Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
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: | yes |
Analytic conductor: | \(78.2533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 22x^{8} - 16x^{7} + 146x^{6} + 200x^{5} - 206x^{4} - 440x^{3} - 124x^{2} + 72x + 28 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{41}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 1960) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.92302\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.12212 | 0.647857 | 0.323929 | − | 0.946081i | \(-0.394996\pi\) | ||||
0.323929 | + | 0.946081i | \(0.394996\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.74084 | −0.580281 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.94252 | −1.49023 | −0.745113 | − | 0.666938i | \(-0.767604\pi\) | ||||
−0.745113 | + | 0.666938i | \(0.767604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.64101 | −1.28718 | −0.643592 | − | 0.765369i | \(-0.722557\pi\) | ||||
−0.643592 | + | 0.765369i | \(0.722557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.72505 | 1.38853 | 0.694264 | − | 0.719720i | \(-0.255730\pi\) | ||||
0.694264 | + | 0.719720i | \(0.255730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.53763 | −1.72925 | −0.864625 | − | 0.502417i | \(-0.832444\pi\) | ||||
−0.864625 | + | 0.502417i | \(0.832444\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.87122 | −1.43275 | −0.716374 | − | 0.697716i | \(-0.754200\pi\) | ||||
−0.716374 | + | 0.697716i | \(0.754200\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.31980 | −1.02380 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.11636 | 1.50717 | 0.753585 | − | 0.657350i | \(-0.228323\pi\) | ||||
0.753585 | + | 0.657350i | \(0.228323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.87614 | 0.696175 | 0.348087 | − | 0.937462i | \(-0.386831\pi\) | ||||
0.348087 | + | 0.937462i | \(0.386831\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.54611 | −0.965454 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.18786 | 0.852879 | 0.426439 | − | 0.904516i | \(-0.359768\pi\) | ||||
0.426439 | + | 0.904516i | \(0.359768\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.20778 | −0.833912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.45170 | 1.47611 | 0.738054 | − | 0.674742i | \(-0.235745\pi\) | ||||
0.738054 | + | 0.674742i | \(0.235745\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.706904 | −0.107802 | −0.0539009 | − | 0.998546i | \(-0.517166\pi\) | ||||
−0.0539009 | + | 0.998546i | \(0.517166\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.20616 | −0.321802 | −0.160901 | − | 0.986971i | \(-0.551440\pi\) | ||||
−0.160901 | + | 0.986971i | \(0.551440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.42420 | 0.899568 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.32166 | −0.181544 | −0.0907721 | − | 0.995872i | \(-0.528933\pi\) | ||||
−0.0907721 | + | 0.995872i | \(0.528933\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.45814 | −1.12031 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.94064 | 0.513027 | 0.256514 | − | 0.966541i | \(-0.417426\pi\) | ||||
0.256514 | + | 0.966541i | \(0.417426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.07542 | 0.777878 | 0.388939 | − | 0.921264i | \(-0.372842\pi\) | ||||
0.388939 | + | 0.921264i | \(0.372842\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.24674 | −1.00750 | −0.503750 | − | 0.863850i | \(-0.668047\pi\) | ||||
−0.503750 | + | 0.863850i | \(0.668047\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.71035 | −0.928217 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.50952 | −0.535182 | −0.267591 | − | 0.963533i | \(-0.586228\pi\) | ||||
−0.267591 | + | 0.963533i | \(0.586228\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.93470 | −0.343481 | −0.171741 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171741 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0249 | −1.24040 | −0.620201 | − | 0.784443i | \(-0.712949\pi\) | ||||
−0.620201 | + | 0.784443i | \(0.712949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.746943 | −0.0829937 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.27356 | 0.578848 | 0.289424 | − | 0.957201i | \(-0.406536\pi\) | ||||
0.289424 | + | 0.957201i | \(0.406536\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.10755 | 0.976432 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.49970 | 1.00697 | 0.503483 | − | 0.864005i | \(-0.332052\pi\) | ||||
0.503483 | + | 0.864005i | \(0.332052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.34950 | 0.451022 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.74808 | 0.177491 | 0.0887454 | − | 0.996054i | \(-0.471714\pi\) | ||||
0.0887454 | + | 0.996054i | \(0.471714\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.60415 | 0.864749 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.22585 | −0.519991 | −0.259996 | − | 0.965610i | \(-0.583721\pi\) | ||||
−0.259996 | + | 0.965610i | \(0.583721\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.15144 | 0.409053 | 0.204527 | − | 0.978861i | \(-0.434434\pi\) | ||||
0.204527 | + | 0.978861i | \(0.434434\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.7234 | 1.61671 | 0.808356 | − | 0.588694i | \(-0.200358\pi\) | ||||
0.808356 | + | 0.588694i | \(0.200358\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.3182 | 1.08409 | 0.542045 | − | 0.840349i | \(-0.317650\pi\) | ||||
0.542045 | + | 0.840349i | \(0.317650\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.82141 | 0.552544 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.614757 | −0.0578315 | −0.0289157 | − | 0.999582i | \(-0.509205\pi\) | ||||
−0.0289157 | + | 0.999582i | \(0.509205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.07926 | 0.746928 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.4285 | 1.22077 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.6060 | 0.956307 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.32166 | 0.472221 | 0.236111 | − | 0.971726i | \(-0.424127\pi\) | ||||
0.236111 | + | 0.971726i | \(0.424127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.793233 | −0.0698402 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.30041 | 0.637840 | 0.318920 | − | 0.947782i | \(-0.396680\pi\) | ||||
0.318920 | + | 0.947782i | \(0.396680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.9675 | 1.87681 | 0.938403 | − | 0.345542i | \(-0.112305\pi\) | ||||
0.938403 | + | 0.345542i | \(0.112305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.46849 | −0.803107 | −0.401553 | − | 0.915836i | \(-0.631530\pi\) | ||||
−0.401553 | + | 0.915836i | \(0.631530\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.47558 | −0.208482 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.9383 | 1.91820 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.7823 | −1.29293 | −0.646467 | − | 0.762942i | \(-0.723754\pi\) | ||||
−0.646467 | + | 0.762942i | \(0.723754\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2669 | 0.916884 | 0.458442 | − | 0.888724i | \(-0.348408\pi\) | ||||
0.458442 | + | 0.888724i | \(0.348408\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.96640 | −0.805736 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.66981 | 0.691926 | 0.345963 | − | 0.938248i | \(-0.387552\pi\) | ||||
0.345963 | + | 0.938248i | \(0.387552\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.48307 | −0.117615 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.1275 | 1.88981 | 0.944905 | − | 0.327344i | \(-0.106154\pi\) | ||||
0.944905 | + | 0.327344i | \(0.106154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9825 | 1.31414 | 0.657071 | − | 0.753829i | \(-0.271795\pi\) | ||||
0.657071 | + | 0.753829i | \(0.271795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.53896 | 0.656843 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.1218 | 1.00345 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.7691 | −1.50302 | −0.751509 | − | 0.659723i | \(-0.770673\pi\) | ||||
−0.751509 | + | 0.659723i | \(0.770673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.42188 | 0.332368 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.11496 | −0.158080 | −0.0790398 | − | 0.996871i | \(-0.525185\pi\) | ||||
−0.0790398 | + | 0.996871i | \(0.525185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.23706 | −0.686585 | −0.343293 | − | 0.939229i | \(-0.611542\pi\) | ||||
−0.343293 | + | 0.939229i | \(0.611542\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.81736 | 0.503954 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.2962 | −2.06922 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.75734 | −0.488944 | −0.244472 | − | 0.969656i | \(-0.578615\pi\) | ||||
−0.244472 | + | 0.969656i | \(0.578615\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.71570 | 0.195480 | 0.0977402 | − | 0.995212i | \(-0.468839\pi\) | ||||
0.0977402 | + | 0.995212i | \(0.468839\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.2189 | 1.22680 | 0.613398 | − | 0.789774i | \(-0.289802\pi\) | ||||
0.613398 | + | 0.789774i | \(0.289802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0215 | 0.993956 | 0.496978 | − | 0.867763i | \(-0.334443\pi\) | ||||
0.496978 | + | 0.867763i | \(0.334443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.25385 | −0.652716 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.9617 | 0.831396 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 37.2549 | 2.57697 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.78518 | −0.673639 | −0.336820 | − | 0.941569i | \(-0.609351\pi\) | ||||
−0.336820 | + | 0.941569i | \(0.609351\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.06023 | −0.346721 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.29310 | −0.222527 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.5700 | −1.78729 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.13608 | −0.477867 | −0.238934 | − | 0.971036i | \(-0.576798\pi\) | ||||
−0.238934 | + | 0.971036i | \(0.576798\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.773180 | 0.0513178 | 0.0256589 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256589 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.2336 | −0.940580 | −0.470290 | − | 0.882512i | \(-0.655851\pi\) | ||||
−0.470290 | + | 0.882512i | \(0.655851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −11.7275 | −0.768294 | −0.384147 | − | 0.923272i | \(-0.625504\pi\) | ||||
−0.384147 | + | 0.923272i | \(0.625504\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.3713 | −0.803604 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.3330 | −0.927124 | −0.463562 | − | 0.886065i | \(-0.653429\pi\) | ||||
−0.463562 | + | 0.886065i | \(0.653429\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.07456 | −0.133634 | −0.0668171 | − | 0.997765i | \(-0.521284\pi\) | ||||
−0.0668171 | + | 0.997765i | \(0.521284\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.1212 | 0.970029 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 34.9822 | 2.22586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.91758 | 0.375011 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.81192 | 0.177487 | 0.0887435 | − | 0.996055i | \(-0.471715\pi\) | ||||
0.0887435 | + | 0.996055i | \(0.471715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 33.9611 | 2.13512 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −21.5852 | −1.34644 | −0.673222 | − | 0.739440i | \(-0.735090\pi\) | ||||
−0.673222 | + | 0.739440i | \(0.735090\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.1293 | −0.874582 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 16.9163 | 1.04310 | 0.521551 | − | 0.853220i | \(-0.325354\pi\) | ||||
0.521551 | + | 0.853220i | \(0.325354\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.6598 | 0.652370 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3325 | 0.690953 | 0.345477 | − | 0.938427i | \(-0.387717\pi\) | ||||
0.345477 | + | 0.938427i | \(0.387717\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.11364 | 0.189140 | 0.0945701 | − | 0.995518i | \(-0.469852\pi\) | ||||
0.0945701 | + | 0.995518i | \(0.469852\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.6607 | 1.60189 | 0.800945 | − | 0.598739i | \(-0.204331\pi\) | ||||
0.800945 | + | 0.598739i | \(0.204331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.74774 | −0.403977 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.2579 | 1.68572 | 0.842861 | − | 0.538131i | \(-0.180869\pi\) | ||||
0.842861 | + | 0.538131i | \(0.180869\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.9531 | −0.829428 | −0.414714 | − | 0.909952i | \(-0.636118\pi\) | ||||
−0.414714 | + | 0.909952i | \(0.636118\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.7762 | 0.928011 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96156 | 0.114989 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.50405 | −0.379970 | −0.189985 | − | 0.981787i | \(-0.560844\pi\) | ||||
−0.189985 | + | 0.981787i | \(0.560844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 26.2932 | 1.52569 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31.8894 | 1.84421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.86404 | −0.336880 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.4580 | −1.62418 | −0.812091 | − | 0.583531i | \(-0.801671\pi\) | ||||
−0.812091 | + | 0.583531i | \(0.801671\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.65842 | 0.265008 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.10465 | 0.346163 | 0.173081 | − | 0.984908i | \(-0.444628\pi\) | ||||
0.173081 | + | 0.984908i | \(0.444628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.42029 | −0.249850 | −0.124925 | − | 0.992166i | \(-0.539869\pi\) | ||||
−0.124925 | + | 0.992166i | \(0.539869\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.67611 | −0.318802 | −0.159401 | − | 0.987214i | \(-0.550956\pi\) | ||||
−0.159401 | + | 0.987214i | \(0.550956\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −40.1153 | −2.24602 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.7657 | 1.04740 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −43.1533 | −2.40111 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.7004 | 0.702336 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.4091 | −1.34165 | −0.670823 | − | 0.741618i | \(-0.734059\pi\) | ||||
−0.670823 | + | 0.741618i | \(0.734059\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.03124 | −0.494909 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.84018 | 0.154714 | 0.0773572 | − | 0.997003i | \(-0.475352\pi\) | ||||
0.0773572 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.689832 | −0.0374666 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.1579 | −1.03746 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.47921 | 0.294139 | 0.147070 | − | 0.989126i | \(-0.453016\pi\) | ||||
0.147070 | + | 0.989126i | \(0.453016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.5197 | 0.616637 | 0.308318 | − | 0.951283i | \(-0.400234\pi\) | ||||
0.308318 | + | 0.951283i | \(0.400234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.6893 | 1.31781 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1927 | 0.595726 | 0.297863 | − | 0.954609i | \(-0.403726\pi\) | ||||
0.297863 | + | 0.954609i | \(0.403726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.2726 | 1.86161 | 0.930807 | − | 0.365511i | \(-0.119106\pi\) | ||||
0.930807 | + | 0.365511i | \(0.119106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.8159 | 1.99031 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.0684 | 0.790887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1383 | 1.62541 | 0.812704 | − | 0.582677i | \(-0.197995\pi\) | ||||
0.812704 | + | 0.582677i | \(0.197995\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.4539 | −0.856557 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.9531 | 0.567131 | 0.283565 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283565 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −37.6681 | −1.94001 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.34338 | 0.377204 | 0.188602 | − | 0.982054i | \(-0.439604\pi\) | ||||
0.188602 | + | 0.982054i | \(0.439604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.97155 | 0.305932 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.73491 | 0.190845 | 0.0954224 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954224 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.23061 | 0.0625553 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.29745 | 0.471399 | 0.235700 | − | 0.971826i | \(-0.424262\pi\) | ||||
0.235700 | + | 0.971826i | \(0.424262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.3381 | −1.98941 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.19195 | 0.413229 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2764 | −0.666325 | −0.333163 | − | 0.942869i | \(-0.608116\pi\) | ||||
−0.333163 | + | 0.942869i | \(0.608116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.01019 | −0.200260 | −0.100130 | − | 0.994974i | \(-0.531926\pi\) | ||||
−0.100130 | + | 0.994974i | \(0.531926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.9892 | −0.896105 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.6411 | −1.27098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.2260 | −1.44513 | −0.722567 | − | 0.691301i | \(-0.757038\pi\) | ||||
−0.722567 | + | 0.691301i | \(0.757038\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.6502 | 1.21590 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.6248 | −0.520299 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.8552 | −1.45852 | −0.729260 | − | 0.684237i | \(-0.760136\pi\) | ||||
−0.729260 | + | 0.684237i | \(0.760136\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.81281 | −0.478247 | −0.239124 | − | 0.970989i | \(-0.576860\pi\) | ||||
−0.239124 | + | 0.970989i | \(0.576860\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.84058 | 0.186735 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 25.7395 | 1.24272 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.0840 | −0.822908 | −0.411454 | − | 0.911430i | \(-0.634979\pi\) | ||||
−0.411454 | + | 0.911430i | \(0.634979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.70709 | 0.466493 | 0.233246 | − | 0.972418i | \(-0.425065\pi\) | ||||
0.233246 | + | 0.972418i | \(0.425065\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51.7927 | 2.47758 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.4222 | 0.497425 | 0.248713 | − | 0.968577i | \(-0.419993\pi\) | ||||
0.248713 | + | 0.968577i | \(0.419993\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.8412 | 1.65535 | 0.827677 | − | 0.561205i | \(-0.189662\pi\) | ||||
0.827677 | + | 0.561205i | \(0.189662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.7096 | −0.837637 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.64043 | −0.407767 | −0.203883 | − | 0.978995i | \(-0.565356\pi\) | ||||
−0.203883 | + | 0.978995i | \(0.565356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −46.7152 | −2.19973 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.6428 | 0.594010 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.6058 | 1.19779 | 0.598893 | − | 0.800829i | \(-0.295607\pi\) | ||||
0.598893 | + | 0.800829i | \(0.295607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −30.4561 | −1.42157 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.8105 | −1.10896 | −0.554482 | − | 0.832196i | \(-0.687083\pi\) | ||||
−0.554482 | + | 0.832196i | \(0.687083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.27660 | 0.152276 | 0.0761382 | − | 0.997097i | \(-0.475741\pi\) | ||||
0.0761382 | + | 0.997097i | \(0.475741\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −29.1321 | −1.34807 | −0.674036 | − | 0.738699i | \(-0.735441\pi\) | ||||
−0.674036 | + | 0.738699i | \(0.735441\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.72859 | 0.448270 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.49389 | 0.160649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.30080 | 0.105347 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.58771 | 0.346692 | 0.173346 | − | 0.984861i | \(-0.444542\pi\) | ||||
0.173346 | + | 0.984861i | \(0.444542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0769 | −1.09781 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.86118 | 0.220281 | 0.110140 | − | 0.993916i | \(-0.464870\pi\) | ||||
0.110140 | + | 0.993916i | \(0.464870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27.0740 | 1.22433 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.95002 | 0.268521 | 0.134260 | − | 0.990946i | \(-0.457134\pi\) | ||||
0.134260 | + | 0.990946i | \(0.457134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.4666 | 2.09275 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.08297 | −0.0932467 | −0.0466234 | − | 0.998913i | \(-0.514846\pi\) | ||||
−0.0466234 | + | 0.998913i | \(0.514846\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.0564 | 0.851377 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.22949 | 0.0994081 | 0.0497041 | − | 0.998764i | \(-0.484172\pi\) | ||||
0.0497041 | + | 0.998764i | \(0.484172\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.58176 | 0.425541 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.75149 | 0.0776334 | 0.0388167 | − | 0.999246i | \(-0.487641\pi\) | ||||
0.0388167 | + | 0.999246i | \(0.487641\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 40.0987 | 1.77040 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.9040 | 0.479557 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.1833 | −0.973741 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.7933 | −0.735727 | −0.367864 | − | 0.929880i | \(-0.619911\pi\) | ||||
−0.367864 | + | 0.929880i | \(0.619911\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −20.3763 | −0.890995 | −0.445497 | − | 0.895283i | \(-0.646973\pi\) | ||||
−0.445497 | + | 0.895283i | \(0.646973\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.1911 | 0.966658 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.2137 | 1.05277 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.86002 | −0.297700 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −43.8654 | −1.90002 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.37324 | −0.102413 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4407 | −0.534867 | −0.267434 | − | 0.963576i | \(-0.586176\pi\) | ||||
−0.267434 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.3651 | −0.444809 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.2004 | 1.41955 | 0.709773 | − | 0.704431i | \(-0.248798\pi\) | ||||
0.709773 | + | 0.704431i | \(0.248798\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.5763 | −0.451388 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −61.1781 | −2.60628 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.0813 | −1.10510 | −0.552551 | − | 0.833479i | \(-0.686345\pi\) | ||||
−0.552551 | + | 0.833479i | \(0.686345\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.28075 | 0.138761 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.7517 | −1.34056 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.4346 | 1.66197 | 0.830986 | − | 0.556294i | \(-0.187777\pi\) | ||||
0.830986 | + | 0.556294i | \(0.187777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.09101 | −0.255348 | −0.127674 | − | 0.991816i | \(-0.540751\pi\) | ||||
−0.127674 | + | 0.991816i | \(0.540751\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.9957 | −1.04604 | −0.523019 | − | 0.852321i | \(-0.675194\pi\) | ||||
−0.523019 | + | 0.852321i | \(0.675194\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.58256 | −0.316766 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.4463 | −0.976083 | −0.488042 | − | 0.872820i | \(-0.662289\pi\) | ||||
−0.488042 | + | 0.872820i | \(0.662289\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.04735 | 0.126643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.53234 | 0.270542 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.6033 | −1.13931 | −0.569656 | − | 0.821884i | \(-0.692923\pi\) | ||||
−0.569656 | + | 0.821884i | \(0.692923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29.2169 | −1.20386 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.3217 | 0.794789 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.40275 | −0.221864 | −0.110932 | − | 0.993828i | \(-0.535384\pi\) | ||||
−0.110932 | + | 0.993828i | \(0.535384\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.7338 | 0.643942 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.1269 | 1.72126 | 0.860628 | − | 0.509234i | \(-0.170071\pi\) | ||||
0.860628 | + | 0.509234i | \(0.170071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.70777 | −0.0696615 | −0.0348307 | − | 0.999393i | \(-0.511089\pi\) | ||||
−0.0348307 | + | 0.999393i | \(0.511089\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.3563 | 0.584632 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1419 | 0.533412 | 0.266706 | − | 0.963778i | \(-0.414065\pi\) | ||||
0.266706 | + | 0.963778i | \(0.414065\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2388 | 0.414218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.3179 | 1.54764 | 0.773822 | − | 0.633403i | \(-0.218342\pi\) | ||||
0.773822 | + | 0.633403i | \(0.218342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.55459 | −0.384653 | −0.192327 | − | 0.981331i | \(-0.561603\pi\) | ||||
−0.192327 | + | 0.981331i | \(0.561603\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.6354 | −1.23134 | −0.615670 | − | 0.788004i | \(-0.711115\pi\) | ||||
−0.615670 | + | 0.788004i | \(0.711115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 36.5535 | 1.46684 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 41.8045 | 1.66951 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7007 | 1.18425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.4786 | −1.25314 | −0.626571 | − | 0.779364i | \(-0.715542\pi\) | ||||
−0.626571 | + | 0.779364i | \(0.715542\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.9802 | −0.436422 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.85036 | 0.310556 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.4201 | 0.846041 | 0.423021 | − | 0.906120i | \(-0.360970\pi\) | ||||
0.423021 | + | 0.906120i | \(0.360970\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.83210 | 0.229996 | 0.114998 | − | 0.993366i | \(-0.463314\pi\) | ||||
0.114998 | + | 0.993366i | \(0.463314\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.1428 | 1.02778 | 0.513890 | − | 0.857856i | \(-0.328204\pi\) | ||||
0.513890 | + | 0.857856i | \(0.328204\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.4767 | −0.764526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.1019 | −1.45191 | −0.725955 | − | 0.687742i | \(-0.758602\pi\) | ||||
−0.725955 | + | 0.687742i | \(0.758602\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.10886 | 0.199315 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −49.4758 | −1.92730 | −0.963652 | − | 0.267159i | \(-0.913915\pi\) | ||||
−0.963652 | + | 0.267159i | \(0.913915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.1885 | 1.09640 | 0.548202 | − | 0.836346i | \(-0.315313\pi\) | ||||
0.548202 | + | 0.836346i | \(0.315313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −29.8148 | −1.15791 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −55.7693 | −2.15940 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00755 | −0.309590 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0279 | −1.15921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0752 | −0.542558 | −0.271279 | − | 0.962501i | \(-0.587447\pi\) | ||||
−0.271279 | + | 0.962501i | \(0.587447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.9999 | −1.07612 | −0.538062 | − | 0.842906i | \(-0.680843\pi\) | ||||
−0.538062 | + | 0.842906i | \(0.680843\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.867603 | 0.0332466 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1558 | −0.962562 | −0.481281 | − | 0.876566i | \(-0.659828\pi\) | ||||
−0.481281 | + | 0.876566i | \(0.659828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.9718 | −0.609362 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.13384 | 0.233681 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.6990 | 0.711344 | 0.355672 | − | 0.934611i | \(-0.384252\pi\) | ||||
0.355672 | + | 0.934611i | \(0.384252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.1114 | 2.04962 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.1597 | −0.497745 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1354 | 0.949351 | 0.474676 | − | 0.880161i | \(-0.342565\pi\) | ||||
0.474676 | + | 0.880161i | \(0.342565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.1042 | −1.47484 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.6659 | 0.663458 | 0.331729 | − | 0.943375i | \(-0.392368\pi\) | ||||
0.331729 | + | 0.943375i | \(0.392368\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.1927 | 0.719782 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.6338 | −0.997443 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0834 | −0.600644 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.06812 | 0.151715 | 0.0758576 | − | 0.997119i | \(-0.475831\pi\) | ||||
0.0758576 | + | 0.997119i | \(0.475831\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.32791 | −0.0865760 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.5626 | 1.31894 | 0.659471 | − | 0.751730i | \(-0.270780\pi\) | ||||
0.659471 | + | 0.751730i | \(0.270780\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.2087 | 0.711434 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.04706 | −0.149686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.90581 | 0.0703929 | 0.0351964 | − | 0.999380i | \(-0.488794\pi\) | ||||
0.0351964 | + | 0.999380i | \(0.488794\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 40.7597 | 1.50140 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.44004 | −0.200115 | −0.100058 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100058 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 39.2543 | 1.44204 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 42.7120 | 1.56695 | 0.783475 | − | 0.621423i | \(-0.213445\pi\) | ||||
0.783475 | + | 0.621423i | \(0.213445\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.18043 | −0.335895 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.9029 | −0.580306 | −0.290153 | − | 0.956980i | \(-0.593706\pi\) | ||||
−0.290153 | + | 0.956980i | \(0.593706\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.15532 | 0.114986 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.28840 | 0.0468277 | 0.0234138 | − | 0.999726i | \(-0.492546\pi\) | ||||
0.0234138 | + | 0.999726i | \(0.492546\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 38.1085 | 1.38325 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7660 | 0.680266 | 0.340133 | − | 0.940377i | \(-0.389528\pi\) | ||||
0.340133 | + | 0.940377i | \(0.389528\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18.2885 | −0.660360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.3190 | −1.41788 | −0.708939 | − | 0.705269i | \(-0.750826\pi\) | ||||
−0.708939 | + | 0.705269i | \(0.750826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.2212 | −0.872304 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.9516 | −0.429868 | −0.214934 | − | 0.976629i | \(-0.568954\pi\) | ||||
−0.214934 | + | 0.976629i | \(0.568954\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −71.2434 | −2.55256 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.2884 | 0.797541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.1774 | −1.54304 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 36.6318 | 1.30578 | 0.652892 | − | 0.757451i | \(-0.273555\pi\) | ||||
0.652892 | + | 0.757451i | \(0.273555\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.9821 | 0.675782 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.1961 | −1.00127 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.35871 | 0.0481281 | 0.0240641 | − | 0.999710i | \(-0.492339\pi\) | ||||
0.0240641 | + | 0.999710i | \(0.492339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.6304 | −0.446831 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.5375 | −0.584323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.5048 | 0.511864 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.7164 | 0.447639 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.6391 | 1.95617 | 0.978084 | − | 0.208211i | \(-0.0667642\pi\) | ||||
0.978084 | + | 0.208211i | \(0.0667642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1690 | 1.90213 | 0.951065 | − | 0.308990i | \(-0.0999909\pi\) | ||||
0.951065 | + | 0.308990i | \(0.0999909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.49389 | 0.122536 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.32838 | 0.186416 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.2489 | 1.61410 | 0.807048 | − | 0.590486i | \(-0.201064\pi\) | ||||
0.807048 | + | 0.590486i | \(0.201064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.1540 | 1.88769 | 0.943845 | − | 0.330388i | \(-0.107179\pi\) | ||||
0.943845 | + | 0.330388i | \(0.107179\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.0834 | 0.350632 | 0.175316 | − | 0.984512i | \(-0.443905\pi\) | ||||
0.175316 | + | 0.984512i | \(0.443905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.0572 | −1.35651 | −0.678256 | − | 0.734825i | \(-0.737264\pi\) | ||||
−0.678256 | + | 0.734825i | \(0.737264\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.9166 | 1.03780 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −20.6203 | −0.712741 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4278 | −1.53382 | −0.766909 | − | 0.641756i | \(-0.778206\pi\) | ||||
−0.766909 | + | 0.641756i | \(0.778206\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.8753 | 1.27156 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 31.7088 | 1.09211 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.6571 | −0.537351 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.6469 | −1.22196 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 49.0774 | 1.68038 | 0.840189 | − | 0.542293i | \(-0.182444\pi\) | ||||
0.840189 | + | 0.542293i | \(0.182444\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −33.7257 | −1.15205 | −0.576025 | − | 0.817432i | \(-0.695397\pi\) | ||||
−0.576025 | + | 0.817432i | \(0.695397\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.8680 | 0.950843 | 0.475421 | − | 0.879758i | \(-0.342296\pi\) | ||||
0.475421 | + | 0.879758i | \(0.342296\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.3459 | −0.794702 | −0.397351 | − | 0.917667i | \(-0.630070\pi\) | ||||
−0.397351 | + | 0.917667i | \(0.630070\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.7028 | 0.601219 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 54.4910 | 1.84848 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.2732 | 1.29684 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.04313 | −0.102994 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.4536 | 0.758206 | 0.379103 | − | 0.925355i | \(-0.376233\pi\) | ||||
0.379103 | + | 0.925355i | \(0.376233\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.29833 | −0.246167 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.44467 | 0.0823629 | 0.0411814 | − | 0.999152i | \(-0.486888\pi\) | ||||
0.0411814 | + | 0.999152i | \(0.486888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.2730 | 1.42260 | 0.711299 | − | 0.702889i | \(-0.248107\pi\) | ||||
0.711299 | + | 0.702889i | \(0.248107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.29839 | 0.0771725 | 0.0385863 | − | 0.999255i | \(-0.487715\pi\) | ||||
0.0385863 | + | 0.999255i | \(0.487715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.69178 | 0.123679 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.6292 | 0.556476 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.7838 | 1.19479 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.4601 | 1.04925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.56657 | −0.252079 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.1626 | 1.79844 | 0.899220 | − | 0.437497i | \(-0.144135\pi\) | ||||
0.899220 | + | 0.437497i | \(0.144135\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.09738 | 0.301741 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.71481 | 0.255603 | 0.127801 | − | 0.991800i | \(-0.459208\pi\) | ||||
0.127801 | + | 0.991800i | \(0.459208\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.0647 | −0.862615 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.86010 | 0.226294 | 0.113147 | − | 0.993578i | \(-0.463907\pi\) | ||||
0.113147 | + | 0.993578i | \(0.463907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.9333 | −1.05224 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.9287 | 0.688877 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.22700 | −0.237366 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.2013 | −0.629975 | −0.314988 | − | 0.949096i | \(-0.602000\pi\) | ||||
−0.314988 | + | 0.949096i | \(0.602000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.85016 | 0.224264 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.3868 | −0.666009 | −0.333004 | − | 0.942925i | \(-0.608062\pi\) | ||||
−0.333004 | + | 0.942925i | \(0.608062\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.96011 | −0.161867 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.2362 | −1.44206 | −0.721030 | − | 0.692904i | \(-0.756331\pi\) | ||||
−0.721030 | + | 0.692904i | \(0.756331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.9447 | −2.11489 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.4842 | 1.18558 | 0.592788 | − | 0.805359i | \(-0.298027\pi\) | ||||
0.592788 | + | 0.805359i | \(0.298027\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6200 | 0.442123 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.36929 | −0.206538 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.51474 | 0.0814606 | 0.0407303 | − | 0.999170i | \(-0.487032\pi\) | ||||
0.0407303 | + | 0.999170i | \(0.487032\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −45.0142 | −1.45510 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.9756 | −0.515341 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −29.1128 | −0.938147 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.49369 | 0.0801915 | 0.0400958 | − | 0.999196i | \(-0.487234\pi\) | ||||
0.0400958 | + | 0.999196i | \(0.487234\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48.4233 | −1.55558 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.3021 | −0.491069 | −0.245534 | − | 0.969388i | \(-0.578963\pi\) | ||||
−0.245534 | + | 0.969388i | \(0.578963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.5170 | −1.23227 | −0.616134 | − | 0.787641i | \(-0.711302\pi\) | ||||
−0.616134 | + | 0.787641i | \(0.711302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.9524 | −1.50061 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.7033 | −0.629077 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.9438 | −0.636107 | −0.318054 | − | 0.948073i | \(-0.603029\pi\) | ||||
−0.318054 | + | 0.948073i | \(0.603029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.85729 | 0.154453 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.09531 | −0.0347937 | −0.0173968 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173968 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.3900 | −0.869195 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.8274 | 1.38803 | 0.694014 | − | 0.719961i | \(-0.255841\pi\) | ||||
0.694014 | + | 0.719961i | \(0.255841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −27.5984 | −0.873175 |
(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 | 9800.2.a.dc.1.7 | 10 | ||
5.2 | odd | 4 | 1960.2.g.g.1569.7 | ✓ | 20 | ||
5.3 | odd | 4 | 1960.2.g.g.1569.13 | yes | 20 | ||
5.4 | even | 2 | 9800.2.a.db.1.4 | 10 | |||
7.6 | odd | 2 | inner | 9800.2.a.dc.1.4 | 10 | ||
35.13 | even | 4 | 1960.2.g.g.1569.8 | yes | 20 | ||
35.27 | even | 4 | 1960.2.g.g.1569.14 | yes | 20 | ||
35.34 | odd | 2 | 9800.2.a.db.1.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.g.g.1569.7 | ✓ | 20 | 5.2 | odd | 4 | ||
1960.2.g.g.1569.8 | yes | 20 | 35.13 | even | 4 | ||
1960.2.g.g.1569.13 | yes | 20 | 5.3 | odd | 4 | ||
1960.2.g.g.1569.14 | yes | 20 | 35.27 | even | 4 | ||
9800.2.a.db.1.4 | 10 | 5.4 | even | 2 | |||
9800.2.a.db.1.7 | 10 | 35.34 | odd | 2 | |||
9800.2.a.dc.1.4 | 10 | 7.6 | odd | 2 | inner | ||
9800.2.a.dc.1.7 | 10 | 1.1 | even | 1 | trivial |