Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.12 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.f.151.12 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77209 | + | 4.80141i | 0.980083 | + | 1.69755i | 0.662025 | + | 0.749482i | \(0.269697\pi\) |
0.318058 | + | 0.948071i | \(0.396969\pi\) | |||||||
\(3\) | −0.320819 | − | 5.18624i | −0.0617417 | − | 0.998092i | ||||
\(4\) | −11.3690 | + | 19.6917i | −1.42112 | + | 2.46146i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 24.0119 | − | 15.9171i | 1.63380 | − | 1.08302i | ||||
\(7\) | −12.8563 | − | 22.2678i | −0.694177 | − | 1.20235i | −0.970457 | − | 0.241272i | \(-0.922435\pi\) |
0.276281 | − | 0.961077i | \(-0.410898\pi\) | |||||||
\(8\) | −81.7101 | −3.61111 | ||||||||
\(9\) | −26.7942 | + | 3.32769i | −0.992376 | + | 0.123248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.12792 | − | 5.41771i | −0.0857366 | − | 0.148500i | 0.819968 | − | 0.572409i | \(-0.193991\pi\) |
−0.905705 | + | 0.423909i | \(0.860658\pi\) | |||||||
\(12\) | 105.773 | + | 52.6449i | 2.54451 | + | 1.26644i | ||||
\(13\) | 7.62998 | − | 13.2155i | 0.162783 | − | 0.281948i | −0.773083 | − | 0.634305i | \(-0.781286\pi\) |
0.935866 | + | 0.352357i | \(0.114620\pi\) | |||||||
\(14\) | 71.2779 | − | 123.457i | 1.36070 | − | 2.35680i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −135.556 | − | 234.790i | −2.11806 | − | 3.66859i | ||||
\(17\) | −36.0074 | −0.513710 | −0.256855 | − | 0.966450i | \(-0.582686\pi\) | ||||
−0.256855 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(18\) | −90.2535 | − | 119.425i | −1.18183 | − | 1.56382i | ||||
\(19\) | −52.7512 | −0.636945 | −0.318472 | − | 0.947932i | \(-0.603170\pi\) | ||||
−0.318472 | + | 0.947932i | \(0.603170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −111.362 | + | 73.8199i | −1.15720 | + | 0.767087i | ||||
\(22\) | 17.3418 | − | 30.0368i | 0.168058 | − | 0.291085i | ||||
\(23\) | 41.8670 | − | 72.5158i | 0.379560 | − | 0.657417i | −0.611438 | − | 0.791292i | \(-0.709409\pi\) |
0.990998 | + | 0.133875i | \(0.0427420\pi\) | |||||||
\(24\) | 26.2142 | + | 423.768i | 0.222956 | + | 3.60422i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 84.6040 | 0.638162 | ||||||||
\(27\) | 25.8543 | + | 137.893i | 0.184284 | + | 0.982873i | ||||
\(28\) | 584.654 | 3.94604 | ||||||||
\(29\) | −59.5457 | − | 103.136i | −0.381288 | − | 0.660411i | 0.609958 | − | 0.792433i | \(-0.291186\pi\) |
−0.991247 | + | 0.132023i | \(0.957853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −138.331 | + | 239.596i | −0.801449 | + | 1.38815i | 0.117214 | + | 0.993107i | \(0.462604\pi\) |
−0.918663 | + | 0.395043i | \(0.870730\pi\) | |||||||
\(32\) | 424.708 | − | 735.615i | 2.34620 | − | 4.06374i | ||||
\(33\) | −27.0941 | + | 17.9602i | −0.142923 | + | 0.0947417i | ||||
\(34\) | −99.8157 | − | 172.886i | −0.503478 | − | 0.872050i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 239.095 | − | 565.454i | 1.10692 | − | 2.61784i | ||||
\(37\) | −117.553 | −0.522315 | −0.261158 | − | 0.965296i | \(-0.584104\pi\) | ||||
−0.261158 | + | 0.965296i | \(0.584104\pi\) | |||||||
\(38\) | −146.231 | − | 253.280i | −0.624258 | − | 1.08125i | ||||
\(39\) | −70.9867 | − | 35.3311i | −0.291461 | − | 0.145064i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 79.6608 | − | 137.977i | 0.303437 | − | 0.525569i | −0.673475 | − | 0.739210i | \(-0.735199\pi\) |
0.976912 | + | 0.213641i | \(0.0685324\pi\) | |||||||
\(42\) | −663.144 | − | 330.057i | −2.43632 | − | 1.21259i | ||||
\(43\) | 147.482 | + | 255.446i | 0.523040 | + | 0.905932i | 0.999640 | + | 0.0268122i | \(0.00853561\pi\) |
−0.476600 | + | 0.879120i | \(0.658131\pi\) | |||||||
\(44\) | 142.245 | 0.487370 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 464.237 | 1.48800 | ||||||||
\(47\) | −41.6458 | − | 72.1327i | −0.129248 | − | 0.223865i | 0.794137 | − | 0.607738i | \(-0.207923\pi\) |
−0.923386 | + | 0.383874i | \(0.874590\pi\) | |||||||
\(48\) | −1174.19 | + | 778.352i | −3.53082 | + | 2.34053i | ||||
\(49\) | −159.070 | + | 275.518i | −0.463762 | + | 0.803260i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.5519 | + | 186.743i | 0.0317173 | + | 0.512730i | ||||
\(52\) | 173.490 | + | 300.494i | 0.462669 | + | 0.801366i | ||||
\(53\) | 149.018 | 0.386212 | 0.193106 | − | 0.981178i | \(-0.438144\pi\) | ||||
0.193106 | + | 0.981178i | \(0.438144\pi\) | |||||||
\(54\) | −590.411 | + | 506.390i | −1.48787 | + | 1.27613i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1050.49 | + | 1819.51i | 2.50675 | + | 4.34182i | ||||
\(57\) | 16.9236 | + | 273.580i | 0.0393260 | + | 0.635729i | ||||
\(58\) | 330.132 | − | 571.806i | 0.747388 | − | 1.29451i | ||||
\(59\) | −317.731 | + | 550.325i | −0.701102 | + | 1.21434i | 0.266978 | + | 0.963703i | \(0.413975\pi\) |
−0.968080 | + | 0.250641i | \(0.919359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −298.575 | − | 517.148i | −0.626699 | − | 1.08548i | −0.988210 | − | 0.153107i | \(-0.951072\pi\) |
0.361510 | − | 0.932368i | \(-0.382261\pi\) | |||||||
\(62\) | −1533.86 | −3.14194 | ||||||||
\(63\) | 418.575 | + | 553.865i | 0.837071 | + | 1.10763i | ||||
\(64\) | 2540.42 | 4.96175 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −161.342 | − | 80.3021i | −0.300906 | − | 0.149765i | ||||
\(67\) | 165.008 | − | 285.802i | 0.300879 | − | 0.521138i | −0.675456 | − | 0.737400i | \(-0.736053\pi\) |
0.976335 | + | 0.216262i | \(0.0693867\pi\) | |||||||
\(68\) | 409.367 | − | 709.045i | 0.730045 | − | 1.26448i | ||||
\(69\) | −389.516 | − | 193.868i | −0.679598 | − | 0.338246i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1149.79 | −1.92189 | −0.960947 | − | 0.276732i | \(-0.910749\pi\) | ||||
−0.960947 | + | 0.276732i | \(0.910749\pi\) | |||||||
\(72\) | 2189.35 | − | 271.906i | 3.58358 | − | 0.445062i | ||||
\(73\) | −130.284 | −0.208885 | −0.104442 | − | 0.994531i | \(-0.533306\pi\) | ||||
−0.104442 | + | 0.994531i | \(0.533306\pi\) | |||||||
\(74\) | −325.869 | − | 564.422i | −0.511912 | − | 0.886658i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 599.728 | − | 1038.76i | 0.905177 | − | 1.56781i | ||||
\(77\) | −80.4271 | + | 139.304i | −0.119033 | + | 0.206171i | ||||
\(78\) | −27.1426 | − | 438.777i | −0.0394012 | − | 0.636945i | ||||
\(79\) | 368.918 | + | 638.984i | 0.525398 | + | 0.910017i | 0.999562 | + | 0.0295801i | \(0.00941703\pi\) |
−0.474164 | + | 0.880437i | \(0.657250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 706.853 | − | 178.325i | 0.969620 | − | 0.244616i | ||||
\(82\) | 883.309 | 1.18957 | ||||||||
\(83\) | 184.951 | + | 320.345i | 0.244591 | + | 0.423644i | 0.962016 | − | 0.272991i | \(-0.0880130\pi\) |
−0.717426 | + | 0.696635i | \(0.754680\pi\) | |||||||
\(84\) | −187.568 | − | 3032.16i | −0.243635 | − | 3.93852i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −817.665 | + | 1416.24i | −1.02525 | + | 1.77578i | ||||
\(87\) | −515.785 | + | 341.906i | −0.635609 | + | 0.421336i | ||||
\(88\) | 255.583 | + | 442.682i | 0.309605 | + | 0.536251i | ||||
\(89\) | −225.638 | −0.268737 | −0.134369 | − | 0.990931i | \(-0.542901\pi\) | ||||
−0.134369 | + | 0.990931i | \(0.542901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −392.374 | −0.452000 | ||||||||
\(92\) | 951.972 | + | 1648.86i | 1.07880 | + | 1.86854i | ||||
\(93\) | 1286.98 | + | 640.549i | 1.43498 | + | 0.714213i | ||||
\(94\) | 230.892 | − | 399.917i | 0.253348 | − | 0.438812i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3951.33 | − | 1966.64i | −4.20084 | − | 2.09082i | ||||
\(97\) | 5.95671 | + | 10.3173i | 0.00623518 | + | 0.0107996i | 0.869126 | − | 0.494590i | \(-0.164682\pi\) |
−0.862891 | + | 0.505390i | \(0.831349\pi\) | |||||||
\(98\) | −1763.83 | −1.81810 | ||||||||
\(99\) | 101.838 | + | 134.754i | 0.103385 | + | 0.136801i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −383.267 | − | 663.838i | −0.377589 | − | 0.654003i | 0.613122 | − | 0.789988i | \(-0.289913\pi\) |
−0.990711 | + | 0.135985i | \(0.956580\pi\) | |||||||
\(102\) | −864.605 | + | 573.133i | −0.839300 | + | 0.556359i | ||||
\(103\) | 774.737 | − | 1341.88i | 0.741137 | − | 1.28369i | −0.210841 | − | 0.977520i | \(-0.567620\pi\) |
0.951978 | − | 0.306166i | \(-0.0990463\pi\) | |||||||
\(104\) | −623.447 | + | 1079.84i | −0.587827 | + | 1.01815i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 413.093 | + | 715.497i | 0.378520 | + | 0.655615i | ||||
\(107\) | −1218.43 | −1.10084 | −0.550421 | − | 0.834887i | \(-0.685533\pi\) | ||||
−0.550421 | + | 0.834887i | \(0.685533\pi\) | |||||||
\(108\) | −3009.29 | − | 1058.59i | −2.68119 | − | 0.943178i | ||||
\(109\) | −1327.27 | −1.16633 | −0.583163 | − | 0.812355i | \(-0.698185\pi\) | ||||
−0.583163 | + | 0.812355i | \(0.698185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 37.7134 | + | 609.660i | 0.0322486 | + | 0.521319i | ||||
\(112\) | −3485.51 | + | 6037.08i | −2.94062 | + | 5.09330i | ||||
\(113\) | 216.828 | − | 375.557i | 0.180509 | − | 0.312650i | −0.761545 | − | 0.648112i | \(-0.775559\pi\) |
0.942054 | + | 0.335462i | \(0.108892\pi\) | |||||||
\(114\) | −1266.66 | + | 839.646i | −1.04064 | + | 0.689825i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2707.90 | 2.16743 | ||||||||
\(117\) | −160.462 | + | 379.489i | −0.126792 | + | 0.299861i | ||||
\(118\) | −3523.11 | −2.74855 | ||||||||
\(119\) | 462.922 | + | 801.805i | 0.356605 | + | 0.617658i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 645.932 | − | 1118.79i | 0.485298 | − | 0.840562i | ||||
\(122\) | 1655.36 | − | 2867.16i | 1.22843 | − | 2.12771i | ||||
\(123\) | −741.136 | − | 368.875i | −0.543301 | − | 0.270409i | ||||
\(124\) | −3145.36 | − | 5447.92i | −2.27792 | − | 3.94547i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1499.00 | + | 3545.11i | −1.05986 | + | 2.50654i | ||||
\(127\) | 1850.18 | 1.29273 | 0.646365 | − | 0.763028i | \(-0.276288\pi\) | ||||
0.646365 | + | 0.763028i | \(0.276288\pi\) | |||||||
\(128\) | 3644.61 | + | 6312.65i | 2.51673 | + | 4.35910i | ||||
\(129\) | 1277.49 | − | 846.827i | 0.871911 | − | 0.577976i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 638.716 | − | 1106.29i | 0.425991 | − | 0.737839i | −0.570521 | − | 0.821283i | \(-0.693259\pi\) |
0.996512 | + | 0.0834443i | \(0.0265921\pi\) | |||||||
\(132\) | −45.6350 | − | 737.717i | −0.0300910 | − | 0.486440i | ||||
\(133\) | 678.186 | + | 1174.65i | 0.442152 | + | 0.765830i | ||||
\(134\) | 1829.67 | 1.17954 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2942.17 | 1.85506 | ||||||||
\(137\) | −766.766 | − | 1328.08i | −0.478170 | − | 0.828214i | 0.521517 | − | 0.853241i | \(-0.325366\pi\) |
−0.999687 | + | 0.0250268i | \(0.992033\pi\) | |||||||
\(138\) | −148.936 | − | 2407.64i | −0.0918717 | − | 1.48516i | ||||
\(139\) | −766.669 | + | 1327.91i | −0.467828 | + | 0.810301i | −0.999324 | − | 0.0367593i | \(-0.988297\pi\) |
0.531497 | + | 0.847060i | \(0.321630\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −360.737 | + | 239.127i | −0.215457 | + | 0.142823i | ||||
\(142\) | −3187.31 | − | 5520.59i | −1.88362 | − | 3.26252i | ||||
\(143\) | −95.4638 | −0.0558258 | ||||||||
\(144\) | 4413.42 | + | 5839.91i | 2.55406 | + | 3.37958i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −361.159 | − | 625.545i | −0.204724 | − | 0.354593i | ||||
\(147\) | 1479.94 | + | 736.586i | 0.830361 | + | 0.413283i | ||||
\(148\) | 1336.46 | − | 2314.82i | 0.742275 | − | 1.28566i | ||||
\(149\) | 1251.54 | − | 2167.73i | 0.688120 | − | 1.19186i | −0.284325 | − | 0.958728i | \(-0.591770\pi\) |
0.972445 | − | 0.233131i | \(-0.0748971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 760.321 | + | 1316.92i | 0.409762 | + | 0.709729i | 0.994863 | − | 0.101232i | \(-0.0322784\pi\) |
−0.585101 | + | 0.810961i | \(0.698945\pi\) | |||||||
\(152\) | 4310.30 | 2.30008 | ||||||||
\(153\) | 964.786 | − | 119.821i | 0.509793 | − | 0.0633136i | ||||
\(154\) | −891.805 | −0.466648 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1502.78 | − | 996.167i | 0.771271 | − | 0.511264i | ||||
\(157\) | 1296.44 | − | 2245.50i | 0.659026 | − | 1.14147i | −0.321842 | − | 0.946793i | \(-0.604302\pi\) |
0.980868 | − | 0.194674i | \(-0.0623647\pi\) | |||||||
\(158\) | −2045.35 | + | 3542.65i | −1.02987 | + | 1.78378i | ||||
\(159\) | −47.8079 | − | 772.845i | −0.0238454 | − | 0.385475i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2153.03 | −1.05393 | ||||||||
\(162\) | 2815.67 | + | 2899.55i | 1.36556 | + | 1.40624i | ||||
\(163\) | 675.580 | 0.324635 | 0.162318 | − | 0.986739i | \(-0.448103\pi\) | ||||
0.162318 | + | 0.986739i | \(0.448103\pi\) | |||||||
\(164\) | 1811.33 | + | 3137.31i | 0.862444 | + | 1.49380i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1025.40 | + | 1776.05i | −0.479438 | + | 0.830412i | ||||
\(167\) | −1947.97 | + | 3373.97i | −0.902623 | + | 1.56339i | −0.0785470 | + | 0.996910i | \(0.525028\pi\) |
−0.824076 | + | 0.566479i | \(0.808305\pi\) | |||||||
\(168\) | 9099.38 | − | 6031.84i | 4.17876 | − | 2.77004i | ||||
\(169\) | 982.067 | + | 1700.99i | 0.447004 | + | 0.774233i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1413.42 | − | 175.540i | 0.632088 | − | 0.0785020i | ||||
\(172\) | −6706.87 | −2.97322 | ||||||||
\(173\) | −25.8304 | − | 44.7396i | −0.0113517 | − | 0.0196618i | 0.860294 | − | 0.509799i | \(-0.170280\pi\) |
−0.871645 | + | 0.490137i | \(0.836947\pi\) | |||||||
\(174\) | −3071.44 | − | 1528.70i | −1.33819 | − | 0.666037i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −848.017 | + | 1468.81i | −0.363191 | + | 0.629066i | ||||
\(177\) | 2956.05 | + | 1471.27i | 1.25531 | + | 0.624788i | ||||
\(178\) | −625.490 | − | 1083.38i | −0.263385 | − | 0.456195i | ||||
\(179\) | 4553.37 | 1.90131 | 0.950656 | − | 0.310247i | \(-0.100412\pi\) | ||||
0.950656 | + | 0.310247i | \(0.100412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2441.01 | 1.00243 | 0.501213 | − | 0.865324i | \(-0.332887\pi\) | ||||
0.501213 | + | 0.865324i | \(0.332887\pi\) | |||||||
\(182\) | −1087.70 | − | 1883.95i | −0.442997 | − | 0.767294i | ||||
\(183\) | −2586.26 | + | 1714.39i | −1.04471 | + | 0.692523i | ||||
\(184\) | −3420.96 | + | 5925.28i | −1.37063 | + | 2.37401i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 492.092 | + | 7954.97i | 0.193989 | + | 3.13595i | ||||
\(187\) | 112.628 | + | 195.078i | 0.0440437 | + | 0.0762860i | ||||
\(188\) | 1893.88 | 0.734711 | ||||||||
\(189\) | 2738.19 | − | 2348.52i | 1.05383 | − | 0.903861i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −663.053 | − | 1148.44i | −0.251188 | − | 0.435070i | 0.712665 | − | 0.701504i | \(-0.247488\pi\) |
−0.963853 | + | 0.266434i | \(0.914154\pi\) | |||||||
\(192\) | −815.015 | − | 13175.2i | −0.306347 | − | 4.95229i | ||||
\(193\) | −724.098 | + | 1254.17i | −0.270061 | + | 0.467759i | −0.968877 | − | 0.247542i | \(-0.920377\pi\) |
0.698816 | + | 0.715301i | \(0.253710\pi\) | |||||||
\(194\) | −33.0251 | + | 57.2012i | −0.0122220 | + | 0.0211691i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3616.94 | − | 6264.73i | −1.31813 | − | 2.28306i | ||||
\(197\) | −2398.84 | −0.867564 | −0.433782 | − | 0.901018i | \(-0.642821\pi\) | ||||
−0.433782 | + | 0.901018i | \(0.642821\pi\) | |||||||
\(198\) | −364.704 | + | 862.519i | −0.130901 | + | 0.309578i | ||||
\(199\) | 3109.15 | 1.10755 | 0.553773 | − | 0.832667i | \(-0.313187\pi\) | ||||
0.553773 | + | 0.832667i | \(0.313187\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1535.17 | − | 764.078i | −0.538720 | − | 0.268129i | ||||
\(202\) | 2124.90 | − | 3680.44i | 0.740137 | − | 1.28195i | ||||
\(203\) | −1531.08 | + | 2651.91i | −0.529363 | + | 0.916883i | ||||
\(204\) | −3808.61 | − | 1895.60i | −1.30714 | − | 0.650582i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8590.57 | 2.90550 | ||||||||
\(207\) | −880.481 | + | 2082.32i | −0.295641 | + | 0.699185i | ||||
\(208\) | −4137.16 | −1.37914 | ||||||||
\(209\) | 165.001 | + | 285.791i | 0.0546095 | + | 0.0945864i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1654.80 | − | 2866.19i | 0.539910 | − | 0.935151i | −0.458999 | − | 0.888437i | \(-0.651792\pi\) |
0.998908 | − | 0.0467139i | \(-0.0148749\pi\) | |||||||
\(212\) | −1694.19 | + | 2934.42i | −0.548855 | + | 0.950645i | ||||
\(213\) | 368.873 | + | 5963.07i | 0.118661 | + | 1.91823i | ||||
\(214\) | −3377.60 | − | 5850.18i | −1.07892 | − | 1.86874i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2112.56 | − | 11267.3i | −0.665469 | − | 3.54926i | ||||
\(217\) | 7113.69 | 2.22539 | ||||||||
\(218\) | −3679.32 | − | 6372.76i | −1.14310 | − | 1.97990i | ||||
\(219\) | 41.7976 | + | 675.683i | 0.0128969 | + | 0.208486i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −274.735 | + | 475.856i | −0.0836231 | + | 0.144839i | ||||
\(222\) | −2822.68 | + | 1871.11i | −0.853360 | + | 0.565679i | ||||
\(223\) | −1399.42 | − | 2423.86i | −0.420233 | − | 0.727865i | 0.575729 | − | 0.817641i | \(-0.304718\pi\) |
−0.995962 | + | 0.0897754i | \(0.971385\pi\) | |||||||
\(224\) | −21840.7 | −6.51471 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2404.27 | 0.707653 | ||||||||
\(227\) | −1564.59 | − | 2709.94i | −0.457468 | − | 0.792358i | 0.541358 | − | 0.840792i | \(-0.317910\pi\) |
−0.998826 | + | 0.0484343i | \(0.984577\pi\) | |||||||
\(228\) | −5579.66 | − | 2777.08i | −1.62071 | − | 0.806651i | ||||
\(229\) | −1487.79 | + | 2576.93i | −0.429327 | + | 0.743616i | −0.996814 | − | 0.0797667i | \(-0.974582\pi\) |
0.567487 | + | 0.823383i | \(0.307916\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 748.265 | + | 372.423i | 0.213127 | + | 0.106076i | ||||
\(232\) | 4865.49 | + | 8427.27i | 1.37687 | + | 2.38482i | ||||
\(233\) | −925.895 | −0.260332 | −0.130166 | − | 0.991492i | \(-0.541551\pi\) | ||||
−0.130166 | + | 0.991492i | \(0.541551\pi\) | |||||||
\(234\) | −2266.89 | + | 281.536i | −0.633297 | + | 0.0786521i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7224.55 | − | 12513.3i | −1.99271 | − | 3.45147i | ||||
\(237\) | 3195.57 | − | 2118.29i | 0.875842 | − | 0.580582i | ||||
\(238\) | −2566.53 | + | 4445.36i | −0.699005 | + | 1.21071i | ||||
\(239\) | −1305.41 | + | 2261.04i | −0.353305 | + | 0.611942i | −0.986826 | − | 0.161783i | \(-0.948276\pi\) |
0.633521 | + | 0.773725i | \(0.281609\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 334.737 | + | 579.781i | 0.0894700 | + | 0.154967i | 0.907287 | − | 0.420511i | \(-0.138149\pi\) |
−0.817817 | + | 0.575478i | \(0.804816\pi\) | |||||||
\(242\) | 7162.34 | 1.90253 | ||||||||
\(243\) | −1151.61 | − | 3608.70i | −0.304016 | − | 0.952667i | ||||
\(244\) | 13578.0 | 3.56247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −283.382 | − | 4581.05i | −0.0734464 | − | 1.18731i | ||||
\(247\) | −402.490 | + | 697.134i | −0.103684 | + | 0.179585i | ||||
\(248\) | 11303.0 | − | 19577.4i | 2.89412 | − | 5.01276i | ||||
\(249\) | 1602.05 | − | 1061.97i | 0.407734 | − | 0.270281i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6463.00 | −1.62526 | −0.812631 | − | 0.582778i | \(-0.801966\pi\) | ||||
−0.812631 | + | 0.582778i | \(0.801966\pi\) | |||||||
\(252\) | −15665.3 | + | 1945.55i | −3.91596 | + | 0.486341i | ||||
\(253\) | −523.827 | −0.130169 | ||||||||
\(254\) | 5128.87 | + | 8883.46i | 1.26698 | + | 2.19448i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10044.7 | + | 17398.0i | −2.45233 | + | 4.24755i | ||||
\(257\) | 1417.66 | − | 2455.47i | 0.344091 | − | 0.595984i | −0.641097 | − | 0.767460i | \(-0.721520\pi\) |
0.985188 | + | 0.171476i | \(0.0548536\pi\) | |||||||
\(258\) | 7607.27 | + | 3786.25i | 1.83569 | + | 0.913650i | ||||
\(259\) | 1511.31 | + | 2617.66i | 0.362579 | + | 0.628005i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1938.68 | + | 2565.30i | 0.459775 | + | 0.608383i | ||||
\(262\) | 7082.32 | 1.67003 | ||||||||
\(263\) | 816.837 | + | 1414.80i | 0.191515 | + | 0.331713i | 0.945752 | − | 0.324888i | \(-0.105327\pi\) |
−0.754238 | + | 0.656601i | \(0.771993\pi\) | |||||||
\(264\) | 2213.86 | − | 1467.53i | 0.516112 | − | 0.342123i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3759.99 | + | 6512.49i | −0.866691 | + | 1.50115i | ||||
\(267\) | 72.3891 | + | 1170.21i | 0.0165923 | + | 0.268224i | ||||
\(268\) | 3751.94 | + | 6498.55i | 0.855173 | + | 1.48120i | ||||
\(269\) | −4870.30 | −1.10389 | −0.551947 | − | 0.833880i | \(-0.686115\pi\) | ||||
−0.551947 | + | 0.833880i | \(0.686115\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3913.17 | −0.877153 | −0.438576 | − | 0.898694i | \(-0.644517\pi\) | ||||
−0.438576 | + | 0.898694i | \(0.644517\pi\) | |||||||
\(272\) | 4881.02 | + | 8454.17i | 1.08807 | + | 1.88459i | ||||
\(273\) | 125.881 | + | 2034.95i | 0.0279072 | + | 0.451138i | ||||
\(274\) | 4251.09 | − | 7363.11i | 0.937291 | − | 1.62344i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8245.99 | − | 5466.14i | 1.79837 | − | 1.19211i | ||||
\(277\) | −409.072 | − | 708.534i | −0.0887320 | − | 0.153688i | 0.818243 | − | 0.574872i | \(-0.194948\pi\) |
−0.906975 | + | 0.421184i | \(0.861615\pi\) | |||||||
\(278\) | −8501.11 | −1.83404 | ||||||||
\(279\) | 2909.15 | − | 6880.08i | 0.624252 | − | 1.47634i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2581.48 | + | 4471.25i | 0.548035 | + | 0.949225i | 0.998409 | + | 0.0563851i | \(0.0179574\pi\) |
−0.450374 | + | 0.892840i | \(0.648709\pi\) | |||||||
\(282\) | −2148.14 | − | 1069.16i | −0.453617 | − | 0.225772i | ||||
\(283\) | 3573.29 | − | 6189.11i | 0.750565 | − | 1.30002i | −0.196984 | − | 0.980407i | \(-0.563115\pi\) |
0.947549 | − | 0.319610i | \(-0.103552\pi\) | |||||||
\(284\) | 13071.9 | − | 22641.2i | 2.73125 | − | 4.73067i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −264.635 | − | 458.360i | −0.0547139 | − | 0.0947672i | ||||
\(287\) | −4096.58 | −0.842556 | ||||||||
\(288\) | −8931.78 | + | 21123.5i | −1.82747 | + | 4.32192i | ||||
\(289\) | −3616.47 | −0.736102 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 51.5971 | − | 34.2029i | 0.0103941 | − | 0.00689007i | ||||
\(292\) | 1481.20 | − | 2565.51i | 0.296851 | − | 0.514161i | ||||
\(293\) | 732.548 | − | 1268.81i | 0.146061 | − | 0.252985i | −0.783707 | − | 0.621130i | \(-0.786674\pi\) |
0.929768 | + | 0.368145i | \(0.120007\pi\) | |||||||
\(294\) | 565.871 | + | 9147.65i | 0.112253 | + | 1.81463i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9605.31 | 1.88614 | ||||||||
\(297\) | 666.196 | − | 571.390i | 0.130157 | − | 0.111634i | ||||
\(298\) | 13877.5 | 2.69766 | ||||||||
\(299\) | −638.889 | − | 1106.59i | −0.123572 | − | 0.214032i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3792.14 | − | 6568.19i | 0.726165 | − | 1.25775i | ||||
\(302\) | −4215.36 | + | 7301.22i | −0.803202 | + | 1.39119i | ||||
\(303\) | −3319.86 | + | 2200.68i | −0.629442 | + | 0.417248i | ||||
\(304\) | 7150.74 | + | 12385.4i | 1.34909 | + | 2.33669i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3249.79 | + | 4300.17i | 0.607118 | + | 0.803348i | ||||
\(307\) | −790.554 | −0.146968 | −0.0734842 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734842 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(308\) | −1828.75 | − | 3167.49i | −0.338321 | − | 0.585988i | ||||
\(309\) | −7207.88 | − | 3587.47i | −1.32700 | − | 0.660466i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1962.65 | + | 3399.42i | −0.357852 | + | 0.619817i | −0.987602 | − | 0.156981i | \(-0.949824\pi\) |
0.629750 | + | 0.776798i | \(0.283157\pi\) | |||||||
\(312\) | 5800.33 | + | 2886.91i | 1.05250 | + | 0.523843i | ||||
\(313\) | −2871.19 | − | 4973.04i | −0.518495 | − | 0.898060i | −0.999769 | − | 0.0214900i | \(-0.993159\pi\) |
0.481274 | − | 0.876570i | \(-0.340174\pi\) | |||||||
\(314\) | 14375.4 | 2.58360 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16776.9 | −2.98663 | ||||||||
\(317\) | −4068.35 | − | 7046.59i | −0.720824 | − | 1.24850i | −0.960670 | − | 0.277693i | \(-0.910430\pi\) |
0.239846 | − | 0.970811i | \(-0.422903\pi\) | |||||||
\(318\) | 3578.21 | − | 2371.94i | 0.630994 | − | 0.418276i | ||||
\(319\) | −372.508 | + | 645.203i | −0.0653807 | + | 0.113243i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 390.896 | + | 6319.07i | 0.0679679 | + | 1.09874i | ||||
\(322\) | −5968.39 | − | 10337.5i | −1.03294 | − | 1.78910i | ||||
\(323\) | 1899.43 | 0.327205 | ||||||||
\(324\) | −4524.68 | + | 15946.5i | −0.775837 | + | 2.73431i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1872.77 | + | 3243.73i | 0.318169 | + | 0.551085i | ||||
\(327\) | 425.814 | + | 6883.54i | 0.0720109 | + | 1.16410i | ||||
\(328\) | −6509.10 | + | 11274.1i | −1.09575 | + | 1.89789i | ||||
\(329\) | −1070.83 | + | 1854.72i | −0.179442 | + | 0.310803i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3163.47 | + | 5479.29i | 0.525317 | + | 0.909876i | 0.999565 | + | 0.0294849i | \(0.00938671\pi\) |
−0.474248 | + | 0.880391i | \(0.657280\pi\) | |||||||
\(332\) | −8410.84 | −1.39038 | ||||||||
\(333\) | 3149.74 | − | 391.181i | 0.518333 | − | 0.0643742i | ||||
\(334\) | −21599.8 | −3.53858 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 32427.9 | + | 16139.9i | 5.26515 | + | 2.62054i | ||||
\(337\) | −2387.01 | + | 4134.42i | −0.385842 | + | 0.668297i | −0.991886 | − | 0.127134i | \(-0.959422\pi\) |
0.606044 | + | 0.795431i | \(0.292756\pi\) | |||||||
\(338\) | −5444.76 | + | 9430.60i | −0.876201 | + | 1.51762i | ||||
\(339\) | −2017.29 | − | 1004.04i | −0.323198 | − | 0.160861i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1730.75 | 0.274854 | ||||||||
\(342\) | 4760.97 | + | 6299.80i | 0.752760 | + | 0.996065i | ||||
\(343\) | −639.195 | −0.100622 | ||||||||
\(344\) | −12050.7 | − | 20872.5i | −1.88876 | − | 3.27142i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 143.209 | − | 248.045i | 0.0222513 | − | 0.0385404i | ||||
\(347\) | 909.717 | − | 1575.68i | 0.140738 | − | 0.243766i | −0.787037 | − | 0.616906i | \(-0.788386\pi\) |
0.927775 | + | 0.373141i | \(0.121719\pi\) | |||||||
\(348\) | −868.746 | − | 14043.8i | −0.133821 | − | 2.16330i | ||||
\(349\) | 1488.69 | + | 2578.48i | 0.228331 | + | 0.395481i | 0.957314 | − | 0.289051i | \(-0.0933397\pi\) |
−0.728982 | + | 0.684532i | \(0.760006\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2019.60 | + | 710.445i | 0.307117 | + | 0.108036i | ||||
\(352\) | −5313.80 | −0.804621 | ||||||||
\(353\) | −3473.89 | − | 6016.95i | −0.523786 | − | 0.907223i | −0.999617 | − | 0.0276865i | \(-0.991186\pi\) |
0.475831 | − | 0.879537i | \(-0.342147\pi\) | |||||||
\(354\) | 1130.28 | + | 18271.7i | 0.169700 | + | 2.74331i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2565.28 | − | 4443.19i | 0.381909 | − | 0.661485i | ||||
\(357\) | 4009.84 | − | 2658.06i | 0.594463 | − | 0.394060i | ||||
\(358\) | 12622.4 | + | 21862.6i | 1.86344 | + | 3.22758i | ||||
\(359\) | −3665.56 | −0.538887 | −0.269444 | − | 0.963016i | \(-0.586840\pi\) | ||||
−0.269444 | + | 0.963016i | \(0.586840\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4076.31 | −0.594302 | ||||||||
\(362\) | 6766.71 | + | 11720.3i | 0.982460 | + | 1.70167i | ||||
\(363\) | −6009.53 | − | 2991.03i | −0.868921 | − | 0.432475i | ||||
\(364\) | 4460.90 | − | 7726.50i | 0.642348 | − | 1.11258i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −15400.9 | − | 7665.24i | −2.19950 | − | 1.09472i | ||||
\(367\) | −4831.54 | − | 8368.48i | −0.687206 | − | 1.19028i | −0.972738 | − | 0.231906i | \(-0.925504\pi\) |
0.285532 | − | 0.958369i | \(-0.407830\pi\) | |||||||
\(368\) | −22701.3 | −3.21573 | ||||||||
\(369\) | −1675.30 | + | 3962.05i | −0.236349 | + | 0.558960i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1915.83 | − | 3318.31i | −0.268099 | − | 0.464362i | ||||
\(372\) | −27245.1 | + | 18060.4i | −3.79730 | + | 2.51717i | ||||
\(373\) | 3011.86 | − | 5216.70i | 0.418092 | − | 0.724157i | −0.577655 | − | 0.816281i | \(-0.696032\pi\) |
0.995748 | + | 0.0921237i | \(0.0293655\pi\) | |||||||
\(374\) | −624.431 | + | 1081.55i | −0.0863330 | + | 0.149533i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3402.89 | + | 5893.97i | 0.466730 | + | 0.808400i | ||||
\(377\) | −1817.33 | −0.248269 | ||||||||
\(378\) | 18866.7 | + | 6636.85i | 2.56719 | + | 0.903076i | ||||
\(379\) | −1229.32 | −0.166613 | −0.0833063 | − | 0.996524i | \(-0.526548\pi\) | ||||
−0.0833063 | + | 0.996524i | \(0.526548\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −593.573 | − | 9595.47i | −0.0798154 | − | 1.29026i | ||||
\(382\) | 3676.09 | − | 6367.17i | 0.492369 | − | 0.852809i | ||||
\(383\) | 1066.80 | − | 1847.75i | 0.142326 | − | 0.246515i | −0.786046 | − | 0.618168i | \(-0.787875\pi\) |
0.928372 | + | 0.371652i | \(0.121209\pi\) | |||||||
\(384\) | 31569.7 | − | 20927.0i | 4.19540 | − | 2.78106i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8029.07 | −1.05873 | ||||||||
\(387\) | −4801.69 | − | 6353.67i | −0.630707 | − | 0.834562i | ||||
\(388\) | −270.887 | −0.0354439 | ||||||||
\(389\) | −4920.76 | − | 8523.01i | −0.641369 | − | 1.11088i | −0.985127 | − | 0.171825i | \(-0.945033\pi\) |
0.343759 | − | 0.939058i | \(-0.388300\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1507.52 | + | 2611.10i | −0.194984 | + | 0.337722i | ||||
\(392\) | 12997.7 | − | 22512.6i | 1.67470 | − | 2.90066i | ||||
\(393\) | −5942.39 | − | 2957.61i | −0.762732 | − | 0.379623i | ||||
\(394\) | −6649.80 | − | 11517.8i | −0.850284 | − | 1.47274i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3811.34 | + | 473.348i | −0.483654 | + | 0.0600672i | ||||
\(397\) | −2548.71 | −0.322207 | −0.161104 | − | 0.986938i | \(-0.551505\pi\) | ||||
−0.161104 | + | 0.986938i | \(0.551505\pi\) | |||||||
\(398\) | 8618.85 | + | 14928.3i | 1.08549 | + | 1.88012i | ||||
\(399\) | 5874.46 | − | 3894.09i | 0.737069 | − | 0.488592i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6552.50 | − | 11349.3i | 0.816001 | − | 1.41335i | −0.0926064 | − | 0.995703i | \(-0.529520\pi\) |
0.908607 | − | 0.417652i | \(-0.137147\pi\) | |||||||
\(402\) | −586.992 | − | 9489.08i | −0.0728271 | − | 1.17729i | ||||
\(403\) | 2110.92 | + | 3656.22i | 0.260924 | + | 0.451934i | ||||
\(404\) | 17429.4 | 2.14640 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16977.2 | −2.07528 | ||||||||
\(407\) | 367.697 | + | 636.871i | 0.0447815 | + | 0.0775639i | ||||
\(408\) | −943.903 | − | 15258.8i | −0.114535 | − | 1.85152i | ||||
\(409\) | −3108.62 | + | 5384.29i | −0.375823 | + | 0.650944i | −0.990450 | − | 0.137874i | \(-0.955973\pi\) |
0.614627 | + | 0.788818i | \(0.289306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6641.73 | + | 4402.70i | −0.797111 | + | 0.528393i | ||||
\(412\) | 17616.0 | + | 30511.7i | 2.10649 | + | 3.64856i | ||||
\(413\) | 16339.4 | 1.94675 | ||||||||
\(414\) | −12438.8 | + | 1544.84i | −1.47666 | + | 0.183393i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6481.02 | − | 11225.5i | −0.763842 | − | 1.32301i | ||||
\(417\) | 7132.82 | + | 3550.11i | 0.837640 | + | 0.416906i | ||||
\(418\) | −914.798 | + | 1584.48i | −0.107044 | + | 0.185405i | ||||
\(419\) | −4214.03 | + | 7298.91i | −0.491334 | + | 0.851015i | −0.999950 | − | 0.00997827i | \(-0.996824\pi\) |
0.508617 | + | 0.860993i | \(0.330157\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6389.69 | + | 11067.3i | 0.739702 | + | 1.28120i | 0.952629 | + | 0.304133i | \(0.0983668\pi\) |
−0.212928 | + | 0.977068i | \(0.568300\pi\) | |||||||
\(422\) | 18349.0 | 2.11662 | ||||||||
\(423\) | 1355.90 | + | 1794.15i | 0.155854 | + | 0.206228i | ||||
\(424\) | −12176.3 | −1.39465 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −27608.5 | + | 18301.3i | −3.14000 | + | 2.08146i | ||||
\(427\) | −7677.17 | + | 13297.2i | −0.870080 | + | 1.50702i | ||||
\(428\) | 13852.3 | − | 23992.9i | 1.56443 | − | 2.70968i | ||||
\(429\) | 30.6266 | + | 495.098i | 0.00344678 | + | 0.0557193i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3149.70 | 0.352009 | 0.176005 | − | 0.984389i | \(-0.443683\pi\) | ||||
0.176005 | + | 0.984389i | \(0.443683\pi\) | |||||||
\(432\) | 28871.3 | − | 24762.6i | 3.21544 | − | 2.75785i | ||||
\(433\) | −6999.89 | −0.776890 | −0.388445 | − | 0.921472i | \(-0.626988\pi\) | ||||
−0.388445 | + | 0.921472i | \(0.626988\pi\) | |||||||
\(434\) | 19719.8 | + | 34155.7i | 2.18106 | + | 3.77771i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15089.7 | − | 26136.2i | 1.65749 | − | 2.87086i | ||||
\(437\) | −2208.53 | + | 3825.29i | −0.241759 | + | 0.418738i | ||||
\(438\) | −3128.36 | + | 2073.74i | −0.341276 | + | 0.226227i | ||||
\(439\) | 3861.15 | + | 6687.71i | 0.419778 | + | 0.727077i | 0.995917 | − | 0.0902746i | \(-0.0287745\pi\) |
−0.576139 | + | 0.817352i | \(0.695441\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3345.32 | − | 7911.61i | 0.361226 | − | 0.854293i | ||||
\(442\) | −3046.37 | −0.327830 | ||||||||
\(443\) | 3324.37 | + | 5757.97i | 0.356536 | + | 0.617538i | 0.987380 | − | 0.158372i | \(-0.0506244\pi\) |
−0.630844 | + | 0.775910i | \(0.717291\pi\) | |||||||
\(444\) | −12434.0 | − | 6188.58i | −1.32903 | − | 0.661480i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7758.64 | − | 13438.4i | 0.823727 | − | 1.42674i | ||||
\(447\) | −11643.9 | − | 5795.32i | −1.23207 | − | 0.613220i | ||||
\(448\) | −32660.4 | − | 56569.5i | −3.44433 | − | 5.96576i | ||||
\(449\) | −11416.8 | −1.19998 | −0.599989 | − | 0.800008i | \(-0.704829\pi\) | ||||
−0.599989 | + | 0.800008i | \(0.704829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −996.690 | −0.104063 | ||||||||
\(452\) | 4930.23 | + | 8539.41i | 0.513050 | + | 0.888629i | ||||
\(453\) | 6585.91 | − | 4365.70i | 0.683075 | − | 0.452800i | ||||
\(454\) | 8674.35 | − | 15024.4i | 0.896713 | − | 1.55315i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1382.83 | − | 22354.3i | −0.142011 | − | 2.29569i | ||||
\(457\) | 5595.73 | + | 9692.09i | 0.572773 | + | 0.992072i | 0.996280 | + | 0.0861787i | \(0.0274656\pi\) |
−0.423507 | + | 0.905893i | \(0.639201\pi\) | |||||||
\(458\) | −16497.2 | −1.68310 | ||||||||
\(459\) | −930.944 | − | 4965.17i | −0.0946683 | − | 0.504912i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2450.93 | + | 4245.14i | 0.247617 | + | 0.428885i | 0.962864 | − | 0.269987i | \(-0.0870193\pi\) |
−0.715247 | + | 0.698871i | \(0.753686\pi\) | |||||||
\(462\) | 286.108 | + | 4625.12i | 0.0288116 | + | 0.465757i | ||||
\(463\) | 1065.82 | − | 1846.06i | 0.106982 | − | 0.185299i | −0.807564 | − | 0.589780i | \(-0.799214\pi\) |
0.914546 | + | 0.404481i | \(0.132548\pi\) | |||||||
\(464\) | −16143.6 | + | 27961.5i | −1.61519 | + | 2.79758i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2566.67 | − | 4445.60i | −0.255147 | − | 0.441928i | ||||
\(467\) | −17877.0 | −1.77141 | −0.885707 | − | 0.464246i | \(-0.846325\pi\) | ||||
−0.885707 | + | 0.464246i | \(0.846325\pi\) | |||||||
\(468\) | −5648.48 | − | 7474.16i | −0.557908 | − | 0.738234i | ||||
\(469\) | −8485.57 | −0.835452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12061.6 | − | 6003.24i | −1.17998 | − | 0.587293i | ||||
\(472\) | 25961.8 | − | 44967.2i | 2.53176 | − | 4.38513i | ||||
\(473\) | 922.621 | − | 1598.03i | 0.0896874 | − | 0.155343i | ||||
\(474\) | 19029.2 | + | 9471.11i | 1.84397 | + | 0.917769i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21051.8 | −2.02712 | ||||||||
\(477\) | −3992.82 | + | 495.887i | −0.383268 | + | 0.0475998i | ||||
\(478\) | −14474.9 | −1.38507 | ||||||||
\(479\) | −10208.9 | − | 17682.3i | −0.973811 | − | 1.68669i | −0.683805 | − | 0.729665i | \(-0.739676\pi\) |
−0.290006 | − | 0.957025i | \(-0.593657\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −896.930 | + | 1553.53i | −0.0850239 | + | 0.147266i | ||||
\(482\) | −1855.84 | + | 3214.41i | −0.175376 | + | 0.303760i | ||||
\(483\) | 690.732 | + | 11166.1i | 0.0650712 | + | 1.05192i | ||||
\(484\) | 14687.2 | + | 25439.0i | 1.37934 | + | 2.38908i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14134.5 | − | 15533.0i | 1.31924 | − | 1.44978i | ||||
\(487\) | −8337.59 | −0.775795 | −0.387898 | − | 0.921702i | \(-0.626799\pi\) | ||||
−0.387898 | + | 0.921702i | \(0.626799\pi\) | |||||||
\(488\) | 24396.6 | + | 42256.2i | 2.26308 | + | 3.91977i | ||||
\(489\) | −216.739 | − | 3503.72i | −0.0200435 | − | 0.324016i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8132.34 | + | 14085.6i | −0.747469 | + | 1.29465i | 0.201563 | + | 0.979476i | \(0.435398\pi\) |
−0.949032 | + | 0.315179i | \(0.897935\pi\) | |||||||
\(492\) | 15689.7 | − | 10400.5i | 1.43770 | − | 0.953029i | ||||
\(493\) | 2144.08 | + | 3713.66i | 0.195871 | + | 0.339259i | ||||
\(494\) | −4462.96 | −0.406474 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 75006.2 | 6.79008 | ||||||||
\(497\) | 14782.0 | + | 25603.2i | 1.33413 | + | 2.31079i | ||||
\(498\) | 9540.00 | + | 4748.20i | 0.858429 | + | 0.427253i | ||||
\(499\) | 8055.83 | − | 13953.1i | 0.722702 | − | 1.25176i | −0.237210 | − | 0.971458i | \(-0.576233\pi\) |
0.959913 | − | 0.280299i | \(-0.0904336\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18123.2 | + | 9020.18i | 1.61614 | + | 0.804375i | ||||
\(502\) | −17916.0 | − | 31031.5i | −1.59289 | − | 2.75897i | ||||
\(503\) | −9219.89 | −0.817285 | −0.408643 | − | 0.912695i | \(-0.633998\pi\) | ||||
−0.408643 | + | 0.912695i | \(0.633998\pi\) | |||||||
\(504\) | −34201.8 | − | 45256.4i | −3.02276 | − | 3.99976i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1452.10 | − | 2515.10i | −0.127576 | − | 0.220968i | ||||
\(507\) | 8506.67 | − | 5638.94i | 0.745157 | − | 0.493953i | ||||
\(508\) | −21034.7 | + | 36433.1i | −1.83713 | + | 3.18200i | ||||
\(509\) | −4283.42 | + | 7419.11i | −0.373005 | + | 0.646063i | −0.990026 | − | 0.140883i | \(-0.955006\pi\) |
0.617022 | + | 0.786946i | \(0.288339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1674.97 | + | 2901.14i | 0.145003 | + | 0.251152i | ||||
\(512\) | −53065.9 | −4.58048 | ||||||||
\(513\) | −1363.84 | − | 7274.03i | −0.117378 | − | 0.626036i | ||||
\(514\) | 15719.6 | 1.34895 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2151.69 | + | 34783.4i | 0.183572 | + | 2.96755i | ||||
\(517\) | −260.530 | + | 451.250i | −0.0221626 | + | 0.0383868i | ||||
\(518\) | −8378.96 | + | 14512.8i | −0.710715 | + | 1.23099i | ||||
\(519\) | −223.743 | + | 148.316i | −0.0189234 | + | 0.0125440i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2450.94 | −0.206099 | −0.103050 | − | 0.994676i | \(-0.532860\pi\) | ||||
−0.103050 | + | 0.994676i | \(0.532860\pi\) | |||||||
\(522\) | −6942.82 | + | 16419.6i | −0.582144 | + | 1.37676i | ||||
\(523\) | −20897.8 | −1.74722 | −0.873609 | − | 0.486628i | \(-0.838227\pi\) | ||||
−0.873609 | + | 0.486628i | \(0.838227\pi\) | |||||||
\(524\) | 14523.1 | + | 25154.8i | 1.21077 | + | 2.09712i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4528.70 | + | 7843.94i | −0.375400 | + | 0.650213i | ||||
\(527\) | 4980.92 | − | 8627.20i | 0.411712 | − | 0.713106i | ||||
\(528\) | 7889.65 | + | 3926.80i | 0.650290 | + | 0.323659i | ||||
\(529\) | 2577.80 | + | 4464.89i | 0.211868 | + | 0.366967i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6682.01 | − | 15802.8i | 0.546091 | − | 1.29149i | ||||
\(532\) | −30841.2 | −2.51341 | ||||||||
\(533\) | −1215.62 | − | 2105.52i | −0.0987887 | − | 0.171107i | ||||
\(534\) | −5418.00 | + | 3591.51i | −0.439063 | + | 0.291048i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13482.8 | + | 23352.9i | −1.08651 | + | 1.88189i | ||||
\(537\) | −1460.81 | − | 23614.9i | −0.117390 | − | 1.89768i | ||||
\(538\) | −13500.9 | − | 23384.3i | −1.08191 | − | 1.87392i | ||||
\(539\) | 1990.24 | 0.159046 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9960.84 | −0.791590 | −0.395795 | − | 0.918339i | \(-0.629531\pi\) | ||||
−0.395795 | + | 0.918339i | \(0.629531\pi\) | |||||||
\(542\) | −10847.7 | − | 18788.7i | −0.859682 | − | 1.48901i | ||||
\(543\) | −783.123 | − | 12659.7i | −0.0618914 | − | 1.00051i | ||||
\(544\) | −15292.6 | + | 26487.6i | −1.20527 | + | 2.08758i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9421.65 | + | 6245.47i | −0.738478 | + | 0.489526i | ||||
\(547\) | 4297.17 | + | 7442.93i | 0.335894 | + | 0.581785i | 0.983656 | − | 0.180057i | \(-0.0576283\pi\) |
−0.647762 | + | 0.761843i | \(0.724295\pi\) | |||||||
\(548\) | 34869.4 | 2.71815 | ||||||||
\(549\) | 9720.98 | + | 12863.0i | 0.755704 | + | 0.999960i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3141.10 | + | 5440.55i | 0.242859 | + | 0.420645i | ||||
\(552\) | 31827.4 | + | 15841.0i | 2.45410 | + | 1.22144i | ||||
\(553\) | 9485.85 | − | 16430.0i | 0.729438 | − | 1.26342i | ||||
\(554\) | 2267.97 | − | 3928.24i | 0.173929 | − | 0.301255i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17432.5 | − | 30194.0i | −1.32968 | − | 2.30308i | ||||
\(557\) | 9469.85 | 0.720378 | 0.360189 | − | 0.932879i | \(-0.382712\pi\) | ||||
0.360189 | + | 0.932879i | \(0.382712\pi\) | |||||||
\(558\) | 41098.5 | − | 5104.21i | 3.11799 | − | 0.387238i | ||||
\(559\) | 4501.13 | 0.340568 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 975.585 | − | 646.701i | 0.0734211 | − | 0.0486697i | ||||
\(562\) | −14312.2 | + | 24789.4i | −1.07424 | + | 1.86064i | ||||
\(563\) | −4.38733 | + | 7.59907i | −0.000328426 | + | 0.000568850i | −0.866190 | − | 0.499716i | \(-0.833438\pi\) |
0.865861 | + | 0.500284i | \(0.166771\pi\) | |||||||
\(564\) | −607.595 | − | 9822.14i | −0.0453623 | − | 0.733310i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 39621.9 | 2.94246 | ||||||||
\(567\) | −13058.4 | − | 13447.5i | −0.967202 | − | 0.996015i | ||||
\(568\) | 93949.2 | 6.94018 | ||||||||
\(569\) | 123.467 | + | 213.851i | 0.00909667 | + | 0.0157559i | 0.870538 | − | 0.492101i | \(-0.163771\pi\) |
−0.861441 | + | 0.507857i | \(0.830438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1723.59 | + | 2985.35i | −0.126323 | + | 0.218797i | −0.922249 | − | 0.386596i | \(-0.873651\pi\) |
0.795927 | + | 0.605393i | \(0.206984\pi\) | |||||||
\(572\) | 1085.33 | − | 1879.84i | 0.0793354 | − | 0.137413i | ||||
\(573\) | −5743.37 | + | 3807.19i | −0.418731 | + | 0.277570i | ||||
\(574\) | −11356.1 | − | 19669.4i | −0.825775 | − | 1.43028i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −68068.3 | + | 8453.72i | −4.92392 | + | 0.611525i | ||||
\(577\) | 21137.2 | 1.52505 | 0.762525 | − | 0.646959i | \(-0.223960\pi\) | ||||
0.762525 | + | 0.646959i | \(0.223960\pi\) | |||||||
\(578\) | −10025.2 | − | 17364.1i | −0.721441 | − | 1.24957i | ||||
\(579\) | 6736.76 | + | 3352.98i | 0.483541 | + | 0.240665i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4755.59 | − | 8236.92i | 0.339578 | − | 0.588167i | ||||
\(582\) | 307.254 | + | 152.925i | 0.0218833 | + | 0.0108916i | ||||
\(583\) | −466.117 | − | 807.339i | −0.0331125 | − | 0.0573526i | ||||
\(584\) | 10645.5 | 0.754305 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8122.77 | 0.572608 | ||||||||
\(587\) | −2655.50 | − | 4599.47i | −0.186720 | − | 0.323408i | 0.757435 | − | 0.652910i | \(-0.226452\pi\) |
−0.944155 | + | 0.329503i | \(0.893119\pi\) | |||||||
\(588\) | −31330.0 | + | 20768.2i | −2.19732 | + | 1.45657i | ||||
\(589\) | 7297.10 | − | 12638.9i | 0.510478 | − | 0.884174i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 769.593 | + | 12440.9i | 0.0535648 | + | 0.865908i | ||||
\(592\) | 15935.1 | + | 27600.4i | 1.10630 | + | 1.91616i | ||||
\(593\) | 11575.8 | 0.801624 | 0.400812 | − | 0.916160i | \(-0.368728\pi\) | ||||
0.400812 | + | 0.916160i | \(0.368728\pi\) | |||||||
\(594\) | 4590.23 | + | 1614.73i | 0.317070 | + | 0.111537i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28457.4 | + | 49289.7i | 1.95581 | + | 3.38756i | ||||
\(597\) | −997.475 | − | 16124.8i | −0.0683818 | − | 1.10543i | ||||
\(598\) | 3542.12 | − | 6135.13i | 0.242221 | − | 0.419539i | ||||
\(599\) | 3563.32 | − | 6171.85i | 0.243061 | − | 0.420993i | −0.718524 | − | 0.695502i | \(-0.755182\pi\) |
0.961585 | + | 0.274509i | \(0.0885153\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3860.93 | + | 6687.32i | 0.262047 | + | 0.453879i | 0.966786 | − | 0.255588i | \(-0.0822690\pi\) |
−0.704739 | + | 0.709467i | \(0.748936\pi\) | |||||||
\(602\) | 42048.7 | 2.84681 | ||||||||
\(603\) | −3470.18 | + | 8206.90i | −0.234356 | + | 0.554247i | ||||
\(604\) | −34576.4 | −2.32929 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −19769.3 | − | 9839.49i | −1.32521 | − | 0.659574i | ||||
\(607\) | −7180.72 | + | 12437.4i | −0.480159 | + | 0.831659i | −0.999741 | − | 0.0227612i | \(-0.992754\pi\) |
0.519582 | + | 0.854420i | \(0.326088\pi\) | |||||||
\(608\) | −22403.8 | + | 38804.6i | −1.49440 | + | 2.58838i | ||||
\(609\) | 14244.6 | + | 7089.76i | 0.947817 | + | 0.471743i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1271.03 | −0.0841575 | ||||||||
\(612\) | −8609.17 | + | 20360.5i | −0.568636 | + | 1.34481i | ||||
\(613\) | −12086.0 | −0.796330 | −0.398165 | − | 0.917314i | \(-0.630353\pi\) | ||||
−0.398165 | + | 0.917314i | \(0.630353\pi\) | |||||||
\(614\) | −2191.49 | − | 3795.77i | −0.144041 | − | 0.249487i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6571.71 | − | 11382.5i | 0.429840 | − | 0.744505i | ||||
\(617\) | 12617.9 | − | 21854.8i | 0.823301 | − | 1.42600i | −0.0799090 | − | 0.996802i | \(-0.525463\pi\) |
0.903210 | − | 0.429198i | \(-0.141204\pi\) | |||||||
\(618\) | −2756.02 | − | 44552.7i | −0.179391 | − | 2.89996i | ||||
\(619\) | 2452.72 | + | 4248.24i | 0.159262 | + | 0.275850i | 0.934603 | − | 0.355693i | \(-0.115755\pi\) |
−0.775341 | + | 0.631543i | \(0.782422\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11081.9 | + | 3898.34i | 0.716104 | + | 0.251908i | ||||
\(622\) | −21762.6 | −1.40290 | ||||||||
\(623\) | 2900.88 | + | 5024.47i | 0.186551 | + | 0.323116i | ||||
\(624\) | 1327.28 | + | 21456.3i | 0.0851503 | + | 1.37651i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15918.4 | − | 27571.5i | 1.01634 | − | 1.76035i | ||||
\(627\) | 1429.24 | − | 947.423i | 0.0910342 | − | 0.0603452i | ||||
\(628\) | 29478.4 | + | 51058.1i | 1.87312 | + | 3.24433i | ||||
\(629\) | 4232.79 | 0.268318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11240.9 | −0.709181 | −0.354590 | − | 0.935022i | \(-0.615380\pi\) | ||||
−0.354590 | + | 0.935022i | \(0.615380\pi\) | |||||||
\(632\) | −30144.3 | − | 52211.5i | −1.89727 | − | 3.28617i | ||||
\(633\) | −15395.6 | − | 7662.64i | −0.966702 | − | 0.481142i | ||||
\(634\) | 22555.7 | − | 39067.6i | 1.41293 | − | 2.44727i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 15762.1 | + | 7845.05i | 0.982719 | + | 0.489114i | ||||
\(637\) | 2427.41 | + | 4204.39i | 0.150985 | + | 0.261514i | ||||
\(638\) | −4130.51 | −0.256314 | ||||||||
\(639\) | 30807.5 | − | 3826.13i | 1.90724 | − | 0.236869i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5579.48 | − | 9663.94i | −0.343800 | − | 0.595480i | 0.641335 | − | 0.767261i | \(-0.278381\pi\) |
−0.985135 | + | 0.171781i | \(0.945048\pi\) | |||||||
\(642\) | −29256.8 | + | 19393.9i | −1.79856 | + | 1.19224i | ||||
\(643\) | −13622.4 | + | 23594.7i | −0.835483 | + | 1.44710i | 0.0581529 | + | 0.998308i | \(0.481479\pi\) |
−0.893636 | + | 0.448792i | \(0.851854\pi\) | |||||||
\(644\) | 24477.7 | − | 42396.7i | 1.49776 | − | 2.59420i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5265.40 | + | 9119.93i | 0.320688 | + | 0.555447i | ||||
\(647\) | 31360.6 | 1.90559 | 0.952793 | − | 0.303620i | \(-0.0981955\pi\) | ||||
0.952793 | + | 0.303620i | \(0.0981955\pi\) | |||||||
\(648\) | −57757.1 | + | 14571.0i | −3.50141 | + | 0.883337i | ||||
\(649\) | 3975.34 | 0.240440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2282.21 | − | 36893.3i | −0.137399 | − | 2.22114i | ||||
\(652\) | −7680.67 | + | 13303.3i | −0.461347 | + | 0.799076i | ||||
\(653\) | −3537.24 | + | 6126.67i | −0.211980 | + | 0.367160i | −0.952334 | − | 0.305057i | \(-0.901324\pi\) |
0.740354 | + | 0.672217i | \(0.234658\pi\) | |||||||
\(654\) | −31870.3 | + | 21126.3i | −1.90554 | + | 1.26316i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −43194.0 | −2.57080 | ||||||||
\(657\) | 3490.84 | − | 433.544i | 0.207292 | − | 0.0257446i | ||||
\(658\) | −11873.7 | −0.703473 | ||||||||
\(659\) | −9249.31 | − | 16020.3i | −0.546740 | − | 0.946982i | −0.998495 | − | 0.0548399i | \(-0.982535\pi\) |
0.451755 | − | 0.892142i | \(-0.350798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3200.38 | + | 5543.23i | −0.188321 | + | 0.326182i | −0.944691 | − | 0.327963i | \(-0.893638\pi\) |
0.756369 | + | 0.654145i | \(0.226971\pi\) | |||||||
\(662\) | −17538.9 | + | 30378.2i | −1.02971 | + | 1.78351i | ||||
\(663\) | 2556.04 | + | 1272.18i | 0.149726 | + | 0.0745209i | ||||
\(664\) | −15112.4 | − | 26175.4i | −0.883245 | − | 1.52982i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10609.6 | + | 14038.8i | 0.617288 | + | 0.816806i | ||||
\(667\) | −9972.01 | −0.578887 | ||||||||
\(668\) | −44292.8 | − | 76717.4i | −2.56548 | − | 4.44354i | ||||
\(669\) | −12121.8 | + | 8035.34i | −0.700531 | + | 0.464371i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1867.84 | + | 3235.19i | −0.107462 | + | 0.186130i | ||||
\(672\) | 7006.92 | + | 113271.i | 0.402229 | + | 6.50228i | ||||
\(673\) | 7115.68 | + | 12324.7i | 0.407562 | + | 0.705918i | 0.994616 | − | 0.103630i | \(-0.0330456\pi\) |
−0.587054 | + | 0.809548i | \(0.699712\pi\) | |||||||
\(674\) | −26468.0 | −1.51263 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44660.4 | −2.54099 | ||||||||
\(677\) | 9953.99 | + | 17240.8i | 0.565085 | + | 0.978756i | 0.997042 | + | 0.0768620i | \(0.0244901\pi\) |
−0.431956 | + | 0.901894i | \(0.642177\pi\) | |||||||
\(678\) | −771.336 | − | 12469.1i | −0.0436917 | − | 0.706303i | ||||
\(679\) | 153.163 | − | 265.286i | 0.00865663 | − | 0.0149937i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13552.5 | + | 8983.72i | −0.762601 | + | 0.505517i | ||||
\(682\) | 4797.79 | + | 8310.02i | 0.269380 | + | 0.466579i | ||||
\(683\) | −26204.1 | −1.46804 | −0.734021 | − | 0.679126i | \(-0.762359\pi\) | ||||
−0.734021 | + | 0.679126i | \(0.762359\pi\) | |||||||
\(684\) | −12612.5 | + | 29828.4i | −0.705047 | + | 1.66742i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1771.91 | − | 3069.03i | −0.0986177 | − | 0.170811i | ||||
\(687\) | 13841.9 | + | 6889.30i | 0.768705 | + | 0.382596i | ||||
\(688\) | 39984.1 | − | 69254.4i | 2.21567 | − | 3.83765i | ||||
\(689\) | 1137.01 | − | 1969.35i | 0.0628687 | − | 0.108892i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13281.2 | + | 23003.8i | 0.731176 | + | 1.26643i | 0.956381 | + | 0.292122i | \(0.0943614\pi\) |
−0.225205 | + | 0.974311i | \(0.572305\pi\) | |||||||
\(692\) | 1174.66 | 0.0645289 | ||||||||
\(693\) | 1691.42 | − | 4000.16i | 0.0927151 | − | 0.219269i | ||||
\(694\) | 10087.3 | 0.551741 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 42144.9 | − | 27937.2i | 2.29526 | − | 1.52149i | ||||
\(697\) | −2868.38 | + | 4968.17i | −0.155879 | + | 0.269990i | ||||
\(698\) | −8253.56 | + | 14295.6i | −0.447567 | + | 0.775209i | ||||
\(699\) | 297.045 | + | 4801.91i | 0.0160734 | + | 0.259836i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35417.5 | 1.90827 | 0.954137 | − | 0.299372i | \(-0.0967771\pi\) | ||||
0.954137 | + | 0.299372i | \(0.0967771\pi\) | |||||||
\(702\) | 2187.38 | + | 11666.3i | 0.117603 | + | 0.627232i | ||||
\(703\) | 6201.08 | 0.332686 | ||||||||
\(704\) | −7946.22 | − | 13763.3i | −0.425404 | − | 0.736821i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19259.9 | − | 33359.1i | 1.02671 | − | 1.77831i | ||||
\(707\) | −9854.81 | + | 17069.0i | −0.524227 | + | 0.907987i | ||||
\(708\) | −62579.2 | + | 41482.8i | −3.32185 | + | 2.20200i | ||||
\(709\) | 8339.20 | + | 14443.9i | 0.441728 | + | 0.765096i | 0.997818 | − | 0.0660267i | \(-0.0210322\pi\) |
−0.556090 | + | 0.831122i | \(0.687699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12011.2 | − | 15893.4i | −0.633550 | − | 0.838324i | ||||
\(712\) | 18436.9 | 0.970439 | ||||||||
\(713\) | 11583.0 | + | 20062.3i | 0.608396 | + | 1.05377i | ||||
\(714\) | 23878.1 | + | 11884.5i | 1.25156 | + | 0.622920i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51767.2 | + | 89663.5i | −2.70200 | + | 4.68000i | ||||
\(717\) | 12145.1 | + | 6044.78i | 0.632588 | + | 0.314849i | ||||
\(718\) | −10161.3 | − | 17599.8i | −0.528154 | − | 0.914790i | ||||
\(719\) | 3273.36 | 0.169786 | 0.0848928 | − | 0.996390i | \(-0.472945\pi\) | ||||
0.0848928 | + | 0.996390i | \(0.472945\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −39841.1 | −2.05792 | ||||||||
\(722\) | −11299.9 | − | 19572.0i | −0.582465 | − | 1.00886i | ||||
\(723\) | 2899.49 | − | 1922.03i | 0.149147 | − | 0.0988672i | ||||
\(724\) | −27751.8 | + | 48067.6i | −1.42457 | + | 2.46743i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2297.82 | − | 37145.6i | −0.117465 | − | 1.89890i | ||||
\(727\) | −16970.3 | − | 29393.3i | −0.865738 | − | 1.49950i | −0.866312 | − | 0.499503i | \(-0.833516\pi\) |
0.000573784 | − | 1.00000i | \(-0.499817\pi\) | |||||||
\(728\) | 32060.9 | 1.63222 | ||||||||
\(729\) | −18346.1 | + | 7130.26i | −0.932079 | + | 0.362255i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5310.42 | − | 9197.92i | −0.268691 | − | 0.465386i | ||||
\(732\) | −4356.09 | − | 70418.8i | −0.219953 | − | 3.55567i | ||||
\(733\) | 952.351 | − | 1649.52i | 0.0479890 | − | 0.0831193i | −0.841033 | − | 0.540984i | \(-0.818052\pi\) |
0.889022 | + | 0.457864i | \(0.151385\pi\) | |||||||
\(734\) | 26787.0 | − | 46396.4i | 1.34704 | − | 2.33314i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35562.5 | − | 61596.0i | −1.78105 | − | 3.08486i | ||||
\(737\) | −2064.52 | −0.103185 | ||||||||
\(738\) | −23667.5 | + | 2939.38i | −1.18051 | + | 0.146612i | ||||
\(739\) | 23159.4 | 1.15282 | 0.576408 | − | 0.817162i | \(-0.304454\pi\) | ||||
0.576408 | + | 0.817162i | \(0.304454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3744.63 | + | 1863.76i | 0.185644 | + | 0.0923979i | ||||
\(742\) | 10621.7 | − | 18397.3i | 0.525519 | − | 0.910226i | ||||
\(743\) | 10943.4 | − | 18954.5i | 0.540342 | − | 0.935900i | −0.458542 | − | 0.888673i | \(-0.651628\pi\) |
0.998884 | − | 0.0472272i | \(-0.0150385\pi\) | |||||||
\(744\) | −105159. | − | 52339.3i | −5.18189 | − | 2.57910i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 33396.7 | 1.63906 | ||||||||
\(747\) | −6021.62 | − | 7967.91i | −0.294939 | − | 0.390268i | ||||
\(748\) | −5121.87 | −0.250367 | ||||||||
\(749\) | 15664.5 | + | 27131.8i | 0.764179 | + | 1.32360i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15830.7 | − | 27419.5i | 0.769200 | − | 1.33229i | −0.168797 | − | 0.985651i | \(-0.553988\pi\) |
0.937997 | − | 0.346643i | \(-0.112678\pi\) | |||||||
\(752\) | −11290.7 | + | 19556.1i | −0.547512 | + | 0.948319i | ||||
\(753\) | 2073.45 | + | 33518.7i | 0.100346 | + | 1.62216i | ||||
\(754\) | −5037.81 | − | 8725.74i | −0.243324 | − | 0.421449i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 15115.8 | + | 80619.9i | 0.727191 | + | 3.87846i | ||||
\(757\) | 29482.4 | 1.41553 | 0.707764 | − | 0.706449i | \(-0.249704\pi\) | ||||
0.707764 | + | 0.706449i | \(0.249704\pi\) | |||||||
\(758\) | −3407.80 | − | 5902.48i | −0.163294 | − | 0.282834i | ||||
\(759\) | 168.054 | + | 2716.69i | 0.00803684 | + | 0.129920i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13012.0 | − | 22537.4i | 0.619822 | − | 1.07356i | −0.369696 | − | 0.929153i | \(-0.620538\pi\) |
0.989518 | − | 0.144410i | \(-0.0461284\pi\) | |||||||
\(762\) | 44426.3 | − | 29449.5i | 2.11207 | − | 1.40006i | ||||
\(763\) | 17063.8 | + | 29555.4i | 0.809636 | + | 1.40233i | ||||
\(764\) | 30153.0 | 1.42788 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11829.0 | 0.557964 | ||||||||
\(767\) | 4848.56 | + | 8397.94i | 0.228254 | + | 0.395348i | ||||
\(768\) | 93452.6 | + | 46512.8i | 4.39086 | + | 2.18540i | ||||
\(769\) | −839.198 | + | 1453.53i | −0.0393527 | + | 0.0681609i | −0.885031 | − | 0.465532i | \(-0.845863\pi\) |
0.845678 | + | 0.533693i | \(0.179196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13189.5 | − | 6564.59i | −0.616092 | − | 0.306638i | ||||
\(772\) | −16464.5 | − | 28517.4i | −0.767580 | − | 1.32949i | ||||
\(773\) | 25777.0 | 1.19940 | 0.599698 | − | 0.800226i | \(-0.295287\pi\) | ||||
0.599698 | + | 0.800226i | \(0.295287\pi\) | |||||||
\(774\) | 17195.8 | − | 40667.8i | 0.798568 | − | 1.88860i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −486.724 | − | 843.030i | −0.0225159 | − | 0.0389987i | ||||
\(777\) | 13090.9 | − | 8677.79i | 0.604421 | − | 0.400661i | ||||
\(778\) | 27281.6 | − | 47253.1i | 1.25719 | − | 2.17752i | ||||
\(779\) | −4202.20 | + | 7278.43i | −0.193273 | + | 0.334758i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3596.44 | + | 6229.21i | 0.164777 | + | 0.285402i | ||||
\(782\) | −16716.0 | −0.764401 | ||||||||
\(783\) | 12682.3 | − | 10877.5i | 0.578835 | − | 0.496461i | ||||
\(784\) | 86251.9 | 3.92911 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2272.14 | − | 36730.6i | −0.103110 | − | 1.66684i | ||||
\(787\) | −20408.3 | + | 35348.2i | −0.924368 | + | 1.60105i | −0.131794 | + | 0.991277i | \(0.542074\pi\) |
−0.792574 | + | 0.609775i | \(0.791260\pi\) | |||||||
\(788\) | 27272.4 | − | 47237.1i | 1.23292 | − | 2.13547i | ||||
\(789\) | 7075.45 | − | 4690.21i | 0.319256 | − | 0.211630i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11150.4 | −0.501219 | ||||||||
\(792\) | −8321.23 | − | 11010.8i | −0.373336 | − | 0.494004i | ||||
\(793\) | −9112.50 | −0.408063 | ||||||||
\(794\) | −7065.27 | − | 12237.4i | −0.315790 | − | 0.546964i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −35347.9 | + | 61224.4i | −1.57396 | + | 2.72618i | ||||
\(797\) | 4974.78 | − | 8616.57i | 0.221099 | − | 0.382954i | −0.734043 | − | 0.679103i | \(-0.762369\pi\) |
0.955142 | + | 0.296148i | \(0.0957023\pi\) | |||||||
\(798\) | 34981.6 | + | 17410.9i | 1.55180 | + | 0.772354i | ||||
\(799\) | 1499.56 | + | 2597.31i | 0.0663961 | + | 0.115001i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6045.78 | − | 750.854i | 0.266688 | − | 0.0331212i | ||||
\(802\) | 72656.6 | 3.19899 | ||||||||
\(803\) | 407.517 | + | 705.840i | 0.0179091 | + | 0.0310194i | ||||
\(804\) | 32499.4 | − | 21543.3i | 1.42558 | − | 0.944993i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11703.3 | + | 20270.8i | −0.511454 | + | 0.885865i | ||||
\(807\) | 1562.48 | + | 25258.5i | 0.0681562 | + | 1.10179i | ||||
\(808\) | 31316.8 | + | 54242.3i | 1.36352 | + | 2.36168i | ||||
\(809\) | −32596.2 | −1.41659 | −0.708295 | − | 0.705917i | \(-0.750535\pi\) | ||||
−0.708295 | + | 0.705917i | \(0.750535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7399.23 | −0.320373 | −0.160186 | − | 0.987087i | \(-0.551210\pi\) | ||||
−0.160186 | + | 0.987087i | \(0.551210\pi\) | |||||||
\(812\) | −34813.6 | − | 60299.0i | −1.50458 | − | 2.60601i | ||||
\(813\) | 1255.42 | + | 20294.7i | 0.0541569 | + | 0.875479i | ||||
\(814\) | −2038.58 | + | 3530.93i | −0.0877792 | + | 0.152038i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 42279.4 | − | 28026.4i | 1.81382 | − | 1.20235i | ||||
\(817\) | −7779.83 | − | 13475.1i | −0.333148 | − | 0.577029i | ||||
\(818\) | −34469.6 | −1.47335 | ||||||||
\(819\) | 10513.3 | − | 1305.70i | 0.448554 | − | 0.0557080i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8699.04 | + | 15067.2i | 0.369791 | + | 0.640497i | 0.989533 | − | 0.144309i | \(-0.0460959\pi\) |
−0.619741 | + | 0.784806i | \(0.712763\pi\) | |||||||
\(822\) | −39550.7 | − | 19685.0i | −1.67821 | − | 0.835270i | ||||
\(823\) | 2634.82 | − | 4563.64i | 0.111597 | − | 0.193291i | −0.804818 | − | 0.593522i | \(-0.797737\pi\) |
0.916414 | + | 0.400231i | \(0.131070\pi\) | |||||||
\(824\) | −63303.9 | + | 109645.i | −2.67633 | + | 4.63554i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 45294.3 | + | 78452.1i | 1.90798 | + | 3.30472i | ||||
\(827\) | −9005.90 | −0.378677 | −0.189338 | − | 0.981912i | \(-0.560634\pi\) | ||||
−0.189338 | + | 0.981912i | \(0.560634\pi\) | |||||||
\(828\) | −30994.2 | − | 41012.0i | −1.30087 | − | 1.72134i | ||||
\(829\) | 5545.90 | 0.232349 | 0.116174 | − | 0.993229i | \(-0.462937\pi\) | ||||
0.116174 | + | 0.993229i | \(0.462937\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3543.39 | + | 2348.86i | −0.147917 | + | 0.0980517i | ||||
\(832\) | 19383.3 | − | 33572.9i | 0.807688 | − | 1.39896i | ||||
\(833\) | 5727.71 | − | 9920.68i | 0.238239 | − | 0.412642i | ||||
\(834\) | 2727.32 | + | 44088.8i | 0.113237 | + | 1.83054i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7503.60 | −0.310427 | ||||||||
\(837\) | −36615.1 | − | 12880.3i | −1.51207 | − | 0.531909i | ||||
\(838\) | −46726.7 | −1.92619 | ||||||||
\(839\) | 2041.47 | + | 3535.92i | 0.0840038 | + | 0.145499i | 0.904966 | − | 0.425483i | \(-0.139896\pi\) |
−0.820962 | + | 0.570982i | \(0.806563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5103.12 | − | 8838.86i | 0.209239 | − | 0.362412i | ||||
\(842\) | −35425.6 | + | 61359.0i | −1.44994 | + | 2.51137i | ||||
\(843\) | 22360.8 | − | 14822.6i | 0.913578 | − | 0.605597i | ||||
\(844\) | 37626.8 | + | 65171.4i | 1.53456 | + | 2.65793i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4855.76 | + | 11483.8i | −0.197334 | + | 0.466691i | ||||
\(847\) | −33217.3 | −1.34753 | ||||||||
\(848\) | −20200.3 | − | 34988.0i | −0.818022 | − | 1.41686i | ||||
\(849\) | −33244.6 | − | 16546.3i | −1.34388 | − | 0.668868i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4921.61 | + | 8524.48i | −0.198250 | + | 0.343379i | ||||
\(852\) | −121616. | − | 60530.3i | −4.89027 | − | 2.43396i | ||||
\(853\) | −11838.3 | − | 20504.5i | −0.475188 | − | 0.823049i | 0.524409 | − | 0.851467i | \(-0.324286\pi\) |
−0.999596 | + | 0.0284177i | \(0.990953\pi\) | |||||||
\(854\) | −85127.3 | −3.41100 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 99558.1 | 3.97527 | ||||||||
\(857\) | 8275.86 | + | 14334.2i | 0.329869 | + | 0.571351i | 0.982486 | − | 0.186338i | \(-0.0596619\pi\) |
−0.652616 | + | 0.757689i | \(0.726329\pi\) | |||||||
\(858\) | −2292.27 | + | 1519.51i | −0.0912083 | + | 0.0604606i | ||||
\(859\) | 50.2878 | − | 87.1010i | 0.00199744 | − | 0.00345966i | −0.865025 | − | 0.501729i | \(-0.832698\pi\) |
0.867022 | + | 0.498269i | \(0.166031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1314.26 | + | 21245.9i | 0.0520209 | + | 0.840949i | ||||
\(862\) | 8731.27 | + | 15123.0i | 0.344998 | + | 0.597554i | ||||
\(863\) | 21496.8 | 0.847924 | 0.423962 | − | 0.905680i | \(-0.360639\pi\) | ||||
0.423962 | + | 0.905680i | \(0.360639\pi\) | |||||||
\(864\) | 112417. | + | 39545.5i | 4.42650 | + | 1.55714i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19404.4 | − | 33609.3i | −0.761417 | − | 1.31881i | ||||
\(867\) | 1160.23 | + | 18755.9i | 0.0454482 | + | 0.734698i | ||||
\(868\) | −80875.5 | + | 140081.i | −3.16255 | + | 5.47770i | ||||
\(869\) | 2307.89 | − | 3997.38i | 0.0900918 | − | 0.156044i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2518.01 | − | 4361.32i | −0.0979558 | − | 0.169664i | ||||
\(872\) | 108451. | 4.21173 | ||||||||
\(873\) | −193.938 | − | 256.622i | −0.00751867 | − | 0.00994884i | ||||
\(874\) | −24489.1 | −0.947774 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −13780.5 | − | 6858.77i | −0.531508 | − | 0.264539i | ||||
\(877\) | −7609.29 | + | 13179.7i | −0.292984 | + | 0.507464i | −0.974514 | − | 0.224327i | \(-0.927982\pi\) |
0.681530 | + | 0.731791i | \(0.261315\pi\) | |||||||
\(878\) | −21406.9 | + | 37077.9i | −0.822835 | + | 1.42519i | ||||
\(879\) | −6815.37 | − | 3392.11i | −0.261521 | − | 0.130163i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29944.2 | −1.14511 | −0.572557 | − | 0.819865i | \(-0.694048\pi\) | ||||
−0.572557 | + | 0.819865i | \(0.694048\pi\) | |||||||
\(882\) | 47260.4 | − | 5869.49i | 1.80424 | − | 0.224077i | ||||
\(883\) | 22598.4 | 0.861265 | 0.430633 | − | 0.902527i | \(-0.358290\pi\) | ||||
0.430633 | + | 0.902527i | \(0.358290\pi\) | |||||||
\(884\) | −6246.93 | − | 10820.0i | −0.237678 | − | 0.411670i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18430.9 | + | 31923.3i | −0.698869 | + | 1.21048i | ||||
\(887\) | 18103.2 | − | 31355.7i | 0.685283 | − | 1.18694i | −0.288065 | − | 0.957611i | \(-0.593012\pi\) |
0.973348 | − | 0.229334i | \(-0.0736548\pi\) | |||||||
\(888\) | −3081.57 | − | 49815.4i | −0.116453 | − | 1.88254i | ||||
\(889\) | −23786.5 | − | 41199.4i | −0.897383 | − | 1.55431i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3177.09 | − | 3271.74i | −0.119458 | − | 0.123016i | ||||
\(892\) | 63639.9 | 2.38881 | ||||||||
\(893\) | 2196.87 | + | 3805.08i | 0.0823240 | + | 0.142589i | ||||
\(894\) | −4452.17 | − | 71972.1i | −0.166558 | − | 2.69251i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 93712.6 | − | 162315.i | 3.49411 | − | 6.05197i | ||||
\(897\) | −5534.07 | + | 3668.45i | −0.205994 | + | 0.136551i | ||||
\(898\) | −31648.3 | − | 54816.5i | −1.17608 | − | 2.03703i | ||||
\(899\) | 32948.0 | 1.22233 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5365.76 | −0.198401 | ||||||||
\(902\) | −2762.92 | − | 4785.51i | −0.101990 | − | 0.176652i | ||||
\(903\) | −35280.8 | − | 17559.8i | −1.30019 | − | 0.647123i | ||||
\(904\) | −17717.0 | + | 30686.8i | −0.651836 | + | 1.12901i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39218.3 | + | 19519.5i | 1.43812 | + | 0.715775i | ||||
\(907\) | 14719.9 | + | 25495.6i | 0.538883 | + | 0.933372i | 0.998965 | + | 0.0454956i | \(0.0144867\pi\) |
−0.460082 | + | 0.887876i | \(0.652180\pi\) | |||||||
\(908\) | 71151.1 | 2.60047 | ||||||||
\(909\) | 12478.4 | + | 16511.6i | 0.455314 | + | 0.602480i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18064.0 | + | 31287.8i | 0.656956 | + | 1.13788i | 0.981400 | + | 0.191977i | \(0.0614898\pi\) |
−0.324443 | + | 0.945905i | \(0.605177\pi\) | |||||||
\(912\) | 61939.8 | − | 41058.9i | 2.24894 | − | 1.49079i | ||||
\(913\) | 1157.02 | − | 2004.03i | 0.0419408 | − | 0.0726436i | ||||
\(914\) | −31023.8 | + | 53734.7i | −1.12273 | + | 1.94462i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33829.3 | − | 58594.1i | −1.22025 | − | 2.11354i | ||||
\(917\) | −32846.2 | −1.18285 | ||||||||
\(918\) | 21259.1 | − | 18233.8i | 0.764331 | − | 0.655560i | ||||
\(919\) | −9547.59 | −0.342705 | −0.171353 | − | 0.985210i | \(-0.554814\pi\) | ||||
−0.171353 | + | 0.985210i | \(0.554814\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 253.625 | + | 4100.00i | 0.00907407 | + | 0.146688i | ||||
\(922\) | −13588.4 | + | 23535.8i | −0.485369 | + | 0.840685i | ||||
\(923\) | −8772.84 | + | 15195.0i | −0.312851 | + | 0.541874i | ||||
\(924\) | −15840.7 | + | 10500.5i | −0.563982 | + | 0.373855i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11818.2 | 0.419407 | ||||||||
\(927\) | −16293.0 | + | 38532.7i | −0.577275 | + | 1.36524i | ||||
\(928\) | −101158. | −3.57831 | ||||||||
\(929\) | −9245.91 | − | 16014.4i | −0.326532 | − | 0.565570i | 0.655289 | − | 0.755378i | \(-0.272547\pi\) |
−0.981821 | + | 0.189808i | \(0.939213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8391.15 | − | 14533.9i | 0.295391 | − | 0.511632i | ||||
\(932\) | 10526.5 | − | 18232.4i | 0.369964 | − | 0.640797i | ||||
\(933\) | 18259.8 | + | 9088.19i | 0.640729 | + | 0.318900i | ||||
\(934\) | −49556.8 | − | 85834.8i | −1.73613 | − | 3.00707i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13111.3 | − | 31008.1i | 0.457861 | − | 1.08283i | ||||
\(937\) | 268.075 | 0.00934644 | 0.00467322 | − | 0.999989i | \(-0.498512\pi\) | ||||
0.00467322 | + | 0.999989i | \(0.498512\pi\) | |||||||
\(938\) | −23522.8 | − | 40742.7i | −0.818812 | − | 1.41822i | ||||
\(939\) | −24870.2 | + | 16486.1i | −0.864334 | + | 0.572954i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15216.2 | − | 26355.3i | 0.527137 | − | 0.913027i | −0.472363 | − | 0.881404i | \(-0.656599\pi\) |
0.999500 | − | 0.0316233i | \(-0.0100677\pi\) | |||||||
\(942\) | −4611.90 | − | 74554.3i | −0.159516 | − | 2.57867i | ||||
\(943\) | −6670.33 | − | 11553.3i | −0.230345 | − | 0.398970i | ||||
\(944\) | 172281. | 5.93991 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10230.4 | 0.351604 | ||||||||
\(947\) | −14910.6 | − | 25825.8i | −0.511645 | − | 0.886195i | −0.999909 | − | 0.0134993i | \(-0.995703\pi\) |
0.488264 | − | 0.872696i | \(-0.337630\pi\) | |||||||
\(948\) | 5382.35 | + | 87008.9i | 0.184399 | + | 2.98093i | ||||
\(949\) | −994.063 | + | 1721.77i | −0.0340028 | + | 0.0588946i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −35240.1 | + | 23360.1i | −1.20162 | + | 0.796534i | ||||
\(952\) | −37825.5 | − | 65515.6i | −1.28774 | − | 2.23043i | ||||
\(953\) | −41109.5 | −1.39734 | −0.698671 | − | 0.715443i | \(-0.746225\pi\) | ||||
−0.698671 | + | 0.715443i | \(0.746225\pi\) | |||||||
\(954\) | −13449.4 | − | 17796.5i | −0.456437 | − | 0.603965i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −29682.4 | − | 51411.4i | −1.00418 | − | 1.73929i | ||||
\(957\) | 3465.68 | + | 1724.92i | 0.117063 | + | 0.0582642i | ||||
\(958\) | 56599.9 | − | 98033.9i | 1.90883 | − | 3.30619i | ||||
\(959\) | −19715.6 | + | 34148.4i | −0.663868 | + | 1.14985i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23375.2 | − | 40487.0i | −0.784640 | − | 1.35904i | ||||
\(962\) | −9945.49 | −0.333322 | ||||||||
\(963\) | 32646.8 | − | 4054.56i | 1.09245 | − | 0.135676i | ||||
\(964\) | −15222.5 | −0.508592 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −51698.2 | + | 34270.0i | −1.72191 | + | 1.14143i | ||||
\(967\) | 21303.0 | − | 36897.9i | 0.708437 | − | 1.22705i | −0.256999 | − | 0.966412i | \(-0.582734\pi\) |
0.965437 | − | 0.260638i | \(-0.0839329\pi\) | |||||||
\(968\) | −52779.2 | + | 91416.3i | −1.75247 | + | 3.03536i | ||||
\(969\) | −609.374 | − | 9850.90i | −0.0202022 | − | 0.326580i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33410.2 | −1.10421 | −0.552103 | − | 0.833776i | \(-0.686175\pi\) | ||||
−0.552103 | + | 0.833776i | \(0.686175\pi\) | |||||||
\(972\) | 84154.0 | + | 18350.1i | 2.77700 | + | 0.605536i | ||||
\(973\) | 39426.2 | 1.29902 | ||||||||
\(974\) | −23112.6 | − | 40032.1i | −0.760344 | − | 1.31695i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −80947.4 | + | 140205.i | −2.65478 | + | 4.59821i | ||||
\(977\) | −4192.37 | + | 7261.40i | −0.137283 | + | 0.237782i | −0.926467 | − | 0.376375i | \(-0.877170\pi\) |
0.789184 | + | 0.614157i | \(0.210504\pi\) | |||||||
\(978\) | 16222.0 | − | 10753.3i | 0.530390 | − | 0.351587i | ||||
\(979\) | 705.778 | + | 1222.44i | 0.0230406 | + | 0.0399075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 35563.1 | − | 4416.74i | 1.15743 | − | 0.143747i | ||||
\(982\) | −90174.4 | −2.93033 | ||||||||
\(983\) | 9777.09 | + | 16934.4i | 0.317234 | + | 0.549465i | 0.979910 | − | 0.199441i | \(-0.0639127\pi\) |
−0.662676 | + | 0.748906i | \(0.730579\pi\) | |||||||
\(984\) | 60558.4 | + | 30140.8i | 1.96192 | + | 0.976477i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11887.2 | + | 20589.2i | −0.383941 | + | 0.665004i | ||||
\(987\) | 9962.58 | + | 4958.52i | 0.321289 | + | 0.159910i | ||||
\(988\) | −9151.82 | − | 15851.4i | −0.294695 | − | 0.510426i | ||||
\(989\) | 24698.5 | 0.794101 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32644.3 | 1.04640 | 0.523199 | − | 0.852210i | \(-0.324738\pi\) | ||||
0.523199 | + | 0.852210i | \(0.324738\pi\) | |||||||
\(992\) | 117500. | + | 203516.i | 3.76072 | + | 6.51375i | ||||
\(993\) | 27402.0 | − | 18164.4i | 0.875706 | − | 0.580492i | ||||
\(994\) | −81954.3 | + | 141949.i | −2.61512 | + | 4.52953i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2698.36 | + | 43620.6i | 0.0858441 | + | 1.38772i | ||||
\(997\) | −10695.6 | − | 18525.3i | −0.339752 | − | 0.588469i | 0.644634 | − | 0.764492i | \(-0.277010\pi\) |
−0.984386 | + | 0.176023i | \(0.943677\pi\) | |||||||
\(998\) | 89326.0 | 2.83323 | ||||||||
\(999\) | −3039.26 | − | 16209.8i | −0.0962541 | − | 0.513370i |
(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 | 225.4.e.f.76.12 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.49.1 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.49.24 | 48 | |||
5.4 | even | 2 | 225.4.e.e.76.1 | ✓ | 24 | ||
9.4 | even | 3 | 2025.4.a.bf.1.1 | 12 | |||
9.5 | odd | 6 | 2025.4.a.bj.1.12 | 12 | |||
9.7 | even | 3 | inner | 225.4.e.f.151.12 | yes | 24 | |
45.4 | even | 6 | 2025.4.a.bi.1.12 | 12 | |||
45.7 | odd | 12 | 225.4.k.e.124.24 | 48 | |||
45.14 | odd | 6 | 2025.4.a.be.1.1 | 12 | |||
45.34 | even | 6 | 225.4.e.e.151.1 | yes | 24 | ||
45.43 | odd | 12 | 225.4.k.e.124.1 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.1 | ✓ | 24 | 5.4 | even | 2 | ||
225.4.e.e.151.1 | yes | 24 | 45.34 | even | 6 | ||
225.4.e.f.76.12 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.e.f.151.12 | yes | 24 | 9.7 | even | 3 | inner | |
225.4.k.e.49.1 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.49.24 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.124.1 | 48 | 45.43 | odd | 12 | |||
225.4.k.e.124.24 | 48 | 45.7 | odd | 12 | |||
2025.4.a.be.1.1 | 12 | 45.14 | odd | 6 | |||
2025.4.a.bf.1.1 | 12 | 9.4 | even | 3 | |||
2025.4.a.bi.1.12 | 12 | 45.4 | even | 6 | |||
2025.4.a.bj.1.12 | 12 | 9.5 | odd | 6 |