Properties

Label 1470.2.d.d.1469.4
Level $1470$
Weight $2$
Character 1470.1469
Analytic conductor $11.738$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1470,2,Mod(1469,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.1469");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.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: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1469.4
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 1470.1469
Dual form 1470.2.d.d.1469.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(2.18614 + 0.469882i) q^{5} +(1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.68614 + 0.396143i) q^{3} +1.00000 q^{4} +(2.18614 + 0.469882i) q^{5} +(1.68614 + 0.396143i) q^{6} +1.00000 q^{8} +(2.68614 + 1.33591i) q^{9} +(2.18614 + 0.469882i) q^{10} -0.939764i q^{11} +(1.68614 + 0.396143i) q^{12} -2.00000 q^{13} +(3.50000 + 1.65831i) q^{15} +1.00000 q^{16} -6.63325i q^{17} +(2.68614 + 1.33591i) q^{18} +3.46410i q^{19} +(2.18614 + 0.469882i) q^{20} -0.939764i q^{22} -1.37228 q^{23} +(1.68614 + 0.396143i) q^{24} +(4.55842 + 2.05446i) q^{25} -2.00000 q^{26} +(4.00000 + 3.31662i) q^{27} -3.31662i q^{29} +(3.50000 + 1.65831i) q^{30} +7.57301i q^{31} +1.00000 q^{32} +(0.372281 - 1.58457i) q^{33} -6.63325i q^{34} +(2.68614 + 1.33591i) q^{36} -8.21782i q^{37} +3.46410i q^{38} +(-3.37228 - 0.792287i) q^{39} +(2.18614 + 0.469882i) q^{40} -7.37228 q^{41} +1.08724i q^{43} -0.939764i q^{44} +(5.24456 + 4.18265i) q^{45} -1.37228 q^{46} +8.51278i q^{47} +(1.68614 + 0.396143i) q^{48} +(4.55842 + 2.05446i) q^{50} +(2.62772 - 11.1846i) q^{51} -2.00000 q^{52} -4.37228 q^{53} +(4.00000 + 3.31662i) q^{54} +(0.441578 - 2.05446i) q^{55} +(-1.37228 + 5.84096i) q^{57} -3.31662i q^{58} -13.1168 q^{59} +(3.50000 + 1.65831i) q^{60} +12.7692i q^{61} +7.57301i q^{62} +1.00000 q^{64} +(-4.37228 - 0.939764i) q^{65} +(0.372281 - 1.58457i) q^{66} -2.37686i q^{67} -6.63325i q^{68} +(-2.31386 - 0.543620i) q^{69} -8.51278i q^{71} +(2.68614 + 1.33591i) q^{72} -2.00000 q^{73} -8.21782i q^{74} +(6.87228 + 5.26989i) q^{75} +3.46410i q^{76} +(-3.37228 - 0.792287i) q^{78} +9.11684 q^{79} +(2.18614 + 0.469882i) q^{80} +(5.43070 + 7.17687i) q^{81} -7.37228 q^{82} -11.8294i q^{83} +(3.11684 - 14.5012i) q^{85} +1.08724i q^{86} +(1.31386 - 5.59230i) q^{87} -0.939764i q^{88} -1.37228 q^{89} +(5.24456 + 4.18265i) q^{90} -1.37228 q^{92} +(-3.00000 + 12.7692i) q^{93} +8.51278i q^{94} +(-1.62772 + 7.57301i) q^{95} +(1.68614 + 0.396143i) q^{96} -15.1168 q^{97} +(1.25544 - 2.52434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} + 4 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + q^{3} + 4 q^{4} + 3 q^{5} + q^{6} + 4 q^{8} + 5 q^{9} + 3 q^{10} + q^{12} - 8 q^{13} + 14 q^{15} + 4 q^{16} + 5 q^{18} + 3 q^{20} + 6 q^{23} + q^{24} + q^{25} - 8 q^{26} + 16 q^{27} + 14 q^{30} + 4 q^{32} - 10 q^{33} + 5 q^{36} - 2 q^{39} + 3 q^{40} - 18 q^{41} - 2 q^{45} + 6 q^{46} + q^{48} + q^{50} + 22 q^{51} - 8 q^{52} - 6 q^{53} + 16 q^{54} + 19 q^{55} + 6 q^{57} - 18 q^{59} + 14 q^{60} + 4 q^{64} - 6 q^{65} - 10 q^{66} - 15 q^{69} + 5 q^{72} - 8 q^{73} + 16 q^{75} - 2 q^{78} + 2 q^{79} + 3 q^{80} - 7 q^{81} - 18 q^{82} - 22 q^{85} + 11 q^{87} + 6 q^{89} - 2 q^{90} + 6 q^{92} - 12 q^{93} - 18 q^{95} + q^{96} - 26 q^{97} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.68614 + 0.396143i 0.973494 + 0.228714i
\(4\) 1.00000 0.500000
\(5\) 2.18614 + 0.469882i 0.977672 + 0.210138i
\(6\) 1.68614 + 0.396143i 0.688364 + 0.161725i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 2.68614 + 1.33591i 0.895380 + 0.445302i
\(10\) 2.18614 + 0.469882i 0.691318 + 0.148590i
\(11\) 0.939764i 0.283349i −0.989913 0.141675i \(-0.954751\pi\)
0.989913 0.141675i \(-0.0452487\pi\)
\(12\) 1.68614 + 0.396143i 0.486747 + 0.114357i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) 3.50000 + 1.65831i 0.903696 + 0.428174i
\(16\) 1.00000 0.250000
\(17\) 6.63325i 1.60880i −0.594089 0.804400i \(-0.702487\pi\)
0.594089 0.804400i \(-0.297513\pi\)
\(18\) 2.68614 + 1.33591i 0.633129 + 0.314876i
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 2.18614 + 0.469882i 0.488836 + 0.105069i
\(21\) 0 0
\(22\) 0.939764i 0.200358i
\(23\) −1.37228 −0.286140 −0.143070 0.989713i \(-0.545697\pi\)
−0.143070 + 0.989713i \(0.545697\pi\)
\(24\) 1.68614 + 0.396143i 0.344182 + 0.0808625i
\(25\) 4.55842 + 2.05446i 0.911684 + 0.410891i
\(26\) −2.00000 −0.392232
\(27\) 4.00000 + 3.31662i 0.769800 + 0.638285i
\(28\) 0 0
\(29\) 3.31662i 0.615882i −0.951405 0.307941i \(-0.900360\pi\)
0.951405 0.307941i \(-0.0996399\pi\)
\(30\) 3.50000 + 1.65831i 0.639010 + 0.302765i
\(31\) 7.57301i 1.36015i 0.733141 + 0.680077i \(0.238054\pi\)
−0.733141 + 0.680077i \(0.761946\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.372281 1.58457i 0.0648059 0.275839i
\(34\) 6.63325i 1.13759i
\(35\) 0 0
\(36\) 2.68614 + 1.33591i 0.447690 + 0.222651i
\(37\) 8.21782i 1.35100i −0.737359 0.675501i \(-0.763927\pi\)
0.737359 0.675501i \(-0.236073\pi\)
\(38\) 3.46410i 0.561951i
\(39\) −3.37228 0.792287i −0.539997 0.126867i
\(40\) 2.18614 + 0.469882i 0.345659 + 0.0742949i
\(41\) −7.37228 −1.15136 −0.575678 0.817676i \(-0.695262\pi\)
−0.575678 + 0.817676i \(0.695262\pi\)
\(42\) 0 0
\(43\) 1.08724i 0.165803i 0.996558 + 0.0829013i \(0.0264186\pi\)
−0.996558 + 0.0829013i \(0.973581\pi\)
\(44\) 0.939764i 0.141675i
\(45\) 5.24456 + 4.18265i 0.781813 + 0.623513i
\(46\) −1.37228 −0.202332
\(47\) 8.51278i 1.24172i 0.783923 + 0.620858i \(0.213216\pi\)
−0.783923 + 0.620858i \(0.786784\pi\)
\(48\) 1.68614 + 0.396143i 0.243373 + 0.0571784i
\(49\) 0 0
\(50\) 4.55842 + 2.05446i 0.644658 + 0.290544i
\(51\) 2.62772 11.1846i 0.367954 1.56616i
\(52\) −2.00000 −0.277350
\(53\) −4.37228 −0.600579 −0.300290 0.953848i \(-0.597083\pi\)
−0.300290 + 0.953848i \(0.597083\pi\)
\(54\) 4.00000 + 3.31662i 0.544331 + 0.451335i
\(55\) 0.441578 2.05446i 0.0595424 0.277023i
\(56\) 0 0
\(57\) −1.37228 + 5.84096i −0.181763 + 0.773654i
\(58\) 3.31662i 0.435494i
\(59\) −13.1168 −1.70767 −0.853834 0.520546i \(-0.825729\pi\)
−0.853834 + 0.520546i \(0.825729\pi\)
\(60\) 3.50000 + 1.65831i 0.451848 + 0.214087i
\(61\) 12.7692i 1.63492i 0.575982 + 0.817462i \(0.304620\pi\)
−0.575982 + 0.817462i \(0.695380\pi\)
\(62\) 7.57301i 0.961774i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.37228 0.939764i −0.542315 0.116563i
\(66\) 0.372281 1.58457i 0.0458247 0.195048i
\(67\) 2.37686i 0.290380i −0.989404 0.145190i \(-0.953621\pi\)
0.989404 0.145190i \(-0.0463793\pi\)
\(68\) 6.63325i 0.804400i
\(69\) −2.31386 0.543620i −0.278556 0.0654442i
\(70\) 0 0
\(71\) 8.51278i 1.01028i −0.863037 0.505140i \(-0.831441\pi\)
0.863037 0.505140i \(-0.168559\pi\)
\(72\) 2.68614 + 1.33591i 0.316565 + 0.157438i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 8.21782i 0.955303i
\(75\) 6.87228 + 5.26989i 0.793543 + 0.608515i
\(76\) 3.46410i 0.397360i
\(77\) 0 0
\(78\) −3.37228 0.792287i −0.381836 0.0897088i
\(79\) 9.11684 1.02573 0.512863 0.858471i \(-0.328585\pi\)
0.512863 + 0.858471i \(0.328585\pi\)
\(80\) 2.18614 + 0.469882i 0.244418 + 0.0525344i
\(81\) 5.43070 + 7.17687i 0.603411 + 0.797430i
\(82\) −7.37228 −0.814132
\(83\) 11.8294i 1.29845i −0.760598 0.649223i \(-0.775094\pi\)
0.760598 0.649223i \(-0.224906\pi\)
\(84\) 0 0
\(85\) 3.11684 14.5012i 0.338069 1.57288i
\(86\) 1.08724i 0.117240i
\(87\) 1.31386 5.59230i 0.140861 0.599557i
\(88\) 0.939764i 0.100179i
\(89\) −1.37228 −0.145462 −0.0727308 0.997352i \(-0.523171\pi\)
−0.0727308 + 0.997352i \(0.523171\pi\)
\(90\) 5.24456 + 4.18265i 0.552825 + 0.440890i
\(91\) 0 0
\(92\) −1.37228 −0.143070
\(93\) −3.00000 + 12.7692i −0.311086 + 1.32410i
\(94\) 8.51278i 0.878026i
\(95\) −1.62772 + 7.57301i −0.167000 + 0.776975i
\(96\) 1.68614 + 0.396143i 0.172091 + 0.0404312i
\(97\) −15.1168 −1.53488 −0.767441 0.641119i \(-0.778470\pi\)
−0.767441 + 0.641119i \(0.778470\pi\)
\(98\) 0 0
\(99\) 1.25544 2.52434i 0.126176 0.253705i
\(100\) 4.55842 + 2.05446i 0.455842 + 0.205446i
\(101\) 10.6277 1.05750 0.528749 0.848778i \(-0.322661\pi\)
0.528749 + 0.848778i \(0.322661\pi\)
\(102\) 2.62772 11.1846i 0.260183 1.10744i
\(103\) 2.11684 0.208579 0.104289 0.994547i \(-0.466743\pi\)
0.104289 + 0.994547i \(0.466743\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −4.37228 −0.424674
\(107\) 6.25544 0.604736 0.302368 0.953191i \(-0.402223\pi\)
0.302368 + 0.953191i \(0.402223\pi\)
\(108\) 4.00000 + 3.31662i 0.384900 + 0.319142i
\(109\) −8.11684 −0.777453 −0.388726 0.921353i \(-0.627085\pi\)
−0.388726 + 0.921353i \(0.627085\pi\)
\(110\) 0.441578 2.05446i 0.0421028 0.195885i
\(111\) 3.25544 13.8564i 0.308992 1.31519i
\(112\) 0 0
\(113\) −14.7446 −1.38705 −0.693526 0.720432i \(-0.743944\pi\)
−0.693526 + 0.720432i \(0.743944\pi\)
\(114\) −1.37228 + 5.84096i −0.128526 + 0.547056i
\(115\) −3.00000 0.644810i −0.279751 0.0601289i
\(116\) 3.31662i 0.307941i
\(117\) −5.37228 2.67181i −0.496668 0.247009i
\(118\) −13.1168 −1.20750
\(119\) 0 0
\(120\) 3.50000 + 1.65831i 0.319505 + 0.151383i
\(121\) 10.1168 0.919713
\(122\) 12.7692i 1.15607i
\(123\) −12.4307 2.92048i −1.12084 0.263331i
\(124\) 7.57301i 0.680077i
\(125\) 9.00000 + 6.63325i 0.804984 + 0.593296i
\(126\) 0 0
\(127\) 7.57301i 0.671996i −0.941863 0.335998i \(-0.890926\pi\)
0.941863 0.335998i \(-0.109074\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.430703 + 1.83324i −0.0379213 + 0.161408i
\(130\) −4.37228 0.939764i −0.383474 0.0824227i
\(131\) 10.3723 0.906230 0.453115 0.891452i \(-0.350313\pi\)
0.453115 + 0.891452i \(0.350313\pi\)
\(132\) 0.372281 1.58457i 0.0324029 0.137919i
\(133\) 0 0
\(134\) 2.37686i 0.205330i
\(135\) 7.18614 + 9.13014i 0.618485 + 0.785797i
\(136\) 6.63325i 0.568796i
\(137\) −8.74456 −0.747098 −0.373549 0.927610i \(-0.621859\pi\)
−0.373549 + 0.927610i \(0.621859\pi\)
\(138\) −2.31386 0.543620i −0.196969 0.0462760i
\(139\) 8.21782i 0.697027i 0.937304 + 0.348513i \(0.113313\pi\)
−0.937304 + 0.348513i \(0.886687\pi\)
\(140\) 0 0
\(141\) −3.37228 + 14.3537i −0.283997 + 1.20880i
\(142\) 8.51278i 0.714376i
\(143\) 1.87953i 0.157174i
\(144\) 2.68614 + 1.33591i 0.223845 + 0.111326i
\(145\) 1.55842 7.25061i 0.129420 0.602130i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 8.21782i 0.675501i
\(149\) 9.01011i 0.738137i 0.929402 + 0.369069i \(0.120323\pi\)
−0.929402 + 0.369069i \(0.879677\pi\)
\(150\) 6.87228 + 5.26989i 0.561119 + 0.430285i
\(151\) 9.11684 0.741918 0.370959 0.928649i \(-0.379029\pi\)
0.370959 + 0.928649i \(0.379029\pi\)
\(152\) 3.46410i 0.280976i
\(153\) 8.86141 17.8178i 0.716402 1.44049i
\(154\) 0 0
\(155\) −3.55842 + 16.5557i −0.285819 + 1.32978i
\(156\) −3.37228 0.792287i −0.269999 0.0634337i
\(157\) −8.00000 −0.638470 −0.319235 0.947676i \(-0.603426\pi\)
−0.319235 + 0.947676i \(0.603426\pi\)
\(158\) 9.11684 0.725297
\(159\) −7.37228 1.73205i −0.584660 0.137361i
\(160\) 2.18614 + 0.469882i 0.172830 + 0.0371474i
\(161\) 0 0
\(162\) 5.43070 + 7.17687i 0.426676 + 0.563868i
\(163\) 3.46410i 0.271329i −0.990755 0.135665i \(-0.956683\pi\)
0.990755 0.135665i \(-0.0433170\pi\)
\(164\) −7.37228 −0.575678
\(165\) 1.55842 3.28917i 0.121323 0.256062i
\(166\) 11.8294i 0.918140i
\(167\) 14.6487i 1.13355i −0.823873 0.566775i \(-0.808191\pi\)
0.823873 0.566775i \(-0.191809\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 3.11684 14.5012i 0.239051 1.11219i
\(171\) −4.62772 + 9.30506i −0.353890 + 0.711576i
\(172\) 1.08724i 0.0829013i
\(173\) 17.0256i 1.29443i −0.762308 0.647214i \(-0.775934\pi\)
0.762308 0.647214i \(-0.224066\pi\)
\(174\) 1.31386 5.59230i 0.0996034 0.423951i
\(175\) 0 0
\(176\) 0.939764i 0.0708374i
\(177\) −22.1168 5.19615i −1.66240 0.390567i
\(178\) −1.37228 −0.102857
\(179\) 23.6588i 1.76834i −0.467163 0.884171i \(-0.654724\pi\)
0.467163 0.884171i \(-0.345276\pi\)
\(180\) 5.24456 + 4.18265i 0.390907 + 0.311756i
\(181\) 8.01544i 0.595783i 0.954600 + 0.297892i \(0.0962834\pi\)
−0.954600 + 0.297892i \(0.903717\pi\)
\(182\) 0 0
\(183\) −5.05842 + 21.5306i −0.373929 + 1.59159i
\(184\) −1.37228 −0.101166
\(185\) 3.86141 17.9653i 0.283896 1.32084i
\(186\) −3.00000 + 12.7692i −0.219971 + 0.936281i
\(187\) −6.23369 −0.455852
\(188\) 8.51278i 0.620858i
\(189\) 0 0
\(190\) −1.62772 + 7.57301i −0.118087 + 0.549404i
\(191\) 17.0256i 1.23193i 0.787775 + 0.615963i \(0.211233\pi\)
−0.787775 + 0.615963i \(0.788767\pi\)
\(192\) 1.68614 + 0.396143i 0.121687 + 0.0285892i
\(193\) 17.9653i 1.29317i 0.762841 + 0.646586i \(0.223804\pi\)
−0.762841 + 0.646586i \(0.776196\pi\)
\(194\) −15.1168 −1.08533
\(195\) −7.00000 3.31662i −0.501280 0.237508i
\(196\) 0 0
\(197\) 14.2337 1.01411 0.507054 0.861914i \(-0.330734\pi\)
0.507054 + 0.861914i \(0.330734\pi\)
\(198\) 1.25544 2.52434i 0.0892200 0.179397i
\(199\) 1.28962i 0.0914188i 0.998955 + 0.0457094i \(0.0145548\pi\)
−0.998955 + 0.0457094i \(0.985445\pi\)
\(200\) 4.55842 + 2.05446i 0.322329 + 0.145272i
\(201\) 0.941578 4.00772i 0.0664138 0.282683i
\(202\) 10.6277 0.747764
\(203\) 0 0
\(204\) 2.62772 11.1846i 0.183977 0.783078i
\(205\) −16.1168 3.46410i −1.12565 0.241943i
\(206\) 2.11684 0.147488
\(207\) −3.68614 1.83324i −0.256204 0.127419i
\(208\) −2.00000 −0.138675
\(209\) 3.25544 0.225183
\(210\) 0 0
\(211\) 16.2337 1.11757 0.558787 0.829311i \(-0.311267\pi\)
0.558787 + 0.829311i \(0.311267\pi\)
\(212\) −4.37228 −0.300290
\(213\) 3.37228 14.3537i 0.231065 0.983502i
\(214\) 6.25544 0.427613
\(215\) −0.510875 + 2.37686i −0.0348414 + 0.162101i
\(216\) 4.00000 + 3.31662i 0.272166 + 0.225668i
\(217\) 0 0
\(218\) −8.11684 −0.549742
\(219\) −3.37228 0.792287i −0.227878 0.0535378i
\(220\) 0.441578 2.05446i 0.0297712 0.138511i
\(221\) 13.2665i 0.892401i
\(222\) 3.25544 13.8564i 0.218491 0.929981i
\(223\) −0.883156 −0.0591405 −0.0295703 0.999563i \(-0.509414\pi\)
−0.0295703 + 0.999563i \(0.509414\pi\)
\(224\) 0 0
\(225\) 9.50000 + 11.6082i 0.633333 + 0.773879i
\(226\) −14.7446 −0.980794
\(227\) 20.8395i 1.38317i 0.722297 + 0.691584i \(0.243087\pi\)
−0.722297 + 0.691584i \(0.756913\pi\)
\(228\) −1.37228 + 5.84096i −0.0908816 + 0.386827i
\(229\) 13.8564i 0.915657i −0.889041 0.457829i \(-0.848627\pi\)
0.889041 0.457829i \(-0.151373\pi\)
\(230\) −3.00000 0.644810i −0.197814 0.0425175i
\(231\) 0 0
\(232\) 3.31662i 0.217747i
\(233\) −0.510875 −0.0334685 −0.0167343 0.999860i \(-0.505327\pi\)
−0.0167343 + 0.999860i \(0.505327\pi\)
\(234\) −5.37228 2.67181i −0.351197 0.174662i
\(235\) −4.00000 + 18.6101i −0.260931 + 1.21399i
\(236\) −13.1168 −0.853834
\(237\) 15.3723 + 3.61158i 0.998537 + 0.234597i
\(238\) 0 0
\(239\) 23.6588i 1.53036i −0.643816 0.765180i \(-0.722650\pi\)
0.643816 0.765180i \(-0.277350\pi\)
\(240\) 3.50000 + 1.65831i 0.225924 + 0.107044i
\(241\) 19.2549i 1.24032i −0.784475 0.620160i \(-0.787068\pi\)
0.784475 0.620160i \(-0.212932\pi\)
\(242\) 10.1168 0.650335
\(243\) 6.31386 + 14.2525i 0.405034 + 0.914302i
\(244\) 12.7692i 0.817462i
\(245\) 0 0
\(246\) −12.4307 2.92048i −0.792553 0.186203i
\(247\) 6.92820i 0.440831i
\(248\) 7.57301i 0.480887i
\(249\) 4.68614 19.9460i 0.296972 1.26403i
\(250\) 9.00000 + 6.63325i 0.569210 + 0.419524i
\(251\) 1.11684 0.0704946 0.0352473 0.999379i \(-0.488778\pi\)
0.0352473 + 0.999379i \(0.488778\pi\)
\(252\) 0 0
\(253\) 1.28962i 0.0810777i
\(254\) 7.57301i 0.475173i
\(255\) 11.0000 23.2164i 0.688847 1.45387i
\(256\) 1.00000 0.0625000
\(257\) 1.87953i 0.117242i −0.998280 0.0586209i \(-0.981330\pi\)
0.998280 0.0586209i \(-0.0186703\pi\)
\(258\) −0.430703 + 1.83324i −0.0268144 + 0.114133i
\(259\) 0 0
\(260\) −4.37228 0.939764i −0.271157 0.0582817i
\(261\) 4.43070 8.90892i 0.274254 0.551448i
\(262\) 10.3723 0.640802
\(263\) 7.37228 0.454594 0.227297 0.973825i \(-0.427011\pi\)
0.227297 + 0.973825i \(0.427011\pi\)
\(264\) 0.372281 1.58457i 0.0229123 0.0975238i
\(265\) −9.55842 2.05446i −0.587169 0.126204i
\(266\) 0 0
\(267\) −2.31386 0.543620i −0.141606 0.0332690i
\(268\) 2.37686i 0.145190i
\(269\) −25.9783 −1.58392 −0.791961 0.610572i \(-0.790940\pi\)
−0.791961 + 0.610572i \(0.790940\pi\)
\(270\) 7.18614 + 9.13014i 0.437335 + 0.555642i
\(271\) 8.86263i 0.538367i −0.963089 0.269183i \(-0.913246\pi\)
0.963089 0.269183i \(-0.0867538\pi\)
\(272\) 6.63325i 0.402200i
\(273\) 0 0
\(274\) −8.74456 −0.528278
\(275\) 1.93070 4.28384i 0.116426 0.258325i
\(276\) −2.31386 0.543620i −0.139278 0.0327221i
\(277\) 9.10268i 0.546927i −0.961882 0.273464i \(-0.911831\pi\)
0.961882 0.273464i \(-0.0881693\pi\)
\(278\) 8.21782i 0.492872i
\(279\) −10.1168 + 20.3422i −0.605680 + 1.21785i
\(280\) 0 0
\(281\) 11.3870i 0.679290i 0.940554 + 0.339645i \(0.110307\pi\)
−0.940554 + 0.339645i \(0.889693\pi\)
\(282\) −3.37228 + 14.3537i −0.200816 + 0.854753i
\(283\) 16.0000 0.951101 0.475551 0.879688i \(-0.342249\pi\)
0.475551 + 0.879688i \(0.342249\pi\)
\(284\) 8.51278i 0.505140i
\(285\) −5.74456 + 12.1244i −0.340279 + 0.718185i
\(286\) 1.87953i 0.111139i
\(287\) 0 0
\(288\) 2.68614 + 1.33591i 0.158282 + 0.0787191i
\(289\) −27.0000 −1.58824
\(290\) 1.55842 7.25061i 0.0915137 0.425770i
\(291\) −25.4891 5.98844i −1.49420 0.351049i
\(292\) −2.00000 −0.117041
\(293\) 21.7244i 1.26915i 0.772861 + 0.634576i \(0.218825\pi\)
−0.772861 + 0.634576i \(0.781175\pi\)
\(294\) 0 0
\(295\) −28.6753 6.16337i −1.66954 0.358845i
\(296\) 8.21782i 0.477651i
\(297\) 3.11684 3.75906i 0.180858 0.218123i
\(298\) 9.01011i 0.521942i
\(299\) 2.74456 0.158722
\(300\) 6.87228 + 5.26989i 0.396771 + 0.304257i
\(301\) 0 0
\(302\) 9.11684 0.524615
\(303\) 17.9198 + 4.21010i 1.02947 + 0.241864i
\(304\) 3.46410i 0.198680i
\(305\) −6.00000 + 27.9152i −0.343559 + 1.59842i
\(306\) 8.86141 17.8178i 0.506573 1.01858i
\(307\) −24.1168 −1.37642 −0.688210 0.725511i \(-0.741603\pi\)
−0.688210 + 0.725511i \(0.741603\pi\)
\(308\) 0 0
\(309\) 3.56930 + 0.838574i 0.203050 + 0.0477048i
\(310\) −3.55842 + 16.5557i −0.202105 + 0.940299i
\(311\) 20.2337 1.14735 0.573674 0.819084i \(-0.305518\pi\)
0.573674 + 0.819084i \(0.305518\pi\)
\(312\) −3.37228 0.792287i −0.190918 0.0448544i
\(313\) −3.11684 −0.176174 −0.0880872 0.996113i \(-0.528075\pi\)
−0.0880872 + 0.996113i \(0.528075\pi\)
\(314\) −8.00000 −0.451466
\(315\) 0 0
\(316\) 9.11684 0.512863
\(317\) −1.11684 −0.0627282 −0.0313641 0.999508i \(-0.509985\pi\)
−0.0313641 + 0.999508i \(0.509985\pi\)
\(318\) −7.37228 1.73205i −0.413417 0.0971286i
\(319\) −3.11684 −0.174510
\(320\) 2.18614 + 0.469882i 0.122209 + 0.0262672i
\(321\) 10.5475 + 2.47805i 0.588707 + 0.138311i
\(322\) 0 0
\(323\) 22.9783 1.27854
\(324\) 5.43070 + 7.17687i 0.301706 + 0.398715i
\(325\) −9.11684 4.10891i −0.505712 0.227921i
\(326\) 3.46410i 0.191859i
\(327\) −13.6861 3.21543i −0.756845 0.177814i
\(328\) −7.37228 −0.407066
\(329\) 0 0
\(330\) 1.55842 3.28917i 0.0857883 0.181063i
\(331\) −24.2337 −1.33200 −0.666002 0.745950i \(-0.731996\pi\)
−0.666002 + 0.745950i \(0.731996\pi\)
\(332\) 11.8294i 0.649223i
\(333\) 10.9783 22.0742i 0.601604 1.20966i
\(334\) 14.6487i 0.801541i
\(335\) 1.11684 5.19615i 0.0610197 0.283896i
\(336\) 0 0
\(337\) 0.644810i 0.0351250i −0.999846 0.0175625i \(-0.994409\pi\)
0.999846 0.0175625i \(-0.00559061\pi\)
\(338\) −9.00000 −0.489535
\(339\) −24.8614 5.84096i −1.35029 0.317238i
\(340\) 3.11684 14.5012i 0.169035 0.786439i
\(341\) 7.11684 0.385399
\(342\) −4.62772 + 9.30506i −0.250238 + 0.503160i
\(343\) 0 0
\(344\) 1.08724i 0.0586201i
\(345\) −4.80298 2.27567i −0.258584 0.122518i
\(346\) 17.0256i 0.915299i
\(347\) 1.88316 0.101093 0.0505466 0.998722i \(-0.483904\pi\)
0.0505466 + 0.998722i \(0.483904\pi\)
\(348\) 1.31386 5.59230i 0.0704303 0.299779i
\(349\) 25.7407i 1.37787i −0.724824 0.688934i \(-0.758079\pi\)
0.724824 0.688934i \(-0.241921\pi\)
\(350\) 0 0
\(351\) −8.00000 6.63325i −0.427008 0.354057i
\(352\) 0.939764i 0.0500896i
\(353\) 12.2718i 0.653164i −0.945169 0.326582i \(-0.894103\pi\)
0.945169 0.326582i \(-0.105897\pi\)
\(354\) −22.1168 5.19615i −1.17550 0.276172i
\(355\) 4.00000 18.6101i 0.212298 0.987723i
\(356\) −1.37228 −0.0727308
\(357\) 0 0
\(358\) 23.6588i 1.25041i
\(359\) 27.4179i 1.44706i 0.690293 + 0.723530i \(0.257481\pi\)
−0.690293 + 0.723530i \(0.742519\pi\)
\(360\) 5.24456 + 4.18265i 0.276413 + 0.220445i
\(361\) 7.00000 0.368421
\(362\) 8.01544i 0.421282i
\(363\) 17.0584 + 4.00772i 0.895335 + 0.210351i
\(364\) 0 0
\(365\) −4.37228 0.939764i −0.228856 0.0491895i
\(366\) −5.05842 + 21.5306i −0.264408 + 1.12542i
\(367\) −13.2337 −0.690793 −0.345396 0.938457i \(-0.612256\pi\)
−0.345396 + 0.938457i \(0.612256\pi\)
\(368\) −1.37228 −0.0715351
\(369\) −19.8030 9.84868i −1.03090 0.512702i
\(370\) 3.86141 17.9653i 0.200745 0.933972i
\(371\) 0 0
\(372\) −3.00000 + 12.7692i −0.155543 + 0.662050i
\(373\) 23.3639i 1.20973i 0.796326 + 0.604867i \(0.206774\pi\)
−0.796326 + 0.604867i \(0.793226\pi\)
\(374\) −6.23369 −0.322336
\(375\) 12.5475 + 14.7499i 0.647953 + 0.761681i
\(376\) 8.51278i 0.439013i
\(377\) 6.63325i 0.341630i
\(378\) 0 0
\(379\) −12.2337 −0.628402 −0.314201 0.949356i \(-0.601737\pi\)
−0.314201 + 0.949356i \(0.601737\pi\)
\(380\) −1.62772 + 7.57301i −0.0835002 + 0.388487i
\(381\) 3.00000 12.7692i 0.153695 0.654184i
\(382\) 17.0256i 0.871103i
\(383\) 15.6434i 0.799338i 0.916659 + 0.399669i \(0.130875\pi\)
−0.916659 + 0.399669i \(0.869125\pi\)
\(384\) 1.68614 + 0.396143i 0.0860455 + 0.0202156i
\(385\) 0 0
\(386\) 17.9653i 0.914411i
\(387\) −1.45245 + 2.92048i −0.0738323 + 0.148456i
\(388\) −15.1168 −0.767441
\(389\) 7.51811i 0.381183i 0.981669 + 0.190592i \(0.0610406\pi\)
−0.981669 + 0.190592i \(0.938959\pi\)
\(390\) −7.00000 3.31662i −0.354459 0.167944i
\(391\) 9.10268i 0.460343i
\(392\) 0 0
\(393\) 17.4891 + 4.10891i 0.882210 + 0.207267i
\(394\) 14.2337 0.717083
\(395\) 19.9307 + 4.28384i 1.00282 + 0.215543i
\(396\) 1.25544 2.52434i 0.0630881 0.126853i
\(397\) −8.00000 −0.401508 −0.200754 0.979642i \(-0.564339\pi\)
−0.200754 + 0.979642i \(0.564339\pi\)
\(398\) 1.28962i 0.0646428i
\(399\) 0 0
\(400\) 4.55842 + 2.05446i 0.227921 + 0.102723i
\(401\) 16.5282i 0.825380i −0.910872 0.412690i \(-0.864589\pi\)
0.910872 0.412690i \(-0.135411\pi\)
\(402\) 0.941578 4.00772i 0.0469616 0.199887i
\(403\) 15.1460i 0.754477i
\(404\) 10.6277 0.528749
\(405\) 8.50000 + 18.2414i 0.422368 + 0.906424i
\(406\) 0 0
\(407\) −7.72281 −0.382806
\(408\) 2.62772 11.1846i 0.130091 0.553720i
\(409\) 4.31129i 0.213180i 0.994303 + 0.106590i \(0.0339932\pi\)
−0.994303 + 0.106590i \(0.966007\pi\)
\(410\) −16.1168 3.46410i −0.795954 0.171080i
\(411\) −14.7446 3.46410i −0.727296 0.170872i
\(412\) 2.11684 0.104289
\(413\) 0 0
\(414\) −3.68614 1.83324i −0.181164 0.0900989i
\(415\) 5.55842 25.8607i 0.272852 1.26945i
\(416\) −2.00000 −0.0980581
\(417\) −3.25544 + 13.8564i −0.159419 + 0.678551i
\(418\) 3.25544 0.159229
\(419\) 6.51087 0.318077 0.159039 0.987272i \(-0.449161\pi\)
0.159039 + 0.987272i \(0.449161\pi\)
\(420\) 0 0
\(421\) −2.11684 −0.103169 −0.0515843 0.998669i \(-0.516427\pi\)
−0.0515843 + 0.998669i \(0.516427\pi\)
\(422\) 16.2337 0.790244
\(423\) −11.3723 + 22.8665i −0.552939 + 1.11181i
\(424\) −4.37228 −0.212337
\(425\) 13.6277 30.2372i 0.661041 1.46672i
\(426\) 3.37228 14.3537i 0.163388 0.695441i
\(427\) 0 0
\(428\) 6.25544 0.302368
\(429\) −0.744563 + 3.16915i −0.0359478 + 0.153008i
\(430\) −0.510875 + 2.37686i −0.0246366 + 0.114622i
\(431\) 17.0256i 0.820092i 0.912065 + 0.410046i \(0.134487\pi\)
−0.912065 + 0.410046i \(0.865513\pi\)
\(432\) 4.00000 + 3.31662i 0.192450 + 0.159571i
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 5.50000 11.6082i 0.263705 0.556570i
\(436\) −8.11684 −0.388726
\(437\) 4.75372i 0.227401i
\(438\) −3.37228 0.792287i −0.161134 0.0378569i
\(439\) 2.81929i 0.134557i 0.997734 + 0.0672787i \(0.0214317\pi\)
−0.997734 + 0.0672787i \(0.978568\pi\)
\(440\) 0.441578 2.05446i 0.0210514 0.0979423i
\(441\) 0 0
\(442\) 13.2665i 0.631023i
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 3.25544 13.8564i 0.154496 0.657596i
\(445\) −3.00000 0.644810i −0.142214 0.0305669i
\(446\) −0.883156 −0.0418187
\(447\) −3.56930 + 15.1923i −0.168822 + 0.718572i
\(448\) 0 0
\(449\) 20.3971i 0.962598i −0.876557 0.481299i \(-0.840165\pi\)
0.876557 0.481299i \(-0.159835\pi\)
\(450\) 9.50000 + 11.6082i 0.447834 + 0.547215i
\(451\) 6.92820i 0.326236i
\(452\) −14.7446 −0.693526
\(453\) 15.3723 + 3.61158i 0.722253 + 0.169687i
\(454\) 20.8395i 0.978047i
\(455\) 0 0
\(456\) −1.37228 + 5.84096i −0.0642630 + 0.273528i
\(457\) 2.81929i 0.131881i 0.997824 + 0.0659404i \(0.0210047\pi\)
−0.997824 + 0.0659404i \(0.978995\pi\)
\(458\) 13.8564i 0.647467i
\(459\) 22.0000 26.5330i 1.02687 1.23845i
\(460\) −3.00000 0.644810i −0.139876 0.0300644i
\(461\) 23.4891 1.09400 0.546999 0.837133i \(-0.315770\pi\)
0.546999 + 0.837133i \(0.315770\pi\)
\(462\) 0 0
\(463\) 6.72582i 0.312576i −0.987712 0.156288i \(-0.950047\pi\)
0.987712 0.156288i \(-0.0499527\pi\)
\(464\) 3.31662i 0.153970i
\(465\) −12.5584 + 26.5055i −0.582383 + 1.22917i
\(466\) −0.510875 −0.0236658
\(467\) 36.4280i 1.68569i 0.538160 + 0.842843i \(0.319120\pi\)
−0.538160 + 0.842843i \(0.680880\pi\)
\(468\) −5.37228 2.67181i −0.248334 0.123505i
\(469\) 0 0
\(470\) −4.00000 + 18.6101i −0.184506 + 0.858421i
\(471\) −13.4891 3.16915i −0.621546 0.146027i
\(472\) −13.1168 −0.603752
\(473\) 1.02175 0.0469801
\(474\) 15.3723 + 3.61158i 0.706072 + 0.165885i
\(475\) −7.11684 + 15.7908i −0.326543 + 0.724533i
\(476\) 0 0
\(477\) −11.7446 5.84096i −0.537747 0.267439i
\(478\) 23.6588i 1.08213i
\(479\) 2.74456 0.125402 0.0627011 0.998032i \(-0.480029\pi\)
0.0627011 + 0.998032i \(0.480029\pi\)
\(480\) 3.50000 + 1.65831i 0.159752 + 0.0756913i
\(481\) 16.4356i 0.749401i
\(482\) 19.2549i 0.877038i
\(483\) 0 0
\(484\) 10.1168 0.459857
\(485\) −33.0475 7.10313i −1.50061 0.322537i
\(486\) 6.31386 + 14.2525i 0.286402 + 0.646509i
\(487\) 14.5012i 0.657113i −0.944484 0.328556i \(-0.893438\pi\)
0.944484 0.328556i \(-0.106562\pi\)
\(488\) 12.7692i 0.578033i
\(489\) 1.37228 5.84096i 0.0620567 0.264137i
\(490\) 0 0
\(491\) 30.2372i 1.36458i 0.731080 + 0.682292i \(0.239017\pi\)
−0.731080 + 0.682292i \(0.760983\pi\)
\(492\) −12.4307 2.92048i −0.560419 0.131665i
\(493\) −22.0000 −0.990830
\(494\) 6.92820i 0.311715i
\(495\) 3.93070 4.92865i 0.176672 0.221526i
\(496\) 7.57301i 0.340038i
\(497\) 0 0
\(498\) 4.68614 19.9460i 0.209991 0.893803i
\(499\) −6.23369 −0.279058 −0.139529 0.990218i \(-0.544559\pi\)
−0.139529 + 0.990218i \(0.544559\pi\)
\(500\) 9.00000 + 6.63325i 0.402492 + 0.296648i
\(501\) 5.80298 24.6998i 0.259258 1.10350i
\(502\) 1.11684 0.0498472
\(503\) 6.13592i 0.273587i 0.990600 + 0.136793i \(0.0436797\pi\)
−0.990600 + 0.136793i \(0.956320\pi\)
\(504\) 0 0
\(505\) 23.2337 + 4.99377i 1.03389 + 0.222220i
\(506\) 1.28962i 0.0573306i
\(507\) −15.1753 3.56529i −0.673957 0.158340i
\(508\) 7.57301i 0.335998i
\(509\) −11.7446 −0.520569 −0.260284 0.965532i \(-0.583816\pi\)
−0.260284 + 0.965532i \(0.583816\pi\)
\(510\) 11.0000 23.2164i 0.487088 1.02804i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −11.4891 + 13.8564i −0.507257 + 0.611775i
\(514\) 1.87953i 0.0829024i
\(515\) 4.62772 + 0.994667i 0.203922 + 0.0438303i
\(516\) −0.430703 + 1.83324i −0.0189607 + 0.0807039i
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) 6.74456 28.7075i 0.296053 1.26012i
\(520\) −4.37228 0.939764i −0.191737 0.0412114i
\(521\) −14.7446 −0.645971 −0.322986 0.946404i \(-0.604687\pi\)
−0.322986 + 0.946404i \(0.604687\pi\)
\(522\) 4.43070 8.90892i 0.193927 0.389933i
\(523\) −10.2337 −0.447488 −0.223744 0.974648i \(-0.571828\pi\)
−0.223744 + 0.974648i \(0.571828\pi\)
\(524\) 10.3723 0.453115
\(525\) 0 0
\(526\) 7.37228 0.321447
\(527\) 50.2337 2.18821
\(528\) 0.372281 1.58457i 0.0162015 0.0689597i
\(529\) −21.1168 −0.918124
\(530\) −9.55842 2.05446i −0.415191 0.0892399i
\(531\) −35.2337 17.5229i −1.52901 0.760429i
\(532\) 0 0
\(533\) 14.7446 0.638658
\(534\) −2.31386 0.543620i −0.100130 0.0235248i
\(535\) 13.6753 + 2.93932i 0.591233 + 0.127078i
\(536\) 2.37686i 0.102665i
\(537\) 9.37228 39.8921i 0.404444 1.72147i
\(538\) −25.9783 −1.12000
\(539\) 0 0
\(540\) 7.18614 + 9.13014i 0.309242 + 0.392898i
\(541\) 38.3505 1.64882 0.824409 0.565994i \(-0.191508\pi\)
0.824409 + 0.565994i \(0.191508\pi\)
\(542\) 8.86263i 0.380683i
\(543\) −3.17527 + 13.5152i −0.136264 + 0.579991i
\(544\) 6.63325i 0.284398i
\(545\) −17.7446 3.81396i −0.760094 0.163372i
\(546\) 0 0
\(547\) 9.30506i 0.397856i −0.980014 0.198928i \(-0.936254\pi\)
0.980014 0.198928i \(-0.0637460\pi\)
\(548\) −8.74456 −0.373549
\(549\) −17.0584 + 34.2998i −0.728036 + 1.46388i
\(550\) 1.93070 4.28384i 0.0823255 0.182664i
\(551\) 11.4891 0.489453
\(552\) −2.31386 0.543620i −0.0984844 0.0231380i
\(553\) 0 0
\(554\) 9.10268i 0.386736i
\(555\) 13.6277 28.7624i 0.578464 1.22090i
\(556\) 8.21782i 0.348513i
\(557\) 27.8614 1.18053 0.590263 0.807211i \(-0.299024\pi\)
0.590263 + 0.807211i \(0.299024\pi\)
\(558\) −10.1168 + 20.3422i −0.428280 + 0.861153i
\(559\) 2.17448i 0.0919708i
\(560\) 0 0
\(561\) −10.5109 2.46943i −0.443769 0.104260i
\(562\) 11.3870i 0.480330i
\(563\) 1.43710i 0.0605664i −0.999541 0.0302832i \(-0.990359\pi\)
0.999541 0.0302832i \(-0.00964092\pi\)
\(564\) −3.37228 + 14.3537i −0.141999 + 0.604401i
\(565\) −32.2337 6.92820i −1.35608 0.291472i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 8.51278i 0.357188i
\(569\) 11.3870i 0.477367i 0.971097 + 0.238683i \(0.0767158\pi\)
−0.971097 + 0.238683i \(0.923284\pi\)
\(570\) −5.74456 + 12.1244i −0.240613 + 0.507833i
\(571\) −0.233688 −0.00977954 −0.00488977 0.999988i \(-0.501556\pi\)
−0.00488977 + 0.999988i \(0.501556\pi\)
\(572\) 1.87953i 0.0785870i
\(573\) −6.74456 + 28.7075i −0.281758 + 1.19927i
\(574\) 0 0
\(575\) −6.25544 2.81929i −0.260870 0.117573i
\(576\) 2.68614 + 1.33591i 0.111923 + 0.0556628i
\(577\) 35.1168 1.46193 0.730967 0.682413i \(-0.239069\pi\)
0.730967 + 0.682413i \(0.239069\pi\)
\(578\) −27.0000 −1.12305
\(579\) −7.11684 + 30.2921i −0.295766 + 1.25889i
\(580\) 1.55842 7.25061i 0.0647100 0.301065i
\(581\) 0 0
\(582\) −25.4891 5.98844i −1.05656 0.248229i
\(583\) 4.10891i 0.170174i
\(584\) −2.00000 −0.0827606
\(585\) −10.4891 8.36530i −0.433672 0.345863i
\(586\) 21.7244i 0.897426i
\(587\) 0.0549029i 0.00226608i 0.999999 + 0.00113304i \(0.000360659\pi\)
−0.999999 + 0.00113304i \(0.999639\pi\)
\(588\) 0 0
\(589\) −26.2337 −1.08094
\(590\) −28.6753 6.16337i −1.18054 0.253742i
\(591\) 24.0000 + 5.63858i 0.987228 + 0.231940i
\(592\) 8.21782i 0.337750i
\(593\) 27.4179i 1.12592i −0.826485 0.562958i \(-0.809663\pi\)
0.826485 0.562958i \(-0.190337\pi\)
\(594\) 3.11684 3.75906i 0.127886 0.154236i
\(595\) 0 0
\(596\) 9.01011i 0.369069i
\(597\) −0.510875 + 2.17448i −0.0209087 + 0.0889956i
\(598\) 2.74456 0.112234
\(599\) 1.87953i 0.0767954i 0.999263 + 0.0383977i \(0.0122254\pi\)
−0.999263 + 0.0383977i \(0.987775\pi\)
\(600\) 6.87228 + 5.26989i 0.280560 + 0.215142i
\(601\) 19.2549i 0.785425i 0.919661 + 0.392713i \(0.128463\pi\)
−0.919661 + 0.392713i \(0.871537\pi\)
\(602\) 0 0
\(603\) 3.17527 6.38458i 0.129307 0.260000i
\(604\) 9.11684 0.370959
\(605\) 22.1168 + 4.75372i 0.899178 + 0.193266i
\(606\) 17.9198 + 4.21010i 0.727943 + 0.171024i
\(607\) 41.4674 1.68311 0.841554 0.540172i \(-0.181641\pi\)
0.841554 + 0.540172i \(0.181641\pi\)
\(608\) 3.46410i 0.140488i
\(609\) 0 0
\(610\) −6.00000 + 27.9152i −0.242933 + 1.13025i
\(611\) 17.0256i 0.688780i
\(612\) 8.86141 17.8178i 0.358201 0.720244i
\(613\) 26.8280i 1.08357i −0.840517 0.541785i \(-0.817749\pi\)
0.840517 0.541785i \(-0.182251\pi\)
\(614\) −24.1168 −0.973277
\(615\) −25.8030 12.2255i −1.04048 0.492982i
\(616\) 0 0
\(617\) −46.9783 −1.89127 −0.945637 0.325225i \(-0.894560\pi\)
−0.945637 + 0.325225i \(0.894560\pi\)
\(618\) 3.56930 + 0.838574i 0.143578 + 0.0337324i
\(619\) 16.4356i 0.660604i −0.943875 0.330302i \(-0.892849\pi\)
0.943875 0.330302i \(-0.107151\pi\)
\(620\) −3.55842 + 16.5557i −0.142910 + 0.664892i
\(621\) −5.48913 4.55134i −0.220271 0.182639i
\(622\) 20.2337 0.811297
\(623\) 0 0
\(624\) −3.37228 0.792287i −0.134999 0.0317169i
\(625\) 16.5584 + 18.7302i 0.662337 + 0.749206i
\(626\) −3.11684 −0.124574
\(627\) 5.48913 + 1.28962i 0.219215 + 0.0515025i
\(628\) −8.00000 −0.319235
\(629\) −54.5109 −2.17349
\(630\) 0 0
\(631\) 12.8832 0.512870 0.256435 0.966561i \(-0.417452\pi\)
0.256435 + 0.966561i \(0.417452\pi\)
\(632\) 9.11684 0.362649
\(633\) 27.3723 + 6.43087i 1.08795 + 0.255604i
\(634\) −1.11684 −0.0443555
\(635\) 3.55842 16.5557i 0.141212 0.656992i
\(636\) −7.37228 1.73205i −0.292330 0.0686803i
\(637\) 0 0
\(638\) −3.11684 −0.123397
\(639\) 11.3723 22.8665i 0.449880 0.904585i
\(640\) 2.18614 + 0.469882i 0.0864148 + 0.0185737i
\(641\) 9.01011i 0.355878i 0.984042 + 0.177939i \(0.0569430\pi\)
−0.984042 + 0.177939i \(0.943057\pi\)
\(642\) 10.5475 + 2.47805i 0.416278 + 0.0978009i
\(643\) 18.2337 0.719066 0.359533 0.933132i \(-0.382936\pi\)
0.359533 + 0.933132i \(0.382936\pi\)
\(644\) 0 0
\(645\) −1.80298 + 3.80534i −0.0709925 + 0.149835i
\(646\) 22.9783 0.904067
\(647\) 42.0666i 1.65381i 0.562344 + 0.826903i \(0.309900\pi\)
−0.562344 + 0.826903i \(0.690100\pi\)
\(648\) 5.43070 + 7.17687i 0.213338 + 0.281934i
\(649\) 12.3267i 0.483867i
\(650\) −9.11684 4.10891i −0.357592 0.161165i
\(651\) 0 0
\(652\) 3.46410i 0.135665i
\(653\) −16.3723 −0.640697 −0.320348 0.947300i \(-0.603800\pi\)
−0.320348 + 0.947300i \(0.603800\pi\)
\(654\) −13.6861 3.21543i −0.535170 0.125733i
\(655\) 22.6753 + 4.87375i 0.885996 + 0.190433i
\(656\) −7.37228 −0.287839
\(657\) −5.37228 2.67181i −0.209593 0.104237i
\(658\) 0 0
\(659\) 16.1407i 0.628752i 0.949299 + 0.314376i \(0.101795\pi\)
−0.949299 + 0.314376i \(0.898205\pi\)
\(660\) 1.55842 3.28917i 0.0606615 0.128031i
\(661\) 12.7692i 0.496663i 0.968675 + 0.248331i \(0.0798822\pi\)
−0.968675 + 0.248331i \(0.920118\pi\)
\(662\) −24.2337 −0.941869
\(663\) −5.25544 + 22.3692i −0.204104 + 0.868747i
\(664\) 11.8294i 0.459070i
\(665\) 0 0
\(666\) 10.9783 22.0742i 0.425399 0.855359i
\(667\) 4.55134i 0.176229i
\(668\) 14.6487i 0.566775i
\(669\) −1.48913 0.349857i −0.0575729 0.0135262i
\(670\) 1.11684 5.19615i 0.0431474 0.200745i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 46.9678i 1.81047i 0.424907 + 0.905237i \(0.360307\pi\)
−0.424907 + 0.905237i \(0.639693\pi\)
\(674\) 0.644810i 0.0248372i
\(675\) 11.4198 + 23.3364i 0.439549 + 0.898218i
\(676\) −9.00000 −0.346154
\(677\) 1.82462i 0.0701260i 0.999385 + 0.0350630i \(0.0111632\pi\)
−0.999385 + 0.0350630i \(0.988837\pi\)
\(678\) −24.8614 5.84096i −0.954797 0.224321i
\(679\) 0 0
\(680\) 3.11684 14.5012i 0.119526 0.556096i
\(681\) −8.25544 + 35.1383i −0.316349 + 1.34650i
\(682\) 7.11684 0.272518
\(683\) 31.9783 1.22361 0.611807 0.791007i \(-0.290443\pi\)
0.611807 + 0.791007i \(0.290443\pi\)
\(684\) −4.62772 + 9.30506i −0.176945 + 0.355788i
\(685\) −19.1168 4.10891i −0.730417 0.156993i
\(686\) 0 0
\(687\) 5.48913 23.3639i 0.209423 0.891386i
\(688\) 1.08724i 0.0414507i
\(689\) 8.74456 0.333141
\(690\) −4.80298 2.27567i −0.182847 0.0866333i
\(691\) 9.50744i 0.361680i −0.983513 0.180840i \(-0.942118\pi\)
0.983513 0.180840i \(-0.0578817\pi\)
\(692\) 17.0256i 0.647214i
\(693\) 0 0
\(694\) 1.88316 0.0714836
\(695\) −3.86141 + 17.9653i −0.146472 + 0.681463i
\(696\) 1.31386 5.59230i 0.0498017 0.211975i
\(697\) 48.9022i 1.85230i
\(698\) 25.7407i 0.974300i
\(699\) −0.861407 0.202380i −0.0325814 0.00765470i
\(700\) 0 0
\(701\) 39.2473i 1.48235i −0.671313 0.741174i \(-0.734269\pi\)
0.671313 0.741174i \(-0.265731\pi\)
\(702\) −8.00000 6.63325i −0.301941 0.250356i
\(703\) 28.4674 1.07367
\(704\) 0.939764i 0.0354187i
\(705\) −14.1168 + 29.7947i −0.531671 + 1.12213i
\(706\) 12.2718i 0.461857i
\(707\) 0 0
\(708\) −22.1168 5.19615i −0.831202 0.195283i
\(709\) 12.1168 0.455058 0.227529 0.973771i \(-0.426935\pi\)
0.227529 + 0.973771i \(0.426935\pi\)
\(710\) 4.00000 18.6101i 0.150117 0.698426i
\(711\) 24.4891 + 12.1793i 0.918414 + 0.456758i
\(712\) −1.37228 −0.0514284
\(713\) 10.3923i 0.389195i
\(714\) 0 0
\(715\) −0.883156 + 4.10891i −0.0330282 + 0.153665i
\(716\) 23.6588i 0.884171i
\(717\) 9.37228 39.8921i 0.350014 1.48980i
\(718\) 27.4179i 1.02323i
\(719\) 44.7446 1.66869 0.834345 0.551242i \(-0.185846\pi\)
0.834345 + 0.551242i \(0.185846\pi\)
\(720\) 5.24456 + 4.18265i 0.195453 + 0.155878i
\(721\) 0 0
\(722\) 7.00000 0.260513
\(723\) 7.62772 32.4665i 0.283678 1.20744i
\(724\) 8.01544i 0.297892i
\(725\) 6.81386 15.1186i 0.253060 0.561490i
\(726\) 17.0584 + 4.00772i 0.633097 + 0.148741i
\(727\) 19.0000 0.704671 0.352335 0.935874i \(-0.385388\pi\)
0.352335 + 0.935874i \(0.385388\pi\)
\(728\) 0 0
\(729\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(730\) −4.37228 0.939764i −0.161825 0.0347822i
\(731\) 7.21194 0.266743
\(732\) −5.05842 + 21.5306i −0.186965 + 0.795794i
\(733\) 32.4674 1.19921 0.599605 0.800296i \(-0.295324\pi\)
0.599605 + 0.800296i \(0.295324\pi\)
\(734\) −13.2337 −0.488464
\(735\) 0 0
\(736\) −1.37228 −0.0505830
\(737\) −2.23369 −0.0822790
\(738\) −19.8030 9.84868i −0.728958 0.362535i
\(739\) −1.76631 −0.0649748 −0.0324874 0.999472i \(-0.510343\pi\)
−0.0324874 + 0.999472i \(0.510343\pi\)
\(740\) 3.86141 17.9653i 0.141948 0.660418i
\(741\) 2.74456 11.6819i 0.100824 0.429146i
\(742\) 0 0
\(743\) 21.6060 0.792646 0.396323 0.918111i \(-0.370286\pi\)
0.396323 + 0.918111i \(0.370286\pi\)
\(744\) −3.00000 + 12.7692i −0.109985 + 0.468140i
\(745\) −4.23369 + 19.6974i −0.155110 + 0.721656i
\(746\) 23.3639i 0.855411i
\(747\) 15.8030 31.7754i 0.578201 1.16260i
\(748\) −6.23369 −0.227926
\(749\) 0 0
\(750\) 12.5475 + 14.7499i 0.458172 + 0.538590i
\(751\) 24.8832 0.907999 0.454000 0.891002i \(-0.349997\pi\)
0.454000 + 0.891002i \(0.349997\pi\)
\(752\) 8.51278i 0.310429i
\(753\) 1.88316 + 0.442430i 0.0686260 + 0.0161231i
\(754\) 6.63325i 0.241569i
\(755\) 19.9307 + 4.28384i 0.725353 + 0.155905i
\(756\) 0 0
\(757\) 25.5383i 0.928206i 0.885781 + 0.464103i \(0.153623\pi\)
−0.885781 + 0.464103i \(0.846377\pi\)
\(758\) −12.2337 −0.444348
\(759\) −0.510875 + 2.17448i −0.0185436 + 0.0789287i
\(760\) −1.62772 + 7.57301i −0.0590436 + 0.274702i
\(761\) 7.02175 0.254538 0.127269 0.991868i \(-0.459379\pi\)
0.127269 + 0.991868i \(0.459379\pi\)
\(762\) 3.00000 12.7692i 0.108679 0.462578i
\(763\) 0 0
\(764\) 17.0256i 0.615963i
\(765\) 27.7446 34.7885i 1.00311 1.25778i
\(766\) 15.6434i 0.565218i
\(767\) 26.2337 0.947244
\(768\) 1.68614 + 0.396143i 0.0608434 + 0.0142946i
\(769\) 30.5321i 1.10102i −0.834830 0.550508i \(-0.814434\pi\)
0.834830 0.550508i \(-0.185566\pi\)
\(770\) 0 0
\(771\) 0.744563 3.16915i 0.0268148 0.114134i
\(772\) 17.9653i 0.646586i
\(773\) 8.51278i 0.306183i 0.988212 + 0.153092i \(0.0489230\pi\)
−0.988212 + 0.153092i \(0.951077\pi\)
\(774\) −1.45245 + 2.92048i −0.0522073 + 0.104975i
\(775\) −15.5584 + 34.5210i −0.558875 + 1.24003i
\(776\) −15.1168 −0.542663
\(777\) 0 0
\(778\) 7.51811i 0.269537i
\(779\) 25.5383i 0.915006i
\(780\) −7.00000 3.31662i −0.250640 0.118754i
\(781\) −8.00000 −0.286263
\(782\) 9.10268i 0.325511i
\(783\) 11.0000 13.2665i 0.393108 0.474106i
\(784\) 0 0
\(785\) −17.4891 3.75906i −0.624214 0.134166i
\(786\) 17.4891 + 4.10891i 0.623816 + 0.146560i
\(787\) −9.88316 −0.352296 −0.176148 0.984364i \(-0.556364\pi\)
−0.176148 + 0.984364i \(0.556364\pi\)
\(788\) 14.2337 0.507054
\(789\) 12.4307 + 2.92048i 0.442545 + 0.103972i
\(790\) 19.9307 + 4.28384i 0.709103 + 0.152412i
\(791\) 0 0
\(792\) 1.25544 2.52434i 0.0446100 0.0896984i
\(793\) 25.5383i 0.906893i
\(794\) −8.00000 −0.283909
\(795\) −15.3030 7.25061i −0.542741 0.257153i
\(796\) 1.28962i 0.0457094i
\(797\) 0.939764i 0.0332881i 0.999861 + 0.0166441i \(0.00529822\pi\)
−0.999861 + 0.0166441i \(0.994702\pi\)
\(798\) 0 0
\(799\) 56.4674 1.99767
\(800\) 4.55842 + 2.05446i 0.161165 + 0.0726360i
\(801\) −3.68614 1.83324i −0.130243 0.0647744i
\(802\) 16.5282i 0.583632i
\(803\) 1.87953i 0.0663271i
\(804\) 0.941578 4.00772i 0.0332069 0.141341i
\(805\) 0 0
\(806\) 15.1460i 0.533496i
\(807\) −43.8030 10.2911i −1.54194 0.362264i
\(808\) 10.6277 0.373882
\(809\) 42.0666i 1.47898i −0.673167 0.739491i \(-0.735066\pi\)
0.673167 0.739491i \(-0.264934\pi\)
\(810\) 8.50000 + 18.2414i 0.298660 + 0.640939i
\(811\) 10.3923i 0.364923i −0.983213 0.182462i \(-0.941593\pi\)
0.983213 0.182462i \(-0.0584065\pi\)
\(812\) 0 0
\(813\) 3.51087 14.9436i 0.123132 0.524097i
\(814\) −7.72281 −0.270684
\(815\) 1.62772 7.57301i 0.0570165 0.265271i
\(816\) 2.62772 11.1846i 0.0919886 0.391539i
\(817\) −3.76631 −0.131767
\(818\) 4.31129i 0.150741i
\(819\) 0 0
\(820\) −16.1168 3.46410i −0.562825 0.120972i
\(821\) 4.69882i 0.163990i 0.996633 + 0.0819950i \(0.0261291\pi\)
−0.996633 + 0.0819950i \(0.973871\pi\)
\(822\) −14.7446 3.46410i −0.514276 0.120824i
\(823\) 13.6540i 0.475949i −0.971271 0.237975i \(-0.923516\pi\)
0.971271 0.237975i \(-0.0764835\pi\)
\(824\) 2.11684 0.0737438
\(825\) 4.95245 6.45832i 0.172422 0.224850i
\(826\) 0 0
\(827\) 33.0000 1.14752 0.573761 0.819023i \(-0.305484\pi\)
0.573761 + 0.819023i \(0.305484\pi\)
\(828\) −3.68614 1.83324i −0.128102 0.0637095i
\(829\) 1.28962i 0.0447904i 0.999749 + 0.0223952i \(0.00712920\pi\)
−0.999749 + 0.0223952i \(0.992871\pi\)
\(830\) 5.55842 25.8607i 0.192936 0.897639i
\(831\) 3.60597 15.3484i 0.125090 0.532430i
\(832\) −2.00000 −0.0693375
\(833\) 0 0
\(834\) −3.25544 + 13.8564i −0.112727 + 0.479808i
\(835\) 6.88316 32.0241i 0.238201 1.10824i
\(836\) 3.25544 0.112592
\(837\) −25.1168 + 30.2921i −0.868165 + 1.04705i
\(838\) 6.51087 0.224914
\(839\) 55.7228 1.92377 0.961883 0.273463i \(-0.0881690\pi\)
0.961883 + 0.273463i \(0.0881690\pi\)
\(840\) 0 0
\(841\) 18.0000 0.620690
\(842\) −2.11684 −0.0729513
\(843\) −4.51087 + 19.2000i −0.155363 + 0.661284i
\(844\) 16.2337 0.558787
\(845\) −19.6753 4.22894i −0.676850 0.145480i
\(846\) −11.3723 + 22.8665i −0.390987 + 0.786167i
\(847\) 0 0
\(848\) −4.37228 −0.150145
\(849\) 26.9783 + 6.33830i 0.925891 + 0.217530i
\(850\) 13.6277 30.2372i 0.467427 1.03713i
\(851\) 11.2772i 0.386576i
\(852\) 3.37228 14.3537i 0.115532 0.491751i
\(853\) 38.4674 1.31710 0.658549 0.752538i \(-0.271171\pi\)
0.658549 + 0.752538i \(0.271171\pi\)
\(854\) 0 0
\(855\) −14.4891 + 18.1677i −0.495518 + 0.621322i
\(856\) 6.25544 0.213806
\(857\) 24.5437i 0.838396i 0.907895 + 0.419198i \(0.137689\pi\)
−0.907895 + 0.419198i \(0.862311\pi\)
\(858\) −0.744563 + 3.16915i −0.0254189 + 0.108193i
\(859\) 46.7277i 1.59433i 0.603762 + 0.797164i \(0.293668\pi\)
−0.603762 + 0.797164i \(0.706332\pi\)
\(860\) −0.510875 + 2.37686i −0.0174207 + 0.0810503i
\(861\) 0 0
\(862\) 17.0256i 0.579893i
\(863\) 13.3723 0.455198 0.227599 0.973755i \(-0.426913\pi\)
0.227599 + 0.973755i \(0.426913\pi\)
\(864\) 4.00000 + 3.31662i 0.136083 + 0.112834i
\(865\) 8.00000 37.2203i 0.272008 1.26553i
\(866\) 34.0000 1.15537
\(867\) −45.5258 10.6959i −1.54614 0.363251i
\(868\) 0 0
\(869\) 8.56768i 0.290639i
\(870\) 5.50000 11.6082i 0.186467 0.393554i
\(871\) 4.75372i 0.161074i
\(872\) −8.11684 −0.274871
\(873\) −40.6060 20.1947i −1.37430 0.683487i
\(874\) 4.75372i 0.160797i
\(875\) 0 0
\(876\) −3.37228 0.792287i −0.113939 0.0267689i
\(877\) 28.1176i 0.949463i 0.880131 + 0.474731i \(0.157455\pi\)
−0.880131 + 0.474731i \(0.842545\pi\)
\(878\) 2.81929i 0.0951465i
\(879\) −8.60597 + 36.6303i −0.290272 + 1.23551i
\(880\) 0.441578 2.05446i 0.0148856 0.0692557i
\(881\) −0.350532 −0.0118097 −0.00590486 0.999983i \(-0.501880\pi\)
−0.00590486 + 0.999983i \(0.501880\pi\)
\(882\) 0 0
\(883\) 44.5532i 1.49934i 0.661815 + 0.749668i \(0.269787\pi\)
−0.661815 + 0.749668i \(0.730213\pi\)
\(884\) 13.2665i 0.446201i
\(885\) −45.9090 21.7518i −1.54321 0.731180i
\(886\) 9.00000 0.302361
\(887\) 8.12525i 0.272819i −0.990653 0.136410i \(-0.956444\pi\)
0.990653 0.136410i \(-0.0435563\pi\)
\(888\) 3.25544 13.8564i 0.109245 0.464991i
\(889\) 0 0
\(890\) −3.00000 0.644810i −0.100560 0.0216141i
\(891\) 6.74456 5.10358i 0.225951 0.170976i
\(892\) −0.883156 −0.0295703
\(893\) −29.4891 −0.986816
\(894\) −3.56930 + 15.1923i −0.119375 + 0.508107i
\(895\) 11.1168 51.7215i 0.371595 1.72886i
\(896\) 0 0
\(897\) 4.62772 + 1.08724i 0.154515 + 0.0363019i
\(898\) 20.3971i 0.680659i
\(899\) 25.1168 0.837694
\(900\) 9.50000 + 11.6082i 0.316667 + 0.386940i
\(901\) 29.0024i 0.966211i
\(902\) 6.92820i 0.230684i
\(903\) 0 0
\(904\) −14.7446 −0.490397
\(905\) −3.76631 + 17.5229i −0.125196 + 0.582480i
\(906\) 15.3723 + 3.61158i 0.510710 + 0.119987i
\(907\) 4.95610i 0.164565i −0.996609 0.0822823i \(-0.973779\pi\)
0.996609 0.0822823i \(-0.0262209\pi\)
\(908\) 20.8395i 0.691584i
\(909\) 28.5475 + 14.1976i 0.946862 + 0.470906i
\(910\) 0 0
\(911\) 37.8102i 1.25271i 0.779539 + 0.626353i \(0.215453\pi\)
−0.779539 + 0.626353i \(0.784547\pi\)
\(912\) −1.37228 + 5.84096i −0.0454408 + 0.193414i
\(913\) −11.1168 −0.367914
\(914\) 2.81929i 0.0932539i
\(915\) −21.1753 + 44.6921i −0.700033 + 1.47747i
\(916\) 13.8564i 0.457829i
\(917\) 0 0
\(918\) 22.0000 26.5330i 0.726108 0.875719i
\(919\) 16.2337 0.535500 0.267750 0.963488i \(-0.413720\pi\)
0.267750 + 0.963488i \(0.413720\pi\)
\(920\) −3.00000 0.644810i −0.0989071 0.0212588i
\(921\) −40.6644 9.55373i −1.33994 0.314806i
\(922\) 23.4891 0.773573
\(923\) 17.0256i 0.560403i
\(924\) 0 0
\(925\) 16.8832 37.4603i 0.555115 1.23169i
\(926\) 6.72582i 0.221024i
\(927\) 5.68614 + 2.82791i 0.186757 + 0.0928807i
\(928\) 3.31662i 0.108874i
\(929\) −34.1168 −1.11934 −0.559669 0.828716i \(-0.689072\pi\)
−0.559669 + 0.828716i \(0.689072\pi\)
\(930\) −12.5584 + 26.5055i −0.411807 + 0.869151i
\(931\) 0 0
\(932\) −0.510875 −0.0167343
\(933\) 34.1168 + 8.01544i 1.11694 + 0.262414i
\(934\) 36.4280i 1.19196i
\(935\) −13.6277 2.92910i −0.445674 0.0957917i
\(936\) −5.37228 2.67181i −0.175599 0.0873310i
\(937\) 1.35053 0.0441200 0.0220600 0.999757i \(-0.492978\pi\)
0.0220600 + 0.999757i \(0.492978\pi\)
\(938\) 0 0
\(939\) −5.25544 1.23472i −0.171505 0.0402935i
\(940\) −4.00000 + 18.6101i −0.130466 + 0.606995i
\(941\) −27.3505 −0.891602 −0.445801 0.895132i \(-0.647081\pi\)
−0.445801 + 0.895132i \(0.647081\pi\)
\(942\) −13.4891 3.16915i −0.439499 0.103256i
\(943\) 10.1168 0.329450
\(944\) −13.1168 −0.426917
\(945\) 0 0
\(946\) 1.02175 0.0332199
\(947\) 25.8832 0.841090 0.420545 0.907272i \(-0.361839\pi\)
0.420545 + 0.907272i \(0.361839\pi\)
\(948\) 15.3723 + 3.61158i 0.499268 + 0.117299i
\(949\) 4.00000 0.129845
\(950\) −7.11684 + 15.7908i −0.230901 + 0.512322i
\(951\) −1.88316 0.442430i −0.0610655 0.0143468i
\(952\) 0 0
\(953\) −48.0000 −1.55487 −0.777436 0.628962i \(-0.783480\pi\)
−0.777436 + 0.628962i \(0.783480\pi\)
\(954\) −11.7446 5.84096i −0.380244 0.189108i
\(955\) −8.00000 + 37.2203i −0.258874 + 1.20442i
\(956\) 23.6588i 0.765180i
\(957\) −5.25544 1.23472i −0.169884 0.0399127i
\(958\) 2.74456 0.0886728
\(959\) 0 0
\(960\) 3.50000 + 1.65831i 0.112962 + 0.0535218i
\(961\) −26.3505 −0.850017
\(962\) 16.4356i 0.529907i
\(963\) 16.8030 + 8.35668i 0.541469 + 0.269290i
\(964\) 19.2549i 0.620160i
\(965\) −8.44158 + 39.2747i −0.271744 + 1.26430i
\(966\) 0 0
\(967\) 27.6751i 0.889973i −0.895537 0.444986i \(-0.853209\pi\)
0.895537 0.444986i \(-0.146791\pi\)
\(968\) 10.1168 0.325168
\(969\) 38.7446 + 9.10268i 1.24465 + 0.292420i
\(970\) −33.0475 7.10313i −1.06109 0.228068i
\(971\) −34.3723 −1.10306 −0.551530 0.834155i \(-0.685956\pi\)
−0.551530 + 0.834155i \(0.685956\pi\)
\(972\) 6.31386 + 14.2525i 0.202517 + 0.457151i
\(973\) 0 0
\(974\) 14.5012i 0.464649i
\(975\) −13.7446 10.5398i −0.440178 0.337543i
\(976\) 12.7692i 0.408731i
\(977\) 28.4674 0.910752 0.455376 0.890299i \(-0.349505\pi\)
0.455376 + 0.890299i \(0.349505\pi\)
\(978\) 1.37228 5.84096i 0.0438807 0.186773i
\(979\) 1.28962i 0.0412164i
\(980\) 0 0
\(981\) −21.8030 10.8434i −0.696116 0.346202i
\(982\) 30.2372i 0.964906i
\(983\) 25.0410i 0.798684i −0.916802 0.399342i \(-0.869239\pi\)
0.916802 0.399342i \(-0.130761\pi\)
\(984\) −12.4307 2.92048i −0.396276 0.0931015i
\(985\) 31.1168 + 6.68815i 0.991465 + 0.213102i
\(986\) −22.0000 −0.700623
\(987\) 0 0
\(988\) 6.92820i 0.220416i
\(989\) 1.49200i 0.0474428i
\(990\) 3.93070 4.92865i 0.124926 0.156643i
\(991\) 23.3505 0.741754 0.370877 0.928682i \(-0.379057\pi\)
0.370877 + 0.928682i \(0.379057\pi\)
\(992\) 7.57301i 0.240443i
\(993\) −40.8614 9.60002i −1.29670 0.304647i
\(994\) 0 0
\(995\) −0.605969 + 2.81929i −0.0192105 + 0.0893775i
\(996\) 4.68614 19.9460i 0.148486 0.632014i
\(997\) 38.4674 1.21827 0.609137 0.793065i \(-0.291516\pi\)
0.609137 + 0.793065i \(0.291516\pi\)
\(998\) −6.23369 −0.197324
\(999\) 27.2554 32.8713i 0.862324 1.04000i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1470.2.d.d.1469.4 4
3.2 odd 2 1470.2.d.b.1469.3 4
5.4 even 2 1470.2.d.a.1469.1 4
7.4 even 3 210.2.t.a.89.1 yes 4
7.5 odd 6 210.2.t.b.59.2 yes 4
7.6 odd 2 1470.2.d.c.1469.1 4
15.14 odd 2 1470.2.d.c.1469.2 4
21.5 even 6 210.2.t.d.59.1 yes 4
21.11 odd 6 210.2.t.c.89.1 yes 4
21.20 even 2 1470.2.d.a.1469.2 4
35.4 even 6 210.2.t.d.89.2 yes 4
35.12 even 12 1050.2.s.d.101.3 8
35.18 odd 12 1050.2.s.e.551.4 8
35.19 odd 6 210.2.t.c.59.1 yes 4
35.32 odd 12 1050.2.s.e.551.1 8
35.33 even 12 1050.2.s.d.101.2 8
35.34 odd 2 1470.2.d.b.1469.4 4
105.32 even 12 1050.2.s.d.551.3 8
105.47 odd 12 1050.2.s.e.101.1 8
105.53 even 12 1050.2.s.d.551.2 8
105.68 odd 12 1050.2.s.e.101.4 8
105.74 odd 6 210.2.t.b.89.2 yes 4
105.89 even 6 210.2.t.a.59.2 4
105.104 even 2 inner 1470.2.d.d.1469.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.a.59.2 4 105.89 even 6
210.2.t.a.89.1 yes 4 7.4 even 3
210.2.t.b.59.2 yes 4 7.5 odd 6
210.2.t.b.89.2 yes 4 105.74 odd 6
210.2.t.c.59.1 yes 4 35.19 odd 6
210.2.t.c.89.1 yes 4 21.11 odd 6
210.2.t.d.59.1 yes 4 21.5 even 6
210.2.t.d.89.2 yes 4 35.4 even 6
1050.2.s.d.101.2 8 35.33 even 12
1050.2.s.d.101.3 8 35.12 even 12
1050.2.s.d.551.2 8 105.53 even 12
1050.2.s.d.551.3 8 105.32 even 12
1050.2.s.e.101.1 8 105.47 odd 12
1050.2.s.e.101.4 8 105.68 odd 12
1050.2.s.e.551.1 8 35.32 odd 12
1050.2.s.e.551.4 8 35.18 odd 12
1470.2.d.a.1469.1 4 5.4 even 2
1470.2.d.a.1469.2 4 21.20 even 2
1470.2.d.b.1469.3 4 3.2 odd 2
1470.2.d.b.1469.4 4 35.34 odd 2
1470.2.d.c.1469.1 4 7.6 odd 2
1470.2.d.c.1469.2 4 15.14 odd 2
1470.2.d.d.1469.3 4 105.104 even 2 inner
1470.2.d.d.1469.4 4 1.1 even 1 trivial