Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(59,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.59");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.3317760000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.4 | ||
Root | \(1.01575 + 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.89 |
Dual form | 210.2.t.e.59.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.72286 | − | 0.178197i | 0.994694 | − | 0.102882i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.792893 | + | 2.09077i | 0.354593 | + | 0.935021i | ||||
\(6\) | −0.707107 | + | 1.58114i | −0.288675 | + | 0.645497i | ||||
\(7\) | 1.41421 | − | 2.23607i | 0.534522 | − | 0.845154i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 2.93649 | − | 0.614017i | 0.978831 | − | 0.204672i | ||||
\(10\) | −2.20711 | − | 0.358719i | −0.697948 | − | 0.113437i | ||||
\(11\) | −4.05781 | + | 2.34278i | −1.22348 | + | 0.706374i | −0.965657 | − | 0.259819i | \(-0.916337\pi\) |
−0.257819 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(12\) | −1.01575 | − | 1.40294i | −0.293223 | − | 0.404994i | ||||
\(13\) | 1.04456 | 0.289708 | 0.144854 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144854 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(14\) | 1.22938 | + | 2.34278i | 0.328567 | + | 0.626134i | ||||
\(15\) | 1.73861 | + | 3.46081i | 0.448908 | + | 0.893578i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.73861 | − | 1.58114i | 0.664211 | − | 0.383482i | −0.129668 | − | 0.991557i | \(-0.541391\pi\) |
0.793880 | + | 0.608075i | \(0.208058\pi\) | |||||||
\(18\) | −0.936492 | + | 2.85008i | −0.220733 | + | 0.671771i | ||||
\(19\) | −1.23861 | − | 0.715113i | −0.284157 | − | 0.164058i | 0.351147 | − | 0.936320i | \(-0.385792\pi\) |
−0.635304 | + | 0.772262i | \(0.719125\pi\) | |||||||
\(20\) | 1.41421 | − | 1.73205i | 0.316228 | − | 0.387298i | ||||
\(21\) | 2.03803 | − | 4.10444i | 0.444735 | − | 0.895662i | ||||
\(22\) | − | 4.68556i | − | 0.998964i | ||||||
\(23\) | −2.23861 | + | 3.87739i | −0.466783 | + | 0.808492i | −0.999280 | − | 0.0379400i | \(-0.987920\pi\) |
0.532497 | + | 0.846432i | \(0.321254\pi\) | |||||||
\(24\) | 1.72286 | − | 0.178197i | 0.351677 | − | 0.0363743i | ||||
\(25\) | −3.74264 | + | 3.31552i | −0.748528 | + | 0.663103i | ||||
\(26\) | −0.522278 | + | 0.904612i | −0.102427 | + | 0.177409i | ||||
\(27\) | 4.94975 | − | 1.58114i | 0.952579 | − | 0.304290i | ||||
\(28\) | −2.64360 | − | 0.106711i | −0.499593 | − | 0.0201665i | ||||
\(29\) | − | 6.92163i | − | 1.28531i | −0.766154 | − | 0.642657i | \(-0.777832\pi\) | ||
0.766154 | − | 0.642657i | \(-0.222168\pi\) | |||||||
\(30\) | −3.86646 | − | 0.224724i | −0.705915 | − | 0.0410287i | ||||
\(31\) | −5.73861 | + | 3.31319i | −1.03069 | + | 0.595066i | −0.917181 | − | 0.398471i | \(-0.869541\pi\) |
−0.113504 | + | 0.993537i | \(0.536208\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −6.57357 | + | 4.75937i | −1.14431 | + | 0.828500i | ||||
\(34\) | 3.16228i | 0.542326i | ||||||||
\(35\) | 5.79642 | + | 1.18383i | 0.979775 | + | 0.200104i | ||||
\(36\) | −2.00000 | − | 2.23607i | −0.333333 | − | 0.372678i | ||||
\(37\) | 2.30615 | + | 1.33146i | 0.379129 | + | 0.218890i | 0.677439 | − | 0.735579i | \(-0.263090\pi\) |
−0.298310 | + | 0.954469i | \(0.596423\pi\) | |||||||
\(38\) | 1.23861 | − | 0.715113i | 0.200930 | − | 0.116007i | ||||
\(39\) | 1.79962 | − | 0.186137i | 0.288170 | − | 0.0298057i | ||||
\(40\) | 0.792893 | + | 2.09077i | 0.125367 | + | 0.330580i | ||||
\(41\) | −1.04456 | −0.163132 | −0.0815661 | − | 0.996668i | \(-0.525992\pi\) | ||||
−0.0815661 | + | 0.996668i | \(0.525992\pi\) | |||||||
\(42\) | 2.53553 | + | 3.81721i | 0.391241 | + | 0.589008i | ||||
\(43\) | − | 6.92163i | − | 1.05554i | −0.849388 | − | 0.527769i | \(-0.823029\pi\) | ||
0.849388 | − | 0.527769i | \(-0.176971\pi\) | |||||||
\(44\) | 4.05781 | + | 2.34278i | 0.611738 | + | 0.353187i | ||||
\(45\) | 3.61209 | + | 5.65268i | 0.538459 | + | 0.842652i | ||||
\(46\) | −2.23861 | − | 3.87739i | −0.330065 | − | 0.571690i | ||||
\(47\) | −9.71584 | − | 5.60944i | −1.41720 | − | 0.818221i | −0.421149 | − | 0.906992i | \(-0.638373\pi\) |
−0.996052 | + | 0.0887705i | \(0.971706\pi\) | |||||||
\(48\) | −0.707107 | + | 1.58114i | −0.102062 | + | 0.228218i | ||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | −1.00000 | − | 4.89898i | −0.141421 | − | 0.692820i | ||||
\(51\) | 4.43649 | − | 3.21209i | 0.621233 | − | 0.449783i | ||||
\(52\) | −0.522278 | − | 0.904612i | −0.0724269 | − | 0.125447i | ||||
\(53\) | −2.50000 | − | 4.33013i | −0.343401 | − | 0.594789i | 0.641661 | − | 0.766989i | \(-0.278246\pi\) |
−0.985062 | + | 0.172200i | \(0.944912\pi\) | |||||||
\(54\) | −1.10557 | + | 5.07718i | −0.150449 | + | 0.690916i | ||||
\(55\) | −8.11562 | − | 6.62638i | −1.09431 | − | 0.893501i | ||||
\(56\) | 1.41421 | − | 2.23607i | 0.188982 | − | 0.298807i | ||||
\(57\) | −2.26139 | − | 1.01132i | −0.299528 | − | 0.133953i | ||||
\(58\) | 5.99430 | + | 3.46081i | 0.787091 | + | 0.454427i | ||||
\(59\) | −5.28720 | − | 9.15769i | −0.688334 | − | 1.19223i | −0.972376 | − | 0.233418i | \(-0.925009\pi\) |
0.284042 | − | 0.958812i | \(-0.408324\pi\) | |||||||
\(60\) | 2.12785 | − | 3.23609i | 0.274704 | − | 0.417777i | ||||
\(61\) | 3.00000 | + | 1.73205i | 0.384111 | + | 0.221766i | 0.679605 | − | 0.733578i | \(-0.262151\pi\) |
−0.295495 | + | 0.955344i | \(0.595484\pi\) | |||||||
\(62\) | − | 6.62638i | − | 0.841551i | ||||||
\(63\) | 2.77984 | − | 7.43455i | 0.350227 | − | 0.936665i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.828222 | + | 2.18393i | 0.102728 | + | 0.270883i | ||||
\(66\) | −0.834952 | − | 8.07256i | −0.102776 | − | 0.993663i | ||||
\(67\) | 12.3583 | − | 7.13505i | 1.50980 | − | 0.871685i | 0.509868 | − | 0.860253i | \(-0.329694\pi\) |
0.999935 | − | 0.0114319i | \(-0.00363898\pi\) | |||||||
\(68\) | −2.73861 | − | 1.58114i | −0.332106 | − | 0.191741i | ||||
\(69\) | −3.16588 | + | 7.07912i | −0.381127 | + | 0.852225i | ||||
\(70\) | −3.92344 | + | 4.42793i | −0.468941 | + | 0.529239i | ||||
\(71\) | 6.92163i | 0.821446i | 0.911760 | + | 0.410723i | \(0.134724\pi\) | ||||
−0.911760 | + | 0.410723i | \(0.865276\pi\) | |||||||
\(72\) | 2.93649 | − | 0.614017i | 0.346069 | − | 0.0723626i | ||||
\(73\) | 1.75166 | + | 3.03397i | 0.205017 | + | 0.355099i | 0.950138 | − | 0.311830i | \(-0.100942\pi\) |
−0.745121 | + | 0.666929i | \(0.767608\pi\) | |||||||
\(74\) | −2.30615 | + | 1.33146i | −0.268084 | + | 0.154779i | ||||
\(75\) | −5.85723 | + | 6.37909i | −0.676335 | + | 0.736594i | ||||
\(76\) | 1.43023i | 0.164058i | ||||||||
\(77\) | −0.500000 | + | 12.3867i | −0.0569803 | + | 1.41160i | ||||
\(78\) | −0.738613 | + | 1.65159i | −0.0836314 | + | 0.187006i | ||||
\(79\) | −5.73861 | + | 9.93957i | −0.645644 | + | 1.11829i | 0.338508 | + | 0.940964i | \(0.390078\pi\) |
−0.984152 | + | 0.177325i | \(0.943256\pi\) | |||||||
\(80\) | −2.20711 | − | 0.358719i | −0.246762 | − | 0.0401061i | ||||
\(81\) | 8.24597 | − | 3.60611i | 0.916219 | − | 0.400679i | ||||
\(82\) | 0.522278 | − | 0.904612i | 0.0576760 | − | 0.0998977i | ||||
\(83\) | 4.06775i | 0.446494i | 0.974762 | + | 0.223247i | \(0.0716656\pi\) | ||||
−0.974762 | + | 0.223247i | \(0.928334\pi\) | |||||||
\(84\) | −4.57357 | + | 0.287233i | −0.499017 | + | 0.0313397i | ||||
\(85\) | 5.47723 | + | 4.47214i | 0.594089 | + | 0.485071i | ||||
\(86\) | 5.99430 | + | 3.46081i | 0.646382 | + | 0.373189i | ||||
\(87\) | −1.23341 | − | 11.9250i | −0.132236 | − | 1.27849i | ||||
\(88\) | −4.05781 | + | 2.34278i | −0.432564 | + | 0.249741i | ||||
\(89\) | −2.45877 | + | 4.25871i | −0.260629 | + | 0.451423i | −0.966409 | − | 0.257008i | \(-0.917263\pi\) |
0.705780 | + | 0.708431i | \(0.250597\pi\) | |||||||
\(90\) | −6.70141 | + | 0.301824i | −0.706391 | + | 0.0318150i | ||||
\(91\) | 1.47723 | − | 2.33570i | 0.154855 | − | 0.244848i | ||||
\(92\) | 4.47723 | 0.466783 | ||||||||
\(93\) | −9.29642 | + | 6.73076i | −0.963994 | + | 0.697948i | ||||
\(94\) | 9.71584 | − | 5.60944i | 1.00211 | − | 0.578570i | ||||
\(95\) | 0.513050 | − | 3.15666i | 0.0526378 | − | 0.323867i | ||||
\(96\) | −1.01575 | − | 1.40294i | −0.103670 | − | 0.143187i | ||||
\(97\) | −11.9886 | −1.21726 | −0.608629 | − | 0.793455i | \(-0.708280\pi\) | ||||
−0.608629 | + | 0.793455i | \(0.708280\pi\) | |||||||
\(98\) | 6.97723 | + | 0.564201i | 0.704806 | + | 0.0569930i | ||||
\(99\) | −10.4772 | + | 9.37112i | −1.05300 | + | 0.941833i | ||||
\(100\) | 4.74264 | + | 1.58346i | 0.474264 | + | 0.158346i | ||||
\(101\) | 5.65685 | + | 9.79796i | 0.562878 | + | 0.974933i | 0.997244 | + | 0.0741967i | \(0.0236393\pi\) |
−0.434366 | + | 0.900737i | \(0.643027\pi\) | |||||||
\(102\) | 0.563508 | + | 5.44816i | 0.0557956 | + | 0.539448i | ||||
\(103\) | −2.45877 | + | 4.25871i | −0.242270 | + | 0.419624i | −0.961360 | − | 0.275293i | \(-0.911225\pi\) |
0.719091 | + | 0.694916i | \(0.244559\pi\) | |||||||
\(104\) | 1.04456 | 0.102427 | ||||||||
\(105\) | 10.1974 | + | 1.00667i | 0.995163 | + | 0.0982411i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | 2.73861 | − | 4.74342i | 0.264752 | − | 0.458563i | −0.702747 | − | 0.711440i | \(-0.748043\pi\) |
0.967499 | + | 0.252877i | \(0.0813767\pi\) | |||||||
\(108\) | −3.84418 | − | 3.49604i | −0.369906 | − | 0.336406i | ||||
\(109\) | 10.2158 | + | 17.6944i | 0.978500 | + | 1.69481i | 0.667866 | + | 0.744282i | \(0.267208\pi\) |
0.310634 | + | 0.950529i | \(0.399459\pi\) | |||||||
\(110\) | 9.79642 | − | 3.71515i | 0.934052 | − | 0.354225i | ||||
\(111\) | 4.21043 | + | 1.88296i | 0.399637 | + | 0.178723i | ||||
\(112\) | 1.22938 | + | 2.34278i | 0.116166 | + | 0.221372i | ||||
\(113\) | 17.4772 | 1.64412 | 0.822060 | − | 0.569402i | \(-0.192825\pi\) | ||||
0.822060 | + | 0.569402i | \(0.192825\pi\) | |||||||
\(114\) | 2.00653 | − | 1.45276i | 0.187928 | − | 0.136063i | ||||
\(115\) | −9.88171 | − | 1.60607i | −0.921475 | − | 0.149767i | ||||
\(116\) | −5.99430 | + | 3.46081i | −0.556557 | + | 0.321328i | ||||
\(117\) | 3.06733 | − | 0.641375i | 0.283575 | − | 0.0592951i | ||||
\(118\) | 10.5744 | 0.973452 | ||||||||
\(119\) | 0.337449 | − | 8.35979i | 0.0309339 | − | 0.766341i | ||||
\(120\) | 1.73861 | + | 3.46081i | 0.158713 | + | 0.315928i | ||||
\(121\) | 5.47723 | − | 9.48683i | 0.497930 | − | 0.862439i | ||||
\(122\) | −3.00000 | + | 1.73205i | −0.271607 | + | 0.156813i | ||||
\(123\) | −1.79962 | + | 0.186137i | −0.162267 | + | 0.0167834i | ||||
\(124\) | 5.73861 | + | 3.31319i | 0.515343 | + | 0.297533i | ||||
\(125\) | −9.89949 | − | 5.19615i | −0.885438 | − | 0.464758i | ||||
\(126\) | 5.04858 | + | 6.12469i | 0.449764 | + | 0.545631i | ||||
\(127\) | 8.73085i | 0.774738i | 0.921925 | + | 0.387369i | \(0.126616\pi\) | ||||
−0.921925 | + | 0.387369i | \(0.873384\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.23341 | − | 11.9250i | −0.108596 | − | 1.04994i | ||||
\(130\) | −2.30545 | − | 0.374703i | −0.202201 | − | 0.0328636i | ||||
\(131\) | −6.88624 | + | 11.9273i | −0.601654 | + | 1.04209i | 0.390917 | + | 0.920426i | \(0.372158\pi\) |
−0.992571 | + | 0.121669i | \(0.961175\pi\) | |||||||
\(132\) | 7.40852 | + | 3.31319i | 0.644829 | + | 0.288376i | ||||
\(133\) | −3.35071 | + | 1.75830i | −0.290543 | + | 0.152464i | ||||
\(134\) | 14.2701i | 1.23275i | ||||||||
\(135\) | 7.23042 | + | 9.09511i | 0.622295 | + | 0.782782i | ||||
\(136\) | 2.73861 | − | 1.58114i | 0.234834 | − | 0.135582i | ||||
\(137\) | 1.73861 | + | 3.01137i | 0.148540 | + | 0.257278i | 0.930688 | − | 0.365814i | \(-0.119209\pi\) |
−0.782148 | + | 0.623092i | \(0.785876\pi\) | |||||||
\(138\) | −4.54776 | − | 6.28129i | −0.387131 | − | 0.534699i | ||||
\(139\) | − | 20.1810i | − | 1.71173i | −0.517202 | − | 0.855863i | \(-0.673026\pi\) | ||
0.517202 | − | 0.855863i | \(-0.326974\pi\) | |||||||
\(140\) | −1.87298 | − | 5.61177i | −0.158296 | − | 0.474281i | ||||
\(141\) | −17.7386 | − | 7.93295i | −1.49386 | − | 0.668075i | ||||
\(142\) | −5.99430 | − | 3.46081i | −0.503031 | − | 0.290425i | ||||
\(143\) | −4.23861 | + | 2.44716i | −0.354451 | + | 0.204642i | ||||
\(144\) | −0.936492 | + | 2.85008i | −0.0780410 | + | 0.237507i | ||||
\(145\) | 14.4715 | − | 5.48811i | 1.20180 | − | 0.455763i | ||||
\(146\) | −3.50333 | −0.289937 | ||||||||
\(147\) | −6.29560 | − | 10.3617i | −0.519252 | − | 0.854621i | ||||
\(148\) | − | 2.66291i | − | 0.218890i | ||||||
\(149\) | −2.12132 | − | 1.22474i | −0.173785 | − | 0.100335i | 0.410584 | − | 0.911823i | \(-0.365325\pi\) |
−0.584370 | + | 0.811488i | \(0.698658\pi\) | |||||||
\(150\) | −2.59584 | − | 8.26206i | −0.211950 | − | 0.674594i | ||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | −1.23861 | − | 0.715113i | −0.100465 | − | 0.0580034i | ||||
\(153\) | 7.07107 | − | 6.32456i | 0.571662 | − | 0.511310i | ||||
\(154\) | −10.4772 | − | 6.62638i | −0.844279 | − | 0.533969i | ||||
\(155\) | −11.4772 | − | 9.37112i | −0.921873 | − | 0.752706i | ||||
\(156\) | −1.06101 | − | 1.46545i | −0.0849489 | − | 0.117330i | ||||
\(157\) | 7.22369 | + | 12.5118i | 0.576513 | + | 0.998550i | 0.995875 | + | 0.0907311i | \(0.0289204\pi\) |
−0.419362 | + | 0.907819i | \(0.637746\pi\) | |||||||
\(158\) | −5.73861 | − | 9.93957i | −0.456540 | − | 0.790750i | ||||
\(159\) | −5.07877 | − | 7.01471i | −0.402772 | − | 0.556303i | ||||
\(160\) | 1.41421 | − | 1.73205i | 0.111803 | − | 0.136931i | ||||
\(161\) | 5.50423 | + | 10.4891i | 0.433794 | + | 0.826661i | ||||
\(162\) | −1.00000 | + | 8.94427i | −0.0785674 | + | 0.702728i | ||||
\(163\) | 12.7279 | + | 7.34847i | 0.996928 | + | 0.575577i | 0.907338 | − | 0.420402i | \(-0.138111\pi\) |
0.0895899 | + | 0.995979i | \(0.471444\pi\) | |||||||
\(164\) | 0.522278 | + | 0.904612i | 0.0407831 | + | 0.0706383i | ||||
\(165\) | −15.1629 | − | 9.97014i | −1.18043 | − | 0.776175i | ||||
\(166\) | −3.52277 | − | 2.03387i | −0.273420 | − | 0.157859i | ||||
\(167\) | 4.29068i | 0.332023i | 0.986124 | + | 0.166011i | \(0.0530889\pi\) | ||||
−0.986124 | + | 0.166011i | \(0.946911\pi\) | |||||||
\(168\) | 2.03803 | − | 4.10444i | 0.157238 | − | 0.316664i | ||||
\(169\) | −11.9089 | −0.916069 | ||||||||
\(170\) | −6.61160 | + | 2.50735i | −0.507086 | + | 0.192305i | ||||
\(171\) | −4.07627 | − | 1.33940i | −0.311720 | − | 0.102426i | ||||
\(172\) | −5.99430 | + | 3.46081i | −0.457061 | + | 0.263885i | ||||
\(173\) | 0.977226 | + | 0.564201i | 0.0742971 | + | 0.0428954i | 0.536688 | − | 0.843781i | \(-0.319675\pi\) |
−0.462391 | + | 0.886676i | \(0.653008\pi\) | |||||||
\(174\) | 10.9441 | + | 4.89433i | 0.829666 | + | 0.371038i | ||||
\(175\) | 2.12082 | + | 13.0576i | 0.160319 | + | 0.987065i | ||||
\(176\) | − | 4.68556i | − | 0.353187i | ||||||
\(177\) | −10.7410 | − | 14.8353i | −0.807341 | − | 1.11509i | ||||
\(178\) | −2.45877 | − | 4.25871i | −0.184293 | − | 0.319204i | ||||
\(179\) | 16.7857 | − | 9.69125i | 1.25462 | − | 0.724358i | 0.282600 | − | 0.959238i | \(-0.408803\pi\) |
0.972024 | + | 0.234880i | \(0.0754697\pi\) | |||||||
\(180\) | 3.08932 | − | 5.95450i | 0.230264 | − | 0.443823i | ||||
\(181\) | − | 3.16228i | − | 0.235050i | −0.993070 | − | 0.117525i | \(-0.962504\pi\) | ||
0.993070 | − | 0.117525i | \(-0.0374961\pi\) | |||||||
\(182\) | 1.28416 | + | 2.44716i | 0.0951884 | + | 0.181396i | ||||
\(183\) | 5.47723 | + | 2.44949i | 0.404888 | + | 0.181071i | ||||
\(184\) | −2.23861 | + | 3.87739i | −0.165033 | + | 0.285845i | ||||
\(185\) | −0.955238 | + | 5.87733i | −0.0702305 | + | 0.432110i | ||||
\(186\) | −1.18080 | − | 11.4163i | −0.0865805 | − | 0.837085i | ||||
\(187\) | −7.40852 | + | 12.8319i | −0.541764 | + | 0.938364i | ||||
\(188\) | 11.2189i | 0.818221i | ||||||||
\(189\) | 3.46447 | − | 13.3040i | 0.252003 | − | 0.967726i | ||||
\(190\) | 2.47723 | + | 2.02265i | 0.179717 | + | 0.146738i | ||||
\(191\) | −14.1099 | − | 8.14637i | −1.02096 | − | 0.589451i | −0.106577 | − | 0.994304i | \(-0.533989\pi\) |
−0.914381 | + | 0.404854i | \(0.867322\pi\) | |||||||
\(192\) | 1.72286 | − | 0.178197i | 0.124337 | − | 0.0128603i | ||||
\(193\) | 6.36396 | − | 3.67423i | 0.458088 | − | 0.264477i | −0.253152 | − | 0.967427i | \(-0.581467\pi\) |
0.711240 | + | 0.702949i | \(0.248134\pi\) | |||||||
\(194\) | 5.99430 | − | 10.3824i | 0.430366 | − | 0.745416i | ||||
\(195\) | 1.81608 | + | 3.61501i | 0.130052 | + | 0.258877i | ||||
\(196\) | −3.97723 | + | 5.76035i | −0.284088 | + | 0.411454i | ||||
\(197\) | 9.00000 | 0.641223 | 0.320612 | − | 0.947211i | \(-0.396112\pi\) | ||||
0.320612 | + | 0.947211i | \(0.396112\pi\) | |||||||
\(198\) | −2.87701 | − | 13.7591i | −0.204460 | − | 0.977817i | ||||
\(199\) | 13.4317 | − | 7.75478i | 0.952146 | − | 0.549722i | 0.0583993 | − | 0.998293i | \(-0.481400\pi\) |
0.893747 | + | 0.448571i | \(0.148067\pi\) | |||||||
\(200\) | −3.74264 | + | 3.31552i | −0.264645 | + | 0.234442i | ||||
\(201\) | 20.0201 | − | 14.4949i | 1.41211 | − | 1.02239i | ||||
\(202\) | −11.3137 | −0.796030 | ||||||||
\(203\) | −15.4772 | − | 9.78866i | −1.08629 | − | 0.687029i | ||||
\(204\) | −5.00000 | − | 2.23607i | −0.350070 | − | 0.156556i | ||||
\(205\) | −0.828222 | − | 2.18393i | −0.0578455 | − | 0.152532i | ||||
\(206\) | −2.45877 | − | 4.25871i | −0.171311 | − | 0.296719i | ||||
\(207\) | −4.19288 | + | 12.7605i | −0.291426 | + | 0.886914i | ||||
\(208\) | −0.522278 | + | 0.904612i | −0.0362135 | + | 0.0627236i | ||||
\(209\) | 6.70141 | 0.463546 | ||||||||
\(210\) | −5.97049 | + | 8.32786i | −0.412003 | + | 0.574677i | ||||
\(211\) | 24.4772 | 1.68508 | 0.842541 | − | 0.538632i | \(-0.181059\pi\) | ||||
0.842541 | + | 0.538632i | \(0.181059\pi\) | |||||||
\(212\) | −2.50000 | + | 4.33013i | −0.171701 | + | 0.297394i | ||||
\(213\) | 1.23341 | + | 11.9250i | 0.0845121 | + | 0.817087i | ||||
\(214\) | 2.73861 | + | 4.74342i | 0.187208 | + | 0.324253i | ||||
\(215\) | 14.4715 | − | 5.48811i | 0.986950 | − | 0.374286i | ||||
\(216\) | 4.94975 | − | 1.58114i | 0.336788 | − | 0.107583i | ||||
\(217\) | −0.707107 | + | 17.5175i | −0.0480015 | + | 1.18916i | ||||
\(218\) | −20.4317 | −1.38381 | ||||||||
\(219\) | 3.55851 | + | 4.91496i | 0.240462 | + | 0.332122i | ||||
\(220\) | −1.68080 | + | 10.3415i | −0.113320 | + | 0.697226i | ||||
\(221\) | 2.86064 | − | 1.65159i | 0.192427 | − | 0.111098i | ||||
\(222\) | −3.73591 | + | 2.70486i | −0.250738 | + | 0.181538i | ||||
\(223\) | −21.8881 | −1.46574 | −0.732868 | − | 0.680371i | \(-0.761819\pi\) | ||||
−0.732868 | + | 0.680371i | \(0.761819\pi\) | |||||||
\(224\) | −2.64360 | − | 0.106711i | −0.176633 | − | 0.00712992i | ||||
\(225\) | −8.95445 | + | 12.0340i | −0.596963 | + | 0.802268i | ||||
\(226\) | −8.73861 | + | 15.1357i | −0.581284 | + | 1.00681i | ||||
\(227\) | 9.00000 | − | 5.19615i | 0.597351 | − | 0.344881i | −0.170648 | − | 0.985332i | \(-0.554586\pi\) |
0.767999 | + | 0.640451i | \(0.221253\pi\) | |||||||
\(228\) | 0.254862 | + | 2.46408i | 0.0168787 | + | 0.163188i | ||||
\(229\) | −11.7386 | − | 6.77729i | −0.775709 | − | 0.447856i | 0.0591982 | − | 0.998246i | \(-0.481146\pi\) |
−0.834908 | + | 0.550390i | \(0.814479\pi\) | |||||||
\(230\) | 6.33175 | − | 7.75478i | 0.417503 | − | 0.511335i | ||||
\(231\) | 1.34585 | + | 21.4297i | 0.0885503 | + | 1.40997i | ||||
\(232\) | − | 6.92163i | − | 0.454427i | ||||||
\(233\) | 2.00000 | − | 3.46410i | 0.131024 | − | 0.226941i | −0.793047 | − | 0.609160i | \(-0.791507\pi\) |
0.924072 | + | 0.382219i | \(0.124840\pi\) | |||||||
\(234\) | −0.978218 | + | 2.97707i | −0.0639481 | + | 0.194617i | ||||
\(235\) | 4.02443 | − | 24.7613i | 0.262525 | − | 1.61525i | ||||
\(236\) | −5.28720 | + | 9.15769i | −0.344167 | + | 0.596115i | ||||
\(237\) | −8.11562 | + | 18.1471i | −0.527166 | + | 1.17878i | ||||
\(238\) | 7.07107 | + | 4.47214i | 0.458349 | + | 0.289886i | ||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | −3.86646 | − | 0.224724i | −0.249579 | − | 0.0145058i | ||||
\(241\) | −18.4545 | + | 10.6547i | −1.18876 | + | 0.686328i | −0.958024 | − | 0.286689i | \(-0.907445\pi\) |
−0.230732 | + | 0.973017i | \(0.574112\pi\) | |||||||
\(242\) | 5.47723 | + | 9.48683i | 0.352089 | + | 0.609837i | ||||
\(243\) | 13.5640 | − | 7.68223i | 0.870134 | − | 0.492815i | ||||
\(244\) | − | 3.46410i | − | 0.221766i | ||||||
\(245\) | 10.8445 | − | 11.2870i | 0.692830 | − | 0.721100i | ||||
\(246\) | 0.738613 | − | 1.65159i | 0.0470922 | − | 0.105301i | ||||
\(247\) | −1.29380 | − | 0.746976i | −0.0823226 | − | 0.0475290i | ||||
\(248\) | −5.73861 | + | 3.31319i | −0.364402 | + | 0.210388i | ||||
\(249\) | 0.724861 | + | 7.00816i | 0.0459362 | + | 0.444124i | ||||
\(250\) | 9.44975 | − | 5.97514i | 0.597655 | − | 0.377901i | ||||
\(251\) | −8.85494 | −0.558919 | −0.279459 | − | 0.960158i | \(-0.590155\pi\) | ||||
−0.279459 | + | 0.960158i | \(0.590155\pi\) | |||||||
\(252\) | −7.82843 | + | 1.30986i | −0.493145 | + | 0.0825133i | ||||
\(253\) | − | 20.9783i | − | 1.31889i | ||||||
\(254\) | −7.56114 | − | 4.36543i | −0.474428 | − | 0.273911i | ||||
\(255\) | 10.2334 | + | 6.72884i | 0.640841 | + | 0.421376i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.52277 | − | 5.49798i | −0.594014 | − | 0.342954i | 0.172669 | − | 0.984980i | \(-0.444761\pi\) |
−0.766683 | + | 0.642026i | \(0.778094\pi\) | |||||||
\(258\) | 10.9441 | + | 4.89433i | 0.681347 | + | 0.304708i | ||||
\(259\) | 6.23861 | − | 3.27374i | 0.387649 | − | 0.203421i | ||||
\(260\) | 1.47723 | − | 1.80922i | 0.0916136 | − | 0.112203i | ||||
\(261\) | −4.24999 | − | 20.3253i | −0.263068 | − | 1.25810i | ||||
\(262\) | −6.88624 | − | 11.9273i | −0.425433 | − | 0.736872i | ||||
\(263\) | 1.00000 | + | 1.73205i | 0.0616626 | + | 0.106803i | 0.895209 | − | 0.445647i | \(-0.147026\pi\) |
−0.833546 | + | 0.552450i | \(0.813693\pi\) | |||||||
\(264\) | −6.57357 | + | 4.75937i | −0.404575 | + | 0.292919i | ||||
\(265\) | 7.07107 | − | 8.66025i | 0.434372 | − | 0.531995i | ||||
\(266\) | 0.152621 | − | 3.78095i | 0.00935778 | − | 0.231825i | ||||
\(267\) | −3.47723 | + | 7.77531i | −0.212803 | + | 0.475841i | ||||
\(268\) | −12.3583 | − | 7.13505i | −0.754901 | − | 0.435842i | ||||
\(269\) | 8.79052 | + | 15.2256i | 0.535968 | + | 0.928323i | 0.999116 | + | 0.0420423i | \(0.0133864\pi\) |
−0.463148 | + | 0.886281i | \(0.653280\pi\) | |||||||
\(270\) | −11.4918 | + | 1.71417i | −0.699369 | + | 0.104321i | ||||
\(271\) | −5.47723 | − | 3.16228i | −0.332718 | − | 0.192095i | 0.324329 | − | 0.945944i | \(-0.394861\pi\) |
−0.657047 | + | 0.753850i | \(0.728195\pi\) | |||||||
\(272\) | 3.16228i | 0.191741i | ||||||||
\(273\) | 2.12884 | − | 4.28732i | 0.128843 | − | 0.259480i | ||||
\(274\) | −3.47723 | −0.210067 | ||||||||
\(275\) | 7.41941 | − | 22.2219i | 0.447407 | − | 1.34003i | ||||
\(276\) | 7.71363 | − | 0.797828i | 0.464306 | − | 0.0480236i | ||||
\(277\) | −8.48528 | + | 4.89898i | −0.509831 | + | 0.294351i | −0.732764 | − | 0.680483i | \(-0.761770\pi\) |
0.222933 | + | 0.974834i | \(0.428437\pi\) | |||||||
\(278\) | 17.4772 | + | 10.0905i | 1.04821 | + | 0.605187i | ||||
\(279\) | −14.8170 | + | 13.2528i | −0.887073 | + | 0.793422i | ||||
\(280\) | 5.79642 | + | 1.18383i | 0.346403 | + | 0.0707475i | ||||
\(281\) | 1.80922i | 0.107929i | 0.998543 | + | 0.0539646i | \(0.0171858\pi\) | ||||
−0.998543 | + | 0.0539646i | \(0.982814\pi\) | |||||||
\(282\) | 15.7394 | − | 11.3956i | 0.937270 | − | 0.678599i | ||||
\(283\) | 4.61230 | + | 7.98873i | 0.274173 | + | 0.474881i | 0.969926 | − | 0.243400i | \(-0.0782627\pi\) |
−0.695753 | + | 0.718281i | \(0.744929\pi\) | |||||||
\(284\) | 5.99430 | − | 3.46081i | 0.355696 | − | 0.205361i | ||||
\(285\) | 0.321406 | − | 5.52991i | 0.0190384 | − | 0.327564i | ||||
\(286\) | − | 4.89433i | − | 0.289408i | ||||||
\(287\) | −1.47723 | + | 2.33570i | −0.0871979 | + | 0.137872i | ||||
\(288\) | −2.00000 | − | 2.23607i | −0.117851 | − | 0.131762i | ||||
\(289\) | −3.50000 | + | 6.06218i | −0.205882 | + | 0.356599i | ||||
\(290\) | −2.48292 | + | 15.2768i | −0.145802 | + | 0.897083i | ||||
\(291\) | −20.6547 | + | 2.13633i | −1.21080 | + | 0.125234i | ||||
\(292\) | 1.75166 | − | 3.03397i | 0.102508 | − | 0.177550i | ||||
\(293\) | − | 8.05661i | − | 0.470672i | −0.971914 | − | 0.235336i | \(-0.924381\pi\) | ||
0.971914 | − | 0.235336i | \(-0.0756190\pi\) | |||||||
\(294\) | 12.1213 | − | 0.271281i | 0.706930 | − | 0.0158214i | ||||
\(295\) | 14.9545 | − | 18.3154i | 0.870682 | − | 1.06636i | ||||
\(296\) | 2.30615 | + | 1.33146i | 0.134042 | + | 0.0773893i | ||||
\(297\) | −16.3809 | + | 18.0121i | −0.950515 | + | 1.04517i | ||||
\(298\) | 2.12132 | − | 1.22474i | 0.122885 | − | 0.0709476i | ||||
\(299\) | −2.33836 | + | 4.05015i | −0.135231 | + | 0.234226i | ||||
\(300\) | 8.45307 | + | 1.88296i | 0.488038 | + | 0.108713i | ||||
\(301\) | −15.4772 | − | 9.78866i | −0.892092 | − | 0.564209i | ||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 11.4919 | + | 15.8725i | 0.660194 | + | 0.911850i | ||||
\(304\) | 1.23861 | − | 0.715113i | 0.0710393 | − | 0.0410146i | ||||
\(305\) | −1.24264 | + | 7.64564i | −0.0711534 | + | 0.437788i | ||||
\(306\) | 1.94169 | + | 9.28600i | 0.110999 | + | 0.530845i | ||||
\(307\) | 11.9886 | 0.684226 | 0.342113 | − | 0.939659i | \(-0.388857\pi\) | ||||
0.342113 | + | 0.939659i | \(0.388857\pi\) | |||||||
\(308\) | 10.9772 | − | 5.76035i | 0.625485 | − | 0.328227i | ||||
\(309\) | −3.47723 | + | 7.77531i | −0.197812 | + | 0.442322i | ||||
\(310\) | 13.8542 | − | 5.25401i | 0.786868 | − | 0.298408i | ||||
\(311\) | 8.79052 | + | 15.2256i | 0.498465 | + | 0.863366i | 0.999998 | − | 0.00177176i | \(-0.000563970\pi\) |
−0.501534 | + | 0.865138i | \(0.667231\pi\) | |||||||
\(312\) | 1.79962 | − | 0.186137i | 0.101884 | − | 0.0105379i | ||||
\(313\) | 11.6190 | − | 20.1246i | 0.656742 | − | 1.13751i | −0.324712 | − | 0.945813i | \(-0.605267\pi\) |
0.981454 | − | 0.191697i | \(-0.0613992\pi\) | |||||||
\(314\) | −14.4474 | −0.815313 | ||||||||
\(315\) | 17.7480 | − | 0.0827879i | 0.999989 | − | 0.00466457i | ||||
\(316\) | 11.4772 | 0.645644 | ||||||||
\(317\) | 4.95445 | − | 8.58136i | 0.278270 | − | 0.481977i | −0.692685 | − | 0.721240i | \(-0.743572\pi\) |
0.970955 | + | 0.239263i | \(0.0769058\pi\) | |||||||
\(318\) | 8.61430 | − | 0.890985i | 0.483066 | − | 0.0499640i | ||||
\(319\) | 16.2158 | + | 28.0867i | 0.907913 | + | 1.57255i | ||||
\(320\) | 0.792893 | + | 2.09077i | 0.0443241 | + | 0.116878i | ||||
\(321\) | 3.87298 | − | 8.66025i | 0.216169 | − | 0.483368i | ||||
\(322\) | −11.8360 | − | 0.477769i | −0.659594 | − | 0.0266250i | ||||
\(323\) | −4.52277 | −0.251654 | ||||||||
\(324\) | −7.24597 | − | 5.33816i | −0.402554 | − | 0.296565i | ||||
\(325\) | −3.90940 | + | 3.46324i | −0.216854 | + | 0.192106i | ||||
\(326\) | −12.7279 | + | 7.34847i | −0.704934 | + | 0.406994i | ||||
\(327\) | 20.7535 | + | 28.6645i | 1.14767 | + | 1.58515i | ||||
\(328\) | −1.04456 | −0.0576760 | ||||||||
\(329\) | −26.2834 | + | 13.7923i | −1.44905 | + | 0.760396i | ||||
\(330\) | 16.2158 | − | 8.14637i | 0.892653 | − | 0.448443i | ||||
\(331\) | −10.7158 | + | 18.5604i | −0.588996 | + | 1.02017i | 0.405369 | + | 0.914153i | \(0.367143\pi\) |
−0.994364 | + | 0.106017i | \(0.966190\pi\) | |||||||
\(332\) | 3.52277 | − | 2.03387i | 0.193337 | − | 0.111623i | ||||
\(333\) | 7.58952 | + | 2.49379i | 0.415903 | + | 0.136659i | ||||
\(334\) | −3.71584 | − | 2.14534i | −0.203322 | − | 0.117388i | ||||
\(335\) | 24.7165 | + | 20.1810i | 1.35041 | + | 1.10260i | ||||
\(336\) | 2.53553 | + | 3.81721i | 0.138325 | + | 0.208246i | ||||
\(337\) | − | 17.1464i | − | 0.934025i | −0.884251 | − | 0.467013i | \(-0.845330\pi\) | ||
0.884251 | − | 0.467013i | \(-0.154670\pi\) | |||||||
\(338\) | 5.95445 | − | 10.3134i | 0.323879 | − | 0.560976i | ||||
\(339\) | 30.1108 | − | 3.11439i | 1.63539 | − | 0.169150i | ||||
\(340\) | 1.13437 | − | 6.97948i | 0.0615199 | − | 0.378516i | ||||
\(341\) | 15.5241 | − | 26.8886i | 0.840679 | − | 1.45610i | ||||
\(342\) | 3.19808 | − | 2.86045i | 0.172933 | − | 0.154676i | ||||
\(343\) | −18.3848 | − | 2.23607i | −0.992685 | − | 0.120736i | ||||
\(344\) | − | 6.92163i | − | 0.373189i | ||||||
\(345\) | −17.3110 | − | 1.00614i | −0.931993 | − | 0.0541687i | ||||
\(346\) | −0.977226 | + | 0.564201i | −0.0525360 | + | 0.0303317i | ||||
\(347\) | 8.73861 | + | 15.1357i | 0.469113 | + | 0.812528i | 0.999377 | − | 0.0353049i | \(-0.0112402\pi\) |
−0.530263 | + | 0.847833i | \(0.677907\pi\) | |||||||
\(348\) | −9.71064 | + | 7.03066i | −0.520545 | + | 0.376883i | ||||
\(349\) | 11.7436i | 0.628623i | 0.949320 | + | 0.314311i | \(0.101774\pi\) | ||||
−0.949320 | + | 0.314311i | \(0.898226\pi\) | |||||||
\(350\) | −12.3687 | − | 4.69214i | −0.661133 | − | 0.250805i | ||||
\(351\) | 5.17029 | − | 1.65159i | 0.275970 | − | 0.0881553i | ||||
\(352\) | 4.05781 | + | 2.34278i | 0.216282 | + | 0.124871i | ||||
\(353\) | 0.522774 | − | 0.301824i | 0.0278245 | − | 0.0160645i | −0.486023 | − | 0.873946i | \(-0.661553\pi\) |
0.513848 | + | 0.857881i | \(0.328220\pi\) | |||||||
\(354\) | 18.2182 | − | 1.88433i | 0.968286 | − | 0.100151i | ||||
\(355\) | −14.4715 | + | 5.48811i | −0.768069 | + | 0.291279i | ||||
\(356\) | 4.91754 | 0.260629 | ||||||||
\(357\) | −0.908312 | − | 14.4629i | −0.0480730 | − | 0.765457i | ||||
\(358\) | 19.3825i | 1.02440i | ||||||||
\(359\) | 9.86729 | + | 5.69688i | 0.520775 | + | 0.300670i | 0.737252 | − | 0.675618i | \(-0.236123\pi\) |
−0.216476 | + | 0.976288i | \(0.569456\pi\) | |||||||
\(360\) | 3.61209 | + | 5.65268i | 0.190374 | + | 0.297922i | ||||
\(361\) | −8.47723 | − | 14.6830i | −0.446170 | − | 0.772789i | ||||
\(362\) | 2.73861 | + | 1.58114i | 0.143938 | + | 0.0831028i | ||||
\(363\) | 7.74597 | − | 17.3205i | 0.406558 | − | 0.909091i | ||||
\(364\) | −2.76139 | − | 0.111466i | −0.144736 | − | 0.00584238i | ||||
\(365\) | −4.95445 | + | 6.06794i | −0.259328 | + | 0.317610i | ||||
\(366\) | −4.85993 | + | 3.51867i | −0.254033 | + | 0.183924i | ||||
\(367\) | 0.184829 | + | 0.320133i | 0.00964798 | + | 0.0167108i | 0.870809 | − | 0.491621i | \(-0.163596\pi\) |
−0.861161 | + | 0.508332i | \(0.830262\pi\) | |||||||
\(368\) | −2.23861 | − | 3.87739i | −0.116696 | − | 0.202123i | ||||
\(369\) | −3.06733 | + | 0.641375i | −0.159679 | + | 0.0333887i | ||||
\(370\) | −4.61230 | − | 3.76593i | −0.239782 | − | 0.195781i | ||||
\(371\) | −13.2180 | − | 0.533554i | −0.686244 | − | 0.0277008i | ||||
\(372\) | 10.4772 | + | 4.68556i | 0.543219 | + | 0.242935i | ||||
\(373\) | −20.1042 | − | 11.6072i | −1.04096 | − | 0.600997i | −0.120853 | − | 0.992670i | \(-0.538563\pi\) |
−0.920104 | + | 0.391673i | \(0.871896\pi\) | |||||||
\(374\) | −7.40852 | − | 12.8319i | −0.383085 | − | 0.663523i | ||||
\(375\) | −17.9814 | − | 7.18818i | −0.928554 | − | 0.371196i | ||||
\(376\) | −9.71584 | − | 5.60944i | −0.501056 | − | 0.289285i | ||||
\(377\) | − | 7.23003i | − | 0.372365i | ||||||
\(378\) | 9.78940 | + | 9.65234i | 0.503513 | + | 0.496463i | ||||
\(379\) | −20.4772 | −1.05184 | −0.525922 | − | 0.850533i | \(-0.676280\pi\) | ||||
−0.525922 | + | 0.850533i | \(0.676280\pi\) | |||||||
\(380\) | −2.99028 | + | 1.13402i | −0.153398 | + | 0.0581739i | ||||
\(381\) | 1.55581 | + | 15.0420i | 0.0797066 | + | 0.770627i | ||||
\(382\) | 14.1099 | − | 8.14637i | 0.721927 | − | 0.416805i | ||||
\(383\) | 15.7158 | + | 9.07354i | 0.803042 | + | 0.463636i | 0.844534 | − | 0.535502i | \(-0.179878\pi\) |
−0.0414919 | + | 0.999139i | \(0.513211\pi\) | |||||||
\(384\) | −0.707107 | + | 1.58114i | −0.0360844 | + | 0.0806872i | ||||
\(385\) | −26.2943 | + | 8.77597i | −1.34008 | + | 0.447265i | ||||
\(386\) | 7.34847i | 0.374027i | ||||||||
\(387\) | −4.24999 | − | 20.3253i | −0.216039 | − | 1.03319i | ||||
\(388\) | 5.99430 | + | 10.3824i | 0.304315 | + | 0.527088i | ||||
\(389\) | 6.36396 | − | 3.67423i | 0.322666 | − | 0.186291i | −0.329914 | − | 0.944011i | \(-0.607020\pi\) |
0.652580 | + | 0.757720i | \(0.273687\pi\) | |||||||
\(390\) | −4.03873 | − | 0.234736i | −0.204509 | − | 0.0118863i | ||||
\(391\) | 14.1582i | 0.716012i | ||||||||
\(392\) | −3.00000 | − | 6.32456i | −0.151523 | − | 0.319438i | ||||
\(393\) | −9.73861 | + | 21.7762i | −0.491248 | + | 1.09846i | ||||
\(394\) | −4.50000 | + | 7.79423i | −0.226707 | + | 0.392668i | ||||
\(395\) | −25.3315 | − | 4.11710i | −1.27456 | − | 0.207154i | ||||
\(396\) | 13.3542 | + | 4.38799i | 0.671076 | + | 0.220505i | ||||
\(397\) | 7.44073 | − | 12.8877i | 0.373439 | − | 0.646816i | −0.616653 | − | 0.787235i | \(-0.711512\pi\) |
0.990092 | + | 0.140419i | \(0.0448451\pi\) | |||||||
\(398\) | 15.5096i | 0.777424i | ||||||||
\(399\) | −5.45947 | + | 3.62639i | −0.273315 | + | 0.181547i | ||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | −0.827520 | − | 0.477769i | −0.0413244 | − | 0.0238586i | 0.479195 | − | 0.877708i | \(-0.340928\pi\) |
−0.520520 | + | 0.853850i | \(0.674262\pi\) | |||||||
\(402\) | 2.54289 | + | 24.5854i | 0.126828 | + | 1.22621i | ||||
\(403\) | −5.99430 | + | 3.46081i | −0.298598 | + | 0.172395i | ||||
\(404\) | 5.65685 | − | 9.79796i | 0.281439 | − | 0.487467i | ||||
\(405\) | 14.0777 | + | 14.3812i | 0.699528 | + | 0.714606i | ||||
\(406\) | 16.2158 | − | 8.50934i | 0.804779 | − | 0.422312i | ||||
\(407\) | −12.4772 | −0.618473 | ||||||||
\(408\) | 4.43649 | − | 3.21209i | 0.219639 | − | 0.159022i | ||||
\(409\) | 13.4317 | − | 7.75478i | 0.664154 | − | 0.383449i | −0.129704 | − | 0.991553i | \(-0.541403\pi\) |
0.793858 | + | 0.608103i | \(0.208069\pi\) | |||||||
\(410\) | 2.30545 | + | 0.374703i | 0.113858 | + | 0.0185052i | ||||
\(411\) | 3.53200 | + | 4.87835i | 0.174221 | + | 0.240631i | ||||
\(412\) | 4.91754 | 0.242270 | ||||||||
\(413\) | −27.9545 | − | 1.12840i | −1.37555 | − | 0.0555251i | ||||
\(414\) | −8.95445 | − | 10.0114i | −0.440087 | − | 0.492033i | ||||
\(415\) | −8.50473 | + | 3.22529i | −0.417481 | + | 0.158323i | ||||
\(416\) | −0.522278 | − | 0.904612i | −0.0256068 | − | 0.0443523i | ||||
\(417\) | −3.59619 | − | 34.7690i | −0.176106 | − | 1.70264i | ||||
\(418\) | −3.35071 | + | 5.80359i | −0.163888 | + | 0.283863i | ||||
\(419\) | 8.85494 | 0.432592 | 0.216296 | − | 0.976328i | \(-0.430602\pi\) | ||||
0.216296 | + | 0.976328i | \(0.430602\pi\) | |||||||
\(420\) | −4.22689 | − | 9.33453i | −0.206251 | − | 0.455478i | ||||
\(421\) | 18.9545 | 0.923783 | 0.461892 | − | 0.886936i | \(-0.347171\pi\) | ||||
0.461892 | + | 0.886936i | \(0.347171\pi\) | |||||||
\(422\) | −12.2386 | + | 21.1979i | −0.595766 | + | 1.03190i | ||||
\(423\) | −31.9748 | − | 10.5064i | −1.55467 | − | 0.510838i | ||||
\(424\) | −2.50000 | − | 4.33013i | −0.121411 | − | 0.210290i | ||||
\(425\) | −5.00735 | + | 14.9975i | −0.242892 | + | 0.727488i | ||||
\(426\) | −10.9441 | − | 4.89433i | −0.530241 | − | 0.237131i | ||||
\(427\) | 8.11562 | − | 4.25871i | 0.392743 | − | 0.206094i | ||||
\(428\) | −5.47723 | −0.264752 | ||||||||
\(429\) | −6.86646 | + | 4.97143i | −0.331516 | + | 0.240023i | ||||
\(430\) | −2.48292 | + | 15.2768i | −0.119737 | + | 0.736711i | ||||
\(431\) | 6.63699 | − | 3.83187i | 0.319693 | − | 0.184575i | −0.331563 | − | 0.943433i | \(-0.607576\pi\) |
0.651256 | + | 0.758858i | \(0.274243\pi\) | |||||||
\(432\) | −1.10557 | + | 5.07718i | −0.0531916 | + | 0.244276i | ||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | −14.8170 | − | 9.37112i | −0.711240 | − | 0.449828i | ||||
\(435\) | 23.9545 | − | 12.0340i | 1.14853 | − | 0.576987i | ||||
\(436\) | 10.2158 | − | 17.6944i | 0.489250 | − | 0.847406i | ||||
\(437\) | 5.54555 | − | 3.20172i | 0.265280 | − | 0.153159i | ||||
\(438\) | −6.03574 | + | 0.624282i | −0.288399 | + | 0.0298294i | ||||
\(439\) | −7.69306 | − | 4.44159i | −0.367170 | − | 0.211986i | 0.305051 | − | 0.952336i | \(-0.401326\pi\) |
−0.672221 | + | 0.740350i | \(0.734660\pi\) | |||||||
\(440\) | −8.11562 | − | 6.62638i | −0.386897 | − | 0.315900i | ||||
\(441\) | −12.6929 | − | 16.7300i | −0.604422 | − | 0.796664i | ||||
\(442\) | 3.30318i | 0.157116i | ||||||||
\(443\) | 7.52277 | − | 13.0298i | 0.357418 | − | 0.619066i | −0.630111 | − | 0.776505i | \(-0.716991\pi\) |
0.987529 | + | 0.157439i | \(0.0503239\pi\) | |||||||
\(444\) | −0.474523 | − | 4.58782i | −0.0225199 | − | 0.217728i | ||||
\(445\) | −10.8535 | − | 1.76402i | −0.514507 | − | 0.0836224i | ||||
\(446\) | 10.9441 | − | 18.9557i | 0.518216 | − | 0.897576i | ||||
\(447\) | −3.87298 | − | 1.73205i | −0.183186 | − | 0.0819232i | ||||
\(448\) | 1.41421 | − | 2.23607i | 0.0668153 | − | 0.105644i | ||||
\(449\) | 25.8773i | 1.22122i | 0.791930 | + | 0.610612i | \(0.209077\pi\) | ||||
−0.791930 | + | 0.610612i | \(0.790923\pi\) | |||||||
\(450\) | −5.94455 | − | 13.7718i | −0.280229 | − | 0.649209i | ||||
\(451\) | 4.23861 | − | 2.44716i | 0.199588 | − | 0.115232i | ||||
\(452\) | −8.73861 | − | 15.1357i | −0.411030 | − | 0.711924i | ||||
\(453\) | 2.03151 | + | 2.80588i | 0.0954485 | + | 0.131832i | ||||
\(454\) | 10.3923i | 0.487735i | ||||||||
\(455\) | 6.05469 | + | 1.23658i | 0.283848 | + | 0.0579717i | ||||
\(456\) | −2.26139 | − | 1.01132i | −0.105899 | − | 0.0473595i | ||||
\(457\) | 9.59425 | + | 5.53924i | 0.448800 | + | 0.259115i | 0.707323 | − | 0.706890i | \(-0.249902\pi\) |
−0.258523 | + | 0.966005i | \(0.583236\pi\) | |||||||
\(458\) | 11.7386 | − | 6.77729i | 0.548509 | − | 0.316682i | ||||
\(459\) | 11.0554 | − | 12.1564i | 0.516024 | − | 0.567411i | ||||
\(460\) | 3.54996 | + | 9.36085i | 0.165518 | + | 0.436452i | ||||
\(461\) | 31.7876 | 1.48050 | 0.740248 | − | 0.672334i | \(-0.234708\pi\) | ||||
0.740248 | + | 0.672334i | \(0.234708\pi\) | |||||||
\(462\) | −19.2316 | − | 9.54931i | −0.894735 | − | 0.444274i | ||||
\(463\) | 22.5741i | 1.04911i | 0.851377 | + | 0.524554i | \(0.175768\pi\) | ||||
−0.851377 | + | 0.524554i | \(0.824232\pi\) | |||||||
\(464\) | 5.99430 | + | 3.46081i | 0.278279 | + | 0.160664i | ||||
\(465\) | −21.4436 | − | 14.0999i | −0.994421 | − | 0.653868i | ||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | −24.2614 | − | 14.0073i | −1.12268 | − | 0.648181i | −0.180599 | − | 0.983557i | \(-0.557803\pi\) |
−0.942085 | + | 0.335375i | \(0.891137\pi\) | |||||||
\(468\) | −2.08911 | − | 2.33570i | −0.0965693 | − | 0.107968i | ||||
\(469\) | 1.52277 | − | 37.7244i | 0.0703152 | − | 1.74195i | ||||
\(470\) | 19.4317 | + | 15.8659i | 0.896316 | + | 0.731839i | ||||
\(471\) | 14.6750 | + | 20.2688i | 0.676187 | + | 0.933938i | ||||
\(472\) | −5.28720 | − | 9.15769i | −0.243363 | − | 0.421517i | ||||
\(473\) | 16.2158 | + | 28.0867i | 0.745605 | + | 1.29143i | ||||
\(474\) | −11.6580 | − | 16.1019i | −0.535471 | − | 0.739584i | ||||
\(475\) | 7.00665 | − | 1.43023i | 0.321487 | − | 0.0656233i | ||||
\(476\) | −7.40852 | + | 3.88766i | −0.339569 | + | 0.178190i | ||||
\(477\) | −10.0000 | − | 11.1803i | −0.457869 | − | 0.511913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.1810 | − | 36.6866i | −0.967784 | − | 1.67625i | −0.701940 | − | 0.712236i | \(-0.747683\pi\) |
−0.265844 | − | 0.964016i | \(-0.585651\pi\) | |||||||
\(480\) | 2.12785 | − | 3.23609i | 0.0971224 | − | 0.147707i | ||||
\(481\) | 2.40890 | + | 1.39078i | 0.109836 | + | 0.0634141i | ||||
\(482\) | − | 21.3094i | − | 0.970615i | ||||||
\(483\) | 11.3522 | + | 17.0905i | 0.516541 | + | 0.777644i | ||||
\(484\) | −10.9545 | −0.497930 | ||||||||
\(485\) | −9.50569 | − | 25.0654i | −0.431631 | − | 1.13816i | ||||
\(486\) | −0.129018 | + | 15.5879i | −0.00585235 | + | 0.707083i | ||||
\(487\) | −14.7526 | + | 8.51743i | −0.668505 | + | 0.385962i | −0.795510 | − | 0.605941i | \(-0.792797\pi\) |
0.127005 | + | 0.991902i | \(0.459464\pi\) | |||||||
\(488\) | 3.00000 | + | 1.73205i | 0.135804 | + | 0.0784063i | ||||
\(489\) | 23.2379 | + | 10.3923i | 1.05085 | + | 0.469956i | ||||
\(490\) | 4.35258 | + | 15.0351i | 0.196629 | + | 0.679218i | ||||
\(491\) | − | 13.8433i | − | 0.624737i | −0.949961 | − | 0.312369i | \(-0.898878\pi\) | ||
0.949961 | − | 0.312369i | \(-0.101122\pi\) | |||||||
\(492\) | 1.06101 | + | 1.46545i | 0.0478341 | + | 0.0660677i | ||||
\(493\) | −10.9441 | − | 18.9557i | −0.492895 | − | 0.853720i | ||||
\(494\) | 1.29380 | − | 0.746976i | 0.0582108 | − | 0.0336080i | ||||
\(495\) | −27.9002 | − | 14.4752i | −1.25402 | − | 0.650611i | ||||
\(496\) | − | 6.62638i | − | 0.297533i | ||||||
\(497\) | 15.4772 | + | 9.78866i | 0.694248 | + | 0.439081i | ||||
\(498\) | −6.43168 | − | 2.87633i | −0.288210 | − | 0.128892i | ||||
\(499\) | −0.954451 | + | 1.65316i | −0.0427271 | + | 0.0740055i | −0.886598 | − | 0.462541i | \(-0.846938\pi\) |
0.843871 | + | 0.536546i | \(0.180271\pi\) | |||||||
\(500\) | 0.449747 | + | 11.1713i | 0.0201133 | + | 0.499595i | ||||
\(501\) | 0.764586 | + | 7.39224i | 0.0341592 | + | 0.330261i | ||||
\(502\) | 4.42747 | − | 7.66860i | 0.197608 | − | 0.342266i | ||||
\(503\) | − | 15.5096i | − | 0.691537i | −0.938320 | − | 0.345769i | \(-0.887618\pi\) | ||
0.938320 | − | 0.345769i | \(-0.112382\pi\) | |||||||
\(504\) | 2.77984 | − | 7.43455i | 0.123824 | − | 0.331161i | ||||
\(505\) | −16.0000 | + | 19.5959i | −0.711991 | + | 0.872007i | ||||
\(506\) | 18.1677 | + | 10.4891i | 0.807655 | + | 0.466300i | ||||
\(507\) | −20.5174 | + | 2.12213i | −0.911208 | + | 0.0942471i | ||||
\(508\) | 7.56114 | − | 4.36543i | 0.335471 | − | 0.193684i | ||||
\(509\) | −12.3583 | + | 21.4051i | −0.547770 | + | 0.948766i | 0.450656 | + | 0.892697i | \(0.351190\pi\) |
−0.998427 | + | 0.0560688i | \(0.982143\pi\) | |||||||
\(510\) | −10.9441 | + | 5.49798i | −0.484611 | + | 0.243454i | ||||
\(511\) | 9.26139 | + | 0.373843i | 0.409700 | + | 0.0165378i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −7.26151 | − | 1.58121i | −0.320604 | − | 0.0698122i | ||||
\(514\) | 9.52277 | − | 5.49798i | 0.420032 | − | 0.242505i | ||||
\(515\) | −10.8535 | − | 1.76402i | −0.478264 | − | 0.0777319i | ||||
\(516\) | −9.71064 | + | 7.03066i | −0.427487 | + | 0.309508i | ||||
\(517\) | 52.5667 | 2.31188 | ||||||||
\(518\) | −0.284162 | + | 7.03967i | −0.0124853 | + | 0.309305i | ||||
\(519\) | 1.78416 | + | 0.797901i | 0.0783160 | + | 0.0350240i | ||||
\(520\) | 0.828222 | + | 2.18393i | 0.0363199 | + | 0.0957715i | ||||
\(521\) | −17.7981 | − | 30.8272i | −0.779748 | − | 1.35056i | −0.932087 | − | 0.362235i | \(-0.882014\pi\) |
0.152339 | − | 0.988328i | \(-0.451320\pi\) | |||||||
\(522\) | 19.7272 | + | 6.48204i | 0.863437 | + | 0.283711i | ||||
\(523\) | −8.45307 | + | 14.6412i | −0.369627 | + | 0.640213i | −0.989507 | − | 0.144484i | \(-0.953848\pi\) |
0.619880 | + | 0.784697i | \(0.287181\pi\) | |||||||
\(524\) | 13.7725 | 0.601654 | ||||||||
\(525\) | 5.98072 | + | 22.1186i | 0.261020 | + | 0.965333i | ||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | −10.4772 | + | 18.1471i | −0.456395 | + | 0.790500i | ||||
\(528\) | −0.834952 | − | 8.07256i | −0.0363366 | − | 0.351313i | ||||
\(529\) | 1.47723 | + | 2.55863i | 0.0642272 | + | 0.111245i | ||||
\(530\) | 3.96447 | + | 10.4539i | 0.172205 | + | 0.454086i | ||||
\(531\) | −21.1488 | − | 23.6451i | −0.917779 | − | 1.02611i | ||||
\(532\) | 3.19808 | + | 2.02265i | 0.138655 | + | 0.0876928i | ||||
\(533\) | −1.09110 | −0.0472607 | ||||||||
\(534\) | −4.99501 | − | 6.89902i | −0.216155 | − | 0.298550i | ||||
\(535\) | 12.0888 | + | 1.96479i | 0.522645 | + | 0.0849452i | ||||
\(536\) | 12.3583 | − | 7.13505i | 0.533796 | − | 0.308187i | ||||
\(537\) | 27.1925 | − | 19.6878i | 1.17344 | − | 0.849593i | ||||
\(538\) | −17.5810 | −0.757973 | ||||||||
\(539\) | 26.9905 | + | 18.6355i | 1.16256 | + | 0.802689i | ||||
\(540\) | 4.26139 | − | 10.8093i | 0.183381 | − | 0.465157i | ||||
\(541\) | −4.26139 | + | 7.38094i | −0.183211 | + | 0.317331i | −0.942972 | − | 0.332871i | \(-0.891983\pi\) |
0.759761 | + | 0.650202i | \(0.225316\pi\) | |||||||
\(542\) | 5.47723 | − | 3.16228i | 0.235267 | − | 0.135831i | ||||
\(543\) | −0.563508 | − | 5.44816i | −0.0241825 | − | 0.233803i | ||||
\(544\) | −2.73861 | − | 1.58114i | −0.117417 | − | 0.0677908i | ||||
\(545\) | −28.8948 | + | 35.3887i | −1.23772 | + | 1.51589i | ||||
\(546\) | 2.64851 | + | 3.98729i | 0.113346 | + | 0.170640i | ||||
\(547\) | − | 3.61845i | − | 0.154714i | −0.997003 | − | 0.0773569i | \(-0.975352\pi\) | ||
0.997003 | − | 0.0773569i | \(-0.0246481\pi\) | |||||||
\(548\) | 1.73861 | − | 3.01137i | 0.0742699 | − | 0.128639i | ||||
\(549\) | 9.87298 | + | 3.24410i | 0.421369 | + | 0.138455i | ||||
\(550\) | 15.5350 | + | 17.5364i | 0.662416 | + | 0.747753i | ||||
\(551\) | −4.94975 | + | 8.57321i | −0.210866 | + | 0.365231i | ||||
\(552\) | −3.16588 | + | 7.07912i | −0.134749 | + | 0.301307i | ||||
\(553\) | 14.1099 | + | 26.8886i | 0.600015 | + | 1.14342i | ||||
\(554\) | − | 9.79796i | − | 0.416275i | ||||||
\(555\) | −0.598419 | + | 10.2960i | −0.0254015 | + | 0.437042i | ||||
\(556\) | −17.4772 | + | 10.0905i | −0.741199 | + | 0.427932i | ||||
\(557\) | −13.9317 | − | 24.1304i | −0.590304 | − | 1.02244i | −0.994191 | − | 0.107628i | \(-0.965674\pi\) |
0.403887 | − | 0.914809i | \(-0.367659\pi\) | |||||||
\(558\) | −4.06871 | − | 19.4583i | −0.172242 | − | 0.823736i | ||||
\(559\) | − | 7.23003i | − | 0.305798i | ||||||
\(560\) | −3.92344 | + | 4.42793i | −0.165796 | + | 0.187114i | ||||
\(561\) | −10.4772 | + | 23.4278i | −0.442349 | + | 0.989122i | ||||
\(562\) | −1.56683 | − | 0.904612i | −0.0660929 | − | 0.0381588i | ||||
\(563\) | 9.00000 | − | 5.19615i | 0.379305 | − | 0.218992i | −0.298211 | − | 0.954500i | \(-0.596390\pi\) |
0.677516 | + | 0.735508i | \(0.263057\pi\) | |||||||
\(564\) | 1.99917 | + | 19.3286i | 0.0841803 | + | 0.813879i | ||||
\(565\) | 13.8576 | + | 36.5409i | 0.582993 | + | 1.53729i | ||||
\(566\) | −9.22460 | −0.387739 | ||||||||
\(567\) | 3.59805 | − | 23.5384i | 0.151104 | − | 0.988518i | ||||
\(568\) | 6.92163i | 0.290425i | ||||||||
\(569\) | −6.54879 | − | 3.78095i | −0.274540 | − | 0.158505i | 0.356409 | − | 0.934330i | \(-0.384001\pi\) |
−0.630949 | + | 0.775824i | \(0.717334\pi\) | |||||||
\(570\) | 4.62834 | + | 3.04330i | 0.193860 | + | 0.127470i | ||||
\(571\) | −7.47723 | − | 12.9509i | −0.312912 | − | 0.541980i | 0.666079 | − | 0.745881i | \(-0.267971\pi\) |
−0.978991 | + | 0.203901i | \(0.934638\pi\) | |||||||
\(572\) | 4.23861 | + | 2.44716i | 0.177225 | + | 0.102321i | ||||
\(573\) | −25.7611 | − | 11.5207i | −1.07618 | − | 0.481284i | ||||
\(574\) | −1.28416 | − | 2.44716i | −0.0535999 | − | 0.102143i | ||||
\(575\) | −4.47723 | − | 21.9338i | −0.186713 | − | 0.914704i | ||||
\(576\) | 2.93649 | − | 0.614017i | 0.122354 | − | 0.0255840i | ||||
\(577\) | −0.337449 | − | 0.584480i | −0.0140482 | − | 0.0243322i | 0.858916 | − | 0.512117i | \(-0.171138\pi\) |
−0.872964 | + | 0.487785i | \(0.837805\pi\) | |||||||
\(578\) | −3.50000 | − | 6.06218i | −0.145581 | − | 0.252153i | ||||
\(579\) | 10.3095 | − | 7.46423i | 0.428447 | − | 0.310203i | ||||
\(580\) | −11.9886 | − | 9.78866i | −0.497800 | − | 0.406452i | ||||
\(581\) | 9.09576 | + | 5.75267i | 0.377356 | + | 0.238661i | ||||
\(582\) | 8.47723 | − | 18.9557i | 0.351392 | − | 0.785737i | ||||
\(583\) | 20.2891 | + | 11.7139i | 0.840287 | + | 0.485140i | ||||
\(584\) | 1.75166 | + | 3.03397i | 0.0724843 | + | 0.125547i | ||||
\(585\) | 3.77303 | + | 5.90454i | 0.155996 | + | 0.244123i | ||||
\(586\) | 6.97723 | + | 4.02830i | 0.288227 | + | 0.166408i | ||||
\(587\) | 21.0864i | 0.870330i | 0.900351 | + | 0.435165i | \(0.143310\pi\) | ||||
−0.900351 | + | 0.435165i | \(0.856690\pi\) | |||||||
\(588\) | −5.82572 | + | 10.6330i | −0.240249 | + | 0.438498i | ||||
\(589\) | 9.47723 | 0.390502 | ||||||||
\(590\) | 8.38437 | + | 22.1086i | 0.345179 | + | 0.910198i | ||||
\(591\) | 15.5057 | − | 1.60377i | 0.637821 | − | 0.0659704i | ||||
\(592\) | −2.30615 | + | 1.33146i | −0.0947821 | + | 0.0547225i | ||||
\(593\) | −1.43168 | − | 0.826579i | −0.0587919 | − | 0.0339435i | 0.470316 | − | 0.882498i | \(-0.344140\pi\) |
−0.529108 | + | 0.848555i | \(0.677473\pi\) | |||||||
\(594\) | −7.40852 | − | 23.1923i | −0.303975 | − | 0.951593i | ||||
\(595\) | 17.7460 | − | 5.92289i | 0.727514 | − | 0.242815i | ||||
\(596\) | 2.44949i | 0.100335i | ||||||||
\(597\) | 21.7590 | − | 15.7539i | 0.890537 | − | 0.644764i | ||||
\(598\) | −2.33836 | − | 4.05015i | −0.0956225 | − | 0.165623i | ||||
\(599\) | −20.4739 | + | 11.8206i | −0.836540 | + | 0.482977i | −0.856087 | − | 0.516832i | \(-0.827111\pi\) |
0.0195464 | + | 0.999809i | \(0.493778\pi\) | |||||||
\(600\) | −5.85723 | + | 6.37909i | −0.239120 | + | 0.260425i | ||||
\(601\) | 4.06775i | 0.165927i | 0.996553 | + | 0.0829635i | \(0.0264385\pi\) | ||||
−0.996553 | + | 0.0829635i | \(0.973562\pi\) | |||||||
\(602\) | 16.2158 | − | 8.50934i | 0.660908 | − | 0.346815i | ||||
\(603\) | 31.9089 | − | 28.5402i | 1.29943 | − | 1.16225i | ||||
\(604\) | 1.00000 | − | 1.73205i | 0.0406894 | − | 0.0704761i | ||||
\(605\) | 24.1776 | + | 3.92957i | 0.982961 | + | 0.159760i | ||||
\(606\) | −19.4919 | + | 2.01607i | −0.791806 | + | 0.0818972i | ||||
\(607\) | 6.14692 | − | 10.6468i | 0.249496 | − | 0.432140i | −0.713890 | − | 0.700258i | \(-0.753068\pi\) |
0.963386 | + | 0.268118i | \(0.0864017\pi\) | |||||||
\(608\) | 1.43023i | 0.0580034i | ||||||||
\(609\) | −28.4094 | − | 14.1065i | −1.15121 | − | 0.571624i | ||||
\(610\) | −6.00000 | − | 4.89898i | −0.242933 | − | 0.198354i | ||||
\(611\) | −10.1487 | − | 5.85938i | −0.410574 | − | 0.237045i | ||||
\(612\) | −9.01276 | − | 2.96145i | −0.364319 | − | 0.119709i | ||||
\(613\) | 5.07016 | − | 2.92726i | 0.204782 | − | 0.118231i | −0.394102 | − | 0.919067i | \(-0.628944\pi\) |
0.598884 | + | 0.800836i | \(0.295611\pi\) | |||||||
\(614\) | −5.99430 | + | 10.3824i | −0.241910 | + | 0.419001i | ||||
\(615\) | −1.81608 | − | 3.61501i | −0.0732314 | − | 0.145771i | ||||
\(616\) | −0.500000 | + | 12.3867i | −0.0201456 | + | 0.499076i | ||||
\(617\) | 14.5228 | 0.584665 | 0.292332 | − | 0.956317i | \(-0.405569\pi\) | ||||
0.292332 | + | 0.956317i | \(0.405569\pi\) | |||||||
\(618\) | −4.99501 | − | 6.89902i | −0.200929 | − | 0.277519i | ||||
\(619\) | 26.1475 | − | 15.0963i | 1.05096 | − | 0.606771i | 0.128040 | − | 0.991769i | \(-0.459131\pi\) |
0.922917 | + | 0.384998i | \(0.125798\pi\) | |||||||
\(620\) | −2.37701 | + | 14.6251i | −0.0954631 | + | 0.587359i | ||||
\(621\) | −4.94987 | + | 22.7317i | −0.198632 | + | 0.912190i | ||||
\(622\) | −17.5810 | −0.704936 | ||||||||
\(623\) | 6.04555 | + | 11.5207i | 0.242210 | + | 0.461567i | ||||
\(624\) | −0.738613 | + | 1.65159i | −0.0295682 | + | 0.0661165i | ||||
\(625\) | 3.01472 | − | 24.8176i | 0.120589 | − | 0.992703i | ||||
\(626\) | 11.6190 | + | 20.1246i | 0.464387 | + | 0.804341i | ||||
\(627\) | 11.5456 | − | 1.19417i | 0.461086 | − | 0.0476906i | ||||
\(628\) | 7.22369 | − | 12.5118i | 0.288257 | − | 0.499275i | ||||
\(629\) | 8.42087 | 0.335762 | ||||||||
\(630\) | −8.80233 | + | 15.4117i | −0.350693 | + | 0.614015i | ||||
\(631\) | 3.47723 | 0.138426 | 0.0692131 | − | 0.997602i | \(-0.477951\pi\) | ||||
0.0692131 | + | 0.997602i | \(0.477951\pi\) | |||||||
\(632\) | −5.73861 | + | 9.93957i | −0.228270 | + | 0.395375i | ||||
\(633\) | 42.1708 | − | 4.36177i | 1.67614 | − | 0.173365i | ||||
\(634\) | 4.95445 | + | 8.58136i | 0.196766 | + | 0.340809i | ||||
\(635\) | −18.2542 | + | 6.92263i | −0.724396 | + | 0.274716i | ||||
\(636\) | −3.53553 | + | 7.90569i | −0.140193 | + | 0.313481i | ||||
\(637\) | −3.13367 | − | 6.60635i | −0.124160 | − | 0.261753i | ||||
\(638\) | −32.4317 | −1.28398 | ||||||||
\(639\) | 4.24999 | + | 20.3253i | 0.168127 | + | 0.804056i | ||||
\(640\) | −2.20711 | − | 0.358719i | −0.0872436 | − | 0.0141796i | ||||
\(641\) | 13.9251 | − | 8.03966i | 0.550008 | − | 0.317547i | −0.199117 | − | 0.979976i | \(-0.563807\pi\) |
0.749125 | + | 0.662428i | \(0.230474\pi\) | |||||||
\(642\) | 5.56351 | + | 7.68423i | 0.219574 | + | 0.303272i | ||||
\(643\) | −26.0663 | −1.02796 | −0.513978 | − | 0.857803i | \(-0.671829\pi\) | ||||
−0.513978 | + | 0.857803i | \(0.671829\pi\) | |||||||
\(644\) | 6.33175 | − | 10.0114i | 0.249506 | − | 0.394504i | ||||
\(645\) | 23.9545 | − | 12.0340i | 0.943206 | − | 0.473839i | ||||
\(646\) | 2.26139 | − | 3.91684i | 0.0889731 | − | 0.154106i | ||||
\(647\) | 17.6703 | − | 10.2019i | 0.694691 | − | 0.401080i | −0.110676 | − | 0.993857i | \(-0.535302\pi\) |
0.805367 | + | 0.592777i | \(0.201968\pi\) | |||||||
\(648\) | 8.24597 | − | 3.60611i | 0.323932 | − | 0.141661i | ||||
\(649\) | 42.9089 | + | 24.7735i | 1.68432 | + | 0.972444i | ||||
\(650\) | −1.04456 | − | 5.11726i | −0.0409709 | − | 0.200715i | ||||
\(651\) | 1.90332 | + | 30.3062i | 0.0745969 | + | 1.18779i | ||||
\(652\) | − | 14.6969i | − | 0.575577i | ||||||
\(653\) | −19.9317 | + | 34.5227i | −0.779987 | + | 1.35098i | 0.151962 | + | 0.988386i | \(0.451441\pi\) |
−0.931949 | + | 0.362590i | \(0.881892\pi\) | |||||||
\(654\) | −35.2009 | + | 3.64086i | −1.37646 | + | 0.142369i | ||||
\(655\) | −30.3973 | − | 4.94046i | −1.18772 | − | 0.193040i | ||||
\(656\) | 0.522278 | − | 0.904612i | 0.0203915 | − | 0.0353192i | ||||
\(657\) | 7.00665 | + | 7.83368i | 0.273356 | + | 0.305621i | ||||
\(658\) | 1.19718 | − | 29.6582i | 0.0466708 | − | 1.15620i | ||||
\(659\) | 34.2929i | 1.33586i | 0.744224 | + | 0.667930i | \(0.232819\pi\) | ||||
−0.744224 | + | 0.667930i | \(0.767181\pi\) | |||||||
\(660\) | −1.05296 | + | 18.1165i | −0.0409862 | + | 0.705184i | ||||
\(661\) | 0.522774 | − | 0.301824i | 0.0203336 | − | 0.0117396i | −0.489799 | − | 0.871836i | \(-0.662930\pi\) |
0.510132 | + | 0.860096i | \(0.329596\pi\) | |||||||
\(662\) | −10.7158 | − | 18.5604i | −0.416483 | − | 0.721370i | ||||
\(663\) | 4.63416 | − | 3.35521i | 0.179976 | − | 0.130306i | ||||
\(664\) | 4.06775i | 0.157859i | ||||||||
\(665\) | −6.33295 | − | 5.61141i | −0.245581 | − | 0.217601i | ||||
\(666\) | −5.95445 | + | 5.32582i | −0.230730 | + | 0.206371i | ||||
\(667\) | 26.8378 | + | 15.4948i | 1.03917 | + | 0.599963i | ||||
\(668\) | 3.71584 | − | 2.14534i | 0.143770 | − | 0.0830057i | ||||
\(669\) | −37.7101 | + | 3.90039i | −1.45796 | + | 0.150798i | ||||
\(670\) | −29.8355 | + | 11.3147i | −1.15265 | + | 0.437124i | ||||
\(671\) | −16.2312 | −0.626600 | ||||||||
\(672\) | −4.57357 | + | 0.287233i | −0.176429 | + | 0.0110803i | ||||
\(673\) | 14.1585i | 0.545771i | 0.962047 | + | 0.272885i | \(0.0879780\pi\) | ||||
−0.962047 | + | 0.272885i | \(0.912022\pi\) | |||||||
\(674\) | 14.8492 | + | 8.57321i | 0.571971 | + | 0.330228i | ||||
\(675\) | −13.2828 | + | 22.3286i | −0.511257 | + | 0.859428i | ||||
\(676\) | 5.95445 | + | 10.3134i | 0.229017 | + | 0.396670i | ||||
\(677\) | −28.5000 | − | 16.4545i | −1.09534 | − | 0.632397i | −0.160350 | − | 0.987060i | \(-0.551262\pi\) |
−0.934994 | + | 0.354663i | \(0.884596\pi\) | |||||||
\(678\) | −12.3583 | + | 27.6339i | −0.474616 | + | 1.06127i | ||||
\(679\) | −16.9545 | + | 26.8073i | −0.650652 | + | 1.02877i | ||||
\(680\) | 5.47723 | + | 4.47214i | 0.210042 | + | 0.171499i | ||||
\(681\) | 14.5798 | − | 10.5560i | 0.558699 | − | 0.404507i | ||||
\(682\) | 15.5241 | + | 26.8886i | 0.594450 | + | 1.02962i | ||||
\(683\) | 9.47723 | + | 16.4150i | 0.362636 | + | 0.628104i | 0.988394 | − | 0.151913i | \(-0.0485435\pi\) |
−0.625758 | + | 0.780017i | \(0.715210\pi\) | |||||||
\(684\) | 0.878183 | + | 4.19985i | 0.0335782 | + | 0.160585i | ||||
\(685\) | −4.91754 | + | 6.02273i | −0.187890 | + | 0.230117i | ||||
\(686\) | 11.1289 | − | 14.8036i | 0.424903 | − | 0.565206i | ||||
\(687\) | −21.4317 | − | 9.58454i | −0.817669 | − | 0.365673i | ||||
\(688\) | 5.99430 | + | 3.46081i | 0.228531 | + | 0.131942i | ||||
\(689\) | −2.61139 | − | 4.52306i | −0.0994861 | − | 0.172315i | ||||
\(690\) | 9.52684 | − | 14.4887i | 0.362681 | − | 0.551575i | ||||
\(691\) | 3.00000 | + | 1.73205i | 0.114125 | + | 0.0658903i | 0.555976 | − | 0.831198i | \(-0.312345\pi\) |
−0.441851 | + | 0.897089i | \(0.645678\pi\) | |||||||
\(692\) | − | 1.12840i | − | 0.0428954i | ||||||
\(693\) | 6.13742 | + | 36.6805i | 0.233141 | + | 1.39338i | ||||
\(694\) | −17.4772 | −0.663426 | ||||||||
\(695\) | 42.1938 | − | 16.0013i | 1.60050 | − | 0.606966i | ||||
\(696\) | −1.23341 | − | 11.9250i | −0.0467524 | − | 0.452016i | ||||
\(697\) | −2.86064 | + | 1.65159i | −0.108354 | + | 0.0625584i | ||||
\(698\) | −10.1703 | − | 5.87182i | −0.384951 | − | 0.222252i | ||||
\(699\) | 2.82843 | − | 6.32456i | 0.106981 | − | 0.239217i | ||||
\(700\) | 10.2478 | − | 8.36551i | 0.387332 | − | 0.316187i | ||||
\(701\) | − | 51.7546i | − | 1.95474i | −0.211531 | − | 0.977371i | \(-0.567845\pi\) | ||
0.211531 | − | 0.977371i | \(-0.432155\pi\) | |||||||
\(702\) | −1.15483 | + | 5.30340i | −0.0435861 | + | 0.200164i | ||||
\(703\) | −1.90428 | − | 3.29832i | −0.0718214 | − | 0.124398i | ||||
\(704\) | −4.05781 | + | 2.34278i | −0.152935 | + | 0.0882968i | ||||
\(705\) | 2.52115 | − | 43.3773i | 0.0949519 | − | 1.63369i | ||||
\(706\) | 0.603648i | 0.0227186i | ||||||||
\(707\) | 29.9089 | + | 1.20730i | 1.12484 | + | 0.0454050i | ||||
\(708\) | −7.47723 | + | 16.7196i | −0.281011 | + | 0.628360i | ||||
\(709\) | 11.2158 | − | 19.4264i | 0.421220 | − | 0.729574i | −0.574839 | − | 0.818266i | \(-0.694935\pi\) |
0.996059 | + | 0.0886924i | \(0.0282688\pi\) | |||||||
\(710\) | 2.48292 | − | 15.2768i | 0.0931824 | − | 0.573327i | ||||
\(711\) | −10.7483 | + | 32.7111i | −0.403094 | + | 1.22676i | ||||
\(712\) | −2.45877 | + | 4.25871i | −0.0921463 | + | 0.159602i | ||||
\(713\) | − | 29.6678i | − | 1.11107i | ||||||
\(714\) | 12.9794 | + | 6.44482i | 0.485741 | + | 0.241191i | ||||
\(715\) | −8.47723 | − | 6.92163i | −0.317030 | − | 0.258854i | ||||
\(716\) | −16.7857 | − | 9.69125i | −0.627312 | − | 0.362179i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.86729 | + | 5.69688i | −0.368244 | + | 0.212606i | ||||
\(719\) | 0.401865 | − | 0.696051i | 0.0149870 | − | 0.0259583i | −0.858435 | − | 0.512923i | \(-0.828563\pi\) |
0.873422 | + | 0.486965i | \(0.161896\pi\) | |||||||
\(720\) | −6.70141 | + | 0.301824i | −0.249747 | + | 0.0112483i | ||||
\(721\) | 6.04555 | + | 11.5207i | 0.225148 | + | 0.429054i | ||||
\(722\) | 16.9545 | 0.630979 | ||||||||
\(723\) | −29.8958 | + | 21.6451i | −1.11184 | + | 0.804988i | ||||
\(724\) | −2.73861 | + | 1.58114i | −0.101780 | + | 0.0587626i | ||||
\(725\) | 22.9488 | + | 25.9052i | 0.852295 | + | 0.962093i | ||||
\(726\) | 11.1270 | + | 15.3685i | 0.412962 | + | 0.570377i | ||||
\(727\) | −15.1223 | −0.560854 | −0.280427 | − | 0.959875i | \(-0.590476\pi\) | ||||
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(728\) | 1.47723 | − | 2.33570i | 0.0547496 | − | 0.0865668i | ||||
\(729\) | 22.0000 | − | 15.6525i | 0.814815 | − | 0.579721i | ||||
\(730\) | −2.77776 | − | 7.32465i | −0.102810 | − | 0.271097i | ||||
\(731\) | −10.9441 | − | 18.9557i | −0.404780 | − | 0.701100i | ||||
\(732\) | −0.617292 | − | 5.96816i | −0.0228158 | − | 0.220590i | ||||
\(733\) | 1.19718 | − | 2.07357i | 0.0442187 | − | 0.0765891i | −0.843069 | − | 0.537805i | \(-0.819253\pi\) |
0.887288 | + | 0.461216i | \(0.152587\pi\) | |||||||
\(734\) | −0.369657 | −0.0136443 | ||||||||
\(735\) | 16.6723 | − | 21.3784i | 0.614966 | − | 0.788554i | ||||
\(736\) | 4.47723 | 0.165033 | ||||||||
\(737\) | −33.4317 | + | 57.9054i | −1.23147 | + | 2.13297i | ||||
\(738\) | 0.978218 | − | 2.97707i | 0.0360087 | − | 0.109588i | ||||
\(739\) | −3.23861 | − | 5.60944i | −0.119134 | − | 0.206347i | 0.800291 | − | 0.599612i | \(-0.204679\pi\) |
−0.919425 | + | 0.393266i | \(0.871345\pi\) | |||||||
\(740\) | 5.56754 | − | 2.11140i | 0.204667 | − | 0.0776168i | ||||
\(741\) | −2.36215 | − | 1.05638i | −0.0867756 | − | 0.0388072i | ||||
\(742\) | 7.07107 | − | 11.1803i | 0.259587 | − | 0.410443i | ||||
\(743\) | 13.4317 | 0.492760 | 0.246380 | − | 0.969173i | \(-0.420759\pi\) | ||||
0.246380 | + | 0.969173i | \(0.420759\pi\) | |||||||
\(744\) | −9.29642 | + | 6.73076i | −0.340823 | + | 0.246762i | ||||
\(745\) | 0.878680 | − | 5.40629i | 0.0321923 | − | 0.198071i | ||||
\(746\) | 20.1042 | − | 11.6072i | 0.736068 | − | 0.424969i | ||||
\(747\) | 2.49767 | + | 11.9449i | 0.0913848 | + | 0.437041i | ||||
\(748\) | 14.8170 | 0.541764 | ||||||||
\(749\) | −6.73362 | − | 12.8319i | −0.246041 | − | 0.468868i | ||||
\(750\) | 15.2158 | − | 11.9782i | 0.555604 | − | 0.437384i | ||||
\(751\) | 16.0000 | − | 27.7128i | 0.583848 | − | 1.01125i | −0.411170 | − | 0.911559i | \(-0.634880\pi\) |
0.995018 | − | 0.0996961i | \(-0.0317870\pi\) | |||||||
\(752\) | 9.71584 | − | 5.60944i | 0.354300 | − | 0.204555i | ||||
\(753\) | −15.2558 | + | 1.57792i | −0.555953 | + | 0.0575027i | ||||
\(754\) | 6.26139 | + | 3.61501i | 0.228026 | + | 0.131651i | ||||
\(755\) | −2.82843 | + | 3.46410i | −0.102937 | + | 0.126072i | ||||
\(756\) | −13.2539 | + | 3.65170i | −0.482039 | + | 0.132811i | ||||
\(757\) | 48.1361i | 1.74954i | 0.484541 | + | 0.874768i | \(0.338986\pi\) | ||||
−0.484541 | + | 0.874768i | \(0.661014\pi\) | |||||||
\(758\) | 10.2386 | − | 17.7338i | 0.371883 | − | 0.644121i | ||||
\(759\) | −3.73827 | − | 36.1427i | −0.135691 | − | 1.31190i | ||||
\(760\) | 0.513050 | − | 3.15666i | 0.0186103 | − | 0.114504i | ||||
\(761\) | −0.891935 | + | 1.54488i | −0.0323326 | + | 0.0560018i | −0.881739 | − | 0.471738i | \(-0.843627\pi\) |
0.849406 | + | 0.527739i | \(0.176960\pi\) | |||||||
\(762\) | −13.8047 | − | 6.17364i | −0.500091 | − | 0.223648i | ||||
\(763\) | 54.0131 | + | 2.18028i | 1.95541 | + | 0.0789315i | ||||
\(764\) | 16.2927i | 0.589451i | ||||||||
\(765\) | 18.8298 | + | 9.76928i | 0.680793 | + | 0.353209i | ||||
\(766\) | −15.7158 | + | 9.07354i | −0.567836 | + | 0.327840i | ||||
\(767\) | −5.52277 | − | 9.56573i | −0.199416 | − | 0.345398i | ||||
\(768\) | −1.01575 | − | 1.40294i | −0.0366528 | − | 0.0506243i | ||||
\(769\) | 16.1921i | 0.583902i | 0.956433 | + | 0.291951i | \(0.0943045\pi\) | ||||
−0.956433 | + | 0.291951i | \(0.905696\pi\) | |||||||
\(770\) | 5.54692 | − | 27.1595i | 0.199897 | − | 0.978760i | ||||
\(771\) | −17.3861 | − | 7.77531i | −0.626146 | − | 0.280021i | ||||
\(772\) | −6.36396 | − | 3.67423i | −0.229044 | − | 0.132239i | ||||
\(773\) | −14.0228 | + | 8.09605i | −0.504364 | + | 0.291195i | −0.730514 | − | 0.682898i | \(-0.760719\pi\) |
0.226150 | + | 0.974093i | \(0.427386\pi\) | |||||||
\(774\) | 19.7272 | + | 6.48204i | 0.709080 | + | 0.232992i | ||||
\(775\) | 10.4926 | − | 31.4265i | 0.376907 | − | 1.12887i | ||||
\(776\) | −11.9886 | −0.430366 | ||||||||
\(777\) | 10.1649 | − | 6.75190i | 0.364663 | − | 0.242223i | ||||
\(778\) | 7.34847i | 0.263455i | ||||||||
\(779\) | 1.29380 | + | 0.746976i | 0.0463552 | + | 0.0267632i | ||||
\(780\) | 2.22265 | − | 3.38028i | 0.0795838 | − | 0.121033i | ||||
\(781\) | −16.2158 | − | 28.0867i | −0.580248 | − | 1.00502i | ||||
\(782\) | −12.2614 | − | 7.07912i | −0.438466 | − | 0.253149i | ||||
\(783\) | −10.9441 | − | 34.2603i | −0.391108 | − | 1.22436i | ||||
\(784\) | 6.97723 | + | 0.564201i | 0.249187 | + | 0.0201501i | ||||
\(785\) | −20.4317 | + | 25.0236i | −0.729238 | + | 0.893130i | ||||
\(786\) | −13.9894 | − | 19.3220i | −0.498987 | − | 0.689192i | ||||
\(787\) | −25.0862 | − | 43.4506i | −0.894226 | − | 1.54884i | −0.834760 | − | 0.550615i | \(-0.814393\pi\) |
−0.0594664 | − | 0.998230i | \(-0.518940\pi\) | |||||||
\(788\) | −4.50000 | − | 7.79423i | −0.160306 | − | 0.277658i | ||||
\(789\) | 2.03151 | + | 2.80588i | 0.0723235 | + | 0.0998921i | ||||
\(790\) | 16.2312 | − | 19.8791i | 0.577482 | − | 0.707268i | ||||
\(791\) | 24.7165 | − | 39.0803i | 0.878819 | − | 1.38953i | ||||
\(792\) | −10.4772 | + | 9.37112i | −0.372292 | + | 0.332988i | ||||
\(793\) | 3.13367 | + | 1.80922i | 0.111280 | + | 0.0642474i | ||||
\(794\) | 7.44073 | + | 12.8877i | 0.264061 | + | 0.457368i | ||||
\(795\) | 10.6392 | − | 16.1804i | 0.377335 | − | 0.573861i | ||||
\(796\) | −13.4317 | − | 7.75478i | −0.476073 | − | 0.274861i | ||||
\(797\) | − | 54.2183i | − | 1.92051i | −0.279121 | − | 0.960256i | \(-0.590043\pi\) | ||
0.279121 | − | 0.960256i | \(-0.409957\pi\) | |||||||
\(798\) | −0.410809 | − | 6.54124i | −0.0145425 | − | 0.231557i | ||||
\(799\) | −35.4772 | −1.25509 | ||||||||
\(800\) | 4.74264 | + | 1.58346i | 0.167678 | + | 0.0559839i | ||||
\(801\) | −4.60523 | + | 14.0154i | −0.162718 | + | 0.495210i | ||||
\(802\) | 0.827520 | − | 0.477769i | 0.0292207 | − | 0.0168706i | ||||
\(803\) | −14.2158 | − | 8.20752i | −0.501666 | − | 0.289637i | ||||
\(804\) | −22.5630 | − | 10.0905i | −0.795736 | − | 0.355864i | ||||
\(805\) | −17.5661 | + | 19.8249i | −0.619125 | + | 0.698735i | ||||
\(806\) | − | 6.92163i | − | 0.243804i | ||||||
\(807\) | 17.8580 | + | 24.6652i | 0.628631 | + | 0.868256i | ||||
\(808\) | 5.65685 | + | 9.79796i | 0.199007 | + | 0.344691i | ||||
\(809\) | 7.65776 | − | 4.42121i | 0.269233 | − | 0.155441i | −0.359306 | − | 0.933220i | \(-0.616987\pi\) |
0.628539 | + | 0.777778i | \(0.283653\pi\) | |||||||
\(810\) | −19.4933 | + | 5.00108i | −0.684925 | + | 0.175720i | ||||
\(811\) | 38.3280i | 1.34588i | 0.739697 | + | 0.672940i | \(0.234969\pi\) | ||||
−0.739697 | + | 0.672940i | \(0.765031\pi\) | |||||||
\(812\) | −0.738613 | + | 18.2980i | −0.0259202 | + | 0.642134i | ||||
\(813\) | −10.0000 | − | 4.47214i | −0.350715 | − | 0.156845i | ||||
\(814\) | 6.23861 | − | 10.8056i | 0.218663 | − | 0.378736i | ||||
\(815\) | −5.27208 | + | 32.4377i | −0.184673 | + | 1.13624i | ||||
\(816\) | 0.563508 | + | 5.44816i | 0.0197267 | + | 0.190724i | ||||
\(817\) | −4.94975 | + | 8.57321i | −0.173170 | + | 0.299939i | ||||
\(818\) | 15.5096i | 0.542279i | ||||||||
\(819\) | 2.90370 | − | 7.76580i | 0.101464 | − | 0.271359i | ||||
\(820\) | −1.47723 | + | 1.80922i | −0.0515870 | + | 0.0631809i | ||||
\(821\) | 10.1403 | + | 5.85452i | 0.353900 | + | 0.204324i | 0.666401 | − | 0.745593i | \(-0.267834\pi\) |
−0.312502 | + | 0.949917i | \(0.601167\pi\) | |||||||
\(822\) | −5.99077 | + | 0.619631i | −0.208952 | + | 0.0216121i | ||||
\(823\) | −2.76401 | + | 1.59580i | −0.0963474 | + | 0.0556262i | −0.547400 | − | 0.836871i | \(-0.684382\pi\) |
0.451052 | + | 0.892498i | \(0.351049\pi\) | |||||||
\(824\) | −2.45877 | + | 4.25871i | −0.0856553 | + | 0.148359i | ||||
\(825\) | 8.82273 | − | 39.6074i | 0.307168 | − | 1.37895i | ||||
\(826\) | 14.9545 | − | 23.6451i | 0.520332 | − | 0.822717i | ||||
\(827\) | −3.90890 | −0.135926 | −0.0679629 | − | 0.997688i | \(-0.521650\pi\) | ||||
−0.0679629 | + | 0.997688i | \(0.521650\pi\) | |||||||
\(828\) | 13.1473 | − | 2.74909i | 0.456901 | − | 0.0955375i | ||||
\(829\) | −43.6931 | + | 25.2262i | −1.51752 | + | 0.876142i | −0.517735 | + | 0.855541i | \(0.673225\pi\) |
−0.999788 | + | 0.0206012i | \(0.993442\pi\) | |||||||
\(830\) | 1.45918 | − | 8.97796i | 0.0506489 | − | 0.311629i | ||||
\(831\) | −13.7460 | + | 9.95231i | −0.476842 | + | 0.345242i | ||||
\(832\) | 1.04456 | 0.0362135 | ||||||||
\(833\) | −18.2158 | − | 12.5771i | −0.631141 | − | 0.435770i | ||||
\(834\) | 31.9089 | + | 14.2701i | 1.10491 | + | 0.494133i | ||||
\(835\) | −8.97083 | + | 3.40205i | −0.310448 | + | 0.117733i | ||||
\(836\) | −3.35071 | − | 5.80359i | −0.115887 | − | 0.200721i | ||||
\(837\) | −23.1661 | + | 25.4730i | −0.800737 | + | 0.880476i | ||||
\(838\) | −4.42747 | + | 7.66860i | −0.152944 | + | 0.264907i | ||||
\(839\) | −40.1440 | −1.38593 | −0.692963 | − | 0.720973i | \(-0.743695\pi\) | ||||
−0.692963 | + | 0.720973i | \(0.743695\pi\) | |||||||
\(840\) | 10.1974 | + | 1.00667i | 0.351843 | + | 0.0347335i | ||||
\(841\) | −18.9089 | −0.652031 | ||||||||
\(842\) | −9.47723 | + | 16.4150i | −0.326607 | + | 0.565700i | ||||
\(843\) | 0.322398 | + | 3.11704i | 0.0111040 | + | 0.107357i | ||||
\(844\) | −12.2386 | − | 21.1979i | −0.421270 | − | 0.729662i | ||||
\(845\) | −9.44249 | − | 24.8988i | −0.324831 | − | 0.856544i | ||||
\(846\) | 25.0862 | − | 22.4378i | 0.862481 | − | 0.771426i | ||||
\(847\) | −13.4672 | − | 25.6639i | −0.462740 | − | 0.881821i | ||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | 9.36991 | + | 12.9416i | 0.321575 | + | 0.444154i | ||||
\(850\) | −10.4846 | − | 11.8353i | −0.359618 | − | 0.405946i | ||||
\(851\) | −10.3251 | + | 5.96123i | −0.353942 | + | 0.204348i | ||||
\(852\) | 9.71064 | − | 7.03066i | 0.332681 | − | 0.240867i | ||||
\(853\) | 31.2891 | 1.07132 | 0.535659 | − | 0.844434i | \(-0.320063\pi\) | ||||
0.535659 | + | 0.844434i | \(0.320063\pi\) | |||||||
\(854\) | −0.369657 | + | 9.15769i | −0.0126494 | + | 0.313370i | ||||
\(855\) | −0.431677 | − | 9.58454i | −0.0147630 | − | 0.327784i | ||||
\(856\) | 2.73861 | − | 4.74342i | 0.0936039 | − | 0.162127i | ||||
\(857\) | 13.0455 | − | 7.53185i | 0.445627 | − | 0.257283i | −0.260354 | − | 0.965513i | \(-0.583839\pi\) |
0.705982 | + | 0.708230i | \(0.250506\pi\) | |||||||
\(858\) | −0.872155 | − | 8.43224i | −0.0297749 | − | 0.287872i | ||||
\(859\) | −26.4772 | − | 15.2866i | −0.903391 | − | 0.521573i | −0.0250924 | − | 0.999685i | \(-0.507988\pi\) |
−0.878299 | + | 0.478112i | \(0.841321\pi\) | |||||||
\(860\) | −11.9886 | − | 9.78866i | −0.408808 | − | 0.333790i | ||||
\(861\) | −2.12884 | + | 4.28732i | −0.0725506 | + | 0.146111i | ||||
\(862\) | 7.66374i | 0.261028i | ||||||||
\(863\) | 13.2386 | − | 22.9299i | 0.450648 | − | 0.780545i | −0.547779 | − | 0.836623i | \(-0.684526\pi\) |
0.998426 | + | 0.0560787i | \(0.0178598\pi\) | |||||||
\(864\) | −3.84418 | − | 3.49604i | −0.130782 | − | 0.118938i | ||||
\(865\) | −0.404780 | + | 2.49051i | −0.0137629 | + | 0.0846797i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.94975 | + | 11.0680i | −0.168102 | + | 0.375888i | ||||
\(868\) | 15.5241 | − | 8.14637i | 0.526924 | − | 0.276506i | ||||
\(869\) | − | 53.7772i | − | 1.82427i | ||||||
\(870\) | −1.55545 | + | 26.7622i | −0.0527348 | + | 0.907323i | ||||
\(871\) | 12.9089 | − | 7.45296i | 0.437401 | − | 0.252534i | ||||
\(872\) | 10.2158 | + | 17.6944i | 0.345952 | + | 0.599206i | ||||
\(873\) | −35.2044 | + | 7.36121i | −1.19149 | + | 0.249139i | ||||
\(874\) | 6.40345i | 0.216600i | ||||||||
\(875\) | −25.6190 | + | 14.7875i | −0.866079 | + | 0.499908i | ||||
\(876\) | 2.47723 | − | 5.53924i | 0.0836977 | − | 0.187154i | ||||
\(877\) | −48.2359 | − | 27.8490i | −1.62881 | − | 0.940394i | −0.984449 | − | 0.175673i | \(-0.943790\pi\) |
−0.644361 | − | 0.764721i | \(-0.722877\pi\) | |||||||
\(878\) | 7.69306 | − | 4.44159i | 0.259628 | − | 0.149896i | ||||
\(879\) | −1.43566 | − | 13.8804i | −0.0484237 | − | 0.468174i | ||||
\(880\) | 9.79642 | − | 3.71515i | 0.330237 | − | 0.125238i | ||||
\(881\) | −18.7544 | −0.631853 | −0.315926 | − | 0.948784i | \(-0.602315\pi\) | ||||
−0.315926 | + | 0.948784i | \(0.602315\pi\) | |||||||
\(882\) | 20.8350 | − | 2.62736i | 0.701551 | − | 0.0884678i | ||||
\(883\) | − | 24.3833i | − | 0.820564i | −0.911959 | − | 0.410282i | \(-0.865430\pi\) | ||
0.911959 | − | 0.410282i | \(-0.134570\pi\) | |||||||
\(884\) | −2.86064 | − | 1.65159i | −0.0962136 | − | 0.0555489i | ||||
\(885\) | 22.5007 | − | 34.2197i | 0.756352 | − | 1.15028i | ||||
\(886\) | 7.52277 | + | 13.0298i | 0.252733 | + | 0.437746i | ||||
\(887\) | 3.00000 | + | 1.73205i | 0.100730 | + | 0.0581566i | 0.549519 | − | 0.835481i | \(-0.314811\pi\) |
−0.448789 | + | 0.893638i | \(0.648144\pi\) | |||||||
\(888\) | 4.21043 | + | 1.88296i | 0.141293 | + | 0.0631881i | ||||
\(889\) | 19.5228 | + | 12.3473i | 0.654773 | + | 0.414115i | ||||
\(890\) | 6.95445 | − | 8.51743i | 0.233114 | − | 0.285505i | ||||
\(891\) | −25.0123 | + | 33.9514i | −0.837942 | + | 1.13741i | ||||
\(892\) | 10.9441 | + | 18.9557i | 0.366434 | + | 0.634682i | ||||
\(893\) | 8.02277 | + | 13.8959i | 0.268472 | + | 0.465007i | ||||
\(894\) | 3.43649 | − | 2.48808i | 0.114933 | − | 0.0832137i | ||||
\(895\) | 33.5715 | + | 27.4110i | 1.12217 | + | 0.916248i | ||||
\(896\) | 1.22938 | + | 2.34278i | 0.0410709 | + | 0.0782667i | ||||
\(897\) | −3.30694 | + | 7.39453i | −0.110415 | + | 0.246896i | ||||
\(898\) | −22.4104 | − | 12.9386i | −0.747844 | − | 0.431768i | ||||
\(899\) | 22.9327 | + | 39.7205i | 0.764847 | + | 1.32475i | ||||
\(900\) | 14.8990 | + | 1.73777i | 0.496633 | + | 0.0579256i | ||||
\(901\) | −13.6931 | − | 7.90569i | −0.456182 | − | 0.263377i | ||||
\(902\) | 4.89433i | 0.162963i | ||||||||
\(903\) | −28.4094 | − | 14.1065i | −0.945406 | − | 0.469435i | ||||
\(904\) | 17.4772 | 0.581284 | ||||||||
\(905\) | 6.61160 | − | 2.50735i | 0.219777 | − | 0.0833471i | ||||
\(906\) | −3.44572 | + | 0.356394i | −0.114476 | + | 0.0118404i | ||||
\(907\) | −8.48528 | + | 4.89898i | −0.281749 | + | 0.162668i | −0.634215 | − | 0.773157i | \(-0.718677\pi\) |
0.352466 | + | 0.935825i | \(0.385343\pi\) | |||||||
\(908\) | −9.00000 | − | 5.19615i | −0.298675 | − | 0.172440i | ||||
\(909\) | 22.6274 | + | 25.2982i | 0.750504 | + | 0.839089i | ||||
\(910\) | −4.09826 | + | 4.62523i | −0.135856 | + | 0.153325i | ||||
\(911\) | 24.0681i | 0.797410i | 0.917079 | + | 0.398705i | \(0.130540\pi\) | ||||
−0.917079 | + | 0.398705i | \(0.869460\pi\) | |||||||
\(912\) | 2.00653 | − | 1.45276i | 0.0664427 | − | 0.0481056i | ||||
\(913\) | −9.52984 | − | 16.5062i | −0.315392 | − | 0.546274i | ||||
\(914\) | −9.59425 | + | 5.53924i | −0.317350 | + | 0.183222i | ||||
\(915\) | −0.778465 | + | 13.3938i | −0.0257353 | + | 0.442786i | ||||
\(916\) | 13.5546i | 0.447856i | ||||||||
\(917\) | 16.9317 | + | 32.2659i | 0.559133 | + | 1.06551i | ||||
\(918\) | 5.00000 | + | 15.6525i | 0.165025 | + | 0.516609i | ||||
\(919\) | −0.215838 | + | 0.373843i | −0.00711985 | + | 0.0123319i | −0.869563 | − | 0.493821i | \(-0.835600\pi\) |
0.862444 | + | 0.506153i | \(0.168933\pi\) | |||||||
\(920\) | −9.88171 | − | 1.60607i | −0.325790 | − | 0.0529505i | ||||
\(921\) | 20.6547 | − | 2.13633i | 0.680595 | − | 0.0703946i | ||||
\(922\) | −15.8938 | + | 27.5289i | −0.523434 | + | 0.906615i | ||||
\(923\) | 7.23003i | 0.237979i | ||||||||
\(924\) | 17.8857 | − | 11.8804i | 0.588398 | − | 0.390836i | ||||
\(925\) | −13.0455 | + | 2.66291i | −0.428935 | + | 0.0875560i | ||||
\(926\) | −19.5497 | − | 11.2871i | −0.642444 | − | 0.370916i | ||||
\(927\) | −4.60523 | + | 14.0154i | −0.151256 | + | 0.460326i | ||||
\(928\) | −5.99430 | + | 3.46081i | −0.196773 | + | 0.113607i | ||||
\(929\) | 7.96300 | − | 13.7923i | 0.261258 | − | 0.452512i | −0.705319 | − | 0.708890i | \(-0.749196\pi\) |
0.966576 | + | 0.256379i | \(0.0825294\pi\) | |||||||
\(930\) | 22.9327 | − | 11.5207i | 0.751991 | − | 0.377779i | ||||
\(931\) | −0.806936 | + | 9.97902i | −0.0264463 | + | 0.327049i | ||||
\(932\) | −4.00000 | −0.131024 | ||||||||
\(933\) | 17.8580 | + | 24.6652i | 0.584645 | + | 0.807502i | ||||
\(934\) | 24.2614 | − | 14.0073i | 0.793857 | − | 0.458333i | ||||
\(935\) | −32.7028 | − | 5.31516i | −1.06950 | − | 0.173824i | ||||
\(936\) | 3.06733 | − | 0.641375i | 0.100259 | − | 0.0209640i | ||||
\(937\) | −53.6757 | −1.75351 | −0.876754 | − | 0.480938i | \(-0.840296\pi\) | ||||
−0.876754 | + | 0.480938i | \(0.840296\pi\) | |||||||
\(938\) | 31.9089 | + | 20.1810i | 1.04186 | + | 0.658932i | ||||
\(939\) | 16.4317 | − | 36.7423i | 0.536228 | − | 1.19904i | ||||
\(940\) | −23.4561 | + | 8.89538i | −0.765054 | + | 0.290135i | ||||
\(941\) | −10.2369 | − | 17.7309i | −0.333715 | − | 0.578011i | 0.649522 | − | 0.760343i | \(-0.274969\pi\) |
−0.983237 | + | 0.182331i | \(0.941636\pi\) | |||||||
\(942\) | −24.8908 | + | 2.57448i | −0.810986 | + | 0.0838811i | ||||
\(943\) | 2.33836 | − | 4.05015i | 0.0761474 | − | 0.131891i | ||||
\(944\) | 10.5744 | 0.344167 | ||||||||
\(945\) | 30.5626 | − | 3.30528i | 0.994203 | − | 0.107521i | ||||
\(946\) | −32.4317 | −1.05444 | ||||||||
\(947\) | −16.4317 | + | 28.4605i | −0.533958 | + | 0.924842i | 0.465255 | + | 0.885177i | \(0.345963\pi\) |
−0.999213 | + | 0.0396654i | \(0.987371\pi\) | |||||||
\(948\) | 19.7737 | − | 2.04521i | 0.642218 | − | 0.0664252i | ||||
\(949\) | 1.82971 | + | 3.16915i | 0.0593949 | + | 0.102875i | ||||
\(950\) | −2.26471 | + | 6.78305i | −0.0734770 | + | 0.220071i | ||||
\(951\) | 7.00665 | − | 15.6674i | 0.227206 | − | 0.508049i | ||||
\(952\) | 0.337449 | − | 8.35979i | 0.0109368 | − | 0.270942i | ||||
\(953\) | 46.9545 | 1.52100 | 0.760502 | − | 0.649336i | \(-0.224953\pi\) | ||||
0.760502 | + | 0.649336i | \(0.224953\pi\) | |||||||
\(954\) | 14.6825 | − | 3.07008i | 0.475362 | − | 0.0993976i | ||||
\(955\) | 5.84452 | − | 35.9598i | 0.189124 | − | 1.16363i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.9426 | + | 45.4998i | 1.06488 | + | 1.47080i | ||||
\(958\) | 42.3620 | 1.36865 | ||||||||
\(959\) | 9.19239 | + | 0.371058i | 0.296838 | + | 0.0119821i | ||||
\(960\) | 1.73861 | + | 3.46081i | 0.0561135 | + | 0.111697i | ||||
\(961\) | 6.45445 | − | 11.1794i | 0.208208 | − | 0.360627i | ||||
\(962\) | −2.40890 | + | 1.39078i | −0.0776661 | + | 0.0448406i | ||||
\(963\) | 5.12938 | − | 15.6106i | 0.165292 | − | 0.503043i | ||||
\(964\) | 18.4545 | + | 10.6547i | 0.594378 | + | 0.343164i | ||||
\(965\) | 12.7279 | + | 10.3923i | 0.409726 | + | 0.334540i | ||||
\(966\) | −20.4769 | + | 1.28601i | −0.658833 | + | 0.0413766i | ||||
\(967\) | − | 7.23690i | − | 0.232723i | −0.993207 | − | 0.116361i | \(-0.962877\pi\) | ||
0.993207 | − | 0.116361i | \(-0.0371231\pi\) | |||||||
\(968\) | 5.47723 | − | 9.48683i | 0.176045 | − | 0.304918i | ||||
\(969\) | −7.79211 | + | 0.805945i | −0.250319 | + | 0.0258907i | ||||
\(970\) | 26.4601 | + | 4.30055i | 0.849584 | + | 0.138082i | ||||
\(971\) | −18.8748 | + | 32.6922i | −0.605723 | + | 1.04914i | 0.386214 | + | 0.922409i | \(0.373783\pi\) |
−0.991937 | + | 0.126733i | \(0.959551\pi\) | |||||||
\(972\) | −13.4350 | − | 7.90569i | −0.430929 | − | 0.253575i | ||||
\(973\) | −45.1260 | − | 28.5402i | −1.44667 | − | 0.914956i | ||||
\(974\) | − | 17.0349i | − | 0.545832i | ||||||
\(975\) | −6.11821 | + | 6.66332i | −0.195939 | + | 0.213397i | ||||
\(976\) | −3.00000 | + | 1.73205i | −0.0960277 | + | 0.0554416i | ||||
\(977\) | −1.95445 | − | 3.38521i | −0.0625284 | − | 0.108302i | 0.833067 | − | 0.553173i | \(-0.186583\pi\) |
−0.895595 | + | 0.444870i | \(0.853250\pi\) | |||||||
\(978\) | −20.6190 | + | 14.9285i | −0.659321 | + | 0.477359i | ||||
\(979\) | − | 23.0414i | − | 0.736407i | ||||||
\(980\) | −15.1971 | − | 3.74812i | −0.485453 | − | 0.119729i | ||||
\(981\) | 40.8634 | + | 45.6866i | 1.30467 | + | 1.45866i | ||||
\(982\) | 11.9886 | + | 6.92163i | 0.382572 | + | 0.220878i | ||||
\(983\) | −45.7158 | + | 26.3941i | −1.45811 | + | 0.841840i | −0.998918 | − | 0.0464984i | \(-0.985194\pi\) |
−0.459190 | + | 0.888338i | \(0.651860\pi\) | |||||||
\(984\) | −1.79962 | + | 0.186137i | −0.0573699 | + | 0.00593382i | ||||
\(985\) | 7.13604 | + | 18.8169i | 0.227373 | + | 0.599557i | ||||
\(986\) | 21.8881 | 0.697059 | ||||||||
\(987\) | −42.8248 | + | 28.4459i | −1.36313 | + | 0.905442i | ||||
\(988\) | 1.49395i | 0.0475290i | ||||||||
\(989\) | 26.8378 | + | 15.4948i | 0.853394 | + | 0.492707i | ||||
\(990\) | 26.4860 | − | 16.9247i | 0.841779 | − | 0.537901i | ||||
\(991\) | −5.26139 | − | 9.11299i | −0.167133 | − | 0.289484i | 0.770277 | − | 0.637709i | \(-0.220118\pi\) |
−0.937411 | + | 0.348225i | \(0.886784\pi\) | |||||||
\(992\) | 5.73861 | + | 3.31319i | 0.182201 | + | 0.105194i | ||||
\(993\) | −15.1545 | + | 33.8865i | −0.480913 | + | 1.07535i | ||||
\(994\) | −16.2158 | + | 8.50934i | −0.514335 | + | 0.269900i | ||||
\(995\) | 26.8634 | + | 21.9338i | 0.851626 | + | 0.695349i | ||||
\(996\) | 5.70682 | − | 4.13183i | 0.180827 | − | 0.130922i | ||||
\(997\) | 7.74597 | + | 13.4164i | 0.245317 | + | 0.424902i | 0.962221 | − | 0.272270i | \(-0.0877745\pi\) |
−0.716904 | + | 0.697172i | \(0.754441\pi\) | |||||||
\(998\) | −0.954451 | − | 1.65316i | −0.0302126 | − | 0.0523298i | ||||
\(999\) | 13.5201 | + | 2.94403i | 0.427756 | + | 0.0931449i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 210.2.t.e.89.4 | yes | 8 | |
3.2 | odd | 2 | 210.2.t.f.89.2 | yes | 8 | ||
5.2 | odd | 4 | 1050.2.s.i.551.2 | 16 | |||
5.3 | odd | 4 | 1050.2.s.i.551.7 | 16 | |||
5.4 | even | 2 | 210.2.t.f.89.1 | yes | 8 | ||
7.2 | even | 3 | 1470.2.d.f.1469.3 | 8 | |||
7.3 | odd | 6 | inner | 210.2.t.e.59.3 | ✓ | 8 | |
7.5 | odd | 6 | 1470.2.d.f.1469.6 | 8 | |||
15.2 | even | 4 | 1050.2.s.i.551.8 | 16 | |||
15.8 | even | 4 | 1050.2.s.i.551.1 | 16 | |||
15.14 | odd | 2 | inner | 210.2.t.e.89.3 | yes | 8 | |
21.2 | odd | 6 | 1470.2.d.e.1469.2 | 8 | |||
21.5 | even | 6 | 1470.2.d.e.1469.7 | 8 | |||
21.17 | even | 6 | 210.2.t.f.59.1 | yes | 8 | ||
35.3 | even | 12 | 1050.2.s.i.101.1 | 16 | |||
35.9 | even | 6 | 1470.2.d.e.1469.6 | 8 | |||
35.17 | even | 12 | 1050.2.s.i.101.8 | 16 | |||
35.19 | odd | 6 | 1470.2.d.e.1469.3 | 8 | |||
35.24 | odd | 6 | 210.2.t.f.59.2 | yes | 8 | ||
105.17 | odd | 12 | 1050.2.s.i.101.2 | 16 | |||
105.38 | odd | 12 | 1050.2.s.i.101.7 | 16 | |||
105.44 | odd | 6 | 1470.2.d.f.1469.7 | 8 | |||
105.59 | even | 6 | inner | 210.2.t.e.59.4 | yes | 8 | |
105.89 | even | 6 | 1470.2.d.f.1469.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.e.59.3 | ✓ | 8 | 7.3 | odd | 6 | inner | |
210.2.t.e.59.4 | yes | 8 | 105.59 | even | 6 | inner | |
210.2.t.e.89.3 | yes | 8 | 15.14 | odd | 2 | inner | |
210.2.t.e.89.4 | yes | 8 | 1.1 | even | 1 | trivial | |
210.2.t.f.59.1 | yes | 8 | 21.17 | even | 6 | ||
210.2.t.f.59.2 | yes | 8 | 35.24 | odd | 6 | ||
210.2.t.f.89.1 | yes | 8 | 5.4 | even | 2 | ||
210.2.t.f.89.2 | yes | 8 | 3.2 | odd | 2 | ||
1050.2.s.i.101.1 | 16 | 35.3 | even | 12 | |||
1050.2.s.i.101.2 | 16 | 105.17 | odd | 12 | |||
1050.2.s.i.101.7 | 16 | 105.38 | odd | 12 | |||
1050.2.s.i.101.8 | 16 | 35.17 | even | 12 | |||
1050.2.s.i.551.1 | 16 | 15.8 | even | 4 | |||
1050.2.s.i.551.2 | 16 | 5.2 | odd | 4 | |||
1050.2.s.i.551.7 | 16 | 5.3 | odd | 4 | |||
1050.2.s.i.551.8 | 16 | 15.2 | even | 4 | |||
1470.2.d.e.1469.2 | 8 | 21.2 | odd | 6 | |||
1470.2.d.e.1469.3 | 8 | 35.19 | odd | 6 | |||
1470.2.d.e.1469.6 | 8 | 35.9 | even | 6 | |||
1470.2.d.e.1469.7 | 8 | 21.5 | even | 6 | |||
1470.2.d.f.1469.2 | 8 | 105.89 | even | 6 | |||
1470.2.d.f.1469.3 | 8 | 7.2 | even | 3 | |||
1470.2.d.f.1469.6 | 8 | 7.5 | odd | 6 | |||
1470.2.d.f.1469.7 | 8 | 105.44 | odd | 6 |