Properties

Label 731.2.e.a.307.13
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.13
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.13

$q$-expansion

\(f(q)\) \(=\) \(q-0.546292 q^{2} +(0.344032 - 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 - 1.16347i) q^{5} +(-0.187942 + 0.325525i) q^{6} +(0.618902 + 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 + 2.18807i) q^{9} +O(q^{10})\) \(q-0.546292 q^{2} +(0.344032 - 0.595881i) q^{3} -1.70156 q^{4} +(0.671732 - 1.16347i) q^{5} +(-0.187942 + 0.325525i) q^{6} +(0.618902 + 1.07197i) q^{7} +2.02214 q^{8} +(1.26328 + 2.18807i) q^{9} +(-0.366962 + 0.635597i) q^{10} -0.376735 q^{11} +(-0.585392 + 1.01393i) q^{12} +(-0.470269 - 0.814530i) q^{13} +(-0.338101 - 0.585609i) q^{14} +(-0.462195 - 0.800545i) q^{15} +2.29845 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.690122 - 1.19533i) q^{18} +(-2.39780 + 4.15311i) q^{19} +(-1.14300 + 1.97973i) q^{20} +0.851688 q^{21} +0.205807 q^{22} +(3.55543 - 6.15818i) q^{23} +(0.695679 - 1.20495i) q^{24} +(1.59755 + 2.76704i) q^{25} +(0.256904 + 0.444971i) q^{26} +3.80263 q^{27} +(-1.05310 - 1.82403i) q^{28} +(1.90315 + 3.29634i) q^{29} +(0.252493 + 0.437331i) q^{30} +(-1.39144 + 2.41005i) q^{31} -5.29990 q^{32} +(-0.129609 + 0.224489i) q^{33} +(-0.273146 - 0.473103i) q^{34} +1.66295 q^{35} +(-2.14956 - 3.72315i) q^{36} +(4.86114 - 8.41974i) q^{37} +(1.30990 - 2.26881i) q^{38} -0.647150 q^{39} +(1.35833 - 2.35270i) q^{40} +6.95562 q^{41} -0.465271 q^{42} +(6.12810 + 2.33375i) q^{43} +0.641038 q^{44} +3.39436 q^{45} +(-1.94230 + 3.36417i) q^{46} +6.61167 q^{47} +(0.790741 - 1.36960i) q^{48} +(2.73392 - 4.73529i) q^{49} +(-0.872730 - 1.51161i) q^{50} +0.688064 q^{51} +(0.800193 + 1.38597i) q^{52} +(3.05510 - 5.29158i) q^{53} -2.07735 q^{54} +(-0.253065 + 0.438321i) q^{55} +(1.25150 + 2.16767i) q^{56} +(1.64984 + 2.85760i) q^{57} +(-1.03967 - 1.80077i) q^{58} +0.791761 q^{59} +(0.786454 + 1.36218i) q^{60} +(-1.45666 - 2.52301i) q^{61} +(0.760134 - 1.31659i) q^{62} +(-1.56370 + 2.70840i) q^{63} -1.70161 q^{64} -1.26358 q^{65} +(0.0708042 - 0.122637i) q^{66} +(-5.93843 + 10.2857i) q^{67} +(-0.850782 - 1.47360i) q^{68} +(-2.44636 - 4.23722i) q^{69} -0.908454 q^{70} +(-3.31931 - 5.74921i) q^{71} +(2.55453 + 4.42458i) q^{72} +(2.39725 + 4.15217i) q^{73} +(-2.65560 + 4.59964i) q^{74} +2.19843 q^{75} +(4.08001 - 7.06679i) q^{76} +(-0.233162 - 0.403848i) q^{77} +0.353533 q^{78} +(2.59411 + 4.49313i) q^{79} +(1.54394 - 2.67419i) q^{80} +(-2.48163 + 4.29830i) q^{81} -3.79980 q^{82} +(3.70861 - 6.42350i) q^{83} -1.44920 q^{84} +1.34346 q^{85} +(-3.34773 - 1.27491i) q^{86} +2.61897 q^{87} -0.761809 q^{88} +(-7.18187 + 12.4394i) q^{89} -1.85431 q^{90} +(0.582101 - 1.00823i) q^{91} +(-6.04979 + 10.4785i) q^{92} +(0.957400 + 1.65827i) q^{93} -3.61190 q^{94} +(3.22136 + 5.57956i) q^{95} +(-1.82333 + 3.15811i) q^{96} +9.03956 q^{97} +(-1.49352 + 2.58685i) q^{98} +(-0.475923 - 0.824323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.546292 −0.386287 −0.193143 0.981171i \(-0.561868\pi\)
−0.193143 + 0.981171i \(0.561868\pi\)
\(3\) 0.344032 0.595881i 0.198627 0.344032i −0.749457 0.662054i \(-0.769685\pi\)
0.948083 + 0.318022i \(0.103018\pi\)
\(4\) −1.70156 −0.850782
\(5\) 0.671732 1.16347i 0.300408 0.520322i −0.675821 0.737066i \(-0.736211\pi\)
0.976228 + 0.216745i \(0.0695439\pi\)
\(6\) −0.187942 + 0.325525i −0.0767270 + 0.132895i
\(7\) 0.618902 + 1.07197i 0.233923 + 0.405166i 0.958959 0.283544i \(-0.0915103\pi\)
−0.725036 + 0.688711i \(0.758177\pi\)
\(8\) 2.02214 0.714933
\(9\) 1.26328 + 2.18807i 0.421095 + 0.729357i
\(10\) −0.366962 + 0.635597i −0.116044 + 0.200993i
\(11\) −0.376735 −0.113590 −0.0567949 0.998386i \(-0.518088\pi\)
−0.0567949 + 0.998386i \(0.518088\pi\)
\(12\) −0.585392 + 1.01393i −0.168988 + 0.292696i
\(13\) −0.470269 0.814530i −0.130429 0.225910i 0.793413 0.608684i \(-0.208302\pi\)
−0.923842 + 0.382774i \(0.874969\pi\)
\(14\) −0.338101 0.585609i −0.0903614 0.156511i
\(15\) −0.462195 0.800545i −0.119338 0.206700i
\(16\) 2.29845 0.574613
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −0.690122 1.19533i −0.162663 0.281741i
\(19\) −2.39780 + 4.15311i −0.550093 + 0.952789i 0.448174 + 0.893946i \(0.352074\pi\)
−0.998267 + 0.0588427i \(0.981259\pi\)
\(20\) −1.14300 + 1.97973i −0.255582 + 0.442680i
\(21\) 0.851688 0.185854
\(22\) 0.205807 0.0438782
\(23\) 3.55543 6.15818i 0.741358 1.28407i −0.210519 0.977590i \(-0.567515\pi\)
0.951877 0.306480i \(-0.0991513\pi\)
\(24\) 0.695679 1.20495i 0.142005 0.245960i
\(25\) 1.59755 + 2.76704i 0.319510 + 0.553408i
\(26\) 0.256904 + 0.444971i 0.0503831 + 0.0872660i
\(27\) 3.80263 0.731817
\(28\) −1.05310 1.82403i −0.199018 0.344708i
\(29\) 1.90315 + 3.29634i 0.353405 + 0.612116i 0.986844 0.161677i \(-0.0516904\pi\)
−0.633438 + 0.773793i \(0.718357\pi\)
\(30\) 0.252493 + 0.437331i 0.0460988 + 0.0798454i
\(31\) −1.39144 + 2.41005i −0.249910 + 0.432857i −0.963501 0.267706i \(-0.913734\pi\)
0.713590 + 0.700563i \(0.247068\pi\)
\(32\) −5.29990 −0.936899
\(33\) −0.129609 + 0.224489i −0.0225620 + 0.0390785i
\(34\) −0.273146 0.473103i −0.0468442 0.0811365i
\(35\) 1.66295 0.281089
\(36\) −2.14956 3.72315i −0.358260 0.620524i
\(37\) 4.86114 8.41974i 0.799167 1.38420i −0.120993 0.992653i \(-0.538608\pi\)
0.920159 0.391544i \(-0.128059\pi\)
\(38\) 1.30990 2.26881i 0.212494 0.368050i
\(39\) −0.647150 −0.103627
\(40\) 1.35833 2.35270i 0.214771 0.371995i
\(41\) 6.95562 1.08629 0.543143 0.839640i \(-0.317234\pi\)
0.543143 + 0.839640i \(0.317234\pi\)
\(42\) −0.465271 −0.0717928
\(43\) 6.12810 + 2.33375i 0.934526 + 0.355894i
\(44\) 0.641038 0.0966402
\(45\) 3.39436 0.506001
\(46\) −1.94230 + 3.36417i −0.286377 + 0.496019i
\(47\) 6.61167 0.964411 0.482205 0.876058i \(-0.339836\pi\)
0.482205 + 0.876058i \(0.339836\pi\)
\(48\) 0.790741 1.36960i 0.114134 0.197685i
\(49\) 2.73392 4.73529i 0.390560 0.676470i
\(50\) −0.872730 1.51161i −0.123423 0.213774i
\(51\) 0.688064 0.0963482
\(52\) 0.800193 + 1.38597i 0.110967 + 0.192200i
\(53\) 3.05510 5.29158i 0.419650 0.726855i −0.576254 0.817270i \(-0.695486\pi\)
0.995904 + 0.0904156i \(0.0288195\pi\)
\(54\) −2.07735 −0.282691
\(55\) −0.253065 + 0.438321i −0.0341233 + 0.0591032i
\(56\) 1.25150 + 2.16767i 0.167239 + 0.289667i
\(57\) 1.64984 + 2.85760i 0.218526 + 0.378499i
\(58\) −1.03967 1.80077i −0.136516 0.236452i
\(59\) 0.791761 0.103079 0.0515393 0.998671i \(-0.483587\pi\)
0.0515393 + 0.998671i \(0.483587\pi\)
\(60\) 0.786454 + 1.36218i 0.101531 + 0.175856i
\(61\) −1.45666 2.52301i −0.186507 0.323039i 0.757577 0.652746i \(-0.226383\pi\)
−0.944083 + 0.329707i \(0.893050\pi\)
\(62\) 0.760134 1.31659i 0.0965371 0.167207i
\(63\) −1.56370 + 2.70840i −0.197007 + 0.341227i
\(64\) −1.70161 −0.212701
\(65\) −1.26358 −0.156728
\(66\) 0.0708042 0.122637i 0.00871540 0.0150955i
\(67\) −5.93843 + 10.2857i −0.725494 + 1.25659i 0.233276 + 0.972411i \(0.425055\pi\)
−0.958770 + 0.284182i \(0.908278\pi\)
\(68\) −0.850782 1.47360i −0.103173 0.178700i
\(69\) −2.44636 4.23722i −0.294507 0.510102i
\(70\) −0.908454 −0.108581
\(71\) −3.31931 5.74921i −0.393929 0.682306i 0.599035 0.800723i \(-0.295551\pi\)
−0.992964 + 0.118418i \(0.962218\pi\)
\(72\) 2.55453 + 4.42458i 0.301055 + 0.521442i
\(73\) 2.39725 + 4.15217i 0.280577 + 0.485974i 0.971527 0.236929i \(-0.0761407\pi\)
−0.690950 + 0.722903i \(0.742807\pi\)
\(74\) −2.65560 + 4.59964i −0.308708 + 0.534697i
\(75\) 2.19843 0.253853
\(76\) 4.08001 7.06679i 0.468009 0.810616i
\(77\) −0.233162 0.403848i −0.0265713 0.0460228i
\(78\) 0.353533 0.0400297
\(79\) 2.59411 + 4.49313i 0.291860 + 0.505517i 0.974250 0.225472i \(-0.0723924\pi\)
−0.682389 + 0.730989i \(0.739059\pi\)
\(80\) 1.54394 2.67419i 0.172618 0.298984i
\(81\) −2.48163 + 4.29830i −0.275736 + 0.477589i
\(82\) −3.79980 −0.419618
\(83\) 3.70861 6.42350i 0.407073 0.705071i −0.587488 0.809233i \(-0.699883\pi\)
0.994560 + 0.104163i \(0.0332162\pi\)
\(84\) −1.44920 −0.158121
\(85\) 1.34346 0.145719
\(86\) −3.34773 1.27491i −0.360995 0.137477i
\(87\) 2.61897 0.280783
\(88\) −0.761809 −0.0812091
\(89\) −7.18187 + 12.4394i −0.761276 + 1.31857i 0.180917 + 0.983498i \(0.442094\pi\)
−0.942193 + 0.335071i \(0.891240\pi\)
\(90\) −1.85431 −0.195461
\(91\) 0.582101 1.00823i 0.0610207 0.105691i
\(92\) −6.04979 + 10.4785i −0.630734 + 1.09246i
\(93\) 0.957400 + 1.65827i 0.0992778 + 0.171954i
\(94\) −3.61190 −0.372539
\(95\) 3.22136 + 5.57956i 0.330504 + 0.572450i
\(96\) −1.82333 + 3.15811i −0.186093 + 0.322323i
\(97\) 9.03956 0.917828 0.458914 0.888481i \(-0.348239\pi\)
0.458914 + 0.888481i \(0.348239\pi\)
\(98\) −1.49352 + 2.58685i −0.150868 + 0.261312i
\(99\) −0.475923 0.824323i −0.0478321 0.0828476i
\(100\) −2.71834 4.70830i −0.271834 0.470830i
\(101\) 7.14481 + 12.3752i 0.710936 + 1.23138i 0.964506 + 0.264060i \(0.0850616\pi\)
−0.253571 + 0.967317i \(0.581605\pi\)
\(102\) −0.375884 −0.0372180
\(103\) −7.07308 12.2509i −0.696931 1.20712i −0.969525 0.244991i \(-0.921215\pi\)
0.272594 0.962129i \(-0.412118\pi\)
\(104\) −0.950948 1.64709i −0.0932481 0.161510i
\(105\) 0.572106 0.990917i 0.0558319 0.0967036i
\(106\) −1.66898 + 2.89075i −0.162105 + 0.280775i
\(107\) −14.2119 −1.37391 −0.686956 0.726699i \(-0.741054\pi\)
−0.686956 + 0.726699i \(0.741054\pi\)
\(108\) −6.47042 −0.622617
\(109\) 3.34958 5.80164i 0.320831 0.555696i −0.659828 0.751416i \(-0.729371\pi\)
0.980660 + 0.195720i \(0.0627044\pi\)
\(110\) 0.138247 0.239451i 0.0131814 0.0228308i
\(111\) −3.34478 5.79332i −0.317472 0.549878i
\(112\) 1.42252 + 2.46387i 0.134415 + 0.232814i
\(113\) −11.8684 −1.11649 −0.558243 0.829678i \(-0.688524\pi\)
−0.558243 + 0.829678i \(0.688524\pi\)
\(114\) −0.901294 1.56109i −0.0844139 0.146209i
\(115\) −4.77659 8.27330i −0.445420 0.771489i
\(116\) −3.23833 5.60894i −0.300671 0.520777i
\(117\) 1.18817 2.05796i 0.109846 0.190259i
\(118\) −0.432533 −0.0398179
\(119\) −0.618902 + 1.07197i −0.0567347 + 0.0982673i
\(120\) −0.934620 1.61881i −0.0853188 0.147776i
\(121\) −10.8581 −0.987097
\(122\) 0.795764 + 1.37830i 0.0720451 + 0.124786i
\(123\) 2.39296 4.14472i 0.215766 0.373717i
\(124\) 2.36763 4.10085i 0.212619 0.368267i
\(125\) 11.0098 0.984749
\(126\) 0.854236 1.47958i 0.0761014 0.131812i
\(127\) −10.2894 −0.913040 −0.456520 0.889713i \(-0.650904\pi\)
−0.456520 + 0.889713i \(0.650904\pi\)
\(128\) 11.5294 1.01906
\(129\) 3.49890 2.84873i 0.308061 0.250817i
\(130\) 0.690283 0.0605419
\(131\) 20.9025 1.82626 0.913128 0.407673i \(-0.133660\pi\)
0.913128 + 0.407673i \(0.133660\pi\)
\(132\) 0.220538 0.381982i 0.0191953 0.0332473i
\(133\) −5.93601 −0.514717
\(134\) 3.24412 5.61897i 0.280249 0.485405i
\(135\) 2.55435 4.42426i 0.219843 0.380780i
\(136\) 1.01107 + 1.75122i 0.0866984 + 0.150166i
\(137\) −4.25668 −0.363672 −0.181836 0.983329i \(-0.558204\pi\)
−0.181836 + 0.983329i \(0.558204\pi\)
\(138\) 1.33643 + 2.31476i 0.113764 + 0.197046i
\(139\) −8.55711 + 14.8214i −0.725805 + 1.25713i 0.232837 + 0.972516i \(0.425199\pi\)
−0.958642 + 0.284615i \(0.908134\pi\)
\(140\) −2.82961 −0.239146
\(141\) 2.27462 3.93977i 0.191558 0.331788i
\(142\) 1.81331 + 3.14075i 0.152170 + 0.263566i
\(143\) 0.177167 + 0.306862i 0.0148154 + 0.0256611i
\(144\) 2.90360 + 5.02918i 0.241967 + 0.419098i
\(145\) 5.11362 0.424663
\(146\) −1.30960 2.26830i −0.108383 0.187726i
\(147\) −1.88111 3.25818i −0.155151 0.268730i
\(148\) −8.27155 + 14.3267i −0.679917 + 1.17765i
\(149\) −1.75004 + 3.03115i −0.143368 + 0.248322i −0.928763 0.370674i \(-0.879127\pi\)
0.785395 + 0.618995i \(0.212460\pi\)
\(150\) −1.20099 −0.0980602
\(151\) −1.07338 −0.0873505 −0.0436752 0.999046i \(-0.513907\pi\)
−0.0436752 + 0.999046i \(0.513907\pi\)
\(152\) −4.84868 + 8.39815i −0.393280 + 0.681180i
\(153\) −1.26328 + 2.18807i −0.102130 + 0.176895i
\(154\) 0.127375 + 0.220619i 0.0102641 + 0.0177780i
\(155\) 1.86935 + 3.23781i 0.150150 + 0.260067i
\(156\) 1.10117 0.0881640
\(157\) 9.73171 + 16.8558i 0.776675 + 1.34524i 0.933848 + 0.357669i \(0.116428\pi\)
−0.157173 + 0.987571i \(0.550238\pi\)
\(158\) −1.41714 2.45456i −0.112742 0.195275i
\(159\) −2.10210 3.64095i −0.166707 0.288746i
\(160\) −3.56011 + 6.16630i −0.281452 + 0.487489i
\(161\) 8.80185 0.693683
\(162\) 1.35569 2.34813i 0.106513 0.184486i
\(163\) −9.69133 16.7859i −0.759084 1.31477i −0.943318 0.331890i \(-0.892314\pi\)
0.184234 0.982882i \(-0.441019\pi\)
\(164\) −11.8354 −0.924193
\(165\) 0.174125 + 0.301593i 0.0135556 + 0.0234790i
\(166\) −2.02598 + 3.50911i −0.157247 + 0.272360i
\(167\) 2.62914 4.55381i 0.203449 0.352384i −0.746188 0.665735i \(-0.768118\pi\)
0.949638 + 0.313351i \(0.101451\pi\)
\(168\) 1.72223 0.132873
\(169\) 6.05769 10.4922i 0.465976 0.807095i
\(170\) −0.733924 −0.0562894
\(171\) −12.1164 −0.926565
\(172\) −10.4274 3.97103i −0.795078 0.302789i
\(173\) −10.7383 −0.816420 −0.408210 0.912888i \(-0.633847\pi\)
−0.408210 + 0.912888i \(0.633847\pi\)
\(174\) −1.43072 −0.108463
\(175\) −1.97746 + 3.42505i −0.149482 + 0.258910i
\(176\) −0.865907 −0.0652702
\(177\) 0.272391 0.471795i 0.0204742 0.0354623i
\(178\) 3.92340 6.79552i 0.294071 0.509346i
\(179\) 10.5108 + 18.2052i 0.785613 + 1.36072i 0.928632 + 0.371001i \(0.120985\pi\)
−0.143020 + 0.989720i \(0.545681\pi\)
\(180\) −5.77572 −0.430496
\(181\) −11.8457 20.5173i −0.880482 1.52504i −0.850806 0.525479i \(-0.823886\pi\)
−0.0296752 0.999560i \(-0.509447\pi\)
\(182\) −0.317997 + 0.550787i −0.0235715 + 0.0408271i
\(183\) −2.00455 −0.148181
\(184\) 7.18956 12.4527i 0.530021 0.918024i
\(185\) −6.53077 11.3116i −0.480152 0.831647i
\(186\) −0.523020 0.905898i −0.0383497 0.0664237i
\(187\) −0.188367 0.326262i −0.0137748 0.0238586i
\(188\) −11.2502 −0.820504
\(189\) 2.35346 + 4.07631i 0.171189 + 0.296508i
\(190\) −1.75980 3.04807i −0.127670 0.221130i
\(191\) −6.48004 + 11.2238i −0.468880 + 0.812123i −0.999367 0.0355695i \(-0.988675\pi\)
0.530488 + 0.847693i \(0.322009\pi\)
\(192\) −0.585408 + 1.01396i −0.0422482 + 0.0731761i
\(193\) 1.13960 0.0820302 0.0410151 0.999159i \(-0.486941\pi\)
0.0410151 + 0.999159i \(0.486941\pi\)
\(194\) −4.93824 −0.354545
\(195\) −0.434711 + 0.752942i −0.0311303 + 0.0539193i
\(196\) −4.65194 + 8.05740i −0.332282 + 0.575529i
\(197\) 0.807859 + 1.39925i 0.0575576 + 0.0996926i 0.893368 0.449325i \(-0.148335\pi\)
−0.835811 + 0.549017i \(0.815002\pi\)
\(198\) 0.259993 + 0.450321i 0.0184769 + 0.0320029i
\(199\) −13.2722 −0.940838 −0.470419 0.882443i \(-0.655897\pi\)
−0.470419 + 0.882443i \(0.655897\pi\)
\(200\) 3.23047 + 5.59533i 0.228428 + 0.395650i
\(201\) 4.08601 + 7.07719i 0.288205 + 0.499186i
\(202\) −3.90316 6.76047i −0.274625 0.475665i
\(203\) −2.35572 + 4.08023i −0.165339 + 0.286376i
\(204\) −1.17078 −0.0819713
\(205\) 4.67232 8.09269i 0.326329 0.565218i
\(206\) 3.86397 + 6.69259i 0.269215 + 0.466295i
\(207\) 17.9661 1.24873
\(208\) −1.08089 1.87216i −0.0749463 0.129811i
\(209\) 0.903334 1.56462i 0.0624849 0.108227i
\(210\) −0.312537 + 0.541330i −0.0215671 + 0.0373553i
\(211\) −6.07480 −0.418206 −0.209103 0.977894i \(-0.567054\pi\)
−0.209103 + 0.977894i \(0.567054\pi\)
\(212\) −5.19845 + 9.00397i −0.357031 + 0.618395i
\(213\) −4.56779 −0.312980
\(214\) 7.76383 0.530724
\(215\) 6.83171 5.56223i 0.465918 0.379341i
\(216\) 7.68944 0.523200
\(217\) −3.44466 −0.233839
\(218\) −1.82985 + 3.16939i −0.123933 + 0.214658i
\(219\) 3.29893 0.222921
\(220\) 0.430606 0.745832i 0.0290315 0.0502840i
\(221\) 0.470269 0.814530i 0.0316337 0.0547912i
\(222\) 1.82722 + 3.16485i 0.122635 + 0.212411i
\(223\) −17.6313 −1.18068 −0.590340 0.807155i \(-0.701006\pi\)
−0.590340 + 0.807155i \(0.701006\pi\)
\(224\) −3.28012 5.68133i −0.219162 0.379600i
\(225\) −4.03632 + 6.99112i −0.269088 + 0.466074i
\(226\) 6.48362 0.431284
\(227\) 2.01775 3.49484i 0.133922 0.231961i −0.791263 0.611476i \(-0.790576\pi\)
0.925185 + 0.379516i \(0.123909\pi\)
\(228\) −2.80731 4.86240i −0.185918 0.322020i
\(229\) −7.81344 13.5333i −0.516326 0.894303i −0.999820 0.0189558i \(-0.993966\pi\)
0.483494 0.875348i \(-0.339368\pi\)
\(230\) 2.60942 + 4.51964i 0.172060 + 0.298016i
\(231\) −0.320860 −0.0211111
\(232\) 3.84842 + 6.66566i 0.252661 + 0.437622i
\(233\) 7.47200 + 12.9419i 0.489507 + 0.847851i 0.999927 0.0120745i \(-0.00384351\pi\)
−0.510420 + 0.859925i \(0.670510\pi\)
\(234\) −0.649086 + 1.12425i −0.0424321 + 0.0734945i
\(235\) 4.44127 7.69251i 0.289717 0.501804i
\(236\) −1.34723 −0.0876974
\(237\) 3.56983 0.231885
\(238\) 0.338101 0.585609i 0.0219159 0.0379594i
\(239\) −5.60195 + 9.70286i −0.362360 + 0.627626i −0.988349 0.152206i \(-0.951362\pi\)
0.625989 + 0.779832i \(0.284696\pi\)
\(240\) −1.06233 1.84001i −0.0685733 0.118772i
\(241\) −5.56837 9.64469i −0.358690 0.621269i 0.629052 0.777363i \(-0.283443\pi\)
−0.987742 + 0.156094i \(0.950110\pi\)
\(242\) 5.93168 0.381303
\(243\) 7.41146 + 12.8370i 0.475446 + 0.823496i
\(244\) 2.47861 + 4.29307i 0.158677 + 0.274836i
\(245\) −3.67293 6.36169i −0.234655 0.406434i
\(246\) −1.30725 + 2.26423i −0.0833474 + 0.144362i
\(247\) 4.51044 0.286993
\(248\) −2.81368 + 4.87344i −0.178669 + 0.309464i
\(249\) −2.55176 4.41978i −0.161711 0.280092i
\(250\) −6.01458 −0.380396
\(251\) −10.7536 18.6257i −0.678759 1.17565i −0.975355 0.220643i \(-0.929185\pi\)
0.296595 0.955003i \(-0.404149\pi\)
\(252\) 2.66073 4.60853i 0.167610 0.290310i
\(253\) −1.33945 + 2.32000i −0.0842107 + 0.145857i
\(254\) 5.62104 0.352696
\(255\) 0.462195 0.800545i 0.0289437 0.0501320i
\(256\) −2.89519 −0.180949
\(257\) 20.1238 1.25529 0.627643 0.778501i \(-0.284020\pi\)
0.627643 + 0.778501i \(0.284020\pi\)
\(258\) −1.91142 + 1.55624i −0.119000 + 0.0968872i
\(259\) 12.0343 0.747774
\(260\) 2.15006 0.133341
\(261\) −4.80843 + 8.32844i −0.297634 + 0.515517i
\(262\) −11.4189 −0.705459
\(263\) −10.6698 + 18.4806i −0.657925 + 1.13956i 0.323227 + 0.946322i \(0.395232\pi\)
−0.981152 + 0.193238i \(0.938101\pi\)
\(264\) −0.262086 + 0.453947i −0.0161303 + 0.0279385i
\(265\) −4.10441 7.10905i −0.252132 0.436706i
\(266\) 3.24280 0.198829
\(267\) 4.94158 + 8.55907i 0.302420 + 0.523807i
\(268\) 10.1046 17.5017i 0.617238 1.06909i
\(269\) −7.60229 −0.463520 −0.231760 0.972773i \(-0.574448\pi\)
−0.231760 + 0.972773i \(0.574448\pi\)
\(270\) −1.39542 + 2.41694i −0.0849227 + 0.147090i
\(271\) 2.28993 + 3.96628i 0.139104 + 0.240934i 0.927158 0.374672i \(-0.122245\pi\)
−0.788054 + 0.615606i \(0.788911\pi\)
\(272\) 1.14923 + 1.99052i 0.0696821 + 0.120693i
\(273\) −0.400522 0.693725i −0.0242407 0.0419861i
\(274\) 2.32539 0.140482
\(275\) −0.601853 1.04244i −0.0362931 0.0628615i
\(276\) 4.16264 + 7.20991i 0.250562 + 0.433985i
\(277\) 10.6591 18.4622i 0.640445 1.10928i −0.344888 0.938644i \(-0.612083\pi\)
0.985333 0.170640i \(-0.0545834\pi\)
\(278\) 4.67468 8.09679i 0.280369 0.485613i
\(279\) −7.03114 −0.420944
\(280\) 3.36270 0.200960
\(281\) −12.3112 + 21.3236i −0.734425 + 1.27206i 0.220551 + 0.975376i \(0.429215\pi\)
−0.954975 + 0.296685i \(0.904119\pi\)
\(282\) −1.24261 + 2.15226i −0.0739963 + 0.128165i
\(283\) −15.0663 26.0956i −0.895600 1.55122i −0.833060 0.553182i \(-0.813413\pi\)
−0.0625400 0.998042i \(-0.519920\pi\)
\(284\) 5.64802 + 9.78265i 0.335148 + 0.580494i
\(285\) 4.43300 0.262588
\(286\) −0.0967847 0.167636i −0.00572300 0.00991253i
\(287\) 4.30485 + 7.45622i 0.254107 + 0.440127i
\(288\) −6.69528 11.5966i −0.394523 0.683334i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −2.79353 −0.164042
\(291\) 3.10990 5.38650i 0.182305 0.315762i
\(292\) −4.07908 7.06518i −0.238710 0.413458i
\(293\) 17.2906 1.01013 0.505064 0.863082i \(-0.331469\pi\)
0.505064 + 0.863082i \(0.331469\pi\)
\(294\) 1.02764 + 1.77992i 0.0599330 + 0.103807i
\(295\) 0.531852 0.921194i 0.0309656 0.0536340i
\(296\) 9.82989 17.0259i 0.571351 0.989609i
\(297\) −1.43258 −0.0831269
\(298\) 0.956031 1.65589i 0.0553814 0.0959234i
\(299\) −6.68803 −0.386779
\(300\) −3.74078 −0.215974
\(301\) 1.29098 + 8.01350i 0.0744107 + 0.461891i
\(302\) 0.586380 0.0337424
\(303\) 9.83218 0.564844
\(304\) −5.51123 + 9.54573i −0.316091 + 0.547485i
\(305\) −3.91395 −0.224112
\(306\) 0.690122 1.19533i 0.0394517 0.0683323i
\(307\) 6.13975 10.6344i 0.350414 0.606935i −0.635908 0.771765i \(-0.719374\pi\)
0.986322 + 0.164830i \(0.0527075\pi\)
\(308\) 0.396740 + 0.687174i 0.0226064 + 0.0391554i
\(309\) −9.73346 −0.553717
\(310\) −1.02121 1.76879i −0.0580010 0.100461i
\(311\) −3.98889 + 6.90895i −0.226189 + 0.391771i −0.956676 0.291156i \(-0.905960\pi\)
0.730486 + 0.682927i \(0.239293\pi\)
\(312\) −1.30863 −0.0740863
\(313\) 7.48489 12.9642i 0.423071 0.732781i −0.573167 0.819439i \(-0.694285\pi\)
0.996238 + 0.0866578i \(0.0276187\pi\)
\(314\) −5.31636 9.20820i −0.300019 0.519649i
\(315\) 2.10077 + 3.63865i 0.118365 + 0.205014i
\(316\) −4.41405 7.64536i −0.248310 0.430085i
\(317\) 23.9652 1.34602 0.673011 0.739632i \(-0.265001\pi\)
0.673011 + 0.739632i \(0.265001\pi\)
\(318\) 1.14836 + 1.98902i 0.0643969 + 0.111539i
\(319\) −0.716981 1.24185i −0.0401432 0.0695301i
\(320\) −1.14303 + 1.97978i −0.0638972 + 0.110673i
\(321\) −4.88933 + 8.46857i −0.272896 + 0.472670i
\(322\) −4.80838 −0.267961
\(323\) −4.79560 −0.266834
\(324\) 4.22265 7.31384i 0.234592 0.406325i
\(325\) 1.50256 2.60251i 0.0833469 0.144361i
\(326\) 5.29430 + 9.17000i 0.293224 + 0.507879i
\(327\) −2.30472 3.99190i −0.127452 0.220752i
\(328\) 14.0652 0.776622
\(329\) 4.09197 + 7.08751i 0.225598 + 0.390747i
\(330\) −0.0951230 0.164758i −0.00523635 0.00906962i
\(331\) 1.77176 + 3.06877i 0.0973845 + 0.168675i 0.910601 0.413286i \(-0.135619\pi\)
−0.813217 + 0.581961i \(0.802286\pi\)
\(332\) −6.31044 + 10.9300i −0.346330 + 0.599862i
\(333\) 24.5640 1.34610
\(334\) −1.43628 + 2.48771i −0.0785898 + 0.136121i
\(335\) 7.97806 + 13.8184i 0.435888 + 0.754981i
\(336\) 1.95756 0.106794
\(337\) 12.7887 + 22.1507i 0.696646 + 1.20663i 0.969623 + 0.244605i \(0.0786584\pi\)
−0.272977 + 0.962021i \(0.588008\pi\)
\(338\) −3.30927 + 5.73183i −0.180001 + 0.311770i
\(339\) −4.08311 + 7.07215i −0.221764 + 0.384107i
\(340\) −2.28599 −0.123975
\(341\) 0.524204 0.907948i 0.0283873 0.0491682i
\(342\) 6.61910 0.357920
\(343\) 15.4327 0.833290
\(344\) 12.3918 + 4.71917i 0.668124 + 0.254441i
\(345\) −6.57320 −0.353889
\(346\) 5.86627 0.315372
\(347\) −4.93211 + 8.54267i −0.264770 + 0.458594i −0.967503 0.252859i \(-0.918629\pi\)
0.702734 + 0.711453i \(0.251963\pi\)
\(348\) −4.45635 −0.238885
\(349\) 15.7639 27.3039i 0.843822 1.46154i −0.0428181 0.999083i \(-0.513634\pi\)
0.886640 0.462460i \(-0.153033\pi\)
\(350\) 1.08027 1.87108i 0.0577428 0.100013i
\(351\) −1.78826 3.09736i −0.0954502 0.165325i
\(352\) 1.99666 0.106422
\(353\) 1.52728 + 2.64532i 0.0812887 + 0.140796i 0.903804 0.427947i \(-0.140763\pi\)
−0.822515 + 0.568743i \(0.807430\pi\)
\(354\) −0.148805 + 0.257738i −0.00790890 + 0.0136986i
\(355\) −8.91875 −0.473358
\(356\) 12.2204 21.1664i 0.647681 1.12182i
\(357\) 0.425844 + 0.737583i 0.0225381 + 0.0390371i
\(358\) −5.74196 9.94536i −0.303472 0.525629i
\(359\) −9.29311 16.0961i −0.490472 0.849522i 0.509468 0.860489i \(-0.329842\pi\)
−0.999940 + 0.0109678i \(0.996509\pi\)
\(360\) 6.86385 0.361757
\(361\) −1.99889 3.46217i −0.105204 0.182220i
\(362\) 6.47120 + 11.2084i 0.340119 + 0.589103i
\(363\) −3.73552 + 6.47011i −0.196064 + 0.339593i
\(364\) −0.990482 + 1.71557i −0.0519154 + 0.0899200i
\(365\) 6.44125 0.337151
\(366\) 1.09507 0.0572403
\(367\) −14.6450 + 25.3658i −0.764460 + 1.32408i 0.176071 + 0.984377i \(0.443661\pi\)
−0.940531 + 0.339707i \(0.889672\pi\)
\(368\) 8.17198 14.1543i 0.425994 0.737843i
\(369\) 8.78693 + 15.2194i 0.457429 + 0.792291i
\(370\) 3.56771 + 6.17945i 0.185476 + 0.321255i
\(371\) 7.56322 0.392663
\(372\) −1.62908 2.82165i −0.0844638 0.146296i
\(373\) −3.93588 6.81714i −0.203792 0.352978i 0.745955 0.665996i \(-0.231993\pi\)
−0.949747 + 0.313018i \(0.898660\pi\)
\(374\) 0.102904 + 0.178234i 0.00532102 + 0.00921628i
\(375\) 3.78773 6.56054i 0.195598 0.338785i
\(376\) 13.3697 0.689489
\(377\) 1.78998 3.10034i 0.0921887 0.159675i
\(378\) −1.28567 2.22685i −0.0661280 0.114537i
\(379\) 23.8755 1.22640 0.613201 0.789927i \(-0.289882\pi\)
0.613201 + 0.789927i \(0.289882\pi\)
\(380\) −5.48135 9.49398i −0.281187 0.487031i
\(381\) −3.53990 + 6.13128i −0.181354 + 0.314115i
\(382\) 3.54000 6.13146i 0.181122 0.313713i
\(383\) −10.4601 −0.534486 −0.267243 0.963629i \(-0.586113\pi\)
−0.267243 + 0.963629i \(0.586113\pi\)
\(384\) 3.96647 6.87013i 0.202413 0.350590i
\(385\) −0.626489 −0.0319289
\(386\) −0.622555 −0.0316872
\(387\) 2.63511 + 16.3569i 0.133950 + 0.831469i
\(388\) −15.3814 −0.780872
\(389\) 27.1136 1.37471 0.687356 0.726320i \(-0.258771\pi\)
0.687356 + 0.726320i \(0.258771\pi\)
\(390\) 0.237479 0.411327i 0.0120252 0.0208283i
\(391\) 7.11086 0.359612
\(392\) 5.52836 9.57540i 0.279224 0.483631i
\(393\) 7.19111 12.4554i 0.362744 0.628290i
\(394\) −0.441327 0.764401i −0.0222337 0.0385100i
\(395\) 6.97020 0.350709
\(396\) 0.809814 + 1.40264i 0.0406947 + 0.0704852i
\(397\) −3.05135 + 5.28509i −0.153143 + 0.265251i −0.932381 0.361477i \(-0.882273\pi\)
0.779238 + 0.626728i \(0.215606\pi\)
\(398\) 7.25048 0.363434
\(399\) −2.04218 + 3.53715i −0.102237 + 0.177079i
\(400\) 3.67190 + 6.35991i 0.183595 + 0.317996i
\(401\) −6.41013 11.1027i −0.320107 0.554441i 0.660403 0.750911i \(-0.270385\pi\)
−0.980510 + 0.196470i \(0.937052\pi\)
\(402\) −2.23216 3.86621i −0.111330 0.192829i
\(403\) 2.61741 0.130382
\(404\) −12.1574 21.0572i −0.604852 1.04763i
\(405\) 3.33398 + 5.77462i 0.165667 + 0.286943i
\(406\) 1.28691 2.22900i 0.0638684 0.110623i
\(407\) −1.83136 + 3.17201i −0.0907772 + 0.157231i
\(408\) 1.39136 0.0688825
\(409\) −15.6258 −0.772647 −0.386323 0.922363i \(-0.626255\pi\)
−0.386323 + 0.922363i \(0.626255\pi\)
\(410\) −2.55245 + 4.42097i −0.126057 + 0.218336i
\(411\) −1.46443 + 2.53647i −0.0722351 + 0.125115i
\(412\) 12.0353 + 20.8458i 0.592937 + 1.02700i
\(413\) 0.490023 + 0.848744i 0.0241124 + 0.0417640i
\(414\) −9.81472 −0.482367
\(415\) −4.98238 8.62974i −0.244576 0.423617i
\(416\) 2.49238 + 4.31692i 0.122199 + 0.211655i
\(417\) 5.88784 + 10.1980i 0.288329 + 0.499400i
\(418\) −0.493484 + 0.854740i −0.0241371 + 0.0418067i
\(419\) −2.35015 −0.114813 −0.0574063 0.998351i \(-0.518283\pi\)
−0.0574063 + 0.998351i \(0.518283\pi\)
\(420\) −0.973476 + 1.68611i −0.0475008 + 0.0822737i
\(421\) −7.42873 12.8669i −0.362054 0.627096i 0.626244 0.779627i \(-0.284591\pi\)
−0.988299 + 0.152530i \(0.951258\pi\)
\(422\) 3.31861 0.161548
\(423\) 8.35242 + 14.4668i 0.406108 + 0.703400i
\(424\) 6.17782 10.7003i 0.300022 0.519653i
\(425\) −1.59755 + 2.76704i −0.0774926 + 0.134221i
\(426\) 2.49535 0.120900
\(427\) 1.80306 3.12300i 0.0872563 0.151132i
\(428\) 24.1824 1.16890
\(429\) 0.243804 0.0117710
\(430\) −3.73211 + 3.03860i −0.179978 + 0.146534i
\(431\) 27.4875 1.32402 0.662012 0.749493i \(-0.269703\pi\)
0.662012 + 0.749493i \(0.269703\pi\)
\(432\) 8.74017 0.420511
\(433\) 0.257536 0.446066i 0.0123764 0.0214366i −0.859771 0.510680i \(-0.829394\pi\)
0.872147 + 0.489243i \(0.162727\pi\)
\(434\) 1.88179 0.0903289
\(435\) 1.75925 3.04711i 0.0843494 0.146098i
\(436\) −5.69953 + 9.87187i −0.272958 + 0.472777i
\(437\) 17.0504 + 29.5322i 0.815632 + 1.41272i
\(438\) −1.80218 −0.0861114
\(439\) −11.0511 19.1410i −0.527439 0.913551i −0.999489 0.0319793i \(-0.989819\pi\)
0.472049 0.881572i \(-0.343514\pi\)
\(440\) −0.511732 + 0.886345i −0.0243958 + 0.0422548i
\(441\) 13.8149 0.657851
\(442\) −0.256904 + 0.444971i −0.0122197 + 0.0211651i
\(443\) −15.1477 26.2367i −0.719691 1.24654i −0.961122 0.276123i \(-0.910950\pi\)
0.241431 0.970418i \(-0.422383\pi\)
\(444\) 5.69135 + 9.85771i 0.270100 + 0.467826i
\(445\) 9.64858 + 16.7118i 0.457387 + 0.792217i
\(446\) 9.63184 0.456081
\(447\) 1.20414 + 2.08562i 0.0569537 + 0.0986467i
\(448\) −1.05313 1.82408i −0.0497557 0.0861795i
\(449\) −9.49782 + 16.4507i −0.448230 + 0.776357i −0.998271 0.0587805i \(-0.981279\pi\)
0.550041 + 0.835138i \(0.314612\pi\)
\(450\) 2.20501 3.81919i 0.103945 0.180038i
\(451\) −2.62042 −0.123391
\(452\) 20.1949 0.949886
\(453\) −0.369277 + 0.639607i −0.0173502 + 0.0300513i
\(454\) −1.10228 + 1.90920i −0.0517325 + 0.0896033i
\(455\) −0.782032 1.35452i −0.0366622 0.0635008i
\(456\) 3.33620 + 5.77847i 0.156232 + 0.270601i
\(457\) −2.66102 −0.124477 −0.0622385 0.998061i \(-0.519824\pi\)
−0.0622385 + 0.998061i \(0.519824\pi\)
\(458\) 4.26842 + 7.39312i 0.199450 + 0.345458i
\(459\) 1.90132 + 3.29318i 0.0887458 + 0.153712i
\(460\) 8.12768 + 14.0776i 0.378955 + 0.656369i
\(461\) 5.87858 10.1820i 0.273793 0.474223i −0.696037 0.718006i \(-0.745055\pi\)
0.969830 + 0.243783i \(0.0783884\pi\)
\(462\) 0.175284 0.00815493
\(463\) −9.36180 + 16.2151i −0.435080 + 0.753580i −0.997302 0.0734059i \(-0.976613\pi\)
0.562222 + 0.826986i \(0.309946\pi\)
\(464\) 4.37429 + 7.57649i 0.203071 + 0.351730i
\(465\) 2.57247 0.119295
\(466\) −4.08189 7.07005i −0.189090 0.327514i
\(467\) 9.89136 17.1323i 0.457717 0.792790i −0.541123 0.840944i \(-0.682001\pi\)
0.998840 + 0.0481541i \(0.0153338\pi\)
\(468\) −2.02174 + 3.50176i −0.0934551 + 0.161869i
\(469\) −14.7012 −0.678839
\(470\) −2.42623 + 4.20236i −0.111914 + 0.193840i
\(471\) 13.3921 0.617074
\(472\) 1.60105 0.0736942
\(473\) −2.30867 0.879206i −0.106153 0.0404260i
\(474\) −1.95017 −0.0895743
\(475\) −15.3224 −0.703041
\(476\) 1.05310 1.82403i 0.0482688 0.0836041i
\(477\) 15.4378 0.706849
\(478\) 3.06030 5.30060i 0.139975 0.242444i
\(479\) −11.9155 + 20.6382i −0.544431 + 0.942983i 0.454211 + 0.890894i \(0.349921\pi\)
−0.998642 + 0.0520888i \(0.983412\pi\)
\(480\) 2.44958 + 4.24281i 0.111808 + 0.193657i
\(481\) −9.14417 −0.416938
\(482\) 3.04195 + 5.26882i 0.138557 + 0.239988i
\(483\) 3.02812 5.24485i 0.137784 0.238649i
\(484\) 18.4757 0.839805
\(485\) 6.07217 10.5173i 0.275723 0.477566i
\(486\) −4.04882 7.01277i −0.183658 0.318106i
\(487\) −13.5209 23.4189i −0.612691 1.06121i −0.990785 0.135445i \(-0.956754\pi\)
0.378093 0.925767i \(-0.376580\pi\)
\(488\) −2.94557 5.10188i −0.133340 0.230951i
\(489\) −13.3365 −0.603098
\(490\) 2.00649 + 3.47534i 0.0906440 + 0.157000i
\(491\) −13.5858 23.5314i −0.613120 1.06196i −0.990711 0.135983i \(-0.956581\pi\)
0.377591 0.925972i \(-0.376753\pi\)
\(492\) −4.07177 + 7.05251i −0.183570 + 0.317952i
\(493\) −1.90315 + 3.29634i −0.0857134 + 0.148460i
\(494\) −2.46402 −0.110861
\(495\) −1.27877 −0.0574765
\(496\) −3.19816 + 5.53938i −0.143602 + 0.248725i
\(497\) 4.10865 7.11639i 0.184298 0.319214i
\(498\) 1.39401 + 2.41449i 0.0624669 + 0.108196i
\(499\) −16.2616 28.1659i −0.727969 1.26088i −0.957740 0.287634i \(-0.907131\pi\)
0.229771 0.973245i \(-0.426202\pi\)
\(500\) −18.7339 −0.837807
\(501\) −1.80902 3.13331i −0.0808209 0.139986i
\(502\) 5.87459 + 10.1751i 0.262196 + 0.454137i
\(503\) 6.57606 + 11.3901i 0.293212 + 0.507858i 0.974567 0.224095i \(-0.0719424\pi\)
−0.681355 + 0.731953i \(0.738609\pi\)
\(504\) −3.16201 + 5.47676i −0.140847 + 0.243954i
\(505\) 19.1976 0.854283
\(506\) 0.731733 1.26740i 0.0325295 0.0563427i
\(507\) −4.16808 7.21933i −0.185111 0.320622i
\(508\) 17.5082 0.776799
\(509\) −16.7077 28.9385i −0.740554 1.28268i −0.952244 0.305340i \(-0.901230\pi\)
0.211690 0.977337i \(-0.432103\pi\)
\(510\) −0.252493 + 0.437331i −0.0111806 + 0.0193654i
\(511\) −2.96733 + 5.13957i −0.131267 + 0.227361i
\(512\) −21.4771 −0.949164
\(513\) −9.11795 + 15.7927i −0.402567 + 0.697267i
\(514\) −10.9935 −0.484900
\(515\) −19.0049 −0.837455
\(516\) −5.95361 + 4.84730i −0.262093 + 0.213390i
\(517\) −2.49084 −0.109547
\(518\) −6.57423 −0.288855
\(519\) −3.69433 + 6.39876i −0.162163 + 0.280875i
\(520\) −2.55513 −0.112050
\(521\) 8.83174 15.2970i 0.386926 0.670175i −0.605109 0.796143i \(-0.706870\pi\)
0.992034 + 0.125968i \(0.0402037\pi\)
\(522\) 2.62681 4.54976i 0.114972 0.199138i
\(523\) −13.0218 22.5544i −0.569402 0.986234i −0.996625 0.0820873i \(-0.973841\pi\)
0.427223 0.904146i \(-0.359492\pi\)
\(524\) −35.5669 −1.55375
\(525\) 1.36062 + 2.35665i 0.0593821 + 0.102853i
\(526\) 5.82880 10.0958i 0.254148 0.440197i
\(527\) −2.78288 −0.121224
\(528\) −0.297899 + 0.515977i −0.0129644 + 0.0224550i
\(529\) −13.7821 23.8714i −0.599224 1.03789i
\(530\) 2.24221 + 3.88362i 0.0973954 + 0.168694i
\(531\) 1.00022 + 1.73243i 0.0434058 + 0.0751811i
\(532\) 10.1005 0.437913
\(533\) −3.27101 5.66556i −0.141683 0.245403i
\(534\) −2.69955 4.67575i −0.116821 0.202340i
\(535\) −9.54656 + 16.5351i −0.412734 + 0.714876i
\(536\) −12.0083 + 20.7990i −0.518680 + 0.898380i
\(537\) 14.4642 0.624175
\(538\) 4.15307 0.179052
\(539\) −1.02996 + 1.78395i −0.0443636 + 0.0768401i
\(540\) −4.34639 + 7.52817i −0.187039 + 0.323961i
\(541\) 3.28029 + 5.68163i 0.141031 + 0.244272i 0.927885 0.372867i \(-0.121625\pi\)
−0.786854 + 0.617139i \(0.788292\pi\)
\(542\) −1.25097 2.16675i −0.0537339 0.0930698i
\(543\) −16.3011 −0.699549
\(544\) −2.64995 4.58985i −0.113616 0.196788i
\(545\) −4.50004 7.79430i −0.192761 0.333871i
\(546\) 0.218802 + 0.378977i 0.00936387 + 0.0162187i
\(547\) −21.7129 + 37.6079i −0.928377 + 1.60800i −0.142340 + 0.989818i \(0.545463\pi\)
−0.786037 + 0.618179i \(0.787871\pi\)
\(548\) 7.24301 0.309406
\(549\) 3.68036 6.37457i 0.157074 0.272060i
\(550\) 0.328788 + 0.569477i 0.0140196 + 0.0242826i
\(551\) −18.2534 −0.777623
\(552\) −4.94688 8.56824i −0.210553 0.364689i
\(553\) −3.21100 + 5.56162i −0.136546 + 0.236504i
\(554\) −5.82300 + 10.0857i −0.247396 + 0.428502i
\(555\) −8.98717 −0.381484
\(556\) 14.5605 25.2195i 0.617502 1.06954i
\(557\) −15.1135 −0.640382 −0.320191 0.947353i \(-0.603747\pi\)
−0.320191 + 0.947353i \(0.603747\pi\)
\(558\) 3.84106 0.162605
\(559\) −0.980942 6.08901i −0.0414894 0.257538i
\(560\) 3.82220 0.161517
\(561\) −0.259217 −0.0109442
\(562\) 6.72551 11.6489i 0.283699 0.491381i
\(563\) −27.4256 −1.15585 −0.577926 0.816089i \(-0.696138\pi\)
−0.577926 + 0.816089i \(0.696138\pi\)
\(564\) −3.87042 + 6.70377i −0.162974 + 0.282279i
\(565\) −7.97239 + 13.8086i −0.335401 + 0.580932i
\(566\) 8.23062 + 14.2558i 0.345959 + 0.599218i
\(567\) −6.14353 −0.258004
\(568\) −6.71209 11.6257i −0.281633 0.487803i
\(569\) 17.4906 30.2946i 0.733244 1.27002i −0.222245 0.974991i \(-0.571338\pi\)
0.955489 0.295026i \(-0.0953282\pi\)
\(570\) −2.42171 −0.101434
\(571\) −12.1379 + 21.0235i −0.507956 + 0.879806i 0.492002 + 0.870594i \(0.336265\pi\)
−0.999958 + 0.00921123i \(0.997068\pi\)
\(572\) −0.301460 0.522145i −0.0126047 0.0218320i
\(573\) 4.45868 + 7.72267i 0.186264 + 0.322619i
\(574\) −2.35171 4.07327i −0.0981583 0.170015i
\(575\) 22.7199 0.947486
\(576\) −2.14962 3.72325i −0.0895674 0.155135i
\(577\) 5.25256 + 9.09769i 0.218667 + 0.378742i 0.954401 0.298529i \(-0.0964959\pi\)
−0.735734 + 0.677271i \(0.763163\pi\)
\(578\) 0.273146 0.473103i 0.0113614 0.0196785i
\(579\) 0.392059 0.679065i 0.0162934 0.0282210i
\(580\) −8.70115 −0.361296
\(581\) 9.18106 0.380895
\(582\) −1.69891 + 2.94260i −0.0704222 + 0.121975i
\(583\) −1.15096 + 1.99352i −0.0476679 + 0.0825633i
\(584\) 4.84758 + 8.39625i 0.200594 + 0.347439i
\(585\) −1.59626 2.76480i −0.0659972 0.114311i
\(586\) −9.44572 −0.390199
\(587\) 11.4848 + 19.8922i 0.474028 + 0.821040i 0.999558 0.0297348i \(-0.00946629\pi\)
−0.525530 + 0.850775i \(0.676133\pi\)
\(588\) 3.20083 + 5.54401i 0.132000 + 0.228631i
\(589\) −6.67280 11.5576i −0.274948 0.476223i
\(590\) −0.290546 + 0.503241i −0.0119616 + 0.0207181i
\(591\) 1.11172 0.0457299
\(592\) 11.1731 19.3524i 0.459212 0.795378i
\(593\) −19.9373 34.5325i −0.818728 1.41808i −0.906620 0.421948i \(-0.861346\pi\)
0.0878919 0.996130i \(-0.471987\pi\)
\(594\) 0.782609 0.0321108
\(595\) 0.831473 + 1.44015i 0.0340871 + 0.0590405i
\(596\) 2.97780 5.15770i 0.121975 0.211268i
\(597\) −4.56604 + 7.90862i −0.186876 + 0.323678i
\(598\) 3.65362 0.149408
\(599\) −5.81260 + 10.0677i −0.237496 + 0.411356i −0.959995 0.280016i \(-0.909660\pi\)
0.722499 + 0.691372i \(0.242993\pi\)
\(600\) 4.44553 0.181488
\(601\) −16.4549 −0.671209 −0.335605 0.942003i \(-0.608941\pi\)
−0.335605 + 0.942003i \(0.608941\pi\)
\(602\) −0.705251 4.37771i −0.0287439 0.178422i
\(603\) −30.0077 −1.22201
\(604\) 1.82643 0.0743163
\(605\) −7.29372 + 12.6331i −0.296532 + 0.513608i
\(606\) −5.37124 −0.218192
\(607\) −4.83907 + 8.38152i −0.196412 + 0.340195i −0.947362 0.320163i \(-0.896262\pi\)
0.750951 + 0.660358i \(0.229596\pi\)
\(608\) 12.7081 22.0111i 0.515381 0.892667i
\(609\) 1.62089 + 2.80746i 0.0656816 + 0.113764i
\(610\) 2.13816 0.0865716
\(611\) −3.10926 5.38540i −0.125787 0.217870i
\(612\) 2.14956 3.72315i 0.0868908 0.150499i
\(613\) −15.3447 −0.619767 −0.309884 0.950775i \(-0.600290\pi\)
−0.309884 + 0.950775i \(0.600290\pi\)
\(614\) −3.35410 + 5.80947i −0.135360 + 0.234451i
\(615\) −3.21485 5.56829i −0.129635 0.224535i
\(616\) −0.471485 0.816636i −0.0189967 0.0329032i
\(617\) 19.7210 + 34.1578i 0.793938 + 1.37514i 0.923511 + 0.383571i \(0.125306\pi\)
−0.129573 + 0.991570i \(0.541361\pi\)
\(618\) 5.31731 0.213894
\(619\) −10.4125 18.0349i −0.418513 0.724885i 0.577278 0.816548i \(-0.304115\pi\)
−0.995790 + 0.0916631i \(0.970782\pi\)
\(620\) −3.18082 5.50935i −0.127745 0.221261i
\(621\) 13.5200 23.4173i 0.542538 0.939704i
\(622\) 2.17910 3.77431i 0.0873739 0.151336i
\(623\) −17.7795 −0.712320
\(624\) −1.48744 −0.0595454
\(625\) −0.592099 + 1.02554i −0.0236839 + 0.0410218i
\(626\) −4.08894 + 7.08225i −0.163427 + 0.283064i
\(627\) −0.621552 1.07656i −0.0248224 0.0429936i
\(628\) −16.5591 28.6813i −0.660781 1.14451i
\(629\) 9.72228 0.387653
\(630\) −1.14764 1.98776i −0.0457229 0.0791944i
\(631\) 16.1240 + 27.9275i 0.641885 + 1.11178i 0.985012 + 0.172488i \(0.0551806\pi\)
−0.343127 + 0.939289i \(0.611486\pi\)
\(632\) 5.24565 + 9.08573i 0.208661 + 0.361411i
\(633\) −2.08992 + 3.61985i −0.0830670 + 0.143876i
\(634\) −13.0920 −0.519951
\(635\) −6.91175 + 11.9715i −0.274284 + 0.475075i
\(636\) 3.57686 + 6.19531i 0.141832 + 0.245660i
\(637\) −5.14271 −0.203762
\(638\) 0.391681 + 0.678412i 0.0155068 + 0.0268586i
\(639\) 8.38646 14.5258i 0.331763 0.574631i
\(640\) 7.74465 13.4141i 0.306134 0.530240i
\(641\) −34.9428 −1.38016 −0.690079 0.723734i \(-0.742424\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(642\) 2.67100 4.62632i 0.105416 0.182586i
\(643\) 0.854278 0.0336894 0.0168447 0.999858i \(-0.494638\pi\)
0.0168447 + 0.999858i \(0.494638\pi\)
\(644\) −14.9769 −0.590173
\(645\) −0.964099 5.98446i −0.0379614 0.235638i
\(646\) 2.61980 0.103075
\(647\) 25.9415 1.01987 0.509933 0.860214i \(-0.329670\pi\)
0.509933 + 0.860214i \(0.329670\pi\)
\(648\) −5.01819 + 8.69175i −0.197133 + 0.341444i
\(649\) −0.298284 −0.0117087
\(650\) −0.820835 + 1.42173i −0.0321958 + 0.0557648i
\(651\) −1.18507 + 2.05261i −0.0464467 + 0.0804481i
\(652\) 16.4904 + 28.5623i 0.645815 + 1.11858i
\(653\) 26.9885 1.05614 0.528071 0.849200i \(-0.322916\pi\)
0.528071 + 0.849200i \(0.322916\pi\)
\(654\) 1.25905 + 2.18074i 0.0492329 + 0.0852738i
\(655\) 14.0409 24.3195i 0.548622 0.950241i
\(656\) 15.9872 0.624194
\(657\) −6.05683 + 10.4907i −0.236299 + 0.409282i
\(658\) −2.23541 3.87185i −0.0871455 0.150940i
\(659\) −10.3459 17.9196i −0.403019 0.698049i 0.591070 0.806620i \(-0.298706\pi\)
−0.994089 + 0.108571i \(0.965372\pi\)
\(660\) −0.296285 0.513180i −0.0115329 0.0199755i
\(661\) −35.1486 −1.36712 −0.683561 0.729894i \(-0.739570\pi\)
−0.683561 + 0.729894i \(0.739570\pi\)
\(662\) −0.967897 1.67645i −0.0376184 0.0651569i
\(663\) −0.323575 0.560448i −0.0125666 0.0217660i
\(664\) 7.49931 12.9892i 0.291030 0.504078i
\(665\) −3.98741 + 6.90640i −0.154625 + 0.267819i
\(666\) −13.4191 −0.519981
\(667\) 27.0660 1.04800
\(668\) −4.47366 + 7.74860i −0.173091 + 0.299802i
\(669\) −6.06573 + 10.5061i −0.234515 + 0.406191i
\(670\) −4.35835 7.54889i −0.168378 0.291639i
\(671\) 0.548775 + 0.950507i 0.0211852 + 0.0366939i
\(672\) −4.51386 −0.174126
\(673\) 4.76512 + 8.25342i 0.183682 + 0.318146i 0.943131 0.332420i \(-0.107865\pi\)
−0.759450 + 0.650566i \(0.774532\pi\)
\(674\) −6.98638 12.1008i −0.269105 0.466104i
\(675\) 6.07490 + 10.5220i 0.233823 + 0.404993i
\(676\) −10.3076 + 17.8532i −0.396445 + 0.686662i
\(677\) −25.7719 −0.990493 −0.495247 0.868752i \(-0.664922\pi\)
−0.495247 + 0.868752i \(0.664922\pi\)
\(678\) 2.23057 3.86346i 0.0856646 0.148375i
\(679\) 5.59460 + 9.69014i 0.214701 + 0.371873i
\(680\) 2.71667 0.104179
\(681\) −1.38834 2.40467i −0.0532012 0.0921472i
\(682\) −0.286369 + 0.496005i −0.0109656 + 0.0189930i
\(683\) 16.7822 29.0677i 0.642155 1.11224i −0.342796 0.939410i \(-0.611374\pi\)
0.984951 0.172835i \(-0.0552926\pi\)
\(684\) 20.6169 0.788305
\(685\) −2.85935 + 4.95253i −0.109250 + 0.189227i
\(686\) −8.43079 −0.321889
\(687\) −10.7523 −0.410225
\(688\) 14.0851 + 5.36402i 0.536991 + 0.204501i
\(689\) −5.74687 −0.218938
\(690\) 3.59089 0.136703
\(691\) −11.7008 + 20.2663i −0.445118 + 0.770966i −0.998060 0.0622529i \(-0.980171\pi\)
0.552943 + 0.833219i \(0.313505\pi\)
\(692\) 18.2720 0.694596
\(693\) 0.589099 1.02035i 0.0223780 0.0387599i
\(694\) 2.69437 4.66679i 0.102277 0.177149i
\(695\) 11.4962 + 19.9120i 0.436075 + 0.755304i
\(696\) 5.29591 0.200741
\(697\) 3.47781 + 6.02375i 0.131731 + 0.228166i
\(698\) −8.61169 + 14.9159i −0.325957 + 0.564575i
\(699\) 10.2824 0.388917
\(700\) 3.36477 5.82795i 0.127176 0.220276i
\(701\) −23.9234 41.4365i −0.903573 1.56503i −0.822821 0.568301i \(-0.807601\pi\)
−0.0807523 0.996734i \(-0.525732\pi\)
\(702\) 0.976912 + 1.69206i 0.0368712 + 0.0638627i
\(703\) 23.3121 + 40.3777i 0.879232 + 1.52287i
\(704\) 0.641056 0.0241607
\(705\) −3.05588 5.29294i −0.115091 0.199343i
\(706\) −0.834339 1.44512i −0.0314008 0.0543877i
\(707\) −8.84388 + 15.3181i −0.332608 + 0.576095i
\(708\) −0.463491 + 0.802790i −0.0174191 + 0.0301707i
\(709\) 26.9650 1.01269 0.506345 0.862331i \(-0.330996\pi\)
0.506345 + 0.862331i \(0.330996\pi\)
\(710\) 4.87224 0.182852
\(711\) −6.55420 + 11.3522i −0.245802 + 0.425741i
\(712\) −14.5227 + 25.1541i −0.544262 + 0.942689i
\(713\) 9.89434 + 17.1375i 0.370546 + 0.641804i
\(714\) −0.232635 0.402936i −0.00870616 0.0150795i
\(715\) 0.476034 0.0178027
\(716\) −17.8848 30.9773i −0.668385 1.15768i
\(717\) 3.85450 + 6.67619i 0.143949 + 0.249327i
\(718\) 5.07675 + 8.79319i 0.189463 + 0.328159i
\(719\) −0.0144280 + 0.0249901i −0.000538075 + 0.000931974i −0.866294 0.499534i \(-0.833505\pi\)
0.865756 + 0.500466i \(0.166838\pi\)
\(720\) 7.80176 0.290755
\(721\) 8.75509 15.1643i 0.326057 0.564746i
\(722\) 1.09198 + 1.89136i 0.0406391 + 0.0703890i
\(723\) −7.66278 −0.284982
\(724\) 20.1562 + 34.9115i 0.749098 + 1.29748i
\(725\) −6.08075 + 10.5322i −0.225833 + 0.391155i
\(726\) 2.04069 3.53457i 0.0757370 0.131180i
\(727\) −49.0678 −1.81983 −0.909913 0.414800i \(-0.863852\pi\)
−0.909913 + 0.414800i \(0.863852\pi\)
\(728\) 1.17709 2.03877i 0.0436257 0.0755620i
\(729\) −4.69064 −0.173727
\(730\) −3.51881 −0.130237
\(731\) 1.04296 + 6.47397i 0.0385752 + 0.239448i
\(732\) 3.41088 0.126070
\(733\) 9.49167 0.350583 0.175291 0.984517i \(-0.443913\pi\)
0.175291 + 0.984517i \(0.443913\pi\)
\(734\) 8.00042 13.8571i 0.295301 0.511476i
\(735\) −5.05441 −0.186435
\(736\) −18.8434 + 32.6377i −0.694577 + 1.20304i
\(737\) 2.23721 3.87496i 0.0824087 0.142736i
\(738\) −4.80023 8.31424i −0.176699 0.306052i
\(739\) 2.68129 0.0986327 0.0493164 0.998783i \(-0.484296\pi\)
0.0493164 + 0.998783i \(0.484296\pi\)
\(740\) 11.1125 + 19.2475i 0.408505 + 0.707551i
\(741\) 1.55174 2.68768i 0.0570044 0.0987346i
\(742\) −4.13173 −0.151681
\(743\) −16.8294 + 29.1494i −0.617412 + 1.06939i 0.372545 + 0.928014i \(0.378485\pi\)
−0.989956 + 0.141374i \(0.954848\pi\)
\(744\) 1.93599 + 3.35324i 0.0709770 + 0.122936i
\(745\) 2.35111 + 4.07224i 0.0861380 + 0.149195i
\(746\) 2.15014 + 3.72415i 0.0787222 + 0.136351i
\(747\) 18.7401 0.685665
\(748\) 0.320519 + 0.555156i 0.0117193 + 0.0202985i
\(749\) −8.79575 15.2347i −0.321390 0.556663i
\(750\) −2.06921 + 3.58397i −0.0755568 + 0.130868i
\(751\) 6.68818 11.5843i 0.244055 0.422716i −0.717810 0.696239i \(-0.754855\pi\)
0.961866 + 0.273523i \(0.0881888\pi\)
\(752\) 15.1966 0.554163
\(753\) −14.7983 −0.539280
\(754\) −0.977852 + 1.69369i −0.0356113 + 0.0616805i
\(755\) −0.721024 + 1.24885i −0.0262408 + 0.0454503i
\(756\) −4.00456 6.93610i −0.145644 0.252263i
\(757\) 10.2019 + 17.6702i 0.370794 + 0.642234i 0.989688 0.143241i \(-0.0457523\pi\)
−0.618894 + 0.785475i \(0.712419\pi\)
\(758\) −13.0430 −0.473743
\(759\) 0.921629 + 1.59631i 0.0334530 + 0.0579423i
\(760\) 6.51403 + 11.2826i 0.236289 + 0.409264i
\(761\) −9.41279 16.3034i −0.341213 0.590999i 0.643445 0.765492i \(-0.277505\pi\)
−0.984658 + 0.174493i \(0.944171\pi\)
\(762\) 1.93382 3.34947i 0.0700548 0.121338i
\(763\) 8.29224 0.300199
\(764\) 11.0262 19.0980i 0.398914 0.690940i
\(765\) 1.69718 + 2.93960i 0.0613616 + 0.106281i
\(766\) 5.71427 0.206465
\(767\) −0.372341 0.644913i −0.0134444 0.0232865i