Properties

Label 690.3.b.a.599.10
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.10
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.9

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.16793 + 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 + 2.69276i) q^{5} +(3.06591 - 2.93261i) q^{6} +3.87132i q^{7} -2.82843 q^{8} +(0.399825 - 8.99111i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.16793 + 2.07367i) q^{3} +2.00000 q^{4} +(4.21296 + 2.69276i) q^{5} +(3.06591 - 2.93261i) q^{6} +3.87132i q^{7} -2.82843 q^{8} +(0.399825 - 8.99111i) q^{9} +(-5.95803 - 3.80814i) q^{10} -5.04237i q^{11} +(-4.33586 + 4.14733i) q^{12} +15.3444i q^{13} -5.47487i q^{14} +(-14.7173 + 2.89856i) q^{15} +4.00000 q^{16} -10.2474 q^{17} +(-0.565438 + 12.7154i) q^{18} -19.1628 q^{19} +(8.42592 + 5.38552i) q^{20} +(-8.02782 - 8.39274i) q^{21} +7.13098i q^{22} +4.79583 q^{23} +(6.13183 - 5.86521i) q^{24} +(10.4981 + 22.6890i) q^{25} -21.7003i q^{26} +(17.7778 + 20.3212i) q^{27} +7.74264i q^{28} +10.8847i q^{29} +(20.8134 - 4.09918i) q^{30} +0.921869 q^{31} -5.65685 q^{32} +(10.4562 + 10.9315i) q^{33} +14.4920 q^{34} +(-10.4245 + 16.3097i) q^{35} +(0.799650 - 17.9822i) q^{36} +31.4952i q^{37} +27.1003 q^{38} +(-31.8192 - 33.2656i) q^{39} +(-11.9161 - 7.61628i) q^{40} -28.3053i q^{41} +(11.3530 + 11.8691i) q^{42} +26.8720i q^{43} -10.0847i q^{44} +(25.8954 - 36.8026i) q^{45} -6.78233 q^{46} -53.0761 q^{47} +(-8.67171 + 8.29466i) q^{48} +34.0129 q^{49} +(-14.8465 - 32.0871i) q^{50} +(22.2155 - 21.2496i) q^{51} +30.6888i q^{52} -15.1211 q^{53} +(-25.1416 - 28.7385i) q^{54} +(13.5779 - 21.2433i) q^{55} -10.9497i q^{56} +(41.5436 - 39.7372i) q^{57} -15.3934i q^{58} -23.8577i q^{59} +(-29.4346 + 5.79711i) q^{60} -55.3744 q^{61} -1.30372 q^{62} +(34.8075 + 1.54785i) q^{63} +8.00000 q^{64} +(-41.3188 + 64.6454i) q^{65} +(-14.7873 - 15.4595i) q^{66} -43.6001i q^{67} -20.4947 q^{68} +(-10.3970 + 9.94495i) q^{69} +(14.7425 - 23.0654i) q^{70} +2.55319i q^{71} +(-1.13088 + 25.4307i) q^{72} +12.0538i q^{73} -44.5410i q^{74} +(-69.8084 - 27.4186i) q^{75} -38.3256 q^{76} +19.5206 q^{77} +(44.9991 + 47.0447i) q^{78} -101.853 q^{79} +(16.8518 + 10.7710i) q^{80} +(-80.6803 - 7.18975i) q^{81} +40.0298i q^{82} -146.715 q^{83} +(-16.0556 - 16.7855i) q^{84} +(-43.1717 - 27.5937i) q^{85} -38.0027i q^{86} +(-22.5713 - 23.5974i) q^{87} +14.2620i q^{88} +126.637i q^{89} +(-36.6216 + 52.0467i) q^{90} -59.4031 q^{91} +9.59166 q^{92} +(-1.99855 + 1.91165i) q^{93} +75.0609 q^{94} +(-80.7322 - 51.6009i) q^{95} +(12.2637 - 11.7304i) q^{96} -136.772i q^{97} -48.1015 q^{98} +(-45.3365 - 2.01606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.16793 + 2.07367i −0.722643 + 0.691222i
\(4\) 2.00000 0.500000
\(5\) 4.21296 + 2.69276i 0.842592 + 0.538552i
\(6\) 3.06591 2.93261i 0.510986 0.488768i
\(7\) 3.87132i 0.553045i 0.961007 + 0.276523i \(0.0891821\pi\)
−0.961007 + 0.276523i \(0.910818\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0.399825 8.99111i 0.0444250 0.999013i
\(10\) −5.95803 3.80814i −0.595803 0.380814i
\(11\) 5.04237i 0.458397i −0.973380 0.229198i \(-0.926390\pi\)
0.973380 0.229198i \(-0.0736105\pi\)
\(12\) −4.33586 + 4.14733i −0.361321 + 0.345611i
\(13\) 15.3444i 1.18034i 0.807279 + 0.590170i \(0.200939\pi\)
−0.807279 + 0.590170i \(0.799061\pi\)
\(14\) 5.47487i 0.391062i
\(15\) −14.7173 + 2.89856i −0.981152 + 0.193237i
\(16\) 4.00000 0.250000
\(17\) −10.2474 −0.602786 −0.301393 0.953500i \(-0.597452\pi\)
−0.301393 + 0.953500i \(0.597452\pi\)
\(18\) −0.565438 + 12.7154i −0.0314132 + 0.706409i
\(19\) −19.1628 −1.00857 −0.504284 0.863538i \(-0.668244\pi\)
−0.504284 + 0.863538i \(0.668244\pi\)
\(20\) 8.42592 + 5.38552i 0.421296 + 0.269276i
\(21\) −8.02782 8.39274i −0.382277 0.399654i
\(22\) 7.13098i 0.324136i
\(23\) 4.79583 0.208514
\(24\) 6.13183 5.86521i 0.255493 0.244384i
\(25\) 10.4981 + 22.6890i 0.419923 + 0.907560i
\(26\) 21.7003i 0.834626i
\(27\) 17.7778 + 20.3212i 0.658436 + 0.752637i
\(28\) 7.74264i 0.276523i
\(29\) 10.8847i 0.375336i 0.982233 + 0.187668i \(0.0600929\pi\)
−0.982233 + 0.187668i \(0.939907\pi\)
\(30\) 20.8134 4.09918i 0.693779 0.136639i
\(31\) 0.921869 0.0297377 0.0148689 0.999889i \(-0.495267\pi\)
0.0148689 + 0.999889i \(0.495267\pi\)
\(32\) −5.65685 −0.176777
\(33\) 10.4562 + 10.9315i 0.316854 + 0.331257i
\(34\) 14.4920 0.426234
\(35\) −10.4245 + 16.3097i −0.297844 + 0.465992i
\(36\) 0.799650 17.9822i 0.0222125 0.499506i
\(37\) 31.4952i 0.851222i 0.904906 + 0.425611i \(0.139941\pi\)
−0.904906 + 0.425611i \(0.860059\pi\)
\(38\) 27.1003 0.713166
\(39\) −31.8192 33.2656i −0.815876 0.852964i
\(40\) −11.9161 7.61628i −0.297901 0.190407i
\(41\) 28.3053i 0.690374i −0.938534 0.345187i \(-0.887816\pi\)
0.938534 0.345187i \(-0.112184\pi\)
\(42\) 11.3530 + 11.8691i 0.270311 + 0.282598i
\(43\) 26.8720i 0.624930i 0.949929 + 0.312465i \(0.101155\pi\)
−0.949929 + 0.312465i \(0.898845\pi\)
\(44\) 10.0847i 0.229198i
\(45\) 25.8954 36.8026i 0.575453 0.817835i
\(46\) −6.78233 −0.147442
\(47\) −53.0761 −1.12928 −0.564639 0.825338i \(-0.690985\pi\)
−0.564639 + 0.825338i \(0.690985\pi\)
\(48\) −8.67171 + 8.29466i −0.180661 + 0.172805i
\(49\) 34.0129 0.694141
\(50\) −14.8465 32.0871i −0.296930 0.641742i
\(51\) 22.2155 21.2496i 0.435599 0.416659i
\(52\) 30.6888i 0.590170i
\(53\) −15.1211 −0.285304 −0.142652 0.989773i \(-0.545563\pi\)
−0.142652 + 0.989773i \(0.545563\pi\)
\(54\) −25.1416 28.7385i −0.465584 0.532195i
\(55\) 13.5779 21.2433i 0.246871 0.386242i
\(56\) 10.9497i 0.195531i
\(57\) 41.5436 39.7372i 0.728835 0.697145i
\(58\) 15.3934i 0.265403i
\(59\) 23.8577i 0.404368i −0.979348 0.202184i \(-0.935196\pi\)
0.979348 0.202184i \(-0.0648040\pi\)
\(60\) −29.4346 + 5.79711i −0.490576 + 0.0966186i
\(61\) −55.3744 −0.907777 −0.453889 0.891058i \(-0.649964\pi\)
−0.453889 + 0.891058i \(0.649964\pi\)
\(62\) −1.30372 −0.0210277
\(63\) 34.8075 + 1.54785i 0.552499 + 0.0245691i
\(64\) 8.00000 0.125000
\(65\) −41.3188 + 64.6454i −0.635675 + 0.994545i
\(66\) −14.7873 15.4595i −0.224050 0.234234i
\(67\) 43.6001i 0.650748i −0.945585 0.325374i \(-0.894510\pi\)
0.945585 0.325374i \(-0.105490\pi\)
\(68\) −20.4947 −0.301393
\(69\) −10.3970 + 9.94495i −0.150681 + 0.144130i
\(70\) 14.7425 23.0654i 0.210607 0.329506i
\(71\) 2.55319i 0.0359605i 0.999838 + 0.0179802i \(0.00572359\pi\)
−0.999838 + 0.0179802i \(0.994276\pi\)
\(72\) −1.13088 + 25.4307i −0.0157066 + 0.353204i
\(73\) 12.0538i 0.165120i 0.996586 + 0.0825601i \(0.0263097\pi\)
−0.996586 + 0.0825601i \(0.973690\pi\)
\(74\) 44.5410i 0.601905i
\(75\) −69.8084 27.4186i −0.930779 0.365582i
\(76\) −38.3256 −0.504284
\(77\) 19.5206 0.253514
\(78\) 44.9991 + 47.0447i 0.576912 + 0.603137i
\(79\) −101.853 −1.28928 −0.644639 0.764487i \(-0.722992\pi\)
−0.644639 + 0.764487i \(0.722992\pi\)
\(80\) 16.8518 + 10.7710i 0.210648 + 0.134638i
\(81\) −80.6803 7.18975i −0.996053 0.0887623i
\(82\) 40.0298i 0.488168i
\(83\) −146.715 −1.76765 −0.883826 0.467815i \(-0.845041\pi\)
−0.883826 + 0.467815i \(0.845041\pi\)
\(84\) −16.0556 16.7855i −0.191139 0.199827i
\(85\) −43.1717 27.5937i −0.507903 0.324632i
\(86\) 38.0027i 0.441892i
\(87\) −22.5713 23.5974i −0.259441 0.271234i
\(88\) 14.2620i 0.162068i
\(89\) 126.637i 1.42289i 0.702744 + 0.711443i \(0.251958\pi\)
−0.702744 + 0.711443i \(0.748042\pi\)
\(90\) −36.6216 + 52.0467i −0.406907 + 0.578297i
\(91\) −59.4031 −0.652781
\(92\) 9.59166 0.104257
\(93\) −1.99855 + 1.91165i −0.0214897 + 0.0205554i
\(94\) 75.0609 0.798521
\(95\) −80.7322 51.6009i −0.849812 0.543167i
\(96\) 12.2637 11.7304i 0.127746 0.122192i
\(97\) 136.772i 1.41002i −0.709199 0.705009i \(-0.750943\pi\)
0.709199 0.705009i \(-0.249057\pi\)
\(98\) −48.1015 −0.490832
\(99\) −45.3365 2.01606i −0.457944 0.0203643i
\(100\) 20.9961 + 45.3780i 0.209961 + 0.453780i
\(101\) 66.3835i 0.657263i 0.944458 + 0.328631i \(0.106587\pi\)
−0.944458 + 0.328631i \(0.893413\pi\)
\(102\) −31.4175 + 30.0515i −0.308015 + 0.294622i
\(103\) 96.5999i 0.937863i −0.883234 0.468932i \(-0.844639\pi\)
0.883234 0.468932i \(-0.155361\pi\)
\(104\) 43.4006i 0.417313i
\(105\) −11.2212 56.9753i −0.106869 0.542622i
\(106\) 21.3845 0.201741
\(107\) −157.136 −1.46856 −0.734280 0.678846i \(-0.762480\pi\)
−0.734280 + 0.678846i \(0.762480\pi\)
\(108\) 35.5555 + 40.6424i 0.329218 + 0.376318i
\(109\) −142.427 −1.30667 −0.653337 0.757067i \(-0.726631\pi\)
−0.653337 + 0.757067i \(0.726631\pi\)
\(110\) −19.2020 + 30.0425i −0.174564 + 0.273114i
\(111\) −65.3106 68.2794i −0.588383 0.615130i
\(112\) 15.4853i 0.138261i
\(113\) 63.4870 0.561832 0.280916 0.959732i \(-0.409362\pi\)
0.280916 + 0.959732i \(0.409362\pi\)
\(114\) −58.7515 + 56.1970i −0.515364 + 0.492956i
\(115\) 20.2046 + 12.9140i 0.175693 + 0.112296i
\(116\) 21.7695i 0.187668i
\(117\) 137.963 + 6.13508i 1.17917 + 0.0524366i
\(118\) 33.7399i 0.285932i
\(119\) 39.6708i 0.333368i
\(120\) 41.6268 8.19836i 0.346890 0.0683196i
\(121\) 95.5745 0.789872
\(122\) 78.3113 0.641896
\(123\) 58.6958 + 61.3639i 0.477201 + 0.498894i
\(124\) 1.84374 0.0148689
\(125\) −16.8681 + 123.857i −0.134945 + 0.990853i
\(126\) −49.2252 2.18899i −0.390676 0.0173729i
\(127\) 195.570i 1.53992i −0.638090 0.769962i \(-0.720275\pi\)
0.638090 0.769962i \(-0.279725\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −55.7235 58.2565i −0.431965 0.451601i
\(130\) 58.4337 91.4224i 0.449490 0.703249i
\(131\) 67.9207i 0.518479i −0.965813 0.259239i \(-0.916528\pi\)
0.965813 0.259239i \(-0.0834719\pi\)
\(132\) 20.9124 + 21.8630i 0.158427 + 0.165629i
\(133\) 74.1853i 0.557784i
\(134\) 61.6599i 0.460148i
\(135\) 20.1769 + 133.484i 0.149459 + 0.988768i
\(136\) 28.9839 0.213117
\(137\) −95.4416 −0.696654 −0.348327 0.937373i \(-0.613250\pi\)
−0.348327 + 0.937373i \(0.613250\pi\)
\(138\) 14.7036 14.0643i 0.106548 0.101915i
\(139\) 20.1287 0.144811 0.0724053 0.997375i \(-0.476932\pi\)
0.0724053 + 0.997375i \(0.476932\pi\)
\(140\) −20.8491 + 32.6194i −0.148922 + 0.232996i
\(141\) 115.065 110.062i 0.816065 0.780582i
\(142\) 3.61076i 0.0254279i
\(143\) 77.3722 0.541064
\(144\) 1.59930 35.9645i 0.0111063 0.249753i
\(145\) −29.3100 + 45.8570i −0.202138 + 0.316255i
\(146\) 17.0466i 0.116758i
\(147\) −73.7375 + 70.5314i −0.501616 + 0.479805i
\(148\) 62.9904i 0.425611i
\(149\) 3.49799i 0.0234764i −0.999931 0.0117382i \(-0.996264\pi\)
0.999931 0.0117382i \(-0.00373648\pi\)
\(150\) 98.7241 + 38.7758i 0.658160 + 0.258505i
\(151\) 256.597 1.69932 0.849660 0.527331i \(-0.176807\pi\)
0.849660 + 0.527331i \(0.176807\pi\)
\(152\) 54.2006 0.356583
\(153\) −4.09715 + 92.1352i −0.0267788 + 0.602191i
\(154\) −27.6063 −0.179262
\(155\) 3.88380 + 2.48237i 0.0250568 + 0.0160153i
\(156\) −63.6384 66.5312i −0.407938 0.426482i
\(157\) 4.85732i 0.0309384i 0.999880 + 0.0154692i \(0.00492419\pi\)
−0.999880 + 0.0154692i \(0.995076\pi\)
\(158\) 144.042 0.911657
\(159\) 32.7815 31.3562i 0.206173 0.197209i
\(160\) −23.8321 15.2326i −0.148951 0.0952035i
\(161\) 18.5662i 0.115318i
\(162\) 114.099 + 10.1678i 0.704316 + 0.0627644i
\(163\) 219.553i 1.34695i 0.739210 + 0.673475i \(0.235199\pi\)
−0.739210 + 0.673475i \(0.764801\pi\)
\(164\) 56.6107i 0.345187i
\(165\) 14.6156 + 74.2099i 0.0885793 + 0.449757i
\(166\) 207.487 1.24992
\(167\) −329.137 −1.97088 −0.985440 0.170025i \(-0.945615\pi\)
−0.985440 + 0.170025i \(0.945615\pi\)
\(168\) 22.7061 + 23.7383i 0.135155 + 0.141299i
\(169\) −66.4511 −0.393202
\(170\) 61.0540 + 39.0234i 0.359141 + 0.229549i
\(171\) −7.66177 + 172.295i −0.0448057 + 1.00757i
\(172\) 53.7439i 0.312465i
\(173\) 159.612 0.922611 0.461306 0.887241i \(-0.347381\pi\)
0.461306 + 0.887241i \(0.347381\pi\)
\(174\) 31.9207 + 33.3717i 0.183452 + 0.191791i
\(175\) −87.8363 + 40.6414i −0.501922 + 0.232236i
\(176\) 20.1695i 0.114599i
\(177\) 49.4730 + 51.7219i 0.279508 + 0.292214i
\(178\) 179.091i 1.00613i
\(179\) 46.3952i 0.259191i −0.991567 0.129595i \(-0.958632\pi\)
0.991567 0.129595i \(-0.0413679\pi\)
\(180\) 51.7907 73.6052i 0.287726 0.408918i
\(181\) 221.770 1.22525 0.612625 0.790373i \(-0.290113\pi\)
0.612625 + 0.790373i \(0.290113\pi\)
\(182\) 84.0087 0.461586
\(183\) 120.048 114.828i 0.655999 0.627475i
\(184\) −13.5647 −0.0737210
\(185\) −84.8091 + 132.688i −0.458428 + 0.717233i
\(186\) 2.82637 2.70348i 0.0151955 0.0145348i
\(187\) 51.6709i 0.276315i
\(188\) −106.152 −0.564639
\(189\) −78.6698 + 68.8234i −0.416242 + 0.364145i
\(190\) 114.173 + 72.9746i 0.600908 + 0.384077i
\(191\) 14.2887i 0.0748099i 0.999300 + 0.0374050i \(0.0119091\pi\)
−0.999300 + 0.0374050i \(0.988091\pi\)
\(192\) −17.3434 + 16.5893i −0.0903303 + 0.0864027i
\(193\) 283.329i 1.46802i 0.679136 + 0.734012i \(0.262355\pi\)
−0.679136 + 0.734012i \(0.737645\pi\)
\(194\) 193.424i 0.997033i
\(195\) −44.4767 225.828i −0.228085 1.15809i
\(196\) 68.0258 0.347070
\(197\) 145.276 0.737439 0.368720 0.929541i \(-0.379796\pi\)
0.368720 + 0.929541i \(0.379796\pi\)
\(198\) 64.1155 + 2.85115i 0.323816 + 0.0143997i
\(199\) 134.005 0.673390 0.336695 0.941614i \(-0.390691\pi\)
0.336695 + 0.941614i \(0.390691\pi\)
\(200\) −29.6930 64.1742i −0.148465 0.320871i
\(201\) 90.4120 + 94.5219i 0.449811 + 0.470258i
\(202\) 93.8805i 0.464755i
\(203\) −42.1383 −0.207578
\(204\) 44.4311 42.4992i 0.217799 0.208329i
\(205\) 76.2195 119.249i 0.371802 0.581704i
\(206\) 136.613i 0.663170i
\(207\) 1.91749 43.1199i 0.00926326 0.208309i
\(208\) 61.3777i 0.295085i
\(209\) 96.6259i 0.462325i
\(210\) 15.8692 + 80.5752i 0.0755677 + 0.383691i
\(211\) −143.378 −0.679516 −0.339758 0.940513i \(-0.610345\pi\)
−0.339758 + 0.940513i \(0.610345\pi\)
\(212\) −30.2423 −0.142652
\(213\) −5.29447 5.53514i −0.0248567 0.0259866i
\(214\) 222.224 1.03843
\(215\) −72.3598 + 113.211i −0.336557 + 0.526561i
\(216\) −50.2831 57.4770i −0.232792 0.266097i
\(217\) 3.56885i 0.0164463i
\(218\) 201.423 0.923958
\(219\) −24.9955 26.1317i −0.114135 0.119323i
\(220\) 27.1558 42.4866i 0.123435 0.193121i
\(221\) 157.240i 0.711492i
\(222\) 92.3631 + 96.5616i 0.416050 + 0.434962i
\(223\) 87.2841i 0.391409i −0.980663 0.195704i \(-0.937301\pi\)
0.980663 0.195704i \(-0.0626993\pi\)
\(224\) 21.8995i 0.0977655i
\(225\) 208.197 85.3178i 0.925319 0.379190i
\(226\) −89.7841 −0.397275
\(227\) −73.6779 −0.324572 −0.162286 0.986744i \(-0.551887\pi\)
−0.162286 + 0.986744i \(0.551887\pi\)
\(228\) 83.0872 79.4745i 0.364417 0.348572i
\(229\) 60.3596 0.263579 0.131789 0.991278i \(-0.457928\pi\)
0.131789 + 0.991278i \(0.457928\pi\)
\(230\) −28.5737 18.2632i −0.124233 0.0794052i
\(231\) −42.3193 + 40.4792i −0.183200 + 0.175235i
\(232\) 30.7867i 0.132701i
\(233\) 23.4620 0.100695 0.0503477 0.998732i \(-0.483967\pi\)
0.0503477 + 0.998732i \(0.483967\pi\)
\(234\) −195.110 8.67632i −0.833802 0.0370783i
\(235\) −223.608 142.921i −0.951521 0.608176i
\(236\) 47.7155i 0.202184i
\(237\) 220.810 211.209i 0.931687 0.891177i
\(238\) 56.1030i 0.235727i
\(239\) 63.7138i 0.266585i −0.991077 0.133293i \(-0.957445\pi\)
0.991077 0.133293i \(-0.0425550\pi\)
\(240\) −58.8691 + 11.5942i −0.245288 + 0.0483093i
\(241\) 112.211 0.465606 0.232803 0.972524i \(-0.425210\pi\)
0.232803 + 0.972524i \(0.425210\pi\)
\(242\) −135.163 −0.558524
\(243\) 189.818 151.717i 0.781145 0.624350i
\(244\) −110.749 −0.453889
\(245\) 143.295 + 91.5886i 0.584878 + 0.373831i
\(246\) −83.0084 86.7817i −0.337432 0.352771i
\(247\) 294.042i 1.19045i
\(248\) −2.60744 −0.0105139
\(249\) 318.068 304.238i 1.27738 1.22184i
\(250\) 23.8551 175.160i 0.0954202 0.700639i
\(251\) 363.290i 1.44737i 0.690130 + 0.723685i \(0.257553\pi\)
−0.690130 + 0.723685i \(0.742447\pi\)
\(252\) 69.6149 + 3.09570i 0.276250 + 0.0122845i
\(253\) 24.1823i 0.0955824i
\(254\) 276.578i 1.08889i
\(255\) 150.813 29.7025i 0.591424 0.116481i
\(256\) 16.0000 0.0625000
\(257\) −30.3795 −0.118208 −0.0591040 0.998252i \(-0.518824\pi\)
−0.0591040 + 0.998252i \(0.518824\pi\)
\(258\) 78.8049 + 82.3871i 0.305445 + 0.319330i
\(259\) −121.928 −0.470765
\(260\) −82.6377 + 129.291i −0.317837 + 0.497272i
\(261\) 97.8660 + 4.35200i 0.374966 + 0.0166743i
\(262\) 96.0544i 0.366620i
\(263\) 276.122 1.04989 0.524946 0.851135i \(-0.324085\pi\)
0.524946 + 0.851135i \(0.324085\pi\)
\(264\) −29.5745 30.9189i −0.112025 0.117117i
\(265\) −63.7047 40.7176i −0.240395 0.153651i
\(266\) 104.914i 0.394413i
\(267\) −262.602 274.539i −0.983529 1.02824i
\(268\) 87.2002i 0.325374i
\(269\) 89.7539i 0.333658i −0.985986 0.166829i \(-0.946647\pi\)
0.985986 0.166829i \(-0.0533527\pi\)
\(270\) −28.5345 188.774i −0.105683 0.699165i
\(271\) −317.625 −1.17205 −0.586023 0.810294i \(-0.699307\pi\)
−0.586023 + 0.810294i \(0.699307\pi\)
\(272\) −40.9894 −0.150696
\(273\) 128.782 123.182i 0.471728 0.451217i
\(274\) 134.975 0.492609
\(275\) 114.406 52.9351i 0.416023 0.192491i
\(276\) −20.7940 + 19.8899i −0.0753407 + 0.0720648i
\(277\) 143.086i 0.516557i −0.966071 0.258279i \(-0.916845\pi\)
0.966071 0.258279i \(-0.0831552\pi\)
\(278\) −28.4663 −0.102397
\(279\) 0.368587 8.28863i 0.00132110 0.0297084i
\(280\) 29.4850 46.1308i 0.105304 0.164753i
\(281\) 445.282i 1.58463i 0.610111 + 0.792316i \(0.291125\pi\)
−0.610111 + 0.792316i \(0.708875\pi\)
\(282\) −162.727 + 155.651i −0.577045 + 0.551955i
\(283\) 418.790i 1.47982i 0.672704 + 0.739912i \(0.265133\pi\)
−0.672704 + 0.739912i \(0.734867\pi\)
\(284\) 5.10639i 0.0179802i
\(285\) 282.024 55.5445i 0.989559 0.194893i
\(286\) −109.421 −0.382590
\(287\) 109.579 0.381808
\(288\) −2.26175 + 50.8614i −0.00785331 + 0.176602i
\(289\) −183.992 −0.636649
\(290\) 41.4506 64.8516i 0.142933 0.223626i
\(291\) 283.619 + 296.511i 0.974635 + 1.01894i
\(292\) 24.1076i 0.0825601i
\(293\) −68.5934 −0.234107 −0.117054 0.993126i \(-0.537345\pi\)
−0.117054 + 0.993126i \(0.537345\pi\)
\(294\) 104.281 99.7464i 0.354696 0.339273i
\(295\) 64.2432 100.512i 0.217774 0.340718i
\(296\) 89.0819i 0.300953i
\(297\) 102.467 89.6420i 0.345006 0.301825i
\(298\) 4.94690i 0.0166004i
\(299\) 73.5892i 0.246118i
\(300\) −139.617 54.8372i −0.465390 0.182791i
\(301\) −104.030 −0.345614
\(302\) −362.883 −1.20160
\(303\) −137.657 143.915i −0.454314 0.474966i
\(304\) −76.6512 −0.252142
\(305\) −233.290 149.110i −0.764886 0.488886i
\(306\) 5.79425 130.299i 0.0189354 0.425813i
\(307\) 402.815i 1.31210i 0.754717 + 0.656050i \(0.227774\pi\)
−0.754717 + 0.656050i \(0.772226\pi\)
\(308\) 39.0412 0.126757
\(309\) 200.316 + 209.422i 0.648272 + 0.677740i
\(310\) −5.49252 3.51061i −0.0177178 0.0113245i
\(311\) 468.326i 1.50587i 0.658094 + 0.752936i \(0.271363\pi\)
−0.658094 + 0.752936i \(0.728637\pi\)
\(312\) 89.9982 + 94.0893i 0.288456 + 0.301568i
\(313\) 555.209i 1.77383i 0.461933 + 0.886915i \(0.347156\pi\)
−0.461933 + 0.886915i \(0.652844\pi\)
\(314\) 6.86929i 0.0218767i
\(315\) 142.474 + 100.249i 0.452300 + 0.318252i
\(316\) −203.706 −0.644639
\(317\) −441.805 −1.39371 −0.696854 0.717213i \(-0.745417\pi\)
−0.696854 + 0.717213i \(0.745417\pi\)
\(318\) −46.3601 + 44.3443i −0.145786 + 0.139447i
\(319\) 54.8849 0.172053
\(320\) 33.7037 + 21.5421i 0.105324 + 0.0673190i
\(321\) 340.660 325.847i 1.06124 1.01510i
\(322\) 26.2566i 0.0815421i
\(323\) 196.368 0.607951
\(324\) −161.361 14.3795i −0.498026 0.0443812i
\(325\) −348.149 + 161.087i −1.07123 + 0.495652i
\(326\) 310.495i 0.952437i
\(327\) 308.772 295.347i 0.944258 0.903201i
\(328\) 80.0596i 0.244084i
\(329\) 205.474i 0.624542i
\(330\) −20.6696 104.949i −0.0626350 0.318026i
\(331\) −5.74801 −0.0173656 −0.00868280 0.999962i \(-0.502764\pi\)
−0.00868280 + 0.999962i \(0.502764\pi\)
\(332\) −293.430 −0.883826
\(333\) 283.177 + 12.5926i 0.850382 + 0.0378156i
\(334\) 465.470 1.39362
\(335\) 117.405 183.686i 0.350462 0.548315i
\(336\) −32.1113 33.5710i −0.0955693 0.0999136i
\(337\) 168.422i 0.499768i −0.968276 0.249884i \(-0.919608\pi\)
0.968276 0.249884i \(-0.0803924\pi\)
\(338\) 93.9760 0.278036
\(339\) −137.635 + 131.651i −0.406004 + 0.388350i
\(340\) −86.3434 55.1874i −0.253951 0.162316i
\(341\) 4.64840i 0.0136317i
\(342\) 10.8354 243.662i 0.0316824 0.712462i
\(343\) 321.369i 0.936937i
\(344\) 76.0054i 0.220946i
\(345\) −70.5816 + 13.9010i −0.204584 + 0.0402927i
\(346\) −225.725 −0.652385
\(347\) −43.0406 −0.124036 −0.0620182 0.998075i \(-0.519754\pi\)
−0.0620182 + 0.998075i \(0.519754\pi\)
\(348\) −45.1427 47.1947i −0.129720 0.135617i
\(349\) 0.727200 0.00208367 0.00104183 0.999999i \(-0.499668\pi\)
0.00104183 + 0.999999i \(0.499668\pi\)
\(350\) 124.219 57.4756i 0.354912 0.164216i
\(351\) −311.817 + 272.789i −0.888367 + 0.777178i
\(352\) 28.5239i 0.0810339i
\(353\) 629.821 1.78420 0.892098 0.451843i \(-0.149233\pi\)
0.892098 + 0.451843i \(0.149233\pi\)
\(354\) −69.9653 73.1458i −0.197642 0.206626i
\(355\) −6.87514 + 10.7565i −0.0193666 + 0.0303000i
\(356\) 253.274i 0.711443i
\(357\) 82.2639 + 86.0034i 0.230431 + 0.240906i
\(358\) 65.6127i 0.183276i
\(359\) 583.627i 1.62570i −0.582471 0.812851i \(-0.697914\pi\)
0.582471 0.812851i \(-0.302086\pi\)
\(360\) −73.2432 + 104.093i −0.203453 + 0.289148i
\(361\) 6.21317 0.0172110
\(362\) −313.631 −0.866383
\(363\) −207.199 + 198.190i −0.570795 + 0.545977i
\(364\) −118.806 −0.326391
\(365\) −32.4580 + 50.7821i −0.0889259 + 0.139129i
\(366\) −169.773 + 162.391i −0.463861 + 0.443692i
\(367\) 373.566i 1.01789i −0.860799 0.508946i \(-0.830035\pi\)
0.860799 0.508946i \(-0.169965\pi\)
\(368\) 19.1833 0.0521286
\(369\) −254.496 11.3172i −0.689692 0.0306699i
\(370\) 119.938 187.649i 0.324157 0.507160i
\(371\) 58.5387i 0.157786i
\(372\) −3.99709 + 3.82330i −0.0107449 + 0.0102777i
\(373\) 216.748i 0.581094i 0.956861 + 0.290547i \(0.0938372\pi\)
−0.956861 + 0.290547i \(0.906163\pi\)
\(374\) 73.0737i 0.195384i
\(375\) −220.268 303.491i −0.587383 0.809309i
\(376\) 150.122 0.399260
\(377\) −167.020 −0.443024
\(378\) 111.256 97.3310i 0.294328 0.257489i
\(379\) 206.231 0.544145 0.272072 0.962277i \(-0.412291\pi\)
0.272072 + 0.962277i \(0.412291\pi\)
\(380\) −161.464 103.202i −0.424906 0.271583i
\(381\) 405.547 + 423.982i 1.06443 + 1.11281i
\(382\) 20.2073i 0.0528986i
\(383\) 95.6645 0.249777 0.124888 0.992171i \(-0.460143\pi\)
0.124888 + 0.992171i \(0.460143\pi\)
\(384\) 24.5273 23.4608i 0.0638732 0.0610959i
\(385\) 82.2395 + 52.5643i 0.213609 + 0.136531i
\(386\) 400.687i 1.03805i
\(387\) 241.609 + 10.7441i 0.624313 + 0.0277625i
\(388\) 273.543i 0.705009i
\(389\) 173.495i 0.446003i −0.974818 0.223001i \(-0.928415\pi\)
0.974818 0.223001i \(-0.0715854\pi\)
\(390\) 62.8995 + 319.369i 0.161281 + 0.818895i
\(391\) −49.1446 −0.125690
\(392\) −96.2030 −0.245416
\(393\) 140.845 + 147.247i 0.358384 + 0.374675i
\(394\) −205.451 −0.521448
\(395\) −429.102 274.266i −1.08634 0.694343i
\(396\) −90.6730 4.03213i −0.228972 0.0101821i
\(397\) 341.235i 0.859533i 0.902940 + 0.429767i \(0.141404\pi\)
−0.902940 + 0.429767i \(0.858596\pi\)
\(398\) −189.511 −0.476158
\(399\) 153.836 + 160.828i 0.385553 + 0.403079i
\(400\) 41.9923 + 90.7560i 0.104981 + 0.226890i
\(401\) 335.722i 0.837213i −0.908168 0.418606i \(-0.862519\pi\)
0.908168 0.418606i \(-0.137481\pi\)
\(402\) −127.862 133.674i −0.318064 0.332523i
\(403\) 14.1455i 0.0351006i
\(404\) 132.767i 0.328631i
\(405\) −320.543 247.543i −0.791463 0.611217i
\(406\) 59.5926 0.146780
\(407\) 158.810 0.390198
\(408\) −62.8350 + 60.1029i −0.154007 + 0.147311i
\(409\) −132.366 −0.323634 −0.161817 0.986821i \(-0.551735\pi\)
−0.161817 + 0.986821i \(0.551735\pi\)
\(410\) −107.791 + 168.644i −0.262904 + 0.411327i
\(411\) 206.911 197.914i 0.503432 0.481542i
\(412\) 193.200i 0.468932i
\(413\) 92.3609 0.223634
\(414\) −2.71175 + 60.9807i −0.00655011 + 0.147296i
\(415\) −618.105 395.069i −1.48941 0.951973i
\(416\) 86.8011i 0.208657i
\(417\) −43.6375 + 41.7402i −0.104646 + 0.100096i
\(418\) 136.650i 0.326913i
\(419\) 545.122i 1.30101i 0.759504 + 0.650503i \(0.225442\pi\)
−0.759504 + 0.650503i \(0.774558\pi\)
\(420\) −22.4425 113.951i −0.0534345 0.271311i
\(421\) 41.9780 0.0997102 0.0498551 0.998756i \(-0.484124\pi\)
0.0498551 + 0.998756i \(0.484124\pi\)
\(422\) 202.767 0.480490
\(423\) −21.2212 + 477.213i −0.0501682 + 1.12816i
\(424\) 42.7690 0.100870
\(425\) −107.578 232.502i −0.253124 0.547064i
\(426\) 7.48751 + 7.82787i 0.0175763 + 0.0183753i
\(427\) 214.372i 0.502042i
\(428\) −314.272 −0.734280
\(429\) −167.737 + 160.444i −0.390996 + 0.373995i
\(430\) 102.332 160.104i 0.237982 0.372335i
\(431\) 106.166i 0.246324i 0.992387 + 0.123162i \(0.0393036\pi\)
−0.992387 + 0.123162i \(0.960696\pi\)
\(432\) 71.1111 + 81.2848i 0.164609 + 0.188159i
\(433\) 616.452i 1.42368i 0.702343 + 0.711838i \(0.252137\pi\)
−0.702343 + 0.711838i \(0.747863\pi\)
\(434\) 5.04712i 0.0116293i
\(435\) −31.5501 160.194i −0.0725289 0.368262i
\(436\) −284.855 −0.653337
\(437\) −91.9016 −0.210301
\(438\) 35.3490 + 36.9558i 0.0807054 + 0.0843741i
\(439\) 649.727 1.48002 0.740008 0.672598i \(-0.234822\pi\)
0.740008 + 0.672598i \(0.234822\pi\)
\(440\) −38.4041 + 60.0851i −0.0872820 + 0.136557i
\(441\) 13.5992 305.814i 0.0308372 0.693455i
\(442\) 222.371i 0.503101i
\(443\) −215.853 −0.487252 −0.243626 0.969869i \(-0.578337\pi\)
−0.243626 + 0.969869i \(0.578337\pi\)
\(444\) −130.621 136.559i −0.294192 0.307565i
\(445\) −341.003 + 533.516i −0.766298 + 1.19891i
\(446\) 123.438i 0.276768i
\(447\) 7.25366 + 7.58339i 0.0162274 + 0.0169651i
\(448\) 30.9705i 0.0691307i
\(449\) 655.202i 1.45925i −0.683849 0.729623i \(-0.739695\pi\)
0.683849 0.729623i \(-0.260305\pi\)
\(450\) −294.435 + 120.658i −0.654299 + 0.268128i
\(451\) −142.726 −0.316465
\(452\) 126.974 0.280916
\(453\) −556.284 + 532.097i −1.22800 + 1.17461i
\(454\) 104.196 0.229507
\(455\) −250.263 159.958i −0.550029 0.351557i
\(456\) −117.503 + 112.394i −0.257682 + 0.246478i
\(457\) 96.6236i 0.211430i 0.994396 + 0.105715i \(0.0337132\pi\)
−0.994396 + 0.105715i \(0.966287\pi\)
\(458\) −85.3613 −0.186378
\(459\) −182.175 208.239i −0.396896 0.453679i
\(460\) 40.4093 + 25.8281i 0.0878463 + 0.0561480i
\(461\) 732.435i 1.58880i 0.607397 + 0.794398i \(0.292214\pi\)
−0.607397 + 0.794398i \(0.707786\pi\)
\(462\) 59.8485 57.2462i 0.129542 0.123910i
\(463\) 160.728i 0.347145i −0.984821 0.173572i \(-0.944469\pi\)
0.984821 0.173572i \(-0.0555311\pi\)
\(464\) 43.5390i 0.0938340i
\(465\) −13.5674 + 2.67209i −0.0291772 + 0.00574643i
\(466\) −33.1803 −0.0712024
\(467\) −614.619 −1.31610 −0.658050 0.752974i \(-0.728618\pi\)
−0.658050 + 0.752974i \(0.728618\pi\)
\(468\) 275.927 + 12.2702i 0.589587 + 0.0262183i
\(469\) 168.790 0.359893
\(470\) 316.229 + 202.121i 0.672827 + 0.430045i
\(471\) −10.0725 10.5303i −0.0213853 0.0223574i
\(472\) 67.4799i 0.142966i
\(473\) 135.498 0.286466
\(474\) −312.272 + 298.694i −0.658802 + 0.630157i
\(475\) −201.173 434.785i −0.423521 0.915336i
\(476\) 79.3416i 0.166684i
\(477\) −6.04581 + 135.956i −0.0126746 + 0.285023i
\(478\) 90.1050i 0.188504i
\(479\) 328.068i 0.684902i 0.939536 + 0.342451i \(0.111257\pi\)
−0.939536 + 0.342451i \(0.888743\pi\)
\(480\) 83.2535 16.3967i 0.173445 0.0341598i
\(481\) −483.276 −1.00473
\(482\) −158.690 −0.329233
\(483\) −38.5001 40.2502i −0.0797103 0.0833337i
\(484\) 191.149 0.394936
\(485\) 368.293 576.214i 0.759368 1.18807i
\(486\) −268.443 + 214.560i −0.552353 + 0.441482i
\(487\) 183.987i 0.377796i 0.981997 + 0.188898i \(0.0604916\pi\)
−0.981997 + 0.188898i \(0.939508\pi\)
\(488\) 156.623 0.320948
\(489\) −455.279 475.975i −0.931041 0.973363i
\(490\) −202.650 129.526i −0.413571 0.264338i
\(491\) 152.142i 0.309862i −0.987925 0.154931i \(-0.950484\pi\)
0.987925 0.154931i \(-0.0495156\pi\)
\(492\) 117.392 + 122.728i 0.238601 + 0.249447i
\(493\) 111.540i 0.226247i
\(494\) 415.838i 0.841778i
\(495\) −185.572 130.574i −0.374893 0.263786i
\(496\) 3.68748 0.00743443
\(497\) −9.88422 −0.0198878
\(498\) −449.816 + 430.258i −0.903245 + 0.863971i
\(499\) 320.913 0.643111 0.321556 0.946891i \(-0.395794\pi\)
0.321556 + 0.946891i \(0.395794\pi\)
\(500\) −33.7361 + 247.713i −0.0674723 + 0.495427i
\(501\) 713.545 682.520i 1.42424 1.36231i
\(502\) 513.770i 1.02345i
\(503\) 783.001 1.55666 0.778331 0.627855i \(-0.216067\pi\)
0.778331 + 0.627855i \(0.216067\pi\)
\(504\) −98.4504 4.37798i −0.195338 0.00868647i
\(505\) −178.755 + 279.671i −0.353970 + 0.553804i
\(506\) 34.1990i 0.0675869i
\(507\) 144.061 137.797i 0.284144 0.271790i
\(508\) 391.141i 0.769962i
\(509\) 15.4948i 0.0304417i 0.999884 + 0.0152209i \(0.00484514\pi\)
−0.999884 + 0.0152209i \(0.995155\pi\)
\(510\) −213.282 + 42.0057i −0.418200 + 0.0823642i
\(511\) −46.6640 −0.0913190
\(512\) −22.6274 −0.0441942
\(513\) −340.672 389.411i −0.664078 0.759086i
\(514\) 42.9631 0.0835857
\(515\) 260.121 406.972i 0.505088 0.790236i
\(516\) −111.447 116.513i −0.215982 0.225800i
\(517\) 267.629i 0.517658i
\(518\) 172.432 0.332881
\(519\) −346.027 + 330.981i −0.666718 + 0.637729i
\(520\) 116.867 182.845i 0.224745 0.351625i
\(521\) 689.773i 1.32394i 0.749530 + 0.661970i \(0.230280\pi\)
−0.749530 + 0.661970i \(0.769720\pi\)
\(522\) −138.403 6.15465i −0.265141 0.0117905i
\(523\) 59.6203i 0.113997i 0.998374 + 0.0569984i \(0.0181530\pi\)
−0.998374 + 0.0569984i \(0.981847\pi\)
\(524\) 135.841i 0.259239i
\(525\) 106.146 270.251i 0.202183 0.514763i
\(526\) −390.495 −0.742386
\(527\) −9.44673 −0.0179255
\(528\) 41.8247 + 43.7259i 0.0792135 + 0.0828143i
\(529\) 23.0000 0.0434783
\(530\) 90.0921 + 57.5834i 0.169985 + 0.108648i
\(531\) −214.508 9.53892i −0.403969 0.0179641i
\(532\) 148.371i 0.278892i
\(533\) 434.329 0.814876
\(534\) 371.376 + 388.257i 0.695460 + 0.727074i
\(535\) −662.008 423.130i −1.23740 0.790897i
\(536\) 123.320i 0.230074i
\(537\) 96.2081 + 100.581i 0.179158 + 0.187302i
\(538\) 126.931i 0.235932i
\(539\) 171.505i 0.318192i
\(540\) 40.3538 + 266.967i 0.0747293 + 0.494384i
\(541\) −146.409 −0.270626 −0.135313 0.990803i \(-0.543204\pi\)
−0.135313 + 0.990803i \(0.543204\pi\)
\(542\) 449.189 0.828762
\(543\) −480.782 + 459.878i −0.885419 + 0.846920i
\(544\) 57.9678 0.106558
\(545\) −600.041 383.523i −1.10099 0.703712i
\(546\) −182.125 + 174.206i −0.333562 + 0.319058i
\(547\) 750.940i 1.37283i 0.727209 + 0.686416i \(0.240817\pi\)
−0.727209 + 0.686416i \(0.759183\pi\)
\(548\) −190.883 −0.348327
\(549\) −22.1401 + 497.878i −0.0403280 + 0.906881i
\(550\) −161.795 + 74.8616i −0.294172 + 0.136112i
\(551\) 208.582i 0.378552i
\(552\) 29.4072 28.1286i 0.0532739 0.0509575i
\(553\) 394.305i 0.713029i
\(554\) 202.355i 0.365261i
\(555\) −91.2907 463.524i −0.164488 0.835179i
\(556\) 40.2574 0.0724053
\(557\) 579.005 1.03951 0.519753 0.854317i \(-0.326024\pi\)
0.519753 + 0.854317i \(0.326024\pi\)
\(558\) −0.521260 + 11.7219i −0.000934158 + 0.0210070i
\(559\) −412.335 −0.737629
\(560\) −41.6981 + 65.2388i −0.0744610 + 0.116498i
\(561\) −107.148 112.019i −0.190995 0.199677i
\(562\) 629.724i 1.12050i
\(563\) 15.5541 0.0276272 0.0138136 0.999905i \(-0.495603\pi\)
0.0138136 + 0.999905i \(0.495603\pi\)
\(564\) 230.130 220.124i 0.408033 0.390291i
\(565\) 267.468 + 170.955i 0.473395 + 0.302576i
\(566\) 592.259i 1.04639i
\(567\) 27.8338 312.339i 0.0490896 0.550862i
\(568\) 7.22152i 0.0127139i
\(569\) 858.739i 1.50921i −0.656181 0.754604i \(-0.727829\pi\)
0.656181 0.754604i \(-0.272171\pi\)
\(570\) −398.843 + 78.5518i −0.699724 + 0.137810i
\(571\) 807.796 1.41470 0.707352 0.706862i \(-0.249890\pi\)
0.707352 + 0.706862i \(0.249890\pi\)
\(572\) 154.744 0.270532
\(573\) −29.6300 30.9769i −0.0517103 0.0540609i
\(574\) −154.968 −0.269979
\(575\) 50.3470 + 108.813i 0.0875600 + 0.189239i
\(576\) 3.19860 71.9289i 0.00555313 0.124877i
\(577\) 1032.87i 1.79007i 0.445999 + 0.895033i \(0.352848\pi\)
−0.445999 + 0.895033i \(0.647152\pi\)
\(578\) 260.204 0.450179
\(579\) −587.529 614.237i −1.01473 1.06086i
\(580\) −58.6201 + 91.7140i −0.101069 + 0.158128i
\(581\) 567.981i 0.977592i
\(582\) −401.097 419.330i −0.689171 0.720499i
\(583\) 76.2463i 0.130783i
\(584\) 34.0932i 0.0583788i
\(585\) 564.714 + 397.349i 0.965323 + 0.679230i
\(586\) 97.0057 0.165539
\(587\) 235.989 0.402026 0.201013 0.979589i \(-0.435577\pi\)
0.201013 + 0.979589i \(0.435577\pi\)
\(588\) −147.475 + 141.063i −0.250808 + 0.239903i
\(589\) −17.6656 −0.0299925
\(590\) −90.8536 + 142.145i −0.153989 + 0.240924i
\(591\) −314.947 + 301.253i −0.532905 + 0.509734i
\(592\) 125.981i 0.212806i
\(593\) −361.012 −0.608789 −0.304395 0.952546i \(-0.598454\pi\)
−0.304395 + 0.952546i \(0.598454\pi\)
\(594\) −144.910 + 126.773i −0.243956 + 0.213422i
\(595\) 106.824 167.131i 0.179536 0.280893i
\(596\) 6.99598i 0.0117382i
\(597\) −290.512 + 277.881i −0.486620 + 0.465462i
\(598\) 104.071i 0.174032i
\(599\) 727.245i 1.21410i 0.794664 + 0.607049i \(0.207647\pi\)
−0.794664 + 0.607049i \(0.792353\pi\)
\(600\) 197.448 + 77.5516i 0.329080 + 0.129253i
\(601\) 222.405 0.370058 0.185029 0.982733i \(-0.440762\pi\)
0.185029 + 0.982733i \(0.440762\pi\)
\(602\) 147.121 0.244386
\(603\) −392.014 17.4324i −0.650105 0.0289095i
\(604\) 513.195 0.849660
\(605\) 402.652 + 257.359i 0.665540 + 0.425387i
\(606\) 194.677 + 203.526i 0.321249 + 0.335852i
\(607\) 339.105i 0.558657i −0.960196 0.279329i \(-0.909888\pi\)
0.960196 0.279329i \(-0.0901119\pi\)
\(608\) 108.401 0.178291
\(609\) 91.3529 87.3808i 0.150005 0.143482i
\(610\) 329.922 + 210.874i 0.540856 + 0.345694i
\(611\) 814.422i 1.33293i
\(612\) −8.19430 + 184.270i −0.0133894 + 0.301095i
\(613\) 411.286i 0.670940i −0.942051 0.335470i \(-0.891105\pi\)
0.942051 0.335470i \(-0.108895\pi\)
\(614\) 569.666i 0.927795i
\(615\) 82.0446 + 416.577i 0.133406 + 0.677362i
\(616\) −55.2126 −0.0896309
\(617\) 268.904 0.435825 0.217912 0.975968i \(-0.430075\pi\)
0.217912 + 0.975968i \(0.430075\pi\)
\(618\) −283.290 296.167i −0.458397 0.479235i
\(619\) −242.398 −0.391597 −0.195798 0.980644i \(-0.562730\pi\)
−0.195798 + 0.980644i \(0.562730\pi\)
\(620\) 7.76760 + 4.96475i 0.0125284 + 0.00800766i
\(621\) 85.2592 + 97.4570i 0.137293 + 0.156936i
\(622\) 662.313i 1.06481i
\(623\) −490.251 −0.786920
\(624\) −127.277 133.062i −0.203969 0.213241i
\(625\) −404.581 + 476.381i −0.647329 + 0.762210i
\(626\) 785.184i 1.25429i
\(627\) −200.370 209.478i −0.319569 0.334096i
\(628\) 9.71464i 0.0154692i
\(629\) 322.743i 0.513105i
\(630\) −201.489 141.774i −0.319824 0.225038i
\(631\) 19.5182 0.0309322 0.0154661 0.999880i \(-0.495077\pi\)
0.0154661 + 0.999880i \(0.495077\pi\)
\(632\) 288.084 0.455828
\(633\) 310.833 297.318i 0.491047 0.469696i
\(634\) 624.807 0.985500
\(635\) 526.624 823.930i 0.829329 1.29753i
\(636\) 65.5630 62.7123i 0.103087 0.0986043i
\(637\) 521.908i 0.819322i
\(638\) −77.6190 −0.121660
\(639\) 22.9561 + 1.02083i 0.0359250 + 0.00159754i
\(640\) −47.6642 30.4651i −0.0744753 0.0476017i
\(641\) 889.107i 1.38706i −0.720426 0.693531i \(-0.756054\pi\)
0.720426 0.693531i \(-0.243946\pi\)
\(642\) −481.765 + 460.818i −0.750413 + 0.717785i
\(643\) 78.9605i 0.122800i −0.998113 0.0614001i \(-0.980443\pi\)
0.998113 0.0614001i \(-0.0195566\pi\)
\(644\) 37.1324i 0.0576590i
\(645\) −77.8899 395.482i −0.120760 0.613151i
\(646\) −277.706 −0.429886
\(647\) −844.151 −1.30472 −0.652358 0.757911i \(-0.726220\pi\)
−0.652358 + 0.757911i \(0.726220\pi\)
\(648\) 228.198 + 20.3357i 0.352158 + 0.0313822i
\(649\) −120.299 −0.185361
\(650\) 492.358 227.811i 0.757473 0.350479i
\(651\) −7.40060 7.73701i −0.0113680 0.0118848i
\(652\) 439.106i 0.673475i
\(653\) 1045.45 1.60099 0.800497 0.599336i \(-0.204569\pi\)
0.800497 + 0.599336i \(0.204569\pi\)
\(654\) −436.670 + 417.683i −0.667691 + 0.638660i
\(655\) 182.894 286.147i 0.279228 0.436866i
\(656\) 113.221i 0.172593i
\(657\) 108.377 + 4.81940i 0.164957 + 0.00733547i
\(658\) 290.585i 0.441618i
\(659\) 1221.83i 1.85407i 0.374976 + 0.927035i \(0.377651\pi\)
−0.374976 + 0.927035i \(0.622349\pi\)
\(660\) 29.2312 + 148.420i 0.0442897 + 0.224879i
\(661\) −431.226 −0.652384 −0.326192 0.945303i \(-0.605766\pi\)
−0.326192 + 0.945303i \(0.605766\pi\)
\(662\) 8.12892 0.0122793
\(663\) 326.063 + 340.884i 0.491799 + 0.514154i
\(664\) 414.973 0.624960
\(665\) 199.763 312.540i 0.300396 0.469985i
\(666\) −400.473 17.8086i −0.601311 0.0267396i
\(667\) 52.2014i 0.0782630i
\(668\) −658.274 −0.985440
\(669\) 180.998 + 189.226i 0.270550 + 0.282849i
\(670\) −166.035 + 259.771i −0.247814 + 0.387717i
\(671\) 279.218i 0.416122i
\(672\) 45.4122 + 47.4765i 0.0675777 + 0.0706496i
\(673\) 1314.26i 1.95284i −0.215880 0.976420i \(-0.569262\pi\)
0.215880 0.976420i \(-0.430738\pi\)
\(674\) 238.184i 0.353389i
\(675\) −274.435 + 616.693i −0.406571 + 0.913619i
\(676\) −132.902 −0.196601
\(677\) 572.358 0.845432 0.422716 0.906262i \(-0.361077\pi\)
0.422716 + 0.906262i \(0.361077\pi\)
\(678\) 194.646 186.182i 0.287088 0.274605i
\(679\) 529.487 0.779804
\(680\) 122.108 + 78.0467i 0.179571 + 0.114775i
\(681\) 159.728 152.783i 0.234550 0.224351i
\(682\) 6.57383i 0.00963905i
\(683\) 1159.23 1.69726 0.848628 0.528990i \(-0.177429\pi\)
0.848628 + 0.528990i \(0.177429\pi\)
\(684\) −15.3235 + 344.590i −0.0224028 + 0.503787i
\(685\) −402.092 257.001i −0.586995 0.375185i
\(686\) 454.485i 0.662514i
\(687\) −130.855 + 125.166i −0.190473 + 0.182192i
\(688\) 107.488i 0.156232i
\(689\) 232.025i 0.336756i
\(690\) 99.8175 19.6590i 0.144663 0.0284913i
\(691\) 982.871 1.42239 0.711195 0.702995i \(-0.248155\pi\)
0.711195 + 0.702995i \(0.248155\pi\)
\(692\) 319.223 0.461306
\(693\) 7.80483 175.512i 0.0112624 0.253264i
\(694\) 60.8686 0.0877069
\(695\) 84.8014 + 54.2017i 0.122016 + 0.0779881i
\(696\) 63.8413 + 66.7434i 0.0917261 + 0.0958957i
\(697\) 290.055i 0.416147i
\(698\) −1.02842 −0.00147338
\(699\) −50.8640 + 48.6524i −0.0727668 + 0.0696029i
\(700\) −175.673 + 81.2828i −0.250961 + 0.116118i
\(701\) 354.669i 0.505948i 0.967473 + 0.252974i \(0.0814087\pi\)
−0.967473 + 0.252974i \(0.918591\pi\)
\(702\) 440.976 385.783i 0.628170 0.549548i
\(703\) 603.537i 0.858516i
\(704\) 40.3389i 0.0572996i
\(705\) 781.136 153.844i 1.10799 0.218219i
\(706\) −890.701 −1.26162
\(707\) −256.992 −0.363496
\(708\) 98.9459 + 103.444i 0.139754 + 0.146107i
\(709\) 1097.20 1.54754 0.773769 0.633467i \(-0.218369\pi\)
0.773769 + 0.633467i \(0.218369\pi\)
\(710\) 9.72292 15.2120i 0.0136942 0.0214253i
\(711\) −40.7234 + 915.771i −0.0572762 + 1.28800i
\(712\) 358.183i 0.503066i
\(713\) 4.42113 0.00620074
\(714\) −116.339 121.627i −0.162939 0.170346i
\(715\) 325.966 + 208.345i 0.455896 + 0.291391i
\(716\) 92.7904i 0.129595i
\(717\) 132.121 + 138.127i 0.184269 + 0.192646i
\(718\) 825.374i 1.14955i
\(719\) 702.947i 0.977674i 0.872375 + 0.488837i \(0.162579\pi\)
−0.872375 + 0.488837i \(0.837421\pi\)
\(720\) 103.581 147.210i 0.143863 0.204459i
\(721\) 373.969 0.518681
\(722\) −8.78675 −0.0121700
\(723\) −243.266 + 232.688i −0.336467 + 0.321837i
\(724\) 443.541 0.612625
\(725\) −246.964 + 114.269i −0.340640 + 0.157612i
\(726\) 293.023 280.282i 0.403613 0.386064i
\(727\) 783.325i 1.07748i −0.842473 0.538738i \(-0.818901\pi\)
0.842473 0.538738i \(-0.181099\pi\)
\(728\) 168.017 0.230793
\(729\) −96.9019 + 722.531i −0.132924 + 0.991126i
\(730\) 45.9025 71.8167i 0.0628801 0.0983791i
\(731\) 275.367i 0.376699i
\(732\) 240.096 229.656i 0.327999 0.313738i
\(733\) 111.554i 0.152188i 0.997101 + 0.0760938i \(0.0242448\pi\)
−0.997101 + 0.0760938i \(0.975755\pi\)
\(734\) 528.302i 0.719758i
\(735\) −500.577 + 98.5883i −0.681058 + 0.134134i
\(736\) −27.1293 −0.0368605
\(737\) −219.848 −0.298301
\(738\) 359.912 + 16.0049i 0.487686 + 0.0216869i
\(739\) 457.432 0.618988 0.309494 0.950901i \(-0.399840\pi\)
0.309494 + 0.950901i \(0.399840\pi\)
\(740\) −169.618 + 265.376i −0.229214 + 0.358617i
\(741\) 609.745 + 637.462i 0.822868 + 0.860273i
\(742\) 82.7862i 0.111572i
\(743\) −975.746 −1.31325 −0.656626 0.754216i \(-0.728017\pi\)
−0.656626 + 0.754216i \(0.728017\pi\)
\(744\) 5.65274 5.40696i 0.00759777 0.00726742i
\(745\) 9.41925 14.7369i 0.0126433 0.0197811i
\(746\) 306.528i 0.410895i
\(747\) −58.6604 + 1319.13i −0.0785280 + 1.76591i
\(748\) 103.342i 0.138158i
\(749\) 608.323i 0.812181i
\(750\) 311.507 + 429.201i 0.415342 + 0.572268i
\(751\) −897.353 −1.19488 −0.597438 0.801915i \(-0.703815\pi\)
−0.597438 + 0.801915i \(0.703815\pi\)
\(752\) −212.304 −0.282320
\(753\) −753.342 787.587i −1.00045 1.04593i
\(754\) 236.202 0.313265
\(755\) 1081.03 + 690.955i 1.43183 + 0.915172i
\(756\) −157.340 + 137.647i −0.208121 + 0.182072i
\(757\) 809.753i 1.06969i 0.844951 + 0.534843i \(0.179629\pi\)
−0.844951 + 0.534843i \(0.820371\pi\)
\(758\) −291.655 −0.384769
\(759\) 50.1461 + 52.4256i 0.0660686 + 0.0690719i
\(760\) 228.345 + 145.949i 0.300454 + 0.192039i
\(761\) 814.133i 1.06982i 0.844909 + 0.534910i \(0.179655\pi\)
−0.844909 + 0.534910i \(0.820345\pi\)
\(762\) −573.531 599.602i −0.752665 0.786879i
\(763\) 551.382i 0.722650i
\(764\) 28.5774i 0.0374050i
\(765\) −265.359 + 377.129i −0.346875 + 0.492979i
\(766\) −135.290 −0.176619
\(767\) 366.083 0.477292
\(768\) −34.6869 + 33.1786i −0.0451652 + 0.0432014i
\(769\) 538.649 0.700454 0.350227 0.936665i \(-0.386104\pi\)
0.350227 + 0.936665i \(0.386104\pi\)
\(770\) −116.304 74.3372i −0.151044 0.0965418i
\(771\) 65.8605 62.9969i 0.0854222 0.0817080i
\(772\) 566.658i 0.734012i
\(773\) 642.229 0.830826 0.415413 0.909633i \(-0.363637\pi\)
0.415413 + 0.909633i \(0.363637\pi\)
\(774\) −341.687 15.1944i −0.441456 0.0196311i
\(775\) 9.67785 + 20.9163i 0.0124876 + 0.0269888i
\(776\) 386.849i 0.498516i
\(777\) 264.331 252.838i 0.340195 0.325403i
\(778\) 245.359i 0.315372i
\(779\) 542.409i 0.696289i
\(780\) −88.9533 451.656i −0.114043 0.579046i
\(781\) 12.8741 0.0164842
\(782\) 69.5010 0.0888759
\(783\) −221.191 + 193.