Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.d (of order \(2\), degree \(1\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 38x^{14} + 1016x^{12} + 13512x^{10} + 130640x^{8} + 569472x^{6} + 1783808x^{4} + 352256x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.7 | ||
Root | \(-2.23772 - 3.87585i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.5.d.b.55.8 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.988828 | − | 3.87585i | −0.247207 | − | 0.968963i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −14.0444 | + | 7.66510i | −0.877777 | + | 0.479069i | ||||
\(5\) | 20.7568 | 0.830274 | 0.415137 | − | 0.909759i | \(-0.363734\pi\) | ||||
0.415137 | + | 0.909759i | \(0.363734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.38785i | − | 0.109956i | −0.998488 | − | 0.0549780i | \(-0.982491\pi\) | ||
0.998488 | − | 0.0549780i | \(-0.0175089\pi\) | |||||||
\(8\) | 43.5963 | + | 46.8547i | 0.681192 | + | 0.732104i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −20.5250 | − | 80.4504i | −0.205250 | − | 0.804504i | ||||
\(11\) | 115.619i | 0.955527i | 0.878488 | + | 0.477764i | \(0.158552\pi\) | ||||
−0.878488 | + | 0.477764i | \(0.841448\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 207.234 | 1.22624 | 0.613119 | − | 0.789991i | \(-0.289915\pi\) | ||||
0.613119 | + | 0.789991i | \(0.289915\pi\) | |||||||
\(14\) | −20.8825 | + | 5.32765i | −0.106543 | + | 0.0271819i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 138.493 | − | 215.304i | 0.540986 | − | 0.841031i | ||||
\(17\) | 383.437 | 1.32677 | 0.663385 | − | 0.748278i | \(-0.269119\pi\) | ||||
0.663385 | + | 0.748278i | \(0.269119\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 618.390i | − | 1.71299i | −0.516155 | − | 0.856495i | \(-0.672637\pi\) | ||
0.516155 | − | 0.856495i | \(-0.327363\pi\) | |||||||
\(20\) | −291.518 | + | 159.103i | −0.728796 | + | 0.397758i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 448.121 | − | 114.327i | 0.925870 | − | 0.236213i | ||||
\(23\) | − | 82.9899i | − | 0.156881i | −0.996919 | − | 0.0784403i | \(-0.975006\pi\) | ||
0.996919 | − | 0.0784403i | \(-0.0249940\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −194.153 | −0.310645 | ||||||||
\(26\) | −204.919 | − | 803.209i | −0.303135 | − | 1.18818i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 41.2984 | + | 75.6693i | 0.0526765 | + | 0.0965170i | ||||
\(29\) | 201.949 | 0.240130 | 0.120065 | − | 0.992766i | \(-0.461690\pi\) | ||||
0.120065 | + | 0.992766i | \(0.461690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 196.140i | − | 0.204100i | −0.994779 | − | 0.102050i | \(-0.967460\pi\) | ||
0.994779 | − | 0.102050i | \(-0.0325402\pi\) | |||||||
\(32\) | −971.432 | − | 323.878i | −0.948664 | − | 0.316287i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −379.153 | − | 1486.14i | −0.327987 | − | 1.28559i | ||||
\(35\) | − | 111.835i | − | 0.0912937i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 340.480 | 0.248707 | 0.124354 | − | 0.992238i | \(-0.460314\pi\) | ||||
0.124354 | + | 0.992238i | \(0.460314\pi\) | |||||||
\(38\) | −2396.79 | + | 611.481i | −1.65982 | + | 0.423463i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 904.922 | + | 972.556i | 0.565576 | + | 0.607847i | ||||
\(41\) | 2797.22 | 1.66402 | 0.832011 | − | 0.554758i | \(-0.187189\pi\) | ||||
0.832011 | + | 0.554758i | \(0.187189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 254.774i | − | 0.137790i | −0.997624 | − | 0.0688951i | \(-0.978053\pi\) | ||
0.997624 | − | 0.0688951i | \(-0.0219474\pi\) | |||||||
\(44\) | −886.230 | − | 1623.80i | −0.457763 | − | 0.838740i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −321.656 | + | 82.0627i | −0.152011 | + | 0.0387820i | ||||
\(47\) | 2257.41i | 1.02191i | 0.859607 | + | 0.510956i | \(0.170709\pi\) | ||||
−0.859607 | + | 0.510956i | \(0.829291\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2371.97 | 0.987910 | ||||||||
\(50\) | 191.984 | + | 752.509i | 0.0767937 | + | 0.301004i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2910.49 | + | 1588.47i | −1.07636 | + | 0.587452i | ||||
\(53\) | 4111.23 | 1.46359 | 0.731796 | − | 0.681524i | \(-0.238683\pi\) | ||||
0.731796 | + | 0.681524i | \(0.238683\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2399.88i | 0.793349i | ||||||||
\(56\) | 252.446 | − | 234.890i | 0.0804993 | − | 0.0749012i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −199.693 | − | 782.726i | −0.0593618 | − | 0.232677i | ||||
\(59\) | − | 1598.57i | − | 0.459226i | −0.973282 | − | 0.229613i | \(-0.926254\pi\) | ||
0.973282 | − | 0.229613i | \(-0.0737461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6081.09 | −1.63426 | −0.817131 | − | 0.576452i | \(-0.804437\pi\) | ||||
−0.817131 | + | 0.576452i | \(0.804437\pi\) | |||||||
\(62\) | −760.210 | + | 193.949i | −0.197765 | + | 0.0504549i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −294.723 | + | 4085.38i | −0.0719539 | + | 0.997408i | ||||
\(65\) | 4301.53 | 1.01811 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7383.67i | 1.64484i | 0.568884 | + | 0.822418i | \(0.307375\pi\) | ||||
−0.568884 | + | 0.822418i | \(0.692625\pi\) | |||||||
\(68\) | −5385.15 | + | 2939.08i | −1.16461 | + | 0.635614i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −433.455 | + | 110.585i | −0.0884602 | + | 0.0225684i | ||||
\(71\) | 9347.39i | 1.85427i | 0.374723 | + | 0.927137i | \(0.377738\pi\) | ||||
−0.374723 | + | 0.927137i | \(0.622262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5320.95 | −0.998490 | −0.499245 | − | 0.866461i | \(-0.666389\pi\) | ||||
−0.499245 | + | 0.866461i | \(0.666389\pi\) | |||||||
\(74\) | −336.676 | − | 1319.65i | −0.0614822 | − | 0.240988i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4740.02 | + | 8684.94i | 0.820640 | + | 1.50362i | ||||
\(77\) | 622.936 | 0.105066 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5971.42i | − | 0.956806i | −0.878141 | − | 0.478403i | \(-0.841216\pi\) | ||
0.878141 | − | 0.478403i | \(-0.158784\pi\) | |||||||
\(80\) | 2874.67 | − | 4469.03i | 0.449167 | − | 0.698286i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2765.97 | − | 10841.6i | −0.411358 | − | 1.61238i | ||||
\(83\) | − | 10091.0i | − | 1.46480i | −0.680876 | − | 0.732399i | \(-0.738401\pi\) | ||
0.680876 | − | 0.732399i | \(-0.261599\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7958.94 | 1.10158 | ||||||||
\(86\) | −987.466 | + | 251.928i | −0.133514 | + | 0.0340627i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5417.28 | + | 5040.55i | −0.699546 | + | 0.650898i | ||||
\(89\) | −13611.5 | −1.71841 | −0.859206 | − | 0.511631i | \(-0.829042\pi\) | ||||
−0.859206 | + | 0.511631i | \(0.829042\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 1116.55i | − | 0.134832i | ||||||
\(92\) | 636.126 | + | 1165.55i | 0.0751566 | + | 0.137706i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8749.37 | − | 2232.19i | 0.990195 | − | 0.252624i | ||||
\(95\) | − | 12835.8i | − | 1.42225i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2179.54 | 0.231645 | 0.115822 | − | 0.993270i | \(-0.463050\pi\) | ||||
0.115822 | + | 0.993270i | \(0.463050\pi\) | |||||||
\(98\) | −2345.47 | − | 9193.41i | −0.244218 | − | 0.957248i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2726.77 | − | 1488.20i | 0.272677 | − | 0.148820i | ||||
\(101\) | −3242.55 | −0.317866 | −0.158933 | − | 0.987289i | \(-0.550805\pi\) | ||||
−0.158933 | + | 0.987289i | \(0.550805\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 3261.34i | − | 0.307412i | −0.988117 | − | 0.153706i | \(-0.950879\pi\) | ||
0.988117 | − | 0.153706i | \(-0.0491209\pi\) | |||||||
\(104\) | 9034.65 | + | 9709.89i | 0.835304 | + | 0.897734i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4065.30 | − | 15934.5i | −0.361810 | − | 1.41817i | ||||
\(107\) | 15927.7i | 1.39119i | 0.718434 | + | 0.695595i | \(0.244859\pi\) | ||||
−0.718434 | + | 0.695595i | \(0.755141\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7377.06 | 0.620913 | 0.310456 | − | 0.950588i | \(-0.399518\pi\) | ||||
0.310456 | + | 0.950588i | \(0.399518\pi\) | |||||||
\(110\) | 9301.58 | − | 2373.07i | 0.768726 | − | 0.196122i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1160.03 | − | 746.177i | −0.0924765 | − | 0.0594847i | ||||
\(113\) | −7121.69 | −0.557733 | −0.278867 | − | 0.960330i | \(-0.589959\pi\) | ||||
−0.278867 | + | 0.960330i | \(0.589959\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1722.61i | − | 0.130254i | ||||||
\(116\) | −2836.27 | + | 1547.96i | −0.210781 | + | 0.115039i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6195.80 | + | 1580.71i | −0.444973 | + | 0.113524i | ||||
\(119\) | − | 2065.90i | − | 0.145886i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1273.29 | 0.0869676 | ||||||||
\(122\) | 6013.15 | + | 23569.4i | 0.404001 | + | 1.58354i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1503.43 | + | 2754.68i | 0.0977779 | + | 0.179154i | ||||
\(125\) | −17003.0 | −1.08819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16366.5i | − | 1.01472i | −0.861733 | − | 0.507362i | \(-0.830621\pi\) | ||
0.861733 | − | 0.507362i | \(-0.169379\pi\) | |||||||
\(128\) | 16125.8 | − | 2897.44i | 0.984239 | − | 0.176846i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4253.47 | − | 16672.1i | −0.251685 | − | 0.986514i | ||||
\(131\) | − | 17497.0i | − | 1.01958i | −0.860299 | − | 0.509790i | \(-0.829723\pi\) | ||
0.860299 | − | 0.509790i | \(-0.170277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3331.79 | −0.188354 | ||||||||
\(134\) | 28618.0 | − | 7301.18i | 1.59378 | − | 0.406615i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16716.4 | + | 17965.8i | 0.903786 | + | 0.971334i | ||||
\(137\) | −8028.61 | −0.427759 | −0.213880 | − | 0.976860i | \(-0.568610\pi\) | ||||
−0.213880 | + | 0.976860i | \(0.568610\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15001.1i | − | 0.776417i | −0.921572 | − | 0.388208i | \(-0.873094\pi\) | ||
0.921572 | − | 0.388208i | \(-0.126906\pi\) | |||||||
\(140\) | 857.224 | + | 1570.66i | 0.0437359 | + | 0.0801355i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36229.1 | − | 9242.96i | 1.79672 | − | 0.458389i | ||||
\(143\) | 23960.2i | 1.17170i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4191.83 | 0.199374 | ||||||||
\(146\) | 5261.50 | + | 20623.2i | 0.246834 | + | 0.967499i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4781.85 | + | 2609.81i | −0.218310 | + | 0.119148i | ||||
\(149\) | −1457.01 | −0.0656279 | −0.0328140 | − | 0.999461i | \(-0.510447\pi\) | ||||
−0.0328140 | + | 0.999461i | \(0.510447\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15413.9i | 0.676019i | 0.941143 | + | 0.338009i | \(0.109754\pi\) | ||||
−0.941143 | + | 0.338009i | \(0.890246\pi\) | |||||||
\(152\) | 28974.5 | − | 26959.5i | 1.25409 | − | 1.16688i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −615.977 | − | 2414.41i | −0.0259731 | − | 0.101805i | ||||
\(155\) | − | 4071.25i | − | 0.169459i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23328.9 | −0.946443 | −0.473222 | − | 0.880943i | \(-0.656909\pi\) | ||||
−0.473222 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(158\) | −23144.3 | + | 5904.71i | −0.927109 | + | 0.236529i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −20163.9 | − | 6722.68i | −0.787651 | − | 0.262605i | ||||
\(161\) | −447.137 | −0.0172500 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31514.9i | 1.18615i | 0.805146 | + | 0.593077i | \(0.202087\pi\) | ||||
−0.805146 | + | 0.593077i | \(0.797913\pi\) | |||||||
\(164\) | −39285.4 | + | 21441.0i | −1.46064 | + | 0.797181i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −39111.2 | + | 9978.26i | −1.41933 | + | 0.362108i | ||||
\(167\) | − | 45156.1i | − | 1.61914i | −0.587025 | − | 0.809569i | \(-0.699701\pi\) | ||
0.587025 | − | 0.809569i | \(-0.300299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14385.0 | 0.503659 | ||||||||
\(170\) | −7870.02 | − | 30847.6i | −0.272319 | − | 1.06739i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1952.87 | + | 3578.16i | 0.0660109 | + | 0.120949i | ||||
\(173\) | −39788.6 | −1.32943 | −0.664716 | − | 0.747096i | \(-0.731447\pi\) | ||||
−0.664716 | + | 0.747096i | \(0.731447\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1046.07i | 0.0341573i | ||||||||
\(176\) | 24893.2 | + | 16012.3i | 0.803628 | + | 0.516927i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 13459.5 | + | 52756.3i | 0.424803 | + | 1.66508i | ||||
\(179\) | 22082.3i | 0.689188i | 0.938752 | + | 0.344594i | \(0.111983\pi\) | ||||
−0.938752 | + | 0.344594i | \(0.888017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9867.01 | −0.301181 | −0.150591 | − | 0.988596i | \(-0.548118\pi\) | ||||
−0.150591 | + | 0.988596i | \(0.548118\pi\) | |||||||
\(182\) | −4327.57 | + | 1104.07i | −0.130647 | + | 0.0333315i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3888.46 | − | 3618.05i | 0.114853 | − | 0.106866i | ||||
\(185\) | 7067.30 | 0.206495 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 44332.5i | 1.26777i | ||||||||
\(188\) | −17303.2 | − | 31704.0i | −0.489566 | − | 0.897012i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −49749.7 | + | 12692.4i | −1.37811 | + | 0.351590i | ||||
\(191\) | 6985.96i | 0.191496i | 0.995406 | + | 0.0957479i | \(0.0305243\pi\) | ||||
−0.995406 | + | 0.0957479i | \(0.969476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −39647.8 | −1.06440 | −0.532199 | − | 0.846619i | \(-0.678634\pi\) | ||||
−0.532199 | + | 0.846619i | \(0.678634\pi\) | |||||||
\(194\) | −2155.19 | − | 8447.59i | −0.0572642 | − | 0.224455i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −33313.0 | + | 18181.4i | −0.867165 | + | 0.473277i | ||||
\(197\) | 25520.9 | 0.657602 | 0.328801 | − | 0.944399i | \(-0.393355\pi\) | ||||
0.328801 | + | 0.944399i | \(0.393355\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20635.7i | − | 0.521091i | −0.965462 | − | 0.260546i | \(-0.916098\pi\) | ||
0.965462 | − | 0.260546i | \(-0.0839024\pi\) | |||||||
\(200\) | −8464.36 | − | 9096.99i | −0.211609 | − | 0.227425i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3206.32 | + | 12567.6i | 0.0785786 | + | 0.308000i | ||||
\(203\) | − | 1088.07i | − | 0.0264038i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 58061.5 | 1.38159 | ||||||||
\(206\) | −12640.5 | + | 3224.90i | −0.297871 | + | 0.0759944i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 28700.4 | − | 44618.4i | 0.663378 | − | 1.03130i | ||||
\(209\) | 71497.5 | 1.63681 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 37403.1i | 0.840123i | 0.907496 | + | 0.420062i | \(0.137992\pi\) | ||||
−0.907496 | + | 0.420062i | \(0.862008\pi\) | |||||||
\(212\) | −57739.9 | + | 31513.0i | −1.28471 | + | 0.701161i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 61733.5 | − | 15749.8i | 1.34801 | − | 0.343912i | ||||
\(215\) | − | 5288.31i | − | 0.114404i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1056.77 | −0.0224420 | ||||||||
\(218\) | −7294.65 | − | 28592.4i | −0.153494 | − | 0.601641i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −18395.3 | − | 33705.0i | −0.380069 | − | 0.696384i | ||||
\(221\) | 79461.2 | 1.62694 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 63893.4i | − | 1.28483i | −0.766356 | − | 0.642416i | \(-0.777932\pi\) | ||
0.766356 | − | 0.642416i | \(-0.222068\pi\) | |||||||
\(224\) | −1745.00 | + | 5233.92i | −0.0347777 | + | 0.104311i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7042.13 | + | 27602.6i | 0.137876 | + | 0.540423i | ||||
\(227\) | 52128.0i | 1.01162i | 0.862644 | + | 0.505812i | \(0.168807\pi\) | ||||
−0.862644 | + | 0.505812i | \(0.831193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −30234.6 | −0.576545 | −0.288272 | − | 0.957548i | \(-0.593081\pi\) | ||||
−0.288272 | + | 0.957548i | \(0.593081\pi\) | |||||||
\(230\) | −6676.57 | + | 1703.36i | −0.126211 | + | 0.0321997i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8804.25 | + | 9462.28i | 0.163575 | + | 0.175800i | ||||
\(233\) | 5080.01 | 0.0935735 | 0.0467868 | − | 0.998905i | \(-0.485102\pi\) | ||||
0.0467868 | + | 0.998905i | \(0.485102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 46856.6i | 0.848468i | ||||||||
\(236\) | 12253.2 | + | 22451.0i | 0.220001 | + | 0.403098i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8007.11 | + | 2042.82i | −0.141359 | + | 0.0360641i | ||||
\(239\) | 40740.6i | 0.713234i | 0.934251 | + | 0.356617i | \(0.116070\pi\) | ||||
−0.934251 | + | 0.356617i | \(0.883930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −34834.0 | −0.599749 | −0.299875 | − | 0.953979i | \(-0.596945\pi\) | ||||
−0.299875 | + | 0.953979i | \(0.596945\pi\) | |||||||
\(242\) | −1259.07 | − | 4935.09i | −0.0214990 | − | 0.0842684i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 85405.5 | − | 46612.2i | 1.43452 | − | 0.782924i | ||||
\(245\) | 49234.6 | 0.820236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 128151.i | − | 2.10053i | ||||||
\(248\) | 9190.08 | − | 8550.98i | 0.149422 | − | 0.139031i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16813.1 | + | 65901.2i | 0.269009 | + | 1.05442i | ||||
\(251\) | 71105.6i | 1.12864i | 0.825555 | + | 0.564321i | \(0.190862\pi\) | ||||
−0.825555 | + | 0.564321i | \(0.809138\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9595.19 | 0.149904 | ||||||||
\(254\) | −63434.1 | + | 16183.6i | −0.983230 | + | 0.250847i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −27175.6 | − | 59636.0i | −0.414667 | − | 0.909973i | ||||
\(257\) | −4341.02 | −0.0657242 | −0.0328621 | − | 0.999460i | \(-0.510462\pi\) | ||||
−0.0328621 | + | 0.999460i | \(0.510462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1834.46i | − | 0.0273469i | ||||||
\(260\) | −60412.6 | + | 32971.6i | −0.893677 | + | 0.487746i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −67815.8 | + | 17301.5i | −0.987934 | + | 0.252047i | ||||
\(263\) | − | 112382.i | − | 1.62475i | −0.583135 | − | 0.812375i | \(-0.698174\pi\) | ||
0.583135 | − | 0.812375i | \(-0.301826\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 85336.1 | 1.21518 | ||||||||
\(266\) | 3294.57 | + | 12913.5i | 0.0465624 | + | 0.182508i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −56596.5 | − | 103699.i | −0.787989 | − | 1.44380i | ||||
\(269\) | 67178.9 | 0.928385 | 0.464193 | − | 0.885734i | \(-0.346345\pi\) | ||||
0.464193 | + | 0.885734i | \(0.346345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30451.7i | − | 0.414641i | −0.978273 | − | 0.207321i | \(-0.933526\pi\) | ||
0.978273 | − | 0.207321i | \(-0.0664744\pi\) | |||||||
\(272\) | 53103.1 | − | 82555.4i | 0.717765 | − | 1.11586i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7938.92 | + | 31117.7i | 0.105745 | + | 0.414483i | ||||
\(275\) | − | 22447.8i | − | 0.296830i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16480.0 | 0.214782 | 0.107391 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107391 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(278\) | −58142.2 | + | 14833.6i | −0.752319 | + | 0.191936i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5239.98 | − | 4875.58i | 0.0668365 | − | 0.0621885i | ||||
\(281\) | 22525.2 | 0.285270 | 0.142635 | − | 0.989775i | \(-0.454442\pi\) | ||||
0.142635 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 69282.8i | 0.865073i | 0.901616 | + | 0.432537i | \(0.142381\pi\) | ||||
−0.901616 | + | 0.432537i | \(0.857619\pi\) | |||||||
\(284\) | −71648.7 | − | 131279.i | −0.888324 | − | 1.62764i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 92866.0 | − | 23692.5i | 1.13534 | − | 0.289653i | ||||
\(287\) | − | 15071.0i | − | 0.182969i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 63502.6 | 0.760319 | ||||||||
\(290\) | −4145.00 | − | 16246.9i | −0.0492866 | − | 0.193186i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 74729.8 | − | 40785.6i | 0.876452 | − | 0.478345i | ||||
\(293\) | −92504.8 | −1.07753 | −0.538764 | − | 0.842456i | \(-0.681109\pi\) | ||||
−0.538764 | + | 0.842456i | \(0.681109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 33181.2i | − | 0.381283i | ||||||
\(296\) | 14843.7 | + | 15953.1i | 0.169417 | + | 0.182080i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1440.73 | + | 5647.13i | 0.0162237 | + | 0.0635910i | ||||
\(299\) | − | 17198.3i | − | 0.192373i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1372.68 | −0.0151509 | ||||||||
\(302\) | 59742.0 | − | 15241.7i | 0.655037 | − | 0.167117i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −133142. | − | 85642.3i | −1.44068 | − | 0.926705i | ||||
\(305\) | −126224. | −1.35689 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 79741.9i | − | 0.846077i | −0.906112 | − | 0.423038i | \(-0.860964\pi\) | ||
0.906112 | − | 0.423038i | \(-0.139036\pi\) | |||||||
\(308\) | −8748.79 | + | 4774.87i | −0.0922246 | + | 0.0503338i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15779.6 | + | 4025.76i | −0.164199 | + | 0.0418914i | ||||
\(311\) | 115631.i | 1.19551i | 0.801679 | + | 0.597755i | \(0.203940\pi\) | ||||
−0.801679 | + | 0.597755i | \(0.796060\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25857.6 | −0.263936 | −0.131968 | − | 0.991254i | \(-0.542130\pi\) | ||||
−0.131968 | + | 0.991254i | \(0.542130\pi\) | |||||||
\(314\) | 23068.2 | + | 90419.2i | 0.233967 | + | 0.917068i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45771.6 | + | 83865.3i | 0.458376 | + | 0.839862i | ||||
\(317\) | −78300.9 | −0.779198 | −0.389599 | − | 0.920985i | \(-0.627386\pi\) | ||||
−0.389599 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23349.1i | 0.229451i | ||||||||
\(320\) | −6117.53 | + | 84799.7i | −0.0597415 | + | 0.828122i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 442.141 | + | 1733.04i | 0.00426432 | + | 0.0167146i | ||||
\(323\) | − | 237113.i | − | 2.27274i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40235.2 | −0.380925 | ||||||||
\(326\) | 122147. | − | 31162.8i | 1.14934 | − | 0.293226i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 121949. | + | 131063.i | 1.13352 | + | 1.21824i | ||||
\(329\) | 12162.6 | 0.112366 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 159345.i | 1.45439i | 0.686429 | + | 0.727197i | \(0.259177\pi\) | ||||
−0.686429 | + | 0.727197i | \(0.740823\pi\) | |||||||
\(332\) | 77348.5 | + | 141722.i | 0.701739 | + | 1.28577i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −175018. | + | 44651.6i | −1.56888 | + | 0.400262i | ||||
\(335\) | 153262.i | 1.36566i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32887.8 | 0.289584 | 0.144792 | − | 0.989462i | \(-0.453749\pi\) | ||||
0.144792 | + | 0.989462i | \(0.453749\pi\) | |||||||
\(338\) | −14224.3 | − | 55754.2i | −0.124508 | − | 0.488027i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −111779. | + | 61006.0i | −0.966944 | + | 0.527734i | ||||
\(341\) | 22677.5 | 0.195023 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 25716.0i | − | 0.218583i | ||||||
\(344\) | 11937.4 | − | 11107.2i | 0.100877 | − | 0.0938616i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 39344.0 | + | 154215.i | 0.328645 | + | 1.28817i | ||||
\(347\) | 68679.4i | 0.570385i | 0.958470 | + | 0.285192i | \(0.0920575\pi\) | ||||
−0.958470 | + | 0.285192i | \(0.907943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −228554. | −1.87645 | −0.938226 | − | 0.346024i | \(-0.887532\pi\) | ||||
−0.938226 | + | 0.346024i | \(0.887532\pi\) | |||||||
\(350\) | 4054.40 | − | 1034.38i | 0.0330972 | − | 0.00844393i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 37446.4 | − | 112316.i | 0.302221 | − | 0.906474i | ||||
\(353\) | −46025.5 | −0.369359 | −0.184680 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184680 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 194022.i | 1.53956i | ||||||||
\(356\) | 191166. | − | 104334.i | 1.50838 | − | 0.823237i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 85587.6 | − | 21835.6i | 0.667797 | − | 0.170372i | ||||
\(359\) | − | 131445.i | − | 1.01990i | −0.860205 | − | 0.509948i | \(-0.829665\pi\) | ||
0.860205 | − | 0.509948i | \(-0.170335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −252085. | −1.93434 | ||||||||
\(362\) | 9756.77 | + | 38243.0i | 0.0744542 | + | 0.291834i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8558.44 | + | 15681.3i | 0.0645939 | + | 0.118353i | ||||
\(365\) | −110446. | −0.829020 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 120649.i | − | 0.895756i | −0.894095 | − | 0.447878i | \(-0.852180\pi\) | ||
0.894095 | − | 0.447878i | \(-0.147820\pi\) | |||||||
\(368\) | −17868.1 | − | 11493.5i | −0.131942 | − | 0.0848703i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6988.34 | − | 27391.8i | −0.0510470 | − | 0.200086i | ||||
\(371\) | − | 22150.7i | − | 0.160931i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 183241. | 1.31706 | 0.658530 | − | 0.752555i | \(-0.271179\pi\) | ||||
0.658530 | + | 0.752555i | \(0.271179\pi\) | |||||||
\(374\) | 171826. | − | 43837.2i | 1.22842 | − | 0.313400i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −105770. | + | 98414.6i | −0.748147 | + | 0.696119i | ||||
\(377\) | 41850.8 | 0.294457 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 210539.i | 1.46573i | 0.680374 | + | 0.732865i | \(0.261817\pi\) | ||||
−0.680374 | + | 0.732865i | \(0.738183\pi\) | |||||||
\(380\) | 98387.8 | + | 180272.i | 0.681356 | + | 1.24842i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 27076.5 | − | 6907.91i | 0.185552 | − | 0.0473391i | ||||
\(383\) | 115027.i | 0.784153i | 0.919933 | + | 0.392076i | \(0.128243\pi\) | ||||
−0.919933 | + | 0.392076i | \(0.871757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12930.2 | 0.0872336 | ||||||||
\(386\) | 39204.8 | + | 153669.i | 0.263127 | + | 1.03136i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −30610.5 | + | 16706.4i | −0.203332 | + | 0.110974i | ||||
\(389\) | −227952. | −1.50641 | −0.753206 | − | 0.657785i | \(-0.771493\pi\) | ||||
−0.753206 | + | 0.657785i | \(0.771493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 31821.4i | − | 0.208145i | ||||||
\(392\) | 103409. | + | 111138.i | 0.672957 | + | 0.723253i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25235.8 | − | 98915.2i | −0.162564 | − | 0.637192i | ||||
\(395\) | − | 123948.i | − | 0.794411i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 253211. | 1.60657 | 0.803287 | − | 0.595592i | \(-0.203082\pi\) | ||||
0.803287 | + | 0.595592i | \(0.203082\pi\) | |||||||
\(398\) | −79981.0 | + | 20405.2i | −0.504918 | + | 0.128817i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26888.8 | + | 41802.0i | −0.168055 | + | 0.261262i | ||||
\(401\) | −113054. | −0.703071 | −0.351535 | − | 0.936175i | \(-0.614340\pi\) | ||||
−0.351535 | + | 0.936175i | \(0.614340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 40646.9i | − | 0.250275i | ||||||
\(404\) | 45539.7 | − | 24854.4i | 0.279015 | − | 0.152279i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4217.21 | + | 1075.92i | −0.0255843 | + | 0.00652719i | ||||
\(407\) | 39365.9i | 0.237647i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 77602.4 | 0.463905 | 0.231952 | − | 0.972727i | \(-0.425489\pi\) | ||||
0.231952 | + | 0.972727i | \(0.425489\pi\) | |||||||
\(410\) | −57412.9 | − | 225038.i | −0.341540 | − | 1.33871i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24998.5 | + | 45803.6i | 0.147272 | + | 0.269839i | ||||
\(413\) | −8612.83 | −0.0504947 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 209457.i | − | 1.21618i | ||||||
\(416\) | −201314. | − | 67118.5i | −1.16329 | − | 0.387843i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −70698.7 | − | 277114.i | −0.404631 | − | 1.58601i | ||||
\(419\) | 46895.2i | 0.267116i | 0.991041 | + | 0.133558i | \(0.0426403\pi\) | ||||
−0.991041 | + | 0.133558i | \(0.957360\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40148.2 | 0.226518 | 0.113259 | − | 0.993566i | \(-0.463871\pi\) | ||||
0.113259 | + | 0.993566i | \(0.463871\pi\) | |||||||
\(422\) | 144969. | − | 36985.3i | 0.814048 | − | 0.207684i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 179234. | + | 192630.i | 0.996987 | + | 1.07150i | ||||
\(425\) | −74445.5 | −0.412155 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32764.0i | 0.179697i | ||||||||
\(428\) | −122088. | − | 223696.i | −0.666475 | − | 1.22115i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −20496.7 | + | 5229.22i | −0.110853 | + | 0.0282814i | ||||
\(431\) | − | 257425.i | − | 1.38579i | −0.721040 | − | 0.692893i | \(-0.756336\pi\) | ||
0.721040 | − | 0.692893i | \(-0.243664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29760.6 | −0.158732 | −0.0793661 | − | 0.996846i | \(-0.525290\pi\) | ||||
−0.0793661 | + | 0.996846i | \(0.525290\pi\) | |||||||
\(434\) | 1044.97 | + | 4095.89i | 0.00554783 | + | 0.0217455i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −103607. | + | 56545.9i | −0.545023 | + | 0.297460i | ||||
\(437\) | −51320.1 | −0.268735 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 249198.i | − | 1.29305i | −0.762892 | − | 0.646526i | \(-0.776221\pi\) | ||
0.762892 | − | 0.646526i | \(-0.223779\pi\) | |||||||
\(440\) | −112446. | + | 104626.i | −0.580815 | + | 0.540424i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −78573.4 | − | 307980.i | −0.402190 | − | 1.57644i | ||||
\(443\) | 53833.8i | 0.274314i | 0.990549 | + | 0.137157i | \(0.0437964\pi\) | ||||
−0.990549 | + | 0.137157i | \(0.956204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −282533. | −1.42675 | ||||||||
\(446\) | −247641. | + | 63179.6i | −1.24495 | + | 0.317619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22011.4 | + | 1587.92i | 0.109671 | + | 0.00791177i | ||||
\(449\) | 127961. | 0.634726 | 0.317363 | − | 0.948304i | \(-0.397203\pi\) | ||||
0.317363 | + | 0.948304i | \(0.397203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 323412.i | 1.59002i | ||||||||
\(452\) | 100020. | − | 54588.5i | 0.489566 | − | 0.267192i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 202040. | − | 51545.6i | 0.980227 | − | 0.250081i | ||||
\(455\) | − | 23176.0i | − | 0.111948i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 138874. | 0.664951 | 0.332475 | − | 0.943112i | \(-0.392116\pi\) | ||||
0.332475 | + | 0.943112i | \(0.392116\pi\) | |||||||
\(458\) | 29896.8 | + | 117185.i | 0.142526 | + | 0.558650i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 13204.0 | + | 24193.1i | 0.0624006 | + | 0.114334i | ||||
\(461\) | 242960. | 1.14323 | 0.571613 | − | 0.820523i | \(-0.306318\pi\) | ||||
0.571613 | + | 0.820523i | \(0.306318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 277264.i | − | 1.29340i | −0.762746 | − | 0.646699i | \(-0.776149\pi\) | ||
0.762746 | − | 0.646699i | \(-0.223851\pi\) | |||||||
\(464\) | 27968.5 | − | 43480.5i | 0.129907 | − | 0.201957i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5023.26 | − | 19689.4i | −0.0231320 | − | 0.0906692i | ||||
\(467\) | − | 123580.i | − | 0.566649i | −0.959024 | − | 0.283325i | \(-0.908563\pi\) | ||
0.959024 | − | 0.283325i | \(-0.0914374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39782.1 | 0.180860 | ||||||||
\(470\) | 181609. | − | 46333.1i | 0.822133 | − | 0.209747i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 74900.3 | − | 69691.6i | 0.336202 | − | 0.312821i | ||||
\(473\) | 29456.7 | 0.131662 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 120062.i | 0.532132i | ||||||||
\(476\) | 15835.3 | + | 29014.4i | 0.0698896 | + | 0.128056i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 157905. | − | 40285.5i | 0.691097 | − | 0.176316i | ||||
\(479\) | 56214.6i | 0.245007i | 0.992468 | + | 0.122503i | \(0.0390922\pi\) | ||||
−0.992468 | + | 0.122503i | \(0.960908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 70559.1 | 0.304974 | ||||||||
\(482\) | 34444.9 | + | 135011.i | 0.148262 | + | 0.581134i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17882.7 | + | 9759.92i | −0.0763382 | + | 0.0416635i | ||||
\(485\) | 45240.5 | 0.192328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 271980.i | − | 1.14678i | −0.819283 | − | 0.573389i | \(-0.805628\pi\) | ||
0.819283 | − | 0.573389i | \(-0.194372\pi\) | |||||||
\(488\) | −265113. | − | 284928.i | −1.11325 | − | 1.19645i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −48684.6 | − | 190826.i | −0.202768 | − | 0.794778i | ||||
\(491\) | 335208.i | 1.39044i | 0.718798 | + | 0.695219i | \(0.244693\pi\) | ||||
−0.718798 | + | 0.695219i | \(0.755307\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 77434.8 | 0.318597 | ||||||||
\(494\) | −496696. | + | 126720.i | −2.03534 | + | 0.519267i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −42229.7 | − | 27163.9i | −0.171654 | − | 0.110415i | ||||
\(497\) | 50362.3 | 0.203889 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 287692.i | − | 1.15538i | −0.816255 | − | 0.577692i | \(-0.803953\pi\) | ||
0.816255 | − | 0.577692i | \(-0.196047\pi\) | |||||||
\(500\) | 238798. | − | 130330.i | 0.955193 | − | 0.521320i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 275595. | − | 70311.2i | 1.09361 | − | 0.279008i | ||||
\(503\) | 338788.i | 1.33903i | 0.742797 | + | 0.669517i | \(0.233499\pi\) | ||||
−0.742797 | + | 0.669517i | \(0.766501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −67305.0 | −0.263915 | ||||||||
\(506\) | −9487.99 | − | 37189.5i | −0.0370572 | − | 0.145251i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 125451. | + | 229858.i | 0.486123 | + | 0.890702i | ||||
\(509\) | 444920. | 1.71730 | 0.858651 | − | 0.512561i | \(-0.171303\pi\) | ||||
0.858651 | + | 0.512561i | \(0.171303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28668.5i | 0.109790i | ||||||||
\(512\) | −204268. | + | 164298.i | −0.779221 | + | 0.626749i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4292.52 | + | 16825.1i | 0.0162475 | + | 0.0636843i | ||||
\(515\) | − | 67695.1i | − | 0.255236i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −260999. | −0.976466 | ||||||||
\(518\) | −7110.08 | + | 1813.96i | −0.0264981 | + | 0.00676034i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 187531. | + | 201547.i | 0.693531 | + | 0.745365i | ||||
\(521\) | 275911. | 1.01647 | 0.508233 | − | 0.861220i | \(-0.330299\pi\) | ||||
0.508233 | + | 0.861220i | \(0.330299\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 85712.3i | − | 0.313357i | −0.987650 | − | 0.156679i | \(-0.949921\pi\) | ||
0.987650 | − | 0.156679i | \(-0.0500787\pi\) | |||||||
\(524\) | 134116. | + | 245736.i | 0.488448 | + | 0.894964i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −435577. | + | 111127.i | −1.57432 | + | 0.401650i | ||||
\(527\) | − | 75207.3i | − | 0.270794i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 272954. | 0.975388 | ||||||||
\(530\) | −84382.7 | − | 330750.i | −0.300401 | − | 1.17747i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 46793.1 | − | 25538.5i | 0.165333 | − | 0.0902344i | ||||
\(533\) | 579680. | 2.04049 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 330610.i | 1.15507i | ||||||||
\(536\) | −345959. | + | 321901.i | −1.20419 | + | 1.12045i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −66428.4 | − | 260375.i | −0.229503 | − | 0.899571i | ||||
\(539\) | 274244.i | 0.943975i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 250046. | 0.854331 | 0.427165 | − | 0.904174i | \(-0.359512\pi\) | ||||
0.427165 | + | 0.904174i | \(0.359512\pi\) | |||||||
\(542\) | −118026. | + | 30111.5i | −0.401772 | + | 0.102502i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −372482. | − | 124187.i | −1.25866 | − | 0.419640i | ||||
\(545\) | 153125. | 0.515528 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 435437.i | 1.45529i | 0.685951 | + | 0.727647i | \(0.259386\pi\) | ||||
−0.685951 | + | 0.727647i | \(0.740614\pi\) | |||||||
\(548\) | 112757. | − | 61540.1i | 0.375477 | − | 0.204926i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −87004.2 | + | 22197.0i | −0.287617 | + | 0.0733784i | ||||
\(551\) | − | 124883.i | − | 0.411341i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −32173.1 | −0.105207 | ||||||||
\(554\) | −16295.9 | − | 63874.2i | −0.0530957 | − | 0.208116i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 114985. | + | 210683.i | 0.371957 | + | 0.681521i | ||||
\(557\) | −466836. | −1.50471 | −0.752356 | − | 0.658756i | \(-0.771083\pi\) | ||||
−0.752356 | + | 0.658756i | \(0.771083\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 52797.9i | − | 0.168964i | ||||||
\(560\) | −24078.5 | − | 15488.3i | −0.0767808 | − | 0.0493886i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −22273.6 | − | 87304.4i | −0.0705208 | − | 0.276416i | ||||
\(563\) | − | 75191.2i | − | 0.237219i | −0.992941 | − | 0.118610i | \(-0.962156\pi\) | ||
0.992941 | − | 0.118610i | \(-0.0378437\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −147824. | −0.463071 | ||||||||
\(566\) | 268530. | − | 68508.8i | 0.838224 | − | 0.213852i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −437969. | + | 407512.i | −1.35752 | + | 1.26312i | ||||
\(569\) | −66289.8 | −0.204749 | −0.102375 | − | 0.994746i | \(-0.532644\pi\) | ||||
−0.102375 | + | 0.994746i | \(0.532644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 377844.i | 1.15888i | 0.815014 | + | 0.579442i | \(0.196729\pi\) | ||||
−0.815014 | + | 0.579442i | \(0.803271\pi\) | |||||||
\(572\) | −183657. | − | 336507.i | −0.561327 | − | 1.02850i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −58413.0 | + | 14902.6i | −0.177291 | + | 0.0452313i | ||||
\(575\) | 16112.8i | 0.0487342i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −415556. | −1.24818 | −0.624091 | − | 0.781352i | \(-0.714530\pi\) | ||||
−0.624091 | + | 0.781352i | \(0.714530\pi\) | |||||||
\(578\) | −62793.2 | − | 246127.i | −0.187956 | − | 0.736721i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −58872.0 | + | 32130.8i | −0.175006 | + | 0.0955137i | ||||
\(581\) | −54368.7 | −0.161063 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 475335.i | 1.39850i | ||||||||
\(584\) | −231974. | − | 249311.i | −0.680163 | − | 0.730999i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 91471.3 | + | 358535.i | 0.266373 | + | 1.04409i | ||||
\(587\) | − | 342605.i | − | 0.994301i | −0.867664 | − | 0.497151i | \(-0.834380\pi\) | ||
0.867664 | − | 0.497151i | \(-0.165620\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −121291. | −0.349621 | ||||||||
\(590\) | −128605. | + | 32810.5i | −0.369449 | + | 0.0942559i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 47154.0 | − | 73306.8i | 0.134547 | − | 0.209171i | ||||
\(593\) | 125568. | 0.357082 | 0.178541 | − | 0.983932i | \(-0.442862\pi\) | ||||
0.178541 | + | 0.983932i | \(0.442862\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 42881.5i | − | 0.121126i | ||||||
\(596\) | 20462.8 | − | 11168.1i | 0.0576067 | − | 0.0314403i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −66658.2 | + | 17006.2i | −0.186402 | + | 0.0475559i | ||||
\(599\) | − | 317723.i | − | 0.885512i | −0.896642 | − | 0.442756i | \(-0.854001\pi\) | ||
0.896642 | − | 0.442756i | \(-0.145999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −168972. | −0.467806 | −0.233903 | − | 0.972260i | \(-0.575150\pi\) | ||||
−0.233903 | + | 0.972260i | \(0.575150\pi\) | |||||||
\(602\) | 1357.35 | + | 5320.32i | 0.00374540 | + | 0.0146806i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −118149. | − | 216480.i | −0.323859 | − | 0.593394i | ||||
\(605\) | 26429.5 | 0.0722070 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 644373.i | − | 1.74888i | −0.485135 | − | 0.874440i | \(-0.661229\pi\) | ||
0.485135 | − | 0.874440i | \(-0.338771\pi\) | |||||||
\(608\) | −200283. | + | 600723.i | −0.541796 | + | 1.62505i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 124814. | + | 489227.i | 0.335432 | + | 1.31477i | ||||
\(611\) | 467812.i | 1.25311i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 228892. | 0.609129 | 0.304564 | − | 0.952492i | \(-0.401489\pi\) | ||||
0.304564 | + | 0.952492i | \(0.401489\pi\) | |||||||
\(614\) | −309068. | + | 78851.0i | −0.819817 | + | 0.209156i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27157.7 | + | 29187.5i | 0.0715702 | + | 0.0769193i | ||||
\(617\) | −329605. | −0.865813 | −0.432906 | − | 0.901439i | \(-0.642512\pi\) | ||||
−0.432906 | + | 0.901439i | \(0.642512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 223932.i | − | 0.584434i | −0.956352 | − | 0.292217i | \(-0.905607\pi\) | ||
0.956352 | − | 0.292217i | \(-0.0943930\pi\) | |||||||
\(620\) | 31206.5 | + | 57178.4i | 0.0811824 | + | 0.148747i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 448168. | − | 114339.i | 1.15840 | − | 0.295538i | ||||
\(623\) | 73336.9i | 0.188950i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −231584. | −0.592854 | ||||||||
\(626\) | 25568.7 | + | 100220.i | 0.0652468 | + | 0.255744i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 327641. | − | 178818.i | 0.830766 | − | 0.453411i | ||||
\(629\) | 130553. | 0.329977 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 681430.i | 1.71144i | 0.517437 | + | 0.855721i | \(0.326886\pi\) | ||||
−0.517437 | + | 0.855721i | \(0.673114\pi\) | |||||||
\(632\) | 279789. | − | 260332.i | 0.700482 | − | 0.651769i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 77426.1 | + | 303482.i | 0.192623 | + | 0.755014i | ||||
\(635\) | − | 339717.i | − | 0.842499i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 491554. | 1.21141 | ||||||||
\(638\) | 90497.8 | − | 23088.3i | 0.222329 | − | 0.0567219i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 334720. | − | 60141.7i | 0.817188 | − | 0.146830i | ||||
\(641\) | −346761. | −0.843945 | −0.421973 | − | 0.906609i | \(-0.638662\pi\) | ||||
−0.421973 | + | 0.906609i | \(0.638662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 124932.i | − | 0.302169i | −0.988521 | − | 0.151085i | \(-0.951723\pi\) | ||
0.988521 | − | 0.151085i | \(-0.0482766\pi\) | |||||||
\(644\) | 6279.78 | − | 3427.35i | 0.0151416 | − | 0.00826392i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −919015. | + | 234464.i | −2.20221 | + | 0.561838i | ||||
\(647\) | 43450.9i | 0.103798i | 0.998652 | + | 0.0518992i | \(0.0165274\pi\) | ||||
−0.998652 | + | 0.0518992i | \(0.983473\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 184824. | 0.438803 | ||||||||
\(650\) | 39785.7 | + | 155946.i | 0.0941673 | + | 0.369102i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −241565. | − | 442609.i | −0.568249 | − | 1.04118i | ||||
\(653\) | −344790. | −0.808589 | −0.404294 | − | 0.914629i | \(-0.632483\pi\) | ||||
−0.404294 | + | 0.914629i | \(0.632483\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 363183.i | − | 0.846530i | ||||||
\(656\) | 387394. | − | 602253.i | 0.900214 | − | 1.39950i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12026.7 | − | 47140.3i | −0.0277775 | − | 0.108878i | ||||
\(659\) | 670185.i | 1.54321i | 0.636105 | + | 0.771603i | \(0.280545\pi\) | ||||
−0.636105 | + | 0.771603i | \(0.719455\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −619584. | −1.41807 | −0.709034 | − | 0.705174i | \(-0.750869\pi\) | ||||
−0.709034 | + | 0.705174i | \(0.750869\pi\) | |||||||
\(662\) | 617597. | − | 157565.i | 1.40925 | − | 0.359536i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 472810. | − | 439930.i | 1.07239 | − | 0.997809i | ||||
\(665\) | −69157.4 | −0.156385 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 16759.8i | − | 0.0376718i | ||||||
\(668\) | 346126. | + | 634193.i | 0.775678 | + | 1.42124i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 594019. | − | 151549.i | 1.32328 | − | 0.337602i | ||||
\(671\) | − | 703088.i | − | 1.56158i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −233848. | −0.516302 | −0.258151 | − | 0.966105i | \(-0.583113\pi\) | ||||
−0.258151 | + | 0.966105i | \(0.583113\pi\) | |||||||
\(674\) | −32520.3 | − | 127468.i | −0.0715872 | − | 0.280596i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −202029. | + | 110263.i | −0.442101 | + | 0.241287i | ||||
\(677\) | −703621. | −1.53519 | −0.767594 | − | 0.640936i | \(-0.778546\pi\) | ||||
−0.767594 | + | 0.640936i | \(0.778546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 11743.0i | − | 0.0254707i | ||||||
\(680\) | 346980. | + | 372913.i | 0.750390 | + | 0.806474i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22424.1 | − | 87894.5i | −0.0482111 | − | 0.188970i | ||||
\(683\) | − | 8903.15i | − | 0.0190855i | −0.999954 | − | 0.00954273i | \(-0.996962\pi\) | ||
0.999954 | − | 0.00954273i | \(-0.00303759\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −166649. | −0.355157 | ||||||||
\(686\) | −99671.5 | + | 25428.7i | −0.211799 | + | 0.0540352i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −54853.9 | − | 35284.3i | −0.115886 | − | 0.0745426i | ||||
\(689\) | 851987. | 1.79471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 186507.i | − | 0.390606i | −0.980743 | − | 0.195303i | \(-0.937431\pi\) | ||
0.980743 | − | 0.195303i | \(-0.0625690\pi\) | |||||||
\(692\) | 558808. | − | 304983.i | 1.16694 | − | 0.636889i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 266191. | − | 67912.1i | 0.552681 | − | 0.141003i | ||||
\(695\) | − | 311376.i | − | 0.644638i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.07256e6 | 2.20778 | ||||||||
\(698\) | 226000. | + | 885840.i | 0.463872 | + | 1.81821i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8018.21 | − | 14691.4i | −0.0163637 | − | 0.0299825i | ||||
\(701\) | −498328. | −1.01410 | −0.507048 | − | 0.861918i | \(-0.669264\pi\) | ||||
−0.507048 | + | 0.861918i | \(0.669264\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 210549.i | − | 0.426033i | ||||||
\(704\) | −472347. | − | 34075.5i | −0.953051 | − | 0.0687539i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 45511.3 | + | 178388.i | 0.0913082 | + | 0.357895i | ||||
\(707\) | 17470.3i | 0.0349512i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 84448.4 | 0.167996 | 0.0839980 | − | 0.996466i | \(-0.473231\pi\) | ||||
0.0839980 | + | 0.996466i | \(0.473231\pi\) | |||||||
\(710\) | 752002. | − | 191855.i | 1.49177 | − | 0.380589i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −593413. | − | 637764.i | −1.17057 | − | 1.25806i | ||||
\(713\) | −16277.6 | −0.0320193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 497338.i | 0.972835i | ||||||||
\(716\) | −169263. | − | 310133.i | −0.330168 | − | 0.604954i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −509462. | + | 129977.i | −0.988241 | + | 0.252125i | ||||
\(719\) | 563153.i | 1.08935i | 0.838646 | + | 0.544677i | \(0.183348\pi\) | ||||
−0.838646 | + | 0.544677i | \(0.816652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17571.6 | −0.0338018 | ||||||||
\(722\) | 249268. | + | 977043.i | 0.478182 | + | 1.87430i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 138577. | − | 75631.6i | 0.264370 | − | 0.144287i | ||||
\(725\) | −39209.1 | −0.0745953 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 829063.i | − | 1.56862i | −0.620367 | − | 0.784312i | \(-0.713016\pi\) | ||
0.620367 | − | 0.784312i | \(-0.286984\pi\) | |||||||
\(728\) | 52315.4 | − | 48677.3i | 0.0987113 | − | 0.0918467i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 109212. | + | 428073.i | 0.204939 | + | 0.803289i | ||||
\(731\) | − | 97689.7i | − | 0.182816i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 345658. | 0.643338 | 0.321669 | − | 0.946852i | \(-0.395756\pi\) | ||||
0.321669 | + | 0.946852i | \(0.395756\pi\) | |||||||
\(734\) | −467616. | + | 119301.i | −0.867954 | + | 0.221437i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26878.6 | + | 80619.0i | −0.0496193 | + | 0.148827i | ||||
\(737\) | −853691. | −1.57169 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 662859.i | − | 1.21376i | −0.794794 | − | 0.606879i | \(-0.792421\pi\) | ||
0.794794 | − | 0.606879i | \(-0.207579\pi\) | |||||||
\(740\) | −99256.2 | + | 54171.5i | −0.181257 | + | 0.0989253i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −85852.7 | + | 21903.2i | −0.155936 | + | 0.0397832i | ||||
\(743\) | 346708.i | 0.628039i | 0.949417 | + | 0.314019i | \(0.101676\pi\) | ||||
−0.949417 | + | 0.314019i | \(0.898324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30242.8 | −0.0544891 | ||||||||
\(746\) | −181194. | − | 710216.i | −0.325586 | − | 1.27618i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −339813. | − | 622625.i | −0.607347 | − | 1.11282i | ||||
\(749\) | 85816.2 | 0.152970 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 218129.i | 0.386752i | 0.981125 | + | 0.193376i | \(0.0619438\pi\) | ||||
−0.981125 | + | 0.193376i | \(0.938056\pi\) | |||||||
\(752\) | 486028. | + | 312634.i | 0.859461 | + | 0.552841i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −41383.3 | − | 162208.i | −0.0727917 | − | 0.285318i | ||||
\(755\) | 319944.i | 0.561281i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 454177. | 0.792563 | 0.396281 | − | 0.918129i | \(-0.370300\pi\) | ||||
0.396281 | + | 0.918129i | \(0.370300\pi\) | |||||||
\(758\) | 816017. | − | 208187.i | 1.42024 | − | 0.362339i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 601418. | − | 559594.i | 1.04124 | − | 0.968827i | ||||
\(761\) | −779754. | −1.34644 | −0.673222 | − | 0.739441i | \(-0.735090\pi\) | ||||
−0.673222 | + | 0.739441i | \(0.735090\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 39746.5i | − | 0.0682731i | ||||||
\(764\) | −53548.1 | − | 98113.9i | −0.0917396 | − | 0.168091i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 445826. | − | 113742.i | 0.759815 | − | 0.193848i | ||||
\(767\) | − | 331278.i | − | 0.563120i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.04561e6 | 1.76814 | 0.884072 | − | 0.467350i | \(-0.154791\pi\) | ||||
0.884072 | + | 0.467350i | \(0.154791\pi\) | |||||||
\(770\) | −12785.7 | − | 50115.5i | −0.0215647 | − | 0.0845261i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 556831. | − | 303904.i | 0.934305 | − | 0.509920i | ||||
\(773\) | 240697. | 0.402820 | 0.201410 | − | 0.979507i | \(-0.435448\pi\) | ||||
0.201410 | + | 0.979507i | \(0.435448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38081.2i | 0.0634027i | ||||||||
\(776\) | 95020.1 | + | 102122.i | 0.157795 | + | 0.169588i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 225405. | + | 883506.i | 0.372395 | + | 1.45966i | ||||
\(779\) | − | 1.72977e6i | − | 2.85046i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.08073e6 | −1.77181 | ||||||||
\(782\) | −123335. | + | 31465.8i | −0.201684 | + | 0.0514548i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 328500. | − | 510695.i | 0.534446 | − | 0.830863i | ||||
\(785\) | −484234. | −0.785807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 453844.i | − | 0.732753i | −0.930467 | − | 0.366376i | \(-0.880598\pi\) | ||
0.930467 | − | 0.366376i | \(-0.119402\pi\) | |||||||
\(788\) | −358427. | + | 195620.i | −0.577229 | + | 0.315037i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −480404. | + | 122563.i | −0.769754 | + | 0.196384i | ||||
\(791\) | 38370.6i | 0.0613261i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.26021e6 | −2.00399 | ||||||||
\(794\) | −250382. | − | 981406.i | −0.397156 | − | 1.55671i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 158175. | + | 289817.i | 0.249638 | + | 0.457402i | ||||
\(797\) | −595530. | −0.937534 | −0.468767 | − | 0.883322i | \(-0.655302\pi\) | ||||
−0.468767 | + | 0.883322i | \(0.655302\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 865572.i | 1.35584i | ||||||||
\(800\) | 188607. | + | 62881.9i | 0.294698 | + | 0.0982530i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 111791. | + | 438182.i | 0.173804 | + | 0.681249i | ||||
\(803\) | − | 615202.i | − | 0.954084i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9281.15 | −0.0143222 | ||||||||
\(806\) | −157541. | + | 40192.8i | −0.242507 | + | 0.0618697i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −141363. | − | 151928.i | −0.216528 | − | 0.232711i | ||||
\(809\) | 238455. | 0.364342 | 0.182171 | − | 0.983267i | \(-0.441688\pi\) | ||||
0.182171 | + | 0.983267i | \(0.441688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 325863.i | 0.495443i | 0.968831 | + | 0.247721i | \(0.0796817\pi\) | ||||
−0.968831 | + | 0.247721i | \(0.920318\pi\) | |||||||
\(812\) | 8340.18 | + | 15281.4i | 0.0126492 | + | 0.0231766i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 152576. | − | 38926.1i | 0.230271 | − | 0.0587479i | ||||
\(815\) | 654151.i | 0.984833i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −157550. | −0.236033 | ||||||||
\(818\) | −76735.4 | − | 300775.i | −0.114680 | − | 0.449506i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −815442. | + | 445047.i | −1.21273 | + | 0.661879i | ||||
\(821\) | 376943. | 0.559228 | 0.279614 | − | 0.960113i | \(-0.409794\pi\) | ||||
0.279614 | + | 0.960113i | \(0.409794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.10349e6i | 1.62918i | 0.580040 | + | 0.814588i | \(0.303037\pi\) | ||||
−0.580040 | + | 0.814588i | \(0.696963\pi\) | |||||||
\(824\) | 152809. | − | 142182.i | 0.225058 | − | 0.209407i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8516.61 | + | 33382.0i | 0.0124826 | + | 0.0489275i | ||||
\(827\) | 251807.i | 0.368177i | 0.982910 | + | 0.184089i | \(0.0589334\pi\) | ||||
−0.982910 | + | 0.184089i | \(0.941067\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 595280. | 0.866189 | 0.433094 | − | 0.901349i | \(-0.357422\pi\) | ||||
0.433094 | + | 0.901349i | \(0.357422\pi\) | |||||||
\(830\) | −811825. | + | 207117.i | −1.17844 | + | 0.300649i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −61076.7 | + | 846631.i | −0.0882326 | + | 1.22306i | ||||
\(833\) | 909501. | 1.31073 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 937299.i | − | 1.34433i | ||||||
\(836\) | −1.00414e6 | + | 548035.i | −1.43675 | + | 0.784144i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 181759. | − | 46371.3i | 0.258826 | − | 0.0660330i | ||||
\(839\) | 937926.i | 1.33243i | 0.745760 | + | 0.666215i | \(0.232087\pi\) | ||||
−0.745760 | + | 0.666215i | \(0.767913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −666497. | −0.942338 | ||||||||
\(842\) | −39699.7 | − | 155609.i | −0.0559967 | − | 0.219487i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −286699. | − | 525306.i | −0.402477 | − | 0.737441i | ||||
\(845\) | 298588. | 0.418175 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6860.31i | − | 0.00956262i | ||||||
\(848\) | 569374. | − | 885164.i | 0.791783 | − | 1.23093i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 73613.7 | + | 288539.i | 0.101888 | + | 0.399363i | ||||
\(851\) | − | 28256.4i | − | 0.0390174i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17614.3 | −0.0242085 | −0.0121042 | − | 0.999927i | \(-0.503853\pi\) | ||||
−0.0121042 | + | 0.999927i | \(0.503853\pi\) | |||||||
\(854\) | 126988. | − | 32397.9i | 0.174120 | − | 0.0444224i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −746289. | + | 694390.i | −1.01850 | + | 0.947668i | ||||
\(857\) | 203626. | 0.277251 | 0.138625 | − | 0.990345i | \(-0.455732\pi\) | ||||
0.138625 | + | 0.990345i | \(0.455732\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 110138.i | − | 0.149262i | −0.997211 | − | 0.0746310i | \(-0.976222\pi\) | ||
0.997211 | − | 0.0746310i | \(-0.0237779\pi\) | |||||||
\(860\) | 40535.4 | + | 74271.3i | 0.0548072 | + | 0.100421i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −997741. | + | 254549.i | −1.34278 | + | 0.342576i | ||||
\(863\) | 366628.i | 0.492271i | 0.969235 | + | 0.246136i | \(0.0791609\pi\) | ||||
−0.969235 | + | 0.246136i | \(0.920839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −825885. | −1.10379 | ||||||||
\(866\) | 29428.1 | + | 115347.i | 0.0392397 | + | 0.153806i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14841.8 | − | 8100.27i | 0.0196991 | − | 0.0107513i | ||||
\(869\) | 690409. | 0.914254 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.53015e6i | 2.01696i | ||||||||
\(872\) | 321613. | + | 345650.i | 0.422961 | + | 0.454573i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 50746.7 | + | 198909.i | 0.0664332 | + | 0.260394i | ||||
\(875\) | 91609.8i | 0.119654i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −556086. | −0.723007 | −0.361503 | − | 0.932371i | \(-0.617736\pi\) | ||||
−0.361503 | + | 0.932371i | \(0.617736\pi\) | |||||||
\(878\) | −965855. | + | 246414.i | −1.25292 | + | 0.319651i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 516704. | + | 332366.i | 0.667232 | + | 0.429191i | ||||
\(881\) | −246117. | −0.317096 | −0.158548 | − | 0.987351i | \(-0.550681\pi\) | ||||
−0.158548 | + | 0.987351i | \(0.550681\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 317186.i | − | 0.406810i | −0.979095 | − | 0.203405i | \(-0.934799\pi\) | ||
0.979095 | − | 0.203405i | \(-0.0652009\pi\) | |||||||
\(884\) | −1.11599e6 | + | 609078.i | −1.42809 | + | 0.779414i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 208652. | − | 53232.3i | 0.265800 | − | 0.0678122i | ||||
\(887\) | − | 84967.8i | − | 0.107996i | −0.998541 | − | 0.0539979i | \(-0.982804\pi\) | ||
0.998541 | − | 0.0539979i | \(-0.0171964\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −88180.2 | −0.111575 | ||||||||
\(890\) | 279376. | + | 1.09505e6i | 0.352703 | + | 1.38247i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 489749. | + | 897347.i | 0.615523 | + | 1.12780i | ||||
\(893\) | 1.39596e6 | 1.75053 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 458358.i | 0.572215i | ||||||||
\(896\) | −15610.9 | − | 86883.2i | −0.0194452 | − | 0.108223i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −126532. | − | 495959.i | −0.156909 | − | 0.615026i | ||||
\(899\) | − | 39610.4i | − | 0.0490105i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.57640e6 | 1.94185 | ||||||||
\(902\) | 1.25349e6 | − | 319798.i | 1.54067 | − | 0.393064i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −310480. | − | 333685.i | −0.379924 | − | 0.408319i | ||||
\(905\) | −204808. | −0.250063 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 384478.i | 0.467366i | 0.972313 | + | 0.233683i | \(0.0750778\pi\) | ||||
−0.972313 | + | 0.233683i | \(0.924922\pi\) | |||||||
\(908\) | −399566. | − | 732109.i | −0.484638 | − | 0.887981i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −89826.7 | + | 22917.1i | −0.108473 | + | 0.0276743i | ||||
\(911\) | − | 1.24116e6i | − | 1.49552i | −0.663972 | − | 0.747758i | \(-0.731130\pi\) | ||
0.663972 | − | 0.747758i | \(-0.268870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16671e6 | 1.39965 | ||||||||
\(914\) | −137323. | − | 538256.i | −0.164380 | − | 0.644312i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 424628. | − | 231751.i | 0.506078 | − | 0.276205i | ||||
\(917\) | −94271.2 | −0.112109 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 698308.i | 0.826829i | 0.910543 | + | 0.413415i | \(0.135664\pi\) | ||||
−0.910543 | + | 0.413415i | \(0.864336\pi\) | |||||||
\(920\) | 80712.3 | − | 75099.4i | 0.0953595 | − | 0.0887280i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −240245. | − | 941675.i | −0.282614 | − | 1.10774i | ||||
\(923\) | 1.93710e6i | 2.27378i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −66105.3 | −0.0772597 | ||||||||
\(926\) | −1.07463e6 | + | 274167.i | −1.25325 | + | 0.319737i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −196180. | − | 65406.9i | −0.227803 | − | 0.0759500i | ||||
\(929\) | 1.40938e6 | 1.63304 | 0.816519 | − | 0.577318i | \(-0.195901\pi\) | ||||
0.816519 | + | 0.577318i | \(0.195901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.46680e6i | − | 1.69228i | ||||||
\(932\) | −71345.9 | + | 38938.8i | −0.0821367 | + | 0.0448281i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −478978. | + | 122199.i | −0.549062 | + | 0.140080i | ||||
\(935\) | 920203.i | 1.05259i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −98815.5 | −0.112550 | −0.0562751 | − | 0.998415i | \(-0.517922\pi\) | ||||
−0.0562751 | + | 0.998415i | \(0.517922\pi\) | |||||||
\(938\) | −39337.6 | − | 154189.i | −0.0447098 | − | 0.175246i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −359161. | − | 658075.i | −0.406474 | − | 0.744766i | ||||
\(941\) | 1.30446e6 | 1.47316 | 0.736581 | − | 0.676350i | \(-0.236439\pi\) | ||||
0.736581 | + | 0.676350i | \(0.236439\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 232141.i | − | 0.261053i | ||||||
\(944\) | −344178. | − | 221389.i | −0.386224 | − | 0.248435i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29127.6 | − | 114170.i | −0.0325478 | − | 0.127576i | ||||
\(947\) | 146295.i | 0.163128i | 0.996668 | + | 0.0815641i | \(0.0259915\pi\) | ||||
−0.996668 | + | 0.0815641i | \(0.974008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.10268e6 | −1.22439 | ||||||||
\(950\) | 465344. | − | 118721.i | 0.515616 | − | 0.131547i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 96797.0 | − | 90065.5i | 0.106804 | − | 0.0993767i | ||||
\(953\) | 1.65688e6 | 1.82433 | 0.912167 | − | 0.409818i | \(-0.134408\pi\) | ||||
0.912167 | + | 0.409818i | \(0.134408\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 145006.i | 0.158994i | ||||||||
\(956\) | −312281. | − | 572179.i | −0.341688 | − | 0.626061i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 217879. | − | 55586.5i | 0.237402 | − | 0.0605674i | ||||
\(959\) | 43256.9i | 0.0470347i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 885050. | 0.958343 | ||||||||
\(962\) | −69770.8 | − | 273477.i | −0.0753918 | − | 0.295509i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 489224. | − | 267006.i | 0.526446 | − | 0.287321i | ||||
\(965\) | −822963. | −0.883742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 532588.i | 0.569559i | 0.958593 | + | 0.284780i | \(0.0919204\pi\) | ||||
−0.958593 | + | 0.284780i | \(0.908080\pi\) | |||||||
\(968\) | 55510.9 | + | 59659.7i | 0.0592417 | + | 0.0636694i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −44735.0 | − | 175345.i | −0.0475449 | − | 0.186359i | ||||
\(971\) | − | 1.26243e6i | − | 1.33896i | −0.742828 | − | 0.669482i | \(-0.766516\pi\) | ||
0.742828 | − | 0.669482i | \(-0.233484\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −80823.9 | −0.0853717 | ||||||||
\(974\) | −1.05416e6 | + | 268942.i | −1.11119 | + | 0.283492i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −842186. | + | 1.30928e6i | −0.884114 | + | 1.37447i | ||||
\(977\) | −995130. | −1.04254 | −0.521268 | − | 0.853393i | \(-0.674541\pi\) | ||||
−0.521268 | + | 0.853393i | \(0.674541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.57375e6i | − | 1.64199i | ||||||
\(980\) | −691473. | + | 377388.i | −0.719984 | + | 0.392949i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.29922e6 | − | 331463.i | 1.34728 | − | 0.343726i | ||||
\(983\) | 706269.i | 0.730909i | 0.930829 | + | 0.365454i | \(0.119086\pi\) | ||||
−0.930829 | + | 0.365454i | \(0.880914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 529733. | 0.545990 | ||||||||
\(986\) | −76569.7 | − | 300126.i | −0.0787595 | − | 0.308709i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 982294. | + | 1.79982e6i | 1.00630 | + | 1.84380i | ||||
\(989\) | −21143.7 | −0.0216166 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 6734.63i | − | 0.00685751i | −0.999994 | − | 0.00342875i | \(-0.998909\pi\) | ||
0.999994 | − | 0.00342875i | \(-0.00109141\pi\) | |||||||
\(992\) | −63525.4 | + | 190537.i | −0.0645541 | + | 0.193622i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49799.7 | − | 195197.i | −0.0504027 | − | 0.197560i | ||||
\(995\) | − | 428333.i | − | 0.432648i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −525528. | −0.528696 | −0.264348 | − | 0.964427i | \(-0.585157\pi\) | ||||
−0.264348 | + | 0.964427i | \(0.585157\pi\) | |||||||
\(998\) | −1.11505e6 | + | 284478.i | −1.11952 | + | 0.285619i | ||||
\(999\) | 0 | 0 |
(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 | 108.5.d.b.55.7 | ✓ | 16 | |
3.2 | odd | 2 | inner | 108.5.d.b.55.10 | yes | 16 | |
4.3 | odd | 2 | inner | 108.5.d.b.55.8 | yes | 16 | |
12.11 | even | 2 | inner | 108.5.d.b.55.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.d.b.55.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
108.5.d.b.55.8 | yes | 16 | 4.3 | odd | 2 | inner | |
108.5.d.b.55.9 | yes | 16 | 12.11 | even | 2 | inner | |
108.5.d.b.55.10 | yes | 16 | 3.2 | odd | 2 | inner |