Properties

Label 1078.2.e.k.177.1
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.k.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.00000 q^{6} -1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} +1.00000 q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +9.00000 q^{29} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 + 0.866025i) q^{33} -6.00000 q^{34} -2.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(0.500000 + 0.866025i) q^{39} +6.00000 q^{41} -4.00000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} -1.00000 q^{48} +5.00000 q^{50} +(3.00000 - 5.19615i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(2.50000 - 4.33013i) q^{54} +2.00000 q^{57} +(4.50000 - 7.79423i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(5.50000 - 9.52628i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{66} +(-5.50000 - 9.52628i) q^{67} +(-3.00000 + 5.19615i) q^{68} +6.00000 q^{69} +(-1.00000 + 1.73205i) q^{72} +(1.00000 + 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(4.50000 + 7.79423i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(-9.00000 + 15.5885i) q^{89} -6.00000 q^{92} +(2.00000 - 3.46410i) q^{93} +(3.00000 + 5.19615i) q^{94} +(-0.500000 + 0.866025i) q^{96} +13.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} - q^{4} + 2 q^{6} - 2 q^{8} + 2 q^{9} + q^{11} + q^{12} + 2 q^{13} - q^{16} - 6 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{22} + 6 q^{23} - q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 18 q^{29} - 4 q^{31} + q^{32} - q^{33} - 12 q^{34} - 4 q^{36} - 2 q^{37} - 2 q^{38} + q^{39} + 12 q^{41} - 8 q^{43} + q^{44} - 6 q^{46} - 6 q^{47} - 2 q^{48} + 10 q^{50} + 6 q^{51} - q^{52} + 5 q^{54} + 4 q^{57} + 9 q^{58} - 3 q^{59} + 11 q^{61} - 8 q^{62} + 2 q^{64} + q^{66} - 11 q^{67} - 6 q^{68} + 12 q^{69} - 2 q^{72} + 2 q^{73} + 2 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{78} - 5 q^{79} - q^{81} + 6 q^{82} + 12 q^{83} - 4 q^{86} + 9 q^{87} - q^{88} - 18 q^{89} - 12 q^{92} + 4 q^{93} + 6 q^{94} - q^{96} + 26 q^{97} + 4 q^{99}+O(q^{100}) \) 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
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −1.00000 1.73205i −0.235702 0.408248i
\(19\) 1.00000 1.73205i 0.229416 0.397360i −0.728219 0.685344i \(-0.759652\pi\)
0.957635 + 0.287984i \(0.0929851\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 3.00000 5.19615i 0.625543 1.08347i −0.362892 0.931831i \(-0.618211\pi\)
0.988436 0.151642i \(-0.0484560\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) 0.500000 0.866025i 0.0980581 0.169842i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) 0 0
\(31\) −2.00000 3.46410i −0.359211 0.622171i 0.628619 0.777714i \(-0.283621\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) −0.500000 + 0.866025i −0.0870388 + 0.150756i
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −1.00000 1.73205i −0.162221 0.280976i
\(39\) 0.500000 + 0.866025i 0.0800641 + 0.138675i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0.500000 0.866025i 0.0753778 0.130558i
\(45\) 0 0
\(46\) −3.00000 5.19615i −0.442326 0.766131i
\(47\) −3.00000 + 5.19615i −0.437595 + 0.757937i −0.997503 0.0706177i \(-0.977503\pi\)
0.559908 + 0.828554i \(0.310836\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) 5.00000 0.707107
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −0.500000 0.866025i −0.0693375 0.120096i
\(53\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(54\) 2.50000 4.33013i 0.340207 0.589256i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 4.50000 7.79423i 0.590879 1.02343i
\(59\) −1.50000 2.59808i −0.195283 0.338241i 0.751710 0.659494i \(-0.229229\pi\)
−0.946993 + 0.321253i \(0.895896\pi\)
\(60\) 0 0
\(61\) 5.50000 9.52628i 0.704203 1.21972i −0.262776 0.964857i \(-0.584638\pi\)
0.966978 0.254858i \(-0.0820288\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.500000 + 0.866025i 0.0615457 + 0.106600i
\(67\) −5.50000 9.52628i −0.671932 1.16382i −0.977356 0.211604i \(-0.932131\pi\)
0.305424 0.952217i \(-0.401202\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.00000 + 1.73205i −0.117851 + 0.204124i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) −2.50000 + 4.33013i −0.288675 + 0.500000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 4.50000 + 7.79423i 0.482451 + 0.835629i
\(88\) −0.500000 0.866025i −0.0533002 0.0923186i
\(89\) −9.00000 + 15.5885i −0.953998 + 1.65237i −0.217354 + 0.976093i \(0.569742\pi\)
−0.736644 + 0.676280i \(0.763591\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −6.00000 −0.625543
\(93\) 2.00000 3.46410i 0.207390 0.359211i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) −3.00000 5.19615i −0.297044 0.514496i
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) −2.50000 4.33013i −0.240563 0.416667i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 1.00000 1.73205i 0.0936586 0.162221i
\(115\) 0 0
\(116\) −4.50000 7.79423i −0.417815 0.723676i
\(117\) 1.00000 1.73205i 0.0924500 0.160128i
\(118\) −3.00000 −0.276172
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) −5.50000 9.52628i −0.497947 0.862469i
\(123\) 3.00000 + 5.19615i 0.270501 + 0.468521i
\(124\) −2.00000 + 3.46410i −0.179605 + 0.311086i
\(125\) 0 0
\(126\) 0 0
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) −2.00000 3.46410i −0.176090 0.304997i
\(130\) 0 0
\(131\) 9.00000 15.5885i 0.786334 1.36197i −0.141865 0.989886i \(-0.545310\pi\)
0.928199 0.372084i \(-0.121357\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) −11.0000 −0.950255
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) 4.50000 + 7.79423i 0.384461 + 0.665906i 0.991694 0.128618i \(-0.0410540\pi\)
−0.607233 + 0.794524i \(0.707721\pi\)
\(138\) 3.00000 5.19615i 0.255377 0.442326i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 0.500000 + 0.866025i 0.0418121 + 0.0724207i
\(144\) 1.00000 + 1.73205i 0.0833333 + 0.144338i
\(145\) 0 0
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 2.50000 + 4.33013i 0.204124 + 0.353553i
\(151\) 9.50000 + 16.4545i 0.773099 + 1.33905i 0.935857 + 0.352381i \(0.114628\pi\)
−0.162758 + 0.986666i \(0.552039\pi\)
\(152\) −1.00000 + 1.73205i −0.0811107 + 0.140488i
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) 0 0
\(156\) 0.500000 0.866025i 0.0400320 0.0693375i
\(157\) −2.00000 3.46410i −0.159617 0.276465i 0.775113 0.631822i \(-0.217693\pi\)
−0.934731 + 0.355357i \(0.884359\pi\)
\(158\) 2.50000 + 4.33013i 0.198889 + 0.344486i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −8.50000 + 14.7224i −0.665771 + 1.15315i 0.313304 + 0.949653i \(0.398564\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) 3.00000 5.19615i 0.232845 0.403300i
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) 2.00000 + 3.46410i 0.152499 + 0.264135i
\(173\) −10.5000 + 18.1865i −0.798300 + 1.38270i 0.122422 + 0.992478i \(0.460934\pi\)
−0.920722 + 0.390218i \(0.872399\pi\)
\(174\) 9.00000 0.682288
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 1.50000 2.59808i 0.112747 0.195283i
\(178\) 9.00000 + 15.5885i 0.674579 + 1.16840i
\(179\) 7.50000 + 12.9904i 0.560576 + 0.970947i 0.997446 + 0.0714220i \(0.0227537\pi\)
−0.436870 + 0.899525i \(0.643913\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 11.0000 0.813143
\(184\) −3.00000 + 5.19615i −0.221163 + 0.383065i
\(185\) 0 0
\(186\) −2.00000 3.46410i −0.146647 0.254000i
\(187\) 3.00000 5.19615i 0.219382 0.379980i
\(188\) 6.00000 0.437595
\(189\) 0 0
\(190\) 0 0
\(191\) −3.00000 + 5.19615i −0.217072 + 0.375980i −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 6.50000 11.2583i 0.466673 0.808301i
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) 7.00000 + 12.1244i 0.496217 + 0.859473i 0.999990 0.00436292i \(-0.00138876\pi\)
−0.503774 + 0.863836i \(0.668055\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) 5.50000 9.52628i 0.387940 0.671932i
\(202\) −15.0000 −1.05540
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) −6.00000 10.3923i −0.417029 0.722315i
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) −10.0000 −0.688428 −0.344214 0.938891i \(-0.611855\pi\)
−0.344214 + 0.938891i \(0.611855\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −1.00000 + 1.73205i −0.0675737 + 0.117041i
\(220\) 0 0
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) −1.00000 + 1.73205i −0.0671156 + 0.116248i
\(223\) −26.0000 −1.74109 −0.870544 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 0 0
\(225\) 10.0000 0.666667
\(226\) 4.50000 7.79423i 0.299336 0.518464i
\(227\) 9.00000 + 15.5885i 0.597351 + 1.03464i 0.993210 + 0.116331i \(0.0371134\pi\)
−0.395860 + 0.918311i \(0.629553\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) −8.00000 + 13.8564i −0.528655 + 0.915657i 0.470787 + 0.882247i \(0.343970\pi\)
−0.999442 + 0.0334101i \(0.989363\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) −1.00000 1.73205i −0.0653720 0.113228i
\(235\) 0 0
\(236\) −1.50000 + 2.59808i −0.0976417 + 0.169120i
\(237\) −5.00000 −0.324785
\(238\) 0 0
\(239\) −9.00000 −0.582162 −0.291081 0.956698i \(-0.594015\pi\)
−0.291081 + 0.956698i \(0.594015\pi\)
\(240\) 0 0
\(241\) 13.0000 + 22.5167i 0.837404 + 1.45043i 0.892058 + 0.451920i \(0.149261\pi\)
−0.0546547 + 0.998505i \(0.517406\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 8.00000 13.8564i 0.513200 0.888889i
\(244\) −11.0000 −0.704203
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 1.00000 1.73205i 0.0636285 0.110208i
\(248\) 2.00000 + 3.46410i 0.127000 + 0.219971i
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) −3.50000 + 6.06218i −0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) 0 0
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) −9.00000 15.5885i −0.556022 0.963058i
\(263\) 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i \(-0.0771668\pi\)
−0.693276 + 0.720672i \(0.743833\pi\)
\(264\) 0.500000 0.866025i 0.0307729 0.0533002i
\(265\) 0 0
\(266\) 0 0
\(267\) −18.0000 −1.10158
\(268\) −5.50000 + 9.52628i −0.335966 + 0.581910i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 14.5000 25.1147i 0.880812 1.52561i 0.0303728 0.999539i \(-0.490331\pi\)
0.850439 0.526073i \(-0.176336\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) 9.00000 0.543710
\(275\) −2.50000 + 4.33013i −0.150756 + 0.261116i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) −14.5000 25.1147i −0.871221 1.50900i −0.860735 0.509053i \(-0.829996\pi\)
−0.0104855 0.999945i \(-0.503338\pi\)
\(278\) −4.00000 + 6.92820i −0.239904 + 0.415526i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) −3.00000 + 5.19615i −0.178647 + 0.309426i
\(283\) −5.00000 8.66025i −0.297219 0.514799i 0.678280 0.734804i \(-0.262726\pi\)
−0.975499 + 0.220005i \(0.929393\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.00000 0.0591312
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) 6.50000 + 11.2583i 0.381037 + 0.659975i
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 2.50000 + 4.33013i 0.145065 + 0.251259i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 3.00000 5.19615i 0.173494 0.300501i
\(300\) 5.00000 0.288675
\(301\) 0 0
\(302\) 19.0000 1.09333
\(303\) 7.50000 12.9904i 0.430864 0.746278i
\(304\) 1.00000 + 1.73205i 0.0573539 + 0.0993399i
\(305\) 0 0
\(306\) −6.00000 + 10.3923i −0.342997 + 0.594089i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) −0.500000 0.866025i −0.0283069 0.0490290i
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) −4.00000 −0.225733
\(315\) 0 0
\(316\) 5.00000 0.281272
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) −0.500000 + 0.866025i −0.0277778 + 0.0481125i
\(325\) 2.50000 + 4.33013i 0.138675 + 0.240192i
\(326\) 8.50000 + 14.7224i 0.470771 + 0.815400i
\(327\) 1.00000 1.73205i 0.0553001 0.0957826i
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −17.5000 + 30.3109i −0.961887 + 1.66604i −0.244131 + 0.969742i \(0.578503\pi\)
−0.717756 + 0.696295i \(0.754831\pi\)
\(332\) −3.00000 5.19615i −0.164646 0.285176i
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) −1.50000 + 2.59808i −0.0820763 + 0.142160i
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −6.00000 + 10.3923i −0.326357 + 0.565267i
\(339\) 4.50000 + 7.79423i 0.244406 + 0.423324i
\(340\) 0 0
\(341\) 2.00000 3.46410i 0.108306 0.187592i
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) 10.5000 + 18.1865i 0.564483 + 0.977714i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 4.50000 7.79423i 0.241225 0.417815i
\(349\) −2.00000 −0.107058 −0.0535288 0.998566i \(-0.517047\pi\)
−0.0535288 + 0.998566i \(0.517047\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) −1.50000 2.59808i −0.0797241 0.138086i
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) 15.0000 0.792775
\(359\) 1.50000 2.59808i 0.0791670 0.137121i −0.823724 0.566991i \(-0.808107\pi\)
0.902891 + 0.429870i \(0.141441\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 0 0
\(366\) 5.50000 9.52628i 0.287490 0.497947i
\(367\) −5.00000 8.66025i −0.260998 0.452062i 0.705509 0.708700i \(-0.250718\pi\)
−0.966507 + 0.256639i \(0.917385\pi\)
\(368\) 3.00000 + 5.19615i 0.156386 + 0.270868i
\(369\) 6.00000 10.3923i 0.312348 0.541002i
\(370\) 0 0
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) 15.5000 26.8468i 0.802560 1.39007i −0.115367 0.993323i \(-0.536804\pi\)
0.917926 0.396751i \(-0.129862\pi\)
\(374\) −3.00000 5.19615i −0.155126 0.268687i
\(375\) 0 0
\(376\) 3.00000 5.19615i 0.154713 0.267971i
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0 0
\(381\) −3.50000 6.06218i −0.179310 0.310575i
\(382\) 3.00000 + 5.19615i 0.153493 + 0.265858i
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) −6.50000 11.2583i −0.329988 0.571555i
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 0 0
\(391\) −36.0000 −1.82060
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) −1.50000 + 2.59808i −0.0755689 + 0.130889i
\(395\) 0 0
\(396\) −1.00000 1.73205i −0.0502519 0.0870388i
\(397\) −11.0000 + 19.0526i −0.552074 + 0.956221i 0.446051 + 0.895008i \(0.352830\pi\)
−0.998125 + 0.0612128i \(0.980503\pi\)
\(398\) 14.0000 0.701757
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 16.5000 28.5788i 0.823971 1.42716i −0.0787327 0.996896i \(-0.525087\pi\)
0.902703 0.430263i \(-0.141579\pi\)
\(402\) −5.50000 9.52628i −0.274315 0.475128i
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) −7.50000 + 12.9904i −0.373139 + 0.646296i
\(405\) 0 0
\(406\) 0 0
\(407\) −2.00000 −0.0991363
\(408\) −3.00000 + 5.19615i −0.148522 + 0.257248i
\(409\) −2.00000 3.46410i −0.0988936 0.171289i 0.812333 0.583193i \(-0.198197\pi\)
−0.911227 + 0.411905i \(0.864864\pi\)
\(410\) 0 0
\(411\) −4.50000 + 7.79423i −0.221969 + 0.384461i
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) −12.0000 −0.589768
\(415\) 0 0
\(416\) 0.500000 + 0.866025i 0.0245145 + 0.0424604i
\(417\) −4.00000 6.92820i −0.195881 0.339276i
\(418\) 1.00000 1.73205i 0.0489116 0.0847174i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) −5.00000 + 8.66025i −0.243396 + 0.421575i
\(423\) 6.00000 + 10.3923i 0.291730 + 0.505291i
\(424\) 0 0
\(425\) 15.0000 25.9808i 0.727607 1.26025i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) −0.500000 + 0.866025i −0.0241402 + 0.0418121i
\(430\) 0 0
\(431\) 1.50000 + 2.59808i 0.0722525 + 0.125145i 0.899888 0.436121i \(-0.143648\pi\)
−0.827636 + 0.561266i \(0.810315\pi\)
\(432\) −2.50000 + 4.33013i −0.120281 + 0.208333i
\(433\) 34.0000 1.63394 0.816968 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) −6.00000 10.3923i −0.287019 0.497131i
\(438\) 1.00000 + 1.73205i 0.0477818 + 0.0827606i
\(439\) −0.500000 + 0.866025i −0.0238637 + 0.0413331i −0.877711 0.479191i \(-0.840930\pi\)
0.853847 + 0.520524i \(0.174263\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) 0 0
\(446\) −13.0000 + 22.5167i −0.615568 + 1.06619i
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 5.00000 8.66025i 0.235702 0.408248i
\(451\) 3.00000 + 5.19615i 0.141264 + 0.244677i
\(452\) −4.50000 7.79423i −0.211662 0.366610i
\(453\) −9.50000 + 16.4545i −0.446349 + 0.773099i
\(454\) 18.0000 0.844782
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) 11.0000 19.0526i 0.514558 0.891241i −0.485299 0.874348i \(-0.661289\pi\)
0.999857 0.0168929i \(-0.00537742\pi\)
\(458\) 8.00000 + 13.8564i 0.373815 + 0.647467i
\(459\) −15.0000 25.9808i −0.700140 1.21268i
\(460\) 0 0
\(461\) −21.0000 −0.978068 −0.489034 0.872265i \(-0.662651\pi\)
−0.489034 + 0.872265i \(0.662651\pi\)
\(462\) 0 0
\(463\) −22.0000 −1.02243 −0.511213 0.859454i \(-0.670804\pi\)
−0.511213 + 0.859454i \(0.670804\pi\)
\(464\) −4.50000 + 7.79423i −0.208907 + 0.361838i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) 1.50000 + 2.59808i 0.0690431 + 0.119586i
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) −2.50000 + 4.33013i −0.114829 + 0.198889i
\(475\) 10.0000 0.458831
\(476\) 0 0
\(477\) 0 0
\(478\) −4.50000 + 7.79423i −0.205825 + 0.356500i
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) −1.00000 + 1.73205i −0.0455961 + 0.0789747i
\(482\) 26.0000 1.18427
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 0 0
\(486\) −8.00000 13.8564i −0.362887 0.628539i
\(487\) −10.0000 17.3205i −0.453143 0.784867i 0.545436 0.838152i \(-0.316364\pi\)
−0.998579 + 0.0532853i \(0.983031\pi\)
\(488\) −5.50000 + 9.52628i −0.248973 + 0.431234i
\(489\) −17.0000 −0.768767
\(490\) 0 0
\(491\) 42.0000 1.89543 0.947717 0.319113i \(-0.103385\pi\)
0.947717 + 0.319113i \(0.103385\pi\)
\(492\) 3.00000 5.19615i 0.135250 0.234261i
\(493\) −27.0000 46.7654i −1.21602 2.10621i
\(494\) −1.00000 1.73205i −0.0449921 0.0779287i
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 6.00000 0.268866
\(499\) 20.0000 34.6410i 0.895323 1.55074i 0.0619186 0.998081i \(-0.480278\pi\)
0.833404 0.552664i \(-0.186389\pi\)
\(500\) 0 0
\(501\) −1.50000 2.59808i −0.0670151 0.116073i
\(502\) 6.00000 10.3923i 0.267793 0.463831i
\(503\) 33.0000 1.47140 0.735699 0.677309i \(-0.236854\pi\)
0.735699 + 0.677309i \(0.236854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) −6.00000 10.3923i −0.266469 0.461538i
\(508\) 3.50000 + 6.06218i 0.155287 + 0.268966i
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 5.00000 8.66025i 0.220755 0.382360i
\(514\) −1.50000 2.59808i −0.0661622 0.114596i
\(515\) 0 0
\(516\) −2.00000 + 3.46410i −0.0880451 + 0.152499i
\(517\) −6.00000 −0.263880
\(518\) 0 0
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) −21.0000 36.3731i −0.920027 1.59353i −0.799370 0.600839i \(-0.794833\pi\)
−0.120656 0.992694i \(-0.538500\pi\)
\(522\) −9.00000 15.5885i −0.393919 0.682288i
\(523\) −8.00000 + 13.8564i −0.349816 + 0.605898i −0.986216 0.165460i \(-0.947089\pi\)
0.636401 + 0.771358i \(0.280422\pi\)
\(524\) −18.0000 −0.786334
\(525\) 0 0
\(526\) 9.00000 0.392419
\(527\) −12.0000 + 20.7846i −0.522728 + 0.905392i
\(528\) −0.500000 0.866025i −0.0217597 0.0376889i
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) −9.00000 + 15.5885i −0.389468 + 0.674579i
\(535\) 0 0
\(536\) 5.50000 + 9.52628i 0.237564 + 0.411473i
\(537\) −7.50000 + 12.9904i −0.323649 + 0.560576i
\(538\) 12.0000 0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) −14.5000 25.1147i −0.622828 1.07877i
\(543\) −1.00000 1.73205i −0.0429141 0.0743294i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) −11.0000 19.0526i −0.469469 0.813143i
\(550\) 2.50000 + 4.33013i 0.106600 + 0.184637i
\(551\) 9.00000 15.5885i 0.383413 0.664091i
\(552\) −6.00000 −0.255377
\(553\) 0 0
\(554\) −29.0000 −1.23209
\(555\) 0 0
\(556\) 4.00000 + 6.92820i 0.169638 + 0.293821i
\(557\) 9.00000 + 15.5885i 0.381342 + 0.660504i 0.991254 0.131965i \(-0.0421286\pi\)
−0.609912 + 0.792469i \(0.708795\pi\)
\(558\) −4.00000 + 6.92820i −0.169334 + 0.293294i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 6.00000 0.253320
\(562\) 9.00000 15.5885i 0.379642 0.657559i
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 3.00000 + 5.19615i 0.126323 + 0.218797i
\(565\) 0 0
\(566\) −10.0000 −0.420331
\(567\) 0 0
\(568\) 0 0
\(569\) 18.0000 31.1769i 0.754599 1.30700i −0.190974 0.981595i \(-0.561165\pi\)
0.945573 0.325409i \(-0.105502\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0.500000 0.866025i 0.0209061 0.0362103i
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 30.0000 1.25109
\(576\) 1.00000 1.73205i 0.0416667 0.0721688i
\(577\) −3.50000 6.06218i −0.145707 0.252372i 0.783930 0.620850i \(-0.213212\pi\)
−0.929636 + 0.368478i \(0.879879\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 7.00000 12.1244i 0.290910 0.503871i
\(580\) 0 0
\(581\) 0 0
\(582\) 13.0000 0.538867
\(583\) 0 0
\(584\) −1.00000 1.73205i −0.0413803 0.0716728i
\(585\) 0 0
\(586\) 15.0000 25.9808i 0.619644 1.07326i
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −1.50000 2.59808i −0.0617018 0.106871i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 18.0000 31.1769i 0.739171 1.28028i −0.213697 0.976900i \(-0.568551\pi\)
0.952869 0.303383i \(-0.0981160\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) −7.00000 + 12.1244i −0.286491 + 0.496217i
\(598\) −3.00000 5.19615i −0.122679 0.212486i
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 2.50000 4.33013i 0.102062 0.176777i
\(601\) −2.00000 −0.0815817 −0.0407909 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) −22.0000 −0.895909
\(604\) 9.50000 16.4545i 0.386550 0.669523i
\(605\) 0 0
\(606\) −7.50000 12.9904i −0.304667 0.527698i
\(607\) −20.0000 + 34.6410i −0.811775 + 1.40604i 0.0998457 + 0.995003i \(0.468165\pi\)
−0.911621 + 0.411033i \(0.865168\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 5.00000 + 8.66025i 0.201948 + 0.349784i 0.949156 0.314806i \(-0.101939\pi\)
−0.747208 + 0.664590i \(0.768606\pi\)
\(614\) −10.0000 + 17.3205i −0.403567 + 0.698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 21.0000 0.845428 0.422714 0.906263i \(-0.361077\pi\)
0.422714 + 0.906263i \(0.361077\pi\)
\(618\) −8.00000 + 13.8564i −0.321807 + 0.557386i
\(619\) 10.0000 + 17.3205i 0.401934 + 0.696170i 0.993959 0.109749i \(-0.0350048\pi\)
−0.592025 + 0.805919i \(0.701671\pi\)
\(620\) 0 0
\(621\) 15.0000 25.9808i 0.601929 1.04257i
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −8.50000 14.7224i −0.339728 0.588427i
\(627\) 1.00000 + 1.73205i 0.0399362 + 0.0691714i
\(628\) −2.00000 + 3.46410i −0.0798087 + 0.138233i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 2.50000 4.33013i 0.0994447 0.172243i
\(633\) −5.00000 8.66025i −0.198732 0.344214i
\(634\) 6.00000 + 10.3923i 0.238290 + 0.412731i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 9.00000 0.356313
\(639\) 0 0
\(640\) 0 0
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) −6.00000 + 10.3923i −0.236801 + 0.410152i
\(643\) −5.00000 −0.197181 −0.0985904 0.995128i \(-0.531433\pi\)
−0.0985904 + 0.995128i \(0.531433\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.00000 + 10.3923i −0.236067 + 0.408880i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) 1.50000 2.59808i 0.0588802 0.101983i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 17.0000 0.665771
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) −1.00000 1.73205i −0.0391031 0.0677285i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 7.00000 + 12.1244i 0.272268 + 0.471583i 0.969442 0.245319i \(-0.0788928\pi\)
−0.697174 + 0.716902i \(0.745559\pi\)
\(662\) 17.5000 + 30.3109i 0.680157 + 1.17807i
\(663\) 3.00000 5.19615i 0.116510 0.201802i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) 1.50000 + 2.59808i 0.0580367 + 0.100523i
\(669\) −13.0000 22.5167i −0.502609 0.870544i
\(670\) 0 0
\(671\) 11.0000 0.424650
\(672\) 0 0
\(673\) −28.0000 −1.07932 −0.539660 0.841883i \(-0.681447\pi\)
−0.539660 + 0.841883i \(0.681447\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 12.5000 + 21.6506i 0.481125 + 0.833333i
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 9.00000 0.345643
\(679\) 0 0
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) −2.00000 3.46410i −0.0765840 0.132647i
\(683\) 10.5000 + 18.1865i 0.401771 + 0.695888i 0.993940 0.109926i \(-0.0350613\pi\)
−0.592168 + 0.805814i \(0.701728\pi\)
\(684\) −2.00000 + 3.46410i −0.0764719 + 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) 2.00000 3.46410i 0.0762493 0.132068i
\(689\) 0 0
\(690\) 0 0
\(691\) 5.50000 9.52628i 0.209230 0.362397i −0.742242 0.670132i \(-0.766238\pi\)
0.951472 + 0.307735i \(0.0995710\pi\)
\(692\) 21.0000 0.798300
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) −4.50000 7.79423i −0.170572 0.295439i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −1.00000 + 1.73205i −0.0378506 + 0.0655591i
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 39.0000 1.47301 0.736505 0.676432i \(-0.236475\pi\)
0.736505 + 0.676432i \(0.236475\pi\)
\(702\) 2.50000 4.33013i 0.0943564 0.163430i
\(703\) 2.00000 + 3.46410i 0.0754314 + 0.130651i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) −3.00000 −0.112747
\(709\) −13.0000 + 22.5167i −0.488225 + 0.845631i −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 0 0
\(711\) 5.00000 + 8.66025i 0.187515 + 0.324785i
\(712\) 9.00000 15.5885i 0.337289 0.584202i
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) 7.50000 12.9904i 0.280288 0.485473i
\(717\) −4.50000 7.79423i −0.168056 0.291081i
\(718\) −1.50000 2.59808i −0.0559795 0.0969593i
\(719\) −21.0000 + 36.3731i −0.783168 + 1.35649i 0.146920 + 0.989148i \(0.453064\pi\)
−0.930087 + 0.367338i \(0.880269\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) −13.0000 + 22.5167i −0.483475 + 0.837404i
\(724\) 1.00000 + 1.73205i 0.0371647 + 0.0643712i
\(725\) 22.5000 + 38.9711i 0.835629 + 1.44735i
\(726\) −0.500000 + 0.866025i −0.0185567 + 0.0321412i
\(727\) −14.0000 −0.519231 −0.259616 0.965712i \(-0.583596\pi\)
−0.259616 + 0.965712i \(0.583596\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 12.0000 + 20.7846i 0.443836 + 0.768747i
\(732\) −5.50000 9.52628i −0.203286 0.352101i
\(733\) −12.5000 + 21.6506i −0.461698 + 0.799684i −0.999046 0.0436764i \(-0.986093\pi\)
0.537348 + 0.843361i \(0.319426\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 5.50000 9.52628i 0.202595 0.350905i
\(738\) −6.00000 10.3923i −0.220863 0.382546i
\(739\) −25.0000 43.3013i −0.919640 1.59286i −0.799962 0.600050i \(-0.795147\pi\)
−0.119677 0.992813i \(-0.538186\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) −2.00000 + 3.46410i −0.0733236 + 0.127000i
\(745\) 0 0
\(746\) −15.5000 26.8468i −0.567495 0.982931i
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) −6.00000 −0.219382
\(749\) 0 0
\(750\) 0 0
\(751\) 2.00000 3.46410i 0.0729810 0.126407i −0.827225 0.561870i \(-0.810082\pi\)
0.900207 + 0.435463i \(0.143415\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 6.00000 + 10.3923i 0.218652 + 0.378717i
\(754\) 4.50000 7.79423i 0.163880 0.283849i
\(755\) 0 0
\(756\) 0 0
\(757\) −46.0000 −1.67190 −0.835949 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 11.5000 19.9186i 0.417699 0.723476i
\(759\) 3.00000 + 5.19615i 0.108893 + 0.188608i
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) −7.00000 −0.253583
\(763\) 0 0
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 18.0000 + 31.1769i 0.650366 + 1.12647i
\(767\) −1.50000 2.59808i −0.0541619 0.0938111i
\(768\) 0.500000 0.866025i 0.0180422 0.0312500i
\(769\) 22.0000 0.793340 0.396670 0.917961i \(-0.370166\pi\)
0.396670 + 0.917961i \(0.370166\pi\)
\(770\) 0 0
\(771\) 3.00000 0.108042
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 12.0000 + 20.7846i 0.431610 + 0.747570i 0.997012 0.0772449i \(-0.0246123\pi\)
−0.565402 + 0.824815i \(0.691279\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) 10.0000 17.3205i 0.359211 0.622171i
\(776\) −13.0000 −0.466673
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) 6.00000 10.3923i 0.214972 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) −18.0000 + 31.1769i −0.643679 + 1.11488i
\(783\) 45.0000 1.60817