Properties

Label 882.2.l.a.509.1
Level $882$
Weight $2$
Character 882.509
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 509.1
Root \(-1.62181 + 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 882.509
Dual form 882.2.l.a.227.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +(-1.33750 - 1.10050i) q^{3} -1.00000 q^{4} +(-1.94556 - 3.36980i) q^{5} +(-1.10050 + 1.33750i) q^{6} +1.00000i q^{8} +(0.577806 + 2.94383i) q^{9} +(-3.36980 + 1.94556i) q^{10} +(-3.41614 - 1.97231i) q^{11} +(1.33750 + 1.10050i) q^{12} +(-2.46687 - 1.42425i) q^{13} +(-1.10628 + 6.64819i) q^{15} +1.00000 q^{16} +(0.371058 + 0.642692i) q^{17} +(2.94383 - 0.577806i) q^{18} +(-1.54563 - 0.892369i) q^{19} +(1.94556 + 3.36980i) q^{20} +(-1.97231 + 3.41614i) q^{22} +(5.41535 - 3.12656i) q^{23} +(1.10050 - 1.33750i) q^{24} +(-5.07039 + 8.78217i) q^{25} +(-1.42425 + 2.46687i) q^{26} +(2.46687 - 4.57324i) q^{27} +(-2.50079 + 1.44383i) q^{29} +(6.64819 + 1.10628i) q^{30} +3.51174i q^{31} -1.00000i q^{32} +(2.39856 + 6.39742i) q^{33} +(0.642692 - 0.371058i) q^{34} +(-0.577806 - 2.94383i) q^{36} +(-1.50079 + 2.59944i) q^{37} +(-0.892369 + 1.54563i) q^{38} +(1.73205 + 4.61971i) q^{39} +(3.36980 - 1.94556i) q^{40} +(5.24705 - 9.08816i) q^{41} +(0.471521 + 0.816699i) q^{43} +(3.41614 + 1.97231i) q^{44} +(8.79598 - 7.67448i) q^{45} +(-3.12656 - 5.41535i) q^{46} +2.18525 q^{47} +(-1.33750 - 1.10050i) q^{48} +(8.78217 + 5.07039i) q^{50} +(0.210992 - 1.26795i) q^{51} +(2.46687 + 1.42425i) q^{52} +(-4.57324 - 2.46687i) q^{54} +15.3490i q^{55} +(1.08523 + 2.89450i) q^{57} +(1.44383 + 2.50079i) q^{58} +0.0211346 q^{59} +(1.10628 - 6.64819i) q^{60} +2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} +11.0838i q^{65} +(6.39742 - 2.39856i) q^{66} +13.4493 q^{67} +(-0.371058 - 0.642692i) q^{68} +(-10.6838 - 1.77782i) q^{69} -1.94304i q^{71} +(-2.94383 + 0.577806i) q^{72} +(-4.20443 + 2.42743i) q^{73} +(2.59944 + 1.50079i) q^{74} +(16.4464 - 6.16618i) q^{75} +(1.54563 + 0.892369i) q^{76} +(4.61971 - 1.73205i) q^{78} +3.63613 q^{79} +(-1.94556 - 3.36980i) q^{80} +(-8.33228 + 3.40192i) q^{81} +(-9.08816 - 5.24705i) q^{82} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} +(0.816699 - 0.471521i) q^{86} +(4.93374 + 0.820992i) q^{87} +(1.97231 - 3.41614i) q^{88} +(-4.63323 + 8.02499i) q^{89} +(-7.67448 - 8.79598i) q^{90} +(-5.41535 + 3.12656i) q^{92} +(3.86466 - 4.69694i) q^{93} -2.18525i q^{94} +6.94462i q^{95} +(-1.10050 + 1.33750i) q^{96} +(-16.2983 + 9.40980i) q^{97} +(3.83228 - 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 12 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.33750 1.10050i −0.772205 0.635373i
\(4\) −1.00000 −0.500000
\(5\) −1.94556 3.36980i −0.870080 1.50702i −0.861913 0.507056i \(-0.830734\pi\)
−0.00816625 0.999967i \(-0.502599\pi\)
\(6\) −1.10050 + 1.33750i −0.449277 + 0.546032i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.577806 + 2.94383i 0.192602 + 0.981277i
\(10\) −3.36980 + 1.94556i −1.06563 + 0.615239i
\(11\) −3.41614 1.97231i −1.03001 0.594674i −0.113019 0.993593i \(-0.536052\pi\)
−0.916986 + 0.398919i \(0.869385\pi\)
\(12\) 1.33750 + 1.10050i 0.386103 + 0.317687i
\(13\) −2.46687 1.42425i −0.684186 0.395015i 0.117244 0.993103i \(-0.462594\pi\)
−0.801430 + 0.598088i \(0.795927\pi\)
\(14\) 0 0
\(15\) −1.10628 + 6.64819i −0.285641 + 1.71656i
\(16\) 1.00000 0.250000
\(17\) 0.371058 + 0.642692i 0.0899949 + 0.155876i 0.907509 0.420033i \(-0.137982\pi\)
−0.817514 + 0.575909i \(0.804648\pi\)
\(18\) 2.94383 0.577806i 0.693868 0.136190i
\(19\) −1.54563 0.892369i −0.354591 0.204723i 0.312114 0.950045i \(-0.398963\pi\)
−0.666706 + 0.745321i \(0.732296\pi\)
\(20\) 1.94556 + 3.36980i 0.435040 + 0.753511i
\(21\) 0 0
\(22\) −1.97231 + 3.41614i −0.420498 + 0.728324i
\(23\) 5.41535 3.12656i 1.12918 0.651932i 0.185451 0.982654i \(-0.440626\pi\)
0.943728 + 0.330722i \(0.107292\pi\)
\(24\) 1.10050 1.33750i 0.224638 0.273016i
\(25\) −5.07039 + 8.78217i −1.01408 + 1.75643i
\(26\) −1.42425 + 2.46687i −0.279318 + 0.483793i
\(27\) 2.46687 4.57324i 0.474749 0.880121i
\(28\) 0 0
\(29\) −2.50079 + 1.44383i −0.464385 + 0.268113i −0.713886 0.700262i \(-0.753067\pi\)
0.249501 + 0.968374i \(0.419733\pi\)
\(30\) 6.64819 + 1.10628i 1.21379 + 0.201979i
\(31\) 3.51174i 0.630726i 0.948971 + 0.315363i \(0.102126\pi\)
−0.948971 + 0.315363i \(0.897874\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.39856 + 6.39742i 0.417536 + 1.11365i
\(34\) 0.642692 0.371058i 0.110221 0.0636360i
\(35\) 0 0
\(36\) −0.577806 2.94383i −0.0963009 0.490638i
\(37\) −1.50079 + 2.59944i −0.246728 + 0.427346i −0.962616 0.270870i \(-0.912689\pi\)
0.715888 + 0.698215i \(0.246022\pi\)
\(38\) −0.892369 + 1.54563i −0.144761 + 0.250734i
\(39\) 1.73205 + 4.61971i 0.277350 + 0.739746i
\(40\) 3.36980 1.94556i 0.532813 0.307620i
\(41\) 5.24705 9.08816i 0.819452 1.41933i −0.0866345 0.996240i \(-0.527611\pi\)
0.906087 0.423092i \(-0.139055\pi\)
\(42\) 0 0
\(43\) 0.471521 + 0.816699i 0.0719063 + 0.124545i 0.899737 0.436433i \(-0.143758\pi\)
−0.827830 + 0.560978i \(0.810425\pi\)
\(44\) 3.41614 + 1.97231i 0.515003 + 0.297337i
\(45\) 8.79598 7.67448i 1.31123 1.14404i
\(46\) −3.12656 5.41535i −0.460985 0.798450i
\(47\) 2.18525 0.318752 0.159376 0.987218i \(-0.449052\pi\)
0.159376 + 0.987218i \(0.449052\pi\)
\(48\) −1.33750 1.10050i −0.193051 0.158843i
\(49\) 0 0
\(50\) 8.78217 + 5.07039i 1.24199 + 0.717061i
\(51\) 0.210992 1.26795i 0.0295447 0.177548i
\(52\) 2.46687 + 1.42425i 0.342093 + 0.197507i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −4.57324 2.46687i −0.622340 0.335698i
\(55\) 15.3490i 2.06965i
\(56\) 0 0
\(57\) 1.08523 + 2.89450i 0.143742 + 0.383386i
\(58\) 1.44383 + 2.50079i 0.189584 + 0.328370i
\(59\) 0.0211346 0.00275149 0.00137575 0.999999i \(-0.499562\pi\)
0.00137575 + 0.999999i \(0.499562\pi\)
\(60\) 1.10628 6.64819i 0.142821 0.858278i
\(61\) 2.46911i 0.316138i 0.987428 + 0.158069i \(0.0505268\pi\)
−0.987428 + 0.158069i \(0.949473\pi\)
\(62\) 3.51174 0.445991
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 11.0838i 1.37478i
\(66\) 6.39742 2.39856i 0.787468 0.295242i
\(67\) 13.4493 1.64309 0.821544 0.570144i \(-0.193113\pi\)
0.821544 + 0.570144i \(0.193113\pi\)
\(68\) −0.371058 0.642692i −0.0449974 0.0779379i
\(69\) −10.6838 1.77782i −1.28618 0.214025i
\(70\) 0 0
\(71\) 1.94304i 0.230597i −0.993331 0.115298i \(-0.963218\pi\)
0.993331 0.115298i \(-0.0367824\pi\)
\(72\) −2.94383 + 0.577806i −0.346934 + 0.0680950i
\(73\) −4.20443 + 2.42743i −0.492092 + 0.284109i −0.725442 0.688284i \(-0.758364\pi\)
0.233350 + 0.972393i \(0.425031\pi\)
\(74\) 2.59944 + 1.50079i 0.302179 + 0.174463i
\(75\) 16.4464 6.16618i 1.89907 0.712009i
\(76\) 1.54563 + 0.892369i 0.177296 + 0.102362i
\(77\) 0 0
\(78\) 4.61971 1.73205i 0.523079 0.196116i
\(79\) 3.63613 0.409096 0.204548 0.978856i \(-0.434427\pi\)
0.204548 + 0.978856i \(0.434427\pi\)
\(80\) −1.94556 3.36980i −0.217520 0.376756i
\(81\) −8.33228 + 3.40192i −0.925809 + 0.377992i
\(82\) −9.08816 5.24705i −1.00362 0.579440i
\(83\) 4.02998 + 6.98012i 0.442347 + 0.766168i 0.997863 0.0653378i \(-0.0208125\pi\)
−0.555516 + 0.831506i \(0.687479\pi\)
\(84\) 0 0
\(85\) 1.44383 2.50079i 0.156605 0.271249i
\(86\) 0.816699 0.471521i 0.0880669 0.0508454i
\(87\) 4.93374 + 0.820992i 0.528952 + 0.0880196i
\(88\) 1.97231 3.41614i 0.210249 0.364162i
\(89\) −4.63323 + 8.02499i −0.491122 + 0.850647i −0.999948 0.0102218i \(-0.996746\pi\)
0.508826 + 0.860869i \(0.330080\pi\)
\(90\) −7.67448 8.79598i −0.808962 0.927178i
\(91\) 0 0
\(92\) −5.41535 + 3.12656i −0.564589 + 0.325966i
\(93\) 3.86466 4.69694i 0.400747 0.487050i
\(94\) 2.18525i 0.225392i
\(95\) 6.94462i 0.712503i
\(96\) −1.10050 + 1.33750i −0.112319 + 0.136508i
\(97\) −16.2983 + 9.40980i −1.65484 + 0.955421i −0.679794 + 0.733403i \(0.737931\pi\)
−0.975043 + 0.222018i \(0.928736\pi\)
\(98\) 0 0
\(99\) 3.83228 11.1962i 0.385159 1.12526i
\(100\) 5.07039 8.78217i 0.507039 0.878217i
\(101\) −4.14079 + 7.17206i −0.412024 + 0.713647i −0.995111 0.0987631i \(-0.968511\pi\)
0.583087 + 0.812410i \(0.301845\pi\)
\(102\) −1.26795 0.210992i −0.125546 0.0208913i
\(103\) −14.7646 + 8.52435i −1.45480 + 0.839929i −0.998748 0.0500247i \(-0.984070\pi\)
−0.456051 + 0.889953i \(0.650737\pi\)
\(104\) 1.42425 2.46687i 0.139659 0.241896i
\(105\) 0 0
\(106\) 0 0
\(107\) −12.4161 7.16846i −1.20031 0.693001i −0.239689 0.970850i \(-0.577045\pi\)
−0.960625 + 0.277848i \(0.910379\pi\)
\(108\) −2.46687 + 4.57324i −0.237374 + 0.440061i
\(109\) −5.63998 9.76874i −0.540212 0.935675i −0.998891 0.0470733i \(-0.985011\pi\)
0.458679 0.888602i \(-0.348323\pi\)
\(110\) 15.3490 1.46347
\(111\) 4.86799 1.82513i 0.462049 0.173234i
\(112\) 0 0
\(113\) −8.51501 4.91614i −0.801024 0.462472i 0.0428049 0.999083i \(-0.486371\pi\)
−0.843829 + 0.536612i \(0.819704\pi\)
\(114\) 2.89450 1.08523i 0.271095 0.101641i
\(115\) −21.0718 12.1658i −1.96495 1.13447i
\(116\) 2.50079 1.44383i 0.232192 0.134056i
\(117\) 2.76737 8.08498i 0.255844 0.747457i
\(118\) 0.0211346i 0.00194560i
\(119\) 0 0
\(120\) −6.64819 1.10628i −0.606894 0.100989i
\(121\) 2.28001 + 3.94910i 0.207274 + 0.359009i
\(122\) 2.46911 0.223543
\(123\) −17.0194 + 6.38103i −1.53459 + 0.575358i
\(124\) 3.51174i 0.315363i
\(125\) 20.0033 1.78915
\(126\) 0 0
\(127\) 2.94462 0.261293 0.130646 0.991429i \(-0.458295\pi\)
0.130646 + 0.991429i \(0.458295\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.268117 1.61124i 0.0236064 0.141862i
\(130\) 11.0838 0.972115
\(131\) −7.53255 13.0468i −0.658122 1.13990i −0.981101 0.193495i \(-0.938018\pi\)
0.322979 0.946406i \(-0.395316\pi\)
\(132\) −2.39856 6.39742i −0.208768 0.556824i
\(133\) 0 0
\(134\) 13.4493i 1.16184i
\(135\) −20.2104 + 0.584648i −1.73943 + 0.0503185i
\(136\) −0.642692 + 0.371058i −0.0551104 + 0.0318180i
\(137\) 13.6139 + 7.85997i 1.16311 + 0.671523i 0.952048 0.305950i \(-0.0989739\pi\)
0.211064 + 0.977472i \(0.432307\pi\)
\(138\) −1.77782 + 10.6838i −0.151338 + 0.909465i
\(139\) −2.86373 1.65337i −0.242898 0.140237i 0.373610 0.927586i \(-0.378120\pi\)
−0.616508 + 0.787349i \(0.711453\pi\)
\(140\) 0 0
\(141\) −2.92277 2.40487i −0.246142 0.202526i
\(142\) −1.94304 −0.163056
\(143\) 5.61811 + 9.73085i 0.469810 + 0.813735i
\(144\) 0.577806 + 2.94383i 0.0481505 + 0.245319i
\(145\) 9.73085 + 5.61811i 0.808103 + 0.466559i
\(146\) 2.42743 + 4.20443i 0.200896 + 0.347961i
\(147\) 0 0
\(148\) 1.50079 2.59944i 0.123364 0.213673i
\(149\) −9.52765 + 5.50079i −0.780535 + 0.450642i −0.836620 0.547784i \(-0.815472\pi\)
0.0560848 + 0.998426i \(0.482138\pi\)
\(150\) −6.16618 16.4464i −0.503467 1.34284i
\(151\) 0.719988 1.24706i 0.0585918 0.101484i −0.835242 0.549883i \(-0.814672\pi\)
0.893834 + 0.448399i \(0.148006\pi\)
\(152\) 0.892369 1.54563i 0.0723807 0.125367i
\(153\) −1.67758 + 1.46368i −0.135624 + 0.118332i
\(154\) 0 0
\(155\) 11.8339 6.83228i 0.950518 0.548782i
\(156\) −1.73205 4.61971i −0.138675 0.369873i
\(157\) 16.6071i 1.32539i 0.748890 + 0.662695i \(0.230587\pi\)
−0.748890 + 0.662695i \(0.769413\pi\)
\(158\) 3.63613i 0.289275i
\(159\) 0 0
\(160\) −3.36980 + 1.94556i −0.266406 + 0.153810i
\(161\) 0 0
\(162\) 3.40192 + 8.33228i 0.267280 + 0.654646i
\(163\) 6.19773 10.7348i 0.485444 0.840813i −0.514416 0.857541i \(-0.671991\pi\)
0.999860 + 0.0167274i \(0.00532476\pi\)
\(164\) −5.24705 + 9.08816i −0.409726 + 0.709666i
\(165\) 16.8915 20.5292i 1.31500 1.59820i
\(166\) 6.98012 4.02998i 0.541763 0.312787i
\(167\) 5.86087 10.1513i 0.453528 0.785534i −0.545074 0.838388i \(-0.683498\pi\)
0.998602 + 0.0528541i \(0.0168318\pi\)
\(168\) 0 0
\(169\) −2.44304 4.23147i −0.187926 0.325498i
\(170\) −2.50079 1.44383i −0.191802 0.110737i
\(171\) 1.73391 5.06568i 0.132595 0.387383i
\(172\) −0.471521 0.816699i −0.0359532 0.0622727i
\(173\) −16.7710 −1.27507 −0.637536 0.770420i \(-0.720046\pi\)
−0.637536 + 0.770420i \(0.720046\pi\)
\(174\) 0.820992 4.93374i 0.0622393 0.374026i
\(175\) 0 0
\(176\) −3.41614 1.97231i −0.257501 0.148668i
\(177\) −0.0282675 0.0232586i −0.00212472 0.00174822i
\(178\) 8.02499 + 4.63323i 0.601499 + 0.347275i
\(179\) −5.00158 + 2.88766i −0.373835 + 0.215834i −0.675133 0.737696i \(-0.735914\pi\)
0.301297 + 0.953530i \(0.402580\pi\)
\(180\) −8.79598 + 7.67448i −0.655614 + 0.572022i
\(181\) 5.53310i 0.411272i −0.978629 0.205636i \(-0.934074\pi\)
0.978629 0.205636i \(-0.0659263\pi\)
\(182\) 0 0
\(183\) 2.71726 3.30244i 0.200865 0.244123i
\(184\) 3.12656 + 5.41535i 0.230493 + 0.399225i
\(185\) 11.6795 0.858692
\(186\) −4.69694 3.86466i −0.344396 0.283371i
\(187\) 2.92737i 0.214070i
\(188\) −2.18525 −0.159376
\(189\) 0 0
\(190\) 6.94462 0.503816
\(191\) 6.21372i 0.449609i −0.974404 0.224805i \(-0.927826\pi\)
0.974404 0.224805i \(-0.0721744\pi\)
\(192\) 1.33750 + 1.10050i 0.0965257 + 0.0794216i
\(193\) −7.80542 −0.561847 −0.280923 0.959730i \(-0.590641\pi\)
−0.280923 + 0.959730i \(0.590641\pi\)
\(194\) 9.40980 + 16.2983i 0.675584 + 1.17015i
\(195\) 12.1977 14.8246i 0.873497 1.06161i
\(196\) 0 0
\(197\) 12.7737i 0.910092i 0.890468 + 0.455046i \(0.150377\pi\)
−0.890468 + 0.455046i \(0.849623\pi\)
\(198\) −11.1962 3.83228i −0.795676 0.272348i
\(199\) −1.56925 + 0.906005i −0.111241 + 0.0642250i −0.554588 0.832125i \(-0.687124\pi\)
0.443347 + 0.896350i \(0.353791\pi\)
\(200\) −8.78217 5.07039i −0.620993 0.358530i
\(201\) −17.9884 14.8009i −1.26880 1.04397i
\(202\) 7.17206 + 4.14079i 0.504624 + 0.291345i
\(203\) 0 0
\(204\) −0.210992 + 1.26795i −0.0147724 + 0.0887742i
\(205\) −40.8338 −2.85195
\(206\) 8.52435 + 14.7646i 0.593919 + 1.02870i
\(207\) 12.3331 + 14.1353i 0.857208 + 0.982474i
\(208\) −2.46687 1.42425i −0.171047 0.0987537i
\(209\) 3.52006 + 6.09692i 0.243487 + 0.421732i
\(210\) 0 0
\(211\) −1.88766 + 3.26953i −0.129952 + 0.225083i −0.923658 0.383218i \(-0.874816\pi\)
0.793706 + 0.608302i \(0.208149\pi\)
\(212\) 0 0
\(213\) −2.13832 + 2.59882i −0.146515 + 0.178068i
\(214\) −7.16846 + 12.4161i −0.490026 + 0.848750i
\(215\) 1.83474 3.17787i 0.125128 0.216729i
\(216\) 4.57324 + 2.46687i 0.311170 + 0.167849i
\(217\) 0 0
\(218\) −9.76874 + 5.63998i −0.661622 + 0.381988i
\(219\) 8.29481 + 1.38029i 0.560511 + 0.0932712i
\(220\) 15.3490i 1.03483i
\(221\) 2.11392i 0.142197i
\(222\) −1.82513 4.86799i −0.122495 0.326718i
\(223\) −11.0662 + 6.38910i −0.741051 + 0.427846i −0.822451 0.568836i \(-0.807394\pi\)
0.0814006 + 0.996681i \(0.474061\pi\)
\(224\) 0 0
\(225\) −28.7829 9.85197i −1.91886 0.656798i
\(226\) −4.91614 + 8.51501i −0.327017 + 0.566410i
\(227\) 9.99110 17.3051i 0.663133 1.14858i −0.316655 0.948541i \(-0.602560\pi\)
0.979788 0.200039i \(-0.0641068\pi\)
\(228\) −1.08523 2.89450i −0.0718708 0.191693i
\(229\) 8.77402 5.06568i 0.579804 0.334750i −0.181252 0.983437i \(-0.558015\pi\)
0.761055 + 0.648687i \(0.224682\pi\)
\(230\) −12.1658 + 21.0718i −0.802188 + 1.38943i
\(231\) 0 0
\(232\) −1.44383 2.50079i −0.0947921 0.164185i
\(233\) −6.33070 3.65503i −0.414738 0.239449i 0.278085 0.960556i \(-0.410300\pi\)
−0.692824 + 0.721107i \(0.743634\pi\)
\(234\) −8.08498 2.76737i −0.528532 0.180909i
\(235\) −4.25153 7.36387i −0.277339 0.480366i
\(236\) −0.0211346 −0.00137575
\(237\) −4.86332 4.00156i −0.315906 0.259929i
\(238\) 0 0
\(239\) 7.28317 + 4.20494i 0.471109 + 0.271995i 0.716704 0.697378i \(-0.245650\pi\)
−0.245595 + 0.969373i \(0.578983\pi\)
\(240\) −1.10628 + 6.64819i −0.0714103 + 0.429139i
\(241\) −7.75277 4.47607i −0.499400 0.288329i 0.229066 0.973411i \(-0.426433\pi\)
−0.728466 + 0.685082i \(0.759766\pi\)
\(242\) 3.94910 2.28001i 0.253858 0.146565i
\(243\) 14.8882 + 4.61960i 0.955080 + 0.296347i
\(244\) 2.46911i 0.158069i
\(245\) 0 0
\(246\) 6.38103 + 17.0194i 0.406840 + 1.08512i
\(247\) 2.54191 + 4.40271i 0.161738 + 0.280138i
\(248\) −3.51174 −0.222995
\(249\) 2.29153 13.7709i 0.145220 0.872695i
\(250\) 20.0033i 1.26512i
\(251\) −12.6432 −0.798033 −0.399017 0.916944i \(-0.630648\pi\)
−0.399017 + 0.916944i \(0.630648\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) 2.94462i 0.184762i
\(255\) −4.68324 + 1.75587i −0.293276 + 0.109957i
\(256\) 1.00000 0.0625000
\(257\) 8.15329 + 14.1219i 0.508588 + 0.880900i 0.999951 + 0.00994523i \(0.00316572\pi\)
−0.491362 + 0.870955i \(0.663501\pi\)
\(258\) −1.61124 0.268117i −0.100312 0.0166922i
\(259\) 0 0
\(260\) 11.0838i 0.687389i
\(261\) −5.69536 6.52765i −0.352534 0.404051i
\(262\) −13.0468 + 7.53255i −0.806032 + 0.465363i
\(263\) −20.5434 11.8608i −1.26676 0.731366i −0.292389 0.956300i \(-0.594450\pi\)
−0.974374 + 0.224934i \(0.927783\pi\)
\(264\) −6.39742 + 2.39856i −0.393734 + 0.147621i
\(265\) 0 0
\(266\) 0 0
\(267\) 15.0284 5.63455i 0.919725 0.344829i
\(268\) −13.4493 −0.821544
\(269\) 3.64144 + 6.30716i 0.222022 + 0.384554i 0.955422 0.295244i \(-0.0954009\pi\)
−0.733400 + 0.679798i \(0.762068\pi\)
\(270\) 0.584648 + 20.2104i 0.0355805 + 1.22996i
\(271\) 19.6483 + 11.3440i 1.19355 + 0.689097i 0.959110 0.283033i \(-0.0913407\pi\)
0.234441 + 0.972130i \(0.424674\pi\)
\(272\) 0.371058 + 0.642692i 0.0224987 + 0.0389689i
\(273\) 0 0
\(274\) 7.85997 13.6139i 0.474838 0.822444i
\(275\) 34.6423 20.0007i 2.08901 1.20609i
\(276\) 10.6838 + 1.77782i 0.643089 + 0.107012i
\(277\) −12.0838 + 20.9298i −0.726046 + 1.25755i 0.232496 + 0.972597i \(0.425311\pi\)
−0.958542 + 0.284951i \(0.908023\pi\)
\(278\) −1.65337 + 2.86373i −0.0991628 + 0.171755i
\(279\) −10.3380 + 2.02910i −0.618917 + 0.121479i
\(280\) 0 0
\(281\) −4.11229 + 2.37423i −0.245319 + 0.141635i −0.617619 0.786478i \(-0.711903\pi\)
0.372300 + 0.928112i \(0.378569\pi\)
\(282\) −2.40487 + 2.92277i −0.143208 + 0.174049i
\(283\) 29.3853i 1.74677i −0.487027 0.873387i \(-0.661919\pi\)
0.487027 0.873387i \(-0.338081\pi\)
\(284\) 1.94304i 0.115298i
\(285\) 7.64254 9.28842i 0.452705 0.550198i
\(286\) 9.73085 5.61811i 0.575398 0.332206i
\(287\) 0 0
\(288\) 2.94383 0.577806i 0.173467 0.0340475i
\(289\) 8.22463 14.2455i 0.483802 0.837969i
\(290\) 5.61811 9.73085i 0.329907 0.571415i
\(291\) 32.1544 + 5.35061i 1.88492 + 0.313658i
\(292\) 4.20443 2.42743i 0.246046 0.142055i
\(293\) −3.31206 + 5.73666i −0.193493 + 0.335139i −0.946405 0.322981i \(-0.895315\pi\)
0.752913 + 0.658121i \(0.228648\pi\)
\(294\) 0 0
\(295\) −0.0411186 0.0712195i −0.00239402 0.00414656i
\(296\) −2.59944 1.50079i −0.151090 0.0872316i
\(297\) −17.4470 + 10.7574i −1.01238 + 0.624209i
\(298\) 5.50079 + 9.52765i 0.318652 + 0.551922i
\(299\) −17.8119 −1.03009
\(300\) −16.4464 + 6.16618i −0.949533 + 0.356005i
\(301\) 0 0
\(302\) −1.24706 0.719988i −0.0717600 0.0414307i
\(303\) 13.4311 5.03569i 0.771599 0.289293i
\(304\) −1.54563 0.892369i −0.0886479 0.0511809i
\(305\) 8.32043 4.80380i 0.476426 0.275065i
\(306\) 1.46368 + 1.67758i 0.0836733 + 0.0959007i
\(307\) 21.7242i 1.23987i 0.784655 + 0.619933i \(0.212840\pi\)
−0.784655 + 0.619933i \(0.787160\pi\)
\(308\) 0 0
\(309\) 29.1287 + 4.84712i 1.65707 + 0.275743i
\(310\) −6.83228 11.8339i −0.388048 0.672118i
\(311\) 6.29800 0.357127 0.178563 0.983928i \(-0.442855\pi\)
0.178563 + 0.983928i \(0.442855\pi\)
\(312\) −4.61971 + 1.73205i −0.261540 + 0.0980581i
\(313\) 22.2191i 1.25590i 0.778256 + 0.627948i \(0.216105\pi\)
−0.778256 + 0.627948i \(0.783895\pi\)
\(314\) 16.6071 0.937192
\(315\) 0 0
\(316\) −3.63613 −0.204548
\(317\) 15.6614i 0.879632i 0.898088 + 0.439816i \(0.144956\pi\)
−0.898088 + 0.439816i \(0.855044\pi\)
\(318\) 0 0
\(319\) 11.3907 0.637758
\(320\) 1.94556 + 3.36980i 0.108760 + 0.188378i
\(321\) 8.71769 + 23.2518i 0.486574 + 1.29779i
\(322\) 0 0
\(323\) 1.32448i 0.0736963i
\(324\) 8.33228 3.40192i 0.462905 0.188996i
\(325\) 25.0159 14.4430i 1.38763 0.801151i
\(326\) −10.7348 6.19773i −0.594545 0.343260i
\(327\) −3.20701 + 19.2725i −0.177348 + 1.06577i
\(328\) 9.08816 + 5.24705i 0.501810 + 0.289720i
\(329\) 0 0
\(330\) −20.5292 16.8915i −1.13010 0.929847i
\(331\) 1.27226 0.0699296 0.0349648 0.999389i \(-0.488868\pi\)
0.0349648 + 0.999389i \(0.488868\pi\)
\(332\) −4.02998 6.98012i −0.221174 0.383084i
\(333\) −8.51948 2.91610i −0.466865 0.159801i
\(334\) −10.1513 5.86087i −0.555456 0.320693i
\(335\) −26.1663 45.3214i −1.42962 2.47617i
\(336\) 0 0
\(337\) −3.78001 + 6.54717i −0.205910 + 0.356647i −0.950422 0.310962i \(-0.899349\pi\)
0.744512 + 0.667609i \(0.232682\pi\)
\(338\) −4.23147 + 2.44304i −0.230162 + 0.132884i
\(339\) 5.97860 + 15.9461i 0.324713 + 0.866072i
\(340\) −1.44383 + 2.50079i −0.0783027 + 0.135624i
\(341\) 6.92623 11.9966i 0.375076 0.649651i
\(342\) −5.06568 1.73391i −0.273921 0.0937592i
\(343\) 0 0
\(344\) −0.816699 + 0.471521i −0.0440334 + 0.0254227i
\(345\) 14.7950 + 39.4612i 0.796537 + 2.12452i
\(346\) 16.7710i 0.901613i
\(347\) 22.1091i 1.18688i −0.804879 0.593439i \(-0.797770\pi\)
0.804879 0.593439i \(-0.202230\pi\)
\(348\) −4.93374 0.820992i −0.264476 0.0440098i
\(349\) 12.7682 7.37173i 0.683467 0.394600i −0.117693 0.993050i \(-0.537550\pi\)
0.801160 + 0.598450i \(0.204217\pi\)
\(350\) 0 0
\(351\) −12.5989 + 7.76816i −0.672478 + 0.414634i
\(352\) −1.97231 + 3.41614i −0.105124 + 0.182081i
\(353\) −8.63881 + 14.9629i −0.459798 + 0.796393i −0.998950 0.0458154i \(-0.985411\pi\)
0.539152 + 0.842208i \(0.318745\pi\)
\(354\) −0.0232586 + 0.0282675i −0.00123618 + 0.00150240i
\(355\) −6.54767 + 3.78030i −0.347514 + 0.200638i
\(356\) 4.63323 8.02499i 0.245561 0.425324i
\(357\) 0 0
\(358\) 2.88766 + 5.00158i 0.152618 + 0.264342i
\(359\) −9.45088 5.45647i −0.498799 0.287982i 0.229419 0.973328i \(-0.426318\pi\)
−0.728217 + 0.685346i \(0.759651\pi\)
\(360\) 7.67448 + 8.79598i 0.404481 + 0.463589i
\(361\) −7.90736 13.6959i −0.416177 0.720839i
\(362\) −5.53310 −0.290813
\(363\) 1.29646 7.79106i 0.0680466 0.408925i
\(364\) 0 0
\(365\) 16.3599 + 9.44541i 0.856318 + 0.494395i
\(366\) −3.30244 2.71726i −0.172621 0.142033i
\(367\) 30.9407 + 17.8636i 1.61509 + 0.932472i 0.988166 + 0.153391i \(0.0490194\pi\)
0.626923 + 0.779081i \(0.284314\pi\)
\(368\) 5.41535 3.12656i 0.282295 0.162983i
\(369\) 29.7858 + 10.1952i 1.55059 + 0.530743i
\(370\) 11.6795i 0.607187i
\(371\) 0 0
\(372\) −3.86466 + 4.69694i −0.200373 + 0.243525i
\(373\) 16.0300 + 27.7648i 0.830003 + 1.43761i 0.898035 + 0.439923i \(0.144994\pi\)
−0.0680328 + 0.997683i \(0.521672\pi\)
\(374\) −2.92737 −0.151371
\(375\) −26.7544 22.0136i −1.38159 1.13678i
\(376\) 2.18525i 0.112696i
\(377\) 8.22549 0.423634
\(378\) 0 0
\(379\) 34.8891 1.79214 0.896068 0.443918i \(-0.146412\pi\)
0.896068 + 0.443918i \(0.146412\pi\)
\(380\) 6.94462i 0.356251i
\(381\) −3.93842 3.24055i −0.201772 0.166018i
\(382\) −6.21372 −0.317922
\(383\) 8.76711 + 15.1851i 0.447978 + 0.775921i 0.998254 0.0590616i \(-0.0188108\pi\)
−0.550276 + 0.834983i \(0.685477\pi\)
\(384\) 1.10050 1.33750i 0.0561596 0.0682539i
\(385\) 0 0
\(386\) 7.80542i 0.397286i
\(387\) −2.13178 + 1.85997i −0.108364 + 0.0945477i
\(388\) 16.2983 9.40980i 0.827418 0.477710i
\(389\) 6.60060 + 3.81086i 0.334664 + 0.193218i 0.657910 0.753097i \(-0.271441\pi\)
−0.323246 + 0.946315i \(0.604774\pi\)
\(390\) −14.8246 12.1977i −0.750672 0.617656i
\(391\) 4.01882 + 2.32027i 0.203241 + 0.117341i
\(392\) 0 0
\(393\) −4.28317 + 25.7396i −0.216057 + 1.29839i
\(394\) 12.7737 0.643532
\(395\) −7.07430 12.2530i −0.355947 0.616517i
\(396\) −3.83228 + 11.1962i −0.192579 + 0.562628i
\(397\) −32.6032 18.8234i −1.63631 0.944722i −0.982090 0.188414i \(-0.939665\pi\)
−0.654216 0.756307i \(-0.727001\pi\)
\(398\) 0.906005 + 1.56925i 0.0454139 + 0.0786592i
\(399\) 0 0
\(400\) −5.07039 + 8.78217i −0.253519 + 0.439108i
\(401\) −18.5689 + 10.7207i −0.927284 + 0.535368i −0.885952 0.463778i \(-0.846494\pi\)
−0.0413326 + 0.999145i \(0.513160\pi\)
\(402\) −14.8009 + 17.9884i −0.738202 + 0.897178i
\(403\) 5.00158 8.66299i 0.249146 0.431534i
\(404\) 4.14079 7.17206i 0.206012 0.356823i
\(405\) 27.6747 + 21.4595i 1.37517 + 1.06633i
\(406\) 0 0
\(407\) 10.2538 5.92004i 0.508262 0.293445i
\(408\) 1.26795 + 0.210992i 0.0627728 + 0.0104456i
\(409\) 29.5703i 1.46216i −0.682293 0.731079i \(-0.739017\pi\)
0.682293 0.731079i \(-0.260983\pi\)
\(410\) 40.8338i 2.01664i
\(411\) −9.55865 25.4947i −0.471493 1.25756i
\(412\) 14.7646 8.52435i 0.727400 0.419964i
\(413\) 0 0
\(414\) 14.1353 12.3331i 0.694714 0.606137i
\(415\) 15.6811 27.1605i 0.769755 1.33325i
\(416\) −1.42425 + 2.46687i −0.0698294 + 0.120948i
\(417\) 2.01070 + 5.36291i 0.0984642 + 0.262623i
\(418\) 6.09692 3.52006i 0.298210 0.172172i
\(419\) −3.56481 + 6.17443i −0.174152 + 0.301641i −0.939868 0.341539i \(-0.889052\pi\)
0.765715 + 0.643180i \(0.222385\pi\)
\(420\) 0 0
\(421\) −2.31007 4.00115i −0.112586 0.195004i 0.804226 0.594323i \(-0.202580\pi\)
−0.916812 + 0.399319i \(0.869247\pi\)
\(422\) 3.26953 + 1.88766i 0.159158 + 0.0918899i
\(423\) 1.26265 + 6.43301i 0.0613922 + 0.312784i
\(424\) 0 0
\(425\) −7.52564 −0.365047
\(426\) 2.59882 + 2.13832i 0.125913 + 0.103602i
\(427\) 0 0
\(428\) 12.4161 + 7.16846i 0.600157 + 0.346501i
\(429\) 3.19458 19.1977i 0.154236 0.926875i
\(430\) −3.17787 1.83474i −0.153250 0.0884792i
\(431\) −3.47078 + 2.00385i −0.167181 + 0.0965223i −0.581256 0.813721i \(-0.697439\pi\)
0.414075 + 0.910243i \(0.364105\pi\)
\(432\) 2.46687 4.57324i 0.118687 0.220030i
\(433\) 29.4125i 1.41348i −0.707475 0.706738i \(-0.750166\pi\)
0.707475 0.706738i \(-0.249834\pi\)
\(434\) 0 0
\(435\) −6.83228 18.2230i −0.327583 0.873726i
\(436\) 5.63998 + 9.76874i 0.270106 + 0.467838i
\(437\) −11.1602 −0.533863
\(438\) 1.38029 8.29481i 0.0659527 0.396341i
\(439\) 21.3769i 1.02027i −0.860096 0.510133i \(-0.829596\pi\)
0.860096 0.510133i \(-0.170404\pi\)
\(440\) −15.3490 −0.731733
\(441\) 0 0
\(442\) −2.11392 −0.100549
\(443\) 5.83386i 0.277175i 0.990350 + 0.138587i \(0.0442562\pi\)
−0.990350 + 0.138587i \(0.955744\pi\)
\(444\) −4.86799 + 1.82513i −0.231024 + 0.0866171i
\(445\) 36.0569 1.70926
\(446\) 6.38910 + 11.0662i 0.302533 + 0.524002i
\(447\) 18.7968 + 3.12786i 0.889059 + 0.147943i
\(448\) 0 0
\(449\) 22.5823i 1.06573i −0.846202 0.532863i \(-0.821116\pi\)
0.846202 0.532863i \(-0.178884\pi\)
\(450\) −9.85197 + 28.7829i −0.464427 + 1.35684i
\(451\) −35.8493 + 20.6976i −1.68808 + 0.974613i
\(452\) 8.51501 + 4.91614i 0.400512 + 0.231236i
\(453\) −2.33537 + 0.875590i −0.109725 + 0.0411388i
\(454\) −17.3051 9.99110i −0.812168 0.468906i
\(455\) 0 0
\(456\) −2.89450 + 1.08523i −0.135548 + 0.0508203i
\(457\) 39.8623 1.86468 0.932340 0.361584i \(-0.117764\pi\)
0.932340 + 0.361584i \(0.117764\pi\)
\(458\) −5.06568 8.77402i −0.236704 0.409983i
\(459\) 3.85454 0.111505i 0.179915 0.00520459i
\(460\) 21.0718 + 12.1658i 0.982476 + 0.567233i
\(461\) −3.68254 6.37834i −0.171513 0.297069i 0.767436 0.641125i \(-0.221532\pi\)
−0.938949 + 0.344056i \(0.888199\pi\)
\(462\) 0 0
\(463\) −14.3457 + 24.8475i −0.666702 + 1.15476i 0.312119 + 0.950043i \(0.398961\pi\)
−0.978821 + 0.204718i \(0.934372\pi\)
\(464\) −2.50079 + 1.44383i −0.116096 + 0.0670282i
\(465\) −23.3467 3.88498i −1.08268 0.180162i
\(466\) −3.65503 + 6.33070i −0.169316 + 0.293264i
\(467\) 6.83519 11.8389i 0.316295 0.547839i −0.663417 0.748250i \(-0.730894\pi\)
0.979712 + 0.200411i \(0.0642278\pi\)
\(468\) −2.76737 + 8.08498i −0.127922 + 0.373728i
\(469\) 0 0
\(470\) −7.36387 + 4.25153i −0.339670 + 0.196109i
\(471\) 18.2761 22.2119i 0.842117 1.02347i
\(472\) 0.0211346i 0.000972799i
\(473\) 3.71994i 0.171043i
\(474\) −4.00156 + 4.86332i −0.183798 + 0.223380i
\(475\) 15.6739 9.04931i 0.719166 0.415211i
\(476\) 0 0
\(477\) 0 0
\(478\) 4.20494 7.28317i 0.192329 0.333124i
\(479\) 5.20537 9.01596i 0.237839 0.411950i −0.722255 0.691627i \(-0.756894\pi\)
0.960094 + 0.279677i \(0.0902275\pi\)
\(480\) 6.64819 + 1.10628i 0.303447 + 0.0504947i
\(481\) 7.40449 4.27499i 0.337616 0.194923i
\(482\) −4.47607 + 7.75277i −0.203879 + 0.353129i
\(483\) 0 0
\(484\) −2.28001 3.94910i −0.103637 0.179504i
\(485\) 63.4184 + 36.6146i 2.87968 + 1.66258i
\(486\) 4.61960 14.8882i 0.209549 0.675344i
\(487\) −1.16925 2.02520i −0.0529838 0.0917707i 0.838317 0.545183i \(-0.183540\pi\)
−0.891301 + 0.453412i \(0.850207\pi\)
\(488\) −2.46911 −0.111772
\(489\) −20.1031 + 7.53716i −0.909092 + 0.340842i
\(490\) 0 0
\(491\) −29.3448 16.9422i −1.32431 0.764591i −0.339898 0.940462i \(-0.610392\pi\)
−0.984413 + 0.175871i \(0.943726\pi\)
\(492\) 17.0194 6.38103i 0.767295 0.287679i
\(493\) −1.85588 1.07149i −0.0835845 0.0482575i
\(494\) 4.40271 2.54191i 0.198087 0.114366i
\(495\) −45.1848 + 8.86872i −2.03090 + 0.398619i
\(496\) 3.51174i 0.157682i
\(497\) 0 0
\(498\) −13.7709 2.29153i −0.617088 0.102686i
\(499\) 8.30223 + 14.3799i 0.371659 + 0.643732i 0.989821 0.142319i \(-0.0454558\pi\)
−0.618162 + 0.786051i \(0.712123\pi\)
\(500\) −20.0033 −0.894576
\(501\) −19.0104 + 7.12751i −0.849324 + 0.318434i
\(502\) 12.6432i 0.564295i
\(503\) −35.3661 −1.57690 −0.788449 0.615100i \(-0.789115\pi\)
−0.788449 + 0.615100i \(0.789115\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 24.6661i 1.09654i
\(507\) −1.38916 + 8.34816i −0.0616950 + 0.370755i
\(508\) −2.94462 −0.130646
\(509\) −18.5291 32.0933i −0.821287 1.42251i −0.904724 0.425998i \(-0.859923\pi\)
0.0834371 0.996513i \(-0.473410\pi\)
\(510\) 1.75587 + 4.68324i 0.0777511 + 0.207377i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −7.89388 + 4.86718i −0.348523 + 0.214891i
\(514\) 14.1219 8.15329i 0.622891 0.359626i
\(515\) 57.4507 + 33.1692i 2.53158 + 1.46161i
\(516\) −0.268117 + 1.61124i −0.0118032 + 0.0709310i
\(517\) −7.46513 4.30999i −0.328316 0.189553i
\(518\) 0 0
\(519\) 22.4311 + 18.4564i 0.984618 + 0.810147i
\(520\) −11.0838 −0.486057
\(521\) −0.891547 1.54420i −0.0390594 0.0676528i 0.845835 0.533445i \(-0.179103\pi\)
−0.884894 + 0.465792i \(0.845769\pi\)
\(522\) −6.52765 + 5.69536i −0.285707 + 0.249279i
\(523\) 20.8312 + 12.0269i 0.910886 + 0.525901i 0.880716 0.473644i \(-0.157062\pi\)
0.0301702 + 0.999545i \(0.490395\pi\)
\(524\) 7.53255 + 13.0468i 0.329061 + 0.569950i
\(525\) 0 0
\(526\) −11.8608 + 20.5434i −0.517154 + 0.895737i
\(527\) −2.25696 + 1.30306i −0.0983149 + 0.0567621i
\(528\) 2.39856 + 6.39742i 0.104384 + 0.278412i
\(529\) 8.05069 13.9442i 0.350030 0.606270i
\(530\) 0 0
\(531\) 0.0122117 + 0.0622167i 0.000529942 + 0.00269998i
\(532\) 0 0
\(533\) −25.8876 + 14.9462i −1.12132 + 0.647392i
\(534\) −5.63455 15.0284i −0.243831 0.650344i
\(535\) 55.7866i 2.41187i
\(536\) 13.4493i 0.580920i
\(537\) 9.86747 + 1.64198i 0.425813 + 0.0708569i
\(538\) 6.30716 3.64144i 0.271921 0.156994i
\(539\) 0 0
\(540\) 20.2104 0.584648i 0.869716 0.0251592i
\(541\) −15.0016 + 25.9835i −0.644968 + 1.11712i 0.339341 + 0.940664i \(0.389796\pi\)
−0.984309 + 0.176454i \(0.943537\pi\)
\(542\) 11.3440 19.6483i 0.487265 0.843968i
\(543\) −6.08917 + 7.40051i −0.261311 + 0.317586i
\(544\) 0.642692 0.371058i 0.0275552 0.0159090i
\(545\) −21.9458 + 38.0113i −0.940056 + 1.62822i
\(546\) 0 0
\(547\) −10.7816 18.6743i −0.460987 0.798454i 0.538023 0.842930i \(-0.319171\pi\)
−0.999010 + 0.0444765i \(0.985838\pi\)
\(548\) −13.6139 7.85997i −0.581556 0.335761i
\(549\) −7.26865 + 1.42667i −0.310219 + 0.0608887i
\(550\) −20.0007 34.6423i −0.852835 1.47715i
\(551\) 5.15372 0.219556
\(552\) 1.77782 10.6838i 0.0756692 0.454733i
\(553\) 0 0
\(554\) 20.9298 + 12.0838i 0.889221 + 0.513392i
\(555\) −15.6213 12.8533i −0.663087 0.545590i
\(556\) 2.86373 + 1.65337i 0.121449 + 0.0701187i
\(557\) −31.9976 + 18.4738i −1.35578 + 0.782762i −0.989052 0.147565i \(-0.952856\pi\)
−0.366731 + 0.930327i \(0.619523\pi\)
\(558\) 2.02910 + 10.3380i 0.0858987 + 0.437640i
\(559\) 2.68625i 0.113616i
\(560\) 0 0
\(561\) −3.22157 + 3.91535i −0.136015 + 0.165306i
\(562\) 2.37423 + 4.11229i 0.100151 + 0.173467i
\(563\) −15.1684 −0.639273 −0.319637 0.947540i \(-0.603561\pi\)
−0.319637 + 0.947540i \(0.603561\pi\)
\(564\) 2.92277 + 2.40487i 0.123071 + 0.101263i
\(565\) 38.2585i 1.60955i
\(566\) −29.3853 −1.23516
\(567\) 0 0
\(568\) 1.94304 0.0815282
\(569\) 36.7292i 1.53977i −0.638183 0.769885i \(-0.720314\pi\)
0.638183 0.769885i \(-0.279686\pi\)
\(570\) −9.28842 7.64254i −0.389049 0.320111i
\(571\) 11.2277 0.469866 0.234933 0.972012i \(-0.424513\pi\)
0.234933 + 0.972012i \(0.424513\pi\)
\(572\) −5.61811 9.73085i −0.234905 0.406867i
\(573\) −6.83819 + 8.31085i −0.285670 + 0.347191i
\(574\) 0 0
\(575\) 63.4114i 2.64444i
\(576\) −0.577806 2.94383i −0.0240752 0.122660i
\(577\) 31.6545 18.2757i 1.31780 0.760829i 0.334422 0.942424i \(-0.391459\pi\)
0.983374 + 0.181594i \(0.0581257\pi\)
\(578\) −14.2455 8.22463i −0.592534 0.342100i
\(579\) 10.4397 + 8.58986i 0.433861 + 0.356982i
\(580\) −9.73085 5.61811i −0.404052 0.233279i
\(581\) 0 0
\(582\) 5.35061 32.1544i 0.221790 1.33284i
\(583\) 0 0
\(584\) −2.42743 4.20443i −0.100448 0.173981i
\(585\) −32.6289 + 6.40429i −1.34904 + 0.264785i
\(586\) 5.73666 + 3.31206i 0.236979 + 0.136820i
\(587\) 4.99738 + 8.65571i 0.206264 + 0.357259i 0.950535 0.310619i \(-0.100536\pi\)
−0.744271 + 0.667878i \(0.767203\pi\)
\(588\) 0 0
\(589\) 3.13376 5.42784i 0.129124 0.223650i
\(590\) −0.0712195 + 0.0411186i −0.00293206 + 0.00169283i
\(591\) 14.0575 17.0849i 0.578248 0.702778i
\(592\) −1.50079 + 2.59944i −0.0616820 + 0.106836i
\(593\) −3.89111 + 6.73961i −0.159789 + 0.276763i −0.934792 0.355194i \(-0.884415\pi\)
0.775004 + 0.631957i \(0.217748\pi\)
\(594\) 10.7574 + 17.4470i 0.441382 + 0.715860i
\(595\) 0 0
\(596\) 9.52765 5.50079i 0.390268 0.225321i
\(597\) 3.09592 + 0.515173i 0.126708 + 0.0210846i
\(598\) 17.8119i 0.728385i
\(599\) 25.0124i 1.02198i −0.859586 0.510990i \(-0.829279\pi\)
0.859586 0.510990i \(-0.170721\pi\)
\(600\) 6.16618 + 16.4464i 0.251733 + 0.671421i
\(601\) 25.9925 15.0068i 1.06026 0.612139i 0.134753 0.990879i \(-0.456976\pi\)
0.925503 + 0.378740i \(0.123643\pi\)
\(602\) 0 0
\(603\) 7.77106 + 39.5924i 0.316462 + 1.61233i
\(604\) −0.719988 + 1.24706i −0.0292959 + 0.0507420i
\(605\) 8.87179 15.3664i 0.360689 0.624732i
\(606\) −5.03569 13.4311i −0.204561 0.545603i
\(607\) −3.96882 + 2.29140i −0.161089 + 0.0930050i −0.578378 0.815769i \(-0.696314\pi\)
0.417288 + 0.908774i \(0.362981\pi\)
\(608\) −0.892369 + 1.54563i −0.0361903 + 0.0626835i
\(609\) 0 0
\(610\) −4.80380 8.32043i −0.194500 0.336884i
\(611\) −5.39073 3.11234i −0.218085 0.125912i
\(612\) 1.67758 1.46368i 0.0678120 0.0591659i
\(613\) −15.2761 26.4590i −0.616996 1.06867i −0.990031 0.140852i \(-0.955016\pi\)
0.373034 0.927818i \(-0.378317\pi\)
\(614\) 21.7242 0.876717
\(615\) 54.6151 + 44.9375i 2.20229 + 1.81206i
\(616\) 0 0
\(617\) −28.2484 16.3092i −1.13724 0.656585i −0.191493 0.981494i \(-0.561333\pi\)
−0.945745 + 0.324909i \(0.894666\pi\)
\(618\) 4.84712 29.1287i 0.194980 1.17173i
\(619\) 17.3244 + 10.0023i 0.696327 + 0.402024i 0.805978 0.591946i \(-0.201640\pi\)
−0.109651 + 0.993970i \(0.534973\pi\)
\(620\) −11.8339 + 6.83228i −0.475259 + 0.274391i
\(621\) −0.939542 32.4785i −0.0377025 1.30332i
\(622\) 6.29800i 0.252527i
\(623\) 0 0
\(624\) 1.73205 + 4.61971i 0.0693375 + 0.184937i
\(625\) −13.5657 23.4965i −0.542628 0.939859i
\(626\) 22.2191 0.888052
\(627\) 2.00158 12.0284i 0.0799353 0.480369i
\(628\) 16.6071i 0.662695i
\(629\) −2.22752 −0.0888171
\(630\) 0 0
\(631\) 6.09634 0.242692 0.121346 0.992610i \(-0.461279\pi\)
0.121346 + 0.992610i \(0.461279\pi\)
\(632\) 3.63613i 0.144637i
\(633\) 6.12285 2.29562i 0.243362 0.0912426i
\(634\) 15.6614 0.621994
\(635\) −5.72893 9.92279i −0.227345 0.393774i
\(636\) 0 0
\(637\) 0 0
\(638\) 11.3907i 0.450963i
\(639\) 5.71999 1.12270i 0.226279 0.0444134i
\(640\) 3.36980 1.94556i 0.133203 0.0769049i
\(641\) −28.9612 16.7207i −1.14390 0.660429i −0.196504 0.980503i \(-0.562959\pi\)
−0.947393 + 0.320074i \(0.896292\pi\)
\(642\) 23.2518 8.71769i 0.917674 0.344060i
\(643\) −16.6022 9.58527i −0.654726 0.378006i 0.135539 0.990772i \(-0.456724\pi\)
−0.790264 + 0.612766i \(0.790057\pi\)
\(644\) 0 0
\(645\) −5.95121 + 2.23126i −0.234328 + 0.0878559i
\(646\) −1.32448 −0.0521111
\(647\) −22.3025 38.6290i −0.876800 1.51866i −0.854832 0.518904i \(-0.826340\pi\)
−0.0219681 0.999759i \(-0.506993\pi\)
\(648\) −3.40192 8.33228i −0.133640 0.327323i
\(649\) −0.0721988 0.0416840i −0.00283405 0.00163624i
\(650\) −14.4430 25.0159i −0.566500 0.981206i
\(651\) 0 0
\(652\) −6.19773 + 10.7348i −0.242722 + 0.420407i
\(653\) 0.564755 0.326061i 0.0221006 0.0127598i −0.488909 0.872335i \(-0.662605\pi\)
0.511010 + 0.859575i \(0.329272\pi\)
\(654\) 19.2725 + 3.20701i 0.753613 + 0.125404i
\(655\) −29.3100 + 50.7664i −1.14524 + 1.98361i
\(656\) 5.24705 9.08816i 0.204863 0.354833i
\(657\) −9.57529 10.9746i −0.373568 0.428158i
\(658\) 0 0
\(659\) 26.2738 15.1692i 1.02348 0.590908i 0.108372 0.994110i \(-0.465436\pi\)
0.915111 + 0.403202i \(0.132103\pi\)
\(660\) −16.8915 + 20.5292i −0.657501 + 0.799099i
\(661\) 12.8176i 0.498548i −0.968433 0.249274i \(-0.919808\pi\)
0.968433 0.249274i \(-0.0801919\pi\)
\(662\) 1.27226i 0.0494477i
\(663\) −2.32636 + 2.82736i −0.0903484 + 0.109806i
\(664\) −6.98012 + 4.02998i −0.270881 + 0.156393i
\(665\) 0 0
\(666\) −2.91610 + 8.51948i −0.112996 + 0.330123i
\(667\) −9.02843 + 15.6377i −0.349582 + 0.605494i
\(668\) −5.86087 + 10.1513i −0.226764 + 0.392767i
\(669\) 21.8323 + 3.63297i 0.844085 + 0.140459i
\(670\) −45.3214 + 26.1663i −1.75092 + 1.01089i
\(671\) 4.86986 8.43484i 0.187999 0.325623i
\(672\) 0 0
\(673\) 11.2246 + 19.4416i 0.432678 + 0.749420i 0.997103 0.0760644i \(-0.0242355\pi\)
−0.564425 + 0.825484i \(0.690902\pi\)
\(674\) 6.54717 + 3.78001i 0.252188 + 0.145601i
\(675\) 27.6550 + 44.8526i 1.06444 + 1.72638i
\(676\) 2.44304 + 4.23147i 0.0939632 + 0.162749i
\(677\) 51.1807 1.96703 0.983516 0.180820i \(-0.0578752\pi\)
0.983516 + 0.180820i \(0.0578752\pi\)
\(678\) 15.9461 5.97860i 0.612406 0.229607i
\(679\) 0 0
\(680\) 2.50079 + 1.44383i 0.0959009 + 0.0553684i
\(681\) −32.4073 + 12.1503i −1.24185 + 0.465602i
\(682\) −11.9966 6.92623i −0.459373 0.265219i
\(683\) −12.6107 + 7.28080i −0.482536 + 0.278592i −0.721473 0.692443i \(-0.756534\pi\)
0.238937 + 0.971035i \(0.423201\pi\)
\(684\) −1.73391 + 5.06568i −0.0662977 + 0.193691i
\(685\) 61.1681i 2.33711i
\(686\) 0 0
\(687\) −17.3100 2.88045i −0.660419 0.109896i
\(688\) 0.471521 + 0.816699i 0.0179766 + 0.0311363i
\(689\) 0 0
\(690\) 39.4612 14.7950i 1.50226 0.563237i
\(691\) 24.4515i 0.930180i 0.885263 + 0.465090i \(0.153978\pi\)
−0.885263 + 0.465090i \(0.846022\pi\)
\(692\) 16.7710 0.637536
\(693\) 0 0
\(694\) −22.1091 −0.839250
\(695\) 12.8669i 0.488071i
\(696\) −0.820992 + 4.93374i −0.0311196 + 0.187013i
\(697\) 7.78785 0.294986
\(698\) −7.37173 12.7682i −0.279024 0.483284i
\(699\) 4.44495 + 11.8555i 0.168123 + 0.448417i
\(700\) 0 0
\(701\) 2.21697i 0.0837337i −0.999123 0.0418669i \(-0.986669\pi\)
0.999123 0.0418669i \(-0.0133305\pi\)
\(702\) 7.76816 + 12.5989i 0.293190 + 0.475514i
\(703\) 4.63932 2.67851i 0.174975 0.101022i
\(704\) 3.41614 + 1.97231i 0.128751 + 0.0743342i
\(705\) −2.41751 + 14.5280i −0.0910487 + 0.547155i
\(706\) 14.9629 + 8.63881i 0.563135 + 0.325126i
\(707\) 0 0
\(708\) 0.0282675 + 0.0232586i 0.00106236 + 0.000874112i
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) 3.78030 + 6.54767i 0.141872 + 0.245730i
\(711\) 2.10098 + 10.7041i 0.0787927 + 0.401437i
\(712\) −8.02499 4.63323i −0.300749 0.173638i
\(713\) 10.9796 + 19.0173i 0.411190 + 0.712203i
\(714\) 0 0
\(715\) 21.8607 37.8639i 0.817544 1.41603i
\(716\) 5.00158 2.88766i 0.186918 0.107917i
\(717\) −5.11370 13.6392i −0.190975 0.509366i
\(718\) −5.45647 + 9.45088i −0.203634 + 0.352704i
\(719\) −1.11376 + 1.92909i −0.0415363 + 0.0719429i −0.886046 0.463597i \(-0.846559\pi\)
0.844510 + 0.535540i \(0.179892\pi\)
\(720\) 8.79598 7.67448i 0.327807 0.286011i
\(721\) 0 0
\(722\) −13.6959 + 7.90736i −0.509710 + 0.294281i
\(723\) 5.44342 + 14.5186i 0.202443 + 0.539954i
\(724\) 5.53310i 0.205636i
\(725\) 29.2831i 1.08755i
\(726\) −7.79106 1.29646i −0.289153 0.0481162i
\(727\) −10.4880 + 6.05523i −0.388977 + 0.224576i −0.681717 0.731616i \(-0.738766\pi\)
0.292740 + 0.956192i \(0.405433\pi\)
\(728\) 0 0
\(729\) −14.8291 22.5632i −0.549227 0.835673i
\(730\) 9.44541 16.3599i 0.349590 0.605508i
\(731\) −0.349924 + 0.606086i −0.0129424 + 0.0224169i
\(732\) −2.71726 + 3.30244i −0.100433 + 0.122062i
\(733\) 13.5673 7.83306i 0.501118 0.289321i −0.228057 0.973648i \(-0.573237\pi\)
0.729175 + 0.684327i \(0.239904\pi\)
\(734\) 17.8636 30.9407i 0.659357 1.14204i
\(735\) 0 0
\(736\) −3.12656 5.41535i −0.115246 0.199613i
\(737\) −45.9446 26.5261i −1.69239 0.977102i
\(738\) 10.1952 29.7858i 0.375292 1.09643i
\(739\) 4.05227 + 7.01874i 0.149065 + 0.258188i 0.930882 0.365319i \(-0.119040\pi\)
−0.781817 + 0.623508i \(0.785707\pi\)
\(740\) −11.6795 −0.429346
\(741\) 1.44538 8.68599i 0.0530974 0.319088i
\(742\) 0 0
\(743\) −10.5429 6.08697i −0.386783 0.223309i 0.293982 0.955811i \(-0.405019\pi\)
−0.680765 + 0.732502i \(0.738353\pi\)
\(744\) 4.69694 + 3.86466i 0.172198 + 0.141685i
\(745\) 37.0732 + 21.4042i 1.35826 + 0.784189i
\(746\) 27.7648 16.0300i 1.01654 0.586900i
\(747\) −18.2198 + 15.8967i −0.666626 + 0.581631i
\(748\) 2.92737i 0.107035i
\(749\) 0 0
\(750\) −22.0136 + 26.7544i −0.803824 + 0.976934i
\(751\) −17.3062 29.9752i −0.631511 1.09381i −0.987243 0.159221i \(-0.949102\pi\)
0.355732 0.934588i \(-0.384232\pi\)
\(752\) 2.18525 0.0796879
\(753\) 16.9103 + 13.9139i 0.616246 + 0.507049i
\(754\) 8.22549i 0.299555i
\(755\) −5.60311 −0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) 34.8891i 1.26723i
\(759\) 32.9909 + 27.1451i 1.19749 + 0.985303i
\(760\) −6.94462 −0.251908
\(761\) −5.11262 8.85532i −0.185332 0.321005i 0.758356 0.651840i \(-0.226003\pi\)
−0.943688 + 0.330835i \(0.892670\pi\)
\(762\) −3.24055 + 3.93842i −0.117393 + 0.142674i
\(763\) 0 0
\(764\) 6.21372i 0.224805i
\(765\) 8.19615 + 2.80542i 0.296333 + 0.101430i
\(766\) 15.1851 8.76711i 0.548659 0.316769i
\(767\) −0.0521363 0.0301009i −0.00188253 0.00108688i
\(768\) −1.33750 1.10050i −0.0482628 0.0397108i
\(769\) 26.6746 + 15.4006i 0.961910 + 0.555359i 0.896760 0.442517i \(-0.145914\pi\)
0.0651494 + 0.997876i \(0.479248\pi\)
\(770\) 0 0
\(771\) 4.63613 27.8607i 0.166966 1.00338i
\(772\) 7.80542 0.280923
\(773\) −17.8916 30.9892i −0.643518 1.11461i −0.984642 0.174587i \(-0.944141\pi\)
0.341124 0.940018i \(-0.389192\pi\)
\(774\) 1.85997 + 2.13178i 0.0668553 + 0.0766251i
\(775\) −30.8406 17.8059i −1.10783 0.639605i
\(776\) −9.40980 16.2983i −0.337792 0.585073i
\(777\) 0 0
\(778\) 3.81086 6.60060i 0.136626 0.236643i
\(779\) −16.2200 + 9.36461i −0.581141 + 0.335522i
\(780\) −12.1977 + 14.8246i −0.436749 + 0.530805i