Properties

Label 637.2.e.o.508.4
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + 43 x^{2} + 6 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.4
Root \(-0.602377 - 1.04335i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.o.79.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +O(q^{10})\) \(q+(0.328092 + 0.568272i) q^{2} +(-0.102377 + 0.177322i) q^{3} +(0.784711 - 1.35916i) q^{4} +(-0.679981 - 1.17776i) q^{5} -0.134356 q^{6} +2.34220 q^{8} +(1.47904 + 2.56177i) q^{9} +(0.446193 - 0.772828i) q^{10} +(0.952756 - 1.65022i) q^{11} +(0.160672 + 0.278293i) q^{12} -1.00000 q^{13} +0.278457 q^{15} +(-0.800966 - 1.38731i) q^{16} +(1.78317 - 3.08854i) q^{17} +(-0.970521 + 1.68099i) q^{18} +(0.492627 + 0.853255i) q^{19} -2.13436 q^{20} +1.25037 q^{22} +(-0.848026 - 1.46882i) q^{23} +(-0.239786 + 0.415322i) q^{24} +(1.57525 - 2.72841i) q^{25} +(-0.328092 - 0.568272i) q^{26} -1.21994 q^{27} +6.54835 q^{29} +(0.0913595 + 0.158239i) q^{30} +(3.84775 - 6.66450i) q^{31} +(2.86778 - 4.96714i) q^{32} +(0.195080 + 0.337889i) q^{33} +2.34017 q^{34} +4.64247 q^{36} +(1.01003 + 1.74942i) q^{37} +(-0.323254 + 0.559893i) q^{38} +(0.102377 - 0.177322i) q^{39} +(-1.59265 - 2.75855i) q^{40} -9.88779 q^{41} -3.16639 q^{43} +(-1.49528 - 2.58990i) q^{44} +(2.01144 - 3.48391i) q^{45} +(0.556461 - 0.963819i) q^{46} +(3.88208 + 6.72396i) q^{47} +0.328001 q^{48} +2.06731 q^{50} +(0.365109 + 0.632388i) q^{51} +(-0.784711 + 1.35916i) q^{52} +(-0.177097 + 0.306741i) q^{53} +(-0.400251 - 0.693255i) q^{54} -2.59143 q^{55} -0.201734 q^{57} +(2.14846 + 3.72124i) q^{58} +(1.08192 - 1.87395i) q^{59} +(0.218508 - 0.378467i) q^{60} +(6.10010 + 10.5657i) q^{61} +5.04967 q^{62} +0.559715 q^{64} +(0.679981 + 1.17776i) q^{65} +(-0.128008 + 0.221717i) q^{66} +(-5.65670 + 9.79769i) q^{67} +(-2.79854 - 4.84722i) q^{68} +0.347272 q^{69} -9.05268 q^{71} +(3.46420 + 6.00017i) q^{72} +(-3.56809 + 6.18012i) q^{73} +(-0.662763 + 1.14794i) q^{74} +(0.322538 + 0.558652i) q^{75} +1.54628 q^{76} +0.134356 q^{78} +(2.69815 + 4.67333i) q^{79} +(-1.08928 + 1.88670i) q^{80} +(-4.31222 + 7.46899i) q^{81} +(-3.24411 - 5.61896i) q^{82} +2.03494 q^{83} -4.85008 q^{85} +(-1.03887 - 1.79937i) q^{86} +(-0.670398 + 1.16116i) q^{87} +(2.23154 - 3.86515i) q^{88} +(-3.44932 - 5.97440i) q^{89} +2.63974 q^{90} -2.66182 q^{92} +(0.787840 + 1.36458i) q^{93} +(-2.54736 + 4.41216i) q^{94} +(0.669955 - 1.16040i) q^{95} +(0.587187 + 1.01704i) q^{96} +14.6223 q^{97} +5.63665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + O(q^{10}) \) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + 4q^{10} - 4q^{11} - 4q^{12} - 12q^{13} + 24q^{15} + 16q^{17} + 4q^{18} + 2q^{19} - 32q^{20} - 24q^{22} + 6q^{23} + 12q^{24} + 4q^{25} - 40q^{27} - 12q^{29} + 6q^{31} + 20q^{32} + 4q^{33} - 48q^{36} + 8q^{38} - 8q^{39} + 4q^{40} + 16q^{41} + 4q^{43} + 4q^{44} + 14q^{45} - 8q^{46} + 30q^{47} + 16q^{48} + 16q^{50} + 4q^{51} + 4q^{52} + 14q^{53} - 48q^{54} + 16q^{55} + 8q^{57} + 8q^{58} + 24q^{59} - 12q^{60} - 56q^{62} - 40q^{64} - 6q^{65} - 4q^{66} - 16q^{67} + 28q^{68} + 40q^{69} + 16q^{71} - 28q^{72} - 6q^{73} + 12q^{74} + 12q^{75} + 32q^{76} + 8q^{78} + 22q^{79} - 28q^{80} - 46q^{81} - 40q^{82} - 100q^{83} - 16q^{85} + 16q^{86} - 16q^{87} + 44q^{88} + 26q^{89} + 80q^{90} + 40q^{92} - 16q^{93} - 32q^{94} + 6q^{95} - 20q^{96} + 28q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.328092 + 0.568272i 0.231996 + 0.401829i 0.958395 0.285444i \(-0.0921410\pi\)
−0.726399 + 0.687273i \(0.758808\pi\)
\(3\) −0.102377 + 0.177322i −0.0591072 + 0.102377i −0.894065 0.447937i \(-0.852159\pi\)
0.834958 + 0.550314i \(0.185492\pi\)
\(4\) 0.784711 1.35916i 0.392356 0.679580i
\(5\) −0.679981 1.17776i −0.304097 0.526711i 0.672963 0.739676i \(-0.265021\pi\)
−0.977060 + 0.212965i \(0.931688\pi\)
\(6\) −0.134356 −0.0548505
\(7\) 0 0
\(8\) 2.34220 0.828092
\(9\) 1.47904 + 2.56177i 0.493013 + 0.853923i
\(10\) 0.446193 0.772828i 0.141099 0.244390i
\(11\) 0.952756 1.65022i 0.287267 0.497561i −0.685890 0.727706i \(-0.740587\pi\)
0.973156 + 0.230145i \(0.0739200\pi\)
\(12\) 0.160672 + 0.278293i 0.0463821 + 0.0803361i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0.278457 0.0718972
\(16\) −0.800966 1.38731i −0.200242 0.346829i
\(17\) 1.78317 3.08854i 0.432482 0.749080i −0.564605 0.825361i \(-0.690971\pi\)
0.997086 + 0.0762814i \(0.0243047\pi\)
\(18\) −0.970521 + 1.68099i −0.228754 + 0.396214i
\(19\) 0.492627 + 0.853255i 0.113016 + 0.195750i 0.916985 0.398921i \(-0.130615\pi\)
−0.803969 + 0.594672i \(0.797282\pi\)
\(20\) −2.13436 −0.477256
\(21\) 0 0
\(22\) 1.25037 0.266579
\(23\) −0.848026 1.46882i −0.176826 0.306271i 0.763966 0.645257i \(-0.223250\pi\)
−0.940792 + 0.338986i \(0.889916\pi\)
\(24\) −0.239786 + 0.415322i −0.0489462 + 0.0847773i
\(25\) 1.57525 2.72841i 0.315050 0.545683i
\(26\) −0.328092 0.568272i −0.0643441 0.111447i
\(27\) −1.21994 −0.234777
\(28\) 0 0
\(29\) 6.54835 1.21600 0.607999 0.793938i \(-0.291972\pi\)
0.607999 + 0.793938i \(0.291972\pi\)
\(30\) 0.0913595 + 0.158239i 0.0166799 + 0.0288904i
\(31\) 3.84775 6.66450i 0.691077 1.19698i −0.280409 0.959881i \(-0.590470\pi\)
0.971485 0.237099i \(-0.0761966\pi\)
\(32\) 2.86778 4.96714i 0.506957 0.878074i
\(33\) 0.195080 + 0.337889i 0.0339591 + 0.0588188i
\(34\) 2.34017 0.401336
\(35\) 0 0
\(36\) 4.64247 0.773745
\(37\) 1.01003 + 1.74942i 0.166047 + 0.287602i 0.937027 0.349258i \(-0.113566\pi\)
−0.770979 + 0.636860i \(0.780233\pi\)
\(38\) −0.323254 + 0.559893i −0.0524387 + 0.0908266i
\(39\) 0.102377 0.177322i 0.0163934 0.0283942i
\(40\) −1.59265 2.75855i −0.251820 0.436165i
\(41\) −9.88779 −1.54421 −0.772107 0.635493i \(-0.780797\pi\)
−0.772107 + 0.635493i \(0.780797\pi\)
\(42\) 0 0
\(43\) −3.16639 −0.482869 −0.241435 0.970417i \(-0.577618\pi\)
−0.241435 + 0.970417i \(0.577618\pi\)
\(44\) −1.49528 2.58990i −0.225422 0.390442i
\(45\) 2.01144 3.48391i 0.299847 0.519351i
\(46\) 0.556461 0.963819i 0.0820457 0.142107i
\(47\) 3.88208 + 6.72396i 0.566260 + 0.980791i 0.996931 + 0.0782818i \(0.0249434\pi\)
−0.430672 + 0.902509i \(0.641723\pi\)
\(48\) 0.328001 0.0473429
\(49\) 0 0
\(50\) 2.06731 0.292362
\(51\) 0.365109 + 0.632388i 0.0511255 + 0.0885520i
\(52\) −0.784711 + 1.35916i −0.108820 + 0.188482i
\(53\) −0.177097 + 0.306741i −0.0243261 + 0.0421341i −0.877932 0.478785i \(-0.841077\pi\)
0.853606 + 0.520919i \(0.174411\pi\)
\(54\) −0.400251 0.693255i −0.0544673 0.0943401i
\(55\) −2.59143 −0.349428
\(56\) 0 0
\(57\) −0.201734 −0.0267203
\(58\) 2.14846 + 3.72124i 0.282107 + 0.488623i
\(59\) 1.08192 1.87395i 0.140854 0.243967i −0.786964 0.616999i \(-0.788348\pi\)
0.927819 + 0.373032i \(0.121682\pi\)
\(60\) 0.218508 0.378467i 0.0282093 0.0488599i
\(61\) 6.10010 + 10.5657i 0.781037 + 1.35280i 0.931338 + 0.364156i \(0.118642\pi\)
−0.150301 + 0.988640i \(0.548024\pi\)
\(62\) 5.04967 0.641308
\(63\) 0 0
\(64\) 0.559715 0.0699644
\(65\) 0.679981 + 1.17776i 0.0843413 + 0.146083i
\(66\) −0.128008 + 0.221717i −0.0157567 + 0.0272915i
\(67\) −5.65670 + 9.79769i −0.691076 + 1.19698i 0.280410 + 0.959880i \(0.409530\pi\)
−0.971486 + 0.237098i \(0.923804\pi\)
\(68\) −2.79854 4.84722i −0.339373 0.587812i
\(69\) 0.347272 0.0418067
\(70\) 0 0
\(71\) −9.05268 −1.07436 −0.537178 0.843469i \(-0.680510\pi\)
−0.537178 + 0.843469i \(0.680510\pi\)
\(72\) 3.46420 + 6.00017i 0.408260 + 0.707127i
\(73\) −3.56809 + 6.18012i −0.417614 + 0.723328i −0.995699 0.0926481i \(-0.970467\pi\)
0.578085 + 0.815977i \(0.303800\pi\)
\(74\) −0.662763 + 1.14794i −0.0770447 + 0.133445i
\(75\) 0.322538 + 0.558652i 0.0372435 + 0.0645076i
\(76\) 1.54628 0.177371
\(77\) 0 0
\(78\) 0.134356 0.0152128
\(79\) 2.69815 + 4.67333i 0.303565 + 0.525790i 0.976941 0.213510i \(-0.0684897\pi\)
−0.673376 + 0.739300i \(0.735156\pi\)
\(80\) −1.08928 + 1.88670i −0.121786 + 0.210939i
\(81\) −4.31222 + 7.46899i −0.479136 + 0.829887i
\(82\) −3.24411 5.61896i −0.358251 0.620510i
\(83\) 2.03494 0.223364 0.111682 0.993744i \(-0.464376\pi\)
0.111682 + 0.993744i \(0.464376\pi\)
\(84\) 0 0
\(85\) −4.85008 −0.526065
\(86\) −1.03887 1.79937i −0.112024 0.194031i
\(87\) −0.670398 + 1.16116i −0.0718743 + 0.124490i
\(88\) 2.23154 3.86515i 0.237883 0.412026i
\(89\) −3.44932 5.97440i −0.365627 0.633285i 0.623249 0.782023i \(-0.285812\pi\)
−0.988877 + 0.148738i \(0.952479\pi\)
\(90\) 2.63974 0.278253
\(91\) 0 0
\(92\) −2.66182 −0.277514
\(93\) 0.787840 + 1.36458i 0.0816952 + 0.141500i
\(94\) −2.54736 + 4.41216i −0.262740 + 0.455079i
\(95\) 0.669955 1.16040i 0.0687359 0.119054i
\(96\) 0.587187 + 1.01704i 0.0599296 + 0.103801i
\(97\) 14.6223 1.48467 0.742334 0.670030i \(-0.233719\pi\)
0.742334 + 0.670030i \(0.233719\pi\)
\(98\) 0 0
\(99\) 5.63665 0.566505
\(100\) −2.47223 4.28204i −0.247223 0.428204i
\(101\) 1.40684 2.43672i 0.139986 0.242463i −0.787505 0.616308i \(-0.788628\pi\)
0.927491 + 0.373845i \(0.121961\pi\)
\(102\) −0.239579 + 0.414963i −0.0237218 + 0.0410874i
\(103\) 3.02494 + 5.23935i 0.298056 + 0.516248i 0.975691 0.219150i \(-0.0703285\pi\)
−0.677635 + 0.735398i \(0.736995\pi\)
\(104\) −2.34220 −0.229671
\(105\) 0 0
\(106\) −0.232416 −0.0225743
\(107\) −8.66018 14.9999i −0.837211 1.45009i −0.892218 0.451606i \(-0.850851\pi\)
0.0550067 0.998486i \(-0.482482\pi\)
\(108\) −0.957298 + 1.65809i −0.0921160 + 0.159550i
\(109\) −5.28811 + 9.15928i −0.506509 + 0.877300i 0.493462 + 0.869767i \(0.335731\pi\)
−0.999972 + 0.00753267i \(0.997602\pi\)
\(110\) −0.850226 1.47263i −0.0810659 0.140410i
\(111\) −0.413613 −0.0392584
\(112\) 0 0
\(113\) −2.34665 −0.220755 −0.110377 0.993890i \(-0.535206\pi\)
−0.110377 + 0.993890i \(0.535206\pi\)
\(114\) −0.0661874 0.114640i −0.00619901 0.0107370i
\(115\) −1.15328 + 1.99755i −0.107544 + 0.186272i
\(116\) 5.13857 8.90026i 0.477104 0.826368i
\(117\) −1.47904 2.56177i −0.136737 0.236836i
\(118\) 1.41988 0.130711
\(119\) 0 0
\(120\) 0.652201 0.0595375
\(121\) 3.68451 + 6.38176i 0.334956 + 0.580160i
\(122\) −4.00278 + 6.93303i −0.362395 + 0.627687i
\(123\) 1.01228 1.75332i 0.0912741 0.158091i
\(124\) −6.03875 10.4594i −0.542296 0.939284i
\(125\) −11.0844 −0.991417
\(126\) 0 0
\(127\) −18.1639 −1.61179 −0.805894 0.592060i \(-0.798315\pi\)
−0.805894 + 0.592060i \(0.798315\pi\)
\(128\) −5.55192 9.61621i −0.490725 0.849961i
\(129\) 0.324164 0.561469i 0.0285411 0.0494346i
\(130\) −0.446193 + 0.772828i −0.0391337 + 0.0677815i
\(131\) 5.05068 + 8.74804i 0.441280 + 0.764320i 0.997785 0.0665248i \(-0.0211911\pi\)
−0.556505 + 0.830845i \(0.687858\pi\)
\(132\) 0.612326 0.0532961
\(133\) 0 0
\(134\) −7.42367 −0.641308
\(135\) 0.829534 + 1.43679i 0.0713949 + 0.123660i
\(136\) 4.17653 7.23396i 0.358134 0.620307i
\(137\) −3.27800 + 5.67767i −0.280059 + 0.485076i −0.971399 0.237453i \(-0.923687\pi\)
0.691340 + 0.722529i \(0.257021\pi\)
\(138\) 0.113937 + 0.197345i 0.00969899 + 0.0167991i
\(139\) 13.8243 1.17256 0.586281 0.810108i \(-0.300591\pi\)
0.586281 + 0.810108i \(0.300591\pi\)
\(140\) 0 0
\(141\) −1.58974 −0.133880
\(142\) −2.97011 5.14439i −0.249246 0.431707i
\(143\) −0.952756 + 1.65022i −0.0796735 + 0.137999i
\(144\) 2.36932 4.10378i 0.197443 0.341982i
\(145\) −4.45276 7.71240i −0.369781 0.640480i
\(146\) −4.68265 −0.387539
\(147\) 0 0
\(148\) 3.17032 0.260598
\(149\) −4.04695 7.00952i −0.331539 0.574242i 0.651275 0.758842i \(-0.274234\pi\)
−0.982814 + 0.184600i \(0.940901\pi\)
\(150\) −0.211644 + 0.366578i −0.0172807 + 0.0299310i
\(151\) −6.01827 + 10.4239i −0.489760 + 0.848289i −0.999931 0.0117843i \(-0.996249\pi\)
0.510171 + 0.860073i \(0.329582\pi\)
\(152\) 1.15383 + 1.99849i 0.0935880 + 0.162099i
\(153\) 10.5495 0.852876
\(154\) 0 0
\(155\) −10.4656 −0.840617
\(156\) −0.160672 0.278293i −0.0128641 0.0222812i
\(157\) −9.19677 + 15.9293i −0.733982 + 1.27129i 0.221186 + 0.975232i \(0.429007\pi\)
−0.955168 + 0.296063i \(0.904326\pi\)
\(158\) −1.77048 + 3.06656i −0.140852 + 0.243963i
\(159\) −0.0362612 0.0628062i −0.00287570 0.00498085i
\(160\) −7.80014 −0.616655
\(161\) 0 0
\(162\) −5.65922 −0.444630
\(163\) −1.25643 2.17620i −0.0984114 0.170454i 0.812616 0.582800i \(-0.198043\pi\)
−0.911027 + 0.412346i \(0.864709\pi\)
\(164\) −7.75906 + 13.4391i −0.605881 + 1.04942i
\(165\) 0.265302 0.459516i 0.0206537 0.0357732i
\(166\) 0.667649 + 1.15640i 0.0518196 + 0.0897542i
\(167\) −17.9095 −1.38588 −0.692941 0.720995i \(-0.743685\pi\)
−0.692941 + 0.720995i \(0.743685\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −1.59127 2.75616i −0.122045 0.211388i
\(171\) −1.45723 + 2.52399i −0.111437 + 0.193015i
\(172\) −2.48470 + 4.30363i −0.189457 + 0.328148i
\(173\) 3.25991 + 5.64632i 0.247846 + 0.429282i 0.962928 0.269759i \(-0.0869439\pi\)
−0.715082 + 0.699041i \(0.753611\pi\)
\(174\) −0.879809 −0.0666982
\(175\) 0 0
\(176\) −3.05250 −0.230091
\(177\) 0.221527 + 0.383697i 0.0166510 + 0.0288404i
\(178\) 2.26339 3.92030i 0.169648 0.293839i
\(179\) 13.3007 23.0375i 0.994141 1.72190i 0.403461 0.914997i \(-0.367807\pi\)
0.590680 0.806906i \(-0.298859\pi\)
\(180\) −3.15679 5.46773i −0.235293 0.407540i
\(181\) 24.6402 1.83149 0.915746 0.401758i \(-0.131601\pi\)
0.915746 + 0.401758i \(0.131601\pi\)
\(182\) 0 0
\(183\) −2.49803 −0.184660
\(184\) −1.98625 3.44028i −0.146428 0.253621i
\(185\) 1.37360 2.37914i 0.100989 0.174918i
\(186\) −0.516968 + 0.895415i −0.0379059 + 0.0656550i
\(187\) −3.39785 5.88524i −0.248475 0.430372i
\(188\) 12.1853 0.888701
\(189\) 0 0
\(190\) 0.879227 0.0637858
\(191\) −1.51049 2.61625i −0.109295 0.189305i 0.806190 0.591657i \(-0.201526\pi\)
−0.915485 + 0.402352i \(0.868193\pi\)
\(192\) −0.0573018 + 0.0992496i −0.00413540 + 0.00716273i
\(193\) −10.6261 + 18.4050i −0.764884 + 1.32482i 0.175424 + 0.984493i \(0.443870\pi\)
−0.940308 + 0.340325i \(0.889463\pi\)
\(194\) 4.79746 + 8.30944i 0.344437 + 0.596583i
\(195\) −0.278457 −0.0199407
\(196\) 0 0
\(197\) −2.72191 −0.193928 −0.0969639 0.995288i \(-0.530913\pi\)
−0.0969639 + 0.995288i \(0.530913\pi\)
\(198\) 1.84934 + 3.20315i 0.131427 + 0.227638i
\(199\) −10.8335 + 18.7642i −0.767967 + 1.33016i 0.170697 + 0.985324i \(0.445398\pi\)
−0.938664 + 0.344834i \(0.887935\pi\)
\(200\) 3.68955 6.39049i 0.260891 0.451876i
\(201\) −1.15823 2.00611i −0.0816951 0.141500i
\(202\) 1.84629 0.129905
\(203\) 0 0
\(204\) 1.14602 0.0802376
\(205\) 6.72351 + 11.6455i 0.469591 + 0.813355i
\(206\) −1.98492 + 3.43797i −0.138296 + 0.239535i
\(207\) 2.50853 4.34489i 0.174355 0.301991i
\(208\) 0.800966 + 1.38731i 0.0555370 + 0.0961930i
\(209\) 1.87741 0.129864
\(210\) 0 0
\(211\) 18.3885 1.26592 0.632959 0.774186i \(-0.281840\pi\)
0.632959 + 0.774186i \(0.281840\pi\)
\(212\) 0.277940 + 0.481406i 0.0190890 + 0.0330631i
\(213\) 0.926784 1.60524i 0.0635022 0.109989i
\(214\) 5.68267 9.84267i 0.388459 0.672831i
\(215\) 2.15308 + 3.72925i 0.146839 + 0.254333i
\(216\) −2.85733 −0.194417
\(217\) 0 0
\(218\) −6.93995 −0.470033
\(219\) −0.730579 1.26540i −0.0493680 0.0855078i
\(220\) −2.03352 + 3.52216i −0.137100 + 0.237464i
\(221\) −1.78317 + 3.08854i −0.119949 + 0.207757i
\(222\) −0.135703 0.235044i −0.00910779 0.0157752i
\(223\) −22.2216 −1.48807 −0.744035 0.668141i \(-0.767090\pi\)
−0.744035 + 0.668141i \(0.767090\pi\)
\(224\) 0 0
\(225\) 9.31943 0.621295
\(226\) −0.769918 1.33354i −0.0512142 0.0887056i
\(227\) 13.3687 23.1553i 0.887313 1.53687i 0.0442740 0.999019i \(-0.485903\pi\)
0.843039 0.537852i \(-0.180764\pi\)
\(228\) −0.158303 + 0.274189i −0.0104839 + 0.0181586i
\(229\) −8.35039 14.4633i −0.551809 0.955761i −0.998144 0.0608954i \(-0.980604\pi\)
0.446335 0.894866i \(-0.352729\pi\)
\(230\) −1.51353 −0.0997994
\(231\) 0 0
\(232\) 15.3375 1.00696
\(233\) 6.93878 + 12.0183i 0.454575 + 0.787346i 0.998664 0.0516812i \(-0.0164580\pi\)
−0.544089 + 0.839027i \(0.683125\pi\)
\(234\) 0.970521 1.68099i 0.0634449 0.109890i
\(235\) 5.27948 9.14433i 0.344396 0.596511i
\(236\) −1.69800 2.94101i −0.110530 0.191444i
\(237\) −1.10491 −0.0717715
\(238\) 0 0
\(239\) 0.465845 0.0301330 0.0150665 0.999886i \(-0.495204\pi\)
0.0150665 + 0.999886i \(0.495204\pi\)
\(240\) −0.223035 0.386307i −0.0143968 0.0249360i
\(241\) 2.84657 4.93040i 0.183364 0.317595i −0.759660 0.650320i \(-0.774635\pi\)
0.943024 + 0.332725i \(0.107968\pi\)
\(242\) −2.41772 + 4.18761i −0.155417 + 0.269190i
\(243\) −2.71285 4.69879i −0.174029 0.301427i
\(244\) 19.1473 1.22578
\(245\) 0 0
\(246\) 1.32848 0.0847010
\(247\) −0.492627 0.853255i −0.0313451 0.0542913i
\(248\) 9.01220 15.6096i 0.572275 0.991209i
\(249\) −0.208331 + 0.360840i −0.0132024 + 0.0228673i
\(250\) −3.63669 6.29894i −0.230005 0.398380i
\(251\) −17.9066 −1.13025 −0.565126 0.825005i \(-0.691172\pi\)
−0.565126 + 0.825005i \(0.691172\pi\)
\(252\) 0 0
\(253\) −3.23185 −0.203185
\(254\) −5.95944 10.3221i −0.373929 0.647663i
\(255\) 0.496535 0.860024i 0.0310942 0.0538568i
\(256\) 4.20280 7.27946i 0.262675 0.454966i
\(257\) 12.9878 + 22.4955i 0.810156 + 1.40323i 0.912754 + 0.408509i \(0.133951\pi\)
−0.102598 + 0.994723i \(0.532715\pi\)
\(258\) 0.425423 0.0264857
\(259\) 0 0
\(260\) 2.13436 0.132367
\(261\) 9.68526 + 16.7754i 0.599503 + 1.03837i
\(262\) −3.31418 + 5.74032i −0.204751 + 0.354638i
\(263\) −13.9201 + 24.1103i −0.858349 + 1.48670i 0.0151543 + 0.999885i \(0.495176\pi\)
−0.873503 + 0.486819i \(0.838157\pi\)
\(264\) 0.456916 + 0.791402i 0.0281212 + 0.0487074i
\(265\) 0.481690 0.0295900
\(266\) 0 0
\(267\) 1.41252 0.0864448
\(268\) 8.87775 + 15.3767i 0.542295 + 0.939283i
\(269\) 2.95243 5.11375i 0.180013 0.311791i −0.761872 0.647728i \(-0.775719\pi\)
0.941885 + 0.335937i \(0.109053\pi\)
\(270\) −0.544327 + 0.942801i −0.0331267 + 0.0573771i
\(271\) −2.17466 3.76662i −0.132101 0.228806i 0.792385 0.610021i \(-0.208839\pi\)
−0.924486 + 0.381215i \(0.875506\pi\)
\(272\) −5.71303 −0.346403
\(273\) 0 0
\(274\) −4.30195 −0.259890
\(275\) −3.00166 5.19903i −0.181007 0.313513i
\(276\) 0.272509 0.471999i 0.0164031 0.0284110i
\(277\) −0.540257 + 0.935752i −0.0324609 + 0.0562239i −0.881799 0.471625i \(-0.843668\pi\)
0.849339 + 0.527848i \(0.177001\pi\)
\(278\) 4.53564 + 7.85596i 0.272030 + 0.471169i
\(279\) 22.7639 1.36284
\(280\) 0 0
\(281\) 14.4912 0.864473 0.432236 0.901760i \(-0.357725\pi\)
0.432236 + 0.901760i \(0.357725\pi\)
\(282\) −0.521580 0.903403i −0.0310597 0.0537969i
\(283\) 12.2489 21.2158i 0.728123 1.26115i −0.229552 0.973296i \(-0.573726\pi\)
0.957676 0.287850i \(-0.0929404\pi\)
\(284\) −7.10374 + 12.3040i −0.421530 + 0.730111i
\(285\) 0.137175 + 0.237595i 0.00812557 + 0.0140739i
\(286\) −1.25037 −0.0739357
\(287\) 0 0
\(288\) 16.9662 0.999744
\(289\) 2.14063 + 3.70768i 0.125919 + 0.218099i
\(290\) 2.92183 5.06075i 0.171576 0.297178i
\(291\) −1.49698 + 2.59285i −0.0877546 + 0.151995i
\(292\) 5.59985 + 9.69922i 0.327706 + 0.567604i
\(293\) −1.16105 −0.0678296 −0.0339148 0.999425i \(-0.510797\pi\)
−0.0339148 + 0.999425i \(0.510797\pi\)
\(294\) 0 0
\(295\) −2.94275 −0.171334
\(296\) 2.36568 + 4.09748i 0.137502 + 0.238161i
\(297\) −1.16230 + 2.01317i −0.0674436 + 0.116816i
\(298\) 2.65554 4.59953i 0.153831 0.266444i
\(299\) 0.848026 + 1.46882i 0.0490426 + 0.0849443i
\(300\) 1.01240 0.0584507
\(301\) 0 0
\(302\) −7.89818 −0.454489
\(303\) 0.288055 + 0.498926i 0.0165483 + 0.0286626i
\(304\) 0.789156 1.36686i 0.0452612 0.0783947i
\(305\) 8.29590 14.3689i 0.475022 0.822762i
\(306\) 3.46120 + 5.99498i 0.197864 + 0.342710i
\(307\) −25.3731 −1.44812 −0.724060 0.689737i \(-0.757726\pi\)
−0.724060 + 0.689737i \(0.757726\pi\)
\(308\) 0 0
\(309\) −1.23873 −0.0704690
\(310\) −3.43368 5.94730i −0.195020 0.337784i
\(311\) 12.2323 21.1869i 0.693628 1.20140i −0.277012 0.960866i \(-0.589344\pi\)
0.970641 0.240533i \(-0.0773224\pi\)
\(312\) 0.239786 0.415322i 0.0135752 0.0235130i
\(313\) 3.30832 + 5.73018i 0.186997 + 0.323889i 0.944248 0.329236i \(-0.106791\pi\)
−0.757250 + 0.653125i \(0.773458\pi\)
\(314\) −12.0695 −0.681124
\(315\) 0 0
\(316\) 8.46906 0.476422
\(317\) −4.09901 7.09970i −0.230224 0.398759i 0.727650 0.685948i \(-0.240612\pi\)
−0.957874 + 0.287189i \(0.907279\pi\)
\(318\) 0.0237940 0.0412124i 0.00133430 0.00231108i
\(319\) 6.23898 10.8062i 0.349316 0.605033i
\(320\) −0.380596 0.659212i −0.0212760 0.0368510i
\(321\) 3.54640 0.197941
\(322\) 0 0
\(323\) 3.51375 0.195510
\(324\) 6.76770 + 11.7220i 0.375983 + 0.651222i
\(325\) −1.57525 + 2.72841i −0.0873792 + 0.151345i
\(326\) 0.824451 1.42799i 0.0456621 0.0790891i
\(327\) −1.08276 1.87539i −0.0598767 0.103709i
\(328\) −23.1592 −1.27875
\(329\) 0 0
\(330\) 0.348173 0.0191663
\(331\) 0.362357 + 0.627621i 0.0199170 + 0.0344972i 0.875812 0.482652i \(-0.160326\pi\)
−0.855895 + 0.517149i \(0.826993\pi\)
\(332\) 1.59684 2.76581i 0.0876382 0.151794i
\(333\) −2.98774 + 5.17491i −0.163727 + 0.283583i
\(334\) −5.87597 10.1775i −0.321519 0.556887i
\(335\) 15.3858 0.840616
\(336\) 0 0
\(337\) −8.58299 −0.467545 −0.233773 0.972291i \(-0.575107\pi\)
−0.233773 + 0.972291i \(0.575107\pi\)
\(338\) 0.328092 + 0.568272i 0.0178459 + 0.0309099i
\(339\) 0.240243 0.416112i 0.0130482 0.0226001i
\(340\) −3.80591 + 6.59203i −0.206405 + 0.357503i
\(341\) −7.33194 12.6993i −0.397047 0.687705i
\(342\) −1.91242 −0.103412
\(343\) 0 0
\(344\) −7.41630 −0.399860
\(345\) −0.236139 0.409004i −0.0127133 0.0220200i
\(346\) −2.13910 + 3.70503i −0.114999 + 0.199183i
\(347\) 12.9625 22.4517i 0.695864 1.20527i −0.274024 0.961723i \(-0.588355\pi\)
0.969888 0.243550i \(-0.0783119\pi\)
\(348\) 1.05214 + 1.82236i 0.0564005 + 0.0976886i
\(349\) −17.1403 −0.917501 −0.458750 0.888565i \(-0.651703\pi\)
−0.458750 + 0.888565i \(0.651703\pi\)
\(350\) 0 0
\(351\) 1.21994 0.0651154
\(352\) −5.46459 9.46495i −0.291264 0.504483i
\(353\) −9.45506 + 16.3766i −0.503242 + 0.871641i 0.496751 + 0.867893i \(0.334526\pi\)
−0.999993 + 0.00374752i \(0.998807\pi\)
\(354\) −0.145363 + 0.251776i −0.00772594 + 0.0133817i
\(355\) 6.15566 + 10.6619i 0.326708 + 0.565875i
\(356\) −10.8269 −0.573823
\(357\) 0 0
\(358\) 17.4554 0.922547
\(359\) −7.05247 12.2152i −0.372215 0.644696i 0.617691 0.786421i \(-0.288068\pi\)
−0.989906 + 0.141725i \(0.954735\pi\)
\(360\) 4.71118 8.16001i 0.248301 0.430070i
\(361\) 9.01464 15.6138i 0.474455 0.821779i
\(362\) 8.08425 + 14.0023i 0.424899 + 0.735946i
\(363\) −1.50883 −0.0791931
\(364\) 0 0
\(365\) 9.70495 0.507980
\(366\) −0.819584 1.41956i −0.0428403 0.0742016i
\(367\) 0.180129 0.311993i 0.00940266 0.0162859i −0.861286 0.508121i \(-0.830340\pi\)
0.870688 + 0.491835i \(0.163674\pi\)
\(368\) −1.35848 + 2.35296i −0.0708157 + 0.122656i
\(369\) −14.6244 25.3302i −0.761317 1.31864i
\(370\) 1.80267 0.0937162
\(371\) 0 0
\(372\) 2.47291 0.128214
\(373\) 12.5840 + 21.7961i 0.651575 + 1.12856i 0.982741 + 0.184989i \(0.0592249\pi\)
−0.331165 + 0.943573i \(0.607442\pi\)
\(374\) 2.22961 3.86180i 0.115291 0.199689i
\(375\) 1.13478 1.96550i 0.0585999 0.101498i
\(376\) 9.09260 + 15.7488i 0.468915 + 0.812185i
\(377\) −6.54835 −0.337257
\(378\) 0 0
\(379\) 31.8947 1.63832 0.819161 0.573564i \(-0.194440\pi\)
0.819161 + 0.573564i \(0.194440\pi\)
\(380\) −1.05144 1.82115i −0.0539378 0.0934231i
\(381\) 1.85956 3.22086i 0.0952683 0.165010i
\(382\) 0.991161 1.71674i 0.0507122 0.0878361i
\(383\) 16.4086 + 28.4205i 0.838440 + 1.45222i 0.891199 + 0.453613i \(0.149865\pi\)
−0.0527590 + 0.998607i \(0.516801\pi\)
\(384\) 2.27355 0.116022
\(385\) 0 0
\(386\) −13.9454 −0.709800
\(387\) −4.68321 8.11155i −0.238061 0.412333i
\(388\) 11.4743 19.8740i 0.582518 1.00895i
\(389\) 12.6543 21.9179i 0.641600 1.11128i −0.343476 0.939162i \(-0.611604\pi\)
0.985076 0.172122i \(-0.0550623\pi\)
\(390\) −0.0913595 0.158239i −0.00462617 0.00801275i
\(391\) −6.04869 −0.305895
\(392\) 0 0
\(393\) −2.06829 −0.104331
\(394\) −0.893035 1.54678i −0.0449905 0.0779258i
\(395\) 3.66938 6.35555i 0.184626 0.319782i
\(396\) 4.42314 7.66111i 0.222271 0.384985i
\(397\) −2.64698 4.58470i −0.132848 0.230099i 0.791925 0.610618i \(-0.209079\pi\)
−0.924773 + 0.380518i \(0.875746\pi\)
\(398\) −14.2175 −0.712661
\(399\) 0 0
\(400\) −5.04689 −0.252345
\(401\) 12.3168 + 21.3333i 0.615070 + 1.06533i 0.990372 + 0.138430i \(0.0442055\pi\)
−0.375303 + 0.926902i \(0.622461\pi\)
\(402\) 0.760011 1.31638i 0.0379059 0.0656549i
\(403\) −3.84775 + 6.66450i −0.191670 + 0.331982i
\(404\) −2.20793 3.82424i −0.109849 0.190263i
\(405\) 11.7289 0.582815
\(406\) 0 0
\(407\) 3.84924 0.190800
\(408\) 0.855158 + 1.48118i 0.0423366 + 0.0733292i
\(409\) 5.11113 8.85273i 0.252729 0.437739i −0.711547 0.702638i \(-0.752005\pi\)
0.964276 + 0.264899i \(0.0853386\pi\)
\(410\) −4.41186 + 7.64157i −0.217886 + 0.377390i
\(411\) −0.671182 1.16252i −0.0331070 0.0573430i
\(412\) 9.49481 0.467776
\(413\) 0 0
\(414\) 3.29211 0.161798
\(415\) −1.38372 2.39668i −0.0679243 0.117648i
\(416\) −2.86778 + 4.96714i −0.140604 + 0.243534i
\(417\) −1.41529 + 2.45135i −0.0693069 + 0.120043i
\(418\) 0.615965 + 1.06688i 0.0301278 + 0.0521829i
\(419\) −30.6503 −1.49736 −0.748682 0.662929i \(-0.769313\pi\)
−0.748682 + 0.662929i \(0.769313\pi\)
\(420\) 0 0
\(421\) 25.9764 1.26601 0.633007 0.774146i \(-0.281820\pi\)
0.633007 + 0.774146i \(0.281820\pi\)
\(422\) 6.03312 + 10.4497i 0.293688 + 0.508682i
\(423\) −11.4835 + 19.8900i −0.558346 + 0.967084i
\(424\) −0.414796 + 0.718447i −0.0201443 + 0.0348909i
\(425\) −5.61787 9.73044i −0.272507 0.471996i
\(426\) 1.21628 0.0589290
\(427\) 0 0
\(428\) −27.1830 −1.31394
\(429\) −0.195080 0.337889i −0.00941855 0.0163134i
\(430\) −1.41282 + 2.44707i −0.0681322 + 0.118008i
\(431\) −7.44088 + 12.8880i −0.358415 + 0.620792i −0.987696 0.156385i \(-0.950016\pi\)
0.629282 + 0.777177i \(0.283349\pi\)
\(432\) 0.977128 + 1.69243i 0.0470121 + 0.0814273i
\(433\) 40.0871 1.92647 0.963233 0.268669i \(-0.0865837\pi\)
0.963233 + 0.268669i \(0.0865837\pi\)
\(434\) 0 0
\(435\) 1.82343 0.0874269
\(436\) 8.29928 + 14.3748i 0.397464 + 0.688427i
\(437\) 0.835522 1.44717i 0.0399684 0.0692273i
\(438\) 0.479394 0.830335i 0.0229063 0.0396750i
\(439\) −1.50121 2.60018i −0.0716491 0.124100i 0.827975 0.560765i \(-0.189493\pi\)
−0.899624 + 0.436665i \(0.856159\pi\)
\(440\) −6.06963 −0.289358
\(441\) 0 0
\(442\) −2.34017 −0.111311
\(443\) −0.717828 1.24332i −0.0341051 0.0590717i 0.848469 0.529245i \(-0.177525\pi\)
−0.882574 + 0.470173i \(0.844191\pi\)
\(444\) −0.324567 + 0.562166i −0.0154032 + 0.0266792i
\(445\) −4.69094 + 8.12495i −0.222372 + 0.385160i
\(446\) −7.29073 12.6279i −0.345226 0.597949i
\(447\) 1.65725 0.0783853
\(448\) 0 0
\(449\) 19.6313 0.926460 0.463230 0.886238i \(-0.346690\pi\)
0.463230 + 0.886238i \(0.346690\pi\)
\(450\) 3.05763 + 5.29597i 0.144138 + 0.249654i
\(451\) −9.42066 + 16.3171i −0.443601 + 0.768340i
\(452\) −1.84145 + 3.18948i −0.0866143 + 0.150020i
\(453\) −1.23226 2.13434i −0.0578967 0.100280i
\(454\) 17.5447 0.823413
\(455\) 0 0
\(456\) −0.472501 −0.0221269
\(457\) −5.32103 9.21630i −0.248907 0.431120i 0.714316 0.699824i \(-0.246738\pi\)
−0.963223 + 0.268703i \(0.913405\pi\)
\(458\) 5.47939 9.49058i 0.256035 0.443466i
\(459\) −2.17535 + 3.76782i −0.101537 + 0.175867i
\(460\) 1.80999 + 3.13499i 0.0843912 + 0.146170i
\(461\) 38.5930 1.79745 0.898727 0.438509i \(-0.144493\pi\)
0.898727 + 0.438509i \(0.144493\pi\)
\(462\) 0 0
\(463\) −27.9993 −1.30124 −0.650618 0.759405i \(-0.725490\pi\)
−0.650618 + 0.759405i \(0.725490\pi\)
\(464\) −5.24501 9.08462i −0.243493 0.421743i
\(465\) 1.07143 1.85578i 0.0496865 0.0860596i
\(466\) −4.55312 + 7.88623i −0.210919 + 0.365322i
\(467\) −12.9099 22.3607i −0.597401 1.03473i −0.993203 0.116393i \(-0.962867\pi\)
0.395802 0.918336i \(-0.370467\pi\)
\(468\) −4.64247 −0.214598
\(469\) 0 0
\(470\) 6.92862 0.319594
\(471\) −1.88307 3.26157i −0.0867673 0.150285i
\(472\) 2.53408 4.38915i 0.116640 0.202027i
\(473\) −3.01679 + 5.22524i −0.138712 + 0.240257i
\(474\) −0.362512 0.627889i −0.0166507 0.0288399i
\(475\) 3.10405 0.142423
\(476\) 0 0
\(477\) −1.04773 −0.0479723
\(478\) 0.152840 + 0.264726i 0.00699073 + 0.0121083i
\(479\) −19.7035 + 34.1275i −0.900277 + 1.55933i −0.0731431 + 0.997321i \(0.523303\pi\)
−0.827134 + 0.562005i \(0.810030\pi\)
\(480\) 0.798553 1.38313i 0.0364488 0.0631311i
\(481\) −1.01003 1.74942i −0.0460533 0.0797666i
\(482\) 3.73575 0.170159
\(483\) 0 0
\(484\) 11.5651 0.525687
\(485\) −9.94288 17.2216i −0.451483 0.781991i
\(486\) 1.78013 3.08327i 0.0807481 0.139860i
\(487\) 17.0480 29.5280i 0.772517 1.33804i −0.163662 0.986516i \(-0.552331\pi\)
0.936179 0.351523i \(-0.114336\pi\)
\(488\) 14.2876 + 24.7469i 0.646771 + 1.12024i
\(489\) 0.514517 0.0232673
\(490\) 0 0
\(491\) −9.70414 −0.437942 −0.218971 0.975731i \(-0.570270\pi\)
−0.218971 + 0.975731i \(0.570270\pi\)
\(492\) −1.58869 2.75170i −0.0716239 0.124056i
\(493\) 11.6768 20.2248i 0.525897 0.910880i
\(494\) 0.323254 0.559893i 0.0145439 0.0251908i
\(495\) −3.83282 6.63863i −0.172272 0.298384i
\(496\) −12.3277 −0.553529
\(497\) 0 0
\(498\) −0.273407 −0.0122516
\(499\) −9.02313 15.6285i −0.403931 0.699629i 0.590265 0.807209i \(-0.299023\pi\)
−0.994196 + 0.107580i \(0.965690\pi\)
\(500\) −8.69804 + 15.0654i −0.388988 + 0.673747i
\(501\) 1.83352 3.17575i 0.0819156 0.141882i
\(502\) −5.87500 10.1758i −0.262214 0.454168i
\(503\) −16.4922 −0.735352 −0.367676 0.929954i \(-0.619846\pi\)
−0.367676 + 0.929954i \(0.619846\pi\)
\(504\) 0 0
\(505\) −3.82650 −0.170277
\(506\) −1.06034 1.83657i −0.0471380 0.0816455i
\(507\) −0.102377 + 0.177322i −0.00454671 + 0.00787513i
\(508\) −14.2534 + 24.6877i −0.632394 + 1.09534i
\(509\) −9.59883 16.6257i −0.425460 0.736919i 0.571003 0.820948i \(-0.306555\pi\)
−0.996463 + 0.0840290i \(0.973221\pi\)
\(510\) 0.651637 0.0288550
\(511\) 0 0
\(512\) −16.6921 −0.737692
\(513\) −0.600974 1.04092i −0.0265336 0.0459576i
\(514\) −8.52238 + 14.7612i −0.375906 + 0.651089i
\(515\) 4.11380 7.12531i 0.181276 0.313979i
\(516\) −0.508750 0.881182i −0.0223965 0.0387919i
\(517\) 14.7947 0.650670
\(518\) 0 0
\(519\) −1.33495 −0.0585979
\(520\) 1.59265 + 2.75855i 0.0698423 + 0.120970i
\(521\) −4.38017 + 7.58668i −0.191899 + 0.332378i −0.945879 0.324518i \(-0.894798\pi\)
0.753981 + 0.656897i \(0.228131\pi\)
\(522\) −6.35531 + 11.0077i −0.278164 + 0.481795i
\(523\) −5.87030 10.1677i −0.256690 0.444601i 0.708663 0.705547i \(-0.249299\pi\)
−0.965353 + 0.260946i \(0.915965\pi\)
\(524\) 15.8533 0.692555
\(525\) 0 0
\(526\) −18.2683 −0.796534
\(527\) −13.7224 23.7678i −0.597756 1.03534i
\(528\) 0.312505 0.541275i 0.0136000 0.0235560i
\(529\) 10.0617 17.4274i 0.437465 0.757712i
\(530\) 0.158039 + 0.273731i 0.00686476 + 0.0118901i
\(531\) 6.40082 0.277772
\(532\) 0 0
\(533\) 9.88779 0.428288
\(534\) 0.463436 + 0.802695i 0.0200548 + 0.0347360i
\(535\) −11.7775 + 20.3993i −0.509186 + 0.881937i
\(536\) −13.2491 + 22.9481i −0.572274 + 0.991208i
\(537\) 2.72336 + 4.71700i 0.117522 + 0.203554i
\(538\) 3.87467 0.167049
\(539\) 0 0
\(540\) 2.60378 0.112049
\(541\) −8.22934 14.2536i −0.353807 0.612812i 0.633106 0.774065i \(-0.281780\pi\)
−0.986913 + 0.161253i \(0.948446\pi\)
\(542\) 1.42698 2.47160i 0.0612939 0.106164i
\(543\) −2.52258 + 4.36924i −0.108254 + 0.187502i
\(544\) −10.2275 17.7145i −0.438499 0.759502i
\(545\) 14.3833 0.616112
\(546\) 0 0
\(547\) −8.19375 −0.350339 −0.175170 0.984538i \(-0.556047\pi\)
−0.175170 + 0.984538i \(0.556047\pi\)
\(548\) 5.14457 + 8.91066i 0.219765 + 0.380645i
\(549\) −18.0445 + 31.2541i −0.770123 + 1.33389i
\(550\) 1.96964 3.41152i 0.0839858 0.145468i
\(551\) 3.22590 + 5.58742i 0.137428 + 0.238032i
\(552\) 0.813381 0.0346198
\(553\) 0 0
\(554\) −0.709015 −0.0301232
\(555\) 0.281249 + 0.487137i 0.0119383 + 0.0206778i
\(556\) 10.8481 18.7894i 0.460061 0.796850i
\(557\) 6.90720 11.9636i 0.292667 0.506915i −0.681772 0.731565i \(-0.738790\pi\)
0.974440 + 0.224650i \(0.0721238\pi\)
\(558\) 7.46865 + 12.9361i 0.316173 + 0.547628i
\(559\) 3.16639 0.133924
\(560\) 0 0
\(561\) 1.39144 0.0587467
\(562\) 4.75445 + 8.23494i 0.200554 + 0.347370i
\(563\) 4.87780 8.44859i 0.205575 0.356066i −0.744741 0.667354i \(-0.767427\pi\)
0.950316 + 0.311288i \(0.100760\pi\)
\(564\) −1.24749 + 2.16071i −0.0525286 + 0.0909822i
\(565\) 1.59568 + 2.76380i 0.0671308 + 0.116274i
\(566\) 16.0751 0.675687
\(567\) 0 0
\(568\) −21.2032 −0.889666
\(569\) 0.716319 + 1.24070i 0.0300296 + 0.0520129i 0.880650 0.473768i \(-0.157106\pi\)
−0.850620 + 0.525781i \(0.823773\pi\)
\(570\) −0.0900123 + 0.155906i −0.00377020 + 0.00653018i
\(571\) −8.14359 + 14.1051i −0.340799 + 0.590281i −0.984581 0.174928i \(-0.944031\pi\)
0.643783 + 0.765209i \(0.277364\pi\)
\(572\) 1.49528 + 2.58990i 0.0625207 + 0.108289i
\(573\) 0.618557 0.0258406
\(574\) 0 0
\(575\) −5.34342 −0.222836
\(576\) 0.827840 + 1.43386i 0.0344934 + 0.0597442i
\(577\) −2.40923 + 4.17291i −0.100297 + 0.173720i −0.911807 0.410619i \(-0.865313\pi\)
0.811510 + 0.584339i \(0.198646\pi\)
\(578\) −1.40465 + 2.43292i −0.0584256 + 0.101196i
\(579\) −2.17573 3.76848i −0.0904203 0.156613i
\(580\) −13.9765 −0.580343
\(581\) 0 0
\(582\) −1.96459 −0.0814349
\(583\) 0.337460 + 0.584498i 0.0139762 + 0.0242074i
\(584\) −8.35718 + 14.4751i −0.345823 + 0.598982i
\(585\) −2.01144 + 3.48391i −0.0831626 + 0.144042i
\(586\) −0.380933 0.659795i −0.0157362 0.0272559i
\(587\) −36.6215 −1.51153 −0.755765 0.654843i \(-0.772735\pi\)
−0.755765 + 0.654843i \(0.772735\pi\)
\(588\) 0 0
\(589\) 7.58203 0.312412
\(590\) −0.965493 1.67228i −0.0397487 0.0688468i
\(591\) 0.278660 0.482653i 0.0114625 0.0198537i
\(592\) 1.61799 2.80245i 0.0664992 0.115180i
\(593\) −9.35407 16.2017i −0.384125 0.665325i 0.607522 0.794303i \(-0.292164\pi\)
−0.991647 + 0.128978i \(0.958830\pi\)
\(594\) −1.52537 −0.0625866
\(595\) 0 0
\(596\) −12.7027 −0.520325
\(597\) −2.21820 3.84203i −0.0907847 0.157244i
\(598\) −0.556461 + 0.963819i −0.0227554 + 0.0394135i
\(599\) 12.7097 22.0139i 0.519305 0.899463i −0.480443 0.877026i \(-0.659524\pi\)
0.999748 0.0224368i \(-0.00714245\pi\)
\(600\) 0.755448 + 1.30847i 0.0308410 + 0.0534182i
\(601\) −17.7790 −0.725219 −0.362609 0.931941i \(-0.618114\pi\)
−0.362609 + 0.931941i \(0.618114\pi\)
\(602\) 0 0
\(603\) −33.4659 −1.36284
\(604\) 9.44521 + 16.3596i 0.384320 + 0.665662i
\(605\) 5.01080 8.67895i 0.203718 0.352850i
\(606\) −0.189017 + 0.327388i −0.00767830 + 0.0132992i
\(607\) 13.0024 + 22.5208i 0.527750 + 0.914089i 0.999477 + 0.0323446i \(0.0102974\pi\)
−0.471727 + 0.881745i \(0.656369\pi\)
\(608\) 5.65098 0.229178
\(609\) 0 0
\(610\) 10.8873 0.440813
\(611\) −3.88208 6.72396i −0.157052 0.272022i
\(612\) 8.27830 14.3384i 0.334631 0.579597i
\(613\) −13.4115 + 23.2294i −0.541685 + 0.938226i 0.457123 + 0.889404i \(0.348880\pi\)
−0.998807 + 0.0488222i \(0.984453\pi\)
\(614\) −8.32471 14.4188i −0.335958 0.581896i
\(615\) −2.75332 −0.111025
\(616\) 0 0
\(617\) −18.6491 −0.750784 −0.375392 0.926866i \(-0.622492\pi\)
−0.375392 + 0.926866i \(0.622492\pi\)
\(618\) −0.406418 0.703937i −0.0163485 0.0283165i
\(619\) 6.53427 11.3177i 0.262634 0.454896i −0.704307 0.709896i \(-0.748742\pi\)
0.966941 + 0.255000i \(0.0820753\pi\)
\(620\) −8.21247 + 14.2244i −0.329821 + 0.571266i
\(621\) 1.03454 + 1.79187i 0.0415146 + 0.0719053i
\(622\) 16.0532 0.643676
\(623\) 0 0
\(624\) −0.328001 −0.0131306
\(625\) −0.339088 0.587317i −0.0135635 0.0234927i
\(626\) −2.17087 + 3.76005i −0.0867654 + 0.150282i
\(627\) −0.192203 + 0.332906i −0.00767587 + 0.0132950i
\(628\) 14.4336 + 24.9998i 0.575964 + 0.997599i
\(629\) 7.20418 0.287250
\(630\) 0 0
\(631\) −49.1745 −1.95761 −0.978804 0.204801i \(-0.934345\pi\)
−0.978804 + 0.204801i \(0.934345\pi\)
\(632\) 6.31959 + 10.9459i 0.251380 + 0.435403i
\(633\) −1.88255 + 3.26068i −0.0748248 + 0.129600i
\(634\) 2.68971 4.65871i 0.106822 0.185021i
\(635\) 12.3511 + 21.3928i 0.490140 + 0.848947i
\(636\) −0.113818 −0.00451318
\(637\) 0 0
\(638\) 8.18784 0.324160
\(639\) −13.3893 23.1909i −0.529671 0.917417i
\(640\) −7.55040 + 13.0777i −0.298456 + 0.516941i
\(641\) −2.18751 + 3.78888i −0.0864016 + 0.149652i −0.905988 0.423304i \(-0.860870\pi\)
0.819586 + 0.572956i \(0.194203\pi\)
\(642\) 1.16355 + 2.01532i 0.0459215 + 0.0795383i
\(643\) 5.34651 0.210846 0.105423 0.994427i \(-0.466380\pi\)
0.105423 + 0.994427i \(0.466380\pi\)
\(644\) 0 0
\(645\) −0.881702 −0.0347170
\(646\) 1.15283 + 1.99676i 0.0453576 + 0.0785616i
\(647\) −14.8673 + 25.7509i −0.584493 + 1.01237i 0.410445 + 0.911885i \(0.365373\pi\)
−0.994938 + 0.100487i \(0.967960\pi\)
\(648\) −10.1001 + 17.4938i −0.396768 + 0.687223i
\(649\) −2.06162 3.57083i −0.0809256 0.140167i
\(650\) −2.06731 −0.0810865
\(651\) 0 0
\(652\) −3.94375 −0.154449
\(653\) 1.27131 + 2.20198i 0.0497503 + 0.0861700i 0.889828 0.456296i \(-0.150824\pi\)
−0.840078 + 0.542466i \(0.817491\pi\)
\(654\) 0.710489 1.23060i 0.0277823 0.0481204i
\(655\) 6.86874 11.8970i 0.268384 0.464854i
\(656\) 7.91979 + 13.7175i 0.309216 + 0.535578i
\(657\) −21.1094 −0.823556
\(658\) 0 0
\(659\) 1.87019 0.0728523 0.0364261 0.999336i \(-0.488403\pi\)
0.0364261 + 0.999336i \(0.488403\pi\)
\(660\) −0.416370 0.721174i −0.0162072 0.0280717i
\(661\) −6.03815 + 10.4584i −0.234857 + 0.406784i −0.959231 0.282623i \(-0.908795\pi\)
0.724374 + 0.689407i \(0.242129\pi\)
\(662\) −0.237773 + 0.411835i −0.00924131 + 0.0160064i
\(663\) −0.365109 0.632388i −0.0141797 0.0245599i
\(664\) 4.76624 0.184966
\(665\) 0 0
\(666\) −3.92101 −0.151936
\(667\) −5.55317 9.61838i −0.215020 0.372425i
\(668\) −14.0538 + 24.3419i −0.543758 + 0.941817i
\(669\) 2.27498 3.94037i 0.0879556 0.152344i
\(670\) 5.04796 + 8.74332i 0.195020 + 0.337784i
\(671\) 23.2476 0.897464
\(672\) 0 0
\(673\) −7.81691 −0.301320 −0.150660 0.988586i \(-0.548140\pi\)
−0.150660 + 0.988586i \(0.548140\pi\)
\(674\) −2.81601 4.87747i −0.108469 0.187873i
\(675\) −1.92171 + 3.32849i −0.0739665 + 0.128114i
\(676\) 0.784711 1.35916i 0.0301812 0.0522754i
\(677\) 3.12814 + 5.41809i 0.120224 + 0.208234i 0.919856 0.392256i \(-0.128305\pi\)
−0.799632 + 0.600491i \(0.794972\pi\)
\(678\) 0.315287 0.0121085
\(679\) 0 0
\(680\) −11.3598 −0.435630
\(681\) 2.73729 + 4.74113i 0.104893 + 0.181680i
\(682\) 4.81110 8.33307i 0.184227 0.319090i
\(683\) −11.1828 + 19.3692i −0.427898 + 0.741140i −0.996686 0.0813435i \(-0.974079\pi\)
0.568789 + 0.822484i \(0.307412\pi\)
\(684\) 2.28701 + 3.96121i 0.0874459 + 0.151461i
\(685\) 8.91593 0.340660
\(686\) 0 0
\(687\) 3.41954 0.130464
\(688\) 2.53617 + 4.39277i 0.0966905 + 0.167473i
\(689\) 0.177097 0.306741i 0.00674685 0.0116859i
\(690\) 0.154950 0.268382i 0.00589886 0.0102171i
\(691\) −1.90385 3.29757i −0.0724260 0.125445i 0.827538 0.561410i \(-0.189741\pi\)
−0.899964 + 0.435964i \(0.856407\pi\)
\(692\) 10.2323 0.388975
\(693\) 0 0
\(694\) 17.0116 0.645751
\(695\) −9.40027 16.2817i −0.356572 0.617602i
\(696\) −1.57021 + 2.71968i −0.0595185 + 0.103089i
\(697\) −17.6316 + 30.5388i −0.667844 + 1.15674i
\(698\) −5.62360 9.74037i −0.212857 0.368678i
\(699\) −2.84148 −0.107475
\(700\) 0 0
\(701\) −8.14218 −0.307526 −0.153763 0.988108i \(-0.549139\pi\)
−0.153763 + 0.988108i \(0.549139\pi\)
\(702\) 0.400251 + 0.693255i 0.0151065 + 0.0261652i
\(703\) −0.995133 + 1.72362i −0.0375322 + 0.0650076i
\(704\) 0.533272 0.923655i 0.0200985 0.0348116i
\(705\) 1.08099 + 1.87233i 0.0407125 + 0.0705161i
\(706\) −12.4085 −0.467001
\(707\) 0 0
\(708\) 0.695340 0.0261325
\(709\) 12.0159 + 20.8122i 0.451268 + 0.781619i 0.998465 0.0553845i \(-0.0176385\pi\)
−0.547197 + 0.837004i \(0.684305\pi\)
\(710\) −4.03924 + 6.99617i −0.151590 + 0.262562i
\(711\) −7.98132 + 13.8241i −0.299323 + 0.518442i
\(712\) −8.07899 13.9932i −0.302773 0.524418i
\(713\) −13.0520 −0.488800
\(714\) 0 0
\(715\) 2.59143 0.0969138
\(716\) −20.8744 36.1556i −0.780114 1.35120i
\(717\) −0.0476916 + 0.0826043i −0.00178108 + 0.00308492i
\(718\) 4.62772 8.01544i 0.172705 0.299134i
\(719\) −16.3480 28.3156i −0.609678 1.05599i −0.991293 0.131672i \(-0.957965\pi\)
0.381615 0.924321i \(-0.375368\pi\)
\(720\) −6.44437 −0.240168
\(721\) 0 0
\(722\) 11.8305 0.440286
\(723\) 0.582845 + 1.00952i 0.0216762 + 0.0375443i
\(724\) 19.3354 33.4900i 0.718596 1.24465i
\(725\) 10.3153 17.8666i 0.383101 0.663550i
\(726\) −0.495036 0.857427i −0.0183725 0.0318221i
\(727\) 15.7712 0.584921 0.292460 0.956278i \(-0.405526\pi\)
0.292460 + 0.956278i \(0.405526\pi\)
\(728\) 0 0
\(729\) −24.7624 −0.917126
\(730\) 3.18412 + 5.51505i 0.117849 + 0.204121i
\(731\) −5.64620 + 9.77950i −0.208832 + 0.361708i
\(732\) −1.96023 + 3.39522i −0.0724523 + 0.125491i
\(733\) 11.7547 + 20.3598i 0.434170 + 0.752005i 0.997228 0.0744131i \(-0.0237083\pi\)
−0.563057 + 0.826418i \(0.690375\pi\)
\(734\) 0.236396 0.00872552
\(735\) 0 0
\(736\) −9.72781 −0.358572
\(737\) 10.7789 + 18.6696i 0.397046 + 0.687705i
\(738\) 9.59631 16.6213i 0.353245 0.611838i
\(739\) 11.2633 19.5087i 0.414329 0.717639i −0.581029 0.813883i \(-0.697350\pi\)
0.995358 + 0.0962443i \(0.0306830\pi\)
\(740\) −2.15576 3.73388i −0.0792472 0.137260i
\(741\) 0.201734 0.00741089
\(742\) 0 0
\(743\) −13.9795 −0.512857 −0.256429 0.966563i \(-0.582546\pi\)
−0.256429 + 0.966563i \(0.582546\pi\)
\(744\) 1.84528 + 3.19611i 0.0676511 + 0.117175i
\(745\) −5.50370 + 9.53268i −0.201640 + 0.349250i
\(746\) −8.25743 + 14.3023i −0.302326 + 0.523644i
\(747\) 3.00976 + 5.21306i 0.110121 + 0.190736i
\(748\) −10.6653 −0.389963
\(749\) 0 0
\(750\) 1.48925 0.0543798
\(751\) −1.27296 2.20483i −0.0464509 0.0804552i 0.841865 0.539688i \(-0.181458\pi\)
−0.888316 + 0.459233i \(0.848124\pi\)
\(752\) 6.21883 10.7713i 0.226777 0.392790i
\(753\) 1.83321 3.17522i 0.0668060 0.115711i
\(754\) −2.14846 3.72124i −0.0782424 0.135520i
\(755\) 16.3692 0.595738
\(756\) 0 0
\(757\) 19.6921 0.715721 0.357861 0.933775i \(-0.383506\pi\)
0.357861 + 0.933775i \(0.383506\pi\)
\(758\) 10.4644 + 18.1249i 0.380084 + 0.658325i
\(759\) 0.330866 0.573077i 0.0120097 0.0208014i
\(760\) 1.56917 2.71788i 0.0569196 0.0985877i
\(761\) −19.5453 33.8534i −0.708515 1.22718i −0.965408 0.260744i \(-0.916032\pi\)
0.256893 0.966440i \(-0.417301\pi\)
\(762\) 2.44043 0.0884075
\(763\) 0 0
\(764\) −4.74120 −0.171531
\(765\) −7.17345 12.4248i −0.259357 0.449219i
\(766\) −10.7671 + 18.6491i −0.389029 + 0.673819i
\(767\) −1.08192 + 1.87395i −0.0390660 + 0.0676643i
\(768\) 0.860536 + 1.49049i 0.0310519 + 0.0537835i
\(769\) 21.7389 0.783926 0.391963 0.919981i \(-0.371796\pi\)
0.391963 + 0.919981i \(0.371796\pi\)
\(770\) 0 0
\(771\) −5.31859 −0.191544
\(772\) 16.6769 + 28.8852i 0.600213 + 1.03960i
\(773\) 2.06403 3.57501i 0.0742381 0.128584i −0.826517 0.562912i \(-0.809681\pi\)
0.900755 + 0.434328i \(0.143014\pi\)
\(774\) 3.07304 5.32267i 0.110458 0.191319i
\(775\) −12.1224 20.9965i −0.435448 0.754218i
\(776\) 34.2483 1.22944
\(777\) 0 0
\(778\) 16.6071 0.595395
\(779\) −4.87100 8.43681i −0.174522 0.302280i
\(780\) −0.218508 + 0.378467i −0.00782385 + 0.0135513i
\(781\) −8.62500 + 14.9389i −0.308627 + 0.534557i
\(782\) −1.98453 3.43730i −0.0709665 0.122918i
\(783\) −7.98857 −0.285488
\(784\) 0 0