Properties

Label 570.2.m.b.493.10
Level $570$
Weight $2$
Character 570.493
Analytic conductor $4.551$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.m (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 493.10
Root \(0.850665 + 0.850665i\) of defining polynomial
Character \(\chi\) \(=\) 570.493
Dual form 570.2.m.b.37.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.23583 + 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 + 3.17648i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(2.23583 + 0.0328054i) q^{5} -1.00000 q^{6} +(-3.17648 + 3.17648i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000i q^{9} +(1.55777 + 1.60417i) q^{10} +1.49820 q^{11} +(-0.707107 - 0.707107i) q^{12} +(-2.38967 + 2.38967i) q^{13} -4.49222 q^{14} +(-1.60417 + 1.55777i) q^{15} -1.00000 q^{16} +(0.853306 - 0.853306i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-4.34485 - 0.349716i) q^{19} +(-0.0328054 + 2.23583i) q^{20} -4.49222i q^{21} +(1.05939 + 1.05939i) q^{22} +(4.67468 + 4.67468i) q^{23} -1.00000i q^{24} +(4.99785 + 0.146694i) q^{25} -3.37950 q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.17648 - 3.17648i) q^{28} -5.40423 q^{29} +(-2.23583 - 0.0328054i) q^{30} -0.364245i q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.05939 + 1.05939i) q^{33} +1.20676 q^{34} +(-7.20626 + 6.99785i) q^{35} +1.00000 q^{36} +(4.29845 + 4.29845i) q^{37} +(-2.82498 - 3.31956i) q^{38} -3.37950i q^{39} +(-1.60417 + 1.55777i) q^{40} -1.79412i q^{41} +(3.17648 - 3.17648i) q^{42} +(0.623738 + 0.623738i) q^{43} +1.49820i q^{44} +(0.0328054 - 2.23583i) q^{45} +6.61099i q^{46} +(-5.24209 + 5.24209i) q^{47} +(0.707107 - 0.707107i) q^{48} -13.1800i q^{49} +(3.43028 + 3.63774i) q^{50} +1.20676i q^{51} +(-2.38967 - 2.38967i) q^{52} +(5.27391 - 5.27391i) q^{53} +1.00000i q^{54} +(3.34972 + 0.0491491i) q^{55} -4.49222i q^{56} +(3.31956 - 2.82498i) q^{57} +(-3.82137 - 3.82137i) q^{58} -1.49134 q^{59} +(-1.55777 - 1.60417i) q^{60} +15.2432 q^{61} +(0.257560 - 0.257560i) q^{62} +(3.17648 + 3.17648i) q^{63} -1.00000i q^{64} +(-5.42128 + 5.26449i) q^{65} -1.49820 q^{66} +(0.989147 + 0.989147i) q^{67} +(0.853306 + 0.853306i) q^{68} -6.61099 q^{69} +(-10.0438 - 0.147369i) q^{70} +8.98443i q^{71} +(0.707107 + 0.707107i) q^{72} +(-11.2572 - 11.2572i) q^{73} +6.07893i q^{74} +(-3.63774 + 3.43028i) q^{75} +(0.349716 - 4.34485i) q^{76} +(-4.75900 + 4.75900i) q^{77} +(2.38967 - 2.38967i) q^{78} +7.95317 q^{79} +(-2.23583 - 0.0328054i) q^{80} -1.00000 q^{81} +(1.26863 - 1.26863i) q^{82} +(3.94546 + 3.94546i) q^{83} +4.49222 q^{84} +(1.93584 - 1.87985i) q^{85} +0.882099i q^{86} +(3.82137 - 3.82137i) q^{87} +(-1.05939 + 1.05939i) q^{88} +9.30909 q^{89} +(1.60417 - 1.55777i) q^{90} -15.1814i q^{91} +(-4.67468 + 4.67468i) q^{92} +(0.257560 + 0.257560i) q^{93} -7.41343 q^{94} +(-9.70286 - 0.924440i) q^{95} +1.00000 q^{96} +(8.79952 + 8.79952i) q^{97} +(9.31967 - 9.31967i) q^{98} -1.49820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \) \( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 2.23583 + 0.0328054i 0.999892 + 0.0146710i
\(6\) −1.00000 −0.408248
\(7\) −3.17648 + 3.17648i −1.20060 + 1.20060i −0.226610 + 0.973986i \(0.572764\pi\)
−0.973986 + 0.226610i \(0.927236\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) 1.55777 + 1.60417i 0.492611 + 0.507282i
\(11\) 1.49820 0.451724 0.225862 0.974159i \(-0.427480\pi\)
0.225862 + 0.974159i \(0.427480\pi\)
\(12\) −0.707107 0.707107i −0.204124 0.204124i
\(13\) −2.38967 + 2.38967i −0.662774 + 0.662774i −0.956033 0.293259i \(-0.905260\pi\)
0.293259 + 0.956033i \(0.405260\pi\)
\(14\) −4.49222 −1.20060
\(15\) −1.60417 + 1.55777i −0.414194 + 0.402215i
\(16\) −1.00000 −0.250000
\(17\) 0.853306 0.853306i 0.206957 0.206957i −0.596016 0.802973i \(-0.703250\pi\)
0.802973 + 0.596016i \(0.203250\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) −4.34485 0.349716i −0.996776 0.0802304i
\(20\) −0.0328054 + 2.23583i −0.00733551 + 0.499946i
\(21\) 4.49222i 0.980282i
\(22\) 1.05939 + 1.05939i 0.225862 + 0.225862i
\(23\) 4.67468 + 4.67468i 0.974737 + 0.974737i 0.999689 0.0249512i \(-0.00794305\pi\)
−0.0249512 + 0.999689i \(0.507943\pi\)
\(24\) 1.00000i 0.204124i
\(25\) 4.99785 + 0.146694i 0.999570 + 0.0293389i
\(26\) −3.37950 −0.662774
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −3.17648 3.17648i −0.600298 0.600298i
\(29\) −5.40423 −1.00354 −0.501771 0.865001i \(-0.667318\pi\)
−0.501771 + 0.865001i \(0.667318\pi\)
\(30\) −2.23583 0.0328054i −0.408204 0.00598942i
\(31\) 0.364245i 0.0654204i −0.999465 0.0327102i \(-0.989586\pi\)
0.999465 0.0327102i \(-0.0104138\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −1.05939 + 1.05939i −0.184416 + 0.184416i
\(34\) 1.20676 0.206957
\(35\) −7.20626 + 6.99785i −1.21808 + 1.18285i
\(36\) 1.00000 0.166667
\(37\) 4.29845 + 4.29845i 0.706661 + 0.706661i 0.965832 0.259170i \(-0.0834491\pi\)
−0.259170 + 0.965832i \(0.583449\pi\)
\(38\) −2.82498 3.31956i −0.458273 0.538503i
\(39\) 3.37950i 0.541153i
\(40\) −1.60417 + 1.55777i −0.253641 + 0.246305i
\(41\) 1.79412i 0.280194i −0.990138 0.140097i \(-0.955259\pi\)
0.990138 0.140097i \(-0.0447415\pi\)
\(42\) 3.17648 3.17648i 0.490141 0.490141i
\(43\) 0.623738 + 0.623738i 0.0951192 + 0.0951192i 0.753065 0.657946i \(-0.228574\pi\)
−0.657946 + 0.753065i \(0.728574\pi\)
\(44\) 1.49820i 0.225862i
\(45\) 0.0328054 2.23583i 0.00489034 0.333297i
\(46\) 6.61099i 0.974737i
\(47\) −5.24209 + 5.24209i −0.764637 + 0.764637i −0.977157 0.212520i \(-0.931833\pi\)
0.212520 + 0.977157i \(0.431833\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 13.1800i 1.88286i
\(50\) 3.43028 + 3.63774i 0.485115 + 0.514454i
\(51\) 1.20676i 0.168980i
\(52\) −2.38967 2.38967i −0.331387 0.331387i
\(53\) 5.27391 5.27391i 0.724427 0.724427i −0.245077 0.969504i \(-0.578813\pi\)
0.969504 + 0.245077i \(0.0788132\pi\)
\(54\) 1.00000i 0.136083i
\(55\) 3.34972 + 0.0491491i 0.451676 + 0.00662726i
\(56\) 4.49222i 0.600298i
\(57\) 3.31956 2.82498i 0.439686 0.374178i
\(58\) −3.82137 3.82137i −0.501771 0.501771i
\(59\) −1.49134 −0.194156 −0.0970781 0.995277i \(-0.530950\pi\)
−0.0970781 + 0.995277i \(0.530950\pi\)
\(60\) −1.55777 1.60417i −0.201107 0.207097i
\(61\) 15.2432 1.95169 0.975844 0.218468i \(-0.0701060\pi\)
0.975844 + 0.218468i \(0.0701060\pi\)
\(62\) 0.257560 0.257560i 0.0327102 0.0327102i
\(63\) 3.17648 + 3.17648i 0.400198 + 0.400198i
\(64\) 1.00000i 0.125000i
\(65\) −5.42128 + 5.26449i −0.672426 + 0.652979i
\(66\) −1.49820 −0.184416
\(67\) 0.989147 + 0.989147i 0.120844 + 0.120844i 0.764942 0.644099i \(-0.222767\pi\)
−0.644099 + 0.764942i \(0.722767\pi\)
\(68\) 0.853306 + 0.853306i 0.103478 + 0.103478i
\(69\) −6.61099 −0.795870
\(70\) −10.0438 0.147369i −1.20047 0.0176140i
\(71\) 8.98443i 1.06626i 0.846035 + 0.533128i \(0.178984\pi\)
−0.846035 + 0.533128i \(0.821016\pi\)
\(72\) 0.707107 + 0.707107i 0.0833333 + 0.0833333i
\(73\) −11.2572 11.2572i −1.31756 1.31756i −0.915706 0.401850i \(-0.868367\pi\)
−0.401850 0.915706i \(-0.631633\pi\)
\(74\) 6.07893i 0.706661i
\(75\) −3.63774 + 3.43028i −0.420050 + 0.396095i
\(76\) 0.349716 4.34485i 0.0401152 0.498388i
\(77\) −4.75900 + 4.75900i −0.542338 + 0.542338i
\(78\) 2.38967 2.38967i 0.270576 0.270576i
\(79\) 7.95317 0.894801 0.447401 0.894334i \(-0.352350\pi\)
0.447401 + 0.894334i \(0.352350\pi\)
\(80\) −2.23583 0.0328054i −0.249973 0.00366776i
\(81\) −1.00000 −0.111111
\(82\) 1.26863 1.26863i 0.140097 0.140097i
\(83\) 3.94546 + 3.94546i 0.433071 + 0.433071i 0.889672 0.456601i \(-0.150933\pi\)
−0.456601 + 0.889672i \(0.650933\pi\)
\(84\) 4.49222 0.490141
\(85\) 1.93584 1.87985i 0.209971 0.203898i
\(86\) 0.882099i 0.0951192i
\(87\) 3.82137 3.82137i 0.409694 0.409694i
\(88\) −1.05939 + 1.05939i −0.112931 + 0.112931i
\(89\) 9.30909 0.986762 0.493381 0.869813i \(-0.335761\pi\)
0.493381 + 0.869813i \(0.335761\pi\)
\(90\) 1.60417 1.55777i 0.169094 0.164204i
\(91\) 15.1814i 1.59145i
\(92\) −4.67468 + 4.67468i −0.487369 + 0.487369i
\(93\) 0.257560 + 0.257560i 0.0267078 + 0.0267078i
\(94\) −7.41343 −0.764637
\(95\) −9.70286 0.924440i −0.995492 0.0948455i
\(96\) 1.00000 0.102062
\(97\) 8.79952 + 8.79952i 0.893456 + 0.893456i 0.994847 0.101391i \(-0.0323292\pi\)
−0.101391 + 0.994847i \(0.532329\pi\)
\(98\) 9.31967 9.31967i 0.941429 0.941429i
\(99\) 1.49820i 0.150575i
\(100\) −0.146694 + 4.99785i −0.0146694 + 0.499785i
\(101\) 2.17827 0.216746 0.108373 0.994110i \(-0.465436\pi\)
0.108373 + 0.994110i \(0.465436\pi\)
\(102\) −0.853306 + 0.853306i −0.0844898 + 0.0844898i
\(103\) 9.44827 9.44827i 0.930966 0.930966i −0.0668005 0.997766i \(-0.521279\pi\)
0.997766 + 0.0668005i \(0.0212791\pi\)
\(104\) 3.37950i 0.331387i
\(105\) 0.147369 10.0438i 0.0143817 0.980176i
\(106\) 7.45843 0.724427
\(107\) 0.300245 + 0.300245i 0.0290258 + 0.0290258i 0.721471 0.692445i \(-0.243466\pi\)
−0.692445 + 0.721471i \(0.743466\pi\)
\(108\) −0.707107 + 0.707107i −0.0680414 + 0.0680414i
\(109\) 7.83545 0.750500 0.375250 0.926924i \(-0.377557\pi\)
0.375250 + 0.926924i \(0.377557\pi\)
\(110\) 2.33385 + 2.40336i 0.222524 + 0.229151i
\(111\) −6.07893 −0.576987
\(112\) 3.17648 3.17648i 0.300149 0.300149i
\(113\) 12.3606 12.3606i 1.16279 1.16279i 0.178928 0.983862i \(-0.442737\pi\)
0.983862 0.178928i \(-0.0572631\pi\)
\(114\) 4.34485 + 0.349716i 0.406932 + 0.0327539i
\(115\) 10.2984 + 10.6051i 0.960332 + 0.988933i
\(116\) 5.40423i 0.501771i
\(117\) 2.38967 + 2.38967i 0.220925 + 0.220925i
\(118\) −1.05454 1.05454i −0.0970781 0.0970781i
\(119\) 5.42101i 0.496943i
\(120\) 0.0328054 2.23583i 0.00299471 0.204102i
\(121\) −8.75540 −0.795945
\(122\) 10.7786 + 10.7786i 0.975844 + 0.975844i
\(123\) 1.26863 + 1.26863i 0.114389 + 0.114389i
\(124\) 0.364245 0.0327102
\(125\) 11.1695 + 0.491940i 0.999032 + 0.0440004i
\(126\) 4.49222i 0.400198i
\(127\) 8.31864 + 8.31864i 0.738160 + 0.738160i 0.972222 0.234062i \(-0.0752017\pi\)
−0.234062 + 0.972222i \(0.575202\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) −0.882099 −0.0776645
\(130\) −7.55598 0.110866i −0.662703 0.00972358i
\(131\) 8.07719 0.705707 0.352854 0.935679i \(-0.385211\pi\)
0.352854 + 0.935679i \(0.385211\pi\)
\(132\) −1.05939 1.05939i −0.0922078 0.0922078i
\(133\) 14.9122 12.6904i 1.29305 1.10040i
\(134\) 1.39887i 0.120844i
\(135\) 1.55777 + 1.60417i 0.134072 + 0.138065i
\(136\) 1.20676i 0.103478i
\(137\) 6.99785 6.99785i 0.597866 0.597866i −0.341878 0.939744i \(-0.611063\pi\)
0.939744 + 0.341878i \(0.111063\pi\)
\(138\) −4.67468 4.67468i −0.397935 0.397935i
\(139\) 10.8866i 0.923393i −0.887038 0.461696i \(-0.847241\pi\)
0.887038 0.461696i \(-0.152759\pi\)
\(140\) −6.99785 7.20626i −0.591426 0.609040i
\(141\) 7.41343i 0.624324i
\(142\) −6.35295 + 6.35295i −0.533128 + 0.533128i
\(143\) −3.58020 + 3.58020i −0.299391 + 0.299391i
\(144\) 1.00000i 0.0833333i
\(145\) −12.0829 0.177288i −1.00343 0.0147230i
\(146\) 15.9201i 1.31756i
\(147\) 9.31967 + 9.31967i 0.768674 + 0.768674i
\(148\) −4.29845 + 4.29845i −0.353331 + 0.353331i
\(149\) 12.6624i 1.03735i 0.854972 + 0.518674i \(0.173574\pi\)
−0.854972 + 0.518674i \(0.826426\pi\)
\(150\) −4.99785 0.146694i −0.408073 0.0119776i
\(151\) 15.4280i 1.25551i −0.778411 0.627755i \(-0.783974\pi\)
0.778411 0.627755i \(-0.216026\pi\)
\(152\) 3.31956 2.82498i 0.269252 0.229136i
\(153\) −0.853306 0.853306i −0.0689857 0.0689857i
\(154\) −6.73024 −0.542338
\(155\) 0.0119492 0.814389i 0.000959784 0.0654133i
\(156\) 3.37950 0.270576
\(157\) −13.2948 + 13.2948i −1.06104 + 1.06104i −0.0630301 + 0.998012i \(0.520076\pi\)
−0.998012 + 0.0630301i \(0.979924\pi\)
\(158\) 5.62374 + 5.62374i 0.447401 + 0.447401i
\(159\) 7.45843i 0.591492i
\(160\) −1.55777 1.60417i −0.123153 0.126820i
\(161\) −29.6980 −2.34053
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 0.0438073 + 0.0438073i 0.00343125 + 0.00343125i 0.708820 0.705389i \(-0.249228\pi\)
−0.705389 + 0.708820i \(0.749228\pi\)
\(164\) 1.79412 0.140097
\(165\) −2.40336 + 2.33385i −0.187101 + 0.181690i
\(166\) 5.57973i 0.433071i
\(167\) −6.61861 6.61861i −0.512164 0.512164i 0.403025 0.915189i \(-0.367959\pi\)
−0.915189 + 0.403025i \(0.867959\pi\)
\(168\) 3.17648 + 3.17648i 0.245070 + 0.245070i
\(169\) 1.57899i 0.121461i
\(170\) 2.69810 + 0.0395881i 0.206935 + 0.00303627i
\(171\) −0.349716 + 4.34485i −0.0267435 + 0.332259i
\(172\) −0.623738 + 0.623738i −0.0475596 + 0.0475596i
\(173\) −17.7594 + 17.7594i −1.35022 + 1.35022i −0.464807 + 0.885412i \(0.653876\pi\)
−0.885412 + 0.464807i \(0.846124\pi\)
\(174\) 5.40423 0.409694
\(175\) −16.3415 + 15.4096i −1.23530 + 1.16485i
\(176\) −1.49820 −0.112931
\(177\) 1.05454 1.05454i 0.0792640 0.0792640i
\(178\) 6.58252 + 6.58252i 0.493381 + 0.493381i
\(179\) −9.00631 −0.673164 −0.336582 0.941654i \(-0.609271\pi\)
−0.336582 + 0.941654i \(0.609271\pi\)
\(180\) 2.23583 + 0.0328054i 0.166649 + 0.00244517i
\(181\) 18.7616i 1.39454i −0.716808 0.697271i \(-0.754398\pi\)
0.716808 0.697271i \(-0.245602\pi\)
\(182\) 10.7349 10.7349i 0.795724 0.795724i
\(183\) −10.7786 + 10.7786i −0.796773 + 0.796773i
\(184\) −6.61099 −0.487369
\(185\) 9.46959 + 9.75161i 0.696218 + 0.716953i
\(186\) 0.364245i 0.0267078i
\(187\) 1.27842 1.27842i 0.0934875 0.0934875i
\(188\) −5.24209 5.24209i −0.382319 0.382319i
\(189\) −4.49222 −0.326761
\(190\) −6.20728 7.51463i −0.450323 0.545169i
\(191\) −6.38310 −0.461865 −0.230932 0.972970i \(-0.574178\pi\)
−0.230932 + 0.972970i \(0.574178\pi\)
\(192\) 0.707107 + 0.707107i 0.0510310 + 0.0510310i
\(193\) −15.6976 + 15.6976i −1.12994 + 1.12994i −0.139754 + 0.990186i \(0.544631\pi\)
−0.990186 + 0.139754i \(0.955369\pi\)
\(194\) 12.4444i 0.893456i
\(195\) 0.110866 7.55598i 0.00793927 0.541095i
\(196\) 13.1800 0.941429
\(197\) 2.62159 2.62159i 0.186780 0.186780i −0.607522 0.794303i \(-0.707836\pi\)
0.794303 + 0.607522i \(0.207836\pi\)
\(198\) 1.05939 1.05939i 0.0752874 0.0752874i
\(199\) 6.73685i 0.477563i −0.971073 0.238781i \(-0.923252\pi\)
0.971073 0.238781i \(-0.0767479\pi\)
\(200\) −3.63774 + 3.43028i −0.257227 + 0.242558i
\(201\) −1.39887 −0.0986684
\(202\) 1.54027 + 1.54027i 0.108373 + 0.108373i
\(203\) 17.1664 17.1664i 1.20485 1.20485i
\(204\) −1.20676 −0.0844898
\(205\) 0.0588568 4.01134i 0.00411073 0.280164i
\(206\) 13.3619 0.930966
\(207\) 4.67468 4.67468i 0.324912 0.324912i
\(208\) 2.38967 2.38967i 0.165694 0.165694i
\(209\) −6.50945 0.523945i −0.450268 0.0362420i
\(210\) 7.20626 6.99785i 0.497279 0.482897i
\(211\) 15.1654i 1.04403i −0.852937 0.522013i \(-0.825181\pi\)
0.852937 0.522013i \(-0.174819\pi\)
\(212\) 5.27391 + 5.27391i 0.362213 + 0.362213i
\(213\) −6.35295 6.35295i −0.435297 0.435297i
\(214\) 0.424610i 0.0290258i
\(215\) 1.37411 + 1.41503i 0.0937135 + 0.0965045i
\(216\) −1.00000 −0.0680414
\(217\) 1.15702 + 1.15702i 0.0785434 + 0.0785434i
\(218\) 5.54050 + 5.54050i 0.375250 + 0.375250i
\(219\) 15.9201 1.07578
\(220\) −0.0491491 + 3.34972i −0.00331363 + 0.225838i
\(221\) 4.07823i 0.274332i
\(222\) −4.29845 4.29845i −0.288493 0.288493i
\(223\) −1.90756 + 1.90756i −0.127739 + 0.127739i −0.768086 0.640347i \(-0.778791\pi\)
0.640347 + 0.768086i \(0.278791\pi\)
\(224\) 4.49222 0.300149
\(225\) 0.146694 4.99785i 0.00977963 0.333190i
\(226\) 17.4806 1.16279
\(227\) 19.8625 + 19.8625i 1.31832 + 1.31832i 0.915106 + 0.403212i \(0.132106\pi\)
0.403212 + 0.915106i \(0.367894\pi\)
\(228\) 2.82498 + 3.31956i 0.187089 + 0.219843i
\(229\) 19.0279i 1.25740i −0.777648 0.628700i \(-0.783587\pi\)
0.777648 0.628700i \(-0.216413\pi\)
\(230\) −0.216876 + 14.7810i −0.0143004 + 0.974633i
\(231\) 6.73024i 0.442817i
\(232\) 3.82137 3.82137i 0.250885 0.250885i
\(233\) −8.22028 8.22028i −0.538529 0.538529i 0.384568 0.923097i \(-0.374350\pi\)
−0.923097 + 0.384568i \(0.874350\pi\)
\(234\) 3.37950i 0.220925i
\(235\) −11.8924 + 11.5484i −0.775773 + 0.753337i
\(236\) 1.49134i 0.0970781i
\(237\) −5.62374 + 5.62374i −0.365301 + 0.365301i
\(238\) −3.83323 + 3.83323i −0.248472 + 0.248472i
\(239\) 5.40164i 0.349403i −0.984621 0.174702i \(-0.944104\pi\)
0.984621 0.174702i \(-0.0558961\pi\)
\(240\) 1.60417 1.55777i 0.103548 0.100554i
\(241\) 24.3252i 1.56692i 0.621440 + 0.783462i \(0.286548\pi\)
−0.621440 + 0.783462i \(0.713452\pi\)
\(242\) −6.19100 6.19100i −0.397973 0.397973i
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) 15.2432i 0.975844i
\(245\) 0.432375 29.4682i 0.0276235 1.88266i
\(246\) 1.79412i 0.114389i
\(247\) 11.2184 9.54703i 0.713812 0.607463i
\(248\) 0.257560 + 0.257560i 0.0163551 + 0.0163551i
\(249\) −5.57973 −0.353601
\(250\) 7.55018 + 8.24589i 0.477516 + 0.521516i
\(251\) −28.4372 −1.79494 −0.897470 0.441075i \(-0.854597\pi\)
−0.897470 + 0.441075i \(0.854597\pi\)
\(252\) −3.17648 + 3.17648i −0.200099 + 0.200099i
\(253\) 7.00360 + 7.00360i 0.440313 + 0.440313i
\(254\) 11.7643i 0.738160i
\(255\) −0.0395881 + 2.69810i −0.00247910 + 0.168961i
\(256\) 1.00000 0.0625000
\(257\) −14.1711 14.1711i −0.883966 0.883966i 0.109969 0.993935i \(-0.464925\pi\)
−0.993935 + 0.109969i \(0.964925\pi\)
\(258\) −0.623738 0.623738i −0.0388323 0.0388323i
\(259\) −27.3079 −1.69683
\(260\) −5.26449 5.42128i −0.326490 0.336213i
\(261\) 5.40423i 0.334514i
\(262\) 5.71144 + 5.71144i 0.352854 + 0.352854i
\(263\) −3.16396 3.16396i −0.195098 0.195098i 0.602797 0.797895i \(-0.294053\pi\)
−0.797895 + 0.602797i \(0.794053\pi\)
\(264\) 1.49820i 0.0922078i
\(265\) 11.9646 11.6185i 0.734977 0.713721i
\(266\) 19.5180 + 1.57100i 1.19673 + 0.0963243i
\(267\) −6.58252 + 6.58252i −0.402844 + 0.402844i
\(268\) −0.989147 + 0.989147i −0.0604218 + 0.0604218i
\(269\) 5.14967 0.313981 0.156990 0.987600i \(-0.449821\pi\)
0.156990 + 0.987600i \(0.449821\pi\)
\(270\) −0.0328054 + 2.23583i −0.00199647 + 0.136068i
\(271\) −9.33799 −0.567242 −0.283621 0.958936i \(-0.591536\pi\)
−0.283621 + 0.958936i \(0.591536\pi\)
\(272\) −0.853306 + 0.853306i −0.0517392 + 0.0517392i
\(273\) 10.7349 + 10.7349i 0.649706 + 0.649706i
\(274\) 9.89645 0.597866
\(275\) 7.48777 + 0.219778i 0.451530 + 0.0132531i
\(276\) 6.61099i 0.397935i
\(277\) 6.94186 6.94186i 0.417096 0.417096i −0.467106 0.884202i \(-0.654703\pi\)
0.884202 + 0.467106i \(0.154703\pi\)
\(278\) 7.69802 7.69802i 0.461696 0.461696i
\(279\) −0.364245 −0.0218068
\(280\) 0.147369 10.0438i 0.00880698 0.600233i
\(281\) 13.9366i 0.831390i 0.909504 + 0.415695i \(0.136462\pi\)
−0.909504 + 0.415695i \(0.863538\pi\)
\(282\) 5.24209 5.24209i 0.312162 0.312162i
\(283\) −13.0086 13.0086i −0.773280 0.773280i 0.205399 0.978678i \(-0.434151\pi\)
−0.978678 + 0.205399i \(0.934151\pi\)
\(284\) −8.98443 −0.533128
\(285\) 7.51463 6.20728i 0.445128 0.367687i
\(286\) −5.06316 −0.299391
\(287\) 5.69897 + 5.69897i 0.336400 + 0.336400i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 15.5437i 0.914338i
\(290\) −8.41856 8.66929i −0.494355 0.509078i
\(291\) −12.4444 −0.729504
\(292\) 11.2572 11.2572i 0.658778 0.658778i
\(293\) −11.5186 + 11.5186i −0.672924 + 0.672924i −0.958389 0.285465i \(-0.907852\pi\)
0.285465 + 0.958389i \(0.407852\pi\)
\(294\) 13.1800i 0.768674i
\(295\) −3.33438 0.0489241i −0.194135 0.00284847i
\(296\) −6.07893 −0.353331
\(297\) 1.05939 + 1.05939i 0.0614719 + 0.0614719i
\(298\) −8.95370 + 8.95370i −0.518674 + 0.518674i
\(299\) −22.3418 −1.29206
\(300\) −3.43028 3.63774i −0.198047 0.210025i
\(301\) −3.96258 −0.228399
\(302\) 10.9092 10.9092i 0.627755 0.627755i
\(303\) −1.54027 + 1.54027i −0.0884860 + 0.0884860i
\(304\) 4.34485 + 0.349716i 0.249194 + 0.0200576i
\(305\) 34.0811 + 0.500058i 1.95148 + 0.0286333i
\(306\) 1.20676i 0.0689857i
\(307\) −19.8832 19.8832i −1.13480 1.13480i −0.989369 0.145427i \(-0.953545\pi\)
−0.145427 0.989369i \(-0.546455\pi\)
\(308\) −4.75900 4.75900i −0.271169 0.271169i
\(309\) 13.3619i 0.760130i
\(310\) 0.584310 0.567411i 0.0331866 0.0322268i
\(311\) 25.6191 1.45272 0.726362 0.687312i \(-0.241210\pi\)
0.726362 + 0.687312i \(0.241210\pi\)
\(312\) 2.38967 + 2.38967i 0.135288 + 0.135288i
\(313\) −1.42367 1.42367i −0.0804705 0.0804705i 0.665726 0.746196i \(-0.268122\pi\)
−0.746196 + 0.665726i \(0.768122\pi\)
\(314\) −18.8017 −1.06104
\(315\) 6.99785 + 7.20626i 0.394284 + 0.406027i
\(316\) 7.95317i 0.447401i
\(317\) −22.0096 22.0096i −1.23618 1.23618i −0.961550 0.274630i \(-0.911445\pi\)
−0.274630 0.961550i \(-0.588555\pi\)
\(318\) −5.27391 + 5.27391i −0.295746 + 0.295746i
\(319\) −8.09662 −0.453324
\(320\) 0.0328054 2.23583i 0.00183388 0.124987i
\(321\) −0.424610 −0.0236994
\(322\) −20.9997 20.9997i −1.17027 1.17027i
\(323\) −4.00590 + 3.40907i −0.222894 + 0.189686i
\(324\) 1.00000i 0.0555556i
\(325\) −12.2937 + 11.5926i −0.681934 + 0.643044i
\(326\) 0.0619528i 0.00343125i
\(327\) −5.54050 + 5.54050i −0.306390 + 0.306390i
\(328\) 1.26863 + 1.26863i 0.0700485 + 0.0700485i
\(329\) 33.3027i 1.83604i
\(330\) −3.34972 0.0491491i −0.184396 0.00270557i
\(331\) 19.0483i 1.04699i 0.852028 + 0.523496i \(0.175372\pi\)
−0.852028 + 0.523496i \(0.824628\pi\)
\(332\) −3.94546 + 3.94546i −0.216535 + 0.216535i
\(333\) 4.29845 4.29845i 0.235554 0.235554i
\(334\) 9.36013i 0.512164i
\(335\) 2.17911 + 2.24401i 0.119058 + 0.122603i
\(336\) 4.49222i 0.245070i
\(337\) 10.2649 + 10.2649i 0.559164 + 0.559164i 0.929069 0.369905i \(-0.120610\pi\)
−0.369905 + 0.929069i \(0.620610\pi\)
\(338\) −1.11651 + 1.11651i −0.0607304 + 0.0607304i
\(339\) 17.4806i 0.949414i
\(340\) 1.87985 + 1.93584i 0.101949 + 0.104985i
\(341\) 0.545712i 0.0295520i
\(342\) −3.31956 + 2.82498i −0.179501 + 0.152758i
\(343\) 19.6306 + 19.6306i 1.05996 + 1.05996i
\(344\) −0.882099 −0.0475596
\(345\) −14.7810 0.216876i −0.795784 0.0116762i
\(346\) −25.1155 −1.35022
\(347\) −21.2020 + 21.2020i −1.13818 + 1.13818i −0.149404 + 0.988776i \(0.547736\pi\)
−0.988776 + 0.149404i \(0.952264\pi\)
\(348\) 3.82137 + 3.82137i 0.204847 + 0.204847i
\(349\) 19.7333i 1.05630i −0.849152 0.528148i \(-0.822886\pi\)
0.849152 0.528148i \(-0.177114\pi\)
\(350\) −22.4514 0.658983i −1.20008 0.0352241i
\(351\) −3.37950 −0.180384
\(352\) −1.05939 1.05939i −0.0564655 0.0564655i
\(353\) 18.4563 + 18.4563i 0.982329 + 0.982329i 0.999847 0.0175180i \(-0.00557644\pi\)
−0.0175180 + 0.999847i \(0.505576\pi\)
\(354\) 1.49134 0.0792640
\(355\) −0.294738 + 20.0876i −0.0156431 + 1.06614i
\(356\) 9.30909i 0.493381i
\(357\) −3.83323 3.83323i −0.202876 0.202876i
\(358\) −6.36843 6.36843i −0.336582 0.336582i
\(359\) 1.52209i 0.0803327i −0.999193 0.0401663i \(-0.987211\pi\)
0.999193 0.0401663i \(-0.0127888\pi\)
\(360\) 1.55777 + 1.60417i 0.0821018 + 0.0845469i
\(361\) 18.7554 + 3.03893i 0.987126 + 0.159944i
\(362\) 13.2665 13.2665i 0.697271 0.697271i
\(363\) 6.19100 6.19100i 0.324943 0.324943i
\(364\) 15.1814 0.795724
\(365\) −24.7999 25.5384i −1.29808 1.33674i
\(366\) −15.2432 −0.796773
\(367\) −15.6342 + 15.6342i −0.816099 + 0.816099i −0.985540 0.169442i \(-0.945804\pi\)
0.169442 + 0.985540i \(0.445804\pi\)
\(368\) −4.67468 4.67468i −0.243684 0.243684i
\(369\) −1.79412 −0.0933980
\(370\) −0.199422 + 13.5914i −0.0103674 + 0.706585i
\(371\) 33.5049i 1.73949i
\(372\) −0.257560 + 0.257560i −0.0133539 + 0.0133539i
\(373\) 10.2074 10.2074i 0.528520 0.528520i −0.391611 0.920131i \(-0.628082\pi\)
0.920131 + 0.391611i \(0.128082\pi\)
\(374\) 1.80796 0.0934875
\(375\) −8.24589 + 7.55018i −0.425816 + 0.389890i
\(376\) 7.41343i 0.382319i
\(377\) 12.9143 12.9143i 0.665121 0.665121i
\(378\) −3.17648 3.17648i −0.163380 0.163380i
\(379\) 17.3997 0.893762 0.446881 0.894593i \(-0.352535\pi\)
0.446881 + 0.894593i \(0.352535\pi\)
\(380\) 0.924440 9.70286i 0.0474228 0.497746i
\(381\) −11.7643 −0.602705
\(382\) −4.51353 4.51353i −0.230932 0.230932i
\(383\) 14.2959 14.2959i 0.730485 0.730485i −0.240231 0.970716i \(-0.577223\pi\)
0.970716 + 0.240231i \(0.0772230\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −10.7964 + 10.4842i −0.550236 + 0.534323i
\(386\) −22.1998 −1.12994
\(387\) 0.623738 0.623738i 0.0317064 0.0317064i
\(388\) −8.79952 + 8.79952i −0.446728 + 0.446728i
\(389\) 11.0275i 0.559116i 0.960129 + 0.279558i \(0.0901879\pi\)
−0.960129 + 0.279558i \(0.909812\pi\)
\(390\) 5.42128 5.26449i 0.274517 0.266578i
\(391\) 7.97786 0.403457
\(392\) 9.31967 + 9.31967i 0.470715 + 0.470715i
\(393\) −5.71144 + 5.71144i −0.288104 + 0.288104i
\(394\) 3.70748 0.186780
\(395\) 17.7819 + 0.260907i 0.894705 + 0.0131276i
\(396\) 1.49820 0.0752874
\(397\) −1.09266 + 1.09266i −0.0548392 + 0.0548392i −0.733995 0.679155i \(-0.762346\pi\)
0.679155 + 0.733995i \(0.262346\pi\)
\(398\) 4.76367 4.76367i 0.238781 0.238781i
\(399\) −1.57100 + 19.5180i −0.0786484 + 0.977122i
\(400\) −4.99785 0.146694i −0.249892 0.00733472i
\(401\) 13.6821i 0.683249i −0.939836 0.341625i \(-0.889023\pi\)
0.939836 0.341625i \(-0.110977\pi\)
\(402\) −0.989147 0.989147i −0.0493342 0.0493342i
\(403\) 0.870424 + 0.870424i 0.0433589 + 0.0433589i
\(404\) 2.17827i 0.108373i
\(405\) −2.23583 0.0328054i −0.111099 0.00163011i
\(406\) 24.2770 1.20485
\(407\) 6.43994 + 6.43994i 0.319216 + 0.319216i
\(408\) −0.853306 0.853306i −0.0422449 0.0422449i
\(409\) 13.9275 0.688673 0.344336 0.938846i \(-0.388104\pi\)
0.344336 + 0.938846i \(0.388104\pi\)
\(410\) 2.87806 2.79483i 0.142137 0.138027i
\(411\) 9.89645i 0.488156i
\(412\) 9.44827 + 9.44827i 0.465483 + 0.465483i
\(413\) 4.73721 4.73721i 0.233103 0.233103i
\(414\) 6.61099 0.324912
\(415\) 8.69194 + 8.95080i 0.426670 + 0.439378i
\(416\) 3.37950 0.165694
\(417\) 7.69802 + 7.69802i 0.376974 + 0.376974i
\(418\) −4.23239 4.97336i −0.207013 0.243255i
\(419\) 31.7859i 1.55284i −0.630215 0.776421i \(-0.717033\pi\)
0.630215 0.776421i \(-0.282967\pi\)
\(420\) 10.0438 + 0.147369i 0.490088 + 0.00719087i
\(421\) 29.9617i 1.46025i 0.683316 + 0.730123i \(0.260537\pi\)
−0.683316 + 0.730123i \(0.739463\pi\)
\(422\) 10.7235 10.7235i 0.522013 0.522013i
\(423\) 5.24209 + 5.24209i 0.254879 + 0.254879i
\(424\) 7.45843i 0.362213i
\(425\) 4.38987 4.13952i 0.212940 0.200796i
\(426\) 8.98443i 0.435297i
\(427\) −48.4196 + 48.4196i −2.34319 + 2.34319i
\(428\) −0.300245 + 0.300245i −0.0145129 + 0.0145129i
\(429\) 5.06316i 0.244452i
\(430\) −0.0289376 + 1.97222i −0.00139550 + 0.0951090i
\(431\) 19.4154i 0.935207i −0.883938 0.467603i \(-0.845118\pi\)
0.883938 0.467603i \(-0.154882\pi\)
\(432\) −0.707107 0.707107i −0.0340207 0.0340207i
\(433\) 5.53848 5.53848i 0.266162 0.266162i −0.561390 0.827552i \(-0.689733\pi\)
0.827552 + 0.561390i \(0.189733\pi\)
\(434\) 1.63627i 0.0785434i
\(435\) 8.66929 8.41856i 0.415661 0.403639i
\(436\) 7.83545i 0.375250i
\(437\) −18.6759 21.9456i −0.893392 1.04980i
\(438\) 11.2572 + 11.2572i 0.537890 + 0.537890i
\(439\) 19.2533 0.918908 0.459454 0.888202i \(-0.348045\pi\)
0.459454 + 0.888202i \(0.348045\pi\)
\(440\) −2.40336 + 2.33385i −0.114576 + 0.111262i
\(441\) −13.1800 −0.627619
\(442\) −2.88374 + 2.88374i −0.137166 + 0.137166i
\(443\) −0.822360 0.822360i −0.0390715 0.0390715i 0.687301 0.726373i \(-0.258795\pi\)
−0.726373 + 0.687301i \(0.758795\pi\)
\(444\) 6.07893i 0.288493i
\(445\) 20.8135 + 0.305388i 0.986655 + 0.0144768i
\(446\) −2.69769 −0.127739
\(447\) −8.95370 8.95370i −0.423495 0.423495i
\(448\) 3.17648 + 3.17648i 0.150074 + 0.150074i
\(449\) 34.0243 1.60570 0.802852 0.596178i \(-0.203315\pi\)
0.802852 + 0.596178i \(0.203315\pi\)
\(450\) 3.63774 3.43028i 0.171485 0.161705i
\(451\) 2.68795i 0.126570i
\(452\) 12.3606 + 12.3606i 0.581395 + 0.581395i
\(453\) 10.9092 + 10.9092i 0.512560 + 0.512560i
\(454\) 28.0898i 1.31832i
\(455\) 0.498033 33.9431i 0.0233482 1.59128i
\(456\) −0.349716 + 4.34485i −0.0163770 + 0.203466i
\(457\) 26.2360 26.2360i 1.22727 1.22727i 0.262273 0.964994i \(-0.415528\pi\)
0.964994 0.262273i \(-0.0844722\pi\)
\(458\) 13.4548 13.4548i 0.628700 0.628700i
\(459\) 1.20676 0.0563266
\(460\) −10.6051 + 10.2984i −0.494466 + 0.480166i
\(461\) −26.7535 −1.24604 −0.623018 0.782207i \(-0.714094\pi\)
−0.623018 + 0.782207i \(0.714094\pi\)
\(462\) 4.75900 4.75900i 0.221409 0.221409i
\(463\) −16.5215 16.5215i −0.767820 0.767820i 0.209902 0.977722i \(-0.432685\pi\)
−0.977722 + 0.209902i \(0.932685\pi\)
\(464\) 5.40423 0.250885
\(465\) 0.567411 + 0.584310i 0.0263130 + 0.0270967i
\(466\) 11.6252i 0.538529i
\(467\) 6.89955 6.89955i 0.319273 0.319273i −0.529215 0.848488i \(-0.677513\pi\)
0.848488 + 0.529215i \(0.177513\pi\)
\(468\) −2.38967 + 2.38967i −0.110462 + 0.110462i
\(469\) −6.28401 −0.290168
\(470\) −16.5752 0.243201i −0.764555 0.0112180i
\(471\) 18.8017i 0.866337i
\(472\) 1.05454 1.05454i 0.0485391 0.0485391i
\(473\) 0.934485 + 0.934485i 0.0429677 + 0.0429677i
\(474\) −7.95317 −0.365301
\(475\) −21.6636 2.38519i −0.993993 0.109440i
\(476\) −5.42101 −0.248472
\(477\) −5.27391 5.27391i −0.241476 0.241476i
\(478\) 3.81954 3.81954i 0.174702 0.174702i
\(479\) 10.1104i 0.461958i 0.972959 + 0.230979i \(0.0741929\pi\)
−0.972959 + 0.230979i \(0.925807\pi\)
\(480\) 2.23583 + 0.0328054i 0.102051 + 0.00149735i
\(481\) −20.5437 −0.936714
\(482\) −17.2005 + 17.2005i −0.783462 + 0.783462i
\(483\) 20.9997 20.9997i 0.955518 0.955518i
\(484\) 8.75540i 0.397973i
\(485\) 19.3855 + 19.9629i 0.880252 + 0.906468i
\(486\) 1.00000 0.0453609
\(487\) 19.5066 + 19.5066i 0.883928 + 0.883928i 0.993931 0.110003i \(-0.0350860\pi\)
−0.110003 + 0.993931i \(0.535086\pi\)
\(488\) −10.7786 + 10.7786i −0.487922 + 0.487922i
\(489\) −0.0619528 −0.00280160
\(490\) 21.1429 20.5314i 0.955140 0.927516i
\(491\) −14.0700 −0.634970 −0.317485 0.948263i \(-0.602838\pi\)
−0.317485 + 0.948263i \(0.602838\pi\)
\(492\) −1.26863 + 1.26863i −0.0571944 + 0.0571944i
\(493\) −4.61146 + 4.61146i −0.207690 + 0.207690i
\(494\) 14.6834 + 1.18187i 0.660638 + 0.0531747i
\(495\) 0.0491491 3.34972i 0.00220909 0.150559i
\(496\) 0.364245i 0.0163551i
\(497\) −28.5388 28.5388i −1.28014 1.28014i
\(498\) −3.94546 3.94546i −0.176800 0.176800i
\(499\) 4.43607i 0.198586i 0.995058 + 0.0992929i \(0.0316581\pi\)
−0.995058 + 0.0992929i \(0.968342\pi\)
\(500\) −0.491940 + 11.1695i −0.0220002 + 0.499516i
\(501\) 9.36013 0.418180
\(502\) −20.1081 20.1081i −0.897470 0.897470i
\(503\) −3.35985 3.35985i −0.149808 0.149808i 0.628224 0.778032i \(-0.283782\pi\)
−0.778032 + 0.628224i \(0.783782\pi\)
\(504\) −4.49222 −0.200099
\(505\) 4.87023 + 0.0714589i 0.216722 + 0.00317988i
\(506\) 9.90459i 0.440313i
\(507\) −1.11651 1.11651i −0.0495861 0.0495861i
\(508\) −8.31864 + 8.31864i −0.369080 + 0.369080i
\(509\) −37.6552 −1.66904 −0.834519 0.550979i \(-0.814254\pi\)
−0.834519 + 0.550979i \(0.814254\pi\)
\(510\) −1.93584 + 1.87985i −0.0857203 + 0.0832412i
\(511\) 71.5164 3.16370
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) −2.82498 3.31956i −0.124726 0.146562i
\(514\) 20.0409i 0.883966i
\(515\) 21.4347 20.8147i 0.944524 0.917207i
\(516\) 0.882099i 0.0388323i
\(517\) −7.85370 + 7.85370i −0.345405 + 0.345405i
\(518\) −19.3096 19.3096i −0.848414 0.848414i
\(519\) 25.1155i 1.10245i
\(520\) 0.110866 7.55598i 0.00486179 0.331351i
\(521\) 27.2139i 1.19226i 0.802887 + 0.596131i \(0.203296\pi\)
−0.802887 + 0.596131i \(0.796704\pi\)
\(522\) −3.82137 + 3.82137i −0.167257 + 0.167257i
\(523\) 11.9984 11.9984i 0.524655 0.524655i −0.394319 0.918974i \(-0.629019\pi\)
0.918974 + 0.394319i \(0.129019\pi\)
\(524\) 8.07719i 0.352854i
\(525\) 0.658983 22.4514i 0.0287604 0.979860i
\(526\) 4.47451i 0.195098i
\(527\) −0.310812 0.310812i −0.0135392 0.0135392i
\(528\) 1.05939 1.05939i 0.0461039 0.0461039i
\(529\) 20.7052i 0.900226i
\(530\) 16.6758 + 0.244677i 0.724349 + 0.0106281i
\(531\) 1.49134i 0.0647187i
\(532\) 12.6904 + 14.9122i 0.550200 + 0.646525i
\(533\) 4.28734 + 4.28734i 0.185705 + 0.185705i
\(534\) −9.30909 −0.402844
\(535\) 0.661446 + 0.681146i 0.0285968 + 0.0294485i
\(536\) −1.39887 −0.0604218
\(537\) 6.36843 6.36843i 0.274818 0.274818i
\(538\) 3.64136 + 3.64136i 0.156990 + 0.156990i
\(539\) 19.7463i 0.850533i
\(540\) −1.60417 + 1.55777i −0.0690323 + 0.0670358i
\(541\) −2.33439 −0.100363 −0.0501816 0.998740i \(-0.515980\pi\)
−0.0501816 + 0.998740i \(0.515980\pi\)
\(542\) −6.60295 6.60295i −0.283621 0.283621i
\(543\) 13.2665 + 13.2665i 0.569319 + 0.569319i
\(544\) −1.20676 −0.0517392
\(545\) 17.5187 + 0.257045i 0.750420 + 0.0110106i
\(546\) 15.1814i 0.649706i
\(547\) −8.46036 8.46036i −0.361739 0.361739i 0.502714 0.864453i \(-0.332335\pi\)
−0.864453 + 0.502714i \(0.832335\pi\)
\(548\) 6.99785 + 6.99785i 0.298933 + 0.298933i
\(549\) 15.2432i 0.650563i
\(550\) 5.13925 + 5.45006i 0.219138 + 0.232391i
\(551\) 23.4806 + 1.88995i 1.00031 + 0.0805145i
\(552\) 4.67468 4.67468i 0.198967 0.198967i
\(553\) −25.2630 + 25.2630i −1.07429 + 1.07429i
\(554\) 9.81727 0.417096
\(555\) −13.5914 0.199422i −0.576925 0.00846498i
\(556\) 10.8866 0.461696
\(557\) 14.2030 14.2030i 0.601801 0.601801i −0.338989 0.940790i \(-0.610085\pi\)
0.940790 + 0.338989i \(0.110085\pi\)
\(558\) −0.257560 0.257560i −0.0109034 0.0109034i
\(559\) −2.98105 −0.126085
\(560\) 7.20626 6.99785i 0.304520 0.295713i
\(561\) 1.80796i 0.0763322i
\(562\) −9.85468 + 9.85468i −0.415695 + 0.415695i
\(563\) −30.8429 + 30.8429i −1.29987 + 1.29987i −0.371401 + 0.928472i \(0.621123\pi\)
−0.928472 + 0.371401i \(0.878877\pi\)
\(564\) 7.41343 0.312162
\(565\) 28.0417 27.2307i 1.17972 1.14561i
\(566\) 18.3969i 0.773280i
\(567\) 3.17648 3.17648i 0.133399 0.133399i
\(568\) −6.35295 6.35295i −0.266564 0.266564i
\(569\) 13.5457 0.567864 0.283932 0.958844i \(-0.408361\pi\)
0.283932 + 0.958844i \(0.408361\pi\)
\(570\) 9.70286 + 0.924440i 0.406408 + 0.0387205i
\(571\) 10.5825 0.442863 0.221431 0.975176i \(-0.428927\pi\)
0.221431 + 0.975176i \(0.428927\pi\)
\(572\) −3.58020 3.58020i −0.149696 0.149696i
\(573\) 4.51353 4.51353i 0.188556 0.188556i
\(574\) 8.05956i 0.336400i
\(575\) 22.6776 + 24.0491i 0.945720 + 1.00292i
\(576\) −1.00000 −0.0416667
\(577\) −4.85640 + 4.85640i −0.202175 + 0.202175i −0.800931 0.598757i \(-0.795662\pi\)
0.598757 + 0.800931i \(0.295662\pi\)
\(578\) −10.9911 + 10.9911i −0.457169 + 0.457169i
\(579\) 22.1998i 0.922592i
\(580\) 0.177288 12.0829i 0.00736149 0.501717i
\(581\) −25.0653 −1.03989
\(582\) −8.79952 8.79952i −0.364752 0.364752i
\(583\) 7.90137 7.90137i 0.327241 0.327241i
\(584\) 15.9201 0.658778
\(585\) 5.26449 + 5.42128i 0.217660 + 0.224142i
\(586\) −16.2898 −0.672924
\(587\) 7.59468 7.59468i 0.313466 0.313466i −0.532785 0.846251i \(-0.678854\pi\)
0.846251 + 0.532785i \(0.178854\pi\)
\(588\) −9.31967 + 9.31967i −0.384337 + 0.384337i
\(589\) −0.127383 + 1.58259i −0.00524870 + 0.0652095i
\(590\) −2.32317 2.39236i −0.0956434 0.0984919i
\(591\) 3.70748i 0.152505i
\(592\) −4.29845 4.29845i −0.176665 0.176665i
\(593\) 16.8852 + 16.8852i 0.693392 + 0.693392i 0.962977 0.269585i \(-0.0868865\pi\)
−0.269585 + 0.962977i \(0.586886\pi\)
\(594\) 1.49820i 0.0614719i
\(595\) −0.177838 + 12.1204i −0.00729066 + 0.496890i
\(596\) −12.6624 −0.518674
\(597\) 4.76367 + 4.76367i 0.194964 + 0.194964i
\(598\) −15.7981 15.7981i −0.646031 0.646031i
\(599\) 40.3029 1.64673 0.823365 0.567512i \(-0.192094\pi\)
0.823365 + 0.567512i \(0.192094\pi\)
\(600\) 0.146694 4.99785i 0.00598878 0.204036i
\(601\) 37.1125i 1.51385i −0.653503 0.756924i \(-0.726701\pi\)
0.653503 0.756924i \(-0.273299\pi\)
\(602\) −2.80197 2.80197i −0.114200 0.114200i
\(603\) 0.989147 0.989147i 0.0402812 0.0402812i
\(604\) 15.4280 0.627755
\(605\) −19.5756 0.287224i −0.795860 0.0116773i
\(606\) −2.17827 −0.0884860
\(607\) −21.9049 21.9049i −0.889091 0.889091i 0.105345 0.994436i \(-0.466405\pi\)
−0.994436 + 0.105345i \(0.966405\pi\)
\(608\) 2.82498 + 3.31956i 0.114568 + 0.134626i
\(609\) 24.2770i 0.983753i
\(610\) 23.7454 + 24.4526i 0.961422 + 0.990056i
\(611\) 25.0537i 1.01356i
\(612\) 0.853306 0.853306i 0.0344928 0.0344928i
\(613\) 3.66633 + 3.66633i 0.148082 + 0.148082i 0.777261 0.629179i \(-0.216609\pi\)
−0.629179 + 0.777261i \(0.716609\pi\)
\(614\) 28.1191i 1.13480i
\(615\) 2.79483 + 2.87806i 0.112698 + 0.116055i
\(616\) 6.73024i 0.271169i
\(617\) −21.5484 + 21.5484i −0.867507 + 0.867507i −0.992196 0.124689i \(-0.960207\pi\)
0.124689 + 0.992196i \(0.460207\pi\)
\(618\) −9.44827 + 9.44827i −0.380065 + 0.380065i
\(619\) 23.0888i 0.928017i −0.885831 0.464008i \(-0.846411\pi\)
0.885831 0.464008i \(-0.153589\pi\)
\(620\) 0.814389 + 0.0119492i 0.0327067 + 0.000479892i
\(621\) 6.61099i 0.265290i
\(622\) 18.1154 + 18.1154i 0.726362 + 0.726362i
\(623\) −29.5701 + 29.5701i −1.18470 + 1.18470i
\(624\) 3.37950i 0.135288i
\(625\) 24.9570 + 1.46631i 0.998278 + 0.0586525i
\(626\) 2.01337i 0.0804705i
\(627\) 4.97336 4.23239i 0.198617 0.169025i
\(628\) −13.2948 13.2948i −0.530521 0.530521i
\(629\) 7.33579 0.292497
\(630\) −0.147369 + 10.0438i −0.00587132 + 0.400155i
\(631\) 37.3658 1.48751 0.743754 0.668453i \(-0.233043\pi\)
0.743754 + 0.668453i \(0.233043\pi\)
\(632\) −5.62374 + 5.62374i −0.223700 + 0.223700i
\(633\) 10.7235 + 10.7235i 0.426222 + 0.426222i
\(634\) 31.1262i 1.23618i
\(635\) 18.3262 + 18.8719i 0.727251 + 0.748910i
\(636\) −7.45843 −0.295746
\(637\) 31.4958 + 31.4958i 1.24791 + 1.24791i
\(638\) −5.72518 5.72518i −0.226662 0.226662i
\(639\) 8.98443 0.355419
\(640\) 1.60417 1.55777i 0.0634102 0.0615763i
\(641\) 35.6140i 1.40667i −0.710859 0.703335i \(-0.751693\pi\)
0.710859 0.703335i \(-0.248307\pi\)
\(642\) −0.300245 0.300245i −0.0118497 0.0118497i
\(643\) −35.3543 35.3543i −1.39424 1.39424i −0.815545 0.578694i \(-0.803563\pi\)
−0.578694 0.815545i \(-0.696437\pi\)
\(644\) 29.6980i 1.17027i
\(645\) −1.97222 0.0289376i −0.0776561 0.00113942i
\(646\) −5.24317 0.422022i −0.206290 0.0166042i
\(647\) 20.9716 20.9716i 0.824480 0.824480i −0.162267 0.986747i \(-0.551880\pi\)
0.986747 + 0.162267i \(0.0518804\pi\)
\(648\) 0.707107 0.707107i 0.0277778 0.0277778i
\(649\) −2.23433 −0.0877051
\(650\) −16.8902 0.495754i −0.662489 0.0194451i
\(651\) −1.63627 −0.0641304
\(652\) −0.0438073 + 0.0438073i −0.00171563 + 0.00171563i
\(653\) 31.2511 + 31.2511i 1.22295 + 1.22295i 0.966578 + 0.256372i \(0.0825272\pi\)
0.256372 + 0.966578i \(0.417473\pi\)
\(654\) −7.83545 −0.306390
\(655\) 18.0592 + 0.264975i 0.705631 + 0.0103534i
\(656\) 1.79412i 0.0700485i
\(657\) −11.2572 + 11.2572i −0.439185 + 0.439185i
\(658\) 23.5486 23.5486i 0.918020 0.918020i
\(659\) 32.1135 1.25097 0.625483 0.780238i \(-0.284902\pi\)
0.625483 + 0.780238i \(0.284902\pi\)
\(660\) −2.33385 2.40336i −0.0908451 0.0935507i
\(661\) 1.31818i 0.0512712i 0.999671 + 0.0256356i \(0.00816097\pi\)
−0.999671 + 0.0256356i \(0.991839\pi\)
\(662\) −13.4692 + 13.4692i −0.523496 + 0.523496i
\(663\) −2.88374 2.88374i −0.111995 0.111995i
\(664\) −5.57973 −0.216535
\(665\) 33.7574 27.8844i 1.30905 1.08131i
\(666\) 6.07893 0.235554
\(667\) −25.2630 25.2630i −0.978189 0.978189i
\(668\) 6.61861 6.61861i 0.256082 0.256082i
\(669\) 2.69769i 0.104299i
\(670\) −0.0458903 + 3.12762i −0.00177290 + 0.120831i
\(671\) 22.8373 0.881625
\(672\) −3.17648 + 3.17648i −0.122535 + 0.122535i
\(673\) 2.51419 2.51419i 0.0969147 0.0969147i −0.656987 0.753902i \(-0.728169\pi\)
0.753902 + 0.656987i \(0.228169\pi\)
\(674\) 14.5167i 0.559164i
\(675\) 3.43028 + 3.63774i 0.132032 + 0.140017i
\(676\) −1.57899 −0.0607304
\(677\) −18.7510 18.7510i −0.720658 0.720658i 0.248081 0.968739i \(-0.420200\pi\)
−0.968739 + 0.248081i \(0.920200\pi\)
\(678\) −12.3606 + 12.3606i −0.474707 + 0.474707i
\(679\) −55.9030 −2.14536
\(680\) −0.0395881 + 2.69810i −0.00151814 + 0.103467i
\(681\) −28.0898 −1.07640
\(682\) 0.385877 0.385877i 0.0147760 0.0147760i
\(683\) −17.3262 + 17.3262i −0.662968 + 0.662968i −0.956079 0.293110i \(-0.905310\pi\)
0.293110 + 0.956079i \(0.405310\pi\)
\(684\) −4.34485 0.349716i −0.166129 0.0133717i
\(685\) 15.8755 15.4164i 0.606573 0.589031i
\(686\) 27.7619i 1.05996i
\(687\) 13.4548 + 13.4548i 0.513331 + 0.513331i
\(688\) −0.623738 0.623738i −0.0237798 0.0237798i
\(689\) 25.2058i 0.960263i
\(690\) −10.2984 10.6051i −0.392054 0.403730i
\(691\) −10.3859 −0.395097 −0.197549 0.980293i \(-0.563298\pi\)
−0.197549 + 0.980293i \(0.563298\pi\)
\(692\) −17.7594 17.7594i −0.675110 0.675110i
\(693\) 4.75900 + 4.75900i 0.180779 + 0.180779i
\(694\) −29.9841 −1.13818
\(695\) 0.357141 24.3406i 0.0135471 0.923293i
\(696\) 5.40423i 0.204847i
\(697\) −1.53093 1.53093i −0.0579881 0.0579881i
\(698\) 13.9535 13.9535i 0.528148 0.528148i
\(699\) 11.6252 0.439707
\(700\) −15.4096 16.3415i −0.582427 0.617651i
\(701\) 31.8741 1.20387 0.601934 0.798546i \(-0.294397\pi\)
0.601934 + 0.798546i \(0.294397\pi\)
\(702\) −2.38967 2.38967i −0.0901921 0.0901921i
\(703\) −17.1729 20.1794i −0.647688 0.761079i
\(704\) 1.49820i 0.0564655i
\(705\) 0.243201 16.5752i 0.00915946 0.624256i
\(706\) 26.1011i 0.982329i
\(707\) −6.91921 + 6.91921i −0.260224 + 0.260224i
\(708\) 1.05454 + 1.05454i 0.0396320 + 0.0396320i
\(709\) 13.1134i 0.492483i −0.969209 0.246241i \(-0.920804\pi\)
0.969209 0.246241i \(-0.0791956\pi\)
\(710\) −14.4125 + 13.9957i −0.540892 + 0.525249i
\(711\) 7.95317i 0.298267i
\(712\) −6.58252 + 6.58252i −0.246690 + 0.246690i
\(713\) 1.70273 1.70273i 0.0637677 0.0637677i
\(714\) 5.42101i 0.202876i
\(715\) −8.12215 + 7.88725i −0.303751 + 0.294967i
\(716\) 9.00631i 0.336582i
\(717\) 3.81954 + 3.81954i 0.142643 + 0.142643i
\(718\) 1.07628 1.07628i 0.0401663 0.0401663i
\(719\) 16.8894i 0.629869i 0.949113 + 0.314935i \(0.101983\pi\)
−0.949113 + 0.314935i \(0.898017\pi\)
\(720\) −0.0328054 + 2.23583i −0.00122259 + 0.0833244i
\(721\) 60.0244i 2.23543i
\(722\) 11.1132 + 15.4109i 0.413591 + 0.573535i
\(723\) −17.2005 17.2005i −0.639694 0.639694i
\(724\) 18.7616 0.697271
\(725\) −27.0095 0.792771i −1.00311 0.0294428i
\(726\) 8.75540 0.324943
\(727\) 10.7209 10.7209i 0.397617 0.397617i −0.479775 0.877392i \(-0.659282\pi\)
0.877392 + 0.479775i \(0.159282\pi\)
\(728\) 10.7349 + 10.7349i 0.397862 + 0.397862i
\(729\) 1.00000i 0.0370370i
\(730\) 0.522265 35.5946i 0.0193299 1.31741i
\(731\) 1.06448 0.0393712
\(732\) −10.7786 10.7786i −0.398387 0.398387i
\(733\) −24.7783 24.7783i −0.915207 0.915207i 0.0814690 0.996676i \(-0.474039\pi\)
−0.996676 + 0.0814690i \(0.974039\pi\)
\(734\) −22.1101 −0.816099
\(735\) 20.5314 + 21.1429i 0.757314 + 0.779868i
\(736\) 6.61099i 0.243684i
\(737\) 1.48194 + 1.48194i 0.0545880 + 0.0545880i
\(738\) −1.26863 1.26863i −0.0466990 0.0466990i
\(739\) 0.497280i 0.0182928i 0.999958 + 0.00914638i \(0.00291142\pi\)
−0.999958 + 0.00914638i \(0.997089\pi\)
\(740\) −9.75161 + 9.46959i −0.358476 + 0.348109i
\(741\) −1.18187 + 14.6834i −0.0434169 + 0.539408i
\(742\) −23.6915 + 23.6915i −0.869743 + 0.869743i
\(743\) −15.6060 + 15.6060i −0.572529 + 0.572529i −0.932835 0.360305i \(-0.882673\pi\)
0.360305 + 0.932835i \(0.382673\pi\)
\(744\) −0.364245 −0.0133539
\(745\) −0.415396 + 28.3110i −0.0152189 + 1.03724i
\(746\) 14.4355 0.528520
\(747\) 3.94546 3.94546i 0.144357 0.144357i
\(748\) 1.27842 + 1.27842i 0.0467438 + 0.0467438i
\(749\) −1.90744 −0.0696964
\(750\) −11.1695 0.491940i −0.407853 0.0179631i
\(751\) 5.39804i 0.196977i −0.995138 0.0984887i \(-0.968599\pi\)
0.995138 0.0984887i \(-0.0314008\pi\)
\(752\) 5.24209 5.24209i 0.191159 0.191159i
\(753\) 20.1081 20.1081i 0.732781 0.732781i
\(754\) 18.2636 0.665121
\(755\) 0.506121 34.4943i 0.0184196 1.25538i
\(756\) 4.49222i 0.163380i
\(757\) −3.00432 + 3.00432i −0.109194 + 0.109194i −0.759593 0.650399i \(-0.774602\pi\)
0.650399 + 0.759593i \(0.274602\pi\)
\(758\) 12.3034 + 12.3034i 0.446881 + 0.446881i
\(759\) −9.90459 −0.359514
\(760\) 7.51463 6.20728i 0.272584 0.225162i
\(761\) −9.42821 −0.341772 −0.170886 0.985291i \(-0.554663\pi\)
−0.170886 + 0.985291i \(0.554663\pi\)
\(762\) −8.31864 8.31864i −0.301353 0.301353i
\(763\) −24.8891 + 24.8891i −0.901047 + 0.901047i
\(764\) 6.38310i 0.230932i
\(765\) −1.87985 1.93584i −0.0679662 0.0699903i
\(766\) 20.2174 0.730485
\(767\) 3.56381 3.56381i 0.128682 0.128682i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 25.1986i 0.908683i 0.890828 + 0.454342i \(0.150125\pi\)
−0.890828 + 0.454342i \(0.849875\pi\)
\(770\) −15.0477 0.220788i −0.542280 0.00795665i
\(771\) 20.0409 0.721755
\(772\) −15.6976 15.6976i −0.564970 0.564970i
\(773\) −8.32250 + 8.32250i −0.299340 + 0.299340i −0.840755 0.541416i \(-0.817889\pi\)
0.541416 + 0.840755i \(0.317889\pi\)
\(774\) 0.882099 0.0317064
\(775\) 0.0534327 1.82044i 0.00191936 0.0653922i
\(776\) −12.4444 −0.446728
\(777\) 19.3096 19.3096i 0.692727 0.692727i
\(778\) −7.79761 + 7.79761i −0.279558 + 0.279558i