Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 313.5 | ||
Character | \(\chi\) | \(=\) | 735.313 |
Dual form | 735.2.v.a.472.5 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.197706 | + | 0.737849i | 0.139799 | + | 0.521738i | 0.999932 | + | 0.0116677i | \(0.00371404\pi\) |
−0.860133 | + | 0.510071i | \(0.829619\pi\) | |||||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | 1.22672 | − | 0.708245i | 0.613358 | − | 0.354123i | ||||
\(5\) | 2.23413 | + | 0.0930365i | 0.999134 | + | 0.0416072i | ||||
\(6\) | − | 0.763878i | − | 0.311852i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.84539 | + | 1.84539i | 0.652445 | + | 0.652445i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0.373055 | + | 1.66685i | 0.117970 | + | 0.527103i | ||||
\(11\) | 1.92568 | + | 3.33538i | 0.580615 | + | 1.00565i | 0.995407 | + | 0.0957376i | \(0.0305210\pi\) |
−0.414792 | + | 0.909916i | \(0.636146\pi\) | |||||||
\(12\) | −1.36822 | + | 0.366615i | −0.394973 | + | 0.105833i | ||||
\(13\) | −3.66816 | + | 3.66816i | −1.01737 | + | 1.01737i | −0.0175187 | + | 0.999847i | \(0.505577\pi\) |
−0.999847 | + | 0.0175187i | \(0.994423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.13393 | − | 0.668102i | −0.550977 | − | 0.172503i | ||||
\(16\) | 0.419714 | − | 0.726965i | 0.104928 | − | 0.181741i | ||||
\(17\) | 0.545404 | − | 2.03548i | 0.132280 | − | 0.493675i | −0.867714 | − | 0.497063i | \(-0.834412\pi\) |
0.999994 | + | 0.00338789i | \(0.00107840\pi\) | |||||||
\(18\) | −0.197706 | + | 0.737849i | −0.0465998 | + | 0.173913i | ||||
\(19\) | −0.0348837 | + | 0.0604203i | −0.00800286 | + | 0.0138614i | −0.869999 | − | 0.493053i | \(-0.835881\pi\) |
0.861996 | + | 0.506915i | \(0.169214\pi\) | |||||||
\(20\) | 2.80654 | − | 1.46818i | 0.627561 | − | 0.328296i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.08029 | + | 2.08029i | −0.443519 | + | 0.443519i | ||||
\(23\) | 0.729698 | − | 0.195522i | 0.152153 | − | 0.0407692i | −0.181939 | − | 0.983310i | \(-0.558237\pi\) |
0.334091 | + | 0.942541i | \(0.391571\pi\) | |||||||
\(24\) | −1.30489 | − | 2.26014i | −0.266360 | − | 0.461349i | ||||
\(25\) | 4.98269 | + | 0.415712i | 0.996538 | + | 0.0831423i | ||||
\(26\) | −3.43177 | − | 1.98133i | −0.673025 | − | 0.388571i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.77107i | − | 0.514576i | −0.966335 | − | 0.257288i | \(-0.917171\pi\) | ||
0.966335 | − | 0.257288i | \(-0.0828288\pi\) | |||||||
\(30\) | 0.0710685 | − | 1.70660i | 0.0129753 | − | 0.311582i | ||||
\(31\) | 2.07564 | − | 1.19837i | 0.372795 | − | 0.215233i | −0.301884 | − | 0.953345i | \(-0.597615\pi\) |
0.674679 | + | 0.738111i | \(0.264282\pi\) | |||||||
\(32\) | 5.66108 | + | 1.51688i | 1.00075 | + | 0.268149i | ||||
\(33\) | −0.996806 | − | 3.72013i | −0.173522 | − | 0.647591i | ||||
\(34\) | 1.60970 | 0.276062 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.41649 | 0.236082 | ||||||||
\(37\) | 2.26481 | + | 8.45237i | 0.372332 | + | 1.38956i | 0.857204 | + | 0.514976i | \(0.172199\pi\) |
−0.484872 | + | 0.874585i | \(0.661134\pi\) | |||||||
\(38\) | −0.0514778 | − | 0.0137934i | −0.00835080 | − | 0.00223759i | ||||
\(39\) | 4.49256 | − | 2.59378i | 0.719386 | − | 0.415338i | ||||
\(40\) | 3.95116 | + | 4.29454i | 0.624734 | + | 0.679027i | ||||
\(41\) | − | 8.68077i | − | 1.35571i | −0.735196 | − | 0.677854i | \(-0.762910\pi\) | ||
0.735196 | − | 0.677854i | \(-0.237090\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.77107 | − | 2.77107i | −0.422585 | − | 0.422585i | 0.463508 | − | 0.886093i | \(-0.346591\pi\) |
−0.886093 | + | 0.463508i | \(0.846591\pi\) | |||||||
\(44\) | 4.72453 | + | 2.72771i | 0.712250 | + | 0.411218i | ||||
\(45\) | 1.88830 | + | 1.19764i | 0.281491 | + | 0.178533i | ||||
\(46\) | 0.288532 | + | 0.499752i | 0.0425417 | + | 0.0736843i | ||||
\(47\) | −7.50006 | + | 2.00963i | −1.09400 | + | 0.293135i | −0.760317 | − | 0.649552i | \(-0.774957\pi\) |
−0.333678 | + | 0.942687i | \(0.608290\pi\) | |||||||
\(48\) | −0.593565 | + | 0.593565i | −0.0856737 | + | 0.0856737i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.678376 | + | 3.75866i | 0.0959368 | + | 0.531555i | ||||
\(51\) | −1.05364 | + | 1.82496i | −0.147539 | + | 0.255545i | ||||
\(52\) | −1.90184 | + | 7.09776i | −0.263737 | + | 0.984282i | ||||
\(53\) | 2.24675 | − | 8.38498i | 0.308615 | − | 1.15177i | −0.621174 | − | 0.783673i | \(-0.713344\pi\) |
0.929789 | − | 0.368093i | \(-0.119989\pi\) | |||||||
\(54\) | 0.381939 | − | 0.661538i | 0.0519753 | − | 0.0900239i | ||||
\(55\) | 3.99191 | + | 7.63083i | 0.538269 | + | 1.02894i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0493330 | − | 0.0493330i | 0.00653431 | − | 0.00653431i | ||||
\(58\) | 2.04464 | − | 0.547858i | 0.268474 | − | 0.0719373i | ||||
\(59\) | 3.48720 | + | 6.04001i | 0.453995 | + | 0.786342i | 0.998630 | − | 0.0523310i | \(-0.0166651\pi\) |
−0.544635 | + | 0.838673i | \(0.683332\pi\) | |||||||
\(60\) | −3.09090 | + | 0.691771i | −0.399034 | + | 0.0893072i | ||||
\(61\) | 12.3935 | + | 7.15536i | 1.58682 | + | 0.916150i | 0.993827 | + | 0.110942i | \(0.0353869\pi\) |
0.592992 | + | 0.805208i | \(0.297946\pi\) | |||||||
\(62\) | 1.29458 | + | 1.29458i | 0.164412 | + | 0.164412i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.79807i | 0.349758i | ||||||||
\(65\) | −8.53643 | + | 7.85389i | −1.05881 | + | 0.974155i | ||||
\(66\) | 2.54782 | − | 1.47098i | 0.313615 | − | 0.181066i | ||||
\(67\) | −0.568937 | − | 0.152446i | −0.0695067 | − | 0.0186243i | 0.223898 | − | 0.974613i | \(-0.428122\pi\) |
−0.293405 | + | 0.955988i | \(0.594788\pi\) | |||||||
\(68\) | −0.772560 | − | 2.88323i | −0.0936866 | − | 0.349643i | ||||
\(69\) | −0.755439 | −0.0909442 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.12783 | −0.964595 | −0.482298 | − | 0.876007i | \(-0.660198\pi\) | ||||
−0.482298 | + | 0.876007i | \(0.660198\pi\) | |||||||
\(72\) | 0.675461 | + | 2.52086i | 0.0796039 | + | 0.297086i | ||||
\(73\) | −13.0484 | − | 3.49631i | −1.52720 | − | 0.409212i | −0.605096 | − | 0.796152i | \(-0.706865\pi\) |
−0.922105 | + | 0.386940i | \(0.873532\pi\) | |||||||
\(74\) | −5.78881 | + | 3.34217i | −0.672936 | + | 0.388520i | ||||
\(75\) | −4.70531 | − | 1.69116i | −0.543323 | − | 0.195278i | ||||
\(76\) | 0.0988248i | 0.0113360i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.80203 | + | 2.80203i | 0.317267 | + | 0.317267i | ||||
\(79\) | −8.54186 | − | 4.93165i | −0.961035 | − | 0.554854i | −0.0645434 | − | 0.997915i | \(-0.520559\pi\) |
−0.896491 | + | 0.443061i | \(0.853892\pi\) | |||||||
\(80\) | 1.00533 | − | 1.58509i | 0.112399 | − | 0.177218i | ||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.40510 | − | 1.71624i | 0.707325 | − | 0.189527i | ||||
\(83\) | 1.63570 | − | 1.63570i | 0.179541 | − | 0.179541i | −0.611615 | − | 0.791156i | \(-0.709480\pi\) |
0.791156 | + | 0.611615i | \(0.209480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40788 | − | 4.49678i | 0.152706 | − | 0.487744i | ||||
\(86\) | 1.49678 | − | 2.59249i | 0.161402 | − | 0.279556i | ||||
\(87\) | −0.717207 | + | 2.67665i | −0.0768926 | + | 0.286967i | ||||
\(88\) | −2.60144 | + | 9.70872i | −0.277315 | + | 1.03495i | ||||
\(89\) | 2.52657 | − | 4.37614i | 0.267815 | − | 0.463870i | −0.700482 | − | 0.713670i | \(-0.747032\pi\) |
0.968297 | + | 0.249800i | \(0.0803649\pi\) | |||||||
\(90\) | −0.510348 | + | 1.63006i | −0.0537954 | + | 0.171823i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.756656 | − | 0.756656i | 0.0788868 | − | 0.0788868i | ||||
\(93\) | −2.31507 | + | 0.620321i | −0.240062 | + | 0.0643243i | ||||
\(94\) | −2.96561 | − | 5.13659i | −0.305880 | − | 0.529799i | ||||
\(95\) | −0.0835560 | + | 0.131741i | −0.00857267 | + | 0.0135164i | ||||
\(96\) | −5.07559 | − | 2.93039i | −0.518025 | − | 0.299082i | ||||
\(97\) | 6.85851 | + | 6.85851i | 0.696376 | + | 0.696376i | 0.963627 | − | 0.267251i | \(-0.0861152\pi\) |
−0.267251 | + | 0.963627i | \(0.586115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.85136i | 0.387076i | ||||||||
\(100\) | 6.40677 | − | 3.01901i | 0.640677 | − | 0.301901i | ||||
\(101\) | 16.6236 | − | 9.59763i | 1.65411 | − | 0.955000i | 0.678752 | − | 0.734368i | \(-0.262521\pi\) |
0.975357 | − | 0.220632i | \(-0.0708121\pi\) | |||||||
\(102\) | −1.55485 | − | 0.416622i | −0.153954 | − | 0.0412517i | ||||
\(103\) | 0.855857 | + | 3.19410i | 0.0843301 | + | 0.314724i | 0.995186 | − | 0.0979992i | \(-0.0312443\pi\) |
−0.910856 | + | 0.412723i | \(0.864578\pi\) | |||||||
\(104\) | −13.5384 | −1.32755 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.63105 | 0.644064 | ||||||||
\(107\) | −2.34164 | − | 8.73911i | −0.226375 | − | 0.844841i | −0.981849 | − | 0.189663i | \(-0.939260\pi\) |
0.755475 | − | 0.655178i | \(-0.227406\pi\) | |||||||
\(108\) | −1.36822 | − | 0.366615i | −0.131658 | − | 0.0352775i | ||||
\(109\) | 1.87111 | − | 1.08029i | 0.179220 | − | 0.103473i | −0.407706 | − | 0.913113i | \(-0.633671\pi\) |
0.586926 | + | 0.809641i | \(0.300338\pi\) | |||||||
\(110\) | −4.84118 | + | 4.45409i | −0.461588 | + | 0.424681i | ||||
\(111\) | − | 8.75054i | − | 0.830564i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.13823 | − | 4.13823i | −0.389292 | − | 0.389292i | 0.485143 | − | 0.874435i | \(-0.338768\pi\) |
−0.874435 | + | 0.485143i | \(0.838768\pi\) | |||||||
\(114\) | 0.0461537 | + | 0.0266469i | 0.00432269 | + | 0.00249571i | ||||
\(115\) | 1.64843 | − | 0.368934i | 0.153717 | − | 0.0344032i | ||||
\(116\) | −1.96260 | − | 3.39932i | −0.182223 | − | 0.315619i | ||||
\(117\) | −5.01080 | + | 1.34264i | −0.463249 | + | 0.124127i | ||||
\(118\) | −3.76718 | + | 3.76718i | −0.346797 | + | 0.346797i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.70502 | − | 5.17085i | −0.246934 | − | 0.472032i | ||||
\(121\) | −1.91649 | + | 3.31946i | −0.174226 | + | 0.301769i | ||||
\(122\) | −2.82932 | + | 10.5592i | −0.256154 | + | 0.955981i | ||||
\(123\) | −2.24675 | + | 8.38498i | −0.202583 | + | 0.756048i | ||||
\(124\) | 1.69748 | − | 2.94012i | 0.152438 | − | 0.264030i | ||||
\(125\) | 11.0933 | + | 1.39233i | 0.992215 | + | 0.124533i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.83298 | + | 4.83298i | −0.428858 | + | 0.428858i | −0.888239 | − | 0.459381i | \(-0.848071\pi\) |
0.459381 | + | 0.888239i | \(0.348071\pi\) | |||||||
\(128\) | 9.25761 | − | 2.48057i | 0.818265 | − | 0.219253i | ||||
\(129\) | 1.95945 | + | 3.39386i | 0.172520 | + | 0.298813i | ||||
\(130\) | −7.48269 | − | 4.74584i | −0.656275 | − | 0.416238i | ||||
\(131\) | 0.560750 | + | 0.323749i | 0.0489930 | + | 0.0282861i | 0.524296 | − | 0.851536i | \(-0.324328\pi\) |
−0.475303 | + | 0.879822i | \(0.657662\pi\) | |||||||
\(132\) | −3.85756 | − | 3.85756i | −0.335758 | − | 0.335758i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.449929i | − | 0.0388680i | ||||||
\(135\) | −1.51398 | − | 1.64556i | −0.130303 | − | 0.141627i | ||||
\(136\) | 4.76274 | − | 2.74977i | 0.408402 | − | 0.235791i | ||||
\(137\) | −13.9839 | − | 3.74696i | −1.19472 | − | 0.320125i | −0.393971 | − | 0.919123i | \(-0.628899\pi\) |
−0.800751 | + | 0.598998i | \(0.795566\pi\) | |||||||
\(138\) | −0.149355 | − | 0.557400i | −0.0127139 | − | 0.0474491i | ||||
\(139\) | −22.1663 | −1.88012 | −0.940060 | − | 0.341009i | \(-0.889231\pi\) | ||||
−0.940060 | + | 0.341009i | \(0.889231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.76463 | 0.653900 | ||||||||
\(142\) | −1.60692 | − | 5.99711i | −0.134850 | − | 0.503266i | ||||
\(143\) | −19.2984 | − | 5.17099i | −1.61381 | − | 0.432420i | ||||
\(144\) | 0.726965 | − | 0.419714i | 0.0605804 | − | 0.0349761i | ||||
\(145\) | 0.257811 | − | 6.19095i | 0.0214100 | − | 0.514130i | ||||
\(146\) | − | 10.3190i | − | 0.854007i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.76463 | + | 8.76463i | 0.720448 | + | 0.720448i | ||||
\(149\) | −9.56745 | − | 5.52377i | −0.783796 | − | 0.452525i | 0.0539779 | − | 0.998542i | \(-0.482810\pi\) |
−0.837774 | + | 0.546017i | \(0.816143\pi\) | |||||||
\(150\) | 0.317553 | − | 3.80617i | 0.0259281 | − | 0.310772i | ||||
\(151\) | −9.19950 | − | 15.9340i | −0.748645 | − | 1.29669i | −0.948472 | − | 0.316859i | \(-0.897372\pi\) |
0.199828 | − | 0.979831i | \(-0.435962\pi\) | |||||||
\(152\) | −0.175873 | + | 0.0471251i | −0.0142652 | + | 0.00382235i | ||||
\(153\) | 1.49007 | − | 1.49007i | 0.120465 | − | 0.120465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.74873 | − | 2.48420i | 0.381428 | − | 0.199536i | ||||
\(156\) | 3.67407 | − | 6.36367i | 0.294161 | − | 0.509502i | ||||
\(157\) | −0.384306 | + | 1.43425i | −0.0306709 | + | 0.114465i | −0.979564 | − | 0.201132i | \(-0.935538\pi\) |
0.948893 | + | 0.315597i | \(0.102205\pi\) | |||||||
\(158\) | 1.95003 | − | 7.27763i | 0.155136 | − | 0.578977i | ||||
\(159\) | −4.34039 | + | 7.51777i | −0.344215 | + | 0.596198i | ||||
\(160\) | 12.5065 | + | 3.91560i | 0.988724 | + | 0.309555i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.540143 | + | 0.540143i | −0.0424377 | + | 0.0424377i | ||||
\(163\) | −7.52050 | + | 2.01511i | −0.589051 | + | 0.157836i | −0.541020 | − | 0.841010i | \(-0.681962\pi\) |
−0.0480317 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(164\) | −6.14812 | − | 10.6488i | −0.480087 | − | 0.831535i | ||||
\(165\) | −1.88089 | − | 8.40400i | −0.146427 | − | 0.654250i | ||||
\(166\) | 1.53028 | + | 0.883510i | 0.118773 | + | 0.0685737i | ||||
\(167\) | 1.88968 | + | 1.88968i | 0.146228 | + | 0.146228i | 0.776431 | − | 0.630203i | \(-0.217028\pi\) |
−0.630203 | + | 0.776431i | \(0.717028\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.9108i | − | 1.07006i | ||||||
\(170\) | 3.59629 | + | 0.149761i | 0.275823 | + | 0.0114862i | ||||
\(171\) | −0.0604203 | + | 0.0348837i | −0.00462046 | + | 0.00266762i | ||||
\(172\) | −5.36192 | − | 1.43672i | −0.408843 | − | 0.109549i | ||||
\(173\) | −1.79627 | − | 6.70378i | −0.136568 | − | 0.509679i | −0.999987 | − | 0.00519041i | \(-0.998348\pi\) |
0.863419 | − | 0.504488i | \(-0.168319\pi\) | |||||||
\(174\) | −2.11676 | −0.160471 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.23294 | 0.243692 | ||||||||
\(177\) | −1.80511 | − | 6.73676i | −0.135680 | − | 0.506366i | ||||
\(178\) | 3.72845 | + | 0.999035i | 0.279459 | + | 0.0748808i | ||||
\(179\) | −16.0957 | + | 9.29284i | −1.20305 | + | 0.694579i | −0.961231 | − | 0.275743i | \(-0.911076\pi\) |
−0.241815 | + | 0.970322i | \(0.577743\pi\) | |||||||
\(180\) | 3.16463 | + | 0.131785i | 0.235877 | + | 0.00982270i | ||||
\(181\) | − | 8.48528i | − | 0.630706i | −0.948974 | − | 0.315353i | \(-0.897877\pi\) | ||
0.948974 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.1192 | − | 10.1192i | −0.748034 | − | 0.748034i | ||||
\(184\) | 1.70740 | + | 0.985766i | 0.125871 | + | 0.0726716i | ||||
\(185\) | 4.27350 | + | 19.0944i | 0.314194 | + | 1.40385i | ||||
\(186\) | −0.915407 | − | 1.58553i | −0.0671209 | − | 0.116257i | ||||
\(187\) | 7.83935 | − | 2.10055i | 0.573270 | − | 0.153607i | ||||
\(188\) | −7.77713 | + | 7.77713i | −0.567206 | + | 0.567206i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.113725 | − | 0.0356057i | −0.00825047 | − | 0.00258311i | ||||
\(191\) | 2.69676 | − | 4.67092i | 0.195130 | − | 0.337976i | −0.751813 | − | 0.659377i | \(-0.770820\pi\) |
0.946943 | + | 0.321401i | \(0.104154\pi\) | |||||||
\(192\) | 0.724193 | − | 2.70273i | 0.0522641 | − | 0.195052i | ||||
\(193\) | −1.75911 | + | 6.56510i | −0.126624 | + | 0.472566i | −0.999892 | − | 0.0146728i | \(-0.995329\pi\) |
0.873269 | + | 0.487239i | \(0.161996\pi\) | |||||||
\(194\) | −3.70458 | + | 6.41652i | −0.265973 | + | 0.460679i | ||||
\(195\) | 10.2783 | − | 5.37688i | 0.736044 | − | 0.385046i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6739 | − | 12.6739i | 0.902981 | − | 0.902981i | −0.0927124 | − | 0.995693i | \(-0.529554\pi\) |
0.995693 | + | 0.0927124i | \(0.0295537\pi\) | |||||||
\(198\) | −2.84172 | + | 0.761438i | −0.201953 | + | 0.0541130i | ||||
\(199\) | 1.33556 | + | 2.31325i | 0.0946750 | + | 0.163982i | 0.909473 | − | 0.415763i | \(-0.136485\pi\) |
−0.814798 | + | 0.579745i | \(0.803152\pi\) | |||||||
\(200\) | 8.42787 | + | 9.96218i | 0.595941 | + | 0.704432i | ||||
\(201\) | 0.510095 | + | 0.294503i | 0.0359793 | + | 0.0207727i | ||||
\(202\) | 10.3682 | + | 10.3682i | 0.729503 | + | 0.729503i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.98494i | 0.208988i | ||||||||
\(205\) | 0.807629 | − | 19.3940i | 0.0564072 | − | 1.35453i | ||||
\(206\) | −2.18756 | + | 1.26299i | −0.152414 | + | 0.0879965i | ||||
\(207\) | 0.729698 | + | 0.195522i | 0.0507175 | + | 0.0135897i | ||||
\(208\) | 1.12705 | + | 4.20621i | 0.0781468 | + | 0.291648i | ||||
\(209\) | −0.268699 | −0.0185863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0239 | −0.827757 | −0.413879 | − | 0.910332i | \(-0.635826\pi\) | ||||
−0.413879 | + | 0.910332i | \(0.635826\pi\) | |||||||
\(212\) | −3.18250 | − | 11.8772i | −0.218575 | − | 0.815733i | ||||
\(213\) | 7.85088 | + | 2.10364i | 0.537933 | + | 0.144139i | ||||
\(214\) | 5.98519 | − | 3.45555i | 0.409139 | − | 0.236217i | ||||
\(215\) | −5.93313 | − | 6.44876i | −0.404636 | − | 0.439802i | ||||
\(216\) | − | 2.60978i | − | 0.177573i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.16702 | + | 1.16702i | 0.0790405 | + | 0.0790405i | ||||
\(219\) | 11.6989 | + | 6.75436i | 0.790538 | + | 0.456417i | ||||
\(220\) | 10.3014 | + | 6.53361i | 0.694523 | + | 0.440496i | ||||
\(221\) | 5.46582 | + | 9.46708i | 0.367671 | + | 0.636825i | ||||
\(222\) | 6.45658 | − | 1.73004i | 0.433337 | − | 0.116112i | ||||
\(223\) | −11.6925 | + | 11.6925i | −0.782988 | + | 0.782988i | −0.980334 | − | 0.197346i | \(-0.936768\pi\) |
0.197346 | + | 0.980334i | \(0.436768\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.10728 | + | 2.85136i | 0.273819 | + | 0.190091i | ||||
\(226\) | 2.23524 | − | 3.87155i | 0.148686 | − | 0.257531i | ||||
\(227\) | 0.404524 | − | 1.50971i | 0.0268492 | − | 0.100203i | −0.951201 | − | 0.308572i | \(-0.900149\pi\) |
0.978050 | + | 0.208369i | \(0.0668156\pi\) | |||||||
\(228\) | 0.0255777 | − | 0.0954574i | 0.00169393 | − | 0.00632182i | ||||
\(229\) | −3.91654 | + | 6.78365i | −0.258812 | + | 0.448276i | −0.965924 | − | 0.258826i | \(-0.916664\pi\) |
0.707112 | + | 0.707102i | \(0.249998\pi\) | |||||||
\(230\) | 0.598123 | + | 1.14335i | 0.0394390 | + | 0.0753906i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.11372 | − | 5.11372i | 0.335732 | − | 0.335732i | ||||
\(233\) | −1.37692 | + | 0.368944i | −0.0902048 | + | 0.0241703i | −0.303639 | − | 0.952787i | \(-0.598202\pi\) |
0.213434 | + | 0.976957i | \(0.431535\pi\) | |||||||
\(234\) | −1.98133 | − | 3.43177i | −0.129524 | − | 0.224342i | ||||
\(235\) | −16.9431 | + | 3.79201i | −1.10524 | + | 0.247363i | ||||
\(236\) | 8.55562 | + | 4.93959i | 0.556923 | + | 0.321540i | ||||
\(237\) | 6.97440 | + | 6.97440i | 0.453036 | + | 0.453036i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.2805i | 1.31183i | 0.754833 | + | 0.655917i | \(0.227718\pi\) | ||||
−0.754833 | + | 0.655917i | \(0.772282\pi\) | |||||||
\(240\) | −1.38132 | + | 1.27088i | −0.0891641 | + | 0.0820349i | ||||
\(241\) | −2.39883 | + | 1.38497i | −0.154522 | + | 0.0892136i | −0.575268 | − | 0.817965i | \(-0.695102\pi\) |
0.420745 | + | 0.907179i | \(0.361769\pi\) | |||||||
\(242\) | −2.82816 | − | 0.757804i | −0.181801 | − | 0.0487135i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | 20.2710 | 1.29772 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.63105 | −0.422780 | ||||||||
\(247\) | −0.0936725 | − | 0.349590i | −0.00596024 | − | 0.0222439i | ||||
\(248\) | 6.04183 | + | 1.61890i | 0.383656 | + | 0.102800i | ||||
\(249\) | −2.00331 | + | 1.15661i | −0.126955 | + | 0.0732973i | ||||
\(250\) | 1.16589 | + | 8.46046i | 0.0737372 | + | 0.535086i | ||||
\(251\) | 6.09982i | 0.385017i | 0.981295 | + | 0.192509i | \(0.0616623\pi\) | ||||
−0.981295 | + | 0.192509i | \(0.938338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.05731 | + | 2.05731i | 0.129342 | + | 0.129342i | ||||
\(254\) | −4.52152 | − | 2.61050i | −0.283706 | − | 0.163797i | ||||
\(255\) | −2.52376 | + | 3.97917i | −0.158044 | + | 0.249185i | ||||
\(256\) | 6.45864 | + | 11.1867i | 0.403665 | + | 0.699168i | ||||
\(257\) | 2.75722 | − | 0.738795i | 0.171991 | − | 0.0460848i | −0.171796 | − | 0.985133i | \(-0.554957\pi\) |
0.343787 | + | 0.939048i | \(0.388290\pi\) | |||||||
\(258\) | −2.11676 | + | 2.11676i | −0.131784 | + | 0.131784i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4.90931 | + | 15.6804i | −0.304462 | + | 0.972456i | ||||
\(261\) | 1.38554 | − | 2.39982i | 0.0857626 | − | 0.148545i | ||||
\(262\) | −0.128014 | + | 0.477756i | −0.00790876 | + | 0.0295159i | ||||
\(263\) | 6.13773 | − | 22.9063i | 0.378469 | − | 1.41246i | −0.469741 | − | 0.882804i | \(-0.655653\pi\) |
0.848210 | − | 0.529660i | \(-0.177681\pi\) | |||||||
\(264\) | 5.02561 | − | 8.70460i | 0.309305 | − | 0.535731i | ||||
\(265\) | 5.79964 | − | 18.5241i | 0.356269 | − | 1.13793i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.57310 | + | 3.57310i | −0.218670 | + | 0.218670i | ||||
\(268\) | −0.805894 | + | 0.215939i | −0.0492278 | + | 0.0131905i | ||||
\(269\) | −12.3676 | − | 21.4213i | −0.754064 | − | 1.30608i | −0.945838 | − | 0.324638i | \(-0.894758\pi\) |
0.191774 | − | 0.981439i | \(-0.438576\pi\) | |||||||
\(270\) | 0.914849 | − | 1.44243i | 0.0556759 | − | 0.0877834i | ||||
\(271\) | 3.58076 | + | 2.06735i | 0.217515 | + | 0.125583i | 0.604799 | − | 0.796378i | \(-0.293253\pi\) |
−0.387284 | + | 0.921961i | \(0.626587\pi\) | |||||||
\(272\) | −1.25081 | − | 1.25081i | −0.0758413 | − | 0.0758413i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.0588i | − | 0.668085i | ||||||
\(275\) | 8.20851 | + | 17.4197i | 0.494992 | + | 1.05045i | ||||
\(276\) | −0.926710 | + | 0.535036i | −0.0557814 | + | 0.0322054i | ||||
\(277\) | 16.5463 | + | 4.43358i | 0.994174 | + | 0.266388i | 0.719003 | − | 0.695007i | \(-0.244599\pi\) |
0.275171 | + | 0.961395i | \(0.411266\pi\) | |||||||
\(278\) | −4.38241 | − | 16.3554i | −0.262840 | − | 0.980931i | ||||
\(279\) | 2.39674 | 0.143489 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.25279 | 0.313355 | 0.156678 | − | 0.987650i | \(-0.449922\pi\) | ||||
0.156678 | + | 0.987650i | \(0.449922\pi\) | |||||||
\(282\) | 1.53511 | + | 5.72913i | 0.0914147 | + | 0.341164i | ||||
\(283\) | 2.27756 | + | 0.610271i | 0.135387 | + | 0.0362768i | 0.325876 | − | 0.945412i | \(-0.394341\pi\) |
−0.190489 | + | 0.981689i | \(0.561007\pi\) | |||||||
\(284\) | −9.97054 | + | 5.75649i | −0.591643 | + | 0.341585i | ||||
\(285\) | 0.114806 | − | 0.105627i | 0.00680053 | − | 0.00625678i | ||||
\(286\) | − | 15.2617i | − | 0.902441i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.14420 | + | 4.14420i | 0.244199 | + | 0.244199i | ||||
\(289\) | 10.8767 | + | 6.27969i | 0.639808 | + | 0.369393i | ||||
\(290\) | 4.61896 | − | 1.03376i | 0.271234 | − | 0.0607046i | ||||
\(291\) | −4.84970 | − | 8.39993i | −0.284294 | − | 0.492412i | ||||
\(292\) | −18.4830 | + | 4.95249i | −1.08163 | + | 0.289823i | ||||
\(293\) | −15.2556 | + | 15.2556i | −0.891240 | + | 0.891240i | −0.994640 | − | 0.103400i | \(-0.967028\pi\) |
0.103400 | + | 0.994640i | \(0.467028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.22893 | + | 13.8186i | 0.420884 | + | 0.804551i | ||||
\(296\) | −11.4185 | + | 19.7774i | −0.663687 | + | 1.14954i | ||||
\(297\) | 0.996806 | − | 3.72013i | 0.0578405 | − | 0.215864i | ||||
\(298\) | 2.18417 | − | 8.15142i | 0.126525 | − | 0.472199i | ||||
\(299\) | −1.95945 | + | 3.39386i | −0.113318 | + | 0.196272i | ||||
\(300\) | −6.96984 | + | 1.25794i | −0.402404 | + | 0.0726272i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.93809 | − | 9.93809i | 0.571873 | − | 0.571873i | ||||
\(303\) | −18.5412 | + | 4.96810i | −1.06516 | + | 0.285410i | ||||
\(304\) | 0.0292823 | + | 0.0507184i | 0.00167946 | + | 0.00290890i | ||||
\(305\) | 27.0229 | + | 17.1391i | 1.54733 | + | 0.981380i | ||||
\(306\) | 1.39404 | + | 0.804852i | 0.0796922 | + | 0.0460103i | ||||
\(307\) | −14.6198 | − | 14.6198i | −0.834394 | − | 0.834394i | 0.153721 | − | 0.988114i | \(-0.450874\pi\) |
−0.988114 | + | 0.153721i | \(0.950874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 3.30678i | − | 0.188116i | ||||||
\(310\) | 2.77182 | + | 3.01271i | 0.157429 | + | 0.171110i | ||||
\(311\) | −2.47872 | + | 1.43109i | −0.140555 | + | 0.0811497i | −0.568629 | − | 0.822594i | \(-0.692526\pi\) |
0.428073 | + | 0.903744i | \(0.359193\pi\) | |||||||
\(312\) | 13.0771 | + | 3.50400i | 0.740345 | + | 0.198375i | ||||
\(313\) | −3.44732 | − | 12.8656i | −0.194854 | − | 0.727204i | −0.992305 | − | 0.123820i | \(-0.960485\pi\) |
0.797451 | − | 0.603384i | \(-0.206181\pi\) | |||||||
\(314\) | −1.13424 | −0.0640088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −13.9713 | −0.785945 | ||||||||
\(317\) | 2.70240 | + | 10.0855i | 0.151782 | + | 0.566459i | 0.999359 | + | 0.0357866i | \(0.0113937\pi\) |
−0.847577 | + | 0.530672i | \(0.821940\pi\) | |||||||
\(318\) | −6.40510 | − | 1.71624i | −0.359180 | − | 0.0962421i | ||||
\(319\) | 9.24258 | − | 5.33620i | 0.517485 | − | 0.298770i | ||||
\(320\) | −0.260322 | + | 6.25125i | −0.0145525 | + | 0.349456i | ||||
\(321\) | 9.04739i | 0.504976i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.103958 | + | 0.103958i | 0.00578440 | + | 0.00578440i | ||||
\(324\) | 1.22672 | + | 0.708245i | 0.0681509 | + | 0.0393470i | ||||
\(325\) | −19.8022 | + | 16.7524i | −1.09843 | + | 0.929257i | ||||
\(326\) | −2.97370 | − | 5.15060i | −0.164698 | − | 0.285265i | ||||
\(327\) | −2.08695 | + | 0.559197i | −0.115409 | + | 0.0309237i | ||||
\(328\) | 16.0194 | − | 16.0194i | 0.884526 | − | 0.884526i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 5.82902 | − | 3.04933i | 0.320877 | − | 0.167860i | ||||
\(331\) | −11.8100 | + | 20.4555i | −0.649136 | + | 1.12434i | 0.334193 | + | 0.942505i | \(0.391536\pi\) |
−0.983330 | + | 0.181833i | \(0.941797\pi\) | |||||||
\(332\) | 0.848062 | − | 3.16501i | 0.0465435 | − | 0.173703i | ||||
\(333\) | −2.26481 | + | 8.45237i | −0.124111 | + | 0.463187i | ||||
\(334\) | −1.02070 | + | 1.76790i | −0.0558500 | + | 0.0967351i | ||||
\(335\) | −1.25690 | − | 0.393517i | −0.0686716 | − | 0.0215001i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.93809 | + | 4.93809i | −0.268995 | + | 0.268995i | −0.828695 | − | 0.559700i | \(-0.810916\pi\) |
0.559700 | + | 0.828695i | \(0.310916\pi\) | |||||||
\(338\) | 10.2641 | − | 2.75026i | 0.558293 | − | 0.149594i | ||||
\(339\) | 2.92617 | + | 5.06828i | 0.158928 | + | 0.275271i | ||||
\(340\) | −1.45775 | − | 6.51340i | −0.0790578 | − | 0.353238i | ||||
\(341\) | 7.99402 | + | 4.61535i | 0.432900 | + | 0.249935i | ||||
\(342\) | −0.0376844 | − | 0.0376844i | −0.00203774 | − | 0.00203774i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 10.2274i | − | 0.551427i | ||||||
\(345\) | −1.68775 | − | 0.0702834i | −0.0908655 | − | 0.00378393i | ||||
\(346\) | 4.59124 | − | 2.65076i | 0.246827 | − | 0.142505i | ||||
\(347\) | −7.97341 | − | 2.13647i | −0.428035 | − | 0.114692i | 0.0383685 | − | 0.999264i | \(-0.487784\pi\) |
−0.466404 | + | 0.884572i | \(0.654451\pi\) | |||||||
\(348\) | 1.01592 | + | 3.79145i | 0.0544589 | + | 0.203243i | ||||
\(349\) | −16.9121 | −0.905282 | −0.452641 | − | 0.891693i | \(-0.649518\pi\) | ||||
−0.452641 | + | 0.891693i | \(0.649518\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.18757 | 0.276892 | ||||||||
\(352\) | 5.84206 | + | 21.8029i | 0.311383 | + | 1.16210i | ||||
\(353\) | 15.1990 | + | 4.07257i | 0.808963 | + | 0.216761i | 0.639516 | − | 0.768778i | \(-0.279135\pi\) |
0.169448 | + | 0.985539i | \(0.445802\pi\) | |||||||
\(354\) | 4.61383 | − | 2.66380i | 0.245222 | − | 0.141579i | ||||
\(355\) | −18.1586 | − | 0.756184i | −0.963760 | − | 0.0401341i | ||||
\(356\) | − | 7.15771i | − | 0.379358i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0389 | − | 10.0389i | −0.530574 | − | 0.530574i | ||||
\(359\) | −7.05693 | − | 4.07432i | −0.372450 | − | 0.215034i | 0.302078 | − | 0.953283i | \(-0.402320\pi\) |
−0.674528 | + | 0.738249i | \(0.735653\pi\) | |||||||
\(360\) | 1.27454 | + | 5.69477i | 0.0671740 | + | 0.300140i | ||||
\(361\) | 9.49757 | + | 16.4503i | 0.499872 | + | 0.865804i | ||||
\(362\) | 6.26086 | − | 1.67759i | 0.329063 | − | 0.0881723i | ||||
\(363\) | 2.71033 | − | 2.71033i | 0.142255 | − | 0.142255i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.8266 | − | 9.02520i | −1.50885 | − | 0.472401i | ||||
\(366\) | 5.46582 | − | 9.46708i | 0.285703 | − | 0.494852i | ||||
\(367\) | 5.39815 | − | 20.1462i | 0.281781 | − | 1.05162i | −0.669378 | − | 0.742922i | \(-0.733439\pi\) |
0.951160 | − | 0.308700i | \(-0.0998938\pi\) | |||||||
\(368\) | 0.164127 | − | 0.612529i | 0.00855569 | − | 0.0319303i | ||||
\(369\) | 4.34039 | − | 7.51777i | 0.225951 | − | 0.391359i | ||||
\(370\) | −13.2439 | + | 6.92828i | −0.688518 | + | 0.360184i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.40060 | + | 2.40060i | −0.124465 | + | 0.124465i | ||||
\(373\) | −2.04168 | + | 0.547065i | −0.105714 | + | 0.0283260i | −0.311288 | − | 0.950316i | \(-0.600760\pi\) |
0.205574 | + | 0.978642i | \(0.434094\pi\) | |||||||
\(374\) | 3.09977 | + | 5.36897i | 0.160286 | + | 0.277623i | ||||
\(375\) | −10.3549 | − | 4.21604i | −0.534727 | − | 0.217716i | ||||
\(376\) | −17.5491 | − | 10.1320i | −0.905027 | − | 0.522518i | ||||
\(377\) | 10.1648 | + | 10.1648i | 0.523511 | + | 0.523511i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.7135i | 0.961248i | 0.876927 | + | 0.480624i | \(0.159590\pi\) | ||||
−0.876927 | + | 0.480624i | \(0.840410\pi\) | |||||||
\(380\) | −0.00919431 | + | 0.220788i | −0.000471658 | + | 0.0113262i | ||||
\(381\) | 5.91917 | − | 3.41743i | 0.303248 | − | 0.175080i | ||||
\(382\) | 3.97960 | + | 1.06633i | 0.203614 | + | 0.0545582i | ||||
\(383\) | 7.66288 | + | 28.5983i | 0.391555 | + | 1.46130i | 0.827569 | + | 0.561364i | \(0.189723\pi\) |
−0.436014 | + | 0.899940i | \(0.643610\pi\) | |||||||
\(384\) | −9.58418 | −0.489091 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.19184 | −0.264258 | ||||||||
\(387\) | −1.01428 | − | 3.78536i | −0.0515589 | − | 0.192421i | ||||
\(388\) | 13.2710 | + | 3.55594i | 0.673731 | + | 0.180526i | ||||
\(389\) | 22.2232 | − | 12.8305i | 1.12676 | − | 0.650535i | 0.183641 | − | 0.982993i | \(-0.441212\pi\) |
0.943118 | + | 0.332459i | \(0.107878\pi\) | |||||||
\(390\) | 5.99941 | + | 6.52079i | 0.303792 | + | 0.330193i | ||||
\(391\) | − | 1.59192i | − | 0.0805069i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.457851 | − | 0.457851i | −0.0230955 | − | 0.0230955i | ||||
\(394\) | 11.8572 | + | 6.84574i | 0.597356 | + | 0.344883i | ||||
\(395\) | −18.6248 | − | 11.8127i | −0.937117 | − | 0.594359i | ||||
\(396\) | 2.72771 | + | 4.72453i | 0.137073 | + | 0.237417i | ||||
\(397\) | −9.20135 | + | 2.46549i | −0.461802 | + | 0.123740i | −0.482217 | − | 0.876052i | \(-0.660168\pi\) |
0.0204142 | + | 0.999792i | \(0.493502\pi\) | |||||||
\(398\) | −1.44278 | + | 1.44278i | −0.0723201 | + | 0.0723201i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.39351 | − | 3.44776i | 0.119676 | − | 0.172388i | ||||
\(401\) | −7.37513 | + | 12.7741i | −0.368296 | + | 0.637908i | −0.989299 | − | 0.145900i | \(-0.953392\pi\) |
0.621003 | + | 0.783808i | \(0.286726\pi\) | |||||||
\(402\) | −0.116450 | + | 0.434598i | −0.00580801 | + | 0.0216758i | ||||
\(403\) | −3.21796 | + | 12.0096i | −0.160298 | + | 0.598240i | ||||
\(404\) | 13.5950 | − | 23.5472i | 0.676374 | − | 1.17151i | ||||
\(405\) | 1.03649 | + | 1.98133i | 0.0515038 | + | 0.0984532i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.8305 | + | 23.8305i | −1.18124 | + | 1.18124i | ||||
\(408\) | −5.31215 | + | 1.42339i | −0.262990 | + | 0.0704681i | ||||
\(409\) | −5.28021 | − | 9.14560i | −0.261090 | − | 0.452221i | 0.705442 | − | 0.708768i | \(-0.250749\pi\) |
−0.966532 | + | 0.256547i | \(0.917415\pi\) | |||||||
\(410\) | 14.4695 | − | 3.23840i | 0.714598 | − | 0.159933i | ||||
\(411\) | 12.5376 | + | 7.23858i | 0.618434 | + | 0.357053i | ||||
\(412\) | 3.31210 | + | 3.31210i | 0.163176 | + | 0.163176i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.577063i | 0.0283611i | ||||||||
\(415\) | 3.80654 | − | 3.50218i | 0.186856 | − | 0.171915i | ||||
\(416\) | −26.3299 | + | 15.2016i | −1.29093 | + | 0.745320i | ||||
\(417\) | 21.4110 | + | 5.73706i | 1.04850 | + | 0.280945i | ||||
\(418\) | −0.0531235 | − | 0.198260i | −0.00259835 | − | 0.00969719i | ||||
\(419\) | 15.5472 | 0.759532 | 0.379766 | − | 0.925083i | \(-0.376004\pi\) | ||||
0.379766 | + | 0.925083i | \(0.376004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29886 | 0.160776 | 0.0803882 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803882 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(422\) | −2.37719 | − | 8.87180i | −0.115720 | − | 0.431873i | ||||
\(423\) | −7.50006 | − | 2.00963i | −0.364665 | − | 0.0977117i | ||||
\(424\) | 19.6197 | − | 11.3275i | 0.952818 | − | 0.550110i | ||||
\(425\) | 3.56375 | − | 9.91541i | 0.172867 | − | 0.480968i | ||||
\(426\) | 6.20867i | 0.300811i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −9.06196 | − | 9.06196i | −0.438026 | − | 0.438026i | ||||
\(429\) | 17.3025 | + | 9.98959i | 0.835372 | + | 0.482302i | ||||
\(430\) | 3.58519 | − | 5.65272i | 0.172893 | − | 0.272598i | ||||
\(431\) | 7.04553 | + | 12.2032i | 0.339371 | + | 0.587809i | 0.984315 | − | 0.176422i | \(-0.0564523\pi\) |
−0.644943 | + | 0.764230i | \(0.723119\pi\) | |||||||
\(432\) | −0.810825 | + | 0.217260i | −0.0390108 | + | 0.0104529i | ||||
\(433\) | −1.72650 | + | 1.72650i | −0.0829702 | + | 0.0829702i | −0.747374 | − | 0.664404i | \(-0.768686\pi\) |
0.664404 | + | 0.747374i | \(0.268686\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.85136 | + | 5.91327i | −0.0887660 | + | 0.283519i | ||||
\(436\) | 1.53022 | − | 2.65041i | 0.0732840 | − | 0.126932i | ||||
\(437\) | −0.0136411 | + | 0.0509091i | −0.000652540 | + | 0.00243531i | ||||
\(438\) | −2.67075 | + | 9.96739i | −0.127614 | + | 0.476260i | ||||
\(439\) | 13.5586 | − | 23.4841i | 0.647116 | − | 1.12084i | −0.336693 | − | 0.941615i | \(-0.609308\pi\) |
0.983809 | − | 0.179223i | \(-0.0573582\pi\) | |||||||
\(440\) | −6.71524 | + | 21.4485i | −0.320136 | + | 1.02252i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.90465 | + | 5.90465i | −0.280856 | + | 0.280856i | ||||
\(443\) | 32.9897 | − | 8.83957i | 1.56739 | − | 0.419981i | 0.632396 | − | 0.774645i | \(-0.282072\pi\) |
0.934994 | + | 0.354664i | \(0.115405\pi\) | |||||||
\(444\) | −6.19753 | − | 10.7344i | −0.294122 | − | 0.509434i | ||||
\(445\) | 6.05182 | − | 9.54181i | 0.286884 | − | 0.452325i | ||||
\(446\) | −10.9390 | − | 6.31563i | −0.517976 | − | 0.299054i | ||||
\(447\) | 7.81179 | + | 7.81179i | 0.369485 | + | 0.369485i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 9.80267i | − | 0.462617i | −0.972881 | − | 0.231308i | \(-0.925699\pi\) | ||
0.972881 | − | 0.231308i | \(-0.0743006\pi\) | |||||||
\(450\) | −1.29184 | + | 3.59428i | −0.0608979 | + | 0.169436i | ||||
\(451\) | 28.9536 | − | 16.7164i | 1.36337 | − | 0.787144i | ||||
\(452\) | −8.00732 | − | 2.14556i | −0.376633 | − | 0.100918i | ||||
\(453\) | 4.76201 | + | 17.7721i | 0.223739 | + | 0.835005i | ||||
\(454\) | 1.19391 | 0.0560331 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.182078 | 0.00852656 | ||||||||
\(457\) | 0.201340 | + | 0.751411i | 0.00941828 | + | 0.0351495i | 0.970475 | − | 0.241201i | \(-0.0775415\pi\) |
−0.961057 | + | 0.276351i | \(0.910875\pi\) | |||||||
\(458\) | −5.77964 | − | 1.54865i | −0.270065 | − | 0.0723636i | ||||
\(459\) | −1.82496 | + | 1.05364i | −0.0851817 | + | 0.0491797i | ||||
\(460\) | 1.76087 | − | 1.62007i | 0.0821008 | − | 0.0755363i | ||||
\(461\) | − | 0.831786i | − | 0.0387401i | −0.999812 | − | 0.0193701i | \(-0.993834\pi\) | ||
0.999812 | − | 0.0193701i | \(-0.00616607\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.45140 | + | 5.45140i | 0.253348 | + | 0.253348i | 0.822342 | − | 0.568994i | \(-0.192667\pi\) |
−0.568994 | + | 0.822342i | \(0.692667\pi\) | |||||||
\(464\) | −2.01448 | − | 1.16306i | −0.0935197 | − | 0.0539936i | ||||
\(465\) | −5.22988 | + | 1.17049i | −0.242530 | + | 0.0542803i | ||||
\(466\) | −0.544450 | − | 0.943015i | −0.0252211 | − | 0.0436843i | ||||
\(467\) | 31.8048 | − | 8.52208i | 1.47175 | − | 0.394355i | 0.568220 | − | 0.822876i | \(-0.307632\pi\) |
0.903531 | + | 0.428522i | \(0.140965\pi\) | |||||||
\(468\) | −5.19592 | + | 5.19592i | −0.240181 | + | 0.240181i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.14768 | − | 11.7517i | −0.283571 | − | 0.542067i | ||||
\(471\) | 0.742422 | − | 1.28591i | 0.0342090 | − | 0.0592517i | ||||
\(472\) | −4.71094 | + | 17.5815i | −0.216838 | + | 0.809252i | ||||
\(473\) | 3.90637 | − | 14.5788i | 0.179615 | − | 0.670333i | ||||
\(474\) | −3.76718 | + | 6.52494i | −0.173032 | + | 0.299700i | ||||
\(475\) | −0.198932 | + | 0.286554i | −0.00912762 | + | 0.0131480i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.13823 | − | 6.13823i | 0.281050 | − | 0.281050i | ||||
\(478\) | −14.9639 | + | 4.00957i | −0.684434 | + | 0.183394i | ||||
\(479\) | 20.2160 | + | 35.0151i | 0.923691 | + | 1.59988i | 0.793653 | + | 0.608371i | \(0.208177\pi\) |
0.130038 | + | 0.991509i | \(0.458490\pi\) | |||||||
\(480\) | −11.0669 | − | 7.01909i | −0.505132 | − | 0.320376i | ||||
\(481\) | −39.3123 | − | 22.6970i | −1.79249 | − | 1.03489i | ||||
\(482\) | −1.49616 | − | 1.49616i | −0.0681483 | − | 0.0681483i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.42938i | 0.246790i | ||||||||
\(485\) | 14.6847 | + | 15.9609i | 0.666799 | + | 0.724748i | ||||
\(486\) | 0.661538 | − | 0.381939i | 0.0300080 | − | 0.0173251i | ||||
\(487\) | 9.87490 | + | 2.64597i | 0.447474 | + | 0.119900i | 0.475517 | − | 0.879706i | \(-0.342261\pi\) |
−0.0280431 | + | 0.999607i | \(0.508928\pi\) | |||||||
\(488\) | 9.66634 | + | 36.0753i | 0.437575 | + | 1.63305i | ||||
\(489\) | 7.78580 | 0.352086 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.1040 | 0.907279 | 0.453639 | − | 0.891185i | \(-0.350125\pi\) | ||||
0.453639 | + | 0.891185i | \(0.350125\pi\) | |||||||
\(492\) | 3.18250 | + | 11.8772i | 0.143478 | + | 0.535468i | ||||
\(493\) | −5.64045 | − | 1.51135i | −0.254033 | − | 0.0680680i | ||||
\(494\) | 0.239425 | − | 0.138232i | 0.0107723 | − | 0.00621937i | ||||
\(495\) | −0.358317 | + | 8.60445i | −0.0161052 | + | 0.386741i | ||||
\(496\) | − | 2.01189i | − | 0.0903364i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.24947 | − | 1.24947i | −0.0559902 | − | 0.0559902i | ||||
\(499\) | −13.3564 | − | 7.71133i | −0.597916 | − | 0.345207i | 0.170306 | − | 0.985391i | \(-0.445525\pi\) |
−0.768221 | + | 0.640185i | \(0.778858\pi\) | |||||||
\(500\) | 14.5945 | − | 6.14879i | 0.652684 | − | 0.274982i | ||||
\(501\) | −1.33620 | − | 2.31437i | −0.0596972 | − | 0.103399i | ||||
\(502\) | −4.50075 | + | 1.20597i | −0.200878 | + | 0.0538252i | ||||
\(503\) | 25.9985 | − | 25.9985i | 1.15922 | − | 1.15922i | 0.174573 | − | 0.984644i | \(-0.444145\pi\) |
0.984644 | − | 0.174573i | \(-0.0558546\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.0322 | − | 19.8958i | 1.69241 | − | 0.885350i | ||||
\(506\) | −1.11124 | + | 1.92472i | −0.0494006 | + | 0.0855644i | ||||
\(507\) | −3.60039 | + | 13.4368i | −0.159899 | + | 0.596751i | ||||
\(508\) | −2.50576 | + | 9.35164i | −0.111175 | + | 0.414912i | ||||
\(509\) | −18.5636 | + | 32.1530i | −0.822816 | + | 1.42516i | 0.0807619 | + | 0.996733i | \(0.474265\pi\) |
−0.903577 | + | 0.428425i | \(0.859069\pi\) | |||||||
\(510\) | −3.43499 | − | 1.07545i | −0.152104 | − | 0.0476216i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.57690 | − | 6.57690i | 0.290661 | − | 0.290661i | ||||
\(513\) | 0.0673901 | − | 0.0180571i | 0.00297535 | − | 0.000797241i | ||||
\(514\) | 1.09024 | + | 1.88835i | 0.0480884 | + | 0.0832915i | ||||
\(515\) | 1.61493 | + | 7.21567i | 0.0711623 | + | 0.317960i | ||||
\(516\) | 4.80737 | + | 2.77554i | 0.211633 | + | 0.122186i | ||||
\(517\) | −21.1456 | − | 21.1456i | −0.929982 | − | 0.929982i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.94026i | 0.304644i | ||||||||
\(520\) | −30.2466 | − | 1.25957i | −1.32640 | − | 0.0552356i | ||||
\(521\) | 2.24415 | − | 1.29566i | 0.0983180 | − | 0.0567639i | −0.450035 | − | 0.893011i | \(-0.648588\pi\) |
0.548353 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(522\) | 2.04464 | + | 0.547858i | 0.0894913 | + | 0.0239791i | ||||
\(523\) | −2.22856 | − | 8.31711i | −0.0974482 | − | 0.363682i | 0.899931 | − | 0.436032i | \(-0.143617\pi\) |
−0.997379 | + | 0.0723506i | \(0.976950\pi\) | |||||||
\(524\) | 0.917176 | 0.0400670 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.1149 | 0.789846 | ||||||||
\(527\) | −1.30719 | − | 4.87850i | −0.0569421 | − | 0.212511i | ||||
\(528\) | −3.12278 | − | 0.836746i | −0.135901 | − | 0.0364147i | ||||
\(529\) | −19.4244 | + | 11.2147i | −0.844537 | + | 0.487594i | ||||
\(530\) | 14.8146 | + | 0.616930i | 0.643507 | + | 0.0267977i | ||||
\(531\) | 6.97440i | 0.302663i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 31.8425 | + | 31.8425i | 1.37925 | + | 1.37925i | ||||
\(534\) | −3.34284 | − | 1.92999i | −0.144659 | − | 0.0835187i | ||||
\(535\) | −4.41847 | − | 19.7422i | −0.191027 | − | 0.853529i | ||||
\(536\) | −0.768589 | − | 1.33124i | −0.0331980 | − | 0.0575006i | ||||
\(537\) | 17.9524 | − | 4.81033i | 0.774703 | − | 0.207581i | ||||
\(538\) | 13.3605 | − | 13.3605i | 0.576013 | − | 0.576013i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.02269 | − | 0.946361i | −0.130076 | − | 0.0407249i | ||||
\(541\) | 16.7319 | − | 28.9805i | 0.719360 | − | 1.24597i | −0.241894 | − | 0.970303i | \(-0.577769\pi\) |
0.961254 | − | 0.275665i | \(-0.0888980\pi\) | |||||||
\(542\) | −0.817456 | + | 3.05079i | −0.0351127 | + | 0.131042i | ||||
\(543\) | −2.19615 | + | 8.19615i | −0.0942459 | + | 0.351731i | ||||
\(544\) | 6.17515 | − | 10.6957i | 0.264757 | − | 0.458573i | ||||
\(545\) | 4.28081 | − | 2.23942i | 0.183370 | − | 0.0959262i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.828381 | + | 0.828381i | −0.0354190 | + | 0.0354190i | −0.724594 | − | 0.689175i | \(-0.757973\pi\) |
0.689175 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(548\) | −19.8080 | + | 5.30754i | −0.846156 | + | 0.226727i | ||||
\(549\) | 7.15536 | + | 12.3935i | 0.305383 | + | 0.528940i | ||||
\(550\) | −11.2302 | + | 9.50062i | −0.478858 | + | 0.405108i | ||||
\(551\) | 0.167429 | + | 0.0966653i | 0.00713272 | + | 0.00411808i | ||||
\(552\) | −1.39408 | − | 1.39408i | −0.0593361 | − | 0.0593361i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0853i | 0.555939i | ||||||||
\(555\) | 0.814119 | − | 19.5499i | 0.0345574 | − | 0.829845i | ||||
\(556\) | −27.1918 | + | 15.6992i | −1.15319 | + | 0.665793i | ||||
\(557\) | −20.0969 | − | 5.38496i | −0.851534 | − | 0.228168i | −0.193448 | − | 0.981111i | \(-0.561967\pi\) |
−0.658086 | + | 0.752943i | \(0.728634\pi\) | |||||||
\(558\) | 0.473850 | + | 1.76843i | 0.0200597 | + | 0.0748636i | ||||
\(559\) | 20.3295 | 0.859846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.11589 | −0.342653 | ||||||||
\(562\) | 1.03851 | + | 3.87577i | 0.0438069 | + | 0.163489i | ||||
\(563\) | 32.7427 | + | 8.77338i | 1.37994 | + | 0.369754i | 0.871100 | − | 0.491106i | \(-0.163407\pi\) |
0.508841 | + | 0.860860i | \(0.330074\pi\) | |||||||
\(564\) | 9.52500 | − | 5.49926i | 0.401075 | − | 0.231561i | ||||
\(565\) | −8.86035 | − | 9.63036i | −0.372758 | − | 0.405152i | ||||
\(566\) | 1.80115i | 0.0757080i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.9990 | − | 14.9990i | −0.629346 | − | 0.629346i | ||||
\(569\) | −13.5671 | − | 7.83298i | −0.568763 | − | 0.328376i | 0.187892 | − | 0.982190i | \(-0.439835\pi\) |
−0.756655 | + | 0.653814i | \(0.773168\pi\) | |||||||
\(570\) | 0.100634 | + | 0.0638266i | 0.00421511 | + | 0.00267340i | ||||
\(571\) | −18.4943 | − | 32.0331i | −0.773964 | − | 1.34055i | −0.935375 | − | 0.353658i | \(-0.884938\pi\) |
0.161411 | − | 0.986887i | \(-0.448396\pi\) | |||||||
\(572\) | −27.3360 | + | 7.32466i | −1.14298 | + | 0.306260i | ||||
\(573\) | −3.81379 | + | 3.81379i | −0.159323 | + | 0.159323i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.71714 | − | 0.670882i | 0.155015 | − | 0.0279777i | ||||
\(576\) | −1.39903 | + | 2.42320i | −0.0582931 | + | 0.100967i | ||||
\(577\) | 5.69488 | − | 21.2536i | 0.237081 | − | 0.884798i | −0.740119 | − | 0.672476i | \(-0.765231\pi\) |
0.977200 | − | 0.212322i | \(-0.0681025\pi\) | |||||||
\(578\) | −2.48307 | + | 9.26693i | −0.103282 | + | 0.385453i | ||||
\(579\) | 3.39835 | − | 5.88611i | 0.141230 | − | 0.244618i | ||||
\(580\) | −4.06845 | − | 7.77713i | −0.168933 | − | 0.322928i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 5.23907 | − | 5.23907i | 0.217166 | − | 0.217166i | ||||
\(583\) | 32.2936 | − | 8.65304i | 1.33746 | − | 0.358372i | ||||
\(584\) | −17.6274 | − | 30.5315i | −0.729427 | − | 1.26340i | ||||
\(585\) | −11.3197 | + | 2.53345i | −0.468012 | + | 0.104745i | ||||
\(586\) | −14.2724 | − | 8.24019i | −0.589589 | − | 0.340399i | ||||
\(587\) | −15.7111 | − | 15.7111i | −0.648468 | − | 0.648468i | 0.304155 | − | 0.952623i | \(-0.401626\pi\) |
−0.952623 | + | 0.304155i | \(0.901626\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.167214i | 0.00688993i | ||||||||
\(590\) | −8.76685 | + | 8.06588i | −0.360926 | + | 0.332067i | ||||
\(591\) | −15.5223 | + | 8.96183i | −0.638504 | + | 0.368640i | ||||
\(592\) | 7.09515 | + | 1.90114i | 0.291609 | + | 0.0781364i | ||||
\(593\) | −0.677877 | − | 2.52987i | −0.0278371 | − | 0.103889i | 0.950610 | − | 0.310389i | \(-0.100459\pi\) |
−0.978447 | + | 0.206500i | \(0.933793\pi\) | |||||||
\(594\) | 2.94197 | 0.120710 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.6487 | −0.640997 | ||||||||
\(597\) | −0.691334 | − | 2.58009i | −0.0282944 | − | 0.105596i | ||||
\(598\) | −2.89155 | − | 0.774789i | −0.118244 | − | 0.0316835i | ||||
\(599\) | −40.9761 | + | 23.6576i | −1.67424 | + | 0.966622i | −0.709015 | + | 0.705193i | \(0.750860\pi\) |
−0.965223 | + | 0.261429i | \(0.915806\pi\) | |||||||
\(600\) | −5.56230 | − | 11.8040i | −0.227080 | − | 0.481897i | ||||
\(601\) | 11.0819i | 0.452041i | 0.974123 | + | 0.226021i | \(0.0725717\pi\) | ||||
−0.974123 | + | 0.226021i | \(0.927428\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.416491 | − | 0.416491i | −0.0169608 | − | 0.0169608i | ||||
\(604\) | −22.5704 | − | 13.0310i | −0.918375 | − | 0.530224i | ||||
\(605\) | −4.59052 | + | 7.23781i | −0.186631 | + | 0.294259i | ||||
\(606\) | −7.33142 | − | 12.6984i | −0.297819 | − | 0.515837i | ||||
\(607\) | −10.3088 | + | 2.76222i | −0.418419 | + | 0.112115i | −0.461885 | − | 0.886940i | \(-0.652827\pi\) |
0.0434656 | + | 0.999055i | \(0.486160\pi\) | |||||||
\(608\) | −0.289130 | + | 0.289130i | −0.0117258 | + | 0.0117258i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.30346 | + | 23.3273i | −0.295708 | + | 0.944496i | ||||
\(611\) | 20.1398 | − | 34.8831i | 0.814767 | − | 1.41122i | ||||
\(612\) | 0.772560 | − | 2.88323i | 0.0312289 | − | 0.116548i | ||||
\(613\) | −0.960769 | + | 3.58564i | −0.0388051 | + | 0.144823i | −0.982610 | − | 0.185679i | \(-0.940551\pi\) |
0.943805 | + | 0.330502i | \(0.107218\pi\) | |||||||
\(614\) | 7.89676 | − | 13.6776i | 0.318687 | − | 0.551983i | ||||
\(615\) | −5.79964 | + | 18.5241i | −0.233864 | + | 0.746965i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.3212 | − | 11.3212i | 0.455774 | − | 0.455774i | −0.441491 | − | 0.897266i | \(-0.645550\pi\) |
0.897266 | + | 0.441491i | \(0.145550\pi\) | |||||||
\(618\) | 2.43990 | − | 0.653770i | 0.0981473 | − | 0.0262985i | ||||
\(619\) | 4.53385 | + | 7.85287i | 0.182231 | + | 0.315633i | 0.942640 | − | 0.333811i | \(-0.108335\pi\) |
−0.760409 | + | 0.649445i | \(0.775001\pi\) | |||||||
\(620\) | 4.06593 | − | 6.41068i | 0.163292 | − | 0.257459i | ||||
\(621\) | −0.654230 | − | 0.377720i | −0.0262533 | − | 0.0151574i | ||||
\(622\) | −1.54599 | − | 1.54599i | −0.0619884 | − | 0.0619884i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.35458i | − | 0.174323i | ||||||
\(625\) | 24.6544 | + | 4.14272i | 0.986175 | + | 0.165709i | ||||
\(626\) | 8.81129 | − | 5.08720i | 0.352170 | − | 0.203325i | ||||
\(627\) | 0.259544 | + | 0.0695445i | 0.0103652 | + | 0.00277734i | ||||
\(628\) | 0.544366 | + | 2.03160i | 0.0217225 | + | 0.0810697i | ||||
\(629\) | 18.4398 | 0.735244 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.67260 | −0.385060 | −0.192530 | − | 0.981291i | \(-0.561669\pi\) | ||||
−0.192530 | + | 0.981291i | \(0.561669\pi\) | |||||||
\(632\) | −6.66227 | − | 24.8639i | −0.265011 | − | 0.989034i | ||||
\(633\) | 11.6142 | + | 3.11201i | 0.461622 | + | 0.123691i | ||||
\(634\) | −6.90730 | + | 3.98793i | −0.274324 | + | 0.158381i | ||||
\(635\) | −11.2472 | + | 10.3479i | −0.446330 | + | 0.410643i | ||||
\(636\) | 12.2962i | 0.487577i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.76463 | + | 5.76463i | 0.228224 | + | 0.228224i | ||||
\(639\) | −7.03890 | − | 4.06391i | −0.278455 | − | 0.160766i | ||||
\(640\) | 20.9135 | − | 4.68062i | 0.826679 | − | 0.185018i | ||||
\(641\) | 20.2924 | + | 35.1474i | 0.801500 | + | 1.38824i | 0.918629 | + | 0.395122i | \(0.129298\pi\) |
−0.117129 | + | 0.993117i | \(0.537369\pi\) | |||||||
\(642\) | −6.67561 | + | 1.78872i | −0.263465 | + | 0.0705953i | ||||
\(643\) | 3.89544 | − | 3.89544i | 0.153621 | − | 0.153621i | −0.626112 | − | 0.779733i | \(-0.715355\pi\) |
0.779733 | + | 0.626112i | \(0.215355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.06191 | + | 7.76463i | 0.159937 | + | 0.305732i | ||||
\(646\) | −0.0561524 | + | 0.0972588i | −0.00220929 | + | 0.00382660i | ||||
\(647\) | 6.16438 | − | 23.0058i | 0.242347 | − | 0.904450i | −0.732352 | − | 0.680927i | \(-0.761577\pi\) |
0.974698 | − | 0.223524i | \(-0.0717561\pi\) | |||||||
\(648\) | −0.675461 | + | 2.52086i | −0.0265346 | + | 0.0990285i | ||||
\(649\) | −13.4305 | + | 23.2623i | −0.527192 | + | 0.913123i | ||||
\(650\) | −16.2758 | − | 11.2990i | −0.638388 | − | 0.443183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.79833 | + | 7.79833i | −0.305406 | + | 0.305406i | ||||
\(653\) | 31.4119 | − | 8.41678i | 1.22924 | − | 0.329374i | 0.414957 | − | 0.909841i | \(-0.363797\pi\) |
0.814284 | + | 0.580467i | \(0.197130\pi\) | |||||||
\(654\) | −0.825207 | − | 1.42930i | −0.0322681 | − | 0.0558901i | ||||
\(655\) | 1.22267 | + | 0.775469i | 0.0477737 | + | 0.0303001i | ||||
\(656\) | −6.31062 | − | 3.64344i | −0.246388 | − | 0.142252i | ||||
\(657\) | −9.55210 | − | 9.55210i | −0.372663 | − | 0.372663i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.7543i | − | 1.27593i | −0.770067 | − | 0.637963i | \(-0.779777\pi\) | ||
0.770067 | − | 0.637963i | \(-0.220223\pi\) | |||||||
\(660\) | −8.25941 | − | 8.97720i | −0.321497 | − | 0.349437i | ||||
\(661\) | −28.1609 | + | 16.2587i | −1.09533 | + | 0.632391i | −0.934991 | − | 0.354671i | \(-0.884593\pi\) |
−0.160341 | + | 0.987062i | \(0.551260\pi\) | |||||||
\(662\) | −17.4280 | − | 4.66982i | −0.677359 | − | 0.181498i | ||||
\(663\) | −2.82932 | − | 10.5592i | −0.109882 | − | 0.410084i | ||||
\(664\) | 6.03701 | 0.234281 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.68434 | −0.259013 | ||||||||
\(667\) | −0.541806 | − | 2.02205i | −0.0209788 | − | 0.0782940i | ||||
\(668\) | 3.65646 | + | 0.979744i | 0.141473 | + | 0.0379075i | ||||
\(669\) | 14.3203 | − | 8.26785i | 0.553656 | − | 0.319654i | ||||
\(670\) | 0.0418598 | − | 1.00520i | 0.00161719 | − | 0.0388343i | ||||
\(671\) | 55.1158i | 2.12772i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.7534 | − | 16.7534i | −0.645796 | − | 0.645796i | 0.306179 | − | 0.951974i | \(-0.400950\pi\) |
−0.951974 | + | 0.306179i | \(0.900950\pi\) | |||||||
\(674\) | −4.61986 | − | 2.66728i | −0.177950 | − | 0.102740i | ||||
\(675\) | −3.22934 | − | 3.81725i | −0.124297 | − | 0.146926i | ||||
\(676\) | −9.85228 | − | 17.0647i | −0.378934 | − | 0.656333i | ||||
\(677\) | 9.36503 | − | 2.50935i | 0.359927 | − | 0.0964422i | −0.0743237 | − | 0.997234i | \(-0.523680\pi\) |
0.434251 | + | 0.900792i | \(0.357013\pi\) | |||||||
\(678\) | −3.16110 | + | 3.16110i | −0.121401 | + | 0.121401i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 10.8964 | − | 5.70024i | 0.417858 | − | 0.218594i | ||||
\(681\) | −0.781481 | + | 1.35357i | −0.0299464 | + | 0.0518687i | ||||
\(682\) | −1.82497 | + | 6.81087i | −0.0698816 | + | 0.260802i | ||||
\(683\) | 8.50440 | − | 31.7389i | 0.325412 | − | 1.21445i | −0.588485 | − | 0.808508i | \(-0.700275\pi\) |
0.913897 | − | 0.405946i | \(-0.133058\pi\) | |||||||
\(684\) | −0.0494124 | + | 0.0855848i | −0.00188933 | + | 0.00327242i | ||||
\(685\) | −30.8932 | − | 9.67222i | −1.18037 | − | 0.369557i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.53883 | − | 5.53883i | 0.211319 | − | 0.211319i | ||||
\(688\) | −3.17753 | + | 0.851417i | −0.121142 | + | 0.0324600i | ||||
\(689\) | 22.5160 | + | 38.9989i | 0.857793 | + | 1.48574i | ||||
\(690\) | −0.281820 | − | 1.25920i | −0.0107287 | − | 0.0479370i | ||||
\(691\) | 36.7813 | + | 21.2357i | 1.39923 | + | 0.807845i | 0.994312 | − | 0.106509i | \(-0.0339673\pi\) |
0.404916 | + | 0.914354i | \(0.367301\pi\) | |||||||
\(692\) | −6.95144 | − | 6.95144i | −0.264254 | − | 0.264254i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.30557i | − | 0.239356i | ||||||
\(695\) | −49.5224 | − | 2.06227i | −1.87849 | − | 0.0782265i | ||||
\(696\) | −6.26301 | + | 3.61595i | −0.237399 | + | 0.137062i | ||||
\(697\) | −17.6695 | − | 4.73453i | −0.669280 | − | 0.179333i | ||||
\(698\) | −3.34362 | − | 12.4786i | −0.126558 | − | 0.472320i | ||||
\(699\) | 1.42549 | 0.0539169 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0793 | 0.645077 | 0.322539 | − | 0.946556i | \(-0.395464\pi\) | ||||
0.322539 | + | 0.946556i | \(0.395464\pi\) | |||||||
\(702\) | 1.02561 | + | 3.82764i | 0.0387093 | + | 0.144465i | ||||
\(703\) | −0.589700 | − | 0.158010i | −0.0222409 | − | 0.00595944i | ||||
\(704\) | −9.33261 | + | 5.38818i | −0.351736 | + | 0.203075i | ||||
\(705\) | 17.3472 | + | 0.722394i | 0.653333 | + | 0.0272069i | ||||
\(706\) | 12.0198i | 0.452370i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.98563 | − | 6.98563i | −0.262536 | − | 0.262536i | ||||
\(709\) | 28.2967 | + | 16.3371i | 1.06270 | + | 0.613552i | 0.926179 | − | 0.377084i | \(-0.123073\pi\) |
0.136525 | + | 0.990637i | \(0.456407\pi\) | |||||||
\(710\) | −3.03212 | − | 13.5478i | −0.113794 | − | 0.508441i | ||||
\(711\) | −4.93165 | − | 8.54186i | −0.184951 | − | 0.320345i | ||||
\(712\) | 12.7382 | − | 3.41319i | 0.477385 | − | 0.127915i | ||||
\(713\) | 1.28028 | − | 1.28028i | 0.0479469 | − | 0.0479469i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −42.6341 | − | 13.3481i | −1.59443 | − | 0.499192i | ||||
\(716\) | −13.1632 | + | 22.7994i | −0.491933 | + | 0.852052i | ||||
\(717\) | 5.24897 | − | 19.5894i | 0.196027 | − | 0.731581i | ||||
\(718\) | 1.61104 | − | 6.01247i | 0.0601233 | − | 0.224383i | ||||
\(719\) | 9.66239 | − | 16.7357i | 0.360346 | − | 0.624138i | −0.627671 | − | 0.778478i | \(-0.715992\pi\) |
0.988018 | + | 0.154340i | \(0.0493252\pi\) | |||||||
\(720\) | 1.66319 | − | 0.870061i | 0.0619832 | − | 0.0324253i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.2601 | + | 10.2601i | −0.381841 | + | 0.381841i | ||||
\(723\) | 2.67555 | − | 0.716912i | 0.0995048 | − | 0.0266622i | ||||
\(724\) | −6.00966 | − | 10.4090i | −0.223347 | − | 0.386849i | ||||
\(725\) | 1.15197 | − | 13.8074i | 0.0427830 | − | 0.512794i | ||||
\(726\) | 2.53566 | + | 1.46396i | 0.0941072 | + | 0.0543328i | ||||
\(727\) | 2.71795 | + | 2.71795i | 0.100803 | + | 0.100803i | 0.755710 | − | 0.654907i | \(-0.227292\pi\) |
−0.654907 | + | 0.755710i | \(0.727292\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0.960044 | − | 23.0540i | 0.0355328 | − | 0.853267i | ||||
\(731\) | −7.15181 | + | 4.12910i | −0.264519 | + | 0.152720i | ||||
\(732\) | −19.5803 | − | 5.24652i | −0.723709 | − | 0.193917i | ||||
\(733\) | −0.872739 | − | 3.25711i | −0.0322354 | − | 0.120304i | 0.947933 | − | 0.318469i | \(-0.103169\pi\) |
−0.980169 | + | 0.198165i | \(0.936502\pi\) | |||||||
\(734\) | 15.9321 | 0.588064 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.42747 | 0.163199 | ||||||||
\(737\) | −0.587125 | − | 2.19118i | −0.0216270 | − | 0.0807132i | ||||
\(738\) | 6.40510 | + | 1.71624i | 0.235775 | + | 0.0631757i | ||||
\(739\) | −4.29271 | + | 2.47840i | −0.157910 | + | 0.0911693i | −0.576873 | − | 0.816834i | \(-0.695727\pi\) |
0.418963 | + | 0.908003i | \(0.362394\pi\) | |||||||
\(740\) | 18.7659 | + | 20.3968i | 0.689848 | + | 0.749800i | ||||
\(741\) | 0.361923i | 0.0132956i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6556 | + | 15.6556i | 0.574347 | + | 0.574347i | 0.933340 | − | 0.358993i | \(-0.116880\pi\) |
−0.358993 | + | 0.933340i | \(0.616880\pi\) | |||||||
\(744\) | −5.41695 | − | 3.12748i | −0.198595 | − | 0.114659i | ||||
\(745\) | −20.8610 | − | 13.2310i | −0.764289 | − | 0.484745i | ||||
\(746\) | −0.807303 | − | 1.39829i | −0.0295575 | − | 0.0511950i | ||||
\(747\) | 2.23440 | − | 0.598706i | 0.0817525 | − | 0.0219055i | ||||
\(748\) | 8.12896 | − | 8.12896i | 0.297224 | − | 0.297224i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.06357 | − | 8.47393i | 0.0388360 | − | 0.309424i | ||||
\(751\) | 5.59544 | − | 9.69159i | 0.204181 | − | 0.353651i | −0.745691 | − | 0.666292i | \(-0.767880\pi\) |
0.949871 | + | 0.312641i | \(0.101214\pi\) | |||||||
\(752\) | −1.68694 | + | 6.29575i | −0.0615164 | + | 0.229582i | ||||
\(753\) | 1.57875 | − | 5.89197i | 0.0575328 | − | 0.214715i | ||||
\(754\) | −5.49042 | + | 9.50969i | −0.199949 | + | 0.346322i | ||||
\(755\) | −19.0704 | − | 36.4545i | −0.694045 | − | 1.32672i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4977 | − | 29.4977i | 1.07211 | − | 1.07211i | 0.0749214 | − | 0.997189i | \(-0.476129\pi\) |
0.997189 | − | 0.0749214i | \(-0.0238706\pi\) | |||||||
\(758\) | −13.8077 | + | 3.69977i | −0.501520 | + | 0.134382i | ||||
\(759\) | −1.45473 | − | 2.51967i | −0.0528035 | − | 0.0914584i | ||||
\(760\) | −0.397309 | + | 0.0889211i | −0.0144119 | + | 0.00322551i | ||||
\(761\) | 24.3504 | + | 14.0587i | 0.882703 | + | 0.509629i | 0.871549 | − | 0.490309i | \(-0.163116\pi\) |
0.0111541 | + | 0.999938i | \(0.496449\pi\) | |||||||
\(762\) | 3.69181 | + | 3.69181i | 0.133740 | + | 0.133740i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 7.63986i | − | 0.276400i | ||||||
\(765\) | 3.46765 | − | 3.19038i | 0.125373 | − | 0.115349i | ||||
\(766\) | −19.5862 | + | 11.3081i | −0.707679 | + | 0.408579i | ||||
\(767\) | −34.9474 | − | 9.36412i | −1.26188 | − | 0.338119i | ||||
\(768\) | −3.34324 | − | 12.4771i | −0.120639 | − | 0.450230i | ||||
\(769\) | 6.61248 | 0.238452 | 0.119226 | − | 0.992867i | \(-0.461959\pi\) | ||||
0.119226 | + | 0.992867i | \(0.461959\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.85449 | −0.102802 | ||||||||
\(772\) | 2.49177 | + | 9.29941i | 0.0896807 | + | 0.334693i | ||||
\(773\) | −43.3367 | − | 11.6120i | −1.55871 | − | 0.417656i | −0.626457 | − | 0.779456i | \(-0.715496\pi\) |
−0.932256 | + | 0.361800i | \(0.882162\pi\) | |||||||
\(774\) | 2.59249 | − | 1.49678i | 0.0931853 | − | 0.0538005i | ||||
\(775\) | 10.8404 | − | 5.10823i | 0.389399 | − | 0.183493i | ||||
\(776\) | 25.3133i | 0.908695i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.8607 | + | 13.8607i | 0.496929 | + | 0.496929i | ||||
\(779\) | 0.524495 | + | 0.302817i | 0.0187920 | + | 0.0108496i | ||||
\(780\) | 8.80041 | − | 13.8755i | 0.315105 | − | 0.496821i | ||||
\(781\) | −15.6516 | − | 27.1094i | −0.560058 | − | 0.970049i | ||||
\(782\) | 1.17460 | − | 0.314733i | 0.0420035 | − | 0.0112548i | ||||
\(783\) | −1.95945 | + | 1.95945i | −0.0700249 | + | 0.0700249i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.992027 | + | 3.16855i | −0.0354070 | + | 0.113090i | ||||
\(786\) | 0.247305 | − | 0.428345i | 0.00882108 | − | 0.0152786i | ||||
\(787\) | 8.21624 | − | 30.6634i | 0.292877 | − | 1.09303i | −0.650011 | − | 0.759924i | \(-0.725236\pi\) |
0.942889 | − | 0.333108i | \(-0.108097\pi\) | |||||||
\(788\) | 6.57108 | − | 24.5236i | 0.234085 | − | 0.873617i | ||||
\(789\) | −11.8572 | + | 20.5372i | −0.422127 | + | 0.731145i | ||||
\(790\) | 5.03372 | − | 16.0777i | 0.179092 | − | 0.572021i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −7.10728 | + | 7.10728i | −0.252546 | + | 0.252546i | ||||
\(793\) | −71.7082 | + | 19.2142i | −2.54643 | + | 0.682315i | ||||
\(794\) | −3.63833 | − | 6.30177i | −0.129119 | − | 0.223641i | ||||
\(795\) | −10.3964 | + | 16.3919i | −0.368723 | + | 0.581360i | ||||
\(796\) | 3.27670 | + | 1.89180i | 0.116139 | + | 0.0670531i | ||||
\(797\) | 5.14677 | + | 5.14677i | 0.182308 | + | 0.182308i | 0.792361 | − | 0.610053i | \(-0.208852\pi\) |
−0.610053 | + | 0.792361i | \(0.708852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3622i | 0.578854i | ||||||||
\(800\) | 27.5768 | + | 9.91153i | 0.974988 | + | 0.350425i | ||||
\(801\) | 4.37614 | − | 2.52657i | 0.154623 | − | 0.0892718i | ||||
\(802\) | −10.8835 | − | 2.91622i | −0.384309 | − | 0.102975i | ||||
\(803\) | −13.4656 | − | 50.2541i | −0.475189 | − | 1.77343i | ||||
\(804\) | 0.834323 | 0.0294243 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.49747 | −0.334534 | ||||||||
\(807\) | 6.40192 | + | 23.8923i | 0.225358 | + | 0.841049i | ||||
\(808\) | 48.3885 | + | 12.9657i | 1.70230 | + | 0.456130i | ||||
\(809\) | −19.5042 | + | 11.2608i | −0.685732 | + | 0.395907i | −0.802011 | − | 0.597309i | \(-0.796237\pi\) |
0.116279 | + | 0.993217i | \(0.462903\pi\) | |||||||
\(810\) | −1.25700 | + | 1.15650i | −0.0441666 | + | 0.0406352i | ||||
\(811\) | 34.9145i | 1.22602i | 0.790077 | + | 0.613008i | \(0.210040\pi\) | ||||
−0.790077 | + | 0.613008i | \(0.789960\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.92367 | − | 2.92367i | −0.102538 | − | 0.102538i | ||||
\(814\) | −22.2948 | − | 12.8719i | −0.781432 | − | 0.451160i | ||||
\(815\) | −16.9893 | + | 3.80235i | −0.595108 | + | 0.133190i | ||||
\(816\) | 0.884454 | + | 1.53192i | 0.0309621 | + | 0.0536279i | ||||
\(817\) | 0.264094 | − | 0.0707639i | 0.00923949 | − | 0.00247572i | ||||
\(818\) | 5.70414 | − | 5.70414i | 0.199441 | − | 0.199441i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.7450 | − | 24.3629i | −0.445074 | − | 0.850790i | ||||
\(821\) | −4.26320 | + | 7.38408i | −0.148787 | + | 0.257706i | −0.930779 | − | 0.365582i | \(-0.880870\pi\) |
0.781993 | + | 0.623288i | \(0.214203\pi\) | |||||||
\(822\) | −2.86222 | + | 10.6820i | −0.0998315 | + | 0.372576i | ||||
\(823\) | −12.4099 | + | 46.3143i | −0.432581 | + | 1.61441i | 0.314209 | + | 0.949354i | \(0.398261\pi\) |
−0.746790 | + | 0.665060i | \(0.768406\pi\) | |||||||
\(824\) | −4.31498 | + | 7.47377i | −0.150320 | + | 0.260361i | ||||
\(825\) | −3.42027 | − | 18.9506i | −0.119079 | − | 0.659776i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37.8440 | + | 37.8440i | −1.31597 | + | 1.31597i | −0.399025 | + | 0.916940i | \(0.630651\pi\) |
−0.916940 | + | 0.399025i | \(0.869349\pi\) | |||||||
\(828\) | 1.03361 | − | 0.276955i | 0.0359205 | − | 0.00962486i | ||||
\(829\) | 16.8570 | + | 29.1972i | 0.585469 | + | 1.01406i | 0.994817 | + | 0.101683i | \(0.0324228\pi\) |
−0.409348 | + | 0.912378i | \(0.634244\pi\) | |||||||
\(830\) | 3.33666 | + | 2.11625i | 0.115817 | + | 0.0734561i | ||||
\(831\) | −14.8350 | − | 8.56502i | −0.514622 | − | 0.297117i | ||||
\(832\) | −10.2638 | − | 10.2638i | −0.355832 | − | 0.355832i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.9323i | 0.586319i | ||||||||
\(835\) | 4.04598 | + | 4.39760i | 0.140017 | + | 0.152185i | ||||
\(836\) | −0.329618 | + | 0.190305i | −0.0114001 | + | 0.00658184i | ||||
\(837\) | −2.31507 | − | 0.620321i | −0.0800205 | − | 0.0214414i | ||||
\(838\) | 3.07378 | + | 11.4715i | 0.106182 | + | 0.396277i | ||||
\(839\) | −16.0665 | −0.554679 | −0.277339 | − | 0.960772i | \(-0.589453\pi\) | ||||
−0.277339 | + | 0.960772i | \(0.589453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3211 | 0.735212 | ||||||||
\(842\) | 0.652204 | + | 2.43406i | 0.0224764 | + | 0.0838832i | ||||
\(843\) | −5.07381 | − | 1.35952i | −0.174751 | − | 0.0468245i | ||||
\(844\) | −14.7499 | + | 8.51585i | −0.507712 | + | 0.293128i | ||||
\(845\) | 1.29422 | − | 31.0786i | 0.0445224 | − | 1.06914i | ||||
\(846\) | − | 5.93123i | − | 0.203920i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.15260 | − | 5.15260i | −0.176941 | − | 0.176941i | ||||
\(849\) | −2.04201 | − | 1.17895i | −0.0700814 | − | 0.0404615i | ||||
\(850\) | 8.02065 | + | 0.669172i | 0.275106 | + | 0.0229524i | ||||
\(851\) | 3.30525 | + | 5.72486i | 0.113303 | + | 0.196246i | ||||
\(852\) | 11.1207 | − | 2.97978i | 0.380989 | − | 0.102086i | ||||
\(853\) | 5.14393 | − | 5.14393i | 0.176125 | − | 0.176125i | −0.613539 | − | 0.789664i | \(-0.710255\pi\) |
0.789664 | + | 0.613539i | \(0.210255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.138232 | + | 0.0723134i | −0.00472745 | + | 0.00247307i | ||||
\(856\) | 11.8059 | − | 20.4483i | 0.403516 | − | 0.698910i | ||||
\(857\) | −2.06832 | + | 7.71909i | −0.0706526 | + | 0.263679i | −0.992212 | − | 0.124557i | \(-0.960249\pi\) |
0.921560 | + | 0.388236i | \(0.126916\pi\) | |||||||
\(858\) | −3.95001 | + | 14.7416i | −0.134851 | + | 0.503271i | ||||
\(859\) | −21.0400 | + | 36.4424i | −0.717877 | + | 1.24340i | 0.243963 | + | 0.969785i | \(0.421553\pi\) |
−0.961839 | + | 0.273615i | \(0.911781\pi\) | |||||||
\(860\) | −11.8456 | − | 3.70868i | −0.403931 | − | 0.126465i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.61119 | + | 7.61119i | −0.259238 | + | 0.259238i | ||||
\(863\) | 16.3618 | − | 4.38413i | 0.556962 | − | 0.149237i | 0.0306516 | − | 0.999530i | \(-0.490242\pi\) |
0.526310 | + | 0.850293i | \(0.323575\pi\) | |||||||
\(864\) | −2.93039 | − | 5.07559i | −0.0996939 | − | 0.172675i | ||||
\(865\) | −3.38941 | − | 15.1442i | −0.115243 | − | 0.514920i | ||||
\(866\) | −1.61524 | − | 0.932557i | −0.0548879 | − | 0.0316896i | ||||
\(867\) | −8.88082 | − | 8.88082i | −0.301608 | − | 0.301608i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 37.9871i | − | 1.28862i | ||||||
\(870\) | −4.72913 | − | 0.196936i | −0.160332 | − | 0.00667676i | ||||
\(871\) | 2.64615 | − | 1.52776i | 0.0896614 | − | 0.0517660i | ||||
\(872\) | 5.44649 | + | 1.45938i | 0.184441 | + | 0.0494209i | ||||
\(873\) | 2.51039 | + | 9.36890i | 0.0849638 | + | 0.317089i | ||||
\(874\) | −0.0402602 | −0.00136182 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.1350 | 0.646510 | ||||||||
\(877\) | −4.23918 | − | 15.8208i | −0.143147 | − | 0.534232i | −0.999831 | − | 0.0183902i | \(-0.994146\pi\) |
0.856684 | − | 0.515842i | \(-0.172521\pi\) | |||||||
\(878\) | 20.0084 | + | 5.36123i | 0.675250 | + | 0.180933i | ||||
\(879\) | 18.6842 | − | 10.7873i | 0.630202 | − | 0.363847i | ||||
\(880\) | 7.22281 | + | 0.300781i | 0.243481 | + | 0.0101393i | ||||
\(881\) | − | 8.72058i | − | 0.293804i | −0.989151 | − | 0.146902i | \(-0.953070\pi\) | ||
0.989151 | − | 0.146902i | \(-0.0469301\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.0876 | + | 17.0876i | 0.575044 | + | 0.575044i | 0.933534 | − | 0.358490i | \(-0.116708\pi\) |
−0.358490 | + | 0.933534i | \(0.616708\pi\) | |||||||
\(884\) | 13.4100 | + | 7.74229i | 0.451028 | + | 0.260401i | ||||
\(885\) | −3.40609 | − | 15.2187i | −0.114494 | − | 0.511572i | ||||
\(886\) | 13.0445 | + | 22.5938i | 0.438240 | + | 0.759054i | ||||
\(887\) | −36.0664 | + | 9.66396i | −1.21099 | + | 0.324484i | −0.807151 | − | 0.590346i | \(-0.798991\pi\) |
−0.403840 | + | 0.914830i | \(0.632325\pi\) | |||||||
\(888\) | 16.1482 | − | 16.1482i | 0.541898 | − | 0.541898i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 8.23690 | + | 2.57886i | 0.276101 | + | 0.0864435i | ||||
\(891\) | −1.92568 | + | 3.33538i | −0.0645127 | + | 0.111739i | ||||
\(892\) | −6.06223 | + | 22.6246i | −0.202979 | + | 0.757526i | ||||
\(893\) | 0.140207 | − | 0.523259i | 0.00469184 | − | 0.0175102i | ||||
\(894\) | −4.21949 | + | 7.30836i | −0.141121 | + | 0.244428i | ||||
\(895\) | −36.8244 | + | 19.2639i | −1.23090 | + | 0.643922i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.77107 | − | 2.77107i | 0.0925235 | − | 0.0925235i | ||||
\(898\) | 7.23289 | − | 1.93805i | 0.241365 | − | 0.0646735i | ||||
\(899\) | −3.32077 | − | 5.75174i | −0.110754 | − | 0.191831i | ||||
\(900\) | 7.05793 | + | 0.588852i | 0.235264 | + | 0.0196284i | ||||
\(901\) | −15.8420 | − | 9.14640i | −0.527775 | − | 0.304711i | ||||
\(902\) | 18.0585 | + | 18.0585i | 0.601282 | + | 0.601282i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 15.2733i | − | 0.507984i | ||||||
\(905\) | 0.789441 | − | 18.9572i | 0.0262419 | − | 0.630160i | ||||
\(906\) | −12.1716 | + | 7.02729i | −0.404375 | + | 0.233466i | ||||
\(907\) | 32.3002 | + | 8.65482i | 1.07251 | + | 0.287379i | 0.751525 | − | 0.659705i | \(-0.229319\pi\) |
0.320987 | + | 0.947084i | \(0.395985\pi\) | |||||||
\(908\) | −0.573005 | − | 2.13848i | −0.0190158 | − | 0.0709681i | ||||
\(909\) | 19.1953 | 0.636667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8226 | −0.590490 | −0.295245 | − | 0.955422i | \(-0.595401\pi\) | ||||
−0.295245 | + | 0.955422i | \(0.595401\pi\) | |||||||
\(912\) | −0.0151576 | − | 0.0565691i | −0.000501920 | − | 0.00187319i | ||||
\(913\) | 8.60549 | + | 2.30583i | 0.284800 | + | 0.0763120i | ||||
\(914\) | −0.514622 | + | 0.297117i | −0.0170222 | + | 0.00982776i | ||||
\(915\) | −21.6662 | − | 23.5491i | −0.716262 | − | 0.778510i | ||||
\(916\) | 11.0955i | 0.366605i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.13823 | − | 1.13823i | −0.0375673 | − | 0.0375673i | ||||
\(919\) | 18.6847 | + | 10.7876i | 0.616351 | + | 0.355850i | 0.775447 | − | 0.631413i | \(-0.217525\pi\) |
−0.159096 | + | 0.987263i | \(0.550858\pi\) | |||||||
\(920\) | 3.72284 | + | 2.36118i | 0.122738 | + | 0.0778458i | ||||
\(921\) | 10.3377 | + | 17.9055i | 0.340640 | + | 0.590005i | ||||
\(922\) | 0.613733 | − | 0.164449i | 0.0202122 | − | 0.00541585i | ||||
\(923\) | 29.8142 | − | 29.8142i | 0.981346 | − | 0.981346i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.77107 | + | 43.0570i | 0.255511 | + | 1.41571i | ||||
\(926\) | −2.94454 | + | 5.10009i | −0.0967636 | + | 0.167599i | ||||
\(927\) | −0.855857 | + | 3.19410i | −0.0281100 | + | 0.104908i | ||||
\(928\) | 4.20339 | − | 15.6873i | 0.137983 | − | 0.514960i | ||||
\(929\) | −19.1535 | + | 33.1748i | −0.628405 | + | 1.08843i | 0.359467 | + | 0.933158i | \(0.382959\pi\) |
−0.987872 | + | 0.155272i | \(0.950375\pi\) | |||||||
\(930\) | −1.89763 | − | 3.62745i | −0.0622257 | − | 0.118949i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.42778 | + | 1.42778i | −0.0467686 | + | 0.0467686i | ||||
\(933\) | 2.76465 | − | 0.740787i | 0.0905107 | − | 0.0242523i | ||||
\(934\) | 12.5760 | + | 21.7823i | 0.411500 | + | 0.712739i | ||||
\(935\) | 17.7096 | − | 3.96355i | 0.579165 | − | 0.129622i | ||||
\(936\) | −11.7246 | − | 6.76921i | −0.383231 | − | 0.221258i | ||||
\(937\) | 13.2317 | + | 13.2317i | 0.432262 | + | 0.432262i | 0.889397 | − | 0.457135i | \(-0.151125\pi\) |
−0.457135 | + | 0.889397i | \(0.651125\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.3194i | 0.434662i | ||||||||
\(940\) | −18.0987 | + | 16.6516i | −0.590314 | + | 0.543115i | ||||
\(941\) | 2.23517 | − | 1.29048i | 0.0728645 | − | 0.0420683i | −0.463125 | − | 0.886293i | \(-0.653272\pi\) |
0.535990 | + | 0.844225i | \(0.319939\pi\) | |||||||
\(942\) | 1.09559 | + | 0.293563i | 0.0356963 | + | 0.00956479i | ||||
\(943\) | −1.69728 | − | 6.33435i | −0.0552711 | − | 0.206275i | ||||
\(944\) | 5.85450 | 0.190548 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.5293 | 0.374848 | ||||||||
\(947\) | 1.80892 | + | 6.75097i | 0.0587819 | + | 0.219377i | 0.989069 | − | 0.147456i | \(-0.0471086\pi\) |
−0.930287 | + | 0.366833i | \(0.880442\pi\) | |||||||
\(948\) | 13.4952 | + | 3.61603i | 0.438304 | + | 0.117443i | ||||
\(949\) | 60.6887 | − | 35.0387i | 1.97004 | − | 1.13740i | ||||
\(950\) | −0.250764 | − | 0.0901283i | −0.00813585 | − | 0.00292415i | ||||
\(951\) | − | 10.4413i | − | 0.338582i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16.3558 | − | 16.3558i | −0.529818 | − | 0.529818i | 0.390700 | − | 0.920518i | \(-0.372233\pi\) |
−0.920518 | + | 0.390700i | \(0.872233\pi\) | |||||||
\(954\) | 5.74266 | + | 3.31552i | 0.185925 | + | 0.107344i | ||||
\(955\) | 6.45947 | − | 10.1845i | 0.209024 | − | 0.329564i | ||||
\(956\) | 14.3636 | + | 24.8784i | 0.464551 | + | 0.804625i | ||||
\(957\) | −10.3088 | + | 2.76222i | −0.333235 | + | 0.0892900i | ||||
\(958\) | −21.8390 | + | 21.8390i | −0.705587 | + | 0.705587i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.86939 | − | 5.97087i | 0.0603345 | − | 0.192709i | ||||
\(961\) | −12.6278 | + | 21.8720i | −0.407349 | + | 0.705550i | ||||
\(962\) | 8.97467 | − | 33.4939i | 0.289355 | − | 1.07989i | ||||
\(963\) | 2.34164 | − | 8.73911i | 0.0754582 | − | 0.281614i | ||||
\(964\) | −1.96179 | + | 3.39793i | −0.0631851 | + | 0.109440i | ||||
\(965\) | −4.54089 | + | 14.5036i | −0.146176 | + | 0.466889i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.66781 | − | 8.66781i | 0.278738 | − | 0.278738i | −0.553867 | − | 0.832605i | \(-0.686848\pi\) |
0.832605 | + | 0.553867i | \(0.186848\pi\) | |||||||
\(968\) | −9.66239 | + | 2.58903i | −0.310561 | + | 0.0832146i | ||||
\(969\) | −0.0735096 | − | 0.127322i | −0.00236147 | − | 0.00409019i | ||||
\(970\) | −8.87349 | + | 13.9907i | −0.284910 | + | 0.449214i | ||||
\(971\) | −11.4195 | − | 6.59307i | −0.366470 | − | 0.211582i | 0.305445 | − | 0.952210i | \(-0.401195\pi\) |
−0.671915 | + | 0.740628i | \(0.734528\pi\) | |||||||
\(972\) | −1.00161 | − | 1.00161i | −0.0321267 | − | 0.0321267i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.80931i | 0.250226i | ||||||||
\(975\) | 23.4633 | − | 11.0564i | 0.751427 | − | 0.354088i | ||||
\(976\) | 10.4034 | − | 6.00641i | 0.333005 | − | 0.192260i | ||||
\(977\) | 33.4574 | + | 8.96490i | 1.07040 | + | 0.286812i | 0.750657 | − | 0.660692i | \(-0.229737\pi\) |
0.319742 | + | 0.947505i | \(0.396404\pi\) | |||||||
\(978\) | 1.53930 | + | 5.74475i | 0.0492214 | + | 0.183697i | ||||
\(979\) | 19.4614 | 0.621990 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.16057 | 0.0689818 | ||||||||
\(982\) | 3.97468 | + | 14.8337i | 0.126837 | + | 0.473362i | ||||
\(983\) | −21.4961 | − | 5.75986i | −0.685618 | − | 0.183711i | −0.100838 | − | 0.994903i | \(-0.532152\pi\) |
−0.584780 | + | 0.811192i | \(0.698819\pi\) | |||||||
\(984\) | −19.6197 | + | 11.3275i | −0.625454 | + | 0.361106i | ||||
\(985\) | 29.4944 | − | 27.1361i | 0.939769 | − | 0.864628i | ||||
\(986\) | − | 4.46061i | − | 0.142055i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.362505 | − | 0.362505i | −0.0115328 | − | 0.0115328i | ||||
\(989\) | −2.56386 | − | 1.48024i | −0.0815259 | − | 0.0470690i | ||||
\(990\) | −6.41963 | + | 1.43677i | −0.204029 | + | 0.0456635i | ||||
\(991\) | 15.0516 | + | 26.0701i | 0.478128 | + | 0.828142i | 0.999686 | − | 0.0250738i | \(-0.00798206\pi\) |
−0.521557 | + | 0.853216i | \(0.674649\pi\) | |||||||
\(992\) | 13.5681 | − | 3.63557i | 0.430788 | − | 0.115429i | ||||
\(993\) | 16.7019 | − | 16.7019i | 0.530018 | − | 0.530018i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.76859 | + | 5.29236i | 0.0877702 | + | 0.167779i | ||||
\(996\) | −1.63833 | + | 2.83767i | −0.0519125 | + | 0.0899150i | ||||
\(997\) | −8.37177 | + | 31.2439i | −0.265137 | + | 0.989503i | 0.697030 | + | 0.717042i | \(0.254504\pi\) |
−0.962167 | + | 0.272461i | \(0.912162\pi\) | |||||||
\(998\) | 3.04916 | − | 11.3796i | 0.0965194 | − | 0.360215i | ||||
\(999\) | 4.37527 | − | 7.57819i | 0.138427 | − | 0.239763i |
(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 | 735.2.v.a.313.5 | 32 | ||
5.2 | odd | 4 | inner | 735.2.v.a.607.3 | 32 | ||
7.2 | even | 3 | 105.2.m.a.13.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 735.2.v.a.178.3 | 32 | ||
7.4 | even | 3 | inner | 735.2.v.a.178.4 | 32 | ||
7.5 | odd | 6 | 105.2.m.a.13.5 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 735.2.v.a.313.6 | 32 | ||
21.2 | odd | 6 | 315.2.p.e.118.4 | 16 | |||
21.5 | even | 6 | 315.2.p.e.118.3 | 16 | |||
28.19 | even | 6 | 1680.2.cz.d.433.7 | 16 | |||
28.23 | odd | 6 | 1680.2.cz.d.433.2 | 16 | |||
35.2 | odd | 12 | 105.2.m.a.97.5 | yes | 16 | ||
35.9 | even | 6 | 525.2.m.b.118.3 | 16 | |||
35.12 | even | 12 | 105.2.m.a.97.6 | yes | 16 | ||
35.17 | even | 12 | inner | 735.2.v.a.472.5 | 32 | ||
35.19 | odd | 6 | 525.2.m.b.118.4 | 16 | |||
35.23 | odd | 12 | 525.2.m.b.307.4 | 16 | |||
35.27 | even | 4 | inner | 735.2.v.a.607.4 | 32 | ||
35.32 | odd | 12 | inner | 735.2.v.a.472.6 | 32 | ||
35.33 | even | 12 | 525.2.m.b.307.3 | 16 | |||
105.2 | even | 12 | 315.2.p.e.307.3 | 16 | |||
105.47 | odd | 12 | 315.2.p.e.307.4 | 16 | |||
140.47 | odd | 12 | 1680.2.cz.d.97.2 | 16 | |||
140.107 | even | 12 | 1680.2.cz.d.97.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.5 | ✓ | 16 | 7.5 | odd | 6 | ||
105.2.m.a.13.6 | yes | 16 | 7.2 | even | 3 | ||
105.2.m.a.97.5 | yes | 16 | 35.2 | odd | 12 | ||
105.2.m.a.97.6 | yes | 16 | 35.12 | even | 12 | ||
315.2.p.e.118.3 | 16 | 21.5 | even | 6 | |||
315.2.p.e.118.4 | 16 | 21.2 | odd | 6 | |||
315.2.p.e.307.3 | 16 | 105.2 | even | 12 | |||
315.2.p.e.307.4 | 16 | 105.47 | odd | 12 | |||
525.2.m.b.118.3 | 16 | 35.9 | even | 6 | |||
525.2.m.b.118.4 | 16 | 35.19 | odd | 6 | |||
525.2.m.b.307.3 | 16 | 35.33 | even | 12 | |||
525.2.m.b.307.4 | 16 | 35.23 | odd | 12 | |||
735.2.v.a.178.3 | 32 | 7.3 | odd | 6 | inner | ||
735.2.v.a.178.4 | 32 | 7.4 | even | 3 | inner | ||
735.2.v.a.313.5 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.a.313.6 | 32 | 7.6 | odd | 2 | inner | ||
735.2.v.a.472.5 | 32 | 35.17 | even | 12 | inner | ||
735.2.v.a.472.6 | 32 | 35.32 | odd | 12 | inner | ||
735.2.v.a.607.3 | 32 | 5.2 | odd | 4 | inner | ||
735.2.v.a.607.4 | 32 | 35.27 | even | 4 | inner | ||
1680.2.cz.d.97.2 | 16 | 140.47 | odd | 12 | |||
1680.2.cz.d.97.7 | 16 | 140.107 | even | 12 | |||
1680.2.cz.d.433.2 | 16 | 28.23 | odd | 6 | |||
1680.2.cz.d.433.7 | 16 | 28.19 | even | 6 |