Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(57,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.57");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.m (of order \(4\), degree \(2\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.31678304256.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 8x^{5} + 32x^{4} - 20x^{3} + 8x^{2} + 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 57.1 | ||
Root | \(2.13456 + 2.13456i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.57 |
Dual form | 1300.2.m.c.593.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.13456 | + | 2.13456i | −1.23239 | + | 1.23239i | −0.269344 | + | 0.963044i | \(0.586807\pi\) |
−0.963044 | + | 0.269344i | \(0.913193\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.84356i | 1.07477i | 0.843338 | + | 0.537383i | \(0.180587\pi\) | ||||
−0.843338 | + | 0.537383i | \(0.819413\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 6.11268i | − | 2.03756i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.66608 | + | 2.66608i | 0.803853 | + | 0.803853i | 0.983695 | − | 0.179843i | \(-0.0575589\pi\) |
−0.179843 | + | 0.983695i | \(0.557559\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.134559 | + | 3.60304i | 0.0373198 | + | 0.999303i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.80064 | − | 2.80064i | 0.679254 | − | 0.679254i | −0.280577 | − | 0.959831i | \(-0.590526\pi\) |
0.959831 | + | 0.280577i | \(0.0905259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.97812 | + | 3.97812i | 0.912644 | + | 0.912644i | 0.996480 | − | 0.0838357i | \(-0.0267171\pi\) |
−0.0838357 | + | 0.996480i | \(0.526717\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.06975 | − | 6.06975i | −1.32453 | − | 1.32453i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.66608 | + | 3.66608i | 0.764430 | + | 0.764430i | 0.977120 | − | 0.212690i | \(-0.0682224\pi\) |
−0.212690 | + | 0.977120i | \(0.568222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 6.64420 | + | 6.64420i | 1.27868 | + | 1.27868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.17572i | 1.51819i | 0.650978 | + | 0.759096i | \(0.274359\pi\) | ||||
−0.650978 | + | 0.759096i | \(0.725641\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.60304 | + | 3.60304i | −0.647125 | + | 0.647125i | −0.952297 | − | 0.305172i | \(-0.901286\pi\) |
0.305172 | + | 0.952297i | \(0.401286\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.3818 | −1.98132 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.11268i | − | 0.511722i | −0.966714 | − | 0.255861i | \(-0.917641\pi\) | ||
0.966714 | − | 0.255861i | \(-0.0823589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.97812 | − | 7.40368i | −1.27752 | − | 1.18554i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.64420 | − | 3.64420i | 0.569128 | − | 0.569128i | −0.362756 | − | 0.931884i | \(-0.618164\pi\) |
0.931884 | + | 0.362756i | \(0.118164\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.998233 | − | 0.998233i | −0.152229 | − | 0.152229i | 0.626884 | − | 0.779113i | \(-0.284330\pi\) |
−0.779113 | + | 0.626884i | \(0.784330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.46765i | − | 1.38100i | −0.723333 | − | 0.690500i | \(-0.757391\pi\) | ||
0.723333 | − | 0.690500i | \(-0.242609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.08585 | −0.155122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.9562i | 1.67421i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.78053 | + | 2.78053i | −0.381935 | + | 0.381935i | −0.871799 | − | 0.489864i | \(-0.837046\pi\) |
0.489864 | + | 0.871799i | \(0.337046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.9831 | −2.24946 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.97812 | − | 3.97812i | 0.517907 | − | 0.517907i | −0.399030 | − | 0.916938i | \(-0.630653\pi\) |
0.916938 | + | 0.399030i | \(0.130653\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.9866 | −1.40669 | −0.703345 | − | 0.710848i | \(-0.748311\pi\) | ||||
−0.703345 | + | 0.710848i | \(0.748311\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.3818 | 2.18990 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.574447 | −0.0701798 | −0.0350899 | − | 0.999384i | \(-0.511172\pi\) | ||||
−0.0350899 | + | 0.999384i | \(0.511172\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.6509 | −1.88415 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.73937 | + | 4.73937i | −0.562459 | + | 0.562459i | −0.930005 | − | 0.367546i | \(-0.880198\pi\) |
0.367546 | + | 0.930005i | \(0.380198\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.92588 | 1.04470 | 0.522348 | − | 0.852732i | \(-0.325056\pi\) | ||||
0.522348 | + | 0.852732i | \(0.325056\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.58116 | + | 7.58116i | −0.863954 | + | 0.863954i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.51895i | − | 0.620931i | −0.950585 | − | 0.310465i | \(-0.899515\pi\) | ||
0.950585 | − | 0.310465i | \(-0.100485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.0268 | −1.11409 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.75771i | 0.302698i | 0.988480 | + | 0.151349i | \(0.0483617\pi\) | ||||
−0.988480 | + | 0.151349i | \(0.951638\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.4516 | − | 17.4516i | −1.87100 | − | 1.87100i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.36252 | + | 3.36252i | −0.356426 | + | 0.356426i | −0.862494 | − | 0.506068i | \(-0.831099\pi\) |
0.506068 | + | 0.862494i | \(0.331099\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.2455 | + | 0.382626i | −1.07402 | + | 0.0401101i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 15.3818i | − | 1.59502i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.12022 | −0.926018 | −0.463009 | − | 0.886353i | \(-0.653230\pi\) | ||||
−0.463009 | + | 0.886353i | \(0.653230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.2969 | − | 16.2969i | 1.63790 | − | 1.63790i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.1395i | − | 1.00892i | −0.863435 | − | 0.504459i | \(-0.831692\pi\) | ||
0.863435 | − | 0.504459i | \(-0.168308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.57940 | − | 8.57940i | −0.845353 | − | 0.845353i | 0.144196 | − | 0.989549i | \(-0.453940\pi\) |
−0.989549 | + | 0.144196i | \(0.953940\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.04788 | + | 5.04788i | 0.487997 | + | 0.487997i | 0.907674 | − | 0.419677i | \(-0.137857\pi\) |
−0.419677 | + | 0.907674i | \(0.637857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.73760 | − | 5.73760i | −0.549562 | − | 0.549562i | 0.376752 | − | 0.926314i | \(-0.377041\pi\) |
−0.926314 | + | 0.376752i | \(0.877041\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.64420 | + | 6.64420i | 0.630640 | + | 0.630640i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.55835 | + | 7.55835i | −0.711029 | + | 0.711029i | −0.966751 | − | 0.255721i | \(-0.917687\pi\) |
0.255721 | + | 0.966751i | \(0.417687\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 22.0242 | − | 0.822514i | 2.03614 | − | 0.0760414i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.96379 | + | 7.96379i | 0.730039 | + | 0.730039i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.21594i | 0.292358i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.5575i | 1.40277i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3103 | + | 10.3103i | −0.914889 | + | 0.914889i | −0.996652 | − | 0.0817626i | \(-0.973945\pi\) |
0.0817626 | + | 0.996652i | \(0.473945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.26157 | 0.375211 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0386 | −0.877074 | −0.438537 | − | 0.898713i | \(-0.644503\pi\) | ||||
−0.438537 | + | 0.898713i | \(0.644503\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.3120 | + | 11.3120i | −0.980879 | + | 0.980879i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 7.41801i | − | 0.633763i | −0.948465 | − | 0.316882i | \(-0.897364\pi\) | ||
0.948465 | − | 0.316882i | \(-0.102636\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.26912i | 0.192464i | 0.995359 | + | 0.0962320i | \(0.0306791\pi\) | ||||
−0.995359 | + | 0.0962320i | \(0.969321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.2093 | + | 20.2093i | 1.70193 | + | 1.70193i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.24724 | + | 9.96473i | −0.773293 | + | 0.833292i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.31782 | − | 2.31782i | 0.191171 | − | 0.191171i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.976355 | − | 0.976355i | −0.0799862 | − | 0.0799862i | 0.665982 | − | 0.745968i | \(-0.268013\pi\) |
−0.745968 | + | 0.665982i | \(0.768013\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.79887 | − | 3.79887i | −0.309148 | − | 0.309148i | 0.535431 | − | 0.844579i | \(-0.320149\pi\) |
−0.844579 | + | 0.535431i | \(0.820149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.1194 | − | 17.1194i | −1.38402 | − | 1.38402i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0698 | + | 11.0698i | 0.883463 | + | 0.883463i | 0.993885 | − | 0.110422i | \(-0.0352203\pi\) |
−0.110422 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 11.8704i | − | 0.941383i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.4247 | + | 10.4247i | −0.821583 | + | 0.821583i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.4776 | 1.68225 | 0.841126 | − | 0.540840i | \(-0.181893\pi\) | ||||
0.841126 | + | 0.540840i | \(0.181893\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.71749i | 0.210285i | 0.994457 | + | 0.105143i | \(0.0335299\pi\) | ||||
−0.994457 | + | 0.105143i | \(0.966470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9638 | + | 0.969640i | −0.997214 | + | 0.0745877i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.3170 | − | 24.3170i | 1.85957 | − | 1.85957i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.24983 | + | 4.24983i | 0.323109 | + | 0.323109i | 0.849959 | − | 0.526850i | \(-0.176627\pi\) |
−0.526850 | + | 0.849959i | \(0.676627\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9831i | 1.27653i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.8109 | 1.25650 | 0.628252 | − | 0.778010i | \(-0.283771\pi\) | ||||
0.628252 | + | 0.778010i | \(0.283771\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 21.6509i | − | 1.60930i | −0.593750 | − | 0.804650i | \(-0.702353\pi\) | ||
0.593750 | − | 0.804650i | \(-0.297647\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 23.4516 | − | 23.4516i | 1.73359 | − | 1.73359i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.9334 | 1.09204 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.8932 | + | 18.8932i | −1.37428 | + | 1.37428i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.10094 | −0.152019 | −0.0760094 | − | 0.997107i | \(-0.524218\pi\) | ||||
−0.0760094 | + | 0.997107i | \(0.524218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.39288 | 0.388188 | 0.194094 | − | 0.980983i | \(-0.437823\pi\) | ||||
0.194094 | + | 0.980983i | \(0.437823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.66784 | 0.617558 | 0.308779 | − | 0.951134i | \(-0.400080\pi\) | ||||
0.308779 | + | 0.951134i | \(0.400080\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5154 | 0.816306 | 0.408153 | − | 0.912913i | \(-0.366173\pi\) | ||||
0.408153 | + | 0.912913i | \(0.366173\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.22619 | − | 1.22619i | 0.0864888 | − | 0.0864888i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −23.2482 | −1.63170 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.4096 | − | 22.4096i | 1.55757 | − | 1.55757i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.2120i | 1.46726i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.4886 | 1.75471 | 0.877355 | − | 0.479842i | \(-0.159306\pi\) | ||||
0.877355 | + | 0.479842i | \(0.159306\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 20.2329i | − | 1.38634i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.2455 | − | 10.2455i | −0.695508 | − | 0.695508i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −19.0528 | + | 19.0528i | −1.28747 | + | 1.28747i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.4677 | + | 9.71395i | 0.704131 | + | 0.653431i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.50787i | 0.100975i | 0.998725 | + | 0.0504874i | \(0.0160775\pi\) | ||||
−0.998725 | + | 0.0504874i | \(0.983923\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.7542 | −0.846524 | −0.423262 | − | 0.906007i | \(-0.639115\pi\) | ||||
−0.423262 | + | 0.906007i | \(0.639115\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.0461 | − | 17.0461i | 1.12644 | − | 1.12644i | 0.135687 | − | 0.990752i | \(-0.456676\pi\) |
0.990752 | − | 0.135687i | \(-0.0433241\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 32.3649i | − | 2.12945i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.9755 | + | 19.9755i | 1.30864 | + | 1.30864i | 0.922397 | + | 0.386243i | \(0.126228\pi\) |
0.386243 | + | 0.922397i | \(0.373772\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.7805 | + | 11.7805i | 0.765227 | + | 0.765227i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.96555 | + | 1.96555i | 0.127141 | + | 0.127141i | 0.767814 | − | 0.640673i | \(-0.221344\pi\) |
−0.640673 | + | 0.767814i | \(0.721344\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.3751 | − | 13.3751i | −0.861565 | − | 0.861565i | 0.129955 | − | 0.991520i | \(-0.458517\pi\) |
−0.991520 | + | 0.129955i | \(0.958517\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.47025 | − | 1.47025i | 0.0943164 | − | 0.0943164i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.7980 | + | 14.8686i | −0.877948 | + | 0.946068i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.88649 | − | 5.88649i | −0.373041 | − | 0.373041i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1588i | 1.33553i | 0.744372 | + | 0.667765i | \(0.232749\pi\) | ||||
−0.744372 | + | 0.667765i | \(0.767251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.5481i | 1.22898i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.9638 | − | 14.9638i | 0.933415 | − | 0.933415i | −0.0645021 | − | 0.997918i | \(-0.520546\pi\) |
0.997918 | + | 0.0645021i | \(0.0205459\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.85111 | 0.549981 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.9756 | 3.09341 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.80240 | + | 2.80240i | −0.172804 | + | 0.172804i | −0.788210 | − | 0.615406i | \(-0.788992\pi\) |
0.615406 | + | 0.788210i | \(0.288992\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 14.3550i | − | 0.878510i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.0993i | 1.34742i | 0.738997 | + | 0.673709i | \(0.235300\pi\) | ||||
−0.738997 | + | 0.673709i | \(0.764700\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2969 | + | 14.2969i | 0.868474 | + | 0.868474i | 0.992303 | − | 0.123830i | \(-0.0395177\pi\) |
−0.123830 | + | 0.992303i | \(0.539518\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.0528 | − | 22.6863i | 1.27417 | − | 1.37304i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.01928 | − | 4.01928i | 0.241495 | − | 0.241495i | −0.575973 | − | 0.817469i | \(-0.695377\pi\) |
0.817469 | + | 0.575973i | \(0.195377\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0242 | + | 22.0242i | 1.31856 | + | 1.31856i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2262 | − | 10.2262i | −0.610043 | − | 0.610043i | 0.332914 | − | 0.942957i | \(-0.391968\pi\) |
−0.942957 | + | 0.332914i | \(0.891968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4734 | − | 20.4734i | −1.21702 | − | 1.21702i | −0.968671 | − | 0.248348i | \(-0.920112\pi\) |
−0.248348 | − | 0.968671i | \(-0.579888\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3625 | + | 10.3625i | 0.611680 | + | 0.611680i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.31287i | 0.0772278i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 19.4677 | − | 19.4677i | 1.14121 | − | 1.14121i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.7770 | −1.38907 | −0.694533 | − | 0.719461i | \(-0.744389\pi\) | ||||
−0.694533 | + | 0.719461i | \(0.744389\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 35.4279i | 2.05574i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7157 | + | 13.7023i | −0.735369 | + | 0.792426i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.83854 | − | 2.83854i | 0.163611 | − | 0.163611i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.6434 | + | 21.6434i | 1.24338 | + | 1.24338i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.46931i | − | 0.0838579i | −0.999121 | − | 0.0419289i | \(-0.986650\pi\) | ||
0.999121 | − | 0.0419289i | \(-0.0133503\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.6264 | 2.08361 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.708066i | 0.0401507i | 0.999798 | + | 0.0200754i | \(0.00639062\pi\) | ||||
−0.999798 | + | 0.0200754i | \(0.993609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.7376 | − | 13.7376i | 0.776495 | − | 0.776495i | −0.202738 | − | 0.979233i | \(-0.564984\pi\) |
0.979233 | + | 0.202738i | \(0.0649840\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.3853 | 0.639464 | 0.319732 | − | 0.947508i | \(-0.396407\pi\) | ||||
0.319732 | + | 0.947508i | \(0.396407\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7971 | + | 21.7971i | −1.22040 | + | 1.22040i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.5500 | −1.20280 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 22.2825 | 1.23983 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.4945 | 1.35455 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.9219 | 1.48425 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.8056 | + | 14.8056i | −0.813789 | + | 0.813789i | −0.985200 | − | 0.171411i | \(-0.945167\pi\) |
0.171411 | + | 0.985200i | \(0.445167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.0268 | −1.04266 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.22972 | + | 2.22972i | −0.121461 | + | 0.121461i | −0.765224 | − | 0.643764i | \(-0.777372\pi\) |
0.643764 | + | 0.765224i | \(0.277372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 32.2675i | − | 1.75253i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.2120 | −1.04039 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8172i | 0.908046i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.3162 | + | 14.3162i | 0.768532 | + | 0.768532i | 0.977848 | − | 0.209316i | \(-0.0671237\pi\) |
−0.209316 | + | 0.977848i | \(0.567124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.93696 | + | 5.93696i | −0.317798 | + | 0.317798i | −0.847921 | − | 0.530123i | \(-0.822146\pi\) |
0.530123 | + | 0.847921i | \(0.322146\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.0453 | + | 24.8334i | −1.23007 | + | 1.32551i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 22.5020i | − | 1.19766i | −0.800875 | − | 0.598831i | \(-0.795632\pi\) | ||
0.800875 | − | 0.598831i | \(-0.204368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −33.9983 | −1.79938 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.1369 | + | 21.1369i | −1.11556 | + | 1.11556i | −0.123179 | + | 0.992384i | \(0.539309\pi\) |
−0.992384 | + | 0.123179i | \(0.960691\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.6509i | 0.665838i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.86461 | − | 6.86461i | −0.360299 | − | 0.360299i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.5695 | − | 25.5695i | −1.33472 | − | 1.33472i | −0.901093 | − | 0.433626i | \(-0.857234\pi\) |
−0.433626 | − | 0.901093i | \(-0.642766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −22.2758 | − | 22.2758i | −1.15963 | − | 1.15963i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.90660 | − | 7.90660i | −0.410490 | − | 0.410490i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.17843 | + | 6.17843i | −0.319907 | + | 0.319907i | −0.848731 | − | 0.528824i | \(-0.822633\pi\) |
0.528824 | + | 0.848731i | \(0.322633\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.4574 | + | 1.10011i | −1.51714 | + | 0.0566587i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.75594 | − | 8.75594i | −0.449763 | − | 0.449763i | 0.445513 | − | 0.895275i | \(-0.353021\pi\) |
−0.895275 | + | 0.445513i | \(0.853021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 44.0158i | − | 2.25500i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 11.9586i | − | 0.611056i | −0.952183 | − | 0.305528i | \(-0.901167\pi\) | ||
0.952183 | − | 0.305528i | \(-0.0988329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.10188 | + | 6.10188i | −0.310176 | + | 0.310176i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.1640 | 0.566036 | 0.283018 | − | 0.959115i | \(-0.408664\pi\) | ||||
0.283018 | + | 0.959115i | \(0.408664\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.5347 | 1.03848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.4279 | − | 21.4279i | 1.08089 | − | 1.08089i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 22.0040i | − | 1.10435i | −0.833728 | − | 0.552175i | \(-0.813798\pi\) | ||
0.833728 | − | 0.552175i | \(-0.186202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 48.2924i | − | 2.41765i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.2767 | + | 17.2767i | 0.862755 | + | 0.862755i | 0.991657 | − | 0.128902i | \(-0.0411453\pi\) |
−0.128902 | + | 0.991657i | \(0.541145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.4667 | − | 12.4971i | −0.670825 | − | 0.622524i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.29865 | − | 8.29865i | 0.411349 | − | 0.411349i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.7400 | − | 17.7400i | −0.877184 | − | 0.877184i | 0.116058 | − | 0.993242i | \(-0.462974\pi\) |
−0.993242 | + | 0.116058i | \(0.962974\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.8342 | + | 15.8342i | 0.781042 | + | 0.781042i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.3120 | + | 11.3120i | 0.556629 | + | 0.556629i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.84356 | − | 4.84356i | −0.237190 | − | 0.237190i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 12.4338i | − | 0.607429i | −0.952763 | − | 0.303714i | \(-0.901773\pi\) | ||
0.952763 | − | 0.303714i | \(-0.0982269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6938 | − | 15.6938i | 0.764871 | − | 0.764871i | −0.212327 | − | 0.977199i | \(-0.568104\pi\) |
0.977199 | + | 0.212327i | \(0.0681043\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −57.8727 | −2.81387 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 31.2411i | − | 1.51186i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.53152 | − | 41.0091i | −0.0739424 | − | 1.97994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.08409 | − | 6.08409i | 0.293060 | − | 0.293060i | −0.545228 | − | 0.838288i | \(-0.683557\pi\) |
0.838288 | + | 0.545228i | \(0.183557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3684 | − | 11.3684i | −0.546331 | − | 0.546331i | 0.379047 | − | 0.925377i | \(-0.376252\pi\) |
−0.925377 | + | 0.379047i | \(0.876252\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 29.1682i | 1.39530i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.91249 | 0.0912781 | 0.0456391 | − | 0.998958i | \(-0.485468\pi\) | ||||
0.0456391 | + | 0.998958i | \(0.485468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.63748i | 0.316071i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.5333 | − | 10.5333i | 0.500452 | − | 0.500452i | −0.411127 | − | 0.911578i | \(-0.634865\pi\) |
0.911578 | + | 0.411127i | \(0.134865\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.16818 | 0.197148 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.4842 | − | 12.4842i | 0.589167 | − | 0.589167i | −0.348239 | − | 0.937406i | \(-0.613220\pi\) |
0.937406 | + | 0.348239i | \(0.113220\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4314 | 0.914991 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.2178 | 0.761980 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.2061 | −1.08553 | −0.542767 | − | 0.839883i | \(-0.682623\pi\) | ||||
−0.542767 | + | 0.839883i | \(0.682623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 37.2160 | 1.73709 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.5154 | + | 18.5154i | −0.862349 | + | 0.862349i | −0.991611 | − | 0.129262i | \(-0.958739\pi\) |
0.129262 | + | 0.991611i | \(0.458739\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.0654 | −0.700148 | −0.350074 | − | 0.936722i | \(-0.613844\pi\) | ||||
−0.350074 | + | 0.936722i | \(0.613844\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.0569 | + | 17.0569i | −0.789300 | + | 0.789300i | −0.981379 | − | 0.192080i | \(-0.938477\pi\) |
0.192080 | + | 0.981379i | \(0.438477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.63348i | − | 0.0754269i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −47.2581 | −2.17754 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.32273i | − | 0.244740i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.9965 | + | 16.9965i | 0.778215 | + | 0.778215i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.91155 | + | 6.91155i | −0.315797 | + | 0.315797i | −0.847150 | − | 0.531353i | \(-0.821684\pi\) |
0.531353 | + | 0.847150i | \(0.321684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.2151 | − | 0.418838i | 0.511365 | − | 0.0190974i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 44.5044i | − | 2.02502i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.6737 | −0.846188 | −0.423094 | − | 0.906086i | \(-0.639056\pi\) | ||||
−0.423094 | + | 0.906086i | \(0.639056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −45.8451 | + | 45.8451i | −2.07319 | + | 2.07319i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 28.0706i | − | 1.26681i | −0.773821 | − | 0.633405i | \(-0.781657\pi\) | ||
0.773821 | − | 0.633405i | \(-0.218343\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.8972 | + | 22.8972i | 1.03124 | + | 1.03124i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4767 | − | 13.4767i | −0.604512 | − | 0.604512i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8276 | + | 20.8276i | 0.932370 | + | 0.932370i | 0.997854 | − | 0.0654834i | \(-0.0208589\pi\) |
−0.0654834 | + | 0.997854i | \(0.520859\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.80064 | − | 5.80064i | −0.259153 | − | 0.259153i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.528262 | + | 0.528262i | −0.0235540 | + | 0.0235540i | −0.718786 | − | 0.695232i | \(-0.755302\pi\) |
0.695232 | + | 0.718786i | \(0.255302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.6022 | − | 29.7417i | 1.13703 | − | 1.32088i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.3305 | + | 16.3305i | 0.723837 | + | 0.723837i | 0.969384 | − | 0.245548i | \(-0.0789678\pi\) |
−0.245548 | + | 0.969384i | \(0.578968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.3813i | 1.12280i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 52.8629i | 2.33395i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.2415 | − | 25.2415i | 1.11012 | − | 1.11012i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.1430 | −0.796391 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.5785 | −1.20824 | −0.604118 | − | 0.796895i | \(-0.706474\pi\) | ||||
−0.604118 | + | 0.796895i | \(0.706474\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.83909 | + | 2.83909i | −0.124145 | + | 0.124145i | −0.766449 | − | 0.642305i | \(-0.777978\pi\) |
0.642305 | + | 0.766449i | \(0.277978\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.1816i | 0.879125i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.88025i | 0.168707i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.3170 | − | 24.3170i | −1.05527 | − | 1.05527i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.6206 | + | 12.6398i | 0.589972 | + | 0.547492i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35.8838 | + | 35.8838i | −1.54850 | + | 1.54850i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.89497 | − | 2.89497i | −0.124695 | − | 0.124695i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.13196 | + | 9.13196i | 0.392614 | + | 0.392614i | 0.875618 | − | 0.483004i | \(-0.160454\pi\) |
−0.483004 | + | 0.875618i | \(0.660454\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.2151 | + | 46.2151i | 1.98328 | + | 1.98328i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.28428 | + | 4.28428i | 0.183183 | + | 0.183183i | 0.792741 | − | 0.609559i | \(-0.208653\pi\) |
−0.609559 | + | 0.792741i | \(0.708653\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 67.1576i | 2.86622i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.5240 | + | 32.5240i | −1.38557 | + | 1.38557i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.6935 | 0.667355 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2159i | 0.432863i | 0.976298 | + | 0.216432i | \(0.0694418\pi\) | ||||
−0.976298 | + | 0.216432i | \(0.930558\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46235 | − | 3.73099i | 0.146442 | − | 0.157804i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.8763 | + | 31.8763i | −1.34582 | + | 1.34582i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.19088 | + | 2.19088i | 0.0923346 | + | 0.0923346i | 0.751765 | − | 0.659431i | \(-0.229203\pi\) |
−0.659431 | + | 0.751765i | \(0.729203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 28.5119i | − | 1.19739i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1338 | −0.592521 | −0.296261 | − | 0.955107i | \(-0.595740\pi\) | ||||
−0.296261 | + | 0.955107i | \(0.595740\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 31.7222i | − | 1.32753i | −0.747941 | − | 0.663766i | \(-0.768957\pi\) | ||
0.747941 | − | 0.663766i | \(-0.231043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.48458 | − | 4.48458i | 0.187346 | − | 0.187346i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.9259 | 1.03768 | 0.518839 | − | 0.854872i | \(-0.326364\pi\) | ||||
0.518839 | + | 0.854872i | \(0.326364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5114 | + | 11.5114i | −0.478398 | + | 0.478398i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.84172 | −0.325329 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.8262 | −0.614038 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.8873 | 1.19231 | 0.596154 | − | 0.802870i | \(-0.296695\pi\) | ||||
0.596154 | + | 0.802870i | \(0.296695\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.6667 | −1.18119 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.5020 | + | 18.5020i | −0.761072 | + | 0.761072i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.65210 | 0.149974 | 0.0749868 | − | 0.997185i | \(-0.476109\pi\) | ||||
0.0749868 | + | 0.997185i | \(0.476109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.5803 | + | 24.5803i | −1.00601 | + | 1.00601i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 20.4810i | − | 0.836833i | −0.908255 | − | 0.418416i | \(-0.862585\pi\) | ||
0.908255 | − | 0.418416i | \(-0.137415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6154 | 1.41199 | 0.705995 | − | 0.708217i | \(-0.250500\pi\) | ||||
0.705995 | + | 0.708217i | \(0.250500\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.51141i | 0.142996i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.3800 | + | 12.3800i | 0.502490 | + | 0.502490i | 0.912211 | − | 0.409721i | \(-0.134374\pi\) |
−0.409721 | + | 0.912211i | \(0.634374\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 49.6246 | − | 49.6246i | 2.01089 | − | 2.01089i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.1123 | − | 1.27395i | 1.38004 | − | 0.0515387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.906637i | 0.0366187i | 0.999832 | + | 0.0183094i | \(0.00582838\pi\) | ||||
−0.999832 | + | 0.0183094i | \(0.994172\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.1880 | 1.53739 | 0.768695 | − | 0.639616i | \(-0.220906\pi\) | ||||
0.768695 | + | 0.639616i | \(0.220906\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.38038 | + | 2.38038i | −0.0956757 | + | 0.0956757i | −0.753325 | − | 0.657649i | \(-0.771551\pi\) |
0.657649 | + | 0.753325i | \(0.271551\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.7163i | 1.95492i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.56153 | − | 9.56153i | −0.383074 | − | 0.383074i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −45.2782 | − | 45.2782i | −1.80824 | − | 1.80824i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.71749 | − | 8.71749i | −0.347589 | − | 0.347589i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.726798 | − | 0.726798i | −0.0289334 | − | 0.0289334i | 0.692492 | − | 0.721425i | \(-0.256513\pi\) |
−0.721425 | + | 0.692492i | \(0.756513\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −54.4070 | + | 54.4070i | −2.16248 | + | 2.16248i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.146111 | − | 3.91238i | −0.00578913 | − | 0.155014i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.9702 | + | 28.9702i | 1.14604 | + | 1.14604i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 27.5067i | − | 1.08645i | −0.839587 | − | 0.543225i | \(-0.817203\pi\) | ||
0.839587 | − | 0.543225i | \(-0.182797\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.23997i | 0.246081i | 0.992402 | + | 0.123040i | \(0.0392644\pi\) | ||||
−0.992402 | + | 0.123040i | \(0.960736\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.0569 | − | 17.0569i | 0.670576 | − | 0.670576i | −0.287273 | − | 0.957849i | \(-0.592749\pi\) |
0.957849 | + | 0.287273i | \(0.0927485\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.2120 | 0.832643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 43.7391 | 1.71427 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.3558 | + | 12.3558i | −0.483520 | + | 0.483520i | −0.906254 | − | 0.422734i | \(-0.861070\pi\) |
0.422734 | + | 0.906254i | \(0.361070\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 54.5611i | − | 2.12863i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.97906i | 0.193957i | 0.995286 | + | 0.0969784i | \(0.0309178\pi\) | ||||
−0.995286 | + | 0.0969784i | \(0.969082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.06622 | − | 5.06622i | −0.197053 | − | 0.197053i | 0.601682 | − | 0.798735i | \(-0.294497\pi\) |
−0.798735 | + | 0.601682i | \(0.794497\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −43.0788 | + | 1.60882i | −1.67304 | + | 0.0624812i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −29.9728 | + | 29.9728i | −1.16055 | + | 1.16055i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.21865 | − | 3.21865i | −0.124440 | − | 0.124440i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.2911 | − | 29.2911i | −1.13077 | − | 1.13077i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.39838 | − | 2.39838i | −0.0924506 | − | 0.0924506i | 0.659369 | − | 0.751820i | \(-0.270824\pi\) |
−0.751820 | + | 0.659369i | \(0.770824\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.5114 | + | 16.5114i | 0.634585 | + | 0.634585i | 0.949215 | − | 0.314630i | \(-0.101880\pi\) |
−0.314630 | + | 0.949215i | \(0.601880\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 25.9339i | − | 0.995253i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2245 | − | 27.2245i | 1.04325 | − | 1.04325i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.6982 | −0.983314 | −0.491657 | − | 0.870789i | \(-0.663609\pi\) | ||||
−0.491657 | + | 0.870789i | \(0.663609\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 72.7718i | 2.77642i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.3925 | − | 9.64420i | −0.395922 | − | 0.367415i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.68536 | + | 3.68536i | −0.140198 | + | 0.140198i | −0.773722 | − | 0.633525i | \(-0.781607\pi\) |
0.633525 | + | 0.773722i | \(0.281607\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 46.3412 | + | 46.3412i | 1.76036 | + | 1.76036i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 20.4122i | − | 0.773166i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −85.2779 | −3.22551 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.4122i | 0.922034i | 0.887391 | + | 0.461017i | \(0.152515\pi\) | ||||
−0.887391 | + | 0.461017i | \(0.847485\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3826 | − | 12.3826i | 0.467020 | − | 0.467020i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.8323 | 1.08435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.9370 | − | 22.9370i | 0.861417 | − | 0.861417i | −0.130086 | − | 0.991503i | \(-0.541525\pi\) |
0.991503 | + | 0.130086i | \(0.0415253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.7356 | −1.26518 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.4180 | −0.989364 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.39118 | −0.313375 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.4886 | 1.17433 | 0.587164 | − | 0.809468i | \(-0.300244\pi\) | ||||
0.587164 | + | 0.809468i | \(0.300244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.3961 | − | 24.3961i | 0.908557 | − | 0.908557i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 57.0998 | 2.12356 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.1780 | − | 13.1780i | 0.488744 | − | 0.488744i | −0.419166 | − | 0.907910i | \(-0.637677\pi\) |
0.907910 | + | 0.419166i | \(0.137677\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 23.8038i | − | 0.881623i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.59138 | −0.206804 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 37.8822i | − | 1.39921i | −0.714530 | − | 0.699605i | \(-0.753359\pi\) | ||
0.714530 | − | 0.699605i | \(-0.246641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.53152 | − | 1.53152i | −0.0564142 | − | 0.0564142i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.49036 | − | 8.49036i | 0.312323 | − | 0.312323i | −0.533486 | − | 0.845809i | \(-0.679118\pi\) |
0.845809 | + | 0.533486i | \(0.179118\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.28522 | − | 61.1907i | −0.0839496 | − | 2.24790i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4331i | 1.40997i | 0.709220 | + | 0.704987i | \(0.249047\pi\) | ||||
−0.709220 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.8570 | 0.616765 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3540 | + | 14.3540i | −0.524482 | + | 0.524482i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.4961i | 0.747915i | 0.927446 | + | 0.373957i | \(0.121999\pi\) | ||||
−0.927446 | + | 0.373957i | \(0.878001\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45.1647 | − | 45.1647i | −1.64589 | − | 1.64589i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.3305 | + | 10.3305i | 0.375468 | + | 0.375468i | 0.869464 | − | 0.493996i | \(-0.164464\pi\) |
−0.493996 | + | 0.869464i | \(0.664464\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −41.7266 | − | 41.7266i | −1.51458 | − | 1.51458i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0344 | + | 12.0344i | 0.436246 | + | 0.436246i | 0.890746 | − | 0.454501i | \(-0.150182\pi\) |
−0.454501 | + | 0.890746i | \(0.650182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.3152 | − | 16.3152i | 0.590651 | − | 0.590651i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8686 | + | 13.7980i | 0.536875 | + | 0.498218i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.7408 | − | 36.7408i | −1.32491 | − | 1.32491i | −0.909750 | − | 0.415156i | \(-0.863727\pi\) |
−0.415156 | − | 0.909750i | \(-0.636273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 63.8822i | 2.30066i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 21.0047i | − | 0.755486i | −0.925911 | − | 0.377743i | \(-0.876700\pi\) | ||
0.925911 | − | 0.377743i | \(-0.123300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.8932 | + | 18.8932i | −0.677790 | + | 0.677790i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 28.9941 | 1.03882 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25.2710 | −0.904269 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −54.3211 | + | 54.3211i | −1.94128 | + | 1.94128i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.9942i | 1.63952i | 0.572710 | + | 0.819758i | \(0.305892\pi\) | ||||
−0.572710 | + | 0.819758i | \(0.694108\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 11.9638i | − | 0.425922i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.4926 | − | 21.4926i | −0.764190 | − | 0.764190i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.47834 | − | 39.5852i | −0.0524975 | − | 1.40571i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.79478 | + | 1.79478i | −0.0635745 | + | 0.0635745i | −0.738179 | − | 0.674605i | \(-0.764314\pi\) |
0.674605 | + | 0.738179i | \(0.264314\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.5155 | − | 26.5155i | −0.938049 | − | 0.938049i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.5540 | + | 20.5540i | 0.726239 | + | 0.726239i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.7971 | + | 23.7971i | 0.839782 | + | 0.839782i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −47.1722 | − | 47.1722i | −1.66054 | − | 1.66054i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.9702i | 1.47559i | 0.675024 | + | 0.737796i | \(0.264133\pi\) | ||||
−0.675024 | + | 0.737796i | \(0.735867\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5522 | + | 21.5522i | −0.756801 | + | 0.756801i | −0.975739 | − | 0.218938i | \(-0.929741\pi\) |
0.218938 | + | 0.975739i | \(0.429741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −61.0351 | −2.14059 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 7.94219i | − | 0.277862i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.33887 | + | 62.6273i | 0.0817268 | + | 2.18838i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.98221 | − | 7.98221i | 0.278581 | − | 0.278581i | −0.553961 | − | 0.832542i | \(-0.686884\pi\) |
0.832542 | + | 0.553961i | \(0.186884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.95531 | + | 5.95531i | 0.207589 | + | 0.207589i | 0.803242 | − | 0.595653i | \(-0.203107\pi\) |
−0.595653 | + | 0.803242i | \(0.703107\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9.00821i | − | 0.313246i | −0.987658 | − | 0.156623i | \(-0.949939\pi\) | ||
0.987658 | − | 0.156623i | \(-0.0500608\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.2837 | 1.64223 | 0.821115 | − | 0.570763i | \(-0.193352\pi\) | ||||
0.821115 | + | 0.570763i | \(0.193352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.1588i | 0.595232i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.04108 | + | 3.04108i | −0.105367 | + | 0.105367i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −47.8786 | −1.65493 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.6334 | + | 20.6334i | −0.712344 | + | 0.712344i | −0.967025 | − | 0.254681i | \(-0.918030\pi\) |
0.254681 | + | 0.967025i | \(0.418030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.8424 | −1.30491 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.6568 | 1.50362 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.14473 | −0.314217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 87.4035 | 2.99968 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4113 | − | 11.4113i | 0.391175 | − | 0.391175i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.5422 | −0.840310 | −0.420155 | − | 0.907452i | \(-0.638024\pi\) | ||||
−0.420155 | + | 0.907452i | \(0.638024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.2312 | − | 27.2312i | 0.930202 | − | 0.930202i | −0.0675164 | − | 0.997718i | \(-0.521507\pi\) |
0.997718 | + | 0.0675164i | \(0.0215075\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.87746i | − | 0.337015i | −0.985700 | − | 0.168507i | \(-0.946105\pi\) | ||
0.985700 | − | 0.168507i | \(-0.0538947\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44.2388 | −1.50765 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.46931i | − | 0.254258i | −0.991886 | − | 0.127129i | \(-0.959424\pi\) | ||
0.991886 | − | 0.127129i | \(-0.0405763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.80240 | − | 2.80240i | −0.0951746 | − | 0.0951746i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.7140 | − | 14.7140i | 0.499137 | − | 0.499137i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0772967 | − | 2.06975i | −0.00261910 | − | 0.0701309i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 55.7490i | 1.88682i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.1762 | 0.546231 | 0.273116 | − | 0.961981i | \(-0.411946\pi\) | ||||
0.273116 | + | 0.961981i | \(0.411946\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 50.7534 | − | 50.7534i | 1.71187 | − | 1.71187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.0765i | 1.08068i | 0.841445 | + | 0.540342i | \(0.181705\pi\) | ||||
−0.841445 | + | 0.540342i | \(0.818295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.7870 | + | 29.7870i | 1.00241 | + | 1.00241i | 0.999997 | + | 0.00241408i | \(0.000768428\pi\) |
0.00241408 | + | 0.999997i | \(0.499232\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.13290 | + | 6.13290i | 0.205923 | + | 0.205923i | 0.802532 | − | 0.596609i | \(-0.203486\pi\) |
−0.596609 | + | 0.802532i | \(0.703486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.3179 | − | 29.3179i | −0.983292 | − | 0.983292i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.7323 | − | 26.7323i | −0.895566 | − | 0.895566i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 37.6635 | − | 37.6635i | 1.26036 | − | 1.26036i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.10597 | − | 56.3909i | −0.0703161 | − | 1.88284i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.4574 | − | 29.4574i | −0.982461 | − | 0.982461i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.5745i | 0.518861i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.1181i | 0.403264i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.2823 | + | 35.2823i | −1.17153 | + | 1.17153i | −0.189683 | + | 0.981845i | \(0.560746\pi\) |
−0.981845 | + | 0.189683i | \(0.939254\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −61.9796 | −2.05573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.1710 | 1.33092 | 0.665462 | − | 0.746431i | \(-0.268234\pi\) | ||||
0.665462 | + | 0.746431i | \(0.268234\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.35227 | + | 7.35227i | −0.243324 | + | 0.243324i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 28.5453i | − | 0.942649i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.33757i | − | 0.0441223i | −0.999757 | − | 0.0220611i | \(-0.992977\pi\) | ||
0.999757 | − | 0.0220611i | \(-0.00702285\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.13633 | + | 3.13633i | 0.103345 | + | 0.103345i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.7138 | − | 16.4384i | −0.583058 | − | 0.541076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −52.4431 | + | 52.4431i | −1.72246 | + | 1.72246i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.1253 | + | 23.1253i | 0.758716 | + | 0.758716i | 0.976089 | − | 0.217373i | \(-0.0697487\pi\) |
−0.217373 | + | 0.976089i | \(0.569749\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.31966 | − | 4.31966i | −0.141571 | − | 0.141571i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.51141 | − | 1.51141i | −0.0494813 | − | 0.0494813i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.50552 | + | 6.50552i | 0.212526 | + | 0.212526i | 0.805340 | − | 0.592814i | \(-0.201983\pi\) |
−0.592814 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 58.6474i | 1.91389i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.4625 | + | 28.4625i | −0.927850 | + | 0.927850i | −0.997567 | − | 0.0697170i | \(-0.977790\pi\) |
0.0697170 | + | 0.997567i | \(0.477790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.7198 | 0.870118 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.5474i | 0.407737i | 0.978998 | + | 0.203868i | \(0.0653515\pi\) | ||||
−0.978998 | + | 0.203868i | \(0.934649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.20105 | + | 32.1603i | 0.0389879 | + | 1.04397i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.3027 | + | 24.3027i | −0.788068 | + | 0.788068i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.341577 | − | 0.341577i | −0.0110648 | − | 0.0110648i | 0.701553 | − | 0.712618i | \(-0.252490\pi\) |
−0.712618 | + | 0.701553i | \(0.752490\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 93.0544i | − | 3.00802i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.0936 | 0.681147 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.03621i | 0.162458i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.8561 | − | 30.8561i | 0.994322 | − | 0.994322i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.5634 | −0.950695 | −0.475348 | − | 0.879798i | \(-0.657678\pi\) | ||||
−0.475348 | + | 0.879798i | \(0.657678\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −47.5634 | + | 47.5634i | −1.52796 | + | 1.52796i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.7660 | 1.53288 | 0.766442 | − | 0.642314i | \(-0.222025\pi\) | ||||
0.766442 | + | 0.642314i | \(0.222025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.45238 | −0.206854 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.4601 | 1.10248 | 0.551239 | − | 0.834347i | \(-0.314155\pi\) | ||||
0.551239 | + | 0.834347i | \(0.314155\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.9295 | −0.573028 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.0721 | + | 35.0721i | −1.11977 | + | 1.11977i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.0637 | 1.05457 | 0.527285 | − | 0.849689i | \(-0.323210\pi\) | ||||
0.527285 | + | 0.849689i | \(0.323210\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −57.4663 | + | 57.4663i | −1.82917 | + | 1.82917i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 7.31920i | − | 0.232737i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.5406 | 1.95490 | 0.977451 | − | 0.211162i | \(-0.0677246\pi\) | ||||
0.977451 | + | 0.211162i | \(0.0677246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 63.2068i | − | 2.00581i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.82494 | − | 9.82494i | −0.311159 | − | 0.311159i | 0.534199 | − | 0.845358i | \(-0.320613\pi\) |
−0.845358 | + | 0.534199i | \(0.820613\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.6813 | − | 20.6813i | 0.654327 | − | 0.654327i |
(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 | 1300.2.m.c.57.1 | 8 | ||
5.2 | odd | 4 | 260.2.r.c.213.4 | yes | 8 | ||
5.3 | odd | 4 | 1300.2.r.c.993.1 | 8 | |||
5.4 | even | 2 | 260.2.m.c.57.4 | ✓ | 8 | ||
13.8 | odd | 4 | 1300.2.r.c.957.1 | 8 | |||
15.2 | even | 4 | 2340.2.bp.g.1513.4 | 8 | |||
15.14 | odd | 2 | 2340.2.u.g.577.3 | 8 | |||
20.7 | even | 4 | 1040.2.cd.m.993.1 | 8 | |||
20.19 | odd | 2 | 1040.2.bg.m.577.1 | 8 | |||
65.8 | even | 4 | inner | 1300.2.m.c.593.1 | 8 | ||
65.34 | odd | 4 | 260.2.r.c.177.4 | yes | 8 | ||
65.47 | even | 4 | 260.2.m.c.73.4 | yes | 8 | ||
195.47 | odd | 4 | 2340.2.u.g.73.3 | 8 | |||
195.164 | even | 4 | 2340.2.bp.g.1477.4 | 8 | |||
260.47 | odd | 4 | 1040.2.bg.m.593.1 | 8 | |||
260.99 | even | 4 | 1040.2.cd.m.177.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.m.c.57.4 | ✓ | 8 | 5.4 | even | 2 | ||
260.2.m.c.73.4 | yes | 8 | 65.47 | even | 4 | ||
260.2.r.c.177.4 | yes | 8 | 65.34 | odd | 4 | ||
260.2.r.c.213.4 | yes | 8 | 5.2 | odd | 4 | ||
1040.2.bg.m.577.1 | 8 | 20.19 | odd | 2 | |||
1040.2.bg.m.593.1 | 8 | 260.47 | odd | 4 | |||
1040.2.cd.m.177.1 | 8 | 260.99 | even | 4 | |||
1040.2.cd.m.993.1 | 8 | 20.7 | even | 4 | |||
1300.2.m.c.57.1 | 8 | 1.1 | even | 1 | trivial | ||
1300.2.m.c.593.1 | 8 | 65.8 | even | 4 | inner | ||
1300.2.r.c.957.1 | 8 | 13.8 | odd | 4 | |||
1300.2.r.c.993.1 | 8 | 5.3 | odd | 4 | |||
2340.2.u.g.73.3 | 8 | 195.47 | odd | 4 | |||
2340.2.u.g.577.3 | 8 | 15.14 | odd | 2 | |||
2340.2.bp.g.1477.4 | 8 | 195.164 | even | 4 | |||
2340.2.bp.g.1513.4 | 8 | 15.2 | even | 4 |