Properties

Label 168.2.i.e.125.2
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 125.2
Root \(-0.578737 - 0.965926i\) of \(x^{8} - 8 x^{6} + 13 x^{4} + 12 x^{2} + 36\)
Character \(\chi\) \(=\) 168.125
Dual form 168.2.i.e.125.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} +1.41421i q^{5} +(-2.15988 - 1.15539i) q^{6} +(1.00000 - 2.44949i) q^{7} +(2.59808 - 1.11803i) q^{8} +(2.00000 - 2.23607i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 1.11803i) q^{2} +(1.58114 - 0.707107i) q^{3} +(-0.500000 + 1.93649i) q^{4} +1.41421i q^{5} +(-2.15988 - 1.15539i) 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} +(0.578737 + 3.41542i) q^{12} -3.16228 q^{13} +(-3.60464 + 1.00329i) q^{14} +(1.00000 + 2.23607i) q^{15} +(-3.50000 - 1.93649i) q^{16} +(-4.23205 - 0.299576i) 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} +(3.31735 - 3.60488i) q^{24} +3.00000 q^{25} +(2.73861 + 3.53553i) q^{26} +(1.58114 - 4.94975i) q^{27} +(4.24342 + 3.16124i) q^{28} -6.92820 q^{29} +(1.63397 - 3.05453i) q^{30} +4.89898i q^{31} +(0.866025 + 5.59017i) q^{32} +(5.47723 - 2.44949i) q^{33} +(3.46410 + 1.41421i) q^{35} +(3.33013 + 4.99102i) q^{36} +(2.73861 + 3.53553i) q^{38} +(-5.00000 + 2.23607i) q^{39} +(1.58114 + 3.67423i) q^{40} -10.9545 q^{41} +(-4.99000 + 4.13520i) 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} +(-6.90329 - 0.586988i) q^{48} +(-5.00000 - 4.89898i) q^{49} +(-2.59808 - 3.35410i) q^{50} +(1.58114 - 6.12372i) q^{52} +(-6.90329 + 2.51884i) q^{54} +4.89898i q^{55} +(-0.140537 - 7.48200i) q^{56} +(-5.00000 + 2.23607i) q^{57} +(6.00000 + 7.74597i) q^{58} +9.89949i q^{59} +(-4.83013 + 0.818458i) 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} +(-7.48203 - 4.00240i) q^{66} -7.74597i q^{67} +(3.16228 + 7.07107i) q^{69} +(-1.41886 - 5.09773i) q^{70} -8.94427i q^{71} +(2.69615 - 8.04554i) q^{72} +14.6969i q^{73} +(4.74342 - 2.12132i) q^{75} +(1.58114 - 6.12372i) q^{76} +(3.46410 - 8.48528i) q^{77} +(6.83013 + 3.65368i) 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} +(8.94476 + 1.99781i) q^{84} +(8.66025 - 6.70820i) q^{86} +(-10.9545 + 4.89898i) q^{87} +(9.00000 - 3.87298i) q^{88} +(0.423665 - 5.98502i) 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} +(5.32215 + 8.22646i) q^{96} -4.89898i q^{97} +(-1.14710 + 9.83281i) 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 \(0.102416\pi\)
−0.948683 + 0.316228i \(0.897584\pi\)
\(6\) −2.15988 1.15539i −0.881766 0.471688i
\(7\) 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 \(-0.325099\pi\)
0.522233 + 0.852803i \(0.325099\pi\)
\(12\) 0.578737 + 3.41542i 0.167067 + 0.985946i
\(13\) −3.16228 −0.877058 −0.438529 0.898717i \(-0.644500\pi\)
−0.438529 + 0.898717i \(0.644500\pi\)
\(14\) −3.60464 + 1.00329i −0.963380 + 0.268140i
\(15\) 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 \(0.5\pi\)
\(18\) −4.23205 0.299576i −0.997504 0.0706108i
\(19\) −3.16228 −0.725476 −0.362738 0.931891i \(-0.618158\pi\)
−0.362738 + 0.931891i \(0.618158\pi\)
\(20\) −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 \(0.845604\pi\)
\(24\) 3.31735 3.60488i 0.677151 0.735844i
\(25\) 3.00000 0.600000
\(26\) 2.73861 + 3.53553i 0.537086 + 0.693375i
\(27\) 1.58114 4.94975i 0.304290 0.952579i
\(28\) 4.24342 + 3.16124i 0.801930 + 0.597418i
\(29\) −6.92820 −1.28654 −0.643268 0.765641i \(-0.722422\pi\)
−0.643268 + 0.765641i \(0.722422\pi\)
\(30\) 1.63397 3.05453i 0.298322 0.557678i
\(31\) 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
\(36\) 3.33013 + 4.99102i 0.555021 + 0.831836i
\(37\) 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 \(0.826688\pi\)
\(42\) −4.99000 + 4.13520i −0.769974 + 0.638075i
\(43\) 7.74597i 1.18125i 0.806947 + 0.590624i \(0.201119\pi\)
−0.806947 + 0.590624i \(0.798881\pi\)
\(44\) −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 \(0.205397\pi\)
\(48\) −6.90329 0.586988i −0.996404 0.0847245i
\(49\) −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 \(0.5\pi\)
\(54\) −6.90329 + 2.51884i −0.939419 + 0.342771i
\(55\) 4.89898i 0.660578i
\(56\) −0.140537 7.48200i −0.0187800 0.999824i
\(57\) −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 \(0.222894\pi\)
−0.764687 + 0.644402i \(0.777106\pi\)
\(60\) −4.83013 + 0.818458i −0.623567 + 0.105662i
\(61\) −3.16228 −0.404888 −0.202444 0.979294i \(-0.564888\pi\)
−0.202444 + 0.979294i \(0.564888\pi\)
\(62\) 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
\(66\) −7.48203 4.00240i −0.920974 0.492662i
\(67\) 7.74597i 0.946320i −0.880976 0.473160i \(-0.843113\pi\)
0.880976 0.473160i \(-0.156887\pi\)
\(68\) 0 0
\(69\) 3.16228 + 7.07107i 0.380693 + 0.851257i
\(70\) −1.41886 5.09773i −0.169586 0.609295i
\(71\) 8.94427i 1.06149i −0.847532 0.530745i \(-0.821912\pi\)
0.847532 0.530745i \(-0.178088\pi\)
\(72\) 2.69615 8.04554i 0.317745 0.948176i
\(73\) 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
\(78\) 6.83013 + 3.65368i 0.773360 + 0.413698i
\(79\) −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 \(-0.873140\pi\)
0.921628 0.388075i \(-0.126860\pi\)
\(84\) 8.94476 + 1.99781i 0.975954 + 0.217978i
\(85\) 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 \(0.5\pi\)
\(90\) 0.423665 5.98502i 0.0446582 0.630877i
\(91\) −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
\(96\) 5.32215 + 8.22646i 0.543190 + 0.839610i
\(97\) 4.89898i 0.497416i −0.968579 0.248708i \(-0.919994\pi\)
0.968579 0.248708i \(-0.0800060\pi\)
\(98\) −1.14710 + 9.83281i −0.115874 + 0.993264i
\(99\) 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 \(-0.718274\pi\)
0.633238 0.773957i \(-0.281726\pi\)
\(102\) 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 \(-0.667524\pi\)
−0.502331 + 0.864675i \(0.667524\pi\)
\(108\) 8.79458 + 5.53674i 0.846258 + 0.532773i
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 5.47723 4.24264i 0.522233 0.404520i
\(111\) 0 0
\(112\) −8.24342 + 6.63672i −0.778930 + 0.627111i
\(113\) 4.47214i 0.420703i 0.977626 + 0.210352i \(0.0674609\pi\)
−0.977626 + 0.210352i \(0.932539\pi\)
\(114\) 6.83013 + 3.65368i 0.639700 + 0.342198i
\(115\) −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
\(120\) 5.09808 + 4.69144i 0.465389 + 0.428268i
\(121\) 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
\(126\) −4.96586 + 10.0668i −0.442394 + 0.896821i
\(127\) 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 \(0.0196778\pi\)
−0.998090 + 0.0617802i \(0.980322\pi\)
\(132\) 2.00480 + 11.8313i 0.174496 + 1.02979i
\(133\) −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 \(0.723153\pi\)
\(138\) 5.16708 9.65926i 0.439851 0.822251i
\(139\) 15.8114 1.34110 0.670552 0.741862i \(-0.266057\pi\)
0.670552 + 0.741862i \(0.266057\pi\)
\(140\) −4.47066 + 6.00110i −0.377840 + 0.507185i
\(141\) 17.3205 7.74597i 1.45865 0.652328i
\(142\) −10.0000 + 7.74597i −0.839181 + 0.650027i
\(143\) −10.9545 −0.916057
\(144\) −11.3301 + 3.95325i −0.944177 + 0.329438i
\(145\) 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 \(-0.408408\pi\)
0.283790 + 0.958886i \(0.408408\pi\)
\(150\) −6.47963 3.46618i −0.529059 0.283013i
\(151\) 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
\(154\) −12.4868 + 3.47549i −1.00622 + 0.280063i
\(155\) −6.92820 −0.556487
\(156\) −1.83013 10.8005i −0.146527 0.864731i
\(157\) 15.8114 1.26189 0.630943 0.775829i \(-0.282668\pi\)
0.630943 + 0.775829i \(0.282668\pi\)
\(158\) 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
\(162\) −9.13397 + 8.86400i −0.717633 + 0.696422i
\(163\) 23.2379i 1.82013i −0.414462 0.910066i \(-0.636030\pi\)
0.414462 0.910066i \(-0.363970\pi\)
\(164\) 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 \(0.177998\pi\)
\(168\) −5.51278 11.7307i −0.425320 0.905043i
\(169\) −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 \(-0.913372\pi\)
0.963196 0.268802i \(-0.0866276\pi\)
\(174\) 14.9641 + 8.00481i 1.13442 + 0.606843i
\(175\) 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 \(-0.373035\pi\)
0.388379 + 0.921500i \(0.373035\pi\)
\(180\) −7.05836 + 4.70951i −0.526099 + 0.351026i
\(181\) −3.16228 −0.235050 −0.117525 0.993070i \(-0.537496\pi\)
−0.117525 + 0.993070i \(0.537496\pi\)
\(182\) 11.3989 3.17267i 0.844940 0.235174i
\(183\) −5.00000 + 2.23607i −0.369611 + 0.165295i
\(184\) 5.00000 + 11.6190i 0.368605 + 0.856560i
\(185\) 0 0
\(186\) 5.66025 10.5812i 0.415030 0.775850i
\(187\) 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 \(-0.104891\pi\)
\(192\) 4.58834 13.0747i 0.331135 0.943583i
\(193\) −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
\(196\) 11.9868 7.23297i 0.856202 0.516641i
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) −14.6603 1.03776i −1.04186 0.0737506i
\(199\) 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
\(210\) −5.84805 7.05693i −0.403554 0.486974i
\(211\) 7.74597i 0.533254i −0.963800 0.266627i \(-0.914091\pi\)
0.963800 0.266627i \(-0.0859092\pi\)
\(212\) 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
\(216\) −1.42607 14.6276i −0.0970316 0.995281i
\(217\) 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 \(0.893605\pi\)
\(224\) 14.5591 + 3.46885i 0.972770 + 0.231772i
\(225\) 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 \(0.106552\pi\)
−0.944495 + 0.328526i \(0.893448\pi\)
\(228\) −1.83013 10.8005i −0.121203 0.715280i
\(229\) 15.8114 1.04485 0.522423 0.852686i \(-0.325028\pi\)
0.522423 + 0.852686i \(0.325028\pi\)
\(230\) 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 \(-0.0946467\pi\)
\(234\) 13.3829 + 0.947343i 0.874869 + 0.0619298i
\(235\) 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 \(0.953798\pi\)
\(240\) 0.830127 9.76273i 0.0535845 0.630181i
\(241\) 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
\(246\) 23.6603 + 12.6567i 1.50852 + 0.806963i
\(247\) 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 \(-0.836648\pi\)
0.871185 0.490954i \(-0.163352\pi\)
\(252\) 15.5556 3.16609i 0.979909 0.199445i
\(253\) 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 \(0.610989\pi\)
\(258\) 8.94965 16.7303i 0.557181 1.04158i
\(259\) 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 \(-0.0889307\pi\)
\(264\) 11.4916 12.4877i 0.707261 0.768564i
\(265\) 0 0
\(266\) 11.3989 3.17267i 0.698909 0.194529i
\(267\) 0 0
\(268\) 15.0000 + 3.87298i 0.916271 + 0.236580i
\(269\) 9.89949i 0.603583i 0.953374 + 0.301791i \(0.0975846\pi\)
−0.953374 + 0.301791i \(0.902415\pi\)
\(270\) −3.56218 9.76273i −0.216787 0.594141i
\(271\) 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
\(276\) −15.2742 + 2.58819i −0.919399 + 0.155791i
\(277\) 15.4919i 0.930820i −0.885095 0.465410i \(-0.845907\pi\)
0.885095 0.465410i \(-0.154093\pi\)
\(278\) −13.6931 17.6777i −0.821255 1.06024i
\(279\) 10.9545 + 9.79796i 0.655826 + 0.586588i
\(280\) 10.5811 0.198749i 0.632344 0.0118775i
\(281\) 8.94427i 0.533571i −0.963756 0.266785i \(-0.914039\pi\)
0.963756 0.266785i \(-0.0859614\pi\)
\(282\) −23.6603 12.6567i −1.40895 0.753696i
\(283\) 15.8114 0.939889 0.469945 0.882696i \(-0.344274\pi\)
0.469945 + 0.882696i \(0.344274\pi\)
\(284\) 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
\(288\) 14.2321 + 9.24385i 0.838632 + 0.544699i
\(289\) −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 \(0.287277\pi\)
−0.619644 + 0.784883i \(0.712723\pi\)
\(294\) 5.13913 + 16.3582i 0.299720 + 0.954027i
\(295\) −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
\(300\) 1.73621 + 10.2462i 0.100240 + 0.591567i
\(301\) 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 \(-0.528764\pi\)
−0.0902404 + 0.995920i \(0.528764\pi\)
\(308\) 14.6996 + 10.9508i 0.837589 + 0.623982i
\(309\) −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 \(0.600525\pi\)
\(312\) −10.4904 + 11.3996i −0.593901 + 0.645378i
\(313\) 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 \(-0.562329\pi\)
−0.194563 + 0.980890i \(0.562329\pi\)
\(318\) 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
\(322\) −4.48683 16.1204i −0.250041 0.898357i
\(323\) 0 0
\(324\) 17.8205 + 2.53564i 0.990028 + 0.140869i
\(325\) −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
\(330\) 5.66025 10.5812i 0.311587 0.582475i
\(331\) 7.74597i 0.425757i 0.977079 + 0.212878i \(0.0682838\pi\)
−0.977079 + 0.212878i \(0.931716\pi\)
\(332\) 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
\(336\) −8.34111 + 16.3226i −0.455045 + 0.890468i
\(337\) 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
\(342\) 13.3829 + 0.947343i 0.723665 + 0.0512265i
\(343\) −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 \(-0.346088\pi\)
0.464907 + 0.885360i \(0.346088\pi\)
\(348\) −4.00961 23.6627i −0.214938 1.26845i
\(349\) −22.1359 −1.18491 −0.592455 0.805604i \(-0.701841\pi\)
−0.592455 + 0.805604i \(0.701841\pi\)
\(350\) −10.8139 + 3.00986i −0.578028 + 0.160884i
\(351\) −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 \(0.405838\pi\)
\(354\) 11.4378 21.3817i 0.607913 1.13642i
\(355\) 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 \(0.690551\pi\)
\(360\) 11.3781 + 3.81294i 0.599679 + 0.200959i
\(361\) −9.00000 −0.473684
\(362\) 2.73861 + 3.53553i 0.143938 + 0.185824i
\(363\) 1.58114 0.707107i 0.0829883 0.0371135i
\(364\) −13.4189 9.99671i −0.703339 0.523970i
\(365\) −20.7846 −1.08792
\(366\) 6.83013 + 3.65368i 0.357016 + 0.190981i
\(367\) 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
\(372\) −16.7321 + 2.83522i −0.867516 + 0.146999i
\(373\) 30.9839i 1.60428i −0.597133 0.802142i \(-0.703694\pi\)
0.597133 0.802142i \(-0.296306\pi\)
\(374\) 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
\(378\) −0.733419 + 19.4284i −0.0377230 + 0.999288i
\(379\) 23.2379i 1.19365i 0.802371 + 0.596825i \(0.203571\pi\)
−0.802371 + 0.596825i \(0.796429\pi\)
\(380\) 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 \(0.590292\pi\)
\(384\) −18.5916 + 6.19307i −0.948746 + 0.316039i
\(385\) 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 \(-0.747954\pi\)
−0.702548 + 0.711637i \(0.747954\pi\)
\(390\) −5.16708 + 9.65926i −0.261645 + 0.489116i
\(391\) 0 0
\(392\) −18.4676 7.13775i −0.932755 0.360511i
\(393\) 1.00000 + 2.23607i 0.0504433 + 0.112795i
\(394\) 0 0
\(395\) 14.1421i 0.711568i
\(396\) 11.5359 + 17.2894i 0.579701 + 0.868825i
\(397\) −22.1359 −1.11097 −0.555486 0.831526i \(-0.687468\pi\)
−0.555486 + 0.831526i \(0.687468\pi\)
\(398\) 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 \(0.964382\pi\)
\(402\) −8.94965 + 16.7303i −0.446368 + 0.834433i
\(403\) 15.4919i 0.771708i
\(404\) 30.1247 + 7.77817i 1.49876 + 0.386979i
\(405\) 12.6491 1.41421i 0.628539 0.0702728i
\(406\) 24.9737 6.95097i 1.23942 0.344971i
\(407\) 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
\(414\) 1.33975 18.9263i 0.0658449 0.930177i
\(415\) 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 \(-0.800208\pi\)
0.809402 0.587255i \(-0.199792\pi\)
\(420\) −2.82532 + 12.6498i −0.137862 + 0.617247i
\(421\) 30.9839i 1.51006i 0.655690 + 0.755031i \(0.272378\pi\)
−0.655690 + 0.755031i \(0.727622\pi\)
\(422\) −8.66025 + 6.70820i −0.421575 + 0.326550i
\(423\) 21.9089 24.4949i 1.06525 1.19098i
\(424\) 0 0
\(425\) 0 0
\(426\) −10.3342 + 19.3185i −0.500692 + 0.935985i
\(427\) −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 \(-0.181023\pi\)
\(432\) −15.1191 + 14.2623i −0.727420 + 0.686193i
\(433\) 14.6969i 0.706290i −0.935569 0.353145i \(-0.885112\pi\)
0.935569 0.353145i \(-0.114888\pi\)
\(434\) −4.91508 17.6590i −0.235931 0.847661i
\(435\) −6.92820 15.4919i −0.332182 0.742781i
\(436\) 0 0
\(437\) 14.1421i 0.676510i
\(438\) 16.9808 31.7436i 0.811372 1.51677i
\(439\) 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 \(-0.634981\pi\)
−0.411461 + 0.911427i \(0.634981\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 10.9545 8.48528i 0.518708 0.401790i
\(447\) 10.9545 4.89898i 0.518128 0.231714i
\(448\) −8.73025 19.2817i −0.412466 0.910973i
\(449\) 8.94427i 0.422106i −0.977475 0.211053i \(-0.932311\pi\)
0.977475 0.211053i \(-0.0676893\pi\)
\(450\) −12.6962 0.898729i −0.598502 0.0423665i
\(451\) −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
\(456\) −10.4904 + 11.3996i −0.491257 + 0.533837i
\(457\) 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 \(-0.882003\pi\)
0.932075 0.362266i \(-0.117997\pi\)
\(462\) −17.2859 + 14.3247i −0.804212 + 0.666448i
\(463\) 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 \(-0.947688\pi\)
0.986526 0.163605i \(-0.0523123\pi\)
\(468\) −10.5308 15.7830i −0.486786 0.729569i
\(469\) −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
\(474\) 21.5988 + 11.5539i 0.992064 + 0.530690i
\(475\) −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 \(0.419484\pi\)
\(480\) −11.6340 + 7.52666i −0.531016 + 0.343544i
\(481\) 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
\(486\) −8.17429 + 20.4739i −0.370793 + 0.928715i
\(487\) 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
\(490\) −13.9057 1.62224i −0.628195 0.0732854i
\(491\) −3.46410 −0.156333 −0.0781664 0.996940i \(-0.524907\pi\)
−0.0781664 + 0.996940i \(0.524907\pi\)
\(492\) −6.33975 37.4140i −0.285818 1.68675i
\(493\) 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
\(498\) −8.16987 + 15.2726i −0.366101 + 0.684383i
\(499\) 7.74597i 0.346757i −0.984855 0.173379i \(-0.944532\pi\)
0.984855 0.173379i \(-0.0554684\pi\)
\(500\) −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 \(0.761718\pi\)
\(504\) −17.0113 14.6497i −0.757745 0.652551i
\(505\) 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 \(0.0704079\pi\)
−0.975636 + 0.219394i \(0.929592\pi\)
\(510\) 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
\(516\) −26.4557 + 4.48288i −1.16465 + 0.197348i
\(517\) 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 \(0.244195\pi\)
\(522\) 29.3205 + 2.07553i 1.28332 + 0.0908433i
\(523\) −3.16228 −0.138277 −0.0691384 0.997607i \(-0.522025\pi\)
−0.0691384 + 0.997607i \(0.522025\pi\)
\(524\) −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
\(528\) −23.9137 2.03339i −1.04071 0.0884918i
\(529\) 3.00000 0.130435
\(530\) 0 0
\(531\) 22.1359 + 19.7990i 0.960618 + 0.859203i
\(532\) −13.4189 9.99671i −0.581781 0.433412i
\(533\) 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
\(540\) −7.83013 + 12.4374i −0.336955 + 0.535221i
\(541\) 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
\(546\) 15.7798 13.0766i 0.675312 0.559629i
\(547\) 7.74597i 0.331194i 0.986194 + 0.165597i \(0.0529550\pi\)
−0.986194 + 0.165597i \(0.947045\pi\)
\(548\) −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
\(552\) 16.1215 + 14.8356i 0.686178 + 0.631447i
\(553\) −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 \(0.5\pi\)
\(558\) 1.46762 20.7327i 0.0621292 0.877686i
\(559\) 24.4949i 1.03602i
\(560\) −9.38574 11.6580i −0.396620 0.492638i
\(561\) 0 0
\(562\) −10.0000 + 7.74597i −0.421825 + 0.326744i
\(563\) 1.41421i 0.0596020i 0.999556 + 0.0298010i \(0.00948736\pi\)
−0.999556 + 0.0298010i \(0.990513\pi\)
\(564\) 6.33975 + 37.4140i 0.266951 + 1.57541i
\(565\) −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 \(-0.155279\pi\)
\(570\) −5.16708 + 9.65926i −0.216425 + 0.404582i
\(571\) 7.74597i 0.324159i −0.986778 0.162079i \(-0.948180\pi\)
0.986778 0.162079i \(-0.0518200\pi\)
\(572\) 5.47723 21.2132i 0.229014 0.886969i
\(573\) −6.32456 14.1421i −0.264212 0.590796i
\(574\) 39.4868 10.9905i 1.64815 0.458733i
\(575\) 13.4164i 0.559503i
\(576\) −1.99038 23.9173i −0.0829325 0.996555i
\(577\) 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
\(582\) −5.66025 + 10.5812i −0.234625 + 0.438604i
\(583\) 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 \(0.260310\pi\)
−0.683836 + 0.729636i \(0.739690\pi\)
\(588\) 13.8384 19.9123i 0.570685 0.821169i
\(589\) 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 \(0.264244\pi\)
\(594\) −23.9137 + 8.72552i −0.981191 + 0.358012i
\(595\) 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 \(-0.0584923\pi\)
\(600\) 9.95205 10.8147i 0.406291 0.441506i
\(601\) 24.4949i 0.999168i 0.866266 + 0.499584i \(0.166514\pi\)
−0.866266 + 0.499584i \(0.833486\pi\)
\(602\) −7.77142 27.9214i −0.316740 1.13799i
\(603\) −17.3205 15.4919i −0.705346 0.630880i
\(604\) −4.00000 + 15.4919i −0.162758 + 0.630358i
\(605\) 1.41421i 0.0574960i
\(606\) −17.9737 + 33.5998i −0.730132 + 1.36490i
\(607\) 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 \(0.387849\pi\)
−0.345089 + 0.938570i \(0.612151\pi\)
\(614\) 2.73861 + 3.53553i 0.110521 + 0.142683i
\(615\) −10.9545 24.4949i −0.441726 0.987730i
\(616\) −0.486833 25.9184i −0.0196151 1.04428i
\(617\) 31.3050i 1.26029i 0.776478 + 0.630145i \(0.217005\pi\)
−0.776478 + 0.630145i \(0.782995\pi\)
\(618\) −11.3205 + 21.1624i −0.455378 + 0.851276i
\(619\) −3.16228 −0.127103 −0.0635513 0.997979i \(-0.520243\pi\)
−0.0635513 + 0.997979i \(0.520243\pi\)
\(620\) 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
\(624\) 21.8301 + 1.85622i 0.873904 + 0.0743083i
\(625\) −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
\(630\) −14.2366 7.02279i −0.567199 0.279795i
\(631\) −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 \(0.787848\pi\)
\(642\) 22.4461 + 12.0072i 0.885876 + 0.473887i
\(643\) −3.16228 −0.124708 −0.0623540 0.998054i \(-0.519861\pi\)
−0.0623540 + 0.998054i \(0.519861\pi\)
\(644\) −14.1375 + 18.9771i −0.557095 + 0.747804i
\(645\) −17.3205 + 7.74597i −0.681994 + 0.304997i
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) −12.5981 22.1199i −0.494899 0.868950i
\(649\) 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 \(-0.102172\pi\)
0.948925 + 0.315501i \(0.102172\pi\)
\(654\) 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
\(658\) −39.4868 + 10.9905i −1.53936 + 0.428452i
\(659\) 24.2487 0.944596 0.472298 0.881439i \(-0.343425\pi\)
0.472298 + 0.881439i \(0.343425\pi\)
\(660\) −16.7321 + 2.83522i −0.651294 + 0.110361i
\(661\) −41.1096 −1.59898 −0.799489 0.600680i \(-0.794896\pi\)
−0.799489 + 0.600680i \(0.794896\pi\)
\(662\) 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
\(672\) 25.4728 4.81010i 0.982634 0.185554i
\(673\) −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 \(-0.956613\pi\)
0.990725 0.135882i \(-0.0433867\pi\)
\(678\) 5.16708 9.65926i 0.198441 0.370962i
\(679\) −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 \(-0.703433\pi\)
−0.596476 + 0.802631i \(0.703433\pi\)
\(684\) −10.5308 15.7830i −0.402655 0.603477i
\(685\) −25.2982 −0.966595
\(686\) 22.9383 + 12.6426i 0.875787 + 0.482697i
\(687\) 25.0000 11.1803i 0.953809 0.426557i
\(688\) 15.0000 27.1109i 0.571870 1.03359i
\(689\) 0 0
\(690\) 13.6603 + 7.30736i 0.520037 + 0.278186i
\(691\) −3.16228 −0.120299 −0.0601494 0.998189i \(-0.519158\pi\)
−0.0601494 + 0.998189i \(0.519158\pi\)
\(692\) 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
\(696\) −22.9833 + 24.9754i −0.871179 + 0.946689i
\(697\) 0 0
\(698\) 19.1703 + 24.7487i 0.725606 + 0.936754i
\(699\) −6.32456 14.1421i −0.239217 0.534905i
\(700\) 12.7302 + 9.48371i 0.481158 + 0.358451i
\(701\) 20.7846 0.785024 0.392512 0.919747i \(-0.371606\pi\)
0.392512 + 0.919747i \(0.371606\pi\)
\(702\) 21.8301 7.96527i 0.823925 0.300630i
\(703\) 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
\(708\) −33.8109 + 5.72920i −1.27069 + 0.215317i
\(709\) 30.9839i 1.16362i 0.813323 + 0.581812i \(0.197656\pi\)
−0.813323 + 0.581812i \(0.802344\pi\)
\(710\) −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 \(0.709956\pi\)
\(720\) −5.59075 16.0232i −0.208355 0.597150i
\(721\) −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
\(726\) −2.15988 1.15539i −0.0801605 0.0428807i
\(727\) 19.5959i 0.726772i −0.931639 0.363386i \(-0.881621\pi\)
0.931639 0.363386i \(-0.118379\pi\)
\(728\) 0.444416 + 23.6601i 0.0164711 + 0.876903i
\(729\) −22.0000 15.6525i −0.814815 0.579721i
\(730\) 18.0000 + 23.2379i 0.666210 + 0.860073i
\(731\) 0 0
\(732\) −1.83013 10.8005i −0.0676434 0.399198i
\(733\) 15.8114 0.584007 0.292003 0.956417i \(-0.405678\pi\)
0.292003 + 0.956417i \(0.405678\pi\)
\(734\) −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
\(738\) 46.3598 + 3.28169i 1.70653 + 0.120801i
\(739\) 23.2379i 0.854820i 0.904058 + 0.427410i \(0.140574\pi\)
−0.904058 + 0.427410i \(0.859426\pi\)
\(740\) 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 \(-0.358172\pi\)
\(744\) 17.6603 + 16.2516i 0.647456 + 0.595814i
\(745\) 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
\(750\) 13.0718 24.4362i 0.477315 0.892284i
\(751\) −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
\(756\) 22.3568 16.0055i 0.813107 0.582114i
\(757\) 46.4758i 1.68919i −0.535404 0.844596i \(-0.679841\pi\)
0.535404 0.844596i \(-0.320159\pi\)
\(758\) 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 \(0.563623\pi\)
\(762\) −17.2790 9.24316i −0.625952 0.334844i
\(763\) 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
\(768\) 23.0248 + 15.4226i 0.830837 + 0.556516i
\(769\) 24.4949i 0.883309i −0.897185 0.441654i \(-0.854392\pi\)
0.897185 0.441654i \(-0.145608\pi\)
\(770\) −4.91508 17.6590i −0.177127 0.636388i
\(771\) −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 \(0.219339\pi\)
−0.771836 + 0.635822i \(0.780661\pi\)
\(774\) 2.32051 32.7813i 0.0834089 1.17830i
\(775\) 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
\(780\) 15.2742 2.58819i 0.546904 0.0926721i
\(781\) 30.9839i 1.10869i
\(782\) 0 0
\(783\) −10.9545 + 34.2929i −0.391480 +