Properties

Label 882.2.l.a.509.4
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 509.4
Root \(1.62181 - 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 882.509
Dual form 882.2.l.a.227.8

$q$-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 \(0.169266\pi\)
0.00816625 + 0.999967i \(0.497401\pi\)
\(6\) 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 0.801430 0.598088i \(-0.204073\pi\)
−0.117244 + 0.993103i \(0.537406\pi\)
\(14\) 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 0.817514 0.575909i \(-0.195352\pi\)
−0.907509 + 0.420033i \(0.862018\pi\)
\(18\) 2.94383 0.577806i 0.693868 0.136190i
\(19\) 1.54563 + 0.892369i 0.354591 + 0.204723i 0.666706 0.745321i \(-0.267704\pi\)
−0.312114 + 0.950045i \(0.601037\pi\)
\(20\) −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 \(-0.897874\pi\)
0.948971 0.315363i \(-0.102126\pi\)
\(32\) 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 \(0.472389\pi\)
−0.906087 + 0.423092i \(0.860945\pi\)
\(42\) 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 \(-0.550948\pi\)
−0.159376 + 0.987218i \(0.550948\pi\)
\(48\) 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 \(-0.500438\pi\)
−0.00137575 + 0.999999i \(0.500438\pi\)
\(60\) 1.10628 6.64819i 0.142821 0.858278i
\(61\) 2.46911i 0.316138i −0.987428 0.158069i \(-0.949473\pi\)
0.987428 0.158069i \(-0.0505268\pi\)
\(62\) −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 −0.233350 0.972393i \(-0.574969\pi\)
0.725442 + 0.688284i \(0.241636\pi\)
\(74\) 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 0.555516 0.831506i \(-0.312521\pi\)
−0.997863 + 0.0653378i \(0.979188\pi\)
\(84\) 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 −0.508826 0.860869i \(-0.669920\pi\)
0.999948 + 0.0102218i \(0.00325375\pi\)
\(90\) 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 \(-0.262069\pi\)
0.975043 0.222018i \(-0.0712643\pi\)
\(98\) 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 −0.583087 0.812410i \(-0.698155\pi\)
0.995111 + 0.0987631i \(0.0314886\pi\)
\(102\) −1.26795 0.210992i −0.125546 0.0208913i
\(103\) 14.7646 8.52435i 1.45480 0.839929i 0.456051 0.889953i \(-0.349263\pi\)
0.998748 + 0.0500247i \(0.0159300\pi\)
\(104\) −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 \(0.0619823\pi\)
−0.322979 + 0.946406i \(0.604684\pi\)
\(132\) 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 0.616508 0.787349i \(-0.288547\pi\)
−0.373610 + 0.927586i \(0.621880\pi\)
\(140\) 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 \(-0.769413\pi\)
0.748890 0.662695i \(-0.230587\pi\)
\(158\) 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 −0.998602 0.0528541i \(-0.983168\pi\)
0.545074 + 0.838388i \(0.316502\pi\)
\(168\) 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 \(-0.279954\pi\)
0.637536 + 0.770420i \(0.279954\pi\)
\(174\) −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 \(0.0659263\pi\)
−0.978629 + 0.205636i \(0.934074\pi\)
\(182\) 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 −0.443347 0.896350i \(-0.646209\pi\)
0.554588 + 0.832125i \(0.312876\pi\)
\(200\) −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 −0.0814006 0.996681i \(-0.525939\pi\)
0.822451 + 0.568836i \(0.192606\pi\)
\(224\) 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 \(0.397440\pi\)
−0.979788 + 0.200039i \(0.935893\pi\)
\(228\) −1.08523 2.89450i −0.0718708 0.191693i
\(229\) −8.77402 + 5.06568i −0.579804 + 0.334750i −0.761055 0.648687i \(-0.775318\pi\)
0.181252 + 0.983437i \(0.441985\pi\)
\(230\) 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 0.728466 0.685082i \(-0.240234\pi\)
−0.229066 + 0.973411i \(0.573567\pi\)
\(242\) 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 \(-0.369352\pi\)
0.399017 + 0.916944i \(0.369352\pi\)
\(252\) 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 \(-0.996834\pi\)
0.491362 0.870955i \(-0.336499\pi\)
\(258\) 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 0.733400 0.679798i \(-0.237932\pi\)
−0.955422 + 0.295244i \(0.904599\pi\)
\(270\) 0.584648 + 20.2104i 0.0355805 + 1.22996i
\(271\) −19.6483 11.3440i −1.19355 0.689097i −0.234441 0.972130i \(-0.575326\pi\)
−0.959110 + 0.283033i \(0.908659\pi\)
\(272\) −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 \(0.338081\pi\)
−0.487027 + 0.873387i \(0.661919\pi\)
\(284\) 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 −0.752913 0.658121i \(-0.771352\pi\)
0.946405 + 0.322981i \(0.104685\pi\)
\(294\) 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 \(-0.787160\pi\)
0.784655 0.619933i \(-0.212840\pi\)
\(308\) 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 \(-0.557145\pi\)
−0.178563 + 0.983928i \(0.557145\pi\)
\(312\) −4.61971 + 1.73205i −0.261540 + 0.0980581i
\(313\) 22.2191i 1.25590i −0.778256 0.627948i \(-0.783895\pi\)
0.778256 0.627948i \(-0.216105\pi\)
\(314\) −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 −0.801160 0.598450i \(-0.795783\pi\)
0.117693 + 0.993050i \(0.462450\pi\)
\(350\) 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 −0.539152 0.842208i \(-0.681255\pi\)
0.998950 + 0.0458154i \(0.0145886\pi\)
\(354\) −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 \(-0.950981\pi\)
−0.626923 0.779081i \(-0.715686\pi\)
\(368\) 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 0.550276 0.834983i \(-0.314523\pi\)
−0.998254 + 0.0590616i \(0.981189\pi\)
\(384\) −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 \(0.0603348\pi\)
0.654216 + 0.756307i \(0.272999\pi\)
\(398\) −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 \(0.260983\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(410\) 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 −0.765715 0.643180i \(-0.777615\pi\)
0.939868 + 0.341539i \(0.110948\pi\)
\(420\) 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 \(0.249834\pi\)
−0.707475 + 0.706738i \(0.750166\pi\)
\(434\) 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 \(0.170404\pi\)
−0.860096 + 0.510133i \(0.829596\pi\)
\(440\) 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 0.938949 0.344056i \(-0.111801\pi\)
−0.767436 + 0.641125i \(0.778468\pi\)
\(462\) 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 −0.979712 0.200411i \(-0.935772\pi\)
0.663417 + 0.748250i \(0.269106\pi\)
\(468\) 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 −0.960094 0.279677i \(-0.909773\pi\)
0.722255 + 0.691627i \(0.243106\pi\)
\(480\) 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 \(-0.210885\pi\)
0.788449 + 0.615100i \(0.210885\pi\)
\(504\) 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 \(0.140077\pi\)
−0.0834371 + 0.996513i \(0.526590\pi\)
\(510\) −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 0.884894 0.465792i \(-0.154231\pi\)
−0.845835 + 0.533445i \(0.820897\pi\)
\(522\) −6.52765 + 5.69536i −0.285707 + 0.249279i
\(523\) −20.8312 12.0269i −0.910886 0.525901i −0.0301702 0.999545i \(-0.509605\pi\)
−0.880716 + 0.473644i \(0.842938\pi\)
\(524\) −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 \(-0.396439\pi\)
0.319637 + 0.947540i \(0.396439\pi\)
\(564\) 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 −0.983374 0.181594i \(-0.941874\pi\)
−0.334422 + 0.942424i \(0.608541\pi\)
\(578\) −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 0.744271 0.667878i \(-0.232797\pi\)
−0.950535 + 0.310619i \(0.899464\pi\)
\(588\) 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 −0.775004 0.631957i \(-0.782252\pi\)
0.934792 + 0.355194i \(0.115585\pi\)
\(594\) −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 −0.925503 0.378740i \(-0.876357\pi\)
−0.134753 + 0.990879i \(0.543024\pi\)
\(602\) 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 −0.417288 0.908774i \(-0.637019\pi\)
0.578378 + 0.815769i \(0.303686\pi\)
\(608\) 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 0.109651 0.993970i \(-0.465027\pi\)
−0.805978 + 0.591946i \(0.798360\pi\)
\(620\) −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 0.790264 0.612766i \(-0.209943\pi\)
−0.135539 + 0.990772i \(0.543276\pi\)
\(644\) 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 \(0.173660\pi\)
0.0219681 + 0.999759i \(0.493007\pi\)
\(648\) −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 \(0.0801919\pi\)
−0.968433 + 0.249274i \(0.919808\pi\)
\(662\) 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 \(-0.942125\pi\)
−0.983516 + 0.180820i \(0.942125\pi\)
\(678\) −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 \(-0.846022\pi\)
0.885263 0.465090i \(-0.153978\pi\)
\(692\) −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 −0.844510 0.535540i \(-0.820108\pi\)
0.886046 + 0.463597i \(0.153441\pi\)
\(720\) −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 −0.292740 0.956192i \(-0.594567\pi\)
0.681717 + 0.731616i \(0.261234\pi\)
\(728\) 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 −0.729175 0.684327i \(-0.760096\pi\)
0.228057 + 0.973648i \(0.426763\pi\)
\(734\) −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 0.943688 0.330835i \(-0.107330\pi\)
−0.758356 + 0.651840i \(0.773997\pi\)
\(762\) 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 −0.0651494 0.997876i \(-0.520752\pi\)
−0.896760 + 0.442517i \(0.854086\pi\)
\(770\) 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 \(0.0558590\pi\)
−0.341124 + 0.940018i \(0.610808\pi\)
\(774\) 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
\(781\)