Properties

Label 187.2.e.a.166.2
Level $187$
Weight $2$
Character 187.166
Analytic conductor $1.493$
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] = [187,2,Mod(89,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.e (of order \(4\), 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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{8})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 166.2
Root \(0.707107 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 187.166
Dual form 187.2.e.a.89.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000i q^{2} +(0.414214 + 0.414214i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.828427 + 0.828427i) q^{6} +(0.707107 - 0.707107i) q^{7} -2.65685i q^{9} +O(q^{10})\) \(q+2.00000i q^{2} +(0.414214 + 0.414214i) q^{3} -2.00000 q^{4} +(2.00000 + 2.00000i) q^{5} +(-0.828427 + 0.828427i) q^{6} +(0.707107 - 0.707107i) q^{7} -2.65685i q^{9} +(-4.00000 + 4.00000i) q^{10} +(0.707107 - 0.707107i) q^{11} +(-0.828427 - 0.828427i) q^{12} -3.41421 q^{13} +(1.41421 + 1.41421i) q^{14} +1.65685i q^{15} -4.00000 q^{16} +(-2.12132 - 3.53553i) q^{17} +5.31371 q^{18} +2.58579i q^{19} +(-4.00000 - 4.00000i) q^{20} +0.585786 q^{21} +(1.41421 + 1.41421i) q^{22} +(3.00000 - 3.00000i) q^{23} +3.00000i q^{25} -6.82843i q^{26} +(2.34315 - 2.34315i) q^{27} +(-1.41421 + 1.41421i) q^{28} +(2.70711 + 2.70711i) q^{29} -3.31371 q^{30} +(-4.82843 - 4.82843i) q^{31} -8.00000i q^{32} +0.585786 q^{33} +(7.07107 - 4.24264i) q^{34} +2.82843 q^{35} +5.31371i q^{36} +(6.65685 + 6.65685i) q^{37} -5.17157 q^{38} +(-1.41421 - 1.41421i) q^{39} +(-3.53553 + 3.53553i) q^{41} +1.17157i q^{42} -5.41421i q^{43} +(-1.41421 + 1.41421i) q^{44} +(5.31371 - 5.31371i) q^{45} +(6.00000 + 6.00000i) q^{46} +11.4853 q^{47} +(-1.65685 - 1.65685i) q^{48} +6.00000i q^{49} -6.00000 q^{50} +(0.585786 - 2.34315i) q^{51} +6.82843 q^{52} +3.48528i q^{53} +(4.68629 + 4.68629i) q^{54} +2.82843 q^{55} +(-1.07107 + 1.07107i) q^{57} +(-5.41421 + 5.41421i) q^{58} -4.65685i q^{59} -3.31371i q^{60} +(-4.82843 + 4.82843i) q^{61} +(9.65685 - 9.65685i) q^{62} +(-1.87868 - 1.87868i) q^{63} +8.00000 q^{64} +(-6.82843 - 6.82843i) q^{65} +1.17157i q^{66} +1.00000 q^{67} +(4.24264 + 7.07107i) q^{68} +2.48528 q^{69} +5.65685i q^{70} +(-11.0711 - 11.0711i) q^{71} +(-5.77817 - 5.77817i) q^{73} +(-13.3137 + 13.3137i) q^{74} +(-1.24264 + 1.24264i) q^{75} -5.17157i q^{76} -1.00000i q^{77} +(2.82843 - 2.82843i) q^{78} +(-2.24264 + 2.24264i) q^{79} +(-8.00000 - 8.00000i) q^{80} -6.02944 q^{81} +(-7.07107 - 7.07107i) q^{82} +4.82843i q^{83} -1.17157 q^{84} +(2.82843 - 11.3137i) q^{85} +10.8284 q^{86} +2.24264i q^{87} -1.82843 q^{89} +(10.6274 + 10.6274i) q^{90} +(-2.41421 + 2.41421i) q^{91} +(-6.00000 + 6.00000i) q^{92} -4.00000i q^{93} +22.9706i q^{94} +(-5.17157 + 5.17157i) q^{95} +(3.31371 - 3.31371i) q^{96} +(-5.41421 - 5.41421i) q^{97} -12.0000 q^{98} +(-1.87868 - 1.87868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 8 q^{4} + 8 q^{5} + 8 q^{6} - 16 q^{10} + 8 q^{12} - 8 q^{13} - 16 q^{16} - 24 q^{18} - 16 q^{20} + 8 q^{21} + 12 q^{23} + 32 q^{27} + 8 q^{29} + 32 q^{30} - 8 q^{31} + 8 q^{33} + 4 q^{37} - 32 q^{38} - 24 q^{45} + 24 q^{46} + 12 q^{47} + 16 q^{48} - 24 q^{50} + 8 q^{51} + 16 q^{52} + 64 q^{54} + 24 q^{57} - 16 q^{58} - 8 q^{61} + 16 q^{62} - 16 q^{63} + 32 q^{64} - 16 q^{65} + 4 q^{67} - 24 q^{69} - 16 q^{71} + 8 q^{73} - 8 q^{74} + 12 q^{75} + 8 q^{79} - 32 q^{80} - 92 q^{81} - 16 q^{84} + 32 q^{86} + 4 q^{89} - 48 q^{90} - 4 q^{91} - 24 q^{92} - 32 q^{95} - 32 q^{96} - 16 q^{97} - 48 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 1.41421i 0.707107 + 0.707107i \(0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 0.414214 + 0.414214i 0.239146 + 0.239146i 0.816497 0.577350i \(-0.195913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) −2.00000 −1.00000
\(5\) 2.00000 + 2.00000i 0.894427 + 0.894427i 0.994936 0.100509i \(-0.0320471\pi\)
−0.100509 + 0.994936i \(0.532047\pi\)
\(6\) −0.828427 + 0.828427i −0.338204 + 0.338204i
\(7\) 0.707107 0.707107i 0.267261 0.267261i −0.560734 0.827996i \(-0.689481\pi\)
0.827996 + 0.560734i \(0.189481\pi\)
\(8\) 0 0
\(9\) 2.65685i 0.885618i
\(10\) −4.00000 + 4.00000i −1.26491 + 1.26491i
\(11\) 0.707107 0.707107i 0.213201 0.213201i
\(12\) −0.828427 0.828427i −0.239146 0.239146i
\(13\) −3.41421 −0.946932 −0.473466 0.880812i \(-0.656997\pi\)
−0.473466 + 0.880812i \(0.656997\pi\)
\(14\) 1.41421 + 1.41421i 0.377964 + 0.377964i
\(15\) 1.65685i 0.427798i
\(16\) −4.00000 −1.00000
\(17\) −2.12132 3.53553i −0.514496 0.857493i
\(18\) 5.31371 1.25245
\(19\) 2.58579i 0.593220i 0.954999 + 0.296610i \(0.0958562\pi\)
−0.954999 + 0.296610i \(0.904144\pi\)
\(20\) −4.00000 4.00000i −0.894427 0.894427i
\(21\) 0.585786 0.127829
\(22\) 1.41421 + 1.41421i 0.301511 + 0.301511i
\(23\) 3.00000 3.00000i 0.625543 0.625543i −0.321400 0.946943i \(-0.604153\pi\)
0.946943 + 0.321400i \(0.104153\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) 6.82843i 1.33916i
\(27\) 2.34315 2.34315i 0.450939 0.450939i
\(28\) −1.41421 + 1.41421i −0.267261 + 0.267261i
\(29\) 2.70711 + 2.70711i 0.502697 + 0.502697i 0.912275 0.409578i \(-0.134324\pi\)
−0.409578 + 0.912275i \(0.634324\pi\)
\(30\) −3.31371 −0.604998
\(31\) −4.82843 4.82843i −0.867211 0.867211i 0.124952 0.992163i \(-0.460122\pi\)
−0.992163 + 0.124952i \(0.960122\pi\)
\(32\) 8.00000i 1.41421i
\(33\) 0.585786 0.101972
\(34\) 7.07107 4.24264i 1.21268 0.727607i
\(35\) 2.82843 0.478091
\(36\) 5.31371i 0.885618i
\(37\) 6.65685 + 6.65685i 1.09438 + 1.09438i 0.995055 + 0.0993251i \(0.0316684\pi\)
0.0993251 + 0.995055i \(0.468332\pi\)
\(38\) −5.17157 −0.838940
\(39\) −1.41421 1.41421i −0.226455 0.226455i
\(40\) 0 0
\(41\) −3.53553 + 3.53553i −0.552158 + 0.552158i −0.927063 0.374905i \(-0.877675\pi\)
0.374905 + 0.927063i \(0.377675\pi\)
\(42\) 1.17157i 0.180778i
\(43\) 5.41421i 0.825660i −0.910808 0.412830i \(-0.864540\pi\)
0.910808 0.412830i \(-0.135460\pi\)
\(44\) −1.41421 + 1.41421i −0.213201 + 0.213201i
\(45\) 5.31371 5.31371i 0.792121 0.792121i
\(46\) 6.00000 + 6.00000i 0.884652 + 0.884652i
\(47\) 11.4853 1.67530 0.837650 0.546207i \(-0.183929\pi\)
0.837650 + 0.546207i \(0.183929\pi\)
\(48\) −1.65685 1.65685i −0.239146 0.239146i
\(49\) 6.00000i 0.857143i
\(50\) −6.00000 −0.848528
\(51\) 0.585786 2.34315i 0.0820265 0.328106i
\(52\) 6.82843 0.946932
\(53\) 3.48528i 0.478740i 0.970928 + 0.239370i \(0.0769409\pi\)
−0.970928 + 0.239370i \(0.923059\pi\)
\(54\) 4.68629 + 4.68629i 0.637723 + 0.637723i
\(55\) 2.82843 0.381385
\(56\) 0 0
\(57\) −1.07107 + 1.07107i −0.141866 + 0.141866i
\(58\) −5.41421 + 5.41421i −0.710921 + 0.710921i
\(59\) 4.65685i 0.606271i −0.952947 0.303135i \(-0.901967\pi\)
0.952947 0.303135i \(-0.0980334\pi\)
\(60\) 3.31371i 0.427798i
\(61\) −4.82843 + 4.82843i −0.618217 + 0.618217i −0.945074 0.326857i \(-0.894010\pi\)
0.326857 + 0.945074i \(0.394010\pi\)
\(62\) 9.65685 9.65685i 1.22642 1.22642i
\(63\) −1.87868 1.87868i −0.236691 0.236691i
\(64\) 8.00000 1.00000
\(65\) −6.82843 6.82843i −0.846962 0.846962i
\(66\) 1.17157i 0.144211i
\(67\) 1.00000 0.122169 0.0610847 0.998133i \(-0.480544\pi\)
0.0610847 + 0.998133i \(0.480544\pi\)
\(68\) 4.24264 + 7.07107i 0.514496 + 0.857493i
\(69\) 2.48528 0.299193
\(70\) 5.65685i 0.676123i
\(71\) −11.0711 11.0711i −1.31389 1.31389i −0.918520 0.395374i \(-0.870615\pi\)
−0.395374 0.918520i \(-0.629385\pi\)
\(72\) 0 0
\(73\) −5.77817 5.77817i −0.676284 0.676284i 0.282873 0.959157i \(-0.408712\pi\)
−0.959157 + 0.282873i \(0.908712\pi\)
\(74\) −13.3137 + 13.3137i −1.54769 + 1.54769i
\(75\) −1.24264 + 1.24264i −0.143488 + 0.143488i
\(76\) 5.17157i 0.593220i
\(77\) 1.00000i 0.113961i
\(78\) 2.82843 2.82843i 0.320256 0.320256i
\(79\) −2.24264 + 2.24264i −0.252317 + 0.252317i −0.821920 0.569603i \(-0.807097\pi\)
0.569603 + 0.821920i \(0.307097\pi\)
\(80\) −8.00000 8.00000i −0.894427 0.894427i
\(81\) −6.02944 −0.669937
\(82\) −7.07107 7.07107i −0.780869 0.780869i
\(83\) 4.82843i 0.529989i 0.964250 + 0.264994i \(0.0853701\pi\)
−0.964250 + 0.264994i \(0.914630\pi\)
\(84\) −1.17157 −0.127829
\(85\) 2.82843 11.3137i 0.306786 1.22714i
\(86\) 10.8284 1.16766
\(87\) 2.24264i 0.240436i
\(88\) 0 0
\(89\) −1.82843 −0.193813 −0.0969064 0.995293i \(-0.530895\pi\)
−0.0969064 + 0.995293i \(0.530895\pi\)
\(90\) 10.6274 + 10.6274i 1.12023 + 1.12023i
\(91\) −2.41421 + 2.41421i −0.253078 + 0.253078i
\(92\) −6.00000 + 6.00000i −0.625543 + 0.625543i
\(93\) 4.00000i 0.414781i
\(94\) 22.9706i 2.36923i
\(95\) −5.17157 + 5.17157i −0.530592 + 0.530592i
\(96\) 3.31371 3.31371i 0.338204 0.338204i
\(97\) −5.41421 5.41421i −0.549730 0.549730i 0.376633 0.926363i \(-0.377082\pi\)
−0.926363 + 0.376633i \(0.877082\pi\)
\(98\) −12.0000 −1.21218
\(99\) −1.87868 1.87868i −0.188814 0.188814i
\(100\) 6.00000i 0.600000i
\(101\) −10.7279 −1.06747 −0.533734 0.845652i \(-0.679212\pi\)
−0.533734 + 0.845652i \(0.679212\pi\)
\(102\) 4.68629 + 1.17157i 0.464012 + 0.116003i
\(103\) 16.6569 1.64125 0.820624 0.571468i \(-0.193626\pi\)
0.820624 + 0.571468i \(0.193626\pi\)
\(104\) 0 0
\(105\) 1.17157 + 1.17157i 0.114334 + 0.114334i
\(106\) −6.97056 −0.677041
\(107\) −0.464466 0.464466i −0.0449016 0.0449016i 0.684299 0.729201i \(-0.260108\pi\)
−0.729201 + 0.684299i \(0.760108\pi\)
\(108\) −4.68629 + 4.68629i −0.450939 + 0.450939i
\(109\) −10.9497 + 10.9497i −1.04880 + 1.04880i −0.0500488 + 0.998747i \(0.515938\pi\)
−0.998747 + 0.0500488i \(0.984062\pi\)
\(110\) 5.65685i 0.539360i
\(111\) 5.51472i 0.523434i
\(112\) −2.82843 + 2.82843i −0.267261 + 0.267261i
\(113\) −5.41421 + 5.41421i −0.509326 + 0.509326i −0.914320 0.404993i \(-0.867274\pi\)
0.404993 + 0.914320i \(0.367274\pi\)
\(114\) −2.14214 2.14214i −0.200629 0.200629i
\(115\) 12.0000 1.11901
\(116\) −5.41421 5.41421i −0.502697 0.502697i
\(117\) 9.07107i 0.838621i
\(118\) 9.31371 0.857396
\(119\) −4.00000 1.00000i −0.366679 0.0916698i
\(120\) 0 0
\(121\) 1.00000i 0.0909091i
\(122\) −9.65685 9.65685i −0.874291 0.874291i
\(123\) −2.92893 −0.264093
\(124\) 9.65685 + 9.65685i 0.867211 + 0.867211i
\(125\) 4.00000 4.00000i 0.357771 0.357771i
\(126\) 3.75736 3.75736i 0.334732 0.334732i
\(127\) 5.75736i 0.510883i 0.966825 + 0.255442i \(0.0822208\pi\)
−0.966825 + 0.255442i \(0.917779\pi\)
\(128\) 0 0
\(129\) 2.24264 2.24264i 0.197454 0.197454i
\(130\) 13.6569 13.6569i 1.19779 1.19779i
\(131\) −1.53553 1.53553i −0.134160 0.134160i 0.636838 0.770998i \(-0.280242\pi\)
−0.770998 + 0.636838i \(0.780242\pi\)
\(132\) −1.17157 −0.101972
\(133\) 1.82843 + 1.82843i 0.158545 + 0.158545i
\(134\) 2.00000i 0.172774i
\(135\) 9.37258 0.806664
\(136\) 0 0
\(137\) 9.82843 0.839699 0.419850 0.907594i \(-0.362083\pi\)
0.419850 + 0.907594i \(0.362083\pi\)
\(138\) 4.97056i 0.423122i
\(139\) 4.36396 + 4.36396i 0.370146 + 0.370146i 0.867530 0.497384i \(-0.165706\pi\)
−0.497384 + 0.867530i \(0.665706\pi\)
\(140\) −5.65685 −0.478091
\(141\) 4.75736 + 4.75736i 0.400642 + 0.400642i
\(142\) 22.1421 22.1421i 1.85813 1.85813i
\(143\) −2.41421 + 2.41421i −0.201887 + 0.201887i
\(144\) 10.6274i 0.885618i
\(145\) 10.8284i 0.899252i
\(146\) 11.5563 11.5563i 0.956410 0.956410i
\(147\) −2.48528 + 2.48528i −0.204983 + 0.204983i
\(148\) −13.3137 13.3137i −1.09438 1.09438i
\(149\) 20.2426 1.65834 0.829171 0.558995i \(-0.188813\pi\)
0.829171 + 0.558995i \(0.188813\pi\)
\(150\) −2.48528 2.48528i −0.202922 0.202922i
\(151\) 6.48528i 0.527765i −0.964555 0.263882i \(-0.914997\pi\)
0.964555 0.263882i \(-0.0850031\pi\)
\(152\) 0 0
\(153\) −9.39340 + 5.63604i −0.759411 + 0.455647i
\(154\) 2.00000 0.161165
\(155\) 19.3137i 1.55131i
\(156\) 2.82843 + 2.82843i 0.226455 + 0.226455i
\(157\) −20.3137 −1.62121 −0.810605 0.585593i \(-0.800862\pi\)
−0.810605 + 0.585593i \(0.800862\pi\)
\(158\) −4.48528 4.48528i −0.356830 0.356830i
\(159\) −1.44365 + 1.44365i −0.114489 + 0.114489i
\(160\) 16.0000 16.0000i 1.26491 1.26491i
\(161\) 4.24264i 0.334367i
\(162\) 12.0589i 0.947435i
\(163\) −5.00000 + 5.00000i −0.391630 + 0.391630i −0.875268 0.483638i \(-0.839315\pi\)
0.483638 + 0.875268i \(0.339315\pi\)
\(164\) 7.07107 7.07107i 0.552158 0.552158i
\(165\) 1.17157 + 1.17157i 0.0912068 + 0.0912068i
\(166\) −9.65685 −0.749517
\(167\) 2.92893 + 2.92893i 0.226648 + 0.226648i 0.811291 0.584643i \(-0.198765\pi\)
−0.584643 + 0.811291i \(0.698765\pi\)
\(168\) 0 0
\(169\) −1.34315 −0.103319
\(170\) 22.6274 + 5.65685i 1.73544 + 0.433861i
\(171\) 6.87006 0.525366
\(172\) 10.8284i 0.825660i
\(173\) 0.121320 + 0.121320i 0.00922381 + 0.00922381i 0.711704 0.702480i \(-0.247924\pi\)
−0.702480 + 0.711704i \(0.747924\pi\)
\(174\) −4.48528 −0.340028
\(175\) 2.12132 + 2.12132i 0.160357 + 0.160357i
\(176\) −2.82843 + 2.82843i −0.213201 + 0.213201i
\(177\) 1.92893 1.92893i 0.144987 0.144987i
\(178\) 3.65685i 0.274093i
\(179\) 25.6274i 1.91548i 0.287630 + 0.957742i \(0.407133\pi\)
−0.287630 + 0.957742i \(0.592867\pi\)
\(180\) −10.6274 + 10.6274i −0.792121 + 0.792121i
\(181\) −13.0711 + 13.0711i −0.971565 + 0.971565i −0.999607 0.0280419i \(-0.991073\pi\)
0.0280419 + 0.999607i \(0.491073\pi\)
\(182\) −4.82843 4.82843i −0.357907 0.357907i
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) 26.6274i 1.95769i
\(186\) 8.00000 0.586588
\(187\) −4.00000 1.00000i −0.292509 0.0731272i
\(188\) −22.9706 −1.67530
\(189\) 3.31371i 0.241037i
\(190\) −10.3431 10.3431i −0.750371 0.750371i
\(191\) 7.17157 0.518917 0.259458 0.965754i \(-0.416456\pi\)
0.259458 + 0.965754i \(0.416456\pi\)
\(192\) 3.31371 + 3.31371i 0.239146 + 0.239146i
\(193\) 9.17157 9.17157i 0.660184 0.660184i −0.295239 0.955423i \(-0.595399\pi\)
0.955423 + 0.295239i \(0.0953993\pi\)
\(194\) 10.8284 10.8284i 0.777436 0.777436i
\(195\) 5.65685i 0.405096i
\(196\) 12.0000i 0.857143i
\(197\) 13.6569 13.6569i 0.973011 0.973011i −0.0266347 0.999645i \(-0.508479\pi\)
0.999645 + 0.0266347i \(0.00847908\pi\)
\(198\) 3.75736 3.75736i 0.267024 0.267024i
\(199\) −15.4142 15.4142i −1.09268 1.09268i −0.995241 0.0974436i \(-0.968933\pi\)
−0.0974436 0.995241i \(-0.531067\pi\)
\(200\) 0 0
\(201\) 0.414214 + 0.414214i 0.0292164 + 0.0292164i
\(202\) 21.4558i 1.50963i
\(203\) 3.82843 0.268703
\(204\) −1.17157 + 4.68629i −0.0820265 + 0.328106i
\(205\) −14.1421 −0.987730
\(206\) 33.3137i 2.32108i
\(207\) −7.97056 7.97056i −0.553992 0.553992i
\(208\) 13.6569 0.946932
\(209\) 1.82843 + 1.82843i 0.126475 + 0.126475i
\(210\) −2.34315 + 2.34315i −0.161692 + 0.161692i
\(211\) 6.36396 6.36396i 0.438113 0.438113i −0.453263 0.891377i \(-0.649740\pi\)
0.891377 + 0.453263i \(0.149740\pi\)
\(212\) 6.97056i 0.478740i
\(213\) 9.17157i 0.628426i
\(214\) 0.928932 0.928932i 0.0635005 0.0635005i
\(215\) 10.8284 10.8284i 0.738493 0.738493i
\(216\) 0 0
\(217\) −6.82843 −0.463544
\(218\) −21.8995 21.8995i −1.48322 1.48322i
\(219\) 4.78680i 0.323462i
\(220\) −5.65685 −0.381385
\(221\) 7.24264 + 12.0711i 0.487193 + 0.811988i
\(222\) −11.0294 −0.740247
\(223\) 6.00000i 0.401790i −0.979613 0.200895i \(-0.935615\pi\)
0.979613 0.200895i \(-0.0643850\pi\)
\(224\) −5.65685 5.65685i −0.377964 0.377964i
\(225\) 7.97056 0.531371
\(226\) −10.8284 10.8284i −0.720296 0.720296i
\(227\) −9.77817 + 9.77817i −0.649000 + 0.649000i −0.952751 0.303751i \(-0.901761\pi\)
0.303751 + 0.952751i \(0.401761\pi\)
\(228\) 2.14214 2.14214i 0.141866 0.141866i
\(229\) 4.65685i 0.307734i 0.988092 + 0.153867i \(0.0491727\pi\)
−0.988092 + 0.153867i \(0.950827\pi\)
\(230\) 24.0000i 1.58251i
\(231\) 0.414214 0.414214i 0.0272533 0.0272533i
\(232\) 0 0
\(233\) −15.5355 15.5355i −1.01777 1.01777i −0.999839 0.0179274i \(-0.994293\pi\)
−0.0179274 0.999839i \(-0.505707\pi\)
\(234\) −18.1421 −1.18599
\(235\) 22.9706 + 22.9706i 1.49843 + 1.49843i
\(236\) 9.31371i 0.606271i
\(237\) −1.85786 −0.120681
\(238\) 2.00000 8.00000i 0.129641 0.518563i
\(239\) 25.0711 1.62171 0.810856 0.585245i \(-0.199002\pi\)
0.810856 + 0.585245i \(0.199002\pi\)
\(240\) 6.62742i 0.427798i
\(241\) 9.43503 + 9.43503i 0.607764 + 0.607764i 0.942361 0.334598i \(-0.108600\pi\)
−0.334598 + 0.942361i \(0.608600\pi\)
\(242\) 2.00000 0.128565
\(243\) −9.52691 9.52691i −0.611152 0.611152i
\(244\) 9.65685 9.65685i 0.618217 0.618217i
\(245\) −12.0000 + 12.0000i −0.766652 + 0.766652i
\(246\) 5.85786i 0.373484i
\(247\) 8.82843i 0.561739i
\(248\) 0 0
\(249\) −2.00000 + 2.00000i −0.126745 + 0.126745i
\(250\) 8.00000 + 8.00000i 0.505964 + 0.505964i
\(251\) 6.00000 0.378717 0.189358 0.981908i \(-0.439359\pi\)
0.189358 + 0.981908i \(0.439359\pi\)
\(252\) 3.75736 + 3.75736i 0.236691 + 0.236691i
\(253\) 4.24264i 0.266733i
\(254\) −11.5147 −0.722498
\(255\) 5.85786 3.51472i 0.366834 0.220100i
\(256\) 16.0000 1.00000
\(257\) 10.5147i 0.655890i 0.944697 + 0.327945i \(0.106356\pi\)
−0.944697 + 0.327945i \(0.893644\pi\)
\(258\) 4.48528 + 4.48528i 0.279241 + 0.279241i
\(259\) 9.41421 0.584971
\(260\) 13.6569 + 13.6569i 0.846962 + 0.846962i
\(261\) 7.19239 7.19239i 0.445198 0.445198i
\(262\) 3.07107 3.07107i 0.189731 0.189731i
\(263\) 5.55635i 0.342619i −0.985217 0.171310i \(-0.945200\pi\)
0.985217 0.171310i \(-0.0547998\pi\)
\(264\) 0 0
\(265\) −6.97056 + 6.97056i −0.428198 + 0.428198i
\(266\) −3.65685 + 3.65685i −0.224216 + 0.224216i
\(267\) −0.757359 0.757359i −0.0463496 0.0463496i
\(268\) −2.00000 −0.122169
\(269\) 16.0711 + 16.0711i 0.979870 + 0.979870i 0.999801 0.0199311i \(-0.00634467\pi\)
−0.0199311 + 0.999801i \(0.506345\pi\)
\(270\) 18.7452i 1.14079i
\(271\) −29.3137 −1.78068 −0.890340 0.455295i \(-0.849534\pi\)
−0.890340 + 0.455295i \(0.849534\pi\)
\(272\) 8.48528 + 14.1421i 0.514496 + 0.857493i
\(273\) −2.00000 −0.121046
\(274\) 19.6569i 1.18751i
\(275\) 2.12132 + 2.12132i 0.127920 + 0.127920i
\(276\) −4.97056 −0.299193
\(277\) −10.4645 10.4645i −0.628749 0.628749i 0.319004 0.947753i \(-0.396652\pi\)
−0.947753 + 0.319004i \(0.896652\pi\)
\(278\) −8.72792 + 8.72792i −0.523466 + 0.523466i
\(279\) −12.8284 + 12.8284i −0.768018 + 0.768018i
\(280\) 0 0
\(281\) 16.4853i 0.983429i 0.870756 + 0.491715i \(0.163630\pi\)
−0.870756 + 0.491715i \(0.836370\pi\)
\(282\) −9.51472 + 9.51472i −0.566593 + 0.566593i
\(283\) −1.07107 + 1.07107i −0.0636684 + 0.0636684i −0.738224 0.674556i \(-0.764335\pi\)
0.674556 + 0.738224i \(0.264335\pi\)
\(284\) 22.1421 + 22.1421i 1.31389 + 1.31389i
\(285\) −4.28427 −0.253778
\(286\) −4.82843 4.82843i −0.285511 0.285511i
\(287\) 5.00000i 0.295141i
\(288\) −21.2548 −1.25245
\(289\) −8.00000 + 15.0000i −0.470588 + 0.882353i
\(290\) −21.6569 −1.27173
\(291\) 4.48528i 0.262932i
\(292\) 11.5563 + 11.5563i 0.676284 + 0.676284i
\(293\) 10.9289 0.638475 0.319238 0.947675i \(-0.396573\pi\)
0.319238 + 0.947675i \(0.396573\pi\)
\(294\) −4.97056 4.97056i −0.289889 0.289889i
\(295\) 9.31371 9.31371i 0.542265 0.542265i
\(296\) 0 0
\(297\) 3.31371i 0.192281i
\(298\) 40.4853i 2.34525i
\(299\) −10.2426 + 10.2426i −0.592347 + 0.592347i
\(300\) 2.48528 2.48528i 0.143488 0.143488i
\(301\) −3.82843 3.82843i −0.220667 0.220667i
\(302\) 12.9706 0.746372
\(303\) −4.44365 4.44365i −0.255281 0.255281i
\(304\) 10.3431i 0.593220i
\(305\) −19.3137 −1.10590
\(306\) −11.2721 18.7868i −0.644382 1.07397i
\(307\) −22.2426 −1.26945 −0.634727 0.772736i \(-0.718888\pi\)
−0.634727 + 0.772736i \(0.718888\pi\)
\(308\) 2.00000i 0.113961i
\(309\) 6.89949 + 6.89949i 0.392499 + 0.392499i
\(310\) 38.6274 2.19389
\(311\) 1.65685 + 1.65685i 0.0939516 + 0.0939516i 0.752520 0.658569i \(-0.228838\pi\)
−0.658569 + 0.752520i \(0.728838\pi\)
\(312\) 0 0
\(313\) −10.4142 + 10.4142i −0.588646 + 0.588646i −0.937265 0.348619i \(-0.886651\pi\)
0.348619 + 0.937265i \(0.386651\pi\)
\(314\) 40.6274i 2.29274i
\(315\) 7.51472i 0.423406i
\(316\) 4.48528 4.48528i 0.252317 0.252317i
\(317\) 8.58579 8.58579i 0.482226 0.482226i −0.423616 0.905842i \(-0.639239\pi\)
0.905842 + 0.423616i \(0.139239\pi\)
\(318\) −2.88730 2.88730i −0.161912 0.161912i
\(319\) 3.82843 0.214351
\(320\) 16.0000 + 16.0000i 0.894427 + 0.894427i
\(321\) 0.384776i 0.0214761i
\(322\) 8.48528 0.472866
\(323\) 9.14214 5.48528i 0.508682 0.305209i
\(324\) 12.0589 0.669937
\(325\) 10.2426i 0.568159i
\(326\) −10.0000 10.0000i −0.553849 0.553849i
\(327\) −9.07107 −0.501631
\(328\) 0 0
\(329\) 8.12132 8.12132i 0.447743 0.447743i
\(330\) −2.34315 + 2.34315i −0.128986 + 0.128986i
\(331\) 11.6569i 0.640719i −0.947296 0.320359i \(-0.896196\pi\)
0.947296 0.320359i \(-0.103804\pi\)
\(332\) 9.65685i 0.529989i
\(333\) 17.6863 17.6863i 0.969203 0.969203i
\(334\) −5.85786 + 5.85786i −0.320528 + 0.320528i
\(335\) 2.00000 + 2.00000i 0.109272 + 0.109272i
\(336\) −2.34315 −0.127829
\(337\) 22.2635 + 22.2635i 1.21277 + 1.21277i 0.970113 + 0.242655i \(0.0780183\pi\)
0.242655 + 0.970113i \(0.421982\pi\)
\(338\) 2.68629i 0.146115i
\(339\) −4.48528 −0.243607
\(340\) −5.65685 + 22.6274i −0.306786 + 1.22714i
\(341\) −6.82843 −0.369780
\(342\) 13.7401i 0.742980i
\(343\) 9.19239 + 9.19239i 0.496342 + 0.496342i
\(344\) 0 0
\(345\) 4.97056 + 4.97056i 0.267606 + 0.267606i
\(346\) −0.242641 + 0.242641i −0.0130444 + 0.0130444i
\(347\) 15.4350 15.4350i 0.828596 0.828596i −0.158727 0.987323i \(-0.550739\pi\)
0.987323 + 0.158727i \(0.0507389\pi\)
\(348\) 4.48528i 0.240436i
\(349\) 35.6985i 1.91090i −0.295159 0.955448i \(-0.595373\pi\)
0.295159 0.955448i \(-0.404627\pi\)
\(350\) −4.24264 + 4.24264i −0.226779 + 0.226779i
\(351\) −8.00000 + 8.00000i −0.427008 + 0.427008i
\(352\) −5.65685 5.65685i −0.301511 0.301511i
\(353\) −12.1716 −0.647827 −0.323914 0.946087i \(-0.604999\pi\)
−0.323914 + 0.946087i \(0.604999\pi\)
\(354\) 3.85786 + 3.85786i 0.205043 + 0.205043i
\(355\) 44.2843i 2.35037i
\(356\) 3.65685 0.193813
\(357\) −1.24264 2.07107i −0.0657675 0.109613i
\(358\) −51.2548 −2.70890
\(359\) 32.1421i 1.69640i −0.529678 0.848199i \(-0.677687\pi\)
0.529678 0.848199i \(-0.322313\pi\)
\(360\) 0 0
\(361\) 12.3137 0.648090
\(362\) −26.1421 26.1421i −1.37400 1.37400i
\(363\) 0.414214 0.414214i 0.0217406 0.0217406i
\(364\) 4.82843 4.82843i 0.253078 0.253078i
\(365\) 23.1127i 1.20977i
\(366\) 8.00000i 0.418167i
\(367\) −12.8284 + 12.8284i −0.669638 + 0.669638i −0.957632 0.287994i \(-0.907012\pi\)
0.287994 + 0.957632i \(0.407012\pi\)
\(368\) −12.0000 + 12.0000i −0.625543 + 0.625543i
\(369\) 9.39340 + 9.39340i 0.489001 + 0.489001i
\(370\) −53.2548 −2.76859
\(371\) 2.46447 + 2.46447i 0.127949 + 0.127949i
\(372\) 8.00000i 0.414781i
\(373\) 28.7279 1.48748 0.743738 0.668472i \(-0.233051\pi\)
0.743738 + 0.668472i \(0.233051\pi\)
\(374\) 2.00000 8.00000i 0.103418 0.413670i
\(375\) 3.31371 0.171119
\(376\) 0 0
\(377\) −9.24264 9.24264i −0.476020 0.476020i
\(378\) 6.62742 0.340878
\(379\) −24.5563 24.5563i −1.26137 1.26137i −0.950427 0.310948i \(-0.899353\pi\)
−0.310948 0.950427i \(-0.600647\pi\)
\(380\) 10.3431 10.3431i 0.530592 0.530592i
\(381\) −2.38478 + 2.38478i −0.122176 + 0.122176i
\(382\) 14.3431i 0.733859i
\(383\) 31.4558i 1.60732i 0.595090 + 0.803659i \(0.297117\pi\)
−0.595090 + 0.803659i \(0.702883\pi\)
\(384\) 0 0
\(385\) 2.00000 2.00000i 0.101929 0.101929i
\(386\) 18.3431 + 18.3431i 0.933642 + 0.933642i
\(387\) −14.3848 −0.731219
\(388\) 10.8284 + 10.8284i 0.549730 + 0.549730i
\(389\) 9.00000i 0.456318i −0.973624 0.228159i \(-0.926729\pi\)
0.973624 0.228159i \(-0.0732706\pi\)
\(390\) 11.3137 0.572892
\(391\) −16.9706 4.24264i −0.858238 0.214560i
\(392\) 0 0
\(393\) 1.27208i 0.0641678i
\(394\) 27.3137 + 27.3137i 1.37604 + 1.37604i
\(395\) −8.97056 −0.451358
\(396\) 3.75736 + 3.75736i 0.188814 + 0.188814i
\(397\) −0.272078 + 0.272078i −0.0136552 + 0.0136552i −0.713901 0.700246i \(-0.753074\pi\)
0.700246 + 0.713901i \(0.253074\pi\)
\(398\) 30.8284 30.8284i 1.54529 1.54529i
\(399\) 1.51472i 0.0758308i
\(400\) 12.0000i 0.600000i
\(401\) −8.48528 + 8.48528i −0.423735 + 0.423735i −0.886487 0.462753i \(-0.846862\pi\)
0.462753 + 0.886487i \(0.346862\pi\)
\(402\) −0.828427 + 0.828427i −0.0413182 + 0.0413182i
\(403\) 16.4853 + 16.4853i 0.821190 + 0.821190i
\(404\) 21.4558 1.06747
\(405\) −12.0589 12.0589i −0.599210 0.599210i
\(406\) 7.65685i 0.380003i
\(407\) 9.41421 0.466645
\(408\) 0 0
\(409\) 10.1421 0.501496 0.250748 0.968052i \(-0.419323\pi\)
0.250748 + 0.968052i \(0.419323\pi\)
\(410\) 28.2843i 1.39686i
\(411\) 4.07107 + 4.07107i 0.200811 + 0.200811i
\(412\) −33.3137 −1.64125
\(413\) −3.29289 3.29289i −0.162033 0.162033i
\(414\) 15.9411 15.9411i 0.783464 0.783464i
\(415\) −9.65685 + 9.65685i −0.474036 + 0.474036i
\(416\) 27.3137i 1.33916i
\(417\) 3.61522i 0.177038i
\(418\) −3.65685 + 3.65685i −0.178863 + 0.178863i
\(419\) 8.34315 8.34315i 0.407589 0.407589i −0.473308 0.880897i \(-0.656940\pi\)
0.880897 + 0.473308i \(0.156940\pi\)
\(420\) −2.34315 2.34315i −0.114334 0.114334i
\(421\) −20.3137 −0.990030 −0.495015 0.868885i \(-0.664837\pi\)
−0.495015 + 0.868885i \(0.664837\pi\)
\(422\) 12.7279 + 12.7279i 0.619586 + 0.619586i
\(423\) 30.5147i 1.48368i
\(424\) 0 0
\(425\) 10.6066 6.36396i 0.514496 0.308697i
\(426\) 18.3431 0.888728
\(427\) 6.82843i 0.330451i
\(428\) 0.928932 + 0.928932i 0.0449016 + 0.0449016i
\(429\) −2.00000 −0.0965609
\(430\) 21.6569 + 21.6569i 1.04439 + 1.04439i
\(431\) 6.84924 6.84924i 0.329916 0.329916i −0.522638 0.852555i \(-0.675052\pi\)
0.852555 + 0.522638i \(0.175052\pi\)
\(432\) −9.37258 + 9.37258i −0.450939 + 0.450939i
\(433\) 11.4853i 0.551947i −0.961165 0.275974i \(-0.911000\pi\)
0.961165 0.275974i \(-0.0890003\pi\)
\(434\) 13.6569i 0.655550i
\(435\) −4.48528 + 4.48528i −0.215053 + 0.215053i
\(436\) 21.8995 21.8995i 1.04880 1.04880i
\(437\) 7.75736 + 7.75736i 0.371085 + 0.371085i
\(438\) 9.57359 0.457444
\(439\) 13.7782 + 13.7782i 0.657596 + 0.657596i 0.954811 0.297214i \(-0.0960576\pi\)
−0.297214 + 0.954811i \(0.596058\pi\)
\(440\) 0 0
\(441\) 15.9411 0.759101
\(442\) −24.1421 + 14.4853i −1.14832 + 0.688995i
\(443\) 12.9706 0.616250 0.308125 0.951346i \(-0.400298\pi\)
0.308125 + 0.951346i \(0.400298\pi\)
\(444\) 11.0294i 0.523434i
\(445\) −3.65685 3.65685i −0.173352 0.173352i
\(446\) 12.0000 0.568216
\(447\) 8.38478 + 8.38478i 0.396586 + 0.396586i
\(448\) 5.65685 5.65685i 0.267261 0.267261i
\(449\) −11.3137 + 11.3137i −0.533927 + 0.533927i −0.921739 0.387812i \(-0.873231\pi\)
0.387812 + 0.921739i \(0.373231\pi\)
\(450\) 15.9411i 0.751472i
\(451\) 5.00000i 0.235441i
\(452\) 10.8284 10.8284i 0.509326 0.509326i
\(453\) 2.68629 2.68629i 0.126213 0.126213i
\(454\) −19.5563 19.5563i −0.917825 0.917825i
\(455\) −9.65685 −0.452720
\(456\) 0 0
\(457\) 36.4853i 1.70671i 0.521331 + 0.853355i \(0.325436\pi\)
−0.521331 + 0.853355i \(0.674564\pi\)
\(458\) −9.31371 −0.435201
\(459\) −13.2548 3.31371i −0.618683 0.154671i
\(460\) −24.0000 −1.11901
\(461\) 33.6985i 1.56949i −0.619816 0.784747i \(-0.712793\pi\)
0.619816 0.784747i \(-0.287207\pi\)
\(462\) 0.828427 + 0.828427i 0.0385419 + 0.0385419i
\(463\) 40.1127 1.86420 0.932098 0.362207i \(-0.117977\pi\)
0.932098 + 0.362207i \(0.117977\pi\)
\(464\) −10.8284 10.8284i −0.502697 0.502697i
\(465\) 8.00000 8.00000i 0.370991 0.370991i
\(466\) 31.0711 31.0711i 1.43934 1.43934i
\(467\) 28.1127i 1.30090i 0.759549 + 0.650450i \(0.225420\pi\)
−0.759549 + 0.650450i \(0.774580\pi\)
\(468\) 18.1421i 0.838621i
\(469\) 0.707107 0.707107i 0.0326512 0.0326512i
\(470\) −45.9411 + 45.9411i −2.11911 + 2.11911i
\(471\) −8.41421 8.41421i −0.387706 0.387706i
\(472\) 0 0
\(473\) −3.82843 3.82843i −0.176031 0.176031i
\(474\) 3.71573i 0.170669i
\(475\) −7.75736 −0.355932
\(476\) 8.00000 + 2.00000i 0.366679 + 0.0916698i
\(477\) 9.25988 0.423981
\(478\) 50.1421i 2.29345i
\(479\) 18.9497 + 18.9497i 0.865836 + 0.865836i 0.992008 0.126172i \(-0.0402692\pi\)
−0.126172 + 0.992008i \(0.540269\pi\)
\(480\) 13.2548 0.604998
\(481\) −22.7279 22.7279i −1.03630 1.03630i
\(482\) −18.8701 + 18.8701i −0.859508 + 0.859508i
\(483\) 1.75736 1.75736i 0.0799626 0.0799626i
\(484\) 2.00000i 0.0909091i
\(485\) 21.6569i 0.983387i
\(486\) 19.0538 19.0538i 0.864299 0.864299i
\(487\) 5.82843 5.82843i 0.264111 0.264111i −0.562611 0.826722i \(-0.690203\pi\)
0.826722 + 0.562611i \(0.190203\pi\)
\(488\) 0 0
\(489\) −4.14214 −0.187314
\(490\) −24.0000 24.0000i −1.08421 1.08421i
\(491\) 38.3848i 1.73228i 0.499801 + 0.866140i \(0.333407\pi\)
−0.499801 + 0.866140i \(0.666593\pi\)
\(492\) 5.85786 0.264093
\(493\) 3.82843 15.3137i 0.172424 0.689695i
\(494\) 17.6569 0.794419
\(495\) 7.51472i 0.337761i
\(496\) 19.3137 + 19.3137i 0.867211 + 0.867211i
\(497\) −15.6569 −0.702306
\(498\) −4.00000 4.00000i −0.179244 0.179244i
\(499\) −9.07107 + 9.07107i −0.406077 + 0.406077i −0.880368 0.474291i \(-0.842704\pi\)
0.474291 + 0.880368i \(0.342704\pi\)
\(500\) −8.00000 + 8.00000i −0.357771 + 0.357771i
\(501\) 2.42641i 0.108404i
\(502\) 12.0000i 0.535586i
\(503\) 16.0208 16.0208i 0.714333 0.714333i −0.253106 0.967439i \(-0.581452\pi\)
0.967439 + 0.253106i \(0.0814521\pi\)
\(504\) 0 0
\(505\) −21.4558 21.4558i −0.954773 0.954773i
\(506\) 8.48528 0.377217
\(507\) −0.556349 0.556349i −0.0247083 0.0247083i
\(508\) 11.5147i 0.510883i
\(509\) 40.3137 1.78687 0.893437 0.449189i \(-0.148287\pi\)
0.893437 + 0.449189i \(0.148287\pi\)
\(510\) 7.02944 + 11.7157i 0.311269 + 0.518781i
\(511\) −8.17157 −0.361489
\(512\) 32.0000i 1.41421i
\(513\) 6.05887 + 6.05887i 0.267506 + 0.267506i
\(514\) −21.0294 −0.927569
\(515\) 33.3137 + 33.3137i 1.46798 + 1.46798i
\(516\) −4.48528 + 4.48528i −0.197454 + 0.197454i
\(517\) 8.12132 8.12132i 0.357175 0.357175i
\(518\) 18.8284i 0.827274i
\(519\) 0.100505i 0.00441168i
\(520\) 0 0
\(521\) 3.24264 3.24264i 0.142063 0.142063i −0.632499 0.774561i \(-0.717971\pi\)
0.774561 + 0.632499i \(0.217971\pi\)
\(522\) 14.3848 + 14.3848i 0.629605 + 0.629605i
\(523\) −6.34315 −0.277366 −0.138683 0.990337i \(-0.544287\pi\)
−0.138683 + 0.990337i \(0.544287\pi\)
\(524\) 3.07107 + 3.07107i 0.134160 + 0.134160i
\(525\) 1.75736i 0.0766974i
\(526\) 11.1127 0.484537
\(527\) −6.82843 + 27.3137i −0.297451 + 1.18980i
\(528\) −2.34315 −0.101972
\(529\) 5.00000i 0.217391i
\(530\) −13.9411 13.9411i −0.605564 0.605564i
\(531\) −12.3726 −0.536924
\(532\) −3.65685 3.65685i −0.158545 0.158545i
\(533\) 12.0711 12.0711i 0.522856 0.522856i
\(534\) 1.51472 1.51472i 0.0655483 0.0655483i
\(535\) 1.85786i 0.0803225i
\(536\) 0 0
\(537\) −10.6152 + 10.6152i −0.458081 + 0.458081i
\(538\) −32.1421 + 32.1421i −1.38575 + 1.38575i
\(539\) 4.24264 + 4.24264i 0.182743 + 0.182743i
\(540\) −18.7452 −0.806664
\(541\) 5.43503 + 5.43503i 0.233670 + 0.233670i 0.814223 0.580553i \(-0.197163\pi\)
−0.580553 + 0.814223i \(0.697163\pi\)
\(542\) 58.6274i 2.51826i
\(543\) −10.8284 −0.464692
\(544\) −28.2843 + 16.9706i −1.21268 + 0.727607i
\(545\) −43.7990 −1.87614
\(546\) 4.00000i 0.171184i
\(547\) −6.10051 6.10051i −0.260839 0.260839i 0.564556 0.825395i \(-0.309047\pi\)
−0.825395 + 0.564556i \(0.809047\pi\)
\(548\) −19.6569 −0.839699
\(549\) 12.8284 + 12.8284i 0.547504 + 0.547504i
\(550\) −4.24264 + 4.24264i −0.180907 + 0.180907i
\(551\) −7.00000 + 7.00000i −0.298210 + 0.298210i
\(552\) 0 0
\(553\) 3.17157i 0.134869i
\(554\) 20.9289 20.9289i 0.889185 0.889185i
\(555\) −11.0294 + 11.0294i −0.468174 + 0.468174i
\(556\) −8.72792 8.72792i −0.370146 0.370146i
\(557\) 24.2843 1.02896 0.514479 0.857503i \(-0.327985\pi\)
0.514479 + 0.857503i \(0.327985\pi\)
\(558\) −25.6569 25.6569i −1.08614 1.08614i
\(559\) 18.4853i 0.781844i
\(560\) −11.3137 −0.478091
\(561\) −1.24264 2.07107i −0.0524643 0.0874406i
\(562\) −32.9706 −1.39078
\(563\) 16.8701i 0.710988i −0.934679 0.355494i \(-0.884313\pi\)
0.934679 0.355494i \(-0.115687\pi\)
\(564\) −9.51472 9.51472i −0.400642 0.400642i
\(565\) −21.6569 −0.911111
\(566\) −2.14214 2.14214i −0.0900407 0.0900407i
\(567\) −4.26346 + 4.26346i −0.179048 + 0.179048i
\(568\) 0 0
\(569\) 19.5147i 0.818100i −0.912512 0.409050i \(-0.865860\pi\)
0.912512 0.409050i \(-0.134140\pi\)
\(570\) 8.56854i 0.358897i
\(571\) −12.2635 + 12.2635i −0.513210 + 0.513210i −0.915508 0.402299i \(-0.868211\pi\)
0.402299 + 0.915508i \(0.368211\pi\)
\(572\) 4.82843 4.82843i 0.201887 0.201887i
\(573\) 2.97056 + 2.97056i 0.124097 + 0.124097i
\(574\) −10.0000 −0.417392
\(575\) 9.00000 + 9.00000i 0.375326 + 0.375326i
\(576\) 21.2548i 0.885618i
\(577\) 21.6863 0.902812 0.451406 0.892319i \(-0.350923\pi\)
0.451406 + 0.892319i \(0.350923\pi\)
\(578\) −30.0000 16.0000i −1.24784 0.665512i
\(579\) 7.59798 0.315761
\(580\) 21.6569i 0.899252i
\(581\) 3.41421 + 3.41421i 0.141645 + 0.141645i
\(582\) 8.97056 0.371842
\(583\) 2.46447 + 2.46447i 0.102068 + 0.102068i
\(584\) 0 0
\(585\) −18.1421 + 18.1421i −0.750085 + 0.750085i
\(586\) 21.8579i 0.902940i
\(587\) 37.1127i 1.53180i 0.642957 + 0.765902i \(0.277707\pi\)
−0.642957 + 0.765902i \(0.722293\pi\)
\(588\) 4.97056 4.97056i 0.204983 0.204983i
\(589\) 12.4853 12.4853i 0.514447 0.514447i
\(590\) 18.6274 + 18.6274i 0.766879 + 0.766879i
\(591\) 11.3137 0.465384
\(592\) −26.6274 26.6274i −1.09438 1.09438i
\(593\) 25.3137i 1.03951i 0.854316 + 0.519755i \(0.173977\pi\)
−0.854316 + 0.519755i \(0.826023\pi\)
\(594\) 6.62742 0.271926
\(595\) −6.00000 10.0000i −0.245976 0.409960i
\(596\) −40.4853 −1.65834
\(597\) 12.7696i 0.522623i
\(598\) −20.4853 20.4853i −0.837705 0.837705i
\(599\) −5.97056 −0.243951 −0.121975 0.992533i \(-0.538923\pi\)
−0.121975 + 0.992533i \(0.538923\pi\)
\(600\) 0 0
\(601\) −19.3137 + 19.3137i −0.787823 + 0.787823i −0.981137 0.193314i \(-0.938076\pi\)
0.193314 + 0.981137i \(0.438076\pi\)
\(602\) 7.65685 7.65685i 0.312070 0.312070i
\(603\) 2.65685i 0.108195i
\(604\) 12.9706i 0.527765i
\(605\) 2.00000 2.00000i 0.0813116 0.0813116i
\(606\) 8.88730 8.88730i 0.361022 0.361022i
\(607\) 32.7279 + 32.7279i 1.32839 + 1.32839i 0.906779 + 0.421606i \(0.138534\pi\)
0.421606 + 0.906779i \(0.361466\pi\)
\(608\) 20.6863 0.838940
\(609\) 1.58579 + 1.58579i 0.0642593 + 0.0642593i
\(610\) 38.6274i 1.56398i
\(611\) −39.2132 −1.58640
\(612\) 18.7868 11.2721i 0.759411 0.455647i
\(613\) 11.2721 0.455275 0.227637 0.973746i \(-0.426900\pi\)
0.227637 + 0.973746i \(0.426900\pi\)
\(614\) 44.4853i 1.79528i
\(615\) −5.85786 5.85786i −0.236212 0.236212i
\(616\) 0 0
\(617\) 16.9706 + 16.9706i 0.683209 + 0.683209i 0.960722 0.277513i \(-0.0895101\pi\)
−0.277513 + 0.960722i \(0.589510\pi\)
\(618\) −13.7990 + 13.7990i −0.555077 + 0.555077i
\(619\) −21.0711 + 21.0711i −0.846918 + 0.846918i −0.989747 0.142830i \(-0.954380\pi\)
0.142830 + 0.989747i \(0.454380\pi\)
\(620\) 38.6274i 1.55131i
\(621\) 14.0589i 0.564163i
\(622\) −3.31371 + 3.31371i −0.132868 + 0.132868i
\(623\) −1.29289 + 1.29289i −0.0517987 + 0.0517987i
\(624\) 5.65685 + 5.65685i 0.226455 + 0.226455i
\(625\) 31.0000 1.24000
\(626\) −20.8284 20.8284i −0.832471 0.832471i
\(627\) 1.51472i 0.0604920i
\(628\) 40.6274 1.62121
\(629\) 9.41421 37.6569i 0.375369 1.50148i
\(630\) 15.0294 0.598787
\(631\) 9.34315i 0.371945i −0.982555 0.185972i \(-0.940457\pi\)
0.982555 0.185972i \(-0.0595435\pi\)
\(632\) 0 0
\(633\) 5.27208 0.209546
\(634\) 17.1716 + 17.1716i 0.681970 + 0.681970i
\(635\) −11.5147 + 11.5147i −0.456948 + 0.456948i
\(636\) 2.88730 2.88730i 0.114489 0.114489i
\(637\) 20.4853i 0.811656i
\(638\) 7.65685i 0.303138i
\(639\) −29.4142 + 29.4142i −1.16361 + 1.16361i
\(640\) 0 0
\(641\) 4.41421 + 4.41421i 0.174351 + 0.174351i 0.788888 0.614537i \(-0.210657\pi\)
−0.614537 + 0.788888i \(0.710657\pi\)
\(642\) 0.769553 0.0303718
\(643\) 5.72792 + 5.72792i 0.225887 + 0.225887i 0.810972 0.585085i \(-0.198939\pi\)
−0.585085 + 0.810972i \(0.698939\pi\)
\(644\) 8.48528i 0.334367i
\(645\) 8.97056 0.353216
\(646\) 10.9706 + 18.2843i 0.431631 + 0.719385i
\(647\) −28.4558 −1.11871 −0.559357 0.828927i \(-0.688952\pi\)
−0.559357 + 0.828927i \(0.688952\pi\)
\(648\) 0 0
\(649\) −3.29289 3.29289i −0.129257 0.129257i
\(650\) 20.4853 0.803499
\(651\) −2.82843 2.82843i −0.110855 0.110855i
\(652\) 10.0000 10.0000i 0.391630 0.391630i
\(653\) 1.89949 1.89949i 0.0743330 0.0743330i −0.668963 0.743296i \(-0.733261\pi\)
0.743296 + 0.668963i \(0.233261\pi\)
\(654\) 18.1421i 0.709414i
\(655\) 6.14214i 0.239993i
\(656\) 14.1421 14.1421i 0.552158 0.552158i
\(657\) −15.3518 + 15.3518i −0.598930 + 0.598930i
\(658\) 16.2426 + 16.2426i 0.633204 + 0.633204i
\(659\) 42.5269 1.65661 0.828307 0.560275i \(-0.189305\pi\)
0.828307 + 0.560275i \(0.189305\pi\)
\(660\) −2.34315 2.34315i −0.0912068 0.0912068i
\(661\) 21.0000i 0.816805i −0.912802 0.408403i \(-0.866086\pi\)
0.912802 0.408403i \(-0.133914\pi\)
\(662\) 23.3137 0.906113
\(663\) −2.00000 + 8.00000i −0.0776736 + 0.310694i
\(664\) 0 0
\(665\) 7.31371i 0.283613i
\(666\) 35.3726 + 35.3726i 1.37066 + 1.37066i
\(667\) 16.2426 0.628918
\(668\) −5.85786 5.85786i −0.226648 0.226648i
\(669\) 2.48528 2.48528i 0.0960865 0.0960865i
\(670\) −4.00000 + 4.00000i −0.154533 + 0.154533i
\(671\) 6.82843i 0.263609i
\(672\) 4.68629i 0.180778i
\(673\) 20.9497 20.9497i 0.807553 0.807553i −0.176710 0.984263i \(-0.556545\pi\)
0.984263 + 0.176710i \(0.0565453\pi\)
\(674\) −44.5269 + 44.5269i −1.71511 + 1.71511i
\(675\) 7.02944 + 7.02944i 0.270563 + 0.270563i
\(676\) 2.68629 0.103319
\(677\) −27.9203 27.9203i −1.07306 1.07306i −0.997111 0.0759533i \(-0.975800\pi\)
−0.0759533 0.997111i \(-0.524200\pi\)
\(678\) 8.97056i 0.344512i
\(679\) −7.65685 −0.293843
\(680\) 0 0
\(681\) −8.10051 −0.310412
\(682\) 13.6569i 0.522948i
\(683\) −36.2132 36.2132i −1.38566 1.38566i −0.834204 0.551455i \(-0.814073\pi\)
−0.551455 0.834204i \(-0.685927\pi\)
\(684\) −13.7401 −0.525366
\(685\) 19.6569 + 19.6569i 0.751050 + 0.751050i
\(686\) −18.3848 + 18.3848i −0.701934 + 0.701934i
\(687\) −1.92893 + 1.92893i −0.0735934 + 0.0735934i
\(688\) 21.6569i 0.825660i
\(689\) 11.8995i 0.453335i
\(690\) −9.94113 + 9.94113i −0.378452 + 0.378452i
\(691\) 27.2426 27.2426i 1.03636 1.03636i 0.0370453 0.999314i \(-0.488205\pi\)
0.999314 0.0370453i \(-0.0117946\pi\)
\(692\) −0.242641 0.242641i −0.00922381 0.00922381i
\(693\) −2.65685 −0.100926
\(694\) 30.8701 + 30.8701i 1.17181 + 1.17181i
\(695\) 17.4558i 0.662138i
\(696\) 0 0
\(697\) 20.0000 + 5.00000i 0.757554 + 0.189389i
\(698\) 71.3970 2.70242
\(699\) 12.8701i 0.486790i
\(700\) −4.24264 4.24264i −0.160357 0.160357i
\(701\) −9.85786 −0.372326 −0.186163 0.982519i \(-0.559605\pi\)
−0.186163 + 0.982519i \(0.559605\pi\)
\(702\) −16.0000 16.0000i −0.603881 0.603881i
\(703\) −17.2132 + 17.2132i −0.649208 + 0.649208i
\(704\) 5.65685 5.65685i 0.213201 0.213201i
\(705\) 19.0294i 0.716690i
\(706\) 24.3431i 0.916166i
\(707\) −7.58579 + 7.58579i −0.285293 + 0.285293i
\(708\) −3.85786 + 3.85786i −0.144987 + 0.144987i
\(709\) 12.0711 + 12.0711i 0.453338 + 0.453338i 0.896461 0.443123i \(-0.146129\pi\)
−0.443123 + 0.896461i \(0.646129\pi\)
\(710\) 88.5685 3.32392
\(711\) 5.95837 + 5.95837i 0.223456 + 0.223456i
\(712\) 0 0
\(713\) −28.9706 −1.08496
\(714\) 4.14214 2.48528i 0.155016 0.0930093i
\(715\) −9.65685 −0.361146
\(716\) 51.2548i 1.91548i
\(717\) 10.3848 + 10.3848i 0.387827 + 0.387827i
\(718\) 64.2843 2.39907
\(719\) −16.5563 16.5563i −0.617448 0.617448i 0.327428 0.944876i \(-0.393818\pi\)
−0.944876 + 0.327428i \(0.893818\pi\)
\(720\) −21.2548 + 21.2548i −0.792121 + 0.792121i
\(721\) 11.7782 11.7782i 0.438642 0.438642i
\(722\) 24.6274i 0.916538i
\(723\) 7.81623i 0.290689i
\(724\) 26.1421 26.1421i 0.971565 0.971565i
\(725\) −8.12132 + 8.12132i −0.301618 + 0.301618i
\(726\) 0.828427 + 0.828427i 0.0307458 + 0.0307458i
\(727\) −5.14214 −0.190711 −0.0953556 0.995443i \(-0.530399\pi\)
−0.0953556 + 0.995443i \(0.530399\pi\)
\(728\) 0 0
\(729\) 10.1960i 0.377628i
\(730\) 46.2254 1.71088
\(731\) −19.1421 + 11.4853i −0.707997 + 0.424798i
\(732\) 8.00000 0.295689
\(733\) 33.7990i 1.24839i −0.781267 0.624197i \(-0.785426\pi\)
0.781267 0.624197i \(-0.214574\pi\)
\(734\) −25.6569 25.6569i −0.947012 0.947012i
\(735\) −9.94113 −0.366684
\(736\) −24.0000 24.0000i −0.884652 0.884652i
\(737\) 0.707107 0.707107i 0.0260466 0.0260466i
\(738\) −18.7868 + 18.7868i −0.691552 + 0.691552i
\(739\) 35.3137i 1.29904i −0.760346 0.649518i \(-0.774971\pi\)
0.760346 0.649518i \(-0.225029\pi\)
\(740\) 53.2548i 1.95769i
\(741\) 3.65685 3.65685i 0.134338 0.134338i
\(742\) −4.92893 + 4.92893i −0.180947 + 0.180947i
\(743\) −5.43503 5.43503i −0.199392 0.199392i 0.600347 0.799739i \(-0.295029\pi\)
−0.799739 + 0.600347i \(0.795029\pi\)
\(744\) 0 0
\(745\) 40.4853 + 40.4853i 1.48327 + 1.48327i
\(746\) 57.4558i 2.10361i
\(747\) 12.8284 0.469368
\(748\) 8.00000 + 2.00000i 0.292509 + 0.0731272i
\(749\) −0.656854 −0.0240009
\(750\) 6.62742i 0.241999i
\(751\) −19.3848 19.3848i −0.707361 0.707361i 0.258619 0.965979i \(-0.416733\pi\)
−0.965979 + 0.258619i \(0.916733\pi\)
\(752\) −45.9411 −1.67530
\(753\) 2.48528 + 2.48528i 0.0905687 + 0.0905687i
\(754\) 18.4853 18.4853i 0.673194 0.673194i
\(755\) 12.9706 12.9706i 0.472047 0.472047i
\(756\) 6.62742i 0.241037i
\(757\) 17.1716i 0.624111i −0.950064 0.312056i \(-0.898982\pi\)
0.950064 0.312056i \(-0.101018\pi\)
\(758\) 49.1127 49.1127i 1.78385 1.78385i
\(759\) 1.75736 1.75736i 0.0637881 0.0637881i
\(760\) 0 0
\(761\) 4.92893 0.178674 0.0893368 0.996001i \(-0.471525\pi\)
0.0893368 + 0.996001i \(0.471525\pi\)
\(762\) −4.76955 4.76955i −0.172783 0.172783i
\(763\) 15.4853i 0.560605i
\(764\) −14.3431 −0.518917
\(765\) −30.0589 7.51472i −1.08678 0.271695i
\(766\) −62.9117 −2.27309
\(767\) 15.8995i 0.574097i
\(768\) 6.62742 + 6.62742i 0.239146 + 0.239146i
\(769\) −14.0416 −0.506354 −0.253177 0.967420i \(-0.581476\pi\)
−0.253177 + 0.967420i \(0.581476\pi\)
\(770\) 4.00000 + 4.00000i 0.144150 + 0.144150i
\(771\) −4.35534 + 4.35534i −0.156854 + 0.156854i
\(772\) −18.3431 + 18.3431i −0.660184 + 0.660184i
\(773\) 41.5980i 1.49618i 0.663600 + 0.748088i \(0.269028\pi\)
−0.663600 + 0.748088i \(0.730972\pi\)
\(774\) 28.7696i 1.03410i
\(775\) 14.4853 14.4853i 0.520327 0.520327i
\(776\) 0 0
\(777\) 3.89949 + 3.89949i 0.139894 + 0.139894i
\(778\) 18.0000 0.645331
\(779\) −9.14214 9.14214i −0.327551 0.327551i
\(780\) 11.3137i 0.405096i
\(781\) −15.6569 −0.560246
\(782\) 8.48528 33.9411i 0.303433 1.21373i
\(783\) 12.6863 0.453371
\(784\) 24.0000i 0.857143i
\(785\) −40.6274 40.6274i −1.45005 1.45005i
\(786\) 2.54416 0.0907470
\(787\) −8.36396 8.36396i −0.298143 0.298143i 0.542143 0.840286i \(-0.317613\pi\)
−0.840286 + 0.542143i \(0.817613\pi\)
\(788\) −27.3137 + 27.3137i −0.973011 + 0.973011i
\(789\) 2.30152 2.30152i 0.0819361 0.0819361i
\(790\) 17.9411i 0.638317i
\(791\) 7.65685i 0.272246i
\(792\) 0 0
\(793\) 16.4853 16.4853i 0.585410 0.585410i
\(794\) −0.544156 0.544156i −0.0193114 0.0193114i
\(795\) −5.77460 −0.204804
\(796\) 30.8284 + 30.8284i 1.09268 + 1.09268i
\(797\) 19.5147i 0.691247i 0.938373 + 0.345623i \(0.112333\pi\)
−0.938373 + 0.345623i \(0.887667\pi\)
\(798\) −3.02944 −0.107241
\(799\) −24.3640 40.6066i −0.861935 1.43656i
\(800\) 24.0000 0.848528
\(801\) 4.85786i 0.171644i
\(802\) −16.9706 16.9706i −0.599251 0.599251i
\(803\) −8.17157 −0.288369
\(804\) −0.828427 0.828427i −0.0292164 0.0292164i
\(805\) 8.48528 8.48528i 0.299067 0.299067i
\(806\) −32.9706 + 32.9706i −1.16134 + 1.16134i
\(807\) 13.3137i 0.468665i
\(808\) 0 0
\(809\) −32.6066 + 32.6066i −1.14639 + 1.14639i −0.159129 + 0.987258i \(0.550869\pi\)
−0.987258 + 0.159129i \(0.949131\pi\)
\(810\) 24.1177 24.1177i 0.847411 0.847411i
\(811\) −23.0711 23.0711i −0.810135 0.810135i 0.174519 0.984654i \(-0.444163\pi\)
−0.984654 + 0.174519i \(0.944163\pi\)
\(812\) −7.65685 −0.268703
\(813\) −12.1421 12.1421i −0.425843 0.425843i
\(814\) 18.8284i 0.659936i
\(815\) −20.0000 −0.700569
\(816\) −2.34315 + 9.37258i −0.0820265 + 0.328106i
\(817\) 14.0000 0.489798
\(818\) 20.2843i 0.709223i
\(819\) 6.41421 + 6.41421i 0.224131 + 0.224131i
\(820\) 28.2843 0.987730
\(821\) −17.1716 17.1716i −0.599292 0.599292i 0.340832 0.940124i \(-0.389291\pi\)
−0.940124 + 0.340832i \(0.889291\pi\)
\(822\) −8.14214 + 8.14214i −0.283990 + 0.283990i
\(823\) 20.6274 20.6274i 0.719027 0.719027i −0.249379 0.968406i \(-0.580227\pi\)
0.968406 + 0.249379i \(0.0802266\pi\)
\(824\) 0 0
\(825\) 1.75736i 0.0611834i
\(826\) 6.58579 6.58579i 0.229149 0.229149i
\(827\) 14.7487 14.7487i 0.512864 0.512864i −0.402539 0.915403i \(-0.631872\pi\)
0.915403 + 0.402539i \(0.131872\pi\)
\(828\) 15.9411 + 15.9411i 0.553992 + 0.553992i
\(829\) 32.9706 1.14511 0.572557 0.819865i \(-0.305951\pi\)
0.572557 + 0.819865i \(0.305951\pi\)
\(830\) −19.3137 19.3137i −0.670389 0.670389i
\(831\) 8.66905i 0.300726i
\(832\) −27.3137 −0.946932
\(833\) 21.2132 12.7279i 0.734994 0.440996i
\(834\) −7.23045 −0.250370
\(835\) 11.7157i 0.405440i
\(836\) −3.65685 3.65685i −0.126475 0.126475i
\(837\) −22.6274 −0.782118
\(838\) 16.6863 + 16.6863i 0.576418 + 0.576418i
\(839\) −25.3848 + 25.3848i −0.876380 + 0.876380i −0.993158 0.116778i \(-0.962743\pi\)
0.116778 + 0.993158i \(0.462743\pi\)
\(840\) 0 0
\(841\) 14.3431i 0.494591i
\(842\) 40.6274i 1.40011i
\(843\) −6.82843 + 6.82843i −0.235184 + 0.235184i
\(844\) −12.7279 + 12.7279i −0.438113 + 0.438113i
\(845\) −2.68629 2.68629i −0.0924112 0.0924112i
\(846\) 61.0294 2.09824
\(847\) −0.707107 0.707107i −0.0242965 0.0242965i
\(848\) 13.9411i 0.478740i
\(849\) −0.887302 −0.0304521
\(850\) 12.7279 + 21.2132i 0.436564 + 0.727607i
\(851\) 39.9411 1.36916
\(852\) 18.3431i 0.628426i
\(853\) 15.9203 + 15.9203i 0.545101 + 0.545101i 0.925020 0.379919i \(-0.124048\pi\)
−0.379919 + 0.925020i \(0.624048\pi\)
\(854\) −13.6569 −0.467328
\(855\) 13.7401 + 13.7401i 0.469902 + 0.469902i
\(856\) 0 0
\(857\) 39.4558 39.4558i 1.34779 1.34779i 0.459724 0.888062i \(-0.347948\pi\)
0.888062 0.459724i \(-0.152052\pi\)
\(858\) 4.00000i 0.136558i
\(859\) 10.3137i 0.351899i −0.984399 0.175950i \(-0.943700\pi\)
0.984399 0.175950i \(-0.0562996\pi\)
\(860\) −21.6569 + 21.6569i −0.738493 + 0.738493i
\(861\) −2.07107 + 2.07107i −0.0705818 + 0.0705818i
\(862\) 13.6985 + 13.6985i 0.466572 + 0.466572i
\(863\) −30.6863 −1.04457 −0.522287 0.852770i \(-0.674921\pi\)
−0.522287 + 0.852770i \(0.674921\pi\)
\(864\) −18.7452 18.7452i −0.637723 0.637723i
\(865\) 0.485281i 0.0165001i
\(866\) 22.9706 0.780571
\(867\) −9.52691 + 2.89949i −0.323551 + 0.0984720i
\(868\) 13.6569 0.463544
\(869\) 3.17157i 0.107588i
\(870\) −8.97056 8.97056i −0.304131 0.304131i
\(871\) −3.41421 −0.115686
\(872\) 0 0
\(873\) −14.3848 + 14.3848i −0.486851 + 0.486851i
\(874\) −15.5147 + 15.5147i −0.524793 + 0.524793i
\(875\) 5.65685i 0.191237i
\(876\) 9.57359i 0.323462i
\(877\) −11.5563 + 11.5563i −0.390230 + 0.390230i −0.874769 0.484539i \(-0.838987\pi\)
0.484539 + 0.874769i \(0.338987\pi\)
\(878\) −27.5563 + 27.5563i −0.929982 + 0.929982i
\(879\) 4.52691 + 4.52691i 0.152689 + 0.152689i
\(880\) −11.3137 −0.381385
\(881\) −15.4142 15.4142i −0.519318 0.519318i 0.398047 0.917365i \(-0.369688\pi\)
−0.917365 + 0.398047i \(0.869688\pi\)
\(882\) 31.8823i 1.07353i
\(883\) 20.6569 0.695158 0.347579 0.937651i \(-0.387004\pi\)
0.347579 + 0.937651i \(0.387004\pi\)
\(884\) −14.4853 24.1421i −0.487193 0.811988i
\(885\) 7.71573 0.259361
\(886\) 25.9411i 0.871509i
\(887\) −3.51472 3.51472i −0.118013 0.118013i 0.645634 0.763647i \(-0.276593\pi\)
−0.763647 + 0.645634i \(0.776593\pi\)
\(888\) 0 0
\(889\) 4.07107 + 4.07107i 0.136539 + 0.136539i
\(890\) 7.31371 7.31371i 0.245156 0.245156i
\(891\) −4.26346 + 4.26346i −0.142831 + 0.142831i
\(892\) 12.0000i 0.401790i
\(893\) 29.6985i 0.993822i
\(894\) −16.7696 + 16.7696i −0.560858 + 0.560858i
\(895\) −51.2548 + 51.2548i −1.71326 + 1.71326i
\(896\) 0 0
\(897\) −8.48528 −0.283315
\(898\) −22.6274 22.6274i −0.755087 0.755087i
\(899\) 26.1421i 0.871889i
\(900\) −15.9411 −0.531371
\(901\) 12.3223 7.39340i 0.410516 0.246310i
\(902\) −10.0000 −0.332964
\(903\) 3.17157i 0.105543i
\(904\) 0 0
\(905\) −52.2843 −1.73799
\(906\) 5.37258 + 5.37258i 0.178492 + 0.178492i
\(907\) 10.7279 10.7279i 0.356215 0.356215i −0.506201 0.862416i \(-0.668951\pi\)
0.862416 + 0.506201i \(0.168951\pi\)
\(908\) 19.5563 19.5563i 0.649000 0.649000i
\(909\) 28.5025i 0.945369i
\(910\) 19.3137i 0.640243i
\(911\) 5.24264 5.24264i 0.173696 0.173696i −0.614905 0.788601i \(-0.710806\pi\)
0.788601 + 0.614905i \(0.210806\pi\)
\(912\) 4.28427 4.28427i 0.141866 0.141866i
\(913\) 3.41421 + 3.41421i 0.112994 + 0.112994i
\(914\) −72.9706 −2.41365
\(915\) −8.00000 8.00000i −0.264472 0.264472i
\(916\) 9.31371i 0.307734i
\(917\) −2.17157 −0.0717117
\(918\) 6.62742 26.5097i 0.218737 0.874949i
\(919\) 18.0416 0.595138 0.297569 0.954700i \(-0.403824\pi\)
0.297569 + 0.954700i \(0.403824\pi\)
\(920\) 0 0
\(921\) −9.21320 9.21320i −0.303585 0.303585i
\(922\) 67.3970 2.21960
\(923\) 37.7990 + 37.7990i 1.24417 + 1.24417i
\(924\) −0.828427 + 0.828427i −0.0272533 + 0.0272533i
\(925\) −19.9706 + 19.9706i −0.656628 + 0.656628i
\(926\) 80.2254i 2.63637i
\(927\) 44.2548i 1.45352i
\(928\) 21.6569 21.6569i 0.710921 0.710921i
\(929\) −18.1716 + 18.1716i −0.596190 + 0.596190i −0.939296 0.343107i \(-0.888521\pi\)
0.343107 + 0.939296i \(0.388521\pi\)
\(930\) 16.0000 + 16.0000i 0.524661 + 0.524661i
\(931\) −15.5147 −0.508474
\(932\) 31.0711 + 31.0711i 1.01777 + 1.01777i
\(933\) 1.37258i 0.0449364i
\(934\) −56.2254 −1.83975
\(935\) −6.00000 10.0000i −0.196221 0.327035i
\(936\) 0 0
\(937\) 18.6863i 0.610455i 0.952280 + 0.305227i \(0.0987324\pi\)
−0.952280 + 0.305227i \(0.901268\pi\)
\(938\) 1.41421 + 1.41421i 0.0461757 + 0.0461757i
\(939\) −8.62742 −0.281545
\(940\) −45.9411 45.9411i −1.49843 1.49843i
\(941\) −3.05025 + 3.05025i −0.0994354 + 0.0994354i −0.755074 0.655639i \(-0.772399\pi\)
0.655639 + 0.755074i \(0.272399\pi\)
\(942\) 16.8284 16.8284i 0.548300 0.548300i
\(943\) 21.2132i 0.690797i
\(944\) 18.6274i 0.606271i
\(945\) 6.62742 6.62742i 0.215590 0.215590i
\(946\) 7.65685 7.65685i 0.248946 0.248946i
\(947\) 8.10051 + 8.10051i 0.263231 + 0.263231i 0.826365 0.563134i \(-0.190405\pi\)
−0.563134 + 0.826365i \(0.690405\pi\)
\(948\) 3.71573 0.120681
\(949\) 19.7279 + 19.7279i 0.640395 + 0.640395i
\(950\) 15.5147i 0.503364i
\(951\) 7.11270 0.230645
\(952\) 0 0
\(953\) −41.6569 −1.34940 −0.674699 0.738093i \(-0.735727\pi\)
−0.674699 + 0.738093i \(0.735727\pi\)
\(954\) 18.5198i 0.599600i
\(955\) 14.3431 + 14.3431i 0.464133 + 0.464133i
\(956\) −50.1421 −1.62171
\(957\) 1.58579 + 1.58579i 0.0512612 + 0.0512612i
\(958\) −37.8995 + 37.8995i −1.22448 + 1.22448i
\(959\) 6.94975 6.94975i 0.224419 0.224419i
\(960\) 13.2548i 0.427798i
\(961\) 15.6274i 0.504110i
\(962\) 45.4558 45.4558i 1.46556 1.46556i
\(963\) −1.23402 + 1.23402i −0.0397657 + 0.0397657i
\(964\) −18.8701 18.8701i −0.607764 0.607764i
\(965\) 36.6863 1.18097
\(966\) 3.51472 + 3.51472i 0.113084 + 0.113084i
\(967\) 23.2132i 0.746486i −0.927734 0.373243i \(-0.878246\pi\)
0.927734 0.373243i \(-0.121754\pi\)
\(968\) 0 0
\(969\) 6.05887 + 1.51472i 0.194639 + 0.0486598i
\(970\) 43.3137 1.39072
\(971\) 56.4264i 1.81081i 0.424549 + 0.905405i \(0.360433\pi\)
−0.424549 + 0.905405i \(0.639567\pi\)
\(972\) 19.0538 + 19.0538i 0.611152 + 0.611152i
\(973\) 6.17157 0.197852
\(974\) 11.6569 + 11.6569i 0.373510 + 0.373510i
\(975\) 4.24264 4.24264i 0.135873 0.135873i
\(976\) 19.3137 19.3137i 0.618217 0.618217i
\(977\) 30.8579i 0.987231i −0.869680 0.493615i \(-0.835675\pi\)
0.869680 0.493615i \(-0.164325\pi\)
\(978\) 8.28427i 0.264902i
\(979\) −1.29289 + 1.29289i −0.0413210 + 0.0413210i
\(980\) 24.0000 24.0000i 0.766652 0.766652i
\(981\) 29.0919 + 29.0919i 0.928832 + 0.928832i
\(982\) −76.7696 −2.44981
\(983\) 9.75736 + 9.75736i 0.311211 + 0.311211i 0.845379 0.534167i \(-0.179375\pi\)
−0.534167 + 0.845379i \(0.679375\pi\)
\(984\) 0 0
\(985\) 54.6274 1.74057
\(986\) 30.6274 + 7.65685i 0.975376 + 0.243844i
\(987\) 6.72792 0.214152
\(988\) 17.6569i 0.561739i
\(989\) −16.2426 16.2426i −0.516486 0.516486i
\(990\) 15.0294 0.477667
\(991\) 38.4558 + 38.4558i 1.22159 + 1.22159i 0.967067 + 0.254524i \(0.0819186\pi\)
0.254524 + 0.967067i \(0.418081\pi\)
\(992\) −38.6274 + 38.6274i −1.22642 + 1.22642i
\(993\) 4.82843 4.82843i 0.153226 0.153226i
\(994\) 31.3137i 0.993211i
\(995\) 61.6569i 1.95465i
\(996\) 4.00000 4.00000i 0.126745 0.126745i
\(997\) −8.46447 + 8.46447i −0.268072 + 0.268072i −0.828323 0.560251i \(-0.810705\pi\)
0.560251 + 0.828323i \(0.310705\pi\)
\(998\) −18.1421 18.1421i −0.574279 0.574279i
\(999\) 31.1960 0.986996
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 187.2.e.a.166.2 yes 4
17.2 even 8 3179.2.a.i.1.1 2
17.4 even 4 inner 187.2.e.a.89.2 4
17.15 even 8 3179.2.a.h.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.e.a.89.2 4 17.4 even 4 inner
187.2.e.a.166.2 yes 4 1.1 even 1 trivial
3179.2.a.h.1.2 2 17.15 even 8
3179.2.a.i.1.1 2 17.2 even 8