721659 | + | 0.293066i | ||||
\(479\) | −7800.06 | + | 4503.37i | −0.744038 | + | 0.429570i | −0.823535 | − | 0.567265i | \(-0.808002\pi\) |
0.0794979 | + | 0.996835i | \(0.474668\pi\) | |||||||
\(480\) | 205.839 | + | 1231.43i | 0.0195734 | + | 0.117097i | ||||
\(481\) | −5000.00 | − | 8660.25i | −0.473972 | − | 0.820943i | ||||
\(482\) | −611.013 | − | 4404.52i | −0.0577404 | − | 0.416224i | ||||
\(483\) | 884.490 | 0.0833244 | ||||||||
\(484\) | −1653.34 | − | 1608.04i | −0.155272 | − | 0.151018i | ||||
\(485\) | −1414.06 | + | 816.407i | −0.132390 | + | 0.0764354i | ||||
\(486\) | −10964.2 | + | 1521.00i | −1.02335 | + | 0.141963i | ||||
\(487\) | 4682.36 | 0.435683 | 0.217842 | − | 0.975984i | \(-0.430098\pi\) | ||||
0.217842 | + | 0.975984i | \(0.430098\pi\) | |||||||
\(488\) | −3350.15 | − | 2461.49i | −0.310767 | − | 0.228333i | ||||
\(489\) | 4312.76 | + | 2489.97i | 0.398834 | + | 0.230267i | ||||
\(490\) | −4078.91 | − | 5239.98i | −0.376054 | − | 0.483098i | ||||
\(491\) | −13460.3 | − | 7771.32i | −1.23718 | − | 0.714287i | −0.268664 | − | 0.963234i | \(-0.586582\pi\) |
−0.968517 | + | 0.248947i | \(0.919915\pi\) | |||||||
\(492\) | −9002.82 | − | 2278.76i | −0.824957 | − | 0.208810i | ||||
\(493\) | 4185.29i | 0.382344i | ||||||||
\(494\) | 6144.94 | − | 3472.40i | 0.559664 | − | 0.316256i | ||||
\(495\) | 1697.13i | 0.154101i | ||||||||
\(496\) | −367.343 | − | 13220.2i | −0.0332544 | − | 1.19679i | ||||
\(497\) | −523.672 | − | 302.342i | −0.0472634 | − | 0.0272875i | ||||
\(498\) | 6183.15 | − | 4813.09i | 0.556373 | − | 0.433092i | ||||
\(499\) | −15320.8 | − | 8845.45i | −1.37445 | − | 0.793541i | −0.382968 | − | 0.923762i | \(-0.625098\pi\) |
−0.991485 | + | 0.130221i | \(0.958431\pi\) | |||||||
\(500\) | −3652.20 | − | 3552.12i | −0.326662 | − | 0.317712i | ||||
\(501\) | −2977.03 | −0.265477 | ||||||||
\(502\) | 431.877 | + | 3113.20i | 0.0383976 | + | 0.276791i | ||||
\(503\) | 11621.0 | − | 6709.41i | 1.03013 | − | 0.594747i | 0.113110 | − | 0.993582i | \(-0.463919\pi\) |
0.917023 | + | 0.398835i | \(0.130585\pi\) | |||||||
\(504\) | −9464.25 | + | 12881.1i | −0.836451 | + | 1.13843i | ||||
\(505\) | 1872.98 | 0.165043 | ||||||||
\(506\) | −863.155 | + | 119.741i | −0.0758339 | + | 0.0105200i | ||||
\(507\) | 1697.28 | + | 2939.78i | 0.148676 | + | 0.257515i | ||||
\(508\) | −1416.15 | + | 5594.84i | −0.123684 | + | 0.488644i | ||||
\(509\) | −1459.47 | + | 842.628i | −0.127092 | + | 0.0733769i | −0.562198 | − | 0.827002i | \(-0.690044\pi\) |
0.435106 | + | 0.900379i | \(0.356711\pi\) | |||||||
\(510\) | −307.347 | + | 756.825i | −0.0266854 | + | 0.0657113i | ||||
\(511\) | 27240.7 | + | 15727.4i | 2.35823 | + | 1.36152i | ||||
\(512\) | 3756.26 | − | 10959.4i | 0.324228 | − | 0.945979i | ||||
\(513\) | −3773.92 | − | 9545.38i | −0.324800 | − | 0.821518i | ||||
\(514\) | 2174.51 | + | 15675.0i | 0.186602 | + | 1.34513i | ||||
\(515\) | −889.231 | + | 1540.19i | −0.0760858 | + | 0.131784i | ||||
\(516\) | 4045.12 | + | 1023.89i | 0.345110 | + | 0.0873530i | ||||
\(517\) | 5723.63 | + | 9913.61i | 0.486895 | + | 0.843327i | ||||
\(518\) | −12434.0 | + | 30618.0i | −1.05467 | + | 2.59706i | ||||
\(519\) | −4777.46 | + | 2758.27i | −0.404060 | + | 0.233284i | ||||
\(520\) | −717.608 | − | 1635.24i | −0.0605177 | − | 0.137904i | ||||
\(521\) | 1695.97i | 0.142614i | 0.997454 | + | 0.0713068i | \(0.0227169\pi\) | ||||
−0.997454 | + | 0.0713068i | \(0.977283\pi\) | |||||||
\(522\) | −4476.47 | + | 3484.57i | −0.375344 | + | 0.292175i | ||||
\(523\) | −11140.9 | − | 19296.5i | −0.931464 | − | 1.61334i | −0.780822 | − | 0.624754i | \(-0.785199\pi\) |
−0.150642 | − | 0.988588i | \(-0.548134\pi\) | |||||||
\(524\) | −3437.18 | − | 12150.1i | −0.286553 | − | 1.01294i | ||||
\(525\) | 10951.8i | 0.910430i | ||||||||
\(526\) | 13505.9 | − | 10513.2i | 1.11955 | − | 0.871482i | ||||
\(527\) | 4326.40 | − | 7493.54i | 0.357611 | − | 0.619400i | ||||
\(528\) | −2589.02 | + | 4786.63i | −0.213395 | + | 0.394529i | ||||
\(529\) | −6037.98 | + | 10458.1i | −0.496259 | + | 0.859546i | ||||
\(530\) | −1762.19 | − | 715.625i | −0.144424 | − | 0.0586505i | ||||
\(531\) | −3938.67 | −0.321890 | ||||||||
\(532\) | −21528.6 | − | 8975.62i | −1.75448 | − | 0.731471i | ||||
\(533\) | 13283.0 | 1.07946 | ||||||||
\(534\) | 7280.65 | + | 2956.68i | 0.590009 | + | 0.239603i | ||||
\(535\) | 1302.55 | − | 2256.08i | 0.105260 | − | 0.182315i | ||||
\(536\) | 8911.32 | + | 6547.52i | 0.718117 | + | 0.527630i | ||||
\(537\) | 5782.54 | − | 10015.7i | 0.464684 | − | 0.804856i | ||||
\(538\) | −8364.91 | + | 6511.41i | −0.670329 | + | 0.521797i | ||||
\(539\) | − | 28943.8i | − | 2.31298i | ||||||
\(540\) | −2498.89 | + | 706.918i | −0.199139 | + | 0.0563350i | ||||
\(541\) | 7123.20 | + | 12337.7i | 0.566082 | + | 0.980483i | 0.996948 | + | 0.0780669i | \(0.0248748\pi\) |
−0.430866 | + | 0.902416i | \(0.641792\pi\) | |||||||
\(542\) | −10485.3 | + | 8161.97i | −0.830964 | + | 0.646839i | ||||
\(543\) | − | 4203.17i | − | 0.332183i | ||||||
\(544\) | 5849.60 | − | 4820.24i | 0.461028 | − | 0.379901i | ||||
\(545\) | −162.141 | + | 93.6121i | −0.0127438 | + | 0.00735762i | ||||
\(546\) | −2972.61 | + | 7319.89i | −0.232996 | + | 0.573741i | ||||
\(547\) | 6488.68 | + | 11238.7i | 0.507196 | + | 0.878489i | 0.999965 | + | 0.00832897i | \(0.00265123\pi\) |
−0.492770 | + | 0.870160i | \(0.664015\pi\) | |||||||
\(548\) | 4936.15 | − | 19501.5i | 0.384784 | − | 1.52019i | ||||
\(549\) | 1843.30 | − | 3192.70i | 0.143297 | − | 0.248198i | ||||
\(550\) | −1482.64 | − | 10687.6i | −0.114945 | − | 0.828587i | ||||
\(551\) | −6484.92 | − | 5145.02i | −0.501392 | − | 0.397795i | ||||
\(552\) | −228.451 | − | 520.581i | −0.0176151 | − | 0.0401402i | ||||
\(553\) | 14561.6 | + | 8407.15i | 1.11975 | + | 0.646489i | ||||
\(554\) | 7898.12 | − | 19448.7i | 0.605702 | − | 1.49151i | ||||
\(555\) | −1982.36 | + | 1144.51i | −0.151615 | + | 0.0875350i | ||||
\(556\) | −5043.23 | − | 1276.53i | −0.384677 | − | 0.0973682i | ||||
\(557\) | −12082.3 | − | 20927.1i | −0.919108 | − | 1.59194i | −0.800774 | − | 0.598967i | \(-0.795578\pi\) |
−0.118334 | − | 0.992974i | \(-0.537755\pi\) | |||||||
\(558\) | 11616.9 | − | 1611.55i | 0.881334 | − | 0.122262i | ||||
\(559\) | −5968.28 | −0.451577 | ||||||||
\(560\) | −2807.57 | + | 5190.69i | −0.211860 | + | 0.391690i | ||||
\(561\) | −3083.44 | + | 1780.22i | −0.232055 | + | 0.133977i | ||||
\(562\) | −1224.18 | − | 8824.52i | −0.0918838 | − | 0.662349i | ||||
\(563\) | 17145.3 | 1.28346 | 0.641732 | − | 0.766929i | \(-0.278216\pi\) | ||||
0.641732 | + | 0.766929i | \(0.278216\pi\) | |||||||
\(564\) | −5206.83 | + | 5353.51i | −0.388736 | + | 0.399687i | ||||
\(565\) | 2137.55 | + | 1234.12i | 0.159164 | + | 0.0918931i | ||||
\(566\) | −4151.65 | + | 3231.73i | −0.308316 | + | 0.239999i | ||||
\(567\) | −6567.74 | − | 3791.89i | −0.486453 | − | 0.280854i | ||||
\(568\) | −42.6914 | + | 386.306i | −0.00315368 | + | 0.0285371i | ||||
\(569\) | 4852.05i | 0.357484i | 0.983896 | + | 0.178742i | \(0.0572027\pi\) | ||||
−0.983896 | + | 0.178742i | \(0.942797\pi\) | |||||||
\(570\) | −794.842 | − | 1406.59i | −0.0584075 | − | 0.103361i | ||||
\(571\) | 2444.38i | 0.179149i | 0.995980 | + | 0.0895744i | \(0.0285507\pi\) | ||||
−0.995980 | + | 0.0895744i | \(0.971449\pi\) | |||||||
\(572\) | 1909.96 | − | 7545.76i | 0.139614 | − | 0.551580i | ||||
\(573\) | −8445.68 | − | 4876.12i | −0.615748 | − | 0.355502i | ||||
\(574\) | −26963.1 | − | 34638.3i | −1.96066 | − | 2.51877i | ||||
\(575\) | 976.177 | + | 563.596i | 0.0707990 | + | 0.0408758i | ||||
\(576\) | 10025.8 | + | 2243.35i | 0.725249 | + | 0.162279i | ||||
\(577\) | 13542.8 | 0.977111 | 0.488555 | − | 0.872533i | \(-0.337524\pi\) | ||||
0.488555 | + | 0.872533i | \(0.337524\pi\) | |||||||
\(578\) | −8852.17 | + | 1228.01i | −0.637027 | + | 0.0883712i | ||||
\(579\) | −10425.8 | + | 6019.36i | −0.748330 | + | 0.432049i | ||||
\(580\) | −1460.25 | + | 1501.39i | −0.104541 | + | 0.107486i | ||||
\(581\) | 37036.6 | 2.64464 | ||||||||
\(582\) | −637.992 | − | 4598.99i | −0.0454392 | − | 0.327551i | ||||
\(583\) | −4145.06 | − | 7179.46i | −0.294461 | − | 0.510022i | ||||
\(584\) | 2220.75 | − | 20095.1i | 0.157355 | − | 1.42387i | ||||
\(585\) | 1371.45 | − | 791.809i | 0.0969275 | − | 0.0559611i | ||||
\(586\) | −11267.5 | − | 4575.75i | −0.794297 | − | 0.322564i | ||||
\(587\) | −8886.86 | − | 5130.83i | −0.624872 | − | 0.360770i | 0.153891 | − | 0.988088i | \(-0.450819\pi\) |
−0.778763 | + | 0.627318i | \(0.784153\pi\) | |||||||
\(588\) | 18169.4 | − | 5140.00i | 1.27431 | − | 0.360493i | ||||
\(589\) | 6292.43 | + | 15915.5i | 0.440195 | + | 1.11339i | ||||
\(590\) | −1440.36 | + | 199.813i | −0.100506 | + | 0.0139426i | ||||
\(591\) | −6541.22 | + | 11329.7i | −0.455279 | + | 0.788566i | ||||
\(592\) | 21232.2 | − | 589.968i | 1.47405 | − | 0.0409586i | ||||
\(593\) | −3359.92 | − | 5819.56i | −0.232674 | − | 0.403003i | 0.725920 | − | 0.687779i | \(-0.241414\pi\) |
−0.958594 | + | 0.284776i | \(0.908081\pi\) | |||||||
\(594\) | −10487.7 | − | 4259.05i | −0.724435 | − | 0.294193i | ||||
\(595\) | −3343.72 | + | 1930.50i | −0.230385 | + | 0.133013i | ||||
\(596\) | 8969.61 | − | 2537.44i | 0.616459 | − | 0.174392i | ||||
\(597\) | − | 3578.60i | − | 0.245331i | ||||||
\(598\) | 499.476 | + | 641.653i | 0.0341556 | + | 0.0438782i | ||||
\(599\) | 13228.1 | + | 22911.7i | 0.902313 | + | 1.56285i | 0.824485 | + | 0.565884i | \(0.191465\pi\) |
0.0778279 | + | 0.996967i | \(0.475202\pi\) | |||||||
\(600\) | 6445.86 | − | 2828.69i | 0.438585 | − | 0.192468i | ||||
\(601\) | 4055.99i | 0.275286i | 0.990482 | + | 0.137643i | \(0.0439527\pi\) | ||||
−0.990482 | + | 0.137643i | \(0.956047\pi\) | |||||||
\(602\) | 12115.0 | + | 15563.6i | 0.820216 | + | 1.05369i | ||||
\(603\) | −4903.15 | + | 8492.50i | −0.331130 | + | 0.573535i | ||||
\(604\) | 3041.16 | + | 2957.83i | 0.204873 | + | 0.199259i | ||||
\(605\) | 377.557 | − | 653.947i | 0.0253717 | − | 0.0439450i | ||||
\(606\) | −2003.94 | + | 4934.59i | −0.134331 | + | 0.330782i | ||||
\(607\) | 11424.8 | 0.763949 | 0.381974 | − | 0.924173i | \(-0.375244\pi\) | ||||
0.381974 | + | 0.924173i | \(0.375244\pi\) | |||||||
\(608\) | 277.783 | + | 14989.3i | 0.0185289 | + | 0.999828i | ||||
\(609\) | 9265.86 | 0.616538 | ||||||||
\(610\) | 512.121 | − | 1261.07i | 0.0339921 | − | 0.0837037i | ||||
\(611\) | 5340.82 | − | 9250.56i | 0.353627 | − | 0.612500i | ||||
\(612\) | 4818.51 | + | 4686.48i | 0.318263 | + | 0.309542i | ||||
\(613\) | 5739.18 | − | 9940.56i | 0.378146 | − | 0.654968i | −0.612647 | − | 0.790357i | \(-0.709895\pi\) |
0.990793 | + | 0.135389i | \(0.0432284\pi\) | |||||||
\(614\) | −9164.13 | − | 11772.7i | −0.602336 | − | 0.773793i | ||||
\(615\) | − | 3040.52i | − | 0.199359i | ||||||
\(616\) | −23554.2 | + | 10336.5i | −1.54062 | + | 0.676086i | ||||
\(617\) | 6334.37 | + | 10971.5i | 0.413310 | + | 0.715874i | 0.995249 | − | 0.0973584i | \(-0.0310393\pi\) |
−0.581940 | + | 0.813232i | \(0.697706\pi\) | |||||||
\(618\) | −3106.41 | − | 3990.66i | −0.202198 | − | 0.259754i | ||||
\(619\) | 13348.3i | 0.866744i | 0.901215 | + | 0.433372i | \(0.142676\pi\) | ||||
−0.901215 | + | 0.433372i | \(0.857324\pi\) | |||||||
\(620\) | 4166.52 | − | 1178.68i | 0.269889 | − | 0.0763497i | ||||
\(621\) | 1024.08 | − | 591.253i | 0.0661754 | − | 0.0382064i | ||||
\(622\) | −2267.38 | − | 920.782i | −0.146163 | − | 0.0593569i | ||||
\(623\) | 18571.4 | + | 32166.6i | 1.19430 | + | 2.06858i | ||||
\(624\) | 5076.02 | − | 141.045i | 0.325647 | − | 0.00904856i | ||||
\(625\) | −6549.71 | + | 11344.4i | −0.419181 | + | 0.726044i | ||||
\(626\) | 14337.7 | − | 1988.99i | 0.915417 | − | 0.126991i | ||||
\(627\) | 1032.13 | − | 6966.10i | 0.0657402 | − | 0.443699i | ||||
\(628\) | −12782.8 | + | 3616.15i | −0.812242 | + | 0.229777i | ||||
\(629\) | 12034.9 | + | 6948.37i | 0.762900 | + | 0.440460i | ||||
\(630\) | −4848.72 | − | 1969.07i | −0.306631 | − | 0.124523i | ||||
\(631\) | 1087.29 | − | 627.747i | 0.0685963 | − | 0.0396041i | −0.465310 | − | 0.885148i | \(-0.654057\pi\) |
0.533906 | + | 0.845544i | \(0.320724\pi\) | |||||||
\(632\) | 1187.11 | − | 10741.9i | 0.0747162 | − | 0.676093i | ||||
\(633\) | −2232.05 | − | 3866.03i | −0.140152 | − | 0.242750i | ||||
\(634\) | 1550.14 | + | 11174.3i | 0.0971042 | + | 0.699980i | ||||
\(635\) | −1889.54 | −0.118085 | ||||||||
\(636\) | 3770.79 | − | 3877.02i | 0.235097 | − | 0.241720i | ||||
\(637\) | −23389.6 | + | 13504.0i | −1.45483 | + | 0.839949i | ||||
\(638\) | −9042.36 | + | 1254.39i | −0.561114 | + | 0.0778401i | ||||
\(639\) | −344.661 | −0.0213374 | ||||||||
\(640\) | 3780.22 | + | 311.763i | 0.233479 | + | 0.0192555i | ||||
\(641\) | −25390.6 | − | 14659.3i | −1.56454 | − | 0.903287i | −0.996788 | − | 0.0800870i | \(-0.974480\pi\) |
−0.567751 | − | 0.823200i | \(-0.692186\pi\) | |||||||
\(642\) | 4550.28 | + | 5845.53i | 0.279728 | + | 0.359353i | ||||
\(643\) | −16446.2 | − | 9495.22i | −1.00867 | − | 0.582356i | −0.0978682 | − | 0.995199i | \(-0.531202\pi\) |
−0.910802 | + | 0.412843i | \(0.864536\pi\) | |||||||
\(644\) | 659.363 | − | 2604.98i | 0.0403456 | − | 0.159395i | ||||
\(645\) | 1366.16i | 0.0833990i | ||||||||
\(646\) | −4982.64 | + | 8448.74i | −0.303466 | + | 0.514568i | ||||
\(647\) | − | 20452.3i | − | 1.24276i | −0.783511 | − | 0.621378i | \(-0.786573\pi\) | ||
0.783511 | − | 0.621378i | \(-0.213427\pi\) | |||||||
\(648\) | −535.423 | + | 4844.94i | −0.0324590 | + | 0.293715i | ||||
\(649\) | −5489.11 | − | 3169.14i | −0.331997 | − | 0.191679i | ||||
\(650\) | −7944.99 | + | 6184.54i | −0.479428 | + | 0.373196i | ||||
\(651\) | −16590.1 | − | 9578.27i | −0.998795 | − | 0.576654i | ||||
\(652\) | 10548.4 | − | 10845.6i | 0.633603 | − | 0.651453i | ||||
\(653\) | −17242.8 | −1.03332 | −0.516662 | − | 0.856189i | \(-0.672826\pi\) | ||||
−0.516662 | + | 0.856189i | \(0.672826\pi\) | |||||||
\(654\) | −73.1544 | − | 527.337i | −0.00437395 | − | 0.0315298i | ||||
\(655\) | 3580.25 | − | 2067.06i | 0.213575 | − | 0.123308i | ||||
\(656\) | −13422.7 | + | 24816.1i | −0.798886 | + | 1.47699i | ||||
\(657\) | 17928.8 | 1.06464 | ||||||||
\(658\) | −34964.1 | + | 4850.37i | −2.07149 | + | 0.287366i | ||||
\(659\) | 4082.78 | + | 7071.59i | 0.241339 | + | 0.418012i | 0.961096 | − | 0.276214i | \(-0.0890800\pi\) |
−0.719757 | + | 0.694226i | \(0.755747\pi\) | |||||||
\(660\) | −1727.25 | − | 437.195i | −0.101868 | − | 0.0257845i | ||||
\(661\) | 5235.08 | − | 3022.48i | 0.308050 | − | 0.177853i | −0.338003 | − | 0.941145i | \(-0.609752\pi\) |
0.646054 | + | 0.763292i | \(0.276418\pi\) | |||||||
\(662\) | −840.264 | + | 2069.10i | −0.0493320 | + | 0.121477i | ||||
\(663\) | 2877.21 | + | 1661.16i | 0.168539 | + | 0.0973062i | ||||
\(664\) | −9566.02 | − | 21798.5i | −0.559087 | − | 1.27401i | ||||
\(665\) | 1119.25 | − | 7554.14i | 0.0652672 | − | 0.440507i | ||||
\(666\) | 2588.22 | + | 18657.3i | 0.150588 | + | 1.08552i | ||||
\(667\) | 476.835 | − | 825.902i | 0.0276808 | − | 0.0479446i | ||||
\(668\) | −2219.29 | + | 8767.87i | −0.128543 | + | 0.507843i | ||||
\(669\) | −4410.72 | − | 7639.58i | −0.254900 | − | 0.441500i | ||||
\(670\) | −1362.23 | + | 3354.42i | −0.0785486 | + | 0.193422i | ||||
\(671\) | 5137.82 | − | 2966.32i | 0.295594 | − | 0.170661i | ||||
\(672\) | −10671.6 | − | 12950.5i | −0.612598 | − | 0.743417i | ||||
\(673\) | 4687.57i | 0.268488i | 0.990948 | + | 0.134244i | \(0.0428606\pi\) | ||||
−0.990948 | + | 0.134244i | \(0.957139\pi\) | |||||||
\(674\) | −17128.7 | + | 13333.4i | −0.978894 | + | 0.761991i | ||||
\(675\) | 7320.93 | + | 12680.2i | 0.417456 | + | 0.723055i | ||||
\(676\) | 9923.43 | − | 2807.27i | 0.564601 | − | 0.159722i | ||||
\(677\) | 14057.2i | 0.798025i | 0.916945 | + | 0.399013i | \(0.130647\pi\) | ||||
−0.916945 | + | 0.399013i | \(0.869353\pi\) | |||||||
\(678\) | −5538.43 | + | 4311.22i | −0.313720 | + | 0.244206i | ||||
\(679\) | 10973.1 | − | 19005.9i | 0.620189 | − | 1.07420i | ||||
\(680\) | 1999.86 | + | 1469.38i | 0.112781 | + | 0.0828651i | ||||
\(681\) | −6626.76 | + | 11477.9i | −0.372890 | + | 0.645864i | ||||
\(682\) | 17486.6 | + | 7101.31i | 0.981812 | + | 0.398714i | ||||
\(683\) | −2335.41 | −0.130838 | −0.0654188 | − | 0.997858i | \(-0.520838\pi\) | ||||
−0.0654188 | + | 0.997858i | \(0.520838\pi\) | |||||||
\(684\) | −13185.0 | + | 1704.93i | −0.737046 | + | 0.0953065i | ||||
\(685\) | 6586.22 | 0.367367 | ||||||||
\(686\) | 51049.2 | + | 20731.1i | 2.84121 | + | 1.15382i | ||||
\(687\) | −2330.61 | + | 4036.73i | −0.129430 | + | 0.224179i | ||||
\(688\) | 6031.06 | − | 11150.3i | 0.334203 | − | 0.617881i | ||||
\(689\) | −3867.83 | + | 6699.28i | −0.213864 | + | 0.370424i | ||||
\(690\) | 146.876 | − | 114.331i | 0.00810360 | − | 0.00630800i | ||||
\(691\) | 16886.2i | 0.929638i | 0.885406 | + | 0.464819i | \(0.153881\pi\) | ||||
−0.885406 | + | 0.464819i | \(0.846119\pi\) | |||||||
\(692\) | 4562.11 | + | 16126.7i | 0.250615 | + | 0.885901i | ||||
\(693\) | −11405.3 | − | 19754.5i | −0.625181 | − | 1.08285i | ||||
\(694\) | 13048.0 | − | 10156.8i | 0.713682 | − | 0.555544i | ||||
\(695\) | − | 1703.25i | − | 0.0929609i | ||||||
\(696\) | −2393.24 | − | 5453.57i | −0.130338 | − | 0.297007i | ||||
\(697\) | −15986.0 | + | 9229.52i | −0.868741 | + | 0.501568i | ||||
\(698\) | −10074.2 | + | 24807.2i | −0.546296 | + | 1.34522i | ||||
\(699\) | −1792.91 | − | 3105.41i | −0.0970159 | − | 0.168036i | ||||
\(700\) | 32255.0 | + | 8164.27i | 1.74161 | + | 0.440829i | ||||
\(701\) | 15216.0 | − | 26354.9i | 0.819830 | − | 1.41999i | −0.0859765 | − | 0.996297i | \(-0.527401\pi\) |
0.905807 | − | 0.423691i | \(-0.139266\pi\) | |||||||
\(702\) | 1451.36 | + | 10462.2i | 0.0780316 | + | 0.562494i | ||||
\(703\) | −25560.9 | + | 10105.9i | −1.37133 | + | 0.542178i | ||||
\(704\) | 12167.4 | + | 11193.4i | 0.651387 | + | 0.599245i | ||||
\(705\) | −2117.48 | − | 1222.53i | −0.113119 | − | 0.0653093i | ||||
\(706\) | 6142.51 | − | 15125.6i | 0.327445 | − | 0.806316i | ||||
\(707\) | −21801.5 | + | 12587.1i | −1.15973 | + | 0.669570i | ||||
\(708\) | 1014.64 | − | 4008.57i | 0.0538593 | − | 0.212785i | ||||
\(709\) | −7249.79 | − | 12557.0i | −0.384022 | − | 0.665145i | 0.607611 | − | 0.794235i | \(-0.292128\pi\) |
−0.991633 | + | 0.129089i | \(0.958795\pi\) | |||||||
\(710\) | −126.041 | + | 17.4850i | −0.00666232 | + | 0.000924225i | ||||
\(711\) | 9583.89 | 0.505519 | ||||||||
\(712\) | 14135.5 | − | 19238.7i | 0.744029 | − | 1.01264i | ||||
\(713\) | −1707.50 | + | 985.824i | −0.0896862 | + | 0.0517804i | ||||
\(714\) | −1508.61 | − | 10874.9i | −0.0790735 | − | 0.570005i | ||||
\(715\) | 2548.42 | 0.133295 | ||||||||
\(716\) | −25187.1 | − | 24497.0i | −1.31465 | − | 1.27863i | ||||
\(717\) | −6562.98 | − | 3789.14i | −0.341840 | − | 0.197361i | ||||
\(718\) | −20003.7 | + | 15571.3i | −1.03974 | + | 0.809351i | ||||
\(719\) | 14024.3 | + | 8096.92i | 0.727423 | + | 0.419978i | 0.817479 | − | 0.575959i | \(-0.195371\pi\) |
−0.0900555 | + | 0.995937i | \(0.528704\pi\) | |||||||
\(720\) | 93.4283 | + | 3362.37i | 0.00483593 | + | 0.174039i | ||||
\(721\) | − | 23903.8i | − | 1.23471i | ||||||
\(722\) | −6965.74 | − | 18106.5i | −0.359055 | − | 0.933316i | ||||
\(723\) | 4139.87i | 0.212951i | ||||||||
\(724\) | −12379.1 | − | 3133.35i | −0.635448 | − | 0.160842i | ||||
\(725\) | 10226.4 | + | 5904.20i | 0.523859 | + | 0.302450i | ||||
\(726\) | 1318.95 | + | 1694.39i | 0.0674251 | + | 0.0866179i | ||||
\(727\) | −9479.44 | − | 5472.96i | −0.483594 | − | 0.279203i | 0.238319 | − | 0.971187i | \(-0.423404\pi\) |
−0.721913 | + | 0.691984i | \(0.756737\pi\) | |||||||
\(728\) | 19342.4 | + | 14211.6i | 0.984719 | + | 0.723514i | ||||
\(729\) | 4489.05 | 0.228067 | ||||||||
\(730\) | 6556.48 | − | 909.543i | 0.332420 | − | 0.0461147i | ||||
\(731\) | 7182.78 | − | 4146.98i | 0.363427 | − | 0.209824i | ||||
\(732\) | 2774.51 | + | 2698.49i | 0.140094 | + | 0.136255i | ||||
\(733\) | −35573.7 | −1.79256 | −0.896278 | − | 0.443492i | \(-0.853739\pi\) | ||||
−0.896278 | + | 0.443492i | \(0.853739\pi\) | |||||||
\(734\) | −774.385 | − | 5582.19i | −0.0389415 | − | 0.280712i | ||||
\(735\) | 3091.10 | + | 5353.94i | 0.155125 | + | 0.268685i | ||||
\(736\) | −1703.51 | + | 284.749i | −0.0853153 | + | 0.0142609i | ||||
\(737\) | −13666.5 | + | 7890.35i | −0.683055 | + | 0.394362i | ||||
\(738\) | −23181.2 | − | 9413.90i | −1.15625 | − | 0.469553i | ||||
\(739\) | 2622.62 | + | 1514.17i | 0.130547 | + | 0.0753716i | 0.563851 | − | 0.825876i | \(-0.309319\pi\) |
−0.433304 | + | 0.901248i | \(0.642652\pi\) | |||||||
\(740\) | 1893.00 | + | 6691.59i | 0.0940381 | + | 0.332416i | ||||
\(741\) | −6110.88 | + | 2416.03i | −0.302954 | + | 0.119778i | ||||
\(742\) | 25321.1 | − | 3512.65i | 1.25278 | − | 0.173792i | ||||
\(743\) | 9261.66 | − | 16041.7i | 0.457304 | − | 0.792075i | −0.541513 | − | 0.840692i | \(-0.682148\pi\) |
0.998817 | + | 0.0486178i | \(0.0154816\pi\) | |||||||
\(744\) | −1352.47 | + | 12238.3i | −0.0666453 | + | 0.603060i | ||||
\(745\) | 1525.97 | + | 2643.05i | 0.0750432 | + | 0.129979i | ||||
\(746\) | 32376.5 | + | 13148.1i | 1.58899 | + | 0.645290i | ||||
\(747\) | 18282.1 | − | 10555.1i | 0.895455 | − | 0.516991i | ||||
\(748\) | 2944.45 | + | 10408.4i | 0.143930 | + | 0.508780i | ||||
\(749\) | 35014.3i | 1.70814i | ||||||||
\(750\) | 2913.52 | + | 3742.87i | 0.141849 | + | 0.182227i | ||||
\(751\) | −6527.11 | − | 11305.3i | −0.317147 | − | 0.549315i | 0.662744 | − | 0.748846i | \(-0.269392\pi\) |
−0.979892 | + | 0.199530i | \(0.936058\pi\) | |||||||
\(752\) | 11885.5 | + | 19325.9i | 0.576355 | + | 0.937159i | ||||
\(753\) | − | 2926.15i | − | 0.141613i | ||||||
\(754\) | 5232.47 | + | 6721.91i | 0.252726 | + | 0.324665i | ||||
\(755\) | −694.479 | + | 1202.87i | −0.0334764 | + | 0.0579829i | ||||
\(756\) | 24336.3 | − | 25021.9i | 1.17077 | − | 1.20376i | ||||
\(757\) | 11903.2 | − | 20617.0i | 0.571507 | − | 0.989879i | −0.424905 | − | 0.905238i | \(-0.639692\pi\) |
0.996412 | − | 0.0846408i | \(-0.0269743\pi\) | |||||||
\(758\) | 12552.7 | − | 30910.4i | 0.601499 | − | 1.48116i | ||||
\(759\) | 811.292 | 0.0387985 | ||||||||
\(760\) | −4735.20 | + | 1292.37i | −0.226005 | + | 0.0616833i | ||||
\(761\) | −17949.5 | −0.855019 | −0.427510 | − | 0.904011i | \(-0.640609\pi\) | ||||
−0.427510 | + | 0.904011i | \(0.640609\pi\) | |||||||
\(762\) | 2021.66 | − | 4978.22i | 0.0961114 | − | 0.236669i | ||||
\(763\) | 1258.21 | − | 2179.29i | 0.0596990 | − | 0.103402i | ||||
\(764\) | −20657.1 | + | 21239.0i | −0.978201 | + | 1.00576i | ||||
\(765\) | −1100.36 | + | 1905.87i | −0.0520045 | + | 0.0900744i | ||||
\(766\) | −18283.6 | − | 23488.1i | −0.862421 | − | 1.10791i | ||||
\(767\) | 5914.36i | 0.278429i | ||||||||
\(768\) | −4865.91 | + | 9625.87i | −0.228624 | + | 0.452270i | ||||
\(769\) | 7993.33 | + | 13844.9i | 0.374834 | + | 0.649231i | 0.990302 | − | 0.138931i | \(-0.0443665\pi\) |
−0.615469 | + | 0.788161i | \(0.711033\pi\) | |||||||
\(770\) | −5173.04 | − | 6645.56i | −0.242108 | − | 0.311025i | ||||
\(771\) | − | 14733.2i | − | 0.688201i | ||||||
\(772\) | 9955.90 | + | 35193.2i | 0.464146 | + | 1.64071i | ||||
\(773\) | 21879.1 | − | 12631.9i | 1.01803 | − | 0.587758i | 0.104495 | − | 0.994525i | \(-0.466677\pi\) |
0.913532 | + | 0.406767i | \(0.133344\pi\) | |||||||
\(774\) | 10415.7 | + | 4229.83i | 0.483702 | + | 0.196431i | ||||
\(775\) | −12206.5 | − | 21142.3i | −0.565770 | − | 0.979942i | ||||
\(776\) | −14020.4 | − | 1549.43i | −0.648589 | − | 0.0716767i | ||||
\(777\) | 15383.1 | − | 26644.3i | 0.710251 | − | 1.23019i | ||||
\(778\) | 842.601 | − | 116.889i | 0.0388287 | − | 0.00538648i | ||||
\(779\) | 5351.02 | − | 36115.6i | 0.246111 | − | 1.66107i | ||||
\(780\) | 452.563 | + | 1599.77i | 0.0207748 | + | 0.0734371i | ||||
\(781\) | −480.335 | − | 277.321i | −0.0220073 | − | 0.0127059i | ||||
\(782\) | −1046.96 | − | 425.171i | −0.0478762 | − | 0.0194425i | ||||
\(783\) | 10728.2 | − | 6193.93i | 0.489648 | − | 0.282699i | ||||
\(784\) | −1593.38 | − | 57343.9i | −0.0725849 | − | 2.61224i | ||||
\(785\) | −2174.69 | − | 3766.67i | −0.0988763 | − | 0.171259i | ||||
\(786\) | 1615.33 | + | 11644.2i | 0.0733038 | + | 0.528414i | ||||
\(787\) | 6251.77 | 0.283166 | 0.141583 | − | 0.989926i | \(-0.454781\pi\) | ||||
0.141583 | + | 0.989926i | \(0.454781\pi\) | |||||||
\(788\) | 28491.7 | + | 27711.0i | 1.28804 | + | 1.25275i | ||||
\(789\) | −13799.6 | + | 7967.21i | −0.622661 | + | 0.359493i | ||||
\(790\) | 3504.80 | − | 486.200i | 0.157842 | − | 0.0218965i | ||||
\(791\) | −33174.8 | −1.49122 | ||||||||
\(792\) | −8681.02 | + | 11815.1i | −0.389478 | + | 0.530089i | ||||
\(793\) | −4794.19 | − | 2767.93i | −0.214687 | − | 0.123950i | ||||
\(794\) | −14371.9 | − | 18462.9i | −0.642366 | − | 0.825217i | ||||
\(795\) | 1533.48 | + | 885.357i | 0.0684114 | + | 0.0394973i | ||||
\(796\) | −10539.6 | − | 2667.75i | −0.469305 | − | 0.118789i | ||||
\(797\) | − | 28414.0i | − | 1.26283i | −0.775446 | − | 0.631414i | \(-0.782475\pi\) | ||
0.775446 | − | 0.631414i | \(-0.217525\pi\) | |||||||
\(798\) | 18704.8 | + | 11031.1i | 0.829751 | + | 0.489345i | ||||
\(799\) | 14844.0i | 0.657249i | ||||||||
\(800\) | −3525.79 | − | 21092.9i | −0.155819 | − | 0.932184i | ||||
\(801\) | 18334.5 | + | 10585.4i | 0.808760 | + | 0.466938i | ||||
\(802\) | 15593.8 | − | 12138.5i | 0.686579 | − | 0.534447i | ||||
\(803\) | 24986.3 | + | 14425.9i | 1.09807 | + | 0.633969i | ||||
\(804\) | −7380.13 | − | 7177.91i | −0.323728 | − | 0.314858i | ||||
\(805\) | 879.777 | 0.0385193 | ||||||||
\(806\) | −2419.93 | − | 17444.1i | −0.105755 | − | 0.762337i | ||||
\(807\) | 8546.84 | − | 4934.52i | 0.372816 | − | 0.215246i | ||||
\(808\) | 13039.3 | + | 9580.55i | 0.567726 | + | 0.417132i | ||||
\(809\) | −25258.2 | −1.09769 | −0.548845 | − | 0.835924i | \(-0.684932\pi\) | ||||
−0.548845 | + | 0.835924i | \(0.684932\pi\) | |||||||
\(810\) | −1580.77 | + | 219.291i | −0.0685712 | + | 0.00951249i | ||||
\(811\) | −16.6604 | − | 28.8566i | −0.000721363 | − | 0.00124944i | 0.865664 | − | 0.500625i | \(-0.166896\pi\) |
−0.866386 | + | 0.499375i | \(0.833563\pi\) | |||||||
\(812\) | 6907.44 | − | 27289.6i | 0.298527 | − | 1.17940i | ||||
\(813\) | 10713.3 | − | 6185.36i | 0.462157 | − | 0.266826i | ||||
\(814\) | −11405.0 | + | 28084.1i | −0.491086 | + | 1.20927i | ||||
\(815\) | 4289.78 | + | 2476.71i | 0.184374 | + | 0.106448i | ||||
\(816\) | −6010.95 | + | 3696.75i | −0.257874 | + | 0.158593i | ||||
\(817\) | −2404.31 | + | 16227.3i | −0.102957 | + | 0.694887i | ||||
\(818\) | −3532.36 | − | 25463.2i | −0.150986 | − | 1.08839i | ||||
\(819\) | −10642.5 | + | 18433.3i | −0.454063 | + | 0.786461i | ||||
\(820\) | −8954.86 | − | 2266.62i | −0.381362 | − | 0.0965292i | ||||
\(821\) | −3843.61 | − | 6657.34i | −0.163390 | − | 0.283000i | 0.772692 | − | 0.634781i | \(-0.218910\pi\) |
−0.936082 | + | 0.351781i | \(0.885576\pi\) | |||||||
\(822\) | −7046.72 | + | 17352.2i | −0.299006 | + | 0.736285i | ||||
\(823\) | −8835.14 | + | 5100.97i | −0.374208 | + | 0.216049i | −0.675295 | − | 0.737547i | \(-0.735984\pi\) |
0.301087 | + | 0.953597i | \(0.402651\pi\) | |||||||
\(824\) | −14068.9 | + | 6174.00i | −0.594800 | + | 0.261021i | ||||
\(825\) | 10045.5i | 0.423925i | ||||||||
\(826\) | 15422.9 | − | 12005.5i | 0.649676 | − | 0.505721i | ||||
\(827\) | −12625.1 | − | 21867.3i | −0.530855 | − | 0.919468i | −0.999352 | − | 0.0360029i | \(-0.988537\pi\) |
0.468496 | − | 0.883465i | \(-0.344796\pi\) | |||||||
\(828\) | −416.923 | − | 1473.79i | −0.0174989 | − | 0.0618570i | ||||
\(829\) | 7364.89i | 0.308556i | 0.988027 | + | 0.154278i | \(0.0493052\pi\) | ||||
−0.988027 | + | 0.154278i | \(0.950695\pi\) | |||||||
\(830\) | 6150.21 | − | 4787.45i | 0.257201 | − | 0.200210i | ||||
\(831\) | −9771.41 | + | 16924.6i | −0.407902 | + | 0.706507i | ||||
\(832\) | 3368.63 | − | 15054.9i | 0.140368 | − | 0.627326i | ||||
\(833\) | 18766.1 | − | 32503.9i | 0.780562 | − | 1.35197i | ||||
\(834\) | 4487.40 | + | 1822.34i | 0.186314 | + | 0.0756623i | ||||
\(835\) | −2961.17 | −0.122725 | ||||||||
\(836\) | −19747.0 | − | 8232.83i | −0.816942 | − | 0.340596i | ||||
\(837\) | −25611.1 | −1.05764 | ||||||||
\(838\) | 5068.06 | + | 2058.14i | 0.208918 | + | 0.0848416i | ||||
\(839\) | −5958.64 | + | 10320.7i | −0.245191 | + | 0.424683i | −0.962185 | − | 0.272396i | \(-0.912184\pi\) |
0.716995 | + | 0.697079i | \(0.245517\pi\) | |||||||
\(840\) | 3253.08 | − | 4427.52i | 0.133622 | − | 0.181862i | ||||
\(841\) | −7199.21 | + | 12469.4i | −0.295183 | + | 0.511271i | ||||
\(842\) | 4703.23 | − | 3661.09i | 0.192499 | − | 0.149845i | ||||
\(843\) | 8294.30i | 0.338874i | ||||||||
\(844\) | −13050.1 | + | 3691.77i | −0.532230 | + | 0.150564i | ||||
\(845\) | 1688.24 | + | 2924.11i | 0.0687303 | + | 0.119044i | ||||
\(846\) | −15876.7 | + | 12358.8i | −0.645216 | + | 0.502249i | ||||
\(847\) | 10149.2i | 0.411726i | ||||||||
\(848\) | −8607.49 | − | 13995.9i | −0.348564 | − | 0.566769i | ||||
\(849\) | 4241.94 | − | 2449.09i | 0.171476 | − | 0.0990017i | ||||
\(850\) | 5264.49 | − | 12963.5i | 0.212436 | − | 0.523112i | ||||
\(851\) | −1583.27 | − | 2742.31i | −0.0637766 | − | 0.110464i | ||||
\(852\) | 88.7877 | − | 350.778i | 0.00357021 | − | 0.0141050i | ||||
\(853\) | −17429.2 | + | 30188.2i | −0.699605 | + | 1.21175i | 0.268998 | + | 0.963141i | \(0.413308\pi\) |
−0.968603 | + | 0.248611i | \(0.920026\pi\) | |||||||
\(854\) | 2513.75 | + | 18120.5i | 0.100725 | + | 0.726077i | ||||
\(855\) | −1600.39 | − | 4047.86i | −0.0640141 | − | 0.161911i | ||||
\(856\) | 20608.2 | − | 9043.69i | 0.822868 | − | 0.361106i | ||||
\(857\) | 10491.2 | + | 6057.11i | 0.418172 | + | 0.241431i | 0.694295 | − | 0.719691i | \(-0.255716\pi\) |
−0.276123 | + | 0.961122i | \(0.589050\pi\) | |||||||
\(858\) | −2726.61 | + | 6714.12i | −0.108490 | + | 0.267152i | ||||
\(859\) | 7561.24 | − | 4365.48i | 0.300333 | − | 0.173397i | −0.342259 | − | 0.939606i | \(-0.611192\pi\) |
0.642593 | + | 0.766208i | \(0.277859\pi\) | |||||||
\(860\) | 4023.57 | + | 1018.43i | 0.159538 | + | 0.0403817i | ||||
\(861\) | 20433.3 | + | 35391.6i | 0.808788 | + | 1.40086i | ||||
\(862\) | 6441.73 | − | 893.624i | 0.254532 | − | 0.0353097i | ||||
\(863\) | −14814.1 | −0.584332 | −0.292166 | − | 0.956368i | \(-0.594376\pi\) | ||||
−0.292166 | + | 0.956368i | \(0.594376\pi\) | |||||||
\(864\) | −21012.8 | − | 7860.73i | −0.827395 | − | 0.309523i | ||||
\(865\) | −4752.00 | + | 2743.57i | −0.186790 | + | 0.107843i | ||||
\(866\) | 2445.85 | + | 17631.0i | 0.0959738 | + | 0.691832i | ||||
\(867\) | 8320.29 | 0.325919 | ||||||||
\(868\) | −40577.1 | + | 41720.3i | −1.58672 | + | 1.63143i | ||||
\(869\) | 13356.5 | + | 7711.40i | 0.521392 | + | 0.301026i | ||||
\(870\) | 1538.67 | − | 1197.73i | 0.0599605 | − | 0.0466745i | ||||
\(871\) | 12752.4 | + | 7362.63i | 0.496097 | + | 0.286421i | ||||
\(872\) | −1607.63 | − | 177.663i | −0.0624327 | − | 0.00689956i | ||||
\(873\) | − | 12509.0i | − | 0.484954i | ||||||
\(874\) | 1945.82 | − | 1099.55i | 0.0753071 | − | 0.0425548i | ||||
\(875\) | 22419.5i | 0.866191i | ||||||||
\(876\) | −4618.61 | + | 18246.9i | −0.178137 | + | 0.703775i | ||||
\(877\) | 11448.5 | + | 6609.79i | 0.440808 | + | 0.254500i | 0.703940 | − | 0.710259i | \(-0.251422\pi\) |
−0.263132 | + | 0.964760i | \(0.584756\pi\) | |||||||
\(878\) | −16483.7 | − | 21175.9i | −0.633597 | − | 0.813953i | ||||
\(879\) | 9805.20 | + | 5661.04i | 0.376247 | + | 0.217226i | ||||
\(880\) | −2575.23 | + | 4761.13i | −0.0986488 | + | 0.182384i | ||||
\(881\) | 9181.87 | 0.351129 | 0.175565 | − | 0.984468i | \(-0.443825\pi\) | ||||
0.175565 | + | 0.984468i | \(0.443825\pi\) | |||||||
\(882\) | 50389.5 | − | 6990.25i | 1.92370 | − | 0.266864i | ||||
\(883\) | 14364.3 | − | 8293.26i | 0.547450 | − | 0.316071i | −0.200643 | − | 0.979665i | \(-0.564303\pi\) |
0.748093 | + | 0.663594i | \(0.230970\pi\) | |||||||
\(884\) | 7037.28 | − | 7235.54i | 0.267748 | − | 0.275291i | ||||
\(885\) | 1353.81 | 0.0514214 | ||||||||
\(886\) | 2673.85 | + | 19274.6i | 0.101388 | + | 0.730860i | ||||
\(887\) | −5955.03 | − | 10314.4i | −0.225423 | − | 0.390445i | 0.731023 | − | 0.682353i | \(-0.239043\pi\) |
−0.956446 | + | 0.291908i | \(0.905710\pi\) | |||||||
\(888\) | −19655.1 | − | 2172.13i | −0.742774 | − | 0.0820853i | ||||
\(889\) | 21994.3 | − | 12698.4i | 0.829768 | − | 0.479067i | ||||
\(890\) | 7241.86 | + | 2940.92i | 0.272750 | + | 0.110764i | ||||
\(891\) | −6024.21 | − | 3478.08i | −0.226508 | − | 0.130775i | ||||
\(892\) | −25788.0 | + | 7295.23i | −0.967988 | + | 0.273837i | ||||
\(893\) | −23000.1 | − | 18247.9i | −0.861892 | − | 0.683809i | ||||
\(894\) | −8596.10 | + | 1192.49i | −0.321584 | + | 0.0446116i | ||||
\(895\) | 5751.73 | − | 9962.29i | 0.214815 | − | 0.372070i | ||||
\(896\) | −46096.9 | + | 21775.5i | −1.71874 | + | 0.811906i | ||||
\(897\) | −378.516 | − | 655.608i | −0.0140895 | − | 0.0244037i | ||||
\(898\) | 2062.78 | + | 837.698i | 0.0766548 | + | 0.0311295i | ||||
\(899\) | −17887.6 | + | 10327.4i | −0.663611 | + | 0.383136i | ||||
\(900\) | 18248.5 | − | 5162.37i | 0.675871 | − | 0.191199i | ||||
\(901\) | − | 10750.0i | − | 0.397487i | ||||||
\(902\) | −24731.7 | − | 31771.7i | −0.912945 | − | 1.17282i | ||||
\(903\) | −9181.05 | − | 15902.1i | −0.338346 | − | 0.586032i | ||||
\(904\) | 8568.56 | + | 19525.5i | 0.315250 | + | 0.718374i | ||||
\(905\) | − | 4180.78i | − | 0.153562i | ||||||
\(906\) | −2426.07 | − | 3116.66i | −0.0889635 | − | 0.114287i | ||||
\(907\) | 13757.1 | − | 23828.0i | 0.503636 | − | 0.872323i | −0.496355 | − | 0.868119i | \(-0.665329\pi\) |
0.999991 | − | 0.00420323i | \(-0.00133793\pi\) | |||||||
\(908\) | 28864.3 | + | 28073.4i | 1.05495 | + | 1.02605i | ||||
\(909\) | −7174.45 | + | 12426.5i | −0.261784 | + | 0.453423i | ||||
\(910\) | −2956.77 | + | 7280.89i | −0.107710 | + | 0.265230i | ||||
\(911\) | 14978.4 | 0.544740 | 0.272370 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272370 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(912\) | 1661.37 | − | 13858.2i | 0.0603219 | − | 0.503169i | ||||
\(913\) | 33971.6 | 1.23143 | ||||||||
\(914\) | −12015.7 | + | 29588.1i | −0.434841 | + | 1.07077i | ||||
\(915\) | −633.587 | + | 1097.40i | −0.0228915 | + | 0.0396493i | ||||
\(916\) | 10151.5 | + | 9873.32i | 0.366173 | + | 0.356140i | ||||
\(917\) | −27782.7 | + | 48121.0i | −1.00051 | + | 1.73293i | ||||
\(918\) | −9016.23 | − | 11582.7i | −0.324161 | − | 0.416435i | ||||
\(919\) | − | 6190.26i | − | 0.222196i | −0.993809 | − | 0.111098i | \(-0.964563\pi\) | ||
0.993809 | − | 0.111098i | \(-0.0354367\pi\) | |||||||
\(920\) | −227.234 | − | 517.807i | −0.00814313 | − | 0.0185561i | ||||
\(921\) | 6944.82 | + | 12028.8i | 0.248468 | + | 0.430360i | ||||
\(922\) | −6156.60 | − | 7909.09i | −0.219910 | − | 0.282508i | ||||
\(923\) | 517.547i | 0.0184564i | ||||||||
\(924\) | 23043.2 | − | 6518.76i | 0.820418 | − | 0.232090i | ||||
\(925\) | 33955.4 | − | 19604.2i | 1.20697 | − | 0.696845i | ||||
\(926\) | −28440.3 | − | 11549.6i | −1.00929 | − | 0.409874i | ||||
\(927\) | −6812.39 | − | 11799.4i | −0.241368 | − | 0.418062i | ||||
\(928\) | −17845.8 | + | 2983.02i | −0.631269 | + | 0.105520i | ||||
\(929\) | −14652.9 | + | 25379.6i | −0.517487 | + | 0.896314i | 0.482306 | + | 0.876003i | \(0.339799\pi\) |
−0.999794 | + | 0.0203118i | \(0.993534\pi\) | |||||||
\(930\) | −3993.02 | + | 553.928i | −0.140792 | + | 0.0195312i | ||||
\(931\) | 27294.0 | + | 69034.7i | 0.960820 | + | 2.43021i | ||||
\(932\) | −10482.6 | + | 2965.44i | −0.368420 | + | 0.104223i | ||||
\(933\) | 1973.11 | + | 1139.17i | 0.0692354 | + | 0.0399731i | ||||
\(934\) | −35461.6 | − | 14401.0i | −1.24233 | − | 0.504512i | ||||
\(935\) | −3067.01 | + | 1770.74i | −0.107275 | + | 0.0619351i | ||||
\(936\) | 13598.0 | + | 1502.74i | 0.474856 | + | 0.0524772i | ||||
\(937\) | −1809.54 | − | 3134.21i | −0.0630897 | − | 0.109275i | 0.832755 | − | 0.553641i | \(-0.186762\pi\) |
−0.895845 | + | 0.444367i | \(0.853429\pi\) | |||||||
\(938\) | −6686.52 | − | 48200.1i | −0.232753 | − | 1.67781i | ||||
\(939\) | −13476.2 | −0.468350 | ||||||||
\(940\) | −5179.08 | + | 5324.99i | −0.179705 | + | 0.184768i | ||||
\(941\) | 43981.4 | − | 25392.7i | 1.52365 | − | 0.879679i | 0.524040 | − | 0.851694i | \(-0.324424\pi\) |
0.999608 | − | 0.0279849i | \(-0.00890904\pi\) | |||||||
\(942\) | 12250.5 | − | 1699.44i | 0.423717 | − | 0.0587799i | ||||
\(943\) | 4206.12 | 0.145249 | ||||||||
\(944\) | −11049.6 | − | 5976.57i | −0.380967 | − | 0.206060i | ||||
\(945\) | 9896.95 | + | 5714.01i | 0.340686 | + | 0.196695i | ||||
\(946\) | 11112.4 | + | 14275.6i | 0.381919 | + | 0.490633i | ||||
\(947\) | 14499.4 | + | 8371.21i | 0.497535 | + | 0.287252i | 0.727695 | − | 0.685901i | \(-0.240592\pi\) |
−0.230160 | + | 0.973153i | \(0.573925\pi\) | |||||||
\(948\) | −2468.90 | + | 9753.99i | −0.0845844 | + | 0.334172i | ||||
\(949\) | − | 26922.0i | − | 0.920892i | ||||||
\(950\) | 13614.7 | + | 24093.3i | 0.464968 | + | 0.822831i | ||||
\(951\) | − | 10502.9i | − | 0.358127i | ||||||
\(952\) | −33153.2 | − | 3663.82i | −1.12868 | − | 0.124732i | ||||
\(953\) | 23390.3 | + | 13504.4i | 0.795055 | + | 0.459025i | 0.841739 | − | 0.539885i | \(-0.181532\pi\) |
−0.0466842 | + | 0.998910i | \(0.514865\pi\) | |||||||
\(954\) | 11497.9 | − | 8950.23i | 0.390209 | − | 0.303747i | ||||
\(955\) | −8400.69 | − | 4850.14i | −0.284649 | − | 0.164342i | ||||
\(956\) | −16052.2 | + | 16504.4i | −0.543060 | + | 0.558359i | ||||
\(957\) | 8499.05 | 0.287080 | ||||||||
\(958\) | −3500.47 | − | 25233.3i | −0.118053 | − | 0.850991i | ||||
\(959\) | −76663.5 | + | 44261.7i | −2.58143 | + | 1.49039i | ||||
\(960\) | −3446.11 | − | 771.090i | −0.115857 | − | 0.0259238i | ||||
\(961\) | 12911.5 | 0.433404 | ||||||||
\(962\) | 28016.0 | − | 3886.50i | 0.938952 | − | 0.130255i | ||||
\(963\) | 9978.81 | + | 17283.8i | 0.333918 | + | 0.578362i | ||||
\(964\) | 12192.6 | + | 3086.16i | 0.407363 | + | 0.103110i | ||||
\(965\) | −10370.3 | + | 5987.29i | −0.345940 | + | 0.199728i | ||||
\(966\) | −941.290 | + | 2317.88i | −0.0313515 | + | 0.0772013i | ||||
\(967\) | −9165.59 | − | 5291.75i | −0.304804 | − | 0.175979i | 0.339795 | − | 0.940500i | \(-0.389642\pi\) |
−0.644599 | + | 0.764521i | \(0.722976\pi\) | |||||||
\(968\) | 5973.50 | − | 2621.41i | 0.198343 | − | 0.0870404i | ||||
\(969\) | 5675.65 | − | 7153.74i | 0.188161 | − | 0.237163i | ||||
\(970\) | −634.593 | − | 4574.49i | −0.0210057 | − | 0.151421i | ||||
\(971\) | −2048.59 | + | 3548.26i | −0.0677058 | + | 0.117270i | −0.897891 | − | 0.440218i | \(-0.854901\pi\) |
0.830185 | + | 0.557488i | \(0.188235\pi\) | |||||||
\(972\) | 7682.41 | − | 30351.3i | 0.253512 | − | 1.00156i | ||||
\(973\) | 11446.4 | + | 19825.8i | 0.377138 | + | 0.653222i | ||||
\(974\) | −4983.05 | + | 12270.5i | −0.163929 | + | 0.403667i | ||||
\(975\) | 8117.78 | − | 4686.80i | 0.266643 | − | 0.153946i | ||||
\(976\) | 10015.8 | − | 6159.77i | 0.328483 | − | 0.202018i | ||||
\(977\) | − | 41698.3i | − | 1.36545i | −0.730675 | − | 0.682726i | \(-0.760794\pi\) | ||
0.730675 | − | 0.682726i | \(-0.239206\pi\) | |||||||
\(978\) | −11114.9 | + | 8652.05i | −0.363410 | + | 0.282886i | ||||
\(979\) | 17034.5 | + | 29504.6i | 0.556103 | + | 0.963199i | ||||
\(980\) | 18072.6 | − | 5112.62i | 0.589091 | − | 0.166650i | ||||
\(981\) | − | 1434.32i | − | 0.0466814i | ||||||
\(982\) | 34690.1 | − | 27003.5i | 1.12730 | − | 0.877510i | ||||
\(983\) | −8614.30 | + | 14920.4i | −0.279505 | + | 0.484117i | −0.971262 | − | 0.238013i | \(-0.923504\pi\) |
0.691757 | + | 0.722131i | \(0.256837\pi\) | |||||||
\(984\) | 15552.7 | − | 21167.5i | 0.503862 | − | 0.685768i | ||||
\(985\) | −6506.37 | + | 11269.4i | −0.210467 | + | 0.364540i | ||||
\(986\) | −10967.9 | − | 4454.06i | −0.354248 | − | 0.143860i | ||||
\(987\) | 32863.3 | 1.05983 | ||||||||
\(988\) | 2560.14 | + | 19798.7i | 0.0824383 | + | 0.637531i | ||||
\(989\) | −1889.88 | −0.0607632 | ||||||||
\(990\) | −4447.45 | − | 1806.11i | −0.142777 | − | 0.0579818i | ||||
\(991\) | 2279.31 | − | 3947.88i | 0.0730623 | − | 0.126548i | −0.827180 | − | 0.561937i | \(-0.810056\pi\) |
0.900242 | + | 0.435390i | \(0.143389\pi\) | |||||||
\(992\) | 35035.6 | + | 13106.6i | 1.12135 | + | 0.419490i | ||||
\(993\) | 1039.56 | − | 1800.57i | 0.0332220 | − | 0.0575421i | ||||
\(994\) | 1349.61 | − | 1050.57i | 0.0430655 | − | 0.0335231i | ||||
\(995\) | − | 3559.54i | − | 0.113412i | ||||||
\(996\) | 6032.86 | + | 21325.6i | 0.191926 | + | 0.678442i | ||||
\(997\) | −3940.09 | − | 6824.44i | −0.125159 | − | 0.216782i | 0.796636 | − | 0.604460i | \(-0.206611\pi\) |
−0.921795 | + | 0.387677i | \(0.873278\pi\) | |||||||
\(998\) | 39484.9 | − | 30735.8i | 1.25238 | − | 0.974875i | ||||
\(999\) | − | 41132.4i | − | 1.30267i |
(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 | 76.4.f.a.27.11 | ✓ | 56 | |
4.3 | odd | 2 | inner | 76.4.f.a.27.20 | yes | 56 | |
19.12 | odd | 6 | inner | 76.4.f.a.31.20 | yes | 56 | |
76.31 | even | 6 | inner | 76.4.f.a.31.11 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.f.a.27.11 | ✓ | 56 | 1.1 | even | 1 | trivial | |
76.4.f.a.27.20 | yes | 56 | 4.3 | odd | 2 | inner | |
76.4.f.a.31.11 | yes | 56 | 76.31 | even | 6 | inner | |
76.4.f.a.31.20 | yes | 56 | 19.12 | odd | 6 | inner |