Properties

Label 24.3.h.c.5.3
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 5.3
Root \(0.707107 - 1.87083i\) of defining polynomial
Character \(\chi\) \(=\) 24.5
Dual form 24.3.h.c.5.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.87083i) q^{2} +(1.41421 + 2.64575i) q^{3} +(-3.00000 - 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 - 0.774923i) q^{6} +4.00000 q^{7} +(-7.07107 + 3.74166i) q^{8} +(-5.00000 + 7.48331i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.87083i) q^{2} +(1.41421 + 2.64575i) q^{3} +(-3.00000 - 2.64575i) q^{4} -5.65685 q^{5} +(5.94975 - 0.774923i) 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} +(2.75736 - 11.6789i) 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} +(10.4645 + 14.6456i) 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} +(-19.8995 - 13.4168i) 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} +(-33.6569 + 4.38362i) 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} +(34.7990 - 9.22119i) 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} +(23.7990 - 3.09969i) q^{42} +5.29150i q^{43} +(-25.4558 - 22.4499i) q^{44} +(28.2843 - 42.3320i) q^{45} +(56.0000 + 21.1660i) q^{46} +(-39.1716 + 27.7414i) 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} +(-23.9497 + 48.3984i) 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} +(-15.5980 + 66.0659i) 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} +(50.4853 - 6.57544i) 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} +(7.35534 - 71.6233i) 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} +(-8.20101 - 62.9662i) 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} +(11.0294 - 46.7156i) 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} +(-59.1960 - 82.8483i) q^{90} -42.3320i q^{91} +(79.1960 - 89.7998i) q^{92} +(-5.65685 - 10.5830i) q^{93} +29.9333i q^{95} +(24.2010 + 92.8995i) 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 \(-0.691388\pi\)
−0.565685 + 0.824621i \(0.691388\pi\)
\(6\) 5.94975 0.774923i 0.991625 0.129154i
\(7\) 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 \(-0.373962\pi\)
0.385695 + 0.922627i \(0.373962\pi\)
\(12\) 2.75736 11.6789i 0.229780 0.973243i
\(13\) 10.5830i 0.814077i −0.913411 0.407039i \(-0.866561\pi\)
0.913411 0.407039i \(-0.133439\pi\)
\(14\) 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 \(-0.145091\pi\)
\(18\) 10.4645 + 14.6456i 0.581359 + 0.813647i
\(19\) 5.29150i 0.278500i −0.990257 0.139250i \(-0.955531\pi\)
0.990257 0.139250i \(-0.0444692\pi\)
\(20\) 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 \(0.774466\pi\)
\(24\) −19.8995 13.4168i −0.829146 0.559033i
\(25\) 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 \(-0.405481\pi\)
0.292596 + 0.956236i \(0.405481\pi\)
\(30\) −33.6569 + 4.38362i −1.12190 + 0.146121i
\(31\) −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
\(36\) 34.7990 9.22119i 0.966639 0.256144i
\(37\) 52.9150i 1.43014i 0.699055 + 0.715068i \(0.253604\pi\)
−0.699055 + 0.715068i \(0.746396\pi\)
\(38\) −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 \(-0.118945\pi\)
\(42\) 23.7990 3.09969i 0.566643 0.0738022i
\(43\) 5.29150i 0.123058i 0.998105 + 0.0615291i \(0.0195977\pi\)
−0.998105 + 0.0615291i \(0.980402\pi\)
\(44\) −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 \(\pi\)
\(48\) −39.1716 + 27.7414i −0.816074 + 0.577947i
\(49\) −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 \(-0.659472\pi\)
−0.480299 + 0.877105i \(0.659472\pi\)
\(54\) −23.9497 + 48.3984i −0.443514 + 0.896268i
\(55\) −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 \(-0.366406\pi\)
0.407485 + 0.913212i \(0.366406\pi\)
\(60\) −15.5980 + 66.0659i −0.259966 + 1.10110i
\(61\) 95.2470i 1.56143i −0.624889 0.780714i \(-0.714856\pi\)
0.624889 0.780714i \(-0.285144\pi\)
\(62\) −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
\(66\) 50.4853 6.57544i 0.764929 0.0996278i
\(67\) 47.6235i 0.710799i 0.934715 + 0.355399i \(0.115655\pi\)
−0.934715 + 0.355399i \(0.884345\pi\)
\(68\) −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 \(-0.217927\pi\)
\(72\) 7.35534 71.6233i 0.102157 0.994768i
\(73\) −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
\(78\) −8.20101 62.9662i −0.105141 0.807259i
\(79\) 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 \(-0.505424\pi\)
−0.0170387 + 0.999855i \(0.505424\pi\)
\(84\) 11.0294 46.7156i 0.131303 0.556139i
\(85\) 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 \(0.799689\pi\)
\(90\) −59.1960 82.8483i −0.657733 0.920537i
\(91\) 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
\(96\) 24.2010 + 92.8995i 0.252094 + 0.967703i
\(97\) 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 \(-0.400325\pi\)
0.308047 + 0.951371i \(0.400325\pi\)
\(102\) −11.5980 89.0477i −0.113706 0.873016i
\(103\) −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 \(-0.735453\pi\)
−0.674064 + 0.738673i \(0.735453\pi\)
\(108\) 73.6102 + 79.0287i 0.681576 + 0.731748i
\(109\) 52.9150i 0.485459i −0.970094 0.242729i \(-0.921957\pi\)
0.970094 0.242729i \(-0.0780427\pi\)
\(110\) −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 \(-0.130068\pi\)
\(114\) −4.10051 31.4831i −0.0359693 0.276168i
\(115\) 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
\(120\) 112.569 + 75.8968i 0.938071 + 0.632473i
\(121\) −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
\(126\) 41.8579 + 58.5826i 0.332205 + 0.464941i
\(127\) 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 \(-0.482810\pi\)
0.0539776 + 0.998542i \(0.482810\pi\)
\(132\) 23.3970 99.0988i 0.177250 0.750749i
\(133\) 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 \(\pi\)
\(138\) 23.1960 + 178.095i 0.168087 + 1.29055i
\(139\) 121.705i 0.875572i 0.899079 + 0.437786i \(0.144237\pi\)
−0.899079 + 0.437786i \(0.855763\pi\)
\(140\) 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
\(144\) −128.794 64.4059i −0.894402 0.447263i
\(145\) −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 \(-0.715485\pi\)
−0.626430 + 0.779478i \(0.715485\pi\)
\(150\) 41.6482 5.42446i 0.277655 0.0361631i
\(151\) −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
\(156\) −123.598 29.1811i −0.792295 0.187059i
\(157\) 116.413i 0.741484i 0.928736 + 0.370742i \(0.120897\pi\)
−0.928736 + 0.370742i \(0.879103\pi\)
\(158\) 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
\(162\) −161.920 + 5.08066i −0.999508 + 0.0313621i
\(163\) 291.033i 1.78548i 0.450576 + 0.892738i \(0.351219\pi\)
−0.450576 + 0.892738i \(0.648781\pi\)
\(164\) −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 \(0.553657\pi\)
\(168\) −79.5980 53.6671i −0.473797 0.319447i
\(169\) 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 \(-0.681397\pi\)
−0.539527 + 0.841969i \(0.681397\pi\)
\(174\) 100.971 13.1509i 0.580291 0.0755797i
\(175\) 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 \(-0.148758\pi\)
0.892772 + 0.450509i \(0.148758\pi\)
\(180\) −196.853 + 52.1629i −1.09363 + 0.289794i
\(181\) 116.413i 0.643166i −0.946881 0.321583i \(-0.895785\pi\)
0.946881 0.321583i \(-0.104215\pi\)
\(182\) −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
\(186\) −23.7990 + 3.09969i −0.127952 + 0.0166650i
\(187\) 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 \(-0.0500916\pi\)
\(192\) 190.912 + 20.4139i 0.994332 + 0.106322i
\(193\) −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 \(-0.288197\pi\)
0.617372 + 0.786671i \(0.288197\pi\)
\(198\) 88.7939 + 124.272i 0.448454 + 0.627639i
\(199\) −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
\(204\) −174.794 41.2684i −0.856833 0.202296i
\(205\) 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
\(210\) −134.627 + 17.5345i −0.641083 + 0.0834976i
\(211\) 248.701i 1.17868i −0.807887 0.589338i \(-0.799389\pi\)
0.807887 0.589338i \(-0.200611\pi\)
\(212\) 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
\(216\) 199.899 81.8303i 0.925461 0.378844i
\(217\) −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
\(222\) 41.0051 + 314.831i 0.184707 + 1.41816i
\(223\) 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 \(-0.825532\pi\)
−0.853512 + 0.521073i \(0.825532\pi\)
\(228\) −61.7990 14.5906i −0.271048 0.0639937i
\(229\) 243.409i 1.06292i −0.847083 0.531461i \(-0.821643\pi\)
0.847083 0.531461i \(-0.178357\pi\)
\(230\) −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 \(0.927820\pi\)
\(234\) 154.995 110.745i 0.662372 0.473271i
\(235\) 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 \(0.729349\pi\)
\(240\) 221.588 156.929i 0.923283 0.653872i
\(241\) 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
\(246\) −23.1960 178.095i −0.0942925 0.723965i
\(247\) −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 \(-0.604071\pi\)
−0.321156 + 0.947026i \(0.604071\pi\)
\(252\) 139.196 36.8848i 0.552365 0.146368i
\(253\) 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 \(-0.338181\pi\)
\(258\) 4.10051 + 31.4831i 0.0158934 + 0.122028i
\(259\) 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 \(-0.130418\pi\)
\(264\) −168.853 113.845i −0.639594 0.431232i
\(265\) 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 \(-0.530167\pi\)
−0.0946314 + 0.995512i \(0.530167\pi\)
\(270\) 135.480 273.783i 0.501779 1.01401i
\(271\) 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
\(276\) 349.588 + 82.5368i 1.26662 + 0.299046i
\(277\) 243.409i 0.878733i −0.898308 0.439367i \(-0.855203\pi\)
0.898308 0.439367i \(-0.144797\pi\)
\(278\) 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 \(-0.949195\pi\)
0.987290 0.158932i \(-0.0508051\pi\)
\(284\) −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
\(288\) −211.563 + 195.410i −0.734595 + 0.678505i
\(289\) 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 \(-0.490780\pi\)
0.0289600 + 0.999581i \(0.490780\pi\)
\(294\) −196.342 + 25.5724i −0.667829 + 0.0869811i
\(295\) −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
\(300\) 19.3015 81.7524i 0.0643384 0.272508i
\(301\) 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
\(306\) 219.196 156.618i 0.716327 0.511823i
\(307\) 460.361i 1.49955i −0.661695 0.749773i \(-0.730163\pi\)
0.661695 0.749773i \(-0.269837\pi\)
\(308\) −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 \(-0.0773511\pi\)
\(312\) −141.990 + 210.596i −0.455096 + 0.674989i
\(313\) −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 \(-0.502840\pi\)
−0.00892248 + 0.999960i \(0.502840\pi\)
\(318\) −302.912 + 39.4526i −0.952552 + 0.124065i
\(319\) 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
\(324\) −104.990 + 306.518i −0.324043 + 0.946042i
\(325\) 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
\(330\) −285.588 + 37.1963i −0.865418 + 0.112716i
\(331\) 418.029i 1.26293i 0.775406 + 0.631463i \(0.217545\pi\)
−0.775406 + 0.631463i \(0.782455\pi\)
\(332\) 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
\(336\) −156.686 + 110.966i −0.466328 + 0.330255i
\(337\) −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
\(342\) 77.4975 55.3727i 0.226601 0.161909i
\(343\) −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 \(-0.326828\pi\)
0.517594 + 0.855626i \(0.326828\pi\)
\(348\) 46.7939 198.198i 0.134465 0.569534i
\(349\) 116.413i 0.333562i 0.985994 + 0.166781i \(0.0533373\pi\)
−0.985994 + 0.166781i \(0.946663\pi\)
\(350\) 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 \(0.918125\pi\)
\(354\) 286.083 37.2608i 0.808145 0.105257i
\(355\) 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 \(-0.151644\pi\)
\(360\) −41.6081 + 405.163i −0.115578 + 1.12545i
\(361\) 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
\(366\) −73.8091 566.696i −0.201664 1.54835i
\(367\) −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
\(372\) −11.0294 + 46.7156i −0.0296490 + 0.125580i
\(373\) 137.579i 0.368845i 0.982847 + 0.184422i \(0.0590414\pi\)
−0.982847 + 0.184422i \(0.940959\pi\)
\(374\) −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
\(378\) −95.7990 + 193.594i −0.253436 + 0.512153i
\(379\) 164.037i 0.432814i −0.976303 0.216407i \(-0.930566\pi\)
0.976303 0.216407i \(-0.0694338\pi\)
\(380\) 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 \(0.924666\pi\)
\(384\) 173.186 342.728i 0.451005 0.892522i
\(385\) −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 \(-0.539446\pi\)
−0.123607 + 0.992331i \(0.539446\pi\)
\(390\) 46.3919 + 356.191i 0.118954 + 0.913309i
\(391\) 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
\(396\) 295.279 78.2444i 0.745655 0.197587i
\(397\) 52.9150i 0.133287i −0.997777 0.0666436i \(-0.978771\pi\)
0.997777 0.0666436i \(-0.0212291\pi\)
\(398\) −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 \(0.946284\pi\)
\(402\) 36.9045 + 283.348i 0.0918024 + 0.704846i
\(403\) 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
\(408\) −200.804 + 297.828i −0.492167 + 0.729971i
\(409\) −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
\(414\) −438.392 + 313.236i −1.05892 + 0.756608i
\(415\) 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 \(-0.629221\pi\)
−0.394900 + 0.918724i \(0.629221\pi\)
\(420\) −62.3919 + 264.264i −0.148552 + 0.629199i
\(421\) 518.567i 1.23175i 0.787843 + 0.615876i \(0.211198\pi\)
−0.787843 + 0.615876i \(0.788802\pi\)
\(422\) −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
\(426\) −69.5879 534.286i −0.163352 1.25419i
\(427\) 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 \(-0.136815\pi\)
\(432\) −11.7401 431.840i −0.0271762 0.999631i
\(433\) 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
\(438\) −35.6985 + 4.64954i −0.0815034 + 0.0106154i
\(439\) −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 \(-0.423041\pi\)
0.239427 + 0.970914i \(0.423041\pi\)
\(444\) 617.990 + 145.906i 1.39187 + 0.328617i
\(445\) 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 \(-0.185372\pi\)
\(450\) 73.2513 + 102.520i 0.162781 + 0.227821i
\(451\) 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
\(456\) −70.9949 + 105.298i −0.155691 + 0.230917i
\(457\) 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 \(-0.292210\pi\)
0.607406 + 0.794391i \(0.292210\pi\)
\(462\) 201.941 26.3017i 0.437102 0.0569302i
\(463\) −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 \(-0.247949\pi\)
0.711649 + 0.702535i \(0.247949\pi\)
\(468\) −97.5879 368.278i −0.208521 0.786919i
\(469\) 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
\(474\) 737.769 96.0904i 1.55647 0.202722i
\(475\) 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 \(0.919581\pi\)
\(480\) −136.902 525.519i −0.285212 1.09483i
\(481\) 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
\(486\) −242.432 421.216i −0.498831 0.866699i
\(487\) 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 \(-0.462322\pi\)
0.118091 + 0.993003i \(0.462322\pi\)
\(492\) −349.588 82.5368i −0.710544 0.167758i
\(493\) 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
\(498\) −16.8284 + 2.19181i −0.0337920 + 0.00440123i
\(499\) 333.365i 0.668065i −0.942561 0.334033i \(-0.891590\pi\)
0.942561 0.334033i \(-0.108410\pi\)
\(500\) −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 \(0.852734\pi\)
\(504\) 29.4214 286.493i 0.0583757 0.568439i
\(505\) −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 \(-0.602588\pi\)
−0.316739 + 0.948513i \(0.602588\pi\)
\(510\) 65.6081 + 503.730i 0.128643 + 0.987705i
\(511\) −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
\(516\) 61.7990 + 14.5906i 0.119765 + 0.0282763i
\(517\) 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 \(0.944861\pi\)
\(522\) 177.588 + 248.545i 0.340207 + 0.476140i
\(523\) 555.608i 1.06235i 0.847263 + 0.531174i \(0.178249\pi\)
−0.847263 + 0.531174i \(0.821751\pi\)
\(524\) −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
\(528\) −332.382 + 235.394i −0.629511 + 0.445822i
\(529\) −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
\(534\) 81.1859 + 623.334i 0.152033 + 1.16729i
\(535\) 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
\(540\) −416.402 447.054i −0.771115 0.827878i
\(541\) 772.559i 1.42802i −0.700135 0.714011i \(-0.746877\pi\)
0.700135 0.714011i \(-0.253123\pi\)
\(542\) 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
\(546\) −32.8040 251.865i −0.0600807 0.461291i
\(547\) 502.693i 0.919000i 0.888178 + 0.459500i \(0.151971\pi\)
−0.888178 + 0.459500i \(0.848029\pi\)
\(548\) 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
\(552\) 401.608 595.657i 0.727551 1.07909i
\(553\) 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 \(-0.656558\pi\)
−0.472251 + 0.881464i \(0.656558\pi\)
\(558\) −41.8579 58.5826i −0.0750141 0.104987i
\(559\) 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 \(-0.497601\pi\)
0.00753577 + 0.999972i \(0.497601\pi\)
\(564\) 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 \(-0.102219\pi\)
\(570\) 23.1960 + 178.095i 0.0406947 + 0.312448i
\(571\) 5.29150i 0.00926708i −0.999989 0.00463354i \(-0.998525\pi\)
0.999989 0.00463354i \(-0.00147491\pi\)
\(572\) −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
\(576\) 215.980 + 533.974i 0.374965 + 0.927039i
\(577\) −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
\(582\) 702.070 91.4409i 1.20631 0.157115i
\(583\) −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 \(-0.533035\pi\)
−0.103597 + 0.994619i \(0.533035\pi\)
\(588\) −90.9929 + 385.404i −0.154750 + 0.655449i
\(589\) 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 \(-0.207120\pi\)
\(594\) −203.220 + 410.674i −0.342122 + 0.691371i
\(595\) 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 \(-0.194873\pi\)
\(600\) −139.296 93.9175i −0.232161 0.156529i
\(601\) −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
\(606\) 370.225 48.2199i 0.610933 0.0795707i
\(607\) −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
\(612\) −138.010 520.824i −0.225507 0.851019i
\(613\) 391.571i 0.638778i 0.947624 + 0.319389i \(0.103478\pi\)
−0.947624 + 0.319389i \(0.896522\pi\)
\(614\) −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 \(-0.0270570\pi\)
\(618\) −642.573 + 83.6916i −1.03976 + 0.135423i
\(619\) 682.604i 1.10275i −0.834257 0.551376i \(-0.814103\pi\)
0.834257 0.551376i \(-0.185897\pi\)
\(620\) −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
\(624\) 293.588 + 414.553i 0.470493 + 0.664348i
\(625\) −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
\(630\) −236.784 331.393i −0.375847 0.526021i
\(631\) −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
\(636\) −140.382 + 594.593i −0.220726 + 0.934895i
\(637\) 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 \(0.787641\pi\)
\(642\) −858.250 + 111.782i −1.33684 + 0.174116i
\(643\) 851.932i 1.32493i −0.749092 0.662467i \(-0.769510\pi\)
0.749092 0.662467i \(-0.230490\pi\)
\(644\) 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 \(0.887205\pi\)
\(648\) 499.203 + 413.159i 0.770375 + 0.637591i
\(649\) 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 \(-0.179821\pi\)
0.844630 + 0.535351i \(0.179821\pi\)
\(654\) −41.0051 314.831i −0.0626989 0.481393i
\(655\) −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 \(-0.747594\pi\)
−0.701742 + 0.712431i \(0.747594\pi\)
\(660\) −132.353 + 560.588i −0.200535 + 0.849375i
\(661\) 433.903i 0.656435i 0.944602 + 0.328217i \(0.106448\pi\)
−0.944602 + 0.328217i \(0.893552\pi\)
\(662\) 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
\(666\) −774.975 + 553.727i −1.16363 + 0.831423i
\(667\) 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
\(672\) 96.8040 + 371.598i 0.144054 + 0.552973i
\(673\) 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 \(-0.700510\pi\)
−0.589082 + 0.808074i \(0.700510\pi\)
\(678\) −69.5879 534.286i −0.102637 0.788032i
\(679\) 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 \(-0.404316\pi\)
0.296094 + 0.955159i \(0.404316\pi\)
\(684\) −48.7939 184.139i −0.0713362 0.269209i
\(685\) 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
\(690\) −131.216 1007.46i −0.190168 1.46009i
\(691\) 121.705i 0.176128i 0.996115 + 0.0880641i \(0.0280680\pi\)
−0.996115 + 0.0880641i \(0.971932\pi\)
\(692\) 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
\(696\) −337.706 227.690i −0.485209 0.327141i
\(697\) −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 \(-0.423490\pi\)
0.238056 + 0.971251i \(0.423490\pi\)
\(702\) 512.201 + 253.460i 0.729631 + 0.361055i
\(703\) 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
\(708\) 132.583 561.560i 0.187264 0.793164i
\(709\) 370.405i 0.522433i −0.965280 0.261217i \(-0.915876\pi\)
0.965280 0.261217i \(-0.0841237\pi\)
\(710\) 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
\(714\) −46.3919 356.191i −0.0649747 0.498866i
\(715\) 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 \(0.749715\pi\)
\(720\) 728.569 + 364.335i 1.01190 + 0.506021i
\(721\) −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
\(726\) −291.538 + 37.9712i −0.401567 + 0.0523019i
\(727\) 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
\(732\) −1112.38 262.630i −1.51965 0.358785i
\(733\) 370.405i 0.505328i 0.967554 + 0.252664i \(0.0813067\pi\)
−0.967554 + 0.252664i \(0.918693\pi\)
\(734\) −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
\(738\) 438.392 313.236i 0.594027 0.424438i
\(739\) 5.29150i 0.00716036i 0.999994 + 0.00358018i \(0.00113961\pi\)
−0.999994 + 0.00358018i \(0.998860\pi\)
\(740\) −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 \(-0.167987\pi\)
\(744\) 79.5980 + 53.6671i 0.106987 + 0.0721332i
\(745\) 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
\(750\) 605.823 78.9052i 0.807765 0.105207i
\(751\) −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
\(756\) 294.441 + 316.115i 0.389472 + 0.418142i
\(757\) 1047.72i 1.38404i −0.721879 0.692019i \(-0.756721\pi\)
0.721879 0.692019i \(-0.243279\pi\)
\(758\) −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 \(0.679193\pi\)
\(762\) 452.181 58.8941i 0.593413 0.0772889i
\(763\) 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
\(768\) −518.725 566.347i −0.675423 0.737430i
\(769\) 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 \(-0.487185\pi\)
0.0402493 + 0.999190i \(0.487185\pi\)
\(774\) −77.4975 + 55.3727i −0.100126 + 0.0715410i
\(775\) −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
\(780\) 699.176 + 165.074i 0.896379 + 0.211633i
\(781\) 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