Properties

Label 504.2.bm.c.107.17
Level $504$
Weight $2$
Character 504.107
Analytic conductor $4.024$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [504,2,Mod(107,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.107");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 107.17
Character \(\chi\) \(=\) 504.107
Dual form 504.2.bm.c.179.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.830529 - 1.14465i) q^{2} +(-0.620442 - 1.90133i) q^{4} +(1.88256 - 3.26069i) q^{5} +(2.23426 - 1.41706i) q^{7} +(-2.69165 - 0.868922i) q^{8} +O(q^{10})\) \(q+(0.830529 - 1.14465i) q^{2} +(-0.620442 - 1.90133i) q^{4} +(1.88256 - 3.26069i) q^{5} +(2.23426 - 1.41706i) q^{7} +(-2.69165 - 0.868922i) q^{8} +(-2.16882 - 4.86297i) q^{10} +(-1.47084 + 0.849192i) q^{11} +5.64222i q^{13} +(0.233580 - 3.73436i) q^{14} +(-3.23010 + 2.35933i) q^{16} +(2.26012 - 1.30488i) q^{17} +(-1.18076 + 2.04513i) q^{19} +(-7.36767 - 1.55630i) q^{20} +(-0.249553 + 2.38888i) q^{22} +(-0.653873 + 1.13254i) q^{23} +(-4.58807 - 7.94677i) q^{25} +(6.45836 + 4.68603i) q^{26} +(-4.08053 - 3.36886i) q^{28} +6.80944 q^{29} +(-4.75107 + 2.74303i) q^{31} +(0.0179044 + 5.65683i) q^{32} +(0.383465 - 3.67078i) q^{34} +(-0.414472 - 9.95295i) q^{35} +(5.20109 + 3.00285i) q^{37} +(1.36030 + 3.05010i) q^{38} +(-7.90048 + 7.14084i) q^{40} -6.10456i q^{41} -6.49804 q^{43} +(2.52717 + 2.26968i) q^{44} +(0.753301 + 1.68906i) q^{46} +(3.53360 - 6.12038i) q^{47} +(2.98386 - 6.33219i) q^{49} +(-12.9068 - 1.34830i) q^{50} +(10.7277 - 3.50067i) q^{52} +(-0.488913 - 0.846821i) q^{53} +6.39462i q^{55} +(-7.24517 + 1.87284i) q^{56} +(5.65544 - 7.79442i) q^{58} +(-6.67395 + 3.85320i) q^{59} +(-7.64484 - 4.41375i) q^{61} +(-0.806095 + 7.71647i) q^{62} +(6.48995 + 4.67767i) q^{64} +(18.3975 + 10.6218i) q^{65} +(6.69828 + 11.6018i) q^{67} +(-3.88327 - 3.48762i) q^{68} +(-11.7369 - 7.79179i) q^{70} +9.40544 q^{71} +(-1.09003 - 1.88798i) q^{73} +(7.75687 - 3.45947i) q^{74} +(4.62106 + 0.976124i) q^{76} +(-2.08289 + 3.98160i) q^{77} +(15.0908 + 8.71267i) q^{79} +(1.61217 + 14.9739i) q^{80} +(-6.98758 - 5.07002i) q^{82} +11.8864i q^{83} -9.82605i q^{85} +(-5.39682 + 7.43798i) q^{86} +(4.69688 - 1.00768i) q^{88} +(-9.58642 - 5.53472i) q^{89} +(7.99538 + 12.6062i) q^{91} +(2.55902 + 0.540552i) q^{92} +(-4.07092 - 9.12788i) q^{94} +(4.44570 + 7.70018i) q^{95} +15.0631 q^{97} +(-4.76995 - 8.67454i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.830529 1.14465i 0.587273 0.809389i
\(3\) 0 0
\(4\) −0.620442 1.90133i −0.310221 0.950665i
\(5\) 1.88256 3.26069i 0.841907 1.45823i −0.0463738 0.998924i \(-0.514767\pi\)
0.888281 0.459301i \(-0.151900\pi\)
\(6\) 0 0
\(7\) 2.23426 1.41706i 0.844472 0.535600i
\(8\) −2.69165 0.868922i −0.951642 0.307210i
\(9\) 0 0
\(10\) −2.16882 4.86297i −0.685842 1.53781i
\(11\) −1.47084 + 0.849192i −0.443476 + 0.256041i −0.705071 0.709137i \(-0.749085\pi\)
0.261595 + 0.965178i \(0.415752\pi\)
\(12\) 0 0
\(13\) 5.64222i 1.56487i 0.622733 + 0.782435i \(0.286022\pi\)
−0.622733 + 0.782435i \(0.713978\pi\)
\(14\) 0.233580 3.73436i 0.0624270 0.998050i
\(15\) 0 0
\(16\) −3.23010 + 2.35933i −0.807526 + 0.589832i
\(17\) 2.26012 1.30488i 0.548158 0.316479i −0.200220 0.979751i \(-0.564166\pi\)
0.748379 + 0.663271i \(0.230833\pi\)
\(18\) 0 0
\(19\) −1.18076 + 2.04513i −0.270885 + 0.469186i −0.969089 0.246713i \(-0.920649\pi\)
0.698204 + 0.715899i \(0.253983\pi\)
\(20\) −7.36767 1.55630i −1.64746 0.347999i
\(21\) 0 0
\(22\) −0.249553 + 2.38888i −0.0532048 + 0.509311i
\(23\) −0.653873 + 1.13254i −0.136342 + 0.236151i −0.926109 0.377255i \(-0.876868\pi\)
0.789767 + 0.613406i \(0.210201\pi\)
\(24\) 0 0
\(25\) −4.58807 7.94677i −0.917614 1.58935i
\(26\) 6.45836 + 4.68603i 1.26659 + 0.919006i
\(27\) 0 0
\(28\) −4.08053 3.36886i −0.771149 0.636655i
\(29\) 6.80944 1.26448 0.632241 0.774772i \(-0.282135\pi\)
0.632241 + 0.774772i \(0.282135\pi\)
\(30\) 0 0
\(31\) −4.75107 + 2.74303i −0.853317 + 0.492663i −0.861769 0.507302i \(-0.830643\pi\)
0.00845183 + 0.999964i \(0.497310\pi\)
\(32\) 0.0179044 + 5.65683i 0.00316508 + 0.999995i
\(33\) 0 0
\(34\) 0.383465 3.67078i 0.0657637 0.629533i
\(35\) −0.414472 9.95295i −0.0700586 1.68236i
\(36\) 0 0
\(37\) 5.20109 + 3.00285i 0.855054 + 0.493666i 0.862353 0.506308i \(-0.168990\pi\)
−0.00729899 + 0.999973i \(0.502323\pi\)
\(38\) 1.36030 + 3.05010i 0.220671 + 0.494791i
\(39\) 0 0
\(40\) −7.90048 + 7.14084i −1.24918 + 1.12907i
\(41\) 6.10456i 0.953373i −0.879073 0.476686i \(-0.841838\pi\)
0.879073 0.476686i \(-0.158162\pi\)
\(42\) 0 0
\(43\) −6.49804 −0.990943 −0.495471 0.868624i \(-0.665005\pi\)
−0.495471 + 0.868624i \(0.665005\pi\)
\(44\) 2.52717 + 2.26968i 0.380985 + 0.342168i
\(45\) 0 0
\(46\) 0.753301 + 1.68906i 0.111068 + 0.249039i
\(47\) 3.53360 6.12038i 0.515429 0.892749i −0.484411 0.874841i \(-0.660966\pi\)
0.999840 0.0179081i \(-0.00570062\pi\)
\(48\) 0 0
\(49\) 2.98386 6.33219i 0.426266 0.904598i
\(50\) −12.9068 1.34830i −1.82530 0.190678i
\(51\) 0 0
\(52\) 10.7277 3.50067i 1.48767 0.485455i
\(53\) −0.488913 0.846821i −0.0671573 0.116320i 0.830492 0.557031i \(-0.188060\pi\)
−0.897649 + 0.440711i \(0.854726\pi\)
\(54\) 0 0
\(55\) 6.39462i 0.862251i
\(56\) −7.24517 + 1.87284i −0.968176 + 0.250269i
\(57\) 0 0
\(58\) 5.65544 7.79442i 0.742596 1.02346i
\(59\) −6.67395 + 3.85320i −0.868874 + 0.501645i −0.866974 0.498354i \(-0.833938\pi\)
−0.00190001 + 0.999998i \(0.500605\pi\)
\(60\) 0 0
\(61\) −7.64484 4.41375i −0.978822 0.565123i −0.0769075 0.997038i \(-0.524505\pi\)
−0.901914 + 0.431915i \(0.857838\pi\)
\(62\) −0.806095 + 7.71647i −0.102374 + 0.979993i
\(63\) 0 0
\(64\) 6.48995 + 4.67767i 0.811244 + 0.584708i
\(65\) 18.3975 + 10.6218i 2.28193 + 1.31747i
\(66\) 0 0
\(67\) 6.69828 + 11.6018i 0.818325 + 1.41738i 0.906916 + 0.421312i \(0.138430\pi\)
−0.0885910 + 0.996068i \(0.528236\pi\)
\(68\) −3.88327 3.48762i −0.470916 0.422936i
\(69\) 0 0
\(70\) −11.7369 7.79179i −1.40282 0.931297i
\(71\) 9.40544 1.11622 0.558110 0.829767i \(-0.311527\pi\)
0.558110 + 0.829767i \(0.311527\pi\)
\(72\) 0 0
\(73\) −1.09003 1.88798i −0.127578 0.220971i 0.795160 0.606400i \(-0.207387\pi\)
−0.922738 + 0.385429i \(0.874054\pi\)
\(74\) 7.75687 3.45947i 0.901717 0.402155i
\(75\) 0 0
\(76\) 4.62106 + 0.976124i 0.530072 + 0.111969i
\(77\) −2.08289 + 3.98160i −0.237368 + 0.453745i
\(78\) 0 0
\(79\) 15.0908 + 8.71267i 1.69785 + 0.980252i 0.947800 + 0.318865i \(0.103302\pi\)
0.750045 + 0.661386i \(0.230032\pi\)
\(80\) 1.61217 + 14.9739i 0.180246 + 1.67414i
\(81\) 0 0
\(82\) −6.98758 5.07002i −0.771649 0.559890i
\(83\) 11.8864i 1.30471i 0.757915 + 0.652353i \(0.226218\pi\)
−0.757915 + 0.652353i \(0.773782\pi\)
\(84\) 0 0
\(85\) 9.82605i 1.06578i
\(86\) −5.39682 + 7.43798i −0.581954 + 0.802058i
\(87\) 0 0
\(88\) 4.69688 1.00768i 0.500689 0.107419i
\(89\) −9.58642 5.53472i −1.01616 0.586679i −0.103170 0.994664i \(-0.532898\pi\)
−0.912989 + 0.407984i \(0.866232\pi\)
\(90\) 0 0
\(91\) 7.99538 + 12.6062i 0.838144 + 1.32149i
\(92\) 2.55902 + 0.540552i 0.266797 + 0.0563564i
\(93\) 0 0
\(94\) −4.07092 9.12788i −0.419883 0.941469i
\(95\) 4.44570 + 7.70018i 0.456119 + 0.790021i
\(96\) 0 0
\(97\) 15.0631 1.52943 0.764715 0.644369i \(-0.222880\pi\)
0.764715 + 0.644369i \(0.222880\pi\)
\(98\) −4.76995 8.67454i −0.481837 0.876261i
\(99\) 0 0
\(100\) −12.2628 + 13.6539i −1.22628 + 1.36539i
\(101\) 0.777899 + 1.34736i 0.0774039 + 0.134067i 0.902129 0.431466i \(-0.142004\pi\)
−0.824725 + 0.565534i \(0.808670\pi\)
\(102\) 0 0
\(103\) −6.94066 4.00719i −0.683883 0.394840i 0.117433 0.993081i \(-0.462533\pi\)
−0.801317 + 0.598240i \(0.795867\pi\)
\(104\) 4.90265 15.1869i 0.480744 1.48919i
\(105\) 0 0
\(106\) −1.37537 0.143677i −0.133588 0.0139551i
\(107\) −12.6257 7.28943i −1.22057 0.704696i −0.255530 0.966801i \(-0.582250\pi\)
−0.965039 + 0.262105i \(0.915583\pi\)
\(108\) 0 0
\(109\) 0.655188 0.378273i 0.0627556 0.0362320i −0.468294 0.883573i \(-0.655131\pi\)
0.531050 + 0.847341i \(0.321798\pi\)
\(110\) 7.31960 + 5.31092i 0.697896 + 0.506377i
\(111\) 0 0
\(112\) −3.87358 + 9.84862i −0.366019 + 0.930607i
\(113\) 9.87390i 0.928859i 0.885610 + 0.464429i \(0.153741\pi\)
−0.885610 + 0.464429i \(0.846259\pi\)
\(114\) 0 0
\(115\) 2.46191 + 4.26416i 0.229574 + 0.397635i
\(116\) −4.22486 12.9470i −0.392268 1.20210i
\(117\) 0 0
\(118\) −1.13234 + 10.8395i −0.104241 + 0.997859i
\(119\) 3.20060 6.11817i 0.293398 0.560852i
\(120\) 0 0
\(121\) −4.05774 + 7.02822i −0.368886 + 0.638929i
\(122\) −11.4015 + 5.08491i −1.03224 + 0.460366i
\(123\) 0 0
\(124\) 8.16316 + 7.33145i 0.733074 + 0.658384i
\(125\) −15.7237 −1.40637
\(126\) 0 0
\(127\) 4.50847i 0.400062i −0.979790 0.200031i \(-0.935896\pi\)
0.979790 0.200031i \(-0.0641043\pi\)
\(128\) 10.7444 3.54377i 0.949678 0.313228i
\(129\) 0 0
\(130\) 27.4379 12.2370i 2.40647 1.07325i
\(131\) −14.0673 8.12176i −1.22907 0.709601i −0.262231 0.965005i \(-0.584458\pi\)
−0.966835 + 0.255404i \(0.917792\pi\)
\(132\) 0 0
\(133\) 0.259961 + 6.24258i 0.0225414 + 0.541300i
\(134\) 18.8431 + 1.96843i 1.62779 + 0.170046i
\(135\) 0 0
\(136\) −7.21727 + 1.54841i −0.618876 + 0.132775i
\(137\) −3.63470 + 2.09849i −0.310533 + 0.179286i −0.647165 0.762350i \(-0.724046\pi\)
0.336632 + 0.941636i \(0.390712\pi\)
\(138\) 0 0
\(139\) −5.70274 −0.483700 −0.241850 0.970314i \(-0.577754\pi\)
−0.241850 + 0.970314i \(0.577754\pi\)
\(140\) −18.6667 + 6.96327i −1.57762 + 0.588504i
\(141\) 0 0
\(142\) 7.81150 10.7659i 0.655526 0.903457i
\(143\) −4.79133 8.29882i −0.400671 0.693982i
\(144\) 0 0
\(145\) 12.8192 22.2035i 1.06458 1.84390i
\(146\) −3.06637 0.320326i −0.253775 0.0265104i
\(147\) 0 0
\(148\) 2.48243 11.7521i 0.204055 0.966015i
\(149\) 6.74195 11.6774i 0.552322 0.956650i −0.445784 0.895140i \(-0.647075\pi\)
0.998106 0.0615095i \(-0.0195915\pi\)
\(150\) 0 0
\(151\) 18.4727 10.6652i 1.50329 0.867924i 0.503295 0.864115i \(-0.332121\pi\)
0.999993 0.00380878i \(-0.00121238\pi\)
\(152\) 4.95525 4.47879i 0.401924 0.363278i
\(153\) 0 0
\(154\) 2.82763 + 5.69102i 0.227857 + 0.458595i
\(155\) 20.6557i 1.65910i
\(156\) 0 0
\(157\) 7.97251 4.60293i 0.636276 0.367354i −0.146903 0.989151i \(-0.546930\pi\)
0.783179 + 0.621797i \(0.213597\pi\)
\(158\) 22.5063 10.0375i 1.79050 0.798542i
\(159\) 0 0
\(160\) 18.4789 + 10.5909i 1.46088 + 0.837287i
\(161\) 0.143959 + 3.45697i 0.0113456 + 0.272448i
\(162\) 0 0
\(163\) 0.0600325 0.103979i 0.00470211 0.00814429i −0.863665 0.504067i \(-0.831837\pi\)
0.868367 + 0.495922i \(0.165170\pi\)
\(164\) −11.6068 + 3.78753i −0.906338 + 0.295756i
\(165\) 0 0
\(166\) 13.6058 + 9.87204i 1.05601 + 0.766219i
\(167\) −12.9810 −1.00450 −0.502251 0.864722i \(-0.667495\pi\)
−0.502251 + 0.864722i \(0.667495\pi\)
\(168\) 0 0
\(169\) −18.8346 −1.44882
\(170\) −11.2474 8.16082i −0.862634 0.625907i
\(171\) 0 0
\(172\) 4.03166 + 12.3549i 0.307411 + 0.942054i
\(173\) −3.44458 + 5.96618i −0.261886 + 0.453600i −0.966743 0.255749i \(-0.917678\pi\)
0.704857 + 0.709350i \(0.251011\pi\)
\(174\) 0 0
\(175\) −21.5120 11.2536i −1.62616 0.850691i
\(176\) 2.74746 6.21318i 0.207097 0.468336i
\(177\) 0 0
\(178\) −14.2971 + 6.37634i −1.07161 + 0.477927i
\(179\) 13.6043 7.85445i 1.01683 0.587070i 0.103649 0.994614i \(-0.466948\pi\)
0.913185 + 0.407544i \(0.133615\pi\)
\(180\) 0 0
\(181\) 15.6714i 1.16485i 0.812886 + 0.582423i \(0.197895\pi\)
−0.812886 + 0.582423i \(0.802105\pi\)
\(182\) 21.0701 + 1.31791i 1.56182 + 0.0976901i
\(183\) 0 0
\(184\) 2.74409 2.48024i 0.202297 0.182846i
\(185\) 19.5827 11.3061i 1.43975 0.831241i
\(186\) 0 0
\(187\) −2.21618 + 3.83854i −0.162063 + 0.280702i
\(188\) −13.8292 2.92120i −1.00860 0.213051i
\(189\) 0 0
\(190\) 12.5063 + 1.30646i 0.907301 + 0.0947805i
\(191\) −12.0633 + 20.8943i −0.872873 + 1.51186i −0.0138617 + 0.999904i \(0.504412\pi\)
−0.859011 + 0.511957i \(0.828921\pi\)
\(192\) 0 0
\(193\) −4.80306 8.31914i −0.345732 0.598825i 0.639755 0.768579i \(-0.279036\pi\)
−0.985486 + 0.169754i \(0.945703\pi\)
\(194\) 12.5104 17.2420i 0.898193 1.23790i
\(195\) 0 0
\(196\) −13.8909 1.74455i −0.992206 0.124610i
\(197\) 2.05305 0.146274 0.0731371 0.997322i \(-0.476699\pi\)
0.0731371 + 0.997322i \(0.476699\pi\)
\(198\) 0 0
\(199\) −8.62103 + 4.97735i −0.611128 + 0.352835i −0.773407 0.633910i \(-0.781449\pi\)
0.162279 + 0.986745i \(0.448116\pi\)
\(200\) 5.44435 + 25.3766i 0.384974 + 1.79440i
\(201\) 0 0
\(202\) 2.18832 + 0.228602i 0.153970 + 0.0160844i
\(203\) 15.2141 9.64941i 1.06782 0.677256i
\(204\) 0 0
\(205\) −19.9051 11.4922i −1.39023 0.802651i
\(206\) −10.3512 + 4.61653i −0.721206 + 0.321649i
\(207\) 0 0
\(208\) −13.3118 18.2249i −0.923010 1.26367i
\(209\) 4.01076i 0.277430i
\(210\) 0 0
\(211\) −13.9757 −0.962128 −0.481064 0.876685i \(-0.659750\pi\)
−0.481064 + 0.876685i \(0.659750\pi\)
\(212\) −1.30674 + 1.45499i −0.0897476 + 0.0999289i
\(213\) 0 0
\(214\) −18.8298 + 8.39787i −1.28718 + 0.574066i
\(215\) −12.2330 + 21.1881i −0.834281 + 1.44502i
\(216\) 0 0
\(217\) −6.72808 + 12.8612i −0.456732 + 0.873076i
\(218\) 0.111163 1.06413i 0.00752893 0.0720718i
\(219\) 0 0
\(220\) 12.1583 3.96749i 0.819711 0.267488i
\(221\) 7.36241 + 12.7521i 0.495249 + 0.857796i
\(222\) 0 0
\(223\) 15.8817i 1.06352i −0.846896 0.531759i \(-0.821531\pi\)
0.846896 0.531759i \(-0.178469\pi\)
\(224\) 8.05609 + 12.6135i 0.538270 + 0.842772i
\(225\) 0 0
\(226\) 11.3022 + 8.20057i 0.751808 + 0.545494i
\(227\) 0.620059 0.357991i 0.0411548 0.0237607i −0.479281 0.877661i \(-0.659103\pi\)
0.520436 + 0.853901i \(0.325769\pi\)
\(228\) 0 0
\(229\) −3.89913 2.25117i −0.257662 0.148761i 0.365606 0.930770i \(-0.380862\pi\)
−0.623268 + 0.782009i \(0.714195\pi\)
\(230\) 6.92565 + 0.723483i 0.456664 + 0.0477051i
\(231\) 0 0
\(232\) −18.3286 5.91687i −1.20333 0.388462i
\(233\) 6.69604 + 3.86596i 0.438672 + 0.253267i 0.703034 0.711156i \(-0.251828\pi\)
−0.264362 + 0.964423i \(0.585161\pi\)
\(234\) 0 0
\(235\) −13.3044 23.0440i −0.867886 1.50322i
\(236\) 11.4670 + 10.2987i 0.746438 + 0.670387i
\(237\) 0 0
\(238\) −4.34496 8.74488i −0.281642 0.566846i
\(239\) −21.3788 −1.38288 −0.691440 0.722433i \(-0.743024\pi\)
−0.691440 + 0.722433i \(0.743024\pi\)
\(240\) 0 0
\(241\) 4.25688 + 7.37313i 0.274210 + 0.474945i 0.969935 0.243362i \(-0.0782504\pi\)
−0.695726 + 0.718308i \(0.744917\pi\)
\(242\) 4.67477 + 10.4818i 0.300505 + 0.673798i
\(243\) 0 0
\(244\) −3.64882 + 17.2738i −0.233592 + 1.10584i
\(245\) −15.0300 21.6502i −0.960232 1.38318i
\(246\) 0 0
\(247\) −11.5391 6.66209i −0.734215 0.423899i
\(248\) 15.1717 3.25497i 0.963403 0.206691i
\(249\) 0 0
\(250\) −13.0590 + 17.9981i −0.825922 + 1.13830i
\(251\) 0.778871i 0.0491619i 0.999698 + 0.0245810i \(0.00782515\pi\)
−0.999698 + 0.0245810i \(0.992175\pi\)
\(252\) 0 0
\(253\) 2.22106i 0.139637i
\(254\) −5.16062 3.74442i −0.323806 0.234946i
\(255\) 0 0
\(256\) 4.86715 15.2417i 0.304197 0.952609i
\(257\) −10.6901 6.17195i −0.666832 0.384996i 0.128043 0.991769i \(-0.459130\pi\)
−0.794875 + 0.606773i \(0.792464\pi\)
\(258\) 0 0
\(259\) 15.8758 0.661120i 0.986476 0.0410800i
\(260\) 8.78098 41.5700i 0.544573 2.57806i
\(261\) 0 0
\(262\) −20.9799 + 9.35676i −1.29614 + 0.578062i
\(263\) −1.01432 1.75686i −0.0625458 0.108333i 0.833057 0.553187i \(-0.186589\pi\)
−0.895603 + 0.444855i \(0.853255\pi\)
\(264\) 0 0
\(265\) −3.68163 −0.226161
\(266\) 7.36146 + 4.88708i 0.451360 + 0.299646i
\(267\) 0 0
\(268\) 17.9029 19.9338i 1.09359 1.21765i
\(269\) 13.1346 + 22.7498i 0.800833 + 1.38708i 0.919069 + 0.394097i \(0.128943\pi\)
−0.118236 + 0.992986i \(0.537724\pi\)
\(270\) 0 0
\(271\) 7.01591 + 4.05064i 0.426186 + 0.246059i 0.697720 0.716370i \(-0.254198\pi\)
−0.271535 + 0.962429i \(0.587531\pi\)
\(272\) −4.22177 + 9.54724i −0.255983 + 0.578887i
\(273\) 0 0
\(274\) −0.616685 + 5.90331i −0.0372553 + 0.356632i
\(275\) 13.4967 + 7.79231i 0.813880 + 0.469894i
\(276\) 0 0
\(277\) 8.45693 4.88261i 0.508127 0.293368i −0.223936 0.974604i \(-0.571891\pi\)
0.732064 + 0.681236i \(0.238557\pi\)
\(278\) −4.73630 + 6.52764i −0.284064 + 0.391502i
\(279\) 0 0
\(280\) −7.53272 + 27.1500i −0.450166 + 1.62252i
\(281\) 1.88752i 0.112600i −0.998414 0.0562999i \(-0.982070\pi\)
0.998414 0.0562999i \(-0.0179303\pi\)
\(282\) 0 0
\(283\) 3.28892 + 5.69657i 0.195506 + 0.338626i 0.947066 0.321038i \(-0.104032\pi\)
−0.751560 + 0.659664i \(0.770698\pi\)
\(284\) −5.83553 17.8828i −0.346275 1.06115i
\(285\) 0 0
\(286\) −13.4786 1.40803i −0.797005 0.0832585i
\(287\) −8.65056 13.6392i −0.510626 0.805097i
\(288\) 0 0
\(289\) −5.09459 + 8.82408i −0.299682 + 0.519064i
\(290\) −14.7685 33.1141i −0.867235 1.94453i
\(291\) 0 0
\(292\) −2.91337 + 3.24388i −0.170492 + 0.189834i
\(293\) −14.1311 −0.825545 −0.412772 0.910834i \(-0.635440\pi\)
−0.412772 + 0.910834i \(0.635440\pi\)
\(294\) 0 0
\(295\) 29.0156i 1.68935i
\(296\) −11.3903 12.6020i −0.662046 0.732474i
\(297\) 0 0
\(298\) −7.76713 17.4156i −0.449938 1.00886i
\(299\) −6.39004 3.68929i −0.369546 0.213357i
\(300\) 0 0
\(301\) −14.5183 + 9.20814i −0.836823 + 0.530749i
\(302\) 3.13419 30.0025i 0.180353 1.72645i
\(303\) 0 0
\(304\) −1.01117 9.39179i −0.0579944 0.538656i
\(305\) −28.7838 + 16.6183i −1.64815 + 0.951562i
\(306\) 0 0
\(307\) −17.5973 −1.00433 −0.502167 0.864771i \(-0.667464\pi\)
−0.502167 + 0.864771i \(0.667464\pi\)
\(308\) 8.86264 + 1.48991i 0.504996 + 0.0848958i
\(309\) 0 0
\(310\) 23.6435 + 17.1552i 1.34286 + 0.974347i
\(311\) −5.44683 9.43418i −0.308861 0.534963i 0.669252 0.743035i \(-0.266615\pi\)
−0.978114 + 0.208072i \(0.933281\pi\)
\(312\) 0 0
\(313\) −1.76535 + 3.05768i −0.0997835 + 0.172830i −0.911595 0.411090i \(-0.865148\pi\)
0.811811 + 0.583920i \(0.198482\pi\)
\(314\) 1.35267 12.9486i 0.0763354 0.730732i
\(315\) 0 0
\(316\) 7.20270 34.0982i 0.405183 1.91818i
\(317\) −8.09426 + 14.0197i −0.454619 + 0.787423i −0.998666 0.0516316i \(-0.983558\pi\)
0.544047 + 0.839055i \(0.316891\pi\)
\(318\) 0 0
\(319\) −10.0156 + 5.78252i −0.560767 + 0.323759i
\(320\) 27.4701 12.3557i 1.53563 0.690706i
\(321\) 0 0
\(322\) 4.07658 + 2.70634i 0.227179 + 0.150818i
\(323\) 6.16298i 0.342918i
\(324\) 0 0
\(325\) 44.8374 25.8869i 2.48713 1.43595i
\(326\) −0.0691610 0.155074i −0.00383048 0.00858875i
\(327\) 0 0
\(328\) −5.30439 + 16.4313i −0.292886 + 0.907269i
\(329\) −0.777972 18.6819i −0.0428910 1.02996i
\(330\) 0 0
\(331\) 5.79835 10.0430i 0.318706 0.552016i −0.661512 0.749935i \(-0.730085\pi\)
0.980218 + 0.197919i \(0.0634183\pi\)
\(332\) 22.6000 7.37484i 1.24034 0.404747i
\(333\) 0 0
\(334\) −10.7811 + 14.8587i −0.589917 + 0.813033i
\(335\) 50.4397 2.75581
\(336\) 0 0
\(337\) 2.81073 0.153110 0.0765550 0.997065i \(-0.475608\pi\)
0.0765550 + 0.997065i \(0.475608\pi\)
\(338\) −15.6427 + 21.5590i −0.850851 + 1.17266i
\(339\) 0 0
\(340\) −18.6826 + 6.09649i −1.01320 + 0.330629i
\(341\) 4.65872 8.06914i 0.252284 0.436968i
\(342\) 0 0
\(343\) −2.30639 18.3761i −0.124533 0.992215i
\(344\) 17.4905 + 5.64629i 0.943022 + 0.304428i
\(345\) 0 0
\(346\) 3.96836 + 8.89792i 0.213340 + 0.478355i
\(347\) −18.7883 + 10.8474i −1.00861 + 0.582320i −0.910784 0.412884i \(-0.864522\pi\)
−0.0978242 + 0.995204i \(0.531188\pi\)
\(348\) 0 0
\(349\) 7.44465i 0.398503i 0.979948 + 0.199251i \(0.0638511\pi\)
−0.979948 + 0.199251i \(0.936149\pi\)
\(350\) −30.7478 + 15.2773i −1.64354 + 0.816606i
\(351\) 0 0
\(352\) −4.83007 8.30511i −0.257443 0.442664i
\(353\) 13.0365 7.52665i 0.693865 0.400603i −0.111193 0.993799i \(-0.535467\pi\)
0.805058 + 0.593196i \(0.202134\pi\)
\(354\) 0 0
\(355\) 17.7063 30.6682i 0.939754 1.62770i
\(356\) −4.57551 + 21.6609i −0.242502 + 1.14803i
\(357\) 0 0
\(358\) 2.30819 22.0955i 0.121992 1.16778i
\(359\) 9.01876 15.6210i 0.475992 0.824442i −0.523630 0.851946i \(-0.675422\pi\)
0.999622 + 0.0275035i \(0.00875575\pi\)
\(360\) 0 0
\(361\) 6.71162 + 11.6249i 0.353243 + 0.611835i
\(362\) 17.9383 + 13.0156i 0.942814 + 0.684083i
\(363\) 0 0
\(364\) 19.0079 23.0233i 0.996282 1.20675i
\(365\) −8.20816 −0.429635
\(366\) 0 0
\(367\) 3.38897 1.95662i 0.176903 0.102135i −0.408934 0.912564i \(-0.634099\pi\)
0.585837 + 0.810429i \(0.300766\pi\)
\(368\) −0.559958 5.20093i −0.0291898 0.271117i
\(369\) 0 0
\(370\) 3.32253 31.8054i 0.172730 1.65348i
\(371\) −2.29236 1.19920i −0.119013 0.0622594i
\(372\) 0 0
\(373\) −15.8513 9.15178i −0.820752 0.473861i 0.0299239 0.999552i \(-0.490473\pi\)
−0.850676 + 0.525691i \(0.823807\pi\)
\(374\) 2.55318 + 5.72478i 0.132022 + 0.296021i
\(375\) 0 0
\(376\) −14.8293 + 13.4035i −0.764765 + 0.691232i
\(377\) 38.4203i 1.97875i
\(378\) 0 0
\(379\) 25.8073 1.32563 0.662816 0.748783i \(-0.269361\pi\)
0.662816 + 0.748783i \(0.269361\pi\)
\(380\) 11.8823 13.2302i 0.609548 0.678697i
\(381\) 0 0
\(382\) 13.8977 + 31.1616i 0.711068 + 1.59437i
\(383\) 7.37665 12.7767i 0.376929 0.652860i −0.613685 0.789551i \(-0.710313\pi\)
0.990614 + 0.136691i \(0.0436467\pi\)
\(384\) 0 0
\(385\) 9.06159 + 14.2873i 0.461822 + 0.728147i
\(386\) −13.5116 1.41148i −0.687721 0.0718423i
\(387\) 0 0
\(388\) −9.34580 28.6400i −0.474461 1.45397i
\(389\) −8.70264 15.0734i −0.441242 0.764253i 0.556540 0.830821i \(-0.312128\pi\)
−0.997782 + 0.0665677i \(0.978795\pi\)
\(390\) 0 0
\(391\) 3.41290i 0.172598i
\(392\) −13.5337 + 14.4513i −0.683554 + 0.729900i
\(393\) 0 0
\(394\) 1.70512 2.35003i 0.0859028 0.118393i
\(395\) 56.8186 32.8042i 2.85886 1.65056i
\(396\) 0 0
\(397\) −10.0273 5.78926i −0.503255 0.290554i 0.226802 0.973941i \(-0.427173\pi\)
−0.730057 + 0.683387i \(0.760506\pi\)
\(398\) −1.46270 + 14.0019i −0.0733184 + 0.701851i
\(399\) 0 0
\(400\) 33.5690 + 14.8441i 1.67845 + 0.742207i
\(401\) −31.1453 17.9818i −1.55532 0.897967i −0.997694 0.0678773i \(-0.978377\pi\)
−0.557630 0.830089i \(-0.688289\pi\)
\(402\) 0 0
\(403\) −15.4768 26.8065i −0.770953 1.33533i
\(404\) 2.07914 2.31500i 0.103441 0.115176i
\(405\) 0 0
\(406\) 1.59055 25.4289i 0.0789378 1.26201i
\(407\) −10.2000 −0.505595
\(408\) 0 0
\(409\) 12.1615 + 21.0644i 0.601349 + 1.04157i 0.992617 + 0.121290i \(0.0387031\pi\)
−0.391268 + 0.920277i \(0.627964\pi\)
\(410\) −29.6863 + 13.2397i −1.46610 + 0.653863i
\(411\) 0 0
\(412\) −3.31272 + 15.6827i −0.163206 + 0.772631i
\(413\) −9.45111 + 18.0665i −0.465059 + 0.888993i
\(414\) 0 0
\(415\) 38.7580 + 22.3769i 1.90256 + 1.09844i
\(416\) −31.9170 + 0.101021i −1.56486 + 0.00495294i
\(417\) 0 0
\(418\) −4.59092 3.33106i −0.224549 0.162927i
\(419\) 6.92954i 0.338530i 0.985571 + 0.169265i \(0.0541394\pi\)
−0.985571 + 0.169265i \(0.945861\pi\)
\(420\) 0 0
\(421\) 12.6192i 0.615024i 0.951544 + 0.307512i \(0.0994965\pi\)
−0.951544 + 0.307512i \(0.900504\pi\)
\(422\) −11.6072 + 15.9973i −0.565032 + 0.778736i
\(423\) 0 0
\(424\) 0.580159 + 2.70417i 0.0281750 + 0.131326i
\(425\) −20.7391 11.9737i −1.00600 0.580812i
\(426\) 0 0
\(427\) −23.3352 + 0.971750i −1.12927 + 0.0470263i
\(428\) −6.02612 + 28.5282i −0.291284 + 1.37896i
\(429\) 0 0
\(430\) 14.0931 + 31.5998i 0.679630 + 1.52388i
\(431\) 11.1759 + 19.3571i 0.538322 + 0.932401i 0.998995 + 0.0448306i \(0.0142748\pi\)
−0.460673 + 0.887570i \(0.652392\pi\)
\(432\) 0 0
\(433\) −32.2813 −1.55134 −0.775671 0.631138i \(-0.782588\pi\)
−0.775671 + 0.631138i \(0.782588\pi\)
\(434\) 9.13370 + 18.3829i 0.438432 + 0.882408i
\(435\) 0 0
\(436\) −1.12573 1.01103i −0.0539126 0.0484196i
\(437\) −1.54413 2.67451i −0.0738658 0.127939i
\(438\) 0 0
\(439\) 2.42798 + 1.40180i 0.115881 + 0.0669041i 0.556820 0.830633i \(-0.312021\pi\)
−0.440939 + 0.897537i \(0.645355\pi\)
\(440\) 5.55643 17.2121i 0.264892 0.820554i
\(441\) 0 0
\(442\) 20.7113 + 2.16359i 0.985137 + 0.102912i
\(443\) 16.2066 + 9.35689i 0.769999 + 0.444559i 0.832874 0.553462i \(-0.186694\pi\)
−0.0628752 + 0.998021i \(0.520027\pi\)
\(444\) 0 0
\(445\) −36.0940 + 20.8389i −1.71102 + 0.987859i
\(446\) −18.1790 13.1902i −0.860799 0.624575i
\(447\) 0 0
\(448\) 21.1288 + 1.25446i 0.998242 + 0.0592678i
\(449\) 13.8950i 0.655747i 0.944722 + 0.327874i \(0.106332\pi\)
−0.944722 + 0.327874i \(0.893668\pi\)
\(450\) 0 0
\(451\) 5.18395 + 8.97886i 0.244103 + 0.422798i
\(452\) 18.7735 6.12618i 0.883033 0.288151i
\(453\) 0 0
\(454\) 0.105203 1.00707i 0.00493742 0.0472642i
\(455\) 56.1567 2.33854i 2.63267 0.109633i
\(456\) 0 0
\(457\) 2.88922 5.00428i 0.135152 0.234090i −0.790503 0.612458i \(-0.790181\pi\)
0.925656 + 0.378367i \(0.123514\pi\)
\(458\) −5.81514 + 2.59348i −0.271724 + 0.121185i
\(459\) 0 0
\(460\) 6.58009 7.32656i 0.306798 0.341603i
\(461\) 15.4222 0.718285 0.359142 0.933283i \(-0.383069\pi\)
0.359142 + 0.933283i \(0.383069\pi\)
\(462\) 0 0
\(463\) 11.5902i 0.538644i 0.963050 + 0.269322i \(0.0867996\pi\)
−0.963050 + 0.269322i \(0.913200\pi\)
\(464\) −21.9952 + 16.0657i −1.02110 + 0.745831i
\(465\) 0 0
\(466\) 9.98642 4.45382i 0.462612 0.206319i
\(467\) −1.98153 1.14404i −0.0916943 0.0529397i 0.453452 0.891281i \(-0.350192\pi\)
−0.545146 + 0.838341i \(0.683526\pi\)
\(468\) 0 0
\(469\) 31.4061 + 16.4295i 1.45020 + 0.758643i
\(470\) −37.4270 3.90978i −1.72638 0.180345i
\(471\) 0 0
\(472\) 21.3121 4.57234i 0.980967 0.210459i
\(473\) 9.55761 5.51809i 0.439459 0.253722i
\(474\) 0 0
\(475\) 21.6696 0.994270
\(476\) −13.6184 2.28942i −0.624200 0.104935i
\(477\) 0 0
\(478\) −17.7557 + 24.4712i −0.812129 + 1.11929i
\(479\) −9.42948 16.3323i −0.430844 0.746244i 0.566102 0.824335i \(-0.308451\pi\)
−0.996946 + 0.0780912i \(0.975117\pi\)
\(480\) 0 0
\(481\) −16.9427 + 29.3457i −0.772522 + 1.33805i
\(482\) 11.9751 + 1.25097i 0.545451 + 0.0569802i
\(483\) 0 0
\(484\) 15.8806 + 3.35451i 0.721843 + 0.152478i
\(485\) 28.3573 49.1162i 1.28764 2.23025i
\(486\) 0 0
\(487\) 26.9019 15.5318i 1.21904 0.703813i 0.254327 0.967118i \(-0.418146\pi\)
0.964713 + 0.263305i \(0.0848126\pi\)
\(488\) 16.7420 + 18.5230i 0.757876 + 0.838499i
\(489\) 0 0
\(490\) −37.2647 0.777026i −1.68345 0.0351025i
\(491\) 7.52948i 0.339801i −0.985461 0.169900i \(-0.945655\pi\)
0.985461 0.169900i \(-0.0543446\pi\)
\(492\) 0 0
\(493\) 15.3901 8.88549i 0.693136 0.400182i
\(494\) −17.2093 + 7.67514i −0.774283 + 0.345321i
\(495\) 0 0
\(496\) 8.87474 20.0696i 0.398487 0.901151i
\(497\) 21.0142 13.3281i 0.942617 0.597848i
\(498\) 0 0
\(499\) −0.883277 + 1.52988i −0.0395409 + 0.0684869i −0.885119 0.465366i \(-0.845923\pi\)
0.845578 + 0.533852i \(0.179256\pi\)
\(500\) 9.75562 + 29.8959i 0.436285 + 1.33698i
\(501\) 0 0
\(502\) 0.891534 + 0.646876i 0.0397911 + 0.0288715i
\(503\) −16.9584 −0.756136 −0.378068 0.925778i \(-0.623411\pi\)
−0.378068 + 0.925778i \(0.623411\pi\)
\(504\) 0 0
\(505\) 5.85777 0.260667
\(506\) −2.54233 1.84465i −0.113020 0.0820048i
\(507\) 0 0
\(508\) −8.57209 + 2.79724i −0.380325 + 0.124108i
\(509\) −5.13114 + 8.88739i −0.227434 + 0.393927i −0.957047 0.289934i \(-0.906367\pi\)
0.729613 + 0.683860i \(0.239700\pi\)
\(510\) 0 0
\(511\) −5.11079 2.67361i −0.226088 0.118273i
\(512\) −13.4041 18.2299i −0.592385 0.805655i
\(513\) 0 0
\(514\) −15.9432 + 7.11046i −0.703224 + 0.313629i
\(515\) −26.1324 + 15.0876i −1.15153 + 0.664837i
\(516\) 0 0
\(517\) 12.0028i 0.527884i
\(518\) 12.4286 18.7213i 0.546081 0.822568i
\(519\) 0 0
\(520\) −40.2902 44.5762i −1.76684 1.95480i
\(521\) −32.7368 + 18.9006i −1.43423 + 0.828051i −0.997440 0.0715138i \(-0.977217\pi\)
−0.436787 + 0.899565i \(0.643884\pi\)
\(522\) 0 0
\(523\) 19.6691 34.0679i 0.860070 1.48968i −0.0117911 0.999930i \(-0.503753\pi\)
0.871861 0.489754i \(-0.162913\pi\)
\(524\) −6.71420 + 31.7856i −0.293311 + 1.38856i
\(525\) 0 0
\(526\) −2.85341 0.298080i −0.124415 0.0129969i
\(527\) −7.15864 + 12.3991i −0.311835 + 0.540114i
\(528\) 0 0
\(529\) 10.6449 + 18.4375i 0.462822 + 0.801631i
\(530\) −3.05770 + 4.21417i −0.132818 + 0.183052i
\(531\) 0 0
\(532\) 11.7079 4.36742i 0.507602 0.189352i
\(533\) 34.4433 1.49190
\(534\) 0 0
\(535\) −47.5372 + 27.4456i −2.05521 + 1.18658i
\(536\) −7.94839 37.0481i −0.343318 1.60024i
\(537\) 0 0
\(538\) 36.9493 + 3.85988i 1.59300 + 0.166411i
\(539\) 0.988451 + 11.8475i 0.0425756 + 0.510309i
\(540\) 0 0
\(541\) −12.8385 7.41231i −0.551970 0.318680i 0.197946 0.980213i \(-0.436573\pi\)
−0.749916 + 0.661533i \(0.769906\pi\)
\(542\) 10.4635 4.66658i 0.449445 0.200447i
\(543\) 0 0
\(544\) 7.42193 + 12.7617i 0.318213 + 0.547154i
\(545\) 2.84849i 0.122016i
\(546\) 0 0
\(547\) −16.2017 −0.692736 −0.346368 0.938099i \(-0.612585\pi\)
−0.346368 + 0.938099i \(0.612585\pi\)
\(548\) 6.24505 + 5.60876i 0.266775 + 0.239595i
\(549\) 0 0
\(550\) 20.1288 8.97721i 0.858297 0.382790i
\(551\) −8.04030 + 13.9262i −0.342528 + 0.593277i
\(552\) 0 0
\(553\) 46.0632 1.91822i 1.95881 0.0815708i
\(554\) 1.43485 13.7354i 0.0609611 0.583560i
\(555\) 0 0
\(556\) 3.53822 + 10.8428i 0.150054 + 0.459837i
\(557\) 1.17534 + 2.03574i 0.0498006 + 0.0862572i 0.889851 0.456251i \(-0.150808\pi\)
−0.840051 + 0.542508i \(0.817475\pi\)
\(558\) 0 0
\(559\) 36.6634i 1.55070i
\(560\) 24.8211 + 31.1712i 1.04888 + 1.31722i
\(561\) 0 0
\(562\) −2.16054 1.56764i −0.0911370 0.0661268i
\(563\) −6.40537 + 3.69814i −0.269954 + 0.155858i −0.628867 0.777513i \(-0.716481\pi\)
0.358913 + 0.933371i \(0.383148\pi\)
\(564\) 0 0
\(565\) 32.1957 + 18.5882i 1.35449 + 0.782012i
\(566\) 9.25211 + 0.966515i 0.388895 + 0.0406257i
\(567\) 0 0
\(568\) −25.3161 8.17260i −1.06224 0.342914i
\(569\) −30.2952 17.4909i −1.27004 0.733258i −0.295045 0.955483i \(-0.595334\pi\)
−0.974995 + 0.222226i \(0.928668\pi\)
\(570\) 0 0
\(571\) 16.4081 + 28.4197i 0.686659 + 1.18933i 0.972912 + 0.231174i \(0.0742567\pi\)
−0.286254 + 0.958154i \(0.592410\pi\)
\(572\) −12.8061 + 14.2588i −0.535448 + 0.596191i
\(573\) 0 0
\(574\) −22.7966 1.42591i −0.951513 0.0595162i
\(575\) 12.0001 0.500437
\(576\) 0 0
\(577\) 4.58139 + 7.93520i 0.190726 + 0.330347i 0.945491 0.325648i \(-0.105583\pi\)
−0.754765 + 0.655995i \(0.772249\pi\)
\(578\) 5.86927 + 13.1602i 0.244130 + 0.547391i
\(579\) 0 0
\(580\) −50.1697 10.5975i −2.08318 0.440038i
\(581\) 16.8438 + 26.5574i 0.698800 + 1.10179i
\(582\) 0 0
\(583\) 1.43823 + 0.830362i 0.0595653 + 0.0343901i
\(584\) 1.29346 + 6.02893i 0.0535237 + 0.249479i
\(585\) 0 0
\(586\) −11.7363 + 16.1751i −0.484820 + 0.668187i
\(587\) 17.4528i 0.720354i −0.932884 0.360177i \(-0.882716\pi\)
0.932884 0.360177i \(-0.117284\pi\)
\(588\) 0 0
\(589\) 12.9554i 0.533819i
\(590\) 33.2126 + 24.0983i 1.36734 + 0.992111i
\(591\) 0 0
\(592\) −23.8848 + 2.57155i −0.981658 + 0.105690i
\(593\) −17.0385 9.83721i −0.699689 0.403966i 0.107542 0.994200i \(-0.465702\pi\)
−0.807232 + 0.590235i \(0.799035\pi\)
\(594\) 0 0
\(595\) −13.9241 21.9540i −0.570834 0.900025i
\(596\) −26.3856 5.57352i −1.08079 0.228300i
\(597\) 0 0
\(598\) −9.53006 + 4.25029i −0.389713 + 0.173807i
\(599\) 2.68048 + 4.64273i 0.109521 + 0.189697i 0.915576 0.402144i \(-0.131735\pi\)
−0.806055 + 0.591841i \(0.798402\pi\)
\(600\) 0 0
\(601\) 12.4609 0.508291 0.254145 0.967166i \(-0.418206\pi\)
0.254145 + 0.967166i \(0.418206\pi\)
\(602\) −1.51782 + 24.2660i −0.0618616 + 0.989010i
\(603\) 0 0
\(604\) −31.7393 28.5055i −1.29146 1.15987i
\(605\) 15.2779 + 26.4621i 0.621135 + 1.07584i
\(606\) 0 0
\(607\) −10.6807 6.16649i −0.433515 0.250290i 0.267328 0.963606i \(-0.413859\pi\)
−0.700843 + 0.713315i \(0.747193\pi\)
\(608\) −11.5901 6.64273i −0.470041 0.269398i
\(609\) 0 0
\(610\) −4.88363 + 46.7493i −0.197732 + 1.89282i
\(611\) 34.5325 + 19.9373i 1.39704 + 0.806579i
\(612\) 0 0
\(613\) −3.55744 + 2.05389i −0.143683 + 0.0829557i −0.570118 0.821563i \(-0.693103\pi\)
0.426435 + 0.904518i \(0.359769\pi\)
\(614\) −14.6151 + 20.1428i −0.589818 + 0.812896i
\(615\) 0 0
\(616\) 9.06612 8.90720i 0.365284 0.358881i
\(617\) 36.1255i 1.45436i 0.686447 + 0.727180i \(0.259169\pi\)
−0.686447 + 0.727180i \(0.740831\pi\)
\(618\) 0 0
\(619\) −0.802674 1.39027i −0.0322622 0.0558798i 0.849443 0.527680i \(-0.176938\pi\)
−0.881706 + 0.471800i \(0.843604\pi\)
\(620\) 39.2732 12.8156i 1.57725 0.514689i
\(621\) 0 0
\(622\) −15.3226 1.60066i −0.614379 0.0641807i
\(623\) −29.2616 + 1.21855i −1.17234 + 0.0488201i
\(624\) 0 0
\(625\) −6.66043 + 11.5362i −0.266417 + 0.461448i
\(626\) 2.03379 + 4.56020i 0.0812866 + 0.182262i
\(627\) 0 0
\(628\) −13.6982 12.3025i −0.546616 0.490924i
\(629\) 15.6734 0.624940
\(630\) 0 0
\(631\) 8.98270i 0.357596i 0.983886 + 0.178798i \(0.0572208\pi\)
−0.983886 + 0.178798i \(0.942779\pi\)
\(632\) −33.0485 36.5642i −1.31460 1.45444i
\(633\) 0 0
\(634\) 9.32507 + 20.9088i 0.370346 + 0.830396i
\(635\) −14.7007 8.48748i −0.583381 0.336815i
\(636\) 0 0
\(637\) 35.7276 + 16.8356i 1.41558 + 0.667050i
\(638\) −1.69931 + 16.2669i −0.0672764 + 0.644014i
\(639\) 0 0
\(640\) 8.67180 41.7055i 0.342783 1.64855i
\(641\) 34.1214 19.7000i 1.34772 0.778104i 0.359790 0.933033i \(-0.382848\pi\)
0.987926 + 0.154929i \(0.0495149\pi\)
\(642\) 0 0
\(643\) 40.0002 1.57745 0.788726 0.614745i \(-0.210741\pi\)
0.788726 + 0.614745i \(0.210741\pi\)
\(644\) 6.48353 2.41856i 0.255487 0.0953048i
\(645\) 0 0
\(646\) 7.05445 + 5.11854i 0.277554 + 0.201386i
\(647\) −19.8854 34.4425i −0.781775 1.35407i −0.930907 0.365257i \(-0.880981\pi\)
0.149132 0.988817i \(-0.452352\pi\)
\(648\) 0 0
\(649\) 6.54422 11.3349i 0.256883 0.444935i
\(650\) 7.60739 72.8229i 0.298386 2.85635i
\(651\) 0 0
\(652\) −0.234946 0.0496284i −0.00920118 0.00194360i
\(653\) 1.64003 2.84061i 0.0641792 0.111162i −0.832150 0.554550i \(-0.812890\pi\)
0.896330 + 0.443388i \(0.146224\pi\)
\(654\) 0 0
\(655\) −52.9651 + 30.5794i −2.06952 + 1.19484i
\(656\) 14.4027 + 19.7184i 0.562330 + 0.769873i
\(657\) 0 0
\(658\) −22.0303 14.6253i −0.858831 0.570155i
\(659\) 16.7484i 0.652425i 0.945297 + 0.326212i \(0.105772\pi\)
−0.945297 + 0.326212i \(0.894228\pi\)
\(660\) 0 0
\(661\) −4.50164 + 2.59902i −0.175093 + 0.101090i −0.584985 0.811044i \(-0.698900\pi\)
0.409892 + 0.912134i \(0.365566\pi\)
\(662\) −6.68005 14.9781i −0.259628 0.582141i
\(663\) 0 0
\(664\) 10.3284 31.9941i 0.400819 1.24161i
\(665\) 20.8445 + 10.9044i 0.808315 + 0.422854i
\(666\) 0 0
\(667\) −4.45251 + 7.71197i −0.172402 + 0.298609i
\(668\) 8.05397 + 24.6812i 0.311618 + 0.954945i
\(669\) 0 0
\(670\) 41.8916 57.7357i 1.61841 2.23052i
\(671\) 14.9925 0.578779
\(672\) 0 0
\(673\) −29.9571 −1.15476 −0.577380 0.816475i \(-0.695925\pi\)
−0.577380 + 0.816475i \(0.695925\pi\)
\(674\) 2.33439 3.21729i 0.0899174 0.123926i
\(675\) 0 0
\(676\) 11.6858 + 35.8108i 0.449453 + 1.37734i
\(677\) 15.2704 26.4492i 0.586891 1.01652i −0.407746 0.913095i \(-0.633685\pi\)
0.994637 0.103429i \(-0.0329816\pi\)
\(678\) 0 0
\(679\) 33.6550 21.3454i 1.29156 0.819162i
\(680\) −8.53807 + 26.4483i −0.327420 + 1.01425i
\(681\) 0 0
\(682\) −5.36713 12.0343i −0.205518 0.460815i
\(683\) 11.1942 6.46296i 0.428333 0.247298i −0.270303 0.962775i \(-0.587124\pi\)
0.698636 + 0.715477i \(0.253791\pi\)
\(684\) 0 0
\(685\) 15.8022i 0.603770i
\(686\) −22.9497 12.6219i −0.876223 0.481906i
\(687\) 0 0
\(688\) 20.9894 15.3310i 0.800212 0.584489i
\(689\) 4.77795 2.75855i 0.182025 0.105092i
\(690\) 0 0
\(691\) −8.33676 + 14.4397i −0.317145 + 0.549312i −0.979891 0.199533i \(-0.936058\pi\)
0.662746 + 0.748844i \(0.269391\pi\)
\(692\) 13.4808 + 2.84761i 0.512464 + 0.108250i
\(693\) 0 0
\(694\) −3.18774 + 30.5151i −0.121005 + 1.15834i
\(695\) −10.7358 + 18.5949i −0.407231 + 0.705344i
\(696\) 0 0
\(697\) −7.96571 13.7970i −0.301723 0.522599i
\(698\) 8.52151 + 6.18300i 0.322544 + 0.234030i
\(699\) 0 0
\(700\) −8.04980 + 47.8837i −0.304254 + 1.80983i
\(701\) 24.5914 0.928805 0.464403 0.885624i \(-0.346269\pi\)
0.464403 + 0.885624i \(0.346269\pi\)
\(702\) 0 0
\(703\) −12.2825 + 7.09128i −0.463242 + 0.267453i
\(704\) −13.5179 1.36890i −0.509477 0.0515925i
\(705\) 0 0
\(706\) 2.21186 21.1734i 0.0832444 0.796870i
\(707\) 3.64733 + 1.90803i 0.137172 + 0.0717587i
\(708\) 0 0
\(709\) 4.59843 + 2.65490i 0.172698 + 0.0997070i 0.583857 0.811856i \(-0.301543\pi\)
−0.411160 + 0.911563i \(0.634876\pi\)
\(710\) −20.3987 45.7384i −0.765551 1.71653i
\(711\) 0 0
\(712\) 20.9940 + 23.2274i 0.786785 + 0.870483i
\(713\) 7.17437i 0.268682i
\(714\) 0 0
\(715\) −36.0799 −1.34931
\(716\) −23.3746 20.9930i −0.873549 0.784547i
\(717\) 0 0
\(718\) −10.3902 23.2970i −0.387757 0.869436i
\(719\) 5.16456 8.94528i 0.192606 0.333603i −0.753507 0.657439i \(-0.771640\pi\)
0.946113 + 0.323837i \(0.104973\pi\)
\(720\) 0 0
\(721\) −21.1857 + 0.882240i −0.788997 + 0.0328563i
\(722\) 18.8806 + 1.97235i 0.702663 + 0.0734031i
\(723\) 0 0
\(724\) 29.7965 9.72319i 1.10738 0.361360i
\(725\) −31.2422 54.1131i −1.16031 2.00971i
\(726\) 0 0
\(727\) 28.6727i 1.06341i −0.846929 0.531706i \(-0.821551\pi\)
0.846929 0.531706i \(-0.178449\pi\)
\(728\) −10.5670 40.8788i −0.391638 1.51507i
\(729\) 0 0
\(730\) −6.81712 + 9.39546i −0.252313 + 0.347742i
\(731\) −14.6863 + 8.47916i −0.543193 + 0.313613i
\(732\) 0 0
\(733\) −33.6091 19.4042i −1.24138 0.716710i −0.272004 0.962296i \(-0.587686\pi\)
−0.969375 + 0.245586i \(0.921020\pi\)
\(734\) 0.574993 5.50421i 0.0212234 0.203164i
\(735\) 0 0
\(736\) −6.41830 3.67857i −0.236582 0.135594i
\(737\) −19.7042 11.3763i −0.725815 0.419050i
\(738\) 0 0
\(739\) −5.59773 9.69556i −0.205916 0.356657i 0.744508 0.667613i \(-0.232684\pi\)
−0.950424 + 0.310956i \(0.899351\pi\)
\(740\) −33.6466 30.2184i −1.23687 1.11085i
\(741\) 0 0
\(742\) −3.27654 + 1.62797i −0.120285 + 0.0597648i
\(743\) 6.68201 0.245139 0.122570 0.992460i \(-0.460887\pi\)
0.122570 + 0.992460i \(0.460887\pi\)
\(744\) 0 0
\(745\) −25.3843 43.9668i −0.930007 1.61082i
\(746\) −23.6406 + 10.5434i −0.865543 + 0.386021i
\(747\) 0 0
\(748\) 8.67335 + 1.83210i 0.317129 + 0.0669883i
\(749\) −38.5387 + 1.60487i −1.40817 + 0.0586407i
\(750\) 0 0
\(751\) 43.2883 + 24.9925i 1.57961 + 0.911990i 0.994913 + 0.100741i \(0.0321215\pi\)
0.584701 + 0.811249i \(0.301212\pi\)
\(752\) 3.02607 + 28.1064i 0.110349 + 1.02493i
\(753\) 0 0
\(754\) 43.9778 + 31.9092i 1.60158 + 1.16207i
\(755\) 80.3117i 2.92284i
\(756\) 0 0
\(757\) 32.8378i 1.19351i −0.802424 0.596755i \(-0.796457\pi\)
0.802424 0.596755i \(-0.203543\pi\)
\(758\) 21.4337 29.5403i 0.778507 1.07295i
\(759\) 0 0
\(760\) −5.27541 24.5891i −0.191359 0.891942i
\(761\) 28.7157 + 16.5790i 1.04094 + 0.600988i 0.920100 0.391683i \(-0.128107\pi\)
0.120842 + 0.992672i \(0.461440\pi\)
\(762\) 0 0
\(763\) 0.927825 1.77360i 0.0335895 0.0642088i
\(764\) 47.2116 + 9.97268i 1.70806 + 0.360799i
\(765\) 0 0
\(766\) −8.49835 19.0551i −0.307058 0.688490i
\(767\) −21.7406 37.6559i −0.785008 1.35967i
\(768\) 0 0
\(769\) −48.1183 −1.73519 −0.867596 0.497270i \(-0.834336\pi\)
−0.867596 + 0.497270i \(0.834336\pi\)
\(770\) 23.8798 + 1.49366i 0.860569 + 0.0538277i
\(771\) 0 0
\(772\) −12.8374 + 14.2937i −0.462028 + 0.514443i
\(773\) −14.2293 24.6458i −0.511791 0.886449i −0.999907 0.0136695i \(-0.995649\pi\)
0.488115 0.872779i \(-0.337685\pi\)
\(774\) 0 0
\(775\) 43.5965 + 25.1704i 1.56603 + 0.904148i
\(776\) −40.5447 13.0887i −1.45547 0.469857i
\(777\) 0 0
\(778\) −24.4816 2.55745i −0.877707 0.0916890i
\(779\) 12.4847 + 7.20802i 0.447309 + 0.258254i
\(780\) 0 0
\(781\) −13.8339 + 7.98703i −0.495017 + 0.285798i
\(782\) 3.90657 + 2.83451i 0.139699 + 0.101362i
\(783\) 0 0
\(784\) 5.30152 + 27.4935i 0.189340 + 0.981912i
\(785\) 34.6612i 1.23711i
\(786\) 0 0
\(787\) −11.0597 19.1559i −0.394234 0.682834i 0.598769 0.800922i \(-0.295657\pi\)
−0.993003 + 0.118088i \(0.962323\pi\)
\(788\) −1.27380 3.90353i −0.0453773 0.139058i
\(789\) 0 0
\(790\) 9.64020 92.2823i 0.342983 3.28326i
\(791\) 13.9920 + 22.0609i 0.497497 + 0.784395i
\(792\) 0 0
\(793\) 24.9033 43.1339i 0.884344 1.53173i
\(794\) −14.9546 + 6.66957i −0.530720 + 0.236694i
\(795\) 0 0
\(796\) 14.8124 + 13.3033i 0.525013 + 0.471521i
\(797\) −25.7820 −0.913247 −0.456623 0.889660i \(-0.650941\pi\)
−0.456623 + 0.889660i \(0.650941\pi\)
\(798\) 0 0
\(799\) 18.4437i 0.652490i
\(800\) 44.8714 26.0962i 1.58644 0.922640i
\(801\) 0 0
\(802\) −46.4499 + 20.7161i −1.64020 + 0.731510i
\(803\) 3.20652 + 1.85128i 0.113156 + 0.0653304i
\(804\) 0 0
\(805\) 11.5431 + 6.03856i 0.406842 + 0.212831i
\(806\) −43.5380 4.54816i −1.53356 0.160202i
\(807\) 0 0
\(808\) −0.923080 4.30256i −0.0324738 0.151363i
\(809\) 2.56573 1.48132i 0.0902062 0.0520806i −0.454218 0.890890i \(-0.650081\pi\)
0.544425 + 0.838810i \(0.316748\pi\)
\(810\) 0 0
\(811\) −51.9174 −1.82307 −0.911533 0.411228i \(-0.865100\pi\)
−0.911533 + 0.411228i \(0.865100\pi\)
\(812\) −27.7862 22.9401i −0.975103 0.805039i
\(813\) 0 0
\(814\) −8.47139 + 11.6754i −0.296922 + 0.409223i
\(815\) −0.226030 0.391495i −0.00791747 0.0137135i
\(816\) 0 0
\(817\) 7.67262 13.2894i 0.268431 0.464936i
\(818\) 34.2118 + 3.57391i 1.19619 + 0.124959i
\(819\) 0 0
\(820\) −9.50053 + 44.9764i −0.331773 + 1.57064i
\(821\) −10.7741 + 18.6612i −0.376017 + 0.651281i −0.990479 0.137666i \(-0.956040\pi\)
0.614462 + 0.788947i \(0.289373\pi\)
\(822\) 0 0
\(823\) 30.0162 17.3299i 1.04630 0.604082i 0.124689 0.992196i \(-0.460207\pi\)
0.921611 + 0.388114i \(0.126873\pi\)
\(824\) 15.1999 + 16.8168i 0.529513 + 0.585843i
\(825\) 0 0
\(826\) 12.8303 + 25.8229i 0.446425 + 0.898495i
\(827\) 40.6029i 1.41190i −0.708260 0.705951i \(-0.750520\pi\)
0.708260 0.705951i \(-0.249480\pi\)
\(828\) 0 0
\(829\) −28.2837 + 16.3296i −0.982334 + 0.567151i −0.902974 0.429695i \(-0.858621\pi\)
−0.0793604 + 0.996846i \(0.525288\pi\)
\(830\) 57.8034 25.7796i 2.00639 0.894823i
\(831\) 0 0
\(832\) −26.3924 + 36.6177i −0.914992 + 1.26949i
\(833\) −1.51886 18.2050i −0.0526256 0.630767i
\(834\) 0 0
\(835\) −24.4376 + 42.3271i −0.845697 + 1.46479i
\(836\) −7.62578 + 2.48844i −0.263743 + 0.0860647i
\(837\) 0 0
\(838\) 7.93189 + 5.75519i 0.274002 + 0.198810i
\(839\) 35.4704 1.22458 0.612288 0.790635i \(-0.290249\pi\)
0.612288 + 0.790635i \(0.290249\pi\)
\(840\) 0 0
\(841\) 17.3685 0.598913
\(842\) 14.4446 + 10.4807i 0.497794 + 0.361187i
\(843\) 0 0
\(844\) 8.67112 + 26.5724i 0.298472 + 0.914661i
\(845\) −35.4573 + 61.4138i −1.21977 + 2.11270i
\(846\) 0 0
\(847\) 0.893370 + 21.4530i 0.0306965 + 0.737133i
\(848\) 3.57717 + 1.58182i 0.122840 + 0.0543198i
\(849\) 0 0
\(850\) −30.9302 + 13.7945i −1.06090 + 0.473147i
\(851\) −6.80170 + 3.92697i −0.233159 + 0.134615i
\(852\) 0 0
\(853\) 2.87597i 0.0984714i 0.998787 + 0.0492357i \(0.0156786\pi\)
−0.998787 + 0.0492357i \(0.984321\pi\)
\(854\) −18.2682 + 27.5176i −0.625126 + 0.941634i
\(855\) 0 0
\(856\) 27.6499 + 30.5913i 0.945055 + 1.04559i
\(857\) 5.76468 3.32824i 0.196918 0.113691i −0.398299 0.917256i \(-0.630399\pi\)
0.595217 + 0.803565i \(0.297066\pi\)
\(858\) 0 0
\(859\) 10.2685 17.7855i 0.350355 0.606833i −0.635956 0.771725i \(-0.719394\pi\)
0.986312 + 0.164892i \(0.0527276\pi\)
\(860\) 47.8754 + 10.1129i 1.63254 + 0.344847i
\(861\) 0 0
\(862\) 31.4390 + 3.28425i 1.07082 + 0.111862i
\(863\) −15.7546 + 27.2877i −0.536292 + 0.928886i 0.462807 + 0.886459i \(0.346842\pi\)
−0.999100 + 0.0424266i \(0.986491\pi\)
\(864\) 0 0
\(865\) 12.9692 + 22.4634i 0.440968 + 0.763778i
\(866\) −26.8106 + 36.9508i −0.911061 + 1.25564i
\(867\) 0 0
\(868\) 28.6278 + 4.81267i 0.971690 + 0.163353i
\(869\) −29.5949 −1.00394
\(870\) 0 0
\(871\) −65.4596 + 37.7931i −2.21801 + 1.28057i
\(872\) −2.09223 + 0.448871i −0.0708517 + 0.0152007i
\(873\) 0 0
\(874\) −4.34383 0.453775i −0.146932 0.0153492i
\(875\) −35.1308 + 22.2815i −1.18764 + 0.753251i
\(876\) 0 0
\(877\) −48.3067 27.8899i −1.63120 0.941774i −0.983723 0.179689i \(-0.942491\pi\)
−0.647477 0.762085i \(-0.724176\pi\)
\(878\) 3.62107 1.61495i 0.122205 0.0545020i
\(879\) 0 0
\(880\) −15.0870 20.6553i −0.508583 0.696290i
\(881\) 21.9485i 0.739464i 0.929138 + 0.369732i \(0.120550\pi\)
−0.929138 + 0.369732i \(0.879450\pi\)
\(882\) 0 0
\(883\) 33.4287 1.12497 0.562483 0.826809i \(-0.309846\pi\)
0.562483 + 0.826809i \(0.309846\pi\)
\(884\) 19.6779 21.9103i 0.661840 0.736922i
\(885\) 0 0
\(886\) 24.1704 10.7797i 0.812021 0.362151i
\(887\) −6.18309 + 10.7094i −0.207608 + 0.359587i −0.950960 0.309313i \(-0.899901\pi\)
0.743353 + 0.668900i \(0.233234\pi\)
\(888\) 0 0
\(889\) −6.38880 10.0731i −0.214273 0.337841i
\(890\) −6.12394 + 58.6223i −0.205275 + 1.96502i
\(891\) 0 0
\(892\) −30.1963 + 9.85367i −1.01105 + 0.329925i
\(893\) 8.34466 + 14.4534i 0.279243 + 0.483664i
\(894\) 0 0
\(895\) 59.1460i 1.97703i
\(896\) 18.9840 23.1432i 0.634211 0.773160i
\(897\) 0 0
\(898\) 15.9049 + 11.5402i 0.530755 + 0.385103i
\(899\) −32.3521 + 18.6785i −1.07900 + 0.622963i
\(900\) 0 0
\(901\) −2.21000 1.27594i −0.0736257 0.0425078i
\(902\) 14.5831 + 1.52341i 0.485563 + 0.0507240i
\(903\) 0 0
\(904\) 8.57965 26.5771i 0.285355 0.883941i
\(905\) 51.0996 + 29.5024i 1.69861 + 0.980692i
\(906\) 0 0
\(907\) −6.85914 11.8804i −0.227754 0.394481i 0.729388 0.684100i \(-0.239805\pi\)
−0.957142 + 0.289619i \(0.906471\pi\)
\(908\) −1.06537 0.956823i −0.0353555 0.0317533i
\(909\) 0 0
\(910\) 43.9630 66.2219i 1.45736 2.19524i
\(911\) 9.02706 0.299080 0.149540 0.988756i \(-0.452221\pi\)
0.149540 + 0.988756i \(0.452221\pi\)
\(912\) 0 0
\(913\) −10.0939 17.4831i −0.334058 0.578606i
\(914\) −3.32856 7.46335i −0.110099 0.246866i
\(915\) 0 0
\(916\) −1.86102 + 8.81025i −0.0614899 + 0.291099i
\(917\) −42.9391 + 1.78812i −1.41797 + 0.0590489i
\(918\) 0 0
\(919\) −37.8104 21.8298i −1.24725 0.720100i −0.276689 0.960959i \(-0.589237\pi\)
−0.970560 + 0.240860i \(0.922571\pi\)
\(920\) −2.92138 13.6168i −0.0963151 0.448933i
\(921\) 0 0
\(922\) 12.8086 17.6530i 0.421829 0.581372i
\(923\) 53.0675i 1.74674i
\(924\) 0 0
\(925\) 55.1092i 1.81198i
\(926\) 13.2668 + 9.62603i 0.435973 + 0.316331i
\(927\) 0 0
\(928\) 0.121919 + 38.5198i 0.00400218 + 1.26447i
\(929\) 43.0944 + 24.8806i 1.41388 + 0.816304i 0.995751 0.0920830i \(-0.0293525\pi\)
0.418129 + 0.908387i \(0.362686\pi\)
\(930\) 0 0
\(931\) 9.42695 + 13.5792i 0.308956 + 0.445039i
\(932\) 3.19596 15.1300i 0.104687 0.495599i
\(933\) 0 0
\(934\) −2.95524 + 1.31800i −0.0966984 + 0.0431263i
\(935\) 8.34421 + 14.4526i 0.272885 + 0.472650i
\(936\) 0 0
\(937\) 40.5415 1.32443 0.662216 0.749313i \(-0.269616\pi\)
0.662216 + 0.749313i \(0.269616\pi\)
\(938\) 44.8897 22.3038i 1.46570 0.728246i
\(939\) 0 0
\(940\) −35.5595 + 39.5935i −1.15982 + 1.29140i
\(941\) 27.1914 + 47.0968i 0.886414 + 1.53531i 0.844085 + 0.536209i \(0.180144\pi\)
0.0423286 + 0.999104i \(0.486522\pi\)
\(942\) 0 0
\(943\) 6.91367 + 3.99161i 0.225140 + 0.129985i
\(944\) 12.4666 28.1923i 0.405752 0.917581i
\(945\) 0 0
\(946\) 1.62160 15.5230i 0.0527229 0.504698i
\(947\) −12.3501 7.13032i −0.401323 0.231704i 0.285732 0.958310i \(-0.407763\pi\)
−0.687055 + 0.726606i \(0.741097\pi\)
\(948\) 0 0
\(949\) 10.6524 6.15016i 0.345791 0.199643i
\(950\) 17.9972 24.8041i 0.583908 0.804751i
\(951\) 0 0
\(952\) −13.9311 + 13.6869i −0.451509 + 0.443595i
\(953\) 3.31610i 0.107419i −0.998557 0.0537095i \(-0.982896\pi\)
0.998557 0.0537095i \(-0.0171045\pi\)
\(954\) 0 0
\(955\) 45.4200 + 78.6697i 1.46976 + 2.54569i
\(956\) 13.2643 + 40.6482i 0.428998 + 1.31466i
\(957\) 0 0
\(958\) −26.5263 2.77105i −0.857025 0.0895285i
\(959\) −5.14717 + 9.83919i −0.166211 + 0.317724i
\(960\) 0 0
\(961\) −0.451578 + 0.782157i −0.0145670 + 0.0252309i
\(962\) 19.5191 + 43.7659i 0.629319 + 1.41107i
\(963\) 0 0
\(964\) 11.3776 12.6683i 0.366448 0.408019i
\(965\) −36.1682 −1.16430
\(966\) 0 0
\(967\) 18.6637i 0.600185i 0.953910 + 0.300092i \(0.0970175\pi\)
−0.953910 + 0.300092i \(0.902982\pi\)
\(968\) 17.0290 15.3916i 0.547333 0.494706i
\(969\) 0 0
\(970\) −32.6693 73.2516i −1.04895 2.35197i
\(971\) 4.93811 + 2.85102i 0.158472 + 0.0914936i 0.577139 0.816646i \(-0.304169\pi\)
−0.418667 + 0.908140i \(0.637503\pi\)
\(972\) 0 0
\(973\) −12.7414 + 8.08115i −0.408471 + 0.259070i
\(974\) 4.56434 43.6928i 0.146251 1.40001i
\(975\) 0 0
\(976\) 35.1071 3.77981i 1.12375 0.120989i
\(977\) −3.52730 + 2.03649i −0.112848 + 0.0651530i −0.555362 0.831609i \(-0.687420\pi\)
0.442514 + 0.896762i \(0.354087\pi\)
\(978\) 0 0
\(979\) 18.8002 0.600856
\(980\) −31.8389 + 42.0097i −1.01705 + 1.34195i
\(981\) 0 0
\(982\) −8.61861 6.25345i −0.275031 0.199556i
\(983\) −13.6318 23.6109i −0.434786 0.753071i 0.562492 0.826803i \(-0.309843\pi\)
−0.997278 + 0.0737313i \(0.976509\pi\)
\(984\) 0 0
\(985\) 3.86500 6.69438i 0.123149 0.213301i
\(986\) 2.61118 24.9959i 0.0831570 0.796033i
\(987\) 0 0
\(988\) −5.50750 + 26.0730i −0.175217 + 0.829494i
\(989\) 4.24890 7.35930i 0.135107 0.234012i
\(990\) 0 0
\(991\) −7.91978 + 4.57249i −0.251580 + 0.145250i −0.620488 0.784216i \(-0.713065\pi\)
0.368907 + 0.929466i \(0.379732\pi\)
\(992\) −15.6019 26.8268i −0.495361 0.851753i
\(993\) 0 0
\(994\) 2.19693 35.1233i 0.0696823 1.11404i
\(995\) 37.4807i 1.18822i
\(996\) 0 0
\(997\) 40.5025 23.3841i 1.28273 0.740583i 0.305381 0.952230i \(-0.401216\pi\)
0.977346 + 0.211647i \(0.0678827\pi\)
\(998\) 1.01759 + 2.28165i 0.0322112 + 0.0722245i
\(999\) 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 504.2.bm.c.107.17 yes 48
3.2 odd 2 inner 504.2.bm.c.107.8 48
4.3 odd 2 2016.2.bu.c.1871.23 48
7.4 even 3 inner 504.2.bm.c.179.15 yes 48
8.3 odd 2 inner 504.2.bm.c.107.10 yes 48
8.5 even 2 2016.2.bu.c.1871.1 48
12.11 even 2 2016.2.bu.c.1871.2 48
21.11 odd 6 inner 504.2.bm.c.179.10 yes 48
24.5 odd 2 2016.2.bu.c.1871.24 48
24.11 even 2 inner 504.2.bm.c.107.15 yes 48
28.11 odd 6 2016.2.bu.c.431.24 48
56.11 odd 6 inner 504.2.bm.c.179.8 yes 48
56.53 even 6 2016.2.bu.c.431.2 48
84.11 even 6 2016.2.bu.c.431.1 48
168.11 even 6 inner 504.2.bm.c.179.17 yes 48
168.53 odd 6 2016.2.bu.c.431.23 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bm.c.107.8 48 3.2 odd 2 inner
504.2.bm.c.107.10 yes 48 8.3 odd 2 inner
504.2.bm.c.107.15 yes 48 24.11 even 2 inner
504.2.bm.c.107.17 yes 48 1.1 even 1 trivial
504.2.bm.c.179.8 yes 48 56.11 odd 6 inner
504.2.bm.c.179.10 yes 48 21.11 odd 6 inner
504.2.bm.c.179.15 yes 48 7.4 even 3 inner
504.2.bm.c.179.17 yes 48 168.11 even 6 inner
2016.2.bu.c.431.1 48 84.11 even 6
2016.2.bu.c.431.2 48 56.53 even 6
2016.2.bu.c.431.23 48 168.53 odd 6
2016.2.bu.c.431.24 48 28.11 odd 6
2016.2.bu.c.1871.1 48 8.5 even 2
2016.2.bu.c.1871.2 48 12.11 even 2
2016.2.bu.c.1871.23 48 4.3 odd 2
2016.2.bu.c.1871.24 48 24.5 odd 2