Properties

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

$q$-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 \(-0.910818\pi\)
0.961007 0.276523i \(-0.0891821\pi\)
\(8\) −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 \(0.0736105\pi\)
−0.973380 + 0.229198i \(0.926390\pi\)
\(12\) −4.33586 4.14733i −0.361321 0.345611i
\(13\) 15.3444i 1.18034i −0.807279 0.590170i \(-0.799061\pi\)
0.807279 0.590170i \(-0.200939\pi\)
\(14\) 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 \(-0.939907\pi\)
0.982233 0.187668i \(-0.0600929\pi\)
\(30\) 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 \(-0.860059\pi\)
0.904906 0.425611i \(-0.139941\pi\)
\(38\) 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 \(0.112184\pi\)
−0.938534 + 0.345187i \(0.887816\pi\)
\(42\) 11.3530 11.8691i 0.270311 0.282598i
\(43\) 26.8720i 0.624930i −0.949929 0.312465i \(-0.898845\pi\)
0.949929 0.312465i \(-0.101155\pi\)
\(44\) 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 \(0.0648040\pi\)
−0.979348 + 0.202184i \(0.935196\pi\)
\(60\) −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 \(0.105490\pi\)
−0.945585 + 0.325374i \(0.894510\pi\)
\(68\) −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 \(-0.994276\pi\)
0.999838 0.0179802i \(-0.00572359\pi\)
\(72\) −1.13088 25.4307i −0.0157066 0.353204i
\(73\) 12.0538i 0.165120i −0.996586 0.0825601i \(-0.973690\pi\)
0.996586 0.0825601i \(-0.0263097\pi\)
\(74\) 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 \(-0.748042\pi\)
0.702744 0.711443i \(-0.251958\pi\)
\(90\) −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 \(0.249057\pi\)
−0.709199 + 0.705009i \(0.750943\pi\)
\(98\) −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 \(-0.893413\pi\)
0.944458 0.328631i \(-0.106587\pi\)
\(102\) −31.4175 30.0515i −0.308015 0.294622i
\(103\) 96.5999i 0.937863i 0.883234 + 0.468932i \(0.155361\pi\)
−0.883234 + 0.468932i \(0.844639\pi\)
\(104\) 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 \(0.279725\pi\)
−0.638090 + 0.769962i \(0.720275\pi\)
\(128\) −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 \(0.0834719\pi\)
−0.965813 + 0.259239i \(0.916528\pi\)
\(132\) 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 \(0.00373648\pi\)
−0.999931 + 0.0117382i \(0.996264\pi\)
\(150\) 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 \(-0.995076\pi\)
0.999880 0.0154692i \(-0.00492419\pi\)
\(158\) 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 \(-0.764801\pi\)
0.739210 0.673475i \(-0.235199\pi\)
\(164\) 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 \(0.0413679\pi\)
−0.991567 + 0.129595i \(0.958632\pi\)
\(180\) 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 \(-0.988091\pi\)
0.999300 0.0374050i \(-0.0119091\pi\)
\(192\) −17.3434 16.5893i −0.0903303 0.0864027i
\(193\) 283.329i 1.46802i −0.679136 0.734012i \(-0.737645\pi\)
0.679136 0.734012i \(-0.262355\pi\)
\(194\) 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 \(0.0626993\pi\)
−0.980663 + 0.195704i \(0.937301\pi\)
\(224\) 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 \(0.0425550\pi\)
−0.991077 + 0.133293i \(0.957445\pi\)
\(240\) −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 \(-0.742447\pi\)
0.690130 0.723685i \(-0.257553\pi\)
\(252\) 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 \(0.0533527\pi\)
−0.985986 + 0.166829i \(0.946647\pi\)
\(270\) −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 \(0.0831552\pi\)
−0.966071 + 0.258279i \(0.916845\pi\)
\(278\) −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 \(-0.708875\pi\)
0.610111 0.792316i \(-0.291125\pi\)
\(282\) −162.727 155.651i −0.577045 0.551955i
\(283\) 418.790i 1.47982i −0.672704 0.739912i \(-0.734867\pi\)
0.672704 0.739912i \(-0.265133\pi\)
\(284\) 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 \(-0.772226\pi\)
0.754717 0.656050i \(-0.227774\pi\)
\(308\) 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 \(-0.728637\pi\)
0.658094 0.752936i \(-0.271363\pi\)
\(312\) 89.9982 94.0893i 0.288456 0.301568i
\(313\) 555.209i 1.77383i −0.461933 0.886915i \(-0.652844\pi\)
0.461933 0.886915i \(-0.347156\pi\)
\(314\) 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 \(0.0803924\pi\)
−0.968276 + 0.249884i \(0.919608\pi\)
\(338\) 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 \(0.302086\pi\)
−0.582471 + 0.812851i \(0.697914\pi\)
\(360\) −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 \(0.169965\pi\)
−0.860799 + 0.508946i \(0.830035\pi\)
\(368\) 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 \(-0.906163\pi\)
0.956861 0.290547i \(-0.0938372\pi\)
\(374\) 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 \(0.0715854\pi\)
−0.974818 + 0.223001i \(0.928415\pi\)
\(390\) 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 \(-0.858596\pi\)
0.902940 0.429767i \(-0.141404\pi\)
\(398\) −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 \(0.137481\pi\)
−0.908168 + 0.418606i \(0.862519\pi\)
\(402\) −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 \(-0.774558\pi\)
0.759504 0.650503i \(-0.225442\pi\)
\(420\) −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 \(-0.960696\pi\)
0.992387 0.123162i \(-0.0393036\pi\)
\(432\) 71.1111 81.2848i 0.164609 0.188159i
\(433\) 616.452i 1.42368i −0.702343 0.711838i \(-0.747863\pi\)
0.702343 0.711838i \(-0.252137\pi\)
\(434\) 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 \(0.260305\pi\)
−0.683849 + 0.729623i \(0.739695\pi\)
\(450\) −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 \(-0.966287\pi\)
0.994396 0.105715i \(-0.0337132\pi\)
\(458\) −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 \(-0.707786\pi\)
0.607397 0.794398i \(-0.292214\pi\)
\(462\) 59.8485 + 57.2462i 0.129542 + 0.123910i
\(463\) 160.728i 0.347145i 0.984821 + 0.173572i \(0.0555311\pi\)
−0.984821 + 0.173572i \(0.944469\pi\)
\(464\) 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 \(-0.888743\pi\)
0.939536 0.342451i \(-0.111257\pi\)
\(480\) 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 \(-0.939508\pi\)
0.981997 0.188898i \(-0.0604916\pi\)
\(488\) 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 \(0.0495156\pi\)
−0.987925 + 0.154931i \(0.950484\pi\)
\(492\) 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 \(-0.995155\pi\)
0.999884 0.0152209i \(-0.00484514\pi\)
\(510\) −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 \(-0.769720\pi\)
0.749530 0.661970i \(-0.230280\pi\)
\(522\) −138.403 + 6.15465i −0.265141 + 0.0117905i
\(523\) 59.6203i 0.113997i −0.998374 0.0569984i \(-0.981847\pi\)
0.998374 0.0569984i \(-0.0181530\pi\)
\(524\) 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 \(-0.759183\pi\)
0.727209 0.686416i \(-0.240817\pi\)
\(548\) −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 \(0.272171\pi\)
−0.656181 + 0.754604i \(0.727829\pi\)
\(570\) −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 \(-0.647152\pi\)
0.445999 0.895033i \(-0.352848\pi\)
\(578\) 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 \(-0.792353\pi\)
0.794664 0.607049i \(-0.207647\pi\)
\(600\) 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 \(0.0901119\pi\)
−0.960196 + 0.279329i \(0.909888\pi\)
\(608\) 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 \(0.108895\pi\)
−0.942051 + 0.335470i \(0.891105\pi\)
\(614\) 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 \(0.243946\pi\)
−0.720426 + 0.693531i \(0.756054\pi\)
\(642\) −481.765 460.818i −0.750413 0.717785i
\(643\) 78.9605i 0.122800i 0.998113 + 0.0614001i \(0.0195566\pi\)
−0.998113 + 0.0614001i \(0.980443\pi\)
\(644\) 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 \(-0.622349\pi\)
0.374976 0.927035i \(-0.377651\pi\)
\(660\) 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 \(0.430738\pi\)
−0.215880 + 0.976420i \(0.569262\pi\)
\(674\) 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 \(-0.918591\pi\)
0.967473 0.252974i \(-0.0814087\pi\)
\(702\) 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 \(-0.837421\pi\)
0.872375 0.488837i \(-0.162579\pi\)
\(720\) 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 \(0.181099\pi\)
−0.842473 + 0.538738i \(0.818901\pi\)
\(728\) 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 \(-0.975755\pi\)
0.997101 0.0760938i \(-0.0242448\pi\)
\(734\) 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 \(-0.820371\pi\)
0.844951 0.534843i \(-0.179629\pi\)
\(758\) −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 \(-0.820345\pi\)
0.844909 0.534910i \(-0.179655\pi\)
\(762\) −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
\(783\)