Properties

Label 539.2.e.l.177.3
Level $539$
Weight $2$
Character 539.177
Analytic conductor $4.304$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [539,2,Mod(67,539)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(539, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("539.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 539.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: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.3
Root \(0.356769 + 0.617942i\) of defining polynomial
Character \(\chi\) \(=\) 539.177
Dual form 539.2.e.l.67.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.24543 - 2.15715i) q^{2} +(-0.356769 - 0.617942i) q^{3} +(-2.10220 - 3.64112i) q^{4} +(1.10220 - 1.90907i) q^{5} -1.77733 q^{6} -5.49086 q^{8} +(1.24543 - 2.15715i) q^{9} +O(q^{10})\) \(q+(1.24543 - 2.15715i) q^{2} +(-0.356769 - 0.617942i) q^{3} +(-2.10220 - 3.64112i) q^{4} +(1.10220 - 1.90907i) q^{5} -1.77733 q^{6} -5.49086 q^{8} +(1.24543 - 2.15715i) q^{9} +(-2.74543 - 4.75523i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.50000 + 2.59808i) q^{12} +3.28646 q^{13} -1.57292 q^{15} +(-2.63409 + 4.56239i) q^{16} +(0.745432 + 1.29113i) q^{17} +(-3.10220 - 5.37317i) q^{18} +(-3.45897 + 5.99111i) q^{19} -9.26819 q^{20} +2.49086 q^{22} +(-3.24543 + 5.62125i) q^{23} +(1.95897 + 3.39304i) q^{24} +(0.0703069 + 0.121775i) q^{25} +(4.09306 - 7.08940i) q^{26} -3.91794 q^{27} -1.64975 q^{29} +(-1.95897 + 3.39304i) q^{30} +(-1.17512 - 2.03538i) q^{31} +(1.07031 + 1.85383i) q^{32} +(0.356769 - 0.617942i) q^{33} +3.71354 q^{34} -10.4726 q^{36} +(2.77733 - 4.81047i) q^{37} +(8.61582 + 14.9230i) q^{38} +(-1.17251 - 2.03084i) q^{39} +(-6.05203 + 10.4824i) q^{40} +11.2499 q^{41} +5.26819 q^{43} +(2.10220 - 3.64112i) q^{44} +(-2.74543 - 4.75523i) q^{45} +(8.08393 + 14.0018i) q^{46} +(0.745432 - 1.29113i) q^{47} +3.75905 q^{48} +0.350250 q^{50} +(0.531894 - 0.921267i) q^{51} +(-6.90880 - 11.9664i) q^{52} +(-0.152367 - 0.263908i) q^{53} +(-4.87953 + 8.45159i) q^{54} +2.20440 q^{55} +4.93621 q^{57} +(-2.05465 + 3.55876i) q^{58} +(-6.32936 - 10.9628i) q^{59} +(3.30660 + 5.72720i) q^{60} +(-6.49086 + 11.2425i) q^{61} -5.85415 q^{62} -5.20440 q^{64} +(3.62234 - 6.27408i) q^{65} +(-0.888663 - 1.53921i) q^{66} +(2.28646 + 3.96027i) q^{67} +(3.13409 - 5.42841i) q^{68} +4.63148 q^{69} +11.3267 q^{71} +(-6.83850 + 11.8446i) q^{72} +(-4.28384 - 7.41984i) q^{73} +(-6.91794 - 11.9822i) q^{74} +(0.0501666 - 0.0868912i) q^{75} +29.0858 q^{76} -5.84111 q^{78} +(-2.31574 + 4.01098i) q^{79} +(5.80660 + 10.0573i) q^{80} +(-2.33850 - 4.05039i) q^{81} +(14.0110 - 24.2678i) q^{82} +1.93621 q^{83} +3.28646 q^{85} +(6.56117 - 11.3643i) q^{86} +(0.588580 + 1.01945i) q^{87} +(-2.74543 - 4.75523i) q^{88} +(1.60220 - 2.77509i) q^{89} -13.6770 q^{90} +27.2902 q^{92} +(-0.838496 + 1.45232i) q^{93} +(-1.85677 - 3.21602i) q^{94} +(7.62496 + 13.2068i) q^{95} +(0.763705 - 1.32278i) q^{96} -1.85939 q^{97} +2.49086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{3} - 4 q^{4} - 2 q^{5} + 2 q^{6} - 18 q^{8} - 9 q^{10} + 3 q^{11} - 9 q^{12} + 22 q^{13} - 14 q^{15} - 2 q^{16} - 3 q^{17} - 10 q^{18} - 11 q^{19} - 28 q^{20} - 12 q^{23} + 2 q^{24} - 3 q^{25} + q^{26} - 4 q^{27} - 18 q^{29} - 2 q^{30} - 3 q^{31} + 3 q^{32} + q^{33} + 20 q^{34} - 18 q^{36} + 4 q^{37} + 8 q^{38} + 5 q^{39} - 3 q^{40} + 10 q^{41} + 4 q^{43} + 4 q^{44} - 9 q^{45} + 10 q^{46} - 3 q^{47} - 20 q^{48} - 6 q^{50} - 2 q^{51} - 7 q^{52} - 17 q^{53} - 8 q^{54} - 4 q^{55} + 40 q^{57} + 13 q^{58} + 8 q^{59} - 6 q^{60} - 24 q^{61} - 26 q^{62} - 14 q^{64} - 15 q^{65} + q^{66} + 16 q^{67} + 5 q^{68} + 6 q^{69} + 14 q^{71} - 10 q^{72} - 20 q^{73} - 22 q^{74} + 25 q^{75} + 78 q^{76} - 12 q^{78} - 3 q^{79} + 9 q^{80} + 17 q^{81} + 41 q^{82} + 22 q^{83} + 22 q^{85} + 21 q^{86} + 30 q^{87} - 9 q^{88} + q^{89} - 20 q^{90} + 50 q^{92} + 26 q^{93} - 10 q^{94} + 17 q^{95} + 27 q^{96} - 18 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24543 2.15715i 0.880653 1.52534i 0.0300373 0.999549i \(-0.490437\pi\)
0.850616 0.525787i \(-0.176229\pi\)
\(3\) −0.356769 0.617942i −0.205981 0.356769i 0.744464 0.667663i \(-0.232705\pi\)
−0.950445 + 0.310894i \(0.899372\pi\)
\(4\) −2.10220 3.64112i −1.05110 1.82056i
\(5\) 1.10220 1.90907i 0.492919 0.853761i −0.507048 0.861918i \(-0.669263\pi\)
0.999967 + 0.00815703i \(0.00259649\pi\)
\(6\) −1.77733 −0.725590
\(7\) 0 0
\(8\) −5.49086 −1.94131
\(9\) 1.24543 2.15715i 0.415144 0.719050i
\(10\) −2.74543 4.75523i −0.868182 1.50373i
\(11\) 0.500000 + 0.866025i 0.150756 + 0.261116i
\(12\) −1.50000 + 2.59808i −0.433013 + 0.750000i
\(13\) 3.28646 0.911501 0.455750 0.890108i \(-0.349371\pi\)
0.455750 + 0.890108i \(0.349371\pi\)
\(14\) 0 0
\(15\) −1.57292 −0.406127
\(16\) −2.63409 + 4.56239i −0.658524 + 1.14060i
\(17\) 0.745432 + 1.29113i 0.180794 + 0.313144i 0.942151 0.335189i \(-0.108800\pi\)
−0.761357 + 0.648333i \(0.775467\pi\)
\(18\) −3.10220 5.37317i −0.731196 1.26647i
\(19\) −3.45897 + 5.99111i −0.793542 + 1.37446i 0.130219 + 0.991485i \(0.458432\pi\)
−0.923761 + 0.382970i \(0.874901\pi\)
\(20\) −9.26819 −2.07243
\(21\) 0 0
\(22\) 2.49086 0.531054
\(23\) −3.24543 + 5.62125i −0.676719 + 1.17211i 0.299244 + 0.954177i \(0.403266\pi\)
−0.975963 + 0.217936i \(0.930068\pi\)
\(24\) 1.95897 + 3.39304i 0.399873 + 0.692600i
\(25\) 0.0703069 + 0.121775i 0.0140614 + 0.0243550i
\(26\) 4.09306 7.08940i 0.802716 1.39034i
\(27\) −3.91794 −0.754008
\(28\) 0 0
\(29\) −1.64975 −0.306351 −0.153175 0.988199i \(-0.548950\pi\)
−0.153175 + 0.988199i \(0.548950\pi\)
\(30\) −1.95897 + 3.39304i −0.357657 + 0.619481i
\(31\) −1.17512 2.03538i −0.211059 0.365564i 0.740987 0.671519i \(-0.234358\pi\)
−0.952046 + 0.305955i \(0.901024\pi\)
\(32\) 1.07031 + 1.85383i 0.189205 + 0.327713i
\(33\) 0.356769 0.617942i 0.0621055 0.107570i
\(34\) 3.71354 0.636867
\(35\) 0 0
\(36\) −10.4726 −1.74543
\(37\) 2.77733 4.81047i 0.456590 0.790836i −0.542189 0.840257i \(-0.682404\pi\)
0.998778 + 0.0494206i \(0.0157375\pi\)
\(38\) 8.61582 + 14.9230i 1.39767 + 2.42084i
\(39\) −1.17251 2.03084i −0.187751 0.325195i
\(40\) −6.05203 + 10.4824i −0.956911 + 1.65742i
\(41\) 11.2499 1.75694 0.878471 0.477796i \(-0.158564\pi\)
0.878471 + 0.477796i \(0.158564\pi\)
\(42\) 0 0
\(43\) 5.26819 0.803391 0.401696 0.915773i \(-0.368421\pi\)
0.401696 + 0.915773i \(0.368421\pi\)
\(44\) 2.10220 3.64112i 0.316919 0.548919i
\(45\) −2.74543 4.75523i −0.409265 0.708867i
\(46\) 8.08393 + 14.0018i 1.19191 + 2.06445i
\(47\) 0.745432 1.29113i 0.108732 0.188330i −0.806525 0.591201i \(-0.798654\pi\)
0.915257 + 0.402871i \(0.131988\pi\)
\(48\) 3.75905 0.542573
\(49\) 0 0
\(50\) 0.350250 0.0495328
\(51\) 0.531894 0.921267i 0.0744800 0.129003i
\(52\) −6.90880 11.9664i −0.958079 1.65944i
\(53\) −0.152367 0.263908i −0.0209293 0.0362506i 0.855371 0.518016i \(-0.173329\pi\)
−0.876300 + 0.481765i \(0.839996\pi\)
\(54\) −4.87953 + 8.45159i −0.664019 + 1.15012i
\(55\) 2.20440 0.297241
\(56\) 0 0
\(57\) 4.93621 0.653817
\(58\) −2.05465 + 3.55876i −0.269789 + 0.467288i
\(59\) −6.32936 10.9628i −0.824012 1.42723i −0.902672 0.430330i \(-0.858397\pi\)
0.0786592 0.996902i \(-0.474936\pi\)
\(60\) 3.30660 + 5.72720i 0.426881 + 0.739379i
\(61\) −6.49086 + 11.2425i −0.831070 + 1.43946i 0.0661206 + 0.997812i \(0.478938\pi\)
−0.897191 + 0.441644i \(0.854396\pi\)
\(62\) −5.85415 −0.743478
\(63\) 0 0
\(64\) −5.20440 −0.650550
\(65\) 3.62234 6.27408i 0.449296 0.778204i
\(66\) −0.888663 1.53921i −0.109387 0.189464i
\(67\) 2.28646 + 3.96027i 0.279336 + 0.483824i 0.971220 0.238185i \(-0.0765524\pi\)
−0.691884 + 0.722009i \(0.743219\pi\)
\(68\) 3.13409 5.42841i 0.380065 0.658292i
\(69\) 4.63148 0.557564
\(70\) 0 0
\(71\) 11.3267 1.34424 0.672119 0.740444i \(-0.265385\pi\)
0.672119 + 0.740444i \(0.265385\pi\)
\(72\) −6.83850 + 11.8446i −0.805925 + 1.39590i
\(73\) −4.28384 7.41984i −0.501386 0.868426i −0.999999 0.00160129i \(-0.999490\pi\)
0.498613 0.866825i \(-0.333843\pi\)
\(74\) −6.91794 11.9822i −0.804194 1.39291i
\(75\) 0.0501666 0.0868912i 0.00579274 0.0100333i
\(76\) 29.0858 3.33637
\(77\) 0 0
\(78\) −5.84111 −0.661376
\(79\) −2.31574 + 4.01098i −0.260541 + 0.451270i −0.966386 0.257096i \(-0.917234\pi\)
0.705845 + 0.708366i \(0.250568\pi\)
\(80\) 5.80660 + 10.0573i 0.649198 + 1.12444i
\(81\) −2.33850 4.05039i −0.259833 0.450044i
\(82\) 14.0110 24.2678i 1.54726 2.67993i
\(83\) 1.93621 0.212527 0.106263 0.994338i \(-0.466111\pi\)
0.106263 + 0.994338i \(0.466111\pi\)
\(84\) 0 0
\(85\) 3.28646 0.356467
\(86\) 6.56117 11.3643i 0.707509 1.22544i
\(87\) 0.588580 + 1.01945i 0.0631024 + 0.109297i
\(88\) −2.74543 4.75523i −0.292664 0.506909i
\(89\) 1.60220 2.77509i 0.169833 0.294159i −0.768528 0.639816i \(-0.779011\pi\)
0.938361 + 0.345657i \(0.112344\pi\)
\(90\) −13.6770 −1.44168
\(91\) 0 0
\(92\) 27.2902 2.84520
\(93\) −0.838496 + 1.45232i −0.0869480 + 0.150598i
\(94\) −1.85677 3.21602i −0.191511 0.331707i
\(95\) 7.62496 + 13.2068i 0.782304 + 1.35499i
\(96\) 0.763705 1.32278i 0.0779453 0.135005i
\(97\) −1.85939 −0.188792 −0.0943960 0.995535i \(-0.530092\pi\)
−0.0943960 + 0.995535i \(0.530092\pi\)
\(98\) 0 0
\(99\) 2.49086 0.250341
\(100\) 0.295598 0.511992i 0.0295598 0.0511992i
\(101\) 3.02276 + 5.23557i 0.300776 + 0.520959i 0.976312 0.216368i \(-0.0694211\pi\)
−0.675536 + 0.737327i \(0.736088\pi\)
\(102\) −1.32488 2.29475i −0.131182 0.227214i
\(103\) −0.531894 + 0.921267i −0.0524091 + 0.0907752i −0.891040 0.453925i \(-0.850023\pi\)
0.838631 + 0.544700i \(0.183357\pi\)
\(104\) −18.0455 −1.76951
\(105\) 0 0
\(106\) −0.759053 −0.0737257
\(107\) 3.16599 5.48365i 0.306068 0.530125i −0.671431 0.741067i \(-0.734320\pi\)
0.977498 + 0.210943i \(0.0676533\pi\)
\(108\) 8.23630 + 14.2657i 0.792538 + 1.37272i
\(109\) 1.40694 + 2.43688i 0.134760 + 0.233411i 0.925506 0.378734i \(-0.123640\pi\)
−0.790746 + 0.612145i \(0.790307\pi\)
\(110\) 2.74543 4.75523i 0.261767 0.453393i
\(111\) −3.96345 −0.376194
\(112\) 0 0
\(113\) −12.7538 −1.19978 −0.599889 0.800083i \(-0.704789\pi\)
−0.599889 + 0.800083i \(0.704789\pi\)
\(114\) 6.14772 10.6482i 0.575786 0.997291i
\(115\) 7.15423 + 12.3915i 0.667136 + 1.15551i
\(116\) 3.46811 + 6.00694i 0.322006 + 0.557730i
\(117\) 4.09306 7.08940i 0.378404 0.655415i
\(118\) −31.5311 −2.90268
\(119\) 0 0
\(120\) 8.63671 0.788420
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 16.1679 + 28.0035i 1.46377 + 2.53532i
\(123\) −4.01362 6.95180i −0.361896 0.626822i
\(124\) −4.94070 + 8.55754i −0.443688 + 0.768490i
\(125\) 11.3320 1.01356
\(126\) 0 0
\(127\) −12.3775 −1.09832 −0.549162 0.835716i \(-0.685053\pi\)
−0.549162 + 0.835716i \(0.685053\pi\)
\(128\) −8.62234 + 14.9343i −0.762114 + 1.32002i
\(129\) −1.87953 3.25544i −0.165483 0.286625i
\(130\) −9.02276 15.6279i −0.791348 1.37066i
\(131\) 0.379526 0.657359i 0.0331594 0.0574337i −0.848969 0.528442i \(-0.822776\pi\)
0.882129 + 0.471008i \(0.156110\pi\)
\(132\) −3.00000 −0.261116
\(133\) 0 0
\(134\) 11.3905 0.983992
\(135\) −4.31836 + 7.47961i −0.371665 + 0.643742i
\(136\) −4.09306 7.08940i −0.350977 0.607911i
\(137\) 2.92056 + 5.05855i 0.249520 + 0.432181i 0.963393 0.268094i \(-0.0863938\pi\)
−0.713873 + 0.700275i \(0.753060\pi\)
\(138\) 5.76819 9.99080i 0.491021 0.850473i
\(139\) 5.57292 0.472689 0.236345 0.971669i \(-0.424051\pi\)
0.236345 + 0.971669i \(0.424051\pi\)
\(140\) 0 0
\(141\) −1.06379 −0.0895871
\(142\) 14.1067 24.4335i 1.18381 2.05041i
\(143\) 1.64323 + 2.84616i 0.137414 + 0.238008i
\(144\) 6.56117 + 11.3643i 0.546764 + 0.947023i
\(145\) −1.81836 + 3.14948i −0.151006 + 0.261550i
\(146\) −21.3409 −1.76619
\(147\) 0 0
\(148\) −23.3540 −1.91969
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) −0.124958 0.216434i −0.0102028 0.0176718i
\(151\) −7.42056 12.8528i −0.603876 1.04594i −0.992228 0.124433i \(-0.960289\pi\)
0.388352 0.921511i \(-0.373045\pi\)
\(152\) 18.9927 32.8964i 1.54051 2.66825i
\(153\) 3.71354 0.300222
\(154\) 0 0
\(155\) −5.18089 −0.416139
\(156\) −4.92969 + 8.53848i −0.394691 + 0.683625i
\(157\) 3.19527 + 5.53436i 0.255010 + 0.441690i 0.964898 0.262624i \(-0.0845879\pi\)
−0.709888 + 0.704314i \(0.751255\pi\)
\(158\) 5.76819 + 9.99080i 0.458893 + 0.794825i
\(159\) −0.108720 + 0.188308i −0.00862205 + 0.0149338i
\(160\) 4.71877 0.373052
\(161\) 0 0
\(162\) −11.6498 −0.915291
\(163\) −4.97259 + 8.61278i −0.389483 + 0.674605i −0.992380 0.123214i \(-0.960680\pi\)
0.602897 + 0.797819i \(0.294013\pi\)
\(164\) −23.6496 40.9623i −1.84672 3.19862i
\(165\) −0.786462 1.36219i −0.0612260 0.106047i
\(166\) 2.41142 4.17670i 0.187163 0.324175i
\(167\) 1.94145 0.150234 0.0751168 0.997175i \(-0.476067\pi\)
0.0751168 + 0.997175i \(0.476067\pi\)
\(168\) 0 0
\(169\) −2.19917 −0.169167
\(170\) 4.09306 7.08940i 0.313924 0.543732i
\(171\) 8.61582 + 14.9230i 0.658868 + 1.14119i
\(172\) −11.0748 19.1821i −0.844445 1.46262i
\(173\) 3.21616 5.57054i 0.244520 0.423521i −0.717477 0.696582i \(-0.754703\pi\)
0.961996 + 0.273062i \(0.0880364\pi\)
\(174\) 2.93214 0.222285
\(175\) 0 0
\(176\) −5.26819 −0.397105
\(177\) −4.51624 + 7.82235i −0.339461 + 0.587964i
\(178\) −3.99086 6.91238i −0.299128 0.518105i
\(179\) 1.79298 + 3.10553i 0.134014 + 0.232119i 0.925220 0.379430i \(-0.123880\pi\)
−0.791207 + 0.611549i \(0.790547\pi\)
\(180\) −11.5429 + 19.9929i −0.860357 + 1.49018i
\(181\) −12.2134 −0.907813 −0.453906 0.891049i \(-0.649970\pi\)
−0.453906 + 0.891049i \(0.649970\pi\)
\(182\) 0 0
\(183\) 9.26295 0.684737
\(184\) 17.8202 30.8655i 1.31372 2.27544i
\(185\) −6.12234 10.6042i −0.450123 0.779637i
\(186\) 2.08858 + 3.61753i 0.153142 + 0.265250i
\(187\) −0.745432 + 1.29113i −0.0545114 + 0.0944165i
\(188\) −6.26819 −0.457155
\(189\) 0 0
\(190\) 37.9855 2.75576
\(191\) −6.05465 + 10.4870i −0.438099 + 0.758810i −0.997543 0.0700583i \(-0.977681\pi\)
0.559444 + 0.828868i \(0.311015\pi\)
\(192\) 1.85677 + 3.21602i 0.134001 + 0.232096i
\(193\) 5.96997 + 10.3403i 0.429728 + 0.744311i 0.996849 0.0793237i \(-0.0252761\pi\)
−0.567121 + 0.823635i \(0.691943\pi\)
\(194\) −2.31574 + 4.01098i −0.166260 + 0.287971i
\(195\) −5.16936 −0.370185
\(196\) 0 0
\(197\) 12.1626 0.866551 0.433275 0.901262i \(-0.357358\pi\)
0.433275 + 0.901262i \(0.357358\pi\)
\(198\) 3.10220 5.37317i 0.220464 0.381855i
\(199\) 0.952451 + 1.64969i 0.0675174 + 0.116944i 0.897808 0.440387i \(-0.145159\pi\)
−0.830290 + 0.557331i \(0.811826\pi\)
\(200\) −0.386046 0.668651i −0.0272975 0.0472807i
\(201\) 1.63148 2.82580i 0.115076 0.199317i
\(202\) 15.0586 1.05952
\(203\) 0 0
\(204\) −4.47259 −0.313144
\(205\) 12.3997 21.4769i 0.866030 1.50001i
\(206\) 1.32488 + 2.29475i 0.0923084 + 0.159883i
\(207\) 8.08393 + 14.0018i 0.561872 + 0.973191i
\(208\) −8.65685 + 14.9941i −0.600245 + 1.03965i
\(209\) −6.91794 −0.478524
\(210\) 0 0
\(211\) −16.2447 −1.11833 −0.559165 0.829056i \(-0.688878\pi\)
−0.559165 + 0.829056i \(0.688878\pi\)
\(212\) −0.640614 + 1.10958i −0.0439975 + 0.0762060i
\(213\) −4.04103 6.99927i −0.276887 0.479582i
\(214\) −7.88605 13.6590i −0.539079 0.933712i
\(215\) 5.80660 10.0573i 0.396007 0.685904i
\(216\) 21.5129 1.46377
\(217\) 0 0
\(218\) 7.00897 0.474707
\(219\) −3.05669 + 5.29434i −0.206552 + 0.357758i
\(220\) −4.63409 8.02649i −0.312431 0.541146i
\(221\) 2.44983 + 4.24324i 0.164794 + 0.285431i
\(222\) −4.93621 + 8.54977i −0.331297 + 0.573823i
\(223\) −3.03655 −0.203342 −0.101671 0.994818i \(-0.532419\pi\)
−0.101671 + 0.994818i \(0.532419\pi\)
\(224\) 0 0
\(225\) 0.350250 0.0233500
\(226\) −15.8840 + 27.5119i −1.05659 + 1.83007i
\(227\) 9.22454 + 15.9774i 0.612254 + 1.06046i 0.990860 + 0.134897i \(0.0430705\pi\)
−0.378605 + 0.925558i \(0.623596\pi\)
\(228\) −10.3769 17.9733i −0.687228 1.19031i
\(229\) −12.7499 + 22.0835i −0.842538 + 1.45932i 0.0452039 + 0.998978i \(0.485606\pi\)
−0.887742 + 0.460341i \(0.847727\pi\)
\(230\) 35.6404 2.35006
\(231\) 0 0
\(232\) 9.05855 0.594723
\(233\) −1.90880 + 3.30614i −0.125050 + 0.216593i −0.921752 0.387779i \(-0.873242\pi\)
0.796703 + 0.604372i \(0.206576\pi\)
\(234\) −10.1953 17.6587i −0.666485 1.15439i
\(235\) −1.64323 2.84616i −0.107193 0.185663i
\(236\) −26.6112 + 46.0919i −1.73224 + 3.00033i
\(237\) 3.30473 0.214666
\(238\) 0 0
\(239\) 13.0037 0.841142 0.420571 0.907260i \(-0.361830\pi\)
0.420571 + 0.907260i \(0.361830\pi\)
\(240\) 4.14323 7.17629i 0.267444 0.463227i
\(241\) −0.225292 0.390216i −0.0145123 0.0251360i 0.858678 0.512515i \(-0.171286\pi\)
−0.873190 + 0.487379i \(0.837953\pi\)
\(242\) 1.24543 + 2.15715i 0.0800594 + 0.138667i
\(243\) −7.54551 + 13.0692i −0.484045 + 0.838391i
\(244\) 54.5804 3.49415
\(245\) 0 0
\(246\) −19.9948 −1.27482
\(247\) −11.3678 + 19.6896i −0.723314 + 1.25282i
\(248\) 6.45245 + 11.1760i 0.409731 + 0.709675i
\(249\) −0.690780 1.19647i −0.0437764 0.0758230i
\(250\) 14.1132 24.4448i 0.892597 1.54602i
\(251\) −1.11861 −0.0706058 −0.0353029 0.999377i \(-0.511240\pi\)
−0.0353029 + 0.999377i \(0.511240\pi\)
\(252\) 0 0
\(253\) −6.49086 −0.408077
\(254\) −15.4153 + 26.7001i −0.967243 + 1.67531i
\(255\) −1.17251 2.03084i −0.0734253 0.127176i
\(256\) 16.2727 + 28.1851i 1.01704 + 1.76157i
\(257\) −11.4198 + 19.7797i −0.712348 + 1.23382i 0.251626 + 0.967825i \(0.419035\pi\)
−0.963974 + 0.265998i \(0.914298\pi\)
\(258\) −9.36329 −0.582933
\(259\) 0 0
\(260\) −30.4596 −1.88902
\(261\) −2.05465 + 3.55876i −0.127180 + 0.220282i
\(262\) −0.945349 1.63739i −0.0584038 0.101158i
\(263\) 4.59568 + 7.95995i 0.283382 + 0.490832i 0.972215 0.234088i \(-0.0752103\pi\)
−0.688834 + 0.724919i \(0.741877\pi\)
\(264\) −1.95897 + 3.39304i −0.120566 + 0.208827i
\(265\) −0.671758 −0.0412658
\(266\) 0 0
\(267\) −2.28646 −0.139929
\(268\) 9.61320 16.6506i 0.587220 1.01709i
\(269\) −7.80660 13.5214i −0.475977 0.824416i 0.523644 0.851937i \(-0.324572\pi\)
−0.999621 + 0.0275208i \(0.991239\pi\)
\(270\) 10.7564 + 18.6307i 0.654616 + 1.13383i
\(271\) 13.8723 24.0275i 0.842680 1.45956i −0.0449415 0.998990i \(-0.514310\pi\)
0.887621 0.460574i \(-0.152357\pi\)
\(272\) −7.85415 −0.476228
\(273\) 0 0
\(274\) 14.5494 0.878962
\(275\) −0.0703069 + 0.121775i −0.00423967 + 0.00734332i
\(276\) −9.73630 16.8638i −0.586056 1.01508i
\(277\) −7.40619 12.8279i −0.444995 0.770753i 0.553057 0.833143i \(-0.313461\pi\)
−0.998052 + 0.0623900i \(0.980128\pi\)
\(278\) 6.94070 12.0216i 0.416275 0.721010i
\(279\) −5.85415 −0.350479
\(280\) 0 0
\(281\) 15.2227 0.908109 0.454054 0.890974i \(-0.349977\pi\)
0.454054 + 0.890974i \(0.349977\pi\)
\(282\) −1.32488 + 2.29475i −0.0788952 + 0.136650i
\(283\) 10.8586 + 18.8077i 0.645479 + 1.11800i 0.984191 + 0.177112i \(0.0566755\pi\)
−0.338712 + 0.940890i \(0.609991\pi\)
\(284\) −23.8111 41.2420i −1.41293 2.44726i
\(285\) 5.44070 9.42356i 0.322279 0.558204i
\(286\) 8.18613 0.484056
\(287\) 0 0
\(288\) 5.33198 0.314190
\(289\) 7.38866 12.7975i 0.434627 0.752796i
\(290\) 4.52928 + 7.84494i 0.265968 + 0.460671i
\(291\) 0.663371 + 1.14899i 0.0388875 + 0.0673551i
\(292\) −18.0110 + 31.1960i −1.05401 + 1.82561i
\(293\) −11.1276 −0.650080 −0.325040 0.945700i \(-0.605378\pi\)
−0.325040 + 0.945700i \(0.605378\pi\)
\(294\) 0 0
\(295\) −27.9049 −1.62469
\(296\) −15.2499 + 26.4136i −0.886383 + 1.53526i
\(297\) −1.95897 3.39304i −0.113671 0.196884i
\(298\) −1.24543 2.15715i −0.0721459 0.124960i
\(299\) −10.6660 + 18.4740i −0.616830 + 1.06838i
\(300\) −0.421841 −0.0243550
\(301\) 0 0
\(302\) −36.9672 −2.12722
\(303\) 2.15685 3.73578i 0.123908 0.214615i
\(304\) −18.2225 31.5623i −1.04513 1.81022i
\(305\) 14.3085 + 24.7830i 0.819301 + 1.41907i
\(306\) 4.62496 8.01066i 0.264391 0.457939i
\(307\) −24.9855 −1.42600 −0.712998 0.701166i \(-0.752663\pi\)
−0.712998 + 0.701166i \(0.752663\pi\)
\(308\) 0 0
\(309\) 0.759053 0.0431810
\(310\) −6.45245 + 11.1760i −0.366475 + 0.634753i
\(311\) 17.3704 + 30.0864i 0.984984 + 1.70604i 0.642005 + 0.766700i \(0.278103\pi\)
0.342979 + 0.939343i \(0.388564\pi\)
\(312\) 6.43808 + 11.1511i 0.364484 + 0.631306i
\(313\) 11.8547 20.5330i 0.670069 1.16059i −0.307815 0.951446i \(-0.599598\pi\)
0.977884 0.209148i \(-0.0670689\pi\)
\(314\) 15.9179 0.898301
\(315\) 0 0
\(316\) 19.4726 1.09542
\(317\) −9.83850 + 17.0408i −0.552585 + 0.957105i 0.445502 + 0.895281i \(0.353025\pi\)
−0.998087 + 0.0618244i \(0.980308\pi\)
\(318\) 0.270807 + 0.469051i 0.0151861 + 0.0263031i
\(319\) −0.824875 1.42873i −0.0461841 0.0799933i
\(320\) −5.73630 + 9.93556i −0.320669 + 0.555414i
\(321\) −4.51811 −0.252176
\(322\) 0 0
\(323\) −10.3137 −0.573870
\(324\) −9.83198 + 17.0295i −0.546221 + 0.946082i
\(325\) 0.231061 + 0.400209i 0.0128170 + 0.0221996i
\(326\) 12.3860 + 21.4533i 0.686000 + 1.18819i
\(327\) 1.00390 1.73881i 0.0555159 0.0961564i
\(328\) −61.7718 −3.41077
\(329\) 0 0
\(330\) −3.91794 −0.215675
\(331\) 14.0949 24.4131i 0.774728 1.34187i −0.160220 0.987081i \(-0.551220\pi\)
0.934947 0.354786i \(-0.115446\pi\)
\(332\) −4.07031 7.04998i −0.223387 0.386918i
\(333\) −6.91794 11.9822i −0.379101 0.656622i
\(334\) 2.41794 4.18799i 0.132304 0.229157i
\(335\) 10.0806 0.550760
\(336\) 0 0
\(337\) 21.7460 1.18458 0.592290 0.805725i \(-0.298224\pi\)
0.592290 + 0.805725i \(0.298224\pi\)
\(338\) −2.73891 + 4.74394i −0.148977 + 0.258036i
\(339\) 4.55017 + 7.88112i 0.247131 + 0.428044i
\(340\) −6.90880 11.9664i −0.374682 0.648969i
\(341\) 1.17512 2.03538i 0.0636366 0.110222i
\(342\) 42.9217 2.32094
\(343\) 0 0
\(344\) −28.9269 −1.55963
\(345\) 5.10482 8.84180i 0.274834 0.476027i
\(346\) −8.01100 13.8755i −0.430674 0.745950i
\(347\) 1.97072 + 3.41339i 0.105794 + 0.183241i 0.914062 0.405574i \(-0.132928\pi\)
−0.808268 + 0.588814i \(0.799595\pi\)
\(348\) 2.47463 4.28618i 0.132654 0.229763i
\(349\) 14.1093 0.755254 0.377627 0.925958i \(-0.376740\pi\)
0.377627 + 0.925958i \(0.376740\pi\)
\(350\) 0 0
\(351\) −12.8762 −0.687279
\(352\) −1.07031 + 1.85383i −0.0570475 + 0.0988093i
\(353\) −2.48434 4.30301i −0.132228 0.229026i 0.792307 0.610123i \(-0.208880\pi\)
−0.924535 + 0.381097i \(0.875547\pi\)
\(354\) 11.2493 + 19.4844i 0.597895 + 1.03559i
\(355\) 12.4843 21.6235i 0.662600 1.14766i
\(356\) −13.4726 −0.714046
\(357\) 0 0
\(358\) 8.93214 0.472078
\(359\) 2.03580 3.52610i 0.107445 0.186101i −0.807289 0.590156i \(-0.799066\pi\)
0.914735 + 0.404055i \(0.132400\pi\)
\(360\) 15.0748 + 26.1103i 0.794511 + 1.37613i
\(361\) −14.4289 24.9917i −0.759418 1.31535i
\(362\) −15.2109 + 26.3461i −0.799468 + 1.38472i
\(363\) 0.713538 0.0374510
\(364\) 0 0
\(365\) −18.8866 −0.988571
\(366\) 11.5364 19.9816i 0.603016 1.04445i
\(367\) −9.01100 15.6075i −0.470371 0.814706i 0.529055 0.848587i \(-0.322546\pi\)
−0.999426 + 0.0338816i \(0.989213\pi\)
\(368\) −17.0975 29.6138i −0.891271 1.54373i
\(369\) 14.0110 24.2678i 0.729384 1.26333i
\(370\) −30.4998 −1.58561
\(371\) 0 0
\(372\) 7.05075 0.365564
\(373\) −14.4582 + 25.0424i −0.748618 + 1.29664i 0.199867 + 0.979823i \(0.435949\pi\)
−0.948485 + 0.316822i \(0.897384\pi\)
\(374\) 1.85677 + 3.21602i 0.0960112 + 0.166296i
\(375\) −4.04290 7.00250i −0.208774 0.361608i
\(376\) −4.09306 + 7.08940i −0.211084 + 0.365608i
\(377\) −5.42184 −0.279239
\(378\) 0 0
\(379\) 4.30847 0.221311 0.110656 0.993859i \(-0.464705\pi\)
0.110656 + 0.993859i \(0.464705\pi\)
\(380\) 32.0584 55.5268i 1.64456 2.84846i
\(381\) 4.41591 + 7.64857i 0.226234 + 0.391848i
\(382\) 15.0813 + 26.1216i 0.771627 + 1.33650i
\(383\) −6.17438 + 10.6943i −0.315496 + 0.546455i −0.979543 0.201236i \(-0.935504\pi\)
0.664047 + 0.747691i \(0.268837\pi\)
\(384\) 12.3047 0.627923
\(385\) 0 0
\(386\) 29.7408 1.51377
\(387\) 6.56117 11.3643i 0.333523 0.577679i
\(388\) 3.90880 + 6.77025i 0.198439 + 0.343707i
\(389\) −14.7115 25.4811i −0.745903 1.29194i −0.949772 0.312943i \(-0.898685\pi\)
0.203869 0.978998i \(-0.434648\pi\)
\(390\) −6.43808 + 11.1511i −0.326005 + 0.564657i
\(391\) −9.67699 −0.489387
\(392\) 0 0
\(393\) −0.541613 −0.0273208
\(394\) 15.1477 26.2366i 0.763131 1.32178i
\(395\) 5.10482 + 8.84180i 0.256851 + 0.444879i
\(396\) −5.23630 9.06953i −0.263134 0.455761i
\(397\) −8.64975 + 14.9818i −0.434119 + 0.751915i −0.997223 0.0744702i \(-0.976273\pi\)
0.563105 + 0.826386i \(0.309607\pi\)
\(398\) 4.74485 0.237838
\(399\) 0 0
\(400\) −0.740780 −0.0370390
\(401\) 12.4752 21.6077i 0.622982 1.07904i −0.365945 0.930636i \(-0.619254\pi\)
0.988927 0.148400i \(-0.0474124\pi\)
\(402\) −4.06379 7.03869i −0.202683 0.351058i
\(403\) −3.86200 6.68919i −0.192380 0.333212i
\(404\) 12.7089 22.0124i 0.632291 1.09516i
\(405\) −10.3100 −0.512306
\(406\) 0 0
\(407\) 5.55465 0.275334
\(408\) −2.92056 + 5.05855i −0.144589 + 0.250436i
\(409\) −19.2792 33.3925i −0.953295 1.65115i −0.738223 0.674557i \(-0.764335\pi\)
−0.215072 0.976598i \(-0.568999\pi\)
\(410\) −30.8859 53.4959i −1.52534 2.64197i
\(411\) 2.08393 3.60947i 0.102793 0.178042i
\(412\) 4.47259 0.220349
\(413\) 0 0
\(414\) 40.2719 1.97926
\(415\) 2.13409 3.69636i 0.104759 0.181447i
\(416\) 3.51752 + 6.09253i 0.172461 + 0.298711i
\(417\) −1.98825 3.44374i −0.0973648 0.168641i
\(418\) −8.61582 + 14.9230i −0.421414 + 0.729910i
\(419\) −0.908970 −0.0444061 −0.0222030 0.999753i \(-0.507068\pi\)
−0.0222030 + 0.999753i \(0.507068\pi\)
\(420\) 0 0
\(421\) 15.5532 0.758014 0.379007 0.925394i \(-0.376266\pi\)
0.379007 + 0.925394i \(0.376266\pi\)
\(422\) −20.2316 + 35.0422i −0.984861 + 1.70583i
\(423\) −1.85677 3.21602i −0.0902792 0.156368i
\(424\) 0.836629 + 1.44908i 0.0406303 + 0.0703737i
\(425\) −0.104818 + 0.181550i −0.00508442 + 0.00880647i
\(426\) −20.1313 −0.975365
\(427\) 0 0
\(428\) −26.6222 −1.28683
\(429\) 1.17251 2.03084i 0.0566092 0.0980500i
\(430\) −14.4635 25.0514i −0.697490 1.20809i
\(431\) −1.76819 3.06259i −0.0851707 0.147520i 0.820293 0.571943i \(-0.193810\pi\)
−0.905464 + 0.424423i \(0.860477\pi\)
\(432\) 10.3202 17.8752i 0.496532 0.860019i
\(433\) −17.6457 −0.847997 −0.423999 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(434\) 0 0
\(435\) 2.59493 0.124417
\(436\) 5.91532 10.2456i 0.283293 0.490677i
\(437\) −22.4517 38.8875i −1.07401 1.86024i
\(438\) 7.61379 + 13.1875i 0.363801 + 0.630122i
\(439\) 7.51362 13.0140i 0.358606 0.621123i −0.629123 0.777306i \(-0.716586\pi\)
0.987728 + 0.156183i \(0.0499190\pi\)
\(440\) −12.1041 −0.577039
\(441\) 0 0
\(442\) 12.2044 0.580504
\(443\) −6.61134 + 11.4512i −0.314114 + 0.544062i −0.979249 0.202662i \(-0.935041\pi\)
0.665135 + 0.746723i \(0.268374\pi\)
\(444\) 8.33198 + 14.4314i 0.395418 + 0.684884i
\(445\) −3.53189 6.11742i −0.167428 0.289994i
\(446\) −3.78181 + 6.55029i −0.179074 + 0.310165i
\(447\) −0.713538 −0.0337492
\(448\) 0 0
\(449\) −9.90864 −0.467617 −0.233809 0.972283i \(-0.575119\pi\)
−0.233809 + 0.972283i \(0.575119\pi\)
\(450\) 0.436212 0.755542i 0.0205632 0.0356166i
\(451\) 5.62496 + 9.74271i 0.264869 + 0.458766i
\(452\) 26.8111 + 46.4382i 1.26109 + 2.18427i
\(453\) −5.29485 + 9.17095i −0.248774 + 0.430889i
\(454\) 45.9542 2.15674
\(455\) 0 0
\(456\) −27.1041 −1.26926
\(457\) −5.17251 + 8.95905i −0.241960 + 0.419087i −0.961272 0.275600i \(-0.911124\pi\)
0.719313 + 0.694686i \(0.244457\pi\)
\(458\) 31.7583 + 55.0070i 1.48397 + 2.57031i
\(459\) −2.92056 5.05855i −0.136320 0.236113i
\(460\) 30.0793 52.0988i 1.40245 2.42912i
\(461\) 15.3372 0.714325 0.357163 0.934042i \(-0.383744\pi\)
0.357163 + 0.934042i \(0.383744\pi\)
\(462\) 0 0
\(463\) −25.1313 −1.16795 −0.583976 0.811771i \(-0.698504\pi\)
−0.583976 + 0.811771i \(0.698504\pi\)
\(464\) 4.34560 7.52680i 0.201739 0.349423i
\(465\) 1.84838 + 3.20149i 0.0857167 + 0.148466i
\(466\) 4.75457 + 8.23515i 0.220251 + 0.381486i
\(467\) −0.373007 + 0.646068i −0.0172607 + 0.0298964i −0.874527 0.484977i \(-0.838828\pi\)
0.857266 + 0.514874i \(0.172161\pi\)
\(468\) −34.4178 −1.59096
\(469\) 0 0
\(470\) −8.18613 −0.377598
\(471\) 2.27994 3.94898i 0.105054 0.181959i
\(472\) 34.7537 + 60.1951i 1.59967 + 2.77070i
\(473\) 2.63409 + 4.56239i 0.121116 + 0.209779i
\(474\) 4.11582 7.12881i 0.189046 0.327437i
\(475\) −0.972758 −0.0446332
\(476\) 0 0
\(477\) −0.759053 −0.0347546
\(478\) 16.1953 28.0510i 0.740754 1.28302i
\(479\) −10.0565 17.4184i −0.459494 0.795867i 0.539440 0.842024i \(-0.318636\pi\)
−0.998934 + 0.0461569i \(0.985303\pi\)
\(480\) −1.68351 2.91593i −0.0768414 0.133093i
\(481\) 9.12758 15.8094i 0.416182 0.720848i
\(482\) −1.12234 −0.0511212
\(483\) 0 0
\(484\) 4.20440 0.191109
\(485\) −2.04942 + 3.54969i −0.0930592 + 0.161183i
\(486\) 18.7948 + 32.5536i 0.852552 + 1.47666i
\(487\) 2.12496 + 3.68054i 0.0962911 + 0.166781i 0.910147 0.414286i \(-0.135969\pi\)
−0.813856 + 0.581067i \(0.802635\pi\)
\(488\) 35.6404 61.7311i 1.61337 2.79443i
\(489\) 7.09626 0.320904
\(490\) 0 0
\(491\) 30.3279 1.36868 0.684340 0.729163i \(-0.260091\pi\)
0.684340 + 0.729163i \(0.260091\pi\)
\(492\) −16.8749 + 29.2281i −0.760778 + 1.31771i
\(493\) −1.22978 2.13003i −0.0553863 0.0959320i
\(494\) 28.3156 + 49.0440i 1.27398 + 2.20659i
\(495\) 2.74543 4.75523i 0.123398 0.213732i
\(496\) 12.3816 0.555948
\(497\) 0 0
\(498\) −3.44128 −0.154207
\(499\) −7.22064 + 12.5065i −0.323240 + 0.559869i −0.981155 0.193224i \(-0.938106\pi\)
0.657914 + 0.753093i \(0.271439\pi\)
\(500\) −23.8221 41.2611i −1.06536 1.84525i
\(501\) −0.692648 1.19970i −0.0309452 0.0535987i
\(502\) −1.39315 + 2.41300i −0.0621792 + 0.107698i
\(503\) 2.95822 0.131901 0.0659503 0.997823i \(-0.478992\pi\)
0.0659503 + 0.997823i \(0.478992\pi\)
\(504\) 0 0
\(505\) 13.3267 0.593032
\(506\) −8.08393 + 14.0018i −0.359374 + 0.622455i
\(507\) 0.784595 + 1.35896i 0.0348451 + 0.0603534i
\(508\) 26.0200 + 45.0679i 1.15445 + 1.99957i
\(509\) −12.4953 + 21.6426i −0.553847 + 0.959290i 0.444146 + 0.895955i \(0.353507\pi\)
−0.997992 + 0.0633358i \(0.979826\pi\)
\(510\) −5.84111 −0.258649
\(511\) 0 0
\(512\) 46.5767 2.05842
\(513\) 13.5520 23.4728i 0.598337 1.03635i
\(514\) 28.4452 + 49.2685i 1.25466 + 2.17314i
\(515\) 1.17251 + 2.03084i 0.0516669 + 0.0894896i
\(516\) −7.90228 + 13.6872i −0.347879 + 0.602544i
\(517\) 1.49086 0.0655681
\(518\) 0 0
\(519\) −4.58970 −0.201465
\(520\) −19.8898 + 34.4501i −0.872225 + 1.51074i
\(521\) 14.4316 + 24.9962i 0.632258 + 1.09510i 0.987089 + 0.160173i \(0.0512051\pi\)
−0.354831 + 0.934931i \(0.615462\pi\)
\(522\) 5.11786 + 8.86439i 0.224002 + 0.387984i
\(523\) 0.236295 0.409276i 0.0103325 0.0178964i −0.860813 0.508921i \(-0.830044\pi\)
0.871145 + 0.491025i \(0.163378\pi\)
\(524\) −3.19136 −0.139415
\(525\) 0 0
\(526\) 22.8944 0.998245
\(527\) 1.75195 3.03447i 0.0763162 0.132184i
\(528\) 1.87953 + 3.25544i 0.0817959 + 0.141675i
\(529\) −9.56566 16.5682i −0.415898 0.720357i
\(530\) −0.836629 + 1.44908i −0.0363408 + 0.0629442i
\(531\) −31.5311 −1.36834
\(532\) 0 0
\(533\) 36.9724 1.60145
\(534\) −2.84763 + 4.93224i −0.123229 + 0.213439i
\(535\) −6.97911 12.0882i −0.301733 0.522617i
\(536\) −12.5547 21.7453i −0.542278 0.939254i
\(537\) 1.27936 2.21592i 0.0552085 0.0956239i
\(538\) −38.8904 −1.67668
\(539\) 0 0
\(540\) 36.3122 1.56263
\(541\) −7.72978 + 13.3884i −0.332329 + 0.575611i −0.982968 0.183776i \(-0.941168\pi\)
0.650639 + 0.759387i \(0.274501\pi\)
\(542\) −34.5539 59.8491i −1.48422 2.57074i
\(543\) 4.35735 + 7.54715i 0.186992 + 0.323879i
\(544\) −1.59568 + 2.76380i −0.0684143 + 0.118497i
\(545\) 6.20290 0.265703
\(546\) 0 0
\(547\) −35.0440 −1.49837 −0.749187 0.662359i \(-0.769556\pi\)
−0.749187 + 0.662359i \(0.769556\pi\)
\(548\) 12.2792 21.2682i 0.524541 0.908532i
\(549\) 16.1679 + 28.0035i 0.690027 + 1.19516i
\(550\) 0.175125 + 0.303325i 0.00746735 + 0.0129338i
\(551\) 5.70644 9.88384i 0.243102 0.421066i
\(552\) −25.4308 −1.08241
\(553\) 0 0
\(554\) −36.8956 −1.56754
\(555\) −4.36852 + 7.56650i −0.185433 + 0.321180i
\(556\) −11.7154 20.2917i −0.496844 0.860559i
\(557\) −5.26632 9.12154i −0.223141 0.386492i 0.732619 0.680639i \(-0.238298\pi\)
−0.955760 + 0.294147i \(0.904964\pi\)
\(558\) −7.29095 + 12.6283i −0.308650 + 0.534598i
\(559\) 17.3137 0.732292
\(560\) 0 0
\(561\) 1.06379 0.0449132
\(562\) 18.9588 32.8376i 0.799729 1.38517i
\(563\) −15.3574 26.5997i −0.647235 1.12104i −0.983780 0.179377i \(-0.942592\pi\)
0.336545 0.941667i \(-0.390742\pi\)
\(564\) 2.23630 + 3.87338i 0.0941650 + 0.163099i
\(565\) −14.0573 + 24.3479i −0.591394 + 1.02432i
\(566\) 54.0948 2.27377
\(567\) 0 0
\(568\) −62.1936 −2.60959
\(569\) 15.3860 26.6494i 0.645017 1.11720i −0.339281 0.940685i \(-0.610184\pi\)
0.984298 0.176516i \(-0.0564829\pi\)
\(570\) −13.5520 23.4728i −0.567632 0.983168i
\(571\) 3.75847 + 6.50986i 0.157287 + 0.272429i 0.933889 0.357562i \(-0.116392\pi\)
−0.776602 + 0.629991i \(0.783059\pi\)
\(572\) 6.90880 11.9664i 0.288872 0.500340i
\(573\) 8.64045 0.360960
\(574\) 0 0
\(575\) −0.912705 −0.0380624
\(576\) −6.48173 + 11.2267i −0.270072 + 0.467778i
\(577\) 13.8092 + 23.9183i 0.574885 + 0.995731i 0.996054 + 0.0887483i \(0.0282867\pi\)
−0.421169 + 0.906982i \(0.638380\pi\)
\(578\) −18.4042 31.8769i −0.765512 1.32591i
\(579\) 4.25980 7.37819i 0.177031 0.306627i
\(580\) 15.2902 0.634891
\(581\) 0 0
\(582\) 3.30473 0.136986
\(583\) 0.152367 0.263908i 0.00631041 0.0109300i
\(584\) 23.5220 + 40.7413i 0.973348 + 1.68589i
\(585\) −9.02276 15.6279i −0.373045 0.646133i
\(586\) −13.8586 + 24.0039i −0.572495 + 0.991590i
\(587\) 29.9582 1.23651 0.618254 0.785978i \(-0.287840\pi\)
0.618254 + 0.785978i \(0.287840\pi\)
\(588\) 0 0
\(589\) 16.2589 0.669936
\(590\) −34.7537 + 60.1951i −1.43079 + 2.47819i
\(591\) −4.33925 7.51579i −0.178493 0.309158i
\(592\) 14.6315 + 25.3425i 0.601350 + 1.04157i
\(593\) 6.33401 10.9708i 0.260107 0.450518i −0.706163 0.708049i \(-0.749576\pi\)
0.966270 + 0.257531i \(0.0829089\pi\)
\(594\) −9.75905 −0.400419
\(595\) 0 0
\(596\) −4.20440 −0.172219
\(597\) 0.679610 1.17712i 0.0278146 0.0481762i
\(598\) 26.5675 + 46.0163i 1.08643 + 1.88175i
\(599\) −0.647133 1.12087i −0.0264411 0.0457974i 0.852502 0.522724i \(-0.175084\pi\)
−0.878943 + 0.476926i \(0.841751\pi\)
\(600\) −0.275458 + 0.477108i −0.0112455 + 0.0194778i
\(601\) 41.0220 1.67332 0.836661 0.547721i \(-0.184504\pi\)
0.836661 + 0.547721i \(0.184504\pi\)
\(602\) 0 0
\(603\) 11.3905 0.463858
\(604\) −31.1990 + 54.0383i −1.26947 + 2.19879i
\(605\) 1.10220 + 1.90907i 0.0448108 + 0.0776146i
\(606\) −5.37242 9.30531i −0.218240 0.378002i
\(607\) −10.5884 + 18.3397i −0.429770 + 0.744384i −0.996853 0.0792770i \(-0.974739\pi\)
0.567082 + 0.823661i \(0.308072\pi\)
\(608\) −14.8086 −0.600570
\(609\) 0 0
\(610\) 71.2809 2.88608
\(611\) 2.44983 4.24324i 0.0991096 0.171663i
\(612\) −7.80660 13.5214i −0.315563 0.546571i
\(613\) −3.38156 5.85704i −0.136580 0.236563i 0.789620 0.613596i \(-0.210278\pi\)
−0.926200 + 0.377033i \(0.876944\pi\)
\(614\) −31.1177 + 53.8974i −1.25581 + 2.17512i
\(615\) −17.6953 −0.713542
\(616\) 0 0
\(617\) −41.0728 −1.65353 −0.826763 0.562550i \(-0.809820\pi\)
−0.826763 + 0.562550i \(0.809820\pi\)
\(618\) 0.945349 1.63739i 0.0380275 0.0658656i
\(619\) −15.2134 26.3503i −0.611477 1.05911i −0.990992 0.133924i \(-0.957242\pi\)
0.379515 0.925186i \(-0.376091\pi\)
\(620\) 10.8913 + 18.8643i 0.437404 + 0.757607i
\(621\) 12.7154 22.0237i 0.510252 0.883782i
\(622\) 86.5345 3.46972
\(623\) 0 0
\(624\) 12.3540 0.494555
\(625\) 12.1386 21.0246i 0.485543 0.840985i
\(626\) −29.5285 51.1449i −1.18020 2.04416i
\(627\) 2.46811 + 4.27489i 0.0985667 + 0.170722i
\(628\) 13.4342 23.2687i 0.536082 0.928521i
\(629\) 8.28123 0.330194
\(630\) 0 0
\(631\) 12.3670 0.492323 0.246162 0.969229i \(-0.420831\pi\)
0.246162 + 0.969229i \(0.420831\pi\)
\(632\) 12.7154 22.0237i 0.505792 0.876057i
\(633\) 5.79560 + 10.0383i 0.230354 + 0.398985i
\(634\) 24.5064 + 42.4462i 0.973272 + 1.68576i
\(635\) −13.6425 + 23.6295i −0.541385 + 0.937707i
\(636\) 0.914205 0.0362506
\(637\) 0 0
\(638\) −4.10930 −0.162689
\(639\) 14.1067 24.4335i 0.558052 0.966574i
\(640\) 19.0071 + 32.9213i 0.751322 + 1.30133i
\(641\) 23.5657 + 40.8169i 0.930787 + 1.61217i 0.781979 + 0.623305i \(0.214211\pi\)
0.148809 + 0.988866i \(0.452456\pi\)
\(642\) −5.62699 + 9.74624i −0.222080 + 0.384653i
\(643\) −1.87242 −0.0738412 −0.0369206 0.999318i \(-0.511755\pi\)
−0.0369206 + 0.999318i \(0.511755\pi\)
\(644\) 0 0
\(645\) −8.28646 −0.326279
\(646\) −12.8450 + 22.2482i −0.505380 + 0.875344i
\(647\) −0.917939 1.58992i −0.0360879 0.0625061i 0.847417 0.530927i \(-0.178156\pi\)
−0.883505 + 0.468421i \(0.844823\pi\)
\(648\) 12.8404 + 22.2402i 0.504417 + 0.873676i
\(649\) 6.32936 10.9628i 0.248449 0.430326i
\(650\) 1.15108 0.0451492
\(651\) 0 0
\(652\) 41.8135 1.63754
\(653\) 9.08858 15.7419i 0.355664 0.616027i −0.631568 0.775321i \(-0.717588\pi\)
0.987231 + 0.159293i \(0.0509216\pi\)
\(654\) −2.50058 4.33114i −0.0977805 0.169361i
\(655\) −0.836629 1.44908i −0.0326898 0.0566204i
\(656\) −29.6333 + 51.3265i −1.15699 + 2.00396i
\(657\) −21.3409 −0.832590
\(658\) 0 0
\(659\) −16.8997 −0.658318 −0.329159 0.944275i \(-0.606765\pi\)
−0.329159 + 0.944275i \(0.606765\pi\)
\(660\) −3.30660 + 5.72720i −0.128709 + 0.222931i
\(661\) −22.6516 39.2338i −0.881046 1.52602i −0.850180 0.526493i \(-0.823507\pi\)
−0.0308661 0.999524i \(-0.509827\pi\)
\(662\) −35.1086 60.8098i −1.36453 2.36344i
\(663\) 1.74805 3.02771i 0.0678886 0.117587i
\(664\) −10.6315 −0.412581
\(665\) 0 0
\(666\) −34.4633 −1.33543
\(667\) 5.35415 9.27366i 0.207314 0.359078i
\(668\) −4.08131 7.06904i −0.157911 0.273509i
\(669\) 1.08335 + 1.87641i 0.0418845 + 0.0725462i
\(670\) 12.5547 21.7453i 0.485028 0.840094i
\(671\) −12.9817 −0.501154
\(672\) 0 0
\(673\) 39.5076 1.52291 0.761454 0.648219i \(-0.224486\pi\)
0.761454 + 0.648219i \(0.224486\pi\)
\(674\) 27.0832 46.9094i 1.04321 1.80688i
\(675\) −0.275458 0.477108i −0.0106024 0.0183639i
\(676\) 4.62309 + 8.00743i 0.177811 + 0.307978i
\(677\) −17.0669 + 29.5608i −0.655936 + 1.13611i 0.325723 + 0.945465i \(0.394392\pi\)
−0.981658 + 0.190649i \(0.938941\pi\)
\(678\) 22.6677 0.870547
\(679\) 0 0
\(680\) −18.0455 −0.692014
\(681\) 6.58206 11.4005i 0.252225 0.436867i
\(682\) −2.92708 5.06984i −0.112084 0.194134i
\(683\) −11.8931 20.5995i −0.455079 0.788219i 0.543614 0.839335i \(-0.317056\pi\)
−0.998693 + 0.0511160i \(0.983722\pi\)
\(684\) 36.2244 62.7425i 1.38507 2.39902i
\(685\) 12.8762 0.491973
\(686\) 0 0
\(687\) 18.1951 0.694186
\(688\) −13.8769 + 24.0355i −0.529052 + 0.916345i
\(689\) −0.500750 0.867324i −0.0190770 0.0330424i
\(690\) −12.7154 22.0237i −0.484067 0.838429i
\(691\) −10.2812 + 17.8076i −0.391116 + 0.677433i −0.992597 0.121454i \(-0.961244\pi\)
0.601481 + 0.798887i \(0.294578\pi\)
\(692\) −27.0440 −1.02806
\(693\) 0 0
\(694\) 9.81761 0.372671
\(695\) 6.14248 10.6391i 0.232998 0.403564i
\(696\) −3.23181 5.59766i −0.122501 0.212179i
\(697\) 8.38605 + 14.5251i 0.317644 + 0.550176i
\(698\) 17.5722 30.4359i 0.665117 1.15202i
\(699\) 2.72401 0.103031
\(700\) 0 0
\(701\) −23.9907 −0.906116 −0.453058 0.891481i \(-0.649667\pi\)
−0.453058 + 0.891481i \(0.649667\pi\)
\(702\) −16.0364 + 27.7758i −0.605254 + 1.04833i
\(703\) 19.2134 + 33.2785i 0.724646 + 1.25512i
\(704\) −2.60220 4.50714i −0.0980741 0.169869i
\(705\) −1.17251 + 2.03084i −0.0441592 + 0.0764860i
\(706\) −12.3763 −0.465789
\(707\) 0 0
\(708\) 37.9762 1.42723
\(709\) 25.8559 44.7836i 0.971037 1.68189i 0.278599 0.960407i \(-0.410130\pi\)
0.692437 0.721478i \(-0.256537\pi\)
\(710\) −31.0968 53.8612i −1.16704 2.02138i
\(711\) 5.76819 + 9.99080i 0.216324 + 0.374684i
\(712\) −8.79747 + 15.2377i −0.329699 + 0.571055i
\(713\) 15.2552 0.571310
\(714\) 0 0
\(715\) 7.24468 0.270936
\(716\) 7.53841 13.0569i 0.281724 0.487960i
\(717\) −4.63933 8.03555i −0.173259 0.300093i
\(718\) −5.07089 8.78304i −0.189244 0.327780i
\(719\) 12.8926 22.3306i 0.480812 0.832790i −0.518946 0.854807i \(-0.673675\pi\)
0.999758 + 0.0220170i \(0.00700879\pi\)
\(720\) 28.9269 1.07804
\(721\) 0 0
\(722\) −71.8811 −2.67514
\(723\) −0.160754 + 0.278434i −0.00597851 + 0.0103551i
\(724\) 25.6750 + 44.4703i 0.954202 + 1.65273i
\(725\) −0.115989 0.200899i −0.00430772 0.00746118i
\(726\) 0.888663 1.53921i 0.0329814 0.0571254i
\(727\) −32.7330 −1.21400 −0.606999 0.794702i \(-0.707627\pi\)
−0.606999 + 0.794702i \(0.707627\pi\)
\(728\) 0 0
\(729\) −3.26295 −0.120850
\(730\) −23.5220 + 40.7413i −0.870589 + 1.50790i
\(731\) 3.92708 + 6.80189i 0.145248 + 0.251577i
\(732\) −19.4726 33.7275i −0.719728 1.24660i
\(733\) −4.64136 + 8.03908i −0.171433 + 0.296930i −0.938921 0.344133i \(-0.888173\pi\)
0.767488 + 0.641063i \(0.221506\pi\)
\(734\) −44.8904 −1.65693
\(735\) 0 0
\(736\) −13.8944 −0.512156
\(737\) −2.28646 + 3.96027i −0.0842229 + 0.145878i
\(738\) −34.8995 60.4477i −1.28467 2.22511i
\(739\) 25.0466 + 43.3820i 0.921355 + 1.59583i 0.797320 + 0.603556i \(0.206250\pi\)
0.124035 + 0.992278i \(0.460417\pi\)
\(740\) −25.7408 + 44.5843i −0.946250 + 1.63895i
\(741\) 16.2227 0.595955
\(742\) 0 0
\(743\) 13.1679 0.483082 0.241541 0.970391i \(-0.422347\pi\)
0.241541 + 0.970391i \(0.422347\pi\)
\(744\) 4.60407 7.97448i 0.168793 0.292359i
\(745\) −1.10220 1.90907i −0.0403815 0.0699428i
\(746\) 36.0135 + 62.3771i 1.31855 + 2.28379i
\(747\) 2.41142 4.17670i 0.0882293 0.152818i
\(748\) 6.26819 0.229188
\(749\) 0 0
\(750\) −20.1406 −0.735431
\(751\) −20.6569 + 35.7787i −0.753779 + 1.30558i 0.192200 + 0.981356i \(0.438438\pi\)
−0.945979 + 0.324228i \(0.894895\pi\)
\(752\) 3.92708 + 6.80189i 0.143206 + 0.248040i
\(753\) 0.399084 + 0.691234i 0.0145434 + 0.0251900i
\(754\) −6.75253 + 11.6957i −0.245913 + 0.425933i
\(755\) −32.7158 −1.19065
\(756\) 0 0
\(757\) −45.5114 −1.65414 −0.827069 0.562100i \(-0.809994\pi\)
−0.827069 + 0.562100i \(0.809994\pi\)
\(758\) 5.36591 9.29402i 0.194898 0.337574i
\(759\) 2.31574 + 4.01098i 0.0840560 + 0.145589i
\(760\) −41.8676 72.5168i −1.51870 2.63046i
\(761\) 15.6360 27.0823i 0.566803 0.981732i −0.430076 0.902793i \(-0.641513\pi\)
0.996879 0.0789393i \(-0.0251533\pi\)
\(762\) 21.9988 0.796934
\(763\) 0 0
\(764\) 50.9124 1.84194
\(765\) 4.09306 7.08940i 0.147985 0.256318i
\(766\) 15.3795 + 26.6381i 0.555685 + 0.962474i
\(767\) −20.8012 36.0287i −0.751088 1.30092i
\(768\) 11.6112 20.1111i 0.418982 0.725698i
\(769\) −42.0467 −1.51624 −0.758121 0.652114i \(-0.773882\pi\)
−0.758121 + 0.652114i \(0.773882\pi\)
\(770\) 0 0
\(771\) 16.2969 0.586920
\(772\) 25.1002 43.4748i 0.903375 1.56469i
\(773\) 3.82226 + 6.62034i 0.137477 + 0.238117i 0.926541 0.376194i \(-0.122767\pi\)
−0.789064 + 0.614311i \(0.789434\pi\)
\(774\) −16.3430 28.3069i −0.587436 1.01747i
\(775\) 0.165239 0.286202i 0.00593555 0.0102807i
\(776\) 10.2096 0.366505
\(777\) 0 0
\(778\) −73.2887 −2.62753
\(779\) −38.9131 + 67.3995i −1.39421 + 2.41484i
\(780\) 10.8670 + 18.8222i 0.389102 + 0.673944i
\(781\) 5.66337 + 9.80925i 0.202651 + 0.351002i
\(782\) −12.0520 + 20.8747i −0.430980 + 0.746479i
\(783\) 6.46362 0.230991
\(784\) 0 0
\(785\) 14.0873 0.502797
\(786\) −0.674542 + 1.16834i −0.0240601 + 0.0416734i
\(787\) −13.9517 24.1651i −0.497324 0.861391i 0.502671 0.864478i \(-0.332351\pi\)
−0.999995 + 0.00308674i \(0.999017\pi\)
\(788\) −25.5683 44.2855i −0.910832 1.57761i
\(789\) 3.27919 5.67973i 0.116742 0.202204i
\(790\) 25.4308 0.904788
\(791\) 0 0
\(792\) −13.6770 −0.485991
\(793\) −21.3320 + 36.9481i −0.757521 + 1.31206i
\(794\) 21.5453 + 37.3176i 0.764616 + 1.32435i
\(795\) 0.239662 + 0.415107i 0.00849995 + 0.0147223i
\(796\) 4.00448 6.93597i 0.141935 0.245839i
\(797\) −10.0560 −0.356201 −0.178101 0.984012i \(-0.556995\pi\)
−0.178101 + 0.984012i \(0.556995\pi\)
\(798\) 0 0
\(799\) 2.22267 0.0786326
\(800\) −0.150500 + 0.260674i −0.00532098 + 0.00921620i
\(801\) −3.99086 6.91238i −0.141010 0.244237i
\(802\) −31.0740 53.8218i −1.09726 1.90051i
\(803\) 4.28384 7.41984i 0.151174 0.261840i
\(804\) −13.7188 −0.483824
\(805\) 0 0
\(806\) −19.2394 −0.677681
\(807\) −5.57031 + 9.64805i −0.196084 + 0.339628i
\(808\) −16.5975 28.7478i −0.583900 1.01134i
\(809\) −19.2863 33.4048i −0.678070 1.17445i −0.975561 0.219727i \(-0.929483\pi\)
0.297491 0.954725i \(-0.403850\pi\)
\(810\) −12.8404 + 22.2402i −0.451164 + 0.781440i
\(811\) −12.3760 −0.434580 −0.217290 0.976107i \(-0.569722\pi\)
−0.217290 + 0.976107i \(0.569722\pi\)
\(812\) 0 0
\(813\) −19.7968 −0.694303
\(814\) 6.91794 11.9822i 0.242474 0.419977i
\(815\) 10.9616 + 18.9860i 0.383968 + 0.665051i
\(816\) 2.80212 + 4.85341i 0.0980937 + 0.169903i
\(817\) −18.2225 + 31.5623i −0.637525 + 1.10423i
\(818\) −96.0437 −3.35809
\(819\) 0 0
\(820\) −104.266 −3.64114
\(821\) −14.8691 + 25.7540i −0.518934 + 0.898820i 0.480824 + 0.876817i \(0.340338\pi\)
−0.999758 + 0.0220025i \(0.992996\pi\)
\(822\) −5.19078 8.99070i −0.181049 0.313587i
\(823\) −20.3885 35.3139i −0.710698 1.23097i −0.964595 0.263734i \(-0.915046\pi\)
0.253897 0.967231i \(-0.418288\pi\)
\(824\) 2.92056 5.05855i 0.101742 0.176223i
\(825\) 0.100333 0.00349316
\(826\) 0 0
\(827\) −18.8411 −0.655170 −0.327585 0.944822i \(-0.606235\pi\)
−0.327585 + 0.944822i \(0.606235\pi\)
\(828\) 33.9881 58.8691i 1.18117 2.04584i
\(829\) −15.5703 26.9686i −0.540779 0.936657i −0.998860 0.0477461i \(-0.984796\pi\)
0.458080 0.888911i \(-0.348537\pi\)
\(830\) −5.31574 9.20713i −0.184512 0.319584i
\(831\) −5.28459 + 9.15319i −0.183321 + 0.317521i
\(832\) −17.1041 −0.592977
\(833\) 0 0
\(834\) −9.90490 −0.342979
\(835\) 2.13986 3.70635i 0.0740530 0.128264i
\(836\) 14.5429 + 25.1890i 0.502977 + 0.871181i
\(837\) 4.60407 + 7.97448i 0.159140 + 0.275638i
\(838\) −1.13206 + 1.96079i −0.0391064 + 0.0677342i
\(839\) −10.2589 −0.354176 −0.177088 0.984195i \(-0.556668\pi\)
−0.177088 + 0.984195i \(0.556668\pi\)
\(840\) 0 0
\(841\) −26.2783 −0.906149
\(842\) 19.3704 33.5505i 0.667548 1.15623i
\(843\) −5.43098 9.40673i −0.187053 0.323985i
\(844\) 34.1496 + 59.1488i 1.17548 + 2.03599i
\(845\) −2.42392 + 4.19836i −0.0833855 + 0.144428i
\(846\) −9.24992 −0.318019
\(847\) 0 0
\(848\) 1.60540 0.0551297
\(849\) 7.74805 13.4200i 0.265912 0.460574i
\(850\) 0.261087 + 0.452217i 0.00895522 + 0.0155109i
\(851\) 18.0272 + 31.2241i 0.617966 + 1.07035i
\(852\) −16.9901 + 29.4277i −0.582072 + 1.00818i
\(853\) −3.04435 −0.104237 −0.0521183 0.998641i \(-0.516597\pi\)
−0.0521183 + 0.998641i \(0.516597\pi\)
\(854\) 0 0
\(855\) 37.9855 1.29908
\(856\) −17.3840 + 30.1100i −0.594173 + 1.02914i
\(857\) 24.7766 + 42.9143i 0.846352 + 1.46592i 0.884442 + 0.466650i \(0.154539\pi\)
−0.0380904 + 0.999274i \(0.512127\pi\)
\(858\) −2.92056 5.05855i −0.0997062 0.172696i
\(859\) 18.4373 31.9344i 0.629074 1.08959i −0.358664 0.933467i \(-0.616768\pi\)
0.987738 0.156121i \(-0.0498989\pi\)
\(860\) −48.8266 −1.66497
\(861\) 0 0
\(862\) −8.80864 −0.300023
\(863\) 23.2115 40.2035i 0.790129 1.36854i −0.135758 0.990742i \(-0.543347\pi\)
0.925887 0.377801i \(-0.123320\pi\)
\(864\) −4.19340 7.26318i −0.142662 0.247098i
\(865\) −7.08970 12.2797i −0.241057 0.417523i
\(866\) −21.9765 + 38.0644i −0.746792 + 1.29348i
\(867\) −10.5442 −0.358099
\(868\) 0 0
\(869\) −4.63148 −0.157112
\(870\) 3.23181 5.59766i 0.109569 0.189778i
\(871\) 7.51437 + 13.0153i 0.254615 + 0.441006i
\(872\) −7.72529 13.3806i −0.261611 0.453124i
\(873\) −2.31574 + 4.01098i −0.0783759 + 0.135751i
\(874\) −111.848 −3.78332
\(875\) 0 0
\(876\) 25.7031 0.868426
\(877\) −19.5155 + 33.8018i −0.658991 + 1.14141i 0.321886 + 0.946778i \(0.395683\pi\)
−0.980877 + 0.194628i \(0.937650\pi\)
\(878\) −18.7154 32.4160i −0.631614 1.09399i
\(879\) 3.96997 + 6.87620i 0.133904 + 0.231928i
\(880\) −5.80660 + 10.0573i −0.195741 + 0.339033i
\(881\) 44.0049 1.48256 0.741281 0.671194i \(-0.234218\pi\)
0.741281 + 0.671194i \(0.234218\pi\)
\(882\) 0 0
\(883\) −23.3596 −0.786112 −0.393056 0.919515i \(-0.628582\pi\)
−0.393056 + 0.919515i \(0.628582\pi\)
\(884\) 10.3001 17.8403i 0.346429 0.600033i
\(885\) 9.95560 + 17.2436i 0.334654 + 0.579638i
\(886\) 16.4679 + 28.5233i 0.553251 + 0.958259i
\(887\) 20.9588 36.3017i 0.703728 1.21889i −0.263421 0.964681i \(-0.584851\pi\)
0.967149 0.254211i \(-0.0818158\pi\)
\(888\) 21.7628 0.730311
\(889\) 0 0
\(890\) −17.5949 −0.589783
\(891\) 2.33850 4.05039i 0.0783426 0.135693i
\(892\) 6.38343 + 11.0564i 0.213733 + 0.370196i
\(893\) 5.15685 + 8.93193i 0.172567 + 0.298896i
\(894\) −0.888663 + 1.53921i −0.0297213 + 0.0514789i
\(895\) 7.90490 0.264232
\(896\) 0 0
\(897\) 15.2212 0.508220
\(898\) −12.3405 + 21.3744i −0.411809 + 0.713274i
\(899\) 1.93866 + 3.35786i 0.0646580 + 0.111991i
\(900\) −0.736295 1.27530i −0.0245432 0.0425100i
\(901\) 0.227159 0.393451i 0.00756776 0.0131078i
\(902\) 28.0220 0.933031
\(903\) 0 0
\(904\) 70.0295 2.32915
\(905\) −13.4616 + 23.3162i −0.447478 + 0.775055i
\(906\) 13.1887 + 22.8436i 0.438167 + 0.758927i
\(907\) 10.2591 + 17.7692i 0.340646 + 0.590017i 0.984553 0.175087i \(-0.0560208\pi\)
−0.643907 + 0.765104i \(0.722687\pi\)
\(908\) 38.7837 67.1753i 1.28708 2.22929i
\(909\) 15.0586 0.499461
\(910\) 0 0
\(911\) 27.6755 0.916930 0.458465 0.888712i \(-0.348399\pi\)
0.458465 + 0.888712i \(0.348399\pi\)
\(912\) −13.0025 + 22.5209i −0.430554 + 0.745742i
\(913\) 0.968106 + 1.67681i 0.0320396 + 0.0554943i
\(914\) 12.8840 + 22.3158i 0.426165 + 0.738140i
\(915\) 10.2096 17.6836i 0.337520 0.584602i
\(916\) 107.212 3.54237
\(917\) 0 0
\(918\) −14.5494 −0.480202
\(919\) −0.481727 + 0.834376i −0.0158907 + 0.0275235i −0.873861 0.486175i \(-0.838392\pi\)
0.857971 + 0.513699i \(0.171725\pi\)
\(920\) −39.2829 68.0400i −1.29512 2.24321i
\(921\) 8.91404 + 15.4396i 0.293728 + 0.508751i
\(922\) 19.1015 33.0847i 0.629073 1.08959i
\(923\) 37.2249 1.22527
\(924\) 0 0
\(925\) 0.781061 0.0256811
\(926\) −31.2993 + 54.2120i −1.02856 + 1.78152i
\(927\) 1.32488 + 2.29475i 0.0435146 + 0.0753695i
\(928\) −1.76574 3.05835i −0.0579632 0.100395i
\(929\) 13.1660 22.8042i 0.431962 0.748180i −0.565080 0.825036i \(-0.691155\pi\)
0.997042 + 0.0768558i \(0.0244881\pi\)
\(930\) 9.20814 0.301947
\(931\) 0 0
\(932\) 16.0507 0.525760
\(933\) 12.3944 21.4678i 0.405775 0.702824i
\(934\) 0.929110 + 1.60927i 0.0304014 + 0.0526568i
\(935\) 1.64323 + 2.84616i 0.0537394 + 0.0930794i
\(936\) −22.4745 + 38.9269i −0.734601 + 1.27237i
\(937\) 21.3865 0.698665 0.349333 0.936999i \(-0.386408\pi\)
0.349333 + 0.936999i \(0.386408\pi\)
\(938\) 0 0
\(939\) −16.9176 −0.552085
\(940\) −6.90880 + 11.9664i −0.225340 + 0.390301i
\(941\) 7.41142 + 12.8370i 0.241605 + 0.418473i 0.961172 0.275951i \(-0.0889927\pi\)
−0.719566 + 0.694424i \(0.755659\pi\)
\(942\) −5.67903 9.83636i −0.185033 0.320486i
\(943\) −36.5108 + 63.2386i −1.18896 + 2.05933i
\(944\) 66.6885 2.17053
\(945\) 0 0
\(946\) 13.1223 0.426644
\(947\) −15.8560 + 27.4634i −0.515251 + 0.892442i 0.484592 + 0.874740i \(0.338968\pi\)
−0.999843 + 0.0177013i \(0.994365\pi\)
\(948\) −6.94722 12.0329i −0.225635 0.390811i
\(949\) −14.0787 24.3850i −0.457014 0.791571i
\(950\) −1.21150 + 2.09839i −0.0393064 + 0.0680806i
\(951\) 14.0403 0.455287
\(952\) 0 0
\(953\) 49.9620 1.61843 0.809213 0.587515i \(-0.199894\pi\)
0.809213 + 0.587515i \(0.199894\pi\)
\(954\) −0.945349 + 1.63739i −0.0306068 + 0.0530125i
\(955\) 13.3469 + 23.1175i 0.431895 + 0.748064i
\(956\) −27.3365 47.3481i −0.884124 1.53135i
\(957\) −0.588580 + 1.01945i −0.0190261 + 0.0329541i
\(958\) −50.0988 −1.61862
\(959\) 0 0
\(960\) 8.18613 0.264206
\(961\) 12.7382 22.0631i 0.410908 0.711714i
\(962\) −22.7355 39.3791i −0.733023 1.26963i
\(963\) −7.88605 13.6590i −0.254124 0.440156i
\(964\) −0.947216 + 1.64063i −0.0305078 + 0.0528410i
\(965\) 26.3204 0.847285
\(966\) 0 0
\(967\) −52.4581 −1.68694 −0.843469 0.537178i \(-0.819490\pi\)
−0.843469 + 0.537178i \(0.819490\pi\)
\(968\) 2.74543 4.75523i 0.0882415 0.152839i
\(969\) 3.67961 + 6.37327i 0.118206 + 0.204739i
\(970\) 5.10482 + 8.84180i 0.163906 + 0.283893i
\(971\) 15.4133 26.6966i 0.494636 0.856735i −0.505345 0.862917i \(-0.668635\pi\)
0.999981 + 0.00618284i \(0.00196807\pi\)
\(972\) 63.4487 2.03512
\(973\) 0 0
\(974\) 10.5860 0.339196
\(975\) 0.164871 0.285565i 0.00528009 0.00914538i
\(976\) −34.1951 59.2276i −1.09456 1.89583i
\(977\) −12.3678 21.4216i −0.395680 0.685338i 0.597508 0.801863i \(-0.296158\pi\)
−0.993188 + 0.116525i \(0.962824\pi\)
\(978\) 8.83791 15.3077i 0.282605 0.489487i
\(979\) 3.20440 0.102413
\(980\) 0 0
\(981\) 7.00897 0.223779
\(982\) 37.7713 65.4219i 1.20533 2.08770i
\(983\) 6.11192 + 10.5862i 0.194940 + 0.337646i 0.946881 0.321585i \(-0.104215\pi\)
−0.751941 + 0.659231i \(0.770882\pi\)
\(984\) 22.0382 + 38.1714i 0.702554 + 1.21686i
\(985\) 13.4057 23.2193i 0.427140 0.739827i
\(986\) −6.12641 −0.195105
\(987\) 0 0
\(988\) 95.5894 3.04110
\(989\) −17.0975 + 29.6138i −0.543670 + 0.941665i
\(990\) −6.83850 11.8446i −0.217342 0.376447i
\(991\) −2.30008 3.98386i −0.0730645 0.126552i 0.827178 0.561939i \(-0.189945\pi\)
−0.900243 + 0.435388i \(0.856611\pi\)
\(992\) 2.51549 4.35695i 0.0798668 0.138333i
\(993\) −20.1145 −0.638316
\(994\) 0 0
\(995\) 4.19917 0.133123
\(996\) −2.90432 + 5.03043i −0.0920268 + 0.159395i
\(997\) −17.2382 29.8574i −0.545938 0.945593i −0.998547 0.0538835i \(-0.982840\pi\)
0.452609 0.891709i \(-0.350493\pi\)
\(998\) 17.9856 + 31.1520i 0.569325 + 0.986100i
\(999\) −10.8814 + 18.8471i −0.344272 + 0.596297i
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 539.2.e.l.177.3 6
7.2 even 3 539.2.a.i.1.1 3
7.3 odd 6 77.2.e.b.67.3 yes 6
7.4 even 3 inner 539.2.e.l.67.3 6
7.5 odd 6 539.2.a.h.1.1 3
7.6 odd 2 77.2.e.b.23.3 6
21.2 odd 6 4851.2.a.bn.1.3 3
21.5 even 6 4851.2.a.bo.1.3 3
21.17 even 6 693.2.i.g.298.1 6
21.20 even 2 693.2.i.g.100.1 6
28.3 even 6 1232.2.q.k.529.2 6
28.19 even 6 8624.2.a.cl.1.2 3
28.23 odd 6 8624.2.a.ck.1.2 3
28.27 even 2 1232.2.q.k.177.2 6
77.3 odd 30 847.2.n.e.130.3 24
77.6 even 10 847.2.n.d.366.1 24
77.10 even 6 847.2.e.d.606.1 6
77.13 even 10 847.2.n.d.807.3 24
77.17 even 30 847.2.n.d.487.3 24
77.20 odd 10 847.2.n.e.807.1 24
77.24 even 30 847.2.n.d.81.1 24
77.27 odd 10 847.2.n.e.366.3 24
77.31 odd 30 847.2.n.e.81.3 24
77.38 odd 30 847.2.n.e.487.1 24
77.41 even 10 847.2.n.d.9.3 24
77.48 odd 10 847.2.n.e.632.3 24
77.52 even 30 847.2.n.d.130.1 24
77.54 even 6 5929.2.a.v.1.3 3
77.59 odd 30 847.2.n.e.753.1 24
77.62 even 10 847.2.n.d.632.1 24
77.65 odd 6 5929.2.a.w.1.3 3
77.69 odd 10 847.2.n.e.9.1 24
77.73 even 30 847.2.n.d.753.3 24
77.76 even 2 847.2.e.d.485.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
77.2.e.b.23.3 6 7.6 odd 2
77.2.e.b.67.3 yes 6 7.3 odd 6
539.2.a.h.1.1 3 7.5 odd 6
539.2.a.i.1.1 3 7.2 even 3
539.2.e.l.67.3 6 7.4 even 3 inner
539.2.e.l.177.3 6 1.1 even 1 trivial
693.2.i.g.100.1 6 21.20 even 2
693.2.i.g.298.1 6 21.17 even 6
847.2.e.d.485.1 6 77.76 even 2
847.2.e.d.606.1 6 77.10 even 6
847.2.n.d.9.3 24 77.41 even 10
847.2.n.d.81.1 24 77.24 even 30
847.2.n.d.130.1 24 77.52 even 30
847.2.n.d.366.1 24 77.6 even 10
847.2.n.d.487.3 24 77.17 even 30
847.2.n.d.632.1 24 77.62 even 10
847.2.n.d.753.3 24 77.73 even 30
847.2.n.d.807.3 24 77.13 even 10
847.2.n.e.9.1 24 77.69 odd 10
847.2.n.e.81.3 24 77.31 odd 30
847.2.n.e.130.3 24 77.3 odd 30
847.2.n.e.366.3 24 77.27 odd 10
847.2.n.e.487.1 24 77.38 odd 30
847.2.n.e.632.3 24 77.48 odd 10
847.2.n.e.753.1 24 77.59 odd 30
847.2.n.e.807.1 24 77.20 odd 10
1232.2.q.k.177.2 6 28.27 even 2
1232.2.q.k.529.2 6 28.3 even 6
4851.2.a.bn.1.3 3 21.2 odd 6
4851.2.a.bo.1.3 3 21.5 even 6
5929.2.a.v.1.3 3 77.54 even 6
5929.2.a.w.1.3 3 77.65 odd 6
8624.2.a.ck.1.2 3 28.23 odd 6
8624.2.a.cl.1.2 3 28.19 even 6