Properties

Label 490.2.i.b.79.1
Level $490$
Weight $2$
Character 490.79
Analytic conductor $3.913$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [490,2,Mod(79,490)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(490, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("490.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\), 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: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 490.79
Dual form 490.2.i.b.459.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} +3.00000 q^{6} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.23205 + 0.133975i) q^{5} +3.00000 q^{6} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(-1.86603 - 1.23205i) q^{10} +(-2.59808 - 1.50000i) q^{12} -2.00000i q^{13} +(-6.00000 + 3.00000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(1.00000 - 1.73205i) q^{19} +(1.00000 + 2.00000i) q^{20} +(-0.866025 - 0.500000i) q^{23} +(1.50000 + 2.59808i) q^{24} +(4.96410 + 0.598076i) q^{25} +(-1.00000 + 1.73205i) q^{26} +9.00000i q^{27} +1.00000 q^{29} +(6.69615 + 0.401924i) q^{30} +(5.00000 + 8.66025i) q^{31} +(0.866025 - 0.500000i) q^{32} -2.00000 q^{34} +6.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(3.00000 + 5.19615i) q^{39} +(0.133975 - 2.23205i) q^{40} +3.00000 q^{41} -5.00000i q^{43} +(7.39230 - 11.1962i) q^{45} +(0.500000 + 0.866025i) q^{46} +(6.92820 + 4.00000i) q^{47} -3.00000i q^{48} +(-4.00000 - 3.00000i) q^{50} +(-3.00000 + 5.19615i) q^{51} +(1.73205 - 1.00000i) q^{52} +(5.19615 - 3.00000i) q^{53} +(4.50000 - 7.79423i) q^{54} +6.00000i q^{57} +(-0.866025 - 0.500000i) q^{58} +(-1.00000 - 1.73205i) q^{59} +(-5.59808 - 3.69615i) q^{60} +(-4.50000 + 7.79423i) q^{61} -10.0000i q^{62} -1.00000 q^{64} +(0.267949 - 4.46410i) q^{65} +(-6.06218 + 3.50000i) q^{67} +(1.73205 + 1.00000i) q^{68} +3.00000 q^{69} +6.00000 q^{71} +(-5.19615 - 3.00000i) q^{72} +(-8.66025 + 5.00000i) q^{73} +(-4.00000 - 6.92820i) q^{74} +(-13.7942 + 5.89230i) q^{75} +2.00000 q^{76} -6.00000i q^{78} +(-5.00000 + 8.66025i) q^{79} +(-1.23205 + 1.86603i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.59808 - 1.50000i) q^{82} -9.00000i q^{83} +(4.00000 - 2.00000i) q^{85} +(-2.50000 + 4.33013i) q^{86} +(-2.59808 + 1.50000i) q^{87} +(3.50000 - 6.06218i) q^{89} +(-12.0000 + 6.00000i) q^{90} -1.00000i q^{92} +(-25.9808 - 15.0000i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(2.46410 - 3.73205i) q^{95} +(-1.50000 + 2.59808i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 2 q^{5} + 12 q^{6} + 12 q^{9} - 4 q^{10} - 24 q^{15} - 2 q^{16} + 4 q^{19} + 4 q^{20} + 6 q^{24} + 6 q^{25} - 4 q^{26} + 4 q^{29} + 6 q^{30} + 20 q^{31} - 8 q^{34} + 24 q^{36} + 12 q^{39} + 4 q^{40} + 12 q^{41} - 12 q^{45} + 2 q^{46} - 16 q^{50} - 12 q^{51} + 18 q^{54} - 4 q^{59} - 12 q^{60} - 18 q^{61} - 4 q^{64} + 8 q^{65} + 12 q^{69} + 24 q^{71} - 16 q^{74} - 24 q^{75} + 8 q^{76} - 20 q^{79} + 2 q^{80} - 18 q^{81} + 16 q^{85} - 10 q^{86} + 14 q^{89} - 48 q^{90} - 16 q^{94} - 4 q^{95} - 6 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −2.59808 + 1.50000i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 2.23205 + 0.133975i 0.998203 + 0.0599153i
\(6\) 3.00000 1.22474
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 5.19615i 1.00000 1.73205i
\(10\) −1.86603 1.23205i −0.590089 0.389609i
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) −2.59808 1.50000i −0.750000 0.433013i
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 0 0
\(15\) −6.00000 + 3.00000i −1.54919 + 0.774597i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) −5.19615 + 3.00000i −1.22474 + 0.707107i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 1.00000 + 2.00000i 0.223607 + 0.447214i
\(21\) 0 0
\(22\) 0 0
\(23\) −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i \(-0.366580\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 9.00000i 1.73205i
\(28\) 0 0
\(29\) 1.00000 0.185695 0.0928477 0.995680i \(-0.470403\pi\)
0.0928477 + 0.995680i \(0.470403\pi\)
\(30\) 6.69615 + 0.401924i 1.22254 + 0.0733809i
\(31\) 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) 6.92820 + 4.00000i 1.13899 + 0.657596i 0.946180 0.323640i \(-0.104907\pi\)
0.192809 + 0.981236i \(0.438240\pi\)
\(38\) −1.73205 + 1.00000i −0.280976 + 0.162221i
\(39\) 3.00000 + 5.19615i 0.480384 + 0.832050i
\(40\) 0.133975 2.23205i 0.0211832 0.352918i
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 0 0
\(43\) 5.00000i 0.762493i −0.924473 0.381246i \(-0.875495\pi\)
0.924473 0.381246i \(-0.124505\pi\)
\(44\) 0 0
\(45\) 7.39230 11.1962i 1.10198 1.66902i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) 6.92820 + 4.00000i 1.01058 + 0.583460i 0.911362 0.411606i \(-0.135032\pi\)
0.0992202 + 0.995066i \(0.468365\pi\)
\(48\) 3.00000i 0.433013i
\(49\) 0 0
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) −3.00000 + 5.19615i −0.420084 + 0.727607i
\(52\) 1.73205 1.00000i 0.240192 0.138675i
\(53\) 5.19615 3.00000i 0.713746 0.412082i −0.0987002 0.995117i \(-0.531468\pi\)
0.812447 + 0.583036i \(0.198135\pi\)
\(54\) 4.50000 7.79423i 0.612372 1.06066i
\(55\) 0 0
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) −0.866025 0.500000i −0.113715 0.0656532i
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) −5.59808 3.69615i −0.722709 0.477171i
\(61\) −4.50000 + 7.79423i −0.576166 + 0.997949i 0.419748 + 0.907641i \(0.362118\pi\)
−0.995914 + 0.0903080i \(0.971215\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.267949 4.46410i 0.0332350 0.553704i
\(66\) 0 0
\(67\) −6.06218 + 3.50000i −0.740613 + 0.427593i −0.822292 0.569066i \(-0.807305\pi\)
0.0816792 + 0.996659i \(0.473972\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) −5.19615 3.00000i −0.612372 0.353553i
\(73\) −8.66025 + 5.00000i −1.01361 + 0.585206i −0.912245 0.409644i \(-0.865653\pi\)
−0.101361 + 0.994850i \(0.532320\pi\)
\(74\) −4.00000 6.92820i −0.464991 0.805387i
\(75\) −13.7942 + 5.89230i −1.59282 + 0.680385i
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 6.00000i 0.679366i
\(79\) −5.00000 + 8.66025i −0.562544 + 0.974355i 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) −1.23205 + 1.86603i −0.137747 + 0.208628i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −2.59808 1.50000i −0.286910 0.165647i
\(83\) 9.00000i 0.987878i −0.869496 0.493939i \(-0.835557\pi\)
0.869496 0.493939i \(-0.164443\pi\)
\(84\) 0 0
\(85\) 4.00000 2.00000i 0.433861 0.216930i
\(86\) −2.50000 + 4.33013i −0.269582 + 0.466930i
\(87\) −2.59808 + 1.50000i −0.278543 + 0.160817i
\(88\) 0 0
\(89\) 3.50000 6.06218i 0.370999 0.642590i −0.618720 0.785611i \(-0.712349\pi\)
0.989720 + 0.143022i \(0.0456819\pi\)
\(90\) −12.0000 + 6.00000i −1.26491 + 0.632456i
\(91\) 0 0
\(92\) 1.00000i 0.104257i
\(93\) −25.9808 15.0000i −2.69408 1.55543i
\(94\) −4.00000 6.92820i −0.412568 0.714590i
\(95\) 2.46410 3.73205i 0.252811 0.382900i
\(96\) −1.50000 + 2.59808i −0.153093 + 0.265165i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.96410 + 4.59808i 0.196410 + 0.459808i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 5.19615 3.00000i 0.514496 0.297044i
\(103\) 9.52628 + 5.50000i 0.938652 + 0.541931i 0.889538 0.456862i \(-0.151027\pi\)
0.0491146 + 0.998793i \(0.484360\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 6.06218 + 3.50000i 0.586053 + 0.338358i 0.763535 0.645766i \(-0.223462\pi\)
−0.177482 + 0.984124i \(0.556795\pi\)
\(108\) −7.79423 + 4.50000i −0.750000 + 0.433013i
\(109\) 2.50000 + 4.33013i 0.239457 + 0.414751i 0.960558 0.278078i \(-0.0896974\pi\)
−0.721102 + 0.692829i \(0.756364\pi\)
\(110\) 0 0
\(111\) −24.0000 −2.27798
\(112\) 0 0
\(113\) 10.0000i 0.940721i 0.882474 + 0.470360i \(0.155876\pi\)
−0.882474 + 0.470360i \(0.844124\pi\)
\(114\) 3.00000 5.19615i 0.280976 0.486664i
\(115\) −1.86603 1.23205i −0.174008 0.114889i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) −10.3923 6.00000i −0.960769 0.554700i
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) 3.00000 + 6.00000i 0.273861 + 0.547723i
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 7.79423 4.50000i 0.705656 0.407411i
\(123\) −7.79423 + 4.50000i −0.702782 + 0.405751i
\(124\) −5.00000 + 8.66025i −0.449013 + 0.777714i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 7.50000 + 12.9904i 0.660338 + 1.14374i
\(130\) −2.46410 + 3.73205i −0.216116 + 0.327323i
\(131\) 10.0000 17.3205i 0.873704 1.51330i 0.0155672 0.999879i \(-0.495045\pi\)
0.858137 0.513421i \(-0.171622\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.00000 0.604708
\(135\) −1.20577 + 20.0885i −0.103776 + 1.72894i
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) 13.8564 8.00000i 1.18383 0.683486i 0.226935 0.973910i \(-0.427130\pi\)
0.956898 + 0.290424i \(0.0937963\pi\)
\(138\) −2.59808 1.50000i −0.221163 0.127688i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −24.0000 −2.02116
\(142\) −5.19615 3.00000i −0.436051 0.251754i
\(143\) 0 0
\(144\) 3.00000 + 5.19615i 0.250000 + 0.433013i
\(145\) 2.23205 + 0.133975i 0.185362 + 0.0111260i
\(146\) 10.0000 0.827606
\(147\) 0 0
\(148\) 8.00000i 0.657596i
\(149\) −7.50000 + 12.9904i −0.614424 + 1.06421i 0.376061 + 0.926595i \(0.377278\pi\)
−0.990485 + 0.137619i \(0.956055\pi\)
\(150\) 14.8923 + 1.79423i 1.21595 + 0.146498i
\(151\) −3.00000 5.19615i −0.244137 0.422857i 0.717752 0.696299i \(-0.245171\pi\)
−0.961888 + 0.273442i \(0.911838\pi\)
\(152\) −1.73205 1.00000i −0.140488 0.0811107i
\(153\) 12.0000i 0.970143i
\(154\) 0 0
\(155\) 10.0000 + 20.0000i 0.803219 + 1.60644i
\(156\) −3.00000 + 5.19615i −0.240192 + 0.416025i
\(157\) 10.3923 6.00000i 0.829396 0.478852i −0.0242497 0.999706i \(-0.507720\pi\)
0.853646 + 0.520854i \(0.174386\pi\)
\(158\) 8.66025 5.00000i 0.688973 0.397779i
\(159\) −9.00000 + 15.5885i −0.713746 + 1.23625i
\(160\) 2.00000 1.00000i 0.158114 0.0790569i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 10.3923 + 6.00000i 0.813988 + 0.469956i 0.848339 0.529454i \(-0.177603\pi\)
−0.0343508 + 0.999410i \(0.510936\pi\)
\(164\) 1.50000 + 2.59808i 0.117130 + 0.202876i
\(165\) 0 0
\(166\) −4.50000 + 7.79423i −0.349268 + 0.604949i
\(167\) 9.00000i 0.696441i 0.937413 + 0.348220i \(0.113214\pi\)
−0.937413 + 0.348220i \(0.886786\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −4.46410 0.267949i −0.342381 0.0205508i
\(171\) −6.00000 10.3923i −0.458831 0.794719i
\(172\) 4.33013 2.50000i 0.330169 0.190623i
\(173\) −10.3923 6.00000i −0.790112 0.456172i 0.0498898 0.998755i \(-0.484113\pi\)
−0.840002 + 0.542583i \(0.817446\pi\)
\(174\) 3.00000 0.227429
\(175\) 0 0
\(176\) 0 0
\(177\) 5.19615 + 3.00000i 0.390567 + 0.225494i
\(178\) −6.06218 + 3.50000i −0.454379 + 0.262336i
\(179\) −13.0000 22.5167i −0.971666 1.68297i −0.690526 0.723307i \(-0.742621\pi\)
−0.281139 0.959667i \(-0.590712\pi\)
\(180\) 13.3923 + 0.803848i 0.998203 + 0.0599153i
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) 0 0
\(183\) 27.0000i 1.99590i
\(184\) −0.500000 + 0.866025i −0.0368605 + 0.0638442i
\(185\) 14.9282 + 9.85641i 1.09754 + 0.724657i
\(186\) 15.0000 + 25.9808i 1.09985 + 1.90500i
\(187\) 0 0
\(188\) 8.00000i 0.583460i
\(189\) 0 0
\(190\) −4.00000 + 2.00000i −0.290191 + 0.145095i
\(191\) 10.0000 17.3205i 0.723575 1.25327i −0.235983 0.971757i \(-0.575831\pi\)
0.959558 0.281511i \(-0.0908356\pi\)
\(192\) 2.59808 1.50000i 0.187500 0.108253i
\(193\) −17.3205 + 10.0000i −1.24676 + 0.719816i −0.970461 0.241257i \(-0.922440\pi\)
−0.276296 + 0.961073i \(0.589107\pi\)
\(194\) 0 0
\(195\) 6.00000 + 12.0000i 0.429669 + 0.859338i
\(196\) 0 0
\(197\) 8.00000i 0.569976i −0.958531 0.284988i \(-0.908010\pi\)
0.958531 0.284988i \(-0.0919897\pi\)
\(198\) 0 0
\(199\) −6.00000 10.3923i −0.425329 0.736691i 0.571122 0.820865i \(-0.306508\pi\)
−0.996451 + 0.0841740i \(0.973175\pi\)
\(200\) 0.598076 4.96410i 0.0422904 0.351015i
\(201\) 10.5000 18.1865i 0.740613 1.28278i
\(202\) 15.0000i 1.05540i
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 6.69615 + 0.401924i 0.467680 + 0.0280716i
\(206\) −5.50000 9.52628i −0.383203 0.663727i
\(207\) −5.19615 + 3.00000i −0.361158 + 0.208514i
\(208\) 1.73205 + 1.00000i 0.120096 + 0.0693375i
\(209\) 0 0
\(210\) 0 0
\(211\) −18.0000 −1.23917 −0.619586 0.784929i \(-0.712699\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(212\) 5.19615 + 3.00000i 0.356873 + 0.206041i
\(213\) −15.5885 + 9.00000i −1.06810 + 0.616670i
\(214\) −3.50000 6.06218i −0.239255 0.414402i
\(215\) 0.669873 11.1603i 0.0456850 0.761123i
\(216\) 9.00000 0.612372
\(217\) 0 0
\(218\) 5.00000i 0.338643i
\(219\) 15.0000 25.9808i 1.01361 1.75562i
\(220\) 0 0
\(221\) −2.00000 3.46410i −0.134535 0.233021i
\(222\) 20.7846 + 12.0000i 1.39497 + 0.805387i
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 18.0000 24.0000i 1.20000 1.60000i
\(226\) 5.00000 8.66025i 0.332595 0.576072i
\(227\) −10.3923 + 6.00000i −0.689761 + 0.398234i −0.803523 0.595274i \(-0.797043\pi\)
0.113761 + 0.993508i \(0.463710\pi\)
\(228\) −5.19615 + 3.00000i −0.344124 + 0.198680i
\(229\) −5.00000 + 8.66025i −0.330409 + 0.572286i −0.982592 0.185776i \(-0.940520\pi\)
0.652183 + 0.758062i \(0.273853\pi\)
\(230\) 1.00000 + 2.00000i 0.0659380 + 0.131876i
\(231\) 0 0
\(232\) 1.00000i 0.0656532i
\(233\) −12.1244 7.00000i −0.794293 0.458585i 0.0471787 0.998886i \(-0.484977\pi\)
−0.841472 + 0.540301i \(0.818310\pi\)
\(234\) 6.00000 + 10.3923i 0.392232 + 0.679366i
\(235\) 14.9282 + 9.85641i 0.973809 + 0.642961i
\(236\) 1.00000 1.73205i 0.0650945 0.112747i
\(237\) 30.0000i 1.94871i
\(238\) 0 0
\(239\) 10.0000 0.646846 0.323423 0.946254i \(-0.395166\pi\)
0.323423 + 0.946254i \(0.395166\pi\)
\(240\) 0.401924 6.69615i 0.0259441 0.432235i
\(241\) 9.00000 + 15.5885i 0.579741 + 1.00414i 0.995509 + 0.0946700i \(0.0301796\pi\)
−0.415768 + 0.909471i \(0.636487\pi\)
\(242\) −9.52628 + 5.50000i −0.612372 + 0.353553i
\(243\) 0 0
\(244\) −9.00000 −0.576166
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) −3.46410 2.00000i −0.220416 0.127257i
\(248\) 8.66025 5.00000i 0.549927 0.317500i
\(249\) 13.5000 + 23.3827i 0.855528 + 1.48182i
\(250\) −8.52628 7.23205i −0.539249 0.457395i
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −4.00000 + 6.92820i −0.250982 + 0.434714i
\(255\) −7.39230 + 11.1962i −0.462924 + 0.701130i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.3923 + 6.00000i 0.648254 + 0.374270i 0.787787 0.615948i \(-0.211227\pi\)
−0.139533 + 0.990217i \(0.544560\pi\)
\(258\) 15.0000i 0.933859i
\(259\) 0 0
\(260\) 4.00000 2.00000i 0.248069 0.124035i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) −17.3205 + 10.0000i −1.07006 + 0.617802i
\(263\) −18.1865 + 10.5000i −1.12143 + 0.647458i −0.941766 0.336270i \(-0.890834\pi\)
−0.179664 + 0.983728i \(0.557501\pi\)
\(264\) 0 0
\(265\) 12.0000 6.00000i 0.737154 0.368577i
\(266\) 0 0
\(267\) 21.0000i 1.28518i
\(268\) −6.06218 3.50000i −0.370306 0.213797i
\(269\) −2.50000 4.33013i −0.152428 0.264013i 0.779692 0.626164i \(-0.215376\pi\)
−0.932119 + 0.362151i \(0.882042\pi\)
\(270\) 11.0885 16.7942i 0.674822 1.02206i
\(271\) 3.00000 5.19615i 0.182237 0.315644i −0.760405 0.649449i \(-0.775000\pi\)
0.942642 + 0.333805i \(0.108333\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) 1.50000 + 2.59808i 0.0902894 + 0.156386i
\(277\) −22.5167 + 13.0000i −1.35290 + 0.781094i −0.988654 0.150210i \(-0.952005\pi\)
−0.364241 + 0.931305i \(0.618672\pi\)
\(278\) 6.92820 + 4.00000i 0.415526 + 0.239904i
\(279\) 60.0000 3.59211
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 20.7846 + 12.0000i 1.23771 + 0.714590i
\(283\) 6.92820 4.00000i 0.411839 0.237775i −0.279741 0.960076i \(-0.590248\pi\)
0.691580 + 0.722300i \(0.256915\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) −0.803848 + 13.3923i −0.0476158 + 0.793292i
\(286\) 0 0
\(287\) 0 0
\(288\) 6.00000i 0.353553i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) −1.86603 1.23205i −0.109577 0.0723485i
\(291\) 0 0
\(292\) −8.66025 5.00000i −0.506803 0.292603i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 0 0
\(295\) −2.00000 4.00000i −0.116445 0.232889i
\(296\) 4.00000 6.92820i 0.232495 0.402694i
\(297\) 0 0
\(298\) 12.9904 7.50000i 0.752513 0.434463i
\(299\) −1.00000 + 1.73205i −0.0578315 + 0.100167i
\(300\) −12.0000 9.00000i −0.692820 0.519615i
\(301\) 0 0
\(302\) 6.00000i 0.345261i
\(303\) 38.9711 + 22.5000i 2.23883 + 1.29259i
\(304\) 1.00000 + 1.73205i 0.0573539 + 0.0993399i
\(305\) −11.0885 + 16.7942i −0.634923 + 0.961635i
\(306\) −6.00000 + 10.3923i −0.342997 + 0.594089i
\(307\) 19.0000i 1.08439i 0.840254 + 0.542194i \(0.182406\pi\)
−0.840254 + 0.542194i \(0.817594\pi\)
\(308\) 0 0
\(309\) −33.0000 −1.87730
\(310\) 1.33975 22.3205i 0.0760925 1.26772i
\(311\) 3.00000 + 5.19615i 0.170114 + 0.294647i 0.938460 0.345389i \(-0.112253\pi\)
−0.768345 + 0.640036i \(0.778920\pi\)
\(312\) 5.19615 3.00000i 0.294174 0.169842i
\(313\) −6.92820 4.00000i −0.391605 0.226093i 0.291250 0.956647i \(-0.405929\pi\)
−0.682855 + 0.730554i \(0.739262\pi\)
\(314\) −12.0000 −0.677199
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −19.0526 11.0000i −1.07010 0.617822i −0.141890 0.989882i \(-0.545318\pi\)
−0.928208 + 0.372061i \(0.878651\pi\)
\(318\) 15.5885 9.00000i 0.874157 0.504695i
\(319\) 0 0
\(320\) −2.23205 0.133975i −0.124775 0.00748941i
\(321\) −21.0000 −1.17211
\(322\) 0 0
\(323\) 4.00000i 0.222566i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 1.19615 9.92820i 0.0663506 0.550718i
\(326\) −6.00000 10.3923i −0.332309 0.575577i
\(327\) −12.9904 7.50000i −0.718370 0.414751i
\(328\) 3.00000i 0.165647i
\(329\) 0 0
\(330\) 0 0
\(331\) −7.00000 + 12.1244i −0.384755 + 0.666415i −0.991735 0.128302i \(-0.959047\pi\)
0.606980 + 0.794717i \(0.292381\pi\)
\(332\) 7.79423 4.50000i 0.427764 0.246970i
\(333\) 41.5692 24.0000i 2.27798 1.31519i
\(334\) 4.50000 7.79423i 0.246229 0.426481i
\(335\) −14.0000 + 7.00000i −0.764902 + 0.382451i
\(336\) 0 0
\(337\) 2.00000i 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) −7.79423 4.50000i −0.423950 0.244768i
\(339\) −15.0000 25.9808i −0.814688 1.41108i
\(340\) 3.73205 + 2.46410i 0.202399 + 0.133635i
\(341\) 0 0
\(342\) 12.0000i 0.648886i
\(343\) 0 0
\(344\) −5.00000 −0.269582
\(345\) 6.69615 + 0.401924i 0.360509 + 0.0216388i
\(346\) 6.00000 + 10.3923i 0.322562 + 0.558694i
\(347\) 18.1865 10.5000i 0.976304 0.563670i 0.0751519 0.997172i \(-0.476056\pi\)
0.901152 + 0.433503i \(0.142722\pi\)
\(348\) −2.59808 1.50000i −0.139272 0.0804084i
\(349\) −9.00000 −0.481759 −0.240879 0.970555i \(-0.577436\pi\)
−0.240879 + 0.970555i \(0.577436\pi\)
\(350\) 0 0
\(351\) 18.0000 0.960769
\(352\) 0 0
\(353\) −5.19615 + 3.00000i −0.276563 + 0.159674i −0.631867 0.775077i \(-0.717711\pi\)
0.355303 + 0.934751i \(0.384378\pi\)
\(354\) −3.00000 5.19615i −0.159448 0.276172i
\(355\) 13.3923 + 0.803848i 0.710790 + 0.0426638i
\(356\) 7.00000 0.370999
\(357\) 0 0
\(358\) 26.0000i 1.37414i
\(359\) −7.00000 + 12.1244i −0.369446 + 0.639899i −0.989479 0.144677i \(-0.953786\pi\)
0.620033 + 0.784576i \(0.287119\pi\)
\(360\) −11.1962 7.39230i −0.590089 0.389609i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 4.33013 + 2.50000i 0.227586 + 0.131397i
\(363\) 33.0000i 1.73205i
\(364\) 0 0
\(365\) −20.0000 + 10.0000i −1.04685 + 0.523424i
\(366\) −13.5000 + 23.3827i −0.705656 + 1.22223i
\(367\) 19.9186 11.5000i 1.03974 0.600295i 0.119982 0.992776i \(-0.461716\pi\)
0.919760 + 0.392481i \(0.128383\pi\)
\(368\) 0.866025 0.500000i 0.0451447 0.0260643i
\(369\) 9.00000 15.5885i 0.468521 0.811503i
\(370\) −8.00000 16.0000i −0.415900 0.831800i
\(371\) 0 0
\(372\) 30.0000i 1.55543i
\(373\) 6.92820 + 4.00000i 0.358729 + 0.207112i 0.668523 0.743691i \(-0.266927\pi\)
−0.309794 + 0.950804i \(0.600260\pi\)
\(374\) 0 0
\(375\) −31.5788 + 11.3038i −1.63072 + 0.583728i
\(376\) 4.00000 6.92820i 0.206284 0.357295i
\(377\) 2.00000i 0.103005i
\(378\) 0 0
\(379\) 2.00000 0.102733 0.0513665 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) 4.46410 + 0.267949i 0.229004 + 0.0137455i
\(381\) 12.0000 + 20.7846i 0.614779 + 1.06483i
\(382\) −17.3205 + 10.0000i −0.886194 + 0.511645i
\(383\) 7.79423 + 4.50000i 0.398266 + 0.229939i 0.685736 0.727851i \(-0.259481\pi\)
−0.287469 + 0.957790i \(0.592814\pi\)
\(384\) −3.00000 −0.153093
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) −25.9808 15.0000i −1.32068 0.762493i
\(388\) 0 0
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0.803848 13.3923i 0.0407044 0.678146i
\(391\) −2.00000 −0.101144
\(392\) 0 0
\(393\) 60.0000i 3.02660i
\(394\) −4.00000 + 6.92820i −0.201517 + 0.349038i
\(395\) −12.3205 + 18.6603i −0.619912 + 0.938899i
\(396\) 0 0
\(397\) −27.7128 16.0000i −1.39087 0.803017i −0.397455 0.917622i \(-0.630107\pi\)
−0.993411 + 0.114605i \(0.963440\pi\)
\(398\) 12.0000i 0.601506i
\(399\) 0 0
\(400\) −3.00000 + 4.00000i −0.150000 + 0.200000i
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) −18.1865 + 10.5000i −0.907062 + 0.523692i
\(403\) 17.3205 10.0000i 0.862796 0.498135i
\(404\) 7.50000 12.9904i 0.373139 0.646296i
\(405\) −9.00000 18.0000i −0.447214 0.894427i
\(406\) 0 0
\(407\) 0 0
\(408\) 5.19615 + 3.00000i 0.257248 + 0.148522i
\(409\) 8.50000 + 14.7224i 0.420298 + 0.727977i 0.995968 0.0897044i \(-0.0285922\pi\)
−0.575670 + 0.817682i \(0.695259\pi\)
\(410\) −5.59808 3.69615i −0.276469 0.182540i
\(411\) −24.0000 + 41.5692i −1.18383 + 2.05046i
\(412\) 11.0000i 0.541931i
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 1.20577 20.0885i 0.0591890 0.986104i
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 20.7846 12.0000i 1.01783 0.587643i
\(418\) 0 0
\(419\) −40.0000 −1.95413 −0.977064 0.212946i \(-0.931694\pi\)
−0.977064 + 0.212946i \(0.931694\pi\)
\(420\) 0 0
\(421\) 31.0000 1.51085 0.755424 0.655237i \(-0.227431\pi\)
0.755424 + 0.655237i \(0.227431\pi\)
\(422\) 15.5885 + 9.00000i 0.758834 + 0.438113i
\(423\) 41.5692 24.0000i 2.02116 1.16692i
\(424\) −3.00000 5.19615i −0.145693 0.252347i
\(425\) 9.19615 3.92820i 0.446079 0.190546i
\(426\) 18.0000 0.872103
\(427\) 0 0
\(428\) 7.00000i 0.338358i
\(429\) 0 0
\(430\) −6.16025 + 9.33013i −0.297074 + 0.449939i
\(431\) −16.0000 27.7128i −0.770693 1.33488i −0.937184 0.348836i \(-0.886577\pi\)
0.166491 0.986043i \(-0.446756\pi\)
\(432\) −7.79423 4.50000i −0.375000 0.216506i
\(433\) 14.0000i 0.672797i −0.941720 0.336399i \(-0.890791\pi\)
0.941720 0.336399i \(-0.109209\pi\)
\(434\) 0 0
\(435\) −6.00000 + 3.00000i −0.287678 + 0.143839i
\(436\) −2.50000 + 4.33013i −0.119728 + 0.207375i
\(437\) −1.73205 + 1.00000i −0.0828552 + 0.0478365i
\(438\) −25.9808 + 15.0000i −1.24141 + 0.716728i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 4.00000i 0.190261i
\(443\) −2.59808 1.50000i −0.123438 0.0712672i 0.437009 0.899457i \(-0.356038\pi\)
−0.560448 + 0.828190i \(0.689371\pi\)
\(444\) −12.0000 20.7846i −0.569495 0.986394i
\(445\) 8.62436 13.0622i 0.408834 0.619207i
\(446\) −4.00000 + 6.92820i −0.189405 + 0.328060i
\(447\) 45.0000i 2.12843i
\(448\) 0 0
\(449\) −23.0000 −1.08544 −0.542719 0.839915i \(-0.682605\pi\)
−0.542719 + 0.839915i \(0.682605\pi\)
\(450\) −27.5885 + 11.7846i −1.30053 + 0.555532i
\(451\) 0 0
\(452\) −8.66025 + 5.00000i −0.407344 + 0.235180i
\(453\) 15.5885 + 9.00000i 0.732410 + 0.422857i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) −27.7128 16.0000i −1.29635 0.748448i −0.316579 0.948566i \(-0.602534\pi\)
−0.979772 + 0.200118i \(0.935868\pi\)
\(458\) 8.66025 5.00000i 0.404667 0.233635i
\(459\) 9.00000 + 15.5885i 0.420084 + 0.727607i
\(460\) 0.133975 2.23205i 0.00624660 0.104070i
\(461\) 14.0000 0.652045 0.326023 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 0 0
\(463\) 25.0000i 1.16185i −0.813958 0.580924i \(-0.802691\pi\)
0.813958 0.580924i \(-0.197309\pi\)
\(464\) −0.500000 + 0.866025i −0.0232119 + 0.0402042i
\(465\) −55.9808 36.9615i −2.59605 1.71405i
\(466\) 7.00000 + 12.1244i 0.324269 + 0.561650i
\(467\) 0.866025 + 0.500000i 0.0400749 + 0.0231372i 0.519904 0.854225i \(-0.325968\pi\)
−0.479829 + 0.877362i \(0.659301\pi\)
\(468\) 12.0000i 0.554700i
\(469\) 0 0
\(470\) −8.00000 16.0000i −0.369012 0.738025i
\(471\) −18.0000 + 31.1769i −0.829396 + 1.43656i
\(472\) −1.73205 + 1.00000i −0.0797241 + 0.0460287i
\(473\) 0 0
\(474\) −15.0000 + 25.9808i −0.688973 + 1.19334i
\(475\) 6.00000 8.00000i 0.275299 0.367065i
\(476\) 0 0
\(477\) 36.0000i 1.64833i
\(478\) −8.66025 5.00000i −0.396111 0.228695i
\(479\) −9.00000 15.5885i −0.411220 0.712255i 0.583803 0.811895i \(-0.301564\pi\)
−0.995023 + 0.0996406i \(0.968231\pi\)
\(480\) −3.69615 + 5.59808i −0.168706 + 0.255516i
\(481\) 8.00000 13.8564i 0.364769 0.631798i
\(482\) 18.0000i 0.819878i
\(483\) 0 0
\(484\) 11.0000 0.500000
\(485\) 0 0
\(486\) 0 0
\(487\) 3.46410 2.00000i 0.156973 0.0906287i −0.419456 0.907776i \(-0.637779\pi\)
0.576429 + 0.817147i \(0.304446\pi\)
\(488\) 7.79423 + 4.50000i 0.352828 + 0.203705i
\(489\) −36.0000 −1.62798
\(490\) 0 0
\(491\) −18.0000 −0.812329 −0.406164 0.913800i \(-0.633134\pi\)
−0.406164 + 0.913800i \(0.633134\pi\)
\(492\) −7.79423 4.50000i −0.351391 0.202876i
\(493\) 1.73205 1.00000i 0.0780076 0.0450377i
\(494\) 2.00000 + 3.46410i 0.0899843 + 0.155857i
\(495\) 0 0
\(496\) −10.0000 −0.449013
\(497\) 0 0
\(498\) 27.0000i 1.20990i
\(499\) 8.00000 13.8564i 0.358129 0.620298i −0.629519 0.776985i \(-0.716748\pi\)
0.987648 + 0.156687i \(0.0500814\pi\)
\(500\) 3.76795 + 10.5263i 0.168508 + 0.470750i
\(501\) −13.5000 23.3827i −0.603136 1.04466i
\(502\) −8.66025 5.00000i −0.386526 0.223161i
\(503\) 5.00000i 0.222939i −0.993768 0.111469i \(-0.964444\pi\)
0.993768 0.111469i \(-0.0355557\pi\)
\(504\) 0 0
\(505\) −15.0000 30.0000i −0.667491 1.33498i
\(506\) 0 0
\(507\) −23.3827 + 13.5000i −1.03846 + 0.599556i
\(508\) 6.92820 4.00000i 0.307389 0.177471i
\(509\) −17.5000 + 30.3109i −0.775674 + 1.34351i 0.158741 + 0.987320i \(0.449256\pi\)
−0.934415 + 0.356186i \(0.884077\pi\)
\(510\) 12.0000 6.00000i 0.531369 0.265684i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 15.5885 + 9.00000i 0.688247 + 0.397360i
\(514\) −6.00000 10.3923i −0.264649 0.458385i
\(515\) 20.5263 + 13.5526i 0.904496 + 0.597197i
\(516\) −7.50000 + 12.9904i −0.330169 + 0.571870i
\(517\) 0 0
\(518\) 0 0
\(519\) 36.0000 1.58022
\(520\) −4.46410 0.267949i −0.195764 0.0117503i
\(521\) −9.00000 15.5885i −0.394297 0.682943i 0.598714 0.800963i \(-0.295679\pi\)
−0.993011 + 0.118020i \(0.962345\pi\)
\(522\) −5.19615 + 3.00000i −0.227429 + 0.131306i
\(523\) −3.46410 2.00000i −0.151475 0.0874539i 0.422347 0.906434i \(-0.361206\pi\)
−0.573822 + 0.818980i \(0.694540\pi\)
\(524\) 20.0000 0.873704
\(525\) 0 0
\(526\) 21.0000 0.915644
\(527\) 17.3205 + 10.0000i 0.754493 + 0.435607i
\(528\) 0 0
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) −13.3923 0.803848i −0.581725 0.0349169i
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 6.00000i 0.259889i
\(534\) 10.5000 18.1865i 0.454379 0.787008i
\(535\) 13.0622 + 8.62436i 0.564727 + 0.372863i
\(536\) 3.50000 + 6.06218i 0.151177 + 0.261846i
\(537\) 67.5500 + 39.0000i 2.91500 + 1.68297i
\(538\) 5.00000i 0.215565i
\(539\) 0 0
\(540\) −18.0000 + 9.00000i −0.774597 + 0.387298i
\(541\) −2.50000 + 4.33013i −0.107483 + 0.186167i −0.914750 0.404020i \(-0.867613\pi\)
0.807267 + 0.590187i \(0.200946\pi\)
\(542\) −5.19615 + 3.00000i −0.223194 + 0.128861i
\(543\) 12.9904 7.50000i 0.557471 0.321856i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 5.00000 + 10.0000i 0.214176 + 0.428353i
\(546\) 0 0
\(547\) 37.0000i 1.58201i 0.611812 + 0.791003i \(0.290441\pi\)
−0.611812 + 0.791003i \(0.709559\pi\)
\(548\) 13.8564 + 8.00000i 0.591916 + 0.341743i
\(549\) 27.0000 + 46.7654i 1.15233 + 1.99590i
\(550\) 0 0
\(551\) 1.00000 1.73205i 0.0426014 0.0737878i
\(552\) 3.00000i 0.127688i
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) −53.5692 3.21539i −2.27389 0.136486i
\(556\) −4.00000 6.92820i −0.169638 0.293821i
\(557\) −3.46410 + 2.00000i −0.146779 + 0.0847427i −0.571591 0.820539i \(-0.693674\pi\)
0.424812 + 0.905282i \(0.360340\pi\)
\(558\) −51.9615 30.0000i −2.19971 1.27000i
\(559\) −10.0000 −0.422955
\(560\) 0 0
\(561\) 0 0
\(562\) −15.5885 9.00000i −0.657559 0.379642i
\(563\) 9.52628 5.50000i 0.401485 0.231797i −0.285640 0.958337i \(-0.592206\pi\)
0.687124 + 0.726540i \(0.258873\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) −1.33975 + 22.3205i −0.0563635 + 0.939031i
\(566\) −8.00000 −0.336265
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) −9.00000 + 15.5885i −0.377300 + 0.653502i −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 7.39230 11.1962i 0.309630 0.468955i
\(571\) 5.00000 + 8.66025i 0.209243 + 0.362420i 0.951476 0.307722i \(-0.0995665\pi\)
−0.742233 + 0.670142i \(0.766233\pi\)
\(572\) 0 0
\(573\) 60.0000i 2.50654i
\(574\) 0 0
\(575\) −4.00000 3.00000i −0.166812 0.125109i
\(576\) −3.00000 + 5.19615i −0.125000 + 0.216506i
\(577\) 13.8564 8.00000i 0.576850 0.333044i −0.183031 0.983107i \(-0.558591\pi\)
0.759880 + 0.650063i \(0.225257\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) 30.0000 51.9615i 1.24676 2.15945i
\(580\) 1.00000 + 2.00000i 0.0415227 + 0.0830455i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 5.00000 + 8.66025i 0.206901 + 0.358364i
\(585\) −22.3923 14.7846i −0.925808 0.611268i
\(586\) 12.0000 20.7846i 0.495715 0.858604i
\(587\) 28.0000i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(588\) 0 0
\(589\) 20.0000 0.824086
\(590\) −0.267949 + 4.46410i −0.0110313 + 0.183784i
\(591\) 12.0000 + 20.7846i 0.493614 + 0.854965i
\(592\) −6.92820 + 4.00000i −0.284747 + 0.164399i
\(593\) −36.3731 21.0000i −1.49366 0.862367i −0.493689 0.869638i \(-0.664352\pi\)
−0.999974 + 0.00727173i \(0.997685\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) 31.1769 + 18.0000i 1.27599 + 0.736691i
\(598\) 1.73205 1.00000i 0.0708288 0.0408930i
\(599\) 18.0000 + 31.1769i 0.735460 + 1.27385i 0.954521 + 0.298143i \(0.0963673\pi\)
−0.219061 + 0.975711i \(0.570299\pi\)
\(600\) 5.89230 + 13.7942i 0.240552 + 0.563147i
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 42.0000i 1.71037i
\(604\) 3.00000 5.19615i 0.122068 0.211428i
\(605\) 13.5526 20.5263i 0.550990 0.834512i
\(606\) −22.5000 38.9711i −0.914000 1.58309i
\(607\) 4.33013 + 2.50000i 0.175754 + 0.101472i 0.585296 0.810819i \(-0.300978\pi\)
−0.409542 + 0.912291i \(0.634311\pi\)
\(608\) 2.00000i 0.0811107i
\(609\) 0 0
\(610\) 18.0000 9.00000i 0.728799 0.364399i
\(611\) 8.00000 13.8564i 0.323645 0.560570i
\(612\) 10.3923 6.00000i 0.420084 0.242536i
\(613\) −15.5885 + 9.00000i −0.629612 + 0.363507i −0.780602 0.625029i \(-0.785087\pi\)
0.150990 + 0.988535i \(0.451754\pi\)
\(614\) 9.50000 16.4545i 0.383389 0.664049i
\(615\) −18.0000 + 9.00000i −0.725830 + 0.362915i
\(616\) 0 0
\(617\) 20.0000i 0.805170i 0.915383 + 0.402585i \(0.131888\pi\)
−0.915383 + 0.402585i \(0.868112\pi\)
\(618\) 28.5788 + 16.5000i 1.14961 + 0.663727i
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) −12.3205 + 18.6603i −0.494804 + 0.749414i
\(621\) 4.50000 7.79423i 0.180579 0.312772i
\(622\) 6.00000i 0.240578i
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 4.00000 + 6.92820i 0.159872 + 0.276907i
\(627\) 0 0
\(628\) 10.3923 + 6.00000i 0.414698 + 0.239426i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) −24.0000 −0.955425 −0.477712 0.878516i \(-0.658534\pi\)
−0.477712 + 0.878516i \(0.658534\pi\)
\(632\) 8.66025 + 5.00000i 0.344486 + 0.198889i
\(633\) 46.7654 27.0000i 1.85876 1.07315i
\(634\) 11.0000 + 19.0526i 0.436866 + 0.756674i
\(635\) 1.07180 17.8564i 0.0425330 0.708610i
\(636\) −18.0000 −0.713746
\(637\) 0 0
\(638\) 0 0
\(639\) 18.0000 31.1769i 0.712069 1.23334i
\(640\) 1.86603 + 1.23205i 0.0737611 + 0.0487011i
\(641\) 17.5000 + 30.3109i 0.691208 + 1.19721i 0.971442 + 0.237276i \(0.0762547\pi\)
−0.280234 + 0.959932i \(0.590412\pi\)
\(642\) 18.1865 + 10.5000i 0.717765 + 0.414402i
\(643\) 20.0000i 0.788723i −0.918955 0.394362i \(-0.870966\pi\)
0.918955 0.394362i \(-0.129034\pi\)
\(644\) 0 0
\(645\) 15.0000 + 30.0000i 0.590624 + 1.18125i
\(646\) −2.00000 + 3.46410i −0.0786889 + 0.136293i
\(647\) −18.1865 + 10.5000i −0.714986 + 0.412798i −0.812905 0.582397i \(-0.802115\pi\)
0.0979182 + 0.995194i \(0.468782\pi\)
\(648\) −7.79423 + 4.50000i −0.306186 + 0.176777i
\(649\) 0 0
\(650\) −6.00000 + 8.00000i −0.235339 + 0.313786i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 36.3731 + 21.0000i 1.42339 + 0.821794i 0.996587 0.0825519i \(-0.0263070\pi\)
0.426801 + 0.904345i \(0.359640\pi\)
\(654\) 7.50000 + 12.9904i 0.293273 + 0.507964i
\(655\) 24.6410 37.3205i 0.962804 1.45823i
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 60.0000i 2.34082i
\(658\) 0 0
\(659\) −30.0000 −1.16863 −0.584317 0.811525i \(-0.698638\pi\)
−0.584317 + 0.811525i \(0.698638\pi\)
\(660\) 0 0
\(661\) −20.5000 35.5070i −0.797358 1.38106i −0.921331 0.388778i \(-0.872897\pi\)
0.123974 0.992286i \(-0.460436\pi\)
\(662\) 12.1244 7.00000i 0.471226 0.272063i
\(663\) 10.3923 + 6.00000i 0.403604 + 0.233021i
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −48.0000 −1.85996
\(667\) −0.866025 0.500000i −0.0335326 0.0193601i
\(668\) −7.79423 + 4.50000i −0.301568 + 0.174110i
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 15.6244 + 0.937822i 0.603622 + 0.0362312i
\(671\) 0 0
\(672\) 0 0
\(673\) 20.0000i 0.770943i −0.922720 0.385472i \(-0.874039\pi\)
0.922720 0.385472i \(-0.125961\pi\)
\(674\) −1.00000 + 1.73205i −0.0385186 + 0.0667161i
\(675\) −5.38269 + 44.6769i −0.207180 + 1.71962i
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −1.73205 1.00000i −0.0665681 0.0384331i 0.466347 0.884602i \(-0.345570\pi\)
−0.532915 + 0.846169i \(0.678903\pi\)
\(678\) 30.0000i 1.15214i
\(679\) 0 0
\(680\) −2.00000 4.00000i −0.0766965 0.153393i
\(681\) 18.0000 31.1769i 0.689761 1.19470i
\(682\) 0 0
\(683\) −21.6506 + 12.5000i −0.828439 + 0.478299i −0.853318 0.521391i \(-0.825413\pi\)
0.0248792 + 0.999690i \(0.492080\pi\)
\(684\) 6.00000 10.3923i 0.229416 0.397360i
\(685\) 32.0000 16.0000i 1.22266 0.611329i
\(686\) 0 0
\(687\) 30.0000i 1.14457i
\(688\) 4.33013 + 2.50000i 0.165085 + 0.0953116i
\(689\) −6.00000 10.3923i −0.228582 0.395915i
\(690\) −5.59808 3.69615i −0.213115 0.140710i
\(691\) −10.0000 + 17.3205i −0.380418 + 0.658903i −0.991122 0.132956i \(-0.957553\pi\)
0.610704 + 0.791859i \(0.290887\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) −21.0000 −0.797149
\(695\) −17.8564 1.07180i −0.677332 0.0406556i
\(696\) 1.50000 + 2.59808i 0.0568574 + 0.0984798i
\(697\) 5.19615 3.00000i 0.196818 0.113633i
\(698\) 7.79423 + 4.50000i 0.295016 + 0.170328i
\(699\) 42.0000 1.58859
\(700\) 0 0
\(701\) −1.00000 −0.0377695 −0.0188847 0.999822i \(-0.506012\pi\)
−0.0188847 + 0.999822i \(0.506012\pi\)
\(702\) −15.5885 9.00000i −0.588348 0.339683i
\(703\) 13.8564 8.00000i 0.522604 0.301726i
\(704\) 0 0
\(705\) −53.5692 3.21539i −2.01753 0.121099i
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 6.00000i 0.225494i
\(709\) −4.50000 + 7.79423i −0.169001 + 0.292718i −0.938069 0.346449i \(-0.887387\pi\)
0.769068 + 0.639167i \(0.220721\pi\)
\(710\) −11.1962 7.39230i −0.420184 0.277428i
\(711\) 30.0000 + 51.9615i 1.12509 + 1.94871i
\(712\) −6.06218 3.50000i −0.227190 0.131168i
\(713\) 10.0000i 0.374503i
\(714\) 0 0
\(715\) 0 0
\(716\) 13.0000 22.5167i 0.485833 0.841487i
\(717\) −25.9808 + 15.0000i −0.970269 + 0.560185i
\(718\) 12.1244 7.00000i 0.452477 0.261238i
\(719\) −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i \(-0.954983\pi\)
0.617079 + 0.786901i \(0.288316\pi\)
\(720\) 6.00000 + 12.0000i 0.223607 + 0.447214i
\(721\) 0 0
\(722\) 15.0000i 0.558242i
\(723\) −46.7654 27.0000i −1.73922 1.00414i
\(724\) −2.50000 4.33013i −0.0929118 0.160928i
\(725\) 4.96410 + 0.598076i 0.184362 + 0.0222120i
\(726\) 16.5000 28.5788i 0.612372 1.06066i
\(727\) 29.0000i 1.07555i 0.843088 + 0.537775i \(0.180735\pi\)
−0.843088 + 0.537775i \(0.819265\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 22.3205 + 1.33975i 0.826119 + 0.0495862i
\(731\) −5.00000 8.66025i −0.184932 0.320311i
\(732\) 23.3827 13.5000i 0.864249 0.498974i
\(733\) 13.8564 + 8.00000i 0.511798 + 0.295487i 0.733572 0.679611i \(-0.237852\pi\)
−0.221774 + 0.975098i \(0.571185\pi\)
\(734\) −23.0000 −0.848945
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) −15.5885 + 9.00000i −0.573819 + 0.331295i
\(739\) −16.0000 27.7128i −0.588570 1.01943i −0.994420 0.105493i \(-0.966358\pi\)
0.405851 0.913939i \(-0.366975\pi\)
\(740\) −1.07180 + 17.8564i −0.0394000 + 0.656415i
\(741\) 12.0000 0.440831
\(742\) 0 0
\(743\) 3.00000i 0.110059i 0.998485 + 0.0550297i \(0.0175253\pi\)
−0.998485 + 0.0550297i \(0.982475\pi\)
\(744\) −15.0000 + 25.9808i −0.549927 + 0.952501i
\(745\) −18.4808 + 27.9904i −0.677083 + 1.02549i
\(746\) −4.00000 6.92820i −0.146450 0.253660i
\(747\) −46.7654 27.0000i −1.71106 0.987878i
\(748\) 0 0
\(749\) 0 0
\(750\) 33.0000 + 6.00000i 1.20499 + 0.219089i
\(751\) −2.00000 + 3.46410i −0.0729810 + 0.126407i −0.900207 0.435463i \(-0.856585\pi\)
0.827225 + 0.561870i \(0.189918\pi\)
\(752\) −6.92820 + 4.00000i −0.252646 + 0.145865i
\(753\) −25.9808 + 15.0000i −0.946792 + 0.546630i
\(754\) −1.00000 + 1.73205i −0.0364179 + 0.0630776i
\(755\) −6.00000 12.0000i −0.218362 0.436725i
\(756\) 0 0
\(757\) 6.00000i 0.218074i −0.994038 0.109037i \(-0.965223\pi\)
0.994038 0.109037i \(-0.0347767\pi\)
\(758\) −1.73205 1.00000i −0.0629109 0.0363216i
\(759\) 0 0
\(760\) −3.73205 2.46410i −0.135376 0.0893824i
\(761\) −25.0000 + 43.3013i −0.906249 + 1.56967i −0.0870179 + 0.996207i \(0.527734\pi\)
−0.819231 + 0.573463i \(0.805600\pi\)
\(762\) 24.0000i 0.869428i
\(763\) 0 0
\(764\) 20.0000 0.723575
\(765\) 1.60770 26.7846i 0.0581263 0.968400i
\(766\) −4.50000 7.79423i −0.162592 0.281617i
\(767\) −3.46410 + 2.00000i −0.125081 + 0.0722158i
\(768\) 2.59808 + 1.50000i 0.0937500 + 0.0541266i
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −36.0000 −1.29651
\(772\) −17.3205 10.0000i −0.623379 0.359908i
\(773\) −15.5885 + 9.00000i −0.560678 + 0.323708i −0.753418 0.657542i \(-0.771596\pi\)
0.192740 + 0.981250i \(0.438263\pi\)
\(774\) 15.0000 + 25.9808i 0.539164 + 0.933859i
\(775\) 19.6410 + 45.9808i 0.705526 + 1.65168i
\(776\) 0 0
\(777\) 0 0
\(778\) 18.0000i 0.645331i
\(779\) 3.00000 5.19615i 0.107486 0.186171i
\(780\) −7.39230 + 11.1962i −0.264687 + 0.400887i
\(781\) 0 0
\(782\) 1.73205 + 1.00000i 0.0619380 + 0.0357599i
\(783\) 9.00000i 0.321634i
\(784\) 0 0
\(785\) 24.0000 12.0000i 0.856597 0.428298i
\(786\) 30.0000 51.9615i 1.07006 1.85341i
\(787\) −18.1865 + 10.5000i −0.648280 + 0.374285i −0.787797 0.615935i \(-0.788778\pi\)
0.139517 + 0.990220i \(0.455445\pi\)
\(788\) 6.92820 4.00000i 0.246807 0.142494i
\(789\) 31.5000 54.5596i 1.12143 1.94237i
\(790\) 20.0000 10.0000i 0.711568 0.355784i
\(791\) 0 0
\(792\) 0 0
\(793\) 15.5885 + 9.00000i 0.553562 + 0.319599i
\(794\) 16.0000 + 27.7128i 0.567819 + 0.983491i
\(795\) −22.1769 + 33.5885i −0.786534 + 1.19126i
\(796\) 6.00000 10.3923i 0.212664 0.368345i
\(797\) 8.00000i 0.283375i 0.989911 + 0.141687i \(0.0452527\pi\)
−0.989911 + 0.141687i \(0.954747\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 4.59808 1.96410i 0.162567 0.0694415i
\(801\) −21.0000 36.3731i −0.741999 1.28518i
\(802\) 2.59808 1.50000i 0.0917413 0.0529668i
\(803\) 0 0
\(804\) 21.0000 0.740613
\(805\) 0 0
\(806\) −20.0000 −0.704470
\(807\) 12.9904 + 7.50000i 0.457283 + 0.264013i
\(808\) −12.9904 + 7.50000i −0.457000 + 0.263849i
\(809\) 12.5000 + 21.6506i 0.439477 + 0.761196i 0.997649 0.0685291i \(-0.0218306\pi\)
−0.558173 + 0.829725i \(0.688497\pi\)
\(810\) −1.20577 + 20.0885i −0.0423665 + 0.705836i
\(811\) −6.00000 −0.210688 −0.105344 0.994436i \(-0.533594\pi\)
−0.105344 + 0.994436i \(0.533594\pi\)
\(812\) 0 0
\(813\) 18.0000i 0.631288i
\(814\) 0 0
\(815\) 22.3923 + 14.7846i 0.784368 + 0.517882i
\(816\) −3.00000 5.19615i −0.105021 0.181902i
\(817\) −8.66025 5.00000i −0.302984 0.174928i
\(818\) 17.0000i 0.594391i
\(819\) 0 0
\(820\) 3.00000 + 6.00000i 0.104765 + 0.209529i
\(821\) 21.0000 36.3731i 0.732905 1.26943i −0.222731 0.974880i \(-0.571497\pi\)
0.955636 0.294549i \(-0.0951694\pi\)
\(822\) 41.5692 24.0000i 1.44989 0.837096i
\(823\) 38.9711 22.5000i 1.35845 0.784301i 0.369034 0.929416i \(-0.379689\pi\)
0.989415 + 0.145115i \(0.0463553\pi\)
\(824\) 5.50000 9.52628i 0.191602 0.331864i
\(825\) 0 0
\(826\) 0 0
\(827\) 37.0000i 1.28662i −0.765607 0.643308i \(-0.777561\pi\)
0.765607 0.643308i \(-0.222439\pi\)
\(828\) −5.19615 3.00000i −0.180579 0.104257i
\(829\) −17.0000 29.4449i −0.590434 1.02266i −0.994174 0.107788i \(-0.965623\pi\)
0.403739 0.914874i \(-0.367710\pi\)
\(830\) −11.0885 + 16.7942i −0.384886 + 0.582936i
\(831\) 39.0000 67.5500i 1.35290 2.34328i
\(832\) 2.00000i 0.0693375i
\(833\) 0 0
\(834\) −24.0000 −0.831052
\(835\) −1.20577 + 20.0885i −0.0417274 + 0.695190i
\(836\) 0 0
\(837\) −77.9423 + 45.0000i −2.69408 + 1.55543i
\(838\) 34.6410 + 20.0000i 1.19665 + 0.690889i
\(839\) 32.0000 1.10476 0.552381 0.833592i \(-0.313719\pi\)
0.552381 + 0.833592i \(0.313719\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) −26.8468 15.5000i −0.925201 0.534165i
\(843\) −46.7654 + 27.0000i −1.61068 + 0.929929i
\(844\) −9.00000 15.5885i −0.309793 0.536577i
\(845\) 20.0885 + 1.20577i 0.691064 + 0.0414798i
\(846\) −48.0000 −1.65027
\(847\) 0 0
\(848\) 6.00000i 0.206041i
\(849\) −12.0000 + 20.7846i −0.411839 + 0.713326i
\(850\) −9.92820 1.19615i −0.340535 0.0410277i
\(851\) −4.00000 6.92820i −0.137118 0.237496i
\(852\) −15.5885 9.00000i −0.534052 0.308335i
\(853\) 10.0000i 0.342393i −0.985237 0.171197i \(-0.945237\pi\)
0.985237 0.171197i \(-0.0547634\pi\)
\(854\) 0 0
\(855\) −12.0000 24.0000i −0.410391 0.820783i
\(856\) 3.50000 6.06218i 0.119628 0.207201i
\(857\) 3.46410 2.00000i 0.118331 0.0683187i −0.439666 0.898161i \(-0.644903\pi\)
0.557998 + 0.829843i \(0.311570\pi\)
\(858\) 0 0
\(859\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(860\) 10.0000 5.00000i 0.340997 0.170499i
\(861\) 0 0
\(862\) 32.0000i 1.08992i
\(863\) −9.52628 5.50000i −0.324278 0.187222i 0.329020 0.944323i \(-0.393282\pi\)
−0.653298 + 0.757101i \(0.726615\pi\)
\(864\) 4.50000 + 7.79423i 0.153093 + 0.265165i
\(865\) −22.3923 14.7846i −0.761361 0.502692i
\(866\) −7.00000 + 12.1244i −0.237870 + 0.412002i
\(867\) 39.0000i 1.32451i
\(868\) 0 0
\(869\) 0 0
\(870\) 6.69615 + 0.401924i 0.227021 + 0.0136265i
\(871\) 7.00000 + 12.1244i 0.237186 + 0.410818i
\(872\) 4.33013 2.50000i 0.146637 0.0846607i
\(873\) 0 0
\(874\) 2.00000 0.0676510
\(875\) 0 0
\(876\) 30.0000 1.01361
\(877\) 12.1244 + 7.00000i 0.409410 + 0.236373i 0.690536 0.723298i \(-0.257375\pi\)
−0.281126 + 0.959671i \(0.590708\pi\)
\(878\) 6.92820 4.00000i 0.233816 0.134993i
\(879\) −36.0000 62.3538i −1.21425 2.10314i
\(880\) 0 0
\(881\) 3.00000 0.101073 0.0505363 0.998722i \(-0.483907\pi\)
0.0505363 + 0.998722i \(0.483907\pi\)
\(882\) 0 0
\(883\) 4.00000i 0.134611i −0.997732 0.0673054i \(-0.978560\pi\)
0.997732 0.0673054i \(-0.0214402\pi\)
\(884\) 2.00000 3.46410i 0.0672673 0.116510i
\(885\) 11.1962 + 7.39230i 0.376355 + 0.248490i
\(886\) 1.50000 + 2.59808i 0.0503935 + 0.0872841i
\(887\) 7.79423 + 4.50000i 0.261705 + 0.151095i 0.625112 0.780535i \(-0.285053\pi\)
−0.363407 + 0.931630i \(0.618387\pi\)
\(888\) 24.0000i 0.805387i
\(889\) 0 0
\(890\) −14.0000 + 7.00000i −0.469281 + 0.234641i
\(891\) 0 0
\(892\) 6.92820 4.00000i 0.231973 0.133930i
\(893\) 13.8564 8.00000i 0.463687 0.267710i
\(894\) −22.5000 + 38.9711i −0.752513 + 1.30339i
\(895\) −26.0000 52.0000i −0.869084 1.73817i
\(896\) 0 0
\(897\) 6.00000i 0.200334i
\(898\) 19.9186 + 11.5000i 0.664692 + 0.383760i
\(899\) 5.00000 + 8.66025i 0.166759 + 0.288836i
\(900\) 29.7846 + 3.58846i 0.992820 + 0.119615i
\(901\) 6.00000 10.3923i 0.199889 0.346218i
\(902\) 0 0
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) −11.1603 0.669873i −0.370979 0.0222673i
\(906\) −9.00000 15.5885i −0.299005 0.517892i
\(907\) −21.6506 + 12.5000i −0.718898 + 0.415056i −0.814347 0.580379i \(-0.802905\pi\)
0.0954492 + 0.995434i \(0.469571\pi\)
\(908\) −10.3923 6.00000i −0.344881 0.199117i
\(909\) −90.0000 −2.98511
\(910\) 0 0
\(911\) 8.00000 0.265052 0.132526 0.991180i \(-0.457691\pi\)
0.132526 + 0.991180i \(0.457691\pi\)
\(912\) −5.19615 3.00000i −0.172062 0.0993399i
\(913\) 0 0
\(914\) 16.0000 + 27.7128i 0.529233 + 0.916658i
\(915\) 3.61731 60.2654i 0.119585 1.99231i
\(916\) −10.0000 −0.330409
\(917\) 0 0
\(918\) 18.0000i 0.594089i
\(919\) 13.0000 22.5167i 0.428830 0.742756i −0.567939 0.823071i \(-0.692259\pi\)
0.996770 + 0.0803145i \(0.0255924\pi\)
\(920\) −1.23205 + 1.86603i −0.0406195 + 0.0615210i
\(921\) −28.5000 49.3634i −0.939107 1.62658i
\(922\) −12.1244 7.00000i −0.399294 0.230533i
\(923\) 12.0000i 0.394985i
\(924\) 0 0
\(925\) 32.0000 + 24.0000i 1.05215 + 0.789115i
\(926\) −12.5000 + 21.6506i −0.410775 + 0.711484i
\(927\) 57.1577 33.0000i 1.87730 1.08386i
\(928\) 0.866025 0.500000i 0.0284287 0.0164133i
\(929\) −13.5000 + 23.3827i −0.442921 + 0.767161i −0.997905 0.0646999i \(-0.979391\pi\)
0.554984 + 0.831861i \(0.312724\pi\)
\(930\) 30.0000 + 60.0000i 0.983739 + 1.96748i
\(931\) 0 0
\(932\) 14.0000i 0.458585i
\(933\) −15.5885 9.00000i −0.510343 0.294647i
\(934\) −0.500000 0.866025i −0.0163605 0.0283372i
\(935\) 0 0
\(936\) −6.00000 + 10.3923i −0.196116 + 0.339683i
\(937\) 56.0000i 1.82944i 0.404088 + 0.914720i \(0.367589\pi\)
−0.404088 + 0.914720i \(0.632411\pi\)
\(938\) 0 0
\(939\) 24.0000 0.783210
\(940\) −1.07180 + 17.8564i −0.0349582 + 0.582412i
\(941\) 7.00000 + 12.1244i 0.228193 + 0.395243i 0.957273 0.289187i \(-0.0933848\pi\)
−0.729079 + 0.684429i \(0.760051\pi\)
\(942\) 31.1769 18.0000i 1.01580 0.586472i
\(943\) −2.59808 1.50000i −0.0846050 0.0488467i
\(944\) 2.00000 0.0650945
\(945\) 0 0
\(946\) 0 0
\(947\) 2.59808 + 1.50000i 0.0844261 + 0.0487435i 0.541619 0.840624i \(-0.317812\pi\)
−0.457193 + 0.889368i \(0.651145\pi\)
\(948\) 25.9808 15.0000i 0.843816 0.487177i
\(949\) 10.0000 + 17.3205i 0.324614 + 0.562247i
\(950\) −9.19615 + 3.92820i −0.298363 + 0.127448i
\(951\) 66.0000 2.14020
\(952\) 0 0
\(953\) 36.0000i 1.16615i −0.812417 0.583077i \(-0.801849\pi\)
0.812417 0.583077i \(-0.198151\pi\)
\(954\) −18.0000 + 31.1769i −0.582772 + 1.00939i
\(955\) 24.6410 37.3205i 0.797365 1.20766i
\(956\) 5.00000 + 8.66025i 0.161712 + 0.280093i
\(957\) 0 0
\(958\) 18.0000i 0.581554i
\(959\) 0 0
\(960\) 6.00000 3.00000i 0.193649 0.0968246i
\(961\) −34.5000 + 59.7558i −1.11290 + 1.92760i
\(962\) −13.8564 + 8.00000i −0.446748 + 0.257930i
\(963\) 36.3731 21.0000i 1.17211 0.676716i
\(964\) −9.00000 + 15.5885i −0.289870 + 0.502070i
\(965\) −40.0000 + 20.0000i −1.28765 + 0.643823i
\(966\) 0 0
\(967\) 17.0000i 0.546683i 0.961917 + 0.273342i \(0.0881289\pi\)
−0.961917 + 0.273342i \(0.911871\pi\)
\(968\) −9.52628 5.50000i −0.306186 0.176777i
\(969\) 6.00000 + 10.3923i 0.192748 + 0.333849i
\(970\) 0 0
\(971\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −4.00000 −0.128168
\(975\) 11.7846 + 27.5885i 0.377410 + 0.883538i
\(976\) −4.50000 7.79423i −0.144041 0.249487i
\(977\) 31.1769 18.0000i 0.997438 0.575871i 0.0899487 0.995946i \(-0.471330\pi\)
0.907489 + 0.420075i \(0.137996\pi\)
\(978\) 31.1769 + 18.0000i 0.996928 + 0.575577i
\(979\) 0 0
\(980\) 0 0
\(981\) 30.0000 0.957826
\(982\) 15.5885 + 9.00000i 0.497448 + 0.287202i
\(983\) 21.6506 12.5000i 0.690548 0.398688i −0.113269 0.993564i \(-0.536132\pi\)
0.803817 + 0.594876i \(0.202799\pi\)
\(984\) 4.50000 + 7.79423i 0.143455 + 0.248471i
\(985\) 1.07180 17.8564i 0.0341503 0.568952i
\(986\) −2.00000 −0.0636930
\(987\) 0 0
\(988\) 4.00000i 0.127257i
\(989\) −2.50000 + 4.33013i −0.0794954 + 0.137690i
\(990\) 0 0
\(991\) 13.0000 + 22.5167i 0.412959 + 0.715265i 0.995212 0.0977423i \(-0.0311621\pi\)
−0.582253 + 0.813008i \(0.697829\pi\)
\(992\) 8.66025 + 5.00000i 0.274963 + 0.158750i
\(993\) 42.0000i 1.33283i
\(994\) 0 0
\(995\) −12.0000 24.0000i −0.380426 0.760851i
\(996\) −13.5000 + 23.3827i −0.427764 + 0.740909i
\(997\) −29.4449 + 17.0000i −0.932528 + 0.538395i −0.887610 0.460595i \(-0.847636\pi\)
−0.0449179 + 0.998991i \(0.514303\pi\)
\(998\) −13.8564 + 8.00000i −0.438617 + 0.253236i
\(999\) −36.0000 + 62.3538i −1.13899 + 1.97279i
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 490.2.i.b.79.1 4
5.4 even 2 inner 490.2.i.b.79.2 4
7.2 even 3 490.2.c.b.99.2 2
7.3 odd 6 70.2.i.a.39.2 yes 4
7.4 even 3 inner 490.2.i.b.459.2 4
7.5 odd 6 490.2.c.c.99.2 2
7.6 odd 2 70.2.i.a.9.1 4
21.17 even 6 630.2.u.b.109.1 4
21.20 even 2 630.2.u.b.289.2 4
28.3 even 6 560.2.bw.c.529.2 4
28.27 even 2 560.2.bw.c.289.1 4
35.2 odd 12 2450.2.a.c.1.1 1
35.3 even 12 350.2.e.f.151.1 2
35.4 even 6 inner 490.2.i.b.459.1 4
35.9 even 6 490.2.c.b.99.1 2
35.12 even 12 2450.2.a.r.1.1 1
35.13 even 4 350.2.e.f.51.1 2
35.17 even 12 350.2.e.g.151.1 2
35.19 odd 6 490.2.c.c.99.1 2
35.23 odd 12 2450.2.a.bh.1.1 1
35.24 odd 6 70.2.i.a.39.1 yes 4
35.27 even 4 350.2.e.g.51.1 2
35.33 even 12 2450.2.a.s.1.1 1
35.34 odd 2 70.2.i.a.9.2 yes 4
105.59 even 6 630.2.u.b.109.2 4
105.104 even 2 630.2.u.b.289.1 4
140.59 even 6 560.2.bw.c.529.1 4
140.139 even 2 560.2.bw.c.289.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
70.2.i.a.9.1 4 7.6 odd 2
70.2.i.a.9.2 yes 4 35.34 odd 2
70.2.i.a.39.1 yes 4 35.24 odd 6
70.2.i.a.39.2 yes 4 7.3 odd 6
350.2.e.f.51.1 2 35.13 even 4
350.2.e.f.151.1 2 35.3 even 12
350.2.e.g.51.1 2 35.27 even 4
350.2.e.g.151.1 2 35.17 even 12
490.2.c.b.99.1 2 35.9 even 6
490.2.c.b.99.2 2 7.2 even 3
490.2.c.c.99.1 2 35.19 odd 6
490.2.c.c.99.2 2 7.5 odd 6
490.2.i.b.79.1 4 1.1 even 1 trivial
490.2.i.b.79.2 4 5.4 even 2 inner
490.2.i.b.459.1 4 35.4 even 6 inner
490.2.i.b.459.2 4 7.4 even 3 inner
560.2.bw.c.289.1 4 28.27 even 2
560.2.bw.c.289.2 4 140.139 even 2
560.2.bw.c.529.1 4 140.59 even 6
560.2.bw.c.529.2 4 28.3 even 6
630.2.u.b.109.1 4 21.17 even 6
630.2.u.b.109.2 4 105.59 even 6
630.2.u.b.289.1 4 105.104 even 2
630.2.u.b.289.2 4 21.20 even 2
2450.2.a.c.1.1 1 35.2 odd 12
2450.2.a.r.1.1 1 35.12 even 12
2450.2.a.s.1.1 1 35.33 even 12
2450.2.a.bh.1.1 1 35.23 odd 12