Properties

Label 1470.2.d.a.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 \(-1.18614 - 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 1470.1469
Dual form 1470.2.d.a.1469.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +(1.18614 + 1.26217i) q^{3} +1.00000 q^{4} +(-0.686141 - 2.12819i) q^{5} +(-1.18614 - 1.26217i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(1.18614 + 1.26217i) q^{3} +1.00000 q^{4} +(-0.686141 - 2.12819i) q^{5} +(-1.18614 - 1.26217i) q^{6} -1.00000 q^{8} +(-0.186141 + 2.99422i) q^{9} +(0.686141 + 2.12819i) q^{10} -4.25639i q^{11} +(1.18614 + 1.26217i) q^{12} +2.00000 q^{13} +(1.87228 - 3.39036i) q^{15} +1.00000 q^{16} -6.63325i q^{17} +(0.186141 - 2.99422i) q^{18} +3.46410i q^{19} +(-0.686141 - 2.12819i) q^{20} +4.25639i q^{22} -4.37228 q^{23} +(-1.18614 - 1.26217i) q^{24} +(-4.05842 + 2.92048i) q^{25} -2.00000 q^{26} +(-4.00000 + 3.31662i) q^{27} +3.31662i q^{29} +(-1.87228 + 3.39036i) q^{30} -2.37686i q^{31} -1.00000 q^{32} +(5.37228 - 5.04868i) q^{33} +6.63325i q^{34} +(-0.186141 + 2.99422i) q^{36} -11.6819i q^{37} -3.46410i q^{38} +(2.37228 + 2.52434i) q^{39} +(0.686141 + 2.12819i) q^{40} -1.62772 q^{41} -11.0371i q^{43} -4.25639i q^{44} +(6.50000 - 1.65831i) q^{45} +4.37228 q^{46} -1.87953i q^{47} +(1.18614 + 1.26217i) q^{48} +(4.05842 - 2.92048i) q^{50} +(8.37228 - 7.86797i) q^{51} +2.00000 q^{52} -1.37228 q^{53} +(4.00000 - 3.31662i) q^{54} +(-9.05842 + 2.92048i) q^{55} +(-4.37228 + 4.10891i) q^{57} -3.31662i q^{58} +4.11684 q^{59} +(1.87228 - 3.39036i) q^{60} +2.81929i q^{61} +2.37686i q^{62} +1.00000 q^{64} +(-1.37228 - 4.25639i) q^{65} +(-5.37228 + 5.04868i) q^{66} -7.57301i q^{67} -6.63325i q^{68} +(-5.18614 - 5.51856i) q^{69} -1.87953i q^{71} +(0.186141 - 2.99422i) q^{72} +2.00000 q^{73} +11.6819i q^{74} +(-8.50000 - 1.65831i) q^{75} +3.46410i q^{76} +(-2.37228 - 2.52434i) q^{78} -8.11684 q^{79} +(-0.686141 - 2.12819i) q^{80} +(-8.93070 - 1.11469i) q^{81} +1.62772 q^{82} -1.43710i q^{83} +(-14.1168 + 4.55134i) q^{85} +11.0371i q^{86} +(-4.18614 + 3.93398i) q^{87} +4.25639i q^{88} +4.37228 q^{89} +(-6.50000 + 1.65831i) q^{90} -4.37228 q^{92} +(3.00000 - 2.81929i) q^{93} +1.87953i q^{94} +(7.37228 - 2.37686i) q^{95} +(-1.18614 - 1.26217i) q^{96} -2.11684 q^{97} +(12.7446 + 0.792287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} - q^{3} + 4 q^{4} + 3 q^{5} + q^{6} - 4 q^{8} + 5 q^{9} - 3 q^{10} - q^{12} + 8 q^{13} - 4 q^{15} + 4 q^{16} - 5 q^{18} + 3 q^{20} - 6 q^{23} + q^{24} + q^{25} - 8 q^{26} - 16 q^{27} + 4 q^{30} - 4 q^{32} + 10 q^{33} + 5 q^{36} - 2 q^{39} - 3 q^{40} - 18 q^{41} + 26 q^{45} + 6 q^{46} - q^{48} - q^{50} + 22 q^{51} + 8 q^{52} + 6 q^{53} + 16 q^{54} - 19 q^{55} - 6 q^{57} - 18 q^{59} - 4 q^{60} + 4 q^{64} + 6 q^{65} - 10 q^{66} - 15 q^{69} - 5 q^{72} + 8 q^{73} - 34 q^{75} + 2 q^{78} + 2 q^{79} + 3 q^{80} - 7 q^{81} + 18 q^{82} - 22 q^{85} - 11 q^{87} + 6 q^{89} - 26 q^{90} - 6 q^{92} + 12 q^{93} + 18 q^{95} + q^{96} + 26 q^{97} + 28 q^{99}+O(q^{100}) \) 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
\(3\) 1.18614 + 1.26217i 0.684819 + 0.728714i
\(4\) 1.00000 0.500000
\(5\) −0.686141 2.12819i −0.306851 0.951757i
\(6\) −1.18614 1.26217i −0.484240 0.515278i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.186141 + 2.99422i −0.0620469 + 0.998073i
\(10\) 0.686141 + 2.12819i 0.216977 + 0.672994i
\(11\) 4.25639i 1.28335i −0.766977 0.641675i \(-0.778240\pi\)
0.766977 0.641675i \(-0.221760\pi\)
\(12\) 1.18614 + 1.26217i 0.342409 + 0.364357i
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 1.87228 3.39036i 0.483421 0.875388i
\(16\) 1.00000 0.250000
\(17\) 6.63325i 1.60880i −0.594089 0.804400i \(-0.702487\pi\)
0.594089 0.804400i \(-0.297513\pi\)
\(18\) 0.186141 2.99422i 0.0438738 0.705744i
\(19\) 3.46410i 0.794719i 0.917663 + 0.397360i \(0.130073\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −0.686141 2.12819i −0.153426 0.475879i
\(21\) 0 0
\(22\) 4.25639i 0.907465i
\(23\) −4.37228 −0.911684 −0.455842 0.890061i \(-0.650662\pi\)
−0.455842 + 0.890061i \(0.650662\pi\)
\(24\) −1.18614 1.26217i −0.242120 0.257639i
\(25\) −4.05842 + 2.92048i −0.811684 + 0.584096i
\(26\) −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 \(0.0996399\pi\)
−0.951405 + 0.307941i \(0.900360\pi\)
\(30\) −1.87228 + 3.39036i −0.341830 + 0.618993i
\(31\) 2.37686i 0.426897i −0.976954 0.213448i \(-0.931530\pi\)
0.976954 0.213448i \(-0.0684695\pi\)
\(32\) −1.00000 −0.176777
\(33\) 5.37228 5.04868i 0.935194 0.878862i
\(34\) 6.63325i 1.13759i
\(35\) 0 0
\(36\) −0.186141 + 2.99422i −0.0310234 + 0.499037i
\(37\) 11.6819i 1.92050i −0.279147 0.960248i \(-0.590052\pi\)
0.279147 0.960248i \(-0.409948\pi\)
\(38\) 3.46410i 0.561951i
\(39\) 2.37228 + 2.52434i 0.379869 + 0.404218i
\(40\) 0.686141 + 2.12819i 0.108488 + 0.336497i
\(41\) −1.62772 −0.254207 −0.127103 0.991889i \(-0.540568\pi\)
−0.127103 + 0.991889i \(0.540568\pi\)
\(42\) 0 0
\(43\) 11.0371i 1.68314i −0.540145 0.841572i \(-0.681631\pi\)
0.540145 0.841572i \(-0.318369\pi\)
\(44\) 4.25639i 0.641675i
\(45\) 6.50000 1.65831i 0.968963 0.247207i
\(46\) 4.37228 0.644658
\(47\) 1.87953i 0.274157i −0.990560 0.137079i \(-0.956229\pi\)
0.990560 0.137079i \(-0.0437713\pi\)
\(48\) 1.18614 + 1.26217i 0.171205 + 0.182178i
\(49\) 0 0
\(50\) 4.05842 2.92048i 0.573948 0.413018i
\(51\) 8.37228 7.86797i 1.17235 1.10174i
\(52\) 2.00000 0.277350
\(53\) −1.37228 −0.188497 −0.0942487 0.995549i \(-0.530045\pi\)
−0.0942487 + 0.995549i \(0.530045\pi\)
\(54\) 4.00000 3.31662i 0.544331 0.451335i
\(55\) −9.05842 + 2.92048i −1.22144 + 0.393798i
\(56\) 0 0
\(57\) −4.37228 + 4.10891i −0.579123 + 0.544239i
\(58\) 3.31662i 0.435494i
\(59\) 4.11684 0.535967 0.267984 0.963423i \(-0.413643\pi\)
0.267984 + 0.963423i \(0.413643\pi\)
\(60\) 1.87228 3.39036i 0.241710 0.437694i
\(61\) 2.81929i 0.360973i 0.983577 + 0.180487i \(0.0577673\pi\)
−0.983577 + 0.180487i \(0.942233\pi\)
\(62\) 2.37686i 0.301862i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.37228 4.25639i −0.170211 0.527940i
\(66\) −5.37228 + 5.04868i −0.661282 + 0.621449i
\(67\) 7.57301i 0.925191i −0.886569 0.462595i \(-0.846918\pi\)
0.886569 0.462595i \(-0.153082\pi\)
\(68\) 6.63325i 0.804400i
\(69\) −5.18614 5.51856i −0.624338 0.664356i
\(70\) 0 0
\(71\) 1.87953i 0.223059i −0.993761 0.111529i \(-0.964425\pi\)
0.993761 0.111529i \(-0.0355749\pi\)
\(72\) 0.186141 2.99422i 0.0219369 0.352872i
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 11.6819i 1.35800i
\(75\) −8.50000 1.65831i −0.981495 0.191485i
\(76\) 3.46410i 0.397360i
\(77\) 0 0
\(78\) −2.37228 2.52434i −0.268608 0.285825i
\(79\) −8.11684 −0.913216 −0.456608 0.889668i \(-0.650936\pi\)
−0.456608 + 0.889668i \(0.650936\pi\)
\(80\) −0.686141 2.12819i −0.0767129 0.237939i
\(81\) −8.93070 1.11469i −0.992300 0.123855i
\(82\) 1.62772 0.179751
\(83\) 1.43710i 0.157742i −0.996885 0.0788710i \(-0.974868\pi\)
0.996885 0.0788710i \(-0.0251315\pi\)
\(84\) 0 0
\(85\) −14.1168 + 4.55134i −1.53119 + 0.493662i
\(86\) 11.0371i 1.19016i
\(87\) −4.18614 + 3.93398i −0.448801 + 0.421767i
\(88\) 4.25639i 0.453733i
\(89\) 4.37228 0.463461 0.231730 0.972780i \(-0.425561\pi\)
0.231730 + 0.972780i \(0.425561\pi\)
\(90\) −6.50000 + 1.65831i −0.685160 + 0.174801i
\(91\) 0 0
\(92\) −4.37228 −0.455842
\(93\) 3.00000 2.81929i 0.311086 0.292347i
\(94\) 1.87953i 0.193858i
\(95\) 7.37228 2.37686i 0.756380 0.243861i
\(96\) −1.18614 1.26217i −0.121060 0.128820i
\(97\) −2.11684 −0.214933 −0.107466 0.994209i \(-0.534274\pi\)
−0.107466 + 0.994209i \(0.534274\pi\)
\(98\) 0 0
\(99\) 12.7446 + 0.792287i 1.28088 + 0.0796278i
\(100\) −4.05842 + 2.92048i −0.405842 + 0.292048i
\(101\) 16.3723 1.62910 0.814551 0.580091i \(-0.196983\pi\)
0.814551 + 0.580091i \(0.196983\pi\)
\(102\) −8.37228 + 7.86797i −0.828979 + 0.779045i
\(103\) 15.1168 1.48951 0.744753 0.667340i \(-0.232567\pi\)
0.744753 + 0.667340i \(0.232567\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 1.37228 0.133288
\(107\) −17.7446 −1.71543 −0.857716 0.514124i \(-0.828117\pi\)
−0.857716 + 0.514124i \(0.828117\pi\)
\(108\) −4.00000 + 3.31662i −0.384900 + 0.319142i
\(109\) 9.11684 0.873235 0.436618 0.899647i \(-0.356176\pi\)
0.436618 + 0.899647i \(0.356176\pi\)
\(110\) 9.05842 2.92048i 0.863687 0.278457i
\(111\) 14.7446 13.8564i 1.39949 1.31519i
\(112\) 0 0
\(113\) 3.25544 0.306246 0.153123 0.988207i \(-0.451067\pi\)
0.153123 + 0.988207i \(0.451067\pi\)
\(114\) 4.37228 4.10891i 0.409502 0.384835i
\(115\) 3.00000 + 9.30506i 0.279751 + 0.867702i
\(116\) 3.31662i 0.307941i
\(117\) −0.372281 + 5.98844i −0.0344174 + 0.553631i
\(118\) −4.11684 −0.378986
\(119\) 0 0
\(120\) −1.87228 + 3.39036i −0.170915 + 0.309496i
\(121\) −7.11684 −0.646986
\(122\) 2.81929i 0.255247i
\(123\) −1.93070 2.05446i −0.174086 0.185244i
\(124\) 2.37686i 0.213448i
\(125\) 9.00000 + 6.63325i 0.804984 + 0.593296i
\(126\) 0 0
\(127\) 2.37686i 0.210912i −0.994424 0.105456i \(-0.966370\pi\)
0.994424 0.105456i \(-0.0336303\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 13.9307 13.0916i 1.22653 1.15265i
\(130\) 1.37228 + 4.25639i 0.120357 + 0.373310i
\(131\) 4.62772 0.404326 0.202163 0.979352i \(-0.435203\pi\)
0.202163 + 0.979352i \(0.435203\pi\)
\(132\) 5.37228 5.04868i 0.467597 0.439431i
\(133\) 0 0
\(134\) 7.57301i 0.654209i
\(135\) 9.80298 + 6.23711i 0.843707 + 0.536805i
\(136\) 6.63325i 0.568796i
\(137\) −2.74456 −0.234484 −0.117242 0.993103i \(-0.537405\pi\)
−0.117242 + 0.993103i \(0.537405\pi\)
\(138\) 5.18614 + 5.51856i 0.441474 + 0.469771i
\(139\) 11.6819i 0.990848i −0.868651 0.495424i \(-0.835013\pi\)
0.868651 0.495424i \(-0.164987\pi\)
\(140\) 0 0
\(141\) 2.37228 2.22938i 0.199782 0.187748i
\(142\) 1.87953i 0.157726i
\(143\) 8.51278i 0.711874i
\(144\) −0.186141 + 2.99422i −0.0155117 + 0.249518i
\(145\) 7.05842 2.27567i 0.586170 0.188984i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 11.6819i 0.960248i
\(149\) 14.2063i 1.16382i −0.813252 0.581911i \(-0.802305\pi\)
0.813252 0.581911i \(-0.197695\pi\)
\(150\) 8.50000 + 1.65831i 0.694022 + 0.135401i
\(151\) −8.11684 −0.660539 −0.330270 0.943887i \(-0.607140\pi\)
−0.330270 + 0.943887i \(0.607140\pi\)
\(152\) 3.46410i 0.280976i
\(153\) 19.8614 + 1.23472i 1.60570 + 0.0998210i
\(154\) 0 0
\(155\) −5.05842 + 1.63086i −0.406302 + 0.130994i
\(156\) 2.37228 + 2.52434i 0.189935 + 0.202109i
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 8.11684 0.645741
\(159\) −1.62772 1.73205i −0.129086 0.137361i
\(160\) 0.686141 + 2.12819i 0.0542442 + 0.168249i
\(161\) 0 0
\(162\) 8.93070 + 1.11469i 0.701662 + 0.0875785i
\(163\) 3.46410i 0.271329i 0.990755 + 0.135665i \(0.0433170\pi\)
−0.990755 + 0.135665i \(0.956683\pi\)
\(164\) −1.62772 −0.127103
\(165\) −14.4307 7.96916i −1.12343 0.620398i
\(166\) 1.43710i 0.111540i
\(167\) 11.3321i 0.876902i 0.898755 + 0.438451i \(0.144473\pi\)
−0.898755 + 0.438451i \(0.855527\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 14.1168 4.55134i 1.08271 0.349072i
\(171\) −10.3723 0.644810i −0.793188 0.0493099i
\(172\) 11.0371i 0.841572i
\(173\) 3.75906i 0.285796i 0.989737 + 0.142898i \(0.0456420\pi\)
−0.989737 + 0.142898i \(0.954358\pi\)
\(174\) 4.18614 3.93398i 0.317351 0.298235i
\(175\) 0 0
\(176\) 4.25639i 0.320837i
\(177\) 4.88316 + 5.19615i 0.367040 + 0.390567i
\(178\) −4.37228 −0.327716
\(179\) 2.87419i 0.214827i 0.994214 + 0.107414i \(0.0342569\pi\)
−0.994214 + 0.107414i \(0.965743\pi\)
\(180\) 6.50000 1.65831i 0.484481 0.123603i
\(181\) 17.9653i 1.33535i 0.744452 + 0.667676i \(0.232711\pi\)
−0.744452 + 0.667676i \(0.767289\pi\)
\(182\) 0 0
\(183\) −3.55842 + 3.34408i −0.263046 + 0.247201i
\(184\) 4.37228 0.322329
\(185\) −24.8614 + 8.01544i −1.82785 + 0.589307i
\(186\) −3.00000 + 2.81929i −0.219971 + 0.206720i
\(187\) −28.2337 −2.06465
\(188\) 1.87953i 0.137079i
\(189\) 0 0
\(190\) −7.37228 + 2.37686i −0.534842 + 0.172436i
\(191\) 3.75906i 0.271996i 0.990709 + 0.135998i \(0.0434240\pi\)
−0.990709 + 0.135998i \(0.956576\pi\)
\(192\) 1.18614 + 1.26217i 0.0856023 + 0.0910892i
\(193\) 8.01544i 0.576964i −0.957485 0.288482i \(-0.906849\pi\)
0.957485 0.288482i \(-0.0931506\pi\)
\(194\) 2.11684 0.151981
\(195\) 3.74456 6.78073i 0.268154 0.485578i
\(196\) 0 0
\(197\) 20.2337 1.44159 0.720795 0.693148i \(-0.243777\pi\)
0.720795 + 0.693148i \(0.243777\pi\)
\(198\) −12.7446 0.792287i −0.905717 0.0563054i
\(199\) 18.6101i 1.31924i −0.751601 0.659619i \(-0.770718\pi\)
0.751601 0.659619i \(-0.229282\pi\)
\(200\) 4.05842 2.92048i 0.286974 0.206509i
\(201\) 9.55842 8.98266i 0.674199 0.633588i
\(202\) −16.3723 −1.15195
\(203\) 0 0
\(204\) 8.37228 7.86797i 0.586177 0.550868i
\(205\) 1.11684 + 3.46410i 0.0780038 + 0.241943i
\(206\) −15.1168 −1.05324
\(207\) 0.813859 13.0916i 0.0565671 0.909927i
\(208\) 2.00000 0.138675
\(209\) 14.7446 1.01990
\(210\) 0 0
\(211\) −18.2337 −1.25526 −0.627629 0.778512i \(-0.715975\pi\)
−0.627629 + 0.778512i \(0.715975\pi\)
\(212\) −1.37228 −0.0942487
\(213\) 2.37228 2.22938i 0.162546 0.152755i
\(214\) 17.7446 1.21299
\(215\) −23.4891 + 7.57301i −1.60195 + 0.516475i
\(216\) 4.00000 3.31662i 0.272166 0.225668i
\(217\) 0 0
\(218\) −9.11684 −0.617471
\(219\) 2.37228 + 2.52434i 0.160304 + 0.170579i
\(220\) −9.05842 + 2.92048i −0.610719 + 0.196899i
\(221\) 13.2665i 0.892401i
\(222\) −14.7446 + 13.8564i −0.989590 + 0.929981i
\(223\) 18.1168 1.21319 0.606597 0.795010i \(-0.292534\pi\)
0.606597 + 0.795010i \(0.292534\pi\)
\(224\) 0 0
\(225\) −7.98913 12.6954i −0.532608 0.846362i
\(226\) −3.25544 −0.216548
\(227\) 15.6434i 1.03829i 0.854687 + 0.519143i \(0.173749\pi\)
−0.854687 + 0.519143i \(0.826251\pi\)
\(228\) −4.37228 + 4.10891i −0.289561 + 0.272119i
\(229\) 13.8564i 0.915657i −0.889041 0.457829i \(-0.848627\pi\)
0.889041 0.457829i \(-0.151373\pi\)
\(230\) −3.00000 9.30506i −0.197814 0.613558i
\(231\) 0 0
\(232\) 3.31662i 0.217747i
\(233\) 23.4891 1.53882 0.769412 0.638753i \(-0.220549\pi\)
0.769412 + 0.638753i \(0.220549\pi\)
\(234\) 0.372281 5.98844i 0.0243368 0.391477i
\(235\) −4.00000 + 1.28962i −0.260931 + 0.0841256i
\(236\) 4.11684 0.267984
\(237\) −9.62772 10.2448i −0.625388 0.665473i
\(238\) 0 0
\(239\) 2.87419i 0.185916i 0.995670 + 0.0929581i \(0.0296323\pi\)
−0.995670 + 0.0929581i \(0.970368\pi\)
\(240\) 1.87228 3.39036i 0.120855 0.218847i
\(241\) 10.5947i 0.682464i 0.939979 + 0.341232i \(0.110844\pi\)
−0.939979 + 0.341232i \(0.889156\pi\)
\(242\) 7.11684 0.457488
\(243\) −9.18614 12.5942i −0.589291 0.807921i
\(244\) 2.81929i 0.180487i
\(245\) 0 0
\(246\) 1.93070 + 2.05446i 0.123097 + 0.130987i
\(247\) 6.92820i 0.440831i
\(248\) 2.37686i 0.150931i
\(249\) 1.81386 1.70460i 0.114949 0.108025i
\(250\) −9.00000 6.63325i −0.569210 0.419524i
\(251\) −16.1168 −1.01729 −0.508643 0.860977i \(-0.669853\pi\)
−0.508643 + 0.860977i \(0.669853\pi\)
\(252\) 0 0
\(253\) 18.6101i 1.17001i
\(254\) 2.37686i 0.149138i
\(255\) −22.4891 12.4193i −1.40832 0.777727i
\(256\) 1.00000 0.0625000
\(257\) 8.51278i 0.531012i 0.964109 + 0.265506i \(0.0855391\pi\)
−0.964109 + 0.265506i \(0.914461\pi\)
\(258\) −13.9307 + 13.0916i −0.867288 + 0.815046i
\(259\) 0 0
\(260\) −1.37228 4.25639i −0.0851053 0.263970i
\(261\) −9.93070 0.617359i −0.614695 0.0382135i
\(262\) −4.62772 −0.285901
\(263\) −1.62772 −0.100369 −0.0501847 0.998740i \(-0.515981\pi\)
−0.0501847 + 0.998740i \(0.515981\pi\)
\(264\) −5.37228 + 5.04868i −0.330641 + 0.310725i
\(265\) 0.941578 + 2.92048i 0.0578407 + 0.179404i
\(266\) 0 0
\(267\) 5.18614 + 5.51856i 0.317387 + 0.337730i
\(268\) 7.57301i 0.462595i
\(269\) 19.9783 1.21810 0.609048 0.793134i \(-0.291552\pi\)
0.609048 + 0.793134i \(0.291552\pi\)
\(270\) −9.80298 6.23711i −0.596591 0.379578i
\(271\) 20.9870i 1.27487i 0.770505 + 0.637434i \(0.220004\pi\)
−0.770505 + 0.637434i \(0.779996\pi\)
\(272\) 6.63325i 0.402200i
\(273\) 0 0
\(274\) 2.74456 0.165805
\(275\) 12.4307 + 17.2742i 0.749600 + 1.04167i
\(276\) −5.18614 5.51856i −0.312169 0.332178i
\(277\) 29.0024i 1.74259i 0.490762 + 0.871294i \(0.336718\pi\)
−0.490762 + 0.871294i \(0.663282\pi\)
\(278\) 11.6819i 0.700635i
\(279\) 7.11684 + 0.442430i 0.426074 + 0.0264876i
\(280\) 0 0
\(281\) 21.7793i 1.29924i −0.760258 0.649621i \(-0.774927\pi\)
0.760258 0.649621i \(-0.225073\pi\)
\(282\) −2.37228 + 2.22938i −0.141267 + 0.132758i
\(283\) −16.0000 −0.951101 −0.475551 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 1.87953i 0.111529i
\(285\) 11.7446 + 6.48577i 0.695688 + 0.384184i
\(286\) 8.51278i 0.503371i
\(287\) 0 0
\(288\) 0.186141 2.99422i 0.0109684 0.176436i
\(289\) −27.0000 −1.58824
\(290\) −7.05842 + 2.27567i −0.414485 + 0.133632i
\(291\) −2.51087 2.67181i −0.147190 0.156625i
\(292\) 2.00000 0.117041
\(293\) 25.0410i 1.46291i −0.681889 0.731455i \(-0.738841\pi\)
0.681889 0.731455i \(-0.261159\pi\)
\(294\) 0 0
\(295\) −2.82473 8.76144i −0.164462 0.510111i
\(296\) 11.6819i 0.678998i
\(297\) 14.1168 + 17.0256i 0.819142 + 0.987923i
\(298\) 14.2063i 0.822947i
\(299\) −8.74456 −0.505711
\(300\) −8.50000 1.65831i −0.490748 0.0957427i
\(301\) 0 0
\(302\) 8.11684 0.467072
\(303\) 19.4198 + 20.6646i 1.11564 + 1.18715i
\(304\) 3.46410i 0.198680i
\(305\) 6.00000 1.93443i 0.343559 0.110765i
\(306\) −19.8614 1.23472i −1.13540 0.0705841i
\(307\) 6.88316 0.392842 0.196421 0.980520i \(-0.437068\pi\)
0.196421 + 0.980520i \(0.437068\pi\)
\(308\) 0 0
\(309\) 17.9307 + 19.0800i 1.02004 + 1.08542i
\(310\) 5.05842 1.63086i 0.287299 0.0926267i
\(311\) −14.2337 −0.807118 −0.403559 0.914954i \(-0.632227\pi\)
−0.403559 + 0.914954i \(0.632227\pi\)
\(312\) −2.37228 2.52434i −0.134304 0.142912i
\(313\) −14.1168 −0.797931 −0.398966 0.916966i \(-0.630631\pi\)
−0.398966 + 0.916966i \(0.630631\pi\)
\(314\) −8.00000 −0.451466
\(315\) 0 0
\(316\) −8.11684 −0.456608
\(317\) −16.1168 −0.905212 −0.452606 0.891711i \(-0.649506\pi\)
−0.452606 + 0.891711i \(0.649506\pi\)
\(318\) 1.62772 + 1.73205i 0.0912779 + 0.0971286i
\(319\) 14.1168 0.790392
\(320\) −0.686141 2.12819i −0.0383564 0.118970i
\(321\) −21.0475 22.3966i −1.17476 1.25006i
\(322\) 0 0
\(323\) 22.9783 1.27854
\(324\) −8.93070 1.11469i −0.496150 0.0619273i
\(325\) −8.11684 + 5.84096i −0.450241 + 0.323998i
\(326\) 3.46410i 0.191859i
\(327\) 10.8139 + 11.5070i 0.598008 + 0.636338i
\(328\) 1.62772 0.0898757
\(329\) 0 0
\(330\) 14.4307 + 7.96916i 0.794384 + 0.438688i
\(331\) 10.2337 0.562494 0.281247 0.959635i \(-0.409252\pi\)
0.281247 + 0.959635i \(0.409252\pi\)
\(332\) 1.43710i 0.0788710i
\(333\) 34.9783 + 2.17448i 1.91680 + 0.119161i
\(334\) 11.3321i 0.620063i
\(335\) −16.1168 + 5.19615i −0.880557 + 0.283896i
\(336\) 0 0
\(337\) 9.30506i 0.506879i −0.967351 0.253440i \(-0.918438\pi\)
0.967351 0.253440i \(-0.0815619\pi\)
\(338\) 9.00000 0.489535
\(339\) 3.86141 + 4.10891i 0.209723 + 0.223165i
\(340\) −14.1168 + 4.55134i −0.765593 + 0.246831i
\(341\) −10.1168 −0.547858
\(342\) 10.3723 + 0.644810i 0.560869 + 0.0348673i
\(343\) 0 0
\(344\) 11.0371i 0.595081i
\(345\) −8.18614 + 14.8236i −0.440727 + 0.798077i
\(346\) 3.75906i 0.202088i
\(347\) −19.1168 −1.02625 −0.513123 0.858315i \(-0.671512\pi\)
−0.513123 + 0.858315i \(0.671512\pi\)
\(348\) −4.18614 + 3.93398i −0.224401 + 0.210884i
\(349\) 24.0087i 1.28515i 0.766221 + 0.642577i \(0.222135\pi\)
−0.766221 + 0.642577i \(0.777865\pi\)
\(350\) 0 0
\(351\) −8.00000 + 6.63325i −0.427008 + 0.354057i
\(352\) 4.25639i 0.226866i
\(353\) 18.9051i 1.00622i 0.864224 + 0.503108i \(0.167810\pi\)
−0.864224 + 0.503108i \(0.832190\pi\)
\(354\) −4.88316 5.19615i −0.259537 0.276172i
\(355\) −4.00000 + 1.28962i −0.212298 + 0.0684459i
\(356\) 4.37228 0.231730
\(357\) 0 0
\(358\) 2.87419i 0.151906i
\(359\) 14.1514i 0.746880i 0.927654 + 0.373440i \(0.121822\pi\)
−0.927654 + 0.373440i \(0.878178\pi\)
\(360\) −6.50000 + 1.65831i −0.342580 + 0.0874007i
\(361\) 7.00000 0.368421
\(362\) 17.9653i 0.944236i
\(363\) −8.44158 8.98266i −0.443068 0.471467i
\(364\) 0 0
\(365\) −1.37228 4.25639i −0.0718285 0.222790i
\(366\) 3.55842 3.34408i 0.186002 0.174798i
\(367\) −21.2337 −1.10839 −0.554195 0.832387i \(-0.686974\pi\)
−0.554195 + 0.832387i \(0.686974\pi\)
\(368\) −4.37228 −0.227921
\(369\) 0.302985 4.87375i 0.0157727 0.253717i
\(370\) 24.8614 8.01544i 1.29248 0.416703i
\(371\) 0 0
\(372\) 3.00000 2.81929i 0.155543 0.146173i
\(373\) 16.4356i 0.851006i 0.904957 + 0.425503i \(0.139903\pi\)
−0.904957 + 0.425503i \(0.860097\pi\)
\(374\) 28.2337 1.45993
\(375\) 2.30298 + 19.2275i 0.118926 + 0.992903i
\(376\) 1.87953i 0.0969292i
\(377\) 6.63325i 0.341630i
\(378\) 0 0
\(379\) 22.2337 1.14207 0.571034 0.820926i \(-0.306542\pi\)
0.571034 + 0.820926i \(0.306542\pi\)
\(380\) 7.37228 2.37686i 0.378190 0.121930i
\(381\) 3.00000 2.81929i 0.153695 0.144437i
\(382\) 3.75906i 0.192330i
\(383\) 20.8395i 1.06485i 0.846477 + 0.532425i \(0.178719\pi\)
−0.846477 + 0.532425i \(0.821281\pi\)
\(384\) −1.18614 1.26217i −0.0605300 0.0644098i
\(385\) 0 0
\(386\) 8.01544i 0.407975i
\(387\) 33.0475 + 2.05446i 1.67990 + 0.104434i
\(388\) −2.11684 −0.107466
\(389\) 34.0511i 1.72646i 0.504811 + 0.863230i \(0.331562\pi\)
−0.504811 + 0.863230i \(0.668438\pi\)
\(390\) −3.74456 + 6.78073i −0.189613 + 0.343355i
\(391\) 29.0024i 1.46672i
\(392\) 0 0
\(393\) 5.48913 + 5.84096i 0.276890 + 0.294638i
\(394\) −20.2337 −1.01936
\(395\) 5.56930 + 17.2742i 0.280222 + 0.869160i
\(396\) 12.7446 + 0.792287i 0.640438 + 0.0398139i
\(397\) 8.00000 0.401508 0.200754 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 18.6101i 0.932841i
\(399\) 0 0
\(400\) −4.05842 + 2.92048i −0.202921 + 0.146024i
\(401\) 19.8448i 0.991004i −0.868607 0.495502i \(-0.834984\pi\)
0.868607 0.495502i \(-0.165016\pi\)
\(402\) −9.55842 + 8.98266i −0.476731 + 0.448014i
\(403\) 4.75372i 0.236800i
\(404\) 16.3723 0.814551
\(405\) 3.75544 + 19.7711i 0.186609 + 0.982434i
\(406\) 0 0
\(407\) −49.7228 −2.46467
\(408\) −8.37228 + 7.86797i −0.414490 + 0.389522i
\(409\) 35.4882i 1.75478i −0.479779 0.877389i \(-0.659283\pi\)
0.479779 0.877389i \(-0.340717\pi\)
\(410\) −1.11684 3.46410i −0.0551570 0.171080i
\(411\) −3.25544 3.46410i −0.160579 0.170872i
\(412\) 15.1168 0.744753
\(413\) 0 0
\(414\) −0.813859 + 13.0916i −0.0399990 + 0.643416i
\(415\) −3.05842 + 0.986051i −0.150132 + 0.0484033i
\(416\) −2.00000 −0.0980581
\(417\) 14.7446 13.8564i 0.722044 0.678551i
\(418\) −14.7446 −0.721180
\(419\) 29.4891 1.44064 0.720319 0.693643i \(-0.243995\pi\)
0.720319 + 0.693643i \(0.243995\pi\)
\(420\) 0 0
\(421\) 15.1168 0.736750 0.368375 0.929677i \(-0.379914\pi\)
0.368375 + 0.929677i \(0.379914\pi\)
\(422\) 18.2337 0.887602
\(423\) 5.62772 + 0.349857i 0.273629 + 0.0170106i
\(424\) 1.37228 0.0666439
\(425\) 19.3723 + 26.9205i 0.939694 + 1.30584i
\(426\) −2.37228 + 2.22938i −0.114937 + 0.108014i
\(427\) 0 0
\(428\) −17.7446 −0.857716
\(429\) 10.7446 10.0974i 0.518752 0.487505i
\(430\) 23.4891 7.57301i 1.13275 0.365203i
\(431\) 3.75906i 0.181067i 0.995893 + 0.0905337i \(0.0288573\pi\)
−0.995893 + 0.0905337i \(0.971143\pi\)
\(432\) −4.00000 + 3.31662i −0.192450 + 0.159571i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 11.2446 + 6.20965i 0.539136 + 0.297730i
\(436\) 9.11684 0.436618
\(437\) 15.1460i 0.724533i
\(438\) −2.37228 2.52434i −0.113352 0.120618i
\(439\) 12.7692i 0.609439i 0.952442 + 0.304720i \(0.0985627\pi\)
−0.952442 + 0.304720i \(0.901437\pi\)
\(440\) 9.05842 2.92048i 0.431843 0.139228i
\(441\) 0 0
\(442\) 13.2665i 0.631023i
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 14.7446 13.8564i 0.699746 0.657596i
\(445\) −3.00000 9.30506i −0.142214 0.441102i
\(446\) −18.1168 −0.857857
\(447\) 17.9307 16.8506i 0.848093 0.797007i
\(448\) 0 0
\(449\) 35.9855i 1.69826i 0.528182 + 0.849131i \(0.322874\pi\)
−0.528182 + 0.849131i \(0.677126\pi\)
\(450\) 7.98913 + 12.6954i 0.376611 + 0.598468i
\(451\) 6.92820i 0.326236i
\(452\) 3.25544 0.153123
\(453\) −9.62772 10.2448i −0.452350 0.481344i
\(454\) 15.6434i 0.734179i
\(455\) 0 0
\(456\) 4.37228 4.10891i 0.204751 0.192417i
\(457\) 12.7692i 0.597316i −0.954360 0.298658i \(-0.903461\pi\)
0.954360 0.298658i \(-0.0965390\pi\)
\(458\) 13.8564i 0.647467i
\(459\) 22.0000 + 26.5330i 1.02687 + 1.23845i
\(460\) 3.00000 + 9.30506i 0.139876 + 0.433851i
\(461\) 0.510875 0.0237938 0.0118969 0.999929i \(-0.496213\pi\)
0.0118969 + 0.999929i \(0.496213\pi\)
\(462\) 0 0
\(463\) 36.5754i 1.69981i 0.526940 + 0.849903i \(0.323339\pi\)
−0.526940 + 0.849903i \(0.676661\pi\)
\(464\) 3.31662i 0.153970i
\(465\) −8.05842 4.45015i −0.373700 0.206371i
\(466\) −23.4891 −1.08811
\(467\) 0.0549029i 0.00254060i 0.999999 + 0.00127030i \(0.000404349\pi\)
−0.999999 + 0.00127030i \(0.999596\pi\)
\(468\) −0.372281 + 5.98844i −0.0172087 + 0.276816i
\(469\) 0 0
\(470\) 4.00000 1.28962i 0.184506 0.0594858i
\(471\) 9.48913 + 10.0974i 0.437236 + 0.465261i
\(472\) −4.11684 −0.189493
\(473\) −46.9783 −2.16006
\(474\) 9.62772 + 10.2448i 0.442216 + 0.470561i
\(475\) −10.1168 14.0588i −0.464193 0.645061i
\(476\) 0 0
\(477\) 0.255437 4.10891i 0.0116957 0.188134i
\(478\) 2.87419i 0.131463i
\(479\) −8.74456 −0.399549 −0.199775 0.979842i \(-0.564021\pi\)
−0.199775 + 0.979842i \(0.564021\pi\)
\(480\) −1.87228 + 3.39036i −0.0854576 + 0.154748i
\(481\) 23.3639i 1.06530i
\(482\) 10.5947i 0.482575i
\(483\) 0 0
\(484\) −7.11684 −0.323493
\(485\) 1.45245 + 4.50506i 0.0659525 + 0.204564i
\(486\) 9.18614 + 12.5942i 0.416692 + 0.571286i
\(487\) 4.55134i 0.206241i 0.994669 + 0.103121i \(0.0328827\pi\)
−0.994669 + 0.103121i \(0.967117\pi\)
\(488\) 2.81929i 0.127623i
\(489\) −4.37228 + 4.10891i −0.197721 + 0.185811i
\(490\) 0 0
\(491\) 26.9205i 1.21491i 0.794355 + 0.607453i \(0.207809\pi\)
−0.794355 + 0.607453i \(0.792191\pi\)
\(492\) −1.93070 2.05446i −0.0870428 0.0926220i
\(493\) 22.0000 0.990830
\(494\) 6.92820i 0.311715i
\(495\) −7.05842 27.6665i −0.317252 1.24352i
\(496\) 2.37686i 0.106724i
\(497\) 0 0
\(498\) −1.81386 + 1.70460i −0.0812810 + 0.0763849i
\(499\) 28.2337 1.26391 0.631957 0.775004i \(-0.282252\pi\)
0.631957 + 0.775004i \(0.282252\pi\)
\(500\) 9.00000 + 6.63325i 0.402492 + 0.296648i
\(501\) −14.3030 + 13.4414i −0.639010 + 0.600519i
\(502\) 16.1168 0.719330
\(503\) 9.45254i 0.421468i −0.977543 0.210734i \(-0.932415\pi\)
0.977543 0.210734i \(-0.0675854\pi\)
\(504\) 0 0
\(505\) −11.2337 34.8434i −0.499893 1.55051i
\(506\) 18.6101i 0.827321i
\(507\) −10.6753 11.3595i −0.474105 0.504494i
\(508\) 2.37686i 0.105456i
\(509\) −0.255437 −0.0113221 −0.00566103 0.999984i \(-0.501802\pi\)
−0.00566103 + 0.999984i \(0.501802\pi\)
\(510\) 22.4891 + 12.4193i 0.995835 + 0.549936i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −11.4891 13.8564i −0.507257 0.611775i
\(514\) 8.51278i 0.375483i
\(515\) −10.3723 32.1716i −0.457057 1.41765i
\(516\) 13.9307 13.0916i 0.613265 0.576324i
\(517\) −8.00000 −0.351840
\(518\) 0 0
\(519\) −4.74456 + 4.45877i −0.208263 + 0.195718i
\(520\) 1.37228 + 4.25639i 0.0601785 + 0.186655i
\(521\) −3.25544 −0.142623 −0.0713116 0.997454i \(-0.522718\pi\)
−0.0713116 + 0.997454i \(0.522718\pi\)
\(522\) 9.93070 + 0.617359i 0.434655 + 0.0270211i
\(523\) −24.2337 −1.05967 −0.529833 0.848102i \(-0.677745\pi\)
−0.529833 + 0.848102i \(0.677745\pi\)
\(524\) 4.62772 0.202163
\(525\) 0 0
\(526\) 1.62772 0.0709719
\(527\) −15.7663 −0.686791
\(528\) 5.37228 5.04868i 0.233799 0.219715i
\(529\) −3.88316 −0.168833
\(530\) −0.941578 2.92048i −0.0408995 0.126858i
\(531\) −0.766312 + 12.3267i −0.0332551 + 0.534935i
\(532\) 0 0
\(533\) −3.25544 −0.141009
\(534\) −5.18614 5.51856i −0.224426 0.238811i
\(535\) 12.1753 + 37.7639i 0.526383 + 1.63267i
\(536\) 7.57301i 0.327104i
\(537\) −3.62772 + 3.40920i −0.156548 + 0.147118i
\(538\) −19.9783 −0.861324
\(539\) 0 0
\(540\) 9.80298 + 6.23711i 0.421853 + 0.268402i
\(541\) −13.3505 −0.573984 −0.286992 0.957933i \(-0.592655\pi\)
−0.286992 + 0.957933i \(0.592655\pi\)
\(542\) 20.9870i 0.901468i
\(543\) −22.6753 + 21.3094i −0.973089 + 0.914474i
\(544\) 6.63325i 0.284398i
\(545\) −6.25544 19.4024i −0.267953 0.831108i
\(546\) 0 0
\(547\) 0.644810i 0.0275701i −0.999905 0.0137850i \(-0.995612\pi\)
0.999905 0.0137850i \(-0.00438806\pi\)
\(548\) −2.74456 −0.117242
\(549\) −8.44158 0.524785i −0.360278 0.0223973i
\(550\) −12.4307 17.2742i −0.530047 0.736575i
\(551\) −11.4891 −0.489453
\(552\) 5.18614 + 5.51856i 0.220737 + 0.234885i
\(553\) 0 0
\(554\) 29.0024i 1.23220i
\(555\) −39.6060 21.8719i −1.68118 0.928408i
\(556\) 11.6819i 0.495424i
\(557\) 0.861407 0.0364990 0.0182495 0.999833i \(-0.494191\pi\)
0.0182495 + 0.999833i \(0.494191\pi\)
\(558\) −7.11684 0.442430i −0.301280 0.0187296i
\(559\) 22.0742i 0.933640i
\(560\) 0 0
\(561\) −33.4891 35.6357i −1.41391 1.50454i
\(562\) 21.7793i 0.918703i
\(563\) 11.8294i 0.498550i −0.968433 0.249275i \(-0.919808\pi\)
0.968433 0.249275i \(-0.0801923\pi\)
\(564\) 2.37228 2.22938i 0.0998911 0.0938740i
\(565\) −2.23369 6.92820i −0.0939720 0.291472i
\(566\) 16.0000 0.672530
\(567\) 0 0
\(568\) 1.87953i 0.0788632i
\(569\) 21.7793i 0.913035i −0.889714 0.456517i \(-0.849097\pi\)
0.889714 0.456517i \(-0.150903\pi\)
\(570\) −11.7446 6.48577i −0.491926 0.271659i
\(571\) 34.2337 1.43264 0.716318 0.697774i \(-0.245826\pi\)
0.716318 + 0.697774i \(0.245826\pi\)
\(572\) 8.51278i 0.355937i
\(573\) −4.74456 + 4.45877i −0.198207 + 0.186268i
\(574\) 0 0
\(575\) 17.7446 12.7692i 0.739999 0.532511i
\(576\) −0.186141 + 2.99422i −0.00775586 + 0.124759i
\(577\) −17.8832 −0.744486 −0.372243 0.928135i \(-0.621411\pi\)
−0.372243 + 0.928135i \(0.621411\pi\)
\(578\) 27.0000 1.12305
\(579\) 10.1168 9.50744i 0.420442 0.395116i
\(580\) 7.05842 2.27567i 0.293085 0.0944921i
\(581\) 0 0
\(582\) 2.51087 + 2.67181i 0.104079 + 0.110750i
\(583\) 5.84096i 0.241908i
\(584\) −2.00000 −0.0827606
\(585\) 13.0000 3.31662i 0.537484 0.137126i
\(586\) 25.0410i 1.03443i
\(587\) 36.4280i 1.50354i 0.659424 + 0.751772i \(0.270800\pi\)
−0.659424 + 0.751772i \(0.729200\pi\)
\(588\) 0 0
\(589\) 8.23369 0.339263
\(590\) 2.82473 + 8.76144i 0.116292 + 0.360703i
\(591\) 24.0000 + 25.5383i 0.987228 + 1.05051i
\(592\) 11.6819i 0.480124i
\(593\) 14.1514i 0.581127i 0.956856 + 0.290563i \(0.0938427\pi\)
−0.956856 + 0.290563i \(0.906157\pi\)
\(594\) −14.1168 17.0256i −0.579221 0.698567i
\(595\) 0 0
\(596\) 14.2063i 0.581911i
\(597\) 23.4891 22.0742i 0.961346 0.903438i
\(598\) 8.74456 0.357592
\(599\) 8.51278i 0.347823i 0.984761 + 0.173911i \(0.0556406\pi\)
−0.984761 + 0.173911i \(0.944359\pi\)
\(600\) 8.50000 + 1.65831i 0.347011 + 0.0677003i
\(601\) 10.5947i 0.432166i −0.976375 0.216083i \(-0.930672\pi\)
0.976375 0.216083i \(-0.0693282\pi\)
\(602\) 0 0
\(603\) 22.6753 + 1.40965i 0.923408 + 0.0574052i
\(604\) −8.11684 −0.330270
\(605\) 4.88316 + 15.1460i 0.198529 + 0.615774i
\(606\) −19.4198 20.6646i −0.788877 0.839441i
\(607\) 27.4674 1.11487 0.557433 0.830222i \(-0.311786\pi\)
0.557433 + 0.830222i \(0.311786\pi\)
\(608\) 3.46410i 0.140488i
\(609\) 0 0
\(610\) −6.00000 + 1.93443i −0.242933 + 0.0783228i
\(611\) 3.75906i 0.152075i
\(612\) 19.8614 + 1.23472i 0.802850 + 0.0499105i
\(613\) 12.9715i 0.523916i −0.965079 0.261958i \(-0.915632\pi\)
0.965079 0.261958i \(-0.0843682\pi\)
\(614\) −6.88316 −0.277782
\(615\) −3.04755 + 5.51856i −0.122889 + 0.222530i
\(616\) 0 0
\(617\) 1.02175 0.0411341 0.0205670 0.999788i \(-0.493453\pi\)
0.0205670 + 0.999788i \(0.493453\pi\)
\(618\) −17.9307 19.0800i −0.721279 0.767511i
\(619\) 23.3639i 0.939072i 0.882913 + 0.469536i \(0.155579\pi\)
−0.882913 + 0.469536i \(0.844421\pi\)
\(620\) −5.05842 + 1.63086i −0.203151 + 0.0654970i
\(621\) 17.4891 14.5012i 0.701814 0.581914i
\(622\) 14.2337 0.570719
\(623\) 0 0
\(624\) 2.37228 + 2.52434i 0.0949673 + 0.101054i
\(625\) 7.94158 23.7051i 0.317663 0.948204i
\(626\) 14.1168 0.564223
\(627\) 17.4891 + 18.6101i 0.698448 + 0.743217i
\(628\) 8.00000 0.319235
\(629\) −77.4891 −3.08969
\(630\) 0 0
\(631\) 30.1168 1.19893 0.599466 0.800400i \(-0.295380\pi\)
0.599466 + 0.800400i \(0.295380\pi\)
\(632\) 8.11684 0.322871
\(633\) −21.6277 23.0140i −0.859625 0.914724i
\(634\) 16.1168 0.640082
\(635\) −5.05842 + 1.63086i −0.200737 + 0.0647187i
\(636\) −1.62772 1.73205i −0.0645432 0.0686803i
\(637\) 0 0
\(638\) −14.1168 −0.558891
\(639\) 5.62772 + 0.349857i 0.222629 + 0.0138401i
\(640\) 0.686141 + 2.12819i 0.0271221 + 0.0841243i
\(641\) 14.2063i 0.561114i −0.959837 0.280557i \(-0.909481\pi\)
0.959837 0.280557i \(-0.0905191\pi\)
\(642\) 21.0475 + 22.3966i 0.830680 + 0.883925i
\(643\) 16.2337 0.640194 0.320097 0.947385i \(-0.396284\pi\)
0.320097 + 0.947385i \(0.396284\pi\)
\(644\) 0 0
\(645\) −37.4198 20.6646i −1.47340 0.813667i
\(646\) −22.9783 −0.904067
\(647\) 25.4834i 1.00186i −0.865489 0.500928i \(-0.832992\pi\)
0.865489 0.500928i \(-0.167008\pi\)
\(648\) 8.93070 + 1.11469i 0.350831 + 0.0437892i
\(649\) 17.5229i 0.687834i
\(650\) 8.11684 5.84096i 0.318369 0.229101i
\(651\) 0 0
\(652\) 3.46410i 0.135665i
\(653\) 10.6277 0.415895 0.207947 0.978140i \(-0.433322\pi\)
0.207947 + 0.978140i \(0.433322\pi\)
\(654\) −10.8139 11.5070i −0.422855 0.449959i
\(655\) −3.17527 9.84868i −0.124068 0.384820i
\(656\) −1.62772 −0.0635517
\(657\) −0.372281 + 5.98844i −0.0145241 + 0.233631i
\(658\) 0 0
\(659\) 36.9253i 1.43841i −0.694800 0.719203i \(-0.744507\pi\)
0.694800 0.719203i \(-0.255493\pi\)
\(660\) −14.4307 7.96916i −0.561714 0.310199i
\(661\) 2.81929i 0.109658i 0.998496 + 0.0548289i \(0.0174613\pi\)
−0.998496 + 0.0548289i \(0.982539\pi\)
\(662\) −10.2337 −0.397744
\(663\) 16.7446 15.7359i 0.650305 0.611133i
\(664\) 1.43710i 0.0557702i
\(665\) 0 0
\(666\) −34.9783 2.17448i −1.35538 0.0842594i
\(667\) 14.5012i 0.561489i
\(668\) 11.3321i 0.438451i
\(669\) 21.4891 + 22.8665i 0.830818 + 0.884071i
\(670\) 16.1168 5.19615i 0.622648 0.200745i
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 17.1181i 0.659855i −0.944006 0.329928i \(-0.892976\pi\)
0.944006 0.329928i \(-0.107024\pi\)
\(674\) 9.30506i 0.358418i
\(675\) 6.54755 25.1422i 0.252015 0.967723i
\(676\) −9.00000 −0.346154
\(677\) 44.9407i 1.72721i −0.504166 0.863607i \(-0.668200\pi\)
0.504166 0.863607i \(-0.331800\pi\)
\(678\) −3.86141 4.10891i −0.148296 0.157802i
\(679\) 0 0
\(680\) 14.1168 4.55134i 0.541356 0.174536i
\(681\) −19.7446 + 18.5552i −0.756613 + 0.711038i
\(682\) 10.1168 0.387394
\(683\) 13.9783 0.534863 0.267431 0.963577i \(-0.413825\pi\)
0.267431 + 0.963577i \(0.413825\pi\)
\(684\) −10.3723 0.644810i −0.396594 0.0246549i
\(685\) 1.88316 + 5.84096i 0.0719517 + 0.223172i
\(686\) 0 0
\(687\) 17.4891 16.4356i 0.667252 0.627059i
\(688\) 11.0371i 0.420786i
\(689\) −2.74456 −0.104560
\(690\) 8.18614 14.8236i 0.311641 0.564326i
\(691\) 30.2921i 1.15236i 0.817321 + 0.576182i \(0.195458\pi\)
−0.817321 + 0.576182i \(0.804542\pi\)
\(692\) 3.75906i 0.142898i
\(693\) 0 0
\(694\) 19.1168 0.725665
\(695\) −24.8614 + 8.01544i −0.943047 + 0.304043i
\(696\) 4.18614 3.93398i 0.158675 0.149117i
\(697\) 10.7971i 0.408968i
\(698\) 24.0087i 0.908741i
\(699\) 27.8614 + 29.6472i 1.05382 + 1.12136i
\(700\) 0 0
\(701\) 12.7143i 0.480211i −0.970747 0.240106i \(-0.922818\pi\)
0.970747 0.240106i \(-0.0771821\pi\)
\(702\) 8.00000 6.63325i 0.301941 0.250356i
\(703\) 40.4674 1.52626
\(704\) 4.25639i 0.160419i
\(705\) −6.37228 3.51900i −0.239994 0.132533i
\(706\) 18.9051i 0.711502i
\(707\) 0 0
\(708\) 4.88316 + 5.19615i 0.183520 + 0.195283i
\(709\) −5.11684 −0.192167 −0.0960836 0.995373i \(-0.530632\pi\)
−0.0960836 + 0.995373i \(0.530632\pi\)
\(710\) 4.00000 1.28962i 0.150117 0.0483986i
\(711\) 1.51087 24.3036i 0.0566622 0.911457i
\(712\) −4.37228 −0.163858
\(713\) 10.3923i 0.389195i
\(714\) 0 0
\(715\) −18.1168 + 5.84096i −0.677532 + 0.218440i
\(716\) 2.87419i 0.107414i
\(717\) −3.62772 + 3.40920i −0.135480 + 0.127319i
\(718\) 14.1514i 0.528124i
\(719\) 33.2554 1.24022 0.620109 0.784515i \(-0.287088\pi\)
0.620109 + 0.784515i \(0.287088\pi\)
\(720\) 6.50000 1.65831i 0.242241 0.0618017i
\(721\) 0 0
\(722\) −7.00000 −0.260513
\(723\) −13.3723 + 12.5668i −0.497320 + 0.467364i
\(724\) 17.9653i 0.667676i
\(725\) −9.68614 13.4603i −0.359734 0.499902i
\(726\) 8.44158 + 8.98266i 0.313296 + 0.333378i
\(727\) −19.0000 −0.704671 −0.352335 0.935874i \(-0.614612\pi\)
−0.352335 + 0.935874i \(0.614612\pi\)
\(728\) 0 0
\(729\) 5.00000 26.5330i 0.185185 0.982704i
\(730\) 1.37228 + 4.25639i 0.0507904 + 0.157536i
\(731\) −73.2119 −2.70784
\(732\) −3.55842 + 3.34408i −0.131523 + 0.123601i
\(733\) 36.4674 1.34695 0.673477 0.739209i \(-0.264800\pi\)
0.673477 + 0.739209i \(0.264800\pi\)
\(734\) 21.2337 0.783750
\(735\) 0 0
\(736\) 4.37228 0.161164
\(737\) −32.2337 −1.18734
\(738\) −0.302985 + 4.87375i −0.0111530 + 0.179405i
\(739\) −36.2337 −1.33288 −0.666439 0.745560i \(-0.732182\pi\)
−0.666439 + 0.745560i \(0.732182\pi\)
\(740\) −24.8614 + 8.01544i −0.913923 + 0.294654i
\(741\) −8.74456 + 8.21782i −0.321240 + 0.301889i
\(742\) 0 0
\(743\) 18.6060 0.682587 0.341293 0.939957i \(-0.389135\pi\)
0.341293 + 0.939957i \(0.389135\pi\)
\(744\) −3.00000 + 2.81929i −0.109985 + 0.103360i
\(745\) −30.2337 + 9.74749i −1.10768 + 0.357121i
\(746\) 16.4356i 0.601752i
\(747\) 4.30298 + 0.267502i 0.157438 + 0.00978739i
\(748\) −28.2337 −1.03233
\(749\) 0 0
\(750\) −2.30298 19.2275i −0.0840931 0.702089i
\(751\) 42.1168 1.53687 0.768433 0.639931i \(-0.221037\pi\)
0.768433 + 0.639931i \(0.221037\pi\)
\(752\) 1.87953i 0.0685393i
\(753\) −19.1168 20.3422i −0.696657 0.741310i
\(754\) 6.63325i 0.241569i
\(755\) 5.56930 + 17.2742i 0.202687 + 0.628673i
\(756\) 0 0
\(757\) 5.63858i 0.204938i −0.994736 0.102469i \(-0.967326\pi\)
0.994736 0.102469i \(-0.0326742\pi\)
\(758\) −22.2337 −0.807564
\(759\) −23.4891 + 22.0742i −0.852601 + 0.801244i
\(760\) −7.37228 + 2.37686i −0.267421 + 0.0862178i
\(761\) 52.9783 1.92046 0.960230 0.279210i \(-0.0900726\pi\)
0.960230 + 0.279210i \(0.0900726\pi\)
\(762\) −3.00000 + 2.81929i −0.108679 + 0.102132i
\(763\) 0 0
\(764\) 3.75906i 0.135998i
\(765\) −11.0000 43.1161i −0.397706 1.55887i
\(766\) 20.8395i 0.752962i
\(767\) 8.23369 0.297301
\(768\) 1.18614 + 1.26217i 0.0428012 + 0.0455446i
\(769\) 40.4820i 1.45982i −0.683545 0.729909i \(-0.739563\pi\)
0.683545 0.729909i \(-0.260437\pi\)
\(770\) 0 0
\(771\) −10.7446 + 10.0974i −0.386956 + 0.363647i
\(772\) 8.01544i 0.288482i
\(773\) 1.87953i 0.0676019i −0.999429 0.0338010i \(-0.989239\pi\)
0.999429 0.0338010i \(-0.0107612\pi\)
\(774\) −33.0475 2.05446i −1.18787 0.0738459i
\(775\) 6.94158 + 9.64630i 0.249349 + 0.346505i
\(776\) 2.11684 0.0759903
\(777\) 0 0
\(778\) 34.0511i 1.22079i
\(779\) 5.63858i 0.202023i
\(780\) 3.74456 6.78073i 0.134077 0.242789i
\(781\) −8.00000 −0.286263
\(782\) 29.0024i 1.03712i
\(783\) −11.0000 13.2665i −0.393108 0.474106i
\(784\) 0 0
\(785\) −5.48913 17.0256i −0.195915 0.607668i
\(786\) −5.48913 5.84096i −0.195791 0.208340i
\(787\) 27.1168 0.966611 0.483306 0.875452i \(-0.339436\pi\)
0.483306 + 0.875452i \(0.339436\pi\)
\(788\) 20.2337 0.720795
\(789\) −1.93070 2.05446i −0.0687349 0.0731406i
\(790\) −5.56930 17.2742i −0.198147 0.614589i
\(791\) 0 0
\(792\) −12.7446 0.792287i −0.452858 0.0281527i
\(793\) 5.63858i 0.200232i
\(794\) −8.00000 −0.283909
\(795\) −2.56930 + 4.65253i −0.0911236 + 0.165008i
\(796\) 18.6101i 0.659619i
\(797\) 4.25639i 0.150769i −0.997155 0.0753845i \(-0.975982\pi\)
0.997155 0.0753845i \(-0.0240184\pi\)
\(798\) 0 0
\(799\) −12.4674 −0.441064
\(800\) 4.05842 2.92048i 0.143487 0.103255i
\(801\) −0.813859 + 13.0916i −0.0287563 + 0.462568i
\(802\) 19.8448i 0.700746i
\(803\) 8.51278i 0.300409i
\(804\) 9.55842 8.98266i 0.337100 0.316794i
\(805\) 0 0
\(806\) 4.75372i 0.167443i
\(807\) 23.6970 + 25.2159i 0.834174 + 0.887643i
\(808\) −16.3723 −0.575975
\(809\) 25.4834i 0.895950i −0.894046 0.447975i \(-0.852145\pi\)
0.894046 0.447975i \(-0.147855\pi\)
\(810\) −3.75544 19.7711i −0.131953 0.694686i
\(811\) 10.3923i 0.364923i −0.983213 0.182462i \(-0.941593\pi\)
0.983213 0.182462i \(-0.0584065\pi\)
\(812\) 0 0
\(813\) −26.4891 + 24.8935i −0.929014 + 0.873054i
\(814\) 49.7228 1.74278
\(815\) 7.37228 2.37686i 0.258240 0.0832578i
\(816\) 8.37228 7.86797i 0.293088 0.275434i
\(817\) 38.2337 1.33763
\(818\) 35.4882i 1.24082i
\(819\) 0 0
\(820\) 1.11684 + 3.46410i 0.0390019 + 0.120972i
\(821\) 21.2819i 0.742745i 0.928484 + 0.371372i \(0.121113\pi\)
−0.928484 + 0.371372i \(0.878887\pi\)
\(822\) 3.25544 + 3.46410i 0.113546 + 0.120824i
\(823\) 43.5036i 1.51644i 0.651998 + 0.758221i \(0.273931\pi\)
−0.651998 + 0.758221i \(0.726069\pi\)
\(824\) −15.1168 −0.526620
\(825\) −7.05842 + 36.1793i −0.245743 + 1.25960i
\(826\) 0 0
\(827\) −33.0000 −1.14752 −0.573761 0.819023i \(-0.694516\pi\)
−0.573761 + 0.819023i \(0.694516\pi\)
\(828\) 0.813859 13.0916i 0.0282836 0.454964i
\(829\) 18.6101i 0.646356i −0.946338 0.323178i \(-0.895249\pi\)
0.946338 0.323178i \(-0.104751\pi\)
\(830\) 3.05842 0.986051i 0.106159 0.0342263i
\(831\) −36.6060 + 34.4010i −1.26985 + 1.19336i
\(832\) 2.00000 0.0693375
\(833\) 0 0
\(834\) −14.7446 + 13.8564i −0.510562 + 0.479808i
\(835\) 24.1168 7.77539i 0.834598 0.269079i
\(836\) 14.7446 0.509951
\(837\) 7.88316 + 9.50744i 0.272482 + 0.328625i
\(838\) −29.4891 −1.01868
\(839\) −1.72281 −0.0594781 −0.0297391 0.999558i \(-0.509468\pi\)
−0.0297391 + 0.999558i \(0.509468\pi\)
\(840\) 0 0
\(841\) 18.0000 0.620690
\(842\) −15.1168 −0.520961
\(843\) 27.4891 25.8333i 0.946776 0.889746i
\(844\) −18.2337 −0.627629
\(845\) 6.17527 + 19.1537i 0.212436 + 0.658909i
\(846\) −5.62772 0.349857i −0.193485 0.0120283i
\(847\) 0 0
\(848\) −1.37228 −0.0471243
\(849\) −18.9783 20.1947i −0.651332 0.693080i
\(850\) −19.3723 26.9205i −0.664464 0.923366i
\(851\) 51.0767i 1.75089i
\(852\) 2.37228 2.22938i 0.0812730 0.0763774i
\(853\) 30.4674 1.04318 0.521592 0.853195i \(-0.325339\pi\)
0.521592 + 0.853195i \(0.325339\pi\)
\(854\) 0 0
\(855\) 5.74456 + 22.5167i 0.196460 + 0.770054i
\(856\) 17.7446 0.606497
\(857\) 37.8102i 1.29157i −0.763519 0.645785i \(-0.776530\pi\)
0.763519 0.645785i \(-0.223470\pi\)
\(858\) −10.7446 + 10.0974i −0.366813 + 0.344718i
\(859\) 32.8713i 1.12155i −0.827967 0.560777i \(-0.810502\pi\)
0.827967 0.560777i \(-0.189498\pi\)
\(860\) −23.4891 + 7.57301i −0.800973 + 0.258238i
\(861\) 0 0
\(862\) 3.75906i 0.128034i
\(863\) −7.62772 −0.259651 −0.129825 0.991537i \(-0.541442\pi\)
−0.129825 + 0.991537i \(0.541442\pi\)
\(864\) 4.00000 3.31662i 0.136083 0.112834i
\(865\) 8.00000 2.57924i 0.272008 0.0876968i
\(866\) 34.0000 1.15537
\(867\) −32.0258 34.0786i −1.08765 1.15737i
\(868\) 0 0
\(869\) 34.5484i 1.17198i
\(870\) −11.2446 6.20965i −0.381226 0.210527i
\(871\) 15.1460i 0.513204i
\(872\) −9.11684 −0.308735
\(873\) 0.394031 6.33830i 0.0133359 0.214519i
\(874\) 15.1460i 0.512322i
\(875\) 0 0
\(876\) 2.37228 + 2.52434i 0.0801520 + 0.0852895i
\(877\) 31.5817i 1.06644i 0.845977 + 0.533219i \(0.179018\pi\)
−0.845977 + 0.533219i \(0.820982\pi\)
\(878\) 12.7692i 0.430938i
\(879\) 31.6060 29.7021i 1.06604 1.00183i
\(880\) −9.05842 + 2.92048i −0.305359 + 0.0984494i
\(881\) 51.3505 1.73004 0.865022 0.501734i \(-0.167305\pi\)
0.865022 + 0.501734i \(0.167305\pi\)
\(882\) 0 0
\(883\) 54.9455i 1.84906i 0.381104 + 0.924532i \(0.375544\pi\)
−0.381104 + 0.924532i \(0.624456\pi\)
\(884\) 13.2665i 0.446201i
\(885\) 7.70789 13.9576i 0.259098 0.469179i
\(886\) 9.00000 0.302361
\(887\) 54.8906i 1.84305i −0.388323 0.921523i \(-0.626945\pi\)
0.388323 0.921523i \(-0.373055\pi\)
\(888\) −14.7446 + 13.8564i −0.494795 + 0.464991i
\(889\) 0 0
\(890\) 3.00000 + 9.30506i 0.100560 + 0.311906i
\(891\) −4.74456 + 38.0125i −0.158949 + 1.27347i
\(892\) 18.1168 0.606597
\(893\) 6.51087 0.217878
\(894\) −17.9307 + 16.8506i −0.599692 + 0.563569i
\(895\) 6.11684 1.97210i 0.204464 0.0659201i
\(896\) 0 0
\(897\) −10.3723 11.0371i −0.346320 0.368519i
\(898\) 35.9855i 1.20085i
\(899\) 7.88316 0.262918
\(900\) −7.98913 12.6954i −0.266304 0.423181i
\(901\) 9.10268i 0.303254i
\(902\) 6.92820i 0.230684i
\(903\) 0 0
\(904\) −3.25544 −0.108274
\(905\) 38.2337 12.3267i 1.27093 0.409755i
\(906\) 9.62772 + 10.2448i 0.319860 + 0.340362i
\(907\) 44.7933i 1.48734i −0.668549 0.743668i \(-0.733084\pi\)
0.668549 0.743668i \(-0.266916\pi\)
\(908\) 15.6434i 0.519143i
\(909\) −3.04755 + 49.0222i −0.101081 + 1.62596i
\(910\) 0 0
\(911\) 24.5437i 0.813168i 0.913613 + 0.406584i \(0.133280\pi\)
−0.913613 + 0.406584i \(0.866720\pi\)
\(912\) −4.37228 + 4.10891i −0.144781 + 0.136060i
\(913\) −6.11684 −0.202438
\(914\) 12.7692i 0.422366i
\(915\) 9.55842 + 5.27851i 0.315992 + 0.174502i
\(916\) 13.8564i 0.457829i
\(917\) 0 0
\(918\) −22.0000 26.5330i −0.726108 0.875719i
\(919\) −18.2337 −0.601474 −0.300737 0.953707i \(-0.597233\pi\)
−0.300737 + 0.953707i \(0.597233\pi\)
\(920\) −3.00000 9.30506i −0.0989071 0.306779i
\(921\) 8.16439 + 8.68771i 0.269026 + 0.286270i
\(922\) −0.510875 −0.0168248
\(923\) 3.75906i 0.123731i
\(924\) 0 0
\(925\) 34.1168 + 47.4102i 1.12175 + 1.55884i
\(926\) 36.5754i 1.20194i
\(927\) −2.81386 + 45.2632i −0.0924193 + 1.48664i
\(928\) 3.31662i 0.108874i
\(929\) −16.8832 −0.553918 −0.276959 0.960882i \(-0.589327\pi\)
−0.276959 + 0.960882i \(0.589327\pi\)
\(930\) 8.05842 + 4.45015i 0.264246 + 0.145926i
\(931\) 0 0
\(932\) 23.4891 0.769412
\(933\) −16.8832 17.9653i −0.552730 0.588158i
\(934\) 0.0549029i 0.00179648i
\(935\) 19.3723 + 60.0868i 0.633541 + 1.96505i
\(936\) 0.372281 5.98844i 0.0121684 0.195738i
\(937\) 50.3505 1.64488 0.822440 0.568852i \(-0.192612\pi\)
0.822440 + 0.568852i \(0.192612\pi\)
\(938\) 0 0
\(939\) −16.7446 17.8178i −0.546438 0.581463i
\(940\) −4.00000 + 1.28962i −0.130466 + 0.0420628i
\(941\) 24.3505 0.793805 0.396902 0.917861i \(-0.370085\pi\)
0.396902 + 0.917861i \(0.370085\pi\)
\(942\) −9.48913 10.0974i −0.309172 0.328989i
\(943\) 7.11684 0.231756
\(944\) 4.11684 0.133992
\(945\) 0 0
\(946\) 46.9783 1.52739
\(947\) −43.1168 −1.40111 −0.700555 0.713599i \(-0.747064\pi\)
−0.700555 + 0.713599i \(0.747064\pi\)
\(948\) −9.62772 10.2448i −0.312694 0.332737i
\(949\) 4.00000 0.129845
\(950\) 10.1168 + 14.0588i 0.328234 + 0.456127i
\(951\) −19.1168 20.3422i −0.619906 0.659640i
\(952\) 0 0
\(953\) 48.0000 1.55487 0.777436 0.628962i \(-0.216520\pi\)
0.777436 + 0.628962i \(0.216520\pi\)
\(954\) −0.255437 + 4.10891i −0.00827009 + 0.133031i
\(955\) 8.00000 2.57924i 0.258874 0.0834623i
\(956\) 2.87419i 0.0929581i
\(957\) 16.7446 + 17.8178i 0.541275 + 0.575969i
\(958\) 8.74456 0.282524
\(959\) 0 0
\(960\) 1.87228 3.39036i 0.0604276 0.109424i
\(961\) 25.3505 0.817759
\(962\) 23.3639i 0.753281i
\(963\) 3.30298 53.1311i 0.106437 1.71213i
\(964\) 10.5947i 0.341232i
\(965\) −17.0584 + 5.49972i −0.549130 + 0.177042i
\(966\) 0 0
\(967\) 51.9239i 1.66976i −0.550433 0.834879i \(-0.685537\pi\)
0.550433 0.834879i \(-0.314463\pi\)
\(968\) 7.11684 0.228744
\(969\) 27.2554 + 29.0024i 0.875571 + 0.931692i
\(970\) −1.45245 4.50506i −0.0466354 0.144649i
\(971\) −28.6277 −0.918707 −0.459354 0.888253i \(-0.651919\pi\)
−0.459354 + 0.888253i \(0.651919\pi\)
\(972\) −9.18614 12.5942i −0.294646 0.403960i
\(973\) 0 0
\(974\) 4.55134i 0.145834i
\(975\) −17.0000 3.31662i −0.544436 0.106217i
\(976\) 2.81929i 0.0902433i
\(977\) 40.4674 1.29467 0.647333 0.762207i \(-0.275884\pi\)
0.647333 + 0.762207i \(0.275884\pi\)
\(978\) 4.37228 4.10891i 0.139810 0.131389i
\(979\) 18.6101i 0.594782i
\(980\) 0 0
\(981\) −1.69702 + 27.2978i −0.0541815 + 0.871553i
\(982\) 26.9205i 0.859069i
\(983\) 21.7244i 0.692900i 0.938068 + 0.346450i \(0.112613\pi\)
−0.938068 + 0.346450i \(0.887387\pi\)
\(984\) 1.93070 + 2.05446i 0.0615486 + 0.0654937i
\(985\) −13.8832 43.0612i −0.442354 1.37204i
\(986\) −22.0000 −0.700623
\(987\) 0 0
\(988\) 6.92820i 0.220416i
\(989\) 48.2574i 1.53450i
\(990\) 7.05842 + 27.6665i 0.224331 + 0.879300i
\(991\) −28.3505 −0.900584 −0.450292 0.892881i \(-0.648680\pi\)
−0.450292 + 0.892881i \(0.648680\pi\)
\(992\) 2.37686i 0.0754654i
\(993\) 12.1386 + 12.9166i 0.385207 + 0.409897i
\(994\) 0 0
\(995\) −39.6060 + 12.7692i −1.25559 + 0.404810i
\(996\) 1.81386 1.70460i 0.0574743 0.0540123i
\(997\) 30.4674 0.964911 0.482456 0.875920i \(-0.339745\pi\)
0.482456 + 0.875920i \(0.339745\pi\)
\(998\) −28.2337 −0.893722
\(999\) 38.7446 + 46.7277i 1.22582 + 1.47840i
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.a.1469.4 4
3.2 odd 2 1470.2.d.c.1469.3 4
5.4 even 2 1470.2.d.d.1469.1 4
7.4 even 3 210.2.t.d.89.1 yes 4
7.5 odd 6 210.2.t.c.59.2 yes 4
7.6 odd 2 1470.2.d.b.1469.1 4
15.14 odd 2 1470.2.d.b.1469.2 4
21.5 even 6 210.2.t.a.59.1 4
21.11 odd 6 210.2.t.b.89.1 yes 4
21.20 even 2 1470.2.d.d.1469.2 4
35.4 even 6 210.2.t.a.89.2 yes 4
35.12 even 12 1050.2.s.d.101.1 8
35.18 odd 12 1050.2.s.e.551.2 8
35.19 odd 6 210.2.t.b.59.1 yes 4
35.32 odd 12 1050.2.s.e.551.3 8
35.33 even 12 1050.2.s.d.101.4 8
35.34 odd 2 1470.2.d.c.1469.4 4
105.32 even 12 1050.2.s.d.551.1 8
105.47 odd 12 1050.2.s.e.101.3 8
105.53 even 12 1050.2.s.d.551.4 8
105.68 odd 12 1050.2.s.e.101.2 8
105.74 odd 6 210.2.t.c.89.2 yes 4
105.89 even 6 210.2.t.d.59.2 yes 4
105.104 even 2 inner 1470.2.d.a.1469.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.t.a.59.1 4 21.5 even 6
210.2.t.a.89.2 yes 4 35.4 even 6
210.2.t.b.59.1 yes 4 35.19 odd 6
210.2.t.b.89.1 yes 4 21.11 odd 6
210.2.t.c.59.2 yes 4 7.5 odd 6
210.2.t.c.89.2 yes 4 105.74 odd 6
210.2.t.d.59.2 yes 4 105.89 even 6
210.2.t.d.89.1 yes 4 7.4 even 3
1050.2.s.d.101.1 8 35.12 even 12
1050.2.s.d.101.4 8 35.33 even 12
1050.2.s.d.551.1 8 105.32 even 12
1050.2.s.d.551.4 8 105.53 even 12
1050.2.s.e.101.2 8 105.68 odd 12
1050.2.s.e.101.3 8 105.47 odd 12
1050.2.s.e.551.2 8 35.18 odd 12
1050.2.s.e.551.3 8 35.32 odd 12
1470.2.d.a.1469.3 4 105.104 even 2 inner
1470.2.d.a.1469.4 4 1.1 even 1 trivial
1470.2.d.b.1469.1 4 7.6 odd 2
1470.2.d.b.1469.2 4 15.14 odd 2
1470.2.d.c.1469.3 4 3.2 odd 2
1470.2.d.c.1469.4 4 35.34 odd 2
1470.2.d.d.1469.1 4 5.4 even 2
1470.2.d.d.1469.2 4 21.20 even 2