Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,3,Mod(2,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.n (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: | \(1.71662566547\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 32.5 | ||
Character | \(\chi\) | \(=\) | 63.32 |
Dual form | 63.3.n.b.2.5 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11793 | − | 0.645440i | −0.558967 | − | 0.322720i | 0.193764 | − | 0.981048i | \(-0.437931\pi\) |
−0.752731 | + | 0.658328i | \(0.771264\pi\) | |||||||
\(3\) | −0.401800 | + | 2.97297i | −0.133933 | + | 0.990990i | ||||
\(4\) | −1.16681 | − | 2.02098i | −0.291704 | − | 0.505246i | ||||
\(5\) | 4.83636i | 0.967271i | 0.875269 | + | 0.483636i | \(0.160684\pi\) | ||||
−0.875269 | + | 0.483636i | \(0.839316\pi\) | |||||||
\(6\) | 2.36806 | − | 3.06425i | 0.394677 | − | 0.510708i | ||||
\(7\) | −1.74042 | + | 6.78019i | −0.248632 | + | 0.968598i | ||||
\(8\) | 8.17595i | 1.02199i | ||||||||
\(9\) | −8.67711 | − | 2.38908i | −0.964124 | − | 0.265453i | ||||
\(10\) | 3.12158 | − | 5.40673i | 0.312158 | − | 0.540673i | ||||
\(11\) | 13.6810i | 1.24373i | 0.783126 | + | 0.621863i | \(0.213624\pi\) | ||||
−0.783126 | + | 0.621863i | \(0.786376\pi\) | |||||||
\(12\) | 6.47715 | − | 2.65687i | 0.539762 | − | 0.221406i | ||||
\(13\) | 8.59380 | − | 14.8849i | 0.661062 | − | 1.14499i | −0.319275 | − | 0.947662i | \(-0.603439\pi\) |
0.980337 | − | 0.197330i | \(-0.0632272\pi\) | |||||||
\(14\) | 6.32188 | − | 6.45647i | 0.451563 | − | 0.461176i | ||||
\(15\) | −14.3784 | − | 1.94325i | −0.958557 | − | 0.129550i | ||||
\(16\) | 0.609829 | − | 1.05626i | 0.0381143 | − | 0.0660160i | ||||
\(17\) | 7.11684 | + | 4.10891i | 0.418638 | + | 0.241700i | 0.694494 | − | 0.719498i | \(-0.255628\pi\) |
−0.275857 | + | 0.961199i | \(0.588962\pi\) | |||||||
\(18\) | 8.15844 | + | 8.27139i | 0.453247 | + | 0.459522i | ||||
\(19\) | −6.93167 | − | 12.0060i | −0.364825 | − | 0.631895i | 0.623923 | − | 0.781486i | \(-0.285538\pi\) |
−0.988748 | + | 0.149591i | \(0.952204\pi\) | |||||||
\(20\) | 9.77419 | − | 5.64313i | 0.488710 | − | 0.282157i | ||||
\(21\) | −19.4580 | − | 7.89850i | −0.926571 | − | 0.376119i | ||||
\(22\) | 8.83026 | − | 15.2945i | 0.401375 | − | 0.695202i | ||||
\(23\) | − | 18.5326i | − | 0.805766i | −0.915251 | − | 0.402883i | \(-0.868008\pi\) | ||
0.915251 | − | 0.402883i | \(-0.131992\pi\) | |||||||
\(24\) | −24.3069 | − | 3.28510i | −1.01279 | − | 0.136879i | ||||
\(25\) | 1.60965 | 0.0643859 | ||||||||
\(26\) | −19.2146 | + | 11.0936i | −0.739024 | + | 0.426676i | ||||
\(27\) | 10.5891 | − | 24.8369i | 0.392190 | − | 0.919884i | ||||
\(28\) | 15.7334 | − | 4.39386i | 0.561907 | − | 0.156924i | ||||
\(29\) | −18.1723 | + | 10.4918i | −0.626631 | + | 0.361786i | −0.779446 | − | 0.626469i | \(-0.784499\pi\) |
0.152815 | + | 0.988255i | \(0.451166\pi\) | |||||||
\(30\) | 14.8198 | + | 11.4528i | 0.493994 | + | 0.381760i | ||||
\(31\) | 25.7776 | + | 44.6481i | 0.831536 | + | 1.44026i | 0.896820 | + | 0.442395i | \(0.145871\pi\) |
−0.0652846 | + | 0.997867i | \(0.520796\pi\) | |||||||
\(32\) | 26.9588 | − | 15.5647i | 0.842464 | − | 0.486397i | ||||
\(33\) | −40.6732 | − | 5.49702i | −1.23252 | − | 0.166577i | ||||
\(34\) | −5.30411 | − | 9.18698i | −0.156003 | − | 0.270205i | ||||
\(35\) | −32.7914 | − | 8.41730i | −0.936897 | − | 0.240494i | ||||
\(36\) | 5.29629 | + | 20.3239i | 0.147119 | + | 0.564553i | ||||
\(37\) | 13.8496 | + | 23.9882i | 0.374314 | + | 0.648331i | 0.990224 | − | 0.139486i | \(-0.0445449\pi\) |
−0.615910 | + | 0.787816i | \(0.711212\pi\) | |||||||
\(38\) | 17.8959i | 0.470945i | ||||||||
\(39\) | 40.7994 | + | 31.5299i | 1.04614 | + | 0.808458i | ||||
\(40\) | −39.5418 | −0.988546 | ||||||||
\(41\) | 18.4583 | + | 10.6569i | 0.450202 | + | 0.259924i | 0.707915 | − | 0.706297i | \(-0.249636\pi\) |
−0.257714 | + | 0.966221i | \(0.582969\pi\) | |||||||
\(42\) | 16.6548 | + | 21.3890i | 0.396542 | + | 0.509261i | ||||
\(43\) | 18.1984 | + | 31.5205i | 0.423218 | + | 0.733035i | 0.996252 | − | 0.0864962i | \(-0.0275670\pi\) |
−0.573034 | + | 0.819532i | \(0.694234\pi\) | |||||||
\(44\) | 27.6490 | − | 15.9632i | 0.628387 | − | 0.362799i | ||||
\(45\) | 11.5544 | − | 41.9656i | 0.256766 | − | 0.932569i | ||||
\(46\) | −11.9617 | + | 20.7183i | −0.260037 | + | 0.450397i | ||||
\(47\) | 51.4255 | + | 29.6905i | 1.09416 | + | 0.631713i | 0.934681 | − | 0.355488i | \(-0.115685\pi\) |
0.159479 | + | 0.987201i | \(0.449019\pi\) | |||||||
\(48\) | 2.89519 | + | 2.23741i | 0.0603164 | + | 0.0466127i | ||||
\(49\) | −42.9419 | − | 23.6008i | −0.876365 | − | 0.481648i | ||||
\(50\) | −1.79948 | − | 1.03893i | −0.0359896 | − | 0.0207786i | ||||
\(51\) | −15.0752 | + | 19.5072i | −0.295592 | + | 0.382494i | ||||
\(52\) | −40.1095 | −0.771336 | ||||||||
\(53\) | −81.0775 | − | 46.8101i | −1.52976 | − | 0.883210i | −0.999371 | − | 0.0354576i | \(-0.988711\pi\) |
−0.530393 | − | 0.847752i | \(-0.677956\pi\) | |||||||
\(54\) | −27.8687 | + | 20.9314i | −0.516087 | + | 0.387618i | ||||
\(55\) | −66.1662 | −1.20302 | ||||||||
\(56\) | −55.4345 | − | 14.2296i | −0.989902 | − | 0.254100i | ||||
\(57\) | 38.4786 | − | 15.7836i | 0.675064 | − | 0.276906i | ||||
\(58\) | 27.0873 | 0.467022 | ||||||||
\(59\) | −1.45171 | + | 0.838143i | −0.0246052 | + | 0.0142058i | −0.512252 | − | 0.858835i | \(-0.671189\pi\) |
0.487647 | + | 0.873041i | \(0.337855\pi\) | |||||||
\(60\) | 12.8496 | + | 31.3258i | 0.214160 | + | 0.522097i | ||||
\(61\) | 32.7357 | − | 56.6998i | 0.536650 | − | 0.929506i | −0.462431 | − | 0.886655i | \(-0.653023\pi\) |
0.999082 | − | 0.0428504i | \(-0.0136439\pi\) | |||||||
\(62\) | − | 66.5516i | − | 1.07341i | ||||||
\(63\) | 31.3002 | − | 54.6744i | 0.496829 | − | 0.867848i | ||||
\(64\) | −45.0629 | −0.704108 | ||||||||
\(65\) | 71.9887 | + | 41.5627i | 1.10752 | + | 0.639426i | ||||
\(66\) | 41.9220 | + | 32.3974i | 0.635181 | + | 0.490870i | ||||
\(67\) | 27.6096 | + | 47.8212i | 0.412083 | + | 0.713749i | 0.995117 | − | 0.0986986i | \(-0.0314680\pi\) |
−0.583034 | + | 0.812448i | \(0.698135\pi\) | |||||||
\(68\) | − | 19.1773i | − | 0.282020i | ||||||
\(69\) | 55.0969 | + | 7.44641i | 0.798506 | + | 0.107919i | ||||
\(70\) | 31.2258 | + | 30.5749i | 0.446083 | + | 0.436784i | ||||
\(71\) | 14.2603i | 0.200849i | 0.994945 | + | 0.100425i | \(0.0320202\pi\) | ||||
−0.994945 | + | 0.100425i | \(0.967980\pi\) | |||||||
\(72\) | 19.5330 | − | 70.9437i | 0.271292 | − | 0.985329i | ||||
\(73\) | 32.6549 | − | 56.5599i | 0.447327 | − | 0.774794i | −0.550884 | − | 0.834582i | \(-0.685709\pi\) |
0.998211 | + | 0.0597882i | \(0.0190425\pi\) | |||||||
\(74\) | − | 35.7564i | − | 0.483194i | ||||||
\(75\) | −0.646757 | + | 4.78544i | −0.00862343 | + | 0.0638058i | ||||
\(76\) | −16.1759 | + | 28.0176i | −0.212841 | + | 0.368652i | ||||
\(77\) | −92.7597 | − | 23.8107i | −1.20467 | − | 0.309230i | ||||
\(78\) | −25.2604 | − | 61.5819i | −0.323851 | − | 0.789512i | ||||
\(79\) | 3.35204 | − | 5.80590i | 0.0424309 | − | 0.0734924i | −0.844030 | − | 0.536296i | \(-0.819823\pi\) |
0.886461 | + | 0.462804i | \(0.153156\pi\) | |||||||
\(80\) | 5.10843 | + | 2.94935i | 0.0638554 | + | 0.0368669i | ||||
\(81\) | 69.5846 | + | 41.4606i | 0.859069 | + | 0.511860i | ||||
\(82\) | −13.7568 | − | 23.8274i | −0.167765 | − | 0.290578i | ||||
\(83\) | 11.6006 | − | 6.69762i | 0.139767 | − | 0.0806943i | −0.428486 | − | 0.903548i | \(-0.640953\pi\) |
0.568253 | + | 0.822854i | \(0.307620\pi\) | |||||||
\(84\) | 6.74114 | + | 48.5404i | 0.0802517 | + | 0.577861i | ||||
\(85\) | −19.8721 | + | 34.4196i | −0.233790 | + | 0.404936i | ||||
\(86\) | − | 46.9839i | − | 0.546324i | ||||||
\(87\) | −23.8901 | − | 58.2413i | −0.274599 | − | 0.669441i | ||||
\(88\) | −111.855 | −1.27108 | ||||||||
\(89\) | −13.7259 | + | 7.92464i | −0.154223 | + | 0.0890410i | −0.575126 | − | 0.818065i | \(-0.695047\pi\) |
0.420902 | + | 0.907106i | \(0.361714\pi\) | |||||||
\(90\) | −40.0034 | + | 39.4571i | −0.444482 | + | 0.438412i | ||||
\(91\) | 85.9656 | + | 84.1736i | 0.944677 | + | 0.924984i | ||||
\(92\) | −37.4541 | + | 21.6241i | −0.407110 | + | 0.235045i | ||||
\(93\) | −143.095 | + | 58.6964i | −1.53866 | + | 0.631145i | ||||
\(94\) | −38.3269 | − | 66.3841i | −0.407733 | − | 0.706214i | ||||
\(95\) | 58.0653 | − | 33.5240i | 0.611214 | − | 0.352884i | ||||
\(96\) | 35.4413 | + | 86.4017i | 0.369180 | + | 0.900018i | ||||
\(97\) | −40.7574 | − | 70.5938i | −0.420179 | − | 0.727771i | 0.575778 | − | 0.817606i | \(-0.304699\pi\) |
−0.995957 | + | 0.0898349i | \(0.971366\pi\) | |||||||
\(98\) | 32.7733 | + | 54.1005i | 0.334422 | + | 0.552046i | ||||
\(99\) | 32.6850 | − | 118.711i | 0.330151 | − | 1.19911i | ||||
\(100\) | −1.87816 | − | 3.25307i | −0.0187816 | − | 0.0325307i | ||||
\(101\) | − | 14.8904i | − | 0.147430i | −0.997279 | − | 0.0737150i | \(-0.976514\pi\) | ||
0.997279 | − | 0.0737150i | \(-0.0234855\pi\) | |||||||
\(102\) | 29.4438 | − | 12.0776i | 0.288665 | − | 0.118408i | ||||
\(103\) | 77.9753 | 0.757041 | 0.378521 | − | 0.925593i | \(-0.376433\pi\) | ||||
0.378521 | + | 0.925593i | \(0.376433\pi\) | |||||||
\(104\) | 121.698 | + | 70.2625i | 1.17018 | + | 0.675601i | ||||
\(105\) | 38.2000 | − | 94.1058i | 0.363809 | − | 0.896246i | ||||
\(106\) | 60.4262 | + | 104.661i | 0.570059 | + | 0.987371i | ||||
\(107\) | −73.0945 | + | 42.2012i | −0.683127 | + | 0.394403i | −0.801032 | − | 0.598622i | \(-0.795715\pi\) |
0.117905 | + | 0.993025i | \(0.462382\pi\) | |||||||
\(108\) | −62.5504 | + | 7.57957i | −0.579171 | + | 0.0701812i | ||||
\(109\) | −18.7753 | + | 32.5198i | −0.172251 | + | 0.298347i | −0.939206 | − | 0.343353i | \(-0.888437\pi\) |
0.766956 | + | 0.641700i | \(0.221771\pi\) | |||||||
\(110\) | 73.9694 | + | 42.7063i | 0.672450 | + | 0.388239i | ||||
\(111\) | −76.8811 | + | 31.5360i | −0.692623 | + | 0.284108i | ||||
\(112\) | 6.10025 | + | 5.97309i | 0.0544665 | + | 0.0533311i | ||||
\(113\) | −9.59066 | − | 5.53717i | −0.0848731 | − | 0.0490015i | 0.456963 | − | 0.889486i | \(-0.348937\pi\) |
−0.541836 | + | 0.840484i | \(0.682271\pi\) | |||||||
\(114\) | −53.2040 | − | 7.19058i | −0.466702 | − | 0.0630752i | ||||
\(115\) | 89.6304 | 0.779394 | ||||||||
\(116\) | 42.4074 | + | 24.4839i | 0.365581 | + | 0.211068i | ||||
\(117\) | −110.131 | + | 108.627i | −0.941287 | + | 0.928433i | ||||
\(118\) | 2.16388 | 0.0183380 | ||||||||
\(119\) | −40.2455 | + | 41.1023i | −0.338197 | + | 0.345397i | ||||
\(120\) | 15.8879 | − | 117.557i | 0.132399 | − | 0.979639i | ||||
\(121\) | −66.1695 | −0.546855 | ||||||||
\(122\) | −73.1927 | + | 42.2578i | −0.599940 | + | 0.346376i | ||||
\(123\) | −39.0992 | + | 50.5940i | −0.317879 | + | 0.411333i | ||||
\(124\) | 60.1554 | − | 104.192i | 0.485124 | − | 0.840259i | ||||
\(125\) | 128.694i | 1.02955i | ||||||||
\(126\) | −70.2807 | + | 40.9200i | −0.557783 | + | 0.324762i | ||||
\(127\) | 240.533 | 1.89396 | 0.946982 | − | 0.321287i | \(-0.104116\pi\) | ||||
0.946982 | + | 0.321287i | \(0.104116\pi\) | |||||||
\(128\) | −57.4579 | − | 33.1734i | −0.448890 | − | 0.259167i | ||||
\(129\) | −101.022 | + | 41.4383i | −0.783114 | + | 0.321227i | ||||
\(130\) | −53.6524 | − | 92.9288i | −0.412711 | − | 0.714837i | ||||
\(131\) | − | 25.0287i | − | 0.191059i | −0.995427 | − | 0.0955294i | \(-0.969546\pi\) | ||
0.995427 | − | 0.0955294i | \(-0.0304544\pi\) | |||||||
\(132\) | 36.3487 | + | 88.6138i | 0.275369 | + | 0.671317i | ||||
\(133\) | 93.4670 | − | 26.1025i | 0.702759 | − | 0.196259i | ||||
\(134\) | − | 71.2813i | − | 0.531950i | ||||||
\(135\) | 120.120 | + | 51.2128i | 0.889778 | + | 0.379354i | ||||
\(136\) | −33.5942 | + | 58.1869i | −0.247017 | + | 0.427845i | ||||
\(137\) | − | 255.996i | − | 1.86859i | −0.356507 | − | 0.934293i | \(-0.616032\pi\) | ||
0.356507 | − | 0.934293i | \(-0.383968\pi\) | |||||||
\(138\) | −56.7886 | − | 43.8864i | −0.411511 | − | 0.318017i | ||||
\(139\) | 25.1689 | − | 43.5938i | 0.181071 | − | 0.313625i | −0.761174 | − | 0.648547i | \(-0.775377\pi\) |
0.942246 | + | 0.334923i | \(0.108710\pi\) | |||||||
\(140\) | 21.2503 | + | 76.0923i | 0.151788 | + | 0.543516i | ||||
\(141\) | −108.932 | + | 140.957i | −0.772566 | + | 0.999694i | ||||
\(142\) | 9.20417 | − | 15.9421i | 0.0648181 | − | 0.112268i | ||||
\(143\) | 203.640 | + | 117.572i | 1.42406 | + | 0.822180i | ||||
\(144\) | −7.81504 | + | 7.70832i | −0.0542711 | + | 0.0535300i | ||||
\(145\) | −50.7420 | − | 87.8877i | −0.349945 | − | 0.606122i | ||||
\(146\) | −73.0121 | + | 42.1536i | −0.500083 | + | 0.288723i | ||||
\(147\) | 87.4184 | − | 118.182i | 0.594683 | − | 0.803960i | ||||
\(148\) | 32.3199 | − | 55.9797i | 0.218377 | − | 0.378241i | ||||
\(149\) | 132.023i | 0.886060i | 0.896507 | + | 0.443030i | \(0.146096\pi\) | ||||
−0.896507 | + | 0.443030i | \(0.853904\pi\) | |||||||
\(150\) | 3.81174 | − | 4.93236i | 0.0254116 | − | 0.0328824i | ||||
\(151\) | −288.084 | −1.90784 | −0.953922 | − | 0.300055i | \(-0.902995\pi\) | ||||
−0.953922 | + | 0.300055i | \(0.902995\pi\) | |||||||
\(152\) | 98.1605 | − | 56.6730i | 0.645793 | − | 0.372849i | ||||
\(153\) | −51.9371 | − | 52.6562i | −0.339458 | − | 0.344158i | ||||
\(154\) | 88.3309 | + | 86.4896i | 0.573577 | + | 0.561621i | ||||
\(155\) | −215.934 | + | 124.670i | −1.39312 | + | 0.804321i | ||||
\(156\) | 16.1160 | − | 119.244i | 0.103308 | − | 0.764387i | ||||
\(157\) | −4.26687 | − | 7.39044i | −0.0271775 | − | 0.0470729i | 0.852117 | − | 0.523352i | \(-0.175319\pi\) |
−0.879294 | + | 0.476279i | \(0.841985\pi\) | |||||||
\(158\) | −7.49472 | + | 4.32708i | −0.0474349 | + | 0.0273866i | ||||
\(159\) | 171.742 | − | 222.233i | 1.08014 | − | 1.39769i | ||||
\(160\) | 75.2764 | + | 130.383i | 0.470478 | + | 0.814891i | ||||
\(161\) | 125.655 | + | 32.2546i | 0.780463 | + | 0.200339i | ||||
\(162\) | −51.0307 | − | 91.2630i | −0.315004 | − | 0.563352i | ||||
\(163\) | −96.2204 | − | 166.659i | −0.590309 | − | 1.02245i | −0.994191 | − | 0.107634i | \(-0.965672\pi\) |
0.403881 | − | 0.914811i | \(-0.367661\pi\) | |||||||
\(164\) | − | 49.7385i | − | 0.303283i | ||||||
\(165\) | 26.5856 | − | 196.710i | 0.161125 | − | 1.19218i | ||||
\(166\) | −17.2917 | −0.104167 | ||||||||
\(167\) | −125.010 | − | 72.1747i | −0.748564 | − | 0.432184i | 0.0766107 | − | 0.997061i | \(-0.475590\pi\) |
−0.825175 | + | 0.564877i | \(0.808923\pi\) | |||||||
\(168\) | 64.5778 | − | 159.088i | 0.384392 | − | 0.946951i | ||||
\(169\) | −63.2069 | − | 109.477i | −0.374005 | − | 0.647796i | ||||
\(170\) | 44.4315 | − | 25.6526i | 0.261362 | − | 0.150897i | ||||
\(171\) | 31.4636 | + | 120.738i | 0.183997 | + | 0.706069i | ||||
\(172\) | 42.4683 | − | 73.5572i | 0.246909 | − | 0.427658i | ||||
\(173\) | 265.669 | + | 153.384i | 1.53566 | + | 0.886612i | 0.999085 | + | 0.0427579i | \(0.0136144\pi\) |
0.536572 | + | 0.843854i | \(0.319719\pi\) | |||||||
\(174\) | −10.8837 | + | 80.5297i | −0.0625498 | + | 0.462814i | ||||
\(175\) | −2.80147 | + | 10.9137i | −0.0160084 | + | 0.0623641i | ||||
\(176\) | 14.4506 | + | 8.34307i | 0.0821058 | + | 0.0474038i | ||||
\(177\) | −1.90848 | − | 4.65265i | −0.0107824 | − | 0.0262861i | ||||
\(178\) | 20.4595 | 0.114941 | ||||||||
\(179\) | −180.597 | − | 104.268i | −1.00892 | − | 0.582502i | −0.0980467 | − | 0.995182i | \(-0.531259\pi\) |
−0.910876 | + | 0.412680i | \(0.864593\pi\) | |||||||
\(180\) | −98.2937 | + | 25.6148i | −0.546076 | + | 0.142304i | ||||
\(181\) | −132.399 | −0.731485 | −0.365742 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365742 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(182\) | −41.7749 | − | 149.586i | −0.229532 | − | 0.821902i | ||||
\(183\) | 155.414 | + | 120.104i | 0.849256 | + | 0.656307i | ||||
\(184\) | 151.522 | 0.823488 | ||||||||
\(185\) | −116.016 | + | 66.9817i | −0.627112 | + | 0.362063i | ||||
\(186\) | 197.856 | + | 26.7404i | 1.06374 | + | 0.143766i | ||||
\(187\) | −56.2139 | + | 97.3654i | −0.300609 | + | 0.520671i | ||||
\(188\) | − | 138.573i | − | 0.737092i | ||||||
\(189\) | 149.969 | + | 115.023i | 0.793487 | + | 0.608587i | ||||
\(190\) | −86.5510 | −0.455531 | ||||||||
\(191\) | −92.3441 | − | 53.3149i | −0.483477 | − | 0.279136i | 0.238387 | − | 0.971170i | \(-0.423381\pi\) |
−0.721864 | + | 0.692035i | \(0.756715\pi\) | |||||||
\(192\) | 18.1063 | − | 133.971i | 0.0943036 | − | 0.697765i | ||||
\(193\) | 63.8462 | + | 110.585i | 0.330809 | + | 0.572978i | 0.982671 | − | 0.185360i | \(-0.0593450\pi\) |
−0.651862 | + | 0.758338i | \(0.726012\pi\) | |||||||
\(194\) | 105.226i | 0.542401i | ||||||||
\(195\) | −152.490 | + | 197.320i | −0.781999 | + | 1.01190i | ||||
\(196\) | 2.40847 | + | 114.322i | 0.0122881 | + | 0.583278i | ||||
\(197\) | 0.117739i | 0.000597658i | 1.00000 | 0.000298829i | \(9.51202e-5\pi\) | |||||
−1.00000 | 0.000298829i | \(0.999905\pi\) | ||||||||
\(198\) | −113.161 | + | 111.616i | −0.571519 | + | 0.563715i | ||||
\(199\) | 53.3999 | − | 92.4913i | 0.268341 | − | 0.464780i | −0.700093 | − | 0.714052i | \(-0.746858\pi\) |
0.968434 | + | 0.249272i | \(0.0801913\pi\) | |||||||
\(200\) | 13.1604i | 0.0658020i | ||||||||
\(201\) | −153.265 | + | 62.8679i | −0.762510 | + | 0.312776i | ||||
\(202\) | −9.61088 | + | 16.6465i | −0.0475786 | + | 0.0824086i | ||||
\(203\) | −39.5088 | − | 141.472i | −0.194625 | − | 0.696905i | ||||
\(204\) | 57.0137 | + | 7.70546i | 0.279479 | + | 0.0377719i | ||||
\(205\) | −51.5405 | + | 89.2708i | −0.251417 | + | 0.435467i | ||||
\(206\) | −87.1713 | − | 50.3283i | −0.423161 | − | 0.244312i | ||||
\(207\) | −44.2759 | + | 160.810i | −0.213893 | + | 0.776858i | ||||
\(208\) | −10.4815 | − | 18.1545i | −0.0503919 | − | 0.0872813i | ||||
\(209\) | 164.254 | − | 94.8321i | 0.785904 | − | 0.453742i | ||||
\(210\) | −103.445 | + | 80.5484i | −0.492594 | + | 0.383564i | ||||
\(211\) | −35.3849 | + | 61.2884i | −0.167701 | + | 0.290466i | −0.937611 | − | 0.347686i | \(-0.886968\pi\) |
0.769910 | + | 0.638152i | \(0.220301\pi\) | |||||||
\(212\) | 218.475i | 1.03054i | ||||||||
\(213\) | −42.3955 | − | 5.72980i | −0.199040 | − | 0.0269005i | ||||
\(214\) | 108.953 | 0.509127 | ||||||||
\(215\) | −152.445 | + | 88.0139i | −0.709044 | + | 0.409367i | ||||
\(216\) | 203.065 | + | 86.5763i | 0.940116 | + | 0.400816i | ||||
\(217\) | −347.586 | + | 97.0704i | −1.60178 | + | 0.447329i | ||||
\(218\) | 41.9791 | − | 24.2367i | 0.192565 | − | 0.111177i | ||||
\(219\) | 155.030 | + | 119.808i | 0.707901 | + | 0.547068i | ||||
\(220\) | 77.2036 | + | 133.721i | 0.350926 | + | 0.607821i | ||||
\(221\) | 122.321 | − | 70.6223i | 0.553490 | − | 0.319558i | ||||
\(222\) | 106.303 | + | 14.3669i | 0.478841 | + | 0.0647159i | ||||
\(223\) | 118.725 | + | 205.638i | 0.532399 | + | 0.922142i | 0.999284 | + | 0.0378245i | \(0.0120428\pi\) |
−0.466885 | + | 0.884318i | \(0.654624\pi\) | |||||||
\(224\) | 58.6118 | + | 209.875i | 0.261660 | + | 0.936942i | ||||
\(225\) | −13.9671 | − | 3.84558i | −0.0620760 | − | 0.0170915i | ||||
\(226\) | 7.14782 | + | 12.3804i | 0.0316275 | + | 0.0547805i | ||||
\(227\) | − | 317.326i | − | 1.39791i | −0.715165 | − | 0.698956i | \(-0.753648\pi\) | ||
0.715165 | − | 0.698956i | \(-0.246352\pi\) | |||||||
\(228\) | −76.7959 | − | 59.3481i | −0.336824 | − | 0.260299i | ||||
\(229\) | −76.6612 | −0.334765 | −0.167383 | − | 0.985892i | \(-0.553532\pi\) | ||||
−0.167383 | + | 0.985892i | \(0.553532\pi\) | |||||||
\(230\) | −100.201 | − | 57.8510i | −0.435656 | − | 0.251526i | ||||
\(231\) | 108.059 | − | 266.205i | 0.467789 | − | 1.15240i | ||||
\(232\) | −85.7803 | − | 148.576i | −0.369743 | − | 0.640413i | ||||
\(233\) | 285.287 | − | 164.710i | 1.22441 | − | 0.706912i | 0.258553 | − | 0.965997i | \(-0.416754\pi\) |
0.965854 | + | 0.259085i | \(0.0834211\pi\) | |||||||
\(234\) | 193.231 | − | 50.3548i | 0.825773 | − | 0.215192i | ||||
\(235\) | −143.594 | + | 248.712i | −0.611038 | + | 1.05835i | ||||
\(236\) | 3.38774 | + | 1.95591i | 0.0143548 | + | 0.00828777i | ||||
\(237\) | 15.9139 | + | 12.2983i | 0.0671473 | + | 0.0518917i | ||||
\(238\) | 71.5208 | − | 19.9736i | 0.300508 | − | 0.0839228i | ||||
\(239\) | 50.1733 | + | 28.9676i | 0.209930 | + | 0.121203i | 0.601279 | − | 0.799039i | \(-0.294658\pi\) |
−0.391349 | + | 0.920242i | \(0.627991\pi\) | |||||||
\(240\) | −10.8209 | + | 14.0022i | −0.0450871 | + | 0.0583423i | ||||
\(241\) | 79.8163 | 0.331188 | 0.165594 | − | 0.986194i | \(-0.447046\pi\) | ||||
0.165594 | + | 0.986194i | \(0.447046\pi\) | |||||||
\(242\) | 73.9732 | + | 42.7084i | 0.305674 | + | 0.176481i | ||||
\(243\) | −151.220 | + | 190.214i | −0.622306 | + | 0.782774i | ||||
\(244\) | −152.786 | −0.626171 | ||||||||
\(245\) | 114.142 | − | 207.682i | 0.465885 | − | 0.847682i | ||||
\(246\) | 76.3657 | − | 31.3246i | 0.310430 | − | 0.127336i | ||||
\(247\) | −238.278 | −0.964686 | ||||||||
\(248\) | −365.041 | + | 210.757i | −1.47194 | + | 0.849825i | ||||
\(249\) | 15.2507 | + | 37.1794i | 0.0612478 | + | 0.149315i | ||||
\(250\) | 83.0641 | − | 143.871i | 0.332256 | − | 0.575485i | ||||
\(251\) | − | 186.751i | − | 0.744029i | −0.928227 | − | 0.372014i | \(-0.878667\pi\) | ||
0.928227 | − | 0.372014i | \(-0.121333\pi\) | |||||||
\(252\) | −147.018 | + | 0.537693i | −0.583403 | + | 0.00213370i | ||||
\(253\) | 253.545 | 1.00215 | ||||||||
\(254\) | −268.901 | − | 155.250i | −1.05866 | − | 0.611220i | ||||
\(255\) | −94.3438 | − | 72.9091i | −0.369975 | − | 0.285918i | ||||
\(256\) | 132.949 | + | 230.274i | 0.519331 | + | 0.899507i | ||||
\(257\) | − | 361.599i | − | 1.40700i | −0.710695 | − | 0.703500i | \(-0.751619\pi\) | ||
0.710695 | − | 0.703500i | \(-0.248381\pi\) | |||||||
\(258\) | 139.682 | + | 18.8781i | 0.541402 | + | 0.0731710i | ||||
\(259\) | −186.749 | + | 52.1533i | −0.721038 | + | 0.201364i | ||||
\(260\) | − | 193.984i | − | 0.746092i | ||||||
\(261\) | 182.749 | − | 47.6233i | 0.700187 | − | 0.182465i | ||||
\(262\) | −16.1545 | + | 27.9805i | −0.0616585 | + | 0.106796i | ||||
\(263\) | 383.169i | 1.45692i | 0.685090 | + | 0.728458i | \(0.259763\pi\) | ||||
−0.685090 | + | 0.728458i | \(0.740237\pi\) | |||||||
\(264\) | 44.9434 | − | 332.542i | 0.170240 | − | 1.25963i | ||||
\(265\) | 226.390 | − | 392.120i | 0.854303 | − | 1.47970i | ||||
\(266\) | −121.338 | − | 31.1464i | −0.456156 | − | 0.117092i | ||||
\(267\) | −18.0447 | − | 43.9908i | −0.0675831 | − | 0.164760i | ||||
\(268\) | 64.4305 | − | 111.597i | 0.240412 | − | 0.416406i | ||||
\(269\) | 70.7645 | + | 40.8559i | 0.263065 | + | 0.151881i | 0.625732 | − | 0.780038i | \(-0.284800\pi\) |
−0.362667 | + | 0.931919i | \(0.618134\pi\) | |||||||
\(270\) | −101.232 | − | 134.783i | −0.374932 | − | 0.499196i | ||||
\(271\) | 187.954 | + | 325.546i | 0.693558 | + | 1.20128i | 0.970665 | + | 0.240438i | \(0.0772910\pi\) |
−0.277107 | + | 0.960839i | \(0.589376\pi\) | |||||||
\(272\) | 8.68012 | − | 5.01147i | 0.0319122 | − | 0.0184245i | ||||
\(273\) | −284.787 | + | 221.752i | −1.04317 | + | 0.812279i | ||||
\(274\) | −165.230 | + | 286.187i | −0.603030 | + | 1.04448i | ||||
\(275\) | 22.0216i | 0.0800785i | ||||||||
\(276\) | −49.2388 | − | 120.039i | −0.178402 | − | 0.434922i | ||||
\(277\) | 111.107 | 0.401107 | 0.200554 | − | 0.979683i | \(-0.435726\pi\) | ||||
0.200554 | + | 0.979683i | \(0.435726\pi\) | |||||||
\(278\) | −56.2744 | + | 32.4900i | −0.202426 | + | 0.116871i | ||||
\(279\) | −117.007 | − | 449.002i | −0.419381 | − | 1.60932i | ||||
\(280\) | 68.8195 | − | 268.101i | 0.245784 | − | 0.957504i | ||||
\(281\) | 88.6512 | − | 51.1828i | 0.315485 | − | 0.182145i | −0.333893 | − | 0.942611i | \(-0.608363\pi\) |
0.649378 | + | 0.760466i | \(0.275029\pi\) | |||||||
\(282\) | 212.758 | − | 87.2716i | 0.754461 | − | 0.309474i | ||||
\(283\) | −57.0283 | − | 98.7759i | −0.201513 | − | 0.349031i | 0.747503 | − | 0.664259i | \(-0.231253\pi\) |
−0.949016 | + | 0.315227i | \(0.897919\pi\) | |||||||
\(284\) | 28.8198 | − | 16.6391i | 0.101478 | − | 0.0585885i | ||||
\(285\) | 76.3353 | + | 186.096i | 0.267843 | + | 0.652970i | ||||
\(286\) | −151.771 | − | 262.875i | −0.530668 | − | 0.919143i | ||||
\(287\) | −104.381 | + | 106.603i | −0.363696 | + | 0.371439i | ||||
\(288\) | −271.110 | + | 70.6498i | −0.941355 | + | 0.245312i | ||||
\(289\) | −110.734 | − | 191.796i | −0.383162 | − | 0.663656i | ||||
\(290\) | 131.004i | 0.451737i | ||||||||
\(291\) | 226.250 | − | 92.8059i | 0.777490 | − | 0.318920i | ||||
\(292\) | −152.409 | −0.521948 | ||||||||
\(293\) | 98.3627 | + | 56.7897i | 0.335709 | + | 0.193822i | 0.658373 | − | 0.752692i | \(-0.271245\pi\) |
−0.322664 | + | 0.946514i | \(0.604578\pi\) | |||||||
\(294\) | −174.008 | + | 75.6966i | −0.591863 | + | 0.257471i | ||||
\(295\) | −4.05356 | − | 7.02097i | −0.0137409 | − | 0.0237999i | ||||
\(296\) | −196.127 | + | 113.234i | −0.662590 | + | 0.382547i | ||||
\(297\) | 339.793 | + | 144.870i | 1.14408 | + | 0.487777i | ||||
\(298\) | 85.2129 | − | 147.593i | 0.285949 | − | 0.495278i | ||||
\(299\) | −275.856 | − | 159.266i | −0.922596 | − | 0.532661i | ||||
\(300\) | 10.4259 | − | 4.27663i | 0.0347531 | − | 0.0142554i | ||||
\(301\) | −245.388 | + | 68.5294i | −0.815242 | + | 0.227673i | ||||
\(302\) | 322.060 | + | 185.941i | 1.06642 | + | 0.615699i | ||||
\(303\) | 44.2688 | + | 5.98298i | 0.146102 | + | 0.0197458i | ||||
\(304\) | −16.9085 | −0.0556202 | ||||||||
\(305\) | 274.221 | + | 158.321i | 0.899084 | + | 0.519087i | ||||
\(306\) | 24.0759 | + | 92.3884i | 0.0786794 | + | 0.301923i | ||||
\(307\) | 375.302 | 1.22248 | 0.611241 | − | 0.791445i | \(-0.290671\pi\) | ||||
0.611241 | + | 0.791445i | \(0.290671\pi\) | |||||||
\(308\) | 60.1124 | + | 215.248i | 0.195170 | + | 0.698858i | ||||
\(309\) | −31.3305 | + | 231.818i | −0.101393 | + | 0.750221i | ||||
\(310\) | 321.867 | 1.03828 | ||||||||
\(311\) | 477.504 | − | 275.687i | 1.53538 | − | 0.886453i | 0.536281 | − | 0.844039i | \(-0.319829\pi\) |
0.999100 | − | 0.0424134i | \(-0.0135046\pi\) | |||||||
\(312\) | −257.787 | + | 333.574i | −0.826240 | + | 1.06915i | ||||
\(313\) | 94.4409 | − | 163.576i | 0.301728 | − | 0.522609i | −0.674799 | − | 0.738001i | \(-0.735770\pi\) |
0.976528 | + | 0.215393i | \(0.0691032\pi\) | |||||||
\(314\) | 11.0160i | 0.0350829i | ||||||||
\(315\) | 264.425 | + | 151.379i | 0.839445 | + | 0.480569i | ||||
\(316\) | −15.6448 | −0.0495089 | ||||||||
\(317\) | 399.628 | + | 230.726i | 1.26066 | + | 0.727841i | 0.973202 | − | 0.229953i | \(-0.0738573\pi\) |
0.287456 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(318\) | −335.434 | + | 137.592i | −1.05482 | + | 0.432681i | ||||
\(319\) | −143.538 | − | 248.615i | −0.449962 | − | 0.779358i | ||||
\(320\) | − | 217.940i | − | 0.681064i | ||||||
\(321\) | −96.0934 | − | 234.264i | −0.299356 | − | 0.729796i | ||||
\(322\) | −119.655 | − | 117.161i | −0.371600 | − | 0.363854i | ||||
\(323\) | − | 113.926i | − | 0.352713i | ||||||
\(324\) | 2.59892 | − | 189.006i | 0.00802137 | − | 0.583352i | ||||
\(325\) | 13.8330 | − | 23.9594i | 0.0425631 | − | 0.0737214i | ||||
\(326\) | 248.418i | 0.762018i | ||||||||
\(327\) | −89.1365 | − | 68.8849i | −0.272589 | − | 0.210657i | ||||
\(328\) | −87.1302 | + | 150.914i | −0.265641 | + | 0.460104i | ||||
\(329\) | −290.809 | + | 297.000i | −0.883919 | + | 0.902737i | ||||
\(330\) | −156.685 | + | 202.750i | −0.474804 | + | 0.614393i | ||||
\(331\) | −73.1980 | + | 126.783i | −0.221142 | + | 0.383029i | −0.955155 | − | 0.296106i | \(-0.904312\pi\) |
0.734013 | + | 0.679135i | \(0.237645\pi\) | |||||||
\(332\) | −27.0716 | − | 15.6298i | −0.0815408 | − | 0.0470776i | ||||
\(333\) | −62.8648 | − | 241.237i | −0.188783 | − | 0.724434i | ||||
\(334\) | 93.1689 | + | 161.373i | 0.278949 | + | 0.483153i | ||||
\(335\) | −231.280 | + | 133.530i | −0.690389 | + | 0.398596i | ||||
\(336\) | −20.2089 | + | 15.7359i | −0.0601455 | + | 0.0468330i | ||||
\(337\) | 122.785 | − | 212.670i | 0.364348 | − | 0.631070i | −0.624323 | − | 0.781166i | \(-0.714625\pi\) |
0.988671 | + | 0.150097i | \(0.0479585\pi\) | |||||||
\(338\) | 163.185i | 0.482796i | ||||||||
\(339\) | 20.3154 | − | 26.2879i | 0.0599273 | − | 0.0775454i | ||||
\(340\) | 92.7484 | 0.272790 | ||||||||
\(341\) | −610.830 | + | 352.663i | −1.79129 | + | 1.03420i | ||||
\(342\) | 42.7548 | − | 155.285i | 0.125014 | − | 0.454049i | ||||
\(343\) | 234.755 | − | 250.079i | 0.684416 | − | 0.729092i | ||||
\(344\) | −257.710 | + | 148.789i | −0.749158 | + | 0.432527i | ||||
\(345\) | −36.0135 | + | 266.468i | −0.104387 | + | 0.772372i | ||||
\(346\) | −198.000 | − | 342.946i | −0.572255 | − | 0.991175i | ||||
\(347\) | −19.5639 | + | 11.2952i | −0.0563802 | + | 0.0325511i | −0.527925 | − | 0.849291i | \(-0.677030\pi\) |
0.471545 | + | 0.881842i | \(0.343697\pi\) | |||||||
\(348\) | −89.8293 | + | 116.238i | −0.258130 | + | 0.334018i | ||||
\(349\) | 167.280 | + | 289.738i | 0.479313 | + | 0.830195i | 0.999719 | − | 0.0237246i | \(-0.00755249\pi\) |
−0.520405 | + | 0.853919i | \(0.674219\pi\) | |||||||
\(350\) | 10.1760 | − | 10.3926i | 0.0290743 | − | 0.0296933i | ||||
\(351\) | −278.693 | − | 371.061i | −0.793999 | − | 1.05715i | ||||
\(352\) | 212.940 | + | 368.824i | 0.604944 | + | 1.04779i | ||||
\(353\) | 380.072i | 1.07669i | 0.842724 | + | 0.538346i | \(0.180951\pi\) | ||||
−0.842724 | + | 0.538346i | \(0.819049\pi\) | |||||||
\(354\) | −0.869449 | + | 6.43316i | −0.00245607 | + | 0.0181728i | ||||
\(355\) | −68.9680 | −0.194276 | ||||||||
\(356\) | 32.0311 | + | 18.4932i | 0.0899751 | + | 0.0519471i | ||||
\(357\) | −106.025 | − | 136.163i | −0.296989 | − | 0.381410i | ||||
\(358\) | 134.597 | + | 233.129i | 0.375970 | + | 0.651199i | ||||
\(359\) | −1.25505 | + | 0.724605i | −0.00349597 | + | 0.00201840i | −0.501747 | − | 0.865014i | \(-0.667309\pi\) |
0.498251 | + | 0.867033i | \(0.333976\pi\) | |||||||
\(360\) | 343.109 | + | 94.4686i | 0.953081 | + | 0.262413i | ||||
\(361\) | 84.4039 | − | 146.192i | 0.233806 | − | 0.404964i | ||||
\(362\) | 148.013 | + | 85.4554i | 0.408876 | + | 0.236065i | ||||
\(363\) | 26.5869 | − | 196.720i | 0.0732422 | − | 0.541928i | ||||
\(364\) | 69.8074 | − | 271.950i | 0.191779 | − | 0.747115i | ||||
\(365\) | 273.544 | + | 157.931i | 0.749436 | + | 0.432687i | ||||
\(366\) | −96.2224 | − | 234.579i | −0.262903 | − | 0.640926i | ||||
\(367\) | −430.855 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(368\) | −19.5752 | − | 11.3017i | −0.0531934 | − | 0.0307112i | ||||
\(369\) | −134.704 | − | 136.569i | −0.365052 | − | 0.370107i | ||||
\(370\) | 172.931 | 0.467380 | ||||||||
\(371\) | 458.490 | − | 468.251i | 1.23582 | − | 1.26213i | ||||
\(372\) | 285.590 | + | 220.705i | 0.767715 | + | 0.593292i | ||||
\(373\) | 35.9863 | 0.0964780 | 0.0482390 | − | 0.998836i | \(-0.484639\pi\) | ||||
0.0482390 | + | 0.998836i | \(0.484639\pi\) | |||||||
\(374\) | 125.687 | − | 72.5654i | 0.336062 | − | 0.194025i | ||||
\(375\) | −382.603 | − | 51.7092i | −1.02027 | − | 0.137891i | ||||
\(376\) | −242.748 | + | 420.452i | −0.645607 | + | 1.11822i | ||||
\(377\) | 360.657i | 0.956650i | ||||||||
\(378\) | −93.4153 | − | 225.384i | −0.247130 | − | 0.596254i | ||||
\(379\) | −694.643 | −1.83283 | −0.916415 | − | 0.400229i | \(-0.868931\pi\) | ||||
−0.916415 | + | 0.400229i | \(0.868931\pi\) | |||||||
\(380\) | −135.503 | − | 78.2326i | −0.356587 | − | 0.205875i | ||||
\(381\) | −96.6464 | + | 715.099i | −0.253665 | + | 1.87690i | ||||
\(382\) | 68.8231 | + | 119.205i | 0.180165 | + | 0.312055i | ||||
\(383\) | − | 344.907i | − | 0.900540i | −0.892892 | − | 0.450270i | \(-0.851328\pi\) | ||
0.892892 | − | 0.450270i | \(-0.148672\pi\) | |||||||
\(384\) | 121.710 | − | 157.492i | 0.316953 | − | 0.410135i | ||||
\(385\) | 115.157 | − | 448.619i | 0.299109 | − | 1.16524i | ||||
\(386\) | − | 164.835i | − | 0.427035i | ||||||
\(387\) | −82.6043 | − | 316.985i | −0.213448 | − | 0.819082i | ||||
\(388\) | −95.1126 | + | 164.740i | −0.245136 | + | 0.424587i | ||||
\(389\) | 441.484i | 1.13492i | 0.823401 | + | 0.567460i | \(0.192074\pi\) | ||||
−0.823401 | + | 0.567460i | \(0.807926\pi\) | |||||||
\(390\) | 297.832 | − | 122.168i | 0.763672 | − | 0.313252i | ||||
\(391\) | 76.1488 | − | 131.894i | 0.194754 | − | 0.337324i | ||||
\(392\) | 192.959 | − | 351.091i | 0.492242 | − | 0.895640i | ||||
\(393\) | 74.4096 | + | 10.0565i | 0.189337 | + | 0.0255892i | ||||
\(394\) | 0.0759932 | − | 0.131624i | 0.000192876 | − | 0.000334071i | ||||
\(395\) | 28.0794 | + | 16.2117i | 0.0710871 | + | 0.0410422i | ||||
\(396\) | −278.051 | + | 72.4585i | −0.702149 | + | 0.182976i | ||||
\(397\) | 43.5787 | + | 75.4806i | 0.109770 | + | 0.190127i | 0.915677 | − | 0.401915i | \(-0.131655\pi\) |
−0.805907 | + | 0.592042i | \(0.798322\pi\) | |||||||
\(398\) | −119.395 | + | 68.9328i | −0.299988 | + | 0.173198i | ||||
\(399\) | 40.0469 | + | 288.363i | 0.100368 | + | 0.722713i | ||||
\(400\) | 0.981611 | − | 1.70020i | 0.00245403 | − | 0.00425050i | ||||
\(401\) | − | 658.483i | − | 1.64210i | −0.570855 | − | 0.821051i | \(-0.693388\pi\) | ||
0.570855 | − | 0.821051i | \(-0.306612\pi\) | |||||||
\(402\) | 211.917 | + | 28.6408i | 0.527157 | + | 0.0712459i | ||||
\(403\) | 886.110 | 2.19879 | ||||||||
\(404\) | −30.0933 | + | 17.3744i | −0.0744884 | + | 0.0430059i | ||||
\(405\) | −200.519 | + | 336.536i | −0.495107 | + | 0.830953i | ||||
\(406\) | −47.1433 | + | 183.657i | −0.116116 | + | 0.452356i | ||||
\(407\) | −328.183 | + | 189.476i | −0.806346 | + | 0.465544i | ||||
\(408\) | −159.490 | − | 123.254i | −0.390907 | − | 0.302094i | ||||
\(409\) | 308.519 | + | 534.370i | 0.754324 | + | 1.30653i | 0.945710 | + | 0.325013i | \(0.105369\pi\) |
−0.191385 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(410\) | 115.238 | − | 66.5326i | 0.281068 | − | 0.162275i | ||||
\(411\) | 761.069 | + | 102.859i | 1.85175 | + | 0.250266i | ||||
\(412\) | −90.9827 | − | 157.587i | −0.220832 | − | 0.382492i | ||||
\(413\) | −3.15618 | − | 11.3016i | −0.00764209 | − | 0.0273645i | ||||
\(414\) | 153.291 | − | 151.197i | 0.370267 | − | 0.365211i | ||||
\(415\) | 32.3921 | + | 56.1048i | 0.0780533 | + | 0.135192i | ||||
\(416\) | − | 535.040i | − | 1.28615i | ||||||
\(417\) | 119.490 | + | 92.3425i | 0.286548 | + | 0.221445i | ||||
\(418\) | −244.834 | −0.585726 | ||||||||
\(419\) | 186.805 | + | 107.852i | 0.445835 | + | 0.257403i | 0.706069 | − | 0.708143i | \(-0.250467\pi\) |
−0.260235 | + | 0.965545i | \(0.583800\pi\) | |||||||
\(420\) | −234.758 | + | 32.6026i | −0.558949 | + | 0.0776252i | ||||
\(421\) | −277.485 | − | 480.618i | −0.659110 | − | 1.14161i | −0.980847 | − | 0.194782i | \(-0.937600\pi\) |
0.321737 | − | 0.946829i | \(-0.395733\pi\) | |||||||
\(422\) | 79.1160 | − | 45.6776i | 0.187479 | − | 0.108241i | ||||
\(423\) | −375.292 | − | 380.488i | −0.887215 | − | 0.899498i | ||||
\(424\) | 382.717 | − | 662.886i | 0.902635 | − | 1.56341i | ||||
\(425\) | 11.4556 | + | 6.61390i | 0.0269544 | + | 0.0155621i | ||||
\(426\) | 43.6972 | + | 33.7693i | 0.102575 | + | 0.0792706i | ||||
\(427\) | 327.462 | + | 320.636i | 0.766889 | + | 0.750903i | ||||
\(428\) | 170.576 | + | 98.4818i | 0.398541 | + | 0.230098i | ||||
\(429\) | −431.360 | + | 558.176i | −1.00550 | + | 1.30111i | ||||
\(430\) | 227.231 | 0.528443 | ||||||||
\(431\) | −702.016 | − | 405.309i | −1.62881 | − | 0.940392i | −0.984450 | − | 0.175667i | \(-0.943792\pi\) |
−0.644357 | − | 0.764725i | \(-0.722875\pi\) | |||||||
\(432\) | −19.7765 | − | 26.3311i | −0.0457790 | − | 0.0609516i | ||||
\(433\) | −352.669 | −0.814477 | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(434\) | 451.232 | + | 115.828i | 1.03971 | + | 0.266884i | ||||
\(435\) | 281.676 | − | 115.541i | 0.647531 | − | 0.265612i | ||||
\(436\) | 87.6292 | 0.200984 | ||||||||
\(437\) | −222.503 | + | 128.462i | −0.509159 | + | 0.293963i | ||||
\(438\) | −95.9850 | − | 234.000i | −0.219144 | − | 0.534247i | ||||
\(439\) | −195.124 | + | 337.965i | −0.444475 | + | 0.769853i | −0.998015 | − | 0.0629691i | \(-0.979943\pi\) |
0.553541 | + | 0.832822i | \(0.313276\pi\) | |||||||
\(440\) | − | 540.971i | − | 1.22948i | ||||||
\(441\) | 316.227 | + | 307.378i | 0.717069 | + | 0.697002i | ||||
\(442\) | −182.330 | −0.412511 | ||||||||
\(443\) | −158.958 | − | 91.7743i | −0.358821 | − | 0.207165i | 0.309742 | − | 0.950821i | \(-0.399757\pi\) |
−0.668563 | + | 0.743655i | \(0.733091\pi\) | |||||||
\(444\) | 153.440 | + | 118.579i | 0.345585 | + | 0.267069i | ||||
\(445\) | −38.3264 | − | 66.3833i | −0.0861268 | − | 0.149176i | ||||
\(446\) | − | 306.519i | − | 0.687263i | ||||||
\(447\) | −392.500 | − | 53.0468i | −0.878077 | − | 0.118673i | ||||
\(448\) | 78.4285 | − | 305.535i | 0.175064 | − | 0.681998i | ||||
\(449\) | − | 653.190i | − | 1.45477i | −0.686231 | − | 0.727383i | \(-0.740736\pi\) | ||
0.686231 | − | 0.727383i | \(-0.259264\pi\) | |||||||
\(450\) | 13.1322 | + | 13.3140i | 0.0291827 | + | 0.0295867i | ||||
\(451\) | −145.797 | + | 252.527i | −0.323275 | + | 0.559928i | ||||
\(452\) | 25.8434i | 0.0571756i | ||||||||
\(453\) | 115.752 | − | 856.467i | 0.255524 | − | 1.89065i | ||||
\(454\) | −204.815 | + | 354.750i | −0.451134 | + | 0.781387i | ||||
\(455\) | −407.094 | + | 415.760i | −0.894711 | + | 0.913759i | ||||
\(456\) | 129.046 | + | 314.600i | 0.282996 | + | 0.689911i | ||||
\(457\) | −72.8642 | + | 126.204i | −0.159440 | + | 0.276158i | −0.934667 | − | 0.355525i | \(-0.884302\pi\) |
0.775227 | + | 0.631683i | \(0.217636\pi\) | |||||||
\(458\) | 85.7023 | + | 49.4802i | 0.187123 | + | 0.108035i | ||||
\(459\) | 177.414 | − | 133.250i | 0.386522 | − | 0.290305i | ||||
\(460\) | −104.582 | − | 181.141i | −0.227352 | − | 0.393786i | ||||
\(461\) | −6.30986 | + | 3.64300i | −0.0136873 | + | 0.00790238i | −0.506828 | − | 0.862047i | \(-0.669182\pi\) |
0.493141 | + | 0.869950i | \(0.335849\pi\) | |||||||
\(462\) | −292.622 | + | 227.854i | −0.633382 | + | 0.493190i | ||||
\(463\) | −22.2343 | + | 38.5110i | −0.0480223 | + | 0.0831771i | −0.889037 | − | 0.457835i | \(-0.848625\pi\) |
0.841015 | + | 0.541012i | \(0.181959\pi\) | |||||||
\(464\) | 25.5928i | 0.0551569i | ||||||||
\(465\) | −283.877 | − | 692.059i | −0.610488 | − | 1.48830i | ||||
\(466\) | −425.243 | −0.912538 | ||||||||
\(467\) | −174.902 | + | 100.980i | −0.374523 | + | 0.216231i | −0.675433 | − | 0.737422i | \(-0.736043\pi\) |
0.300909 | + | 0.953653i | \(0.402710\pi\) | |||||||
\(468\) | 348.035 | + | 95.8248i | 0.743664 | + | 0.204754i | ||||
\(469\) | −372.289 | + | 103.969i | −0.793793 | + | 0.221682i | ||||
\(470\) | 321.057 | − | 185.363i | 0.683101 | − | 0.394388i | ||||
\(471\) | 23.6860 | − | 9.71581i | 0.0502887 | − | 0.0206280i | ||||
\(472\) | −6.85262 | − | 11.8691i | −0.0145183 | − | 0.0251464i | ||||
\(473\) | −431.232 | + | 248.972i | −0.911695 | + | 0.526368i | ||||
\(474\) | −9.85290 | − | 24.0202i | −0.0207867 | − | 0.0506755i | ||||
\(475\) | −11.1575 | − | 19.3254i | −0.0234896 | − | 0.0406851i | ||||
\(476\) | 130.026 | + | 33.3766i | 0.273164 | + | 0.0701190i | ||||
\(477\) | 591.685 | + | 599.877i | 1.24043 | + | 1.25760i | ||||
\(478\) | −37.3936 | − | 64.7677i | −0.0782294 | − | 0.135497i | ||||
\(479\) | − | 190.784i | − | 0.398297i | −0.979969 | − | 0.199149i | \(-0.936182\pi\) | ||
0.979969 | − | 0.199149i | \(-0.0638176\pi\) | |||||||
\(480\) | −417.870 | + | 171.407i | −0.870562 | + | 0.357098i | ||||
\(481\) | 476.083 | 0.989778 | ||||||||
\(482\) | −89.2294 | − | 51.5166i | −0.185123 | − | 0.106881i | ||||
\(483\) | −146.380 | + | 360.608i | −0.303064 | + | 0.746600i | ||||
\(484\) | 77.2075 | + | 133.727i | 0.159520 | + | 0.276296i | ||||
\(485\) | 341.417 | − | 197.117i | 0.703953 | − | 0.406427i | ||||
\(486\) | 291.826 | − | 115.043i | 0.600466 | − | 0.236714i | ||||
\(487\) | −60.9902 | + | 105.638i | −0.125236 | + | 0.216916i | −0.921825 | − | 0.387605i | \(-0.873302\pi\) |
0.796589 | + | 0.604521i | \(0.206636\pi\) | |||||||
\(488\) | 463.575 | + | 267.645i | 0.949949 | + | 0.548454i | ||||
\(489\) | 534.133 | − | 219.097i | 1.09230 | − | 0.448051i | ||||
\(490\) | −261.649 | + | 158.504i | −0.533978 | + | 0.323477i | ||||
\(491\) | −121.061 | − | 69.8948i | −0.246561 | − | 0.142352i | 0.371628 | − | 0.928382i | \(-0.378800\pi\) |
−0.618189 | + | 0.786030i | \(0.712133\pi\) | |||||||
\(492\) | 147.871 | + | 19.9849i | 0.300551 | + | 0.0406198i | ||||
\(493\) | −172.439 | −0.349775 | ||||||||
\(494\) | 266.379 | + | 153.794i | 0.539228 | + | 0.311324i | ||||
\(495\) | 574.131 | + | 158.076i | 1.15986 | + | 0.319346i | ||||
\(496\) | 62.8798 | 0.126774 | ||||||||
\(497\) | −96.6876 | − | 24.8190i | −0.194542 | − | 0.0499375i | ||||
\(498\) | 6.94779 | − | 51.4076i | 0.0139514 | − | 0.103228i | ||||
\(499\) | −227.450 | −0.455811 | −0.227906 | − | 0.973683i | \(-0.573188\pi\) | ||||
−0.227906 | + | 0.973683i | \(0.573188\pi\) | |||||||
\(500\) | 260.088 | − | 150.162i | 0.520176 | − | 0.300324i | ||||
\(501\) | 264.802 | − | 342.652i | 0.528548 | − | 0.683936i | ||||
\(502\) | −120.537 | + | 208.776i | −0.240113 | + | 0.415888i | ||||
\(503\) | 911.427i | 1.81198i | 0.423298 | + | 0.905991i | \(0.360872\pi\) | ||||
−0.423298 | + | 0.905991i | \(0.639128\pi\) | |||||||
\(504\) | 447.016 | + | 255.909i | 0.886936 | + | 0.507757i | ||||
\(505\) | 72.0155 | 0.142605 | ||||||||
\(506\) | −283.446 | − | 163.648i | −0.560171 | − | 0.323415i | ||||
\(507\) | 350.870 | − | 143.924i | 0.692051 | − | 0.283874i | ||||
\(508\) | −280.658 | − | 486.114i | −0.552476 | − | 0.956917i | ||||
\(509\) | − | 72.9480i | − | 0.143316i | −0.997429 | − | 0.0716581i | \(-0.977171\pi\) | ||
0.997429 | − | 0.0716581i | \(-0.0228291\pi\) | |||||||
\(510\) | 58.4117 | + | 142.401i | 0.114533 | + | 0.279217i | ||||
\(511\) | 326.654 | + | 319.844i | 0.639244 | + | 0.625919i | ||||
\(512\) | − | 77.8547i | − | 0.152060i | ||||||
\(513\) | −371.592 | + | 45.0278i | −0.724351 | + | 0.0877735i | ||||
\(514\) | −233.391 | + | 404.244i | −0.454067 | + | 0.786467i | ||||
\(515\) | 377.116i | 0.732264i | ||||||||
\(516\) | 201.620 | + | 155.812i | 0.390736 | + | 0.301962i | ||||
\(517\) | −406.196 | + | 703.552i | −0.785678 | + | 1.36083i | ||||
\(518\) | 242.435 | + | 62.2312i | 0.468021 | + | 0.120137i | ||||
\(519\) | −562.752 | + | 728.196i | −1.08430 | + | 1.40307i | ||||
\(520\) | −339.815 | + | 588.576i | −0.653490 | + | 1.13188i | ||||
\(521\) | −317.781 | − | 183.471i | −0.609944 | − | 0.352152i | 0.162999 | − | 0.986626i | \(-0.447883\pi\) |
−0.772944 | + | 0.634475i | \(0.781216\pi\) | |||||||
\(522\) | −235.039 | − | 64.7137i | −0.450267 | − | 0.123973i | ||||
\(523\) | −52.6461 | − | 91.1858i | −0.100662 | − | 0.174351i | 0.811296 | − | 0.584636i | \(-0.198763\pi\) |
−0.911958 | + | 0.410285i | \(0.865429\pi\) | |||||||
\(524\) | −50.5826 | + | 29.2039i | −0.0965316 | + | 0.0557326i | ||||
\(525\) | −31.3205 | − | 12.7138i | −0.0596581 | − | 0.0242168i | ||||
\(526\) | 247.313 | − | 428.358i | 0.470176 | − | 0.814369i | ||||
\(527\) | 423.671i | 0.803930i | ||||||||
\(528\) | −30.6100 | + | 39.6090i | −0.0579734 | + | 0.0750171i | ||||
\(529\) | 185.542 | 0.350741 | ||||||||
\(530\) | −506.179 | + | 292.243i | −0.955056 | + | 0.551402i | ||||
\(531\) | 14.5990 | − | 3.80442i | 0.0274934 | − | 0.00716463i | ||||
\(532\) | −161.811 | − | 158.438i | −0.304157 | − | 0.297816i | ||||
\(533\) | 317.254 | − | 183.166i | 0.595222 | − | 0.343652i | ||||
\(534\) | −8.22064 | + | 60.8256i | −0.0153945 | + | 0.113906i | ||||
\(535\) | −204.100 | − | 353.511i | −0.381495 | − | 0.660769i | ||||
\(536\) | −390.984 | + | 225.735i | −0.729447 | + | 0.421147i | ||||
\(537\) | 382.549 | − | 495.015i | 0.712382 | − | 0.921816i | ||||
\(538\) | −52.7400 | − | 91.3484i | −0.0980298 | − | 0.169793i | ||||
\(539\) | 322.882 | − | 587.487i | 0.599039 | − | 1.08996i | ||||
\(540\) | −36.6575 | − | 302.516i | −0.0678843 | − | 0.560215i | ||||
\(541\) | 65.3800 | + | 113.242i | 0.120850 | + | 0.209319i | 0.920103 | − | 0.391676i | \(-0.128105\pi\) |
−0.799253 | + | 0.600995i | \(0.794771\pi\) | |||||||
\(542\) | − | 485.252i | − | 0.895299i | ||||||
\(543\) | 53.1978 | − | 393.618i | 0.0979703 | − | 0.724894i | ||||
\(544\) | 255.816 | 0.470249 | ||||||||
\(545\) | −157.277 | − | 90.8041i | −0.288582 | − | 0.166613i | ||||
\(546\) | 461.501 | − | 64.0918i | 0.845239 | − | 0.117384i | ||||
\(547\) | 36.9358 | + | 63.9746i | 0.0675242 | + | 0.116955i | 0.897811 | − | 0.440381i | \(-0.145157\pi\) |
−0.830287 | + | 0.557337i | \(0.811823\pi\) | |||||||
\(548\) | −517.364 | + | 298.700i | −0.944094 | + | 0.545073i | ||||
\(549\) | −419.512 | + | 413.783i | −0.764138 | + | 0.753703i | ||||
\(550\) | 14.2136 | − | 24.6187i | 0.0258429 | − | 0.0447612i | ||||
\(551\) | 251.929 | + | 145.451i | 0.457221 | + | 0.263977i | ||||
\(552\) | −60.8815 | + | 450.470i | −0.110293 | + | 0.816069i | ||||
\(553\) | 33.5311 | + | 32.8322i | 0.0606349 | + | 0.0593710i | ||||
\(554\) | −124.210 | − | 71.7127i | −0.224206 | − | 0.129445i | ||||
\(555\) | −152.519 | − | 371.825i | −0.274810 | − | 0.669954i | ||||
\(556\) | −117.470 | −0.211277 | ||||||||
\(557\) | −220.844 | − | 127.504i | −0.396488 | − | 0.228912i | 0.288480 | − | 0.957486i | \(-0.406850\pi\) |
−0.684968 | + | 0.728574i | \(0.740184\pi\) | |||||||
\(558\) | −158.997 | + | 577.476i | −0.284941 | + | 1.03490i | ||||
\(559\) | 625.573 | 1.11909 | ||||||||
\(560\) | −28.8880 | + | 29.5030i | −0.0515857 | + | 0.0526839i | ||||
\(561\) | −266.878 | − | 206.244i | −0.475718 | − | 0.367636i | ||||
\(562\) | −132.142 | −0.235128 | ||||||||
\(563\) | −238.040 | + | 137.432i | −0.422806 | + | 0.244107i | −0.696277 | − | 0.717773i | \(-0.745162\pi\) |
0.273471 | + | 0.961880i | \(0.411828\pi\) | |||||||
\(564\) | 411.974 | + | 55.6788i | 0.730451 | + | 0.0987213i | ||||
\(565\) | 26.7797 | − | 46.3838i | 0.0473977 | − | 0.0820953i | ||||
\(566\) | 147.233i | 0.260130i | ||||||||
\(567\) | −402.217 | + | 399.637i | −0.709378 | + | 0.704828i | ||||
\(568\) | −116.592 | −0.205267 | ||||||||
\(569\) | −227.449 | − | 131.317i | −0.399734 | − | 0.230786i | 0.286635 | − | 0.958040i | \(-0.407463\pi\) |
−0.686369 | + | 0.727253i | \(0.740797\pi\) | |||||||
\(570\) | 34.7762 | − | 257.314i | 0.0610109 | − | 0.451427i | ||||
\(571\) | 215.712 | + | 373.624i | 0.377779 | + | 0.654333i | 0.990739 | − | 0.135781i | \(-0.0433545\pi\) |
−0.612960 | + | 0.790114i | \(0.710021\pi\) | |||||||
\(572\) | − | 548.738i | − | 0.959331i | ||||||
\(573\) | 195.608 | − | 253.114i | 0.341374 | − | 0.441736i | ||||
\(574\) | 185.497 | − | 51.8037i | 0.323165 | − | 0.0902503i | ||||
\(575\) | − | 29.8310i | − | 0.0518800i | ||||||
\(576\) | 391.016 | + | 107.659i | 0.678848 | + | 0.186908i | ||||
\(577\) | 389.031 | − | 673.821i | 0.674230 | − | 1.16780i | −0.302463 | − | 0.953161i | \(-0.597809\pi\) |
0.976693 | − | 0.214640i | \(-0.0688578\pi\) | |||||||
\(578\) | 285.888i | 0.494616i | ||||||||
\(579\) | −354.419 | + | 145.380i | −0.612122 | + | 0.251088i | ||||
\(580\) | −118.413 | + | 205.097i | −0.204160 | + | 0.353616i | ||||
\(581\) | 25.2212 | + | 90.3111i | 0.0434099 | + | 0.155441i | ||||
\(582\) | −312.833 | − | 42.2797i | −0.537514 | − | 0.0726456i | ||||
\(583\) | 640.409 | − | 1109.22i | 1.09847 | − | 1.90261i | ||||
\(584\) | 462.432 | + | 266.985i | 0.791835 | + | 0.457166i | ||||
\(585\) | −525.357 | − | 532.631i | −0.898047 | − | 0.910480i | ||||
\(586\) | −73.3087 | − | 126.974i | −0.125100 | − | 0.216680i | ||||
\(587\) | −743.197 | + | 429.085i | −1.26609 | + | 0.730980i | −0.974247 | − | 0.225485i | \(-0.927603\pi\) |
−0.291847 | + | 0.956465i | \(0.594270\pi\) | |||||||
\(588\) | −340.845 | − | 38.7745i | −0.579668 | − | 0.0659430i | ||||
\(589\) | 357.364 | − | 618.972i | 0.606729 | − | 1.05089i | ||||
\(590\) | 10.4653i | 0.0177378i | ||||||||
\(591\) | −0.350034 | − | 0.0473074i | −0.000592273 | − | 8.00464e-5i | ||||
\(592\) | 33.7836 | 0.0570669 | ||||||||
\(593\) | 362.591 | − | 209.342i | 0.611452 | − | 0.353022i | −0.162081 | − | 0.986777i | \(-0.551821\pi\) |
0.773534 | + | 0.633755i | \(0.218487\pi\) | |||||||
\(594\) | −286.362 | − | 381.271i | −0.482090 | − | 0.641870i | ||||
\(595\) | −198.785 | − | 194.641i | −0.334093 | − | 0.327128i | ||||
\(596\) | 266.816 | − | 154.046i | 0.447678 | − | 0.258467i | ||||
\(597\) | 253.518 | + | 195.919i | 0.424653 | + | 0.328173i | ||||
\(598\) | 205.593 | + | 356.097i | 0.343801 | + | 0.595480i | ||||
\(599\) | 582.638 | − | 336.386i | 0.972685 | − | 0.561580i | 0.0726311 | − | 0.997359i | \(-0.476860\pi\) |
0.900054 | + | 0.435779i | \(0.143527\pi\) | |||||||
\(600\) | −39.1255 | − | 5.28785i | −0.0652092 | − | 0.00881309i | ||||
\(601\) | 66.6761 | + | 115.486i | 0.110942 | + | 0.192157i | 0.916150 | − | 0.400835i | \(-0.131280\pi\) |
−0.805208 | + | 0.592992i | \(0.797947\pi\) | |||||||
\(602\) | 318.559 | + | 81.7717i | 0.529168 | + | 0.135833i | ||||
\(603\) | −125.323 | − | 480.911i | −0.207832 | − | 0.797531i | ||||
\(604\) | 336.141 | + | 582.213i | 0.556525 | + | 0.963929i | ||||
\(605\) | − | 320.019i | − | 0.528957i | ||||||
\(606\) | −45.6280 | − | 35.2615i | −0.0752938 | − | 0.0581872i | ||||
\(607\) | 779.315 | 1.28388 | 0.641940 | − | 0.766755i | \(-0.278130\pi\) | ||||
0.641940 | + | 0.766755i | \(0.278130\pi\) | |||||||
\(608\) | −373.739 | − | 215.779i | −0.614703 | − | 0.354899i | ||||
\(609\) | 436.466 | − | 60.6151i | 0.716693 | − | 0.0995322i | ||||
\(610\) | −204.374 | − | 353.986i | −0.335039 | − | 0.580305i | ||||
\(611\) | 883.881 | − | 510.309i | 1.44661 | − | 0.835203i | ||||
\(612\) | −45.8162 | + | 166.404i | −0.0748631 | + | 0.271902i | ||||
\(613\) | 38.9459 | − | 67.4563i | 0.0635333 | − | 0.110043i | −0.832509 | − | 0.554011i | \(-0.813096\pi\) |
0.896042 | + | 0.443968i | \(0.146430\pi\) | |||||||
\(614\) | −419.563 | − | 242.235i | −0.683327 | − | 0.394519i | ||||
\(615\) | −244.691 | − | 189.098i | −0.397871 | − | 0.307476i | ||||
\(616\) | 194.675 | − | 758.399i | 0.316031 | − | 1.23117i | ||||
\(617\) | 956.905 | + | 552.470i | 1.55090 | + | 0.895413i | 0.998069 | + | 0.0621194i | \(0.0197859\pi\) |
0.552831 | + | 0.833293i | \(0.313547\pi\) | |||||||
\(618\) | 184.650 | − | 238.936i | 0.298787 | − | 0.386627i | ||||
\(619\) | −315.310 | −0.509386 | −0.254693 | − | 0.967022i | \(-0.581974\pi\) | ||||
−0.254693 | + | 0.967022i | \(0.581974\pi\) | |||||||
\(620\) | 503.910 | + | 290.933i | 0.812759 | + | 0.469247i | ||||
\(621\) | −460.292 | − | 196.244i | −0.741211 | − | 0.316014i | ||||
\(622\) | −711.757 | −1.14430 | ||||||||
\(623\) | −29.8417 | − | 106.856i | −0.0479001 | − | 0.171519i | ||||
\(624\) | 58.1843 | − | 23.8667i | 0.0932440 | − | 0.0382480i | ||||
\(625\) | −582.168 | −0.931469 | ||||||||
\(626\) | −211.158 | + | 121.912i | −0.337312 | + | 0.194747i | ||||
\(627\) | 215.936 | + | 526.426i | 0.344395 | + | 0.839595i | ||||
\(628\) | −9.95730 | + | 17.2465i | −0.0158556 | + | 0.0274627i | ||||
\(629\) | 227.627i | 0.361887i | ||||||||
\(630\) | −197.904 | − | 339.903i | −0.314133 | − | 0.539528i | ||||
\(631\) | −154.111 | −0.244234 | −0.122117 | − | 0.992516i | \(-0.538968\pi\) | ||||
−0.122117 | + | 0.992516i | \(0.538968\pi\) | |||||||
\(632\) | 47.4688 | + | 27.4061i | 0.0751088 | + | 0.0433641i | ||||
\(633\) | −167.991 | − | 129.824i | −0.265389 | − | 0.205093i | ||||
\(634\) | −297.839 | − | 515.872i | −0.469778 | − | 0.813679i | ||||
\(635\) | 1163.31i | 1.83198i | ||||||||
\(636\) | −649.519 | − | 87.7833i | −1.02126 | − | 0.138024i | ||||
\(637\) | −720.329 | + | 436.365i | −1.13081 | + | 0.685032i | ||||
\(638\) | 370.581i | 0.580847i | ||||||||
\(639\) | 34.0690 | − | 123.738i | 0.0533162 | − | 0.193644i | ||||
\(640\) | 160.438 | − | 277.887i | 0.250685 | − | 0.434199i | ||||
\(641\) | − | 645.715i | − | 1.00736i | −0.863891 | − | 0.503678i | \(-0.831980\pi\) | ||
0.863891 | − | 0.503678i | \(-0.168020\pi\) | |||||||
\(642\) | −43.7774 | + | 323.915i | −0.0681892 | + | 0.504540i | ||||
\(643\) | 153.144 | − | 265.252i | 0.238170 | − | 0.412523i | −0.722019 | − | 0.691873i | \(-0.756786\pi\) |
0.960189 | + | 0.279350i | \(0.0901190\pi\) | |||||||
\(644\) | −81.4297 | − | 291.581i | −0.126444 | − | 0.452765i | ||||
\(645\) | −200.410 | − | 488.577i | −0.310714 | − | 0.757484i | ||||
\(646\) | −73.5326 | + | 127.362i | −0.113828 | + | 0.197155i | ||||
\(647\) | 483.124 | + | 278.932i | 0.746715 | + | 0.431116i | 0.824506 | − | 0.565854i | \(-0.191453\pi\) |
−0.0777910 | + | 0.996970i | \(0.524787\pi\) | |||||||
\(648\) | −338.980 | + | 568.920i | −0.523118 | + | 0.877964i | ||||
\(649\) | −11.4666 | − | 19.8608i | −0.0176681 | − | 0.0306021i | ||||
\(650\) | −30.9288 | + | 17.8567i | −0.0475827 | + | 0.0274719i | ||||
\(651\) | −148.927 | − | 1072.37i | −0.228767 | − | 1.64726i | ||||
\(652\) | −224.543 | + | 388.920i | −0.344391 | + | 0.596502i | ||||
\(653\) | − | 149.393i | − | 0.228779i | −0.993436 | − | 0.114390i | \(-0.963509\pi\) | ||
0.993436 | − | 0.114390i | \(-0.0364912\pi\) | |||||||
\(654\) | 55.1877 | + | 134.541i | 0.0843848 | + | 0.205720i | ||||
\(655\) | 121.048 | 0.184806 | ||||||||
\(656\) | 22.5128 | − | 12.9978i | 0.0343183 | − | 0.0198137i | ||||
\(657\) | −418.477 | + | 412.762i | −0.636951 | + | 0.628252i | ||||
\(658\) | 516.802 | − | 144.327i | 0.785413 | − | 0.219342i | ||||
\(659\) | −462.734 | + | 267.160i | −0.702176 | + | 0.405401i | −0.808157 | − | 0.588967i | \(-0.799535\pi\) |
0.105981 | + | 0.994368i | \(0.466202\pi\) | |||||||
\(660\) | −428.568 | + | 175.795i | −0.649345 | + | 0.266356i | ||||
\(661\) | −94.5251 | − | 163.722i | −0.143003 | − | 0.247689i | 0.785623 | − | 0.618705i | \(-0.212343\pi\) |
−0.928626 | + | 0.371017i | \(0.879009\pi\) | |||||||
\(662\) | 163.661 | − | 94.4898i | 0.247222 | − | 0.142734i | ||||
\(663\) | 160.809 | + | 392.034i | 0.242548 | + | 0.591303i | ||||
\(664\) | 54.7595 | + | 94.8462i | 0.0824691 | + | 0.142841i | ||||
\(665\) | 126.241 | + | 452.040i | 0.189836 | + | 0.679759i | ||||
\(666\) | −85.4249 | + | 310.262i | −0.128266 | + | 0.465859i | ||||
\(667\) | 194.440 | + | 336.780i | 0.291515 | + | 0.504918i | ||||
\(668\) | 336.858i | 0.504278i | ||||||||
\(669\) | −659.059 | + | 270.341i | −0.985140 | + | 0.404097i | ||||
\(670\) | 344.742 | 0.514540 | ||||||||
\(671\) | 775.710 | + | 447.856i | 1.15605 | + | 0.667446i | ||||
\(672\) | −647.503 | + | 89.9233i | −0.963546 | + | 0.133814i | ||||
\(673\) | 429.674 | + | 744.217i | 0.638446 | + | 1.10582i | 0.985774 | + | 0.168077i | \(0.0537557\pi\) |
−0.347328 | + | 0.937744i | \(0.612911\pi\) | |||||||
\(674\) | −274.532 | + | 158.501i | −0.407318 | + | 0.235165i | ||||
\(675\) | 17.0448 | − | 39.9786i | 0.0252515 | − | 0.0592276i | ||||
\(676\) | −147.501 | + | 255.480i | −0.218197 | + | 0.377929i | ||||
\(677\) | −914.866 | − | 528.198i | −1.35135 | − | 0.780204i | −0.362915 | − | 0.931822i | \(-0.618218\pi\) |
−0.988439 | + | 0.151618i | \(0.951552\pi\) | |||||||
\(678\) | −39.6785 | + | 16.2758i | −0.0585229 | + | 0.0240056i | ||||
\(679\) | 549.574 | − | 153.480i | 0.809388 | − | 0.226038i | ||||
\(680\) | −281.413 | − | 162.474i | −0.413842 | − | 0.238932i | ||||
\(681\) | 943.401 | + | 127.502i | 1.38532 | + | 0.187227i | ||||
\(682\) | 910.492 | 1.33503 | ||||||||
\(683\) | −70.7663 | − | 40.8570i | −0.103611 | − | 0.0598199i | 0.447299 | − | 0.894384i | \(-0.352386\pi\) |
−0.550910 | + | 0.834565i | \(0.685719\pi\) | |||||||
\(684\) | 207.297 | − | 204.466i | 0.303065 | − | 0.298927i | ||||
\(685\) | 1238.09 | 1.80743 | ||||||||
\(686\) | −423.851 | + | 128.052i | −0.617859 | + | 0.186664i | ||||
\(687\) | 30.8025 | − | 227.912i | 0.0448363 | − | 0.331749i | ||||
\(688\) | 44.3916 | 0.0645227 | ||||||||
\(689\) | −1393.53 | + | 804.554i | −2.02254 | + | 1.16771i | ||||
\(690\) | 212.250 | − | 274.650i | 0.307609 | − | 0.398043i | ||||
\(691\) | −179.603 | + | 311.081i | −0.259917 | + | 0.450189i | −0.966219 | − | 0.257721i | \(-0.917028\pi\) |
0.706303 | + | 0.707910i | \(0.250362\pi\) | |||||||
\(692\) | − | 715.882i | − | 1.03451i | ||||||
\(693\) | 748.000 | + | 428.218i | 1.07937 | + | 0.617920i | ||||
\(694\) | 29.1616 | 0.0420196 | ||||||||
\(695\) | 210.835 | + | 121.726i | 0.303360 | + | 0.175145i | ||||
\(696\) | 476.178 | − | 195.325i | 0.684164 | − | 0.280639i | ||||
\(697\) | 87.5764 | + | 151.687i | 0.125648 | + | 0.217628i | ||||
\(698\) | − | 431.878i | − | 0.618736i | ||||||
\(699\) | 375.051 | + | 914.330i | 0.536554 | + | 1.30805i | ||||
\(700\) | 25.3252 | − | 7.07257i | 0.0361789 | − | 0.0101037i | ||||
\(701\) | 894.651i | 1.27625i | 0.769933 | + | 0.638125i | \(0.220290\pi\) | ||||
−0.769933 | + | 0.638125i | \(0.779710\pi\) | |||||||
\(702\) | 72.0633 | + | 594.702i | 0.102654 | + | 0.847154i | ||||
\(703\) | 192.002 | − | 332.557i | 0.273118 | − | 0.473054i | ||||
\(704\) | − | 616.506i | − | 0.875718i | ||||||
\(705\) | −681.718 | − | 526.833i | −0.966975 | − | 0.747281i | ||||
\(706\) | 245.314 | − | 424.896i | 0.347470 | − | 0.601836i | ||||
\(707\) | 100.960 | + | 25.9156i | 0.142800 | + | 0.0366558i | ||||
\(708\) | −7.17607 | + | 9.28578i | −0.0101357 | + | 0.0131155i | ||||
\(709\) | 130.275 | − | 225.643i | 0.183745 | − | 0.318256i | −0.759408 | − | 0.650615i | \(-0.774511\pi\) |
0.943153 | + | 0.332359i | \(0.107845\pi\) | |||||||
\(710\) | 77.1017 | + | 44.5147i | 0.108594 | + | 0.0626967i | ||||
\(711\) | −42.9568 | + | 42.3702i | −0.0604174 | + | 0.0595923i | ||||
\(712\) | −64.7915 | − | 112.222i | −0.0909993 | − | 0.157615i | ||||
\(713\) | 827.447 | − | 477.727i | 1.16051 | − | 0.670023i | ||||
\(714\) | 30.6439 | + | 220.655i | 0.0429186 | + | 0.309040i | ||||
\(715\) | −568.619 | + | 984.877i | −0.795271 | + | 1.37745i | ||||
\(716\) | 486.645i | 0.679672i | ||||||||
\(717\) | −106.279 | + | 137.525i | −0.148228 | + | 0.191805i | ||||
\(718\) | 1.87076 | 0.00260551 | ||||||||
\(719\) | 775.636 | − | 447.814i | 1.07877 | − | 0.622829i | 0.148206 | − | 0.988956i | \(-0.452650\pi\) |
0.930565 | + | 0.366128i | \(0.119317\pi\) | |||||||
\(720\) | −37.2802 | − | 37.7963i | −0.0517780 | − | 0.0524949i | ||||
\(721\) | −135.710 | + | 528.687i | −0.188224 | + | 0.733269i | ||||
\(722\) | −188.716 | + | 108.955i | −0.261380 | + | 0.150908i | ||||
\(723\) | −32.0702 | + | 237.291i | −0.0443571 | + | 0.328204i | ||||
\(724\) | 154.485 | + | 267.575i | 0.213377 | + | 0.369579i | ||||
\(725\) | −29.2510 | + | 16.8881i | −0.0403462 | + | 0.0232939i | ||||
\(726\) | −156.693 | + | 202.760i | −0.215831 | + | 0.279283i | ||||
\(727\) | −409.883 | − | 709.938i | −0.563800 | − | 0.976531i | −0.997160 | − | 0.0753098i | \(-0.976005\pi\) |
0.433360 | − | 0.901221i | \(-0.357328\pi\) | |||||||
\(728\) | −688.199 | + | 702.851i | −0.945329 | + | 0.965454i | ||||
\(729\) | −504.740 | − | 526.002i | −0.692374 | − | 0.721539i | ||||
\(730\) | −203.870 | − | 353.113i | −0.279274 | − | 0.483716i | ||||
\(731\) | 299.102i | 0.409168i | ||||||||
\(732\) | 61.3894 | − | 454.228i | 0.0838653 | − | 0.620530i | ||||
\(733\) | −1148.34 | −1.56663 | −0.783313 | − | 0.621627i | \(-0.786472\pi\) | ||||
−0.783313 | + | 0.621627i | \(0.786472\pi\) | |||||||
\(734\) | 481.667 | + | 278.091i | 0.656223 | + | 0.378870i | ||||
\(735\) | 571.571 | + | 422.787i | 0.777648 | + | 0.575220i | ||||
\(736\) | −288.455 | − | 499.618i | −0.391922 | − | 0.678829i | ||||
\(737\) | −654.241 | + | 377.726i | −0.887708 | + | 0.512519i | ||||
\(738\) | 62.4434 | + | 239.619i | 0.0846116 | + | 0.324687i | ||||
\(739\) | −322.085 | + | 557.868i | −0.435839 | + | 0.754895i | −0.997364 | − | 0.0725646i | \(-0.976882\pi\) |
0.561525 | + | 0.827460i | \(0.310215\pi\) | |||||||
\(740\) | 270.738 | + | 156.310i | 0.365862 | + | 0.211230i | ||||
\(741\) | 95.7400 | − | 708.392i | 0.129204 | − | 0.955995i | ||||
\(742\) | −814.790 | + | 227.546i | −1.09810 | + | 0.306666i | ||||
\(743\) | −599.923 | − | 346.366i | −0.807434 | − | 0.466172i | 0.0386303 | − | 0.999254i | \(-0.487701\pi\) |
−0.846064 | + | 0.533082i | \(0.821034\pi\) | |||||||
\(744\) | −479.899 | − | 1169.94i | −0.645026 | − | 1.57250i | ||||
\(745\) | −638.510 | −0.857060 | ||||||||
\(746\) | −40.2303 | − | 23.2270i | −0.0539280 | − | 0.0311354i | ||||
\(747\) | −116.661 | + | 30.4012i | −0.156173 | + | 0.0406977i | ||||
\(748\) | 262.365 | 0.350755 | ||||||||
\(749\) | −158.916 | − | 569.042i | −0.212171 | − | 0.759736i | ||||
\(750\) | 394.350 | + | 304.755i | 0.525800 | + | 0.406340i | ||||
\(751\) | −868.794 | −1.15685 | −0.578425 | − | 0.815736i | \(-0.696332\pi\) | ||||
−0.578425 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(752\) | 62.7216 | − | 36.2123i | 0.0834063 | − | 0.0481547i | ||||
\(753\) | 555.206 | + | 75.0367i | 0.737325 | + | 0.0996503i | ||||
\(754\) | 232.783 | − | 403.191i | 0.308730 | − | 0.534736i | ||||
\(755\) | − | 1393.28i | − | 1.84540i | ||||||
\(756\) | 57.4732 | − | 437.295i | 0.0760227 | − | 0.578433i | ||||
\(757\) | 878.499 | 1.16050 | 0.580250 | − | 0.814438i | \(-0.302955\pi\) | ||||
0.580250 | + | 0.814438i | \(0.302955\pi\) | |||||||
\(758\) | 776.565 | + | 448.350i | 1.02449 | + | 0.591491i | ||||
\(759\) | −101.874 | + | 753.781i | −0.134222 | + | 0.993123i | ||||
\(760\) | 274.091 | + | 474.739i | 0.360646 | + | 0.624657i | ||||
\(761\) | − | 49.1883i | − | 0.0646364i | −0.999478 | − | 0.0323182i | \(-0.989711\pi\) | ||
0.999478 | − | 0.0323182i | \(-0.0102890\pi\) | |||||||
\(762\) | 569.598 | − | 737.054i | 0.747503 | − | 0.967263i | ||||
\(763\) | −187.813 | − | 183.898i | −0.246151 | − | 0.241020i | ||||
\(764\) | 248.834i | 0.325700i | ||||||||
\(765\) | 254.664 | − | 251.186i | 0.332894 | − | 0.328348i | ||||
\(766\) | −222.617 | + | 385.583i | −0.290622 | + | 0.503372i | ||||
\(767\) | 28.8113i | 0.0375637i | ||||||||
\(768\) | −738.016 | + | 302.728i | −0.960959 | + | 0.394178i | ||||
\(769\) | 231.085 | − | 400.251i | 0.300501 | − | 0.520482i | −0.675749 | − | 0.737132i | \(-0.736180\pi\) |
0.976249 | + | 0.216650i | \(0.0695130\pi\) | |||||||
\(770\) | −418.295 | + | 427.200i | −0.543240 | + | 0.554805i | ||||
\(771\) | 1075.02 | + | 145.291i | 1.39432 | + | 0.188444i | ||||
\(772\) | 148.993 | − | 258.064i | 0.192996 | − | 0.334280i | ||||
\(773\) | 469.184 | + | 270.883i | 0.606965 | + | 0.350431i | 0.771777 | − | 0.635894i | \(-0.219368\pi\) |
−0.164812 | + | 0.986325i | \(0.552702\pi\) | |||||||
\(774\) | −112.248 | + | 407.684i | −0.145024 | + | 0.526724i | ||||
\(775\) | 41.4929 | + | 71.8678i | 0.0535392 | + | 0.0927326i | ||||
\(776\) | 577.172 | − | 333.230i | 0.743778 | − | 0.429421i | ||||
\(777\) | −80.0146 | − | 576.154i | −0.102979 | − | 0.741511i | ||||
\(778\) | 284.951 | − | 493.550i | 0.366261 | − | 0.634384i | ||||
\(779\) | − | 295.480i | − | 0.379307i | ||||||
\(780\) | 576.708 | + | 77.9427i | 0.739370 | + | 0.0999266i | ||||
\(781\) | −195.095 | −0.249802 | ||||||||
\(782\) | −170.259 | + | 98.2990i | −0.217722 | + | 0.125702i | ||||
\(783\) | 68.1541 | + | 562.442i | 0.0870423 | + | 0.718317i | ||||
\(784\) | −51.1157 | + | 30.9651i | −0.0651985 | + | 0.0394964i | ||||
\(785\) | 35.7428 | − | 20.6361i | 0.0455322 | − | 0.0262881i | ||||
\(786\) | −76.6942 | − | 59.2695i | −0.0975753 | − | 0.0754065i | ||||
\(787\) | −266.117 | − | 460.928i | −0.338141 | − | 0.585678i | 0.645942 | − | 0.763387i | \(-0.276465\pi\) |
−0.984083 | + | 0.177709i | \(0.943131\pi\) | |||||||
\(788\) | 0.237948 | − | 0.137379i | 0.000301964 | − | 0.000174339i | ||||
\(789\) | −1139.15 | − | 153.957i | −1.44379 | − | 0.195130i | ||||
\(790\) | −20.9273 | − | 36.2471i | −0.0264902 | − | 0.0458825i | ||||
\(791\) | 54.2348 | − | 55.3894i | 0.0685649 | − | 0.0700246i | ||||
\(792\) | 970.580 | + | 267.231i | 1.22548 | + | 0.337413i | ||||
\(793\) | −562.648 | − | 974.534i | −0.709518 | − | 1.22892i | ||||
\(794\) | − | 112.510i | − | 0.141700i | ||||||
\(795\) | 1074.80 | + | 830.606i | 1.35195 | + | 1.04479i | ||||
\(796\) | −249.231 | −0.313104 | ||||||||
\(797\) | −1209.31 | − | 698.198i | −1.51733 | − | 0.876032i | −0.999792 | − | 0.0203733i | \(-0.993515\pi\) |
−0.517540 | − | 0.855659i | \(-0.673152\pi\) | |||||||
\(798\) | 141.351 | − | 348.218i | 0.177131 | − | 0.436364i | ||||
\(799\) | 243.991 | + | 422.605i | 0.305371 | + | 0.528918i | ||||
\(800\) | 43.3942 | − | 25.0537i | 0.0542428 | − | 0.0313171i | ||||
\(801\) | 138.034 | − | 35.9708i | 0.172327 | − | 0.0449073i | ||||
\(802\) | −425.011 | + | 736.141i | −0.529939 | + | 0.917881i | ||||
\(803\) | 773.796 | + | 446.751i | 0.963631 | + | 0.556353i | ||||
\(804\) | 305.886 | + | 236.390i | 0.380455 | + | 0.294017i | ||||
\(805\) | −155.995 | + | 607.711i | −0.193782 | + | 0.754920i | ||||
\(806\) | −990.614 | − | 571.931i | −1.22905 | − | 0.709592i | ||||
\(807\) | −149.897 | + | 193.965i | −0.185745 | + | 0.240353i | ||||
\(808\) | 121.744 | 0.150673 | ||||||||
\(809\) | 587.272 | + | 339.062i | 0.725924 | + | 0.419112i | 0.816929 | − | 0.576738i | \(-0.195675\pi\) |
−0.0910054 | + | 0.995850i | \(0.529008\pi\) | |||||||
\(810\) | 441.380 | − | 246.803i | 0.544914 | − | 0.304695i | ||||
\(811\) | −877.972 | −1.08258 | −0.541290 | − | 0.840836i | \(-0.682064\pi\) | ||||
−0.541290 | + | 0.840836i | \(0.682064\pi\) | |||||||
\(812\) | −239.812 | + | 244.918i | −0.295335 | + | 0.301623i | ||||
\(813\) | −1043.36 | + | 427.978i | −1.28334 | + | 0.526418i | ||||
\(814\) | 489.183 | 0.600962 | ||||||||
\(815\) | 806.021 | − | 465.356i | 0.988983 | − | 0.570989i | ||||
\(816\) | 11.4113 | + | 27.8193i | 0.0139844 | + | 0.0340923i | ||||
\(817\) | 252.290 | − | 436.980i | 0.308801 | − | 0.534859i | ||||
\(818\) | − | 796.521i | − | 0.973742i | ||||||
\(819\) | −544.836 | − | 935.762i | −0.665245 | − | 1.14257i | ||||
\(820\) | 240.553 | 0.293357 | ||||||||
\(821\) | −347.814 | − | 200.810i | −0.423646 | − | 0.244592i | 0.272990 | − | 0.962017i | \(-0.411987\pi\) |
−0.696636 | + | 0.717425i | \(0.745321\pi\) | |||||||
\(822\) | −784.436 | − | 606.215i | −0.954302 | − | 0.737487i | ||||
\(823\) | 60.8798 | + | 105.447i | 0.0739730 | + | 0.128125i | 0.900639 | − | 0.434568i | \(-0.143099\pi\) |
−0.826666 | + | 0.562693i | \(0.809765\pi\) | |||||||
\(824\) | 637.522i | 0.773692i | ||||||||
\(825\) | −65.4695 | − | 8.84827i | −0.0793570 | − | 0.0107252i | ||||
\(826\) | −3.76607 | + | 14.6715i | −0.00455941 | + | 0.0177621i | ||||
\(827\) | − | 1365.90i | − | 1.65163i | −0.563941 | − | 0.825815i | \(-0.690715\pi\) | ||
0.563941 | − | 0.825815i | \(-0.309285\pi\) | |||||||
\(828\) | 376.655 | − | 98.1542i | 0.454898 | − | 0.118544i | ||||
\(829\) | −452.116 | + | 783.089i | −0.545376 | + | 0.944618i | 0.453208 | + | 0.891405i | \(0.350280\pi\) |
−0.998583 | + | 0.0532133i | \(0.983054\pi\) | |||||||
\(830\) | − | 83.6286i | − | 0.100757i | ||||||
\(831\) | −44.6427 | + | 330.317i | −0.0537217 | + | 0.397494i | ||||
\(832\) | −387.262 | + | 670.757i | −0.465459 | + | 0.806199i | ||||
\(833\) | −208.637 | − | 344.407i | −0.250464 | − | 0.413454i | ||||
\(834\) | −73.9809 | − | 180.357i | −0.0887061 | − | 0.216255i | ||||
\(835\) | 349.063 | − | 604.594i | 0.418039 | − | 0.724065i | ||||
\(836\) | −383.308 | − | 221.303i | −0.458502 | − | 0.264716i | ||||
\(837\) | 1381.88 | − | 167.450i | 1.65099 | − | 0.200060i | ||||
\(838\) | −139.224 | − | 241.142i | −0.166138 | − | 0.287759i | ||||
\(839\) | 115.048 | − | 66.4230i | 0.137125 | − | 0.0791692i | −0.429868 | − | 0.902892i | \(-0.641440\pi\) |
0.566993 | + | 0.823723i | \(0.308107\pi\) | |||||||
\(840\) | 769.405 | + | 312.321i | 0.915958 | + | 0.371811i | ||||
\(841\) | −200.345 | + | 347.008i | −0.238222 | + | 0.412613i | ||||
\(842\) | 716.400i | 0.850831i | ||||||||
\(843\) | 116.545 | + | 284.123i | 0.138250 | + | 0.337038i | ||||
\(844\) | 165.150 | 0.195676 | ||||||||
\(845\) | 529.472 | − | 305.691i | 0.626594 | − | 0.361764i | ||||
\(846\) | 173.970 | + | 667.589i | 0.205638 | + | 0.789112i | ||||
\(847\) | 115.163 | − | 448.641i | 0.135965 | − | 0.529683i | ||||
\(848\) | −98.8869 | + | 57.0924i | −0.116612 | + | 0.0673259i | ||||
\(849\) | 316.572 | − | 129.855i | 0.372876 | − | 0.152951i | ||||
\(850\) | −8.53774 | − | 14.7878i | −0.0100444 | − | 0.0173974i | ||||
\(851\) | 444.565 | − | 256.670i | 0.522403 | − | 0.301609i | ||||
\(852\) | 37.8879 | + | 92.3661i | 0.0444693 | + | 0.108411i | ||||
\(853\) | −324.186 | − | 561.507i | −0.380054 | − | 0.658273i | 0.611016 | − | 0.791619i | \(-0.290761\pi\) |
−0.991070 | + | 0.133346i | \(0.957428\pi\) | |||||||
\(854\) | −159.130 | − | 569.806i | −0.186335 | − | 0.667221i | ||||
\(855\) | −583.931 | + | 152.169i | −0.682960 | + | 0.177975i | ||||
\(856\) | −345.035 | − | 597.618i | −0.403078 | − | 0.698151i | ||||
\(857\) | − | 407.461i | − | 0.475450i | −0.971332 | − | 0.237725i | \(-0.923598\pi\) | ||
0.971332 | − | 0.237725i | \(-0.0764017\pi\) | |||||||
\(858\) | 842.501 | − | 345.587i | 0.981936 | − | 0.402783i | ||||
\(859\) | −336.523 | −0.391762 | −0.195881 | − | 0.980628i | \(-0.562757\pi\) | ||||
−0.195881 | + | 0.980628i | \(0.562757\pi\) | |||||||
\(860\) | 355.749 | + | 205.392i | 0.413662 | + | 0.238828i | ||||
\(861\) | −274.988 | − | 353.154i | −0.319382 | − | 0.410168i | ||||
\(862\) | 523.205 | + | 906.218i | 0.606966 | + | 1.05130i | ||||
\(863\) | −604.222 | + | 348.847i | −0.700141 | + | 0.404227i | −0.807400 | − | 0.590005i | \(-0.799126\pi\) |
0.107259 | + | 0.994231i | \(0.465793\pi\) | |||||||
\(864\) | −101.108 | − | 834.390i | −0.117023 | − | 0.965729i | ||||
\(865\) | −741.820 | + | 1284.87i | −0.857595 | + | 1.48540i | ||||
\(866\) | 394.261 | + | 227.626i | 0.455266 | + | 0.262848i | ||||
\(867\) | 614.698 | − | 252.144i | 0.708994 | − | 0.290824i | ||||
\(868\) | 601.747 | + | 589.203i | 0.693256 | + | 0.678805i | ||||
\(869\) | 79.4304 | + | 45.8592i | 0.0914044 | + | 0.0527724i | ||||
\(870\) | −389.470 | − | 52.6373i | −0.447667 | − | 0.0605027i | ||||
\(871\) | 949.085 | 1.08965 | ||||||||
\(872\) | −265.880 | − | 153.506i | −0.304909 | − | 0.176039i | ||||
\(873\) | 185.002 | + | 709.923i | 0.211915 | + | 0.813200i | ||||
\(874\) | 331.658 | 0.379471 | ||||||||
\(875\) | −872.568 | − | 223.981i | −0.997220 | − | 0.255979i | ||||
\(876\) | 61.2379 | − | 453.107i | 0.0699063 | − | 0.517246i | ||||
\(877\) | 1612.26 | 1.83838 | 0.919190 | − | 0.393814i | \(-0.128845\pi\) | ||||
0.919190 | + | 0.393814i | \(0.128845\pi\) | |||||||
\(878\) | 436.273 | − | 251.882i | 0.496894 | − | 0.286882i | ||||
\(879\) | −208.356 | + | 269.611i | −0.237038 | + | 0.306725i | ||||
\(880\) | −40.3501 | + | 69.8884i | −0.0458524 | + | 0.0794186i | ||||
\(881\) | 667.659i | 0.757842i | 0.925429 | + | 0.378921i | \(0.123705\pi\) | ||||
−0.925429 | + | 0.378921i | \(0.876295\pi\) | |||||||
\(882\) | −155.127 | − | 547.734i | −0.175881 | − | 0.621014i | ||||
\(883\) | −779.788 | −0.883112 | −0.441556 | − | 0.897234i | \(-0.645573\pi\) | ||||
−0.441556 | + | 0.897234i | \(0.645573\pi\) | |||||||
\(884\) | −285.453 | − | 164.806i | −0.322910 | − | 0.186432i | ||||
\(885\) | 22.5019 | − | 9.23008i | 0.0254258 | − | 0.0104295i | ||||
\(886\) | 118.470 | + | 205.195i | 0.133713 | + | 0.231597i | ||||
\(887\) | 570.512i | 0.643193i | 0.946877 | + | 0.321596i | \(0.104219\pi\) | ||||
−0.946877 | + | 0.321596i | \(0.895781\pi\) | |||||||
\(888\) | −257.837 | − | 628.577i | −0.290357 | − | 0.707856i | ||||
\(889\) | −418.629 | + | 1630.86i | −0.470899 | + | 1.83449i | ||||
\(890\) | 98.9496i | 0.111179i | ||||||||
\(891\) | −567.223 | + | 951.986i | −0.636614 | + | 1.06845i | ||||
\(892\) | 277.060 | − | 479.882i | 0.310606 | − | 0.537985i | ||||
\(893\) | − | 823.219i | − | 0.921858i | ||||||
\(894\) | 404.551 | + | 312.638i | 0.452518 | + | 0.349707i | ||||
\(895\) | 504.276 | − | 873.432i | 0.563437 | − | 0.975902i | ||||
\(896\) | 324.923 | − | 331.840i | 0.362637 | − | 0.370357i | ||||
\(897\) | 584.331 | − | 756.120i | 0.651428 | − | 0.842943i | ||||
\(898\) | −421.595 | + | 730.224i | −0.469482 | + | 0.813167i | ||||
\(899\) | −936.877 | − | 540.906i | −1.04213 | − | 0.601675i | ||||
\(900\) | 8.52517 | + | 32.7143i | 0.00947241 | + | 0.0363493i | ||||
\(901\) | −384.677 | − | 666.280i | −0.426944 | − | 0.739489i | ||||
\(902\) | 325.983 | − | 188.206i | 0.361400 | − | 0.208654i | ||||
\(903\) | −105.139 | − | 757.066i | −0.116433 | − | 0.838390i | ||||
\(904\) | 45.2716 | − | 78.4128i | 0.0500792 | − | 0.0867398i | ||||
\(905\) | − | 640.328i | − | 0.707544i | ||||||
\(906\) | −682.201 | + | 882.763i | −0.752982 | + | 0.974352i | ||||
\(907\) | −1433.01 | −1.57994 | −0.789970 | − | 0.613146i | \(-0.789904\pi\) | ||||
−0.789970 | + | 0.613146i | \(0.789904\pi\) | |||||||
\(908\) | −641.310 | + | 370.261i | −0.706289 | + | 0.407776i | ||||
\(909\) | −35.5745 | + | 129.206i | −0.0391358 | + | 0.142141i | ||||
\(910\) | 723.452 | − | 202.038i | 0.795003 | − | 0.222020i | ||||
\(911\) | −866.010 | + | 499.991i | −0.950615 | + | 0.548838i | −0.893272 | − | 0.449517i | \(-0.851596\pi\) |
−0.0573431 | + | 0.998355i | \(0.518263\pi\) | |||||||
\(912\) | 6.79386 | − | 50.2686i | 0.00744940 | − | 0.0551191i | ||||
\(913\) | 91.6301 | + | 158.708i | 0.100362 | + | 0.173831i | ||||
\(914\) | 162.915 | − | 94.0589i | 0.178244 | − | 0.102909i | ||||
\(915\) | −580.867 | + | 751.637i | −0.634827 | + | 0.821461i | ||||
\(916\) | 89.4495 | + | 154.931i | 0.0976522 | + | 0.169139i | ||||
\(917\) | 169.699 | + | 43.5605i | 0.185059 | + | 0.0475033i | ||||
\(918\) | −284.342 | + | 34.4552i | −0.309741 | + | 0.0375329i | ||||
\(919\) | −100.551 | − | 174.159i | −0.109413 | − | 0.189509i | 0.806120 | − | 0.591753i | \(-0.201564\pi\) |
−0.915533 | + | 0.402244i | \(0.868230\pi\) | |||||||
\(920\) | 732.814i | 0.796537i | ||||||||
\(921\) | −150.796 | + | 1115.76i | −0.163731 | + | 1.21147i | ||||
\(922\) | 9.40534 | 0.0102010 | ||||||||
\(923\) | 212.263 | + | 122.550i | 0.229971 | + | 0.132774i | ||||
\(924\) | −664.080 | + | 92.2255i | −0.718701 | + | 0.0998111i | ||||
\(925\) | 22.2930 | + | 38.6126i | 0.0241005 | + | 0.0417434i | ||||
\(926\) | 49.7130 | − | 28.7018i | 0.0536858 | − | 0.0309955i | ||||
\(927\) | −676.600 | − | 186.289i | −0.729881 | − | 0.200959i | ||||
\(928\) | −326.603 | + | 565.693i | −0.351943 | + | 0.609583i | ||||
\(929\) | −574.180 | − | 331.503i | −0.618062 | − | 0.356838i | 0.158052 | − | 0.987431i | \(-0.449479\pi\) |
−0.776114 | + | 0.630592i | \(0.782812\pi\) | |||||||
\(930\) | −129.326 | + | 956.902i | −0.139061 | + | 1.02893i | ||||
\(931\) | 14.3080 | + | 679.153i | 0.0153684 | + | 0.729487i | ||||
\(932\) | −665.754 | − | 384.373i | −0.714328 | − | 0.412417i | ||||
\(933\) | 627.748 | + | 1530.38i | 0.672827 | + | 1.64027i | ||||
\(934\) | 260.706 | 0.279129 | ||||||||
\(935\) | −470.894 | − | 271.871i | −0.503630 | − | 0.290771i | ||||
\(936\) | −888.127 | − | 900.423i | −0.948853 | − | 0.961990i | ||||
\(937\) | 251.201 | 0.268091 | 0.134045 | − | 0.990975i | \(-0.457203\pi\) | ||||
0.134045 | + | 0.990975i | \(0.457203\pi\) | |||||||
\(938\) | 483.300 | + | 124.059i | 0.515246 | + | 0.132260i | ||||
\(939\) | 448.362 | + | 346.495i | 0.477489 | + | 0.369004i | ||||
\(940\) | 670.190 | 0.712968 | ||||||||
\(941\) | 596.921 | − | 344.633i | 0.634348 | − | 0.366241i | −0.148086 | − | 0.988974i | \(-0.547311\pi\) |
0.782434 | + | 0.622734i | \(0.213978\pi\) | |||||||
\(942\) | −32.7504 | − | 4.42625i | −0.0347668 | − | 0.00469878i | ||||
\(943\) | 197.500 | − | 342.080i | 0.209438 | − | 0.362757i | ||||
\(944\) | 2.04450i | 0.00216578i | ||||||||
\(945\) | −556.292 | + | 725.304i | −0.588669 | + | 0.767518i | ||||
\(946\) | 642.786 | 0.679477 | ||||||||
\(947\) | 1379.86 | + | 796.662i | 1.45708 | + | 0.841248i | 0.998867 | − | 0.0475928i | \(-0.0151550\pi\) |
0.458217 | + | 0.888840i | \(0.348488\pi\) | |||||||
\(948\) | 6.28609 | − | 46.5116i | 0.00663090 | − | 0.0490629i | ||||
\(949\) | −561.260 | − | 972.130i | −0.591422 | − | 1.02437i | ||||
\(950\) | 28.8061i | 0.0303222i | ||||||||
\(951\) | −846.511 | + | 1095.38i | −0.890127 | + | 1.15182i | ||||
\(952\) | −336.050 | − | 329.045i | −0.352994 | − | 0.345636i | ||||
\(953\) | 820.886i | 0.861370i | 0.902502 | + | 0.430685i | \(0.141728\pi\) | ||||
−0.902502 | + | 0.430685i | \(0.858272\pi\) | |||||||
\(954\) | −274.281 | − | 1052.52i | −0.287506 | − | 1.10327i | ||||
\(955\) | 257.850 | − | 446.609i | 0.270000 | − | 0.467654i | ||||
\(956\) | − | 135.199i | − | 0.141422i | ||||||
\(957\) | 796.799 | − | 326.841i | 0.832601 | − | 0.341526i | ||||
\(958\) | −123.140 | + | 213.284i | −0.128538 | + | 0.222635i | ||||
\(959\) | 1735.70 | + | 445.541i | 1.80991 | + | 0.464589i | ||||
\(960\) | 647.931 | + | 87.5685i | 0.674928 | + | 0.0912172i | ||||
\(961\) | −848.470 | + | 1469.59i | −0.882903 | + | 1.52923i | ||||
\(962\) | −532.230 | − | 307.283i | −0.553254 | − | 0.319421i | ||||
\(963\) | 735.072 | − | 191.555i | 0.763314 | − | 0.198915i | ||||
\(964\) | −93.1308 | − | 161.307i | −0.0966087 | − | 0.167331i | ||||
\(965\) | −534.828 | + | 308.783i | −0.554225 | + | 0.319982i | ||||
\(966\) | 396.394 | − | 308.656i | 0.410346 | − | 0.319520i | ||||
\(967\) | 194.448 | − | 336.793i | 0.201083 | − | 0.348287i | −0.747794 | − | 0.663930i | \(-0.768887\pi\) |
0.948878 | + | 0.315644i | \(0.102220\pi\) | |||||||
\(968\) | − | 540.999i | − | 0.558883i | ||||||
\(969\) | 338.700 | + | 45.7756i | 0.349535 | + | 0.0472401i | ||||
\(970\) | −508.909 | −0.524649 | ||||||||
\(971\) | 503.065 | − | 290.445i | 0.518090 | − | 0.299119i | −0.218063 | − | 0.975935i | \(-0.569974\pi\) |
0.736153 | + | 0.676815i | \(0.236641\pi\) | |||||||
\(972\) | 560.865 | + | 83.6692i | 0.577022 | + | 0.0860794i | ||||
\(973\) | 251.770 | + | 246.522i | 0.258756 | + | 0.253362i | ||||
\(974\) | 136.366 | − | 78.7310i | 0.140006 | − | 0.0808326i | ||||
\(975\) | 65.6726 | + | 50.7520i | 0.0673566 | + | 0.0520533i | ||||
\(976\) | −39.9264 | − | 69.1545i | −0.0409081 | − | 0.0708550i | ||||
\(977\) | 165.895 | − | 95.7795i | 0.169800 | − | 0.0980343i | −0.412691 | − | 0.910871i | \(-0.635411\pi\) |
0.582492 | + | 0.812837i | \(0.302078\pi\) | |||||||
\(978\) | −738.540 | − | 99.8144i | −0.755153 | − | 0.102060i | ||||
\(979\) | −108.417 | − | 187.784i | −0.110743 | − | 0.191812i | ||||
\(980\) | −552.904 | + | 11.6482i | −0.564188 | + | 0.0118860i | ||||
\(981\) | 240.608 | − | 237.322i | 0.245268 | − | 0.241919i | ||||
\(982\) | 90.2258 | + | 156.276i | 0.0918797 | + | 0.159140i | ||||
\(983\) | 1317.45i | 1.34024i | 0.742254 | + | 0.670119i | \(0.233757\pi\) | ||||
−0.742254 | + | 0.670119i | \(0.766243\pi\) | |||||||
\(984\) | −413.654 | − | 319.673i | −0.420380 | − | 0.324871i | ||||
\(985\) | −0.569426 | −0.000578098 | ||||||||
\(986\) | 192.776 | + | 111.299i | 0.195513 | + | 0.112879i | ||||
\(987\) | −766.126 | − | 983.902i | −0.776217 | − | 0.996862i | ||||
\(988\) | 278.026 | + | 481.555i | 0.281403 | + | 0.487403i | ||||
\(989\) | 584.158 | − | 337.264i | 0.590655 | − | 0.341015i | ||||
\(990\) | −539.812 | − | 547.286i | −0.545265 | − | 0.552814i | ||||
\(991\) | 711.008 | − | 1231.50i | 0.717465 | − | 1.24269i | −0.244536 | − | 0.969640i | \(-0.578636\pi\) |
0.962001 | − | 0.273046i | \(-0.0880310\pi\) | |||||||
\(992\) | 1389.87 | + | 802.441i | 1.40108 | + | 0.808912i | ||||
\(993\) | −347.510 | − | 268.557i | −0.349960 | − | 0.270450i | ||||
\(994\) | 92.0713 | + | 90.1520i | 0.0926270 | + | 0.0906962i | ||||
\(995\) | 447.321 | + | 258.261i | 0.449569 | + | 0.259559i | ||||
\(996\) | 57.3442 | − | 74.2029i | 0.0575745 | − | 0.0745009i | ||||
\(997\) | 1178.44 | 1.18198 | 0.590991 | − | 0.806678i | \(-0.298737\pi\) | ||||
0.590991 | + | 0.806678i | \(0.298737\pi\) | |||||||
\(998\) | 254.274 | + | 146.805i | 0.254784 | + | 0.147099i | ||||
\(999\) | 742.448 | − | 89.9665i | 0.743191 | − | 0.0900565i |
(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 | 63.3.n.b.32.5 | yes | 22 | |
3.2 | odd | 2 | 189.3.n.b.179.7 | 22 | |||
7.2 | even | 3 | 63.3.j.b.23.7 | yes | 22 | ||
7.3 | odd | 6 | 441.3.r.f.50.7 | 22 | |||
7.4 | even | 3 | 441.3.r.g.50.7 | 22 | |||
7.5 | odd | 6 | 441.3.j.f.275.7 | 22 | |||
7.6 | odd | 2 | 441.3.n.f.410.5 | 22 | |||
9.2 | odd | 6 | 63.3.j.b.11.5 | ✓ | 22 | ||
9.7 | even | 3 | 189.3.j.b.116.7 | 22 | |||
21.2 | odd | 6 | 189.3.j.b.44.5 | 22 | |||
63.2 | odd | 6 | inner | 63.3.n.b.2.5 | yes | 22 | |
63.11 | odd | 6 | 441.3.r.g.344.7 | 22 | |||
63.16 | even | 3 | 189.3.n.b.170.7 | 22 | |||
63.20 | even | 6 | 441.3.j.f.263.5 | 22 | |||
63.38 | even | 6 | 441.3.r.f.344.7 | 22 | |||
63.47 | even | 6 | 441.3.n.f.128.5 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.3.j.b.11.5 | ✓ | 22 | 9.2 | odd | 6 | ||
63.3.j.b.23.7 | yes | 22 | 7.2 | even | 3 | ||
63.3.n.b.2.5 | yes | 22 | 63.2 | odd | 6 | inner | |
63.3.n.b.32.5 | yes | 22 | 1.1 | even | 1 | trivial | |
189.3.j.b.44.5 | 22 | 21.2 | odd | 6 | |||
189.3.j.b.116.7 | 22 | 9.7 | even | 3 | |||
189.3.n.b.170.7 | 22 | 63.16 | even | 3 | |||
189.3.n.b.179.7 | 22 | 3.2 | odd | 2 | |||
441.3.j.f.263.5 | 22 | 63.20 | even | 6 | |||
441.3.j.f.275.7 | 22 | 7.5 | odd | 6 | |||
441.3.n.f.128.5 | 22 | 63.47 | even | 6 | |||
441.3.n.f.410.5 | 22 | 7.6 | odd | 2 | |||
441.3.r.f.50.7 | 22 | 7.3 | odd | 6 | |||
441.3.r.f.344.7 | 22 | 63.38 | even | 6 | |||
441.3.r.g.50.7 | 22 | 7.4 | even | 3 | |||
441.3.r.g.344.7 | 22 | 63.11 | odd | 6 |