Properties

Label 931.2.x.b.655.1
Level $931$
Weight $2$
Character 931.655
Analytic conductor $7.434$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.x (of order \(9\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.43407242818\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 19)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 655.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 931.655
Dual form 931.2.x.b.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.03209 + 0.866025i) q^{2} +(0.500000 + 2.83564i) q^{3} +(-0.0320889 + 0.181985i) q^{4} +(-0.152704 - 0.866025i) q^{5} +(-2.97178 - 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(-4.97178 + 1.80958i) q^{9} +O(q^{10})\) \(q+(-1.03209 + 0.866025i) q^{2} +(0.500000 + 2.83564i) q^{3} +(-0.0320889 + 0.181985i) q^{4} +(-0.152704 - 0.866025i) q^{5} +(-2.97178 - 2.49362i) q^{6} +(-1.47178 - 2.54920i) q^{8} +(-4.97178 + 1.80958i) q^{9} +(0.907604 + 0.761570i) q^{10} -2.22668 q^{11} -0.532089 q^{12} +(-1.97178 - 1.65452i) q^{13} +(2.37939 - 0.866025i) q^{15} +(3.37939 + 1.23000i) q^{16} +(0.439693 + 0.160035i) q^{17} +(3.56418 - 6.17334i) q^{18} +(-1.52094 - 4.08494i) q^{19} +0.162504 q^{20} +(2.29813 - 1.92836i) q^{22} +(-2.06418 - 1.73205i) q^{23} +(6.49273 - 5.44804i) q^{24} +(3.97178 - 1.44561i) q^{25} +3.46791 q^{26} +(-3.29813 - 5.71253i) q^{27} +(-1.19459 + 6.77487i) q^{29} +(-1.70574 + 2.95442i) q^{30} +(-3.55303 - 6.15403i) q^{31} +(0.979055 - 0.356347i) q^{32} +(-1.11334 - 6.31407i) q^{33} +(-0.592396 + 0.215615i) q^{34} +(-0.169778 - 0.962858i) q^{36} +(-2.47178 - 4.28125i) q^{37} +(5.10741 + 2.89884i) q^{38} +(3.70574 - 6.41852i) q^{39} +(-1.98293 + 1.66387i) q^{40} +(-1.89646 + 1.59132i) q^{41} +(-3.66637 - 1.33445i) q^{43} +(0.0714517 - 0.405223i) q^{44} +(2.32635 + 4.02936i) q^{45} +3.63041 q^{46} +(-6.85117 + 2.49362i) q^{47} +(-1.79813 + 10.1977i) q^{48} +(-2.84730 + 4.93166i) q^{50} +(-0.233956 + 1.32683i) q^{51} +(0.364370 - 0.305743i) q^{52} +(-0.492726 + 2.79439i) q^{53} +(8.35117 + 3.03958i) q^{54} +(0.340022 + 1.92836i) q^{55} +(10.8229 - 6.35532i) q^{57} +(-4.63429 - 8.02682i) q^{58} +(-5.92514 - 2.15658i) q^{59} +(0.0812519 + 0.460802i) q^{60} +(-6.99273 - 5.86759i) q^{61} +(8.99660 + 3.27449i) q^{62} +(-4.29813 + 7.44459i) q^{64} +(-1.13176 + 1.96026i) q^{65} +(6.61721 + 5.55250i) q^{66} +(5.87939 + 4.93339i) q^{67} +(-0.0432332 + 0.0748822i) q^{68} +(3.87939 - 6.71929i) q^{69} +(8.74422 + 3.18264i) q^{71} +(11.9304 + 10.0108i) q^{72} +(-0.241230 - 1.36808i) q^{73} +(6.25877 + 2.27801i) q^{74} +(6.08512 + 10.5397i) q^{75} +(0.792204 - 0.145708i) q^{76} +(1.73396 + 9.83375i) q^{78} +(11.1309 + 4.05131i) q^{79} +(0.549163 - 3.11446i) q^{80} +(2.39053 - 2.00589i) q^{81} +(0.579193 - 3.28476i) q^{82} +(-7.41534 + 12.8438i) q^{83} +(0.0714517 - 0.405223i) q^{85} +(4.93969 - 1.79790i) q^{86} -19.8084 q^{87} +(3.27719 + 5.67626i) q^{88} +(1.78699 - 10.1345i) q^{89} +(-5.89053 - 2.14398i) q^{90} +(0.381445 - 0.320070i) q^{92} +(15.6741 - 13.1521i) q^{93} +(4.91147 - 8.50692i) q^{94} +(-3.30541 + 1.94096i) q^{95} +(1.50000 + 2.59808i) q^{96} +(-1.64156 - 9.30975i) q^{97} +(11.0706 - 4.02936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} - 15 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 3 q^{2} + 3 q^{3} + 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} - 15 q^{9} + 9 q^{10} + 6 q^{12} + 3 q^{13} + 3 q^{15} + 9 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 6 q^{23} + 21 q^{24} + 9 q^{25} + 30 q^{26} - 6 q^{27} - 3 q^{29} - 9 q^{31} + 9 q^{32} - 24 q^{36} - 3 q^{38} + 12 q^{39} + 9 q^{40} - 21 q^{41} - 3 q^{43} + 15 q^{45} + 36 q^{46} - 15 q^{47} + 3 q^{48} - 15 q^{50} - 6 q^{51} + 21 q^{52} + 15 q^{53} + 24 q^{54} - 18 q^{55} + 24 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} - 24 q^{61} + 12 q^{62} - 12 q^{64} - 12 q^{65} + 9 q^{66} + 24 q^{67} + 15 q^{68} + 12 q^{69} - 6 q^{71} - 3 q^{72} - 24 q^{73} + 15 q^{74} + 15 q^{75} - 36 q^{76} + 15 q^{78} + 15 q^{79} + 15 q^{80} - 3 q^{81} - 45 q^{82} + 24 q^{86} - 42 q^{87} + 9 q^{88} + 3 q^{89} - 18 q^{90} + 42 q^{92} + 27 q^{93} + 9 q^{94} - 24 q^{95} + 9 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).

\(n\) \(248\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.03209 + 0.866025i −0.729797 + 0.612372i −0.930076 0.367366i \(-0.880260\pi\)
0.200279 + 0.979739i \(0.435815\pi\)
\(3\) 0.500000 + 2.83564i 0.288675 + 1.63716i 0.691854 + 0.722037i \(0.256794\pi\)
−0.403179 + 0.915121i \(0.632095\pi\)
\(4\) −0.0320889 + 0.181985i −0.0160444 + 0.0909926i
\(5\) −0.152704 0.866025i −0.0682911 0.387298i −0.999726 0.0233912i \(-0.992554\pi\)
0.931435 0.363907i \(-0.118557\pi\)
\(6\) −2.97178 2.49362i −1.21322 1.01802i
\(7\) 0 0
\(8\) −1.47178 2.54920i −0.520353 0.901278i
\(9\) −4.97178 + 1.80958i −1.65726 + 0.603193i
\(10\) 0.907604 + 0.761570i 0.287010 + 0.240830i
\(11\) −2.22668 −0.671370 −0.335685 0.941974i \(-0.608968\pi\)
−0.335685 + 0.941974i \(0.608968\pi\)
\(12\) −0.532089 −0.153601
\(13\) −1.97178 1.65452i −0.546874 0.458882i 0.327007 0.945022i \(-0.393960\pi\)
−0.873881 + 0.486140i \(0.838404\pi\)
\(14\) 0 0
\(15\) 2.37939 0.866025i 0.614355 0.223607i
\(16\) 3.37939 + 1.23000i 0.844846 + 0.307499i
\(17\) 0.439693 + 0.160035i 0.106641 + 0.0388142i 0.394790 0.918772i \(-0.370817\pi\)
−0.288149 + 0.957586i \(0.593040\pi\)
\(18\) 3.56418 6.17334i 0.840085 1.45507i
\(19\) −1.52094 4.08494i −0.348929 0.937149i
\(20\) 0.162504 0.0363370
\(21\) 0 0
\(22\) 2.29813 1.92836i 0.489964 0.411128i
\(23\) −2.06418 1.73205i −0.430411 0.361158i 0.401696 0.915773i \(-0.368421\pi\)
−0.832107 + 0.554616i \(0.812865\pi\)
\(24\) 6.49273 5.44804i 1.32532 1.11208i
\(25\) 3.97178 1.44561i 0.794356 0.289122i
\(26\) 3.46791 0.680113
\(27\) −3.29813 5.71253i −0.634726 1.09938i
\(28\) 0 0
\(29\) −1.19459 + 6.77487i −0.221830 + 1.25806i 0.646822 + 0.762641i \(0.276097\pi\)
−0.868653 + 0.495421i \(0.835014\pi\)
\(30\) −1.70574 + 2.95442i −0.311424 + 0.539401i
\(31\) −3.55303 6.15403i −0.638144 1.10530i −0.985840 0.167690i \(-0.946369\pi\)
0.347696 0.937607i \(-0.386964\pi\)
\(32\) 0.979055 0.356347i 0.173074 0.0629939i
\(33\) −1.11334 6.31407i −0.193808 1.09914i
\(34\) −0.592396 + 0.215615i −0.101595 + 0.0369776i
\(35\) 0 0
\(36\) −0.169778 0.962858i −0.0282963 0.160476i
\(37\) −2.47178 4.28125i −0.406358 0.703833i 0.588120 0.808774i \(-0.299868\pi\)
−0.994479 + 0.104940i \(0.966535\pi\)
\(38\) 5.10741 + 2.89884i 0.828531 + 0.470255i
\(39\) 3.70574 6.41852i 0.593393 1.02779i
\(40\) −1.98293 + 1.66387i −0.313528 + 0.263081i
\(41\) −1.89646 + 1.59132i −0.296177 + 0.248522i −0.778751 0.627333i \(-0.784146\pi\)
0.482574 + 0.875855i \(0.339702\pi\)
\(42\) 0 0
\(43\) −3.66637 1.33445i −0.559117 0.203502i 0.0469757 0.998896i \(-0.485042\pi\)
−0.606093 + 0.795394i \(0.707264\pi\)
\(44\) 0.0714517 0.405223i 0.0107718 0.0610897i
\(45\) 2.32635 + 4.02936i 0.346792 + 0.600661i
\(46\) 3.63041 0.535275
\(47\) −6.85117 + 2.49362i −0.999345 + 0.363732i −0.789332 0.613967i \(-0.789573\pi\)
−0.210013 + 0.977699i \(0.567351\pi\)
\(48\) −1.79813 + 10.1977i −0.259538 + 1.47191i
\(49\) 0 0
\(50\) −2.84730 + 4.93166i −0.402669 + 0.697442i
\(51\) −0.233956 + 1.32683i −0.0327603 + 0.185793i
\(52\) 0.364370 0.305743i 0.0505291 0.0423989i
\(53\) −0.492726 + 2.79439i −0.0676811 + 0.383839i 0.932086 + 0.362238i \(0.117987\pi\)
−0.999767 + 0.0216005i \(0.993124\pi\)
\(54\) 8.35117 + 3.03958i 1.13645 + 0.413634i
\(55\) 0.340022 + 1.92836i 0.0458486 + 0.260020i
\(56\) 0 0
\(57\) 10.8229 6.35532i 1.43353 0.841783i
\(58\) −4.63429 8.02682i −0.608511 1.05397i
\(59\) −5.92514 2.15658i −0.771388 0.280762i −0.0738112 0.997272i \(-0.523516\pi\)
−0.697577 + 0.716510i \(0.745738\pi\)
\(60\) 0.0812519 + 0.460802i 0.0104896 + 0.0594893i
\(61\) −6.99273 5.86759i −0.895327 0.751268i 0.0739445 0.997262i \(-0.476441\pi\)
−0.969271 + 0.245994i \(0.920886\pi\)
\(62\) 8.99660 + 3.27449i 1.14257 + 0.415861i
\(63\) 0 0
\(64\) −4.29813 + 7.44459i −0.537267 + 0.930573i
\(65\) −1.13176 + 1.96026i −0.140377 + 0.243141i
\(66\) 6.61721 + 5.55250i 0.814522 + 0.683465i
\(67\) 5.87939 + 4.93339i 0.718281 + 0.602710i 0.926909 0.375286i \(-0.122455\pi\)
−0.208628 + 0.977995i \(0.566900\pi\)
\(68\) −0.0432332 + 0.0748822i −0.00524280 + 0.00908080i
\(69\) 3.87939 6.71929i 0.467023 0.808908i
\(70\) 0 0
\(71\) 8.74422 + 3.18264i 1.03775 + 0.377709i 0.804026 0.594594i \(-0.202687\pi\)
0.233722 + 0.972303i \(0.424909\pi\)
\(72\) 11.9304 + 10.0108i 1.40601 + 1.17978i
\(73\) −0.241230 1.36808i −0.0282338 0.160122i 0.967431 0.253134i \(-0.0814614\pi\)
−0.995665 + 0.0930125i \(0.970350\pi\)
\(74\) 6.25877 + 2.27801i 0.727567 + 0.264813i
\(75\) 6.08512 + 10.5397i 0.702649 + 1.21702i
\(76\) 0.792204 0.145708i 0.0908720 0.0167139i
\(77\) 0 0
\(78\) 1.73396 + 9.83375i 0.196332 + 1.11345i
\(79\) 11.1309 + 4.05131i 1.25232 + 0.455808i 0.881186 0.472770i \(-0.156746\pi\)
0.371136 + 0.928578i \(0.378968\pi\)
\(80\) 0.549163 3.11446i 0.0613983 0.348207i
\(81\) 2.39053 2.00589i 0.265614 0.222877i
\(82\) 0.579193 3.28476i 0.0639611 0.362742i
\(83\) −7.41534 + 12.8438i −0.813940 + 1.40979i 0.0961469 + 0.995367i \(0.469348\pi\)
−0.910087 + 0.414418i \(0.863985\pi\)
\(84\) 0 0
\(85\) 0.0714517 0.405223i 0.00775003 0.0439526i
\(86\) 4.93969 1.79790i 0.532661 0.193873i
\(87\) −19.8084 −2.12368
\(88\) 3.27719 + 5.67626i 0.349349 + 0.605091i
\(89\) 1.78699 10.1345i 0.189420 1.07426i −0.730723 0.682674i \(-0.760817\pi\)
0.920143 0.391582i \(-0.128072\pi\)
\(90\) −5.89053 2.14398i −0.620916 0.225995i
\(91\) 0 0
\(92\) 0.381445 0.320070i 0.0397684 0.0333696i
\(93\) 15.6741 13.1521i 1.62533 1.36381i
\(94\) 4.91147 8.50692i 0.506580 0.877422i
\(95\) −3.30541 + 1.94096i −0.339128 + 0.199138i
\(96\) 1.50000 + 2.59808i 0.153093 + 0.265165i
\(97\) −1.64156 9.30975i −0.166675 0.945261i −0.947320 0.320287i \(-0.896221\pi\)
0.780645 0.624974i \(-0.214891\pi\)
\(98\) 0 0
\(99\) 11.0706 4.02936i 1.11263 0.404966i
\(100\) 0.135630 + 0.769193i 0.0135630 + 0.0769193i
\(101\) −8.69119 + 3.16333i −0.864806 + 0.314764i −0.736062 0.676914i \(-0.763317\pi\)
−0.128744 + 0.991678i \(0.541095\pi\)
\(102\) −0.907604 1.57202i −0.0898662 0.155653i
\(103\) −2.75490 + 4.77163i −0.271448 + 0.470162i −0.969233 0.246145i \(-0.920836\pi\)
0.697785 + 0.716308i \(0.254169\pi\)
\(104\) −1.31567 + 7.46156i −0.129012 + 0.731666i
\(105\) 0 0
\(106\) −1.91147 3.31077i −0.185659 0.321570i
\(107\) 10.2344 0.989399 0.494699 0.869064i \(-0.335278\pi\)
0.494699 + 0.869064i \(0.335278\pi\)
\(108\) 1.14543 0.416902i 0.110219 0.0401164i
\(109\) −1.39646 + 1.17177i −0.133757 + 0.112235i −0.707212 0.707002i \(-0.750047\pi\)
0.573455 + 0.819237i \(0.305603\pi\)
\(110\) −2.02094 1.69577i −0.192690 0.161686i
\(111\) 10.9042 9.14971i 1.03498 0.868452i
\(112\) 0 0
\(113\) −17.6878 −1.66393 −0.831963 0.554830i \(-0.812783\pi\)
−0.831963 + 0.554830i \(0.812783\pi\)
\(114\) −5.66637 + 15.9322i −0.530705 + 1.49219i
\(115\) −1.18479 + 2.05212i −0.110482 + 0.191361i
\(116\) −1.19459 0.434796i −0.110915 0.0403698i
\(117\) 12.7973 + 4.65782i 1.18311 + 0.430616i
\(118\) 7.98293 2.90555i 0.734888 0.267477i
\(119\) 0 0
\(120\) −5.70961 4.79093i −0.521213 0.437350i
\(121\) −6.04189 −0.549263
\(122\) 12.2986 1.11346
\(123\) −5.46064 4.58202i −0.492369 0.413147i
\(124\) 1.23396 0.449123i 0.110812 0.0403324i
\(125\) −4.05690 7.02676i −0.362861 0.628493i
\(126\) 0 0
\(127\) 8.88919 + 7.45891i 0.788788 + 0.661871i 0.945445 0.325782i \(-0.105627\pi\)
−0.156657 + 0.987653i \(0.550072\pi\)
\(128\) −1.64930 9.35365i −0.145779 0.826753i
\(129\) 1.95084 11.0637i 0.171762 0.974109i
\(130\) −0.529563 3.00330i −0.0464457 0.263407i
\(131\) −1.41353 + 1.18610i −0.123501 + 0.103630i −0.702446 0.711737i \(-0.747909\pi\)
0.578945 + 0.815366i \(0.303464\pi\)
\(132\) 1.18479 0.103123
\(133\) 0 0
\(134\) −10.3405 −0.893282
\(135\) −4.44356 + 3.72859i −0.382441 + 0.320906i
\(136\) −0.239170 1.35640i −0.0205087 0.116310i
\(137\) 0.0444153 0.251892i 0.00379465 0.0215206i −0.982852 0.184398i \(-0.940966\pi\)
0.986646 + 0.162878i \(0.0520775\pi\)
\(138\) 1.81521 + 10.2946i 0.154521 + 0.876331i
\(139\) −3.26604 2.74054i −0.277022 0.232449i 0.493682 0.869643i \(-0.335651\pi\)
−0.770704 + 0.637193i \(0.780095\pi\)
\(140\) 0 0
\(141\) −10.4966 18.1806i −0.883973 1.53109i
\(142\) −11.7811 + 4.28795i −0.988645 + 0.359837i
\(143\) 4.39053 + 3.68409i 0.367155 + 0.308079i
\(144\) −19.0273 −1.58561
\(145\) 6.04963 0.502394
\(146\) 1.43376 + 1.20307i 0.118659 + 0.0995668i
\(147\) 0 0
\(148\) 0.858441 0.312447i 0.0705634 0.0256830i
\(149\) −15.5608 5.66366i −1.27479 0.463985i −0.386083 0.922464i \(-0.626172\pi\)
−0.888705 + 0.458479i \(0.848394\pi\)
\(150\) −15.4081 5.60808i −1.25806 0.457898i
\(151\) 2.18092 3.77747i 0.177481 0.307406i −0.763536 0.645765i \(-0.776539\pi\)
0.941017 + 0.338359i \(0.109872\pi\)
\(152\) −8.17483 + 9.88933i −0.663066 + 0.802131i
\(153\) −2.47565 −0.200145
\(154\) 0 0
\(155\) −4.78699 + 4.01676i −0.384500 + 0.322634i
\(156\) 1.04916 + 0.880352i 0.0840003 + 0.0704846i
\(157\) 7.36824 6.18269i 0.588050 0.493432i −0.299530 0.954087i \(-0.596830\pi\)
0.887579 + 0.460655i \(0.152385\pi\)
\(158\) −14.9966 + 5.45831i −1.19307 + 0.434240i
\(159\) −8.17024 −0.647943
\(160\) −0.458111 0.793471i −0.0362168 0.0627294i
\(161\) 0 0
\(162\) −0.730085 + 4.14052i −0.0573609 + 0.325310i
\(163\) −4.17752 + 7.23567i −0.327209 + 0.566742i −0.981957 0.189105i \(-0.939441\pi\)
0.654748 + 0.755847i \(0.272775\pi\)
\(164\) −0.228741 0.396191i −0.0178617 0.0309373i
\(165\) −5.29813 + 1.92836i −0.412459 + 0.150123i
\(166\) −3.46972 19.6778i −0.269303 1.52729i
\(167\) 3.79174 1.38008i 0.293413 0.106794i −0.191120 0.981567i \(-0.561212\pi\)
0.484533 + 0.874773i \(0.338990\pi\)
\(168\) 0 0
\(169\) −1.10694 6.27779i −0.0851496 0.482907i
\(170\) 0.277189 + 0.480105i 0.0212594 + 0.0368224i
\(171\) 14.9538 + 17.5572i 1.14355 + 1.34263i
\(172\) 0.360500 0.624404i 0.0274879 0.0476104i
\(173\) 15.4311 12.9482i 1.17320 0.984434i 0.173203 0.984886i \(-0.444588\pi\)
1.00000 0.000452057i \(0.000143894\pi\)
\(174\) 20.4440 17.1546i 1.54986 1.30049i
\(175\) 0 0
\(176\) −7.52481 2.73881i −0.567204 0.206445i
\(177\) 3.15270 17.8799i 0.236972 1.34393i
\(178\) 6.93242 + 12.0073i 0.519607 + 0.899985i
\(179\) −11.5125 −0.860484 −0.430242 0.902714i \(-0.641572\pi\)
−0.430242 + 0.902714i \(0.641572\pi\)
\(180\) −0.807934 + 0.294064i −0.0602198 + 0.0219182i
\(181\) −1.48246 + 8.40744i −0.110190 + 0.624920i 0.878829 + 0.477136i \(0.158325\pi\)
−0.989020 + 0.147784i \(0.952786\pi\)
\(182\) 0 0
\(183\) 13.1420 22.7627i 0.971487 1.68266i
\(184\) −1.37733 + 7.81120i −0.101538 + 0.575850i
\(185\) −3.33022 + 2.79439i −0.244843 + 0.205448i
\(186\) −4.78699 + 27.1484i −0.350999 + 1.99061i
\(187\) −0.979055 0.356347i −0.0715956 0.0260587i
\(188\) −0.233956 1.32683i −0.0170630 0.0967689i
\(189\) 0 0
\(190\) 1.73055 4.86581i 0.125547 0.353003i
\(191\) −9.16772 15.8790i −0.663353 1.14896i −0.979729 0.200327i \(-0.935800\pi\)
0.316376 0.948634i \(-0.397534\pi\)
\(192\) −23.2592 8.46567i −1.67859 0.610957i
\(193\) 0.0516892 + 0.293144i 0.00372067 + 0.0211010i 0.986612 0.163088i \(-0.0521454\pi\)
−0.982891 + 0.184189i \(0.941034\pi\)
\(194\) 9.75671 + 8.18685i 0.700491 + 0.587782i
\(195\) −6.12449 2.22913i −0.438583 0.159631i
\(196\) 0 0
\(197\) −6.57057 + 11.3806i −0.468134 + 0.810832i −0.999337 0.0364128i \(-0.988407\pi\)
0.531203 + 0.847245i \(0.321740\pi\)
\(198\) −7.93629 + 13.7461i −0.564008 + 0.976890i
\(199\) 0.196652 + 0.165011i 0.0139403 + 0.0116973i 0.649731 0.760164i \(-0.274881\pi\)
−0.635791 + 0.771861i \(0.719326\pi\)
\(200\) −9.53074 7.99724i −0.673925 0.565491i
\(201\) −11.0496 + 19.1385i −0.779381 + 1.34993i
\(202\) 6.23055 10.7916i 0.438380 0.759297i
\(203\) 0 0
\(204\) −0.233956 0.0851529i −0.0163802 0.00596189i
\(205\) 1.66772 + 1.39938i 0.116479 + 0.0977371i
\(206\) −1.28905 7.31056i −0.0898123 0.509351i
\(207\) 13.3969 + 4.87608i 0.931151 + 0.338911i
\(208\) −4.62836 8.01655i −0.320919 0.555848i
\(209\) 3.38666 + 9.09586i 0.234260 + 0.629174i
\(210\) 0 0
\(211\) 0.425145 + 2.41112i 0.0292682 + 0.165988i 0.995938 0.0900364i \(-0.0286983\pi\)
−0.966670 + 0.256024i \(0.917587\pi\)
\(212\) −0.492726 0.179338i −0.0338406 0.0123170i
\(213\) −4.65270 + 26.3868i −0.318798 + 1.80799i
\(214\) −10.5628 + 8.86327i −0.722060 + 0.605881i
\(215\) −0.595800 + 3.37895i −0.0406332 + 0.230442i
\(216\) −9.70826 + 16.8152i −0.660564 + 1.14413i
\(217\) 0 0
\(218\) 0.426489 2.41874i 0.0288855 0.163818i
\(219\) 3.75877 1.36808i 0.253994 0.0924463i
\(220\) −0.361844 −0.0243955
\(221\) −0.602196 1.04303i −0.0405081 0.0701621i
\(222\) −3.33022 + 18.8866i −0.223510 + 1.26759i
\(223\) −7.99660 2.91052i −0.535492 0.194903i 0.0600971 0.998193i \(-0.480859\pi\)
−0.595589 + 0.803289i \(0.703081\pi\)
\(224\) 0 0
\(225\) −17.1309 + 14.3745i −1.14206 + 0.958301i
\(226\) 18.2554 15.3181i 1.21433 1.01894i
\(227\) −7.07532 + 12.2548i −0.469606 + 0.813381i −0.999396 0.0347477i \(-0.988937\pi\)
0.529790 + 0.848129i \(0.322271\pi\)
\(228\) 0.809278 + 2.17355i 0.0535957 + 0.143947i
\(229\) −10.2665 17.7821i −0.678430 1.17508i −0.975454 0.220205i \(-0.929327\pi\)
0.297023 0.954870i \(-0.404006\pi\)
\(230\) −0.554378 3.14403i −0.0365546 0.207311i
\(231\) 0 0
\(232\) 19.0287 6.92588i 1.24929 0.454706i
\(233\) 3.06506 + 17.3828i 0.200798 + 1.13878i 0.903916 + 0.427711i \(0.140680\pi\)
−0.703117 + 0.711074i \(0.748209\pi\)
\(234\) −17.2417 + 6.27546i −1.12712 + 0.410240i
\(235\) 3.20574 + 5.55250i 0.209119 + 0.362205i
\(236\) 0.582596 1.00909i 0.0379238 0.0656859i
\(237\) −5.92262 + 33.5888i −0.384715 + 2.18183i
\(238\) 0 0
\(239\) −1.17617 2.03719i −0.0760804 0.131775i 0.825475 0.564438i \(-0.190907\pi\)
−0.901556 + 0.432663i \(0.857574\pi\)
\(240\) 9.10607 0.587794
\(241\) 12.9684 4.72010i 0.835367 0.304049i 0.111307 0.993786i \(-0.464496\pi\)
0.724060 + 0.689737i \(0.242274\pi\)
\(242\) 6.23577 5.23243i 0.400850 0.336353i
\(243\) −8.27584 6.94426i −0.530896 0.445474i
\(244\) 1.29220 1.08429i 0.0827249 0.0694144i
\(245\) 0 0
\(246\) 9.60401 0.612329
\(247\) −3.75965 + 10.5710i −0.239221 + 0.672619i
\(248\) −10.4586 + 18.1148i −0.664120 + 1.15029i
\(249\) −40.1279 14.6054i −2.54301 0.925578i
\(250\) 10.2724 + 3.73886i 0.649686 + 0.236466i
\(251\) −3.91400 + 1.42458i −0.247050 + 0.0899187i −0.462577 0.886579i \(-0.653075\pi\)
0.215528 + 0.976498i \(0.430853\pi\)
\(252\) 0 0
\(253\) 4.59627 + 3.85673i 0.288965 + 0.242470i
\(254\) −15.6340 −0.980967
\(255\) 1.18479 0.0741946
\(256\) −3.36753 2.82569i −0.210470 0.176606i
\(257\) 0.627011 0.228213i 0.0391119 0.0142356i −0.322390 0.946607i \(-0.604486\pi\)
0.361502 + 0.932371i \(0.382264\pi\)
\(258\) 7.56805 + 13.1082i 0.471166 + 0.816084i
\(259\) 0 0
\(260\) −0.320422 0.268866i −0.0198717 0.0166744i
\(261\) −6.32042 35.8449i −0.391224 2.21874i
\(262\) 0.431703 2.44831i 0.0266707 0.151257i
\(263\) 1.97952 + 11.2264i 0.122063 + 0.692251i 0.983009 + 0.183556i \(0.0587609\pi\)
−0.860947 + 0.508695i \(0.830128\pi\)
\(264\) −14.4572 + 12.1311i −0.889781 + 0.746615i
\(265\) 2.49525 0.153282
\(266\) 0 0
\(267\) 29.6313 1.81341
\(268\) −1.08647 + 0.911654i −0.0663665 + 0.0556881i
\(269\) −3.36706 19.0955i −0.205293 1.16428i −0.896978 0.442076i \(-0.854242\pi\)
0.691684 0.722200i \(-0.256869\pi\)
\(270\) 1.35710 7.69648i 0.0825903 0.468393i
\(271\) 2.32588 + 13.1907i 0.141287 + 0.801281i 0.970273 + 0.242011i \(0.0778072\pi\)
−0.828986 + 0.559269i \(0.811082\pi\)
\(272\) 1.28905 + 1.08164i 0.0781600 + 0.0655841i
\(273\) 0 0
\(274\) 0.172304 + 0.298439i 0.0104093 + 0.0180294i
\(275\) −8.84389 + 3.21891i −0.533307 + 0.194108i
\(276\) 1.09833 + 0.921605i 0.0661115 + 0.0554741i
\(277\) 17.7469 1.06631 0.533154 0.846018i \(-0.321007\pi\)
0.533154 + 0.846018i \(0.321007\pi\)
\(278\) 5.74422 0.344516
\(279\) 28.8011 + 24.1670i 1.72428 + 1.44684i
\(280\) 0 0
\(281\) −17.1766 + 6.25179i −1.02467 + 0.372950i −0.799050 0.601265i \(-0.794664\pi\)
−0.225622 + 0.974215i \(0.572442\pi\)
\(282\) 26.5783 + 9.67372i 1.58272 + 0.576061i
\(283\) 7.22416 + 2.62938i 0.429431 + 0.156300i 0.547688 0.836683i \(-0.315508\pi\)
−0.118256 + 0.992983i \(0.537730\pi\)
\(284\) −0.859785 + 1.48919i −0.0510188 + 0.0883672i
\(285\) −7.15657 8.40247i −0.423919 0.497719i
\(286\) −7.72193 −0.456608
\(287\) 0 0
\(288\) −4.22281 + 3.54336i −0.248832 + 0.208794i
\(289\) −12.8550 10.7867i −0.756179 0.634509i
\(290\) −6.24376 + 5.23913i −0.366646 + 0.307652i
\(291\) 25.5783 9.30975i 1.49943 0.545747i
\(292\) 0.256711 0.0150229
\(293\) −5.25150 9.09586i −0.306796 0.531386i 0.670864 0.741581i \(-0.265924\pi\)
−0.977660 + 0.210195i \(0.932590\pi\)
\(294\) 0 0
\(295\) −0.962859 + 5.46064i −0.0560598 + 0.317931i
\(296\) −7.27584 + 12.6021i −0.422900 + 0.732484i
\(297\) 7.34389 + 12.7200i 0.426136 + 0.738089i
\(298\) 20.9650 7.63063i 1.21447 0.442030i
\(299\) 1.20439 + 6.83045i 0.0696518 + 0.395015i
\(300\) −2.11334 + 0.769193i −0.122014 + 0.0444094i
\(301\) 0 0
\(302\) 1.02048 + 5.78742i 0.0587219 + 0.333028i
\(303\) −13.3157 23.0634i −0.764966 1.32496i
\(304\) −0.115400 15.6753i −0.00661865 0.899042i
\(305\) −4.01367 + 6.95188i −0.229822 + 0.398064i
\(306\) 2.55509 2.14398i 0.146065 0.122563i
\(307\) 8.95929 7.51774i 0.511334 0.429060i −0.350264 0.936651i \(-0.613908\pi\)
0.861598 + 0.507591i \(0.169464\pi\)
\(308\) 0 0
\(309\) −14.9081 5.42609i −0.848091 0.308680i
\(310\) 1.46198 8.29131i 0.0830350 0.470915i
\(311\) 7.98293 + 13.8268i 0.452670 + 0.784048i 0.998551 0.0538151i \(-0.0171382\pi\)
−0.545881 + 0.837863i \(0.683805\pi\)
\(312\) −21.8161 −1.23510
\(313\) −25.0228 + 9.10754i −1.41437 + 0.514788i −0.932409 0.361404i \(-0.882297\pi\)
−0.481961 + 0.876193i \(0.660075\pi\)
\(314\) −2.25031 + 12.7622i −0.126993 + 0.720211i
\(315\) 0 0
\(316\) −1.09446 + 1.89565i −0.0615679 + 0.106639i
\(317\) 5.12819 29.0834i 0.288028 1.63349i −0.406236 0.913768i \(-0.633159\pi\)
0.694264 0.719720i \(-0.255730\pi\)
\(318\) 8.43242 7.07564i 0.472867 0.396782i
\(319\) 2.65998 15.0855i 0.148930 0.844625i
\(320\) 7.10354 + 2.58548i 0.397100 + 0.144533i
\(321\) 5.11721 + 29.0211i 0.285615 + 1.61980i
\(322\) 0 0
\(323\) −0.0150147 2.03952i −0.000835443 0.113482i
\(324\) 0.288333 + 0.499408i 0.0160185 + 0.0277449i
\(325\) −10.2233 3.72097i −0.567085 0.206402i
\(326\) −1.95471 11.0857i −0.108261 0.613980i
\(327\) −4.02094 3.37397i −0.222359 0.186581i
\(328\) 6.84776 + 2.49238i 0.378104 + 0.137619i
\(329\) 0 0
\(330\) 3.79813 6.57856i 0.209080 0.362138i
\(331\) −13.8327 + 23.9590i −0.760317 + 1.31691i 0.182371 + 0.983230i \(0.441623\pi\)
−0.942687 + 0.333677i \(0.891710\pi\)
\(332\) −2.09942 1.76162i −0.115221 0.0966817i
\(333\) 20.0364 + 16.8126i 1.09799 + 0.921322i
\(334\) −2.71823 + 4.70810i −0.148735 + 0.257616i
\(335\) 3.37464 5.84504i 0.184376 0.319349i
\(336\) 0 0
\(337\) −16.7827 6.10841i −0.914212 0.332746i −0.158279 0.987394i \(-0.550594\pi\)
−0.755934 + 0.654648i \(0.772817\pi\)
\(338\) 6.57919 + 5.52060i 0.357861 + 0.300281i
\(339\) −8.84389 50.1562i −0.480334 2.72411i
\(340\) 0.0714517 + 0.0260063i 0.00387501 + 0.00141039i
\(341\) 7.91147 + 13.7031i 0.428430 + 0.742063i
\(342\) −30.6386 5.17015i −1.65675 0.279569i
\(343\) 0 0
\(344\) 1.99432 + 11.3103i 0.107526 + 0.609813i
\(345\) −6.41147 2.33359i −0.345182 0.125636i
\(346\) −4.71276 + 26.7274i −0.253360 + 1.43687i
\(347\) −4.44356 + 3.72859i −0.238543 + 0.200161i −0.754220 0.656622i \(-0.771985\pi\)
0.515677 + 0.856783i \(0.327540\pi\)
\(348\) 0.635630 3.60483i 0.0340733 0.193239i
\(349\) 2.68614 4.65253i 0.143786 0.249044i −0.785134 0.619326i \(-0.787406\pi\)
0.928919 + 0.370282i \(0.120739\pi\)
\(350\) 0 0
\(351\) −2.94831 + 16.7207i −0.157369 + 0.892485i
\(352\) −2.18004 + 0.793471i −0.116197 + 0.0422922i
\(353\) 25.2344 1.34309 0.671546 0.740963i \(-0.265630\pi\)
0.671546 + 0.740963i \(0.265630\pi\)
\(354\) 12.2306 + 21.1839i 0.650047 + 1.12591i
\(355\) 1.42097 8.05872i 0.0754172 0.427712i
\(356\) 1.78699 + 0.650411i 0.0947102 + 0.0344717i
\(357\) 0 0
\(358\) 11.8819 9.97011i 0.627979 0.526937i
\(359\) 5.12243 4.29823i 0.270351 0.226852i −0.497525 0.867449i \(-0.665758\pi\)
0.767877 + 0.640598i \(0.221313\pi\)
\(360\) 6.84776 11.8607i 0.360909 0.625112i
\(361\) −14.3735 + 12.4259i −0.756498 + 0.653996i
\(362\) −5.75103 9.96108i −0.302267 0.523543i
\(363\) −3.02094 17.1326i −0.158558 0.899230i
\(364\) 0 0
\(365\) −1.14796 + 0.417822i −0.0600868 + 0.0218698i
\(366\) 6.14930 + 34.8744i 0.321429 + 1.82291i
\(367\) 7.62923 2.77681i 0.398243 0.144948i −0.135132 0.990828i \(-0.543146\pi\)
0.533375 + 0.845879i \(0.320924\pi\)
\(368\) −4.84524 8.39220i −0.252575 0.437473i
\(369\) 6.54916 11.3435i 0.340936 0.590518i
\(370\) 1.01707 5.76811i 0.0528752 0.299870i
\(371\) 0 0
\(372\) 1.89053 + 3.27449i 0.0980194 + 0.169775i
\(373\) 34.8976 1.80693 0.903463 0.428665i \(-0.141016\pi\)
0.903463 + 0.428665i \(0.141016\pi\)
\(374\) 1.31908 0.480105i 0.0682079 0.0248256i
\(375\) 17.8969 15.0173i 0.924193 0.775490i
\(376\) 16.4402 + 13.7949i 0.847836 + 0.711419i
\(377\) 13.5646 11.3821i 0.698615 0.586207i
\(378\) 0 0
\(379\) 1.70140 0.0873950 0.0436975 0.999045i \(-0.486086\pi\)
0.0436975 + 0.999045i \(0.486086\pi\)
\(380\) −0.247159 0.663818i −0.0126790 0.0340532i
\(381\) −16.7062 + 28.9360i −0.855885 + 1.48244i
\(382\) 23.2135 + 8.44901i 1.18770 + 0.432289i
\(383\) 2.75965 + 1.00443i 0.141011 + 0.0513240i 0.411562 0.911382i \(-0.364983\pi\)
−0.270550 + 0.962706i \(0.587206\pi\)
\(384\) 25.6989 9.35365i 1.31144 0.477326i
\(385\) 0 0
\(386\) −0.307218 0.257787i −0.0156370 0.0131210i
\(387\) 20.6432 1.04935
\(388\) 1.74691 0.0886860
\(389\) −18.8195 15.7915i −0.954189 0.800659i 0.0258092 0.999667i \(-0.491784\pi\)
−0.979998 + 0.199007i \(0.936228\pi\)
\(390\) 8.25150 3.00330i 0.417831 0.152078i
\(391\) −0.630415 1.09191i −0.0318815 0.0552203i
\(392\) 0 0
\(393\) −4.07011 3.41523i −0.205310 0.172275i
\(394\) −3.07444 17.4360i −0.154888 0.878415i
\(395\) 1.80881 10.2583i 0.0910112 0.516150i
\(396\) 0.378041 + 2.14398i 0.0189973 + 0.107739i
\(397\) 24.3876 20.4636i 1.22398 1.02704i 0.225371 0.974273i \(-0.427640\pi\)
0.998607 0.0527667i \(-0.0168040\pi\)
\(398\) −0.345866 −0.0173367
\(399\) 0 0
\(400\) 15.2003 0.760014
\(401\) −0.0662372 + 0.0555796i −0.00330773 + 0.00277551i −0.644440 0.764655i \(-0.722909\pi\)
0.641132 + 0.767430i \(0.278465\pi\)
\(402\) −5.17024 29.3219i −0.257868 1.46244i
\(403\) −3.17617 + 18.0130i −0.158217 + 0.897290i
\(404\) −0.296789 1.68317i −0.0147658 0.0837411i
\(405\) −2.10220 1.76395i −0.104459 0.0876515i
\(406\) 0 0
\(407\) 5.50387 + 9.53298i 0.272817 + 0.472532i
\(408\) 3.72668 1.35640i 0.184498 0.0671519i
\(409\) −15.3255 12.8596i −0.757796 0.635866i 0.179756 0.983711i \(-0.442469\pi\)
−0.937552 + 0.347845i \(0.886914\pi\)
\(410\) −2.93313 −0.144857
\(411\) 0.736482 0.0363280
\(412\) −0.779963 0.654467i −0.0384260 0.0322433i
\(413\) 0 0
\(414\) −18.0496 + 6.56953i −0.887091 + 0.322875i
\(415\) 12.2554 + 4.46059i 0.601592 + 0.218962i
\(416\) −2.52007 0.917229i −0.123556 0.0449709i
\(417\) 6.13816 10.6316i 0.300587 0.520632i
\(418\) −11.3726 6.45480i −0.556251 0.315715i
\(419\) −25.4097 −1.24135 −0.620673 0.784070i \(-0.713141\pi\)
−0.620673 + 0.784070i \(0.713141\pi\)
\(420\) 0 0
\(421\) 3.34730 2.80872i 0.163137 0.136888i −0.557565 0.830134i \(-0.688264\pi\)
0.720702 + 0.693245i \(0.243820\pi\)
\(422\) −2.52687 2.12030i −0.123006 0.103215i
\(423\) 29.5501 24.7955i 1.43677 1.20560i
\(424\) 7.84864 2.85667i 0.381164 0.138732i
\(425\) 1.97771 0.0959331
\(426\) −18.0496 31.2629i −0.874507 1.51469i
\(427\) 0 0
\(428\) −0.328411 + 1.86251i −0.0158744 + 0.0900279i
\(429\) −8.25150 + 14.2920i −0.398386 + 0.690025i
\(430\) −2.31134 4.00335i −0.111463 0.193059i
\(431\) 35.9962 13.1015i 1.73388 0.631079i 0.734981 0.678088i \(-0.237191\pi\)
0.998894 + 0.0470089i \(0.0149689\pi\)
\(432\) −4.11927 23.3615i −0.198188 1.12398i
\(433\) −17.0376 + 6.20118i −0.818775 + 0.298010i −0.717244 0.696823i \(-0.754597\pi\)
−0.101532 + 0.994832i \(0.532374\pi\)
\(434\) 0 0
\(435\) 3.02481 + 17.1546i 0.145029 + 0.822499i
\(436\) −0.168434 0.291736i −0.00806651 0.0139716i
\(437\) −3.93582 + 11.0664i −0.188276 + 0.529377i
\(438\) −2.69459 + 4.66717i −0.128753 + 0.223006i
\(439\) 4.66566 3.91495i 0.222680 0.186850i −0.524622 0.851335i \(-0.675793\pi\)
0.747302 + 0.664485i \(0.231349\pi\)
\(440\) 4.41534 3.70491i 0.210493 0.176625i
\(441\) 0 0
\(442\) 1.52481 + 0.554987i 0.0725280 + 0.0263981i
\(443\) −5.19088 + 29.4390i −0.246626 + 1.39869i 0.570059 + 0.821604i \(0.306920\pi\)
−0.816685 + 0.577084i \(0.804191\pi\)
\(444\) 1.31521 + 2.27801i 0.0624170 + 0.108109i
\(445\) −9.04963 −0.428994
\(446\) 10.7738 3.92134i 0.510154 0.185681i
\(447\) 8.27972 46.9566i 0.391617 2.22097i
\(448\) 0 0
\(449\) 5.62495 9.74270i 0.265458 0.459787i −0.702226 0.711955i \(-0.747810\pi\)
0.967683 + 0.252168i \(0.0811435\pi\)
\(450\) 5.23190 29.6716i 0.246634 1.39873i
\(451\) 4.22281 3.54336i 0.198844 0.166850i
\(452\) 0.567581 3.21891i 0.0266968 0.151405i
\(453\) 11.8020 + 4.29558i 0.554507 + 0.201824i
\(454\) −3.31062 18.7755i −0.155375 0.881176i
\(455\) 0 0
\(456\) −32.1300 18.2362i −1.50463 0.853989i
\(457\) 11.6951 + 20.2564i 0.547072 + 0.947556i 0.998473 + 0.0552352i \(0.0175909\pi\)
−0.451402 + 0.892321i \(0.649076\pi\)
\(458\) 25.9957 + 9.46167i 1.21470 + 0.442115i
\(459\) −0.535959 3.03958i −0.0250164 0.141875i
\(460\) −0.335437 0.281465i −0.0156398 0.0131234i
\(461\) −34.4149 12.5260i −1.60286 0.583395i −0.622853 0.782339i \(-0.714026\pi\)
−0.980011 + 0.198945i \(0.936249\pi\)
\(462\) 0 0
\(463\) 21.4932 37.2273i 0.998873 1.73010i 0.458340 0.888777i \(-0.348444\pi\)
0.540534 0.841322i \(-0.318222\pi\)
\(464\) −12.3701 + 21.4256i −0.574265 + 0.994657i
\(465\) −13.7836 11.5658i −0.639198 0.536351i
\(466\) −18.2173 15.2862i −0.843902 0.708118i
\(467\) 12.7981 22.1670i 0.592227 1.02577i −0.401705 0.915769i \(-0.631582\pi\)
0.993932 0.109998i \(-0.0350845\pi\)
\(468\) −1.25830 + 2.17945i −0.0581651 + 0.100745i
\(469\) 0 0
\(470\) −8.11721 2.95442i −0.374419 0.136277i
\(471\) 21.2160 + 17.8023i 0.977582 + 0.820289i
\(472\) 3.22297 + 18.2784i 0.148349 + 0.841331i
\(473\) 8.16385 + 2.97140i 0.375374 + 0.136625i
\(474\) −22.9761 39.7958i −1.05533 1.82788i
\(475\) −11.9461 14.0258i −0.548124 0.643548i
\(476\) 0 0
\(477\) −2.60694 14.7847i −0.119364 0.676946i
\(478\) 2.97818 + 1.08397i 0.136219 + 0.0495796i
\(479\) −6.62923 + 37.5962i −0.302897 + 1.71782i 0.330343 + 0.943861i \(0.392836\pi\)
−0.633240 + 0.773955i \(0.718275\pi\)
\(480\) 2.02094 1.69577i 0.0922431 0.0774011i
\(481\) −2.20961 + 12.5313i −0.100749 + 0.571378i
\(482\) −9.29679 + 16.1025i −0.423457 + 0.733449i
\(483\) 0 0
\(484\) 0.193877 1.09953i 0.00881261 0.0499788i
\(485\) −7.81180 + 2.84326i −0.354716 + 0.129106i
\(486\) 14.5553 0.660242
\(487\) −3.88191 6.72367i −0.175906 0.304678i 0.764568 0.644543i \(-0.222952\pi\)
−0.940475 + 0.339864i \(0.889619\pi\)
\(488\) −4.66591 + 26.4617i −0.211216 + 1.19786i
\(489\) −22.6065 8.22811i −1.02230 0.372088i
\(490\) 0 0
\(491\) −28.1313 + 23.6050i −1.26955 + 1.06528i −0.274954 + 0.961457i \(0.588663\pi\)
−0.994596 + 0.103822i \(0.966893\pi\)
\(492\) 1.00908 0.846723i 0.0454931 0.0381732i
\(493\) −1.60947 + 2.78768i −0.0724869 + 0.125551i
\(494\) −5.27450 14.1662i −0.237311 0.637368i
\(495\) −5.18004 8.97210i −0.232826 0.403266i
\(496\) −4.43763 25.1671i −0.199256 1.13003i
\(497\) 0 0
\(498\) 54.0642 19.6778i 2.42268 0.881782i
\(499\) 0.855448 + 4.85148i 0.0382951 + 0.217182i 0.997950 0.0639981i \(-0.0203852\pi\)
−0.959655 + 0.281180i \(0.909274\pi\)
\(500\) 1.40895 0.512815i 0.0630101 0.0229338i
\(501\) 5.80928 + 10.0620i 0.259539 + 0.449535i
\(502\) 2.80587 4.85992i 0.125232 0.216909i
\(503\) −5.72163 + 32.4490i −0.255115 + 1.44683i 0.540663 + 0.841239i \(0.318173\pi\)
−0.795778 + 0.605589i \(0.792938\pi\)
\(504\) 0 0
\(505\) 4.06670 + 7.04374i 0.180966 + 0.313442i
\(506\) −8.08378 −0.359368
\(507\) 17.2481 6.27779i 0.766015 0.278807i
\(508\) −1.64266 + 1.37835i −0.0728810 + 0.0611544i
\(509\) 28.2939 + 23.7414i 1.25410 + 1.05232i 0.996284 + 0.0861240i \(0.0274481\pi\)
0.257819 + 0.966193i \(0.416996\pi\)
\(510\) −1.22281 + 1.02606i −0.0541470 + 0.0454347i
\(511\) 0 0
\(512\) 24.9186 1.10126
\(513\) −18.3191 + 22.1611i −0.808807 + 0.978437i
\(514\) −0.449493 + 0.778544i −0.0198263 + 0.0343401i
\(515\) 4.55303 + 1.65717i 0.200631 + 0.0730236i
\(516\) 1.95084 + 0.710047i 0.0858808 + 0.0312581i
\(517\) 15.2554 5.55250i 0.670930 0.244199i
\(518\) 0 0
\(519\) 44.4320 + 37.2829i 1.95035 + 1.63654i
\(520\) 6.66281 0.292183
\(521\) −9.29179 −0.407081 −0.203540 0.979067i \(-0.565245\pi\)
−0.203540 + 0.979067i \(0.565245\pi\)
\(522\) 37.5658 + 31.5215i 1.64421 + 1.37966i
\(523\) −26.7015 + 9.71854i −1.16757 + 0.424962i −0.851797 0.523872i \(-0.824487\pi\)
−0.315776 + 0.948834i \(0.602265\pi\)
\(524\) −0.170493 0.295303i −0.00744802 0.0129004i
\(525\) 0 0
\(526\) −11.7654 9.87236i −0.512996 0.430455i
\(527\) −0.577382 3.27449i −0.0251511 0.142639i
\(528\) 4.00387 22.7071i 0.174246 0.988199i
\(529\) −2.73308 15.5001i −0.118829 0.673916i
\(530\) −2.57532 + 2.16095i −0.111865 + 0.0938657i
\(531\) 33.3610 1.44775
\(532\) 0 0
\(533\) 6.37227 0.276014
\(534\) −30.5822 + 25.6615i −1.32342 + 1.11048i
\(535\) −1.56283 8.86327i −0.0675672 0.383193i
\(536\) 3.92303 22.2486i 0.169449 0.960993i
\(537\) −5.75624 32.6453i −0.248400 1.40875i
\(538\) 20.0123 + 16.7923i 0.862793 + 0.723969i
\(539\) 0 0
\(540\) −0.535959 0.928309i −0.0230640 0.0399480i
\(541\) −14.0817 + 5.12533i −0.605420 + 0.220355i −0.626498 0.779423i \(-0.715512\pi\)
0.0210779 + 0.999778i \(0.493290\pi\)
\(542\) −13.8240 11.5998i −0.593794 0.498252i
\(543\) −24.5817 −1.05490
\(544\) 0.487511 0.0209019
\(545\) 1.22803 + 1.03044i 0.0526028 + 0.0441390i
\(546\) 0 0
\(547\) 3.65270 1.32948i 0.156178 0.0568443i −0.262748 0.964864i \(-0.584629\pi\)
0.418926 + 0.908020i \(0.362407\pi\)
\(548\) 0.0444153 + 0.0161658i 0.00189733 + 0.000690571i
\(549\) 45.3842 + 16.5185i 1.93695 + 0.704992i
\(550\) 6.34002 10.9812i 0.270339 0.468242i
\(551\) 29.4918 5.42437i 1.25639 0.231086i
\(552\) −22.8384 −0.972068
\(553\) 0 0
\(554\) −18.3164 + 15.3693i −0.778189 + 0.652978i
\(555\) −9.58899 8.04612i −0.407030 0.341539i
\(556\) 0.603541 0.506431i 0.0255958 0.0214774i
\(557\) −12.4081 + 4.51617i −0.525747 + 0.191356i −0.591238 0.806497i \(-0.701361\pi\)
0.0654914 + 0.997853i \(0.479138\pi\)
\(558\) −50.6546 −2.14438
\(559\) 5.02141 + 8.69734i 0.212383 + 0.367858i
\(560\) 0 0
\(561\) 0.520945 2.95442i 0.0219943 0.124736i
\(562\) 12.3136 21.3278i 0.519418 0.899659i
\(563\) 5.35638 + 9.27752i 0.225745 + 0.391001i 0.956543 0.291593i \(-0.0941852\pi\)
−0.730798 + 0.682594i \(0.760852\pi\)
\(564\) 3.64543 1.32683i 0.153500 0.0558695i
\(565\) 2.70099 + 15.3181i 0.113631 + 0.644436i
\(566\) −9.73308 + 3.54255i −0.409112 + 0.148905i
\(567\) 0 0
\(568\) −4.75641 26.9749i −0.199574 1.13184i
\(569\) 6.73530 + 11.6659i 0.282358 + 0.489059i 0.971965 0.235125i \(-0.0755499\pi\)
−0.689607 + 0.724184i \(0.742217\pi\)
\(570\) 14.6630 + 2.47432i 0.614164 + 0.103638i
\(571\) −6.33275 + 10.9686i −0.265017 + 0.459023i −0.967568 0.252610i \(-0.918711\pi\)
0.702551 + 0.711634i \(0.252044\pi\)
\(572\) −0.811337 + 0.680793i −0.0339237 + 0.0284654i
\(573\) 40.4432 33.9358i 1.68954 1.41769i
\(574\) 0 0
\(575\) −10.7023 3.89533i −0.446318 0.162447i
\(576\) 7.89780 44.7907i 0.329075 1.86628i
\(577\) −5.27719 9.14036i −0.219692 0.380518i 0.735022 0.678044i \(-0.237172\pi\)
−0.954714 + 0.297526i \(0.903839\pi\)
\(578\) 22.6091 0.940413
\(579\) −0.805407 + 0.293144i −0.0334716 + 0.0121827i
\(580\) −0.194126 + 1.10094i −0.00806064 + 0.0457142i
\(581\) 0 0
\(582\) −18.3366 + 31.7600i −0.760077 + 1.31649i
\(583\) 1.09714 6.22221i 0.0454391 0.257698i
\(584\) −3.13247 + 2.62846i −0.129623 + 0.108766i
\(585\) 2.07960 11.7940i 0.0859810 0.487623i
\(586\) 13.2973 + 4.83981i 0.549305 + 0.199931i
\(587\) 3.32619 + 18.8638i 0.137287 + 0.778591i 0.973240 + 0.229791i \(0.0738041\pi\)
−0.835954 + 0.548800i \(0.815085\pi\)
\(588\) 0 0
\(589\) −19.7349 + 23.8739i −0.813162 + 0.983706i
\(590\) −3.73530 6.46973i −0.153780 0.266355i
\(591\) −35.5565 12.9415i −1.46260 0.532342i
\(592\) −3.08718 17.5083i −0.126882 0.719586i
\(593\) 6.66044 + 5.58878i 0.273512 + 0.229504i 0.769218 0.638987i \(-0.220646\pi\)
−0.495706 + 0.868490i \(0.665091\pi\)
\(594\) −18.5954 6.76817i −0.762978 0.277701i
\(595\) 0 0
\(596\) 1.53003 2.65009i 0.0626724 0.108552i
\(597\) −0.369585 + 0.640140i −0.0151261 + 0.0261992i
\(598\) −7.15839 6.00660i −0.292728 0.245628i
\(599\) 15.1919 + 12.7475i 0.620724 + 0.520850i 0.898031 0.439932i \(-0.144997\pi\)
−0.277307 + 0.960781i \(0.589442\pi\)
\(600\) 17.9119 31.0244i 0.731252 1.26657i
\(601\) −16.8807 + 29.2383i −0.688579 + 1.19265i 0.283718 + 0.958908i \(0.408432\pi\)
−0.972298 + 0.233747i \(0.924901\pi\)
\(602\) 0 0
\(603\) −38.1584 13.8885i −1.55393 0.565584i
\(604\) 0.617460 + 0.518110i 0.0251241 + 0.0210816i
\(605\) 0.922618 + 5.23243i 0.0375098 + 0.212729i
\(606\) 33.7165 + 12.2718i 1.36964 + 0.498507i
\(607\) 17.6425 + 30.5577i 0.716087 + 1.24030i 0.962539 + 0.271144i \(0.0874018\pi\)
−0.246452 + 0.969155i \(0.579265\pi\)
\(608\) −2.94475 3.45740i −0.119425 0.140216i
\(609\) 0 0
\(610\) −1.87804 10.6509i −0.0760397 0.431242i
\(611\) 17.6348 + 6.41852i 0.713426 + 0.259666i
\(612\) 0.0794409 0.450532i 0.00321121 0.0182117i
\(613\) 14.1361 11.8616i 0.570952 0.479085i −0.311010 0.950407i \(-0.600667\pi\)
0.881962 + 0.471321i \(0.156223\pi\)
\(614\) −2.73623 + 15.5180i −0.110425 + 0.626254i
\(615\) −3.13429 + 5.42874i −0.126387 + 0.218908i
\(616\) 0 0
\(617\) −6.19671 + 35.1433i −0.249470 + 1.41482i 0.560408 + 0.828217i \(0.310644\pi\)
−0.809878 + 0.586598i \(0.800467\pi\)
\(618\) 20.0856 7.31056i 0.807961 0.294074i
\(619\) −3.65951 −0.147088 −0.0735441 0.997292i \(-0.523431\pi\)
−0.0735441 + 0.997292i \(0.523431\pi\)
\(620\) −0.577382 1.00005i −0.0231882 0.0401631i
\(621\) −3.08647 + 17.5042i −0.123856 + 0.702420i
\(622\) −20.2135 7.35710i −0.810487 0.294993i
\(623\) 0 0
\(624\) 20.4179 17.1326i 0.817369 0.685854i
\(625\) 10.7233 8.99790i 0.428931 0.359916i
\(626\) 17.9383 31.0701i 0.716961 1.24181i
\(627\) −24.0993 + 14.1513i −0.962432 + 0.565148i
\(628\) 0.888719 + 1.53931i 0.0354637 + 0.0614250i
\(629\) −0.401674 2.27801i −0.0160158 0.0908301i
\(630\) 0 0
\(631\) 0.745977 0.271514i 0.0296969 0.0108088i −0.327129 0.944980i \(-0.606081\pi\)
0.356826 + 0.934171i \(0.383859\pi\)
\(632\) −6.05463 34.3375i −0.240840 1.36587i
\(633\) −6.62449 + 2.41112i −0.263300 + 0.0958332i
\(634\) 19.8942 + 34.4578i 0.790101 + 1.36850i
\(635\) 5.10220 8.83726i 0.202474 0.350696i
\(636\) 0.262174 1.48686i 0.0103959 0.0589579i
\(637\) 0 0
\(638\) 10.3191 + 17.8732i 0.408536 + 0.707605i
\(639\) −49.2336 −1.94765
\(640\) −7.84864 + 2.85667i −0.310245 + 0.112920i
\(641\) 22.5082 18.8866i 0.889021 0.745977i −0.0789927 0.996875i \(-0.525170\pi\)
0.968013 + 0.250898i \(0.0807259\pi\)
\(642\) −30.4145 25.5208i −1.20036 1.00722i
\(643\) −17.0168 + 14.2788i −0.671078 + 0.563101i −0.913384 0.407098i \(-0.866541\pi\)
0.242306 + 0.970200i \(0.422096\pi\)
\(644\) 0 0
\(645\) −9.87939 −0.389000
\(646\) 1.78177 + 2.09196i 0.0701030 + 0.0823073i
\(647\) 5.62954 9.75065i 0.221320 0.383337i −0.733889 0.679269i \(-0.762297\pi\)
0.955209 + 0.295932i \(0.0956302\pi\)
\(648\) −8.63176 3.14170i −0.339088 0.123418i
\(649\) 13.1934 + 4.80201i 0.517887 + 0.188495i
\(650\) 13.7738 5.01325i 0.540252 0.196636i
\(651\) 0 0
\(652\) −1.18273 0.992431i −0.0463194 0.0388666i
\(653\) 27.0000 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) 7.07192 0.276534
\(655\) 1.24304 + 1.04303i 0.0485696 + 0.0407547i
\(656\) −8.36618 + 3.04504i −0.326645 + 0.118889i
\(657\) 3.67499 + 6.36527i 0.143375 + 0.248333i
\(658\) 0 0
\(659\) 21.4691 + 18.0147i 0.836317 + 0.701753i 0.956732 0.290970i \(-0.0939781\pi\)
−0.120415 + 0.992724i \(0.538423\pi\)
\(660\) −0.180922 1.02606i −0.00704238 0.0399393i
\(661\) −1.97400 + 11.1951i −0.0767798 + 0.435440i 0.922050 + 0.387071i \(0.126513\pi\)
−0.998830 + 0.0483686i \(0.984598\pi\)
\(662\) −6.47250 36.7074i −0.251561 1.42667i
\(663\) 2.65657 2.22913i 0.103173 0.0865722i
\(664\) 43.6551 1.69415
\(665\) 0 0
\(666\) −35.2395 −1.36550
\(667\) 14.2003 11.9154i 0.549837 0.461368i
\(668\) 0.129481 + 0.734325i 0.00500978 + 0.0284119i
\(669\) 4.25490 24.1307i 0.164504 0.932948i
\(670\) 1.57903 + 8.95513i 0.0610033 + 0.345967i
\(671\) 15.5706 + 13.0653i 0.601095 + 0.504379i
\(672\) 0 0
\(673\) 8.28359 + 14.3476i 0.319309 + 0.553059i 0.980344 0.197296i \(-0.0632160\pi\)
−0.661035 + 0.750355i \(0.729883\pi\)
\(674\) 22.6113 8.22983i 0.870954 0.317001i
\(675\) −21.3576 17.9211i −0.822053 0.689784i
\(676\) 1.17799 0.0453071
\(677\) 9.04963 0.347806 0.173903 0.984763i \(-0.444362\pi\)
0.173903 + 0.984763i \(0.444362\pi\)
\(678\) 52.5642 + 44.1066i 2.01872 + 1.69390i
\(679\) 0 0
\(680\) −1.13816 + 0.414255i −0.0436463 + 0.0158859i
\(681\) −38.2879 13.9357i −1.46720 0.534016i
\(682\) −20.0326 7.29125i −0.767086 0.279197i
\(683\) −4.36571 + 7.56164i −0.167049 + 0.289338i −0.937381 0.348305i \(-0.886757\pi\)
0.770332 + 0.637643i \(0.220091\pi\)
\(684\) −3.67499 + 2.15799i −0.140517 + 0.0825126i
\(685\) −0.224927 −0.00859402
\(686\) 0 0
\(687\) 45.2904 38.0032i 1.72794 1.44991i
\(688\) −10.7487 9.01925i −0.409791 0.343856i
\(689\) 5.59492 4.69470i 0.213150 0.178854i
\(690\) 8.63816 3.14403i 0.328849 0.119691i
\(691\) −34.7202 −1.32082 −0.660409 0.750906i \(-0.729617\pi\)
−0.660409 + 0.750906i \(0.729617\pi\)
\(692\) 1.86122 + 3.22372i 0.0707528 + 0.122547i
\(693\) 0 0
\(694\) 1.35710 7.69648i 0.0515147 0.292154i
\(695\) −1.87464 + 3.24697i −0.0711091 + 0.123164i
\(696\) 29.1536 + 50.4956i 1.10507 + 1.91403i
\(697\) −1.08853 + 0.396191i −0.0412309 + 0.0150068i
\(698\) 1.25687 + 7.12808i 0.0475734 + 0.269802i
\(699\) −47.7588 + 17.3828i −1.80640 + 0.657478i
\(700\) 0 0
\(701\) 6.84436 + 38.8163i 0.258508 + 1.46607i 0.786905 + 0.617074i \(0.211682\pi\)
−0.528397 + 0.848997i \(0.677207\pi\)
\(702\) −11.4376 19.8106i −0.431686 0.747701i
\(703\) −13.7292 + 16.6086i −0.517807 + 0.626406i
\(704\) 9.57057 16.5767i 0.360705 0.624759i
\(705\) −14.1420 + 11.8666i −0.532620 + 0.446921i
\(706\) −26.0442 + 21.8537i −0.980185 + 0.822473i
\(707\) 0 0
\(708\) 3.15270 + 1.14749i 0.118486 + 0.0431253i
\(709\) −7.14068 + 40.4968i −0.268174 + 1.52089i 0.491668 + 0.870783i \(0.336387\pi\)
−0.759842 + 0.650107i \(0.774724\pi\)
\(710\) 5.51249 + 9.54791i 0.206880 + 0.358327i
\(711\) −62.6715 −2.35036
\(712\) −28.4650 + 10.3604i −1.06677 + 0.388273i
\(713\) −3.32501 + 18.8571i −0.124523 + 0.706202i
\(714\) 0 0
\(715\) 2.52007 4.36488i 0.0942452 0.163237i
\(716\) 0.369423 2.09510i 0.0138060 0.0782976i
\(717\) 5.18866 4.35381i 0.193774 0.162596i
\(718\) −1.56443 + 8.87230i −0.0583839 + 0.331111i
\(719\) −39.8387 14.5001i −1.48573 0.540763i −0.533411 0.845856i \(-0.679090\pi\)
−0.952323 + 0.305093i \(0.901312\pi\)
\(720\) 2.90554 + 16.4782i 0.108283 + 0.614105i
\(721\) 0 0
\(722\) 4.07351 25.2724i 0.151600 0.940543i
\(723\) 19.8687 + 34.4136i 0.738925 + 1.27986i
\(724\) −1.48246 0.539571i −0.0550952 0.0200530i
\(725\) 5.04916 + 28.6352i 0.187521 + 1.06349i
\(726\) 17.9552 + 15.0662i 0.666379 + 0.559158i
\(727\) 48.5411 + 17.6675i 1.80029 + 0.655251i 0.998324 + 0.0578805i \(0.0184342\pi\)
0.801965 + 0.597371i \(0.203788\pi\)
\(728\) 0 0
\(729\) 20.2344 35.0470i 0.749423 1.29804i
\(730\) 0.822948 1.42539i 0.0304587 0.0527560i
\(731\) −1.39852 1.17350i −0.0517261 0.0434033i
\(732\) 3.72075 + 3.12208i 0.137523 + 0.115395i
\(733\) −11.4581 + 19.8460i −0.423215 + 0.733030i −0.996252 0.0864997i \(-0.972432\pi\)
0.573037 + 0.819530i \(0.305765\pi\)
\(734\) −5.46926 + 9.47303i −0.201874 + 0.349656i
\(735\) 0 0
\(736\) −2.63816 0.960210i −0.0972437 0.0353938i
\(737\) −13.0915 10.9851i −0.482232 0.404641i
\(738\) 3.06443 + 17.3792i 0.112803 + 0.639738i
\(739\) −26.4304 9.61986i −0.972256 0.353872i −0.193432 0.981114i \(-0.561962\pi\)
−0.778825 + 0.627241i \(0.784184\pi\)
\(740\) −0.401674 0.695720i −0.0147658 0.0255752i
\(741\) −31.8555 5.37549i −1.17024 0.197474i
\(742\) 0 0
\(743\) 1.06489 + 6.03931i 0.0390671 + 0.221561i 0.998091 0.0617657i \(-0.0196731\pi\)
−0.959024 + 0.283326i \(0.908562\pi\)
\(744\) −56.5963 20.5994i −2.07492 0.755210i
\(745\) −2.52869 + 14.3409i −0.0926439 + 0.525409i
\(746\) −36.0174 + 30.2222i −1.31869 + 1.10651i
\(747\) 13.6257 77.2750i 0.498537 2.82734i
\(748\) 0.0962667 0.166739i 0.00351986 0.00609657i
\(749\) 0 0
\(750\) −5.46585 + 30.9984i −0.199585 + 1.13190i
\(751\) −5.30066 + 1.92928i −0.193424 + 0.0704005i −0.436916 0.899502i \(-0.643929\pi\)
0.243492 + 0.969903i \(0.421707\pi\)
\(752\) −26.2199 −0.956140
\(753\) −5.99660 10.3864i −0.218528 0.378502i
\(754\) −4.14274 + 23.4947i −0.150870 + 0.855625i
\(755\) −3.60442 1.31190i −0.131178 0.0477450i
\(756\) 0 0
\(757\) 12.0207 10.0866i 0.436900 0.366602i −0.397648 0.917538i \(-0.630173\pi\)
0.834548 + 0.550936i \(0.185729\pi\)
\(758\) −1.75600 + 1.47346i −0.0637806 + 0.0535183i
\(759\) −8.63816 + 14.9617i −0.313545 + 0.543076i
\(760\) 9.81274 + 5.56947i 0.355945 + 0.202026i
\(761\) 2.43242 + 4.21307i 0.0881751 + 0.152724i 0.906740 0.421691i \(-0.138563\pi\)
−0.818565 + 0.574414i \(0.805230\pi\)
\(762\) −7.81702 44.3325i −0.283181 1.60600i
\(763\) 0 0
\(764\) 3.18392 1.15885i 0.115190 0.0419257i
\(765\) 0.378041 + 2.14398i 0.0136681 + 0.0775157i
\(766\) −3.71806 + 1.35326i −0.134339 + 0.0488954i
\(767\) 8.11499 + 14.0556i 0.293015 + 0.507517i
\(768\) 6.32888 10.9619i 0.228374 0.395555i
\(769\) −3.91266 + 22.1898i −0.141094 + 0.800184i 0.829327 + 0.558764i \(0.188724\pi\)
−0.970421 + 0.241420i \(0.922387\pi\)
\(770\) 0 0
\(771\) 0.960637 + 1.66387i 0.0345965 + 0.0599229i
\(772\) −0.0550065 −0.00197973
\(773\) −24.8380 + 9.04028i −0.893359 + 0.325156i −0.747589 0.664162i \(-0.768788\pi\)
−0.145771 + 0.989318i \(0.546566\pi\)
\(774\) −21.3056 + 17.8775i −0.765815 + 0.642595i