Properties

Label 867.2.h.d.712.1
Level $867$
Weight $2$
Character 867.712
Analytic conductor $6.923$
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] = [867,2,Mod(688,867)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(867, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("867.688");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 867 = 3 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 867.h (of order \(8\), degree \(4\), not 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: \(6.92302985525\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{8})\)
Coefficient field: \(\Q(\zeta_{16})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 51)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 712.1
Root \(0.923880 + 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 867.712
Dual form 867.2.h.d.688.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.00000i q^{4} +(0.382683 - 0.923880i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.00000i q^{4} +(0.382683 - 0.923880i) q^{6} +(-3.69552 - 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-1.53073 + 3.69552i) q^{11} +(-0.923880 + 0.382683i) q^{12} -2.00000i q^{13} +(-1.53073 - 3.69552i) q^{14} +1.00000 q^{16} -1.00000 q^{18} +(-2.82843 - 2.82843i) q^{19} +4.00000i q^{21} +(-3.69552 + 1.53073i) q^{22} +(-1.53073 + 3.69552i) q^{23} +(-2.77164 - 1.14805i) q^{24} +(-3.53553 + 3.53553i) q^{25} +(1.41421 - 1.41421i) q^{26} +(0.923880 + 0.382683i) q^{27} +(-1.53073 + 3.69552i) q^{28} +(-1.53073 - 3.69552i) q^{31} +(-3.53553 - 3.53553i) q^{32} +4.00000 q^{33} +(0.707107 + 0.707107i) q^{36} +(-3.06147 - 7.39104i) q^{37} -4.00000i q^{38} +(-1.84776 + 0.765367i) q^{39} +(-7.39104 - 3.06147i) q^{41} +(-2.82843 + 2.82843i) q^{42} +(-2.82843 + 2.82843i) q^{43} +(3.69552 + 1.53073i) q^{44} +(-3.69552 + 1.53073i) q^{46} +8.00000i q^{47} +(-0.382683 - 0.923880i) q^{48} +(6.36396 + 6.36396i) q^{49} -5.00000 q^{50} -2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} +(0.382683 + 0.923880i) q^{54} +(-11.0866 + 4.59220i) q^{56} +(-1.53073 + 3.69552i) q^{57} +(8.48528 - 8.48528i) q^{59} +(7.39104 + 3.06147i) q^{61} +(1.53073 - 3.69552i) q^{62} +(3.69552 - 1.53073i) q^{63} -7.00000i q^{64} +(2.82843 + 2.82843i) q^{66} -12.0000 q^{67} +4.00000 q^{69} +(-4.59220 - 11.0866i) q^{71} +3.00000i q^{72} +(3.06147 - 7.39104i) q^{74} +(4.61940 + 1.91342i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(11.3137 - 11.3137i) q^{77} +(-1.84776 - 0.765367i) q^{78} +(1.53073 - 3.69552i) q^{79} -1.00000i q^{81} +(-3.06147 - 7.39104i) q^{82} +(-8.48528 - 8.48528i) q^{83} +4.00000 q^{84} -4.00000 q^{86} +(4.59220 + 11.0866i) q^{88} -10.0000i q^{89} +(-3.06147 + 7.39104i) q^{91} +(3.69552 + 1.53073i) q^{92} +(-2.82843 + 2.82843i) q^{93} +(-5.65685 + 5.65685i) q^{94} +(-1.91342 + 4.61940i) q^{96} +(14.7821 - 6.12293i) q^{97} +9.00000i q^{98} +(-1.53073 - 3.69552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{16} - 8 q^{18} + 32 q^{33} - 40 q^{50} - 16 q^{52} - 96 q^{67} + 32 q^{69} + 32 q^{84} - 32 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).

\(n\) \(290\) \(292\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{8}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i 0.911438 0.411438i \(-0.134973\pi\)
−0.411438 + 0.911438i \(0.634973\pi\)
\(3\) −0.382683 0.923880i −0.220942 0.533402i
\(4\) 1.00000i 0.500000i
\(5\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(6\) 0.382683 0.923880i 0.156230 0.377172i
\(7\) −3.69552 1.53073i −1.39677 0.578563i −0.447862 0.894103i \(-0.647814\pi\)
−0.948912 + 0.315540i \(0.897814\pi\)
\(8\) 2.12132 2.12132i 0.750000 0.750000i
\(9\) −0.707107 + 0.707107i −0.235702 + 0.235702i
\(10\) 0 0
\(11\) −1.53073 + 3.69552i −0.461534 + 1.11424i 0.506234 + 0.862396i \(0.331037\pi\)
−0.967768 + 0.251845i \(0.918963\pi\)
\(12\) −0.923880 + 0.382683i −0.266701 + 0.110471i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) −1.53073 3.69552i −0.409106 0.987669i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0
\(18\) −1.00000 −0.235702
\(19\) −2.82843 2.82843i −0.648886 0.648886i 0.303838 0.952724i \(-0.401732\pi\)
−0.952724 + 0.303838i \(0.901732\pi\)
\(20\) 0 0
\(21\) 4.00000i 0.872872i
\(22\) −3.69552 + 1.53073i −0.787887 + 0.326354i
\(23\) −1.53073 + 3.69552i −0.319180 + 0.770569i 0.680118 + 0.733103i \(0.261929\pi\)
−0.999298 + 0.0374660i \(0.988071\pi\)
\(24\) −2.77164 1.14805i −0.565758 0.234345i
\(25\) −3.53553 + 3.53553i −0.707107 + 0.707107i
\(26\) 1.41421 1.41421i 0.277350 0.277350i
\(27\) 0.923880 + 0.382683i 0.177801 + 0.0736475i
\(28\) −1.53073 + 3.69552i −0.289281 + 0.698387i
\(29\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(30\) 0 0
\(31\) −1.53073 3.69552i −0.274928 0.663735i 0.724753 0.689009i \(-0.241954\pi\)
−0.999681 + 0.0252745i \(0.991954\pi\)
\(32\) −3.53553 3.53553i −0.625000 0.625000i
\(33\) 4.00000 0.696311
\(34\) 0 0
\(35\) 0 0
\(36\) 0.707107 + 0.707107i 0.117851 + 0.117851i
\(37\) −3.06147 7.39104i −0.503302 1.21508i −0.947675 0.319237i \(-0.896573\pi\)
0.444373 0.895842i \(-0.353427\pi\)
\(38\) 4.00000i 0.648886i
\(39\) −1.84776 + 0.765367i −0.295878 + 0.122557i
\(40\) 0 0
\(41\) −7.39104 3.06147i −1.15429 0.478121i −0.278317 0.960489i \(-0.589777\pi\)
−0.875969 + 0.482368i \(0.839777\pi\)
\(42\) −2.82843 + 2.82843i −0.436436 + 0.436436i
\(43\) −2.82843 + 2.82843i −0.431331 + 0.431331i −0.889081 0.457750i \(-0.848656\pi\)
0.457750 + 0.889081i \(0.348656\pi\)
\(44\) 3.69552 + 1.53073i 0.557120 + 0.230767i
\(45\) 0 0
\(46\) −3.69552 + 1.53073i −0.544874 + 0.225694i
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) −0.382683 0.923880i −0.0552356 0.133351i
\(49\) 6.36396 + 6.36396i 0.909137 + 0.909137i
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) −2.00000 −0.277350
\(53\) 4.24264 + 4.24264i 0.582772 + 0.582772i 0.935664 0.352892i \(-0.114802\pi\)
−0.352892 + 0.935664i \(0.614802\pi\)
\(54\) 0.382683 + 0.923880i 0.0520766 + 0.125724i
\(55\) 0 0
\(56\) −11.0866 + 4.59220i −1.48150 + 0.613659i
\(57\) −1.53073 + 3.69552i −0.202751 + 0.489483i
\(58\) 0 0
\(59\) 8.48528 8.48528i 1.10469 1.10469i 0.110853 0.993837i \(-0.464642\pi\)
0.993837 0.110853i \(-0.0353582\pi\)
\(60\) 0 0
\(61\) 7.39104 + 3.06147i 0.946325 + 0.391981i 0.801848 0.597527i \(-0.203850\pi\)
0.144477 + 0.989508i \(0.453850\pi\)
\(62\) 1.53073 3.69552i 0.194403 0.469331i
\(63\) 3.69552 1.53073i 0.465592 0.192854i
\(64\) 7.00000i 0.875000i
\(65\) 0 0
\(66\) 2.82843 + 2.82843i 0.348155 + 0.348155i
\(67\) −12.0000 −1.46603 −0.733017 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) −4.59220 11.0866i −0.544994 1.31573i −0.921162 0.389180i \(-0.872758\pi\)
0.376168 0.926552i \(-0.377242\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(74\) 3.06147 7.39104i 0.355888 0.859191i
\(75\) 4.61940 + 1.91342i 0.533402 + 0.220942i
\(76\) −2.82843 + 2.82843i −0.324443 + 0.324443i
\(77\) 11.3137 11.3137i 1.28932 1.28932i
\(78\) −1.84776 0.765367i −0.209218 0.0866607i
\(79\) 1.53073 3.69552i 0.172221 0.415778i −0.814076 0.580759i \(-0.802756\pi\)
0.986297 + 0.164980i \(0.0527560\pi\)
\(80\) 0 0
\(81\) 1.00000i 0.111111i
\(82\) −3.06147 7.39104i −0.338083 0.816203i
\(83\) −8.48528 8.48528i −0.931381 0.931381i 0.0664117 0.997792i \(-0.478845\pi\)
−0.997792 + 0.0664117i \(0.978845\pi\)
\(84\) 4.00000 0.436436
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 4.59220 + 11.0866i 0.489530 + 1.18183i
\(89\) 10.0000i 1.06000i −0.847998 0.529999i \(-0.822192\pi\)
0.847998 0.529999i \(-0.177808\pi\)
\(90\) 0 0
\(91\) −3.06147 + 7.39104i −0.320929 + 0.774791i
\(92\) 3.69552 + 1.53073i 0.385284 + 0.159590i
\(93\) −2.82843 + 2.82843i −0.293294 + 0.293294i
\(94\) −5.65685 + 5.65685i −0.583460 + 0.583460i
\(95\) 0 0
\(96\) −1.91342 + 4.61940i −0.195287 + 0.471465i
\(97\) 14.7821 6.12293i 1.50089 0.621690i 0.527238 0.849718i \(-0.323228\pi\)
0.973655 + 0.228028i \(0.0732278\pi\)
\(98\) 9.00000i 0.909137i
\(99\) −1.53073 3.69552i −0.153845 0.371414i
\(100\) 3.53553 + 3.53553i 0.353553 + 0.353553i
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) −4.24264 4.24264i −0.416025 0.416025i
\(105\) 0 0
\(106\) 6.00000i 0.582772i
\(107\) 11.0866 4.59220i 1.07178 0.443945i 0.224160 0.974552i \(-0.428036\pi\)
0.847618 + 0.530608i \(0.178036\pi\)
\(108\) 0.382683 0.923880i 0.0368237 0.0889003i
\(109\) 7.39104 + 3.06147i 0.707933 + 0.293235i 0.707449 0.706764i \(-0.249846\pi\)
0.000483966 1.00000i \(0.499846\pi\)
\(110\) 0 0
\(111\) −5.65685 + 5.65685i −0.536925 + 0.536925i
\(112\) −3.69552 1.53073i −0.349194 0.144641i
\(113\) 3.06147 7.39104i 0.287999 0.695290i −0.711977 0.702202i \(-0.752200\pi\)
0.999976 + 0.00691210i \(0.00220021\pi\)
\(114\) −3.69552 + 1.53073i −0.346117 + 0.143366i
\(115\) 0 0
\(116\) 0 0
\(117\) 1.41421 + 1.41421i 0.130744 + 0.130744i
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) 0 0
\(121\) −3.53553 3.53553i −0.321412 0.321412i
\(122\) 3.06147 + 7.39104i 0.277172 + 0.669153i
\(123\) 8.00000i 0.721336i
\(124\) −3.69552 + 1.53073i −0.331867 + 0.137464i
\(125\) 0 0
\(126\) 3.69552 + 1.53073i 0.329223 + 0.136369i
\(127\) −5.65685 + 5.65685i −0.501965 + 0.501965i −0.912048 0.410083i \(-0.865500\pi\)
0.410083 + 0.912048i \(0.365500\pi\)
\(128\) −2.12132 + 2.12132i −0.187500 + 0.187500i
\(129\) 3.69552 + 1.53073i 0.325372 + 0.134774i
\(130\) 0 0
\(131\) 3.69552 1.53073i 0.322879 0.133741i −0.215356 0.976536i \(-0.569091\pi\)
0.538235 + 0.842795i \(0.319091\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 6.12293 + 14.7821i 0.530926 + 1.28177i
\(134\) −8.48528 8.48528i −0.733017 0.733017i
\(135\) 0 0
\(136\) 0 0
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 2.82843 + 2.82843i 0.240772 + 0.240772i
\(139\) −1.53073 3.69552i −0.129835 0.313450i 0.845572 0.533862i \(-0.179260\pi\)
−0.975407 + 0.220412i \(0.929260\pi\)
\(140\) 0 0
\(141\) 7.39104 3.06147i 0.622438 0.257822i
\(142\) 4.59220 11.0866i 0.385369 0.930363i
\(143\) 7.39104 + 3.06147i 0.618070 + 0.256013i
\(144\) −0.707107 + 0.707107i −0.0589256 + 0.0589256i
\(145\) 0 0
\(146\) 0 0
\(147\) 3.44415 8.31492i 0.284069 0.685803i
\(148\) −7.39104 + 3.06147i −0.607539 + 0.251651i
\(149\) 6.00000i 0.491539i −0.969328 0.245770i \(-0.920959\pi\)
0.969328 0.245770i \(-0.0790407\pi\)
\(150\) 1.91342 + 4.61940i 0.156230 + 0.377172i
\(151\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(152\) −12.0000 −0.973329
\(153\) 0 0
\(154\) 16.0000 1.28932
\(155\) 0 0
\(156\) 0.765367 + 1.84776i 0.0612784 + 0.147939i
\(157\) 2.00000i 0.159617i −0.996810 0.0798087i \(-0.974569\pi\)
0.996810 0.0798087i \(-0.0254309\pi\)
\(158\) 3.69552 1.53073i 0.294000 0.121779i
\(159\) 2.29610 5.54328i 0.182093 0.439610i
\(160\) 0 0
\(161\) 11.3137 11.3137i 0.891645 0.891645i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −18.4776 7.65367i −1.44728 0.599482i −0.485726 0.874111i \(-0.661445\pi\)
−0.961550 + 0.274629i \(0.911445\pi\)
\(164\) −3.06147 + 7.39104i −0.239060 + 0.577143i
\(165\) 0 0
\(166\) 12.0000i 0.931381i
\(167\) 4.59220 + 11.0866i 0.355355 + 0.857903i 0.995940 + 0.0900162i \(0.0286919\pi\)
−0.640585 + 0.767887i \(0.721308\pi\)
\(168\) 8.48528 + 8.48528i 0.654654 + 0.654654i
\(169\) 9.00000 0.692308
\(170\) 0 0
\(171\) 4.00000 0.305888
\(172\) 2.82843 + 2.82843i 0.215666 + 0.215666i
\(173\) 6.12293 + 14.7821i 0.465518 + 1.12386i 0.966099 + 0.258171i \(0.0831197\pi\)
−0.500581 + 0.865690i \(0.666880\pi\)
\(174\) 0 0
\(175\) 18.4776 7.65367i 1.39677 0.578563i
\(176\) −1.53073 + 3.69552i −0.115383 + 0.278560i
\(177\) −11.0866 4.59220i −0.833316 0.345171i
\(178\) 7.07107 7.07107i 0.529999 0.529999i
\(179\) 2.82843 2.82843i 0.211407 0.211407i −0.593458 0.804865i \(-0.702238\pi\)
0.804865 + 0.593458i \(0.202238\pi\)
\(180\) 0 0
\(181\) 3.06147 7.39104i 0.227557 0.549371i −0.768322 0.640064i \(-0.778908\pi\)
0.995879 + 0.0906923i \(0.0289080\pi\)
\(182\) −7.39104 + 3.06147i −0.547860 + 0.226931i
\(183\) 8.00000i 0.591377i
\(184\) 4.59220 + 11.0866i 0.338542 + 0.817312i
\(185\) 0 0
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 8.00000 0.583460
\(189\) −2.82843 2.82843i −0.205738 0.205738i
\(190\) 0 0
\(191\) 8.00000i 0.578860i −0.957199 0.289430i \(-0.906534\pi\)
0.957199 0.289430i \(-0.0934657\pi\)
\(192\) −6.46716 + 2.67878i −0.466727 + 0.193325i
\(193\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(194\) 14.7821 + 6.12293i 1.06129 + 0.439601i
\(195\) 0 0
\(196\) 6.36396 6.36396i 0.454569 0.454569i
\(197\) −14.7821 6.12293i −1.05318 0.436241i −0.212153 0.977236i \(-0.568048\pi\)
−0.841026 + 0.540995i \(0.818048\pi\)
\(198\) 1.53073 3.69552i 0.108785 0.262629i
\(199\) −18.4776 + 7.65367i −1.30984 + 0.542554i −0.924838 0.380361i \(-0.875800\pi\)
−0.385004 + 0.922915i \(0.625800\pi\)
\(200\) 15.0000i 1.06066i
\(201\) 4.59220 + 11.0866i 0.323909 + 0.781985i
\(202\) 4.24264 + 4.24264i 0.298511 + 0.298511i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.53073 3.69552i −0.106393 0.256856i
\(208\) 2.00000i 0.138675i
\(209\) 14.7821 6.12293i 1.02250 0.423532i
\(210\) 0 0
\(211\) 3.69552 + 1.53073i 0.254410 + 0.105380i 0.506244 0.862390i \(-0.331034\pi\)
−0.251834 + 0.967771i \(0.581034\pi\)
\(212\) 4.24264 4.24264i 0.291386 0.291386i
\(213\) −8.48528 + 8.48528i −0.581402 + 0.581402i
\(214\) 11.0866 + 4.59220i 0.757861 + 0.313916i
\(215\) 0 0
\(216\) 2.77164 1.14805i 0.188586 0.0781149i
\(217\) 16.0000i 1.08615i
\(218\) 3.06147 + 7.39104i 0.207349 + 0.500584i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) −8.00000 −0.536925
\(223\) 11.3137 + 11.3137i 0.757622 + 0.757622i 0.975889 0.218267i \(-0.0700404\pi\)
−0.218267 + 0.975889i \(0.570040\pi\)
\(224\) 7.65367 + 18.4776i 0.511382 + 1.23459i
\(225\) 5.00000i 0.333333i
\(226\) 7.39104 3.06147i 0.491644 0.203646i
\(227\) −4.59220 + 11.0866i −0.304795 + 0.735840i 0.695062 + 0.718950i \(0.255377\pi\)
−0.999857 + 0.0168909i \(0.994623\pi\)
\(228\) 3.69552 + 1.53073i 0.244742 + 0.101375i
\(229\) −7.07107 + 7.07107i −0.467269 + 0.467269i −0.901029 0.433759i \(-0.857187\pi\)
0.433759 + 0.901029i \(0.357187\pi\)
\(230\) 0 0
\(231\) −14.7821 6.12293i −0.972589 0.402860i
\(232\) 0 0
\(233\) 7.39104 3.06147i 0.484203 0.200563i −0.127209 0.991876i \(-0.540602\pi\)
0.611412 + 0.791313i \(0.290602\pi\)
\(234\) 2.00000i 0.130744i
\(235\) 0 0
\(236\) −8.48528 8.48528i −0.552345 0.552345i
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 6.12293 + 14.7821i 0.394413 + 0.952197i 0.988966 + 0.148141i \(0.0473289\pi\)
−0.594553 + 0.804056i \(0.702671\pi\)
\(242\) 5.00000i 0.321412i
\(243\) −0.923880 + 0.382683i −0.0592669 + 0.0245492i
\(244\) 3.06147 7.39104i 0.195990 0.473163i
\(245\) 0 0
\(246\) −5.65685 + 5.65685i −0.360668 + 0.360668i
\(247\) −5.65685 + 5.65685i −0.359937 + 0.359937i
\(248\) −11.0866 4.59220i −0.703997 0.291605i
\(249\) −4.59220 + 11.0866i −0.291019 + 0.702582i
\(250\) 0 0
\(251\) 12.0000i 0.757433i −0.925513 0.378717i \(-0.876365\pi\)
0.925513 0.378717i \(-0.123635\pi\)
\(252\) −1.53073 3.69552i −0.0964272 0.232796i
\(253\) −11.3137 11.3137i −0.711287 0.711287i
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −1.41421 1.41421i −0.0882162 0.0882162i 0.661622 0.749838i \(-0.269869\pi\)
−0.749838 + 0.661622i \(0.769869\pi\)
\(258\) 1.53073 + 3.69552i 0.0952993 + 0.230073i
\(259\) 32.0000i 1.98838i
\(260\) 0 0
\(261\) 0 0
\(262\) 3.69552 + 1.53073i 0.228310 + 0.0945690i
\(263\) −16.9706 + 16.9706i −1.04645 + 1.04645i −0.0475824 + 0.998867i \(0.515152\pi\)
−0.998867 + 0.0475824i \(0.984848\pi\)
\(264\) 8.48528 8.48528i 0.522233 0.522233i
\(265\) 0 0
\(266\) −6.12293 + 14.7821i −0.375421 + 0.906347i
\(267\) −9.23880 + 3.82683i −0.565405 + 0.234198i
\(268\) 12.0000i 0.733017i
\(269\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 8.00000 0.484182
\(274\) −7.07107 7.07107i −0.427179 0.427179i
\(275\) −7.65367 18.4776i −0.461534 1.11424i
\(276\) 4.00000i 0.240772i
\(277\) 7.39104 3.06147i 0.444084 0.183946i −0.149425 0.988773i \(-0.547742\pi\)
0.593509 + 0.804827i \(0.297742\pi\)
\(278\) 1.53073 3.69552i 0.0918073 0.221642i
\(279\) 3.69552 + 1.53073i 0.221245 + 0.0916426i
\(280\) 0 0
\(281\) 7.07107 7.07107i 0.421825 0.421825i −0.464007 0.885832i \(-0.653589\pi\)
0.885832 + 0.464007i \(0.153589\pi\)
\(282\) 7.39104 + 3.06147i 0.440130 + 0.182308i
\(283\) −1.53073 + 3.69552i −0.0909927 + 0.219676i −0.962823 0.270131i \(-0.912933\pi\)
0.871831 + 0.489807i \(0.162933\pi\)
\(284\) −11.0866 + 4.59220i −0.657866 + 0.272497i
\(285\) 0 0
\(286\) 3.06147 + 7.39104i 0.181028 + 0.437041i
\(287\) 22.6274 + 22.6274i 1.33565 + 1.33565i
\(288\) 5.00000 0.294628
\(289\) 0 0
\(290\) 0 0
\(291\) −11.3137 11.3137i −0.663221 0.663221i
\(292\) 0 0
\(293\) 10.0000i 0.584206i −0.956387 0.292103i \(-0.905645\pi\)
0.956387 0.292103i \(-0.0943550\pi\)
\(294\) 8.31492 3.44415i 0.484936 0.200867i
\(295\) 0 0
\(296\) −22.1731 9.18440i −1.28879 0.533833i
\(297\) −2.82843 + 2.82843i −0.164122 + 0.164122i
\(298\) 4.24264 4.24264i 0.245770 0.245770i
\(299\) 7.39104 + 3.06147i 0.427435 + 0.177049i
\(300\) 1.91342 4.61940i 0.110471 0.266701i
\(301\) 14.7821 6.12293i 0.852024 0.352920i
\(302\) 0 0
\(303\) −2.29610 5.54328i −0.131908 0.318453i
\(304\) −2.82843 2.82843i −0.162221 0.162221i
\(305\) 0 0
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −11.3137 11.3137i −0.644658 0.644658i
\(309\) 0 0
\(310\) 0 0
\(311\) −11.0866 + 4.59220i −0.628661 + 0.260400i −0.674184 0.738563i \(-0.735505\pi\)
0.0455232 + 0.998963i \(0.485505\pi\)
\(312\) −2.29610 + 5.54328i −0.129991 + 0.313826i
\(313\) −14.7821 6.12293i −0.835532 0.346089i −0.0764418 0.997074i \(-0.524356\pi\)
−0.759090 + 0.650985i \(0.774356\pi\)
\(314\) 1.41421 1.41421i 0.0798087 0.0798087i
\(315\) 0 0
\(316\) −3.69552 1.53073i −0.207889 0.0861105i
\(317\) 12.2459 29.5641i 0.687797 1.66049i −0.0613775 0.998115i \(-0.519549\pi\)
0.749174 0.662373i \(-0.230451\pi\)
\(318\) 5.54328 2.29610i 0.310852 0.128759i
\(319\) 0 0
\(320\) 0 0
\(321\) −8.48528 8.48528i −0.473602 0.473602i
\(322\) 16.0000 0.891645
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 7.07107 + 7.07107i 0.392232 + 0.392232i
\(326\) −7.65367 18.4776i −0.423898 1.02338i
\(327\) 8.00000i 0.442401i
\(328\) −22.1731 + 9.18440i −1.22431 + 0.507124i
\(329\) 12.2459 29.5641i 0.675137 1.62992i
\(330\) 0 0
\(331\) 14.1421 14.1421i 0.777322 0.777322i −0.202053 0.979375i \(-0.564761\pi\)
0.979375 + 0.202053i \(0.0647612\pi\)
\(332\) −8.48528 + 8.48528i −0.465690 + 0.465690i
\(333\) 7.39104 + 3.06147i 0.405026 + 0.167767i
\(334\) −4.59220 + 11.0866i −0.251274 + 0.606629i
\(335\) 0 0
\(336\) 4.00000i 0.218218i
\(337\) −6.12293 14.7821i −0.333538 0.805231i −0.998306 0.0581814i \(-0.981470\pi\)
0.664769 0.747049i \(-0.268530\pi\)
\(338\) 6.36396 + 6.36396i 0.346154 + 0.346154i
\(339\) −8.00000 −0.434500
\(340\) 0 0
\(341\) 16.0000 0.866449
\(342\) 2.82843 + 2.82843i 0.152944 + 0.152944i
\(343\) −3.06147 7.39104i −0.165304 0.399078i
\(344\) 12.0000i 0.646997i
\(345\) 0 0
\(346\) −6.12293 + 14.7821i −0.329171 + 0.794689i
\(347\) 3.69552 + 1.53073i 0.198386 + 0.0821741i 0.479664 0.877452i \(-0.340758\pi\)
−0.281278 + 0.959626i \(0.590758\pi\)
\(348\) 0 0
\(349\) −1.41421 + 1.41421i −0.0757011 + 0.0757011i −0.743944 0.668242i \(-0.767047\pi\)
0.668242 + 0.743944i \(0.267047\pi\)
\(350\) 18.4776 + 7.65367i 0.987669 + 0.409106i
\(351\) 0.765367 1.84776i 0.0408523 0.0986261i
\(352\) 18.4776 7.65367i 0.984859 0.407942i
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) −4.59220 11.0866i −0.244073 0.589244i
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 4.00000 0.211407
\(359\) 22.6274 + 22.6274i 1.19423 + 1.19423i 0.975868 + 0.218361i \(0.0700712\pi\)
0.218361 + 0.975868i \(0.429929\pi\)
\(360\) 0 0
\(361\) 3.00000i 0.157895i
\(362\) 7.39104 3.06147i 0.388464 0.160907i
\(363\) −1.91342 + 4.61940i −0.100428 + 0.242455i
\(364\) 7.39104 + 3.06147i 0.387396 + 0.160464i
\(365\) 0 0
\(366\) 5.65685 5.65685i 0.295689 0.295689i
\(367\) −11.0866 4.59220i −0.578713 0.239711i 0.0740732 0.997253i \(-0.476400\pi\)
−0.652787 + 0.757542i \(0.726400\pi\)
\(368\) −1.53073 + 3.69552i −0.0797950 + 0.192642i
\(369\) 7.39104 3.06147i 0.384762 0.159374i
\(370\) 0 0
\(371\) −9.18440 22.1731i −0.476830 1.15117i
\(372\) 2.82843 + 2.82843i 0.146647 + 0.146647i
\(373\) −26.0000 −1.34623 −0.673114 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 16.9706 + 16.9706i 0.875190 + 0.875190i
\(377\) 0 0
\(378\) 4.00000i 0.205738i
\(379\) −18.4776 + 7.65367i −0.949130 + 0.393143i −0.802904 0.596109i \(-0.796713\pi\)
−0.146226 + 0.989251i \(0.546713\pi\)
\(380\) 0 0
\(381\) 7.39104 + 3.06147i 0.378654 + 0.156844i
\(382\) 5.65685 5.65685i 0.289430 0.289430i
\(383\) −11.3137 + 11.3137i −0.578103 + 0.578103i −0.934380 0.356277i \(-0.884046\pi\)
0.356277 + 0.934380i \(0.384046\pi\)
\(384\) 2.77164 + 1.14805i 0.141440 + 0.0585862i
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) −6.12293 14.7821i −0.310845 0.750446i
\(389\) 4.24264 + 4.24264i 0.215110 + 0.215110i 0.806434 0.591324i \(-0.201394\pi\)
−0.591324 + 0.806434i \(0.701394\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 27.0000 1.36371
\(393\) −2.82843 2.82843i −0.142675 0.142675i
\(394\) −6.12293 14.7821i −0.308469 0.744710i
\(395\) 0 0
\(396\) −3.69552 + 1.53073i −0.185707 + 0.0769223i
\(397\) −3.06147 + 7.39104i −0.153651 + 0.370945i −0.981896 0.189420i \(-0.939339\pi\)
0.828246 + 0.560365i \(0.189339\pi\)
\(398\) −18.4776 7.65367i −0.926198 0.383644i
\(399\) 11.3137 11.3137i 0.566394 0.566394i
\(400\) −3.53553 + 3.53553i −0.176777 + 0.176777i
\(401\) 22.1731 + 9.18440i 1.10727 + 0.458647i 0.859997 0.510298i \(-0.170465\pi\)
0.247275 + 0.968945i \(0.420465\pi\)
\(402\) −4.59220 + 11.0866i −0.229038 + 0.552947i
\(403\) −7.39104 + 3.06147i −0.368174 + 0.152503i
\(404\) 6.00000i 0.298511i
\(405\) 0 0
\(406\) 0 0
\(407\) 32.0000 1.58618
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 3.82683 + 9.23880i 0.188764 + 0.455716i
\(412\) 0 0
\(413\) −44.3462 + 18.3688i −2.18213 + 0.903870i
\(414\) 1.53073 3.69552i 0.0752315 0.181625i
\(415\) 0 0
\(416\) −7.07107 + 7.07107i −0.346688 + 0.346688i
\(417\) −2.82843 + 2.82843i −0.138509 + 0.138509i
\(418\) 14.7821 + 6.12293i 0.723015 + 0.299483i
\(419\) −1.53073 + 3.69552i −0.0747812 + 0.180538i −0.956850 0.290583i \(-0.906151\pi\)
0.882068 + 0.471121i \(0.156151\pi\)
\(420\) 0 0
\(421\) 22.0000i 1.07221i 0.844150 + 0.536107i \(0.180106\pi\)
−0.844150 + 0.536107i \(0.819894\pi\)
\(422\) 1.53073 + 3.69552i 0.0745150 + 0.179895i
\(423\) −5.65685 5.65685i −0.275046 0.275046i
\(424\) 18.0000 0.874157
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) −22.6274 22.6274i −1.09502 1.09502i
\(428\) −4.59220 11.0866i −0.221972 0.535889i
\(429\) 8.00000i 0.386244i
\(430\) 0 0
\(431\) −7.65367 + 18.4776i −0.368664 + 0.890034i 0.625306 + 0.780380i \(0.284974\pi\)
−0.993970 + 0.109654i \(0.965026\pi\)
\(432\) 0.923880 + 0.382683i 0.0444502 + 0.0184119i
\(433\) 1.41421 1.41421i 0.0679628 0.0679628i −0.672308 0.740271i \(-0.734697\pi\)
0.740271 + 0.672308i \(0.234697\pi\)
\(434\) −11.3137 + 11.3137i −0.543075 + 0.543075i
\(435\) 0 0
\(436\) 3.06147 7.39104i 0.146618 0.353966i
\(437\) 14.7821 6.12293i 0.707122 0.292900i
\(438\) 0 0
\(439\) −13.7766 33.2597i −0.657521 1.58740i −0.801620 0.597834i \(-0.796028\pi\)
0.144099 0.989563i \(-0.453972\pi\)
\(440\) 0 0
\(441\) −9.00000 −0.428571
\(442\) 0 0
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 5.65685 + 5.65685i 0.268462 + 0.268462i
\(445\) 0 0
\(446\) 16.0000i 0.757622i
\(447\) −5.54328 + 2.29610i −0.262188 + 0.108602i
\(448\) −10.7151 + 25.8686i −0.506243 + 1.22218i
\(449\) 7.39104 + 3.06147i 0.348805 + 0.144480i 0.550205 0.835029i \(-0.314549\pi\)
−0.201401 + 0.979509i \(0.564549\pi\)
\(450\) 3.53553 3.53553i 0.166667 0.166667i
\(451\) 22.6274 22.6274i 1.06548 1.06548i
\(452\) −7.39104 3.06147i −0.347645 0.143999i
\(453\) 0 0
\(454\) −11.0866 + 4.59220i −0.520318 + 0.215523i
\(455\) 0 0
\(456\) 4.59220 + 11.0866i 0.215050 + 0.519175i
\(457\) −26.8701 26.8701i −1.25693 1.25693i −0.952552 0.304376i \(-0.901552\pi\)
−0.304376 0.952552i \(-0.598448\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) −24.0416 24.0416i −1.11973 1.11973i −0.991781 0.127950i \(-0.959160\pi\)
−0.127950 0.991781i \(-0.540840\pi\)
\(462\) −6.12293 14.7821i −0.284865 0.687724i
\(463\) 40.0000i 1.85896i −0.368875 0.929479i \(-0.620257\pi\)
0.368875 0.929479i \(-0.379743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 7.39104 + 3.06147i 0.342383 + 0.141820i
\(467\) −2.82843 + 2.82843i −0.130884 + 0.130884i −0.769514 0.638630i \(-0.779501\pi\)
0.638630 + 0.769514i \(0.279501\pi\)
\(468\) 1.41421 1.41421i 0.0653720 0.0653720i
\(469\) 44.3462 + 18.3688i 2.04772 + 0.848193i
\(470\) 0 0
\(471\) −1.84776 + 0.765367i −0.0851402 + 0.0352662i
\(472\) 36.0000i 1.65703i
\(473\) −6.12293 14.7821i −0.281533 0.679680i
\(474\) −2.82843 2.82843i −0.129914 0.129914i
\(475\) 20.0000 0.917663
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) −5.65685 5.65685i −0.258738 0.258738i
\(479\) −4.59220 11.0866i −0.209823 0.506558i 0.783572 0.621301i \(-0.213395\pi\)
−0.993395 + 0.114743i \(0.963395\pi\)
\(480\) 0 0
\(481\) −14.7821 + 6.12293i −0.674004 + 0.279182i
\(482\) −6.12293 + 14.7821i −0.278892 + 0.673305i
\(483\) −14.7821 6.12293i −0.672608 0.278603i
\(484\) −3.53553 + 3.53553i −0.160706 + 0.160706i
\(485\) 0 0
\(486\) −0.923880 0.382683i −0.0419080 0.0173589i
\(487\) 1.53073 3.69552i 0.0693642 0.167460i −0.885395 0.464839i \(-0.846112\pi\)
0.954760 + 0.297379i \(0.0961124\pi\)
\(488\) 22.1731 9.18440i 1.00373 0.415758i
\(489\) 20.0000i 0.904431i
\(490\) 0 0
\(491\) 14.1421 + 14.1421i 0.638226 + 0.638226i 0.950118 0.311892i \(-0.100963\pi\)
−0.311892 + 0.950118i \(0.600963\pi\)
\(492\) 8.00000 0.360668
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) −1.53073 3.69552i −0.0687320 0.165934i
\(497\) 48.0000i 2.15309i
\(498\) −11.0866 + 4.59220i −0.496800 + 0.205781i
\(499\) 13.7766 33.2597i 0.616725 1.48891i −0.238759 0.971079i \(-0.576741\pi\)
0.855485 0.517828i \(-0.173259\pi\)
\(500\) 0 0
\(501\) 8.48528 8.48528i 0.379094 0.379094i
\(502\) 8.48528 8.48528i 0.378717 0.378717i
\(503\) −11.0866 4.59220i −0.494325 0.204756i 0.121572 0.992583i \(-0.461206\pi\)
−0.615897 + 0.787826i \(0.711206\pi\)
\(504\) 4.59220 11.0866i 0.204553 0.493834i
\(505\) 0 0
\(506\) 16.0000i 0.711287i
\(507\) −3.44415 8.31492i −0.152960 0.369278i
\(508\) 5.65685 + 5.65685i 0.250982 + 0.250982i
\(509\) 18.0000 0.797836 0.398918 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −7.77817 7.77817i −0.343750 0.343750i
\(513\) −1.53073 3.69552i −0.0675835 0.163161i
\(514\) 2.00000i 0.0882162i
\(515\) 0 0
\(516\) 1.53073 3.69552i 0.0673868 0.162686i
\(517\) −29.5641 12.2459i −1.30023 0.538573i
\(518\) −22.6274 + 22.6274i −0.994192 + 0.994192i
\(519\) 11.3137 11.3137i 0.496617 0.496617i
\(520\) 0 0
\(521\) −9.18440 + 22.1731i −0.402376 + 0.971422i 0.584712 + 0.811241i \(0.301208\pi\)
−0.987088 + 0.160180i \(0.948792\pi\)
\(522\) 0 0
\(523\) 12.0000i 0.524723i 0.964970 + 0.262362i \(0.0845013\pi\)
−0.964970 + 0.262362i \(0.915499\pi\)
\(524\) −1.53073 3.69552i −0.0668704 0.161439i
\(525\) −14.1421 14.1421i −0.617213 0.617213i
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) 4.00000 0.174078
\(529\) 4.94975 + 4.94975i 0.215206 + 0.215206i
\(530\) 0 0
\(531\) 12.0000i 0.520756i
\(532\) 14.7821 6.12293i 0.640884 0.265463i
\(533\) −6.12293 + 14.7821i −0.265214 + 0.640283i
\(534\) −9.23880 3.82683i −0.399802 0.165603i
\(535\) 0 0
\(536\) −25.4558 + 25.4558i −1.09952 + 1.09952i
\(537\) −3.69552 1.53073i −0.159473 0.0660560i
\(538\) 0 0
\(539\) −33.2597 + 13.7766i −1.43260 + 0.593400i
\(540\) 0 0
\(541\) 15.3073 + 36.9552i 0.658114 + 1.58883i 0.800714 + 0.599047i \(0.204454\pi\)
−0.142600 + 0.989780i \(0.545546\pi\)
\(542\) 0 0
\(543\) −8.00000 −0.343313
\(544\) 0 0
\(545\) 0 0
\(546\) 5.65685 + 5.65685i 0.242091 + 0.242091i
\(547\) −13.7766 33.2597i −0.589045 1.42208i −0.884417 0.466698i \(-0.845443\pi\)
0.295372 0.955382i \(-0.404557\pi\)
\(548\) 10.0000i 0.427179i
\(549\) −7.39104 + 3.06147i −0.315442 + 0.130660i
\(550\) 7.65367 18.4776i 0.326354 0.787887i
\(551\) 0 0
\(552\) 8.48528 8.48528i 0.361158 0.361158i
\(553\) −11.3137 + 11.3137i −0.481108 + 0.481108i
\(554\) 7.39104 + 3.06147i 0.314015 + 0.130069i
\(555\) 0 0
\(556\) −3.69552 + 1.53073i −0.156725 + 0.0649176i
\(557\) 18.0000i 0.762684i −0.924434 0.381342i \(-0.875462\pi\)
0.924434 0.381342i \(-0.124538\pi\)
\(558\) 1.53073 + 3.69552i 0.0648011 + 0.156444i
\(559\) 5.65685 + 5.65685i 0.239259 + 0.239259i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000 0.421825
\(563\) 31.1127 + 31.1127i 1.31124 + 1.31124i 0.920499 + 0.390745i \(0.127783\pi\)
0.390745 + 0.920499i \(0.372217\pi\)
\(564\) −3.06147 7.39104i −0.128911 0.311219i
\(565\) 0 0
\(566\) −3.69552 + 1.53073i −0.155334 + 0.0643415i
\(567\) −1.53073 + 3.69552i −0.0642848 + 0.155197i
\(568\) −33.2597 13.7766i −1.39554 0.578053i
\(569\) −18.3848 + 18.3848i −0.770730 + 0.770730i −0.978234 0.207504i \(-0.933466\pi\)
0.207504 + 0.978234i \(0.433466\pi\)
\(570\) 0 0
\(571\) −18.4776 7.65367i −0.773263 0.320296i −0.0390697 0.999236i \(-0.512439\pi\)
−0.734193 + 0.678940i \(0.762439\pi\)
\(572\) 3.06147 7.39104i 0.128006 0.309035i
\(573\) −7.39104 + 3.06147i −0.308765 + 0.127895i
\(574\) 32.0000i 1.33565i
\(575\) −7.65367 18.4776i −0.319180 0.770569i
\(576\) 4.94975 + 4.94975i 0.206239 + 0.206239i
\(577\) −30.0000 −1.24892 −0.624458 0.781058i \(-0.714680\pi\)
−0.624458 + 0.781058i \(0.714680\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 18.3688 + 44.3462i 0.762066 + 1.83979i
\(582\) 16.0000i 0.663221i
\(583\) −22.1731 + 9.18440i −0.918316 + 0.380379i
\(584\) 0 0
\(585\) 0 0
\(586\) 7.07107 7.07107i 0.292103 0.292103i
\(587\) 8.48528 8.48528i 0.350225 0.350225i −0.509968 0.860193i \(-0.670343\pi\)
0.860193 + 0.509968i \(0.170343\pi\)
\(588\) −8.31492 3.44415i −0.342901 0.142034i
\(589\) −6.12293 + 14.7821i −0.252291 + 0.609085i
\(590\) 0 0
\(591\) 16.0000i 0.658152i
\(592\) −3.06147 7.39104i −0.125826 0.303770i
\(593\) 32.5269 + 32.5269i 1.33572 + 1.33572i 0.900159 + 0.435561i \(0.143450\pi\)
0.435561 + 0.900159i \(0.356550\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 14.1421 + 14.1421i 0.578799 + 0.578799i
\(598\) 3.06147 + 7.39104i 0.125193 + 0.302242i
\(599\) 8.00000i 0.326871i −0.986554 0.163436i \(-0.947742\pi\)
0.986554 0.163436i \(-0.0522576\pi\)
\(600\) 13.8582 5.74025i 0.565758 0.234345i
\(601\) 6.12293 14.7821i 0.249760 0.602973i −0.748424 0.663221i \(-0.769189\pi\)
0.998183 + 0.0602475i \(0.0191890\pi\)
\(602\) 14.7821 + 6.12293i 0.602472 + 0.249552i
\(603\) 8.48528 8.48528i 0.345547 0.345547i
\(604\) 0 0
\(605\) 0 0
\(606\) 2.29610 5.54328i 0.0932727 0.225180i
\(607\) −3.69552 + 1.53073i −0.149996 + 0.0621306i −0.456419 0.889765i \(-0.650868\pi\)
0.306422 + 0.951896i \(0.400868\pi\)
\(608\) 20.0000i 0.811107i
\(609\) 0 0
\(610\) 0 0
\(611\) 16.0000 0.647291
\(612\) 0 0
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) −8.48528 8.48528i −0.342438 0.342438i
\(615\) 0 0
\(616\) 48.0000i 1.93398i
\(617\) 22.1731 9.18440i 0.892656 0.369750i 0.111264 0.993791i \(-0.464510\pi\)
0.781392 + 0.624041i \(0.214510\pi\)
\(618\) 0 0
\(619\) 33.2597 + 13.7766i 1.33682 + 0.553728i 0.932593 0.360931i \(-0.117541\pi\)
0.404226 + 0.914659i \(0.367541\pi\)
\(620\) 0 0
\(621\) −2.82843 + 2.82843i −0.113501 + 0.113501i
\(622\) −11.0866 4.59220i −0.444530 0.184130i
\(623\) −15.3073 + 36.9552i −0.613276 + 1.48058i
\(624\) −1.84776 + 0.765367i −0.0739696 + 0.0306392i
\(625\) 25.0000i 1.00000i
\(626\) −6.12293 14.7821i −0.244722 0.590810i
\(627\) −11.3137 11.3137i −0.451826 0.451826i
\(628\) −2.00000 −0.0798087
\(629\) 0 0
\(630\) 0 0
\(631\) −5.65685 5.65685i −0.225196 0.225196i 0.585486 0.810682i \(-0.300904\pi\)
−0.810682 + 0.585486i \(0.800904\pi\)
\(632\) −4.59220 11.0866i −0.182668 0.440999i
\(633\) 4.00000i 0.158986i
\(634\) 29.5641 12.2459i 1.17414 0.486346i
\(635\) 0 0
\(636\) −5.54328 2.29610i −0.219805 0.0910463i
\(637\) 12.7279 12.7279i 0.504299 0.504299i
\(638\) 0 0
\(639\) 11.0866 + 4.59220i 0.438577 + 0.181665i
\(640\) 0 0
\(641\) 7.39104 3.06147i 0.291928 0.120921i −0.231913 0.972737i \(-0.574498\pi\)
0.523841 + 0.851816i \(0.324498\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 1.53073 + 3.69552i 0.0603662 + 0.145737i 0.951185 0.308623i \(-0.0998681\pi\)
−0.890818 + 0.454360i \(0.849868\pi\)
\(644\) −11.3137 11.3137i −0.445823 0.445823i
\(645\) 0 0
\(646\) 0 0
\(647\) 32.0000 1.25805 0.629025 0.777385i \(-0.283454\pi\)
0.629025 + 0.777385i \(0.283454\pi\)
\(648\) −2.12132 2.12132i −0.0833333 0.0833333i
\(649\) 18.3688 + 44.3462i 0.721039 + 1.74074i
\(650\) 10.0000i 0.392232i
\(651\) 14.7821 6.12293i 0.579355 0.239977i
\(652\) −7.65367 + 18.4776i −0.299741 + 0.723638i
\(653\) −29.5641 12.2459i −1.15693 0.479218i −0.280081 0.959976i \(-0.590361\pi\)
−0.876853 + 0.480758i \(0.840361\pi\)
\(654\) 5.65685 5.65685i 0.221201 0.221201i
\(655\) 0 0
\(656\) −7.39104 3.06147i −0.288571 0.119530i
\(657\) 0 0
\(658\) 29.5641 12.2459i 1.15253 0.477394i
\(659\) 4.00000i 0.155818i 0.996960 + 0.0779089i \(0.0248243\pi\)
−0.996960 + 0.0779089i \(0.975176\pi\)
\(660\) 0 0
\(661\) 29.6985 + 29.6985i 1.15514 + 1.15514i 0.985508 + 0.169629i \(0.0542570\pi\)
0.169629 + 0.985508i \(0.445743\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) −36.0000 −1.39707
\(665\) 0 0
\(666\) 3.06147 + 7.39104i 0.118629 + 0.286397i
\(667\) 0 0
\(668\) 11.0866 4.59220i 0.428952 0.177678i
\(669\) 6.12293 14.7821i 0.236726 0.571508i
\(670\) 0 0
\(671\) −22.6274 + 22.6274i −0.873522 + 0.873522i
\(672\) 14.1421 14.1421i 0.545545 0.545545i
\(673\) −29.5641 12.2459i −1.13961 0.472044i −0.268576 0.963259i \(-0.586553\pi\)
−0.871038 + 0.491215i \(0.836553\pi\)
\(674\) 6.12293 14.7821i 0.235847 0.569384i
\(675\) −4.61940 + 1.91342i −0.177801 + 0.0736475i
\(676\) 9.00000i 0.346154i
\(677\) 18.3688 + 44.3462i 0.705971 + 1.70436i 0.709832 + 0.704371i \(0.248771\pi\)
−0.00386145 + 0.999993i \(0.501229\pi\)
\(678\) −5.65685 5.65685i −0.217250 0.217250i
\(679\) −64.0000 −2.45609
\(680\) 0 0
\(681\) 12.0000 0.459841
\(682\) 11.3137 + 11.3137i 0.433224 + 0.433224i
\(683\) 4.59220 + 11.0866i 0.175716 + 0.424215i 0.987060 0.160354i \(-0.0512636\pi\)
−0.811344 + 0.584569i \(0.801264\pi\)
\(684\) 4.00000i 0.152944i
\(685\) 0 0
\(686\) 3.06147 7.39104i 0.116887 0.282191i
\(687\) 9.23880 + 3.82683i 0.352482 + 0.146003i
\(688\) −2.82843 + 2.82843i −0.107833 + 0.107833i
\(689\) 8.48528 8.48528i 0.323263 0.323263i
\(690\) 0 0
\(691\) −7.65367 + 18.4776i −0.291159 + 0.702921i −0.999997 0.00245092i \(-0.999220\pi\)
0.708838 + 0.705372i \(0.249220\pi\)
\(692\) 14.7821 6.12293i 0.561930 0.232759i
\(693\) 16.0000i 0.607790i
\(694\) 1.53073 + 3.69552i 0.0581059 + 0.140280i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −2.00000 −0.0757011
\(699\) −5.65685 5.65685i −0.213962 0.213962i
\(700\) −7.65367 18.4776i −0.289281 0.698387i
\(701\) 34.0000i 1.28416i 0.766637 + 0.642081i \(0.221929\pi\)
−0.766637 + 0.642081i \(0.778071\pi\)
\(702\) 1.84776 0.765367i 0.0697392 0.0288869i
\(703\) −12.2459 + 29.5641i −0.461862 + 1.11503i
\(704\) 25.8686 + 10.7151i 0.974961 + 0.403842i
\(705\) 0 0
\(706\) 12.7279 12.7279i 0.479022 0.479022i
\(707\) −22.1731 9.18440i −0.833906 0.345415i
\(708\) −4.59220 + 11.0866i −0.172585 + 0.416658i
\(709\) −36.9552 + 15.3073i −1.38788 + 0.574879i −0.946577 0.322478i \(-0.895484\pi\)
−0.441304 + 0.897358i \(0.645484\pi\)
\(710\) 0 0
\(711\) 1.53073 + 3.69552i 0.0574070 + 0.138593i
\(712\) −21.2132 21.2132i −0.794998 0.794998i
\(713\) 16.0000 0.599205
\(714\) 0 0
\(715\) 0 0
\(716\) −2.82843 2.82843i −0.105703 0.105703i
\(717\) 3.06147 + 7.39104i 0.114333 + 0.276023i
\(718\) 32.0000i 1.19423i
\(719\) 33.2597 13.7766i 1.24038 0.513781i 0.336544 0.941668i \(-0.390742\pi\)
0.903832 + 0.427887i \(0.140742\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.12132 2.12132i 0.0789474 0.0789474i
\(723\) 11.3137 11.3137i 0.420761 0.420761i
\(724\) −7.39104 3.06147i −0.274686 0.113779i
\(725\) 0 0
\(726\) −4.61940 + 1.91342i −0.171442 + 0.0710136i
\(727\) 8.00000i 0.296704i −0.988935 0.148352i \(-0.952603\pi\)
0.988935 0.148352i \(-0.0473968\pi\)
\(728\) 9.18440 + 22.1731i 0.340397 + 0.821790i
\(729\) 0.707107 + 0.707107i 0.0261891 + 0.0261891i
\(730\) 0 0
\(731\) 0 0
\(732\) −8.00000 −0.295689
\(733\) −24.0416 24.0416i −0.887998 0.887998i 0.106333 0.994331i \(-0.466089\pi\)
−0.994331 + 0.106333i \(0.966089\pi\)
\(734\) −4.59220 11.0866i −0.169501 0.409212i
\(735\) 0 0
\(736\) 18.4776 7.65367i 0.681093 0.282118i
\(737\) 18.3688 44.3462i 0.676624 1.63351i
\(738\) 7.39104 + 3.06147i 0.272068 + 0.112694i
\(739\) 2.82843 2.82843i 0.104045 0.104045i −0.653168 0.757213i \(-0.726560\pi\)
0.757213 + 0.653168i \(0.226560\pi\)
\(740\) 0 0
\(741\) 7.39104 + 3.06147i 0.271517 + 0.112466i
\(742\) 9.18440 22.1731i 0.337170 0.814000i
\(743\) −33.2597 + 13.7766i −1.22018 + 0.505415i −0.897467 0.441083i \(-0.854595\pi\)
−0.322712 + 0.946497i \(0.604595\pi\)
\(744\) 12.0000i 0.439941i
\(745\) 0 0
\(746\) −18.3848 18.3848i −0.673114 0.673114i
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) −48.0000 −1.75388
\(750\) 0 0
\(751\) 7.65367 + 18.4776i 0.279286 + 0.674257i 0.999816 0.0191669i \(-0.00610140\pi\)
−0.720530 + 0.693424i \(0.756101\pi\)
\(752\) 8.00000i 0.291730i
\(753\) −11.0866 + 4.59220i −0.404017 + 0.167349i
\(754\) 0 0
\(755\) 0 0
\(756\) −2.82843 + 2.82843i −0.102869 + 0.102869i
\(757\) −26.8701 + 26.8701i −0.976609 + 0.976609i −0.999733 0.0231238i \(-0.992639\pi\)
0.0231238 + 0.999733i \(0.492639\pi\)
\(758\) −18.4776 7.65367i −0.671136 0.277994i
\(759\) −6.12293 + 14.7821i −0.222248 + 0.536555i
\(760\) 0 0
\(761\) 6.00000i 0.217500i −0.994069 0.108750i \(-0.965315\pi\)
0.994069 0.108750i \(-0.0346848\pi\)
\(762\) 3.06147 + 7.39104i 0.110905 + 0.267749i
\(763\) −22.6274 22.6274i −0.819167 0.819167i
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) −16.0000 −0.578103
\(767\) −16.9706 16.9706i −0.612772 0.612772i
\(768\) 6.50562 + 15.7060i 0.234751 + 0.566740i
\(769\) 34.0000i 1.22607i −0.790055 0.613036i \(-0.789948\pi\)
0.790055 0.613036i \(-0.210052\pi\)
\(770\) 0 0
\(771\) −0.765367 + 1.84776i −0.0275640 + 0.0665454i
\(772\) 0 0
\(773\) 4.24264 4.24264i 0.152597 0.152597i −0.626680 0.779277i \(-0.715587\pi\)
0.779277 + 0.626680i \(0.215587\pi\)
\(774\) 2.82843 2.82843i 0.101666 0.101666i
\(775\) 18.4776 + 7.65367i 0.663735 + 0.274928i
\(776\) 18.3688 44.3462i 0.659402 1.59194i
\(777\) 29.5641 12.2459i 1.06061 0.439318i
\(778\) 6.00000i 0.215110i
\(779\) 12.2459 + 29.5641i 0.438754 + 1.05925i
\(780\) 0 0
\(781\) 48.0000 1.71758
\(782\) 0 0
\(783\) 0 0
\(784\) 6.36396 + 6.36396i 0.227284 + 0.227284i
\(785\) 0 0
\(786\) 4.00000i 0.142675i
\(787\) 11.0866 4.59220i 0.395193 0.163694i −0.176232 0.984349i \(-0.556391\pi\)
0.571425 + 0.820654i \(0.306391\pi\)
\(788\) −6.12293 + 14.7821i −0.218121 + 0.526590i
\(789\) 22.1731 + 9.18440i 0.789384 + 0.326973i
\(790\) 0 0
\(791\) −22.6274 + 22.6274i −0.804538 + 0.804538i
\(792\) −11.0866 4.59220i −0.393944 0.163177i
\(793\) 6.12293 14.7821i 0.217432 0.524927i
\(794\) −7.39104 + 3.06147i −0.262298 + 0.108647i
\(795\) 0 0
\(796\) 7.65367 + 18.4776i 0.271277 + 0.654921i
\(797\) 12.7279 + 12.7279i 0.450846 + 0.450846i 0.895635 0.444789i \(-0.146721\pi\)
−0.444789 + 0.895635i \(0.646721\pi\)
\(798\) 16.0000 0.566394
\(799\) 0 0
\(800\) 25.0000 0.883883
\(801\) 7.07107 + 7.07107i 0.249844 + 0.249844i
\(802\) 9.18440 + 22.1731i 0.324313 + 0.782960i
\(803\) 0 0
\(804\) 11.0866 4.59220i 0.390993 0.161954i
\(805\) 0 0
\(806\) −7.39104 3.06147i −0.260338 0.107836i
\(807\) 0 0
\(808\) 12.7279 12.7279i 0.447767 0.447767i
\(809\) 36.9552 + 15.3073i 1.29927 + 0.538177i 0.921737 0.387817i \(-0.126771\pi\)
0.377538 + 0.925994i \(0.376771\pi\)
\(810\) 0 0
\(811\) 3.69552 1.53073i 0.129767 0.0537513i −0.316855 0.948474i \(-0.602627\pi\)
0.446622 + 0.894723i \(0.352627\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 22.6274 + 22.6274i 0.793091 + 0.793091i
\(815\) 0 0
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) 7.07107 + 7.07107i 0.247234 + 0.247234i
\(819\) −3.06147 7.39104i −0.106976 0.258264i
\(820\) 0 0
\(821\) −29.5641 + 12.2459i −1.03180 + 0.427384i −0.833360 0.552730i \(-0.813586\pi\)
−0.198435 + 0.980114i \(0.563586\pi\)
\(822\) −3.82683 + 9.23880i −0.133476 + 0.322240i
\(823\) 40.6507 + 16.8381i 1.41699 + 0.586938i 0.954104 0.299477i \(-0.0968122\pi\)
0.462891 + 0.886415i \(0.346812\pi\)
\(824\) 0 0
\(825\) −14.1421 + 14.1421i −0.492366 + 0.492366i
\(826\) −44.3462 18.3688i −1.54300 0.639132i
\(827\) 4.59220 11.0866i 0.159686 0.385517i −0.823704 0.567020i \(-0.808096\pi\)
0.983390 + 0.181503i \(0.0580962\pi\)
\(828\) −3.69552 + 1.53073i −0.128428 + 0.0531967i
\(829\) 2.00000i 0.0694629i 0.999397 + 0.0347314i \(0.0110576\pi\)
−0.999397 + 0.0347314i \(0.988942\pi\)
\(830\) 0 0
\(831\) −5.65685 5.65685i −0.196234 0.196234i
\(832\) −14.0000 −0.485363
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) −6.12293 14.7821i −0.211766 0.511249i
\(837\) 4.00000i 0.138260i
\(838\) −3.69552 + 1.53073i −0.127660 + 0.0528783i
\(839\) 16.8381 40.6507i 0.581315 1.40342i −0.310307 0.950636i \(-0.600432\pi\)
0.891622 0.452782i \(-0.149568\pi\)
\(840\) 0 0
\(841\) −20.5061 + 20.5061i −0.707107 + 0.707107i
\(842\) −15.5563 + 15.5563i −0.536107 + 0.536107i
\(843\) −9.23880 3.82683i −0.318201 0.131803i
\(844\) 1.53073 3.69552i 0.0526900 0.127205i
\(845\) 0 0
\(846\) 8.00000i 0.275046i
\(847\) 7.65367 + 18.4776i 0.262983 + 0.634898i
\(848\) 4.24264 + 4.24264i 0.145693 + 0.145693i
\(849\) 4.00000 0.137280
\(850\) 0 0
\(851\) 32.0000 1.09695
\(852\) 8.48528 + 8.48528i 0.290701 + 0.290701i
\(853\) 9.18440 + 22.1731i 0.314468 + 0.759193i 0.999528 + 0.0307066i \(0.00977575\pi\)
−0.685060 + 0.728486i \(0.740224\pi\)
\(854\) 32.0000i 1.09502i
\(855\) 0 0
\(856\) 13.7766 33.2597i 0.470875 1.13679i
\(857\) 7.39104 + 3.06147i 0.252473 + 0.104578i 0.505331 0.862926i \(-0.331370\pi\)
−0.252858 + 0.967503i \(0.581370\pi\)
\(858\) 5.65685 5.65685i 0.193122 0.193122i
\(859\) −2.82843 + 2.82843i −0.0965047 + 0.0965047i −0.753711 0.657206i \(-0.771738\pi\)
0.657206 + 0.753711i \(0.271738\pi\)
\(860\) 0 0
\(861\) 12.2459 29.5641i 0.417338 1.00754i
\(862\) −18.4776 + 7.65367i −0.629349 + 0.260685i
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) −1.91342 4.61940i −0.0650958 0.157155i
\(865\) 0 0
\(866\) 2.00000 0.0679628
\(867\) 0 0
\(868\) 16.0000 0.543075
\(869\) 11.3137 + 11.3137i 0.383791 + 0.383791i
\(870\) 0 0
\(871\) 24.0000i 0.813209i
\(872\) 22.1731 9.18440i 0.750876 0.311023i
\(873\) −6.12293 + 14.7821i −0.207230 + 0.500297i
\(874\) 14.7821 + 6.12293i 0.500011 + 0.207111i
\(875\) 0 0
\(876\) 0 0
\(877\) 36.9552 + 15.3073i 1.24789 + 0.516892i 0.906171 0.422911i \(-0.138992\pi\)
0.341717 + 0.939803i \(0.388992\pi\)
\(878\) 13.7766 33.2597i 0.464938 1.12246i
\(879\) −9.23880 + 3.82683i −0.311617 + 0.129076i
\(880\) 0 0
\(881\) 9.18440 + 22.1731i 0.309430 + 0.747031i 0.999724 + 0.0235015i \(0.00748144\pi\)
−0.690293 + 0.723530i \(0.742519\pi\)
\(882\) −6.36396 6.36396i −0.214286 0.214286i
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −14.1421 14.1421i −0.475114 0.475114i
\(887\) 1.53073 + 3.69552i 0.0513970 + 0.124083i 0.947493 0.319778i \(-0.103608\pi\)
−0.896096 + 0.443861i \(0.853608\pi\)
\(888\) 24.0000i 0.805387i
\(889\) 29.5641 12.2459i 0.991550 0.410713i
\(890\) 0 0
\(891\) 3.69552 + 1.53073i 0.123805 + 0.0512815i
\(892\) 11.3137 11.3137i 0.378811 0.378811i
\(893\) 22.6274 22.6274i 0.757198 0.757198i
\(894\) −5.54328 2.29610i −0.185395 0.0767931i
\(895\) 0 0
\(896\) 11.0866 4.59220i 0.370376 0.153415i
\(897\) 8.00000i 0.267112i
\(898\) 3.06147 + 7.39104i 0.102162 + 0.246642i
\(899\) 0 0
\(900\) −5.00000 −0.166667
\(901\) 0 0
\(902\) 32.0000 1.06548
\(903\) −11.3137 11.3137i −0.376497 0.376497i
\(904\) −9.18440 22.1731i −0.305469 0.737467i
\(905\) 0 0
\(906\) 0 0
\(907\) −10.7151 + 25.8686i −0.355790 + 0.858954i 0.640092 + 0.768298i \(0.278896\pi\)
−0.995882 + 0.0906554i \(0.971104\pi\)
\(908\) 11.0866 + 4.59220i 0.367920 + 0.152398i
\(909\) −4.24264 + 4.24264i −0.140720 + 0.140720i
\(910\) 0 0
\(911\) −25.8686 10.7151i −0.857066 0.355008i −0.0895065 0.995986i \(-0.528529\pi\)
−0.767559 + 0.640978i \(0.778529\pi\)
\(912\) −1.53073 + 3.69552i −0.0506877 + 0.122371i
\(913\) 44.3462 18.3688i 1.46765 0.607919i
\(914\) 38.0000i 1.25693i
\(915\) 0 0
\(916\) 7.07107 + 7.07107i 0.233635 + 0.233635i
\(917\) −16.0000 −0.528367
\(918\) 0 0
\(919\) 24.0000 0.791687 0.395843 0.918318i \(-0.370452\pi\)
0.395843 + 0.918318i \(0.370452\pi\)
\(920\) 0 0
\(921\) 4.59220 + 11.0866i 0.151318 + 0.365314i
\(922\) 34.0000i 1.11973i
\(923\) −22.1731 + 9.18440i −0.729837 + 0.302308i
\(924\) −6.12293 + 14.7821i −0.201430 + 0.486294i
\(925\) 36.9552 + 15.3073i 1.21508 + 0.503302i
\(926\) 28.2843 28.2843i 0.929479 0.929479i
\(927\) 0 0
\(928\) 0 0
\(929\) −9.18440 + 22.1731i −0.301330 + 0.727476i 0.698598 + 0.715514i \(0.253808\pi\)
−0.999928 + 0.0119617i \(0.996192\pi\)
\(930\) 0 0
\(931\) 36.0000i 1.17985i
\(932\) −3.06147 7.39104i −0.100282 0.242101i
\(933\) 8.48528 + 8.48528i 0.277796 + 0.277796i
\(934\) −4.00000 −0.130884
\(935\) 0 0
\(936\) 6.00000 0.196116
\(937\) 18.3848 + 18.3848i 0.600604 + 0.600604i 0.940473 0.339869i \(-0.110383\pi\)
−0.339869 + 0.940473i \(0.610383\pi\)
\(938\) 18.3688 + 44.3462i 0.599763 + 1.44796i
\(939\) 16.0000i 0.522140i
\(940\) 0 0
\(941\) −18.3688 + 44.3462i −0.598806 + 1.44565i 0.275993 + 0.961160i \(0.410993\pi\)
−0.874799 + 0.484486i \(0.839007\pi\)
\(942\) −1.84776 0.765367i −0.0602032 0.0249370i
\(943\) 22.6274 22.6274i 0.736850 0.736850i
\(944\) 8.48528 8.48528i 0.276172 0.276172i
\(945\) 0 0
\(946\) 6.12293 14.7821i 0.199074 0.480607i
\(947\) −11.0866 + 4.59220i −0.360265 + 0.149226i −0.555471 0.831536i \(-0.687462\pi\)
0.195207 + 0.980762i \(0.437462\pi\)
\(948\) 4.00000i 0.129914i
\(949\) 0 0
\(950\) 14.1421 + 14.1421i 0.458831 + 0.458831i
\(951\) −32.0000 −1.03767
\(952\) 0 0
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) −4.24264 4.24264i −0.137361 0.137361i
\(955\) 0 0
\(956\) 8.00000i 0.258738i
\(957\) 0 0
\(958\) 4.59220 11.0866i 0.148367 0.358190i
\(959\) 36.9552 + 15.3073i 1.19335 + 0.494300i
\(960\) 0 0
\(961\) 10.6066 10.6066i 0.342148 0.342148i
\(962\) −14.7821 6.12293i −0.476593 0.197411i
\(963\) −4.59220 + 11.0866i −0.147982 + 0.357259i
\(964\) 14.7821 6.12293i 0.476098 0.197206i
\(965\) 0 0
\(966\) −6.12293 14.7821i −0.197002 0.475605i
\(967\) −16.9706 16.9706i −0.545737 0.545737i 0.379468 0.925205i \(-0.376107\pi\)
−0.925205 + 0.379468i \(0.876107\pi\)
\(968\) −15.0000 −0.482118
\(969\) 0 0
\(970\) 0 0
\(971\) 25.4558 + 25.4558i 0.816917 + 0.816917i 0.985660 0.168743i \(-0.0539708\pi\)
−0.168743 + 0.985660i \(0.553971\pi\)
\(972\) 0.382683 + 0.923880i 0.0122746 + 0.0296334i
\(973\) 16.0000i 0.512936i
\(974\) 3.69552 1.53073i 0.118412 0.0490479i
\(975\) 3.82683 9.23880i 0.122557 0.295878i
\(976\) 7.39104 + 3.06147i 0.236581 + 0.0979952i
\(977\) 32.5269 32.5269i 1.04063 1.04063i 0.0414892 0.999139i \(-0.486790\pi\)
0.999139 0.0414892i \(-0.0132102\pi\)
\(978\) −14.1421 + 14.1421i −0.452216 + 0.452216i
\(979\) 36.9552 + 15.3073i 1.18109 + 0.489225i
\(980\) 0 0
\(981\) −7.39104 + 3.06147i −0.235978 + 0.0977451i
\(982\) 20.0000i 0.638226i
\(983\) −7.65367 18.4776i −0.244114 0.589344i 0.753570 0.657368i \(-0.228330\pi\)
−0.997684 + 0.0680246i \(0.978330\pi\)
\(984\) 16.9706 + 16.9706i 0.541002 + 0.541002i
\(985\) 0 0
\(986\) 0 0
\(987\) −32.0000 −1.01857
\(988\) 5.65685 + 5.65685i 0.179969 + 0.179969i
\(989\) −6.12293 14.7821i −0.194698 0.470043i
\(990\) 0 0
\(991\) −11.0866 + 4.59220i −0.352176 + 0.145876i −0.551756 0.834005i \(-0.686042\pi\)
0.199580 + 0.979881i \(0.436042\pi\)
\(992\) −7.65367 + 18.4776i −0.243004 + 0.586664i
\(993\) −18.4776 7.65367i −0.586369 0.242882i
\(994\) −33.9411 + 33.9411i −1.07655 + 1.07655i
\(995\) 0 0
\(996\) 11.0866 + 4.59220i 0.351291 + 0.145509i
\(997\) −3.06147 + 7.39104i −0.0969576 + 0.234076i −0.964915 0.262562i \(-0.915433\pi\)
0.867957 + 0.496639i \(0.165433\pi\)
\(998\) 33.2597 13.7766i 1.05282 0.436091i
\(999\) 8.00000i 0.253109i
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 867.2.h.d.712.1 8
17.2 even 8 inner 867.2.h.d.757.1 8
17.3 odd 16 51.2.d.b.16.1 2
17.4 even 4 inner 867.2.h.d.733.1 8
17.5 odd 16 867.2.a.b.1.1 1
17.6 odd 16 867.2.e.d.829.1 4
17.7 odd 16 867.2.e.d.616.1 4
17.8 even 8 inner 867.2.h.d.688.1 8
17.9 even 8 inner 867.2.h.d.688.2 8
17.10 odd 16 867.2.e.d.616.2 4
17.11 odd 16 867.2.e.d.829.2 4
17.12 odd 16 867.2.a.a.1.1 1
17.13 even 4 inner 867.2.h.d.733.2 8
17.14 odd 16 51.2.d.b.16.2 yes 2
17.15 even 8 inner 867.2.h.d.757.2 8
17.16 even 2 inner 867.2.h.d.712.2 8
51.5 even 16 2601.2.a.j.1.1 1
51.14 even 16 153.2.d.a.118.1 2
51.20 even 16 153.2.d.a.118.2 2
51.29 even 16 2601.2.a.i.1.1 1
68.3 even 16 816.2.c.c.577.2 2
68.31 even 16 816.2.c.c.577.1 2
85.3 even 16 1275.2.d.d.424.1 2
85.14 odd 16 1275.2.g.a.526.1 2
85.37 even 16 1275.2.d.b.424.2 2
85.48 even 16 1275.2.d.b.424.1 2
85.54 odd 16 1275.2.g.a.526.2 2
85.82 even 16 1275.2.d.d.424.2 2
136.3 even 16 3264.2.c.d.577.1 2
136.37 odd 16 3264.2.c.e.577.2 2
136.99 even 16 3264.2.c.d.577.2 2
136.133 odd 16 3264.2.c.e.577.1 2
204.71 odd 16 2448.2.c.j.577.1 2
204.167 odd 16 2448.2.c.j.577.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.2.d.b.16.1 2 17.3 odd 16
51.2.d.b.16.2 yes 2 17.14 odd 16
153.2.d.a.118.1 2 51.14 even 16
153.2.d.a.118.2 2 51.20 even 16
816.2.c.c.577.1 2 68.31 even 16
816.2.c.c.577.2 2 68.3 even 16
867.2.a.a.1.1 1 17.12 odd 16
867.2.a.b.1.1 1 17.5 odd 16
867.2.e.d.616.1 4 17.7 odd 16
867.2.e.d.616.2 4 17.10 odd 16
867.2.e.d.829.1 4 17.6 odd 16
867.2.e.d.829.2 4 17.11 odd 16
867.2.h.d.688.1 8 17.8 even 8 inner
867.2.h.d.688.2 8 17.9 even 8 inner
867.2.h.d.712.1 8 1.1 even 1 trivial
867.2.h.d.712.2 8 17.16 even 2 inner
867.2.h.d.733.1 8 17.4 even 4 inner
867.2.h.d.733.2 8 17.13 even 4 inner
867.2.h.d.757.1 8 17.2 even 8 inner
867.2.h.d.757.2 8 17.15 even 8 inner
1275.2.d.b.424.1 2 85.48 even 16
1275.2.d.b.424.2 2 85.37 even 16
1275.2.d.d.424.1 2 85.3 even 16
1275.2.d.d.424.2 2 85.82 even 16
1275.2.g.a.526.1 2 85.14 odd 16
1275.2.g.a.526.2 2 85.54 odd 16
2448.2.c.j.577.1 2 204.71 odd 16
2448.2.c.j.577.2 2 204.167 odd 16
2601.2.a.i.1.1 1 51.29 even 16
2601.2.a.j.1.1 1 51.5 even 16
3264.2.c.d.577.1 2 136.3 even 16
3264.2.c.d.577.2 2 136.99 even 16
3264.2.c.e.577.1 2 136.133 odd 16
3264.2.c.e.577.2 2 136.37 odd 16