Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(37,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.37");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.v (of order \(12\), degree \(4\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 163.5 | ||
Character | \(\chi\) | \(=\) | 210.163 |
Dual form | 210.3.v.a.67.5 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0.448288 | − | 1.67303i | 0.149429 | − | 0.557678i | ||||
\(4\) | −1.73205 | + | 1.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | −4.09442 | + | 2.86979i | −0.818884 | + | 0.573959i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −3.46105 | − | 6.08450i | −0.494436 | − | 0.869214i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.59808 | − | 1.50000i | −0.288675 | − | 0.166667i | ||||
\(10\) | −5.41887 | − | 4.54267i | −0.541887 | − | 0.454267i | ||||
\(11\) | −5.62423 | − | 9.74146i | −0.511294 | − | 0.885587i | −0.999914 | − | 0.0130905i | \(-0.995833\pi\) |
0.488620 | − | 0.872496i | \(-0.337500\pi\) | |||||||
\(12\) | 0.896575 | + | 3.34607i | 0.0747146 | + | 0.278839i | ||||
\(13\) | −5.84142 | − | 5.84142i | −0.449340 | − | 0.449340i | 0.445795 | − | 0.895135i | \(-0.352921\pi\) |
−0.895135 | + | 0.445795i | \(0.852921\pi\) | |||||||
\(14\) | 7.04475 | − | 6.95496i | 0.503196 | − | 0.496783i | ||||
\(15\) | 2.96578 | + | 8.13659i | 0.197719 | + | 0.542440i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | 24.8241 | + | 6.65160i | 1.46024 | + | 0.391270i | 0.899573 | − | 0.436770i | \(-0.143878\pi\) |
0.560668 | + | 0.828041i | \(0.310544\pi\) | |||||||
\(18\) | 1.09808 | − | 4.09808i | 0.0610042 | − | 0.227671i | ||||
\(19\) | −27.5095 | − | 15.8826i | −1.44787 | − | 0.835926i | −0.449513 | − | 0.893274i | \(-0.648402\pi\) |
−0.998354 | + | 0.0573477i | \(0.981736\pi\) | |||||||
\(20\) | 4.22195 | − | 9.06505i | 0.211098 | − | 0.453252i | ||||
\(21\) | −11.7311 | + | 3.06284i | −0.558624 | + | 0.145850i | ||||
\(22\) | 11.2485 | − | 11.2485i | 0.511294 | − | 0.511294i | ||||
\(23\) | −39.8193 | + | 10.6696i | −1.73127 | + | 0.463894i | −0.980476 | − | 0.196638i | \(-0.936998\pi\) |
−0.750798 | + | 0.660532i | \(0.770331\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 8.52858 | − | 23.5003i | 0.341143 | − | 0.940011i | ||||
\(26\) | 5.84142 | − | 10.1176i | 0.224670 | − | 0.389140i | ||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 12.0792 | + | 7.07761i | 0.431400 | + | 0.252772i | ||||
\(29\) | − | 8.29704i | − | 0.286105i | −0.989715 | − | 0.143052i | \(-0.954308\pi\) | ||
0.989715 | − | 0.143052i | \(-0.0456917\pi\) | |||||||
\(30\) | −10.0292 | + | 7.02953i | −0.334308 | + | 0.234318i | ||||
\(31\) | 6.00177 | + | 10.3954i | 0.193605 | + | 0.335334i | 0.946442 | − | 0.322873i | \(-0.104649\pi\) |
−0.752837 | + | 0.658207i | \(0.771315\pi\) | |||||||
\(32\) | 5.46410 | + | 1.46410i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −18.8190 | + | 5.04255i | −0.570274 | + | 0.152805i | ||||
\(34\) | 36.3450i | 1.06897i | ||||||||
\(35\) | 31.6323 | + | 14.9800i | 0.903779 | + | 0.428000i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 6.32737 | + | 23.6141i | 0.171010 | + | 0.638218i | 0.997197 | + | 0.0748217i | \(0.0238388\pi\) |
−0.826187 | + | 0.563396i | \(0.809495\pi\) | |||||||
\(38\) | 11.6269 | − | 43.3921i | 0.305970 | − | 1.14190i | ||||
\(39\) | −12.3915 | + | 7.15424i | −0.317731 | + | 0.183442i | ||||
\(40\) | 13.9284 | + | 2.44926i | 0.348211 | + | 0.0612314i | ||||
\(41\) | 42.9567 | 1.04772 | 0.523862 | − | 0.851803i | \(-0.324491\pi\) | ||||
0.523862 | + | 0.851803i | \(0.324491\pi\) | |||||||
\(42\) | −8.47781 | − | 14.9039i | −0.201853 | − | 0.354855i | ||||
\(43\) | −37.4962 | − | 37.4962i | −0.872005 | − | 0.872005i | 0.120685 | − | 0.992691i | \(-0.461491\pi\) |
−0.992691 | + | 0.120685i | \(0.961491\pi\) | |||||||
\(44\) | 19.4829 | + | 11.2485i | 0.442793 | + | 0.255647i | ||||
\(45\) | 14.9423 | − | 1.31431i | 0.332051 | − | 0.0292069i | ||||
\(46\) | −29.1498 | − | 50.4889i | −0.633690 | − | 1.09758i | ||||
\(47\) | 9.60246 | + | 35.8369i | 0.204308 | + | 0.762487i | 0.989659 | + | 0.143437i | \(0.0458154\pi\) |
−0.785352 | + | 0.619050i | \(0.787518\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | −25.0423 | + | 42.1175i | −0.511067 | + | 0.859541i | ||||
\(50\) | 35.2237 | + | 3.04855i | 0.704473 | + | 0.0609710i | ||||
\(51\) | 22.2567 | − | 38.5497i | 0.436405 | − | 0.755876i | ||||
\(52\) | 15.9590 | + | 4.27621i | 0.306905 | + | 0.0822349i | ||||
\(53\) | −2.96326 | + | 11.0590i | −0.0559106 | + | 0.208661i | −0.988230 | − | 0.152974i | \(-0.951115\pi\) |
0.932320 | + | 0.361635i | \(0.117781\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 50.9839 | + | 23.7452i | 0.926981 | + | 0.431732i | ||||
\(56\) | −5.24690 | + | 19.0911i | −0.0936946 | + | 0.340912i | ||||
\(57\) | −38.9043 | + | 38.9043i | −0.682531 | + | 0.682531i | ||||
\(58\) | 11.3340 | − | 3.03693i | 0.195413 | − | 0.0523608i | ||||
\(59\) | 52.5762 | − | 30.3549i | 0.891121 | − | 0.514489i | 0.0168122 | − | 0.999859i | \(-0.494648\pi\) |
0.874309 | + | 0.485370i | \(0.161315\pi\) | |||||||
\(60\) | −13.2735 | − | 11.1272i | −0.221225 | − | 0.185454i | ||||
\(61\) | 18.8287 | − | 32.6122i | 0.308667 | − | 0.534627i | −0.669404 | − | 0.742898i | \(-0.733451\pi\) |
0.978071 | + | 0.208272i | \(0.0667839\pi\) | |||||||
\(62\) | −12.0035 | + | 12.0035i | −0.193605 | + | 0.193605i | ||||
\(63\) | −0.134677 | + | 20.9996i | −0.00213774 | + | 0.333326i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 40.6809 | + | 7.15356i | 0.625860 | + | 0.110055i | ||||
\(66\) | −13.7765 | − | 23.8616i | −0.208735 | − | 0.361539i | ||||
\(67\) | −78.8176 | − | 21.1191i | −1.17638 | − | 0.315211i | −0.382892 | − | 0.923793i | \(-0.625072\pi\) |
−0.793491 | + | 0.608583i | \(0.791738\pi\) | |||||||
\(68\) | −49.6482 | + | 13.3032i | −0.730120 | + | 0.195635i | ||||
\(69\) | 71.4020i | 1.03481i | ||||||||
\(70\) | −8.88486 | + | 48.6935i | −0.126927 | + | 0.695622i | ||||
\(71\) | 1.19909 | 0.0168886 | 0.00844432 | − | 0.999964i | \(-0.497312\pi\) | ||||
0.00844432 | + | 0.999964i | \(0.497312\pi\) | |||||||
\(72\) | 2.19615 | + | 8.19615i | 0.0305021 | + | 0.113835i | ||||
\(73\) | −18.5123 | + | 69.0889i | −0.253593 | + | 0.946423i | 0.715274 | + | 0.698844i | \(0.246302\pi\) |
−0.968868 | + | 0.247579i | \(0.920365\pi\) | |||||||
\(74\) | −29.9414 | + | 17.2867i | −0.404614 | + | 0.233604i | ||||
\(75\) | −35.4935 | − | 24.8035i | −0.473247 | − | 0.330713i | ||||
\(76\) | 63.5304 | 0.835926 | ||||||||
\(77\) | −39.8061 | + | 67.9363i | −0.516963 | + | 0.882290i | ||||
\(78\) | −14.3085 | − | 14.3085i | −0.183442 | − | 0.183442i | ||||
\(79\) | −71.0156 | − | 41.0009i | −0.898932 | − | 0.518999i | −0.0220786 | − | 0.999756i | \(-0.507028\pi\) |
−0.876854 | + | 0.480757i | \(0.840362\pi\) | |||||||
\(80\) | 1.75241 | + | 19.9231i | 0.0219051 | + | 0.249038i | ||||
\(81\) | 4.50000 | + | 7.79423i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 15.7232 | + | 58.6799i | 0.191747 | + | 0.715609i | ||||
\(83\) | 103.192 | + | 103.192i | 1.24328 | + | 1.24328i | 0.958631 | + | 0.284651i | \(0.0918777\pi\) |
0.284651 | + | 0.958631i | \(0.408122\pi\) | |||||||
\(84\) | 17.2560 | − | 17.0361i | 0.205429 | − | 0.202811i | ||||
\(85\) | −120.729 | + | 44.0056i | −1.42034 | + | 0.517713i | ||||
\(86\) | 37.4962 | − | 64.9454i | 0.436003 | − | 0.755179i | ||||
\(87\) | −13.8812 | − | 3.71946i | −0.159554 | − | 0.0427524i | ||||
\(88\) | −8.23445 | + | 30.7314i | −0.0935733 | + | 0.349220i | ||||
\(89\) | −12.6471 | − | 7.30178i | −0.142102 | − | 0.0820425i | 0.427264 | − | 0.904127i | \(-0.359478\pi\) |
−0.569365 | + | 0.822085i | \(0.692811\pi\) | |||||||
\(90\) | 7.26464 | + | 19.9305i | 0.0807183 | + | 0.221450i | ||||
\(91\) | −15.3247 | + | 55.7595i | −0.168403 | + | 0.612742i | ||||
\(92\) | 58.2995 | − | 58.2995i | 0.633690 | − | 0.633690i | ||||
\(93\) | 20.0823 | − | 5.38104i | 0.215939 | − | 0.0578606i | ||||
\(94\) | −45.4393 | + | 26.2344i | −0.483397 | + | 0.279090i | ||||
\(95\) | 158.215 | − | 13.9164i | 1.66542 | − | 0.146489i | ||||
\(96\) | 4.89898 | − | 8.48528i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 24.6424 | − | 24.6424i | 0.254045 | − | 0.254045i | −0.568582 | − | 0.822627i | \(-0.692508\pi\) |
0.822627 | + | 0.568582i | \(0.192508\pi\) | |||||||
\(98\) | −66.6997 | − | 18.7923i | −0.680609 | − | 0.191758i | ||||
\(99\) | 33.7454i | 0.340863i | ||||||||
\(100\) | 8.72836 | + | 49.2323i | 0.0872836 | + | 0.492323i | ||||
\(101\) | −80.5667 | − | 139.546i | −0.797690 | − | 1.38164i | −0.921117 | − | 0.389286i | \(-0.872722\pi\) |
0.123427 | − | 0.992354i | \(-0.460612\pi\) | |||||||
\(102\) | 60.8064 | + | 16.2930i | 0.596141 | + | 0.159735i | ||||
\(103\) | −65.6221 | + | 17.5834i | −0.637108 | + | 0.170712i | −0.562893 | − | 0.826530i | \(-0.690312\pi\) |
−0.0742147 | + | 0.997242i | \(0.523645\pi\) | |||||||
\(104\) | 23.3657i | 0.224670i | ||||||||
\(105\) | 39.2424 | − | 46.2064i | 0.373737 | − | 0.440061i | ||||
\(106\) | −16.1916 | −0.152751 | ||||||||
\(107\) | −7.60901 | − | 28.3972i | −0.0711122 | − | 0.265394i | 0.921211 | − | 0.389062i | \(-0.127201\pi\) |
−0.992324 | + | 0.123668i | \(0.960534\pi\) | |||||||
\(108\) | 2.68973 | − | 10.0382i | 0.0249049 | − | 0.0929463i | ||||
\(109\) | 147.093 | − | 84.9242i | 1.34948 | − | 0.779121i | 0.361302 | − | 0.932449i | \(-0.382332\pi\) |
0.988175 | + | 0.153327i | \(0.0489989\pi\) | |||||||
\(110\) | −13.7752 | + | 78.3367i | −0.125229 | + | 0.712152i | ||||
\(111\) | 42.3436 | 0.381473 | ||||||||
\(112\) | −27.9994 | − | 0.179570i | −0.249995 | − | 0.00160330i | ||||
\(113\) | −79.5633 | − | 79.5633i | −0.704100 | − | 0.704100i | 0.261188 | − | 0.965288i | \(-0.415886\pi\) |
−0.965288 | + | 0.261188i | \(0.915886\pi\) | |||||||
\(114\) | −67.3842 | − | 38.9043i | −0.591089 | − | 0.341265i | ||||
\(115\) | 132.418 | − | 157.959i | 1.15146 | − | 1.37355i | ||||
\(116\) | 8.29704 | + | 14.3709i | 0.0715262 | + | 0.123887i | ||||
\(117\) | 6.41432 | + | 23.9386i | 0.0548232 | + | 0.204603i | ||||
\(118\) | 60.7097 | + | 60.7097i | 0.514489 | + | 0.514489i | ||||
\(119\) | −45.4458 | − | 174.064i | −0.381897 | − | 1.46272i | ||||
\(120\) | 10.3416 | − | 22.2047i | 0.0861803 | − | 0.185040i | ||||
\(121\) | −2.76398 | + | 4.78736i | −0.0228428 | + | 0.0395649i | ||||
\(122\) | 51.4409 | + | 13.7835i | 0.421647 | + | 0.112980i | ||||
\(123\) | 19.2569 | − | 71.8679i | 0.156561 | − | 0.584292i | ||||
\(124\) | −20.7907 | − | 12.0035i | −0.167667 | − | 0.0968027i | ||||
\(125\) | 32.5214 | + | 120.695i | 0.260171 | + | 0.965563i | ||||
\(126\) | −28.7352 | + | 7.50240i | −0.228057 | + | 0.0595429i | ||||
\(127\) | 76.9204 | − | 76.9204i | 0.605673 | − | 0.605673i | −0.336140 | − | 0.941812i | \(-0.609121\pi\) |
0.941812 | + | 0.336140i | \(0.109121\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | −79.5415 | + | 45.9233i | −0.616601 | + | 0.355995i | ||||
\(130\) | 5.11828 | + | 58.1895i | 0.0393714 | + | 0.447611i | ||||
\(131\) | 89.9974 | − | 155.880i | 0.687003 | − | 1.18992i | −0.285800 | − | 0.958289i | \(-0.592259\pi\) |
0.972803 | − | 0.231635i | \(-0.0744074\pi\) | |||||||
\(132\) | 27.5530 | − | 27.5530i | 0.208735 | − | 0.208735i | ||||
\(133\) | −1.42602 | + | 222.352i | −0.0107219 | + | 1.67182i | ||||
\(134\) | − | 115.397i | − | 0.861172i | ||||||
\(135\) | 4.49957 | − | 25.5882i | 0.0333302 | − | 0.189542i | ||||
\(136\) | −36.3450 | − | 62.9514i | −0.267243 | − | 0.462878i | ||||
\(137\) | −226.592 | − | 60.7150i | −1.65395 | − | 0.443175i | −0.693237 | − | 0.720709i | \(-0.743816\pi\) |
−0.960716 | + | 0.277534i | \(0.910483\pi\) | |||||||
\(138\) | −97.5370 | + | 26.1350i | −0.706790 | + | 0.189384i | ||||
\(139\) | − | 224.218i | − | 1.61308i | −0.591182 | − | 0.806538i | \(-0.701339\pi\) | ||
0.591182 | − | 0.806538i | \(-0.298661\pi\) | |||||||
\(140\) | −69.7687 | + | 5.68612i | −0.498348 | + | 0.0406151i | ||||
\(141\) | 64.2609 | 0.455751 | ||||||||
\(142\) | 0.438899 | + | 1.63799i | 0.00309083 | + | 0.0115352i | ||||
\(143\) | −24.0504 | + | 89.7574i | −0.168185 | + | 0.627674i | ||||
\(144\) | −10.3923 | + | 6.00000i | −0.0721688 | + | 0.0416667i | ||||
\(145\) | 23.8108 | + | 33.9716i | 0.164212 | + | 0.234287i | ||||
\(146\) | −101.153 | −0.692830 | ||||||||
\(147\) | 59.2378 | + | 60.7773i | 0.402978 | + | 0.413451i | ||||
\(148\) | −34.5734 | − | 34.5734i | −0.233604 | − | 0.233604i | ||||
\(149\) | 99.1675 | + | 57.2544i | 0.665554 | + | 0.384258i | 0.794390 | − | 0.607408i | \(-0.207791\pi\) |
−0.128836 | + | 0.991666i | \(0.541124\pi\) | |||||||
\(150\) | 20.8907 | − | 57.5637i | 0.139271 | − | 0.383758i | ||||
\(151\) | −48.4855 | − | 83.9793i | −0.321096 | − | 0.556154i | 0.659619 | − | 0.751601i | \(-0.270718\pi\) |
−0.980714 | + | 0.195446i | \(0.937385\pi\) | |||||||
\(152\) | 23.2537 | + | 86.7841i | 0.152985 | + | 0.570948i | ||||
\(153\) | −54.5175 | − | 54.5175i | −0.356324 | − | 0.356324i | ||||
\(154\) | −107.373 | − | 29.5098i | −0.697226 | − | 0.191622i | ||||
\(155\) | −54.4063 | − | 25.3392i | −0.351008 | − | 0.163479i | ||||
\(156\) | 14.3085 | − | 24.7830i | 0.0917211 | − | 0.158866i | ||||
\(157\) | 124.509 | + | 33.3622i | 0.793052 | + | 0.212498i | 0.632531 | − | 0.774535i | \(-0.282016\pi\) |
0.160521 | + | 0.987032i | \(0.448683\pi\) | |||||||
\(158\) | 30.0147 | − | 112.017i | 0.189967 | − | 0.708965i | ||||
\(159\) | 17.1737 | + | 9.91526i | 0.108011 | + | 0.0623602i | ||||
\(160\) | −26.5740 | + | 9.68619i | −0.166088 | + | 0.0605387i | ||||
\(161\) | 202.735 | + | 205.353i | 1.25923 | + | 1.27548i | ||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 248.548 | − | 66.5982i | 1.52483 | − | 0.408578i | 0.603503 | − | 0.797360i | \(-0.293771\pi\) |
0.921329 | + | 0.388783i | \(0.127104\pi\) | |||||||
\(164\) | −74.4031 | + | 42.9567i | −0.453678 | + | 0.261931i | ||||
\(165\) | 62.5820 | − | 74.6531i | 0.379285 | − | 0.452443i | ||||
\(166\) | −103.192 | + | 178.735i | −0.621641 | + | 1.07671i | ||||
\(167\) | −20.8857 | + | 20.8857i | −0.125064 | + | 0.125064i | −0.766868 | − | 0.641804i | \(-0.778186\pi\) |
0.641804 | + | 0.766868i | \(0.278186\pi\) | |||||||
\(168\) | 29.5879 | + | 17.3365i | 0.176119 | + | 0.103194i | ||||
\(169\) | − | 100.756i | − | 0.596188i | ||||||
\(170\) | −104.303 | − | 148.812i | −0.613545 | − | 0.875363i | ||||
\(171\) | 47.6478 | + | 82.5284i | 0.278642 | + | 0.482622i | ||||
\(172\) | 102.442 | + | 27.4491i | 0.595591 | + | 0.159588i | ||||
\(173\) | −208.410 | + | 55.8433i | −1.20468 | + | 0.322794i | −0.804673 | − | 0.593718i | \(-0.797660\pi\) |
−0.400009 | + | 0.916511i | \(0.630993\pi\) | |||||||
\(174\) | − | 20.3235i | − | 0.116802i | ||||||
\(175\) | −172.505 | + | 29.4436i | −0.985745 | + | 0.168249i | ||||
\(176\) | −44.9939 | −0.255647 | ||||||||
\(177\) | −27.2154 | − | 101.569i | −0.153759 | − | 0.573838i | ||||
\(178\) | 5.34528 | − | 19.9488i | 0.0300296 | − | 0.112072i | ||||
\(179\) | −132.468 | + | 76.4803i | −0.740044 | + | 0.427264i | −0.822085 | − | 0.569364i | \(-0.807189\pi\) |
0.0820415 | + | 0.996629i | \(0.473856\pi\) | |||||||
\(180\) | −24.5665 | + | 17.2188i | −0.136481 | + | 0.0956598i | ||||
\(181\) | −61.7819 | −0.341336 | −0.170668 | − | 0.985329i | \(-0.554593\pi\) | ||||
−0.170668 | + | 0.985329i | \(0.554593\pi\) | |||||||
\(182\) | −81.7781 | − | 0.524471i | −0.449330 | − | 0.00288171i | ||||
\(183\) | −46.1206 | − | 46.1206i | −0.252025 | − | 0.252025i | ||||
\(184\) | 100.978 | + | 58.2995i | 0.548792 | + | 0.316845i | ||||
\(185\) | −93.6743 | − | 78.5276i | −0.506348 | − | 0.424474i | ||||
\(186\) | 14.7013 | + | 25.4633i | 0.0790390 | + | 0.136900i | ||||
\(187\) | −74.8202 | − | 279.233i | −0.400108 | − | 1.49322i | ||||
\(188\) | −52.4688 | − | 52.4688i | −0.279090 | − | 0.279090i | ||||
\(189\) | 35.0726 | + | 9.63917i | 0.185569 | + | 0.0510009i | ||||
\(190\) | 76.9210 | + | 211.032i | 0.404847 | + | 1.11070i | ||||
\(191\) | 11.1433 | − | 19.3007i | 0.0583417 | − | 0.101051i | −0.835379 | − | 0.549674i | \(-0.814752\pi\) |
0.893721 | + | 0.448623i | \(0.148085\pi\) | |||||||
\(192\) | 13.3843 | + | 3.58630i | 0.0697097 | + | 0.0186787i | ||||
\(193\) | 60.8969 | − | 227.270i | 0.315528 | − | 1.17757i | −0.607969 | − | 0.793961i | \(-0.708016\pi\) |
0.923497 | − | 0.383606i | \(-0.125318\pi\) | |||||||
\(194\) | 42.6818 | + | 24.6424i | 0.220009 | + | 0.127023i | ||||
\(195\) | 30.2049 | − | 64.8536i | 0.154897 | − | 0.332582i | ||||
\(196\) | 1.25696 | − | 97.9919i | 0.00641308 | − | 0.499959i | ||||
\(197\) | −144.812 | + | 144.812i | −0.735086 | + | 0.735086i | −0.971623 | − | 0.236537i | \(-0.923988\pi\) |
0.236537 | + | 0.971623i | \(0.423988\pi\) | |||||||
\(198\) | −46.0971 | + | 12.3517i | −0.232813 | + | 0.0623822i | ||||
\(199\) | −166.521 | + | 96.1408i | −0.836787 | + | 0.483119i | −0.856171 | − | 0.516693i | \(-0.827163\pi\) |
0.0193836 | + | 0.999812i | \(0.493830\pi\) | |||||||
\(200\) | −64.0577 | + | 29.9434i | −0.320289 | + | 0.149717i | ||||
\(201\) | −70.6659 | + | 122.397i | −0.351572 | + | 0.608940i | ||||
\(202\) | 161.133 | − | 161.133i | 0.797690 | − | 0.797690i | ||||
\(203\) | −50.4833 | + | 28.7165i | −0.248686 | + | 0.141460i | ||||
\(204\) | 89.0267i | 0.436405i | ||||||||
\(205\) | −175.883 | + | 123.277i | −0.857964 | + | 0.601350i | ||||
\(206\) | −48.0387 | − | 83.2055i | −0.233198 | − | 0.403910i | ||||
\(207\) | 119.458 | + | 32.0087i | 0.577091 | + | 0.154631i | ||||
\(208\) | −31.9181 | + | 8.55243i | −0.153452 | + | 0.0411174i | ||||
\(209\) | 357.310i | 1.70962i | ||||||||
\(210\) | 77.4829 | + | 36.6934i | 0.368966 | + | 0.174730i | ||||
\(211\) | −1.49392 | −0.00708017 | −0.00354009 | − | 0.999994i | \(-0.501127\pi\) | ||||
−0.00354009 | + | 0.999994i | \(0.501127\pi\) | |||||||
\(212\) | −5.92652 | − | 22.1181i | −0.0279553 | − | 0.104331i | ||||
\(213\) | 0.537539 | − | 2.00612i | 0.00252366 | − | 0.00941841i | ||||
\(214\) | 36.0062 | − | 20.7882i | 0.168253 | − | 0.0971411i | ||||
\(215\) | 261.132 | + | 45.9189i | 1.21457 | + | 0.213576i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 42.4782 | − | 72.4966i | 0.195752 | − | 0.334086i | ||||
\(218\) | 169.848 | + | 169.848i | 0.779121 | + | 0.779121i | ||||
\(219\) | 107.289 | + | 61.9434i | 0.489905 | + | 0.282847i | ||||
\(220\) | −112.052 | + | 9.85597i | −0.509327 | + | 0.0447999i | ||||
\(221\) | −106.153 | − | 183.863i | −0.480331 | − | 0.831957i | ||||
\(222\) | 15.4988 | + | 57.8424i | 0.0698145 | + | 0.260551i | ||||
\(223\) | 186.552 | + | 186.552i | 0.836555 | + | 0.836555i | 0.988404 | − | 0.151849i | \(-0.0485227\pi\) |
−0.151849 | + | 0.988404i | \(0.548523\pi\) | |||||||
\(224\) | −10.0032 | − | 38.3137i | −0.0446572 | − | 0.171043i | ||||
\(225\) | −57.4083 | + | 48.2627i | −0.255148 | + | 0.214501i | ||||
\(226\) | 79.5633 | − | 137.808i | 0.352050 | − | 0.609769i | ||||
\(227\) | −44.7381 | − | 11.9875i | −0.197084 | − | 0.0528085i | 0.158927 | − | 0.987290i | \(-0.449197\pi\) |
−0.356011 | + | 0.934482i | \(0.615863\pi\) | |||||||
\(228\) | 28.4799 | − | 106.288i | 0.124912 | − | 0.466177i | ||||
\(229\) | −146.091 | − | 84.3456i | −0.637951 | − | 0.368321i | 0.145874 | − | 0.989303i | \(-0.453401\pi\) |
−0.783825 | + | 0.620982i | \(0.786734\pi\) | |||||||
\(230\) | 264.244 | + | 123.069i | 1.14889 | + | 0.535082i | ||||
\(231\) | 95.8151 | + | 97.0520i | 0.414784 | + | 0.420138i | ||||
\(232\) | −16.5941 | + | 16.5941i | −0.0715262 | + | 0.0715262i | ||||
\(233\) | 214.579 | − | 57.4964i | 0.920942 | − | 0.246766i | 0.232954 | − | 0.972488i | \(-0.425161\pi\) |
0.687988 | + | 0.725722i | \(0.258494\pi\) | |||||||
\(234\) | −30.3529 | + | 17.5242i | −0.129713 | + | 0.0748899i | ||||
\(235\) | −142.161 | − | 119.174i | −0.604940 | − | 0.507124i | ||||
\(236\) | −60.7097 | + | 105.152i | −0.257245 | + | 0.445561i | ||||
\(237\) | −100.431 | + | 100.431i | −0.423761 | + | 0.423761i | ||||
\(238\) | 221.141 | − | 125.792i | 0.929164 | − | 0.528537i | ||||
\(239\) | − | 42.6023i | − | 0.178252i | −0.996020 | − | 0.0891262i | \(-0.971593\pi\) | ||
0.996020 | − | 0.0891262i | \(-0.0284074\pi\) | |||||||
\(240\) | 34.1175 | + | 5.99943i | 0.142156 | + | 0.0249976i | ||||
\(241\) | 110.433 | + | 191.275i | 0.458227 | + | 0.793672i | 0.998867 | − | 0.0475819i | \(-0.0151515\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(242\) | −7.55134 | − | 2.02337i | −0.0312039 | − | 0.00836105i | ||||
\(243\) | 15.0573 | − | 4.03459i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 75.3147i | 0.308667i | ||||||||
\(245\) | −18.3350 | − | 244.313i | −0.0748366 | − | 0.997196i | ||||
\(246\) | 105.222 | 0.427731 | ||||||||
\(247\) | 67.9174 | + | 253.471i | 0.274969 | + | 1.02620i | ||||
\(248\) | 8.78719 | − | 32.7943i | 0.0354322 | − | 0.132235i | ||||
\(249\) | 218.904 | − | 126.384i | 0.879133 | − | 0.507568i | ||||
\(250\) | −152.969 | + | 88.6026i | −0.611877 | + | 0.354410i | ||||
\(251\) | −165.088 | −0.657720 | −0.328860 | − | 0.944379i | \(-0.606664\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606664\pi\) | |||||||
\(252\) | −20.7663 | − | 36.5070i | −0.0824060 | − | 0.144869i | ||||
\(253\) | 327.890 | + | 327.890i | 1.29601 | + | 1.29601i | ||||
\(254\) | 133.230 | + | 76.9204i | 0.524528 | + | 0.302836i | ||||
\(255\) | 19.5014 | + | 221.711i | 0.0764762 | + | 0.869454i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 32.9883 | + | 123.114i | 0.128359 | + | 0.479042i | 0.999937 | − | 0.0112144i | \(-0.00356974\pi\) |
−0.871578 | + | 0.490257i | \(0.836903\pi\) | |||||||
\(258\) | −91.8466 | − | 91.8466i | −0.355995 | − | 0.355995i | ||||
\(259\) | 121.780 | − | 120.228i | 0.470194 | − | 0.464202i | ||||
\(260\) | −77.6149 | + | 28.2905i | −0.298519 | + | 0.108810i | ||||
\(261\) | −12.4456 | + | 21.5563i | −0.0476841 | + | 0.0825913i | ||||
\(262\) | 245.877 | + | 65.8827i | 0.938463 | + | 0.251461i | ||||
\(263\) | −113.007 | + | 421.747i | −0.429683 | + | 1.60360i | 0.323796 | + | 0.946127i | \(0.395041\pi\) |
−0.753479 | + | 0.657472i | \(0.771626\pi\) | |||||||
\(264\) | 47.7232 | + | 27.5530i | 0.180770 | + | 0.104367i | ||||
\(265\) | −19.6043 | − | 53.7843i | −0.0739786 | − | 0.202960i | ||||
\(266\) | −304.260 | + | 79.4384i | −1.14384 | + | 0.298641i | ||||
\(267\) | −17.8856 | + | 17.8856i | −0.0669874 | + | 0.0669874i | ||||
\(268\) | 157.635 | − | 42.2382i | 0.588191 | − | 0.157605i | ||||
\(269\) | −8.01022 | + | 4.62470i | −0.0297778 | + | 0.0171922i | −0.514815 | − | 0.857301i | \(-0.672139\pi\) |
0.485037 | + | 0.874494i | \(0.338806\pi\) | |||||||
\(270\) | 36.6010 | − | 3.21939i | 0.135559 | − | 0.0119237i | ||||
\(271\) | 48.2949 | − | 83.6492i | 0.178210 | − | 0.308669i | −0.763058 | − | 0.646331i | \(-0.776303\pi\) |
0.941267 | + | 0.337662i | \(0.109636\pi\) | |||||||
\(272\) | 72.6900 | − | 72.6900i | 0.267243 | − | 0.267243i | ||||
\(273\) | 86.4176 | + | 50.6350i | 0.316548 | + | 0.185476i | ||||
\(274\) | − | 331.753i | − | 1.21078i | ||||||
\(275\) | −276.894 | + | 49.0903i | −1.00689 | + | 0.178510i | ||||
\(276\) | −71.4020 | − | 123.672i | −0.258703 | − | 0.448087i | ||||
\(277\) | −146.599 | − | 39.2810i | −0.529237 | − | 0.141809i | −0.0157013 | − | 0.999877i | \(-0.504998\pi\) |
−0.513536 | + | 0.858068i | \(0.671665\pi\) | |||||||
\(278\) | 306.287 | − | 82.0693i | 1.10175 | − | 0.295213i | ||||
\(279\) | − | 36.0106i | − | 0.129070i | ||||||
\(280\) | −33.3045 | − | 93.2245i | −0.118945 | − | 0.332945i | ||||
\(281\) | −52.8654 | −0.188133 | −0.0940665 | − | 0.995566i | \(-0.529987\pi\) | ||||
−0.0940665 | + | 0.995566i | \(0.529987\pi\) | |||||||
\(282\) | 23.5211 | + | 87.7821i | 0.0834083 | + | 0.311284i | ||||
\(283\) | 42.6656 | − | 159.230i | 0.150762 | − | 0.562651i | −0.848669 | − | 0.528924i | \(-0.822596\pi\) |
0.999431 | − | 0.0337273i | \(-0.0107378\pi\) | |||||||
\(284\) | −2.07689 | + | 1.19909i | −0.00731299 | + | 0.00422216i | ||||
\(285\) | 47.6433 | − | 270.938i | 0.167169 | − | 0.950658i | ||||
\(286\) | −131.414 | −0.459489 | ||||||||
\(287\) | −148.675 | − | 261.370i | −0.518032 | − | 0.910696i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 321.711 | + | 185.740i | 1.11319 | + | 0.642698i | ||||
\(290\) | −37.6907 | + | 44.9606i | −0.129968 | + | 0.155037i | ||||
\(291\) | −30.1806 | − | 52.2744i | −0.103713 | − | 0.179637i | ||||
\(292\) | −37.0246 | − | 138.178i | −0.126797 | − | 0.473212i | ||||
\(293\) | −251.280 | − | 251.280i | −0.857612 | − | 0.857612i | 0.133445 | − | 0.991056i | \(-0.457396\pi\) |
−0.991056 | + | 0.133445i | \(0.957396\pi\) | |||||||
\(294\) | −61.3408 | + | 103.166i | −0.208642 | + | 0.350906i | ||||
\(295\) | −128.157 | + | 275.168i | −0.434430 | + | 0.932774i | ||||
\(296\) | 34.5734 | − | 59.8828i | 0.116802 | − | 0.202307i | ||||
\(297\) | 56.4571 | + | 15.1276i | 0.190091 | + | 0.0509348i | ||||
\(298\) | −41.9131 | + | 156.422i | −0.140648 | + | 0.524906i | ||||
\(299\) | 294.926 | + | 170.276i | 0.986376 | + | 0.569484i | ||||
\(300\) | 86.2800 | + | 7.46739i | 0.287600 | + | 0.0248913i | ||||
\(301\) | −98.3695 | + | 357.922i | −0.326809 | + | 1.18911i | ||||
\(302\) | 96.9710 | − | 96.9710i | 0.321096 | − | 0.321096i | ||||
\(303\) | −269.581 | + | 72.2341i | −0.889708 | + | 0.238396i | ||||
\(304\) | −110.038 | + | 63.5304i | −0.361967 | + | 0.208982i | ||||
\(305\) | 16.4978 | + | 187.563i | 0.0540911 | + | 0.614959i | ||||
\(306\) | 54.5175 | − | 94.4271i | 0.178162 | − | 0.308585i | ||||
\(307\) | 279.604 | − | 279.604i | 0.910762 | − | 0.910762i | −0.0855701 | − | 0.996332i | \(-0.527271\pi\) |
0.996332 | + | 0.0855701i | \(0.0272712\pi\) | |||||||
\(308\) | 1.00994 | − | 157.475i | 0.00327903 | − | 0.511283i | ||||
\(309\) | 117.670i | 0.380810i | ||||||||
\(310\) | 14.6999 | − | 83.5952i | 0.0474189 | − | 0.269662i | ||||
\(311\) | 215.478 | + | 373.218i | 0.692854 | + | 1.20006i | 0.970899 | + | 0.239490i | \(0.0769803\pi\) |
−0.278045 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(312\) | 39.0915 | + | 10.4745i | 0.125293 | + | 0.0335722i | ||||
\(313\) | −162.483 | + | 43.5371i | −0.519114 | + | 0.139096i | −0.508857 | − | 0.860851i | \(-0.669932\pi\) |
−0.0102571 | + | 0.999947i | \(0.503265\pi\) | |||||||
\(314\) | 182.294i | 0.580555i | ||||||||
\(315\) | −59.7130 | − | 86.3676i | −0.189565 | − | 0.274183i | ||||
\(316\) | 164.004 | 0.518999 | ||||||||
\(317\) | 44.9330 | + | 167.692i | 0.141744 | + | 0.528997i | 0.999879 | + | 0.0155721i | \(0.00495695\pi\) |
−0.858134 | + | 0.513425i | \(0.828376\pi\) | |||||||
\(318\) | −7.25848 | + | 27.0890i | −0.0228254 | + | 0.0851856i | ||||
\(319\) | −80.8252 | + | 46.6645i | −0.253371 | + | 0.146284i | ||||
\(320\) | −22.9583 | − | 32.7554i | −0.0717448 | − | 0.102361i | ||||
\(321\) | −50.9205 | −0.158631 | ||||||||
\(322\) | −206.311 | + | 352.106i | −0.640716 | + | 1.09350i | ||||
\(323\) | −577.253 | − | 577.253i | −1.78716 | − | 1.78716i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | −187.094 | + | 87.4560i | −0.575674 | + | 0.269095i | ||||
\(326\) | 181.950 | + | 315.146i | 0.558128 | + | 0.966705i | ||||
\(327\) | −76.1410 | − | 284.162i | −0.232847 | − | 0.868997i | ||||
\(328\) | −85.9133 | − | 85.9133i | −0.261931 | − | 0.261931i | ||||
\(329\) | 184.815 | − | 182.459i | 0.561747 | − | 0.554588i | ||||
\(330\) | 124.885 | + | 58.1637i | 0.378438 | + | 0.176254i | ||||
\(331\) | −201.616 | + | 349.209i | −0.609112 | + | 1.05501i | 0.382275 | + | 0.924048i | \(0.375141\pi\) |
−0.991387 | + | 0.130964i | \(0.958193\pi\) | |||||||
\(332\) | −281.927 | − | 75.5421i | −0.849178 | − | 0.227536i | ||||
\(333\) | 18.9821 | − | 70.8422i | 0.0570033 | − | 0.212739i | ||||
\(334\) | −36.1751 | − | 20.8857i | −0.108309 | − | 0.0625320i | ||||
\(335\) | 383.320 | − | 139.720i | 1.14424 | − | 0.417074i | ||||
\(336\) | −12.8522 | + | 46.7635i | −0.0382507 | + | 0.139177i | ||||
\(337\) | −140.687 | + | 140.687i | −0.417468 | + | 0.417468i | −0.884330 | − | 0.466862i | \(-0.845385\pi\) |
0.466862 | + | 0.884330i | \(0.345385\pi\) | |||||||
\(338\) | 137.635 | − | 36.8792i | 0.407204 | − | 0.109110i | ||||
\(339\) | −168.779 | + | 97.4448i | −0.497874 | + | 0.287448i | ||||
\(340\) | 165.103 | − | 196.949i | 0.485598 | − | 0.579261i | ||||
\(341\) | 67.5106 | − | 116.932i | 0.197978 | − | 0.342909i | ||||
\(342\) | −95.2956 | + | 95.2956i | −0.278642 | + | 0.278642i | ||||
\(343\) | 342.937 | + | 6.59883i | 0.999815 | + | 0.0192386i | ||||
\(344\) | 149.985i | 0.436003i | ||||||||
\(345\) | −204.909 | − | 292.350i | −0.593939 | − | 0.847391i | ||||
\(346\) | −152.567 | − | 264.253i | −0.440944 | − | 0.763738i | ||||
\(347\) | −425.251 | − | 113.946i | −1.22551 | − | 0.328373i | −0.412678 | − | 0.910877i | \(-0.635407\pi\) |
−0.812828 | + | 0.582503i | \(0.802073\pi\) | |||||||
\(348\) | 27.7624 | − | 7.43892i | 0.0797771 | − | 0.0213762i | ||||
\(349\) | − | 283.692i | − | 0.812870i | −0.913680 | − | 0.406435i | \(-0.866772\pi\) | ||
0.913680 | − | 0.406435i | \(-0.133228\pi\) | |||||||
\(350\) | −103.362 | − | 224.870i | −0.295320 | − | 0.642484i | ||||
\(351\) | 42.9255 | 0.122295 | ||||||||
\(352\) | −16.4689 | − | 61.4628i | −0.0467866 | − | 0.174610i | ||||
\(353\) | −14.1270 | + | 52.7227i | −0.0400199 | + | 0.149356i | −0.983045 | − | 0.183366i | \(-0.941301\pi\) |
0.943025 | + | 0.332722i | \(0.107967\pi\) | |||||||
\(354\) | 128.785 | − | 74.3539i | 0.363799 | − | 0.210039i | ||||
\(355\) | −4.90959 | + | 3.44115i | −0.0138298 | + | 0.00969338i | ||||
\(356\) | 29.2071 | 0.0820425 | ||||||||
\(357\) | −311.587 | − | 1.99831i | −0.872793 | − | 0.00559752i | ||||
\(358\) | −152.961 | − | 152.961i | −0.427264 | − | 0.427264i | ||||
\(359\) | −255.462 | − | 147.491i | −0.711594 | − | 0.410839i | 0.100057 | − | 0.994982i | \(-0.468097\pi\) |
−0.811651 | + | 0.584143i | \(0.801431\pi\) | |||||||
\(360\) | −32.5132 | − | 27.2560i | −0.0903145 | − | 0.0757111i | ||||
\(361\) | 324.014 | + | 561.209i | 0.897546 | + | 1.55459i | ||||
\(362\) | −22.6137 | − | 84.3956i | −0.0624689 | − | 0.233137i | ||||
\(363\) | 6.77034 | + | 6.77034i | 0.0186511 | + | 0.0186511i | ||||
\(364\) | −29.2164 | − | 111.903i | −0.0802649 | − | 0.307426i | ||||
\(365\) | −122.474 | − | 336.006i | −0.335544 | − | 0.920563i | ||||
\(366\) | 46.1206 | − | 79.8833i | 0.126013 | − | 0.218260i | ||||
\(367\) | −9.37230 | − | 2.51130i | −0.0255376 | − | 0.00684278i | 0.246028 | − | 0.969263i | \(-0.420875\pi\) |
−0.271565 | + | 0.962420i | \(0.587541\pi\) | |||||||
\(368\) | −42.6782 | + | 159.277i | −0.115973 | + | 0.432819i | ||||
\(369\) | −111.605 | − | 64.4350i | −0.302452 | − | 0.174621i | ||||
\(370\) | 72.9836 | − | 156.705i | 0.197253 | − | 0.423526i | ||||
\(371\) | 77.5447 | − | 20.2459i | 0.209015 | − | 0.0545712i | ||||
\(372\) | −29.4025 | + | 29.4025i | −0.0790390 | + | 0.0790390i | ||||
\(373\) | 11.8859 | − | 3.18482i | 0.0318658 | − | 0.00853840i | −0.242851 | − | 0.970064i | \(-0.578083\pi\) |
0.274717 | + | 0.961525i | \(0.411416\pi\) | |||||||
\(374\) | 354.053 | − | 204.413i | 0.946666 | − | 0.546558i | ||||
\(375\) | 216.506 | − | 0.303090i | 0.577350 | − | 0.000808239i | ||||
\(376\) | 52.4688 | − | 90.8787i | 0.139545 | − | 0.241699i | ||||
\(377\) | −48.4665 | + | 48.4665i | −0.128558 | + | 0.128558i | ||||
\(378\) | −0.329891 | + | 51.4382i | −0.000872727 | + | 0.136080i | ||||
\(379\) | 287.766i | 0.759278i | 0.925135 | + | 0.379639i | \(0.123952\pi\) | ||||
−0.925135 | + | 0.379639i | \(0.876048\pi\) | |||||||
\(380\) | −260.120 | + | 182.319i | −0.684527 | + | 0.479787i | ||||
\(381\) | −94.2079 | − | 163.173i | −0.247265 | − | 0.428275i | ||||
\(382\) | 30.4440 | + | 8.15744i | 0.0796963 | + | 0.0213546i | ||||
\(383\) | 625.764 | − | 167.673i | 1.63385 | − | 0.437788i | 0.678820 | − | 0.734305i | \(-0.262492\pi\) |
0.955028 | + | 0.296516i | \(0.0958249\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | −31.9800 | − | 392.395i | −0.0830651 | − | 1.01921i | ||||
\(386\) | 332.747 | 0.862038 | ||||||||
\(387\) | 41.1737 | + | 153.662i | 0.106392 | + | 0.397060i | ||||
\(388\) | −18.0395 | + | 67.3242i | −0.0464935 | + | 0.173516i | ||||
\(389\) | −117.516 | + | 67.8481i | −0.302099 | + | 0.174417i | −0.643385 | − | 0.765543i | \(-0.722471\pi\) |
0.341287 | + | 0.939959i | \(0.389137\pi\) | |||||||
\(390\) | 99.6474 | + | 17.5226i | 0.255506 | + | 0.0449297i | ||||
\(391\) | −1059.45 | −2.70959 | ||||||||
\(392\) | 134.320 | − | 34.1505i | 0.342652 | − | 0.0871186i | ||||
\(393\) | −220.448 | − | 220.448i | −0.560936 | − | 0.560936i | ||||
\(394\) | −250.822 | − | 144.812i | −0.636603 | − | 0.367543i | ||||
\(395\) | 408.432 | − | 35.9252i | 1.03401 | − | 0.0909500i | ||||
\(396\) | −33.7454 | − | 58.4487i | −0.0852156 | − | 0.147598i | ||||
\(397\) | −89.9718 | − | 335.779i | −0.226629 | − | 0.845791i | −0.981745 | − | 0.190200i | \(-0.939086\pi\) |
0.755116 | − | 0.655591i | \(-0.227580\pi\) | |||||||
\(398\) | −192.282 | − | 192.282i | −0.483119 | − | 0.483119i | ||||
\(399\) | 371.363 | + | 102.063i | 0.930733 | + | 0.255798i | ||||
\(400\) | −64.3502 | − | 76.5444i | −0.160876 | − | 0.191361i | ||||
\(401\) | 103.629 | − | 179.491i | 0.258427 | − | 0.447609i | −0.707394 | − | 0.706820i | \(-0.750129\pi\) |
0.965821 | + | 0.259211i | \(0.0834624\pi\) | |||||||
\(402\) | −193.063 | − | 51.7311i | −0.480256 | − | 0.128684i | ||||
\(403\) | 25.6648 | − | 95.7824i | 0.0636844 | − | 0.237674i | ||||
\(404\) | 279.091 | + | 161.133i | 0.690820 | + | 0.398845i | ||||
\(405\) | −40.7927 | − | 18.9988i | −0.100723 | − | 0.0469106i | ||||
\(406\) | −57.7056 | − | 58.4506i | −0.142132 | − | 0.143967i | ||||
\(407\) | 194.449 | − | 194.449i | 0.477761 | − | 0.477761i | ||||
\(408\) | −121.613 | + | 32.5860i | −0.298070 | + | 0.0798677i | ||||
\(409\) | 226.963 | − | 131.037i | 0.554921 | − | 0.320384i | −0.196183 | − | 0.980567i | \(-0.562855\pi\) |
0.751105 | + | 0.660183i | \(0.229521\pi\) | |||||||
\(410\) | −232.777 | − | 195.138i | −0.567748 | − | 0.475946i | ||||
\(411\) | −203.156 | + | 351.877i | −0.494298 | + | 0.856149i | ||||
\(412\) | 96.0774 | − | 96.0774i | 0.233198 | − | 0.233198i | ||||
\(413\) | −366.663 | − | 214.840i | −0.887803 | − | 0.520193i | ||||
\(414\) | 174.899i | 0.422460i | ||||||||
\(415\) | −718.654 | − | 126.372i | −1.73170 | − | 0.304512i | ||||
\(416\) | −23.3657 | − | 40.4705i | −0.0561675 | − | 0.0972849i | ||||
\(417\) | −375.123 | − | 100.514i | −0.899576 | − | 0.241041i | ||||
\(418\) | −488.094 | + | 130.784i | −1.16769 | + | 0.312881i | ||||
\(419\) | − | 143.688i | − | 0.342931i | −0.985190 | − | 0.171465i | \(-0.945150\pi\) | ||
0.985190 | − | 0.171465i | \(-0.0548502\pi\) | |||||||
\(420\) | −21.7634 | + | 119.274i | −0.0518176 | + | 0.283986i | ||||
\(421\) | 305.872 | 0.726537 | 0.363269 | − | 0.931684i | \(-0.381661\pi\) | ||||
0.363269 | + | 0.931684i | \(0.381661\pi\) | |||||||
\(422\) | −0.546811 | − | 2.04073i | −0.00129576 | − | 0.00483585i | ||||
\(423\) | 28.8074 | − | 107.511i | 0.0681026 | − | 0.254162i | ||||
\(424\) | 28.0446 | − | 16.1916i | 0.0661429 | − | 0.0381876i | ||||
\(425\) | 368.029 | − | 526.645i | 0.865950 | − | 1.23916i | ||||
\(426\) | 2.93717 | 0.00689476 | ||||||||
\(427\) | −263.596 | − | 1.69053i | −0.617321 | − | 0.00395909i | ||||
\(428\) | 41.5764 | + | 41.5764i | 0.0971411 | + | 0.0971411i | ||||
\(429\) | 139.386 | + | 80.4743i | 0.324908 | + | 0.187586i | ||||
\(430\) | 32.8544 | + | 373.520i | 0.0764056 | + | 0.868651i | ||||
\(431\) | 314.493 | + | 544.718i | 0.729683 | + | 1.26385i | 0.957017 | + | 0.290031i | \(0.0936656\pi\) |
−0.227334 | + | 0.973817i | \(0.573001\pi\) | |||||||
\(432\) | 5.37945 | + | 20.0764i | 0.0124524 | + | 0.0464731i | ||||
\(433\) | 215.672 | + | 215.672i | 0.498087 | + | 0.498087i | 0.910842 | − | 0.412755i | \(-0.135433\pi\) |
−0.412755 | + | 0.910842i | \(0.635433\pi\) | |||||||
\(434\) | 114.580 | + | 31.4907i | 0.264010 | + | 0.0725591i | ||||
\(435\) | 67.5096 | − | 24.6072i | 0.155195 | − | 0.0565682i | ||||
\(436\) | −169.848 | + | 294.186i | −0.389561 | + | 0.674739i | ||||
\(437\) | 1264.87 | + | 338.920i | 2.89444 | + | 0.775562i | ||||
\(438\) | −45.3457 | + | 169.233i | −0.103529 | + | 0.386376i | ||||
\(439\) | 356.713 | + | 205.949i | 0.812559 | + | 0.469131i | 0.847844 | − | 0.530246i | \(-0.177901\pi\) |
−0.0352848 | + | 0.999377i | \(0.511234\pi\) | |||||||
\(440\) | −54.4774 | − | 149.458i | −0.123812 | − | 0.339678i | ||||
\(441\) | 128.238 | − | 71.8611i | 0.290789 | − | 0.162950i | ||||
\(442\) | 212.306 | − | 212.306i | 0.480331 | − | 0.480331i | ||||
\(443\) | 403.971 | − | 108.244i | 0.911898 | − | 0.244342i | 0.227779 | − | 0.973713i | \(-0.426854\pi\) |
0.684119 | + | 0.729370i | \(0.260187\pi\) | |||||||
\(444\) | −73.3412 | + | 42.3436i | −0.165183 | + | 0.0953684i | ||||
\(445\) | 72.7370 | − | 6.39786i | 0.163454 | − | 0.0143772i | ||||
\(446\) | −186.552 | + | 323.117i | −0.418277 | + | 0.724478i | ||||
\(447\) | 140.244 | − | 140.244i | 0.313745 | − | 0.313745i | ||||
\(448\) | 48.6760 | − | 27.6884i | 0.108652 | − | 0.0618045i | ||||
\(449\) | − | 142.091i | − | 0.316460i | −0.987402 | − | 0.158230i | \(-0.949421\pi\) | ||
0.987402 | − | 0.158230i | \(-0.0505788\pi\) | |||||||
\(450\) | −86.9409 | − | 60.7559i | −0.193202 | − | 0.135013i | ||||
\(451\) | −241.598 | − | 418.460i | −0.535695 | − | 0.927850i | ||||
\(452\) | 217.371 | + | 58.2444i | 0.480909 | + | 0.128859i | ||||
\(453\) | −162.236 | + | 43.4709i | −0.358136 | + | 0.0959622i | ||||
\(454\) | − | 65.5011i | − | 0.144275i | ||||||
\(455\) | −97.2727 | − | 272.282i | −0.213786 | − | 0.598421i | ||||
\(456\) | 155.617 | 0.341265 | ||||||||
\(457\) | 18.3636 | + | 68.5338i | 0.0401829 | + | 0.149965i | 0.983103 | − | 0.183056i | \(-0.0585989\pi\) |
−0.942920 | + | 0.333020i | \(0.891932\pi\) | |||||||
\(458\) | 61.7452 | − | 230.436i | 0.134815 | − | 0.503136i | ||||
\(459\) | −115.649 | + | 66.7700i | −0.251959 | + | 0.145468i | ||||
\(460\) | −71.3952 | + | 406.010i | −0.155207 | + | 0.882631i | ||||
\(461\) | 75.0514 | 0.162801 | 0.0814007 | − | 0.996681i | \(-0.474061\pi\) | ||||
0.0814007 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(462\) | −97.5047 | + | 166.409i | −0.211049 | + | 0.360193i | ||||
\(463\) | 345.058 | + | 345.058i | 0.745267 | + | 0.745267i | 0.973586 | − | 0.228320i | \(-0.0733231\pi\) |
−0.228320 | + | 0.973586i | \(0.573323\pi\) | |||||||
\(464\) | −28.7418 | − | 16.5941i | −0.0619435 | − | 0.0357631i | ||||
\(465\) | −66.7829 | + | 79.6643i | −0.143619 | + | 0.171321i | ||||
\(466\) | 157.083 | + | 272.076i | 0.337088 | + | 0.583854i | ||||
\(467\) | 156.462 | + | 583.925i | 0.335037 | + | 1.25037i | 0.903829 | + | 0.427894i | \(0.140744\pi\) |
−0.568792 | + | 0.822481i | \(0.692589\pi\) | |||||||
\(468\) | −35.0485 | − | 35.0485i | −0.0748899 | − | 0.0748899i | ||||
\(469\) | 144.292 | + | 552.660i | 0.307660 | + | 1.17838i | ||||
\(470\) | 110.760 | − | 237.816i | 0.235661 | − | 0.505992i | ||||
\(471\) | 111.632 | − | 193.352i | 0.237010 | − | 0.410514i | ||||
\(472\) | −165.862 | − | 44.4426i | −0.351403 | − | 0.0941580i | ||||
\(473\) | −154.380 | + | 576.155i | −0.326386 | + | 1.21809i | ||||
\(474\) | −173.952 | − | 100.431i | −0.366988 | − | 0.211880i | ||||
\(475\) | −607.862 | + | 511.024i | −1.27971 | + | 1.07584i | ||||
\(476\) | 252.778 | + | 256.041i | 0.531046 | + | 0.537902i | ||||
\(477\) | 24.2873 | − | 24.2873i | 0.0509169 | − | 0.0509169i | ||||
\(478\) | 58.1958 | − | 15.5935i | 0.121749 | − | 0.0326224i | ||||
\(479\) | −485.140 | + | 280.096i | −1.01282 | + | 0.584751i | −0.912016 | − | 0.410155i | \(-0.865474\pi\) |
−0.100803 | + | 0.994906i | \(0.532141\pi\) | |||||||
\(480\) | 4.29251 | + | 48.8014i | 0.00894274 | + | 0.101670i | ||||
\(481\) | 100.979 | − | 174.900i | 0.209935 | − | 0.363618i | ||||
\(482\) | −220.865 | + | 220.865i | −0.458227 | + | 0.458227i | ||||
\(483\) | 434.446 | − | 247.126i | 0.899473 | − | 0.511648i | ||||
\(484\) | − | 11.0559i | − | 0.0228428i | ||||||
\(485\) | −30.1777 | + | 171.615i | −0.0622221 | + | 0.353845i | ||||
\(486\) | 11.0227 | + | 19.0919i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −676.511 | − | 181.271i | −1.38914 | − | 0.372219i | −0.514707 | − | 0.857366i | \(-0.672099\pi\) |
−0.874433 | + | 0.485147i | \(0.838766\pi\) | |||||||
\(488\) | −102.882 | + | 27.5671i | −0.210823 | + | 0.0564899i | ||||
\(489\) | − | 445.684i | − | 0.911419i | ||||||
\(490\) | 327.027 | − | 114.471i | 0.667401 | − | 0.233614i | ||||
\(491\) | 285.090 | 0.580632 | 0.290316 | − | 0.956931i | \(-0.406240\pi\) | ||||
0.290316 | + | 0.956931i | \(0.406240\pi\) | |||||||
\(492\) | 38.5139 | + | 143.736i | 0.0782803 | + | 0.292146i | ||||
\(493\) | 55.1886 | − | 205.966i | 0.111944 | − | 0.417782i | ||||
\(494\) | −321.389 | + | 185.554i | −0.650584 | + | 0.375615i | ||||
\(495\) | −96.8423 | − | 138.168i | −0.195641 | − | 0.279127i | ||||
\(496\) | 48.0141 | 0.0968027 | ||||||||
\(497\) | −4.15012 | − | 7.29588i | −0.00835034 | − | 0.0146798i | ||||
\(498\) | 252.769 | + | 252.769i | 0.507568 | + | 0.507568i | ||||
\(499\) | −659.973 | − | 381.035i | −1.32259 | − | 0.763598i | −0.338449 | − | 0.940985i | \(-0.609902\pi\) |
−0.984141 | + | 0.177387i | \(0.943236\pi\) | |||||||
\(500\) | −177.024 | − | 176.529i | −0.354048 | − | 0.353058i | ||||
\(501\) | 25.5797 | + | 44.3053i | 0.0510572 | + | 0.0884337i | ||||
\(502\) | −60.4263 | − | 225.514i | −0.120371 | − | 0.449231i | ||||
\(503\) | −242.900 | − | 242.900i | −0.482902 | − | 0.482902i | 0.423155 | − | 0.906057i | \(-0.360922\pi\) |
−0.906057 | + | 0.423155i | \(0.860922\pi\) | |||||||
\(504\) | 42.2685 | − | 41.7298i | 0.0838661 | − | 0.0827972i | ||||
\(505\) | 730.341 | + | 340.149i | 1.44622 | + | 0.673562i | ||||
\(506\) | −327.890 | + | 567.922i | −0.648004 | + | 1.12238i | ||||
\(507\) | −168.568 | − | 45.1676i | −0.332480 | − | 0.0890879i | ||||
\(508\) | −56.3097 | + | 210.150i | −0.110846 | + | 0.413682i | ||||
\(509\) | −110.550 | − | 63.8262i | −0.217191 | − | 0.125395i | 0.387458 | − | 0.921887i | \(-0.373353\pi\) |
−0.604649 | + | 0.796492i | \(0.706687\pi\) | |||||||
\(510\) | −295.724 | + | 107.791i | −0.579852 | + | 0.211355i | ||||
\(511\) | 484.443 | − | 126.482i | 0.948030 | − | 0.247518i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 159.433 | − | 42.7198i | 0.310785 | − | 0.0832746i | ||||
\(514\) | −156.102 | + | 90.1256i | −0.303701 | + | 0.175342i | ||||
\(515\) | 218.224 | − | 260.316i | 0.423736 | − | 0.505467i | ||||
\(516\) | 91.8466 | − | 159.083i | 0.177997 | − | 0.308300i | ||||
\(517\) | 295.097 | − | 295.097i | 0.570787 | − | 0.570787i | ||||
\(518\) | 208.810 | + | 122.348i | 0.403107 | + | 0.236194i | ||||
\(519\) | 373.711i | 0.720059i | ||||||||
\(520\) | −67.0546 | − | 95.6689i | −0.128951 | − | 0.183979i | ||||
\(521\) | −371.561 | − | 643.563i | −0.713170 | − | 1.23525i | −0.963661 | − | 0.267127i | \(-0.913926\pi\) |
0.250492 | − | 0.968119i | \(-0.419408\pi\) | |||||||
\(522\) | −34.0019 | − | 9.11078i | −0.0651377 | − | 0.0174536i | ||||
\(523\) | 907.753 | − | 243.232i | 1.73566 | − | 0.465070i | 0.754189 | − | 0.656657i | \(-0.228030\pi\) |
0.981476 | + | 0.191587i | \(0.0613636\pi\) | |||||||
\(524\) | 359.990i | 0.687003i | ||||||||
\(525\) | −28.0720 | + | 301.806i | −0.0534704 | + | 0.574869i | ||||
\(526\) | −617.480 | −1.17392 | ||||||||
\(527\) | 79.8426 | + | 297.977i | 0.151504 | + | 0.565421i | ||||
\(528\) | −20.1702 | + | 75.2762i | −0.0382011 | + | 0.142569i | ||||
\(529\) | 1013.61 | − | 585.208i | 1.91609 | − | 1.10625i | ||||
\(530\) | 66.2951 | − | 46.4664i | 0.125085 | − | 0.0876725i | ||||
\(531\) | −182.129 | −0.342993 | ||||||||
\(532\) | −219.882 | − | 386.551i | −0.413312 | − | 0.726599i | ||||
\(533\) | −250.928 | − | 250.928i | −0.470784 | − | 0.470784i | ||||
\(534\) | −30.9788 | − | 17.8856i | −0.0580128 | − | 0.0334937i | ||||
\(535\) | 112.649 | + | 94.4338i | 0.210558 | + | 0.176512i | ||||
\(536\) | 115.397 | + | 199.873i | 0.215293 | + | 0.372898i | ||||
\(537\) | 68.5704 | + | 255.908i | 0.127692 | + | 0.476552i | ||||
\(538\) | −9.24940 | − | 9.24940i | −0.0171922 | − | 0.0171922i | ||||
\(539\) | 551.129 | + | 7.06945i | 1.02250 | + | 0.0131159i | ||||
\(540\) | 17.7947 | + | 48.8196i | 0.0329531 | + | 0.0904066i | ||||
\(541\) | 151.264 | − | 261.997i | 0.279600 | − | 0.484282i | −0.691685 | − | 0.722199i | \(-0.743131\pi\) |
0.971285 | + | 0.237917i | \(0.0764647\pi\) | |||||||
\(542\) | 131.944 | + | 35.3543i | 0.243439 | + | 0.0652294i | ||||
\(543\) | −27.6960 | + | 103.363i | −0.0510056 | + | 0.190356i | ||||
\(544\) | 125.903 | + | 72.6900i | 0.231439 | + | 0.133621i | ||||
\(545\) | −358.546 | + | 769.842i | −0.657883 | + | 1.41255i | ||||
\(546\) | −37.5376 | + | 136.582i | −0.0687502 | + | 0.250151i | ||||
\(547\) | −471.627 | + | 471.627i | −0.862206 | + | 0.862206i | −0.991594 | − | 0.129388i | \(-0.958699\pi\) |
0.129388 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(548\) | 453.183 | − | 121.430i | 0.826977 | − | 0.221588i | ||||
\(549\) | −97.8367 | + | 56.4860i | −0.178209 | + | 0.102889i | ||||
\(550\) | −168.409 | − | 360.276i | −0.306198 | − | 0.655046i | ||||
\(551\) | −131.779 | + | 228.247i | −0.239163 | + | 0.414242i | ||||
\(552\) | 142.804 | − | 142.804i | 0.258703 | − | 0.258703i | ||||
\(553\) | −3.68126 | + | 574.001i | −0.00665690 | + | 1.03798i | ||||
\(554\) | − | 214.635i | − | 0.387429i | ||||||
\(555\) | −173.372 | + | 121.517i | −0.312383 | + | 0.218950i | ||||
\(556\) | 224.218 | + | 388.356i | 0.403269 | + | 0.698482i | ||||
\(557\) | −42.8563 | − | 11.4833i | −0.0769413 | − | 0.0206164i | 0.220143 | − | 0.975468i | \(-0.429348\pi\) |
−0.297084 | + | 0.954851i | \(0.596014\pi\) | |||||||
\(558\) | 49.1914 | − | 13.1808i | 0.0881566 | − | 0.0236215i | ||||
\(559\) | 438.062i | 0.783653i | ||||||||
\(560\) | 115.157 | − | 79.6173i | 0.205637 | − | 0.142174i | ||||
\(561\) | −500.707 | −0.892526 | ||||||||
\(562\) | −19.3501 | − | 72.2154i | −0.0344307 | − | 0.128497i | ||||
\(563\) | −21.4182 | + | 79.9337i | −0.0380429 | + | 0.141978i | −0.982335 | − | 0.187130i | \(-0.940081\pi\) |
0.944292 | + | 0.329108i | \(0.106748\pi\) | |||||||
\(564\) | −111.303 | + | 64.2609i | −0.197346 | + | 0.113938i | ||||
\(565\) | 554.096 | + | 97.4355i | 0.980701 | + | 0.172452i | ||||
\(566\) | 233.129 | 0.411889 | ||||||||
\(567\) | 31.8493 | − | 54.3565i | 0.0561715 | − | 0.0958668i | ||||
\(568\) | −2.39819 | − | 2.39819i | −0.00422216 | − | 0.00422216i | ||||
\(569\) | −497.115 | − | 287.010i | −0.873665 | − | 0.504410i | −0.00510028 | − | 0.999987i | \(-0.501623\pi\) |
−0.868564 | + | 0.495577i | \(0.834957\pi\) | |||||||
\(570\) | 387.546 | − | 34.0881i | 0.679906 | − | 0.0598038i | ||||
\(571\) | −231.337 | − | 400.688i | −0.405144 | − | 0.701730i | 0.589194 | − | 0.807992i | \(-0.299445\pi\) |
−0.994338 | + | 0.106261i | \(0.966112\pi\) | |||||||
\(572\) | −48.1008 | − | 179.515i | −0.0840924 | − | 0.313837i | ||||
\(573\) | −27.2953 | − | 27.2953i | −0.0476358 | − | 0.0476358i | ||||
\(574\) | 302.619 | − | 298.762i | 0.527211 | − | 0.520491i | ||||
\(575\) | −88.8645 | + | 1026.76i | −0.154547 | + | 1.78567i | ||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 200.509 | + | 53.7263i | 0.347503 | + | 0.0931131i | 0.428349 | − | 0.903614i | \(-0.359095\pi\) |
−0.0808459 | + | 0.996727i | \(0.525762\pi\) | |||||||
\(578\) | −135.971 | + | 507.450i | −0.235244 | + | 0.877942i | ||||
\(579\) | −352.931 | − | 203.765i | −0.609553 | − | 0.351926i | ||||
\(580\) | −75.2131 | − | 35.0297i | −0.129678 | − | 0.0603961i | ||||
\(581\) | 270.720 | − | 985.028i | 0.465955 | − | 1.69540i | ||||
\(582\) | 60.3612 | − | 60.3612i | 0.103713 | − | 0.103713i | ||||
\(583\) | 124.397 | − | 33.3321i | 0.213374 | − | 0.0571735i | ||||
\(584\) | 175.202 | − | 101.153i | 0.300004 | − | 0.173207i | ||||
\(585\) | −94.9617 | − | 79.6068i | −0.162328 | − | 0.136080i | ||||
\(586\) | 251.280 | − | 435.230i | 0.428806 | − | 0.742714i | ||||
\(587\) | 275.657 | − | 275.657i | 0.469603 | − | 0.469603i | −0.432183 | − | 0.901786i | \(-0.642256\pi\) |
0.901786 | + | 0.432183i | \(0.142256\pi\) | |||||||
\(588\) | −163.380 | − | 46.0315i | −0.277858 | − | 0.0782849i | ||||
\(589\) | − | 381.295i | − | 0.647359i | ||||||
\(590\) | −422.795 | − | 74.3468i | −0.716603 | − | 0.126012i | ||||
\(591\) | 177.358 | + | 307.192i | 0.300098 | + | 0.519784i | ||||
\(592\) | 94.4562 | + | 25.3095i | 0.159554 | + | 0.0427525i | ||||
\(593\) | −233.497 | + | 62.5653i | −0.393755 | + | 0.105506i | −0.450264 | − | 0.892896i | \(-0.648670\pi\) |
0.0565081 | + | 0.998402i | \(0.482003\pi\) | |||||||
\(594\) | 82.6590i | 0.139157i | ||||||||
\(595\) | 685.601 | + | 582.270i | 1.15227 | + | 0.978605i | ||||
\(596\) | −229.018 | −0.384258 | ||||||||
\(597\) | 86.1974 | + | 321.693i | 0.144384 | + | 0.538850i | ||||
\(598\) | −124.651 | + | 465.202i | −0.208446 | + | 0.777930i | ||||
\(599\) | −678.246 | + | 391.586i | −1.13230 | + | 0.653732i | −0.944512 | − | 0.328478i | \(-0.893464\pi\) |
−0.187786 | + | 0.982210i | \(0.560131\pi\) | |||||||
\(600\) | 21.3800 | + | 120.594i | 0.0356334 | + | 0.200990i | ||||
\(601\) | −970.347 | −1.61455 | −0.807277 | − | 0.590172i | \(-0.799060\pi\) | ||||
−0.807277 | + | 0.590172i | \(0.799060\pi\) | |||||||
\(602\) | −524.936 | − | 3.36660i | −0.871987 | − | 0.00559235i | ||||
\(603\) | 173.096 | + | 173.096i | 0.287057 | + | 0.287057i | ||||
\(604\) | 167.959 | + | 96.9710i | 0.278077 | + | 0.160548i | ||||
\(605\) | −2.42182 | − | 27.5335i | −0.00400300 | − | 0.0455099i | ||||
\(606\) | −197.347 | − | 341.816i | −0.325656 | − | 0.564052i | ||||
\(607\) | −4.32679 | − | 16.1478i | −0.00712816 | − | 0.0266027i | 0.962270 | − | 0.272096i | \(-0.0877168\pi\) |
−0.969398 | + | 0.245493i | \(0.921050\pi\) | |||||||
\(608\) | −127.061 | − | 127.061i | −0.208982 | − | 0.208982i | ||||
\(609\) | 25.4125 | + | 97.3335i | 0.0417283 | + | 0.159825i | ||||
\(610\) | −250.177 | + | 91.1891i | −0.410126 | + | 0.149490i | ||||
\(611\) | 153.246 | − | 265.430i | 0.250812 | − | 0.434419i | ||||
\(612\) | 148.945 | + | 39.9096i | 0.243373 | + | 0.0652117i | ||||
\(613\) | −231.054 | + | 862.305i | −0.376923 | + | 1.40670i | 0.473591 | + | 0.880745i | \(0.342958\pi\) |
−0.850514 | + | 0.525952i | \(0.823709\pi\) | |||||||
\(614\) | 484.288 | + | 279.604i | 0.788743 | + | 0.455381i | ||||
\(615\) | 127.400 | + | 349.521i | 0.207154 | + | 0.568327i | ||||
\(616\) | 215.485 | − | 56.2603i | 0.349813 | − | 0.0913317i | ||||
\(617\) | 698.494 | − | 698.494i | 1.13208 | − | 1.13208i | 0.142251 | − | 0.989831i | \(-0.454566\pi\) |
0.989831 | − | 0.142251i | \(-0.0454339\pi\) | |||||||
\(618\) | −160.741 | + | 43.0703i | −0.260098 | + | 0.0696931i | ||||
\(619\) | −637.279 | + | 367.933i | −1.02953 | + | 0.594399i | −0.916850 | − | 0.399232i | \(-0.869277\pi\) |
−0.112679 | + | 0.993631i | \(0.535943\pi\) | |||||||
\(620\) | 119.574 | − | 10.5176i | 0.192861 | − | 0.0169638i | ||||
\(621\) | 107.103 | − | 185.508i | 0.172469 | − | 0.298725i | ||||
\(622\) | −430.955 | + | 430.955i | −0.692854 | + | 0.692854i | ||||
\(623\) | −0.655590 | + | 102.223i | −0.00105231 | + | 0.164082i | ||||
\(624\) | 57.2340i | 0.0917211i | ||||||||
\(625\) | −479.527 | − | 400.848i | −0.767243 | − | 0.641357i | ||||
\(626\) | −118.946 | − | 206.020i | −0.190009 | − | 0.329105i | ||||
\(627\) | 597.791 | + | 160.178i | 0.953414 | + | 0.255467i | ||||
\(628\) | −249.018 | + | 66.7243i | −0.396526 | + | 0.106249i | ||||
\(629\) | 628.285i | 0.998863i | ||||||||
\(630\) | 96.1238 | − | 113.182i | 0.152578 | − | 0.179654i | ||||
\(631\) | 395.464 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(632\) | 60.0295 | + | 224.033i | 0.0949834 | + | 0.354483i | ||||
\(633\) | −0.669704 | + | 2.49937i | −0.00105798 | + | 0.00394845i | ||||
\(634\) | −212.625 | + | 122.759i | −0.335371 | + | 0.193626i | ||||
\(635\) | −94.1989 | + | 535.690i | −0.148345 | + | 0.843607i | ||||
\(636\) | −39.6611 | −0.0623602 | ||||||||
\(637\) | 392.308 | − | 99.7436i | 0.615868 | − | 0.156583i | ||||
\(638\) | −93.3290 | − | 93.3290i | −0.146284 | − | 0.146284i | ||||
\(639\) | −3.11534 | − | 1.79864i | −0.00487533 | − | 0.00281477i | ||||
\(640\) | 36.3413 | − | 43.3510i | 0.0567833 | − | 0.0677359i | ||||
\(641\) | −99.9972 | − | 173.200i | −0.156002 | − | 0.270203i | 0.777421 | − | 0.628980i | \(-0.216527\pi\) |
−0.933423 | + | 0.358777i | \(0.883194\pi\) | |||||||
\(642\) | −18.6382 | − | 69.5587i | −0.0290314 | − | 0.108347i | ||||
\(643\) | −854.979 | − | 854.979i | −1.32967 | − | 1.32967i | −0.905653 | − | 0.424019i | \(-0.860619\pi\) |
−0.424019 | − | 0.905653i | \(-0.639381\pi\) | |||||||
\(644\) | −556.501 | − | 152.946i | −0.864132 | − | 0.237494i | ||||
\(645\) | 193.886 | − | 416.297i | 0.300599 | − | 0.645422i | ||||
\(646\) | 577.253 | − | 999.832i | 0.893581 | − | 1.54773i | ||||
\(647\) | 487.329 | + | 130.579i | 0.753213 | + | 0.201823i | 0.614943 | − | 0.788572i | \(-0.289179\pi\) |
0.138270 | + | 0.990395i | \(0.455846\pi\) | |||||||
\(648\) | 6.58846 | − | 24.5885i | 0.0101674 | − | 0.0379452i | ||||
\(649\) | −591.401 | − | 341.446i | −0.911250 | − | 0.526110i | ||||
\(650\) | −187.948 | − | 223.564i | −0.289151 | − | 0.343944i | ||||
\(651\) | −102.247 | − | 103.567i | −0.157061 | − | 0.159089i | ||||
\(652\) | −363.899 | + | 363.899i | −0.558128 | + | 0.558128i | ||||
\(653\) | 357.612 | − | 95.8220i | 0.547645 | − | 0.146741i | 0.0256211 | − | 0.999672i | \(-0.491844\pi\) |
0.522024 | + | 0.852931i | \(0.325177\pi\) | |||||||
\(654\) | 360.303 | − | 208.021i | 0.550922 | − | 0.318075i | ||||
\(655\) | 78.8562 | + | 896.512i | 0.120391 | + | 1.36872i | ||||
\(656\) | 85.9133 | − | 148.806i | 0.130965 | − | 0.226839i | ||||
\(657\) | 151.730 | − | 151.730i | 0.230943 | − | 0.230943i | ||||
\(658\) | 316.891 | + | 185.677i | 0.481597 | + | 0.282184i | ||||
\(659\) | − | 328.877i | − | 0.499055i | −0.968368 | − | 0.249528i | \(-0.919725\pi\) | ||
0.968368 | − | 0.249528i | \(-0.0802753\pi\) | |||||||
\(660\) | −33.7422 | + | 191.885i | −0.0511245 | + | 0.290735i | ||||
\(661\) | −174.842 | − | 302.835i | −0.264511 | − | 0.458147i | 0.702924 | − | 0.711265i | \(-0.251877\pi\) |
−0.967435 | + | 0.253118i | \(0.918544\pi\) | |||||||
\(662\) | −550.825 | − | 147.593i | −0.832062 | − | 0.222950i | ||||
\(663\) | −355.195 | + | 95.1743i | −0.535739 | + | 0.143551i | ||||
\(664\) | − | 412.770i | − | 0.621641i | ||||||
\(665\) | −632.265 | − | 914.495i | −0.950774 | − | 1.37518i | ||||
\(666\) | 103.720 | 0.155736 | ||||||||
\(667\) | 88.5257 | + | 330.382i | 0.132722 | + | 0.495326i | ||||
\(668\) | 15.2894 | − | 57.0608i | 0.0228883 | − | 0.0854203i | ||||
\(669\) | 395.736 | − | 228.478i | 0.591533 | − | 0.341522i | ||||
\(670\) | 331.166 | + | 472.484i | 0.494277 | + | 0.705200i | ||||
\(671\) | −423.587 | −0.631278 | ||||||||
\(672\) | −68.5843 | − | 0.439855i | −0.102060 | − | 0.000654545i | ||||
\(673\) | −861.883 | − | 861.883i | −1.28066 | − | 1.28066i | −0.940294 | − | 0.340364i | \(-0.889450\pi\) |
−0.340364 | − | 0.940294i | \(-0.610550\pi\) | |||||||
\(674\) | −243.677 | − | 140.687i | −0.361538 | − | 0.208734i | ||||
\(675\) | 55.0096 | + | 117.682i | 0.0814957 | + | 0.174343i | ||||
\(676\) | 100.756 | + | 174.514i | 0.149047 | + | 0.258157i | ||||
\(677\) | −255.699 | − | 954.281i | −0.377694 | − | 1.40957i | −0.849368 | − | 0.527801i | \(-0.823017\pi\) |
0.471674 | − | 0.881773i | \(-0.343650\pi\) | |||||||
\(678\) | −194.890 | − | 194.890i | −0.287448 | − | 0.287448i | ||||
\(679\) | −235.225 | − | 64.6480i | −0.346428 | − | 0.0952106i | ||||
\(680\) | 329.469 | + | 153.447i | 0.484513 | + | 0.225657i | ||||
\(681\) | −40.1110 | + | 69.4744i | −0.0589002 | + | 0.102018i | ||||
\(682\) | 184.443 | + | 49.4212i | 0.270444 | + | 0.0724651i | ||||
\(683\) | −142.519 | + | 531.889i | −0.208666 | + | 0.778753i | 0.779634 | + | 0.626235i | \(0.215405\pi\) |
−0.988301 | + | 0.152518i | \(0.951262\pi\) | |||||||
\(684\) | −165.057 | − | 95.2956i | −0.241311 | − | 0.139321i | ||||
\(685\) | 1102.00 | − | 401.678i | 1.60876 | − | 0.586391i | ||||
\(686\) | 116.509 | + | 470.875i | 0.169839 | + | 0.686407i | ||||
\(687\) | −206.604 | + | 206.604i | −0.300733 | + | 0.300733i | ||||
\(688\) | −204.883 | + | 54.8983i | −0.297795 | + | 0.0797940i | ||||
\(689\) | 81.9101 | − | 47.2908i | 0.118883 | − | 0.0686369i | ||||
\(690\) | 324.356 | − | 386.919i | 0.470081 | − | 0.560751i | ||||
\(691\) | 81.0298 | − | 140.348i | 0.117265 | − | 0.203108i | −0.801418 | − | 0.598104i | \(-0.795921\pi\) |
0.918683 | + | 0.394996i | \(0.129254\pi\) | |||||||
\(692\) | 305.133 | − | 305.133i | 0.440944 | − | 0.440944i | ||||
\(693\) | 205.324 | − | 116.794i | 0.296283 | − | 0.168535i | ||||
\(694\) | − | 622.610i | − | 0.897133i | ||||||
\(695\) | 643.458 | + | 918.041i | 0.925839 | + | 1.32092i | ||||
\(696\) | 20.3235 | + | 35.2014i | 0.0292004 | + | 0.0505767i | ||||
\(697\) | 1066.36 | + | 285.730i | 1.52993 | + | 0.409943i | ||||
\(698\) | 387.530 | − | 103.838i | 0.555201 | − | 0.148766i | ||||
\(699\) | − | 384.773i | − | 0.550462i | ||||||
\(700\) | 269.344 | − | 223.503i | 0.384778 | − | 0.319290i | ||||
\(701\) | −106.422 | −0.151815 | −0.0759076 | − | 0.997115i | \(-0.524185\pi\) | ||||
−0.0759076 | + | 0.997115i | \(0.524185\pi\) | |||||||
\(702\) | 15.7118 | + | 58.6373i | 0.0223815 | + | 0.0835289i | ||||
\(703\) | 200.990 | − | 750.105i | 0.285903 | − | 1.06701i | ||||
\(704\) | 77.9317 | − | 44.9939i | 0.110698 | − | 0.0639117i | ||||
\(705\) | −263.111 | + | 184.416i | −0.373208 | + | 0.261582i | ||||
\(706\) | −77.1914 | −0.109336 | ||||||||
\(707\) | −570.220 | + | 973.182i | −0.806534 | + | 1.37650i | ||||
\(708\) | 148.708 | + | 148.708i | 0.210039 | + | 0.210039i | ||||
\(709\) | −517.345 | − | 298.689i | −0.729682 | − | 0.421282i | 0.0886236 | − | 0.996065i | \(-0.471753\pi\) |
−0.818306 | + | 0.574783i | \(0.805087\pi\) | |||||||
\(710\) | −6.49773 | − | 5.44708i | −0.00915174 | − | 0.00767194i | ||||
\(711\) | 123.003 | + | 213.047i | 0.173000 | + | 0.299644i | ||||
\(712\) | 10.6906 | + | 39.8977i | 0.0150148 | + | 0.0560361i | ||||
\(713\) | −349.900 | − | 349.900i | −0.490743 | − | 0.490743i | ||||
\(714\) | −111.319 | − | 426.367i | −0.155909 | − | 0.597153i | ||||
\(715\) | −159.113 | − | 436.524i | −0.222535 | − | 0.610523i | ||||
\(716\) | 152.961 | − | 264.936i | 0.213632 | − | 0.370022i | ||||
\(717\) | −71.2751 | − | 19.0981i | −0.0994073 | − | 0.0266361i | ||||
\(718\) | 107.971 | − | 402.953i | 0.150377 | − | 0.561216i | ||||
\(719\) | −781.019 | − | 450.921i | −1.08626 | − | 0.627151i | −0.153680 | − | 0.988121i | \(-0.549112\pi\) |
−0.932577 | + | 0.360970i | \(0.882446\pi\) | |||||||
\(720\) | 25.3317 | − | 54.3903i | 0.0351829 | − | 0.0755421i | ||||
\(721\) | 334.107 | + | 338.421i | 0.463394 | + | 0.469377i | ||||
\(722\) | −648.028 | + | 648.028i | −0.897546 | + | 0.897546i | ||||
\(723\) | 369.515 | − | 99.0112i | 0.511085 | − | 0.136945i | ||||
\(724\) | 107.009 | − | 61.7819i | 0.147803 | − | 0.0853341i | ||||
\(725\) | −194.983 | − | 70.7619i | −0.268942 | − | 0.0976027i | ||||
\(726\) | −6.77034 | + | 11.7266i | −0.00932554 | + | 0.0161523i | ||||
\(727\) | 985.007 | − | 985.007i | 1.35489 | − | 1.35489i | 0.474798 | − | 0.880095i | \(-0.342521\pi\) |
0.880095 | − | 0.474798i | \(-0.157479\pi\) | |||||||
\(728\) | 142.168 | − | 80.8697i | 0.195286 | − | 0.111085i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 414.164 | − | 290.289i | 0.567347 | − | 0.397656i | ||||
\(731\) | −681.400 | − | 1180.22i | −0.932148 | − | 1.61453i | ||||
\(732\) | 126.004 | + | 33.7627i | 0.172137 | + | 0.0461238i | ||||
\(733\) | −1105.78 | + | 296.294i | −1.50857 | + | 0.404220i | −0.915960 | − | 0.401269i | \(-0.868569\pi\) |
−0.592611 | + | 0.805489i | \(0.701903\pi\) | |||||||
\(734\) | − | 13.7220i | − | 0.0186948i | ||||||
\(735\) | −416.963 | − | 78.8475i | −0.567296 | − | 0.107276i | ||||
\(736\) | −233.198 | −0.316845 | ||||||||
\(737\) | 237.558 | + | 886.577i | 0.322331 | + | 1.20295i | ||||
\(738\) | 47.1697 | − | 176.040i | 0.0639156 | − | 0.238536i | ||||
\(739\) | 1074.61 | − | 620.424i | 1.45413 | − | 0.839545i | 0.455422 | − | 0.890276i | \(-0.349488\pi\) |
0.998712 | + | 0.0507308i | \(0.0161550\pi\) | |||||||
\(740\) | 240.776 | + | 42.3395i | 0.325373 | + | 0.0572156i | ||||
\(741\) | 454.512 | 0.613377 | ||||||||
\(742\) | 56.0398 | + | 98.5175i | 0.0755253 | + | 0.132773i | ||||
\(743\) | 452.213 | + | 452.213i | 0.608631 | + | 0.608631i | 0.942588 | − | 0.333957i | \(-0.108384\pi\) |
−0.333957 | + | 0.942588i | \(0.608384\pi\) | |||||||
\(744\) | −50.9267 | − | 29.4025i | −0.0684498 | − | 0.0395195i | ||||
\(745\) | −570.342 | + | 50.1666i | −0.765560 | + | 0.0673378i | ||||
\(746\) | 8.70110 | + | 15.0708i | 0.0116637 | + | 0.0202021i | ||||
\(747\) | −113.313 | − | 422.890i | −0.151691 | − | 0.566118i | ||||
\(748\) | 408.825 | + | 408.825i | 0.546558 | + | 0.546558i | ||||
\(749\) | −146.448 | + | 144.581i | −0.195524 | + | 0.193032i | ||||
\(750\) | 79.6608 | + | 295.642i | 0.106214 | + | 0.394189i | ||||
\(751\) | −169.151 | + | 292.978i | −0.225234 | + | 0.390118i | −0.956390 | − | 0.292093i | \(-0.905648\pi\) |
0.731155 | + | 0.682211i | \(0.238981\pi\) | |||||||
\(752\) | 143.348 | + | 38.4098i | 0.190622 | + | 0.0510769i | ||||
\(753\) | −74.0068 | + | 276.197i | −0.0982826 | + | 0.366796i | ||||
\(754\) | −83.9464 | − | 48.4665i | −0.111335 | − | 0.0642791i | ||||
\(755\) | 439.523 | + | 204.703i | 0.582150 | + | 0.271130i | ||||
\(756\) | −70.3867 | + | 18.3771i | −0.0931041 | + | 0.0243083i | ||||
\(757\) | 295.501 | − | 295.501i | 0.390357 | − | 0.390357i | −0.484457 | − | 0.874815i | \(-0.660983\pi\) |
0.874815 | + | 0.484457i | \(0.160983\pi\) | |||||||
\(758\) | −393.096 | + | 105.330i | −0.518597 | + | 0.138958i | ||||
\(759\) | 695.560 | − | 401.582i | 0.916416 | − | 0.529093i | ||||
\(760\) | −344.263 | − | 288.597i | −0.452978 | − | 0.379733i | ||||
\(761\) | −43.0586 | + | 74.5798i | −0.0565817 | + | 0.0980023i | −0.892929 | − | 0.450198i | \(-0.851353\pi\) |
0.836347 | + | 0.548200i | \(0.184687\pi\) | |||||||
\(762\) | 188.416 | − | 188.416i | 0.247265 | − | 0.247265i | ||||
\(763\) | −1025.82 | − | 601.061i | −1.34445 | − | 0.787760i | ||||
\(764\) | 44.5731i | 0.0583417i | ||||||||
\(765\) | 379.672 | + | 66.7637i | 0.496303 | + | 0.0872728i | ||||
\(766\) | 458.091 | + | 793.437i | 0.598030 | + | 1.03582i | ||||
\(767\) | −484.435 | − | 129.804i | −0.631597 | − | 0.169236i | ||||
\(768\) | −26.7685 | + | 7.17260i | −0.0348548 | + | 0.00933933i | ||||
\(769\) | 1217.54i | 1.58328i | 0.610988 | + | 0.791640i | \(0.290772\pi\) | ||||
−0.610988 | + | 0.791640i | \(0.709228\pi\) | |||||||
\(770\) | 524.316 | − | 187.312i | 0.680930 | − | 0.243263i | ||||
\(771\) | 220.762 | 0.286332 | ||||||||
\(772\) | 121.794 | + | 454.541i | 0.157764 | + | 0.588783i | ||||
\(773\) | −219.423 | + | 818.896i | −0.283859 | + | 1.05937i | 0.665811 | + | 0.746121i | \(0.268086\pi\) |
−0.949669 | + | 0.313254i | \(0.898581\pi\) | |||||||
\(774\) | −194.836 | + | 112.489i | −0.251726 | + | 0.145334i | ||||
\(775\) | 295.480 | − | 52.3856i | 0.381265 | − | 0.0675943i | ||||
\(776\) | −98.5695 | −0.127023 | ||||||||
\(777\) | −146.553 | − | 257.639i | −0.188614 | − | 0.331582i | ||||
\(778\) | −135.696 | − | 135.696i | −0.174417 | − | 0.174417i | ||||
\(779\) | −1181.72 | − | 682.264i | −1.51696 | − | 0.875820i | ||||
\(780\) | 12.5372 | + | 142.535i | 0.0160733 | + | 0.182737i | ||||
\(781\) | −6.74398 | − | 11.6809i | −0.00863506 | − | 0.0149564i | ||||
\(782\) | −387.785 | − | 1447.23i | −0.495889 | − | 1.85068i | ||||
\(783\) | 30.4853 | + | 30.4853i | 0.0389339 | + | 0.0389339i | ||||
\(784\) | 95.8148 | + | 170.984i | 0.122213 | + | 0.218092i | ||||
\(785\) | −605.536 | + | 220.717i | −0.771383 | + | 0.281168i | ||||
\(786\) | 220.448 | − | 381.827i | 0.280468 | − | 0.485784i | ||||
\(787\) | −639.837 | − | 171.444i | −0.813008 | − | 0.217845i | −0.171721 | − | 0.985146i | \(-0.554933\pi\) |
−0.641287 | + | 0.767301i | \(0.721599\pi\) | |||||||
\(788\) | 106.010 | − | 395.634i | 0.134530 | − | 0.502073i | ||||
\(789\) | 654.936 | + | 378.128i | 0.830084 | + | 0.479249i | ||||
\(790\) | 198.571 | + | 544.779i | 0.251356 | + | 0.689594i | ||||
\(791\) | −208.730 | + | 759.476i | −0.263882 | + | 0.960146i | ||||
\(792\) | 67.4908 | − | 67.4908i | 0.0852156 | − | 0.0852156i | ||||
\(793\) | −300.488 | + | 80.5154i | −0.378925 | + | 0.101533i | ||||
\(794\) | 425.751 | − | 245.807i | 0.536210 | − | 0.309581i | ||||
\(795\) | −98.7713 | + | 8.68781i | −0.124241 | + | 0.0109281i | ||||
\(796\) | 192.282 | − | 333.041i | 0.241560 | − | 0.418394i | ||||
\(797\) | −72.1342 | + | 72.1342i | −0.0905072 | + | 0.0905072i | −0.750911 | − | 0.660404i | \(-0.770385\pi\) |
0.660404 | + | 0.750911i | \(0.270385\pi\) | |||||||
\(798\) | −3.49302 | + | 544.649i | −0.00437721 | + | 0.682517i | ||||
\(799\) | 953.490i | 1.19335i | ||||||||
\(800\) | 81.0078 | − | 115.921i | 0.101260 | − | 0.144902i | ||||
\(801\) | 21.9053 | + | 37.9412i | 0.0273475 | + | 0.0473673i | ||||
\(802\) | 283.121 | + | 75.8619i | 0.353018 | + | 0.0945909i | ||||
\(803\) | 777.144 | − | 208.235i | 0.967801 | − | 0.259321i | ||||
\(804\) | − | 282.664i | − | 0.351572i | ||||||
\(805\) | −1419.40 | − | 258.992i | −1.76324 | − | 0.321729i | ||||
\(806\) | 140.235 | 0.173989 | ||||||||
\(807\) | 4.14639 | + | 15.4746i | 0.00513803 | + | 0.0191754i | ||||
\(808\) | −117.958 | + | 440.225i | −0.145987 | + | 0.544832i | ||||
\(809\) | −541.028 | + | 312.363i | −0.668762 | + | 0.386110i | −0.795607 | − | 0.605813i | \(-0.792848\pi\) |
0.126845 | + | 0.991923i | \(0.459515\pi\) | |||||||
\(810\) | 11.0217 | − | 62.6779i | 0.0136070 | − | 0.0773802i | ||||
\(811\) | −429.920 | −0.530111 | −0.265056 | − | 0.964233i | \(-0.585390\pi\) | ||||
−0.265056 | + | 0.964233i | \(0.585390\pi\) | |||||||
\(812\) | 58.7232 | − | 100.222i | 0.0723192 | − | 0.123426i | ||||
\(813\) | −118.298 | − | 118.298i | −0.145508 | − | 0.145508i | ||||
\(814\) | 336.795 | + | 194.449i | 0.413753 | + | 0.238880i | ||||
\(815\) | −826.536 | + | 985.962i | −1.01415 | + | 1.20977i | ||||
\(816\) | −89.0267 | − | 154.199i | −0.109101 | − | 0.188969i | ||||
\(817\) | 435.964 | + | 1627.04i | 0.533615 | + | 1.99148i | ||||
\(818\) | 262.074 | + | 262.074i | 0.320384 | + | 0.320384i | ||||
\(819\) | 123.454 | − | 121.881i | 0.150737 | − | 0.148816i | ||||
\(820\) | 181.361 | − | 389.404i | 0.221172 | − | 0.474883i | ||||
\(821\) | 625.295 | − | 1083.04i | 0.761626 | − | 1.31918i | −0.180385 | − | 0.983596i | \(-0.557734\pi\) |
0.942012 | − | 0.335580i | \(-0.108932\pi\) | |||||||
\(822\) | −555.034 | − | 148.721i | −0.675224 | − | 0.180926i | ||||
\(823\) | 94.7993 | − | 353.796i | 0.115188 | − | 0.429886i | −0.884113 | − | 0.467272i | \(-0.845237\pi\) |
0.999301 | + | 0.0373868i | \(0.0119034\pi\) | |||||||
\(824\) | 166.411 | + | 96.0774i | 0.201955 | + | 0.116599i | ||||
\(825\) | −41.9983 | + | 485.259i | −0.0509071 | + | 0.588192i | ||||
\(826\) | 159.269 | − | 579.508i | 0.192819 | − | 0.701583i | ||||
\(827\) | 458.173 | − | 458.173i | 0.554018 | − | 0.554018i | −0.373580 | − | 0.927598i | \(-0.621870\pi\) |
0.927598 | + | 0.373580i | \(0.121870\pi\) | |||||||
\(828\) | −238.916 | + | 64.0173i | −0.288546 | + | 0.0773156i | ||||
\(829\) | −228.961 | + | 132.190i | −0.276189 | + | 0.159458i | −0.631697 | − | 0.775216i | \(-0.717641\pi\) |
0.355508 | + | 0.934673i | \(0.384308\pi\) | |||||||
\(830\) | −90.4178 | − | 1027.96i | −0.108937 | − | 1.23850i | ||||
\(831\) | −131.437 | + | 227.655i | −0.158167 | + | 0.273953i | ||||
\(832\) | 46.7313 | − | 46.7313i | 0.0561675 | − | 0.0561675i | ||||
\(833\) | −901.800 | + | 878.958i | −1.08259 | + | 1.05517i | ||||
\(834\) | − | 549.219i | − | 0.658536i | ||||||
\(835\) | 25.5772 | − | 145.452i | 0.0306314 | − | 0.174195i | ||||
\(836\) | −357.310 | − | 618.879i | −0.427404 | − | 0.740285i | ||||
\(837\) | −60.2469 | − | 16.1431i | −0.0719796 | − | 0.0192869i | ||||
\(838\) | 196.282 | − | 52.5935i | 0.234226 | − | 0.0627607i | ||||
\(839\) | − | 1042.00i | − | 1.24196i | −0.783827 | − | 0.620980i | \(-0.786735\pi\) | ||
0.783827 | − | 0.620980i | \(-0.213265\pi\) | |||||||
\(840\) | −170.898 | + | 13.9281i | −0.203450 | + | 0.0165811i | ||||
\(841\) | 772.159 | 0.918144 | ||||||||
\(842\) | 111.957 | + | 417.829i | 0.132966 | + | 0.496234i | ||||
\(843\) | −23.6989 | + | 88.4455i | −0.0281126 | + | 0.104918i | ||||
\(844\) | 2.58754 | − | 1.49392i | 0.00306580 | − | 0.00177004i | ||||
\(845\) | 289.148 | + | 412.536i | 0.342187 | + | 0.488209i | ||||
\(846\) | 157.406 | 0.186060 | ||||||||
\(847\) | 38.6949 | + | 0.248164i | 0.0456847 | + | 0.000292992i | ||||
\(848\) | 32.3831 | + | 32.3831i | 0.0381876 | + | 0.0381876i | ||||
\(849\) | −247.271 | − | 142.762i | −0.291250 | − | 0.168153i | ||||
\(850\) | 854.118 | + | 309.971i | 1.00484 | + | 0.364672i | ||||
\(851\) | −503.903 | − | 872.785i | −0.592130 | − | 1.02560i | ||||
\(852\) | 1.07508 | + | 4.01224i | 0.00126183 | + | 0.00470921i | ||||
\(853\) | 559.421 | + | 559.421i | 0.655828 | + | 0.655828i | 0.954390 | − | 0.298562i | \(-0.0965071\pi\) |
−0.298562 | + | 0.954390i | \(0.596507\pi\) | |||||||
\(854\) | −94.1735 | − | 360.698i | −0.110273 | − | 0.422363i | ||||
\(855\) | −431.930 | − | 201.167i | −0.505181 | − | 0.235283i | ||||
\(856\) | −41.5764 | + | 72.0124i | −0.0485705 | + | 0.0841267i | ||||
\(857\) | −1099.94 | − | 294.728i | −1.28348 | − | 0.343906i | −0.448297 | − | 0.893885i | \(-0.647969\pi\) |
−0.835179 | + | 0.549978i | \(0.814636\pi\) | |||||||
\(858\) | −58.9113 | + | 219.860i | −0.0686611 | + | 0.256247i | ||||
\(859\) | 127.974 | + | 73.8859i | 0.148980 | + | 0.0860139i | 0.572637 | − | 0.819809i | \(-0.305920\pi\) |
−0.423657 | + | 0.905823i | \(0.639254\pi\) | |||||||
\(860\) | −498.212 | + | 181.598i | −0.579317 | + | 0.211160i | ||||
\(861\) | −503.929 | + | 131.570i | −0.585284 | + | 0.152810i | ||||
\(862\) | −628.987 | + | 628.987i | −0.729683 | + | 0.729683i | ||||
\(863\) | 103.370 | − | 27.6980i | 0.119780 | − | 0.0320950i | −0.198431 | − | 0.980115i | \(-0.563585\pi\) |
0.318211 | + | 0.948020i | \(0.396918\pi\) | |||||||
\(864\) | −25.4558 | + | 14.6969i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 693.060 | − | 826.739i | 0.801225 | − | 0.955768i | ||||
\(866\) | −215.672 | + | 373.554i | −0.249044 | + | 0.431356i | ||||
\(867\) | 454.967 | − | 454.967i | 0.524761 | − | 0.524761i | ||||
\(868\) | −1.07774 | + | 168.046i | −0.00124163 | + | 0.193601i | ||||
\(869\) | 922.394i | 1.06144i | ||||||||
\(870\) | 58.3243 | + | 83.2130i | 0.0670394 | + | 0.0956472i | ||||
\(871\) | 337.041 | + | 583.772i | 0.386959 | + | 0.670232i | ||||
\(872\) | −464.035 | − | 124.338i | −0.532150 | − | 0.142589i | ||||
\(873\) | −100.986 | + | 27.0592i | −0.115677 | + | 0.0309956i | ||||
\(874\) | 1851.90i | 2.11887i | ||||||||
\(875\) | 621.812 | − | 615.609i | 0.710643 | − | 0.703553i | ||||
\(876\) | −247.774 | −0.282847 | ||||||||
\(877\) | 332.675 | + | 1241.56i | 0.379333 | + | 1.41569i | 0.846909 | + | 0.531738i | \(0.178461\pi\) |
−0.467576 | + | 0.883953i | \(0.654872\pi\) | |||||||
\(878\) | −150.765 | + | 562.662i | −0.171714 | + | 0.640845i | ||||
\(879\) | −533.046 | + | 307.754i | −0.606423 | + | 0.350119i | ||||
\(880\) | 184.224 | − | 129.123i | 0.209345 | − | 0.146731i | ||||
\(881\) | 1358.66 | 1.54217 | 0.771087 | − | 0.636729i | \(-0.219713\pi\) | ||||
0.771087 | + | 0.636729i | \(0.219713\pi\) | |||||||
\(882\) | 145.102 | + | 148.873i | 0.164515 | + | 0.168791i | ||||
\(883\) | 434.614 | + | 434.614i | 0.492201 | + | 0.492201i | 0.908999 | − | 0.416798i | \(-0.136848\pi\) |
−0.416798 | + | 0.908999i | \(0.636848\pi\) | |||||||
\(884\) | 367.725 | + | 212.306i | 0.415979 | + | 0.240165i | ||||
\(885\) | 402.914 | + | 337.765i | 0.455270 | + | 0.381655i | ||||
\(886\) | 295.727 | + | 512.215i | 0.333778 | + | 0.578120i | ||||
\(887\) | 225.904 | + | 843.084i | 0.254683 | + | 0.950489i | 0.968267 | + | 0.249919i | \(0.0804041\pi\) |
−0.713584 | + | 0.700570i | \(0.752929\pi\) | |||||||
\(888\) | −84.6871 | − | 84.6871i | −0.0953684 | − | 0.0953684i | ||||
\(889\) | −734.248 | − | 201.797i | −0.825925 | − | 0.226993i | ||||
\(890\) | 35.3632 | + | 97.0188i | 0.0397340 | + | 0.109010i | ||||
\(891\) | 50.6181 | − | 87.6731i | 0.0568104 | − | 0.0983985i | ||||
\(892\) | −509.669 | − | 136.565i | −0.571377 | − | 0.153100i | ||||
\(893\) | 305.024 | − | 1138.37i | 0.341572 | − | 1.27477i | ||||
\(894\) | 242.910 | + | 140.244i | 0.271711 | + | 0.156873i | ||||
\(895\) | 322.896 | − | 693.298i | 0.360778 | − | 0.774635i | ||||
\(896\) | 55.6397 | + | 56.3580i | 0.0620979 | + | 0.0628995i | ||||
\(897\) | 417.089 | − | 417.089i | 0.464982 | − | 0.464982i | ||||
\(898\) | 194.100 | − | 52.0088i | 0.216146 | − | 0.0579163i | ||||
\(899\) | 86.2507 | − | 49.7969i | 0.0959407 | − | 0.0553914i | ||||
\(900\) | 51.1715 | − | 141.002i | 0.0568572 | − | 0.156669i | ||||
\(901\) | −147.121 | + | 254.820i | −0.163286 | + | 0.282819i | ||||
\(902\) | 483.197 | − | 483.197i | 0.535695 | − | 0.535695i | ||||
\(903\) | 554.718 | + | 325.027i | 0.614305 | + | 0.359942i | ||||
\(904\) | 318.253i | 0.352050i | ||||||||
\(905\) | 252.961 | − | 177.301i | 0.279515 | − | 0.195913i | ||||
\(906\) | −118.765 | − | 205.706i | −0.131087 | − | 0.227049i | ||||
\(907\) | −1443.18 | − | 386.699i | −1.59116 | − | 0.426350i | −0.648802 | − | 0.760957i | \(-0.724730\pi\) |
−0.942358 | + | 0.334607i | \(0.891396\pi\) | |||||||
\(908\) | 89.4761 | − | 23.9751i | 0.0985420 | − | 0.0264042i | ||||
\(909\) | 483.400i | 0.531793i | ||||||||
\(910\) | 336.339 | − | 232.539i | 0.369604 | − | 0.255537i | ||||
\(911\) | −692.019 | −0.759626 | −0.379813 | − | 0.925063i | \(-0.624012\pi\) | ||||
−0.379813 | + | 0.925063i | \(0.624012\pi\) | |||||||
\(912\) | 56.9598 | + | 212.577i | 0.0624559 | + | 0.233089i | ||||
\(913\) | 424.866 | − | 1585.62i | 0.465352 | − | 1.73672i | ||||
\(914\) | −86.8974 | + | 50.1703i | −0.0950738 | + | 0.0548909i | ||||
\(915\) | 321.194 | + | 56.4807i | 0.351032 | + | 0.0617275i | ||||
\(916\) | 337.382 | 0.368321 | ||||||||
\(917\) | −1259.94 | − | 8.08041i | −1.37398 | − | 0.00881179i | ||||
\(918\) | −133.540 | − | 133.540i | −0.145468 | − | 0.145468i | ||||
\(919\) | −405.065 | − | 233.864i | −0.440767 | − | 0.254477i | 0.263156 | − | 0.964753i | \(-0.415237\pi\) |
−0.703923 | + | 0.710276i | \(0.748570\pi\) | |||||||
\(920\) | −580.753 | + | 51.0824i | −0.631253 | + | 0.0555243i | ||||
\(921\) | −342.443 | − | 593.130i | −0.371817 | − | 0.644006i | ||||
\(922\) | 27.4707 | + | 102.522i | 0.0297947 | + | 0.111195i | ||||
\(923\) | −7.00440 | − | 7.00440i | −0.00758873 | − | 0.00758873i | ||||
\(924\) | −263.009 | − | 72.2839i | −0.284641 | − | 0.0782293i | ||||
\(925\) | 608.900 | + | 52.6993i | 0.658271 | + | 0.0569722i | ||||
\(926\) | −345.058 | + | 597.659i | −0.372633 | + | 0.645420i | ||||
\(927\) | 196.866 | + | 52.7502i | 0.212369 | + | 0.0569042i | ||||
\(928\) | 12.1477 | − | 45.3359i | 0.0130902 | − | 0.0488533i | ||||
\(929\) | 306.947 | + | 177.216i | 0.330406 | + | 0.190760i | 0.656021 | − | 0.754742i | \(-0.272238\pi\) |
−0.325615 | + | 0.945502i | \(0.605571\pi\) | |||||||
\(930\) | −133.268 | − | 62.0680i | −0.143299 | − | 0.0667398i | ||||
\(931\) | 1357.84 | − | 760.894i | 1.45847 | − | 0.817287i | ||||
\(932\) | −314.166 | + | 314.166i | −0.337088 | + | 0.337088i | ||||
\(933\) | 721.002 | − | 193.192i | 0.772778 | − | 0.207065i | ||||
\(934\) | −740.387 | + | 427.463i | −0.792706 | + | 0.457669i | ||||
\(935\) | 1107.69 | + | 928.579i | 1.18469 | + | 0.993132i | ||||
\(936\) | 35.0485 | − | 60.7058i | 0.0374450 | − | 0.0648566i | ||||
\(937\) | −546.542 | + | 546.542i | −0.583289 | + | 0.583289i | −0.935806 | − | 0.352517i | \(-0.885326\pi\) |
0.352517 | + | 0.935806i | \(0.385326\pi\) | |||||||
\(938\) | −702.133 | + | 399.395i | −0.748543 | + | 0.425794i | ||||
\(939\) | 291.356i | 0.310283i | ||||||||
\(940\) | 365.404 | + | 64.2548i | 0.388728 | + | 0.0683562i | ||||
\(941\) | 385.947 | + | 668.480i | 0.410146 | + | 0.710394i | 0.994905 | − | 0.100813i | \(-0.0321444\pi\) |
−0.584759 | + | 0.811207i | \(0.698811\pi\) | |||||||
\(942\) | 304.984 | + | 81.7202i | 0.323762 | + | 0.0867519i | ||||
\(943\) | −1710.50 | + | 458.328i | −1.81390 | + | 0.486032i | ||||
\(944\) | − | 242.839i | − | 0.257245i | ||||||
\(945\) | −171.264 | + | 61.1843i | −0.181232 | + | 0.0647452i | ||||
\(946\) | −843.550 | −0.891702 | ||||||||
\(947\) | 89.9315 | + | 335.629i | 0.0949647 | + | 0.354413i | 0.997014 | − | 0.0772198i | \(-0.0246043\pi\) |
−0.902049 | + | 0.431633i | \(0.857938\pi\) | |||||||
\(948\) | 73.5208 | − | 274.383i | 0.0775536 | − | 0.289434i | ||||
\(949\) | 511.715 | − | 295.439i | 0.539215 | − | 0.311316i | ||||
\(950\) | −920.565 | − | 643.307i | −0.969016 | − | 0.677166i | ||||
\(951\) | 300.697 | 0.316191 | ||||||||
\(952\) | −257.236 | + | 439.019i | −0.270206 | + | 0.461154i | ||||
\(953\) | 190.549 | + | 190.549i | 0.199946 | + | 0.199946i | 0.799977 | − | 0.600031i | \(-0.204845\pi\) |
−0.600031 | + | 0.799977i | \(0.704845\pi\) | |||||||
\(954\) | 42.0669 | + | 24.2873i | 0.0440953 | + | 0.0254584i | ||||
\(955\) | 9.76380 | + | 111.004i | 0.0102239 | + | 0.116235i | ||||
\(956\) | 42.6023 | + | 73.7894i | 0.0445631 | + | 0.0771855i | ||||
\(957\) | 41.8382 | + | 156.142i | 0.0437181 | + | 0.163158i | ||||
\(958\) | −560.192 | − | 560.192i | −0.584751 | − | 0.584751i | ||||
\(959\) | 414.824 | + | 1588.83i | 0.432559 | + | 1.65676i | ||||
\(960\) | −65.0928 | + | 23.7262i | −0.0678049 | + | 0.0247148i | ||||
\(961\) | 408.458 | − | 707.469i | 0.425034 | − | 0.736180i | ||||
\(962\) | 275.879 | + | 73.9216i | 0.286777 | + | 0.0768415i | ||||
\(963\) | −22.8270 | + | 85.1916i | −0.0237041 | + | 0.0884648i | ||||
\(964\) | −382.550 | − | 220.865i | −0.396836 | − | 0.229113i | ||||
\(965\) | 402.881 | + | 1105.30i | 0.417494 | + | 1.14539i | ||||
\(966\) | 496.599 | + | 503.009i | 0.514077 | + | 0.520714i | ||||
\(967\) | 697.702 | − | 697.702i | 0.721511 | − | 0.721511i | −0.247402 | − | 0.968913i | \(-0.579577\pi\) |
0.968913 | + | 0.247402i | \(0.0795767\pi\) | |||||||
\(968\) | 15.1027 | − | 4.04675i | 0.0156019 | − | 0.00418053i | ||||
\(969\) | −1224.54 | + | 706.988i | −1.26371 | + | 0.729605i | ||||
\(970\) | −245.476 | + | 21.5918i | −0.253068 | + | 0.0222596i | ||||
\(971\) | −605.244 | + | 1048.31i | −0.623320 | + | 1.07962i | 0.365543 | + | 0.930794i | \(0.380883\pi\) |
−0.988863 | + | 0.148828i | \(0.952450\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −1364.25 | + | 776.028i | −1.40211 | + | 0.797562i | ||||
\(974\) | − | 990.481i | − | 1.01692i | ||||||
\(975\) | 62.4448 | + | 352.220i | 0.0640460 | + | 0.361251i | ||||
\(976\) | −75.3147 | − | 130.449i | −0.0771667 | − | 0.133657i | ||||
\(977\) | 1004.34 | + | 269.113i | 1.02799 | + | 0.275448i | 0.733126 | − | 0.680093i | \(-0.238060\pi\) |
0.294860 | + | 0.955541i | \(0.404727\pi\) | |||||||
\(978\) | 608.815 | − | 163.132i | 0.622510 | − | 0.166801i | ||||
\(979\) | 164.268i | 0.167791i | ||||||||
\(980\) | 276.070 | + | 404.828i | 0.281704 | + | 0.413089i | ||||
\(981\) | −509.545 | −0.519414 | ||||||||
\(982\) | 104.350 | + | 389.441i | 0.106263 | + | 0.396579i | ||||
\(983\) | −256.541 | + | 957.423i | −0.260977 | + | 0.973980i | 0.703690 | + | 0.710508i | \(0.251535\pi\) |
−0.964667 | + | 0.263473i | \(0.915132\pi\) | |||||||
\(984\) | −182.250 | + | 105.222i | −0.185213 | + | 0.106933i | ||||
\(985\) | 177.341 | − | 1008.50i | 0.180041 | − | 1.02386i | ||||
\(986\) | 301.556 | 0.305838 | ||||||||
\(987\) | −222.410 | − | 390.996i | −0.225340 | − | 0.396145i | ||||
\(988\) | −371.108 | − | 371.108i | −0.375615 | − | 0.375615i | ||||
\(989\) | 1893.14 | + | 1093.01i | 1.91420 | + | 1.10516i | ||||
\(990\) | 153.294 | − | 182.862i | 0.154843 | − | 0.184709i | ||||
\(991\) | 185.301 | + | 320.951i | 0.186984 | + | 0.323866i | 0.944243 | − | 0.329249i | \(-0.106795\pi\) |
−0.757259 | + | 0.653114i | \(0.773462\pi\) | |||||||
\(992\) | 17.5744 | + | 65.5885i | 0.0177161 | + | 0.0661174i | ||||
\(993\) | 493.856 | + | 493.856i | 0.497338 | + | 0.497338i | ||||
\(994\) | 8.44731 | − | 8.33965i | 0.00849830 | − | 0.00838999i | ||||
\(995\) | 405.902 | − | 871.521i | 0.407941 | − | 0.875900i | ||||
\(996\) | −252.769 | + | 437.808i | −0.253784 | + | 0.439567i | ||||
\(997\) | 356.099 | + | 95.4166i | 0.357171 | + | 0.0957037i | 0.432943 | − | 0.901422i | \(-0.357475\pi\) |
−0.0757716 | + | 0.997125i | \(0.524142\pi\) | |||||||
\(998\) | 278.937 | − | 1041.01i | 0.279496 | − | 1.04309i | ||||
\(999\) | −110.012 | − | 63.5153i | −0.110122 | − | 0.0635789i |
(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 | 210.3.v.a.163.5 | yes | 32 | |
5.2 | odd | 4 | inner | 210.3.v.a.37.3 | ✓ | 32 | |
7.4 | even | 3 | inner | 210.3.v.a.193.3 | yes | 32 | |
35.32 | odd | 12 | inner | 210.3.v.a.67.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.v.a.37.3 | ✓ | 32 | 5.2 | odd | 4 | inner | |
210.3.v.a.67.5 | yes | 32 | 35.32 | odd | 12 | inner | |
210.3.v.a.163.5 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.v.a.193.3 | yes | 32 | 7.4 | even | 3 | inner |