Properties

Label 168.2.i.e.125.5
Level 168
Weight 2
Character 168.125
Analytic conductor 1.341
Analytic rank 0
Dimension 8
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.1
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 125.5
Root \(-2.15988 - 0.258819i\) of \(x^{8} - 8 x^{6} + 13 x^{4} + 12 x^{2} + 36\)
Character \(\chi\) \(=\) 168.125
Dual form 168.2.i.e.125.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 1.11803i) q^{2} +(-1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})\) \(q+(0.866025 - 1.11803i) q^{2} +(-1.58114 + 0.707107i) q^{3} +(-0.500000 - 1.93649i) q^{4} -1.41421i q^{5} +(-0.578737 + 2.38014i) q^{6} +(1.00000 - 2.44949i) q^{7} +(-2.59808 - 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +(-1.58114 - 1.22474i) q^{10} -3.46410 q^{11} +(2.15988 + 2.70831i) q^{12} +3.16228 q^{13} +(-1.87259 - 3.23935i) q^{14} +(1.00000 + 2.23607i) q^{15} +(-3.50000 + 1.93649i) q^{16} +(-0.767949 - 4.17256i) q^{18} +3.16228 q^{19} +(-2.73861 + 0.707107i) q^{20} +(0.150912 + 4.58009i) q^{21} +(-3.00000 + 3.87298i) q^{22} +4.47214i q^{23} +(4.89849 - 0.0693504i) q^{24} +3.00000 q^{25} +(2.73861 - 3.53553i) q^{26} +(-1.58114 + 4.94975i) q^{27} +(-5.24342 - 0.711747i) q^{28} +6.92820 q^{29} +(3.36603 + 0.818458i) q^{30} +4.89898i q^{31} +(-0.866025 + 5.59017i) q^{32} +(5.47723 - 2.44949i) q^{33} +(-3.46410 - 1.41421i) q^{35} +(-5.33013 - 2.75495i) q^{36} +(2.73861 - 3.53553i) q^{38} +(-5.00000 + 2.23607i) q^{39} +(-1.58114 + 3.67423i) q^{40} -10.9545 q^{41} +(5.25139 + 3.79775i) q^{42} -7.74597i q^{43} +(1.73205 + 6.70820i) q^{44} +(-3.16228 - 2.82843i) q^{45} +(5.00000 + 3.87298i) q^{46} +10.9545 q^{47} +(4.16468 - 5.53674i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(2.59808 - 3.35410i) q^{50} +(-1.58114 - 6.12372i) q^{52} +(4.16468 + 6.05437i) q^{54} +4.89898i q^{55} +(-5.33669 + 5.24593i) q^{56} +(-5.00000 + 2.23607i) q^{57} +(6.00000 - 7.74597i) q^{58} -9.89949i q^{59} +(3.83013 - 3.05453i) q^{60} +3.16228 q^{61} +(5.47723 + 4.24264i) q^{62} +(-3.47723 - 7.13505i) q^{63} +(5.50000 + 5.80948i) q^{64} -4.47214i q^{65} +(2.00480 - 8.24504i) q^{66} +7.74597i q^{67} +(-3.16228 - 7.07107i) q^{69} +(-4.58114 + 2.64824i) q^{70} -8.94427i q^{71} +(-7.69615 + 3.57341i) q^{72} +14.6969i q^{73} +(-4.74342 + 2.12132i) q^{75} +(-1.58114 - 6.12372i) q^{76} +(-3.46410 + 8.48528i) q^{77} +(-1.83013 + 7.52666i) q^{78} -10.0000 q^{79} +(2.73861 + 4.94975i) q^{80} +(-1.00000 - 8.94427i) q^{81} +(-9.48683 + 12.2474i) q^{82} +7.07107i q^{83} +(8.79385 - 2.58228i) q^{84} +(-8.66025 - 6.70820i) q^{86} +(-10.9545 + 4.89898i) q^{87} +(9.00000 + 3.87298i) q^{88} +(-5.90089 + 1.08604i) q^{90} +(3.16228 - 7.74597i) q^{91} +(8.66025 - 2.23607i) q^{92} +(-3.46410 - 7.74597i) q^{93} +(9.48683 - 12.2474i) q^{94} -4.47214i q^{95} +(-2.58354 - 9.45121i) q^{96} -4.89898i q^{97} +(-9.80735 + 1.34753i) q^{98} +(-6.92820 + 7.74597i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{4} + 8q^{7} + 16q^{9} + O(q^{10}) \) \( 8q - 4q^{4} + 8q^{7} + 16q^{9} + 8q^{15} - 28q^{16} - 20q^{18} - 24q^{22} + 24q^{25} - 4q^{28} + 20q^{30} - 8q^{36} - 40q^{39} + 12q^{42} + 40q^{46} - 40q^{49} - 40q^{57} + 48q^{58} - 4q^{60} + 16q^{63} + 44q^{64} - 24q^{70} - 20q^{72} + 20q^{78} - 80q^{79} - 8q^{81} + 60q^{84} + 72q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 1.11803i 0.612372 0.790569i
\(3\) −1.58114 + 0.707107i −0.912871 + 0.408248i
\(4\) −0.500000 1.93649i −0.250000 0.968246i
\(5\) 1.41421i 0.632456i −0.948683 0.316228i \(-0.897584\pi\)
0.948683 0.316228i \(-0.102416\pi\)
\(6\) −0.578737 + 2.38014i −0.236268 + 0.971688i
\(7\) 1.00000 2.44949i 0.377964 0.925820i
\(8\) −2.59808 1.11803i −0.918559 0.395285i
\(9\) 2.00000 2.23607i 0.666667 0.745356i
\(10\) −1.58114 1.22474i −0.500000 0.387298i
\(11\) −3.46410 −1.04447 −0.522233 0.852803i \(-0.674901\pi\)
−0.522233 + 0.852803i \(0.674901\pi\)
\(12\) 2.15988 + 2.70831i 0.623502 + 0.781821i
\(13\) 3.16228 0.877058 0.438529 0.898717i \(-0.355500\pi\)
0.438529 + 0.898717i \(0.355500\pi\)
\(14\) −1.87259 3.23935i −0.500470 0.865754i
\(15\) 1.00000 + 2.23607i 0.258199 + 0.577350i
\(16\) −3.50000 + 1.93649i −0.875000 + 0.484123i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.767949 4.17256i −0.181007 0.983482i
\(19\) 3.16228 0.725476 0.362738 0.931891i \(-0.381842\pi\)
0.362738 + 0.931891i \(0.381842\pi\)
\(20\) −2.73861 + 0.707107i −0.612372 + 0.158114i
\(21\) 0.150912 + 4.58009i 0.0329317 + 0.999458i
\(22\) −3.00000 + 3.87298i −0.639602 + 0.825723i
\(23\) 4.47214i 0.932505i 0.884652 + 0.466252i \(0.154396\pi\)
−0.884652 + 0.466252i \(0.845604\pi\)
\(24\) 4.89849 0.0693504i 0.999900 0.0141561i
\(25\) 3.00000 0.600000
\(26\) 2.73861 3.53553i 0.537086 0.693375i
\(27\) −1.58114 + 4.94975i −0.304290 + 0.952579i
\(28\) −5.24342 0.711747i −0.990913 0.134508i
\(29\) 6.92820 1.28654 0.643268 0.765641i \(-0.277578\pi\)
0.643268 + 0.765641i \(0.277578\pi\)
\(30\) 3.36603 + 0.818458i 0.614549 + 0.149429i
\(31\) 4.89898i 0.879883i 0.898027 + 0.439941i \(0.145001\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) −0.866025 + 5.59017i −0.153093 + 0.988212i
\(33\) 5.47723 2.44949i 0.953463 0.426401i
\(34\) 0 0
\(35\) −3.46410 1.41421i −0.585540 0.239046i
\(36\) −5.33013 2.75495i −0.888355 0.459158i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 2.73861 3.53553i 0.444262 0.573539i
\(39\) −5.00000 + 2.23607i −0.800641 + 0.358057i
\(40\) −1.58114 + 3.67423i −0.250000 + 0.580948i
\(41\) −10.9545 −1.71080 −0.855399 0.517970i \(-0.826688\pi\)
−0.855399 + 0.517970i \(0.826688\pi\)
\(42\) 5.25139 + 3.79775i 0.810307 + 0.586005i
\(43\) 7.74597i 1.18125i −0.806947 0.590624i \(-0.798881\pi\)
0.806947 0.590624i \(-0.201119\pi\)
\(44\) 1.73205 + 6.70820i 0.261116 + 1.01130i
\(45\) −3.16228 2.82843i −0.471405 0.421637i
\(46\) 5.00000 + 3.87298i 0.737210 + 0.571040i
\(47\) 10.9545 1.59787 0.798935 0.601417i \(-0.205397\pi\)
0.798935 + 0.601417i \(0.205397\pi\)
\(48\) 4.16468 5.53674i 0.601120 0.799159i
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 2.59808 3.35410i 0.367423 0.474342i
\(51\) 0 0
\(52\) −1.58114 6.12372i −0.219265 0.849208i
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 4.16468 + 6.05437i 0.566741 + 0.823896i
\(55\) 4.89898i 0.660578i
\(56\) −5.33669 + 5.24593i −0.713145 + 0.701016i
\(57\) −5.00000 + 2.23607i −0.662266 + 0.296174i
\(58\) 6.00000 7.74597i 0.787839 1.01710i
\(59\) 9.89949i 1.28880i −0.764687 0.644402i \(-0.777106\pi\)
0.764687 0.644402i \(-0.222894\pi\)
\(60\) 3.83013 3.05453i 0.494467 0.394338i
\(61\) 3.16228 0.404888 0.202444 0.979294i \(-0.435112\pi\)
0.202444 + 0.979294i \(0.435112\pi\)
\(62\) 5.47723 + 4.24264i 0.695608 + 0.538816i
\(63\) −3.47723 7.13505i −0.438089 0.898931i
\(64\) 5.50000 + 5.80948i 0.687500 + 0.726184i
\(65\) 4.47214i 0.554700i
\(66\) 2.00480 8.24504i 0.246774 1.01489i
\(67\) 7.74597i 0.946320i 0.880976 + 0.473160i \(0.156887\pi\)
−0.880976 + 0.473160i \(0.843113\pi\)
\(68\) 0 0
\(69\) −3.16228 7.07107i −0.380693 0.851257i
\(70\) −4.58114 + 2.64824i −0.547551 + 0.316525i
\(71\) 8.94427i 1.06149i −0.847532 0.530745i \(-0.821912\pi\)
0.847532 0.530745i \(-0.178088\pi\)
\(72\) −7.69615 + 3.57341i −0.907000 + 0.421130i
\(73\) 14.6969i 1.72015i 0.510171 + 0.860073i \(0.329582\pi\)
−0.510171 + 0.860073i \(0.670418\pi\)
\(74\) 0 0
\(75\) −4.74342 + 2.12132i −0.547723 + 0.244949i
\(76\) −1.58114 6.12372i −0.181369 0.702439i
\(77\) −3.46410 + 8.48528i −0.394771 + 0.966988i
\(78\) −1.83013 + 7.52666i −0.207221 + 0.852227i
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 2.73861 + 4.94975i 0.306186 + 0.553399i
\(81\) −1.00000 8.94427i −0.111111 0.993808i
\(82\) −9.48683 + 12.2474i −1.04765 + 1.35250i
\(83\) 7.07107i 0.776151i 0.921628 + 0.388075i \(0.126860\pi\)
−0.921628 + 0.388075i \(0.873140\pi\)
\(84\) 8.79385 2.58228i 0.959488 0.281750i
\(85\) 0 0
\(86\) −8.66025 6.70820i −0.933859 0.723364i
\(87\) −10.9545 + 4.89898i −1.17444 + 0.525226i
\(88\) 9.00000 + 3.87298i 0.959403 + 0.412861i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −5.90089 + 1.08604i −0.622008 + 0.114479i
\(91\) 3.16228 7.74597i 0.331497 0.811998i
\(92\) 8.66025 2.23607i 0.902894 0.233126i
\(93\) −3.46410 7.74597i −0.359211 0.803219i
\(94\) 9.48683 12.2474i 0.978492 1.26323i
\(95\) 4.47214i 0.458831i
\(96\) −2.58354 9.45121i −0.263682 0.964610i
\(97\) 4.89898i 0.497416i −0.968579 0.248708i \(-0.919994\pi\)
0.968579 0.248708i \(-0.0800060\pi\)
\(98\) −9.80735 + 1.34753i −0.990692 + 0.136121i
\(99\) −6.92820 + 7.74597i −0.696311 + 0.778499i
\(100\) −1.50000 5.80948i −0.150000 0.580948i
\(101\) 15.5563i 1.54791i 0.633238 + 0.773957i \(0.281726\pi\)
−0.633238 + 0.773957i \(0.718274\pi\)
\(102\) 0 0
\(103\) 9.79796i 0.965422i −0.875780 0.482711i \(-0.839652\pi\)
0.875780 0.482711i \(-0.160348\pi\)
\(104\) −8.21584 3.53553i −0.805629 0.346688i
\(105\) 6.47723 0.213422i 0.632112 0.0208278i
\(106\) 0 0
\(107\) 10.3923 1.00466 0.502331 0.864675i \(-0.332476\pi\)
0.502331 + 0.864675i \(0.332476\pi\)
\(108\) 10.3757 + 0.586988i 0.998404 + 0.0564830i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 5.47723 + 4.24264i 0.522233 + 0.404520i
\(111\) 0 0
\(112\) 1.24342 + 10.5097i 0.117492 + 0.993074i
\(113\) 4.47214i 0.420703i 0.977626 + 0.210352i \(0.0674609\pi\)
−0.977626 + 0.210352i \(0.932539\pi\)
\(114\) −1.83013 + 7.52666i −0.171407 + 0.704936i
\(115\) 6.32456 0.589768
\(116\) −3.46410 13.4164i −0.321634 1.24568i
\(117\) 6.32456 7.07107i 0.584705 0.653720i
\(118\) −11.0680 8.57321i −1.01889 0.789228i
\(119\) 0 0
\(120\) −0.0980762 6.92751i −0.00895309 0.632392i
\(121\) 1.00000 0.0909091
\(122\) 2.73861 3.53553i 0.247942 0.320092i
\(123\) 17.3205 7.74597i 1.56174 0.698430i
\(124\) 9.48683 2.44949i 0.851943 0.219971i
\(125\) 11.3137i 1.01193i
\(126\) −10.9886 2.29148i −0.978942 0.204141i
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 11.2583 1.11803i 0.995105 0.0988212i
\(129\) 5.47723 + 12.2474i 0.482243 + 1.07833i
\(130\) −5.00000 3.87298i −0.438529 0.339683i
\(131\) 1.41421i 0.123560i −0.998090 0.0617802i \(-0.980322\pi\)
0.998090 0.0617802i \(-0.0196778\pi\)
\(132\) −7.48203 9.38186i −0.651227 0.816586i
\(133\) 3.16228 7.74597i 0.274204 0.671660i
\(134\) 8.66025 + 6.70820i 0.748132 + 0.579501i
\(135\) 7.00000 + 2.23607i 0.602464 + 0.192450i
\(136\) 0 0
\(137\) 17.8885i 1.52832i 0.645026 + 0.764161i \(0.276847\pi\)
−0.645026 + 0.764161i \(0.723153\pi\)
\(138\) −10.6443 2.58819i −0.906104 0.220321i
\(139\) −15.8114 −1.34110 −0.670552 0.741862i \(-0.733943\pi\)
−0.670552 + 0.741862i \(0.733943\pi\)
\(140\) −1.00656 + 7.41531i −0.0850700 + 0.626708i
\(141\) −17.3205 + 7.74597i −1.45865 + 0.652328i
\(142\) −10.0000 7.74597i −0.839181 0.650027i
\(143\) −10.9545 −0.916057
\(144\) −2.66987 + 11.6992i −0.222489 + 0.974935i
\(145\) 9.79796i 0.813676i
\(146\) 16.4317 + 12.7279i 1.35990 + 1.05337i
\(147\) 11.3698 + 4.21043i 0.937765 + 0.347271i
\(148\) 0 0
\(149\) −6.92820 −0.567581 −0.283790 0.958886i \(-0.591592\pi\)
−0.283790 + 0.958886i \(0.591592\pi\)
\(150\) −1.73621 + 7.14042i −0.141761 + 0.583013i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −8.21584 3.53553i −0.666392 0.286770i
\(153\) 0 0
\(154\) 6.48683 + 11.2215i 0.522724 + 0.904250i
\(155\) 6.92820 0.556487
\(156\) 6.83013 + 8.56442i 0.546848 + 0.685703i
\(157\) −15.8114 −1.26189 −0.630943 0.775829i \(-0.717332\pi\)
−0.630943 + 0.775829i \(0.717332\pi\)
\(158\) −8.66025 + 11.1803i −0.688973 + 0.889460i
\(159\) 0 0
\(160\) 7.90569 + 1.22474i 0.625000 + 0.0968246i
\(161\) 10.9545 + 4.47214i 0.863332 + 0.352454i
\(162\) −10.8660 6.62793i −0.853716 0.520740i
\(163\) 23.2379i 1.82013i 0.414462 + 0.910066i \(0.363970\pi\)
−0.414462 + 0.910066i \(0.636030\pi\)
\(164\) 5.47723 + 21.2132i 0.427699 + 1.65647i
\(165\) −3.46410 7.74597i −0.269680 0.603023i
\(166\) 7.90569 + 6.12372i 0.613601 + 0.475293i
\(167\) 21.9089 1.69536 0.847681 0.530506i \(-0.177998\pi\)
0.847681 + 0.530506i \(0.177998\pi\)
\(168\) 4.72862 12.0681i 0.364821 0.931078i
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 6.32456 7.07107i 0.483651 0.540738i
\(172\) −15.0000 + 3.87298i −1.14374 + 0.295312i
\(173\) 7.07107i 0.537603i 0.963196 + 0.268802i \(0.0866276\pi\)
−0.963196 + 0.268802i \(0.913372\pi\)
\(174\) −4.00961 + 16.4901i −0.303968 + 1.25011i
\(175\) 3.00000 7.34847i 0.226779 0.555492i
\(176\) 12.1244 6.70820i 0.913908 0.505650i
\(177\) 7.00000 + 15.6525i 0.526152 + 1.17651i
\(178\) 0 0
\(179\) −10.3923 −0.776757 −0.388379 0.921500i \(-0.626965\pi\)
−0.388379 + 0.921500i \(0.626965\pi\)
\(180\) −3.89609 + 7.53794i −0.290397 + 0.561845i
\(181\) 3.16228 0.235050 0.117525 0.993070i \(-0.462504\pi\)
0.117525 + 0.993070i \(0.462504\pi\)
\(182\) −5.92164 10.2437i −0.438941 0.759316i
\(183\) −5.00000 + 2.23607i −0.369611 + 0.165295i
\(184\) 5.00000 11.6190i 0.368605 0.856560i
\(185\) 0 0
\(186\) −11.6603 2.83522i −0.854971 0.207888i
\(187\) 0 0
\(188\) −5.47723 21.2132i −0.399468 1.54713i
\(189\) 10.5432 + 8.82273i 0.766906 + 0.641759i
\(190\) −5.00000 3.87298i −0.362738 0.280976i
\(191\) 8.94427i 0.647185i −0.946197 0.323592i \(-0.895109\pi\)
0.946197 0.323592i \(-0.104891\pi\)
\(192\) −12.8042 5.29650i −0.924062 0.382242i
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) −5.47723 4.24264i −0.393242 0.304604i
\(195\) 3.16228 + 7.07107i 0.226455 + 0.506370i
\(196\) −6.98683 + 12.1319i −0.499059 + 0.866568i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 2.66025 + 14.4542i 0.189056 + 1.02721i
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −7.79423 3.35410i −0.551135 0.237171i
\(201\) −5.47723 12.2474i −0.386334 0.863868i
\(202\) 17.3925 + 13.4722i 1.22373 + 0.947900i
\(203\) 6.92820 16.9706i 0.486265 1.19110i
\(204\) 0 0
\(205\) 15.4919i 1.08200i
\(206\) −10.9545 8.48528i −0.763233 0.591198i
\(207\) 10.0000 + 8.94427i 0.695048 + 0.621670i
\(208\) −11.0680 + 6.12372i −0.767426 + 0.424604i
\(209\) −10.9545 −0.757735
\(210\) 5.37083 7.42659i 0.370622 0.512483i
\(211\) 7.74597i 0.533254i 0.963800 + 0.266627i \(0.0859092\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 0 0
\(213\) 6.32456 + 14.1421i 0.433351 + 0.969003i
\(214\) 9.00000 11.6190i 0.615227 0.794255i
\(215\) −10.9545 −0.747087
\(216\) 9.64191 11.0921i 0.656049 0.754719i
\(217\) 12.0000 + 4.89898i 0.814613 + 0.332564i
\(218\) 0 0
\(219\) −10.3923 23.2379i −0.702247 1.57027i
\(220\) 9.48683 2.44949i 0.639602 0.165145i
\(221\) 0 0
\(222\) 0 0
\(223\) 9.79796i 0.656120i 0.944657 + 0.328060i \(0.106395\pi\)
−0.944657 + 0.328060i \(0.893605\pi\)
\(224\) 12.8270 + 7.71149i 0.857043 + 0.515246i
\(225\) 6.00000 6.70820i 0.400000 0.447214i
\(226\) 5.00000 + 3.87298i 0.332595 + 0.257627i
\(227\) 9.89949i 0.657053i −0.944495 0.328526i \(-0.893448\pi\)
0.944495 0.328526i \(-0.106552\pi\)
\(228\) 6.83013 + 8.56442i 0.452336 + 0.567193i
\(229\) −15.8114 −1.04485 −0.522423 0.852686i \(-0.674972\pi\)
−0.522423 + 0.852686i \(0.674972\pi\)
\(230\) 5.47723 7.07107i 0.361158 0.466252i
\(231\) −0.522774 15.8659i −0.0343960 1.04390i
\(232\) −18.0000 7.74597i −1.18176 0.508548i
\(233\) 8.94427i 0.585959i −0.956119 0.292979i \(-0.905353\pi\)
0.956119 0.292979i \(-0.0946467\pi\)
\(234\) −2.42847 13.1948i −0.158754 0.862571i
\(235\) 15.4919i 1.01058i
\(236\) −19.1703 + 4.94975i −1.24788 + 0.322201i
\(237\) 15.8114 7.07107i 1.02706 0.459315i
\(238\) 0 0
\(239\) 4.47214i 0.289278i 0.989484 + 0.144639i \(0.0462022\pi\)
−0.989484 + 0.144639i \(0.953798\pi\)
\(240\) −7.83013 5.88975i −0.505433 0.380181i
\(241\) 4.89898i 0.315571i −0.987473 0.157786i \(-0.949565\pi\)
0.987473 0.157786i \(-0.0504355\pi\)
\(242\) 0.866025 1.11803i 0.0556702 0.0718699i
\(243\) 7.90569 + 13.4350i 0.507151 + 0.861858i
\(244\) −1.58114 6.12372i −0.101222 0.392031i
\(245\) −6.92820 + 7.07107i −0.442627 + 0.451754i
\(246\) 6.33975 26.0731i 0.404207 1.66236i
\(247\) 10.0000 0.636285
\(248\) 5.47723 12.7279i 0.347804 0.808224i
\(249\) −5.00000 11.1803i −0.316862 0.708525i
\(250\) −12.6491 9.79796i −0.800000 0.619677i
\(251\) 15.5563i 0.981908i 0.871185 + 0.490954i \(0.163352\pi\)
−0.871185 + 0.490954i \(0.836648\pi\)
\(252\) −12.0783 + 10.3011i −0.760864 + 0.648911i
\(253\) 15.4919i 0.973970i
\(254\) 6.92820 8.94427i 0.434714 0.561214i
\(255\) 0 0
\(256\) 8.50000 13.5554i 0.531250 0.847215i
\(257\) −10.9545 −0.683320 −0.341660 0.939824i \(-0.610989\pi\)
−0.341660 + 0.939824i \(0.610989\pi\)
\(258\) 18.4365 + 4.48288i 1.14781 + 0.279092i
\(259\) 0 0
\(260\) −8.66025 + 2.23607i −0.537086 + 0.138675i
\(261\) 13.8564 15.4919i 0.857690 0.958927i
\(262\) −1.58114 1.22474i −0.0976831 0.0756650i
\(263\) 8.94427i 0.551527i −0.961225 0.275764i \(-0.911069\pi\)
0.961225 0.275764i \(-0.0889307\pi\)
\(264\) −16.9689 + 0.240237i −1.04436 + 0.0147855i
\(265\) 0 0
\(266\) −5.92164 10.2437i −0.363079 0.628084i
\(267\) 0 0
\(268\) 15.0000 3.87298i 0.916271 0.236580i
\(269\) 9.89949i 0.603583i −0.953374 0.301791i \(-0.902415\pi\)
0.953374 0.301791i \(-0.0975846\pi\)
\(270\) 8.56218 5.88975i 0.521078 0.358439i
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0 0
\(273\) 0.477226 + 14.4835i 0.0288830 + 0.876582i
\(274\) 20.0000 + 15.4919i 1.20824 + 0.935902i
\(275\) −10.3923 −0.626680
\(276\) −12.1119 + 9.65926i −0.729052 + 0.581419i
\(277\) 15.4919i 0.930820i 0.885095 + 0.465410i \(0.154093\pi\)
−0.885095 + 0.465410i \(0.845907\pi\)
\(278\) −13.6931 + 17.6777i −0.821255 + 1.06024i
\(279\) 10.9545 + 9.79796i 0.655826 + 0.586588i
\(280\) 7.41886 + 7.54722i 0.443362 + 0.451033i
\(281\) 8.94427i 0.533571i −0.963756 0.266785i \(-0.914039\pi\)
0.963756 0.266785i \(-0.0859614\pi\)
\(282\) −6.33975 + 26.0731i −0.377526 + 1.55263i
\(283\) −15.8114 −0.939889 −0.469945 0.882696i \(-0.655726\pi\)
−0.469945 + 0.882696i \(0.655726\pi\)
\(284\) −17.3205 + 4.47214i −1.02778 + 0.265372i
\(285\) 3.16228 + 7.07107i 0.187317 + 0.418854i
\(286\) −9.48683 + 12.2474i −0.560968 + 0.724207i
\(287\) −10.9545 + 26.8328i −0.646621 + 1.58389i
\(288\) 10.7679 + 13.1168i 0.634507 + 0.772917i
\(289\) −17.0000 −1.00000
\(290\) −10.9545 8.48528i −0.643268 0.498273i
\(291\) 3.46410 + 7.74597i 0.203069 + 0.454077i
\(292\) 28.4605 7.34847i 1.66552 0.430037i
\(293\) 26.8701i 1.56977i −0.619644 0.784883i \(-0.712723\pi\)
0.619644 0.784883i \(-0.287277\pi\)
\(294\) 14.5539 9.06548i 0.848803 0.528709i
\(295\) −14.0000 −0.815112
\(296\) 0 0
\(297\) 5.47723 17.1464i 0.317821 0.994937i
\(298\) −6.00000 + 7.74597i −0.347571 + 0.448712i
\(299\) 14.1421i 0.817861i
\(300\) 6.47963 + 8.12493i 0.374101 + 0.469093i
\(301\) −18.9737 7.74597i −1.09362 0.446470i
\(302\) 6.92820 8.94427i 0.398673 0.514685i
\(303\) −11.0000 24.5967i −0.631933 1.41305i
\(304\) −11.0680 + 6.12372i −0.634792 + 0.351220i
\(305\) 4.47214i 0.256074i
\(306\) 0 0
\(307\) 3.16228 0.180481 0.0902404 0.995920i \(-0.471236\pi\)
0.0902404 + 0.995920i \(0.471236\pi\)
\(308\) 18.1637 + 2.46556i 1.03497 + 0.140489i
\(309\) 6.92820 + 15.4919i 0.394132 + 0.881305i
\(310\) 6.00000 7.74597i 0.340777 0.439941i
\(311\) −10.9545 −0.621170 −0.310585 0.950546i \(-0.600525\pi\)
−0.310585 + 0.950546i \(0.600525\pi\)
\(312\) 15.4904 0.219305i 0.876970 0.0124157i
\(313\) 9.79796i 0.553813i 0.960897 + 0.276907i \(0.0893093\pi\)
−0.960897 + 0.276907i \(0.910691\pi\)
\(314\) −13.6931 + 17.6777i −0.772744 + 0.997609i
\(315\) −10.0905 + 4.91754i −0.568534 + 0.277072i
\(316\) 5.00000 + 19.3649i 0.281272 + 1.08936i
\(317\) 6.92820 0.389127 0.194563 0.980890i \(-0.437671\pi\)
0.194563 + 0.980890i \(0.437671\pi\)
\(318\) 0 0
\(319\) −24.0000 −1.34374
\(320\) 8.21584 7.77817i 0.459279 0.434813i
\(321\) −16.4317 + 7.34847i −0.917127 + 0.410152i
\(322\) 14.4868 8.37447i 0.807320 0.466691i
\(323\) 0 0
\(324\) −16.8205 + 6.40863i −0.934473 + 0.356035i
\(325\) 9.48683 0.526235
\(326\) 25.9808 + 20.1246i 1.43894 + 1.11460i
\(327\) 0 0
\(328\) 28.4605 + 12.2474i 1.57147 + 0.676252i
\(329\) 10.9545 26.8328i 0.603938 1.47934i
\(330\) −11.6603 2.83522i −0.641876 0.156074i
\(331\) 7.74597i 0.425757i −0.977079 0.212878i \(-0.931716\pi\)
0.977079 0.212878i \(-0.0682838\pi\)
\(332\) 13.6931 3.53553i 0.751505 0.194038i
\(333\) 0 0
\(334\) 18.9737 24.4949i 1.03819 1.34030i
\(335\) 10.9545 0.598506
\(336\) −9.39750 15.7381i −0.512676 0.858582i
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −2.59808 + 3.35410i −0.141317 + 0.182439i
\(339\) −3.16228 7.07107i −0.171751 0.384048i
\(340\) 0 0
\(341\) 16.9706i 0.919007i
\(342\) −2.42847 13.1948i −0.131317 0.713493i
\(343\) −17.0000 + 7.34847i −0.917914 + 0.396780i
\(344\) −8.66025 + 20.1246i −0.466930 + 1.08505i
\(345\) −10.0000 + 4.47214i −0.538382 + 0.240772i
\(346\) 7.90569 + 6.12372i 0.425013 + 0.329213i
\(347\) −17.3205 −0.929814 −0.464907 0.885360i \(-0.653912\pi\)
−0.464907 + 0.885360i \(0.653912\pi\)
\(348\) 14.9641 + 18.7637i 0.802158 + 1.00584i
\(349\) 22.1359 1.18491 0.592455 0.805604i \(-0.298159\pi\)
0.592455 + 0.805604i \(0.298159\pi\)
\(350\) −5.61776 9.71806i −0.300282 0.519452i
\(351\) −5.00000 + 15.6525i −0.266880 + 0.835467i
\(352\) 3.00000 19.3649i 0.159901 1.03215i
\(353\) 10.9545 0.583047 0.291523 0.956564i \(-0.405838\pi\)
0.291523 + 0.956564i \(0.405838\pi\)
\(354\) 23.5622 + 5.72920i 1.25232 + 0.304504i
\(355\) −12.6491 −0.671345
\(356\) 0 0
\(357\) 0 0
\(358\) −9.00000 + 11.6190i −0.475665 + 0.614081i
\(359\) 31.3050i 1.65221i 0.563515 + 0.826106i \(0.309449\pi\)
−0.563515 + 0.826106i \(0.690551\pi\)
\(360\) 5.05356 + 10.8840i 0.266346 + 0.573637i
\(361\) −9.00000 −0.473684
\(362\) 2.73861 3.53553i 0.143938 0.185824i
\(363\) −1.58114 + 0.707107i −0.0829883 + 0.0371135i
\(364\) −16.5811 2.25074i −0.869088 0.117971i
\(365\) 20.7846 1.08792
\(366\) −1.83013 + 7.52666i −0.0956623 + 0.393425i
\(367\) 19.5959i 1.02290i −0.859313 0.511449i \(-0.829109\pi\)
0.859313 0.511449i \(-0.170891\pi\)
\(368\) −8.66025 15.6525i −0.451447 0.815942i
\(369\) −21.9089 + 24.4949i −1.14053 + 1.27515i
\(370\) 0 0
\(371\) 0 0
\(372\) −13.2679 + 10.5812i −0.687911 + 0.548609i
\(373\) 30.9839i 1.60428i 0.597133 + 0.802142i \(0.296306\pi\)
−0.597133 + 0.802142i \(0.703694\pi\)
\(374\) 0 0
\(375\) 8.00000 + 17.8885i 0.413118 + 0.923760i
\(376\) −28.4605 12.2474i −1.46774 0.631614i
\(377\) 21.9089 1.12837
\(378\) 18.9948 4.14697i 0.976987 0.213297i
\(379\) 23.2379i 1.19365i −0.802371 0.596825i \(-0.796429\pi\)
0.802371 0.596825i \(-0.203571\pi\)
\(380\) −8.66025 + 2.23607i −0.444262 + 0.114708i
\(381\) −12.6491 + 5.65685i −0.648034 + 0.289809i
\(382\) −10.0000 7.74597i −0.511645 0.396318i
\(383\) −10.9545 −0.559746 −0.279873 0.960037i \(-0.590292\pi\)
−0.279873 + 0.960037i \(0.590292\pi\)
\(384\) −17.0104 + 9.72861i −0.868059 + 0.496461i
\(385\) 12.0000 + 4.89898i 0.611577 + 0.249675i
\(386\) −3.46410 + 4.47214i −0.176318 + 0.227626i
\(387\) −17.3205 15.4919i −0.880451 0.787499i
\(388\) −9.48683 + 2.44949i −0.481621 + 0.124354i
\(389\) 27.7128 1.40510 0.702548 0.711637i \(-0.252046\pi\)
0.702548 + 0.711637i \(0.252046\pi\)
\(390\) 10.6443 + 2.58819i 0.538995 + 0.131058i
\(391\) 0 0
\(392\) 7.51316 + 18.3181i 0.379472 + 0.925203i
\(393\) 1.00000 + 2.23607i 0.0504433 + 0.112795i
\(394\) 0 0
\(395\) 14.1421i 0.711568i
\(396\) 18.4641 + 9.54342i 0.927856 + 0.479575i
\(397\) 22.1359 1.11097 0.555486 0.831526i \(-0.312532\pi\)
0.555486 + 0.831526i \(0.312532\pi\)
\(398\) 0 0
\(399\) 0.477226 + 14.4835i 0.0238912 + 0.725083i
\(400\) −10.5000 + 5.80948i −0.525000 + 0.290474i
\(401\) 4.47214i 0.223328i 0.993746 + 0.111664i \(0.0356180\pi\)
−0.993746 + 0.111664i \(0.964382\pi\)
\(402\) −18.4365 4.48288i −0.919528 0.223586i
\(403\) 15.4919i 0.771708i
\(404\) 30.1247 7.77817i 1.49876 0.386979i
\(405\) −12.6491 + 1.41421i −0.628539 + 0.0702728i
\(406\) −12.9737 22.4429i −0.643872 1.11382i
\(407\) 0 0
\(408\) 0 0
\(409\) 9.79796i 0.484478i −0.970217 0.242239i \(-0.922118\pi\)
0.970217 0.242239i \(-0.0778818\pi\)
\(410\) 17.3205 + 13.4164i 0.855399 + 0.662589i
\(411\) −12.6491 28.2843i −0.623935 1.39516i
\(412\) −18.9737 + 4.89898i −0.934765 + 0.241355i
\(413\) −24.2487 9.89949i −1.19320 0.487122i
\(414\) 18.6603 3.43437i 0.917101 0.168790i
\(415\) 10.0000 0.490881
\(416\) −2.73861 + 17.6777i −0.134272 + 0.866719i
\(417\) 25.0000 11.1803i 1.22426 0.547504i
\(418\) −9.48683 + 12.2474i −0.464016 + 0.599042i
\(419\) 24.0416i 1.17451i 0.809402 + 0.587255i \(0.199792\pi\)
−0.809402 + 0.587255i \(0.800208\pi\)
\(420\) −3.65190 12.4364i −0.178195 0.606833i
\(421\) 30.9839i 1.51006i −0.655690 0.755031i \(-0.727622\pi\)
0.655690 0.755031i \(-0.272378\pi\)
\(422\) 8.66025 + 6.70820i 0.421575 + 0.326550i
\(423\) 21.9089 24.4949i 1.06525 1.19098i
\(424\) 0 0
\(425\) 0 0
\(426\) 21.2886 + 5.17638i 1.03144 + 0.250796i
\(427\) 3.16228 7.74597i 0.153033 0.374854i
\(428\) −5.19615 20.1246i −0.251166 0.972760i
\(429\) 17.3205 7.74597i 0.836242 0.373979i
\(430\) −9.48683 + 12.2474i −0.457496 + 0.590624i
\(431\) 22.3607i 1.07708i −0.842601 0.538538i \(-0.818977\pi\)
0.842601 0.538538i \(-0.181023\pi\)
\(432\) −4.05116 20.3860i −0.194911 0.980821i
\(433\) 14.6969i 0.706290i −0.935569 0.353145i \(-0.885112\pi\)
0.935569 0.353145i \(-0.114888\pi\)
\(434\) 15.8695 9.17377i 0.761762 0.440355i
\(435\) 6.92820 + 15.4919i 0.332182 + 0.742781i
\(436\) 0 0
\(437\) 14.1421i 0.676510i
\(438\) −34.9808 8.50566i −1.67145 0.406416i
\(439\) 24.4949i 1.16908i 0.811366 + 0.584539i \(0.198725\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 5.47723 12.7279i 0.261116 0.606780i
\(441\) −20.9545 + 1.38238i −0.997831 + 0.0658277i
\(442\) 0 0
\(443\) 17.3205 0.822922 0.411461 0.911427i \(-0.365019\pi\)
0.411461 + 0.911427i \(0.365019\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 10.9545 + 8.48528i 0.518708 + 0.401790i
\(447\) 10.9545 4.89898i 0.518128 0.231714i
\(448\) 19.7302 7.66272i 0.932167 0.362029i
\(449\) 8.94427i 0.422106i −0.977475 0.211053i \(-0.932311\pi\)
0.977475 0.211053i \(-0.0676893\pi\)
\(450\) −2.30385 12.5177i −0.108604 0.590089i
\(451\) 37.9473 1.78687
\(452\) 8.66025 2.23607i 0.407344 0.105176i
\(453\) −12.6491 + 5.65685i −0.594307 + 0.265782i
\(454\) −11.0680 8.57321i −0.519446 0.402361i
\(455\) −10.9545 4.47214i −0.513553 0.209657i
\(456\) 15.4904 0.219305i 0.725404 0.0102699i
\(457\) 8.00000 0.374224 0.187112 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) −13.6931 + 17.6777i −0.639835 + 0.826023i
\(459\) 0 0
\(460\) −3.16228 12.2474i −0.147442 0.571040i
\(461\) 15.5563i 0.724531i 0.932075 + 0.362266i \(0.117997\pi\)
−0.932075 + 0.362266i \(0.882003\pi\)
\(462\) −18.1913 13.1558i −0.846338 0.612063i
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) −24.2487 + 13.4164i −1.12572 + 0.622841i
\(465\) −10.9545 + 4.89898i −0.508001 + 0.227185i
\(466\) −10.0000 7.74597i −0.463241 0.358825i
\(467\) 7.07107i 0.327210i 0.986526 + 0.163605i \(0.0523123\pi\)
−0.986526 + 0.163605i \(0.947688\pi\)
\(468\) −16.8553 8.71191i −0.779138 0.402708i
\(469\) 18.9737 + 7.74597i 0.876122 + 0.357676i
\(470\) −17.3205 13.4164i −0.798935 0.618853i
\(471\) 25.0000 11.1803i 1.15194 0.515163i
\(472\) −11.0680 + 25.7196i −0.509445 + 1.18384i
\(473\) 26.8328i 1.23377i
\(474\) 5.78737 23.8014i 0.265823 1.09323i
\(475\) 9.48683 0.435286
\(476\) 0 0
\(477\) 0 0
\(478\) 5.00000 + 3.87298i 0.228695 + 0.177146i
\(479\) 10.9545 0.500522 0.250261 0.968178i \(-0.419484\pi\)
0.250261 + 0.968178i \(0.419484\pi\)
\(480\) −13.3660 + 3.65368i −0.610073 + 0.166767i
\(481\) 0 0
\(482\) −5.47723 4.24264i −0.249481 0.193247i
\(483\) −20.4828 + 0.674899i −0.931999 + 0.0307090i
\(484\) −0.500000 1.93649i −0.0227273 0.0880223i
\(485\) −6.92820 −0.314594
\(486\) 21.8674 + 2.79624i 0.991923 + 0.126840i
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) −8.21584 3.53553i −0.371914 0.160046i
\(489\) −16.4317 36.7423i −0.743066 1.66155i
\(490\) 1.90569 + 13.8697i 0.0860905 + 0.626569i
\(491\) 3.46410 0.156333 0.0781664 0.996940i \(-0.475093\pi\)
0.0781664 + 0.996940i \(0.475093\pi\)
\(492\) −23.6603 29.6680i −1.06669 1.33754i
\(493\) 0 0
\(494\) 8.66025 11.1803i 0.389643 0.503027i
\(495\) 10.9545 + 9.79796i 0.492366 + 0.440386i
\(496\) −9.48683 17.1464i −0.425971 0.769897i
\(497\) −21.9089 8.94427i −0.982749 0.401205i
\(498\) −16.8301 4.09229i −0.754176 0.183380i
\(499\) 7.74597i 0.346757i 0.984855 + 0.173379i \(0.0554684\pi\)
−0.984855 + 0.173379i \(0.944532\pi\)
\(500\) −21.9089 + 5.65685i −0.979796 + 0.252982i
\(501\) −34.6410 + 15.4919i −1.54765 + 0.692129i
\(502\) 17.3925 + 13.4722i 0.776266 + 0.601293i
\(503\) −32.8634 −1.46530 −0.732652 0.680603i \(-0.761718\pi\)
−0.732652 + 0.680603i \(0.761718\pi\)
\(504\) 1.05687 + 22.4251i 0.0470768 + 0.998891i
\(505\) 22.0000 0.978987
\(506\) −17.3205 13.4164i −0.769991 0.596432i
\(507\) 4.74342 2.12132i 0.210663 0.0942111i
\(508\) −4.00000 15.4919i −0.177471 0.687343i
\(509\) 9.89949i 0.438787i −0.975636 0.219394i \(-0.929592\pi\)
0.975636 0.219394i \(-0.0704079\pi\)
\(510\) 0 0
\(511\) 36.0000 + 14.6969i 1.59255 + 0.650154i
\(512\) −7.79423 21.2426i −0.344459 0.938801i
\(513\) −5.00000 + 15.6525i −0.220755 + 0.691074i
\(514\) −9.48683 + 12.2474i −0.418446 + 0.540212i
\(515\) −13.8564 −0.610586
\(516\) 20.9785 16.7303i 0.923526 0.736512i
\(517\) −37.9473 −1.66892
\(518\) 0 0
\(519\) −5.00000 11.1803i −0.219476 0.490762i
\(520\) −5.00000 + 11.6190i −0.219265 + 0.509525i
\(521\) 32.8634 1.43977 0.719885 0.694094i \(-0.244195\pi\)
0.719885 + 0.694094i \(0.244195\pi\)
\(522\) −5.32051 28.9083i −0.232872 1.26528i
\(523\) 3.16228 0.138277 0.0691384 0.997607i \(-0.477975\pi\)
0.0691384 + 0.997607i \(0.477975\pi\)
\(524\) −2.73861 + 0.707107i −0.119637 + 0.0308901i
\(525\) 0.452736 + 13.7403i 0.0197590 + 0.599675i
\(526\) −10.0000 7.74597i −0.436021 0.337740i
\(527\) 0 0
\(528\) −14.4269 + 19.1798i −0.627849 + 0.834694i
\(529\) 3.00000 0.130435
\(530\) 0 0
\(531\) −22.1359 19.7990i −0.960618 0.859203i
\(532\) −16.5811 2.25074i −0.718884 0.0975820i
\(533\) −34.6410 −1.50047
\(534\) 0 0
\(535\) 14.6969i 0.635404i
\(536\) 8.66025 20.1246i 0.374066 0.869251i
\(537\) 16.4317 7.34847i 0.709079 0.317110i
\(538\) −11.0680 8.57321i −0.477174 0.369618i
\(539\) 17.3205 + 16.9706i 0.746047 + 0.730974i
\(540\) 0.830127 14.6735i 0.0357230 0.631446i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −5.00000 + 2.23607i −0.214571 + 0.0959589i
\(544\) 0 0
\(545\) 0 0
\(546\) 16.6064 + 12.0095i 0.710686 + 0.513961i
\(547\) 7.74597i 0.331194i −0.986194 0.165597i \(-0.947045\pi\)
0.986194 0.165597i \(-0.0529550\pi\)
\(548\) 34.6410 8.94427i 1.47979 0.382080i
\(549\) 6.32456 7.07107i 0.269925 0.301786i
\(550\) −9.00000 + 11.6190i −0.383761 + 0.495434i
\(551\) 21.9089 0.933351
\(552\) 0.310144 + 21.9067i 0.0132006 + 0.932411i
\(553\) −10.0000 + 24.4949i −0.425243 + 1.04163i
\(554\) 17.3205 + 13.4164i 0.735878 + 0.570009i
\(555\) 0 0
\(556\) 7.90569 + 30.6186i 0.335276 + 1.29852i
\(557\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(558\) 20.4413 3.76217i 0.865349 0.159265i
\(559\) 24.4949i 1.03602i
\(560\) 14.8630 1.75846i 0.628075 0.0743083i
\(561\) 0 0
\(562\) −10.0000 7.74597i −0.421825 0.326744i
\(563\) 1.41421i 0.0596020i −0.999556 0.0298010i \(-0.990513\pi\)
0.999556 0.0298010i \(-0.00948736\pi\)
\(564\) 23.6603 + 29.6680i 0.996276 + 1.24925i
\(565\) 6.32456 0.266076
\(566\) −13.6931 + 17.6777i −0.575562 + 0.743048i
\(567\) −22.9089 6.49478i −0.962083 0.272755i
\(568\) −10.0000 + 23.2379i −0.419591 + 0.975041i
\(569\) 22.3607i 0.937408i −0.883355 0.468704i \(-0.844721\pi\)
0.883355 0.468704i \(-0.155279\pi\)
\(570\) 10.6443 + 2.58819i 0.445841 + 0.108407i
\(571\) 7.74597i 0.324159i 0.986778 + 0.162079i \(0.0518200\pi\)
−0.986778 + 0.162079i \(0.948180\pi\)
\(572\) 5.47723 + 21.2132i 0.229014 + 0.886969i
\(573\) 6.32456 + 14.1421i 0.264212 + 0.590796i
\(574\) 20.5132 + 35.4853i 0.856203 + 1.48113i
\(575\) 13.4164i 0.559503i
\(576\) 23.9904 0.679424i 0.999599 0.0283093i
\(577\) 29.3939i 1.22368i −0.790980 0.611842i \(-0.790429\pi\)
0.790980 0.611842i \(-0.209571\pi\)
\(578\) −14.7224 + 19.0066i −0.612372 + 0.790569i
\(579\) 6.32456 2.82843i 0.262840 0.117545i
\(580\) −18.9737 + 4.89898i −0.787839 + 0.203419i
\(581\) 17.3205 + 7.07107i 0.718576 + 0.293357i
\(582\) 11.6603 + 2.83522i 0.483333 + 0.117524i
\(583\) 0 0
\(584\) 16.4317 38.1838i 0.679948 1.58006i
\(585\) −10.0000 8.94427i −0.413449 0.369800i
\(586\) −30.0416 23.2702i −1.24101 0.961281i
\(587\) 35.3553i 1.45927i −0.683836 0.729636i \(-0.739690\pi\)
0.683836 0.729636i \(-0.260310\pi\)
\(588\) 2.46857 24.1227i 0.101802 0.994805i
\(589\) 15.4919i 0.638334i
\(590\) −12.1244 + 15.6525i −0.499152 + 0.644402i
\(591\) 0 0
\(592\) 0 0
\(593\) 32.8634 1.34954 0.674768 0.738030i \(-0.264244\pi\)
0.674768 + 0.738030i \(0.264244\pi\)
\(594\) −14.4269 20.9730i −0.591942 0.860531i
\(595\) 0 0
\(596\) 3.46410 + 13.4164i 0.141895 + 0.549557i
\(597\) 0 0
\(598\) 15.8114 + 12.2474i 0.646576 + 0.500835i
\(599\) 8.94427i 0.365453i −0.983164 0.182727i \(-0.941508\pi\)
0.983164 0.182727i \(-0.0584923\pi\)
\(600\) 14.6955 0.208051i 0.599940 0.00849365i
\(601\) 24.4949i 0.999168i 0.866266 + 0.499584i \(0.166514\pi\)
−0.866266 + 0.499584i \(0.833486\pi\)
\(602\) −25.0919 + 14.5050i −1.02267 + 0.591180i
\(603\) 17.3205 + 15.4919i 0.705346 + 0.630880i
\(604\) −4.00000 15.4919i −0.162758 0.630358i
\(605\) 1.41421i 0.0574960i
\(606\) −37.0263 9.00303i −1.50409 0.365723i
\(607\) 19.5959i 0.795374i 0.917521 + 0.397687i \(0.130187\pi\)
−0.917521 + 0.397687i \(0.869813\pi\)
\(608\) −2.73861 + 17.6777i −0.111065 + 0.716924i
\(609\) 1.04555 + 31.7318i 0.0423678 + 1.28584i
\(610\) −5.00000 3.87298i −0.202444 0.156813i
\(611\) 34.6410 1.40143
\(612\) 0 0
\(613\) 46.4758i 1.87714i −0.345089 0.938570i \(-0.612151\pi\)
0.345089 0.938570i \(-0.387849\pi\)
\(614\) 2.73861 3.53553i 0.110521 0.142683i
\(615\) −10.9545 24.4949i −0.441726 0.987730i
\(616\) 18.4868 18.1724i 0.744856 0.732188i
\(617\) 31.3050i 1.26029i 0.776478 + 0.630145i \(0.217005\pi\)
−0.776478 + 0.630145i \(0.782995\pi\)
\(618\) 23.3205 + 5.67044i 0.938088 + 0.228099i
\(619\) 3.16228 0.127103 0.0635513 0.997979i \(-0.479757\pi\)
0.0635513 + 0.997979i \(0.479757\pi\)
\(620\) −3.46410 13.4164i −0.139122 0.538816i
\(621\) −22.1359 7.07107i −0.888285 0.283752i
\(622\) −9.48683 + 12.2474i −0.380387 + 0.491078i
\(623\) 0 0
\(624\) 13.1699 17.5087i 0.527217 0.700909i
\(625\) −1.00000 −0.0400000
\(626\) 10.9545 + 8.48528i 0.437828 + 0.339140i
\(627\) 17.3205 7.74597i 0.691714 0.309344i
\(628\) 7.90569 + 30.6186i 0.315472 + 1.22182i
\(629\) 0 0
\(630\) −3.24064 + 15.5402i −0.129110 + 0.619137i
\(631\) −10.0000 −0.398094 −0.199047 0.979990i \(-0.563785\pi\)
−0.199047 + 0.979990i \(0.563785\pi\)
\(632\) 25.9808 + 11.1803i 1.03346 + 0.444730i
\(633\) −5.47723 12.2474i −0.217700 0.486792i
\(634\) 6.00000 7.74597i 0.238290 0.307632i
\(635\) 11.3137i 0.448971i
\(636\) 0 0
\(637\) −15.8114 15.4919i −0.626470 0.613813i
\(638\) −20.7846 + 26.8328i −0.822871 + 1.06232i
\(639\) −20.0000 17.8885i −0.791188 0.707660i
\(640\) −1.58114 15.9217i −0.0625000 0.629360i
\(641\) 31.3050i 1.23647i 0.785993 + 0.618236i \(0.212152\pi\)
−0.785993 + 0.618236i \(0.787848\pi\)
\(642\) −6.01441 + 24.7351i −0.237370 + 0.976218i
\(643\) 3.16228 0.124708 0.0623540 0.998054i \(-0.480139\pi\)
0.0623540 + 0.998054i \(0.480139\pi\)
\(644\) 3.18303 23.4493i 0.125429 0.924031i
\(645\) 17.3205 7.74597i 0.681994 0.304997i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −7.40192 + 24.3559i −0.290775 + 0.956791i
\(649\) 34.2929i 1.34611i
\(650\) 8.21584 10.6066i 0.322252 0.416025i
\(651\) −22.4378 + 0.739315i −0.879405 + 0.0289760i
\(652\) 45.0000 11.6190i 1.76234 0.455033i
\(653\) −48.4974 −1.89785 −0.948925 0.315501i \(-0.897828\pi\)
−0.948925 + 0.315501i \(0.897828\pi\)
\(654\) 0 0
\(655\) −2.00000 −0.0781465
\(656\) 38.3406 21.2132i 1.49695 0.828236i
\(657\) 32.8634 + 29.3939i 1.28212 + 1.14676i
\(658\) −20.5132 35.4853i −0.799687 1.38336i
\(659\) −24.2487 −0.944596 −0.472298 0.881439i \(-0.656575\pi\)
−0.472298 + 0.881439i \(0.656575\pi\)
\(660\) −13.2679 + 10.5812i −0.516454 + 0.411872i
\(661\) 41.1096 1.59898 0.799489 0.600680i \(-0.205104\pi\)
0.799489 + 0.600680i \(0.205104\pi\)
\(662\) −8.66025 6.70820i −0.336590 0.260722i
\(663\) 0 0
\(664\) 7.90569 18.3712i 0.306800 0.712940i
\(665\) −10.9545 4.47214i −0.424795 0.173422i
\(666\) 0 0
\(667\) 30.9839i 1.19970i
\(668\) −10.9545 42.4264i −0.423840 1.64153i
\(669\) −6.92820 15.4919i −0.267860 0.598953i
\(670\) 9.48683 12.2474i 0.366508 0.473160i
\(671\) −10.9545 −0.422892
\(672\) −25.7342 3.12285i −0.992717 0.120467i
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 6.92820 8.94427i 0.266864 0.344520i
\(675\) −4.74342 + 14.8492i −0.182574 + 0.571548i
\(676\) 1.50000 + 5.80948i 0.0576923 + 0.223441i
\(677\) 7.07107i 0.271763i 0.990725 + 0.135882i \(0.0433867\pi\)
−0.990725 + 0.135882i \(0.956613\pi\)
\(678\) −10.6443 2.58819i −0.408792 0.0993989i
\(679\) −12.0000 4.89898i −0.460518 0.188006i
\(680\) 0 0
\(681\) 7.00000 + 15.6525i 0.268241 + 0.599804i
\(682\) −18.9737 14.6969i −0.726539 0.562775i
\(683\) 31.1769 1.19295 0.596476 0.802631i \(-0.296567\pi\)
0.596476 + 0.802631i \(0.296567\pi\)
\(684\) −16.8553 8.71191i −0.644480 0.333108i
\(685\) 25.2982 0.966595
\(686\) −6.50659 + 25.3705i −0.248423 + 0.968652i
\(687\) 25.0000 11.1803i 0.953809 0.426557i
\(688\) 15.0000 + 27.1109i 0.571870 + 1.03359i
\(689\) 0 0
\(690\) −3.66025 + 15.0533i −0.139343 + 0.573070i
\(691\) 3.16228 0.120299 0.0601494 0.998189i \(-0.480842\pi\)
0.0601494 + 0.998189i \(0.480842\pi\)
\(692\) 13.6931 3.53553i 0.520532 0.134401i
\(693\) 12.0455 + 24.7165i 0.457569 + 0.938903i
\(694\) −15.0000 + 19.3649i −0.569392 + 0.735082i
\(695\) 22.3607i 0.848189i
\(696\) 33.9377 0.480473i 1.28641 0.0182123i
\(697\) 0 0
\(698\) 19.1703 24.7487i 0.725606 0.936754i
\(699\) 6.32456 + 14.1421i 0.239217 + 0.534905i
\(700\) −15.7302 2.13524i −0.594548 0.0807045i
\(701\) −20.7846 −0.785024 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(702\) 13.1699 + 19.1456i 0.497065 + 0.722605i
\(703\) 0 0
\(704\) −19.0526 20.1246i −0.718070 0.758475i
\(705\) 10.9545 + 24.4949i 0.412568 + 0.922531i
\(706\) 9.48683 12.2474i 0.357042 0.460939i
\(707\) 38.1051 + 15.5563i 1.43309 + 0.585057i
\(708\) 26.8109 21.3817i 1.00761 0.803573i
\(709\) 30.9839i 1.16362i −0.813323 0.581812i \(-0.802344\pi\)
0.813323 0.581812i \(-0.197656\pi\)
\(710\) −10.9545 + 14.1421i −0.411113 + 0.530745i
\(711\) −20.0000 + 22.3607i −0.750059 + 0.838591i
\(712\) 0 0
\(713\) −21.9089 −0.820495
\(714\) 0 0
\(715\) 15.4919i 0.579365i
\(716\) 5.19615 + 20.1246i 0.194189 + 0.752092i
\(717\) −3.16228 7.07107i −0.118097 0.264074i
\(718\) 35.0000 + 27.1109i 1.30619 + 1.01177i
\(719\) −32.8634 −1.22560 −0.612798 0.790239i \(-0.709956\pi\)
−0.612798 + 0.790239i \(0.709956\pi\)
\(720\) 16.5452 + 3.77577i 0.616603 + 0.140715i
\(721\) −24.0000 9.79796i −0.893807 0.364895i
\(722\) −7.79423 + 10.0623i −0.290071 + 0.374480i
\(723\) 3.46410 + 7.74597i 0.128831 + 0.288076i
\(724\) −1.58114 6.12372i −0.0587626 0.227586i
\(725\) 20.7846 0.771921
\(726\) −0.578737 + 2.38014i −0.0214789 + 0.0883353i
\(727\) 19.5959i 0.726772i −0.931639 0.363386i \(-0.881621\pi\)
0.931639 0.363386i \(-0.118379\pi\)
\(728\) −16.8761 + 16.5891i −0.625470 + 0.614832i
\(729\) −22.0000 15.6525i −0.814815 0.579721i
\(730\) 18.0000 23.2379i 0.666210 0.860073i
\(731\) 0 0
\(732\) 6.83013 + 8.56442i 0.252449 + 0.316550i
\(733\) −15.8114 −0.584007 −0.292003 0.956417i \(-0.594322\pi\)
−0.292003 + 0.956417i \(0.594322\pi\)
\(734\) −21.9089 16.9706i −0.808672 0.626395i
\(735\) 5.95445 16.0793i 0.219633 0.593095i
\(736\) −25.0000 3.87298i −0.921512 0.142760i
\(737\) 26.8328i 0.988399i
\(738\) 8.41246 + 45.7081i 0.309667 + 1.68254i
\(739\) 23.2379i 0.854820i −0.904058 0.427410i \(-0.859426\pi\)
0.904058 0.427410i \(-0.140574\pi\)
\(740\) 0 0
\(741\) −15.8114 + 7.07107i −0.580846 + 0.259762i
\(742\) 0 0
\(743\) 49.1935i 1.80473i −0.430968 0.902367i \(-0.641828\pi\)
0.430968 0.902367i \(-0.358172\pi\)
\(744\) 0.339746 + 23.9976i 0.0124557 + 0.879795i
\(745\) 9.79796i 0.358969i
\(746\) 34.6410 + 26.8328i 1.26830 + 0.982419i
\(747\) 15.8114 + 14.1421i 0.578508 + 0.517434i
\(748\) 0 0
\(749\) 10.3923 25.4558i 0.379727 0.930136i
\(750\) 26.9282 + 6.54766i 0.983279 + 0.239087i
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) −38.3406 + 21.2132i −1.39814 + 0.773566i
\(753\) −11.0000 24.5967i −0.400862 0.896355i
\(754\) 18.9737 24.4949i 0.690980 0.892052i
\(755\) 11.3137i 0.411748i
\(756\) 11.8135 24.8282i 0.429654 0.902994i
\(757\) 46.4758i 1.68919i 0.535404 + 0.844596i \(0.320159\pi\)
−0.535404 + 0.844596i \(0.679841\pi\)
\(758\) −25.9808 20.1246i −0.943664 0.730959i
\(759\) 10.9545 + 24.4949i 0.397621 + 0.889108i
\(760\) −5.00000 + 11.6190i −0.181369 + 0.421464i
\(761\) −10.9545 −0.397099 −0.198549 0.980091i \(-0.563623\pi\)
−0.198549 + 0.980091i \(0.563623\pi\)
\(762\) −4.62990 + 19.0411i −0.167723 + 0.689787i
\(763\) 0 0
\(764\) −17.3205 + 4.47214i −0.626634 + 0.161796i
\(765\) 0 0
\(766\) −9.48683 + 12.2474i −0.342773 + 0.442518i
\(767\) 31.3050i 1.13036i
\(768\) −3.85454 + 27.4434i −0.139089 + 0.990280i
\(769\) 24.4949i 0.883309i −0.897185 0.441654i \(-0.854392\pi\)
0.897185 0.441654i \(-0.145608\pi\)
\(770\) 15.8695 9.17377i 0.571898 0.330600i
\(771\) 17.3205 7.74597i 0.623783 0.278964i
\(772\) 2.00000 + 7.74597i 0.0719816 + 0.278783i
\(773\) 35.3553i 1.27164i −0.771836 0.635822i \(-0.780661\pi\)
0.771836 0.635822i \(-0.219339\pi\)
\(774\) −32.3205 + 5.94851i −1.16174 + 0.213815i
\(775\) 14.6969i 0.527930i
\(776\) −5.47723 + 12.7279i −0.196621 + 0.456906i
\(777\) 0 0
\(778\) 24.0000 30.9839i 0.860442 1.11083i
\(779\) −34.6410 −1.24114
\(780\) 12.1119 9.65926i 0.433676 0.345857i
\(781\) 30.9839i 1.10869i
\(782\) 0 0
\(783\) −10.9545 + 34.2929i −0.391480 +