Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.1 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.b.1249.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 4.47214i | − 1.69031i | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
0.534522 | − | 0.845154i | \(-0.320491\pi\) | |||||||
\(8\) | − 3.00000i | − 1.06066i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 3.38197i | 0.937989i | 0.883201 | + | 0.468994i | \(0.155384\pi\) | ||||
−0.883201 | + | 0.468994i | \(0.844616\pi\) | |||||||
\(14\) | −4.47214 | −1.19523 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.85410i | 0.692221i | 0.938194 | + | 0.346111i | \(0.112498\pi\) | ||||
−0.938194 | + | 0.346111i | \(0.887502\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 3.23607 | 0.742405 | 0.371202 | − | 0.928552i | \(-0.378946\pi\) | ||||
0.371202 | + | 0.928552i | \(0.378946\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.47214 | 0.975900 | ||||||||
\(22\) | − 3.23607i | − 0.689932i | ||||||||
\(23\) | − 4.47214i | − 0.932505i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
0.884652 | − | 0.466252i | \(-0.154396\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.38197 | 0.663258 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 4.47214i | − 0.845154i | ||||||||
\(29\) | −4.38197 | −0.813711 | −0.406855 | − | 0.913493i | \(-0.633375\pi\) | ||||
−0.406855 | + | 0.913493i | \(0.633375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23607 | 1.29964 | 0.649818 | − | 0.760090i | \(-0.274845\pi\) | ||||
0.649818 | + | 0.760090i | \(0.274845\pi\) | |||||||
\(32\) | − 5.00000i | − 0.883883i | ||||||||
\(33\) | 3.23607i | 0.563327i | ||||||||
\(34\) | 2.85410 | 0.489474 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 8.09017i | − 1.33002i | −0.746836 | − | 0.665008i | \(-0.768428\pi\) | ||||
0.746836 | − | 0.665008i | \(-0.231572\pi\) | |||||||
\(38\) | − 3.23607i | − 0.524960i | ||||||||
\(39\) | −3.38197 | −0.541548 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.38197 | −0.215827 | −0.107913 | − | 0.994160i | \(-0.534417\pi\) | ||||
−0.107913 | + | 0.994160i | \(0.534417\pi\) | |||||||
\(42\) | − 4.47214i | − 0.690066i | ||||||||
\(43\) | − 5.70820i | − 0.870493i | −0.900311 | − | 0.435246i | \(-0.856661\pi\) | ||||
0.900311 | − | 0.435246i | \(-0.143339\pi\) | |||||||
\(44\) | 3.23607 | 0.487856 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.47214 | −0.659380 | ||||||||
\(47\) | 5.23607i | 0.763759i | 0.924212 | + | 0.381880i | \(0.124723\pi\) | ||||
−0.924212 | + | 0.381880i | \(0.875277\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | −13.0000 | −1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.85410 | −0.399654 | ||||||||
\(52\) | 3.38197i | 0.468994i | ||||||||
\(53\) | 1.38197i | 0.189828i | 0.995485 | + | 0.0949138i | \(0.0302576\pi\) | ||||
−0.995485 | + | 0.0949138i | \(0.969742\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.4164 | −1.79284 | ||||||||
\(57\) | 3.23607i | 0.428628i | ||||||||
\(58\) | 4.38197i | 0.575380i | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.618034 | −0.0791311 | −0.0395656 | − | 0.999217i | \(-0.512597\pi\) | ||||
−0.0395656 | + | 0.999217i | \(0.512597\pi\) | |||||||
\(62\) | − 7.23607i | − 0.918982i | ||||||||
\(63\) | 4.47214i | 0.563436i | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.23607 | 0.398332 | ||||||||
\(67\) | − 5.23607i | − 0.639688i | −0.947470 | − | 0.319844i | \(-0.896370\pi\) | ||||
0.947470 | − | 0.319844i | \(-0.103630\pi\) | |||||||
\(68\) | 2.85410i | 0.346111i | ||||||||
\(69\) | 4.47214 | 0.538382 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.763932 | −0.0906621 | −0.0453310 | − | 0.998972i | \(-0.514434\pi\) | ||||
−0.0453310 | + | 0.998972i | \(0.514434\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | 3.09017i | 0.361677i | 0.983513 | + | 0.180839i | \(0.0578811\pi\) | ||||
−0.983513 | + | 0.180839i | \(0.942119\pi\) | |||||||
\(74\) | −8.09017 | −0.940463 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | − 14.4721i | − 1.64925i | ||||||||
\(78\) | 3.38197i | 0.382932i | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.38197i | 0.152613i | ||||||||
\(83\) | 3.52786i | 0.387233i | 0.981077 | + | 0.193617i | \(0.0620218\pi\) | ||||
−0.981077 | + | 0.193617i | \(0.937978\pi\) | |||||||
\(84\) | 4.47214 | 0.487950 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.70820 | −0.615531 | ||||||||
\(87\) | − 4.38197i | − 0.469796i | ||||||||
\(88\) | − 9.70820i | − 1.03490i | ||||||||
\(89\) | −7.61803 | −0.807510 | −0.403755 | − | 0.914867i | \(-0.632295\pi\) | ||||
−0.403755 | + | 0.914867i | \(0.632295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.1246 | 1.58549 | ||||||||
\(92\) | − 4.47214i | − 0.466252i | ||||||||
\(93\) | 7.23607i | 0.750345i | ||||||||
\(94\) | 5.23607 | 0.540059 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.00000 | 0.510310 | ||||||||
\(97\) | − 8.85410i | − 0.898998i | −0.893281 | − | 0.449499i | \(-0.851603\pi\) | ||||
0.893281 | − | 0.449499i | \(-0.148397\pi\) | |||||||
\(98\) | 13.0000i | 1.31320i | ||||||||
\(99\) | −3.23607 | −0.325237 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5623 | −1.64801 | −0.824006 | − | 0.566582i | \(-0.808266\pi\) | ||||
−0.824006 | + | 0.566582i | \(0.808266\pi\) | |||||||
\(102\) | 2.85410i | 0.282598i | ||||||||
\(103\) | − 1.23607i | − 0.121793i | −0.998144 | − | 0.0608967i | \(-0.980604\pi\) | ||||
0.998144 | − | 0.0608967i | \(-0.0193960\pi\) | |||||||
\(104\) | 10.1459 | 0.994887 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.38197 | 0.134228 | ||||||||
\(107\) | − 16.4721i | − 1.59242i | −0.605019 | − | 0.796211i | \(-0.706835\pi\) | ||||
0.605019 | − | 0.796211i | \(-0.293165\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | 19.0902 | 1.82851 | 0.914253 | − | 0.405143i | \(-0.132778\pi\) | ||||
0.914253 | + | 0.405143i | \(0.132778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.09017 | 0.767885 | ||||||||
\(112\) | 4.47214i | 0.422577i | ||||||||
\(113\) | 2.67376i | 0.251526i | 0.992060 | + | 0.125763i | \(0.0401380\pi\) | ||||
−0.992060 | + | 0.125763i | \(0.959862\pi\) | |||||||
\(114\) | 3.23607 | 0.303086 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.38197 | −0.406855 | ||||||||
\(117\) | − 3.38197i | − 0.312663i | ||||||||
\(118\) | − 4.00000i | − 0.368230i | ||||||||
\(119\) | 12.7639 | 1.17007 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0.618034i | 0.0559542i | ||||||||
\(123\) | − 1.38197i | − 0.124608i | ||||||||
\(124\) | 7.23607 | 0.649818 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.47214 | 0.398410 | ||||||||
\(127\) | − 9.70820i | − 0.861464i | −0.902480 | − | 0.430732i | \(-0.858255\pi\) | ||||
0.902480 | − | 0.430732i | \(-0.141745\pi\) | |||||||
\(128\) | − 3.00000i | − 0.265165i | ||||||||
\(129\) | 5.70820 | 0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.1803 | 1.23894 | 0.619471 | − | 0.785020i | \(-0.287347\pi\) | ||||
0.619471 | + | 0.785020i | \(0.287347\pi\) | |||||||
\(132\) | 3.23607i | 0.281664i | ||||||||
\(133\) | − 14.4721i | − 1.25489i | ||||||||
\(134\) | −5.23607 | −0.452327 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.56231 | 0.734212 | ||||||||
\(137\) | 5.38197i | 0.459812i | 0.973213 | + | 0.229906i | \(0.0738419\pi\) | ||||
−0.973213 | + | 0.229906i | \(0.926158\pi\) | |||||||
\(138\) | − 4.47214i | − 0.380693i | ||||||||
\(139\) | 5.05573 | 0.428821 | 0.214411 | − | 0.976744i | \(-0.431217\pi\) | ||||
0.214411 | + | 0.976744i | \(0.431217\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.23607 | −0.440956 | ||||||||
\(142\) | 0.763932i | 0.0641078i | ||||||||
\(143\) | 10.9443i | 0.915206i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.09017 | 0.255744 | ||||||||
\(147\) | − 13.0000i | − 1.07222i | ||||||||
\(148\) | − 8.09017i | − 0.665008i | ||||||||
\(149\) | 12.1459 | 0.995031 | 0.497515 | − | 0.867455i | \(-0.334246\pi\) | ||||
0.497515 | + | 0.867455i | \(0.334246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4721 | 1.34048 | 0.670242 | − | 0.742143i | \(-0.266190\pi\) | ||||
0.670242 | + | 0.742143i | \(0.266190\pi\) | |||||||
\(152\) | − 9.70820i | − 0.787439i | ||||||||
\(153\) | − 2.85410i | − 0.230740i | ||||||||
\(154\) | −14.4721 | −1.16620 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.38197 | −0.270774 | ||||||||
\(157\) | 13.7984i | 1.10123i | 0.834759 | + | 0.550615i | \(0.185607\pi\) | ||||
−0.834759 | + | 0.550615i | \(0.814393\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.38197 | −0.109597 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.0000 | −1.57622 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 2.94427i | 0.230613i | 0.993330 | + | 0.115307i | \(0.0367850\pi\) | ||||
−0.993330 | + | 0.115307i | \(0.963215\pi\) | |||||||
\(164\) | −1.38197 | −0.107913 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.52786 | 0.273815 | ||||||||
\(167\) | 23.4164i | 1.81202i | 0.423261 | + | 0.906008i | \(0.360886\pi\) | ||||
−0.423261 | + | 0.906008i | \(0.639114\pi\) | |||||||
\(168\) | − 13.4164i | − 1.03510i | ||||||||
\(169\) | 1.56231 | 0.120177 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.23607 | −0.247468 | ||||||||
\(172\) | − 5.70820i | − 0.435246i | ||||||||
\(173\) | 9.90983i | 0.753430i | 0.926329 | + | 0.376715i | \(0.122946\pi\) | ||||
−0.926329 | + | 0.376715i | \(0.877054\pi\) | |||||||
\(174\) | −4.38197 | −0.332196 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.23607 | −0.243928 | ||||||||
\(177\) | 4.00000i | 0.300658i | ||||||||
\(178\) | 7.61803i | 0.570996i | ||||||||
\(179\) | −6.18034 | −0.461940 | −0.230970 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230970 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.79837 | −0.728307 | −0.364154 | − | 0.931339i | \(-0.618642\pi\) | ||||
−0.364154 | + | 0.931339i | \(0.618642\pi\) | |||||||
\(182\) | − 15.1246i | − 1.12111i | ||||||||
\(183\) | − 0.618034i | − 0.0456864i | ||||||||
\(184\) | −13.4164 | −0.989071 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.23607 | 0.530574 | ||||||||
\(187\) | 9.23607i | 0.675408i | ||||||||
\(188\) | 5.23607i | 0.381880i | ||||||||
\(189\) | −4.47214 | −0.325300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.6525 | −1.78379 | −0.891895 | − | 0.452242i | \(-0.850624\pi\) | ||||
−0.891895 | + | 0.452242i | \(0.850624\pi\) | |||||||
\(192\) | − 7.00000i | − 0.505181i | ||||||||
\(193\) | 7.67376i | 0.552369i | 0.961105 | + | 0.276185i | \(0.0890702\pi\) | ||||
−0.961105 | + | 0.276185i | \(0.910930\pi\) | |||||||
\(194\) | −8.85410 | −0.635687 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.0000 | −0.928571 | ||||||||
\(197\) | − 5.38197i | − 0.383449i | −0.981449 | − | 0.191725i | \(-0.938592\pi\) | ||||
0.981449 | − | 0.191725i | \(-0.0614080\pi\) | |||||||
\(198\) | 3.23607i | 0.229977i | ||||||||
\(199\) | 18.6525 | 1.32224 | 0.661119 | − | 0.750281i | \(-0.270082\pi\) | ||||
0.661119 | + | 0.750281i | \(0.270082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.23607 | 0.369324 | ||||||||
\(202\) | 16.5623i | 1.16532i | ||||||||
\(203\) | 19.5967i | 1.37542i | ||||||||
\(204\) | −2.85410 | −0.199827 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.23607 | −0.0861209 | ||||||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | − 3.38197i | − 0.234497i | ||||||||
\(209\) | 10.4721 | 0.724373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8885 | −1.23150 | −0.615749 | − | 0.787942i | \(-0.711146\pi\) | ||||
−0.615749 | + | 0.787942i | \(0.711146\pi\) | |||||||
\(212\) | 1.38197i | 0.0949138i | ||||||||
\(213\) | − 0.763932i | − 0.0523438i | ||||||||
\(214\) | −16.4721 | −1.12601 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | − 32.3607i | − 2.19679i | ||||||||
\(218\) | − 19.0902i | − 1.29295i | ||||||||
\(219\) | −3.09017 | −0.208814 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.65248 | −0.649296 | ||||||||
\(222\) | − 8.09017i | − 0.542977i | ||||||||
\(223\) | − 14.1803i | − 0.949586i | −0.880098 | − | 0.474793i | \(-0.842523\pi\) | ||||
0.880098 | − | 0.474793i | \(-0.157477\pi\) | |||||||
\(224\) | −22.3607 | −1.49404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.67376 | 0.177856 | ||||||||
\(227\) | 20.0000i | 1.32745i | 0.747978 | + | 0.663723i | \(0.231025\pi\) | ||||
−0.747978 | + | 0.663723i | \(0.768975\pi\) | |||||||
\(228\) | 3.23607i | 0.214314i | ||||||||
\(229\) | 24.9787 | 1.65064 | 0.825320 | − | 0.564665i | \(-0.190995\pi\) | ||||
0.825320 | + | 0.564665i | \(0.190995\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.4721 | 0.952197 | ||||||||
\(232\) | 13.1459i | 0.863070i | ||||||||
\(233\) | 14.6180i | 0.957659i | 0.877908 | + | 0.478830i | \(0.158939\pi\) | ||||
−0.877908 | + | 0.478830i | \(0.841061\pi\) | |||||||
\(234\) | −3.38197 | −0.221086 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 12.7639i | − 0.827363i | ||||||||
\(239\) | 7.05573 | 0.456397 | 0.228199 | − | 0.973615i | \(-0.426716\pi\) | ||||
0.228199 | + | 0.973615i | \(0.426716\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.03444 | −0.0666343 | −0.0333171 | − | 0.999445i | \(-0.510607\pi\) | ||||
−0.0333171 | + | 0.999445i | \(0.510607\pi\) | |||||||
\(242\) | 0.527864i | 0.0339324i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −0.618034 | −0.0395656 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.38197 | −0.0881109 | ||||||||
\(247\) | 10.9443i | 0.696367i | ||||||||
\(248\) | − 21.7082i | − 1.37847i | ||||||||
\(249\) | −3.52786 | −0.223569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.9443 | −1.70071 | −0.850354 | − | 0.526212i | \(-0.823612\pi\) | ||||
−0.850354 | + | 0.526212i | \(0.823612\pi\) | |||||||
\(252\) | 4.47214i | 0.281718i | ||||||||
\(253\) | − 14.4721i | − 0.909855i | ||||||||
\(254\) | −9.70820 | −0.609147 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 12.7984i | 0.798341i | 0.916877 | + | 0.399170i | \(0.130702\pi\) | ||||
−0.916877 | + | 0.399170i | \(0.869298\pi\) | |||||||
\(258\) | − 5.70820i | − 0.355377i | ||||||||
\(259\) | −36.1803 | −2.24814 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.38197 | 0.271237 | ||||||||
\(262\) | − 14.1803i | − 0.876064i | ||||||||
\(263\) | 11.8885i | 0.733079i | 0.930402 | + | 0.366540i | \(0.119458\pi\) | ||||
−0.930402 | + | 0.366540i | \(0.880542\pi\) | |||||||
\(264\) | 9.70820 | 0.597499 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.4721 | −0.887344 | ||||||||
\(267\) | − 7.61803i | − 0.466216i | ||||||||
\(268\) | − 5.23607i | − 0.319844i | ||||||||
\(269\) | 0.145898 | 0.00889556 | 0.00444778 | − | 0.999990i | \(-0.498584\pi\) | ||||
0.00444778 | + | 0.999990i | \(0.498584\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1803 | 1.34736 | 0.673680 | − | 0.739023i | \(-0.264713\pi\) | ||||
0.673680 | + | 0.739023i | \(0.264713\pi\) | |||||||
\(272\) | − 2.85410i | − 0.173055i | ||||||||
\(273\) | 15.1246i | 0.915383i | ||||||||
\(274\) | 5.38197 | 0.325136 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | 5.79837i | 0.348391i | 0.984711 | + | 0.174195i | \(0.0557324\pi\) | ||||
−0.984711 | + | 0.174195i | \(0.944268\pi\) | |||||||
\(278\) | − 5.05573i | − 0.303222i | ||||||||
\(279\) | −7.23607 | −0.433212 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.3820 | −1.03692 | −0.518461 | − | 0.855102i | \(-0.673495\pi\) | ||||
−0.518461 | + | 0.855102i | \(0.673495\pi\) | |||||||
\(282\) | 5.23607i | 0.311803i | ||||||||
\(283\) | 0.291796i | 0.0173455i | 0.999962 | + | 0.00867274i | \(0.00276065\pi\) | ||||
−0.999962 | + | 0.00867274i | \(0.997239\pi\) | |||||||
\(284\) | −0.763932 | −0.0453310 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.9443 | 0.647148 | ||||||||
\(287\) | 6.18034i | 0.364814i | ||||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | 8.85410 | 0.520830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.85410 | 0.519037 | ||||||||
\(292\) | 3.09017i | 0.180839i | ||||||||
\(293\) | 3.79837i | 0.221903i | 0.993826 | + | 0.110952i | \(0.0353899\pi\) | ||||
−0.993826 | + | 0.110952i | \(0.964610\pi\) | |||||||
\(294\) | −13.0000 | −0.758175 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −24.2705 | −1.41069 | ||||||||
\(297\) | − 3.23607i | − 0.187776i | ||||||||
\(298\) | − 12.1459i | − 0.703593i | ||||||||
\(299\) | 15.1246 | 0.874679 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.5279 | −1.47140 | ||||||||
\(302\) | − 16.4721i | − 0.947865i | ||||||||
\(303\) | − 16.5623i | − 0.951480i | ||||||||
\(304\) | −3.23607 | −0.185601 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.85410 | −0.163158 | ||||||||
\(307\) | − 1.34752i | − 0.0769073i | −0.999260 | − | 0.0384536i | \(-0.987757\pi\) | ||||
0.999260 | − | 0.0384536i | \(-0.0122432\pi\) | |||||||
\(308\) | − 14.4721i | − 0.824626i | ||||||||
\(309\) | 1.23607 | 0.0703175 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.29180 | 0.243365 | 0.121683 | − | 0.992569i | \(-0.461171\pi\) | ||||
0.121683 | + | 0.992569i | \(0.461171\pi\) | |||||||
\(312\) | 10.1459i | 0.574398i | ||||||||
\(313\) | 8.47214i | 0.478873i | 0.970912 | + | 0.239437i | \(0.0769628\pi\) | ||||
−0.970912 | + | 0.239437i | \(0.923037\pi\) | |||||||
\(314\) | 13.7984 | 0.778687 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.8328i | 1.39475i | 0.716706 | + | 0.697375i | \(0.245649\pi\) | ||||
−0.716706 | + | 0.697375i | \(0.754351\pi\) | |||||||
\(318\) | 1.38197i | 0.0774968i | ||||||||
\(319\) | −14.1803 | −0.793947 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.4721 | 0.919385 | ||||||||
\(322\) | 20.0000i | 1.11456i | ||||||||
\(323\) | 9.23607i | 0.513909i | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.94427 | 0.163068 | ||||||||
\(327\) | 19.0902i | 1.05569i | ||||||||
\(328\) | 4.14590i | 0.228919i | ||||||||
\(329\) | 23.4164 | 1.29099 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.9443 | 0.601552 | 0.300776 | − | 0.953695i | \(-0.402754\pi\) | ||||
0.300776 | + | 0.953695i | \(0.402754\pi\) | |||||||
\(332\) | 3.52786i | 0.193617i | ||||||||
\(333\) | 8.09017i | 0.443339i | ||||||||
\(334\) | 23.4164 | 1.28129 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.47214 | −0.243975 | ||||||||
\(337\) | 14.9443i | 0.814066i | 0.913413 | + | 0.407033i | \(0.133437\pi\) | ||||
−0.913413 | + | 0.407033i | \(0.866563\pi\) | |||||||
\(338\) | − 1.56231i | − 0.0849782i | ||||||||
\(339\) | −2.67376 | −0.145219 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 23.4164 | 1.26807 | ||||||||
\(342\) | 3.23607i | 0.174987i | ||||||||
\(343\) | 26.8328i | 1.44884i | ||||||||
\(344\) | −17.1246 | −0.923297 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.90983 | 0.532756 | ||||||||
\(347\) | 33.7082i | 1.80955i | 0.425889 | + | 0.904776i | \(0.359962\pi\) | ||||
−0.425889 | + | 0.904776i | \(0.640038\pi\) | |||||||
\(348\) | − 4.38197i | − 0.234898i | ||||||||
\(349\) | −25.0344 | −1.34006 | −0.670031 | − | 0.742333i | \(-0.733719\pi\) | ||||
−0.670031 | + | 0.742333i | \(0.733719\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.38197 | 0.180516 | ||||||||
\(352\) | − 16.1803i | − 0.862415i | ||||||||
\(353\) | − 30.3607i | − 1.61594i | −0.589226 | − | 0.807968i | \(-0.700567\pi\) | ||||
0.589226 | − | 0.807968i | \(-0.299433\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.61803 | −0.403755 | ||||||||
\(357\) | 12.7639i | 0.675539i | ||||||||
\(358\) | 6.18034i | 0.326641i | ||||||||
\(359\) | 10.5836 | 0.558581 | 0.279290 | − | 0.960207i | \(-0.409901\pi\) | ||||
0.279290 | + | 0.960207i | \(0.409901\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.52786 | −0.448835 | ||||||||
\(362\) | 9.79837i | 0.514991i | ||||||||
\(363\) | − 0.527864i | − 0.0277057i | ||||||||
\(364\) | 15.1246 | 0.792745 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.618034 | −0.0323052 | ||||||||
\(367\) | 6.00000i | 0.313197i | 0.987662 | + | 0.156599i | \(0.0500529\pi\) | ||||
−0.987662 | + | 0.156599i | \(0.949947\pi\) | |||||||
\(368\) | 4.47214i | 0.233126i | ||||||||
\(369\) | 1.38197 | 0.0719423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.18034 | 0.320867 | ||||||||
\(372\) | 7.23607i | 0.375173i | ||||||||
\(373\) | 29.4164i | 1.52312i | 0.648092 | + | 0.761562i | \(0.275567\pi\) | ||||
−0.648092 | + | 0.761562i | \(0.724433\pi\) | |||||||
\(374\) | 9.23607 | 0.477586 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7082 | 0.810089 | ||||||||
\(377\) | − 14.8197i | − 0.763251i | ||||||||
\(378\) | 4.47214i | 0.230022i | ||||||||
\(379\) | −23.4164 | −1.20282 | −0.601410 | − | 0.798941i | \(-0.705394\pi\) | ||||
−0.601410 | + | 0.798941i | \(0.705394\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.70820 | 0.497366 | ||||||||
\(382\) | 24.6525i | 1.26133i | ||||||||
\(383\) | 20.8328i | 1.06451i | 0.846585 | + | 0.532254i | \(0.178655\pi\) | ||||
−0.846585 | + | 0.532254i | \(0.821345\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.67376 | 0.390584 | ||||||||
\(387\) | 5.70820i | 0.290164i | ||||||||
\(388\) | − 8.85410i | − 0.449499i | ||||||||
\(389\) | 37.0902 | 1.88055 | 0.940273 | − | 0.340421i | \(-0.110570\pi\) | ||||
0.940273 | + | 0.340421i | \(0.110570\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7639 | 0.645500 | ||||||||
\(392\) | 39.0000i | 1.96980i | ||||||||
\(393\) | 14.1803i | 0.715304i | ||||||||
\(394\) | −5.38197 | −0.271140 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.23607 | −0.162619 | ||||||||
\(397\) | − 10.9443i | − 0.549277i | −0.961548 | − | 0.274639i | \(-0.911442\pi\) | ||||
0.961548 | − | 0.274639i | \(-0.0885582\pi\) | |||||||
\(398\) | − 18.6525i | − 0.934964i | ||||||||
\(399\) | 14.4721 | 0.724513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.4508 | 1.67046 | 0.835228 | − | 0.549904i | \(-0.185336\pi\) | ||||
0.835228 | + | 0.549904i | \(0.185336\pi\) | |||||||
\(402\) | − 5.23607i | − 0.261151i | ||||||||
\(403\) | 24.4721i | 1.21904i | ||||||||
\(404\) | −16.5623 | −0.824006 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 19.5967 | 0.972570 | ||||||||
\(407\) | − 26.1803i | − 1.29771i | ||||||||
\(408\) | 8.56231i | 0.423897i | ||||||||
\(409\) | −25.7984 | −1.27565 | −0.637824 | − | 0.770182i | \(-0.720165\pi\) | ||||
−0.637824 | + | 0.770182i | \(0.720165\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.38197 | −0.265473 | ||||||||
\(412\) | − 1.23607i | − 0.0608967i | ||||||||
\(413\) | − 17.8885i | − 0.880238i | ||||||||
\(414\) | 4.47214 | 0.219793 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.9098 | 0.829073 | ||||||||
\(417\) | 5.05573i | 0.247580i | ||||||||
\(418\) | − 10.4721i | − 0.512209i | ||||||||
\(419\) | −32.9443 | −1.60943 | −0.804717 | − | 0.593659i | \(-0.797683\pi\) | ||||
−0.804717 | + | 0.593659i | \(0.797683\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1459 | 1.12806 | 0.564031 | − | 0.825754i | \(-0.309250\pi\) | ||||
0.564031 | + | 0.825754i | \(0.309250\pi\) | |||||||
\(422\) | 17.8885i | 0.870801i | ||||||||
\(423\) | − 5.23607i | − 0.254586i | ||||||||
\(424\) | 4.14590 | 0.201343 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.763932 | −0.0370126 | ||||||||
\(427\) | 2.76393i | 0.133756i | ||||||||
\(428\) | − 16.4721i | − 0.796211i | ||||||||
\(429\) | −10.9443 | −0.528394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6525 | −0.513112 | −0.256556 | − | 0.966529i | \(-0.582588\pi\) | ||||
−0.256556 | + | 0.966529i | \(0.582588\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 24.9787i | 1.20040i | 0.799850 | + | 0.600200i | \(0.204912\pi\) | ||||
−0.799850 | + | 0.600200i | \(0.795088\pi\) | |||||||
\(434\) | −32.3607 | −1.55336 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.0902 | 0.914253 | ||||||||
\(437\) | − 14.4721i | − 0.692296i | ||||||||
\(438\) | 3.09017i | 0.147654i | ||||||||
\(439\) | 6.18034 | 0.294972 | 0.147486 | − | 0.989064i | \(-0.452882\pi\) | ||||
0.147486 | + | 0.989064i | \(0.452882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | 0.619048 | ||||||||
\(442\) | 9.65248i | 0.459121i | ||||||||
\(443\) | − 30.7639i | − 1.46164i | −0.682571 | − | 0.730819i | \(-0.739138\pi\) | ||||
0.682571 | − | 0.730819i | \(-0.260862\pi\) | |||||||
\(444\) | 8.09017 | 0.383942 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −14.1803 | −0.671459 | ||||||||
\(447\) | 12.1459i | 0.574481i | ||||||||
\(448\) | 31.3050i | 1.47902i | ||||||||
\(449\) | 7.79837 | 0.368028 | 0.184014 | − | 0.982924i | \(-0.441091\pi\) | ||||
0.184014 | + | 0.982924i | \(0.441091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.47214 | −0.210585 | ||||||||
\(452\) | 2.67376i | 0.125763i | ||||||||
\(453\) | 16.4721i | 0.773928i | ||||||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.70820 | 0.454628 | ||||||||
\(457\) | − 22.3607i | − 1.04599i | −0.852336 | − | 0.522994i | \(-0.824815\pi\) | ||||
0.852336 | − | 0.522994i | \(-0.175185\pi\) | |||||||
\(458\) | − 24.9787i | − 1.16718i | ||||||||
\(459\) | 2.85410 | 0.133218 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.20163 | −0.381988 | −0.190994 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190994 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(462\) | − 14.4721i | − 0.673305i | ||||||||
\(463\) | 23.2361i | 1.07987i | 0.841706 | + | 0.539936i | \(0.181552\pi\) | ||||
−0.841706 | + | 0.539936i | \(0.818448\pi\) | |||||||
\(464\) | 4.38197 | 0.203428 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.6180 | 0.677167 | ||||||||
\(467\) | − 5.81966i | − 0.269302i | −0.990893 | − | 0.134651i | \(-0.957009\pi\) | ||||
0.990893 | − | 0.134651i | \(-0.0429913\pi\) | |||||||
\(468\) | − 3.38197i | − 0.156331i | ||||||||
\(469\) | −23.4164 | −1.08127 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.7984 | −0.635796 | ||||||||
\(472\) | − 12.0000i | − 0.552345i | ||||||||
\(473\) | − 18.4721i | − 0.849350i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.7639 | 0.585034 | ||||||||
\(477\) | − 1.38197i | − 0.0632759i | ||||||||
\(478\) | − 7.05573i | − 0.322721i | ||||||||
\(479\) | −1.05573 | −0.0482374 | −0.0241187 | − | 0.999709i | \(-0.507678\pi\) | ||||
−0.0241187 | + | 0.999709i | \(0.507678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.3607 | 1.24754 | ||||||||
\(482\) | 1.03444i | 0.0471175i | ||||||||
\(483\) | − 20.0000i | − 0.910032i | ||||||||
\(484\) | −0.527864 | −0.0239938 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 3.70820i | 0.168035i | 0.996464 | + | 0.0840174i | \(0.0267751\pi\) | ||||
−0.996464 | + | 0.0840174i | \(0.973225\pi\) | |||||||
\(488\) | 1.85410i | 0.0839313i | ||||||||
\(489\) | −2.94427 | −0.133145 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8885 | −1.34885 | −0.674426 | − | 0.738343i | \(-0.735609\pi\) | ||||
−0.674426 | + | 0.738343i | \(0.735609\pi\) | |||||||
\(492\) | − 1.38197i | − 0.0623038i | ||||||||
\(493\) | − 12.5066i | − 0.563268i | ||||||||
\(494\) | 10.9443 | 0.492406 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.23607 | −0.324909 | ||||||||
\(497\) | 3.41641i | 0.153247i | ||||||||
\(498\) | 3.52786i | 0.158087i | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.4164 | −1.04617 | ||||||||
\(502\) | 26.9443i | 1.20258i | ||||||||
\(503\) | 35.4164i | 1.57914i | 0.613661 | + | 0.789570i | \(0.289696\pi\) | ||||
−0.613661 | + | 0.789570i | \(0.710304\pi\) | |||||||
\(504\) | 13.4164 | 0.597614 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.4721 | −0.643365 | ||||||||
\(507\) | 1.56231i | 0.0693844i | ||||||||
\(508\) | − 9.70820i | − 0.430732i | ||||||||
\(509\) | −26.8541 | −1.19029 | −0.595144 | − | 0.803619i | \(-0.702905\pi\) | ||||
−0.595144 | + | 0.803619i | \(0.702905\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8197 | 0.611346 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | − 3.23607i | − 0.142876i | ||||||||
\(514\) | 12.7984 | 0.564512 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.70820 | 0.251290 | ||||||||
\(517\) | 16.9443i | 0.745208i | ||||||||
\(518\) | 36.1803i | 1.58967i | ||||||||
\(519\) | −9.90983 | −0.434993 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.03444 | 0.0891305 | 0.0445653 | − | 0.999006i | \(-0.485810\pi\) | ||||
0.0445653 | + | 0.999006i | \(0.485810\pi\) | |||||||
\(522\) | − 4.38197i | − 0.191793i | ||||||||
\(523\) | − 12.2918i | − 0.537483i | −0.963212 | − | 0.268741i | \(-0.913392\pi\) | ||||
0.963212 | − | 0.268741i | \(-0.0866077\pi\) | |||||||
\(524\) | 14.1803 | 0.619471 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8885 | 0.518365 | ||||||||
\(527\) | 20.6525i | 0.899636i | ||||||||
\(528\) | − 3.23607i | − 0.140832i | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | − 14.4721i | − 0.627447i | ||||||||
\(533\) | − 4.67376i | − 0.202443i | ||||||||
\(534\) | −7.61803 | −0.329665 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.7082 | −0.678491 | ||||||||
\(537\) | − 6.18034i | − 0.266701i | ||||||||
\(538\) | − 0.145898i | − 0.00629011i | ||||||||
\(539\) | −42.0689 | −1.81204 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.3262 | −1.51879 | −0.759397 | − | 0.650628i | \(-0.774506\pi\) | ||||
−0.759397 | + | 0.650628i | \(0.774506\pi\) | |||||||
\(542\) | − 22.1803i | − 0.952727i | ||||||||
\(543\) | − 9.79837i | − 0.420488i | ||||||||
\(544\) | 14.2705 | 0.611843 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.1246 | 0.647274 | ||||||||
\(547\) | 2.36068i | 0.100935i | 0.998726 | + | 0.0504677i | \(0.0160712\pi\) | ||||
−0.998726 | + | 0.0504677i | \(0.983929\pi\) | |||||||
\(548\) | 5.38197i | 0.229906i | ||||||||
\(549\) | 0.618034 | 0.0263770 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.1803 | −0.604103 | ||||||||
\(552\) | − 13.4164i | − 0.571040i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.79837 | 0.246349 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.05573 | 0.214411 | ||||||||
\(557\) | − 22.2705i | − 0.943632i | −0.881697 | − | 0.471816i | \(-0.843599\pi\) | ||||
0.881697 | − | 0.471816i | \(-0.156401\pi\) | |||||||
\(558\) | 7.23607i | 0.306327i | ||||||||
\(559\) | 19.3050 | 0.816512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.23607 | −0.389947 | ||||||||
\(562\) | 17.3820i | 0.733214i | ||||||||
\(563\) | − 17.5279i | − 0.738711i | −0.929288 | − | 0.369356i | \(-0.879578\pi\) | ||||
0.929288 | − | 0.369356i | \(-0.120422\pi\) | |||||||
\(564\) | −5.23607 | −0.220478 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.291796 | 0.0122651 | ||||||||
\(567\) | − 4.47214i | − 0.187812i | ||||||||
\(568\) | 2.29180i | 0.0961616i | ||||||||
\(569\) | 30.2705 | 1.26901 | 0.634503 | − | 0.772920i | \(-0.281205\pi\) | ||||
0.634503 | + | 0.772920i | \(0.281205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2361 | −0.888702 | −0.444351 | − | 0.895853i | \(-0.646566\pi\) | ||||
−0.444351 | + | 0.895853i | \(0.646566\pi\) | |||||||
\(572\) | 10.9443i | 0.457603i | ||||||||
\(573\) | − 24.6525i | − 1.02987i | ||||||||
\(574\) | 6.18034 | 0.257962 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 30.9443i | 1.28823i | 0.764930 | + | 0.644113i | \(0.222774\pi\) | ||||
−0.764930 | + | 0.644113i | \(0.777226\pi\) | |||||||
\(578\) | − 8.85410i | − 0.368282i | ||||||||
\(579\) | −7.67376 | −0.318911 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.7771 | 0.654544 | ||||||||
\(582\) | − 8.85410i | − 0.367014i | ||||||||
\(583\) | 4.47214i | 0.185217i | ||||||||
\(584\) | 9.27051 | 0.383616 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.79837 | 0.156909 | ||||||||
\(587\) | 14.5836i | 0.601929i | 0.953635 | + | 0.300965i | \(0.0973086\pi\) | ||||
−0.953635 | + | 0.300965i | \(0.902691\pi\) | |||||||
\(588\) | − 13.0000i | − 0.536111i | ||||||||
\(589\) | 23.4164 | 0.964856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.38197 | 0.221384 | ||||||||
\(592\) | 8.09017i | 0.332504i | ||||||||
\(593\) | − 32.7426i | − 1.34458i | −0.740288 | − | 0.672290i | \(-0.765311\pi\) | ||||
0.740288 | − | 0.672290i | \(-0.234689\pi\) | |||||||
\(594\) | −3.23607 | −0.132777 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.1459 | 0.497515 | ||||||||
\(597\) | 18.6525i | 0.763395i | ||||||||
\(598\) | − 15.1246i | − 0.618491i | ||||||||
\(599\) | 12.4721 | 0.509598 | 0.254799 | − | 0.966994i | \(-0.417991\pi\) | ||||
0.254799 | + | 0.966994i | \(0.417991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.3262 | −0.992288 | −0.496144 | − | 0.868240i | \(-0.665251\pi\) | ||||
−0.496144 | + | 0.868240i | \(0.665251\pi\) | |||||||
\(602\) | 25.5279i | 1.04044i | ||||||||
\(603\) | 5.23607i | 0.213229i | ||||||||
\(604\) | 16.4721 | 0.670242 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.5623 | −0.672798 | ||||||||
\(607\) | 39.2361i | 1.59254i | 0.604940 | + | 0.796271i | \(0.293197\pi\) | ||||
−0.604940 | + | 0.796271i | \(0.706803\pi\) | |||||||
\(608\) | − 16.1803i | − 0.656199i | ||||||||
\(609\) | −19.5967 | −0.794100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −17.7082 | −0.716397 | ||||||||
\(612\) | − 2.85410i | − 0.115370i | ||||||||
\(613\) | 39.5066i | 1.59566i | 0.602885 | + | 0.797828i | \(0.294018\pi\) | ||||
−0.602885 | + | 0.797828i | \(0.705982\pi\) | |||||||
\(614\) | −1.34752 | −0.0543816 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −43.4164 | −1.74930 | ||||||||
\(617\) | − 26.9787i | − 1.08612i | −0.839693 | − | 0.543061i | \(-0.817265\pi\) | ||||
0.839693 | − | 0.543061i | \(-0.182735\pi\) | |||||||
\(618\) | − 1.23607i | − 0.0497219i | ||||||||
\(619\) | −28.3607 | −1.13991 | −0.569956 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569956 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.47214 | −0.179461 | ||||||||
\(622\) | − 4.29180i | − 0.172085i | ||||||||
\(623\) | 34.0689i | 1.36494i | ||||||||
\(624\) | 3.38197 | 0.135387 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.47214 | 0.338615 | ||||||||
\(627\) | 10.4721i | 0.418217i | ||||||||
\(628\) | 13.7984i | 0.550615i | ||||||||
\(629\) | 23.0902 | 0.920665 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2918 | 0.409710 | 0.204855 | − | 0.978792i | \(-0.434328\pi\) | ||||
0.204855 | + | 0.978792i | \(0.434328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 17.8885i | − 0.711006i | ||||||||
\(634\) | 24.8328 | 0.986237 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.38197 | −0.0547985 | ||||||||
\(637\) | − 43.9656i | − 1.74198i | ||||||||
\(638\) | 14.1803i | 0.561405i | ||||||||
\(639\) | 0.763932 | 0.0302207 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.9443 | 1.53821 | 0.769103 | − | 0.639125i | \(-0.220703\pi\) | ||||
0.769103 | + | 0.639125i | \(0.220703\pi\) | |||||||
\(642\) | − 16.4721i | − 0.650103i | ||||||||
\(643\) | 13.8885i | 0.547711i | 0.961771 | + | 0.273855i | \(0.0882990\pi\) | ||||
−0.961771 | + | 0.273855i | \(0.911701\pi\) | |||||||
\(644\) | −20.0000 | −0.788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.23607 | 0.363388 | ||||||||
\(647\) | − 10.3607i | − 0.407320i | −0.979042 | − | 0.203660i | \(-0.934716\pi\) | ||||
0.979042 | − | 0.203660i | \(-0.0652838\pi\) | |||||||
\(648\) | − 3.00000i | − 0.117851i | ||||||||
\(649\) | 12.9443 | 0.508107 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.3607 | 1.26832 | ||||||||
\(652\) | 2.94427i | 0.115307i | ||||||||
\(653\) | 45.1033i | 1.76503i | 0.470285 | + | 0.882515i | \(0.344151\pi\) | ||||
−0.470285 | + | 0.882515i | \(0.655849\pi\) | |||||||
\(654\) | 19.0902 | 0.746485 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.38197 | 0.0539567 | ||||||||
\(657\) | − 3.09017i | − 0.120559i | ||||||||
\(658\) | − 23.4164i | − 0.912867i | ||||||||
\(659\) | 6.58359 | 0.256460 | 0.128230 | − | 0.991744i | \(-0.459070\pi\) | ||||
0.128230 | + | 0.991744i | \(0.459070\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4164 | 0.988584 | 0.494292 | − | 0.869296i | \(-0.335427\pi\) | ||||
0.494292 | + | 0.869296i | \(0.335427\pi\) | |||||||
\(662\) | − 10.9443i | − 0.425361i | ||||||||
\(663\) | − 9.65248i | − 0.374871i | ||||||||
\(664\) | 10.5836 | 0.410723 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.09017 | 0.313488 | ||||||||
\(667\) | 19.5967i | 0.758789i | ||||||||
\(668\) | 23.4164i | 0.906008i | ||||||||
\(669\) | 14.1803 | 0.548244 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | − 22.3607i | − 0.862582i | ||||||||
\(673\) | 29.7984i | 1.14864i | 0.818630 | + | 0.574321i | \(0.194734\pi\) | ||||
−0.818630 | + | 0.574321i | \(0.805266\pi\) | |||||||
\(674\) | 14.9443 | 0.575632 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.56231 | 0.0600887 | ||||||||
\(677\) | − 37.4164i | − 1.43803i | −0.694995 | − | 0.719015i | \(-0.744593\pi\) | ||||
0.694995 | − | 0.719015i | \(-0.255407\pi\) | |||||||
\(678\) | 2.67376i | 0.102685i | ||||||||
\(679\) | −39.5967 | −1.51958 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | − 23.4164i | − 0.896661i | ||||||||
\(683\) | 7.41641i | 0.283781i | 0.989882 | + | 0.141890i | \(0.0453181\pi\) | ||||
−0.989882 | + | 0.141890i | \(0.954682\pi\) | |||||||
\(684\) | −3.23607 | −0.123734 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.8328 | 1.02448 | ||||||||
\(687\) | 24.9787i | 0.952997i | ||||||||
\(688\) | 5.70820i | 0.217623i | ||||||||
\(689\) | −4.67376 | −0.178056 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.2361 | −0.807858 | −0.403929 | − | 0.914790i | \(-0.632356\pi\) | ||||
−0.403929 | + | 0.914790i | \(0.632356\pi\) | |||||||
\(692\) | 9.90983i | 0.376715i | ||||||||
\(693\) | 14.4721i | 0.549751i | ||||||||
\(694\) | 33.7082 | 1.27955 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −13.1459 | −0.498294 | ||||||||
\(697\) | − 3.94427i | − 0.149400i | ||||||||
\(698\) | 25.0344i | 0.947568i | ||||||||
\(699\) | −14.6180 | −0.552905 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.437694 | 0.0165315 | 0.00826574 | − | 0.999966i | \(-0.497369\pi\) | ||||
0.00826574 | + | 0.999966i | \(0.497369\pi\) | |||||||
\(702\) | − 3.38197i | − 0.127644i | ||||||||
\(703\) | − 26.1803i | − 0.987410i | ||||||||
\(704\) | −22.6525 | −0.853747 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −30.3607 | −1.14264 | ||||||||
\(707\) | 74.0689i | 2.78565i | ||||||||
\(708\) | 4.00000i | 0.150329i | ||||||||
\(709\) | 6.72949 | 0.252731 | 0.126366 | − | 0.991984i | \(-0.459669\pi\) | ||||
0.126366 | + | 0.991984i | \(0.459669\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.8541i | 0.856494i | ||||||||
\(713\) | − 32.3607i | − 1.21192i | ||||||||
\(714\) | 12.7639 | 0.477678 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.18034 | −0.230970 | ||||||||
\(717\) | 7.05573i | 0.263501i | ||||||||
\(718\) | − 10.5836i | − 0.394976i | ||||||||
\(719\) | 35.8885 | 1.33842 | 0.669208 | − | 0.743075i | \(-0.266633\pi\) | ||||
0.669208 | + | 0.743075i | \(0.266633\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.52786 | −0.205868 | ||||||||
\(722\) | 8.52786i | 0.317374i | ||||||||
\(723\) | − 1.03444i | − 0.0384713i | ||||||||
\(724\) | −9.79837 | −0.364154 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.527864 | −0.0195909 | ||||||||
\(727\) | − 15.3475i | − 0.569208i | −0.958645 | − | 0.284604i | \(-0.908138\pi\) | ||||
0.958645 | − | 0.284604i | \(-0.0918621\pi\) | |||||||
\(728\) | − 45.3738i | − 1.68167i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.2918 | 0.602574 | ||||||||
\(732\) | − 0.618034i | − 0.0228432i | ||||||||
\(733\) | 2.58359i | 0.0954272i | 0.998861 | + | 0.0477136i | \(0.0151935\pi\) | ||||
−0.998861 | + | 0.0477136i | \(0.984807\pi\) | |||||||
\(734\) | 6.00000 | 0.221464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22.3607 | −0.824226 | ||||||||
\(737\) | − 16.9443i | − 0.624150i | ||||||||
\(738\) | − 1.38197i | − 0.0508709i | ||||||||
\(739\) | −17.7082 | −0.651407 | −0.325703 | − | 0.945472i | \(-0.605601\pi\) | ||||
−0.325703 | + | 0.945472i | \(0.605601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.9443 | −0.402048 | ||||||||
\(742\) | − 6.18034i | − 0.226887i | ||||||||
\(743\) | 0.875388i | 0.0321149i | 0.999871 | + | 0.0160574i | \(0.00511146\pi\) | ||||
−0.999871 | + | 0.0160574i | \(0.994889\pi\) | |||||||
\(744\) | 21.7082 | 0.795861 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.4164 | 1.07701 | ||||||||
\(747\) | − 3.52786i | − 0.129078i | ||||||||
\(748\) | 9.23607i | 0.337704i | ||||||||
\(749\) | −73.6656 | −2.69168 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.34752 | 0.195134 | 0.0975670 | − | 0.995229i | \(-0.468894\pi\) | ||||
0.0975670 | + | 0.995229i | \(0.468894\pi\) | |||||||
\(752\) | − 5.23607i | − 0.190940i | ||||||||
\(753\) | − 26.9443i | − 0.981904i | ||||||||
\(754\) | −14.8197 | −0.539700 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.47214 | −0.162650 | ||||||||
\(757\) | − 27.3820i | − 0.995214i | −0.867402 | − | 0.497607i | \(-0.834212\pi\) | ||||
0.867402 | − | 0.497607i | \(-0.165788\pi\) | |||||||
\(758\) | 23.4164i | 0.850522i | ||||||||
\(759\) | 14.4721 | 0.525305 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.74265 | −0.353171 | −0.176585 | − | 0.984285i | \(-0.556505\pi\) | ||||
−0.176585 | + | 0.984285i | \(0.556505\pi\) | |||||||
\(762\) | − 9.70820i | − 0.351691i | ||||||||
\(763\) | − 85.3738i | − 3.09074i | ||||||||
\(764\) | −24.6525 | −0.891895 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.8328 | 0.752720 | ||||||||
\(767\) | 13.5279i | 0.488463i | ||||||||
\(768\) | − 17.0000i | − 0.613435i | ||||||||
\(769\) | 5.63932 | 0.203359 | 0.101680 | − | 0.994817i | \(-0.467578\pi\) | ||||
0.101680 | + | 0.994817i | \(0.467578\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.7984 | −0.460922 | ||||||||
\(772\) | 7.67376i | 0.276185i | ||||||||
\(773\) | − 35.9230i | − 1.29206i | −0.763312 | − | 0.646030i | \(-0.776428\pi\) | ||||
0.763312 | − | 0.646030i | \(-0.223572\pi\) | |||||||
\(774\) | 5.70820 | 0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −26.5623 | −0.953531 | ||||||||
\(777\) | − 36.1803i | − 1.29796i | ||||||||
\(778\) | − 37.0902i | − 1.32975i | ||||||||
\(779\) | −4.47214 | −0.160231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.47214 | −0.0884600 | ||||||||
\(782\) | − 12.7639i | − 0.456437i | ||||||||
\(783\) | 4.38197i | 0.156599i | ||||||||
\(784\) | 13.0000 | 0.464286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 14.1803 | 0.505796 | ||||||||
\(787\) | − 8.18034i | − 0.291598i | −0.989314 | − | 0.145799i | \(-0.953425\pi\) | ||||
0.989314 | − | 0.145799i | \(-0.0465752\pi\) | |||||||
\(788\) | − 5.38197i | − 0.191725i | ||||||||
\(789\) | −11.8885 | −0.423243 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.9574 | 0.425157 | ||||||||
\(792\) | 9.70820i | 0.344966i | ||||||||
\(793\) | − 2.09017i | − 0.0742241i | ||||||||
\(794\) | −10.9443 | −0.388398 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.6525 | 0.661119 | ||||||||
\(797\) | − 38.1033i | − 1.34969i | −0.737960 | − | 0.674845i | \(-0.764211\pi\) | ||||
0.737960 | − | 0.674845i | \(-0.235789\pi\) | |||||||
\(798\) | − 14.4721i | − 0.512308i | ||||||||
\(799\) | −14.9443 | −0.528690 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.61803 | 0.269170 | ||||||||
\(802\) | − 33.4508i | − 1.18119i | ||||||||
\(803\) | 10.0000i | 0.352892i | ||||||||
\(804\) | 5.23607 | 0.184662 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.4721 | 0.861994 | ||||||||
\(807\) | 0.145898i | 0.00513585i | ||||||||
\(808\) | 49.6869i | 1.74798i | ||||||||
\(809\) | 23.2148 | 0.816188 | 0.408094 | − | 0.912940i | \(-0.366194\pi\) | ||||
0.408094 | + | 0.912940i | \(0.366194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.23607 | 0.324322 | 0.162161 | − | 0.986764i | \(-0.448154\pi\) | ||||
0.162161 | + | 0.986764i | \(0.448154\pi\) | |||||||
\(812\) | 19.5967i | 0.687711i | ||||||||
\(813\) | 22.1803i | 0.777898i | ||||||||
\(814\) | −26.1803 | −0.917620 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.85410 | 0.0999136 | ||||||||
\(817\) | − 18.4721i | − 0.646258i | ||||||||
\(818\) | 25.7984i | 0.902019i | ||||||||
\(819\) | −15.1246 | −0.528497 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.05573 | 0.176446 | 0.0882231 | − | 0.996101i | \(-0.471881\pi\) | ||||
0.0882231 | + | 0.996101i | \(0.471881\pi\) | |||||||
\(822\) | 5.38197i | 0.187718i | ||||||||
\(823\) | − 14.7639i | − 0.514638i | −0.966326 | − | 0.257319i | \(-0.917161\pi\) | ||||
0.966326 | − | 0.257319i | \(-0.0828392\pi\) | |||||||
\(824\) | −3.70820 | −0.129181 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.8885 | −0.622422 | ||||||||
\(827\) | − 22.0689i | − 0.767410i | −0.923456 | − | 0.383705i | \(-0.874648\pi\) | ||||
0.923456 | − | 0.383705i | \(-0.125352\pi\) | |||||||
\(828\) | 4.47214i | 0.155417i | ||||||||
\(829\) | 26.5066 | 0.920611 | 0.460306 | − | 0.887760i | \(-0.347740\pi\) | ||||
0.460306 | + | 0.887760i | \(0.347740\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.79837 | −0.201143 | ||||||||
\(832\) | − 23.6738i | − 0.820740i | ||||||||
\(833\) | − 37.1033i | − 1.28555i | ||||||||
\(834\) | 5.05573 | 0.175066 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.4721 | 0.362186 | ||||||||
\(837\) | − 7.23607i | − 0.250115i | ||||||||
\(838\) | 32.9443i | 1.13804i | ||||||||
\(839\) | 44.0689 | 1.52143 | 0.760713 | − | 0.649088i | \(-0.224849\pi\) | ||||
0.760713 | + | 0.649088i | \(0.224849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.79837 | −0.337875 | ||||||||
\(842\) | − 23.1459i | − 0.797660i | ||||||||
\(843\) | − 17.3820i | − 0.598667i | ||||||||
\(844\) | −17.8885 | −0.615749 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.23607 | −0.180020 | ||||||||
\(847\) | 2.36068i | 0.0811139i | ||||||||
\(848\) | − 1.38197i | − 0.0474569i | ||||||||
\(849\) | −0.291796 | −0.0100144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.1803 | −1.24025 | ||||||||
\(852\) | − 0.763932i | − 0.0261719i | ||||||||
\(853\) | 29.8541i | 1.02218i | 0.859526 | + | 0.511092i | \(0.170759\pi\) | ||||
−0.859526 | + | 0.511092i | \(0.829241\pi\) | |||||||
\(854\) | 2.76393 | 0.0945798 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −49.4164 | −1.68902 | ||||||||
\(857\) | 3.52786i | 0.120510i | 0.998183 | + | 0.0602548i | \(0.0191913\pi\) | ||||
−0.998183 | + | 0.0602548i | \(0.980809\pi\) | |||||||
\(858\) | 10.9443i | 0.373631i | ||||||||
\(859\) | −3.41641 | −0.116566 | −0.0582832 | − | 0.998300i | \(-0.518563\pi\) | ||||
−0.0582832 | + | 0.998300i | \(0.518563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.18034 | −0.210625 | ||||||||
\(862\) | 10.6525i | 0.362825i | ||||||||
\(863\) | 51.1246i | 1.74030i | 0.492785 | + | 0.870151i | \(0.335979\pi\) | ||||
−0.492785 | + | 0.870151i | \(0.664021\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.9787 | 0.848811 | ||||||||
\(867\) | 8.85410i | 0.300701i | ||||||||
\(868\) | − 32.3607i | − 1.09839i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.7082 | 0.600020 | ||||||||
\(872\) | − 57.2705i | − 1.93942i | ||||||||
\(873\) | 8.85410i | 0.299666i | ||||||||
\(874\) | −14.4721 | −0.489527 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.09017 | −0.104407 | ||||||||
\(877\) | − 18.2148i | − 0.615069i | −0.951537 | − | 0.307535i | \(-0.900496\pi\) | ||||
0.951537 | − | 0.307535i | \(-0.0995040\pi\) | |||||||
\(878\) | − 6.18034i | − 0.208576i | ||||||||
\(879\) | −3.79837 | −0.128116 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.0557 | 0.844149 | 0.422074 | − | 0.906561i | \(-0.361302\pi\) | ||||
0.422074 | + | 0.906561i | \(0.361302\pi\) | |||||||
\(882\) | − 13.0000i | − 0.437733i | ||||||||
\(883\) | − 0.180340i | − 0.00606892i | −0.999995 | − | 0.00303446i | \(-0.999034\pi\) | ||||
0.999995 | − | 0.00303446i | \(-0.000965900\pi\) | |||||||
\(884\) | −9.65248 | −0.324648 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30.7639 | −1.03353 | ||||||||
\(887\) | − 17.1246i | − 0.574988i | −0.957782 | − | 0.287494i | \(-0.907178\pi\) | ||||
0.957782 | − | 0.287494i | \(-0.0928222\pi\) | |||||||
\(888\) | − 24.2705i | − 0.814465i | ||||||||
\(889\) | −43.4164 | −1.45614 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.23607 | 0.108412 | ||||||||
\(892\) | − 14.1803i | − 0.474793i | ||||||||
\(893\) | 16.9443i | 0.567018i | ||||||||
\(894\) | 12.1459 | 0.406220 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.4164 | −0.448211 | ||||||||
\(897\) | 15.1246i | 0.504996i | ||||||||
\(898\) | − 7.79837i | − 0.260235i | ||||||||
\(899\) | −31.7082 | −1.05753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.94427 | −0.131403 | ||||||||
\(902\) | 4.47214i | 0.148906i | ||||||||
\(903\) | − 25.5279i | − 0.849514i | ||||||||
\(904\) | 8.02129 | 0.266784 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16.4721 | 0.547250 | ||||||||
\(907\) | 33.1246i | 1.09988i | 0.835203 | + | 0.549942i | \(0.185350\pi\) | ||||
−0.835203 | + | 0.549942i | \(0.814650\pi\) | |||||||
\(908\) | 20.0000i | 0.663723i | ||||||||
\(909\) | 16.5623 | 0.549337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.18034 | −0.138501 | −0.0692504 | − | 0.997599i | \(-0.522061\pi\) | ||||
−0.0692504 | + | 0.997599i | \(0.522061\pi\) | |||||||
\(912\) | − 3.23607i | − 0.107157i | ||||||||
\(913\) | 11.4164i | 0.377828i | ||||||||
\(914\) | −22.3607 | −0.739626 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.9787 | 0.825320 | ||||||||
\(917\) | − 63.4164i | − 2.09419i | ||||||||
\(918\) | − 2.85410i | − 0.0941994i | ||||||||
\(919\) | 49.1935 | 1.62274 | 0.811372 | − | 0.584530i | \(-0.198721\pi\) | ||||
0.811372 | + | 0.584530i | \(0.198721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.34752 | 0.0444024 | ||||||||
\(922\) | 8.20163i | 0.270106i | ||||||||
\(923\) | − 2.58359i | − 0.0850400i | ||||||||
\(924\) | 14.4721 | 0.476098 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23.2361 | 0.763585 | ||||||||
\(927\) | 1.23607i | 0.0405978i | ||||||||
\(928\) | 21.9098i | 0.719225i | ||||||||
\(929\) | −2.09017 | −0.0685763 | −0.0342881 | − | 0.999412i | \(-0.510916\pi\) | ||||
−0.0342881 | + | 0.999412i | \(0.510916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.0689 | −1.37875 | ||||||||
\(932\) | 14.6180i | 0.478830i | ||||||||
\(933\) | 4.29180i | 0.140507i | ||||||||
\(934\) | −5.81966 | −0.190425 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −10.1459 | −0.331629 | ||||||||
\(937\) | − 11.6869i | − 0.381795i | −0.981610 | − | 0.190897i | \(-0.938860\pi\) | ||||
0.981610 | − | 0.190897i | \(-0.0611398\pi\) | |||||||
\(938\) | 23.4164i | 0.764573i | ||||||||
\(939\) | −8.47214 | −0.276478 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.32624 | 0.173630 | 0.0868152 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868152 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(942\) | 13.7984i | 0.449575i | ||||||||
\(943\) | 6.18034i | 0.201260i | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.4721 | −0.600581 | ||||||||
\(947\) | − 29.4164i | − 0.955905i | −0.878386 | − | 0.477952i | \(-0.841379\pi\) | ||||
0.878386 | − | 0.477952i | \(-0.158621\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.4508 | −0.339249 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.8328 | −0.805259 | ||||||||
\(952\) | − 38.2918i | − 1.24104i | ||||||||
\(953\) | 10.0902i | 0.326853i | 0.986556 | + | 0.163426i | \(0.0522546\pi\) | ||||
−0.986556 | + | 0.163426i | \(0.947745\pi\) | |||||||
\(954\) | −1.38197 | −0.0447428 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.05573 | 0.228199 | ||||||||
\(957\) | − 14.1803i | − 0.458385i | ||||||||
\(958\) | 1.05573i | 0.0341090i | ||||||||
\(959\) | 24.0689 | 0.777225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.3607 | 0.689054 | ||||||||
\(962\) | − 27.3607i | − 0.882144i | ||||||||
\(963\) | 16.4721i | 0.530807i | ||||||||
\(964\) | −1.03444 | −0.0333171 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.0000 | −0.643489 | ||||||||
\(967\) | − 34.8328i | − 1.12015i | −0.828443 | − | 0.560074i | \(-0.810773\pi\) | ||||
0.828443 | − | 0.560074i | \(-0.189227\pi\) | |||||||
\(968\) | 1.58359i | 0.0508986i | ||||||||
\(969\) | −9.23607 | −0.296705 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.58359 | −0.211278 | −0.105639 | − | 0.994405i | \(-0.533689\pi\) | ||||
−0.105639 | + | 0.994405i | \(0.533689\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 22.6099i | − 0.724840i | ||||||||
\(974\) | 3.70820 | 0.118819 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.618034 | 0.0197828 | ||||||||
\(977\) | 45.7426i | 1.46344i | 0.681607 | + | 0.731718i | \(0.261281\pi\) | ||||
−0.681607 | + | 0.731718i | \(0.738719\pi\) | |||||||
\(978\) | 2.94427i | 0.0941474i | ||||||||
\(979\) | −24.6525 | −0.787897 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.0902 | −0.609502 | ||||||||
\(982\) | 29.8885i | 0.953782i | ||||||||
\(983\) | 21.7082i | 0.692384i | 0.938164 | + | 0.346192i | \(0.112525\pi\) | ||||
−0.938164 | + | 0.346192i | \(0.887475\pi\) | |||||||
\(984\) | −4.14590 | −0.132166 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −12.5066 | −0.398291 | ||||||||
\(987\) | 23.4164i | 0.745352i | ||||||||
\(988\) | 10.9443i | 0.348184i | ||||||||
\(989\) | −25.5279 | −0.811739 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.12461 | −0.0992566 | −0.0496283 | − | 0.998768i | \(-0.515804\pi\) | ||||
−0.0496283 | + | 0.998768i | \(0.515804\pi\) | |||||||
\(992\) | − 36.1803i | − 1.14873i | ||||||||
\(993\) | 10.9443i | 0.347306i | ||||||||
\(994\) | 3.41641 | 0.108362 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.52786 | −0.111785 | ||||||||
\(997\) | − 9.41641i | − 0.298221i | −0.988821 | − | 0.149110i | \(-0.952359\pi\) | ||||
0.988821 | − | 0.149110i | \(-0.0476410\pi\) | |||||||
\(998\) | − 6.00000i | − 0.189927i | ||||||||
\(999\) | −8.09017 | −0.255962 |
(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 | 1875.2.b.b.1249.1 | 4 | ||
5.2 | odd | 4 | 1875.2.a.d.1.2 | 2 | |||
5.3 | odd | 4 | 1875.2.a.a.1.1 | 2 | |||
5.4 | even | 2 | inner | 1875.2.b.b.1249.4 | 4 | ||
15.2 | even | 4 | 5625.2.a.a.1.2 | 2 | |||
15.8 | even | 4 | 5625.2.a.h.1.1 | 2 | |||
25.3 | odd | 20 | 375.2.g.a.76.1 | 4 | |||
25.4 | even | 10 | 375.2.i.a.49.2 | 8 | |||
25.6 | even | 5 | 375.2.i.a.199.2 | 8 | |||
25.8 | odd | 20 | 375.2.g.a.301.1 | 4 | |||
25.17 | odd | 20 | 75.2.g.a.61.1 | yes | 4 | ||
25.19 | even | 10 | 375.2.i.a.199.1 | 8 | |||
25.21 | even | 5 | 375.2.i.a.49.1 | 8 | |||
25.22 | odd | 20 | 75.2.g.a.16.1 | ✓ | 4 | ||
75.17 | even | 20 | 225.2.h.a.136.1 | 4 | |||
75.47 | even | 20 | 225.2.h.a.91.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.16.1 | ✓ | 4 | 25.22 | odd | 20 | ||
75.2.g.a.61.1 | yes | 4 | 25.17 | odd | 20 | ||
225.2.h.a.91.1 | 4 | 75.47 | even | 20 | |||
225.2.h.a.136.1 | 4 | 75.17 | even | 20 | |||
375.2.g.a.76.1 | 4 | 25.3 | odd | 20 | |||
375.2.g.a.301.1 | 4 | 25.8 | odd | 20 | |||
375.2.i.a.49.1 | 8 | 25.21 | even | 5 | |||
375.2.i.a.49.2 | 8 | 25.4 | even | 10 | |||
375.2.i.a.199.1 | 8 | 25.19 | even | 10 | |||
375.2.i.a.199.2 | 8 | 25.6 | even | 5 | |||
1875.2.a.a.1.1 | 2 | 5.3 | odd | 4 | |||
1875.2.a.d.1.2 | 2 | 5.2 | odd | 4 | |||
1875.2.b.b.1249.1 | 4 | 1.1 | even | 1 | trivial | ||
1875.2.b.b.1249.4 | 4 | 5.4 | even | 2 | inner | ||
5625.2.a.a.1.2 | 2 | 15.2 | even | 4 | |||
5625.2.a.h.1.1 | 2 | 15.8 | even | 4 |