Properties

Label 867.2.h.d.712.2
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 712.2
Root \(-0.923880 - 0.382683i\) of defining polynomial
Character \(\chi\) \(=\) 867.712
Dual form 867.2.h.d.688.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{6} +(3.69552 + 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-0.707107 + 0.707107i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(0.382683 + 0.923880i) q^{3} -1.00000i q^{4} +(-0.382683 + 0.923880i) q^{6} +(3.69552 + 1.53073i) q^{7} +(2.12132 - 2.12132i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(1.53073 - 3.69552i) q^{11} +(0.923880 - 0.382683i) q^{12} -2.00000i q^{13} +(1.53073 + 3.69552i) q^{14} +1.00000 q^{16} -1.00000 q^{18} +(-2.82843 - 2.82843i) q^{19} +4.00000i q^{21} +(3.69552 - 1.53073i) q^{22} +(1.53073 - 3.69552i) q^{23} +(2.77164 + 1.14805i) q^{24} +(-3.53553 + 3.53553i) q^{25} +(1.41421 - 1.41421i) q^{26} +(-0.923880 - 0.382683i) q^{27} +(1.53073 - 3.69552i) q^{28} +(1.53073 + 3.69552i) q^{31} +(-3.53553 - 3.53553i) q^{32} +4.00000 q^{33} +(0.707107 + 0.707107i) q^{36} +(3.06147 + 7.39104i) q^{37} -4.00000i q^{38} +(1.84776 - 0.765367i) q^{39} +(7.39104 + 3.06147i) q^{41} +(-2.82843 + 2.82843i) q^{42} +(-2.82843 + 2.82843i) q^{43} +(-3.69552 - 1.53073i) q^{44} +(3.69552 - 1.53073i) q^{46} +8.00000i q^{47} +(0.382683 + 0.923880i) q^{48} +(6.36396 + 6.36396i) q^{49} -5.00000 q^{50} -2.00000 q^{52} +(4.24264 + 4.24264i) q^{53} +(-0.382683 - 0.923880i) q^{54} +(11.0866 - 4.59220i) q^{56} +(1.53073 - 3.69552i) q^{57} +(8.48528 - 8.48528i) q^{59} +(-7.39104 - 3.06147i) q^{61} +(-1.53073 + 3.69552i) q^{62} +(-3.69552 + 1.53073i) q^{63} -7.00000i q^{64} +(2.82843 + 2.82843i) q^{66} -12.0000 q^{67} +4.00000 q^{69} +(4.59220 + 11.0866i) q^{71} +3.00000i q^{72} +(-3.06147 + 7.39104i) q^{74} +(-4.61940 - 1.91342i) q^{75} +(-2.82843 + 2.82843i) q^{76} +(11.3137 - 11.3137i) q^{77} +(1.84776 + 0.765367i) q^{78} +(-1.53073 + 3.69552i) q^{79} -1.00000i q^{81} +(3.06147 + 7.39104i) q^{82} +(-8.48528 - 8.48528i) q^{83} +4.00000 q^{84} -4.00000 q^{86} +(-4.59220 - 11.0866i) q^{88} -10.0000i q^{89} +(3.06147 - 7.39104i) q^{91} +(-3.69552 - 1.53073i) q^{92} +(-2.82843 + 2.82843i) q^{93} +(-5.65685 + 5.65685i) q^{94} +(1.91342 - 4.61940i) q^{96} +(-14.7821 + 6.12293i) q^{97} +9.00000i q^{98} +(1.53073 + 3.69552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) 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 0.948912 0.315540i \(-0.102186\pi\)
0.447862 + 0.894103i \(0.352186\pi\)
\(8\) 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 \(-0.668963\pi\)
0.967768 0.251845i \(-0.0810372\pi\)
\(12\) 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 \(-0.738071\pi\)
0.999298 0.0374660i \(-0.0119286\pi\)
\(24\) 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 0.999681 0.0252745i \(-0.00804598\pi\)
−0.724753 + 0.689009i \(0.758046\pi\)
\(32\) −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 \(0.103427\pi\)
−0.444373 + 0.895842i \(0.646573\pi\)
\(38\) 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 0.875969 0.482368i \(-0.160223\pi\)
0.278317 + 0.960489i \(0.410223\pi\)
\(42\) −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 −0.144477 0.989508i \(-0.546150\pi\)
−0.801848 + 0.597527i \(0.796150\pi\)
\(62\) −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 \(0.127242\pi\)
−0.376168 + 0.926552i \(0.622758\pi\)
\(72\) 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 −0.986297 0.164980i \(-0.947244\pi\)
0.814076 + 0.580759i \(0.197244\pi\)
\(80\) 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 −0.973655 0.228028i \(-0.926772\pi\)
−0.527238 + 0.849718i \(0.676772\pi\)
\(98\) 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 −0.847618 0.530608i \(-0.821964\pi\)
−0.224160 + 0.974552i \(0.571964\pi\)
\(108\) −0.382683 + 0.923880i −0.0368237 + 0.0889003i
\(109\) −7.39104 3.06147i −0.707933 0.293235i −0.000483966 1.00000i \(-0.500154\pi\)
−0.707449 + 0.706764i \(0.750154\pi\)
\(110\) 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 −0.999976 0.00691210i \(-0.997800\pi\)
0.711977 + 0.702202i \(0.247800\pi\)
\(114\) 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 −0.538235 0.842795i \(-0.680909\pi\)
0.215356 + 0.976536i \(0.430909\pi\)
\(132\) 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 0.975407 0.220412i \(-0.0707402\pi\)
−0.845572 + 0.533862i \(0.820740\pi\)
\(140\) 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 0.961550 0.274629i \(-0.0885551\pi\)
0.485726 + 0.874111i \(0.338555\pi\)
\(164\) 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 \(-0.971308\pi\)
0.640585 0.767887i \(-0.278692\pi\)
\(168\) 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 \(-0.916880\pi\)
0.500581 0.865690i \(-0.333120\pi\)
\(174\) 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 −0.995879 0.0906923i \(-0.971092\pi\)
0.768322 + 0.640064i \(0.221092\pi\)
\(182\) 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 0.841026 0.540995i \(-0.181952\pi\)
0.212153 + 0.977236i \(0.431952\pi\)
\(198\) −1.53073 + 3.69552i −0.108785 + 0.262629i
\(199\) 18.4776 7.65367i 1.30984 0.542554i 0.385004 0.922915i \(-0.374200\pi\)
0.924838 + 0.380361i \(0.124200\pi\)
\(200\) 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 0.251834 0.967771i \(-0.418966\pi\)
−0.506244 + 0.862390i \(0.668966\pi\)
\(212\) 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 \(-0.744623\pi\)
0.999857 0.0168909i \(-0.00537679\pi\)
\(228\) −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 −0.611412 0.791313i \(-0.709398\pi\)
0.127209 + 0.991876i \(0.459398\pi\)
\(234\) 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 \(-0.952671\pi\)
0.594553 0.804056i \(-0.297329\pi\)
\(242\) 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 −0.593509 0.804827i \(-0.702258\pi\)
0.149425 + 0.988773i \(0.452258\pi\)
\(278\) −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 −0.871831 0.489807i \(-0.837067\pi\)
0.962823 + 0.270131i \(0.0870672\pi\)
\(284\) 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 −0.0455232 0.998963i \(-0.514495\pi\)
0.674184 + 0.738563i \(0.264495\pi\)
\(312\) 2.29610 5.54328i 0.129991 0.313826i
\(313\) 14.7821 + 6.12293i 0.835532 + 0.346089i 0.759090 0.650985i \(-0.225644\pi\)
0.0764418 + 0.997074i \(0.475644\pi\)
\(314\) 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 \(0.480451\pi\)
−0.749174 + 0.662373i \(0.769549\pi\)
\(318\) −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 \(0.0185302\pi\)
−0.664769 + 0.747049i \(0.731470\pi\)
\(338\) 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 0.281278 0.959626i \(-0.409242\pi\)
−0.479664 + 0.877452i \(0.659242\pi\)
\(348\) 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 0.652787 0.757542i \(-0.273600\pi\)
−0.0740732 + 0.997253i \(0.523600\pi\)
\(368\) 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 0.146226 0.989251i \(-0.453287\pi\)
0.802904 + 0.596109i \(0.203287\pi\)
\(380\) 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 −0.828246 0.560365i \(-0.810661\pi\)
0.981896 + 0.189420i \(0.0606607\pi\)
\(398\) 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 −0.247275 0.968945i \(-0.579535\pi\)
−0.859997 + 0.510298i \(0.829535\pi\)
\(402\) 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 −0.882068 0.471121i \(-0.843849\pi\)
0.956850 + 0.290583i \(0.0938494\pi\)
\(420\) 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 \(-0.715026\pi\)
0.993970 0.109654i \(-0.0349743\pi\)
\(432\) −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 \(0.203972\pi\)
−0.144099 + 0.989563i \(0.546028\pi\)
\(440\) 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 0.201401 0.979509i \(-0.435451\pi\)
−0.550205 + 0.835029i \(0.685451\pi\)
\(450\) 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 0.993395 0.114743i \(-0.0366045\pi\)
−0.783572 + 0.621301i \(0.786605\pi\)
\(480\) 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 −0.954760 0.297379i \(-0.903888\pi\)
0.885395 + 0.464839i \(0.153888\pi\)
\(488\) −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 \(0.423259\pi\)
−0.855485 + 0.517828i \(0.826741\pi\)
\(500\) 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 0.615897 0.787826i \(-0.288794\pi\)
−0.121572 + 0.992583i \(0.538794\pi\)
\(504\) −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 \(-0.698792\pi\)
0.987088 0.160180i \(-0.0512076\pi\)
\(522\) 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 \(-0.795546\pi\)
0.142600 0.989780i \(-0.454454\pi\)
\(542\) 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 \(0.154557\pi\)
−0.295372 + 0.955382i \(0.595443\pi\)
\(548\) 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 0.734193 0.678940i \(-0.237561\pi\)
0.0390697 + 0.999236i \(0.487561\pi\)
\(572\) −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 −0.998183 0.0602475i \(-0.980811\pi\)
0.748424 + 0.663221i \(0.230811\pi\)
\(602\) −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 −0.306422 0.951896i \(-0.599132\pi\)
0.456419 + 0.889765i \(0.349132\pi\)
\(608\) 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 −0.781392 0.624041i \(-0.785490\pi\)
−0.111264 + 0.993791i \(0.535490\pi\)
\(618\) 0 0
\(619\) −33.2597 13.7766i −1.33682 0.553728i −0.404226 0.914659i \(-0.632459\pi\)
−0.932593 + 0.360931i \(0.882459\pi\)
\(620\) 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 −0.523841 0.851816i \(-0.675502\pi\)
0.231913 + 0.972737i \(0.425502\pi\)
\(642\) 12.0000i 0.473602i
\(643\) −1.53073 3.69552i −0.0603662 0.145737i 0.890818 0.454360i \(-0.150132\pi\)
−0.951185 + 0.308623i \(0.900132\pi\)
\(644\) −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 0.876853 0.480758i \(-0.159639\pi\)
0.280081 + 0.959976i \(0.409639\pi\)
\(654\) 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 0.871038 0.491215i \(-0.163447\pi\)
0.268576 + 0.963259i \(0.413447\pi\)
\(674\) −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 \(-0.751229\pi\)
0.00386145 0.999993i \(-0.498771\pi\)
\(678\) −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 0.811344 0.584569i \(-0.198736\pi\)
−0.987060 + 0.160354i \(0.948736\pi\)
\(684\) 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 −0.708838 0.705372i \(-0.750780\pi\)
0.999997 + 0.00245092i \(0.000780153\pi\)
\(692\) −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 0.441304 0.897358i \(-0.354516\pi\)
0.946577 + 0.322478i \(0.104516\pi\)
\(710\) 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 −0.903832 0.427887i \(-0.859258\pi\)
−0.336544 + 0.941668i \(0.609258\pi\)
\(720\) 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 0.322712 0.946497i \(-0.395405\pi\)
0.897467 + 0.441083i \(0.145405\pi\)
\(744\) 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 0.720530 0.693424i \(-0.243899\pi\)
−0.999816 + 0.0191669i \(0.993899\pi\)
\(752\) 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 −0.571425 0.820654i \(-0.693609\pi\)
0.176232 + 0.984349i \(0.443609\pi\)
\(788\) 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 −0.377538 0.925994i \(-0.623229\pi\)
−0.921737 + 0.387817i \(0.873229\pi\)
\(810\) 0 0
\(811\) −3.69552 + 1.53073i −0.129767 + 0.0537513i −0.446622 0.894723i \(-0.647373\pi\)
0.316855 + 0.948474i \(0.397373\pi\)
\(812\) 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 0.198435 0.980114i \(-0.436414\pi\)
0.833360 + 0.552730i \(0.186414\pi\)
\(822\) 3.82683 9.23880i 0.133476 0.322240i
\(823\) −40.6507 16.8381i −1.41699 0.586938i −0.462891 0.886415i \(-0.653188\pi\)
−0.954104 + 0.299477i \(0.903188\pi\)
\(824\) 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 −0.983390 0.181503i \(-0.941904\pi\)
0.823704 + 0.567020i \(0.191904\pi\)
\(828\) 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 \(0.399568\pi\)
−0.891622 + 0.452782i \(0.850432\pi\)
\(840\) 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 \(-0.990224\pi\)
0.685060 0.728486i \(-0.259776\pi\)
\(854\) 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 0.252858 0.967503i \(-0.418630\pi\)
−0.505331 + 0.862926i \(0.668630\pi\)
\(858\) 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 −0.341717 0.939803i \(-0.611008\pi\)
−0.906171 + 0.422911i \(0.861008\pi\)
\(878\) −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 \(-0.992519\pi\)
0.690293 0.723530i \(-0.257481\pi\)
\(882\) −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 0.896096 0.443861i \(-0.146392\pi\)
−0.947493 + 0.319778i \(0.896392\pi\)
\(888\) 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 \(-0.721104\pi\)
0.995882 0.0906554i \(-0.0288962\pi\)
\(908\) −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 0.767559 0.640978i \(-0.221471\pi\)
0.0895065 + 0.995986i \(0.471471\pi\)
\(912\) 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 \(-0.746192\pi\)
0.999928 0.0119617i \(-0.00380762\pi\)
\(930\) 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 \(-0.589007\pi\)
0.874799 0.484486i \(-0.160993\pi\)
\(942\) 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 −0.195207 0.980762i \(-0.562538\pi\)
0.555471 + 0.831536i \(0.312538\pi\)
\(948\) 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 0.997684 0.0680246i \(-0.0216696\pi\)
−0.753570 + 0.657368i \(0.771670\pi\)
\(984\) 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 −0.199580 0.979881i \(-0.563958\pi\)
0.551756 + 0.834005i \(0.313958\pi\)
\(992\) 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 −0.867957 0.496639i \(-0.834567\pi\)
0.964915 + 0.262562i \(0.0845675\pi\)
\(998\) −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.712.2 8
17.2 even 8 inner 867.2.h.d.757.2 8
17.3 odd 16 51.2.d.b.16.2 yes 2
17.4 even 4 inner 867.2.h.d.733.2 8
17.5 odd 16 867.2.a.a.1.1 1
17.6 odd 16 867.2.e.d.829.2 4
17.7 odd 16 867.2.e.d.616.2 4
17.8 even 8 inner 867.2.h.d.688.2 8
17.9 even 8 inner 867.2.h.d.688.1 8
17.10 odd 16 867.2.e.d.616.1 4
17.11 odd 16 867.2.e.d.829.1 4
17.12 odd 16 867.2.a.b.1.1 1
17.13 even 4 inner 867.2.h.d.733.1 8
17.14 odd 16 51.2.d.b.16.1 2
17.15 even 8 inner 867.2.h.d.757.1 8
17.16 even 2 inner 867.2.h.d.712.1 8
51.5 even 16 2601.2.a.i.1.1 1
51.14 even 16 153.2.d.a.118.2 2
51.20 even 16 153.2.d.a.118.1 2
51.29 even 16 2601.2.a.j.1.1 1
68.3 even 16 816.2.c.c.577.1 2
68.31 even 16 816.2.c.c.577.2 2
85.3 even 16 1275.2.d.b.424.1 2
85.14 odd 16 1275.2.g.a.526.2 2
85.37 even 16 1275.2.d.d.424.2 2
85.48 even 16 1275.2.d.d.424.1 2
85.54 odd 16 1275.2.g.a.526.1 2
85.82 even 16 1275.2.d.b.424.2 2
136.3 even 16 3264.2.c.d.577.2 2
136.37 odd 16 3264.2.c.e.577.1 2
136.99 even 16 3264.2.c.d.577.1 2
136.133 odd 16 3264.2.c.e.577.2 2
204.71 odd 16 2448.2.c.j.577.2 2
204.167 odd 16 2448.2.c.j.577.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
51.2.d.b.16.1 2 17.14 odd 16
51.2.d.b.16.2 yes 2 17.3 odd 16
153.2.d.a.118.1 2 51.20 even 16
153.2.d.a.118.2 2 51.14 even 16
816.2.c.c.577.1 2 68.3 even 16
816.2.c.c.577.2 2 68.31 even 16
867.2.a.a.1.1 1 17.5 odd 16
867.2.a.b.1.1 1 17.12 odd 16
867.2.e.d.616.1 4 17.10 odd 16
867.2.e.d.616.2 4 17.7 odd 16
867.2.e.d.829.1 4 17.11 odd 16
867.2.e.d.829.2 4 17.6 odd 16
867.2.h.d.688.1 8 17.9 even 8 inner
867.2.h.d.688.2 8 17.8 even 8 inner
867.2.h.d.712.1 8 17.16 even 2 inner
867.2.h.d.712.2 8 1.1 even 1 trivial
867.2.h.d.733.1 8 17.13 even 4 inner
867.2.h.d.733.2 8 17.4 even 4 inner
867.2.h.d.757.1 8 17.15 even 8 inner
867.2.h.d.757.2 8 17.2 even 8 inner
1275.2.d.b.424.1 2 85.3 even 16
1275.2.d.b.424.2 2 85.82 even 16
1275.2.d.d.424.1 2 85.48 even 16
1275.2.d.d.424.2 2 85.37 even 16
1275.2.g.a.526.1 2 85.54 odd 16
1275.2.g.a.526.2 2 85.14 odd 16
2448.2.c.j.577.1 2 204.167 odd 16
2448.2.c.j.577.2 2 204.71 odd 16
2601.2.a.i.1.1 1 51.5 even 16
2601.2.a.j.1.1 1 51.29 even 16
3264.2.c.d.577.1 2 136.99 even 16
3264.2.c.d.577.2 2 136.3 even 16
3264.2.c.e.577.1 2 136.37 odd 16
3264.2.c.e.577.2 2 136.133 odd 16