Properties

Label 24.3.h.c.5.1
Level $24$
Weight $3$
Character 24.5
Analytic conductor $0.654$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 24.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.653952634465\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-7})\)
Defining polynomial: \(x^{4} + 6 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-0.707107 - 1.87083i\) of defining polynomial
Character \(\chi\) \(=\) 24.5
Dual form 24.3.h.c.5.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 1.87083i) q^{2} +(-1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} +5.65685 q^{5} +(-3.94975 + 4.51658i) q^{6} +4.00000 q^{7} +(7.07107 + 3.74166i) q^{8} +(-5.00000 + 7.48331i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 1.87083i) q^{2} +(-1.41421 - 2.64575i) q^{3} +(-3.00000 + 2.64575i) q^{4} +5.65685 q^{5} +(-3.94975 + 4.51658i) q^{6} +4.00000 q^{7} +(7.07107 + 3.74166i) q^{8} +(-5.00000 + 7.48331i) q^{9} +(-4.00000 - 10.5830i) q^{10} -8.48528 q^{11} +(11.2426 + 4.19560i) q^{12} +10.5830i q^{13} +(-2.82843 - 7.48331i) q^{14} +(-8.00000 - 14.9666i) q^{15} +(2.00000 - 15.8745i) q^{16} -14.9666i q^{17} +(17.5355 + 4.06264i) q^{18} +5.29150i q^{19} +(-16.9706 + 14.9666i) q^{20} +(-5.65685 - 10.5830i) q^{21} +(6.00000 + 15.8745i) q^{22} +29.9333i q^{23} +(-0.100505 - 23.9998i) q^{24} +7.00000 q^{25} +(19.7990 - 7.48331i) q^{26} +(26.8701 + 2.64575i) q^{27} +(-12.0000 + 10.5830i) q^{28} -16.9706 q^{29} +(-22.3431 + 25.5496i) q^{30} -4.00000 q^{31} +(-31.1127 + 7.48331i) q^{32} +(12.0000 + 22.4499i) q^{33} +(-28.0000 + 10.5830i) q^{34} +22.6274 q^{35} +(-4.79899 - 35.6787i) q^{36} -52.9150i q^{37} +(9.89949 - 3.74166i) q^{38} +(28.0000 - 14.9666i) q^{39} +(40.0000 + 21.1660i) q^{40} -29.9333i q^{41} +(-15.7990 + 18.0663i) q^{42} -5.29150i q^{43} +(25.4558 - 22.4499i) q^{44} +(-28.2843 + 42.3320i) q^{45} +(56.0000 - 21.1660i) q^{46} +(-44.8284 + 17.1584i) q^{48} -33.0000 q^{49} +(-4.94975 - 13.0958i) q^{50} +(-39.5980 + 21.1660i) q^{51} +(-28.0000 - 31.7490i) q^{52} +50.9117 q^{53} +(-14.0503 - 52.1401i) q^{54} -48.0000 q^{55} +(28.2843 + 14.9666i) q^{56} +(14.0000 - 7.48331i) q^{57} +(12.0000 + 31.7490i) q^{58} -48.0833 q^{59} +(63.5980 + 23.7339i) q^{60} +95.2470i q^{61} +(2.82843 + 7.48331i) q^{62} +(-20.0000 + 29.9333i) q^{63} +(36.0000 + 52.9150i) q^{64} +59.8665i q^{65} +(33.5147 - 38.3245i) q^{66} -47.6235i q^{67} +(39.5980 + 44.8999i) q^{68} +(79.1960 - 42.3320i) q^{69} +(-16.0000 - 42.3320i) q^{70} -89.7998i q^{71} +(-63.3553 + 34.2067i) q^{72} -6.00000 q^{73} +(-98.9949 + 37.4166i) q^{74} +(-9.89949 - 18.5203i) q^{75} +(-14.0000 - 15.8745i) q^{76} -33.9411 q^{77} +(-47.7990 - 41.8002i) q^{78} +124.000 q^{79} +(11.3137 - 89.7998i) q^{80} +(-31.0000 - 74.8331i) q^{81} +(-56.0000 + 21.1660i) q^{82} +2.82843 q^{83} +(44.9706 + 16.7824i) q^{84} -84.6640i q^{85} +(-9.89949 + 3.74166i) q^{86} +(24.0000 + 44.8999i) q^{87} +(-60.0000 - 31.7490i) q^{88} +104.766i q^{89} +(99.1960 + 22.9818i) q^{90} +42.3320i q^{91} +(-79.1960 - 89.7998i) q^{92} +(5.65685 + 10.5830i) q^{93} +29.9333i q^{95} +(63.7990 + 71.7335i) q^{96} +118.000 q^{97} +(23.3345 + 61.7373i) q^{98} +(42.4264 - 63.4980i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 12q^{4} + 4q^{6} + 16q^{7} - 20q^{9} + O(q^{10}) \) \( 4q - 12q^{4} + 4q^{6} + 16q^{7} - 20q^{9} - 16q^{10} + 28q^{12} - 32q^{15} + 8q^{16} + 56q^{18} + 24q^{22} - 40q^{24} + 28q^{25} - 48q^{28} - 112q^{30} - 16q^{31} + 48q^{33} - 112q^{34} + 60q^{36} + 112q^{39} + 160q^{40} + 16q^{42} + 224q^{46} - 168q^{48} - 132q^{49} - 112q^{52} - 76q^{54} - 192q^{55} + 56q^{57} + 48q^{58} + 96q^{60} - 80q^{63} + 144q^{64} + 168q^{66} - 64q^{70} - 112q^{72} - 24q^{73} - 56q^{76} - 112q^{78} + 496q^{79} - 124q^{81} - 224q^{82} + 112q^{84} + 96q^{87} - 240q^{88} + 80q^{90} + 176q^{96} + 472q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/24\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(13\) \(17\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 1.87083i −0.353553 0.935414i
\(3\) −1.41421 2.64575i −0.471405 0.881917i
\(4\) −3.00000 + 2.64575i −0.750000 + 0.661438i
\(5\) 5.65685 1.13137 0.565685 0.824621i \(-0.308612\pi\)
0.565685 + 0.824621i \(0.308612\pi\)
\(6\) −3.94975 + 4.51658i −0.658291 + 0.752763i
\(7\) 4.00000 0.571429 0.285714 0.958315i \(-0.407769\pi\)
0.285714 + 0.958315i \(0.407769\pi\)
\(8\) 7.07107 + 3.74166i 0.883883 + 0.467707i
\(9\) −5.00000 + 7.48331i −0.555556 + 0.831479i
\(10\) −4.00000 10.5830i −0.400000 1.05830i
\(11\) −8.48528 −0.771389 −0.385695 0.922627i \(-0.626038\pi\)
−0.385695 + 0.922627i \(0.626038\pi\)
\(12\) 11.2426 + 4.19560i 0.936887 + 0.349633i
\(13\) 10.5830i 0.814077i 0.913411 + 0.407039i \(0.133439\pi\)
−0.913411 + 0.407039i \(0.866561\pi\)
\(14\) −2.82843 7.48331i −0.202031 0.534522i
\(15\) −8.00000 14.9666i −0.533333 0.997775i
\(16\) 2.00000 15.8745i 0.125000 0.992157i
\(17\) 14.9666i 0.880390i −0.897902 0.440195i \(-0.854909\pi\)
0.897902 0.440195i \(-0.145091\pi\)
\(18\) 17.5355 + 4.06264i 0.974196 + 0.225702i
\(19\) 5.29150i 0.278500i 0.990257 + 0.139250i \(0.0444692\pi\)
−0.990257 + 0.139250i \(0.955531\pi\)
\(20\) −16.9706 + 14.9666i −0.848528 + 0.748331i
\(21\) −5.65685 10.5830i −0.269374 0.503953i
\(22\) 6.00000 + 15.8745i 0.272727 + 0.721569i
\(23\) 29.9333i 1.30145i 0.759315 + 0.650723i \(0.225534\pi\)
−0.759315 + 0.650723i \(0.774466\pi\)
\(24\) −0.100505 23.9998i −0.00418771 0.999991i
\(25\) 7.00000 0.280000
\(26\) 19.7990 7.48331i 0.761500 0.287820i
\(27\) 26.8701 + 2.64575i 0.995187 + 0.0979908i
\(28\) −12.0000 + 10.5830i −0.428571 + 0.377964i
\(29\) −16.9706 −0.585192 −0.292596 0.956236i \(-0.594519\pi\)
−0.292596 + 0.956236i \(0.594519\pi\)
\(30\) −22.3431 + 25.5496i −0.744772 + 0.851654i
\(31\) −4.00000 −0.129032 −0.0645161 0.997917i \(-0.520550\pi\)
−0.0645161 + 0.997917i \(0.520550\pi\)
\(32\) −31.1127 + 7.48331i −0.972272 + 0.233854i
\(33\) 12.0000 + 22.4499i 0.363636 + 0.680301i
\(34\) −28.0000 + 10.5830i −0.823529 + 0.311265i
\(35\) 22.6274 0.646498
\(36\) −4.79899 35.6787i −0.133305 0.991075i
\(37\) 52.9150i 1.43014i −0.699055 0.715068i \(-0.746396\pi\)
0.699055 0.715068i \(-0.253604\pi\)
\(38\) 9.89949 3.74166i 0.260513 0.0984647i
\(39\) 28.0000 14.9666i 0.717949 0.383760i
\(40\) 40.0000 + 21.1660i 1.00000 + 0.529150i
\(41\) 29.9333i 0.730079i −0.930992 0.365040i \(-0.881055\pi\)
0.930992 0.365040i \(-0.118945\pi\)
\(42\) −15.7990 + 18.0663i −0.376166 + 0.430150i
\(43\) 5.29150i 0.123058i −0.998105 0.0615291i \(-0.980402\pi\)
0.998105 0.0615291i \(-0.0195977\pi\)
\(44\) 25.4558 22.4499i 0.578542 0.510226i
\(45\) −28.2843 + 42.3320i −0.628539 + 0.940712i
\(46\) 56.0000 21.1660i 1.21739 0.460131i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) −44.8284 + 17.1584i −0.933926 + 0.357468i
\(49\) −33.0000 −0.673469
\(50\) −4.94975 13.0958i −0.0989949 0.261916i
\(51\) −39.5980 + 21.1660i −0.776431 + 0.415020i
\(52\) −28.0000 31.7490i −0.538462 0.610558i
\(53\) 50.9117 0.960598 0.480299 0.877105i \(-0.340528\pi\)
0.480299 + 0.877105i \(0.340528\pi\)
\(54\) −14.0503 52.1401i −0.260190 0.965557i
\(55\) −48.0000 −0.872727
\(56\) 28.2843 + 14.9666i 0.505076 + 0.267261i
\(57\) 14.0000 7.48331i 0.245614 0.131286i
\(58\) 12.0000 + 31.7490i 0.206897 + 0.547397i
\(59\) −48.0833 −0.814971 −0.407485 0.913212i \(-0.633594\pi\)
−0.407485 + 0.913212i \(0.633594\pi\)
\(60\) 63.5980 + 23.7339i 1.05997 + 0.395565i
\(61\) 95.2470i 1.56143i 0.624889 + 0.780714i \(0.285144\pi\)
−0.624889 + 0.780714i \(0.714856\pi\)
\(62\) 2.82843 + 7.48331i 0.0456198 + 0.120699i
\(63\) −20.0000 + 29.9333i −0.317460 + 0.475131i
\(64\) 36.0000 + 52.9150i 0.562500 + 0.826797i
\(65\) 59.8665i 0.921023i
\(66\) 33.5147 38.3245i 0.507799 0.580674i
\(67\) 47.6235i 0.710799i −0.934715 0.355399i \(-0.884345\pi\)
0.934715 0.355399i \(-0.115655\pi\)
\(68\) 39.5980 + 44.8999i 0.582323 + 0.660292i
\(69\) 79.1960 42.3320i 1.14777 0.613508i
\(70\) −16.0000 42.3320i −0.228571 0.604743i
\(71\) 89.7998i 1.26479i −0.774648 0.632393i \(-0.782073\pi\)
0.774648 0.632393i \(-0.217927\pi\)
\(72\) −63.3553 + 34.2067i −0.879935 + 0.475094i
\(73\) −6.00000 −0.0821918 −0.0410959 0.999155i \(-0.513085\pi\)
−0.0410959 + 0.999155i \(0.513085\pi\)
\(74\) −98.9949 + 37.4166i −1.33777 + 0.505629i
\(75\) −9.89949 18.5203i −0.131993 0.246937i
\(76\) −14.0000 15.8745i −0.184211 0.208875i
\(77\) −33.9411 −0.440794
\(78\) −47.7990 41.8002i −0.612808 0.535900i
\(79\) 124.000 1.56962 0.784810 0.619736i \(-0.212760\pi\)
0.784810 + 0.619736i \(0.212760\pi\)
\(80\) 11.3137 89.7998i 0.141421 1.12250i
\(81\) −31.0000 74.8331i −0.382716 0.923866i
\(82\) −56.0000 + 21.1660i −0.682927 + 0.258122i
\(83\) 2.82843 0.0340774 0.0170387 0.999855i \(-0.494576\pi\)
0.0170387 + 0.999855i \(0.494576\pi\)
\(84\) 44.9706 + 16.7824i 0.535364 + 0.199790i
\(85\) 84.6640i 0.996048i
\(86\) −9.89949 + 3.74166i −0.115110 + 0.0435076i
\(87\) 24.0000 + 44.8999i 0.275862 + 0.516091i
\(88\) −60.0000 31.7490i −0.681818 0.360784i
\(89\) 104.766i 1.17715i 0.808442 + 0.588575i \(0.200311\pi\)
−0.808442 + 0.588575i \(0.799689\pi\)
\(90\) 99.1960 + 22.9818i 1.10218 + 0.255353i
\(91\) 42.3320i 0.465187i
\(92\) −79.1960 89.7998i −0.860826 0.976085i
\(93\) 5.65685 + 10.5830i 0.0608264 + 0.113796i
\(94\) 0 0
\(95\) 29.9333i 0.315087i
\(96\) 63.7990 + 71.7335i 0.664573 + 0.747224i
\(97\) 118.000 1.21649 0.608247 0.793747i \(-0.291873\pi\)
0.608247 + 0.793747i \(0.291873\pi\)
\(98\) 23.3345 + 61.7373i 0.238107 + 0.629973i
\(99\) 42.4264 63.4980i 0.428550 0.641394i
\(100\) −21.0000 + 18.5203i −0.210000 + 0.185203i
\(101\) −62.2254 −0.616093 −0.308047 0.951371i \(-0.599675\pi\)
−0.308047 + 0.951371i \(0.599675\pi\)
\(102\) 67.5980 + 59.1144i 0.662725 + 0.579553i
\(103\) −108.000 −1.04854 −0.524272 0.851551i \(-0.675662\pi\)
−0.524272 + 0.851551i \(0.675662\pi\)
\(104\) −39.5980 + 74.8331i −0.380750 + 0.719549i
\(105\) −32.0000 59.8665i −0.304762 0.570157i
\(106\) −36.0000 95.2470i −0.339623 0.898557i
\(107\) 144.250 1.34813 0.674064 0.738673i \(-0.264547\pi\)
0.674064 + 0.738673i \(0.264547\pi\)
\(108\) −87.6102 + 63.1542i −0.811205 + 0.584761i
\(109\) 52.9150i 0.485459i 0.970094 + 0.242729i \(0.0780427\pi\)
−0.970094 + 0.242729i \(0.921957\pi\)
\(110\) 33.9411 + 89.7998i 0.308556 + 0.816362i
\(111\) −140.000 + 74.8331i −1.26126 + 0.674173i
\(112\) 8.00000 63.4980i 0.0714286 0.566947i
\(113\) 89.7998i 0.794688i −0.917670 0.397344i \(-0.869932\pi\)
0.917670 0.397344i \(-0.130068\pi\)
\(114\) −23.8995 20.9001i −0.209645 0.183334i
\(115\) 169.328i 1.47242i
\(116\) 50.9117 44.8999i 0.438894 0.387068i
\(117\) −79.1960 52.9150i −0.676889 0.452265i
\(118\) 34.0000 + 89.9555i 0.288136 + 0.762335i
\(119\) 59.8665i 0.503080i
\(120\) −0.568542 135.763i −0.00473785 1.13136i
\(121\) −49.0000 −0.404959
\(122\) 178.191 67.3498i 1.46058 0.552048i
\(123\) −79.1960 + 42.3320i −0.643870 + 0.344163i
\(124\) 12.0000 10.5830i 0.0967742 0.0853468i
\(125\) −101.823 −0.814587
\(126\) 70.1421 + 16.2506i 0.556684 + 0.128973i
\(127\) 76.0000 0.598425 0.299213 0.954186i \(-0.403276\pi\)
0.299213 + 0.954186i \(0.403276\pi\)
\(128\) 73.5391 104.766i 0.574524 0.818488i
\(129\) −14.0000 + 7.48331i −0.108527 + 0.0580102i
\(130\) 112.000 42.3320i 0.861538 0.325631i
\(131\) −14.1421 −0.107955 −0.0539776 0.998542i \(-0.517190\pi\)
−0.0539776 + 0.998542i \(0.517190\pi\)
\(132\) −95.3970 35.6008i −0.722704 0.269703i
\(133\) 21.1660i 0.159143i
\(134\) −89.0955 + 33.6749i −0.664891 + 0.251305i
\(135\) 152.000 + 14.9666i 1.12593 + 0.110864i
\(136\) 56.0000 105.830i 0.411765 0.778162i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −135.196 118.229i −0.979681 0.856731i
\(139\) 121.705i 0.875572i −0.899079 0.437786i \(-0.855763\pi\)
0.899079 0.437786i \(-0.144237\pi\)
\(140\) −67.8823 + 59.8665i −0.484873 + 0.427618i
\(141\) 0 0
\(142\) −168.000 + 63.4980i −1.18310 + 0.447169i
\(143\) 89.7998i 0.627970i
\(144\) 108.794 + 94.3392i 0.755513 + 0.655133i
\(145\) −96.0000 −0.662069
\(146\) 4.24264 + 11.2250i 0.0290592 + 0.0768834i
\(147\) 46.6690 + 87.3098i 0.317477 + 0.593944i
\(148\) 140.000 + 158.745i 0.945946 + 1.07260i
\(149\) 186.676 1.25286 0.626430 0.779478i \(-0.284515\pi\)
0.626430 + 0.779478i \(0.284515\pi\)
\(150\) −27.6482 + 31.6161i −0.184322 + 0.210774i
\(151\) −60.0000 −0.397351 −0.198675 0.980065i \(-0.563664\pi\)
−0.198675 + 0.980065i \(0.563664\pi\)
\(152\) −19.7990 + 37.4166i −0.130257 + 0.246162i
\(153\) 112.000 + 74.8331i 0.732026 + 0.489106i
\(154\) 24.0000 + 63.4980i 0.155844 + 0.412325i
\(155\) −22.6274 −0.145983
\(156\) −44.4020 + 118.981i −0.284628 + 0.762698i
\(157\) 116.413i 0.741484i −0.928736 0.370742i \(-0.879103\pi\)
0.928736 0.370742i \(-0.120897\pi\)
\(158\) −87.6812 231.983i −0.554945 1.46825i
\(159\) −72.0000 134.700i −0.452830 0.847168i
\(160\) −176.000 + 42.3320i −1.10000 + 0.264575i
\(161\) 119.733i 0.743683i
\(162\) −118.080 + 110.911i −0.728887 + 0.684634i
\(163\) 291.033i 1.78548i −0.450576 0.892738i \(-0.648781\pi\)
0.450576 0.892738i \(-0.351219\pi\)
\(164\) 79.1960 + 89.7998i 0.482902 + 0.547560i
\(165\) 67.8823 + 126.996i 0.411408 + 0.769673i
\(166\) −2.00000 5.29150i −0.0120482 0.0318765i
\(167\) 329.266i 1.97165i 0.167772 + 0.985826i \(0.446343\pi\)
−0.167772 + 0.985826i \(0.553657\pi\)
\(168\) −0.402020 95.9992i −0.00239298 0.571424i
\(169\) 57.0000 0.337278
\(170\) −158.392 + 59.8665i −0.931717 + 0.352156i
\(171\) −39.5980 26.4575i −0.231567 0.154722i
\(172\) 14.0000 + 15.8745i 0.0813953 + 0.0922937i
\(173\) 186.676 1.07905 0.539527 0.841969i \(-0.318603\pi\)
0.539527 + 0.841969i \(0.318603\pi\)
\(174\) 67.0294 76.6489i 0.385227 0.440511i
\(175\) 28.0000 0.160000
\(176\) −16.9706 + 134.700i −0.0964237 + 0.765339i
\(177\) 68.0000 + 127.216i 0.384181 + 0.718736i
\(178\) 196.000 74.0810i 1.10112 0.416186i
\(179\) −319.612 −1.78554 −0.892772 0.450509i \(-0.851242\pi\)
−0.892772 + 0.450509i \(0.851242\pi\)
\(180\) −27.1472 201.829i −0.150818 1.12127i
\(181\) 116.413i 0.643166i 0.946881 + 0.321583i \(0.104215\pi\)
−0.946881 + 0.321583i \(0.895785\pi\)
\(182\) 79.1960 29.9333i 0.435143 0.164468i
\(183\) 252.000 134.700i 1.37705 0.736064i
\(184\) −112.000 + 211.660i −0.608696 + 1.15033i
\(185\) 299.333i 1.61801i
\(186\) 15.7990 18.0663i 0.0849408 0.0971308i
\(187\) 126.996i 0.679123i
\(188\) 0 0
\(189\) 107.480 + 10.5830i 0.568678 + 0.0559947i
\(190\) 56.0000 21.1660i 0.294737 0.111400i
\(191\) 59.8665i 0.313437i −0.987643 0.156719i \(-0.949908\pi\)
0.987643 0.156719i \(-0.0500916\pi\)
\(192\) 89.0883 170.080i 0.464002 0.885834i
\(193\) −102.000 −0.528497 −0.264249 0.964455i \(-0.585124\pi\)
−0.264249 + 0.964455i \(0.585124\pi\)
\(194\) −83.4386 220.758i −0.430096 1.13793i
\(195\) 158.392 84.6640i 0.812266 0.434175i
\(196\) 99.0000 87.3098i 0.505102 0.445458i
\(197\) −243.245 −1.23474 −0.617372 0.786671i \(-0.711803\pi\)
−0.617372 + 0.786671i \(0.711803\pi\)
\(198\) −148.794 34.4727i −0.751485 0.174104i
\(199\) −188.000 −0.944724 −0.472362 0.881405i \(-0.656598\pi\)
−0.472362 + 0.881405i \(0.656598\pi\)
\(200\) 49.4975 + 26.1916i 0.247487 + 0.130958i
\(201\) −126.000 + 67.3498i −0.626866 + 0.335074i
\(202\) 44.0000 + 116.413i 0.217822 + 0.576302i
\(203\) −67.8823 −0.334395
\(204\) 62.7939 168.264i 0.307813 0.824826i
\(205\) 169.328i 0.825991i
\(206\) 76.3675 + 202.049i 0.370716 + 0.980823i
\(207\) −224.000 149.666i −1.08213 0.723026i
\(208\) 168.000 + 21.1660i 0.807692 + 0.101760i
\(209\) 44.8999i 0.214832i
\(210\) −89.3726 + 102.199i −0.425584 + 0.486660i
\(211\) 248.701i 1.17868i 0.807887 + 0.589338i \(0.200611\pi\)
−0.807887 + 0.589338i \(0.799389\pi\)
\(212\) −152.735 + 134.700i −0.720448 + 0.635376i
\(213\) −237.588 + 126.996i −1.11544 + 0.596226i
\(214\) −102.000 269.867i −0.476636 1.26106i
\(215\) 29.9333i 0.139224i
\(216\) 180.101 + 119.247i 0.833799 + 0.552069i
\(217\) −16.0000 −0.0737327
\(218\) 98.9949 37.4166i 0.454105 0.171636i
\(219\) 8.48528 + 15.8745i 0.0387456 + 0.0724863i
\(220\) 144.000 126.996i 0.654545 0.577255i
\(221\) 158.392 0.716706
\(222\) 238.995 + 209.001i 1.07655 + 0.941446i
\(223\) 188.000 0.843049 0.421525 0.906817i \(-0.361495\pi\)
0.421525 + 0.906817i \(0.361495\pi\)
\(224\) −124.451 + 29.9333i −0.555584 + 0.133631i
\(225\) −35.0000 + 52.3832i −0.155556 + 0.232814i
\(226\) −168.000 + 63.4980i −0.743363 + 0.280965i
\(227\) 387.495 1.70702 0.853512 0.521073i \(-0.174468\pi\)
0.853512 + 0.521073i \(0.174468\pi\)
\(228\) −22.2010 + 59.4905i −0.0973729 + 0.260923i
\(229\) 243.409i 1.06292i 0.847083 + 0.531461i \(0.178357\pi\)
−0.847083 + 0.531461i \(0.821643\pi\)
\(230\) 316.784 119.733i 1.37732 0.520578i
\(231\) 48.0000 + 89.7998i 0.207792 + 0.388744i
\(232\) −120.000 63.4980i −0.517241 0.273698i
\(233\) 104.766i 0.449641i 0.974400 + 0.224821i \(0.0721796\pi\)
−0.974400 + 0.224821i \(0.927820\pi\)
\(234\) −42.9949 + 185.579i −0.183739 + 0.793071i
\(235\) 0 0
\(236\) 144.250 127.216i 0.611228 0.539052i
\(237\) −175.362 328.073i −0.739926 1.38427i
\(238\) −112.000 + 42.3320i −0.470588 + 0.177866i
\(239\) 359.199i 1.50293i 0.659776 + 0.751463i \(0.270651\pi\)
−0.659776 + 0.751463i \(0.729349\pi\)
\(240\) −253.588 + 97.0628i −1.05662 + 0.404428i
\(241\) 122.000 0.506224 0.253112 0.967437i \(-0.418546\pi\)
0.253112 + 0.967437i \(0.418546\pi\)
\(242\) 34.6482 + 91.6706i 0.143175 + 0.378804i
\(243\) −154.149 + 187.848i −0.634359 + 0.773038i
\(244\) −252.000 285.741i −1.03279 1.17107i
\(245\) −186.676 −0.761944
\(246\) 135.196 + 118.229i 0.549577 + 0.480605i
\(247\) −56.0000 −0.226721
\(248\) −28.2843 14.9666i −0.114049 0.0603493i
\(249\) −4.00000 7.48331i −0.0160643 0.0300535i
\(250\) 72.0000 + 190.494i 0.288000 + 0.761976i
\(251\) 161.220 0.642312 0.321156 0.947026i \(-0.395929\pi\)
0.321156 + 0.947026i \(0.395929\pi\)
\(252\) −19.1960 142.715i −0.0761744 0.566329i
\(253\) 253.992i 1.00392i
\(254\) −53.7401 142.183i −0.211575 0.559776i
\(255\) −224.000 + 119.733i −0.878431 + 0.469541i
\(256\) −248.000 63.4980i −0.968750 0.248039i
\(257\) 448.999i 1.74708i −0.486755 0.873539i \(-0.661819\pi\)
0.486755 0.873539i \(-0.338181\pi\)
\(258\) 23.8995 + 20.9001i 0.0926337 + 0.0810081i
\(259\) 211.660i 0.817220i
\(260\) −158.392 179.600i −0.609200 0.690768i
\(261\) 84.8528 126.996i 0.325107 0.486575i
\(262\) 10.0000 + 26.4575i 0.0381679 + 0.100983i
\(263\) 209.533i 0.796703i −0.917233 0.398351i \(-0.869582\pi\)
0.917233 0.398351i \(-0.130418\pi\)
\(264\) 0.852814 + 203.645i 0.00323036 + 0.771382i
\(265\) 288.000 1.08679
\(266\) 39.5980 14.9666i 0.148865 0.0562655i
\(267\) 277.186 148.162i 1.03815 0.554914i
\(268\) 126.000 + 142.871i 0.470149 + 0.533099i
\(269\) 50.9117 0.189263 0.0946314 0.995512i \(-0.469833\pi\)
0.0946314 + 0.995512i \(0.469833\pi\)
\(270\) −79.4802 294.949i −0.294371 1.09240i
\(271\) 348.000 1.28413 0.642066 0.766649i \(-0.278077\pi\)
0.642066 + 0.766649i \(0.278077\pi\)
\(272\) −237.588 29.9333i −0.873485 0.110049i
\(273\) 112.000 59.8665i 0.410256 0.219291i
\(274\) 0 0
\(275\) −59.3970 −0.215989
\(276\) −125.588 + 336.529i −0.455029 + 1.21931i
\(277\) 243.409i 0.878733i 0.898308 + 0.439367i \(0.144797\pi\)
−0.898308 + 0.439367i \(0.855203\pi\)
\(278\) −227.688 + 86.0581i −0.819023 + 0.309562i
\(279\) 20.0000 29.9333i 0.0716846 0.107288i
\(280\) 160.000 + 84.6640i 0.571429 + 0.302372i
\(281\) 314.299i 1.11850i 0.828998 + 0.559251i \(0.188911\pi\)
−0.828998 + 0.559251i \(0.811089\pi\)
\(282\) 0 0
\(283\) 89.9555i 0.317864i 0.987290 + 0.158932i \(0.0508051\pi\)
−0.987290 + 0.158932i \(0.949195\pi\)
\(284\) 237.588 + 269.399i 0.836577 + 0.948589i
\(285\) 79.1960 42.3320i 0.277881 0.148533i
\(286\) −168.000 + 63.4980i −0.587413 + 0.222021i
\(287\) 119.733i 0.417188i
\(288\) 99.5635 270.243i 0.345707 0.938343i
\(289\) 65.0000 0.224913
\(290\) 67.8823 + 179.600i 0.234077 + 0.619309i
\(291\) −166.877 312.199i −0.573461 1.07285i
\(292\) 18.0000 15.8745i 0.0616438 0.0543648i
\(293\) −16.9706 −0.0579200 −0.0289600 0.999581i \(-0.509220\pi\)
−0.0289600 + 0.999581i \(0.509220\pi\)
\(294\) 130.342 149.047i 0.443339 0.506963i
\(295\) −272.000 −0.922034
\(296\) 197.990 374.166i 0.668885 1.26407i
\(297\) −228.000 22.4499i −0.767677 0.0755890i
\(298\) −132.000 349.239i −0.442953 1.17194i
\(299\) −316.784 −1.05948
\(300\) 78.6985 + 29.3692i 0.262328 + 0.0978973i
\(301\) 21.1660i 0.0703190i
\(302\) 42.4264 + 112.250i 0.140485 + 0.371688i
\(303\) 88.0000 + 164.633i 0.290429 + 0.543343i
\(304\) 84.0000 + 10.5830i 0.276316 + 0.0348125i
\(305\) 538.799i 1.76655i
\(306\) 60.8040 262.448i 0.198706 0.857673i
\(307\) 460.361i 1.49955i 0.661695 + 0.749773i \(0.269837\pi\)
−0.661695 + 0.749773i \(0.730163\pi\)
\(308\) 101.823 89.7998i 0.330595 0.291558i
\(309\) 152.735 + 285.741i 0.494288 + 0.924729i
\(310\) 16.0000 + 42.3320i 0.0516129 + 0.136555i
\(311\) 149.666i 0.481242i −0.970619 0.240621i \(-0.922649\pi\)
0.970619 0.240621i \(-0.0773511\pi\)
\(312\) 253.990 1.06365i 0.814070 0.00340912i
\(313\) −562.000 −1.79553 −0.897764 0.440478i \(-0.854809\pi\)
−0.897764 + 0.440478i \(0.854809\pi\)
\(314\) −217.789 + 82.3165i −0.693595 + 0.262154i
\(315\) −113.137 + 169.328i −0.359165 + 0.537549i
\(316\) −372.000 + 328.073i −1.17722 + 1.03821i
\(317\) 5.65685 0.0178450 0.00892248 0.999960i \(-0.497160\pi\)
0.00892248 + 0.999960i \(0.497160\pi\)
\(318\) −201.088 + 229.947i −0.632353 + 0.723103i
\(319\) 144.000 0.451411
\(320\) 203.647 + 299.333i 0.636396 + 0.935414i
\(321\) −204.000 381.649i −0.635514 1.18894i
\(322\) 224.000 84.6640i 0.695652 0.262932i
\(323\) 79.1960 0.245189
\(324\) 290.990 + 142.481i 0.898117 + 0.439757i
\(325\) 74.0810i 0.227942i
\(326\) −544.472 + 205.791i −1.67016 + 0.631261i
\(327\) 140.000 74.8331i 0.428135 0.228848i
\(328\) 112.000 211.660i 0.341463 0.645305i
\(329\) 0 0
\(330\) 189.588 216.796i 0.574509 0.656957i
\(331\) 418.029i 1.26293i −0.775406 0.631463i \(-0.782455\pi\)
0.775406 0.631463i \(-0.217545\pi\)
\(332\) −8.48528 + 7.48331i −0.0255581 + 0.0225401i
\(333\) 395.980 + 264.575i 1.18913 + 0.794520i
\(334\) 616.000 232.826i 1.84431 0.697084i
\(335\) 269.399i 0.804177i
\(336\) −179.314 + 68.6338i −0.533672 + 0.204267i
\(337\) −50.0000 −0.148368 −0.0741840 0.997245i \(-0.523635\pi\)
−0.0741840 + 0.997245i \(0.523635\pi\)
\(338\) −40.3051 106.637i −0.119246 0.315495i
\(339\) −237.588 + 126.996i −0.700849 + 0.374620i
\(340\) 224.000 + 253.992i 0.658824 + 0.747036i
\(341\) 33.9411 0.0995341
\(342\) −21.4975 + 92.7893i −0.0628581 + 0.271314i
\(343\) −328.000 −0.956268
\(344\) 19.7990 37.4166i 0.0575552 0.108769i
\(345\) 448.000 239.466i 1.29855 0.694105i
\(346\) −132.000 349.239i −0.381503 1.00936i
\(347\) −359.210 −1.03519 −0.517594 0.855626i \(-0.673172\pi\)
−0.517594 + 0.855626i \(0.673172\pi\)
\(348\) −190.794 71.2016i −0.548258 0.204602i
\(349\) 116.413i 0.333562i −0.985994 0.166781i \(-0.946663\pi\)
0.985994 0.166781i \(-0.0533373\pi\)
\(350\) −19.7990 52.3832i −0.0565685 0.149666i
\(351\) −28.0000 + 284.366i −0.0797721 + 0.810159i
\(352\) 264.000 63.4980i 0.750000 0.180392i
\(353\) 179.600i 0.508781i 0.967102 + 0.254390i \(0.0818748\pi\)
−0.967102 + 0.254390i \(0.918125\pi\)
\(354\) 189.917 217.172i 0.536488 0.613480i
\(355\) 507.984i 1.43094i
\(356\) −277.186 314.299i −0.778612 0.882863i
\(357\) −158.392 + 84.6640i −0.443675 + 0.237154i
\(358\) 226.000 + 597.940i 0.631285 + 1.67022i
\(359\) 329.266i 0.917175i −0.888649 0.458588i \(-0.848356\pi\)
0.888649 0.458588i \(-0.151644\pi\)
\(360\) −358.392 + 193.503i −0.995533 + 0.537507i
\(361\) 333.000 0.922438
\(362\) 217.789 82.3165i 0.601627 0.227394i
\(363\) 69.2965 + 129.642i 0.190899 + 0.357140i
\(364\) −112.000 126.996i −0.307692 0.348890i
\(365\) −33.9411 −0.0929894
\(366\) −430.191 376.202i −1.17538 1.02787i
\(367\) −228.000 −0.621253 −0.310627 0.950532i \(-0.600539\pi\)
−0.310627 + 0.950532i \(0.600539\pi\)
\(368\) 475.176 + 59.8665i 1.29124 + 0.162681i
\(369\) 224.000 + 149.666i 0.607046 + 0.405600i
\(370\) −560.000 + 211.660i −1.51351 + 0.572054i
\(371\) 203.647 0.548913
\(372\) −44.9706 16.7824i −0.120889 0.0451139i
\(373\) 137.579i 0.368845i −0.982847 0.184422i \(-0.940959\pi\)
0.982847 0.184422i \(-0.0590414\pi\)
\(374\) 237.588 89.7998i 0.635262 0.240106i
\(375\) 144.000 + 269.399i 0.384000 + 0.718398i
\(376\) 0 0
\(377\) 179.600i 0.476391i
\(378\) −56.2010 208.560i −0.148680 0.551747i
\(379\) 164.037i 0.432814i 0.976303 + 0.216407i \(0.0694338\pi\)
−0.976303 + 0.216407i \(0.930566\pi\)
\(380\) −79.1960 89.7998i −0.208410 0.236315i
\(381\) −107.480 201.077i −0.282100 0.527761i
\(382\) −112.000 + 42.3320i −0.293194 + 0.110817i
\(383\) 179.600i 0.468928i 0.972125 + 0.234464i \(0.0753336\pi\)
−0.972125 + 0.234464i \(0.924666\pi\)
\(384\) −381.186 46.4041i −0.992672 0.120844i
\(385\) −192.000 −0.498701
\(386\) 72.1249 + 190.825i 0.186852 + 0.494364i
\(387\) 39.5980 + 26.4575i 0.102320 + 0.0683657i
\(388\) −354.000 + 312.199i −0.912371 + 0.804636i
\(389\) 96.1665 0.247215 0.123607 0.992331i \(-0.460554\pi\)
0.123607 + 0.992331i \(0.460554\pi\)
\(390\) −270.392 236.458i −0.693313 0.606302i
\(391\) 448.000 1.14578
\(392\) −233.345 123.475i −0.595268 0.314986i
\(393\) 20.0000 + 37.4166i 0.0508906 + 0.0952076i
\(394\) 172.000 + 455.069i 0.436548 + 1.15500i
\(395\) 701.450 1.77582
\(396\) 40.7208 + 302.744i 0.102830 + 0.764505i
\(397\) 52.9150i 0.133287i 0.997777 + 0.0666436i \(0.0212291\pi\)
−0.997777 + 0.0666436i \(0.978771\pi\)
\(398\) 132.936 + 351.716i 0.334010 + 0.883708i
\(399\) 56.0000 29.9333i 0.140351 0.0750207i
\(400\) 14.0000 111.122i 0.0350000 0.277804i
\(401\) 134.700i 0.335909i 0.985795 + 0.167955i \(0.0537162\pi\)
−0.985795 + 0.167955i \(0.946284\pi\)
\(402\) 215.095 + 188.101i 0.535063 + 0.467913i
\(403\) 42.3320i 0.105042i
\(404\) 186.676 164.633i 0.462070 0.407507i
\(405\) −175.362 423.320i −0.432994 1.04524i
\(406\) 48.0000 + 126.996i 0.118227 + 0.312798i
\(407\) 448.999i 1.10319i
\(408\) −359.196 + 1.50422i −0.880382 + 0.00368682i
\(409\) −158.000 −0.386308 −0.193154 0.981168i \(-0.561872\pi\)
−0.193154 + 0.981168i \(0.561872\pi\)
\(410\) −316.784 + 119.733i −0.772644 + 0.292032i
\(411\) 0 0
\(412\) 324.000 285.741i 0.786408 0.693546i
\(413\) −192.333 −0.465697
\(414\) −121.608 + 524.896i −0.293739 + 1.26786i
\(415\) 16.0000 0.0385542
\(416\) −79.1960 329.266i −0.190375 0.791504i
\(417\) −322.000 + 172.116i −0.772182 + 0.412749i
\(418\) −84.0000 + 31.7490i −0.200957 + 0.0759546i
\(419\) 330.926 0.789799 0.394900 0.918724i \(-0.370779\pi\)
0.394900 + 0.918724i \(0.370779\pi\)
\(420\) 254.392 + 94.9355i 0.605695 + 0.226037i
\(421\) 518.567i 1.23175i −0.787843 0.615876i \(-0.788802\pi\)
0.787843 0.615876i \(-0.211198\pi\)
\(422\) 465.276 175.858i 1.10255 0.416725i
\(423\) 0 0
\(424\) 360.000 + 190.494i 0.849057 + 0.449279i
\(425\) 104.766i 0.246509i
\(426\) 405.588 + 354.686i 0.952084 + 0.832597i
\(427\) 380.988i 0.892244i
\(428\) −432.749 + 381.649i −1.01110 + 0.891703i
\(429\) −237.588 + 126.996i −0.553818 + 0.296028i
\(430\) −56.0000 + 21.1660i −0.130233 + 0.0492233i
\(431\) 359.199i 0.833409i −0.909042 0.416704i \(-0.863185\pi\)
0.909042 0.416704i \(-0.136815\pi\)
\(432\) 95.7401 421.257i 0.221621 0.975133i
\(433\) 86.0000 0.198614 0.0993072 0.995057i \(-0.468337\pi\)
0.0993072 + 0.995057i \(0.468337\pi\)
\(434\) 11.3137 + 29.9333i 0.0260685 + 0.0689706i
\(435\) 135.765 + 253.992i 0.312102 + 0.583890i
\(436\) −140.000 158.745i −0.321101 0.364094i
\(437\) −158.392 −0.362453
\(438\) 23.6985 27.0995i 0.0541061 0.0618710i
\(439\) −156.000 −0.355353 −0.177677 0.984089i \(-0.556858\pi\)
−0.177677 + 0.984089i \(0.556858\pi\)
\(440\) −339.411 179.600i −0.771389 0.408181i
\(441\) 165.000 246.949i 0.374150 0.559976i
\(442\) −112.000 296.324i −0.253394 0.670417i
\(443\) −212.132 −0.478853 −0.239427 0.970914i \(-0.576959\pi\)
−0.239427 + 0.970914i \(0.576959\pi\)
\(444\) 222.010 594.905i 0.500023 1.33988i
\(445\) 592.648i 1.33179i
\(446\) −132.936 351.716i −0.298063 0.788600i
\(447\) −264.000 493.899i −0.590604 1.10492i
\(448\) 144.000 + 211.660i 0.321429 + 0.472456i
\(449\) 493.899i 1.10000i −0.835166 0.549999i \(-0.814628\pi\)
0.835166 0.549999i \(-0.185372\pi\)
\(450\) 122.749 + 28.4385i 0.272775 + 0.0631966i
\(451\) 253.992i 0.563175i
\(452\) 237.588 + 269.399i 0.525637 + 0.596016i
\(453\) 84.8528 + 158.745i 0.187313 + 0.350431i
\(454\) −274.000 724.936i −0.603524 1.59678i
\(455\) 239.466i 0.526299i
\(456\) 126.995 0.531823i 0.278498 0.00116628i
\(457\) 194.000 0.424508 0.212254 0.977215i \(-0.431920\pi\)
0.212254 + 0.977215i \(0.431920\pi\)
\(458\) 455.377 172.116i 0.994272 0.375800i
\(459\) 39.5980 402.154i 0.0862701 0.876153i
\(460\) −448.000 507.984i −0.973913 1.10431i
\(461\) −560.029 −1.21481 −0.607406 0.794391i \(-0.707790\pi\)
−0.607406 + 0.794391i \(0.707790\pi\)
\(462\) 134.059 153.298i 0.290171 0.331813i
\(463\) −404.000 −0.872570 −0.436285 0.899808i \(-0.643706\pi\)
−0.436285 + 0.899808i \(0.643706\pi\)
\(464\) −33.9411 + 269.399i −0.0731490 + 0.580602i
\(465\) 32.0000 + 59.8665i 0.0688172 + 0.128745i
\(466\) 196.000 74.0810i 0.420601 0.158972i
\(467\) −664.680 −1.42330 −0.711649 0.702535i \(-0.752051\pi\)
−0.711649 + 0.702535i \(0.752051\pi\)
\(468\) 377.588 50.7877i 0.806812 0.108521i
\(469\) 190.494i 0.406171i
\(470\) 0 0
\(471\) −308.000 + 164.633i −0.653928 + 0.349539i
\(472\) −340.000 179.911i −0.720339 0.381168i
\(473\) 44.8999i 0.0949258i
\(474\) −489.769 + 560.056i −1.03327 + 1.18155i
\(475\) 37.0405i 0.0779800i
\(476\) 158.392 + 179.600i 0.332756 + 0.377310i
\(477\) −254.558 + 380.988i −0.533665 + 0.798717i
\(478\) 672.000 253.992i 1.40586 0.531364i
\(479\) 239.466i 0.499929i 0.968255 + 0.249965i \(0.0804190\pi\)
−0.968255 + 0.249965i \(0.919581\pi\)
\(480\) 360.902 + 405.786i 0.751878 + 0.845387i
\(481\) 560.000 1.16424
\(482\) −86.2670 228.241i −0.178977 0.473529i
\(483\) 316.784 169.328i 0.655867 0.350576i
\(484\) 147.000 129.642i 0.303719 0.267855i
\(485\) 667.509 1.37631
\(486\) 460.432 + 155.558i 0.947391 + 0.320078i
\(487\) 500.000 1.02669 0.513347 0.858181i \(-0.328405\pi\)
0.513347 + 0.858181i \(0.328405\pi\)
\(488\) −356.382 + 673.498i −0.730291 + 1.38012i
\(489\) −770.000 + 411.582i −1.57464 + 0.841682i
\(490\) 132.000 + 349.239i 0.269388 + 0.712733i
\(491\) −115.966 −0.236182 −0.118091 0.993003i \(-0.537678\pi\)
−0.118091 + 0.993003i \(0.537678\pi\)
\(492\) 125.588 336.529i 0.255260 0.684002i
\(493\) 253.992i 0.515197i
\(494\) 39.5980 + 104.766i 0.0801579 + 0.212078i
\(495\) 240.000 359.199i 0.484848 0.725655i
\(496\) −8.00000 + 63.4980i −0.0161290 + 0.128020i
\(497\) 359.199i 0.722735i
\(498\) −11.1716 + 12.7748i −0.0224329 + 0.0256522i
\(499\) 333.365i 0.668065i 0.942561 + 0.334033i \(0.108410\pi\)
−0.942561 + 0.334033i \(0.891590\pi\)
\(500\) 305.470 269.399i 0.610940 0.538799i
\(501\) 871.156 465.652i 1.73883 0.929446i
\(502\) −114.000 301.616i −0.227092 0.600828i
\(503\) 448.999i 0.892642i 0.894873 + 0.446321i \(0.147266\pi\)
−0.894873 + 0.446321i \(0.852734\pi\)
\(504\) −253.421 + 136.827i −0.502820 + 0.271482i
\(505\) −352.000 −0.697030
\(506\) −475.176 + 179.600i −0.939083 + 0.354940i
\(507\) −80.6102 150.808i −0.158994 0.297451i
\(508\) −228.000 + 201.077i −0.448819 + 0.395821i
\(509\) 322.441 0.633479 0.316739 0.948513i \(-0.397412\pi\)
0.316739 + 0.948513i \(0.397412\pi\)
\(510\) 382.392 + 334.402i 0.749788 + 0.655689i
\(511\) −24.0000 −0.0469667
\(512\) 56.5685 + 508.865i 0.110485 + 0.993878i
\(513\) −14.0000 + 142.183i −0.0272904 + 0.277160i
\(514\) −840.000 + 317.490i −1.63424 + 0.617685i
\(515\) −610.940 −1.18629
\(516\) 22.2010 59.4905i 0.0430252 0.115292i
\(517\) 0 0
\(518\) −395.980 + 149.666i −0.764440 + 0.288931i
\(519\) −264.000 493.899i −0.508671 0.951635i
\(520\) −224.000 + 423.320i −0.430769 + 0.814077i
\(521\) 179.600i 0.344721i 0.985034 + 0.172360i \(0.0551394\pi\)
−0.985034 + 0.172360i \(0.944861\pi\)
\(522\) −297.588 68.9453i −0.570092 0.132079i
\(523\) 555.608i 1.06235i −0.847263 0.531174i \(-0.821751\pi\)
0.847263 0.531174i \(-0.178249\pi\)
\(524\) 42.4264 37.4166i 0.0809664 0.0714057i
\(525\) −39.5980 74.0810i −0.0754247 0.141107i
\(526\) −392.000 + 148.162i −0.745247 + 0.281677i
\(527\) 59.8665i 0.113599i
\(528\) 380.382 145.594i 0.720420 0.275747i
\(529\) −367.000 −0.693762
\(530\) −203.647 538.799i −0.384239 1.01660i
\(531\) 240.416 359.822i 0.452761 0.677631i
\(532\) −56.0000 63.4980i −0.105263 0.119357i
\(533\) 316.784 0.594341
\(534\) −473.186 413.801i −0.886116 0.774908i
\(535\) 816.000 1.52523
\(536\) 178.191 336.749i 0.332446 0.628263i
\(537\) 452.000 + 845.615i 0.841713 + 1.57470i
\(538\) −36.0000 95.2470i −0.0669145 0.177039i
\(539\) 280.014 0.519507
\(540\) −495.598 + 357.254i −0.917774 + 0.661582i
\(541\) 772.559i 1.42802i 0.700135 + 0.714011i \(0.253123\pi\)
−0.700135 + 0.714011i \(0.746877\pi\)
\(542\) −246.073 651.048i −0.454010 1.20120i
\(543\) 308.000 164.633i 0.567219 0.303191i
\(544\) 112.000 + 465.652i 0.205882 + 0.855978i
\(545\) 299.333i 0.549234i
\(546\) −191.196 167.201i −0.350176 0.306229i
\(547\) 502.693i 0.919000i −0.888178 0.459500i \(-0.848029\pi\)
0.888178 0.459500i \(-0.151971\pi\)
\(548\) 0 0
\(549\) −712.764 476.235i −1.29829 0.867459i
\(550\) 42.0000 + 111.122i 0.0763636 + 0.202039i
\(551\) 89.7998i 0.162976i
\(552\) 718.392 3.00844i 1.30143 0.00545008i
\(553\) 496.000 0.896926
\(554\) 455.377 172.116i 0.821980 0.310679i
\(555\) −791.960 + 423.320i −1.42695 + 0.762739i
\(556\) 322.000 + 365.114i 0.579137 + 0.656679i
\(557\) 526.087 0.944502 0.472251 0.881464i \(-0.343442\pi\)
0.472251 + 0.881464i \(0.343442\pi\)
\(558\) −70.1421 16.2506i −0.125703 0.0291229i
\(559\) 56.0000 0.100179
\(560\) 45.2548 359.199i 0.0808122 0.641427i
\(561\) 336.000 179.600i 0.598930 0.320142i
\(562\) 588.000 222.243i 1.04626 0.395450i
\(563\) −8.48528 −0.0150715 −0.00753577 0.999972i \(-0.502399\pi\)
−0.00753577 + 0.999972i \(0.502399\pi\)
\(564\) 0 0
\(565\) 507.984i 0.899087i
\(566\) 168.291 63.6082i 0.297335 0.112382i
\(567\) −124.000 299.333i −0.218695 0.527923i
\(568\) 336.000 634.980i 0.591549 1.11792i
\(569\) 359.199i 0.631281i −0.948879 0.315641i \(-0.897781\pi\)
0.948879 0.315641i \(-0.102219\pi\)
\(570\) −135.196 118.229i −0.237186 0.207419i
\(571\) 5.29150i 0.00926708i 0.999989 + 0.00463354i \(0.00147491\pi\)
−0.999989 + 0.00463354i \(0.998525\pi\)
\(572\) 237.588 + 269.399i 0.415363 + 0.470978i
\(573\) −158.392 + 84.6640i −0.276426 + 0.147756i
\(574\) −224.000 + 84.6640i −0.390244 + 0.147498i
\(575\) 209.533i 0.364405i
\(576\) −575.980 + 4.82420i −0.999965 + 0.00837535i
\(577\) −18.0000 −0.0311958 −0.0155979 0.999878i \(-0.504965\pi\)
−0.0155979 + 0.999878i \(0.504965\pi\)
\(578\) −45.9619 121.604i −0.0795189 0.210387i
\(579\) 144.250 + 269.867i 0.249136 + 0.466091i
\(580\) 288.000 253.992i 0.496552 0.437917i
\(581\) 11.3137 0.0194728
\(582\) −466.070 + 532.956i −0.800808 + 0.915733i
\(583\) −432.000 −0.740995
\(584\) −42.4264 22.4499i −0.0726480 0.0384417i
\(585\) −448.000 299.333i −0.765812 0.511680i
\(586\) 12.0000 + 31.7490i 0.0204778 + 0.0541792i
\(587\) 121.622 0.207193 0.103597 0.994619i \(-0.466965\pi\)
0.103597 + 0.994619i \(0.466965\pi\)
\(588\) −371.007 138.455i −0.630965 0.235467i
\(589\) 21.1660i 0.0359355i
\(590\) 192.333 + 508.865i 0.325988 + 0.862484i
\(591\) 344.000 + 643.565i 0.582064 + 1.08894i
\(592\) −840.000 105.830i −1.41892 0.178767i
\(593\) 718.398i 1.21146i −0.795669 0.605732i \(-0.792880\pi\)
0.795669 0.605732i \(-0.207120\pi\)
\(594\) 119.220 + 442.423i 0.200708 + 0.744821i
\(595\) 338.656i 0.569170i
\(596\) −560.029 + 493.899i −0.939645 + 0.828689i
\(597\) 265.872 + 497.401i 0.445347 + 0.833168i
\(598\) 224.000 + 592.648i 0.374582 + 0.991051i
\(599\) 688.465i 1.14936i −0.818379 0.574679i \(-0.805127\pi\)
0.818379 0.574679i \(-0.194873\pi\)
\(600\) −0.703535 167.999i −0.00117256 0.279998i
\(601\) −358.000 −0.595674 −0.297837 0.954617i \(-0.596265\pi\)
−0.297837 + 0.954617i \(0.596265\pi\)
\(602\) −39.5980 + 14.9666i −0.0657774 + 0.0248615i
\(603\) 356.382 + 238.118i 0.591015 + 0.394888i
\(604\) 180.000 158.745i 0.298013 0.262823i
\(605\) −277.186 −0.458158
\(606\) 245.775 281.046i 0.405569 0.463772i
\(607\) −884.000 −1.45634 −0.728171 0.685395i \(-0.759629\pi\)
−0.728171 + 0.685395i \(0.759629\pi\)
\(608\) −39.5980 164.633i −0.0651283 0.270778i
\(609\) 96.0000 + 179.600i 0.157635 + 0.294909i
\(610\) 1008.00 380.988i 1.65246 0.624571i
\(611\) 0 0
\(612\) −533.990 + 71.8247i −0.872533 + 0.117361i
\(613\) 391.571i 0.638778i −0.947624 0.319389i \(-0.896522\pi\)
0.947624 0.319389i \(-0.103478\pi\)
\(614\) 861.256 325.524i 1.40270 0.530170i
\(615\) −448.000 + 239.466i −0.728455 + 0.389376i
\(616\) −240.000 126.996i −0.389610 0.206162i
\(617\) 104.766i 0.169800i −0.996389 0.0848998i \(-0.972943\pi\)
0.996389 0.0848998i \(-0.0270570\pi\)
\(618\) 426.573 487.791i 0.690247 0.789305i
\(619\) 682.604i 1.10275i 0.834257 + 0.551376i \(0.185897\pi\)
−0.834257 + 0.551376i \(0.814103\pi\)
\(620\) 67.8823 59.8665i 0.109488 0.0965589i
\(621\) −79.1960 + 804.308i −0.127530 + 1.29518i
\(622\) −280.000 + 105.830i −0.450161 + 0.170145i
\(623\) 419.066i 0.672658i
\(624\) −181.588 474.419i −0.291006 0.760288i
\(625\) −751.000 −1.20160
\(626\) 397.394 + 1051.41i 0.634815 + 1.67956i
\(627\) −118.794 + 63.4980i −0.189464 + 0.101273i
\(628\) 308.000 + 349.239i 0.490446 + 0.556113i
\(629\) −791.960 −1.25908
\(630\) 396.784 + 91.9271i 0.629816 + 0.145916i
\(631\) −428.000 −0.678288 −0.339144 0.940734i \(-0.610137\pi\)
−0.339144 + 0.940734i \(0.610137\pi\)
\(632\) 876.812 + 463.966i 1.38736 + 0.734123i
\(633\) 658.000 351.716i 1.03949 0.555633i
\(634\) −4.00000 10.5830i −0.00630915 0.0166924i
\(635\) 429.921 0.677041
\(636\) 572.382 + 213.605i 0.899971 + 0.335857i
\(637\) 349.239i 0.548256i
\(638\) −101.823 269.399i −0.159598 0.422256i
\(639\) 672.000 + 448.999i 1.05164 + 0.702659i
\(640\) 416.000 592.648i 0.650000 0.926013i
\(641\) 793.231i 1.23749i 0.785592 + 0.618745i \(0.212359\pi\)
−0.785592 + 0.618745i \(0.787641\pi\)
\(642\) −569.750 + 651.516i −0.887461 + 1.01482i
\(643\) 851.932i 1.32493i 0.749092 + 0.662467i \(0.230490\pi\)
−0.749092 + 0.662467i \(0.769510\pi\)
\(644\) −316.784 359.199i −0.491900 0.557763i
\(645\) −79.1960 + 42.3320i −0.122784 + 0.0656310i
\(646\) −56.0000 148.162i −0.0866873 0.229353i
\(647\) 448.999i 0.693970i 0.937871 + 0.346985i \(0.112795\pi\)
−0.937871 + 0.346985i \(0.887205\pi\)
\(648\) 60.7969 645.142i 0.0938224 0.995589i
\(649\) 408.000 0.628659
\(650\) 138.593 52.3832i 0.213220 0.0805895i
\(651\) 22.6274 + 42.3320i 0.0347579 + 0.0650261i
\(652\) 770.000 + 873.098i 1.18098 + 1.33911i
\(653\) −1103.09 −1.68926 −0.844630 0.535351i \(-0.820179\pi\)
−0.844630 + 0.535351i \(0.820179\pi\)
\(654\) −238.995 209.001i −0.365436 0.319573i
\(655\) −80.0000 −0.122137
\(656\) −475.176 59.8665i −0.724353 0.0912599i
\(657\) 30.0000 44.8999i 0.0456621 0.0683408i
\(658\) 0 0
\(659\) 924.896 1.40348 0.701742 0.712431i \(-0.252406\pi\)
0.701742 + 0.712431i \(0.252406\pi\)
\(660\) −539.647 201.389i −0.817647 0.305134i
\(661\) 433.903i 0.656435i −0.944602 0.328217i \(-0.893552\pi\)
0.944602 0.328217i \(-0.106448\pi\)
\(662\) −782.060 + 295.591i −1.18136 + 0.446512i
\(663\) −224.000 419.066i −0.337858 0.632075i
\(664\) 20.0000 + 10.5830i 0.0301205 + 0.0159383i
\(665\) 119.733i 0.180050i
\(666\) 214.975 927.893i 0.322785 1.39323i
\(667\) 507.984i 0.761596i
\(668\) −871.156 987.798i −1.30413 1.47874i
\(669\) −265.872 497.401i −0.397417 0.743500i
\(670\) −504.000 + 190.494i −0.752239 + 0.284320i
\(671\) 808.198i 1.20447i
\(672\) 255.196 + 286.934i 0.379756 + 0.426985i
\(673\) 566.000 0.841010 0.420505 0.907290i \(-0.361853\pi\)
0.420505 + 0.907290i \(0.361853\pi\)
\(674\) 35.3553 + 93.5414i 0.0524560 + 0.138786i
\(675\) 188.090 + 18.5203i 0.278652 + 0.0274374i
\(676\) −171.000 + 150.808i −0.252959 + 0.223088i
\(677\) 797.616 1.17816 0.589082 0.808074i \(-0.299490\pi\)
0.589082 + 0.808074i \(0.299490\pi\)
\(678\) 405.588 + 354.686i 0.598212 + 0.523136i
\(679\) 472.000 0.695140
\(680\) 316.784 598.665i 0.465859 0.880390i
\(681\) −548.000 1025.21i −0.804699 1.50545i
\(682\) −24.0000 63.4980i −0.0351906 0.0931056i
\(683\) −404.465 −0.592189 −0.296094 0.955159i \(-0.595684\pi\)
−0.296094 + 0.955159i \(0.595684\pi\)
\(684\) 188.794 25.3939i 0.276015 0.0371255i
\(685\) 0 0
\(686\) 231.931 + 613.632i 0.338092 + 0.894507i
\(687\) 644.000 344.232i 0.937409 0.501066i
\(688\) −84.0000 10.5830i −0.122093 0.0153823i
\(689\) 538.799i 0.782001i
\(690\) −764.784 668.803i −1.10838 0.969280i
\(691\) 121.705i 0.176128i −0.996115 0.0880641i \(-0.971932\pi\)
0.996115 0.0880641i \(-0.0280680\pi\)
\(692\) −560.029 + 493.899i −0.809290 + 0.713727i
\(693\) 169.706 253.992i 0.244885 0.366511i
\(694\) 254.000 + 672.021i 0.365994 + 0.968330i
\(695\) 688.465i 0.990597i
\(696\) 1.70563 + 407.290i 0.00245061 + 0.585187i
\(697\) −448.000 −0.642755
\(698\) −217.789 + 82.3165i −0.312018 + 0.117932i
\(699\) 277.186 148.162i 0.396546 0.211963i
\(700\) −84.0000 + 74.0810i −0.120000 + 0.105830i
\(701\) −333.754 −0.476112 −0.238056 0.971251i \(-0.576510\pi\)
−0.238056 + 0.971251i \(0.576510\pi\)
\(702\) 551.799 148.694i 0.786038 0.211815i
\(703\) 280.000 0.398293
\(704\) −305.470 448.999i −0.433906 0.637783i
\(705\) 0 0
\(706\) 336.000 126.996i 0.475921 0.179881i
\(707\) −248.902 −0.352053
\(708\) −540.583 201.738i −0.763535 0.284941i
\(709\) 370.405i 0.522433i 0.965280 + 0.261217i \(0.0841237\pi\)
−0.965280 + 0.261217i \(0.915876\pi\)
\(710\) −950.352 + 359.199i −1.33852 + 0.505914i
\(711\) −620.000 + 927.931i −0.872011 + 1.30511i
\(712\) −392.000 + 740.810i −0.550562 + 1.04046i
\(713\) 119.733i 0.167929i
\(714\) 270.392 + 236.458i 0.378700 + 0.331173i
\(715\) 507.984i 0.710467i
\(716\) 958.837 845.615i 1.33916 1.18103i
\(717\) 950.352 507.984i 1.32546 0.708486i
\(718\) −616.000 + 232.826i −0.857939 + 0.324270i
\(719\) 1017.73i 1.41548i 0.706473 + 0.707740i \(0.250285\pi\)
−0.706473 + 0.707740i \(0.749715\pi\)
\(720\) 615.431 + 533.663i 0.854766 + 0.741199i
\(721\) −432.000 −0.599168
\(722\) −235.467 622.986i −0.326131 0.862861i
\(723\) −172.534 322.782i −0.238636 0.446448i
\(724\) −308.000 349.239i −0.425414 0.482375i
\(725\) −118.794 −0.163854
\(726\) 193.538 221.312i 0.266581 0.304838i
\(727\) 1140.00 1.56809 0.784044 0.620705i \(-0.213154\pi\)
0.784044 + 0.620705i \(0.213154\pi\)
\(728\) −158.392 + 299.333i −0.217571 + 0.411171i
\(729\) 715.000 + 142.183i 0.980796 + 0.195038i
\(730\) 24.0000 + 63.4980i 0.0328767 + 0.0869836i
\(731\) −79.1960 −0.108339
\(732\) −399.618 + 1070.83i −0.545926 + 1.46288i
\(733\) 370.405i 0.505328i −0.967554 0.252664i \(-0.918693\pi\)
0.967554 0.252664i \(-0.0813067\pi\)
\(734\) 161.220 + 426.549i 0.219646 + 0.581129i
\(735\) 264.000 + 493.899i 0.359184 + 0.671971i
\(736\) −224.000 931.304i −0.304348 1.26536i
\(737\) 404.099i 0.548303i
\(738\) 121.608 524.896i 0.164781 0.711241i
\(739\) 5.29150i 0.00716036i −0.999994 0.00358018i \(-0.998860\pi\)
0.999994 0.00358018i \(-0.00113961\pi\)
\(740\) 791.960 + 897.998i 1.07022 + 1.21351i
\(741\) 79.1960 + 148.162i 0.106877 + 0.199949i
\(742\) −144.000 380.988i −0.194070 0.513461i
\(743\) 748.331i 1.00718i −0.863944 0.503588i \(-0.832013\pi\)
0.863944 0.503588i \(-0.167987\pi\)
\(744\) 0.402020 + 95.9992i 0.000540350 + 0.129031i
\(745\) 1056.00 1.41745
\(746\) −257.387 + 97.2831i −0.345023 + 0.130406i
\(747\) −14.1421 + 21.1660i −0.0189319 + 0.0283347i
\(748\) −336.000 380.988i −0.449198 0.509342i
\(749\) 576.999 0.770359
\(750\) 402.177 459.893i 0.536235 0.613191i
\(751\) −1108.00 −1.47537 −0.737683 0.675147i \(-0.764080\pi\)
−0.737683 + 0.675147i \(0.764080\pi\)
\(752\) 0 0
\(753\) −228.000 426.549i −0.302789 0.566466i
\(754\) −336.000 + 126.996i −0.445623 + 0.168430i
\(755\) −339.411 −0.449551
\(756\) −350.441 + 252.617i −0.463546 + 0.334149i
\(757\) 1047.72i 1.38404i 0.721879 + 0.692019i \(0.243279\pi\)
−0.721879 + 0.692019i \(0.756721\pi\)
\(758\) 306.884 115.991i 0.404861 0.153023i
\(759\) −672.000 + 359.199i −0.885375 + 0.473253i
\(760\) −112.000 + 211.660i −0.147368 + 0.278500i
\(761\) 1287.13i 1.69137i 0.533685 + 0.845683i \(0.320807\pi\)
−0.533685 + 0.845683i \(0.679193\pi\)
\(762\) −300.181 + 343.260i −0.393938 + 0.450473i
\(763\) 211.660i 0.277405i
\(764\) 158.392 + 179.600i 0.207319 + 0.235078i
\(765\) 633.568 + 423.320i 0.828193 + 0.553360i
\(766\) 336.000 126.996i 0.438642 0.165791i
\(767\) 508.865i 0.663449i
\(768\) 182.725 + 745.946i 0.237923 + 0.971284i
\(769\) 538.000 0.699610 0.349805 0.936823i \(-0.386248\pi\)
0.349805 + 0.936823i \(0.386248\pi\)
\(770\) 135.765 + 359.199i 0.176318 + 0.466492i
\(771\) −1187.94 + 634.980i −1.54078 + 0.823580i
\(772\) 306.000 269.867i 0.396373 0.349568i
\(773\) −62.2254 −0.0804986 −0.0402493 0.999190i \(-0.512815\pi\)
−0.0402493 + 0.999190i \(0.512815\pi\)
\(774\) 21.4975 92.7893i 0.0277745 0.119883i
\(775\) −28.0000 −0.0361290
\(776\) 834.386 + 441.516i 1.07524 + 0.568963i
\(777\) −560.000 + 299.333i −0.720721 + 0.385241i
\(778\) −68.0000 179.911i −0.0874036 0.231248i
\(779\) 158.392 0.203327
\(780\) −251.176 + 673.058i −0.322020 + 0.862895i
\(781\) 761.976i 0.975642i
\(782\) −316.784 838.131i −0.405094 1.07178i
\(783\) −456.000 44.8999i −0.582375 0.0573434i
\(784\) −66.0000 + 523.859i −0.0841837 + 0.668187i
\(785\) 658.532i 0.838894i