Properties

Label 360.2.bd.a.299.2
Level $360$
Weight $2$
Character 360.299
Analytic conductor $2.875$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [360,2,Mod(59,360)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(360, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("360.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 360.bd (of order \(6\), 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: \(2.87461447277\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.2
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 360.299
Dual form 360.2.bd.a.59.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.67303 + 1.48356i) q^{5} +(-2.12132 + 1.22474i) q^{6} +(-1.22474 + 2.12132i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.67303 + 1.48356i) q^{5} +(-2.12132 + 1.22474i) q^{6} +(-1.22474 + 2.12132i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-1.00000 - 3.00000i) q^{10} +(4.50000 + 2.59808i) q^{11} +3.46410 q^{12} +(1.22474 + 2.12132i) q^{13} +(3.00000 - 1.73205i) q^{14} +(3.67423 - 1.22474i) q^{15} +(-2.00000 + 3.46410i) q^{16} +5.19615 q^{17} +4.24264i q^{18} -5.00000 q^{19} +(-0.896575 + 4.38134i) q^{20} +(2.12132 + 3.67423i) q^{21} +(-3.67423 - 6.36396i) q^{22} +(-2.44949 + 1.41421i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(0.598076 + 4.96410i) q^{25} -3.46410i q^{26} -5.19615 q^{27} -4.89898 q^{28} +(4.24264 - 7.34847i) q^{29} +(-5.36603 - 1.09808i) q^{30} +(6.36396 - 3.67423i) q^{31} +(4.89898 - 2.82843i) q^{32} +(7.79423 - 4.50000i) q^{33} +(-6.36396 - 3.67423i) q^{34} +(-5.19615 + 1.73205i) q^{35} +(3.00000 - 5.19615i) q^{36} +(6.12372 + 3.53553i) q^{38} +4.24264 q^{39} +(4.19615 - 4.73205i) q^{40} +(1.50000 - 0.866025i) q^{41} -6.00000i q^{42} +(-7.79423 - 4.50000i) q^{43} +10.3923i q^{44} +(1.34486 - 6.57201i) q^{45} +4.00000 q^{46} +(-6.12372 - 3.53553i) q^{47} +(3.46410 + 6.00000i) q^{48} +(0.500000 + 0.866025i) q^{49} +(2.77766 - 6.50266i) q^{50} +(4.50000 - 7.79423i) q^{51} +(-2.44949 + 4.24264i) q^{52} -1.41421i q^{53} +(6.36396 + 3.67423i) q^{54} +(3.67423 + 11.0227i) q^{55} +(6.00000 + 3.46410i) q^{56} +(-4.33013 + 7.50000i) q^{57} +(-10.3923 + 6.00000i) q^{58} +(-1.50000 + 0.866025i) q^{59} +(5.79555 + 5.13922i) q^{60} +(-6.36396 - 3.67423i) q^{61} -10.3923 q^{62} +7.34847 q^{63} -8.00000 q^{64} +(-1.09808 + 5.36603i) q^{65} -12.7279 q^{66} +(2.59808 - 1.50000i) q^{67} +(5.19615 + 9.00000i) q^{68} +4.89898i q^{69} +(7.58871 + 1.55291i) q^{70} +4.24264 q^{71} +(-7.34847 + 4.24264i) q^{72} +3.00000i q^{73} +(7.96410 + 3.40192i) q^{75} +(-5.00000 - 8.66025i) q^{76} +(-11.0227 + 6.36396i) q^{77} +(-5.19615 - 3.00000i) q^{78} +(-6.36396 - 3.67423i) q^{79} +(-8.48528 + 2.82843i) q^{80} +(-4.50000 + 7.79423i) q^{81} -2.44949 q^{82} +(-4.24264 + 7.34847i) q^{84} +(8.69333 + 7.70882i) q^{85} +(6.36396 + 11.0227i) q^{86} +(-7.34847 - 12.7279i) q^{87} +(7.34847 - 12.7279i) q^{88} -10.3923i q^{89} +(-6.29423 + 7.09808i) q^{90} -6.00000 q^{91} +(-4.89898 - 2.82843i) q^{92} -12.7279i q^{93} +(5.00000 + 8.66025i) q^{94} +(-8.36516 - 7.41782i) q^{95} -9.79796i q^{96} +(2.59808 + 1.50000i) q^{97} -1.41421i q^{98} -15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{4} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{4} - 12 q^{9} - 8 q^{10} + 36 q^{11} + 24 q^{14} - 16 q^{16} - 40 q^{19} - 16 q^{25} - 36 q^{30} + 24 q^{36} - 8 q^{40} + 12 q^{41} + 32 q^{46} + 4 q^{49} + 36 q^{51} + 48 q^{56} - 12 q^{59} - 64 q^{64} + 12 q^{65} + 36 q^{75} - 40 q^{76} - 36 q^{81} + 12 q^{90} - 48 q^{91} + 40 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).

\(n\) \(181\) \(217\) \(271\) \(281\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.866025 0.500000i
\(3\) 0.866025 1.50000i 0.500000 0.866025i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 1.67303 + 1.48356i 0.748203 + 0.663470i
\(6\) −2.12132 + 1.22474i −0.866025 + 0.500000i
\(7\) −1.22474 + 2.12132i −0.462910 + 0.801784i −0.999104 0.0423108i \(-0.986528\pi\)
0.536194 + 0.844094i \(0.319861\pi\)
\(8\) 2.82843i 1.00000i
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −1.00000 3.00000i −0.316228 0.948683i
\(11\) 4.50000 + 2.59808i 1.35680 + 0.783349i 0.989191 0.146631i \(-0.0468429\pi\)
0.367610 + 0.929980i \(0.380176\pi\)
\(12\) 3.46410 1.00000
\(13\) 1.22474 + 2.12132i 0.339683 + 0.588348i 0.984373 0.176096i \(-0.0563468\pi\)
−0.644690 + 0.764444i \(0.723014\pi\)
\(14\) 3.00000 1.73205i 0.801784 0.462910i
\(15\) 3.67423 1.22474i 0.948683 0.316228i
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 5.19615 1.26025 0.630126 0.776493i \(-0.283003\pi\)
0.630126 + 0.776493i \(0.283003\pi\)
\(18\) 4.24264i 1.00000i
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) −0.896575 + 4.38134i −0.200480 + 0.979698i
\(21\) 2.12132 + 3.67423i 0.462910 + 0.801784i
\(22\) −3.67423 6.36396i −0.783349 1.35680i
\(23\) −2.44949 + 1.41421i −0.510754 + 0.294884i −0.733144 0.680074i \(-0.761948\pi\)
0.222390 + 0.974958i \(0.428614\pi\)
\(24\) −4.24264 2.44949i −0.866025 0.500000i
\(25\) 0.598076 + 4.96410i 0.119615 + 0.992820i
\(26\) 3.46410i 0.679366i
\(27\) −5.19615 −1.00000
\(28\) −4.89898 −0.925820
\(29\) 4.24264 7.34847i 0.787839 1.36458i −0.139450 0.990229i \(-0.544533\pi\)
0.927289 0.374347i \(-0.122133\pi\)
\(30\) −5.36603 1.09808i −0.979698 0.200480i
\(31\) 6.36396 3.67423i 1.14300 0.659912i 0.195829 0.980638i \(-0.437260\pi\)
0.947172 + 0.320726i \(0.103927\pi\)
\(32\) 4.89898 2.82843i 0.866025 0.500000i
\(33\) 7.79423 4.50000i 1.35680 0.783349i
\(34\) −6.36396 3.67423i −1.09141 0.630126i
\(35\) −5.19615 + 1.73205i −0.878310 + 0.292770i
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 6.12372 + 3.53553i 0.993399 + 0.573539i
\(39\) 4.24264 0.679366
\(40\) 4.19615 4.73205i 0.663470 0.748203i
\(41\) 1.50000 0.866025i 0.234261 0.135250i −0.378275 0.925693i \(-0.623483\pi\)
0.612536 + 0.790443i \(0.290149\pi\)
\(42\) 6.00000i 0.925820i
\(43\) −7.79423 4.50000i −1.18861 0.686244i −0.230618 0.973044i \(-0.574075\pi\)
−0.957990 + 0.286801i \(0.907408\pi\)
\(44\) 10.3923i 1.56670i
\(45\) 1.34486 6.57201i 0.200480 0.979698i
\(46\) 4.00000 0.589768
\(47\) −6.12372 3.53553i −0.893237 0.515711i −0.0182371 0.999834i \(-0.505805\pi\)
−0.875000 + 0.484123i \(0.839139\pi\)
\(48\) 3.46410 + 6.00000i 0.500000 + 0.866025i
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 2.77766 6.50266i 0.392820 0.919615i
\(51\) 4.50000 7.79423i 0.630126 1.09141i
\(52\) −2.44949 + 4.24264i −0.339683 + 0.588348i
\(53\) 1.41421i 0.194257i −0.995272 0.0971286i \(-0.969034\pi\)
0.995272 0.0971286i \(-0.0309658\pi\)
\(54\) 6.36396 + 3.67423i 0.866025 + 0.500000i
\(55\) 3.67423 + 11.0227i 0.495434 + 1.48630i
\(56\) 6.00000 + 3.46410i 0.801784 + 0.462910i
\(57\) −4.33013 + 7.50000i −0.573539 + 0.993399i
\(58\) −10.3923 + 6.00000i −1.36458 + 0.787839i
\(59\) −1.50000 + 0.866025i −0.195283 + 0.112747i −0.594454 0.804130i \(-0.702632\pi\)
0.399170 + 0.916877i \(0.369298\pi\)
\(60\) 5.79555 + 5.13922i 0.748203 + 0.663470i
\(61\) −6.36396 3.67423i −0.814822 0.470438i 0.0338058 0.999428i \(-0.489237\pi\)
−0.848628 + 0.528991i \(0.822571\pi\)
\(62\) −10.3923 −1.31982
\(63\) 7.34847 0.925820
\(64\) −8.00000 −1.00000
\(65\) −1.09808 + 5.36603i −0.136200 + 0.665574i
\(66\) −12.7279 −1.56670
\(67\) 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i \(-0.608004\pi\)
0.650236 + 0.759733i \(0.274670\pi\)
\(68\) 5.19615 + 9.00000i 0.630126 + 1.09141i
\(69\) 4.89898i 0.589768i
\(70\) 7.58871 + 1.55291i 0.907024 + 0.185609i
\(71\) 4.24264 0.503509 0.251754 0.967791i \(-0.418992\pi\)
0.251754 + 0.967791i \(0.418992\pi\)
\(72\) −7.34847 + 4.24264i −0.866025 + 0.500000i
\(73\) 3.00000i 0.351123i 0.984468 + 0.175562i \(0.0561742\pi\)
−0.984468 + 0.175562i \(0.943826\pi\)
\(74\) 0 0
\(75\) 7.96410 + 3.40192i 0.919615 + 0.392820i
\(76\) −5.00000 8.66025i −0.573539 0.993399i
\(77\) −11.0227 + 6.36396i −1.25615 + 0.725241i
\(78\) −5.19615 3.00000i −0.588348 0.339683i
\(79\) −6.36396 3.67423i −0.716002 0.413384i 0.0972777 0.995257i \(-0.468987\pi\)
−0.813279 + 0.581874i \(0.802320\pi\)
\(80\) −8.48528 + 2.82843i −0.948683 + 0.316228i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −2.44949 −0.270501
\(83\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(84\) −4.24264 + 7.34847i −0.462910 + 0.801784i
\(85\) 8.69333 + 7.70882i 0.942924 + 0.836139i
\(86\) 6.36396 + 11.0227i 0.686244 + 1.18861i
\(87\) −7.34847 12.7279i −0.787839 1.36458i
\(88\) 7.34847 12.7279i 0.783349 1.35680i
\(89\) 10.3923i 1.10158i −0.834643 0.550791i \(-0.814326\pi\)
0.834643 0.550791i \(-0.185674\pi\)
\(90\) −6.29423 + 7.09808i −0.663470 + 0.748203i
\(91\) −6.00000 −0.628971
\(92\) −4.89898 2.82843i −0.510754 0.294884i
\(93\) 12.7279i 1.31982i
\(94\) 5.00000 + 8.66025i 0.515711 + 0.893237i
\(95\) −8.36516 7.41782i −0.858248 0.761052i
\(96\) 9.79796i 1.00000i
\(97\) 2.59808 + 1.50000i 0.263795 + 0.152302i 0.626064 0.779771i \(-0.284665\pi\)
−0.362270 + 0.932073i \(0.617998\pi\)
\(98\) 1.41421i 0.142857i
\(99\) 15.5885i 1.56670i
\(100\) −8.00000 + 6.00000i −0.800000 + 0.600000i
\(101\) −4.24264 + 7.34847i −0.422159 + 0.731200i −0.996150 0.0876610i \(-0.972061\pi\)
0.573992 + 0.818861i \(0.305394\pi\)
\(102\) −11.0227 + 6.36396i −1.09141 + 0.630126i
\(103\) 8.57321 + 14.8492i 0.844744 + 1.46314i 0.885843 + 0.463984i \(0.153581\pi\)
−0.0410996 + 0.999155i \(0.513086\pi\)
\(104\) 6.00000 3.46410i 0.588348 0.339683i
\(105\) −1.90192 + 9.29423i −0.185609 + 0.907024i
\(106\) −1.00000 + 1.73205i −0.0971286 + 0.168232i
\(107\) −15.5885 −1.50699 −0.753497 0.657452i \(-0.771634\pi\)
−0.753497 + 0.657452i \(0.771634\pi\)
\(108\) −5.19615 9.00000i −0.500000 0.866025i
\(109\) 14.6969i 1.40771i 0.710343 + 0.703856i \(0.248540\pi\)
−0.710343 + 0.703856i \(0.751460\pi\)
\(110\) 3.29423 16.0981i 0.314092 1.53489i
\(111\) 0 0
\(112\) −4.89898 8.48528i −0.462910 0.801784i
\(113\) 5.19615 + 9.00000i 0.488813 + 0.846649i 0.999917 0.0128699i \(-0.00409674\pi\)
−0.511104 + 0.859519i \(0.670763\pi\)
\(114\) 10.6066 6.12372i 0.993399 0.573539i
\(115\) −6.19615 1.26795i −0.577794 0.118237i
\(116\) 16.9706 1.57568
\(117\) 3.67423 6.36396i 0.339683 0.588348i
\(118\) 2.44949 0.225494
\(119\) −6.36396 + 11.0227i −0.583383 + 1.01045i
\(120\) −3.46410 10.3923i −0.316228 0.948683i
\(121\) 8.00000 + 13.8564i 0.727273 + 1.25967i
\(122\) 5.19615 + 9.00000i 0.470438 + 0.814822i
\(123\) 3.00000i 0.270501i
\(124\) 12.7279 + 7.34847i 1.14300 + 0.659912i
\(125\) −6.36396 + 9.19239i −0.569210 + 0.822192i
\(126\) −9.00000 5.19615i −0.801784 0.462910i
\(127\) 4.89898 0.434714 0.217357 0.976092i \(-0.430256\pi\)
0.217357 + 0.976092i \(0.430256\pi\)
\(128\) 9.79796 + 5.65685i 0.866025 + 0.500000i
\(129\) −13.5000 + 7.79423i −1.18861 + 0.686244i
\(130\) 5.13922 5.79555i 0.450739 0.508304i
\(131\) −6.00000 + 3.46410i −0.524222 + 0.302660i −0.738661 0.674078i \(-0.764541\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(132\) 15.5885 + 9.00000i 1.35680 + 0.783349i
\(133\) 6.12372 10.6066i 0.530994 0.919709i
\(134\) −4.24264 −0.366508
\(135\) −8.69333 7.70882i −0.748203 0.663470i
\(136\) 14.6969i 1.26025i
\(137\) 7.79423 13.5000i 0.665906 1.15338i −0.313133 0.949709i \(-0.601379\pi\)
0.979039 0.203674i \(-0.0652881\pi\)
\(138\) 3.46410 6.00000i 0.294884 0.510754i
\(139\) −8.50000 14.7224i −0.720961 1.24874i −0.960615 0.277882i \(-0.910368\pi\)
0.239655 0.970858i \(-0.422966\pi\)
\(140\) −8.19615 7.26795i −0.692701 0.614254i
\(141\) −10.6066 + 6.12372i −0.893237 + 0.515711i
\(142\) −5.19615 3.00000i −0.436051 0.251754i
\(143\) 12.7279i 1.06436i
\(144\) 12.0000 1.00000
\(145\) 18.0000 6.00000i 1.49482 0.498273i
\(146\) 2.12132 3.67423i 0.175562 0.304082i
\(147\) 1.73205 0.142857
\(148\) 0 0
\(149\) −6.36396 11.0227i −0.521356 0.903015i −0.999691 0.0248379i \(-0.992093\pi\)
0.478335 0.878177i \(-0.341240\pi\)
\(150\) −7.34847 9.79796i −0.600000 0.800000i
\(151\) −12.7279 7.34847i −1.03578 0.598010i −0.117147 0.993115i \(-0.537375\pi\)
−0.918636 + 0.395105i \(0.870708\pi\)
\(152\) 14.1421i 1.14708i
\(153\) −7.79423 13.5000i −0.630126 1.09141i
\(154\) 18.0000 1.45048
\(155\) 16.0981 + 3.29423i 1.29303 + 0.264599i
\(156\) 4.24264 + 7.34847i 0.339683 + 0.588348i
\(157\) 2.44949 + 4.24264i 0.195491 + 0.338600i 0.947061 0.321053i \(-0.104037\pi\)
−0.751571 + 0.659653i \(0.770703\pi\)
\(158\) 5.19615 + 9.00000i 0.413384 + 0.716002i
\(159\) −2.12132 1.22474i −0.168232 0.0971286i
\(160\) 12.3923 + 2.53590i 0.979698 + 0.200480i
\(161\) 6.92820i 0.546019i
\(162\) 11.0227 6.36396i 0.866025 0.500000i
\(163\) 6.00000i 0.469956i −0.972001 0.234978i \(-0.924498\pi\)
0.972001 0.234978i \(-0.0755019\pi\)
\(164\) 3.00000 + 1.73205i 0.234261 + 0.135250i
\(165\) 19.7160 + 4.03459i 1.53489 + 0.314092i
\(166\) 0 0
\(167\) 1.22474 0.707107i 0.0947736 0.0547176i −0.451864 0.892087i \(-0.649241\pi\)
0.546638 + 0.837369i \(0.315907\pi\)
\(168\) 10.3923 6.00000i 0.801784 0.462910i
\(169\) 3.50000 6.06218i 0.269231 0.466321i
\(170\) −5.19615 15.5885i −0.398527 1.19558i
\(171\) 7.50000 + 12.9904i 0.573539 + 0.993399i
\(172\) 18.0000i 1.37249i
\(173\) −17.1464 9.89949i −1.30362 0.752645i −0.322596 0.946537i \(-0.604555\pi\)
−0.981023 + 0.193892i \(0.937889\pi\)
\(174\) 20.7846i 1.57568i
\(175\) −11.2629 4.81105i −0.851398 0.363681i
\(176\) −18.0000 + 10.3923i −1.35680 + 0.783349i
\(177\) 3.00000i 0.225494i
\(178\) −7.34847 + 12.7279i −0.550791 + 0.953998i
\(179\) 6.92820i 0.517838i 0.965899 + 0.258919i \(0.0833663\pi\)
−0.965899 + 0.258919i \(0.916634\pi\)
\(180\) 12.7279 4.24264i 0.948683 0.316228i
\(181\) 7.34847i 0.546207i −0.961985 0.273104i \(-0.911950\pi\)
0.961985 0.273104i \(-0.0880502\pi\)
\(182\) 7.34847 + 4.24264i 0.544705 + 0.314485i
\(183\) −11.0227 + 6.36396i −0.814822 + 0.470438i
\(184\) 4.00000 + 6.92820i 0.294884 + 0.510754i
\(185\) 0 0
\(186\) −9.00000 + 15.5885i −0.659912 + 1.14300i
\(187\) 23.3827 + 13.5000i 1.70991 + 0.987218i
\(188\) 14.1421i 1.03142i
\(189\) 6.36396 11.0227i 0.462910 0.801784i
\(190\) 5.00000 + 15.0000i 0.362738 + 1.08821i
\(191\) 10.6066 18.3712i 0.767467 1.32929i −0.171466 0.985190i \(-0.554850\pi\)
0.938933 0.344101i \(-0.111816\pi\)
\(192\) −6.92820 + 12.0000i −0.500000 + 0.866025i
\(193\) −7.79423 + 4.50000i −0.561041 + 0.323917i −0.753563 0.657376i \(-0.771667\pi\)
0.192522 + 0.981293i \(0.438333\pi\)
\(194\) −2.12132 3.67423i −0.152302 0.263795i
\(195\) 7.09808 + 6.29423i 0.508304 + 0.450739i
\(196\) −1.00000 + 1.73205i −0.0714286 + 0.123718i
\(197\) 11.3137i 0.806068i −0.915185 0.403034i \(-0.867956\pi\)
0.915185 0.403034i \(-0.132044\pi\)
\(198\) −11.0227 + 19.0919i −0.783349 + 1.35680i
\(199\) 7.34847i 0.520919i 0.965485 + 0.260460i \(0.0838741\pi\)
−0.965485 + 0.260460i \(0.916126\pi\)
\(200\) 14.0406 1.69161i 0.992820 0.119615i
\(201\) 5.19615i 0.366508i
\(202\) 10.3923 6.00000i 0.731200 0.422159i
\(203\) 10.3923 + 18.0000i 0.729397 + 1.26335i
\(204\) 18.0000 1.26025
\(205\) 3.79435 + 0.776457i 0.265009 + 0.0542301i
\(206\) 24.2487i 1.68949i
\(207\) 7.34847 + 4.24264i 0.510754 + 0.294884i
\(208\) −9.79796 −0.679366
\(209\) −22.5000 12.9904i −1.55636 0.898563i
\(210\) 8.90138 10.0382i 0.614254 0.692701i
\(211\) −4.00000 6.92820i −0.275371 0.476957i 0.694857 0.719148i \(-0.255467\pi\)
−0.970229 + 0.242190i \(0.922134\pi\)
\(212\) 2.44949 1.41421i 0.168232 0.0971286i
\(213\) 3.67423 6.36396i 0.251754 0.436051i
\(214\) 19.0919 + 11.0227i 1.30509 + 0.753497i
\(215\) −6.36396 19.0919i −0.434019 1.30206i
\(216\) 14.6969i 1.00000i
\(217\) 18.0000i 1.22192i
\(218\) 10.3923 18.0000i 0.703856 1.21911i
\(219\) 4.50000 + 2.59808i 0.304082 + 0.175562i
\(220\) −15.4176 + 17.3867i −1.03946 + 1.17221i
\(221\) 6.36396 + 11.0227i 0.428086 + 0.741467i
\(222\) 0 0
\(223\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(224\) 13.8564i 0.925820i
\(225\) 12.0000 9.00000i 0.800000 0.600000i
\(226\) 14.6969i 0.977626i
\(227\) 12.9904 22.5000i 0.862202 1.49338i −0.00759708 0.999971i \(-0.502418\pi\)
0.869799 0.493406i \(-0.164248\pi\)
\(228\) −17.3205 −1.14708
\(229\) −6.36396 + 3.67423i −0.420542 + 0.242800i −0.695309 0.718711i \(-0.744733\pi\)
0.274767 + 0.961511i \(0.411399\pi\)
\(230\) 6.69213 + 5.93426i 0.441266 + 0.391293i
\(231\) 22.0454i 1.45048i
\(232\) −20.7846 12.0000i −1.36458 0.787839i
\(233\) 5.19615 0.340411 0.170206 0.985409i \(-0.445557\pi\)
0.170206 + 0.985409i \(0.445557\pi\)
\(234\) −9.00000 + 5.19615i −0.588348 + 0.339683i
\(235\) −5.00000 15.0000i −0.326164 0.978492i
\(236\) −3.00000 1.73205i −0.195283 0.112747i
\(237\) −11.0227 + 6.36396i −0.716002 + 0.413384i
\(238\) 15.5885 9.00000i 1.01045 0.583383i
\(239\) 4.24264 + 7.34847i 0.274434 + 0.475333i 0.969992 0.243137i \(-0.0781763\pi\)
−0.695558 + 0.718470i \(0.744843\pi\)
\(240\) −3.10583 + 15.1774i −0.200480 + 0.979698i
\(241\) 8.50000 14.7224i 0.547533 0.948355i −0.450910 0.892570i \(-0.648900\pi\)
0.998443 0.0557856i \(-0.0177663\pi\)
\(242\) 22.6274i 1.45455i
\(243\) 7.79423 + 13.5000i 0.500000 + 0.866025i
\(244\) 14.6969i 0.940875i
\(245\) −0.448288 + 2.19067i −0.0286401 + 0.139957i
\(246\) −2.12132 + 3.67423i −0.135250 + 0.234261i
\(247\) −6.12372 10.6066i −0.389643 0.674882i
\(248\) −10.3923 18.0000i −0.659912 1.14300i
\(249\) 0 0
\(250\) 14.2942 6.75833i 0.904046 0.427434i
\(251\) 19.0526i 1.20259i 0.799028 + 0.601293i \(0.205348\pi\)
−0.799028 + 0.601293i \(0.794652\pi\)
\(252\) 7.34847 + 12.7279i 0.462910 + 0.801784i
\(253\) −14.6969 −0.923989
\(254\) −6.00000 3.46410i −0.376473 0.217357i
\(255\) 19.0919 6.36396i 1.19558 0.398527i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −12.9904 22.5000i −0.810318 1.40351i −0.912642 0.408760i \(-0.865961\pi\)
0.102324 0.994751i \(-0.467372\pi\)
\(258\) 22.0454 1.37249
\(259\) 0 0
\(260\) −10.3923 + 3.46410i −0.644503 + 0.214834i
\(261\) −25.4558 −1.57568
\(262\) 9.79796 0.605320
\(263\) 6.12372 + 3.53553i 0.377605 + 0.218010i 0.676776 0.736189i \(-0.263377\pi\)
−0.299171 + 0.954200i \(0.596710\pi\)
\(264\) −12.7279 22.0454i −0.783349 1.35680i
\(265\) 2.09808 2.36603i 0.128884 0.145344i
\(266\) −15.0000 + 8.66025i −0.919709 + 0.530994i
\(267\) −15.5885 9.00000i −0.953998 0.550791i
\(268\) 5.19615 + 3.00000i 0.317406 + 0.183254i
\(269\) −12.7279 −0.776035 −0.388018 0.921652i \(-0.626840\pi\)
−0.388018 + 0.921652i \(0.626840\pi\)
\(270\) 5.19615 + 15.5885i 0.316228 + 0.948683i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) −10.3923 + 18.0000i −0.630126 + 1.09141i
\(273\) −5.19615 + 9.00000i −0.314485 + 0.544705i
\(274\) −19.0919 + 11.0227i −1.15338 + 0.665906i
\(275\) −10.2058 + 23.8923i −0.615431 + 1.44076i
\(276\) −8.48528 + 4.89898i −0.510754 + 0.294884i
\(277\) −9.79796 + 16.9706i −0.588702 + 1.01966i 0.405700 + 0.914006i \(0.367028\pi\)
−0.994403 + 0.105656i \(0.966306\pi\)
\(278\) 24.0416i 1.44192i
\(279\) −19.0919 11.0227i −1.14300 0.659912i
\(280\) 4.89898 + 14.6969i 0.292770 + 0.878310i
\(281\) −15.0000 8.66025i −0.894825 0.516627i −0.0193073 0.999814i \(-0.506146\pi\)
−0.875518 + 0.483186i \(0.839479\pi\)
\(282\) 17.3205 1.03142
\(283\) −5.19615 + 3.00000i −0.308879 + 0.178331i −0.646425 0.762978i \(-0.723737\pi\)
0.337546 + 0.941309i \(0.390403\pi\)
\(284\) 4.24264 + 7.34847i 0.251754 + 0.436051i
\(285\) −18.3712 + 6.12372i −1.08821 + 0.362738i
\(286\) 9.00000 15.5885i 0.532181 0.921765i
\(287\) 4.24264i 0.250435i
\(288\) −14.6969 8.48528i −0.866025 0.500000i
\(289\) 10.0000 0.588235
\(290\) −26.2880 5.37945i −1.54369 0.315892i
\(291\) 4.50000 2.59808i 0.263795 0.152302i
\(292\) −5.19615 + 3.00000i −0.304082 + 0.175562i
\(293\) 19.5959 11.3137i 1.14481 0.660954i 0.197190 0.980365i \(-0.436819\pi\)
0.947616 + 0.319411i \(0.103485\pi\)
\(294\) −2.12132 1.22474i −0.123718 0.0714286i
\(295\) −3.79435 0.776457i −0.220916 0.0452071i
\(296\) 0 0
\(297\) −23.3827 13.5000i −1.35680 0.783349i
\(298\) 18.0000i 1.04271i
\(299\) −6.00000 3.46410i −0.346989 0.200334i
\(300\) 2.07180 + 17.1962i 0.119615 + 0.992820i
\(301\) 19.0919 11.0227i 1.10044 0.635338i
\(302\) 10.3923 + 18.0000i 0.598010 + 1.03578i
\(303\) 7.34847 + 12.7279i 0.422159 + 0.731200i
\(304\) 10.0000 17.3205i 0.573539 0.993399i
\(305\) −5.19615 15.5885i −0.297531 0.892592i
\(306\) 22.0454i 1.26025i
\(307\) 15.0000i 0.856095i 0.903756 + 0.428048i \(0.140798\pi\)
−0.903756 + 0.428048i \(0.859202\pi\)
\(308\) −22.0454 12.7279i −1.25615 0.725241i
\(309\) 29.6985 1.68949
\(310\) −17.3867 15.4176i −0.987496 0.875664i
\(311\) 8.48528 + 14.6969i 0.481156 + 0.833387i 0.999766 0.0216240i \(-0.00688367\pi\)
−0.518610 + 0.855011i \(0.673550\pi\)
\(312\) 12.0000i 0.679366i
\(313\) −12.9904 7.50000i −0.734260 0.423925i 0.0857188 0.996319i \(-0.472681\pi\)
−0.819979 + 0.572394i \(0.806015\pi\)
\(314\) 6.92820i 0.390981i
\(315\) 12.2942 + 10.9019i 0.692701 + 0.614254i
\(316\) 14.6969i 0.826767i
\(317\) 28.1691 + 16.2635i 1.58214 + 0.913447i 0.994547 + 0.104287i \(0.0332561\pi\)
0.587589 + 0.809160i \(0.300077\pi\)
\(318\) 1.73205 + 3.00000i 0.0971286 + 0.168232i
\(319\) 38.1838 22.0454i 2.13788 1.23431i
\(320\) −13.3843 11.8685i −0.748203 0.663470i
\(321\) −13.5000 + 23.3827i −0.753497 + 1.30509i
\(322\) −4.89898 + 8.48528i −0.273009 + 0.472866i
\(323\) −25.9808 −1.44561
\(324\) −18.0000 −1.00000
\(325\) −9.79796 + 7.34847i −0.543493 + 0.407620i
\(326\) −4.24264 + 7.34847i −0.234978 + 0.406994i
\(327\) 22.0454 + 12.7279i 1.21911 + 0.703856i
\(328\) −2.44949 4.24264i −0.135250 0.234261i
\(329\) 15.0000 8.66025i 0.826977 0.477455i
\(330\) −21.2942 18.8827i −1.17221 1.03946i
\(331\) −5.00000 + 8.66025i −0.274825 + 0.476011i −0.970091 0.242742i \(-0.921953\pi\)
0.695266 + 0.718752i \(0.255287\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −2.00000 −0.109435
\(335\) 6.57201 + 1.34486i 0.359067 + 0.0734777i
\(336\) −16.9706 −0.925820
\(337\) −2.59808 + 1.50000i −0.141526 + 0.0817102i −0.569091 0.822274i \(-0.692705\pi\)
0.427565 + 0.903985i \(0.359372\pi\)
\(338\) −8.57321 + 4.94975i −0.466321 + 0.269231i
\(339\) 18.0000 0.977626
\(340\) −4.65874 + 22.7661i −0.252656 + 1.23467i
\(341\) 38.1838 2.06777
\(342\) 21.2132i 1.14708i
\(343\) −19.5959 −1.05808
\(344\) −12.7279 + 22.0454i −0.686244 + 1.18861i
\(345\) −7.26795 + 8.19615i −0.391293 + 0.441266i
\(346\) 14.0000 + 24.2487i 0.752645 + 1.30362i
\(347\) 2.59808 + 4.50000i 0.139472 + 0.241573i 0.927297 0.374327i \(-0.122126\pi\)
−0.787825 + 0.615899i \(0.788793\pi\)
\(348\) 14.6969 25.4558i 0.787839 1.36458i
\(349\) −12.7279 7.34847i −0.681310 0.393355i 0.119038 0.992890i \(-0.462019\pi\)
−0.800348 + 0.599535i \(0.795352\pi\)
\(350\) 10.3923 + 13.8564i 0.555492 + 0.740656i
\(351\) −6.36396 11.0227i −0.339683 0.588348i
\(352\) 29.3939 1.56670
\(353\) −12.9904 + 22.5000i −0.691408 + 1.19755i 0.279968 + 0.960009i \(0.409676\pi\)
−0.971377 + 0.237545i \(0.923657\pi\)
\(354\) 2.12132 3.67423i 0.112747 0.195283i
\(355\) 7.09808 + 6.29423i 0.376727 + 0.334063i
\(356\) 18.0000 10.3923i 0.953998 0.550791i
\(357\) 11.0227 + 19.0919i 0.583383 + 1.01045i
\(358\) 4.89898 8.48528i 0.258919 0.448461i
\(359\) −4.24264 −0.223918 −0.111959 0.993713i \(-0.535713\pi\)
−0.111959 + 0.993713i \(0.535713\pi\)
\(360\) −18.5885 3.80385i −0.979698 0.200480i
\(361\) 6.00000 0.315789
\(362\) −5.19615 + 9.00000i −0.273104 + 0.473029i
\(363\) 27.7128 1.45455
\(364\) −6.00000 10.3923i −0.314485 0.544705i
\(365\) −4.45069 + 5.01910i −0.232960 + 0.262712i
\(366\) 18.0000 0.940875
\(367\) 7.34847 12.7279i 0.383587 0.664392i −0.607985 0.793948i \(-0.708022\pi\)
0.991572 + 0.129556i \(0.0413553\pi\)
\(368\) 11.3137i 0.589768i
\(369\) −4.50000 2.59808i −0.234261 0.135250i
\(370\) 0 0
\(371\) 3.00000 + 1.73205i 0.155752 + 0.0899236i
\(372\) 22.0454 12.7279i 1.14300 0.659912i
\(373\) −7.34847 12.7279i −0.380489 0.659027i 0.610643 0.791906i \(-0.290911\pi\)
−0.991132 + 0.132879i \(0.957578\pi\)
\(374\) −19.0919 33.0681i −0.987218 1.70991i
\(375\) 8.27723 + 17.5068i 0.427434 + 0.904046i
\(376\) −10.0000 + 17.3205i −0.515711 + 0.893237i
\(377\) 20.7846 1.07046
\(378\) −15.5885 + 9.00000i −0.801784 + 0.462910i
\(379\) −13.0000 −0.667765 −0.333883 0.942615i \(-0.608359\pi\)
−0.333883 + 0.942615i \(0.608359\pi\)
\(380\) 4.48288 21.9067i 0.229967 1.12379i
\(381\) 4.24264 7.34847i 0.217357 0.376473i
\(382\) −25.9808 + 15.0000i −1.32929 + 0.767467i
\(383\) 2.44949 1.41421i 0.125163 0.0722629i −0.436111 0.899893i \(-0.643645\pi\)
0.561274 + 0.827630i \(0.310311\pi\)
\(384\) 16.9706 9.79796i 0.866025 0.500000i
\(385\) −27.8827 5.70577i −1.42103 0.290793i
\(386\) 12.7279 0.647834
\(387\) 27.0000i 1.37249i
\(388\) 6.00000i 0.304604i
\(389\) −2.12132 + 3.67423i −0.107555 + 0.186291i −0.914779 0.403954i \(-0.867636\pi\)
0.807224 + 0.590245i \(0.200969\pi\)
\(390\) −4.24264 12.7279i −0.214834 0.644503i
\(391\) −12.7279 + 7.34847i −0.643679 + 0.371628i
\(392\) 2.44949 1.41421i 0.123718 0.0714286i
\(393\) 12.0000i 0.605320i
\(394\) −8.00000 + 13.8564i −0.403034 + 0.698076i
\(395\) −5.19615 15.5885i −0.261447 0.784340i
\(396\) 27.0000 15.5885i 1.35680 0.783349i
\(397\) 29.3939 1.47524 0.737618 0.675218i \(-0.235950\pi\)
0.737618 + 0.675218i \(0.235950\pi\)
\(398\) 5.19615 9.00000i 0.260460 0.451129i
\(399\) −10.6066 18.3712i −0.530994 0.919709i
\(400\) −18.3923 7.85641i −0.919615 0.392820i
\(401\) 19.5000 11.2583i 0.973784 0.562214i 0.0733959 0.997303i \(-0.476616\pi\)
0.900388 + 0.435089i \(0.143283\pi\)
\(402\) −3.67423 + 6.36396i −0.183254 + 0.317406i
\(403\) 15.5885 + 9.00000i 0.776516 + 0.448322i
\(404\) −16.9706 −0.844317
\(405\) −19.0919 + 6.36396i −0.948683 + 0.316228i
\(406\) 29.3939i 1.45879i
\(407\) 0 0
\(408\) −22.0454 12.7279i −1.09141 0.630126i
\(409\) 0.500000 + 0.866025i 0.0247234 + 0.0428222i 0.878122 0.478436i \(-0.158796\pi\)
−0.853399 + 0.521258i \(0.825463\pi\)
\(410\) −4.09808 3.63397i −0.202390 0.179469i
\(411\) −13.5000 23.3827i −0.665906 1.15338i
\(412\) −17.1464 + 29.6985i −0.844744 + 1.46314i
\(413\) 4.24264i 0.208767i
\(414\) −6.00000 10.3923i −0.294884 0.510754i
\(415\) 0 0
\(416\) 12.0000 + 6.92820i 0.588348 + 0.339683i
\(417\) −29.4449 −1.44192
\(418\) 18.3712 + 31.8198i 0.898563 + 1.55636i
\(419\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(420\) −18.0000 + 6.00000i −0.878310 + 0.292770i
\(421\) −6.36396 3.67423i −0.310160 0.179071i 0.336838 0.941563i \(-0.390643\pi\)
−0.646998 + 0.762491i \(0.723976\pi\)
\(422\) 11.3137i 0.550743i
\(423\) 21.2132i 1.03142i
\(424\) −4.00000 −0.194257
\(425\) 3.10770 + 25.7942i 0.150745 + 1.25120i
\(426\) −9.00000 + 5.19615i −0.436051 + 0.251754i
\(427\) 15.5885 9.00000i 0.754378 0.435541i
\(428\) −15.5885 27.0000i −0.753497 1.30509i
\(429\) 19.0919 + 11.0227i 0.921765 + 0.532181i
\(430\) −5.70577 + 27.8827i −0.275157 + 1.34462i
\(431\) 4.24264 0.204361 0.102180 0.994766i \(-0.467418\pi\)
0.102180 + 0.994766i \(0.467418\pi\)
\(432\) 10.3923 18.0000i 0.500000 0.866025i
\(433\) 15.0000i 0.720854i −0.932787 0.360427i \(-0.882631\pi\)
0.932787 0.360427i \(-0.117369\pi\)
\(434\) 12.7279 22.0454i 0.610960 1.05821i
\(435\) 6.58846 32.1962i 0.315892 1.54369i
\(436\) −25.4558 + 14.6969i −1.21911 + 0.703856i
\(437\) 12.2474 7.07107i 0.585875 0.338255i
\(438\) −3.67423 6.36396i −0.175562 0.304082i
\(439\) 31.8198 + 18.3712i 1.51868 + 0.876808i 0.999758 + 0.0219843i \(0.00699839\pi\)
0.518918 + 0.854824i \(0.326335\pi\)
\(440\) 31.1769 10.3923i 1.48630 0.495434i
\(441\) 1.50000 2.59808i 0.0714286 0.123718i
\(442\) 18.0000i 0.856173i
\(443\) 7.79423 13.5000i 0.370315 0.641404i −0.619299 0.785155i \(-0.712583\pi\)
0.989614 + 0.143751i \(0.0459164\pi\)
\(444\) 0 0
\(445\) 15.4176 17.3867i 0.730867 0.824207i
\(446\) 0 0
\(447\) −22.0454 −1.04271
\(448\) 9.79796 16.9706i 0.462910 0.801784i
\(449\) 19.0526i 0.899146i 0.893244 + 0.449573i \(0.148424\pi\)
−0.893244 + 0.449573i \(0.851576\pi\)
\(450\) −21.0609 + 2.53742i −0.992820 + 0.119615i
\(451\) 9.00000 0.423793
\(452\) −10.3923 + 18.0000i −0.488813 + 0.846649i
\(453\) −22.0454 + 12.7279i −1.03578 + 0.598010i
\(454\) −31.8198 + 18.3712i −1.49338 + 0.862202i
\(455\) −10.0382 8.90138i −0.470598 0.417303i
\(456\) 21.2132 + 12.2474i 0.993399 + 0.573539i
\(457\) 23.3827 + 13.5000i 1.09380 + 0.631503i 0.934585 0.355741i \(-0.115772\pi\)
0.159211 + 0.987245i \(0.449105\pi\)
\(458\) 10.3923 0.485601
\(459\) −27.0000 −1.26025
\(460\) −4.00000 12.0000i −0.186501 0.559503i
\(461\) 6.36396 11.0227i 0.296399 0.513378i −0.678910 0.734221i \(-0.737547\pi\)
0.975309 + 0.220843i \(0.0708808\pi\)
\(462\) 15.5885 27.0000i 0.725241 1.25615i
\(463\) 9.79796 + 16.9706i 0.455350 + 0.788689i 0.998708 0.0508118i \(-0.0161809\pi\)
−0.543358 + 0.839501i \(0.682848\pi\)
\(464\) 16.9706 + 29.3939i 0.787839 + 1.36458i
\(465\) 18.8827 21.2942i 0.875664 0.987496i
\(466\) −6.36396 3.67423i −0.294805 0.170206i
\(467\) 25.9808 1.20225 0.601123 0.799156i \(-0.294720\pi\)
0.601123 + 0.799156i \(0.294720\pi\)
\(468\) 14.6969 0.679366
\(469\) 7.34847i 0.339321i
\(470\) −4.48288 + 21.9067i −0.206780 + 1.01048i
\(471\) 8.48528 0.390981
\(472\) 2.44949 + 4.24264i 0.112747 + 0.195283i
\(473\) −23.3827 40.5000i −1.07514 1.86219i
\(474\) 18.0000 0.826767
\(475\) −2.99038 24.8205i −0.137208 1.13884i
\(476\) −25.4558 −1.16677
\(477\) −3.67423 + 2.12132i −0.168232 + 0.0971286i
\(478\) 12.0000i 0.548867i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 14.5359 16.3923i 0.663470 0.748203i
\(481\) 0 0
\(482\) −20.8207 + 12.0208i −0.948355 + 0.547533i
\(483\) −10.3923 6.00000i −0.472866 0.273009i
\(484\) −16.0000 + 27.7128i −0.727273 + 1.25967i
\(485\) 2.12132 + 6.36396i 0.0963242 + 0.288973i
\(486\) 22.0454i 1.00000i
\(487\) −19.5959 −0.887976 −0.443988 0.896033i \(-0.646437\pi\)
−0.443988 + 0.896033i \(0.646437\pi\)
\(488\) −10.3923 + 18.0000i −0.470438 + 0.814822i
\(489\) −9.00000 5.19615i −0.406994 0.234978i
\(490\) 2.09808 2.36603i 0.0947814 0.106886i
\(491\) 19.5000 11.2583i 0.880023 0.508081i 0.00935679 0.999956i \(-0.497022\pi\)
0.870666 + 0.491875i \(0.163688\pi\)
\(492\) 5.19615 3.00000i 0.234261 0.135250i
\(493\) 22.0454 38.1838i 0.992875 1.71971i
\(494\) 17.3205i 0.779287i
\(495\) 23.1265 26.0800i 1.03946 1.17221i
\(496\) 29.3939i 1.31982i
\(497\) −5.19615 + 9.00000i −0.233079 + 0.403705i
\(498\) 0 0
\(499\) 8.50000 + 14.7224i 0.380512 + 0.659067i 0.991136 0.132855i \(-0.0424144\pi\)
−0.610623 + 0.791921i \(0.709081\pi\)
\(500\) −22.2856 1.83032i −0.996644 0.0818542i
\(501\) 2.44949i 0.109435i
\(502\) 13.4722 23.3345i 0.601293 1.04147i
\(503\) 7.07107i 0.315283i 0.987496 + 0.157642i \(0.0503891\pi\)
−0.987496 + 0.157642i \(0.949611\pi\)
\(504\) 20.7846i 0.925820i
\(505\) −18.0000 + 6.00000i −0.800989 + 0.266996i
\(506\) 18.0000 + 10.3923i 0.800198 + 0.461994i
\(507\) −6.06218 10.5000i −0.269231 0.466321i
\(508\) 4.89898 + 8.48528i 0.217357 + 0.376473i
\(509\) −8.48528 14.6969i −0.376103 0.651430i 0.614388 0.789004i \(-0.289403\pi\)
−0.990492 + 0.137574i \(0.956070\pi\)
\(510\) −27.8827 5.70577i −1.23467 0.252656i
\(511\) −6.36396 3.67423i −0.281525 0.162539i
\(512\) 22.6274i 1.00000i
\(513\) 25.9808 1.14708
\(514\) 36.7423i 1.62064i
\(515\) −7.68653 + 37.5622i −0.338709 + 1.65519i
\(516\) −27.0000 15.5885i −1.18861 0.686244i
\(517\) −18.3712 31.8198i −0.807963 1.39943i
\(518\) 0 0
\(519\) −29.6985 + 17.1464i −1.30362 + 0.752645i
\(520\) 15.1774 + 3.10583i 0.665574 + 0.136200i
\(521\) 29.4449i 1.29000i 0.764181 + 0.645001i \(0.223143\pi\)
−0.764181 + 0.645001i \(0.776857\pi\)
\(522\) 31.1769 + 18.0000i 1.36458 + 0.787839i
\(523\) 6.00000i 0.262362i −0.991358 0.131181i \(-0.958123\pi\)
0.991358 0.131181i \(-0.0418769\pi\)
\(524\) −12.0000 6.92820i −0.524222 0.302660i
\(525\) −16.9706 + 12.7279i −0.740656 + 0.555492i
\(526\) −5.00000 8.66025i −0.218010 0.377605i
\(527\) 33.0681 19.0919i 1.44047 0.831655i
\(528\) 36.0000i 1.56670i
\(529\) −7.50000 + 12.9904i −0.326087 + 0.564799i
\(530\) −4.24264 + 1.41421i −0.184289 + 0.0614295i
\(531\) 4.50000 + 2.59808i 0.195283 + 0.112747i
\(532\) 24.4949 1.06199
\(533\) 3.67423 + 2.12132i 0.159149 + 0.0918846i
\(534\) 12.7279 + 22.0454i 0.550791 + 0.953998i
\(535\) −26.0800 23.1265i −1.12754 0.999845i
\(536\) −4.24264 7.34847i −0.183254 0.317406i
\(537\) 10.3923 + 6.00000i 0.448461 + 0.258919i
\(538\) 15.5885 + 9.00000i 0.672066 + 0.388018i
\(539\) 5.19615i 0.223814i
\(540\) 4.65874 22.7661i 0.200480 0.979698i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −11.0227 6.36396i −0.473029 0.273104i
\(544\) 25.4558 14.6969i 1.09141 0.630126i
\(545\) −21.8038 + 24.5885i −0.933974 + 1.05325i
\(546\) 12.7279 7.34847i 0.544705 0.314485i
\(547\) −28.5788 16.5000i −1.22194 0.705489i −0.256611 0.966515i \(-0.582606\pi\)
−0.965332 + 0.261026i \(0.915939\pi\)
\(548\) 31.1769 1.33181
\(549\) 22.0454i 0.940875i
\(550\) 29.3939 22.0454i 1.25336 0.940019i
\(551\) −21.2132 + 36.7423i −0.903713 + 1.56528i
\(552\) 13.8564 0.589768
\(553\) 15.5885 9.00000i 0.662889 0.382719i
\(554\) 24.0000 13.8564i 1.01966 0.588702i
\(555\) 0 0
\(556\) 17.0000 29.4449i 0.720961 1.24874i
\(557\) 24.0416i 1.01868i 0.860566 + 0.509338i \(0.170110\pi\)
−0.860566 + 0.509338i \(0.829890\pi\)
\(558\) 15.5885 + 27.0000i 0.659912 + 1.14300i
\(559\) 22.0454i 0.932421i
\(560\) 4.39230 21.4641i 0.185609 0.907024i
\(561\) 40.5000 23.3827i 1.70991 0.987218i
\(562\) 12.2474 + 21.2132i 0.516627 + 0.894825i
\(563\) −2.59808 4.50000i −0.109496 0.189652i 0.806070 0.591820i \(-0.201590\pi\)
−0.915566 + 0.402167i \(0.868257\pi\)
\(564\) −21.2132 12.2474i −0.893237 0.515711i
\(565\) −4.65874 + 22.7661i −0.195995 + 0.957778i
\(566\) 8.48528 0.356663
\(567\) −11.0227 19.0919i −0.462910 0.801784i
\(568\) 12.0000i 0.503509i
\(569\) 19.5000 + 11.2583i 0.817483 + 0.471974i 0.849548 0.527512i \(-0.176875\pi\)
−0.0320650 + 0.999486i \(0.510208\pi\)
\(570\) 26.8301 + 5.49038i 1.12379 + 0.229967i
\(571\) −6.50000 11.2583i −0.272017 0.471146i 0.697362 0.716720i \(-0.254357\pi\)
−0.969378 + 0.245573i \(0.921024\pi\)
\(572\) −22.0454 + 12.7279i −0.921765 + 0.532181i
\(573\) −18.3712 31.8198i −0.767467 1.32929i
\(574\) 3.00000 5.19615i 0.125218 0.216883i
\(575\) −8.48528 11.3137i −0.353861 0.471814i
\(576\) 12.0000 + 20.7846i 0.500000 + 0.866025i
\(577\) 3.00000i 0.124892i −0.998048 0.0624458i \(-0.980110\pi\)
0.998048 0.0624458i \(-0.0198901\pi\)
\(578\) −12.2474 7.07107i −0.509427 0.294118i
\(579\) 15.5885i 0.647834i
\(580\) 28.3923 + 25.1769i 1.17893 + 1.04541i
\(581\) 0 0
\(582\) −7.34847 −0.304604
\(583\) 3.67423 6.36396i 0.152171 0.263568i
\(584\) 8.48528 0.351123
\(585\) 15.5885 5.19615i 0.644503 0.214834i
\(586\) −32.0000 −1.32191
\(587\) 12.9904 22.5000i 0.536170 0.928674i −0.462935 0.886392i \(-0.653204\pi\)
0.999106 0.0422823i \(-0.0134629\pi\)
\(588\) 1.73205 + 3.00000i 0.0714286 + 0.123718i
\(589\) −31.8198 + 18.3712i −1.31111 + 0.756971i
\(590\) 4.09808 + 3.63397i 0.168715 + 0.149608i
\(591\) −16.9706 9.79796i −0.698076 0.403034i
\(592\) 0 0
\(593\) 31.1769 1.28028 0.640141 0.768257i \(-0.278876\pi\)
0.640141 + 0.768257i \(0.278876\pi\)
\(594\) 19.0919 + 33.0681i 0.783349 + 1.35680i
\(595\) −27.0000 + 9.00000i −1.10689 + 0.368964i
\(596\) 12.7279 22.0454i 0.521356 0.903015i
\(597\) 11.0227 + 6.36396i 0.451129 + 0.260460i
\(598\) 4.89898 + 8.48528i 0.200334 + 0.346989i
\(599\) 16.9706 + 29.3939i 0.693398 + 1.20100i 0.970718 + 0.240223i \(0.0772207\pi\)
−0.277319 + 0.960778i \(0.589446\pi\)
\(600\) 9.62209 22.5259i 0.392820 0.919615i
\(601\) −12.5000 + 21.6506i −0.509886 + 0.883148i 0.490049 + 0.871695i \(0.336979\pi\)
−0.999934 + 0.0114528i \(0.996354\pi\)
\(602\) −31.1769 −1.27068
\(603\) −7.79423 4.50000i −0.317406 0.183254i
\(604\) 29.3939i 1.19602i
\(605\) −7.17260 + 35.0507i −0.291608 + 1.42501i
\(606\) 20.7846i 0.844317i
\(607\) 14.6969 + 25.4558i 0.596530 + 1.03322i 0.993329 + 0.115315i \(0.0367878\pi\)
−0.396799 + 0.917906i \(0.629879\pi\)
\(608\) −24.4949 + 14.1421i −0.993399 + 0.573539i
\(609\) 36.0000 1.45879
\(610\) −4.65874 + 22.7661i −0.188627 + 0.921773i
\(611\) 17.3205i 0.700713i
\(612\) 15.5885 27.0000i 0.630126 1.09141i
\(613\) −41.6413 −1.68188 −0.840939 0.541130i \(-0.817997\pi\)
−0.840939 + 0.541130i \(0.817997\pi\)
\(614\) 10.6066 18.3712i 0.428048 0.741400i
\(615\) 4.45069 5.01910i 0.179469 0.202390i
\(616\) 18.0000 + 31.1769i 0.725241 + 1.25615i
\(617\) −2.59808 4.50000i −0.104595 0.181163i 0.808978 0.587839i \(-0.200021\pi\)
−0.913573 + 0.406676i \(0.866688\pi\)
\(618\) −36.3731 21.0000i −1.46314 0.844744i
\(619\) −5.50000 + 9.52628i −0.221064 + 0.382893i −0.955131 0.296183i \(-0.904286\pi\)
0.734068 + 0.679076i \(0.237620\pi\)
\(620\) 10.3923 + 31.1769i 0.417365 + 1.25210i
\(621\) 12.7279 7.34847i 0.510754 0.294884i
\(622\) 24.0000i 0.962312i
\(623\) 22.0454 + 12.7279i 0.883231 + 0.509933i
\(624\) −8.48528 + 14.6969i −0.339683 + 0.588348i
\(625\) −24.2846 + 5.93782i −0.971384 + 0.237513i
\(626\) 10.6066 + 18.3712i 0.423925 + 0.734260i
\(627\) −38.9711 + 22.5000i −1.55636 + 0.898563i
\(628\) −4.89898 + 8.48528i −0.195491 + 0.338600i
\(629\) 0 0
\(630\) −7.34847 22.0454i −0.292770 0.878310i
\(631\) 7.34847i 0.292538i 0.989245 + 0.146269i \(0.0467265\pi\)
−0.989245 + 0.146269i \(0.953274\pi\)
\(632\) −10.3923 + 18.0000i −0.413384 + 0.716002i
\(633\) −13.8564 −0.550743
\(634\) −23.0000 39.8372i −0.913447 1.58214i
\(635\) 8.19615 + 7.26795i 0.325254 + 0.288420i
\(636\) 4.89898i 0.194257i
\(637\) −1.22474 + 2.12132i −0.0485262 + 0.0840498i
\(638\) −62.3538 −2.46861
\(639\) −6.36396 11.0227i −0.251754 0.436051i
\(640\) 8.00000 + 24.0000i 0.316228 + 0.948683i
\(641\) −4.50000 2.59808i −0.177739 0.102618i 0.408491 0.912762i \(-0.366055\pi\)
−0.586230 + 0.810145i \(0.699389\pi\)
\(642\) 33.0681 19.0919i 1.30509 0.753497i
\(643\) 18.1865 10.5000i 0.717207 0.414080i −0.0965169 0.995331i \(-0.530770\pi\)
0.813724 + 0.581252i \(0.197437\pi\)
\(644\) 12.0000 6.92820i 0.472866 0.273009i
\(645\) −34.1492 6.98811i −1.34462 0.275157i
\(646\) 31.8198 + 18.3712i 1.25193 + 0.722804i
\(647\) 5.65685i 0.222394i −0.993798 0.111197i \(-0.964532\pi\)
0.993798 0.111197i \(-0.0354684\pi\)
\(648\) 22.0454 + 12.7279i 0.866025 + 0.500000i
\(649\) −9.00000 −0.353281
\(650\) 17.1962 2.07180i 0.674489 0.0812626i
\(651\) 27.0000 + 15.5885i 1.05821 + 0.610960i
\(652\) 10.3923 6.00000i 0.406994 0.234978i
\(653\) −9.79796 + 5.65685i −0.383424 + 0.221370i −0.679307 0.733854i \(-0.737719\pi\)
0.295883 + 0.955224i \(0.404386\pi\)
\(654\) −18.0000 31.1769i −0.703856 1.21911i
\(655\) −15.1774 3.10583i −0.593031 0.121355i
\(656\) 6.92820i 0.270501i
\(657\) 7.79423 4.50000i 0.304082 0.175562i
\(658\) −24.4949 −0.954911
\(659\) 33.0000 + 19.0526i 1.28550 + 0.742182i 0.977848 0.209317i \(-0.0671242\pi\)
0.307650 + 0.951500i \(0.400458\pi\)
\(660\) 12.7279 + 38.1838i 0.495434 + 1.48630i
\(661\) 25.4558 14.6969i 0.990118 0.571645i 0.0848081 0.996397i \(-0.472972\pi\)
0.905309 + 0.424753i \(0.139639\pi\)
\(662\) 12.2474 7.07107i 0.476011 0.274825i
\(663\) 22.0454 0.856173
\(664\) 0 0
\(665\) 25.9808 8.66025i 1.00749 0.335830i
\(666\) 0 0
\(667\) 24.0000i 0.929284i
\(668\) 2.44949 + 1.41421i 0.0947736 + 0.0547176i
\(669\) 0 0
\(670\) −7.09808 6.29423i −0.274223 0.243167i
\(671\) −19.0919 33.0681i −0.737034 1.27658i
\(672\) 20.7846 + 12.0000i 0.801784 + 0.462910i
\(673\) 20.7846 + 12.0000i 0.801188 + 0.462566i 0.843886 0.536522i \(-0.180262\pi\)
−0.0426985 + 0.999088i \(0.513595\pi\)
\(674\) 4.24264 0.163420
\(675\) −3.10770 25.7942i −0.119615 0.992820i
\(676\) 14.0000 0.538462
\(677\) −26.9444 15.5563i −1.03556 0.597879i −0.116985 0.993134i \(-0.537323\pi\)
−0.918572 + 0.395255i \(0.870656\pi\)
\(678\) −22.0454 12.7279i −0.846649 0.488813i
\(679\) −6.36396 + 3.67423i −0.244226 + 0.141004i
\(680\) 21.8038 24.5885i 0.836139 0.942924i
\(681\) −22.5000 38.9711i −0.862202 1.49338i
\(682\) −46.7654 27.0000i −1.79074 1.03388i
\(683\) −15.5885 −0.596476 −0.298238 0.954492i \(-0.596399\pi\)
−0.298238 + 0.954492i \(0.596399\pi\)
\(684\) −15.0000 + 25.9808i −0.573539 + 0.993399i
\(685\) 33.0681 11.0227i 1.26347 0.421156i
\(686\) 24.0000 + 13.8564i 0.916324 + 0.529040i
\(687\) 12.7279i 0.485601i
\(688\) 31.1769 18.0000i 1.18861 0.686244i
\(689\) 3.00000 1.73205i 0.114291 0.0659859i
\(690\) 14.6969 4.89898i 0.559503 0.186501i
\(691\) −8.00000 + 13.8564i −0.304334 + 0.527123i −0.977113 0.212721i \(-0.931767\pi\)
0.672779 + 0.739844i \(0.265101\pi\)
\(692\) 39.5980i 1.50529i
\(693\) 33.0681 + 19.0919i 1.25615 + 0.725241i
\(694\) 7.34847i 0.278944i
\(695\) 7.62089 37.2414i 0.289077 1.41265i
\(696\) −36.0000 + 20.7846i −1.36458 + 0.787839i
\(697\) 7.79423 4.50000i 0.295227 0.170450i
\(698\) 10.3923 + 18.0000i 0.393355 + 0.681310i
\(699\) 4.50000 7.79423i 0.170206 0.294805i
\(700\) −2.92996 24.3190i −0.110742 0.919173i
\(701\) −50.9117 −1.92291 −0.961454 0.274966i \(-0.911333\pi\)
−0.961454 + 0.274966i \(0.911333\pi\)
\(702\) 18.0000i 0.679366i
\(703\) 0 0
\(704\) −36.0000 20.7846i −1.35680 0.783349i
\(705\) −26.8301 5.49038i −1.01048 0.206780i
\(706\) 31.8198 18.3712i 1.19755 0.691408i
\(707\) −10.3923 18.0000i −0.390843 0.676960i
\(708\) −5.19615 + 3.00000i −0.195283 + 0.112747i
\(709\) −31.8198 18.3712i −1.19502 0.689944i −0.235578 0.971856i \(-0.575698\pi\)
−0.959440 + 0.281912i \(0.909031\pi\)
\(710\) −4.24264 12.7279i −0.159223 0.477670i
\(711\) 22.0454i 0.826767i
\(712\) −29.3939 −1.10158
\(713\) −10.3923 + 18.0000i −0.389195 + 0.674105i
\(714\) 31.1769i 1.16677i
\(715\) −18.8827 + 21.2942i −0.706172 + 0.796359i
\(716\) −12.0000 + 6.92820i −0.448461 + 0.258919i
\(717\) 14.6969 0.548867
\(718\) 5.19615 + 3.00000i 0.193919 + 0.111959i
\(719\) 25.4558 0.949343 0.474671 0.880163i \(-0.342567\pi\)
0.474671 + 0.880163i \(0.342567\pi\)
\(720\) 20.0764 + 17.8028i 0.748203 + 0.663470i
\(721\) −42.0000 −1.56416
\(722\) −7.34847 4.24264i −0.273482 0.157895i
\(723\) −14.7224 25.5000i −0.547533 0.948355i
\(724\) 12.7279 7.34847i 0.473029 0.273104i
\(725\) 39.0160 + 16.6660i 1.44902 + 0.618958i
\(726\) −33.9411 19.5959i −1.25967 0.727273i
\(727\) 13.4722 23.3345i 0.499656 0.865430i −0.500344 0.865827i \(-0.666793\pi\)
1.00000 0.000397168i \(0.000126423\pi\)
\(728\) 16.9706i 0.628971i
\(729\) 27.0000 1.00000
\(730\) 9.00000 3.00000i 0.333105 0.111035i
\(731\) −40.5000 23.3827i −1.49795 0.864840i
\(732\) −22.0454 12.7279i −0.814822 0.470438i
\(733\) 18.3712 + 31.8198i 0.678555 + 1.17529i 0.975416 + 0.220371i \(0.0707267\pi\)
−0.296861 + 0.954921i \(0.595940\pi\)
\(734\) −18.0000 + 10.3923i −0.664392 + 0.383587i
\(735\) 2.89778 + 2.56961i 0.106886 + 0.0947814i
\(736\) −8.00000 + 13.8564i −0.294884 + 0.510754i
\(737\) 15.5885 0.574208
\(738\) 3.67423 + 6.36396i 0.135250 + 0.234261i
\(739\) 43.0000 1.58178 0.790890 0.611958i \(-0.209618\pi\)
0.790890 + 0.611958i \(0.209618\pi\)
\(740\) 0 0
\(741\) −21.2132 −0.779287
\(742\) −2.44949 4.24264i −0.0899236 0.155752i
\(743\) −12.2474 + 7.07107i −0.449315 + 0.259412i −0.707541 0.706672i \(-0.750196\pi\)
0.258226 + 0.966085i \(0.416862\pi\)
\(744\) −36.0000 −1.31982
\(745\) 5.70577 27.8827i 0.209043 1.02154i
\(746\) 20.7846i 0.760979i
\(747\) 0 0
\(748\) 54.0000i 1.97444i
\(749\) 19.0919 33.0681i 0.697602 1.20828i
\(750\) 2.24167 27.2942i 0.0818542 0.996644i
\(751\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(752\) 24.4949 14.1421i 0.893237 0.515711i
\(753\) 28.5788 + 16.5000i 1.04147 + 0.601293i
\(754\) −25.4558 14.6969i −0.927047 0.535231i
\(755\) −10.3923 31.1769i −0.378215 1.13464i
\(756\) 25.4558 0.925820
\(757\) −19.5959 −0.712226 −0.356113 0.934443i \(-0.615898\pi\)
−0.356113 + 0.934443i \(0.615898\pi\)
\(758\) 15.9217 + 9.19239i 0.578302 + 0.333883i
\(759\) −12.7279 + 22.0454i −0.461994 + 0.800198i
\(760\) −20.9808 + 23.6603i −0.761052 + 0.858248i
\(761\) 3.00000 1.73205i 0.108750 0.0627868i −0.444639 0.895710i \(-0.646668\pi\)
0.553388 + 0.832923i \(0.313335\pi\)
\(762\) −10.3923 + 6.00000i −0.376473 + 0.217357i
\(763\) −31.1769 18.0000i −1.12868 0.651644i
\(764\) 42.4264 1.53493
\(765\) 6.98811 34.1492i 0.252656 1.23467i
\(766\) −4.00000 −0.144526
\(767\) −3.67423 2.12132i −0.132669 0.0765964i
\(768\) −27.7128 −1.00000
\(769\) −2.00000 3.46410i −0.0721218 0.124919i 0.827709 0.561157i \(-0.189644\pi\)
−0.899831 + 0.436239i \(0.856310\pi\)
\(770\) 30.1146 + 26.7042i 1.08525 + 0.962351i
\(771\) −45.0000 −1.62064
\(772\) −15.5885 9.00000i −0.561041 0.323917i
\(773\) 45.2548i 1.62770i −0.581073 0.813852i \(-0.697367\pi\)
0.581073 0.813852i \(-0.302633\pi\)
\(774\) 19.0919 33.0681i 0.686244 1.18861i
\(775\) 22.0454 + 29.3939i 0.791894 + 1.05586i
\(776\) 4.24264 7.34847i 0.152302 0.263795i
\(777\) 0 0
\(778\) 5.19615 3.00000i 0.186291 0.107555i
\(779\) −7.50000 + 4.33013i −0.268715 + 0.155143i
\(780\) −3.80385 + 18.5885i −0.136200 + 0.665574i
\(781\) 19.0919 + 11.0227i 0.683161 + 0.394423i
\(782\) 20.7846 0.743256
\(783\) −22.0454 + 38.1838i −0.787839 + 1.36458i
\(784\) −4.00000 −0.142857
\(785\) −2.19615 + 10.7321i −0.0783840 + 0.383043i
\(786\) 8.48528 14.6969i 0.302660 0.524222i
\(787\) −41.5692 + 24.0000i −1.48178 + 0.855508i −0.999786 0.0206657i \(-0.993421\pi\)
−0.481996 + 0.876173i \(0.660088\pi\)
\(788\) 19.5959 11.3137i 0.698076 0.403034i
\(789\) 10.6066 6.12372i 0.377605 0.218010i
\(790\) −4.65874 + 22.7661i −0.165751 + 0.809982i
\(791\) −25.4558 −0.905106
\(792\) −44.0908 −1.56670
\(793\) 18.0000i 0.639199i
\(794\) −36.0000 20.7846i −1.27759 0.737618i
\(795\) −1.73205 5.19615i −0.0614295 0.184289i
\(796\) −12.7279 + 7.34847i −0.451129 + 0.260460i
\(797\) −12.2474 + 7.07107i −0.433827 + 0.250470i −0.700976 0.713185i \(-0.747252\pi\)
0.267149 + 0.963655i \(0.413919\pi\)
\(798\) 30.0000i 1.06199i
\(799\) −31.8198 18.3712i −1.12570 0.649925i
\(800\) 16.9706 + 22.6274i 0.600000 + 0.800000i
\(801\) −27.0000 + 15.5885i −0.953998 + 0.550791i
\(802\) −31.8434 −1.12443
\(803\) −7.79423 + 13.5000i −0.275052 + 0.476405i
\(804\) 9.00000 5.19615i 0.317406 0.183254i
\(805\) 10.2784 11.5911i 0.362267 0.408533i
\(806\) −12.7279 22.0454i −0.448322 0.776516i
\(807\) −11.0227 + 19.0919i −0.388018 + 0.672066i
\(808\) 20.7846 + 12.0000i 0.731200 + 0.422159i
\(809\) 32.9090i 1.15702i 0.815676 + 0.578509i \(0.196365\pi\)
−0.815676 + 0.578509i \(0.803635\pi\)
\(810\) 27.8827 + 5.70577i 0.979698 + 0.200480i
\(811\) 47.0000 1.65039 0.825197 0.564846i \(-0.191064\pi\)
0.825197 + 0.564846i \(0.191064\pi\)
\(812\) −20.7846 + 36.0000i −0.729397 + 1.26335i
\(813\) 0 0
\(814\) 0 0
\(815\) 8.90138 10.0382i 0.311802 0.351623i
\(816\) 18.0000 + 31.1769i 0.630126 + 1.09141i
\(817\) 38.9711 + 22.5000i 1.36343 + 0.787175i
\(818\) 1.41421i 0.0494468i
\(819\) 9.00000 + 15.5885i 0.314485 + 0.544705i
\(820\) 2.44949 + 7.34847i 0.0855399 + 0.256620i
\(821\) −10.6066 + 18.3712i −0.370173 + 0.641158i −0.989592 0.143902i \(-0.954035\pi\)
0.619419 + 0.785061i \(0.287368\pi\)
\(822\) 38.1838i 1.33181i
\(823\) −14.6969 25.4558i −0.512303 0.887335i −0.999898 0.0142651i \(-0.995459\pi\)
0.487595 0.873070i \(-0.337874\pi\)
\(824\) 42.0000 24.2487i 1.46314 0.844744i
\(825\) 27.0000 + 36.0000i 0.940019 + 1.25336i
\(826\) −3.00000 + 5.19615i −0.104383 + 0.180797i
\(827\) −20.7846 −0.722752 −0.361376 0.932420i \(-0.617693\pi\)
−0.361376 + 0.932420i \(0.617693\pi\)
\(828\) 16.9706i 0.589768i
\(829\) 51.4393i 1.78656i 0.449500 + 0.893280i \(0.351602\pi\)
−0.449500 + 0.893280i \(0.648398\pi\)
\(830\) 0 0
\(831\) 16.9706 + 29.3939i 0.588702 + 1.01966i
\(832\) −9.79796 16.9706i −0.339683 0.588348i
\(833\) 2.59808 + 4.50000i 0.0900180 + 0.155916i
\(834\) 36.0624 + 20.8207i 1.24874 + 0.720961i
\(835\) 3.09808 + 0.633975i 0.107213 + 0.0219396i
\(836\) 51.9615i 1.79713i
\(837\) −33.0681 + 19.0919i −1.14300 + 0.659912i
\(838\) 0 0
\(839\) −14.8492 + 25.7196i −0.512653 + 0.887941i 0.487240 + 0.873268i \(0.338004\pi\)
−0.999892 + 0.0146723i \(0.995329\pi\)
\(840\) 26.2880 + 5.37945i 0.907024 + 0.185609i
\(841\) −21.5000 37.2391i −0.741379 1.28411i
\(842\) 5.19615 + 9.00000i 0.179071 + 0.310160i
\(843\) −25.9808 + 15.0000i −0.894825 + 0.516627i
\(844\) 8.00000 13.8564i 0.275371 0.476957i
\(845\) 14.8492 4.94975i 0.510829 0.170276i
\(846\) 15.0000 25.9808i 0.515711 0.893237i
\(847\) −39.1918 −1.34665
\(848\) 4.89898 + 2.82843i 0.168232 + 0.0971286i
\(849\) 10.3923i 0.356663i
\(850\) 14.4331 33.7888i 0.495053 1.15895i
\(851\) 0 0
\(852\) 14.6969 0.503509
\(853\) −11.0227 + 19.0919i −0.377410 + 0.653694i −0.990685 0.136176i \(-0.956519\pi\)
0.613274 + 0.789870i \(0.289852\pi\)
\(854\) −25.4558 −0.871081
\(855\) −6.72432 + 32.8601i −0.229967 + 1.12379i
\(856\) 44.0908i 1.50699i
\(857\) −15.5885 + 27.0000i −0.532492 + 0.922302i 0.466789 + 0.884369i \(0.345411\pi\)
−0.999280 + 0.0379336i \(0.987922\pi\)
\(858\) −15.5885 27.0000i −0.532181 0.921765i
\(859\) 24.5000 + 42.4352i 0.835929 + 1.44787i 0.893272 + 0.449517i \(0.148404\pi\)
−0.0573424 + 0.998355i \(0.518263\pi\)
\(860\) 26.7042 30.1146i 0.910604 1.02690i
\(861\) 6.36396 + 3.67423i 0.216883 + 0.125218i
\(862\) −5.19615 3.00000i −0.176982 0.102180i
\(863\) 24.0416i 0.818387i −0.912448 0.409193i \(-0.865810\pi\)
0.912448 0.409193i \(-0.134190\pi\)
\(864\) −25.4558 + 14.6969i −0.866025 + 0.500000i
\(865\) −14.0000 42.0000i −0.476014 1.42804i
\(866\) −10.6066 + 18.3712i −0.360427 + 0.624278i
\(867\) 8.66025 15.0000i 0.294118 0.509427i
\(868\) −31.1769 + 18.0000i −1.05821 + 0.610960i
\(869\) −19.0919 33.0681i −0.647648 1.12176i
\(870\) −30.8353 + 34.7733i −1.04541 + 1.17893i
\(871\) 6.36396 + 3.67423i 0.215635 + 0.124497i
\(872\) 41.5692 1.40771
\(873\) 9.00000i 0.304604i
\(874\) −20.0000 −0.676510
\(875\) −11.7058 24.7583i −0.395727 0.836984i
\(876\) 10.3923i 0.351123i
\(877\) −1.22474 2.12132i −0.0413567 0.0716319i 0.844606 0.535388i \(-0.179835\pi\)
−0.885963 + 0.463756i \(0.846501\pi\)
\(878\) −25.9808 45.0000i −0.876808 1.51868i
\(879\) 39.1918i 1.32191i
\(880\) −45.5322 9.31749i −1.53489 0.314092i
\(881\) 41.5692i 1.40050i 0.713896 + 0.700251i \(0.246929\pi\)
−0.713896 + 0.700251i \(0.753071\pi\)
\(882\) −3.67423 + 2.12132i −0.123718 + 0.0714286i
\(883\) 9.00000i 0.302874i −0.988467 0.151437i \(-0.951610\pi\)
0.988467 0.151437i \(-0.0483901\pi\)
\(884\) −12.7279 + 22.0454i −0.428086 + 0.741467i
\(885\) −4.45069 + 5.01910i −0.149608 + 0.168715i
\(886\) −19.0919 + 11.0227i −0.641404 + 0.370315i
\(887\) −35.5176 + 20.5061i −1.19256 + 0.688527i −0.958887 0.283787i \(-0.908409\pi\)
−0.233677 + 0.972314i \(0.575076\pi\)
\(888\) 0 0
\(889\) −6.00000 + 10.3923i −0.201234 + 0.348547i
\(890\) −31.1769 + 10.3923i −1.04505 + 0.348351i
\(891\) −40.5000 + 23.3827i −1.35680 + 0.783349i
\(892\) 0 0
\(893\) 30.6186 + 17.6777i 1.02461 + 0.591561i
\(894\) 27.0000 + 15.5885i 0.903015 + 0.521356i
\(895\) −10.2784 + 11.5911i −0.343570 + 0.387448i
\(896\) −24.0000 + 13.8564i −0.801784 + 0.462910i
\(897\) −10.3923 + 6.00000i −0.346989 + 0.200334i
\(898\) 13.4722 23.3345i 0.449573 0.778683i
\(899\) 62.3538i 2.07962i
\(900\) 27.5885 + 11.7846i 0.919615 + 0.392820i
\(901\) 7.34847i 0.244813i
\(902\) −11.0227 6.36396i −0.367016 0.211897i
\(903\) 38.1838i 1.27068i
\(904\) 25.4558 14.6969i 0.846649 0.488813i
\(905\) 10.9019 12.2942i 0.362392 0.408674i
\(906\) 36.0000 1.19602
\(907\) 44.1673 + 25.5000i 1.46655 + 0.846714i 0.999300 0.0374111i \(-0.0119111\pi\)
0.467251 + 0.884125i \(0.345244\pi\)
\(908\) 51.9615 1.72440
\(909\) 25.4558 0.844317
\(910\) 6.00000 + 18.0000i 0.198898 + 0.596694i
\(911\) 23.3345 40.4166i 0.773107 1.33906i −0.162745 0.986668i \(-0.552035\pi\)
0.935852 0.352393i \(-0.114632\pi\)
\(912\) −17.3205 30.0000i −0.573539 0.993399i
\(913\) 0 0
\(914\) −19.0919 33.0681i −0.631503 1.09380i
\(915\) −27.8827 5.70577i −0.921773 0.188627i
\(916\) −12.7279 7.34847i −0.420542 0.242800i
\(917\) 16.9706i 0.560417i
\(918\) 33.0681 + 19.0919i 1.09141 + 0.630126i
\(919\) 58.7878i 1.93923i −0.244638 0.969615i \(-0.578669\pi\)
0.244638 0.969615i \(-0.421331\pi\)
\(920\) −3.58630 + 17.5254i −0.118237 + 0.577794i
\(921\) 22.5000 + 12.9904i 0.741400 + 0.428048i
\(922\) −15.5885 + 9.00000i −0.513378 + 0.296399i
\(923\) 5.19615 + 9.00000i 0.171033 + 0.296239i
\(924\) −38.1838 + 22.0454i −1.25615 + 0.725241i
\(925\) 0 0
\(926\) 27.7128i 0.910700i
\(927\) 25.7196 44.5477i 0.844744 1.46314i
\(928\) 48.0000i 1.57568i
\(929\) 27.0000 + 15.5885i 0.885841 + 0.511441i 0.872580 0.488471i \(-0.162445\pi\)
0.0132613 + 0.999912i \(0.495779\pi\)
\(930\) −38.1838 + 12.7279i −1.25210 + 0.417365i
\(931\) −2.50000 4.33013i −0.0819342 0.141914i
\(932\) 5.19615 + 9.00000i 0.170206 + 0.294805i
\(933\) 29.3939 0.962312
\(934\) −31.8198 18.3712i −1.04118 0.601123i
\(935\) 19.0919 + 57.2756i 0.624371 + 1.87311i
\(936\) −18.0000 10.3923i −0.588348 0.339683i
\(937\) 36.0000i 1.17607i 0.808836 + 0.588034i \(0.200098\pi\)
−0.808836 + 0.588034i \(0.799902\pi\)
\(938\) 5.19615 9.00000i 0.169660 0.293860i
\(939\) −22.5000 + 12.9904i −0.734260 + 0.423925i
\(940\) 20.9808 23.6603i 0.684317 0.771712i
\(941\) 16.9706 + 29.3939i 0.553225 + 0.958213i 0.998039 + 0.0625904i \(0.0199362\pi\)
−0.444815 + 0.895623i \(0.646730\pi\)
\(942\) −10.3923 6.00000i −0.338600 0.195491i
\(943\) −2.44949 + 4.24264i −0.0797664 + 0.138159i
\(944\) 6.92820i 0.225494i
\(945\) 27.0000 9.00000i 0.878310 0.292770i
\(946\) 66.1362i 2.15027i
\(947\) 18.1865 31.5000i 0.590983 1.02361i −0.403117 0.915148i \(-0.632073\pi\)
0.994100 0.108464i \(-0.0345933\pi\)
\(948\) −22.0454 12.7279i −0.716002 0.413384i
\(949\) −6.36396 + 3.67423i −0.206583 + 0.119271i
\(950\) −13.8883 + 32.5133i −0.450596 + 1.05487i
\(951\) 48.7904 28.1691i 1.58214 0.913447i
\(952\) 31.1769 + 18.0000i 1.01045 + 0.583383i
\(953\) −15.5885 −0.504960 −0.252480 0.967602i \(-0.581246\pi\)
−0.252480 + 0.967602i \(0.581246\pi\)
\(954\) 6.00000 0.194257
\(955\) 45.0000 15.0000i 1.45617 0.485389i
\(956\) −8.48528 + 14.6969i −0.274434 + 0.475333i
\(957\) 76.3675i 2.46861i
\(958\) 0 0
\(959\) 19.0919 + 33.0681i 0.616509 + 1.06783i
\(960\) −29.3939 + 9.79796i −0.948683 + 0.316228i
\(961\) 11.5000 19.9186i 0.370968 0.642535i
\(962\) 0 0
\(963\) 23.3827 + 40.5000i 0.753497 + 1.30509i
\(964\) 34.0000 1.09507
\(965\) −19.7160 4.03459i −0.634682 0.129878i
\(966\) 8.48528 + 14.6969i 0.273009 + 0.472866i
\(967\) 14.6969 + 25.4558i 0.472622 + 0.818605i 0.999509 0.0313303i \(-0.00997439\pi\)
−0.526887 + 0.849935i \(0.676641\pi\)
\(968\) 39.1918 22.6274i 1.25967 0.727273i
\(969\) −22.5000 + 38.9711i −0.722804 + 1.25193i
\(970\) 1.90192 9.29423i 0.0610671 0.298420i
\(971\) 3.46410i 0.111168i −0.998454 0.0555842i \(-0.982298\pi\)
0.998454 0.0555842i \(-0.0177021\pi\)
\(972\) −15.5885 + 27.0000i −0.500000 + 0.866025i
\(973\) 41.6413 1.33496
\(974\) 24.0000 + 13.8564i 0.769010 + 0.443988i
\(975\) 2.53742 + 21.0609i 0.0812626 + 0.674489i
\(976\) 25.4558 14.6969i 0.814822 0.470438i
\(977\) −28.5788 49.5000i −0.914318 1.58365i −0.807897 0.589324i \(-0.799394\pi\)
−0.106421 0.994321i \(-0.533939\pi\)
\(978\) 7.34847 + 12.7279i 0.234978 + 0.406994i
\(979\) 27.0000 46.7654i 0.862924 1.49463i
\(980\) −4.24264 + 1.41421i −0.135526 + 0.0451754i
\(981\) 38.1838 22.0454i 1.21911 0.703856i
\(982\) −31.8434 −1.01616
\(983\) −24.4949 14.1421i −0.781266 0.451064i 0.0556128 0.998452i \(-0.482289\pi\)
−0.836879 + 0.547388i \(0.815622\pi\)
\(984\) −8.48528 −0.270501
\(985\) 16.7846 18.9282i 0.534802 0.603103i
\(986\) −54.0000 + 31.1769i −1.71971 + 0.992875i
\(987\) 30.0000i 0.954911i
\(988\) 12.2474 21.2132i 0.389643 0.674882i
\(989\) 25.4558 0.809449
\(990\) −46.7654 + 15.5885i −1.48630 + 0.495434i
\(991\) 44.0908i 1.40059i 0.713853 + 0.700295i \(0.246948\pi\)
−0.713853 + 0.700295i \(0.753052\pi\)
\(992\) 20.7846 36.0000i 0.659912 1.14300i
\(993\) 8.66025 + 15.0000i 0.274825 + 0.476011i
\(994\) 12.7279 7.34847i 0.403705 0.233079i
\(995\) −10.9019 + 12.2942i −0.345614 + 0.389753i
\(996\) 0 0
\(997\) −20.8207 + 36.0624i −0.659397 + 1.14211i 0.321375 + 0.946952i \(0.395855\pi\)
−0.980772 + 0.195157i \(0.937478\pi\)
\(998\) 24.0416i 0.761025i
\(999\) 0 0
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 360.2.bd.a.299.2 yes 8
5.4 even 2 inner 360.2.bd.a.299.3 yes 8
8.3 odd 2 inner 360.2.bd.a.299.4 yes 8
9.5 odd 6 inner 360.2.bd.a.59.1 8
40.19 odd 2 inner 360.2.bd.a.299.1 yes 8
45.14 odd 6 inner 360.2.bd.a.59.4 yes 8
72.59 even 6 inner 360.2.bd.a.59.3 yes 8
360.59 even 6 inner 360.2.bd.a.59.2 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
360.2.bd.a.59.1 8 9.5 odd 6 inner
360.2.bd.a.59.2 yes 8 360.59 even 6 inner
360.2.bd.a.59.3 yes 8 72.59 even 6 inner
360.2.bd.a.59.4 yes 8 45.14 odd 6 inner
360.2.bd.a.299.1 yes 8 40.19 odd 2 inner
360.2.bd.a.299.2 yes 8 1.1 even 1 trivial
360.2.bd.a.299.3 yes 8 5.4 even 2 inner
360.2.bd.a.299.4 yes 8 8.3 odd 2 inner