Properties

Label 14.4.c.a.9.1
Level 14
Weight 4
Character 14.9
Analytic conductor 0.826
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.c (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.826026740080\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.1
Root \(0.500000 + 0.866025i\)
Character \(\chi\) = 14.9
Dual form 14.4.c.a.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 + 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -10.0000 q^{6} +(-14.0000 - 12.1244i) q^{7} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(2.50000 + 4.33013i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(4.50000 - 7.79423i) q^{5} -10.0000 q^{6} +(-14.0000 - 12.1244i) q^{7} +8.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(9.00000 + 15.5885i) q^{10} +(28.5000 + 49.3634i) q^{11} +(10.0000 - 17.3205i) q^{12} -70.0000 q^{13} +(35.0000 - 12.1244i) q^{14} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-25.5000 - 44.1673i) q^{17} +(2.00000 + 3.46410i) q^{18} +(-2.50000 + 4.33013i) q^{19} -36.0000 q^{20} +(17.5000 - 90.9327i) q^{21} -114.000 q^{22} +(-34.5000 + 59.7558i) q^{23} +(20.0000 + 34.6410i) q^{24} +(22.0000 + 38.1051i) q^{25} +(70.0000 - 121.244i) q^{26} +145.000 q^{27} +(-14.0000 + 72.7461i) q^{28} +114.000 q^{29} +(-45.0000 + 77.9423i) q^{30} +(-11.5000 - 19.9186i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(-142.500 + 246.817i) q^{33} +102.000 q^{34} +(-157.500 + 54.5596i) q^{35} -8.00000 q^{36} +(126.500 - 219.104i) q^{37} +(-5.00000 - 8.66025i) q^{38} +(-175.000 - 303.109i) q^{39} +(36.0000 - 62.3538i) q^{40} -42.0000 q^{41} +(140.000 + 121.244i) q^{42} -124.000 q^{43} +(114.000 - 197.454i) q^{44} +(-9.00000 - 15.5885i) q^{45} +(-69.0000 - 119.512i) q^{46} +(-100.500 + 174.071i) q^{47} -80.0000 q^{48} +(49.0000 + 339.482i) q^{49} -88.0000 q^{50} +(127.500 - 220.836i) q^{51} +(140.000 + 242.487i) q^{52} +(196.500 + 340.348i) q^{53} +(-145.000 + 251.147i) q^{54} +513.000 q^{55} +(-112.000 - 96.9948i) q^{56} -25.0000 q^{57} +(-114.000 + 197.454i) q^{58} +(-109.500 - 189.660i) q^{59} +(-90.0000 - 155.885i) q^{60} +(354.500 - 614.012i) q^{61} +46.0000 q^{62} +(-35.0000 + 12.1244i) q^{63} +64.0000 q^{64} +(-315.000 + 545.596i) q^{65} +(-285.000 - 493.634i) q^{66} +(-209.500 - 362.865i) q^{67} +(-102.000 + 176.669i) q^{68} -345.000 q^{69} +(63.0000 - 327.358i) q^{70} -96.0000 q^{71} +(8.00000 - 13.8564i) q^{72} +(156.500 + 271.066i) q^{73} +(253.000 + 438.209i) q^{74} +(-110.000 + 190.526i) q^{75} +20.0000 q^{76} +(199.500 - 1036.63i) q^{77} +700.000 q^{78} +(-230.500 + 399.238i) q^{79} +(72.0000 + 124.708i) q^{80} +(335.500 + 581.103i) q^{81} +(42.0000 - 72.7461i) q^{82} -588.000 q^{83} +(-350.000 + 121.244i) q^{84} -459.000 q^{85} +(124.000 - 214.774i) q^{86} +(285.000 + 493.634i) q^{87} +(228.000 + 394.908i) q^{88} +(508.500 - 880.748i) q^{89} +36.0000 q^{90} +(980.000 + 848.705i) q^{91} +276.000 q^{92} +(57.5000 - 99.5929i) q^{93} +(-201.000 - 348.142i) q^{94} +(22.5000 + 38.9711i) q^{95} +(80.0000 - 138.564i) q^{96} -1834.00 q^{97} +(-637.000 - 254.611i) q^{98} +114.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} + 5q^{3} - 4q^{4} + 9q^{5} - 20q^{6} - 28q^{7} + 16q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} + 5q^{3} - 4q^{4} + 9q^{5} - 20q^{6} - 28q^{7} + 16q^{8} + 2q^{9} + 18q^{10} + 57q^{11} + 20q^{12} - 140q^{13} + 70q^{14} + 90q^{15} - 16q^{16} - 51q^{17} + 4q^{18} - 5q^{19} - 72q^{20} + 35q^{21} - 228q^{22} - 69q^{23} + 40q^{24} + 44q^{25} + 140q^{26} + 290q^{27} - 28q^{28} + 228q^{29} - 90q^{30} - 23q^{31} - 32q^{32} - 285q^{33} + 204q^{34} - 315q^{35} - 16q^{36} + 253q^{37} - 10q^{38} - 350q^{39} + 72q^{40} - 84q^{41} + 280q^{42} - 248q^{43} + 228q^{44} - 18q^{45} - 138q^{46} - 201q^{47} - 160q^{48} + 98q^{49} - 176q^{50} + 255q^{51} + 280q^{52} + 393q^{53} - 290q^{54} + 1026q^{55} - 224q^{56} - 50q^{57} - 228q^{58} - 219q^{59} - 180q^{60} + 709q^{61} + 92q^{62} - 70q^{63} + 128q^{64} - 630q^{65} - 570q^{66} - 419q^{67} - 204q^{68} - 690q^{69} + 126q^{70} - 192q^{71} + 16q^{72} + 313q^{73} + 506q^{74} - 220q^{75} + 40q^{76} + 399q^{77} + 1400q^{78} - 461q^{79} + 144q^{80} + 671q^{81} + 84q^{82} - 1176q^{83} - 700q^{84} - 918q^{85} + 248q^{86} + 570q^{87} + 456q^{88} + 1017q^{89} + 72q^{90} + 1960q^{91} + 552q^{92} + 115q^{93} - 402q^{94} + 45q^{95} + 160q^{96} - 3668q^{97} - 1274q^{98} + 228q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.353553 + 0.612372i
\(3\) 2.50000 + 4.33013i 0.481125 + 0.833333i 0.999765 0.0216593i \(-0.00689490\pi\)
−0.518640 + 0.854993i \(0.673562\pi\)
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 4.50000 7.79423i 0.402492 0.697137i −0.591534 0.806280i \(-0.701477\pi\)
0.994026 + 0.109143i \(0.0348107\pi\)
\(6\) −10.0000 −0.680414
\(7\) −14.0000 12.1244i −0.755929 0.654654i
\(8\) 8.00000 0.353553
\(9\) 1.00000 1.73205i 0.0370370 0.0641500i
\(10\) 9.00000 + 15.5885i 0.284605 + 0.492950i
\(11\) 28.5000 + 49.3634i 0.781188 + 1.35306i 0.931250 + 0.364381i \(0.118720\pi\)
−0.150061 + 0.988677i \(0.547947\pi\)
\(12\) 10.0000 17.3205i 0.240563 0.416667i
\(13\) −70.0000 −1.49342 −0.746712 0.665148i \(-0.768369\pi\)
−0.746712 + 0.665148i \(0.768369\pi\)
\(14\) 35.0000 12.1244i 0.668153 0.231455i
\(15\) 45.0000 0.774597
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −25.5000 44.1673i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 2.00000 + 3.46410i 0.0261891 + 0.0453609i
\(19\) −2.50000 + 4.33013i −0.0301863 + 0.0522842i −0.880724 0.473630i \(-0.842943\pi\)
0.850538 + 0.525914i \(0.176277\pi\)
\(20\) −36.0000 −0.402492
\(21\) 17.5000 90.9327i 0.181848 0.944911i
\(22\) −114.000 −1.10477
\(23\) −34.5000 + 59.7558i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 20.0000 + 34.6410i 0.170103 + 0.294628i
\(25\) 22.0000 + 38.1051i 0.176000 + 0.304841i
\(26\) 70.0000 121.244i 0.528005 0.914531i
\(27\) 145.000 1.03353
\(28\) −14.0000 + 72.7461i −0.0944911 + 0.490990i
\(29\) 114.000 0.729975 0.364987 0.931012i \(-0.381073\pi\)
0.364987 + 0.931012i \(0.381073\pi\)
\(30\) −45.0000 + 77.9423i −0.273861 + 0.474342i
\(31\) −11.5000 19.9186i −0.0666278 0.115403i 0.830787 0.556590i \(-0.187891\pi\)
−0.897415 + 0.441188i \(0.854557\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) −142.500 + 246.817i −0.751699 + 1.30198i
\(34\) 102.000 0.514496
\(35\) −157.500 + 54.5596i −0.760639 + 0.263493i
\(36\) −8.00000 −0.0370370
\(37\) 126.500 219.104i 0.562067 0.973528i −0.435249 0.900310i \(-0.643340\pi\)
0.997316 0.0732182i \(-0.0233270\pi\)
\(38\) −5.00000 8.66025i −0.0213449 0.0369705i
\(39\) −175.000 303.109i −0.718524 1.24452i
\(40\) 36.0000 62.3538i 0.142302 0.246475i
\(41\) −42.0000 −0.159983 −0.0799914 0.996796i \(-0.525489\pi\)
−0.0799914 + 0.996796i \(0.525489\pi\)
\(42\) 140.000 + 121.244i 0.514344 + 0.445435i
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) 114.000 197.454i 0.390594 0.676529i
\(45\) −9.00000 15.5885i −0.0298142 0.0516398i
\(46\) −69.0000 119.512i −0.221163 0.383065i
\(47\) −100.500 + 174.071i −0.311903 + 0.540231i −0.978774 0.204941i \(-0.934300\pi\)
0.666871 + 0.745173i \(0.267633\pi\)
\(48\) −80.0000 −0.240563
\(49\) 49.0000 + 339.482i 0.142857 + 0.989743i
\(50\) −88.0000 −0.248902
\(51\) 127.500 220.836i 0.350070 0.606339i
\(52\) 140.000 + 242.487i 0.373356 + 0.646671i
\(53\) 196.500 + 340.348i 0.509271 + 0.882083i 0.999942 + 0.0107383i \(0.00341816\pi\)
−0.490672 + 0.871345i \(0.663249\pi\)
\(54\) −145.000 + 251.147i −0.365407 + 0.632904i
\(55\) 513.000 1.25769
\(56\) −112.000 96.9948i −0.267261 0.231455i
\(57\) −25.0000 −0.0580935
\(58\) −114.000 + 197.454i −0.258085 + 0.447016i
\(59\) −109.500 189.660i −0.241622 0.418501i 0.719555 0.694436i \(-0.244346\pi\)
−0.961176 + 0.275935i \(0.911013\pi\)
\(60\) −90.0000 155.885i −0.193649 0.335410i
\(61\) 354.500 614.012i 0.744083 1.28879i −0.206539 0.978438i \(-0.566220\pi\)
0.950622 0.310351i \(-0.100447\pi\)
\(62\) 46.0000 0.0942259
\(63\) −35.0000 + 12.1244i −0.0699934 + 0.0242464i
\(64\) 64.0000 0.125000
\(65\) −315.000 + 545.596i −0.601091 + 1.04112i
\(66\) −285.000 493.634i −0.531531 0.920639i
\(67\) −209.500 362.865i −0.382007 0.661656i 0.609342 0.792908i \(-0.291434\pi\)
−0.991349 + 0.131251i \(0.958100\pi\)
\(68\) −102.000 + 176.669i −0.181902 + 0.315063i
\(69\) −345.000 −0.601929
\(70\) 63.0000 327.358i 0.107571 0.558953i
\(71\) −96.0000 −0.160466 −0.0802331 0.996776i \(-0.525566\pi\)
−0.0802331 + 0.996776i \(0.525566\pi\)
\(72\) 8.00000 13.8564i 0.0130946 0.0226805i
\(73\) 156.500 + 271.066i 0.250917 + 0.434601i 0.963779 0.266704i \(-0.0859346\pi\)
−0.712862 + 0.701305i \(0.752601\pi\)
\(74\) 253.000 + 438.209i 0.397441 + 0.688388i
\(75\) −110.000 + 190.526i −0.169356 + 0.293333i
\(76\) 20.0000 0.0301863
\(77\) 199.500 1036.63i 0.295261 1.53422i
\(78\) 700.000 1.01615
\(79\) −230.500 + 399.238i −0.328269 + 0.568579i −0.982169 0.188003i \(-0.939799\pi\)
0.653899 + 0.756582i \(0.273132\pi\)
\(80\) 72.0000 + 124.708i 0.100623 + 0.174284i
\(81\) 335.500 + 581.103i 0.460219 + 0.797124i
\(82\) 42.0000 72.7461i 0.0565625 0.0979691i
\(83\) −588.000 −0.777607 −0.388804 0.921321i \(-0.627112\pi\)
−0.388804 + 0.921321i \(0.627112\pi\)
\(84\) −350.000 + 121.244i −0.454621 + 0.157485i
\(85\) −459.000 −0.585712
\(86\) 124.000 214.774i 0.155480 0.269299i
\(87\) 285.000 + 493.634i 0.351209 + 0.608312i
\(88\) 228.000 + 394.908i 0.276192 + 0.478378i
\(89\) 508.500 880.748i 0.605628 1.04898i −0.386324 0.922363i \(-0.626255\pi\)
0.991952 0.126615i \(-0.0404114\pi\)
\(90\) 36.0000 0.0421637
\(91\) 980.000 + 848.705i 1.12892 + 0.977675i
\(92\) 276.000 0.312772
\(93\) 57.5000 99.5929i 0.0641126 0.111046i
\(94\) −201.000 348.142i −0.220549 0.382001i
\(95\) 22.5000 + 38.9711i 0.0242995 + 0.0420879i
\(96\) 80.0000 138.564i 0.0850517 0.147314i
\(97\) −1834.00 −1.91974 −0.959868 0.280451i \(-0.909516\pi\)
−0.959868 + 0.280451i \(0.909516\pi\)
\(98\) −637.000 254.611i −0.656599 0.262445i
\(99\) 114.000 0.115732
\(100\) 88.0000 152.420i 0.0880000 0.152420i
\(101\) 142.500 + 246.817i 0.140389 + 0.243161i 0.927643 0.373468i \(-0.121831\pi\)
−0.787254 + 0.616629i \(0.788498\pi\)
\(102\) 255.000 + 441.673i 0.247537 + 0.428746i
\(103\) 249.500 432.147i 0.238679 0.413405i −0.721656 0.692252i \(-0.756619\pi\)
0.960336 + 0.278847i \(0.0899522\pi\)
\(104\) −560.000 −0.528005
\(105\) −630.000 545.596i −0.585540 0.507093i
\(106\) −786.000 −0.720218
\(107\) 553.500 958.690i 0.500083 0.866169i −0.499917 0.866073i \(-0.666636\pi\)
1.00000 9.56665e-5i \(-3.04516e-5\pi\)
\(108\) −290.000 502.295i −0.258382 0.447531i
\(109\) −461.500 799.341i −0.405538 0.702413i 0.588846 0.808246i \(-0.299583\pi\)
−0.994384 + 0.105832i \(0.966249\pi\)
\(110\) −513.000 + 888.542i −0.444660 + 0.770174i
\(111\) 1265.00 1.08170
\(112\) 280.000 96.9948i 0.236228 0.0818317i
\(113\) 1542.00 1.28371 0.641855 0.766826i \(-0.278165\pi\)
0.641855 + 0.766826i \(0.278165\pi\)
\(114\) 25.0000 43.3013i 0.0205392 0.0355749i
\(115\) 310.500 + 537.802i 0.251776 + 0.436089i
\(116\) −228.000 394.908i −0.182494 0.316088i
\(117\) −70.0000 + 121.244i −0.0553120 + 0.0958032i
\(118\) 438.000 0.341705
\(119\) −178.500 + 927.513i −0.137505 + 0.714496i
\(120\) 360.000 0.273861
\(121\) −959.000 + 1661.04i −0.720511 + 1.24796i
\(122\) 709.000 + 1228.02i 0.526146 + 0.911312i
\(123\) −105.000 181.865i −0.0769718 0.133319i
\(124\) −46.0000 + 79.6743i −0.0333139 + 0.0577013i
\(125\) 1521.00 1.08834
\(126\) 14.0000 72.7461i 0.00989856 0.0514344i
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) −64.0000 + 110.851i −0.0441942 + 0.0765466i
\(129\) −310.000 536.936i −0.211581 0.366469i
\(130\) −630.000 1091.19i −0.425036 0.736184i
\(131\) −1024.50 + 1774.49i −0.683290 + 1.18349i 0.290681 + 0.956820i \(0.406118\pi\)
−0.973971 + 0.226673i \(0.927215\pi\)
\(132\) 1140.00 0.751699
\(133\) 87.5000 30.3109i 0.0570467 0.0197616i
\(134\) 838.000 0.540240
\(135\) 652.500 1130.16i 0.415987 0.720511i
\(136\) −204.000 353.338i −0.128624 0.222783i
\(137\) 70.5000 + 122.110i 0.0439651 + 0.0761498i 0.887171 0.461442i \(-0.152668\pi\)
−0.843205 + 0.537591i \(0.819334\pi\)
\(138\) 345.000 597.558i 0.212814 0.368605i
\(139\) 1484.00 0.905548 0.452774 0.891625i \(-0.350434\pi\)
0.452774 + 0.891625i \(0.350434\pi\)
\(140\) 504.000 + 436.477i 0.304256 + 0.263493i
\(141\) −1005.00 −0.600257
\(142\) 96.0000 166.277i 0.0567334 0.0982651i
\(143\) −1995.00 3455.44i −1.16665 2.02069i
\(144\) 16.0000 + 27.7128i 0.00925926 + 0.0160375i
\(145\) 513.000 888.542i 0.293809 0.508892i
\(146\) −626.000 −0.354850
\(147\) −1347.50 + 1060.88i −0.756054 + 0.595238i
\(148\) −1012.00 −0.562067
\(149\) 28.5000 49.3634i 0.0156699 0.0271410i −0.858084 0.513509i \(-0.828345\pi\)
0.873754 + 0.486368i \(0.161679\pi\)
\(150\) −220.000 381.051i −0.119753 0.207418i
\(151\) −419.500 726.595i −0.226082 0.391586i 0.730561 0.682847i \(-0.239258\pi\)
−0.956644 + 0.291261i \(0.905925\pi\)
\(152\) −20.0000 + 34.6410i −0.0106725 + 0.0184852i
\(153\) −102.000 −0.0538968
\(154\) 1596.00 + 1382.18i 0.835126 + 0.723240i
\(155\) −207.000 −0.107269
\(156\) −700.000 + 1212.44i −0.359262 + 0.622260i
\(157\) 1416.50 + 2453.45i 0.720057 + 1.24718i 0.960976 + 0.276631i \(0.0892179\pi\)
−0.240919 + 0.970545i \(0.577449\pi\)
\(158\) −461.000 798.475i −0.232121 0.402046i
\(159\) −982.500 + 1701.74i −0.490046 + 0.848785i
\(160\) −288.000 −0.142302
\(161\) 1207.50 418.290i 0.591083 0.204757i
\(162\) −1342.00 −0.650849
\(163\) 1155.50 2001.38i 0.555250 0.961721i −0.442634 0.896702i \(-0.645956\pi\)
0.997884 0.0650188i \(-0.0207107\pi\)
\(164\) 84.0000 + 145.492i 0.0399957 + 0.0692746i
\(165\) 1282.50 + 2221.36i 0.605106 + 1.04807i
\(166\) 588.000 1018.45i 0.274926 0.476185i
\(167\) 1260.00 0.583843 0.291921 0.956442i \(-0.405705\pi\)
0.291921 + 0.956442i \(0.405705\pi\)
\(168\) 140.000 727.461i 0.0642931 0.334077i
\(169\) 2703.00 1.23031
\(170\) 459.000 795.011i 0.207081 0.358674i
\(171\) 5.00000 + 8.66025i 0.00223602 + 0.00387290i
\(172\) 248.000 + 429.549i 0.109941 + 0.190423i
\(173\) −1633.50 + 2829.30i −0.717877 + 1.24340i 0.243962 + 0.969785i \(0.421553\pi\)
−0.961839 + 0.273615i \(0.911781\pi\)
\(174\) −1140.00 −0.496685
\(175\) 154.000 800.207i 0.0665217 0.345657i
\(176\) −912.000 −0.390594
\(177\) 547.500 948.298i 0.232501 0.402703i
\(178\) 1017.00 + 1761.50i 0.428244 + 0.741740i
\(179\) −643.500 1114.57i −0.268701 0.465403i 0.699826 0.714314i \(-0.253261\pi\)
−0.968527 + 0.248910i \(0.919928\pi\)
\(180\) −36.0000 + 62.3538i −0.0149071 + 0.0258199i
\(181\) −2674.00 −1.09810 −0.549052 0.835788i \(-0.685011\pi\)
−0.549052 + 0.835788i \(0.685011\pi\)
\(182\) −2450.00 + 848.705i −0.997836 + 0.345660i
\(183\) 3545.00 1.43199
\(184\) −276.000 + 478.046i −0.110581 + 0.191533i
\(185\) −1138.50 1971.94i −0.452455 0.783675i
\(186\) 115.000 + 199.186i 0.0453345 + 0.0785216i
\(187\) 1453.50 2517.54i 0.568398 0.984494i
\(188\) 804.000 0.311903
\(189\) −2030.00 1758.03i −0.781274 0.676603i
\(190\) −90.0000 −0.0343647
\(191\) −2092.50 + 3624.32i −0.792712 + 1.37302i 0.131570 + 0.991307i \(0.457998\pi\)
−0.924282 + 0.381711i \(0.875335\pi\)
\(192\) 160.000 + 277.128i 0.0601407 + 0.104167i
\(193\) 42.5000 + 73.6122i 0.0158509 + 0.0274545i 0.873842 0.486210i \(-0.161621\pi\)
−0.857991 + 0.513664i \(0.828288\pi\)
\(194\) 1834.00 3176.58i 0.678730 1.17559i
\(195\) −3150.00 −1.15680
\(196\) 1078.00 848.705i 0.392857 0.309295i
\(197\) −390.000 −0.141047 −0.0705237 0.997510i \(-0.522467\pi\)
−0.0705237 + 0.997510i \(0.522467\pi\)
\(198\) −114.000 + 197.454i −0.0409173 + 0.0708709i
\(199\) 1416.50 + 2453.45i 0.504588 + 0.873972i 0.999986 + 0.00530596i \(0.00168895\pi\)
−0.495398 + 0.868666i \(0.664978\pi\)
\(200\) 176.000 + 304.841i 0.0622254 + 0.107778i
\(201\) 1047.50 1814.32i 0.367587 0.636679i
\(202\) −570.000 −0.198540
\(203\) −1596.00 1382.18i −0.551809 0.477881i
\(204\) −1020.00 −0.350070
\(205\) −189.000 + 327.358i −0.0643919 + 0.111530i
\(206\) 499.000 + 864.293i 0.168772 + 0.292321i
\(207\) 69.0000 + 119.512i 0.0231683 + 0.0401286i
\(208\) 560.000 969.948i 0.186678 0.323336i
\(209\) −285.000 −0.0943247
\(210\) 1575.00 545.596i 0.517549 0.179284i
\(211\) −124.000 −0.0404574 −0.0202287 0.999795i \(-0.506439\pi\)
−0.0202287 + 0.999795i \(0.506439\pi\)
\(212\) 786.000 1361.39i 0.254635 0.441041i
\(213\) −240.000 415.692i −0.0772044 0.133722i
\(214\) 1107.00 + 1917.38i 0.353612 + 0.612474i
\(215\) −558.000 + 966.484i −0.177001 + 0.306575i
\(216\) 1160.00 0.365407
\(217\) −80.5000 + 418.290i −0.0251829 + 0.130854i
\(218\) 1846.00 0.573518
\(219\) −782.500 + 1355.33i −0.241445 + 0.418195i
\(220\) −1026.00 1777.08i −0.314422 0.544595i
\(221\) 1785.00 + 3091.71i 0.543313 + 0.941045i
\(222\) −1265.00 + 2191.04i −0.382438 + 0.662402i
\(223\) 56.0000 0.0168163 0.00840816 0.999965i \(-0.497324\pi\)
0.00840816 + 0.999965i \(0.497324\pi\)
\(224\) −112.000 + 581.969i −0.0334077 + 0.173591i
\(225\) 88.0000 0.0260741
\(226\) −1542.00 + 2670.82i −0.453860 + 0.786108i
\(227\) 1528.50 + 2647.44i 0.446917 + 0.774083i 0.998184 0.0602465i \(-0.0191887\pi\)
−0.551267 + 0.834329i \(0.685855\pi\)
\(228\) 50.0000 + 86.6025i 0.0145234 + 0.0251552i
\(229\) 480.500 832.250i 0.138656 0.240160i −0.788332 0.615250i \(-0.789055\pi\)
0.926988 + 0.375090i \(0.122388\pi\)
\(230\) −1242.00 −0.356065
\(231\) 4987.50 1727.72i 1.42058 0.492102i
\(232\) 912.000 0.258085
\(233\) 1414.50 2449.99i 0.397712 0.688858i −0.595731 0.803184i \(-0.703138\pi\)
0.993443 + 0.114326i \(0.0364709\pi\)
\(234\) −140.000 242.487i −0.0391115 0.0677431i
\(235\) 904.500 + 1566.64i 0.251077 + 0.434878i
\(236\) −438.000 + 758.638i −0.120811 + 0.209251i
\(237\) −2305.00 −0.631755
\(238\) −1428.00 1236.68i −0.388922 0.336817i
\(239\) −3540.00 −0.958090 −0.479045 0.877790i \(-0.659017\pi\)
−0.479045 + 0.877790i \(0.659017\pi\)
\(240\) −360.000 + 623.538i −0.0968246 + 0.167705i
\(241\) −2615.50 4530.18i −0.699084 1.21085i −0.968785 0.247904i \(-0.920258\pi\)
0.269701 0.962944i \(-0.413075\pi\)
\(242\) −1918.00 3322.07i −0.509478 0.882442i
\(243\) 280.000 484.974i 0.0739177 0.128029i
\(244\) −2836.00 −0.744083
\(245\) 2866.50 + 1145.75i 0.747486 + 0.298773i
\(246\) 420.000 0.108855
\(247\) 175.000 303.109i 0.0450809 0.0780824i
\(248\) −92.0000 159.349i −0.0235565 0.0408010i
\(249\) −1470.00 2546.11i −0.374126 0.648006i
\(250\) −1521.00 + 2634.45i −0.384786 + 0.666469i
\(251\) 5040.00 1.26742 0.633709 0.773571i \(-0.281532\pi\)
0.633709 + 0.773571i \(0.281532\pi\)
\(252\) 112.000 + 96.9948i 0.0279974 + 0.0242464i
\(253\) −3933.00 −0.977334
\(254\) 2056.00 3561.10i 0.507893 0.879697i
\(255\) −1147.50 1987.53i −0.281801 0.488094i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 718.500 1244.48i 0.174392 0.302056i −0.765559 0.643366i \(-0.777537\pi\)
0.939951 + 0.341310i \(0.110871\pi\)
\(258\) 1240.00 0.299221
\(259\) −4427.50 + 1533.73i −1.06221 + 0.367959i
\(260\) 2520.00 0.601091
\(261\) 114.000 197.454i 0.0270361 0.0468279i
\(262\) −2049.00 3548.97i −0.483159 0.836856i
\(263\) 1162.50 + 2013.51i 0.272558 + 0.472085i 0.969516 0.245027i \(-0.0787969\pi\)
−0.696958 + 0.717112i \(0.745464\pi\)
\(264\) −1140.00 + 1974.54i −0.265766 + 0.460320i
\(265\) 3537.00 0.819910
\(266\) −35.0000 + 181.865i −0.00806762 + 0.0419206i
\(267\) 5085.00 1.16553
\(268\) −838.000 + 1451.46i −0.191004 + 0.330828i
\(269\) 1192.50 + 2065.47i 0.270290 + 0.468156i 0.968936 0.247311i \(-0.0795471\pi\)
−0.698646 + 0.715467i \(0.746214\pi\)
\(270\) 1305.00 + 2260.33i 0.294147 + 0.509478i
\(271\) 165.500 286.654i 0.0370975 0.0642547i −0.846881 0.531783i \(-0.821522\pi\)
0.883978 + 0.467528i \(0.154855\pi\)
\(272\) 816.000 0.181902
\(273\) −1225.00 + 6365.29i −0.271576 + 1.41115i
\(274\) −282.000 −0.0621761
\(275\) −1254.00 + 2171.99i −0.274978 + 0.476276i
\(276\) 690.000 + 1195.12i 0.150482 + 0.260643i
\(277\) −2435.50 4218.41i −0.528285 0.915017i −0.999456 0.0329750i \(-0.989502\pi\)
0.471171 0.882042i \(-0.343831\pi\)
\(278\) −1484.00 + 2570.36i −0.320160 + 0.554533i
\(279\) −46.0000 −0.00987078
\(280\) −1260.00 + 436.477i −0.268926 + 0.0931589i
\(281\) −7026.00 −1.49159 −0.745794 0.666177i \(-0.767930\pi\)
−0.745794 + 0.666177i \(0.767930\pi\)
\(282\) 1005.00 1740.71i 0.212223 0.367581i
\(283\) 2676.50 + 4635.83i 0.562196 + 0.973752i 0.997305 + 0.0733738i \(0.0233766\pi\)
−0.435109 + 0.900378i \(0.643290\pi\)
\(284\) 192.000 + 332.554i 0.0401166 + 0.0694839i
\(285\) −112.500 + 194.856i −0.0233822 + 0.0404991i
\(286\) 7980.00 1.64989
\(287\) 588.000 + 509.223i 0.120936 + 0.104733i
\(288\) −64.0000 −0.0130946
\(289\) 1156.00 2002.25i 0.235294 0.407541i
\(290\) 1026.00 + 1777.08i 0.207754 + 0.359841i
\(291\) −4585.00 7941.45i −0.923634 1.59978i
\(292\) 626.000 1084.26i 0.125458 0.217300i
\(293\) 4158.00 0.829054 0.414527 0.910037i \(-0.363947\pi\)
0.414527 + 0.910037i \(0.363947\pi\)
\(294\) −490.000 3394.82i −0.0972020 0.673435i
\(295\) −1971.00 −0.389004
\(296\) 1012.00 1752.84i 0.198721 0.344194i
\(297\) 4132.50 + 7157.70i 0.807380 + 1.39842i
\(298\) 57.0000 + 98.7269i 0.0110803 + 0.0191916i
\(299\) 2415.00 4182.90i 0.467101 0.809042i
\(300\) 880.000 0.169356
\(301\) 1736.00 + 1503.42i 0.332430 + 0.287893i
\(302\) 1678.00 0.319729
\(303\) −712.500 + 1234.09i −0.135089 + 0.233982i
\(304\) −40.0000 69.2820i −0.00754657 0.0130710i
\(305\) −3190.50 5526.11i −0.598975 1.03746i
\(306\) 102.000 176.669i 0.0190554 0.0330049i
\(307\) −9604.00 −1.78544 −0.892719 0.450615i \(-0.851205\pi\)
−0.892719 + 0.450615i \(0.851205\pi\)
\(308\) −3990.00 + 1382.18i −0.738154 + 0.255704i
\(309\) 2495.00 0.459338
\(310\) 207.000 358.535i 0.0379252 0.0656884i
\(311\) −5065.50 8773.70i −0.923595 1.59971i −0.793805 0.608173i \(-0.791903\pi\)
−0.129791 0.991541i \(-0.541430\pi\)
\(312\) −1400.00 2424.87i −0.254037 0.440004i
\(313\) −5399.50 + 9352.21i −0.975073 + 1.68888i −0.295378 + 0.955380i \(0.595446\pi\)
−0.679695 + 0.733495i \(0.737888\pi\)
\(314\) −5666.00 −1.01831
\(315\) −63.0000 + 327.358i −0.0112687 + 0.0585540i
\(316\) 1844.00 0.328269
\(317\) −265.500 + 459.859i −0.0470409 + 0.0814772i −0.888587 0.458708i \(-0.848312\pi\)
0.841546 + 0.540185i \(0.181646\pi\)
\(318\) −1965.00 3403.48i −0.346515 0.600181i
\(319\) 3249.00 + 5627.43i 0.570248 + 0.987698i
\(320\) 288.000 498.831i 0.0503115 0.0871421i
\(321\) 5535.00 0.962410
\(322\) −483.000 + 2509.74i −0.0835917 + 0.434355i
\(323\) 255.000 0.0439275
\(324\) 1342.00 2324.41i 0.230110 0.398562i
\(325\) −1540.00 2667.36i −0.262843 0.455257i
\(326\) 2311.00 + 4002.77i 0.392621 + 0.680040i
\(327\) 2307.50 3996.71i 0.390229 0.675897i
\(328\) −336.000 −0.0565625
\(329\) 3517.50 1218.50i 0.589441 0.204188i
\(330\) −5130.00 −0.855749
\(331\) 3507.50 6075.17i 0.582446 1.00883i −0.412743 0.910848i \(-0.635429\pi\)
0.995189 0.0979784i \(-0.0312376\pi\)
\(332\) 1176.00 + 2036.89i 0.194402 + 0.336714i
\(333\) −253.000 438.209i −0.0416346 0.0721132i
\(334\) −1260.00 + 2182.38i −0.206420 + 0.357529i
\(335\) −3771.00 −0.615020
\(336\) 1120.00 + 969.948i 0.181848 + 0.157485i
\(337\) 8990.00 1.45316 0.726582 0.687079i \(-0.241108\pi\)
0.726582 + 0.687079i \(0.241108\pi\)
\(338\) −2703.00 + 4681.73i −0.434982 + 0.753410i
\(339\) 3855.00 + 6677.06i 0.617625 + 1.06976i
\(340\) 918.000 + 1590.02i 0.146428 + 0.253621i
\(341\) 655.500 1135.36i 0.104098 0.180303i
\(342\) −20.0000 −0.00316221
\(343\) 3430.00 5346.84i 0.539949 0.841698i
\(344\) −992.000 −0.155480
\(345\) −1552.50 + 2689.01i −0.242272 + 0.419627i
\(346\) −3267.00 5658.61i −0.507616 0.879216i
\(347\) 4354.50 + 7542.22i 0.673665 + 1.16682i 0.976857 + 0.213893i \(0.0686143\pi\)
−0.303192 + 0.952929i \(0.598052\pi\)
\(348\) 1140.00 1974.54i 0.175605 0.304156i
\(349\) 6482.00 0.994193 0.497097 0.867695i \(-0.334399\pi\)
0.497097 + 0.867695i \(0.334399\pi\)
\(350\) 1232.00 + 1066.94i 0.188152 + 0.162944i
\(351\) −10150.0 −1.54350
\(352\) 912.000 1579.63i 0.138096 0.239189i
\(353\) 1066.50 + 1847.23i 0.160805 + 0.278522i 0.935158 0.354232i \(-0.115258\pi\)
−0.774353 + 0.632754i \(0.781924\pi\)
\(354\) 1095.00 + 1896.60i 0.164403 + 0.284754i
\(355\) −432.000 + 748.246i −0.0645864 + 0.111867i
\(356\) −4068.00 −0.605628
\(357\) −4462.50 + 1545.86i −0.661570 + 0.229175i
\(358\) 2574.00 0.380000
\(359\) −1924.50 + 3333.33i −0.282928 + 0.490046i −0.972105 0.234548i \(-0.924639\pi\)
0.689176 + 0.724594i \(0.257972\pi\)
\(360\) −72.0000 124.708i −0.0105409 0.0182574i
\(361\) 3417.00 + 5918.42i 0.498178 + 0.862869i
\(362\) 2674.00 4631.50i 0.388238 0.672449i
\(363\) −9590.00 −1.38662
\(364\) 980.000 5092.23i 0.141115 0.733256i
\(365\) 2817.00 0.403969
\(366\) −3545.00 + 6140.12i −0.506284 + 0.876910i
\(367\) −3245.50 5621.37i −0.461618 0.799545i 0.537424 0.843312i \(-0.319397\pi\)
−0.999042 + 0.0437668i \(0.986064\pi\)
\(368\) −552.000 956.092i −0.0781929 0.135434i
\(369\) −42.0000 + 72.7461i −0.00592529 + 0.0102629i
\(370\) 4554.00 0.639868
\(371\) 1375.50 7147.31i 0.192486 1.00019i
\(372\) −460.000 −0.0641126
\(373\) −461.500 + 799.341i −0.0640632 + 0.110961i −0.896278 0.443493i \(-0.853739\pi\)
0.832215 + 0.554453i \(0.187073\pi\)
\(374\) 2907.00 + 5035.07i 0.401918 + 0.696143i
\(375\) 3802.50 + 6586.12i 0.523627 + 0.906949i
\(376\) −804.000 + 1392.57i −0.110274 + 0.191001i
\(377\) −7980.00 −1.09016
\(378\) 5075.00 1758.03i 0.690555 0.239215i
\(379\) 6344.00 0.859814 0.429907 0.902873i \(-0.358546\pi\)
0.429907 + 0.902873i \(0.358546\pi\)
\(380\) 90.0000 155.885i 0.0121497 0.0210440i
\(381\) −5140.00 8902.74i −0.691155 1.19712i
\(382\) −4185.00 7248.63i −0.560532 0.970870i
\(383\) 2503.50 4336.19i 0.334002 0.578509i −0.649290 0.760541i \(-0.724934\pi\)
0.983293 + 0.182032i \(0.0582673\pi\)
\(384\) −640.000 −0.0850517
\(385\) −7182.00 6219.79i −0.950724 0.823351i
\(386\) −170.000 −0.0224165
\(387\) −124.000 + 214.774i −0.0162875 + 0.0282108i
\(388\) 3668.00 + 6353.16i 0.479934 + 0.831270i
\(389\) −6145.50 10644.3i −0.801001 1.38737i −0.918958 0.394355i \(-0.870968\pi\)
0.117958 0.993019i \(-0.462365\pi\)
\(390\) 3150.00 5455.96i 0.408991 0.708393i
\(391\) 3519.00 0.455150
\(392\) 392.000 + 2715.86i 0.0505076 + 0.349927i
\(393\) −10245.0 −1.31499
\(394\) 390.000 675.500i 0.0498678 0.0863736i
\(395\) 2074.50 + 3593.14i 0.264252 + 0.457697i
\(396\) −228.000 394.908i −0.0289329 0.0501133i
\(397\) −443.500 + 768.165i −0.0560671 + 0.0971110i −0.892697 0.450658i \(-0.851189\pi\)
0.836630 + 0.547769i \(0.184523\pi\)
\(398\) −5666.00 −0.713595
\(399\) 350.000 + 303.109i 0.0439146 + 0.0380311i
\(400\) −704.000 −0.0880000
\(401\) −5977.50 + 10353.3i −0.744394 + 1.28933i 0.206083 + 0.978535i \(0.433928\pi\)
−0.950477 + 0.310794i \(0.899405\pi\)
\(402\) 2095.00 + 3628.65i 0.259923 + 0.450200i
\(403\) 805.000 + 1394.30i 0.0995035 + 0.172345i
\(404\) 570.000 987.269i 0.0701945 0.121580i
\(405\) 6039.00 0.740939
\(406\) 3990.00 1382.18i 0.487735 0.168956i
\(407\) 14421.0 1.75632
\(408\) 1020.00 1766.69i 0.123768 0.214373i
\(409\) 1710.50 + 2962.67i 0.206794 + 0.358178i 0.950703 0.310103i \(-0.100364\pi\)
−0.743909 + 0.668281i \(0.767030\pi\)
\(410\) −378.000 654.715i −0.0455319 0.0788636i
\(411\) −352.500 + 610.548i −0.0423055 + 0.0732752i
\(412\) −1996.00 −0.238679
\(413\) −766.500 + 3982.85i −0.0913245 + 0.474536i
\(414\) −276.000 −0.0327649
\(415\) −2646.00 + 4583.01i −0.312981 + 0.542099i
\(416\) 1120.00 + 1939.90i 0.132001 + 0.228633i
\(417\) 3710.00 + 6425.91i 0.435682 + 0.754624i
\(418\) 285.000 493.634i 0.0333488 0.0577618i
\(419\) −5460.00 −0.636607 −0.318304 0.947989i \(-0.603113\pi\)
−0.318304 + 0.947989i \(0.603113\pi\)
\(420\) −630.000 + 3273.58i −0.0731925 + 0.380319i
\(421\) 7730.00 0.894863 0.447431 0.894318i \(-0.352339\pi\)
0.447431 + 0.894318i \(0.352339\pi\)
\(422\) 124.000 214.774i 0.0143039 0.0247750i
\(423\) 201.000 + 348.142i 0.0231039 + 0.0400171i
\(424\) 1572.00 + 2722.78i 0.180054 + 0.311863i
\(425\) 1122.00 1943.36i 0.128059 0.221804i
\(426\) 960.000 0.109183
\(427\) −12407.5 + 4298.08i −1.40619 + 0.487117i
\(428\) −4428.00 −0.500083
\(429\) 9975.00 17277.2i 1.12260 1.94441i
\(430\) −1116.00 1932.97i −0.125159 0.216781i
\(431\) 5656.50 + 9797.35i 0.632167 + 1.09495i 0.987108 + 0.160057i \(0.0511677\pi\)
−0.354941 + 0.934889i \(0.615499\pi\)
\(432\) −1160.00 + 2009.18i −0.129191 + 0.223765i
\(433\) 4214.00 0.467695 0.233847 0.972273i \(-0.424868\pi\)
0.233847 + 0.972273i \(0.424868\pi\)
\(434\) −644.000 557.720i −0.0712281 0.0616853i
\(435\) 5130.00 0.565436
\(436\) −1846.00 + 3197.37i −0.202769 + 0.351207i
\(437\) −172.500 298.779i −0.0188828 0.0327060i
\(438\) −1565.00 2710.66i −0.170727 0.295708i
\(439\) −8276.50 + 14335.3i −0.899808 + 1.55851i −0.0720696 + 0.997400i \(0.522960\pi\)
−0.827739 + 0.561114i \(0.810373\pi\)
\(440\) 4104.00 0.444660
\(441\) 637.000 + 254.611i 0.0687831 + 0.0274929i
\(442\) −7140.00 −0.768360
\(443\) 8197.50 14198.5i 0.879176 1.52278i 0.0269294 0.999637i \(-0.491427\pi\)
0.852247 0.523140i \(-0.175240\pi\)
\(444\) −2530.00 4382.09i −0.270425 0.468389i
\(445\) −4576.50 7926.73i −0.487521 0.844411i
\(446\) −56.0000 + 96.9948i −0.00594546 + 0.0102978i
\(447\) 285.000 0.0301567
\(448\) −896.000 775.959i −0.0944911 0.0818317i
\(449\) −15090.0 −1.58606 −0.793030 0.609182i \(-0.791498\pi\)
−0.793030 + 0.609182i \(0.791498\pi\)
\(450\) −88.0000 + 152.420i −0.00921858 + 0.0159670i
\(451\) −1197.00 2073.26i −0.124977 0.216466i
\(452\) −3084.00 5341.64i −0.320927 0.555862i
\(453\) 2097.50 3632.98i 0.217548 0.376804i
\(454\) −6114.00 −0.632036
\(455\) 11025.0 3819.17i 1.13596 0.393507i
\(456\) −200.000 −0.0205392
\(457\) 7392.50 12804.2i 0.756688 1.31062i −0.187842 0.982199i \(-0.560149\pi\)
0.944531 0.328423i \(-0.106517\pi\)
\(458\) 961.000 + 1664.50i 0.0980449 + 0.169819i
\(459\) −3697.50 6404.26i −0.376001 0.651253i
\(460\) 1242.00 2151.21i 0.125888 0.218045i
\(461\) 2898.00 0.292784 0.146392 0.989227i \(-0.453234\pi\)
0.146392 + 0.989227i \(0.453234\pi\)
\(462\) −1995.00 + 10366.3i −0.200900 + 1.04391i
\(463\) 464.000 0.0465743 0.0232872 0.999729i \(-0.492587\pi\)
0.0232872 + 0.999729i \(0.492587\pi\)
\(464\) −912.000 + 1579.63i −0.0912468 + 0.158044i
\(465\) −517.500 896.336i −0.0516097 0.0893905i
\(466\) 2829.00 + 4899.97i 0.281225 + 0.487096i
\(467\) −2116.50 + 3665.89i −0.209721 + 0.363248i −0.951627 0.307256i \(-0.900589\pi\)
0.741905 + 0.670505i \(0.233922\pi\)
\(468\) 560.000 0.0553120
\(469\) −1466.50 + 7620.16i −0.144385 + 0.750248i
\(470\) −3618.00 −0.355076
\(471\) −7082.50 + 12267.2i −0.692876 + 1.20010i
\(472\) −876.000 1517.28i −0.0854262 0.147963i
\(473\) −3534.00 6121.07i −0.343538 0.595025i
\(474\) 2305.00 3992.38i 0.223359 0.386869i
\(475\) −220.000 −0.0212511
\(476\) 3570.00 1236.68i 0.343762 0.119083i
\(477\) 786.000 0.0754475
\(478\) 3540.00 6131.46i 0.338736 0.586708i
\(479\) −1369.50 2372.04i −0.130635 0.226266i 0.793287 0.608848i \(-0.208368\pi\)
−0.923921 + 0.382582i \(0.875035\pi\)
\(480\) −720.000 1247.08i −0.0684653 0.118585i
\(481\) −8855.00 + 15337.3i −0.839404 + 1.45389i
\(482\) 10462.0 0.988654
\(483\) 4830.00 + 4182.90i 0.455016 + 0.394055i
\(484\) 7672.00 0.720511
\(485\) −8253.00 + 14294.6i −0.772679 + 1.33832i
\(486\) 560.000 + 969.948i 0.0522677 + 0.0905304i
\(487\) −8525.50 14766.6i −0.793280 1.37400i −0.923926 0.382572i \(-0.875038\pi\)
0.130646 0.991429i \(-0.458295\pi\)
\(488\) 2836.00 4912.10i 0.263073 0.455656i
\(489\) 11555.0 1.06858
\(490\) −4851.00 + 3819.17i −0.447236 + 0.352107i
\(491\) −4296.00 −0.394859 −0.197429 0.980317i \(-0.563259\pi\)
−0.197429 + 0.980317i \(0.563259\pi\)
\(492\) −420.000 + 727.461i −0.0384859 + 0.0666595i
\(493\) −2907.00 5035.07i −0.265567 0.459976i
\(494\) 350.000 + 606.218i 0.0318770 + 0.0552126i
\(495\) 513.000 888.542i 0.0465811 0.0806808i
\(496\) 368.000 0.0333139
\(497\) 1344.00 + 1163.94i 0.121301 + 0.105050i
\(498\) 5880.00 0.529095
\(499\) −1700.50 + 2945.35i −0.152555 + 0.264233i −0.932166 0.362031i \(-0.882083\pi\)
0.779611 + 0.626264i \(0.215417\pi\)
\(500\) −3042.00 5268.90i −0.272085 0.471265i
\(501\) 3150.00 + 5455.96i 0.280901 + 0.486536i
\(502\) −5040.00 + 8729.54i −0.448100 + 0.776132i
\(503\) 16800.0 1.48921 0.744607 0.667503i \(-0.232637\pi\)
0.744607 + 0.667503i \(0.232637\pi\)
\(504\) −280.000 + 96.9948i −0.0247464 + 0.00857241i
\(505\) 2565.00 0.226022
\(506\) 3933.00 6812.16i 0.345540 0.598493i
\(507\) 6757.50 + 11704.3i 0.591935 + 1.02526i
\(508\) 4112.00 + 7122.19i 0.359135 + 0.622040i
\(509\) −919.500 + 1592.62i −0.0800710 + 0.138687i −0.903280 0.429051i \(-0.858848\pi\)
0.823209 + 0.567738i \(0.192181\pi\)
\(510\) 4590.00 0.398527
\(511\) 1095.50 5692.38i 0.0948377 0.492791i
\(512\) 512.000 0.0441942
\(513\) −362.500 + 627.868i −0.0311984 + 0.0540372i
\(514\) 1437.00 + 2488.96i 0.123314 + 0.213586i
\(515\) −2245.50 3889.32i −0.192133 0.332784i
\(516\) −1240.00 + 2147.74i −0.105791 + 0.183235i
\(517\) −11457.0 −0.974620
\(518\) 1771.00 9202.39i 0.150219 0.780559i
\(519\) −16335.0 −1.38155
\(520\) −2520.00 + 4364.77i −0.212518 + 0.368092i
\(521\) −151.500 262.406i −0.0127396 0.0220656i 0.859585 0.510992i \(-0.170722\pi\)
−0.872325 + 0.488927i \(0.837389\pi\)
\(522\) 228.000 + 394.908i 0.0191174 + 0.0331123i
\(523\) 10833.5 18764.2i 0.905767 1.56883i 0.0858815 0.996305i \(-0.472629\pi\)
0.819885 0.572528i \(-0.194037\pi\)
\(524\) 8196.00 0.683290
\(525\) 3850.00 1333.68i 0.320053 0.110870i
\(526\) −4650.00 −0.385456
\(527\) −586.500 + 1015.85i −0.0484788 + 0.0839678i
\(528\) −2280.00 3949.08i −0.187925 0.325495i
\(529\) 3703.00 + 6413.78i 0.304348 + 0.527146i
\(530\) −3537.00 + 6126.26i −0.289882 + 0.502090i
\(531\) −438.000 −0.0357958
\(532\) −280.000 242.487i −0.0228187 0.0197616i
\(533\) 2940.00 0.238922
\(534\) −5085.00 + 8807.48i −0.412078 + 0.713739i
\(535\) −4981.50 8628.21i −0.402559 0.697253i
\(536\) −1676.00 2902.92i −0.135060 0.233931i
\(537\) 3217.50 5572.87i 0.258557 0.447835i
\(538\) −4770.00 −0.382248
\(539\) −15361.5 + 12094.0i −1.22758 + 0.966470i
\(540\) −5220.00 −0.415987
\(541\) −2519.50 + 4363.90i −0.200225 + 0.346800i −0.948601 0.316475i \(-0.897501\pi\)
0.748376 + 0.663275i \(0.230834\pi\)
\(542\) 331.000 + 573.309i 0.0262319 + 0.0454349i
\(543\) −6685.00 11578.8i −0.528326 0.915087i
\(544\) −816.000 + 1413.35i −0.0643120 + 0.111392i
\(545\) −8307.00 −0.652904
\(546\) −9800.00 8487.05i −0.768134 0.665224i
\(547\) −2392.00 −0.186974 −0.0934868 0.995621i \(-0.529801\pi\)
−0.0934868 + 0.995621i \(0.529801\pi\)
\(548\) 282.000 488.438i 0.0219826 0.0380749i
\(549\) −709.000 1228.02i −0.0551173 0.0954659i
\(550\) −2508.00 4343.98i −0.194439 0.336778i
\(551\) −285.000 + 493.634i −0.0220352 + 0.0381661i
\(552\) −2760.00 −0.212814
\(553\) 8067.50 2794.66i 0.620371 0.214903i
\(554\) 9742.00 0.747108
\(555\) 5692.50 9859.70i 0.435375 0.754092i
\(556\) −2968.00 5140.73i −0.226387 0.392114i
\(557\) 11074.5 + 19181.6i 0.842445 + 1.45916i 0.887822 + 0.460187i \(0.152218\pi\)
−0.0453775 + 0.998970i \(0.514449\pi\)
\(558\) 46.0000 79.6743i 0.00348985 0.00604459i
\(559\) 8680.00 0.656753
\(560\) 504.000 2618.86i 0.0380319 0.197620i
\(561\) 14535.0 1.09388
\(562\) 7026.00 12169.4i 0.527356 0.913407i
\(563\) 4174.50 + 7230.45i 0.312494 + 0.541256i 0.978902 0.204332i \(-0.0655022\pi\)
−0.666408 + 0.745588i \(0.732169\pi\)
\(564\) 2010.00 + 3481.42i 0.150064 + 0.259919i
\(565\) 6939.00 12018.7i 0.516683 0.894921i
\(566\) −10706.0 −0.795065
\(567\) 2348.50 12203.2i 0.173947 0.903853i
\(568\) −768.000 −0.0567334
\(569\) 7672.50 13289.2i 0.565286 0.979105i −0.431737 0.902000i \(-0.642099\pi\)
0.997023 0.0771050i \(-0.0245677\pi\)
\(570\) −225.000 389.711i −0.0165337 0.0286372i
\(571\) 5796.50 + 10039.8i 0.424827 + 0.735821i 0.996404 0.0847268i \(-0.0270017\pi\)
−0.571578 + 0.820548i \(0.693668\pi\)
\(572\) −7980.00 + 13821.8i −0.583323 + 1.01034i
\(573\) −20925.0 −1.52557
\(574\) −1470.00 + 509.223i −0.106893 + 0.0370288i
\(575\) −3036.00 −0.220191
\(576\) 64.0000 110.851i 0.00462963 0.00801875i
\(577\) 7296.50 + 12637.9i 0.526442 + 0.911825i 0.999525 + 0.0308071i \(0.00980776\pi\)
−0.473083 + 0.881018i \(0.656859\pi\)
\(578\) 2312.00 + 4004.50i 0.166378 + 0.288175i
\(579\) −212.500 + 368.061i −0.0152525 + 0.0264181i
\(580\) −4104.00 −0.293809
\(581\) 8232.00 + 7129.12i 0.587816 + 0.509063i
\(582\) 18340.0 1.30622
\(583\) −11200.5 + 19399.8i −0.795673 + 1.37815i
\(584\) 1252.00 + 2168.53i 0.0887125 + 0.153655i
\(585\) 630.000 + 1091.19i 0.0445253 + 0.0771201i
\(586\) −4158.00 + 7201.87i −0.293115 + 0.507690i
\(587\) −15372.0 −1.08087 −0.540435 0.841386i \(-0.681740\pi\)
−0.540435 + 0.841386i \(0.681740\pi\)
\(588\) 6370.00 + 2546.11i 0.446759 + 0.178571i
\(589\) 115.000 0.00804498
\(590\) 1971.00 3413.87i 0.137534 0.238215i
\(591\) −975.000 1688.75i −0.0678615 0.117540i
\(592\) 2024.00 + 3505.67i 0.140517 + 0.243382i
\(593\) 7186.50 12447.4i 0.497663 0.861978i −0.502333 0.864674i \(-0.667525\pi\)
0.999996 + 0.00269639i \(0.000858288\pi\)
\(594\) −16530.0 −1.14181
\(595\) 6426.00 + 5565.08i 0.442757 + 0.383439i
\(596\) −228.000 −0.0156699
\(597\) −7082.50 + 12267.2i −0.485540 + 0.840980i
\(598\) 4830.00 + 8365.81i 0.330290 + 0.572079i
\(599\) −1273.50 2205.77i −0.0868678 0.150459i 0.819318 0.573340i \(-0.194352\pi\)
−0.906186 + 0.422880i \(0.861019\pi\)
\(600\) −880.000 + 1524.20i −0.0598764 + 0.103709i
\(601\) −7042.00 −0.477952 −0.238976 0.971025i \(-0.576812\pi\)
−0.238976 + 0.971025i \(0.576812\pi\)
\(602\) −4340.00 + 1503.42i −0.293829 + 0.101785i
\(603\) −838.000 −0.0565937
\(604\) −1678.00 + 2906.38i −0.113041 + 0.195793i
\(605\) 8631.00 + 14949.3i 0.580000 + 1.00459i
\(606\) −1425.00 2468.17i −0.0955226 0.165450i
\(607\) 11295.5 19564.4i 0.755305 1.30823i −0.189917 0.981800i \(-0.560822\pi\)
0.945223 0.326427i \(-0.105845\pi\)
\(608\) 160.000 0.0106725
\(609\) 1995.00 10366.3i 0.132745 0.689761i
\(610\) 12762.0 0.847079
\(611\) 7035.00 12185.0i 0.465803 0.806794i
\(612\) 204.000 + 353.338i 0.0134742 + 0.0233380i
\(613\) 4242.50 + 7348.23i 0.279532 + 0.484163i 0.971268 0.237987i \(-0.0764874\pi\)
−0.691737 + 0.722150i \(0.743154\pi\)
\(614\) 9604.00 16634.6i 0.631247 1.09335i
\(615\) −1890.00 −0.123922
\(616\) 1596.00 8293.06i 0.104391 0.542430i
\(617\) −18282.0 −1.19288 −0.596439 0.802658i \(-0.703418\pi\)
−0.596439 + 0.802658i \(0.703418\pi\)
\(618\) −2495.00 + 4321.47i −0.162401 + 0.281286i
\(619\) −1145.50 1984.06i −0.0743805 0.128831i 0.826436 0.563030i \(-0.190365\pi\)
−0.900817 + 0.434200i \(0.857031\pi\)
\(620\) 414.000 + 717.069i 0.0268172 + 0.0464487i
\(621\) −5002.50 + 8664.58i −0.323258 + 0.559900i
\(622\) 20262.0 1.30616
\(623\) −17797.5 + 6165.23i −1.14453 + 0.396477i
\(624\) 5600.00 0.359262
\(625\) 4094.50 7091.88i 0.262048 0.453880i
\(626\) −10799.0 18704.4i −0.689481 1.19422i
\(627\) −712.500 1234.09i −0.0453820 0.0786039i
\(628\) 5666.00 9813.80i 0.360029 0.623588i
\(629\) −12903.0 −0.817927
\(630\) −504.000 436.477i −0.0318728 0.0276026i
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) −1844.00 + 3193.90i −0.116061 + 0.201023i
\(633\) −310.000 536.936i −0.0194651 0.0337145i
\(634\) −531.000 919.719i −0.0332629 0.0576131i
\(635\) −9252.00 + 16024.9i −0.578196 + 1.00146i
\(636\) 7860.00 0.490046
\(637\) −3430.00 23763.7i −0.213346 1.47811i
\(638\) −12996.0 −0.806452
\(639\) −96.0000 + 166.277i −0.00594319 + 0.0102939i
\(640\) 576.000 + 997.661i 0.0355756 + 0.0616188i
\(641\) −12487.5 21629.0i −0.769464 1.33275i −0.937854 0.347031i \(-0.887190\pi\)
0.168390 0.985721i \(-0.446143\pi\)
\(642\) −5535.00 + 9586.90i −0.340263 + 0.589353i
\(643\) 9548.00 0.585593 0.292797 0.956175i \(-0.405414\pi\)
0.292797 + 0.956175i \(0.405414\pi\)
\(644\) −3864.00 3346.32i −0.236433 0.204757i
\(645\) −5580.00 −0.340639
\(646\) −255.000 + 441.673i −0.0155307 + 0.0269000i
\(647\) −5065.50 8773.70i −0.307798 0.533122i 0.670082 0.742287i \(-0.266259\pi\)
−0.977880 + 0.209165i \(0.932925\pi\)
\(648\) 2684.00 + 4648.82i 0.162712 + 0.281826i
\(649\) 6241.50 10810.6i 0.377504 0.653857i
\(650\) 6160.00 0.371716
\(651\) −2012.50 + 697.150i −0.121161 + 0.0419716i
\(652\) −9244.00 −0.555250
\(653\) −8329.50 + 14427.1i −0.499171 + 0.864589i −1.00000 0.000957229i \(-0.999695\pi\)
0.500829 + 0.865546i \(0.333029\pi\)
\(654\) 4615.00 + 7993.41i 0.275934 + 0.477932i
\(655\) 9220.50 + 15970.4i 0.550038 + 0.952693i
\(656\) 336.000 581.969i 0.0199979 0.0346373i
\(657\) 626.000 0.0371729
\(658\) −1407.00 + 7310.99i −0.0833595 + 0.433149i
\(659\) 29556.0 1.74710 0.873550 0.486735i \(-0.161812\pi\)
0.873550 + 0.486735i \(0.161812\pi\)
\(660\) 5130.00 8885.42i 0.302553 0.524037i
\(661\) −95.5000 165.411i −0.00561955 0.00973334i 0.863202 0.504859i \(-0.168455\pi\)
−0.868822 + 0.495125i \(0.835122\pi\)
\(662\) 7015.00 + 12150.3i 0.411852 + 0.713348i
\(663\) −8925.00 + 15458.6i −0.522803 + 0.905521i
\(664\) −4704.00 −0.274926
\(665\) 157.500 818.394i 0.00918434 0.0477232i
\(666\) 1012.00 0.0588802
\(667\) −3933.00 + 6812.16i −0.228315 + 0.395454i
\(668\) −2520.00 4364.77i −0.145961 0.252811i
\(669\) 140.000 + 242.487i 0.00809075 + 0.0140136i
\(670\) 3771.00 6531.56i 0.217442 0.376621i
\(671\) 40413.0 2.32508
\(672\) −2800.00 + 969.948i −0.160733 + 0.0556794i
\(673\) 2606.00 0.149263 0.0746314 0.997211i \(-0.476222\pi\)
0.0746314 + 0.997211i \(0.476222\pi\)
\(674\) −8990.00 + 15571.1i −0.513771 + 0.889878i
\(675\) 3190.00 + 5525.24i 0.181901 + 0.315062i
\(676\) −5406.00 9363.47i −0.307579 0.532742i
\(677\) 2104.50 3645.10i 0.119472 0.206931i −0.800087 0.599885i \(-0.795213\pi\)
0.919559 + 0.392953i \(0.128547\pi\)
\(678\) −15420.0 −0.873454
\(679\) 25676.0 + 22236.1i 1.45118 + 1.25676i
\(680\) −3672.00 −0.207081
\(681\) −7642.50 + 13237.2i −0.430046 + 0.744861i
\(682\) 1311.00 + 2270.72i 0.0736082 + 0.127493i
\(683\) −12151.5 21047.0i −0.680768 1.17912i −0.974747 0.223312i \(-0.928313\pi\)
0.293979 0.955812i \(-0.405020\pi\)
\(684\) 20.0000 34.6410i 0.00111801 0.00193645i
\(685\) 1269.00 0.0707825
\(686\) 5831.00 + 11287.8i 0.324532 + 0.628235i
\(687\) 4805.00 0.266845
\(688\) 992.000 1718.19i 0.0549704 0.0952116i
\(689\) −13755.0 23824.4i −0.760557 1.31732i
\(690\) −3105.00 5378.02i −0.171312 0.296721i
\(691\) −7520.50 + 13025.9i −0.414028 + 0.717117i −0.995326 0.0965734i \(-0.969212\pi\)
0.581298 + 0.813691i \(0.302545\pi\)
\(692\) 13068.0 0.717877
\(693\) −1596.00 1382.18i −0.0874849 0.0757641i
\(694\) −17418.0 −0.952706
\(695\) 6678.00 11566.6i 0.364476 0.631291i
\(696\) 2280.00 + 3949.08i 0.124171 + 0.215071i
\(697\) 1071.00 + 1855.03i 0.0582023 + 0.100809i
\(698\) −6482.00 + 11227.2i −0.351500 + 0.608817i
\(699\) 14145.0 0.765398
\(700\) −3080.00 + 1066.94i −0.166304 + 0.0576095i
\(701\) 24726.0 1.33222 0.666111 0.745852i \(-0.267958\pi\)
0.666111 + 0.745852i \(0.267958\pi\)
\(702\) 10150.0 17580.3i 0.545708 0.945194i
\(703\) 632.500 + 1095.52i 0.0339334 + 0.0587744i
\(704\) 1824.00 + 3159.26i 0.0976486 + 0.169132i
\(705\) −4522.50 + 7833.20i −0.241599 + 0.418462i
\(706\) −4266.00 −0.227412
\(707\) 997.500 5183.16i 0.0530620 0.275718i
\(708\) −4380.00 −0.232501
\(709\) 2478.50 4292.89i 0.131286 0.227395i −0.792886 0.609370i \(-0.791423\pi\)
0.924173 + 0.381975i \(0.124756\pi\)
\(710\) −864.000 1496.49i −0.0456695 0.0791019i
\(711\) 461.000 + 798.475i 0.0243162 + 0.0421170i
\(712\) 4068.00 7045.98i 0.214122 0.370870i
\(713\) 1587.00 0.0833571
\(714\) 1785.00 9275.13i 0.0935601 0.486153i
\(715\) −35910.0 −1.87826
\(716\) −2574.00 + 4458.30i −0.134350 + 0.232702i
\(717\) −8850.00 15328.6i −0.460961 0.798409i
\(718\) −3849.00 6666.66i −0.200060 0.346515i
\(719\) −13834.5 + 23962.1i −0.717580 + 1.24288i 0.244376 + 0.969680i \(0.421417\pi\)
−0.961956 + 0.273204i \(0.911917\pi\)
\(720\) 288.000 0.0149071
\(721\) −8732.50 + 3025.03i −0.451061 + 0.156252i
\(722\) −13668.0 −0.704529
\(723\) 13077.5 22650.9i 0.672694 1.16514i
\(724\) 5348.00 + 9263.01i 0.274526 + 0.475493i
\(725\) 2508.00 + 4343.98i 0.128476 + 0.222526i
\(726\) 9590.00 16610.4i 0.490246 0.849130i
\(727\) −13888.0 −0.708497 −0.354249 0.935151i \(-0.615263\pi\)
−0.354249 + 0.935151i \(0.615263\pi\)
\(728\) 7840.00 + 6789.64i 0.399134 + 0.345660i
\(729\) 20917.0 1.06269
\(730\) −2817.00 + 4879.19i −0.142824 + 0.247379i
\(731\) 3162.00 + 5476.74i 0.159987 + 0.277106i
\(732\) −7090.00 12280.2i −0.357997 0.620069i
\(733\) −7121.50 + 12334.8i −0.358852 + 0.621550i −0.987769 0.155922i \(-0.950165\pi\)
0.628917 + 0.777472i \(0.283498\pi\)
\(734\) 12982.0 0.652826
\(735\) 2205.00 + 15276.7i 0.110657 + 0.766652i
\(736\) 2208.00 0.110581
\(737\) 11941.5 20683.3i 0.596840 1.03376i
\(738\) −84.0000 145.492i −0.00418981 0.00725697i
\(739\) −18479.5 32007.4i −0.919864 1.59325i −0.799620 0.600507i \(-0.794966\pi\)
−0.120244 0.992744i \(-0.538368\pi\)
\(740\) −4554.00 + 7887.76i −0.226228 + 0.391838i
\(741\) 1750.00 0.0867582
\(742\) 11004.0 + 9529.74i 0.544433 + 0.471493i
\(743\) −12528.0 −0.618584 −0.309292 0.950967i \(-0.600092\pi\)
−0.309292 + 0.950967i \(0.600092\pi\)
\(744\) 460.000 796.743i 0.0226672 0.0392608i
\(745\) −256.500 444.271i −0.0126140 0.0218481i
\(746\) −923.000 1598.68i −0.0452995 0.0784610i
\(747\) −588.000 + 1018.45i −0.0288003 + 0.0498835i
\(748\) −11628.0 −0.568398
\(749\) −19372.5 + 6710.83i −0.945068 + 0.327381i
\(750\) −15210.0 −0.740521
\(751\) 8883.50 15386.7i 0.431643 0.747627i −0.565372 0.824836i \(-0.691268\pi\)
0.997015 + 0.0772090i \(0.0246009\pi\)
\(752\) −1608.00 2785.14i −0.0779757 0.135058i
\(753\) 12600.0 + 21823.8i 0.609787 + 1.05618i
\(754\) 7980.00 13821.8i 0.385430 0.667585i
\(755\) −7551.00 −0.363985
\(756\) −2030.00 + 10548.2i −0.0976592 + 0.507452i
\(757\) −28726.0 −1.37921 −0.689606 0.724184i \(-0.742216\pi\)
−0.689606 + 0.724184i \(0.742216\pi\)
\(758\) −6344.00 + 10988.1i −0.303990 + 0.526526i
\(759\) −9832.50 17030.4i −0.470220 0.814445i
\(760\) 180.000 + 311.769i 0.00859117 + 0.0148803i
\(761\) 13234.5 22922.8i 0.630421 1.09192i −0.357045 0.934087i \(-0.616216\pi\)
0.987466 0.157834i \(-0.0504510\pi\)
\(762\) 20560.0 0.977441
\(763\) −3230.50 + 16786.2i −0.153279 + 0.796462i
\(764\) 16740.0 0.792712
\(765\) −459.000 + 795.011i −0.0216930 + 0.0375735i
\(766\) 5007.00 + 8672.38i 0.236175 + 0.409068i
\(767\) 7665.00 + 13276.2i 0.360844 + 0.625000i
\(768\) 640.000 1108.51i 0.0300703 0.0520833i
\(769\) 5054.00 0.236999 0.118499 0.992954i \(-0.462192\pi\)
0.118499 + 0.992954i \(0.462192\pi\)
\(770\) 17955.0 6219.79i 0.840329 0.291098i
\(771\) 7185.00 0.335618
\(772\) 170.000 294.449i 0.00792543 0.0137273i
\(773\) 17782.5 + 30800.2i 0.827415 + 1.43313i 0.900059 + 0.435767i \(0.143523\pi\)
−0.0726439 + 0.997358i \(0.523144\pi\)
\(774\) −248.000 429.549i −0.0115170 0.0199481i
\(775\) 506.000 876.418i 0.0234530 0.0406217i
\(776\) −14672.0 −0.678730
\(777\) −17710.0 15337.3i −0.817687 0.708138i
\(778\) 24582.0 1.13279
\(779\) 105.000 181.865i 0.00482929 0.00836457i
\(780\) 6300.00 + 10911.9i 0.289200 + 0.500910i
\(781\) −2736.00 4738.89i −0.125354 0.217120i
\(782\) −3519.00 + 6095.09i −0.160920 + 0.278721i
\(783\) 16530.0 0.754450
\(784\) −5096.00 2036.89i −0.232143 0.0927884i
\(785\) 25497.0 1.15927
\(786\) 10245.0 17744.9i 0.464920