Properties

Label 1170.2.bp.d.289.1
Level $1170$
Weight $2$
Character 1170.289
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
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] = [1170,2,Mod(289,1170)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("1170.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bp (of order \(6\), degree \(2\), 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: \(9.34249703649\)
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.289
Dual form 1170.2.bp.d.919.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.23205 - 0.133975i) q^{5} +(-2.36603 - 1.36603i) q^{7} +1.00000i q^{8} +(-1.86603 + 1.23205i) q^{10} +(0.366025 + 0.633975i) q^{11} +(-3.59808 - 0.232051i) q^{13} +2.73205 q^{14} +(-0.500000 - 0.866025i) q^{16} +(3.86603 + 2.23205i) q^{17} +(0.633975 - 1.09808i) q^{19} +(1.00000 - 2.00000i) q^{20} +(-0.633975 - 0.366025i) q^{22} +(5.36603 - 3.09808i) q^{23} +(4.96410 - 0.598076i) q^{25} +(3.23205 - 1.59808i) q^{26} +(-2.36603 + 1.36603i) q^{28} +(3.23205 + 5.59808i) q^{29} +4.00000 q^{31} +(0.866025 + 0.500000i) q^{32} -4.46410 q^{34} +(-5.46410 - 2.73205i) q^{35} +(6.86603 - 3.96410i) q^{37} +1.26795i q^{38} +(0.133975 + 2.23205i) q^{40} +(-4.59808 - 7.96410i) q^{41} +(-2.83013 - 1.63397i) q^{43} +0.732051 q^{44} +(-3.09808 + 5.36603i) q^{46} -7.66025i q^{47} +(0.232051 + 0.401924i) q^{49} +(-4.00000 + 3.00000i) q^{50} +(-2.00000 + 3.00000i) q^{52} +7.73205i q^{53} +(0.901924 + 1.36603i) q^{55} +(1.36603 - 2.36603i) q^{56} +(-5.59808 - 3.23205i) q^{58} +(6.19615 - 10.7321i) q^{59} +(5.06218 - 8.76795i) q^{61} +(-3.46410 + 2.00000i) q^{62} -1.00000 q^{64} +(-8.06218 - 0.0358984i) q^{65} +(6.63397 - 3.83013i) q^{67} +(3.86603 - 2.23205i) q^{68} +(6.09808 - 0.366025i) q^{70} +(0.633975 - 1.09808i) q^{71} +4.66025i q^{73} +(-3.96410 + 6.86603i) q^{74} +(-0.633975 - 1.09808i) q^{76} -2.00000i q^{77} -12.0000 q^{79} +(-1.23205 - 1.86603i) q^{80} +(7.96410 + 4.59808i) q^{82} +5.26795i q^{83} +(8.92820 + 4.46410i) q^{85} +3.26795 q^{86} +(-0.633975 + 0.366025i) q^{88} +(2.46410 + 4.26795i) q^{89} +(8.19615 + 5.46410i) q^{91} -6.19615i q^{92} +(3.83013 + 6.63397i) q^{94} +(1.26795 - 2.53590i) q^{95} +(8.66025 + 5.00000i) q^{97} +(-0.401924 - 0.232051i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{4} + 2 q^{5} - 6 q^{7} - 4 q^{10} - 2 q^{11} - 4 q^{13} + 4 q^{14} - 2 q^{16} + 12 q^{17} + 6 q^{19} + 4 q^{20} - 6 q^{22} + 18 q^{23} + 6 q^{25} + 6 q^{26} - 6 q^{28} + 6 q^{29} + 16 q^{31} - 4 q^{34} - 8 q^{35} + 24 q^{37} + 4 q^{40} - 8 q^{41} + 6 q^{43} - 4 q^{44} - 2 q^{46} - 6 q^{49} - 16 q^{50} - 8 q^{52} + 14 q^{55} + 2 q^{56} - 12 q^{58} + 4 q^{59} - 4 q^{61} - 4 q^{64} - 8 q^{65} + 30 q^{67} + 12 q^{68} + 14 q^{70} + 6 q^{71} - 2 q^{74} - 6 q^{76} - 48 q^{79} + 2 q^{80} + 18 q^{82} + 8 q^{85} + 20 q^{86} - 6 q^{88} - 4 q^{89} + 12 q^{91} - 2 q^{94} + 12 q^{95} - 12 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 2.23205 0.133975i 0.998203 0.0599153i
\(6\) 0 0
\(7\) −2.36603 1.36603i −0.894274 0.516309i −0.0189356 0.999821i \(-0.506028\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.86603 + 1.23205i −0.590089 + 0.389609i
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0 0
\(13\) −3.59808 0.232051i −0.997927 0.0643593i
\(14\) 2.73205 0.730171
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.86603 + 2.23205i 0.937649 + 0.541352i 0.889223 0.457475i \(-0.151246\pi\)
0.0484264 + 0.998827i \(0.484579\pi\)
\(18\) 0 0
\(19\) 0.633975 1.09808i 0.145444 0.251916i −0.784095 0.620641i \(-0.786872\pi\)
0.929538 + 0.368725i \(0.120206\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) −0.633975 0.366025i −0.135164 0.0780369i
\(23\) 5.36603 3.09808i 1.11889 0.645994i 0.177775 0.984071i \(-0.443110\pi\)
0.941118 + 0.338078i \(0.109777\pi\)
\(24\) 0 0
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) 3.23205 1.59808i 0.633857 0.313409i
\(27\) 0 0
\(28\) −2.36603 + 1.36603i −0.447137 + 0.258155i
\(29\) 3.23205 + 5.59808i 0.600177 + 1.03954i 0.992794 + 0.119835i \(0.0382364\pi\)
−0.392617 + 0.919702i \(0.628430\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −4.46410 −0.765587
\(35\) −5.46410 2.73205i −0.923602 0.461801i
\(36\) 0 0
\(37\) 6.86603 3.96410i 1.12877 0.651694i 0.185143 0.982712i \(-0.440725\pi\)
0.943625 + 0.331017i \(0.107392\pi\)
\(38\) 1.26795i 0.205689i
\(39\) 0 0
\(40\) 0.133975 + 2.23205i 0.0211832 + 0.352918i
\(41\) −4.59808 7.96410i −0.718099 1.24378i −0.961752 0.273921i \(-0.911679\pi\)
0.243653 0.969862i \(-0.421654\pi\)
\(42\) 0 0
\(43\) −2.83013 1.63397i −0.431590 0.249179i 0.268434 0.963298i \(-0.413494\pi\)
−0.700024 + 0.714119i \(0.746827\pi\)
\(44\) 0.732051 0.110361
\(45\) 0 0
\(46\) −3.09808 + 5.36603i −0.456786 + 0.791177i
\(47\) 7.66025i 1.11736i −0.829382 0.558681i \(-0.811307\pi\)
0.829382 0.558681i \(-0.188693\pi\)
\(48\) 0 0
\(49\) 0.232051 + 0.401924i 0.0331501 + 0.0574177i
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) −2.00000 + 3.00000i −0.277350 + 0.416025i
\(53\) 7.73205i 1.06208i 0.847347 + 0.531039i \(0.178198\pi\)
−0.847347 + 0.531039i \(0.821802\pi\)
\(54\) 0 0
\(55\) 0.901924 + 1.36603i 0.121615 + 0.184195i
\(56\) 1.36603 2.36603i 0.182543 0.316173i
\(57\) 0 0
\(58\) −5.59808 3.23205i −0.735063 0.424389i
\(59\) 6.19615 10.7321i 0.806670 1.39719i −0.108487 0.994098i \(-0.534601\pi\)
0.915158 0.403096i \(-0.132066\pi\)
\(60\) 0 0
\(61\) 5.06218 8.76795i 0.648145 1.12262i −0.335420 0.942069i \(-0.608878\pi\)
0.983565 0.180552i \(-0.0577885\pi\)
\(62\) −3.46410 + 2.00000i −0.439941 + 0.254000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −8.06218 0.0358984i −0.999990 0.00445265i
\(66\) 0 0
\(67\) 6.63397 3.83013i 0.810469 0.467924i −0.0366497 0.999328i \(-0.511669\pi\)
0.847119 + 0.531404i \(0.178335\pi\)
\(68\) 3.86603 2.23205i 0.468824 0.270676i
\(69\) 0 0
\(70\) 6.09808 0.366025i 0.728860 0.0437484i
\(71\) 0.633975 1.09808i 0.0752389 0.130318i −0.825951 0.563742i \(-0.809361\pi\)
0.901190 + 0.433424i \(0.142695\pi\)
\(72\) 0 0
\(73\) 4.66025i 0.545441i 0.962093 + 0.272721i \(0.0879235\pi\)
−0.962093 + 0.272721i \(0.912076\pi\)
\(74\) −3.96410 + 6.86603i −0.460817 + 0.798159i
\(75\) 0 0
\(76\) −0.633975 1.09808i −0.0727219 0.125958i
\(77\) 2.00000i 0.227921i
\(78\) 0 0
\(79\) −12.0000 −1.35011 −0.675053 0.737769i \(-0.735879\pi\)
−0.675053 + 0.737769i \(0.735879\pi\)
\(80\) −1.23205 1.86603i −0.137747 0.208628i
\(81\) 0 0
\(82\) 7.96410 + 4.59808i 0.879488 + 0.507773i
\(83\) 5.26795i 0.578233i 0.957294 + 0.289116i \(0.0933614\pi\)
−0.957294 + 0.289116i \(0.906639\pi\)
\(84\) 0 0
\(85\) 8.92820 + 4.46410i 0.968400 + 0.484200i
\(86\) 3.26795 0.352392
\(87\) 0 0
\(88\) −0.633975 + 0.366025i −0.0675819 + 0.0390184i
\(89\) 2.46410 + 4.26795i 0.261194 + 0.452402i 0.966560 0.256442i \(-0.0825504\pi\)
−0.705365 + 0.708844i \(0.749217\pi\)
\(90\) 0 0
\(91\) 8.19615 + 5.46410i 0.859190 + 0.572793i
\(92\) 6.19615i 0.645994i
\(93\) 0 0
\(94\) 3.83013 + 6.63397i 0.395047 + 0.684242i
\(95\) 1.26795 2.53590i 0.130089 0.260178i
\(96\) 0 0
\(97\) 8.66025 + 5.00000i 0.879316 + 0.507673i 0.870433 0.492287i \(-0.163839\pi\)
0.00888289 + 0.999961i \(0.497172\pi\)
\(98\) −0.401924 0.232051i −0.0406004 0.0234407i
\(99\) 0 0
\(100\) 1.96410 4.59808i 0.196410 0.459808i
\(101\) 6.96410 + 12.0622i 0.692954 + 1.20023i 0.970866 + 0.239625i \(0.0770245\pi\)
−0.277912 + 0.960607i \(0.589642\pi\)
\(102\) 0 0
\(103\) 9.26795i 0.913198i −0.889673 0.456599i \(-0.849067\pi\)
0.889673 0.456599i \(-0.150933\pi\)
\(104\) 0.232051 3.59808i 0.0227545 0.352820i
\(105\) 0 0
\(106\) −3.86603 6.69615i −0.375502 0.650388i
\(107\) −1.09808 + 0.633975i −0.106155 + 0.0612886i −0.552138 0.833753i \(-0.686188\pi\)
0.445983 + 0.895042i \(0.352854\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −1.46410 0.732051i −0.139597 0.0697983i
\(111\) 0 0
\(112\) 2.73205i 0.258155i
\(113\) −7.79423 4.50000i −0.733219 0.423324i 0.0863794 0.996262i \(-0.472470\pi\)
−0.819599 + 0.572938i \(0.805804\pi\)
\(114\) 0 0
\(115\) 11.5622 7.63397i 1.07818 0.711872i
\(116\) 6.46410 0.600177
\(117\) 0 0
\(118\) 12.3923i 1.14080i
\(119\) −6.09808 10.5622i −0.559010 0.968233i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) 10.1244i 0.916616i
\(123\) 0 0
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 3.46410 2.00000i 0.307389 0.177471i −0.338368 0.941014i \(-0.609875\pi\)
0.645758 + 0.763542i \(0.276542\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 7.00000 4.00000i 0.613941 0.350823i
\(131\) 13.8564 1.21064 0.605320 0.795982i \(-0.293045\pi\)
0.605320 + 0.795982i \(0.293045\pi\)
\(132\) 0 0
\(133\) −3.00000 + 1.73205i −0.260133 + 0.150188i
\(134\) −3.83013 + 6.63397i −0.330873 + 0.573088i
\(135\) 0 0
\(136\) −2.23205 + 3.86603i −0.191397 + 0.331509i
\(137\) 15.9904 + 9.23205i 1.36615 + 0.788747i 0.990434 0.137987i \(-0.0440633\pi\)
0.375716 + 0.926735i \(0.377397\pi\)
\(138\) 0 0
\(139\) −0.535898 + 0.928203i −0.0454543 + 0.0787292i −0.887857 0.460119i \(-0.847807\pi\)
0.842403 + 0.538848i \(0.181140\pi\)
\(140\) −5.09808 + 3.36603i −0.430866 + 0.284481i
\(141\) 0 0
\(142\) 1.26795i 0.106404i
\(143\) −1.16987 2.36603i −0.0978297 0.197857i
\(144\) 0 0
\(145\) 7.96410 + 12.0622i 0.661383 + 1.00171i
\(146\) −2.33013 4.03590i −0.192843 0.334013i
\(147\) 0 0
\(148\) 7.92820i 0.651694i
\(149\) −9.96410 + 17.2583i −0.816291 + 1.41386i 0.0921062 + 0.995749i \(0.470640\pi\)
−0.908397 + 0.418108i \(0.862693\pi\)
\(150\) 0 0
\(151\) −5.12436 −0.417014 −0.208507 0.978021i \(-0.566860\pi\)
−0.208507 + 0.978021i \(0.566860\pi\)
\(152\) 1.09808 + 0.633975i 0.0890657 + 0.0514221i
\(153\) 0 0
\(154\) 1.00000 + 1.73205i 0.0805823 + 0.139573i
\(155\) 8.92820 0.535898i 0.717131 0.0430444i
\(156\) 0 0
\(157\) 9.39230i 0.749588i 0.927108 + 0.374794i \(0.122286\pi\)
−0.927108 + 0.374794i \(0.877714\pi\)
\(158\) 10.3923 6.00000i 0.826767 0.477334i
\(159\) 0 0
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) −16.9282 −1.33413
\(162\) 0 0
\(163\) −11.6603 6.73205i −0.913302 0.527295i −0.0318096 0.999494i \(-0.510127\pi\)
−0.881492 + 0.472199i \(0.843460\pi\)
\(164\) −9.19615 −0.718099
\(165\) 0 0
\(166\) −2.63397 4.56218i −0.204436 0.354094i
\(167\) 12.0000 6.92820i 0.928588 0.536120i 0.0422232 0.999108i \(-0.486556\pi\)
0.886365 + 0.462988i \(0.153223\pi\)
\(168\) 0 0
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) −9.96410 + 0.598076i −0.764212 + 0.0458704i
\(171\) 0 0
\(172\) −2.83013 + 1.63397i −0.215795 + 0.124589i
\(173\) 16.2679 + 9.39230i 1.23683 + 0.714084i 0.968445 0.249228i \(-0.0801769\pi\)
0.268384 + 0.963312i \(0.413510\pi\)
\(174\) 0 0
\(175\) −12.5622 5.36603i −0.949611 0.405633i
\(176\) 0.366025 0.633975i 0.0275902 0.0477876i
\(177\) 0 0
\(178\) −4.26795 2.46410i −0.319896 0.184692i
\(179\) −9.09808 15.7583i −0.680022 1.17783i −0.974974 0.222321i \(-0.928637\pi\)
0.294951 0.955512i \(-0.404697\pi\)
\(180\) 0 0
\(181\) −16.1244 −1.19851 −0.599257 0.800557i \(-0.704537\pi\)
−0.599257 + 0.800557i \(0.704537\pi\)
\(182\) −9.83013 0.633975i −0.728657 0.0469933i
\(183\) 0 0
\(184\) 3.09808 + 5.36603i 0.228393 + 0.395589i
\(185\) 14.7942 9.76795i 1.08769 0.718154i
\(186\) 0 0
\(187\) 3.26795i 0.238976i
\(188\) −6.63397 3.83013i −0.483832 0.279341i
\(189\) 0 0
\(190\) 0.169873 + 2.83013i 0.0123239 + 0.205319i
\(191\) −4.73205 + 8.19615i −0.342399 + 0.593053i −0.984878 0.173251i \(-0.944573\pi\)
0.642479 + 0.766304i \(0.277906\pi\)
\(192\) 0 0
\(193\) 9.23205 5.33013i 0.664538 0.383671i −0.129466 0.991584i \(-0.541326\pi\)
0.794004 + 0.607913i \(0.207993\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 0.464102 0.0331501
\(197\) −8.53590 + 4.92820i −0.608158 + 0.351120i −0.772244 0.635326i \(-0.780866\pi\)
0.164086 + 0.986446i \(0.447532\pi\)
\(198\) 0 0
\(199\) −14.0263 + 24.2942i −0.994297 + 1.72217i −0.404786 + 0.914411i \(0.632654\pi\)
−0.589510 + 0.807761i \(0.700679\pi\)
\(200\) 0.598076 + 4.96410i 0.0422904 + 0.351015i
\(201\) 0 0
\(202\) −12.0622 6.96410i −0.848692 0.489992i
\(203\) 17.6603i 1.23951i
\(204\) 0 0
\(205\) −11.3301 17.1603i −0.791330 1.19852i
\(206\) 4.63397 + 8.02628i 0.322864 + 0.559217i
\(207\) 0 0
\(208\) 1.59808 + 3.23205i 0.110807 + 0.224102i
\(209\) 0.928203 0.0642052
\(210\) 0 0
\(211\) 10.7321 + 18.5885i 0.738825 + 1.27968i 0.953025 + 0.302892i \(0.0979523\pi\)
−0.214200 + 0.976790i \(0.568714\pi\)
\(212\) 6.69615 + 3.86603i 0.459894 + 0.265520i
\(213\) 0 0
\(214\) 0.633975 1.09808i 0.0433376 0.0750629i
\(215\) −6.53590 3.26795i −0.445745 0.222872i
\(216\) 0 0
\(217\) −9.46410 5.46410i −0.642465 0.370927i
\(218\) 8.66025 5.00000i 0.586546 0.338643i
\(219\) 0 0
\(220\) 1.63397 0.0980762i 0.110163 0.00661230i
\(221\) −13.3923 8.92820i −0.900864 0.600576i
\(222\) 0 0
\(223\) 0.339746 0.196152i 0.0227511 0.0131353i −0.488581 0.872518i \(-0.662485\pi\)
0.511332 + 0.859383i \(0.329152\pi\)
\(224\) −1.36603 2.36603i −0.0912714 0.158087i
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) −3.63397 2.09808i −0.241195 0.139254i 0.374531 0.927215i \(-0.377804\pi\)
−0.615726 + 0.787960i \(0.711137\pi\)
\(228\) 0 0
\(229\) −28.7846 −1.90214 −0.951070 0.308975i \(-0.900014\pi\)
−0.951070 + 0.308975i \(0.900014\pi\)
\(230\) −6.19615 + 12.3923i −0.408562 + 0.817124i
\(231\) 0 0
\(232\) −5.59808 + 3.23205i −0.367532 + 0.212195i
\(233\) 12.3923i 0.811847i 0.913907 + 0.405923i \(0.133050\pi\)
−0.913907 + 0.405923i \(0.866950\pi\)
\(234\) 0 0
\(235\) −1.02628 17.0981i −0.0669471 1.11536i
\(236\) −6.19615 10.7321i −0.403335 0.698597i
\(237\) 0 0
\(238\) 10.5622 + 6.09808i 0.684644 + 0.395280i
\(239\) −4.58846 −0.296803 −0.148401 0.988927i \(-0.547413\pi\)
−0.148401 + 0.988927i \(0.547413\pi\)
\(240\) 0 0
\(241\) 4.69615 8.13397i 0.302506 0.523955i −0.674197 0.738551i \(-0.735510\pi\)
0.976703 + 0.214596i \(0.0688435\pi\)
\(242\) 10.4641i 0.672658i
\(243\) 0 0
\(244\) −5.06218 8.76795i −0.324073 0.561310i
\(245\) 0.571797 + 0.866025i 0.0365308 + 0.0553283i
\(246\) 0 0
\(247\) −2.53590 + 3.80385i −0.161355 + 0.242033i
\(248\) 4.00000i 0.254000i
\(249\) 0 0
\(250\) −8.52628 + 7.23205i −0.539249 + 0.457395i
\(251\) −10.7321 + 18.5885i −0.677401 + 1.17329i 0.298360 + 0.954453i \(0.403560\pi\)
−0.975761 + 0.218840i \(0.929773\pi\)
\(252\) 0 0
\(253\) 3.92820 + 2.26795i 0.246964 + 0.142585i
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 2.59808 1.50000i 0.162064 0.0935674i −0.416775 0.909010i \(-0.636840\pi\)
0.578838 + 0.815442i \(0.303506\pi\)
\(258\) 0 0
\(259\) −21.6603 −1.34590
\(260\) −4.06218 + 6.96410i −0.251926 + 0.431895i
\(261\) 0 0
\(262\) −12.0000 + 6.92820i −0.741362 + 0.428026i
\(263\) −14.8301 + 8.56218i −0.914465 + 0.527967i −0.881865 0.471502i \(-0.843712\pi\)
−0.0325998 + 0.999468i \(0.510379\pi\)
\(264\) 0 0
\(265\) 1.03590 + 17.2583i 0.0636347 + 1.06017i
\(266\) 1.73205 3.00000i 0.106199 0.183942i
\(267\) 0 0
\(268\) 7.66025i 0.467924i
\(269\) −2.19615 + 3.80385i −0.133902 + 0.231925i −0.925177 0.379535i \(-0.876084\pi\)
0.791276 + 0.611460i \(0.209417\pi\)
\(270\) 0 0
\(271\) −2.92820 5.07180i −0.177876 0.308090i 0.763277 0.646071i \(-0.223589\pi\)
−0.941153 + 0.337982i \(0.890256\pi\)
\(272\) 4.46410i 0.270676i
\(273\) 0 0
\(274\) −18.4641 −1.11546
\(275\) 2.19615 + 2.92820i 0.132433 + 0.176577i
\(276\) 0 0
\(277\) −10.6699 6.16025i −0.641091 0.370134i 0.143944 0.989586i \(-0.454021\pi\)
−0.785034 + 0.619452i \(0.787355\pi\)
\(278\) 1.07180i 0.0642821i
\(279\) 0 0
\(280\) 2.73205 5.46410i 0.163271 0.326543i
\(281\) −1.73205 −0.103325 −0.0516627 0.998665i \(-0.516452\pi\)
−0.0516627 + 0.998665i \(0.516452\pi\)
\(282\) 0 0
\(283\) −6.63397 + 3.83013i −0.394349 + 0.227677i −0.684043 0.729442i \(-0.739780\pi\)
0.289694 + 0.957119i \(0.406447\pi\)
\(284\) −0.633975 1.09808i −0.0376195 0.0651588i
\(285\) 0 0
\(286\) 2.19615 + 1.46410i 0.129861 + 0.0865741i
\(287\) 25.1244i 1.48304i
\(288\) 0 0
\(289\) 1.46410 + 2.53590i 0.0861236 + 0.149170i
\(290\) −12.9282 6.46410i −0.759170 0.379585i
\(291\) 0 0
\(292\) 4.03590 + 2.33013i 0.236183 + 0.136360i
\(293\) −11.8923 6.86603i −0.694756 0.401117i 0.110635 0.993861i \(-0.464711\pi\)
−0.805391 + 0.592744i \(0.798045\pi\)
\(294\) 0 0
\(295\) 12.3923 24.7846i 0.721508 1.44302i
\(296\) 3.96410 + 6.86603i 0.230409 + 0.399080i
\(297\) 0 0
\(298\) 19.9282i 1.15441i
\(299\) −20.0263 + 9.90192i −1.15815 + 0.572643i
\(300\) 0 0
\(301\) 4.46410 + 7.73205i 0.257307 + 0.445668i
\(302\) 4.43782 2.56218i 0.255368 0.147437i
\(303\) 0 0
\(304\) −1.26795 −0.0727219
\(305\) 10.1244 20.2487i 0.579719 1.15944i
\(306\) 0 0
\(307\) 19.2679i 1.09968i −0.835270 0.549840i \(-0.814689\pi\)
0.835270 0.549840i \(-0.185311\pi\)
\(308\) −1.73205 1.00000i −0.0986928 0.0569803i
\(309\) 0 0
\(310\) −7.46410 + 4.92820i −0.423932 + 0.279903i
\(311\) −3.12436 −0.177166 −0.0885830 0.996069i \(-0.528234\pi\)
−0.0885830 + 0.996069i \(0.528234\pi\)
\(312\) 0 0
\(313\) 14.0000i 0.791327i 0.918396 + 0.395663i \(0.129485\pi\)
−0.918396 + 0.395663i \(0.870515\pi\)
\(314\) −4.69615 8.13397i −0.265019 0.459027i
\(315\) 0 0
\(316\) −6.00000 + 10.3923i −0.337526 + 0.584613i
\(317\) 29.7321i 1.66992i −0.550312 0.834959i \(-0.685491\pi\)
0.550312 0.834959i \(-0.314509\pi\)
\(318\) 0 0
\(319\) −2.36603 + 4.09808i −0.132472 + 0.229448i
\(320\) −2.23205 + 0.133975i −0.124775 + 0.00748941i
\(321\) 0 0
\(322\) 14.6603 8.46410i 0.816984 0.471686i
\(323\) 4.90192 2.83013i 0.272750 0.157472i
\(324\) 0 0
\(325\) −18.0000 + 1.00000i −0.998460 + 0.0554700i
\(326\) 13.4641 0.745708
\(327\) 0 0
\(328\) 7.96410 4.59808i 0.439744 0.253886i
\(329\) −10.4641 + 18.1244i −0.576905 + 0.999228i
\(330\) 0 0
\(331\) 14.3923 24.9282i 0.791073 1.37018i −0.134231 0.990950i \(-0.542856\pi\)
0.925303 0.379228i \(-0.123810\pi\)
\(332\) 4.56218 + 2.63397i 0.250382 + 0.144558i
\(333\) 0 0
\(334\) −6.92820 + 12.0000i −0.379094 + 0.656611i
\(335\) 14.2942 9.43782i 0.780977 0.515643i
\(336\) 0 0
\(337\) 11.0526i 0.602071i 0.953613 + 0.301036i \(0.0973323\pi\)
−0.953613 + 0.301036i \(0.902668\pi\)
\(338\) −12.0000 + 5.00000i −0.652714 + 0.271964i
\(339\) 0 0
\(340\) 8.33013 5.50000i 0.451765 0.298279i
\(341\) 1.46410 + 2.53590i 0.0792855 + 0.137327i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) 1.63397 2.83013i 0.0880980 0.152590i
\(345\) 0 0
\(346\) −18.7846 −1.00987
\(347\) −4.90192 2.83013i −0.263149 0.151929i 0.362621 0.931937i \(-0.381882\pi\)
−0.625770 + 0.780007i \(0.715215\pi\)
\(348\) 0 0
\(349\) −9.53590 16.5167i −0.510445 0.884117i −0.999927 0.0121031i \(-0.996147\pi\)
0.489482 0.872014i \(-0.337186\pi\)
\(350\) 13.5622 1.63397i 0.724929 0.0873396i
\(351\) 0 0
\(352\) 0.732051i 0.0390184i
\(353\) −21.8660 + 12.6244i −1.16381 + 0.671927i −0.952214 0.305430i \(-0.901200\pi\)
−0.211597 + 0.977357i \(0.567866\pi\)
\(354\) 0 0
\(355\) 1.26795 2.53590i 0.0672958 0.134592i
\(356\) 4.92820 0.261194
\(357\) 0 0
\(358\) 15.7583 + 9.09808i 0.832854 + 0.480848i
\(359\) 8.87564 0.468439 0.234219 0.972184i \(-0.424747\pi\)
0.234219 + 0.972184i \(0.424747\pi\)
\(360\) 0 0
\(361\) 8.69615 + 15.0622i 0.457692 + 0.792746i
\(362\) 13.9641 8.06218i 0.733937 0.423739i
\(363\) 0 0
\(364\) 8.83013 4.36603i 0.462824 0.228842i
\(365\) 0.624356 + 10.4019i 0.0326803 + 0.544462i
\(366\) 0 0
\(367\) 28.5622 16.4904i 1.49093 0.860791i 0.490987 0.871167i \(-0.336636\pi\)
0.999946 + 0.0103758i \(0.00330278\pi\)
\(368\) −5.36603 3.09808i −0.279723 0.161498i
\(369\) 0 0
\(370\) −7.92820 + 15.8564i −0.412168 + 0.824335i
\(371\) 10.5622 18.2942i 0.548361 0.949789i
\(372\) 0 0
\(373\) 20.3827 + 11.7679i 1.05538 + 0.609321i 0.924149 0.382031i \(-0.124775\pi\)
0.131226 + 0.991352i \(0.458109\pi\)
\(374\) −1.63397 2.83013i −0.0844908 0.146342i
\(375\) 0 0
\(376\) 7.66025 0.395047
\(377\) −10.3301 20.8923i −0.532029 1.07601i
\(378\) 0 0
\(379\) 13.1244 + 22.7321i 0.674153 + 1.16767i 0.976716 + 0.214538i \(0.0688244\pi\)
−0.302563 + 0.953129i \(0.597842\pi\)
\(380\) −1.56218 2.36603i −0.0801380 0.121375i
\(381\) 0 0
\(382\) 9.46410i 0.484226i
\(383\) −23.3205 13.4641i −1.19162 0.687983i −0.232948 0.972489i \(-0.574837\pi\)
−0.958674 + 0.284506i \(0.908171\pi\)
\(384\) 0 0
\(385\) −0.267949 4.46410i −0.0136560 0.227512i
\(386\) −5.33013 + 9.23205i −0.271296 + 0.469899i
\(387\) 0 0
\(388\) 8.66025 5.00000i 0.439658 0.253837i
\(389\) −24.0718 −1.22049 −0.610244 0.792213i \(-0.708929\pi\)
−0.610244 + 0.792213i \(0.708929\pi\)
\(390\) 0 0
\(391\) 27.6603 1.39884
\(392\) −0.401924 + 0.232051i −0.0203002 + 0.0117203i
\(393\) 0 0
\(394\) 4.92820 8.53590i 0.248279 0.430032i
\(395\) −26.7846 + 1.60770i −1.34768 + 0.0808919i
\(396\) 0 0
\(397\) 16.7321 + 9.66025i 0.839758 + 0.484834i 0.857182 0.515014i \(-0.172213\pi\)
−0.0174242 + 0.999848i \(0.505547\pi\)
\(398\) 28.0526i 1.40615i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) −4.52628 7.83975i −0.226032 0.391498i 0.730597 0.682809i \(-0.239242\pi\)
−0.956628 + 0.291311i \(0.905909\pi\)
\(402\) 0 0
\(403\) −14.3923 0.928203i −0.716932 0.0462371i
\(404\) 13.9282 0.692954
\(405\) 0 0
\(406\) 8.83013 + 15.2942i 0.438232 + 0.759040i
\(407\) 5.02628 + 2.90192i 0.249143 + 0.143843i
\(408\) 0 0
\(409\) 8.03590 13.9186i 0.397350 0.688230i −0.596048 0.802949i \(-0.703263\pi\)
0.993398 + 0.114719i \(0.0365967\pi\)
\(410\) 18.3923 + 9.19615i 0.908331 + 0.454166i
\(411\) 0 0
\(412\) −8.02628 4.63397i −0.395426 0.228300i
\(413\) −29.3205 + 16.9282i −1.44277 + 0.832982i
\(414\) 0 0
\(415\) 0.705771 + 11.7583i 0.0346450 + 0.577194i
\(416\) −3.00000 2.00000i −0.147087 0.0980581i
\(417\) 0 0
\(418\) −0.803848 + 0.464102i −0.0393175 + 0.0227000i
\(419\) 3.26795 + 5.66025i 0.159650 + 0.276522i 0.934742 0.355326i \(-0.115630\pi\)
−0.775093 + 0.631848i \(0.782297\pi\)
\(420\) 0 0
\(421\) 17.0526 0.831091 0.415545 0.909572i \(-0.363591\pi\)
0.415545 + 0.909572i \(0.363591\pi\)
\(422\) −18.5885 10.7321i −0.904872 0.522428i
\(423\) 0 0
\(424\) −7.73205 −0.375502
\(425\) 20.5263 + 8.76795i 0.995671 + 0.425308i
\(426\) 0 0
\(427\) −23.9545 + 13.8301i −1.15924 + 0.669287i
\(428\) 1.26795i 0.0612886i
\(429\) 0 0
\(430\) 7.29423 0.437822i 0.351759 0.0211137i
\(431\) −3.90192 6.75833i −0.187949 0.325537i 0.756617 0.653858i \(-0.226851\pi\)
−0.944566 + 0.328321i \(0.893517\pi\)
\(432\) 0 0
\(433\) −12.8205 7.40192i −0.616114 0.355714i 0.159240 0.987240i \(-0.449096\pi\)
−0.775355 + 0.631526i \(0.782429\pi\)
\(434\) 10.9282 0.524571
\(435\) 0 0
\(436\) −5.00000 + 8.66025i −0.239457 + 0.414751i
\(437\) 7.85641i 0.375823i
\(438\) 0 0
\(439\) 4.90192 + 8.49038i 0.233956 + 0.405224i 0.958969 0.283512i \(-0.0914995\pi\)
−0.725013 + 0.688735i \(0.758166\pi\)
\(440\) −1.36603 + 0.901924i −0.0651227 + 0.0429975i
\(441\) 0 0
\(442\) 16.0622 + 1.03590i 0.764000 + 0.0492727i
\(443\) 34.6410i 1.64584i 0.568154 + 0.822922i \(0.307658\pi\)
−0.568154 + 0.822922i \(0.692342\pi\)
\(444\) 0 0
\(445\) 6.07180 + 9.19615i 0.287831 + 0.435939i
\(446\) −0.196152 + 0.339746i −0.00928809 + 0.0160874i
\(447\) 0 0
\(448\) 2.36603 + 1.36603i 0.111784 + 0.0645386i
\(449\) 3.92820 6.80385i 0.185383 0.321093i −0.758322 0.651880i \(-0.773981\pi\)
0.943706 + 0.330786i \(0.107314\pi\)
\(450\) 0 0
\(451\) 3.36603 5.83013i 0.158500 0.274530i
\(452\) −7.79423 + 4.50000i −0.366610 + 0.211662i
\(453\) 0 0
\(454\) 4.19615 0.196935
\(455\) 19.0263 + 11.0981i 0.891966 + 0.520286i
\(456\) 0 0
\(457\) −7.62436 + 4.40192i −0.356652 + 0.205913i −0.667611 0.744510i \(-0.732683\pi\)
0.310959 + 0.950423i \(0.399350\pi\)
\(458\) 24.9282 14.3923i 1.16482 0.672508i
\(459\) 0 0
\(460\) −0.830127 13.8301i −0.0387049 0.644833i
\(461\) 13.0359 22.5788i 0.607142 1.05160i −0.384567 0.923097i \(-0.625649\pi\)
0.991709 0.128504i \(-0.0410176\pi\)
\(462\) 0 0
\(463\) 6.33975i 0.294633i 0.989089 + 0.147316i \(0.0470636\pi\)
−0.989089 + 0.147316i \(0.952936\pi\)
\(464\) 3.23205 5.59808i 0.150044 0.259884i
\(465\) 0 0
\(466\) −6.19615 10.7321i −0.287031 0.497153i
\(467\) 22.0526i 1.02047i 0.860035 + 0.510235i \(0.170442\pi\)
−0.860035 + 0.510235i \(0.829558\pi\)
\(468\) 0 0
\(469\) −20.9282 −0.966375
\(470\) 9.43782 + 14.2942i 0.435334 + 0.659344i
\(471\) 0 0
\(472\) 10.7321 + 6.19615i 0.493983 + 0.285201i
\(473\) 2.39230i 0.109998i
\(474\) 0 0
\(475\) 2.49038 5.83013i 0.114267 0.267505i
\(476\) −12.1962 −0.559010
\(477\) 0 0
\(478\) 3.97372 2.29423i 0.181754 0.104936i
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) −25.6244 + 12.6699i −1.16837 + 0.577696i
\(482\) 9.39230i 0.427808i
\(483\) 0 0
\(484\) −5.23205 9.06218i −0.237820 0.411917i
\(485\) 20.0000 + 10.0000i 0.908153 + 0.454077i
\(486\) 0 0
\(487\) −33.2942 19.2224i −1.50871 0.871052i −0.999949 0.0101413i \(-0.996772\pi\)
−0.508757 0.860910i \(-0.669895\pi\)
\(488\) 8.76795 + 5.06218i 0.396906 + 0.229154i
\(489\) 0 0
\(490\) −0.928203 0.464102i −0.0419319 0.0209660i
\(491\) 10.9019 + 18.8827i 0.491997 + 0.852164i 0.999958 0.00921662i \(-0.00293378\pi\)
−0.507961 + 0.861380i \(0.669600\pi\)
\(492\) 0 0
\(493\) 28.8564i 1.29963i
\(494\) 0.294229 4.56218i 0.0132380 0.205262i
\(495\) 0 0
\(496\) −2.00000 3.46410i −0.0898027 0.155543i
\(497\) −3.00000 + 1.73205i −0.134568 + 0.0776931i
\(498\) 0 0
\(499\) −40.3923 −1.80821 −0.904104 0.427313i \(-0.859460\pi\)
−0.904104 + 0.427313i \(0.859460\pi\)
\(500\) 3.76795 10.5263i 0.168508 0.470750i
\(501\) 0 0
\(502\) 21.4641i 0.957990i
\(503\) −18.8827 10.9019i −0.841937 0.486093i 0.0159849 0.999872i \(-0.494912\pi\)
−0.857922 + 0.513779i \(0.828245\pi\)
\(504\) 0 0
\(505\) 17.1603 + 25.9904i 0.763621 + 1.15656i
\(506\) −4.53590 −0.201645
\(507\) 0 0
\(508\) 4.00000i 0.177471i
\(509\) 15.3564 + 26.5981i 0.680661 + 1.17894i 0.974780 + 0.223170i \(0.0716405\pi\)
−0.294119 + 0.955769i \(0.595026\pi\)
\(510\) 0 0
\(511\) 6.36603 11.0263i 0.281616 0.487774i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −1.50000 + 2.59808i −0.0661622 + 0.114596i
\(515\) −1.24167 20.6865i −0.0547145 0.911558i
\(516\) 0 0
\(517\) 4.85641 2.80385i 0.213585 0.123313i
\(518\) 18.7583 10.8301i 0.824194 0.475848i
\(519\) 0 0
\(520\) 0.0358984 8.06218i 0.00157425 0.353550i
\(521\) 19.4449 0.851895 0.425947 0.904748i \(-0.359941\pi\)
0.425947 + 0.904748i \(0.359941\pi\)
\(522\) 0 0
\(523\) 31.5622 18.2224i 1.38012 0.796811i 0.387945 0.921683i \(-0.373185\pi\)
0.992173 + 0.124871i \(0.0398518\pi\)
\(524\) 6.92820 12.0000i 0.302660 0.524222i
\(525\) 0 0
\(526\) 8.56218 14.8301i 0.373329 0.646624i
\(527\) 15.4641 + 8.92820i 0.673627 + 0.388919i
\(528\) 0 0
\(529\) 7.69615 13.3301i 0.334615 0.579571i
\(530\) −9.52628 14.4282i −0.413795 0.626721i
\(531\) 0 0
\(532\) 3.46410i 0.150188i
\(533\) 14.6962 + 29.7224i 0.636561 + 1.28742i
\(534\) 0 0
\(535\) −2.36603 + 1.56218i −0.102292 + 0.0675388i
\(536\) 3.83013 + 6.63397i 0.165436 + 0.286544i
\(537\) 0 0
\(538\) 4.39230i 0.189366i
\(539\) −0.169873 + 0.294229i −0.00731695 + 0.0126733i
\(540\) 0 0
\(541\) −1.19615 −0.0514266 −0.0257133 0.999669i \(-0.508186\pi\)
−0.0257133 + 0.999669i \(0.508186\pi\)
\(542\) 5.07180 + 2.92820i 0.217852 + 0.125777i
\(543\) 0 0
\(544\) 2.23205 + 3.86603i 0.0956984 + 0.165754i
\(545\) −22.3205 + 1.33975i −0.956106 + 0.0573884i
\(546\) 0 0
\(547\) 25.8038i 1.10329i 0.834078 + 0.551646i \(0.186000\pi\)
−0.834078 + 0.551646i \(0.814000\pi\)
\(548\) 15.9904 9.23205i 0.683075 0.394374i
\(549\) 0 0
\(550\) −3.36603 1.43782i −0.143528 0.0613089i
\(551\) 8.19615 0.349168
\(552\) 0 0
\(553\) 28.3923 + 16.3923i 1.20736 + 0.697072i
\(554\) 12.3205 0.523448
\(555\) 0 0
\(556\) 0.535898 + 0.928203i 0.0227272 + 0.0393646i
\(557\) 12.6962 7.33013i 0.537953 0.310587i −0.206296 0.978490i \(-0.566141\pi\)
0.744249 + 0.667902i \(0.232808\pi\)
\(558\) 0 0
\(559\) 9.80385 + 6.53590i 0.414659 + 0.276439i
\(560\) 0.366025 + 6.09808i 0.0154674 + 0.257691i
\(561\) 0 0
\(562\) 1.50000 0.866025i 0.0632737 0.0365311i
\(563\) −6.92820 4.00000i −0.291989 0.168580i 0.346850 0.937921i \(-0.387251\pi\)
−0.638838 + 0.769341i \(0.720585\pi\)
\(564\) 0 0
\(565\) −18.0000 9.00000i −0.757266 0.378633i
\(566\) 3.83013 6.63397i 0.160992 0.278847i
\(567\) 0 0
\(568\) 1.09808 + 0.633975i 0.0460743 + 0.0266010i
\(569\) −9.07180 15.7128i −0.380310 0.658715i 0.610797 0.791787i \(-0.290849\pi\)
−0.991106 + 0.133072i \(0.957516\pi\)
\(570\) 0 0
\(571\) −25.6603 −1.07385 −0.536924 0.843631i \(-0.680414\pi\)
−0.536924 + 0.843631i \(0.680414\pi\)
\(572\) −2.63397 0.169873i −0.110132 0.00710275i
\(573\) 0 0
\(574\) −12.5622 21.7583i −0.524335 0.908175i
\(575\) 24.7846 18.5885i 1.03359 0.775192i
\(576\) 0 0
\(577\) 23.9808i 0.998332i 0.866506 + 0.499166i \(0.166360\pi\)
−0.866506 + 0.499166i \(0.833640\pi\)
\(578\) −2.53590 1.46410i −0.105479 0.0608986i
\(579\) 0 0
\(580\) 14.4282 0.866025i 0.599099 0.0359597i
\(581\) 7.19615 12.4641i 0.298547 0.517098i
\(582\) 0 0
\(583\) −4.90192 + 2.83013i −0.203017 + 0.117212i
\(584\) −4.66025 −0.192843
\(585\) 0 0
\(586\) 13.7321 0.567266
\(587\) −8.78461 + 5.07180i −0.362580 + 0.209335i −0.670212 0.742170i \(-0.733797\pi\)
0.307632 + 0.951505i \(0.400463\pi\)
\(588\) 0 0
\(589\) 2.53590 4.39230i 0.104490 0.180982i
\(590\) 1.66025 + 27.6603i 0.0683516 + 1.13875i
\(591\) 0 0
\(592\) −6.86603 3.96410i −0.282192 0.162924i
\(593\) 19.3923i 0.796347i 0.917310 + 0.398173i \(0.130356\pi\)
−0.917310 + 0.398173i \(0.869644\pi\)
\(594\) 0 0
\(595\) −15.0263 22.7583i −0.616017 0.933001i
\(596\) 9.96410 + 17.2583i 0.408146 + 0.706929i
\(597\) 0 0
\(598\) 12.3923 18.5885i 0.506759 0.760139i
\(599\) 8.78461 0.358929 0.179465 0.983764i \(-0.442563\pi\)
0.179465 + 0.983764i \(0.442563\pi\)
\(600\) 0 0
\(601\) −8.50000 14.7224i −0.346722 0.600541i 0.638943 0.769254i \(-0.279372\pi\)
−0.985665 + 0.168714i \(0.946039\pi\)
\(602\) −7.73205 4.46410i −0.315135 0.181943i
\(603\) 0 0
\(604\) −2.56218 + 4.43782i −0.104254 + 0.180572i
\(605\) 10.4641 20.9282i 0.425426 0.850852i
\(606\) 0 0
\(607\) −41.9090 24.1962i −1.70103 0.982092i −0.944718 0.327883i \(-0.893665\pi\)
−0.756314 0.654209i \(-0.773002\pi\)
\(608\) 1.09808 0.633975i 0.0445329 0.0257111i
\(609\) 0 0
\(610\) 1.35641 + 22.5981i 0.0549193 + 0.914969i
\(611\) −1.77757 + 27.5622i −0.0719127 + 1.11505i
\(612\) 0 0
\(613\) −18.8660 + 10.8923i −0.761992 + 0.439936i −0.830010 0.557748i \(-0.811666\pi\)
0.0680188 + 0.997684i \(0.478332\pi\)
\(614\) 9.63397 + 16.6865i 0.388796 + 0.673414i
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) −28.3301 16.3564i −1.14053 0.658484i −0.193967 0.981008i \(-0.562135\pi\)
−0.946561 + 0.322524i \(0.895469\pi\)
\(618\) 0 0
\(619\) 36.1051 1.45119 0.725594 0.688123i \(-0.241565\pi\)
0.725594 + 0.688123i \(0.241565\pi\)
\(620\) 4.00000 8.00000i 0.160644 0.321288i
\(621\) 0 0
\(622\) 2.70577 1.56218i 0.108492 0.0626376i
\(623\) 13.4641i 0.539428i
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) −7.00000 12.1244i −0.279776 0.484587i
\(627\) 0 0
\(628\) 8.13397 + 4.69615i 0.324581 + 0.187397i
\(629\) 35.3923 1.41118
\(630\) 0 0
\(631\) −4.92820 + 8.53590i −0.196189 + 0.339809i −0.947290 0.320379i \(-0.896190\pi\)
0.751101 + 0.660187i \(0.229523\pi\)
\(632\) 12.0000i 0.477334i
\(633\) 0 0
\(634\) 14.8660 + 25.7487i 0.590405 + 1.02261i
\(635\) 7.46410 4.92820i 0.296204 0.195570i
\(636\) 0 0
\(637\) −0.741670 1.50000i −0.0293860 0.0594322i
\(638\) 4.73205i 0.187344i
\(639\) 0 0
\(640\) 1.86603 1.23205i 0.0737611 0.0487011i
\(641\) 4.52628 7.83975i 0.178777 0.309651i −0.762685 0.646770i \(-0.776119\pi\)
0.941462 + 0.337119i \(0.109453\pi\)
\(642\) 0 0
\(643\) −7.60770 4.39230i −0.300018 0.173216i 0.342433 0.939542i \(-0.388749\pi\)
−0.642451 + 0.766327i \(0.722082\pi\)
\(644\) −8.46410 + 14.6603i −0.333532 + 0.577695i
\(645\) 0 0
\(646\) −2.83013 + 4.90192i −0.111350 + 0.192864i
\(647\) 20.1962 11.6603i 0.793993 0.458412i −0.0473736 0.998877i \(-0.515085\pi\)
0.841366 + 0.540465i \(0.181752\pi\)
\(648\) 0 0
\(649\) 9.07180 0.356099
\(650\) 15.0885 9.86603i 0.591818 0.386977i
\(651\) 0 0
\(652\) −11.6603 + 6.73205i −0.456651 + 0.263647i
\(653\) 28.2679 16.3205i 1.10621 0.638671i 0.168365 0.985725i \(-0.446151\pi\)
0.937845 + 0.347054i \(0.112818\pi\)
\(654\) 0 0
\(655\) 30.9282 1.85641i 1.20846 0.0725358i
\(656\) −4.59808 + 7.96410i −0.179525 + 0.310946i
\(657\) 0 0
\(658\) 20.9282i 0.815866i
\(659\) 20.7321 35.9090i 0.807606 1.39881i −0.106912 0.994269i \(-0.534096\pi\)
0.914518 0.404546i \(-0.132570\pi\)
\(660\) 0 0
\(661\) 19.2583 + 33.3564i 0.749062 + 1.29741i 0.948273 + 0.317457i \(0.102829\pi\)
−0.199210 + 0.979957i \(0.563838\pi\)
\(662\) 28.7846i 1.11875i
\(663\) 0 0
\(664\) −5.26795 −0.204436
\(665\) −6.46410 + 4.26795i −0.250667 + 0.165504i
\(666\) 0 0
\(667\) 34.6865 + 20.0263i 1.34307 + 0.775421i
\(668\) 13.8564i 0.536120i
\(669\) 0 0
\(670\) −7.66025 + 15.3205i −0.295941 + 0.591883i
\(671\) 7.41154 0.286119
\(672\) 0 0
\(673\) −8.89230 + 5.13397i −0.342773 + 0.197900i −0.661498 0.749947i \(-0.730079\pi\)
0.318725 + 0.947847i \(0.396746\pi\)
\(674\) −5.52628 9.57180i −0.212864 0.368692i
\(675\) 0 0
\(676\) 7.89230 10.3301i 0.303550 0.397313i
\(677\) 48.6410i 1.86943i 0.355403 + 0.934713i \(0.384344\pi\)
−0.355403 + 0.934713i \(0.615656\pi\)
\(678\) 0 0
\(679\) −13.6603 23.6603i −0.524232 0.907997i
\(680\) −4.46410 + 8.92820i −0.171190 + 0.342381i
\(681\) 0 0
\(682\) −2.53590 1.46410i −0.0971046 0.0560633i
\(683\) 23.3205 + 13.4641i 0.892334 + 0.515190i 0.874705 0.484655i \(-0.161055\pi\)
0.0176291 + 0.999845i \(0.494388\pi\)
\(684\) 0 0
\(685\) 36.9282 + 18.4641i 1.41095 + 0.705477i
\(686\) −8.92820 15.4641i −0.340880 0.590422i
\(687\) 0 0
\(688\) 3.26795i 0.124589i
\(689\) 1.79423 27.8205i 0.0683547 1.05988i
\(690\) 0 0
\(691\) −20.2942 35.1506i −0.772029 1.33719i −0.936449 0.350803i \(-0.885909\pi\)
0.164420 0.986390i \(-0.447425\pi\)
\(692\) 16.2679 9.39230i 0.618415 0.357042i
\(693\) 0 0
\(694\) 5.66025 0.214860
\(695\) −1.07180 + 2.14359i −0.0406556 + 0.0813111i
\(696\) 0 0
\(697\) 41.0526i 1.55498i
\(698\) 16.5167 + 9.53590i 0.625165 + 0.360939i
\(699\) 0 0
\(700\) −10.9282 + 8.19615i −0.413047 + 0.309785i
\(701\) 13.4641 0.508532 0.254266 0.967134i \(-0.418166\pi\)
0.254266 + 0.967134i \(0.418166\pi\)
\(702\) 0 0
\(703\) 10.0526i 0.379139i
\(704\) −0.366025 0.633975i −0.0137951 0.0238938i
\(705\) 0 0
\(706\) 12.6244 21.8660i 0.475124 0.822939i
\(707\) 38.0526i 1.43111i
\(708\) 0 0
\(709\) 18.5263 32.0885i 0.695769 1.20511i −0.274152 0.961686i \(-0.588397\pi\)
0.969921 0.243421i \(-0.0782696\pi\)
\(710\) 0.169873 + 2.83013i 0.00637522 + 0.106213i
\(711\) 0 0
\(712\) −4.26795 + 2.46410i −0.159948 + 0.0923461i
\(713\) 21.4641 12.3923i 0.803837 0.464095i
\(714\) 0 0
\(715\) −2.92820 5.12436i −0.109509 0.191640i
\(716\) −18.1962 −0.680022
\(717\) 0 0
\(718\) −7.68653 + 4.43782i −0.286859 + 0.165618i
\(719\) 16.1962 28.0526i 0.604015 1.04618i −0.388192 0.921579i \(-0.626900\pi\)
0.992206 0.124605i \(-0.0397665\pi\)
\(720\) 0 0
\(721\) −12.6603 + 21.9282i −0.471492 + 0.816649i
\(722\) −15.0622 8.69615i −0.560556 0.323637i
\(723\) 0 0
\(724\) −8.06218 + 13.9641i −0.299628 + 0.518972i
\(725\) 19.3923 + 25.8564i 0.720212 + 0.960283i
\(726\) 0 0
\(727\) 13.2679i 0.492081i −0.969260 0.246040i \(-0.920870\pi\)
0.969260 0.246040i \(-0.0791296\pi\)
\(728\) −5.46410 + 8.19615i −0.202513 + 0.303770i
\(729\) 0 0
\(730\) −5.74167 8.69615i −0.212509 0.321859i
\(731\) −7.29423 12.6340i −0.269787 0.467284i
\(732\) 0 0
\(733\) 45.3923i 1.67660i −0.545207 0.838302i \(-0.683549\pi\)
0.545207 0.838302i \(-0.316451\pi\)
\(734\) −16.4904 + 28.5622i −0.608671 + 1.05425i
\(735\) 0 0
\(736\) 6.19615 0.228393
\(737\) 4.85641 + 2.80385i 0.178888 + 0.103281i
\(738\) 0 0
\(739\) 1.07180 + 1.85641i 0.0394267 + 0.0682890i 0.885065 0.465467i \(-0.154114\pi\)
−0.845639 + 0.533756i \(0.820780\pi\)
\(740\) −1.06218 17.6962i −0.0390464 0.650524i
\(741\) 0 0
\(742\) 21.1244i 0.775499i
\(743\) −18.5885 + 10.7321i −0.681944 + 0.393721i −0.800587 0.599216i \(-0.795479\pi\)
0.118643 + 0.992937i \(0.462146\pi\)
\(744\) 0 0
\(745\) −19.9282 + 39.8564i −0.730113 + 1.46023i
\(746\) −23.5359 −0.861710
\(747\) 0 0
\(748\) 2.83013 + 1.63397i 0.103480 + 0.0597440i
\(749\) 3.46410 0.126576
\(750\) 0 0
\(751\) −18.0263 31.2224i −0.657788 1.13932i −0.981187 0.193060i \(-0.938159\pi\)
0.323399 0.946263i \(-0.395175\pi\)
\(752\) −6.63397 + 3.83013i −0.241916 + 0.139670i
\(753\) 0 0
\(754\) 19.3923 + 12.9282i 0.706226 + 0.470817i
\(755\) −11.4378 + 0.686533i −0.416265 + 0.0249855i
\(756\) 0 0
\(757\) −34.7321 + 20.0526i −1.26236 + 0.728823i −0.973530 0.228558i \(-0.926599\pi\)
−0.288828 + 0.957381i \(0.593265\pi\)
\(758\) −22.7321 13.1244i −0.825665 0.476698i
\(759\) 0 0
\(760\) 2.53590 + 1.26795i 0.0919867 + 0.0459934i
\(761\) 11.5359 19.9808i 0.418176 0.724302i −0.577580 0.816334i \(-0.696003\pi\)
0.995756 + 0.0920320i \(0.0293362\pi\)
\(762\) 0 0
\(763\) 23.6603 + 13.6603i 0.856559 + 0.494534i
\(764\) 4.73205 + 8.19615i 0.171200 + 0.296526i
\(765\) 0 0
\(766\) 26.9282 0.972956
\(767\) −24.7846 + 37.1769i −0.894920 + 1.34238i
\(768\) 0 0
\(769\) 22.7321 + 39.3731i 0.819739 + 1.41983i 0.905875 + 0.423546i \(0.139215\pi\)
−0.0861360 + 0.996283i \(0.527452\pi\)
\(770\) 2.46410 + 3.73205i 0.0888001 + 0.134494i
\(771\) 0 0
\(772\) 10.6603i 0.383671i
\(773\) −35.1962 20.3205i −1.26592 0.730878i −0.291705 0.956508i \(-0.594222\pi\)
−0.974213 + 0.225631i \(0.927556\pi\)
\(774\) 0 0
\(775\) 19.8564 2.39230i 0.713263 0.0859341i
\(776\) −5.00000 + 8.66025i −0.179490 + 0.310885i
\(777\) 0 0
\(778\) 20.8468 12.0359i 0.747394 0.431508i
\(779\) −11.6603 −0.417772
\(780\) 0 0
\(781\) 0.928203 0.0332137
\(782\) −23.9545 + 13.8301i −0.856611 + 0.494564i
\(783\) 0 0
\(784\) 0.232051 0.401924i 0.00828753 0.0143544i
\(785\) 1.25833 + 20.9641i 0.0449117 + 0.748241i
\(786\) 0 0
\(787\) 16.7321 + 9.66025i 0.596433 + 0.344351i 0.767637 0.640885i \(-0.221432\pi\)
−0.171204 + 0.985236i \(0.554766\pi\)
\(788\) 9.85641i 0.351120i
\(789\) 0 0
\(790\) 22.3923 14.7846i 0.796682 0.526013i
\(791\) 12.2942 + 21.2942i 0.437132 + 0.757136i
\(792\) 0 0
\(793\) −20.2487 + 30.3731i −0.719053 + 1.07858i
\(794\) −19.3205 −0.685659
\(795\) 0 0
\(796\) 14.0263 + 24.2942i 0.497148 + 0.861086i
\(797\) −0.928203 0.535898i −0.0328786 0.0189825i 0.483471 0.875361i \(-0.339376\pi\)
−0.516349 + 0.856378i \(0.672709\pi\)
\(798\) 0 0
\(799\) 17.0981 29.6147i 0.604886 1.04769i
\(800\) 4.59808 + 1.96410i 0.162567 + 0.0694415i
\(801\) 0 0
\(802\) 7.83975 + 4.52628i 0.276831 + 0.159828i
\(803\) −2.95448 + 1.70577i −0.104261 + 0.0601954i
\(804\) 0 0
\(805\) −37.7846 + 2.26795i −1.33173 + 0.0799347i
\(806\) 12.9282 6.39230i 0.455377 0.225159i
\(807\) 0 0
\(808\) −12.0622 + 6.96410i −0.424346 + 0.244996i
\(809\) −0.990381 1.71539i −0.0348199 0.0603099i 0.848090 0.529852i \(-0.177752\pi\)
−0.882910 + 0.469542i \(0.844419\pi\)
\(810\) 0 0
\(811\) −33.8564 −1.18886 −0.594430 0.804148i \(-0.702622\pi\)
−0.594430 + 0.804148i \(0.702622\pi\)
\(812\) −15.2942 8.83013i −0.536722 0.309877i
\(813\) 0 0
\(814\) −5.80385 −0.203425
\(815\) −26.9282 13.4641i −0.943254 0.471627i
\(816\) 0 0
\(817\) −3.58846 + 2.07180i −0.125544 + 0.0724830i
\(818\) 16.0718i 0.561937i
\(819\) 0 0
\(820\) −20.5263 + 1.23205i −0.716809 + 0.0430251i
\(821\) 5.12436 + 8.87564i 0.178841 + 0.309762i 0.941484 0.337058i \(-0.109432\pi\)
−0.762643 + 0.646820i \(0.776098\pi\)
\(822\) 0 0
\(823\) −34.9808 20.1962i −1.21935 0.703994i −0.254573 0.967054i \(-0.581935\pi\)
−0.964780 + 0.263060i \(0.915268\pi\)
\(824\) 9.26795 0.322864
\(825\) 0 0
\(826\) 16.9282 29.3205i 0.589008 1.02019i
\(827\) 48.7846i 1.69641i −0.529670 0.848204i \(-0.677684\pi\)
0.529670 0.848204i \(-0.322316\pi\)
\(828\) 0 0
\(829\) 8.93782 + 15.4808i 0.310423 + 0.537669i 0.978454 0.206465i \(-0.0661958\pi\)
−0.668031 + 0.744134i \(0.732863\pi\)
\(830\) −6.49038 9.83013i −0.225284 0.341209i
\(831\) 0 0
\(832\) 3.59808 + 0.232051i 0.124741 + 0.00804491i
\(833\) 2.07180i 0.0717835i
\(834\) 0 0
\(835\) 25.8564 17.0718i 0.894798 0.590794i
\(836\) 0.464102 0.803848i 0.0160513 0.0278016i
\(837\) 0 0
\(838\) −5.66025 3.26795i −0.195530 0.112889i
\(839\) −24.0526 + 41.6603i −0.830387 + 1.43827i 0.0673455 + 0.997730i \(0.478547\pi\)
−0.897732 + 0.440542i \(0.854786\pi\)
\(840\) 0 0
\(841\) −6.39230 + 11.0718i −0.220424 + 0.381786i
\(842\) −14.7679 + 8.52628i −0.508937 + 0.293835i
\(843\) 0 0
\(844\) 21.4641 0.738825
\(845\) 29.0000 + 2.00000i 0.997630 + 0.0688021i
\(846\) 0 0
\(847\) −24.7583 + 14.2942i −0.850706 + 0.491156i
\(848\) 6.69615 3.86603i 0.229947 0.132760i
\(849\) 0 0
\(850\) −22.1603 + 2.66987i −0.760090 + 0.0915759i
\(851\) 24.5622 42.5429i 0.841981 1.45835i
\(852\) 0 0
\(853\) 12.0718i 0.413330i 0.978412 + 0.206665i \(0.0662611\pi\)
−0.978412 + 0.206665i \(0.933739\pi\)
\(854\) 13.8301 23.9545i 0.473257 0.819706i
\(855\) 0 0
\(856\) −0.633975 1.09808i −0.0216688 0.0375315i
\(857\) 3.92820i 0.134185i −0.997747 0.0670924i \(-0.978628\pi\)
0.997747 0.0670924i \(-0.0213722\pi\)
\(858\) 0 0
\(859\) 44.3013 1.51154 0.755770 0.654837i \(-0.227263\pi\)
0.755770 + 0.654837i \(0.227263\pi\)
\(860\) −6.09808 + 4.02628i −0.207943 + 0.137295i
\(861\) 0 0
\(862\) 6.75833 + 3.90192i 0.230190 + 0.132900i
\(863\) 21.1244i 0.719081i 0.933129 + 0.359541i \(0.117067\pi\)
−0.933129 + 0.359541i \(0.882933\pi\)
\(864\) 0 0
\(865\) 37.5692 + 18.7846i 1.27739 + 0.638696i
\(866\) 14.8038 0.503055
\(867\) 0 0
\(868\) −9.46410 + 5.46410i −0.321233 + 0.185464i
\(869\) −4.39230 7.60770i −0.148999 0.258073i
\(870\) 0 0
\(871\) −24.7583 + 12.2417i −0.838904 + 0.414793i
\(872\) 10.0000i 0.338643i
\(873\) 0 0
\(874\) 3.92820 + 6.80385i 0.132873 + 0.230144i
\(875\) −28.7583 10.2942i −0.972209 0.348008i
\(876\) 0 0
\(877\) 8.25833 + 4.76795i 0.278864 + 0.161002i 0.632909 0.774226i \(-0.281861\pi\)
−0.354045 + 0.935228i \(0.615194\pi\)
\(878\) −8.49038 4.90192i −0.286536 0.165432i
\(879\) 0 0
\(880\) 0.732051 1.46410i 0.0246774 0.0493549i
\(881\) 8.93782 + 15.4808i 0.301123 + 0.521560i 0.976391 0.216013i \(-0.0693052\pi\)
−0.675268 + 0.737573i \(0.735972\pi\)
\(882\) 0 0
\(883\) 18.2487i 0.614118i 0.951690 + 0.307059i \(0.0993449\pi\)
−0.951690 + 0.307059i \(0.900655\pi\)
\(884\) −14.4282 + 7.13397i −0.485273 + 0.239942i
\(885\) 0 0
\(886\) −17.3205 30.0000i −0.581894 1.00787i
\(887\) −25.1769 + 14.5359i −0.845358 + 0.488068i −0.859082 0.511838i \(-0.828965\pi\)
0.0137239 + 0.999906i \(0.495631\pi\)
\(888\) 0 0
\(889\) −10.9282 −0.366520
\(890\) −9.85641 4.92820i −0.330387 0.165194i
\(891\) 0 0
\(892\) 0.392305i 0.0131353i
\(893\) −8.41154 4.85641i −0.281482 0.162513i
\(894\) 0 0
\(895\) −22.4186 33.9545i −0.749371 1.13497i
\(896\) −2.73205 −0.0912714
\(897\) 0 0
\(898\) 7.85641i 0.262172i
\(899\) 12.9282 + 22.3923i 0.431180 + 0.746825i
\(900\) 0 0
\(901\) −17.2583 + 29.8923i −0.574958 + 0.995857i
\(902\) 6.73205i 0.224153i
\(903\) 0 0
\(904\) 4.50000 7.79423i 0.149668 0.259232i
\(905\) −35.9904 + 2.16025i −1.19636 + 0.0718093i
\(906\) 0 0
\(907\) 6.00000 3.46410i 0.199227 0.115024i −0.397068 0.917789i \(-0.629972\pi\)
0.596295 + 0.802766i \(0.296639\pi\)
\(908\) −3.63397 + 2.09808i −0.120598 + 0.0696271i
\(909\) 0 0
\(910\) −22.0263 0.0980762i −0.730164 0.00325119i
\(911\) −44.1051 −1.46127 −0.730634 0.682769i \(-0.760775\pi\)
−0.730634 + 0.682769i \(0.760775\pi\)
\(912\) 0 0
\(913\) −3.33975 + 1.92820i −0.110529 + 0.0638142i
\(914\) 4.40192 7.62436i 0.145603 0.252191i
\(915\) 0 0
\(916\) −14.3923 + 24.9282i −0.475535 + 0.823651i
\(917\) −32.7846 18.9282i −1.08264 0.625064i
\(918\) 0 0
\(919\) −28.7321 + 49.7654i −0.947783 + 1.64161i −0.197702 + 0.980262i \(0.563348\pi\)
−0.750081 + 0.661346i \(0.769986\pi\)
\(920\) 7.63397 + 11.5622i 0.251685 + 0.381194i
\(921\) 0 0
\(922\) 26.0718i 0.858629i
\(923\) −2.53590 + 3.80385i −0.0834701 + 0.125205i
\(924\) 0 0
\(925\) 31.7128 23.7846i 1.04271 0.782033i
\(926\) −3.16987 5.49038i −0.104168 0.180425i
\(927\) 0 0
\(928\) 6.46410i 0.212195i
\(929\) −19.7942 + 34.2846i −0.649428 + 1.12484i 0.333832 + 0.942633i \(0.391658\pi\)
−0.983260 + 0.182209i \(0.941675\pi\)
\(930\) 0 0
\(931\) 0.588457 0.0192859
\(932\) 10.7321 + 6.19615i 0.351540 + 0.202962i
\(933\) 0 0
\(934\) −11.0263 19.0981i −0.360791 0.624908i
\(935\) 0.437822 + 7.29423i 0.0143183 + 0.238547i
\(936\) 0 0
\(937\) 17.0526i 0.557083i −0.960424 0.278541i \(-0.910149\pi\)
0.960424 0.278541i \(-0.0898509\pi\)
\(938\) 18.1244 10.4641i 0.591781 0.341665i
\(939\) 0 0
\(940\) −15.3205 7.66025i −0.499700 0.249850i
\(941\) −12.3923 −0.403978 −0.201989 0.979388i \(-0.564740\pi\)
−0.201989 + 0.979388i \(0.564740\pi\)
\(942\) 0 0
\(943\) −49.3468 28.4904i −1.60695 0.927774i
\(944\) −12.3923 −0.403335
\(945\) 0 0
\(946\) 1.19615 + 2.07180i 0.0388903 + 0.0673599i
\(947\) −24.0000 + 13.8564i −0.779895 + 0.450273i −0.836393 0.548130i \(-0.815340\pi\)
0.0564979 + 0.998403i \(0.482007\pi\)
\(948\) 0 0
\(949\) 1.08142 16.7679i 0.0351042 0.544311i
\(950\) 0.758330 + 6.29423i 0.0246035 + 0.204212i
\(951\) 0 0
\(952\) 10.5622 6.09808i 0.342322 0.197640i
\(953\) 32.6603 + 18.8564i 1.05797 + 0.610819i 0.924870 0.380284i \(-0.124174\pi\)
0.133100 + 0.991103i \(0.457507\pi\)
\(954\) 0 0
\(955\) −9.46410 + 18.9282i −0.306251 + 0.612502i
\(956\) −2.29423 + 3.97372i −0.0742007 + 0.128519i
\(957\) 0 0
\(958\) −13.8564 8.00000i −0.447680 0.258468i
\(959\) −25.2224 43.6865i −0.814475 1.41071i
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 15.8564 23.7846i 0.511231 0.766847i
\(963\) 0 0
\(964\) −4.69615 8.13397i −0.151253 0.261978i
\(965\) 19.8923 13.1340i 0.640356 0.422798i
\(966\) 0 0
\(967\) 16.5885i 0.533449i −0.963773 0.266724i \(-0.914059\pi\)
0.963773 0.266724i \(-0.0859413\pi\)
\(968\) 9.06218 + 5.23205i 0.291269 + 0.168164i
\(969\) 0 0
\(970\) −22.3205 + 1.33975i −0.716668 + 0.0430167i
\(971\) −27.4641 + 47.5692i −0.881365 + 1.52657i −0.0315409 + 0.999502i \(0.510041\pi\)
−0.849824 + 0.527066i \(0.823292\pi\)
\(972\) 0 0
\(973\) 2.53590 1.46410i 0.0812972 0.0469369i
\(974\) 38.4449 1.23185
\(975\) 0 0
\(976\) −10.1244 −0.324073
\(977\) −18.4019 + 10.6244i −0.588730 + 0.339903i −0.764595 0.644511i \(-0.777061\pi\)
0.175865 + 0.984414i \(0.443728\pi\)
\(978\) 0 0
\(979\) −1.80385 + 3.12436i −0.0576512 + 0.0998548i
\(980\) 1.03590 0.0621778i 0.0330906 0.00198620i
\(981\) 0 0
\(982\) −18.8827 10.9019i −0.602571 0.347894i
\(983\) 31.7128i 1.01148i −0.862685 0.505741i \(-0.831219\pi\)
0.862685 0.505741i \(-0.168781\pi\)
\(984\) 0 0
\(985\) −18.3923 + 12.1436i −0.586028 + 0.386927i
\(986\) −14.4282 24.9904i −0.459488 0.795856i
\(987\) 0 0
\(988\) 2.02628 + 4.09808i 0.0644645 + 0.130377i
\(989\) −20.2487 −0.643872
\(990\) 0 0
\(991\) −4.02628 6.97372i −0.127899 0.221528i 0.794963 0.606657i \(-0.207490\pi\)
−0.922862 + 0.385130i \(0.874157\pi\)
\(992\) 3.46410 + 2.00000i 0.109985 + 0.0635001i
\(993\) 0 0
\(994\) 1.73205 3.00000i 0.0549373 0.0951542i
\(995\) −28.0526 + 56.1051i −0.889326 + 1.77865i
\(996\) 0 0
\(997\) 13.7942 + 7.96410i 0.436868 + 0.252226i 0.702268 0.711913i \(-0.252171\pi\)
−0.265400 + 0.964138i \(0.585504\pi\)
\(998\) 34.9808 20.1962i 1.10730 0.639298i
\(999\) 0 0
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 1170.2.bp.d.289.1 4
3.2 odd 2 390.2.y.b.289.2 yes 4
5.4 even 2 1170.2.bp.e.289.2 4
13.9 even 3 1170.2.bp.e.919.2 4
15.2 even 4 1950.2.i.bh.601.2 4
15.8 even 4 1950.2.i.y.601.1 4
15.14 odd 2 390.2.y.c.289.1 yes 4
39.35 odd 6 390.2.y.c.139.1 yes 4
65.9 even 6 inner 1170.2.bp.d.919.1 4
195.74 odd 6 390.2.y.b.139.2 4
195.113 even 12 1950.2.i.y.451.1 4
195.152 even 12 1950.2.i.bh.451.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
390.2.y.b.139.2 4 195.74 odd 6
390.2.y.b.289.2 yes 4 3.2 odd 2
390.2.y.c.139.1 yes 4 39.35 odd 6
390.2.y.c.289.1 yes 4 15.14 odd 2
1170.2.bp.d.289.1 4 1.1 even 1 trivial
1170.2.bp.d.919.1 4 65.9 even 6 inner
1170.2.bp.e.289.2 4 5.4 even 2
1170.2.bp.e.919.2 4 13.9 even 3
1950.2.i.y.451.1 4 195.113 even 12
1950.2.i.y.601.1 4 15.8 even 4
1950.2.i.bh.451.2 4 195.152 even 12
1950.2.i.bh.601.2 4 15.2 even 4