Properties

Label 882.2.f.j.589.2
Level $882$
Weight $2$
Character 882.589
Analytic conductor $7.043$
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] = [882,2,Mod(295,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 589.2
Root \(1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.589
Dual form 882.2.f.j.295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-1.00000 + 1.41421i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.724745 + 1.25529i) q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.44949 q^{10} +(-1.00000 - 1.73205i) q^{11} +(-0.724745 - 1.57313i) q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.00000 q^{17} +(-1.94949 + 2.28024i) q^{18} -2.55051 q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-1.00000 + 1.41421i) q^{24} +(1.44949 + 2.51059i) q^{25} -4.89898 q^{26} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(-1.44949 + 2.04989i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.44949 + 0.317837i) q^{33} +(1.00000 + 1.73205i) q^{34} +(2.94949 + 0.548188i) q^{36} +11.7980 q^{37} +(1.27526 + 2.20881i) q^{38} +(3.55051 + 7.70674i) q^{39} +(-0.724745 + 1.25529i) q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +2.00000 q^{44} +(4.27526 + 0.794593i) q^{45} -1.00000 q^{46} +(4.89898 + 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(1.44949 - 2.51059i) q^{50} +(2.00000 - 2.82843i) q^{51} +(2.44949 + 4.24264i) q^{52} -10.8990 q^{53} +(-1.27526 - 5.03723i) q^{54} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} +(3.44949 - 5.97469i) q^{58} +(-1.00000 + 1.73205i) q^{59} +(2.50000 + 0.230351i) q^{60} +(3.27526 + 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 + 6.14966i) q^{65} +(-1.44949 - 3.14626i) q^{66} +(6.44949 - 11.1708i) q^{67} +(1.00000 - 1.73205i) q^{68} +(0.724745 + 1.57313i) q^{69} +0.101021 q^{71} +(-1.00000 - 2.82843i) q^{72} +6.89898 q^{73} +(-5.89898 - 10.2173i) q^{74} +(-5.00000 - 0.460702i) q^{75} +(1.27526 - 2.20881i) q^{76} +(4.89898 - 6.92820i) q^{78} +(0.949490 + 1.64456i) q^{79} +1.44949 q^{80} +(-7.00000 + 5.65685i) q^{81} -9.79796 q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(-3.44949 + 5.97469i) q^{86} +(-11.8990 - 1.09638i) q^{87} +(-1.00000 - 1.73205i) q^{88} +16.8990 q^{89} +(-1.44949 - 4.09978i) q^{90} +(0.500000 + 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} +(4.89898 - 8.48528i) q^{94} +(1.84847 - 3.20164i) q^{95} +(-0.724745 - 1.57313i) q^{96} +(1.44949 + 2.51059i) q^{97} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} - 2 q^{16} - 8 q^{17} + 2 q^{18} - 20 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} - 4 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} + 4 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} + 8 q^{37} + 10 q^{38} + 24 q^{39} + 2 q^{40} - 4 q^{43} + 8 q^{44} + 22 q^{45} - 4 q^{46} + 2 q^{48} - 4 q^{50} + 8 q^{51} - 24 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} - 4 q^{59} + 10 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} - 4 q^{72} + 8 q^{73} - 4 q^{74} - 20 q^{75} + 10 q^{76} - 6 q^{79} - 4 q^{80} - 28 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} - 28 q^{87} - 4 q^{88} + 48 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} - 22 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −1.00000 + 1.41421i −0.577350 + 0.816497i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.724745 + 1.25529i −0.324116 + 0.561385i −0.981333 0.192316i \(-0.938400\pi\)
0.657217 + 0.753701i \(0.271733\pi\)
\(6\) 1.72474 + 0.158919i 0.704124 + 0.0648783i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −1.00000 2.82843i −0.333333 0.942809i
\(10\) 1.44949 0.458369
\(11\) −1.00000 1.73205i −0.301511 0.522233i 0.674967 0.737848i \(-0.264158\pi\)
−0.976478 + 0.215615i \(0.930824\pi\)
\(12\) −0.724745 1.57313i −0.209216 0.454124i
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) 0 0
\(15\) −1.05051 2.28024i −0.271241 0.588755i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) −1.94949 + 2.28024i −0.459499 + 0.537457i
\(19\) −2.55051 −0.585127 −0.292564 0.956246i \(-0.594508\pi\)
−0.292564 + 0.956246i \(0.594508\pi\)
\(20\) −0.724745 1.25529i −0.162058 0.280692i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) −1.00000 + 1.41421i −0.204124 + 0.288675i
\(25\) 1.44949 + 2.51059i 0.289898 + 0.502118i
\(26\) −4.89898 −0.960769
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) 3.44949 + 5.97469i 0.640554 + 1.10947i 0.985309 + 0.170780i \(0.0546286\pi\)
−0.344755 + 0.938693i \(0.612038\pi\)
\(30\) −1.44949 + 2.04989i −0.264639 + 0.374257i
\(31\) 3.00000 5.19615i 0.538816 0.933257i −0.460152 0.887840i \(-0.652205\pi\)
0.998968 0.0454165i \(-0.0144615\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 3.44949 + 0.317837i 0.600479 + 0.0553284i
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 0 0
\(36\) 2.94949 + 0.548188i 0.491582 + 0.0913647i
\(37\) 11.7980 1.93957 0.969786 0.243956i \(-0.0784453\pi\)
0.969786 + 0.243956i \(0.0784453\pi\)
\(38\) 1.27526 + 2.20881i 0.206874 + 0.358316i
\(39\) 3.55051 + 7.70674i 0.568537 + 1.23407i
\(40\) −0.724745 + 1.25529i −0.114592 + 0.198480i
\(41\) 4.89898 8.48528i 0.765092 1.32518i −0.175106 0.984550i \(-0.556027\pi\)
0.940198 0.340629i \(-0.110640\pi\)
\(42\) 0 0
\(43\) −3.44949 5.97469i −0.526042 0.911132i −0.999540 0.0303367i \(-0.990342\pi\)
0.473497 0.880795i \(-0.342991\pi\)
\(44\) 2.00000 0.301511
\(45\) 4.27526 + 0.794593i 0.637317 + 0.118451i
\(46\) −1.00000 −0.147442
\(47\) 4.89898 + 8.48528i 0.714590 + 1.23771i 0.963118 + 0.269081i \(0.0867199\pi\)
−0.248528 + 0.968625i \(0.579947\pi\)
\(48\) 1.72474 + 0.158919i 0.248945 + 0.0229379i
\(49\) 0 0
\(50\) 1.44949 2.51059i 0.204989 0.355051i
\(51\) 2.00000 2.82843i 0.280056 0.396059i
\(52\) 2.44949 + 4.24264i 0.339683 + 0.588348i
\(53\) −10.8990 −1.49709 −0.748545 0.663084i \(-0.769247\pi\)
−0.748545 + 0.663084i \(0.769247\pi\)
\(54\) −1.27526 5.03723i −0.173540 0.685481i
\(55\) 2.89898 0.390898
\(56\) 0 0
\(57\) 2.55051 3.60697i 0.337823 0.477754i
\(58\) 3.44949 5.97469i 0.452940 0.784515i
\(59\) −1.00000 + 1.73205i −0.130189 + 0.225494i −0.923749 0.382998i \(-0.874892\pi\)
0.793560 + 0.608492i \(0.208225\pi\)
\(60\) 2.50000 + 0.230351i 0.322749 + 0.0297382i
\(61\) 3.27526 + 5.67291i 0.419353 + 0.726341i 0.995875 0.0907408i \(-0.0289235\pi\)
−0.576521 + 0.817082i \(0.695590\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.55051 + 6.14966i 0.440387 + 0.762772i
\(66\) −1.44949 3.14626i −0.178420 0.387278i
\(67\) 6.44949 11.1708i 0.787931 1.36474i −0.139302 0.990250i \(-0.544486\pi\)
0.927233 0.374486i \(-0.122181\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0.724745 + 1.57313i 0.0872490 + 0.189383i
\(70\) 0 0
\(71\) 0.101021 0.0119889 0.00599446 0.999982i \(-0.498092\pi\)
0.00599446 + 0.999982i \(0.498092\pi\)
\(72\) −1.00000 2.82843i −0.117851 0.333333i
\(73\) 6.89898 0.807464 0.403732 0.914877i \(-0.367713\pi\)
0.403732 + 0.914877i \(0.367713\pi\)
\(74\) −5.89898 10.2173i −0.685742 1.18774i
\(75\) −5.00000 0.460702i −0.577350 0.0531973i
\(76\) 1.27526 2.20881i 0.146282 0.253368i
\(77\) 0 0
\(78\) 4.89898 6.92820i 0.554700 0.784465i
\(79\) 0.949490 + 1.64456i 0.106826 + 0.185028i 0.914483 0.404625i \(-0.132598\pi\)
−0.807657 + 0.589653i \(0.799265\pi\)
\(80\) 1.44949 0.162058
\(81\) −7.00000 + 5.65685i −0.777778 + 0.628539i
\(82\) −9.79796 −1.08200
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) 1.44949 2.51059i 0.157219 0.272312i
\(86\) −3.44949 + 5.97469i −0.371968 + 0.644268i
\(87\) −11.8990 1.09638i −1.27570 0.117544i
\(88\) −1.00000 1.73205i −0.106600 0.184637i
\(89\) 16.8990 1.79129 0.895644 0.444771i \(-0.146715\pi\)
0.895644 + 0.444771i \(0.146715\pi\)
\(90\) −1.44949 4.09978i −0.152790 0.432154i
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 4.34847 + 9.43879i 0.450915 + 0.978757i
\(94\) 4.89898 8.48528i 0.505291 0.875190i
\(95\) 1.84847 3.20164i 0.189649 0.328482i
\(96\) −0.724745 1.57313i −0.0739690 0.160557i
\(97\) 1.44949 + 2.51059i 0.147173 + 0.254912i 0.930182 0.367099i \(-0.119649\pi\)
−0.783008 + 0.622011i \(0.786316\pi\)
\(98\) 0 0
\(99\) −3.89898 + 4.56048i −0.391862 + 0.458345i
\(100\) −2.89898 −0.289898
\(101\) −8.62372 14.9367i −0.858093 1.48626i −0.873746 0.486383i \(-0.838316\pi\)
0.0156533 0.999877i \(-0.495017\pi\)
\(102\) −3.44949 0.317837i −0.341550 0.0314706i
\(103\) 7.00000 12.1244i 0.689730 1.19465i −0.282194 0.959357i \(-0.591062\pi\)
0.971925 0.235291i \(-0.0756043\pi\)
\(104\) 2.44949 4.24264i 0.240192 0.416025i
\(105\) 0 0
\(106\) 5.44949 + 9.43879i 0.529301 + 0.916777i
\(107\) −12.0000 −1.16008 −0.580042 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −3.72474 + 3.62302i −0.358414 + 0.348625i
\(109\) 12.6969 1.21615 0.608073 0.793881i \(-0.291943\pi\)
0.608073 + 0.793881i \(0.291943\pi\)
\(110\) −1.44949 2.51059i −0.138203 0.239375i
\(111\) −11.7980 + 16.6848i −1.11981 + 1.58365i
\(112\) 0 0
\(113\) 3.05051 5.28364i 0.286968 0.497043i −0.686117 0.727492i \(-0.740686\pi\)
0.973084 + 0.230449i \(0.0740194\pi\)
\(114\) −4.39898 0.405324i −0.412002 0.0379620i
\(115\) 0.724745 + 1.25529i 0.0675828 + 0.117057i
\(116\) −6.89898 −0.640554
\(117\) −14.4495 2.68556i −1.33586 0.248280i
\(118\) 2.00000 0.184115
\(119\) 0 0
\(120\) −1.05051 2.28024i −0.0958980 0.208156i
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 3.27526 5.67291i 0.296528 0.513601i
\(123\) 7.10102 + 15.4135i 0.640277 + 1.38979i
\(124\) 3.00000 + 5.19615i 0.269408 + 0.466628i
\(125\) −11.4495 −1.02407
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 11.8990 + 1.09638i 1.04765 + 0.0965306i
\(130\) 3.55051 6.14966i 0.311400 0.539361i
\(131\) −4.27526 + 7.40496i −0.373531 + 0.646974i −0.990106 0.140322i \(-0.955186\pi\)
0.616575 + 0.787296i \(0.288520\pi\)
\(132\) −2.00000 + 2.82843i −0.174078 + 0.246183i
\(133\) 0 0
\(134\) −12.8990 −1.11430
\(135\) −5.39898 + 5.25153i −0.464670 + 0.451980i
\(136\) −2.00000 −0.171499
\(137\) −3.89898 6.75323i −0.333112 0.576967i 0.650008 0.759927i \(-0.274765\pi\)
−0.983120 + 0.182960i \(0.941432\pi\)
\(138\) 1.00000 1.41421i 0.0851257 0.120386i
\(139\) 2.27526 3.94086i 0.192985 0.334259i −0.753253 0.657730i \(-0.771517\pi\)
0.946238 + 0.323471i \(0.104850\pi\)
\(140\) 0 0
\(141\) −16.8990 1.55708i −1.42315 0.131130i
\(142\) −0.0505103 0.0874863i −0.00423873 0.00734169i
\(143\) −9.79796 −0.819346
\(144\) −1.94949 + 2.28024i −0.162457 + 0.190020i
\(145\) −10.0000 −0.830455
\(146\) −3.44949 5.97469i −0.285482 0.494469i
\(147\) 0 0
\(148\) −5.89898 + 10.2173i −0.484893 + 0.839860i
\(149\) 3.00000 5.19615i 0.245770 0.425685i −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 2.10102 + 4.56048i 0.171548 + 0.372361i
\(151\) 2.50000 + 4.33013i 0.203447 + 0.352381i 0.949637 0.313353i \(-0.101452\pi\)
−0.746190 + 0.665733i \(0.768119\pi\)
\(152\) −2.55051 −0.206874
\(153\) 2.00000 + 5.65685i 0.161690 + 0.457330i
\(154\) 0 0
\(155\) 4.34847 + 7.53177i 0.349277 + 0.604966i
\(156\) −8.44949 0.778539i −0.676501 0.0623330i
\(157\) −4.17423 + 7.22999i −0.333140 + 0.577016i −0.983126 0.182931i \(-0.941442\pi\)
0.649986 + 0.759947i \(0.274775\pi\)
\(158\) 0.949490 1.64456i 0.0755373 0.130835i
\(159\) 10.8990 15.4135i 0.864345 1.22237i
\(160\) −0.724745 1.25529i −0.0572961 0.0992398i
\(161\) 0 0
\(162\) 8.39898 + 3.23375i 0.659886 + 0.254067i
\(163\) −19.7980 −1.55070 −0.775348 0.631534i \(-0.782425\pi\)
−0.775348 + 0.631534i \(0.782425\pi\)
\(164\) 4.89898 + 8.48528i 0.382546 + 0.662589i
\(165\) −2.89898 + 4.09978i −0.225685 + 0.319167i
\(166\) 1.00000 1.73205i 0.0776151 0.134433i
\(167\) −5.34847 + 9.26382i −0.413877 + 0.716856i −0.995310 0.0967384i \(-0.969159\pi\)
0.581433 + 0.813594i \(0.302492\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) −2.89898 −0.222342
\(171\) 2.55051 + 7.21393i 0.195042 + 0.551663i
\(172\) 6.89898 0.526042
\(173\) −1.55051 2.68556i −0.117883 0.204180i 0.801045 0.598604i \(-0.204277\pi\)
−0.918929 + 0.394424i \(0.870944\pi\)
\(174\) 5.00000 + 10.8530i 0.379049 + 0.822764i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) −1.44949 3.14626i −0.108950 0.236488i
\(178\) −8.44949 14.6349i −0.633316 1.09694i
\(179\) 20.6969 1.54696 0.773481 0.633820i \(-0.218514\pi\)
0.773481 + 0.633820i \(0.218514\pi\)
\(180\) −2.82577 + 3.30518i −0.210620 + 0.246354i
\(181\) 10.3485 0.769196 0.384598 0.923084i \(-0.374340\pi\)
0.384598 + 0.923084i \(0.374340\pi\)
\(182\) 0 0
\(183\) −11.2980 1.04100i −0.835169 0.0769528i
\(184\) 0.500000 0.866025i 0.0368605 0.0638442i
\(185\) −8.55051 + 14.8099i −0.628646 + 1.08885i
\(186\) 6.00000 8.48528i 0.439941 0.622171i
\(187\) 2.00000 + 3.46410i 0.146254 + 0.253320i
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) −3.69694 −0.268204
\(191\) −2.05051 3.55159i −0.148370 0.256984i 0.782255 0.622958i \(-0.214069\pi\)
−0.930625 + 0.365974i \(0.880736\pi\)
\(192\) −1.00000 + 1.41421i −0.0721688 + 0.102062i
\(193\) 8.94949 15.5010i 0.644198 1.11578i −0.340288 0.940321i \(-0.610524\pi\)
0.984486 0.175463i \(-0.0561422\pi\)
\(194\) 1.44949 2.51059i 0.104067 0.180250i
\(195\) −12.2474 1.12848i −0.877058 0.0808124i
\(196\) 0 0
\(197\) 16.6969 1.18961 0.594804 0.803871i \(-0.297230\pi\)
0.594804 + 0.803871i \(0.297230\pi\)
\(198\) 5.89898 + 1.09638i 0.419222 + 0.0779161i
\(199\) 2.89898 0.205503 0.102752 0.994707i \(-0.467235\pi\)
0.102752 + 0.994707i \(0.467235\pi\)
\(200\) 1.44949 + 2.51059i 0.102494 + 0.177526i
\(201\) 9.34847 + 20.2918i 0.659390 + 1.43127i
\(202\) −8.62372 + 14.9367i −0.606763 + 1.05094i
\(203\) 0 0
\(204\) 1.44949 + 3.14626i 0.101485 + 0.220283i
\(205\) 7.10102 + 12.2993i 0.495957 + 0.859022i
\(206\) −14.0000 −0.975426
\(207\) −2.94949 0.548188i −0.205004 0.0381017i
\(208\) −4.89898 −0.339683
\(209\) 2.55051 + 4.41761i 0.176422 + 0.305573i
\(210\) 0 0
\(211\) −6.44949 + 11.1708i −0.444001 + 0.769033i −0.997982 0.0634968i \(-0.979775\pi\)
0.553981 + 0.832529i \(0.313108\pi\)
\(212\) 5.44949 9.43879i 0.374272 0.648259i
\(213\) −0.101021 + 0.142865i −0.00692181 + 0.00978892i
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 10.0000 0.681994
\(216\) 5.00000 + 1.41421i 0.340207 + 0.0962250i
\(217\) 0 0
\(218\) −6.34847 10.9959i −0.429973 0.744734i
\(219\) −6.89898 + 9.75663i −0.466190 + 0.659292i
\(220\) −1.44949 + 2.51059i −0.0977246 + 0.169264i
\(221\) −4.89898 + 8.48528i −0.329541 + 0.570782i
\(222\) 20.3485 + 1.87492i 1.36570 + 0.125836i
\(223\) −5.55051 9.61377i −0.371690 0.643785i 0.618136 0.786071i \(-0.287888\pi\)
−0.989826 + 0.142286i \(0.954555\pi\)
\(224\) 0 0
\(225\) 5.65153 6.61037i 0.376769 0.440691i
\(226\) −6.10102 −0.405834
\(227\) −2.72474 4.71940i −0.180848 0.313237i 0.761322 0.648374i \(-0.224551\pi\)
−0.942169 + 0.335137i \(0.891217\pi\)
\(228\) 1.84847 + 4.01229i 0.122418 + 0.265720i
\(229\) 0.623724 1.08032i 0.0412169 0.0713897i −0.844681 0.535270i \(-0.820210\pi\)
0.885898 + 0.463880i \(0.153543\pi\)
\(230\) 0.724745 1.25529i 0.0477883 0.0827717i
\(231\) 0 0
\(232\) 3.44949 + 5.97469i 0.226470 + 0.392258i
\(233\) −7.00000 −0.458585 −0.229293 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 4.89898 + 13.8564i 0.320256 + 0.905822i
\(235\) −14.2020 −0.926439
\(236\) −1.00000 1.73205i −0.0650945 0.112747i
\(237\) −3.27526 0.301783i −0.212751 0.0196029i
\(238\) 0 0
\(239\) −3.39898 + 5.88721i −0.219862 + 0.380812i −0.954766 0.297360i \(-0.903894\pi\)
0.734904 + 0.678171i \(0.237227\pi\)
\(240\) −1.44949 + 2.04989i −0.0935642 + 0.132320i
\(241\) 0.449490 + 0.778539i 0.0289542 + 0.0501501i 0.880139 0.474715i \(-0.157449\pi\)
−0.851185 + 0.524865i \(0.824116\pi\)
\(242\) −7.00000 −0.449977
\(243\) −1.00000 15.5563i −0.0641500 0.997940i
\(244\) −6.55051 −0.419353
\(245\) 0 0
\(246\) 9.79796 13.8564i 0.624695 0.883452i
\(247\) −6.24745 + 10.8209i −0.397516 + 0.688517i
\(248\) 3.00000 5.19615i 0.190500 0.329956i
\(249\) −3.44949 0.317837i −0.218603 0.0201421i
\(250\) 5.72474 + 9.91555i 0.362065 + 0.627114i
\(251\) −17.4495 −1.10140 −0.550701 0.834703i \(-0.685640\pi\)
−0.550701 + 0.834703i \(0.685640\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 1.50000 + 2.59808i 0.0941184 + 0.163018i
\(255\) 2.10102 + 4.56048i 0.131571 + 0.285588i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.10102 7.10318i 0.255815 0.443084i −0.709302 0.704905i \(-0.750990\pi\)
0.965116 + 0.261821i \(0.0843230\pi\)
\(258\) −5.00000 10.8530i −0.311286 0.675679i
\(259\) 0 0
\(260\) −7.10102 −0.440387
\(261\) 13.4495 15.7313i 0.832503 0.973744i
\(262\) 8.55051 0.528252
\(263\) −12.9495 22.4292i −0.798500 1.38304i −0.920593 0.390523i \(-0.872294\pi\)
0.122093 0.992519i \(-0.461039\pi\)
\(264\) 3.44949 + 0.317837i 0.212301 + 0.0195615i
\(265\) 7.89898 13.6814i 0.485230 0.840444i
\(266\) 0 0
\(267\) −16.8990 + 23.8988i −1.03420 + 1.46258i
\(268\) 6.44949 + 11.1708i 0.393965 + 0.682368i
\(269\) 18.3485 1.11873 0.559363 0.828923i \(-0.311046\pi\)
0.559363 + 0.828923i \(0.311046\pi\)
\(270\) 7.24745 + 2.04989i 0.441066 + 0.124752i
\(271\) −7.10102 −0.431356 −0.215678 0.976465i \(-0.569196\pi\)
−0.215678 + 0.976465i \(0.569196\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −3.89898 + 6.75323i −0.235546 + 0.407978i
\(275\) 2.89898 5.02118i 0.174815 0.302789i
\(276\) −1.72474 0.158919i −0.103817 0.00956578i
\(277\) 9.34847 + 16.1920i 0.561695 + 0.972884i 0.997349 + 0.0727700i \(0.0231839\pi\)
−0.435654 + 0.900114i \(0.643483\pi\)
\(278\) −4.55051 −0.272921
\(279\) −17.6969 3.28913i −1.05949 0.196915i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 7.10102 + 15.4135i 0.422860 + 0.917860i
\(283\) −12.7247 + 22.0399i −0.756408 + 1.31014i 0.188264 + 0.982118i \(0.439714\pi\)
−0.944672 + 0.328018i \(0.893619\pi\)
\(284\) −0.0505103 + 0.0874863i −0.00299723 + 0.00519136i
\(285\) 2.67934 + 5.81577i 0.158710 + 0.344497i
\(286\) 4.89898 + 8.48528i 0.289683 + 0.501745i
\(287\) 0 0
\(288\) 2.94949 + 0.548188i 0.173800 + 0.0323023i
\(289\) −13.0000 −0.764706
\(290\) 5.00000 + 8.66025i 0.293610 + 0.508548i
\(291\) −5.00000 0.460702i −0.293105 0.0270068i
\(292\) −3.44949 + 5.97469i −0.201866 + 0.349642i
\(293\) 1.37628 2.38378i 0.0804029 0.139262i −0.823020 0.568012i \(-0.807713\pi\)
0.903423 + 0.428750i \(0.141046\pi\)
\(294\) 0 0
\(295\) −1.44949 2.51059i −0.0843926 0.146172i
\(296\) 11.7980 0.685742
\(297\) −2.55051 10.0745i −0.147996 0.584580i
\(298\) −6.00000 −0.347571
\(299\) −2.44949 4.24264i −0.141658 0.245358i
\(300\) 2.89898 4.09978i 0.167373 0.236701i
\(301\) 0 0
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) 29.7474 + 2.74094i 1.70895 + 0.157463i
\(304\) 1.27526 + 2.20881i 0.0731409 + 0.126684i
\(305\) −9.49490 −0.543676
\(306\) 3.89898 4.56048i 0.222890 0.260705i
\(307\) −25.2474 −1.44095 −0.720474 0.693482i \(-0.756076\pi\)
−0.720474 + 0.693482i \(0.756076\pi\)
\(308\) 0 0
\(309\) 10.1464 + 22.0239i 0.577210 + 1.25289i
\(310\) 4.34847 7.53177i 0.246976 0.427776i
\(311\) 15.3485 26.5843i 0.870332 1.50746i 0.00867810 0.999962i \(-0.497238\pi\)
0.861654 0.507497i \(-0.169429\pi\)
\(312\) 3.55051 + 7.70674i 0.201008 + 0.436308i
\(313\) −2.34847 4.06767i −0.132743 0.229918i 0.791990 0.610534i \(-0.209045\pi\)
−0.924733 + 0.380616i \(0.875712\pi\)
\(314\) 8.34847 0.471131
\(315\) 0 0
\(316\) −1.89898 −0.106826
\(317\) −10.3485 17.9241i −0.581228 1.00672i −0.995334 0.0964878i \(-0.969239\pi\)
0.414106 0.910229i \(-0.364094\pi\)
\(318\) −18.7980 1.73205i −1.05414 0.0971286i
\(319\) 6.89898 11.9494i 0.386269 0.669037i
\(320\) −0.724745 + 1.25529i −0.0405145 + 0.0701731i
\(321\) 12.0000 16.9706i 0.669775 0.947204i
\(322\) 0 0
\(323\) 5.10102 0.283828
\(324\) −1.39898 8.89060i −0.0777211 0.493922i
\(325\) 14.2020 0.787787
\(326\) 9.89898 + 17.1455i 0.548254 + 0.949603i
\(327\) −12.6969 + 17.9562i −0.702142 + 0.992979i
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) 0 0
\(330\) 5.00000 + 0.460702i 0.275241 + 0.0253608i
\(331\) −2.34847 4.06767i −0.129084 0.223579i 0.794238 0.607606i \(-0.207870\pi\)
−0.923322 + 0.384027i \(0.874537\pi\)
\(332\) −2.00000 −0.109764
\(333\) −11.7980 33.3697i −0.646524 1.82865i
\(334\) 10.6969 0.585310
\(335\) 9.34847 + 16.1920i 0.510761 + 0.884665i
\(336\) 0 0
\(337\) 11.6969 20.2597i 0.637173 1.10362i −0.348877 0.937168i \(-0.613437\pi\)
0.986050 0.166447i \(-0.0532296\pi\)
\(338\) −5.50000 + 9.52628i −0.299161 + 0.518161i
\(339\) 4.42168 + 9.59771i 0.240153 + 0.521276i
\(340\) 1.44949 + 2.51059i 0.0786096 + 0.136156i
\(341\) −12.0000 −0.649836
\(342\) 4.97219 5.81577i 0.268865 0.314481i
\(343\) 0 0
\(344\) −3.44949 5.97469i −0.185984 0.322134i
\(345\) −2.50000 0.230351i −0.134595 0.0124017i
\(346\) −1.55051 + 2.68556i −0.0833559 + 0.144377i
\(347\) −9.79796 + 16.9706i −0.525982 + 0.911028i 0.473560 + 0.880762i \(0.342969\pi\)
−0.999542 + 0.0302659i \(0.990365\pi\)
\(348\) 6.89898 9.75663i 0.369824 0.523010i
\(349\) 5.55051 + 9.61377i 0.297112 + 0.514613i 0.975474 0.220115i \(-0.0706432\pi\)
−0.678362 + 0.734728i \(0.737310\pi\)
\(350\) 0 0
\(351\) 18.2474 17.7491i 0.973977 0.947377i
\(352\) 2.00000 0.106600
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) −2.00000 + 2.82843i −0.106299 + 0.150329i
\(355\) −0.0732141 + 0.126811i −0.00388580 + 0.00673040i
\(356\) −8.44949 + 14.6349i −0.447822 + 0.775651i
\(357\) 0 0
\(358\) −10.3485 17.9241i −0.546934 0.947317i
\(359\) −8.79796 −0.464339 −0.232169 0.972675i \(-0.574582\pi\)
−0.232169 + 0.972675i \(0.574582\pi\)
\(360\) 4.27526 + 0.794593i 0.225326 + 0.0418787i
\(361\) −12.4949 −0.657626
\(362\) −5.17423 8.96204i −0.271952 0.471034i
\(363\) 5.07321 + 11.0119i 0.266275 + 0.577976i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 4.74745 + 10.3048i 0.248153 + 0.538641i
\(367\) −6.89898 11.9494i −0.360124 0.623753i 0.627857 0.778329i \(-0.283932\pi\)
−0.987981 + 0.154576i \(0.950599\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −28.8990 5.37113i −1.50442 0.279610i
\(370\) 17.1010 0.889040
\(371\) 0 0
\(372\) −10.3485 0.953512i −0.536543 0.0494373i
\(373\) 3.44949 5.97469i 0.178608 0.309358i −0.762796 0.646639i \(-0.776174\pi\)
0.941404 + 0.337281i \(0.109507\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 11.4495 16.1920i 0.591249 0.836153i
\(376\) 4.89898 + 8.48528i 0.252646 + 0.437595i
\(377\) 33.7980 1.74068
\(378\) 0 0
\(379\) 22.4949 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(380\) 1.84847 + 3.20164i 0.0948245 + 0.164241i
\(381\) 3.00000 4.24264i 0.153695 0.217357i
\(382\) −2.05051 + 3.55159i −0.104913 + 0.181715i
\(383\) −1.44949 + 2.51059i −0.0740655 + 0.128285i −0.900679 0.434484i \(-0.856931\pi\)
0.826614 + 0.562769i \(0.190264\pi\)
\(384\) 1.72474 + 0.158919i 0.0880155 + 0.00810978i
\(385\) 0 0
\(386\) −17.8990 −0.911034
\(387\) −13.4495 + 15.7313i −0.683676 + 0.799668i
\(388\) −2.89898 −0.147173
\(389\) 12.4495 + 21.5631i 0.631214 + 1.09330i 0.987304 + 0.158843i \(0.0507764\pi\)
−0.356090 + 0.934452i \(0.615890\pi\)
\(390\) 5.14643 + 11.1708i 0.260600 + 0.565658i
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) −6.19694 13.4511i −0.312594 0.678517i
\(394\) −8.34847 14.4600i −0.420590 0.728483i
\(395\) −2.75255 −0.138496
\(396\) −2.00000 5.65685i −0.100504 0.284268i
\(397\) −38.6969 −1.94214 −0.971072 0.238788i \(-0.923250\pi\)
−0.971072 + 0.238788i \(0.923250\pi\)
\(398\) −1.44949 2.51059i −0.0726564 0.125844i
\(399\) 0 0
\(400\) 1.44949 2.51059i 0.0724745 0.125529i
\(401\) 9.94949 17.2330i 0.496854 0.860576i −0.503140 0.864205i \(-0.667822\pi\)
0.999993 + 0.00362911i \(0.00115518\pi\)
\(402\) 12.8990 18.2419i 0.643343 0.909824i
\(403\) −14.6969 25.4558i −0.732107 1.26805i
\(404\) 17.2474 0.858093
\(405\) −2.02781 12.8868i −0.100763 0.640352i
\(406\) 0 0
\(407\) −11.7980 20.4347i −0.584803 1.01291i
\(408\) 2.00000 2.82843i 0.0990148 0.140028i
\(409\) −6.89898 + 11.9494i −0.341133 + 0.590859i −0.984643 0.174578i \(-0.944144\pi\)
0.643511 + 0.765437i \(0.277477\pi\)
\(410\) 7.10102 12.2993i 0.350694 0.607421i
\(411\) 13.4495 + 1.23924i 0.663414 + 0.0611272i
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 0 0
\(414\) 1.00000 + 2.82843i 0.0491473 + 0.139010i
\(415\) −2.89898 −0.142305
\(416\) 2.44949 + 4.24264i 0.120096 + 0.208013i
\(417\) 3.29796 + 7.15855i 0.161502 + 0.350556i
\(418\) 2.55051 4.41761i 0.124750 0.216073i
\(419\) 14.7247 25.5040i 0.719351 1.24595i −0.241906 0.970300i \(-0.577773\pi\)
0.961257 0.275653i \(-0.0888940\pi\)
\(420\) 0 0
\(421\) −11.4495 19.8311i −0.558014 0.966509i −0.997662 0.0683385i \(-0.978230\pi\)
0.439648 0.898170i \(-0.355103\pi\)
\(422\) 12.8990 0.627912
\(423\) 19.1010 22.3417i 0.928723 1.08629i
\(424\) −10.8990 −0.529301
\(425\) −2.89898 5.02118i −0.140621 0.243563i
\(426\) 0.174235 + 0.0160540i 0.00844169 + 0.000777821i
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 9.79796 13.8564i 0.473050 0.668994i
\(430\) −5.00000 8.66025i −0.241121 0.417635i
\(431\) 31.5959 1.52192 0.760961 0.648798i \(-0.224728\pi\)
0.760961 + 0.648798i \(0.224728\pi\)
\(432\) −1.27526 5.03723i −0.0613557 0.242354i
\(433\) 7.79796 0.374746 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(434\) 0 0
\(435\) 10.0000 14.1421i 0.479463 0.678064i
\(436\) −6.34847 + 10.9959i −0.304037 + 0.526607i
\(437\) −1.27526 + 2.20881i −0.0610037 + 0.105662i
\(438\) 11.8990 + 1.09638i 0.568555 + 0.0523869i
\(439\) 1.10102 + 1.90702i 0.0525488 + 0.0910173i 0.891103 0.453801i \(-0.149932\pi\)
−0.838554 + 0.544818i \(0.816599\pi\)
\(440\) 2.89898 0.138203
\(441\) 0 0
\(442\) 9.79796 0.466041
\(443\) 7.44949 + 12.9029i 0.353936 + 0.613035i 0.986935 0.161117i \(-0.0515098\pi\)
−0.632999 + 0.774152i \(0.718176\pi\)
\(444\) −8.55051 18.5597i −0.405789 0.880807i
\(445\) −12.2474 + 21.2132i −0.580585 + 1.00560i
\(446\) −5.55051 + 9.61377i −0.262824 + 0.455225i
\(447\) 4.34847 + 9.43879i 0.205676 + 0.446440i
\(448\) 0 0
\(449\) 20.5959 0.971981 0.485991 0.873964i \(-0.338459\pi\)
0.485991 + 0.873964i \(0.338459\pi\)
\(450\) −8.55051 1.58919i −0.403075 0.0749150i
\(451\) −19.5959 −0.922736
\(452\) 3.05051 + 5.28364i 0.143484 + 0.248521i
\(453\) −8.62372 0.794593i −0.405178 0.0373332i
\(454\) −2.72474 + 4.71940i −0.127879 + 0.221492i
\(455\) 0 0
\(456\) 2.55051 3.60697i 0.119439 0.168912i
\(457\) 8.74745 + 15.1510i 0.409188 + 0.708735i 0.994799 0.101857i \(-0.0324785\pi\)
−0.585611 + 0.810593i \(0.699145\pi\)
\(458\) −1.24745 −0.0582895
\(459\) −10.0000 2.82843i −0.466760 0.132020i
\(460\) −1.44949 −0.0675828
\(461\) 2.82577 + 4.89437i 0.131609 + 0.227954i 0.924297 0.381674i \(-0.124652\pi\)
−0.792688 + 0.609628i \(0.791319\pi\)
\(462\) 0 0
\(463\) −1.84847 + 3.20164i −0.0859057 + 0.148793i −0.905777 0.423755i \(-0.860712\pi\)
0.819871 + 0.572548i \(0.194045\pi\)
\(464\) 3.44949 5.97469i 0.160139 0.277368i
\(465\) −15.0000 1.38211i −0.695608 0.0640936i
\(466\) 3.50000 + 6.06218i 0.162134 + 0.280825i
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) 9.55051 11.1708i 0.441472 0.516372i
\(469\) 0 0
\(470\) 7.10102 + 12.2993i 0.327546 + 0.567326i
\(471\) −6.05051 13.1332i −0.278793 0.605148i
\(472\) −1.00000 + 1.73205i −0.0460287 + 0.0797241i
\(473\) −6.89898 + 11.9494i −0.317215 + 0.549433i
\(474\) 1.37628 + 2.98735i 0.0632144 + 0.137213i
\(475\) −3.69694 6.40329i −0.169627 0.293803i
\(476\) 0 0
\(477\) 10.8990 + 30.8270i 0.499030 + 1.41147i
\(478\) 6.79796 0.310931
\(479\) 4.79796 + 8.31031i 0.219224 + 0.379708i 0.954571 0.297983i \(-0.0963140\pi\)
−0.735347 + 0.677691i \(0.762981\pi\)
\(480\) 2.50000 + 0.230351i 0.114109 + 0.0105140i
\(481\) 28.8990 50.0545i 1.31768 2.28229i
\(482\) 0.449490 0.778539i 0.0204737 0.0354615i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) −4.20204 −0.190805
\(486\) −12.9722 + 8.64420i −0.588431 + 0.392109i
\(487\) −36.3939 −1.64916 −0.824582 0.565742i \(-0.808590\pi\)
−0.824582 + 0.565742i \(0.808590\pi\)
\(488\) 3.27526 + 5.67291i 0.148264 + 0.256800i
\(489\) 19.7980 27.9985i 0.895295 1.26614i
\(490\) 0 0
\(491\) −7.89898 + 13.6814i −0.356476 + 0.617434i −0.987369 0.158435i \(-0.949355\pi\)
0.630893 + 0.775869i \(0.282688\pi\)
\(492\) −16.8990 1.55708i −0.761865 0.0701985i
\(493\) −6.89898 11.9494i −0.310714 0.538173i
\(494\) 12.4949 0.562172
\(495\) −2.89898 8.19955i −0.130299 0.368542i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 1.44949 + 3.14626i 0.0649532 + 0.140987i
\(499\) 12.6969 21.9917i 0.568393 0.984486i −0.428332 0.903621i \(-0.640899\pi\)
0.996725 0.0808642i \(-0.0257680\pi\)
\(500\) 5.72474 9.91555i 0.256018 0.443437i
\(501\) −7.75255 16.8277i −0.346358 0.751806i
\(502\) 8.72474 + 15.1117i 0.389404 + 0.674468i
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) 1.00000 + 1.73205i 0.0444554 + 0.0769991i
\(507\) 18.9722 + 1.74810i 0.842585 + 0.0776361i
\(508\) 1.50000 2.59808i 0.0665517 0.115271i
\(509\) −3.55051 + 6.14966i −0.157374 + 0.272579i −0.933921 0.357480i \(-0.883636\pi\)
0.776547 + 0.630059i \(0.216969\pi\)
\(510\) 2.89898 4.09978i 0.128369 0.181541i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −12.7526 3.60697i −0.563039 0.159251i
\(514\) −8.20204 −0.361777
\(515\) 10.1464 + 17.5741i 0.447105 + 0.774409i
\(516\) −6.89898 + 9.75663i −0.303711 + 0.429512i
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 0 0
\(519\) 5.34847 + 0.492810i 0.234772 + 0.0216320i
\(520\) 3.55051 + 6.14966i 0.155700 + 0.269681i
\(521\) 9.30306 0.407575 0.203787 0.979015i \(-0.434675\pi\)
0.203787 + 0.979015i \(0.434675\pi\)
\(522\) −20.3485 3.78194i −0.890628 0.165531i
\(523\) 14.3485 0.627415 0.313707 0.949520i \(-0.398429\pi\)
0.313707 + 0.949520i \(0.398429\pi\)
\(524\) −4.27526 7.40496i −0.186765 0.323487i
\(525\) 0 0
\(526\) −12.9495 + 22.4292i −0.564625 + 0.977958i
\(527\) −6.00000 + 10.3923i −0.261364 + 0.452696i
\(528\) −1.44949 3.14626i −0.0630809 0.136924i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) −15.7980 −0.686219
\(531\) 5.89898 + 1.09638i 0.255994 + 0.0475787i
\(532\) 0 0
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) 29.1464 + 2.68556i 1.26129 + 0.116216i
\(535\) 8.69694 15.0635i 0.376001 0.651254i
\(536\) 6.44949 11.1708i 0.278576 0.482507i
\(537\) −20.6969 + 29.2699i −0.893139 + 1.26309i
\(538\) −9.17423 15.8902i −0.395529 0.685077i
\(539\) 0 0
\(540\) −1.84847 7.30142i −0.0795455 0.314203i
\(541\) −18.4949 −0.795158 −0.397579 0.917568i \(-0.630149\pi\)
−0.397579 + 0.917568i \(0.630149\pi\)
\(542\) 3.55051 + 6.14966i 0.152507 + 0.264151i
\(543\) −10.3485 + 14.6349i −0.444095 + 0.628046i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) −9.20204 + 15.9384i −0.394172 + 0.682726i
\(546\) 0 0
\(547\) 3.79796 + 6.57826i 0.162389 + 0.281266i 0.935725 0.352730i \(-0.114747\pi\)
−0.773336 + 0.633996i \(0.781413\pi\)
\(548\) 7.79796 0.333112
\(549\) 12.7702 14.9367i 0.545017 0.637484i
\(550\) −5.79796 −0.247226
\(551\) −8.79796 15.2385i −0.374806 0.649182i
\(552\) 0.724745 + 1.57313i 0.0308472 + 0.0669570i
\(553\) 0 0
\(554\) 9.34847 16.1920i 0.397178 0.687933i
\(555\) −12.3939 26.9022i −0.526091 1.14193i
\(556\) 2.27526 + 3.94086i 0.0964923 + 0.167130i
\(557\) −12.8990 −0.546547 −0.273274 0.961936i \(-0.588106\pi\)
−0.273274 + 0.961936i \(0.588106\pi\)
\(558\) 6.00000 + 16.9706i 0.254000 + 0.718421i
\(559\) −33.7980 −1.42950
\(560\) 0 0
\(561\) −6.89898 0.635674i −0.291275 0.0268382i
\(562\) 9.50000 16.4545i 0.400733 0.694090i
\(563\) −19.9722 + 34.5929i −0.841728 + 1.45791i 0.0467054 + 0.998909i \(0.485128\pi\)
−0.888433 + 0.459006i \(0.848206\pi\)
\(564\) 9.79796 13.8564i 0.412568 0.583460i
\(565\) 4.42168 + 7.65858i 0.186022 + 0.322199i
\(566\) 25.4495 1.06972
\(567\) 0 0
\(568\) 0.101021 0.00423873
\(569\) 15.0000 + 25.9808i 0.628833 + 1.08917i 0.987786 + 0.155815i \(0.0498003\pi\)
−0.358954 + 0.933355i \(0.616866\pi\)
\(570\) 3.69694 5.22826i 0.154848 0.218988i
\(571\) −16.8990 + 29.2699i −0.707200 + 1.22491i 0.258691 + 0.965960i \(0.416709\pi\)
−0.965892 + 0.258947i \(0.916625\pi\)
\(572\) 4.89898 8.48528i 0.204837 0.354787i
\(573\) 7.07321 + 0.651729i 0.295488 + 0.0272263i
\(574\) 0 0
\(575\) 2.89898 0.120896
\(576\) −1.00000 2.82843i −0.0416667 0.117851i
\(577\) 15.5959 0.649267 0.324633 0.945840i \(-0.394759\pi\)
0.324633 + 0.945840i \(0.394759\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 12.9722 + 28.1575i 0.539106 + 1.17018i
\(580\) 5.00000 8.66025i 0.207614 0.359597i
\(581\) 0 0
\(582\) 2.10102 + 4.56048i 0.0870901 + 0.189038i
\(583\) 10.8990 + 18.8776i 0.451390 + 0.781830i
\(584\) 6.89898 0.285482
\(585\) 13.8434 16.1920i 0.572353 0.669458i
\(586\) −2.75255 −0.113707
\(587\) 8.07321 + 13.9832i 0.333217 + 0.577149i 0.983141 0.182850i \(-0.0585324\pi\)
−0.649924 + 0.760000i \(0.725199\pi\)
\(588\) 0 0
\(589\) −7.65153 + 13.2528i −0.315276 + 0.546074i
\(590\) −1.44949 + 2.51059i −0.0596745 + 0.103359i
\(591\) −16.6969 + 23.6130i −0.686820 + 0.971311i
\(592\) −5.89898 10.2173i −0.242447 0.419930i
\(593\) −14.6969 −0.603531 −0.301765 0.953382i \(-0.597576\pi\)
−0.301765 + 0.953382i \(0.597576\pi\)
\(594\) −7.44949 + 7.24604i −0.305656 + 0.297309i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) −2.89898 + 4.09978i −0.118647 + 0.167793i
\(598\) −2.44949 + 4.24264i −0.100167 + 0.173494i
\(599\) 16.8990 29.2699i 0.690474 1.19594i −0.281209 0.959646i \(-0.590736\pi\)
0.971683 0.236289i \(-0.0759312\pi\)
\(600\) −5.00000 0.460702i −0.204124 0.0188081i
\(601\) 8.34847 + 14.4600i 0.340541 + 0.589835i 0.984533 0.175198i \(-0.0560564\pi\)
−0.643992 + 0.765032i \(0.722723\pi\)
\(602\) 0 0
\(603\) −38.0454 7.07107i −1.54933 0.287956i
\(604\) −5.00000 −0.203447
\(605\) 5.07321 + 8.78706i 0.206255 + 0.357245i
\(606\) −12.5000 27.1325i −0.507778 1.10218i
\(607\) 10.3485 17.9241i 0.420031 0.727516i −0.575911 0.817513i \(-0.695352\pi\)
0.995942 + 0.0899969i \(0.0286857\pi\)
\(608\) 1.27526 2.20881i 0.0517184 0.0895789i
\(609\) 0 0
\(610\) 4.74745 + 8.22282i 0.192219 + 0.332932i
\(611\) 48.0000 1.94187
\(612\) −5.89898 1.09638i −0.238452 0.0443184i
\(613\) −14.6969 −0.593604 −0.296802 0.954939i \(-0.595920\pi\)
−0.296802 + 0.954939i \(0.595920\pi\)
\(614\) 12.6237 + 21.8649i 0.509452 + 0.882397i
\(615\) −24.4949 2.25697i −0.987730 0.0910098i
\(616\) 0 0
\(617\) 7.69694 13.3315i 0.309867 0.536706i −0.668466 0.743743i \(-0.733049\pi\)
0.978333 + 0.207037i \(0.0663821\pi\)
\(618\) 14.0000 19.7990i 0.563163 0.796432i
\(619\) 15.0732 + 26.1076i 0.605844 + 1.04935i 0.991918 + 0.126884i \(0.0404976\pi\)
−0.386074 + 0.922468i \(0.626169\pi\)
\(620\) −8.69694 −0.349277
\(621\) 3.72474 3.62302i 0.149469 0.145387i
\(622\) −30.6969 −1.23084
\(623\) 0 0
\(624\) 4.89898 6.92820i 0.196116 0.277350i
\(625\) 1.05051 1.81954i 0.0420204 0.0727815i
\(626\) −2.34847 + 4.06767i −0.0938637 + 0.162577i
\(627\) −8.79796 0.810647i −0.351357 0.0323741i
\(628\) −4.17423 7.22999i −0.166570 0.288508i
\(629\) −23.5959 −0.940831
\(630\) 0 0
\(631\) 27.8990 1.11064 0.555320 0.831636i \(-0.312596\pi\)
0.555320 + 0.831636i \(0.312596\pi\)
\(632\) 0.949490 + 1.64456i 0.0377687 + 0.0654173i
\(633\) −9.34847 20.2918i −0.371568 0.806527i
\(634\) −10.3485 + 17.9241i −0.410990 + 0.711856i
\(635\) 2.17423 3.76588i 0.0862819 0.149445i
\(636\) 7.89898 + 17.1455i 0.313215 + 0.679865i
\(637\) 0 0
\(638\) −13.7980 −0.546266
\(639\) −0.101021 0.285729i −0.00399631 0.0113033i
\(640\) 1.44949 0.0572961
\(641\) 3.74745 + 6.49077i 0.148015 + 0.256370i 0.930494 0.366308i \(-0.119378\pi\)
−0.782479 + 0.622678i \(0.786045\pi\)
\(642\) −20.6969 1.90702i −0.816843 0.0752642i
\(643\) −19.6969 + 34.1161i −0.776771 + 1.34541i 0.157022 + 0.987595i \(0.449811\pi\)
−0.933793 + 0.357812i \(0.883523\pi\)
\(644\) 0 0
\(645\) −10.0000 + 14.1421i −0.393750 + 0.556846i
\(646\) −2.55051 4.41761i −0.100348 0.173809i
\(647\) 50.6969 1.99310 0.996551 0.0829807i \(-0.0264440\pi\)
0.996551 + 0.0829807i \(0.0264440\pi\)
\(648\) −7.00000 + 5.65685i −0.274986 + 0.222222i
\(649\) 4.00000 0.157014
\(650\) −7.10102 12.2993i −0.278525 0.482419i
\(651\) 0 0
\(652\) 9.89898 17.1455i 0.387674 0.671471i
\(653\) −4.89898 + 8.48528i −0.191712 + 0.332055i −0.945818 0.324698i \(-0.894737\pi\)
0.754106 + 0.656753i \(0.228071\pi\)
\(654\) 21.8990 + 2.01778i 0.856318 + 0.0789014i
\(655\) −6.19694 10.7334i −0.242134 0.419389i
\(656\) −9.79796 −0.382546
\(657\) −6.89898 19.5133i −0.269155 0.761285i
\(658\) 0 0
\(659\) 12.3485 + 21.3882i 0.481028 + 0.833165i 0.999763 0.0217701i \(-0.00693018\pi\)
−0.518735 + 0.854935i \(0.673597\pi\)
\(660\) −2.10102 4.56048i −0.0817821 0.177516i
\(661\) 2.27526 3.94086i 0.0884972 0.153282i −0.818379 0.574679i \(-0.805127\pi\)
0.906876 + 0.421397i \(0.138460\pi\)
\(662\) −2.34847 + 4.06767i −0.0912758 + 0.158094i
\(663\) −7.10102 15.4135i −0.275781 0.598610i
\(664\) 1.00000 + 1.73205i 0.0388075 + 0.0672166i
\(665\) 0 0
\(666\) −23.0000 + 26.9022i −0.891232 + 1.04244i
\(667\) 6.89898 0.267130
\(668\) −5.34847 9.26382i −0.206938 0.358428i
\(669\) 19.1464 + 1.76416i 0.740244 + 0.0682063i
\(670\) 9.34847 16.1920i 0.361163 0.625552i
\(671\) 6.55051 11.3458i 0.252880 0.438000i
\(672\) 0 0
\(673\) 4.29796 + 7.44428i 0.165674 + 0.286956i 0.936894 0.349612i \(-0.113687\pi\)
−0.771220 + 0.636568i \(0.780353\pi\)
\(674\) −23.3939 −0.901098
\(675\) 3.69694 + 14.6028i 0.142295 + 0.562063i
\(676\) 11.0000 0.423077
\(677\) 7.34847 + 12.7279i 0.282425 + 0.489174i 0.971981 0.235058i \(-0.0755280\pi\)
−0.689557 + 0.724232i \(0.742195\pi\)
\(678\) 6.10102 8.62815i 0.234308 0.331362i
\(679\) 0 0
\(680\) 1.44949 2.51059i 0.0555854 0.0962767i
\(681\) 9.39898 + 0.866025i 0.360170 + 0.0331862i
\(682\) 6.00000 + 10.3923i 0.229752 + 0.397942i
\(683\) 51.7980 1.98199 0.990997 0.133885i \(-0.0427452\pi\)
0.990997 + 0.133885i \(0.0427452\pi\)
\(684\) −7.52270 1.39816i −0.287638 0.0534600i
\(685\) 11.3031 0.431868
\(686\) 0 0
\(687\) 0.904082 + 1.96240i 0.0344929 + 0.0748703i
\(688\) −3.44949 + 5.97469i −0.131511 + 0.227783i
\(689\) −26.6969 + 46.2405i −1.01707 + 1.76162i
\(690\) 1.05051 + 2.28024i 0.0399922 + 0.0868072i
\(691\) 25.5227 + 44.2066i 0.970929 + 1.68170i 0.692762 + 0.721167i \(0.256394\pi\)
0.278168 + 0.960533i \(0.410273\pi\)
\(692\) 3.10102 0.117883
\(693\) 0 0
\(694\) 19.5959 0.743851
\(695\) 3.29796 + 5.71223i 0.125099 + 0.216677i
\(696\) −11.8990 1.09638i −0.451030 0.0415580i
\(697\) −9.79796 + 16.9706i −0.371124 + 0.642806i
\(698\) 5.55051 9.61377i 0.210090 0.363886i
\(699\) 7.00000 9.89949i 0.264764 0.374433i
\(700\) 0 0
\(701\) −7.39388 −0.279263 −0.139631 0.990204i \(-0.544592\pi\)
−0.139631 + 0.990204i \(0.544592\pi\)
\(702\) −24.4949 6.92820i −0.924500 0.261488i
\(703\) −30.0908 −1.13490
\(704\) −1.00000 1.73205i −0.0376889 0.0652791i
\(705\) 14.2020 20.0847i 0.534880 0.756434i
\(706\) −3.00000 + 5.19615i −0.112906 + 0.195560i
\(707\) 0 0
\(708\) 3.44949 + 0.317837i 0.129640 + 0.0119451i
\(709\) −13.7980 23.8988i −0.518193 0.897537i −0.999777 0.0211367i \(-0.993271\pi\)
0.481583 0.876400i \(-0.340062\pi\)
\(710\) 0.146428 0.00549535
\(711\) 3.70204 4.33013i 0.138837 0.162392i
\(712\) 16.8990 0.633316
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 7.10102 12.2993i 0.265563 0.459969i
\(716\) −10.3485 + 17.9241i −0.386740 + 0.669854i
\(717\) −4.92679 10.6941i −0.183994 0.399378i
\(718\) 4.39898 + 7.61926i 0.164168 + 0.284348i
\(719\) −9.79796 −0.365402 −0.182701 0.983169i \(-0.558484\pi\)
−0.182701 + 0.983169i \(0.558484\pi\)
\(720\) −1.44949 4.09978i −0.0540193 0.152790i
\(721\) 0 0
\(722\) 6.24745 + 10.8209i 0.232506 + 0.402712i
\(723\) −1.55051 0.142865i −0.0576641 0.00531319i
\(724\) −5.17423 + 8.96204i −0.192299 + 0.333071i
\(725\) −10.0000 + 17.3205i −0.371391 + 0.643268i
\(726\) 7.00000 9.89949i 0.259794 0.367405i
\(727\) −4.24745 7.35680i −0.157529 0.272848i 0.776448 0.630181i \(-0.217019\pi\)
−0.933977 + 0.357333i \(0.883686\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) 10.0000 0.370117
\(731\) 6.89898 + 11.9494i 0.255168 + 0.441964i
\(732\) 6.55051 9.26382i 0.242114 0.342401i
\(733\) −8.72474 + 15.1117i −0.322256 + 0.558163i −0.980953 0.194245i \(-0.937774\pi\)
0.658697 + 0.752408i \(0.271108\pi\)
\(734\) −6.89898 + 11.9494i −0.254646 + 0.441060i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) −25.7980 −0.950280
\(738\) 9.79796 + 27.7128i 0.360668 + 1.02012i
\(739\) 13.5959 0.500134 0.250067 0.968229i \(-0.419547\pi\)
0.250067 + 0.968229i \(0.419547\pi\)
\(740\) −8.55051 14.8099i −0.314323 0.544423i
\(741\) −9.05561 19.6561i −0.332666 0.722086i
\(742\) 0 0
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) 4.34847 + 9.43879i 0.159423 + 0.346043i
\(745\) 4.34847 + 7.53177i 0.159316 + 0.275943i
\(746\) −6.89898 −0.252590
\(747\) 3.89898 4.56048i 0.142656 0.166859i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) −19.7474 1.81954i −0.721075 0.0664401i
\(751\) −0.702041 + 1.21597i −0.0256178 + 0.0443714i −0.878550 0.477650i \(-0.841489\pi\)
0.852932 + 0.522022i \(0.174822\pi\)
\(752\) 4.89898 8.48528i 0.178647 0.309426i
\(753\) 17.4495 24.6773i 0.635895 0.899291i
\(754\) −16.8990 29.2699i −0.615425 1.06595i
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) −11.2474 19.4812i −0.408526 0.707587i
\(759\) 2.00000 2.82843i 0.0725954 0.102665i
\(760\) 1.84847 3.20164i 0.0670510 0.116136i
\(761\) 1.00000 1.73205i 0.0362500 0.0627868i −0.847331 0.531065i \(-0.821792\pi\)
0.883581 + 0.468278i \(0.155125\pi\)
\(762\) −5.17423 0.476756i −0.187443 0.0172710i
\(763\) 0 0
\(764\) 4.10102 0.148370
\(765\) −8.55051 1.58919i −0.309144 0.0574571i
\(766\) 2.89898 0.104744
\(767\) 4.89898 + 8.48528i 0.176892 + 0.306386i
\(768\) −0.724745 1.57313i −0.0261520 0.0567655i
\(769\) −17.0454 + 29.5235i −0.614673 + 1.06465i 0.375769 + 0.926714i \(0.377379\pi\)
−0.990442 + 0.137932i \(0.955955\pi\)
\(770\) 0 0
\(771\) 5.94439 + 12.9029i 0.214082 + 0.464686i
\(772\) 8.94949 + 15.5010i 0.322099 + 0.557892i
\(773\) −33.9444 −1.22089 −0.610447 0.792057i \(-0.709010\pi\)
−0.610447 + 0.792057i \(0.709010\pi\)
\(774\) 20.3485 + 3.78194i 0.731411 + 0.135939i
\(775\) 17.3939 0.624807
\(776\) 1.44949 + 2.51059i 0.0520336 + 0.0901249i
\(777\) 0 0
\(778\) 12.4495 21.5631i 0.446336 0.773076i
\(779\) −12.4949 + 21.6418i −0.447676 + 0.775398i
\(780\) 7.10102 10.0424i 0.254257 0.359574i
\(781\) −0.101021 0.174973i −0.00361480 0.00626101i
\(782\) 2.00000 0.0715199
\(783\) 8.79796 + 34.7518i 0.314413 + 1.24193i
\(784\) 0 0
\(785\) −6.05051 10.4798i −0.215952 0.374040i
\(786\) −8.55051 + 12.0922i −0.304987 + 0.431316i
\(787\) −5.69694 + 9.86739i −0.203074 + 0.351734i −0.949517 0.313715i \(-0.898427\pi\)
0.746443 + 0.665449i \(0.231760\pi\)
\(788\) −8.34847 + 14.4600i −0.297402 + 0.515115i
\(789\) 44.6691 + 4.11583i 1.59026 + 0.146527i
\(790\) 1.37628 + 2.38378i 0.0489657 + 0.0848111i
\(791\) 0 0
\(792\) −3.89898 + 4.56048i −0.138544 + 0.162050i
\(793\) 32.0908 1.13958
\(794\) 19.3485 + 33.5125i 0.686651 + 1.18932i
\(795\) 11.4495 + 24.8523i 0.406072 + 0.881419i
\(796\) −1.44949 + 2.51059i −0.0513758 + 0.0889855i
\(797\) −8.97219 + 15.5403i −0.317811 + 0.550465i −0.980031 0.198844i \(-0.936281\pi\)
0.662220 + 0.749310i \(0.269615\pi\)
\(798\) 0 0
\(799\) −9.79796 16.9706i −0.346627 0.600375i
\(800\) −2.89898 −0.102494
\(801\) −16.8990 47.7975i −0.597096 1.68884i
\(802\) −19.8990 −0.702657
\(803\) −6.89898 11.9494i −0.243460 0.421685i
\(804\) −22.2474 2.04989i −0.784607 0.0722940i
\(805\) 0 0
\(806\) −14.6969 + 25.4558i −0.517678 + 0.896644i
\(807\) −18.3485 + 25.9487i −0.645897 + 0.913436i
\(808\) −8.62372 14.9367i −0.303382 0.525472i
\(809\) −16.2020 −0.569633 −0.284817 0.958582i \(-0.591933\pi\)
−0.284817 + 0.958582i \(0.591933\pi\)
\(810\) −10.1464 + 8.19955i −0.356509 + 0.288103i
\(811\) 2.00000 0.0702295 0.0351147 0.999383i \(-0.488820\pi\)
0.0351147 + 0.999383i \(0.488820\pi\)
\(812\) 0 0
\(813\) 7.10102 10.0424i 0.249044 0.352201i
\(814\) −11.7980 + 20.4347i −0.413518 + 0.716235i
\(815\) 14.3485 24.8523i 0.502605 0.870537i
\(816\) −3.44949 0.317837i −0.120756 0.0111265i
\(817\) 8.79796 + 15.2385i 0.307802 + 0.533128i
\(818\) 13.7980 0.482434
\(819\) 0 0
\(820\) −14.2020 −0.495957
\(821\) −0.202041 0.349945i −0.00705128 0.0122132i 0.862478 0.506094i \(-0.168911\pi\)
−0.869530 + 0.493881i \(0.835578\pi\)
\(822\) −5.65153 12.2672i −0.197120 0.427868i
\(823\) 6.69694 11.5994i 0.233441 0.404331i −0.725378 0.688351i \(-0.758335\pi\)
0.958818 + 0.284020i \(0.0916682\pi\)
\(824\) 7.00000 12.1244i 0.243857 0.422372i
\(825\) 4.20204 + 9.12096i 0.146296 + 0.317551i
\(826\) 0 0
\(827\) −36.4949 −1.26905 −0.634526 0.772902i \(-0.718805\pi\)
−0.634526 + 0.772902i \(0.718805\pi\)
\(828\) 1.94949 2.28024i 0.0677495 0.0792438i
\(829\) −1.30306 −0.0452572 −0.0226286 0.999744i \(-0.507204\pi\)
−0.0226286 + 0.999744i \(0.507204\pi\)
\(830\) 1.44949 + 2.51059i 0.0503125 + 0.0871438i
\(831\) −32.2474 2.97129i −1.11865 0.103073i
\(832\) 2.44949 4.24264i 0.0849208 0.147087i
\(833\) 0 0
\(834\) 4.55051 6.43539i 0.157571 0.222839i
\(835\) −7.75255 13.4278i −0.268288 0.464689i
\(836\) −5.10102 −0.176422
\(837\) 22.3485 21.7381i 0.772476 0.751379i
\(838\) −29.4495 −1.01732
\(839\) −17.5505 30.3984i −0.605911 1.04947i −0.991907 0.126968i \(-0.959475\pi\)
0.385996 0.922500i \(-0.373858\pi\)
\(840\) 0 0
\(841\) −9.29796 + 16.1045i −0.320619 + 0.555329i
\(842\) −11.4495 + 19.8311i −0.394575 + 0.683425i
\(843\) −32.7702 3.01945i −1.12866 0.103996i
\(844\) −6.44949 11.1708i −0.222001 0.384516i
\(845\) 15.9444 0.548504
\(846\) −28.8990 5.37113i −0.993567 0.184663i
\(847\) 0 0
\(848\) 5.44949 + 9.43879i 0.187136 + 0.324129i
\(849\) −18.4444 40.0354i −0.633010 1.37401i
\(850\) −2.89898 + 5.02118i −0.0994342 + 0.172225i
\(851\) 5.89898 10.2173i 0.202214 0.350246i
\(852\) −0.0732141 0.158919i −0.00250827 0.00544446i
\(853\) 12.4217 + 21.5150i 0.425310 + 0.736659i 0.996449 0.0841942i \(-0.0268316\pi\)
−0.571139 + 0.820853i \(0.693498\pi\)
\(854\) 0 0
\(855\) −10.9041 2.02662i −0.372912 0.0693089i
\(856\) −12.0000 −0.410152
\(857\) −17.4495 30.2234i −0.596063 1.03241i −0.993396 0.114737i \(-0.963397\pi\)
0.397333 0.917675i \(-0.369936\pi\)
\(858\) −16.8990 1.55708i −0.576922 0.0531578i
\(859\) −5.00000 + 8.66025i −0.170598 + 0.295484i −0.938629 0.344928i \(-0.887903\pi\)
0.768031 + 0.640412i \(0.221237\pi\)
\(860\) −5.00000 + 8.66025i −0.170499 + 0.295312i
\(861\) 0 0
\(862\) −15.7980 27.3629i −0.538081 0.931983i
\(863\) 11.8990 0.405046 0.202523 0.979278i \(-0.435086\pi\)
0.202523 + 0.979278i \(0.435086\pi\)
\(864\) −3.72474 + 3.62302i −0.126718 + 0.123258i
\(865\) 4.49490 0.152831
\(866\) −3.89898 6.75323i −0.132493 0.229484i
\(867\) 13.0000 18.3848i 0.441503 0.624380i
\(868\) 0 0
\(869\) 1.89898 3.28913i 0.0644185 0.111576i
\(870\) −17.2474 1.58919i −0.584743 0.0538785i
\(871\) −31.5959 54.7257i −1.07059 1.85431i
\(872\) 12.6969 0.429973
\(873\) 5.65153 6.61037i 0.191275 0.223727i
\(874\) 2.55051 0.0862723
\(875\) 0 0
\(876\) −5.00000 10.8530i −0.168934 0.366689i
\(877\) −11.2474 + 19.4812i −0.379799 + 0.657832i −0.991033 0.133619i \(-0.957340\pi\)
0.611233 + 0.791450i \(0.290674\pi\)
\(878\) 1.10102 1.90702i 0.0371576 0.0643589i
\(879\) 1.99490 + 4.33013i 0.0672862 + 0.146052i
\(880\) −1.44949 2.51059i −0.0488623 0.0846320i
\(881\) −19.5959 −0.660203 −0.330102 0.943945i \(-0.607083\pi\)
−0.330102 + 0.943945i \(0.607083\pi\)
\(882\) 0 0
\(883\) −19.7980 −0.666254 −0.333127 0.942882i \(-0.608104\pi\)
−0.333127 + 0.942882i \(0.608104\pi\)
\(884\) −4.89898 8.48528i −0.164771 0.285391i
\(885\) 5.00000 + 0.460702i 0.168073 + 0.0154863i
\(886\) 7.44949 12.9029i 0.250271 0.433481i
\(887\) −7.10102 + 12.2993i −0.238429 + 0.412971i −0.960264 0.279094i \(-0.909966\pi\)
0.721835 + 0.692065i \(0.243299\pi\)
\(888\) −11.7980 + 16.6848i −0.395914 + 0.559906i
\(889\) 0 0
\(890\) 24.4949 0.821071
\(891\) 16.7980 + 6.46750i 0.562753 + 0.216669i
\(892\) 11.1010 0.371690
\(893\) −12.4949 21.6418i −0.418126 0.724215i
\(894\) 6.00000 8.48528i 0.200670 0.283790i
\(895\) −15.0000 + 25.9808i −0.501395 + 0.868441i
\(896\) 0 0
\(897\) 8.44949 + 0.778539i 0.282120 + 0.0259947i
\(898\) −10.2980 17.8366i −0.343647 0.595215i
\(899\) 41.3939 1.38056
\(900\) 2.89898 + 8.19955i 0.0966326 + 0.273318i
\(901\) 21.7980 0.726195
\(902\) 9.79796 + 16.9706i 0.326236 + 0.565058i
\(903\) 0 0
\(904\) 3.05051 5.28364i 0.101458 0.175731i
\(905\) −7.50000 + 12.9904i −0.249308 + 0.431815i
\(906\) 3.62372 + 7.86566i 0.120390 + 0.261319i
\(907\) −1.34847 2.33562i −0.0447752 0.0775529i 0.842769 0.538275i \(-0.180924\pi\)
−0.887544 + 0.460722i \(0.847590\pi\)
\(908\) 5.44949 0.180848
\(909\) −33.6237 + 39.3283i −1.11523 + 1.30444i
\(910\) 0 0
\(911\) −25.9949 45.0245i −0.861249 1.49173i −0.870724 0.491773i \(-0.836349\pi\)
0.00947432 0.999955i \(-0.496984\pi\)
\(912\) −4.39898 0.405324i −0.145665 0.0134216i
\(913\) 2.00000 3.46410i 0.0661903 0.114645i
\(914\) 8.74745 15.1510i 0.289340 0.501151i
\(915\) 9.49490 13.4278i 0.313892 0.443910i
\(916\) 0.623724 + 1.08032i 0.0206084 + 0.0356949i
\(917\) 0 0
\(918\) 2.55051 + 10.0745i 0.0841794 + 0.332507i
\(919\) −25.6969 −0.847664 −0.423832 0.905741i \(-0.639315\pi\)
−0.423832 + 0.905741i \(0.639315\pi\)
\(920\) 0.724745 + 1.25529i 0.0238941 + 0.0413858i
\(921\) 25.2474 35.7053i 0.831932 1.17653i
\(922\) 2.82577 4.89437i 0.0930616 0.161187i
\(923\) 0.247449 0.428594i 0.00814487 0.0141073i
\(924\) 0 0
\(925\) 17.1010 + 29.6198i 0.562278 + 0.973894i
\(926\) 3.69694 0.121489
\(927\) −41.2929 7.67463i −1.35624 0.252068i
\(928\) −6.89898 −0.226470
\(929\) 17.1464 + 29.6985i 0.562556 + 0.974376i 0.997272 + 0.0738083i \(0.0235153\pi\)
−0.434716 + 0.900567i \(0.643151\pi\)
\(930\) 6.30306 + 13.6814i 0.206686 + 0.448632i
\(931\) 0 0
\(932\) 3.50000 6.06218i 0.114646 0.198573i
\(933\) 22.2474 + 48.2903i 0.728349 + 1.58095i
\(934\) 5.00000 + 8.66025i 0.163605 + 0.283372i
\(935\) −5.79796 −0.189614
\(936\) −14.4495 2.68556i −0.472296 0.0877804i
\(937\) −45.5959 −1.48955 −0.744777 0.667314i \(-0.767444\pi\)
−0.744777 + 0.667314i \(0.767444\pi\)
\(938\) 0 0
\(939\) 8.10102 + 0.746431i 0.264367 + 0.0243589i
\(940\) 7.10102 12.2993i 0.231610 0.401160i
\(941\) −0.724745 + 1.25529i −0.0236260 + 0.0409214i −0.877597 0.479400i \(-0.840854\pi\)
0.853971 + 0.520321i \(0.174188\pi\)
\(942\) −8.34847 + 11.8065i −0.272008 + 0.384677i
\(943\) −4.89898 8.48528i −0.159533 0.276319i
\(944\) 2.00000 0.0650945
\(945\) 0 0
\(946\) 13.7980 0.448610
\(947\) −26.2474 45.4619i −0.852927 1.47731i −0.878554 0.477642i \(-0.841492\pi\)
0.0256270 0.999672i \(-0.491842\pi\)
\(948\) 1.89898 2.68556i 0.0616760 0.0872230i
\(949\) 16.8990 29.2699i 0.548564 0.950141i
\(950\) −3.69694 + 6.40329i −0.119945 + 0.207750i
\(951\) 35.6969 + 3.28913i 1.15755 + 0.106657i
\(952\) 0 0
\(953\) −3.39388 −0.109938 −0.0549692 0.998488i \(-0.517506\pi\)
−0.0549692 + 0.998488i \(0.517506\pi\)
\(954\) 21.2474 24.8523i 0.687912 0.804622i
\(955\) 5.94439 0.192356
\(956\) −3.39898 5.88721i −0.109931 0.190406i
\(957\) 10.0000 + 21.7060i 0.323254 + 0.701656i
\(958\) 4.79796 8.31031i 0.155015 0.268494i
\(959\) 0 0
\(960\) −1.05051 2.28024i −0.0339051 0.0735944i
\(961\) −2.50000 4.33013i −0.0806452 0.139682i
\(962\) −57.7980 −1.86348
\(963\) 12.0000 + 33.9411i 0.386695 + 1.09374i
\(964\) −0.898979 −0.0289542
\(965\) 12.9722 + 22.4685i 0.417590 + 0.723287i
\(966\) 0 0
\(967\) −12.2980 + 21.3007i −0.395476 + 0.684984i −0.993162 0.116746i \(-0.962754\pi\)
0.597686 + 0.801730i \(0.296087\pi\)
\(968\) 3.50000 6.06218i 0.112494 0.194846i
\(969\) −5.10102 + 7.21393i −0.163868 + 0.231745i
\(970\) 2.10102 + 3.63907i 0.0674597 + 0.116844i
\(971\) 0.0556128 0.00178470 0.000892350 1.00000i \(-0.499716\pi\)
0.000892350 1.00000i \(0.499716\pi\)
\(972\) 13.9722 + 6.91215i 0.448158 + 0.221707i
\(973\) 0 0
\(974\) 18.1969 + 31.5180i 0.583068 + 1.00990i
\(975\) −14.2020 + 20.0847i −0.454829 + 0.643226i
\(976\) 3.27526 5.67291i 0.104838 0.181585i
\(977\) 18.7980 32.5590i 0.601400 1.04166i −0.391209 0.920302i \(-0.627943\pi\)
0.992609 0.121354i \(-0.0387235\pi\)
\(978\) −34.1464 3.14626i −1.09188 0.100606i
\(979\) −16.8990 29.2699i −0.540094 0.935470i
\(980\) 0 0
\(981\) −12.6969 35.9124i −0.405382 1.14659i
\(982\) 15.7980 0.504133
\(983\) −16.5959 28.7450i −0.529328 0.916822i −0.999415 0.0342024i \(-0.989111\pi\)
0.470087 0.882620i \(-0.344222\pi\)
\(984\) 7.10102 + 15.4135i 0.226372 + 0.491364i
\(985\) −12.1010 + 20.9596i −0.385571 + 0.667828i
\(986\) −6.89898 + 11.9494i −0.219708 + 0.380546i
\(987\) 0 0
\(988\) −6.24745 10.8209i −0.198758 0.344259i
\(989\) −6.89898 −0.219375
\(990\) −5.65153 + 6.61037i −0.179617 + 0.210091i
\(991\) −1.79796 −0.0571140 −0.0285570 0.999592i \(-0.509091\pi\)
−0.0285570 + 0.999592i \(0.509091\pi\)
\(992\) 3.00000 + 5.19615i 0.0952501 + 0.164978i
\(993\) 8.10102 + 0.746431i 0.257078 + 0.0236873i
\(994\) 0 0
\(995\) −2.10102 + 3.63907i −0.0666068 + 0.115366i
\(996\) 2.00000 2.82843i 0.0633724 0.0896221i
\(997\) 26.0732 + 45.1601i 0.825747 + 1.43024i 0.901347 + 0.433097i \(0.142579\pi\)
−0.0756001 + 0.997138i \(0.524087\pi\)
\(998\) −25.3939 −0.803829
\(999\) 58.9898 + 16.6848i 1.86635 + 0.527885i
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 882.2.f.j.589.2 4
3.2 odd 2 2646.2.f.k.1765.2 4
7.2 even 3 882.2.h.l.67.1 4
7.3 odd 6 882.2.e.m.373.1 4
7.4 even 3 882.2.e.n.373.2 4
7.5 odd 6 882.2.h.k.67.2 4
7.6 odd 2 126.2.f.c.85.1 yes 4
9.2 odd 6 2646.2.f.k.883.2 4
9.4 even 3 7938.2.a.bn.1.2 2
9.5 odd 6 7938.2.a.bm.1.1 2
9.7 even 3 inner 882.2.f.j.295.1 4
21.2 odd 6 2646.2.h.n.361.1 4
21.5 even 6 2646.2.h.m.361.2 4
21.11 odd 6 2646.2.e.k.1549.2 4
21.17 even 6 2646.2.e.l.1549.1 4
21.20 even 2 378.2.f.d.253.1 4
28.27 even 2 1008.2.r.e.337.2 4
63.2 odd 6 2646.2.e.k.2125.2 4
63.11 odd 6 2646.2.h.n.667.1 4
63.13 odd 6 1134.2.a.p.1.1 2
63.16 even 3 882.2.e.n.655.2 4
63.20 even 6 378.2.f.d.127.1 4
63.25 even 3 882.2.h.l.79.1 4
63.34 odd 6 126.2.f.c.43.2 4
63.38 even 6 2646.2.h.m.667.2 4
63.41 even 6 1134.2.a.i.1.2 2
63.47 even 6 2646.2.e.l.2125.1 4
63.52 odd 6 882.2.h.k.79.2 4
63.61 odd 6 882.2.e.m.655.1 4
84.83 odd 2 3024.2.r.e.1009.1 4
252.83 odd 6 3024.2.r.e.2017.1 4
252.139 even 6 9072.2.a.bk.1.1 2
252.167 odd 6 9072.2.a.bd.1.2 2
252.223 even 6 1008.2.r.e.673.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.f.c.43.2 4 63.34 odd 6
126.2.f.c.85.1 yes 4 7.6 odd 2
378.2.f.d.127.1 4 63.20 even 6
378.2.f.d.253.1 4 21.20 even 2
882.2.e.m.373.1 4 7.3 odd 6
882.2.e.m.655.1 4 63.61 odd 6
882.2.e.n.373.2 4 7.4 even 3
882.2.e.n.655.2 4 63.16 even 3
882.2.f.j.295.1 4 9.7 even 3 inner
882.2.f.j.589.2 4 1.1 even 1 trivial
882.2.h.k.67.2 4 7.5 odd 6
882.2.h.k.79.2 4 63.52 odd 6
882.2.h.l.67.1 4 7.2 even 3
882.2.h.l.79.1 4 63.25 even 3
1008.2.r.e.337.2 4 28.27 even 2
1008.2.r.e.673.1 4 252.223 even 6
1134.2.a.i.1.2 2 63.41 even 6
1134.2.a.p.1.1 2 63.13 odd 6
2646.2.e.k.1549.2 4 21.11 odd 6
2646.2.e.k.2125.2 4 63.2 odd 6
2646.2.e.l.1549.1 4 21.17 even 6
2646.2.e.l.2125.1 4 63.47 even 6
2646.2.f.k.883.2 4 9.2 odd 6
2646.2.f.k.1765.2 4 3.2 odd 2
2646.2.h.m.361.2 4 21.5 even 6
2646.2.h.m.667.2 4 63.38 even 6
2646.2.h.n.361.1 4 21.2 odd 6
2646.2.h.n.667.1 4 63.11 odd 6
3024.2.r.e.1009.1 4 84.83 odd 2
3024.2.r.e.2017.1 4 252.83 odd 6
7938.2.a.bm.1.1 2 9.5 odd 6
7938.2.a.bn.1.2 2 9.4 even 3
9072.2.a.bd.1.2 2 252.167 odd 6
9072.2.a.bk.1.1 2 252.139 even 6