Properties

Label 731.2.j.a.135.13
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.13
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.13

$q$-expansion

\(f(q)\) \(=\) \(q-2.04963 q^{2} +(-1.14468 - 0.660879i) q^{3} +2.20099 q^{4} +(-1.07261 - 0.619273i) q^{5} +(2.34616 + 1.35456i) q^{6} +(0.325723 - 0.188056i) q^{7} -0.411958 q^{8} +(-0.626478 - 1.08509i) q^{9} +O(q^{10})\) \(q-2.04963 q^{2} +(-1.14468 - 0.660879i) q^{3} +2.20099 q^{4} +(-1.07261 - 0.619273i) q^{5} +(2.34616 + 1.35456i) q^{6} +(0.325723 - 0.188056i) q^{7} -0.411958 q^{8} +(-0.626478 - 1.08509i) q^{9} +(2.19846 + 1.26928i) q^{10} +3.21595i q^{11} +(-2.51942 - 1.45459i) q^{12} +(-1.51925 - 2.63143i) q^{13} +(-0.667612 + 0.385446i) q^{14} +(0.818530 + 1.41773i) q^{15} -3.55762 q^{16} +(1.69471 - 3.75872i) q^{17} +(1.28405 + 2.22404i) q^{18} +(2.17636 - 3.76957i) q^{19} +(-2.36081 - 1.36302i) q^{20} -0.497130 q^{21} -6.59151i q^{22} +(6.19848 + 3.57870i) q^{23} +(0.471559 + 0.272254i) q^{24} +(-1.73300 - 3.00165i) q^{25} +(3.11391 + 5.39346i) q^{26} +5.62138i q^{27} +(0.716913 - 0.413910i) q^{28} +(2.12867 - 1.22899i) q^{29} +(-1.67768 - 2.90583i) q^{30} +(-4.76401 - 2.75050i) q^{31} +8.11573 q^{32} +(2.12535 - 3.68122i) q^{33} +(-3.47353 + 7.70399i) q^{34} -0.465833 q^{35} +(-1.37887 - 2.38828i) q^{36} +(-0.0633372 - 0.0365677i) q^{37} +(-4.46074 + 7.72623i) q^{38} +4.01618i q^{39} +(0.441871 + 0.255115i) q^{40} -4.40087i q^{41} +1.01893 q^{42} +(-6.23169 + 2.04110i) q^{43} +7.07828i q^{44} +1.55184i q^{45} +(-12.7046 - 7.33501i) q^{46} +1.26040 q^{47} +(4.07232 + 2.35116i) q^{48} +(-3.42927 + 5.93967i) q^{49} +(3.55201 + 6.15227i) q^{50} +(-4.42395 + 3.18251i) q^{51} +(-3.34387 - 5.79175i) q^{52} +(-0.0597063 + 0.103414i) q^{53} -11.5218i q^{54} +(1.99155 - 3.44947i) q^{55} +(-0.134184 + 0.0774713i) q^{56} +(-4.98246 + 2.87663i) q^{57} +(-4.36298 + 2.51897i) q^{58} -6.51628 q^{59} +(1.80158 + 3.12042i) q^{60} +(-9.01943 + 5.20737i) q^{61} +(9.76446 + 5.63752i) q^{62} +(-0.408116 - 0.235626i) q^{63} -9.51902 q^{64} +3.76334i q^{65} +(-4.35619 + 7.54515i) q^{66} +(5.84305 - 10.1205i) q^{67} +(3.73004 - 8.27290i) q^{68} +(-4.73017 - 8.19290i) q^{69} +0.954786 q^{70} +(-6.83335 + 3.94524i) q^{71} +(0.258083 + 0.447012i) q^{72} +(-8.42147 + 4.86214i) q^{73} +(0.129818 + 0.0749504i) q^{74} +4.58122i q^{75} +(4.79016 - 8.29679i) q^{76} +(0.604779 + 1.04751i) q^{77} -8.23168i q^{78} +(-3.72882 + 2.15284i) q^{79} +(3.81595 + 2.20314i) q^{80} +(1.83562 - 3.17938i) q^{81} +9.02017i q^{82} +(-8.85769 + 15.3420i) q^{83} -1.09418 q^{84} +(-4.14544 + 2.98216i) q^{85} +(12.7727 - 4.18350i) q^{86} -3.24885 q^{87} -1.32484i q^{88} +(-2.49935 + 4.32901i) q^{89} -3.18071i q^{90} +(-0.989712 - 0.571411i) q^{91} +(13.6428 + 7.87668i) q^{92} +(3.63550 + 6.29687i) q^{93} -2.58335 q^{94} +(-4.66879 + 2.69553i) q^{95} +(-9.28988 - 5.36351i) q^{96} +13.4689i q^{97} +(7.02874 - 12.1741i) q^{98} +(3.48960 - 2.01472i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.04963 −1.44931 −0.724654 0.689113i \(-0.758001\pi\)
−0.724654 + 0.689113i \(0.758001\pi\)
\(3\) −1.14468 0.660879i −0.660879 0.381559i 0.131733 0.991285i \(-0.457946\pi\)
−0.792612 + 0.609727i \(0.791279\pi\)
\(4\) 2.20099 1.10050
\(5\) −1.07261 0.619273i −0.479687 0.276947i 0.240599 0.970625i \(-0.422656\pi\)
−0.720286 + 0.693677i \(0.755989\pi\)
\(6\) 2.34616 + 1.35456i 0.957818 + 0.552996i
\(7\) 0.325723 0.188056i 0.123112 0.0710786i −0.437180 0.899374i \(-0.644023\pi\)
0.560291 + 0.828296i \(0.310689\pi\)
\(8\) −0.411958 −0.145649
\(9\) −0.626478 1.08509i −0.208826 0.361697i
\(10\) 2.19846 + 1.26928i 0.695215 + 0.401382i
\(11\) 3.21595i 0.969645i 0.874612 + 0.484823i \(0.161116\pi\)
−0.874612 + 0.484823i \(0.838884\pi\)
\(12\) −2.51942 1.45459i −0.727295 0.419904i
\(13\) −1.51925 2.63143i −0.421365 0.729826i 0.574708 0.818359i \(-0.305116\pi\)
−0.996073 + 0.0885322i \(0.971782\pi\)
\(14\) −0.667612 + 0.385446i −0.178427 + 0.103015i
\(15\) 0.818530 + 1.41773i 0.211343 + 0.366058i
\(16\) −3.55762 −0.889405
\(17\) 1.69471 3.75872i 0.411028 0.911623i
\(18\) 1.28405 + 2.22404i 0.302653 + 0.524211i
\(19\) 2.17636 3.76957i 0.499292 0.864799i −0.500708 0.865616i \(-0.666927\pi\)
1.00000 0.000817420i \(0.000260193\pi\)
\(20\) −2.36081 1.36302i −0.527893 0.304779i
\(21\) −0.497130 −0.108483
\(22\) 6.59151i 1.40532i
\(23\) 6.19848 + 3.57870i 1.29247 + 0.746210i 0.979092 0.203418i \(-0.0652050\pi\)
0.313381 + 0.949627i \(0.398538\pi\)
\(24\) 0.471559 + 0.272254i 0.0962565 + 0.0555737i
\(25\) −1.73300 3.00165i −0.346600 0.600329i
\(26\) 3.11391 + 5.39346i 0.610689 + 1.05774i
\(27\) 5.62138i 1.08183i
\(28\) 0.716913 0.413910i 0.135484 0.0782217i
\(29\) 2.12867 1.22899i 0.395283 0.228217i −0.289163 0.957280i \(-0.593377\pi\)
0.684447 + 0.729063i \(0.260044\pi\)
\(30\) −1.67768 2.90583i −0.306302 0.530530i
\(31\) −4.76401 2.75050i −0.855641 0.494005i 0.00690913 0.999976i \(-0.497801\pi\)
−0.862550 + 0.505972i \(0.831134\pi\)
\(32\) 8.11573 1.43467
\(33\) 2.12535 3.68122i 0.369977 0.640818i
\(34\) −3.47353 + 7.70399i −0.595706 + 1.32122i
\(35\) −0.465833 −0.0787401
\(36\) −1.37887 2.38828i −0.229812 0.398046i
\(37\) −0.0633372 0.0365677i −0.0104126 0.00601170i 0.494785 0.869016i \(-0.335247\pi\)
−0.505197 + 0.863004i \(0.668580\pi\)
\(38\) −4.46074 + 7.72623i −0.723628 + 1.25336i
\(39\) 4.01618i 0.643103i
\(40\) 0.441871 + 0.255115i 0.0698660 + 0.0403372i
\(41\) 4.40087i 0.687301i −0.939098 0.343650i \(-0.888337\pi\)
0.939098 0.343650i \(-0.111663\pi\)
\(42\) 1.01893 0.157225
\(43\) −6.23169 + 2.04110i −0.950323 + 0.311264i
\(44\) 7.07828i 1.06709i
\(45\) 1.55184i 0.231335i
\(46\) −12.7046 7.33501i −1.87319 1.08149i
\(47\) 1.26040 0.183848 0.0919240 0.995766i \(-0.470698\pi\)
0.0919240 + 0.995766i \(0.470698\pi\)
\(48\) 4.07232 + 2.35116i 0.587789 + 0.339360i
\(49\) −3.42927 + 5.93967i −0.489896 + 0.848524i
\(50\) 3.55201 + 6.15227i 0.502331 + 0.870062i
\(51\) −4.42395 + 3.18251i −0.619477 + 0.445641i
\(52\) −3.34387 5.79175i −0.463711 0.803171i
\(53\) −0.0597063 + 0.103414i −0.00820129 + 0.0142050i −0.870097 0.492881i \(-0.835944\pi\)
0.861896 + 0.507086i \(0.169277\pi\)
\(54\) 11.5218i 1.56791i
\(55\) 1.99155 3.44947i 0.268541 0.465126i
\(56\) −0.134184 + 0.0774713i −0.0179311 + 0.0103525i
\(57\) −4.98246 + 2.87663i −0.659943 + 0.381018i
\(58\) −4.36298 + 2.51897i −0.572888 + 0.330757i
\(59\) −6.51628 −0.848348 −0.424174 0.905581i \(-0.639435\pi\)
−0.424174 + 0.905581i \(0.639435\pi\)
\(60\) 1.80158 + 3.12042i 0.232582 + 0.402845i
\(61\) −9.01943 + 5.20737i −1.15482 + 0.666735i −0.950057 0.312077i \(-0.898975\pi\)
−0.204762 + 0.978812i \(0.565642\pi\)
\(62\) 9.76446 + 5.63752i 1.24009 + 0.715965i
\(63\) −0.408116 0.235626i −0.0514178 0.0296861i
\(64\) −9.51902 −1.18988
\(65\) 3.76334i 0.466784i
\(66\) −4.35619 + 7.54515i −0.536210 + 0.928744i
\(67\) 5.84305 10.1205i 0.713842 1.23641i −0.249563 0.968359i \(-0.580287\pi\)
0.963405 0.268052i \(-0.0863798\pi\)
\(68\) 3.73004 8.27290i 0.452334 1.00324i
\(69\) −4.73017 8.19290i −0.569446 0.986309i
\(70\) 0.954786 0.114119
\(71\) −6.83335 + 3.94524i −0.810969 + 0.468213i −0.847292 0.531127i \(-0.821769\pi\)
0.0363230 + 0.999340i \(0.488435\pi\)
\(72\) 0.258083 + 0.447012i 0.0304153 + 0.0526809i
\(73\) −8.42147 + 4.86214i −0.985658 + 0.569070i −0.903974 0.427588i \(-0.859363\pi\)
−0.0816845 + 0.996658i \(0.526030\pi\)
\(74\) 0.129818 + 0.0749504i 0.0150910 + 0.00871280i
\(75\) 4.58122i 0.528993i
\(76\) 4.79016 8.29679i 0.549469 0.951707i
\(77\) 0.604779 + 1.04751i 0.0689210 + 0.119375i
\(78\) 8.23168i 0.932054i
\(79\) −3.72882 + 2.15284i −0.419525 + 0.242213i −0.694874 0.719131i \(-0.744540\pi\)
0.275349 + 0.961344i \(0.411207\pi\)
\(80\) 3.81595 + 2.20314i 0.426636 + 0.246318i
\(81\) 1.83562 3.17938i 0.203958 0.353265i
\(82\) 9.02017i 0.996111i
\(83\) −8.85769 + 15.3420i −0.972257 + 1.68400i −0.283554 + 0.958956i \(0.591513\pi\)
−0.688704 + 0.725043i \(0.741820\pi\)
\(84\) −1.09418 −0.119385
\(85\) −4.14544 + 2.98216i −0.449636 + 0.323461i
\(86\) 12.7727 4.18350i 1.37731 0.451118i
\(87\) −3.24885 −0.348313
\(88\) 1.32484i 0.141228i
\(89\) −2.49935 + 4.32901i −0.264931 + 0.458874i −0.967546 0.252697i \(-0.918682\pi\)
0.702615 + 0.711571i \(0.252016\pi\)
\(90\) 3.18071i 0.335276i
\(91\) −0.989712 0.571411i −0.103750 0.0599001i
\(92\) 13.6428 + 7.87668i 1.42236 + 0.821200i
\(93\) 3.63550 + 6.29687i 0.376984 + 0.652955i
\(94\) −2.58335 −0.266452
\(95\) −4.66879 + 2.69553i −0.479008 + 0.276555i
\(96\) −9.28988 5.36351i −0.948144 0.547411i
\(97\) 13.4689i 1.36756i 0.729688 + 0.683780i \(0.239665\pi\)
−0.729688 + 0.683780i \(0.760335\pi\)
\(98\) 7.02874 12.1741i 0.710010 1.22977i
\(99\) 3.48960 2.01472i 0.350718 0.202487i
\(100\) −3.81432 6.60660i −0.381432 0.660660i
\(101\) −8.58843 14.8756i −0.854581 1.48018i −0.877033 0.480430i \(-0.840481\pi\)
0.0224525 0.999748i \(-0.492853\pi\)
\(102\) 9.06748 6.52298i 0.897814 0.645872i
\(103\) −5.49172 9.51193i −0.541115 0.937239i −0.998840 0.0481451i \(-0.984669\pi\)
0.457725 0.889094i \(-0.348664\pi\)
\(104\) 0.625869 + 1.08404i 0.0613715 + 0.106299i
\(105\) 0.533228 + 0.307859i 0.0520377 + 0.0300440i
\(106\) 0.122376 0.211961i 0.0118862 0.0205875i
\(107\) 5.14270i 0.497163i −0.968611 0.248582i \(-0.920036\pi\)
0.968611 0.248582i \(-0.0799644\pi\)
\(108\) 12.3726i 1.19055i
\(109\) −12.1557 7.01809i −1.16430 0.672211i −0.211972 0.977276i \(-0.567989\pi\)
−0.952332 + 0.305064i \(0.901322\pi\)
\(110\) −4.08195 + 7.07014i −0.389199 + 0.674112i
\(111\) 0.0483337 + 0.0837164i 0.00458763 + 0.00794601i
\(112\) −1.15880 + 0.669033i −0.109496 + 0.0632176i
\(113\) 10.9538i 1.03044i 0.857057 + 0.515221i \(0.172290\pi\)
−0.857057 + 0.515221i \(0.827710\pi\)
\(114\) 10.2122 5.89602i 0.956461 0.552213i
\(115\) −4.43238 7.67711i −0.413322 0.715894i
\(116\) 4.68518 2.70499i 0.435008 0.251152i
\(117\) −1.90356 + 3.29706i −0.175984 + 0.304813i
\(118\) 13.3560 1.22952
\(119\) −0.154844 1.54300i −0.0141945 0.141447i
\(120\) −0.337200 0.584047i −0.0307820 0.0533160i
\(121\) 0.657665 0.0597878
\(122\) 18.4865 10.6732i 1.67369 0.966305i
\(123\) −2.90844 + 5.03757i −0.262246 + 0.454223i
\(124\) −10.4855 6.05383i −0.941629 0.543650i
\(125\) 10.4855i 0.937855i
\(126\) 0.836488 + 0.482947i 0.0745203 + 0.0430243i
\(127\) 11.9806 1.06311 0.531555 0.847024i \(-0.321608\pi\)
0.531555 + 0.847024i \(0.321608\pi\)
\(128\) 3.27902 0.289827
\(129\) 8.48218 + 1.78200i 0.746814 + 0.156896i
\(130\) 7.71345i 0.676515i
\(131\) 11.1928i 0.977924i −0.872305 0.488962i \(-0.837376\pi\)
0.872305 0.488962i \(-0.162624\pi\)
\(132\) 4.67789 8.10234i 0.407158 0.705218i
\(133\) 1.63711i 0.141956i
\(134\) −11.9761 + 20.7432i −1.03458 + 1.79194i
\(135\) 3.48117 6.02956i 0.299611 0.518942i
\(136\) −0.698150 + 1.54843i −0.0598659 + 0.132777i
\(137\) 0.0782270 0.00668339 0.00334169 0.999994i \(-0.498936\pi\)
0.00334169 + 0.999994i \(0.498936\pi\)
\(138\) 9.69511 + 16.7924i 0.825302 + 1.42947i
\(139\) −10.4665 6.04283i −0.887755 0.512546i −0.0145478 0.999894i \(-0.504631\pi\)
−0.873208 + 0.487348i \(0.837964\pi\)
\(140\) −1.02529 −0.0866531
\(141\) −1.44275 0.832971i −0.121501 0.0701488i
\(142\) 14.0059 8.08628i 1.17534 0.678586i
\(143\) 8.46254 4.88585i 0.707673 0.408575i
\(144\) 2.22877 + 3.86034i 0.185731 + 0.321695i
\(145\) −3.04431 −0.252816
\(146\) 17.2609 9.96559i 1.42852 0.824758i
\(147\) 7.85081 4.53267i 0.647524 0.373848i
\(148\) −0.139405 0.0804852i −0.0114590 0.00661585i
\(149\) −4.80098 + 8.31555i −0.393312 + 0.681236i −0.992884 0.119085i \(-0.962004\pi\)
0.599572 + 0.800321i \(0.295337\pi\)
\(150\) 9.38981i 0.766675i
\(151\) 15.3351 1.24796 0.623978 0.781442i \(-0.285515\pi\)
0.623978 + 0.781442i \(0.285515\pi\)
\(152\) −0.896570 + 1.55291i −0.0727215 + 0.125957i
\(153\) −5.14025 + 0.515837i −0.415565 + 0.0417029i
\(154\) −1.23958 2.14701i −0.0998878 0.173011i
\(155\) 3.40662 + 5.90045i 0.273627 + 0.473935i
\(156\) 8.83957i 0.707732i
\(157\) 6.67036 + 11.5534i 0.532352 + 0.922062i 0.999286 + 0.0377693i \(0.0120252\pi\)
−0.466934 + 0.884292i \(0.654641\pi\)
\(158\) 7.64271 4.41252i 0.608022 0.351041i
\(159\) 0.136689 0.0789173i 0.0108401 0.00625855i
\(160\) −8.70503 5.02585i −0.688193 0.397329i
\(161\) 2.69198 0.212158
\(162\) −3.76234 + 6.51657i −0.295598 + 0.511990i
\(163\) 14.4359 8.33457i 1.13071 0.652814i 0.186595 0.982437i \(-0.440255\pi\)
0.944113 + 0.329623i \(0.106922\pi\)
\(164\) 9.68628i 0.756371i
\(165\) −4.55936 + 2.63235i −0.354946 + 0.204928i
\(166\) 18.1550 31.4454i 1.40910 2.44063i
\(167\) 10.1806 + 5.87776i 0.787797 + 0.454835i 0.839186 0.543844i \(-0.183032\pi\)
−0.0513896 + 0.998679i \(0.516365\pi\)
\(168\) 0.204797 0.0158004
\(169\) 1.88373 3.26272i 0.144902 0.250978i
\(170\) 8.49663 6.11233i 0.651662 0.468794i
\(171\) −5.45377 −0.417060
\(172\) −13.7159 + 4.49244i −1.04583 + 0.342545i
\(173\) 6.07931i 0.462201i −0.972930 0.231101i \(-0.925767\pi\)
0.972930 0.231101i \(-0.0742326\pi\)
\(174\) 6.65894 0.504813
\(175\) −1.12896 0.651803i −0.0853411 0.0492717i
\(176\) 11.4411i 0.862407i
\(177\) 7.45903 + 4.30647i 0.560655 + 0.323694i
\(178\) 5.12275 8.87287i 0.383967 0.665050i
\(179\) 8.56881 + 14.8416i 0.640463 + 1.10931i 0.985330 + 0.170663i \(0.0545908\pi\)
−0.344867 + 0.938652i \(0.612076\pi\)
\(180\) 3.41559i 0.254583i
\(181\) −7.38275 + 4.26244i −0.548756 + 0.316824i −0.748620 0.662999i \(-0.769283\pi\)
0.199864 + 0.979824i \(0.435950\pi\)
\(182\) 2.02855 + 1.17118i 0.150366 + 0.0868138i
\(183\) 13.7658 1.01759
\(184\) −2.55351 1.47427i −0.188248 0.108685i
\(185\) 0.0452908 + 0.0784460i 0.00332985 + 0.00576747i
\(186\) −7.45143 12.9063i −0.546365 0.946333i
\(187\) 12.0878 + 5.45011i 0.883951 + 0.398551i
\(188\) 2.77412 0.202324
\(189\) 1.05714 + 1.83101i 0.0768953 + 0.133187i
\(190\) 9.56930 5.52484i 0.694230 0.400814i
\(191\) −6.53911 + 11.3261i −0.473154 + 0.819526i −0.999528 0.0307268i \(-0.990218\pi\)
0.526374 + 0.850253i \(0.323551\pi\)
\(192\) 10.8962 + 6.29092i 0.786365 + 0.454008i
\(193\) 23.8529i 1.71697i −0.512841 0.858484i \(-0.671407\pi\)
0.512841 0.858484i \(-0.328593\pi\)
\(194\) 27.6063i 1.98202i
\(195\) 2.48711 4.30780i 0.178106 0.308488i
\(196\) −7.54779 + 13.0732i −0.539128 + 0.933797i
\(197\) −10.8322 + 6.25395i −0.771760 + 0.445576i −0.833502 0.552517i \(-0.813668\pi\)
0.0617424 + 0.998092i \(0.480334\pi\)
\(198\) −7.15239 + 4.12944i −0.508298 + 0.293466i
\(199\) 21.7920i 1.54480i −0.635139 0.772398i \(-0.719057\pi\)
0.635139 0.772398i \(-0.280943\pi\)
\(200\) 0.713924 + 1.23655i 0.0504820 + 0.0874375i
\(201\) −13.3768 + 7.72310i −0.943526 + 0.544745i
\(202\) 17.6031 + 30.4895i 1.23855 + 2.14523i
\(203\) 0.462237 0.800618i 0.0324427 0.0561924i
\(204\) −9.73708 + 7.00469i −0.681732 + 0.490426i
\(205\) −2.72534 + 4.72043i −0.190346 + 0.329689i
\(206\) 11.2560 + 19.4960i 0.784243 + 1.35835i
\(207\) 8.96789i 0.623312i
\(208\) 5.40493 + 9.36162i 0.374765 + 0.649111i
\(209\) 12.1228 + 6.99907i 0.838548 + 0.484136i
\(210\) −1.09292 0.630998i −0.0754187 0.0435430i
\(211\) 28.1289i 1.93647i 0.250040 + 0.968235i \(0.419556\pi\)
−0.250040 + 0.968235i \(0.580444\pi\)
\(212\) −0.131413 + 0.227614i −0.00902548 + 0.0156326i
\(213\) 10.4293 0.714604
\(214\) 10.5406i 0.720543i
\(215\) 7.94818 + 1.66981i 0.542062 + 0.113880i
\(216\) 2.31577i 0.157568i
\(217\) −2.06900 −0.140453
\(218\) 24.9147 + 14.3845i 1.68744 + 0.974242i
\(219\) 12.8531 0.868534
\(220\) 4.38339 7.59225i 0.295528 0.511869i
\(221\) −12.4655 + 1.25094i −0.838519 + 0.0841475i
\(222\) −0.0990663 0.171588i −0.00664889 0.0115162i
\(223\) −13.1603 −0.881278 −0.440639 0.897684i \(-0.645248\pi\)
−0.440639 + 0.897684i \(0.645248\pi\)
\(224\) 2.64348 1.52621i 0.176625 0.101974i
\(225\) −2.17137 + 3.76093i −0.144758 + 0.250729i
\(226\) 22.4512i 1.49343i
\(227\) −23.5426 13.5923i −1.56258 0.902153i −0.996995 0.0774598i \(-0.975319\pi\)
−0.565580 0.824693i \(-0.691348\pi\)
\(228\) −10.9664 + 6.33143i −0.726265 + 0.419309i
\(229\) −14.5518 25.2045i −0.961613 1.66556i −0.718452 0.695576i \(-0.755149\pi\)
−0.243161 0.969986i \(-0.578184\pi\)
\(230\) 9.08475 + 15.7352i 0.599031 + 1.03755i
\(231\) 1.59874i 0.105190i
\(232\) −0.876921 + 0.506291i −0.0575727 + 0.0332396i
\(233\) 1.62790 0.939871i 0.106648 0.0615730i −0.445728 0.895169i \(-0.647055\pi\)
0.552375 + 0.833596i \(0.313722\pi\)
\(234\) 3.90159 6.75776i 0.255055 0.441769i
\(235\) −1.35192 0.780531i −0.0881895 0.0509162i
\(236\) −14.3423 −0.933603
\(237\) 5.69106 0.369674
\(238\) 0.317373 + 3.16258i 0.0205722 + 0.205000i
\(239\) 7.35673 12.7422i 0.475867 0.824226i −0.523751 0.851872i \(-0.675468\pi\)
0.999618 + 0.0276455i \(0.00880095\pi\)
\(240\) −2.91202 5.04376i −0.187970 0.325573i
\(241\) −8.24038 + 4.75758i −0.530809 + 0.306463i −0.741346 0.671123i \(-0.765812\pi\)
0.210537 + 0.977586i \(0.432479\pi\)
\(242\) −1.34797 −0.0866509
\(243\) 10.4024 6.00582i 0.667314 0.385274i
\(244\) −19.8517 + 11.4614i −1.27087 + 0.733739i
\(245\) 7.35656 4.24731i 0.469993 0.271351i
\(246\) 5.96124 10.3252i 0.380075 0.658309i
\(247\) −13.2258 −0.841538
\(248\) 1.96257 + 1.13309i 0.124623 + 0.0719514i
\(249\) 20.2784 11.7077i 1.28509 0.741947i
\(250\) 21.4915i 1.35924i
\(251\) −3.29683 5.71027i −0.208094 0.360429i 0.743020 0.669269i \(-0.233393\pi\)
−0.951114 + 0.308840i \(0.900059\pi\)
\(252\) −0.898260 0.518611i −0.0565851 0.0326694i
\(253\) −11.5089 + 19.9340i −0.723559 + 1.25324i
\(254\) −24.5559 −1.54077
\(255\) 6.71603 0.673970i 0.420574 0.0422057i
\(256\) 12.3172 0.769828
\(257\) −3.83620 −0.239295 −0.119648 0.992816i \(-0.538177\pi\)
−0.119648 + 0.992816i \(0.538177\pi\)
\(258\) −17.3854 3.65244i −1.08236 0.227391i
\(259\) −0.0275072 −0.00170921
\(260\) 8.28307i 0.513694i
\(261\) −2.66712 1.53986i −0.165091 0.0953152i
\(262\) 22.9412i 1.41731i
\(263\) 1.12700 1.95202i 0.0694938 0.120367i −0.829185 0.558975i \(-0.811195\pi\)
0.898679 + 0.438608i \(0.144528\pi\)
\(264\) −0.875557 + 1.51651i −0.0538868 + 0.0933347i
\(265\) 0.128083 0.0739490i 0.00786810 0.00454265i
\(266\) 3.35548i 0.205738i
\(267\) 5.72190 3.30354i 0.350175 0.202173i
\(268\) 12.8605 22.2750i 0.785580 1.36066i
\(269\) 19.6404i 1.19749i 0.800938 + 0.598747i \(0.204335\pi\)
−0.800938 + 0.598747i \(0.795665\pi\)
\(270\) −7.13512 + 12.3584i −0.434229 + 0.752107i
\(271\) −11.0573 19.1519i −0.671685 1.16339i −0.977426 0.211278i \(-0.932238\pi\)
0.305741 0.952115i \(-0.401096\pi\)
\(272\) −6.02914 + 13.3721i −0.365570 + 0.810802i
\(273\) 0.755267 + 1.30816i 0.0457108 + 0.0791735i
\(274\) −0.160337 −0.00968629
\(275\) 9.65314 5.57325i 0.582106 0.336079i
\(276\) −10.4111 18.0325i −0.626672 1.08543i
\(277\) 13.5522 + 7.82434i 0.814270 + 0.470119i 0.848437 0.529297i \(-0.177544\pi\)
−0.0341663 + 0.999416i \(0.510878\pi\)
\(278\) 21.4524 + 12.3856i 1.28663 + 0.742837i
\(279\) 6.89251i 0.412644i
\(280\) 0.191904 0.0114684
\(281\) 12.7626 22.1055i 0.761355 1.31871i −0.180797 0.983520i \(-0.557868\pi\)
0.942152 0.335186i \(-0.108799\pi\)
\(282\) 2.95710 + 1.70728i 0.176093 + 0.101667i
\(283\) −1.41447 + 0.816646i −0.0840816 + 0.0485445i −0.541451 0.840732i \(-0.682125\pi\)
0.457370 + 0.889277i \(0.348792\pi\)
\(284\) −15.0401 + 8.68343i −0.892468 + 0.515267i
\(285\) 7.12567 0.422088
\(286\) −17.3451 + 10.0142i −1.02564 + 0.592151i
\(287\) −0.827611 1.43346i −0.0488523 0.0846147i
\(288\) −5.08432 8.80630i −0.299597 0.518916i
\(289\) −11.2559 12.7399i −0.662112 0.749405i
\(290\) 6.23972 0.366409
\(291\) 8.90132 15.4175i 0.521804 0.903792i
\(292\) −18.5356 + 10.7015i −1.08471 + 0.626259i
\(293\) −5.50109 −0.321377 −0.160688 0.987005i \(-0.551371\pi\)
−0.160688 + 0.987005i \(0.551371\pi\)
\(294\) −16.0913 + 9.29030i −0.938462 + 0.541821i
\(295\) 6.98945 + 4.03536i 0.406941 + 0.234948i
\(296\) 0.0260922 + 0.0150644i 0.00151658 + 0.000875599i
\(297\) −18.0781 −1.04900
\(298\) 9.84025 17.0438i 0.570030 0.987321i
\(299\) 21.7478i 1.25771i
\(300\) 10.0832i 0.582155i
\(301\) −1.64596 + 1.83674i −0.0948717 + 0.105868i
\(302\) −31.4314 −1.80867
\(303\) 22.7037i 1.30429i
\(304\) −7.74267 + 13.4107i −0.444073 + 0.769157i
\(305\) 12.8991 0.738602
\(306\) 10.5356 1.05728i 0.602281 0.0604404i
\(307\) −15.3065 + 26.5116i −0.873587 + 1.51310i −0.0153261 + 0.999883i \(0.504879\pi\)
−0.858261 + 0.513214i \(0.828455\pi\)
\(308\) 1.33111 + 2.30556i 0.0758473 + 0.131371i
\(309\) 14.5174i 0.825869i
\(310\) −6.98232 12.0937i −0.396569 0.686878i
\(311\) −27.8979 16.1069i −1.58194 0.913336i −0.994576 0.104016i \(-0.966831\pi\)
−0.587369 0.809320i \(-0.699836\pi\)
\(312\) 1.65450i 0.0936674i
\(313\) −2.01012 1.16054i −0.113619 0.0655978i 0.442114 0.896959i \(-0.354229\pi\)
−0.555732 + 0.831361i \(0.687562\pi\)
\(314\) −13.6718 23.6802i −0.771543 1.33635i
\(315\) 0.291834 + 0.505471i 0.0164430 + 0.0284801i
\(316\) −8.20710 + 4.73837i −0.461686 + 0.266554i
\(317\) 22.8348i 1.28253i 0.767318 + 0.641266i \(0.221591\pi\)
−0.767318 + 0.641266i \(0.778409\pi\)
\(318\) −0.280162 + 0.161751i −0.0157107 + 0.00907056i
\(319\) 3.95236 + 6.84569i 0.221290 + 0.383285i
\(320\) 10.2102 + 5.89487i 0.570769 + 0.329533i
\(321\) −3.39870 + 5.88672i −0.189697 + 0.328565i
\(322\) −5.51758 −0.307483
\(323\) −10.4804 14.5687i −0.583148 0.810622i
\(324\) 4.04018 6.99780i 0.224454 0.388767i
\(325\) −5.26574 + 9.12053i −0.292091 + 0.505916i
\(326\) −29.5883 + 17.0828i −1.63874 + 0.946129i
\(327\) 9.27622 + 16.0669i 0.512976 + 0.888501i
\(328\) 1.81297i 0.100105i
\(329\) 0.410541 0.237026i 0.0226338 0.0130676i
\(330\) 9.34502 5.39535i 0.514426 0.297004i
\(331\) −5.73060 9.92569i −0.314982 0.545565i 0.664452 0.747331i \(-0.268665\pi\)
−0.979434 + 0.201766i \(0.935332\pi\)
\(332\) −19.4957 + 33.7675i −1.06996 + 1.85323i
\(333\) 0.0916354i 0.00502159i
\(334\) −20.8664 12.0472i −1.14176 0.659196i
\(335\) −12.5347 + 7.23689i −0.684841 + 0.395393i
\(336\) 1.76860 0.0964850
\(337\) 19.3232 11.1562i 1.05260 0.607720i 0.129225 0.991615i \(-0.458751\pi\)
0.923376 + 0.383896i \(0.125418\pi\)
\(338\) −3.86095 + 6.68737i −0.210008 + 0.363745i
\(339\) 7.23911 12.5385i 0.393174 0.680998i
\(340\) −9.12408 + 6.56371i −0.494823 + 0.355967i
\(341\) 8.84547 15.3208i 0.479009 0.829668i
\(342\) 11.1782 0.604449
\(343\) 5.21237i 0.281441i
\(344\) 2.56719 0.840846i 0.138414 0.0453354i
\(345\) 11.7171i 0.630826i
\(346\) 12.4603i 0.669872i
\(347\) 3.39401 + 1.95953i 0.182200 + 0.105193i 0.588326 0.808624i \(-0.299787\pi\)
−0.406126 + 0.913817i \(0.633121\pi\)
\(348\) −7.15068 −0.383317
\(349\) −15.4174 + 26.7038i −0.825277 + 1.42942i 0.0764304 + 0.997075i \(0.475648\pi\)
−0.901707 + 0.432347i \(0.857686\pi\)
\(350\) 2.31395 + 1.33596i 0.123686 + 0.0714099i
\(351\) 14.7922 8.54031i 0.789552 0.455848i
\(352\) 26.0998i 1.39112i
\(353\) −2.56002 4.43408i −0.136256 0.236002i 0.789821 0.613338i \(-0.210174\pi\)
−0.926077 + 0.377336i \(0.876840\pi\)
\(354\) −15.2883 8.82669i −0.812562 0.469133i
\(355\) 9.77272 0.518682
\(356\) −5.50105 + 9.52811i −0.291555 + 0.504989i
\(357\) −0.842491 + 1.86857i −0.0445894 + 0.0988952i
\(358\) −17.5629 30.4198i −0.928229 1.60774i
\(359\) 9.01098 + 15.6075i 0.475581 + 0.823731i 0.999609 0.0279702i \(-0.00890437\pi\)
−0.524027 + 0.851701i \(0.675571\pi\)
\(360\) 0.639294i 0.0336938i
\(361\) 0.0268877 + 0.0465709i 0.00141514 + 0.00245110i
\(362\) 15.1319 8.73642i 0.795317 0.459176i
\(363\) −0.752814 0.434637i −0.0395125 0.0228125i
\(364\) −2.17835 1.25767i −0.114176 0.0659198i
\(365\) 12.0440 0.630410
\(366\) −28.2147 −1.47481
\(367\) 11.1586 + 6.44243i 0.582475 + 0.336292i 0.762117 0.647440i \(-0.224160\pi\)
−0.179641 + 0.983732i \(0.557494\pi\)
\(368\) −22.0518 12.7316i −1.14953 0.663683i
\(369\) −4.77535 + 2.75705i −0.248595 + 0.143526i
\(370\) −0.0928295 0.160785i −0.00482598 0.00835884i
\(371\) 0.0449125i 0.00233174i
\(372\) 8.00170 + 13.8593i 0.414869 + 0.718574i
\(373\) −3.70690 6.42055i −0.191936 0.332443i 0.753956 0.656925i \(-0.228143\pi\)
−0.945892 + 0.324482i \(0.894810\pi\)
\(374\) −24.7756 11.1707i −1.28112 0.577624i
\(375\) 6.92967 12.0025i 0.357847 0.619809i
\(376\) −0.519231 −0.0267773
\(377\) −6.46797 3.73429i −0.333118 0.192326i
\(378\) −2.16674 3.75290i −0.111445 0.193028i
\(379\) 1.27517i 0.0655009i −0.999464 0.0327505i \(-0.989573\pi\)
0.999464 0.0327505i \(-0.0104267\pi\)
\(380\) −10.2760 + 5.93283i −0.527146 + 0.304348i
\(381\) −13.7139 7.91775i −0.702587 0.405639i
\(382\) 13.4028 23.2143i 0.685746 1.18775i
\(383\) −1.85413 −0.0947414 −0.0473707 0.998877i \(-0.515084\pi\)
−0.0473707 + 0.998877i \(0.515084\pi\)
\(384\) −3.75342 2.16704i −0.191541 0.110586i
\(385\) 1.49809i 0.0763500i
\(386\) 48.8896i 2.48842i
\(387\) 6.11879 + 5.48325i 0.311035 + 0.278729i
\(388\) 29.6449i 1.50499i
\(389\) −2.03125 −0.102988 −0.0514942 0.998673i \(-0.516398\pi\)
−0.0514942 + 0.998673i \(0.516398\pi\)
\(390\) −5.09766 + 8.82941i −0.258130 + 0.447094i
\(391\) 23.9559 17.2335i 1.21150 0.871535i
\(392\) 1.41272 2.44689i 0.0713529 0.123587i
\(393\) −7.39712 + 12.8122i −0.373135 + 0.646289i
\(394\) 22.2019 12.8183i 1.11852 0.645777i
\(395\) 5.33278 0.268321
\(396\) 7.68058 4.43438i 0.385963 0.222836i
\(397\) −7.03576 4.06210i −0.353115 0.203871i 0.312942 0.949772i \(-0.398686\pi\)
−0.666056 + 0.745902i \(0.732019\pi\)
\(398\) 44.6657i 2.23889i
\(399\) −1.08193 + 1.87397i −0.0541645 + 0.0938156i
\(400\) 6.16536 + 10.6787i 0.308268 + 0.533936i
\(401\) −15.1797 + 8.76403i −0.758040 + 0.437655i −0.828592 0.559854i \(-0.810857\pi\)
0.0705516 + 0.997508i \(0.477524\pi\)
\(402\) 27.4175 15.8295i 1.36746 0.789504i
\(403\) 16.7148i 0.832626i
\(404\) −18.9031 32.7411i −0.940462 1.62893i
\(405\) −3.93782 + 2.27350i −0.195672 + 0.112971i
\(406\) −0.947416 + 1.64097i −0.0470195 + 0.0814401i
\(407\) 0.117600 0.203689i 0.00582921 0.0100965i
\(408\) 1.82248 1.31106i 0.0902264 0.0649073i
\(409\) 13.4431 0.664721 0.332360 0.943152i \(-0.392155\pi\)
0.332360 + 0.943152i \(0.392155\pi\)
\(410\) 5.58595 9.67515i 0.275870 0.477821i
\(411\) −0.0895446 0.0516986i −0.00441691 0.00255010i
\(412\) −12.0872 20.9357i −0.595495 1.03143i
\(413\) −2.12250 + 1.22543i −0.104442 + 0.0602993i
\(414\) 18.3809i 0.903371i
\(415\) 19.0017 10.9707i 0.932758 0.538528i
\(416\) −12.3299 21.3559i −0.604521 1.04706i
\(417\) 7.98716 + 13.8342i 0.391133 + 0.677462i
\(418\) −24.8472 14.3455i −1.21532 0.701663i
\(419\) 25.5742i 1.24938i 0.780871 + 0.624692i \(0.214775\pi\)
−0.780871 + 0.624692i \(0.785225\pi\)
\(420\) 1.17363 + 0.677595i 0.0572673 + 0.0330633i
\(421\) −9.03038 15.6411i −0.440114 0.762300i 0.557583 0.830121i \(-0.311729\pi\)
−0.997698 + 0.0678210i \(0.978395\pi\)
\(422\) 57.6538i 2.80654i
\(423\) −0.789611 1.36765i −0.0383922 0.0664973i
\(424\) 0.0245965 0.0426024i 0.00119451 0.00206895i
\(425\) −14.2193 + 1.42694i −0.689736 + 0.0692167i
\(426\) −21.3762 −1.03568
\(427\) −1.95856 + 3.39232i −0.0947812 + 0.164166i
\(428\) 11.3190i 0.547126i
\(429\) −12.9158 −0.623582
\(430\) −16.2909 3.42250i −0.785615 0.165048i
\(431\) 9.91132i 0.477411i −0.971092 0.238706i \(-0.923277\pi\)
0.971092 0.238706i \(-0.0767231\pi\)
\(432\) 19.9987i 0.962189i
\(433\) 17.3438 30.0404i 0.833492 1.44365i −0.0617607 0.998091i \(-0.519672\pi\)
0.895253 0.445559i \(-0.146995\pi\)
\(434\) 4.24068 0.203559
\(435\) 3.48475 + 2.01192i 0.167081 + 0.0964643i
\(436\) −26.7546 15.4468i −1.28131 0.739765i
\(437\) 26.9803 15.5771i 1.29064 0.745153i
\(438\) −26.3442 −1.25877
\(439\) 13.6387 7.87429i 0.650938 0.375819i −0.137877 0.990449i \(-0.544028\pi\)
0.788816 + 0.614630i \(0.210695\pi\)
\(440\) −0.820436 + 1.42104i −0.0391127 + 0.0677453i
\(441\) 8.59344 0.409212
\(442\) 25.5497 2.56397i 1.21527 0.121956i
\(443\) −0.154118 0.266940i −0.00732236 0.0126827i 0.862341 0.506328i \(-0.168997\pi\)
−0.869663 + 0.493645i \(0.835664\pi\)
\(444\) 0.106382 + 0.184259i 0.00504867 + 0.00874455i
\(445\) 5.36168 3.09557i 0.254168 0.146744i
\(446\) 26.9737 1.27724
\(447\) 10.9911 6.34574i 0.519863 0.300143i
\(448\) −3.10056 + 1.79011i −0.146488 + 0.0845748i
\(449\) 1.23276 + 0.711732i 0.0581773 + 0.0335887i 0.528807 0.848742i \(-0.322640\pi\)
−0.470629 + 0.882331i \(0.655973\pi\)
\(450\) 4.45052 7.70852i 0.209799 0.363383i
\(451\) 14.1530 0.666438
\(452\) 24.1091i 1.13400i
\(453\) −17.5538 10.1347i −0.824748 0.476168i
\(454\) 48.2536 + 27.8592i 2.26465 + 1.30750i
\(455\) 0.707719 + 1.22580i 0.0331784 + 0.0574666i
\(456\) 2.05257 1.18505i 0.0961202 0.0554950i
\(457\) −11.5614 −0.540822 −0.270411 0.962745i \(-0.587160\pi\)
−0.270411 + 0.962745i \(0.587160\pi\)
\(458\) 29.8259 + 51.6600i 1.39367 + 2.41391i
\(459\) 21.1292 + 9.52661i 0.986225 + 0.444664i
\(460\) −9.75563 16.8973i −0.454859 0.787838i
\(461\) −10.8159 + 18.7337i −0.503748 + 0.872516i 0.496243 + 0.868184i \(0.334713\pi\)
−0.999991 + 0.00433277i \(0.998621\pi\)
\(462\) 3.27684i 0.152452i
\(463\) 4.02199 6.96629i 0.186918 0.323751i −0.757303 0.653063i \(-0.773484\pi\)
0.944221 + 0.329312i \(0.106817\pi\)
\(464\) −7.57299 + 4.37227i −0.351567 + 0.202977i
\(465\) 9.00547i 0.417618i
\(466\) −3.33660 + 1.92639i −0.154565 + 0.0892383i
\(467\) 14.1004 24.4226i 0.652488 1.13014i −0.330029 0.943971i \(-0.607058\pi\)
0.982517 0.186172i \(-0.0596082\pi\)
\(468\) −4.18972 + 7.25680i −0.193670 + 0.335446i
\(469\) 4.39529i 0.202955i
\(470\) 2.77094 + 1.59980i 0.127814 + 0.0737933i
\(471\) 17.6332i 0.812495i
\(472\) 2.68443 0.123561
\(473\) −6.56406 20.0408i −0.301816 0.921477i
\(474\) −11.6646 −0.535772
\(475\) −15.0866 −0.692219
\(476\) −0.340810 3.39613i −0.0156210 0.155661i
\(477\) 0.149619 0.00685056
\(478\) −15.0786 + 26.1169i −0.689678 + 1.19456i
\(479\) 35.8011 + 20.6698i 1.63579 + 0.944425i 0.982259 + 0.187528i \(0.0600474\pi\)
0.653533 + 0.756898i \(0.273286\pi\)
\(480\) 6.64296 + 11.5059i 0.303208 + 0.525172i
\(481\) 0.222223i 0.0101325i
\(482\) 16.8897 9.75130i 0.769307 0.444159i
\(483\) −3.08145 1.77908i −0.140211 0.0809508i
\(484\) 1.44752 0.0657962
\(485\) 8.34093 14.4469i 0.378742 0.656001i
\(486\) −21.3211 + 12.3097i −0.967144 + 0.558381i
\(487\) −0.533301 + 0.307901i −0.0241662 + 0.0139523i −0.512034 0.858965i \(-0.671108\pi\)
0.487868 + 0.872917i \(0.337775\pi\)
\(488\) 3.71562 2.14522i 0.168198 0.0971094i
\(489\) −22.0326 −0.996348
\(490\) −15.0782 + 8.70542i −0.681165 + 0.393271i
\(491\) −0.642989 1.11369i −0.0290177 0.0502601i 0.851152 0.524920i \(-0.175905\pi\)
−0.880170 + 0.474659i \(0.842571\pi\)
\(492\) −6.40146 + 11.0877i −0.288600 + 0.499870i
\(493\) −1.01194 10.0838i −0.0455754 0.454153i
\(494\) 27.1080 1.21965
\(495\) −4.99065 −0.224313
\(496\) 16.9485 + 9.78524i 0.761011 + 0.439370i
\(497\) −1.48385 + 2.57011i −0.0665599 + 0.115285i
\(498\) −41.5632 + 23.9965i −1.86249 + 1.07531i
\(499\) 1.46542 0.846060i 0.0656012 0.0378748i −0.466841 0.884341i \(-0.654608\pi\)
0.532442 + 0.846467i \(0.321275\pi\)
\(500\) 23.0786i 1.03211i
\(501\) −7.76898 13.4563i −0.347092 0.601181i
\(502\) 6.75728 + 11.7040i 0.301592 + 0.522373i
\(503\) 27.9955 16.1632i 1.24826 0.720681i 0.277495 0.960727i \(-0.410496\pi\)
0.970761 + 0.240046i \(0.0771626\pi\)
\(504\) 0.168127 + 0.0970680i 0.00748896 + 0.00432375i
\(505\) 21.2743i 0.946696i
\(506\) 23.5890 40.8574i 1.04866 1.81633i
\(507\) −4.31252 + 2.48983i −0.191526 + 0.110577i
\(508\) 26.3693 1.16995
\(509\) −3.86661 6.69716i −0.171384 0.296846i 0.767520 0.641025i \(-0.221491\pi\)
−0.938904 + 0.344179i \(0.888157\pi\)
\(510\) −13.7654 + 1.38139i −0.609542 + 0.0611690i
\(511\) −1.82871 + 3.16742i −0.0808974 + 0.140118i
\(512\) −31.8039 −1.40555
\(513\) 21.1902 + 12.2342i 0.935570 + 0.540151i
\(514\) 7.86279 0.346813
\(515\) 13.6035i 0.599442i
\(516\) 18.6692 + 3.92216i 0.821866 + 0.172663i
\(517\) 4.05338i 0.178267i
\(518\) 0.0563795 0.00247717
\(519\) −4.01769 + 6.95884i −0.176357 + 0.305459i
\(520\) 1.55034i 0.0679867i
\(521\) −10.6383 6.14204i −0.466074 0.269088i 0.248521 0.968627i \(-0.420056\pi\)
−0.714595 + 0.699539i \(0.753389\pi\)
\(522\) 5.46662 + 3.15616i 0.239268 + 0.138141i
\(523\) 11.2966 + 19.5663i 0.493965 + 0.855572i 0.999976 0.00695469i \(-0.00221376\pi\)
−0.506011 + 0.862527i \(0.668880\pi\)
\(524\) 24.6354i 1.07620i
\(525\) 0.861526 + 1.49221i 0.0376001 + 0.0651253i
\(526\) −2.30994 + 4.00093i −0.100718 + 0.174449i
\(527\) −18.4120 + 13.2453i −0.802038 + 0.576972i
\(528\) −7.56120 + 13.0964i −0.329059 + 0.569947i
\(529\) 14.1141 + 24.4464i 0.613658 + 1.06289i
\(530\) −0.262524 + 0.151568i −0.0114033 + 0.00658370i
\(531\) 4.08230 + 7.07076i 0.177157 + 0.306845i
\(532\) 3.60327i 0.156222i
\(533\) −11.5806 + 6.68604i −0.501610 + 0.289605i
\(534\) −11.7278 + 6.77104i −0.507511 + 0.293012i
\(535\) −3.18473 + 5.51612i −0.137688 + 0.238483i
\(536\) −2.40709 + 4.16920i −0.103970 + 0.180082i
\(537\) 22.6518i 0.977497i
\(538\) 40.2555i 1.73554i
\(539\) −19.1017 11.0284i −0.822768 0.475025i
\(540\) 7.66202 13.2710i 0.329721 0.571094i
\(541\) −28.7477 + 16.5975i −1.23596 + 0.713581i −0.968266 0.249923i \(-0.919595\pi\)
−0.267693 + 0.963504i \(0.586261\pi\)
\(542\) 22.6635 + 39.2542i 0.973479 + 1.68611i
\(543\) 11.2678 0.483548
\(544\) 13.7538 30.5047i 0.589690 1.30788i
\(545\) 8.69223 + 15.0554i 0.372334 + 0.644902i
\(546\) −1.54802 2.68125i −0.0662491 0.114747i
\(547\) 2.76616 + 1.59704i 0.118272 + 0.0682846i 0.557969 0.829862i \(-0.311581\pi\)
−0.439697 + 0.898146i \(0.644914\pi\)
\(548\) 0.172177 0.00735504
\(549\) 11.3009 + 6.52460i 0.482312 + 0.278463i
\(550\) −19.7854 + 11.4231i −0.843652 + 0.487083i
\(551\) 10.6989i 0.455788i
\(552\) 1.94863 + 3.37513i 0.0829393 + 0.143655i
\(553\) −0.809709 + 1.40246i −0.0344323 + 0.0596385i
\(554\) −27.7769 16.0370i −1.18013 0.681348i
\(555\) 0.119727i 0.00508213i
\(556\) −23.0366 13.3002i −0.976971 0.564054i
\(557\) 11.7269 0.496884 0.248442 0.968647i \(-0.420081\pi\)
0.248442 + 0.968647i \(0.420081\pi\)
\(558\) 14.1271i 0.598048i
\(559\) 14.8385 + 13.2973i 0.627602 + 0.562415i
\(560\) 1.65726 0.0700318
\(561\) −10.2348 14.2272i −0.432114 0.600673i
\(562\) −26.1587 + 45.3082i −1.10344 + 1.91121i
\(563\) 4.54836 0.191691 0.0958453 0.995396i \(-0.469445\pi\)
0.0958453 + 0.995396i \(0.469445\pi\)
\(564\) −3.17547 1.83336i −0.133712 0.0771984i
\(565\) 6.78337 11.7491i 0.285378 0.494290i
\(566\) 2.89915 1.67382i 0.121860 0.0703560i
\(567\) 1.38080i 0.0579881i
\(568\) 2.81505 1.62527i 0.118117 0.0681949i
\(569\) 9.68585 16.7764i 0.406052 0.703303i −0.588391 0.808576i \(-0.700238\pi\)
0.994443 + 0.105274i \(0.0335718\pi\)
\(570\) −14.6050 −0.611736
\(571\) −40.8137 23.5638i −1.70800 0.986115i −0.937033 0.349241i \(-0.886439\pi\)
−0.770968 0.636874i \(-0.780227\pi\)
\(572\) 18.6260 10.7537i 0.778791 0.449635i
\(573\) 14.9703 8.64313i 0.625395 0.361072i
\(574\) 1.69630 + 2.93808i 0.0708021 + 0.122633i
\(575\) 24.8075i 1.03455i
\(576\) 5.96345 + 10.3290i 0.248477 + 0.430375i
\(577\) 1.48994 + 2.58065i 0.0620269 + 0.107434i 0.895371 0.445320i \(-0.146910\pi\)
−0.833344 + 0.552754i \(0.813577\pi\)
\(578\) 23.0705 + 26.1121i 0.959605 + 1.08612i
\(579\) −15.7639 + 27.3038i −0.655124 + 1.13471i
\(580\) −6.70051 −0.278223
\(581\) 6.66297i 0.276427i
\(582\) −18.2444 + 31.6003i −0.756256 + 1.30987i
\(583\) −0.332575 0.192012i −0.0137739 0.00795234i
\(584\) 3.46929 2.00300i 0.143560 0.0828846i
\(585\) 4.08356 2.35765i 0.168835 0.0974767i
\(586\) 11.2752 0.465774
\(587\) −5.77778 10.0074i −0.238474 0.413050i 0.721802 0.692099i \(-0.243314\pi\)
−0.960277 + 0.279049i \(0.909981\pi\)
\(588\) 17.2796 9.97636i 0.712597 0.411418i
\(589\) −20.7364 + 11.9722i −0.854429 + 0.493305i
\(590\) −14.3258 8.27100i −0.589784 0.340512i
\(591\) 16.5324 0.680053
\(592\) 0.225330 + 0.130094i 0.00926099 + 0.00534683i
\(593\) −14.5665 25.2299i −0.598174 1.03607i −0.993090 0.117351i \(-0.962560\pi\)
0.394916 0.918717i \(-0.370774\pi\)
\(594\) 37.0534 1.52032
\(595\) −0.789452 + 1.75093i −0.0323644 + 0.0717813i
\(596\) −10.5669 + 18.3024i −0.432838 + 0.749697i
\(597\) −14.4019 + 24.9448i −0.589431 + 1.02092i
\(598\) 44.5750i 1.82281i
\(599\) −1.22249 + 2.11742i −0.0499497 + 0.0865153i −0.889919 0.456118i \(-0.849239\pi\)
0.839970 + 0.542634i \(0.182573\pi\)
\(600\) 1.88727i 0.0770474i
\(601\) 1.62928i 0.0664597i −0.999448 0.0332299i \(-0.989421\pi\)
0.999448 0.0332299i \(-0.0105793\pi\)
\(602\) 3.37362 3.76464i 0.137498 0.153435i
\(603\) −14.6422 −0.596275
\(604\) 33.7525 1.37337
\(605\) −0.705420 0.407275i −0.0286794 0.0165581i
\(606\) 46.5341i 1.89032i
\(607\) 5.98269 + 3.45411i 0.242830 + 0.140198i 0.616477 0.787373i \(-0.288559\pi\)
−0.373647 + 0.927571i \(0.621893\pi\)
\(608\) 17.6628 30.5928i 0.716320 1.24070i
\(609\) −1.05822 + 0.610966i −0.0428814 + 0.0247576i
\(610\) −26.4385 −1.07046
\(611\) −1.91487 3.31664i −0.0774672 0.134177i
\(612\) −11.3136 + 1.13535i −0.457327 + 0.0458939i
\(613\) −3.18755 −0.128744 −0.0643720 0.997926i \(-0.520504\pi\)
−0.0643720 + 0.997926i \(0.520504\pi\)
\(614\) 31.3726 54.3390i 1.26610 2.19294i
\(615\) 6.23927 3.60224i 0.251592 0.145256i
\(616\) −0.249144 0.431530i −0.0100383 0.0173868i
\(617\) 5.06634 2.92505i 0.203963 0.117758i −0.394540 0.918879i \(-0.629096\pi\)
0.598503 + 0.801121i \(0.295763\pi\)
\(618\) 29.7554i 1.19694i
\(619\) 27.5773 15.9218i 1.10842 0.639949i 0.170004 0.985443i \(-0.445622\pi\)
0.938421 + 0.345494i \(0.112289\pi\)
\(620\) 7.49795 + 12.9868i 0.301125 + 0.521564i
\(621\) −20.1172 + 34.8440i −0.807276 + 1.39824i
\(622\) 57.1804 + 33.0131i 2.29273 + 1.32371i
\(623\) 1.88008i 0.0753236i
\(624\) 14.2880i 0.571979i
\(625\) −2.17159 + 3.76131i −0.0868637 + 0.150452i
\(626\) 4.12001 + 2.37869i 0.164669 + 0.0950715i
\(627\) −9.25108 16.0233i −0.369453 0.639911i
\(628\) 14.6814 + 25.4289i 0.585852 + 1.01472i
\(629\) −0.244786 + 0.176095i −0.00976025 + 0.00702136i
\(630\) −0.598152 1.03603i −0.0238309 0.0412764i
\(631\) −1.01344 1.75532i −0.0403443 0.0698784i 0.845148 0.534532i \(-0.179512\pi\)
−0.885492 + 0.464654i \(0.846179\pi\)
\(632\) 1.53612 0.886878i 0.0611035 0.0352781i
\(633\) 18.5898 32.1984i 0.738877 1.27977i
\(634\) 46.8030i 1.85879i
\(635\) −12.8506 7.41929i −0.509960 0.294425i
\(636\) 0.300851 0.173696i 0.0119295 0.00688750i
\(637\) 20.8397 0.825700
\(638\) −8.10088 14.0311i −0.320717 0.555498i
\(639\) 8.56188 + 4.94320i 0.338703 + 0.195550i
\(640\) −3.51712 2.03061i −0.139026 0.0802669i
\(641\) 16.4316i 0.649011i 0.945884 + 0.324505i \(0.105198\pi\)
−0.945884 + 0.324505i \(0.894802\pi\)
\(642\) 6.96608 12.0656i 0.274929 0.476192i
\(643\) 20.0547i 0.790880i −0.918492 0.395440i \(-0.870592\pi\)
0.918492 0.395440i \(-0.129408\pi\)
\(644\) 5.92503 0.233479
\(645\) −7.99455 7.16418i −0.314785 0.282089i
\(646\) 21.4811 + 29.8604i 0.845161 + 1.17484i
\(647\) 29.1917 1.14765 0.573823 0.818979i \(-0.305460\pi\)
0.573823 + 0.818979i \(0.305460\pi\)
\(648\) −0.756198 + 1.30977i −0.0297063 + 0.0514527i
\(649\) 20.9560i 0.822596i
\(650\) 10.7928 18.6937i 0.423330 0.733228i
\(651\) 2.36833 + 1.36736i 0.0928222 + 0.0535909i
\(652\) 31.7733 18.3443i 1.24434 0.718419i
\(653\) 15.1519i 0.592938i 0.955043 + 0.296469i \(0.0958091\pi\)
−0.955043 + 0.296469i \(0.904191\pi\)
\(654\) −19.0128 32.9312i −0.743461 1.28771i
\(655\) −6.93143 + 12.0056i −0.270833 + 0.469097i
\(656\) 15.6566i 0.611289i
\(657\) 10.5517 + 6.09204i 0.411662 + 0.237673i
\(658\) −0.841457 + 0.485815i −0.0328034 + 0.0189391i
\(659\) 23.5992 + 40.8750i 0.919293 + 1.59226i 0.800491 + 0.599345i \(0.204572\pi\)
0.118803 + 0.992918i \(0.462094\pi\)
\(660\) −10.0351 + 5.79378i −0.390617 + 0.225523i
\(661\) 7.59103 0.295257 0.147628 0.989043i \(-0.452836\pi\)
0.147628 + 0.989043i \(0.452836\pi\)
\(662\) 11.7456 + 20.3440i 0.456506 + 0.790692i
\(663\) 15.0957 + 6.80626i 0.586267 + 0.264333i
\(664\) 3.64900 6.32024i 0.141608 0.245273i
\(665\) −1.01382 + 1.75599i −0.0393143 + 0.0680944i
\(666\) 0.187819i 0.00727784i
\(667\) 17.5927 0.681191
\(668\) 22.4074 + 12.9369i 0.866967 + 0.500544i
\(669\) 15.0643 + 8.69736i 0.582418 + 0.336259i
\(670\) 25.6914 14.8330i 0.992547 0.573047i
\(671\) −16.7466 29.0060i −0.646497 1.11977i
\(672\) −4.03457 −0.155637
\(673\) 13.1601 7.59800i 0.507286 0.292882i −0.224431 0.974490i \(-0.572052\pi\)
0.731717 + 0.681608i \(0.238719\pi\)
\(674\) −39.6054 + 22.8662i −1.52554 + 0.880773i
\(675\) 16.8734 9.74186i 0.649457 0.374964i
\(676\) 4.14607 7.18121i 0.159464 0.276200i
\(677\) 36.2706i 1.39399i −0.717075 0.696996i \(-0.754519\pi\)
0.717075 0.696996i \(-0.245481\pi\)
\(678\) −14.8375 + 25.6993i −0.569831 + 0.986976i
\(679\) 2.53291 + 4.38713i 0.0972042 + 0.168363i
\(680\) 1.70775 1.22852i 0.0654891 0.0471118i
\(681\) 17.9657 + 31.1176i 0.688449 + 1.19243i
\(682\) −18.1300 + 31.4020i −0.694232 + 1.20245i
\(683\) −0.285852 0.165037i −0.0109378 0.00631495i 0.494521 0.869166i \(-0.335343\pi\)
−0.505459 + 0.862851i \(0.668677\pi\)
\(684\) −12.0037 −0.458973
\(685\) −0.0839073 0.0484439i −0.00320593 0.00185095i
\(686\) 10.6834i 0.407896i
\(687\) 38.4680i 1.46765i
\(688\) 22.1700 7.26145i 0.845222 0.276840i
\(689\) 0.362836 0.0138230
\(690\) 24.0157i 0.914262i
\(691\) 31.3124 + 18.0782i 1.19118 + 0.687728i 0.958574 0.284843i \(-0.0919415\pi\)
0.232606 + 0.972571i \(0.425275\pi\)
\(692\) 13.3805i 0.508650i
\(693\) 0.757762 1.31248i 0.0287850 0.0498571i
\(694\) −6.95647 4.01632i −0.264064 0.152457i
\(695\) 7.48432 + 12.9632i 0.283897 + 0.491723i
\(696\) 1.33839 0.0507315
\(697\) −16.5416 7.45820i −0.626559 0.282500i
\(698\) 31.6001 54.7330i 1.19608 2.07167i
\(699\) −2.48456 −0.0939748
\(700\) −2.48482 1.43461i −0.0939175 0.0542233i
\(701\) −24.8710 43.0779i −0.939366 1.62703i −0.766658 0.642056i \(-0.778082\pi\)
−0.172707 0.984973i \(-0.555252\pi\)
\(702\) −30.3187 + 17.5045i −1.14430 + 0.660664i
\(703\) −0.275689 + 0.159169i −0.0103978 + 0.00600318i
\(704\) 30.6127i 1.15376i
\(705\) 1.03167 + 1.78691i 0.0388551 + 0.0672989i
\(706\) 5.24709 + 9.08823i 0.197477 + 0.342040i
\(707\) −5.59490 3.23022i −0.210418 0.121485i
\(708\) 16.4173 + 9.47851i 0.616999 + 0.356224i
\(709\) 39.0826i 1.46778i 0.679270 + 0.733888i \(0.262296\pi\)
−0.679270 + 0.733888i \(0.737704\pi\)
\(710\) −20.0305 −0.751730
\(711\) 4.67205 + 2.69741i 0.175215 + 0.101161i
\(712\) 1.02963 1.78337i 0.0385870 0.0668346i
\(713\) −19.6864 34.0979i −0.737262 1.27698i
\(714\) 1.72680 3.82988i 0.0646237 0.143330i
\(715\) −12.1027 −0.452615
\(716\) 18.8599 + 32.6663i 0.704827 + 1.22080i
\(717\) −16.8421 + 9.72382i −0.628981 + 0.363143i
\(718\) −18.4692 31.9896i −0.689264 1.19384i
\(719\) −9.64916 5.57095i −0.359853 0.207761i 0.309163 0.951009i \(-0.399951\pi\)
−0.669016 + 0.743248i \(0.733284\pi\)
\(720\) 5.52087i 0.205751i
\(721\) −3.57756 2.06550i −0.133235 0.0769234i
\(722\) −0.0551100 0.0954532i −0.00205098 0.00355240i
\(723\) 12.5767 0.467734
\(724\) −16.2494 + 9.38158i −0.603903 + 0.348664i
\(725\) −7.37796 4.25967i −0.274011 0.158200i
\(726\) 1.54299 + 0.890847i 0.0572658 + 0.0330624i
\(727\) −39.6986 −1.47234 −0.736169 0.676798i \(-0.763367\pi\)
−0.736169 + 0.676798i \(0.763367\pi\)
\(728\) 0.407720 + 0.235397i 0.0151111 + 0.00872440i
\(729\) −26.8902 −0.995934
\(730\) −24.6857 −0.913658
\(731\) −2.88900 + 26.8822i −0.106854 + 0.994275i
\(732\) 30.2983 1.11986
\(733\) 32.4030 1.19683 0.598415 0.801186i \(-0.295797\pi\)
0.598415 + 0.801186i \(0.295797\pi\)
\(734\) −22.8711 13.2046i −0.844187 0.487391i
\(735\) −11.2278 −0.414145
\(736\) 50.3052 + 29.0437i 1.85427 + 1.07057i
\(737\) 32.5469 + 18.7909i 1.19888 + 0.692174i
\(738\) 9.78770 5.65093i 0.360290 0.208014i
\(739\) 33.2420 1.22283 0.611413 0.791312i \(-0.290601\pi\)
0.611413 + 0.791312i \(0.290601\pi\)
\(740\) 0.0996847 + 0.172659i 0.00366448 + 0.00634707i
\(741\) 15.1393 + 8.74065i 0.556155 + 0.321096i
\(742\) 0.0920542i 0.00337942i
\(743\) −20.1382 11.6268i −0.738800 0.426546i 0.0828331 0.996563i \(-0.473603\pi\)
−0.821633 + 0.570017i \(0.806936\pi\)
\(744\) −1.49767 2.59404i −0.0549073 0.0951023i
\(745\) 10.2992 5.94624i 0.377333 0.217853i
\(746\) 7.59779 + 13.1598i 0.278175 + 0.481813i
\(747\) 22.1966 0.812130
\(748\) 26.6052 + 11.9956i 0.972784 + 0.438604i
\(749\) −0.967116 1.67509i −0.0353376 0.0612066i
\(750\) −14.2033 + 24.6008i −0.518630 + 0.898294i
\(751\) −19.3912 11.1955i −0.707596 0.408531i 0.102575 0.994725i \(-0.467292\pi\)
−0.810170 + 0.586195i \(0.800625\pi\)
\(752\) −4.48402 −0.163515
\(753\) 8.71522i 0.317600i
\(754\) 13.2570 + 7.65391i 0.482790 + 0.278739i
\(755\) −16.4487 9.49664i −0.598628 0.345618i
\(756\) 2.32675 + 4.03004i 0.0846229 + 0.146571i
\(757\) −21.0806 36.5127i −0.766187 1.32708i −0.939617 0.342229i \(-0.888818\pi\)
0.173429 0.984846i \(-0.444515\pi\)
\(758\) 2.61362i 0.0949311i
\(759\) 26.3479 15.2120i 0.956370 0.552160i
\(760\) 1.92335 1.11044i 0.0697671 0.0402800i
\(761\) 2.81584 + 4.87718i 0.102074 + 0.176798i 0.912539 0.408990i \(-0.134119\pi\)
−0.810465 + 0.585787i \(0.800785\pi\)
\(762\) 28.1085 + 16.2285i