Properties

Label 216.3.j.a.125.19
Level $216$
Weight $3$
Character 216.125
Analytic conductor $5.886$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [216,3,Mod(125,216)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(216, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("216.125");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 216.j (of order \(6\), 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: \(5.88557371018\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 72)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 125.19
Character \(\chi\) \(=\) 216.125
Dual form 216.3.j.a.197.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.87413 - 0.698310i) q^{2} +(3.02473 - 2.61745i) q^{4} +(-3.98823 + 6.90782i) q^{5} +(5.64852 + 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +O(q^{10})\) \(q+(1.87413 - 0.698310i) q^{2} +(3.02473 - 2.61745i) q^{4} +(-3.98823 + 6.90782i) q^{5} +(5.64852 + 9.78353i) q^{7} +(3.84094 - 7.01763i) q^{8} +(-2.65067 + 15.7312i) q^{10} +(1.06057 + 1.83697i) q^{11} +(6.03586 + 3.48480i) q^{13} +(17.4180 + 14.3912i) q^{14} +(2.29794 - 15.8341i) q^{16} -4.29594i q^{17} -11.2235i q^{19} +(6.01755 + 31.3333i) q^{20} +(3.27042 + 2.70210i) q^{22} +(3.40068 + 1.96338i) q^{23} +(-19.3120 - 33.4494i) q^{25} +(13.7455 + 2.31608i) q^{26} +(42.6931 + 14.8078i) q^{28} +(0.512348 + 0.887412i) q^{29} +(4.18829 - 7.25434i) q^{31} +(-6.75050 - 31.2799i) q^{32} +(-2.99990 - 8.05114i) q^{34} -90.1105 q^{35} -58.9714i q^{37} +(-7.83749 - 21.0343i) q^{38} +(33.1580 + 54.5205i) q^{40} +(48.6696 + 28.0994i) q^{41} +(-49.8518 + 28.7820i) q^{43} +(8.01611 + 2.78033i) q^{44} +(7.74436 + 1.30491i) q^{46} +(-44.8348 + 25.8854i) q^{47} +(-39.3116 + 68.0897i) q^{49} +(-59.5513 - 49.2027i) q^{50} +(27.3781 - 5.25796i) q^{52} +42.6170 q^{53} -16.9193 q^{55} +(90.3528 - 2.06132i) q^{56} +(1.57990 + 1.30535i) q^{58} +(25.6501 - 44.4272i) q^{59} +(42.9355 - 24.7888i) q^{61} +(2.78363 - 16.5203i) q^{62} +(-34.4944 - 53.9086i) q^{64} +(-48.1448 + 27.7964i) q^{65} +(-85.1906 - 49.1848i) q^{67} +(-11.2444 - 12.9940i) q^{68} +(-168.879 + 62.9251i) q^{70} -31.4710i q^{71} +85.4715 q^{73} +(-41.1803 - 110.520i) q^{74} +(-29.3770 - 33.9480i) q^{76} +(-11.9813 + 20.7523i) q^{77} +(-6.61671 - 11.4605i) q^{79} +(100.215 + 79.0239i) q^{80} +(110.835 + 18.6755i) q^{82} +(-41.8804 - 72.5390i) q^{83} +(29.6756 + 17.1332i) q^{85} +(-73.3301 + 88.7532i) q^{86} +(16.9648 - 0.387037i) q^{88} -105.027i q^{89} +78.7360i q^{91} +(15.4252 - 2.96240i) q^{92} +(-65.9502 + 79.8211i) q^{94} +(77.5300 + 44.7620i) q^{95} +(-9.54179 - 16.5269i) q^{97} +(-26.1273 + 155.061i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.87413 0.698310i 0.937065 0.349155i
\(3\) 0 0
\(4\) 3.02473 2.61745i 0.756182 0.654362i
\(5\) −3.98823 + 6.90782i −0.797647 + 1.38156i 0.123498 + 0.992345i \(0.460589\pi\)
−0.921145 + 0.389220i \(0.872745\pi\)
\(6\) 0 0
\(7\) 5.64852 + 9.78353i 0.806932 + 1.39765i 0.914979 + 0.403501i \(0.132207\pi\)
−0.108047 + 0.994146i \(0.534460\pi\)
\(8\) 3.84094 7.01763i 0.480117 0.877204i
\(9\) 0 0
\(10\) −2.65067 + 15.7312i −0.265067 + 1.57312i
\(11\) 1.06057 + 1.83697i 0.0964157 + 0.166997i 0.910199 0.414172i \(-0.135929\pi\)
−0.813783 + 0.581169i \(0.802596\pi\)
\(12\) 0 0
\(13\) 6.03586 + 3.48480i 0.464297 + 0.268062i 0.713849 0.700299i \(-0.246950\pi\)
−0.249552 + 0.968361i \(0.580284\pi\)
\(14\) 17.4180 + 14.3912i 1.24414 + 1.02794i
\(15\) 0 0
\(16\) 2.29794 15.8341i 0.143621 0.989633i
\(17\) 4.29594i 0.252702i −0.991986 0.126351i \(-0.959673\pi\)
0.991986 0.126351i \(-0.0403266\pi\)
\(18\) 0 0
\(19\) 11.2235i 0.590711i −0.955387 0.295356i \(-0.904562\pi\)
0.955387 0.295356i \(-0.0954381\pi\)
\(20\) 6.01755 + 31.3333i 0.300878 + 1.56666i
\(21\) 0 0
\(22\) 3.27042 + 2.70210i 0.148656 + 0.122823i
\(23\) 3.40068 + 1.96338i 0.147856 + 0.0853645i 0.572103 0.820182i \(-0.306128\pi\)
−0.424247 + 0.905546i \(0.639461\pi\)
\(24\) 0 0
\(25\) −19.3120 33.4494i −0.772480 1.33798i
\(26\) 13.7455 + 2.31608i 0.528671 + 0.0890798i
\(27\) 0 0
\(28\) 42.6931 + 14.8078i 1.52475 + 0.528849i
\(29\) 0.512348 + 0.887412i 0.0176672 + 0.0306004i 0.874724 0.484622i \(-0.161043\pi\)
−0.857057 + 0.515222i \(0.827709\pi\)
\(30\) 0 0
\(31\) 4.18829 7.25434i 0.135106 0.234011i −0.790532 0.612421i \(-0.790196\pi\)
0.925638 + 0.378410i \(0.123529\pi\)
\(32\) −6.75050 31.2799i −0.210953 0.977496i
\(33\) 0 0
\(34\) −2.99990 8.05114i −0.0882322 0.236798i
\(35\) −90.1105 −2.57459
\(36\) 0 0
\(37\) 58.9714i 1.59382i −0.604097 0.796911i \(-0.706466\pi\)
0.604097 0.796911i \(-0.293534\pi\)
\(38\) −7.83749 21.0343i −0.206250 0.553535i
\(39\) 0 0
\(40\) 33.1580 + 54.5205i 0.828950 + 1.36301i
\(41\) 48.6696 + 28.0994i 1.18706 + 0.685351i 0.957638 0.287975i \(-0.0929821\pi\)
0.229425 + 0.973326i \(0.426315\pi\)
\(42\) 0 0
\(43\) −49.8518 + 28.7820i −1.15935 + 0.669348i −0.951147 0.308738i \(-0.900093\pi\)
−0.208198 + 0.978087i \(0.566760\pi\)
\(44\) 8.01611 + 2.78033i 0.182184 + 0.0631892i
\(45\) 0 0
\(46\) 7.74436 + 1.30491i 0.168356 + 0.0283675i
\(47\) −44.8348 + 25.8854i −0.953931 + 0.550752i −0.894300 0.447468i \(-0.852326\pi\)
−0.0596311 + 0.998220i \(0.518992\pi\)
\(48\) 0 0
\(49\) −39.3116 + 68.0897i −0.802278 + 1.38959i
\(50\) −59.5513 49.2027i −1.19103 0.984054i
\(51\) 0 0
\(52\) 27.3781 5.25796i 0.526502 0.101115i
\(53\) 42.6170 0.804094 0.402047 0.915619i \(-0.368299\pi\)
0.402047 + 0.915619i \(0.368299\pi\)
\(54\) 0 0
\(55\) −16.9193 −0.307623
\(56\) 90.3528 2.06132i 1.61344 0.0368094i
\(57\) 0 0
\(58\) 1.57990 + 1.30535i 0.0272396 + 0.0225060i
\(59\) 25.6501 44.4272i 0.434747 0.753003i −0.562528 0.826778i \(-0.690171\pi\)
0.997275 + 0.0737746i \(0.0235046\pi\)
\(60\) 0 0
\(61\) 42.9355 24.7888i 0.703861 0.406374i −0.104923 0.994480i \(-0.533460\pi\)
0.808784 + 0.588106i \(0.200126\pi\)
\(62\) 2.78363 16.5203i 0.0448973 0.266456i
\(63\) 0 0
\(64\) −34.4944 53.9086i −0.538975 0.842322i
\(65\) −48.1448 + 27.7964i −0.740689 + 0.427637i
\(66\) 0 0
\(67\) −85.1906 49.1848i −1.27150 0.734102i −0.296231 0.955116i \(-0.595730\pi\)
−0.975271 + 0.221014i \(0.929063\pi\)
\(68\) −11.2444 12.9940i −0.165359 0.191089i
\(69\) 0 0
\(70\) −168.879 + 62.9251i −2.41255 + 0.898930i
\(71\) 31.4710i 0.443254i −0.975132 0.221627i \(-0.928863\pi\)
0.975132 0.221627i \(-0.0711367\pi\)
\(72\) 0 0
\(73\) 85.4715 1.17084 0.585421 0.810729i \(-0.300929\pi\)
0.585421 + 0.810729i \(0.300929\pi\)
\(74\) −41.1803 110.520i −0.556491 1.49351i
\(75\) 0 0
\(76\) −29.3770 33.9480i −0.386539 0.446685i
\(77\) −11.9813 + 20.7523i −0.155602 + 0.269510i
\(78\) 0 0
\(79\) −6.61671 11.4605i −0.0837558 0.145069i 0.821105 0.570778i \(-0.193358\pi\)
−0.904860 + 0.425708i \(0.860025\pi\)
\(80\) 100.215 + 79.0239i 1.25268 + 0.987799i
\(81\) 0 0
\(82\) 110.835 + 18.6755i 1.35165 + 0.227750i
\(83\) −41.8804 72.5390i −0.504583 0.873964i −0.999986 0.00530047i \(-0.998313\pi\)
0.495403 0.868663i \(-0.335021\pi\)
\(84\) 0 0
\(85\) 29.6756 + 17.1332i 0.349124 + 0.201567i
\(86\) −73.3301 + 88.7532i −0.852675 + 1.03201i
\(87\) 0 0
\(88\) 16.9648 0.387037i 0.192781 0.00439814i
\(89\) 105.027i 1.18008i −0.807374 0.590040i \(-0.799112\pi\)
0.807374 0.590040i \(-0.200888\pi\)
\(90\) 0 0
\(91\) 78.7360i 0.865230i
\(92\) 15.4252 2.96240i 0.167665 0.0322000i
\(93\) 0 0
\(94\) −65.9502 + 79.8211i −0.701597 + 0.849161i
\(95\) 77.5300 + 44.7620i 0.816105 + 0.471179i
\(96\) 0 0
\(97\) −9.54179 16.5269i −0.0983690 0.170380i 0.812641 0.582765i \(-0.198029\pi\)
−0.911010 + 0.412385i \(0.864696\pi\)
\(98\) −26.1273 + 155.061i −0.266605 + 1.58225i
\(99\) 0 0
\(100\) −145.966 50.6270i −1.45966 0.506270i
\(101\) 53.0235 + 91.8395i 0.524985 + 0.909302i 0.999577 + 0.0290952i \(0.00926259\pi\)
−0.474591 + 0.880206i \(0.657404\pi\)
\(102\) 0 0
\(103\) −30.5290 + 52.8778i −0.296398 + 0.513376i −0.975309 0.220844i \(-0.929119\pi\)
0.678911 + 0.734220i \(0.262452\pi\)
\(104\) 47.6384 28.9725i 0.458062 0.278582i
\(105\) 0 0
\(106\) 79.8697 29.7599i 0.753488 0.280753i
\(107\) 7.01531 0.0655636 0.0327818 0.999463i \(-0.489563\pi\)
0.0327818 + 0.999463i \(0.489563\pi\)
\(108\) 0 0
\(109\) 38.1403i 0.349911i 0.984576 + 0.174956i \(0.0559782\pi\)
−0.984576 + 0.174956i \(0.944022\pi\)
\(110\) −31.7089 + 11.8149i −0.288263 + 0.107408i
\(111\) 0 0
\(112\) 167.894 66.9575i 1.49905 0.597835i
\(113\) −120.801 69.7442i −1.06903 0.617205i −0.141115 0.989993i \(-0.545069\pi\)
−0.927917 + 0.372788i \(0.878402\pi\)
\(114\) 0 0
\(115\) −27.1254 + 15.6609i −0.235873 + 0.136181i
\(116\) 3.87247 + 1.34314i 0.0333833 + 0.0115788i
\(117\) 0 0
\(118\) 17.0476 101.174i 0.144471 0.857407i
\(119\) 42.0294 24.2657i 0.353188 0.203913i
\(120\) 0 0
\(121\) 58.2504 100.893i 0.481408 0.833823i
\(122\) 63.1564 76.4398i 0.517676 0.626555i
\(123\) 0 0
\(124\) −6.31941 32.9050i −0.0509630 0.265363i
\(125\) 108.672 0.869373
\(126\) 0 0
\(127\) −11.3165 −0.0891066 −0.0445533 0.999007i \(-0.514186\pi\)
−0.0445533 + 0.999007i \(0.514186\pi\)
\(128\) −102.292 76.9440i −0.799155 0.601125i
\(129\) 0 0
\(130\) −70.8191 + 85.7141i −0.544762 + 0.659339i
\(131\) −33.8613 + 58.6494i −0.258483 + 0.447705i −0.965836 0.259155i \(-0.916556\pi\)
0.707353 + 0.706861i \(0.249889\pi\)
\(132\) 0 0
\(133\) 109.806 63.3962i 0.825605 0.476664i
\(134\) −194.005 32.6893i −1.44780 0.243950i
\(135\) 0 0
\(136\) −30.1473 16.5004i −0.221671 0.121327i
\(137\) 12.4238 7.17291i 0.0906850 0.0523570i −0.453972 0.891016i \(-0.649993\pi\)
0.544657 + 0.838659i \(0.316660\pi\)
\(138\) 0 0
\(139\) 182.816 + 105.549i 1.31522 + 0.759342i 0.982955 0.183844i \(-0.0588541\pi\)
0.332264 + 0.943186i \(0.392187\pi\)
\(140\) −272.560 + 235.860i −1.94685 + 1.68471i
\(141\) 0 0
\(142\) −21.9765 58.9808i −0.154764 0.415358i
\(143\) 14.7836i 0.103382i
\(144\) 0 0
\(145\) −8.17345 −0.0563686
\(146\) 160.185 59.6856i 1.09716 0.408806i
\(147\) 0 0
\(148\) −154.355 178.372i −1.04294 1.20522i
\(149\) 91.6036 158.662i 0.614789 1.06485i −0.375632 0.926769i \(-0.622574\pi\)
0.990421 0.138077i \(-0.0440922\pi\)
\(150\) 0 0
\(151\) 78.9656 + 136.772i 0.522951 + 0.905778i 0.999643 + 0.0267076i \(0.00850231\pi\)
−0.476692 + 0.879070i \(0.658164\pi\)
\(152\) −78.7625 43.1088i −0.518174 0.283611i
\(153\) 0 0
\(154\) −7.96306 + 47.2592i −0.0517082 + 0.306878i
\(155\) 33.4078 + 57.8640i 0.215534 + 0.373316i
\(156\) 0 0
\(157\) 137.812 + 79.5658i 0.877784 + 0.506789i 0.869927 0.493180i \(-0.164166\pi\)
0.00785670 + 0.999969i \(0.497499\pi\)
\(158\) −20.4035 16.8579i −0.129136 0.106696i
\(159\) 0 0
\(160\) 242.998 + 78.1202i 1.51874 + 0.488251i
\(161\) 44.3608i 0.275533i
\(162\) 0 0
\(163\) 127.443i 0.781861i 0.920420 + 0.390930i \(0.127847\pi\)
−0.920420 + 0.390930i \(0.872153\pi\)
\(164\) 220.761 42.3971i 1.34610 0.258519i
\(165\) 0 0
\(166\) −129.144 106.702i −0.777976 0.642783i
\(167\) 14.9753 + 8.64602i 0.0896727 + 0.0517726i 0.544166 0.838978i \(-0.316846\pi\)
−0.454493 + 0.890750i \(0.650180\pi\)
\(168\) 0 0
\(169\) −60.2123 104.291i −0.356286 0.617105i
\(170\) 67.5802 + 11.3871i 0.397530 + 0.0669829i
\(171\) 0 0
\(172\) −75.4529 + 217.542i −0.438679 + 1.26478i
\(173\) 122.607 + 212.361i 0.708709 + 1.22752i 0.965336 + 0.261009i \(0.0840554\pi\)
−0.256627 + 0.966510i \(0.582611\pi\)
\(174\) 0 0
\(175\) 218.169 377.879i 1.24668 2.15931i
\(176\) 31.5239 12.5720i 0.179113 0.0714319i
\(177\) 0 0
\(178\) −73.3415 196.835i −0.412031 1.10581i
\(179\) 245.877 1.37361 0.686807 0.726840i \(-0.259012\pi\)
0.686807 + 0.726840i \(0.259012\pi\)
\(180\) 0 0
\(181\) 53.7077i 0.296728i 0.988933 + 0.148364i \(0.0474007\pi\)
−0.988933 + 0.148364i \(0.952599\pi\)
\(182\) 54.9821 + 147.561i 0.302100 + 0.810777i
\(183\) 0 0
\(184\) 26.8401 16.3235i 0.145870 0.0887146i
\(185\) 407.364 + 235.192i 2.20197 + 1.27131i
\(186\) 0 0
\(187\) 7.89149 4.55615i 0.0422005 0.0243645i
\(188\) −67.8593 + 195.649i −0.360954 + 1.04068i
\(189\) 0 0
\(190\) 176.559 + 29.7498i 0.929258 + 0.156578i
\(191\) −208.549 + 120.406i −1.09188 + 0.630396i −0.934076 0.357075i \(-0.883774\pi\)
−0.157802 + 0.987471i \(0.550441\pi\)
\(192\) 0 0
\(193\) −124.900 + 216.333i −0.647151 + 1.12090i 0.336650 + 0.941630i \(0.390706\pi\)
−0.983800 + 0.179268i \(0.942627\pi\)
\(194\) −29.4234 24.3104i −0.151667 0.125311i
\(195\) 0 0
\(196\) 59.3144 + 308.849i 0.302624 + 1.57576i
\(197\) −327.726 −1.66359 −0.831793 0.555086i \(-0.812685\pi\)
−0.831793 + 0.555086i \(0.812685\pi\)
\(198\) 0 0
\(199\) −229.254 −1.15203 −0.576016 0.817439i \(-0.695393\pi\)
−0.576016 + 0.817439i \(0.695393\pi\)
\(200\) −308.912 + 7.04756i −1.54456 + 0.0352378i
\(201\) 0 0
\(202\) 163.505 + 135.092i 0.809433 + 0.668773i
\(203\) −5.78801 + 10.0251i −0.0285124 + 0.0493849i
\(204\) 0 0
\(205\) −388.211 + 224.134i −1.89371 + 1.09334i
\(206\) −20.2902 + 120.418i −0.0984962 + 0.584556i
\(207\) 0 0
\(208\) 69.0488 87.5647i 0.331966 0.420984i
\(209\) 20.6172 11.9034i 0.0986469 0.0569538i
\(210\) 0 0
\(211\) −135.544 78.2563i −0.642388 0.370883i 0.143146 0.989702i \(-0.454278\pi\)
−0.785534 + 0.618819i \(0.787612\pi\)
\(212\) 128.905 111.548i 0.608041 0.526168i
\(213\) 0 0
\(214\) 13.1476 4.89886i 0.0614374 0.0228919i
\(215\) 459.157i 2.13561i
\(216\) 0 0
\(217\) 94.6307 0.436086
\(218\) 26.6338 + 71.4800i 0.122173 + 0.327890i
\(219\) 0 0
\(220\) −51.1761 + 44.2853i −0.232619 + 0.201297i
\(221\) 14.9705 25.9297i 0.0677398 0.117329i
\(222\) 0 0
\(223\) 120.451 + 208.628i 0.540140 + 0.935550i 0.998895 + 0.0469875i \(0.0149621\pi\)
−0.458755 + 0.888563i \(0.651705\pi\)
\(224\) 267.897 242.729i 1.19597 1.08361i
\(225\) 0 0
\(226\) −275.099 46.3535i −1.21725 0.205104i
\(227\) 44.5553 + 77.1721i 0.196279 + 0.339965i 0.947319 0.320291i \(-0.103781\pi\)
−0.751040 + 0.660257i \(0.770448\pi\)
\(228\) 0 0
\(229\) −144.631 83.5027i −0.631576 0.364641i 0.149786 0.988718i \(-0.452142\pi\)
−0.781362 + 0.624078i \(0.785475\pi\)
\(230\) −39.9004 + 48.2924i −0.173480 + 0.209967i
\(231\) 0 0
\(232\) 8.19543 0.186972i 0.0353251 0.000805913i
\(233\) 136.581i 0.586185i −0.956084 0.293092i \(-0.905316\pi\)
0.956084 0.293092i \(-0.0946844\pi\)
\(234\) 0 0
\(235\) 412.947i 1.75722i
\(236\) −38.7015 201.518i −0.163989 0.853889i
\(237\) 0 0
\(238\) 61.8236 74.8266i 0.259763 0.314398i
\(239\) −133.564 77.1130i −0.558844 0.322648i 0.193838 0.981034i \(-0.437906\pi\)
−0.752681 + 0.658385i \(0.771240\pi\)
\(240\) 0 0
\(241\) −31.9120 55.2732i −0.132415 0.229350i 0.792192 0.610272i \(-0.208940\pi\)
−0.924607 + 0.380922i \(0.875606\pi\)
\(242\) 38.7144 229.763i 0.159977 0.949432i
\(243\) 0 0
\(244\) 64.9847 187.361i 0.266331 0.767872i
\(245\) −313.568 543.115i −1.27987 2.21680i
\(246\) 0 0
\(247\) 39.1117 67.7435i 0.158347 0.274265i
\(248\) −34.8213 57.2554i −0.140409 0.230869i
\(249\) 0 0
\(250\) 203.665 75.8864i 0.814659 0.303546i
\(251\) −99.6131 −0.396865 −0.198432 0.980115i \(-0.563585\pi\)
−0.198432 + 0.980115i \(0.563585\pi\)
\(252\) 0 0
\(253\) 8.32924i 0.0329219i
\(254\) −21.2087 + 7.90245i −0.0834986 + 0.0311120i
\(255\) 0 0
\(256\) −245.439 72.7716i −0.958746 0.284264i
\(257\) −258.303 149.131i −1.00507 0.580277i −0.0953248 0.995446i \(-0.530389\pi\)
−0.909744 + 0.415169i \(0.863722\pi\)
\(258\) 0 0
\(259\) 576.948 333.101i 2.22760 1.28611i
\(260\) −72.8692 + 210.093i −0.280266 + 0.808050i
\(261\) 0 0
\(262\) −22.5049 + 133.562i −0.0858966 + 0.509780i
\(263\) −26.4361 + 15.2629i −0.100518 + 0.0580338i −0.549416 0.835549i \(-0.685150\pi\)
0.448899 + 0.893583i \(0.351816\pi\)
\(264\) 0 0
\(265\) −169.966 + 294.390i −0.641383 + 1.11091i
\(266\) 161.520 195.491i 0.607216 0.734929i
\(267\) 0 0
\(268\) −386.417 + 74.2114i −1.44185 + 0.276908i
\(269\) −218.092 −0.810749 −0.405375 0.914151i \(-0.632859\pi\)
−0.405375 + 0.914151i \(0.632859\pi\)
\(270\) 0 0
\(271\) −343.470 −1.26742 −0.633709 0.773572i \(-0.718468\pi\)
−0.633709 + 0.773572i \(0.718468\pi\)
\(272\) −68.0224 9.87178i −0.250082 0.0362933i
\(273\) 0 0
\(274\) 18.2750 22.1187i 0.0666970 0.0807250i
\(275\) 40.9636 70.9510i 0.148959 0.258004i
\(276\) 0 0
\(277\) 110.463 63.7759i 0.398784 0.230238i −0.287175 0.957878i \(-0.592716\pi\)
0.685959 + 0.727640i \(0.259383\pi\)
\(278\) 416.326 + 70.1499i 1.49757 + 0.252338i
\(279\) 0 0
\(280\) −346.109 + 632.362i −1.23610 + 2.25844i
\(281\) −336.249 + 194.134i −1.19662 + 0.690867i −0.959799 0.280687i \(-0.909438\pi\)
−0.236818 + 0.971554i \(0.576104\pi\)
\(282\) 0 0
\(283\) −215.980 124.696i −0.763180 0.440622i 0.0672566 0.997736i \(-0.478575\pi\)
−0.830436 + 0.557114i \(0.811909\pi\)
\(284\) −82.3737 95.1912i −0.290048 0.335180i
\(285\) 0 0
\(286\) 10.3235 + 27.7063i 0.0360962 + 0.0968752i
\(287\) 634.880i 2.21213i
\(288\) 0 0
\(289\) 270.545 0.936142
\(290\) −15.3181 + 5.70760i −0.0528211 + 0.0196814i
\(291\) 0 0
\(292\) 258.528 223.717i 0.885369 0.766155i
\(293\) −56.0435 + 97.0701i −0.191275 + 0.331297i −0.945673 0.325120i \(-0.894595\pi\)
0.754398 + 0.656417i \(0.227929\pi\)
\(294\) 0 0
\(295\) 204.597 + 354.372i 0.693549 + 1.20126i
\(296\) −413.840 226.506i −1.39811 0.765222i
\(297\) 0 0
\(298\) 60.8817 361.321i 0.204301 1.21249i
\(299\) 13.6840 + 23.7014i 0.0457659 + 0.0792689i
\(300\) 0 0
\(301\) −563.179 325.151i −1.87102 1.08024i
\(302\) 243.501 + 201.187i 0.806296 + 0.666182i
\(303\) 0 0
\(304\) −177.714 25.7909i −0.584587 0.0848385i
\(305\) 395.454i 1.29657i
\(306\) 0 0
\(307\) 425.029i 1.38446i 0.721678 + 0.692229i \(0.243371\pi\)
−0.721678 + 0.692229i \(0.756629\pi\)
\(308\) 18.0778 + 94.1305i 0.0586940 + 0.305619i
\(309\) 0 0
\(310\) 103.018 + 85.1156i 0.332315 + 0.274567i
\(311\) 257.225 + 148.509i 0.827089 + 0.477520i 0.852855 0.522148i \(-0.174869\pi\)
−0.0257662 + 0.999668i \(0.508203\pi\)
\(312\) 0 0
\(313\) −101.171 175.234i −0.323231 0.559852i 0.657922 0.753086i \(-0.271436\pi\)
−0.981153 + 0.193234i \(0.938102\pi\)
\(314\) 313.839 + 52.8811i 0.999488 + 0.168411i
\(315\) 0 0
\(316\) −50.0109 17.3459i −0.158262 0.0548921i
\(317\) −21.4220 37.1039i −0.0675772 0.117047i 0.830257 0.557381i \(-0.188194\pi\)
−0.897834 + 0.440333i \(0.854860\pi\)
\(318\) 0 0
\(319\) −1.08676 + 1.88233i −0.00340678 + 0.00590072i
\(320\) 509.963 23.2809i 1.59363 0.0727527i
\(321\) 0 0
\(322\) 30.9776 + 83.1380i 0.0962038 + 0.258192i
\(323\) −48.2155 −0.149274
\(324\) 0 0
\(325\) 269.194i 0.828290i
\(326\) 88.9950 + 238.845i 0.272991 + 0.732655i
\(327\) 0 0
\(328\) 384.128 233.617i 1.17112 0.712248i
\(329\) −506.500 292.428i −1.53951 0.888839i
\(330\) 0 0
\(331\) −184.989 + 106.804i −0.558880 + 0.322669i −0.752696 0.658369i \(-0.771247\pi\)
0.193816 + 0.981038i \(0.437913\pi\)
\(332\) −316.544 109.791i −0.953445 0.330695i
\(333\) 0 0
\(334\) 34.1033 + 5.74633i 0.102106 + 0.0172046i
\(335\) 679.520 392.321i 2.02842 1.17111i
\(336\) 0 0
\(337\) 111.390 192.934i 0.330535 0.572504i −0.652082 0.758149i \(-0.726104\pi\)
0.982617 + 0.185645i \(0.0594374\pi\)
\(338\) −185.673 153.408i −0.549328 0.453868i
\(339\) 0 0
\(340\) 134.606 25.8510i 0.395899 0.0760324i
\(341\) 17.7680 0.0521055
\(342\) 0 0
\(343\) −334.655 −0.975670
\(344\) 10.5035 + 460.392i 0.0305333 + 1.33835i
\(345\) 0 0
\(346\) 378.075 + 312.375i 1.09270 + 0.902817i
\(347\) −72.3481 + 125.311i −0.208496 + 0.361126i −0.951241 0.308449i \(-0.900190\pi\)
0.742745 + 0.669574i \(0.233523\pi\)
\(348\) 0 0
\(349\) −191.412 + 110.512i −0.548458 + 0.316652i −0.748500 0.663135i \(-0.769226\pi\)
0.200042 + 0.979787i \(0.435892\pi\)
\(350\) 145.000 860.544i 0.414284 2.45870i
\(351\) 0 0
\(352\) 50.3007 45.5750i 0.142900 0.129475i
\(353\) 600.193 346.521i 1.70026 0.981647i 0.754778 0.655981i \(-0.227745\pi\)
0.945485 0.325666i \(-0.105589\pi\)
\(354\) 0 0
\(355\) 217.396 + 125.514i 0.612384 + 0.353560i
\(356\) −274.903 317.678i −0.772200 0.892355i
\(357\) 0 0
\(358\) 460.805 171.698i 1.28717 0.479604i
\(359\) 287.752i 0.801537i 0.916179 + 0.400769i \(0.131257\pi\)
−0.916179 + 0.400769i \(0.868743\pi\)
\(360\) 0 0
\(361\) 235.033 0.651060
\(362\) 37.5046 + 100.655i 0.103604 + 0.278053i
\(363\) 0 0
\(364\) 206.087 + 238.155i 0.566174 + 0.654271i
\(365\) −340.880 + 590.422i −0.933919 + 1.61759i
\(366\) 0 0
\(367\) −328.424 568.847i −0.894888 1.54999i −0.833943 0.551851i \(-0.813922\pi\)
−0.0609450 0.998141i \(-0.519411\pi\)
\(368\) 38.9030 49.3350i 0.105715 0.134063i
\(369\) 0 0
\(370\) 927.690 + 156.313i 2.50727 + 0.422469i
\(371\) 240.723 + 416.944i 0.648849 + 1.12384i
\(372\) 0 0
\(373\) 320.900 + 185.272i 0.860322 + 0.496707i 0.864120 0.503286i \(-0.167876\pi\)
−0.00379823 + 0.999993i \(0.501209\pi\)
\(374\) 11.6081 14.0495i 0.0310376 0.0375656i
\(375\) 0 0
\(376\) 9.44638 + 414.058i 0.0251234 + 1.10122i
\(377\) 7.14173i 0.0189436i
\(378\) 0 0
\(379\) 603.632i 1.59270i −0.604839 0.796348i \(-0.706762\pi\)
0.604839 0.796348i \(-0.293238\pi\)
\(380\) 351.669 67.5381i 0.925445 0.177732i
\(381\) 0 0
\(382\) −306.767 + 371.287i −0.803054 + 0.971956i
\(383\) −285.312 164.725i −0.744939 0.430091i 0.0789230 0.996881i \(-0.474852\pi\)
−0.823862 + 0.566790i \(0.808185\pi\)
\(384\) 0 0
\(385\) −95.5688 165.530i −0.248231 0.429948i
\(386\) −83.0113 + 492.656i −0.215055 + 1.27631i
\(387\) 0 0
\(388\) −72.1195 25.0141i −0.185875 0.0644693i
\(389\) −298.296 516.663i −0.766827 1.32818i −0.939275 0.343164i \(-0.888501\pi\)
0.172449 0.985019i \(-0.444832\pi\)
\(390\) 0 0
\(391\) 8.43457 14.6091i 0.0215718 0.0373634i
\(392\) 326.835 + 537.403i 0.833763 + 1.37093i
\(393\) 0 0
\(394\) −614.202 + 228.855i −1.55889 + 0.580849i
\(395\) 105.556 0.267230
\(396\) 0 0
\(397\) 777.319i 1.95798i 0.203902 + 0.978991i \(0.434637\pi\)
−0.203902 + 0.978991i \(0.565363\pi\)
\(398\) −429.652 + 160.091i −1.07953 + 0.402238i
\(399\) 0 0
\(400\) −574.019 + 228.924i −1.43505 + 0.572311i
\(401\) 433.690 + 250.391i 1.08152 + 0.624417i 0.931307 0.364236i \(-0.118670\pi\)
0.150215 + 0.988653i \(0.452003\pi\)
\(402\) 0 0
\(403\) 50.5599 29.1908i 0.125459 0.0724337i
\(404\) 400.767 + 139.003i 0.991997 + 0.344066i
\(405\) 0 0
\(406\) −3.84684 + 22.8302i −0.00947497 + 0.0562321i
\(407\) 108.328 62.5435i 0.266163 0.153669i
\(408\) 0 0
\(409\) −210.054 + 363.824i −0.513579 + 0.889546i 0.486297 + 0.873794i \(0.338347\pi\)
−0.999876 + 0.0157518i \(0.994986\pi\)
\(410\) −571.043 + 691.148i −1.39279 + 1.68573i
\(411\) 0 0
\(412\) 46.0629 + 239.849i 0.111803 + 0.582157i
\(413\) 579.540 1.40324
\(414\) 0 0
\(415\) 668.115 1.60992
\(416\) 68.2592 212.325i 0.164085 0.510397i
\(417\) 0 0
\(418\) 30.3271 36.7056i 0.0725529 0.0878125i
\(419\) 103.906 179.970i 0.247985 0.429523i −0.714981 0.699143i \(-0.753565\pi\)
0.962967 + 0.269620i \(0.0868982\pi\)
\(420\) 0 0
\(421\) −82.2587 + 47.4921i −0.195389 + 0.112808i −0.594503 0.804094i \(-0.702651\pi\)
0.399114 + 0.916901i \(0.369318\pi\)
\(422\) −308.674 52.0108i −0.731455 0.123248i
\(423\) 0 0
\(424\) 163.689 299.070i 0.386059 0.705354i
\(425\) −143.696 + 82.9632i −0.338109 + 0.195207i
\(426\) 0 0
\(427\) 485.044 + 280.040i 1.13594 + 0.655832i
\(428\) 21.2194 18.3622i 0.0495780 0.0429023i
\(429\) 0 0
\(430\) −320.634 860.520i −0.745660 2.00121i
\(431\) 239.645i 0.556021i −0.960578 0.278010i \(-0.910325\pi\)
0.960578 0.278010i \(-0.0896750\pi\)
\(432\) 0 0
\(433\) 41.9180 0.0968083 0.0484042 0.998828i \(-0.484586\pi\)
0.0484042 + 0.998828i \(0.484586\pi\)
\(434\) 177.350 66.0816i 0.408641 0.152262i
\(435\) 0 0
\(436\) 99.8303 + 115.364i 0.228969 + 0.264597i
\(437\) 22.0360 38.1676i 0.0504257 0.0873399i
\(438\) 0 0
\(439\) −265.485 459.834i −0.604749 1.04746i −0.992091 0.125521i \(-0.959940\pi\)
0.387342 0.921936i \(-0.373393\pi\)
\(440\) −64.9858 + 118.733i −0.147695 + 0.269848i
\(441\) 0 0
\(442\) 9.94971 59.0496i 0.0225107 0.133596i
\(443\) −146.570 253.866i −0.330857 0.573061i 0.651823 0.758371i \(-0.274004\pi\)
−0.982680 + 0.185310i \(0.940671\pi\)
\(444\) 0 0
\(445\) 725.509 + 418.873i 1.63036 + 0.941287i
\(446\) 371.428 + 306.883i 0.832798 + 0.688079i
\(447\) 0 0
\(448\) 332.574 641.981i 0.742353 1.43299i
\(449\) 268.273i 0.597491i 0.954333 + 0.298746i \(0.0965682\pi\)
−0.954333 + 0.298746i \(0.903432\pi\)
\(450\) 0 0
\(451\) 119.206i 0.264315i
\(452\) −547.940 + 105.232i −1.21226 + 0.232814i
\(453\) 0 0
\(454\) 137.393 + 113.517i 0.302627 + 0.250038i
\(455\) −543.894 314.017i −1.19537 0.690148i
\(456\) 0 0
\(457\) 372.941 + 645.954i 0.816064 + 1.41347i 0.908561 + 0.417752i \(0.137182\pi\)
−0.0924966 + 0.995713i \(0.529485\pi\)
\(458\) −329.368 55.4977i −0.719144 0.121174i
\(459\) 0 0
\(460\) −41.0554 + 118.369i −0.0892509 + 0.257324i
\(461\) 331.542 + 574.248i 0.719180 + 1.24566i 0.961325 + 0.275416i \(0.0888157\pi\)
−0.242145 + 0.970240i \(0.577851\pi\)
\(462\) 0 0
\(463\) −142.342 + 246.544i −0.307435 + 0.532493i −0.977800 0.209538i \(-0.932804\pi\)
0.670366 + 0.742031i \(0.266137\pi\)
\(464\) 15.2287 6.07336i 0.0328206 0.0130891i
\(465\) 0 0
\(466\) −95.3759 255.971i −0.204669 0.549293i
\(467\) 174.804 0.374313 0.187157 0.982330i \(-0.440073\pi\)
0.187157 + 0.982330i \(0.440073\pi\)
\(468\) 0 0
\(469\) 1111.29i 2.36948i
\(470\) −288.365 773.917i −0.613543 1.64663i
\(471\) 0 0
\(472\) −213.254 350.645i −0.451808 0.742892i
\(473\) −105.743 61.0508i −0.223558 0.129071i
\(474\) 0 0
\(475\) −375.420 + 216.749i −0.790357 + 0.456313i
\(476\) 63.6133 183.407i 0.133641 0.385309i
\(477\) 0 0
\(478\) −304.164 51.2509i −0.636327 0.107220i
\(479\) −621.273 + 358.692i −1.29702 + 0.748836i −0.979889 0.199545i \(-0.936054\pi\)
−0.317133 + 0.948381i \(0.602720\pi\)
\(480\) 0 0
\(481\) 205.504 355.943i 0.427243 0.740006i
\(482\) −98.4051 81.3047i −0.204160 0.168682i
\(483\) 0 0
\(484\) −87.8897 457.640i −0.181590 0.945537i
\(485\) 152.220 0.313855
\(486\) 0 0
\(487\) 668.869 1.37345 0.686724 0.726919i \(-0.259048\pi\)
0.686724 + 0.726919i \(0.259048\pi\)
\(488\) −9.04622 396.518i −0.0185373 0.812537i
\(489\) 0 0
\(490\) −966.930 798.901i −1.97333 1.63041i
\(491\) −87.6907 + 151.885i −0.178596 + 0.309337i −0.941400 0.337293i \(-0.890489\pi\)
0.762804 + 0.646630i \(0.223822\pi\)
\(492\) 0 0
\(493\) 3.81227 2.20101i 0.00773279 0.00446453i
\(494\) 25.9945 154.272i 0.0526204 0.312292i
\(495\) 0 0
\(496\) −105.242 82.9880i −0.212181 0.167314i
\(497\) 307.898 177.765i 0.619512 0.357676i
\(498\) 0 0
\(499\) −455.645 263.067i −0.913116 0.527188i −0.0316835 0.999498i \(-0.510087\pi\)
−0.881432 + 0.472310i \(0.843420\pi\)
\(500\) 328.702 284.442i 0.657403 0.568884i
\(501\) 0 0
\(502\) −186.688 + 69.5608i −0.371888 + 0.138567i
\(503\) 94.2248i 0.187326i −0.995604 0.0936629i \(-0.970142\pi\)
0.995604 0.0936629i \(-0.0298576\pi\)
\(504\) 0 0
\(505\) −845.881 −1.67501
\(506\) 5.81639 + 15.6101i 0.0114949 + 0.0308500i
\(507\) 0 0
\(508\) −34.2294 + 29.6204i −0.0673807 + 0.0583080i
\(509\) 321.839 557.442i 0.632297 1.09517i −0.354784 0.934948i \(-0.615445\pi\)
0.987081 0.160223i \(-0.0512212\pi\)
\(510\) 0 0
\(511\) 482.788 + 836.213i 0.944790 + 1.63642i
\(512\) −510.802 + 35.0091i −0.997660 + 0.0683772i
\(513\) 0 0
\(514\) −588.233 99.1157i −1.14442 0.192832i
\(515\) −243.513 421.778i −0.472842 0.818986i
\(516\) 0 0
\(517\) −95.1011 54.9066i −0.183948 0.106202i
\(518\) 848.668 1027.16i 1.63836 1.98294i
\(519\) 0 0
\(520\) 10.1438 + 444.627i 0.0195073 + 0.855052i
\(521\) 124.089i 0.238174i −0.992884 0.119087i \(-0.962003\pi\)
0.992884 0.119087i \(-0.0379967\pi\)
\(522\) 0 0
\(523\) 570.827i 1.09145i 0.837965 + 0.545724i \(0.183745\pi\)
−0.837965 + 0.545724i \(0.816255\pi\)
\(524\) 51.0908 + 266.028i 0.0975014 + 0.507688i
\(525\) 0 0
\(526\) −38.8865 + 47.0653i −0.0739287 + 0.0894777i
\(527\) −31.1642 17.9926i −0.0591351 0.0341417i
\(528\) 0 0
\(529\) −256.790 444.774i −0.485426 0.840782i
\(530\) −112.963 + 670.415i −0.213138 + 1.26493i
\(531\) 0 0
\(532\) 166.195 479.167i 0.312397 0.900689i
\(533\) 195.842 + 339.208i 0.367433 + 0.636413i
\(534\) 0 0
\(535\) −27.9787 + 48.4605i −0.0522966 + 0.0905804i
\(536\) −672.373 + 408.921i −1.25443 + 0.762912i
\(537\) 0 0
\(538\) −408.732 + 152.296i −0.759725 + 0.283077i
\(539\) −166.771 −0.309409
\(540\) 0 0
\(541\) 380.160i 0.702699i 0.936244 + 0.351350i \(0.114277\pi\)
−0.936244 + 0.351350i \(0.885723\pi\)
\(542\) −643.708 + 239.849i −1.18765 + 0.442525i
\(543\) 0 0
\(544\) −134.376 + 28.9997i −0.247015 + 0.0533083i
\(545\) −263.467 152.113i −0.483425 0.279106i
\(546\) 0 0
\(547\) −610.683 + 352.578i −1.11642 + 0.644567i −0.940485 0.339835i \(-0.889629\pi\)
−0.175937 + 0.984401i \(0.556296\pi\)
\(548\) 18.8040 54.2149i 0.0343139 0.0989322i
\(549\) 0 0
\(550\) 27.2253 161.577i 0.0495005 0.293776i
\(551\) 9.95988 5.75034i 0.0180760 0.0104362i
\(552\) 0 0
\(553\) 74.7493 129.470i 0.135170 0.234122i
\(554\) 162.487 196.662i 0.293298 0.354985i
\(555\) 0 0
\(556\) 829.235 159.255i 1.49143 0.286429i
\(557\) 450.847 0.809420 0.404710 0.914445i \(-0.367372\pi\)
0.404710 + 0.914445i \(0.367372\pi\)
\(558\) 0 0
\(559\) −401.198 −0.717707
\(560\) −207.068 + 1426.82i −0.369764 + 2.54789i
\(561\) 0 0
\(562\) −494.610 + 598.638i −0.880088 + 1.06519i
\(563\) 50.2105 86.9671i 0.0891838 0.154471i −0.817983 0.575243i \(-0.804907\pi\)
0.907166 + 0.420772i \(0.138241\pi\)
\(564\) 0 0
\(565\) 963.561 556.312i 1.70542 0.984624i
\(566\) −491.851 82.8756i −0.868994 0.146423i
\(567\) 0 0
\(568\) −220.852 120.878i −0.388824 0.212814i
\(569\) 149.043 86.0498i 0.261938 0.151230i −0.363280 0.931680i \(-0.618343\pi\)
0.625218 + 0.780450i \(0.285010\pi\)
\(570\) 0 0
\(571\) 406.657 + 234.784i 0.712184 + 0.411180i 0.811869 0.583839i \(-0.198450\pi\)
−0.0996851 + 0.995019i \(0.531784\pi\)
\(572\) 38.6952 + 44.7162i 0.0676489 + 0.0781752i
\(573\) 0 0
\(574\) 443.343 + 1189.85i 0.772375 + 2.07291i
\(575\) 151.667i 0.263770i
\(576\) 0 0
\(577\) 402.048 0.696791 0.348395 0.937348i \(-0.386727\pi\)
0.348395 + 0.937348i \(0.386727\pi\)
\(578\) 507.036 188.924i 0.877226 0.326859i
\(579\) 0 0
\(580\) −24.7224 + 21.3936i −0.0426249 + 0.0368855i
\(581\) 473.125 819.476i 0.814329 1.41046i
\(582\) 0 0
\(583\) 45.1984 + 78.2859i 0.0775273 + 0.134281i
\(584\) 328.291 599.808i 0.562142 1.02707i
\(585\) 0 0
\(586\) −37.2477 + 221.058i −0.0635626 + 0.377232i
\(587\) −159.999 277.126i −0.272570 0.472105i 0.696949 0.717121i \(-0.254540\pi\)
−0.969519 + 0.245015i \(0.921207\pi\)
\(588\) 0 0
\(589\) −81.4192 47.0074i −0.138233 0.0798088i
\(590\) 630.903 + 521.267i 1.06933 + 0.883504i
\(591\) 0 0
\(592\) −933.760 135.512i −1.57730 0.228906i
\(593\) 700.450i 1.18120i −0.806965 0.590599i \(-0.798892\pi\)
0.806965 0.590599i \(-0.201108\pi\)
\(594\) 0 0
\(595\) 387.109i 0.650603i
\(596\) −138.214 719.677i −0.231902 1.20751i
\(597\) 0 0
\(598\) 42.1965 + 34.8638i 0.0705628 + 0.0583007i
\(599\) 461.232 + 266.292i 0.770003 + 0.444561i 0.832876 0.553460i \(-0.186693\pi\)
−0.0628729 + 0.998022i \(0.520026\pi\)
\(600\) 0 0
\(601\) −440.321 762.658i −0.732647 1.26898i −0.955748 0.294187i \(-0.904951\pi\)
0.223101 0.974795i \(-0.428382\pi\)
\(602\) −1282.53 216.102i −2.13044 0.358974i
\(603\) 0 0
\(604\) 596.844 + 207.011i 0.988153 + 0.342733i
\(605\) 464.632 + 804.766i 0.767987 + 1.33019i
\(606\) 0 0
\(607\) −180.816 + 313.182i −0.297884 + 0.515951i −0.975652 0.219326i \(-0.929614\pi\)
0.677767 + 0.735276i \(0.262948\pi\)
\(608\) −351.070 + 75.7643i −0.577418 + 0.124612i
\(609\) 0 0
\(610\) 276.150 + 741.133i 0.452705 + 1.21497i
\(611\) −360.822 −0.590543
\(612\) 0 0
\(613\) 237.930i 0.388140i 0.980988 + 0.194070i \(0.0621689\pi\)
−0.980988 + 0.194070i \(0.937831\pi\)
\(614\) 296.802 + 796.559i 0.483390 + 1.29733i
\(615\) 0 0
\(616\) 99.6124 + 163.789i 0.161708 + 0.265891i
\(617\) −182.219 105.204i −0.295331 0.170510i 0.345012 0.938598i \(-0.387875\pi\)
−0.640344 + 0.768089i \(0.721208\pi\)
\(618\) 0 0
\(619\) −117.749 + 67.9823i −0.190224 + 0.109826i −0.592088 0.805874i \(-0.701696\pi\)
0.401863 + 0.915700i \(0.368363\pi\)
\(620\) 252.505 + 87.5796i 0.407267 + 0.141257i
\(621\) 0 0
\(622\) 585.777 + 98.7020i 0.941764 + 0.158685i
\(623\) 1027.54 593.248i 1.64934 0.952244i
\(624\) 0 0
\(625\) 49.3927 85.5507i 0.0790284 0.136881i
\(626\) −311.975 257.762i −0.498363 0.411760i
\(627\) 0 0
\(628\) 625.103 120.051i 0.995387 0.191164i
\(629\) −253.337 −0.402762
\(630\) 0 0
\(631\) 368.187 0.583498 0.291749 0.956495i \(-0.405763\pi\)
0.291749 + 0.956495i \(0.405763\pi\)
\(632\) −105.840 + 2.41465i −0.167468 + 0.00382064i
\(633\) 0 0
\(634\) −66.0576 54.5784i −0.104192 0.0860858i
\(635\) 45.1330 78.1726i 0.0710756 0.123106i
\(636\) 0 0
\(637\) −474.559 + 273.986i −0.744990 + 0.430120i
\(638\) −0.722287 + 4.28663i −0.00113211 + 0.00671886i
\(639\) 0 0
\(640\) 939.479 399.743i 1.46794 0.624599i
\(641\) −212.362 + 122.607i −0.331297 + 0.191275i −0.656417 0.754398i \(-0.727929\pi\)
0.325120 + 0.945673i \(0.394595\pi\)
\(642\) 0 0
\(643\) −1052.52 607.675i −1.63690 0.945062i −0.981893 0.189435i \(-0.939334\pi\)
−0.655002 0.755627i \(-0.727332\pi\)
\(644\) 116.112 + 134.179i 0.180298 + 0.208353i
\(645\) 0 0
\(646\) −90.3621 + 33.6694i −0.139879 + 0.0521198i
\(647\) 887.961i 1.37243i 0.727399 + 0.686214i \(0.240729\pi\)
−0.727399 + 0.686214i \(0.759271\pi\)
\(648\) 0 0
\(649\) 108.815 0.167666
\(650\) −187.981 504.505i −0.289202 0.776162i
\(651\) 0 0
\(652\) 333.576 + 385.481i 0.511620 + 0.591229i
\(653\) −467.477 + 809.694i −0.715891 + 1.23996i 0.246723 + 0.969086i \(0.420646\pi\)
−0.962615 + 0.270874i \(0.912687\pi\)
\(654\) 0 0
\(655\) −270.093 467.815i −0.412356 0.714221i
\(656\) 556.769 706.070i 0.848733 1.07633i
\(657\) 0 0
\(658\) −1153.45 194.354i −1.75297 0.295371i
\(659\) −449.326 778.255i −0.681830 1.18096i −0.974422 0.224727i \(-0.927851\pi\)
0.292592 0.956237i \(-0.405482\pi\)
\(660\) 0 0
\(661\) −169.415 97.8116i −0.256301 0.147975i 0.366345 0.930479i \(-0.380609\pi\)
−0.622646 + 0.782504i \(0.713942\pi\)
\(662\) −272.112 + 329.344i −0.411045 + 0.497498i
\(663\) 0 0
\(664\) −669.912 + 15.2835i −1.00890 + 0.0230173i
\(665\) 1011.36i 1.52084i
\(666\) 0 0
\(667\) 4.02374i 0.00603259i
\(668\) 67.9268 13.0453i 0.101687 0.0195290i
\(669\) 0 0
\(670\) 999.547 1209.78i 1.49186 1.80564i
\(671\) 91.0725 + 52.5807i 0.135726 + 0.0783617i
\(672\) 0 0
\(673\) 417.087 + 722.416i 0.619743 + 1.07343i 0.989532 + 0.144311i \(0.0460967\pi\)
−0.369789 + 0.929116i \(0.620570\pi\)
\(674\) 74.0324 439.368i 0.109840 0.651882i
\(675\) 0 0
\(676\) −455.101 157.848i −0.673227 0.233504i
\(677\) 61.6931 + 106.856i 0.0911272 + 0.157837i 0.907986 0.419001i \(-0.137620\pi\)
−0.816859 + 0.576838i \(0.804286\pi\)
\(678\) 0 0
\(679\) 107.794 186.705i 0.158754 0.274970i
\(680\) 234.217 142.445i 0.344436 0.209478i
\(681\) 0 0
\(682\) 33.2995 12.4076i 0.0488262 0.0181929i
\(683\) 799.370 1.17038 0.585191 0.810896i \(-0.301020\pi\)
0.585191 + 0.810896i \(0.301020\pi\)
\(684\) 0 0
\(685\) 114.429i 0.167050i
\(686\) −627.187 + 233.693i −0.914266 + 0.340660i
\(687\) 0 0
\(688\) 341.181 + 855.499i 0.495903 + 1.24346i
\(689\) 257.230 + 148.512i 0.373338 + 0.215547i
\(690\) 0 0
\(691\) 581.995 336.015i 0.842250 0.486273i −0.0157784 0.999876i \(-0.505023\pi\)
0.858028 + 0.513602i \(0.171689\pi\)
\(692\) 926.695 + 321.417i 1.33915 + 0.464476i
\(693\) 0 0
\(694\) −48.0841 + 285.370i −0.0692854 + 0.411196i
\(695\) −1458.22 + 841.905i −2.09816 + 1.21137i
\(696\) 0 0
\(697\) 120.713 209.081i 0.173190 0.299973i
\(698\) −281.559 + 340.778i −0.403380 + 0.488221i
\(699\) 0 0
\(700\) −329.179 1714.03i −0.470255 2.44861i
\(701\) −345.561 −0.492954 −0.246477 0.969149i \(-0.579273\pi\)
−0.246477 + 0.969149i \(0.579273\pi\)
\(702\) 0 0
\(703\) −661.866 −0.941488
\(704\) 62.4445 120.539i 0.0886996 0.171220i
\(705\) 0 0
\(706\) 882.860 1068.55i 1.25051 1.51352i
\(707\) −599.009 + 1037.51i −0.847255 + 1.46749i
\(708\) 0 0
\(709\) 1200.93 693.354i 1.69383 0.977933i 0.742455 0.669896i \(-0.233661\pi\)
0.951374 0.308037i \(-0.0996721\pi\)
\(710\) 495.076 + 83.4191i 0.697290 + 0.117492i
\(711\) 0 0
\(712\) −737.042 403.403i −1.03517 0.566577i
\(713\) 28.4861 16.4465i 0.0399524 0.0230665i
\(714\) 0 0
\(715\) −102.122 58.9603i −0.142828 0.0824619i
\(716\) 743.710 643.570i 1.03870 0.898841i
\(717\) 0 0
\(718\) 200.940 + 539.285i 0.279861 + 0.751093i
\(719\) 226.454i 0.314956i −0.987522 0.157478i \(-0.949664\pi\)
0.987522 0.157478i \(-0.0503364\pi\)
\(720\) 0 0
\(721\) −689.775 −0.956692
\(722\) 440.482 164.126i 0.610086 0.227321i
\(723\) 0 0
\(724\) 140.577 + 162.451i 0.194167 + 0.224380i
\(725\) 19.7889 34.2754i 0.0272951 0.0472765i
\(726\) 0 0
\(727\) −348.940 604.381i −0.479972 0.831336i 0.519764 0.854310i \(-0.326020\pi\)
−0.999736 + 0.0229740i \(0.992687\pi\)
\(728\) 552.540 + 302.420i 0.758984 + 0.415412i
\(729\) 0 0
\(730\) −226.556 + 1344.57i −0.310351 + 1.84187i
\(731\) 123.646 + 214.160i 0.169146 + 0.292969i
\(732\) 0 0
\(733\) 174.486 + 100.740i 0.238044 + 0.137435i 0.614278 0.789090i \(-0.289448\pi\)
−0.376233 + 0.926525i \(0.622781\pi\)
\(734\) −1012.74 836.751i −1.37976 1.13999i
\(735\) 0 0
\(736\) 38.4581 119.627i 0.0522528 0.162536i
\(737\) 208.656i 0.283116i
\(738\) 0 0
\(739\) 914.779i 1.23786i −0.785446 0.618930i \(-0.787566\pi\)
0.785446 0.618930i \(-0.212434\pi\)
\(740\) 1847.77 354.863i 2.49698 0.479545i
\(741\) 0 0
\(742\) 742.302 + 613.309i 1.00041 + 0.826561i
\(743\) 727.202 + 419.850i 0.978738 + 0.565074i 0.901889 0.431968i \(-0.142181\pi\)
0.0768489 + 0.997043i \(0.475514\pi\)
\(744\) 0 0
\(745\) 730.673 + 1265.56i 0.980769 + 1.69874i
\(746\) 730.785 + 123.136i 0.979605 + 0.165061i
\(747\) 0 0
\(748\) 11.9441 34.4367i 0.0159681 0.0460384i
\(749\) 39.6261 + 68.6344i 0.0529054 + 0.0916348i
\(750\) 0 0
\(751\) −92.3794 + 160.006i −0.123008 + 0.213057i −0.920953 0.389674i \(-0.872588\pi\)
0.797944 + 0.602731i \(0.205921\pi\)
\(752\) 306.845 + 769.402i 0.408038 + 1.02314i
\(753\) 0 0
\(754\) 4.98714 + 13.3845i 0.00661424 + 0.0177514i
\(755\) −1259.73 −1.66852
\(756\) 0 0
\(757\) 549.800i 0.726288i −0.931733 0.363144i \(-0.881703\pi\)
0.931733 0.363144i \(-0.118297\pi\)
\(758\) −421.522 1131.28i −0.556098 1.49246i
\(759\) 0 0
\(760\) 611.911 372.149i 0.805146 0.489670i
\(761\) 454.835 + 262.599i 0.597680 + 0.345071i 0.768128 0.640296i \(-0.221188\pi\)
−0.170448 + 0.985367i \(0.554522\pi\)
\(762\) 0 0
\(763\) −373.147 + 215.437i −0.489053 + 0.282355i
\(764\) −315.647 + 910.059i −0.413151 + 1.19118i
\(765\) 0 0
\(766\) −649.740 109.480i −0.848225 0.142924i
\(767\) 309.640 178.771i 0.403703 0.233078i
\(768\) 0 0
\(769\) 70.7173 122.486i 0.0919601 0.159280i −0.816376 0.577521i \(-0.804020\pi\)
0.908336 + 0.418242i \(0.137353\pi\)
\(770\) −294.700 243.488i −0.382727 0.316218i
\(771\) 0 0
\(772\) 188.453 + 981.268i 0.244110 + 1.27107i
\(773\) −746.557 −0.965792 −0.482896 0.875678i \(-0.660415\pi\)
−0.482896 + 0.875678i \(0.660415\pi\)
\(774\) 0 0
\(775\) −323.538 −0.417468
\(776\) −152.629 + 3.48210i −0.196687 + 0.00448724i
\(777\) 0 0
\(778\) −919.836 759.991i −1.18231 0.976852i
\(779\) 315.374 546.244i 0.404845 0.701211i
\(780\) 0 0
\(781\) 57.8112 33.3773i 0.0740220 0.0427366i
\(782\) 5.60579 33.2693i 0.00716853 0.0425439i
\(783\) 0 0
\(784\) 987.805 + 778.931i 1.25996 + 0.993534i
\(785\) −1099.25 + 634.654i −1.40032 + 0.808477i
\(786\) 0 0
\(787\) 515.762 + 297.776i 0.655352 + 0.378368i 0.790504 0.612457i \(-0.209819\pi\)
−0.135151 + 0.990825i \(0.543152\pi\)
\(788\) −991.282 + 857.807i −1.25797 + 1.08859i
\(789\) 0 0
\(790\) 197.825 73.7108i 0.250412 0.0933048i
\(791\) 1575.81i 1.99217i
\(792\) 0 0
\(793\) 345.537 0.435734
\(794\) 542.810 + 1456.80i 0.683639 + 1.83476i
\(795\) 0 0
\(796\) −693.431 + 600.061i −0.871145 + 0.753845i
\(797\) −329.698 + 571.054i −0.413674 + 0.716504i −0.995288 0.0969605i \(-0.969088\pi\)
0.581614 + 0.813465i \(0.302421\pi\)
\(798\) 0 0
\(799\) 111.202 + 192.607i 0.139176 + 0.241060i
\(800\) −915.927 + 829.877i −1.14491 + 1.03735i
\(801\) 0 0
\(802\) 987.643 + 166.415i 1.23147 + 0.207500i
\(803\) 90.6488 + 157.008i 0.112888 + 0.195527i
\(804\) 0 0
\(805\) −306.437 176.921i −0.380667 0.219778i
\(806\) 74.3716 90.0138i 0.0922725 0.111680i
\(807\) 0 0
\(808\) 848.156 19.3500i 1.04970 0.0239480i
\(809\) 1442.15i 1.78263i −0.453382 0.891317i \(-0.649783\pi\)
0.453382 0.891317i \(-0.350217\pi\)
\(810\) 0 0
\(811\) 907.692i 1.11923i 0.828754 + 0.559613i \(0.189050\pi\)
−0.828754 + 0.559613i \(0.810950\pi\)
\(812\) 8.73311 + 45.4731i 0.0107551 + 0.0560014i
\(813\) 0 0
\(814\) 159.347 192.861i 0.195758 0.236931i
\(815\) −880.356 508.274i −1.08019 0.623649i
\(816\) 0 0
\(817\) 323.035 + 559.513i 0.395391 + 0.684838i
\(818\) −139.606 + 828.537i −0.170668 + 1.01288i
\(819\) 0 0
\(820\) −587.574 + 1694.07i −0.716554 + 2.06593i
\(821\) −775.205 1342.69i −0.944221 1.63544i −0.757304 0.653063i \(-0.773484\pi\)
−0.186917 0.982376i \(-0.559850\pi\)
\(822\) 0 0
\(823\) 332.778 576.389i 0.404348 0.700351i −0.589898 0.807478i \(-0.700832\pi\)
0.994245 + 0.107127i \(0.0341652\pi\)
\(824\) 253.817 + 417.342i 0.308030 + 0.506482i
\(825\) 0 0
\(826\) 1086.13 404.698i 1.31493 0.489950i
\(827\) −911.934 −1.10270 −0.551351 0.834274i \(-0.685887\pi\)
−0.551351 + 0.834274i \(0.685887\pi\)
\(828\) 0 0
\(829\) 463.817i 0.559489i −0.960074 0.279745i \(-0.909750\pi\)
0.960074 0.279745i \(-0.0902498\pi\)
\(830\) 1252.14 466.552i 1.50860 0.562111i
\(831\) 0 0
\(832\) −20.3421 445.591i −0.0244497 0.535566i
\(833\) 292.509 + 168.880i 0.351151 + 0.202737i
\(834\) 0 0
\(835\) −119.450 + 68.9647i −0.143054 + 0.0825924i
\(836\) 31.2050 89.9689i 0.0373266 0.107618i
\(837\) 0 0
\(838\) 69.0580 409.846i 0.0824082 0.489076i
\(839\) −54.8140 + 31.6469i −0.0653326 + 0.0377198i −0.532310 0.846549i \(-0.678676\pi\)
0.466978 + 0.884269i \(0.345343\pi\)
\(840\) 0 0
\(841\) 419.975 727.418i 0.499376 0.864944i
\(842\) −120.999 + 146.448i −0.143705 + 0.173929i
\(843\) 0 0
\(844\) −614.815 + 118.075i −0.728454 + 0.139899i
\(845\) 960.563 1.13676
\(846\) 0 0
\(847\) 1316.11 1.55385
\(848\) 97.9310 674.802i 0.115485 0.795758i
\(849\) 0 0
\(850\) −211.372 + 255.828i −0.248673 + 0.300975i
\(851\) 115.783 200.543i 0.136056 0.235655i
\(852\) 0 0
\(853\) −396.697 + 229.033i −0.465061 + 0.268503i −0.714170 0.699972i \(-0.753196\pi\)
0.249109 + 0.968475i \(0.419862\pi\)
\(854\) 1104.59 + 186.121i 1.29343 + 0.217940i
\(855\) 0 0
\(856\) 26.9454 49.2308i 0.0314782 0.0575127i
\(857\) 1107.08 639.171i 1.29181 0.745824i 0.312831 0.949809i \(-0.398723\pi\)
0.978974 + 0.203984i \(0.0653892\pi\)
\(858\) 0 0
\(859\) −363.697 209.981i −0.423396 0.244448i 0.273133 0.961976i \(-0.411940\pi\)
−0.696529 + 0.717528i \(0.745273\pi\)
\(860\) −1201.82 1388.82i −1.39746 1.61491i
\(861\) 0 0
\(862\) −167.346 449.126i −0.194137 0.521028i
\(863\) 918.683i 1.06452i 0.846580 + 0.532261i \(0.178658\pi\)
−0.846580 + 0.532261i \(0.821342\pi\)
\(864\) 0 0
\(865\) −1955.94 −2.26120
\(866\) 78.5598 29.2718i 0.0907157 0.0338011i
\(867\) 0 0
\(868\) 286.232 247.691i 0.329760 0.285358i
\(869\) 14.0350 24.3093i 0.0161508 0.0279739i
\(870\) 0 0
\(871\) −342.799 593.745i −0.393570 0.681682i
\(872\) 267.655 + 146.495i 0.306944 + 0.167999i
\(873\) 0 0
\(874\) 14.6456 86.9189i 0.0167570 0.0994496i
\(875\) 613.834 + 1063.19i 0.701524 + 1.21508i
\(876\) 0 0
\(877\) −1104.62 637.754i −1.25955 0.727200i −0.286561 0.958062i \(-0.592512\pi\)
−0.972986 + 0.230862i \(0.925845\pi\)
\(878\) −818.660 676.397i −0.932414 0.770384i
\(879\) 0 0
\(880\) −38.8793 + 267.902i −0.0441811 + 0.304434i
\(881\) 211.510i 0.240079i 0.992769 + 0.120039i \(0.0383021\pi\)
−0.992769 + 0.120039i \(0.961698\pi\)
\(882\) 0 0
\(883\) 613.635i 0.694943i −0.937690 0.347472i \(-0.887040\pi\)
0.937690 0.347472i \(-0.112960\pi\)
\(884\) −22.5879 117.615i −0.0255519 0.133048i
\(885\) 0 0
\(886\) −451.968 373.427i −0.510122 0.421475i
\(887\) 978.062 + 564.684i 1.10266 + 0.636623i 0.936919 0.349546i \(-0.113664\pi\)
0.165744 + 0.986169i \(0.446997\pi\)
\(888\) 0 0
\(889\) −63.9217 110.716i −0.0719029 0.124540i
\(890\) 1652.20 + 278.392i 1.85641 + 0.312800i
\(891\) 0 0
\(892\) 910.404 + 315.767i 1.02063 + 0.353999i
\(893\) 290.525 + 503.203i 0.325335 + 0.563498i
\(894\) 0 0
\(895\) −980.615 + 1698.47i −1.09566 + 1.89774i
\(896\) 174.986 1435.39i 0.195297 1.60200i
\(897\) 0 0
\(898\) 187.338 + 502.779i 0.208617 + 0.559888i
\(899\) 8.58345 0.00954778
\(900\) 0 0
\(901\) 183.080i 0.203196i
\(902\) 83.2427 + 223.407i 0.0922868 + 0.247680i
\(903\) 0 0
\(904\) −953.427 + 579.851i −1.05468 + 0.641428i
\(905\) −371.003 214.199i −0.409948 0.236684i
\(906\) 0 0
\(907\) 515.588 297.675i 0.568454 0.328197i −0.188078 0.982154i \(-0.560226\pi\)
0.756532 + 0.653957i \(0.226892\pi\)
\(908\) 336.762 + 116.803i 0.370883 + 0.128638i
\(909\) 0 0
\(910\) −1238.61 208.703i −1.36111 0.229344i
\(911\) 316.089 182.494i 0.346969 0.200323i −0.316381 0.948632i \(-0.602468\pi\)
0.663349 + 0.748310i \(0.269134\pi\)
\(912\) 0 0
\(913\) 88.8345 153.866i 0.0972995 0.168528i
\(914\) 1150.02 + 950.172i 1.25822 + 1.03958i
\(915\) 0 0
\(916\) −656.033 + 125.991i −0.716193 + 0.137545i
\(917\) −765.064 −0.834312
\(918\) 0 0
\(919\) 317.896 0.345915 0.172957 0.984929i \(-0.444668\pi\)
0.172957 + 0.984929i \(0.444668\pi\)
\(920\) 5.71514 + 250.509i 0.00621211 + 0.272292i
\(921\) 0 0
\(922\) 1022.36 + 844.695i 1.10885 + 0.916156i
\(923\) 109.670 189.955i 0.118819 0.205801i
\(924\) 0 0
\(925\) −1972.56 + 1138.86i −2.13249 + 1.23120i
\(926\) −94.6038 + 561.455i −0.102164 + 0.606323i
\(927\) 0 0
\(928\) 24.2995 22.0166i 0.0261849 0.0237248i
\(929\) −1405.17 + 811.273i −1.51256 + 0.873276i −0.512666 + 0.858588i \(0.671342\pi\)
−0.999892 + 0.0146874i \(0.995325\pi\)
\(930\) 0 0
\(931\) 764.205 + 441.214i 0.820844 + 0.473914i
\(932\) −357.494 413.120i −0.383577 0.443262i
\(933\) 0 0
\(934\) 327.606 122.068i 0.350756 0.130693i
\(935\) 72.6840i 0.0777369i
\(936\) 0 0
\(937\) −935.489 −0.998387 −0.499194 0.866490i \(-0.666370\pi\)
−0.499194 + 0.866490i \(0.666370\pi\)
\(938\) −776.023 2082.70i −0.827316 2.22036i
\(939\) 0 0
\(940\) −1080.87 1249.05i −1.14986 1.32878i
\(941\) 344.673 596.990i 0.366283 0.634421i −0.622698 0.782462i \(-0.713963\pi\)
0.988981 + 0.148041i \(0.0472968\pi\)
\(942\) 0 0
\(943\) 110.340 + 191.114i 0.117009 + 0.202666i
\(944\) −644.524 508.237i −0.682758 0.538387i
\(945\) 0 0
\(946\) −240.809 40.5757i −0.254555 0.0428918i
\(947\) 571.731 + 990.266i 0.603728 + 1.04569i 0.992251 + 0.124249i \(0.0396521\pi\)
−0.388523 + 0.921439i \(0.627015\pi\)
\(948\) 0 0
\(949\) 515.894 + 297.851i 0.543618 + 0.313858i
\(950\) −552.227 + 668.374i −0.581292 + 0.703552i
\(951\) 0 0
\(952\) −8.85532 388.150i −0.00930180 0.407721i
\(953\) 1635.29i 1.71594i 0.513697 + 0.857972i \(0.328276\pi\)
−0.513697 + 0.857972i \(0.671724\pi\)
\(954\) 0 0
\(955\) 1920.82i 2.01133i
\(956\) −605.833 + 116.350i −0.633716 + 0.121705i
\(957\) 0 0
\(958\) −913.869 + 1106.08i −0.953934 + 1.15457i
\(959\) 140.353 + 81.0327i 0.146353 + 0.0844971i
\(960\) 0 0
\(961\) 445.416 + 771.484i 0.463493 + 0.802793i
\(962\) 136.582 810.589i 0.141977 0.842608i
\(963\) 0 0
\(964\) −241.200 83.6584i −0.250207 0.0867825i
\(965\) −996.261 1725.58i −1.03240 1.78816i
\(966\) 0 0
\(967\) −524.608 + 908.647i −0.542510 + 0.939656i 0.456249 + 0.889852i \(0.349193\pi\)
−0.998759 + 0.0498033i \(0.984141\pi\)
\(968\) −484.291 796.302i −0.500301 0.822626i
\(969\) 0 0
\(970\) 285.279 106.296i 0.294102 0.109584i
\(971\) 1469.41 1.51329 0.756646 0.653824i \(-0.226836\pi\)
0.756646 + 0.653824i \(0.226836\pi\)
\(972\) 0 0
\(973\) 2384.77i 2.45095i
\(974\) 1253.55 467.078i 1.28701 0.479546i
\(975\) 0 0
\(976\) −293.846 736.809i −0.301072 0.754927i
\(977\) 517.184 + 298.596i 0.529359 + 0.305626i 0.740756 0.671775i \(-0.234468\pi\)
−0.211396 + 0.977400i \(0.567801\pi\)
\(978\) 0 0
\(979\) 192.931 111.389i 0.197070 0.113778i
\(980\) −2370.03 822.028i −2.41840 0.838804i
\(981\) 0 0
\(982\) −58.2811 + 345.887i −0.0593494 + 0.352227i
\(983\) −1503.96 + 868.311i −1.52997 + 0.883328i −0.530606 + 0.847619i \(0.678036\pi\)
−0.999362 + 0.0357088i \(0.988631\pi\)
\(984\) 0 0
\(985\) 1307.05 2263.88i 1.32695 2.29835i
\(986\) 5.60769 6.78713i 0.00568732 0.00688350i
\(987\) 0 0
\(988\) −59.0128 307.278i −0.0597296 0.311011i
\(989\) −226.040 −0.228554
\(990\) 0 0
\(991\) 506.650 0.511251 0.255626 0.966776i \(-0.417719\pi\)
0.255626 + 0.966776i \(0.417719\pi\)
\(992\) −255.188 82.0389i −0.257246 0.0827005i
\(993\) 0 0
\(994\) 452.905 548.162i 0.455639 0.551471i
\(995\) 914.319 1583.65i 0.918914 1.59161i
\(996\) 0 0
\(997\) −420.474 + 242.761i −0.421739 + 0.243491i −0.695821 0.718215i \(-0.744959\pi\)
0.274082 + 0.961706i \(0.411626\pi\)
\(998\) −1037.64 174.840i −1.03972 0.175190i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 216.3.j.a.125.19 44
3.2 odd 2 72.3.j.a.5.4 44
4.3 odd 2 864.3.n.a.17.2 44
8.3 odd 2 864.3.n.a.17.21 44
8.5 even 2 inner 216.3.j.a.125.17 44
9.2 odd 6 inner 216.3.j.a.197.17 44
9.4 even 3 648.3.h.a.485.20 44
9.5 odd 6 648.3.h.a.485.25 44
9.7 even 3 72.3.j.a.29.6 yes 44
12.11 even 2 288.3.n.a.113.9 44
24.5 odd 2 72.3.j.a.5.6 yes 44
24.11 even 2 288.3.n.a.113.14 44
36.7 odd 6 288.3.n.a.209.14 44
36.11 even 6 864.3.n.a.305.21 44
36.23 even 6 2592.3.h.a.1457.4 44
36.31 odd 6 2592.3.h.a.1457.42 44
72.5 odd 6 648.3.h.a.485.19 44
72.11 even 6 864.3.n.a.305.2 44
72.13 even 6 648.3.h.a.485.26 44
72.29 odd 6 inner 216.3.j.a.197.19 44
72.43 odd 6 288.3.n.a.209.9 44
72.59 even 6 2592.3.h.a.1457.41 44
72.61 even 6 72.3.j.a.29.4 yes 44
72.67 odd 6 2592.3.h.a.1457.3 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
72.3.j.a.5.4 44 3.2 odd 2
72.3.j.a.5.6 yes 44 24.5 odd 2
72.3.j.a.29.4 yes 44 72.61 even 6
72.3.j.a.29.6 yes 44 9.7 even 3
216.3.j.a.125.17 44 8.5 even 2 inner
216.3.j.a.125.19 44 1.1 even 1 trivial
216.3.j.a.197.17 44 9.2 odd 6 inner
216.3.j.a.197.19 44 72.29 odd 6 inner
288.3.n.a.113.9 44 12.11 even 2
288.3.n.a.113.14 44 24.11 even 2
288.3.n.a.209.9 44 72.43 odd 6
288.3.n.a.209.14 44 36.7 odd 6
648.3.h.a.485.19 44 72.5 odd 6
648.3.h.a.485.20 44 9.4 even 3
648.3.h.a.485.25 44 9.5 odd 6
648.3.h.a.485.26 44 72.13 even 6
864.3.n.a.17.2 44 4.3 odd 2
864.3.n.a.17.21 44 8.3 odd 2
864.3.n.a.305.2 44 72.11 even 6
864.3.n.a.305.21 44 36.11 even 6
2592.3.h.a.1457.3 44 72.67 odd 6
2592.3.h.a.1457.4 44 36.23 even 6
2592.3.h.a.1457.41 44 72.59 even 6
2592.3.h.a.1457.42 44 36.31 odd 6