Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(19,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.r (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.12 | ||
Character | \(\chi\) | \(=\) | 105.19 |
Dual form | 105.3.r.a.94.12 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.71634 | + | 0.990928i | 0.858169 | + | 0.495464i | 0.863399 | − | 0.504522i | \(-0.168331\pi\) |
−0.00522998 | + | 0.999986i | \(0.501665\pi\) | |||||||
\(3\) | 0.866025 | + | 1.50000i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.0361245 | − | 0.0625695i | −0.00903112 | − | 0.0156424i | ||||
\(5\) | 0.266380 | + | 4.99290i | 0.0532761 | + | 0.998580i | ||||
\(6\) | 3.43267i | 0.572112i | ||||||||
\(7\) | 2.11222 | + | 6.67372i | 0.301745 | + | 0.953389i | ||||
\(8\) | − | 8.07061i | − | 1.00883i | ||||||
\(9\) | −1.50000 | + | 2.59808i | −0.166667 | + | 0.288675i | ||||
\(10\) | −4.49040 | + | 8.83346i | −0.449040 | + | 0.883346i | ||||
\(11\) | −3.30124 | − | 5.71792i | −0.300113 | − | 0.519810i | 0.676049 | − | 0.736857i | \(-0.263691\pi\) |
−0.976161 | + | 0.217047i | \(0.930358\pi\) | |||||||
\(12\) | 0.0625695 | − | 0.108373i | 0.00521412 | − | 0.00903112i | ||||
\(13\) | 21.3701 | 1.64385 | 0.821926 | − | 0.569594i | \(-0.192900\pi\) | ||||
0.821926 | + | 0.569594i | \(0.192900\pi\) | |||||||
\(14\) | −2.98790 | + | 13.5474i | −0.213421 | + | 0.967672i | ||||
\(15\) | −7.25866 | + | 4.72355i | −0.483910 | + | 0.314903i | ||||
\(16\) | 7.85289 | − | 13.6016i | 0.490806 | − | 0.850101i | ||||
\(17\) | −7.99915 | − | 13.8549i | −0.470538 | − | 0.814996i | 0.528894 | − | 0.848688i | \(-0.322607\pi\) |
−0.999432 | + | 0.0336921i | \(0.989273\pi\) | |||||||
\(18\) | −5.14901 | + | 2.97278i | −0.286056 | + | 0.165155i | ||||
\(19\) | −17.3295 | − | 10.0052i | −0.912079 | − | 0.526589i | −0.0309794 | − | 0.999520i | \(-0.509863\pi\) |
−0.881099 | + | 0.472931i | \(0.843196\pi\) | |||||||
\(20\) | 0.302780 | − | 0.197033i | 0.0151390 | − | 0.00985166i | ||||
\(21\) | −8.18135 | + | 8.94793i | −0.389588 | + | 0.426092i | ||||
\(22\) | − | 13.0852i | − | 0.594780i | ||||||
\(23\) | −1.58738 | − | 0.916472i | −0.0690164 | − | 0.0398466i | 0.465095 | − | 0.885261i | \(-0.346020\pi\) |
−0.534111 | + | 0.845414i | \(0.679354\pi\) | |||||||
\(24\) | 12.1059 | − | 6.98935i | 0.504413 | − | 0.291223i | ||||
\(25\) | −24.8581 | + | 2.66002i | −0.994323 | + | 0.106401i | ||||
\(26\) | 36.6783 | + | 21.1762i | 1.41070 | + | 0.814469i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 0.341268 | − | 0.373245i | 0.0121882 | − | 0.0133302i | ||||
\(29\) | −4.58193 | −0.157997 | −0.0789987 | − | 0.996875i | \(-0.525172\pi\) | ||||
−0.0789987 | + | 0.996875i | \(0.525172\pi\) | |||||||
\(30\) | −17.1390 | + | 0.914397i | −0.571300 | + | 0.0304799i | ||||
\(31\) | 52.5315 | − | 30.3291i | 1.69456 | − | 0.978357i | 0.743821 | − | 0.668379i | \(-0.233012\pi\) |
0.950744 | − | 0.309978i | \(-0.100322\pi\) | |||||||
\(32\) | −1.00099 | + | 0.577921i | −0.0312809 | + | 0.0180600i | ||||
\(33\) | 5.71792 | − | 9.90372i | 0.173270 | − | 0.300113i | ||||
\(34\) | − | 31.7063i | − | 0.932538i | ||||||
\(35\) | −32.7586 | + | 12.3238i | −0.935959 | + | 0.352109i | ||||
\(36\) | 0.216747 | 0.00602075 | ||||||||
\(37\) | 9.38236 | + | 5.41691i | 0.253577 | + | 0.146403i | 0.621401 | − | 0.783493i | \(-0.286564\pi\) |
−0.367824 | + | 0.929895i | \(0.619897\pi\) | |||||||
\(38\) | −19.8288 | − | 34.3446i | −0.521812 | − | 0.903804i | ||||
\(39\) | 18.5070 | + | 32.0551i | 0.474539 | + | 0.821926i | ||||
\(40\) | 40.2957 | − | 2.14985i | 1.00739 | − | 0.0537463i | ||||
\(41\) | − | 18.1160i | − | 0.441854i | −0.975290 | − | 0.220927i | \(-0.929092\pi\) | ||
0.975290 | − | 0.220927i | \(-0.0709083\pi\) | |||||||
\(42\) | −22.9087 | + | 7.25055i | −0.545445 | + | 0.172632i | ||||
\(43\) | − | 19.8864i | − | 0.462474i | −0.972897 | − | 0.231237i | \(-0.925723\pi\) | ||
0.972897 | − | 0.231237i | \(-0.0742772\pi\) | |||||||
\(44\) | −0.238511 | + | 0.413114i | −0.00542071 | + | 0.00938894i | ||||
\(45\) | −13.3715 | − | 6.79727i | −0.297145 | − | 0.151050i | ||||
\(46\) | −1.81632 | − | 3.14595i | −0.0394851 | − | 0.0683902i | ||||
\(47\) | −43.8498 | + | 75.9500i | −0.932974 | + | 1.61596i | −0.154767 | + | 0.987951i | \(0.549463\pi\) |
−0.778207 | + | 0.628007i | \(0.783871\pi\) | |||||||
\(48\) | 27.2032 | 0.566734 | ||||||||
\(49\) | −40.0771 | + | 28.1927i | −0.817900 | + | 0.575361i | ||||
\(50\) | −45.3007 | − | 20.0671i | −0.906015 | − | 0.401341i | ||||
\(51\) | 13.8549 | − | 23.9974i | 0.271665 | − | 0.470538i | ||||
\(52\) | −0.771983 | − | 1.33711i | −0.0148458 | − | 0.0257137i | ||||
\(53\) | −11.5901 | + | 6.69155i | −0.218681 | + | 0.126256i | −0.605340 | − | 0.795967i | \(-0.706963\pi\) |
0.386658 | + | 0.922223i | \(0.373629\pi\) | |||||||
\(54\) | −8.91835 | − | 5.14901i | −0.165155 | − | 0.0953521i | ||||
\(55\) | 27.6696 | − | 18.0059i | 0.503083 | − | 0.327380i | ||||
\(56\) | 53.8610 | − | 17.0469i | 0.961803 | − | 0.304408i | ||||
\(57\) | − | 34.6590i | − | 0.608053i | ||||||
\(58\) | −7.86413 | − | 4.54036i | −0.135588 | − | 0.0782820i | ||||
\(59\) | −3.31610 | + | 1.91455i | −0.0562051 | + | 0.0324501i | −0.527839 | − | 0.849344i | \(-0.676998\pi\) |
0.471634 | + | 0.881794i | \(0.343664\pi\) | |||||||
\(60\) | 0.557765 | + | 0.283534i | 0.00929609 | + | 0.00472557i | ||||
\(61\) | 31.1884 | + | 18.0066i | 0.511285 | + | 0.295191i | 0.733362 | − | 0.679839i | \(-0.237950\pi\) |
−0.222077 | + | 0.975029i | \(0.571284\pi\) | |||||||
\(62\) | 120.216 | 1.93896 | ||||||||
\(63\) | −20.5072 | − | 4.52288i | −0.325510 | − | 0.0717918i | ||||
\(64\) | −65.1138 | −1.01740 | ||||||||
\(65\) | 5.69257 | + | 106.699i | 0.0875780 | + | 1.64152i | ||||
\(66\) | 19.6277 | − | 11.3321i | 0.297390 | − | 0.171698i | ||||
\(67\) | −25.0204 | + | 14.4455i | −0.373439 | + | 0.215605i | −0.674960 | − | 0.737855i | \(-0.735839\pi\) |
0.301521 | + | 0.953460i | \(0.402506\pi\) | |||||||
\(68\) | −0.577930 | + | 1.00100i | −0.00849897 | + | 0.0147207i | ||||
\(69\) | − | 3.17475i | − | 0.0460109i | ||||||
\(70\) | −68.4368 | − | 11.3095i | −0.977668 | − | 0.161565i | ||||
\(71\) | −98.4282 | −1.38631 | −0.693157 | − | 0.720787i | \(-0.743781\pi\) | ||||
−0.693157 | + | 0.720787i | \(0.743781\pi\) | |||||||
\(72\) | 20.9681 | + | 12.1059i | 0.291223 | + | 0.168138i | ||||
\(73\) | 60.2626 | + | 104.378i | 0.825515 | + | 1.42983i | 0.901525 | + | 0.432727i | \(0.142449\pi\) |
−0.0760099 | + | 0.997107i | \(0.524218\pi\) | |||||||
\(74\) | 10.7355 | + | 18.5945i | 0.145075 | + | 0.251277i | ||||
\(75\) | −25.5178 | − | 34.9835i | −0.340237 | − | 0.466446i | ||||
\(76\) | 1.44573i | 0.0190228i | ||||||||
\(77\) | 31.1868 | − | 34.1090i | 0.405024 | − | 0.442974i | ||||
\(78\) | 73.3565i | 0.940468i | ||||||||
\(79\) | 17.2489 | − | 29.8759i | 0.218340 | − | 0.378176i | −0.735961 | − | 0.677024i | \(-0.763269\pi\) |
0.954301 | + | 0.298848i | \(0.0966024\pi\) | |||||||
\(80\) | 70.0033 | + | 35.5855i | 0.875041 | + | 0.444819i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 17.9517 | − | 31.0932i | 0.218923 | − | 0.379186i | ||||
\(83\) | −70.9960 | −0.855373 | −0.427686 | − | 0.903927i | \(-0.640671\pi\) | ||||
−0.427686 | + | 0.903927i | \(0.640671\pi\) | |||||||
\(84\) | 0.855414 | + | 0.188663i | 0.0101835 | + | 0.00224599i | ||||
\(85\) | 67.0454 | − | 43.6296i | 0.788770 | − | 0.513289i | ||||
\(86\) | 19.7060 | − | 34.1317i | 0.229139 | − | 0.396880i | ||||
\(87\) | −3.96806 | − | 6.87289i | −0.0456099 | − | 0.0789987i | ||||
\(88\) | −46.1471 | + | 26.6430i | −0.524398 | + | 0.302762i | ||||
\(89\) | 115.865 | + | 66.8949i | 1.30186 | + | 0.751628i | 0.980723 | − | 0.195406i | \(-0.0626023\pi\) |
0.321135 | + | 0.947033i | \(0.395936\pi\) | |||||||
\(90\) | −16.2144 | − | 24.9166i | −0.180160 | − | 0.276851i | ||||
\(91\) | 45.1382 | + | 142.618i | 0.496024 | + | 1.56723i | ||||
\(92\) | 0.132428i | 0.00143944i | ||||||||
\(93\) | 90.9872 | + | 52.5315i | 0.978357 | + | 0.564855i | ||||
\(94\) | −150.522 | + | 86.9039i | −1.60130 | + | 0.924510i | ||||
\(95\) | 45.3387 | − | 89.1896i | 0.477249 | − | 0.938838i | ||||
\(96\) | −1.73376 | − | 1.00099i | −0.0180600 | − | 0.0104270i | ||||
\(97\) | −119.662 | −1.23363 | −0.616814 | − | 0.787109i | \(-0.711577\pi\) | ||||
−0.616814 | + | 0.787109i | \(0.711577\pi\) | |||||||
\(98\) | −96.7227 | + | 8.67463i | −0.986966 | + | 0.0885166i | ||||
\(99\) | 19.8074 | 0.200075 | ||||||||
\(100\) | 1.06442 | + | 1.45926i | 0.0106442 | + | 0.0145926i | ||||
\(101\) | 49.6705 | − | 28.6773i | 0.491787 | − | 0.283934i | −0.233528 | − | 0.972350i | \(-0.575027\pi\) |
0.725316 | + | 0.688416i | \(0.241694\pi\) | |||||||
\(102\) | 47.5594 | − | 27.4585i | 0.466269 | − | 0.269201i | ||||
\(103\) | −32.8462 | + | 56.8912i | −0.318895 | + | 0.552342i | −0.980258 | − | 0.197724i | \(-0.936645\pi\) |
0.661363 | + | 0.750066i | \(0.269978\pi\) | |||||||
\(104\) | − | 172.470i | − | 1.65836i | ||||||
\(105\) | −46.8555 | − | 38.4651i | −0.446243 | − | 0.366334i | ||||
\(106\) | −26.5234 | −0.250221 | ||||||||
\(107\) | −110.205 | − | 63.6269i | −1.02995 | − | 0.594644i | −0.112982 | − | 0.993597i | \(-0.536040\pi\) |
−0.916971 | + | 0.398953i | \(0.869374\pi\) | |||||||
\(108\) | 0.187708 | + | 0.325120i | 0.00173804 | + | 0.00301037i | ||||
\(109\) | 32.5728 | + | 56.4178i | 0.298833 | + | 0.517595i | 0.975869 | − | 0.218355i | \(-0.0700692\pi\) |
−0.677036 | + | 0.735950i | \(0.736736\pi\) | |||||||
\(110\) | 65.3329 | − | 3.48563i | 0.593935 | − | 0.0316876i | ||||
\(111\) | 18.7647i | 0.169051i | ||||||||
\(112\) | 107.360 | + | 23.6785i | 0.958574 | + | 0.211415i | ||||
\(113\) | − | 92.2637i | − | 0.816493i | −0.912872 | − | 0.408246i | \(-0.866140\pi\) | ||
0.912872 | − | 0.408246i | \(-0.133860\pi\) | |||||||
\(114\) | 34.3446 | − | 59.4865i | 0.301268 | − | 0.521812i | ||||
\(115\) | 4.15301 | − | 8.16974i | 0.0361131 | − | 0.0710412i | ||||
\(116\) | 0.165520 | + | 0.286689i | 0.00142689 | + | 0.00247145i | ||||
\(117\) | −32.0551 | + | 55.5211i | −0.273975 | + | 0.474539i | ||||
\(118\) | −7.58874 | −0.0643113 | ||||||||
\(119\) | 75.5680 | − | 82.6486i | 0.635025 | − | 0.694526i | ||||
\(120\) | 38.1219 | + | 58.5818i | 0.317683 | + | 0.488181i | ||||
\(121\) | 38.7036 | − | 67.0367i | 0.319865 | − | 0.554022i | ||||
\(122\) | 35.6865 | + | 61.8109i | 0.292513 | + | 0.506647i | ||||
\(123\) | 27.1741 | − | 15.6889i | 0.220927 | − | 0.127552i | ||||
\(124\) | −3.79535 | − | 2.19124i | −0.0306076 | − | 0.0176713i | ||||
\(125\) | −19.9029 | − | 123.405i | −0.159223 | − | 0.987243i | ||||
\(126\) | −30.7153 | − | 28.0839i | −0.243773 | − | 0.222888i | ||||
\(127\) | − | 106.233i | − | 0.836481i | −0.908336 | − | 0.418241i | \(-0.862647\pi\) | ||
0.908336 | − | 0.418241i | \(-0.137353\pi\) | |||||||
\(128\) | −107.753 | − | 62.2114i | −0.841823 | − | 0.486027i | ||||
\(129\) | 29.8296 | − | 17.2221i | 0.231237 | − | 0.133505i | ||||
\(130\) | −95.9603 | + | 188.772i | −0.738156 | + | 1.45209i | ||||
\(131\) | −103.944 | − | 60.0123i | −0.793468 | − | 0.458109i | 0.0477140 | − | 0.998861i | \(-0.484806\pi\) |
−0.841182 | + | 0.540752i | \(0.818140\pi\) | |||||||
\(132\) | −0.826227 | −0.00625930 | ||||||||
\(133\) | 30.1682 | − | 136.785i | 0.226829 | − | 1.02846i | ||||
\(134\) | −57.2579 | −0.427298 | ||||||||
\(135\) | −1.38415 | − | 25.9439i | −0.0102530 | − | 0.192177i | ||||
\(136\) | −111.818 | + | 64.5580i | −0.822189 | + | 0.474691i | ||||
\(137\) | 202.262 | − | 116.776i | 1.47636 | − | 0.852380i | 0.476721 | − | 0.879055i | \(-0.341825\pi\) |
0.999644 | + | 0.0266751i | \(0.00849194\pi\) | |||||||
\(138\) | 3.14595 | − | 5.44895i | 0.0227967 | − | 0.0394851i | ||||
\(139\) | − | 63.8054i | − | 0.459031i | −0.973305 | − | 0.229516i | \(-0.926286\pi\) | ||
0.973305 | − | 0.229516i | \(-0.0737142\pi\) | |||||||
\(140\) | 1.95448 | + | 1.60449i | 0.0139606 | + | 0.0114607i | ||||
\(141\) | −151.900 | −1.07731 | ||||||||
\(142\) | −168.936 | − | 97.5353i | −1.18969 | − | 0.686868i | ||||
\(143\) | −70.5477 | − | 122.192i | −0.493341 | − | 0.854491i | ||||
\(144\) | 23.5587 | + | 40.8048i | 0.163602 | + | 0.283367i | ||||
\(145\) | −1.22054 | − | 22.8771i | −0.00841749 | − | 0.157773i | ||||
\(146\) | 238.864i | 1.63605i | ||||||||
\(147\) | −76.9968 | − | 35.7001i | −0.523788 | − | 0.242858i | ||||
\(148\) | − | 0.782732i | − | 0.00528873i | ||||||
\(149\) | −106.401 | + | 184.291i | −0.714098 | + | 1.23685i | 0.249208 | + | 0.968450i | \(0.419830\pi\) |
−0.963306 | + | 0.268405i | \(0.913504\pi\) | |||||||
\(150\) | −9.13099 | − | 85.3297i | −0.0608733 | − | 0.568865i | ||||
\(151\) | −94.6108 | − | 163.871i | −0.626562 | − | 1.08524i | −0.988237 | − | 0.152933i | \(-0.951128\pi\) |
0.361675 | − | 0.932304i | \(-0.382205\pi\) | |||||||
\(152\) | −80.7480 | + | 139.860i | −0.531237 | + | 0.920129i | ||||
\(153\) | 47.9949 | 0.313692 | ||||||||
\(154\) | 87.3267 | − | 27.6387i | 0.567057 | − | 0.179472i | ||||
\(155\) | 165.423 | + | 254.205i | 1.06725 | + | 1.64003i | ||||
\(156\) | 1.33711 | − | 2.31595i | 0.00857124 | − | 0.0148458i | ||||
\(157\) | 38.2441 | + | 66.2408i | 0.243593 | + | 0.421916i | 0.961735 | − | 0.273981i | \(-0.0883405\pi\) |
−0.718142 | + | 0.695897i | \(0.755007\pi\) | |||||||
\(158\) | 59.2098 | − | 34.1848i | 0.374745 | − | 0.216359i | ||||
\(159\) | −20.0747 | − | 11.5901i | −0.126256 | − | 0.0728938i | ||||
\(160\) | −3.15214 | − | 4.84389i | −0.0197009 | − | 0.0302743i | ||||
\(161\) | 2.76340 | − | 12.5295i | 0.0171640 | − | 0.0778229i | ||||
\(162\) | − | 17.8367i | − | 0.110103i | ||||||
\(163\) | 136.910 | + | 79.0449i | 0.839937 | + | 0.484938i | 0.857243 | − | 0.514912i | \(-0.172176\pi\) |
−0.0173059 | + | 0.999850i | \(0.505509\pi\) | |||||||
\(164\) | −1.13351 | + | 0.654433i | −0.00691165 | + | 0.00399044i | ||||
\(165\) | 50.9714 | + | 25.9108i | 0.308918 | + | 0.157035i | ||||
\(166\) | −121.853 | − | 70.3519i | −0.734054 | − | 0.423806i | ||||
\(167\) | 51.2715 | 0.307015 | 0.153507 | − | 0.988147i | \(-0.450943\pi\) | ||||
0.153507 | + | 0.988147i | \(0.450943\pi\) | |||||||
\(168\) | 72.2153 | + | 66.0285i | 0.429853 | + | 0.393027i | ||||
\(169\) | 287.680 | 1.70225 | ||||||||
\(170\) | 158.306 | − | 8.44594i | 0.931214 | − | 0.0496820i | ||||
\(171\) | 51.9885 | − | 30.0156i | 0.304026 | − | 0.175530i | ||||
\(172\) | −1.24428 | + | 0.718385i | −0.00723418 | + | 0.00417666i | ||||
\(173\) | 45.0981 | − | 78.1122i | 0.260683 | − | 0.451516i | −0.705741 | − | 0.708470i | \(-0.749386\pi\) |
0.966424 | + | 0.256954i | \(0.0827190\pi\) | |||||||
\(174\) | − | 15.7283i | − | 0.0903923i | ||||||
\(175\) | −70.2579 | − | 160.277i | −0.401474 | − | 0.915871i | ||||
\(176\) | −103.697 | −0.589188 | ||||||||
\(177\) | −5.74366 | − | 3.31610i | −0.0324501 | − | 0.0187350i | ||||
\(178\) | 132.576 | + | 229.628i | 0.744809 | + | 1.29005i | ||||
\(179\) | 49.2761 | + | 85.3486i | 0.275285 | + | 0.476808i | 0.970207 | − | 0.242277i | \(-0.0778944\pi\) |
−0.694922 | + | 0.719085i | \(0.744561\pi\) | |||||||
\(180\) | 0.0577372 | + | 1.08220i | 0.000320762 | + | 0.00601220i | ||||
\(181\) | 251.131i | 1.38746i | 0.720234 | + | 0.693731i | \(0.244034\pi\) | ||||
−0.720234 | + | 0.693731i | \(0.755966\pi\) | |||||||
\(182\) | −63.8517 | + | 289.509i | −0.350833 | + | 1.59071i | ||||
\(183\) | 62.3768i | 0.340857i | ||||||||
\(184\) | −7.39649 | + | 12.8111i | −0.0401983 | + | 0.0696255i | ||||
\(185\) | −24.5468 | + | 48.2881i | −0.132685 | + | 0.261017i | ||||
\(186\) | 104.110 | + | 180.324i | 0.559730 | + | 0.969481i | ||||
\(187\) | −52.8142 | + | 91.4769i | −0.282429 | + | 0.489181i | ||||
\(188\) | 6.33620 | 0.0337032 | ||||||||
\(189\) | −10.9754 | − | 34.6777i | −0.0580709 | − | 0.183480i | ||||
\(190\) | 166.197 | − | 108.152i | 0.874721 | − | 0.569222i | ||||
\(191\) | −52.6947 | + | 91.2699i | −0.275888 | + | 0.477853i | −0.970359 | − | 0.241668i | \(-0.922305\pi\) |
0.694470 | + | 0.719521i | \(0.255639\pi\) | |||||||
\(192\) | −56.3902 | − | 97.6708i | −0.293699 | − | 0.508702i | ||||
\(193\) | 60.3612 | − | 34.8496i | 0.312752 | − | 0.180568i | −0.335405 | − | 0.942074i | \(-0.608873\pi\) |
0.648157 | + | 0.761506i | \(0.275540\pi\) | |||||||
\(194\) | −205.380 | − | 118.576i | −1.05866 | − | 0.611218i | ||||
\(195\) | −155.118 | + | 100.943i | −0.795477 | + | 0.517654i | ||||
\(196\) | 3.21176 | + | 1.48916i | 0.0163866 | + | 0.00759773i | ||||
\(197\) | 84.6930i | 0.429914i | 0.976624 | + | 0.214957i | \(0.0689611\pi\) | ||||
−0.976624 | + | 0.214957i | \(0.931039\pi\) | |||||||
\(198\) | 33.9962 | + | 19.6277i | 0.171698 | + | 0.0991300i | ||||
\(199\) | 142.197 | − | 82.0977i | 0.714560 | − | 0.412551i | −0.0981872 | − | 0.995168i | \(-0.531304\pi\) |
0.812747 | + | 0.582617i | \(0.197971\pi\) | |||||||
\(200\) | 21.4680 | + | 200.620i | 0.107340 | + | 1.00310i | ||||
\(201\) | −43.3366 | − | 25.0204i | −0.215605 | − | 0.124480i | ||||
\(202\) | 113.668 | 0.562715 | ||||||||
\(203\) | −9.67802 | − | 30.5785i | −0.0476750 | − | 0.150633i | ||||
\(204\) | −2.00201 | −0.00981377 | ||||||||
\(205\) | 90.4515 | − | 4.82576i | 0.441227 | − | 0.0235403i | ||||
\(206\) | −112.750 | + | 65.0963i | −0.547331 | + | 0.316002i | ||||
\(207\) | 4.76213 | − | 2.74942i | 0.0230055 | − | 0.0132822i | ||||
\(208\) | 167.817 | − | 290.667i | 0.806812 | − | 1.39744i | ||||
\(209\) | 132.118i | 0.632144i | ||||||||
\(210\) | −42.3037 | − | 112.449i | −0.201446 | − | 0.535474i | ||||
\(211\) | −180.173 | −0.853903 | −0.426951 | − | 0.904275i | \(-0.640412\pi\) | ||||
−0.426951 | + | 0.904275i | \(0.640412\pi\) | |||||||
\(212\) | 0.837374 | + | 0.483458i | 0.00394988 | + | 0.00228046i | ||||
\(213\) | −85.2413 | − | 147.642i | −0.400194 | − | 0.693157i | ||||
\(214\) | −126.099 | − | 218.410i | −0.589249 | − | 1.02061i | ||||
\(215\) | 99.2906 | − | 5.29734i | 0.461817 | − | 0.0246388i | ||||
\(216\) | 41.9361i | 0.194149i | ||||||||
\(217\) | 313.366 | + | 286.519i | 1.44408 | + | 1.32036i | ||||
\(218\) | 129.109i | 0.592245i | ||||||||
\(219\) | −104.378 | + | 180.788i | −0.476611 | + | 0.825515i | ||||
\(220\) | −2.12617 | − | 1.08082i | −0.00966440 | − | 0.00491280i | ||||
\(221\) | −170.942 | − | 296.081i | −0.773495 | − | 1.33973i | ||||
\(222\) | −18.5945 | + | 32.2066i | −0.0837589 | + | 0.145075i | ||||
\(223\) | −254.131 | −1.13960 | −0.569801 | − | 0.821783i | \(-0.692980\pi\) | ||||
−0.569801 | + | 0.821783i | \(0.692980\pi\) | |||||||
\(224\) | −5.97118 | − | 5.45962i | −0.0266571 | − | 0.0243733i | ||||
\(225\) | 30.3762 | − | 68.5732i | 0.135005 | − | 0.304770i | ||||
\(226\) | 91.4266 | − | 158.356i | 0.404543 | − | 0.700688i | ||||
\(227\) | −82.2533 | − | 142.467i | −0.362349 | − | 0.627608i | 0.625998 | − | 0.779825i | \(-0.284692\pi\) |
−0.988347 | + | 0.152217i | \(0.951359\pi\) | |||||||
\(228\) | −2.16859 | + | 1.25204i | −0.00951138 | + | 0.00549140i | ||||
\(229\) | 94.5952 | + | 54.6146i | 0.413080 | + | 0.238492i | 0.692112 | − | 0.721790i | \(-0.256680\pi\) |
−0.279033 | + | 0.960282i | \(0.590014\pi\) | |||||||
\(230\) | 15.2236 | − | 9.90670i | 0.0661895 | − | 0.0430726i | ||||
\(231\) | 78.1721 | + | 17.2410i | 0.338407 | + | 0.0746363i | ||||
\(232\) | 36.9789i | 0.159392i | ||||||||
\(233\) | 15.9135 | + | 9.18768i | 0.0682984 | + | 0.0394321i | 0.533760 | − | 0.845636i | \(-0.320778\pi\) |
−0.465462 | + | 0.885068i | \(0.654112\pi\) | |||||||
\(234\) | −110.035 | + | 63.5286i | −0.470234 | + | 0.271490i | ||||
\(235\) | −390.892 | − | 198.706i | −1.66337 | − | 0.845557i | ||||
\(236\) | 0.239585 | + | 0.138325i | 0.00101519 | + | 0.000586121i | ||||
\(237\) | 59.7518 | 0.252117 | ||||||||
\(238\) | 211.599 | − | 66.9705i | 0.889071 | − | 0.281389i | ||||
\(239\) | 83.6340 | 0.349933 | 0.174966 | − | 0.984574i | \(-0.444018\pi\) | ||||
0.174966 | + | 0.984574i | \(0.444018\pi\) | |||||||
\(240\) | 7.24641 | + | 135.823i | 0.0301934 | + | 0.565929i | ||||
\(241\) | −78.8045 | + | 45.4978i | −0.326990 | + | 0.188788i | −0.654504 | − | 0.756059i | \(-0.727122\pi\) |
0.327514 | + | 0.944846i | \(0.393789\pi\) | |||||||
\(242\) | 132.857 | − | 76.7050i | 0.548996 | − | 0.316963i | ||||
\(243\) | 7.79423 | − | 13.5000i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | − | 2.60192i | − | 0.0106636i | ||||||
\(245\) | −151.439 | − | 192.591i | −0.618118 | − | 0.786085i | ||||
\(246\) | 62.1864 | 0.252790 | ||||||||
\(247\) | −370.333 | − | 213.812i | −1.49932 | − | 0.865634i | ||||
\(248\) | −244.774 | − | 423.961i | −0.986992 | − | 1.70952i | ||||
\(249\) | −61.4843 | − | 106.494i | −0.246925 | − | 0.427686i | ||||
\(250\) | 88.1256 | − | 231.528i | 0.352502 | − | 0.926110i | ||||
\(251\) | 405.829i | 1.61685i | 0.588601 | + | 0.808424i | \(0.299679\pi\) | ||||
−0.588601 | + | 0.808424i | \(0.700321\pi\) | |||||||
\(252\) | 0.457816 | + | 1.44651i | 0.00181673 | + | 0.00574011i | ||||
\(253\) | 12.1020i | 0.0478339i | ||||||||
\(254\) | 105.269 | − | 182.332i | 0.414446 | − | 0.717842i | ||||
\(255\) | 123.507 | + | 62.7838i | 0.484343 | + | 0.246211i | ||||
\(256\) | 6.93363 | + | 12.0094i | 0.0270845 | + | 0.0469117i | ||||
\(257\) | 23.1123 | − | 40.0316i | 0.0899309 | − | 0.155765i | −0.817551 | − | 0.575856i | \(-0.804669\pi\) |
0.907482 | + | 0.420092i | \(0.138002\pi\) | |||||||
\(258\) | 68.2634 | 0.264587 | ||||||||
\(259\) | −16.3334 | + | 74.0569i | −0.0630632 | + | 0.285934i | ||||
\(260\) | 6.47043 | − | 4.21062i | 0.0248863 | − | 0.0161947i | ||||
\(261\) | 6.87289 | − | 11.9042i | 0.0263329 | − | 0.0456099i | ||||
\(262\) | −118.936 | − | 206.003i | −0.453953 | − | 0.786269i | ||||
\(263\) | −374.030 | + | 215.946i | −1.42217 | + | 0.821089i | −0.996484 | − | 0.0837824i | \(-0.973300\pi\) |
−0.425684 | + | 0.904872i | \(0.639967\pi\) | |||||||
\(264\) | −79.9290 | − | 46.1471i | −0.302762 | − | 0.174799i | ||||
\(265\) | −36.4976 | − | 56.0858i | −0.137727 | − | 0.211644i | ||||
\(266\) | 187.323 | − | 204.875i | 0.704223 | − | 0.770208i | ||||
\(267\) | 231.731i | 0.867905i | ||||||||
\(268\) | 1.80770 | + | 1.04367i | 0.00674514 | + | 0.00389431i | ||||
\(269\) | 122.369 | − | 70.6497i | 0.454903 | − | 0.262638i | −0.254996 | − | 0.966942i | \(-0.582074\pi\) |
0.709899 | + | 0.704304i | \(0.248741\pi\) | |||||||
\(270\) | 23.3328 | − | 45.9000i | 0.0864179 | − | 0.170000i | ||||
\(271\) | −6.46991 | − | 3.73540i | −0.0238742 | − | 0.0137838i | 0.488015 | − | 0.872835i | \(-0.337721\pi\) |
−0.511890 | + | 0.859051i | \(0.671054\pi\) | |||||||
\(272\) | −251.266 | −0.923771 | ||||||||
\(273\) | −174.836 | + | 191.218i | −0.640425 | + | 0.700432i | ||||
\(274\) | 462.866 | 1.68929 | ||||||||
\(275\) | 97.2723 | + | 133.355i | 0.353717 | + | 0.484927i | ||||
\(276\) | −0.198643 | + | 0.114686i | −0.000719719 | + | 0.000415530i | ||||
\(277\) | 23.4240 | − | 13.5238i | 0.0845631 | − | 0.0488225i | −0.457122 | − | 0.889404i | \(-0.651120\pi\) |
0.541685 | + | 0.840581i | \(0.317786\pi\) | |||||||
\(278\) | 63.2265 | − | 109.512i | 0.227433 | − | 0.393926i | ||||
\(279\) | 181.974i | 0.652238i | ||||||||
\(280\) | 99.4608 | + | 264.382i | 0.355217 | + | 0.944220i | ||||
\(281\) | 498.278 | 1.77323 | 0.886617 | − | 0.462505i | \(-0.153049\pi\) | ||||
0.886617 | + | 0.462505i | \(0.153049\pi\) | |||||||
\(282\) | −260.712 | − | 150.522i | −0.924510 | − | 0.533766i | ||||
\(283\) | 177.970 | + | 308.254i | 0.628870 | + | 1.08924i | 0.987779 | + | 0.155863i | \(0.0498158\pi\) |
−0.358908 | + | 0.933373i | \(0.616851\pi\) | |||||||
\(284\) | 3.55567 | + | 6.15860i | 0.0125200 | + | 0.0216852i | ||||
\(285\) | 173.049 | − | 9.23248i | 0.607189 | − | 0.0323947i | ||||
\(286\) | − | 279.631i | − | 0.977730i | ||||||
\(287\) | 120.901 | − | 38.2650i | 0.421259 | − | 0.133327i | ||||
\(288\) | − | 3.46752i | − | 0.0120400i | ||||||
\(289\) | 16.5274 | − | 28.6262i | 0.0571881 | − | 0.0990527i | ||||
\(290\) | 20.5747 | − | 40.4743i | 0.0709472 | − | 0.139566i | ||||
\(291\) | −103.630 | − | 179.493i | −0.356118 | − | 0.616814i | ||||
\(292\) | 4.35391 | − | 7.54120i | 0.0149107 | − | 0.0258260i | ||||
\(293\) | −11.1221 | −0.0379593 | −0.0189797 | − | 0.999820i | \(-0.506042\pi\) | ||||
−0.0189797 | + | 0.999820i | \(0.506042\pi\) | |||||||
\(294\) | −96.7763 | − | 137.572i | −0.329171 | − | 0.467931i | ||||
\(295\) | −10.4425 | − | 16.0470i | −0.0353984 | − | 0.0543965i | ||||
\(296\) | 43.7177 | − | 75.7213i | 0.147695 | − | 0.255815i | ||||
\(297\) | 17.1537 | + | 29.7112i | 0.0577567 | + | 0.100038i | ||||
\(298\) | −365.239 | + | 210.871i | −1.22563 | + | 0.707620i | ||||
\(299\) | −33.9223 | − | 19.5851i | −0.113453 | − | 0.0655019i | ||||
\(300\) | −1.26708 | + | 2.86039i | −0.00422360 | + | 0.00953464i | ||||
\(301\) | 132.716 | − | 42.0043i | 0.440917 | − | 0.139549i | ||||
\(302\) | − | 375.010i | − | 1.24176i | ||||||
\(303\) | 86.0319 | + | 49.6705i | 0.283934 | + | 0.163929i | ||||
\(304\) | −272.173 | + | 157.139i | −0.895307 | + | 0.516906i | ||||
\(305\) | −81.5973 | + | 160.517i | −0.267532 | + | 0.526286i | ||||
\(306\) | 82.3754 | + | 47.5594i | 0.269201 | + | 0.155423i | ||||
\(307\) | 369.947 | 1.20504 | 0.602519 | − | 0.798105i | \(-0.294164\pi\) | ||||
0.602519 | + | 0.798105i | \(0.294164\pi\) | |||||||
\(308\) | −3.26079 | − | 0.719172i | −0.0105870 | − | 0.00233498i | ||||
\(309\) | −113.782 | −0.368228 | ||||||||
\(310\) | 32.0231 | + | 600.225i | 0.103300 | + | 1.93621i | ||||
\(311\) | 250.461 | − | 144.604i | 0.805340 | − | 0.464963i | −0.0399948 | − | 0.999200i | \(-0.512734\pi\) |
0.845335 | + | 0.534236i | \(0.179401\pi\) | |||||||
\(312\) | 258.704 | − | 149.363i | 0.829180 | − | 0.478728i | ||||
\(313\) | −103.131 | + | 178.629i | −0.329493 | + | 0.570699i | −0.982411 | − | 0.186729i | \(-0.940211\pi\) |
0.652918 | + | 0.757429i | \(0.273545\pi\) | |||||||
\(314\) | 151.589i | 0.482766i | ||||||||
\(315\) | 17.1196 | − | 103.595i | 0.0543479 | − | 0.328873i | ||||
\(316\) | −2.49243 | −0.00788743 | ||||||||
\(317\) | 55.5495 | + | 32.0715i | 0.175235 | + | 0.101172i | 0.585052 | − | 0.810996i | \(-0.301074\pi\) |
−0.409817 | + | 0.912168i | \(0.634407\pi\) | |||||||
\(318\) | −22.9699 | − | 39.7851i | −0.0722325 | − | 0.125110i | ||||
\(319\) | 15.1260 | + | 26.1991i | 0.0474170 | + | 0.0821287i | ||||
\(320\) | −17.3451 | − | 325.107i | −0.0542033 | − | 1.01596i | ||||
\(321\) | − | 220.410i | − | 0.686636i | ||||||
\(322\) | 17.1587 | − | 18.7665i | 0.0532880 | − | 0.0582811i | ||||
\(323\) | 320.132i | 0.991120i | ||||||||
\(324\) | −0.325120 | + | 0.563125i | −0.00100346 | + | 0.00173804i | ||||
\(325\) | −531.219 | + | 56.8449i | −1.63452 | + | 0.174907i | ||||
\(326\) | 156.655 | + | 271.335i | 0.480538 | + | 0.832317i | ||||
\(327\) | −56.4178 | + | 97.7185i | −0.172532 | + | 0.298833i | ||||
\(328\) | −146.207 | −0.445754 | ||||||||
\(329\) | −599.490 | − | 132.218i | −1.82216 | − | 0.401879i | ||||
\(330\) | 61.8084 | + | 94.9807i | 0.187298 | + | 0.287820i | ||||
\(331\) | −80.4769 | + | 139.390i | −0.243133 | + | 0.421118i | −0.961605 | − | 0.274437i | \(-0.911508\pi\) |
0.718472 | + | 0.695556i | \(0.244842\pi\) | |||||||
\(332\) | 2.56469 | + | 4.44218i | 0.00772498 | + | 0.0133801i | ||||
\(333\) | −28.1471 | + | 16.2507i | −0.0845257 | + | 0.0488009i | ||||
\(334\) | 87.9991 | + | 50.8063i | 0.263470 | + | 0.152115i | ||||
\(335\) | −78.7900 | − | 121.076i | −0.235194 | − | 0.361422i | ||||
\(336\) | 57.4591 | + | 181.547i | 0.171009 | + | 0.540317i | ||||
\(337\) | − | 262.731i | − | 0.779616i | −0.920896 | − | 0.389808i | \(-0.872541\pi\) | ||
0.920896 | − | 0.389808i | \(-0.127459\pi\) | |||||||
\(338\) | 493.756 | + | 285.070i | 1.46082 | + | 0.843403i | ||||
\(339\) | 138.395 | − | 79.9027i | 0.408246 | − | 0.235701i | ||||
\(340\) | −5.15186 | − | 2.61890i | −0.0151525 | − | 0.00770264i | ||||
\(341\) | −346.838 | − | 200.247i | −1.01712 | − | 0.587235i | ||||
\(342\) | 118.973 | 0.347874 | ||||||||
\(343\) | −272.801 | − | 207.914i | −0.795340 | − | 0.606164i | ||||
\(344\) | −160.495 | −0.466556 | ||||||||
\(345\) | 15.8512 | − | 0.845692i | 0.0459456 | − | 0.00245128i | ||||
\(346\) | 154.807 | − | 89.3780i | 0.447420 | − | 0.258318i | ||||
\(347\) | 322.912 | − | 186.433i | 0.930582 | − | 0.537272i | 0.0435865 | − | 0.999050i | \(-0.486122\pi\) |
0.886996 | + | 0.461778i | \(0.152788\pi\) | |||||||
\(348\) | −0.286689 | + | 0.496559i | −0.000823818 | + | 0.00142689i | ||||
\(349\) | 522.429i | 1.49693i | 0.663173 | + | 0.748466i | \(0.269209\pi\) | ||||
−0.663173 | + | 0.748466i | \(0.730791\pi\) | |||||||
\(350\) | 38.2371 | − | 344.710i | 0.109249 | − | 0.984887i | ||||
\(351\) | −111.042 | −0.316359 | ||||||||
\(352\) | 6.60900 | + | 3.81571i | 0.0187756 | + | 0.0108401i | ||||
\(353\) | 220.040 | + | 381.121i | 0.623344 | + | 1.07966i | 0.988859 | + | 0.148858i | \(0.0475597\pi\) |
−0.365515 | + | 0.930806i | \(0.619107\pi\) | |||||||
\(354\) | −6.57204 | − | 11.3831i | −0.0185651 | − | 0.0321557i | ||||
\(355\) | −26.2194 | − | 491.442i | −0.0738574 | − | 1.38434i | ||||
\(356\) | − | 9.66617i | − | 0.0271522i | ||||||
\(357\) | 189.417 | + | 41.7762i | 0.530579 | + | 0.117020i | ||||
\(358\) | 195.316i | 0.545576i | ||||||||
\(359\) | 113.027 | − | 195.769i | 0.314839 | − | 0.545318i | −0.664564 | − | 0.747231i | \(-0.731383\pi\) |
0.979403 | + | 0.201914i | \(0.0647160\pi\) | |||||||
\(360\) | −54.8581 | + | 107.916i | −0.152384 | + | 0.299767i | ||||
\(361\) | 19.7077 | + | 34.1347i | 0.0545919 | + | 0.0945559i | ||||
\(362\) | −248.852 | + | 431.025i | −0.687437 | + | 1.19068i | ||||
\(363\) | 134.073 | 0.369348 | ||||||||
\(364\) | 7.29293 | − | 7.97627i | 0.0200355 | − | 0.0219128i | ||||
\(365\) | −505.095 | + | 328.689i | −1.38382 | + | 0.900519i | ||||
\(366\) | −61.8109 | + | 107.060i | −0.168882 | + | 0.292513i | ||||
\(367\) | 71.8470 | + | 124.443i | 0.195768 | + | 0.339081i | 0.947152 | − | 0.320785i | \(-0.103947\pi\) |
−0.751384 | + | 0.659866i | \(0.770613\pi\) | |||||||
\(368\) | −24.9310 | + | 14.3939i | −0.0677472 | + | 0.0391139i | ||||
\(369\) | 47.0668 | + | 27.1741i | 0.127552 | + | 0.0736424i | ||||
\(370\) | −89.9806 | + | 58.5546i | −0.243191 | + | 0.158256i | ||||
\(371\) | −69.1384 | − | 63.2152i | −0.186357 | − | 0.170391i | ||||
\(372\) | − | 7.59069i | − | 0.0204051i | ||||||
\(373\) | −524.499 | − | 302.820i | −1.40616 | − | 0.811849i | −0.411149 | − | 0.911568i | \(-0.634872\pi\) |
−0.995016 | + | 0.0997188i | \(0.968206\pi\) | |||||||
\(374\) | −181.294 | + | 104.670i | −0.484743 | + | 0.279867i | ||||
\(375\) | 167.872 | − | 136.727i | 0.447657 | − | 0.364604i | ||||
\(376\) | 612.963 | + | 353.894i | 1.63022 | + | 0.941209i | ||||
\(377\) | −97.9161 | −0.259724 | ||||||||
\(378\) | 15.5256 | − | 70.3944i | 0.0410730 | − | 0.186229i | ||||
\(379\) | −620.928 | −1.63833 | −0.819167 | − | 0.573555i | \(-0.805564\pi\) | ||||
−0.819167 | + | 0.573555i | \(0.805564\pi\) | |||||||
\(380\) | −7.21838 | + | 0.385114i | −0.0189957 | + | 0.00101346i | ||||
\(381\) | 159.350 | − | 92.0006i | 0.418241 | − | 0.241471i | ||||
\(382\) | −180.884 | + | 104.433i | −0.473518 | + | 0.273386i | ||||
\(383\) | 102.428 | − | 177.410i | 0.267435 | − | 0.463211i | −0.700764 | − | 0.713393i | \(-0.747157\pi\) |
0.968199 | + | 0.250182i | \(0.0804906\pi\) | |||||||
\(384\) | − | 215.507i | − | 0.561215i | ||||||
\(385\) | 178.610 | + | 146.627i | 0.463923 | + | 0.380849i | ||||
\(386\) | 138.134 | 0.357859 | ||||||||
\(387\) | 51.6663 | + | 29.8296i | 0.133505 | + | 0.0770790i | ||||
\(388\) | 4.32272 | + | 7.48718i | 0.0111410 | + | 0.0192969i | ||||
\(389\) | 118.635 | + | 205.482i | 0.304974 | + | 0.528231i | 0.977256 | − | 0.212065i | \(-0.0680188\pi\) |
−0.672281 | + | 0.740296i | \(0.734686\pi\) | |||||||
\(390\) | −366.262 | + | 19.5407i | −0.939132 | + | 0.0501045i | ||||
\(391\) | 29.3240i | 0.0749974i | ||||||||
\(392\) | 227.532 | + | 323.447i | 0.580439 | + | 0.825119i | ||||
\(393\) | − | 207.889i | − | 0.528979i | ||||||
\(394\) | −83.9247 | + | 145.362i | −0.213007 | + | 0.368939i | ||||
\(395\) | 153.762 | + | 78.1635i | 0.389271 | + | 0.197882i | ||||
\(396\) | −0.715534 | − | 1.23934i | −0.00180690 | − | 0.00312965i | ||||
\(397\) | −332.765 | + | 576.367i | −0.838200 | + | 1.45181i | 0.0531979 | + | 0.998584i | \(0.483059\pi\) |
−0.891398 | + | 0.453221i | \(0.850275\pi\) | |||||||
\(398\) | 325.412 | 0.817617 | ||||||||
\(399\) | 231.304 | − | 73.2073i | 0.579710 | − | 0.183477i | ||||
\(400\) | −159.027 | + | 358.999i | −0.397568 | + | 0.897497i | ||||
\(401\) | 189.198 | − | 327.700i | 0.471815 | − | 0.817208i | −0.527665 | − | 0.849453i | \(-0.676932\pi\) |
0.999480 | + | 0.0322448i | \(0.0102656\pi\) | |||||||
\(402\) | −49.5868 | − | 85.8868i | −0.123350 | − | 0.213649i | ||||
\(403\) | 1122.60 | − | 648.135i | 2.78561 | − | 1.60827i | ||||
\(404\) | −3.58864 | − | 2.07190i | −0.00888278 | − | 0.00512848i | ||||
\(405\) | 37.7171 | − | 24.5443i | 0.0931286 | − | 0.0606032i | ||||
\(406\) | 13.6903 | − | 62.0732i | 0.0337201 | − | 0.152890i | ||||
\(407\) | − | 71.5300i | − | 0.175749i | ||||||
\(408\) | −193.674 | − | 111.818i | −0.474691 | − | 0.274063i | ||||
\(409\) | 329.967 | − | 190.507i | 0.806766 | − | 0.465787i | −0.0390652 | − | 0.999237i | \(-0.512438\pi\) |
0.845832 | + | 0.533450i | \(0.179105\pi\) | |||||||
\(410\) | 160.027 | + | 81.3483i | 0.390310 | + | 0.198410i | ||||
\(411\) | 350.328 | + | 202.262i | 0.852380 | + | 0.492122i | ||||
\(412\) | 4.74620 | 0.0115199 | ||||||||
\(413\) | −19.7815 | − | 18.0868i | −0.0478971 | − | 0.0437937i | ||||
\(414\) | 10.8979 | 0.0263234 | ||||||||
\(415\) | −18.9119 | − | 354.476i | −0.0455709 | − | 0.854158i | ||||
\(416\) | −21.3912 | + | 12.3502i | −0.0514211 | + | 0.0296880i | ||||
\(417\) | 95.7080 | − | 55.2571i | 0.229516 | − | 0.132511i | ||||
\(418\) | −130.920 | + | 226.759i | −0.313205 | + | 0.542486i | ||||
\(419\) | − | 368.460i | − | 0.879379i | −0.898150 | − | 0.439690i | \(-0.855088\pi\) | ||
0.898150 | − | 0.439690i | \(-0.144912\pi\) | |||||||
\(420\) | −0.714109 | + | 4.32125i | −0.00170026 | + | 0.0102887i | ||||
\(421\) | 294.472 | 0.699457 | 0.349729 | − | 0.936851i | \(-0.386274\pi\) | ||||
0.349729 | + | 0.936851i | \(0.386274\pi\) | |||||||
\(422\) | −309.238 | − | 178.539i | −0.732792 | − | 0.423078i | ||||
\(423\) | −131.549 | − | 227.850i | −0.310991 | − | 0.538653i | ||||
\(424\) | 54.0049 | + | 93.5393i | 0.127370 | + | 0.220611i | ||||
\(425\) | 235.698 | + | 323.129i | 0.554583 | + | 0.760304i | ||||
\(426\) | − | 337.872i | − | 0.793127i | ||||||
\(427\) | −54.2946 | + | 246.176i | −0.127154 | + | 0.576526i | ||||
\(428\) | 9.19396i | 0.0214812i | ||||||||
\(429\) | 122.192 | − | 211.643i | 0.284830 | − | 0.493341i | ||||
\(430\) | 175.665 | + | 89.2978i | 0.408524 | + | 0.207669i | ||||
\(431\) | 218.472 | + | 378.404i | 0.506895 | + | 0.877968i | 0.999968 | + | 0.00797991i | \(0.00254011\pi\) |
−0.493073 | + | 0.869988i | \(0.664127\pi\) | |||||||
\(432\) | −40.8048 | + | 70.6760i | −0.0944556 | + | 0.163602i | ||||
\(433\) | −678.283 | −1.56647 | −0.783237 | − | 0.621724i | \(-0.786433\pi\) | ||||
−0.783237 | + | 0.621724i | \(0.786433\pi\) | |||||||
\(434\) | 253.921 | + | 802.286i | 0.585072 | + | 1.84858i | ||||
\(435\) | 33.2586 | − | 21.6430i | 0.0764566 | − | 0.0497539i | ||||
\(436\) | 2.35335 | − | 4.07613i | 0.00539760 | − | 0.00934892i | ||||
\(437\) | 18.3390 | + | 31.7640i | 0.0419656 | + | 0.0726865i | ||||
\(438\) | −358.295 | + | 206.862i | −0.818026 | + | 0.472287i | ||||
\(439\) | −283.562 | − | 163.715i | −0.645928 | − | 0.372927i | 0.140966 | − | 0.990014i | \(-0.454979\pi\) |
−0.786894 | + | 0.617088i | \(0.788312\pi\) | |||||||
\(440\) | −145.319 | − | 223.310i | −0.330269 | − | 0.507524i | ||||
\(441\) | −13.1311 | − | 146.412i | −0.0297757 | − | 0.332001i | ||||
\(442\) | − | 677.566i | − | 1.53295i | ||||||
\(443\) | 327.473 | + | 189.067i | 0.739216 | + | 0.426787i | 0.821784 | − | 0.569799i | \(-0.192979\pi\) |
−0.0825680 | + | 0.996585i | \(0.526312\pi\) | |||||||
\(444\) | 1.17410 | − | 0.677866i | 0.00264436 | − | 0.00152672i | ||||
\(445\) | −303.135 | + | 596.323i | −0.681202 | + | 1.34005i | ||||
\(446\) | −436.175 | − | 251.826i | −0.977970 | − | 0.564631i | ||||
\(447\) | −368.583 | −0.824570 | ||||||||
\(448\) | −137.534 | − | 434.552i | −0.306997 | − | 0.969981i | ||||
\(449\) | −84.0926 | −0.187289 | −0.0936444 | − | 0.995606i | \(-0.529852\pi\) | ||||
−0.0936444 | + | 0.995606i | \(0.529852\pi\) | |||||||
\(450\) | 120.087 | − | 87.5942i | 0.266860 | − | 0.194654i | ||||
\(451\) | −103.586 | + | 59.8054i | −0.229681 | + | 0.132606i | ||||
\(452\) | −5.77289 | + | 3.33298i | −0.0127719 | + | 0.00737384i | ||||
\(453\) | 163.871 | − | 283.833i | 0.361746 | − | 0.626562i | ||||
\(454\) | − | 326.028i | − | 0.718124i | ||||||
\(455\) | −700.053 | + | 263.361i | −1.53858 | + | 0.578816i | ||||
\(456\) | −279.719 | −0.613419 | ||||||||
\(457\) | −209.133 | − | 120.743i | −0.457621 | − | 0.264207i | 0.253423 | − | 0.967356i | \(-0.418444\pi\) |
−0.711043 | + | 0.703148i | \(0.751777\pi\) | |||||||
\(458\) | 108.238 | + | 187.474i | 0.236328 | + | 0.409332i | ||||
\(459\) | 41.5648 | + | 71.9923i | 0.0905551 | + | 0.156846i | ||||
\(460\) | −0.661201 | + | 0.0352763i | −0.00143739 | + | 7.66877e-5i | ||||
\(461\) | − | 576.884i | − | 1.25137i | −0.780074 | − | 0.625687i | \(-0.784819\pi\) | ||
0.780074 | − | 0.625687i | \(-0.215181\pi\) | |||||||
\(462\) | 117.085 | + | 107.054i | 0.253431 | + | 0.231719i | ||||
\(463\) | − | 535.082i | − | 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(464\) | −35.9814 | + | 62.3216i | −0.0775461 | + | 0.134314i | ||||
\(465\) | −238.047 | + | 468.283i | −0.511930 | + | 1.00706i | ||||
\(466\) | 18.2087 | + | 31.5383i | 0.0390744 | + | 0.0676788i | ||||
\(467\) | −16.2608 | + | 28.1645i | −0.0348197 | + | 0.0603095i | −0.882910 | − | 0.469542i | \(-0.844419\pi\) |
0.848090 | + | 0.529852i | \(0.177752\pi\) | |||||||
\(468\) | 4.63190 | 0.00989722 | ||||||||
\(469\) | −149.254 | − | 136.467i | −0.318238 | − | 0.290974i | ||||
\(470\) | −473.999 | − | 728.392i | −1.00851 | − | 1.54977i | ||||
\(471\) | −66.2408 | + | 114.732i | −0.140639 | + | 0.243593i | ||||
\(472\) | 15.4516 | + | 26.7630i | 0.0327365 | + | 0.0567012i | ||||
\(473\) | −113.709 | + | 65.6497i | −0.240399 | + | 0.138794i | ||||
\(474\) | 102.554 | + | 59.2098i | 0.216359 | + | 0.124915i | ||||
\(475\) | 457.392 | + | 202.613i | 0.962931 | + | 0.426554i | ||||
\(476\) | −7.90114 | − | 1.74261i | −0.0165990 | − | 0.00366094i | ||||
\(477\) | − | 40.1493i | − | 0.0841705i | ||||||
\(478\) | 143.544 | + | 82.8752i | 0.300301 | + | 0.173379i | ||||
\(479\) | 234.740 | − | 135.527i | 0.490063 | − | 0.282938i | −0.234538 | − | 0.972107i | \(-0.575358\pi\) |
0.724601 | + | 0.689169i | \(0.242024\pi\) | |||||||
\(480\) | 4.53599 | − | 8.92314i | 0.00944998 | − | 0.0185899i | ||||
\(481\) | 200.502 | + | 115.760i | 0.416843 | + | 0.240665i | ||||
\(482\) | −180.340 | −0.374150 | ||||||||
\(483\) | 21.1874 | − | 6.70576i | 0.0438663 | − | 0.0138836i | ||||
\(484\) | −5.59260 | −0.0115550 | ||||||||
\(485\) | −31.8756 | − | 597.460i | −0.0657229 | − | 1.23188i | ||||
\(486\) | 26.7550 | − | 15.4470i | 0.0550515 | − | 0.0317840i | ||||
\(487\) | 448.439 | − | 258.906i | 0.920818 | − | 0.531635i | 0.0369223 | − | 0.999318i | \(-0.488245\pi\) |
0.883896 | + | 0.467683i | \(0.154911\pi\) | |||||||
\(488\) | 145.324 | − | 251.709i | 0.297796 | − | 0.515798i | ||||
\(489\) | 273.819i | 0.559958i | ||||||||
\(490\) | −69.0766 | − | 480.616i | −0.140973 | − | 0.980849i | ||||
\(491\) | 700.753 | 1.42719 | 0.713597 | − | 0.700556i | \(-0.247065\pi\) | ||||
0.713597 | + | 0.700556i | \(0.247065\pi\) | |||||||
\(492\) | −1.96330 | − | 1.13351i | −0.00399044 | − | 0.00230388i | ||||
\(493\) | 36.6515 | + | 63.4823i | 0.0743438 | + | 0.128767i | ||||
\(494\) | −423.744 | − | 733.946i | −0.857781 | − | 1.48572i | ||||
\(495\) | 5.27632 | + | 98.8965i | 0.0106592 | + | 0.199791i | ||||
\(496\) | − | 952.684i | − | 1.92073i | ||||||
\(497\) | −207.902 | − | 656.882i | −0.418313 | − | 1.32170i | ||||
\(498\) | − | 243.706i | − | 0.489369i | ||||||
\(499\) | −106.357 | + | 184.216i | −0.213141 | + | 0.369171i | −0.952696 | − | 0.303925i | \(-0.901703\pi\) |
0.739555 | + | 0.673096i | \(0.235036\pi\) | |||||||
\(500\) | −7.00242 | + | 5.70327i | −0.0140048 | + | 0.0114065i | ||||
\(501\) | 44.4024 | + | 76.9072i | 0.0886275 | + | 0.153507i | ||||
\(502\) | −402.147 | + | 696.539i | −0.801089 | + | 1.38753i | ||||
\(503\) | 614.027 | 1.22073 | 0.610365 | − | 0.792120i | \(-0.291023\pi\) | ||||
0.610365 | + | 0.792120i | \(0.291023\pi\) | |||||||
\(504\) | −36.5024 | + | 165.505i | −0.0724255 | + | 0.328383i | ||||
\(505\) | 156.414 | + | 240.361i | 0.309731 | + | 0.475962i | ||||
\(506\) | −11.9922 | + | 20.7711i | −0.0237000 | + | 0.0410495i | ||||
\(507\) | 249.138 | + | 431.520i | 0.491397 | + | 0.851125i | ||||
\(508\) | −6.64695 | + | 3.83762i | −0.0130845 | + | 0.00755437i | ||||
\(509\) | 536.599 | + | 309.806i | 1.05422 | + | 0.608656i | 0.923829 | − | 0.382806i | \(-0.125042\pi\) |
0.130394 | + | 0.991462i | \(0.458376\pi\) | |||||||
\(510\) | 149.766 | + | 230.145i | 0.293659 | + | 0.451265i | ||||
\(511\) | −569.301 | + | 622.644i | −1.11409 | + | 1.21848i | ||||
\(512\) | 525.174i | 1.02573i | ||||||||
\(513\) | 90.0467 | + | 51.9885i | 0.175530 | + | 0.101342i | ||||
\(514\) | 79.3368 | − | 45.8051i | 0.154352 | − | 0.0891151i | ||||
\(515\) | −292.802 | − | 148.843i | −0.568547 | − | 0.289015i | ||||
\(516\) | −2.15516 | − | 1.24428i | −0.00417666 | − | 0.00241139i | ||||
\(517\) | 579.035 | 1.11999 | ||||||||
\(518\) | −101.419 | + | 110.921i | −0.195789 | + | 0.214134i | ||||
\(519\) | 156.224 | 0.301011 | ||||||||
\(520\) | 861.123 | − | 45.9425i | 1.65601 | − | 0.0883510i | ||||
\(521\) | −893.760 | + | 516.013i | −1.71547 | + | 0.990428i | −0.788719 | + | 0.614753i | \(0.789256\pi\) |
−0.926752 | + | 0.375674i | \(0.877411\pi\) | |||||||
\(522\) | 23.5924 | − | 13.6211i | 0.0451962 | − | 0.0260940i | ||||
\(523\) | 30.3733 | − | 52.6082i | 0.0580752 | − | 0.100589i | −0.835526 | − | 0.549451i | \(-0.814837\pi\) |
0.893601 | + | 0.448861i | \(0.148170\pi\) | |||||||
\(524\) | 8.67165i | 0.0165490i | ||||||||
\(525\) | 179.571 | − | 244.191i | 0.342040 | − | 0.465126i | ||||
\(526\) | −855.949 | −1.62728 | ||||||||
\(527\) | −840.414 | − | 485.213i | −1.59471 | − | 0.920708i | ||||
\(528\) | −89.8043 | − | 155.546i | −0.170084 | − | 0.294594i | ||||
\(529\) | −262.820 | − | 455.218i | −0.496824 | − | 0.860525i | ||||
\(530\) | −7.06531 | − | 132.429i | −0.0133308 | − | 0.249865i | ||||
\(531\) | − | 11.4873i | − | 0.0216334i | ||||||
\(532\) | −9.64840 | + | 3.05369i | −0.0181361 | + | 0.00574002i | ||||
\(533\) | − | 387.141i | − | 0.726343i | ||||||
\(534\) | −229.628 | + | 397.728i | −0.430016 | + | 0.744809i | ||||
\(535\) | 288.326 | − | 567.192i | 0.538928 | − | 1.06017i | ||||
\(536\) | 116.584 | + | 201.930i | 0.217508 | + | 0.376735i | ||||
\(537\) | −85.3486 | + | 147.828i | −0.158936 | + | 0.275285i | ||||
\(538\) | 280.035 | 0.520511 | ||||||||
\(539\) | 293.507 | + | 136.087i | 0.544541 | + | 0.252480i | ||||
\(540\) | −1.57329 | + | 1.02381i | −0.00291350 | + | 0.00189595i | ||||
\(541\) | 64.9714 | − | 112.534i | 0.120095 | − | 0.208011i | −0.799710 | − | 0.600387i | \(-0.795013\pi\) |
0.919805 | + | 0.392376i | \(0.128347\pi\) | |||||||
\(542\) | −7.40303 | − | 12.8224i | −0.0136587 | − | 0.0236576i | ||||
\(543\) | −376.696 | + | 217.485i | −0.693731 | + | 0.400526i | ||||
\(544\) | 16.0141 | + | 9.24574i | 0.0294377 | + | 0.0169959i | ||||
\(545\) | −273.012 | + | 177.661i | −0.500939 | + | 0.325984i | ||||
\(546\) | −489.561 | + | 154.945i | −0.896632 | + | 0.283782i | ||||
\(547\) | 269.262i | 0.492252i | 0.969238 | + | 0.246126i | \(0.0791577\pi\) | ||||
−0.969238 | + | 0.246126i | \(0.920842\pi\) | |||||||
\(548\) | −14.6132 | − | 8.43695i | −0.0266665 | − | 0.0153959i | ||||
\(549\) | −93.5652 | + | 54.0199i | −0.170428 | + | 0.0983969i | ||||
\(550\) | 34.8068 | + | 325.272i | 0.0632851 | + | 0.591404i | ||||
\(551\) | 79.4025 | + | 45.8430i | 0.144106 | + | 0.0831997i | ||||
\(552\) | −25.6222 | −0.0464170 | ||||||||
\(553\) | 235.817 | + | 52.0098i | 0.426432 | + | 0.0940502i | ||||
\(554\) | 53.6046 | 0.0967592 | ||||||||
\(555\) | −93.6903 | + | 4.99855i | −0.168811 | + | 0.00900640i | ||||
\(556\) | −3.99227 | + | 2.30494i | −0.00718034 | + | 0.00414557i | ||||
\(557\) | −160.700 | + | 92.7801i | −0.288510 | + | 0.166571i | −0.637270 | − | 0.770641i | \(-0.719936\pi\) |
0.348760 | + | 0.937212i | \(0.386603\pi\) | |||||||
\(558\) | −180.324 | + | 312.329i | −0.323160 | + | 0.559730i | ||||
\(559\) | − | 424.973i | − | 0.760238i | ||||||
\(560\) | −89.6256 | + | 542.347i | −0.160046 | + | 0.968476i | ||||
\(561\) | −182.954 | −0.326121 | ||||||||
\(562\) | 855.214 | + | 493.758i | 1.52173 | + | 0.878573i | ||||
\(563\) | 256.418 | + | 444.129i | 0.455449 | + | 0.788862i | 0.998714 | − | 0.0507000i | \(-0.0161452\pi\) |
−0.543264 | + | 0.839562i | \(0.682812\pi\) | |||||||
\(564\) | 5.48731 | + | 9.50431i | 0.00972928 | + | 0.0168516i | ||||
\(565\) | 460.663 | − | 24.5772i | 0.815333 | − | 0.0434995i | ||||
\(566\) | 705.423i | 1.24633i | ||||||||
\(567\) | 42.5115 | − | 46.4948i | 0.0749763 | − | 0.0820015i | ||||
\(568\) | 794.376i | 1.39855i | ||||||||
\(569\) | −57.5767 | + | 99.7258i | −0.101189 | + | 0.175265i | −0.912175 | − | 0.409801i | \(-0.865598\pi\) |
0.810986 | + | 0.585066i | \(0.198931\pi\) | |||||||
\(570\) | 306.159 | + | 155.633i | 0.537121 | + | 0.273040i | ||||
\(571\) | 385.360 | + | 667.463i | 0.674886 | + | 1.16894i | 0.976502 | + | 0.215508i | \(0.0691407\pi\) |
−0.301616 | + | 0.953430i | \(0.597526\pi\) | |||||||
\(572\) | −5.09700 | + | 8.82827i | −0.00891084 | + | 0.0154340i | ||||
\(573\) | −182.540 | −0.318569 | ||||||||
\(574\) | 245.425 | + | 54.1289i | 0.427570 | + | 0.0943012i | ||||
\(575\) | 41.8970 | + | 18.5593i | 0.0728643 | + | 0.0322770i | ||||
\(576\) | 97.6708 | − | 169.171i | 0.169567 | − | 0.293699i | ||||
\(577\) | −253.489 | − | 439.056i | −0.439322 | − | 0.760929i | 0.558315 | − | 0.829629i | \(-0.311448\pi\) |
−0.997637 | + | 0.0687005i | \(0.978115\pi\) | |||||||
\(578\) | 56.7330 | − | 32.7548i | 0.0981540 | − | 0.0566693i | ||||
\(579\) | 104.549 | + | 60.3612i | 0.180568 | + | 0.104251i | ||||
\(580\) | −1.38732 | + | 0.902792i | −0.00239192 | + | 0.00155654i | ||||
\(581\) | −149.959 | − | 473.807i | −0.258105 | − | 0.815503i | ||||
\(582\) | − | 410.760i | − | 0.705774i | ||||||
\(583\) | 76.5235 | + | 44.1808i | 0.131258 | + | 0.0757819i | ||||
\(584\) | 842.393 | − | 486.356i | 1.44245 | − | 0.832801i | ||||
\(585\) | −285.750 | − | 145.258i | −0.488462 | − | 0.248305i | ||||
\(586\) | −19.0892 | − | 11.0212i | −0.0325755 | − | 0.0188075i | ||||
\(587\) | 958.495 | 1.63287 | 0.816435 | − | 0.577437i | \(-0.195947\pi\) | ||||
0.816435 | + | 0.577437i | \(0.195947\pi\) | |||||||
\(588\) | 0.547736 | + | 6.10729i | 0.000931524 | + | 0.0103866i | ||||
\(589\) | −1213.79 | −2.06077 | ||||||||
\(590\) | −2.02149 | − | 37.8898i | −0.00342626 | − | 0.0642200i | ||||
\(591\) | −127.040 | + | 73.3463i | −0.214957 | + | 0.124105i | ||||
\(592\) | 147.357 | − | 85.0767i | 0.248914 | − | 0.143711i | ||||
\(593\) | −31.5173 | + | 54.5896i | −0.0531489 | + | 0.0920566i | −0.891376 | − | 0.453265i | \(-0.850259\pi\) |
0.838227 | + | 0.545322i | \(0.183592\pi\) | |||||||
\(594\) | 67.9925i | 0.114465i | ||||||||
\(595\) | 432.786 | + | 355.287i | 0.727372 | + | 0.597122i | ||||
\(596\) | 15.3747 | 0.0257964 | ||||||||
\(597\) | 246.293 | + | 142.197i | 0.412551 | + | 0.238187i | ||||
\(598\) | −38.8148 | − | 67.2292i | −0.0649077 | − | 0.112423i | ||||
\(599\) | 228.895 | + | 396.459i | 0.382129 | + | 0.661867i | 0.991366 | − | 0.131121i | \(-0.0418576\pi\) |
−0.609237 | + | 0.792988i | \(0.708524\pi\) | |||||||
\(600\) | −282.338 | + | 205.944i | −0.470563 | + | 0.343240i | ||||
\(601\) | − | 774.741i | − | 1.28909i | −0.764568 | − | 0.644543i | \(-0.777048\pi\) | ||
0.764568 | − | 0.644543i | \(-0.222952\pi\) | |||||||
\(602\) | 269.409 | + | 59.4185i | 0.447523 | + | 0.0987018i | ||||
\(603\) | − | 86.6732i | − | 0.143737i | ||||||
\(604\) | −6.83554 | + | 11.8395i | −0.0113171 | + | 0.0196018i | ||||
\(605\) | 345.017 | + | 175.386i | 0.570276 | + | 0.289894i | ||||
\(606\) | 98.4398 | + | 170.503i | 0.162442 | + | 0.281358i | ||||
\(607\) | 256.276 | − | 443.882i | 0.422200 | − | 0.731272i | −0.573954 | − | 0.818887i | \(-0.694591\pi\) |
0.996154 | + | 0.0876151i | \(0.0279246\pi\) | |||||||
\(608\) | 23.1288 | 0.0380408 | ||||||||
\(609\) | 37.4863 | − | 40.9988i | 0.0615539 | − | 0.0673215i | ||||
\(610\) | −299.109 | + | 194.644i | −0.490343 | + | 0.319089i | ||||
\(611\) | −937.073 | + | 1623.06i | −1.53367 | + | 2.65640i | ||||
\(612\) | −1.73379 | − | 3.00301i | −0.00283299 | − | 0.00490688i | ||||
\(613\) | −131.925 | + | 76.1668i | −0.215212 | + | 0.124252i | −0.603731 | − | 0.797188i | \(-0.706320\pi\) |
0.388520 | + | 0.921440i | \(0.372987\pi\) | |||||||
\(614\) | 634.953 | + | 366.590i | 1.03413 | + | 0.597053i | ||||
\(615\) | 85.5720 | + | 131.498i | 0.139141 | + | 0.213818i | ||||
\(616\) | −275.281 | − | 251.697i | −0.446884 | − | 0.408599i | ||||
\(617\) | − | 440.775i | − | 0.714384i | −0.934031 | − | 0.357192i | \(-0.883734\pi\) | ||
0.934031 | − | 0.357192i | \(-0.116266\pi\) | |||||||
\(618\) | −195.289 | − | 112.750i | −0.316002 | − | 0.182444i | ||||
\(619\) | −34.6038 | + | 19.9785i | −0.0559028 | + | 0.0322755i | −0.527691 | − | 0.849436i | \(-0.676942\pi\) |
0.471788 | + | 0.881712i | \(0.343609\pi\) | |||||||
\(620\) | 9.92966 | − | 19.5335i | 0.0160156 | − | 0.0315056i | ||||
\(621\) | 8.24825 | + | 4.76213i | 0.0132822 | + | 0.00766848i | ||||
\(622\) | 573.167 | 0.921490 | ||||||||
\(623\) | −201.705 | + | 914.549i | −0.323764 | + | 1.46798i | ||||
\(624\) | 581.335 | 0.931626 | ||||||||
\(625\) | 610.849 | − | 132.246i | 0.977358 | − | 0.211594i | ||||
\(626\) | −354.017 | + | 204.392i | −0.565522 | + | 0.326504i | ||||
\(627\) | −198.177 | + | 114.418i | −0.316072 | + | 0.182484i | ||||
\(628\) | 2.76310 | − | 4.78583i | 0.00439984 | − | 0.00762074i | ||||
\(629\) | − | 173.322i | − | 0.275552i | ||||||
\(630\) | 132.038 | − | 160.840i | 0.209584 | − | 0.255301i | ||||
\(631\) | 384.003 | 0.608562 | 0.304281 | − | 0.952582i | \(-0.401584\pi\) | ||||
0.304281 | + | 0.952582i | \(0.401584\pi\) | |||||||
\(632\) | −241.117 | − | 139.209i | −0.381514 | − | 0.220267i | ||||
\(633\) | −156.035 | − | 270.260i | −0.246500 | − | 0.426951i | ||||
\(634\) | 63.5611 | + | 110.091i | 0.100254 | + | 0.173645i | ||||
\(635\) | 530.411 | − | 28.2984i | 0.835293 | − | 0.0445645i | ||||
\(636\) | 1.67475i | 0.00263325i | ||||||||
\(637\) | −856.451 | + | 602.480i | −1.34451 | + | 0.945808i | ||||
\(638\) | 59.9552i | 0.0939737i | ||||||||
\(639\) | 147.642 | − | 255.724i | 0.231052 | − | 0.400194i | ||||
\(640\) | 281.912 | − | 554.574i | 0.440488 | − | 0.866521i | ||||
\(641\) | −572.373 | − | 991.380i | −0.892938 | − | 1.54661i | −0.836336 | − | 0.548218i | \(-0.815307\pi\) |
−0.0566024 | − | 0.998397i | \(-0.518027\pi\) | |||||||
\(642\) | 218.410 | − | 378.298i | 0.340203 | − | 0.589249i | ||||
\(643\) | −501.070 | −0.779269 | −0.389634 | − | 0.920970i | \(-0.627399\pi\) | ||||
−0.389634 | + | 0.920970i | \(0.627399\pi\) | |||||||
\(644\) | −0.883790 | + | 0.279717i | −0.00137234 | + | 0.000434343i | ||||
\(645\) | 93.9342 | + | 144.348i | 0.145634 | + | 0.223796i | ||||
\(646\) | −317.228 | + | 549.454i | −0.491064 | + | 0.850548i | ||||
\(647\) | −322.214 | − | 558.090i | −0.498012 | − | 0.862582i | 0.501986 | − | 0.864876i | \(-0.332603\pi\) |
−0.999997 | + | 0.00229424i | \(0.999270\pi\) | |||||||
\(648\) | −62.9042 | + | 36.3177i | −0.0970743 | + | 0.0560459i | ||||
\(649\) | 21.8945 | + | 12.6408i | 0.0337358 | + | 0.0194773i | ||||
\(650\) | −968.080 | − | 428.835i | −1.48935 | − | 0.659746i | ||||
\(651\) | −158.396 | + | 718.181i | −0.243312 | + | 1.10320i | ||||
\(652\) | − | 11.4218i | − | 0.0175181i | ||||||
\(653\) | 858.975 | + | 495.930i | 1.31543 | + | 0.759464i | 0.982990 | − | 0.183661i | \(-0.0587949\pi\) |
0.332440 | + | 0.943124i | \(0.392128\pi\) | |||||||
\(654\) | −193.664 | + | 111.812i | −0.296122 | + | 0.170966i | ||||
\(655\) | 271.947 | − | 534.970i | 0.415186 | − | 0.816747i | ||||
\(656\) | −246.407 | − | 142.263i | −0.375621 | − | 0.216865i | ||||
\(657\) | −361.576 | −0.550343 | ||||||||
\(658\) | −897.907 | − | 820.982i | −1.36460 | − | 1.24769i | ||||
\(659\) | −973.378 | −1.47705 | −0.738527 | − | 0.674224i | \(-0.764478\pi\) | ||||
−0.738527 | + | 0.674224i | \(0.764478\pi\) | |||||||
\(660\) | −0.220091 | − | 4.12527i | −0.000333471 | − | 0.00625041i | ||||
\(661\) | 858.076 | − | 495.411i | 1.29815 | − | 0.749486i | 0.318064 | − | 0.948069i | \(-0.396967\pi\) |
0.980084 | + | 0.198583i | \(0.0636338\pi\) | |||||||
\(662\) | −276.251 | + | 159.494i | −0.417298 | + | 0.240927i | ||||
\(663\) | 296.081 | − | 512.827i | 0.446577 | − | 0.773495i | ||||
\(664\) | 572.981i | 0.862923i | ||||||||
\(665\) | 690.992 | + | 114.190i | 1.03909 | + | 0.171714i | ||||
\(666\) | −64.4131 | −0.0967164 | ||||||||
\(667\) | 7.27324 | + | 4.19921i | 0.0109044 | + | 0.00629566i | ||||
\(668\) | −1.85216 | − | 3.20803i | −0.00277269 | − | 0.00480244i | ||||
\(669\) | −220.084 | − | 381.197i | −0.328975 | − | 0.569801i | ||||
\(670\) | −15.2524 | − | 285.883i | −0.0227648 | − | 0.426691i | ||||
\(671\) | − | 237.777i | − | 0.354362i | ||||||
\(672\) | 3.01824 | − | 13.6849i | 0.00449142 | − | 0.0203645i | ||||
\(673\) | 218.787i | 0.325092i | 0.986701 | + | 0.162546i | \(0.0519706\pi\) | ||||
−0.986701 | + | 0.162546i | \(0.948029\pi\) | |||||||
\(674\) | 260.347 | − | 450.934i | 0.386272 | − | 0.669042i | ||||
\(675\) | 129.166 | − | 13.8219i | 0.191358 | − | 0.0204769i | ||||
\(676\) | −10.3923 | − | 18.0000i | −0.0153732 | − | 0.0266272i | ||||
\(677\) | 46.3222 | − | 80.2324i | 0.0684227 | − | 0.118512i | −0.829784 | − | 0.558084i | \(-0.811537\pi\) |
0.898207 | + | 0.439572i | \(0.144870\pi\) | |||||||
\(678\) | 316.711 | 0.467125 | ||||||||
\(679\) | −252.752 | − | 798.590i | −0.372241 | − | 1.17613i | ||||
\(680\) | −352.117 | − | 541.097i | −0.517820 | − | 0.795732i | ||||
\(681\) | 142.467 | − | 246.760i | 0.209203 | − | 0.362349i | ||||
\(682\) | −396.861 | − | 687.383i | −0.581907 | − | 1.00789i | ||||
\(683\) | −855.321 | + | 493.820i | −1.25230 | + | 0.723016i | −0.971566 | − | 0.236770i | \(-0.923911\pi\) |
−0.280734 | + | 0.959785i | \(0.590578\pi\) | |||||||
\(684\) | −3.75612 | − | 2.16859i | −0.00549140 | − | 0.00317046i | ||||
\(685\) | 636.930 | + | 978.767i | 0.929824 | + | 1.42886i | ||||
\(686\) | −262.191 | − | 627.178i | −0.382203 | − | 0.914253i | ||||
\(687\) | 189.190i | 0.275386i | ||||||||
\(688\) | −270.487 | − | 156.166i | −0.393149 | − | 0.226985i | ||||
\(689\) | −247.682 | + | 142.999i | −0.359480 | + | 0.207546i | ||||
\(690\) | 28.0441 | + | 14.2559i | 0.0406436 | + | 0.0206608i | ||||
\(691\) | −619.242 | − | 357.519i | −0.896153 | − | 0.517394i | −0.0202027 | − | 0.999796i | \(-0.506431\pi\) |
−0.875950 | + | 0.482402i | \(0.839764\pi\) | |||||||
\(692\) | −6.51659 | −0.00941703 | ||||||||
\(693\) | 41.8376 | + | 132.189i | 0.0603717 | + | 0.190749i | ||||
\(694\) | 738.968 | 1.06480 | ||||||||
\(695\) | 318.574 | − | 16.9965i | 0.458379 | − | 0.0244554i | ||||
\(696\) | −55.4684 | + | 32.0247i | −0.0796960 | + | 0.0460125i | ||||
\(697\) | −250.996 | + | 144.913i | −0.360109 | + | 0.207909i | ||||
\(698\) | −517.690 | + | 896.665i | −0.741676 | + | 1.28462i | ||||
\(699\) | 31.8271i | 0.0455323i | ||||||||
\(700\) | −7.49044 | + | 10.1859i | −0.0107006 | + | 0.0145513i | ||||
\(701\) | 157.215 | 0.224272 | 0.112136 | − | 0.993693i | \(-0.464231\pi\) | ||||
0.112136 | + | 0.993693i | \(0.464231\pi\) | |||||||
\(702\) | −190.586 | − | 110.035i | −0.271490 | − | 0.156745i | ||||
\(703\) | −108.394 | − | 187.744i | −0.154188 | − | 0.267062i | ||||
\(704\) | 214.956 | + | 372.315i | 0.305336 | + | 0.528857i | ||||
\(705\) | −40.4632 | − | 758.422i | −0.0573946 | − | 1.07578i | ||||
\(706\) | 872.177i | 1.23538i | ||||||||
\(707\) | 296.299 | + | 270.915i | 0.419093 | + | 0.383189i | ||||
\(708\) | 0.479170i | 0.000676794i | ||||||||
\(709\) | 431.110 | − | 746.704i | 0.608054 | − | 1.05318i | −0.383507 | − | 0.923538i | \(-0.625284\pi\) |
0.991561 | − | 0.129642i | \(-0.0413828\pi\) | |||||||
\(710\) | 441.982 | − | 869.462i | 0.622510 | − | 1.22459i | ||||
\(711\) | 51.7466 | + | 89.6278i | 0.0727800 | + | 0.126059i | ||||
\(712\) | 539.882 | − | 935.104i | 0.758262 | − | 1.31335i | ||||
\(713\) | −111.183 | −0.155937 | ||||||||
\(714\) | 283.706 | + | 259.400i | 0.397347 | + | 0.363306i | ||||
\(715\) | 591.301 | − | 384.787i | 0.826995 | − | 0.538164i | ||||
\(716\) | 3.56015 | − | 6.16635i | 0.00497227 | − | 0.00861222i | ||||
\(717\) | 72.4291 | + | 125.451i | 0.101017 | + | 0.174966i | ||||
\(718\) | 387.986 | − | 224.004i | 0.540371 | − | 0.311983i | ||||
\(719\) | −503.718 | − | 290.821i | −0.700581 | − | 0.404481i | 0.106983 | − | 0.994261i | \(-0.465881\pi\) |
−0.807564 | + | 0.589780i | \(0.799214\pi\) | |||||||
\(720\) | −197.459 | + | 128.496i | −0.274248 | + | 0.178466i | ||||
\(721\) | −449.054 | − | 99.0396i | −0.622821 | − | 0.137364i | ||||
\(722\) | 78.1155i | 0.108193i | ||||||||
\(723\) | −136.493 | − | 78.8045i | −0.188788 | − | 0.108997i | ||||
\(724\) | 15.7131 | − | 9.07196i | 0.0217032 | − | 0.0125303i | ||||
\(725\) | 113.898 | − | 12.1880i | 0.157101 | − | 0.0168111i | ||||
\(726\) | 230.115 | + | 132.857i | 0.316963 | + | 0.182999i | ||||
\(727\) | −621.129 | −0.854372 | −0.427186 | − | 0.904164i | \(-0.640495\pi\) | ||||
−0.427186 | + | 0.904164i | \(0.640495\pi\) | |||||||
\(728\) | 1151.01 | − | 364.293i | 1.58106 | − | 0.500402i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −1192.62 | + | 63.6286i | −1.63373 | + | 0.0871624i | ||||
\(731\) | −275.524 | + | 159.074i | −0.376914 | + | 0.217611i | ||||
\(732\) | 3.90288 | − | 2.25333i | 0.00533180 | − | 0.00307832i | ||||
\(733\) | −365.501 | + | 633.067i | −0.498638 | + | 0.863665i | −0.999999 | − | 0.00157256i | \(-0.999499\pi\) |
0.501361 | + | 0.865238i | \(0.332833\pi\) | |||||||
\(734\) | 284.781i | 0.387985i | ||||||||
\(735\) | 157.736 | − | 393.947i | 0.214607 | − | 0.535982i | ||||
\(736\) | 2.11859 | 0.00287852 | ||||||||
\(737\) | 165.197 | + | 95.3763i | 0.224147 | + | 0.129412i | ||||
\(738\) | 53.8550 | + | 93.2797i | 0.0729743 | + | 0.126395i | ||||
\(739\) | 319.505 | + | 553.399i | 0.432348 | + | 0.748849i | 0.997075 | − | 0.0764289i | \(-0.0243518\pi\) |
−0.564727 | + | 0.825278i | \(0.691018\pi\) | |||||||
\(740\) | 3.90810 | − | 0.208504i | 0.00528122 | − | 0.000281763i | ||||
\(741\) | − | 740.665i | − | 0.999548i | ||||||
\(742\) | −56.0231 | − | 177.010i | −0.0755028 | − | 0.238557i | ||||
\(743\) | − | 486.795i | − | 0.655175i | −0.944821 | − | 0.327588i | \(-0.893764\pi\) | ||
0.944821 | − | 0.327588i | \(-0.106236\pi\) | |||||||
\(744\) | 423.961 | − | 734.322i | 0.569840 | − | 0.986992i | ||||
\(745\) | −948.491 | − | 482.156i | −1.27314 | − | 0.647190i | ||||
\(746\) | −600.145 | − | 1039.48i | −0.804484 | − | 1.39341i | ||||
\(747\) | 106.494 | − | 184.453i | 0.142562 | − | 0.246925i | ||||
\(748\) | 7.63154 | 0.0102026 | ||||||||
\(749\) | 191.851 | − | 869.871i | 0.256143 | − | 1.16138i | ||||
\(750\) | 423.610 | − | 68.3203i | 0.564814 | − | 0.0910937i | ||||
\(751\) | −304.031 | + | 526.597i | −0.404835 | + | 0.701195i | −0.994302 | − | 0.106597i | \(-0.966004\pi\) |
0.589467 | + | 0.807792i | \(0.299338\pi\) | |||||||
\(752\) | 688.695 | + | 1192.86i | 0.915818 | + | 1.58624i | ||||
\(753\) | −608.743 | + | 351.458i | −0.808424 | + | 0.466744i | ||||
\(754\) | −168.057 | − | 97.0278i | −0.222887 | − | 0.128684i | ||||
\(755\) | 792.988 | − | 516.034i | 1.05031 | − | 0.683489i | ||||
\(756\) | −1.77328 | + | 1.93944i | −0.00234561 | + | 0.00256539i | ||||
\(757\) | 889.150i | 1.17457i | 0.809380 | + | 0.587285i | \(0.199803\pi\) | ||||
−0.809380 | + | 0.587285i | \(0.800197\pi\) | |||||||
\(758\) | −1065.72 | − | 615.295i | −1.40597 | − | 0.811735i | ||||
\(759\) | −18.1530 | + | 10.4806i | −0.0239169 | + | 0.0138085i | ||||
\(760\) | −719.815 | − | 365.911i | −0.947124 | − | 0.481461i | ||||
\(761\) | 918.591 | + | 530.349i | 1.20708 | + | 0.696910i | 0.962121 | − | 0.272622i | \(-0.0878909\pi\) |
0.244963 | + | 0.969532i | \(0.421224\pi\) | |||||||
\(762\) | 364.664 | 0.478561 | ||||||||
\(763\) | −307.716 | + | 336.549i | −0.403297 | + | 0.441086i | ||||
\(764\) | 7.61428 | 0.00996633 | ||||||||
\(765\) | 12.7849 | + | 239.634i | 0.0167123 | + | 0.313246i | ||||
\(766\) | 351.601 | − | 202.997i | 0.459009 | − | 0.265009i | ||||
\(767\) | −70.8654 | + | 40.9142i | −0.0923929 | + | 0.0533431i | ||||
\(768\) | −12.0094 | + | 20.8009i | −0.0156372 | + | 0.0270845i | ||||
\(769\) | 1226.40i | 1.59480i | 0.603448 | + | 0.797402i | \(0.293793\pi\) | ||||
−0.603448 | + | 0.797402i | \(0.706207\pi\) | |||||||
\(770\) | 161.259 | + | 428.651i | 0.209428 | + | 0.556690i | ||||
\(771\) | 80.0632 | 0.103843 | ||||||||
\(772\) | −4.36104 | − | 2.51784i | −0.00564901 | − | 0.00326146i | ||||
\(773\) | −346.998 | − | 601.018i | −0.448898 | − | 0.777513i | 0.549417 | − | 0.835548i | \(-0.314850\pi\) |
−0.998315 | + | 0.0580349i | \(0.981517\pi\) | |||||||
\(774\) | 59.1179 | + | 102.395i | 0.0763797 | + | 0.132293i | ||||
\(775\) | −1225.16 | + | 893.658i | −1.58085 | + | 1.15311i | ||||
\(776\) | 965.744i | 1.24452i | ||||||||
\(777\) | −125.230 | + | 39.6351i | −0.161172 | + | 0.0510104i | ||||
\(778\) | 470.235i | 0.604415i | ||||||||
\(779\) | −181.254 | + | 313.942i | −0.232676 | + | 0.403006i | ||||
\(780\) | 11.9195 | + | 6.05915i | 0.0152814 | + | 0.00776814i | ||||
\(781\) | 324.935 | + | 562.804i | 0.416050 | + | 0.720620i | ||||
\(782\) | −29.0579 | + | 50.3298i | −0.0371585 | + | 0.0643604i | ||||
\(783\) | 23.8084 | 0.0304066 | ||||||||
\(784\) | 68.7446 | + | 766.507i | 0.0876844 | + | 0.977687i | ||||
\(785\) | −320.546 | + | 208.594i | −0.408339 | + | 0.265725i | ||||
\(786\) | 206.003 | − | 356.807i | 0.262090 | − | 0.453953i | ||||
\(787\) | 187.309 | + | 324.429i | 0.238004 | + | 0.412235i | 0.960142 | − | 0.279514i | \(-0.0901735\pi\) |
−0.722137 | + | 0.691750i | \(0.756840\pi\) | |||||||
\(788\) | 5.29920 | − | 3.05949i | 0.00672487 | − | 0.00388261i | ||||
\(789\) | −647.839 | − | 374.030i | −0.821089 | − | 0.474056i | ||||
\(790\) | 186.453 | + | 286.522i | 0.236017 | + | 0.362686i | ||||
\(791\) | 615.742 | − | 194.881i | 0.778435 | − | 0.246373i | ||||
\(792\) | − | 159.858i | − | 0.201841i | ||||||
\(793\) | 666.498 | + | 384.803i | 0.840477 | + | 0.485250i | ||||
\(794\) | −1142.28 | + | 659.493i | −1.43863 | + | 0.830596i | ||||
\(795\) | 52.5208 | − | 103.318i | 0.0660638 | − | 0.129960i | ||||
\(796\) | −10.2736 | − | 5.93148i | −0.0129066 | − | 0.00745160i | ||||
\(797\) | −1102.96 | −1.38389 | −0.691947 | − | 0.721948i | \(-0.743247\pi\) | ||||
−0.691947 | + | 0.721948i | \(0.743247\pi\) | |||||||
\(798\) | 469.540 | + | 103.558i | 0.588395 | + | 0.129771i | ||||
\(799\) | 1403.04 | 1.75600 | ||||||||
\(800\) | 23.3454 | − | 17.0287i | 0.0291817 | − | 0.0212858i | ||||
\(801\) | −347.596 | + | 200.685i | −0.433953 | + | 0.250543i | ||||
\(802\) | 649.455 | − | 374.963i | 0.809794 | − | 0.467535i | ||||
\(803\) | 397.883 | − | 689.153i | 0.495495 | − | 0.858223i | ||||
\(804\) | 3.61539i | 0.00449676i | ||||||||
\(805\) | 63.2946 | + | 10.4598i | 0.0786268 | + | 0.0129935i | ||||
\(806\) | 2569.02 | 3.18737 | ||||||||
\(807\) | 211.949 | + | 122.369i | 0.262638 | + | 0.151634i | ||||
\(808\) | −231.443 | − | 400.871i | −0.286440 | − | 0.496128i | ||||
\(809\) | −39.6255 | − | 68.6334i | −0.0489808 | − | 0.0848373i | 0.840496 | − | 0.541819i | \(-0.182264\pi\) |
−0.889476 | + | 0.456981i | \(0.848931\pi\) | |||||||
\(810\) | 89.0568 | − | 4.75135i | 0.109947 | − | 0.00586586i | ||||
\(811\) | − | 561.470i | − | 0.692318i | −0.938176 | − | 0.346159i | \(-0.887486\pi\) | ||
0.938176 | − | 0.346159i | \(-0.112514\pi\) | |||||||
\(812\) | −1.56367 | + | 1.71018i | −0.00192570 | + | 0.00210613i | ||||
\(813\) | − | 12.9398i | − | 0.0159161i | ||||||
\(814\) | 70.8811 | − | 122.770i | 0.0870775 | − | 0.150823i | ||||
\(815\) | −358.193 | + | 704.632i | −0.439501 | + | 0.864580i | ||||
\(816\) | −217.602 | − | 376.899i | −0.266670 | − | 0.461885i | ||||
\(817\) | −198.967 | + | 344.621i | −0.243534 | + | 0.421812i | ||||
\(818\) | 755.114 | 0.923122 | ||||||||
\(819\) | −438.240 | − | 96.6544i | −0.535091 | − | 0.118015i | ||||
\(820\) | −3.56946 | − | 5.48517i | −0.00435300 | − | 0.00668924i | ||||
\(821\) | 201.907 | − | 349.713i | 0.245928 | − | 0.425960i | −0.716464 | − | 0.697624i | \(-0.754241\pi\) |
0.962392 | + | 0.271664i | \(0.0875739\pi\) | |||||||
\(822\) | 400.854 | + | 694.300i | 0.487657 | + | 0.844647i | ||||
\(823\) | 1186.85 | − | 685.228i | 1.44210 | − | 0.832598i | 0.444112 | − | 0.895971i | \(-0.353519\pi\) |
0.997990 | + | 0.0633735i | \(0.0201859\pi\) | |||||||
\(824\) | 459.147 | + | 265.088i | 0.557217 | + | 0.321709i | ||||
\(825\) | −115.792 | + | 261.397i | −0.140354 | + | 0.316845i | ||||
\(826\) | −16.0290 | − | 50.6451i | −0.0194056 | − | 0.0613137i | ||||
\(827\) | − | 297.863i | − | 0.360173i | −0.983651 | − | 0.180086i | \(-0.942362\pi\) | ||
0.983651 | − | 0.180086i | \(-0.0576378\pi\) | |||||||
\(828\) | −0.344059 | − | 0.198643i | −0.000415530 | − | 0.000239906i | ||||
\(829\) | −352.766 | + | 203.670i | −0.425532 | + | 0.245681i | −0.697441 | − | 0.716642i | \(-0.745678\pi\) |
0.271909 | + | 0.962323i | \(0.412345\pi\) | |||||||
\(830\) | 318.800 | − | 627.140i | 0.384097 | − | 0.755590i | ||||
\(831\) | 40.5715 | + | 23.4240i | 0.0488225 | + | 0.0281877i | ||||
\(832\) | −1391.49 | −1.67246 | ||||||||
\(833\) | 711.190 | + | 329.748i | 0.853769 | + | 0.395856i | ||||
\(834\) | 219.023 | 0.262618 | ||||||||
\(835\) | 13.6577 | + | 255.993i | 0.0163566 | + | 0.306579i | ||||
\(836\) | 8.26656 | − | 4.77270i | 0.00988823 | − | 0.00570897i | ||||
\(837\) | −272.962 | + | 157.594i | −0.326119 | + | 0.188285i | ||||
\(838\) | 365.117 | − | 632.401i | 0.435701 | − | 0.754656i | ||||
\(839\) | − | 1238.46i | − | 1.47611i | −0.674739 | − | 0.738056i | \(-0.735744\pi\) | ||
0.674739 | − | 0.738056i | \(-0.264256\pi\) | |||||||
\(840\) | −310.437 | + | 378.152i | −0.369568 | + | 0.450181i | ||||
\(841\) | −820.006 | −0.975037 | ||||||||
\(842\) | 505.413 | + | 291.800i | 0.600252 | + | 0.346556i | ||||
\(843\) | 431.522 | + | 747.418i | 0.511888 | + | 0.886617i | ||||
\(844\) | 6.50867 | + | 11.2734i | 0.00771170 | + | 0.0133571i | ||||
\(845\) | 76.6324 | + | 1436.36i | 0.0906892 | + | 1.69983i | ||||
\(846\) | − | 521.424i | − | 0.616340i | ||||||
\(847\) | 529.134 | + | 116.701i | 0.624716 | + | 0.137782i | ||||
\(848\) | 210.192i | 0.247868i | ||||||||
\(849\) | −308.254 | + | 533.911i | −0.363079 | + | 0.628870i | ||||
\(850\) | 84.3394 | + | 788.158i | 0.0992229 | + | 0.927244i | ||||
\(851\) | −9.92888 | − | 17.1973i | −0.0116673 | − | 0.0202084i | ||||
\(852\) | −6.15860 | + | 10.6670i | −0.00722840 | + | 0.0125200i | ||||
\(853\) | −243.147 | −0.285049 | −0.142525 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142525 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(854\) | −337.131 | + | 368.720i | −0.394767 | + | 0.431756i | ||||
\(855\) | 163.713 | + | 251.578i | 0.191478 | + | 0.294243i | ||||
\(856\) | −513.508 | + | 889.422i | −0.599892 | + | 1.03904i | ||||
\(857\) | −76.0495 | − | 131.722i | −0.0887392 | − | 0.153701i | 0.818239 | − | 0.574878i | \(-0.194950\pi\) |
−0.906978 | + | 0.421177i | \(0.861617\pi\) | |||||||
\(858\) | 419.446 | − | 242.167i | 0.488865 | − | 0.282246i | ||||
\(859\) | −1070.00 | − | 617.763i | −1.24563 | − | 0.719165i | −0.275395 | − | 0.961331i | \(-0.588809\pi\) |
−0.970235 | + | 0.242166i | \(0.922142\pi\) | |||||||
\(860\) | −3.91828 | − | 6.02120i | −0.00455613 | − | 0.00700139i | ||||
\(861\) | 162.101 | + | 148.214i | 0.188271 | + | 0.172141i | ||||
\(862\) | 865.959i | 1.00459i | ||||||||
\(863\) | −782.524 | − | 451.790i | −0.906749 | − | 0.523512i | −0.0273650 | − | 0.999626i | \(-0.508712\pi\) |
−0.879384 | + | 0.476114i | \(0.842045\pi\) | |||||||
\(864\) | 5.20129 | − | 3.00296i | 0.00602001 | − | 0.00347565i | ||||
\(865\) | 402.020 | + | 204.363i | 0.464763 | + | 0.236258i | ||||
\(866\) | −1164.16 | − | 672.129i | −1.34430 | − | 0.776131i | ||||
\(867\) | 57.2524 | 0.0660351 | ||||||||
\(868\) | 6.60716 | − | 29.9575i | 0.00761194 | − | 0.0345132i | ||||
\(869\) | −227.771 | −0.262107 | ||||||||
\(870\) | 78.5296 | − | 4.18970i | 0.0902639 | − | 0.00481575i | ||||
\(871\) | −534.687 | + | 308.702i | −0.613878 | + | 0.354422i | ||||
\(872\) | 455.326 | − | 262.883i | 0.522163 | − | 0.301471i | ||||
\(873\) | 179.493 | − | 310.891i | 0.205605 | − | 0.356118i | ||||
\(874\) | 72.6903i | 0.0831697i | ||||||||
\(875\) | 781.533 | − | 393.485i | 0.893181 | − | 0.449697i | ||||
\(876\) | 15.0824 | 0.0172173 | ||||||||
\(877\) | −550.416 | − | 317.783i | −0.627613 | − | 0.362352i | 0.152214 | − | 0.988348i | \(-0.451360\pi\) |
−0.779827 | + | 0.625995i | \(0.784693\pi\) | |||||||
\(878\) | −324.459 | − | 561.980i | −0.369543 | − | 0.640068i | ||||
\(879\) | −9.63200 | − | 16.6831i | −0.0109579 | − | 0.0189797i | ||||
\(880\) | −27.6229 | − | 517.749i | −0.0313896 | − | 0.588351i | ||||
\(881\) | 1453.08i | 1.64935i | 0.565605 | + | 0.824677i | \(0.308643\pi\) | ||||
−0.565605 | + | 0.824677i | \(0.691357\pi\) | |||||||
\(882\) | 122.547 | − | 264.305i | 0.138942 | − | 0.299665i | ||||
\(883\) | 279.559i | 0.316601i | 0.987391 | + | 0.158301i | \(0.0506015\pi\) | ||||
−0.987391 | + | 0.158301i | \(0.949399\pi\) | |||||||
\(884\) | −12.3504 | + | 21.3915i | −0.0139711 | + | 0.0241986i | ||||
\(885\) | 15.0270 | − | 29.5609i | 0.0169796 | − | 0.0334021i | ||||
\(886\) | 374.703 | + | 649.004i | 0.422915 | + | 0.732510i | ||||
\(887\) | 241.249 | − | 417.855i | 0.271983 | − | 0.471088i | −0.697387 | − | 0.716695i | \(-0.745654\pi\) |
0.969369 | + | 0.245607i | \(0.0789874\pi\) | |||||||
\(888\) | 151.443 | 0.170544 | ||||||||
\(889\) | 708.970 | − | 224.387i | 0.797492 | − | 0.252404i | ||||
\(890\) | −1111.20 | + | 723.107i | −1.24853 | + | 0.812480i | ||||
\(891\) | −29.7112 | + | 51.4612i | −0.0333459 | + | 0.0577567i | ||||
\(892\) | 9.18036 | + | 15.9008i | 0.0102919 | + | 0.0178261i | ||||
\(893\) | 1519.79 | − | 877.451i | 1.70189 | − | 0.982588i | ||||
\(894\) | −632.612 | − | 365.239i | −0.707620 | − | 0.408545i | ||||
\(895\) | −413.011 | + | 268.766i | −0.461465 | + | 0.300297i | ||||
\(896\) | 187.583 | − | 850.520i | 0.209356 | − | 0.949241i | ||||
\(897\) | − | 67.8447i | − | 0.0756351i | ||||||
\(898\) | −144.331 | − | 83.3297i | −0.160725 | − | 0.0927948i | ||||
\(899\) | −240.695 | + | 138.966i | −0.267737 | + | 0.154578i | ||||
\(900\) | −5.38791 | + | 0.576552i | −0.00598657 | + | 0.000640613i | ||||
\(901\) | 185.422 | + | 107.053i | 0.205796 | + | 0.118816i | ||||
\(902\) | −237.051 | −0.262806 | ||||||||
\(903\) | 177.942 | + | 162.697i | 0.197056 | + | 0.180174i | ||||
\(904\) | −744.624 | −0.823699 | ||||||||
\(905\) | −1253.87 | + | 66.8963i | −1.38549 | + | 0.0739185i | ||||
\(906\) | 562.515 | − | 324.768i | 0.620878 | − | 0.358464i | ||||
\(907\) | −1039.95 | + | 600.414i | −1.14658 | + | 0.661978i | −0.948051 | − | 0.318118i | \(-0.896949\pi\) |
−0.198528 | + | 0.980095i | \(0.563616\pi\) | |||||||
\(908\) | −5.94272 | + | 10.2931i | −0.00654484 | + | 0.0113360i | ||||
\(909\) | 172.064i | 0.189289i | ||||||||
\(910\) | −1462.50 | − | 241.685i | −1.60714 | − | 0.265588i | ||||
\(911\) | 1298.64 | 1.42551 | 0.712753 | − | 0.701415i | \(-0.247448\pi\) | ||||
0.712753 | + | 0.701415i | \(0.247448\pi\) | |||||||
\(912\) | −471.418 | − | 272.173i | −0.516906 | − | 0.298436i | ||||
\(913\) | 234.375 | + | 405.949i | 0.256708 | + | 0.444632i | ||||
\(914\) | −239.295 | − | 414.471i | −0.261810 | − | 0.453469i | ||||
\(915\) | −311.441 | + | 16.6160i | −0.340373 | + | 0.0181595i | ||||
\(916\) | − | 7.89169i | − | 0.00861539i | ||||||
\(917\) | 180.952 | − | 820.454i | 0.197331 | − | 0.894716i | ||||
\(918\) | 164.751i | 0.179467i | ||||||||
\(919\) | −162.902 | + | 282.155i | −0.177260 | + | 0.307024i | −0.940941 | − | 0.338570i | \(-0.890057\pi\) |
0.763681 | + | 0.645594i | \(0.223390\pi\) | |||||||
\(920\) | −65.9348 | − | 33.5173i | −0.0716682 | − | 0.0364318i | ||||
\(921\) | 320.383 | + | 554.920i | 0.347864 | + | 0.602519i | ||||
\(922\) | 571.650 | − | 990.127i | 0.620011 | − | 1.07389i | ||||
\(923\) | −2103.42 | −2.27889 | ||||||||
\(924\) | −1.74517 | − | 5.51401i | −0.00188871 | − | 0.00596754i | ||||
\(925\) | −247.636 | − | 109.697i | −0.267715 | − | 0.118591i | ||||
\(926\) | 530.227 | − | 918.380i | 0.572600 | − | 0.991772i | ||||
\(927\) | −98.5385 | − | 170.674i | −0.106298 | − | 0.184114i | ||||
\(928\) | 4.58645 | − | 2.64799i | 0.00494230 | − | 0.00285344i | ||||
\(929\) | −1297.10 | − | 748.880i | −1.39623 | − | 0.806114i | −0.402235 | − | 0.915537i | \(-0.631766\pi\) |
−0.993995 | + | 0.109423i | \(0.965100\pi\) | |||||||
\(930\) | −872.604 | + | 567.845i | −0.938284 | + | 0.610586i | ||||
\(931\) | 976.589 | − | 87.5859i | 1.04897 | − | 0.0940772i | ||||
\(932\) | − | 1.32760i | − | 0.00142446i | ||||||
\(933\) | 433.811 | + | 250.461i | 0.464963 | + | 0.268447i | ||||
\(934\) | −55.8180 | + | 32.2265i | −0.0597623 | + | 0.0345038i | ||||
\(935\) | −470.803 | − | 239.328i | −0.503533 | − | 0.255966i | ||||
\(936\) | 448.089 | + | 258.704i | 0.478728 | + | 0.276393i | ||||
\(937\) | 1375.13 | 1.46759 | 0.733796 | − | 0.679370i | \(-0.237747\pi\) | ||||
0.733796 | + | 0.679370i | \(0.237747\pi\) | |||||||
\(938\) | −120.941 | − | 382.123i | −0.128935 | − | 0.407381i | ||||
\(939\) | −357.258 | −0.380466 | ||||||||
\(940\) | 1.68784 | + | 31.6360i | 0.00179558 | + | 0.0336554i | ||||
\(941\) | 110.091 | − | 63.5613i | 0.116994 | − | 0.0675465i | −0.440361 | − | 0.897821i | \(-0.645150\pi\) |
0.557355 | + | 0.830274i | \(0.311816\pi\) | |||||||
\(942\) | −227.383 | + | 131.280i | −0.241383 | + | 0.139363i | ||||
\(943\) | −16.6028 | + | 28.7570i | −0.0176064 | + | 0.0304952i | ||||
\(944\) | 60.1391i | 0.0637067i | ||||||||
\(945\) | 170.218 | − | 64.0365i | 0.180125 | − | 0.0677635i | ||||
\(946\) | −260.216 | −0.275070 | ||||||||
\(947\) | 1063.39 | + | 613.951i | 1.12291 | + | 0.648311i | 0.942142 | − | 0.335215i | \(-0.108809\pi\) |
0.180766 | + | 0.983526i | \(0.442142\pi\) | |||||||
\(948\) | −2.15851 | − | 3.73864i | −0.00227690 | − | 0.00394371i | ||||
\(949\) | 1287.82 | + | 2230.56i | 1.35702 | + | 2.35044i | ||||
\(950\) | 584.264 | + | 800.995i | 0.615015 | + | 0.843152i | ||||
\(951\) | 111.099i | 0.116823i | ||||||||
\(952\) | −667.025 | − | 609.880i | −0.700656 | − | 0.640630i | ||||
\(953\) | 351.252i | 0.368575i | 0.982872 | + | 0.184288i | \(0.0589978\pi\) | ||||
−0.982872 | + | 0.184288i | \(0.941002\pi\) | |||||||
\(954\) | 39.7851 | − | 68.9098i | 0.0417034 | − | 0.0722325i | ||||
\(955\) | −469.738 | − | 238.787i | −0.491872 | − | 0.250039i | ||||
\(956\) | −3.02123 | − | 5.23293i | −0.00316029 | − | 0.00547378i | ||||
\(957\) | −26.1991 | + | 45.3781i | −0.0273762 | + | 0.0474170i | ||||
\(958\) | 537.191 | 0.560742 | ||||||||
\(959\) | 1206.55 | + | 1103.18i | 1.25813 | + | 1.15035i | ||||
\(960\) | 472.639 | − | 307.568i | 0.492332 | − | 0.320384i | ||||
\(961\) | 1359.21 | − | 2354.21i | 1.41437 | − | 2.44975i | ||||
\(962\) | 229.419 | + | 397.365i | 0.238481 | + | 0.413062i | ||||
\(963\) | 330.615 | − | 190.881i | 0.343318 | − | 0.198215i | ||||
\(964\) | 5.69355 | + | 3.28717i | 0.00590617 | + | 0.00340993i | ||||
\(965\) | 190.079 | + | 292.094i | 0.196973 | + | 0.302688i | ||||
\(966\) | 43.0097 | + | 9.48585i | 0.0445235 | + | 0.00981972i | ||||
\(967\) | 809.550i | 0.837177i | 0.908176 | + | 0.418588i | \(0.137475\pi\) | ||||
−0.908176 | + | 0.418588i | \(0.862525\pi\) | |||||||
\(968\) | −541.027 | − | 312.362i | −0.558912 | − | 0.322688i | ||||
\(969\) | −480.198 | + | 277.242i | −0.495560 | + | 0.286112i | ||||
\(970\) | 537.330 | − | 1057.03i | 0.553949 | − | 1.08972i | ||||
\(971\) | −853.738 | − | 492.906i | −0.879236 | − | 0.507627i | −0.00882979 | − | 0.999961i | \(-0.502811\pi\) |
−0.870407 | + | 0.492334i | \(0.836144\pi\) | |||||||
\(972\) | −1.12625 | −0.00115869 | ||||||||
\(973\) | 425.819 | − | 134.771i | 0.437635 | − | 0.138510i | ||||
\(974\) | 1026.23 | 1.05362 | ||||||||
\(975\) | −545.317 | − | 747.600i | −0.559299 | − | 0.766769i | ||||
\(976\) | 489.838 | − | 282.808i | 0.501883 | − | 0.289762i | ||||
\(977\) | −814.008 | + | 469.968i | −0.833171 | + | 0.481031i | −0.854937 | − | 0.518732i | \(-0.826404\pi\) |
0.0217664 | + | 0.999763i | \(0.493071\pi\) | |||||||
\(978\) | −271.335 | + | 469.966i | −0.277439 | + | 0.480538i | ||||
\(979\) | − | 883.344i | − | 0.902292i | ||||||
\(980\) | −6.57965 | + | 16.4327i | −0.00671393 | + | 0.0167681i | ||||
\(981\) | −195.437 | −0.199222 | ||||||||
\(982\) | 1202.73 | + | 694.395i | 1.22477 | + | 0.707123i | ||||
\(983\) | −276.232 | − | 478.448i | −0.281009 | − | 0.486722i | 0.690624 | − | 0.723214i | \(-0.257336\pi\) |
−0.971634 | + | 0.236492i | \(0.924002\pi\) | |||||||
\(984\) | −126.619 | − | 219.311i | −0.128678 | − | 0.222877i | ||||
\(985\) | −422.864 | + | 22.5606i | −0.429303 | + | 0.0229041i | ||||
\(986\) | 145.276i | 0.147339i | ||||||||
\(987\) | −320.846 | − | 1013.74i | −0.325072 | − | 1.02709i | ||||
\(988\) | 30.8954i | 0.0312706i | ||||||||
\(989\) | −18.2253 | + | 31.5672i | −0.0184280 | + | 0.0319183i | ||||
\(990\) | −88.9434 | + | 174.968i | −0.0898418 | + | 0.176736i | ||||
\(991\) | −208.648 | − | 361.389i | −0.210543 | − | 0.364671i | 0.741342 | − | 0.671128i | \(-0.234190\pi\) |
−0.951885 | + | 0.306457i | \(0.900856\pi\) | |||||||
\(992\) | −35.0556 | + | 60.7181i | −0.0353383 | + | 0.0612077i | ||||
\(993\) | −278.780 | −0.280745 | ||||||||
\(994\) | 294.094 | − | 1333.45i | 0.295869 | − | 1.34150i | ||||
\(995\) | 447.784 | + | 688.108i | 0.450034 | + | 0.691566i | ||||
\(996\) | −4.44218 | + | 7.69408i | −0.00446002 | + | 0.00772498i | ||||
\(997\) | −777.245 | − | 1346.23i | −0.779584 | − | 1.35028i | −0.932182 | − | 0.361990i | \(-0.882097\pi\) |
0.152598 | − | 0.988288i | \(-0.451236\pi\) | |||||||
\(998\) | −365.090 | + | 210.785i | −0.365822 | + | 0.211207i | ||||
\(999\) | −48.7521 | − | 28.1471i | −0.0488009 | − | 0.0281752i |
(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 | 105.3.r.a.19.12 | yes | 32 | |
3.2 | odd | 2 | 315.3.bi.e.19.5 | 32 | |||
5.2 | odd | 4 | 525.3.o.q.376.3 | 16 | |||
5.3 | odd | 4 | 525.3.o.p.376.6 | 16 | |||
5.4 | even | 2 | inner | 105.3.r.a.19.5 | ✓ | 32 | |
7.2 | even | 3 | 735.3.e.a.244.3 | 32 | |||
7.3 | odd | 6 | inner | 105.3.r.a.94.5 | yes | 32 | |
7.5 | odd | 6 | 735.3.e.a.244.27 | 32 | |||
15.14 | odd | 2 | 315.3.bi.e.19.12 | 32 | |||
21.17 | even | 6 | 315.3.bi.e.199.12 | 32 | |||
35.3 | even | 12 | 525.3.o.p.451.6 | 16 | |||
35.9 | even | 6 | 735.3.e.a.244.28 | 32 | |||
35.17 | even | 12 | 525.3.o.q.451.3 | 16 | |||
35.19 | odd | 6 | 735.3.e.a.244.4 | 32 | |||
35.24 | odd | 6 | inner | 105.3.r.a.94.12 | yes | 32 | |
105.59 | even | 6 | 315.3.bi.e.199.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.r.a.19.5 | ✓ | 32 | 5.4 | even | 2 | inner | |
105.3.r.a.19.12 | yes | 32 | 1.1 | even | 1 | trivial | |
105.3.r.a.94.5 | yes | 32 | 7.3 | odd | 6 | inner | |
105.3.r.a.94.12 | yes | 32 | 35.24 | odd | 6 | inner | |
315.3.bi.e.19.5 | 32 | 3.2 | odd | 2 | |||
315.3.bi.e.19.12 | 32 | 15.14 | odd | 2 | |||
315.3.bi.e.199.5 | 32 | 105.59 | even | 6 | |||
315.3.bi.e.199.12 | 32 | 21.17 | even | 6 | |||
525.3.o.p.376.6 | 16 | 5.3 | odd | 4 | |||
525.3.o.p.451.6 | 16 | 35.3 | even | 12 | |||
525.3.o.q.376.3 | 16 | 5.2 | odd | 4 | |||
525.3.o.q.451.3 | 16 | 35.17 | even | 12 | |||
735.3.e.a.244.3 | 32 | 7.2 | even | 3 | |||
735.3.e.a.244.4 | 32 | 35.19 | odd | 6 | |||
735.3.e.a.244.27 | 32 | 7.5 | odd | 6 | |||
735.3.e.a.244.28 | 32 | 35.9 | even | 6 |