Properties

Label 20.3.b.a.11.4
Level 20
Weight 3
Character 20.11
Analytic conductor 0.545
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 20 = 2^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 20.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.544960528721\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.4
Root \(0.809017 - 0.587785i\)
Character \(\chi\) = 20.11
Dual form 20.3.b.a.11.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +O(q^{10})\) \(q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +(-1.38197 - 4.25325i) q^{10} +19.9192i q^{11} +(5.52786 + 7.60845i) q^{12} -8.47214 q^{13} +(10.0000 - 3.24920i) q^{14} +5.25731i q^{15} +(4.94427 - 15.2169i) q^{16} +11.8885 q^{17} +(2.14590 + 6.60440i) q^{18} -15.2169i q^{19} +(7.23607 - 5.25731i) q^{20} -12.3607 q^{21} +(-37.8885 + 12.3107i) q^{22} -0.555029i q^{23} +(-11.0557 + 15.2169i) q^{24} +5.00000 q^{25} +(-5.23607 - 16.1150i) q^{26} -29.3238i q^{27} +(12.3607 + 17.0130i) q^{28} -10.9443 q^{29} +(-10.0000 + 3.24920i) q^{30} -8.29451i q^{31} +32.0000 q^{32} +46.8328 q^{33} +(7.34752 + 22.6134i) q^{34} +11.7557i q^{35} +(-11.2361 + 8.16348i) q^{36} -18.3607 q^{37} +(28.9443 - 9.40456i) q^{38} +19.9192i q^{39} +(14.4721 + 10.5146i) q^{40} -14.5836 q^{41} +(-7.63932 - 23.5114i) q^{42} +22.2703i q^{43} +(-46.8328 - 64.4598i) q^{44} -7.76393 q^{45} +(1.05573 - 0.343027i) q^{46} +53.3902i q^{47} +(-35.7771 - 11.6247i) q^{48} +21.3607 q^{49} +(3.09017 + 9.51057i) q^{50} -27.9516i q^{51} +(27.4164 - 19.9192i) q^{52} -66.3607 q^{53} +(55.7771 - 18.1231i) q^{54} -44.5407i q^{55} +(-24.7214 + 34.0260i) q^{56} -35.7771 q^{57} +(-6.76393 - 20.8172i) q^{58} +17.4370i q^{59} +(-12.3607 - 17.0130i) q^{60} +90.1378 q^{61} +(15.7771 - 5.12629i) q^{62} -18.2541i q^{63} +(19.7771 + 60.8676i) q^{64} +18.9443 q^{65} +(28.9443 + 89.0813i) q^{66} +50.2220i q^{67} +(-38.4721 + 27.9516i) q^{68} -1.30495 q^{69} +(-22.3607 + 7.26543i) q^{70} -80.7868i q^{71} +(-22.4721 - 16.3270i) q^{72} -5.55418 q^{73} +(-11.3475 - 34.9241i) q^{74} -11.7557i q^{75} +(35.7771 + 49.2429i) q^{76} +104.721 q^{77} +(-37.8885 + 12.3107i) q^{78} -13.8448i q^{79} +(-11.0557 + 34.0260i) q^{80} -37.6950 q^{81} +(-9.01316 - 27.7396i) q^{82} -76.2155i q^{83} +(40.0000 - 29.0617i) q^{84} -26.5836 q^{85} +(-42.3607 + 13.7638i) q^{86} +25.7315i q^{87} +(93.6656 - 128.920i) q^{88} -111.443 q^{89} +(-4.79837 - 14.7679i) q^{90} +44.5407i q^{91} +(1.30495 + 1.79611i) q^{92} -19.5016 q^{93} +(-101.554 + 32.9970i) q^{94} +34.0260i q^{95} -75.2365i q^{96} -92.8328 q^{97} +(13.2016 + 40.6304i) q^{98} +69.1621i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 4q^{4} - 8q^{8} - 4q^{9} - 10q^{10} + 40q^{12} - 16q^{13} + 40q^{14} - 16q^{16} - 24q^{17} + 22q^{18} + 20q^{20} + 40q^{21} - 80q^{22} - 80q^{24} + 20q^{25} - 12q^{26} - 40q^{28} - 8q^{29} - 40q^{30} + 128q^{32} + 80q^{33} + 92q^{34} - 36q^{36} + 16q^{37} + 80q^{38} + 40q^{40} - 112q^{41} - 120q^{42} - 80q^{44} - 40q^{45} + 40q^{46} - 4q^{49} - 10q^{50} + 56q^{52} - 176q^{53} + 80q^{54} + 80q^{56} - 36q^{58} + 40q^{60} + 128q^{61} - 80q^{62} - 64q^{64} + 40q^{65} + 80q^{66} - 136q^{68} + 120q^{69} - 72q^{72} + 264q^{73} - 108q^{74} + 240q^{77} - 80q^{78} - 80q^{80} - 276q^{81} + 116q^{82} + 160q^{84} - 160q^{85} - 80q^{86} + 160q^{88} - 88q^{89} + 30q^{90} - 120q^{92} - 400q^{93} - 120q^{94} - 264q^{97} + 102q^{98} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(17\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 + 1.90211i 0.309017 + 0.951057i
\(3\) 2.35114i 0.783714i −0.920026 0.391857i \(-0.871833\pi\)
0.920026 0.391857i \(-0.128167\pi\)
\(4\) −3.23607 + 2.35114i −0.809017 + 0.587785i
\(5\) −2.23607 −0.447214
\(6\) 4.47214 1.45309i 0.745356 0.242181i
\(7\) 5.25731i 0.751044i −0.926813 0.375522i \(-0.877463\pi\)
0.926813 0.375522i \(-0.122537\pi\)
\(8\) −6.47214 4.70228i −0.809017 0.587785i
\(9\) 3.47214 0.385793
\(10\) −1.38197 4.25325i −0.138197 0.425325i
\(11\) 19.9192i 1.81084i 0.424522 + 0.905418i \(0.360442\pi\)
−0.424522 + 0.905418i \(0.639558\pi\)
\(12\) 5.52786 + 7.60845i 0.460655 + 0.634038i
\(13\) −8.47214 −0.651703 −0.325851 0.945421i \(-0.605651\pi\)
−0.325851 + 0.945421i \(0.605651\pi\)
\(14\) 10.0000 3.24920i 0.714286 0.232085i
\(15\) 5.25731i 0.350487i
\(16\) 4.94427 15.2169i 0.309017 0.951057i
\(17\) 11.8885 0.699326 0.349663 0.936876i \(-0.386296\pi\)
0.349663 + 0.936876i \(0.386296\pi\)
\(18\) 2.14590 + 6.60440i 0.119217 + 0.366911i
\(19\) 15.2169i 0.800890i −0.916321 0.400445i \(-0.868856\pi\)
0.916321 0.400445i \(-0.131144\pi\)
\(20\) 7.23607 5.25731i 0.361803 0.262866i
\(21\) −12.3607 −0.588604
\(22\) −37.8885 + 12.3107i −1.72221 + 0.559579i
\(23\) 0.555029i 0.0241317i −0.999927 0.0120659i \(-0.996159\pi\)
0.999927 0.0120659i \(-0.00384077\pi\)
\(24\) −11.0557 + 15.2169i −0.460655 + 0.634038i
\(25\) 5.00000 0.200000
\(26\) −5.23607 16.1150i −0.201387 0.619806i
\(27\) 29.3238i 1.08606i
\(28\) 12.3607 + 17.0130i 0.441453 + 0.607608i
\(29\) −10.9443 −0.377389 −0.188694 0.982036i \(-0.560426\pi\)
−0.188694 + 0.982036i \(0.560426\pi\)
\(30\) −10.0000 + 3.24920i −0.333333 + 0.108307i
\(31\) 8.29451i 0.267565i −0.991011 0.133782i \(-0.957288\pi\)
0.991011 0.133782i \(-0.0427123\pi\)
\(32\) 32.0000 1.00000
\(33\) 46.8328 1.41918
\(34\) 7.34752 + 22.6134i 0.216104 + 0.665099i
\(35\) 11.7557i 0.335877i
\(36\) −11.2361 + 8.16348i −0.312113 + 0.226763i
\(37\) −18.3607 −0.496235 −0.248117 0.968730i \(-0.579812\pi\)
−0.248117 + 0.968730i \(0.579812\pi\)
\(38\) 28.9443 9.40456i 0.761691 0.247489i
\(39\) 19.9192i 0.510748i
\(40\) 14.4721 + 10.5146i 0.361803 + 0.262866i
\(41\) −14.5836 −0.355697 −0.177849 0.984058i \(-0.556914\pi\)
−0.177849 + 0.984058i \(0.556914\pi\)
\(42\) −7.63932 23.5114i −0.181889 0.559795i
\(43\) 22.2703i 0.517915i 0.965889 + 0.258957i \(0.0833789\pi\)
−0.965889 + 0.258957i \(0.916621\pi\)
\(44\) −46.8328 64.4598i −1.06438 1.46500i
\(45\) −7.76393 −0.172532
\(46\) 1.05573 0.343027i 0.0229506 0.00745711i
\(47\) 53.3902i 1.13596i 0.823042 + 0.567981i \(0.192275\pi\)
−0.823042 + 0.567981i \(0.807725\pi\)
\(48\) −35.7771 11.6247i −0.745356 0.242181i
\(49\) 21.3607 0.435932
\(50\) 3.09017 + 9.51057i 0.0618034 + 0.190211i
\(51\) 27.9516i 0.548071i
\(52\) 27.4164 19.9192i 0.527239 0.383061i
\(53\) −66.3607 −1.25209 −0.626044 0.779788i \(-0.715327\pi\)
−0.626044 + 0.779788i \(0.715327\pi\)
\(54\) 55.7771 18.1231i 1.03291 0.335612i
\(55\) 44.5407i 0.809830i
\(56\) −24.7214 + 34.0260i −0.441453 + 0.607608i
\(57\) −35.7771 −0.627668
\(58\) −6.76393 20.8172i −0.116620 0.358918i
\(59\) 17.4370i 0.295543i 0.989022 + 0.147771i \(0.0472100\pi\)
−0.989022 + 0.147771i \(0.952790\pi\)
\(60\) −12.3607 17.0130i −0.206011 0.283550i
\(61\) 90.1378 1.47767 0.738834 0.673887i \(-0.235377\pi\)
0.738834 + 0.673887i \(0.235377\pi\)
\(62\) 15.7771 5.12629i 0.254469 0.0826820i
\(63\) 18.2541i 0.289748i
\(64\) 19.7771 + 60.8676i 0.309017 + 0.951057i
\(65\) 18.9443 0.291450
\(66\) 28.9443 + 89.0813i 0.438550 + 1.34972i
\(67\) 50.2220i 0.749582i 0.927109 + 0.374791i \(0.122285\pi\)
−0.927109 + 0.374791i \(0.877715\pi\)
\(68\) −38.4721 + 27.9516i −0.565767 + 0.411054i
\(69\) −1.30495 −0.0189123
\(70\) −22.3607 + 7.26543i −0.319438 + 0.103792i
\(71\) 80.7868i 1.13784i −0.822392 0.568921i \(-0.807361\pi\)
0.822392 0.568921i \(-0.192639\pi\)
\(72\) −22.4721 16.3270i −0.312113 0.226763i
\(73\) −5.55418 −0.0760846 −0.0380423 0.999276i \(-0.512112\pi\)
−0.0380423 + 0.999276i \(0.512112\pi\)
\(74\) −11.3475 34.9241i −0.153345 0.471947i
\(75\) 11.7557i 0.156743i
\(76\) 35.7771 + 49.2429i 0.470751 + 0.647933i
\(77\) 104.721 1.36002
\(78\) −37.8885 + 12.3107i −0.485751 + 0.157830i
\(79\) 13.8448i 0.175251i −0.996154 0.0876253i \(-0.972072\pi\)
0.996154 0.0876253i \(-0.0279278\pi\)
\(80\) −11.0557 + 34.0260i −0.138197 + 0.425325i
\(81\) −37.6950 −0.465371
\(82\) −9.01316 27.7396i −0.109917 0.338288i
\(83\) 76.2155i 0.918260i −0.888369 0.459130i \(-0.848161\pi\)
0.888369 0.459130i \(-0.151839\pi\)
\(84\) 40.0000 29.0617i 0.476190 0.345973i
\(85\) −26.5836 −0.312748
\(86\) −42.3607 + 13.7638i −0.492566 + 0.160044i
\(87\) 25.7315i 0.295765i
\(88\) 93.6656 128.920i 1.06438 1.46500i
\(89\) −111.443 −1.25217 −0.626083 0.779757i \(-0.715343\pi\)
−0.626083 + 0.779757i \(0.715343\pi\)
\(90\) −4.79837 14.7679i −0.0533153 0.164088i
\(91\) 44.5407i 0.489458i
\(92\) 1.30495 + 1.79611i 0.0141843 + 0.0195230i
\(93\) −19.5016 −0.209694
\(94\) −101.554 + 32.9970i −1.08036 + 0.351031i
\(95\) 34.0260i 0.358169i
\(96\) 75.2365i 0.783714i
\(97\) −92.8328 −0.957039 −0.478520 0.878077i \(-0.658826\pi\)
−0.478520 + 0.878077i \(0.658826\pi\)
\(98\) 13.2016 + 40.6304i 0.134710 + 0.414596i
\(99\) 69.1621i 0.698607i
\(100\) −16.1803 + 11.7557i −0.161803 + 0.117557i
\(101\) 64.1115 0.634767 0.317383 0.948297i \(-0.397196\pi\)
0.317383 + 0.948297i \(0.397196\pi\)
\(102\) 53.1672 17.2751i 0.521247 0.169363i
\(103\) 137.769i 1.33757i 0.743458 + 0.668783i \(0.233184\pi\)
−0.743458 + 0.668783i \(0.766816\pi\)
\(104\) 54.8328 + 39.8384i 0.527239 + 0.383061i
\(105\) 27.6393 0.263232
\(106\) −41.0132 126.226i −0.386917 1.19081i
\(107\) 51.3320i 0.479739i −0.970805 0.239869i \(-0.922895\pi\)
0.970805 0.239869i \(-0.0771046\pi\)
\(108\) 68.9443 + 94.8936i 0.638373 + 0.878645i
\(109\) 133.469 1.22449 0.612243 0.790669i \(-0.290267\pi\)
0.612243 + 0.790669i \(0.290267\pi\)
\(110\) 84.7214 27.5276i 0.770194 0.250251i
\(111\) 43.1685i 0.388906i
\(112\) −80.0000 25.9936i −0.714286 0.232085i
\(113\) 170.721 1.51081 0.755404 0.655259i \(-0.227441\pi\)
0.755404 + 0.655259i \(0.227441\pi\)
\(114\) −22.1115 68.0521i −0.193960 0.596948i
\(115\) 1.24108i 0.0107920i
\(116\) 35.4164 25.7315i 0.305314 0.221824i
\(117\) −29.4164 −0.251422
\(118\) −33.1672 + 10.7767i −0.281078 + 0.0913277i
\(119\) 62.5018i 0.525225i
\(120\) 24.7214 34.0260i 0.206011 0.283550i
\(121\) −275.774 −2.27912
\(122\) 55.7082 + 171.452i 0.456625 + 1.40535i
\(123\) 34.2881i 0.278765i
\(124\) 19.5016 + 26.8416i 0.157271 + 0.216464i
\(125\) −11.1803 −0.0894427
\(126\) 34.7214 11.2817i 0.275566 0.0895369i
\(127\) 198.637i 1.56407i −0.623235 0.782035i \(-0.714182\pi\)
0.623235 0.782035i \(-0.285818\pi\)
\(128\) −103.554 + 75.2365i −0.809017 + 0.587785i
\(129\) 52.3607 0.405897
\(130\) 11.7082 + 36.0341i 0.0900631 + 0.277186i
\(131\) 7.77041i 0.0593161i 0.999560 + 0.0296580i \(0.00944183\pi\)
−0.999560 + 0.0296580i \(0.990558\pi\)
\(132\) −151.554 + 110.111i −1.14814 + 0.834171i
\(133\) −80.0000 −0.601504
\(134\) −95.5279 + 31.0389i −0.712895 + 0.231633i
\(135\) 65.5699i 0.485703i
\(136\) −76.9443 55.9033i −0.565767 0.411054i
\(137\) 0.832816 0.00607895 0.00303947 0.999995i \(-0.499033\pi\)
0.00303947 + 0.999995i \(0.499033\pi\)
\(138\) −0.806504 2.48217i −0.00584424 0.0179867i
\(139\) 237.658i 1.70977i −0.518817 0.854885i \(-0.673627\pi\)
0.518817 0.854885i \(-0.326373\pi\)
\(140\) −27.6393 38.0423i −0.197424 0.271730i
\(141\) 125.528 0.890269
\(142\) 153.666 49.9290i 1.08215 0.351613i
\(143\) 168.758i 1.18013i
\(144\) 17.1672 52.8352i 0.119217 0.366911i
\(145\) 24.4721 0.168773
\(146\) −3.43267 10.5647i −0.0235114 0.0723607i
\(147\) 50.2220i 0.341646i
\(148\) 59.4164 43.1685i 0.401462 0.291679i
\(149\) −36.9706 −0.248125 −0.124062 0.992274i \(-0.539592\pi\)
−0.124062 + 0.992274i \(0.539592\pi\)
\(150\) 22.3607 7.26543i 0.149071 0.0484362i
\(151\) 282.723i 1.87234i 0.351552 + 0.936168i \(0.385654\pi\)
−0.351552 + 0.936168i \(0.614346\pi\)
\(152\) −71.5542 + 98.4859i −0.470751 + 0.647933i
\(153\) 41.2786 0.269795
\(154\) 64.7214 + 199.192i 0.420269 + 1.29345i
\(155\) 18.5471i 0.119659i
\(156\) −46.8328 64.4598i −0.300210 0.413204i
\(157\) 204.748 1.30413 0.652063 0.758165i \(-0.273904\pi\)
0.652063 + 0.758165i \(0.273904\pi\)
\(158\) 26.3344 8.55656i 0.166673 0.0541554i
\(159\) 156.023i 0.981279i
\(160\) −71.5542 −0.447214
\(161\) −2.91796 −0.0181240
\(162\) −23.2968 71.7002i −0.143808 0.442594i
\(163\) 107.235i 0.657885i 0.944350 + 0.328943i \(0.106692\pi\)
−0.944350 + 0.328943i \(0.893308\pi\)
\(164\) 47.1935 34.2881i 0.287765 0.209074i
\(165\) −104.721 −0.634675
\(166\) 144.971 47.1038i 0.873317 0.283758i
\(167\) 33.2090i 0.198856i 0.995045 + 0.0994280i \(0.0317013\pi\)
−0.995045 + 0.0994280i \(0.968299\pi\)
\(168\) 80.0000 + 58.1234i 0.476190 + 0.345973i
\(169\) −97.2229 −0.575284
\(170\) −16.4296 50.5650i −0.0966445 0.297441i
\(171\) 52.8352i 0.308978i
\(172\) −52.3607 72.0683i −0.304423 0.419002i
\(173\) −226.361 −1.30844 −0.654222 0.756303i \(-0.727004\pi\)
−0.654222 + 0.756303i \(0.727004\pi\)
\(174\) −48.9443 + 15.9030i −0.281289 + 0.0913963i
\(175\) 26.2866i 0.150209i
\(176\) 303.108 + 98.4859i 1.72221 + 0.559579i
\(177\) 40.9969 0.231621
\(178\) −68.8754 211.977i −0.386940 1.19088i
\(179\) 224.337i 1.25328i 0.779308 + 0.626641i \(0.215571\pi\)
−0.779308 + 0.626641i \(0.784429\pi\)
\(180\) 25.1246 18.2541i 0.139581 0.101412i
\(181\) 86.2229 0.476370 0.238185 0.971220i \(-0.423448\pi\)
0.238185 + 0.971220i \(0.423448\pi\)
\(182\) −84.7214 + 27.5276i −0.465502 + 0.151251i
\(183\) 211.927i 1.15807i
\(184\) −2.60990 + 3.59222i −0.0141843 + 0.0195230i
\(185\) 41.0557 0.221923
\(186\) −12.0526 37.0942i −0.0647990 0.199431i
\(187\) 236.810i 1.26636i
\(188\) −125.528 172.774i −0.667701 0.919012i
\(189\) −154.164 −0.815683
\(190\) −64.7214 + 21.0292i −0.340639 + 0.110680i
\(191\) 31.0198i 0.162407i −0.996698 0.0812036i \(-0.974124\pi\)
0.996698 0.0812036i \(-0.0258764\pi\)
\(192\) 143.108 46.4987i 0.745356 0.242181i
\(193\) 110.223 0.571103 0.285552 0.958363i \(-0.407823\pi\)
0.285552 + 0.958363i \(0.407823\pi\)
\(194\) −57.3738 176.579i −0.295741 0.910198i
\(195\) 44.5407i 0.228414i
\(196\) −69.1246 + 50.2220i −0.352677 + 0.256235i
\(197\) −172.525 −0.875760 −0.437880 0.899033i \(-0.644271\pi\)
−0.437880 + 0.899033i \(0.644271\pi\)
\(198\) −131.554 + 42.7445i −0.664415 + 0.215882i
\(199\) 272.208i 1.36788i −0.729538 0.683940i \(-0.760265\pi\)
0.729538 0.683940i \(-0.239735\pi\)
\(200\) −32.3607 23.5114i −0.161803 0.117557i
\(201\) 118.079 0.587457
\(202\) 39.6231 + 121.947i 0.196154 + 0.603699i
\(203\) 57.5374i 0.283436i
\(204\) 65.7183 + 90.4534i 0.322148 + 0.443399i
\(205\) 32.6099 0.159073
\(206\) −262.053 + 85.1461i −1.27210 + 0.413330i
\(207\) 1.92714i 0.00930984i
\(208\) −41.8885 + 128.920i −0.201387 + 0.619806i
\(209\) 303.108 1.45028
\(210\) 17.0820 + 52.5731i 0.0813430 + 0.250348i
\(211\) 205.266i 0.972826i −0.873729 0.486413i \(-0.838305\pi\)
0.873729 0.486413i \(-0.161695\pi\)
\(212\) 214.748 156.023i 1.01296 0.735959i
\(213\) −189.941 −0.891743
\(214\) 97.6393 31.7249i 0.456259 0.148247i
\(215\) 49.7980i 0.231618i
\(216\) −137.889 + 189.787i −0.638373 + 0.878645i
\(217\) −43.6068 −0.200953
\(218\) 82.4884 + 253.873i 0.378387 + 1.16456i
\(219\) 13.0586i 0.0596285i
\(220\) 104.721 + 144.137i 0.476006 + 0.655166i
\(221\) −100.721 −0.455753
\(222\) −82.1115 + 26.6796i −0.369871 + 0.120179i
\(223\) 235.731i 1.05709i 0.848905 + 0.528545i \(0.177262\pi\)
−0.848905 + 0.528545i \(0.822738\pi\)
\(224\) 168.234i 0.751044i
\(225\) 17.3607 0.0771586
\(226\) 105.512 + 324.731i 0.466865 + 1.43686i
\(227\) 58.5165i 0.257782i −0.991659 0.128891i \(-0.958858\pi\)
0.991659 0.128891i \(-0.0411417\pi\)
\(228\) 115.777 84.1170i 0.507794 0.368934i
\(229\) 162.721 0.710574 0.355287 0.934757i \(-0.384383\pi\)
0.355287 + 0.934757i \(0.384383\pi\)
\(230\) −2.36068 + 0.767031i −0.0102638 + 0.00333492i
\(231\) 246.215i 1.06586i
\(232\) 70.8328 + 51.4631i 0.305314 + 0.221824i
\(233\) 319.050 1.36931 0.684656 0.728867i \(-0.259953\pi\)
0.684656 + 0.728867i \(0.259953\pi\)
\(234\) −18.1803 55.9533i −0.0776938 0.239117i
\(235\) 119.384i 0.508017i
\(236\) −40.9969 56.4274i −0.173716 0.239099i
\(237\) −32.5511 −0.137346
\(238\) 118.885 38.6282i 0.499519 0.162303i
\(239\) 236.810i 0.990837i 0.868654 + 0.495419i \(0.164985\pi\)
−0.868654 + 0.495419i \(0.835015\pi\)
\(240\) 80.0000 + 25.9936i 0.333333 + 0.108307i
\(241\) −0.917961 −0.00380897 −0.00190448 0.999998i \(-0.500606\pi\)
−0.00190448 + 0.999998i \(0.500606\pi\)
\(242\) −170.438 524.553i −0.704288 2.16758i
\(243\) 175.287i 0.721347i
\(244\) −291.692 + 211.927i −1.19546 + 0.868552i
\(245\) −47.7639 −0.194955
\(246\) −65.2198 + 21.1912i −0.265121 + 0.0861431i
\(247\) 128.920i 0.521942i
\(248\) −39.0031 + 53.6832i −0.157271 + 0.216464i
\(249\) −179.193 −0.719653
\(250\) −6.90983 21.2663i −0.0276393 0.0850651i
\(251\) 136.690i 0.544582i −0.962215 0.272291i \(-0.912219\pi\)
0.962215 0.272291i \(-0.0877813\pi\)
\(252\) 42.9180 + 59.0715i 0.170309 + 0.234411i
\(253\) 11.0557 0.0436985
\(254\) 377.830 122.764i 1.48752 0.483324i
\(255\) 62.5018i 0.245105i
\(256\) −207.108 150.473i −0.809017 0.587785i
\(257\) −274.944 −1.06982 −0.534911 0.844908i \(-0.679655\pi\)
−0.534911 + 0.844908i \(0.679655\pi\)
\(258\) 32.3607 + 99.5959i 0.125429 + 0.386031i
\(259\) 96.5278i 0.372694i
\(260\) −61.3050 + 44.5407i −0.235788 + 0.171310i
\(261\) −38.0000 −0.145594
\(262\) −14.7802 + 4.80238i −0.0564130 + 0.0183297i
\(263\) 406.385i 1.54519i 0.634899 + 0.772596i \(0.281042\pi\)
−0.634899 + 0.772596i \(0.718958\pi\)
\(264\) −303.108 220.221i −1.14814 0.834171i
\(265\) 148.387 0.559951
\(266\) −49.4427 152.169i −0.185875 0.572064i
\(267\) 262.018i 0.981339i
\(268\) −118.079 162.522i −0.440593 0.606424i
\(269\) −348.525 −1.29563 −0.647816 0.761797i \(-0.724317\pi\)
−0.647816 + 0.761797i \(0.724317\pi\)
\(270\) −124.721 + 40.5244i −0.461931 + 0.150090i
\(271\) 247.849i 0.914571i −0.889320 0.457286i \(-0.848822\pi\)
0.889320 0.457286i \(-0.151178\pi\)
\(272\) 58.7802 180.907i 0.216104 0.665099i
\(273\) 104.721 0.383595
\(274\) 0.514708 + 1.58411i 0.00187850 + 0.00578142i
\(275\) 99.5959i 0.362167i
\(276\) 4.22291 3.06813i 0.0153004 0.0111164i
\(277\) −54.7539 −0.197667 −0.0988337 0.995104i \(-0.531511\pi\)
−0.0988337 + 0.995104i \(0.531511\pi\)
\(278\) 452.053 146.881i 1.62609 0.528348i
\(279\) 28.7997i 0.103225i
\(280\) 55.2786 76.0845i 0.197424 0.271730i
\(281\) −50.3607 −0.179220 −0.0896098 0.995977i \(-0.528562\pi\)
−0.0896098 + 0.995977i \(0.528562\pi\)
\(282\) 77.5805 + 238.768i 0.275108 + 0.846696i
\(283\) 147.336i 0.520621i −0.965525 0.260310i \(-0.916175\pi\)
0.965525 0.260310i \(-0.0838249\pi\)
\(284\) 189.941 + 261.432i 0.668807 + 0.920534i
\(285\) 80.0000 0.280702
\(286\) 320.997 104.298i 1.12237 0.364679i
\(287\) 76.6705i 0.267145i
\(288\) 111.108 0.385793
\(289\) −147.663 −0.510943
\(290\) 15.1246 + 46.5488i 0.0521538 + 0.160513i
\(291\) 218.263i 0.750045i
\(292\) 17.9737 13.0586i 0.0615537 0.0447214i
\(293\) 178.859 0.610441 0.305220 0.952282i \(-0.401270\pi\)
0.305220 + 0.952282i \(0.401270\pi\)
\(294\) 95.5279 31.0389i 0.324925 0.105574i
\(295\) 38.9904i 0.132171i
\(296\) 118.833 + 86.3371i 0.401462 + 0.291679i
\(297\) 584.105 1.96668
\(298\) −22.8491 70.3222i −0.0766748 0.235981i
\(299\) 4.70228i 0.0157267i
\(300\) 27.6393 + 38.0423i 0.0921311 + 0.126808i
\(301\) 117.082 0.388977
\(302\) −537.771 + 174.732i −1.78070 + 0.578584i
\(303\) 150.735i 0.497475i
\(304\) −231.554 75.2365i −0.761691 0.247489i
\(305\) −201.554 −0.660833
\(306\) 25.5116 + 78.5166i 0.0833713 + 0.256590i
\(307\) 284.550i 0.926873i −0.886130 0.463436i \(-0.846616\pi\)
0.886130 0.463436i \(-0.153384\pi\)
\(308\) −338.885 + 246.215i −1.10028 + 0.799398i
\(309\) 323.915 1.04827
\(310\) −35.2786 + 11.4627i −0.113802 + 0.0369765i
\(311\) 282.199i 0.907392i 0.891157 + 0.453696i \(0.149895\pi\)
−0.891157 + 0.453696i \(0.850105\pi\)
\(312\) 93.6656 128.920i 0.300210 0.413204i
\(313\) −567.548 −1.81325 −0.906626 0.421935i \(-0.861351\pi\)
−0.906626 + 0.421935i \(0.861351\pi\)
\(314\) 126.541 + 389.453i 0.402997 + 1.24030i
\(315\) 40.8174i 0.129579i
\(316\) 32.5511 + 44.8027i 0.103010 + 0.141781i
\(317\) 161.141 0.508331 0.254165 0.967161i \(-0.418199\pi\)
0.254165 + 0.967161i \(0.418199\pi\)
\(318\) −296.774 + 96.4277i −0.933252 + 0.303232i
\(319\) 218.001i 0.683389i
\(320\) −44.2229 136.104i −0.138197 0.425325i
\(321\) −120.689 −0.375978
\(322\) −1.80340 5.55029i −0.00560062 0.0172369i
\(323\) 180.907i 0.560083i
\(324\) 121.984 88.6264i 0.376493 0.273538i
\(325\) −42.3607 −0.130341
\(326\) −203.974 + 66.2751i −0.625686 + 0.203298i
\(327\) 313.805i 0.959647i
\(328\) 94.3870 + 68.5762i 0.287765 + 0.209074i
\(329\) 280.689 0.853158
\(330\) −64.7214 199.192i −0.196125 0.603612i
\(331\) 331.966i 1.00292i 0.865181 + 0.501459i \(0.167203\pi\)
−0.865181 + 0.501459i \(0.832797\pi\)
\(332\) 179.193 + 246.639i 0.539739 + 0.742888i
\(333\) −63.7508 −0.191444
\(334\) −63.1672 + 20.5243i −0.189123 + 0.0614499i
\(335\) 112.300i 0.335223i
\(336\) −61.1146 + 188.091i −0.181889 + 0.559795i
\(337\) −269.108 −0.798541 −0.399271 0.916833i \(-0.630737\pi\)
−0.399271 + 0.916833i \(0.630737\pi\)
\(338\) −60.0871 184.929i −0.177772 0.547127i
\(339\) 401.390i 1.18404i
\(340\) 86.0263 62.5018i 0.253019 0.183829i
\(341\) 165.220 0.484516
\(342\) 100.498 32.6539i 0.293855 0.0954793i
\(343\) 369.908i 1.07845i
\(344\) 104.721 144.137i 0.304423 0.419002i
\(345\) 2.91796 0.00845786
\(346\) −139.899 430.564i −0.404331 1.24440i
\(347\) 503.075i 1.44978i −0.688863 0.724892i \(-0.741890\pi\)
0.688863 0.724892i \(-0.258110\pi\)
\(348\) −60.4984 83.2690i −0.173846 0.239279i
\(349\) −0.504658 −0.00144601 −0.000723006 1.00000i \(-0.500230\pi\)
−0.000723006 1.00000i \(0.500230\pi\)
\(350\) 50.0000 16.2460i 0.142857 0.0464171i
\(351\) 248.435i 0.707791i
\(352\) 637.414i 1.81084i
\(353\) −335.994 −0.951824 −0.475912 0.879493i \(-0.657882\pi\)
−0.475912 + 0.879493i \(0.657882\pi\)
\(354\) 25.3375 + 77.9807i 0.0715748 + 0.220285i
\(355\) 180.645i 0.508859i
\(356\) 360.636 262.018i 1.01302 0.736004i
\(357\) −146.950 −0.411626
\(358\) −426.715 + 138.648i −1.19194 + 0.387285i
\(359\) 98.4859i 0.274334i 0.990548 + 0.137167i \(0.0437997\pi\)
−0.990548 + 0.137167i \(0.956200\pi\)
\(360\) 50.2492 + 36.5082i 0.139581 + 0.101412i
\(361\) 129.446 0.358576
\(362\) 53.2887 + 164.006i 0.147206 + 0.453054i
\(363\) 648.384i 1.78618i
\(364\) −104.721 144.137i −0.287696 0.395980i
\(365\) 12.4195 0.0340261
\(366\) 403.108 130.978i 1.10139 0.357863i
\(367\) 498.473i 1.35824i 0.734029 + 0.679118i \(0.237638\pi\)
−0.734029 + 0.679118i \(0.762362\pi\)
\(368\) −8.44582 2.74421i −0.0229506 0.00745711i
\(369\) −50.6362 −0.137226
\(370\) 25.3738 + 78.0926i 0.0685779 + 0.211061i
\(371\) 348.879i 0.940374i
\(372\) 63.1084 45.8509i 0.169646 0.123255i
\(373\) 600.354 1.60953 0.804765 0.593594i \(-0.202291\pi\)
0.804765 + 0.593594i \(0.202291\pi\)
\(374\) −450.440 + 146.357i −1.20438 + 0.391328i
\(375\) 26.2866i 0.0700975i
\(376\) 251.056 345.549i 0.667701 0.919012i
\(377\) 92.7214 0.245945
\(378\) −95.2786 293.238i −0.252060 0.775761i
\(379\) 303.490i 0.800765i 0.916348 + 0.400383i \(0.131123\pi\)
−0.916348 + 0.400383i \(0.868877\pi\)
\(380\) −80.0000 110.111i −0.210526 0.289765i
\(381\) −467.023 −1.22578
\(382\) 59.0031 19.1713i 0.154458 0.0501866i
\(383\) 332.583i 0.868362i −0.900826 0.434181i \(-0.857038\pi\)
0.900826 0.434181i \(-0.142962\pi\)
\(384\) 176.892 + 243.470i 0.460655 + 0.634038i
\(385\) −234.164 −0.608218
\(386\) 68.1215 + 209.656i 0.176481 + 0.543151i
\(387\) 77.3256i 0.199808i
\(388\) 300.413 218.263i 0.774261 0.562534i
\(389\) 392.354 1.00862 0.504312 0.863522i \(-0.331746\pi\)
0.504312 + 0.863522i \(0.331746\pi\)
\(390\) 84.7214 27.5276i 0.217234 0.0705837i
\(391\) 6.59849i 0.0168759i
\(392\) −138.249 100.444i −0.352677 0.256235i
\(393\) 18.2693 0.0464868
\(394\) −106.626 328.162i −0.270625 0.832897i
\(395\) 30.9579i 0.0783744i
\(396\) −162.610 223.813i −0.410631 0.565185i
\(397\) 334.190 0.841789 0.420895 0.907110i \(-0.361716\pi\)
0.420895 + 0.907110i \(0.361716\pi\)
\(398\) 517.771 168.234i 1.30093 0.422698i
\(399\) 188.091i 0.471407i
\(400\) 24.7214 76.0845i 0.0618034 0.190211i
\(401\) 121.003 0.301753 0.150877 0.988553i \(-0.451790\pi\)
0.150877 + 0.988553i \(0.451790\pi\)
\(402\) 72.9768 + 224.599i 0.181534 + 0.558705i
\(403\) 70.2722i 0.174373i
\(404\) −207.469 + 150.735i −0.513537 + 0.373107i
\(405\) 84.2887 0.208120
\(406\) −109.443 + 35.5601i −0.269563 + 0.0875864i
\(407\) 365.730i 0.898599i
\(408\) −131.437 + 180.907i −0.322148 + 0.443399i
\(409\) −607.410 −1.48511 −0.742555 0.669785i \(-0.766386\pi\)
−0.742555 + 0.669785i \(0.766386\pi\)
\(410\) 20.1540 + 62.0277i 0.0491562 + 0.151287i
\(411\) 1.95807i 0.00476415i
\(412\) −323.915 445.831i −0.786201 1.08211i
\(413\) 91.6718 0.221966
\(414\) 3.66563 1.19104i 0.00885418 0.00287690i
\(415\) 170.423i 0.410658i
\(416\) −271.108 −0.651703
\(417\) −558.768 −1.33997
\(418\) 187.331 + 576.546i 0.448161 + 1.37930i
\(419\) 466.760i 1.11398i −0.830518 0.556992i \(-0.811955\pi\)
0.830518 0.556992i \(-0.188045\pi\)
\(420\) −89.4427 + 64.9839i −0.212959 + 0.154724i
\(421\) −73.0883 −0.173606 −0.0868031 0.996225i \(-0.527665\pi\)
−0.0868031 + 0.996225i \(0.527665\pi\)
\(422\) 390.440 126.862i 0.925212 0.300620i
\(423\) 185.378i 0.438246i
\(424\) 429.495 + 312.047i 1.01296 + 0.735959i
\(425\) 59.4427 0.139865
\(426\) −117.390 361.290i −0.275564 0.848098i
\(427\) 473.882i 1.10979i
\(428\) 120.689 + 166.114i 0.281983 + 0.388117i
\(429\) −396.774 −0.924881
\(430\) 94.7214 30.7768i 0.220282 0.0715740i
\(431\) 463.630i 1.07571i −0.843038 0.537853i \(-0.819235\pi\)
0.843038 0.537853i \(-0.180765\pi\)
\(432\) −446.217 144.985i −1.03291 0.335612i
\(433\) −99.8359 −0.230568 −0.115284 0.993333i \(-0.536778\pi\)
−0.115284 + 0.993333i \(0.536778\pi\)
\(434\) −26.9505 82.9451i −0.0620979 0.191118i
\(435\) 57.5374i 0.132270i
\(436\) −431.915 + 313.805i −0.990630 + 0.719735i
\(437\) −8.44582 −0.0193268
\(438\) −24.8390 + 8.07069i −0.0567101 + 0.0184262i
\(439\) 374.086i 0.852133i 0.904692 + 0.426066i \(0.140101\pi\)
−0.904692 + 0.426066i \(0.859899\pi\)
\(440\) −209.443 + 288.273i −0.476006 + 0.655166i
\(441\) 74.1672 0.168180
\(442\) −62.2492 191.583i −0.140835 0.433447i
\(443\) 290.100i 0.654854i −0.944877 0.327427i \(-0.893818\pi\)
0.944877 0.327427i \(-0.106182\pi\)
\(444\) −101.495 139.696i −0.228593 0.314631i
\(445\) 249.193 0.559985
\(446\) −448.387 + 145.690i −1.00535 + 0.326659i
\(447\) 86.9231i 0.194459i
\(448\) 320.000 103.974i 0.714286 0.232085i
\(449\) 299.921 0.667976 0.333988 0.942577i \(-0.391606\pi\)
0.333988 + 0.942577i \(0.391606\pi\)
\(450\) 10.7295 + 33.0220i 0.0238433 + 0.0733822i
\(451\) 290.493i 0.644109i
\(452\) −552.466 + 401.390i −1.22227 + 0.888031i
\(453\) 664.721 1.46738
\(454\) 111.305 36.1652i 0.245165 0.0796590i
\(455\) 99.5959i 0.218892i
\(456\) 231.554 + 168.234i 0.507794 + 0.368934i
\(457\) 822.328 1.79941 0.899703 0.436503i \(-0.143783\pi\)
0.899703 + 0.436503i \(0.143783\pi\)
\(458\) 100.567 + 309.514i 0.219579 + 0.675796i
\(459\) 348.617i 0.759513i
\(460\) −2.91796 4.01623i −0.00634339 0.00873093i
\(461\) −456.885 −0.991075 −0.495537 0.868587i \(-0.665029\pi\)
−0.495537 + 0.868587i \(0.665029\pi\)
\(462\) 468.328 152.169i 1.01370 0.329370i
\(463\) 400.249i 0.864469i 0.901761 + 0.432234i \(0.142275\pi\)
−0.901761 + 0.432234i \(0.857725\pi\)
\(464\) −54.1115 + 166.538i −0.116620 + 0.358918i
\(465\) 43.6068 0.0937781
\(466\) 197.183 + 606.868i 0.423140 + 1.30229i
\(467\) 913.145i 1.95534i 0.210139 + 0.977672i \(0.432608\pi\)
−0.210139 + 0.977672i \(0.567392\pi\)
\(468\) 95.1935 69.1621i 0.203405 0.147782i
\(469\) 264.033 0.562969
\(470\) 227.082 73.7834i 0.483153 0.156986i
\(471\) 481.391i 1.02206i
\(472\) 81.9938 112.855i 0.173716 0.239099i
\(473\) −443.607 −0.937858
\(474\) −20.1177 61.9158i −0.0424423 0.130624i
\(475\) 76.0845i 0.160178i
\(476\) 146.950 + 202.260i 0.308720 + 0.424916i
\(477\) −230.413 −0.483047
\(478\) −450.440 + 146.357i −0.942342 + 0.306186i
\(479\) 526.131i 1.09840i −0.835692 0.549198i \(-0.814933\pi\)
0.835692 0.549198i \(-0.185067\pi\)
\(480\) 168.234i 0.350487i
\(481\) 155.554 0.323397
\(482\) −0.567331 1.74606i −0.00117704 0.00362254i
\(483\) 6.86054i 0.0142040i
\(484\) 892.423 648.384i 1.84385 1.33964i
\(485\) 207.580 0.428001
\(486\) 333.416 108.334i 0.686042 0.222909i
\(487\) 443.541i 0.910762i 0.890297 + 0.455381i \(0.150497\pi\)
−0.890297 + 0.455381i \(0.849503\pi\)
\(488\) −583.384 423.853i −1.19546 0.868552i
\(489\) 252.125 0.515594
\(490\) −29.5197 90.8524i −0.0602444 0.185413i
\(491\) 287.163i 0.584854i −0.956288 0.292427i \(-0.905537\pi\)
0.956288 0.292427i \(-0.0944628\pi\)
\(492\) −80.6161 110.959i −0.163854 0.225526i
\(493\) −130.111 −0.263918
\(494\) −245.220 + 79.6767i −0.496396 + 0.161289i
\(495\) 154.651i 0.312427i
\(496\) −126.217 41.0103i −0.254469 0.0826820i
\(497\) −424.721 −0.854570
\(498\) −110.748 340.846i −0.222385 0.684430i
\(499\) 810.936i 1.62512i 0.582876 + 0.812561i \(0.301927\pi\)
−0.582876 + 0.812561i \(0.698073\pi\)
\(500\) 36.1803 26.2866i 0.0723607 0.0525731i
\(501\) 78.0789 0.155846
\(502\) 260.000 84.4791i 0.517928 0.168285i
\(503\) 642.471i 1.27728i 0.769506 + 0.638639i \(0.220502\pi\)
−0.769506 + 0.638639i \(0.779498\pi\)
\(504\) −85.8359 + 118.143i −0.170309 + 0.234411i
\(505\) −143.358 −0.283876
\(506\) 6.83282 + 21.0292i 0.0135036 + 0.0415598i
\(507\) 228.585i 0.450858i
\(508\) 467.023 + 642.802i 0.919337 + 1.26536i
\(509\) −915.050 −1.79774 −0.898870 0.438216i \(-0.855611\pi\)
−0.898870 + 0.438216i \(0.855611\pi\)
\(510\) −118.885 + 38.6282i −0.233109 + 0.0757416i
\(511\) 29.2000i 0.0571429i
\(512\) 158.217 486.941i 0.309017 0.951057i
\(513\) −446.217 −0.869818
\(514\) −169.925 522.975i −0.330593 1.01746i
\(515\) 308.061i 0.598177i
\(516\) −169.443 + 123.107i −0.328377 + 0.238580i
\(517\) −1063.49 −2.05704
\(518\) −183.607 + 59.6575i −0.354453 + 0.115169i
\(519\) 532.206i 1.02544i
\(520\) −122.610 89.0813i −0.235788 0.171310i
\(521\) 1006.98 1.93279 0.966396 0.257058i \(-0.0827533\pi\)
0.966396 + 0.257058i \(0.0827533\pi\)
\(522\) −23.4853 72.2803i −0.0449910 0.138468i
\(523\) 774.173i 1.48025i −0.672467 0.740127i \(-0.734765\pi\)
0.672467 0.740127i \(-0.265235\pi\)
\(524\) −18.2693 25.1456i −0.0348651 0.0479877i
\(525\) −61.8034 −0.117721
\(526\) −772.991 + 251.160i −1.46956 + 0.477490i
\(527\) 98.6096i 0.187115i
\(528\) 231.554 712.650i 0.438550 1.34972i
\(529\) 528.692 0.999418
\(530\) 91.7082 + 282.249i 0.173034 + 0.532545i
\(531\) 60.5437i 0.114018i
\(532\) 258.885 188.091i 0.486627 0.353555i
\(533\) 123.554 0.231809
\(534\) −498.387 + 161.936i −0.933309 + 0.303250i
\(535\) 114.782i 0.214546i
\(536\) 236.158 325.043i 0.440593 0.606424i
\(537\) 527.449 0.982214
\(538\) −215.400 662.933i −0.400372 1.23222i
\(539\) 425.487i 0.789401i
\(540\) −154.164 212.189i −0.285489 0.392942i
\(541\) −259.115 −0.478955 −0.239477 0.970902i \(-0.576976\pi\)
−0.239477 + 0.970902i \(0.576976\pi\)
\(542\) 471.437 153.179i 0.869809 0.282618i
\(543\) 202.722i 0.373337i
\(544\) 380.433 0.699326
\(545\) −298.446 −0.547607
\(546\) 64.7214 + 199.192i 0.118537 + 0.364820i
\(547\) 149.818i 0.273890i −0.990579 0.136945i \(-0.956272\pi\)
0.990579 0.136945i \(-0.0437284\pi\)
\(548\) −2.69505 + 1.95807i −0.00491797 + 0.00357312i
\(549\) 312.971 0.570074
\(550\) −189.443 + 61.5537i −0.344441 + 0.111916i
\(551\) 166.538i 0.302247i
\(552\) 8.44582 + 6.13625i 0.0153004 + 0.0111164i
\(553\) −72.7864 −0.131621
\(554\) −33.8398 104.148i −0.0610826 0.187993i
\(555\) 96.5278i 0.173924i
\(556\) 558.768 + 769.078i 1.00498 + 1.38323i
\(557\) 511.698 0.918668 0.459334 0.888264i \(-0.348088\pi\)
0.459334 + 0.888264i \(0.348088\pi\)
\(558\) 54.7802 17.7992i 0.0981724 0.0318981i
\(559\) 188.677i 0.337526i
\(560\) 178.885 + 58.1234i 0.319438 + 0.103792i
\(561\) 556.774 0.992467
\(562\) −31.1246 95.7917i −0.0553819 0.170448i
\(563\) 490.726i 0.871627i 0.900037 + 0.435814i \(0.143539\pi\)
−0.900037 + 0.435814i \(0.856461\pi\)
\(564\) −406.217 + 295.134i −0.720242 + 0.523287i
\(565\) −381.745 −0.675654
\(566\) 280.249 91.0585i 0.495140 0.160881i
\(567\) 198.175i 0.349514i
\(568\) −379.882 + 522.863i −0.668807 + 0.920534i
\(569\) −232.748 −0.409047 −0.204523 0.978862i \(-0.565564\pi\)
−0.204523 + 0.978862i \(0.565564\pi\)
\(570\) 49.4427 + 152.169i 0.0867416 + 0.266963i
\(571\) 210.755i 0.369098i −0.982823 0.184549i \(-0.940918\pi\)
0.982823 0.184549i \(-0.0590824\pi\)
\(572\) 396.774 + 546.113i 0.693661 + 0.954742i
\(573\) −72.9318 −0.127281
\(574\) −145.836 + 47.3850i −0.254070 + 0.0825522i
\(575\) 2.77515i 0.00482634i
\(576\) 68.6687 + 211.341i 0.119217 + 0.366911i
\(577\) 341.712 0.592222 0.296111 0.955154i \(-0.404310\pi\)
0.296111 + 0.955154i \(0.404310\pi\)
\(578\) −91.2605 280.871i −0.157890 0.485936i
\(579\) 259.150i 0.447581i
\(580\) −79.1935 + 57.5374i −0.136541 + 0.0992025i
\(581\) −400.689 −0.689654
\(582\) −415.161 + 134.894i −0.713335 + 0.231777i
\(583\) 1321.85i 2.26733i
\(584\) 35.9474 + 26.1173i 0.0615537 + 0.0447214i
\(585\) 65.7771 0.112439
\(586\) 110.541 + 340.210i 0.188637 + 0.580564i
\(587\) 618.412i 1.05351i 0.850016 + 0.526756i \(0.176592\pi\)
−0.850016 + 0.526756i \(0.823408\pi\)
\(588\) 118.079 + 162.522i 0.200815 + 0.276397i
\(589\) −126.217 −0.214290
\(590\) 74.1641 24.0974i 0.125702 0.0408430i
\(591\) 405.630i 0.686345i
\(592\) −90.7802 + 279.393i −0.153345 + 0.471947i
\(593\) 120.663 0.203478 0.101739 0.994811i \(-0.467559\pi\)
0.101739 + 0.994811i \(0.467559\pi\)
\(594\) 360.997 + 1111.03i 0.607739 + 1.87043i
\(595\) 139.758i 0.234888i
\(596\) 119.639 86.9231i 0.200737 0.145844i
\(597\) −640.000 −1.07203
\(598\) −8.94427 + 2.90617i −0.0149570 + 0.00485982i
\(599\) 849.927i 1.41891i −0.704751 0.709455i \(-0.748941\pi\)
0.704751 0.709455i \(-0.251059\pi\)
\(600\) −55.2786 + 76.0845i −0.0921311 + 0.126808i
\(601\) −11.3576 −0.0188978 −0.00944890 0.999955i \(-0.503008\pi\)
−0.00944890 + 0.999955i \(0.503008\pi\)
\(602\) 72.3607 + 222.703i 0.120200 + 0.369939i
\(603\) 174.378i 0.289183i
\(604\) −664.721 914.910i −1.10053 1.51475i
\(605\) 616.649 1.01926
\(606\) 286.715 93.1594i 0.473127 0.153728i
\(607\) 1115.12i 1.83710i −0.395305 0.918550i \(-0.629361\pi\)
0.395305 0.918550i \(-0.370639\pi\)
\(608\) 486.941i 0.800890i
\(609\) 135.279 0.222132
\(610\) −124.567 383.379i −0.204209 0.628490i
\(611\) 452.329i 0.740309i
\(612\) −133.580 + 97.0519i −0.218269 + 0.158582i
\(613\) 499.475 0.814805 0.407402 0.913249i \(-0.366435\pi\)
0.407402 + 0.913249i \(0.366435\pi\)
\(614\) 541.246 175.862i 0.881508 0.286419i
\(615\) 76.6705i 0.124667i
\(616\) −677.771 492.429i −1.10028 0.799398i
\(617\) 545.935 0.884822 0.442411 0.896813i \(-0.354123\pi\)
0.442411 + 0.896813i \(0.354123\pi\)
\(618\) 200.190 + 616.123i 0.323933 + 0.996962i
\(619\) 455.011i 0.735075i 0.930009 + 0.367537i \(0.119799\pi\)
−0.930009 + 0.367537i \(0.880201\pi\)
\(620\) −43.6068 60.0196i −0.0703335 0.0968058i
\(621\) −16.2755 −0.0262086
\(622\) −536.774 + 174.408i −0.862981 + 0.280399i
\(623\) 585.889i 0.940432i
\(624\) 303.108 + 98.4859i 0.485751 + 0.157830i
\(625\) 25.0000 0.0400000
\(626\) −350.764 1079.54i −0.560326 1.72451i
\(627\) 712.650i 1.13660i
\(628\) −662.577 + 481.391i −1.05506 + 0.766546i
\(629\) −218.282 −0.347030
\(630\) −77.6393 + 25.2265i −0.123237 + 0.0400421i
\(631\) 267.706i 0.424257i 0.977242 + 0.212128i \(0.0680395\pi\)
−0.977242 + 0.212128i \(0.931960\pi\)
\(632\) −65.1021 + 89.6054i −0.103010 + 0.141781i
\(633\) −482.610 −0.762417
\(634\) 99.5905 + 306.508i 0.157083 + 0.483451i
\(635\) 444.165i 0.699473i
\(636\) −366.833 504.902i −0.576781 0.793871i
\(637\) −180.971 −0.284098
\(638\) 414.663 134.732i 0.649941 0.211179i
\(639\) 280.503i 0.438971i
\(640\) 231.554 168.234i 0.361803 0.262866i
\(641\) −418.571 −0.652997 −0.326499 0.945198i \(-0.605869\pi\)
−0.326499 + 0.945198i \(0.605869\pi\)
\(642\) −74.5898 229.564i −0.116183 0.357576i
\(643\) 439.339i 0.683265i 0.939834 + 0.341633i \(0.110980\pi\)
−0.939834 + 0.341633i \(0.889020\pi\)
\(644\) 9.44272 6.86054i 0.0146626 0.0106530i
\(645\) −117.082 −0.181523
\(646\) 344.105 111.807i 0.532671 0.173075i
\(647\) 419.644i 0.648600i 0.945954 + 0.324300i \(0.105129\pi\)
−0.945954 + 0.324300i \(0.894871\pi\)
\(648\) 243.967 + 177.253i 0.376493 + 0.273538i
\(649\) −347.331 −0.535179
\(650\) −26.1803 80.5748i −0.0402774 0.123961i
\(651\) 102.526i 0.157490i
\(652\) −252.125 347.021i −0.386695 0.532240i
\(653\) −370.085 −0.566746 −0.283373 0.959010i \(-0.591453\pi\)
−0.283373 + 0.959010i \(0.591453\pi\)
\(654\) 596.892 193.942i 0.912678 0.296547i
\(655\) 17.3752i 0.0265270i
\(656\) −72.1052 + 221.917i −0.109917 + 0.338288i
\(657\) −19.2849 −0.0293529
\(658\) 173.475 + 533.902i 0.263640 + 0.811401i
\(659\) 322.823i 0.489868i −0.969540 0.244934i \(-0.921234\pi\)
0.969540 0.244934i \(-0.0787664\pi\)
\(660\) 338.885 246.215i 0.513463 0.373053i
\(661\) −812.735 −1.22955 −0.614777 0.788701i \(-0.710754\pi\)
−0.614777 + 0.788701i \(0.710754\pi\)
\(662\) −631.437 + 205.166i −0.953832 + 0.309919i
\(663\) 236.810i 0.357180i
\(664\) −358.387 + 493.277i −0.539739 + 0.742888i
\(665\) 178.885 0.269001
\(666\) −39.4001 121.261i −0.0591594 0.182074i
\(667\) 6.07439i 0.00910703i
\(668\) −78.0789 107.466i −0.116885 0.160878i
\(669\) 554.237 0.828456
\(670\) 213.607 69.4051i 0.318816 0.103590i
\(671\) 1795.47i 2.67581i
\(672\) −395.542 −0.588604
\(673\) 467.378 0.694469 0.347235 0.937778i \(-0.387121\pi\)
0.347235 + 0.937778i \(0.387121\pi\)
\(674\) −166.318 511.875i −0.246763 0.759458i
\(675\) 146.619i 0.217213i
\(676\) 314.620 228.585i 0.465414 0.338143i
\(677\) 548.237 0.809803 0.404902 0.914360i \(-0.367306\pi\)
0.404902 + 0.914360i \(0.367306\pi\)
\(678\) 763.489 248.073i 1.12609 0.365889i
\(679\) 488.051i 0.718779i
\(680\) 172.053 + 125.004i 0.253019 + 0.183829i
\(681\) −137.580 −0.202027
\(682\) 102.111 + 314.267i 0.149724 + 0.460802i
\(683\) 23.9663i 0.0350898i 0.999846 + 0.0175449i \(0.00558500\pi\)
−0.999846 + 0.0175449i \(0.994415\pi\)
\(684\) 124.223 + 170.978i 0.181612 + 0.249968i
\(685\) −1.86223 −0.00271859
\(686\) 703.607 228.616i 1.02567 0.333259i
\(687\) 382.581i 0.556886i
\(688\) 338.885 + 110.111i 0.492566 + 0.160044i
\(689\) 562.217 0.815989
\(690\) 1.80340 + 5.55029i 0.00261362 + 0.00804390i
\(691\) 186.981i 0.270595i −0.990805 0.135298i \(-0.956801\pi\)
0.990805 0.135298i \(-0.0431990\pi\)
\(692\) 732.519 532.206i 1.05855 0.769084i
\(693\) 363.607 0.524685
\(694\) 956.906 310.917i 1.37883 0.448008i
\(695\) 531.420i 0.764633i
\(696\) 120.997 166.538i 0.173846 0.239279i
\(697\) −173.378 −0.248748
\(698\) −0.311896 0.959917i −0.000446842 0.00137524i
\(699\) 750.130i 1.07315i
\(700\) 61.8034 + 85.0651i 0.0882906 + 0.121522i
\(701\) −706.636 −1.00804 −0.504020 0.863692i \(-0.668146\pi\)
−0.504020 + 0.863692i \(0.668146\pi\)
\(702\) −472.551 + 153.541i −0.673150 + 0.218720i
\(703\) 279.393i 0.397429i
\(704\) −1212.43 + 393.943i −1.72221 + 0.559579i
\(705\) −280.689 −0.398140
\(706\) −207.656 639.098i −0.294130 0.905238i
\(707\) 337.054i 0.476738i
\(708\) −132.669 + 96.3895i −0.187385 + 0.136143i
\(709\) −188.597 −0.266005 −0.133002 0.991116i \(-0.542462\pi\)
−0.133002 + 0.991116i \(0.542462\pi\)
\(710\) −343.607 + 111.645i −0.483953 + 0.157246i
\(711\) 48.0710i 0.0676104i
\(712\) 721.272 + 524.035i 1.01302 + 0.736004i
\(713\) −4.60369 −0.00645679
\(714\) −90.8204 279.516i −0.127199 0.391480i
\(715\) 377.354i 0.527769i
\(716\) −527.449 725.971i −0.736661 1.01393i
\(717\) 556.774 0.776533
\(718\) −187.331 + 60.8676i −0.260907 + 0.0847738i
\(719\) 156.085i 0.217086i 0.994092 + 0.108543i \(0.0346186\pi\)
−0.994092 + 0.108543i \(0.965381\pi\)
\(720\) −38.3870 + 118.143i −0.0533153 + 0.164088i
\(721\) 724.296 1.00457
\(722\) 80.0019 + 246.221i 0.110806 + 0.341026i
\(723\) 2.15825i 0.00298514i
\(724\) −279.023 + 202.722i −0.385391 + 0.280003i
\(725\) −54.7214 −0.0754777
\(726\) −1233.30 + 400.723i −1.69876 + 0.551960i
\(727\) 715.164i 0.983719i −0.870675 0.491859i \(-0.836317\pi\)
0.870675 0.491859i \(-0.163683\pi\)
\(728\) 209.443 288.273i 0.287696 0.395980i
\(729\) −751.381 −1.03070
\(730\) 7.67568 + 23.6233i 0.0105146 + 0.0323607i
\(731\) 264.762i 0.362191i
\(732\) 498.269 + 685.809i 0.680696 + 0.936897i
\(733\) 1233.29 1.68252 0.841259 0.540632i \(-0.181815\pi\)
0.841259 + 0.540632i \(0.181815\pi\)
\(734\) −948.152 + 308.073i −1.29176 + 0.419718i
\(735\) 112.300i 0.152789i
\(736\) 17.7609i 0.0241317i
\(737\) −1000.38 −1.35737
\(738\) −31.2949 96.3158i −0.0424050 0.130509i
\(739\) 8.55656i 0.0115786i 0.999983 + 0.00578928i \(0.00184280\pi\)
−0.999983 + 0.00578928i \(0.998157\pi\)
\(740\) −132.859 + 96.5278i −0.179539 + 0.130443i
\(741\) 303.108 0.409053
\(742\) −663.607 + 215.619i −0.894349 + 0.290592i
\(743\) 1010.56i 1.36011i −0.733163 0.680053i \(-0.761957\pi\)
0.733163 0.680053i \(-0.238043\pi\)
\(744\) 126.217 + 91.7018i 0.169646 + 0.123255i
\(745\) 82.6687 0.110965
\(746\) 371.039 + 1141.94i 0.497372 + 1.53075i
\(747\) 264.631i 0.354258i
\(748\) −556.774 766.334i −0.744350 1.02451i
\(749\) −269.868 −0.360305
\(750\) −50.0000 + 16.2460i −0.0666667 + 0.0216613i
\(751\) 1104.31i 1.47046i −0.677820 0.735228i \(-0.737075\pi\)
0.677820 0.735228i \(-0.262925\pi\)
\(752\) 812.433 + 263.976i 1.08036 + 0.351031i
\(753\) −321.378 −0.426796
\(754\) 57.3050 + 176.367i 0.0760013 + 0.233908i
\(755\) 632.188i 0.837335i
\(756\) 498.885 362.461i 0.659901 0.479446i
\(757\) −875.633 −1.15671 −0.578357 0.815783i \(-0.696306\pi\)
−0.578357 + 0.815783i \(0.696306\pi\)
\(758\) −577.272 + 187.567i −0.761573 + 0.247450i
\(759\) 25.9936i 0.0342471i
\(760\) 160.000 220.221i 0.210526 0.289765i
\(761\) −647.207 −0.850470 −0.425235 0.905083i \(-0.639808\pi\)
−0.425235 + 0.905083i \(0.639808\pi\)
\(762\) −288.636 888.331i −0.378788 1.16579i
\(763\) 701.688i 0.919644i
\(764\) 72.9318 + 100.382i 0.0954605 + 0.131390i
\(765\) −92.3018 −0.120656
\(766\) 632.610 205.547i 0.825861 0.268339i
\(767\) 147.729i 0.192606i
\(768\) −353.783 + 486.941i −0.460655 + 0.634038i
\(769\) 631.430 0.821106 0.410553 0.911837i \(-0.365336\pi\)
0.410553 + 0.911837i \(0.365336\pi\)
\(770\) −144.721 445.407i −0.187950 0.578450i
\(771\) 646.433i 0.838434i
\(772\) −356.689 + 259.150i −0.462032 + 0.335686i
\(773\) −421.522 −0.545306 −0.272653 0.962112i \(-0.587901\pi\)
−0.272653 + 0.962112i \(0.587901\pi\)
\(774\) −147.082 + 47.7899i −0.190028 + 0.0617440i
\(775\) 41.4725i 0.0535129i
\(776\) 600.827 + 436.526i 0.774261 + 0.562534i
\(777\) 226.950 0.292086
\(778\) 242.488 + 746.303i 0.311682 + 0.959258i
\(779\) 221.917i 0.284874i
\(780\) 104.721 + 144.137i 0.134258 + 0.184790i
\(781\) 1609.21 2.06044
\(782\) 12.5511 4.07809i 0.0160500 0.00521495i
\(783\) 320.927i 0.409869i
\(784\) 105.613 325.043i 0.134710 0.414596i
\(785\) −457.830 −0.583223
\(786\) 11.2911 + 34.7503i 0.0143652 + 0.0442116i
\(787\) 838.633i 1.06561i 0.846239 + 0.532804i \(0.178862\pi\)