Properties

Label 294.4.e.j.79.1
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
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] = [294,4,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(17.3465615417\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.j.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.00000 - 6.92820i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.00000 - 6.92820i) q^{5} +6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-8.00000 - 13.8564i) q^{10} +(-20.0000 - 34.6410i) q^{11} +(6.00000 - 10.3923i) q^{12} -4.00000 q^{13} +24.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(74.0000 - 128.172i) q^{19} -32.0000 q^{20} -80.0000 q^{22} +(-42.0000 + 72.7461i) q^{23} +(-12.0000 - 20.7846i) q^{24} +(30.5000 + 52.8275i) q^{25} +(-4.00000 + 6.92820i) q^{26} -27.0000 q^{27} +58.0000 q^{29} +(24.0000 - 41.5692i) q^{30} +(-68.0000 - 117.779i) q^{31} +(16.0000 + 27.7128i) q^{32} +(60.0000 - 103.923i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(111.000 - 192.258i) q^{37} +(-148.000 - 256.344i) q^{38} +(-6.00000 - 10.3923i) q^{39} +(-32.0000 + 55.4256i) q^{40} -420.000 q^{41} -164.000 q^{43} +(-80.0000 + 138.564i) q^{44} +(36.0000 + 62.3538i) q^{45} +(84.0000 + 145.492i) q^{46} +(244.000 - 422.620i) q^{47} -48.0000 q^{48} +122.000 q^{50} +(126.000 - 218.238i) q^{51} +(8.00000 + 13.8564i) q^{52} +(-239.000 - 413.960i) q^{53} +(-27.0000 + 46.7654i) q^{54} -320.000 q^{55} +444.000 q^{57} +(58.0000 - 100.459i) q^{58} +(274.000 + 474.582i) q^{59} +(-48.0000 - 83.1384i) q^{60} +(346.000 - 599.290i) q^{61} -272.000 q^{62} +64.0000 q^{64} +(-16.0000 + 27.7128i) q^{65} +(-120.000 - 207.846i) q^{66} +(454.000 + 786.351i) q^{67} +(-168.000 + 290.985i) q^{68} -252.000 q^{69} -524.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(220.000 + 381.051i) q^{73} +(-222.000 - 384.515i) q^{74} +(-91.5000 + 158.483i) q^{75} -592.000 q^{76} -24.0000 q^{78} +(-608.000 + 1053.09i) q^{79} +(64.0000 + 110.851i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-420.000 + 727.461i) q^{82} +684.000 q^{83} -672.000 q^{85} +(-164.000 + 284.056i) q^{86} +(87.0000 + 150.688i) q^{87} +(160.000 + 277.128i) q^{88} +(302.000 - 523.079i) q^{89} +144.000 q^{90} +336.000 q^{92} +(204.000 - 353.338i) q^{93} +(-488.000 - 845.241i) q^{94} +(-592.000 - 1025.37i) q^{95} +(-48.0000 + 83.1384i) q^{96} +832.000 q^{97} +360.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 8 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 8 q^{5} + 12 q^{6} - 16 q^{8} - 9 q^{9} - 16 q^{10} - 40 q^{11} + 12 q^{12} - 8 q^{13} + 48 q^{15} - 16 q^{16} - 84 q^{17} + 18 q^{18} + 148 q^{19} - 64 q^{20} - 160 q^{22} - 84 q^{23} - 24 q^{24} + 61 q^{25} - 8 q^{26} - 54 q^{27} + 116 q^{29} + 48 q^{30} - 136 q^{31} + 32 q^{32} + 120 q^{33} - 336 q^{34} + 72 q^{36} + 222 q^{37} - 296 q^{38} - 12 q^{39} - 64 q^{40} - 840 q^{41} - 328 q^{43} - 160 q^{44} + 72 q^{45} + 168 q^{46} + 488 q^{47} - 96 q^{48} + 244 q^{50} + 252 q^{51} + 16 q^{52} - 478 q^{53} - 54 q^{54} - 640 q^{55} + 888 q^{57} + 116 q^{58} + 548 q^{59} - 96 q^{60} + 692 q^{61} - 544 q^{62} + 128 q^{64} - 32 q^{65} - 240 q^{66} + 908 q^{67} - 336 q^{68} - 504 q^{69} - 1048 q^{71} + 72 q^{72} + 440 q^{73} - 444 q^{74} - 183 q^{75} - 1184 q^{76} - 48 q^{78} - 1216 q^{79} + 128 q^{80} - 81 q^{81} - 840 q^{82} + 1368 q^{83} - 1344 q^{85} - 328 q^{86} + 174 q^{87} + 320 q^{88} + 604 q^{89} + 288 q^{90} + 672 q^{92} + 408 q^{93} - 976 q^{94} - 1184 q^{95} - 96 q^{96} + 1664 q^{97} + 720 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 4.00000 6.92820i 0.357771 0.619677i −0.629817 0.776743i \(-0.716870\pi\)
0.987588 + 0.157066i \(0.0502036\pi\)
\(6\) 6.00000 0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −8.00000 13.8564i −0.252982 0.438178i
\(11\) −20.0000 34.6410i −0.548202 0.949514i −0.998398 0.0565844i \(-0.981979\pi\)
0.450195 0.892930i \(-0.351354\pi\)
\(12\) 6.00000 10.3923i 0.144338 0.250000i
\(13\) −4.00000 −0.0853385 −0.0426692 0.999089i \(-0.513586\pi\)
−0.0426692 + 0.999089i \(0.513586\pi\)
\(14\) 0 0
\(15\) 24.0000 0.413118
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −42.0000 72.7461i −0.599206 1.03785i −0.992939 0.118630i \(-0.962150\pi\)
0.393733 0.919225i \(-0.371183\pi\)
\(18\) 9.00000 + 15.5885i 0.117851 + 0.204124i
\(19\) 74.0000 128.172i 0.893514 1.54761i 0.0578808 0.998324i \(-0.481566\pi\)
0.835633 0.549288i \(-0.185101\pi\)
\(20\) −32.0000 −0.357771
\(21\) 0 0
\(22\) −80.0000 −0.775275
\(23\) −42.0000 + 72.7461i −0.380765 + 0.659505i −0.991172 0.132583i \(-0.957673\pi\)
0.610406 + 0.792088i \(0.291006\pi\)
\(24\) −12.0000 20.7846i −0.102062 0.176777i
\(25\) 30.5000 + 52.8275i 0.244000 + 0.422620i
\(26\) −4.00000 + 6.92820i −0.0301717 + 0.0522589i
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) 58.0000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 24.0000 41.5692i 0.146059 0.252982i
\(31\) −68.0000 117.779i −0.393973 0.682381i 0.598997 0.800752i \(-0.295566\pi\)
−0.992970 + 0.118370i \(0.962233\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 60.0000 103.923i 0.316505 0.548202i
\(34\) −168.000 −0.847405
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) 111.000 192.258i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) −148.000 256.344i −0.631810 1.09433i
\(39\) −6.00000 10.3923i −0.0246351 0.0426692i
\(40\) −32.0000 + 55.4256i −0.126491 + 0.219089i
\(41\) −420.000 −1.59983 −0.799914 0.600114i \(-0.795122\pi\)
−0.799914 + 0.600114i \(0.795122\pi\)
\(42\) 0 0
\(43\) −164.000 −0.581622 −0.290811 0.956780i \(-0.593925\pi\)
−0.290811 + 0.956780i \(0.593925\pi\)
\(44\) −80.0000 + 138.564i −0.274101 + 0.474757i
\(45\) 36.0000 + 62.3538i 0.119257 + 0.206559i
\(46\) 84.0000 + 145.492i 0.269242 + 0.466341i
\(47\) 244.000 422.620i 0.757257 1.31161i −0.186988 0.982362i \(-0.559873\pi\)
0.944245 0.329245i \(-0.106794\pi\)
\(48\) −48.0000 −0.144338
\(49\) 0 0
\(50\) 122.000 0.345068
\(51\) 126.000 218.238i 0.345952 0.599206i
\(52\) 8.00000 + 13.8564i 0.0213346 + 0.0369527i
\(53\) −239.000 413.960i −0.619418 1.07286i −0.989592 0.143902i \(-0.954035\pi\)
0.370174 0.928963i \(-0.379298\pi\)
\(54\) −27.0000 + 46.7654i −0.0680414 + 0.117851i
\(55\) −320.000 −0.784523
\(56\) 0 0
\(57\) 444.000 1.03174
\(58\) 58.0000 100.459i 0.131306 0.227429i
\(59\) 274.000 + 474.582i 0.604606 + 1.04721i 0.992114 + 0.125342i \(0.0400028\pi\)
−0.387507 + 0.921867i \(0.626664\pi\)
\(60\) −48.0000 83.1384i −0.103280 0.178885i
\(61\) 346.000 599.290i 0.726242 1.25789i −0.232219 0.972664i \(-0.574599\pi\)
0.958461 0.285224i \(-0.0920681\pi\)
\(62\) −272.000 −0.557162
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −16.0000 + 27.7128i −0.0305316 + 0.0528823i
\(66\) −120.000 207.846i −0.223803 0.387638i
\(67\) 454.000 + 786.351i 0.827835 + 1.43385i 0.899733 + 0.436440i \(0.143761\pi\)
−0.0718987 + 0.997412i \(0.522906\pi\)
\(68\) −168.000 + 290.985i −0.299603 + 0.518927i
\(69\) −252.000 −0.439670
\(70\) 0 0
\(71\) −524.000 −0.875878 −0.437939 0.899005i \(-0.644291\pi\)
−0.437939 + 0.899005i \(0.644291\pi\)
\(72\) 36.0000 62.3538i 0.0589256 0.102062i
\(73\) 220.000 + 381.051i 0.352727 + 0.610941i 0.986726 0.162393i \(-0.0519212\pi\)
−0.633999 + 0.773334i \(0.718588\pi\)
\(74\) −222.000 384.515i −0.348743 0.604040i
\(75\) −91.5000 + 158.483i −0.140873 + 0.244000i
\(76\) −592.000 −0.893514
\(77\) 0 0
\(78\) −24.0000 −0.0348393
\(79\) −608.000 + 1053.09i −0.865890 + 1.49977i 0.000269874 1.00000i \(0.499914\pi\)
−0.866160 + 0.499766i \(0.833419\pi\)
\(80\) 64.0000 + 110.851i 0.0894427 + 0.154919i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −420.000 + 727.461i −0.565625 + 0.979691i
\(83\) 684.000 0.904563 0.452282 0.891875i \(-0.350610\pi\)
0.452282 + 0.891875i \(0.350610\pi\)
\(84\) 0 0
\(85\) −672.000 −0.857513
\(86\) −164.000 + 284.056i −0.205635 + 0.356170i
\(87\) 87.0000 + 150.688i 0.107211 + 0.185695i
\(88\) 160.000 + 277.128i 0.193819 + 0.335704i
\(89\) 302.000 523.079i 0.359685 0.622992i −0.628223 0.778033i \(-0.716218\pi\)
0.987908 + 0.155041i \(0.0495509\pi\)
\(90\) 144.000 0.168655
\(91\) 0 0
\(92\) 336.000 0.380765
\(93\) 204.000 353.338i 0.227460 0.393973i
\(94\) −488.000 845.241i −0.535461 0.927446i
\(95\) −592.000 1025.37i −0.639347 1.10738i
\(96\) −48.0000 + 83.1384i −0.0510310 + 0.0883883i
\(97\) 832.000 0.870895 0.435447 0.900214i \(-0.356590\pi\)
0.435447 + 0.900214i \(0.356590\pi\)
\(98\) 0 0
\(99\) 360.000 0.365468
\(100\) 122.000 211.310i 0.122000 0.211310i
\(101\) 232.000 + 401.836i 0.228563 + 0.395883i 0.957382 0.288823i \(-0.0932640\pi\)
−0.728819 + 0.684706i \(0.759931\pi\)
\(102\) −252.000 436.477i −0.244625 0.423702i
\(103\) −316.000 + 547.328i −0.302295 + 0.523591i −0.976655 0.214812i \(-0.931086\pi\)
0.674360 + 0.738402i \(0.264420\pi\)
\(104\) 32.0000 0.0301717
\(105\) 0 0
\(106\) −956.000 −0.875990
\(107\) 80.0000 138.564i 0.0722794 0.125192i −0.827621 0.561288i \(-0.810306\pi\)
0.899900 + 0.436096i \(0.143639\pi\)
\(108\) 54.0000 + 93.5307i 0.0481125 + 0.0833333i
\(109\) 1099.00 + 1903.52i 0.965735 + 1.67270i 0.707627 + 0.706586i \(0.249766\pi\)
0.258108 + 0.966116i \(0.416901\pi\)
\(110\) −320.000 + 554.256i −0.277371 + 0.480421i
\(111\) 666.000 0.569495
\(112\) 0 0
\(113\) 770.000 0.641022 0.320511 0.947245i \(-0.396145\pi\)
0.320511 + 0.947245i \(0.396145\pi\)
\(114\) 444.000 769.031i 0.364776 0.631810i
\(115\) 336.000 + 581.969i 0.272454 + 0.471903i
\(116\) −116.000 200.918i −0.0928477 0.160817i
\(117\) 18.0000 31.1769i 0.0142231 0.0246351i
\(118\) 1096.00 0.855042
\(119\) 0 0
\(120\) −192.000 −0.146059
\(121\) −134.500 + 232.961i −0.101052 + 0.175027i
\(122\) −692.000 1198.58i −0.513531 0.889461i
\(123\) −630.000 1091.19i −0.461831 0.799914i
\(124\) −272.000 + 471.118i −0.196986 + 0.341191i
\(125\) 1488.00 1.06473
\(126\) 0 0
\(127\) −184.000 −0.128562 −0.0642809 0.997932i \(-0.520475\pi\)
−0.0642809 + 0.997932i \(0.520475\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) −246.000 426.084i −0.167900 0.290811i
\(130\) 32.0000 + 55.4256i 0.0215891 + 0.0373935i
\(131\) −726.000 + 1257.47i −0.484205 + 0.838668i −0.999835 0.0181429i \(-0.994225\pi\)
0.515630 + 0.856811i \(0.327558\pi\)
\(132\) −480.000 −0.316505
\(133\) 0 0
\(134\) 1816.00 1.17074
\(135\) −108.000 + 187.061i −0.0688530 + 0.119257i
\(136\) 336.000 + 581.969i 0.211851 + 0.366937i
\(137\) −323.000 559.452i −0.201429 0.348885i 0.747560 0.664194i \(-0.231225\pi\)
−0.948989 + 0.315309i \(0.897892\pi\)
\(138\) −252.000 + 436.477i −0.155447 + 0.269242i
\(139\) 3012.00 1.83795 0.918973 0.394320i \(-0.129020\pi\)
0.918973 + 0.394320i \(0.129020\pi\)
\(140\) 0 0
\(141\) 1464.00 0.874405
\(142\) −524.000 + 907.595i −0.309670 + 0.536364i
\(143\) 80.0000 + 138.564i 0.0467828 + 0.0810301i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) 232.000 401.836i 0.132873 0.230142i
\(146\) 880.000 0.498831
\(147\) 0 0
\(148\) −888.000 −0.493197
\(149\) 1585.00 2745.30i 0.871465 1.50942i 0.0109833 0.999940i \(-0.496504\pi\)
0.860482 0.509482i \(-0.170163\pi\)
\(150\) 183.000 + 316.965i 0.0996126 + 0.172534i
\(151\) 940.000 + 1628.13i 0.506597 + 0.877451i 0.999971 + 0.00763414i \(0.00243005\pi\)
−0.493374 + 0.869817i \(0.664237\pi\)
\(152\) −592.000 + 1025.37i −0.315905 + 0.547163i
\(153\) 756.000 0.399470
\(154\) 0 0
\(155\) −1088.00 −0.563808
\(156\) −24.0000 + 41.5692i −0.0123176 + 0.0213346i
\(157\) 302.000 + 523.079i 0.153517 + 0.265900i 0.932518 0.361123i \(-0.117607\pi\)
−0.779001 + 0.627023i \(0.784273\pi\)
\(158\) 1216.00 + 2106.17i 0.612277 + 1.06049i
\(159\) 717.000 1241.88i 0.357621 0.619418i
\(160\) 256.000 0.126491
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) −558.000 + 966.484i −0.268135 + 0.464423i −0.968380 0.249479i \(-0.919741\pi\)
0.700246 + 0.713902i \(0.253074\pi\)
\(164\) 840.000 + 1454.92i 0.399957 + 0.692746i
\(165\) −480.000 831.384i −0.226472 0.392262i
\(166\) 684.000 1184.72i 0.319811 0.553930i
\(167\) 1784.00 0.826647 0.413324 0.910584i \(-0.364368\pi\)
0.413324 + 0.910584i \(0.364368\pi\)
\(168\) 0 0
\(169\) −2181.00 −0.992717
\(170\) −672.000 + 1163.94i −0.303177 + 0.525118i
\(171\) 666.000 + 1153.55i 0.297838 + 0.515870i
\(172\) 328.000 + 568.113i 0.145406 + 0.251850i
\(173\) −172.000 + 297.913i −0.0755891 + 0.130924i −0.901342 0.433107i \(-0.857417\pi\)
0.825753 + 0.564032i \(0.190750\pi\)
\(174\) 348.000 0.151620
\(175\) 0 0
\(176\) 640.000 0.274101
\(177\) −822.000 + 1423.75i −0.349070 + 0.604606i
\(178\) −604.000 1046.16i −0.254335 0.440522i
\(179\) −696.000 1205.51i −0.290623 0.503373i 0.683334 0.730106i \(-0.260529\pi\)
−0.973957 + 0.226732i \(0.927196\pi\)
\(180\) 144.000 249.415i 0.0596285 0.103280i
\(181\) −4052.00 −1.66399 −0.831997 0.554781i \(-0.812802\pi\)
−0.831997 + 0.554781i \(0.812802\pi\)
\(182\) 0 0
\(183\) 2076.00 0.838592
\(184\) 336.000 581.969i 0.134621 0.233170i
\(185\) −888.000 1538.06i −0.352903 0.611246i
\(186\) −408.000 706.677i −0.160839 0.278581i
\(187\) −1680.00 + 2909.85i −0.656972 + 1.13791i
\(188\) −1952.00 −0.757257
\(189\) 0 0
\(190\) −2368.00 −0.904173
\(191\) 1554.00 2691.61i 0.588709 1.01967i −0.405692 0.914010i \(-0.632970\pi\)
0.994402 0.105665i \(-0.0336971\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) −25.0000 43.3013i −0.00932404 0.0161497i 0.861326 0.508053i \(-0.169635\pi\)
−0.870650 + 0.491903i \(0.836301\pi\)
\(194\) 832.000 1441.07i 0.307908 0.533312i
\(195\) −96.0000 −0.0352549
\(196\) 0 0
\(197\) −162.000 −0.0585889 −0.0292945 0.999571i \(-0.509326\pi\)
−0.0292945 + 0.999571i \(0.509326\pi\)
\(198\) 360.000 623.538i 0.129213 0.223803i
\(199\) 772.000 + 1337.14i 0.275003 + 0.476319i 0.970136 0.242562i \(-0.0779878\pi\)
−0.695133 + 0.718881i \(0.744654\pi\)
\(200\) −244.000 422.620i −0.0862670 0.149419i
\(201\) −1362.00 + 2359.05i −0.477951 + 0.827835i
\(202\) 928.000 0.323237
\(203\) 0 0
\(204\) −1008.00 −0.345952
\(205\) −1680.00 + 2909.85i −0.572372 + 0.991378i
\(206\) 632.000 + 1094.66i 0.213755 + 0.370234i
\(207\) −378.000 654.715i −0.126922 0.219835i
\(208\) 32.0000 55.4256i 0.0106673 0.0184763i
\(209\) −5920.00 −1.95931
\(210\) 0 0
\(211\) −1204.00 −0.392828 −0.196414 0.980521i \(-0.562930\pi\)
−0.196414 + 0.980521i \(0.562930\pi\)
\(212\) −956.000 + 1655.84i −0.309709 + 0.536432i
\(213\) −786.000 1361.39i −0.252844 0.437939i
\(214\) −160.000 277.128i −0.0511092 0.0885238i
\(215\) −656.000 + 1136.23i −0.208088 + 0.360418i
\(216\) 216.000 0.0680414
\(217\) 0 0
\(218\) 4396.00 1.36576
\(219\) −660.000 + 1143.15i −0.203647 + 0.352727i
\(220\) 640.000 + 1108.51i 0.196131 + 0.339709i
\(221\) 168.000 + 290.985i 0.0511353 + 0.0885690i
\(222\) 666.000 1153.55i 0.201347 0.348743i
\(223\) −2000.00 −0.600583 −0.300291 0.953848i \(-0.597084\pi\)
−0.300291 + 0.953848i \(0.597084\pi\)
\(224\) 0 0
\(225\) −549.000 −0.162667
\(226\) 770.000 1333.68i 0.226636 0.392544i
\(227\) 194.000 + 336.018i 0.0567235 + 0.0982480i 0.892993 0.450071i \(-0.148601\pi\)
−0.836269 + 0.548319i \(0.815268\pi\)
\(228\) −888.000 1538.06i −0.257935 0.446757i
\(229\) 2090.00 3619.99i 0.603105 1.04461i −0.389243 0.921135i \(-0.627263\pi\)
0.992348 0.123474i \(-0.0394034\pi\)
\(230\) 1344.00 0.385308
\(231\) 0 0
\(232\) −464.000 −0.131306
\(233\) 661.000 1144.89i 0.185852 0.321905i −0.758011 0.652242i \(-0.773829\pi\)
0.943863 + 0.330336i \(0.107162\pi\)
\(234\) −36.0000 62.3538i −0.0100572 0.0174196i
\(235\) −1952.00 3380.96i −0.541849 0.938509i
\(236\) 1096.00 1898.33i 0.302303 0.523604i
\(237\) −3648.00 −0.999844
\(238\) 0 0
\(239\) 2412.00 0.652800 0.326400 0.945232i \(-0.394164\pi\)
0.326400 + 0.945232i \(0.394164\pi\)
\(240\) −192.000 + 332.554i −0.0516398 + 0.0894427i
\(241\) −2168.00 3755.09i −0.579474 1.00368i −0.995540 0.0943434i \(-0.969925\pi\)
0.416066 0.909334i \(-0.363409\pi\)
\(242\) 269.000 + 465.922i 0.0714544 + 0.123763i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −2768.00 −0.726242
\(245\) 0 0
\(246\) −2520.00 −0.653127
\(247\) −296.000 + 512.687i −0.0762511 + 0.132071i
\(248\) 544.000 + 942.236i 0.139290 + 0.241258i
\(249\) 1026.00 + 1777.08i 0.261125 + 0.452282i
\(250\) 1488.00 2577.29i 0.376438 0.652009i
\(251\) −764.000 −0.192125 −0.0960623 0.995375i \(-0.530625\pi\)
−0.0960623 + 0.995375i \(0.530625\pi\)
\(252\) 0 0
\(253\) 3360.00 0.834946
\(254\) −184.000 + 318.697i −0.0454535 + 0.0787278i
\(255\) −1008.00 1745.91i −0.247543 0.428757i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2150.00 3723.91i 0.521842 0.903856i −0.477835 0.878449i \(-0.658579\pi\)
0.999677 0.0254070i \(-0.00808817\pi\)
\(258\) −984.000 −0.237446
\(259\) 0 0
\(260\) 128.000 0.0305316
\(261\) −261.000 + 452.065i −0.0618984 + 0.107211i
\(262\) 1452.00 + 2514.94i 0.342385 + 0.593028i
\(263\) 1930.00 + 3342.86i 0.452505 + 0.783762i 0.998541 0.0539998i \(-0.0171970\pi\)
−0.546036 + 0.837762i \(0.683864\pi\)
\(264\) −480.000 + 831.384i −0.111901 + 0.193819i
\(265\) −3824.00 −0.886439
\(266\) 0 0
\(267\) 1812.00 0.415328
\(268\) 1816.00 3145.40i 0.413917 0.716926i
\(269\) −1400.00 2424.87i −0.317322 0.549617i 0.662607 0.748968i \(-0.269450\pi\)
−0.979928 + 0.199350i \(0.936117\pi\)
\(270\) 216.000 + 374.123i 0.0486864 + 0.0843274i
\(271\) −2440.00 + 4226.20i −0.546935 + 0.947320i 0.451547 + 0.892247i \(0.350872\pi\)
−0.998482 + 0.0550723i \(0.982461\pi\)
\(272\) 1344.00 0.299603
\(273\) 0 0
\(274\) −1292.00 −0.284863
\(275\) 1220.00 2113.10i 0.267523 0.463363i
\(276\) 504.000 + 872.954i 0.109918 + 0.190383i
\(277\) 3337.00 + 5779.85i 0.723830 + 1.25371i 0.959454 + 0.281866i \(0.0909533\pi\)
−0.235624 + 0.971844i \(0.575713\pi\)
\(278\) 3012.00 5216.94i 0.649812 1.12551i
\(279\) 1224.00 0.262649
\(280\) 0 0
\(281\) −9402.00 −1.99600 −0.998001 0.0632056i \(-0.979868\pi\)
−0.998001 + 0.0632056i \(0.979868\pi\)
\(282\) 1464.00 2535.72i 0.309149 0.535461i
\(283\) −4550.00 7880.83i −0.955722 1.65536i −0.732706 0.680545i \(-0.761743\pi\)
−0.223016 0.974815i \(-0.571590\pi\)
\(284\) 1048.00 + 1815.19i 0.218970 + 0.379266i
\(285\) 1776.00 3076.12i 0.369127 0.639347i
\(286\) 320.000 0.0661608
\(287\) 0 0
\(288\) −288.000 −0.0589256
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) −464.000 803.672i −0.0939552 0.162735i
\(291\) 1248.00 + 2161.60i 0.251406 + 0.435447i
\(292\) 880.000 1524.20i 0.176363 0.305470i
\(293\) −5952.00 −1.18676 −0.593378 0.804924i \(-0.702206\pi\)
−0.593378 + 0.804924i \(0.702206\pi\)
\(294\) 0 0
\(295\) 4384.00 0.865242
\(296\) −888.000 + 1538.06i −0.174371 + 0.302020i
\(297\) 540.000 + 935.307i 0.105502 + 0.182734i
\(298\) −3170.00 5490.60i −0.616219 1.06732i
\(299\) 168.000 290.985i 0.0324939 0.0562812i
\(300\) 732.000 0.140873
\(301\) 0 0
\(302\) 3760.00 0.716436
\(303\) −696.000 + 1205.51i −0.131961 + 0.228563i
\(304\) 1184.00 + 2050.75i 0.223378 + 0.386903i
\(305\) −2768.00 4794.32i −0.519656 0.900071i
\(306\) 756.000 1309.43i 0.141234 0.244625i
\(307\) 3004.00 0.558460 0.279230 0.960224i \(-0.409921\pi\)
0.279230 + 0.960224i \(0.409921\pi\)
\(308\) 0 0
\(309\) −1896.00 −0.349060
\(310\) −1088.00 + 1884.47i −0.199336 + 0.345261i
\(311\) 344.000 + 595.825i 0.0627217 + 0.108637i 0.895681 0.444697i \(-0.146689\pi\)
−0.832959 + 0.553334i \(0.813355\pi\)
\(312\) 48.0000 + 83.1384i 0.00870982 + 0.0150859i
\(313\) 2796.00 4842.81i 0.504918 0.874543i −0.495066 0.868855i \(-0.664856\pi\)
0.999984 0.00568790i \(-0.00181052\pi\)
\(314\) 1208.00 0.217106
\(315\) 0 0
\(316\) 4864.00 0.865890
\(317\) 1461.00 2530.53i 0.258858 0.448355i −0.707078 0.707135i \(-0.749987\pi\)
0.965936 + 0.258780i \(0.0833205\pi\)
\(318\) −1434.00 2483.76i −0.252876 0.437995i
\(319\) −1160.00 2009.18i −0.203597 0.352641i
\(320\) 256.000 443.405i 0.0447214 0.0774597i
\(321\) 480.000 0.0834610
\(322\) 0 0
\(323\) −12432.0 −2.14159
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) −122.000 211.310i −0.0208226 0.0360658i
\(326\) 1116.00 + 1932.97i 0.189600 + 0.328396i
\(327\) −3297.00 + 5710.57i −0.557567 + 0.965735i
\(328\) 3360.00 0.565625
\(329\) 0 0
\(330\) −1920.00 −0.320280
\(331\) 3746.00 6488.26i 0.622051 1.07742i −0.367053 0.930200i \(-0.619633\pi\)
0.989103 0.147223i \(-0.0470336\pi\)
\(332\) −1368.00 2369.45i −0.226141 0.391687i
\(333\) 999.000 + 1730.32i 0.164399 + 0.284747i
\(334\) 1784.00 3089.98i 0.292264 0.506216i
\(335\) 7264.00 1.18470
\(336\) 0 0
\(337\) 10766.0 1.74024 0.870121 0.492839i \(-0.164041\pi\)
0.870121 + 0.492839i \(0.164041\pi\)
\(338\) −2181.00 + 3777.60i −0.350979 + 0.607913i
\(339\) 1155.00 + 2000.52i 0.185047 + 0.320511i
\(340\) 1344.00 + 2327.88i 0.214378 + 0.371314i
\(341\) −2720.00 + 4711.18i −0.431954 + 0.748166i
\(342\) 2664.00 0.421206
\(343\) 0 0
\(344\) 1312.00 0.205635
\(345\) −1008.00 + 1745.91i −0.157301 + 0.272454i
\(346\) 344.000 + 595.825i 0.0534496 + 0.0925774i
\(347\) 1992.00 + 3450.25i 0.308173 + 0.533772i 0.977963 0.208779i \(-0.0669490\pi\)
−0.669789 + 0.742551i \(0.733616\pi\)
\(348\) 348.000 602.754i 0.0536056 0.0928477i
\(349\) 180.000 0.0276080 0.0138040 0.999905i \(-0.495606\pi\)
0.0138040 + 0.999905i \(0.495606\pi\)
\(350\) 0 0
\(351\) 108.000 0.0164234
\(352\) 640.000 1108.51i 0.0969094 0.167852i
\(353\) −5214.00 9030.91i −0.786156 1.36166i −0.928306 0.371818i \(-0.878735\pi\)
0.142149 0.989845i \(-0.454599\pi\)
\(354\) 1644.00 + 2847.49i 0.246829 + 0.427521i
\(355\) −2096.00 + 3630.38i −0.313364 + 0.542762i
\(356\) −2416.00 −0.359685
\(357\) 0 0
\(358\) −2784.00 −0.411003
\(359\) −4342.00 + 7520.56i −0.638334 + 1.10563i 0.347464 + 0.937693i \(0.387043\pi\)
−0.985798 + 0.167934i \(0.946290\pi\)
\(360\) −288.000 498.831i −0.0421637 0.0730297i
\(361\) −7522.50 13029.4i −1.09673 1.89960i
\(362\) −4052.00 + 7018.27i −0.588310 + 1.01898i
\(363\) −807.000 −0.116685
\(364\) 0 0
\(365\) 3520.00 0.504781
\(366\) 2076.00 3595.74i 0.296487 0.513531i
\(367\) 2824.00 + 4891.31i 0.401666 + 0.695707i 0.993927 0.110040i \(-0.0350978\pi\)
−0.592261 + 0.805746i \(0.701764\pi\)
\(368\) −672.000 1163.94i −0.0951914 0.164876i
\(369\) 1890.00 3273.58i 0.266638 0.461831i
\(370\) −3552.00 −0.499080
\(371\) 0 0
\(372\) −1632.00 −0.227460
\(373\) 1273.00 2204.90i 0.176712 0.306074i −0.764041 0.645168i \(-0.776787\pi\)
0.940752 + 0.339095i \(0.110121\pi\)
\(374\) 3360.00 + 5819.69i 0.464549 + 0.804623i
\(375\) 2232.00 + 3865.94i 0.307360 + 0.532363i
\(376\) −1952.00 + 3380.96i −0.267731 + 0.463723i
\(377\) −232.000 −0.0316939
\(378\) 0 0
\(379\) 8268.00 1.12058 0.560288 0.828298i \(-0.310690\pi\)
0.560288 + 0.828298i \(0.310690\pi\)
\(380\) −2368.00 + 4101.50i −0.319673 + 0.553690i
\(381\) −276.000 478.046i −0.0371126 0.0642809i
\(382\) −3108.00 5383.21i −0.416280 0.721019i
\(383\) −5436.00 + 9415.43i −0.725239 + 1.25615i 0.233636 + 0.972324i \(0.424938\pi\)
−0.958875 + 0.283827i \(0.908396\pi\)
\(384\) 384.000 0.0510310
\(385\) 0 0
\(386\) −100.000 −0.0131862
\(387\) 738.000 1278.25i 0.0969371 0.167900i
\(388\) −1664.00 2882.13i −0.217724 0.377109i
\(389\) −5217.00 9036.11i −0.679980 1.17776i −0.974986 0.222265i \(-0.928655\pi\)
0.295006 0.955495i \(-0.404678\pi\)
\(390\) −96.0000 + 166.277i −0.0124645 + 0.0215891i
\(391\) 7056.00 0.912627
\(392\) 0 0
\(393\) −4356.00 −0.559112
\(394\) −162.000 + 280.592i −0.0207143 + 0.0358783i
\(395\) 4864.00 + 8424.70i 0.619581 + 1.07315i
\(396\) −720.000 1247.08i −0.0913671 0.158252i
\(397\) −1522.00 + 2636.18i −0.192411 + 0.333265i −0.946049 0.324025i \(-0.894964\pi\)
0.753638 + 0.657290i \(0.228297\pi\)
\(398\) 3088.00 0.388913
\(399\) 0 0
\(400\) −976.000 −0.122000
\(401\) −4455.00 + 7716.29i −0.554793 + 0.960930i 0.443126 + 0.896459i \(0.353869\pi\)
−0.997920 + 0.0644709i \(0.979464\pi\)
\(402\) 2724.00 + 4718.11i 0.337962 + 0.585368i
\(403\) 272.000 + 471.118i 0.0336211 + 0.0582334i
\(404\) 928.000 1607.34i 0.114281 0.197941i
\(405\) −648.000 −0.0795046
\(406\) 0 0
\(407\) −8880.00 −1.08149
\(408\) −1008.00 + 1745.91i −0.122312 + 0.211851i
\(409\) 2808.00 + 4863.60i 0.339478 + 0.587994i 0.984335 0.176310i \(-0.0564161\pi\)
−0.644856 + 0.764304i \(0.723083\pi\)
\(410\) 3360.00 + 5819.69i 0.404728 + 0.701010i
\(411\) 969.000 1678.36i 0.116295 0.201429i
\(412\) 2528.00 0.302295
\(413\) 0 0
\(414\) −1512.00 −0.179495
\(415\) 2736.00 4738.89i 0.323626 0.560537i
\(416\) −64.0000 110.851i −0.00754293 0.0130647i
\(417\) 4518.00 + 7825.41i 0.530569 + 0.918973i
\(418\) −5920.00 + 10253.7i −0.692719 + 1.19983i
\(419\) 8932.00 1.04142 0.520712 0.853732i \(-0.325666\pi\)
0.520712 + 0.853732i \(0.325666\pi\)
\(420\) 0 0
\(421\) −5538.00 −0.641106 −0.320553 0.947231i \(-0.603869\pi\)
−0.320553 + 0.947231i \(0.603869\pi\)
\(422\) −1204.00 + 2085.39i −0.138886 + 0.240557i
\(423\) 2196.00 + 3803.58i 0.252419 + 0.437202i
\(424\) 1912.00 + 3311.68i 0.218997 + 0.379315i
\(425\) 2562.00 4437.51i 0.292412 0.506473i
\(426\) −3144.00 −0.357576
\(427\) 0 0
\(428\) −640.000 −0.0722794
\(429\) −240.000 + 415.692i −0.0270100 + 0.0467828i
\(430\) 1312.00 + 2272.45i 0.147140 + 0.254854i
\(431\) 3350.00 + 5802.37i 0.374394 + 0.648469i 0.990236 0.139400i \(-0.0445174\pi\)
−0.615842 + 0.787870i \(0.711184\pi\)
\(432\) 216.000 374.123i 0.0240563 0.0416667i
\(433\) 5048.00 0.560257 0.280129 0.959962i \(-0.409623\pi\)
0.280129 + 0.959962i \(0.409623\pi\)
\(434\) 0 0
\(435\) 1392.00 0.153428
\(436\) 4396.00 7614.10i 0.482867 0.836351i
\(437\) 6216.00 + 10766.4i 0.680438 + 1.17855i
\(438\) 1320.00 + 2286.31i 0.144000 + 0.249415i
\(439\) −672.000 + 1163.94i −0.0730588 + 0.126542i −0.900240 0.435393i \(-0.856609\pi\)
0.827182 + 0.561935i \(0.189943\pi\)
\(440\) 2560.00 0.277371
\(441\) 0 0
\(442\) 672.000 0.0723162
\(443\) 2196.00 3803.58i 0.235519 0.407932i −0.723904 0.689901i \(-0.757654\pi\)
0.959424 + 0.281969i \(0.0909875\pi\)
\(444\) −1332.00 2307.09i −0.142374 0.246598i
\(445\) −2416.00 4184.63i −0.257369 0.445777i
\(446\) −2000.00 + 3464.10i −0.212338 + 0.367780i
\(447\) 9510.00 1.00628
\(448\) 0 0
\(449\) 3666.00 0.385321 0.192661 0.981265i \(-0.438288\pi\)
0.192661 + 0.981265i \(0.438288\pi\)
\(450\) −549.000 + 950.896i −0.0575114 + 0.0996126i
\(451\) 8400.00 + 14549.2i 0.877030 + 1.51906i
\(452\) −1540.00 2667.36i −0.160256 0.277571i
\(453\) −2820.00 + 4884.38i −0.292484 + 0.506597i
\(454\) 776.000 0.0802191
\(455\) 0 0
\(456\) −3552.00 −0.364776
\(457\) −13.0000 + 22.5167i −0.00133067 + 0.00230478i −0.866690 0.498847i \(-0.833757\pi\)
0.865359 + 0.501152i \(0.167090\pi\)
\(458\) −4180.00 7239.97i −0.426460 0.738650i
\(459\) 1134.00 + 1964.15i 0.115317 + 0.199735i
\(460\) 1344.00 2327.88i 0.136227 0.235952i
\(461\) −7656.00 −0.773483 −0.386741 0.922188i \(-0.626399\pi\)
−0.386741 + 0.922188i \(0.626399\pi\)
\(462\) 0 0
\(463\) 12608.0 1.26554 0.632768 0.774341i \(-0.281919\pi\)
0.632768 + 0.774341i \(0.281919\pi\)
\(464\) −464.000 + 803.672i −0.0464238 + 0.0804084i
\(465\) −1632.00 2826.71i −0.162757 0.281904i
\(466\) −1322.00 2289.77i −0.131417 0.227621i
\(467\) −1534.00 + 2656.97i −0.152002 + 0.263276i −0.931963 0.362552i \(-0.881905\pi\)
0.779961 + 0.625828i \(0.215239\pi\)
\(468\) −144.000 −0.0142231
\(469\) 0 0
\(470\) −7808.00 −0.766290
\(471\) −906.000 + 1569.24i −0.0886333 + 0.153517i
\(472\) −2192.00 3796.66i −0.213761 0.370244i
\(473\) 3280.00 + 5681.13i 0.318847 + 0.552259i
\(474\) −3648.00 + 6318.52i −0.353498 + 0.612277i
\(475\) 9028.00 0.872070
\(476\) 0 0
\(477\) 4302.00 0.412946
\(478\) 2412.00 4177.71i 0.230800 0.399757i
\(479\) 3228.00 + 5591.06i 0.307915 + 0.533324i 0.977906 0.209045i \(-0.0670356\pi\)
−0.669991 + 0.742369i \(0.733702\pi\)
\(480\) 384.000 + 665.108i 0.0365148 + 0.0632456i
\(481\) −444.000 + 769.031i −0.0420887 + 0.0728997i
\(482\) −8672.00 −0.819500
\(483\) 0 0
\(484\) 1076.00 0.101052
\(485\) 3328.00 5764.27i 0.311581 0.539674i
\(486\) −243.000 420.888i −0.0226805 0.0392837i
\(487\) −5948.00 10302.2i −0.553449 0.958602i −0.998022 0.0628592i \(-0.979978\pi\)
0.444574 0.895742i \(-0.353355\pi\)
\(488\) −2768.00 + 4794.32i −0.256765 + 0.444731i
\(489\) −3348.00 −0.309615
\(490\) 0 0
\(491\) −264.000 −0.0242651 −0.0121325 0.999926i \(-0.503862\pi\)
−0.0121325 + 0.999926i \(0.503862\pi\)
\(492\) −2520.00 + 4364.77i −0.230915 + 0.399957i
\(493\) −2436.00 4219.28i −0.222539 0.385450i
\(494\) 592.000 + 1025.37i 0.0539177 + 0.0933882i
\(495\) 1440.00 2494.15i 0.130754 0.226472i
\(496\) 2176.00 0.196986
\(497\) 0 0
\(498\) 4104.00 0.369286
\(499\) 1314.00 2275.91i 0.117881 0.204176i −0.801047 0.598602i \(-0.795723\pi\)
0.918928 + 0.394426i \(0.129056\pi\)
\(500\) −2976.00 5154.58i −0.266182 0.461040i
\(501\) 2676.00 + 4634.97i 0.238632 + 0.413324i
\(502\) −764.000 + 1323.29i −0.0679263 + 0.117652i
\(503\) 13568.0 1.20272 0.601359 0.798979i \(-0.294626\pi\)
0.601359 + 0.798979i \(0.294626\pi\)
\(504\) 0 0
\(505\) 3712.00 0.327093
\(506\) 3360.00 5819.69i 0.295198 0.511298i
\(507\) −3271.50 5666.40i −0.286573 0.496359i
\(508\) 368.000 + 637.395i 0.0321405 + 0.0556689i
\(509\) 10328.0 17888.6i 0.899372 1.55776i 0.0710743 0.997471i \(-0.477357\pi\)
0.828298 0.560288i \(-0.189309\pi\)
\(510\) −4032.00 −0.350078
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) −1998.00 + 3460.64i −0.171957 + 0.297838i
\(514\) −4300.00 7447.82i −0.368998 0.639123i
\(515\) 2528.00 + 4378.62i 0.216305 + 0.374651i
\(516\) −984.000 + 1704.34i −0.0839500 + 0.145406i
\(517\) −19520.0 −1.66052
\(518\) 0 0
\(519\) −1032.00 −0.0872828
\(520\) 128.000 221.703i 0.0107946 0.0186967i
\(521\) 1814.00 + 3141.94i 0.152539 + 0.264205i 0.932160 0.362046i \(-0.117922\pi\)
−0.779621 + 0.626251i \(0.784588\pi\)
\(522\) 522.000 + 904.131i 0.0437688 + 0.0758098i
\(523\) 2426.00 4201.96i 0.202833 0.351317i −0.746607 0.665265i \(-0.768319\pi\)
0.949440 + 0.313948i \(0.101652\pi\)
\(524\) 5808.00 0.484205
\(525\) 0 0
\(526\) 7720.00 0.639939
\(527\) −5712.00 + 9893.47i −0.472142 + 0.817773i
\(528\) 960.000 + 1662.77i 0.0791262 + 0.137051i
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) −3824.00 + 6623.36i −0.313404 + 0.542831i
\(531\) −4932.00 −0.403071
\(532\) 0 0
\(533\) 1680.00 0.136527
\(534\) 1812.00 3138.48i 0.146841 0.254335i
\(535\) −640.000 1108.51i −0.0517189 0.0895798i
\(536\) −3632.00 6290.81i −0.292684 0.506943i
\(537\) 2088.00 3616.52i 0.167791 0.290623i
\(538\) −5600.00 −0.448760
\(539\) 0 0
\(540\) 864.000 0.0688530
\(541\) 3565.00 6174.76i 0.283311 0.490709i −0.688887 0.724869i \(-0.741900\pi\)
0.972198 + 0.234159i \(0.0752338\pi\)
\(542\) 4880.00 + 8452.41i 0.386742 + 0.669856i
\(543\) −6078.00 10527.4i −0.480353 0.831997i
\(544\) 1344.00 2327.88i 0.105926 0.183469i
\(545\) 17584.0 1.38205
\(546\) 0 0
\(547\) −12788.0 −0.999589 −0.499795 0.866144i \(-0.666591\pi\)
−0.499795 + 0.866144i \(0.666591\pi\)
\(548\) −1292.00 + 2237.81i −0.100714 + 0.174443i
\(549\) 3114.00 + 5393.61i 0.242081 + 0.419296i
\(550\) −2440.00 4226.20i −0.189167 0.327647i
\(551\) 4292.00 7433.96i 0.331843 0.574768i
\(552\) 2016.00 0.155447
\(553\) 0 0
\(554\) 13348.0 1.02365
\(555\) 2664.00 4614.18i 0.203749 0.352903i
\(556\) −6024.00 10433.9i −0.459487 0.795854i
\(557\) −1203.00 2083.66i −0.0915130 0.158505i 0.816635 0.577155i \(-0.195837\pi\)
−0.908148 + 0.418649i \(0.862504\pi\)
\(558\) 1224.00 2120.03i 0.0928603 0.160839i
\(559\) 656.000 0.0496348
\(560\) 0 0
\(561\) −10080.0 −0.758606
\(562\) −9402.00 + 16284.7i −0.705693 + 1.22230i
\(563\) −12706.0 22007.4i −0.951144 1.64743i −0.742955 0.669341i \(-0.766577\pi\)
−0.208189 0.978089i \(-0.566757\pi\)
\(564\) −2928.00 5071.44i −0.218601 0.378628i
\(565\) 3080.00 5334.72i 0.229339 0.397227i
\(566\) −18200.0 −1.35160
\(567\) 0 0
\(568\) 4192.00 0.309670
\(569\) 4845.00 8391.79i 0.356965 0.618281i −0.630487 0.776199i \(-0.717145\pi\)
0.987452 + 0.157918i \(0.0504783\pi\)
\(570\) −3552.00 6152.24i −0.261012 0.452086i
\(571\) −2802.00 4853.21i −0.205359 0.355692i 0.744888 0.667190i \(-0.232503\pi\)
−0.950247 + 0.311497i \(0.899170\pi\)
\(572\) 320.000 554.256i 0.0233914 0.0405151i
\(573\) 9324.00 0.679783
\(574\) 0 0
\(575\) −5124.00 −0.371627
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) −10784.0 18678.4i −0.778066 1.34765i −0.933055 0.359733i \(-0.882868\pi\)
0.154990 0.987916i \(-0.450466\pi\)
\(578\) 2143.00 + 3711.78i 0.154216 + 0.267111i
\(579\) 75.0000 129.904i 0.00538324 0.00932404i
\(580\) −1856.00 −0.132873
\(581\) 0 0
\(582\) 4992.00 0.355541
\(583\) −9560.00 + 16558.4i −0.679133 + 1.17629i
\(584\) −1760.00 3048.41i −0.124708 0.216000i
\(585\) −144.000 249.415i −0.0101772 0.0176274i
\(586\) −5952.00 + 10309.2i −0.419582 + 0.726737i
\(587\) −20300.0 −1.42738 −0.713689 0.700463i \(-0.752977\pi\)
−0.713689 + 0.700463i \(0.752977\pi\)
\(588\) 0 0
\(589\) −20128.0 −1.40808
\(590\) 4384.00 7593.31i 0.305909 0.529850i
\(591\) −243.000 420.888i −0.0169132 0.0292945i
\(592\) 1776.00 + 3076.12i 0.123299 + 0.213561i
\(593\) 6906.00 11961.5i 0.478238 0.828333i −0.521450 0.853282i \(-0.674609\pi\)
0.999689 + 0.0249483i \(0.00794212\pi\)
\(594\) 2160.00 0.149202
\(595\) 0 0
\(596\) −12680.0 −0.871465
\(597\) −2316.00 + 4011.43i −0.158773 + 0.275003i
\(598\) −336.000 581.969i −0.0229767 0.0397968i
\(599\) 10998.0 + 19049.1i 0.750194 + 1.29937i 0.947728 + 0.319078i \(0.103373\pi\)
−0.197535 + 0.980296i \(0.563294\pi\)
\(600\) 732.000 1267.86i 0.0498063 0.0862670i
\(601\) −8368.00 −0.567950 −0.283975 0.958832i \(-0.591653\pi\)
−0.283975 + 0.958832i \(0.591653\pi\)
\(602\) 0 0
\(603\) −8172.00 −0.551890
\(604\) 3760.00 6512.51i 0.253298 0.438726i
\(605\) 1076.00 + 1863.69i 0.0723068 + 0.125239i
\(606\) 1392.00 + 2411.01i 0.0933105 + 0.161618i
\(607\) 10752.0 18623.0i 0.718962 1.24528i −0.242449 0.970164i \(-0.577951\pi\)
0.961411 0.275115i \(-0.0887160\pi\)
\(608\) 4736.00 0.315905
\(609\) 0 0
\(610\) −11072.0 −0.734905
\(611\) −976.000 + 1690.48i −0.0646231 + 0.111931i
\(612\) −1512.00 2618.86i −0.0998676 0.172976i
\(613\) 5135.00 + 8894.08i 0.338337 + 0.586017i 0.984120 0.177504i \(-0.0568022\pi\)
−0.645783 + 0.763521i \(0.723469\pi\)
\(614\) 3004.00 5203.08i 0.197446 0.341986i
\(615\) −10080.0 −0.660918
\(616\) 0 0
\(617\) 28358.0 1.85032 0.925162 0.379572i \(-0.123929\pi\)
0.925162 + 0.379572i \(0.123929\pi\)
\(618\) −1896.00 + 3283.97i −0.123411 + 0.213755i
\(619\) 8146.00 + 14109.3i 0.528942 + 0.916155i 0.999430 + 0.0337488i \(0.0107446\pi\)
−0.470488 + 0.882406i \(0.655922\pi\)
\(620\) 2176.00 + 3768.94i 0.140952 + 0.244136i
\(621\) 1134.00 1964.15i 0.0732783 0.126922i
\(622\) 1376.00 0.0887019
\(623\) 0 0
\(624\) 192.000 0.0123176
\(625\) 2139.50 3705.72i 0.136928 0.237166i
\(626\) −5592.00 9685.63i −0.357031 0.618395i
\(627\) −8880.00 15380.6i −0.565603 0.979653i
\(628\) 1208.00 2092.32i 0.0767587 0.132950i
\(629\) −18648.0 −1.18211
\(630\) 0 0
\(631\) 11256.0 0.710134 0.355067 0.934841i \(-0.384458\pi\)
0.355067 + 0.934841i \(0.384458\pi\)
\(632\) 4864.00 8424.70i 0.306138 0.530247i
\(633\) −1806.00 3128.08i −0.113400 0.196414i
\(634\) −2922.00 5061.05i −0.183040 0.317035i
\(635\) −736.000 + 1274.79i −0.0459957 + 0.0796669i
\(636\) −5736.00 −0.357621
\(637\) 0 0
\(638\) −4640.00 −0.287930
\(639\) 2358.00 4084.18i 0.145980 0.252844i
\(640\) −512.000 886.810i −0.0316228 0.0547723i
\(641\) −7759.00 13439.0i −0.478100 0.828093i 0.521585 0.853199i \(-0.325341\pi\)
−0.999685 + 0.0251060i \(0.992008\pi\)
\(642\) 480.000 831.384i 0.0295079 0.0511092i
\(643\) 10452.0 0.641037 0.320518 0.947242i \(-0.396143\pi\)
0.320518 + 0.947242i \(0.396143\pi\)
\(644\) 0 0
\(645\) −3936.00 −0.240279
\(646\) −12432.0 + 21532.9i −0.757168 + 1.31145i
\(647\) 36.0000 + 62.3538i 0.00218749 + 0.00378884i 0.867117 0.498104i \(-0.165970\pi\)
−0.864930 + 0.501893i \(0.832637\pi\)
\(648\) 324.000 + 561.184i 0.0196419 + 0.0340207i
\(649\) 10960.0 18983.3i 0.662893 1.14816i
\(650\) −488.000 −0.0294476
\(651\) 0 0
\(652\) 4464.00 0.268135
\(653\) −5981.00 + 10359.4i −0.358430 + 0.620819i −0.987699 0.156369i \(-0.950021\pi\)
0.629269 + 0.777188i \(0.283354\pi\)
\(654\) 6594.00 + 11421.1i 0.394260 + 0.682878i
\(655\) 5808.00 + 10059.8i 0.346469 + 0.600102i
\(656\) 3360.00 5819.69i 0.199979 0.346373i
\(657\) −3960.00 −0.235151
\(658\) 0 0
\(659\) −6016.00 −0.355615 −0.177807 0.984065i \(-0.556900\pi\)
−0.177807 + 0.984065i \(0.556900\pi\)
\(660\) −1920.00 + 3325.54i −0.113236 + 0.196131i
\(661\) 13034.0 + 22575.6i 0.766965 + 1.32842i 0.939201 + 0.343367i \(0.111567\pi\)
−0.172236 + 0.985056i \(0.555099\pi\)
\(662\) −7492.00 12976.5i −0.439856 0.761853i
\(663\) −504.000 + 872.954i −0.0295230 + 0.0511353i
\(664\) −5472.00 −0.319811
\(665\) 0 0
\(666\) 3996.00 0.232495
\(667\) −2436.00 + 4219.28i −0.141413 + 0.244934i
\(668\) −3568.00 6179.96i −0.206662 0.357949i
\(669\) −3000.00 5196.15i −0.173373 0.300291i
\(670\) 7264.00 12581.6i 0.418855 0.725478i
\(671\) −27680.0 −1.59251
\(672\) 0 0
\(673\) −20530.0 −1.17589 −0.587945 0.808901i \(-0.700063\pi\)
−0.587945 + 0.808901i \(0.700063\pi\)
\(674\) 10766.0 18647.3i 0.615268 1.06568i
\(675\) −823.500 1426.34i −0.0469578 0.0813333i
\(676\) 4362.00 + 7555.21i 0.248179 + 0.429859i
\(677\) −5028.00 + 8708.75i −0.285438 + 0.494394i −0.972715 0.232002i \(-0.925473\pi\)
0.687277 + 0.726395i \(0.258806\pi\)
\(678\) 4620.00 0.261696
\(679\) 0 0
\(680\) 5376.00 0.303177
\(681\) −582.000 + 1008.05i −0.0327493 + 0.0567235i
\(682\) 5440.00 + 9422.36i 0.305437 + 0.529033i
\(683\) −3076.00 5327.79i −0.172328 0.298480i 0.766905 0.641760i \(-0.221795\pi\)
−0.939233 + 0.343280i \(0.888462\pi\)
\(684\) 2664.00 4614.18i 0.148919 0.257935i
\(685\) −5168.00 −0.288262
\(686\) 0 0
\(687\) 12540.0 0.696406
\(688\) 1312.00 2272.45i 0.0727028 0.125925i
\(689\) 956.000 + 1655.84i 0.0528602 + 0.0915566i
\(690\) 2016.00 + 3491.81i 0.111229 + 0.192654i
\(691\) −7358.00 + 12744.4i −0.405082 + 0.701622i −0.994331 0.106329i \(-0.966090\pi\)
0.589249 + 0.807951i \(0.299424\pi\)
\(692\) 1376.00 0.0755891
\(693\) 0 0
\(694\) 7968.00 0.435823
\(695\) 12048.0 20867.7i 0.657564 1.13893i
\(696\) −696.000 1205.51i −0.0379049 0.0656532i
\(697\) 17640.0 + 30553.4i 0.958626 + 1.66039i
\(698\) 180.000 311.769i 0.00976089 0.0169064i
\(699\) 3966.00 0.214604
\(700\) 0 0
\(701\) 28202.0 1.51951 0.759754 0.650211i \(-0.225319\pi\)
0.759754 + 0.650211i \(0.225319\pi\)
\(702\) 108.000 187.061i 0.00580655 0.0100572i
\(703\) −16428.0 28454.1i −0.881357 1.52655i
\(704\) −1280.00 2217.03i −0.0685253 0.118689i
\(705\) 5856.00 10142.9i 0.312836 0.541849i
\(706\) −20856.0 −1.11179
\(707\) 0 0
\(708\) 6576.00 0.349070
\(709\) −11057.0 + 19151.3i −0.585690 + 1.01445i 0.409099 + 0.912490i \(0.365843\pi\)
−0.994789 + 0.101955i \(0.967490\pi\)
\(710\) 4192.00 + 7260.76i 0.221582 + 0.383791i
\(711\) −5472.00 9477.78i −0.288630 0.499922i
\(712\) −2416.00 + 4184.63i −0.127168 + 0.220261i
\(713\) 11424.0 0.600045
\(714\) 0 0
\(715\) 1280.00 0.0669501
\(716\) −2784.00 + 4822.03i −0.145311 + 0.251687i
\(717\) 3618.00 + 6266.56i 0.188447 + 0.326400i
\(718\) 8684.00 + 15041.1i 0.451370 + 0.781797i
\(719\) −4644.00 + 8043.64i −0.240879 + 0.417215i −0.960965 0.276670i \(-0.910769\pi\)
0.720086 + 0.693885i \(0.244102\pi\)
\(720\) −1152.00 −0.0596285
\(721\) 0 0
\(722\) −30090.0 −1.55102
\(723\) 6504.00 11265.3i 0.334559 0.579474i
\(724\) 8104.00 + 14036.5i 0.415998 + 0.720530i
\(725\) 1769.00 + 3064.00i 0.0906193 + 0.156957i
\(726\) −807.000 + 1397.77i −0.0412542 + 0.0714544i
\(727\) −23848.0 −1.21661 −0.608304 0.793704i \(-0.708150\pi\)
−0.608304 + 0.793704i \(0.708150\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 3520.00 6096.82i 0.178467 0.309114i
\(731\) 6888.00 + 11930.4i 0.348511 + 0.603640i
\(732\) −4152.00 7191.47i −0.209648 0.363121i
\(733\) −17378.0 + 30099.6i −0.875677 + 1.51672i −0.0196367 + 0.999807i \(0.506251\pi\)
−0.856040 + 0.516909i \(0.827082\pi\)
\(734\) 11296.0 0.568042
\(735\) 0 0
\(736\) −2688.00 −0.134621
\(737\) 18160.0 31454.0i 0.907642 1.57208i
\(738\) −3780.00 6547.15i −0.188542 0.326564i
\(739\) −13022.0 22554.8i −0.648203 1.12272i −0.983552 0.180626i \(-0.942187\pi\)
0.335349 0.942094i \(-0.391146\pi\)
\(740\) −3552.00 + 6152.24i −0.176452 + 0.305623i
\(741\) −1776.00 −0.0880472
\(742\) 0 0
\(743\) 36204.0 1.78761 0.893806 0.448454i \(-0.148025\pi\)
0.893806 + 0.448454i \(0.148025\pi\)
\(744\) −1632.00 + 2826.71i −0.0804194 + 0.139290i
\(745\) −12680.0 21962.4i −0.623569 1.08005i
\(746\) −2546.00 4409.80i −0.124954 0.216427i
\(747\) −3078.00 + 5331.25i −0.150761 + 0.261125i
\(748\) 13440.0 0.656972
\(749\) 0 0
\(750\) 8928.00 0.434673
\(751\) 5712.00 9893.47i 0.277542 0.480716i −0.693232 0.720715i \(-0.743814\pi\)
0.970773 + 0.239999i \(0.0771470\pi\)
\(752\) 3904.00 + 6761.93i 0.189314 + 0.327902i
\(753\) −1146.00 1984.93i −0.0554616 0.0960623i
\(754\) −232.000 + 401.836i −0.0112055 + 0.0194085i
\(755\) 15040.0 0.724982
\(756\) 0 0
\(757\) −16622.0 −0.798067 −0.399034 0.916936i \(-0.630654\pi\)
−0.399034 + 0.916936i \(0.630654\pi\)
\(758\) 8268.00 14320.6i 0.396184 0.686210i
\(759\) 5040.00 + 8729.54i 0.241028 + 0.417473i
\(760\) 4736.00 + 8202.99i 0.226043 + 0.391518i
\(761\) −19262.0 + 33362.8i −0.917539 + 1.58922i −0.114397 + 0.993435i \(0.536494\pi\)
−0.803141 + 0.595789i \(0.796840\pi\)
\(762\) −1104.00 −0.0524852
\(763\) 0 0
\(764\) −12432.0 −0.588709
\(765\) 3024.00 5237.72i 0.142919 0.247543i
\(766\) 10872.0 + 18830.9i 0.512822 + 0.888233i
\(767\) −1096.00 1898.33i −0.0515962 0.0893672i
\(768\) 384.000 665.108i 0.0180422 0.0312500i
\(769\) 18440.0 0.864712 0.432356 0.901703i \(-0.357682\pi\)
0.432356 + 0.901703i \(0.357682\pi\)
\(770\) 0 0
\(771\) 12900.0 0.602571
\(772\) −100.000 + 173.205i −0.00466202 + 0.00807485i
\(773\) −6984.00 12096.6i −0.324964 0.562854i 0.656541 0.754290i \(-0.272019\pi\)
−0.981505 + 0.191436i \(0.938685\pi\)
\(774\) −1476.00 2556.51i −0.0685449 0.118723i
\(775\) 4148.00 7184.55i 0.192259 0.333002i
\(776\) −6656.00 −0.307908
\(777\) 0 0
\(778\) −20868.0 −0.961638
\(779\) −31080.0 + 53832.1i −1.42947 + 2.47591i
\(780\) 192.000 + 332.554i 0.00881372 + 0.0152658i
\(781\) 10480.0 + 18151.9i 0.480159 + 0.831659i
\(782\) 7056.00 12221.4i 0.322662 0.558868i
\(783\) −1566.00 −0.0714742
\(784\) 0 0
\(785\) 4832.00 0.219696
\(786\) −4356.00 + 7544.81i −0.197676 + 0.342385i
\(787\) 5458.00 + 9453.53i 0.247213 + 0.428186i 0.962752 0.270388i \(-0.0871519\pi\)
−0.715538 + 0.698573i \(0.753819\pi\)
\(788\) 324.000 + 561.184i 0.0146472 + 0.0253698i
\(789\) −5790.00 + 10028.6i −0.261254 + 0.452505i
\(790\) 19456.0 0.876220
\(791\) 0 0
\(792\) −2880.00 −0.129213
\(793\) −1384.00 + 2397.16i −0.0619764 + 0.107346i
\(794\) 3044.00 + 5272.36i 0.136055 + 0.235654i
\(795\) −5736.00 9935.04i −0.255893 0.443220i
\(796\) 3088.00 5348.57i 0.137502 0.238160i
\(797\) −12360.0 −0.549327 −0.274664 0.961540i \(-0.588566\pi\)
−0.274664 + 0.961540i \(0.588566\pi\)
\(798\) 0 0
\(799\) −40992.0 −1.81501
\(800\) −976.000 + 1690.48i −0.0431335 + 0.0747094i
\(801\) 2718.00 + 4707.71i 0.119895 + 0.207664i
\(802\) 8910.00 + 15432.6i 0.392298 + 0.679480i
\(803\) 8800.00 15242.0i 0.386731 0.669838i
\(804\) 10896.0 0.477951
\(805\) 0 0
\(806\) 1088.00 0.0475474
\(807\) 4200.00 7274.61i 0.183206 0.317322i
\(808\) −1856.00 3214.69i −0.0808092 0.139966i
\(809\) −1701.00 2946.22i −0.0739233 0.128039i 0.826694 0.562651i \(-0.190219\pi\)
−0.900618 + 0.434612i \(0.856885\pi\)
\(810\) −648.000 + 1122.37i −0.0281091 + 0.0486864i
\(811\) −292.000 −0.0126430 −0.00632152 0.999980i \(-0.502012\pi\)
−0.00632152 + 0.999980i \(0.502012\pi\)
\(812\) 0 0
\(813\) −14640.0 −0.631546
\(814\) −8880.00 + 15380.6i −0.382363 + 0.662273i
\(815\) 4464.00 + 7731.87i 0.191861 + 0.332314i
\(816\) 2016.00 + 3491.81i 0.0864879 + 0.149801i
\(817\) −12136.0 + 21020.2i −0.519688 + 0.900126i
\(818\) 11232.0 0.480095
\(819\) 0 0
\(820\) 13440.0 0.572372
\(821\) −3455.00 + 5984.24i −0.146870 + 0.254386i −0.930069 0.367385i \(-0.880253\pi\)
0.783199 + 0.621771i \(0.213587\pi\)
\(822\) −1938.00 3356.71i −0.0822330 0.142432i
\(823\) −284.000 491.902i −0.0120287 0.0208343i 0.859948 0.510381i \(-0.170496\pi\)
−0.871977 + 0.489547i \(0.837162\pi\)
\(824\) 2528.00 4378.62i 0.106877 0.185117i
\(825\) 7320.00 0.308909
\(826\) 0 0
\(827\) −12144.0 −0.510627 −0.255313 0.966858i \(-0.582179\pi\)
−0.255313 + 0.966858i \(0.582179\pi\)
\(828\) −1512.00 + 2618.86i −0.0634609 + 0.109918i
\(829\) 7414.00 + 12841.4i 0.310614 + 0.537999i 0.978495 0.206269i \(-0.0661321\pi\)
−0.667882 + 0.744268i \(0.732799\pi\)
\(830\) −5472.00 9477.78i −0.228838 0.396360i
\(831\) −10011.0 + 17339.6i −0.417903 + 0.723830i
\(832\) −256.000 −0.0106673
\(833\) 0 0
\(834\) 18072.0 0.750338
\(835\) 7136.00 12359.9i 0.295750 0.512254i
\(836\) 11840.0 + 20507.5i 0.489827 + 0.848404i
\(837\) 1836.00 + 3180.05i 0.0758201 + 0.131324i
\(838\) 8932.00 15470.7i 0.368199 0.637739i
\(839\) 22824.0 0.939180 0.469590 0.882885i \(-0.344402\pi\)
0.469590 + 0.882885i \(0.344402\pi\)
\(840\) 0 0
\(841\) −21025.0 −0.862069
\(842\) −5538.00 + 9592.10i −0.226665 + 0.392596i
\(843\) −14103.0 24427.1i −0.576196 0.998001i
\(844\) 2408.00 + 4170.78i 0.0982071 + 0.170100i
\(845\) −8724.00 + 15110.4i −0.355165 + 0.615164i
\(846\) 8784.00 0.356974
\(847\) 0 0
\(848\) 7648.00 0.309709
\(849\) 13650.0 23642.5i 0.551787 0.955722i
\(850\) −5124.00 8875.03i −0.206767 0.358131i
\(851\) 9324.00 + 16149.6i 0.375585 + 0.650532i
\(852\) −3144.00 + 5445.57i −0.126422 + 0.218970i
\(853\) 41780.0 1.67705 0.838523 0.544866i \(-0.183420\pi\)
0.838523 + 0.544866i \(0.183420\pi\)
\(854\) 0 0
\(855\) 10656.0 0.426231
\(856\) −640.000 + 1108.51i −0.0255546 + 0.0442619i
\(857\) −10710.0 18550.3i −0.426892 0.739399i 0.569703 0.821851i \(-0.307058\pi\)
−0.996595 + 0.0824518i \(0.973725\pi\)
\(858\) 480.000 + 831.384i 0.0190990 + 0.0330804i
\(859\) −9066.00 + 15702.8i −0.360102 + 0.623716i −0.987977 0.154599i \(-0.950592\pi\)
0.627875 + 0.778314i \(0.283925\pi\)
\(860\) 5248.00 0.208088
\(861\) 0 0
\(862\) 13400.0 0.529473
\(863\) −12018.0 + 20815.8i −0.474041 + 0.821063i −0.999558 0.0297197i \(-0.990539\pi\)
0.525517 + 0.850783i \(0.323872\pi\)
\(864\) −432.000 748.246i −0.0170103 0.0294628i
\(865\) 1376.00 + 2383.30i 0.0540872 + 0.0936817i
\(866\) 5048.00 8743.39i 0.198081 0.343086i
\(867\) −6429.00 −0.251834
\(868\) 0 0
\(869\) 48640.0 1.89873
\(870\) 1392.00 2411.01i 0.0542451 0.0939552i
\(871\) −1816.00 3145.40i −0.0706462 0.122363i
\(872\) −8792.00 15228.2i −0.341439 0.591389i
\(873\) −3744.00 + 6484.80i −0.145149 + 0.251406i
\(874\) 24864.0 0.962285
\(875\) 0 0
\(876\) 5280.00 0.203647
\(877\) 2187.00 3788.00i 0.0842072 0.145851i −0.820846 0.571150i \(-0.806498\pi\)
0.905053 + 0.425299i \(0.139831\pi\)
\(878\) 1344.00 + 2327.88i 0.0516604 + 0.0894784i
\(879\) −8928.00 15463.7i −0.342587 0.593378i
\(880\) 2560.00 4434.05i 0.0980654 0.169854i
\(881\) 46348.0 1.77242 0.886211 0.463282i \(-0.153328\pi\)
0.886211 + 0.463282i \(0.153328\pi\)
\(882\) 0 0
\(883\) −20660.0 −0.787389 −0.393694 0.919241i \(-0.628803\pi\)
−0.393694 + 0.919241i \(0.628803\pi\)
\(884\) 672.000 1163.94i 0.0255677 0.0442845i
\(885\) 6576.00 + 11390.0i 0.249774 + 0.432621i
\(886\) −4392.00 7607.17i −0.166537 0.288451i
\(887\) −900.000 + 1558.85i −0.0340688 + 0.0590089i −0.882557 0.470205i \(-0.844180\pi\)
0.848488 + 0.529214i \(0.177513\pi\)
\(888\) −5328.00 −0.201347
\(889\) 0 0
\(890\) −9664.00 −0.363975
\(891\) −1620.00 + 2805.92i −0.0609114 + 0.105502i
\(892\) 4000.00 + 6928.20i 0.150146 + 0.260060i
\(893\) −36112.0 62547.8i −1.35324 2.34388i
\(894\) 9510.00 16471.8i 0.355774 0.616219i
\(895\) −11136.0 −0.415906
\(896\) 0 0
\(897\) 1008.00 0.0375208
\(898\) 3666.00 6349.70i 0.136232 0.235960i
\(899\) −3944.00 6831.21i −0.146318 0.253430i
\(900\) 1098.00 + 1901.79i 0.0406667 + 0.0704367i
\(901\) −20076.0 + 34772.7i −0.742318 + 1.28573i
\(902\) 33600.0 1.24031
\(903\) 0 0
\(904\) −6160.00 −0.226636
\(905\) −16208.0 + 28073.1i −0.595328 + 1.03114i
\(906\) 5640.00 + 9768.77i 0.206817 + 0.358218i
\(907\) 20998.0 + 36369.6i 0.768718 + 1.33146i 0.938258 + 0.345935i \(0.112438\pi\)
−0.169540 + 0.985523i \(0.554228\pi\)
\(908\) 776.000 1344.07i 0.0283617 0.0491240i
\(909\) −4176.00 −0.152375
\(910\) 0 0
\(911\) −41308.0 −1.50230 −0.751150 0.660132i \(-0.770500\pi\)
−0.751150 + 0.660132i \(0.770500\pi\)
\(912\) −3552.00 + 6152.24i −0.128968 + 0.223378i
\(913\) −13680.0 23694.5i −0.495884 0.858896i
\(914\) 26.0000 + 45.0333i 0.000940923 + 0.00162973i
\(915\) 8304.00 14382.9i 0.300024 0.519656i
\(916\) −16720.0 −0.603105
\(917\) 0 0
\(918\) 4536.00 0.163083
\(919\) −1968.00 + 3408.68i −0.0706402 + 0.122352i −0.899182 0.437575i \(-0.855838\pi\)
0.828542 + 0.559927i \(0.189171\pi\)
\(920\) −2688.00 4655.75i −0.0963269 0.166843i
\(921\) 4506.00 + 7804.62i 0.161214 + 0.279230i
\(922\) −7656.00 + 13260.6i −0.273467 + 0.473659i
\(923\) 2096.00 0.0747461
\(924\) 0 0
\(925\) 13542.0 0.481360
\(926\) 12608.0 21837.7i 0.447435 0.774980i
\(927\) −2844.00 4925.95i −0.100765 0.174530i
\(928\) 928.000 + 1607.34i 0.0328266 + 0.0568574i
\(929\) −3606.00 + 6245.78i −0.127351 + 0.220578i −0.922649 0.385640i \(-0.873981\pi\)
0.795299 + 0.606218i \(0.207314\pi\)
\(930\) −6528.00 −0.230174
\(931\) 0 0
\(932\) −5288.00 −0.185852
\(933\) −1032.00 + 1787.48i −0.0362124 + 0.0627217i
\(934\) 3068.00 + 5313.93i 0.107482 + 0.186164i
\(935\) 13440.0 + 23278.8i 0.470091 + 0.814221i
\(936\) −144.000 + 249.415i −0.00502862 + 0.00870982i
\(937\) 38976.0 1.35890 0.679451 0.733721i \(-0.262218\pi\)
0.679451 + 0.733721i \(0.262218\pi\)
\(938\) 0 0
\(939\) 16776.0 0.583029
\(940\) −7808.00 + 13523.9i −0.270924 + 0.469255i
\(941\) 26772.0 + 46370.5i 0.927463 + 1.60641i 0.787552 + 0.616248i \(0.211348\pi\)
0.139910 + 0.990164i \(0.455319\pi\)
\(942\) 1812.00 + 3138.48i 0.0626732 + 0.108553i
\(943\) 17640.0 30553.4i 0.609160 1.05510i
\(944\) −8768.00 −0.302303
\(945\) 0 0
\(946\) 13120.0 0.450918
\(947\) 10696.0 18526.0i 0.367026 0.635707i −0.622073 0.782959i \(-0.713709\pi\)
0.989099 + 0.147252i \(0.0470428\pi\)
\(948\) 7296.00 + 12637.0i 0.249961 + 0.432945i
\(949\) −880.000 1524.20i −0.0301012 0.0521368i
\(950\) 9028.00 15637.0i 0.308323 0.534031i
\(951\) 8766.00 0.298903
\(952\) 0 0
\(953\) 21162.0 0.719312 0.359656 0.933085i \(-0.382894\pi\)
0.359656 + 0.933085i \(0.382894\pi\)
\(954\) 4302.00 7451.28i 0.145998 0.252876i
\(955\) −12432.0 21532.9i −0.421246 0.729620i
\(956\) −4824.00 8355.41i −0.163200 0.282671i
\(957\) 3480.00 6027.54i 0.117547 0.203597i
\(958\) 12912.0 0.435457
\(959\) 0 0
\(960\) 1536.00 0.0516398
\(961\) 5647.50 9781.76i 0.189571 0.328346i
\(962\) 888.000 + 1538.06i 0.0297612 + 0.0515479i
\(963\) 720.000 + 1247.08i 0.0240931 + 0.0417305i
\(964\) −8672.00 + 15020.3i −0.289737 + 0.501839i
\(965\) −400.000 −0.0133435
\(966\) 0 0
\(967\) 8224.00 0.273491 0.136746 0.990606i \(-0.456336\pi\)
0.136746 + 0.990606i \(0.456336\pi\)
\(968\) 1076.00 1863.69i 0.0357272 0.0618814i
\(969\) −18648.0 32299.3i −0.618225 1.07080i
\(970\) −6656.00 11528.5i −0.220321 0.381607i
\(971\) −4070.00 + 7049.45i −0.134513 + 0.232984i −0.925411 0.378964i \(-0.876280\pi\)
0.790898 + 0.611948i \(0.209614\pi\)
\(972\) −972.000 −0.0320750
\(973\) 0 0
\(974\) −23792.0 −0.782695
\(975\) 366.000 633.931i 0.0120219 0.0208226i
\(976\) 5536.00 + 9588.63i 0.181560 + 0.314472i
\(977\) −16079.0 27849.6i −0.526523 0.911964i −0.999522 0.0309016i \(-0.990162\pi\)
0.473000 0.881063i \(-0.343171\pi\)
\(978\) −3348.00 + 5798.91i −0.109465 + 0.189600i
\(979\) −24160.0 −0.788720
\(980\) 0 0
\(981\) −19782.0 −0.643823
\(982\) −264.000 + 457.261i −0.00857900 + 0.0148593i
\(983\) −20708.0 35867.3i −0.671905 1.16377i −0.977363 0.211568i \(-0.932143\pi\)
0.305458 0.952205i \(-0.401190\pi\)
\(984\) 5040.00 + 8729.54i 0.163282 + 0.282812i
\(985\) −648.000 + 1122.37i −0.0209614 + 0.0363062i
\(986\) −9744.00 −0.314718
\(987\) 0 0
\(988\) 2368.00 0.0762511
\(989\) 6888.00 11930.4i 0.221462 0.383583i
\(990\) −2880.00 4988.31i −0.0924570 0.160140i
\(991\) −6148.00 10648.6i −0.197071 0.341338i 0.750506 0.660863i \(-0.229810\pi\)
−0.947578 + 0.319526i \(0.896476\pi\)
\(992\) 2176.00 3768.94i 0.0696452 0.120629i
\(993\) 22476.0 0.718282
\(994\) 0 0
\(995\) 12352.0 0.393552
\(996\) 4104.00 7108.34i 0.130562 0.226141i
\(997\) 28826.0 + 49928.1i 0.915676 + 1.58600i 0.805909 + 0.592039i \(0.201677\pi\)
0.109766 + 0.993957i \(0.464990\pi\)
\(998\) −2628.00 4551.83i −0.0833546 0.144374i
\(999\) −2997.00 + 5190.96i −0.0949158 + 0.164399i
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 294.4.e.j.79.1 2
3.2 odd 2 882.4.g.c.667.1 2
7.2 even 3 294.4.a.b.1.1 1
7.3 odd 6 294.4.e.f.67.1 2
7.4 even 3 inner 294.4.e.j.67.1 2
7.5 odd 6 294.4.a.f.1.1 yes 1
7.6 odd 2 294.4.e.f.79.1 2
21.2 odd 6 882.4.a.q.1.1 1
21.5 even 6 882.4.a.j.1.1 1
21.11 odd 6 882.4.g.c.361.1 2
21.17 even 6 882.4.g.j.361.1 2
21.20 even 2 882.4.g.j.667.1 2
28.19 even 6 2352.4.a.m.1.1 1
28.23 odd 6 2352.4.a.z.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.b.1.1 1 7.2 even 3
294.4.a.f.1.1 yes 1 7.5 odd 6
294.4.e.f.67.1 2 7.3 odd 6
294.4.e.f.79.1 2 7.6 odd 2
294.4.e.j.67.1 2 7.4 even 3 inner
294.4.e.j.79.1 2 1.1 even 1 trivial
882.4.a.j.1.1 1 21.5 even 6
882.4.a.q.1.1 1 21.2 odd 6
882.4.g.c.361.1 2 21.11 odd 6
882.4.g.c.667.1 2 3.2 odd 2
882.4.g.j.361.1 2 21.17 even 6
882.4.g.j.667.1 2 21.20 even 2
2352.4.a.m.1.1 1 28.19 even 6
2352.4.a.z.1.1 1 28.23 odd 6