Properties

Label 1078.2.e.o.177.1
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), 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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.o.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.41421 - 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} +1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.41421 - 2.44949i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.82843 q^{6} +1.00000 q^{8} +(-2.50000 + 4.33013i) q^{9} +(0.500000 + 0.866025i) q^{11} +(-1.41421 + 2.44949i) q^{12} +4.24264 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.41421 + 2.44949i) q^{17} +(-2.50000 - 4.33013i) q^{18} +(2.12132 - 3.67423i) q^{19} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.41421 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-2.12132 + 3.67423i) q^{26} +5.65685 q^{27} -4.00000 q^{29} +(3.53553 + 6.12372i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.41421 - 2.44949i) q^{33} -2.82843 q^{34} +5.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(2.12132 + 3.67423i) q^{38} +(-6.00000 - 10.3923i) q^{39} +2.82843 q^{41} +10.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(6.36396 - 11.0227i) q^{47} +2.82843 q^{48} -5.00000 q^{50} +(4.00000 - 6.92820i) q^{51} +(-2.12132 - 3.67423i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-2.82843 + 4.89898i) q^{54} -12.0000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-5.65685 - 9.79796i) q^{59} +(4.94975 - 8.57321i) q^{61} -7.07107 q^{62} +1.00000 q^{64} +(1.41421 + 2.44949i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(1.41421 - 2.44949i) q^{68} +16.9706 q^{69} +16.0000 q^{71} +(-2.50000 + 4.33013i) q^{72} +(4.24264 + 7.34847i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(7.07107 - 12.2474i) q^{75} -4.24264 q^{76} +12.0000 q^{78} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.41421 + 2.44949i) q^{82} -12.7279 q^{83} +(-5.00000 + 8.66025i) q^{86} +(5.65685 + 9.79796i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-3.53553 + 6.12372i) q^{89} +6.00000 q^{92} +(10.0000 - 17.3205i) q^{93} +(6.36396 + 11.0227i) q^{94} +(-1.41421 + 2.44949i) q^{96} -7.07107 q^{97} -5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 10 q^{9} + 2 q^{11} - 2 q^{16} - 10 q^{18} - 4 q^{22} - 12 q^{23} + 10 q^{25} - 16 q^{29} - 2 q^{32} + 20 q^{36} - 4 q^{37} - 24 q^{39} + 40 q^{43} + 2 q^{44} - 12 q^{46} - 20 q^{50} + 16 q^{51} - 4 q^{53} - 48 q^{57} + 8 q^{58} + 4 q^{64} - 16 q^{67} + 64 q^{71} - 10 q^{72} - 4 q^{74} + 48 q^{78} + 16 q^{79} - 2 q^{81} - 20 q^{86} + 2 q^{88} + 24 q^{92} + 40 q^{93} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.41421 2.44949i −0.816497 1.41421i −0.908248 0.418432i \(-0.862580\pi\)
0.0917517 0.995782i \(-0.470753\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 2.82843 1.15470
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −2.50000 + 4.33013i −0.833333 + 1.44338i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) −1.41421 + 2.44949i −0.408248 + 0.707107i
\(13\) 4.24264 1.17670 0.588348 0.808608i \(-0.299778\pi\)
0.588348 + 0.808608i \(0.299778\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.41421 + 2.44949i 0.342997 + 0.594089i 0.984988 0.172624i \(-0.0552245\pi\)
−0.641991 + 0.766712i \(0.721891\pi\)
\(18\) −2.50000 4.33013i −0.589256 1.02062i
\(19\) 2.12132 3.67423i 0.486664 0.842927i −0.513218 0.858258i \(-0.671547\pi\)
0.999882 + 0.0153309i \(0.00488018\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) −1.41421 2.44949i −0.288675 0.500000i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −2.12132 + 3.67423i −0.416025 + 0.720577i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 3.53553 + 6.12372i 0.635001 + 1.09985i 0.986515 + 0.163671i \(0.0523335\pi\)
−0.351514 + 0.936182i \(0.614333\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 1.41421 2.44949i 0.246183 0.426401i
\(34\) −2.82843 −0.485071
\(35\) 0 0
\(36\) 5.00000 0.833333
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 2.12132 + 3.67423i 0.344124 + 0.596040i
\(39\) −6.00000 10.3923i −0.960769 1.66410i
\(40\) 0 0
\(41\) 2.82843 0.441726 0.220863 0.975305i \(-0.429113\pi\)
0.220863 + 0.975305i \(0.429113\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) 6.36396 11.0227i 0.928279 1.60783i 0.142078 0.989855i \(-0.454621\pi\)
0.786201 0.617971i \(-0.212045\pi\)
\(48\) 2.82843 0.408248
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 4.00000 6.92820i 0.560112 0.970143i
\(52\) −2.12132 3.67423i −0.294174 0.509525i
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) −2.82843 + 4.89898i −0.384900 + 0.666667i
\(55\) 0 0
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) 2.00000 3.46410i 0.262613 0.454859i
\(59\) −5.65685 9.79796i −0.736460 1.27559i −0.954080 0.299552i \(-0.903163\pi\)
0.217620 0.976034i \(-0.430171\pi\)
\(60\) 0 0
\(61\) 4.94975 8.57321i 0.633750 1.09769i −0.353028 0.935613i \(-0.614848\pi\)
0.986778 0.162075i \(-0.0518186\pi\)
\(62\) −7.07107 −0.898027
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.41421 + 2.44949i 0.174078 + 0.301511i
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 1.41421 2.44949i 0.171499 0.297044i
\(69\) 16.9706 2.04302
\(70\) 0 0
\(71\) 16.0000 1.89885 0.949425 0.313993i \(-0.101667\pi\)
0.949425 + 0.313993i \(0.101667\pi\)
\(72\) −2.50000 + 4.33013i −0.294628 + 0.510310i
\(73\) 4.24264 + 7.34847i 0.496564 + 0.860073i 0.999992 0.00396356i \(-0.00126164\pi\)
−0.503429 + 0.864037i \(0.667928\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 7.07107 12.2474i 0.816497 1.41421i
\(76\) −4.24264 −0.486664
\(77\) 0 0
\(78\) 12.0000 1.35873
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.41421 + 2.44949i −0.156174 + 0.270501i
\(83\) −12.7279 −1.39707 −0.698535 0.715575i \(-0.746165\pi\)
−0.698535 + 0.715575i \(0.746165\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −5.00000 + 8.66025i −0.539164 + 0.933859i
\(87\) 5.65685 + 9.79796i 0.606478 + 1.05045i
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i \(-0.955610\pi\)
0.615526 + 0.788116i \(0.288944\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 10.0000 17.3205i 1.03695 1.79605i
\(94\) 6.36396 + 11.0227i 0.656392 + 1.13691i
\(95\) 0 0
\(96\) −1.41421 + 2.44949i −0.144338 + 0.250000i
\(97\) −7.07107 −0.717958 −0.358979 0.933346i \(-0.616875\pi\)
−0.358979 + 0.933346i \(0.616875\pi\)
\(98\) 0 0
\(99\) −5.00000 −0.502519
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 0.707107 + 1.22474i 0.0703598 + 0.121867i 0.899059 0.437828i \(-0.144252\pi\)
−0.828699 + 0.559694i \(0.810919\pi\)
\(102\) 4.00000 + 6.92820i 0.396059 + 0.685994i
\(103\) 0.707107 1.22474i 0.0696733 0.120678i −0.829084 0.559124i \(-0.811138\pi\)
0.898757 + 0.438446i \(0.144471\pi\)
\(104\) 4.24264 0.416025
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) 7.00000 12.1244i 0.676716 1.17211i −0.299249 0.954175i \(-0.596736\pi\)
0.975964 0.217931i \(-0.0699306\pi\)
\(108\) −2.82843 4.89898i −0.272166 0.471405i
\(109\) 7.00000 + 12.1244i 0.670478 + 1.16130i 0.977769 + 0.209687i \(0.0672444\pi\)
−0.307290 + 0.951616i \(0.599422\pi\)
\(110\) 0 0
\(111\) 5.65685 0.536925
\(112\) 0 0
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 6.00000 10.3923i 0.561951 0.973329i
\(115\) 0 0
\(116\) 2.00000 + 3.46410i 0.185695 + 0.321634i
\(117\) −10.6066 + 18.3712i −0.980581 + 1.69842i
\(118\) 11.3137 1.04151
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 4.94975 + 8.57321i 0.448129 + 0.776182i
\(123\) −4.00000 6.92820i −0.360668 0.624695i
\(124\) 3.53553 6.12372i 0.317500 0.549927i
\(125\) 0 0
\(126\) 0 0
\(127\) −20.0000 −1.77471 −0.887357 0.461084i \(-0.847461\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −14.1421 24.4949i −1.24515 2.15666i
\(130\) 0 0
\(131\) −3.53553 + 6.12372i −0.308901 + 0.535032i −0.978122 0.208031i \(-0.933295\pi\)
0.669221 + 0.743063i \(0.266628\pi\)
\(132\) −2.82843 −0.246183
\(133\) 0 0
\(134\) 8.00000 0.691095
\(135\) 0 0
\(136\) 1.41421 + 2.44949i 0.121268 + 0.210042i
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) −8.48528 + 14.6969i −0.722315 + 1.25109i
\(139\) 18.3848 1.55938 0.779688 0.626168i \(-0.215378\pi\)
0.779688 + 0.626168i \(0.215378\pi\)
\(140\) 0 0
\(141\) −36.0000 −3.03175
\(142\) −8.00000 + 13.8564i −0.671345 + 1.16280i
\(143\) 2.12132 + 3.67423i 0.177394 + 0.307255i
\(144\) −2.50000 4.33013i −0.208333 0.360844i
\(145\) 0 0
\(146\) −8.48528 −0.702247
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −4.00000 + 6.92820i −0.327693 + 0.567581i −0.982054 0.188602i \(-0.939604\pi\)
0.654361 + 0.756182i \(0.272938\pi\)
\(150\) 7.07107 + 12.2474i 0.577350 + 1.00000i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 2.12132 3.67423i 0.172062 0.298020i
\(153\) −14.1421 −1.14332
\(154\) 0 0
\(155\) 0 0
\(156\) −6.00000 + 10.3923i −0.480384 + 0.832050i
\(157\) −4.24264 7.34847i −0.338600 0.586472i 0.645570 0.763701i \(-0.276620\pi\)
−0.984170 + 0.177229i \(0.943287\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) −2.82843 + 4.89898i −0.224309 + 0.388514i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) −1.41421 2.44949i −0.110432 0.191273i
\(165\) 0 0
\(166\) 6.36396 11.0227i 0.493939 0.855528i
\(167\) −14.1421 −1.09435 −0.547176 0.837018i \(-0.684297\pi\)
−0.547176 + 0.837018i \(0.684297\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) 0 0
\(171\) 10.6066 + 18.3712i 0.811107 + 1.40488i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −3.53553 + 6.12372i −0.268802 + 0.465578i −0.968553 0.248809i \(-0.919961\pi\)
0.699751 + 0.714387i \(0.253294\pi\)
\(174\) −11.3137 −0.857690
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −16.0000 + 27.7128i −1.20263 + 2.08302i
\(178\) −3.53553 6.12372i −0.264999 0.458993i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 11.3137 0.840941 0.420471 0.907306i \(-0.361865\pi\)
0.420471 + 0.907306i \(0.361865\pi\)
\(182\) 0 0
\(183\) −28.0000 −2.06982
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) 10.0000 + 17.3205i 0.733236 + 1.27000i
\(187\) −1.41421 + 2.44949i −0.103418 + 0.179124i
\(188\) −12.7279 −0.928279
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) −1.41421 2.44949i −0.102062 0.176777i
\(193\) −3.00000 5.19615i −0.215945 0.374027i 0.737620 0.675216i \(-0.235950\pi\)
−0.953564 + 0.301189i \(0.902616\pi\)
\(194\) 3.53553 6.12372i 0.253837 0.439658i
\(195\) 0 0
\(196\) 0 0
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 2.50000 4.33013i 0.177667 0.307729i
\(199\) −4.94975 8.57321i −0.350878 0.607739i 0.635525 0.772080i \(-0.280784\pi\)
−0.986404 + 0.164341i \(0.947450\pi\)
\(200\) 2.50000 + 4.33013i 0.176777 + 0.306186i
\(201\) −11.3137 + 19.5959i −0.798007 + 1.38219i
\(202\) −1.41421 −0.0995037
\(203\) 0 0
\(204\) −8.00000 −0.560112
\(205\) 0 0
\(206\) 0.707107 + 1.22474i 0.0492665 + 0.0853320i
\(207\) −15.0000 25.9808i −1.04257 1.80579i
\(208\) −2.12132 + 3.67423i −0.147087 + 0.254762i
\(209\) 4.24264 0.293470
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) −1.00000 + 1.73205i −0.0686803 + 0.118958i
\(213\) −22.6274 39.1918i −1.55041 2.68538i
\(214\) 7.00000 + 12.1244i 0.478510 + 0.828804i
\(215\) 0 0
\(216\) 5.65685 0.384900
\(217\) 0 0
\(218\) −14.0000 −0.948200
\(219\) 12.0000 20.7846i 0.810885 1.40449i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) −2.82843 + 4.89898i −0.189832 + 0.328798i
\(223\) 21.2132 1.42054 0.710271 0.703929i \(-0.248573\pi\)
0.710271 + 0.703929i \(0.248573\pi\)
\(224\) 0 0
\(225\) −25.0000 −1.66667
\(226\) −8.00000 + 13.8564i −0.532152 + 0.921714i
\(227\) 3.53553 + 6.12372i 0.234662 + 0.406446i 0.959174 0.282816i \(-0.0912685\pi\)
−0.724513 + 0.689261i \(0.757935\pi\)
\(228\) 6.00000 + 10.3923i 0.397360 + 0.688247i
\(229\) 11.3137 19.5959i 0.747631 1.29493i −0.201325 0.979525i \(-0.564525\pi\)
0.948955 0.315410i \(-0.102142\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −4.00000 −0.262613
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) −10.6066 18.3712i −0.693375 1.20096i
\(235\) 0 0
\(236\) −5.65685 + 9.79796i −0.368230 + 0.637793i
\(237\) −22.6274 −1.46981
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 4.24264 + 7.34847i 0.273293 + 0.473357i 0.969703 0.244287i \(-0.0785540\pi\)
−0.696410 + 0.717644i \(0.745221\pi\)
\(242\) −0.500000 0.866025i −0.0321412 0.0556702i
\(243\) 7.07107 12.2474i 0.453609 0.785674i
\(244\) −9.89949 −0.633750
\(245\) 0 0
\(246\) 8.00000 0.510061
\(247\) 9.00000 15.5885i 0.572656 0.991870i
\(248\) 3.53553 + 6.12372i 0.224507 + 0.388857i
\(249\) 18.0000 + 31.1769i 1.14070 + 1.97576i
\(250\) 0 0
\(251\) −5.65685 −0.357057 −0.178529 0.983935i \(-0.557134\pi\)
−0.178529 + 0.983935i \(0.557134\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 10.0000 17.3205i 0.627456 1.08679i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −3.53553 + 6.12372i −0.220541 + 0.381987i −0.954972 0.296695i \(-0.904115\pi\)
0.734432 + 0.678683i \(0.237449\pi\)
\(258\) 28.2843 1.76090
\(259\) 0 0
\(260\) 0 0
\(261\) 10.0000 17.3205i 0.618984 1.07211i
\(262\) −3.53553 6.12372i −0.218426 0.378325i
\(263\) −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i \(-0.206023\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(264\) 1.41421 2.44949i 0.0870388 0.150756i
\(265\) 0 0
\(266\) 0 0
\(267\) 20.0000 1.22398
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) −5.65685 9.79796i −0.344904 0.597392i 0.640432 0.768015i \(-0.278755\pi\)
−0.985336 + 0.170623i \(0.945422\pi\)
\(270\) 0 0
\(271\) −4.24264 + 7.34847i −0.257722 + 0.446388i −0.965631 0.259916i \(-0.916305\pi\)
0.707909 + 0.706303i \(0.249639\pi\)
\(272\) −2.82843 −0.171499
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) −8.48528 14.6969i −0.510754 0.884652i
\(277\) 4.00000 + 6.92820i 0.240337 + 0.416275i 0.960810 0.277207i \(-0.0894088\pi\)
−0.720473 + 0.693482i \(0.756075\pi\)
\(278\) −9.19239 + 15.9217i −0.551323 + 0.954919i
\(279\) −35.3553 −2.11667
\(280\) 0 0
\(281\) 22.0000 1.31241 0.656205 0.754583i \(-0.272161\pi\)
0.656205 + 0.754583i \(0.272161\pi\)
\(282\) 18.0000 31.1769i 1.07188 1.85656i
\(283\) −3.53553 6.12372i −0.210166 0.364018i 0.741601 0.670842i \(-0.234067\pi\)
−0.951766 + 0.306824i \(0.900734\pi\)
\(284\) −8.00000 13.8564i −0.474713 0.822226i
\(285\) 0 0
\(286\) −4.24264 −0.250873
\(287\) 0 0
\(288\) 5.00000 0.294628
\(289\) 4.50000 7.79423i 0.264706 0.458484i
\(290\) 0 0
\(291\) 10.0000 + 17.3205i 0.586210 + 1.01535i
\(292\) 4.24264 7.34847i 0.248282 0.430037i
\(293\) −21.2132 −1.23929 −0.619644 0.784883i \(-0.712723\pi\)
−0.619644 + 0.784883i \(0.712723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 2.82843 + 4.89898i 0.164122 + 0.284268i
\(298\) −4.00000 6.92820i −0.231714 0.401340i
\(299\) −12.7279 + 22.0454i −0.736075 + 1.27492i
\(300\) −14.1421 −0.816497
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) 2.00000 3.46410i 0.114897 0.199007i
\(304\) 2.12132 + 3.67423i 0.121666 + 0.210732i
\(305\) 0 0
\(306\) 7.07107 12.2474i 0.404226 0.700140i
\(307\) 21.2132 1.21070 0.605351 0.795959i \(-0.293033\pi\)
0.605351 + 0.795959i \(0.293033\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) 0.707107 + 1.22474i 0.0400963 + 0.0694489i 0.885377 0.464873i \(-0.153900\pi\)
−0.845281 + 0.534322i \(0.820567\pi\)
\(312\) −6.00000 10.3923i −0.339683 0.588348i
\(313\) 14.8492 25.7196i 0.839329 1.45376i −0.0511279 0.998692i \(-0.516282\pi\)
0.890457 0.455068i \(-0.150385\pi\)
\(314\) 8.48528 0.478852
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) −2.82843 4.89898i −0.158610 0.274721i
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 0 0
\(321\) −39.5980 −2.21014
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 10.6066 + 18.3712i 0.588348 + 1.01905i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 19.7990 34.2929i 1.09489 1.89640i
\(328\) 2.82843 0.156174
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 6.36396 + 11.0227i 0.349268 + 0.604949i
\(333\) −5.00000 8.66025i −0.273998 0.474579i
\(334\) 7.07107 12.2474i 0.386912 0.670151i
\(335\) 0 0
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −2.50000 + 4.33013i −0.135982 + 0.235528i
\(339\) −22.6274 39.1918i −1.22895 2.12861i
\(340\) 0 0
\(341\) −3.53553 + 6.12372i −0.191460 + 0.331618i
\(342\) −21.2132 −1.14708
\(343\) 0 0
\(344\) 10.0000 0.539164
\(345\) 0 0
\(346\) −3.53553 6.12372i −0.190071 0.329213i
\(347\) −13.0000 22.5167i −0.697877 1.20876i −0.969201 0.246270i \(-0.920795\pi\)
0.271325 0.962488i \(-0.412538\pi\)
\(348\) 5.65685 9.79796i 0.303239 0.525226i
\(349\) −26.8701 −1.43832 −0.719161 0.694844i \(-0.755473\pi\)
−0.719161 + 0.694844i \(0.755473\pi\)
\(350\) 0 0
\(351\) 24.0000 1.28103
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −7.77817 13.4722i −0.413990 0.717053i 0.581331 0.813667i \(-0.302532\pi\)
−0.995322 + 0.0966144i \(0.969199\pi\)
\(354\) −16.0000 27.7128i −0.850390 1.47292i
\(355\) 0 0
\(356\) 7.07107 0.374766
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −6.00000 + 10.3923i −0.316668 + 0.548485i −0.979791 0.200026i \(-0.935897\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(360\) 0 0
\(361\) 0.500000 + 0.866025i 0.0263158 + 0.0455803i
\(362\) −5.65685 + 9.79796i −0.297318 + 0.514969i
\(363\) 2.82843 0.148454
\(364\) 0 0
\(365\) 0 0
\(366\) 14.0000 24.2487i 0.731792 1.26750i
\(367\) 10.6066 + 18.3712i 0.553660 + 0.958967i 0.998006 + 0.0631123i \(0.0201026\pi\)
−0.444346 + 0.895855i \(0.646564\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) −7.07107 + 12.2474i −0.368105 + 0.637577i
\(370\) 0 0
\(371\) 0 0
\(372\) −20.0000 −1.03695
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) −1.41421 2.44949i −0.0731272 0.126660i
\(375\) 0 0
\(376\) 6.36396 11.0227i 0.328196 0.568453i
\(377\) −16.9706 −0.874028
\(378\) 0 0
\(379\) 24.0000 1.23280 0.616399 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) 0 0
\(381\) 28.2843 + 48.9898i 1.44905 + 2.50982i
\(382\) −5.00000 8.66025i −0.255822 0.443097i
\(383\) 7.77817 13.4722i 0.397446 0.688397i −0.595964 0.803011i \(-0.703230\pi\)
0.993410 + 0.114614i \(0.0365632\pi\)
\(384\) 2.82843 0.144338
\(385\) 0 0
\(386\) 6.00000 0.305392
\(387\) −25.0000 + 43.3013i −1.27082 + 2.20113i
\(388\) 3.53553 + 6.12372i 0.179490 + 0.310885i
\(389\) 15.0000 + 25.9808i 0.760530 + 1.31728i 0.942578 + 0.333987i \(0.108394\pi\)
−0.182047 + 0.983290i \(0.558272\pi\)
\(390\) 0 0
\(391\) −16.9706 −0.858238
\(392\) 0 0
\(393\) 20.0000 1.00887
\(394\) 1.00000 1.73205i 0.0503793 0.0872595i
\(395\) 0 0
\(396\) 2.50000 + 4.33013i 0.125630 + 0.217597i
\(397\) −12.7279 + 22.0454i −0.638796 + 1.10643i 0.346901 + 0.937902i \(0.387234\pi\)
−0.985697 + 0.168526i \(0.946099\pi\)
\(398\) 9.89949 0.496217
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 15.0000 25.9808i 0.749064 1.29742i −0.199207 0.979957i \(-0.563837\pi\)
0.948272 0.317460i \(-0.102830\pi\)
\(402\) −11.3137 19.5959i −0.564276 0.977356i
\(403\) 15.0000 + 25.9808i 0.747203 + 1.29419i
\(404\) 0.707107 1.22474i 0.0351799 0.0609333i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) 4.00000 6.92820i 0.198030 0.342997i
\(409\) −14.1421 24.4949i −0.699284 1.21119i −0.968715 0.248175i \(-0.920169\pi\)
0.269432 0.963020i \(-0.413164\pi\)
\(410\) 0 0
\(411\) 8.48528 14.6969i 0.418548 0.724947i
\(412\) −1.41421 −0.0696733
\(413\) 0 0
\(414\) 30.0000 1.47442
\(415\) 0 0
\(416\) −2.12132 3.67423i −0.104006 0.180144i
\(417\) −26.0000 45.0333i −1.27323 2.20529i
\(418\) −2.12132 + 3.67423i −0.103757 + 0.179713i
\(419\) 14.1421 0.690889 0.345444 0.938439i \(-0.387728\pi\)
0.345444 + 0.938439i \(0.387728\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −13.0000 + 22.5167i −0.632830 + 1.09609i
\(423\) 31.8198 + 55.1135i 1.54713 + 2.67971i
\(424\) −1.00000 1.73205i −0.0485643 0.0841158i
\(425\) −7.07107 + 12.2474i −0.342997 + 0.594089i
\(426\) 45.2548 2.19260
\(427\) 0 0
\(428\) −14.0000 −0.676716
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) 0 0
\(431\) −4.00000 6.92820i −0.192673 0.333720i 0.753462 0.657491i \(-0.228382\pi\)
−0.946135 + 0.323772i \(0.895049\pi\)
\(432\) −2.82843 + 4.89898i −0.136083 + 0.235702i
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 7.00000 12.1244i 0.335239 0.580651i
\(437\) 12.7279 + 22.0454i 0.608859 + 1.05457i
\(438\) 12.0000 + 20.7846i 0.573382 + 0.993127i
\(439\) −12.7279 + 22.0454i −0.607471 + 1.05217i 0.384185 + 0.923256i \(0.374482\pi\)
−0.991656 + 0.128914i \(0.958851\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) −2.82843 4.89898i −0.134231 0.232495i
\(445\) 0 0
\(446\) −10.6066 + 18.3712i −0.502237 + 0.869900i
\(447\) 22.6274 1.07024
\(448\) 0 0
\(449\) 16.0000 0.755087 0.377543 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 12.5000 21.6506i 0.589256 1.02062i
\(451\) 1.41421 + 2.44949i 0.0665927 + 0.115342i
\(452\) −8.00000 13.8564i −0.376288 0.651751i
\(453\) 11.3137 19.5959i 0.531564 0.920697i
\(454\) −7.07107 −0.331862
\(455\) 0 0
\(456\) −12.0000 −0.561951
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 11.3137 + 19.5959i 0.528655 + 0.915657i
\(459\) 8.00000 + 13.8564i 0.373408 + 0.646762i
\(460\) 0 0
\(461\) 1.41421 0.0658665 0.0329332 0.999458i \(-0.489515\pi\)
0.0329332 + 0.999458i \(0.489515\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 2.00000 3.46410i 0.0928477 0.160817i
\(465\) 0 0
\(466\) −13.0000 22.5167i −0.602213 1.04306i
\(467\) −12.7279 + 22.0454i −0.588978 + 1.02014i 0.405389 + 0.914144i \(0.367136\pi\)
−0.994367 + 0.105995i \(0.966197\pi\)
\(468\) 21.2132 0.980581
\(469\) 0 0
\(470\) 0 0
\(471\) −12.0000 + 20.7846i −0.552931 + 0.957704i
\(472\) −5.65685 9.79796i −0.260378 0.450988i
\(473\) 5.00000 + 8.66025i 0.229900 + 0.398199i
\(474\) 11.3137 19.5959i 0.519656 0.900070i
\(475\) 21.2132 0.973329
\(476\) 0 0
\(477\) 10.0000 0.457869
\(478\) 0 0
\(479\) 14.1421 + 24.4949i 0.646171 + 1.11920i 0.984030 + 0.178004i \(0.0569639\pi\)
−0.337859 + 0.941197i \(0.609703\pi\)
\(480\) 0 0
\(481\) −4.24264 + 7.34847i −0.193448 + 0.335061i
\(482\) −8.48528 −0.386494
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) 7.07107 + 12.2474i 0.320750 + 0.555556i
\(487\) −19.0000 32.9090i −0.860972 1.49125i −0.870992 0.491298i \(-0.836523\pi\)
0.0100195 0.999950i \(-0.496811\pi\)
\(488\) 4.94975 8.57321i 0.224065 0.388091i
\(489\) −11.3137 −0.511624
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −4.00000 + 6.92820i −0.180334 + 0.312348i
\(493\) −5.65685 9.79796i −0.254772 0.441278i
\(494\) 9.00000 + 15.5885i 0.404929 + 0.701358i
\(495\) 0 0
\(496\) −7.07107 −0.317500
\(497\) 0 0
\(498\) −36.0000 −1.61320
\(499\) −18.0000 + 31.1769i −0.805791 + 1.39567i 0.109965 + 0.993935i \(0.464926\pi\)
−0.915756 + 0.401735i \(0.868407\pi\)
\(500\) 0 0
\(501\) 20.0000 + 34.6410i 0.893534 + 1.54765i
\(502\) 2.82843 4.89898i 0.126239 0.218652i
\(503\) 19.7990 0.882793 0.441397 0.897312i \(-0.354483\pi\)
0.441397 + 0.897312i \(0.354483\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) −7.07107 12.2474i −0.314037 0.543928i
\(508\) 10.0000 + 17.3205i 0.443678 + 0.768473i
\(509\) −8.48528 + 14.6969i −0.376103 + 0.651430i −0.990492 0.137574i \(-0.956070\pi\)
0.614388 + 0.789004i \(0.289403\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 12.0000 20.7846i 0.529813 0.917663i
\(514\) −3.53553 6.12372i −0.155946 0.270106i
\(515\) 0 0
\(516\) −14.1421 + 24.4949i −0.622573 + 1.07833i
\(517\) 12.7279 0.559773
\(518\) 0 0
\(519\) 20.0000 0.877903
\(520\) 0 0
\(521\) 0.707107 + 1.22474i 0.0309789 + 0.0536570i 0.881099 0.472931i \(-0.156804\pi\)
−0.850120 + 0.526589i \(0.823471\pi\)
\(522\) 10.0000 + 17.3205i 0.437688 + 0.758098i
\(523\) −2.12132 + 3.67423i −0.0927589 + 0.160663i −0.908671 0.417513i \(-0.862902\pi\)
0.815912 + 0.578176i \(0.196235\pi\)
\(524\) 7.07107 0.308901
\(525\) 0 0
\(526\) 4.00000 0.174408
\(527\) −10.0000 + 17.3205i −0.435607 + 0.754493i
\(528\) 1.41421 + 2.44949i 0.0615457 + 0.106600i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) 56.5685 2.45487
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) −10.0000 + 17.3205i −0.432742 + 0.749532i
\(535\) 0 0
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) 16.9706 29.3939i 0.732334 1.26844i
\(538\) 11.3137 0.487769
\(539\) 0 0
\(540\) 0 0
\(541\) 15.0000 25.9808i 0.644900 1.11700i −0.339424 0.940633i \(-0.610232\pi\)
0.984325 0.176367i \(-0.0564345\pi\)
\(542\) −4.24264 7.34847i −0.182237 0.315644i
\(543\) −16.0000 27.7128i −0.686626 1.18927i
\(544\) 1.41421 2.44949i 0.0606339 0.105021i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) 24.7487 + 42.8661i 1.05625 + 1.82948i
\(550\) −2.50000 4.33013i −0.106600 0.184637i
\(551\) −8.48528 + 14.6969i −0.361485 + 0.626111i
\(552\) 16.9706 0.722315
\(553\) 0 0
\(554\) −8.00000 −0.339887
\(555\) 0 0
\(556\) −9.19239 15.9217i −0.389844 0.675230i
\(557\) 3.00000 + 5.19615i 0.127114 + 0.220168i 0.922557 0.385860i \(-0.126095\pi\)
−0.795443 + 0.606028i \(0.792762\pi\)
\(558\) 17.6777 30.6186i 0.748355 1.29619i
\(559\) 42.4264 1.79445
\(560\) 0 0
\(561\) 8.00000 0.337760
\(562\) −11.0000 + 19.0526i −0.464007 + 0.803684i
\(563\) −20.5061 35.5176i −0.864229 1.49689i −0.867811 0.496895i \(-0.834473\pi\)
0.00358183 0.999994i \(-0.498860\pi\)
\(564\) 18.0000 + 31.1769i 0.757937 + 1.31278i
\(565\) 0 0
\(566\) 7.07107 0.297219
\(567\) 0 0
\(568\) 16.0000 0.671345
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 2.12132 3.67423i 0.0886969 0.153627i
\(573\) 28.2843 1.18159
\(574\) 0 0
\(575\) −30.0000 −1.25109
\(576\) −2.50000 + 4.33013i −0.104167 + 0.180422i
\(577\) 4.94975 + 8.57321i 0.206061 + 0.356908i 0.950470 0.310816i \(-0.100602\pi\)
−0.744409 + 0.667723i \(0.767269\pi\)
\(578\) 4.50000 + 7.79423i 0.187175 + 0.324197i
\(579\) −8.48528 + 14.6969i −0.352636 + 0.610784i
\(580\) 0 0
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) 1.00000 1.73205i 0.0414158 0.0717342i
\(584\) 4.24264 + 7.34847i 0.175562 + 0.304082i
\(585\) 0 0
\(586\) 10.6066 18.3712i 0.438155 0.758906i
\(587\) 5.65685 0.233483 0.116742 0.993162i \(-0.462755\pi\)
0.116742 + 0.993162i \(0.462755\pi\)
\(588\) 0 0
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) 2.82843 + 4.89898i 0.116346 + 0.201517i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −4.24264 + 7.34847i −0.174224 + 0.301765i −0.939893 0.341470i \(-0.889075\pi\)
0.765668 + 0.643236i \(0.222408\pi\)
\(594\) −5.65685 −0.232104
\(595\) 0 0
\(596\) 8.00000 0.327693
\(597\) −14.0000 + 24.2487i −0.572982 + 0.992434i
\(598\) −12.7279 22.0454i −0.520483 0.901504i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 7.07107 12.2474i 0.288675 0.500000i
\(601\) 11.3137 0.461496 0.230748 0.973014i \(-0.425883\pi\)
0.230748 + 0.973014i \(0.425883\pi\)
\(602\) 0 0
\(603\) 40.0000 1.62893
\(604\) 4.00000 6.92820i 0.162758 0.281905i
\(605\) 0 0
\(606\) 2.00000 + 3.46410i 0.0812444 + 0.140720i
\(607\) 8.48528 14.6969i 0.344407 0.596530i −0.640839 0.767675i \(-0.721413\pi\)
0.985246 + 0.171145i \(0.0547467\pi\)
\(608\) −4.24264 −0.172062
\(609\) 0 0
\(610\) 0 0
\(611\) 27.0000 46.7654i 1.09230 1.89192i
\(612\) 7.07107 + 12.2474i 0.285831 + 0.495074i
\(613\) 8.00000 + 13.8564i 0.323117 + 0.559655i 0.981129 0.193352i \(-0.0619359\pi\)
−0.658012 + 0.753007i \(0.728603\pi\)
\(614\) −10.6066 + 18.3712i −0.428048 + 0.741400i
\(615\) 0 0
\(616\) 0 0
\(617\) 28.0000 1.12724 0.563619 0.826035i \(-0.309409\pi\)
0.563619 + 0.826035i \(0.309409\pi\)
\(618\) 2.00000 3.46410i 0.0804518 0.139347i
\(619\) 7.07107 + 12.2474i 0.284210 + 0.492267i 0.972417 0.233248i \(-0.0749353\pi\)
−0.688207 + 0.725514i \(0.741602\pi\)
\(620\) 0 0
\(621\) −16.9706 + 29.3939i −0.681005 + 1.17954i
\(622\) −1.41421 −0.0567048
\(623\) 0 0
\(624\) 12.0000 0.480384
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 14.8492 + 25.7196i 0.593495 + 1.02796i
\(627\) −6.00000 10.3923i −0.239617 0.415029i
\(628\) −4.24264 + 7.34847i −0.169300 + 0.293236i
\(629\) −5.65685 −0.225554
\(630\) 0 0
\(631\) −30.0000 −1.19428 −0.597141 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) −36.7696 63.6867i −1.46146 2.53132i
\(634\) −9.00000 15.5885i −0.357436 0.619097i
\(635\) 0 0
\(636\) 5.65685 0.224309
\(637\) 0 0
\(638\) 4.00000 0.158362
\(639\) −40.0000 + 69.2820i −1.58238 + 2.74075i
\(640\) 0 0
\(641\) −22.0000 38.1051i −0.868948 1.50506i −0.863073 0.505079i \(-0.831463\pi\)
−0.00587459 0.999983i \(-0.501870\pi\)
\(642\) 19.7990 34.2929i 0.781404 1.35343i
\(643\) −33.9411 −1.33851 −0.669254 0.743034i \(-0.733386\pi\)
−0.669254 + 0.743034i \(0.733386\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) −16.2635 28.1691i −0.639382 1.10744i −0.985569 0.169277i \(-0.945857\pi\)
0.346186 0.938166i \(-0.387477\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 5.65685 9.79796i 0.222051 0.384604i
\(650\) −21.2132 −0.832050
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 15.0000 25.9808i 0.586995 1.01671i −0.407628 0.913148i \(-0.633644\pi\)
0.994623 0.103558i \(-0.0330227\pi\)
\(654\) 19.7990 + 34.2929i 0.774202 + 1.34096i
\(655\) 0 0
\(656\) −1.41421 + 2.44949i −0.0552158 + 0.0956365i
\(657\) −42.4264 −1.65521
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) 8.48528 + 14.6969i 0.330039 + 0.571645i 0.982519 0.186161i \(-0.0596047\pi\)
−0.652480 + 0.757806i \(0.726271\pi\)
\(662\) −4.00000 6.92820i −0.155464 0.269272i
\(663\) 16.9706 29.3939i 0.659082 1.14156i
\(664\) −12.7279 −0.493939
\(665\) 0 0
\(666\) 10.0000 0.387492
\(667\) 12.0000 20.7846i 0.464642 0.804783i
\(668\) 7.07107 + 12.2474i 0.273588 + 0.473868i
\(669\) −30.0000 51.9615i −1.15987 2.00895i
\(670\) 0 0
\(671\) 9.89949 0.382166
\(672\) 0 0
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 11.0000 19.0526i 0.423704 0.733877i
\(675\) 14.1421 + 24.4949i 0.544331 + 0.942809i
\(676\) −2.50000 4.33013i −0.0961538 0.166543i
\(677\) −4.94975 + 8.57321i −0.190234 + 0.329495i −0.945328 0.326122i \(-0.894258\pi\)
0.755094 + 0.655617i \(0.227591\pi\)
\(678\) 45.2548 1.73800
\(679\) 0 0
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) −3.53553 6.12372i −0.135383 0.234490i
\(683\) −16.0000 27.7128i −0.612223 1.06040i −0.990865 0.134858i \(-0.956942\pi\)
0.378642 0.925543i \(-0.376391\pi\)
\(684\) 10.6066 18.3712i 0.405554 0.702439i
\(685\) 0 0
\(686\) 0 0
\(687\) −64.0000 −2.44175
\(688\) −5.00000 + 8.66025i −0.190623 + 0.330169i
\(689\) −4.24264 7.34847i −0.161632 0.279954i
\(690\) 0 0
\(691\) −19.7990 + 34.2929i −0.753189 + 1.30456i 0.193081 + 0.981183i \(0.438152\pi\)
−0.946270 + 0.323379i \(0.895181\pi\)
\(692\) 7.07107 0.268802
\(693\) 0 0
\(694\) 26.0000 0.986947
\(695\) 0 0
\(696\) 5.65685 + 9.79796i 0.214423 + 0.371391i
\(697\) 4.00000 + 6.92820i 0.151511 + 0.262424i
\(698\) 13.4350 23.2702i 0.508523 0.880788i
\(699\) 73.5391 2.78150
\(700\) 0 0
\(701\) −10.0000 −0.377695 −0.188847 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) −12.0000 + 20.7846i −0.452911 + 0.784465i
\(703\) 4.24264 + 7.34847i 0.160014 + 0.277153i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 15.5563 0.585471
\(707\) 0 0
\(708\) 32.0000 1.20263
\(709\) 19.0000 32.9090i 0.713560 1.23592i −0.249952 0.968258i \(-0.580415\pi\)
0.963512 0.267664i \(-0.0862517\pi\)
\(710\) 0 0
\(711\) 20.0000 + 34.6410i 0.750059 + 1.29914i
\(712\) −3.53553 + 6.12372i −0.132500 + 0.229496i
\(713\) −42.4264 −1.58888
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) −6.00000 10.3923i −0.223918 0.387837i
\(719\) −16.2635 + 28.1691i −0.606525 + 1.05053i 0.385284 + 0.922798i \(0.374103\pi\)
−0.991809 + 0.127733i \(0.959230\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.00000 −0.0372161
\(723\) 12.0000 20.7846i 0.446285 0.772988i
\(724\) −5.65685 9.79796i −0.210235 0.364138i
\(725\) −10.0000 17.3205i −0.371391 0.643268i
\(726\) −1.41421 + 2.44949i −0.0524864 + 0.0909091i
\(727\) −46.6690 −1.73086 −0.865430 0.501031i \(-0.832954\pi\)
−0.865430 + 0.501031i \(0.832954\pi\)
\(728\) 0 0
\(729\) −43.0000 −1.59259
\(730\) 0 0
\(731\) 14.1421 + 24.4949i 0.523066 + 0.905977i
\(732\) 14.0000 + 24.2487i 0.517455 + 0.896258i
\(733\) −3.53553 + 6.12372i −0.130588 + 0.226185i −0.923903 0.382626i \(-0.875020\pi\)
0.793315 + 0.608811i \(0.208353\pi\)
\(734\) −21.2132 −0.782994
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 4.00000 6.92820i 0.147342 0.255204i
\(738\) −7.07107 12.2474i −0.260290 0.450835i
\(739\) 6.00000 + 10.3923i 0.220714 + 0.382287i 0.955025 0.296526i \(-0.0958281\pi\)
−0.734311 + 0.678813i \(0.762495\pi\)
\(740\) 0 0
\(741\) −50.9117 −1.87029
\(742\) 0 0
\(743\) −8.00000 −0.293492 −0.146746 0.989174i \(-0.546880\pi\)
−0.146746 + 0.989174i \(0.546880\pi\)
\(744\) 10.0000 17.3205i 0.366618 0.635001i
\(745\) 0 0
\(746\) 5.00000 + 8.66025i 0.183063 + 0.317074i
\(747\) 31.8198 55.1135i 1.16423 2.01650i
\(748\) 2.82843 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) 6.36396 + 11.0227i 0.232070 + 0.401957i
\(753\) 8.00000 + 13.8564i 0.291536 + 0.504956i
\(754\) 8.48528 14.6969i 0.309016 0.535231i
\(755\) 0 0
\(756\) 0 0
\(757\) 46.0000 1.67190 0.835949 0.548807i \(-0.184918\pi\)
0.835949 + 0.548807i \(0.184918\pi\)
\(758\) −12.0000 + 20.7846i −0.435860 + 0.754931i
\(759\) 8.48528 + 14.6969i 0.307996 + 0.533465i
\(760\) 0 0
\(761\) 16.9706 29.3939i 0.615182 1.06553i −0.375170 0.926956i \(-0.622416\pi\)
0.990352 0.138571i \(-0.0442510\pi\)
\(762\) −56.5685 −2.04926
\(763\) 0 0
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) 7.77817 + 13.4722i 0.281037 + 0.486770i
\(767\) −24.0000 41.5692i −0.866590 1.50098i
\(768\) −1.41421 + 2.44949i −0.0510310 + 0.0883883i
\(769\) 5.65685 0.203991 0.101996 0.994785i \(-0.467477\pi\)
0.101996 + 0.994785i \(0.467477\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) −3.00000 + 5.19615i −0.107972 + 0.187014i
\(773\) 24.0416 + 41.6413i 0.864717 + 1.49773i 0.867328 + 0.497738i \(0.165836\pi\)
−0.00261021 + 0.999997i \(0.500831\pi\)
\(774\) −25.0000 43.3013i −0.898606 1.55643i
\(775\) −17.6777 + 30.6186i −0.635001 + 1.09985i
\(776\) −7.07107 −0.253837
\(777\) 0 0
\(778\) −30.0000 −1.07555
\(779\) 6.00000 10.3923i 0.214972 0.372343i
\(780\) 0 0
\(781\) 8.00000 + 13.8564i 0.286263 + 0.495821i
\(782\) 8.48528 14.6969i 0.303433 0.525561i
\(783\) −22.6274 −0.808638
\(784\) 0 0
\(785\) 0 0
\(786\) −10.0000 + 17.3205i −0.356688 + 0.617802i
\(787\) −4.94975 8.57321i −0.176439 0.305602i 0.764219 0.644957i \(-0.223125\pi\)
−0.940658 + 0.339355i \(0.889791\pi\)
\(788\) 1.00000 + 1.73205i 0.0356235 + 0.0617018i
\(789\) −5.65685 + 9.79796i −0.201389 + 0.348817i
\(790\) 0 0
\(791\) 0 0
\(792\) −5.00000 −0.177667
\(793\) 21.0000 36.3731i 0.745732 1.29165i
\(794\) −12.7279 22.0454i −0.451697 0.782362i
\(795\) 0 0
\(796\) −4.94975 + 8.57321i −0.175439 + 0.303870i
\(797\) −2.82843 −0.100188 −0.0500940 0.998745i \(-0.515952\pi\)
−0.0500940 + 0.998745i \(0.515952\pi\)
\(798\) 0 0
\(799\) 36.0000 1.27359
\(800\) 2.50000 4.33013i 0.0883883 0.153093i
\(801\) −17.6777 30.6186i −0.624610 1.08186i
\(802\) 15.0000 + 25.9808i 0.529668 + 0.917413i
\(803\) −4.24264 + 7.34847i −0.149720 + 0.259322i
\(804\) 22.6274 0.798007
\(805\) 0 0
\(806\) −30.0000 −1.05670
\(807\) −16.0000 + 27.7128i −0.563227 + 0.975537i
\(808\) 0.707107 + 1.22474i 0.0248759 + 0.0430864i
\(809\) 3.00000 + 5.19615i 0.105474 + 0.182687i 0.913932 0.405868i \(-0.133031\pi\)
−0.808458 + 0.588555i \(0.799697\pi\)
\(810\) 0 0
\(811\) −15.5563 −0.546257 −0.273129 0.961978i \(-0.588058\pi\)
−0.273129 + 0.961978i \(0.588058\pi\)
\(812\) 0 0
\(813\) 24.0000 0.841717
\(814\) 1.00000 1.73205i 0.0350500 0.0607083i
\(815\) 0 0
\(816\) 4.00000 + 6.92820i 0.140028 + 0.242536i
\(817\) 21.2132 36.7423i 0.742156 1.28545i
\(818\) 28.2843 0.988936
\(819\) 0 0
\(820\) 0 0
\(821\) 4.00000 6.92820i 0.139601 0.241796i −0.787745 0.616002i \(-0.788751\pi\)
0.927346 + 0.374206i \(0.122085\pi\)
\(822\) 8.48528 + 14.6969i 0.295958 + 0.512615i
\(823\) 1.00000 + 1.73205i 0.0348578 + 0.0603755i 0.882928 0.469508i \(-0.155569\pi\)
−0.848070 + 0.529884i \(0.822235\pi\)
\(824\) 0.707107 1.22474i 0.0246332 0.0426660i
\(825\) 14.1421 0.492366
\(826\) 0 0
\(827\) 28.0000 0.973655 0.486828 0.873498i \(-0.338154\pi\)
0.486828 + 0.873498i \(0.338154\pi\)
\(828\) −15.0000 + 25.9808i −0.521286 + 0.902894i
\(829\) −16.9706 29.3939i −0.589412 1.02089i −0.994310 0.106529i \(-0.966026\pi\)
0.404898 0.914362i \(-0.367307\pi\)
\(830\) 0 0
\(831\) 11.3137 19.5959i 0.392468 0.679775i
\(832\) 4.24264 0.147087
\(833\) 0 0
\(834\) 52.0000 1.80061
\(835\) 0 0
\(836\) −2.12132 3.67423i −0.0733674 0.127076i
\(837\) 20.0000 + 34.6410i 0.691301 + 1.19737i
\(838\) −7.07107 + 12.2474i −0.244266 + 0.423081i
\(839\) −43.8406 −1.51355 −0.756773 0.653678i \(-0.773225\pi\)
−0.756773 + 0.653678i \(0.773225\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 1.00000 1.73205i 0.0344623 0.0596904i
\(843\) −31.1127 53.8888i −1.07158 1.85603i
\(844\) −13.0000 22.5167i −0.447478 0.775055i
\(845\) 0 0
\(846\) −63.6396 −2.18797
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) −10.0000 + 17.3205i −0.343199 + 0.594438i
\(850\) −7.07107 12.2474i −0.242536 0.420084i
\(851\) −6.00000 10.3923i −0.205677 0.356244i
\(852\) −22.6274 + 39.1918i −0.775203 + 1.34269i
\(853\) −15.5563 −0.532639 −0.266320 0.963885i \(-0.585808\pi\)
−0.266320 + 0.963885i \(0.585808\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 7.00000 12.1244i 0.239255 0.414402i
\(857\) −8.48528 14.6969i −0.289852 0.502038i 0.683922 0.729555i \(-0.260273\pi\)
−0.973774 + 0.227517i \(0.926939\pi\)
\(858\) 6.00000 + 10.3923i 0.204837 + 0.354787i
\(859\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 8.00000 0.272481
\(863\) −3.00000 + 5.19615i −0.102121 + 0.176879i −0.912558 0.408946i \(-0.865896\pi\)
0.810437 + 0.585826i \(0.199230\pi\)
\(864\) −2.82843 4.89898i −0.0962250 0.166667i
\(865\) 0 0
\(866\) −14.8492 + 25.7196i −0.504598 + 0.873989i
\(867\) −25.4558 −0.864526
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 0 0
\(871\) −16.9706 29.3939i −0.575026 0.995974i
\(872\) 7.00000 + 12.1244i 0.237050 + 0.410582i
\(873\) 17.6777 30.6186i 0.598298 1.03628i
\(874\) −25.4558 −0.861057
\(875\) 0 0
\(876\) −24.0000 −0.810885
\(877\) 1.00000 1.73205i 0.0337676 0.0584872i −0.848648 0.528958i \(-0.822583\pi\)
0.882415 + 0.470471i \(0.155916\pi\)
\(878\) −12.7279 22.0454i −0.429547 0.743996i
\(879\) 30.0000 + 51.9615i 1.01187 + 1.75262i
\(880\) 0 0
\(881\) −12.7279 −0.428815 −0.214407 0.976744i \(-0.568782\pi\)
−0.214407 + 0.976744i \(0.568782\pi\)
\(882\) 0 0
\(883\) −12.0000 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 6.00000 10.3923i 0.201802 0.349531i
\(885\) 0 0
\(886\) −6.00000 10.3923i −0.201574 0.349136i
\(887\) −11.3137 + 19.5959i −0.379877 + 0.657967i −0.991044 0.133535i \(-0.957367\pi\)
0.611167 + 0.791502i \(0.290700\pi\)
\(888\) 5.65685 0.189832
\(889\) 0 0
\(890\) 0 0
\(891\) 0.500000 0.866025i 0.0167506 0.0290129i
\(892\) −10.6066 18.3712i −0.355135 0.615112i
\(893\) −27.0000 46.7654i −0.903521 1.56494i
\(894\) −11.3137 + 19.5959i −0.378387 + 0.655386i
\(895\) 0 0
\(896\) 0 0
\(897\) 72.0000 2.40401
\(898\) −8.00000 + 13.8564i −0.266963 + 0.462394i
\(899\) −14.1421 24.4949i −0.471667 0.816951i
\(900\) 12.5000 + 21.6506i 0.416667 + 0.721688i
\(901\) 2.82843 4.89898i 0.0942286 0.163209i
\(902\) −2.82843 −0.0941763
\(903\) 0 0
\(904\) 16.0000 0.532152
\(905\) 0 0
\(906\) 11.3137 + 19.5959i 0.375873 + 0.651031i
\(907\) −8.00000 13.8564i −0.265636 0.460094i 0.702094 0.712084i \(-0.252248\pi\)
−0.967730 + 0.251990i \(0.918915\pi\)
\(908\) 3.53553 6.12372i 0.117331 0.203223i
\(909\) −7.07107 −0.234533
\(910\) 0 0
\(911\) 30.0000 0.993944 0.496972 0.867766i \(-0.334445\pi\)
0.496972 + 0.867766i \(0.334445\pi\)
\(912\) 6.00000 10.3923i 0.198680 0.344124i
\(913\) −6.36396 11.0227i −0.210616 0.364798i
\(914\) 11.0000 + 19.0526i 0.363848 + 0.630203i
\(915\) 0 0
\(916\) −22.6274 −0.747631
\(917\) 0 0
\(918\) −16.0000 −0.528079
\(919\) 8.00000 13.8564i 0.263896 0.457081i −0.703378 0.710816i \(-0.748326\pi\)
0.967274 + 0.253735i \(0.0816592\pi\)
\(920\) 0 0
\(921\) −30.0000 51.9615i −0.988534 1.71219i
\(922\) −0.707107 + 1.22474i −0.0232873 + 0.0403348i
\(923\) 67.8823 2.23437
\(924\) 0 0
\(925\) −10.0000 −0.328798
\(926\) 8.00000 13.8564i 0.262896 0.455350i
\(927\) 3.53553 + 6.12372i 0.116122 + 0.201129i
\(928\) 2.00000 + 3.46410i 0.0656532 + 0.113715i
\(929\) 13.4350 23.2702i 0.440789 0.763469i −0.556959 0.830540i \(-0.688032\pi\)
0.997748 + 0.0670709i \(0.0213654\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 26.0000 0.851658
\(933\) 2.00000 3.46410i 0.0654771 0.113410i
\(934\) −12.7279 22.0454i −0.416470 0.721348i
\(935\) 0 0
\(936\) −10.6066 + 18.3712i −0.346688 + 0.600481i
\(937\) −8.48528 −0.277202 −0.138601 0.990348i \(-0.544261\pi\)
−0.138601 + 0.990348i \(0.544261\pi\)
\(938\) 0 0
\(939\) −84.0000 −2.74124
\(940\) 0 0
\(941\) −16.2635 28.1691i −0.530174 0.918287i −0.999380 0.0351991i \(-0.988793\pi\)
0.469207 0.883088i \(-0.344540\pi\)
\(942\) −12.0000 20.7846i −0.390981 0.677199i
\(943\) −8.48528 + 14.6969i −0.276319 + 0.478598i
\(944\) 11.3137 0.368230
\(945\) 0 0
\(946\) −10.0000 −0.325128
\(947\) −2.00000 + 3.46410i −0.0649913 + 0.112568i −0.896690 0.442659i \(-0.854035\pi\)
0.831699 + 0.555227i \(0.187369\pi\)
\(948\) 11.3137 + 19.5959i 0.367452 + 0.636446i
\(949\) 18.0000 + 31.1769i 0.584305 + 1.01205i
\(950\) −10.6066 + 18.3712i −0.344124 + 0.596040i
\(951\) 50.9117 1.65092
\(952\) 0 0
\(953\) −46.0000 −1.49009 −0.745043 0.667016i \(-0.767571\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(954\) −5.00000 + 8.66025i −0.161881 + 0.280386i
\(955\) 0 0
\(956\) 0 0
\(957\) −5.65685 + 9.79796i −0.182860 + 0.316723i
\(958\) −28.2843 −0.913823
\(959\) 0 0
\(960\) 0 0
\(961\) −9.50000 + 16.4545i −0.306452 + 0.530790i
\(962\) −4.24264 7.34847i −0.136788 0.236924i
\(963\) 35.0000 + 60.6218i 1.12786 + 1.95351i
\(964\) 4.24264 7.34847i 0.136646 0.236678i
\(965\) 0 0
\(966\) 0 0
\(967\) −52.0000 −1.67221 −0.836104 0.548572i \(-0.815172\pi\)
−0.836104 + 0.548572i \(0.815172\pi\)
\(968\) −0.500000 + 0.866025i −0.0160706 + 0.0278351i
\(969\) −16.9706 29.3939i −0.545173 0.944267i
\(970\) 0 0
\(971\) 7.07107 12.2474i 0.226921 0.393039i −0.729973 0.683476i \(-0.760467\pi\)
0.956894 + 0.290437i \(0.0938006\pi\)
\(972\) −14.1421 −0.453609
\(973\) 0 0
\(974\) 38.0000 1.21760
\(975\) 30.0000 51.9615i 0.960769 1.66410i
\(976\) 4.94975 + 8.57321i 0.158438 + 0.274422i
\(977\) 16.0000 + 27.7128i 0.511885 + 0.886611i 0.999905 + 0.0137788i \(0.00438608\pi\)
−0.488020 + 0.872833i \(0.662281\pi\)
\(978\) 5.65685 9.79796i 0.180886 0.313304i
\(979\) −7.07107 −0.225992
\(980\) 0 0
\(981\) −70.0000 −2.23493
\(982\) −6.00000 + 10.3923i −0.191468 + 0.331632i
\(983\) 13.4350 + 23.2702i 0.428511 + 0.742203i 0.996741 0.0806670i \(-0.0257050\pi\)
−0.568230 + 0.822870i \(0.692372\pi\)
\(984\) −4.00000 6.92820i −0.127515 0.220863i
\(985\) 0 0
\(986\) 11.3137 0.360302
\(987\) 0 0
\(988\) −18.0000 −0.572656
\(989\) −30.0000 + 51.9615i −0.953945 + 1.65228i
\(990\) 0 0
\(991\) 8.00000 + 13.8564i 0.254128 + 0.440163i 0.964658 0.263504i \(-0.0848781\pi\)
−0.710530 + 0.703667i \(0.751545\pi\)
\(992\) 3.53553 6.12372i 0.112253 0.194428i
\(993\) 22.6274 0.718059
\(994\) 0 0
\(995\) 0 0
\(996\) 18.0000 31.1769i 0.570352 0.987878i
\(997\) 10.6066 + 18.3712i 0.335914 + 0.581821i 0.983660 0.180036i \(-0.0576214\pi\)
−0.647746 + 0.761857i \(0.724288\pi\)
\(998\) −18.0000 31.1769i −0.569780 0.986888i
\(999\) −5.65685 + 9.79796i −0.178975 + 0.309994i
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 1078.2.e.o.177.1 4
7.2 even 3 1078.2.a.v.1.2 yes 2
7.3 odd 6 inner 1078.2.e.o.67.2 4
7.4 even 3 inner 1078.2.e.o.67.1 4
7.5 odd 6 1078.2.a.v.1.1 2
7.6 odd 2 inner 1078.2.e.o.177.2 4
21.2 odd 6 9702.2.a.co.1.2 2
21.5 even 6 9702.2.a.co.1.1 2
28.19 even 6 8624.2.a.bz.1.2 2
28.23 odd 6 8624.2.a.bz.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1078.2.a.v.1.1 2 7.5 odd 6
1078.2.a.v.1.2 yes 2 7.2 even 3
1078.2.e.o.67.1 4 7.4 even 3 inner
1078.2.e.o.67.2 4 7.3 odd 6 inner
1078.2.e.o.177.1 4 1.1 even 1 trivial
1078.2.e.o.177.2 4 7.6 odd 2 inner
8624.2.a.bz.1.1 2 28.23 odd 6
8624.2.a.bz.1.2 2 28.19 even 6
9702.2.a.co.1.1 2 21.5 even 6
9702.2.a.co.1.2 2 21.2 odd 6