Properties

Label 210.3.o.a.31.3
Level 210
Weight 3
Character 210.31
Analytic conductor 5.722
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.3317760000.3
Defining polynomial: \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(-1.01575 + 1.40294i\) of defining polynomial
Character \(\chi\) \(=\) 210.31
Dual form 210.3.o.a.61.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(-6.51658 + 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(-6.51658 + 2.55620i) q^{7} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-2.73861 - 1.58114i) q^{10} +(-6.16205 + 10.6730i) q^{11} +(-3.00000 + 1.73205i) q^{12} +7.26007i q^{13} +(-7.73861 - 6.17364i) q^{14} -3.87298 q^{15} +(-2.00000 - 3.46410i) q^{16} +(8.04643 + 4.64561i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(5.26235 - 3.03822i) q^{19} -4.47214i q^{20} +(-11.9886 - 1.80922i) q^{21} -17.4289 q^{22} +(1.12514 + 1.94880i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-8.89173 + 5.13364i) q^{26} +5.19615i q^{27} +(2.08911 - 13.8433i) q^{28} +42.2122 q^{29} +(-2.73861 - 4.74342i) q^{30} +(-1.05527 - 0.609262i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-18.4862 + 10.6730i) q^{33} +13.1398i q^{34} +(9.76139 - 12.2358i) q^{35} -6.00000 q^{36} +(-17.5296 - 30.3622i) q^{37} +(7.44209 + 4.29669i) q^{38} +(-6.28740 + 10.8901i) q^{39} +(5.47723 - 3.16228i) q^{40} +57.8811i q^{41} +(-6.26139 - 15.9623i) q^{42} -34.0190 q^{43} +(-12.3241 - 21.3460i) q^{44} +(-5.80948 - 3.35410i) q^{45} +(-1.59119 + 2.75603i) q^{46} +(49.4411 - 28.5448i) q^{47} -6.92820i q^{48} +(35.9317 - 33.3154i) q^{49} +7.07107 q^{50} +(8.04643 + 13.9368i) q^{51} +(-12.5748 - 7.26007i) q^{52} +(-7.27009 + 12.5922i) q^{53} +(-6.36396 + 3.67423i) q^{54} -27.5575i q^{55} +(18.4317 - 7.23003i) q^{56} +10.5247 q^{57} +(29.8485 + 51.6992i) q^{58} +(50.1067 + 28.9291i) q^{59} +(3.87298 - 6.70820i) q^{60} +(-5.07658 + 2.93096i) q^{61} -1.72325i q^{62} +(-16.4161 - 13.0963i) q^{63} +8.00000 q^{64} +(-8.11700 - 14.0591i) q^{65} +(-26.1434 - 15.0939i) q^{66} +(-24.7355 + 42.8431i) q^{67} +(-16.0929 + 9.29122i) q^{68} +3.89761i q^{69} +(21.8881 + 3.30318i) q^{70} +101.986 q^{71} +(-4.24264 - 7.34847i) q^{72} +(71.2783 + 41.1525i) q^{73} +(24.7906 - 42.9387i) q^{74} +(7.50000 - 4.33013i) q^{75} +12.1529i q^{76} +(12.8732 - 85.3029i) q^{77} -17.7835 q^{78} +(-55.8530 - 96.7403i) q^{79} +(7.74597 + 4.47214i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-70.8895 + 40.9281i) q^{82} +91.6237i q^{83} +(15.1223 - 18.9557i) q^{84} -20.7758 q^{85} +(-24.0551 - 41.6646i) q^{86} +(63.3183 + 36.5568i) q^{87} +(17.4289 - 30.1878i) q^{88} +(110.673 - 63.8973i) q^{89} -9.48683i q^{90} +(-18.5582 - 47.3108i) q^{91} -4.50057 q^{92} +(-1.05527 - 1.82779i) q^{93} +(69.9203 + 40.3685i) q^{94} +(-6.79367 + 11.7670i) q^{95} +(8.48528 - 4.89898i) q^{96} +61.4455i q^{97} +(66.2104 + 20.4496i) q^{98} -36.9723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} + O(q^{10}) \) \( 8q + 12q^{3} - 8q^{4} + 12q^{9} - 4q^{11} - 24q^{12} - 40q^{14} - 16q^{16} + 84q^{17} + 108q^{19} - 48q^{22} + 12q^{23} + 20q^{25} - 96q^{26} + 72q^{29} - 132q^{31} - 12q^{33} + 100q^{35} - 48q^{36} - 96q^{37} - 168q^{38} + 24q^{39} - 72q^{42} - 112q^{43} - 8q^{44} + 8q^{46} - 24q^{47} + 156q^{49} + 84q^{51} + 48q^{52} + 32q^{53} + 16q^{56} + 216q^{57} + 104q^{58} + 132q^{59} + 96q^{61} + 64q^{64} + 20q^{65} - 72q^{66} - 120q^{67} - 168q^{68} + 8q^{71} + 24q^{73} - 16q^{74} + 60q^{75} - 216q^{77} - 192q^{78} + 12q^{79} - 36q^{81} + 24q^{82} + 120q^{85} - 40q^{86} + 108q^{87} + 48q^{88} + 492q^{89} - 308q^{91} - 48q^{92} - 132q^{93} + 480q^{94} - 40q^{95} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 1.22474i 0.353553 + 0.612372i
\(3\) 1.50000 + 0.866025i 0.500000 + 0.288675i
\(4\) −1.00000 + 1.73205i −0.250000 + 0.433013i
\(5\) −1.93649 + 1.11803i −0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) −6.51658 + 2.55620i −0.930940 + 0.365172i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −2.73861 1.58114i −0.273861 0.158114i
\(11\) −6.16205 + 10.6730i −0.560187 + 0.970272i 0.437293 + 0.899319i \(0.355937\pi\)
−0.997480 + 0.0709528i \(0.977396\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 7.26007i 0.558467i 0.960223 + 0.279233i \(0.0900803\pi\)
−0.960223 + 0.279233i \(0.909920\pi\)
\(14\) −7.73861 6.17364i −0.552758 0.440975i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) 8.04643 + 4.64561i 0.473319 + 0.273271i 0.717628 0.696426i \(-0.245228\pi\)
−0.244309 + 0.969697i \(0.578561\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) 5.26235 3.03822i 0.276966 0.159906i −0.355083 0.934835i \(-0.615547\pi\)
0.632049 + 0.774928i \(0.282214\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −11.9886 1.80922i −0.570886 0.0861535i
\(22\) −17.4289 −0.792224
\(23\) 1.12514 + 1.94880i 0.0489192 + 0.0847306i 0.889448 0.457036i \(-0.151089\pi\)
−0.840529 + 0.541767i \(0.817756\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −8.89173 + 5.13364i −0.341990 + 0.197448i
\(27\) 5.19615i 0.192450i
\(28\) 2.08911 13.8433i 0.0746112 0.494402i
\(29\) 42.2122 1.45559 0.727797 0.685793i \(-0.240544\pi\)
0.727797 + 0.685793i \(0.240544\pi\)
\(30\) −2.73861 4.74342i −0.0912871 0.158114i
\(31\) −1.05527 0.609262i −0.0340411 0.0196536i 0.482883 0.875685i \(-0.339590\pi\)
−0.516924 + 0.856031i \(0.672923\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) −18.4862 + 10.6730i −0.560187 + 0.323424i
\(34\) 13.1398i 0.386464i
\(35\) 9.76139 12.2358i 0.278897 0.349595i
\(36\) −6.00000 −0.166667
\(37\) −17.5296 30.3622i −0.473774 0.820600i 0.525775 0.850623i \(-0.323775\pi\)
−0.999549 + 0.0300231i \(0.990442\pi\)
\(38\) 7.44209 + 4.29669i 0.195845 + 0.113071i
\(39\) −6.28740 + 10.8901i −0.161215 + 0.279233i
\(40\) 5.47723 3.16228i 0.136931 0.0790569i
\(41\) 57.8811i 1.41173i 0.708345 + 0.705867i \(0.249442\pi\)
−0.708345 + 0.705867i \(0.750558\pi\)
\(42\) −6.26139 15.9623i −0.149081 0.380055i
\(43\) −34.0190 −0.791140 −0.395570 0.918436i \(-0.629453\pi\)
−0.395570 + 0.918436i \(0.629453\pi\)
\(44\) −12.3241 21.3460i −0.280093 0.485136i
\(45\) −5.80948 3.35410i −0.129099 0.0745356i
\(46\) −1.59119 + 2.75603i −0.0345911 + 0.0599136i
\(47\) 49.4411 28.5448i 1.05194 0.607337i 0.128747 0.991677i \(-0.458904\pi\)
0.923191 + 0.384340i \(0.125571\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 35.9317 33.3154i 0.733300 0.679906i
\(50\) 7.07107 0.141421
\(51\) 8.04643 + 13.9368i 0.157773 + 0.273271i
\(52\) −12.5748 7.26007i −0.241823 0.139617i
\(53\) −7.27009 + 12.5922i −0.137172 + 0.237588i −0.926425 0.376480i \(-0.877134\pi\)
0.789253 + 0.614068i \(0.210468\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 27.5575i 0.501046i
\(56\) 18.4317 7.23003i 0.329137 0.129108i
\(57\) 10.5247 0.184644
\(58\) 29.8485 + 51.6992i 0.514630 + 0.891365i
\(59\) 50.1067 + 28.9291i 0.849266 + 0.490324i 0.860403 0.509614i \(-0.170212\pi\)
−0.0111375 + 0.999938i \(0.503545\pi\)
\(60\) 3.87298 6.70820i 0.0645497 0.111803i
\(61\) −5.07658 + 2.93096i −0.0832226 + 0.0480486i −0.541034 0.841001i \(-0.681967\pi\)
0.457811 + 0.889049i \(0.348634\pi\)
\(62\) 1.72325i 0.0277944i
\(63\) −16.4161 13.0963i −0.260573 0.207877i
\(64\) 8.00000 0.125000
\(65\) −8.11700 14.0591i −0.124877 0.216293i
\(66\) −26.1434 15.0939i −0.396112 0.228695i
\(67\) −24.7355 + 42.8431i −0.369186 + 0.639449i −0.989439 0.144953i \(-0.953697\pi\)
0.620252 + 0.784402i \(0.287030\pi\)
\(68\) −16.0929 + 9.29122i −0.236660 + 0.136636i
\(69\) 3.89761i 0.0564871i
\(70\) 21.8881 + 3.30318i 0.312687 + 0.0471882i
\(71\) 101.986 1.43643 0.718214 0.695822i \(-0.244960\pi\)
0.718214 + 0.695822i \(0.244960\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) 71.2783 + 41.1525i 0.976415 + 0.563733i 0.901186 0.433433i \(-0.142698\pi\)
0.0752290 + 0.997166i \(0.476031\pi\)
\(74\) 24.7906 42.9387i 0.335009 0.580252i
\(75\) 7.50000 4.33013i 0.100000 0.0577350i
\(76\) 12.1529i 0.159906i
\(77\) 12.8732 85.3029i 0.167185 1.10783i
\(78\) −17.7835 −0.227993
\(79\) −55.8530 96.7403i −0.707001 1.22456i −0.965965 0.258674i \(-0.916714\pi\)
0.258964 0.965887i \(-0.416619\pi\)
\(80\) 7.74597 + 4.47214i 0.0968246 + 0.0559017i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −70.8895 + 40.9281i −0.864507 + 0.499123i
\(83\) 91.6237i 1.10390i 0.833877 + 0.551950i \(0.186116\pi\)
−0.833877 + 0.551950i \(0.813884\pi\)
\(84\) 15.1223 18.9557i 0.180027 0.225663i
\(85\) −20.7758 −0.244421
\(86\) −24.0551 41.6646i −0.279710 0.484472i
\(87\) 63.3183 + 36.5568i 0.727797 + 0.420194i
\(88\) 17.4289 30.1878i 0.198056 0.343043i
\(89\) 110.673 63.8973i 1.24352 0.717947i 0.273712 0.961812i \(-0.411748\pi\)
0.969809 + 0.243864i \(0.0784151\pi\)
\(90\) 9.48683i 0.105409i
\(91\) −18.5582 47.3108i −0.203936 0.519899i
\(92\) −4.50057 −0.0489192
\(93\) −1.05527 1.82779i −0.0113470 0.0196536i
\(94\) 69.9203 + 40.3685i 0.743833 + 0.429452i
\(95\) −6.79367 + 11.7670i −0.0715123 + 0.123863i
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 61.4455i 0.633459i 0.948516 + 0.316729i \(0.102585\pi\)
−0.948516 + 0.316729i \(0.897415\pi\)
\(98\) 66.2104 + 20.4496i 0.675616 + 0.208669i
\(99\) −36.9723 −0.373458
\(100\) 5.00000 + 8.66025i 0.0500000 + 0.0866025i
\(101\) 53.8141 + 31.0696i 0.532813 + 0.307620i 0.742161 0.670221i \(-0.233801\pi\)
−0.209348 + 0.977841i \(0.567134\pi\)
\(102\) −11.3794 + 19.7096i −0.111562 + 0.193232i
\(103\) −154.102 + 88.9709i −1.49614 + 0.863795i −0.999990 0.00444312i \(-0.998586\pi\)
−0.496147 + 0.868238i \(0.665252\pi\)
\(104\) 20.5346i 0.197448i
\(105\) 25.2386 9.90012i 0.240368 0.0942869i
\(106\) −20.5629 −0.193990
\(107\) −42.4855 73.5871i −0.397061 0.687730i 0.596301 0.802761i \(-0.296637\pi\)
−0.993362 + 0.115031i \(0.963303\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 86.4291 149.700i 0.792928 1.37339i −0.131219 0.991353i \(-0.541889\pi\)
0.924147 0.382037i \(-0.124777\pi\)
\(110\) 33.7510 19.4861i 0.306827 0.177147i
\(111\) 60.7244i 0.547067i
\(112\) 21.8881 + 17.4617i 0.195429 + 0.155908i
\(113\) −82.0616 −0.726209 −0.363105 0.931748i \(-0.618283\pi\)
−0.363105 + 0.931748i \(0.618283\pi\)
\(114\) 7.44209 + 12.8901i 0.0652815 + 0.113071i
\(115\) −4.35766 2.51590i −0.0378927 0.0218774i
\(116\) −42.2122 + 73.1137i −0.363898 + 0.630290i
\(117\) −18.8622 + 10.8901i −0.161215 + 0.0930778i
\(118\) 81.8238i 0.693422i
\(119\) −64.3103 9.70520i −0.540423 0.0815563i
\(120\) 10.9545 0.0912871
\(121\) −15.4418 26.7460i −0.127618 0.221042i
\(122\) −7.17937 4.14501i −0.0588473 0.0339755i
\(123\) −50.1265 + 86.8216i −0.407532 + 0.705867i
\(124\) 2.11055 1.21852i 0.0170205 0.00982681i
\(125\) 11.1803i 0.0894427i
\(126\) 4.43168 29.3660i 0.0351720 0.233063i
\(127\) −193.480 −1.52346 −0.761732 0.647892i \(-0.775651\pi\)
−0.761732 + 0.647892i \(0.775651\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) −51.0285 29.4613i −0.395570 0.228382i
\(130\) 11.4792 19.8825i 0.0883013 0.152942i
\(131\) −156.850 + 90.5572i −1.19733 + 0.691276i −0.959958 0.280143i \(-0.909618\pi\)
−0.237368 + 0.971420i \(0.576285\pi\)
\(132\) 42.6920i 0.323424i
\(133\) −26.5263 + 33.2504i −0.199446 + 0.250003i
\(134\) −69.9625 −0.522108
\(135\) −5.80948 10.0623i −0.0430331 0.0745356i
\(136\) −22.7587 13.1398i −0.167344 0.0966159i
\(137\) −0.631666 + 1.09408i −0.00461070 + 0.00798597i −0.868322 0.496002i \(-0.834801\pi\)
0.863711 + 0.503988i \(0.168134\pi\)
\(138\) −4.77358 + 2.75603i −0.0345911 + 0.0199712i
\(139\) 12.1327i 0.0872857i 0.999047 + 0.0436428i \(0.0138964\pi\)
−0.999047 + 0.0436428i \(0.986104\pi\)
\(140\) 11.4317 + 29.1430i 0.0816548 + 0.208165i
\(141\) 98.8822 0.701292
\(142\) 72.1153 + 124.907i 0.507854 + 0.879629i
\(143\) −77.4866 44.7369i −0.541865 0.312846i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) −81.7436 + 47.1947i −0.563749 + 0.325481i
\(146\) 116.397i 0.797239i
\(147\) 82.7495 18.8553i 0.562922 0.128268i
\(148\) 70.1185 0.473774
\(149\) −144.863 250.910i −0.972233 1.68396i −0.688780 0.724971i \(-0.741853\pi\)
−0.283453 0.958986i \(-0.591480\pi\)
\(150\) 10.6066 + 6.12372i 0.0707107 + 0.0408248i
\(151\) −58.6516 + 101.588i −0.388421 + 0.672765i −0.992237 0.124358i \(-0.960313\pi\)
0.603816 + 0.797124i \(0.293646\pi\)
\(152\) −14.8842 + 8.59339i −0.0979223 + 0.0565354i
\(153\) 27.8737i 0.182181i
\(154\) 113.577 44.5518i 0.737513 0.289298i
\(155\) 2.72470 0.0175787
\(156\) −12.5748 21.7802i −0.0806077 0.139617i
\(157\) 159.121 + 91.8687i 1.01351 + 0.585151i 0.912218 0.409705i \(-0.134368\pi\)
0.101294 + 0.994857i \(0.467702\pi\)
\(158\) 78.9881 136.811i 0.499925 0.865895i
\(159\) −21.8103 + 12.5922i −0.137172 + 0.0791960i
\(160\) 12.6491i 0.0790569i
\(161\) −12.3136 9.82345i −0.0764821 0.0610152i
\(162\) −12.7279 −0.0785674
\(163\) −60.7854 105.283i −0.372917 0.645911i 0.617096 0.786888i \(-0.288309\pi\)
−0.990013 + 0.140977i \(0.954976\pi\)
\(164\) −100.253 57.8811i −0.611298 0.352933i
\(165\) 23.8655 41.3363i 0.144640 0.250523i
\(166\) −112.216 + 64.7878i −0.675998 + 0.390288i
\(167\) 94.6539i 0.566790i 0.959003 + 0.283395i \(0.0914608\pi\)
−0.959003 + 0.283395i \(0.908539\pi\)
\(168\) 33.9089 + 5.11726i 0.201839 + 0.0304599i
\(169\) 116.291 0.688115
\(170\) −14.6907 25.4450i −0.0864159 0.149677i
\(171\) 15.7871 + 9.11466i 0.0923220 + 0.0533021i
\(172\) 34.0190 58.9227i 0.197785 0.342574i
\(173\) −225.766 + 130.346i −1.30501 + 0.753445i −0.981258 0.192699i \(-0.938276\pi\)
−0.323747 + 0.946144i \(0.604943\pi\)
\(174\) 103.398i 0.594244i
\(175\) −5.22278 + 34.6081i −0.0298445 + 0.197761i
\(176\) 49.2964 0.280093
\(177\) 50.1067 + 86.7873i 0.283089 + 0.490324i
\(178\) 156.516 + 90.3645i 0.879302 + 0.507666i
\(179\) −153.264 + 265.462i −0.856225 + 1.48303i 0.0192782 + 0.999814i \(0.493863\pi\)
−0.875504 + 0.483212i \(0.839470\pi\)
\(180\) 11.6190 6.70820i 0.0645497 0.0372678i
\(181\) 314.885i 1.73970i −0.493318 0.869849i \(-0.664216\pi\)
0.493318 0.869849i \(-0.335784\pi\)
\(182\) 44.8211 56.1828i 0.246270 0.308697i
\(183\) −10.1532 −0.0554817
\(184\) −3.18238 5.51205i −0.0172956 0.0299568i
\(185\) 67.8920 + 39.1974i 0.366984 + 0.211878i
\(186\) 1.49238 2.58488i 0.00802356 0.0138972i
\(187\) −99.1651 + 57.2530i −0.530295 + 0.306166i
\(188\) 114.179i 0.607337i
\(189\) −13.2824 33.8612i −0.0702773 0.179160i
\(190\) −19.2154 −0.101134
\(191\) 45.3946 + 78.6257i 0.237668 + 0.411653i 0.960045 0.279847i \(-0.0902837\pi\)
−0.722377 + 0.691500i \(0.756950\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) 114.828 198.887i 0.594961 1.03050i −0.398591 0.917129i \(-0.630501\pi\)
0.993552 0.113374i \(-0.0361659\pi\)
\(194\) −75.2551 + 43.4485i −0.387913 + 0.223962i
\(195\) 28.1181i 0.144195i
\(196\) 21.7723 + 95.5509i 0.111083 + 0.487504i
\(197\) 227.989 1.15730 0.578652 0.815574i \(-0.303579\pi\)
0.578652 + 0.815574i \(0.303579\pi\)
\(198\) −26.1434 45.2817i −0.132037 0.228695i
\(199\) 9.56623 + 5.52307i 0.0480715 + 0.0277541i 0.523843 0.851815i \(-0.324498\pi\)
−0.475772 + 0.879569i \(0.657831\pi\)
\(200\) −7.07107 + 12.2474i −0.0353553 + 0.0612372i
\(201\) −74.2064 + 42.8431i −0.369186 + 0.213150i
\(202\) 87.8781i 0.435040i
\(203\) −275.079 + 107.903i −1.35507 + 0.531541i
\(204\) −32.1857 −0.157773
\(205\) −64.7130 112.086i −0.315673 0.546762i
\(206\) −217.933 125.824i −1.05793 0.610796i
\(207\) −3.37543 + 5.84641i −0.0163064 + 0.0282435i
\(208\) 25.1496 14.5201i 0.120912 0.0698083i
\(209\) 74.8867i 0.358310i
\(210\) 29.9715 + 23.9104i 0.142722 + 0.113859i
\(211\) 151.187 0.716526 0.358263 0.933621i \(-0.383369\pi\)
0.358263 + 0.933621i \(0.383369\pi\)
\(212\) −14.5402 25.1843i −0.0685858 0.118794i
\(213\) 152.980 + 88.3228i 0.718214 + 0.414661i
\(214\) 60.0836 104.068i 0.280765 0.486298i
\(215\) 65.8775 38.0344i 0.306407 0.176904i
\(216\) 14.6969i 0.0680414i
\(217\) 8.43417 + 1.27282i 0.0388671 + 0.00586552i
\(218\) 244.458 1.12137
\(219\) 71.2783 + 123.458i 0.325472 + 0.563733i
\(220\) 47.7311 + 27.5575i 0.216959 + 0.125262i
\(221\) −33.7274 + 58.4176i −0.152613 + 0.264333i
\(222\) 74.3719 42.9387i 0.335009 0.193417i
\(223\) 308.586i 1.38379i −0.721997 0.691896i \(-0.756776\pi\)
0.721997 0.691896i \(-0.243224\pi\)
\(224\) −5.90890 + 39.1546i −0.0263790 + 0.174797i
\(225\) 15.0000 0.0666667
\(226\) −58.0263 100.505i −0.256754 0.444710i
\(227\) 86.9683 + 50.2112i 0.383120 + 0.221195i 0.679175 0.733976i \(-0.262338\pi\)
−0.296055 + 0.955171i \(0.595671\pi\)
\(228\) −10.5247 + 18.2293i −0.0461610 + 0.0799532i
\(229\) 277.125 159.998i 1.21015 0.698682i 0.247361 0.968923i \(-0.420437\pi\)
0.962793 + 0.270241i \(0.0871034\pi\)
\(230\) 7.11603i 0.0309392i
\(231\) 93.1843 116.806i 0.403395 0.505653i
\(232\) −119.394 −0.514630
\(233\) −155.395 269.151i −0.666929 1.15516i −0.978758 0.205017i \(-0.934275\pi\)
0.311829 0.950138i \(-0.399058\pi\)
\(234\) −26.6752 15.4009i −0.113997 0.0658159i
\(235\) −63.8282 + 110.554i −0.271609 + 0.470441i
\(236\) −100.213 + 57.8582i −0.424633 + 0.245162i
\(237\) 193.481i 0.816374i
\(238\) −33.5879 85.6264i −0.141126 0.359775i
\(239\) 136.263 0.570139 0.285069 0.958507i \(-0.407983\pi\)
0.285069 + 0.958507i \(0.407983\pi\)
\(240\) 7.74597 + 13.4164i 0.0322749 + 0.0559017i
\(241\) 334.441 + 193.090i 1.38772 + 0.801202i 0.993058 0.117623i \(-0.0375274\pi\)
0.394665 + 0.918825i \(0.370861\pi\)
\(242\) 21.8380 37.8246i 0.0902398 0.156300i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 11.7239i 0.0480486i
\(245\) −32.3337 + 104.688i −0.131974 + 0.427297i
\(246\) −141.779 −0.576338
\(247\) 22.0577 + 38.2050i 0.0893024 + 0.154676i
\(248\) 2.98476 + 1.72325i 0.0120353 + 0.00694860i
\(249\) −79.3485 + 137.436i −0.318669 + 0.551950i
\(250\) −13.6931 + 7.90569i −0.0547723 + 0.0316228i
\(251\) 99.3717i 0.395903i −0.980212 0.197952i \(-0.936571\pi\)
0.980212 0.197952i \(-0.0634289\pi\)
\(252\) 39.0995 15.3372i 0.155157 0.0608619i
\(253\) −27.7328 −0.109616
\(254\) −136.811 236.964i −0.538626 0.932928i
\(255\) −31.1637 17.9924i −0.122211 0.0705583i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) 18.2886 10.5589i 0.0711617 0.0410852i −0.463997 0.885837i \(-0.653585\pi\)
0.535159 + 0.844752i \(0.320252\pi\)
\(258\) 83.3292i 0.322982i
\(259\) 191.845 + 153.049i 0.740715 + 0.590921i
\(260\) 32.4680 0.124877
\(261\) 63.3183 + 109.671i 0.242599 + 0.420194i
\(262\) −221.819 128.067i −0.846637 0.488806i
\(263\) 190.259 329.538i 0.723417 1.25299i −0.236205 0.971703i \(-0.575904\pi\)
0.959622 0.281292i \(-0.0907629\pi\)
\(264\) 52.2868 30.1878i 0.198056 0.114348i
\(265\) 32.5128i 0.122690i
\(266\) −59.4802 8.97628i −0.223610 0.0337454i
\(267\) 221.347 0.829014
\(268\) −49.4709 85.6862i −0.184593 0.319725i
\(269\) 14.5415 + 8.39551i 0.0540574 + 0.0312101i 0.526785 0.849998i \(-0.323397\pi\)
−0.472728 + 0.881209i \(0.656731\pi\)
\(270\) 8.21584 14.2302i 0.0304290 0.0527046i
\(271\) 320.146 184.836i 1.18135 0.682052i 0.225023 0.974353i \(-0.427754\pi\)
0.956326 + 0.292301i \(0.0944209\pi\)
\(272\) 37.1649i 0.136636i
\(273\) 13.1351 87.0381i 0.0481139 0.318821i
\(274\) −1.78662 −0.00652051
\(275\) 30.8103 + 53.3650i 0.112037 + 0.194054i
\(276\) −6.75086 3.89761i −0.0244596 0.0141218i
\(277\) −242.912 + 420.736i −0.876940 + 1.51890i −0.0222577 + 0.999752i \(0.507085\pi\)
−0.854682 + 0.519152i \(0.826248\pi\)
\(278\) −14.8595 + 8.57912i −0.0534513 + 0.0308601i
\(279\) 3.65557i 0.0131024i
\(280\) −27.6094 + 34.6081i −0.0986049 + 0.123600i
\(281\) 360.234 1.28197 0.640986 0.767553i \(-0.278526\pi\)
0.640986 + 0.767553i \(0.278526\pi\)
\(282\) 69.9203 + 121.106i 0.247944 + 0.429452i
\(283\) 234.261 + 135.251i 0.827778 + 0.477918i 0.853091 0.521762i \(-0.174725\pi\)
−0.0253131 + 0.999680i \(0.508058\pi\)
\(284\) −101.986 + 176.646i −0.359107 + 0.621992i
\(285\) −20.3810 + 11.7670i −0.0715123 + 0.0412877i
\(286\) 126.535i 0.442431i
\(287\) −147.956 377.187i −0.515525 1.31424i
\(288\) 16.9706 0.0589256
\(289\) −101.337 175.520i −0.350646 0.607336i
\(290\) −115.603 66.7434i −0.398631 0.230150i
\(291\) −53.2134 + 92.1683i −0.182864 + 0.316729i
\(292\) −142.557 + 82.3051i −0.488207 + 0.281867i
\(293\) 9.63230i 0.0328747i −0.999865 0.0164374i \(-0.994768\pi\)
0.999865 0.0164374i \(-0.00523241\pi\)
\(294\) 81.6057 + 88.0143i 0.277570 + 0.299368i
\(295\) −129.375 −0.438559
\(296\) 49.5813 + 85.8773i 0.167504 + 0.290126i
\(297\) −55.4585 32.0190i −0.186729 0.107808i
\(298\) 204.867 354.840i 0.687472 1.19074i
\(299\) −14.1484 + 8.16861i −0.0473192 + 0.0273198i
\(300\) 17.3205i 0.0577350i
\(301\) 221.688 86.9594i 0.736504 0.288902i
\(302\) −165.892 −0.549310
\(303\) 53.8141 + 93.2088i 0.177604 + 0.307620i
\(304\) −21.0494 12.1529i −0.0692415 0.0399766i
\(305\) 6.55383 11.3516i 0.0214880 0.0372183i
\(306\) −34.1381 + 19.7096i −0.111562 + 0.0644106i
\(307\) 46.0412i 0.149971i −0.997185 0.0749857i \(-0.976109\pi\)
0.997185 0.0749857i \(-0.0238911\pi\)
\(308\) 134.876 + 107.600i 0.437908 + 0.349350i
\(309\) −308.204 −0.997425
\(310\) 1.92666 + 3.33707i 0.00621502 + 0.0107647i
\(311\) −378.160 218.331i −1.21595 0.702029i −0.251901 0.967753i \(-0.581056\pi\)
−0.964049 + 0.265724i \(0.914389\pi\)
\(312\) 17.7835 30.8019i 0.0569983 0.0987239i
\(313\) 248.135 143.261i 0.792764 0.457703i −0.0481706 0.998839i \(-0.515339\pi\)
0.840935 + 0.541137i \(0.182006\pi\)
\(314\) 259.844i 0.827529i
\(315\) 46.4317 + 7.00710i 0.147402 + 0.0222447i
\(316\) 223.412 0.707001
\(317\) 0.684418 + 1.18545i 0.00215905 + 0.00373958i 0.867103 0.498129i \(-0.165979\pi\)
−0.864944 + 0.501869i \(0.832646\pi\)
\(318\) −30.8444 17.8080i −0.0969949 0.0560001i
\(319\) −260.114 + 450.531i −0.815404 + 1.41232i
\(320\) −15.4919 + 8.94427i −0.0484123 + 0.0279508i
\(321\) 147.174i 0.458487i
\(322\) 3.32418 22.0273i 0.0103235 0.0684077i
\(323\) 56.4575 0.174791
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 31.4370 + 18.1502i 0.0967293 + 0.0558467i
\(326\) 85.9636 148.893i 0.263692 0.456728i
\(327\) 259.287 149.700i 0.792928 0.457797i
\(328\) 163.712i 0.499123i
\(329\) −249.221 + 312.396i −0.757510 + 0.949533i
\(330\) 67.5019 0.204551
\(331\) 192.017 + 332.583i 0.580111 + 1.00478i 0.995466 + 0.0951223i \(0.0303242\pi\)
−0.415354 + 0.909660i \(0.636342\pi\)
\(332\) −158.697 91.6237i −0.478003 0.275975i
\(333\) 52.5889 91.0866i 0.157925 0.273533i
\(334\) −115.927 + 66.9304i −0.347087 + 0.200391i
\(335\) 110.620i 0.330210i
\(336\) 17.7099 + 45.1482i 0.0527080 + 0.134370i
\(337\) −141.948 −0.421211 −0.210606 0.977571i \(-0.567544\pi\)
−0.210606 + 0.977571i \(0.567544\pi\)
\(338\) 82.2305 + 142.427i 0.243285 + 0.421383i
\(339\) −123.092 71.0675i −0.363105 0.209639i
\(340\) 20.7758 35.9847i 0.0611053 0.105837i
\(341\) 13.0053 7.50861i 0.0381387 0.0220194i
\(342\) 25.7802i 0.0753806i
\(343\) −148.991 + 308.951i −0.434376 + 0.900732i
\(344\) 96.2203 0.279710
\(345\) −4.35766 7.54769i −0.0126309 0.0218774i
\(346\) −319.281 184.337i −0.922778 0.532766i
\(347\) 125.176 216.811i 0.360737 0.624815i −0.627345 0.778741i \(-0.715858\pi\)
0.988082 + 0.153926i \(0.0491918\pi\)
\(348\) −126.637 + 73.1137i −0.363898 + 0.210097i
\(349\) 195.188i 0.559277i 0.960105 + 0.279639i \(0.0902147\pi\)
−0.960105 + 0.279639i \(0.909785\pi\)
\(350\) −46.0792 + 18.0751i −0.131655 + 0.0516431i
\(351\) −37.7244 −0.107477
\(352\) 34.8578 + 60.3756i 0.0990280 + 0.171521i
\(353\) 123.148 + 71.0997i 0.348862 + 0.201416i 0.664184 0.747569i \(-0.268779\pi\)
−0.315322 + 0.948985i \(0.602113\pi\)
\(354\) −70.8615 + 122.736i −0.200174 + 0.346711i
\(355\) −197.496 + 114.024i −0.556326 + 0.321195i
\(356\) 255.589i 0.717947i
\(357\) −88.0605 70.2522i −0.246668 0.196785i
\(358\) −433.497 −1.21089
\(359\) 328.443 + 568.880i 0.914884 + 1.58462i 0.807072 + 0.590453i \(0.201051\pi\)
0.107812 + 0.994171i \(0.465616\pi\)
\(360\) 16.4317 + 9.48683i 0.0456435 + 0.0263523i
\(361\) −162.038 + 280.659i −0.448860 + 0.777448i
\(362\) 385.654 222.658i 1.06534 0.615076i
\(363\) 53.4921i 0.147361i
\(364\) 100.503 + 15.1671i 0.276107 + 0.0416678i
\(365\) −184.040 −0.504218
\(366\) −7.17937 12.4350i −0.0196158 0.0339755i
\(367\) −444.403 256.576i −1.21091 0.699117i −0.247950 0.968773i \(-0.579757\pi\)
−0.962957 + 0.269655i \(0.913090\pi\)
\(368\) 4.50057 7.79522i 0.0122298 0.0211827i
\(369\) −150.379 + 86.8216i −0.407532 + 0.235289i
\(370\) 110.867i 0.299641i
\(371\) 15.1880 100.642i 0.0409381 0.271271i
\(372\) 4.22109 0.0113470
\(373\) 316.262 + 547.782i 0.847887 + 1.46858i 0.883090 + 0.469204i \(0.155459\pi\)
−0.0352027 + 0.999380i \(0.511208\pi\)
\(374\) −140.241 80.9679i −0.374975 0.216492i
\(375\) −9.68246 + 16.7705i −0.0258199 + 0.0447214i
\(376\) −139.841 + 80.7370i −0.371916 + 0.214726i
\(377\) 306.463i 0.812900i
\(378\) 32.0792 40.2110i 0.0848656 0.106378i
\(379\) −617.180 −1.62844 −0.814222 0.580553i \(-0.802836\pi\)
−0.814222 + 0.580553i \(0.802836\pi\)
\(380\) −13.5873 23.5340i −0.0357562 0.0619315i
\(381\) −290.220 167.559i −0.761732 0.439786i
\(382\) −64.1976 + 111.193i −0.168057 + 0.291082i
\(383\) 150.642 86.9735i 0.393322 0.227085i −0.290276 0.956943i \(-0.593747\pi\)
0.683599 + 0.729858i \(0.260414\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 70.4426 + 179.581i 0.182968 + 0.466444i
\(386\) 324.781 0.841402
\(387\) −51.0285 88.3840i −0.131857 0.228382i
\(388\) −106.427 61.4455i −0.274296 0.158365i
\(389\) −98.0961 + 169.907i −0.252175 + 0.436780i −0.964124 0.265451i \(-0.914479\pi\)
0.711949 + 0.702231i \(0.247813\pi\)
\(390\) 34.4375 19.8825i 0.0883013 0.0509808i
\(391\) 20.9079i 0.0534729i
\(392\) −101.630 + 94.2301i −0.259261 + 0.240383i
\(393\) −313.699 −0.798217
\(394\) 161.213 + 279.228i 0.409169 + 0.708702i
\(395\) 216.318 + 124.891i 0.547640 + 0.316180i
\(396\) 36.9723 64.0379i 0.0933645 0.161712i
\(397\) −345.285 + 199.350i −0.869736 + 0.502142i −0.867260 0.497855i \(-0.834121\pi\)
−0.00247542 + 0.999997i \(0.500788\pi\)
\(398\) 15.6216i 0.0392502i
\(399\) −68.5851 + 26.9033i −0.171893 + 0.0674267i
\(400\) −20.0000 −0.0500000
\(401\) −173.599 300.683i −0.432916 0.749833i 0.564207 0.825633i \(-0.309182\pi\)
−0.997123 + 0.0758008i \(0.975849\pi\)
\(402\) −104.944 60.5893i −0.261054 0.150720i
\(403\) 4.42328 7.66135i 0.0109759 0.0190108i
\(404\) −107.628 + 62.1392i −0.266407 + 0.153810i
\(405\) 20.1246i 0.0496904i
\(406\) −326.664 260.603i −0.804591 0.641880i
\(407\) 432.074 1.06161
\(408\) −22.7587 39.4193i −0.0557812 0.0966159i
\(409\) 293.397 + 169.393i 0.717352 + 0.414163i 0.813777 0.581177i \(-0.197408\pi\)
−0.0964252 + 0.995340i \(0.530741\pi\)
\(410\) 91.5180 158.514i 0.223215 0.386619i
\(411\) −1.89500 + 1.09408i −0.00461070 + 0.00266199i
\(412\) 355.884i 0.863795i
\(413\) −400.473 60.4361i −0.969668 0.146334i
\(414\) −9.54715 −0.0230608
\(415\) −102.438 177.429i −0.246840 0.427539i
\(416\) 35.5669 + 20.5346i 0.0854974 + 0.0493619i
\(417\) −10.5072 + 18.1991i −0.0251972 + 0.0436428i
\(418\) −91.7171 + 52.9529i −0.219419 + 0.126682i
\(419\) 369.514i 0.881894i 0.897533 + 0.440947i \(0.145357\pi\)
−0.897533 + 0.440947i \(0.854643\pi\)
\(420\) −8.09110 + 53.6147i −0.0192645 + 0.127654i
\(421\) −217.571 −0.516797 −0.258398 0.966038i \(-0.583195\pi\)
−0.258398 + 0.966038i \(0.583195\pi\)
\(422\) 106.905 + 185.166i 0.253330 + 0.438781i
\(423\) 148.323 + 85.6345i 0.350646 + 0.202446i
\(424\) 20.5629 35.6160i 0.0484975 0.0840001i
\(425\) 40.2322 23.2280i 0.0946639 0.0546542i
\(426\) 249.815i 0.586420i
\(427\) 25.5898 32.0766i 0.0599293 0.0751209i
\(428\) 169.942 0.397061
\(429\) −77.4866 134.211i −0.180622 0.312846i
\(430\) 93.1649 + 53.7888i 0.216663 + 0.125090i
\(431\) 142.916 247.537i 0.331591 0.574332i −0.651233 0.758878i \(-0.725748\pi\)
0.982824 + 0.184546i \(0.0590814\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 643.490i 1.48612i −0.669224 0.743060i \(-0.733374\pi\)
0.669224 0.743060i \(-0.266626\pi\)
\(434\) 4.40498 + 11.2297i 0.0101497 + 0.0258749i
\(435\) −163.487 −0.375833
\(436\) 172.858 + 299.399i 0.396464 + 0.686695i
\(437\) 11.8418 + 6.83686i 0.0270979 + 0.0156450i
\(438\) −100.803 + 174.595i −0.230143 + 0.398620i
\(439\) 494.013 285.218i 1.12531 0.649700i 0.182562 0.983194i \(-0.441561\pi\)
0.942752 + 0.333494i \(0.108228\pi\)
\(440\) 77.9445i 0.177147i
\(441\) 140.453 + 43.3802i 0.318488 + 0.0983677i
\(442\) −95.3956 −0.215827
\(443\) 33.0074 + 57.1705i 0.0745089 + 0.129053i 0.900873 0.434084i \(-0.142928\pi\)
−0.826364 + 0.563137i \(0.809594\pi\)
\(444\) 105.178 + 60.7244i 0.236887 + 0.136767i
\(445\) −142.879 + 247.473i −0.321076 + 0.556120i
\(446\) 377.939 218.203i 0.847396 0.489244i
\(447\) 501.819i 1.12264i
\(448\) −52.1327 + 20.4496i −0.116368 + 0.0456464i
\(449\) 515.072 1.14715 0.573577 0.819152i \(-0.305555\pi\)
0.573577 + 0.819152i \(0.305555\pi\)
\(450\) 10.6066 + 18.3712i 0.0235702 + 0.0408248i
\(451\) −617.764 356.666i −1.36977 0.790834i
\(452\) 82.0616 142.135i 0.181552 0.314458i
\(453\) −175.955 + 101.588i −0.388421 + 0.224255i
\(454\) 142.019i 0.312816i
\(455\) 88.8329 + 70.8683i 0.195237 + 0.155755i
\(456\) −29.7684 −0.0652815
\(457\) −39.5136 68.4395i −0.0864629 0.149758i 0.819551 0.573007i \(-0.194223\pi\)
−0.906014 + 0.423248i \(0.860890\pi\)
\(458\) 391.914 + 226.272i 0.855708 + 0.494043i
\(459\) −24.1393 + 41.8105i −0.0525910 + 0.0910904i
\(460\) 8.71532 5.03179i 0.0189463 0.0109387i
\(461\) 9.58316i 0.0207878i −0.999946 0.0103939i \(-0.996691\pi\)
0.999946 0.0103939i \(-0.00330854\pi\)
\(462\) 208.948 + 31.5328i 0.452269 + 0.0682529i
\(463\) −232.103 −0.501303 −0.250652 0.968077i \(-0.580645\pi\)
−0.250652 + 0.968077i \(0.580645\pi\)
\(464\) −84.4244 146.227i −0.181949 0.315145i
\(465\) 4.08705 + 2.35966i 0.00878937 + 0.00507454i
\(466\) 219.761 380.637i 0.471590 0.816818i
\(467\) 593.692 342.768i 1.27129 0.733979i 0.296058 0.955170i \(-0.404328\pi\)
0.975230 + 0.221191i \(0.0709944\pi\)
\(468\) 43.5604i 0.0930778i
\(469\) 51.6752 342.419i 0.110182 0.730105i
\(470\) −180.533 −0.384114
\(471\) 159.121 + 275.606i 0.337837 + 0.585151i
\(472\) −141.723 81.8238i −0.300261 0.173356i
\(473\) 209.627 363.085i 0.443186 0.767621i
\(474\) 236.964 136.811i 0.499925 0.288632i
\(475\) 30.3822i 0.0639626i
\(476\) 81.1202 101.684i 0.170421 0.213621i
\(477\) −43.6206 −0.0914477
\(478\) 96.3526 + 166.888i 0.201575 + 0.349137i
\(479\) −544.818 314.551i −1.13741 0.656682i −0.191619 0.981469i \(-0.561374\pi\)
−0.945787 + 0.324787i \(0.894707\pi\)
\(480\) −10.9545 + 18.9737i −0.0228218 + 0.0395285i
\(481\) 220.432 127.266i 0.458278 0.264587i
\(482\) 546.140i 1.13307i
\(483\) −9.96307 25.3991i −0.0206275 0.0525861i
\(484\) 61.7673 0.127618
\(485\) −68.6982 118.989i −0.141646 0.245338i
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 249.384 431.946i 0.512083 0.886953i −0.487819 0.872945i \(-0.662207\pi\)
0.999902 0.0140085i \(-0.00445918\pi\)
\(488\) 14.3587 8.29002i 0.0294236 0.0169877i
\(489\) 210.567i 0.430607i
\(490\) −151.079 + 34.4250i −0.308325 + 0.0702550i
\(491\) 166.583 0.339274 0.169637 0.985507i \(-0.445741\pi\)
0.169637 + 0.985507i \(0.445741\pi\)
\(492\) −100.253 173.643i −0.203766 0.352933i
\(493\) 339.658 + 196.101i 0.688961 + 0.397772i
\(494\) −31.1943 + 54.0301i −0.0631463 + 0.109373i
\(495\) 71.5966 41.3363i 0.144640 0.0835077i
\(496\) 4.87410i 0.00982681i
\(497\) −664.603 + 260.698i −1.33723 + 0.524543i
\(498\) −224.431 −0.450665
\(499\) −18.1531 31.4421i −0.0363790 0.0630102i 0.847263 0.531174i \(-0.178249\pi\)
−0.883642 + 0.468164i \(0.844916\pi\)
\(500\) −19.3649 11.1803i −0.0387298 0.0223607i
\(501\) −81.9727 + 141.981i −0.163618 + 0.283395i
\(502\) 121.705 70.2664i 0.242440 0.139973i
\(503\) 634.940i 1.26231i −0.775658 0.631153i \(-0.782582\pi\)
0.775658 0.631153i \(-0.217418\pi\)
\(504\) 46.4317 + 37.0419i 0.0921263 + 0.0734958i
\(505\) −138.947 −0.275143
\(506\) −19.6100 33.9656i −0.0387550 0.0671256i
\(507\) 174.437 + 100.711i 0.344057 + 0.198642i
\(508\) 193.480 335.117i 0.380866 0.659680i
\(509\) 500.864 289.174i 0.984015 0.568121i 0.0805350 0.996752i \(-0.474337\pi\)
0.903480 + 0.428631i \(0.141004\pi\)
\(510\) 50.8901i 0.0997845i
\(511\) −569.685 85.9723i −1.11484 0.168243i
\(512\) −22.6274 −0.0441942
\(513\) 15.7871 + 27.3440i 0.0307740 + 0.0533021i
\(514\) 25.8639 + 14.9325i 0.0503189 + 0.0290516i
\(515\) 198.945 344.583i 0.386301 0.669093i
\(516\) 102.057 58.9227i 0.197785 0.114191i
\(517\) 703.579i 1.36089i
\(518\) −51.7904 + 343.183i −0.0999815 + 0.662516i
\(519\) −451.532 −0.870003
\(520\) 22.9583 + 39.7650i 0.0441507 + 0.0764712i
\(521\) −550.974 318.105i −1.05753 0.610566i −0.132783 0.991145i \(-0.542391\pi\)
−0.924748 + 0.380579i \(0.875725\pi\)
\(522\) −89.5456 + 155.098i −0.171543 + 0.297122i
\(523\) 392.868 226.823i 0.751182 0.433695i −0.0749389 0.997188i \(-0.523876\pi\)
0.826121 + 0.563493i \(0.190543\pi\)
\(524\) 362.229i 0.691276i
\(525\) −37.8057 + 47.3891i −0.0720108 + 0.0902650i
\(526\) 538.133 1.02307
\(527\) −5.66079 9.80477i −0.0107415 0.0186049i
\(528\) 73.9447 + 42.6920i 0.140047 + 0.0808560i
\(529\) 261.968 453.742i 0.495214 0.857735i
\(530\) 39.8199 22.9901i 0.0751320 0.0433775i
\(531\) 173.575i 0.326882i
\(532\) −31.0652 79.1953i −0.0583933 0.148863i
\(533\) −420.220 −0.788406
\(534\) 156.516 + 271.093i 0.293101 + 0.507666i
\(535\) 164.546 + 95.0005i 0.307562 + 0.177571i
\(536\) 69.9625 121.179i 0.130527 0.226079i
\(537\) −459.793 + 265.462i −0.856225 + 0.494342i
\(538\) 23.7461i 0.0441377i
\(539\) 134.162 + 588.790i 0.248909 + 1.09237i
\(540\) 23.2379 0.0430331
\(541\) 288.159 + 499.106i 0.532641 + 0.922562i 0.999274 + 0.0381102i \(0.0121338\pi\)
−0.466632 + 0.884451i \(0.654533\pi\)
\(542\) 452.754 + 261.398i 0.835340 + 0.482284i
\(543\) 272.699 472.328i 0.502208 0.869849i
\(544\) 45.5175 26.2795i 0.0836718 0.0483080i
\(545\) 386.523i 0.709216i
\(546\) 115.887 45.4581i 0.212248 0.0832566i
\(547\) 481.306 0.879901 0.439950 0.898022i \(-0.354996\pi\)
0.439950 + 0.898022i \(0.354996\pi\)
\(548\) −1.26333 2.18815i −0.00230535 0.00399298i
\(549\) −15.2297 8.79289i −0.0277409 0.0160162i
\(550\) −43.5723 + 75.4694i −0.0792224 + 0.137217i
\(551\) 222.136 128.250i 0.403150 0.232759i
\(552\) 11.0241i 0.0199712i
\(553\) 611.259 + 487.645i 1.10535 + 0.881817i
\(554\) −687.060 −1.24018
\(555\) 67.8920 + 117.592i 0.122328 + 0.211878i
\(556\) −21.0145 12.1327i −0.0377958 0.0218214i
\(557\) −54.4056 + 94.2333i −0.0976762 + 0.169180i −0.910722 0.413019i \(-0.864474\pi\)
0.813046 + 0.582199i \(0.197808\pi\)
\(558\) 4.47714 2.58488i 0.00802356 0.00463240i
\(559\) 246.980i 0.441825i
\(560\) −61.9089 9.34279i −0.110552 0.0166836i
\(561\) −198.330 −0.353530
\(562\) 254.724 + 441.195i 0.453245 + 0.785044i
\(563\) 521.516 + 301.097i 0.926316 + 0.534809i 0.885645 0.464364i \(-0.153717\pi\)
0.0406717 + 0.999173i \(0.487050\pi\)
\(564\) −98.8822 + 171.269i −0.175323 + 0.303669i
\(565\) 158.912 91.7477i 0.281260 0.162385i
\(566\) 382.547i 0.675878i
\(567\) 9.40101 62.2946i 0.0165803 0.109867i
\(568\) −288.461 −0.507854
\(569\) 4.76685 + 8.25642i 0.00837759 + 0.0145104i 0.870184 0.492727i \(-0.164000\pi\)
−0.861806 + 0.507238i \(0.830667\pi\)
\(570\) −28.8231 16.6410i −0.0505668 0.0291948i
\(571\) −491.103 + 850.615i −0.860075 + 1.48969i 0.0117813 + 0.999931i \(0.496250\pi\)
−0.871856 + 0.489762i \(0.837084\pi\)
\(572\) 154.973 89.4739i 0.270932 0.156423i
\(573\) 157.251i 0.274435i
\(574\) 357.337 447.919i 0.622538 0.780347i
\(575\) 11.2514 0.0195677
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) −454.001 262.117i −0.786830 0.454276i 0.0520155 0.998646i \(-0.483435\pi\)
−0.838845 + 0.544370i \(0.816769\pi\)
\(578\) 143.312 248.223i 0.247944 0.429452i
\(579\) 344.483 198.887i 0.594961 0.343501i
\(580\) 188.779i 0.325481i
\(581\) −234.209 597.073i −0.403113 1.02767i
\(582\) −150.510 −0.258608
\(583\) −89.5974 155.187i −0.153683 0.266187i
\(584\) −201.605 116.397i −0.345215 0.199310i
\(585\) 24.3510 42.1772i 0.0416256 0.0720977i
\(586\) 11.7971 6.81106i 0.0201316 0.0116230i
\(587\) 651.322i 1.10958i 0.831991 + 0.554789i \(0.187201\pi\)
−0.831991 + 0.554789i \(0.812799\pi\)
\(588\) −50.0911 + 162.182i −0.0851889 + 0.275819i
\(589\) −7.40429 −0.0125710
\(590\) −91.4818 158.451i −0.155054 0.268561i
\(591\) 341.984 + 197.444i 0.578652 + 0.334085i
\(592\) −70.1185 + 121.449i −0.118443 + 0.205150i
\(593\) −610.904 + 352.706i −1.03019 + 0.594782i −0.917040 0.398796i \(-0.869428\pi\)
−0.113152 + 0.993578i \(0.536095\pi\)
\(594\) 90.5633i 0.152464i
\(595\) 135.387 53.1071i 0.227541 0.0892556i
\(596\) 579.451 0.972233
\(597\) 9.56623 + 16.5692i 0.0160238 + 0.0277541i
\(598\) −20.0089 11.5522i −0.0334597 0.0193180i
\(599\) 296.910 514.263i 0.495676 0.858535i −0.504312 0.863522i \(-0.668254\pi\)
0.999988 + 0.00498610i \(0.00158713\pi\)
\(600\) −21.2132 + 12.2474i −0.0353553 + 0.0204124i
\(601\) 12.1644i 0.0202403i 0.999949 + 0.0101202i \(0.00322140\pi\)
−0.999949 + 0.0101202i \(0.996779\pi\)
\(602\) 263.260 + 210.021i 0.437309 + 0.348873i
\(603\) −148.413 −0.246124
\(604\) −117.303 203.175i −0.194211 0.336383i
\(605\) 59.8059 + 34.5290i 0.0988528 + 0.0570727i
\(606\) −76.1047 + 131.817i −0.125585 + 0.217520i
\(607\) 698.521 403.291i 1.15078 0.664401i 0.201700 0.979447i \(-0.435353\pi\)
0.949076 + 0.315047i \(0.102020\pi\)
\(608\) 34.3736i 0.0565354i
\(609\) −506.066 76.3714i −0.830978 0.125405i
\(610\) 18.5370 0.0303886
\(611\) 207.237 + 358.946i 0.339178 + 0.587473i
\(612\) −48.2786 27.8737i −0.0788866 0.0455452i
\(613\) 397.237 688.035i 0.648021 1.12241i −0.335574 0.942014i \(-0.608930\pi\)
0.983595 0.180392i \(-0.0577365\pi\)
\(614\) 56.3887 32.5560i 0.0918383 0.0530229i
\(615\) 224.172i 0.364508i
\(616\) −36.4110 + 241.273i −0.0591087 + 0.391677i
\(617\) 108.982 0.176633 0.0883164 0.996092i \(-0.471851\pi\)
0.0883164 + 0.996092i \(0.471851\pi\)
\(618\) −217.933 377.472i −0.352643 0.610796i
\(619\) −310.725 179.397i −0.501979 0.289818i 0.227551 0.973766i \(-0.426928\pi\)
−0.729531 + 0.683948i \(0.760261\pi\)
\(620\) −2.72470 + 4.71932i −0.00439468 + 0.00761181i
\(621\) −10.1263 + 5.84641i −0.0163064 + 0.00941451i
\(622\) 617.533i 0.992819i
\(623\) −557.878 + 699.296i −0.895470 + 1.12246i
\(624\) 50.2992 0.0806077
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) 350.916 + 202.602i 0.560569 + 0.323645i
\(627\) −64.8538 + 112.330i −0.103435 + 0.179155i
\(628\) −318.243 + 183.737i −0.506756 + 0.292576i
\(629\) 325.743i 0.517875i
\(630\) 24.2502 + 61.8217i 0.0384925 + 0.0981297i
\(631\) −612.351 −0.970446 −0.485223 0.874391i \(-0.661262\pi\)
−0.485223 + 0.874391i \(0.661262\pi\)
\(632\) 157.976 + 273.623i 0.249962 + 0.432948i
\(633\) 226.781 + 130.932i 0.358263 + 0.206843i
\(634\) −0.967913 + 1.67647i −0.00152668 + 0.00264428i
\(635\) 374.672 216.317i 0.590035 0.340657i
\(636\) 50.3687i 0.0791960i
\(637\) 241.872 + 260.866i 0.379705 + 0.409523i
\(638\) −735.713 −1.15316
\(639\) 152.980 + 264.969i 0.239405 + 0.414661i
\(640\) −21.9089 12.6491i −0.0342327 0.0197642i
\(641\) −459.706 + 796.233i −0.717169 + 1.24217i 0.244947 + 0.969536i \(0.421229\pi\)
−0.962117 + 0.272637i \(0.912104\pi\)
\(642\) 180.251 104.068i 0.280765 0.162099i
\(643\) 835.879i 1.29997i 0.759948 + 0.649984i \(0.225224\pi\)
−0.759948 + 0.649984i \(0.774776\pi\)
\(644\) 29.3283 11.5044i 0.0455409 0.0178639i
\(645\) 131.755 0.204271
\(646\) 39.9215 + 69.1461i 0.0617980 + 0.107037i
\(647\) −492.933 284.595i −0.761876 0.439869i 0.0680932 0.997679i \(-0.478308\pi\)
−0.829969 + 0.557810i \(0.811642\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) −617.520 + 356.525i −0.951495 + 0.549346i
\(650\) 51.3364i 0.0789791i
\(651\) 11.5490 + 9.21343i 0.0177403 + 0.0141527i
\(652\) 243.142 0.372917
\(653\) −196.162 339.763i −0.300402 0.520311i 0.675825 0.737062i \(-0.263787\pi\)
−0.976227 + 0.216751i \(0.930454\pi\)
\(654\) 366.688 + 211.707i 0.560684 + 0.323711i
\(655\) 202.492 350.727i 0.309148 0.535460i
\(656\) 200.506 115.762i 0.305649 0.176467i
\(657\) 246.915i 0.375822i
\(658\) −558.831 84.3343i −0.849288 0.128168i
\(659\) 505.063 0.766408 0.383204 0.923664i \(-0.374821\pi\)
0.383204 + 0.923664i \(0.374821\pi\)
\(660\) 47.7311 + 82.6726i 0.0723198 + 0.125262i
\(661\) −255.815 147.695i −0.387013 0.223442i 0.293852 0.955851i \(-0.405063\pi\)
−0.680865 + 0.732409i \(0.738396\pi\)
\(662\) −271.553 + 470.343i −0.410201 + 0.710488i
\(663\) −101.182 + 58.4176i −0.152613 + 0.0881110i
\(664\) 259.151i 0.390288i
\(665\) 14.1927 94.0465i 0.0213425 0.141423i
\(666\) 148.744 0.223339
\(667\) 47.4948 + 82.2633i 0.0712065 + 0.123333i
\(668\) −163.945 94.6539i −0.245427 0.141698i
\(669\) 267.243 462.878i 0.399466 0.691896i
\(670\) 135.482 78.2204i 0.202212 0.116747i
\(671\) 72.2430i 0.107665i
\(672\) −42.7723 + 53.6147i −0.0636492 + 0.0797838i
\(673\) −624.569 −0.928038 −0.464019 0.885825i \(-0.653593\pi\)
−0.464019 + 0.885825i \(0.653593\pi\)
\(674\) −100.373 173.850i −0.148921 0.257938i
\(675\) 22.5000 + 12.9904i 0.0333333 + 0.0192450i
\(676\) −116.291 + 201.423i −0.172029 + 0.297963i
\(677\) −676.847 + 390.778i −0.999774 + 0.577220i −0.908181 0.418577i \(-0.862529\pi\)
−0.0915926 + 0.995797i \(0.529196\pi\)
\(678\) 201.009i 0.296474i
\(679\) −157.067 400.415i −0.231321 0.589712i
\(680\) 58.7628 0.0864159
\(681\) 86.9683 + 150.634i 0.127707 + 0.221195i
\(682\) 18.3923 + 10.6188i 0.0269681 + 0.0155701i
\(683\) −50.8525 + 88.0791i −0.0744546 + 0.128959i −0.900849 0.434133i \(-0.857055\pi\)
0.826394 + 0.563092i \(0.190388\pi\)
\(684\) −31.5741 + 18.2293i −0.0461610 + 0.0266511i
\(685\) 2.82490i 0.00412393i
\(686\) −483.739 + 35.9855i −0.705158 + 0.0524570i
\(687\) 554.250 0.806769
\(688\) 68.0380 + 117.845i 0.0988925 + 0.171287i
\(689\) −91.4200 52.7814i −0.132685 0.0766057i
\(690\) 6.16266 10.6740i 0.00893139 0.0154696i
\(691\) 634.684 366.435i 0.918501 0.530297i 0.0353446 0.999375i \(-0.488747\pi\)
0.883157 + 0.469078i \(0.155414\pi\)
\(692\) 521.384i 0.753445i
\(693\) 240.933 94.5087i 0.347667 0.136376i
\(694\) 354.051 0.510160
\(695\) −13.5648 23.4949i −0.0195177 0.0338056i
\(696\) −179.091 103.398i −0.257315 0.148561i
\(697\) −268.893 + 465.736i −0.385786 + 0.668201i
\(698\) −239.055 + 138.019i −0.342486 + 0.197734i
\(699\) 538.303i 0.770104i
\(700\) −54.7203 43.6543i −0.0781718 0.0623632i
\(701\) −795.928 −1.13542 −0.567709 0.823229i \(-0.692170\pi\)
−0.567709 + 0.823229i \(0.692170\pi\)
\(702\) −26.6752 46.2028i −0.0379988 0.0658159i
\(703\) −184.494 106.518i −0.262438 0.151519i
\(704\) −49.2964 + 85.3839i −0.0700233 + 0.121284i
\(705\) −191.485 + 110.554i −0.271609 + 0.156814i
\(706\) 201.100i 0.284845i
\(707\) −430.104 64.9079i −0.608351 0.0918075i
\(708\) −200.427 −0.283089
\(709\) −514.532 891.196i −0.725715 1.25698i −0.958679 0.284490i \(-0.908176\pi\)
0.232964 0.972485i \(-0.425158\pi\)
\(710\) −279.301 161.255i −0.393382 0.227119i
\(711\) 167.559 290.221i 0.235667 0.408187i
\(712\) −313.032 + 180.729i −0.439651 + 0.253833i
\(713\) 2.74203i 0.00384576i
\(714\) 23.7728 157.527i 0.0332952 0.220627i
\(715\) 200.070 0.279818
\(716\) −306.529 530.923i −0.428113 0.741513i
\(717\) 204.395 + 118.007i 0.285069 + 0.164585i
\(718\) −464.489 + 804.518i −0.646920 + 1.12050i
\(719\) −136.549 + 78.8367i −0.189915 + 0.109648i −0.591943 0.805980i \(-0.701639\pi\)
0.402028 + 0.915628i \(0.368306\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) 776.792 973.702i 1.07738 1.35049i
\(722\) −458.314 −0.634784
\(723\) 334.441 + 579.269i 0.462574 + 0.801202i
\(724\) 545.397 + 314.885i 0.753311 + 0.434925i
\(725\) 105.531 182.784i 0.145559 0.252116i
\(726\) 65.5141 37.8246i 0.0902398 0.0521000i
\(727\) 13.5224i 0.0186003i −0.999957 0.00930013i \(-0.997040\pi\)
0.999957 0.00930013i \(-0.00296037\pi\)
\(728\) 52.4905 + 133.815i 0.0721023 + 0.183812i
\(729\) −27.0000 −0.0370370
\(730\) −130.136 225.402i −0.178268 0.308769i
\(731\) −273.732 158.039i −0.374462 0.216196i
\(732\) 10.1532 17.5858i 0.0138704 0.0240243i
\(733\) 341.622 197.235i 0.466060 0.269080i −0.248529 0.968624i \(-0.579947\pi\)
0.714589 + 0.699545i \(0.246614\pi\)
\(734\) 725.707i 0.988701i
\(735\) −139.163 + 129.030i −0.189337 + 0.175551i
\(736\) 12.7295 0.0172956
\(737\) −304.843 528.003i −0.413626 0.716422i
\(738\) −212.669 122.784i −0.288169 0.166374i
\(739\) −475.080 + 822.863i −0.642869 + 1.11348i 0.341920 + 0.939729i \(0.388923\pi\)
−0.984789 + 0.173753i \(0.944411\pi\)
\(740\) −135.784 + 78.3949i −0.183492 + 0.105939i
\(741\) 76.4101i 0.103118i
\(742\) 134.000 52.5630i 0.180593 0.0708396i
\(743\) 425.883 0.573194 0.286597 0.958051i \(-0.407476\pi\)
0.286597 + 0.958051i \(0.407476\pi\)
\(744\) 2.98476 + 5.16976i 0.00401178 + 0.00694860i
\(745\) 561.051 + 323.923i 0.753088 + 0.434796i
\(746\) −447.262 + 774.680i −0.599547 + 1.03845i
\(747\) −238.045 + 137.436i −0.318669 + 0.183983i
\(748\) 229.012i 0.306166i
\(749\) 464.964 + 370.935i 0.620779 + 0.495240i
\(750\) −27.3861 −0.0365148
\(751\) 315.874 + 547.109i 0.420604 + 0.728508i 0.995999 0.0893683i \(-0.0284848\pi\)
−0.575395 + 0.817876i \(0.695151\pi\)
\(752\) −197.764 114.179i −0.262985 0.151834i
\(753\) 86.0584 149.058i 0.114287 0.197952i
\(754\) −375.340 + 216.702i −0.497798 + 0.287404i
\(755\) 262.298i 0.347414i
\(756\) 71.9316 + 10.8553i 0.0951477 + 0.0143589i
\(757\) 882.903 1.16632 0.583159 0.812358i \(-0.301816\pi\)
0.583159 + 0.812358i \(0.301816\pi\)
\(758\) −436.412 755.889i −0.575742 0.997214i
\(759\) −41.5991 24.0173i −0.0548078 0.0316433i
\(760\) 19.2154 33.2820i 0.0252834 0.0437922i
\(761\) −981.049 + 566.409i −1.28916 + 0.744295i −0.978504 0.206228i \(-0.933881\pi\)
−0.310653 + 0.950523i \(0.600548\pi\)
\(762\) 473.927i 0.621952i
\(763\) −180.560 + 1196.46i −0.236645 + 1.56810i
\(764\) −181.578 −0.237668
\(765\) −31.1637 53.9771i −0.0407368 0.0705583i
\(766\) 213.041 + 122.999i 0.278121 + 0.160573i
\(767\) −210.027 + 363.778i −0.273829 + 0.474287i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 41.6421i 0.0541510i −0.999633 0.0270755i \(-0.991381\pi\)
0.999633 0.0270755i \(-0.00861944\pi\)
\(770\) −170.130 + 213.257i −0.220949 + 0.276957i
\(771\) 36.5771 0.0474411
\(772\) 229.655 + 397.774i 0.297481 + 0.515252i
\(773\) 1114.00 + 643.167i 1.44114 + 0.832041i 0.997926 0.0643767i \(-0.0205059\pi\)
0.443211 + 0.896417i \(0.353839\pi\)
\(774\) 72.1652 124.994i 0.0932367 0.161491i
\(775\) −5.27637 + 3.04631i −0.00680821 + 0.00393072i
\(776\) 173.794i 0.223962i