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: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 17x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-2.37228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.i.199.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.37228i | − 0.838728i | −0.907818 | − | 0.419364i | \(-0.862253\pi\) | ||||
0.907818 | − | 0.419364i | \(-0.137747\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 2.37228 | 0.296535 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.11684 | −0.484240 | ||||||||
\(7\) | 6.74456i | 0.364172i | 0.983283 | + | 0.182086i | \(0.0582850\pi\) | ||||
−0.983283 | + | 0.182086i | \(0.941715\pi\) | |||||||
\(8\) | − 24.6060i | − 1.08744i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | − 7.11684i | − 0.171205i | ||||||||
\(13\) | 60.9783i | 1.30095i | 0.759529 | + | 0.650474i | \(0.225430\pi\) | ||||
−0.759529 | + | 0.650474i | \(0.774570\pi\) | |||||||
\(14\) | 16.0000 | 0.305441 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −39.3940 | −0.615532 | ||||||||
\(17\) | − 99.1684i | − 1.41482i | −0.706805 | − | 0.707408i | \(-0.749864\pi\) | ||||
0.706805 | − | 0.707408i | \(-0.250136\pi\) | |||||||
\(18\) | 21.3505i | 0.279576i | ||||||||
\(19\) | −24.7011 | −0.298253 | −0.149127 | − | 0.988818i | \(-0.547646\pi\) | ||||
−0.149127 | + | 0.988818i | \(0.547646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.2337 | 0.210255 | ||||||||
\(22\) | − 26.0951i | − 0.252886i | ||||||||
\(23\) | − 112.000i | − 1.01537i | −0.861541 | − | 0.507687i | \(-0.830501\pi\) | ||||
0.861541 | − | 0.507687i | \(-0.169499\pi\) | |||||||
\(24\) | −73.8179 | −0.627834 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 144.658 | 1.09114 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 16.0000i | 0.107990i | ||||||||
\(29\) | 21.1249 | 0.135269 | 0.0676345 | − | 0.997710i | \(-0.478455\pi\) | ||||
0.0676345 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −318.717 | −1.84656 | −0.923279 | − | 0.384130i | \(-0.874502\pi\) | ||||
−0.923279 | + | 0.384130i | \(0.874502\pi\) | |||||||
\(32\) | − 103.394i | − 0.571177i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | −235.255 | −1.18665 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −21.3505 | −0.0988451 | ||||||||
\(37\) | − 150.380i | − 0.668172i | −0.942543 | − | 0.334086i | \(-0.891572\pi\) | ||||
0.942543 | − | 0.334086i | \(-0.108428\pi\) | |||||||
\(38\) | 58.5979i | 0.250153i | ||||||||
\(39\) | 182.935 | 0.751103 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −252.745 | −0.962733 | −0.481367 | − | 0.876519i | \(-0.659859\pi\) | ||||
−0.481367 | + | 0.876519i | \(0.659859\pi\) | |||||||
\(42\) | − 48.0000i | − 0.176347i | ||||||||
\(43\) | − 214.016i | − 0.759004i | −0.925191 | − | 0.379502i | \(-0.876095\pi\) | ||||
0.925191 | − | 0.379502i | \(-0.123905\pi\) | |||||||
\(44\) | 26.0951 | 0.0894087 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −265.696 | −0.851623 | ||||||||
\(47\) | 105.870i | 0.328567i | 0.986413 | + | 0.164284i | \(0.0525312\pi\) | ||||
−0.986413 | + | 0.164284i | \(0.947469\pi\) | |||||||
\(48\) | 118.182i | 0.355377i | ||||||||
\(49\) | 297.511 | 0.867379 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −297.505 | −0.816845 | ||||||||
\(52\) | 144.658i | 0.385777i | ||||||||
\(53\) | − 325.652i | − 0.843995i | −0.906597 | − | 0.421998i | \(-0.861329\pi\) | ||||
0.906597 | − | 0.421998i | \(-0.138671\pi\) | |||||||
\(54\) | 64.0516 | 0.161413 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 165.957 | 0.396016 | ||||||||
\(57\) | 74.1032i | 0.172197i | ||||||||
\(58\) | − 50.1143i | − 0.113454i | ||||||||
\(59\) | −196.000 | −0.432492 | −0.216246 | − | 0.976339i | \(-0.569381\pi\) | ||||
−0.216246 | + | 0.976339i | \(0.569381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −402.641 | −0.845130 | −0.422565 | − | 0.906333i | \(-0.638870\pi\) | ||||
−0.422565 | + | 0.906333i | \(0.638870\pi\) | |||||||
\(62\) | 756.087i | 1.54876i | ||||||||
\(63\) | − 60.7011i | − 0.121391i | ||||||||
\(64\) | −560.432 | −1.09459 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −78.2853 | −0.146004 | ||||||||
\(67\) | 27.4132i | 0.0499860i | 0.999688 | + | 0.0249930i | \(0.00795634\pi\) | ||||
−0.999688 | + | 0.0249930i | \(0.992044\pi\) | |||||||
\(68\) | − 235.255i | − 0.419543i | ||||||||
\(69\) | −336.000 | −0.586227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −300.500 | −0.502292 | −0.251146 | − | 0.967949i | \(-0.580807\pi\) | ||||
−0.251146 | + | 0.967949i | \(0.580807\pi\) | |||||||
\(72\) | 221.454i | 0.362480i | ||||||||
\(73\) | − 427.815i | − 0.685917i | −0.939351 | − | 0.342959i | \(-0.888571\pi\) | ||||
0.939351 | − | 0.342959i | \(-0.111429\pi\) | |||||||
\(74\) | −356.745 | −0.560415 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −58.5979 | −0.0884426 | ||||||||
\(77\) | 74.1902i | 0.109802i | ||||||||
\(78\) | − 433.973i | − 0.629971i | ||||||||
\(79\) | −97.5488 | −0.138925 | −0.0694627 | − | 0.997585i | \(-0.522128\pi\) | ||||
−0.0694627 | + | 0.997585i | \(0.522128\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 599.581i | 0.807472i | ||||||||
\(83\) | − 1104.62i | − 1.46082i | −0.683011 | − | 0.730408i | \(-0.739330\pi\) | ||||
0.683011 | − | 0.730408i | \(-0.260670\pi\) | |||||||
\(84\) | 48.0000 | 0.0623480 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −507.707 | −0.636598 | ||||||||
\(87\) | − 63.3748i | − 0.0780976i | ||||||||
\(88\) | − 270.666i | − 0.327876i | ||||||||
\(89\) | −463.022 | −0.551463 | −0.275732 | − | 0.961235i | \(-0.588920\pi\) | ||||
−0.275732 | + | 0.961235i | \(0.588920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −411.272 | −0.473769 | ||||||||
\(92\) | − 265.696i | − 0.301094i | ||||||||
\(93\) | 956.152i | 1.06611i | ||||||||
\(94\) | 251.152 | 0.275578 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −310.182 | −0.329769 | ||||||||
\(97\) | − 1798.36i | − 1.88243i | −0.337810 | − | 0.941214i | \(-0.609686\pi\) | ||||
0.337810 | − | 0.941214i | \(-0.390314\pi\) | |||||||
\(98\) | − 705.779i | − 0.727495i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 741.918 | 0.730927 | 0.365463 | − | 0.930826i | \(-0.380911\pi\) | ||||
0.365463 | + | 0.930826i | \(0.380911\pi\) | |||||||
\(102\) | 705.766i | 0.685111i | ||||||||
\(103\) | − 389.837i | − 0.372930i | −0.982462 | − | 0.186465i | \(-0.940297\pi\) | ||||
0.982462 | − | 0.186465i | \(-0.0597031\pi\) | |||||||
\(104\) | 1500.43 | 1.41470 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −772.538 | −0.707882 | ||||||||
\(107\) | 1538.42i | 1.38995i | 0.719032 | + | 0.694977i | \(0.244585\pi\) | ||||
−0.719032 | + | 0.694977i | \(0.755415\pi\) | |||||||
\(108\) | 64.0516i | 0.0570682i | ||||||||
\(109\) | −779.783 | −0.685226 | −0.342613 | − | 0.939477i | \(-0.611312\pi\) | ||||
−0.342613 | + | 0.939477i | \(0.611312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −451.141 | −0.385770 | ||||||||
\(112\) | − 265.696i | − 0.224160i | ||||||||
\(113\) | 1514.55i | 1.26086i | 0.776246 | + | 0.630430i | \(0.217122\pi\) | ||||
−0.776246 | + | 0.630430i | \(0.782878\pi\) | |||||||
\(114\) | 175.794 | 0.144426 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 50.1143 | 0.0401120 | ||||||||
\(117\) | − 548.804i | − 0.433649i | ||||||||
\(118\) | 464.967i | 0.362743i | ||||||||
\(119\) | 668.848 | 0.515237 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 955.179i | 0.708834i | ||||||||
\(123\) | 758.234i | 0.555834i | ||||||||
\(124\) | −756.087 | −0.547569 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | 2302.74i | 1.60894i | 0.593992 | + | 0.804471i | \(0.297551\pi\) | ||||
−0.593992 | + | 0.804471i | \(0.702449\pi\) | |||||||
\(128\) | 502.350i | 0.346890i | ||||||||
\(129\) | −642.049 | −0.438211 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2020.59 | −1.34763 | −0.673815 | − | 0.738900i | \(-0.735345\pi\) | ||||
−0.673815 | + | 0.738900i | \(0.735345\pi\) | |||||||
\(132\) | − 78.2853i | − 0.0516201i | ||||||||
\(133\) | − 166.598i | − 0.108616i | ||||||||
\(134\) | 65.0319 | 0.0419246 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2440.14 | −1.53853 | ||||||||
\(137\) | 1475.40i | 0.920088i | 0.887896 | + | 0.460044i | \(0.152166\pi\) | ||||
−0.887896 | + | 0.460044i | \(0.847834\pi\) | |||||||
\(138\) | 797.087i | 0.491685i | ||||||||
\(139\) | 1623.71 | 0.990802 | 0.495401 | − | 0.868665i | \(-0.335021\pi\) | ||||
0.495401 | + | 0.868665i | \(0.335021\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 317.609 | 0.189698 | ||||||||
\(142\) | 712.870i | 0.421287i | ||||||||
\(143\) | 670.761i | 0.392251i | ||||||||
\(144\) | 354.546 | 0.205177 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1014.90 | −0.575298 | ||||||||
\(147\) | − 892.533i | − 0.500781i | ||||||||
\(148\) | − 356.745i | − 0.198137i | ||||||||
\(149\) | 1104.11 | 0.607064 | 0.303532 | − | 0.952821i | \(-0.401834\pi\) | ||||
0.303532 | + | 0.952821i | \(0.401834\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2980.07 | 1.60606 | 0.803029 | − | 0.595940i | \(-0.203221\pi\) | ||||
0.803029 | + | 0.595940i | \(0.203221\pi\) | |||||||
\(152\) | 607.794i | 0.324333i | ||||||||
\(153\) | 892.516i | 0.471605i | ||||||||
\(154\) | 176.000 | 0.0920941 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 433.973 | 0.222728 | ||||||||
\(157\) | 2844.67i | 1.44605i | 0.690823 | + | 0.723024i | \(0.257249\pi\) | ||||
−0.690823 | + | 0.723024i | \(0.742751\pi\) | |||||||
\(158\) | 231.413i | 0.116521i | ||||||||
\(159\) | −976.956 | −0.487281 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 755.391 | 0.369771 | ||||||||
\(162\) | − 192.155i | − 0.0931920i | ||||||||
\(163\) | 1528.51i | 0.734492i | 0.930124 | + | 0.367246i | \(0.119699\pi\) | ||||
−0.930124 | + | 0.367246i | \(0.880301\pi\) | |||||||
\(164\) | −599.581 | −0.285484 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2620.47 | −1.22523 | ||||||||
\(167\) | − 383.881i | − 0.177878i | −0.996037 | − | 0.0889388i | \(-0.971652\pi\) | ||||
0.996037 | − | 0.0889388i | \(-0.0283476\pi\) | |||||||
\(168\) | − 497.870i | − 0.228640i | ||||||||
\(169\) | −1521.35 | −0.692466 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 222.310 | 0.0994178 | ||||||||
\(172\) | − 507.707i | − 0.225071i | ||||||||
\(173\) | − 2702.85i | − 1.18783i | −0.804529 | − | 0.593914i | \(-0.797582\pi\) | ||||
0.804529 | − | 0.593914i | \(-0.202418\pi\) | |||||||
\(174\) | −150.343 | −0.0655027 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −433.334 | −0.185590 | ||||||||
\(177\) | 588.000i | 0.249699i | ||||||||
\(178\) | 1098.42i | 0.462528i | ||||||||
\(179\) | 2777.61 | 1.15982 | 0.579911 | − | 0.814680i | \(-0.303087\pi\) | ||||
0.579911 | + | 0.814680i | \(0.303087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3993.61 | −1.64001 | −0.820007 | − | 0.572354i | \(-0.806030\pi\) | ||||
−0.820007 | + | 0.572354i | \(0.806030\pi\) | |||||||
\(182\) | 975.652i | 0.397363i | ||||||||
\(183\) | 1207.92i | 0.487936i | ||||||||
\(184\) | −2755.87 | −1.10416 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2268.26 | 0.894177 | ||||||||
\(187\) | − 1090.85i | − 0.426583i | ||||||||
\(188\) | 251.152i | 0.0974317i | ||||||||
\(189\) | −182.103 | −0.0700850 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 895.587 | 0.339280 | 0.169640 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169640 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(192\) | 1681.30i | 0.631964i | ||||||||
\(193\) | − 1328.24i | − 0.495382i | −0.968839 | − | 0.247691i | \(-0.920328\pi\) | ||||
0.968839 | − | 0.247691i | \(-0.0796718\pi\) | |||||||
\(194\) | −4266.21 | −1.57885 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 705.779 | 0.257208 | ||||||||
\(197\) | 154.114i | 0.0557370i | 0.999612 | + | 0.0278685i | \(0.00887197\pi\) | ||||
−0.999612 | + | 0.0278685i | \(0.991128\pi\) | |||||||
\(198\) | 234.856i | 0.0842953i | ||||||||
\(199\) | −1316.15 | −0.468842 | −0.234421 | − | 0.972135i | \(-0.575319\pi\) | ||||
−0.234421 | + | 0.972135i | \(0.575319\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 82.2397 | 0.0288594 | ||||||||
\(202\) | − 1760.04i | − 0.613049i | ||||||||
\(203\) | 142.478i | 0.0492612i | ||||||||
\(204\) | −705.766 | −0.242223 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −924.803 | −0.312787 | ||||||||
\(207\) | 1008.00i | 0.338458i | ||||||||
\(208\) | − 2402.18i | − 0.800775i | ||||||||
\(209\) | −271.712 | −0.0899268 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1735.76 | −0.566324 | −0.283162 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283162 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(212\) | − 772.538i | − 0.250274i | ||||||||
\(213\) | 901.499i | 0.289999i | ||||||||
\(214\) | 3649.57 | 1.16579 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 664.361 | 0.209278 | ||||||||
\(217\) | − 2149.61i | − 0.672465i | ||||||||
\(218\) | 1849.86i | 0.574718i | ||||||||
\(219\) | −1283.44 | −0.396014 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6047.12 | 1.84060 | ||||||||
\(222\) | 1070.23i | 0.323556i | ||||||||
\(223\) | − 1663.71i | − 0.499597i | −0.968298 | − | 0.249798i | \(-0.919636\pi\) | ||||
0.968298 | − | 0.249798i | \(-0.0803643\pi\) | |||||||
\(224\) | 697.348 | 0.208007 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3592.95 | 1.05752 | ||||||||
\(227\) | − 3658.84i | − 1.06980i | −0.844914 | − | 0.534902i | \(-0.820349\pi\) | ||||
0.844914 | − | 0.534902i | \(-0.179651\pi\) | |||||||
\(228\) | 175.794i | 0.0510624i | ||||||||
\(229\) | −1927.07 | −0.556090 | −0.278045 | − | 0.960568i | \(-0.589686\pi\) | ||||
−0.278045 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 222.571 | 0.0633942 | ||||||||
\(232\) | − 519.800i | − 0.147097i | ||||||||
\(233\) | 2784.27i | 0.782847i | 0.920211 | + | 0.391423i | \(0.128017\pi\) | ||||
−0.920211 | + | 0.391423i | \(0.871983\pi\) | |||||||
\(234\) | −1301.92 | −0.363714 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −464.967 | −0.128249 | ||||||||
\(237\) | 292.646i | 0.0802086i | ||||||||
\(238\) | − 1586.70i | − 0.432144i | ||||||||
\(239\) | −1222.60 | −0.330892 | −0.165446 | − | 0.986219i | \(-0.552906\pi\) | ||||
−0.165446 | + | 0.986219i | \(0.552906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2013.01 | −0.538047 | −0.269024 | − | 0.963134i | \(-0.586701\pi\) | ||||
−0.269024 | + | 0.963134i | \(0.586701\pi\) | |||||||
\(242\) | − 287.046i | − 0.0762480i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −955.179 | −0.250611 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1798.74 | 0.466194 | ||||||||
\(247\) | − 1506.23i | − 0.388012i | ||||||||
\(248\) | 7842.35i | 2.00802i | ||||||||
\(249\) | −3313.86 | −0.843402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2706.63 | 0.680641 | 0.340320 | − | 0.940310i | \(-0.389464\pi\) | ||||
0.340320 | + | 0.940310i | \(0.389464\pi\) | |||||||
\(252\) | − 144.000i | − 0.0359966i | ||||||||
\(253\) | − 1232.00i | − 0.306147i | ||||||||
\(254\) | 5462.76 | 1.34946 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3291.74 | −0.803647 | ||||||||
\(257\) | 225.741i | 0.0547912i | 0.999625 | + | 0.0273956i | \(0.00872138\pi\) | ||||
−0.999625 | + | 0.0273956i | \(0.991279\pi\) | |||||||
\(258\) | 1523.12i | 0.367540i | ||||||||
\(259\) | 1014.25 | 0.243330 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −190.124 | −0.0450897 | ||||||||
\(262\) | 4793.40i | 1.13029i | ||||||||
\(263\) | − 1953.42i | − 0.457997i | −0.973427 | − | 0.228998i | \(-0.926455\pi\) | ||||
0.973427 | − | 0.228998i | \(-0.0735451\pi\) | |||||||
\(264\) | −811.997 | −0.189299 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −395.217 | −0.0910989 | ||||||||
\(267\) | 1389.07i | 0.318387i | ||||||||
\(268\) | 65.0319i | 0.0148226i | ||||||||
\(269\) | 350.848 | 0.0795225 | 0.0397613 | − | 0.999209i | \(-0.487340\pi\) | ||||
0.0397613 | + | 0.999209i | \(0.487340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 254.779 | 0.0571096 | 0.0285548 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285548 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(272\) | 3906.64i | 0.870864i | ||||||||
\(273\) | 1233.81i | 0.273531i | ||||||||
\(274\) | 3500.07 | 0.771704 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −797.087 | −0.173837 | ||||||||
\(277\) | 116.478i | 0.0252654i | 0.999920 | + | 0.0126327i | \(0.00402122\pi\) | ||||
−0.999920 | + | 0.0126327i | \(0.995979\pi\) | |||||||
\(278\) | − 3851.90i | − 0.831013i | ||||||||
\(279\) | 2868.46 | 0.615519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8226.47 | 1.74644 | 0.873221 | − | 0.487325i | \(-0.162027\pi\) | ||||
0.873221 | + | 0.487325i | \(0.162027\pi\) | |||||||
\(282\) | − 753.457i | − 0.159105i | ||||||||
\(283\) | − 1561.52i | − 0.327995i | −0.986461 | − | 0.163997i | \(-0.947561\pi\) | ||||
0.986461 | − | 0.163997i | \(-0.0524389\pi\) | |||||||
\(284\) | −712.870 | −0.148947 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1591.23 | 0.328992 | ||||||||
\(287\) | − 1704.65i | − 0.350601i | ||||||||
\(288\) | 930.546i | 0.190392i | ||||||||
\(289\) | −4921.38 | −1.00171 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5395.07 | −1.08682 | ||||||||
\(292\) | − 1014.90i | − 0.203399i | ||||||||
\(293\) | − 9486.19i | − 1.89143i | −0.324997 | − | 0.945715i | \(-0.605363\pi\) | ||||
0.324997 | − | 0.945715i | \(-0.394637\pi\) | |||||||
\(294\) | −2117.34 | −0.420019 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3700.25 | −0.726598 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | − 2619.27i | − 0.509161i | ||||||||
\(299\) | 6829.56 | 1.32095 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1443.45 | 0.276408 | ||||||||
\(302\) | − 7069.56i | − 1.34705i | ||||||||
\(303\) | − 2225.75i | − 0.422001i | ||||||||
\(304\) | 973.074 | 0.183584 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2117.30 | 0.395549 | ||||||||
\(307\) | − 8443.06i | − 1.56961i | −0.619742 | − | 0.784806i | \(-0.712763\pi\) | ||||
0.619742 | − | 0.784806i | \(-0.287237\pi\) | |||||||
\(308\) | 176.000i | 0.0325602i | ||||||||
\(309\) | −1169.51 | −0.215311 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4447.17 | 0.810856 | 0.405428 | − | 0.914127i | \(-0.367123\pi\) | ||||
0.405428 | + | 0.914127i | \(0.367123\pi\) | |||||||
\(312\) | − 4501.29i | − 0.816779i | ||||||||
\(313\) | − 6480.75i | − 1.17033i | −0.810914 | − | 0.585165i | \(-0.801030\pi\) | ||||
0.810914 | − | 0.585165i | \(-0.198970\pi\) | |||||||
\(314\) | 6748.36 | 1.21284 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −231.413 | −0.0411962 | ||||||||
\(317\) | − 1252.75i | − 0.221960i | −0.993823 | − | 0.110980i | \(-0.964601\pi\) | ||||
0.993823 | − | 0.110980i | \(-0.0353990\pi\) | |||||||
\(318\) | 2317.61i | 0.408696i | ||||||||
\(319\) | 232.374 | 0.0407852 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4615.27 | 0.802490 | ||||||||
\(322\) | − 1792.00i | − 0.310137i | ||||||||
\(323\) | 2449.57i | 0.421974i | ||||||||
\(324\) | 192.155 | 0.0329484 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3626.06 | 0.616039 | ||||||||
\(327\) | 2339.35i | 0.395615i | ||||||||
\(328\) | 6219.02i | 1.04692i | ||||||||
\(329\) | −714.043 | −0.119655 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3801.44 | 0.631258 | 0.315629 | − | 0.948883i | \(-0.397785\pi\) | ||||
0.315629 | + | 0.948883i | \(0.397785\pi\) | |||||||
\(332\) | − 2620.47i | − 0.433183i | ||||||||
\(333\) | 1353.42i | 0.222724i | ||||||||
\(334\) | −910.673 | −0.149191 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −797.087 | −0.129419 | ||||||||
\(337\) | − 5456.53i | − 0.882007i | −0.897506 | − | 0.441003i | \(-0.854623\pi\) | ||||
0.897506 | − | 0.441003i | \(-0.145377\pi\) | |||||||
\(338\) | 3609.06i | 0.580790i | ||||||||
\(339\) | 4543.66 | 0.727958 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3505.89 | −0.556758 | ||||||||
\(342\) | − 527.381i | − 0.0833845i | ||||||||
\(343\) | 4319.97i | 0.680047i | ||||||||
\(344\) | −5266.08 | −0.825371 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6411.93 | −0.996264 | ||||||||
\(347\) | − 4240.53i | − 0.656033i | −0.944672 | − | 0.328017i | \(-0.893620\pi\) | ||||
0.944672 | − | 0.328017i | \(-0.106380\pi\) | |||||||
\(348\) | − 150.343i | − 0.0231587i | ||||||||
\(349\) | 8471.53 | 1.29934 | 0.649672 | − | 0.760215i | \(-0.274906\pi\) | ||||
0.649672 | + | 0.760215i | \(0.274906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1646.41 | −0.250368 | ||||||||
\(352\) | − 1137.33i | − 0.172216i | ||||||||
\(353\) | − 981.282i | − 0.147956i | −0.997260 | − | 0.0739778i | \(-0.976431\pi\) | ||||
0.997260 | − | 0.0739778i | \(-0.0235694\pi\) | |||||||
\(354\) | 1394.90 | 0.209430 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1098.42 | −0.163528 | ||||||||
\(357\) | − 2006.54i | − 0.297472i | ||||||||
\(358\) | − 6589.27i | − 0.972776i | ||||||||
\(359\) | 3020.09 | 0.443995 | 0.221997 | − | 0.975047i | \(-0.428742\pi\) | ||||
0.221997 | + | 0.975047i | \(0.428742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6248.86 | −0.911045 | ||||||||
\(362\) | 9473.96i | 1.37553i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −975.652 | −0.140489 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2865.54 | 0.409246 | ||||||||
\(367\) | 8689.40i | 1.23592i | 0.786209 | + | 0.617960i | \(0.212041\pi\) | ||||
−0.786209 | + | 0.617960i | \(0.787959\pi\) | |||||||
\(368\) | 4412.13i | 0.624995i | ||||||||
\(369\) | 2274.70 | 0.320911 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2196.38 | 0.307360 | ||||||||
\(372\) | 2268.26i | 0.316139i | ||||||||
\(373\) | − 5340.53i | − 0.741346i | −0.928763 | − | 0.370673i | \(-0.879127\pi\) | ||||
0.928763 | − | 0.370673i | \(-0.120873\pi\) | |||||||
\(374\) | −2587.81 | −0.357787 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2605.02 | 0.357297 | ||||||||
\(377\) | 1288.16i | 0.175978i | ||||||||
\(378\) | 432.000i | 0.0587822i | ||||||||
\(379\) | 1603.49 | 0.217324 | 0.108662 | − | 0.994079i | \(-0.465343\pi\) | ||||
0.108662 | + | 0.994079i | \(0.465343\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6908.23 | 0.928923 | ||||||||
\(382\) | − 2124.58i | − 0.284563i | ||||||||
\(383\) | 830.236i | 0.110765i | 0.998465 | + | 0.0553826i | \(0.0176379\pi\) | ||||
−0.998465 | + | 0.0553826i | \(0.982362\pi\) | |||||||
\(384\) | 1507.05 | 0.200277 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3150.96 | −0.415491 | ||||||||
\(387\) | 1926.15i | 0.253001i | ||||||||
\(388\) | − 4266.21i | − 0.558206i | ||||||||
\(389\) | 1746.12 | 0.227588 | 0.113794 | − | 0.993504i | \(-0.463700\pi\) | ||||
0.113794 | + | 0.993504i | \(0.463700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11106.9 | −1.43657 | ||||||||
\(392\) | − 7320.54i | − 0.943223i | ||||||||
\(393\) | 6061.76i | 0.778054i | ||||||||
\(394\) | 365.602 | 0.0467482 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −234.856 | −0.0298029 | ||||||||
\(397\) | − 10016.2i | − 1.26624i | −0.774054 | − | 0.633119i | \(-0.781774\pi\) | ||||
0.774054 | − | 0.633119i | \(-0.218226\pi\) | |||||||
\(398\) | 3122.28i | 0.393231i | ||||||||
\(399\) | −499.794 | −0.0627092 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8228.38 | 1.02470 | 0.512351 | − | 0.858776i | \(-0.328775\pi\) | ||||
0.512351 | + | 0.858776i | \(0.328775\pi\) | |||||||
\(402\) | − 195.096i | − 0.0242052i | ||||||||
\(403\) | − 19434.8i | − 2.40228i | ||||||||
\(404\) | 1760.04 | 0.216746 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 337.999 | 0.0413168 | ||||||||
\(407\) | − 1654.18i | − 0.201462i | ||||||||
\(408\) | 7320.41i | 0.888270i | ||||||||
\(409\) | 12311.5 | 1.48843 | 0.744213 | − | 0.667943i | \(-0.232825\pi\) | ||||
0.744213 | + | 0.667943i | \(0.232825\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4426.21 | 0.531213 | ||||||||
\(412\) | − 924.803i | − 0.110587i | ||||||||
\(413\) | − 1321.93i | − 0.157502i | ||||||||
\(414\) | 2391.26 | 0.283874 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6304.79 | 0.743071 | ||||||||
\(417\) | − 4871.14i | − 0.572040i | ||||||||
\(418\) | 644.577i | 0.0754241i | ||||||||
\(419\) | −13260.4 | −1.54610 | −0.773048 | − | 0.634347i | \(-0.781269\pi\) | ||||
−0.773048 | + | 0.634347i | \(0.781269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6177.74 | −0.715165 | −0.357583 | − | 0.933881i | \(-0.616399\pi\) | ||||
−0.357583 | + | 0.933881i | \(0.616399\pi\) | |||||||
\(422\) | 4117.70i | 0.474992i | ||||||||
\(423\) | − 952.826i | − 0.109522i | ||||||||
\(424\) | −8012.98 | −0.917795 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2138.61 | 0.243230 | ||||||||
\(427\) | − 2715.64i | − 0.307773i | ||||||||
\(428\) | 3649.57i | 0.412170i | ||||||||
\(429\) | 2012.28 | 0.226466 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1668.05 | 0.186421 | 0.0932103 | − | 0.995646i | \(-0.470287\pi\) | ||||
0.0932103 | + | 0.995646i | \(0.470287\pi\) | |||||||
\(432\) | − 1063.64i | − 0.118459i | ||||||||
\(433\) | 731.748i | 0.0812138i | 0.999175 | + | 0.0406069i | \(0.0129291\pi\) | ||||
−0.999175 | + | 0.0406069i | \(0.987071\pi\) | |||||||
\(434\) | −5099.48 | −0.564015 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1849.86 | −0.203194 | ||||||||
\(437\) | 2766.52i | 0.302839i | ||||||||
\(438\) | 3044.69i | 0.332148i | ||||||||
\(439\) | 14248.0 | 1.54902 | 0.774508 | − | 0.632564i | \(-0.217998\pi\) | ||||
0.774508 | + | 0.632564i | \(0.217998\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2677.60 | −0.289126 | ||||||||
\(442\) | − 14345.5i | − 1.54377i | ||||||||
\(443\) | − 174.262i | − 0.0186895i | −0.999956 | − | 0.00934473i | \(-0.997025\pi\) | ||||
0.999956 | − | 0.00934473i | \(-0.00297456\pi\) | |||||||
\(444\) | −1070.23 | −0.114394 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3946.78 | −0.419026 | ||||||||
\(447\) | − 3312.34i | − 0.350488i | ||||||||
\(448\) | − 3779.87i | − 0.398621i | ||||||||
\(449\) | −7469.97 | −0.785144 | −0.392572 | − | 0.919721i | \(-0.628415\pi\) | ||||
−0.392572 | + | 0.919721i | \(0.628415\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2780.19 | −0.290275 | ||||||||
\(452\) | 3592.95i | 0.373890i | ||||||||
\(453\) | − 8940.21i | − 0.927258i | ||||||||
\(454\) | −8679.79 | −0.897275 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1823.38 | 0.187254 | ||||||||
\(457\) | 8762.68i | 0.896939i | 0.893798 | + | 0.448469i | \(0.148031\pi\) | ||||
−0.893798 | + | 0.448469i | \(0.851969\pi\) | |||||||
\(458\) | 4571.56i | 0.466409i | ||||||||
\(459\) | 2677.55 | 0.272282 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4339.67 | 0.438435 | 0.219218 | − | 0.975676i | \(-0.429650\pi\) | ||||
0.219218 | + | 0.975676i | \(0.429650\pi\) | |||||||
\(462\) | − 528.000i | − 0.0531705i | ||||||||
\(463\) | 3932.49i | 0.394726i | 0.980330 | + | 0.197363i | \(0.0632378\pi\) | ||||
−0.980330 | + | 0.197363i | \(0.936762\pi\) | |||||||
\(464\) | −832.197 | −0.0832624 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6605.06 | 0.656596 | ||||||||
\(467\) | − 8383.97i | − 0.830758i | −0.909648 | − | 0.415379i | \(-0.863649\pi\) | ||||
0.909648 | − | 0.415379i | \(-0.136351\pi\) | |||||||
\(468\) | − 1301.92i | − 0.128592i | ||||||||
\(469\) | −184.890 | −0.0182035 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8534.02 | 0.834876 | ||||||||
\(472\) | 4822.77i | 0.470309i | ||||||||
\(473\) | − 2354.18i | − 0.228848i | ||||||||
\(474\) | 694.240 | 0.0672732 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1586.70 | 0.152786 | ||||||||
\(477\) | 2930.87i | 0.281332i | ||||||||
\(478\) | 2900.35i | 0.277529i | ||||||||
\(479\) | −9534.10 | −0.909445 | −0.454722 | − | 0.890633i | \(-0.650261\pi\) | ||||
−0.454722 | + | 0.890633i | \(0.650261\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9169.93 | 0.869258 | ||||||||
\(482\) | 4775.43i | 0.451275i | ||||||||
\(483\) | − 2266.17i | − 0.213487i | ||||||||
\(484\) | 287.046 | 0.0269577 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −576.464 | −0.0538044 | ||||||||
\(487\) | 4451.09i | 0.414164i | 0.978324 | + | 0.207082i | \(0.0663967\pi\) | ||||
−0.978324 | + | 0.207082i | \(0.933603\pi\) | |||||||
\(488\) | 9907.38i | 0.919029i | ||||||||
\(489\) | 4585.53 | 0.424059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9757.40 | −0.896833 | −0.448417 | − | 0.893825i | \(-0.648012\pi\) | ||||
−0.448417 | + | 0.893825i | \(0.648012\pi\) | |||||||
\(492\) | 1798.74i | 0.164824i | ||||||||
\(493\) | − 2094.93i | − 0.191381i | ||||||||
\(494\) | −3573.20 | −0.325437 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12555.6 | 1.13662 | ||||||||
\(497\) | − 2026.74i | − 0.182921i | ||||||||
\(498\) | 7861.40i | 0.707385i | ||||||||
\(499\) | 7173.69 | 0.643564 | 0.321782 | − | 0.946814i | \(-0.395718\pi\) | ||||
0.321782 | + | 0.946814i | \(0.395718\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1151.64 | −0.102698 | ||||||||
\(502\) | − 6420.88i | − 0.570873i | ||||||||
\(503\) | 15617.0i | 1.38435i | 0.721728 | + | 0.692177i | \(0.243348\pi\) | ||||
−0.721728 | + | 0.692177i | \(0.756652\pi\) | |||||||
\(504\) | −1493.61 | −0.132005 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2922.65 | −0.256774 | ||||||||
\(507\) | 4564.04i | 0.399795i | ||||||||
\(508\) | 5462.76i | 0.477108i | ||||||||
\(509\) | 8789.23 | 0.765375 | 0.382688 | − | 0.923878i | \(-0.374999\pi\) | ||||
0.382688 | + | 0.923878i | \(0.374999\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2885.42 | 0.249792 | ||||||||
\(512\) | 11827.7i | 1.02093i | ||||||||
\(513\) | − 666.929i | − 0.0573989i | ||||||||
\(514\) | 535.521 | 0.0459549 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1523.12 | −0.129945 | ||||||||
\(517\) | 1164.56i | 0.0990667i | ||||||||
\(518\) | − 2406.09i | − 0.204088i | ||||||||
\(519\) | −8108.56 | −0.685792 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13099.3 | 1.10152 | 0.550760 | − | 0.834664i | \(-0.314338\pi\) | ||||
0.550760 | + | 0.834664i | \(0.314338\pi\) | |||||||
\(522\) | 451.029i | 0.0378180i | ||||||||
\(523\) | − 16824.2i | − 1.40664i | −0.710876 | − | 0.703318i | \(-0.751701\pi\) | ||||
0.710876 | − | 0.703318i | \(-0.248299\pi\) | |||||||
\(524\) | −4793.40 | −0.399620 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4634.07 | −0.384135 | ||||||||
\(527\) | 31606.7i | 2.61254i | ||||||||
\(528\) | 1300.00i | 0.107150i | ||||||||
\(529\) | −377.000 | −0.0309855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1764.00 | 0.144164 | ||||||||
\(532\) | − 395.217i | − 0.0322083i | ||||||||
\(533\) | − 15411.9i | − 1.25247i | ||||||||
\(534\) | 3295.25 | 0.267040 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 674.529 | 0.0543568 | ||||||||
\(537\) | − 8332.83i | − 0.669624i | ||||||||
\(538\) | − 832.310i | − 0.0666978i | ||||||||
\(539\) | 3272.62 | 0.261525 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18863.1 | 1.49905 | 0.749527 | − | 0.661974i | \(-0.230281\pi\) | ||||
0.749527 | + | 0.661974i | \(0.230281\pi\) | |||||||
\(542\) | − 604.407i | − 0.0478995i | ||||||||
\(543\) | 11980.8i | 0.946862i | ||||||||
\(544\) | −10253.4 | −0.808110 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2926.96 | 0.229418 | ||||||||
\(547\) | − 12283.0i | − 0.960119i | −0.877236 | − | 0.480059i | \(-0.840615\pi\) | ||||
0.877236 | − | 0.480059i | \(-0.159385\pi\) | |||||||
\(548\) | 3500.07i | 0.272839i | ||||||||
\(549\) | 3623.77 | 0.281710 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −521.809 | −0.0403444 | ||||||||
\(552\) | 8267.61i | 0.637487i | ||||||||
\(553\) | − 657.924i | − 0.0505927i | ||||||||
\(554\) | 276.320 | 0.0211908 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3851.90 | 0.293808 | ||||||||
\(557\) | − 9752.05i | − 0.741845i | −0.928664 | − | 0.370923i | \(-0.879042\pi\) | ||||
0.928664 | − | 0.370923i | \(-0.120958\pi\) | |||||||
\(558\) | − 6804.78i | − 0.516253i | ||||||||
\(559\) | 13050.3 | 0.987424 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3272.56 | −0.246288 | ||||||||
\(562\) | − 19515.5i | − 1.46479i | ||||||||
\(563\) | 3447.50i | 0.258072i | 0.991640 | + | 0.129036i | \(0.0411884\pi\) | ||||
−0.991640 | + | 0.129036i | \(0.958812\pi\) | |||||||
\(564\) | 753.457 | 0.0562522 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3704.36 | −0.275098 | ||||||||
\(567\) | 546.310i | 0.0404636i | ||||||||
\(568\) | 7394.09i | 0.546213i | ||||||||
\(569\) | 3371.02 | 0.248366 | 0.124183 | − | 0.992259i | \(-0.460369\pi\) | ||||
0.124183 | + | 0.992259i | \(0.460369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15852.5 | −1.16183 | −0.580916 | − | 0.813964i | \(-0.697305\pi\) | ||||
−0.580916 | + | 0.813964i | \(0.697305\pi\) | |||||||
\(572\) | 1591.23i | 0.116316i | ||||||||
\(573\) | − 2686.76i | − 0.195883i | ||||||||
\(574\) | −4043.91 | −0.294059 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5043.89 | 0.364865 | ||||||||
\(577\) | 1376.35i | 0.0993036i | 0.998767 | + | 0.0496518i | \(0.0158112\pi\) | ||||
−0.998767 | + | 0.0496518i | \(0.984189\pi\) | |||||||
\(578\) | 11674.9i | 0.840159i | ||||||||
\(579\) | −3984.72 | −0.286009 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7450.17 | 0.531988 | ||||||||
\(582\) | 12798.6i | 0.911547i | ||||||||
\(583\) | − 3582.17i | − 0.254474i | ||||||||
\(584\) | −10526.8 | −0.745894 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22503.9 | −1.58640 | ||||||||
\(587\) | − 23021.4i | − 1.61873i | −0.587304 | − | 0.809366i | \(-0.699811\pi\) | ||||
0.587304 | − | 0.809366i | \(-0.300189\pi\) | |||||||
\(588\) | − 2117.34i | − 0.148499i | ||||||||
\(589\) | 7872.66 | 0.550742 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 462.343 | 0.0321798 | ||||||||
\(592\) | 5924.09i | 0.411281i | ||||||||
\(593\) | − 2818.69i | − 0.195194i | −0.995226 | − | 0.0975968i | \(-0.968884\pi\) | ||||
0.995226 | − | 0.0975968i | \(-0.0311156\pi\) | |||||||
\(594\) | 704.568 | 0.0486679 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2619.27 | 0.180016 | ||||||||
\(597\) | 3948.46i | 0.270686i | ||||||||
\(598\) | − 16201.6i | − 1.10792i | ||||||||
\(599\) | 17691.4 | 1.20676 | 0.603380 | − | 0.797454i | \(-0.293820\pi\) | ||||
0.603380 | + | 0.797454i | \(0.293820\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24516.1 | −1.66394 | −0.831972 | − | 0.554817i | \(-0.812788\pi\) | ||||
−0.831972 | + | 0.554817i | \(0.812788\pi\) | |||||||
\(602\) | − 3424.26i | − 0.231831i | ||||||||
\(603\) | − 246.719i | − 0.0166620i | ||||||||
\(604\) | 7069.56 | 0.476252 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5280.12 | −0.353944 | ||||||||
\(607\) | 4288.59i | 0.286768i | 0.989667 | + | 0.143384i | \(0.0457984\pi\) | ||||
−0.989667 | + | 0.143384i | \(0.954202\pi\) | |||||||
\(608\) | 2553.94i | 0.170355i | ||||||||
\(609\) | 427.435 | 0.0284410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6455.74 | −0.427449 | ||||||||
\(612\) | 2117.30i | 0.139848i | ||||||||
\(613\) | 8124.07i | 0.535283i | 0.963519 | + | 0.267641i | \(0.0862442\pi\) | ||||
−0.963519 | + | 0.267641i | \(0.913756\pi\) | |||||||
\(614\) | −20029.3 | −1.31648 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1825.52 | 0.119403 | ||||||||
\(617\) | − 14923.1i | − 0.973714i | −0.873482 | − | 0.486857i | \(-0.838143\pi\) | ||||
0.873482 | − | 0.486857i | \(-0.161857\pi\) | |||||||
\(618\) | 2774.41i | 0.180588i | ||||||||
\(619\) | −3627.68 | −0.235556 | −0.117778 | − | 0.993040i | \(-0.537577\pi\) | ||||
−0.117778 | + | 0.993040i | \(0.537577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3024.00 | 0.195409 | ||||||||
\(622\) | − 10549.9i | − 0.680087i | ||||||||
\(623\) | − 3122.88i | − 0.200827i | ||||||||
\(624\) | −7206.54 | −0.462328 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15374.2 | −0.981589 | ||||||||
\(627\) | 815.135i | 0.0519192i | ||||||||
\(628\) | 6748.36i | 0.428804i | ||||||||
\(629\) | −14913.0 | −0.945341 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12576.5 | 0.793445 | 0.396723 | − | 0.917939i | \(-0.370147\pi\) | ||||
0.396723 | + | 0.917939i | \(0.370147\pi\) | |||||||
\(632\) | 2400.28i | 0.151073i | ||||||||
\(633\) | 5207.27i | 0.326967i | ||||||||
\(634\) | −2971.87 | −0.186164 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2317.61 | −0.144496 | ||||||||
\(637\) | 18141.7i | 1.12841i | ||||||||
\(638\) | − 551.257i | − 0.0342077i | ||||||||
\(639\) | 2704.50 | 0.167431 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7292.77 | −0.449371 | −0.224686 | − | 0.974431i | \(-0.572136\pi\) | ||||
−0.224686 | + | 0.974431i | \(0.572136\pi\) | |||||||
\(642\) | − 10948.7i | − 0.673071i | ||||||||
\(643\) | 12946.3i | 0.794016i | 0.917815 | + | 0.397008i | \(0.129951\pi\) | ||||
−0.917815 | + | 0.397008i | \(0.870049\pi\) | |||||||
\(644\) | 1792.00 | 0.109650 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5811.06 | 0.353921 | ||||||||
\(647\) | 21973.3i | 1.33518i | 0.744530 | + | 0.667589i | \(0.232673\pi\) | ||||
−0.744530 | + | 0.667589i | \(0.767327\pi\) | |||||||
\(648\) | − 1993.08i | − 0.120827i | ||||||||
\(649\) | −2156.00 | −0.130401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6448.83 | −0.388248 | ||||||||
\(652\) | 3626.06i | 0.217803i | ||||||||
\(653\) | 27495.6i | 1.64776i | 0.566764 | + | 0.823880i | \(0.308195\pi\) | ||||
−0.566764 | + | 0.823880i | \(0.691805\pi\) | |||||||
\(654\) | 5549.59 | 0.331814 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9956.63 | 0.592593 | ||||||||
\(657\) | 3850.33i | 0.228639i | ||||||||
\(658\) | 1693.91i | 0.100358i | ||||||||
\(659\) | −5156.28 | −0.304796 | −0.152398 | − | 0.988319i | \(-0.548699\pi\) | ||||
−0.152398 | + | 0.988319i | \(0.548699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9328.59 | 0.548926 | 0.274463 | − | 0.961598i | \(-0.411500\pi\) | ||||
0.274463 | + | 0.961598i | \(0.411500\pi\) | |||||||
\(662\) | − 9018.10i | − 0.529454i | ||||||||
\(663\) | − 18141.4i | − 1.06267i | ||||||||
\(664\) | −27180.2 | −1.58855 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3210.70 | 0.186805 | ||||||||
\(667\) | − 2365.99i | − 0.137349i | ||||||||
\(668\) | − 910.673i | − 0.0527470i | ||||||||
\(669\) | −4991.12 | −0.288442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4429.06 | −0.254816 | ||||||||
\(672\) | − 2092.04i | − 0.120093i | ||||||||
\(673\) | − 22182.4i | − 1.27053i | −0.772293 | − | 0.635267i | \(-0.780890\pi\) | ||||
0.772293 | − | 0.635267i | \(-0.219110\pi\) | |||||||
\(674\) | −12944.4 | −0.739764 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3609.06 | −0.205340 | ||||||||
\(677\) | − 13507.1i | − 0.766797i | −0.923583 | − | 0.383399i | \(-0.874754\pi\) | ||||
0.923583 | − | 0.383399i | \(-0.125246\pi\) | |||||||
\(678\) | − 10778.8i | − 0.610559i | ||||||||
\(679\) | 12129.1 | 0.685528 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10976.5 | −0.617652 | ||||||||
\(682\) | 8316.96i | 0.466969i | ||||||||
\(683\) | 19465.6i | 1.09053i | 0.838264 | + | 0.545264i | \(0.183571\pi\) | ||||
−0.838264 | + | 0.545264i | \(0.816429\pi\) | |||||||
\(684\) | 527.381 | 0.0294809 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10248.2 | 0.570375 | ||||||||
\(687\) | 5781.22i | 0.321059i | ||||||||
\(688\) | 8430.96i | 0.467191i | ||||||||
\(689\) | 19857.7 | 1.09799 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19971.8 | −1.09951 | −0.549757 | − | 0.835324i | \(-0.685280\pi\) | ||||
−0.549757 | + | 0.835324i | \(0.685280\pi\) | |||||||
\(692\) | − 6411.93i | − 0.352233i | ||||||||
\(693\) | − 667.712i | − 0.0366007i | ||||||||
\(694\) | −10059.7 | −0.550234 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1559.40 | −0.0849265 | ||||||||
\(697\) | 25064.3i | 1.36209i | ||||||||
\(698\) | − 20096.9i | − 1.08980i | ||||||||
\(699\) | 8352.80 | 0.451977 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14180.1 | −0.764018 | −0.382009 | − | 0.924159i | \(-0.624768\pi\) | ||||
−0.382009 | + | 0.924159i | \(0.624768\pi\) | |||||||
\(702\) | 3905.75i | 0.209990i | ||||||||
\(703\) | 3714.56i | 0.199285i | ||||||||
\(704\) | −6164.75 | −0.330032 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2327.88 | −0.124095 | ||||||||
\(707\) | 5003.91i | 0.266183i | ||||||||
\(708\) | 1394.90i | 0.0740446i | ||||||||
\(709\) | −15870.6 | −0.840667 | −0.420334 | − | 0.907370i | \(-0.638087\pi\) | ||||
−0.420334 | + | 0.907370i | \(0.638087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 877.939 | 0.0463084 | ||||||||
\(712\) | 11393.1i | 0.599683i | ||||||||
\(713\) | 35696.3i | 1.87495i | ||||||||
\(714\) | −4760.09 | −0.249498 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6589.27 | 0.343928 | ||||||||
\(717\) | 3667.79i | 0.191041i | ||||||||
\(718\) | − 7164.50i | − 0.372391i | ||||||||
\(719\) | 6040.05 | 0.313290 | 0.156645 | − | 0.987655i | \(-0.449932\pi\) | ||||
0.156645 | + | 0.987655i | \(0.449932\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2629.28 | 0.135811 | ||||||||
\(722\) | 14824.0i | 0.764119i | ||||||||
\(723\) | 6039.03i | 0.310642i | ||||||||
\(724\) | −9473.96 | −0.486322 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −861.138 | −0.0440218 | ||||||||
\(727\) | 37252.3i | 1.90043i | 0.311601 | + | 0.950213i | \(0.399135\pi\) | ||||
−0.311601 | + | 0.950213i | \(0.600865\pi\) | |||||||
\(728\) | 10119.7i | 0.515196i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21223.7 | −1.07385 | ||||||||
\(732\) | 2865.54i | 0.144690i | ||||||||
\(733\) | − 6125.52i | − 0.308665i | −0.988019 | − | 0.154332i | \(-0.950677\pi\) | ||||
0.988019 | − | 0.154332i | \(-0.0493227\pi\) | |||||||
\(734\) | 20613.7 | 1.03660 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11580.1 | −0.579958 | ||||||||
\(737\) | 301.546i | 0.0150713i | ||||||||
\(738\) | − 5396.23i | − 0.269157i | ||||||||
\(739\) | 5225.97 | 0.260136 | 0.130068 | − | 0.991505i | \(-0.458480\pi\) | ||||
0.130068 | + | 0.991505i | \(0.458480\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4518.68 | −0.224019 | ||||||||
\(742\) | − 5210.43i | − 0.257791i | ||||||||
\(743\) | − 7062.96i | − 0.348741i | −0.984680 | − | 0.174371i | \(-0.944211\pi\) | ||||
0.984680 | − | 0.174371i | \(-0.0557891\pi\) | |||||||
\(744\) | 23527.0 | 1.15933 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12669.2 | −0.621788 | ||||||||
\(747\) | 9941.57i | 0.486939i | ||||||||
\(748\) | − 2587.81i | − 0.126497i | ||||||||
\(749\) | −10376.0 | −0.506182 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20755.4 | −1.00849 | −0.504244 | − | 0.863561i | \(-0.668229\pi\) | ||||
−0.504244 | + | 0.863561i | \(0.668229\pi\) | |||||||
\(752\) | − 4170.63i | − 0.202243i | ||||||||
\(753\) | − 8119.89i | − 0.392968i | ||||||||
\(754\) | 3055.88 | 0.147598 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −432.000 | −0.0207827 | ||||||||
\(757\) | 31182.9i | 1.49717i | 0.663037 | + | 0.748587i | \(0.269267\pi\) | ||||
−0.663037 | + | 0.748587i | \(0.730733\pi\) | |||||||
\(758\) | − 3803.93i | − 0.182276i | ||||||||
\(759\) | −3696.00 | −0.176754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32047.8 | 1.52659 | 0.763293 | − | 0.646052i | \(-0.223581\pi\) | ||||
0.763293 | + | 0.646052i | \(0.223581\pi\) | |||||||
\(762\) | − 16388.3i | − 0.779114i | ||||||||
\(763\) | − 5259.29i | − 0.249540i | ||||||||
\(764\) | 2124.58 | 0.100608 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1969.55 | 0.0929019 | ||||||||
\(767\) | − 11951.7i | − 0.562650i | ||||||||
\(768\) | 9875.22i | 0.463986i | ||||||||
\(769\) | −2215.88 | −0.103910 | −0.0519548 | − | 0.998649i | \(-0.516545\pi\) | ||||
−0.0519548 | + | 0.998649i | \(0.516545\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 677.223 | 0.0316337 | ||||||||
\(772\) | − 3150.96i | − 0.146898i | ||||||||
\(773\) | − 5300.56i | − 0.246634i | −0.992367 | − | 0.123317i | \(-0.960647\pi\) | ||||
0.992367 | − | 0.123317i | \(-0.0393532\pi\) | |||||||
\(774\) | 4569.36 | 0.212199 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −44250.3 | −2.04703 | ||||||||
\(777\) | − 3042.75i | − 0.140487i | ||||||||
\(778\) | − 4142.29i | − 0.190885i | ||||||||
\(779\) | 6243.06 | 0.287138 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3305.50 | −0.151447 | ||||||||
\(782\) | 26348.6i | 1.20489i | ||||||||
\(783\) | 570.373i | 0.0260325i | ||||||||
\(784\) | −11720.2 | −0.533899 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14380.2 | 0.652576 | ||||||||
\(787\) | 34374.1i | 1.55693i | 0.627687 | + | 0.778466i | \(0.284002\pi\) | ||||
−0.627687 | + | 0.778466i | \(0.715998\pi\) | |||||||
\(788\) | 365.602i | 0.0165280i | ||||||||
\(789\) | −5860.27 | −0.264425 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10215.0 | −0.459170 | ||||||||
\(792\) | 2435.99i | 0.109292i | ||||||||
\(793\) | − 24552.4i | − 1.09947i | ||||||||
\(794\) | −23761.2 | −1.06203 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3122.28 | −0.139028 | ||||||||
\(797\) | 29867.1i | 1.32741i | 0.747993 | + | 0.663707i | \(0.231018\pi\) | ||||
−0.747993 | + | 0.663707i | \(0.768982\pi\) | |||||||
\(798\) | 1185.65i | 0.0525960i | ||||||||
\(799\) | 10498.9 | 0.464862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4167.20 | 0.183821 | ||||||||
\(802\) | − 19520.0i | − 0.859447i | ||||||||
\(803\) | − 4705.96i | − 0.206812i | ||||||||
\(804\) | 195.096 | 0.00855783 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −46104.9 | −2.01486 | ||||||||
\(807\) | − 1052.54i | − 0.0459124i | ||||||||
\(808\) | − 18255.6i | − 0.794839i | ||||||||
\(809\) | 15857.2 | 0.689133 | 0.344566 | − | 0.938762i | \(-0.388026\pi\) | ||||
0.344566 | + | 0.938762i | \(0.388026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36122.6 | 1.56404 | 0.782020 | − | 0.623253i | \(-0.214189\pi\) | ||||
0.782020 | + | 0.623253i | \(0.214189\pi\) | |||||||
\(812\) | 337.999i | 0.0146077i | ||||||||
\(813\) | − 764.337i | − 0.0329723i | ||||||||
\(814\) | −3924.19 | −0.168971 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 11719.9 | 0.502794 | ||||||||
\(817\) | 5286.43i | 0.226375i | ||||||||
\(818\) | − 29206.4i | − 1.24838i | ||||||||
\(819\) | 3701.44 | 0.157923 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25779.6 | 1.09588 | 0.547938 | − | 0.836519i | \(-0.315413\pi\) | ||||
0.547938 | + | 0.836519i | \(0.315413\pi\) | |||||||
\(822\) | − 10500.2i | − 0.445544i | ||||||||
\(823\) | 22130.2i | 0.937315i | 0.883380 | + | 0.468658i | \(0.155262\pi\) | ||||
−0.883380 | + | 0.468658i | \(0.844738\pi\) | |||||||
\(824\) | −9592.32 | −0.405539 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3136.00 | −0.132101 | ||||||||
\(827\) | 18288.6i | 0.768994i | 0.923126 | + | 0.384497i | \(0.125625\pi\) | ||||
−0.923126 | + | 0.384497i | \(0.874375\pi\) | |||||||
\(828\) | 2391.26i | 0.100365i | ||||||||
\(829\) | 34956.6 | 1.46453 | 0.732263 | − | 0.681022i | \(-0.238464\pi\) | ||||
0.732263 | + | 0.681022i | \(0.238464\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 349.435 | 0.0145870 | ||||||||
\(832\) | − 34174.2i | − 1.42401i | ||||||||
\(833\) | − 29503.7i | − 1.22718i | ||||||||
\(834\) | −11555.7 | −0.479786 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −644.577 | −0.0266664 | ||||||||
\(837\) | − 8605.37i | − 0.355370i | ||||||||
\(838\) | 31457.5i | 1.29675i | ||||||||
\(839\) | 14507.5 | 0.596965 | 0.298482 | − | 0.954415i | \(-0.403520\pi\) | ||||
0.298482 | + | 0.954415i | \(0.403520\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23942.7 | −0.981702 | ||||||||
\(842\) | 14655.3i | 0.599829i | ||||||||
\(843\) | − 24679.4i | − 1.00831i | ||||||||
\(844\) | −4117.70 | −0.167935 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2260.37 | −0.0918595 | ||||||||
\(847\) | 816.092i | 0.0331066i | ||||||||
\(848\) | 12828.7i | 0.519506i | ||||||||
\(849\) | −4684.55 | −0.189368 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −16842.6 | −0.678445 | ||||||||
\(852\) | 2138.61i | 0.0859948i | ||||||||
\(853\) | 44146.9i | 1.77205i | 0.463634 | + | 0.886027i | \(0.346545\pi\) | ||||
−0.463634 | + | 0.886027i | \(0.653455\pi\) | |||||||
\(854\) | −6442.26 | −0.258138 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 37854.4 | 1.51149 | ||||||||
\(857\) | − 47679.3i | − 1.90046i | −0.311549 | − | 0.950230i | \(-0.600848\pi\) | ||||
0.311549 | − | 0.950230i | \(-0.399152\pi\) | |||||||
\(858\) | − 4773.70i | − 0.189943i | ||||||||
\(859\) | −7525.09 | −0.298897 | −0.149449 | − | 0.988769i | \(-0.547750\pi\) | ||||
−0.149449 | + | 0.988769i | \(0.547750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5113.95 | −0.202419 | ||||||||
\(862\) | − 3957.09i | − 0.156356i | ||||||||
\(863\) | − 45816.1i | − 1.80718i | −0.428396 | − | 0.903591i | \(-0.640921\pi\) | ||||
0.428396 | − | 0.903591i | \(-0.359079\pi\) | |||||||
\(864\) | 2791.64 | 0.109923 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1735.91 | 0.0681163 | ||||||||
\(867\) | 14764.1i | 0.578335i | ||||||||
\(868\) | − 5099.48i | − 0.199410i | ||||||||
\(869\) | −1073.04 | −0.0418876 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1671.61 | −0.0650292 | ||||||||
\(872\) | 19187.3i | 0.745142i | ||||||||
\(873\) | 16185.2i | 0.627476i | ||||||||
\(874\) | 6562.96 | 0.253999 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3044.69 | −0.117432 | ||||||||
\(877\) | − 34168.3i | − 1.31560i | −0.753192 | − | 0.657801i | \(-0.771487\pi\) | ||||
0.753192 | − | 0.657801i | \(-0.228513\pi\) | |||||||
\(878\) | − 33800.2i | − 1.29920i | ||||||||
\(879\) | −28458.6 | −1.09202 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −100.796 | −0.00385460 | −0.00192730 | − | 0.999998i | \(-0.500613\pi\) | ||||
−0.00192730 | + | 0.999998i | \(0.500613\pi\) | |||||||
\(882\) | 6352.02i | 0.242498i | ||||||||
\(883\) | 12346.1i | 0.470531i | 0.971931 | + | 0.235266i | \(0.0755960\pi\) | ||||
−0.971931 | + | 0.235266i | \(0.924404\pi\) | |||||||
\(884\) | 14345.5 | 0.545803 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −413.398 | −0.0156754 | ||||||||
\(887\) | − 37345.1i | − 1.41367i | −0.707379 | − | 0.706834i | \(-0.750123\pi\) | ||||
0.707379 | − | 0.706834i | \(-0.249877\pi\) | |||||||
\(888\) | 11100.8i | 0.419501i | ||||||||
\(889\) | −15531.0 | −0.585932 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | − 3946.78i | − 0.148148i | ||||||||
\(893\) | − 2615.09i | − 0.0979962i | ||||||||
\(894\) | −7857.80 | −0.293964 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3388.13 | −0.126328 | ||||||||
\(897\) | − 20488.7i | − 0.762651i | ||||||||
\(898\) | 17720.9i | 0.658523i | ||||||||
\(899\) | −6732.88 | −0.249782 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32294.4 | −1.19410 | ||||||||
\(902\) | 6595.39i | 0.243462i | ||||||||
\(903\) | − 4330.34i | − 0.159584i | ||||||||
\(904\) | 37267.1 | 1.37111 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21208.7 | −0.777717 | ||||||||
\(907\) | 10308.6i | 0.377390i | 0.982036 | + | 0.188695i | \(0.0604258\pi\) | ||||
−0.982036 | + | 0.188695i | \(0.939574\pi\) | |||||||
\(908\) | − 8679.79i | − 0.317235i | ||||||||
\(909\) | −6677.26 | −0.243642 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22590.8 | −0.821589 | −0.410795 | − | 0.911728i | \(-0.634749\pi\) | ||||
−0.410795 | + | 0.911728i | \(0.634749\pi\) | |||||||
\(912\) | − 2919.22i | − 0.105992i | ||||||||
\(913\) | − 12150.8i | − 0.440453i | ||||||||
\(914\) | 20787.5 | 0.752288 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4571.56 | −0.164900 | ||||||||
\(917\) | − 13628.0i | − 0.490769i | ||||||||
\(918\) | − 6351.90i | − 0.228370i | ||||||||
\(919\) | −47712.1 | −1.71260 | −0.856299 | − | 0.516481i | \(-0.827242\pi\) | ||||
−0.856299 | + | 0.516481i | \(0.827242\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25329.2 | −0.906216 | ||||||||
\(922\) | − 10294.9i | − 0.367728i | ||||||||
\(923\) | − 18323.9i | − 0.653456i | ||||||||
\(924\) | 528.000 | 0.0187986 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9328.96 | 0.331068 | ||||||||
\(927\) | 3508.53i | 0.124310i | ||||||||
\(928\) | − 2184.19i | − 0.0772625i | ||||||||
\(929\) | −10714.3 | −0.378391 | −0.189196 | − | 0.981939i | \(-0.560588\pi\) | ||||
−0.189196 | + | 0.981939i | \(0.560588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7348.84 | −0.258699 | ||||||||
\(932\) | 6605.06i | 0.232142i | ||||||||
\(933\) | − 13341.5i | − 0.468148i | ||||||||
\(934\) | −19889.1 | −0.696780 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13503.9 | −0.471568 | ||||||||
\(937\) | − 14719.5i | − 0.513197i | −0.966518 | − | 0.256599i | \(-0.917398\pi\) | ||||
0.966518 | − | 0.256599i | \(-0.0826018\pi\) | |||||||
\(938\) | 438.612i | 0.0152678i | ||||||||
\(939\) | −19442.2 | −0.675691 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3694.44 | 0.127987 | 0.0639933 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639933 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(942\) | − 20245.1i | − 0.700234i | ||||||||
\(943\) | 28307.4i | 0.977535i | ||||||||
\(944\) | 7721.23 | 0.266213 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5584.77 | −0.191941 | ||||||||
\(947\) | 36416.7i | 1.24961i | 0.780780 | + | 0.624806i | \(0.214822\pi\) | ||||
−0.780780 | + | 0.624806i | \(0.785178\pi\) | |||||||
\(948\) | 694.240i | 0.0237847i | ||||||||
\(949\) | 26087.4 | 0.892342 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3758.25 | −0.128149 | ||||||||
\(952\) | − 16457.6i | − 0.560289i | ||||||||
\(953\) | − 20779.4i | − 0.706306i | −0.935566 | − | 0.353153i | \(-0.885110\pi\) | ||||
0.935566 | − | 0.353153i | \(-0.114890\pi\) | |||||||
\(954\) | 6952.84 | 0.235961 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2900.35 | −0.0981212 | ||||||||
\(957\) | − 697.123i | − 0.0235473i | ||||||||
\(958\) | 22617.6i | 0.762777i | ||||||||
\(959\) | −9950.94 | −0.335071 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 71789.7 | 2.40978 | ||||||||
\(962\) | − 21753.7i | − 0.729071i | ||||||||
\(963\) | − 13845.8i | − 0.463318i | ||||||||
\(964\) | −4775.43 | −0.159550 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5376.00 | −0.179058 | ||||||||
\(967\) | 56812.8i | 1.88932i | 0.328044 | + | 0.944662i | \(0.393611\pi\) | ||||
−0.328044 | + | 0.944662i | \(0.606389\pi\) | |||||||
\(968\) | − 2977.32i | − 0.0988582i | ||||||||
\(969\) | 7348.70 | 0.243627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26459.7 | −0.874493 | −0.437247 | − | 0.899342i | \(-0.644046\pi\) | ||||
−0.437247 | + | 0.899342i | \(0.644046\pi\) | |||||||
\(972\) | − 576.464i | − 0.0190227i | ||||||||
\(973\) | 10951.2i | 0.360822i | ||||||||
\(974\) | 10559.2 | 0.347371 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15861.7 | 0.520204 | ||||||||
\(977\) | − 21009.2i | − 0.687967i | −0.938976 | − | 0.343984i | \(-0.888224\pi\) | ||||
0.938976 | − | 0.343984i | \(-0.111776\pi\) | |||||||
\(978\) | − 10878.2i | − 0.355670i | ||||||||
\(979\) | −5093.24 | −0.166272 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7018.04 | 0.228409 | ||||||||
\(982\) | 23147.3i | 0.752199i | ||||||||
\(983\) | 9076.80i | 0.294512i | 0.989098 | + | 0.147256i | \(0.0470441\pi\) | ||||
−0.989098 | + | 0.147256i | \(0.952956\pi\) | |||||||
\(984\) | 18657.1 | 0.604437 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4969.76 | −0.160517 | ||||||||
\(987\) | 2142.13i | 0.0690828i | ||||||||
\(988\) | − 3573.20i | − 0.115059i | ||||||||
\(989\) | −23969.8 | −0.770673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2629.24 | 0.0842791 | 0.0421395 | − | 0.999112i | \(-0.486583\pi\) | ||||
0.0421395 | + | 0.999112i | \(0.486583\pi\) | |||||||
\(992\) | 32953.5i | 1.05471i | ||||||||
\(993\) | − 11404.3i | − 0.364457i | ||||||||
\(994\) | −4808.00 | −0.153421 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7861.40 | −0.250098 | ||||||||
\(997\) | − 50423.9i | − 1.60175i | −0.598833 | − | 0.800874i | \(-0.704369\pi\) | ||||
0.598833 | − | 0.800874i | \(-0.295631\pi\) | |||||||
\(998\) | − 17018.0i | − 0.539775i | ||||||||
\(999\) | 4060.27 | 0.128590 |
(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.i.199.2 | 4 | ||
5.2 | odd | 4 | 825.4.a.k.1.2 | 2 | |||
5.3 | odd | 4 | 33.4.a.d.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 825.4.c.i.199.3 | 4 | ||
15.2 | even | 4 | 2475.4.a.o.1.1 | 2 | |||
15.8 | even | 4 | 99.4.a.e.1.2 | 2 | |||
20.3 | even | 4 | 528.4.a.o.1.2 | 2 | |||
35.13 | even | 4 | 1617.4.a.j.1.1 | 2 | |||
40.3 | even | 4 | 2112.4.a.bh.1.1 | 2 | |||
40.13 | odd | 4 | 2112.4.a.ba.1.1 | 2 | |||
55.43 | even | 4 | 363.4.a.j.1.2 | 2 | |||
60.23 | odd | 4 | 1584.4.a.x.1.1 | 2 | |||
165.98 | odd | 4 | 1089.4.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.4.a.d.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
99.4.a.e.1.2 | 2 | 15.8 | even | 4 | |||
363.4.a.j.1.2 | 2 | 55.43 | even | 4 | |||
528.4.a.o.1.2 | 2 | 20.3 | even | 4 | |||
825.4.a.k.1.2 | 2 | 5.2 | odd | 4 | |||
825.4.c.i.199.2 | 4 | 1.1 | even | 1 | trivial | ||
825.4.c.i.199.3 | 4 | 5.4 | even | 2 | inner | ||
1089.4.a.t.1.1 | 2 | 165.98 | odd | 4 | |||
1584.4.a.x.1.1 | 2 | 60.23 | odd | 4 | |||
1617.4.a.j.1.1 | 2 | 35.13 | even | 4 | |||
2112.4.a.ba.1.1 | 2 | 40.13 | odd | 4 | |||
2112.4.a.bh.1.1 | 2 | 40.3 | even | 4 | |||
2475.4.a.o.1.1 | 2 | 15.2 | even | 4 |