Properties

Label 1274.2.f.i.1145.1
Level $1274$
Weight $2$
Character 1274.1145
Analytic conductor $10.173$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1274,2,Mod(79,1274)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1274, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1274.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1274.f (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: \(10.1729412175\)
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 182)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1145.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1274.1145
Dual form 1274.2.f.i.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 - 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{18} +(1.00000 + 1.73205i) q^{19} -3.00000 q^{22} +(1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(0.500000 + 0.866025i) q^{26} +5.00000 q^{27} +(2.50000 - 4.33013i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -2.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{39} -3.00000 q^{41} +8.00000 q^{43} +(1.50000 + 2.59808i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-1.50000 - 2.59808i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(0.500000 - 0.866025i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-2.50000 - 4.33013i) q^{54} +2.00000 q^{57} +(3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{66} +(-2.50000 + 4.33013i) q^{67} +3.00000 q^{69} +12.0000 q^{71} +(1.00000 + 1.73205i) q^{72} +(5.50000 - 9.52628i) q^{73} +(3.50000 - 6.06218i) q^{74} +(-2.50000 - 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(1.50000 + 2.59808i) q^{82} -12.0000 q^{83} +(-4.00000 - 6.92820i) q^{86} +(1.50000 - 2.59808i) q^{88} +(-9.00000 - 15.5885i) q^{89} -3.00000 q^{92} +(-2.50000 - 4.33013i) q^{93} +(-1.50000 + 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} -17.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 3 q^{11} + q^{12} - 2 q^{13} - q^{16} + 2 q^{18} + 2 q^{19} - 6 q^{22} + 3 q^{23} + q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 5 q^{31} - q^{32} - 3 q^{33} - 4 q^{36} + 7 q^{37} + 2 q^{38} - q^{39} - 6 q^{41} + 16 q^{43} + 3 q^{44} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 10 q^{50} + q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} + 6 q^{59} - q^{61} - 10 q^{62} + 2 q^{64} - 3 q^{66} - 5 q^{67} + 6 q^{69} + 24 q^{71} + 2 q^{72} + 11 q^{73} + 7 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{78} + q^{79} - q^{81} + 3 q^{82} - 24 q^{83} - 8 q^{86} + 3 q^{88} - 18 q^{89} - 6 q^{92} - 5 q^{93} - 3 q^{94} + q^{96} - 34 q^{97} + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(885\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 1.00000 1.73205i 0.235702 0.408248i
\(19\) 1.00000 + 1.73205i 0.229416 + 0.397360i 0.957635 0.287984i \(-0.0929851\pi\)
−0.728219 + 0.685344i \(0.759652\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 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
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 2.50000 4.33013i 0.449013 0.777714i −0.549309 0.835619i \(-0.685109\pi\)
0.998322 + 0.0579057i \(0.0184423\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.50000 2.59808i −0.261116 0.452267i
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 1.00000 1.73205i 0.162221 0.280976i
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 1.50000 + 2.59808i 0.226134 + 0.391675i
\(45\) 0 0
\(46\) 1.50000 2.59808i 0.221163 0.383065i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 0.500000 0.866025i 0.0693375 0.120096i
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) −2.50000 4.33013i −0.340207 0.589256i
\(55\) 0 0
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 3.00000 5.19615i 0.390567 0.676481i −0.601958 0.798528i \(-0.705612\pi\)
0.992524 + 0.122047i \(0.0389457\pi\)
\(60\) 0 0
\(61\) −0.500000 0.866025i −0.0640184 0.110883i 0.832240 0.554416i \(-0.187058\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) −5.00000 −0.635001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.50000 + 2.59808i −0.184637 + 0.319801i
\(67\) −2.50000 + 4.33013i −0.305424 + 0.529009i −0.977356 0.211604i \(-0.932131\pi\)
0.671932 + 0.740613i \(0.265465\pi\)
\(68\) 0 0
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 1.00000 + 1.73205i 0.117851 + 0.204124i
\(73\) 5.50000 9.52628i 0.643726 1.11497i −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) 3.50000 6.06218i 0.406867 0.704714i
\(75\) −2.50000 4.33013i −0.288675 0.500000i
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 0.500000 + 0.866025i 0.0562544 + 0.0974355i 0.892781 0.450490i \(-0.148751\pi\)
−0.836527 + 0.547926i \(0.815418\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.50000 + 2.59808i 0.165647 + 0.286910i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 6.92820i −0.431331 0.747087i
\(87\) 0 0
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) −9.00000 15.5885i −0.953998 1.65237i −0.736644 0.676280i \(-0.763591\pi\)
−0.217354 0.976093i \(-0.569742\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.00000 −0.312772
\(93\) −2.50000 4.33013i −0.259238 0.449013i
\(94\) −1.50000 + 2.59808i −0.154713 + 0.267971i
\(95\) 0 0
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) −17.0000 −1.72609 −0.863044 0.505128i \(-0.831445\pi\)
−0.863044 + 0.505128i \(0.831445\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 2.50000 + 4.33013i 0.250000 + 0.433013i
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) 0 0
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −2.50000 + 4.33013i −0.240563 + 0.416667i
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) 7.00000 0.664411
\(112\) 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
\(116\) 0 0
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −0.500000 + 0.866025i −0.0452679 + 0.0784063i
\(123\) −1.50000 + 2.59808i −0.135250 + 0.234261i
\(124\) 2.50000 + 4.33013i 0.224507 + 0.388857i
\(125\) 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
\(129\) 4.00000 6.92820i 0.352180 0.609994i
\(130\) 0 0
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 3.00000 0.261116
\(133\) 0 0
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 5.19615i 0.256307 0.443937i −0.708942 0.705266i \(-0.750827\pi\)
0.965250 + 0.261329i \(0.0841608\pi\)
\(138\) −1.50000 2.59808i −0.127688 0.221163i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) −6.00000 10.3923i −0.503509 0.872103i
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) 1.00000 1.73205i 0.0833333 0.144338i
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) 7.50000 + 12.9904i 0.614424 + 1.06421i 0.990485 + 0.137619i \(0.0439449\pi\)
−0.376061 + 0.926595i \(0.622722\pi\)
\(150\) −2.50000 + 4.33013i −0.204124 + 0.353553i
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 1.00000 + 1.73205i 0.0811107 + 0.140488i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) −6.50000 + 11.2583i −0.518756 + 0.898513i 0.481006 + 0.876717i \(0.340272\pi\)
−0.999762 + 0.0217953i \(0.993062\pi\)
\(158\) 0.500000 0.866025i 0.0397779 0.0688973i
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 0 0
\(166\) 6.00000 + 10.3923i 0.465690 + 0.806599i
\(167\) 24.0000 1.85718 0.928588 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) −4.00000 + 6.92820i −0.304997 + 0.528271i
\(173\) −9.00000 15.5885i −0.684257 1.18517i −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.00000 −0.226134
\(177\) −3.00000 5.19615i −0.225494 0.390567i
\(178\) −9.00000 + 15.5885i −0.674579 + 1.16840i
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 0 0
\(183\) −1.00000 −0.0739221
\(184\) 1.50000 + 2.59808i 0.110581 + 0.191533i
\(185\) 0 0
\(186\) −2.50000 + 4.33013i −0.183309 + 0.317500i
\(187\) 0 0
\(188\) 3.00000 0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 2.00000 3.46410i 0.143963 0.249351i −0.785022 0.619467i \(-0.787349\pi\)
0.928986 + 0.370116i \(0.120682\pi\)
\(194\) 8.50000 + 14.7224i 0.610264 + 1.05701i
\(195\) 0 0
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) −3.00000 5.19615i −0.213201 0.369274i
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 2.50000 4.33013i 0.176777 0.306186i
\(201\) 2.50000 + 4.33013i 0.176336 + 0.305424i
\(202\) 3.00000 0.211079
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) −3.00000 + 5.19615i −0.208514 + 0.361158i
\(208\) 0.500000 + 0.866025i 0.0346688 + 0.0600481i
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 6.00000 10.3923i 0.411113 0.712069i
\(214\) 0 0
\(215\) 0 0
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) −5.50000 9.52628i −0.371656 0.643726i
\(220\) 0 0
\(221\) 0 0
\(222\) −3.50000 6.06218i −0.234905 0.406867i
\(223\) 1.00000 0.0669650 0.0334825 0.999439i \(-0.489340\pi\)
0.0334825 + 0.999439i \(0.489340\pi\)
\(224\) 0 0
\(225\) 10.0000 0.666667
\(226\) −4.50000 7.79423i −0.299336 0.518464i
\(227\) −12.0000 + 20.7846i −0.796468 + 1.37952i 0.125435 + 0.992102i \(0.459967\pi\)
−0.921903 + 0.387421i \(0.873366\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) −1.00000 + 1.73205i −0.0653720 + 0.113228i
\(235\) 0 0
\(236\) 3.00000 + 5.19615i 0.195283 + 0.338241i
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 13.0000 22.5167i 0.837404 1.45043i −0.0546547 0.998505i \(-0.517406\pi\)
0.892058 0.451920i \(-0.149261\pi\)
\(242\) 1.00000 1.73205i 0.0642824 0.111340i
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 1.00000 0.0640184
\(245\) 0 0
\(246\) 3.00000 0.191273
\(247\) −1.00000 1.73205i −0.0636285 0.110208i
\(248\) 2.50000 4.33013i 0.158750 0.274963i
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 3.50000 + 6.06218i 0.219610 + 0.380375i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 12.0000 + 20.7846i 0.748539 + 1.29651i 0.948523 + 0.316709i \(0.102578\pi\)
−0.199983 + 0.979799i \(0.564089\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −12.0000 + 20.7846i −0.739952 + 1.28163i 0.212565 + 0.977147i \(0.431818\pi\)
−0.952517 + 0.304487i \(0.901515\pi\)
\(264\) −1.50000 2.59808i −0.0923186 0.159901i
\(265\) 0 0
\(266\) 0 0
\(267\) −18.0000 −1.10158
\(268\) −2.50000 4.33013i −0.152712 0.264505i
\(269\) −4.50000 + 7.79423i −0.274370 + 0.475223i −0.969976 0.243201i \(-0.921803\pi\)
0.695606 + 0.718423i \(0.255136\pi\)
\(270\) 0 0
\(271\) 5.50000 + 9.52628i 0.334101 + 0.578680i 0.983312 0.181928i \(-0.0582339\pi\)
−0.649211 + 0.760609i \(0.724901\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −7.50000 12.9904i −0.452267 0.783349i
\(276\) −1.50000 + 2.59808i −0.0902894 + 0.156386i
\(277\) −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i \(0.452005\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) 10.0000 0.598684
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 1.50000 + 2.59808i 0.0893237 + 0.154713i
\(283\) −15.5000 + 26.8468i −0.921379 + 1.59588i −0.124096 + 0.992270i \(0.539603\pi\)
−0.797283 + 0.603606i \(0.793730\pi\)
\(284\) −6.00000 + 10.3923i −0.356034 + 0.616670i
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 0 0
\(291\) −8.50000 + 14.7224i −0.498279 + 0.863044i
\(292\) 5.50000 + 9.52628i 0.321863 + 0.557483i
\(293\) −18.0000 −1.05157 −0.525786 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.50000 + 6.06218i 0.203433 + 0.352357i
\(297\) 7.50000 12.9904i 0.435194 0.753778i
\(298\) 7.50000 12.9904i 0.434463 0.752513i
\(299\) −1.50000 2.59808i −0.0867472 0.150251i
\(300\) 5.00000 0.288675
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 1.50000 + 2.59808i 0.0861727 + 0.149256i
\(304\) 1.00000 1.73205i 0.0573539 0.0993399i
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) 0 0
\(309\) 14.0000 0.796432
\(310\) 0 0
\(311\) 15.0000 25.9808i 0.850572 1.47323i −0.0301210 0.999546i \(-0.509589\pi\)
0.880693 0.473688i \(-0.157077\pi\)
\(312\) −0.500000 + 0.866025i −0.0283069 + 0.0490290i
\(313\) 13.0000 + 22.5167i 0.734803 + 1.27272i 0.954810 + 0.297218i \(0.0960589\pi\)
−0.220006 + 0.975499i \(0.570608\pi\)
\(314\) 13.0000 0.733632
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) 1.50000 + 2.59808i 0.0842484 + 0.145922i 0.905071 0.425261i \(-0.139818\pi\)
−0.820822 + 0.571184i \(0.806484\pi\)
\(318\) −6.00000 + 10.3923i −0.336463 + 0.582772i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −2.50000 + 4.33013i −0.138675 + 0.240192i
\(326\) −10.0000 + 17.3205i −0.553849 + 0.959294i
\(327\) 1.00000 + 1.73205i 0.0553001 + 0.0957826i
\(328\) −3.00000 −0.165647
\(329\) 0 0
\(330\) 0 0
\(331\) 9.50000 + 16.4545i 0.522167 + 0.904420i 0.999667 + 0.0257885i \(0.00820965\pi\)
−0.477500 + 0.878632i \(0.658457\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) −7.00000 + 12.1244i −0.383598 + 0.664411i
\(334\) −12.0000 20.7846i −0.656611 1.13728i
\(335\) 0 0
\(336\) 0 0
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) −0.500000 0.866025i −0.0271964 0.0471056i
\(339\) 4.50000 7.79423i 0.244406 0.423324i
\(340\) 0 0
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −9.00000 + 15.5885i −0.483843 + 0.838041i
\(347\) −12.0000 + 20.7846i −0.644194 + 1.11578i 0.340293 + 0.940319i \(0.389474\pi\)
−0.984487 + 0.175457i \(0.943860\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 7.50000 12.9904i 0.399185 0.691408i −0.594441 0.804139i \(-0.702627\pi\)
0.993626 + 0.112731i \(0.0359599\pi\)
\(354\) −3.00000 + 5.19615i −0.159448 + 0.276172i
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 0 0
\(361\) 7.50000 12.9904i 0.394737 0.683704i
\(362\) −3.50000 6.06218i −0.183956 0.318621i
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 0 0
\(366\) 0.500000 + 0.866025i 0.0261354 + 0.0452679i
\(367\) −14.0000 + 24.2487i −0.730794 + 1.26577i 0.225750 + 0.974185i \(0.427517\pi\)
−0.956544 + 0.291587i \(0.905817\pi\)
\(368\) 1.50000 2.59808i 0.0781929 0.135434i
\(369\) −3.00000 5.19615i −0.156174 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 5.00000 0.259238
\(373\) 2.00000 + 3.46410i 0.103556 + 0.179364i 0.913147 0.407630i \(-0.133645\pi\)
−0.809591 + 0.586994i \(0.800311\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.50000 2.59808i −0.0773566 0.133986i
\(377\) 0 0
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −3.50000 + 6.06218i −0.179310 + 0.310575i
\(382\) 0 0
\(383\) 1.50000 + 2.59808i 0.0766464 + 0.132755i 0.901801 0.432151i \(-0.142245\pi\)
−0.825155 + 0.564907i \(0.808912\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) 8.50000 14.7224i 0.431522 0.747418i
\(389\) 18.0000 31.1769i 0.912636 1.58073i 0.102311 0.994753i \(-0.467376\pi\)
0.810326 0.585980i \(-0.199290\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 1.50000 + 2.59808i 0.0755689 + 0.130889i
\(395\) 0 0
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) 10.0000 + 17.3205i 0.501886 + 0.869291i 0.999998 + 0.00217869i \(0.000693499\pi\)
−0.498112 + 0.867113i \(0.665973\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) −12.0000 20.7846i −0.599251 1.03793i −0.992932 0.118686i \(-0.962132\pi\)
0.393680 0.919247i \(-0.371202\pi\)
\(402\) 2.50000 4.33013i 0.124689 0.215967i
\(403\) −2.50000 + 4.33013i −0.124534 + 0.215699i
\(404\) −1.50000 2.59808i −0.0746278 0.129259i
\(405\) 0 0
\(406\) 0 0
\(407\) 21.0000 1.04093
\(408\) 0 0
\(409\) −11.0000 + 19.0526i −0.543915 + 0.942088i 0.454759 + 0.890614i \(0.349725\pi\)
−0.998674 + 0.0514740i \(0.983608\pi\)
\(410\) 0 0
\(411\) −3.00000 5.19615i −0.147979 0.256307i
\(412\) −14.0000 −0.689730
\(413\) 0 0
\(414\) 6.00000 0.294884
\(415\) 0 0
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) −3.00000 5.19615i −0.146735 0.254152i
\(419\) −21.0000 −1.02592 −0.512959 0.858413i \(-0.671451\pi\)
−0.512959 + 0.858413i \(0.671451\pi\)
\(420\) 0 0
\(421\) −37.0000 −1.80327 −0.901635 0.432498i \(-0.857632\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(422\) 11.0000 + 19.0526i 0.535472 + 0.927464i
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) 0 0
\(426\) −12.0000 −0.581402
\(427\) 0 0
\(428\) 0 0
\(429\) 1.50000 + 2.59808i 0.0724207 + 0.125436i
\(430\) 0 0
\(431\) 3.00000 5.19615i 0.144505 0.250290i −0.784683 0.619897i \(-0.787174\pi\)
0.929188 + 0.369607i \(0.120508\pi\)
\(432\) −2.50000 4.33013i −0.120281 0.208333i
\(433\) −38.0000 −1.82616 −0.913082 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 1.73205i −0.0478913 0.0829502i
\(437\) −3.00000 + 5.19615i −0.143509 + 0.248566i
\(438\) −5.50000 + 9.52628i −0.262800 + 0.455183i
\(439\) 13.0000 + 22.5167i 0.620456 + 1.07466i 0.989401 + 0.145210i \(0.0463858\pi\)
−0.368945 + 0.929451i \(0.620281\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.0000 20.7846i −0.570137 0.987507i −0.996551 0.0829786i \(-0.973557\pi\)
0.426414 0.904528i \(-0.359777\pi\)
\(444\) −3.50000 + 6.06218i −0.166103 + 0.287698i
\(445\) 0 0
\(446\) −0.500000 0.866025i −0.0236757 0.0410075i
\(447\) 15.0000 0.709476
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) −5.00000 8.66025i −0.235702 0.408248i
\(451\) −4.50000 + 7.79423i −0.211897 + 0.367016i
\(452\) −4.50000 + 7.79423i −0.211662 + 0.366610i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) 24.0000 1.12638
\(455\) 0 0
\(456\) 2.00000 0.0936586
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) −2.00000 + 3.46410i −0.0934539 + 0.161867i
\(459\) 0 0
\(460\) 0 0
\(461\) −24.0000 −1.11779 −0.558896 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 0 0
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) 6.00000 + 10.3923i 0.277647 + 0.480899i 0.970799 0.239892i \(-0.0771121\pi\)
−0.693153 + 0.720791i \(0.743779\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 6.50000 + 11.2583i 0.299504 + 0.518756i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) 12.0000 20.7846i 0.551761 0.955677i
\(474\) −0.500000 0.866025i −0.0229658 0.0397779i
\(475\) 10.0000 0.458831
\(476\) 0 0
\(477\) 24.0000 1.09888
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) 12.0000 20.7846i 0.548294 0.949673i −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 0 0
\(481\) −3.50000 6.06218i −0.159586 0.276412i
\(482\) −26.0000 −1.18427
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 8.00000 13.8564i 0.362887 0.628539i
\(487\) −1.00000 + 1.73205i −0.0453143 + 0.0784867i −0.887793 0.460243i \(-0.847762\pi\)
0.842479 + 0.538730i \(0.181096\pi\)
\(488\) −0.500000 0.866025i −0.0226339 0.0392031i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −1.50000 2.59808i −0.0676252 0.117130i
\(493\) 0 0
\(494\) −1.00000 + 1.73205i −0.0449921 + 0.0779287i
\(495\) 0 0
\(496\) −5.00000 −0.224507
\(497\) 0 0
\(498\) 12.0000 0.537733
\(499\) −11.5000 19.9186i −0.514811 0.891678i −0.999852 0.0171872i \(-0.994529\pi\)
0.485042 0.874491i \(-0.338804\pi\)
\(500\) 0 0
\(501\) 12.0000 20.7846i 0.536120 0.928588i
\(502\) −7.50000 12.9904i −0.334741 0.579789i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.50000 7.79423i −0.200049 0.346496i
\(507\) 0.500000 0.866025i 0.0222058 0.0384615i
\(508\) 3.50000 6.06218i 0.155287 0.268966i
\(509\) −15.0000 25.9808i −0.664863 1.15158i −0.979322 0.202306i \(-0.935156\pi\)
0.314459 0.949271i \(-0.398177\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 5.00000 + 8.66025i 0.220755 + 0.382360i
\(514\) 12.0000 20.7846i 0.529297 0.916770i
\(515\) 0 0
\(516\) 4.00000 + 6.92820i 0.176090 + 0.304997i
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 3.00000 5.19615i 0.131432 0.227648i −0.792797 0.609486i \(-0.791376\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 0 0
\(523\) −3.50000 6.06218i −0.153044 0.265081i 0.779301 0.626650i \(-0.215574\pi\)
−0.932345 + 0.361569i \(0.882241\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) −1.50000 + 2.59808i −0.0652791 + 0.113067i
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) 3.00000 0.129944
\(534\) 9.00000 + 15.5885i 0.389468 + 0.674579i
\(535\) 0 0
\(536\) −2.50000 + 4.33013i −0.107984 + 0.187033i
\(537\) −3.00000 5.19615i −0.129460 0.224231i
\(538\) 9.00000 0.388018
\(539\) 0 0
\(540\) 0 0
\(541\) 17.0000 + 29.4449i 0.730887 + 1.26593i 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) 5.50000 9.52628i 0.236245 0.409189i
\(543\) 3.50000 6.06218i 0.150199 0.260153i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 3.00000 + 5.19615i 0.128154 + 0.221969i
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) −7.50000 + 12.9904i −0.319801 + 0.553912i
\(551\) 0 0
\(552\) 3.00000 0.127688
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 7.50000 12.9904i 0.317785 0.550420i −0.662240 0.749291i \(-0.730394\pi\)
0.980026 + 0.198871i \(0.0637276\pi\)
\(558\) −5.00000 8.66025i −0.211667 0.366618i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 10.3923i −0.253095 0.438373i
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 1.50000 2.59808i 0.0631614 0.109399i
\(565\) 0 0
\(566\) 31.0000 1.30303
\(567\) 0 0
\(568\) 12.0000 0.503509
\(569\) −10.5000 18.1865i −0.440183 0.762419i 0.557520 0.830164i \(-0.311753\pi\)
−0.997703 + 0.0677445i \(0.978420\pi\)
\(570\) 0 0
\(571\) 11.0000 19.0526i 0.460336 0.797325i −0.538642 0.842535i \(-0.681062\pi\)
0.998978 + 0.0452101i \(0.0143957\pi\)
\(572\) −1.50000 2.59808i −0.0627182 0.108631i
\(573\) 0 0
\(574\) 0 0
\(575\) 15.0000 0.625543
\(576\) 1.00000 + 1.73205i 0.0416667 + 0.0721688i
\(577\) 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i \(-0.820078\pi\)
0.886090 + 0.463513i \(0.153411\pi\)
\(578\) 8.50000 14.7224i 0.353553 0.612372i
\(579\) −2.00000 3.46410i −0.0831172 0.143963i
\(580\) 0 0
\(581\) 0 0
\(582\) 17.0000 0.704673
\(583\) −18.0000 31.1769i −0.745484 1.29122i
\(584\) 5.50000 9.52628i 0.227592 0.394200i
\(585\) 0 0
\(586\) 9.00000 + 15.5885i 0.371787 + 0.643953i
\(587\) −18.0000 −0.742940 −0.371470 0.928445i \(-0.621146\pi\)
−0.371470 + 0.928445i \(0.621146\pi\)
\(588\) 0 0
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) −1.50000 + 2.59808i −0.0617018 + 0.106871i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) −15.0000 −0.615457
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) 8.00000 + 13.8564i 0.327418 + 0.567105i
\(598\) −1.50000 + 2.59808i −0.0613396 + 0.106243i
\(599\) −19.5000 + 33.7750i −0.796748 + 1.38001i 0.124975 + 0.992160i \(0.460115\pi\)
−0.921723 + 0.387849i \(0.873218\pi\)
\(600\) −2.50000 4.33013i −0.102062 0.176777i
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) −10.0000 −0.407231
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 0 0
\(606\) 1.50000 2.59808i 0.0609333 0.105540i
\(607\) 7.00000 + 12.1244i 0.284121 + 0.492112i 0.972396 0.233338i \(-0.0749648\pi\)
−0.688274 + 0.725450i \(0.741632\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 1.50000 + 2.59808i 0.0606835 + 0.105107i
\(612\) 0 0
\(613\) 12.5000 21.6506i 0.504870 0.874461i −0.495114 0.868828i \(-0.664874\pi\)
0.999984 0.00563283i \(-0.00179300\pi\)
\(614\) −8.00000 13.8564i −0.322854 0.559199i
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) −7.00000 12.1244i −0.281581 0.487713i
\(619\) −5.00000 + 8.66025i −0.200967 + 0.348085i −0.948840 0.315757i \(-0.897742\pi\)
0.747873 + 0.663842i \(0.231075\pi\)
\(620\) 0 0
\(621\) 7.50000 + 12.9904i 0.300965 + 0.521286i
\(622\) −30.0000 −1.20289
\(623\) 0 0
\(624\) 1.00000 0.0400320
\(625\) −12.5000 21.6506i −0.500000 0.866025i
\(626\) 13.0000 22.5167i 0.519584 0.899947i
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) −6.50000 11.2583i −0.259378 0.449256i
\(629\) 0 0
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 0.500000 + 0.866025i 0.0198889 + 0.0344486i
\(633\) −11.0000 + 19.0526i −0.437211 + 0.757271i
\(634\) 1.50000 2.59808i 0.0595726 0.103183i
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) 0 0
\(638\) 0 0
\(639\) 12.0000 + 20.7846i 0.474713 + 0.822226i
\(640\) 0 0
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 0 0
\(643\) −32.0000 −1.26196 −0.630978 0.775800i \(-0.717346\pi\)
−0.630978 + 0.775800i \(0.717346\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.00000 10.3923i 0.235884 0.408564i −0.723645 0.690172i \(-0.757535\pi\)
0.959529 + 0.281609i \(0.0908680\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −9.00000 15.5885i −0.353281 0.611900i
\(650\) 5.00000 0.196116
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) −12.0000 20.7846i −0.469596 0.813365i 0.529799 0.848123i \(-0.322267\pi\)
−0.999396 + 0.0347583i \(0.988934\pi\)
\(654\) 1.00000 1.73205i 0.0391031 0.0677285i
\(655\) 0 0
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 22.0000 0.858302
\(658\) 0 0
\(659\) 42.0000 1.63609 0.818044 0.575156i \(-0.195059\pi\)
0.818044 + 0.575156i \(0.195059\pi\)
\(660\) 0 0
\(661\) 16.0000 27.7128i 0.622328 1.07790i −0.366723 0.930330i \(-0.619520\pi\)
0.989051 0.147573i \(-0.0471463\pi\)
\(662\) 9.50000 16.4545i 0.369228 0.639522i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 14.0000 0.542489
\(667\) 0 0
\(668\) −12.0000 + 20.7846i −0.464294 + 0.804181i
\(669\) 0.500000 0.866025i 0.0193311 0.0334825i
\(670\) 0 0
\(671\) −3.00000 −0.115814
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 15.5000 + 26.8468i 0.597038 + 1.03410i
\(675\) 12.5000 21.6506i 0.481125 0.833333i
\(676\) −0.500000 + 0.866025i −0.0192308 + 0.0333087i
\(677\) −19.5000 33.7750i −0.749446 1.29808i −0.948089 0.318006i \(-0.896987\pi\)
0.198643 0.980072i \(-0.436347\pi\)
\(678\) −9.00000 −0.345643
\(679\) 0 0
\(680\) 0 0
\(681\) 12.0000 + 20.7846i 0.459841 + 0.796468i
\(682\) −7.50000 + 12.9904i −0.287190 + 0.497427i
\(683\) 13.5000 23.3827i 0.516563 0.894714i −0.483252 0.875481i \(-0.660544\pi\)
0.999815 0.0192323i \(-0.00612219\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 4.00000 + 6.92820i 0.152167 + 0.263561i 0.932024 0.362397i \(-0.118041\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) 18.0000 0.684257
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −5.00000 8.66025i −0.189253 0.327795i
\(699\) −3.00000 −0.113470
\(700\) 0 0
\(701\) −36.0000 −1.35970 −0.679851 0.733351i \(-0.737955\pi\)
−0.679851 + 0.733351i \(0.737955\pi\)
\(702\) 2.50000 + 4.33013i 0.0943564 + 0.163430i
\(703\) −7.00000 + 12.1244i −0.264010 + 0.457279i
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 0 0
\(706\) −15.0000 −0.564532
\(707\) 0 0
\(708\) 6.00000 0.225494
\(709\) −17.5000 30.3109i −0.657226 1.13835i −0.981331 0.192328i \(-0.938396\pi\)
0.324104 0.946021i \(-0.394937\pi\)
\(710\) 0 0
\(711\) −1.00000 + 1.73205i −0.0375029 + 0.0649570i
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) 15.0000 0.561754
\(714\) 0 0
\(715\) 0 0
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) 3.00000 5.19615i 0.112037 0.194054i
\(718\) 12.0000 20.7846i 0.447836 0.775675i
\(719\) 3.00000 + 5.19615i 0.111881 + 0.193784i 0.916529 0.399969i \(-0.130979\pi\)
−0.804648 + 0.593753i \(0.797646\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 −0.558242
\(723\) −13.0000 22.5167i −0.483475 0.837404i
\(724\) −3.50000 + 6.06218i −0.130076 + 0.225299i
\(725\) 0 0
\(726\) −1.00000 1.73205i −0.0371135 0.0642824i
\(727\) −26.0000 −0.964287 −0.482143 0.876092i \(-0.660142\pi\)
−0.482143 + 0.876092i \(0.660142\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0.500000 0.866025i 0.0184805 0.0320092i
\(733\) −2.00000 3.46410i −0.0738717 0.127950i 0.826723 0.562609i \(-0.190202\pi\)
−0.900595 + 0.434659i \(0.856869\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 7.50000 + 12.9904i 0.276266 + 0.478507i
\(738\) −3.00000 + 5.19615i −0.110432 + 0.191273i
\(739\) 8.00000 13.8564i 0.294285 0.509716i −0.680534 0.732717i \(-0.738252\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) −2.50000 4.33013i −0.0916544 0.158750i
\(745\) 0 0
\(746\) 2.00000 3.46410i 0.0732252 0.126830i
\(747\) −12.0000 20.7846i −0.439057 0.760469i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 15.5000 + 26.8468i 0.565603 + 0.979653i 0.996993 + 0.0774878i \(0.0246899\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 7.50000 12.9904i 0.273315 0.473396i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 8.00000 + 13.8564i 0.290573 + 0.503287i
\(759\) 4.50000 7.79423i 0.163340 0.282913i
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 7.00000 0.253583
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 1.50000 2.59808i 0.0541972 0.0938723i
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) 13.0000 0.468792 0.234396 0.972141i \(-0.424689\pi\)
0.234396 + 0.972141i \(0.424689\pi\)
\(770\) 0 0
\(771\) 24.0000 0.864339
\(772\) 2.00000 + 3.46410i 0.0719816 + 0.124676i
\(773\) −27.0000 + 46.7654i −0.971123 + 1.68203i −0.278944 + 0.960307i \(0.589984\pi\)
−0.692179 + 0.721726i \(0.743349\pi\)
\(774\) 8.00000 13.8564i 0.287554 0.498058i
\(775\) −12.5000 21.6506i −0.449013 0.777714i
\(776\) −17.0000 −0.610264
\(777\) 0 0
\(778\) −36.0000 −1.29066
\(779\) −3.00000 5.19615i −0.107486 0.186171i
\(780\) 0 0
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 16.0000 27.7128i 0.570338 0.987855i −0.426193 0.904632i \(-0.640145\pi\)
0.996531 0.0832226i \(-0.0265213\pi\)
\(788\) 1.50000 2.59808i 0.0534353 0.0925526i
\(789\) 12.0000 + 20.7846i 0.427211 + 0.739952i
\(790\) 0 0
\(791\) 0 0
\(792\) 6.00000 0.213201
\(793\) 0.500000 + 0.866025i 0.0177555 + 0.0307535i
\(794\) 10.0000 17.3205i 0.354887 0.614682i
\(795\) 0 0
\(796\) −8.00000 13.8564i −0.283552 0.491127i
\(797\) −9.00000 −0.318796 −0.159398 0.987214i \(-0.550955\pi\)
−0.159398 + 0.987214i \(0.550955\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 2.50000 + 4.33013i 0.0883883 + 0.153093i
\(801\) 18.0000 31.1769i 0.635999 1.10158i
\(802\) −12.0000 + 20.7846i −0.423735 + 0.733930i
\(803\) −16.5000 28.5788i −0.582272 1.00853i
\(804\) −5.00000 −0.176336
\(805\) 0 0
\(806\) 5.00000 0.176117
\(807\) 4.50000 + 7.79423i 0.158408 + 0.274370i
\(808\) −1.50000 + 2.59808i −0.0527698 + 0.0914000i
\(809\) −15.0000 + 25.9808i −0.527372 + 0.913435i 0.472119 + 0.881535i \(0.343489\pi\)
−0.999491 + 0.0319002i \(0.989844\pi\)
\(810\) 0 0
\(811\) −20.0000 −0.702295 −0.351147 0.936320i \(-0.614208\pi\)
−0.351147 + 0.936320i \(0.614208\pi\)
\(812\) 0 0
\(813\) 11.0000 0.385787
\(814\) −10.5000 18.1865i −0.368025 0.637438i
\(815\) 0 0
\(816\) 0 0
\(817\) 8.00000 + 13.8564i 0.279885 + 0.484774i
\(818\) 22.0000 0.769212
\(819\) 0 0
\(820\) 0 0
\(821\) 3.00000 + 5.19615i 0.104701 + 0.181347i 0.913616 0.406578i \(-0.133278\pi\)
−0.808915 + 0.587925i \(0.799945\pi\)
\(822\) −3.00000 + 5.19615i −0.104637 + 0.181237i
\(823\) −20.5000 + 35.5070i −0.714585 + 1.23770i 0.248534 + 0.968623i \(0.420051\pi\)
−0.963119 + 0.269075i \(0.913282\pi\)
\(824\) 7.00000 + 12.1244i 0.243857 + 0.422372i
\(825\) −15.0000 −0.522233
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) −3.00000 5.19615i −0.104257 0.180579i
\(829\) 19.0000 32.9090i 0.659897 1.14298i −0.320745 0.947166i \(-0.603933\pi\)
0.980642 0.195810i \(-0.0627335\pi\)
\(830\) 0 0
\(831\) 13.0000 + 22.5167i 0.450965 + 0.781094i
\(832\) −1.00000 −0.0346688
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) −3.00000 + 5.19615i −0.103757 + 0.179713i
\(837\) 12.5000 21.6506i 0.432063 0.748355i
\(838\) 10.5000 + 18.1865i 0.362716 + 0.628243i
\(839\) 21.0000 0.725001 0.362500 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 18.5000 + 32.0429i 0.637552 + 1.10427i
\(843\) 6.00000 10.3923i 0.206651 0.357930i
\(844\) 11.0000 19.0526i 0.378636 0.655816i
\(845\) 0 0
\(846\) −6.00000 −0.206284
\(847\) 0 0
\(848\) −12.0000 −0.412082
\(849\) 15.5000 + 26.8468i 0.531959 + 0.921379i
\(850\) 0 0
\(851\) −10.5000 + 18.1865i −0.359935 + 0.623426i
\(852\) 6.00000 + 10.3923i 0.205557 + 0.356034i
\(853\) −44.0000 −1.50653 −0.753266 0.657716i \(-0.771523\pi\)
−0.753266 + 0.657716i \(0.771523\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 27.0000 46.7654i 0.922302 1.59747i 0.126459 0.991972i \(-0.459639\pi\)
0.795843 0.605503i \(-0.207028\pi\)
\(858\) 1.50000 2.59808i 0.0512092 0.0886969i
\(859\) 11.5000 + 19.9186i 0.392375 + 0.679613i 0.992762 0.120096i \(-0.0383202\pi\)
−0.600387 + 0.799709i \(0.704987\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −6.00000 −0.204361
\(863\) −6.00000 10.3923i −0.204242 0.353758i 0.745649 0.666339i \(-0.232140\pi\)
−0.949891 + 0.312581i \(0.898806\pi\)
\(864\) −2.50000 + 4.33013i −0.0850517 + 0.147314i
\(865\) 0 0
\(866\) 19.0000 + 32.9090i 0.645646 + 1.11829i
\(867\) 17.0000 0.577350
\(868\) 0 0
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) 2.50000 4.33013i 0.0847093 0.146721i
\(872\) −1.00000 + 1.73205i −0.0338643 + 0.0586546i
\(873\) −17.0000 29.4449i −0.575363 0.996558i
\(874\) 6.00000 0.202953
\(875\) 0 0
\(876\) 11.0000 0.371656
\(877\) 6.50000 + 11.2583i 0.219489 + 0.380167i 0.954652 0.297724i \(-0.0962275\pi\)
−0.735163 + 0.677891i \(0.762894\pi\)
\(878\) 13.0000 22.5167i 0.438729 0.759900i
\(879\) −9.00000 + 15.5885i −0.303562 + 0.525786i
\(880\) 0 0
\(881\) −6.00000 −0.202145 −0.101073 0.994879i \(-0.532227\pi\)
−0.101073 + 0.994879i \(0.532227\pi\)
\(882\) 0 0
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −12.0000 + 20.7846i −0.403148 + 0.698273i
\(887\) 21.0000 + 36.3731i 0.705111 + 1.22129i 0.966651 + 0.256096i \(0.0824362\pi\)
−0.261540 + 0.965193i \(0.584230\pi\)
\(888\) 7.00000 0.234905
\(889\) 0 0
\(890\) 0 0
\(891\) 1.50000 + 2.59808i 0.0502519 + 0.0870388i
\(892\) −0.500000 + 0.866025i −0.0167412 + 0.0289967i
\(893\) 3.00000 5.19615i 0.100391 0.173883i
\(894\) −7.50000 12.9904i −0.250838 0.434463i
\(895\) 0 0
\(896\) 0 0
\(897\) −3.00000 −0.100167
\(898\) 3.00000 + 5.19615i 0.100111 + 0.173398i
\(899\) 0 0
\(900\) −5.00000 + 8.66025i −0.166667 + 0.288675i
\(901\) 0 0
\(902\) 9.00000 0.299667
\(903\) 0 0
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) 4.00000 6.92820i 0.132891 0.230174i
\(907\) −13.0000 + 22.5167i −0.431658 + 0.747653i −0.997016 0.0771920i \(-0.975405\pi\)
0.565358 + 0.824845i \(0.308738\pi\)
\(908\) −12.0000 20.7846i −0.398234 0.689761i
\(909\) −6.00000 −0.199007
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) −1.00000 1.73205i −0.0331133 0.0573539i
\(913\) −18.0000 + 31.1769i −0.595713 + 1.03181i
\(914\) −13.0000 + 22.5167i −0.430002 + 0.744785i
\(915\) 0 0
\(916\) 4.00000 0.132164
\(917\) 0 0
\(918\) 0 0
\(919\) 12.5000 + 21.6506i 0.412337 + 0.714189i 0.995145 0.0984214i \(-0.0313793\pi\)
−0.582808 + 0.812610i \(0.698046\pi\)
\(920\) 0 0
\(921\) 8.00000 13.8564i 0.263609 0.456584i
\(922\) 12.0000 + 20.7846i 0.395199 + 0.684505i
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) 35.0000 1.15079
\(926\) 20.0000 + 34.6410i 0.657241 + 1.13837i
\(927\) −14.0000 + 24.2487i −0.459820 + 0.796432i
\(928\) 0 0
\(929\) −4.50000 7.79423i −0.147640 0.255720i 0.782715 0.622381i \(-0.213834\pi\)
−0.930355 + 0.366660i \(0.880501\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 3.00000 0.0982683
\(933\) −15.0000 25.9808i −0.491078 0.850572i
\(934\) 6.00000 10.3923i 0.196326 0.340047i
\(935\) 0 0
\(936\) −1.00000 1.73205i −0.0326860 0.0566139i
\(937\) 52.0000 1.69877 0.849383 0.527777i \(-0.176974\pi\)
0.849383 + 0.527777i \(0.176974\pi\)
\(938\) 0 0
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 15.0000 25.9808i 0.488986 0.846949i −0.510934 0.859620i \(-0.670700\pi\)
0.999920 + 0.0126715i \(0.00403357\pi\)
\(942\) 6.50000 11.2583i 0.211781 0.366816i
\(943\) −4.50000 7.79423i −0.146540 0.253815i
\(944\) −6.00000 −0.195283
\(945\) 0 0
\(946\) −24.0000 −0.780307
\(947\) −24.0000 41.5692i −0.779895 1.35082i −0.932002 0.362454i \(-0.881939\pi\)
0.152106 0.988364i \(-0.451394\pi\)
\(948\) −0.500000 + 0.866025i −0.0162392 + 0.0281272i
\(949\) −5.50000 + 9.52628i −0.178538 + 0.309236i
\(950\) −5.00000 8.66025i −0.162221 0.280976i
\(951\) 3.00000 0.0972817
\(952\) 0 0
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) −12.0000 20.7846i −0.388514 0.672927i
\(955\) 0 0
\(956\) −3.00000 + 5.19615i −0.0970269 + 0.168056i
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 0 0
\(960\) 0 0
\(961\) 3.00000 + 5.19615i 0.0967742 + 0.167618i
\(962\) −3.50000 + 6.06218i −0.112845 + 0.195452i
\(963\) 0 0
\(964\) 13.0000 + 22.5167i 0.418702 + 0.725213i
\(965\) 0 0
\(966\) 0 0
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 1.00000 + 1.73205i 0.0321412 + 0.0556702i
\(969\) 0 0
\(970\) 0 0
\(971\) −10.5000 18.1865i −0.336961 0.583634i 0.646899 0.762576i \(-0.276066\pi\)
−0.983860 + 0.178942i \(0.942732\pi\)
\(972\) −16.0000 −0.513200
\(973\) 0 0
\(974\) 2.00000 0.0640841
\(975\) 2.50000 + 4.33013i 0.0800641 + 0.138675i
\(976\) −0.500000 + 0.866025i −0.0160046 + 0.0277208i
\(977\) −9.00000 + 15.5885i −0.287936 + 0.498719i −0.973317 0.229465i \(-0.926302\pi\)
0.685381 + 0.728184i \(0.259636\pi\)
\(978\) 10.0000 + 17.3205i 0.319765 + 0.553849i
\(979\) −54.0000 −1.72585
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) −6.00000 10.3923i −0.191468 0.331632i
\(983\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(984\) −1.50000 + 2.59808i −0.0478183 + 0.0828236i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 2.00000 0.0636285
\(989\) 12.0000 + 20.7846i 0.381578 + 0.660912i
\(990\) 0 0
\(991\) −5.50000 + 9.52628i −0.174713 + 0.302612i −0.940062 0.341004i \(-0.889233\pi\)
0.765349 + 0.643616i \(0.222567\pi\)
\(992\) 2.50000 + 4.33013i 0.0793751 + 0.137482i
\(993\) 19.0000 0.602947
\(994\) 0 0
\(995\) 0 0
\(996\) −6.00000 10.3923i −0.190117 0.329293i
\(997\) −18.5000 + 32.0429i −0.585901 + 1.01481i 0.408862 + 0.912596i \(0.365926\pi\)
−0.994762 + 0.102214i \(0.967407\pi\)
\(998\) −11.5000 + 19.9186i −0.364026 + 0.630512i
\(999\) 17.5000 + 30.3109i 0.553675 + 0.958994i
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 1274.2.f.i.1145.1 2
7.2 even 3 inner 1274.2.f.i.79.1 2
7.3 odd 6 182.2.a.d.1.1 1
7.4 even 3 1274.2.a.j.1.1 1
7.5 odd 6 1274.2.f.d.79.1 2
7.6 odd 2 1274.2.f.d.1145.1 2
21.17 even 6 1638.2.a.f.1.1 1
28.3 even 6 1456.2.a.d.1.1 1
35.24 odd 6 4550.2.a.c.1.1 1
56.3 even 6 5824.2.a.x.1.1 1
56.45 odd 6 5824.2.a.k.1.1 1
91.31 even 12 2366.2.d.e.337.1 2
91.38 odd 6 2366.2.a.e.1.1 1
91.73 even 12 2366.2.d.e.337.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
182.2.a.d.1.1 1 7.3 odd 6
1274.2.a.j.1.1 1 7.4 even 3
1274.2.f.d.79.1 2 7.5 odd 6
1274.2.f.d.1145.1 2 7.6 odd 2
1274.2.f.i.79.1 2 7.2 even 3 inner
1274.2.f.i.1145.1 2 1.1 even 1 trivial
1456.2.a.d.1.1 1 28.3 even 6
1638.2.a.f.1.1 1 21.17 even 6
2366.2.a.e.1.1 1 91.38 odd 6
2366.2.d.e.337.1 2 91.31 even 12
2366.2.d.e.337.2 2 91.73 even 12
4550.2.a.c.1.1 1 35.24 odd 6
5824.2.a.k.1.1 1 56.45 odd 6
5824.2.a.x.1.1 1 56.3 even 6