Properties

Label 441.2.w.a.62.8
Level $441$
Weight $2$
Character 441.62
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(62,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 62.8
Character \(\chi\) \(=\) 441.62
Dual form 441.2.w.a.377.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.843773 + 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(-0.0384932 - 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(2.19977 - 1.75426i) q^{8} +O(q^{10})\) \(q+(-0.843773 + 0.192586i) q^{2} +(-1.12707 + 0.542770i) q^{4} +(-0.0384932 - 0.0482690i) q^{5} +(-2.43436 + 1.03628i) q^{7} +(2.19977 - 1.75426i) q^{8} +(0.0417755 + 0.0333148i) q^{10} +(3.40028 - 0.776091i) q^{11} +(-4.60676 + 1.05146i) q^{13} +(1.85448 - 1.34321i) q^{14} +(0.0416542 - 0.0522327i) q^{16} +(-2.52315 - 1.21509i) q^{17} -3.97727i q^{19} +(0.0695837 + 0.0335097i) q^{20} +(-2.71960 + 1.30969i) q^{22} +(-2.91013 - 6.04296i) q^{23} +(1.11176 - 4.87092i) q^{25} +(3.68457 - 1.77439i) q^{26} +(2.18125 - 2.48926i) q^{28} +(2.79271 - 5.79911i) q^{29} +5.72297i q^{31} +(-2.46665 + 5.12205i) q^{32} +(2.36298 + 0.539334i) q^{34} +(0.143727 + 0.0776146i) q^{35} +(-7.25379 - 3.49324i) q^{37} +(0.765965 + 3.35591i) q^{38} +(-0.169353 - 0.0386537i) q^{40} +(-0.544686 - 0.683014i) q^{41} +(-0.942514 + 1.18188i) q^{43} +(-3.41112 + 2.72028i) q^{44} +(3.61928 + 4.53844i) q^{46} +(-2.98681 - 13.0861i) q^{47} +(4.85225 - 5.04536i) q^{49} +4.32406i q^{50} +(4.62146 - 3.68549i) q^{52} +(2.89428 + 6.01004i) q^{53} +(-0.168349 - 0.134254i) q^{55} +(-3.53714 + 6.55008i) q^{56} +(-1.23958 + 5.43097i) q^{58} +(-4.09325 + 5.13277i) q^{59} +(1.01825 - 2.11443i) q^{61} +(-1.10216 - 4.82889i) q^{62} +(1.06513 - 4.66663i) q^{64} +(0.228082 + 0.181890i) q^{65} -6.92744 q^{67} +3.50329 q^{68} +(-0.136220 - 0.0378094i) q^{70} +(-1.87659 - 3.89678i) q^{71} +(12.7355 + 2.90680i) q^{73} +(6.79330 + 1.55053i) q^{74} +(2.15874 + 4.48267i) q^{76} +(-7.47327 + 5.41293i) q^{77} -6.76297 q^{79} -0.00412462 q^{80} +(0.591130 + 0.471411i) q^{82} +(-0.469890 + 2.05872i) q^{83} +(0.0384733 + 0.168563i) q^{85} +(0.567656 - 1.17875i) q^{86} +(6.11837 - 7.67220i) q^{88} +(-2.55267 + 11.1840i) q^{89} +(10.1249 - 7.33353i) q^{91} +(6.55987 + 5.23132i) q^{92} +(5.04038 + 10.4664i) q^{94} +(-0.191979 + 0.153098i) q^{95} +19.0907i q^{97} +(-3.12254 + 5.19161i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{11}{14}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.843773 + 0.192586i −0.596638 + 0.136179i −0.510167 0.860076i \(-0.670416\pi\)
−0.0864713 + 0.996254i \(0.527559\pi\)
\(3\) 0 0
\(4\) −1.12707 + 0.542770i −0.563537 + 0.271385i
\(5\) −0.0384932 0.0482690i −0.0172147 0.0215866i 0.773150 0.634224i \(-0.218680\pi\)
−0.790364 + 0.612637i \(0.790109\pi\)
\(6\) 0 0
\(7\) −2.43436 + 1.03628i −0.920103 + 0.391677i
\(8\) 2.19977 1.75426i 0.777737 0.620225i
\(9\) 0 0
\(10\) 0.0417755 + 0.0333148i 0.0132106 + 0.0105351i
\(11\) 3.40028 0.776091i 1.02522 0.234000i 0.323332 0.946285i \(-0.395197\pi\)
0.701890 + 0.712285i \(0.252340\pi\)
\(12\) 0 0
\(13\) −4.60676 + 1.05146i −1.27769 + 0.291623i −0.806934 0.590642i \(-0.798875\pi\)
−0.470752 + 0.882266i \(0.656017\pi\)
\(14\) 1.85448 1.34321i 0.495630 0.358988i
\(15\) 0 0
\(16\) 0.0416542 0.0522327i 0.0104135 0.0130582i
\(17\) −2.52315 1.21509i −0.611955 0.294702i 0.102119 0.994772i \(-0.467438\pi\)
−0.714074 + 0.700070i \(0.753152\pi\)
\(18\) 0 0
\(19\) 3.97727i 0.912447i −0.889865 0.456224i \(-0.849202\pi\)
0.889865 0.456224i \(-0.150798\pi\)
\(20\) 0.0695837 + 0.0335097i 0.0155594 + 0.00749300i
\(21\) 0 0
\(22\) −2.71960 + 1.30969i −0.579821 + 0.279227i
\(23\) −2.91013 6.04296i −0.606805 1.26004i −0.947466 0.319857i \(-0.896365\pi\)
0.340661 0.940186i \(-0.389349\pi\)
\(24\) 0 0
\(25\) 1.11176 4.87092i 0.222351 0.974185i
\(26\) 3.68457 1.77439i 0.722603 0.347987i
\(27\) 0 0
\(28\) 2.18125 2.48926i 0.412217 0.470426i
\(29\) 2.79271 5.79911i 0.518592 1.07687i −0.463084 0.886314i \(-0.653257\pi\)
0.981677 0.190554i \(-0.0610284\pi\)
\(30\) 0 0
\(31\) 5.72297i 1.02787i 0.857828 + 0.513937i \(0.171814\pi\)
−0.857828 + 0.513937i \(0.828186\pi\)
\(32\) −2.46665 + 5.12205i −0.436046 + 0.905460i
\(33\) 0 0
\(34\) 2.36298 + 0.539334i 0.405248 + 0.0924951i
\(35\) 0.143727 + 0.0776146i 0.0242942 + 0.0131193i
\(36\) 0 0
\(37\) −7.25379 3.49324i −1.19251 0.574285i −0.270982 0.962584i \(-0.587348\pi\)
−0.921533 + 0.388300i \(0.873063\pi\)
\(38\) 0.765965 + 3.35591i 0.124256 + 0.544401i
\(39\) 0 0
\(40\) −0.169353 0.0386537i −0.0267770 0.00611168i
\(41\) −0.544686 0.683014i −0.0850656 0.106669i 0.737477 0.675372i \(-0.236017\pi\)
−0.822543 + 0.568703i \(0.807445\pi\)
\(42\) 0 0
\(43\) −0.942514 + 1.18188i −0.143732 + 0.180234i −0.848487 0.529217i \(-0.822486\pi\)
0.704754 + 0.709451i \(0.251057\pi\)
\(44\) −3.41112 + 2.72028i −0.514246 + 0.410098i
\(45\) 0 0
\(46\) 3.61928 + 4.53844i 0.533634 + 0.669156i
\(47\) −2.98681 13.0861i −0.435671 1.90880i −0.416852 0.908974i \(-0.636867\pi\)
−0.0188188 0.999823i \(-0.505991\pi\)
\(48\) 0 0
\(49\) 4.85225 5.04536i 0.693179 0.720766i
\(50\) 4.32406i 0.611515i
\(51\) 0 0
\(52\) 4.62146 3.68549i 0.640881 0.511085i
\(53\) 2.89428 + 6.01004i 0.397560 + 0.825542i 0.999633 + 0.0271006i \(0.00862744\pi\)
−0.602073 + 0.798441i \(0.705658\pi\)
\(54\) 0 0
\(55\) −0.168349 0.134254i −0.0227002 0.0181028i
\(56\) −3.53714 + 6.55008i −0.472671 + 0.875292i
\(57\) 0 0
\(58\) −1.23958 + 5.43097i −0.162765 + 0.713122i
\(59\) −4.09325 + 5.13277i −0.532895 + 0.668230i −0.973291 0.229574i \(-0.926267\pi\)
0.440396 + 0.897804i \(0.354838\pi\)
\(60\) 0 0
\(61\) 1.01825 2.11443i 0.130374 0.270725i −0.825555 0.564321i \(-0.809138\pi\)
0.955929 + 0.293597i \(0.0948523\pi\)
\(62\) −1.10216 4.82889i −0.139975 0.613269i
\(63\) 0 0
\(64\) 1.06513 4.66663i 0.133141 0.583328i
\(65\) 0.228082 + 0.181890i 0.0282901 + 0.0225606i
\(66\) 0 0
\(67\) −6.92744 −0.846322 −0.423161 0.906055i \(-0.639079\pi\)
−0.423161 + 0.906055i \(0.639079\pi\)
\(68\) 3.50329 0.424837
\(69\) 0 0
\(70\) −0.136220 0.0378094i −0.0162814 0.00451909i
\(71\) −1.87659 3.89678i −0.222711 0.462463i 0.759436 0.650582i \(-0.225475\pi\)
−0.982146 + 0.188119i \(0.939761\pi\)
\(72\) 0 0
\(73\) 12.7355 + 2.90680i 1.49058 + 0.340215i 0.888743 0.458406i \(-0.151579\pi\)
0.601835 + 0.798620i \(0.294437\pi\)
\(74\) 6.79330 + 1.55053i 0.789705 + 0.180245i
\(75\) 0 0
\(76\) 2.15874 + 4.48267i 0.247625 + 0.514198i
\(77\) −7.47327 + 5.41293i −0.851658 + 0.616860i
\(78\) 0 0
\(79\) −6.76297 −0.760894 −0.380447 0.924803i \(-0.624230\pi\)
−0.380447 + 0.924803i \(0.624230\pi\)
\(80\) −0.00412462 −0.000461147
\(81\) 0 0
\(82\) 0.591130 + 0.471411i 0.0652794 + 0.0520586i
\(83\) −0.469890 + 2.05872i −0.0515772 + 0.225974i −0.994147 0.108034i \(-0.965544\pi\)
0.942570 + 0.334009i \(0.108401\pi\)
\(84\) 0 0
\(85\) 0.0384733 + 0.168563i 0.00417302 + 0.0182832i
\(86\) 0.567656 1.17875i 0.0612119 0.127108i
\(87\) 0 0
\(88\) 6.11837 7.67220i 0.652221 0.817859i
\(89\) −2.55267 + 11.1840i −0.270582 + 1.18550i 0.638746 + 0.769418i \(0.279453\pi\)
−0.909328 + 0.416080i \(0.863404\pi\)
\(90\) 0 0
\(91\) 10.1249 7.33353i 1.06138 0.768763i
\(92\) 6.55987 + 5.23132i 0.683914 + 0.545403i
\(93\) 0 0
\(94\) 5.04038 + 10.4664i 0.519875 + 1.07953i
\(95\) −0.191979 + 0.153098i −0.0196966 + 0.0157075i
\(96\) 0 0
\(97\) 19.0907i 1.93837i 0.246336 + 0.969184i \(0.420773\pi\)
−0.246336 + 0.969184i \(0.579227\pi\)
\(98\) −3.12254 + 5.19161i −0.315424 + 0.524432i
\(99\) 0 0
\(100\) 1.39076 + 6.09332i 0.139076 + 0.609332i
\(101\) −2.82183 3.53847i −0.280783 0.352091i 0.621362 0.783524i \(-0.286580\pi\)
−0.902145 + 0.431433i \(0.858008\pi\)
\(102\) 0 0
\(103\) −6.58862 + 5.25425i −0.649196 + 0.517717i −0.891812 0.452406i \(-0.850566\pi\)
0.242616 + 0.970122i \(0.421995\pi\)
\(104\) −8.28929 + 10.3944i −0.812831 + 1.01926i
\(105\) 0 0
\(106\) −3.59956 4.51371i −0.349621 0.438410i
\(107\) −8.65693 1.97589i −0.836897 0.191016i −0.217466 0.976068i \(-0.569779\pi\)
−0.619430 + 0.785052i \(0.712636\pi\)
\(108\) 0 0
\(109\) −1.66829 7.30926i −0.159793 0.700101i −0.989814 0.142368i \(-0.954528\pi\)
0.830020 0.557733i \(-0.188329\pi\)
\(110\) 0.167904 + 0.0808582i 0.0160090 + 0.00770952i
\(111\) 0 0
\(112\) −0.0472738 + 0.170319i −0.00446695 + 0.0160936i
\(113\) 17.5749 + 4.01136i 1.65331 + 0.377357i 0.944621 0.328163i \(-0.106430\pi\)
0.708689 + 0.705521i \(0.249287\pi\)
\(114\) 0 0
\(115\) −0.179667 + 0.373082i −0.0167540 + 0.0347901i
\(116\) 8.05182i 0.747593i
\(117\) 0 0
\(118\) 2.46527 5.11920i 0.226947 0.471260i
\(119\) 7.40144 + 0.343272i 0.678489 + 0.0314677i
\(120\) 0 0
\(121\) 1.04892 0.505133i 0.0953563 0.0459212i
\(122\) −0.451967 + 1.98020i −0.0409192 + 0.179279i
\(123\) 0 0
\(124\) −3.10625 6.45020i −0.278950 0.579245i
\(125\) −0.556031 + 0.267771i −0.0497330 + 0.0239501i
\(126\) 0 0
\(127\) −3.85424 1.85611i −0.342009 0.164703i 0.254992 0.966943i \(-0.417927\pi\)
−0.597001 + 0.802240i \(0.703641\pi\)
\(128\) 7.22739i 0.638817i
\(129\) 0 0
\(130\) −0.227479 0.109548i −0.0199512 0.00960801i
\(131\) 11.7995 14.7962i 1.03093 1.29275i 0.0756218 0.997137i \(-0.475906\pi\)
0.955309 0.295610i \(-0.0955227\pi\)
\(132\) 0 0
\(133\) 4.12156 + 9.68211i 0.357384 + 0.839546i
\(134\) 5.84519 1.33413i 0.504948 0.115251i
\(135\) 0 0
\(136\) −7.68194 + 1.75335i −0.658721 + 0.150349i
\(137\) 6.23671 + 4.97361i 0.532838 + 0.424924i 0.852593 0.522576i \(-0.175029\pi\)
−0.319754 + 0.947500i \(0.603600\pi\)
\(138\) 0 0
\(139\) −13.9245 + 11.1044i −1.18106 + 0.941863i −0.999141 0.0414500i \(-0.986802\pi\)
−0.181919 + 0.983314i \(0.558231\pi\)
\(140\) −0.204117 0.00946677i −0.0172511 0.000800088i
\(141\) 0 0
\(142\) 2.33388 + 2.92660i 0.195855 + 0.245595i
\(143\) −14.8482 + 7.15054i −1.24167 + 0.597958i
\(144\) 0 0
\(145\) −0.387418 + 0.0884255i −0.0321733 + 0.00734334i
\(146\) −11.3057 −0.935665
\(147\) 0 0
\(148\) 10.0716 0.827878
\(149\) 0.0255145 0.00582353i 0.00209023 0.000477082i −0.221476 0.975166i \(-0.571087\pi\)
0.223566 + 0.974689i \(0.428230\pi\)
\(150\) 0 0
\(151\) 0.0316754 0.0152541i 0.00257771 0.00124136i −0.432594 0.901589i \(-0.642402\pi\)
0.435172 + 0.900347i \(0.356688\pi\)
\(152\) −6.97716 8.74908i −0.565922 0.709644i
\(153\) 0 0
\(154\) 5.26329 6.00653i 0.424128 0.484020i
\(155\) 0.276242 0.220296i 0.0221883 0.0176946i
\(156\) 0 0
\(157\) 1.04529 + 0.833592i 0.0834233 + 0.0665279i 0.664314 0.747454i \(-0.268724\pi\)
−0.580890 + 0.813982i \(0.697295\pi\)
\(158\) 5.70642 1.30245i 0.453978 0.103618i
\(159\) 0 0
\(160\) 0.342186 0.0781017i 0.0270522 0.00617448i
\(161\) 13.3465 + 11.6950i 1.05185 + 0.921699i
\(162\) 0 0
\(163\) 6.98615 8.76035i 0.547197 0.686164i −0.428936 0.903335i \(-0.641112\pi\)
0.976134 + 0.217171i \(0.0696830\pi\)
\(164\) 0.984621 + 0.474168i 0.0768859 + 0.0370263i
\(165\) 0 0
\(166\) 1.82759i 0.141849i
\(167\) −21.3614 10.2871i −1.65300 0.796041i −0.999226 0.0393487i \(-0.987472\pi\)
−0.653771 0.756692i \(-0.726814\pi\)
\(168\) 0 0
\(169\) 8.40408 4.04719i 0.646468 0.311322i
\(170\) −0.0649256 0.134819i −0.00497956 0.0103402i
\(171\) 0 0
\(172\) 0.420796 1.84363i 0.0320854 0.140575i
\(173\) −4.41988 + 2.12850i −0.336037 + 0.161827i −0.594291 0.804250i \(-0.702567\pi\)
0.258254 + 0.966077i \(0.416853\pi\)
\(174\) 0 0
\(175\) 2.34122 + 13.0097i 0.176979 + 0.983440i
\(176\) 0.101098 0.209933i 0.00762059 0.0158243i
\(177\) 0 0
\(178\) 9.92834i 0.744160i
\(179\) 2.68278 5.57086i 0.200521 0.416385i −0.776324 0.630334i \(-0.782918\pi\)
0.976845 + 0.213948i \(0.0686324\pi\)
\(180\) 0 0
\(181\) 7.23695 + 1.65179i 0.537918 + 0.122776i 0.482845 0.875706i \(-0.339604\pi\)
0.0550736 + 0.998482i \(0.482461\pi\)
\(182\) −7.13081 + 8.13776i −0.528571 + 0.603211i
\(183\) 0 0
\(184\) −17.0026 8.18800i −1.25344 0.603627i
\(185\) 0.110607 + 0.484599i 0.00813196 + 0.0356284i
\(186\) 0 0
\(187\) −9.52245 2.17344i −0.696350 0.158937i
\(188\) 10.4691 + 13.1278i 0.763535 + 0.957443i
\(189\) 0 0
\(190\) 0.132502 0.166152i 0.00961271 0.0120540i
\(191\) 4.05359 3.23263i 0.293308 0.233905i −0.465769 0.884906i \(-0.654222\pi\)
0.759077 + 0.651001i \(0.225651\pi\)
\(192\) 0 0
\(193\) −3.39005 4.25099i −0.244021 0.305993i 0.644705 0.764432i \(-0.276980\pi\)
−0.888726 + 0.458439i \(0.848409\pi\)
\(194\) −3.67660 16.1082i −0.263965 1.15650i
\(195\) 0 0
\(196\) −2.73037 + 8.32015i −0.195027 + 0.594296i
\(197\) 22.6860i 1.61631i −0.588968 0.808156i \(-0.700466\pi\)
0.588968 0.808156i \(-0.299534\pi\)
\(198\) 0 0
\(199\) 0.219576 0.175106i 0.0155653 0.0124129i −0.615676 0.787999i \(-0.711117\pi\)
0.631242 + 0.775586i \(0.282546\pi\)
\(200\) −6.09925 12.6652i −0.431282 0.895567i
\(201\) 0 0
\(202\) 3.06245 + 2.44222i 0.215473 + 0.171834i
\(203\) −0.788962 + 17.0112i −0.0553743 + 1.19395i
\(204\) 0 0
\(205\) −0.0120017 + 0.0525829i −0.000838235 + 0.00367255i
\(206\) 4.54741 5.70227i 0.316833 0.397296i
\(207\) 0 0
\(208\) −0.136970 + 0.284421i −0.00949717 + 0.0197211i
\(209\) −3.08672 13.5238i −0.213513 0.935462i
\(210\) 0 0
\(211\) −2.58864 + 11.3416i −0.178209 + 0.780786i 0.804247 + 0.594295i \(0.202569\pi\)
−0.982457 + 0.186491i \(0.940288\pi\)
\(212\) −6.52413 5.20282i −0.448079 0.357331i
\(213\) 0 0
\(214\) 7.68501 0.525337
\(215\) 0.0933284 0.00636494
\(216\) 0 0
\(217\) −5.93059 13.9318i −0.402595 0.945751i
\(218\) 2.81532 + 5.84607i 0.190678 + 0.395946i
\(219\) 0 0
\(220\) 0.262610 + 0.0599391i 0.0177052 + 0.00404110i
\(221\) 12.9012 + 2.94461i 0.867828 + 0.198076i
\(222\) 0 0
\(223\) −10.3037 21.3959i −0.689987 1.43277i −0.891377 0.453262i \(-0.850260\pi\)
0.201390 0.979511i \(-0.435454\pi\)
\(224\) 0.696849 15.0251i 0.0465602 1.00391i
\(225\) 0 0
\(226\) −15.6018 −1.03782
\(227\) 3.52272 0.233811 0.116906 0.993143i \(-0.462702\pi\)
0.116906 + 0.993143i \(0.462702\pi\)
\(228\) 0 0
\(229\) −7.53930 6.01239i −0.498211 0.397310i 0.341890 0.939740i \(-0.388933\pi\)
−0.840101 + 0.542430i \(0.817504\pi\)
\(230\) 0.0797479 0.349398i 0.00525842 0.0230386i
\(231\) 0 0
\(232\) −4.02983 17.6559i −0.264572 1.15916i
\(233\) 9.83501 20.4226i 0.644313 1.33793i −0.281359 0.959603i \(-0.590785\pi\)
0.925672 0.378327i \(-0.123501\pi\)
\(234\) 0 0
\(235\) −0.516679 + 0.647895i −0.0337044 + 0.0422640i
\(236\) 1.82748 8.00670i 0.118959 0.521192i
\(237\) 0 0
\(238\) −6.31125 + 1.13577i −0.409098 + 0.0736210i
\(239\) 0.427038 + 0.340552i 0.0276228 + 0.0220285i 0.637204 0.770695i \(-0.280091\pi\)
−0.609581 + 0.792724i \(0.708662\pi\)
\(240\) 0 0
\(241\) −4.97519 10.3311i −0.320480 0.665485i 0.677034 0.735952i \(-0.263265\pi\)
−0.997514 + 0.0704676i \(0.977551\pi\)
\(242\) −0.787769 + 0.628225i −0.0506397 + 0.0403838i
\(243\) 0 0
\(244\) 2.93579i 0.187945i
\(245\) −0.430313 0.0400011i −0.0274917 0.00255558i
\(246\) 0 0
\(247\) 4.18195 + 18.3223i 0.266091 + 1.16582i
\(248\) 10.0396 + 12.5892i 0.637513 + 0.799416i
\(249\) 0 0
\(250\) 0.417596 0.333021i 0.0264111 0.0210621i
\(251\) 8.15760 10.2293i 0.514903 0.645668i −0.454615 0.890688i \(-0.650223\pi\)
0.969518 + 0.245020i \(0.0787945\pi\)
\(252\) 0 0
\(253\) −14.5852 18.2892i −0.916961 1.14983i
\(254\) 3.60957 + 0.823860i 0.226484 + 0.0516936i
\(255\) 0 0
\(256\) 3.52215 + 15.4315i 0.220134 + 0.964471i
\(257\) −3.19417 1.53823i −0.199247 0.0959523i 0.331600 0.943420i \(-0.392412\pi\)
−0.530847 + 0.847468i \(0.678126\pi\)
\(258\) 0 0
\(259\) 21.2783 + 0.986869i 1.32217 + 0.0613210i
\(260\) −0.355790 0.0812067i −0.0220651 0.00503622i
\(261\) 0 0
\(262\) −7.10661 + 14.7570i −0.439048 + 0.911692i
\(263\) 10.6792i 0.658506i −0.944242 0.329253i \(-0.893203\pi\)
0.944242 0.329253i \(-0.106797\pi\)
\(264\) 0 0
\(265\) 0.178688 0.371050i 0.0109767 0.0227934i
\(266\) −5.34230 7.37576i −0.327557 0.452237i
\(267\) 0 0
\(268\) 7.80774 3.76001i 0.476933 0.229679i
\(269\) −3.32103 + 14.5504i −0.202487 + 0.887154i 0.766929 + 0.641732i \(0.221784\pi\)
−0.969416 + 0.245422i \(0.921073\pi\)
\(270\) 0 0
\(271\) 3.17162 + 6.58594i 0.192662 + 0.400067i 0.974814 0.223021i \(-0.0715919\pi\)
−0.782151 + 0.623088i \(0.785878\pi\)
\(272\) −0.168567 + 0.0811777i −0.0102209 + 0.00492212i
\(273\) 0 0
\(274\) −6.22022 2.99550i −0.375777 0.180965i
\(275\) 17.4253i 1.05079i
\(276\) 0 0
\(277\) 8.65026 + 4.16575i 0.519744 + 0.250296i 0.675315 0.737529i \(-0.264008\pi\)
−0.155571 + 0.987825i \(0.549722\pi\)
\(278\) 9.61056 12.0513i 0.576403 0.722787i
\(279\) 0 0
\(280\) 0.452322 0.0813996i 0.0270314 0.00486456i
\(281\) −7.13655 + 1.62887i −0.425731 + 0.0971703i −0.430018 0.902821i \(-0.641493\pi\)
0.00428673 + 0.999991i \(0.498635\pi\)
\(282\) 0 0
\(283\) −7.64831 + 1.74568i −0.454645 + 0.103770i −0.443710 0.896171i \(-0.646338\pi\)
−0.0109349 + 0.999940i \(0.503481\pi\)
\(284\) 4.23012 + 3.37340i 0.251011 + 0.200175i
\(285\) 0 0
\(286\) 11.1515 8.89299i 0.659400 0.525854i
\(287\) 2.03376 + 1.09826i 0.120049 + 0.0648282i
\(288\) 0 0
\(289\) −5.70946 7.15943i −0.335850 0.421143i
\(290\) 0.309863 0.149222i 0.0181958 0.00876263i
\(291\) 0 0
\(292\) −15.9316 + 3.63628i −0.932325 + 0.212797i
\(293\) −12.7206 −0.743143 −0.371572 0.928404i \(-0.621181\pi\)
−0.371572 + 0.928404i \(0.621181\pi\)
\(294\) 0 0
\(295\) 0.405316 0.0235984
\(296\) −22.0847 + 5.04069i −1.28365 + 0.292984i
\(297\) 0 0
\(298\) −0.0204070 + 0.00982747i −0.00118214 + 0.000569290i
\(299\) 19.7602 + 24.7786i 1.14276 + 1.43298i
\(300\) 0 0
\(301\) 1.06967 3.85382i 0.0616547 0.222131i
\(302\) −0.0237892 + 0.0189712i −0.00136891 + 0.00109167i
\(303\) 0 0
\(304\) −0.207743 0.165670i −0.0119149 0.00950181i
\(305\) −0.141257 + 0.0322410i −0.00808836 + 0.00184612i
\(306\) 0 0
\(307\) −3.00656 + 0.686228i −0.171593 + 0.0391651i −0.307454 0.951563i \(-0.599477\pi\)
0.135861 + 0.990728i \(0.456620\pi\)
\(308\) 5.48495 10.1570i 0.312534 0.578750i
\(309\) 0 0
\(310\) −0.190660 + 0.239080i −0.0108287 + 0.0135788i
\(311\) −22.6761 10.9202i −1.28584 0.619229i −0.338957 0.940802i \(-0.610074\pi\)
−0.946885 + 0.321573i \(0.895788\pi\)
\(312\) 0 0
\(313\) 20.6353i 1.16637i 0.812338 + 0.583187i \(0.198194\pi\)
−0.812338 + 0.583187i \(0.801806\pi\)
\(314\) −1.04253 0.502055i −0.0588332 0.0283326i
\(315\) 0 0
\(316\) 7.62237 3.67074i 0.428792 0.206495i
\(317\) 8.49278 + 17.6354i 0.477002 + 0.990505i 0.991143 + 0.132799i \(0.0423966\pi\)
−0.514141 + 0.857706i \(0.671889\pi\)
\(318\) 0 0
\(319\) 4.99533 21.8860i 0.279685 1.22538i
\(320\) −0.266254 + 0.128221i −0.0148840 + 0.00716777i
\(321\) 0 0
\(322\) −13.5137 7.29762i −0.753091 0.406680i
\(323\) −4.83272 + 10.0353i −0.268900 + 0.558377i
\(324\) 0 0
\(325\) 23.6082i 1.30954i
\(326\) −4.20761 + 8.73718i −0.233038 + 0.483908i
\(327\) 0 0
\(328\) −2.39637 0.546956i −0.132317 0.0302006i
\(329\) 20.8318 + 28.7611i 1.14849 + 1.58565i
\(330\) 0 0
\(331\) 19.2323 + 9.26178i 1.05710 + 0.509074i 0.879929 0.475106i \(-0.157590\pi\)
0.177174 + 0.984180i \(0.443305\pi\)
\(332\) −0.587813 2.57538i −0.0322604 0.141342i
\(333\) 0 0
\(334\) 20.0054 + 4.56609i 1.09464 + 0.249845i
\(335\) 0.266660 + 0.334381i 0.0145692 + 0.0182692i
\(336\) 0 0
\(337\) −9.72244 + 12.1916i −0.529615 + 0.664117i −0.972620 0.232403i \(-0.925341\pi\)
0.443004 + 0.896519i \(0.353913\pi\)
\(338\) −6.31171 + 5.03342i −0.343312 + 0.273782i
\(339\) 0 0
\(340\) −0.134853 0.169100i −0.00731344 0.00917076i
\(341\) 4.44154 + 19.4597i 0.240523 + 1.05380i
\(342\) 0 0
\(343\) −6.58375 + 17.3105i −0.355489 + 0.934681i
\(344\) 4.25327i 0.229321i
\(345\) 0 0
\(346\) 3.31946 2.64718i 0.178455 0.142313i
\(347\) 0.0633374 + 0.131521i 0.00340013 + 0.00706044i 0.902662 0.430350i \(-0.141610\pi\)
−0.899262 + 0.437411i \(0.855896\pi\)
\(348\) 0 0
\(349\) 11.8509 + 9.45081i 0.634366 + 0.505890i 0.887059 0.461656i \(-0.152745\pi\)
−0.252693 + 0.967547i \(0.581316\pi\)
\(350\) −4.48094 10.5263i −0.239516 0.562657i
\(351\) 0 0
\(352\) −4.41212 + 19.3308i −0.235167 + 1.03033i
\(353\) −3.94296 + 4.94431i −0.209862 + 0.263159i −0.875611 0.483017i \(-0.839541\pi\)
0.665749 + 0.746176i \(0.268112\pi\)
\(354\) 0 0
\(355\) −0.115858 + 0.240581i −0.00614909 + 0.0127687i
\(356\) −3.19328 13.9907i −0.169243 0.741503i
\(357\) 0 0
\(358\) −1.19079 + 5.21721i −0.0629354 + 0.275738i
\(359\) 25.2928 + 20.1703i 1.33490 + 1.06455i 0.992141 + 0.125127i \(0.0399339\pi\)
0.342762 + 0.939422i \(0.388638\pi\)
\(360\) 0 0
\(361\) 3.18135 0.167440
\(362\) −6.42446 −0.337662
\(363\) 0 0
\(364\) −7.43111 + 13.7609i −0.389496 + 0.721269i
\(365\) −0.349923 0.726622i −0.0183158 0.0380331i
\(366\) 0 0
\(367\) 9.33500 + 2.13065i 0.487283 + 0.111219i 0.459102 0.888384i \(-0.348171\pi\)
0.0281812 + 0.999603i \(0.491028\pi\)
\(368\) −0.436859 0.0997103i −0.0227729 0.00519776i
\(369\) 0 0
\(370\) −0.186654 0.387591i −0.00970367 0.0201499i
\(371\) −13.2738 11.6313i −0.689142 0.603869i
\(372\) 0 0
\(373\) 13.4756 0.697740 0.348870 0.937171i \(-0.386566\pi\)
0.348870 + 0.937171i \(0.386566\pi\)
\(374\) 8.45336 0.437113
\(375\) 0 0
\(376\) −29.5266 23.5467i −1.52272 1.21433i
\(377\) −6.76777 + 29.6516i −0.348558 + 1.52713i
\(378\) 0 0
\(379\) −1.51751 6.64863i −0.0779490 0.341517i 0.920883 0.389840i \(-0.127470\pi\)
−0.998832 + 0.0483226i \(0.984612\pi\)
\(380\) 0.133277 0.276753i 0.00683697 0.0141971i
\(381\) 0 0
\(382\) −2.79776 + 3.50827i −0.143146 + 0.179499i
\(383\) −4.77281 + 20.9111i −0.243879 + 1.06851i 0.693572 + 0.720388i \(0.256036\pi\)
−0.937451 + 0.348118i \(0.886821\pi\)
\(384\) 0 0
\(385\) 0.548947 + 0.152366i 0.0279769 + 0.00776529i
\(386\) 3.67911 + 2.93399i 0.187262 + 0.149336i
\(387\) 0 0
\(388\) −10.3619 21.5166i −0.526044 1.09234i
\(389\) −8.78880 + 7.00883i −0.445610 + 0.355362i −0.820441 0.571731i \(-0.806272\pi\)
0.374831 + 0.927093i \(0.377701\pi\)
\(390\) 0 0
\(391\) 18.7834i 0.949916i
\(392\) 1.82298 19.6108i 0.0920743 0.990493i
\(393\) 0 0
\(394\) 4.36901 + 19.1419i 0.220107 + 0.964354i
\(395\) 0.260329 + 0.326442i 0.0130986 + 0.0164251i
\(396\) 0 0
\(397\) 23.1518 18.4629i 1.16195 0.926627i 0.163748 0.986502i \(-0.447642\pi\)
0.998206 + 0.0598748i \(0.0190701\pi\)
\(398\) −0.151549 + 0.190037i −0.00759649 + 0.00952569i
\(399\) 0 0
\(400\) −0.208112 0.260964i −0.0104056 0.0130482i
\(401\) 12.7588 + 2.91212i 0.637145 + 0.145424i 0.528878 0.848698i \(-0.322613\pi\)
0.108267 + 0.994122i \(0.465470\pi\)
\(402\) 0 0
\(403\) −6.01749 26.3643i −0.299752 1.31330i
\(404\) 5.10099 + 2.45651i 0.253784 + 0.122216i
\(405\) 0 0
\(406\) −2.61040 14.5055i −0.129552 0.719897i
\(407\) −27.3760 6.24839i −1.35698 0.309721i
\(408\) 0 0
\(409\) 16.9849 35.2695i 0.839848 1.74396i 0.193224 0.981155i \(-0.438106\pi\)
0.646624 0.762809i \(-0.276180\pi\)
\(410\) 0.0466794i 0.00230533i
\(411\) 0 0
\(412\) 4.57401 9.49804i 0.225345 0.467935i
\(413\) 4.64547 16.7368i 0.228589 0.823563i
\(414\) 0 0
\(415\) 0.117460 0.0565658i 0.00576589 0.00277671i
\(416\) 5.97762 26.1897i 0.293077 1.28405i
\(417\) 0 0
\(418\) 5.20899 + 10.8166i 0.254780 + 0.529056i
\(419\) 33.9245 16.3372i 1.65732 0.798123i 0.658351 0.752711i \(-0.271254\pi\)
0.998968 0.0454117i \(-0.0144600\pi\)
\(420\) 0 0
\(421\) 28.6493 + 13.7968i 1.39628 + 0.672414i 0.972403 0.233306i \(-0.0749543\pi\)
0.423878 + 0.905719i \(0.360669\pi\)
\(422\) 10.0683i 0.490115i
\(423\) 0 0
\(424\) 16.9099 + 8.14339i 0.821218 + 0.395478i
\(425\) −8.72373 + 10.9392i −0.423163 + 0.530630i
\(426\) 0 0
\(427\) −0.287665 + 6.20248i −0.0139211 + 0.300159i
\(428\) 10.8294 2.47175i 0.523461 0.119477i
\(429\) 0 0
\(430\) −0.0787480 + 0.0179737i −0.00379757 + 0.000866770i
\(431\) −9.63401 7.68286i −0.464054 0.370071i 0.363373 0.931644i \(-0.381625\pi\)
−0.827427 + 0.561573i \(0.810196\pi\)
\(432\) 0 0
\(433\) 29.2541 23.3294i 1.40586 1.12114i 0.429982 0.902838i \(-0.358520\pi\)
0.975882 0.218301i \(-0.0700514\pi\)
\(434\) 7.68714 + 10.6131i 0.368994 + 0.509446i
\(435\) 0 0
\(436\) 5.84754 + 7.33258i 0.280046 + 0.351167i
\(437\) −24.0344 + 11.5744i −1.14972 + 0.553678i
\(438\) 0 0
\(439\) −27.8246 + 6.35079i −1.32800 + 0.303107i −0.826932 0.562302i \(-0.809916\pi\)
−0.501066 + 0.865409i \(0.667059\pi\)
\(440\) −0.605845 −0.0288825
\(441\) 0 0
\(442\) −11.4528 −0.544753
\(443\) −34.6668 + 7.91248i −1.64707 + 0.375933i −0.942633 0.333831i \(-0.891658\pi\)
−0.704439 + 0.709765i \(0.748801\pi\)
\(444\) 0 0
\(445\) 0.638099 0.307292i 0.0302488 0.0145671i
\(446\) 12.8145 + 16.0689i 0.606786 + 0.760885i
\(447\) 0 0
\(448\) 2.24302 + 12.4640i 0.105973 + 0.588870i
\(449\) −29.2058 + 23.2908i −1.37831 + 1.09916i −0.394703 + 0.918809i \(0.629153\pi\)
−0.983602 + 0.180353i \(0.942276\pi\)
\(450\) 0 0
\(451\) −2.38216 1.89971i −0.112172 0.0894540i
\(452\) −21.9855 + 5.01804i −1.03411 + 0.236029i
\(453\) 0 0
\(454\) −2.97238 + 0.678427i −0.139501 + 0.0318401i
\(455\) −0.743723 0.206428i −0.0348663 0.00967751i
\(456\) 0 0
\(457\) 7.65086 9.59387i 0.357892 0.448782i −0.569993 0.821650i \(-0.693054\pi\)
0.927885 + 0.372867i \(0.121625\pi\)
\(458\) 7.51936 + 3.62113i 0.351357 + 0.169204i
\(459\) 0 0
\(460\) 0.518009i 0.0241523i
\(461\) 34.5881 + 16.6567i 1.61093 + 0.775782i 0.999875 0.0158086i \(-0.00503224\pi\)
0.611052 + 0.791590i \(0.290747\pi\)
\(462\) 0 0
\(463\) −4.90057 + 2.35999i −0.227749 + 0.109678i −0.544279 0.838904i \(-0.683197\pi\)
0.316530 + 0.948583i \(0.397482\pi\)
\(464\) −0.186575 0.387428i −0.00866155 0.0179859i
\(465\) 0 0
\(466\) −4.36542 + 19.1261i −0.202224 + 0.886001i
\(467\) −26.4297 + 12.7279i −1.22302 + 0.588977i −0.930152 0.367176i \(-0.880325\pi\)
−0.292871 + 0.956152i \(0.594611\pi\)
\(468\) 0 0
\(469\) 16.8639 7.17876i 0.778703 0.331484i
\(470\) 0.311185 0.646181i 0.0143539 0.0298061i
\(471\) 0 0
\(472\) 18.4715i 0.850222i
\(473\) −2.28757 + 4.75018i −0.105182 + 0.218414i
\(474\) 0 0
\(475\) −19.3730 4.42175i −0.888892 0.202884i
\(476\) −8.52829 + 3.63039i −0.390893 + 0.166399i
\(477\) 0 0
\(478\) −0.425909 0.205107i −0.0194806 0.00938137i
\(479\) 6.74091 + 29.5338i 0.308000 + 1.34944i 0.857733 + 0.514096i \(0.171872\pi\)
−0.549733 + 0.835340i \(0.685271\pi\)
\(480\) 0 0
\(481\) 37.0895 + 8.46543i 1.69113 + 0.385990i
\(482\) 6.18756 + 7.75895i 0.281836 + 0.353411i
\(483\) 0 0
\(484\) −0.908038 + 1.13864i −0.0412745 + 0.0517565i
\(485\) 0.921490 0.734864i 0.0418427 0.0333684i
\(486\) 0 0
\(487\) 9.46958 + 11.8745i 0.429108 + 0.538084i 0.948636 0.316369i \(-0.102464\pi\)
−0.519528 + 0.854453i \(0.673892\pi\)
\(488\) −1.46933 6.43754i −0.0665133 0.291414i
\(489\) 0 0
\(490\) 0.370791 0.0491204i 0.0167506 0.00221903i
\(491\) 22.0177i 0.993643i −0.867853 0.496821i \(-0.834500\pi\)
0.867853 0.496821i \(-0.165500\pi\)
\(492\) 0 0
\(493\) −14.0928 + 11.2387i −0.634710 + 0.506164i
\(494\) −7.05723 14.6545i −0.317520 0.659337i
\(495\) 0 0
\(496\) 0.298926 + 0.238385i 0.0134222 + 0.0107038i
\(497\) 8.60646 + 7.54152i 0.386053 + 0.338283i
\(498\) 0 0
\(499\) 9.10921 39.9101i 0.407784 1.78662i −0.186597 0.982437i \(-0.559746\pi\)
0.594381 0.804183i \(-0.297397\pi\)
\(500\) 0.481350 0.603594i 0.0215266 0.0269936i
\(501\) 0 0
\(502\) −4.91315 + 10.2023i −0.219284 + 0.455349i
\(503\) −6.99232 30.6353i −0.311772 1.36596i −0.851602 0.524188i \(-0.824369\pi\)
0.539830 0.841774i \(-0.318488\pi\)
\(504\) 0 0
\(505\) −0.0621768 + 0.272414i −0.00276683 + 0.0121223i
\(506\) 15.8288 + 12.6231i 0.703676 + 0.561163i
\(507\) 0 0
\(508\) 5.35145 0.237432
\(509\) 11.4957 0.509537 0.254768 0.967002i \(-0.418001\pi\)
0.254768 + 0.967002i \(0.418001\pi\)
\(510\) 0 0
\(511\) −34.0151 + 6.12134i −1.50474 + 0.270792i
\(512\) 0.327909 + 0.680909i 0.0144916 + 0.0300922i
\(513\) 0 0
\(514\) 2.99140 + 0.682767i 0.131945 + 0.0301156i
\(515\) 0.507235 + 0.115773i 0.0223514 + 0.00510157i
\(516\) 0 0
\(517\) −20.3120 42.1782i −0.893319 1.85500i
\(518\) −18.1441 + 3.26521i −0.797208 + 0.143465i
\(519\) 0 0
\(520\) 0.820811 0.0359949
\(521\) 22.1935 0.972315 0.486157 0.873871i \(-0.338398\pi\)
0.486157 + 0.873871i \(0.338398\pi\)
\(522\) 0 0
\(523\) 17.6618 + 14.0848i 0.772295 + 0.615885i 0.928283 0.371874i \(-0.121285\pi\)
−0.155988 + 0.987759i \(0.549856\pi\)
\(524\) −5.26804 + 23.0808i −0.230135 + 1.00829i
\(525\) 0 0
\(526\) 2.05666 + 9.01080i 0.0896744 + 0.392889i
\(527\) 6.95390 14.4399i 0.302917 0.629013i
\(528\) 0 0
\(529\) −13.7082 + 17.1895i −0.596008 + 0.747370i
\(530\) −0.0793134 + 0.347495i −0.00344515 + 0.0150942i
\(531\) 0 0
\(532\) −9.90046 8.67539i −0.429239 0.376126i
\(533\) 3.22740 + 2.57377i 0.139794 + 0.111482i
\(534\) 0 0
\(535\) 0.237859 + 0.493920i 0.0102835 + 0.0213540i
\(536\) −15.2388 + 12.1525i −0.658216 + 0.524910i
\(537\) 0 0
\(538\) 12.9168i 0.556884i
\(539\) 12.5833 20.9214i 0.542003 0.901149i
\(540\) 0 0
\(541\) −4.83952 21.2033i −0.208067 0.911601i −0.965852 0.259096i \(-0.916575\pi\)
0.757784 0.652505i \(-0.226282\pi\)
\(542\) −3.94449 4.94623i −0.169430 0.212459i
\(543\) 0 0
\(544\) 12.4475 9.92653i 0.533681 0.425597i
\(545\) −0.288593 + 0.361884i −0.0123620 + 0.0155014i
\(546\) 0 0
\(547\) 13.7085 + 17.1899i 0.586131 + 0.734985i 0.983145 0.182827i \(-0.0585249\pi\)
−0.397014 + 0.917813i \(0.629953\pi\)
\(548\) −9.72876 2.22053i −0.415592 0.0948562i
\(549\) 0 0
\(550\) 3.35587 + 14.7030i 0.143095 + 0.626939i
\(551\) −23.0646 11.1073i −0.982585 0.473188i
\(552\) 0 0
\(553\) 16.4635 7.00833i 0.700101 0.298024i
\(554\) −8.10113 1.84903i −0.344184 0.0785577i
\(555\) 0 0
\(556\) 9.66678 20.0733i 0.409963 0.851296i
\(557\) 31.9207i 1.35252i −0.736662 0.676262i \(-0.763599\pi\)
0.736662 0.676262i \(-0.236401\pi\)
\(558\) 0 0
\(559\) 3.09924 6.43564i 0.131084 0.272198i
\(560\) 0.0100408 0.00427426i 0.000424303 0.000180621i
\(561\) 0 0
\(562\) 5.70793 2.74880i 0.240775 0.115951i
\(563\) 2.67208 11.7071i 0.112615 0.493398i −0.886892 0.461978i \(-0.847140\pi\)
0.999506 0.0314198i \(-0.0100029\pi\)
\(564\) 0 0
\(565\) −0.482892 1.00273i −0.0203154 0.0421854i
\(566\) 6.11725 2.94591i 0.257127 0.123826i
\(567\) 0 0
\(568\) −10.9640 5.28001i −0.460041 0.221544i
\(569\) 16.1597i 0.677450i −0.940886 0.338725i \(-0.890004\pi\)
0.940886 0.338725i \(-0.109996\pi\)
\(570\) 0 0
\(571\) −20.1418 9.69978i −0.842908 0.405923i −0.0379679 0.999279i \(-0.512088\pi\)
−0.804940 + 0.593356i \(0.797803\pi\)
\(572\) 12.8540 16.1184i 0.537451 0.673942i
\(573\) 0 0
\(574\) −1.92754 0.535009i −0.0804539 0.0223308i
\(575\) −32.6701 + 7.45675i −1.36244 + 0.310968i
\(576\) 0 0
\(577\) −29.0434 + 6.62897i −1.20909 + 0.275967i −0.779120 0.626875i \(-0.784334\pi\)
−0.429972 + 0.902842i \(0.641477\pi\)
\(578\) 6.19629 + 4.94138i 0.257732 + 0.205534i
\(579\) 0 0
\(580\) 0.388653 0.309941i 0.0161380 0.0128696i
\(581\) −0.989529 5.49862i −0.0410526 0.228121i
\(582\) 0 0
\(583\) 14.5057 + 18.1896i 0.600765 + 0.753335i
\(584\) 33.1145 15.9471i 1.37029 0.659895i
\(585\) 0 0
\(586\) 10.7333 2.44980i 0.443387 0.101200i
\(587\) −21.0093 −0.867148 −0.433574 0.901118i \(-0.642748\pi\)
−0.433574 + 0.901118i \(0.642748\pi\)
\(588\) 0 0
\(589\) 22.7618 0.937882
\(590\) −0.341995 + 0.0780581i −0.0140797 + 0.00321360i
\(591\) 0 0
\(592\) −0.484612 + 0.233377i −0.0199174 + 0.00959173i
\(593\) −5.16895 6.48165i −0.212263 0.266170i 0.664290 0.747475i \(-0.268734\pi\)
−0.876553 + 0.481306i \(0.840163\pi\)
\(594\) 0 0
\(595\) −0.268336 0.370474i −0.0110007 0.0151879i
\(596\) −0.0255959 + 0.0204121i −0.00104845 + 0.000836111i
\(597\) 0 0
\(598\) −21.4452 17.1019i −0.876958 0.699351i
\(599\) 29.1262 6.64786i 1.19006 0.271624i 0.418763 0.908096i \(-0.362464\pi\)
0.771300 + 0.636472i \(0.219607\pi\)
\(600\) 0 0
\(601\) −32.3719 + 7.38868i −1.32048 + 0.301390i −0.823966 0.566640i \(-0.808243\pi\)
−0.496512 + 0.868030i \(0.665386\pi\)
\(602\) −0.160367 + 3.45776i −0.00653609 + 0.140928i
\(603\) 0 0
\(604\) −0.0274211 + 0.0343849i −0.00111575 + 0.00139910i
\(605\) −0.0647586 0.0311861i −0.00263281 0.00126789i
\(606\) 0 0
\(607\) 21.1596i 0.858840i −0.903105 0.429420i \(-0.858718\pi\)
0.903105 0.429420i \(-0.141282\pi\)
\(608\) 20.3718 + 9.81053i 0.826184 + 0.397869i
\(609\) 0 0
\(610\) 0.112980 0.0544082i 0.00457442 0.00220292i
\(611\) 27.5190 + 57.1438i 1.11330 + 2.31179i
\(612\) 0 0
\(613\) −8.60815 + 37.7148i −0.347680 + 1.52329i 0.434752 + 0.900550i \(0.356836\pi\)
−0.782432 + 0.622736i \(0.786021\pi\)
\(614\) 2.40470 1.15804i 0.0970457 0.0467347i
\(615\) 0 0
\(616\) −6.94381 + 25.0173i −0.279774 + 1.00797i
\(617\) 3.14453 6.52968i 0.126594 0.262875i −0.828033 0.560679i \(-0.810540\pi\)
0.954627 + 0.297804i \(0.0962543\pi\)
\(618\) 0 0
\(619\) 2.50182i 0.100557i −0.998735 0.0502784i \(-0.983989\pi\)
0.998735 0.0502784i \(-0.0160109\pi\)
\(620\) −0.191775 + 0.398225i −0.00770187 + 0.0159931i
\(621\) 0 0
\(622\) 21.2365 + 4.84710i 0.851508 + 0.194351i
\(623\) −5.37559 29.8711i −0.215368 1.19676i
\(624\) 0 0
\(625\) −22.4727 10.8223i −0.898909 0.432892i
\(626\) −3.97406 17.4115i −0.158835 0.695903i
\(627\) 0 0
\(628\) −1.63057 0.372167i −0.0650668 0.0148511i
\(629\) 14.0578 + 17.6280i 0.560522 + 0.702873i
\(630\) 0 0
\(631\) −10.5968 + 13.2880i −0.421852 + 0.528986i −0.946660 0.322235i \(-0.895566\pi\)
0.524807 + 0.851221i \(0.324137\pi\)
\(632\) −14.8770 + 11.8640i −0.591775 + 0.471925i
\(633\) 0 0
\(634\) −10.5623 13.2447i −0.419483 0.526015i
\(635\) 0.0587700 + 0.257488i 0.00233221 + 0.0102181i
\(636\) 0 0
\(637\) −17.0482 + 28.3447i −0.675473 + 1.12306i
\(638\) 19.4288i 0.769195i
\(639\) 0 0
\(640\) −0.348859 + 0.278206i −0.0137899 + 0.0109971i
\(641\) −3.78762 7.86507i −0.149602 0.310652i 0.812678 0.582713i \(-0.198009\pi\)
−0.962280 + 0.272062i \(0.912295\pi\)
\(642\) 0 0
\(643\) 22.4798 + 17.9270i 0.886516 + 0.706973i 0.956860 0.290550i \(-0.0938383\pi\)
−0.0703440 + 0.997523i \(0.522410\pi\)
\(644\) −21.3902 5.93709i −0.842893 0.233954i
\(645\) 0 0
\(646\) 2.14508 9.39820i 0.0843969 0.369767i
\(647\) 28.4335 35.6545i 1.11784 1.40172i 0.212432 0.977176i \(-0.431862\pi\)
0.905405 0.424548i \(-0.139567\pi\)
\(648\) 0 0
\(649\) −9.93468 + 20.6296i −0.389970 + 0.809782i
\(650\) −4.54659 19.9199i −0.178332 0.781324i
\(651\) 0 0
\(652\) −3.11905 + 13.6654i −0.122151 + 0.535180i
\(653\) 36.8526 + 29.3890i 1.44215 + 1.15008i 0.962052 + 0.272868i \(0.0879721\pi\)
0.480103 + 0.877212i \(0.340599\pi\)
\(654\) 0 0
\(655\) −1.16840 −0.0456531
\(656\) −0.0583641 −0.00227874
\(657\) 0 0
\(658\) −23.1163 20.2559i −0.901166 0.789657i
\(659\) −9.12325 18.9446i −0.355391 0.737978i 0.644249 0.764816i \(-0.277170\pi\)
−0.999640 + 0.0268386i \(0.991456\pi\)
\(660\) 0 0
\(661\) −2.69086 0.614172i −0.104663 0.0238885i 0.169869 0.985467i \(-0.445666\pi\)
−0.274531 + 0.961578i \(0.588523\pi\)
\(662\) −18.0114 4.11098i −0.700032 0.159778i
\(663\) 0 0
\(664\) 2.57789 + 5.35303i 0.100041 + 0.207738i
\(665\) 0.308694 0.571639i 0.0119706 0.0221672i
\(666\) 0 0
\(667\) −43.1709 −1.67159
\(668\) 29.6594 1.14756
\(669\) 0 0
\(670\) −0.289397 0.230787i −0.0111804 0.00891607i
\(671\) 1.82136 7.97990i 0.0703128 0.308060i
\(672\) 0 0
\(673\) 0.0827287 + 0.362458i 0.00318896 + 0.0139717i 0.976497 0.215529i \(-0.0691477\pi\)
−0.973308 + 0.229501i \(0.926291\pi\)
\(674\) 5.85562 12.1593i 0.225550 0.468359i
\(675\) 0 0
\(676\) −7.27532 + 9.12296i −0.279820 + 0.350883i
\(677\) −6.28042 + 27.5163i −0.241376 + 1.05754i 0.698389 + 0.715718i \(0.253900\pi\)
−0.939765 + 0.341820i \(0.888957\pi\)
\(678\) 0 0
\(679\) −19.7833 46.4737i −0.759214 1.78350i
\(680\) 0.380335 + 0.303307i 0.0145852 + 0.0116313i
\(681\) 0 0
\(682\) −7.49531 15.5642i −0.287010 0.595983i
\(683\) 7.50909 5.98830i 0.287327 0.229136i −0.469210 0.883087i \(-0.655461\pi\)
0.756537 + 0.653951i \(0.226890\pi\)
\(684\) 0 0
\(685\) 0.492490i 0.0188171i
\(686\) 2.22143 15.8741i 0.0848145 0.606076i
\(687\) 0 0
\(688\) 0.0224729 + 0.0984601i 0.000856771 + 0.00375376i
\(689\) −19.6526 24.6436i −0.748704 0.938845i
\(690\) 0 0
\(691\) 18.8209 15.0092i 0.715980 0.570975i −0.196299 0.980544i \(-0.562892\pi\)
0.912279 + 0.409569i \(0.134321\pi\)
\(692\) 3.82624 4.79796i 0.145452 0.182391i
\(693\) 0 0
\(694\) −0.0787716 0.0987765i −0.00299013 0.00374950i
\(695\) 1.07200 + 0.244676i 0.0406632 + 0.00928110i
\(696\) 0 0
\(697\) 0.544404 + 2.38519i 0.0206208 + 0.0903455i
\(698\) −11.8196 5.69202i −0.447378 0.215446i
\(699\) 0 0
\(700\) −9.69999 13.3921i −0.366625 0.506175i
\(701\) 37.8776 + 8.64531i 1.43062 + 0.326529i 0.866504 0.499169i \(-0.166361\pi\)
0.564112 + 0.825698i \(0.309219\pi\)
\(702\) 0 0
\(703\) −13.8935 + 28.8502i −0.524005 + 1.08811i
\(704\) 16.6945i 0.629196i
\(705\) 0 0
\(706\) 2.37476 4.93123i 0.0893752 0.185589i
\(707\) 10.5362 + 5.68971i 0.396255 + 0.213984i
\(708\) 0 0
\(709\) 28.1686 13.5653i 1.05789 0.509455i 0.177707 0.984083i \(-0.443132\pi\)
0.880186 + 0.474629i \(0.157418\pi\)
\(710\) 0.0514252 0.225308i 0.00192995 0.00845568i
\(711\) 0 0
\(712\) 14.0043 + 29.0802i 0.524833 + 1.08983i
\(713\) 34.5836 16.6546i 1.29517 0.623720i
\(714\) 0 0
\(715\) 0.916706 + 0.441462i 0.0342829 + 0.0165098i
\(716\) 7.73490i 0.289067i
\(717\) 0 0
\(718\) −25.2259 12.1482i −0.941423 0.453365i
\(719\) −10.0809 + 12.6411i −0.375955 + 0.471432i −0.933429 0.358762i \(-0.883199\pi\)
0.557474 + 0.830194i \(0.311770\pi\)
\(720\) 0 0
\(721\) 10.5942 19.6184i 0.394550 0.730628i
\(722\) −2.68434 + 0.612684i −0.0999009 + 0.0228017i
\(723\) 0 0
\(724\) −9.05312 + 2.06632i −0.336456 + 0.0767940i
\(725\) −25.1422 20.0503i −0.933759 0.744648i
\(726\) 0 0
\(727\) −22.6368 + 18.0523i −0.839553 + 0.669521i −0.945775 0.324821i \(-0.894696\pi\)
0.106222 + 0.994342i \(0.466124\pi\)
\(728\) 9.40760 33.8938i 0.348669 1.25619i
\(729\) 0 0
\(730\) 0.435193 + 0.545714i 0.0161072 + 0.0201978i
\(731\) 3.81419 1.83682i 0.141073 0.0679371i
\(732\) 0 0
\(733\) 3.00523 0.685925i 0.111001 0.0253352i −0.166660 0.986014i \(-0.553298\pi\)
0.277661 + 0.960679i \(0.410441\pi\)
\(734\) −8.28696 −0.305877
\(735\) 0 0
\(736\) 38.1306 1.40551
\(737\) −23.5552 + 5.37633i −0.867668 + 0.198040i
\(738\) 0 0
\(739\) −36.1985 + 17.4323i −1.33159 + 0.641258i −0.958115 0.286385i \(-0.907546\pi\)
−0.373470 + 0.927642i \(0.621832\pi\)
\(740\) −0.387688 0.486145i −0.0142517 0.0178710i
\(741\) 0 0
\(742\) 13.4401 + 7.25786i 0.493402 + 0.266444i
\(743\) −4.63509 + 3.69636i −0.170045 + 0.135606i −0.704815 0.709392i \(-0.748970\pi\)
0.534770 + 0.844998i \(0.320398\pi\)
\(744\) 0 0
\(745\) −0.00126323 0.00100739i −4.62813e−5 3.69081e-5i
\(746\) −11.3703 + 2.59521i −0.416298 + 0.0950173i
\(747\) 0 0
\(748\) 11.9122 2.71888i 0.435552 0.0994119i
\(749\) 23.1217 4.16096i 0.844848 0.152038i
\(750\) 0 0
\(751\) 24.2461 30.4037i 0.884753 1.10945i −0.108571 0.994089i \(-0.534627\pi\)
0.993324 0.115357i \(-0.0368012\pi\)
\(752\) −0.807933 0.389080i −0.0294623 0.0141883i
\(753\) 0 0
\(754\) 26.3226i 0.958611i
\(755\) −0.00195559 0.000941762i −7.11711e−5 3.42742e-5i
\(756\) 0 0
\(757\) −28.5246 + 13.7367i −1.03674 + 0.499269i −0.873249 0.487275i \(-0.837991\pi\)
−0.163495 + 0.986544i \(0.552277\pi\)
\(758\) 2.56086 + 5.31769i 0.0930147 + 0.193147i
\(759\) 0 0
\(760\) −0.153736 + 0.673561i −0.00557659 + 0.0244326i
\(761\) −35.6689 + 17.1772i −1.29300 + 0.622674i −0.948697 0.316186i \(-0.897598\pi\)
−0.344299 + 0.938860i \(0.611883\pi\)
\(762\) 0 0
\(763\) 11.6357 + 16.0646i 0.421239 + 0.581577i
\(764\) −2.81412 + 5.84358i −0.101811 + 0.211413i
\(765\) 0 0
\(766\) 18.5634i 0.670722i
\(767\) 13.4597 27.9493i 0.486001 1.00919i
\(768\) 0 0
\(769\) −12.5680 2.86855i −0.453212 0.103443i −0.0101794 0.999948i \(-0.503240\pi\)
−0.443033 + 0.896505i \(0.646097\pi\)
\(770\) −0.492530 0.0228431i −0.0177496 0.000823208i
\(771\) 0 0
\(772\) 6.12814 + 2.95116i 0.220557 + 0.106214i
\(773\) −7.48695 32.8025i −0.269287 1.17982i −0.910845 0.412749i \(-0.864569\pi\)
0.641558 0.767075i \(-0.278288\pi\)
\(774\) 0 0
\(775\) 27.8761 + 6.36254i 1.00134 + 0.228549i
\(776\) 33.4901 + 41.9952i 1.20222 + 1.50754i
\(777\) 0 0
\(778\) 6.06595 7.60646i 0.217475 0.272705i
\(779\) −2.71653 + 2.16636i −0.0973298 + 0.0776179i
\(780\) 0 0
\(781\) −9.40520 11.7937i −0.336544 0.422013i
\(782\) −3.61741 15.8489i −0.129358 0.566756i
\(783\) 0 0
\(784\) −0.0614161 0.463607i −0.00219343 0.0165574i
\(785\) 0.0825428i 0.00294608i
\(786\) 0 0
\(787\) 39.1022 31.1830i 1.39384 1.11155i 0.414341 0.910122i \(-0.364012\pi\)
0.979503 0.201431i \(-0.0645593\pi\)
\(788\) 12.3133 + 25.5688i 0.438643 + 0.910852i
\(789\) 0 0
\(790\) −0.282527 0.225307i −0.0100518 0.00801608i
\(791\) −46.9407 + 8.44741i −1.66902 + 0.300355i
\(792\) 0 0
\(793\) −2.46761 + 10.8113i −0.0876275 + 0.383921i
\(794\) −15.9792 + 20.0372i −0.567079 + 0.711094i
\(795\) 0 0
\(796\) −0.152436 + 0.316537i −0.00540295 + 0.0112193i
\(797\) −5.89005 25.8060i −0.208636 0.914095i −0.965475 0.260494i \(-0.916115\pi\)
0.756839 0.653601i \(-0.226743\pi\)
\(798\) 0 0
\(799\) −8.36452 + 36.6474i −0.295916 + 1.29649i
\(800\) 22.2068 + 17.7093i 0.785129 + 0.626120i
\(801\) 0 0
\(802\) −11.3264 −0.399948
\(803\) 45.5602 1.60778
\(804\) 0 0
\(805\) 0.0507574 1.09440i 0.00178896 0.0385726i
\(806\) 10.1548 + 21.0866i 0.357687 + 0.742745i
\(807\) 0 0
\(808\) −12.4148 2.83359i −0.436751 0.0996855i
\(809\) −37.8226 8.63276i −1.32977 0.303512i −0.502141 0.864786i \(-0.667454\pi\)
−0.827630 + 0.561274i \(0.810311\pi\)
\(810\) 0 0
\(811\) −13.6624 28.3702i −0.479751 0.996213i −0.990632 0.136561i \(-0.956395\pi\)
0.510881 0.859652i \(-0.329319\pi\)
\(812\) −8.34393 19.6011i −0.292815 0.687862i
\(813\) 0 0
\(814\) 24.3025 0.851801
\(815\) −0.691773 −0.0242317
\(816\) 0 0
\(817\) 4.70063 + 3.74863i 0.164454 + 0.131148i
\(818\) −7.53899 + 33.0305i −0.263595 + 1.15488i
\(819\) 0 0
\(820\) −0.0150136 0.0657789i −0.000524298 0.00229710i
\(821\) 19.9376 41.4008i 0.695826 1.44490i −0.190430 0.981701i \(-0.560988\pi\)
0.886256 0.463196i \(-0.153297\pi\)
\(822\) 0 0
\(823\) 12.9117 16.1908i 0.450074 0.564376i −0.504093 0.863650i \(-0.668173\pi\)
0.954167 + 0.299274i \(0.0967445\pi\)
\(824\) −5.27615 + 23.1163i −0.183803 + 0.805295i
\(825\) 0 0
\(826\) −0.696460 + 15.0167i −0.0242330 + 0.522498i
\(827\) −4.31401 3.44030i −0.150013 0.119631i 0.545608 0.838041i \(-0.316299\pi\)
−0.695620 + 0.718410i \(0.744870\pi\)
\(828\) 0 0
\(829\) 7.80709 + 16.2116i 0.271152 + 0.563052i 0.991431 0.130632i \(-0.0417007\pi\)
−0.720279 + 0.693684i \(0.755986\pi\)
\(830\) −0.0882160 + 0.0703499i −0.00306202 + 0.00244188i
\(831\) 0 0
\(832\) 22.6180i 0.784137i
\(833\) −18.3735 + 6.83431i −0.636605 + 0.236795i
\(834\) 0 0
\(835\) 0.325721 + 1.42708i 0.0112721 + 0.0493861i
\(836\) 10.8193 + 13.5670i 0.374193 + 0.469223i
\(837\) 0 0
\(838\) −25.4783 + 20.3182i −0.880132 + 0.701882i
\(839\) −3.36402 + 4.21834i −0.116139 + 0.145633i −0.836503 0.547963i \(-0.815403\pi\)
0.720364 + 0.693596i \(0.243975\pi\)
\(840\) 0 0
\(841\) −7.74929 9.71731i −0.267217 0.335079i
\(842\) −26.8306 6.12390i −0.924643 0.211044i
\(843\) 0 0
\(844\) −3.23828 14.1878i −0.111466 0.488365i
\(845\) −0.518854 0.249867i −0.0178491 0.00859569i
\(846\) 0 0
\(847\) −2.02999 + 2.31665i −0.0697514 + 0.0796010i
\(848\) 0.434479 + 0.0991671i 0.0149201 + 0.00340541i
\(849\) 0 0
\(850\) 5.25411 10.9103i 0.180215 0.374220i
\(851\) 54.0001i 1.85110i
\(852\) 0 0
\(853\) −7.13459 + 14.8151i −0.244284 + 0.507260i −0.986674 0.162707i \(-0.947978\pi\)
0.742391 + 0.669967i \(0.233692\pi\)
\(854\) −0.951785 5.28889i −0.0325694 0.180982i
\(855\) 0 0
\(856\) −22.5095 + 10.8400i −0.769359 + 0.370504i
\(857\) 8.82414 38.6611i 0.301427 1.32064i −0.566548 0.824029i \(-0.691721\pi\)
0.867975 0.496609i \(-0.165422\pi\)
\(858\) 0 0
\(859\) 3.27523 + 6.80109i 0.111749 + 0.232050i 0.949342 0.314246i \(-0.101752\pi\)
−0.837592 + 0.546296i \(0.816037\pi\)
\(860\) −0.105188 + 0.0506558i −0.00358688 + 0.00172735i
\(861\) 0 0
\(862\) 9.60853 + 4.62722i 0.327268 + 0.157604i
\(863\) 14.9631i 0.509351i 0.967027 + 0.254675i \(0.0819686\pi\)
−0.967027 + 0.254675i \(0.918031\pi\)
\(864\) 0 0
\(865\) 0.272876 + 0.131410i 0.00927807 + 0.00446808i
\(866\) −20.1909 + 25.3186i −0.686116 + 0.860362i
\(867\) 0 0
\(868\) 14.2460 + 12.4832i 0.483539 + 0.423707i
\(869\) −22.9960 + 5.24868i −0.780086 + 0.178049i
\(870\) 0 0
\(871\) 31.9131 7.28395i 1.08133 0.246807i
\(872\) −16.4922 13.1521i −0.558497 0.445386i
\(873\) 0 0
\(874\) 18.0506 14.3948i 0.610570 0.486913i
\(875\) 1.07610 1.22805i 0.0363787 0.0415158i
\(876\) 0 0
\(877\) 11.8428 + 14.8503i 0.399901 + 0.501460i 0.940488 0.339828i \(-0.110369\pi\)
−0.540586 + 0.841289i \(0.681798\pi\)
\(878\) 22.2546 10.7173i 0.751057 0.361690i
\(879\) 0 0
\(880\) −0.0140249 + 0.00320109i −0.000472778 + 0.000107909i
\(881\) 7.79930 0.262765 0.131382 0.991332i \(-0.458058\pi\)
0.131382 + 0.991332i \(0.458058\pi\)
\(882\) 0 0
\(883\) 14.9421 0.502842 0.251421 0.967878i \(-0.419102\pi\)
0.251421 + 0.967878i \(0.419102\pi\)
\(884\) −16.1388 + 3.68358i −0.542808 + 0.123892i
\(885\) 0 0
\(886\) 27.7271 13.3527i 0.931511 0.448592i
\(887\) −12.3392 15.4728i −0.414308 0.519526i 0.530263 0.847833i \(-0.322093\pi\)
−0.944571 + 0.328307i \(0.893522\pi\)
\(888\) 0 0
\(889\) 11.3061 + 0.524365i 0.379194 + 0.0175866i
\(890\) −0.479231 + 0.382174i −0.0160639 + 0.0128105i
\(891\) 0 0
\(892\) 23.2261 + 18.5222i 0.777666 + 0.620168i
\(893\) −52.0467 + 11.8793i −1.74168 + 0.397526i
\(894\) 0 0
\(895\) −0.372169 + 0.0849451i −0.0124402 + 0.00283940i
\(896\) 7.48960 + 17.5941i 0.250210 + 0.587778i
\(897\) 0 0
\(898\) 20.1576 25.2768i 0.672667 0.843497i
\(899\) 33.1881 + 15.9826i 1.10689 + 0.533048i
\(900\) 0 0
\(901\) 18.6810i 0.622356i
\(902\) 2.37587 + 1.14416i 0.0791077 + 0.0380962i
\(903\) 0 0
\(904\) 45.6978 22.0069i 1.51989 0.731939i
\(905\) −0.198844 0.412903i −0.00660979 0.0137254i
\(906\) 0 0
\(907\) 3.74119 16.3912i 0.124224 0.544262i −0.874066 0.485808i \(-0.838526\pi\)
0.998290 0.0584547i \(-0.0186173\pi\)
\(908\) −3.97037 + 1.91203i −0.131761 + 0.0634529i
\(909\) 0 0
\(910\) 0.667289 + 0.0309482i 0.0221204 + 0.00102592i
\(911\) −7.06895 + 14.6788i −0.234205 + 0.486331i −0.984636 0.174617i \(-0.944131\pi\)
0.750432 + 0.660948i \(0.229846\pi\)
\(912\) 0 0
\(913\) 7.36491i 0.243743i
\(914\) −4.60795 + 9.56850i −0.152417 + 0.316498i
\(915\) 0 0
\(916\) 11.7607 + 2.68430i 0.388584 + 0.0886918i
\(917\) −13.3914 + 48.2468i −0.442224 + 1.59325i
\(918\) 0 0
\(919\) −32.3318 15.5702i −1.06653 0.513612i −0.183541 0.983012i \(-0.558756\pi\)
−0.882985 + 0.469400i \(0.844470\pi\)
\(920\) 0.259257 + 1.13588i 0.00854745 + 0.0374488i
\(921\) 0 0
\(922\) −32.3923 7.39334i −1.06679 0.243487i
\(923\) 12.7423 + 15.9784i 0.419419 + 0.525935i
\(924\) 0 0
\(925\) −25.0797 + 31.4490i −0.824617 + 1.03404i
\(926\) 3.68047 2.93508i 0.120948 0.0964527i
\(927\) 0 0
\(928\) 22.8147 + 28.6088i 0.748930 + 0.939129i
\(929\) 0.313570 + 1.37384i 0.0102879 + 0.0450743i 0.979811 0.199924i \(-0.0640696\pi\)
−0.969523 + 0.244999i \(0.921212\pi\)
\(930\) 0 0
\(931\) −20.0667 19.2987i −0.657661 0.632489i
\(932\) 28.3559i 0.928829i
\(933\) 0 0
\(934\) 19.8495 15.8294i 0.649495 0.517955i
\(935\) 0.261640 + 0.543301i 0.00855655 + 0.0177679i
\(936\) 0 0
\(937\) 8.85736 + 7.06351i 0.289357 + 0.230755i 0.757400 0.652951i \(-0.226469\pi\)
−0.468043 + 0.883706i \(0.655041\pi\)
\(938\) −12.8468 + 9.30500i −0.419463 + 0.303819i
\(939\) 0 0
\(940\) 0.230677 1.01066i 0.00752386 0.0329642i
\(941\) 1.36612 1.71307i 0.0445344 0.0558443i −0.759066 0.651014i \(-0.774344\pi\)
0.803600 + 0.595170i \(0.202915\pi\)
\(942\) 0 0
\(943\) −2.54232 + 5.27918i −0.0827893 + 0.171914i
\(944\) 0.0975975 + 0.427603i 0.00317653 + 0.0139173i
\(945\) 0 0
\(946\) 1.01537 4.44863i 0.0330126 0.144637i
\(947\) 41.5779 + 33.1573i 1.35110 + 1.07747i 0.989407 + 0.145170i \(0.0463730\pi\)
0.361694 + 0.932297i \(0.382198\pi\)
\(948\) 0 0
\(949\) −61.7258 −2.00370
\(950\) 17.1980 0.557975
\(951\) 0 0
\(952\) 16.8837 12.2289i 0.547203 0.396342i
\(953\) −22.5658 46.8584i −0.730979 1.51789i −0.851025 0.525124i \(-0.824019\pi\)
0.120047 0.992768i \(-0.461695\pi\)
\(954\) 0 0
\(955\) −0.312072 0.0712284i −0.0100984 0.00230490i
\(956\) −0.666145 0.152043i −0.0215447 0.00491743i
\(957\) 0 0
\(958\) −11.3756 23.6217i −0.367529 0.763182i
\(959\) −20.3365 5.64461i −0.656699 0.182274i
\(960\) 0 0
\(961\) −1.75234 −0.0565270
\(962\) −32.9254 −1.06156
\(963\) 0 0
\(964\) 11.2148 + 8.94352i 0.361205 + 0.288051i
\(965\) −0.0746969 + 0.327269i −0.00240458 + 0.0105351i
\(966\) 0 0
\(967\) 11.2247 + 49.1785i 0.360961 + 1.58147i 0.750761 + 0.660573i \(0.229687\pi\)
−0.389801 + 0.920899i \(0.627456\pi\)
\(968\) 1.42125 2.95125i 0.0456807 0.0948569i
\(969\) 0 0
\(970\) −0.636004 + 0.797524i −0.0204209 + 0.0256070i
\(971\) 0.427755 1.87412i 0.0137273 0.0601432i −0.967600 0.252487i \(-0.918752\pi\)
0.981328 + 0.192343i \(0.0616088\pi\)
\(972\) 0 0
\(973\) 22.3900 41.4618i 0.717790 1.32920i
\(974\) −10.2770 8.19567i −0.329298 0.262606i
\(975\) 0 0
\(976\) −0.0680276 0.141261i −0.00217751 0.00452165i
\(977\) 43.4478 34.6484i 1.39002 1.10850i 0.409447 0.912334i \(-0.365722\pi\)
0.980570 0.196167i \(-0.0628496\pi\)
\(978\) 0 0
\(979\) 40.0097i 1.27872i
\(980\) 0.506706 0.188477i 0.0161861 0.00602068i
\(981\) 0 0
\(982\) 4.24029 + 18.5779i 0.135313 + 0.592845i
\(983\) −2.18098 2.73487i −0.0695625 0.0872287i 0.745833 0.666133i \(-0.232052\pi\)
−0.815395 + 0.578905i \(0.803480\pi\)
\(984\) 0 0
\(985\) −1.09503 + 0.873259i −0.0348906 + 0.0278243i
\(986\) 9.72676 12.1970i 0.309763 0.388431i
\(987\) 0 0
\(988\) −14.6582 18.3808i −0.466338 0.584770i
\(989\) 9.88487 + 2.25616i 0.314320 + 0.0717416i
\(990\) 0 0
\(991\) 10.8346 + 47.4696i 0.344173 + 1.50792i 0.790170 + 0.612887i \(0.209992\pi\)
−0.445997 + 0.895034i \(0.647151\pi\)
\(992\) −29.3133 14.1166i −0.930699 0.448201i
\(993\) 0 0
\(994\) −8.71429 4.70585i −0.276401 0.149260i
\(995\) −0.0169044 0.00385831i −0.000535905 0.000122317i
\(996\) 0 0
\(997\) 2.50166 5.19474i 0.0792282 0.164519i −0.857592 0.514331i \(-0.828040\pi\)
0.936820 + 0.349812i \(0.113755\pi\)
\(998\) 35.4294i 1.12150i
\(999\) 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 441.2.w.a.62.8 120
3.2 odd 2 inner 441.2.w.a.62.13 yes 120
49.34 odd 14 inner 441.2.w.a.377.13 yes 120
147.83 even 14 inner 441.2.w.a.377.8 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.w.a.62.8 120 1.1 even 1 trivial
441.2.w.a.62.13 yes 120 3.2 odd 2 inner
441.2.w.a.377.8 yes 120 147.83 even 14 inner
441.2.w.a.377.13 yes 120 49.34 odd 14 inner