Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.9935104.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 6x^{3} + 16x^{2} - 8x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.5 | ||
Root | \(1.91004 + 1.91004i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.o.199.2 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82009i | 0.997052i | 0.866875 | + | 0.498526i | \(0.166125\pi\) | ||||
−0.866875 | + | 0.498526i | \(0.833875\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 0.0470959 | 0.00588699 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 8.46027 | 0.575648 | ||||||||
\(7\) | 7.12434i | 0.384678i | 0.981329 | + | 0.192339i | \(0.0616074\pi\) | ||||
−0.981329 | + | 0.192339i | \(0.938393\pi\) | |||||||
\(8\) | 22.6935i | 1.00292i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | − 0.141288i | − 0.00339886i | ||||||||
\(13\) | 66.8837i | 1.42694i | 0.700686 | + | 0.713470i | \(0.252877\pi\) | ||||
−0.700686 | + | 0.713470i | \(0.747123\pi\) | |||||||
\(14\) | −20.0913 | −0.383544 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −63.6210 | −0.994078 | ||||||||
\(17\) | 40.9051i | 0.583585i | 0.956482 | + | 0.291793i | \(0.0942517\pi\) | ||||
−0.956482 | + | 0.291793i | \(0.905748\pi\) | |||||||
\(18\) | − 25.3808i | − 0.332351i | ||||||||
\(19\) | −4.85136 | −0.0585779 | −0.0292889 | − | 0.999571i | \(-0.509324\pi\) | ||||
−0.0292889 | + | 0.999571i | \(0.509324\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.3730 | 0.222094 | ||||||||
\(22\) | − 31.0210i | − 0.300623i | ||||||||
\(23\) | − 128.183i | − 1.16208i | −0.813874 | − | 0.581042i | \(-0.802645\pi\) | ||||
0.813874 | − | 0.581042i | \(-0.197355\pi\) | |||||||
\(24\) | 68.0806 | 0.579037 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −188.618 | −1.42273 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0.335527i | 0.00226460i | ||||||||
\(29\) | 224.689 | 1.43875 | 0.719375 | − | 0.694622i | \(-0.244428\pi\) | ||||
0.719375 | + | 0.694622i | \(0.244428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −267.207 | −1.54812 | −0.774060 | − | 0.633112i | \(-0.781777\pi\) | ||||
−0.774060 | + | 0.633112i | \(0.781777\pi\) | |||||||
\(32\) | 2.13129i | 0.0117738i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | −115.356 | −0.581865 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.423863 | −0.00196233 | ||||||||
\(37\) | − 418.418i | − 1.85912i | −0.368669 | − | 0.929561i | \(-0.620187\pi\) | ||||
0.368669 | − | 0.929561i | \(-0.379813\pi\) | |||||||
\(38\) | − 13.6813i | − 0.0584052i | ||||||||
\(39\) | 200.651 | 0.823844 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −496.282 | −1.89040 | −0.945198 | − | 0.326498i | \(-0.894131\pi\) | ||||
−0.945198 | + | 0.326498i | \(0.894131\pi\) | |||||||
\(42\) | 60.2738i | 0.221439i | ||||||||
\(43\) | − 90.9549i | − 0.322570i | −0.986908 | − | 0.161285i | \(-0.948436\pi\) | ||||
0.986908 | − | 0.161285i | \(-0.0515638\pi\) | |||||||
\(44\) | −0.518055 | −0.00177499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 361.486 | 1.15866 | ||||||||
\(47\) | 203.640i | 0.631998i | 0.948760 | + | 0.315999i | \(0.102340\pi\) | ||||
−0.948760 | + | 0.315999i | \(0.897660\pi\) | |||||||
\(48\) | 190.863i | 0.573931i | ||||||||
\(49\) | 292.244 | 0.852023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 122.715 | 0.336933 | ||||||||
\(52\) | 3.14995i | 0.00840038i | ||||||||
\(53\) | 219.416i | 0.568662i | 0.958726 | + | 0.284331i | \(0.0917714\pi\) | ||||
−0.958726 | + | 0.284331i | \(0.908229\pi\) | |||||||
\(54\) | −76.1424 | −0.191883 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −161.676 | −0.385802 | ||||||||
\(57\) | 14.5541i | 0.0338199i | ||||||||
\(58\) | 633.644i | 1.43451i | ||||||||
\(59\) | −585.745 | −1.29250 | −0.646250 | − | 0.763125i | \(-0.723664\pi\) | ||||
−0.646250 | + | 0.763125i | \(0.723664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 156.973 | 0.329481 | 0.164740 | − | 0.986337i | \(-0.447321\pi\) | ||||
0.164740 | + | 0.986337i | \(0.447321\pi\) | |||||||
\(62\) | − 753.547i | − 1.54356i | ||||||||
\(63\) | − 64.1191i | − 0.128226i | ||||||||
\(64\) | −514.979 | −1.00582 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −93.0629 | −0.173565 | ||||||||
\(67\) | 638.333i | 1.16395i | 0.813206 | + | 0.581976i | \(0.197720\pi\) | ||||
−0.813206 | + | 0.581976i | \(0.802280\pi\) | |||||||
\(68\) | 1.92646i | 0.00343556i | ||||||||
\(69\) | −384.548 | −0.670929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −961.243 | −1.60674 | −0.803371 | − | 0.595479i | \(-0.796962\pi\) | ||||
−0.803371 | + | 0.595479i | \(0.796962\pi\) | |||||||
\(72\) | − 204.242i | − 0.334307i | ||||||||
\(73\) | 223.078i | 0.357662i | 0.983880 | + | 0.178831i | \(0.0572315\pi\) | ||||
−0.983880 | + | 0.178831i | \(0.942769\pi\) | |||||||
\(74\) | 1179.98 | 1.85364 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.228479 | −0.000344847 0 | ||||||||
\(77\) | − 78.3678i | − 0.115985i | ||||||||
\(78\) | 565.854i | 0.821415i | ||||||||
\(79\) | −415.648 | −0.591950 | −0.295975 | − | 0.955196i | \(-0.595644\pi\) | ||||
−0.295975 | + | 0.955196i | \(0.595644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 1399.56i | − 1.88482i | ||||||||
\(83\) | 44.7029i | 0.0591178i | 0.999563 | + | 0.0295589i | \(0.00941027\pi\) | ||||
−0.999563 | + | 0.0295589i | \(0.990590\pi\) | |||||||
\(84\) | 1.00658 | 0.00130747 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 256.501 | 0.321619 | ||||||||
\(87\) | − 674.068i | − 0.830663i | ||||||||
\(88\) | − 249.629i | − 0.302392i | ||||||||
\(89\) | −809.758 | −0.964429 | −0.482214 | − | 0.876053i | \(-0.660167\pi\) | ||||
−0.482214 | + | 0.876053i | \(0.660167\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −476.503 | −0.548913 | ||||||||
\(92\) | − 6.03688i | − 0.00684117i | ||||||||
\(93\) | 801.620i | 0.893808i | ||||||||
\(94\) | −574.282 | −0.630135 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.39387 | 0.00679762 | ||||||||
\(97\) | 429.786i | 0.449878i | 0.974373 | + | 0.224939i | \(0.0722183\pi\) | ||||
−0.974373 | + | 0.224939i | \(0.927782\pi\) | |||||||
\(98\) | 824.154i | 0.849511i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1758.18 | −1.73213 | −0.866067 | − | 0.499928i | \(-0.833360\pi\) | ||||
−0.866067 | + | 0.499928i | \(0.833360\pi\) | |||||||
\(102\) | 346.068i | 0.335940i | ||||||||
\(103\) | 959.852i | 0.918223i | 0.888379 | + | 0.459112i | \(0.151832\pi\) | ||||
−0.888379 | + | 0.459112i | \(0.848168\pi\) | |||||||
\(104\) | −1517.83 | −1.43111 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −618.772 | −0.566985 | ||||||||
\(107\) | 1120.32i | 1.01220i | 0.862476 | + | 0.506098i | \(0.168913\pi\) | ||||
−0.862476 | + | 0.506098i | \(0.831087\pi\) | |||||||
\(108\) | 1.27159i | 0.00113295i | ||||||||
\(109\) | 1811.63 | 1.59195 | 0.795973 | − | 0.605331i | \(-0.206959\pi\) | ||||
0.795973 | + | 0.605331i | \(0.206959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1255.25 | −1.07336 | ||||||||
\(112\) | − 453.258i | − 0.382400i | ||||||||
\(113\) | − 961.487i | − 0.800435i | −0.916420 | − | 0.400217i | \(-0.868935\pi\) | ||||
0.916420 | − | 0.400217i | \(-0.131065\pi\) | |||||||
\(114\) | −41.0438 | −0.0337202 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.5820 | 0.00846991 | ||||||||
\(117\) | − 601.954i | − 0.475646i | ||||||||
\(118\) | − 1651.85i | − 1.28869i | ||||||||
\(119\) | −291.422 | −0.224493 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 442.677i | 0.328509i | ||||||||
\(123\) | 1488.85i | 1.09142i | ||||||||
\(124\) | −12.5843 | −0.00911377 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 180.822 | 0.127848 | ||||||||
\(127\) | 1524.75i | 1.06535i | 0.846320 | + | 0.532675i | \(0.178813\pi\) | ||||
−0.846320 | + | 0.532675i | \(0.821187\pi\) | |||||||
\(128\) | − 1435.24i | − 0.991079i | ||||||||
\(129\) | −272.865 | −0.186236 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −869.085 | −0.579636 | −0.289818 | − | 0.957082i | \(-0.593595\pi\) | ||||
−0.289818 | + | 0.957082i | \(0.593595\pi\) | |||||||
\(132\) | 1.55417i | 0.00102479i | ||||||||
\(133\) | − 34.5628i | − 0.0225336i | ||||||||
\(134\) | −1800.16 | −1.16052 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −928.281 | −0.585290 | ||||||||
\(137\) | − 1050.15i | − 0.654893i | −0.944870 | − | 0.327447i | \(-0.893812\pi\) | ||||
0.944870 | − | 0.327447i | \(-0.106188\pi\) | |||||||
\(138\) | − 1084.46i | − 0.668951i | ||||||||
\(139\) | 272.869 | 0.166507 | 0.0832534 | − | 0.996528i | \(-0.473469\pi\) | ||||
0.0832534 | + | 0.996528i | \(0.473469\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 610.919 | 0.364884 | ||||||||
\(142\) | − 2710.79i | − 1.60200i | ||||||||
\(143\) | − 735.721i | − 0.430238i | ||||||||
\(144\) | 572.589 | 0.331359 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −629.100 | −0.356607 | ||||||||
\(147\) | − 876.731i | − 0.491915i | ||||||||
\(148\) | − 19.7058i | − 0.0109446i | ||||||||
\(149\) | 199.929 | 0.109925 | 0.0549626 | − | 0.998488i | \(-0.482496\pi\) | ||||
0.0549626 | + | 0.998488i | \(0.482496\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2625.47 | −1.41495 | −0.707476 | − | 0.706737i | \(-0.750166\pi\) | ||||
−0.707476 | + | 0.706737i | \(0.750166\pi\) | |||||||
\(152\) | − 110.095i | − 0.0587490i | ||||||||
\(153\) | − 368.146i | − 0.194528i | ||||||||
\(154\) | 221.004 | 0.115643 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.44985 | 0.00484996 | ||||||||
\(157\) | − 1581.68i | − 0.804023i | −0.915635 | − | 0.402012i | \(-0.868311\pi\) | ||||
0.915635 | − | 0.402012i | \(-0.131689\pi\) | |||||||
\(158\) | − 1172.16i | − 0.590205i | ||||||||
\(159\) | 658.247 | 0.328317 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 913.216 | 0.447028 | ||||||||
\(162\) | 228.427i | 0.110784i | ||||||||
\(163\) | 1104.98i | 0.530974i | 0.964114 | + | 0.265487i | \(0.0855328\pi\) | ||||
−0.964114 | + | 0.265487i | \(0.914467\pi\) | |||||||
\(164\) | −23.3729 | −0.0111287 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −126.066 | −0.0589436 | ||||||||
\(167\) | 200.333i | 0.0928276i | 0.998922 | + | 0.0464138i | \(0.0147793\pi\) | ||||
−0.998922 | + | 0.0464138i | \(0.985221\pi\) | |||||||
\(168\) | 485.029i | 0.222743i | ||||||||
\(169\) | −2276.43 | −1.03616 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.6623 | 0.0195260 | ||||||||
\(172\) | − 4.28360i | − 0.00189896i | ||||||||
\(173\) | − 2070.79i | − 0.910052i | −0.890478 | − | 0.455026i | \(-0.849630\pi\) | ||||
0.890478 | − | 0.455026i | \(-0.150370\pi\) | |||||||
\(174\) | 1900.93 | 0.828214 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 699.831 | 0.299726 | ||||||||
\(177\) | 1757.24i | 0.746226i | ||||||||
\(178\) | − 2283.59i | − 0.961586i | ||||||||
\(179\) | −2060.68 | −0.860462 | −0.430231 | − | 0.902719i | \(-0.641568\pi\) | ||||
−0.430231 | + | 0.902719i | \(0.641568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4113.93 | 1.68943 | 0.844713 | − | 0.535220i | \(-0.179771\pi\) | ||||
0.844713 | + | 0.535220i | \(0.179771\pi\) | |||||||
\(182\) | − 1343.78i | − 0.547294i | ||||||||
\(183\) | − 470.918i | − 0.190226i | ||||||||
\(184\) | 2908.91 | 1.16548 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2260.64 | −0.891173 | ||||||||
\(187\) | − 449.956i | − 0.175958i | ||||||||
\(188\) | 9.59060i | 0.00372056i | ||||||||
\(189\) | −192.357 | −0.0740314 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2771.96 | 1.05012 | 0.525058 | − | 0.851066i | \(-0.324044\pi\) | ||||
0.525058 | + | 0.851066i | \(0.324044\pi\) | |||||||
\(192\) | 1544.94i | 0.580709i | ||||||||
\(193\) | 219.884i | 0.0820082i | 0.999159 | + | 0.0410041i | \(0.0130557\pi\) | ||||
−0.999159 | + | 0.0410041i | \(0.986944\pi\) | |||||||
\(194\) | −1212.03 | −0.448552 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.7635 | 0.00501585 | ||||||||
\(197\) | − 2211.07i | − 0.799655i | −0.916590 | − | 0.399827i | \(-0.869070\pi\) | ||||
0.916590 | − | 0.399827i | \(-0.130930\pi\) | |||||||
\(198\) | 279.189i | 0.100208i | ||||||||
\(199\) | 471.758 | 0.168050 | 0.0840252 | − | 0.996464i | \(-0.473222\pi\) | ||||
0.0840252 | + | 0.996464i | \(0.473222\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1915.00 | 0.672008 | ||||||||
\(202\) | − 4958.23i | − 1.72703i | ||||||||
\(203\) | 1600.76i | 0.553456i | ||||||||
\(204\) | 5.77939 | 0.00198352 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2706.87 | −0.915517 | ||||||||
\(207\) | 1153.64i | 0.387361i | ||||||||
\(208\) | − 4255.21i | − 1.41849i | ||||||||
\(209\) | 53.3650 | 0.0176619 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5623.68 | 1.83483 | 0.917417 | − | 0.397928i | \(-0.130271\pi\) | ||||
0.917417 | + | 0.397928i | \(0.130271\pi\) | |||||||
\(212\) | 10.3336i | 0.00334771i | ||||||||
\(213\) | 2883.73i | 0.927652i | ||||||||
\(214\) | −3159.39 | −1.00921 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −612.725 | −0.193012 | ||||||||
\(217\) | − 1903.67i | − 0.595529i | ||||||||
\(218\) | 5108.94i | 1.58725i | ||||||||
\(219\) | 669.234 | 0.206496 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2735.89 | −0.832741 | ||||||||
\(222\) | − 3539.93i | − 1.07020i | ||||||||
\(223\) | − 4421.93i | − 1.32787i | −0.747792 | − | 0.663933i | \(-0.768886\pi\) | ||||
0.747792 | − | 0.663933i | \(-0.231114\pi\) | |||||||
\(224\) | −15.1840 | −0.00452914 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2711.48 | 0.798075 | ||||||||
\(227\) | 3489.83i | 1.02039i | 0.860060 | + | 0.510194i | \(0.170426\pi\) | ||||
−0.860060 | + | 0.510194i | \(0.829574\pi\) | |||||||
\(228\) | 0.685438i | 0 0.000199098i | ||||||||
\(229\) | 84.8948 | 0.0244978 | 0.0122489 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122489 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −235.103 | −0.0669639 | ||||||||
\(232\) | 5099.00i | 1.44295i | ||||||||
\(233\) | 4075.86i | 1.14600i | 0.819555 | + | 0.573001i | \(0.194221\pi\) | ||||
−0.819555 | + | 0.573001i | \(0.805779\pi\) | |||||||
\(234\) | 1697.56 | 0.474244 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −27.5862 | −0.00760894 | ||||||||
\(237\) | 1246.94i | 0.341762i | ||||||||
\(238\) | − 821.836i | − 0.223831i | ||||||||
\(239\) | −763.901 | −0.206747 | −0.103374 | − | 0.994643i | \(-0.532964\pi\) | ||||
−0.103374 | + | 0.994643i | \(0.532964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2526.32 | 0.675248 | 0.337624 | − | 0.941281i | \(-0.390377\pi\) | ||||
0.337624 | + | 0.941281i | \(0.390377\pi\) | |||||||
\(242\) | 341.231i | 0.0906411i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 7.39278 | 0.00193965 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4198.68 | −1.08820 | ||||||||
\(247\) | − 324.477i | − 0.0835870i | ||||||||
\(248\) | − 6063.86i | − 1.55264i | ||||||||
\(249\) | 134.109 | 0.0341317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 963.988 | 0.242416 | 0.121208 | − | 0.992627i | \(-0.461323\pi\) | ||||
0.121208 | + | 0.992627i | \(0.461323\pi\) | |||||||
\(252\) | − 3.01975i | 0 0.000754866i | ||||||||
\(253\) | 1410.01i | 0.350381i | ||||||||
\(254\) | −4299.92 | −1.06221 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −72.3368 | −0.0176604 | ||||||||
\(257\) | − 1517.07i | − 0.368218i | −0.982906 | − | 0.184109i | \(-0.941060\pi\) | ||||
0.982906 | − | 0.184109i | \(-0.0589399\pi\) | |||||||
\(258\) | − 769.503i | − 0.185687i | ||||||||
\(259\) | 2980.95 | 0.715164 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2022.20 | −0.479584 | ||||||||
\(262\) | − 2450.90i | − 0.577927i | ||||||||
\(263\) | − 1420.58i | − 0.333068i | −0.986036 | − | 0.166534i | \(-0.946742\pi\) | ||||
0.986036 | − | 0.166534i | \(-0.0532575\pi\) | |||||||
\(264\) | −748.886 | −0.174586 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 97.4701 | 0.0224672 | ||||||||
\(267\) | 2429.27i | 0.556813i | ||||||||
\(268\) | 30.0629i | 0.00685217i | ||||||||
\(269\) | −6870.16 | −1.55718 | −0.778590 | − | 0.627533i | \(-0.784065\pi\) | ||||
−0.778590 | + | 0.627533i | \(0.784065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2499.86 | 0.560353 | 0.280177 | − | 0.959948i | \(-0.409607\pi\) | ||||
0.280177 | + | 0.959948i | \(0.409607\pi\) | |||||||
\(272\) | − 2602.42i | − 0.580129i | ||||||||
\(273\) | 1429.51i | 0.316915i | ||||||||
\(274\) | 2961.52 | 0.652963 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.1106 | −0.00394975 | ||||||||
\(277\) | 1562.11i | 0.338837i | 0.985544 | + | 0.169419i | \(0.0541890\pi\) | ||||
−0.985544 | + | 0.169419i | \(0.945811\pi\) | |||||||
\(278\) | 769.515i | 0.166016i | ||||||||
\(279\) | 2404.86 | 0.516040 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7476.58 | −1.58724 | −0.793621 | − | 0.608412i | \(-0.791807\pi\) | ||||
−0.793621 | + | 0.608412i | \(0.791807\pi\) | |||||||
\(282\) | 1722.85i | 0.363808i | ||||||||
\(283\) | 2680.33i | 0.563001i | 0.959561 | + | 0.281501i | \(0.0908322\pi\) | ||||
−0.959561 | + | 0.281501i | \(0.909168\pi\) | |||||||
\(284\) | −45.2706 | −0.00945887 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2074.80 | 0.428970 | ||||||||
\(287\) | − 3535.68i | − 0.727194i | ||||||||
\(288\) | − 19.1816i | − 0.00392461i | ||||||||
\(289\) | 3239.77 | 0.659428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1289.36 | 0.259737 | ||||||||
\(292\) | 10.5061i | 0.00210555i | ||||||||
\(293\) | 1320.86i | 0.263363i | 0.991292 | + | 0.131682i | \(0.0420376\pi\) | ||||
−0.991292 | + | 0.131682i | \(0.957962\pi\) | |||||||
\(294\) | 2472.46 | 0.490465 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9495.38 | 1.86455 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | 563.819i | 0.109601i | ||||||||
\(299\) | 8573.33 | 1.65822 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 647.994 | 0.124085 | ||||||||
\(302\) | − 7404.06i | − 1.41078i | ||||||||
\(303\) | 5274.54i | 1.00005i | ||||||||
\(304\) | 308.649 | 0.0582310 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1038.20 | 0.193955 | ||||||||
\(307\) | 6644.48i | 1.23525i | 0.786475 | + | 0.617623i | \(0.211904\pi\) | ||||
−0.786475 | + | 0.617623i | \(0.788096\pi\) | |||||||
\(308\) | − 3.69080i | 0 0.000682802i | ||||||||
\(309\) | 2879.56 | 0.530136 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6911.90 | −1.26025 | −0.630125 | − | 0.776493i | \(-0.716996\pi\) | ||||
−0.630125 | + | 0.776493i | \(0.716996\pi\) | |||||||
\(312\) | 4553.48i | 0.826251i | ||||||||
\(313\) | − 3967.78i | − 0.716524i | −0.933621 | − | 0.358262i | \(-0.883370\pi\) | ||||
0.933621 | − | 0.358262i | \(-0.116630\pi\) | |||||||
\(314\) | 4460.47 | 0.801653 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.5753 | −0.00348480 | ||||||||
\(317\) | 3402.43i | 0.602838i | 0.953492 | + | 0.301419i | \(0.0974602\pi\) | ||||
−0.953492 | + | 0.301419i | \(0.902540\pi\) | |||||||
\(318\) | 1856.32i | 0.327349i | ||||||||
\(319\) | −2471.58 | −0.433800 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3360.95 | 0.584392 | ||||||||
\(322\) | 2575.35i | 0.445710i | ||||||||
\(323\) | − 198.446i | − 0.0341852i | ||||||||
\(324\) | 3.81477 | 0.000654110 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3116.15 | −0.529409 | ||||||||
\(327\) | − 5434.88i | − 0.919111i | ||||||||
\(328\) | − 11262.4i | − 1.89592i | ||||||||
\(329\) | −1450.80 | −0.243116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4518.53 | 0.750335 | 0.375167 | − | 0.926957i | \(-0.377585\pi\) | ||||
0.375167 | + | 0.926957i | \(0.377585\pi\) | |||||||
\(332\) | 2.10532i | 0 0.000348026i | ||||||||
\(333\) | 3765.76i | 0.619707i | ||||||||
\(334\) | −564.956 | −0.0925540 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1359.77 | −0.220779 | ||||||||
\(337\) | 615.717i | 0.0995260i | 0.998761 | + | 0.0497630i | \(0.0158466\pi\) | ||||
−0.998761 | + | 0.0497630i | \(0.984153\pi\) | |||||||
\(338\) | − 6419.75i | − 1.03310i | ||||||||
\(339\) | −2884.46 | −0.462131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2939.27 | 0.466776 | ||||||||
\(342\) | 123.132i | 0.0194684i | ||||||||
\(343\) | 4525.69i | 0.712433i | ||||||||
\(344\) | 2064.09 | 0.323512 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5839.80 | 0.907369 | ||||||||
\(347\) | 8001.58i | 1.23789i | 0.785435 | + | 0.618944i | \(0.212439\pi\) | ||||
−0.785435 | + | 0.618944i | \(0.787561\pi\) | |||||||
\(348\) | − 31.7459i | − 0.00489011i | ||||||||
\(349\) | −934.074 | −0.143266 | −0.0716330 | − | 0.997431i | \(-0.522821\pi\) | ||||
−0.0716330 | + | 0.997431i | \(0.522821\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1805.86 | −0.274615 | ||||||||
\(352\) | − 23.4442i | − 0.00354994i | ||||||||
\(353\) | 11951.7i | 1.80205i | 0.433764 | + | 0.901026i | \(0.357185\pi\) | ||||
−0.433764 | + | 0.901026i | \(0.642815\pi\) | |||||||
\(354\) | −4955.56 | −0.744026 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −38.1363 | −0.00567758 | ||||||||
\(357\) | 874.266i | 0.129611i | ||||||||
\(358\) | − 5811.31i | − 0.857926i | ||||||||
\(359\) | −2014.59 | −0.296173 | −0.148086 | − | 0.988974i | \(-0.547311\pi\) | ||||
−0.148086 | + | 0.988974i | \(0.547311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6835.46 | −0.996569 | ||||||||
\(362\) | 11601.7i | 1.68445i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −22.4413 | −0.00323144 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1328.03 | 0.189665 | ||||||||
\(367\) | − 4133.31i | − 0.587893i | −0.955822 | − | 0.293947i | \(-0.905031\pi\) | ||||
0.955822 | − | 0.293947i | \(-0.0949688\pi\) | |||||||
\(368\) | 8155.10i | 1.15520i | ||||||||
\(369\) | 4466.54 | 0.630132 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1563.19 | −0.218752 | ||||||||
\(372\) | 37.7530i | 0.00526184i | ||||||||
\(373\) | 3255.81i | 0.451955i | 0.974133 | + | 0.225978i | \(0.0725576\pi\) | ||||
−0.974133 | + | 0.225978i | \(0.927442\pi\) | |||||||
\(374\) | 1268.92 | 0.175439 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4621.30 | −0.633844 | ||||||||
\(377\) | 15028.1i | 2.05301i | ||||||||
\(378\) | − 542.465i | − 0.0738131i | ||||||||
\(379\) | 3279.44 | 0.444469 | 0.222234 | − | 0.974993i | \(-0.428665\pi\) | ||||
0.222234 | + | 0.974993i | \(0.428665\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4574.24 | 0.615080 | ||||||||
\(382\) | 7817.18i | 1.04702i | ||||||||
\(383\) | 10824.2i | 1.44410i | 0.691841 | + | 0.722050i | \(0.256800\pi\) | ||||
−0.691841 | + | 0.722050i | \(0.743200\pi\) | |||||||
\(384\) | −4305.71 | −0.572200 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −620.092 | −0.0817664 | ||||||||
\(387\) | 818.594i | 0.107523i | ||||||||
\(388\) | 20.2412i | 0.00264843i | ||||||||
\(389\) | 8828.59 | 1.15071 | 0.575356 | − | 0.817903i | \(-0.304863\pi\) | ||||
0.575356 | + | 0.817903i | \(0.304863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5243.32 | 0.678174 | ||||||||
\(392\) | 6632.04i | 0.854512i | ||||||||
\(393\) | 2607.25i | 0.334653i | ||||||||
\(394\) | 6235.41 | 0.797297 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.66250 | 0.000591665 0 | ||||||||
\(397\) | 8975.60i | 1.13469i | 0.823480 | + | 0.567346i | \(0.192030\pi\) | ||||
−0.823480 | + | 0.567346i | \(0.807970\pi\) | |||||||
\(398\) | 1330.40i | 0.167555i | ||||||||
\(399\) | −103.688 | −0.0130098 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10084.8 | 1.25589 | 0.627947 | − | 0.778257i | \(-0.283896\pi\) | ||||
0.627947 | + | 0.778257i | \(0.283896\pi\) | |||||||
\(402\) | 5400.47i | 0.670027i | ||||||||
\(403\) | − 17871.8i | − 2.20907i | ||||||||
\(404\) | −82.8031 | −0.0101971 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4514.30 | −0.551825 | ||||||||
\(407\) | 4602.60i | 0.560546i | ||||||||
\(408\) | 2784.84i | 0.337917i | ||||||||
\(409\) | −7533.27 | −0.910749 | −0.455374 | − | 0.890300i | \(-0.650495\pi\) | ||||
−0.455374 | + | 0.890300i | \(0.650495\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3150.45 | −0.378103 | ||||||||
\(412\) | 45.2051i | 0.00540557i | ||||||||
\(413\) | − 4173.05i | − 0.497197i | ||||||||
\(414\) | −3253.38 | −0.386219 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −142.549 | −0.0168005 | ||||||||
\(417\) | − 818.607i | − 0.0961327i | ||||||||
\(418\) | 150.494i | 0.0176098i | ||||||||
\(419\) | 1987.86 | 0.231774 | 0.115887 | − | 0.993262i | \(-0.463029\pi\) | ||||
0.115887 | + | 0.993262i | \(0.463029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13280.0 | 1.53736 | 0.768678 | − | 0.639635i | \(-0.220915\pi\) | ||||
0.768678 | + | 0.639635i | \(0.220915\pi\) | |||||||
\(422\) | 15859.3i | 1.82942i | ||||||||
\(423\) | − 1832.76i | − 0.210666i | ||||||||
\(424\) | −4979.32 | −0.570323 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8132.38 | −0.924918 | ||||||||
\(427\) | 1118.33i | 0.126744i | ||||||||
\(428\) | 52.7623i | 0.00595879i | ||||||||
\(429\) | −2207.16 | −0.248398 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11935.3 | −1.33388 | −0.666939 | − | 0.745112i | \(-0.732396\pi\) | ||||
−0.666939 | + | 0.745112i | \(0.732396\pi\) | |||||||
\(432\) | − 1717.77i | − 0.191310i | ||||||||
\(433\) | 12937.5i | 1.43588i | 0.696102 | + | 0.717942i | \(0.254916\pi\) | ||||
−0.696102 | + | 0.717942i | \(0.745084\pi\) | |||||||
\(434\) | 5368.53 | 0.593773 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 85.3202 | 0.00937178 | ||||||||
\(437\) | 621.860i | 0.0680723i | ||||||||
\(438\) | 1887.30i | 0.205887i | ||||||||
\(439\) | 2181.67 | 0.237187 | 0.118594 | − | 0.992943i | \(-0.462161\pi\) | ||||
0.118594 | + | 0.992943i | \(0.462161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2630.19 | −0.284008 | ||||||||
\(442\) | − 7715.45i | − 0.830286i | ||||||||
\(443\) | − 8733.61i | − 0.936673i | −0.883550 | − | 0.468337i | \(-0.844853\pi\) | ||||
0.883550 | − | 0.468337i | \(-0.155147\pi\) | |||||||
\(444\) | −59.1173 | −0.00631888 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12470.2 | 1.32395 | ||||||||
\(447\) | − 599.788i | − 0.0634653i | ||||||||
\(448\) | − 3668.88i | − 0.386916i | ||||||||
\(449\) | 10113.3 | 1.06298 | 0.531490 | − | 0.847065i | \(-0.321632\pi\) | ||||
0.531490 | + | 0.847065i | \(0.321632\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5459.10 | 0.569976 | ||||||||
\(452\) | − 45.2821i | − 0.00471215i | ||||||||
\(453\) | 7876.41i | 0.816923i | ||||||||
\(454\) | −9841.62 | −1.01738 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −330.284 | −0.0339188 | ||||||||
\(457\) | − 18924.7i | − 1.93711i | −0.248793 | − | 0.968557i | \(-0.580034\pi\) | ||||
0.248793 | − | 0.968557i | \(-0.419966\pi\) | |||||||
\(458\) | 239.411i | 0.0244256i | ||||||||
\(459\) | −1104.44 | −0.112311 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12279.2 | 1.24056 | 0.620280 | − | 0.784380i | \(-0.287019\pi\) | ||||
0.620280 | + | 0.784380i | \(0.287019\pi\) | |||||||
\(462\) | − 663.012i | − 0.0667665i | ||||||||
\(463\) | − 2512.53i | − 0.252197i | −0.992018 | − | 0.126098i | \(-0.959755\pi\) | ||||
0.992018 | − | 0.126098i | \(-0.0402455\pi\) | |||||||
\(464\) | −14295.0 | −1.43023 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11494.3 | −1.14262 | ||||||||
\(467\) | − 13924.8i | − 1.37979i | −0.723910 | − | 0.689894i | \(-0.757657\pi\) | ||||
0.723910 | − | 0.689894i | \(-0.242343\pi\) | |||||||
\(468\) | − 28.3496i | − 0.00280013i | ||||||||
\(469\) | −4547.70 | −0.447747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4745.03 | −0.464203 | ||||||||
\(472\) | − 13292.6i | − 1.29628i | ||||||||
\(473\) | 1000.50i | 0.0972584i | ||||||||
\(474\) | −3516.49 | −0.340755 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.7248 | −0.00132159 | ||||||||
\(477\) | − 1974.74i | − 0.189554i | ||||||||
\(478\) | − 2154.27i | − 0.206138i | ||||||||
\(479\) | 17622.0 | 1.68094 | 0.840468 | − | 0.541862i | \(-0.182280\pi\) | ||||
0.840468 | + | 0.541862i | \(0.182280\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27985.4 | 2.65285 | ||||||||
\(482\) | 7124.46i | 0.673257i | ||||||||
\(483\) | − 2739.65i | − 0.258092i | ||||||||
\(484\) | 5.69861 | 0.000535181 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 685.282 | 0.0639609 | ||||||||
\(487\) | 6109.87i | 0.568510i | 0.958749 | + | 0.284255i | \(0.0917463\pi\) | ||||
−0.958749 | + | 0.284255i | \(0.908254\pi\) | |||||||
\(488\) | 3562.27i | 0.330443i | ||||||||
\(489\) | 3314.94 | 0.306558 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4134.23 | 0.379990 | 0.189995 | − | 0.981785i | \(-0.439153\pi\) | ||||
0.189995 | + | 0.981785i | \(0.439153\pi\) | |||||||
\(492\) | 70.1186i | 0.00642518i | ||||||||
\(493\) | 9190.95i | 0.839634i | ||||||||
\(494\) | 915.055 | 0.0833406 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17000.0 | 1.53895 | ||||||||
\(497\) | − 6848.23i | − 0.618078i | ||||||||
\(498\) | 378.199i | 0.0340311i | ||||||||
\(499\) | −16556.0 | −1.48527 | −0.742633 | − | 0.669698i | \(-0.766423\pi\) | ||||
−0.742633 | + | 0.669698i | \(0.766423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 600.998 | 0.0535941 | ||||||||
\(502\) | 2718.53i | 0.241701i | ||||||||
\(503\) | 22181.6i | 1.96626i | 0.182899 | + | 0.983132i | \(0.441452\pi\) | ||||
−0.182899 | + | 0.983132i | \(0.558548\pi\) | |||||||
\(504\) | 1455.09 | 0.128601 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3976.35 | −0.349348 | ||||||||
\(507\) | 6829.30i | 0.598225i | ||||||||
\(508\) | 71.8094i | 0.00627171i | ||||||||
\(509\) | 19760.4 | 1.72076 | 0.860380 | − | 0.509654i | \(-0.170226\pi\) | ||||
0.860380 | + | 0.509654i | \(0.170226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1589.28 | −0.137585 | ||||||||
\(512\) | − 11685.9i | − 1.00869i | ||||||||
\(513\) | − 130.987i | − 0.0112733i | ||||||||
\(514\) | 4278.26 | 0.367132 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.8508 | −0.00109637 | ||||||||
\(517\) | − 2240.04i | − 0.190555i | ||||||||
\(518\) | 8406.55i | 0.713055i | ||||||||
\(519\) | −6212.36 | −0.525419 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10283.0 | −0.864697 | −0.432349 | − | 0.901707i | \(-0.642315\pi\) | ||||
−0.432349 | + | 0.901707i | \(0.642315\pi\) | |||||||
\(522\) | − 5702.80i | − 0.478170i | ||||||||
\(523\) | − 1923.24i | − 0.160798i | −0.996763 | − | 0.0803992i | \(-0.974380\pi\) | ||||
0.996763 | − | 0.0803992i | \(-0.0256195\pi\) | |||||||
\(524\) | −40.9304 | −0.00341231 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4006.17 | 0.332086 | ||||||||
\(527\) | − 10930.1i | − 0.903460i | ||||||||
\(528\) | − 2099.49i | − 0.173047i | ||||||||
\(529\) | −4263.77 | −0.350437 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5271.71 | 0.430834 | ||||||||
\(532\) | − 1.62777i | 0 0.000132655i | ||||||||
\(533\) | − 33193.2i | − 2.69748i | ||||||||
\(534\) | −6850.77 | −0.555172 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14486.0 | −1.16735 | ||||||||
\(537\) | 6182.05i | 0.496788i | ||||||||
\(538\) | − 19374.5i | − 1.55259i | ||||||||
\(539\) | −3214.68 | −0.256894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10243.2 | −0.814027 | −0.407014 | − | 0.913422i | \(-0.633430\pi\) | ||||
−0.407014 | + | 0.913422i | \(0.633430\pi\) | |||||||
\(542\) | 7049.83i | 0.558701i | ||||||||
\(543\) | − 12341.8i | − 0.975391i | ||||||||
\(544\) | −87.1807 | −0.00687103 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4031.34 | −0.315981 | ||||||||
\(547\) | 483.940i | 0.0378277i | 0.999821 | + | 0.0189139i | \(0.00602083\pi\) | ||||
−0.999821 | + | 0.0189139i | \(0.993979\pi\) | |||||||
\(548\) | − 49.4578i | − 0.00385535i | ||||||||
\(549\) | −1412.76 | −0.109827 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1090.05 | −0.0842789 | ||||||||
\(552\) | − 8726.74i | − 0.672889i | ||||||||
\(553\) | − 2961.22i | − 0.227710i | ||||||||
\(554\) | −4405.28 | −0.337839 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8510 | 0.000980223 0 | ||||||||
\(557\) | − 23789.2i | − 1.80966i | −0.425771 | − | 0.904831i | \(-0.639997\pi\) | ||||
0.425771 | − | 0.904831i | \(-0.360003\pi\) | |||||||
\(558\) | 6781.92i | 0.514519i | ||||||||
\(559\) | 6083.40 | 0.460287 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1349.87 | −0.101589 | ||||||||
\(562\) | − 21084.6i | − 1.58256i | ||||||||
\(563\) | 11331.9i | 0.848280i | 0.905597 | + | 0.424140i | \(0.139424\pi\) | ||||
−0.905597 | + | 0.424140i | \(0.860576\pi\) | |||||||
\(564\) | 28.7718 | 0.00214807 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7558.78 | −0.561342 | ||||||||
\(567\) | 577.072i | 0.0427420i | ||||||||
\(568\) | − 21814.0i | − 1.61144i | ||||||||
\(569\) | −2432.39 | −0.179211 | −0.0896056 | − | 0.995977i | \(-0.528561\pi\) | ||||
−0.0896056 | + | 0.995977i | \(0.528561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20528.2 | 1.50451 | 0.752257 | − | 0.658870i | \(-0.228965\pi\) | ||||
0.752257 | + | 0.658870i | \(0.228965\pi\) | |||||||
\(572\) | − 34.6495i | − 0.00253281i | ||||||||
\(573\) | − 8315.89i | − 0.606285i | ||||||||
\(574\) | 9970.94 | 0.725051 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4634.81 | 0.335272 | ||||||||
\(577\) | − 13961.9i | − 1.00735i | −0.863893 | − | 0.503675i | \(-0.831981\pi\) | ||||
0.863893 | − | 0.503675i | \(-0.168019\pi\) | |||||||
\(578\) | 9136.45i | 0.657484i | ||||||||
\(579\) | 659.651 | 0.0473475 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −318.479 | −0.0227413 | ||||||||
\(582\) | 3636.10i | 0.258971i | ||||||||
\(583\) | − 2413.57i | − 0.171458i | ||||||||
\(584\) | −5062.43 | −0.358707 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3724.94 | −0.262587 | ||||||||
\(587\) | 10785.8i | 0.758393i | 0.925316 | + | 0.379196i | \(0.123800\pi\) | ||||
−0.925316 | + | 0.379196i | \(0.876200\pi\) | |||||||
\(588\) | − 41.2905i | − 0.00289590i | ||||||||
\(589\) | 1296.32 | 0.0906856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6633.20 | −0.461681 | ||||||||
\(592\) | 26620.2i | 1.84811i | ||||||||
\(593\) | − 8493.60i | − 0.588179i | −0.955778 | − | 0.294090i | \(-0.904984\pi\) | ||||
0.955778 | − | 0.294090i | \(-0.0950164\pi\) | |||||||
\(594\) | 837.567 | 0.0578548 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.41586 | 0.000647128 0 | ||||||||
\(597\) | − 1415.27i | − 0.0970239i | ||||||||
\(598\) | 24177.6i | 1.65333i | ||||||||
\(599\) | 12058.7 | 0.822549 | 0.411274 | − | 0.911512i | \(-0.365084\pi\) | ||||
0.411274 | + | 0.911512i | \(0.365084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12006.7 | −0.814914 | −0.407457 | − | 0.913224i | \(-0.633584\pi\) | ||||
−0.407457 | + | 0.913224i | \(0.633584\pi\) | |||||||
\(602\) | 1827.40i | 0.123720i | ||||||||
\(603\) | − 5744.99i | − 0.387984i | ||||||||
\(604\) | −123.649 | −0.00832981 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14874.7 | −0.997100 | ||||||||
\(607\) | 27404.7i | 1.83249i | 0.400619 | + | 0.916245i | \(0.368795\pi\) | ||||
−0.400619 | + | 0.916245i | \(0.631205\pi\) | |||||||
\(608\) | − 10.3397i | 0 0.000689686i | ||||||||
\(609\) | 4802.29 | 0.319538 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13620.2 | −0.901822 | ||||||||
\(612\) | − 17.3382i | − 0.00114519i | ||||||||
\(613\) | − 19837.8i | − 1.30708i | −0.756891 | − | 0.653541i | \(-0.773283\pi\) | ||||
0.756891 | − | 0.653541i | \(-0.226717\pi\) | |||||||
\(614\) | −18738.0 | −1.23160 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1778.44 | 0.116324 | ||||||||
\(617\) | 6884.10i | 0.449179i | 0.974453 | + | 0.224589i | \(0.0721041\pi\) | ||||
−0.974453 | + | 0.224589i | \(0.927896\pi\) | |||||||
\(618\) | 8120.60i | 0.528574i | ||||||||
\(619\) | 11903.8 | 0.772944 | 0.386472 | − | 0.922301i | \(-0.373694\pi\) | ||||
0.386472 | + | 0.922301i | \(0.373694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3460.93 | 0.223643 | ||||||||
\(622\) | − 19492.2i | − 1.25654i | ||||||||
\(623\) | − 5768.99i | − 0.370995i | ||||||||
\(624\) | −12765.6 | −0.818965 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11189.5 | 0.714411 | ||||||||
\(627\) | − 160.095i | − 0.0101971i | ||||||||
\(628\) | − 74.4906i | − 0.00473328i | ||||||||
\(629\) | 17115.4 | 1.08496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −912.730 | −0.0575836 | −0.0287918 | − | 0.999585i | \(-0.509166\pi\) | ||||
−0.0287918 | + | 0.999585i | \(0.509166\pi\) | |||||||
\(632\) | − 9432.51i | − 0.593679i | ||||||||
\(633\) | − 16871.0i | − 1.05934i | ||||||||
\(634\) | −9595.16 | −0.601061 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 31.0008 | 0.00193280 | ||||||||
\(637\) | 19546.4i | 1.21578i | ||||||||
\(638\) | − 6970.09i | − 0.432521i | ||||||||
\(639\) | 8651.19 | 0.535580 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17066.1 | 1.05159 | 0.525796 | − | 0.850610i | \(-0.323767\pi\) | ||||
0.525796 | + | 0.850610i | \(0.323767\pi\) | |||||||
\(642\) | 9478.17i | 0.582669i | ||||||||
\(643\) | − 27311.7i | − 1.67507i | −0.546384 | − | 0.837535i | \(-0.683996\pi\) | ||||
0.546384 | − | 0.837535i | \(-0.316004\pi\) | |||||||
\(644\) | 43.0088 | 0.00263165 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 559.634 | 0.0340844 | ||||||||
\(647\) | − 15190.8i | − 0.923050i | −0.887127 | − | 0.461525i | \(-0.847303\pi\) | ||||
0.887127 | − | 0.461525i | \(-0.152697\pi\) | |||||||
\(648\) | 1838.18i | 0.111436i | ||||||||
\(649\) | 6443.20 | 0.389704 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5711.02 | −0.343829 | ||||||||
\(652\) | 52.0401i | 0.00312584i | ||||||||
\(653\) | 9474.30i | 0.567776i | 0.958857 | + | 0.283888i | \(0.0916244\pi\) | ||||
−0.958857 | + | 0.283888i | \(0.908376\pi\) | |||||||
\(654\) | 15326.8 | 0.916402 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 31574.0 | 1.87920 | ||||||||
\(657\) | − 2007.70i | − 0.119221i | ||||||||
\(658\) | − 4091.38i | − 0.242399i | ||||||||
\(659\) | 1220.71 | 0.0721582 | 0.0360791 | − | 0.999349i | \(-0.488513\pi\) | ||||
0.0360791 | + | 0.999349i | \(0.488513\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22686.2 | −1.33494 | −0.667468 | − | 0.744639i | \(-0.732622\pi\) | ||||
−0.667468 | + | 0.744639i | \(0.732622\pi\) | |||||||
\(662\) | 12742.7i | 0.748123i | ||||||||
\(663\) | 8207.66i | 0.480783i | ||||||||
\(664\) | −1014.47 | −0.0592906 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10619.8 | −0.617880 | ||||||||
\(667\) | − 28801.3i | − 1.67195i | ||||||||
\(668\) | 9.43486i | 0 0.000546475i | ||||||||
\(669\) | −13265.8 | −0.766644 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1726.70 | −0.0993421 | ||||||||
\(672\) | 45.5521i | 0.00261490i | ||||||||
\(673\) | − 2761.82i | − 0.158188i | −0.996867 | − | 0.0790938i | \(-0.974797\pi\) | ||||
0.996867 | − | 0.0790938i | \(-0.0252027\pi\) | |||||||
\(674\) | −1736.38 | −0.0992326 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −107.211 | −0.00609984 | ||||||||
\(677\) | − 16975.2i | − 0.963680i | −0.876259 | − | 0.481840i | \(-0.839969\pi\) | ||||
0.876259 | − | 0.481840i | \(-0.160031\pi\) | |||||||
\(678\) | − 8134.44i | − 0.460769i | ||||||||
\(679\) | −3061.94 | −0.173058 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10469.5 | 0.589121 | ||||||||
\(682\) | 8289.02i | 0.465400i | ||||||||
\(683\) | 2447.72i | 0.137130i | 0.997647 | + | 0.0685649i | \(0.0218420\pi\) | ||||
−0.997647 | + | 0.0685649i | \(0.978158\pi\) | |||||||
\(684\) | 2.05632 | 0.000114949 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12762.9 | −0.710333 | ||||||||
\(687\) | − 254.684i | − 0.0141438i | ||||||||
\(688\) | 5786.64i | 0.320659i | ||||||||
\(689\) | −14675.3 | −0.811446 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27460.5 | −1.51179 | −0.755894 | − | 0.654694i | \(-0.772797\pi\) | ||||
−0.755894 | + | 0.654694i | \(0.772797\pi\) | |||||||
\(692\) | − 97.5256i | − 0.00535747i | ||||||||
\(693\) | 705.310i | 0.0386616i | ||||||||
\(694\) | −22565.2 | −1.23424 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15297.0 | 0.833090 | ||||||||
\(697\) | − 20300.5i | − 1.10321i | ||||||||
\(698\) | − 2634.17i | − 0.142844i | ||||||||
\(699\) | 12227.6 | 0.661645 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7980.51 | −0.429986 | −0.214993 | − | 0.976616i | \(-0.568973\pi\) | ||||
−0.214993 | + | 0.976616i | \(0.568973\pi\) | |||||||
\(702\) | − 5092.69i | − 0.273805i | ||||||||
\(703\) | 2029.90i | 0.108903i | ||||||||
\(704\) | 5664.76 | 0.303265 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −33704.9 | −1.79674 | ||||||||
\(707\) | − 12525.9i | − 0.666314i | ||||||||
\(708\) | 82.7586i | 0.00439302i | ||||||||
\(709\) | −4867.53 | −0.257834 | −0.128917 | − | 0.991655i | \(-0.541150\pi\) | ||||
−0.128917 | + | 0.991655i | \(0.541150\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3740.83 | 0.197317 | ||||||||
\(712\) | − 18376.3i | − 0.967247i | ||||||||
\(713\) | 34251.2i | 1.79905i | ||||||||
\(714\) | −2465.51 | −0.129229 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −97.0498 | −0.00506553 | ||||||||
\(717\) | 2291.70i | 0.119366i | ||||||||
\(718\) | − 5681.33i | − 0.295300i | ||||||||
\(719\) | −17353.3 | −0.900094 | −0.450047 | − | 0.893005i | \(-0.648593\pi\) | ||||
−0.450047 | + | 0.893005i | \(0.648593\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6838.31 | −0.353221 | ||||||||
\(722\) | − 19276.6i | − 0.993631i | ||||||||
\(723\) | − 7578.97i | − 0.389855i | ||||||||
\(724\) | 193.749 | 0.00994563 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1023.69 | 0.0523317 | ||||||||
\(727\) | 37570.5i | 1.91666i | 0.285663 | + | 0.958330i | \(0.407786\pi\) | ||||
−0.285663 | + | 0.958330i | \(0.592214\pi\) | |||||||
\(728\) | − 10813.5i | − 0.550516i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3720.52 | 0.188247 | ||||||||
\(732\) | − 22.1783i | − 0.00111986i | ||||||||
\(733\) | 10035.5i | 0.505689i | 0.967507 | + | 0.252845i | \(0.0813661\pi\) | ||||
−0.967507 | + | 0.252845i | \(0.918634\pi\) | |||||||
\(734\) | 11656.3 | 0.586160 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 273.194 | 0.0136822 | ||||||||
\(737\) | − 7021.66i | − 0.350945i | ||||||||
\(738\) | 12596.0i | 0.628274i | ||||||||
\(739\) | 20918.8 | 1.04129 | 0.520643 | − | 0.853775i | \(-0.325692\pi\) | ||||
0.520643 | + | 0.853775i | \(0.325692\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −973.432 | −0.0482590 | ||||||||
\(742\) | − 4408.34i | − 0.218107i | ||||||||
\(743\) | 25389.4i | 1.25363i | 0.779168 | + | 0.626815i | \(0.215642\pi\) | ||||
−0.779168 | + | 0.626815i | \(0.784358\pi\) | |||||||
\(744\) | −18191.6 | −0.896420 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9181.66 | −0.450623 | ||||||||
\(747\) | − 402.326i | − 0.0197059i | ||||||||
\(748\) | − 21.1911i | − 0.00103586i | ||||||||
\(749\) | −7981.51 | −0.389370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14657.0 | 0.712170 | 0.356085 | − | 0.934454i | \(-0.384111\pi\) | ||||
0.356085 | + | 0.934454i | \(0.384111\pi\) | |||||||
\(752\) | − 12955.8i | − 0.628255i | ||||||||
\(753\) | − 2891.96i | − 0.139959i | ||||||||
\(754\) | −42380.5 | −2.04696 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −9.05924 | −0.000435822 0 | ||||||||
\(757\) | − 7874.42i | − 0.378072i | −0.981970 | − | 0.189036i | \(-0.939464\pi\) | ||||
0.981970 | − | 0.189036i | \(-0.0605363\pi\) | |||||||
\(758\) | 9248.33i | 0.443159i | ||||||||
\(759\) | 4230.02 | 0.202293 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20257.8 | −0.964975 | −0.482487 | − | 0.875903i | \(-0.660267\pi\) | ||||
−0.482487 | + | 0.875903i | \(0.660267\pi\) | |||||||
\(762\) | 12899.8i | 0.613267i | ||||||||
\(763\) | 12906.6i | 0.612387i | ||||||||
\(764\) | 130.548 | 0.00618202 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30525.2 | −1.43984 | ||||||||
\(767\) | − 39176.8i | − 1.84432i | ||||||||
\(768\) | 217.010i | 0.0101962i | ||||||||
\(769\) | 39900.7 | 1.87107 | 0.935536 | − | 0.353231i | \(-0.114917\pi\) | ||||
0.935536 | + | 0.353231i | \(0.114917\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4551.20 | −0.212591 | ||||||||
\(772\) | 10.3556i | 0 0.000482781i | ||||||||
\(773\) | 22980.3i | 1.06927i | 0.845083 | + | 0.534635i | \(0.179551\pi\) | ||||
−0.845083 | + | 0.534635i | \(0.820449\pi\) | |||||||
\(774\) | −2308.51 | −0.107206 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9753.36 | −0.451192 | ||||||||
\(777\) | − 8942.86i | − 0.412900i | ||||||||
\(778\) | 24897.4i | 1.14732i | ||||||||
\(779\) | 2407.65 | 0.110735 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10573.7 | 0.484451 | ||||||||
\(782\) | 14786.6i | 0.676175i | ||||||||
\(783\) | 6066.61i | 0.276888i | ||||||||
\(784\) | −18592.8 | −0.846977 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −7352.69 | −0.333666 | ||||||||
\(787\) | 2717.00i | 0.123063i | 0.998105 | + | 0.0615316i | \(0.0195985\pi\) | ||||
−0.998105 | + | 0.0615316i | \(0.980402\pi\) | |||||||
\(788\) | − 104.132i | − 0.00470756i | ||||||||
\(789\) | −4261.75 | −0.192297 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6849.96 | 0.307910 | ||||||||
\(792\) | 2246.66i | 0.100797i | ||||||||
\(793\) | 10498.9i | 0.470149i | ||||||||
\(794\) | −25312.0 | −1.13135 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.2179 | 0.000989311 0 | ||||||||
\(797\) | 29346.0i | 1.30425i | 0.758111 | + | 0.652125i | \(0.226122\pi\) | ||||
−0.758111 | + | 0.652125i | \(0.773878\pi\) | |||||||
\(798\) | − 292.410i | − 0.0129714i | ||||||||
\(799\) | −8329.90 | −0.368825 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7287.82 | 0.321476 | ||||||||
\(802\) | 28440.2i | 1.25219i | ||||||||
\(803\) | − 2453.86i | − 0.107839i | ||||||||
\(804\) | 90.1886 | 0.00395610 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 50400.0 | 2.20256 | ||||||||
\(807\) | 20610.5i | 0.899038i | ||||||||
\(808\) | − 39899.3i | − 1.73719i | ||||||||
\(809\) | 19651.7 | 0.854037 | 0.427019 | − | 0.904243i | \(-0.359564\pi\) | ||||
0.427019 | + | 0.904243i | \(0.359564\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33226.2 | −1.43863 | −0.719316 | − | 0.694683i | \(-0.755544\pi\) | ||||
−0.719316 | + | 0.694683i | \(0.755544\pi\) | |||||||
\(812\) | 75.3895i | 0.00325819i | ||||||||
\(813\) | − 7499.58i | − 0.323520i | ||||||||
\(814\) | −12979.7 | −0.558894 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7807.27 | −0.334938 | ||||||||
\(817\) | 441.255i | 0.0188954i | ||||||||
\(818\) | − 21244.5i | − 0.908064i | ||||||||
\(819\) | 4288.52 | 0.182971 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6761.60 | −0.287432 | −0.143716 | − | 0.989619i | \(-0.545905\pi\) | ||||
−0.143716 | + | 0.989619i | \(0.545905\pi\) | |||||||
\(822\) | − 8884.55i | − 0.376988i | ||||||||
\(823\) | 30624.0i | 1.29707i | 0.761186 | + | 0.648534i | \(0.224617\pi\) | ||||
−0.761186 | + | 0.648534i | \(0.775383\pi\) | |||||||
\(824\) | −21782.4 | −0.920906 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11768.4 | 0.495731 | ||||||||
\(827\) | − 18267.5i | − 0.768106i | −0.923311 | − | 0.384053i | \(-0.874528\pi\) | ||||
0.923311 | − | 0.384053i | \(-0.125472\pi\) | |||||||
\(828\) | 54.3319i | 0.00228039i | ||||||||
\(829\) | 15153.2 | 0.634853 | 0.317427 | − | 0.948283i | \(-0.397181\pi\) | ||||
0.317427 | + | 0.948283i | \(0.397181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4686.32 | 0.195628 | ||||||||
\(832\) | − 34443.7i | − 1.43524i | ||||||||
\(833\) | 11954.3i | 0.497228i | ||||||||
\(834\) | 2308.54 | 0.0958493 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.51327 | 0.000103975 0 | ||||||||
\(837\) | − 7214.58i | − 0.297936i | ||||||||
\(838\) | 5605.93i | 0.231090i | ||||||||
\(839\) | −22328.6 | −0.918794 | −0.459397 | − | 0.888231i | \(-0.651934\pi\) | ||||
−0.459397 | + | 0.888231i | \(0.651934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26096.3 | 1.07000 | ||||||||
\(842\) | 37450.8i | 1.53283i | ||||||||
\(843\) | 22429.7i | 0.916395i | ||||||||
\(844\) | 264.852 | 0.0108016 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5168.54 | 0.210045 | ||||||||
\(847\) | 862.045i | 0.0349708i | ||||||||
\(848\) | − 13959.5i | − 0.565294i | ||||||||
\(849\) | 8041.00 | 0.325049 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −53633.9 | −2.16045 | ||||||||
\(852\) | 135.812i | 0.00546108i | ||||||||
\(853\) | − 888.939i | − 0.0356819i | −0.999841 | − | 0.0178410i | \(-0.994321\pi\) | ||||
0.999841 | − | 0.0178410i | \(-0.00567926\pi\) | |||||||
\(854\) | −3153.79 | −0.126370 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25423.9 | −1.01515 | ||||||||
\(857\) | − 11712.7i | − 0.466861i | −0.972374 | − | 0.233430i | \(-0.925005\pi\) | ||||
0.972374 | − | 0.233430i | \(-0.0749951\pi\) | |||||||
\(858\) | − 6224.40i | − 0.247666i | ||||||||
\(859\) | 9943.60 | 0.394961 | 0.197480 | − | 0.980307i | \(-0.436724\pi\) | ||||
0.197480 | + | 0.980307i | \(0.436724\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10607.0 | −0.419846 | ||||||||
\(862\) | − 33658.5i | − 1.32995i | ||||||||
\(863\) | 21912.2i | 0.864309i | 0.901800 | + | 0.432154i | \(0.142246\pi\) | ||||
−0.901800 | + | 0.432154i | \(0.857754\pi\) | |||||||
\(864\) | −57.5448 | −0.00226587 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −36485.0 | −1.43165 | ||||||||
\(867\) | − 9719.31i | − 0.380721i | ||||||||
\(868\) | − 89.6552i | − 0.00350587i | ||||||||
\(869\) | 4572.13 | 0.178480 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42694.1 | −1.66089 | ||||||||
\(872\) | 41112.2i | 1.59660i | ||||||||
\(873\) | − 3868.07i | − 0.149959i | ||||||||
\(874\) | −1753.70 | −0.0678717 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 31.5182 | 0.00121564 | ||||||||
\(877\) | 3185.48i | 0.122652i | 0.998118 | + | 0.0613261i | \(0.0195330\pi\) | ||||
−0.998118 | + | 0.0613261i | \(0.980467\pi\) | |||||||
\(878\) | 6152.50i | 0.236488i | ||||||||
\(879\) | 3962.58 | 0.152053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2812.86 | −0.107568 | −0.0537842 | − | 0.998553i | \(-0.517128\pi\) | ||||
−0.0537842 | + | 0.998553i | \(0.517128\pi\) | |||||||
\(882\) | − 7417.38i | − 0.283170i | ||||||||
\(883\) | 32216.0i | 1.22781i | 0.789380 | + | 0.613905i | \(0.210402\pi\) | ||||
−0.789380 | + | 0.613905i | \(0.789598\pi\) | |||||||
\(884\) | −128.849 | −0.00490234 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24629.6 | 0.933912 | ||||||||
\(887\) | − 44471.4i | − 1.68343i | −0.539921 | − | 0.841715i | \(-0.681546\pi\) | ||||
0.539921 | − | 0.841715i | \(-0.318454\pi\) | |||||||
\(888\) | − 28486.1i | − 1.07650i | ||||||||
\(889\) | −10862.8 | −0.409817 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | − 208.255i | − 0.00781713i | ||||||||
\(893\) | − 987.930i | − 0.0370211i | ||||||||
\(894\) | 1691.46 | 0.0632782 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 10225.1 | 0.381246 | ||||||||
\(897\) | − 25720.0i | − 0.957375i | ||||||||
\(898\) | 28520.5i | 1.05985i | ||||||||
\(899\) | −60038.5 | −2.22736 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8975.23 | −0.331862 | ||||||||
\(902\) | 15395.2i | 0.568296i | ||||||||
\(903\) | − 1943.98i | − 0.0716408i | ||||||||
\(904\) | 21819.5 | 0.802773 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22212.2 | −0.814515 | ||||||||
\(907\) | 21224.4i | 0.777005i | 0.921448 | + | 0.388502i | \(0.127008\pi\) | ||||
−0.921448 | + | 0.388502i | \(0.872992\pi\) | |||||||
\(908\) | 164.357i | 0.00600701i | ||||||||
\(909\) | 15823.6 | 0.577378 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9599.56 | 0.349119 | 0.174560 | − | 0.984647i | \(-0.444150\pi\) | ||||
0.174560 | + | 0.984647i | \(0.444150\pi\) | |||||||
\(912\) | − 925.946i | − 0.0336197i | ||||||||
\(913\) | − 491.732i | − 0.0178247i | ||||||||
\(914\) | 53369.4 | 1.93140 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.99820 | 0.000144219 0 | ||||||||
\(917\) | − 6191.66i | − 0.222973i | ||||||||
\(918\) | − 3114.61i | − 0.111980i | ||||||||
\(919\) | −51795.7 | −1.85918 | −0.929588 | − | 0.368600i | \(-0.879837\pi\) | ||||
−0.929588 | + | 0.368600i | \(0.879837\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19933.4 | 0.713169 | ||||||||
\(922\) | 34628.4i | 1.23690i | ||||||||
\(923\) | − 64291.6i | − 2.29272i | ||||||||
\(924\) | −11.0724 | −0.000394216 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7085.55 | 0.251453 | ||||||||
\(927\) | − 8638.67i | − 0.306074i | ||||||||
\(928\) | 478.878i | 0.0169396i | ||||||||
\(929\) | 18821.8 | 0.664719 | 0.332360 | − | 0.943153i | \(-0.392155\pi\) | ||||
0.332360 | + | 0.943153i | \(0.392155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1417.78 | −0.0499097 | ||||||||
\(932\) | 191.956i | 0.00674650i | ||||||||
\(933\) | 20735.7i | 0.727606i | ||||||||
\(934\) | 39269.1 | 1.37572 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13660.5 | 0.477036 | ||||||||
\(937\) | 13493.1i | 0.470437i | 0.971943 | + | 0.235218i | \(0.0755805\pi\) | ||||
−0.971943 | + | 0.235218i | \(0.924419\pi\) | |||||||
\(938\) | − 12824.9i | − 0.446427i | ||||||||
\(939\) | −11903.3 | −0.413685 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19364.0 | 0.670826 | 0.335413 | − | 0.942071i | \(-0.391124\pi\) | ||||
0.335413 | + | 0.942071i | \(0.391124\pi\) | |||||||
\(942\) | − 13381.4i | − 0.462835i | ||||||||
\(943\) | 63614.7i | 2.19680i | ||||||||
\(944\) | 37265.7 | 1.28485 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2821.51 | −0.0969717 | ||||||||
\(947\) | − 3304.64i | − 0.113396i | −0.998391 | − | 0.0566982i | \(-0.981943\pi\) | ||||
0.998391 | − | 0.0566982i | \(-0.0180573\pi\) | |||||||
\(948\) | 58.7259i | 0.00201195i | ||||||||
\(949\) | −14920.3 | −0.510361 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10207.3 | 0.348049 | ||||||||
\(952\) | − 6613.39i | − 0.225148i | ||||||||
\(953\) | − 38598.0i | − 1.31197i | −0.754772 | − | 0.655987i | \(-0.772252\pi\) | ||||
0.754772 | − | 0.655987i | \(-0.227748\pi\) | |||||||
\(954\) | 5568.95 | 0.188995 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −35.9766 | −0.00121712 | ||||||||
\(957\) | 7414.75i | 0.250454i | ||||||||
\(958\) | 49695.5i | 1.67598i | ||||||||
\(959\) | 7481.63 | 0.251923 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41608.4 | 1.39668 | ||||||||
\(962\) | 78921.2i | 2.64503i | ||||||||
\(963\) | − 10082.8i | − 0.337399i | ||||||||
\(964\) | 118.979 | 0.00397518 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7726.06 | 0.257331 | ||||||||
\(967\) | 23257.1i | 0.773421i | 0.922201 | + | 0.386710i | \(0.126389\pi\) | ||||
−0.922201 | + | 0.386710i | \(0.873611\pi\) | |||||||
\(968\) | 2745.92i | 0.0911747i | ||||||||
\(969\) | −595.337 | −0.0197368 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32050.7 | 1.05928 | 0.529638 | − | 0.848224i | \(-0.322328\pi\) | ||||
0.529638 | + | 0.848224i | \(0.322328\pi\) | |||||||
\(972\) | − 11.4443i | 0 0.000377651i | ||||||||
\(973\) | 1944.01i | 0.0640515i | ||||||||
\(974\) | −17230.4 | −0.566835 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9986.77 | −0.327529 | ||||||||
\(977\) | 19808.8i | 0.648660i | 0.945944 | + | 0.324330i | \(0.105139\pi\) | ||||
−0.945944 | + | 0.324330i | \(0.894861\pi\) | |||||||
\(978\) | 9348.44i | 0.305655i | ||||||||
\(979\) | 8907.34 | 0.290786 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16304.6 | −0.530649 | ||||||||
\(982\) | 11658.9i | 0.378870i | ||||||||
\(983\) | 10806.7i | 0.350640i | 0.984511 | + | 0.175320i | \(0.0560961\pi\) | ||||
−0.984511 | + | 0.175320i | \(0.943904\pi\) | |||||||
\(984\) | −33787.2 | −1.09461 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25919.3 | −0.837158 | ||||||||
\(987\) | 4352.40i | 0.140363i | ||||||||
\(988\) | − 15.2816i | 0 0.000492076i | ||||||||
\(989\) | −11658.8 | −0.374853 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38387.8 | −1.23050 | −0.615251 | − | 0.788331i | \(-0.710945\pi\) | ||||
−0.615251 | + | 0.788331i | \(0.710945\pi\) | |||||||
\(992\) | − 569.495i | − 0.0182273i | ||||||||
\(993\) | − 13555.6i | − 0.433206i | ||||||||
\(994\) | 19312.6 | 0.616256 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.31597 | 0.000200933 0 | ||||||||
\(997\) | 45526.2i | 1.44617i | 0.690761 | + | 0.723083i | \(0.257276\pi\) | ||||
−0.690761 | + | 0.723083i | \(0.742724\pi\) | |||||||
\(998\) | − 46689.4i | − 1.48089i | ||||||||
\(999\) | 11297.3 | 0.357788 |
(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 | 825.4.c.o.199.5 | 6 | ||
5.2 | odd | 4 | 165.4.a.f.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 825.4.a.n.1.3 | 3 | |||
5.4 | even | 2 | inner | 825.4.c.o.199.2 | 6 | ||
15.2 | even | 4 | 495.4.a.g.1.3 | 3 | |||
15.8 | even | 4 | 2475.4.a.w.1.1 | 3 | |||
55.32 | even | 4 | 1815.4.a.p.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.f.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
495.4.a.g.1.3 | 3 | 15.2 | even | 4 | |||
825.4.a.n.1.3 | 3 | 5.3 | odd | 4 | |||
825.4.c.o.199.2 | 6 | 5.4 | even | 2 | inner | ||
825.4.c.o.199.5 | 6 | 1.1 | even | 1 | trivial | ||
1815.4.a.p.1.3 | 3 | 55.32 | even | 4 | |||
2475.4.a.w.1.1 | 3 | 15.8 | even | 4 |