Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [121,3,Mod(40,121)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(121, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("121.40");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 121 = 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 121.d (of order \(10\), degree \(4\), not 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: | \(3.29701119876\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.64000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 112.2 | ||
Root | \(1.34500 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 121.112 |
Dual form | 121.3.d.e.94.2 |
$q$-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 \(\left(\mathbb{Z}/121\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34500 | + | 0.437016i | 0.672499 | + | 0.218508i | 0.625308 | − | 0.780378i | \(-0.284973\pi\) |
0.0471903 | + | 0.998886i | \(0.484973\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.269672 | − | 0.195928i | −0.444728 | − | 0.895666i | \(-0.646700\pi\) |
0.714400 | + | 0.699737i | \(0.246700\pi\) | |||||||
\(4\) | −1.61803 | − | 1.17557i | −0.404508 | − | 0.293893i | ||||
\(5\) | −2.16312 | − | 6.65740i | −0.432624 | − | 1.33148i | −0.895502 | − | 0.445057i | \(-0.853183\pi\) |
0.462878 | − | 0.886422i | \(-0.346817\pi\) | |||||||
\(6\) | 1.34500 | − | 0.437016i | 0.224166 | − | 0.0728360i | ||||
\(7\) | 4.15627 | − | 5.72061i | 0.593753 | − | 0.817231i | −0.401366 | − | 0.915918i | \(-0.631464\pi\) |
0.995118 | + | 0.0986873i | \(0.0314644\pi\) | |||||||
\(8\) | −4.98752 | − | 6.86474i | −0.623440 | − | 0.858092i | ||||
\(9\) | −2.47214 | + | 7.60845i | −0.274682 | + | 0.845384i | ||||
\(10\) | − | 9.89949i | − | 0.989949i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.00000 | −0.166667 | ||||||||
\(13\) | 16.1400 | + | 5.24419i | 1.24154 | + | 0.403399i | 0.854881 | − | 0.518825i | \(-0.173630\pi\) |
0.386655 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(14\) | 8.09017 | − | 5.87785i | 0.577869 | − | 0.419847i | ||||
\(15\) | −5.66312 | − | 4.11450i | −0.377541 | − | 0.274300i | ||||
\(16\) | −1.23607 | − | 3.80423i | −0.0772542 | − | 0.237764i | ||||
\(17\) | 4.03499 | − | 1.31105i | 0.237352 | − | 0.0771205i | −0.187926 | − | 0.982183i | \(-0.560176\pi\) |
0.425278 | + | 0.905063i | \(0.360176\pi\) | |||||||
\(18\) | −6.65003 | + | 9.15298i | −0.369446 | + | 0.508499i | ||||
\(19\) | 9.97505 | + | 13.7295i | 0.525002 | + | 0.722604i | 0.986359 | − | 0.164611i | \(-0.0526369\pi\) |
−0.461356 | + | 0.887215i | \(0.652637\pi\) | |||||||
\(20\) | −4.32624 | + | 13.3148i | −0.216312 | + | 0.665740i | ||||
\(21\) | − | 7.07107i | − | 0.336718i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.00000 | −0.391304 | −0.195652 | − | 0.980673i | \(-0.562682\pi\) | ||||
−0.195652 | + | 0.980673i | \(0.562682\pi\) | |||||||
\(24\) | −8.06998 | − | 2.62210i | −0.336249 | − | 0.109254i | ||||
\(25\) | −19.4164 | + | 14.1068i | −0.776656 | + | 0.564274i | ||||
\(26\) | 19.4164 | + | 14.1068i | 0.746785 | + | 0.542571i | ||||
\(27\) | 5.25329 | + | 16.1680i | 0.194566 | + | 0.598813i | ||||
\(28\) | −13.4500 | + | 4.37016i | −0.480356 | + | 0.156077i | ||||
\(29\) | 13.3001 | − | 18.3060i | 0.458623 | − | 0.631240i | −0.515600 | − | 0.856830i | \(-0.672431\pi\) |
0.974222 | + | 0.225589i | \(0.0724308\pi\) | |||||||
\(30\) | −5.81878 | − | 8.00886i | −0.193959 | − | 0.266962i | ||||
\(31\) | 15.1418 | − | 46.6018i | 0.488446 | − | 1.50328i | −0.338481 | − | 0.940973i | \(-0.609913\pi\) |
0.826927 | − | 0.562310i | \(-0.190087\pi\) | |||||||
\(32\) | 28.2843i | 0.883883i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | 0.176471 | ||||||||
\(35\) | −47.0749 | − | 15.2956i | −1.34500 | − | 0.437016i | ||||
\(36\) | 12.9443 | − | 9.40456i | 0.359563 | − | 0.261238i | ||||
\(37\) | −13.7533 | − | 9.99235i | −0.371711 | − | 0.270063i | 0.386209 | − | 0.922411i | \(-0.373784\pi\) |
−0.757920 | + | 0.652348i | \(0.773784\pi\) | |||||||
\(38\) | 7.41641 | + | 22.8254i | 0.195169 | + | 0.600667i | ||||
\(39\) | 16.1400 | − | 5.24419i | 0.413845 | − | 0.134466i | ||||
\(40\) | −34.9127 | + | 48.0532i | −0.872817 | + | 1.20133i | ||||
\(41\) | 9.97505 | + | 13.7295i | 0.243294 | + | 0.334865i | 0.913149 | − | 0.407627i | \(-0.133644\pi\) |
−0.669855 | + | 0.742492i | \(0.733644\pi\) | |||||||
\(42\) | 3.09017 | − | 9.51057i | 0.0735755 | − | 0.226442i | ||||
\(43\) | 46.6690i | 1.08533i | 0.839950 | + | 0.542663i | \(0.182584\pi\) | ||||
−0.839950 | + | 0.542663i | \(0.817416\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 56.0000 | 1.24444 | ||||||||
\(46\) | −12.1050 | − | 3.93314i | −0.263152 | − | 0.0855031i | ||||
\(47\) | −25.8885 | + | 18.8091i | −0.550820 | + | 0.400194i | −0.828088 | − | 0.560598i | \(-0.810571\pi\) |
0.277268 | + | 0.960793i | \(0.410571\pi\) | |||||||
\(48\) | −3.23607 | − | 2.35114i | −0.0674181 | − | 0.0489821i | ||||
\(49\) | −0.309017 | − | 0.951057i | −0.00630647 | − | 0.0194093i | ||||
\(50\) | −32.2799 | + | 10.4884i | −0.645599 | + | 0.209768i | ||||
\(51\) | 2.49376 | − | 3.43237i | 0.0488973 | − | 0.0673013i | ||||
\(52\) | −19.9501 | − | 27.4589i | −0.383656 | − | 0.528057i | ||||
\(53\) | 4.94427 | − | 15.2169i | 0.0932881 | − | 0.287111i | −0.893516 | − | 0.449032i | \(-0.851769\pi\) |
0.986804 | + | 0.161921i | \(0.0517689\pi\) | |||||||
\(54\) | 24.0416i | 0.445215i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −60.0000 | −1.07143 | ||||||||
\(57\) | 16.1400 | + | 5.24419i | 0.283157 | + | 0.0920034i | ||||
\(58\) | 25.8885 | − | 18.8091i | 0.446354 | − | 0.324295i | ||||
\(59\) | 57.4402 | + | 41.7328i | 0.973563 | + | 0.707335i | 0.956261 | − | 0.292516i | \(-0.0944923\pi\) |
0.0173020 | + | 0.999850i | \(0.494492\pi\) | |||||||
\(60\) | 4.32624 | + | 13.3148i | 0.0721040 | + | 0.221913i | ||||
\(61\) | −10.7600 | + | 3.49613i | −0.176393 | + | 0.0573136i | −0.395882 | − | 0.918301i | \(-0.629561\pi\) |
0.219489 | + | 0.975615i | \(0.429561\pi\) | |||||||
\(62\) | 40.7314 | − | 56.0620i | 0.656959 | − | 0.904226i | ||||
\(63\) | 33.2502 | + | 45.7649i | 0.527780 | + | 0.726427i | ||||
\(64\) | −17.3050 | + | 53.2592i | −0.270390 | + | 0.832174i | ||||
\(65\) | − | 118.794i | − | 1.82760i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −31.0000 | −0.462687 | −0.231343 | − | 0.972872i | \(-0.574312\pi\) | ||||
−0.231343 | + | 0.972872i | \(0.574312\pi\) | |||||||
\(68\) | −8.06998 | − | 2.62210i | −0.118676 | − | 0.0385602i | ||||
\(69\) | −7.28115 | + | 5.29007i | −0.105524 | + | 0.0766676i | ||||
\(70\) | −56.6312 | − | 41.1450i | −0.809017 | − | 0.587785i | ||||
\(71\) | −22.5582 | − | 69.4271i | −0.317722 | − | 0.977847i | −0.974620 | − | 0.223867i | \(-0.928132\pi\) |
0.656898 | − | 0.753980i | \(-0.271868\pi\) | |||||||
\(72\) | 64.5599 | − | 20.9768i | 0.896665 | − | 0.291344i | ||||
\(73\) | −23.2751 | + | 32.0354i | −0.318837 | + | 0.438842i | −0.938112 | − | 0.346333i | \(-0.887427\pi\) |
0.619275 | + | 0.785174i | \(0.287427\pi\) | |||||||
\(74\) | −14.1313 | − | 19.4501i | −0.190964 | − | 0.262839i | ||||
\(75\) | −7.41641 | + | 22.8254i | −0.0988854 | + | 0.304338i | ||||
\(76\) | − | 33.9411i | − | 0.446594i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 24.0000 | 0.307692 | ||||||||
\(79\) | 149.295 | + | 48.5088i | 1.88981 | + | 0.614035i | 0.979999 | + | 0.199004i | \(0.0637708\pi\) |
0.909807 | + | 0.415031i | \(0.136229\pi\) | |||||||
\(80\) | −22.6525 | + | 16.4580i | −0.283156 | + | 0.205725i | ||||
\(81\) | −44.4959 | − | 32.3282i | −0.549333 | − | 0.399113i | ||||
\(82\) | 7.41641 | + | 22.8254i | 0.0904440 | + | 0.278358i | ||||
\(83\) | 33.6249 | − | 10.9254i | 0.405120 | − | 0.131631i | −0.0993670 | − | 0.995051i | \(-0.531682\pi\) |
0.504487 | + | 0.863420i | \(0.331682\pi\) | |||||||
\(84\) | −8.31254 | + | 11.4412i | −0.0989588 | + | 0.136205i | ||||
\(85\) | −17.4563 | − | 24.0266i | −0.205369 | − | 0.282666i | ||||
\(86\) | −20.3951 | + | 62.7697i | −0.237153 | + | 0.729881i | ||||
\(87\) | − | 22.6274i | − | 0.260085i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.101124 | −0.0505618 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505618 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(90\) | 75.3198 | + | 24.4729i | 0.836887 | + | 0.271921i | ||||
\(91\) | 97.0820 | − | 70.5342i | 1.06684 | − | 0.775101i | ||||
\(92\) | 14.5623 | + | 10.5801i | 0.158286 | + | 0.115001i | ||||
\(93\) | −15.1418 | − | 46.6018i | −0.162815 | − | 0.501094i | ||||
\(94\) | −43.0399 | + | 13.9845i | −0.457871 | + | 0.148771i | ||||
\(95\) | 69.8253 | − | 96.1063i | 0.735003 | − | 1.01165i | ||||
\(96\) | 16.6251 | + | 22.8825i | 0.173178 | + | 0.238359i | ||||
\(97\) | −5.25329 | + | 16.1680i | −0.0541576 | + | 0.166680i | −0.974477 | − | 0.224488i | \(-0.927929\pi\) |
0.920319 | + | 0.391168i | \(0.127929\pi\) | |||||||
\(98\) | − | 1.41421i | − | 0.0144308i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 48.0000 | 0.480000 | ||||||||
\(101\) | −146.605 | − | 47.6347i | −1.45153 | − | 0.471631i | −0.526060 | − | 0.850448i | \(-0.676331\pi\) |
−0.925472 | + | 0.378817i | \(0.876331\pi\) | |||||||
\(102\) | 4.85410 | − | 3.52671i | 0.0475892 | − | 0.0345756i | ||||
\(103\) | 12.9443 | + | 9.40456i | 0.125673 | + | 0.0913064i | 0.648846 | − | 0.760920i | \(-0.275252\pi\) |
−0.523173 | + | 0.852226i | \(0.675252\pi\) | |||||||
\(104\) | −44.4984 | − | 136.952i | −0.427870 | − | 1.31685i | ||||
\(105\) | −47.0749 | + | 15.2956i | −0.448332 | + | 0.145672i | ||||
\(106\) | 13.3001 | − | 18.3060i | 0.125472 | − | 0.172698i | ||||
\(107\) | −108.894 | − | 149.880i | −1.01770 | − | 1.40075i | −0.913802 | − | 0.406161i | \(-0.866867\pi\) |
−0.103902 | − | 0.994588i | \(-0.533133\pi\) | |||||||
\(108\) | 10.5066 | − | 32.3359i | 0.0972831 | − | 0.299407i | ||||
\(109\) | 46.6690i | 0.428156i | 0.976817 | + | 0.214078i | \(0.0686747\pi\) | ||||
−0.976817 | + | 0.214078i | \(0.931325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.0000 | −0.153153 | ||||||||
\(112\) | −26.8999 | − | 8.74032i | −0.240178 | − | 0.0780386i | ||||
\(113\) | −52.5861 | + | 38.2060i | −0.465364 | + | 0.338107i | −0.795632 | − | 0.605781i | \(-0.792861\pi\) |
0.330268 | + | 0.943887i | \(0.392861\pi\) | |||||||
\(114\) | 19.4164 | + | 14.1068i | 0.170319 | + | 0.123744i | ||||
\(115\) | 19.4681 | + | 59.9166i | 0.169288 | + | 0.521014i | ||||
\(116\) | −43.0399 | + | 13.9845i | −0.371034 | + | 0.120556i | ||||
\(117\) | −79.8004 | + | 109.836i | −0.682054 | + | 0.938767i | ||||
\(118\) | 59.0190 | + | 81.2327i | 0.500161 | + | 0.688413i | ||||
\(119\) | 9.27051 | − | 28.5317i | 0.0779034 | − | 0.239762i | ||||
\(120\) | 59.3970i | 0.494975i | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −16.0000 | −0.131148 | ||||||||
\(123\) | 16.1400 | + | 5.24419i | 0.131219 | + | 0.0426357i | ||||
\(124\) | −79.2837 | + | 57.6030i | −0.639384 | + | 0.464540i | ||||
\(125\) | −5.66312 | − | 4.11450i | −0.0453050 | − | 0.0329160i | ||||
\(126\) | 24.7214 | + | 76.0845i | 0.196201 | + | 0.603845i | ||||
\(127\) | 166.780 | − | 54.1900i | 1.31323 | − | 0.426693i | 0.433062 | − | 0.901364i | \(-0.357433\pi\) |
0.880163 | + | 0.474671i | \(0.157433\pi\) | |||||||
\(128\) | 19.9501 | − | 27.4589i | 0.155860 | − | 0.214523i | ||||
\(129\) | 27.4314 | + | 37.7561i | 0.212646 | + | 0.292683i | ||||
\(130\) | 51.9149 | − | 159.777i | 0.399345 | − | 1.22906i | ||||
\(131\) | 140.007i | 1.06876i | 0.845245 | + | 0.534378i | \(0.179454\pi\) | ||||
−0.845245 | + | 0.534378i | \(0.820546\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 120.000 | 0.902256 | ||||||||
\(134\) | −41.6949 | − | 13.5475i | −0.311156 | − | 0.101101i | ||||
\(135\) | 96.2730 | − | 69.9464i | 0.713133 | − | 0.518122i | ||||
\(136\) | −29.1246 | − | 21.1603i | −0.214152 | − | 0.155590i | ||||
\(137\) | 79.4174 | + | 244.422i | 0.579689 | + | 1.78410i | 0.619627 | + | 0.784897i | \(0.287284\pi\) |
−0.0399380 | + | 0.999202i | \(0.512716\pi\) | |||||||
\(138\) | −12.1050 | + | 3.93314i | −0.0877172 | + | 0.0285010i | ||||
\(139\) | −50.7065 | + | 69.7915i | −0.364795 | + | 0.502097i | −0.951477 | − | 0.307720i | \(-0.900434\pi\) |
0.586682 | + | 0.809817i | \(0.300434\pi\) | |||||||
\(140\) | 58.1878 | + | 80.0886i | 0.415627 | + | 0.572061i | ||||
\(141\) | −9.88854 | + | 30.4338i | −0.0701315 | + | 0.215843i | ||||
\(142\) | − | 103.238i | − | 0.727025i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 32.0000 | 0.222222 | ||||||||
\(145\) | −150.640 | − | 48.9458i | −1.03889 | − | 0.337557i | ||||
\(146\) | −45.3050 | + | 32.9160i | −0.310308 | + | 0.225452i | ||||
\(147\) | −0.809017 | − | 0.587785i | −0.00550352 | − | 0.00399854i | ||||
\(148\) | 10.5066 | + | 32.3359i | 0.0709904 | + | 0.218486i | ||||
\(149\) | −262.274 | + | 85.2181i | −1.76023 | + | 0.571934i | −0.997224 | − | 0.0744568i | \(-0.976278\pi\) |
−0.763007 | + | 0.646391i | \(0.776278\pi\) | |||||||
\(150\) | −19.9501 | + | 27.4589i | −0.133001 | + | 0.183060i | ||||
\(151\) | 92.2692 | + | 126.998i | 0.611054 | + | 0.841044i | 0.996664 | − | 0.0816182i | \(-0.0260088\pi\) |
−0.385609 | + | 0.922662i | \(0.626009\pi\) | |||||||
\(152\) | 44.4984 | − | 136.952i | 0.292753 | − | 0.901001i | ||||
\(153\) | 33.9411i | 0.221837i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −343.000 | −2.21290 | ||||||||
\(156\) | −32.2799 | − | 10.4884i | −0.206923 | − | 0.0672332i | ||||
\(157\) | −141.578 | + | 102.862i | −0.901771 | + | 0.655175i | −0.938920 | − | 0.344135i | \(-0.888172\pi\) |
0.0371496 | + | 0.999310i | \(0.488172\pi\) | |||||||
\(158\) | 179.602 | + | 130.488i | 1.13672 | + | 0.825875i | ||||
\(159\) | −4.94427 | − | 15.2169i | −0.0310960 | − | 0.0957038i | ||||
\(160\) | 188.300 | − | 61.1822i | 1.17687 | − | 0.382389i | ||||
\(161\) | −37.4064 | + | 51.4855i | −0.232338 | + | 0.319786i | ||||
\(162\) | −45.7190 | − | 62.9268i | −0.282216 | − | 0.388437i | ||||
\(163\) | −49.4427 | + | 152.169i | −0.303330 | + | 0.933552i | 0.676966 | + | 0.736015i | \(0.263295\pi\) |
−0.980295 | + | 0.197538i | \(0.936705\pi\) | |||||||
\(164\) | − | 33.9411i | − | 0.206958i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 50.0000 | 0.301205 | ||||||||
\(167\) | 16.1400 | + | 5.24419i | 0.0966465 | + | 0.0314023i | 0.356941 | − | 0.934127i | \(-0.383820\pi\) |
−0.260295 | + | 0.965529i | \(0.583820\pi\) | |||||||
\(168\) | −48.5410 | + | 35.2671i | −0.288935 | + | 0.209923i | ||||
\(169\) | 96.2730 | + | 69.9464i | 0.569663 | + | 0.413884i | ||||
\(170\) | −12.9787 | − | 39.9444i | −0.0763454 | − | 0.234967i | ||||
\(171\) | −129.120 | + | 41.9535i | −0.755086 | + | 0.245342i | ||||
\(172\) | 54.8628 | − | 75.5121i | 0.318970 | − | 0.439024i | ||||
\(173\) | −72.3191 | − | 99.5387i | −0.418029 | − | 0.575368i | 0.547124 | − | 0.837051i | \(-0.315722\pi\) |
−0.965154 | + | 0.261683i | \(0.915722\pi\) | |||||||
\(174\) | 9.88854 | − | 30.4338i | 0.0568307 | − | 0.174907i | ||||
\(175\) | 169.706i | 0.969746i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 71.0000 | 0.401130 | ||||||||
\(178\) | −12.1050 | − | 3.93314i | −0.0680055 | − | 0.0220963i | ||||
\(179\) | 160.994 | − | 116.969i | 0.899410 | − | 0.653460i | −0.0389044 | − | 0.999243i | \(-0.512387\pi\) |
0.938314 | + | 0.345783i | \(0.112387\pi\) | |||||||
\(180\) | −90.6099 | − | 65.8319i | −0.503388 | − | 0.365733i | ||||
\(181\) | −22.5582 | − | 69.4271i | −0.124631 | − | 0.383575i | 0.869203 | − | 0.494456i | \(-0.164633\pi\) |
−0.993834 | + | 0.110881i | \(0.964633\pi\) | |||||||
\(182\) | 161.400 | − | 52.4419i | 0.886811 | − | 0.288142i | ||||
\(183\) | −6.65003 | + | 9.15298i | −0.0363390 | + | 0.0500163i | ||||
\(184\) | 44.8877 | + | 61.7826i | 0.243955 | + | 0.335775i | ||||
\(185\) | −36.7730 | + | 113.176i | −0.198773 | + | 0.611761i | ||||
\(186\) | − | 69.2965i | − | 0.372562i | ||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 64.0000 | 0.340426 | ||||||||
\(189\) | 114.325 | + | 37.1464i | 0.604893 | + | 0.196542i | ||||
\(190\) | 135.915 | − | 98.7479i | 0.715341 | − | 0.519726i | ||||
\(191\) | −173.939 | − | 126.374i | −0.910674 | − | 0.661643i | 0.0305116 | − | 0.999534i | \(-0.490286\pi\) |
−0.941185 | + | 0.337891i | \(0.890286\pi\) | |||||||
\(192\) | 17.3050 | + | 53.2592i | 0.0901300 | + | 0.277391i | ||||
\(193\) | −129.120 | + | 41.9535i | −0.669014 | + | 0.217376i | −0.623779 | − | 0.781601i | \(-0.714404\pi\) |
−0.0452348 | + | 0.998976i | \(0.514404\pi\) | |||||||
\(194\) | −14.1313 | + | 19.4501i | −0.0728418 | + | 0.100258i | ||||
\(195\) | −69.8253 | − | 96.1063i | −0.358079 | − | 0.492853i | ||||
\(196\) | −0.618034 | + | 1.90211i | −0.00315323 | + | 0.00970466i | ||||
\(197\) | − | 202.233i | − | 1.02656i | −0.858221 | − | 0.513281i | \(-0.828430\pi\) | ||
0.858221 | − | 0.513281i | \(-0.171570\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 200.000 | 1.00503 | 0.502513 | − | 0.864570i | \(-0.332409\pi\) | ||||
0.502513 | + | 0.864570i | \(0.332409\pi\) | |||||||
\(200\) | 193.680 | + | 62.9303i | 0.968398 | + | 0.314652i | ||||
\(201\) | −25.0795 | + | 18.2213i | −0.124774 | + | 0.0906534i | ||||
\(202\) | −176.366 | − | 128.137i | −0.873098 | − | 0.634342i | ||||
\(203\) | −49.4427 | − | 152.169i | −0.243560 | − | 0.749601i | ||||
\(204\) | −8.06998 | + | 2.62210i | −0.0395587 | + | 0.0128534i | ||||
\(205\) | 69.8253 | − | 96.1063i | 0.340611 | − | 0.468811i | ||||
\(206\) | 13.3001 | + | 18.3060i | 0.0645634 | + | 0.0888639i | ||||
\(207\) | 22.2492 | − | 68.4761i | 0.107484 | − | 0.330802i | ||||
\(208\) | − | 67.8823i | − | 0.326357i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −70.0000 | −0.333333 | ||||||||
\(211\) | 75.3198 | + | 24.4729i | 0.356966 | + | 0.115985i | 0.482010 | − | 0.876166i | \(-0.339907\pi\) |
−0.125044 | + | 0.992151i | \(0.539907\pi\) | |||||||
\(212\) | −25.8885 | + | 18.8091i | −0.122116 | + | 0.0887223i | ||||
\(213\) | −59.0582 | − | 42.9083i | −0.277269 | − | 0.201448i | ||||
\(214\) | −80.9625 | − | 249.177i | −0.378329 | − | 1.16438i | ||||
\(215\) | 310.694 | − | 100.951i | 1.44509 | − | 0.469538i | ||||
\(216\) | 84.7879 | − | 116.701i | 0.392537 | − | 0.540280i | ||||
\(217\) | −203.657 | − | 280.310i | −0.938512 | − | 1.29175i | ||||
\(218\) | −20.3951 | + | 62.7697i | −0.0935556 | + | 0.287935i | ||||
\(219\) | 39.5980i | 0.180813i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.0000 | 0.325792 | ||||||||
\(222\) | −22.8649 | − | 7.42927i | −0.102995 | − | 0.0334652i | ||||
\(223\) | 89.8009 | − | 65.2442i | 0.402695 | − | 0.292575i | −0.367943 | − | 0.929848i | \(-0.619938\pi\) |
0.770638 | + | 0.637274i | \(0.219938\pi\) | |||||||
\(224\) | 161.803 | + | 117.557i | 0.722337 | + | 0.524808i | ||||
\(225\) | −59.3313 | − | 182.603i | −0.263695 | − | 0.811568i | ||||
\(226\) | −87.4248 | + | 28.4060i | −0.386835 | + | 0.125690i | ||||
\(227\) | 77.3066 | − | 106.403i | 0.340558 | − | 0.468738i | −0.604046 | − | 0.796949i | \(-0.706446\pi\) |
0.944604 | + | 0.328212i | \(0.106446\pi\) | |||||||
\(228\) | −19.9501 | − | 27.4589i | −0.0875004 | − | 0.120434i | ||||
\(229\) | −93.6321 | + | 288.170i | −0.408874 | + | 1.25838i | 0.508743 | + | 0.860919i | \(0.330110\pi\) |
−0.917617 | + | 0.397466i | \(0.869890\pi\) | |||||||
\(230\) | 89.0955i | 0.387372i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −192.000 | −0.827586 | ||||||||
\(233\) | 75.3198 | + | 24.4729i | 0.323261 | + | 0.105034i | 0.466152 | − | 0.884705i | \(-0.345640\pi\) |
−0.142891 | + | 0.989738i | \(0.545640\pi\) | |||||||
\(234\) | −155.331 | + | 112.855i | −0.663809 | + | 0.482285i | ||||
\(235\) | 181.220 | + | 131.664i | 0.771148 | + | 0.560272i | ||||
\(236\) | −43.8804 | − | 135.050i | −0.185934 | − | 0.572246i | ||||
\(237\) | 149.295 | − | 48.5088i | 0.629935 | − | 0.204678i | ||||
\(238\) | 24.9376 | − | 34.3237i | 0.104780 | − | 0.144217i | ||||
\(239\) | 165.420 | + | 227.680i | 0.692132 | + | 0.952638i | 0.999999 | + | 0.00120854i | \(0.000384689\pi\) |
−0.307867 | + | 0.951429i | \(0.599615\pi\) | |||||||
\(240\) | −8.65248 | + | 26.6296i | −0.0360520 | + | 0.110957i | ||||
\(241\) | − | 373.352i | − | 1.54918i | −0.632464 | − | 0.774590i | \(-0.717956\pi\) | ||
0.632464 | − | 0.774590i | \(-0.282044\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −208.000 | −0.855967 | ||||||||
\(244\) | 21.5200 | + | 6.99226i | 0.0881965 | + | 0.0286568i | ||||
\(245\) | −5.66312 | + | 4.11450i | −0.0231148 | + | 0.0167939i | ||||
\(246\) | 19.4164 | + | 14.1068i | 0.0789285 | + | 0.0573449i | ||||
\(247\) | 88.9969 | + | 273.904i | 0.360311 | + | 1.10892i | ||||
\(248\) | −395.429 | + | 128.483i | −1.59447 | + | 0.518075i | ||||
\(249\) | 20.7813 | − | 28.6031i | 0.0834592 | − | 0.114872i | ||||
\(250\) | −5.81878 | − | 8.00886i | −0.0232751 | − | 0.0320354i | ||||
\(251\) | 69.5288 | − | 213.988i | 0.277007 | − | 0.852541i | −0.711674 | − | 0.702510i | \(-0.752063\pi\) |
0.988681 | − | 0.150031i | \(-0.0479373\pi\) | |||||||
\(252\) | − | 113.137i | − | 0.448957i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 248.000 | 0.976378 | ||||||||
\(255\) | −28.2449 | − | 9.17734i | −0.110764 | − | 0.0359896i | ||||
\(256\) | 220.053 | − | 159.878i | 0.859581 | − | 0.624522i | ||||
\(257\) | −343.023 | − | 249.221i | −1.33472 | − | 0.969731i | −0.999620 | − | 0.0275488i | \(-0.991230\pi\) |
−0.335100 | − | 0.942183i | \(-0.608770\pi\) | |||||||
\(258\) | 20.3951 | + | 62.7697i | 0.0790509 | + | 0.243294i | ||||
\(259\) | −114.325 | + | 37.1464i | −0.441408 | + | 0.143422i | ||||
\(260\) | −139.651 | + | 192.213i | −0.537118 | + | 0.739279i | ||||
\(261\) | 106.400 | + | 146.448i | 0.407665 | + | 0.561102i | ||||
\(262\) | −61.1854 | + | 188.309i | −0.233532 | + | 0.718737i | ||||
\(263\) | 140.007i | 0.532347i | 0.963925 | + | 0.266173i | \(0.0857593\pi\) | ||||
−0.963925 | + | 0.266173i | \(0.914241\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −112.000 | −0.422642 | ||||||||
\(266\) | 161.400 | + | 52.4419i | 0.606766 | + | 0.197150i | ||||
\(267\) | −7.28115 | + | 5.29007i | −0.0272702 | + | 0.0198130i | ||||
\(268\) | 50.1591 | + | 36.4427i | 0.187161 | + | 0.135980i | ||||
\(269\) | 42.0263 | + | 129.344i | 0.156232 | + | 0.480832i | 0.998284 | − | 0.0585649i | \(-0.0186524\pi\) |
−0.842052 | + | 0.539396i | \(0.818652\pi\) | |||||||
\(270\) | 160.055 | − | 52.0049i | 0.592795 | − | 0.192611i | ||||
\(271\) | −169.576 | + | 233.401i | −0.625741 | + | 0.861258i | −0.997755 | − | 0.0669686i | \(-0.978667\pi\) |
0.372014 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(272\) | −9.97505 | − | 13.7295i | −0.0366730 | − | 0.0504760i | ||||
\(273\) | 37.0820 | − | 114.127i | 0.135832 | − | 0.418047i | ||||
\(274\) | 363.453i | 1.32647i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 18.0000 | 0.0652174 | ||||||||
\(277\) | −117.015 | − | 38.0204i | −0.422436 | − | 0.137258i | 0.0900819 | − | 0.995934i | \(-0.471287\pi\) |
−0.512518 | + | 0.858677i | \(0.671287\pi\) | |||||||
\(278\) | −98.7001 | + | 71.7098i | −0.355036 | + | 0.257949i | ||||
\(279\) | 317.135 | + | 230.412i | 1.13668 | + | 0.825849i | ||||
\(280\) | 129.787 | + | 399.444i | 0.463525 | + | 1.42658i | ||||
\(281\) | 270.344 | − | 87.8402i | 0.962080 | − | 0.312599i | 0.214465 | − | 0.976732i | \(-0.431199\pi\) |
0.747614 | + | 0.664133i | \(0.231199\pi\) | |||||||
\(282\) | −26.6001 | + | 36.6119i | −0.0943267 | + | 0.129830i | ||||
\(283\) | 46.5502 | + | 64.0709i | 0.164488 | + | 0.226399i | 0.883302 | − | 0.468803i | \(-0.155315\pi\) |
−0.718814 | + | 0.695202i | \(0.755315\pi\) | |||||||
\(284\) | −45.1165 | + | 138.854i | −0.158861 | + | 0.488923i | ||||
\(285\) | − | 118.794i | − | 0.416821i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 120.000 | 0.418118 | ||||||||
\(288\) | −215.200 | − | 69.9226i | −0.747221 | − | 0.242787i | ||||
\(289\) | −219.244 | + | 159.290i | −0.758628 | + | 0.551176i | ||||
\(290\) | −181.220 | − | 131.664i | −0.624896 | − | 0.454013i | ||||
\(291\) | 5.25329 | + | 16.1680i | 0.0180525 | + | 0.0555600i | ||||
\(292\) | 75.3198 | − | 24.4729i | 0.257945 | − | 0.0838113i | ||||
\(293\) | −96.4254 | + | 132.718i | −0.329097 | + | 0.452963i | −0.941217 | − | 0.337801i | \(-0.890317\pi\) |
0.612120 | + | 0.790765i | \(0.290317\pi\) | |||||||
\(294\) | −0.831254 | − | 1.14412i | −0.00282739 | − | 0.00389157i | ||||
\(295\) | 153.581 | − | 472.675i | 0.520615 | − | 1.60229i | ||||
\(296\) | 144.250i | 0.487330i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −390.000 | −1.30872 | ||||||||
\(299\) | −145.260 | − | 47.1977i | −0.485818 | − | 0.157852i | ||||
\(300\) | 38.8328 | − | 28.2137i | 0.129443 | − | 0.0940456i | ||||
\(301\) | 266.976 | + | 193.969i | 0.886962 | + | 0.644416i | ||||
\(302\) | 68.6018 | + | 211.135i | 0.227158 | + | 0.699121i | ||||
\(303\) | −146.605 | + | 47.6347i | −0.483844 | + | 0.157210i | ||||
\(304\) | 39.9002 | − | 54.9179i | 0.131251 | − | 0.180651i | ||||
\(305\) | 46.5502 | + | 64.0709i | 0.152624 | + | 0.210068i | ||||
\(306\) | −14.8328 | + | 45.6507i | −0.0484733 | + | 0.149185i | ||||
\(307\) | 186.676i | 0.608066i | 0.952662 | + | 0.304033i | \(0.0983333\pi\) | ||||
−0.952662 | + | 0.304033i | \(0.901667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.0000 | 0.0517799 | ||||||||
\(310\) | −461.334 | − | 149.896i | −1.48817 | − | 0.483537i | ||||
\(311\) | −114.880 | + | 83.4655i | −0.369390 | + | 0.268378i | −0.756958 | − | 0.653463i | \(-0.773315\pi\) |
0.387568 | + | 0.921841i | \(0.373315\pi\) | |||||||
\(312\) | −116.498 | − | 84.6411i | −0.373392 | − | 0.271286i | ||||
\(313\) | −138.131 | − | 425.122i | −0.441312 | − | 1.35822i | −0.886478 | − | 0.462770i | \(-0.846855\pi\) |
0.445166 | − | 0.895448i | \(-0.353145\pi\) | |||||||
\(314\) | −235.374 | + | 76.4778i | −0.749600 | + | 0.243560i | ||||
\(315\) | 232.751 | − | 320.354i | 0.738892 | − | 1.01700i | ||||
\(316\) | −184.538 | − | 253.995i | −0.583982 | − | 0.803782i | ||||
\(317\) | 130.714 | − | 402.297i | 0.412348 | − | 1.26908i | −0.502254 | − | 0.864720i | \(-0.667496\pi\) |
0.914602 | − | 0.404355i | \(-0.132504\pi\) | |||||||
\(318\) | − | 22.6274i | − | 0.0711554i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 392.000 | 1.22500 | ||||||||
\(321\) | −176.195 | − | 57.2491i | −0.548893 | − | 0.178346i | ||||
\(322\) | −72.8115 | + | 52.9007i | −0.226123 | + | 0.164288i | ||||
\(323\) | 58.2492 | + | 42.3205i | 0.180338 | + | 0.131023i | ||||
\(324\) | 33.9919 | + | 104.616i | 0.104913 | + | 0.322890i | ||||
\(325\) | −387.359 | + | 125.861i | −1.19187 | + | 0.387263i | ||||
\(326\) | −133.001 | + | 183.060i | −0.407977 | + | 0.561533i | ||||
\(327\) | 27.4314 | + | 37.7561i | 0.0838880 | + | 0.115462i | ||||
\(328\) | 44.4984 | − | 136.952i | 0.135666 | − | 0.417537i | ||||
\(329\) | 226.274i | 0.687763i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 145.000 | 0.438066 | 0.219033 | − | 0.975717i | \(-0.429710\pi\) | ||||
0.219033 | + | 0.975717i | \(0.429710\pi\) | |||||||
\(332\) | −67.2499 | − | 21.8508i | −0.202560 | − | 0.0658157i | ||||
\(333\) | 110.026 | − | 79.9388i | 0.330409 | − | 0.240056i | ||||
\(334\) | 19.4164 | + | 14.1068i | 0.0581330 | + | 0.0422361i | ||||
\(335\) | 67.0567 | + | 206.379i | 0.200169 | + | 0.616058i | ||||
\(336\) | −26.8999 | + | 8.74032i | −0.0800593 | + | 0.0260129i | ||||
\(337\) | 150.457 | − | 207.086i | 0.446460 | − | 0.614499i | −0.525173 | − | 0.850996i | \(-0.675999\pi\) |
0.971632 | + | 0.236497i | \(0.0759992\pi\) | |||||||
\(338\) | 98.9192 | + | 136.151i | 0.292660 | + | 0.402812i | ||||
\(339\) | −20.0861 | + | 61.8187i | −0.0592510 | + | 0.182356i | ||||
\(340\) | 59.3970i | 0.174697i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −192.000 | −0.561404 | ||||||||
\(343\) | 322.799 | + | 104.884i | 0.941106 | + | 0.305784i | ||||
\(344\) | 320.371 | − | 232.763i | 0.931310 | − | 0.676637i | ||||
\(345\) | 50.9681 | + | 37.0305i | 0.147734 | + | 0.107335i | ||||
\(346\) | −53.7690 | − | 165.484i | −0.155402 | − | 0.478277i | ||||
\(347\) | 521.859 | − | 169.562i | 1.50392 | − | 0.488652i | 0.562759 | − | 0.826621i | \(-0.309740\pi\) |
0.941157 | + | 0.337969i | \(0.109740\pi\) | |||||||
\(348\) | −26.6001 | + | 36.6119i | −0.0764371 | + | 0.105207i | ||||
\(349\) | 256.857 | + | 353.534i | 0.735981 | + | 1.01299i | 0.998840 | + | 0.0481569i | \(0.0153347\pi\) |
−0.262859 | + | 0.964834i | \(0.584665\pi\) | |||||||
\(350\) | −74.1641 | + | 228.254i | −0.211897 | + | 0.652153i | ||||
\(351\) | 288.500i | 0.821936i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 585.000 | 1.65722 | 0.828612 | − | 0.559823i | \(-0.189131\pi\) | ||||
0.828612 | + | 0.559823i | \(0.189131\pi\) | |||||||
\(354\) | 95.4948 | + | 31.0281i | 0.269759 | + | 0.0876501i | ||||
\(355\) | −413.408 | + | 300.358i | −1.16453 | + | 0.846080i | ||||
\(356\) | 14.5623 | + | 10.5801i | 0.0409054 | + | 0.0297195i | ||||
\(357\) | −9.27051 | − | 28.5317i | −0.0259678 | − | 0.0799207i | ||||
\(358\) | 267.654 | − | 86.9662i | 0.747638 | − | 0.242922i | ||||
\(359\) | −242.726 | + | 334.084i | −0.676117 | + | 0.930596i | −0.999879 | − | 0.0155429i | \(-0.995052\pi\) |
0.323762 | + | 0.946139i | \(0.395052\pi\) | |||||||
\(360\) | −279.301 | − | 384.425i | −0.775837 | − | 1.06785i | ||||
\(361\) | 22.5582 | − | 69.4271i | 0.0624882 | − | 0.192319i | ||||
\(362\) | − | 103.238i | − | 0.285187i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −240.000 | −0.659341 | ||||||||
\(365\) | 263.619 | + | 85.6551i | 0.722245 | + | 0.234672i | ||||
\(366\) | −12.9443 | + | 9.40456i | −0.0353669 | + | 0.0256955i | ||||
\(367\) | −440.914 | − | 320.343i | −1.20140 | − | 0.872869i | −0.206979 | − | 0.978345i | \(-0.566363\pi\) |
−0.994422 | + | 0.105476i | \(0.966363\pi\) | |||||||
\(368\) | 11.1246 | + | 34.2380i | 0.0302299 | + | 0.0930381i | ||||
\(369\) | −129.120 | + | 41.9535i | −0.349918 | + | 0.113695i | ||||
\(370\) | −98.9192 | + | 136.151i | −0.267349 | + | 0.367975i | ||||
\(371\) | −66.5003 | − | 91.5298i | −0.179246 | − | 0.246711i | ||||
\(372\) | −30.2837 | + | 93.2035i | −0.0814077 | + | 0.250547i | ||||
\(373\) | − | 233.345i | − | 0.625590i | −0.949821 | − | 0.312795i | \(-0.898735\pi\) | ||
0.949821 | − | 0.312795i | \(-0.101265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.00000 | −0.0186667 | ||||||||
\(376\) | 258.239 | + | 83.9071i | 0.686807 | + | 0.223157i | ||||
\(377\) | 310.663 | − | 225.710i | 0.824039 | − | 0.598699i | ||||
\(378\) | 137.533 | + | 99.9235i | 0.363844 | + | 0.264348i | ||||
\(379\) | −138.131 | − | 425.122i | −0.364461 | − | 1.12169i | −0.950318 | − | 0.311280i | \(-0.899242\pi\) |
0.585857 | − | 0.810414i | \(-0.300758\pi\) | |||||||
\(380\) | −225.960 | + | 73.4187i | −0.594630 | + | 0.193207i | ||||
\(381\) | 103.075 | − | 141.871i | 0.270539 | − | 0.372365i | ||||
\(382\) | −178.720 | − | 245.986i | −0.467852 | − | 0.643943i | ||||
\(383\) | −168.414 | + | 518.326i | −0.439724 | + | 1.35333i | 0.448444 | + | 0.893811i | \(0.351979\pi\) |
−0.888167 | + | 0.459520i | \(0.848021\pi\) | |||||||
\(384\) | − | 33.9411i | − | 0.0883883i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −192.000 | −0.497409 | ||||||||
\(387\) | −355.079 | − | 115.372i | −0.917517 | − | 0.298119i | ||||
\(388\) | 27.5066 | − | 19.9847i | 0.0708932 | − | 0.0515070i | ||||
\(389\) | −173.939 | − | 126.374i | −0.447143 | − | 0.324868i | 0.341324 | − | 0.939946i | \(-0.389125\pi\) |
−0.788467 | + | 0.615077i | \(0.789125\pi\) | |||||||
\(390\) | −51.9149 | − | 159.777i | −0.133115 | − | 0.409686i | ||||
\(391\) | −36.3149 | + | 11.7994i | −0.0928770 | + | 0.0301776i | ||||
\(392\) | −4.98752 | + | 6.86474i | −0.0127233 | + | 0.0175121i | ||||
\(393\) | 82.2941 | + | 113.268i | 0.209400 | + | 0.288214i | ||||
\(394\) | 88.3789 | − | 272.002i | 0.224312 | − | 0.690361i | ||||
\(395\) | − | 1098.84i | − | 2.78188i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −592.000 | −1.49118 | −0.745592 | − | 0.666403i | \(-0.767833\pi\) | ||||
−0.745592 | + | 0.666403i | \(0.767833\pi\) | |||||||
\(398\) | 268.999 | + | 87.4032i | 0.675878 | + | 0.219606i | ||||
\(399\) | 97.0820 | − | 70.5342i | 0.243313 | − | 0.176778i | ||||
\(400\) | 77.6656 | + | 56.4274i | 0.194164 | + | 0.141068i | ||||
\(401\) | 150.800 | + | 464.116i | 0.376061 | + | 1.15740i | 0.942760 | + | 0.333471i | \(0.108220\pi\) |
−0.566700 | + | 0.823924i | \(0.691780\pi\) | |||||||
\(402\) | −41.6949 | + | 13.5475i | −0.103719 | + | 0.0337002i | ||||
\(403\) | 488.777 | − | 672.744i | 1.21285 | − | 1.66934i | ||||
\(404\) | 181.213 | + | 249.419i | 0.448548 | + | 0.617373i | ||||
\(405\) | −118.972 | + | 366.157i | −0.293757 | + | 0.904091i | ||||
\(406\) | − | 226.274i | − | 0.557326i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −36.0000 | −0.0882353 | ||||||||
\(409\) | 149.295 | + | 48.5088i | 0.365024 | + | 0.118603i | 0.485785 | − | 0.874078i | \(-0.338534\pi\) |
−0.120762 | + | 0.992682i | \(0.538534\pi\) | |||||||
\(410\) | 135.915 | − | 98.7479i | 0.331500 | − | 0.240849i | ||||
\(411\) | 207.917 | + | 151.061i | 0.505882 | + | 0.367545i | ||||
\(412\) | −9.88854 | − | 30.4338i | −0.0240013 | − | 0.0738685i | ||||
\(413\) | 477.474 | − | 155.141i | 1.15611 | − | 0.375643i | ||||
\(414\) | 59.8503 | − | 82.3768i | 0.144566 | − | 0.198978i | ||||
\(415\) | −145.469 | − | 200.221i | −0.350529 | − | 0.482461i | ||||
\(416\) | −148.328 | + | 456.507i | −0.356558 | + | 1.09737i | ||||
\(417\) | 86.2670i | 0.206875i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −328.000 | −0.782816 | −0.391408 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391408 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(420\) | 94.1498 | + | 30.5911i | 0.224166 | + | 0.0728360i | ||||
\(421\) | −168.276 | + | 122.259i | −0.399704 | + | 0.290402i | −0.769421 | − | 0.638743i | \(-0.779455\pi\) |
0.369716 | + | 0.929145i | \(0.379455\pi\) | |||||||
\(422\) | 90.6099 | + | 65.8319i | 0.214715 | + | 0.156000i | ||||
\(423\) | −79.1084 | − | 243.470i | −0.187017 | − | 0.575580i | ||||
\(424\) | −129.120 | + | 41.9535i | −0.304528 | + | 0.0989470i | ||||
\(425\) | −59.8503 | + | 82.3768i | −0.140824 | + | 0.193828i | ||||
\(426\) | −60.6815 | − | 83.5210i | −0.142445 | − | 0.196059i | ||||
\(427\) | −24.7214 | + | 76.0845i | −0.0578955 | + | 0.178184i | ||||
\(428\) | 370.524i | 0.865710i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 462.000 | 1.07442 | ||||||||
\(431\) | 533.964 | + | 173.495i | 1.23890 | + | 0.402541i | 0.853929 | − | 0.520389i | \(-0.174213\pi\) |
0.384966 | + | 0.922931i | \(0.374213\pi\) | |||||||
\(432\) | 55.0132 | − | 39.9694i | 0.127345 | − | 0.0925218i | ||||
\(433\) | −31.5517 | − | 22.9236i | −0.0728676 | − | 0.0529414i | 0.550755 | − | 0.834667i | \(-0.314340\pi\) |
−0.623623 | + | 0.781725i | \(0.714340\pi\) | |||||||
\(434\) | −151.418 | − | 466.018i | −0.348890 | − | 1.07377i | ||||
\(435\) | −150.640 | + | 48.9458i | −0.346298 | + | 0.112519i | ||||
\(436\) | 54.8628 | − | 75.5121i | 0.125832 | − | 0.173193i | ||||
\(437\) | −89.7754 | − | 123.565i | −0.205436 | − | 0.282758i | ||||
\(438\) | −17.3050 | + | 53.2592i | −0.0395090 | + | 0.121596i | ||||
\(439\) | − | 248.902i | − | 0.566974i | −0.958976 | − | 0.283487i | \(-0.908509\pi\) | ||
0.958976 | − | 0.283487i | \(-0.0914913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.00000 | 0.0181406 | ||||||||
\(442\) | 96.8398 | + | 31.4652i | 0.219095 | + | 0.0711881i | ||||
\(443\) | −141.578 | + | 102.862i | −0.319589 | + | 0.232195i | −0.736000 | − | 0.676981i | \(-0.763288\pi\) |
0.416411 | + | 0.909176i | \(0.363288\pi\) | |||||||
\(444\) | 27.5066 | + | 19.9847i | 0.0619518 | + | 0.0450106i | ||||
\(445\) | 19.4681 | + | 59.9166i | 0.0437485 | + | 0.134644i | ||||
\(446\) | 149.295 | − | 48.5088i | 0.334741 | − | 0.108764i | ||||
\(447\) | −162.095 | + | 223.104i | −0.362628 | + | 0.499114i | ||||
\(448\) | 232.751 | + | 320.354i | 0.519534 | + | 0.715077i | ||||
\(449\) | 96.7223 | − | 297.681i | 0.215417 | − | 0.662986i | −0.783707 | − | 0.621131i | \(-0.786673\pi\) |
0.999124 | − | 0.0418546i | \(-0.0133266\pi\) | |||||||
\(450\) | − | 271.529i | − | 0.603398i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 130.000 | 0.287611 | ||||||||
\(453\) | 149.295 | + | 48.5088i | 0.329569 | + | 0.107083i | ||||
\(454\) | 150.477 | − | 109.328i | 0.331447 | − | 0.240811i | ||||
\(455\) | −679.574 | − | 493.740i | −1.49357 | − | 1.08514i | ||||
\(456\) | −44.4984 | − | 136.952i | −0.0975843 | − | 0.300334i | ||||
\(457\) | −10.7600 | + | 3.49613i | −0.0235448 | + | 0.00765017i | −0.320766 | − | 0.947159i | \(-0.603940\pi\) |
0.297221 | + | 0.954809i | \(0.403940\pi\) | |||||||
\(458\) | −251.870 | + | 346.669i | −0.549934 | + | 0.756920i | ||||
\(459\) | 42.3939 | + | 58.3503i | 0.0923615 | + | 0.127125i | ||||
\(460\) | 38.9361 | − | 119.833i | 0.0846438 | − | 0.260507i | ||||
\(461\) | 871.156i | 1.88971i | 0.327491 | + | 0.944854i | \(0.393797\pi\) | ||||
−0.327491 | + | 0.944854i | \(0.606203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 321.000 | 0.693305 | 0.346652 | − | 0.937994i | \(-0.387318\pi\) | ||||
0.346652 | + | 0.937994i | \(0.387318\pi\) | |||||||
\(464\) | −86.0798 | − | 27.9690i | −0.185517 | − | 0.0602781i | ||||
\(465\) | −277.493 | + | 201.610i | −0.596759 | + | 0.433571i | ||||
\(466\) | 90.6099 | + | 65.8319i | 0.194442 | + | 0.141270i | ||||
\(467\) | −49.7517 | − | 153.120i | −0.106535 | − | 0.327880i | 0.883553 | − | 0.468331i | \(-0.155145\pi\) |
−0.990088 | + | 0.140451i | \(0.955145\pi\) | |||||||
\(468\) | 258.239 | − | 83.9071i | 0.551794 | − | 0.179289i | ||||
\(469\) | −128.844 | + | 177.339i | −0.274721 | + | 0.378122i | ||||
\(470\) | 186.201 | + | 256.284i | 0.396172 | + | 0.545284i | ||||
\(471\) | −54.0780 | + | 166.435i | −0.114815 | + | 0.353365i | ||||
\(472\) | − | 602.455i | − | 1.27639i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 222.000 | 0.468354 | ||||||||
\(475\) | −387.359 | − | 125.861i | −0.815493 | − | 0.264970i | ||||
\(476\) | −48.5410 | + | 35.2671i | −0.101977 | + | 0.0740906i | ||||
\(477\) | 103.554 | + | 75.2365i | 0.217095 | + | 0.157729i | ||||
\(478\) | 122.989 | + | 378.520i | 0.257299 | + | 0.791884i | ||||
\(479\) | −425.019 | + | 138.097i | −0.887305 | + | 0.288303i | −0.716987 | − | 0.697086i | \(-0.754479\pi\) |
−0.170318 | + | 0.985389i | \(0.554479\pi\) | |||||||
\(480\) | 116.376 | − | 160.177i | 0.242449 | − | 0.333702i | ||||
\(481\) | −169.576 | − | 233.401i | −0.352548 | − | 0.485241i | ||||
\(482\) | 163.161 | − | 502.158i | 0.338508 | − | 1.04182i | ||||
\(483\) | 63.6396i | 0.131759i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 119.000 | 0.245361 | ||||||||
\(486\) | −279.759 | − | 90.8993i | −0.575637 | − | 0.187036i | ||||
\(487\) | 588.155 | − | 427.320i | 1.20771 | − | 0.877454i | 0.212690 | − | 0.977120i | \(-0.431777\pi\) |
0.995021 | + | 0.0996661i | \(0.0317775\pi\) | |||||||
\(488\) | 77.6656 | + | 56.4274i | 0.159151 | + | 0.115630i | ||||
\(489\) | 49.4427 | + | 152.169i | 0.101110 | + | 0.311184i | ||||
\(490\) | −9.41498 | + | 3.05911i | −0.0192142 | + | 0.00624309i | ||||
\(491\) | 305.901 | − | 421.037i | 0.623017 | − | 0.857510i | −0.374551 | − | 0.927206i | \(-0.622203\pi\) |
0.997568 | + | 0.0696967i | \(0.0222032\pi\) | |||||||
\(492\) | −19.9501 | − | 27.4589i | −0.0405490 | − | 0.0558109i | ||||
\(493\) | 29.6656 | − | 91.3014i | 0.0601737 | − | 0.185196i | ||||
\(494\) | 407.294i | 0.824481i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −196.000 | −0.395161 | ||||||||
\(497\) | −490.924 | − | 159.511i | −0.987774 | − | 0.320947i | ||||
\(498\) | 40.4508 | − | 29.3893i | 0.0812266 | − | 0.0590146i | ||||
\(499\) | 297.718 | + | 216.305i | 0.596630 | + | 0.433477i | 0.844681 | − | 0.535270i | \(-0.179790\pi\) |
−0.248051 | + | 0.968747i | \(0.579790\pi\) | |||||||
\(500\) | 4.32624 | + | 13.3148i | 0.00865248 | + | 0.0266296i | ||||
\(501\) | 16.1400 | − | 5.24419i | 0.0322155 | − | 0.0104674i | ||||
\(502\) | 187.032 | − | 257.428i | 0.372574 | − | 0.512804i | ||||
\(503\) | −273.483 | − | 376.416i | −0.543703 | − | 0.748343i | 0.445438 | − | 0.895313i | \(-0.353048\pi\) |
−0.989141 | + | 0.146970i | \(0.953048\pi\) | |||||||
\(504\) | 148.328 | − | 456.507i | 0.294302 | − | 0.905768i | ||||
\(505\) | 1079.04i | 2.13672i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 119.000 | 0.234714 | ||||||||
\(508\) | −333.559 | − | 108.380i | −0.656613 | − | 0.213346i | ||||
\(509\) | 89.8009 | − | 65.2442i | 0.176426 | − | 0.128181i | −0.496068 | − | 0.868284i | \(-0.665223\pi\) |
0.672494 | + | 0.740103i | \(0.265223\pi\) | |||||||
\(510\) | −33.9787 | − | 24.6870i | −0.0666249 | − | 0.0484058i | ||||
\(511\) | 86.5248 | + | 266.296i | 0.169324 | + | 0.521127i | ||||
\(512\) | 236.719 | − | 76.9148i | 0.462343 | − | 0.150224i | ||||
\(513\) | −169.576 | + | 233.401i | −0.330557 | + | 0.454973i | ||||
\(514\) | −352.452 | − | 485.108i | −0.685704 | − | 0.943790i | ||||
\(515\) | 34.6099 | − | 106.518i | 0.0672037 | − | 0.206832i | ||||
\(516\) | − | 93.3381i | − | 0.180888i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −170.000 | −0.328185 | ||||||||
\(519\) | −117.015 | − | 38.0204i | −0.225462 | − | 0.0732570i | ||||
\(520\) | −815.489 | + | 592.488i | −1.56825 | + | 1.13940i | ||||
\(521\) | 413.408 | + | 300.358i | 0.793489 | + | 0.576503i | 0.908997 | − | 0.416803i | \(-0.136850\pi\) |
−0.115508 | + | 0.993307i | \(0.536850\pi\) | |||||||
\(522\) | 79.1084 | + | 243.470i | 0.151549 | + | 0.466419i | ||||
\(523\) | −661.739 | + | 215.012i | −1.26527 | + | 0.411113i | −0.863371 | − | 0.504569i | \(-0.831651\pi\) |
−0.401903 | + | 0.915682i | \(0.631651\pi\) | |||||||
\(524\) | 164.588 | − | 226.536i | 0.314100 | − | 0.432321i | ||||
\(525\) | 99.7505 | + | 137.295i | 0.190001 | + | 0.261514i | ||||
\(526\) | −61.1854 | + | 188.309i | −0.116322 | + | 0.358002i | ||||
\(527\) | − | 207.889i | − | 0.394477i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −448.000 | −0.846881 | ||||||||
\(530\) | −150.640 | − | 48.9458i | −0.284226 | − | 0.0923506i | ||||
\(531\) | −459.522 | + | 333.862i | −0.865389 | + | 0.628742i | ||||
\(532\) | −194.164 | − | 141.068i | −0.364970 | − | 0.265166i | ||||
\(533\) | 88.9969 | + | 273.904i | 0.166974 | + | 0.513892i | ||||
\(534\) | −12.1050 | + | 3.93314i | −0.0226685 | + | 0.00736544i | ||||
\(535\) | −762.260 | + | 1049.16i | −1.42478 | + | 1.96105i | ||||
\(536\) | 154.613 | + | 212.807i | 0.288458 | + | 0.397028i | ||||
\(537\) | 61.4944 | − | 189.260i | 0.114515 | − | 0.352440i | ||||
\(538\) | 192.333i | 0.357496i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −238.000 | −0.440741 | ||||||||
\(541\) | −220.580 | − | 71.6706i | −0.407726 | − | 0.132478i | 0.0979715 | − | 0.995189i | \(-0.468765\pi\) |
−0.505697 | + | 0.862711i | \(0.668765\pi\) | |||||||
\(542\) | −330.079 | + | 239.816i | −0.609002 | + | 0.442466i | ||||
\(543\) | −59.0582 | − | 42.9083i | −0.108763 | − | 0.0790209i | ||||
\(544\) | 37.0820 | + | 114.127i | 0.0681655 | + | 0.209792i | ||||
\(545\) | 310.694 | − | 100.951i | 0.570081 | − | 0.185231i | ||||
\(546\) | 99.7505 | − | 137.295i | 0.182693 | − | 0.251456i | ||||
\(547\) | 412.302 | + | 567.485i | 0.753751 | + | 1.03745i | 0.997708 | + | 0.0676635i | \(0.0215544\pi\) |
−0.243957 | + | 0.969786i | \(0.578446\pi\) | |||||||
\(548\) | 158.835 | − | 488.843i | 0.289844 | − | 0.892049i | ||||
\(549\) | − | 90.5097i | − | 0.164863i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 384.000 | 0.696915 | ||||||||
\(552\) | 72.6298 | + | 23.5989i | 0.131576 | + | 0.0427516i | ||||
\(553\) | 898.009 | − | 652.442i | 1.62389 | − | 1.17982i | ||||
\(554\) | −140.769 | − | 102.275i | −0.254096 | − | 0.184611i | ||||
\(555\) | 36.7730 | + | 113.176i | 0.0662577 | + | 0.203920i | ||||
\(556\) | 164.090 | − | 53.3160i | 0.295125 | − | 0.0958920i | ||||
\(557\) | −123.857 | + | 170.474i | −0.222364 | + | 0.306058i | −0.905594 | − | 0.424145i | \(-0.860575\pi\) |
0.683230 | + | 0.730203i | \(0.260575\pi\) | |||||||
\(558\) | 325.852 | + | 448.496i | 0.583963 | + | 0.803757i | ||||
\(559\) | −244.741 | + | 753.237i | −0.437820 | + | 1.34747i | ||||
\(560\) | 197.990i | 0.353553i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 402.000 | 0.715302 | ||||||||
\(563\) | −516.479 | − | 167.814i | −0.917369 | − | 0.298071i | −0.187982 | − | 0.982172i | \(-0.560195\pi\) |
−0.729387 | + | 0.684101i | \(0.760195\pi\) | |||||||
\(564\) | 51.7771 | − | 37.6183i | 0.0918033 | − | 0.0666990i | ||||
\(565\) | 368.103 | + | 267.442i | 0.651509 | + | 0.473349i | ||||
\(566\) | 34.6099 | + | 106.518i | 0.0611482 | + | 0.188195i | ||||
\(567\) | −369.874 | + | 120.179i | −0.652335 | + | 0.211957i | ||||
\(568\) | −364.089 | + | 501.126i | −0.641002 | + | 0.882264i | ||||
\(569\) | 46.5502 | + | 64.0709i | 0.0818106 | + | 0.112603i | 0.847961 | − | 0.530059i | \(-0.177830\pi\) |
−0.766150 | + | 0.642661i | \(0.777830\pi\) | |||||||
\(570\) | 51.9149 | − | 159.777i | 0.0910787 | − | 0.280311i | ||||
\(571\) | 124.451i | 0.217952i | 0.994044 | + | 0.108976i | \(0.0347572\pi\) | ||||
−0.994044 | + | 0.108976i | \(0.965243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −215.000 | −0.375218 | ||||||||
\(574\) | 161.400 | + | 52.4419i | 0.281184 | + | 0.0913622i | ||||
\(575\) | 174.748 | − | 126.962i | 0.303909 | − | 0.220803i | ||||
\(576\) | −362.440 | − | 263.328i | −0.629235 | − | 0.457166i | ||||
\(577\) | 31.8288 | + | 97.9588i | 0.0551625 | + | 0.169773i | 0.974842 | − | 0.222897i | \(-0.0715515\pi\) |
−0.919679 | + | 0.392670i | \(0.871551\pi\) | |||||||
\(578\) | −364.494 | + | 118.431i | −0.630613 | + | 0.204899i | ||||
\(579\) | −79.8004 | + | 109.836i | −0.137824 | + | 0.189699i | ||||
\(580\) | 186.201 | + | 256.284i | 0.321036 | + | 0.441868i | ||||
\(581\) | 77.2542 | − | 237.764i | 0.132968 | − | 0.409233i | ||||
\(582\) | 24.0416i | 0.0413086i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 336.000 | 0.575342 | ||||||||
\(585\) | 903.838 | + | 293.675i | 1.54502 | + | 0.502008i | ||||
\(586\) | −187.692 | + | 136.366i | −0.320293 | + | 0.232707i | ||||
\(587\) | 511.299 | + | 371.480i | 0.871037 | + | 0.632845i | 0.930865 | − | 0.365363i | \(-0.119055\pi\) |
−0.0598280 | + | 0.998209i | \(0.519055\pi\) | |||||||
\(588\) | 0.618034 | + | 1.90211i | 0.00105108 | + | 0.00323489i | ||||
\(589\) | 790.858 | − | 256.965i | 1.34271 | − | 0.436274i | ||||
\(590\) | 413.133 | − | 568.629i | 0.700226 | − | 0.963778i | ||||
\(591\) | −118.869 | − | 163.610i | −0.201132 | − | 0.276835i | ||||
\(592\) | −21.0132 | + | 64.6718i | −0.0354952 | + | 0.109243i | ||||
\(593\) | − | 497.803i | − | 0.839466i | −0.907648 | − | 0.419733i | \(-0.862124\pi\) | ||
0.907648 | − | 0.419733i | \(-0.137876\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −210.000 | −0.352941 | ||||||||
\(596\) | 524.549 | + | 170.436i | 0.880116 | + | 0.285967i | ||||
\(597\) | 161.803 | − | 117.557i | 0.271027 | − | 0.196913i | ||||
\(598\) | −174.748 | − | 126.962i | −0.292220 | − | 0.212310i | ||||
\(599\) | 96.4133 | + | 296.730i | 0.160957 | + | 0.495375i | 0.998716 | − | 0.0506658i | \(-0.0161343\pi\) |
−0.837759 | + | 0.546041i | \(0.816134\pi\) | |||||||
\(600\) | 193.680 | − | 62.9303i | 0.322799 | − | 0.104884i | ||||
\(601\) | 241.895 | − | 332.940i | 0.402487 | − | 0.553976i | −0.558879 | − | 0.829249i | \(-0.688768\pi\) |
0.961366 | + | 0.275273i | \(0.0887683\pi\) | |||||||
\(602\) | 274.314 | + | 377.561i | 0.455671 | + | 0.627177i | ||||
\(603\) | 76.6362 | − | 235.862i | 0.127092 | − | 0.391148i | ||||
\(604\) | − | 313.955i | − | 0.519794i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −218.000 | −0.359736 | ||||||||
\(607\) | −117.015 | − | 38.0204i | −0.192776 | − | 0.0626366i | 0.211038 | − | 0.977478i | \(-0.432316\pi\) |
−0.403814 | + | 0.914841i | \(0.632316\pi\) | |||||||
\(608\) | −388.328 | + | 282.137i | −0.638698 | + | 0.464041i | ||||
\(609\) | −129.443 | − | 94.0456i | −0.212550 | − | 0.154426i | ||||
\(610\) | 34.6099 | + | 106.518i | 0.0567375 | + | 0.174620i | ||||
\(611\) | −516.479 | + | 167.814i | −0.845301 | + | 0.274655i | ||||
\(612\) | 39.9002 | − | 54.9179i | 0.0651964 | − | 0.0897351i | ||||
\(613\) | −319.201 | − | 439.343i | −0.520720 | − | 0.716710i | 0.464961 | − | 0.885331i | \(-0.346068\pi\) |
−0.985681 | + | 0.168621i | \(0.946068\pi\) | |||||||
\(614\) | −81.5805 | + | 251.079i | −0.132867 | + | 0.408923i | ||||
\(615\) | − | 118.794i | − | 0.193161i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1120.00 | −1.81524 | −0.907618 | − | 0.419798i | \(-0.862101\pi\) | ||||
−0.907618 | + | 0.419798i | \(0.862101\pi\) | |||||||
\(618\) | 21.5200 | + | 6.99226i | 0.0348219 | + | 0.0113143i | ||||
\(619\) | −568.739 | + | 413.213i | −0.918803 | + | 0.667549i | −0.943226 | − | 0.332152i | \(-0.892225\pi\) |
0.0244229 | + | 0.999702i | \(0.492225\pi\) | |||||||
\(620\) | 554.986 | + | 403.221i | 0.895138 | + | 0.650356i | ||||
\(621\) | −47.2796 | − | 145.512i | −0.0761346 | − | 0.234318i | ||||
\(622\) | −190.990 | + | 62.0563i | −0.307057 | + | 0.0997689i | ||||
\(623\) | −37.4064 | + | 51.4855i | −0.0600424 | + | 0.0826413i | ||||
\(624\) | −39.9002 | − | 54.9179i | −0.0639426 | − | 0.0880094i | ||||
\(625\) | −200.552 | + | 617.236i | −0.320883 | + | 0.987577i | ||||
\(626\) | − | 632.153i | − | 1.00983i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 350.000 | 0.557325 | ||||||||
\(629\) | −68.5948 | − | 22.2878i | −0.109054 | − | 0.0354337i | ||||
\(630\) | 453.050 | − | 329.160i | 0.719126 | − | 0.522476i | ||||
\(631\) | −316.326 | − | 229.824i | −0.501308 | − | 0.364222i | 0.308208 | − | 0.951319i | \(-0.400271\pi\) |
−0.809517 | + | 0.587097i | \(0.800271\pi\) | |||||||
\(632\) | −411.611 | − | 1266.81i | −0.651283 | − | 2.00444i | ||||
\(633\) | 75.3198 | − | 24.4729i | 0.118989 | − | 0.0386618i | ||||
\(634\) | 351.620 | − | 483.964i | 0.554606 | − | 0.763350i | ||||
\(635\) | −721.528 | − | 993.099i | −1.13627 | − | 1.56393i | ||||
\(636\) | −9.88854 | + | 30.4338i | −0.0155480 | + | 0.0478519i | ||||
\(637\) | − | 16.9706i | − | 0.0266414i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 584.000 | 0.913928 | ||||||||
\(640\) | −225.960 | − | 73.4187i | −0.353062 | − | 0.114717i | ||||
\(641\) | 18.6074 | − | 13.5191i | 0.0290287 | − | 0.0210906i | −0.573176 | − | 0.819432i | \(-0.694289\pi\) |
0.602205 | + | 0.798341i | \(0.294289\pi\) | |||||||
\(642\) | −211.962 | − | 154.000i | −0.330160 | − | 0.239875i | ||||
\(643\) | −138.131 | − | 425.122i | −0.214822 | − | 0.661154i | −0.999166 | − | 0.0408284i | \(-0.987000\pi\) |
0.784344 | − | 0.620326i | \(-0.213000\pi\) | |||||||
\(644\) | 121.050 | − | 39.3314i | 0.187965 | − | 0.0610737i | ||||
\(645\) | 192.020 | − | 264.292i | 0.297705 | − | 0.409756i | ||||
\(646\) | 59.8503 | + | 82.3768i | 0.0926475 | + | 0.127518i | ||||
\(647\) | −148.019 | + | 455.556i | −0.228778 | + | 0.704105i | 0.769108 | + | 0.639118i | \(0.220701\pi\) |
−0.997886 | + | 0.0649869i | \(0.979299\pi\) | |||||||
\(648\) | 466.690i | 0.720201i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −576.000 | −0.886154 | ||||||||
\(651\) | −329.524 | − | 107.069i | −0.506182 | − | 0.164468i | ||||
\(652\) | 258.885 | − | 188.091i | 0.397064 | − | 0.288484i | ||||
\(653\) | −583.301 | − | 423.793i | −0.893264 | − | 0.648994i | 0.0434632 | − | 0.999055i | \(-0.486161\pi\) |
−0.936727 | + | 0.350061i | \(0.886161\pi\) | |||||||
\(654\) | 20.3951 | + | 62.7697i | 0.0311852 | + | 0.0959782i | ||||
\(655\) | 932.083 | − | 302.852i | 1.42303 | − | 0.462370i | ||||
\(656\) | 39.9002 | − | 54.9179i | 0.0608235 | − | 0.0837163i | ||||
\(657\) | −186.201 | − | 256.284i | −0.283411 | − | 0.390081i | ||||
\(658\) | −98.8854 | + | 304.338i | −0.150282 | + | 0.462520i | ||||
\(659\) | − | 700.036i | − | 1.06227i | −0.847287 | − | 0.531135i | \(-0.821766\pi\) | ||
0.847287 | − | 0.531135i | \(-0.178234\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 607.000 | 0.918306 | 0.459153 | − | 0.888357i | \(-0.348153\pi\) | ||||
0.459153 | + | 0.888357i | \(0.348153\pi\) | |||||||
\(662\) | 195.025 | + | 63.3673i | 0.294599 | + | 0.0957210i | ||||
\(663\) | 58.2492 | − | 42.3205i | 0.0878570 | − | 0.0638319i | ||||
\(664\) | −242.705 | − | 176.336i | −0.365520 | − | 0.265566i | ||||
\(665\) | −259.574 | − | 798.887i | −0.390337 | − | 1.20133i | ||||
\(666\) | 182.920 | − | 59.4342i | 0.274654 | − | 0.0892405i | ||||
\(667\) | −119.701 | + | 164.754i | −0.179461 | + | 0.247007i | ||||
\(668\) | −19.9501 | − | 27.4589i | −0.0298654 | − | 0.0411062i | ||||
\(669\) | 34.3009 | − | 105.567i | 0.0512719 | − | 0.157799i | ||||
\(670\) | 306.884i | 0.458036i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 200.000 | 0.297619 | ||||||||
\(673\) | 948.223 | + | 308.096i | 1.40895 | + | 0.457795i | 0.912074 | − | 0.410026i | \(-0.134481\pi\) |
0.496876 | + | 0.867822i | \(0.334481\pi\) | |||||||
\(674\) | 292.864 | − | 212.778i | 0.434517 | − | 0.315695i | ||||
\(675\) | −330.079 | − | 239.816i | −0.489006 | − | 0.355284i | ||||
\(676\) | −73.5460 | − | 226.351i | −0.108796 | − | 0.334839i | ||||
\(677\) | −735.713 | + | 239.048i | −1.08673 | + | 0.353099i | −0.796980 | − | 0.604005i | \(-0.793571\pi\) |
−0.289745 | + | 0.957104i | \(0.593571\pi\) | |||||||
\(678\) | −54.0315 | + | 74.3680i | −0.0796925 | + | 0.109687i | ||||
\(679\) | 70.6566 | + | 97.2504i | 0.104060 | + | 0.143226i | ||||
\(680\) | −77.8723 | + | 239.666i | −0.114518 | + | 0.352450i | ||||
\(681\) | − | 131.522i | − | 0.193130i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −218.000 | −0.319180 | −0.159590 | − | 0.987183i | \(-0.551017\pi\) | ||||
−0.159590 | + | 0.987183i | \(0.551017\pi\) | |||||||
\(684\) | 258.239 | + | 83.9071i | 0.377543 | + | 0.122671i | ||||
\(685\) | 1455.42 | − | 1057.43i | 2.12470 | − | 1.54369i | ||||
\(686\) | 388.328 | + | 282.137i | 0.566076 | + | 0.411278i | ||||
\(687\) | 93.6321 | + | 288.170i | 0.136291 | + | 0.419462i | ||||
\(688\) | 177.540 | − | 57.6861i | 0.258052 | − | 0.0838461i | ||||
\(689\) | 159.601 | − | 219.672i | 0.231641 | − | 0.318827i | ||||
\(690\) | 52.3690 | + | 72.0797i | 0.0758971 | + | 0.104463i | ||||
\(691\) | 266.682 | − | 820.762i | 0.385936 | − | 1.18779i | −0.549863 | − | 0.835255i | \(-0.685320\pi\) |
0.935799 | − | 0.352534i | \(-0.114680\pi\) | |||||||
\(692\) | 246.073i | 0.355597i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 776.000 | 1.11816 | ||||||||
\(695\) | 574.314 | + | 186.606i | 0.826351 | + | 0.268498i | ||||
\(696\) | −155.331 | + | 112.855i | −0.223177 | + | 0.162148i | ||||
\(697\) | 58.2492 | + | 42.3205i | 0.0835713 | + | 0.0607181i | ||||
\(698\) | 190.973 | + | 587.753i | 0.273600 | + | 0.842053i | ||||
\(699\) | 75.3198 | − | 24.4729i | 0.107754 | − | 0.0350113i | ||||
\(700\) | 199.501 | − | 274.589i | 0.285001 | − | 0.392271i | ||||
\(701\) | −236.907 | − | 326.075i | −0.337956 | − | 0.465157i | 0.605887 | − | 0.795551i | \(-0.292818\pi\) |
−0.943843 | + | 0.330394i | \(0.892818\pi\) | |||||||
\(702\) | −126.079 | + | 388.031i | −0.179600 | + | 0.552751i | ||||
\(703\) | − | 288.500i | − | 0.410383i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 224.000 | 0.317730 | ||||||||
\(706\) | 786.823 | + | 255.654i | 1.11448 | + | 0.362117i | ||||
\(707\) | −881.829 | + | 640.686i | −1.24728 | + | 0.906204i | ||||
\(708\) | −114.880 | − | 83.4655i | −0.162260 | − | 0.117889i | ||||
\(709\) | −192.518 | − | 592.508i | −0.271534 | − | 0.835696i | −0.990116 | − | 0.140253i | \(-0.955208\pi\) |
0.718582 | − | 0.695443i | \(-0.244792\pi\) | |||||||
\(710\) | −687.293 | + | 223.315i | −0.968019 | + | 0.314528i | ||||
\(711\) | −738.153 | + | 1015.98i | −1.03819 | + | 1.42895i | ||||
\(712\) | 44.8877 | + | 61.7826i | 0.0630445 | + | 0.0867734i | ||||
\(713\) | −136.276 | + | 419.416i | −0.191131 | + | 0.588241i | ||||
\(714\) | − | 42.4264i | − | 0.0594207i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −398.000 | −0.555866 | ||||||||
\(717\) | 267.654 | + | 86.9662i | 0.373298 | + | 0.121292i | ||||
\(718\) | −472.466 | + | 343.267i | −0.658031 | + | 0.478087i | ||||
\(719\) | −227.334 | − | 165.168i | −0.316180 | − | 0.229719i | 0.418363 | − | 0.908280i | \(-0.362604\pi\) |
−0.734544 | + | 0.678561i | \(0.762604\pi\) | |||||||
\(720\) | −69.2198 | − | 213.037i | −0.0961386 | − | 0.295884i | ||||
\(721\) | 107.600 | − | 34.9613i | 0.149237 | − | 0.0484900i | ||||
\(722\) | 60.6815 | − | 83.5210i | 0.0840464 | − | 0.115680i | ||||
\(723\) | −219.451 | − | 302.048i | −0.303528 | − | 0.417771i | ||||
\(724\) | −45.1165 | + | 138.854i | −0.0623156 | + | 0.191788i | ||||
\(725\) | 543.058i | 0.749046i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1223.00 | 1.68226 | 0.841128 | − | 0.540836i | \(-0.181892\pi\) | ||||
0.841128 | + | 0.540836i | \(0.181892\pi\) | |||||||
\(728\) | −968.398 | − | 314.652i | −1.33022 | − | 0.432214i | ||||
\(729\) | 232.188 | − | 168.694i | 0.318502 | − | 0.231405i | ||||
\(730\) | 317.135 | + | 230.412i | 0.434431 | + | 0.315633i | ||||
\(731\) | 61.1854 | + | 188.309i | 0.0837009 | + | 0.257605i | ||||
\(732\) | 21.5200 | − | 6.99226i | 0.0293988 | − | 0.00955226i | ||||
\(733\) | 525.352 | − | 723.086i | 0.716715 | − | 0.986474i | −0.282911 | − | 0.959146i | \(-0.591300\pi\) |
0.999627 | − | 0.0273281i | \(-0.00869988\pi\) | |||||||
\(734\) | −453.033 | − | 623.547i | −0.617212 | − | 0.849519i | ||||
\(735\) | −2.16312 | + | 6.65740i | −0.00294302 | + | 0.00905768i | ||||
\(736\) | − | 254.558i | − | 0.345867i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −192.000 | −0.260163 | ||||||||
\(739\) | −915.943 | − | 297.608i | −1.23944 | − | 0.402717i | −0.385312 | − | 0.922786i | \(-0.625906\pi\) |
−0.854124 | + | 0.520069i | \(0.825906\pi\) | |||||||
\(740\) | 192.546 | − | 139.893i | 0.260197 | − | 0.189044i | ||||
\(741\) | 232.997 | + | 169.282i | 0.314436 | + | 0.228451i | ||||
\(742\) | −49.4427 | − | 152.169i | −0.0666344 | − | 0.205080i | ||||
\(743\) | −10.7600 | + | 3.49613i | −0.0144818 | + | 0.00470542i | −0.316249 | − | 0.948676i | \(-0.602423\pi\) |
0.301767 | + | 0.953382i | \(0.402423\pi\) | |||||||
\(744\) | −244.389 | + | 336.372i | −0.328479 | + | 0.452113i | ||||
\(745\) | 1134.66 | + | 1561.73i | 1.52304 | + | 2.09628i | ||||
\(746\) | 101.976 | − | 313.849i | 0.136697 | − | 0.420709i | ||||
\(747\) | 282.843i | 0.378638i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1310.00 | −1.74900 | ||||||||
\(750\) | −9.41498 | − | 3.05911i | −0.0125533 | − | 0.00407882i | ||||
\(751\) | −426.352 | + | 309.763i | −0.567712 | + | 0.412467i | −0.834273 | − | 0.551351i | \(-0.814113\pi\) |
0.266561 | + | 0.963818i | \(0.414113\pi\) | |||||||
\(752\) | 103.554 | + | 75.2365i | 0.137705 | + | 0.100049i | ||||
\(753\) | −69.5288 | − | 213.988i | −0.0923358 | − | 0.284180i | ||||
\(754\) | 516.479 | − | 167.814i | 0.684985 | − | 0.222565i | ||||
\(755\) | 645.884 | − | 888.983i | 0.855476 | − | 1.17746i | ||||
\(756\) | −141.313 | − | 194.501i | −0.186922 | − | 0.257276i | ||||
\(757\) | 11.7426 | − | 36.1401i | 0.0155121 | − | 0.0477413i | −0.943001 | − | 0.332790i | \(-0.892010\pi\) |
0.958513 | + | 0.285049i | \(0.0920099\pi\) | |||||||
\(758\) | − | 632.153i | − | 0.833976i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1008.00 | −1.32632 | ||||||||
\(761\) | −1167.46 | − | 379.330i | −1.53411 | − | 0.498462i | −0.584366 | − | 0.811490i | \(-0.698657\pi\) |
−0.949744 | + | 0.313028i | \(0.898657\pi\) | |||||||
\(762\) | 200.636 | − | 145.771i | 0.263302 | − | 0.191300i | ||||
\(763\) | 266.976 | + | 193.969i | 0.349903 | + | 0.254219i | ||||
\(764\) | 132.877 | + | 408.954i | 0.173923 | + | 0.535281i | ||||
\(765\) | 225.960 | − | 73.4187i | 0.295372 | − | 0.0959721i | ||||
\(766\) | −453.033 | + | 623.547i | −0.591427 | + | 0.814030i | ||||
\(767\) | 708.228 | + | 974.793i | 0.923375 | + | 1.27092i | ||||
\(768\) | 84.0526 | − | 258.687i | 0.109444 | − | 0.336833i | ||||
\(769\) | − | 311.127i | − | 0.404586i | −0.979325 | − | 0.202293i | \(-0.935161\pi\) | ||
0.979325 | − | 0.202293i | \(-0.0648394\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −424.000 | −0.549935 | ||||||||
\(772\) | 258.239 | + | 83.9071i | 0.334507 | + | 0.108688i | ||||
\(773\) | −951.404 | + | 691.235i | −1.23079 | + | 0.894224i | −0.996949 | − | 0.0780495i | \(-0.975131\pi\) |
−0.233845 | + | 0.972274i | \(0.575131\pi\) | |||||||
\(774\) | −427.161 | − | 310.351i | −0.551888 | − | 0.400970i | ||||
\(775\) | 363.404 | + | 1118.44i | 0.468908 | + | 1.44315i | ||||
\(776\) | 137.190 | − | 44.5756i | 0.176791 | − | 0.0574428i | ||||
\(777\) | −70.6566 | + | 97.2504i | −0.0909351 | + | 0.125161i | ||||
\(778\) | −178.720 | − | 245.986i | −0.229717 | − | 0.316178i | ||||
\(779\) | −88.9969 | + | 273.904i | −0.114245 | + | 0.351610i | ||||
\(780\) | 237.588i | 0.304600i | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −54.0000 | −0.0690537 | ||||||||
\(783\) | 365.839 | + | 118.868i | 0.467228 | + | 0.151811i | ||||
\(784\) | −3.23607 | + | 2.35114i | −0.00412764 | + | 0.00299890i | ||||
\(785\) | 991.046 | + | 720.037i | 1.26248 | + | 0.917245i | ||||
\(786\) | 61.1854 | + | 188.309i | 0.0778440 | + | 0.239579i | ||||
\(787\) | −1194.36 | + | 388.070i | −1.51761 | + | 0.493101i | −0.945095 | − | 0.326795i | \(-0.894031\pi\) |
−0.572513 | + | 0.819896i | \(0.694031\pi\) | |||||||
\(788\) | −237.739 | + | 327.219i | −0.301699 | + | 0.415253i | ||||
\(789\) | 82.2941 | + | 113.268i | 0.104302 | + | 0.143559i | ||||
\(790\) | 480.212 | − | 1477.94i | 0.607864 | − | 1.87081i | ||||
\(791\) | 459.619i | 0.581061i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −192.000 | −0.242119 | ||||||||
\(794\) | −796.238 | − | 258.713i | −1.00282 | − | 0.325836i | ||||
\(795\) | −90.6099 | + | 65.8319i | −0.113975 | + | 0.0828075i | ||||
\(796\) | −323.607 | − | 235.114i | −0.406541 | − | 0.295369i | ||||
\(797\) | 59.0222 | + | 181.652i | 0.0740555 | + | 0.227919i | 0.981232 | − | 0.192831i | \(-0.0617669\pi\) |
−0.907176 | + | 0.420750i | \(0.861767\pi\) | |||||||
\(798\) | 161.400 | − | 52.4419i | 0.202255 | − | 0.0657167i | ||||
\(799\) | −79.8004 | + | 109.836i | −0.0998753 | + | 0.137467i | ||||
\(800\) | −399.002 | − | 549.179i | −0.498752 | − | 0.686474i | ||||
\(801\) | 22.2492 | − | 68.4761i | 0.0277768 | − | 0.0854882i | ||||
\(802\) | 690.136i | 0.860519i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 62.0000 | 0.0771144 | ||||||||
\(805\) | 423.674 | + | 137.660i | 0.526303 | + | 0.171006i | ||||
\(806\) | 951.404 | − | 691.235i | 1.18040 | − | 0.857612i | ||||
\(807\) | 110.026 | + | 79.9388i | 0.136340 | + | 0.0990567i | ||||
\(808\) | 404.194 | + | 1243.98i | 0.500240 | + | 1.53958i | ||||
\(809\) | 521.859 | − | 169.562i | 0.645067 | − | 0.209595i | 0.0318290 | − | 0.999493i | \(-0.489867\pi\) |
0.613238 | + | 0.789899i | \(0.289867\pi\) | |||||||
\(810\) | −320.033 | + | 440.487i | −0.395102 | + | 0.543811i | ||||
\(811\) | 238.570 | + | 328.363i | 0.294168 | + | 0.404887i | 0.930362 | − | 0.366642i | \(-0.119492\pi\) |
−0.636195 | + | 0.771529i | \(0.719492\pi\) | |||||||
\(812\) | −98.8854 | + | 304.338i | −0.121780 | + | 0.374801i | ||||
\(813\) | 288.500i | 0.354858i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1120.00 | 1.37423 | ||||||||
\(816\) | −16.1400 | − | 5.24419i | −0.0197794 | − | 0.00642671i | ||||
\(817\) | −640.741 | + | 465.526i | −0.784261 | + | 0.569799i | ||||
\(818\) | 179.602 | + | 130.488i | 0.219562 | + | 0.159521i | ||||
\(819\) | 296.656 | + | 913.014i | 0.362218 | + | 1.11479i | ||||
\(820\) | −225.960 | + | 73.4187i | −0.275560 | + | 0.0895350i | ||||
\(821\) | −32.4189 | + | 44.6208i | −0.0394871 | + | 0.0543493i | −0.828304 | − | 0.560279i | \(-0.810694\pi\) |
0.788817 | + | 0.614628i | \(0.210694\pi\) | |||||||
\(822\) | 213.632 | + | 294.040i | 0.259893 | + | 0.357712i | ||||
\(823\) | 212.295 | − | 653.376i | 0.257952 | − | 0.793895i | −0.735281 | − | 0.677762i | \(-0.762950\pi\) |
0.993234 | − | 0.116133i | \(-0.0370500\pi\) | |||||||
\(824\) | − | 135.765i | − | 0.164763i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 710.000 | 0.859564 | ||||||||
\(827\) | 16.1400 | + | 5.24419i | 0.0195163 | + | 0.00634122i | 0.318759 | − | 0.947836i | \(-0.396734\pi\) |
−0.299243 | + | 0.954177i | \(0.596734\pi\) | |||||||
\(828\) | −116.498 | + | 84.6411i | −0.140699 | + | 0.102224i | ||||
\(829\) | −796.882 | − | 578.968i | −0.961257 | − | 0.698394i | −0.00781437 | − | 0.999969i | \(-0.502487\pi\) |
−0.953442 | + | 0.301576i | \(0.902487\pi\) | |||||||
\(830\) | −108.156 | − | 332.870i | −0.130308 | − | 0.401048i | ||||
\(831\) | −117.015 | + | 38.0204i | −0.140812 | + | 0.0457526i | ||||
\(832\) | −558.603 | + | 768.851i | −0.671397 | + | 0.924099i | ||||
\(833\) | −2.49376 | − | 3.43237i | −0.00299371 | − | 0.00412049i | ||||
\(834\) | −37.7001 | + | 116.029i | −0.0452039 | + | 0.139123i | ||||
\(835\) | − | 118.794i | − | 0.142268i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 833.000 | 0.995221 | ||||||||
\(838\) | −441.159 | − | 143.341i | −0.526443 | − | 0.171052i | ||||
\(839\) | −70.3845 | + | 51.1373i | −0.0838909 | + | 0.0609503i | −0.628940 | − | 0.777454i | \(-0.716511\pi\) |
0.545049 | + | 0.838404i | \(0.316511\pi\) | |||||||
\(840\) | 339.787 | + | 246.870i | 0.404508 | + | 0.293893i | ||||
\(841\) | 101.667 | + | 312.898i | 0.120888 | + | 0.372054i | ||||
\(842\) | −279.759 | + | 90.8993i | −0.332256 | + | 0.107956i | ||||
\(843\) | 167.082 | − | 229.969i | 0.198199 | − | 0.272798i | ||||
\(844\) | −93.1004 | − | 128.142i | −0.110309 | − | 0.151827i | ||||
\(845\) | 257.411 | − | 792.230i | 0.304629 | − | 0.937550i | ||||
\(846\) | − | 362.039i | − | 0.427942i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −64.0000 | −0.0754717 | ||||||||
\(849\) | 75.3198 | + | 24.4729i | 0.0887159 | + | 0.0288256i | ||||
\(850\) | −116.498 | + | 84.6411i | −0.137057 | + | 0.0995777i | ||||
\(851\) | 123.780 | + | 89.9311i | 0.145452 | + | 0.105677i | ||||
\(852\) | 45.1165 | + | 138.854i | 0.0529536 | + | 0.162974i | ||||
\(853\) | 507.064 | − | 164.755i | 0.594448 | − | 0.193148i | 0.00368511 | − | 0.999993i | \(-0.498827\pi\) |
0.590763 | + | 0.806845i | \(0.298827\pi\) | |||||||
\(854\) | −66.5003 | + | 91.5298i | −0.0778692 | + | 0.107178i | ||||
\(855\) | 558.603 | + | 768.851i | 0.653336 | + | 0.899240i | ||||
\(856\) | −485.775 | + | 1495.06i | −0.567494 | + | 1.74657i | ||||
\(857\) | 1368.96i | 1.59738i | 0.601740 | + | 0.798692i | \(0.294475\pi\) | ||||
−0.601740 | + | 0.798692i | \(0.705525\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −977.000 | −1.13737 | −0.568685 | − | 0.822556i | \(-0.692547\pi\) | ||||
−0.568685 | + | 0.822556i | \(0.692547\pi\) | |||||||
\(860\) | −621.389 | − | 201.901i | −0.722545 | − | 0.234769i | ||||
\(861\) | 97.0820 | − | 70.5342i | 0.112755 | − | 0.0819213i | ||||
\(862\) | 642.359 | + | 466.701i | 0.745197 | + | 0.541417i | ||||
\(863\) | −393.070 | − | 1209.74i | −0.455469 | − | 1.40179i | −0.870584 | − | 0.492020i | \(-0.836259\pi\) |
0.415115 | − | 0.909769i | \(-0.363741\pi\) | |||||||
\(864\) | −457.299 | + | 148.585i | −0.529281 | + | 0.171974i | ||||
\(865\) | −506.234 | + | 696.771i | −0.585241 | + | 0.805515i | ||||
\(866\) | −32.4189 | − | 44.6208i | −0.0374352 | − | 0.0515252i | ||||
\(867\) | −83.7436 | + | 257.736i | −0.0965901 | + | 0.297274i | ||||
\(868\) | 692.965i | 0.798346i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −224.000 | −0.257471 | ||||||||
\(871\) | −500.339 | − | 162.570i | −0.574442 | − | 0.186647i | ||||
\(872\) | 320.371 | − | 232.763i | 0.367398 | − | 0.266930i | ||||
\(873\) | −110.026 | − | 79.9388i | −0.126032 | − | 0.0915679i | ||||
\(874\) | −66.7477 | − | 205.428i | −0.0763703 | − | 0.235044i | ||||
\(875\) | −47.0749 | + | 15.2956i | −0.0537999 | + | 0.0174806i | ||||
\(876\) | 46.5502 | − | 64.0709i | 0.0531395 | − | 0.0731403i | ||||
\(877\) | −355.777 | − | 489.685i | −0.405675 | − | 0.558363i | 0.556482 | − | 0.830860i | \(-0.312151\pi\) |
−0.962157 | + | 0.272496i | \(0.912151\pi\) | |||||||
\(878\) | 108.774 | − | 334.772i | 0.123888 | − | 0.381289i | ||||
\(879\) | 164.049i | 0.186631i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −295.000 | −0.334847 | −0.167423 | − | 0.985885i | \(-0.553545\pi\) | ||||
−0.167423 | + | 0.985885i | \(0.553545\pi\) | |||||||
\(882\) | 10.7600 | + | 3.49613i | 0.0121995 | + | 0.00396386i | ||||
\(883\) | 472.466 | − | 343.267i | 0.535069 | − | 0.388750i | −0.287181 | − | 0.957876i | \(-0.592718\pi\) |
0.822250 | + | 0.569126i | \(0.192718\pi\) | |||||||
\(884\) | −116.498 | − | 84.6411i | −0.131786 | − | 0.0957478i | ||||
\(885\) | −153.581 | − | 472.675i | −0.173538 | − | 0.534096i | ||||
\(886\) | −235.374 | + | 76.4778i | −0.265660 | + | 0.0863181i | ||||
\(887\) | 571.071 | − | 786.012i | 0.643823 | − | 0.886147i | −0.354989 | − | 0.934871i | \(-0.615515\pi\) |
0.998812 | + | 0.0487236i | \(0.0155153\pi\) | |||||||
\(888\) | 84.7879 | + | 116.701i | 0.0954819 | + | 0.131420i | ||||
\(889\) | 383.181 | − | 1179.31i | 0.431025 | − | 1.32656i | ||||
\(890\) | 89.0955i | 0.100107i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −222.000 | −0.248879 | ||||||||
\(893\) | −516.479 | − | 167.814i | −0.578364 | − | 0.187922i | ||||
\(894\) | −315.517 | + | 229.236i | −0.352927 | + | 0.256416i | ||||
\(895\) | −1126.96 | − | 818.785i | −1.25917 | − | 0.914843i | ||||
\(896\) | −74.1641 | − | 228.254i | −0.0827724 | − | 0.254747i | ||||
\(897\) | −145.260 | + | 47.1977i | −0.161939 | + | 0.0526173i | ||||
\(898\) | 260.182 | − | 358.110i | 0.289735 | − | 0.398787i | ||||
\(899\) | −651.703 | − | 896.992i | −0.724920 | − | 0.997767i | ||||
\(900\) | −118.663 | + | 365.206i | −0.131847 | + | 0.405784i | ||||
\(901\) | − | 67.8823i | − | 0.0753410i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 330.000 | 0.365449 | ||||||||
\(904\) | 524.549 | + | 170.436i | 0.580253 | + | 0.188536i | ||||
\(905\) | −413.408 | + | 300.358i | −0.456804 | + | 0.331888i | ||||
\(906\) | 179.602 | + | 130.488i | 0.198236 | + | 0.144027i | ||||
\(907\) | −474.650 | − | 1460.82i | −0.523319 | − | 1.61061i | −0.767617 | − | 0.640909i | \(-0.778557\pi\) |
0.244298 | − | 0.969700i | \(-0.421443\pi\) | |||||||
\(908\) | −250.169 | + | 81.2850i | −0.275517 | + | 0.0895209i | ||||
\(909\) | 724.853 | − | 997.675i | 0.797418 | − | 1.09755i | ||||
\(910\) | −698.253 | − | 961.063i | −0.767311 | − | 1.05611i | ||||
\(911\) | 256.484 | − | 789.377i | 0.281541 | − | 0.866495i | −0.705873 | − | 0.708339i | \(-0.749445\pi\) |
0.987414 | − | 0.158156i | \(-0.0505550\pi\) | |||||||
\(912\) | − | 67.8823i | − | 0.0744323i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −16.0000 | −0.0175055 | ||||||||
\(915\) | 75.3198 | + | 24.4729i | 0.0823168 | + | 0.0267463i | ||||
\(916\) | 490.264 | − | 356.198i | 0.535223 | − | 0.388862i | ||||
\(917\) | 800.927 | + | 581.907i | 0.873421 | + | 0.634577i | ||||
\(918\) | 31.5197 | + | 97.0078i | 0.0343352 | + | 0.105673i | ||||
\(919\) | 536.654 | − | 174.369i | 0.583954 | − | 0.189738i | −0.00211708 | − | 0.999998i | \(-0.500674\pi\) |
0.586071 | + | 0.810260i | \(0.300674\pi\) | |||||||
\(920\) | 314.214 | − | 432.478i | 0.341537 | − | 0.470085i | ||||
\(921\) | 109.726 | + | 151.024i | 0.119137 | + | 0.163979i | ||||
\(922\) | −380.709 | + | 1171.70i | −0.412916 | + | 1.27083i | ||||
\(923\) | − | 1238.85i | − | 1.34220i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 408.000 | 0.441081 | ||||||||
\(926\) | 431.744 | + | 140.282i | 0.466246 | + | 0.151493i | ||||
\(927\) | −103.554 | + | 75.2365i | −0.111709 | + | 0.0811613i | ||||
\(928\) | 517.771 | + | 376.183i | 0.557943 | + | 0.405369i | ||||
\(929\) | 477.122 | + | 1468.43i | 0.513587 | + | 1.58066i | 0.785838 | + | 0.618432i | \(0.212232\pi\) |
−0.272252 | + | 0.962226i | \(0.587768\pi\) | |||||||
\(930\) | −461.334 | + | 149.896i | −0.496058 | + | 0.161179i | ||||
\(931\) | 9.97505 | − | 13.7295i | 0.0107143 | − | 0.0147470i | ||||
\(932\) | −93.1004 | − | 128.142i | −0.0998932 | − | 0.137491i | ||||
\(933\) | −43.8804 | + | 135.050i | −0.0470315 | + | 0.144748i | ||||
\(934\) | − | 227.688i | − | 0.243778i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1152.00 | 1.23077 | ||||||||
\(937\) | 844.658 | + | 274.446i | 0.901449 | + | 0.292899i | 0.722835 | − | 0.691020i | \(-0.242839\pi\) |
0.178614 | + | 0.983919i | \(0.442839\pi\) | |||||||
\(938\) | −250.795 | + | 182.213i | −0.267372 | + | 0.194257i | ||||
\(939\) | −361.631 | − | 262.740i | −0.385123 | − | 0.279808i | ||||
\(940\) | −138.440 | − | 426.073i | −0.147276 | − | 0.453269i | ||||
\(941\) | 773.373 | − | 251.284i | 0.821863 | − | 0.267040i | 0.132249 | − | 0.991217i | \(-0.457780\pi\) |
0.689614 | + | 0.724177i | \(0.257780\pi\) | |||||||
\(942\) | −145.469 | + | 200.221i | −0.154426 | + | 0.212549i | ||||
\(943\) | −89.7754 | − | 123.565i | −0.0952019 | − | 0.131034i | ||||
\(944\) | 87.7608 | − | 270.100i | 0.0929670 | − | 0.286123i | ||||
\(945\) | − | 841.457i | − | 0.890431i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 145.000 | 0.153115 | 0.0765576 | − | 0.997065i | \(-0.475607\pi\) | ||||
0.0765576 | + | 0.997065i | \(0.475607\pi\) | |||||||
\(948\) | −298.589 | − | 97.0176i | −0.314968 | − | 0.102339i | ||||
\(949\) | −543.659 | + | 394.992i | −0.572876 | + | 0.416219i | ||||
\(950\) | −465.994 | − | 338.564i | −0.490520 | − | 0.356383i | ||||
\(951\) | −130.714 | − | 402.297i | −0.137449 | − | 0.423025i | ||||
\(952\) | −242.099 | + | 78.6629i | −0.254306 | + | 0.0826291i | ||||
\(953\) | 369.908 | − | 509.135i | 0.388151 | − | 0.534244i | −0.569570 | − | 0.821943i | \(-0.692890\pi\) |
0.957721 | + | 0.287699i | \(0.0928902\pi\) | |||||||
\(954\) | 106.400 | + | 146.448i | 0.111531 | + | 0.153509i | ||||
\(955\) | −465.071 | + | 1431.34i | −0.486985 | + | 1.49879i | ||||
\(956\) | − | 562.857i | − | 0.588763i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −632.000 | −0.659708 | ||||||||
\(959\) | 1728.32 | + | 561.566i | 1.80221 | + | 0.585574i | ||||
\(960\) | 317.135 | − | 230.412i | 0.330349 | − | 0.240012i | ||||
\(961\) | −1164.98 | − | 846.411i | −1.21226 | − | 0.880760i | ||||
\(962\) | −126.079 | − | 388.031i | −0.131059 | − | 0.403359i | ||||
\(963\) | 1409.56 | − | 457.993i | 1.46371 | − | 0.475590i | ||||
\(964\) | −438.902 | + | 604.097i | −0.455293 | + | 0.626656i | ||||
\(965\) | 558.603 | + | 768.851i | 0.578863 | + | 0.796736i | ||||
\(966\) | −27.8115 | + | 85.5951i | −0.0287904 | + | 0.0886077i | ||||
\(967\) | − | 373.352i | − | 0.386093i | −0.981190 | − | 0.193047i | \(-0.938163\pi\) | ||
0.981190 | − | 0.193047i | \(-0.0618369\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.0000 | 0.0743034 | ||||||||
\(970\) | 160.055 | + | 52.0049i | 0.165005 | + | 0.0536133i | ||||
\(971\) | 1371.28 | − | 996.296i | 1.41224 | − | 1.02605i | 0.419246 | − | 0.907872i | \(-0.362294\pi\) |
0.992992 | − | 0.118179i | \(-0.0377057\pi\) | |||||||
\(972\) | 336.551 | + | 244.519i | 0.346246 | + | 0.251562i | ||||
\(973\) | 188.500 | + | 580.144i | 0.193731 | + | 0.596243i | ||||
\(974\) | 977.813 | − | 317.711i | 1.00391 | − | 0.326192i | ||||
\(975\) | −239.401 | + | 329.507i | −0.245540 | + | 0.337956i | ||||
\(976\) | 26.6001 | + | 36.6119i | 0.0272542 | + | 0.0375122i | ||||
\(977\) | −114.027 | + | 350.940i | −0.116712 | + | 0.359201i | −0.992300 | − | 0.123856i | \(-0.960474\pi\) |
0.875589 | + | 0.483058i | \(0.160474\pi\) | |||||||
\(978\) | 226.274i | 0.231364i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.0000 | 0.0142857 | ||||||||
\(981\) | −355.079 | − | 115.372i | −0.361956 | − | 0.117607i | ||||
\(982\) | 595.437 | − | 432.610i | 0.606351 | − | 0.440540i | ||||
\(983\) | −369.721 | − | 268.618i | −0.376115 | − | 0.273263i | 0.383627 | − | 0.923488i | \(-0.374675\pi\) |
−0.759742 | + | 0.650225i | \(0.774675\pi\) | |||||||
\(984\) | −44.4984 | − | 136.952i | −0.0452220 | − | 0.139179i | ||||
\(985\) | −1346.34 | + | 437.453i | −1.36684 | + | 0.444115i | ||||
\(986\) | 79.8004 | − | 109.836i | 0.0809334 | − | 0.111395i | ||||
\(987\) | 133.001 | + | 183.060i | 0.134752 | + | 0.185471i | ||||
\(988\) | 177.994 | − | 547.809i | 0.180156 | − | 0.554462i | ||||
\(989\) | − | 420.021i | − | 0.424693i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1032.00 | −1.04137 | −0.520686 | − | 0.853748i | \(-0.674324\pi\) | ||||
−0.520686 | + | 0.853748i | \(0.674324\pi\) | |||||||
\(992\) | 1318.10 | + | 428.276i | 1.32873 | + | 0.431730i | ||||
\(993\) | 117.307 | − | 85.2289i | 0.118134 | − | 0.0858297i | ||||
\(994\) | −590.582 | − | 429.083i | −0.594147 | − | 0.431673i | ||||
\(995\) | −432.624 | − | 1331.48i | −0.434798 | − | 1.33817i | ||||
\(996\) | −67.2499 | + | 21.8508i | −0.0675199 | + | 0.0219386i | ||||
\(997\) | −416.458 | + | 573.206i | −0.417711 | + | 0.574930i | −0.965078 | − | 0.261963i | \(-0.915630\pi\) |
0.547367 | + | 0.836893i | \(0.315630\pi\) | |||||||
\(998\) | 305.901 | + | 421.037i | 0.306514 | + | 0.421881i | ||||
\(999\) | 89.3059 | − | 274.855i | 0.0893953 | − | 0.275130i |
(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 | 121.3.d.e.112.2 | 8 | ||
11.2 | odd | 10 | inner | 121.3.d.e.118.2 | 8 | ||
11.3 | even | 5 | inner | 121.3.d.e.40.2 | 8 | ||
11.4 | even | 5 | 121.3.b.a.120.2 | yes | 2 | ||
11.5 | even | 5 | inner | 121.3.d.e.94.1 | 8 | ||
11.6 | odd | 10 | inner | 121.3.d.e.94.2 | 8 | ||
11.7 | odd | 10 | 121.3.b.a.120.1 | ✓ | 2 | ||
11.8 | odd | 10 | inner | 121.3.d.e.40.1 | 8 | ||
11.9 | even | 5 | inner | 121.3.d.e.118.1 | 8 | ||
11.10 | odd | 2 | inner | 121.3.d.e.112.1 | 8 | ||
33.26 | odd | 10 | 1089.3.c.a.604.1 | 2 | |||
33.29 | even | 10 | 1089.3.c.a.604.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
121.3.b.a.120.1 | ✓ | 2 | 11.7 | odd | 10 | ||
121.3.b.a.120.2 | yes | 2 | 11.4 | even | 5 | ||
121.3.d.e.40.1 | 8 | 11.8 | odd | 10 | inner | ||
121.3.d.e.40.2 | 8 | 11.3 | even | 5 | inner | ||
121.3.d.e.94.1 | 8 | 11.5 | even | 5 | inner | ||
121.3.d.e.94.2 | 8 | 11.6 | odd | 10 | inner | ||
121.3.d.e.112.1 | 8 | 11.10 | odd | 2 | inner | ||
121.3.d.e.112.2 | 8 | 1.1 | even | 1 | trivial | ||
121.3.d.e.118.1 | 8 | 11.9 | even | 5 | inner | ||
121.3.d.e.118.2 | 8 | 11.2 | odd | 10 | inner | ||
1089.3.c.a.604.1 | 2 | 33.26 | odd | 10 | |||
1089.3.c.a.604.2 | 2 | 33.29 | even | 10 |