Properties

Label 189.2.s.b.89.1
Level $189$
Weight $2$
Character 189.89
Analytic conductor $1.509$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,2,Mod(17,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.s (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: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: 10.0.288778218147.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.1
Root \(0.827154 + 1.43267i\) of defining polynomial
Character \(\chi\) \(=\) 189.89
Dual form 189.2.s.b.17.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.81474 + 1.04774i) q^{2} +(1.19552 - 2.07070i) q^{4} +2.08983 q^{5} +(-0.879217 - 2.49539i) q^{7} +0.819421i q^{8} +O(q^{10})\) \(q+(-1.81474 + 1.04774i) q^{2} +(1.19552 - 2.07070i) q^{4} +2.08983 q^{5} +(-0.879217 - 2.49539i) q^{7} +0.819421i q^{8} +(-3.79250 + 2.18960i) q^{10} -3.22878i q^{11} +(2.68740 - 1.55157i) q^{13} +(4.21007 + 3.60729i) q^{14} +(1.53250 + 2.65437i) q^{16} +(0.816304 + 1.41388i) q^{17} +(4.79094 + 2.76605i) q^{19} +(2.49844 - 4.32742i) q^{20} +(3.38292 + 5.85939i) q^{22} -1.16078i q^{23} -0.632608 q^{25} +(-3.25129 + 5.63139i) q^{26} +(-6.21834 - 1.16270i) q^{28} +(7.05749 + 4.07464i) q^{29} +(-5.16886 - 2.98424i) q^{31} +(-6.98146 - 4.03075i) q^{32} +(-2.96276 - 1.71055i) q^{34} +(-1.83741 - 5.21495i) q^{35} +(2.82656 - 4.89575i) q^{37} -11.5924 q^{38} +1.71245i q^{40} +(1.35369 + 2.34465i) q^{41} +(-0.974903 + 1.68858i) q^{43} +(-6.68583 - 3.86007i) q^{44} +(1.21620 + 2.10652i) q^{46} +(-4.06759 - 7.04527i) q^{47} +(-5.45395 + 4.38798i) q^{49} +(1.14802 - 0.662809i) q^{50} -7.41974i q^{52} +(-5.27766 + 3.04706i) q^{53} -6.74759i q^{55} +(2.04477 - 0.720448i) q^{56} -17.0767 q^{58} +(1.98103 - 3.43124i) q^{59} +(-4.15016 + 2.39609i) q^{61} +12.5068 q^{62} +10.7627 q^{64} +(5.61621 - 3.24252i) q^{65} +(0.336981 - 0.583668i) q^{67} +3.90363 q^{68} +(8.79834 + 7.53864i) q^{70} +7.01535i q^{71} +(-2.96276 + 1.71055i) q^{73} +11.8460i q^{74} +(11.4553 - 6.61374i) q^{76} +(-8.05706 + 2.83879i) q^{77} +(7.07973 + 12.2625i) q^{79} +(3.20267 + 5.54718i) q^{80} +(-4.91318 - 2.83662i) q^{82} +(-1.54535 + 2.67662i) q^{83} +(1.70594 + 2.95477i) q^{85} -4.08578i q^{86} +2.64572 q^{88} +(2.45766 - 4.25679i) q^{89} +(-6.23458 - 5.34194i) q^{91} +(-2.40363 - 1.38774i) q^{92} +(14.7632 + 8.52356i) q^{94} +(10.0122 + 5.78057i) q^{95} +(2.07939 + 1.20054i) q^{97} +(5.30004 - 13.6774i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 4 q^{4} + 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 4 q^{4} + 3 q^{7} - 15 q^{10} + 6 q^{13} + 6 q^{14} - 6 q^{16} + 12 q^{17} + 3 q^{19} + 3 q^{20} + 5 q^{22} - 14 q^{25} - 3 q^{26} + 2 q^{28} + 15 q^{29} - 9 q^{31} - 48 q^{32} + 3 q^{34} + 15 q^{35} + 6 q^{37} - 36 q^{38} + 9 q^{41} + 3 q^{43} - 24 q^{44} - 13 q^{46} - 15 q^{47} - 23 q^{49} - 3 q^{50} + 9 q^{53} + 51 q^{56} - 16 q^{58} + 18 q^{59} + 12 q^{61} - 12 q^{62} + 6 q^{64} + 3 q^{65} - 10 q^{67} + 54 q^{68} + 9 q^{70} + 3 q^{73} + 9 q^{76} - 45 q^{77} + 20 q^{79} + 30 q^{80} + 9 q^{82} + 15 q^{83} + 18 q^{85} + 16 q^{88} - 24 q^{89} - 24 q^{91} - 39 q^{92} - 3 q^{94} + 6 q^{97} - 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81474 + 1.04774i −1.28321 + 0.740865i −0.977435 0.211238i \(-0.932251\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(3\) 0 0
\(4\) 1.19552 2.07070i 0.597760 1.03535i
\(5\) 2.08983 0.934601 0.467300 0.884099i \(-0.345227\pi\)
0.467300 + 0.884099i \(0.345227\pi\)
\(6\) 0 0
\(7\) −0.879217 2.49539i −0.332313 0.943169i
\(8\) 0.819421i 0.289709i
\(9\) 0 0
\(10\) −3.79250 + 2.18960i −1.19929 + 0.692412i
\(11\) 3.22878i 0.973512i −0.873538 0.486756i \(-0.838180\pi\)
0.873538 0.486756i \(-0.161820\pi\)
\(12\) 0 0
\(13\) 2.68740 1.55157i 0.745350 0.430328i −0.0786612 0.996901i \(-0.525065\pi\)
0.824011 + 0.566573i \(0.191731\pi\)
\(14\) 4.21007 + 3.60729i 1.12519 + 0.964090i
\(15\) 0 0
\(16\) 1.53250 + 2.65437i 0.383125 + 0.663593i
\(17\) 0.816304 + 1.41388i 0.197983 + 0.342916i 0.947874 0.318645i \(-0.103228\pi\)
−0.749891 + 0.661561i \(0.769894\pi\)
\(18\) 0 0
\(19\) 4.79094 + 2.76605i 1.09912 + 0.634575i 0.935989 0.352030i \(-0.114509\pi\)
0.163127 + 0.986605i \(0.447842\pi\)
\(20\) 2.49844 4.32742i 0.558667 0.967640i
\(21\) 0 0
\(22\) 3.38292 + 5.85939i 0.721241 + 1.24923i
\(23\) 1.16078i 0.242040i −0.992650 0.121020i \(-0.961384\pi\)
0.992650 0.121020i \(-0.0386165\pi\)
\(24\) 0 0
\(25\) −0.632608 −0.126522
\(26\) −3.25129 + 5.63139i −0.637630 + 1.10441i
\(27\) 0 0
\(28\) −6.21834 1.16270i −1.17516 0.219729i
\(29\) 7.05749 + 4.07464i 1.31054 + 0.756643i 0.982186 0.187911i \(-0.0601717\pi\)
0.328357 + 0.944554i \(0.393505\pi\)
\(30\) 0 0
\(31\) −5.16886 2.98424i −0.928355 0.535986i −0.0420638 0.999115i \(-0.513393\pi\)
−0.886291 + 0.463129i \(0.846727\pi\)
\(32\) −6.98146 4.03075i −1.23416 0.712542i
\(33\) 0 0
\(34\) −2.96276 1.71055i −0.508109 0.293357i
\(35\) −1.83741 5.21495i −0.310580 0.881487i
\(36\) 0 0
\(37\) 2.82656 4.89575i 0.464684 0.804857i −0.534503 0.845167i \(-0.679501\pi\)
0.999187 + 0.0403097i \(0.0128345\pi\)
\(38\) −11.5924 −1.88054
\(39\) 0 0
\(40\) 1.71245i 0.270762i
\(41\) 1.35369 + 2.34465i 0.211410 + 0.366173i 0.952156 0.305612i \(-0.0988611\pi\)
−0.740746 + 0.671785i \(0.765528\pi\)
\(42\) 0 0
\(43\) −0.974903 + 1.68858i −0.148671 + 0.257506i −0.930737 0.365690i \(-0.880833\pi\)
0.782065 + 0.623196i \(0.214166\pi\)
\(44\) −6.68583 3.86007i −1.00793 0.581927i
\(45\) 0 0
\(46\) 1.21620 + 2.10652i 0.179319 + 0.310589i
\(47\) −4.06759 7.04527i −0.593319 1.02766i −0.993782 0.111346i \(-0.964484\pi\)
0.400463 0.916313i \(-0.368849\pi\)
\(48\) 0 0
\(49\) −5.45395 + 4.38798i −0.779136 + 0.626854i
\(50\) 1.14802 0.662809i 0.162354 0.0937353i
\(51\) 0 0
\(52\) 7.41974i 1.02893i
\(53\) −5.27766 + 3.04706i −0.724943 + 0.418546i −0.816569 0.577248i \(-0.804127\pi\)
0.0916264 + 0.995793i \(0.470793\pi\)
\(54\) 0 0
\(55\) 6.74759i 0.909845i
\(56\) 2.04477 0.720448i 0.273245 0.0962740i
\(57\) 0 0
\(58\) −17.0767 −2.24228
\(59\) 1.98103 3.43124i 0.257908 0.446709i −0.707773 0.706439i \(-0.750300\pi\)
0.965681 + 0.259730i \(0.0836336\pi\)
\(60\) 0 0
\(61\) −4.15016 + 2.39609i −0.531373 + 0.306788i −0.741575 0.670869i \(-0.765921\pi\)
0.210202 + 0.977658i \(0.432588\pi\)
\(62\) 12.5068 1.58837
\(63\) 0 0
\(64\) 10.7627 1.34534
\(65\) 5.61621 3.24252i 0.696605 0.402185i
\(66\) 0 0
\(67\) 0.336981 0.583668i 0.0411687 0.0713063i −0.844707 0.535229i \(-0.820225\pi\)
0.885876 + 0.463923i \(0.153559\pi\)
\(68\) 3.90363 0.473385
\(69\) 0 0
\(70\) 8.79834 + 7.53864i 1.05160 + 0.901039i
\(71\) 7.01535i 0.832568i 0.909235 + 0.416284i \(0.136668\pi\)
−0.909235 + 0.416284i \(0.863332\pi\)
\(72\) 0 0
\(73\) −2.96276 + 1.71055i −0.346765 + 0.200205i −0.663259 0.748390i \(-0.730827\pi\)
0.316495 + 0.948594i \(0.397494\pi\)
\(74\) 11.8460i 1.37707i
\(75\) 0 0
\(76\) 11.4553 6.61374i 1.31402 0.758648i
\(77\) −8.05706 + 2.83879i −0.918187 + 0.323511i
\(78\) 0 0
\(79\) 7.07973 + 12.2625i 0.796532 + 1.37963i 0.921862 + 0.387519i \(0.126668\pi\)
−0.125330 + 0.992115i \(0.539999\pi\)
\(80\) 3.20267 + 5.54718i 0.358069 + 0.620194i
\(81\) 0 0
\(82\) −4.91318 2.83662i −0.542570 0.313253i
\(83\) −1.54535 + 2.67662i −0.169624 + 0.293798i −0.938288 0.345856i \(-0.887589\pi\)
0.768664 + 0.639653i \(0.220922\pi\)
\(84\) 0 0
\(85\) 1.70594 + 2.95477i 0.185035 + 0.320490i
\(86\) 4.08578i 0.440581i
\(87\) 0 0
\(88\) 2.64572 0.282035
\(89\) 2.45766 4.25679i 0.260511 0.451219i −0.705867 0.708345i \(-0.749442\pi\)
0.966378 + 0.257126i \(0.0827756\pi\)
\(90\) 0 0
\(91\) −6.23458 5.34194i −0.653562 0.559988i
\(92\) −2.40363 1.38774i −0.250596 0.144682i
\(93\) 0 0
\(94\) 14.7632 + 8.52356i 1.52271 + 0.879138i
\(95\) 10.0122 + 5.78057i 1.02723 + 0.593074i
\(96\) 0 0
\(97\) 2.07939 + 1.20054i 0.211130 + 0.121896i 0.601837 0.798619i \(-0.294436\pi\)
−0.390706 + 0.920515i \(0.627769\pi\)
\(98\) 5.30004 13.6774i 0.535385 1.38162i
\(99\) 0 0
\(100\) −0.756296 + 1.30994i −0.0756296 + 0.130994i
\(101\) 3.52051 0.350304 0.175152 0.984541i \(-0.443958\pi\)
0.175152 + 0.984541i \(0.443958\pi\)
\(102\) 0 0
\(103\) 15.6846i 1.54545i −0.634743 0.772723i \(-0.718894\pi\)
0.634743 0.772723i \(-0.281106\pi\)
\(104\) 1.27139 + 2.20211i 0.124670 + 0.215935i
\(105\) 0 0
\(106\) 6.38506 11.0592i 0.620172 1.07417i
\(107\) 1.41984 + 0.819746i 0.137261 + 0.0792478i 0.567058 0.823678i \(-0.308081\pi\)
−0.429797 + 0.902926i \(0.641415\pi\)
\(108\) 0 0
\(109\) 2.90672 + 5.03459i 0.278414 + 0.482227i 0.970991 0.239117i \(-0.0768581\pi\)
−0.692577 + 0.721344i \(0.743525\pi\)
\(110\) 7.06973 + 12.2451i 0.674072 + 1.16753i
\(111\) 0 0
\(112\) 5.27629 6.15796i 0.498563 0.581872i
\(113\) −13.9931 + 8.07894i −1.31636 + 0.760003i −0.983142 0.182845i \(-0.941469\pi\)
−0.333222 + 0.942848i \(0.608136\pi\)
\(114\) 0 0
\(115\) 2.42584i 0.226210i
\(116\) 16.8748 9.74265i 1.56678 0.904582i
\(117\) 0 0
\(118\) 8.30241i 0.764299i
\(119\) 2.81047 3.28010i 0.257636 0.300687i
\(120\) 0 0
\(121\) 0.575009 0.0522736
\(122\) 5.02097 8.69658i 0.454577 0.787351i
\(123\) 0 0
\(124\) −12.3590 + 7.13545i −1.10987 + 0.640782i
\(125\) −11.7712 −1.05285
\(126\) 0 0
\(127\) −9.59240 −0.851188 −0.425594 0.904914i \(-0.639935\pi\)
−0.425594 + 0.904914i \(0.639935\pi\)
\(128\) −5.56860 + 3.21503i −0.492199 + 0.284171i
\(129\) 0 0
\(130\) −6.79464 + 11.7687i −0.595929 + 1.03218i
\(131\) −2.46122 −0.215038 −0.107519 0.994203i \(-0.534291\pi\)
−0.107519 + 0.994203i \(0.534291\pi\)
\(132\) 0 0
\(133\) 2.69010 14.3872i 0.233261 1.24753i
\(134\) 1.41227i 0.122002i
\(135\) 0 0
\(136\) −1.15856 + 0.668896i −0.0993459 + 0.0573574i
\(137\) 17.3864i 1.48542i 0.669611 + 0.742712i \(0.266461\pi\)
−0.669611 + 0.742712i \(0.733539\pi\)
\(138\) 0 0
\(139\) −8.61174 + 4.97199i −0.730438 + 0.421719i −0.818582 0.574389i \(-0.805240\pi\)
0.0881443 + 0.996108i \(0.471906\pi\)
\(140\) −12.9953 2.42984i −1.09830 0.205359i
\(141\) 0 0
\(142\) −7.35026 12.7310i −0.616820 1.06836i
\(143\) −5.00967 8.67701i −0.418930 0.725608i
\(144\) 0 0
\(145\) 14.7490 + 8.51532i 1.22483 + 0.707159i
\(146\) 3.58442 6.20840i 0.296649 0.513811i
\(147\) 0 0
\(148\) −6.75843 11.7060i −0.555540 0.962223i
\(149\) 9.25717i 0.758377i 0.925319 + 0.379189i \(0.123797\pi\)
−0.925319 + 0.379189i \(0.876203\pi\)
\(150\) 0 0
\(151\) −11.9698 −0.974087 −0.487044 0.873378i \(-0.661925\pi\)
−0.487044 + 0.873378i \(0.661925\pi\)
\(152\) −2.26656 + 3.92579i −0.183842 + 0.318424i
\(153\) 0 0
\(154\) 11.6471 13.5934i 0.938554 1.09539i
\(155\) −10.8020 6.23656i −0.867641 0.500933i
\(156\) 0 0
\(157\) 15.4598 + 8.92569i 1.23382 + 0.712348i 0.967825 0.251626i \(-0.0809651\pi\)
0.265998 + 0.963974i \(0.414298\pi\)
\(158\) −25.6957 14.8354i −2.04424 1.18024i
\(159\) 0 0
\(160\) −14.5901 8.42358i −1.15345 0.665943i
\(161\) −2.89660 + 1.02058i −0.228284 + 0.0804329i
\(162\) 0 0
\(163\) −8.91768 + 15.4459i −0.698486 + 1.20981i 0.270505 + 0.962719i \(0.412809\pi\)
−0.968991 + 0.247095i \(0.920524\pi\)
\(164\) 6.47344 0.505491
\(165\) 0 0
\(166\) 6.47650i 0.502674i
\(167\) 6.16899 + 10.6850i 0.477371 + 0.826830i 0.999664 0.0259359i \(-0.00825657\pi\)
−0.522293 + 0.852766i \(0.674923\pi\)
\(168\) 0 0
\(169\) −1.68526 + 2.91896i −0.129635 + 0.224535i
\(170\) −6.19166 3.57476i −0.474879 0.274171i
\(171\) 0 0
\(172\) 2.33103 + 4.03747i 0.177740 + 0.307854i
\(173\) −4.53368 7.85256i −0.344689 0.597019i 0.640608 0.767868i \(-0.278682\pi\)
−0.985297 + 0.170849i \(0.945349\pi\)
\(174\) 0 0
\(175\) 0.556199 + 1.57860i 0.0420447 + 0.119331i
\(176\) 8.57037 4.94810i 0.646016 0.372977i
\(177\) 0 0
\(178\) 10.2999i 0.772014i
\(179\) 13.0086 7.51051i 0.972307 0.561362i 0.0723682 0.997378i \(-0.476944\pi\)
0.899939 + 0.436016i \(0.143611\pi\)
\(180\) 0 0
\(181\) 2.34159i 0.174049i −0.996206 0.0870246i \(-0.972264\pi\)
0.996206 0.0870246i \(-0.0277359\pi\)
\(182\) 16.9111 + 3.16201i 1.25354 + 0.234384i
\(183\) 0 0
\(184\) 0.951168 0.0701210
\(185\) 5.90704 10.2313i 0.434294 0.752220i
\(186\) 0 0
\(187\) 4.56510 2.63566i 0.333833 0.192739i
\(188\) −19.4516 −1.41865
\(189\) 0 0
\(190\) −24.2262 −1.75755
\(191\) −7.82585 + 4.51825i −0.566258 + 0.326929i −0.755654 0.654972i \(-0.772681\pi\)
0.189395 + 0.981901i \(0.439347\pi\)
\(192\) 0 0
\(193\) 2.74134 4.74815i 0.197326 0.341779i −0.750334 0.661058i \(-0.770108\pi\)
0.947661 + 0.319279i \(0.103441\pi\)
\(194\) −5.03141 −0.361234
\(195\) 0 0
\(196\) 2.56589 + 16.5394i 0.183278 + 1.18139i
\(197\) 2.88946i 0.205865i −0.994688 0.102933i \(-0.967177\pi\)
0.994688 0.102933i \(-0.0328226\pi\)
\(198\) 0 0
\(199\) 4.45419 2.57163i 0.315749 0.182298i −0.333747 0.942663i \(-0.608313\pi\)
0.649496 + 0.760365i \(0.274980\pi\)
\(200\) 0.518372i 0.0366544i
\(201\) 0 0
\(202\) −6.38881 + 3.68858i −0.449515 + 0.259528i
\(203\) 3.96277 21.1937i 0.278132 1.48751i
\(204\) 0 0
\(205\) 2.82897 + 4.89993i 0.197584 + 0.342226i
\(206\) 16.4334 + 28.4634i 1.14497 + 1.98314i
\(207\) 0 0
\(208\) 8.23688 + 4.75557i 0.571125 + 0.329739i
\(209\) 8.93095 15.4689i 0.617767 1.07000i
\(210\) 0 0
\(211\) 7.93224 + 13.7390i 0.546078 + 0.945835i 0.998538 + 0.0540502i \(0.0172131\pi\)
−0.452460 + 0.891785i \(0.649454\pi\)
\(212\) 14.5713i 1.00076i
\(213\) 0 0
\(214\) −3.43552 −0.234848
\(215\) −2.03738 + 3.52885i −0.138948 + 0.240666i
\(216\) 0 0
\(217\) −2.90230 + 15.5221i −0.197021 + 1.05371i
\(218\) −10.5499 6.09099i −0.714529 0.412534i
\(219\) 0 0
\(220\) −13.9723 8.06689i −0.942010 0.543870i
\(221\) 4.38747 + 2.53311i 0.295133 + 0.170395i
\(222\) 0 0
\(223\) 13.5288 + 7.81085i 0.905955 + 0.523053i 0.879127 0.476587i \(-0.158126\pi\)
0.0268275 + 0.999640i \(0.491460\pi\)
\(224\) −3.92008 + 20.9654i −0.261921 + 1.40081i
\(225\) 0 0
\(226\) 16.9293 29.3224i 1.12612 1.95049i
\(227\) −2.08089 −0.138114 −0.0690569 0.997613i \(-0.521999\pi\)
−0.0690569 + 0.997613i \(0.521999\pi\)
\(228\) 0 0
\(229\) 6.43437i 0.425195i 0.977140 + 0.212598i \(0.0681923\pi\)
−0.977140 + 0.212598i \(0.931808\pi\)
\(230\) 2.54165 + 4.40226i 0.167591 + 0.290277i
\(231\) 0 0
\(232\) −3.33885 + 5.78305i −0.219206 + 0.379676i
\(233\) 13.5222 + 7.80704i 0.885868 + 0.511456i 0.872589 0.488456i \(-0.162440\pi\)
0.0132791 + 0.999912i \(0.495773\pi\)
\(234\) 0 0
\(235\) −8.50057 14.7234i −0.554516 0.960450i
\(236\) −4.73672 8.20424i −0.308334 0.534050i
\(237\) 0 0
\(238\) −1.66358 + 8.89719i −0.107834 + 0.576719i
\(239\) 14.8777 8.58964i 0.962358 0.555618i 0.0654600 0.997855i \(-0.479149\pi\)
0.896898 + 0.442238i \(0.145815\pi\)
\(240\) 0 0
\(241\) 11.2184i 0.722642i −0.932441 0.361321i \(-0.882326\pi\)
0.932441 0.361321i \(-0.117674\pi\)
\(242\) −1.04349 + 0.602460i −0.0670782 + 0.0387276i
\(243\) 0 0
\(244\) 11.4583i 0.733544i
\(245\) −11.3978 + 9.17014i −0.728181 + 0.585859i
\(246\) 0 0
\(247\) 17.1669 1.09230
\(248\) 2.44535 4.23547i 0.155280 0.268953i
\(249\) 0 0
\(250\) 21.3617 12.3332i 1.35103 0.780018i
\(251\) −11.3837 −0.718535 −0.359267 0.933235i \(-0.616973\pi\)
−0.359267 + 0.933235i \(0.616973\pi\)
\(252\) 0 0
\(253\) −3.74790 −0.235629
\(254\) 17.4077 10.0504i 1.09226 0.630615i
\(255\) 0 0
\(256\) −4.02567 + 6.97267i −0.251604 + 0.435792i
\(257\) −9.38048 −0.585138 −0.292569 0.956244i \(-0.594510\pi\)
−0.292569 + 0.956244i \(0.594510\pi\)
\(258\) 0 0
\(259\) −14.7020 2.74895i −0.913537 0.170812i
\(260\) 15.5060i 0.961641i
\(261\) 0 0
\(262\) 4.46647 2.57872i 0.275940 0.159314i
\(263\) 8.80306i 0.542820i 0.962464 + 0.271410i \(0.0874899\pi\)
−0.962464 + 0.271410i \(0.912510\pi\)
\(264\) 0 0
\(265\) −11.0294 + 6.36784i −0.677532 + 0.391173i
\(266\) 10.1922 + 28.9276i 0.624926 + 1.77366i
\(267\) 0 0
\(268\) −0.805735 1.39557i −0.0492181 0.0852482i
\(269\) −8.16473 14.1417i −0.497812 0.862236i 0.502184 0.864761i \(-0.332530\pi\)
−0.999997 + 0.00252412i \(0.999197\pi\)
\(270\) 0 0
\(271\) −12.6186 7.28538i −0.766528 0.442555i 0.0651065 0.997878i \(-0.479261\pi\)
−0.831635 + 0.555323i \(0.812595\pi\)
\(272\) −2.50197 + 4.33355i −0.151704 + 0.262760i
\(273\) 0 0
\(274\) −18.2165 31.5519i −1.10050 1.90612i
\(275\) 2.04255i 0.123170i
\(276\) 0 0
\(277\) 28.7137 1.72524 0.862618 0.505855i \(-0.168823\pi\)
0.862618 + 0.505855i \(0.168823\pi\)
\(278\) 10.4187 18.0457i 0.624873 1.08231i
\(279\) 0 0
\(280\) 4.27323 1.50562i 0.255375 0.0899777i
\(281\) 4.76893 + 2.75334i 0.284490 + 0.164251i 0.635455 0.772138i \(-0.280813\pi\)
−0.350964 + 0.936389i \(0.614146\pi\)
\(282\) 0 0
\(283\) −26.2257 15.1414i −1.55896 0.900065i −0.997357 0.0726567i \(-0.976852\pi\)
−0.561601 0.827408i \(-0.689814\pi\)
\(284\) 14.5267 + 8.38699i 0.862001 + 0.497676i
\(285\) 0 0
\(286\) 18.1825 + 10.4977i 1.07515 + 0.620740i
\(287\) 4.66064 5.43943i 0.275109 0.321080i
\(288\) 0 0
\(289\) 7.16730 12.4141i 0.421606 0.730242i
\(290\) −35.6874 −2.09564
\(291\) 0 0
\(292\) 8.17999i 0.478698i
\(293\) 3.54362 + 6.13773i 0.207021 + 0.358570i 0.950775 0.309883i \(-0.100290\pi\)
−0.743754 + 0.668453i \(0.766957\pi\)
\(294\) 0 0
\(295\) 4.14001 7.17071i 0.241041 0.417495i
\(296\) 4.01168 + 2.31615i 0.233174 + 0.134623i
\(297\) 0 0
\(298\) −9.69912 16.7994i −0.561855 0.973161i
\(299\) −1.80103 3.11948i −0.104156 0.180404i
\(300\) 0 0
\(301\) 5.07082 + 0.948135i 0.292277 + 0.0546496i
\(302\) 21.7220 12.5412i 1.24996 0.721667i
\(303\) 0 0
\(304\) 16.9559i 0.972487i
\(305\) −8.67313 + 5.00743i −0.496622 + 0.286725i
\(306\) 0 0
\(307\) 3.11346i 0.177695i 0.996045 + 0.0888473i \(0.0283183\pi\)
−0.996045 + 0.0888473i \(0.971682\pi\)
\(308\) −3.75408 + 20.0776i −0.213909 + 1.14403i
\(309\) 0 0
\(310\) 26.1372 1.48449
\(311\) −9.72605 + 16.8460i −0.551514 + 0.955249i 0.446652 + 0.894708i \(0.352616\pi\)
−0.998166 + 0.0605417i \(0.980717\pi\)
\(312\) 0 0
\(313\) −22.1224 + 12.7724i −1.25043 + 0.721937i −0.971195 0.238285i \(-0.923415\pi\)
−0.279237 + 0.960222i \(0.590081\pi\)
\(314\) −37.4073 −2.11101
\(315\) 0 0
\(316\) 33.8559 1.90454
\(317\) 14.0534 8.11372i 0.789316 0.455712i −0.0504056 0.998729i \(-0.516051\pi\)
0.839722 + 0.543017i \(0.182718\pi\)
\(318\) 0 0
\(319\) 13.1561 22.7871i 0.736601 1.27583i
\(320\) 22.4922 1.25735
\(321\) 0 0
\(322\) 4.18728 4.88697i 0.233348 0.272340i
\(323\) 9.03174i 0.502540i
\(324\) 0 0
\(325\) −1.70007 + 0.981535i −0.0943029 + 0.0544458i
\(326\) 37.3736i 2.06993i
\(327\) 0 0
\(328\) −1.92126 + 1.10924i −0.106084 + 0.0612474i
\(329\) −14.0044 + 16.3446i −0.772089 + 0.901104i
\(330\) 0 0
\(331\) −11.6558 20.1885i −0.640662 1.10966i −0.985285 0.170919i \(-0.945326\pi\)
0.344623 0.938741i \(-0.388007\pi\)
\(332\) 3.69499 + 6.39992i 0.202789 + 0.351241i
\(333\) 0 0
\(334\) −22.3902 12.9270i −1.22514 0.707334i
\(335\) 0.704232 1.21977i 0.0384763 0.0666430i
\(336\) 0 0
\(337\) 5.93515 + 10.2800i 0.323308 + 0.559986i 0.981168 0.193154i \(-0.0618717\pi\)
−0.657860 + 0.753140i \(0.728538\pi\)
\(338\) 7.06286i 0.384169i
\(339\) 0 0
\(340\) 8.15793 0.442426
\(341\) −9.63545 + 16.6891i −0.521789 + 0.903765i
\(342\) 0 0
\(343\) 15.7449 + 9.75176i 0.850147 + 0.526546i
\(344\) −1.38366 0.798855i −0.0746019 0.0430714i
\(345\) 0 0
\(346\) 16.4549 + 9.50024i 0.884621 + 0.510736i
\(347\) −18.7979 10.8530i −1.00913 0.582619i −0.0981903 0.995168i \(-0.531305\pi\)
−0.910936 + 0.412549i \(0.864639\pi\)
\(348\) 0 0
\(349\) 2.20868 + 1.27518i 0.118228 + 0.0682588i 0.557948 0.829876i \(-0.311589\pi\)
−0.439720 + 0.898135i \(0.644922\pi\)
\(350\) −2.66332 2.28200i −0.142361 0.121978i
\(351\) 0 0
\(352\) −13.0144 + 22.5416i −0.693669 + 1.20147i
\(353\) 25.3747 1.35056 0.675279 0.737563i \(-0.264023\pi\)
0.675279 + 0.737563i \(0.264023\pi\)
\(354\) 0 0
\(355\) 14.6609i 0.778119i
\(356\) −5.87636 10.1782i −0.311446 0.539441i
\(357\) 0 0
\(358\) −15.7381 + 27.2592i −0.831786 + 1.44070i
\(359\) 9.73735 + 5.62186i 0.513918 + 0.296711i 0.734443 0.678671i \(-0.237444\pi\)
−0.220525 + 0.975381i \(0.570777\pi\)
\(360\) 0 0
\(361\) 5.80204 + 10.0494i 0.305371 + 0.528917i
\(362\) 2.45338 + 4.24938i 0.128947 + 0.223342i
\(363\) 0 0
\(364\) −18.5151 + 6.52356i −0.970458 + 0.341927i
\(365\) −6.19166 + 3.57476i −0.324086 + 0.187111i
\(366\) 0 0
\(367\) 3.31180i 0.172874i −0.996257 0.0864372i \(-0.972452\pi\)
0.996257 0.0864372i \(-0.0275482\pi\)
\(368\) 3.08114 1.77890i 0.160616 0.0927315i
\(369\) 0 0
\(370\) 24.7562i 1.28701i
\(371\) 12.2438 + 10.4908i 0.635667 + 0.544656i
\(372\) 0 0
\(373\) −6.64541 −0.344087 −0.172043 0.985089i \(-0.555037\pi\)
−0.172043 + 0.985089i \(0.555037\pi\)
\(374\) −5.52298 + 9.56608i −0.285586 + 0.494650i
\(375\) 0 0
\(376\) 5.77304 3.33307i 0.297722 0.171890i
\(377\) 25.2884 1.30242
\(378\) 0 0
\(379\) −3.84940 −0.197730 −0.0988652 0.995101i \(-0.531521\pi\)
−0.0988652 + 0.995101i \(0.531521\pi\)
\(380\) 23.9397 13.8216i 1.22808 0.709033i
\(381\) 0 0
\(382\) 9.46792 16.3989i 0.484421 0.839041i
\(383\) 34.2223 1.74868 0.874339 0.485316i \(-0.161295\pi\)
0.874339 + 0.485316i \(0.161295\pi\)
\(384\) 0 0
\(385\) −16.8379 + 5.93260i −0.858138 + 0.302353i
\(386\) 11.4889i 0.584768i
\(387\) 0 0
\(388\) 4.97191 2.87054i 0.252411 0.145729i
\(389\) 13.4796i 0.683445i −0.939801 0.341723i \(-0.888990\pi\)
0.939801 0.341723i \(-0.111010\pi\)
\(390\) 0 0
\(391\) 1.64121 0.947550i 0.0829993 0.0479197i
\(392\) −3.59560 4.46908i −0.181605 0.225723i
\(393\) 0 0
\(394\) 3.02740 + 5.24361i 0.152518 + 0.264169i
\(395\) 14.7954 + 25.6265i 0.744440 + 1.28941i
\(396\) 0 0
\(397\) −25.5501 14.7513i −1.28232 0.740349i −0.305049 0.952337i \(-0.598673\pi\)
−0.977272 + 0.211988i \(0.932006\pi\)
\(398\) −5.38880 + 9.33367i −0.270116 + 0.467855i
\(399\) 0 0
\(400\) −0.969472 1.67918i −0.0484736 0.0839588i
\(401\) 29.0446i 1.45042i −0.688528 0.725209i \(-0.741743\pi\)
0.688528 0.725209i \(-0.258257\pi\)
\(402\) 0 0
\(403\) −18.5210 −0.922599
\(404\) 4.20884 7.28993i 0.209398 0.362687i
\(405\) 0 0
\(406\) 15.0141 + 42.6130i 0.745138 + 2.11485i
\(407\) −15.8073 9.12634i −0.783538 0.452376i
\(408\) 0 0
\(409\) −26.2193 15.1377i −1.29646 0.748513i −0.316671 0.948536i \(-0.602565\pi\)
−0.979791 + 0.200023i \(0.935898\pi\)
\(410\) −10.2677 5.92806i −0.507086 0.292766i
\(411\) 0 0
\(412\) −32.4781 18.7512i −1.60008 0.923806i
\(413\) −10.3040 1.92663i −0.507029 0.0948035i
\(414\) 0 0
\(415\) −3.22952 + 5.59369i −0.158531 + 0.274583i
\(416\) −25.0160 −1.22651
\(417\) 0 0
\(418\) 37.4293i 1.83073i
\(419\) −18.2902 31.6795i −0.893534 1.54765i −0.835609 0.549325i \(-0.814885\pi\)
−0.0579246 0.998321i \(-0.518448\pi\)
\(420\) 0 0
\(421\) 3.85999 6.68570i 0.188124 0.325841i −0.756501 0.653993i \(-0.773093\pi\)
0.944625 + 0.328152i \(0.106426\pi\)
\(422\) −28.7899 16.6219i −1.40147 0.809140i
\(423\) 0 0
\(424\) −2.49682 4.32463i −0.121256 0.210022i
\(425\) −0.516400 0.894431i −0.0250491 0.0433863i
\(426\) 0 0
\(427\) 9.62808 + 8.24958i 0.465935 + 0.399225i
\(428\) 3.39490 1.96005i 0.164099 0.0947424i
\(429\) 0 0
\(430\) 8.53859i 0.411767i
\(431\) 20.0311 11.5650i 0.964865 0.557065i 0.0671983 0.997740i \(-0.478594\pi\)
0.897667 + 0.440674i \(0.145261\pi\)
\(432\) 0 0
\(433\) 34.9265i 1.67846i −0.543776 0.839230i \(-0.683006\pi\)
0.543776 0.839230i \(-0.316994\pi\)
\(434\) −10.9962 31.2095i −0.527836 1.49810i
\(435\) 0 0
\(436\) 13.9002 0.665699
\(437\) 3.21078 5.56123i 0.153592 0.266030i
\(438\) 0 0
\(439\) 33.6842 19.4476i 1.60766 0.928184i 0.617770 0.786359i \(-0.288036\pi\)
0.989892 0.141824i \(-0.0452969\pi\)
\(440\) 5.52912 0.263590
\(441\) 0 0
\(442\) −10.6161 −0.504959
\(443\) −32.3277 + 18.6644i −1.53594 + 0.886774i −0.536867 + 0.843667i \(0.680392\pi\)
−0.999070 + 0.0431065i \(0.986275\pi\)
\(444\) 0 0
\(445\) 5.13609 8.89596i 0.243474 0.421709i
\(446\) −32.7350 −1.55005
\(447\) 0 0
\(448\) −9.46276 26.8572i −0.447073 1.26888i
\(449\) 23.9224i 1.12897i −0.825445 0.564483i \(-0.809076\pi\)
0.825445 0.564483i \(-0.190924\pi\)
\(450\) 0 0
\(451\) 7.57036 4.37075i 0.356474 0.205810i
\(452\) 38.6342i 1.81720i
\(453\) 0 0
\(454\) 3.77628 2.18024i 0.177230 0.102324i
\(455\) −13.0292 11.1638i −0.610819 0.523365i
\(456\) 0 0
\(457\) −4.99031 8.64348i −0.233437 0.404325i 0.725380 0.688348i \(-0.241664\pi\)
−0.958817 + 0.284024i \(0.908331\pi\)
\(458\) −6.74155 11.6767i −0.315012 0.545617i
\(459\) 0 0
\(460\) −5.02319 2.90014i −0.234207 0.135220i
\(461\) −16.7279 + 28.9735i −0.779094 + 1.34943i 0.153371 + 0.988169i \(0.450987\pi\)
−0.932465 + 0.361261i \(0.882346\pi\)
\(462\) 0 0
\(463\) 11.5353 + 19.9798i 0.536092 + 0.928538i 0.999110 + 0.0421893i \(0.0134333\pi\)
−0.463018 + 0.886349i \(0.653233\pi\)
\(464\) 24.9776i 1.15956i
\(465\) 0 0
\(466\) −32.7190 −1.51568
\(467\) −20.1395 + 34.8827i −0.931946 + 1.61418i −0.151955 + 0.988387i \(0.548557\pi\)
−0.779991 + 0.625791i \(0.784776\pi\)
\(468\) 0 0
\(469\) −1.75276 0.327728i −0.0809349 0.0151331i
\(470\) 30.8527 + 17.8128i 1.42313 + 0.821643i
\(471\) 0 0
\(472\) 2.81163 + 1.62329i 0.129416 + 0.0747182i
\(473\) 5.45205 + 3.14774i 0.250686 + 0.144733i
\(474\) 0 0
\(475\) −3.03078 1.74982i −0.139062 0.0802874i
\(476\) −3.43214 9.74109i −0.157312 0.446482i
\(477\) 0 0
\(478\) −17.9994 + 31.1759i −0.823275 + 1.42595i
\(479\) 0.155503 0.00710509 0.00355255 0.999994i \(-0.498869\pi\)
0.00355255 + 0.999994i \(0.498869\pi\)
\(480\) 0 0
\(481\) 17.5425i 0.799867i
\(482\) 11.7540 + 20.3585i 0.535380 + 0.927305i
\(483\) 0 0
\(484\) 0.687435 1.19067i 0.0312471 0.0541215i
\(485\) 4.34558 + 2.50892i 0.197323 + 0.113924i
\(486\) 0 0
\(487\) 8.25111 + 14.2913i 0.373893 + 0.647602i 0.990161 0.139935i \(-0.0446892\pi\)
−0.616267 + 0.787537i \(0.711356\pi\)
\(488\) −1.96341 3.40072i −0.0888793 0.153944i
\(489\) 0 0
\(490\) 11.0762 28.5834i 0.500371 1.29127i
\(491\) −8.10003 + 4.67655i −0.365549 + 0.211050i −0.671512 0.740993i \(-0.734355\pi\)
0.305963 + 0.952043i \(0.401022\pi\)
\(492\) 0 0
\(493\) 13.3046i 0.599209i
\(494\) −31.1534 + 17.9864i −1.40166 + 0.809248i
\(495\) 0 0
\(496\) 18.2934i 0.821399i
\(497\) 17.5060 6.16801i 0.785253 0.276673i
\(498\) 0 0
\(499\) 1.99623 0.0893637 0.0446818 0.999001i \(-0.485773\pi\)
0.0446818 + 0.999001i \(0.485773\pi\)
\(500\) −14.0727 + 24.3746i −0.629351 + 1.09007i
\(501\) 0 0
\(502\) 20.6585 11.9272i 0.922035 0.532337i
\(503\) 15.7008 0.700063 0.350032 0.936738i \(-0.386171\pi\)
0.350032 + 0.936738i \(0.386171\pi\)
\(504\) 0 0
\(505\) 7.35727 0.327394
\(506\) 6.80147 3.92683i 0.302362 0.174569i
\(507\) 0 0
\(508\) −11.4679 + 19.8630i −0.508807 + 0.881279i
\(509\) 15.1979 0.673633 0.336817 0.941570i \(-0.390650\pi\)
0.336817 + 0.941570i \(0.390650\pi\)
\(510\) 0 0
\(511\) 6.87340 + 5.88930i 0.304061 + 0.260527i
\(512\) 29.7316i 1.31396i
\(513\) 0 0
\(514\) 17.0231 9.82831i 0.750858 0.433508i
\(515\) 32.7781i 1.44437i
\(516\) 0 0
\(517\) −22.7476 + 13.1333i −1.00044 + 0.577603i
\(518\) 29.5605 10.4152i 1.29881 0.457619i
\(519\) 0 0
\(520\) 2.65699 + 4.60204i 0.116517 + 0.201813i
\(521\) −20.6160 35.7080i −0.903204 1.56440i −0.823310 0.567592i \(-0.807875\pi\)
−0.0798940 0.996803i \(-0.525458\pi\)
\(522\) 0 0
\(523\) 37.0311 + 21.3799i 1.61926 + 0.934878i 0.987113 + 0.160026i \(0.0511577\pi\)
0.632143 + 0.774852i \(0.282176\pi\)
\(524\) −2.94244 + 5.09645i −0.128541 + 0.222640i
\(525\) 0 0
\(526\) −9.22332 15.9753i −0.402156 0.696554i
\(527\) 9.74419i 0.424464i
\(528\) 0 0
\(529\) 21.6526 0.941417
\(530\) 13.3437 23.1119i 0.579613 1.00392i
\(531\) 0 0
\(532\) −26.5756 22.7706i −1.15220 0.987231i
\(533\) 7.27579 + 4.20068i 0.315149 + 0.181952i
\(534\) 0 0
\(535\) 2.96723 + 1.71313i 0.128284 + 0.0740650i
\(536\) 0.478269 + 0.276129i 0.0206581 + 0.0119270i
\(537\) 0 0
\(538\) 29.6337 + 17.1090i 1.27760 + 0.737623i
\(539\) 14.1678 + 17.6096i 0.610251 + 0.758499i
\(540\) 0 0
\(541\) 8.04309 13.9310i 0.345800 0.598942i −0.639699 0.768625i \(-0.720941\pi\)
0.985499 + 0.169683i \(0.0542744\pi\)
\(542\) 30.5328 1.31149
\(543\) 0 0
\(544\) 13.1613i 0.564284i
\(545\) 6.07456 + 10.5214i 0.260206 + 0.450689i
\(546\) 0 0
\(547\) −5.94015 + 10.2886i −0.253982 + 0.439910i −0.964619 0.263649i \(-0.915074\pi\)
0.710636 + 0.703560i \(0.248407\pi\)
\(548\) 36.0021 + 20.7858i 1.53794 + 0.887927i
\(549\) 0 0
\(550\) −2.14006 3.70669i −0.0912525 0.158054i
\(551\) 22.5413 + 39.0427i 0.960293 + 1.66328i
\(552\) 0 0
\(553\) 24.3750 28.4481i 1.03653 1.20973i
\(554\) −52.1078 + 30.0845i −2.21385 + 1.27817i
\(555\) 0 0
\(556\) 23.7765i 1.00835i
\(557\) 26.4006 15.2424i 1.11863 0.645841i 0.177579 0.984107i \(-0.443173\pi\)
0.941051 + 0.338265i \(0.109840\pi\)
\(558\) 0 0
\(559\) 6.05052i 0.255910i
\(560\) 11.0266 12.8691i 0.465957 0.543818i
\(561\) 0 0
\(562\) −11.5392 −0.486750
\(563\) 11.2686 19.5177i 0.474914 0.822575i −0.524673 0.851304i \(-0.675813\pi\)
0.999587 + 0.0287288i \(0.00914592\pi\)
\(564\) 0 0
\(565\) −29.2433 + 16.8836i −1.23027 + 0.710300i
\(566\) 63.4572 2.66730
\(567\) 0 0
\(568\) −5.74852 −0.241202
\(569\) −38.5935 + 22.2819i −1.61792 + 0.934108i −0.630465 + 0.776218i \(0.717136\pi\)
−0.987457 + 0.157890i \(0.949531\pi\)
\(570\) 0 0
\(571\) −17.6415 + 30.5560i −0.738274 + 1.27873i 0.214998 + 0.976614i \(0.431025\pi\)
−0.953272 + 0.302113i \(0.902308\pi\)
\(572\) −23.9567 −1.00168
\(573\) 0 0
\(574\) −2.75874 + 14.7543i −0.115147 + 0.615833i
\(575\) 0.734319i 0.0306232i
\(576\) 0 0
\(577\) 3.25158 1.87730i 0.135365 0.0781531i −0.430788 0.902453i \(-0.641764\pi\)
0.566153 + 0.824300i \(0.308431\pi\)
\(578\) 30.0379i 1.24941i
\(579\) 0 0
\(580\) 35.2654 20.3605i 1.46432 0.845423i
\(581\) 8.03792 + 1.50292i 0.333469 + 0.0623516i
\(582\) 0 0
\(583\) 9.83827 + 17.0404i 0.407460 + 0.705741i
\(584\) −1.40166 2.42775i −0.0580011 0.100461i
\(585\) 0 0
\(586\) −12.8615 7.42559i −0.531304 0.306748i
\(587\) 15.8021 27.3700i 0.652222 1.12968i −0.330361 0.943855i \(-0.607171\pi\)
0.982583 0.185826i \(-0.0594961\pi\)
\(588\) 0 0
\(589\) −16.5091 28.5946i −0.680246 1.17822i
\(590\) 17.3506i 0.714314i
\(591\) 0 0
\(592\) 17.3269 0.712129
\(593\) 18.5588 32.1448i 0.762120 1.32003i −0.179636 0.983733i \(-0.557492\pi\)
0.941756 0.336297i \(-0.109175\pi\)
\(594\) 0 0
\(595\) 5.87342 6.85486i 0.240787 0.281022i
\(596\) 19.1689 + 11.0671i 0.785187 + 0.453328i
\(597\) 0 0
\(598\) 6.53682 + 3.77403i 0.267310 + 0.154332i
\(599\) 24.5188 + 14.1559i 1.00181 + 0.578396i 0.908784 0.417267i \(-0.137012\pi\)
0.0930277 + 0.995664i \(0.470345\pi\)
\(600\) 0 0
\(601\) 20.8341 + 12.0286i 0.849840 + 0.490655i 0.860597 0.509287i \(-0.170091\pi\)
−0.0107568 + 0.999942i \(0.503424\pi\)
\(602\) −10.1956 + 3.59229i −0.415543 + 0.146411i
\(603\) 0 0
\(604\) −14.3101 + 24.7859i −0.582271 + 1.00852i
\(605\) 1.20167 0.0488549
\(606\) 0 0
\(607\) 9.52047i 0.386424i 0.981157 + 0.193212i \(0.0618905\pi\)
−0.981157 + 0.193212i \(0.938110\pi\)
\(608\) −22.2985 38.6221i −0.904323 1.56633i
\(609\) 0 0
\(610\) 10.4930 18.1744i 0.424848 0.735859i
\(611\) −21.8625 12.6223i −0.884461 0.510644i
\(612\) 0 0
\(613\) 1.23108 + 2.13230i 0.0497230 + 0.0861227i 0.889816 0.456320i \(-0.150833\pi\)
−0.840093 + 0.542443i \(0.817499\pi\)
\(614\) −3.26210 5.65012i −0.131648 0.228020i
\(615\) 0 0
\(616\) −2.32617 6.60212i −0.0937239 0.266007i
\(617\) −18.7738 + 10.8390i −0.755804 + 0.436364i −0.827787 0.561042i \(-0.810401\pi\)
0.0719831 + 0.997406i \(0.477067\pi\)
\(618\) 0 0
\(619\) 24.1063i 0.968915i 0.874815 + 0.484457i \(0.160983\pi\)
−0.874815 + 0.484457i \(0.839017\pi\)
\(620\) −25.8281 + 14.9119i −1.03728 + 0.598875i
\(621\) 0 0
\(622\) 40.7615i 1.63439i
\(623\) −12.7832 2.39018i −0.512147 0.0957604i
\(624\) 0 0
\(625\) −21.4368 −0.857471
\(626\) 26.7643 46.3571i 1.06972 1.85280i
\(627\) 0 0
\(628\) 36.9649 21.3417i 1.47506 0.851627i
\(629\) 9.22934 0.367998
\(630\) 0 0
\(631\) 3.37520 0.134365 0.0671824 0.997741i \(-0.478599\pi\)
0.0671824 + 0.997741i \(0.478599\pi\)
\(632\) −10.0481 + 5.80128i −0.399692 + 0.230762i
\(633\) 0 0
\(634\) −17.0021 + 29.4486i −0.675242 + 1.16955i
\(635\) −20.0465 −0.795521
\(636\) 0 0
\(637\) −7.84869 + 20.2544i −0.310976 + 0.802510i
\(638\) 55.1368i 2.18289i
\(639\) 0 0
\(640\) −11.6374 + 6.71887i −0.460010 + 0.265587i
\(641\) 35.6978i 1.40998i 0.709218 + 0.704989i \(0.249048\pi\)
−0.709218 + 0.704989i \(0.750952\pi\)
\(642\) 0 0
\(643\) 3.03956 1.75489i 0.119868 0.0692060i −0.438867 0.898552i \(-0.644620\pi\)
0.558735 + 0.829346i \(0.311287\pi\)
\(644\) −1.34963 + 7.21813i −0.0531831 + 0.284434i
\(645\) 0 0
\(646\) −9.46292 16.3903i −0.372314 0.644866i
\(647\) 7.02996 + 12.1762i 0.276376 + 0.478698i 0.970481 0.241176i \(-0.0775331\pi\)
−0.694105 + 0.719874i \(0.744200\pi\)
\(648\) 0 0
\(649\) −11.0787 6.39629i −0.434877 0.251076i
\(650\) 2.05679 3.56246i 0.0806739 0.139731i
\(651\) 0 0
\(652\) 21.3225 + 36.9317i 0.835055 + 1.44636i
\(653\) 11.8558i 0.463955i −0.972721 0.231978i \(-0.925480\pi\)
0.972721 0.231978i \(-0.0745196\pi\)
\(654\) 0 0
\(655\) −5.14353 −0.200974
\(656\) −4.14905 + 7.18637i −0.161993 + 0.280581i
\(657\) 0 0
\(658\) 8.28952 44.3341i 0.323159 1.72832i
\(659\) −5.03144 2.90491i −0.195997 0.113159i 0.398790 0.917042i \(-0.369430\pi\)
−0.594787 + 0.803883i \(0.702764\pi\)
\(660\) 0 0
\(661\) 8.41592 + 4.85893i 0.327341 + 0.188991i 0.654660 0.755923i \(-0.272812\pi\)
−0.327319 + 0.944914i \(0.606145\pi\)
\(662\) 42.3046 + 24.4246i 1.64422 + 0.949288i
\(663\) 0 0
\(664\) −2.19328 1.26629i −0.0851158 0.0491416i
\(665\) 5.62185 30.0668i 0.218006 1.16594i
\(666\) 0 0
\(667\) 4.72977 8.19220i 0.183137 0.317203i
\(668\) 29.5006 1.14141
\(669\) 0 0
\(670\) 2.95141i 0.114023i
\(671\) 7.73645 + 13.3999i 0.298662 + 0.517298i
\(672\) 0 0
\(673\) 13.4646 23.3214i 0.519023 0.898975i −0.480732 0.876867i \(-0.659629\pi\)
0.999756 0.0221072i \(-0.00703750\pi\)
\(674\) −21.5415 12.4370i −0.829747 0.479055i
\(675\) 0 0
\(676\) 4.02953 + 6.97935i 0.154982 + 0.268436i
\(677\) −22.7056 39.3273i −0.872648 1.51147i −0.859247 0.511560i \(-0.829068\pi\)
−0.0134007 0.999910i \(-0.504266\pi\)
\(678\) 0 0
\(679\) 1.16757 6.24443i 0.0448074 0.239639i
\(680\) −2.42120 + 1.39788i −0.0928487 + 0.0536062i
\(681\) 0 0
\(682\) 40.3818i 1.54630i
\(683\) −37.6543 + 21.7397i −1.44080 + 0.831848i −0.997903 0.0647226i \(-0.979384\pi\)
−0.442900 + 0.896571i \(0.646050\pi\)
\(684\) 0 0
\(685\) 36.3347i 1.38828i
\(686\) −38.7903 1.20030i −1.48102 0.0458278i
\(687\) 0 0
\(688\) −5.97616 −0.227839
\(689\) −9.45546 + 16.3773i −0.360224 + 0.623927i
\(690\) 0 0
\(691\) −23.6991 + 13.6827i −0.901557 + 0.520514i −0.877705 0.479201i \(-0.840926\pi\)
−0.0238522 + 0.999715i \(0.507593\pi\)
\(692\) −21.6804 −0.824166
\(693\) 0 0
\(694\) 45.4845 1.72657
\(695\) −17.9971 + 10.3906i −0.682668 + 0.394139i
\(696\) 0 0
\(697\) −2.21004 + 3.82790i −0.0837112 + 0.144992i
\(698\) −5.34423 −0.202282
\(699\) 0 0
\(700\) 3.93377 + 0.735530i 0.148682 + 0.0278004i
\(701\) 8.26437i 0.312141i −0.987746 0.156070i \(-0.950117\pi\)
0.987746 0.156070i \(-0.0498827\pi\)
\(702\) 0 0
\(703\) 27.0838 15.6368i 1.02148 0.589754i
\(704\) 34.7504i 1.30970i
\(705\) 0 0
\(706\) −46.0484 + 26.5861i −1.73306 + 1.00058i
\(707\) −3.09529 8.78505i −0.116410 0.330396i
\(708\) 0 0
\(709\) −21.4086 37.0807i −0.804015 1.39260i −0.916954 0.398994i \(-0.869360\pi\)
0.112938 0.993602i \(-0.463974\pi\)
\(710\) −15.3608 26.6057i −0.576481 0.998494i
\(711\) 0 0
\(712\) 3.48810 + 2.01385i 0.130722 + 0.0754724i
\(713\) −3.46405 + 5.99992i −0.129730 + 0.224699i
\(714\) 0 0
\(715\) −10.4694 18.1335i −0.391532 0.678153i
\(716\) 35.9159i 1.34224i
\(717\) 0 0
\(718\) −23.5610 −0.879289
\(719\) −11.5725 + 20.0442i −0.431583 + 0.747523i −0.997010 0.0772751i \(-0.975378\pi\)
0.565427 + 0.824798i \(0.308711\pi\)
\(720\) 0 0
\(721\) −39.1391 + 13.7901i −1.45762 + 0.513571i
\(722\) −21.0584 12.1581i −0.783712 0.452477i
\(723\) 0 0
\(724\) −4.84874 2.79942i −0.180202 0.104040i
\(725\) −4.46462 2.57765i −0.165812 0.0957316i
\(726\) 0 0
\(727\) 4.76878 + 2.75326i 0.176864 + 0.102113i 0.585819 0.810442i \(-0.300773\pi\)
−0.408954 + 0.912555i \(0.634106\pi\)
\(728\) 4.37730 5.10874i 0.162233 0.189343i
\(729\) 0 0
\(730\) 7.49084 12.9745i 0.277248 0.480208i
\(731\) −3.18327 −0.117737
\(732\) 0 0
\(733\) 3.98999i 0.147373i −0.997281 0.0736867i \(-0.976524\pi\)
0.997281 0.0736867i \(-0.0234765\pi\)
\(734\) 3.46991 + 6.01005i 0.128077 + 0.221835i
\(735\) 0 0
\(736\) −4.67882 + 8.10395i −0.172463 + 0.298716i
\(737\) −1.88453 1.08803i −0.0694176 0.0400783i
\(738\) 0 0
\(739\) 0.871657 + 1.50976i 0.0320644 + 0.0555372i 0.881612 0.471974i \(-0.156458\pi\)
−0.849548 + 0.527512i \(0.823125\pi\)
\(740\) −14.1240 24.4635i −0.519208 0.899295i
\(741\) 0 0
\(742\) −33.2110 6.20974i −1.21921 0.227967i
\(743\) −8.70204 + 5.02413i −0.319247 + 0.184317i −0.651057 0.759029i \(-0.725674\pi\)
0.331810 + 0.943346i \(0.392341\pi\)
\(744\) 0 0
\(745\) 19.3459i 0.708780i
\(746\) 12.0597 6.96267i 0.441537 0.254921i
\(747\) 0 0
\(748\) 12.6040i 0.460846i
\(749\) 0.797238 4.26379i 0.0291304 0.155796i
\(750\) 0 0
\(751\) −23.3450 −0.851872 −0.425936 0.904753i \(-0.640055\pi\)
−0.425936 + 0.904753i \(0.640055\pi\)
\(752\) 12.4672 21.5938i 0.454631 0.787444i
\(753\) 0 0
\(754\) −45.8919 + 26.4957i −1.67128 + 0.964916i
\(755\) −25.0148 −0.910383
\(756\) 0 0
\(757\) −14.3334 −0.520957 −0.260479 0.965480i \(-0.583880\pi\)
−0.260479 + 0.965480i \(0.583880\pi\)
\(758\) 6.98566 4.03317i 0.253730 0.146491i
\(759\) 0 0
\(760\) −4.73672 + 8.20424i −0.171819 + 0.297599i
\(761\) −22.6355 −0.820537 −0.410268 0.911965i \(-0.634565\pi\)
−0.410268 + 0.911965i \(0.634565\pi\)
\(762\) 0 0
\(763\) 10.0076 11.6799i 0.362301 0.422841i
\(764\) 21.6067i 0.781702i
\(765\) 0 0
\(766\) −62.1046 + 35.8561i −2.24393 + 1.29553i
\(767\) 12.2948i 0.443940i
\(768\) 0 0
\(769\) 42.6873 24.6455i 1.53934 0.888741i 0.540468 0.841365i \(-0.318247\pi\)
0.998877 0.0473762i \(-0.0150860\pi\)
\(770\) 24.3406 28.4079i 0.877173 1.02375i
\(771\) 0 0
\(772\) −6.55467 11.3530i −0.235908 0.408604i
\(773\) 11.0083 + 19.0670i 0.395943 + 0.685793i 0.993221 0.116241i \(-0.0370845\pi\)
−0.597278 + 0.802034i \(0.703751\pi\)
\(774\) 0 0
\(775\) 3.26986 + 1.88785i 0.117457 + 0.0678137i
\(776\) −0.983745 + 1.70390i −0.0353144 + 0.0611663i
\(777\) 0 0
\(778\) 14.1232 + 24.4621i 0.506340 + 0.877007i
\(779\) 14.9774i 0.536622i
\(780\) 0 0
\(781\) 22.6510 0.810516
\(782\) −1.98557 + 3.43911i −0.0710040 + 0.122982i
\(783\) 0 0
\(784\) −20.0055 7.75223i −0.714483 0.276865i
\(785\) 32.3083 + 18.6532i 1.15313 + 0.665761i
\(786\) 0 0
\(787\) 9.40107 + 5.42771i 0.335112 + 0.193477i 0.658108 0.752923i \(-0.271357\pi\)
−0.322996 + 0.946400i \(0.604690\pi\)
\(788\) −5.98320 3.45440i −0.213143 0.123058i
\(789\) 0 0
\(790\) −53.6998 31.0036i −1.91055 1.10306i
\(791\) 32.4631 + 27.8152i 1.15426 + 0.988995i
\(792\) 0 0
\(793\) −7.43542 + 12.8785i −0.264039 + 0.457330i
\(794\) 61.8223 2.19399
\(795\) 0 0
\(796\) 12.2977i 0.435882i
\(797\) −1.98299 3.43465i −0.0702412 0.121661i 0.828766 0.559596i \(-0.189044\pi\)
−0.899007 + 0.437934i \(0.855710\pi\)
\(798\) 0 0
\(799\) 6.64078 11.5022i 0.234934 0.406917i
\(800\) 4.41653 + 2.54988i 0.156148 + 0.0901520i
\(801\) 0 0
\(802\) 30.4312 + 52.7084i 1.07456 + 1.86120i
\(803\) 5.52298 + 9.56608i 0.194902 + 0.337580i
\(804\) 0 0
\(805\) −6.05341 + 2.13284i −0.213355 + 0.0751726i
\(806\) 33.6109 19.4053i 1.18389 0.683521i
\(807\) 0 0
\(808\) 2.88478i 0.101486i
\(809\) −36.0199 + 20.7961i −1.26639 + 0.731152i −0.974303 0.225240i \(-0.927683\pi\)
−0.292088 + 0.956391i \(0.594350\pi\)
\(810\) 0 0
\(811\) 13.3293i 0.468056i −0.972230 0.234028i \(-0.924809\pi\)
0.972230 0.234028i \(-0.0751907\pi\)
\(812\) −39.1483 33.5432i −1.37384 1.17714i
\(813\) 0 0
\(814\) 38.2482 1.34060
\(815\) −18.6364 + 32.2792i −0.652806 + 1.13069i
\(816\) 0 0
\(817\) −9.34139 + 5.39326i −0.326814 + 0.188686i
\(818\) 63.4417 2.21819
\(819\) 0 0
\(820\) 13.5284 0.472432
\(821\) 33.4332 19.3027i 1.16683 0.673668i 0.213897 0.976856i \(-0.431384\pi\)
0.952931 + 0.303188i \(0.0980510\pi\)
\(822\) 0 0
\(823\) 5.34881 9.26442i 0.186448 0.322937i −0.757616 0.652701i \(-0.773636\pi\)
0.944063 + 0.329764i \(0.106969\pi\)
\(824\) 12.8523 0.447729
\(825\) 0 0
\(826\) 20.7178 7.29962i 0.720863 0.253986i
\(827\) 11.7079i 0.407125i 0.979062 + 0.203562i \(0.0652520\pi\)
−0.979062 + 0.203562i \(0.934748\pi\)
\(828\) 0 0
\(829\) −15.0948 + 8.71498i −0.524263 + 0.302684i −0.738677 0.674059i \(-0.764549\pi\)
0.214414 + 0.976743i \(0.431216\pi\)
\(830\) 13.5348i 0.469799i
\(831\) 0 0
\(832\) 28.9237 16.6991i 1.00275 0.578937i
\(833\) −10.6562 4.12931i −0.369214 0.143072i
\(834\) 0 0
\(835\) 12.8921 + 22.3298i 0.446151 + 0.772756i
\(836\) −21.3543 36.9867i −0.738553 1.27921i
\(837\) 0 0
\(838\) 66.3838 + 38.3267i 2.29319 + 1.32397i
\(839\) −0.704502 + 1.22023i −0.0243221 + 0.0421271i −0.877930 0.478789i \(-0.841076\pi\)
0.853608 + 0.520916i \(0.174409\pi\)
\(840\) 0 0
\(841\) 18.7055 + 32.3988i 0.645016 + 1.11720i
\(842\) 16.1771i 0.557498i
\(843\) 0 0
\(844\) 37.9326 1.30570
\(845\) −3.52191 + 6.10012i −0.121157 + 0.209851i
\(846\) 0 0
\(847\) −0.505558 1.43487i −0.0173712 0.0493028i
\(848\) −16.1761 9.33925i −0.555488 0.320711i
\(849\) 0 0
\(850\) 1.87426 + 1.08211i 0.0642867 + 0.0371160i
\(851\) −5.68290 3.28102i −0.194807 0.112472i
\(852\) 0 0
\(853\) −28.0716 16.2071i −0.961153 0.554922i −0.0646255 0.997910i \(-0.520585\pi\)
−0.896528 + 0.442987i \(0.853919\pi\)
\(854\) −26.1159 4.88311i −0.893667 0.167097i
\(855\) 0 0
\(856\) −0.671716 + 1.16345i −0.0229588 + 0.0397658i
\(857\) −44.4539 −1.51852 −0.759258 0.650789i \(-0.774438\pi\)
−0.759258 + 0.650789i \(0.774438\pi\)
\(858\) 0 0
\(859\) 15.6494i 0.533952i 0.963703 + 0.266976i \(0.0860245\pi\)
−0.963703 + 0.266976i \(0.913976\pi\)
\(860\) 4.87147 + 8.43763i 0.166116 + 0.287721i
\(861\) 0 0
\(862\) −24.2342 + 41.9748i −0.825420 + 1.42967i
\(863\) 15.6911 + 9.05927i 0.534132 + 0.308381i 0.742697 0.669627i \(-0.233546\pi\)
−0.208565 + 0.978008i \(0.566879\pi\)
\(864\) 0 0
\(865\) −9.47462 16.4105i −0.322147 0.557975i
\(866\) 36.5939 + 63.3825i 1.24351 + 2.15383i
\(867\) 0 0
\(868\) 28.6719 + 24.5668i 0.973189 + 0.833853i
\(869\) 39.5927 22.8589i 1.34309 0.775434i
\(870\) 0 0
\(871\) 2.09140i 0.0708643i
\(872\) −4.12545 + 2.38183i −0.139705 + 0.0806589i
\(873\) 0 0
\(874\) 13.4562i 0.455164i
\(875\) 10.3494 + 29.3737i 0.349875 + 0.993014i
\(876\) 0 0
\(877\) −2.77853 −0.0938243 −0.0469121 0.998899i \(-0.514938\pi\)
−0.0469121 + 0.998899i \(0.514938\pi\)
\(878\) −40.7521 + 70.5847i −1.37532 + 2.38212i
\(879\) 0 0
\(880\) 17.9106 10.3407i 0.603767 0.348585i
\(881\) 1.96106 0.0660696 0.0330348 0.999454i \(-0.489483\pi\)
0.0330348 + 0.999454i \(0.489483\pi\)
\(882\) 0 0
\(883\) −36.9657 −1.24400 −0.621998 0.783019i \(-0.713679\pi\)
−0.621998 + 0.783019i \(0.713679\pi\)
\(884\) 10.4906 6.05676i 0.352838 0.203711i
\(885\) 0 0
\(886\) 39.1110 67.7422i 1.31396 2.27584i
\(887\) 22.5168 0.756040 0.378020 0.925797i \(-0.376605\pi\)
0.378020 + 0.925797i \(0.376605\pi\)
\(888\) 0 0
\(889\) 8.43380 + 23.9368i 0.282861 + 0.802814i
\(890\) 21.5251i 0.721525i
\(891\) 0 0
\(892\) 32.3479 18.6761i 1.08309 0.625321i
\(893\) 45.0046i 1.50602i
\(894\) 0 0
\(895\) 27.1857 15.6957i 0.908719 0.524649i
\(896\) 12.9188 + 11.0691i 0.431586 + 0.369793i
\(897\) 0 0
\(898\) 25.0644 + 43.4129i 0.836411 + 1.44871i
\(899\) −24.3195 42.1225i −0.811099 1.40487i
\(900\) 0 0
\(901\) −8.61635 4.97465i −0.287052 0.165730i
\(902\) −9.15882 + 15.8635i −0.304955 + 0.528198i
\(903\) 0 0
\(904\) −6.62005 11.4663i −0.220180 0.381362i
\(905\) 4.89353i 0.162666i
\(906\) 0 0
\(907\) −19.1196 −0.634857 −0.317428 0.948282i \(-0.602819\pi\)
−0.317428 + 0.948282i \(0.602819\pi\)
\(908\) −2.48775 + 4.30891i −0.0825589 + 0.142996i
\(909\) 0 0
\(910\) 35.3414 + 6.60808i 1.17155 + 0.219056i
\(911\) −4.92610 2.84408i −0.163209 0.0942287i 0.416171 0.909286i \(-0.363372\pi\)
−0.579380 + 0.815058i \(0.696705\pi\)
\(912\) 0 0
\(913\) 8.64222 + 4.98959i 0.286016 + 0.165131i
\(914\) 18.1122 + 10.4571i 0.599100 + 0.345890i
\(915\) 0 0
\(916\) 13.3237 + 7.69242i 0.440226 + 0.254165i
\(917\) 2.16395 + 6.14170i 0.0714598 + 0.202817i
\(918\) 0 0
\(919\) −10.9255 + 18.9235i −0.360399 + 0.624230i −0.988027 0.154284i \(-0.950693\pi\)
0.627627 + 0.778514i \(0.284026\pi\)
\(920\) 1.98778 0.0655352
\(921\) 0 0
\(922\) 70.1058i 2.30881i
\(923\) 10.8848 + 18.8530i 0.358278 + 0.620555i
\(924\) 0 0
\(925\) −1.78811 + 3.09709i −0.0587926 + 0.101832i
\(926\) −41.8672 24.1720i −1.37584 0.794343i
\(927\) 0 0
\(928\) −32.8477 56.8940i −1.07828 1.86764i
\(929\) −8.08806 14.0089i −0.265361 0.459618i 0.702297 0.711884i \(-0.252158\pi\)
−0.967658 + 0.252266i \(0.918824\pi\)
\(930\) 0 0
\(931\) −38.2669 + 5.93663i −1.25415 + 0.194565i
\(932\) 32.3321 18.6669i 1.05907 0.611456i
\(933\) 0 0
\(934\) 84.4040i 2.76178i
\(935\) 9.54029 5.50809i 0.312001 0.180134i
\(936\) 0 0
\(937\) 14.0440i 0.458799i 0.973332 + 0.229400i \(0.0736762\pi\)
−0.973332 + 0.229400i \(0.926324\pi\)
\(938\) 3.52417 1.24169i 0.115068 0.0405428i
\(939\) 0 0
\(940\) −40.6505 −1.32587
\(941\) −21.5934 + 37.4009i −0.703924 + 1.21923i 0.263154 + 0.964754i \(0.415237\pi\)
−0.967078 + 0.254479i \(0.918096\pi\)
\(942\) 0 0
\(943\) 2.72163 1.57133i 0.0886284 0.0511696i
\(944\) 12.1437 0.395244
\(945\) 0 0
\(946\) −13.1921 −0.428911
\(947\) −16.6235 + 9.59758i −0.540191 + 0.311879i −0.745156 0.666890i \(-0.767625\pi\)
0.204965 + 0.978769i \(0.434292\pi\)
\(948\) 0 0
\(949\) −5.30807 + 9.19386i −0.172307 + 0.298445i
\(950\) 7.33344 0.237928
\(951\) 0 0
\(952\) 2.68779 + 2.30296i 0.0871116 + 0.0746394i
\(953\) 5.62718i 0.182282i −0.995838 0.0911411i \(-0.970949\pi\)
0.995838 0.0911411i \(-0.0290514\pi\)
\(954\) 0 0
\(955\) −16.3547 + 9.44239i −0.529225 + 0.305548i
\(956\) 41.0764i 1.32850i
\(957\) 0 0
\(958\) −0.282197 + 0.162926i −0.00911736 + 0.00526391i
\(959\) 43.3860 15.2864i 1.40101 0.493625i
\(960\) 0 0
\(961\) 2.31141 + 4.00348i 0.0745616 + 0.129144i
\(962\) 18.3799 + 31.8350i 0.592593 + 1.02640i
\(963\) 0 0
\(964\) −23.2300 13.4119i −0.748189 0.431967i
\(965\) 5.72894 9.92282i 0.184421 0.319427i
\(966\) 0 0
\(967\) −7.62091 13.1998i −0.245072 0.424477i 0.717080 0.696991i \(-0.245478\pi\)
−0.962152 + 0.272514i \(0.912145\pi\)
\(968\) 0.471174i 0.0151441i
\(969\) 0 0
\(970\) −10.5148 −0.337610
\(971\) 20.4479 35.4168i 0.656205 1.13658i −0.325386 0.945581i \(-0.605494\pi\)
0.981590 0.190998i \(-0.0611725\pi\)
\(972\) 0 0
\(973\) 19.9786 + 17.1182i 0.640486 + 0.548784i
\(974\) −29.9472 17.2900i −0.959571 0.554009i
\(975\) 0 0
\(976\) −12.7202 7.34404i −0.407165 0.235077i
\(977\) −8.98296 5.18631i −0.287390 0.165925i 0.349374 0.936983i \(-0.386394\pi\)
−0.636764 + 0.771058i \(0.719728\pi\)
\(978\) 0 0
\(979\) −13.7442 7.93522i −0.439267 0.253611i
\(980\) 5.36227 + 34.5646i 0.171291 + 1.10413i
\(981\) 0 0
\(982\) 9.79963 16.9735i 0.312719 0.541645i
\(983\) −2.11700 −0.0675219 −0.0337609 0.999430i \(-0.510748\pi\)
−0.0337609 + 0.999430i \(0.510748\pi\)
\(984\) 0 0
\(985\) 6.03847i 0.192402i
\(986\) −13.9398 24.1444i −0.443932 0.768914i
\(987\) 0 0
\(988\) 20.5234 35.5475i 0.652935 1.13092i
\(989\) 1.96007 + 1.13165i 0.0623267 + 0.0359843i
\(990\) 0 0
\(991\) −17.0581 29.5456i −0.541870 0.938546i −0.998797 0.0490418i \(-0.984383\pi\)
0.456927 0.889504i \(-0.348950\pi\)
\(992\) 24.0575 + 41.6688i 0.763825 + 1.32298i
\(993\) 0 0
\(994\) −25.3064 + 29.5351i −0.802671 + 0.936797i
\(995\) 9.30850 5.37427i 0.295099 0.170376i
\(996\) 0 0
\(997\) 45.8235i 1.45125i −0.688093 0.725623i \(-0.741552\pi\)
0.688093 0.725623i \(-0.258448\pi\)
\(998\) −3.62264 + 2.09153i −0.114673 + 0.0662064i
\(999\) 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 189.2.s.b.89.1 10
3.2 odd 2 63.2.s.b.47.5 yes 10
4.3 odd 2 3024.2.df.b.1601.5 10
7.2 even 3 1323.2.o.d.440.5 10
7.3 odd 6 189.2.i.b.143.1 10
7.4 even 3 1323.2.i.b.521.1 10
7.5 odd 6 1323.2.o.c.440.5 10
7.6 odd 2 1323.2.s.b.656.1 10
9.2 odd 6 567.2.p.c.404.1 10
9.4 even 3 63.2.i.b.5.1 10
9.5 odd 6 189.2.i.b.152.5 10
9.7 even 3 567.2.p.d.404.5 10
12.11 even 2 1008.2.df.b.929.3 10
21.2 odd 6 441.2.o.c.146.1 10
21.5 even 6 441.2.o.d.146.1 10
21.11 odd 6 441.2.i.b.227.5 10
21.17 even 6 63.2.i.b.38.5 yes 10
21.20 even 2 441.2.s.b.362.5 10
28.3 even 6 3024.2.ca.b.2033.5 10
36.23 even 6 3024.2.ca.b.2609.5 10
36.31 odd 6 1008.2.ca.b.257.5 10
63.4 even 3 441.2.s.b.374.5 10
63.5 even 6 1323.2.o.d.881.5 10
63.13 odd 6 441.2.i.b.68.1 10
63.23 odd 6 1323.2.o.c.881.5 10
63.31 odd 6 63.2.s.b.59.5 yes 10
63.32 odd 6 1323.2.s.b.962.1 10
63.38 even 6 567.2.p.d.80.5 10
63.40 odd 6 441.2.o.c.293.1 10
63.41 even 6 1323.2.i.b.1097.5 10
63.52 odd 6 567.2.p.c.80.1 10
63.58 even 3 441.2.o.d.293.1 10
63.59 even 6 inner 189.2.s.b.17.1 10
84.59 odd 6 1008.2.ca.b.353.5 10
252.31 even 6 1008.2.df.b.689.3 10
252.59 odd 6 3024.2.df.b.17.5 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.2.i.b.5.1 10 9.4 even 3
63.2.i.b.38.5 yes 10 21.17 even 6
63.2.s.b.47.5 yes 10 3.2 odd 2
63.2.s.b.59.5 yes 10 63.31 odd 6
189.2.i.b.143.1 10 7.3 odd 6
189.2.i.b.152.5 10 9.5 odd 6
189.2.s.b.17.1 10 63.59 even 6 inner
189.2.s.b.89.1 10 1.1 even 1 trivial
441.2.i.b.68.1 10 63.13 odd 6
441.2.i.b.227.5 10 21.11 odd 6
441.2.o.c.146.1 10 21.2 odd 6
441.2.o.c.293.1 10 63.40 odd 6
441.2.o.d.146.1 10 21.5 even 6
441.2.o.d.293.1 10 63.58 even 3
441.2.s.b.362.5 10 21.20 even 2
441.2.s.b.374.5 10 63.4 even 3
567.2.p.c.80.1 10 63.52 odd 6
567.2.p.c.404.1 10 9.2 odd 6
567.2.p.d.80.5 10 63.38 even 6
567.2.p.d.404.5 10 9.7 even 3
1008.2.ca.b.257.5 10 36.31 odd 6
1008.2.ca.b.353.5 10 84.59 odd 6
1008.2.df.b.689.3 10 252.31 even 6
1008.2.df.b.929.3 10 12.11 even 2
1323.2.i.b.521.1 10 7.4 even 3
1323.2.i.b.1097.5 10 63.41 even 6
1323.2.o.c.440.5 10 7.5 odd 6
1323.2.o.c.881.5 10 63.23 odd 6
1323.2.o.d.440.5 10 7.2 even 3
1323.2.o.d.881.5 10 63.5 even 6
1323.2.s.b.656.1 10 7.6 odd 2
1323.2.s.b.962.1 10 63.32 odd 6
3024.2.ca.b.2033.5 10 28.3 even 6
3024.2.ca.b.2609.5 10 36.23 even 6
3024.2.df.b.17.5 10 252.59 odd 6
3024.2.df.b.1601.5 10 4.3 odd 2