Properties

Label 690.2.e.a.551.11
Level $690$
Weight $2$
Character 690.551
Analytic conductor $5.510$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} - 198 x^{7} + 405 x^{6} - 108 x^{5} + 1215 x^{4} - 2916 x^{3} + 2187 x^{2} - 4374 x + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 551.11
Root \(1.53677 - 0.798958i\) of defining polynomial
Character \(\chi\) \(=\) 690.551
Dual form 690.2.e.a.551.3

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-0.798958 - 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 - 0.798958i) q^{6} +0.145234i q^{7} -1.00000i q^{8} +(-1.72333 + 2.45563i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-0.798958 - 1.53677i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.53677 - 0.798958i) q^{6} +0.145234i q^{7} -1.00000i q^{8} +(-1.72333 + 2.45563i) q^{9} -1.00000i q^{10} -3.35877 q^{11} +(0.798958 + 1.53677i) q^{12} +2.96087 q^{13} -0.145234 q^{14} +(0.798958 + 1.53677i) q^{15} +1.00000 q^{16} +5.54307 q^{17} +(-2.45563 - 1.72333i) q^{18} +6.91126i q^{19} +1.00000 q^{20} +(0.223191 - 0.116036i) q^{21} -3.35877i q^{22} +(-3.26171 + 3.51586i) q^{23} +(-1.53677 + 0.798958i) q^{24} +1.00000 q^{25} +2.96087i q^{26} +(5.15061 + 0.686420i) q^{27} -0.145234i q^{28} -3.58666i q^{29} +(-1.53677 + 0.798958i) q^{30} +10.6138 q^{31} +1.00000i q^{32} +(2.68352 + 5.16167i) q^{33} +5.54307i q^{34} -0.145234i q^{35} +(1.72333 - 2.45563i) q^{36} +6.04149i q^{37} -6.91126 q^{38} +(-2.36561 - 4.55019i) q^{39} +1.00000i q^{40} -8.84450i q^{41} +(0.116036 + 0.223191i) q^{42} +8.40616i q^{43} +3.35877 q^{44} +(1.72333 - 2.45563i) q^{45} +(-3.51586 - 3.26171i) q^{46} +9.98664i q^{47} +(-0.798958 - 1.53677i) q^{48} +6.97891 q^{49} +1.00000i q^{50} +(-4.42868 - 8.51843i) q^{51} -2.96087 q^{52} -3.83589 q^{53} +(-0.686420 + 5.15061i) q^{54} +3.35877 q^{55} +0.145234 q^{56} +(10.6210 - 5.52181i) q^{57} +3.58666 q^{58} +7.91338i q^{59} +(-0.798958 - 1.53677i) q^{60} +4.14107i q^{61} +10.6138i q^{62} +(-0.356641 - 0.250286i) q^{63} -1.00000 q^{64} -2.96087 q^{65} +(-5.16167 + 2.68352i) q^{66} +13.0680i q^{67} -5.54307 q^{68} +(8.00904 + 2.20347i) q^{69} +0.145234 q^{70} +1.26558i q^{71} +(2.45563 + 1.72333i) q^{72} -9.24658 q^{73} -6.04149 q^{74} +(-0.798958 - 1.53677i) q^{75} -6.91126i q^{76} -0.487808i q^{77} +(4.55019 - 2.36561i) q^{78} -13.2148i q^{79} -1.00000 q^{80} +(-3.06025 - 8.46374i) q^{81} +8.84450 q^{82} +9.71029 q^{83} +(-0.223191 + 0.116036i) q^{84} -5.54307 q^{85} -8.40616 q^{86} +(-5.51188 + 2.86559i) q^{87} +3.35877i q^{88} -15.3774 q^{89} +(2.45563 + 1.72333i) q^{90} +0.430019i q^{91} +(3.26171 - 3.51586i) q^{92} +(-8.47998 - 16.3110i) q^{93} -9.98664 q^{94} -6.91126i q^{95} +(1.53677 - 0.798958i) q^{96} -11.6097i q^{97} +6.97891i q^{98} +(5.78828 - 8.24791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} + O(q^{10}) \) \( 16q - 16q^{4} - 16q^{5} + 2q^{6} + 2q^{9} - 12q^{11} - 12q^{14} + 16q^{16} + 8q^{18} + 16q^{20} - 4q^{21} + 4q^{23} - 2q^{24} + 16q^{25} + 24q^{27} - 2q^{30} + 4q^{31} - 28q^{33} - 2q^{36} - 16q^{38} - 8q^{39} + 12q^{44} - 2q^{45} - 4q^{46} - 4q^{49} - 2q^{51} - 8q^{53} - 26q^{54} + 12q^{55} + 12q^{56} + 28q^{57} - 8q^{58} - 16q^{64} + 10q^{66} + 30q^{69} + 12q^{70} - 8q^{72} - 16q^{73} - 24q^{74} - 12q^{78} - 16q^{80} + 22q^{81} - 16q^{82} - 40q^{83} + 4q^{84} - 40q^{86} + 20q^{87} + 80q^{89} - 8q^{90} - 4q^{92} - 4q^{93} - 24q^{94} + 2q^{96} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.798958 1.53677i −0.461279 0.887255i
\(4\) −1.00000 −0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.53677 0.798958i 0.627384 0.326173i
\(7\) 0.145234i 0.0548933i 0.999623 + 0.0274466i \(0.00873763\pi\)
−0.999623 + 0.0274466i \(0.991262\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.72333 + 2.45563i −0.574444 + 0.818544i
\(10\) 1.00000i 0.316228i
\(11\) −3.35877 −1.01271 −0.506354 0.862326i \(-0.669007\pi\)
−0.506354 + 0.862326i \(0.669007\pi\)
\(12\) 0.798958 + 1.53677i 0.230639 + 0.443628i
\(13\) 2.96087 0.821199 0.410599 0.911816i \(-0.365320\pi\)
0.410599 + 0.911816i \(0.365320\pi\)
\(14\) −0.145234 −0.0388154
\(15\) 0.798958 + 1.53677i 0.206290 + 0.396793i
\(16\) 1.00000 0.250000
\(17\) 5.54307 1.34439 0.672196 0.740373i \(-0.265351\pi\)
0.672196 + 0.740373i \(0.265351\pi\)
\(18\) −2.45563 1.72333i −0.578798 0.406193i
\(19\) 6.91126i 1.58555i 0.609513 + 0.792776i \(0.291365\pi\)
−0.609513 + 0.792776i \(0.708635\pi\)
\(20\) 1.00000 0.223607
\(21\) 0.223191 0.116036i 0.0487043 0.0253211i
\(22\) 3.35877i 0.716093i
\(23\) −3.26171 + 3.51586i −0.680113 + 0.733107i
\(24\) −1.53677 + 0.798958i −0.313692 + 0.163087i
\(25\) 1.00000 0.200000
\(26\) 2.96087i 0.580675i
\(27\) 5.15061 + 0.686420i 0.991236 + 0.132102i
\(28\) 0.145234i 0.0274466i
\(29\) 3.58666i 0.666026i −0.942922 0.333013i \(-0.891935\pi\)
0.942922 0.333013i \(-0.108065\pi\)
\(30\) −1.53677 + 0.798958i −0.280575 + 0.145869i
\(31\) 10.6138 1.90629 0.953147 0.302506i \(-0.0978233\pi\)
0.953147 + 0.302506i \(0.0978233\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.68352 + 5.16167i 0.467141 + 0.898531i
\(34\) 5.54307i 0.950628i
\(35\) 0.145234i 0.0245490i
\(36\) 1.72333 2.45563i 0.287222 0.409272i
\(37\) 6.04149i 0.993214i 0.867975 + 0.496607i \(0.165421\pi\)
−0.867975 + 0.496607i \(0.834579\pi\)
\(38\) −6.91126 −1.12115
\(39\) −2.36561 4.55019i −0.378801 0.728613i
\(40\) 1.00000i 0.158114i
\(41\) 8.84450i 1.38128i −0.723199 0.690639i \(-0.757329\pi\)
0.723199 0.690639i \(-0.242671\pi\)
\(42\) 0.116036 + 0.223191i 0.0179047 + 0.0344392i
\(43\) 8.40616i 1.28193i 0.767571 + 0.640964i \(0.221465\pi\)
−0.767571 + 0.640964i \(0.778535\pi\)
\(44\) 3.35877 0.506354
\(45\) 1.72333 2.45563i 0.256899 0.366064i
\(46\) −3.51586 3.26171i −0.518385 0.480912i
\(47\) 9.98664i 1.45670i 0.685205 + 0.728351i \(0.259713\pi\)
−0.685205 + 0.728351i \(0.740287\pi\)
\(48\) −0.798958 1.53677i −0.115320 0.221814i
\(49\) 6.97891 0.996987
\(50\) 1.00000i 0.141421i
\(51\) −4.42868 8.51843i −0.620139 1.19282i
\(52\) −2.96087 −0.410599
\(53\) −3.83589 −0.526900 −0.263450 0.964673i \(-0.584860\pi\)
−0.263450 + 0.964673i \(0.584860\pi\)
\(54\) −0.686420 + 5.15061i −0.0934099 + 0.700910i
\(55\) 3.35877 0.452897
\(56\) 0.145234 0.0194077
\(57\) 10.6210 5.52181i 1.40679 0.731382i
\(58\) 3.58666 0.470952
\(59\) 7.91338i 1.03023i 0.857120 + 0.515117i \(0.172252\pi\)
−0.857120 + 0.515117i \(0.827748\pi\)
\(60\) −0.798958 1.53677i −0.103145 0.198396i
\(61\) 4.14107i 0.530209i 0.964220 + 0.265105i \(0.0854065\pi\)
−0.964220 + 0.265105i \(0.914594\pi\)
\(62\) 10.6138i 1.34795i
\(63\) −0.356641 0.250286i −0.0449325 0.0315331i
\(64\) −1.00000 −0.125000
\(65\) −2.96087 −0.367251
\(66\) −5.16167 + 2.68352i −0.635357 + 0.330318i
\(67\) 13.0680i 1.59651i 0.602322 + 0.798253i \(0.294242\pi\)
−0.602322 + 0.798253i \(0.705758\pi\)
\(68\) −5.54307 −0.672196
\(69\) 8.00904 + 2.20347i 0.964175 + 0.265267i
\(70\) 0.145234 0.0173588
\(71\) 1.26558i 0.150196i 0.997176 + 0.0750981i \(0.0239270\pi\)
−0.997176 + 0.0750981i \(0.976073\pi\)
\(72\) 2.45563 + 1.72333i 0.289399 + 0.203097i
\(73\) −9.24658 −1.08223 −0.541115 0.840948i \(-0.681998\pi\)
−0.541115 + 0.840948i \(0.681998\pi\)
\(74\) −6.04149 −0.702309
\(75\) −0.798958 1.53677i −0.0922557 0.177451i
\(76\) 6.91126i 0.792776i
\(77\) 0.487808i 0.0555909i
\(78\) 4.55019 2.36561i 0.515207 0.267853i
\(79\) 13.2148i 1.48678i −0.668857 0.743391i \(-0.733216\pi\)
0.668857 0.743391i \(-0.266784\pi\)
\(80\) −1.00000 −0.111803
\(81\) −3.06025 8.46374i −0.340028 0.940415i
\(82\) 8.84450 0.976711
\(83\) 9.71029 1.06584 0.532921 0.846165i \(-0.321094\pi\)
0.532921 + 0.846165i \(0.321094\pi\)
\(84\) −0.223191 + 0.116036i −0.0243522 + 0.0126605i
\(85\) −5.54307 −0.601230
\(86\) −8.40616 −0.906460
\(87\) −5.51188 + 2.86559i −0.590935 + 0.307224i
\(88\) 3.35877i 0.358046i
\(89\) −15.3774 −1.63000 −0.815001 0.579459i \(-0.803264\pi\)
−0.815001 + 0.579459i \(0.803264\pi\)
\(90\) 2.45563 + 1.72333i 0.258846 + 0.181655i
\(91\) 0.430019i 0.0450783i
\(92\) 3.26171 3.51586i 0.340056 0.366554i
\(93\) −8.47998 16.3110i −0.879333 1.69137i
\(94\) −9.98664 −1.03004
\(95\) 6.91126i 0.709081i
\(96\) 1.53677 0.798958i 0.156846 0.0815433i
\(97\) 11.6097i 1.17879i −0.807845 0.589395i \(-0.799366\pi\)
0.807845 0.589395i \(-0.200634\pi\)
\(98\) 6.97891i 0.704976i
\(99\) 5.78828 8.24791i 0.581744 0.828946i
\(100\) −1.00000 −0.100000
\(101\) 5.20471i 0.517888i 0.965892 + 0.258944i \(0.0833745\pi\)
−0.965892 + 0.258944i \(0.916625\pi\)
\(102\) 8.51843 4.42868i 0.843450 0.438505i
\(103\) 8.68617i 0.855874i −0.903809 0.427937i \(-0.859241\pi\)
0.903809 0.427937i \(-0.140759\pi\)
\(104\) 2.96087i 0.290338i
\(105\) −0.223191 + 0.116036i −0.0217812 + 0.0113239i
\(106\) 3.83589i 0.372574i
\(107\) −11.1465 −1.07757 −0.538785 0.842443i \(-0.681116\pi\)
−0.538785 + 0.842443i \(0.681116\pi\)
\(108\) −5.15061 0.686420i −0.495618 0.0660508i
\(109\) 7.19631i 0.689282i −0.938735 0.344641i \(-0.888001\pi\)
0.938735 0.344641i \(-0.111999\pi\)
\(110\) 3.35877i 0.320246i
\(111\) 9.28438 4.82690i 0.881235 0.458149i
\(112\) 0.145234i 0.0137233i
\(113\) 13.1580 1.23780 0.618902 0.785468i \(-0.287578\pi\)
0.618902 + 0.785468i \(0.287578\pi\)
\(114\) 5.52181 + 10.6210i 0.517165 + 0.994751i
\(115\) 3.26171 3.51586i 0.304156 0.327856i
\(116\) 3.58666i 0.333013i
\(117\) −5.10257 + 7.27082i −0.471733 + 0.672187i
\(118\) −7.91338 −0.728486
\(119\) 0.805042i 0.0737980i
\(120\) 1.53677 0.798958i 0.140287 0.0729346i
\(121\) 0.281357 0.0255779
\(122\) −4.14107 −0.374915
\(123\) −13.5920 + 7.06638i −1.22555 + 0.637154i
\(124\) −10.6138 −0.953147
\(125\) −1.00000 −0.0894427
\(126\) 0.250286 0.356641i 0.0222973 0.0317721i
\(127\) −13.8601 −1.22989 −0.614943 0.788572i \(-0.710821\pi\)
−0.614943 + 0.788572i \(0.710821\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 12.9184 6.71617i 1.13740 0.591326i
\(130\) 2.96087i 0.259686i
\(131\) 3.17761i 0.277629i −0.990318 0.138815i \(-0.955671\pi\)
0.990318 0.138815i \(-0.0443292\pi\)
\(132\) −2.68352 5.16167i −0.233570 0.449265i
\(133\) −1.00375 −0.0870362
\(134\) −13.0680 −1.12890
\(135\) −5.15061 0.686420i −0.443294 0.0590776i
\(136\) 5.54307i 0.475314i
\(137\) 19.0473 1.62732 0.813661 0.581340i \(-0.197471\pi\)
0.813661 + 0.581340i \(0.197471\pi\)
\(138\) −2.20347 + 8.00904i −0.187572 + 0.681775i
\(139\) 10.1337 0.859531 0.429766 0.902940i \(-0.358596\pi\)
0.429766 + 0.902940i \(0.358596\pi\)
\(140\) 0.145234i 0.0122745i
\(141\) 15.3472 7.97891i 1.29247 0.671945i
\(142\) −1.26558 −0.106205
\(143\) −9.94490 −0.831635
\(144\) −1.72333 + 2.45563i −0.143611 + 0.204636i
\(145\) 3.58666i 0.297856i
\(146\) 9.24658i 0.765253i
\(147\) −5.57585 10.7250i −0.459889 0.884582i
\(148\) 6.04149i 0.496607i
\(149\) 19.7755 1.62008 0.810038 0.586378i \(-0.199447\pi\)
0.810038 + 0.586378i \(0.199447\pi\)
\(150\) 1.53677 0.798958i 0.125477 0.0652347i
\(151\) −9.13517 −0.743409 −0.371705 0.928351i \(-0.621227\pi\)
−0.371705 + 0.928351i \(0.621227\pi\)
\(152\) 6.91126 0.560577
\(153\) −9.55255 + 13.6117i −0.772278 + 1.10044i
\(154\) 0.487808 0.0393087
\(155\) −10.6138 −0.852521
\(156\) 2.36561 + 4.55019i 0.189401 + 0.364306i
\(157\) 10.3178i 0.823451i 0.911308 + 0.411726i \(0.135074\pi\)
−0.911308 + 0.411726i \(0.864926\pi\)
\(158\) 13.2148 1.05131
\(159\) 3.06471 + 5.89488i 0.243048 + 0.467494i
\(160\) 1.00000i 0.0790569i
\(161\) −0.510622 0.473711i −0.0402427 0.0373336i
\(162\) 8.46374 3.06025i 0.664974 0.240436i
\(163\) 11.8046 0.924607 0.462303 0.886722i \(-0.347023\pi\)
0.462303 + 0.886722i \(0.347023\pi\)
\(164\) 8.84450i 0.690639i
\(165\) −2.68352 5.16167i −0.208912 0.401835i
\(166\) 9.71029i 0.753664i
\(167\) 11.8429i 0.916428i 0.888842 + 0.458214i \(0.151511\pi\)
−0.888842 + 0.458214i \(0.848489\pi\)
\(168\) −0.116036 0.223191i −0.00895236 0.0172196i
\(169\) −4.23323 −0.325633
\(170\) 5.54307i 0.425134i
\(171\) −16.9715 11.9104i −1.29784 0.910811i
\(172\) 8.40616i 0.640964i
\(173\) 9.94482i 0.756090i 0.925787 + 0.378045i \(0.123404\pi\)
−0.925787 + 0.378045i \(0.876596\pi\)
\(174\) −2.86559 5.51188i −0.217240 0.417854i
\(175\) 0.145234i 0.0109787i
\(176\) −3.35877 −0.253177
\(177\) 12.1611 6.32246i 0.914081 0.475225i
\(178\) 15.3774i 1.15259i
\(179\) 3.37701i 0.252409i 0.992004 + 0.126205i \(0.0402796\pi\)
−0.992004 + 0.126205i \(0.959720\pi\)
\(180\) −1.72333 + 2.45563i −0.128450 + 0.183032i
\(181\) 5.28230i 0.392630i 0.980541 + 0.196315i \(0.0628976\pi\)
−0.980541 + 0.196315i \(0.937102\pi\)
\(182\) −0.430019 −0.0318752
\(183\) 6.36387 3.30854i 0.470431 0.244574i
\(184\) 3.51586 + 3.26171i 0.259193 + 0.240456i
\(185\) 6.04149i 0.444179i
\(186\) 16.3110 8.47998i 1.19598 0.621782i
\(187\) −18.6179 −1.36148
\(188\) 9.98664i 0.728351i
\(189\) −0.0996915 + 0.748044i −0.00725149 + 0.0544122i
\(190\) 6.91126 0.501396
\(191\) −22.1062 −1.59955 −0.799775 0.600300i \(-0.795048\pi\)
−0.799775 + 0.600300i \(0.795048\pi\)
\(192\) 0.798958 + 1.53677i 0.0576598 + 0.110907i
\(193\) 5.62469 0.404874 0.202437 0.979295i \(-0.435114\pi\)
0.202437 + 0.979295i \(0.435114\pi\)
\(194\) 11.6097 0.833530
\(195\) 2.36561 + 4.55019i 0.169405 + 0.325846i
\(196\) −6.97891 −0.498493
\(197\) 4.97721i 0.354611i −0.984156 0.177306i \(-0.943262\pi\)
0.984156 0.177306i \(-0.0567381\pi\)
\(198\) 8.24791 + 5.78828i 0.586153 + 0.411355i
\(199\) 5.07219i 0.359558i 0.983707 + 0.179779i \(0.0575382\pi\)
−0.983707 + 0.179779i \(0.942462\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 20.0825 10.4408i 1.41651 0.736434i
\(202\) −5.20471 −0.366202
\(203\) 0.520905 0.0365603
\(204\) 4.42868 + 8.51843i 0.310070 + 0.596409i
\(205\) 8.84450i 0.617727i
\(206\) 8.68617 0.605194
\(207\) −3.01265 14.0685i −0.209394 0.977831i
\(208\) 2.96087 0.205300
\(209\) 23.2134i 1.60570i
\(210\) −0.116036 0.223191i −0.00800723 0.0154017i
\(211\) −9.58459 −0.659830 −0.329915 0.944011i \(-0.607020\pi\)
−0.329915 + 0.944011i \(0.607020\pi\)
\(212\) 3.83589 0.263450
\(213\) 1.94490 1.01114i 0.133262 0.0692823i
\(214\) 11.1465i 0.761957i
\(215\) 8.40616i 0.573296i
\(216\) 0.686420 5.15061i 0.0467050 0.350455i
\(217\) 1.54148i 0.104643i
\(218\) 7.19631 0.487396
\(219\) 7.38763 + 14.2099i 0.499210 + 0.960215i
\(220\) −3.35877 −0.226448
\(221\) 16.4123 1.10401
\(222\) 4.82690 + 9.28438i 0.323960 + 0.623127i
\(223\) 17.7150 1.18628 0.593142 0.805098i \(-0.297887\pi\)
0.593142 + 0.805098i \(0.297887\pi\)
\(224\) −0.145234 −0.00970385
\(225\) −1.72333 + 2.45563i −0.114889 + 0.163709i
\(226\) 13.1580i 0.875260i
\(227\) −3.72255 −0.247074 −0.123537 0.992340i \(-0.539424\pi\)
−0.123537 + 0.992340i \(0.539424\pi\)
\(228\) −10.6210 + 5.52181i −0.703395 + 0.365691i
\(229\) 4.59060i 0.303355i −0.988430 0.151678i \(-0.951532\pi\)
0.988430 0.151678i \(-0.0484676\pi\)
\(230\) 3.51586 + 3.26171i 0.231829 + 0.215071i
\(231\) −0.749649 + 0.389738i −0.0493233 + 0.0256429i
\(232\) −3.58666 −0.235476
\(233\) 3.65041i 0.239147i 0.992825 + 0.119573i \(0.0381526\pi\)
−0.992825 + 0.119573i \(0.961847\pi\)
\(234\) −7.27082 5.10257i −0.475308 0.333565i
\(235\) 9.98664i 0.651457i
\(236\) 7.91338i 0.515117i
\(237\) −20.3081 + 10.5581i −1.31916 + 0.685821i
\(238\) −0.805042 −0.0521831
\(239\) 2.23114i 0.144321i 0.997393 + 0.0721603i \(0.0229893\pi\)
−0.997393 + 0.0721603i \(0.977011\pi\)
\(240\) 0.798958 + 1.53677i 0.0515725 + 0.0991982i
\(241\) 14.8025i 0.953511i −0.879036 0.476756i \(-0.841813\pi\)
0.879036 0.476756i \(-0.158187\pi\)
\(242\) 0.281357i 0.0180863i
\(243\) −10.5618 + 11.4651i −0.677541 + 0.735485i
\(244\) 4.14107i 0.265105i
\(245\) −6.97891 −0.445866
\(246\) −7.06638 13.5920i −0.450536 0.866592i
\(247\) 20.4634i 1.30205i
\(248\) 10.6138i 0.673977i
\(249\) −7.75811 14.9225i −0.491650 0.945674i
\(250\) 1.00000i 0.0632456i
\(251\) −13.8618 −0.874948 −0.437474 0.899231i \(-0.644127\pi\)
−0.437474 + 0.899231i \(0.644127\pi\)
\(252\) 0.356641 + 0.250286i 0.0224663 + 0.0157666i
\(253\) 10.9553 11.8090i 0.688756 0.742424i
\(254\) 13.8601i 0.869660i
\(255\) 4.42868 + 8.51843i 0.277335 + 0.533445i
\(256\) 1.00000 0.0625000
\(257\) 1.86957i 0.116621i 0.998298 + 0.0583104i \(0.0185713\pi\)
−0.998298 + 0.0583104i \(0.981429\pi\)
\(258\) 6.71617 + 12.9184i 0.418131 + 0.804261i
\(259\) −0.877429 −0.0545208
\(260\) 2.96087 0.183626
\(261\) 8.80752 + 6.18101i 0.545172 + 0.382595i
\(262\) 3.17761 0.196313
\(263\) 21.2810 1.31224 0.656120 0.754656i \(-0.272196\pi\)
0.656120 + 0.754656i \(0.272196\pi\)
\(264\) 5.16167 2.68352i 0.317679 0.165159i
\(265\) 3.83589 0.235637
\(266\) 1.00375i 0.0615439i
\(267\) 12.2859 + 23.6316i 0.751885 + 1.44623i
\(268\) 13.0680i 0.798253i
\(269\) 21.9822i 1.34028i 0.742237 + 0.670138i \(0.233765\pi\)
−0.742237 + 0.670138i \(0.766235\pi\)
\(270\) 0.686420 5.15061i 0.0417742 0.313456i
\(271\) 18.8975 1.14794 0.573971 0.818876i \(-0.305402\pi\)
0.573971 + 0.818876i \(0.305402\pi\)
\(272\) 5.54307 0.336098
\(273\) 0.660841 0.343567i 0.0399959 0.0207936i
\(274\) 19.0473i 1.15069i
\(275\) −3.35877 −0.202542
\(276\) −8.00904 2.20347i −0.482088 0.132633i
\(277\) −8.26393 −0.496532 −0.248266 0.968692i \(-0.579861\pi\)
−0.248266 + 0.968692i \(0.579861\pi\)
\(278\) 10.1337i 0.607780i
\(279\) −18.2911 + 26.0636i −1.09506 + 1.56039i
\(280\) −0.145234 −0.00867939
\(281\) −13.4017 −0.799475 −0.399738 0.916630i \(-0.630899\pi\)
−0.399738 + 0.916630i \(0.630899\pi\)
\(282\) 7.97891 + 15.3472i 0.475137 + 0.913911i
\(283\) 30.2552i 1.79849i −0.437450 0.899243i \(-0.644118\pi\)
0.437450 0.899243i \(-0.355882\pi\)
\(284\) 1.26558i 0.0750981i
\(285\) −10.6210 + 5.52181i −0.629136 + 0.327084i
\(286\) 9.94490i 0.588054i
\(287\) 1.28452 0.0758229
\(288\) −2.45563 1.72333i −0.144699 0.101548i
\(289\) 13.7256 0.807389
\(290\) −3.58666 −0.210616
\(291\) −17.8415 + 9.27569i −1.04589 + 0.543750i
\(292\) 9.24658 0.541115
\(293\) 7.09896 0.414725 0.207363 0.978264i \(-0.433512\pi\)
0.207363 + 0.978264i \(0.433512\pi\)
\(294\) 10.7250 5.57585i 0.625494 0.325190i
\(295\) 7.91338i 0.460735i
\(296\) 6.04149 0.351154
\(297\) −17.2997 2.30553i −1.00383 0.133780i
\(298\) 19.7755i 1.14557i
\(299\) −9.65750 + 10.4100i −0.558508 + 0.602027i
\(300\) 0.798958 + 1.53677i 0.0461279 + 0.0887255i
\(301\) −1.22086 −0.0703692
\(302\) 9.13517i 0.525670i
\(303\) 7.99845 4.15834i 0.459499 0.238891i
\(304\) 6.91126i 0.396388i
\(305\) 4.14107i 0.237117i
\(306\) −13.6117 9.55255i −0.778131 0.546083i
\(307\) −27.6286 −1.57685 −0.788423 0.615133i \(-0.789102\pi\)
−0.788423 + 0.615133i \(0.789102\pi\)
\(308\) 0.487808i 0.0277954i
\(309\) −13.3487 + 6.93989i −0.759379 + 0.394796i
\(310\) 10.6138i 0.602823i
\(311\) 30.1469i 1.70948i −0.519060 0.854738i \(-0.673718\pi\)
0.519060 0.854738i \(-0.326282\pi\)
\(312\) −4.55019 + 2.36561i −0.257604 + 0.133927i
\(313\) 5.35060i 0.302434i 0.988501 + 0.151217i \(0.0483192\pi\)
−0.988501 + 0.151217i \(0.951681\pi\)
\(314\) −10.3178 −0.582268
\(315\) 0.356641 + 0.250286i 0.0200944 + 0.0141020i
\(316\) 13.2148i 0.743391i
\(317\) 20.5865i 1.15625i 0.815947 + 0.578127i \(0.196216\pi\)
−0.815947 + 0.578127i \(0.803784\pi\)
\(318\) −5.89488 + 3.06471i −0.330568 + 0.171861i
\(319\) 12.0468i 0.674490i
\(320\) 1.00000 0.0559017
\(321\) 8.90556 + 17.1296i 0.497060 + 0.956079i
\(322\) 0.473711 0.510622i 0.0263989 0.0284559i
\(323\) 38.3096i 2.13160i
\(324\) 3.06025 + 8.46374i 0.170014 + 0.470208i
\(325\) 2.96087 0.164240
\(326\) 11.8046i 0.653796i
\(327\) −11.0591 + 5.74955i −0.611569 + 0.317951i
\(328\) −8.84450 −0.488356
\(329\) −1.45040 −0.0799631
\(330\) 5.16167 2.68352i 0.284140 0.147723i
\(331\) 0.146593 0.00805747 0.00402874 0.999992i \(-0.498718\pi\)
0.00402874 + 0.999992i \(0.498718\pi\)
\(332\) −9.71029 −0.532921
\(333\) −14.8357 10.4115i −0.812990 0.570546i
\(334\) −11.8429 −0.648012
\(335\) 13.0680i 0.713979i
\(336\) 0.223191 0.116036i 0.0121761 0.00633027i
\(337\) 24.5559i 1.33764i 0.743423 + 0.668821i \(0.233201\pi\)
−0.743423 + 0.668821i \(0.766799\pi\)
\(338\) 4.23323i 0.230257i
\(339\) −10.5127 20.2209i −0.570973 1.09825i
\(340\) 5.54307 0.300615
\(341\) −35.6493 −1.93052
\(342\) 11.9104 16.9715i 0.644041 0.917715i
\(343\) 2.03021i 0.109621i
\(344\) 8.40616 0.453230
\(345\) −8.00904 2.20347i −0.431192 0.118631i
\(346\) −9.94482 −0.534637
\(347\) 9.62040i 0.516450i 0.966085 + 0.258225i \(0.0831376\pi\)
−0.966085 + 0.258225i \(0.916862\pi\)
\(348\) 5.51188 2.86559i 0.295468 0.153612i
\(349\) 23.1850 1.24106 0.620532 0.784181i \(-0.286917\pi\)
0.620532 + 0.784181i \(0.286917\pi\)
\(350\) −0.145234 −0.00776308
\(351\) 15.2503 + 2.03240i 0.814002 + 0.108482i
\(352\) 3.35877i 0.179023i
\(353\) 9.38131i 0.499317i 0.968334 + 0.249658i \(0.0803183\pi\)
−0.968334 + 0.249658i \(0.919682\pi\)
\(354\) 6.32246 + 12.1611i 0.336035 + 0.646353i
\(355\) 1.26558i 0.0671698i
\(356\) 15.3774 0.815001
\(357\) 1.23716 0.643195i 0.0654777 0.0340415i
\(358\) −3.37701 −0.178480
\(359\) 13.9686 0.737234 0.368617 0.929581i \(-0.379831\pi\)
0.368617 + 0.929581i \(0.379831\pi\)
\(360\) −2.45563 1.72333i −0.129423 0.0908276i
\(361\) −28.7656 −1.51398
\(362\) −5.28230 −0.277632
\(363\) −0.224792 0.432381i −0.0117985 0.0226941i
\(364\) 0.430019i 0.0225391i
\(365\) 9.24658 0.483988
\(366\) 3.30854 + 6.36387i 0.172940 + 0.332645i
\(367\) 11.2257i 0.585976i 0.956116 + 0.292988i \(0.0946496\pi\)
−0.956116 + 0.292988i \(0.905350\pi\)
\(368\) −3.26171 + 3.51586i −0.170028 + 0.183277i
\(369\) 21.7188 + 15.2420i 1.13064 + 0.793467i
\(370\) 6.04149 0.314082
\(371\) 0.557101i 0.0289232i
\(372\) 8.47998 + 16.3110i 0.439667 + 0.845685i
\(373\) 6.04006i 0.312743i 0.987698 + 0.156371i \(0.0499797\pi\)
−0.987698 + 0.156371i \(0.950020\pi\)
\(374\) 18.6179i 0.962709i
\(375\) 0.798958 + 1.53677i 0.0412580 + 0.0793585i
\(376\) 9.98664 0.515022
\(377\) 10.6196i 0.546940i
\(378\) −0.748044 0.0996915i −0.0384752 0.00512758i
\(379\) 6.58693i 0.338348i −0.985586 0.169174i \(-0.945890\pi\)
0.985586 0.169174i \(-0.0541099\pi\)
\(380\) 6.91126i 0.354540i
\(381\) 11.0736 + 21.2998i 0.567320 + 1.09122i
\(382\) 22.1062i 1.13105i
\(383\) −25.9655 −1.32677 −0.663387 0.748277i \(-0.730882\pi\)
−0.663387 + 0.748277i \(0.730882\pi\)
\(384\) −1.53677 + 0.798958i −0.0784230 + 0.0407717i
\(385\) 0.487808i 0.0248610i
\(386\) 5.62469i 0.286289i
\(387\) −20.6424 14.4866i −1.04931 0.736396i
\(388\) 11.6097i 0.589395i
\(389\) 25.9332 1.31486 0.657432 0.753514i \(-0.271643\pi\)
0.657432 + 0.753514i \(0.271643\pi\)
\(390\) −4.55019 + 2.36561i −0.230408 + 0.119788i
\(391\) −18.0799 + 19.4887i −0.914338 + 0.985583i
\(392\) 6.97891i 0.352488i
\(393\) −4.88326 + 2.53878i −0.246328 + 0.128064i
\(394\) 4.97721 0.250748
\(395\) 13.2148i 0.664909i
\(396\) −5.78828 + 8.24791i −0.290872 + 0.414473i
\(397\) 11.2187 0.563049 0.281524 0.959554i \(-0.409160\pi\)
0.281524 + 0.959554i \(0.409160\pi\)
\(398\) −5.07219 −0.254246
\(399\) 0.801954 + 1.54253i 0.0401479 + 0.0772233i
\(400\) 1.00000 0.0500000
\(401\) 16.0468 0.801337 0.400669 0.916223i \(-0.368778\pi\)
0.400669 + 0.916223i \(0.368778\pi\)
\(402\) 10.4408 + 20.0825i 0.520738 + 1.00162i
\(403\) 31.4261 1.56545
\(404\) 5.20471i 0.258944i
\(405\) 3.06025 + 8.46374i 0.152065 + 0.420566i
\(406\) 0.520905i 0.0258521i
\(407\) 20.2920i 1.00584i
\(408\) −8.51843 + 4.42868i −0.421725 + 0.219252i
\(409\) −25.0421 −1.23825 −0.619127 0.785291i \(-0.712513\pi\)
−0.619127 + 0.785291i \(0.712513\pi\)
\(410\) −8.84450 −0.436799
\(411\) −15.2180 29.2714i −0.750649 1.44385i
\(412\) 8.68617i 0.427937i
\(413\) −1.14929 −0.0565529
\(414\) 14.0685 3.01265i 0.691431 0.148064i
\(415\) −9.71029 −0.476659
\(416\) 2.96087i 0.145169i
\(417\) −8.09642 15.5732i −0.396483 0.762624i
\(418\) 23.2134 1.13540
\(419\) 0.170219 0.00831576 0.00415788 0.999991i \(-0.498677\pi\)
0.00415788 + 0.999991i \(0.498677\pi\)
\(420\) 0.223191 0.116036i 0.0108906 0.00566197i
\(421\) 3.35189i 0.163361i 0.996659 + 0.0816807i \(0.0260288\pi\)
−0.996659 + 0.0816807i \(0.973971\pi\)
\(422\) 9.58459i 0.466571i
\(423\) −24.5235 17.2103i −1.19237 0.836793i
\(424\) 3.83589i 0.186287i
\(425\) 5.54307 0.268878
\(426\) 1.01114 + 1.94490i 0.0489900 + 0.0942307i
\(427\) −0.601423 −0.0291049
\(428\) 11.1465 0.538785
\(429\) 7.94556 + 15.2830i 0.383615 + 0.737872i
\(430\) 8.40616 0.405381
\(431\) 21.5603 1.03852 0.519262 0.854615i \(-0.326207\pi\)
0.519262 + 0.854615i \(0.326207\pi\)
\(432\) 5.15061 + 0.686420i 0.247809 + 0.0330254i
\(433\) 25.3255i 1.21707i −0.793529 0.608533i \(-0.791758\pi\)
0.793529 0.608533i \(-0.208242\pi\)
\(434\) −1.54148 −0.0739936
\(435\) 5.51188 2.86559i 0.264274 0.137395i
\(436\) 7.19631i 0.344641i
\(437\) −24.2990 22.5425i −1.16238 1.07835i
\(438\) −14.2099 + 7.38763i −0.678974 + 0.352995i
\(439\) −0.917239 −0.0437774 −0.0218887 0.999760i \(-0.506968\pi\)
−0.0218887 + 0.999760i \(0.506968\pi\)
\(440\) 3.35877i 0.160123i
\(441\) −12.0270 + 17.1376i −0.572713 + 0.816077i
\(442\) 16.4123i 0.780655i
\(443\) 4.08632i 0.194147i −0.995277 0.0970734i \(-0.969052\pi\)
0.995277 0.0970734i \(-0.0309482\pi\)
\(444\) −9.28438 + 4.82690i −0.440617 + 0.229074i
\(445\) 15.3774 0.728959
\(446\) 17.7150i 0.838829i
\(447\) −15.7998 30.3905i −0.747306 1.43742i
\(448\) 0.145234i 0.00686166i
\(449\) 5.31513i 0.250836i 0.992104 + 0.125418i \(0.0400273\pi\)
−0.992104 + 0.125418i \(0.959973\pi\)
\(450\) −2.45563 1.72333i −0.115760 0.0812386i
\(451\) 29.7067i 1.39883i
\(452\) −13.1580 −0.618902
\(453\) 7.29861 + 14.0387i 0.342919 + 0.659594i
\(454\) 3.72255i 0.174708i
\(455\) 0.430019i 0.0201596i
\(456\) −5.52181 10.6210i −0.258582 0.497375i
\(457\) 17.8678i 0.835822i 0.908488 + 0.417911i \(0.137238\pi\)
−0.908488 + 0.417911i \(0.862762\pi\)
\(458\) 4.59060 0.214505
\(459\) 28.5502 + 3.80487i 1.33261 + 0.177596i
\(460\) −3.26171 + 3.51586i −0.152078 + 0.163928i
\(461\) 0.958482i 0.0446410i −0.999751 0.0223205i \(-0.992895\pi\)
0.999751 0.0223205i \(-0.00710542\pi\)
\(462\) −0.389738 0.749649i −0.0181323 0.0348768i
\(463\) 41.6838 1.93721 0.968606 0.248603i \(-0.0799714\pi\)
0.968606 + 0.248603i \(0.0799714\pi\)
\(464\) 3.58666i 0.166507i
\(465\) 8.47998 + 16.3110i 0.393250 + 0.756404i
\(466\) −3.65041 −0.169102
\(467\) 7.07758 0.327511 0.163756 0.986501i \(-0.447639\pi\)
0.163756 + 0.986501i \(0.447639\pi\)
\(468\) 5.10257 7.27082i 0.235866 0.336094i
\(469\) −1.89791 −0.0876375
\(470\) 9.98664 0.460649
\(471\) 15.8561 8.24350i 0.730611 0.379840i
\(472\) 7.91338 0.364243
\(473\) 28.2344i 1.29822i
\(474\) −10.5581 20.3081i −0.484949 0.932784i
\(475\) 6.91126i 0.317111i
\(476\) 0.805042i 0.0368990i
\(477\) 6.61051 9.41953i 0.302674 0.431290i
\(478\) −2.23114 −0.102050
\(479\) −12.3246 −0.563125 −0.281562 0.959543i \(-0.590853\pi\)
−0.281562 + 0.959543i \(0.590853\pi\)
\(480\) −1.53677 + 0.798958i −0.0701437 + 0.0364673i
\(481\) 17.8881i 0.815626i
\(482\) 14.8025 0.674234
\(483\) −0.320019 + 1.16318i −0.0145614 + 0.0529267i
\(484\) −0.281357 −0.0127890
\(485\) 11.6097i 0.527171i
\(486\) −11.4651 10.5618i −0.520067 0.479094i
\(487\) 7.63905 0.346159 0.173079 0.984908i \(-0.444628\pi\)
0.173079 + 0.984908i \(0.444628\pi\)
\(488\) 4.14107 0.187457
\(489\) −9.43137 18.1410i −0.426501 0.820362i
\(490\) 6.97891i 0.315275i
\(491\) 30.8151i 1.39067i −0.718688 0.695333i \(-0.755257\pi\)
0.718688 0.695333i \(-0.244743\pi\)
\(492\) 13.5920 7.06638i 0.612773 0.318577i
\(493\) 19.8811i 0.895400i
\(494\) −20.4634 −0.920691
\(495\) −5.78828 + 8.24791i −0.260164 + 0.370716i
\(496\) 10.6138 0.476574
\(497\) −0.183805 −0.00824476
\(498\) 14.9225 7.75811i 0.668693 0.347649i
\(499\) −26.4668 −1.18482 −0.592409 0.805638i \(-0.701823\pi\)
−0.592409 + 0.805638i \(0.701823\pi\)
\(500\) 1.00000 0.0447214
\(501\) 18.1998 9.46194i 0.813105 0.422729i
\(502\) 13.8618i 0.618682i
\(503\) 22.6338 1.00919 0.504595 0.863356i \(-0.331642\pi\)
0.504595 + 0.863356i \(0.331642\pi\)
\(504\) −0.250286 + 0.356641i −0.0111486 + 0.0158861i
\(505\) 5.20471i 0.231607i
\(506\) 11.8090 + 10.9553i 0.524973 + 0.487024i
\(507\) 3.38217 + 6.50550i 0.150207 + 0.288919i
\(508\) 13.8601 0.614943
\(509\) 15.8116i 0.700839i −0.936593 0.350419i \(-0.886039\pi\)
0.936593 0.350419i \(-0.113961\pi\)
\(510\) −8.51843 + 4.42868i −0.377202 + 0.196105i
\(511\) 1.34292i 0.0594072i
\(512\) 1.00000i 0.0441942i
\(513\) −4.74403 + 35.5973i −0.209454 + 1.57166i
\(514\) −1.86957 −0.0824634
\(515\) 8.68617i 0.382758i
\(516\) −12.9184 + 6.71617i −0.568699 + 0.295663i
\(517\) 33.5429i 1.47521i
\(518\) 0.877429i 0.0385520i
\(519\) 15.2829 7.94549i 0.670845 0.348768i
\(520\) 2.96087i 0.129843i
\(521\) 7.86606 0.344618 0.172309 0.985043i \(-0.444877\pi\)
0.172309 + 0.985043i \(0.444877\pi\)
\(522\) −6.18101 + 8.80752i −0.270535 + 0.385495i
\(523\) 1.97457i 0.0863418i −0.999068 0.0431709i \(-0.986254\pi\)
0.999068 0.0431709i \(-0.0137460\pi\)
\(524\) 3.17761i 0.138815i
\(525\) 0.223191 0.116036i 0.00974087 0.00506422i
\(526\) 21.2810i 0.927894i
\(527\) 58.8330 2.56281
\(528\) 2.68352 + 5.16167i 0.116785 + 0.224633i
\(529\) −1.72254 22.9354i −0.0748929 0.997192i
\(530\) 3.83589i 0.166620i
\(531\) −19.4323 13.6374i −0.843292 0.591812i
\(532\) 1.00375 0.0435181
\(533\) 26.1874i 1.13430i
\(534\) −23.6316 + 12.2859i −1.02264 + 0.531663i
\(535\) 11.1465 0.481904
\(536\) 13.0680 0.564450
\(537\) 5.18969 2.69809i 0.223952 0.116431i
\(538\) −21.9822 −0.947718
\(539\) −23.4406 −1.00966
\(540\) 5.15061 + 0.686420i 0.221647 + 0.0295388i
\(541\) 2.33239 0.100277 0.0501387 0.998742i \(-0.484034\pi\)
0.0501387 + 0.998742i \(0.484034\pi\)
\(542\) 18.8975i 0.811717i
\(543\) 8.11769 4.22034i 0.348363 0.181112i
\(544\) 5.54307i 0.237657i
\(545\) 7.19631i 0.308256i
\(546\) 0.343567 + 0.660841i 0.0147033 + 0.0282814i
\(547\) −8.51715 −0.364167 −0.182083 0.983283i \(-0.558284\pi\)
−0.182083 + 0.983283i \(0.558284\pi\)
\(548\) −19.0473 −0.813661
\(549\) −10.1689 7.13643i −0.434000 0.304576i
\(550\) 3.35877i 0.143219i
\(551\) 24.7884 1.05602
\(552\) 2.20347 8.00904i 0.0937860 0.340887i
\(553\) 1.91924 0.0816143
\(554\) 8.26393i 0.351101i
\(555\) −9.28438 + 4.82690i −0.394100 + 0.204890i
\(556\) −10.1337 −0.429766
\(557\) −2.38292 −0.100967 −0.0504837 0.998725i \(-0.516076\pi\)
−0.0504837 + 0.998725i \(0.516076\pi\)
\(558\) −26.0636 18.2911i −1.10336 0.774324i
\(559\) 24.8896i 1.05272i
\(560\) 0.145234i 0.00613725i
\(561\) 14.8749 + 28.6115i 0.628020 + 1.20798i
\(562\) 13.4017i 0.565315i
\(563\) 6.34926 0.267589 0.133795 0.991009i \(-0.457284\pi\)
0.133795 + 0.991009i \(0.457284\pi\)
\(564\) −15.3472 + 7.97891i −0.646233 + 0.335973i
\(565\) −13.1580 −0.553563
\(566\) 30.2552 1.27172
\(567\) 1.22922 0.444453i 0.0516225 0.0186653i
\(568\) 1.26558 0.0531024
\(569\) 25.7123 1.07792 0.538958 0.842333i \(-0.318818\pi\)
0.538958 + 0.842333i \(0.318818\pi\)
\(570\) −5.52181 10.6210i −0.231283 0.444866i
\(571\) 3.97359i 0.166290i 0.996537 + 0.0831448i \(0.0264964\pi\)
−0.996537 + 0.0831448i \(0.973504\pi\)
\(572\) 9.94490 0.415817
\(573\) 17.6619 + 33.9722i 0.737838 + 1.41921i
\(574\) 1.28452i 0.0536149i
\(575\) −3.26171 + 3.51586i −0.136023 + 0.146621i
\(576\) 1.72333 2.45563i 0.0718055 0.102318i
\(577\) 3.74728 0.156001 0.0780007 0.996953i \(-0.475146\pi\)
0.0780007 + 0.996953i \(0.475146\pi\)
\(578\) 13.7256i 0.570910i
\(579\) −4.49389 8.64386i −0.186760 0.359227i
\(580\) 3.58666i 0.148928i
\(581\) 1.41026i 0.0585076i
\(582\) −9.27569 17.8415i −0.384490 0.739554i
\(583\) 12.8839 0.533596
\(584\) 9.24658i 0.382626i
\(585\) 5.10257 7.27082i 0.210965 0.300611i
\(586\) 7.09896i 0.293255i
\(587\) 14.0119i 0.578333i −0.957279 0.289166i \(-0.906622\pi\)
0.957279 0.289166i \(-0.0933781\pi\)
\(588\) 5.57585 + 10.7250i 0.229944 + 0.442291i
\(589\) 73.3548i 3.02253i
\(590\) 7.91338 0.325789
\(591\) −7.64883 + 3.97658i −0.314631 + 0.163575i
\(592\) 6.04149i 0.248304i
\(593\) 37.3930i 1.53555i −0.640722 0.767773i \(-0.721365\pi\)
0.640722 0.767773i \(-0.278635\pi\)
\(594\) 2.30553 17.2997i 0.0945970 0.709817i
\(595\) 0.805042i 0.0330035i
\(596\) −19.7755 −0.810038
\(597\) 7.79479 4.05246i 0.319020 0.165856i
\(598\) −10.4100 9.65750i −0.425697 0.394925i
\(599\) 47.3032i 1.93275i −0.257128 0.966377i \(-0.582776\pi\)
0.257128 0.966377i \(-0.417224\pi\)
\(600\) −1.53677 + 0.798958i −0.0627384 + 0.0326173i
\(601\) −22.4865 −0.917244 −0.458622 0.888631i \(-0.651657\pi\)
−0.458622 + 0.888631i \(0.651657\pi\)
\(602\) 1.22086i 0.0497586i
\(603\) −32.0901 22.5204i −1.30681 0.917104i
\(604\) 9.13517 0.371705
\(605\) −0.281357 −0.0114388
\(606\) 4.15834 + 7.99845i 0.168921 + 0.324915i
\(607\) 37.1285 1.50700 0.753499 0.657449i \(-0.228365\pi\)
0.753499 + 0.657449i \(0.228365\pi\)
\(608\) −6.91126 −0.280289
\(609\) −0.416181 0.800512i −0.0168645 0.0324384i
\(610\) 4.14107 0.167667
\(611\) 29.5692i 1.19624i
\(612\) 9.55255 13.6117i 0.386139 0.550222i
\(613\) 2.91171i 0.117603i −0.998270 0.0588014i \(-0.981272\pi\)
0.998270 0.0588014i \(-0.0187279\pi\)
\(614\) 27.6286i 1.11500i
\(615\) 13.5920 7.06638i 0.548081 0.284944i
\(616\) −0.487808 −0.0196543
\(617\) −16.9070 −0.680651 −0.340325 0.940308i \(-0.610537\pi\)
−0.340325 + 0.940308i \(0.610537\pi\)
\(618\) −6.93989 13.3487i −0.279163 0.536962i
\(619\) 30.6140i 1.23048i −0.788339 0.615241i \(-0.789059\pi\)
0.788339 0.615241i \(-0.210941\pi\)
\(620\) 10.6138 0.426260
\(621\) −19.2132 + 15.8699i −0.770997 + 0.636839i
\(622\) 30.1469 1.20878
\(623\) 2.23332i 0.0894762i
\(624\) −2.36561 4.55019i −0.0947004 0.182153i
\(625\) 1.00000 0.0400000
\(626\) −5.35060 −0.213853
\(627\) −35.6736 + 18.5465i −1.42467 + 0.740676i
\(628\) 10.3178i 0.411726i
\(629\) 33.4884i 1.33527i
\(630\) −0.250286 + 0.356641i −0.00997164 + 0.0142089i
\(631\) 12.9825i 0.516826i −0.966035 0.258413i \(-0.916800\pi\)
0.966035 0.258413i \(-0.0831995\pi\)
\(632\) −13.2148 −0.525657
\(633\) 7.65769 + 14.7293i 0.304366 + 0.585438i
\(634\) −20.5865 −0.817595
\(635\) 13.8601 0.550021
\(636\) −3.06471 5.89488i −0.121524 0.233747i
\(637\) 20.6637 0.818724
\(638\) −12.0468 −0.476937
\(639\) −3.10779 2.18101i −0.122942 0.0862793i
\(640\) 1.00000i 0.0395285i
\(641\) 23.4868 0.927675 0.463837 0.885920i \(-0.346472\pi\)
0.463837 + 0.885920i \(0.346472\pi\)
\(642\) −17.1296 + 8.90556i −0.676050 + 0.351474i
\(643\) 50.0206i 1.97262i −0.164902 0.986310i \(-0.552731\pi\)
0.164902 0.986310i \(-0.447269\pi\)
\(644\) 0.510622 + 0.473711i 0.0201213 + 0.0186668i
\(645\) −12.9184 + 6.71617i −0.508660 + 0.264449i
\(646\) −38.3096 −1.50727
\(647\) 21.4247i 0.842290i 0.906993 + 0.421145i \(0.138372\pi\)
−0.906993 + 0.421145i \(0.861628\pi\)
\(648\) −8.46374 + 3.06025i −0.332487 + 0.120218i
\(649\) 26.5792i 1.04333i
\(650\) 2.96087i 0.116135i
\(651\) 2.36891 1.23158i 0.0928448 0.0482695i
\(652\) −11.8046 −0.462303
\(653\) 28.4131i 1.11189i −0.831219 0.555946i \(-0.812356\pi\)
0.831219 0.555946i \(-0.187644\pi\)
\(654\) −5.74955 11.0591i −0.224825 0.432444i
\(655\) 3.17761i 0.124160i
\(656\) 8.84450i 0.345320i
\(657\) 15.9349 22.7062i 0.621681 0.885853i
\(658\) 1.45040i 0.0565424i
\(659\) −35.0816 −1.36658 −0.683292 0.730146i \(-0.739452\pi\)
−0.683292 + 0.730146i \(0.739452\pi\)
\(660\) 2.68352 + 5.16167i 0.104456 + 0.200918i
\(661\) 13.5864i 0.528450i −0.964461 0.264225i \(-0.914884\pi\)
0.964461 0.264225i \(-0.0851162\pi\)
\(662\) 0.146593i 0.00569749i
\(663\) −13.1128 25.2220i −0.509257 0.979541i
\(664\) 9.71029i 0.376832i
\(665\) 1.00375 0.0389238
\(666\) 10.4115 14.8357i 0.403437 0.574870i
\(667\) 12.6102 + 11.6986i 0.488269 + 0.452973i
\(668\) 11.8429i 0.458214i
\(669\) −14.1535 27.2239i −0.547207 1.05254i
\(670\) 13.0680 0.504860
\(671\) 13.9089i 0.536947i
\(672\) 0.116036 + 0.223191i 0.00447618 + 0.00860979i
\(673\) −32.3448 −1.24680 −0.623400 0.781903i \(-0.714249\pi\)
−0.623400 + 0.781903i \(0.714249\pi\)
\(674\) −24.5559 −0.945856
\(675\) 5.15061 + 0.686420i 0.198247 + 0.0264203i
\(676\) 4.23323 0.162816
\(677\) −17.2030 −0.661164 −0.330582 0.943777i \(-0.607245\pi\)
−0.330582 + 0.943777i \(0.607245\pi\)
\(678\) 20.2209 10.5127i 0.776579 0.403739i
\(679\) 1.68613 0.0647076
\(680\) 5.54307i 0.212567i
\(681\) 2.97416 + 5.72071i 0.113970 + 0.219218i
\(682\) 35.6493i 1.36508i
\(683\) 7.02091i 0.268648i 0.990937 + 0.134324i \(0.0428862\pi\)
−0.990937 + 0.134324i \(0.957114\pi\)
\(684\) 16.9715 + 11.9104i 0.648922 + 0.455406i
\(685\) −19.0473 −0.727760
\(686\) −2.03021 −0.0775138
\(687\) −7.05470 + 3.66770i −0.269154 + 0.139931i
\(688\) 8.40616i 0.320482i
\(689\) −11.3576 −0.432689
\(690\) 2.20347 8.00904i 0.0838848 0.304899i
\(691\) −42.5068 −1.61703 −0.808517 0.588473i \(-0.799729\pi\)
−0.808517 + 0.588473i \(0.799729\pi\)
\(692\) 9.94482i 0.378045i
\(693\) 1.19788 + 0.840655i 0.0455036 + 0.0319338i
\(694\) −9.62040 −0.365185
\(695\) −10.1337 −0.384394
\(696\) 2.86559 + 5.51188i 0.108620 + 0.208927i
\(697\) 49.0257i 1.85698i
\(698\) 23.1850i 0.877565i
\(699\) 5.60985 2.91653i 0.212184 0.110313i
\(700\) 0.145234i 0.00548933i
\(701\) 9.67785 0.365527 0.182764 0.983157i \(-0.441496\pi\)
0.182764 + 0.983157i \(0.441496\pi\)
\(702\) −2.03240 + 15.2503i −0.0767081 + 0.575586i
\(703\) −41.7543 −1.57479
\(704\) 3.35877 0.126589
\(705\) −15.3472 + 7.97891i −0.578008 + 0.300503i
\(706\) −9.38131 −0.353070
\(707\) −0.755900 −0.0284286
\(708\) −12.1611 + 6.32246i −0.457040 + 0.237613i
\(709\) 11.1186i 0.417569i −0.977962 0.208784i \(-0.933049\pi\)
0.977962 0.208784i \(-0.0669507\pi\)
\(710\) 1.26558 0.0474962
\(711\) 32.4507 + 22.7735i 1.21700 + 0.854073i
\(712\) 15.3774i 0.576293i
\(713\) −34.6191 + 37.3166i −1.29650 + 1.39752i
\(714\) 0.643195 + 1.23716i 0.0240710 + 0.0462997i
\(715\) 9.94490 0.371918
\(716\) 3.37701i 0.126205i
\(717\) 3.42876 1.78259i 0.128049 0.0665721i
\(718\) 13.9686i 0.521303i
\(719\) 6.75338i 0.251859i −0.992039 0.125929i \(-0.959809\pi\)
0.992039 0.125929i \(-0.0401913\pi\)
\(720\) 1.72333 2.45563i 0.0642248 0.0915160i
\(721\) 1.26153 0.0469817
\(722\) 28.7656i 1.07054i
\(723\) −22.7480 + 11.8266i −0.846008 + 0.439834i
\(724\) 5.28230i 0.196315i
\(725\) 3.58666i 0.133205i
\(726\) 0.432381 0.224792i 0.0160472 0.00834283i
\(727\) 20.3417i 0.754432i 0.926125 + 0.377216i \(0.123119\pi\)
−0.926125 + 0.377216i \(0.876881\pi\)
\(728\) 0.430019 0.0159376
\(729\) 26.0577 + 7.07097i 0.965098 + 0.261888i
\(730\) 9.24658i 0.342231i
\(731\) 46.5959i 1.72341i
\(732\) −6.36387 + 3.30854i −0.235215 + 0.122287i
\(733\) 38.8545i 1.43512i 0.696496 + 0.717561i \(0.254742\pi\)
−0.696496 + 0.717561i \(0.745258\pi\)
\(734\) −11.2257 −0.414347
\(735\) 5.57585 + 10.7250i 0.205668 + 0.395597i
\(736\) −3.51586 3.26171i −0.129596 0.120228i
\(737\) 43.8923i 1.61680i
\(738\) −15.2420 + 21.7188i −0.561066 + 0.799481i
\(739\) 1.32758 0.0488359 0.0244179 0.999702i \(-0.492227\pi\)
0.0244179 + 0.999702i \(0.492227\pi\)
\(740\) 6.04149i 0.222090i
\(741\) 31.4475 16.3494i 1.15525 0.600610i
\(742\) 0.557101 0.0204518
\(743\) 6.50411 0.238613 0.119306 0.992857i \(-0.461933\pi\)
0.119306 + 0.992857i \(0.461933\pi\)
\(744\) −16.3110 + 8.47998i −0.597990 + 0.310891i
\(745\) −19.7755 −0.724520
\(746\) −6.04006 −0.221142
\(747\) −16.7340 + 23.8449i −0.612267 + 0.872439i
\(748\) 18.6179 0.680738
\(749\) 1.61885i 0.0591513i
\(750\) −1.53677 + 0.798958i −0.0561150 + 0.0291738i
\(751\) 0.826257i 0.0301506i −0.999886 0.0150753i \(-0.995201\pi\)
0.999886 0.0150753i \(-0.00479879\pi\)
\(752\) 9.98664i 0.364175i
\(753\) 11.0750 + 21.3024i 0.403595 + 0.776303i
\(754\) 10.6196 0.386745
\(755\) 9.13517 0.332463
\(756\) 0.0996915 0.748044i 0.00362574 0.0272061i
\(757\) 38.9797i 1.41674i −0.705842 0.708370i \(-0.749431\pi\)
0.705842 0.708370i \(-0.250569\pi\)
\(758\) 6.58693 0.239248
\(759\) −26.9005 7.40097i −0.976428 0.268638i
\(760\) −6.91126 −0.250698
\(761\) 24.3111i 0.881276i 0.897685 + 0.440638i \(0.145248\pi\)
−0.897685 + 0.440638i \(0.854752\pi\)
\(762\) −21.2998 + 11.0736i −0.771610 + 0.401156i
\(763\) 1.04515 0.0378369
\(764\) 22.1062 0.799775
\(765\) 9.55255 13.6117i 0.345373 0.492133i
\(766\) 25.9655i 0.938171i
\(767\) 23.4305i 0.846027i
\(768\) −0.798958 1.53677i −0.0288299 0.0554535i
\(769\) 32.2264i 1.16211i −0.813863 0.581057i \(-0.802639\pi\)
0.813863 0.581057i \(-0.197361\pi\)
\(770\) −0.487808 −0.0175794
\(771\) 2.87311 1.49371i 0.103472 0.0537947i
\(772\) −5.62469 −0.202437
\(773\) 2.00243 0.0720223 0.0360111 0.999351i \(-0.488535\pi\)
0.0360111 + 0.999351i \(0.488535\pi\)
\(774\) 14.4866 20.6424i 0.520710 0.741977i
\(775\) 10.6138 0.381259
\(776\) −11.6097 −0.416765
\(777\) 0.701029 + 1.34841i 0.0251493 + 0.0483739i
\(778\) 25.9332i 0.929750i
\(779\) 61.1267 2.19009
\(780\) −2.36561 4.55019i −0.0847026 0.162923i
\(781\) 4.25078i 0.152105i
\(782\) −19.4887 18.0799i −0.696913 0.646535i
\(783\) 2.46196 18.4735i 0.0879831 0.660189i
\(784\) 6.97891 0.249247