Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(116,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.116");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 85x^{12} - 334x^{10} + 952x^{8} - 1050x^{6} + 853x^{4} - 93x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.1 | ||
Root | \(1.97871 + 1.14241i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.116 |
Dual form | 637.2.r.f.324.1 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97871 | + | 1.14241i | −1.39916 | + | 0.807803i | −0.994304 | − | 0.106579i | \(-0.966010\pi\) |
−0.404852 | + | 0.914382i | \(0.632677\pi\) | |||||||
\(3\) | 1.57521 | − | 2.72835i | 0.909448 | − | 1.57521i | 0.0946163 | − | 0.995514i | \(-0.469838\pi\) |
0.814832 | − | 0.579697i | \(-0.196829\pi\) | |||||||
\(4\) | 1.61019 | − | 2.78892i | 0.805093 | − | 1.39446i | ||||
\(5\) | 1.84030 | − | 1.06250i | 0.823005 | − | 0.475162i | −0.0284464 | − | 0.999595i | \(-0.509056\pi\) |
0.851452 | + | 0.524433i | \(0.175723\pi\) | |||||||
\(6\) | 7.19813i | 2.93862i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.78832i | 0.985820i | ||||||||
\(9\) | −3.46258 | − | 5.99736i | −1.15419 | − | 1.99912i | ||||
\(10\) | −2.42760 | + | 4.20473i | −0.767676 | + | 1.32965i | ||||
\(11\) | −0.267139 | − | 0.154233i | −0.0805454 | − | 0.0465029i | 0.459186 | − | 0.888340i | \(-0.348141\pi\) |
−0.539732 | + | 0.841837i | \(0.681474\pi\) | |||||||
\(12\) | −5.07276 | − | 8.78629i | −1.46438 | − | 2.53638i | ||||
\(13\) | 3.22037 | − | 1.62148i | 0.893170 | − | 0.449718i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.69462i | − | 1.72854i | ||||||
\(16\) | 0.0349749 | + | 0.0605784i | 0.00874373 | + | 0.0151446i | ||||
\(17\) | 0.887368 | − | 1.53697i | 0.215218 | − | 0.372769i | −0.738122 | − | 0.674667i | \(-0.764287\pi\) |
0.953340 | + | 0.301898i | \(0.0976204\pi\) | |||||||
\(18\) | 13.7029 | + | 7.91135i | 3.22979 | + | 1.86472i | ||||
\(19\) | 1.54266 | − | 0.890653i | 0.353909 | − | 0.204330i | −0.312496 | − | 0.949919i | \(-0.601165\pi\) |
0.666406 | + | 0.745589i | \(0.267832\pi\) | |||||||
\(20\) | − | 6.84326i | − | 1.53020i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.704786 | 0.150261 | ||||||||
\(23\) | 0.575211 | + | 0.996294i | 0.119940 | + | 0.207742i | 0.919744 | − | 0.392520i | \(-0.128397\pi\) |
−0.799804 | + | 0.600261i | \(0.795063\pi\) | |||||||
\(24\) | 7.60750 | + | 4.39219i | 1.55288 | + | 0.896553i | ||||
\(25\) | −0.242207 | + | 0.419515i | −0.0484414 | + | 0.0839029i | ||||
\(26\) | −4.51978 | + | 6.88741i | −0.886401 | + | 1.35073i | ||||
\(27\) | −12.3659 | −2.37982 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.01052 | 0.373345 | 0.186672 | − | 0.982422i | \(-0.440230\pi\) | ||||
0.186672 | + | 0.982422i | \(0.440230\pi\) | |||||||
\(30\) | 7.64798 | + | 13.2467i | 1.39632 | + | 2.41850i | ||||
\(31\) | 3.98791 | + | 2.30242i | 0.716251 | + | 0.413527i | 0.813371 | − | 0.581745i | \(-0.197630\pi\) |
−0.0971205 | + | 0.995273i | \(0.530963\pi\) | |||||||
\(32\) | −4.96792 | − | 2.86823i | −0.878213 | − | 0.507037i | ||||
\(33\) | −0.841600 | + | 0.485898i | −0.146504 | + | 0.0845840i | ||||
\(34\) | 4.05494i | 0.695416i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −22.3016 | −3.71693 | ||||||||
\(37\) | −4.79901 | + | 2.77071i | −0.788953 | + | 0.455502i | −0.839594 | − | 0.543215i | \(-0.817207\pi\) |
0.0506410 | + | 0.998717i | \(0.483874\pi\) | |||||||
\(38\) | −2.03497 | + | 3.52468i | −0.330117 | + | 0.571779i | ||||
\(39\) | 0.648799 | − | 11.3405i | 0.103891 | − | 1.81593i | ||||
\(40\) | 2.96258 | + | 5.13134i | 0.468425 | + | 0.811336i | ||||
\(41\) | − | 6.72984i | − | 1.05102i | −0.850786 | − | 0.525512i | \(-0.823874\pi\) | ||
0.850786 | − | 0.525512i | \(-0.176126\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.52611 | −0.232729 | −0.116365 | − | 0.993207i | \(-0.537124\pi\) | ||||
−0.116365 | + | 0.993207i | \(0.537124\pi\) | |||||||
\(44\) | −0.860286 | + | 0.496686i | −0.129693 | + | 0.0748783i | ||||
\(45\) | −12.7443 | − | 7.35795i | −1.89981 | − | 1.09686i | ||||
\(46\) | −2.27635 | − | 1.31425i | −0.335629 | − | 0.193776i | ||||
\(47\) | −8.24297 | + | 4.75908i | −1.20236 | + | 0.694183i | −0.961079 | − | 0.276272i | \(-0.910901\pi\) |
−0.241281 | + | 0.970455i | \(0.577568\pi\) | |||||||
\(48\) | 0.220372 | 0.0318079 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 1.10680i | − | 0.156524i | ||||||
\(51\) | −2.79558 | − | 4.84209i | −0.391460 | − | 0.678028i | ||||
\(52\) | 0.663205 | − | 11.5923i | 0.0919700 | − | 1.60756i | ||||
\(53\) | −3.72037 | + | 6.44387i | −0.511032 | + | 0.885134i | 0.488886 | + | 0.872348i | \(0.337403\pi\) |
−0.999918 | + | 0.0127862i | \(0.995930\pi\) | |||||||
\(54\) | 24.4685 | − | 14.1269i | 3.32974 | − | 1.92243i | ||||
\(55\) | −0.655486 | −0.0883857 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.61186i | − | 0.743309i | ||||||
\(58\) | −3.97823 | + | 2.29683i | −0.522368 | + | 0.301589i | ||||
\(59\) | −7.03304 | − | 4.06053i | −0.915624 | − | 0.528636i | −0.0333877 | − | 0.999442i | \(-0.510630\pi\) |
−0.882236 | + | 0.470807i | \(0.843963\pi\) | |||||||
\(60\) | −18.6708 | − | 10.7796i | −2.41039 | − | 1.39164i | ||||
\(61\) | −1.72037 | − | 2.97977i | −0.220271 | − | 0.381521i | 0.734619 | − | 0.678480i | \(-0.237361\pi\) |
−0.954890 | + | 0.296959i | \(0.904028\pi\) | |||||||
\(62\) | −10.5212 | −1.33620 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.9669 | 1.62086 | ||||||||
\(65\) | 4.20362 | − | 6.40564i | 0.521395 | − | 0.794522i | ||||
\(66\) | 1.11019 | − | 1.92290i | 0.136654 | − | 0.236692i | ||||
\(67\) | 10.9249 | + | 6.30747i | 1.33468 | + | 0.770580i | 0.986014 | − | 0.166665i | \(-0.0532998\pi\) |
0.348671 | + | 0.937245i | \(0.386633\pi\) | |||||||
\(68\) | −2.85765 | − | 4.94960i | −0.346541 | − | 0.600227i | ||||
\(69\) | 3.62431 | 0.436316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.35070i | 0.160299i | 0.996783 | + | 0.0801494i | \(0.0255397\pi\) | ||||
−0.996783 | + | 0.0801494i | \(0.974460\pi\) | |||||||
\(72\) | 16.7226 | − | 9.65478i | 1.97077 | − | 1.13783i | ||||
\(73\) | 10.2894 | + | 5.94059i | 1.20428 | + | 0.695293i | 0.961505 | − | 0.274789i | \(-0.0886079\pi\) |
0.242778 | + | 0.970082i | \(0.421941\pi\) | |||||||
\(74\) | 6.33056 | − | 10.9648i | 0.735912 | − | 1.27464i | ||||
\(75\) | 0.763054 | + | 1.32165i | 0.0881099 | + | 0.152611i | ||||
\(76\) | − | 5.73646i | − | 0.658018i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.6716 | + | 23.1806i | 1.32155 | + | 2.62469i | ||||
\(79\) | 3.96258 | + | 6.86339i | 0.445825 | + | 0.772191i | 0.998109 | − | 0.0614644i | \(-0.0195771\pi\) |
−0.552284 | + | 0.833656i | \(0.686244\pi\) | |||||||
\(80\) | 0.128728 | + | 0.0743214i | 0.0143923 | + | 0.00830939i | ||||
\(81\) | −9.09116 | + | 15.7464i | −1.01013 | + | 1.74960i | ||||
\(82\) | 7.68821 | + | 13.3164i | 0.849021 | + | 1.47055i | ||||
\(83\) | − | 11.2290i | − | 1.23255i | −0.787533 | − | 0.616273i | \(-0.788642\pi\) | ||
0.787533 | − | 0.616273i | \(-0.211358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.77130i | − | 0.409055i | ||||||
\(86\) | 3.01972 | − | 1.74344i | 0.325625 | − | 0.188000i | ||||
\(87\) | 3.16700 | − | 5.48540i | 0.339538 | − | 0.588096i | ||||
\(88\) | 0.430050 | − | 0.744869i | 0.0458435 | − | 0.0794033i | ||||
\(89\) | 1.43688 | − | 0.829583i | 0.152309 | − | 0.0879357i | −0.421909 | − | 0.906638i | \(-0.638640\pi\) |
0.574218 | + | 0.818703i | \(0.305306\pi\) | |||||||
\(90\) | 33.6231 | 3.54418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.70479 | 0.386251 | ||||||||
\(93\) | 12.5636 | − | 7.25360i | 1.30279 | − | 0.752164i | ||||
\(94\) | 10.8736 | − | 18.8336i | 1.12153 | − | 1.94254i | ||||
\(95\) | 1.89263 | − | 3.27813i | 0.194180 | − | 0.336329i | ||||
\(96\) | −15.6511 | + | 9.03614i | −1.59738 | + | 0.922247i | ||||
\(97\) | − | 7.66641i | − | 0.778406i | −0.921152 | − | 0.389203i | \(-0.872750\pi\) | ||
0.921152 | − | 0.389203i | \(-0.127250\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.13617i | 0.214693i | ||||||||
\(100\) | 0.779996 | + | 1.35099i | 0.0779996 | + | 0.135099i | ||||
\(101\) | −4.55864 | + | 7.89579i | −0.453601 | + | 0.785660i | −0.998607 | − | 0.0527721i | \(-0.983194\pi\) |
0.545005 | + | 0.838433i | \(0.316528\pi\) | |||||||
\(102\) | 11.0633 | + | 6.38738i | 1.09543 | + | 0.632445i | ||||
\(103\) | −3.02085 | − | 5.23226i | −0.297653 | − | 0.515550i | 0.677946 | − | 0.735112i | \(-0.262870\pi\) |
−0.975599 | + | 0.219562i | \(0.929537\pi\) | |||||||
\(104\) | 4.52122 | + | 8.97943i | 0.443342 | + | 0.880506i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 17.0007i | − | 1.65125i | ||||||
\(107\) | −6.04305 | − | 10.4669i | −0.584204 | − | 1.01187i | −0.994974 | − | 0.100132i | \(-0.968074\pi\) |
0.410770 | − | 0.911739i | \(-0.365260\pi\) | |||||||
\(108\) | −19.9114 | + | 34.4876i | −1.91598 | + | 3.31857i | ||||
\(109\) | 1.17942 | + | 0.680941i | 0.112968 | + | 0.0652223i | 0.555420 | − | 0.831570i | \(-0.312558\pi\) |
−0.442451 | + | 0.896793i | \(0.645891\pi\) | |||||||
\(110\) | 1.29701 | − | 0.748831i | 0.123665 | − | 0.0713983i | ||||
\(111\) | 17.4578i | 1.65702i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.42009 | −0.886168 | −0.443084 | − | 0.896480i | \(-0.646116\pi\) | ||||
−0.443084 | + | 0.896480i | \(0.646116\pi\) | |||||||
\(114\) | 6.41103 | + | 11.1042i | 0.600448 | + | 1.04001i | ||||
\(115\) | 2.11712 | + | 1.22232i | 0.197422 | + | 0.113982i | ||||
\(116\) | 3.23731 | − | 5.60719i | 0.300577 | − | 0.520615i | ||||
\(117\) | −20.8754 | − | 13.6992i | −1.92993 | − | 1.26649i | ||||
\(118\) | 18.5551 | 1.70814 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 18.6667 | 1.70403 | ||||||||
\(121\) | −5.45242 | − | 9.44388i | −0.495675 | − | 0.858534i | ||||
\(122\) | 6.80822 | + | 3.93073i | 0.616387 | + | 0.355871i | ||||
\(123\) | −18.3613 | − | 10.6009i | −1.65558 | − | 0.955852i | ||||
\(124\) | 12.8426 | − | 7.41466i | 1.15330 | − | 0.665856i | ||||
\(125\) | 11.6543i | 1.04239i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3998 | 1.18904 | 0.594519 | − | 0.804081i | \(-0.297342\pi\) | ||||
0.594519 | + | 0.804081i | \(0.297342\pi\) | |||||||
\(128\) | −15.7217 | + | 9.07695i | −1.38962 | + | 0.802297i | ||||
\(129\) | −2.40394 | + | 4.16375i | −0.211655 | + | 0.366598i | ||||
\(130\) | −0.999884 | + | 17.4771i | −0.0876956 | + | 1.53284i | ||||
\(131\) | 6.69854 | + | 11.6022i | 0.585254 | + | 1.01369i | 0.994844 | + | 0.101420i | \(0.0323385\pi\) |
−0.409590 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(132\) | 3.12954i | 0.272392i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −28.8228 | −2.48991 | ||||||||
\(135\) | −22.7569 | + | 13.1387i | −1.95860 | + | 1.13080i | ||||
\(136\) | 4.28555 | + | 2.47427i | 0.367483 | + | 0.212167i | ||||
\(137\) | −0.433917 | − | 0.250522i | −0.0370720 | − | 0.0214036i | 0.481349 | − | 0.876529i | \(-0.340147\pi\) |
−0.518421 | + | 0.855125i | \(0.673480\pi\) | |||||||
\(138\) | −7.17145 | + | 4.14044i | −0.610475 | + | 0.352458i | ||||
\(139\) | −1.41936 | −0.120388 | −0.0601941 | − | 0.998187i | \(-0.519172\pi\) | ||||
−0.0601941 | + | 0.998187i | \(0.519172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 29.9862i | 2.52529i | ||||||||
\(142\) | −1.54305 | − | 2.67264i | −0.129490 | − | 0.224283i | ||||
\(143\) | −1.11037 | − | 0.0635255i | −0.0928539 | − | 0.00531227i | ||||
\(144\) | 0.242207 | − | 0.419515i | 0.0201839 | − | 0.0349596i | ||||
\(145\) | 3.69996 | − | 2.13617i | 0.307265 | − | 0.177399i | ||||
\(146\) | −27.1463 | −2.24664 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.8454i | 1.46689i | ||||||||
\(149\) | 18.2652 | − | 10.5454i | 1.49635 | − | 0.863916i | 0.496355 | − | 0.868120i | \(-0.334672\pi\) |
0.999991 | + | 0.00420426i | \(0.00133826\pi\) | |||||||
\(150\) | −3.01972 | − | 1.74344i | −0.246559 | − | 0.142351i | ||||
\(151\) | 15.1591 | + | 8.75211i | 1.23363 | + | 0.712236i | 0.967785 | − | 0.251779i | \(-0.0810157\pi\) |
0.265845 | + | 0.964016i | \(0.414349\pi\) | |||||||
\(152\) | 2.48343 | + | 4.30142i | 0.201432 | + | 0.348891i | ||||
\(153\) | −12.2903 | −0.993614 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.78526 | 0.785971 | ||||||||
\(156\) | −30.5830 | − | 20.0697i | −2.44860 | − | 1.60686i | ||||
\(157\) | 0.0377894 | − | 0.0654532i | 0.00301593 | − | 0.00522374i | −0.864514 | − | 0.502610i | \(-0.832373\pi\) |
0.867529 | + | 0.497386i | \(0.165707\pi\) | |||||||
\(158\) | −15.6816 | − | 9.05375i | −1.24756 | − | 0.720278i | ||||
\(159\) | 11.7207 | + | 20.3009i | 0.929515 | + | 1.60997i | ||||
\(160\) | −12.1899 | −0.963699 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 41.5432i | − | 3.26394i | ||||||
\(163\) | −8.73102 | + | 5.04086i | −0.683866 | + | 0.394830i | −0.801310 | − | 0.598249i | \(-0.795863\pi\) |
0.117444 | + | 0.993080i | \(0.462530\pi\) | |||||||
\(164\) | −18.7690 | − | 10.8363i | −1.46561 | − | 0.846172i | ||||
\(165\) | −1.03253 | + | 1.78839i | −0.0803822 | + | 0.139226i | ||||
\(166\) | 12.8281 | + | 22.2189i | 0.995655 | + | 1.72452i | ||||
\(167\) | 5.84989i | 0.452678i | 0.974049 | + | 0.226339i | \(0.0726757\pi\) | ||||
−0.974049 | + | 0.226339i | \(0.927324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.74159 | − | 10.4436i | 0.595507 | − | 0.803350i | ||||
\(170\) | 4.30835 | + | 7.46229i | 0.330436 | + | 0.572331i | ||||
\(171\) | −10.6831 | − | 6.16791i | −0.816960 | − | 0.471672i | ||||
\(172\) | −2.45732 | + | 4.25620i | −0.187369 | + | 0.324532i | ||||
\(173\) | −8.49511 | − | 14.7140i | −0.645871 | − | 1.11868i | −0.984100 | − | 0.177617i | \(-0.943161\pi\) |
0.338229 | − | 0.941064i | \(-0.390172\pi\) | |||||||
\(174\) | 14.4720i | 1.09712i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.0215771i | − | 0.00162644i | ||||||
\(177\) | −22.1570 | + | 12.7924i | −1.66543 | + | 0.961534i | ||||
\(178\) | −1.89544 | + | 3.28300i | −0.142069 | + | 0.246072i | ||||
\(179\) | −7.65079 | + | 13.2516i | −0.571847 | + | 0.990468i | 0.424529 | + | 0.905414i | \(0.360440\pi\) |
−0.996376 | + | 0.0850537i | \(0.972894\pi\) | |||||||
\(180\) | −41.0415 | + | 23.6953i | −3.05905 | + | 1.76615i | ||||
\(181\) | 5.84958 | 0.434796 | 0.217398 | − | 0.976083i | \(-0.430243\pi\) | ||||
0.217398 | + | 0.976083i | \(0.430243\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.8398 | −0.801301 | ||||||||
\(184\) | −2.77799 | + | 1.60387i | −0.204796 | + | 0.118239i | ||||
\(185\) | −5.88774 | + | 10.1979i | −0.432875 | + | 0.749761i | ||||
\(186\) | −16.5731 | + | 28.7055i | −1.21520 | + | 2.10479i | ||||
\(187\) | −0.474101 | + | 0.273722i | −0.0346697 | + | 0.0200165i | ||||
\(188\) | 30.6520i | 2.23553i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.64861i | 0.627436i | ||||||||
\(191\) | 13.4090 | + | 23.2250i | 0.970238 | + | 1.68050i | 0.694831 | + | 0.719173i | \(0.255479\pi\) |
0.275407 | + | 0.961328i | \(0.411188\pi\) | |||||||
\(192\) | 20.4255 | − | 35.3780i | 1.47409 | − | 2.55319i | ||||
\(193\) | 0.185315 | + | 0.106992i | 0.0133393 | + | 0.00770145i | 0.506655 | − | 0.862149i | \(-0.330882\pi\) |
−0.493316 | + | 0.869850i | \(0.664215\pi\) | |||||||
\(194\) | 8.75816 | + | 15.1696i | 0.628799 | + | 1.08911i | ||||
\(195\) | −10.8552 | − | 21.5592i | −0.777358 | − | 1.54388i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.2290i | − | 0.800035i | −0.916508 | − | 0.400017i | \(-0.869004\pi\) | ||
0.916508 | − | 0.400017i | \(-0.130996\pi\) | |||||||
\(198\) | −2.44038 | − | 4.22685i | −0.173430 | − | 0.300389i | ||||
\(199\) | −10.2100 | + | 17.6843i | −0.723771 | + | 1.25361i | 0.235707 | + | 0.971824i | \(0.424259\pi\) |
−0.959478 | + | 0.281784i | \(0.909074\pi\) | |||||||
\(200\) | −1.16974 | − | 0.675351i | −0.0827132 | − | 0.0477545i | ||||
\(201\) | 34.4179 | − | 19.8712i | 2.42765 | − | 1.40161i | ||||
\(202\) | − | 20.8313i | − | 1.46568i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −18.0056 | −1.26065 | ||||||||
\(205\) | −7.15042 | − | 12.3849i | −0.499407 | − | 0.864999i | ||||
\(206\) | 11.9547 | + | 6.90207i | 0.832926 | + | 0.480890i | ||||
\(207\) | 3.98343 | − | 6.89950i | 0.276867 | − | 0.479548i | ||||
\(208\) | 0.210859 | + | 0.138374i | 0.0146204 | + | 0.00959448i | ||||
\(209\) | −0.549471 | −0.0380077 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.41738 | 0.579476 | 0.289738 | − | 0.957106i | \(-0.406432\pi\) | ||||
0.289738 | + | 0.957106i | \(0.406432\pi\) | |||||||
\(212\) | 11.9810 | + | 20.7517i | 0.822857 | + | 1.42523i | ||||
\(213\) | 3.68518 | + | 2.12764i | 0.252504 | + | 0.145783i | ||||
\(214\) | 23.9148 | + | 13.8072i | 1.63479 | + | 0.943844i | ||||
\(215\) | −2.80849 | + | 1.62148i | −0.191537 | + | 0.110584i | ||||
\(216\) | − | 34.4801i | − | 2.34607i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.11164 | −0.210747 | ||||||||
\(219\) | 32.4159 | − | 18.7154i | 2.19047 | − | 1.26467i | ||||
\(220\) | −1.05545 | + | 1.82810i | −0.0711587 | + | 0.123250i | ||||
\(221\) | 0.365490 | − | 6.38845i | 0.0245855 | − | 0.429734i | ||||
\(222\) | −19.9439 | − | 34.5439i | −1.33855 | − | 2.31843i | ||||
\(223\) | 13.6091i | 0.911333i | 0.890151 | + | 0.455666i | \(0.150599\pi\) | ||||
−0.890151 | + | 0.455666i | \(0.849401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.35464 | 0.223643 | ||||||||
\(226\) | 18.6396 | − | 10.7616i | 1.23989 | − | 0.715849i | ||||
\(227\) | 3.12008 | + | 1.80138i | 0.207087 | + | 0.119562i | 0.599957 | − | 0.800032i | \(-0.295184\pi\) |
−0.392870 | + | 0.919594i | \(0.628518\pi\) | |||||||
\(228\) | −15.6511 | − | 9.03614i | −1.03652 | − | 0.598433i | ||||
\(229\) | 15.9212 | − | 9.19208i | 1.05210 | − | 0.607430i | 0.128863 | − | 0.991662i | \(-0.458867\pi\) |
0.923236 | + | 0.384232i | \(0.125534\pi\) | |||||||
\(230\) | −5.58554 | −0.368299 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.60598i | 0.368051i | ||||||||
\(233\) | 10.1348 | + | 17.5541i | 0.663955 | + | 1.15000i | 0.979567 | + | 0.201116i | \(0.0644568\pi\) |
−0.315612 | + | 0.948888i | \(0.602210\pi\) | |||||||
\(234\) | 56.9564 | + | 3.25853i | 3.72336 | + | 0.213017i | ||||
\(235\) | −10.1130 | + | 17.5162i | −0.659699 | + | 1.14263i | ||||
\(236\) | −22.6490 | + | 13.0764i | −1.47432 | + | 0.851202i | ||||
\(237\) | 24.9676 | 1.62182 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.8097i | 1.34607i | 0.739612 | + | 0.673033i | \(0.235009\pi\) | ||||
−0.739612 | + | 0.673033i | \(0.764991\pi\) | |||||||
\(240\) | 0.405549 | − | 0.234144i | 0.0261781 | − | 0.0151139i | ||||
\(241\) | 11.0113 | + | 6.35736i | 0.709299 | + | 0.409514i | 0.810801 | − | 0.585322i | \(-0.199032\pi\) |
−0.101503 | + | 0.994835i | \(0.532365\pi\) | |||||||
\(242\) | 21.5775 | + | 12.4578i | 1.38705 | + | 0.800816i | ||||
\(243\) | 10.0922 | + | 17.4801i | 0.647412 | + | 1.12135i | ||||
\(244\) | −11.0805 | −0.709355 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 48.4422 | 3.08856 | ||||||||
\(247\) | 3.52375 | − | 5.36962i | 0.224211 | − | 0.341661i | ||||
\(248\) | −6.41990 | + | 11.1196i | −0.407664 | + | 0.706094i | ||||
\(249\) | −30.6367 | − | 17.6881i | −1.94152 | − | 1.12094i | ||||
\(250\) | −13.3140 | − | 23.0605i | −0.842050 | − | 1.45847i | ||||
\(251\) | 13.7436 | 0.867486 | 0.433743 | − | 0.901037i | \(-0.357193\pi\) | ||||
0.433743 | + | 0.901037i | \(0.357193\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.354865i | − | 0.0223102i | ||||||
\(254\) | −26.5142 | + | 15.3080i | −1.66365 | + | 0.960510i | ||||
\(255\) | −10.2894 | − | 5.94059i | −0.644347 | − | 0.372014i | ||||
\(256\) | 7.77229 | − | 13.4620i | 0.485768 | − | 0.841375i | ||||
\(257\) | 3.66736 | + | 6.35206i | 0.228764 | + | 0.396231i | 0.957442 | − | 0.288626i | \(-0.0931983\pi\) |
−0.728678 | + | 0.684856i | \(0.759865\pi\) | |||||||
\(258\) | − | 10.9851i | − | 0.683904i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −11.0962 | − | 22.0378i | −0.688159 | − | 1.36673i | ||||
\(261\) | −6.96159 | − | 12.0578i | −0.430912 | − | 0.746361i | ||||
\(262\) | −26.5089 | − | 15.3049i | −1.63772 | − | 0.945540i | ||||
\(263\) | 3.33942 | − | 5.78405i | 0.205918 | − | 0.356660i | −0.744507 | − | 0.667615i | \(-0.767315\pi\) |
0.950425 | + | 0.310955i | \(0.100649\pi\) | |||||||
\(264\) | −1.35484 | − | 2.34665i | −0.0833846 | − | 0.144426i | ||||
\(265\) | 15.8115i | 0.971293i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.22708i | − | 0.319892i | ||||||
\(268\) | 35.1821 | − | 20.3124i | 2.14909 | − | 1.24078i | ||||
\(269\) | 8.11263 | − | 14.0515i | 0.494636 | − | 0.856735i | −0.505345 | − | 0.862917i | \(-0.668635\pi\) |
0.999981 | + | 0.00618287i | \(0.00196808\pi\) | |||||||
\(270\) | 30.0195 | − | 51.9953i | 1.82693 | − | 3.16433i | ||||
\(271\) | −16.2277 | + | 9.36904i | −0.985760 | + | 0.569129i | −0.904004 | − | 0.427524i | \(-0.859386\pi\) |
−0.0817555 | + | 0.996652i | \(0.526053\pi\) | |||||||
\(272\) | 0.124143 | 0.00752725 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.14479 | 0.0691595 | ||||||||
\(275\) | 0.129406 | − | 0.0747124i | 0.00780346 | − | 0.00450533i | ||||
\(276\) | 5.83582 | − | 10.1079i | 0.351275 | − | 0.608426i | ||||
\(277\) | 15.0163 | − | 26.0090i | 0.902243 | − | 1.56273i | 0.0776679 | − | 0.996979i | \(-0.475253\pi\) |
0.824575 | − | 0.565752i | \(-0.191414\pi\) | |||||||
\(278\) | 2.80849 | − | 1.62148i | 0.168442 | − | 0.0972501i | ||||
\(279\) | − | 31.8893i | − | 1.90916i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.23065i | − | 0.133070i | −0.997784 | − | 0.0665348i | \(-0.978806\pi\) | ||
0.997784 | − | 0.0665348i | \(-0.0211943\pi\) | |||||||
\(282\) | −34.2565 | − | 59.3339i | −2.03994 | − | 3.53328i | ||||
\(283\) | −6.88774 | + | 11.9299i | −0.409433 | + | 0.709159i | −0.994826 | − | 0.101590i | \(-0.967607\pi\) |
0.585393 | + | 0.810750i | \(0.300940\pi\) | |||||||
\(284\) | 3.76700 | + | 2.17488i | 0.223531 | + | 0.129055i | ||||
\(285\) | −5.96258 | − | 10.3275i | −0.353193 | − | 0.611748i | ||||
\(286\) | 2.26967 | − | 1.14280i | 0.134208 | − | 0.0675750i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 39.7259i | 2.34087i | ||||||||
\(289\) | 6.92516 | + | 11.9947i | 0.407362 | + | 0.705572i | ||||
\(290\) | −4.88075 | + | 8.45371i | −0.286608 | + | 0.496419i | ||||
\(291\) | −20.9166 | − | 12.0762i | −1.22615 | − | 0.707920i | ||||
\(292\) | 33.1357 | − | 19.1309i | 1.93912 | − | 1.11955i | ||||
\(293\) | − | 1.01231i | − | 0.0591400i | −0.999563 | − | 0.0295700i | \(-0.990586\pi\) | ||
0.999563 | − | 0.0295700i | \(-0.00941380\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.2572 | −1.00475 | ||||||||
\(296\) | −7.72563 | − | 13.3812i | −0.449043 | − | 0.777766i | ||||
\(297\) | 3.30341 | + | 1.90723i | 0.191683 | + | 0.110668i | ||||
\(298\) | −24.0943 | + | 41.7326i | −1.39575 | + | 2.41751i | ||||
\(299\) | 3.46787 | + | 2.27574i | 0.200552 | + | 0.131610i | ||||
\(300\) | 4.91464 | 0.283747 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −39.9939 | −2.30139 | ||||||||
\(303\) | 14.3616 | + | 24.8751i | 0.825054 | + | 1.42904i | ||||
\(304\) | 0.107909 | + | 0.0623010i | 0.00618898 | + | 0.00357321i | ||||
\(305\) | −6.33199 | − | 3.65577i | −0.362568 | − | 0.209329i | ||||
\(306\) | 24.3189 | − | 14.0405i | 1.39022 | − | 0.802645i | ||||
\(307\) | 24.0527i | 1.37276i | 0.727244 | + | 0.686379i | \(0.240801\pi\) | ||||
−0.727244 | + | 0.686379i | \(0.759199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.0339 | −1.08280 | ||||||||
\(310\) | −19.3622 | + | 11.1787i | −1.09970 | + | 0.634910i | ||||
\(311\) | 4.49548 | − | 7.78639i | 0.254915 | − | 0.441526i | −0.709957 | − | 0.704245i | \(-0.751286\pi\) |
0.964872 | + | 0.262719i | \(0.0846192\pi\) | |||||||
\(312\) | 31.6209 | + | 1.80906i | 1.79018 | + | 0.102418i | ||||
\(313\) | −7.61806 | − | 13.1949i | −0.430598 | − | 0.745818i | 0.566326 | − | 0.824181i | \(-0.308364\pi\) |
−0.996925 | + | 0.0783626i | \(0.975031\pi\) | |||||||
\(314\) | 0.172684i | 0.00974510i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.5220 | 1.43572 | ||||||||
\(317\) | 5.91972 | − | 3.41775i | 0.332484 | − | 0.191960i | −0.324459 | − | 0.945900i | \(-0.605182\pi\) |
0.656944 | + | 0.753940i | \(0.271849\pi\) | |||||||
\(318\) | −46.3838 | − | 26.7797i | −2.60107 | − | 1.50173i | ||||
\(319\) | −0.537088 | − | 0.310088i | −0.0300712 | − | 0.0173616i | ||||
\(320\) | 23.8628 | − | 13.7772i | 1.33397 | − | 0.770170i | ||||
\(321\) | −38.0763 | −2.12521 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 3.16135i | − | 0.175902i | ||||||
\(324\) | 29.2769 | + | 50.7091i | 1.62650 | + | 2.81717i | ||||
\(325\) | −0.0997604 | + | 1.74373i | −0.00553371 | + | 0.0967246i | ||||
\(326\) | 11.5174 | − | 19.9487i | 0.637890 | − | 1.10486i | ||||
\(327\) | 3.71568 | − | 2.14525i | 0.205478 | − | 0.118633i | ||||
\(328\) | 18.7649 | 1.03612 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − | 4.71827i | − | 0.259732i | ||||||
\(331\) | 11.9637 | − | 6.90727i | 0.657587 | − | 0.379658i | −0.133770 | − | 0.991012i | \(-0.542708\pi\) |
0.791357 | + | 0.611354i | \(0.209375\pi\) | |||||||
\(332\) | −31.3169 | − | 18.0808i | −1.71874 | − | 0.992314i | ||||
\(333\) | 33.2339 | + | 19.1876i | 1.82121 | + | 1.05147i | ||||
\(334\) | −6.68295 | − | 11.5752i | −0.365675 | − | 0.633367i | ||||
\(335\) | 26.8066 | 1.46460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.0432 | −1.47314 | −0.736568 | − | 0.676364i | \(-0.763555\pi\) | ||||
−0.736568 | + | 0.676364i | \(0.763555\pi\) | |||||||
\(338\) | −3.38754 | + | 29.5088i | −0.184258 | + | 1.60507i | ||||
\(339\) | −14.8386 | + | 25.7013i | −0.805924 | + | 1.39590i | ||||
\(340\) | −10.5179 | − | 6.07249i | −0.570411 | − | 0.329327i | ||||
\(341\) | −0.710218 | − | 1.23013i | −0.0384604 | − | 0.0666154i | ||||
\(342\) | 28.1850 | 1.52407 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 4.25528i | − | 0.229429i | ||||||
\(345\) | 6.66981 | − | 3.85082i | 0.359091 | − | 0.207321i | ||||
\(346\) | 33.6186 | + | 19.4097i | 1.80735 | + | 1.04347i | ||||
\(347\) | 9.65568 | − | 16.7241i | 0.518344 | − | 0.897799i | −0.481429 | − | 0.876485i | \(-0.659882\pi\) |
0.999773 | − | 0.0213132i | \(-0.00678472\pi\) | |||||||
\(348\) | −10.1989 | − | 17.6650i | −0.546719 | − | 0.946944i | ||||
\(349\) | − | 14.1573i | − | 0.757821i | −0.925433 | − | 0.378911i | \(-0.876299\pi\) | ||
0.925433 | − | 0.378911i | \(-0.123701\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −39.8228 | + | 20.0511i | −2.12558 | + | 1.07025i | ||||
\(352\) | 0.884750 | + | 1.53243i | 0.0471573 | + | 0.0816789i | ||||
\(353\) | −14.6919 | − | 8.48235i | −0.781969 | − | 0.451470i | 0.0551585 | − | 0.998478i | \(-0.482434\pi\) |
−0.837128 | + | 0.547008i | \(0.815767\pi\) | |||||||
\(354\) | 29.2282 | − | 50.6247i | 1.55346 | − | 2.69067i | ||||
\(355\) | 1.43511 | + | 2.48569i | 0.0761680 | + | 0.131927i | ||||
\(356\) | − | 5.34313i | − | 0.283186i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 34.9613i | − | 1.84776i | ||||||
\(359\) | −19.7136 | + | 11.3816i | −1.04044 | + | 0.600700i | −0.919959 | − | 0.392016i | \(-0.871778\pi\) |
−0.120484 | + | 0.992715i | \(0.538445\pi\) | |||||||
\(360\) | 20.5163 | − | 35.5353i | 1.08131 | − | 1.87288i | ||||
\(361\) | −7.91348 | + | 13.7065i | −0.416499 | + | 0.721397i | ||||
\(362\) | −11.5746 | + | 6.68260i | −0.608347 | + | 0.351229i | ||||
\(363\) | −34.3549 | −1.80316 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.2474 | 1.32151 | ||||||||
\(366\) | 21.4488 | − | 12.3835i | 1.12114 | − | 0.647293i | ||||
\(367\) | 8.29168 | − | 14.3616i | 0.432822 | − | 0.749670i | −0.564293 | − | 0.825575i | \(-0.690851\pi\) |
0.997115 | + | 0.0759048i | \(0.0241845\pi\) | |||||||
\(368\) | −0.0402359 | + | 0.0696907i | −0.00209744 | + | 0.00363288i | ||||
\(369\) | −40.3613 | + | 23.3026i | −2.10112 | + | 1.21308i | ||||
\(370\) | − | 26.9048i | − | 1.39871i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 46.7186i | − | 2.42225i | ||||||
\(373\) | −13.8230 | − | 23.9422i | −0.715730 | − | 1.23968i | −0.962677 | − | 0.270652i | \(-0.912761\pi\) |
0.246947 | − | 0.969029i | \(-0.420573\pi\) | |||||||
\(374\) | 0.625404 | − | 1.08323i | 0.0323389 | − | 0.0560126i | ||||
\(375\) | 31.7970 | + | 18.3580i | 1.64199 | + | 0.948004i | ||||
\(376\) | −13.2698 | − | 22.9840i | −0.684340 | − | 1.18531i | ||||
\(377\) | 6.47463 | − | 3.26003i | 0.333460 | − | 0.167900i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.24228i | 0.474744i | 0.971419 | + | 0.237372i | \(0.0762860\pi\) | ||||
−0.971419 | + | 0.237372i | \(0.923714\pi\) | |||||||
\(380\) | −6.09497 | − | 10.5568i | −0.312665 | − | 0.541552i | ||||
\(381\) | 21.1075 | − | 36.5592i | 1.08137 | − | 1.87299i | ||||
\(382\) | −53.0648 | − | 30.6369i | −2.71503 | − | 1.56752i | ||||
\(383\) | 6.62358 | − | 3.82413i | 0.338449 | − | 0.195404i | −0.321137 | − | 0.947033i | \(-0.604065\pi\) |
0.659586 | + | 0.751629i | \(0.270732\pi\) | |||||||
\(384\) | 57.1925i | 2.91859i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.488913 | −0.0248850 | ||||||||
\(387\) | 5.28427 | + | 9.15262i | 0.268614 | + | 0.465254i | ||||
\(388\) | −21.3810 | − | 12.3443i | −1.08546 | − | 0.626689i | ||||
\(389\) | 3.26868 | − | 5.66153i | 0.165729 | − | 0.287051i | −0.771185 | − | 0.636611i | \(-0.780336\pi\) |
0.936914 | + | 0.349560i | \(0.113669\pi\) | |||||||
\(390\) | 46.1086 | + | 30.2582i | 2.33480 | + | 1.53218i | ||||
\(391\) | 2.04169 | 0.103253 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 42.2064 | 2.12903 | ||||||||
\(394\) | 12.8281 | + | 22.2189i | 0.646271 | + | 1.11937i | ||||
\(395\) | 14.5846 | + | 8.42044i | 0.733833 | + | 0.423678i | ||||
\(396\) | 5.95762 | + | 3.43963i | 0.299381 | + | 0.172848i | ||||
\(397\) | −25.0548 | + | 14.4654i | −1.25746 | + | 0.725996i | −0.972581 | − | 0.232566i | \(-0.925288\pi\) |
−0.284882 | + | 0.958563i | \(0.591954\pi\) | |||||||
\(398\) | − | 46.6561i | − | 2.33866i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0338847 | −0.00169423 | ||||||||
\(401\) | 23.1603 | − | 13.3716i | 1.15657 | − | 0.667747i | 0.206092 | − | 0.978533i | \(-0.433925\pi\) |
0.950480 | + | 0.310786i | \(0.100592\pi\) | |||||||
\(402\) | −45.4020 | + | 78.6385i | −2.26444 | + | 3.92213i | ||||
\(403\) | 16.5759 | + | 0.948324i | 0.825705 | + | 0.0472394i | ||||
\(404\) | 14.6805 | + | 25.4274i | 0.730382 | + | 1.26506i | ||||
\(405\) | 38.6373i | 1.91990i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70934 | 0.0847287 | ||||||||
\(408\) | 13.5013 | − | 7.79498i | 0.668414 | − | 0.385909i | ||||
\(409\) | 30.1138 | + | 17.3862i | 1.48903 | + | 0.859694i | 0.999922 | − | 0.0125273i | \(-0.00398768\pi\) |
0.489112 | + | 0.872221i | \(0.337321\pi\) | |||||||
\(410\) | 28.2972 | + | 16.3374i | 1.39750 | + | 0.806846i | ||||
\(411\) | −1.36702 | + | 0.789250i | −0.0674302 | + | 0.0389309i | ||||
\(412\) | −19.4565 | −0.958553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 18.2028i | 0.894617i | ||||||||
\(415\) | −11.9308 | − | 20.6647i | −0.585659 | − | 1.01439i | ||||
\(416\) | −20.6494 | − | 1.18137i | −1.01242 | − | 0.0579214i | ||||
\(417\) | −2.23579 | + | 3.87250i | −0.109487 | + | 0.189637i | ||||
\(418\) | 1.08724 | − | 0.627719i | 0.0531787 | − | 0.0307027i | ||||
\(419\) | 4.19246 | 0.204815 | 0.102407 | − | 0.994743i | \(-0.467345\pi\) | ||||
0.102407 | + | 0.994743i | \(0.467345\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.9526i | 1.02117i | 0.859828 | + | 0.510584i | \(0.170571\pi\) | ||||
−0.859828 | + | 0.510584i | \(0.829429\pi\) | |||||||
\(422\) | −16.6555 | + | 9.61607i | −0.810778 | + | 0.468103i | ||||
\(423\) | 57.0838 | + | 32.9574i | 2.77551 | + | 1.60244i | ||||
\(424\) | −17.9676 | − | 10.3736i | −0.872583 | − | 0.503786i | ||||
\(425\) | 0.429853 | + | 0.744528i | 0.0208509 | + | 0.0361149i | ||||
\(426\) | −9.72252 | −0.471058 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −38.9217 | −1.88135 | ||||||||
\(429\) | −1.92239 | + | 2.92941i | −0.0928138 | + | 0.141433i | ||||
\(430\) | 3.70479 | − | 6.41688i | 0.178661 | − | 0.309449i | ||||
\(431\) | 14.6309 | + | 8.44713i | 0.704744 | + | 0.406884i | 0.809112 | − | 0.587655i | \(-0.199949\pi\) |
−0.104368 | + | 0.994539i | \(0.533282\pi\) | |||||||
\(432\) | −0.432497 | − | 0.749106i | −0.0208085 | − | 0.0360414i | ||||
\(433\) | −3.42241 | −0.164471 | −0.0822353 | − | 0.996613i | \(-0.526206\pi\) | ||||
−0.0822353 | + | 0.996613i | \(0.526206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.4597i | − | 0.645342i | ||||||
\(436\) | 3.79818 | − | 2.19288i | 0.181900 | − | 0.105020i | ||||
\(437\) | 1.77470 | + | 1.02463i | 0.0848956 | + | 0.0490145i | ||||
\(438\) | −42.7611 | + | 74.0644i | −2.04320 | + | 3.53893i | ||||
\(439\) | −9.03253 | − | 15.6448i | −0.431099 | − | 0.746685i | 0.565869 | − | 0.824495i | \(-0.308541\pi\) |
−0.996968 | + | 0.0778096i | \(0.975207\pi\) | |||||||
\(440\) | − | 1.82771i | − | 0.0871324i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.57501 | + | 13.0584i | 0.312742 | + | 0.621125i | ||||
\(443\) | −3.22173 | − | 5.58020i | −0.153069 | − | 0.265123i | 0.779285 | − | 0.626669i | \(-0.215582\pi\) |
−0.932354 | + | 0.361546i | \(0.882249\pi\) | |||||||
\(444\) | 48.6885 | + | 28.1103i | 2.31065 | + | 1.33406i | ||||
\(445\) | 1.76286 | − | 3.05336i | 0.0835674 | − | 0.144743i | ||||
\(446\) | −15.5471 | − | 26.9284i | −0.736178 | − | 1.27510i | ||||
\(447\) | − | 66.4451i | − | 3.14275i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.75306i | 0.0827322i | 0.999144 | + | 0.0413661i | \(0.0131710\pi\) | ||||
−0.999144 | + | 0.0413661i | \(0.986829\pi\) | |||||||
\(450\) | −6.63785 | + | 3.83237i | −0.312911 | + | 0.180659i | ||||
\(451\) | −1.03796 | + | 1.79780i | −0.0488757 | + | 0.0846551i | ||||
\(452\) | −15.1681 | + | 26.2719i | −0.713447 | + | 1.23573i | ||||
\(453\) | 47.7575 | − | 27.5728i | 2.24385 | − | 1.29548i | ||||
\(454\) | −8.23163 | −0.386330 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 15.6477 | 0.732770 | ||||||||
\(457\) | −28.3277 | + | 16.3550i | −1.32511 | + | 0.765054i | −0.984539 | − | 0.175164i | \(-0.943954\pi\) |
−0.340573 | + | 0.940218i | \(0.610621\pi\) | |||||||
\(458\) | −21.0022 | + | 36.3769i | −0.981368 | + | 1.69978i | ||||
\(459\) | −10.9731 | + | 19.0060i | −0.512180 | + | 0.887123i | ||||
\(460\) | 6.81790 | − | 3.93632i | 0.317886 | − | 0.183532i | ||||
\(461\) | 7.66641i | 0.357060i | 0.983934 | + | 0.178530i | \(0.0571342\pi\) | ||||
−0.983934 | + | 0.178530i | \(0.942866\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 14.4720i | − | 0.672570i | −0.941760 | − | 0.336285i | \(-0.890829\pi\) | ||
0.941760 | − | 0.336285i | \(-0.109171\pi\) | |||||||
\(464\) | 0.0703179 | + | 0.121794i | 0.00326443 | + | 0.00565415i | ||||
\(465\) | 15.4138 | − | 26.6976i | 0.714800 | − | 1.23807i | ||||
\(466\) | −40.1077 | − | 23.1562i | −1.85795 | − | 1.07269i | ||||
\(467\) | 1.68801 | + | 2.92373i | 0.0781120 | + | 0.135294i | 0.902435 | − | 0.430825i | \(-0.141777\pi\) |
−0.824323 | + | 0.566119i | \(0.808444\pi\) | |||||||
\(468\) | −71.8194 | + | 36.1616i | −3.31985 | + | 1.67157i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 46.2126i | − | 2.13163i | ||||||
\(471\) | −0.119053 | − | 0.206205i | −0.00548566 | − | 0.00950144i | ||||
\(472\) | 11.3221 | − | 19.6104i | 0.521140 | − | 0.902641i | ||||
\(473\) | 0.407683 | + | 0.235376i | 0.0187453 | + | 0.0108226i | ||||
\(474\) | −49.4035 | + | 28.5231i | −2.26918 | + | 1.31011i | ||||
\(475\) | 0.862889i | 0.0395921i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 51.5283 | 2.35932 | ||||||||
\(478\) | −23.7731 | − | 41.1763i | −1.08736 | − | 1.88336i | ||||
\(479\) | 0.125768 | + | 0.0726124i | 0.00574651 | + | 0.00331775i | 0.502871 | − | 0.864362i | \(-0.332277\pi\) |
−0.497124 | + | 0.867680i | \(0.665611\pi\) | |||||||
\(480\) | −19.2017 | + | 33.2584i | −0.876435 | + | 1.51803i | ||||
\(481\) | −10.9619 | + | 16.7042i | −0.499822 | + | 0.761648i | ||||
\(482\) | −29.0508 | −1.32323 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −35.1177 | −1.59626 | ||||||||
\(485\) | −8.14553 | − | 14.1085i | −0.369869 | − | 0.640633i | ||||
\(486\) | −39.9388 | − | 23.0587i | −1.81166 | − | 1.04596i | ||||
\(487\) | −14.2214 | − | 8.21073i | −0.644433 | − | 0.372064i | 0.141887 | − | 0.989883i | \(-0.454683\pi\) |
−0.786320 | + | 0.617819i | \(0.788016\pi\) | |||||||
\(488\) | 8.30856 | − | 4.79695i | 0.376111 | − | 0.217148i | ||||
\(489\) | 31.7616i | 1.43631i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2077 | −0.821701 | −0.410850 | − | 0.911703i | \(-0.634768\pi\) | ||||
−0.410850 | + | 0.911703i | \(0.634768\pi\) | |||||||
\(492\) | −59.1303 | + | 34.1389i | −2.66580 | + | 1.53910i | ||||
\(493\) | 1.78407 | − | 3.09010i | 0.0803506 | − | 0.139171i | ||||
\(494\) | −0.838167 | + | 14.6505i | −0.0377109 | + | 0.659155i | ||||
\(495\) | 2.26967 | + | 3.93119i | 0.102014 | + | 0.176694i | ||||
\(496\) | 0.322108i | 0.0144631i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 80.8279 | 3.62199 | ||||||||
\(499\) | −32.5383 | + | 18.7860i | −1.45661 | + | 0.840976i | −0.998843 | − | 0.0480945i | \(-0.984685\pi\) |
−0.457770 | + | 0.889070i | \(0.651352\pi\) | |||||||
\(500\) | 32.5030 | + | 18.7656i | 1.45358 | + | 0.839225i | ||||
\(501\) | 15.9605 | + | 9.21481i | 0.713063 | + | 0.411687i | ||||
\(502\) | −27.1945 | + | 15.7007i | −1.21375 | + | 0.700758i | ||||
\(503\) | 4.20535 | 0.187507 | 0.0937537 | − | 0.995595i | \(-0.470113\pi\) | ||||
0.0937537 | + | 0.995595i | \(0.470113\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.3741i | 0.862137i | ||||||||
\(506\) | 0.405400 | + | 0.702174i | 0.0180222 | + | 0.0312154i | ||||
\(507\) | −16.2990 | − | 37.5725i | −0.723864 | − | 1.66865i | ||||
\(508\) | 21.5761 | − | 37.3710i | 0.957287 | − | 1.65807i | ||||
\(509\) | −7.30705 | + | 4.21873i | −0.323879 | + | 0.186992i | −0.653120 | − | 0.757254i | \(-0.726540\pi\) |
0.329241 | + | 0.944246i | \(0.393207\pi\) | |||||||
\(510\) | 27.1463 | 1.20206 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 0.791350i | − | 0.0349731i | ||||||
\(513\) | −19.0763 | + | 11.0137i | −0.842240 | + | 0.486268i | ||||
\(514\) | −14.5133 | − | 8.37924i | −0.640153 | − | 0.369593i | ||||
\(515\) | −11.1185 | − | 6.41927i | −0.489940 | − | 0.282867i | ||||
\(516\) | 7.74159 | + | 13.4088i | 0.340804 | + | 0.590290i | ||||
\(517\) | 2.93602 | 0.129126 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −53.5263 | −2.34955 | ||||||||
\(520\) | 17.8610 | + | 11.7210i | 0.783256 | + | 0.514002i | ||||
\(521\) | 12.9140 | − | 22.3677i | 0.565773 | − | 0.979948i | −0.431204 | − | 0.902254i | \(-0.641911\pi\) |
0.996977 | − | 0.0776936i | \(-0.0247556\pi\) | |||||||
\(522\) | 27.5499 | + | 15.9059i | 1.20583 | + | 0.696184i | ||||
\(523\) | −0.378202 | − | 0.655065i | −0.0165376 | − | 0.0286440i | 0.857638 | − | 0.514254i | \(-0.171931\pi\) |
−0.874176 | + | 0.485610i | \(0.838598\pi\) | |||||||
\(524\) | 43.1436 | 1.88473 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.2599i | 0.665364i | ||||||||
\(527\) | 7.07749 | − | 4.08619i | 0.308300 | − | 0.177997i | ||||
\(528\) | −0.0588698 | − | 0.0339885i | −0.00256198 | − | 0.00147916i | ||||
\(529\) | 10.8383 | − | 18.7724i | 0.471229 | − | 0.816192i | ||||
\(530\) | −18.0632 | − | 31.2863i | −0.784614 | − | 1.35899i | ||||
\(531\) | 56.2396i | 2.44059i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9123 | − | 21.6726i | −0.472665 | − | 0.938744i | ||||
\(534\) | 5.97145 | + | 10.3428i | 0.258410 | + | 0.447579i | ||||
\(535\) | −22.2420 | − | 12.8414i | −0.961606 | − | 0.555183i | ||||
\(536\) | −17.5873 | + | 30.4620i | −0.759654 | + | 1.31576i | ||||
\(537\) | 24.1032 | + | 41.7480i | 1.04013 | + | 1.80156i | ||||
\(538\) | 37.0717i | 1.59827i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 84.6231i | 3.64160i | ||||||||
\(541\) | 19.4099 | − | 11.2063i | 0.834496 | − | 0.481797i | −0.0208936 | − | 0.999782i | \(-0.506651\pi\) |
0.855390 | + | 0.517985i | \(0.173318\pi\) | |||||||
\(542\) | 21.4065 | − | 37.0772i | 0.919488 | − | 1.59260i | ||||
\(543\) | 9.21432 | − | 15.9597i | 0.395424 | − | 0.684895i | ||||
\(544\) | −8.81675 | + | 5.09035i | −0.378015 | + | 0.218247i | ||||
\(545\) | 2.89398 | 0.123965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8059 | −0.504784 | −0.252392 | − | 0.967625i | \(-0.581217\pi\) | ||||
−0.252392 | + | 0.967625i | \(0.581217\pi\) | |||||||
\(548\) | −1.39737 | + | 0.806774i | −0.0596929 | + | 0.0344637i | ||||
\(549\) | −11.9138 | + | 20.6354i | −0.508470 | + | 0.880697i | ||||
\(550\) | −0.170704 | + | 0.295668i | −0.00727884 | + | 0.0126073i | ||||
\(551\) | 3.10154 | − | 1.79068i | 0.132130 | − | 0.0762854i | ||||
\(552\) | 10.1058i | 0.430129i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 68.6190i | 2.91534i | ||||||||
\(555\) | 18.5489 | + | 32.1276i | 0.787355 | + | 1.36374i | ||||
\(556\) | −2.28543 | + | 3.95848i | −0.0969238 | + | 0.167877i | ||||
\(557\) | −7.59273 | − | 4.38366i | −0.321714 | − | 0.185742i | 0.330442 | − | 0.943826i | \(-0.392802\pi\) |
−0.652156 | + | 0.758084i | \(0.726135\pi\) | |||||||
\(558\) | 36.4305 | + | 63.0995i | 1.54223 | + | 2.67122i | ||||
\(559\) | −4.91464 | + | 2.47456i | −0.207867 | + | 0.104663i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.72468i | 0.0728161i | ||||||||
\(562\) | 2.54831 | + | 4.41380i | 0.107494 | + | 0.186185i | ||||
\(563\) | −18.3879 | + | 31.8488i | −0.774958 | + | 1.34227i | 0.159860 | + | 0.987140i | \(0.448896\pi\) |
−0.934818 | + | 0.355127i | \(0.884438\pi\) | |||||||
\(564\) | 83.6293 | + | 48.2834i | 3.52143 | + | 2.03310i | ||||
\(565\) | −17.3358 | + | 10.0088i | −0.729321 | + | 0.421074i | ||||
\(566\) | − | 31.4744i | − | 1.32297i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.76619 | −0.158026 | ||||||||
\(569\) | −17.8918 | − | 30.9896i | −0.750065 | − | 1.29915i | −0.947791 | − | 0.318893i | \(-0.896689\pi\) |
0.197726 | − | 0.980257i | \(-0.436644\pi\) | |||||||
\(570\) | 23.5964 | + | 13.6234i | 0.988344 | + | 0.570621i | ||||
\(571\) | 7.46920 | − | 12.9370i | 0.312576 | − | 0.541398i | −0.666343 | − | 0.745645i | \(-0.732141\pi\) |
0.978919 | + | 0.204248i | \(0.0654747\pi\) | |||||||
\(572\) | −1.96507 | + | 2.99445i | −0.0821638 | + | 0.125204i | ||||
\(573\) | 84.4877 | 3.52952 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.557280 | −0.0232402 | ||||||||
\(576\) | −44.8987 | − | 77.7669i | −1.87078 | − | 3.24029i | ||||
\(577\) | −14.5892 | − | 8.42309i | −0.607357 | − | 0.350658i | 0.164573 | − | 0.986365i | \(-0.447375\pi\) |
−0.771930 | + | 0.635707i | \(0.780709\pi\) | |||||||
\(578\) | −27.4057 | − | 15.8227i | −1.13993 | − | 0.658137i | ||||
\(579\) | 0.583822 | − | 0.337070i | 0.0242628 | − | 0.0140081i | ||||
\(580\) | − | 13.7585i | − | 0.571292i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 55.1838 | 2.28744 | ||||||||
\(583\) | 1.98771 | − | 1.14761i | 0.0823226 | − | 0.0475290i | ||||
\(584\) | −16.5643 | + | 28.6901i | −0.685434 | + | 1.18721i | ||||
\(585\) | −52.9723 | − | 3.03060i | −2.19013 | − | 0.125300i | ||||
\(586\) | 1.15647 | + | 2.00307i | 0.0477735 | + | 0.0827461i | ||||
\(587\) | − | 36.8833i | − | 1.52234i | −0.648555 | − | 0.761168i | \(-0.724626\pi\) | ||
0.648555 | − | 0.761168i | \(-0.275374\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.20264 | 0.337984 | ||||||||
\(590\) | 34.1469 | − | 19.7147i | 1.40580 | − | 0.811642i | ||||
\(591\) | −30.6367 | − | 17.6881i | −1.26022 | − | 0.727590i | ||||
\(592\) | −0.335690 | − | 0.193811i | −0.0137968 | − | 0.00796558i | ||||
\(593\) | 13.9894 | − | 8.07676i | 0.574474 | − | 0.331673i | −0.184460 | − | 0.982840i | \(-0.559054\pi\) |
0.758934 | + | 0.651167i | \(0.225720\pi\) | |||||||
\(594\) | −8.71531 | −0.357593 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 67.9204i | − | 2.78213i | ||||||
\(597\) | 32.1660 | + | 55.7131i | 1.31646 | + | 2.28018i | ||||
\(598\) | −9.46172 | − | 0.541314i | −0.386918 | − | 0.0221360i | ||||
\(599\) | 1.24238 | − | 2.15186i | 0.0507622 | − | 0.0879227i | −0.839528 | − | 0.543317i | \(-0.817168\pi\) |
0.890290 | + | 0.455394i | \(0.150502\pi\) | |||||||
\(600\) | −3.68518 | + | 2.12764i | −0.150447 | + | 0.0868605i | ||||
\(601\) | −9.55999 | −0.389960 | −0.194980 | − | 0.980807i | \(-0.562464\pi\) | ||||
−0.194980 | + | 0.980807i | \(0.562464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 87.3605i | − | 3.55759i | ||||||
\(604\) | 48.8179 | − | 28.1850i | 1.98637 | − | 1.14683i | ||||
\(605\) | −20.0682 | − | 11.5864i | −0.815886 | − | 0.471052i | ||||
\(606\) | −56.8349 | − | 32.8136i | −2.30876 | − | 1.33296i | ||||
\(607\) | −9.74294 | − | 16.8753i | −0.395454 | − | 0.684946i | 0.597705 | − | 0.801716i | \(-0.296079\pi\) |
−0.993159 | + | 0.116770i | \(0.962746\pi\) | |||||||
\(608\) | −10.2184 | −0.414411 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.7055 | 0.676387 | ||||||||
\(611\) | −18.8287 | + | 28.6918i | −0.761726 | + | 1.16075i | ||||
\(612\) | −19.7897 | + | 34.2768i | −0.799951 | + | 1.38556i | ||||
\(613\) | 12.7896 | + | 7.38409i | 0.516568 | + | 0.298241i | 0.735529 | − | 0.677493i | \(-0.236934\pi\) |
−0.218962 | + | 0.975733i | \(0.570267\pi\) | |||||||
\(614\) | −27.4779 | − | 47.5931i | −1.10892 | − | 1.92070i | ||||
\(615\) | −45.0537 | −1.81674 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 30.9478i | 1.24591i | 0.782257 | + | 0.622955i | \(0.214068\pi\) | ||||
−0.782257 | + | 0.622955i | \(0.785932\pi\) | |||||||
\(618\) | 37.6625 | − | 21.7444i | 1.51501 | − | 0.874689i | ||||
\(619\) | −11.3297 | − | 6.54123i | −0.455380 | − | 0.262914i | 0.254719 | − | 0.967015i | \(-0.418017\pi\) |
−0.710100 | + | 0.704101i | \(0.751350\pi\) | |||||||
\(620\) | 15.7561 | − | 27.2903i | 0.632780 | − | 1.09601i | ||||
\(621\) | −7.11300 | − | 12.3201i | −0.285435 | − | 0.494388i | ||||
\(622\) | 20.5426i | 0.823685i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.709679 | − | 0.357329i | 0.0284099 | − | 0.0143046i | ||||
\(625\) | 11.1716 | + | 19.3498i | 0.446865 | + | 0.773994i | ||||
\(626\) | 30.1478 | + | 17.4059i | 1.20495 | + | 0.695678i | ||||
\(627\) | −0.865532 | + | 1.49915i | −0.0345660 | + | 0.0598701i | ||||
\(628\) | −0.121696 | − | 0.210784i | −0.00485620 | − | 0.00841119i | ||||
\(629\) | 9.83456i | 0.392130i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.3591i | − | 1.40762i | −0.710387 | − | 0.703812i | \(-0.751480\pi\) | ||
0.710387 | − | 0.703812i | \(-0.248520\pi\) | |||||||
\(632\) | −19.1373 | + | 11.0489i | −0.761242 | + | 0.439503i | ||||
\(633\) | 13.2591 | − | 22.9655i | 0.527004 | − | 0.912797i | ||||
\(634\) | −7.80892 | + | 13.5254i | −0.310132 | + | 0.537164i | ||||
\(635\) | 24.6596 | − | 14.2372i | 0.978585 | − | 0.564986i | ||||
\(636\) | 75.4903 | 2.99338 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.41699 | 0.0560990 | ||||||||
\(639\) | 8.10065 | − | 4.67691i | 0.320457 | − | 0.185016i | ||||
\(640\) | −19.2884 | + | 33.4086i | −0.762443 | + | 1.32059i | ||||
\(641\) | −10.6188 | + | 18.3923i | −0.419417 | + | 0.726452i | −0.995881 | − | 0.0906706i | \(-0.971099\pi\) |
0.576464 | + | 0.817123i | \(0.304432\pi\) | |||||||
\(642\) | 75.3418 | − | 43.4986i | 2.97351 | − | 1.71675i | ||||
\(643\) | 25.4808i | 1.00486i | 0.864617 | + | 0.502432i | \(0.167561\pi\) | ||||
−0.864617 | + | 0.502432i | \(0.832439\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.2167i | 0.402283i | ||||||||
\(646\) | 3.61154 | + | 6.25537i | 0.142094 | + | 0.246114i | ||||
\(647\) | −11.3928 | + | 19.7329i | −0.447897 | + | 0.775781i | −0.998249 | − | 0.0591522i | \(-0.981160\pi\) |
0.550352 | + | 0.834933i | \(0.314494\pi\) | |||||||
\(648\) | −43.9059 | − | 25.3491i | −1.72479 | − | 0.995806i | ||||
\(649\) | 1.25253 | + | 2.16945i | 0.0491662 | + | 0.0851583i | ||||
\(650\) | −1.79465 | − | 3.56429i | −0.0703919 | − | 0.139803i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32.4669i | 1.27150i | ||||||||
\(653\) | −8.13928 | − | 14.0976i | −0.318515 | − | 0.551684i | 0.661664 | − | 0.749801i | \(-0.269851\pi\) |
−0.980178 | + | 0.198117i | \(0.936517\pi\) | |||||||
\(654\) | −4.90150 | + | 8.48964i | −0.191664 | + | 0.331971i | ||||
\(655\) | 24.6546 | + | 14.2343i | 0.963334 | + | 0.556181i | ||||
\(656\) | 0.407683 | − | 0.235376i | 0.0159173 | − | 0.00918988i | ||||
\(657\) | − | 82.2790i | − | 3.21001i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.5596 | 0.800888 | 0.400444 | − | 0.916321i | \(-0.368856\pi\) | ||||
0.400444 | + | 0.916321i | \(0.368856\pi\) | |||||||
\(660\) | 3.32513 | + | 5.75929i | 0.129430 | + | 0.224180i | ||||
\(661\) | −24.0518 | − | 13.8863i | −0.935507 | − | 0.540115i | −0.0469576 | − | 0.998897i | \(-0.514953\pi\) |
−0.888549 | + | 0.458782i | \(0.848286\pi\) | |||||||
\(662\) | −15.7818 | + | 27.3349i | −0.613378 | + | 1.06240i | ||||
\(663\) | −16.8542 | − | 11.0603i | −0.654562 | − | 0.429548i | ||||
\(664\) | 31.3101 | 1.21507 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −87.6802 | −3.39754 | ||||||||
\(667\) | 1.15647 | + | 2.00307i | 0.0447789 | + | 0.0775593i | ||||
\(668\) | 16.3149 | + | 9.41941i | 0.631242 | + | 0.364448i | ||||
\(669\) | 37.1303 | + | 21.4372i | 1.43554 | + | 0.828810i | ||||
\(670\) | −53.0425 | + | 30.6241i | −2.04921 | + | 1.18311i | ||||
\(671\) | 1.06135i | 0.0409730i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.20337 | 0.200575 | 0.100288 | − | 0.994958i | \(-0.468024\pi\) | ||||
0.100288 | + | 0.994958i | \(0.468024\pi\) | |||||||
\(674\) | 53.5105 | − | 30.8943i | 2.06115 | − | 1.19000i | ||||
\(675\) | 2.99511 | − | 5.18768i | 0.115282 | − | 0.199674i | ||||
\(676\) | −16.6609 | − | 38.4068i | −0.640803 | − | 1.47718i | ||||
\(677\) | 22.4239 | + | 38.8394i | 0.861821 | + | 1.49272i | 0.870169 | + | 0.492753i | \(0.164009\pi\) |
−0.00834820 | + | 0.999965i | \(0.502657\pi\) | |||||||
\(678\) | − | 67.8070i | − | 2.60411i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.5156 | 0.403254 | ||||||||
\(681\) | 9.82957 | − | 5.67510i | 0.376670 | − | 0.217470i | ||||
\(682\) | 2.81062 | + | 1.62271i | 0.107624 | + | 0.0621370i | ||||
\(683\) | −16.4318 | − | 9.48691i | −0.628745 | − | 0.363006i | 0.151521 | − | 0.988454i | \(-0.451583\pi\) |
−0.780266 | + | 0.625448i | \(0.784916\pi\) | |||||||
\(684\) | −34.4037 | + | 19.8630i | −1.31546 | + | 0.759479i | ||||
\(685\) | −1.06471 | −0.0406807 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 57.9179i | − | 2.20970i | ||||||
\(688\) | −0.0533755 | − | 0.0924491i | −0.00203492 | − | 0.00352459i | ||||
\(689\) | −1.53235 | + | 26.7842i | −0.0583779 | + | 1.02040i | ||||
\(690\) | −8.79840 | + | 15.2393i | −0.334949 | + | 0.580149i | ||||
\(691\) | 32.4085 | − | 18.7111i | 1.23288 | − | 0.711803i | 0.265250 | − | 0.964180i | \(-0.414545\pi\) |
0.967629 | + | 0.252376i | \(0.0812121\pi\) | |||||||
\(692\) | −54.7148 | −2.07994 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44.1229i | 1.67488i | ||||||||
\(695\) | −2.61204 | + | 1.50806i | −0.0990802 | + | 0.0572040i | ||||
\(696\) | 15.2951 | + | 8.83060i | 0.579757 | + | 0.334723i | ||||
\(697\) | −10.3435 | − | 5.97184i | −0.391789 | − | 0.226200i | ||||
\(698\) | 16.1734 | + | 28.0131i | 0.612171 | + | 1.06031i | ||||
\(699\) | 63.8580 | 2.41533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.5513 | 1.60714 | 0.803570 | − | 0.595210i | \(-0.202931\pi\) | ||||
0.803570 | + | 0.595210i | \(0.202931\pi\) | |||||||
\(702\) | 55.8911 | − | 85.1691i | 2.10947 | − | 3.21450i | ||||
\(703\) | −4.93548 | + | 8.54851i | −0.186145 | + | 0.322413i | ||||
\(704\) | −3.46395 | − | 1.99991i | −0.130552 | − | 0.0753745i | ||||
\(705\) | 31.8602 | + | 55.1835i | 1.19993 | + | 2.07833i | ||||
\(706\) | 38.7612 | 1.45880 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 82.3924i | 3.09650i | ||||||||
\(709\) | −43.5889 | + | 25.1661i | −1.63702 | + | 0.945131i | −0.655163 | + | 0.755488i | \(0.727400\pi\) |
−0.981853 | + | 0.189644i | \(0.939267\pi\) | |||||||
\(710\) | −5.67934 | − | 3.27897i | −0.213142 | − | 0.123057i | ||||
\(711\) | 27.4415 | − | 47.5300i | 1.02914 | − | 1.78252i | ||||
\(712\) | 2.31315 | + | 4.00648i | 0.0866888 | + | 0.150149i | ||||
\(713\) | 5.29752i | 0.198394i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11091 | + | 1.06286i | −0.0789435 | + | 0.0397487i | ||||
\(716\) | 24.6384 | + | 42.6749i | 0.920780 | + | 1.59484i | ||||
\(717\) | 56.7760 | + | 32.7796i | 2.12034 | + | 1.22418i | ||||
\(718\) | 26.0049 | − | 45.0418i | 0.970495 | − | 1.68095i | ||||
\(719\) | −14.4616 | − | 25.0482i | −0.539326 | − | 0.934141i | −0.998940 | − | 0.0460219i | \(-0.985346\pi\) |
0.459614 | − | 0.888119i | \(-0.347988\pi\) | |||||||
\(720\) | − | 1.02938i | − | 0.0383625i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 36.1616i | − | 1.34580i | ||||||
\(723\) | 34.6902 | − | 20.0284i | 1.29014 | − | 0.744863i | ||||
\(724\) | 9.41891 | − | 16.3140i | 0.350051 | − | 0.606306i | ||||
\(725\) | −0.486962 | + | 0.843444i | −0.0180853 | + | 0.0313247i | ||||
\(726\) | 67.9782 | − | 39.2472i | 2.52291 | − | 1.45660i | ||||
\(727\) | −19.8593 | −0.736539 | −0.368269 | − | 0.929719i | \(-0.620050\pi\) | ||||
−0.368269 | + | 0.929719i | \(0.620050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.04209 | 0.334892 | ||||||||
\(730\) | −49.9572 | + | 28.8428i | −1.84900 | + | 1.06752i | ||||
\(731\) | −1.35422 | + | 2.34558i | −0.0500876 | + | 0.0867543i | ||||
\(732\) | −17.4541 | + | 30.2314i | −0.645121 | + | 1.11738i | ||||
\(733\) | 17.6237 | − | 10.1751i | 0.650947 | − | 0.375824i | −0.137872 | − | 0.990450i | \(-0.544026\pi\) |
0.788819 | + | 0.614626i | \(0.210693\pi\) | |||||||
\(734\) | 37.8899i | 1.39854i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 6.59935i | − | 0.243255i | ||||||
\(737\) | −1.94564 | − | 3.36994i | −0.0716684 | − | 0.124133i | ||||
\(738\) | 53.2421 | − | 92.2180i | 1.95987 | − | 3.39459i | ||||
\(739\) | −16.4554 | − | 9.50055i | −0.605323 | − | 0.349483i | 0.165810 | − | 0.986158i | \(-0.446976\pi\) |
−0.771133 | + | 0.636674i | \(0.780310\pi\) | |||||||
\(740\) | 18.9607 | + | 32.8409i | 0.697009 | + | 1.20726i | ||||
\(741\) | −9.09954 | − | 18.0723i | −0.334280 | − | 0.663902i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.15098i | − | 0.299030i | −0.988759 | − | 0.149515i | \(-0.952229\pi\) | ||
0.988759 | − | 0.149515i | \(-0.0477713\pi\) | |||||||
\(744\) | 20.2254 | + | 35.0314i | 0.741498 | + | 1.28431i | ||||
\(745\) | 22.4090 | − | 38.8134i | 0.821000 | − | 1.42201i | ||||
\(746\) | 54.7035 | + | 31.5831i | 2.00284 | + | 1.15634i | ||||
\(747\) | −67.3445 | + | 38.8814i | −2.46401 | + | 1.42260i | ||||
\(748\) | 1.76297i | 0.0644607i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −83.8893 | −3.06320 | ||||||||
\(751\) | 18.3713 | + | 31.8201i | 0.670379 | + | 1.16113i | 0.977797 | + | 0.209556i | \(0.0672020\pi\) |
−0.307417 | + | 0.951575i | \(0.599465\pi\) | |||||||
\(752\) | −0.576595 | − | 0.332897i | −0.0210262 | − | 0.0121395i | ||||
\(753\) | 21.6490 | − | 37.4972i | 0.788934 | − | 1.36647i | ||||
\(754\) | −9.08711 | + | 13.8473i | −0.330933 | + | 0.504289i | ||||
\(755\) | 37.1963 | 1.35371 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.3971 | 1.39557 | 0.697783 | − | 0.716310i | \(-0.254170\pi\) | ||||
0.697783 | + | 0.716310i | \(0.254170\pi\) | |||||||
\(758\) | −10.5584 | − | 18.2878i | −0.383500 | − | 0.664241i | ||||
\(759\) | −0.968195 | − | 0.558987i | −0.0351432 | − | 0.0202900i | ||||
\(760\) | 9.14048 | + | 5.27726i | 0.331560 | + | 0.191426i | ||||
\(761\) | −10.7922 | + | 6.23089i | −0.391218 | + | 0.225870i | −0.682688 | − | 0.730710i | \(-0.739189\pi\) |
0.291470 | + | 0.956580i | \(0.405856\pi\) | |||||||
\(762\) | 96.4533i | 3.49414i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 86.3636 | 3.12453 | ||||||||
\(765\) | −22.6178 | + | 13.0584i | −0.817749 | + | 0.472128i | ||||
\(766\) | −8.73742 | + | 15.1336i | −0.315696 | + | 0.546801i | ||||
\(767\) | −29.2331 | − | 1.67245i | −1.05555 | − | 0.0603888i | ||||
\(768\) | −24.4860 | − | 42.4110i | −0.883562 | − | 1.53037i | ||||
\(769\) | 4.81390i | 0.173594i | 0.996226 | + | 0.0867969i | \(0.0276631\pi\) | ||||
−0.996226 | + | 0.0867969i | \(0.972337\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.1075 | 0.832196 | ||||||||
\(772\) | 0.596785 | − | 0.344554i | 0.0214787 | − | 0.0124008i | ||||
\(773\) | −24.4863 | − | 14.1372i | −0.880713 | − | 0.508480i | −0.00981931 | − | 0.999952i | \(-0.503126\pi\) |
−0.870893 | + | 0.491472i | \(0.836459\pi\) | |||||||
\(774\) | −20.9120 | − | 12.0736i | −0.751668 | − | 0.433975i | ||||
\(775\) | −1.93180 | + | 1.11533i | −0.0693923 | + | 0.0400637i | ||||
\(776\) | 21.3764 | 0.767369 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.9367i | 0.535505i | ||||||||
\(779\) | −5.99395 | − | 10.3818i | −0.214755 | − | 0.371967i | ||||
\(780\) | −77.6057 | − | 4.43990i | −2.77873 | − | 0.158974i | ||||
\(781\) | 0.208322 | − | 0.360825i | 0.00745436 | − | 0.0129113i | ||||
\(782\) | −4.03991 | + | 2.33244i | −0.144467 | + | 0.0834081i | ||||
\(783\) | −24.8619 | −0.888492 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 0.160604i | − | 0.00573222i | ||||||
\(786\) | −83.5141 | + | 48.2169i | −2.97885 | + | 1.71984i | ||||
\(787\) | −43.0053 | − | 24.8291i | −1.53297 | − | 0.885062i | −0.999223 | − | 0.0394193i | \(-0.987449\pi\) |
−0.533749 | − | 0.845643i | \(-0.679217\pi\) | |||||||
\(788\) | −31.3169 | − | 18.0808i | −1.11562 | − | 0.644102i | ||||
\(789\) | −10.5206 | − | 18.2222i | −0.374543 | − | 0.648728i | ||||
\(790\) | −38.4783 | −1.36900 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.95633 | −0.211649 | ||||||||
\(793\) | −10.3719 | − | 6.80642i | −0.368316 | − | 0.241703i | ||||
\(794\) | 33.0507 | − | 57.2455i | 1.17292 | − | 2.03157i | ||||
\(795\) | 43.1393 | + | 24.9065i | 1.52999 | + | 0.883341i | ||||
\(796\) | 32.8801 | + | 56.9501i | 1.16541 | + | 2.01854i | ||||
\(797\) | 5.37263 | 0.190308 | 0.0951542 | − | 0.995463i | \(-0.469666\pi\) | ||||
0.0951542 | + | 0.995463i | \(0.469666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8922i | 0.597604i | ||||||||
\(800\) | 2.40653 | − | 1.38941i | 0.0850837 | − | 0.0491231i | ||||
\(801\) | −9.95062 | − | 5.74500i | −0.351588 | − | 0.202989i | ||||
\(802\) | −30.5517 | + | 52.9170i | −1.07882 | + | 1.86857i | ||||
\(803\) | −1.83246 | − | 3.17392i | −0.0646663 | − | 0.112005i | ||||
\(804\) | − | 127.985i | − | 4.51369i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −33.8822 | + | 17.0600i | −1.19345 | + | 0.600912i | ||||
\(807\) | −25.5582 | − | 44.2681i | −0.899692 | − | 1.55831i | ||||
\(808\) | −22.0160 | − | 12.7109i | −0.774520 | − | 0.447169i | ||||
\(809\) | −20.6184 | + | 35.7122i | −0.724905 | + | 1.25557i | 0.234107 | + | 0.972211i | \(0.424783\pi\) |
−0.959013 | + | 0.283362i | \(0.908550\pi\) | |||||||
\(810\) | −44.1395 | − | 76.4518i | −1.55090 | − | 2.68624i | ||||
\(811\) | 19.4366i | 0.682512i | 0.939970 | + | 0.341256i | \(0.110852\pi\) | ||||
−0.939970 | + | 0.341256i | \(0.889148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 59.0328i | 2.07037i | ||||||||
\(814\) | −3.38227 | + | 1.95276i | −0.118549 | + | 0.0684441i | ||||
\(815\) | −10.7118 | + | 18.5533i | −0.375217 | + | 0.649895i | ||||
\(816\) | 0.195551 | − | 0.338704i | 0.00684564 | − | 0.0118570i | ||||
\(817\) | −2.35426 | + | 1.35923i | −0.0823651 | + | 0.0475535i | ||||
\(818\) | −79.4486 | −2.77785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46.0540 | −1.60828 | ||||||||
\(821\) | 17.4856 | − | 10.0953i | 0.610251 | − | 0.352329i | −0.162813 | − | 0.986657i | \(-0.552057\pi\) |
0.773064 | + | 0.634328i | \(0.218723\pi\) | |||||||
\(822\) | 1.80329 | − | 3.12339i | 0.0628970 | − | 0.108941i | ||||
\(823\) | −21.4049 | + | 37.0743i | −0.746127 | + | 1.29233i | 0.203539 | + | 0.979067i | \(0.434756\pi\) |
−0.949666 | + | 0.313263i | \(0.898578\pi\) | |||||||
\(824\) | 14.5892 | − | 8.42309i | 0.508240 | − | 0.293432i | ||||
\(825\) | − | 0.470751i | − | 0.0163895i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.5376i | 1.16622i | 0.812394 | + | 0.583109i | \(0.198164\pi\) | ||||
−0.812394 | + | 0.583109i | \(0.801836\pi\) | |||||||
\(828\) | −12.8281 | − | 22.2189i | −0.445808 | − | 0.772162i | ||||
\(829\) | 19.8949 | − | 34.4590i | 0.690978 | − | 1.19681i | −0.280540 | − | 0.959842i | \(-0.590513\pi\) |
0.971518 | − | 0.236967i | \(-0.0761533\pi\) | |||||||
\(830\) | 47.2150 | + | 27.2596i | 1.63886 | + | 0.946195i | ||||
\(831\) | −47.3077 | − | 81.9394i | −1.64109 | − | 2.84245i | ||||
\(832\) | 41.7581 | − | 21.0255i | 1.44770 | − | 0.728929i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | − | 10.2167i | − | 0.353776i | ||||||
\(835\) | 6.21548 | + | 10.7655i | 0.215096 | + | 0.372556i | ||||
\(836\) | −0.884750 | + | 1.53243i | −0.0305997 | + | 0.0530003i | ||||
\(837\) | −49.3142 | − | 28.4715i | −1.70455 | − | 0.984120i | ||||
\(838\) | −8.29564 | + | 4.78949i | −0.286568 | + | 0.165450i | ||||
\(839\) | 36.7098i | 1.26736i | 0.773594 | + | 0.633682i | \(0.218457\pi\) | ||||
−0.773594 | + | 0.633682i | \(0.781543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.9578 | −0.860614 | ||||||||
\(842\) | −23.9364 | − | 41.4591i | −0.824903 | − | 1.42877i | ||||
\(843\) | −6.08599 | − | 3.51375i | −0.209613 | − | 0.121020i | ||||
\(844\) | 13.5535 | − | 23.4754i | 0.466532 | − | 0.808058i | ||||
\(845\) | 3.15058 | − | 27.4446i | 0.108383 | − | 0.944124i | ||||
\(846\) | −150.603 | −5.17783 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.520479 | −0.0178733 | ||||||||
\(849\) | 21.6993 | + | 37.5842i | 0.744717 | + | 1.28989i | ||||
\(850\) | −1.70111 | − | 0.982134i | −0.0583475 | − | 0.0336869i | ||||
\(851\) | −5.52089 | − | 3.18749i | −0.189254 | − | 0.109266i | ||||
\(852\) | 11.8676 | − | 6.85179i | 0.406579 | − | 0.234738i | ||||
\(853\) | − | 11.7156i | − | 0.401136i | −0.979680 | − | 0.200568i | \(-0.935721\pi\) | ||
0.979680 | − | 0.200568i | \(-0.0642788\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −26.2135 | −0.896483 | ||||||||
\(856\) | 29.1850 | − | 16.8500i | 0.997523 | − | 0.575920i | ||||
\(857\) | 13.8453 | − | 23.9807i | 0.472945 | − | 0.819164i | −0.526576 | − | 0.850128i | \(-0.676524\pi\) |
0.999521 | + | 0.0309639i | \(0.00985769\pi\) | |||||||
\(858\) | 0.457264 | − | 7.99259i | 0.0156107 | − | 0.272863i | ||||
\(859\) | −19.2819 | − | 33.3972i | −0.657890 | − | 1.13950i | −0.981161 | − | 0.193192i | \(-0.938116\pi\) |
0.323271 | − | 0.946306i | \(-0.395217\pi\) | |||||||
\(860\) | 10.4436i | 0.356122i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −38.6002 | −1.31473 | ||||||||
\(863\) | 15.4613 | − | 8.92660i | 0.526310 | − | 0.303865i | −0.213203 | − | 0.977008i | \(-0.568389\pi\) |
0.739512 | + | 0.673143i | \(0.235056\pi\) | |||||||
\(864\) | 61.4329 | + | 35.4683i | 2.08999 | + | 1.20666i | ||||
\(865\) | −31.2670 | − | 18.0520i | −1.06311 | − | 0.613787i | ||||
\(866\) | 6.77195 | − | 3.90979i | 0.230120 | − | 0.132860i | ||||
\(867\) | 43.6343 | 1.48190 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.44464i | − | 0.0829286i | ||||||
\(870\) | 15.3764 | + | 26.6327i | 0.521310 | + | 0.902935i | ||||
\(871\) | 45.4096 | + | 2.59793i | 1.53864 | + | 0.0880274i | ||||
\(872\) | −1.89868 | + | 3.28861i | −0.0642975 | + | 0.111366i | ||||
\(873\) | −45.9783 | + | 26.5456i | −1.55613 | + | 0.898431i | ||||
\(874\) | −4.68216 | −0.158376 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 120.541i | − | 4.07270i | ||||||
\(877\) | −7.72524 | + | 4.46017i | −0.260863 | + | 0.150609i | −0.624728 | − | 0.780842i | \(-0.714790\pi\) |
0.363865 | + | 0.931452i | \(0.381457\pi\) | |||||||
\(878\) | 35.7454 | + | 20.6376i | 1.20635 | + | 0.696487i | ||||
\(879\) | −2.76194 | − | 1.59461i | −0.0931580 | − | 0.0537848i | ||||
\(880\) | −0.0229256 | − | 0.0397083i | −0.000772821 | − | 0.00133857i | ||||
\(881\) | −54.6144 | −1.84001 | −0.920003 | − | 0.391911i | \(-0.871814\pi\) | ||||
−0.920003 | + | 0.391911i | \(0.871814\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.51632 | −0.252944 | −0.126472 | − | 0.991970i | \(-0.540365\pi\) | ||||
−0.126472 | + | 0.991970i | \(0.540365\pi\) | |||||||
\(884\) | −17.2284 | − | 11.3059i | −0.579454 | − | 0.380259i | ||||
\(885\) | −27.1837 | + | 47.0835i | −0.913770 | + | 1.58270i | ||||
\(886\) | 12.7497 | + | 7.36105i | 0.428335 | + | 0.247299i | ||||
\(887\) | 22.5391 | + | 39.0389i | 0.756790 | + | 1.31080i | 0.944479 | + | 0.328571i | \(0.106567\pi\) |
−0.187689 | + | 0.982229i | \(0.560100\pi\) | |||||||
\(888\) | −48.6780 | −1.63353 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.05560i | 0.270024i | ||||||||
\(891\) | 4.85720 | − | 2.80431i | 0.162722 | − | 0.0939479i | ||||
\(892\) | 37.9547 | + | 21.9132i | 1.27082 | + | 0.733708i | ||||
\(893\) | −8.47737 | + | 14.6832i | −0.283684 | + | 0.491356i | ||||
\(894\) | 75.9074 | + | 131.475i | 2.53872 | + | 4.39720i | ||||
\(895\) | 32.5157i | 1.08688i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.6716 | − | 5.87676i | 0.389705 | − | 0.196219i | ||||
\(898\) | −2.00271 | − | 3.46880i | −0.0668314 | − | 0.115755i | ||||
\(899\) | 8.01779 | + | 4.62907i | 0.267408 | + | 0.154388i | ||||
\(900\) | 5.40160 | − | 9.35584i | 0.180053 | − | 0.311861i | ||||
\(901\) | 6.60268 | + | 11.4362i | 0.219967 | + | 0.380994i | ||||
\(902\) | − | 4.74309i | − | 0.157928i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 26.2662i | − | 0.873602i | ||||||
\(905\) | 10.7650 | − | 6.21515i | 0.357839 | − | 0.206599i | ||||
\(906\) | −62.9988 | + | 109.117i | −2.09299 | + | 3.62517i | ||||
\(907\) | 3.18295 | − | 5.51303i | 0.105688 | − | 0.183057i | −0.808331 | − | 0.588728i | \(-0.799629\pi\) |
0.914019 | + | 0.405671i | \(0.132962\pi\) | |||||||
\(908\) | 10.0478 | − | 5.80111i | 0.333449 | − | 0.192517i | ||||
\(909\) | 63.1385 | 2.09417 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.9161 | 0.692982 | 0.346491 | − | 0.938053i | \(-0.387373\pi\) | ||||
0.346491 | + | 0.938053i | \(0.387373\pi\) | |||||||
\(912\) | 0.339958 | − | 0.196275i | 0.0112571 | − | 0.00649930i | ||||
\(913\) | −1.73188 | + | 2.99971i | −0.0573169 | + | 0.0992758i | ||||
\(914\) | 37.3681 | − | 64.7234i | 1.23603 | − | 2.14086i | ||||
\(915\) | −19.9484 | + | 11.5172i | −0.659475 | + | 0.380748i | ||||
\(916\) | − | 59.2038i | − | 1.95615i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 50.1430i | − | 1.65496i | ||||||
\(919\) | −2.44326 | − | 4.23185i | −0.0805957 | − | 0.139596i | 0.822910 | − | 0.568171i | \(-0.192349\pi\) |
−0.903506 | + | 0.428576i | \(0.859016\pi\) | |||||||
\(920\) | −3.40821 | + | 5.90320i | −0.112366 | + | 0.194623i | ||||
\(921\) | 65.6239 | + | 37.8880i | 2.16238 | + | 1.24845i | ||||
\(922\) | −8.75816 | − | 15.1696i | −0.288435 | − | 0.499584i | ||||
\(923\) | 2.19014 | + | 4.34976i | 0.0720893 | + | 0.143174i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.68434i | − | 0.0882606i | ||||||
\(926\) | 16.5329 | + | 28.6358i | 0.543305 | + | 0.941031i | ||||
\(927\) | −20.9198 | + | 36.2342i | −0.687098 | + | 1.19009i | ||||
\(928\) | −9.98812 | − | 5.76664i | −0.327876 | − | 0.189299i | ||||
\(929\) | −44.6306 | + | 25.7675i | −1.46428 | + | 0.845404i | −0.999205 | − | 0.0398663i | \(-0.987307\pi\) |
−0.465077 | + | 0.885270i | \(0.653973\pi\) | |||||||
\(930\) | 70.4355i | 2.30967i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 65.2759 | 2.13818 | ||||||||
\(933\) | −14.1626 | − | 24.5304i | −0.463664 | − | 0.803090i | ||||
\(934\) | −6.68017 | − | 3.85680i | −0.218582 | − | 0.126198i | ||||
\(935\) | −0.581657 | + | 1.00746i | −0.0190222 | + | 0.0329474i | ||||
\(936\) | 38.1978 | − | 58.2073i | 1.24854 | − | 1.90257i | ||||
\(937\) | −20.3565 | −0.665016 | −0.332508 | − | 0.943100i | \(-0.607895\pi\) | ||||
−0.332508 | + | 0.943100i | \(0.607895\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.0002 | −1.56643 | ||||||||
\(940\) | 32.5676 | + | 56.4088i | 1.06224 | + | 1.83985i | ||||
\(941\) | 29.6730 | + | 17.1317i | 0.967314 | + | 0.558479i | 0.898416 | − | 0.439145i | \(-0.144719\pi\) |
0.0688974 | + | 0.997624i | \(0.478052\pi\) | |||||||
\(942\) | 0.471141 | + | 0.272013i | 0.0153506 | + | 0.00886267i | ||||
\(943\) | 6.70490 | − | 3.87108i | 0.218342 | − | 0.126060i | ||||
\(944\) | − | 0.568067i | − | 0.0184890i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.07558 | −0.0349701 | ||||||||
\(947\) | −47.9046 | + | 27.6578i | −1.55669 | + | 0.898756i | −0.559122 | + | 0.829086i | \(0.688862\pi\) |
−0.997570 | + | 0.0696707i | \(0.977805\pi\) | |||||||
\(948\) | 40.2025 | − | 69.6327i | 1.30572 | − | 2.26156i | ||||
\(949\) | 42.7682 | + | 2.44681i | 1.38832 | + | 0.0794270i | ||||
\(950\) | −0.985770 | − | 1.70740i | −0.0319826 | − | 0.0553955i | ||||
\(951\) | − | 21.5347i | − | 0.698311i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.8378 | −0.480644 | −0.240322 | − | 0.970693i | \(-0.577253\pi\) | ||||
−0.240322 | + | 0.970693i | \(0.577253\pi\) | |||||||
\(954\) | −101.959 | + | 58.8663i | −3.30106 | + | 1.90587i | ||||
\(955\) | 49.3529 | + | 28.4939i | 1.59702 | + | 0.922041i | ||||
\(956\) | 58.0366 | + | 33.5075i | 1.87704 | + | 1.08371i | ||||
\(957\) | −1.69205 | + | 0.976908i | −0.0546964 | + | 0.0315790i | ||||
\(958\) | −0.331812 | −0.0107203 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 86.8081i | − | 2.80172i | ||||||
\(961\) | −4.89769 | − | 8.48305i | −0.157990 | − | 0.273647i | ||||
\(962\) | 2.60744 | − | 45.5758i | 0.0840671 | − | 1.46942i | ||||
\(963\) | −41.8491 | + | 72.4847i | −1.34857 | + | 2.33579i | ||||
\(964\) | 35.4604 | − | 20.4731i | 1.14210 | − | 0.659393i | ||||
\(965\) | 0.454714 | 0.0146378 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.09473i | 0.0995199i | 0.998761 | + | 0.0497600i | \(0.0158456\pi\) | ||||
−0.998761 | + | 0.0497600i | \(0.984154\pi\) | |||||||
\(968\) | 26.3326 | − | 15.2031i | 0.846361 | − | 0.488647i | ||||
\(969\) | −8.62524 | − | 4.97979i | −0.277083 | − | 0.159974i | ||||
\(970\) | 32.2352 | + | 18.6110i | 1.03501 | + | 0.597564i | ||||
\(971\) | 27.4506 | + | 47.5459i | 0.880933 | + | 1.52582i | 0.850305 | + | 0.526290i | \(0.176417\pi\) |
0.0306280 | + | 0.999531i | \(0.490249\pi\) | |||||||
\(972\) | 65.0010 | 2.08491 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 37.5200 | 1.20222 | ||||||||
\(975\) | 4.60035 | + | 3.01892i | 0.147329 | + | 0.0966828i | ||||
\(976\) | 0.120340 | − | 0.208435i | 0.00385198 | − | 0.00667183i | ||||
\(977\) | 37.4196 | + | 21.6042i | 1.19716 | + | 0.691181i | 0.959921 | − | 0.280270i | \(-0.0904242\pi\) |
0.237239 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(978\) | −36.2847 | − | 62.8470i | −1.16026 | − | 2.00962i | ||||
\(979\) | −0.511795 | −0.0163570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 9.43124i | − | 0.301116i | ||||||
\(982\) | 36.0276 | − | 20.8006i | 1.14969 | − | 0.663773i | ||||
\(983\) | −21.5498 | − | 12.4418i | −0.687332 | − | 0.396831i | 0.115280 | − | 0.993333i | \(-0.463224\pi\) |
−0.802612 | + | 0.596502i | \(0.796557\pi\) | |||||||
\(984\) | 29.5588 | − | 51.1973i | 0.942299 | − | 1.63211i | ||||
\(985\) | −11.9308 | − | 20.6647i | −0.380146 | − | 0.658433i | ||||
\(986\) | 8.15254i | 0.259630i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.30158 | − | 18.4735i | −0.295923 | − | 0.587722i | ||||
\(989\) | −0.877834 | − | 1.52045i | −0.0279135 | − | 0.0483476i | ||||
\(990\) | −8.98203 | − | 5.18578i | −0.285468 | − | 0.164815i | ||||
\(991\) | −2.39164 | + | 4.14244i | −0.0759730 | + | 0.131589i | −0.901509 | − | 0.432760i | \(-0.857540\pi\) |
0.825536 | + | 0.564349i | \(0.190873\pi\) | |||||||
\(992\) | −13.2078 | − | 22.8765i | −0.419347 | − | 0.726331i | ||||
\(993\) | − | 43.5216i | − | 1.38112i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43.3925i | 1.37564i | ||||||||
\(996\) | −98.6614 | + | 56.9622i | −3.12621 | + | 1.80492i | ||||
\(997\) | 1.72037 | − | 2.97977i | 0.0544847 | − | 0.0943703i | −0.837497 | − | 0.546442i | \(-0.815982\pi\) |
0.891981 | + | 0.452072i | \(0.149315\pi\) | |||||||
\(998\) | 42.9225 | − | 74.3439i | 1.35869 | − | 2.35331i | ||||
\(999\) | 59.3441 | − | 34.2623i | 1.87756 | − | 1.08401i |
(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 | 637.2.r.f.116.1 | 16 | ||
7.2 | even | 3 | inner | 637.2.r.f.324.8 | 16 | ||
7.3 | odd | 6 | 637.2.c.f.246.1 | 8 | |||
7.4 | even | 3 | 637.2.c.e.246.1 | 8 | |||
7.5 | odd | 6 | 91.2.r.a.51.8 | yes | 16 | ||
7.6 | odd | 2 | 91.2.r.a.25.1 | ✓ | 16 | ||
13.12 | even | 2 | inner | 637.2.r.f.116.8 | 16 | ||
21.5 | even | 6 | 819.2.dl.e.415.1 | 16 | |||
21.20 | even | 2 | 819.2.dl.e.298.8 | 16 | |||
91.5 | even | 12 | 1183.2.e.i.170.8 | 16 | |||
91.12 | odd | 6 | 91.2.r.a.51.1 | yes | 16 | ||
91.18 | odd | 12 | 8281.2.a.cj.1.1 | 8 | |||
91.25 | even | 6 | 637.2.c.e.246.8 | 8 | |||
91.31 | even | 12 | 8281.2.a.ck.1.1 | 8 | |||
91.34 | even | 4 | 1183.2.e.i.508.1 | 16 | |||
91.38 | odd | 6 | 637.2.c.f.246.8 | 8 | |||
91.47 | even | 12 | 1183.2.e.i.170.1 | 16 | |||
91.51 | even | 6 | inner | 637.2.r.f.324.1 | 16 | ||
91.60 | odd | 12 | 8281.2.a.cj.1.8 | 8 | |||
91.73 | even | 12 | 8281.2.a.ck.1.8 | 8 | |||
91.83 | even | 4 | 1183.2.e.i.508.8 | 16 | |||
91.90 | odd | 2 | 91.2.r.a.25.8 | yes | 16 | ||
273.194 | even | 6 | 819.2.dl.e.415.8 | 16 | |||
273.272 | even | 2 | 819.2.dl.e.298.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.r.a.25.1 | ✓ | 16 | 7.6 | odd | 2 | ||
91.2.r.a.25.8 | yes | 16 | 91.90 | odd | 2 | ||
91.2.r.a.51.1 | yes | 16 | 91.12 | odd | 6 | ||
91.2.r.a.51.8 | yes | 16 | 7.5 | odd | 6 | ||
637.2.c.e.246.1 | 8 | 7.4 | even | 3 | |||
637.2.c.e.246.8 | 8 | 91.25 | even | 6 | |||
637.2.c.f.246.1 | 8 | 7.3 | odd | 6 | |||
637.2.c.f.246.8 | 8 | 91.38 | odd | 6 | |||
637.2.r.f.116.1 | 16 | 1.1 | even | 1 | trivial | ||
637.2.r.f.116.8 | 16 | 13.12 | even | 2 | inner | ||
637.2.r.f.324.1 | 16 | 91.51 | even | 6 | inner | ||
637.2.r.f.324.8 | 16 | 7.2 | even | 3 | inner | ||
819.2.dl.e.298.1 | 16 | 273.272 | even | 2 | |||
819.2.dl.e.298.8 | 16 | 21.20 | even | 2 | |||
819.2.dl.e.415.1 | 16 | 21.5 | even | 6 | |||
819.2.dl.e.415.8 | 16 | 273.194 | even | 6 | |||
1183.2.e.i.170.1 | 16 | 91.47 | even | 12 | |||
1183.2.e.i.170.8 | 16 | 91.5 | even | 12 | |||
1183.2.e.i.508.1 | 16 | 91.34 | even | 4 | |||
1183.2.e.i.508.8 | 16 | 91.83 | even | 4 | |||
8281.2.a.cj.1.1 | 8 | 91.18 | odd | 12 | |||
8281.2.a.cj.1.8 | 8 | 91.60 | odd | 12 | |||
8281.2.a.ck.1.1 | 8 | 91.31 | even | 12 | |||
8281.2.a.ck.1.8 | 8 | 91.73 | even | 12 |