Properties

Label 731.2.m.c.87.13
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.13
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.286708 - 0.286708i) q^{2} +(-2.99617 + 1.24105i) q^{3} -1.83560i q^{4} +(-0.918391 - 2.21719i) q^{5} +(1.21484 + 0.503205i) q^{6} +(-1.74237 + 4.20646i) q^{7} +(-1.09970 + 1.09970i) q^{8} +(5.31549 - 5.31549i) q^{9} +O(q^{10})\) \(q+(-0.286708 - 0.286708i) q^{2} +(-2.99617 + 1.24105i) q^{3} -1.83560i q^{4} +(-0.918391 - 2.21719i) q^{5} +(1.21484 + 0.503205i) q^{6} +(-1.74237 + 4.20646i) q^{7} +(-1.09970 + 1.09970i) q^{8} +(5.31549 - 5.31549i) q^{9} +(-0.372376 + 0.898996i) q^{10} +(-5.16669 - 2.14011i) q^{11} +(2.27808 + 5.49976i) q^{12} -4.32837i q^{13} +(1.70558 - 0.706474i) q^{14} +(5.50331 + 5.50331i) q^{15} -3.04061 q^{16} +(-3.09361 + 2.72572i) q^{17} -3.04799 q^{18} +(-1.17381 - 1.17381i) q^{19} +(-4.06987 + 1.68580i) q^{20} -14.7657i q^{21} +(0.867743 + 2.09492i) q^{22} +(-0.709798 - 0.294008i) q^{23} +(1.93009 - 4.65966i) q^{24} +(-0.536960 + 0.536960i) q^{25} +(-1.24098 + 1.24098i) q^{26} +(-5.60614 + 13.5344i) q^{27} +(7.72137 + 3.19830i) q^{28} +(2.37185 + 5.72615i) q^{29} -3.15568i q^{30} +(4.72161 - 1.95575i) q^{31} +(3.07116 + 3.07116i) q^{32} +18.1363 q^{33} +(1.66845 + 0.105478i) q^{34} +10.9267 q^{35} +(-9.75711 - 9.75711i) q^{36} +(8.39726 - 3.47826i) q^{37} +0.673082i q^{38} +(5.37174 + 12.9685i) q^{39} +(3.44819 + 1.42829i) q^{40} +(-1.29038 + 3.11525i) q^{41} +(-4.23343 + 4.23343i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(-3.92839 + 9.48396i) q^{44} +(-16.6672 - 6.90377i) q^{45} +(0.119210 + 0.287799i) q^{46} +8.64397i q^{47} +(9.11019 - 3.77356i) q^{48} +(-9.70872 - 9.70872i) q^{49} +0.307902 q^{50} +(5.88623 - 12.0061i) q^{51} -7.94515 q^{52} +(3.96634 + 3.96634i) q^{53} +(5.48775 - 2.27310i) q^{54} +13.4210i q^{55} +(-2.70975 - 6.54191i) q^{56} +(4.97370 + 2.06018i) q^{57} +(0.961704 - 2.32176i) q^{58} +(2.40335 - 2.40335i) q^{59} +(10.1019 - 10.1019i) q^{60} +(-1.81077 + 4.37160i) q^{61} +(-1.91445 - 0.792992i) q^{62} +(13.0979 + 31.6210i) q^{63} +4.32017i q^{64} +(-9.59683 + 3.97514i) q^{65} +(-5.19981 - 5.19981i) q^{66} +9.52146 q^{67} +(5.00332 + 5.67863i) q^{68} +2.49155 q^{69} +(-3.13277 - 3.13277i) q^{70} +(-0.661153 + 0.273859i) q^{71} +11.6909i q^{72} +(-4.23025 - 10.2127i) q^{73} +(-3.40480 - 1.41032i) q^{74} +(0.942428 - 2.27522i) q^{75} +(-2.15465 + 2.15465i) q^{76} +(18.0046 - 18.0046i) q^{77} +(2.17806 - 5.25830i) q^{78} +(0.123367 + 0.0511002i) q^{79} +(2.79247 + 6.74162i) q^{80} -24.9572i q^{81} +(1.26313 - 0.523205i) q^{82} +(-2.68247 - 2.68247i) q^{83} -27.1038 q^{84} +(8.88459 + 4.35586i) q^{85} +0.405466 q^{86} +(-14.2129 - 14.2129i) q^{87} +(8.03526 - 3.32831i) q^{88} +8.46370i q^{89} +(2.79924 + 6.75797i) q^{90} +(18.2071 + 7.54164i) q^{91} +(-0.539680 + 1.30290i) q^{92} +(-11.7195 + 11.7195i) q^{93} +(2.47829 - 2.47829i) q^{94} +(-1.52455 + 3.68058i) q^{95} +(-13.0132 - 5.39024i) q^{96} +(4.92448 + 11.8887i) q^{97} +5.56713i q^{98} +(-38.8393 + 16.0878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.286708 0.286708i −0.202733 0.202733i 0.598437 0.801170i \(-0.295789\pi\)
−0.801170 + 0.598437i \(0.795789\pi\)
\(3\) −2.99617 + 1.24105i −1.72984 + 0.716523i −0.730400 + 0.683019i \(0.760667\pi\)
−0.999439 + 0.0335036i \(0.989333\pi\)
\(4\) 1.83560i 0.917799i
\(5\) −0.918391 2.21719i −0.410717 0.991558i −0.984946 0.172863i \(-0.944698\pi\)
0.574229 0.818695i \(-0.305302\pi\)
\(6\) 1.21484 + 0.503205i 0.495958 + 0.205433i
\(7\) −1.74237 + 4.20646i −0.658556 + 1.58989i 0.141480 + 0.989941i \(0.454814\pi\)
−0.800036 + 0.599953i \(0.795186\pi\)
\(8\) −1.09970 + 1.09970i −0.388801 + 0.388801i
\(9\) 5.31549 5.31549i 1.77183 1.77183i
\(10\) −0.372376 + 0.898996i −0.117756 + 0.284287i
\(11\) −5.16669 2.14011i −1.55782 0.645268i −0.573107 0.819480i \(-0.694262\pi\)
−0.984708 + 0.174212i \(0.944262\pi\)
\(12\) 2.27808 + 5.49976i 0.657624 + 1.58764i
\(13\) 4.32837i 1.20047i −0.799822 0.600237i \(-0.795073\pi\)
0.799822 0.600237i \(-0.204927\pi\)
\(14\) 1.70558 0.706474i 0.455835 0.188813i
\(15\) 5.50331 + 5.50331i 1.42095 + 1.42095i
\(16\) −3.04061 −0.760153
\(17\) −3.09361 + 2.72572i −0.750312 + 0.661084i
\(18\) −3.04799 −0.718417
\(19\) −1.17381 1.17381i −0.269291 0.269291i 0.559523 0.828814i \(-0.310984\pi\)
−0.828814 + 0.559523i \(0.810984\pi\)
\(20\) −4.06987 + 1.68580i −0.910051 + 0.376955i
\(21\) 14.7657i 3.22213i
\(22\) 0.867743 + 2.09492i 0.185003 + 0.446638i
\(23\) −0.709798 0.294008i −0.148003 0.0613049i 0.307452 0.951563i \(-0.400524\pi\)
−0.455455 + 0.890259i \(0.650524\pi\)
\(24\) 1.93009 4.65966i 0.393978 0.951148i
\(25\) −0.536960 + 0.536960i −0.107392 + 0.107392i
\(26\) −1.24098 + 1.24098i −0.243376 + 0.243376i
\(27\) −5.60614 + 13.5344i −1.07890 + 2.60470i
\(28\) 7.72137 + 3.19830i 1.45920 + 0.604421i
\(29\) 2.37185 + 5.72615i 0.440441 + 1.06332i 0.975794 + 0.218691i \(0.0701786\pi\)
−0.535353 + 0.844629i \(0.679821\pi\)
\(30\) 3.15568i 0.576146i
\(31\) 4.72161 1.95575i 0.848026 0.351264i 0.0840130 0.996465i \(-0.473226\pi\)
0.764013 + 0.645201i \(0.223226\pi\)
\(32\) 3.07116 + 3.07116i 0.542909 + 0.542909i
\(33\) 18.1363 3.15712
\(34\) 1.66845 + 0.105478i 0.286137 + 0.0180893i
\(35\) 10.9267 1.84695
\(36\) −9.75711 9.75711i −1.62618 1.62618i
\(37\) 8.39726 3.47826i 1.38050 0.571822i 0.435886 0.900002i \(-0.356435\pi\)
0.944615 + 0.328180i \(0.106435\pi\)
\(38\) 0.673082i 0.109188i
\(39\) 5.37174 + 12.9685i 0.860167 + 2.07663i
\(40\) 3.44819 + 1.42829i 0.545206 + 0.225832i
\(41\) −1.29038 + 3.11525i −0.201523 + 0.486521i −0.992040 0.125919i \(-0.959812\pi\)
0.790517 + 0.612440i \(0.209812\pi\)
\(42\) −4.23343 + 4.23343i −0.653232 + 0.653232i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) −3.92839 + 9.48396i −0.592226 + 1.42976i
\(45\) −16.6672 6.90377i −2.48459 1.02915i
\(46\) 0.119210 + 0.287799i 0.0175766 + 0.0424336i
\(47\) 8.64397i 1.26085i 0.776249 + 0.630426i \(0.217120\pi\)
−0.776249 + 0.630426i \(0.782880\pi\)
\(48\) 9.11019 3.77356i 1.31494 0.544667i
\(49\) −9.70872 9.70872i −1.38696 1.38696i
\(50\) 0.307902 0.0435438
\(51\) 5.88623 12.0061i 0.824236 1.68118i
\(52\) −7.94515 −1.10179
\(53\) 3.96634 + 3.96634i 0.544819 + 0.544819i 0.924938 0.380119i \(-0.124117\pi\)
−0.380119 + 0.924938i \(0.624117\pi\)
\(54\) 5.48775 2.27310i 0.746788 0.309330i
\(55\) 13.4210i 1.80969i
\(56\) −2.70975 6.54191i −0.362105 0.874200i
\(57\) 4.97370 + 2.06018i 0.658783 + 0.272877i
\(58\) 0.961704 2.32176i 0.126278 0.304862i
\(59\) 2.40335 2.40335i 0.312890 0.312890i −0.533138 0.846028i \(-0.678988\pi\)
0.846028 + 0.533138i \(0.178988\pi\)
\(60\) 10.1019 10.1019i 1.30414 1.30414i
\(61\) −1.81077 + 4.37160i −0.231846 + 0.559725i −0.996395 0.0848406i \(-0.972962\pi\)
0.764549 + 0.644566i \(0.222962\pi\)
\(62\) −1.91445 0.792992i −0.243136 0.100710i
\(63\) 13.0979 + 31.6210i 1.65017 + 3.98387i
\(64\) 4.32017i 0.540022i
\(65\) −9.59683 + 3.97514i −1.19034 + 0.493055i
\(66\) −5.19981 5.19981i −0.640052 0.640052i
\(67\) 9.52146 1.16323 0.581616 0.813464i \(-0.302421\pi\)
0.581616 + 0.813464i \(0.302421\pi\)
\(68\) 5.00332 + 5.67863i 0.606742 + 0.688635i
\(69\) 2.49155 0.299948
\(70\) −3.13277 3.13277i −0.374438 0.374438i
\(71\) −0.661153 + 0.273859i −0.0784644 + 0.0325010i −0.421570 0.906796i \(-0.638521\pi\)
0.343106 + 0.939297i \(0.388521\pi\)
\(72\) 11.6909i 1.37778i
\(73\) −4.23025 10.2127i −0.495114 1.19531i −0.952086 0.305829i \(-0.901066\pi\)
0.456973 0.889481i \(-0.348934\pi\)
\(74\) −3.40480 1.41032i −0.395800 0.163946i
\(75\) 0.942428 2.27522i 0.108822 0.262720i
\(76\) −2.15465 + 2.15465i −0.247155 + 0.247155i
\(77\) 18.0046 18.0046i 2.05182 2.05182i
\(78\) 2.17806 5.25830i 0.246617 0.595385i
\(79\) 0.123367 + 0.0511002i 0.0138799 + 0.00574922i 0.389613 0.920979i \(-0.372609\pi\)
−0.375733 + 0.926728i \(0.622609\pi\)
\(80\) 2.79247 + 6.74162i 0.312208 + 0.753736i
\(81\) 24.9572i 2.77302i
\(82\) 1.26313 0.523205i 0.139489 0.0577783i
\(83\) −2.68247 2.68247i −0.294440 0.294440i 0.544391 0.838831i \(-0.316761\pi\)
−0.838831 + 0.544391i \(0.816761\pi\)
\(84\) −27.1038 −2.95727
\(85\) 8.88459 + 4.35586i 0.963669 + 0.472459i
\(86\) 0.405466 0.0437225
\(87\) −14.2129 14.2129i −1.52379 1.52379i
\(88\) 8.03526 3.32831i 0.856561 0.354799i
\(89\) 8.46370i 0.897150i 0.893745 + 0.448575i \(0.148068\pi\)
−0.893745 + 0.448575i \(0.851932\pi\)
\(90\) 2.79924 + 6.75797i 0.295066 + 0.712353i
\(91\) 18.2071 + 7.54164i 1.90863 + 0.790579i
\(92\) −0.539680 + 1.30290i −0.0562655 + 0.135837i
\(93\) −11.7195 + 11.7195i −1.21526 + 1.21526i
\(94\) 2.47829 2.47829i 0.255617 0.255617i
\(95\) −1.52455 + 3.68058i −0.156415 + 0.377620i
\(96\) −13.0132 5.39024i −1.32815 0.550139i
\(97\) 4.92448 + 11.8887i 0.500005 + 1.20712i 0.949481 + 0.313826i \(0.101611\pi\)
−0.449476 + 0.893292i \(0.648389\pi\)
\(98\) 5.56713i 0.562365i
\(99\) −38.8393 + 16.0878i −3.90349 + 1.61688i
\(100\) 0.985643 + 0.985643i 0.0985643 + 0.0985643i
\(101\) −5.15020 −0.512464 −0.256232 0.966615i \(-0.582481\pi\)
−0.256232 + 0.966615i \(0.582481\pi\)
\(102\) −5.12986 + 1.75460i −0.507932 + 0.173732i
\(103\) −4.67620 −0.460759 −0.230380 0.973101i \(-0.573997\pi\)
−0.230380 + 0.973101i \(0.573997\pi\)
\(104\) 4.75989 + 4.75989i 0.466746 + 0.466746i
\(105\) −32.7383 + 13.5606i −3.19493 + 1.32338i
\(106\) 2.27436i 0.220905i
\(107\) −3.16715 7.64618i −0.306180 0.739184i −0.999822 0.0188644i \(-0.993995\pi\)
0.693642 0.720320i \(-0.256005\pi\)
\(108\) 24.8438 + 10.2906i 2.39059 + 0.990215i
\(109\) 5.34114 12.8947i 0.511589 1.23508i −0.431370 0.902175i \(-0.641970\pi\)
0.942959 0.332910i \(-0.108030\pi\)
\(110\) 3.84790 3.84790i 0.366883 0.366883i
\(111\) −20.8429 + 20.8429i −1.97832 + 1.97832i
\(112\) 5.29788 12.7902i 0.500603 1.20856i
\(113\) 7.44737 + 3.08480i 0.700590 + 0.290194i 0.704404 0.709799i \(-0.251214\pi\)
−0.00381456 + 0.999993i \(0.501214\pi\)
\(114\) −0.835331 2.01667i −0.0782359 0.188878i
\(115\) 1.84377i 0.171932i
\(116\) 10.5109 4.35376i 0.975913 0.404236i
\(117\) −23.0074 23.0074i −2.12704 2.12704i
\(118\) −1.37812 −0.126866
\(119\) −6.07541 17.7624i −0.556932 1.62828i
\(120\) −12.1039 −1.10493
\(121\) 14.3364 + 14.3364i 1.30331 + 1.30331i
\(122\) 1.77253 0.734207i 0.160478 0.0664720i
\(123\) 10.9353i 0.985998i
\(124\) −3.58998 8.66697i −0.322390 0.778317i
\(125\) −9.40227 3.89455i −0.840965 0.348339i
\(126\) 5.31073 12.8212i 0.473118 1.14221i
\(127\) −6.22170 + 6.22170i −0.552087 + 0.552087i −0.927043 0.374956i \(-0.877658\pi\)
0.374956 + 0.927043i \(0.377658\pi\)
\(128\) 7.38094 7.38094i 0.652389 0.652389i
\(129\) 1.24105 2.99617i 0.109269 0.263798i
\(130\) 3.89119 + 1.61178i 0.341280 + 0.141363i
\(131\) −3.21824 7.76952i −0.281179 0.678826i 0.718685 0.695336i \(-0.244744\pi\)
−0.999864 + 0.0165102i \(0.994744\pi\)
\(132\) 33.2909i 2.89760i
\(133\) 6.98282 2.89238i 0.605487 0.250801i
\(134\) −2.72988 2.72988i −0.235825 0.235825i
\(135\) 35.1570 3.02584
\(136\) 0.404571 6.39950i 0.0346917 0.548752i
\(137\) −6.39736 −0.546563 −0.273282 0.961934i \(-0.588109\pi\)
−0.273282 + 0.961934i \(0.588109\pi\)
\(138\) −0.714348 0.714348i −0.0608093 0.0608093i
\(139\) 8.13029 3.36768i 0.689602 0.285643i −0.0102324 0.999948i \(-0.503257\pi\)
0.699834 + 0.714305i \(0.253257\pi\)
\(140\) 20.0570i 1.69513i
\(141\) −10.7276 25.8988i −0.903430 2.18107i
\(142\) 0.268075 + 0.111040i 0.0224964 + 0.00931830i
\(143\) −9.26320 + 22.3634i −0.774628 + 1.87012i
\(144\) −16.1624 + 16.1624i −1.34686 + 1.34686i
\(145\) 10.5177 10.5177i 0.873446 0.873446i
\(146\) −1.71522 + 4.14092i −0.141953 + 0.342705i
\(147\) 41.1380 + 17.0399i 3.39301 + 1.40543i
\(148\) −6.38468 15.4140i −0.524818 1.26702i
\(149\) 14.2238i 1.16526i 0.812737 + 0.582631i \(0.197977\pi\)
−0.812737 + 0.582631i \(0.802023\pi\)
\(150\) −0.922525 + 0.382122i −0.0753238 + 0.0312002i
\(151\) −5.17973 5.17973i −0.421520 0.421520i 0.464207 0.885727i \(-0.346339\pi\)
−0.885727 + 0.464207i \(0.846339\pi\)
\(152\) 2.58167 0.209401
\(153\) −1.95554 + 30.9326i −0.158096 + 2.50076i
\(154\) −10.3241 −0.831942
\(155\) −8.67256 8.67256i −0.696597 0.696597i
\(156\) 23.8050 9.86036i 1.90593 0.789460i
\(157\) 3.29791i 0.263202i 0.991303 + 0.131601i \(0.0420117\pi\)
−0.991303 + 0.131601i \(0.957988\pi\)
\(158\) −0.0207194 0.0500211i −0.00164835 0.00397946i
\(159\) −16.8063 6.96138i −1.33282 0.552073i
\(160\) 3.98882 9.62987i 0.315344 0.761308i
\(161\) 2.47347 2.47347i 0.194936 0.194936i
\(162\) −7.15543 + 7.15543i −0.562184 + 0.562184i
\(163\) −4.14963 + 10.0181i −0.325024 + 0.784677i 0.673923 + 0.738801i \(0.264608\pi\)
−0.998947 + 0.0458759i \(0.985392\pi\)
\(164\) 5.71835 + 2.36862i 0.446528 + 0.184958i
\(165\) −16.6562 40.2116i −1.29668 3.13047i
\(166\) 1.53817i 0.119385i
\(167\) −3.21329 + 1.33099i −0.248652 + 0.102995i −0.503529 0.863979i \(-0.667965\pi\)
0.254877 + 0.966974i \(0.417965\pi\)
\(168\) 16.2377 + 16.2377i 1.25277 + 1.25277i
\(169\) −5.73480 −0.441139
\(170\) −1.29842 3.79614i −0.0995845 0.291151i
\(171\) −12.4788 −0.954276
\(172\) 1.29796 + 1.29796i 0.0989688 + 0.0989688i
\(173\) −4.49102 + 1.86024i −0.341446 + 0.141431i −0.546816 0.837253i \(-0.684160\pi\)
0.205370 + 0.978684i \(0.434160\pi\)
\(174\) 8.14991i 0.617843i
\(175\) −1.32312 3.19429i −0.100018 0.241466i
\(176\) 15.7099 + 6.50725i 1.18418 + 0.490503i
\(177\) −4.21816 + 10.1835i −0.317056 + 0.765441i
\(178\) 2.42661 2.42661i 0.181882 0.181882i
\(179\) 13.2994 13.2994i 0.994045 0.994045i −0.00593736 0.999982i \(-0.501890\pi\)
0.999982 + 0.00593736i \(0.00188993\pi\)
\(180\) −12.6725 + 30.5942i −0.944555 + 2.28036i
\(181\) 7.70684 + 3.19228i 0.572845 + 0.237280i 0.650251 0.759720i \(-0.274664\pi\)
−0.0774060 + 0.997000i \(0.524664\pi\)
\(182\) −3.05788 7.38238i −0.226665 0.547218i
\(183\) 15.3453i 1.13436i
\(184\) 1.10388 0.457242i 0.0813791 0.0337083i
\(185\) −15.4239 15.4239i −1.13399 1.13399i
\(186\) 6.72017 0.492747
\(187\) 21.8171 7.46227i 1.59542 0.545695i
\(188\) 15.8669 1.15721
\(189\) −47.1641 47.1641i −3.43068 3.43068i
\(190\) 1.49235 0.618152i 0.108267 0.0448455i
\(191\) 0.0822586i 0.00595202i 0.999996 + 0.00297601i \(0.000947296\pi\)
−0.999996 + 0.00297601i \(0.999053\pi\)
\(192\) −5.36157 12.9440i −0.386938 0.934151i
\(193\) −6.84388 2.83483i −0.492634 0.204055i 0.122515 0.992467i \(-0.460904\pi\)
−0.615149 + 0.788411i \(0.710904\pi\)
\(194\) 1.99671 4.82048i 0.143355 0.346090i
\(195\) 23.8204 23.8204i 1.70581 1.70581i
\(196\) −17.8213 + 17.8213i −1.27295 + 1.27295i
\(197\) −0.815526 + 1.96885i −0.0581038 + 0.140275i −0.950265 0.311442i \(-0.899188\pi\)
0.892161 + 0.451717i \(0.149188\pi\)
\(198\) 15.7480 + 6.52304i 1.11916 + 0.463572i
\(199\) 4.04060 + 9.75487i 0.286430 + 0.691504i 0.999958 0.00912244i \(-0.00290380\pi\)
−0.713528 + 0.700627i \(0.752904\pi\)
\(200\) 1.18099i 0.0835083i
\(201\) −28.5279 + 11.8166i −2.01220 + 0.833482i
\(202\) 1.47660 + 1.47660i 0.103893 + 0.103893i
\(203\) −28.2195 −1.98062
\(204\) −22.0383 10.8047i −1.54299 0.756483i
\(205\) 8.09218 0.565182
\(206\) 1.34070 + 1.34070i 0.0934112 + 0.0934112i
\(207\) −5.33572 + 2.21013i −0.370858 + 0.153615i
\(208\) 13.1609i 0.912544i
\(209\) 3.55263 + 8.57681i 0.245741 + 0.593271i
\(210\) 13.2743 + 5.49838i 0.916011 + 0.379424i
\(211\) −6.27317 + 15.1448i −0.431863 + 1.04261i 0.546823 + 0.837248i \(0.315837\pi\)
−0.978686 + 0.205361i \(0.934163\pi\)
\(212\) 7.28060 7.28060i 0.500034 0.500034i
\(213\) 1.64105 1.64105i 0.112443 0.112443i
\(214\) −1.28417 + 3.10027i −0.0877843 + 0.211930i
\(215\) 2.21719 + 0.918391i 0.151211 + 0.0626337i
\(216\) −8.71870 21.0488i −0.593232 1.43219i
\(217\) 23.2689i 1.57960i
\(218\) −5.22835 + 2.16565i −0.354108 + 0.146677i
\(219\) 25.3491 + 25.3491i 1.71293 + 1.71293i
\(220\) 24.6355 1.66093
\(221\) 11.7979 + 13.3903i 0.793615 + 0.900730i
\(222\) 11.9516 0.802142
\(223\) 7.08170 + 7.08170i 0.474226 + 0.474226i 0.903279 0.429054i \(-0.141153\pi\)
−0.429054 + 0.903279i \(0.641153\pi\)
\(224\) −18.2698 + 7.56761i −1.22070 + 0.505632i
\(225\) 5.70842i 0.380561i
\(226\) −1.25078 3.01966i −0.0832008 0.200865i
\(227\) −22.0414 9.12986i −1.46294 0.605970i −0.497704 0.867347i \(-0.665823\pi\)
−0.965237 + 0.261377i \(0.915823\pi\)
\(228\) 3.78165 9.12972i 0.250446 0.604630i
\(229\) −11.1342 + 11.1342i −0.735767 + 0.735767i −0.971756 0.235989i \(-0.924167\pi\)
0.235989 + 0.971756i \(0.424167\pi\)
\(230\) 0.528623 0.528623i 0.0348564 0.0348564i
\(231\) −31.6002 + 76.2896i −2.07914 + 5.01948i
\(232\) −8.90533 3.68871i −0.584664 0.242176i
\(233\) −8.58988 20.7378i −0.562742 1.35858i −0.907565 0.419912i \(-0.862061\pi\)
0.344823 0.938668i \(-0.387939\pi\)
\(234\) 13.1928i 0.862442i
\(235\) 19.1653 7.93854i 1.25021 0.517853i
\(236\) −4.41158 4.41158i −0.287170 0.287170i
\(237\) −0.433046 −0.0281294
\(238\) −3.35075 + 6.83449i −0.217197 + 0.443014i
\(239\) 24.9203 1.61196 0.805979 0.591944i \(-0.201639\pi\)
0.805979 + 0.591944i \(0.201639\pi\)
\(240\) −16.7334 16.7334i −1.08014 1.08014i
\(241\) −2.68104 + 1.11053i −0.172701 + 0.0715352i −0.467359 0.884068i \(-0.654794\pi\)
0.294658 + 0.955603i \(0.404794\pi\)
\(242\) 8.22073i 0.528448i
\(243\) 14.1548 + 34.1728i 0.908033 + 2.19218i
\(244\) 8.02449 + 3.32385i 0.513715 + 0.212788i
\(245\) −12.6097 + 30.4425i −0.805603 + 1.94490i
\(246\) −3.13522 + 3.13522i −0.199894 + 0.199894i
\(247\) −5.08070 + 5.08070i −0.323277 + 0.323277i
\(248\) −3.04160 + 7.34307i −0.193142 + 0.466285i
\(249\) 11.3662 + 4.70805i 0.720306 + 0.298361i
\(250\) 1.57911 + 3.81230i 0.0998715 + 0.241111i
\(251\) 0.831872i 0.0525073i 0.999655 + 0.0262536i \(0.00835775\pi\)
−0.999655 + 0.0262536i \(0.991642\pi\)
\(252\) 58.0434 24.0424i 3.65639 1.51453i
\(253\) 3.03809 + 3.03809i 0.191003 + 0.191003i
\(254\) 3.56762 0.223852
\(255\) −32.0256 2.02463i −2.00552 0.126787i
\(256\) 4.40800 0.275500
\(257\) 21.5934 + 21.5934i 1.34696 + 1.34696i 0.888947 + 0.458011i \(0.151438\pi\)
0.458011 + 0.888947i \(0.348562\pi\)
\(258\) −1.21484 + 0.503205i −0.0756329 + 0.0313282i
\(259\) 41.3832i 2.57143i
\(260\) 7.29675 + 17.6159i 0.452525 + 1.09249i
\(261\) 43.0449 + 17.8298i 2.66441 + 1.10363i
\(262\) −1.30489 + 3.15028i −0.0806162 + 0.194625i
\(263\) −6.32219 + 6.32219i −0.389843 + 0.389843i −0.874631 0.484789i \(-0.838897\pi\)
0.484789 + 0.874631i \(0.338897\pi\)
\(264\) −19.9444 + 19.9444i −1.22749 + 1.22749i
\(265\) 5.15148 12.4368i 0.316453 0.763985i
\(266\) −2.83130 1.17276i −0.173598 0.0719066i
\(267\) −10.5039 25.3587i −0.642828 1.55193i
\(268\) 17.4776i 1.06761i
\(269\) −7.15121 + 2.96213i −0.436017 + 0.180604i −0.589885 0.807487i \(-0.700827\pi\)
0.153868 + 0.988091i \(0.450827\pi\)
\(270\) −10.0798 10.0798i −0.613437 0.613437i
\(271\) 21.0463 1.27847 0.639235 0.769011i \(-0.279251\pi\)
0.639235 + 0.769011i \(0.279251\pi\)
\(272\) 9.40648 8.28786i 0.570352 0.502525i
\(273\) −63.9112 −3.86808
\(274\) 1.83417 + 1.83417i 0.110806 + 0.110806i
\(275\) 3.92346 1.62515i 0.236594 0.0980004i
\(276\) 4.57349i 0.275292i
\(277\) 9.72643 + 23.4817i 0.584405 + 1.41088i 0.888784 + 0.458327i \(0.151551\pi\)
−0.304379 + 0.952551i \(0.598449\pi\)
\(278\) −3.29656 1.36548i −0.197714 0.0818959i
\(279\) 14.7019 35.4935i 0.880179 2.12494i
\(280\) −12.0161 + 12.0161i −0.718097 + 0.718097i
\(281\) 0.806536 0.806536i 0.0481139 0.0481139i −0.682640 0.730754i \(-0.739168\pi\)
0.730754 + 0.682640i \(0.239168\pi\)
\(282\) −4.34969 + 10.5011i −0.259020 + 0.625330i
\(283\) −15.0631 6.23936i −0.895411 0.370891i −0.112957 0.993600i \(-0.536032\pi\)
−0.782454 + 0.622708i \(0.786032\pi\)
\(284\) 0.502694 + 1.21361i 0.0298294 + 0.0720145i
\(285\) 12.9197i 0.765297i
\(286\) 9.06758 3.75591i 0.536177 0.222092i
\(287\) −10.8559 10.8559i −0.640802 0.640802i
\(288\) 32.6494 1.92389
\(289\) 2.14090 16.8647i 0.125935 0.992038i
\(290\) −6.03100 −0.354153
\(291\) −29.5091 29.5091i −1.72986 1.72986i
\(292\) −18.7465 + 7.76504i −1.09705 + 0.454415i
\(293\) 31.4338i 1.83638i 0.396139 + 0.918191i \(0.370350\pi\)
−0.396139 + 0.918191i \(0.629650\pi\)
\(294\) −6.90911 16.6801i −0.402947 0.972801i
\(295\) −7.53590 3.12147i −0.438757 0.181739i
\(296\) −5.40940 + 13.0595i −0.314415 + 0.759066i
\(297\) 57.9304 57.9304i 3.36146 3.36146i
\(298\) 4.07808 4.07808i 0.236237 0.236237i
\(299\) −1.27257 + 3.07227i −0.0735949 + 0.177674i
\(300\) −4.17639 1.72992i −0.241124 0.0998768i
\(301\) −1.74237 4.20646i −0.100429 0.242457i
\(302\) 2.97014i 0.170912i
\(303\) 15.4309 6.39168i 0.886480 0.367192i
\(304\) 3.56911 + 3.56911i 0.204702 + 0.204702i
\(305\) 11.3557 0.650223
\(306\) 9.42930 8.30796i 0.539037 0.474934i
\(307\) 11.2028 0.639379 0.319689 0.947522i \(-0.396421\pi\)
0.319689 + 0.947522i \(0.396421\pi\)
\(308\) −33.0492 33.0492i −1.88315 1.88315i
\(309\) 14.0107 5.80341i 0.797040 0.330145i
\(310\) 4.97298i 0.282446i
\(311\) 1.63471 + 3.94655i 0.0926962 + 0.223788i 0.963427 0.267972i \(-0.0863535\pi\)
−0.870730 + 0.491761i \(0.836354\pi\)
\(312\) −20.1687 8.35416i −1.14183 0.472961i
\(313\) −8.85433 + 21.3763i −0.500477 + 1.20826i 0.448748 + 0.893658i \(0.351870\pi\)
−0.949225 + 0.314599i \(0.898130\pi\)
\(314\) 0.945535 0.945535i 0.0533596 0.0533596i
\(315\) 58.0809 58.0809i 3.27249 3.27249i
\(316\) 0.0937994 0.226452i 0.00527663 0.0127389i
\(317\) 16.8901 + 6.99609i 0.948640 + 0.392940i 0.802720 0.596357i \(-0.203386\pi\)
0.145921 + 0.989296i \(0.453386\pi\)
\(318\) 2.82260 + 6.81437i 0.158284 + 0.382131i
\(319\) 34.6613i 1.94066i
\(320\) 9.57865 3.96761i 0.535463 0.221796i
\(321\) 18.9787 + 18.9787i 1.05928 + 1.05928i
\(322\) −1.41832 −0.0790401
\(323\) 6.83081 + 0.431838i 0.380076 + 0.0240281i
\(324\) −45.8114 −2.54508
\(325\) 2.32416 + 2.32416i 0.128921 + 0.128921i
\(326\) 4.06200 1.68253i 0.224973 0.0931869i
\(327\) 45.2632i 2.50306i
\(328\) −2.00680 4.84485i −0.110807 0.267512i
\(329\) −36.3606 15.0610i −2.00462 0.830342i
\(330\) −6.75352 + 16.3044i −0.371769 + 0.897529i
\(331\) 21.3978 21.3978i 1.17613 1.17613i 0.195408 0.980722i \(-0.437397\pi\)
0.980722 0.195408i \(-0.0626031\pi\)
\(332\) −4.92394 + 4.92394i −0.270236 + 0.270236i
\(333\) 26.1469 63.1243i 1.43284 3.45919i
\(334\) 1.30288 + 0.539671i 0.0712904 + 0.0295295i
\(335\) −8.74442 21.1109i −0.477759 1.15341i
\(336\) 44.8966i 2.44931i
\(337\) 0.389486 0.161331i 0.0212167 0.00878824i −0.372050 0.928213i \(-0.621345\pi\)
0.393267 + 0.919425i \(0.371345\pi\)
\(338\) 1.64421 + 1.64421i 0.0894334 + 0.0894334i
\(339\) −26.1420 −1.41984
\(340\) 7.99560 16.3085i 0.433622 0.884454i
\(341\) −28.5806 −1.54773
\(342\) 3.57776 + 3.57776i 0.193463 + 0.193463i
\(343\) 28.3104 11.7265i 1.52862 0.633173i
\(344\) 1.55520i 0.0838510i
\(345\) −2.28822 5.52425i −0.123194 0.297416i
\(346\) 1.82095 + 0.754264i 0.0978951 + 0.0405495i
\(347\) 1.22276 2.95200i 0.0656411 0.158472i −0.887655 0.460509i \(-0.847667\pi\)
0.953296 + 0.302038i \(0.0976668\pi\)
\(348\) −26.0892 + 26.0892i −1.39853 + 1.39853i
\(349\) −9.05965 + 9.05965i −0.484952 + 0.484952i −0.906709 0.421757i \(-0.861414\pi\)
0.421757 + 0.906709i \(0.361414\pi\)
\(350\) −0.536480 + 1.29518i −0.0286760 + 0.0692301i
\(351\) 58.5820 + 24.2655i 3.12688 + 1.29519i
\(352\) −9.29510 22.4403i −0.495430 1.19607i
\(353\) 1.44106i 0.0766999i 0.999264 + 0.0383499i \(0.0122102\pi\)
−0.999264 + 0.0383499i \(0.987790\pi\)
\(354\) 4.12908 1.71032i 0.219458 0.0909024i
\(355\) 1.21439 + 1.21439i 0.0644533 + 0.0644533i
\(356\) 15.5359 0.823403
\(357\) 40.2470 + 45.6792i 2.13010 + 2.41760i
\(358\) −7.62609 −0.403052
\(359\) −6.06951 6.06951i −0.320337 0.320337i 0.528560 0.848896i \(-0.322732\pi\)
−0.848896 + 0.528560i \(0.822732\pi\)
\(360\) 25.9208 10.7368i 1.36615 0.565877i
\(361\) 16.2443i 0.854965i
\(362\) −1.29436 3.12486i −0.0680301 0.164239i
\(363\) −60.7466 25.1621i −3.18837 1.32067i
\(364\) 13.8434 33.4210i 0.725592 1.75173i
\(365\) −18.7586 + 18.7586i −0.981868 + 0.981868i
\(366\) −4.39962 + 4.39962i −0.229972 + 0.229972i
\(367\) −3.06051 + 7.38874i −0.159758 + 0.385689i −0.983408 0.181409i \(-0.941934\pi\)
0.823650 + 0.567098i \(0.191934\pi\)
\(368\) 2.15822 + 0.893964i 0.112505 + 0.0466011i
\(369\) 9.70010 + 23.4181i 0.504967 + 1.21910i
\(370\) 8.84432i 0.459794i
\(371\) −23.5951 + 9.77341i −1.22500 + 0.507410i
\(372\) 21.5124 + 21.5124i 1.11536 + 1.11536i
\(373\) 16.8403 0.871959 0.435979 0.899957i \(-0.356402\pi\)
0.435979 + 0.899957i \(0.356402\pi\)
\(374\) −8.39462 4.11564i −0.434076 0.212815i
\(375\) 33.0041 1.70433
\(376\) −9.50574 9.50574i −0.490221 0.490221i
\(377\) 24.7849 10.2662i 1.27649 0.528739i
\(378\) 27.0446i 1.39102i
\(379\) −12.8898 31.1187i −0.662103 1.59846i −0.794502 0.607262i \(-0.792268\pi\)
0.132399 0.991197i \(-0.457732\pi\)
\(380\) 6.75607 + 2.79846i 0.346579 + 0.143558i
\(381\) 10.9198 26.3627i 0.559438 1.35060i
\(382\) 0.0235842 0.0235842i 0.00120667 0.00120667i
\(383\) 9.38111 9.38111i 0.479352 0.479352i −0.425572 0.904924i \(-0.639927\pi\)
0.904924 + 0.425572i \(0.139927\pi\)
\(384\) −12.9544 + 31.2747i −0.661077 + 1.59598i
\(385\) −56.4549 23.3844i −2.87721 1.19178i
\(386\) 1.14943 + 2.77496i 0.0585043 + 0.141242i
\(387\) 7.51724i 0.382123i
\(388\) 21.8229 9.03935i 1.10789 0.458904i
\(389\) −2.18588 2.18588i −0.110829 0.110829i 0.649518 0.760346i \(-0.274971\pi\)
−0.760346 + 0.649518i \(0.774971\pi\)
\(390\) −13.6590 −0.691649
\(391\) 2.99722 1.02516i 0.151576 0.0518447i
\(392\) 21.3533 1.07850
\(393\) 19.2848 + 19.2848i 0.972788 + 0.972788i
\(394\) 0.798303 0.330668i 0.0402179 0.0166588i
\(395\) 0.320458i 0.0161240i
\(396\) 29.5306 + 71.2932i 1.48397 + 3.58262i
\(397\) 10.8523 + 4.49517i 0.544662 + 0.225606i 0.638011 0.770027i \(-0.279757\pi\)
−0.0933495 + 0.995633i \(0.529757\pi\)
\(398\) 1.63833 3.95527i 0.0821219 0.198260i
\(399\) −17.3321 + 17.3321i −0.867691 + 0.867691i
\(400\) 1.63269 1.63269i 0.0816344 0.0816344i
\(401\) 1.05178 2.53922i 0.0525234 0.126803i −0.895440 0.445183i \(-0.853139\pi\)
0.947963 + 0.318380i \(0.103139\pi\)
\(402\) 11.5671 + 4.79125i 0.576914 + 0.238966i
\(403\) −8.46523 20.4369i −0.421683 1.01803i
\(404\) 9.45369i 0.470339i
\(405\) −55.3349 + 22.9205i −2.74961 + 1.13893i
\(406\) 8.09075 + 8.09075i 0.401537 + 0.401537i
\(407\) −50.8299 −2.51954
\(408\) 6.72996 + 19.6761i 0.333182 + 0.974111i
\(409\) 18.1659 0.898248 0.449124 0.893470i \(-0.351736\pi\)
0.449124 + 0.893470i \(0.351736\pi\)
\(410\) −2.32009 2.32009i −0.114581 0.114581i
\(411\) 19.1676 7.93946i 0.945466 0.391625i
\(412\) 8.58362i 0.422884i
\(413\) 5.92207 + 14.2971i 0.291406 + 0.703516i
\(414\) 2.16345 + 0.896132i 0.106328 + 0.0440425i
\(415\) −3.48400 + 8.41112i −0.171023 + 0.412885i
\(416\) 13.2931 13.2931i 0.651749 0.651749i
\(417\) −20.1803 + 20.1803i −0.988231 + 0.988231i
\(418\) 1.44047 3.47761i 0.0704558 0.170095i
\(419\) 26.9899 + 11.1796i 1.31855 + 0.546159i 0.927366 0.374155i \(-0.122067\pi\)
0.391179 + 0.920315i \(0.372067\pi\)
\(420\) 24.8919 + 60.0943i 1.21460 + 2.93230i
\(421\) 8.73908i 0.425917i 0.977061 + 0.212958i \(0.0683099\pi\)
−0.977061 + 0.212958i \(0.931690\pi\)
\(422\) 6.14069 2.54356i 0.298924 0.123818i
\(423\) 45.9470 + 45.9470i 2.23402 + 2.23402i
\(424\) −8.72353 −0.423652
\(425\) 0.197544 3.12475i 0.00958231 0.151573i
\(426\) −0.941005 −0.0455919
\(427\) −15.2339 15.2339i −0.737221 0.737221i
\(428\) −14.0353 + 5.81362i −0.678422 + 0.281012i
\(429\) 78.5005i 3.79004i
\(430\) −0.372376 0.898996i −0.0179576 0.0433534i
\(431\) 13.5438 + 5.61001i 0.652380 + 0.270225i 0.684228 0.729268i \(-0.260139\pi\)
−0.0318482 + 0.999493i \(0.510139\pi\)
\(432\) 17.0461 41.1529i 0.820131 1.97997i
\(433\) −9.96613 + 9.96613i −0.478942 + 0.478942i −0.904793 0.425852i \(-0.859975\pi\)
0.425852 + 0.904793i \(0.359975\pi\)
\(434\) 6.67139 6.67139i 0.320237 0.320237i
\(435\) −18.4597 + 44.5658i −0.885077 + 2.13677i
\(436\) −23.6694 9.80419i −1.13356 0.469536i
\(437\) 0.488059 + 1.17828i 0.0233470 + 0.0563647i
\(438\) 14.5356i 0.694536i
\(439\) −0.610895 + 0.253041i −0.0291564 + 0.0120770i −0.397214 0.917726i \(-0.630023\pi\)
0.368058 + 0.929803i \(0.380023\pi\)
\(440\) −14.7590 14.7590i −0.703608 0.703608i
\(441\) −103.213 −4.91492
\(442\) 0.456548 7.22167i 0.0217158 0.343500i
\(443\) −12.1011 −0.574939 −0.287470 0.957790i \(-0.592814\pi\)
−0.287470 + 0.957790i \(0.592814\pi\)
\(444\) 38.2592 + 38.2592i 1.81570 + 1.81570i
\(445\) 18.7656 7.77298i 0.889576 0.368475i
\(446\) 4.06076i 0.192282i
\(447\) −17.6525 42.6170i −0.834937 2.01572i
\(448\) −18.1727 7.52736i −0.858577 0.355634i
\(449\) −9.44546 + 22.8034i −0.445759 + 1.07616i 0.528136 + 0.849160i \(0.322891\pi\)
−0.973895 + 0.226998i \(0.927109\pi\)
\(450\) 1.63665 1.63665i 0.0771524 0.0771524i
\(451\) 13.3340 13.3340i 0.627873 0.627873i
\(452\) 5.66245 13.6704i 0.266339 0.643000i
\(453\) 21.9477 + 9.09102i 1.03119 + 0.427133i
\(454\) 3.70185 + 8.93705i 0.173736 + 0.419436i
\(455\) 47.2949i 2.21722i
\(456\) −7.73513 + 3.20399i −0.362231 + 0.150041i
\(457\) 6.21464 + 6.21464i 0.290709 + 0.290709i 0.837360 0.546651i \(-0.184098\pi\)
−0.546651 + 0.837360i \(0.684098\pi\)
\(458\) 6.38451 0.298328
\(459\) −19.5478 57.1511i −0.912414 2.66758i
\(460\) 3.38442 0.157799
\(461\) 4.60808 + 4.60808i 0.214619 + 0.214619i 0.806226 0.591607i \(-0.201506\pi\)
−0.591607 + 0.806226i \(0.701506\pi\)
\(462\) 30.9328 12.8128i 1.43913 0.596105i
\(463\) 8.11992i 0.377365i 0.982038 + 0.188682i \(0.0604217\pi\)
−0.982038 + 0.188682i \(0.939578\pi\)
\(464\) −7.21187 17.4110i −0.334803 0.808285i
\(465\) 36.7476 + 15.2213i 1.70413 + 0.705873i
\(466\) −3.48291 + 8.40848i −0.161343 + 0.389515i
\(467\) 0.912506 0.912506i 0.0422258 0.0422258i −0.685679 0.727904i \(-0.740494\pi\)
0.727904 + 0.685679i \(0.240494\pi\)
\(468\) −42.2324 + 42.2324i −1.95219 + 1.95219i
\(469\) −16.5899 + 40.0517i −0.766052 + 1.84941i
\(470\) −7.77089 3.21881i −0.358445 0.148473i
\(471\) −4.09288 9.88108i −0.188590 0.455296i
\(472\) 5.28591i 0.243304i
\(473\) 5.16669 2.14011i 0.237565 0.0984025i
\(474\) 0.124158 + 0.124158i 0.00570275 + 0.00570275i
\(475\) 1.26058 0.0578395
\(476\) −32.6046 + 11.1520i −1.49443 + 0.511151i
\(477\) 42.1661 1.93065
\(478\) −7.14484 7.14484i −0.326797 0.326797i
\(479\) −26.8502 + 11.1217i −1.22682 + 0.508165i −0.899571 0.436774i \(-0.856121\pi\)
−0.327247 + 0.944939i \(0.606121\pi\)
\(480\) 33.8031i 1.54289i
\(481\) −15.0552 36.3465i −0.686458 1.65726i
\(482\) 1.08707 + 0.450280i 0.0495148 + 0.0205097i
\(483\) −4.34122 + 10.4806i −0.197532 + 0.476885i
\(484\) 26.3159 26.3159i 1.19618 1.19618i
\(485\) 21.8370 21.8370i 0.991567 0.991567i
\(486\) 5.73930 13.8559i 0.260340 0.628516i
\(487\) 31.0084 + 12.8441i 1.40513 + 0.582022i 0.951077 0.308954i \(-0.0999789\pi\)
0.454049 + 0.890976i \(0.349979\pi\)
\(488\) −2.81612 6.79872i −0.127480 0.307764i
\(489\) 35.1658i 1.59025i
\(490\) 12.3434 5.11280i 0.557618 0.230973i
\(491\) 13.4107 + 13.4107i 0.605216 + 0.605216i 0.941692 0.336476i \(-0.109235\pi\)
−0.336476 + 0.941692i \(0.609235\pi\)
\(492\) −20.0727 −0.904948
\(493\) −22.9455 11.2495i −1.03341 0.506652i
\(494\) 2.91335 0.131078
\(495\) 71.3392 + 71.3392i 3.20646 + 3.20646i
\(496\) −14.3566 + 5.94669i −0.644630 + 0.267014i
\(497\) 3.25828i 0.146154i
\(498\) −1.90895 4.60862i −0.0855423 0.206517i
\(499\) −17.3379 7.18159i −0.776151 0.321492i −0.0407897 0.999168i \(-0.512987\pi\)
−0.735361 + 0.677676i \(0.762987\pi\)
\(500\) −7.14882 + 17.2588i −0.319705 + 0.771836i
\(501\) 7.97573 7.97573i 0.356329 0.356329i
\(502\) 0.238504 0.238504i 0.0106450 0.0106450i
\(503\) 7.59224 18.3293i 0.338521 0.817263i −0.659337 0.751848i \(-0.729163\pi\)
0.997858 0.0654153i \(-0.0208372\pi\)
\(504\) −49.1771 20.3698i −2.19052 0.907345i
\(505\) 4.72990 + 11.4190i 0.210478 + 0.508138i
\(506\) 1.74209i 0.0774454i
\(507\) 17.1824 7.11720i 0.763099 0.316086i
\(508\) 11.4205 + 11.4205i 0.506704 + 0.506704i
\(509\) −36.9100 −1.63600 −0.818002 0.575215i \(-0.804918\pi\)
−0.818002 + 0.575215i \(0.804918\pi\)
\(510\) 8.60151 + 9.76246i 0.380881 + 0.432289i
\(511\) 50.3302 2.22648
\(512\) −16.0257 16.0257i −0.708242 0.708242i
\(513\) 22.4674 9.30632i 0.991961 0.410884i
\(514\) 12.3820i 0.546145i
\(515\) 4.29458 + 10.3680i 0.189242 + 0.456870i
\(516\) −5.49976 2.27808i −0.242113 0.100287i
\(517\) 18.4991 44.6607i 0.813588 1.96418i
\(518\) 11.8649 11.8649i 0.521313 0.521313i
\(519\) 11.1472 11.1472i 0.489307 0.489307i
\(520\) 6.18215 14.9250i 0.271105 0.654506i
\(521\) 12.7631 + 5.28666i 0.559163 + 0.231613i 0.644322 0.764755i \(-0.277140\pi\)
−0.0851590 + 0.996367i \(0.527140\pi\)
\(522\) −7.22937 17.4532i −0.316421 0.763907i
\(523\) 8.74761i 0.382506i 0.981541 + 0.191253i \(0.0612552\pi\)
−0.981541 + 0.191253i \(0.938745\pi\)
\(524\) −14.2617 + 5.90739i −0.623025 + 0.258066i
\(525\) 7.92857 + 7.92857i 0.346031 + 0.346031i
\(526\) 3.62524 0.158068
\(527\) −9.27600 + 18.9201i −0.404069 + 0.824174i
\(528\) −55.1454 −2.39989
\(529\) −15.8461 15.8461i −0.688960 0.688960i
\(530\) −5.04269 + 2.08875i −0.219041 + 0.0907295i
\(531\) 25.5500i 1.10877i
\(532\) −5.30924 12.8176i −0.230185 0.555715i
\(533\) 13.4840 + 5.58524i 0.584055 + 0.241924i
\(534\) −4.25898 + 10.2821i −0.184304 + 0.444949i
\(535\) −14.0444 + 14.0444i −0.607191 + 0.607191i
\(536\) −10.4707 + 10.4707i −0.452266 + 0.452266i
\(537\) −23.3420 + 56.3526i −1.00728 + 2.43179i
\(538\) 2.89957 + 1.20104i 0.125010 + 0.0517806i
\(539\) 29.3842 + 70.9397i 1.26567 + 3.05559i
\(540\) 64.5342i 2.77711i
\(541\) 15.5904 6.45777i 0.670285 0.277641i −0.0214742 0.999769i \(-0.506836\pi\)
0.691759 + 0.722128i \(0.256836\pi\)
\(542\) −6.03413 6.03413i −0.259188 0.259188i
\(543\) −27.0528 −1.16095
\(544\) −17.8721 1.12986i −0.766260 0.0484424i
\(545\) −33.4952 −1.43478
\(546\) 18.3239 + 18.3239i 0.784189 + 0.784189i
\(547\) −1.38472 + 0.573570i −0.0592063 + 0.0245241i −0.412090 0.911143i \(-0.635201\pi\)
0.352884 + 0.935667i \(0.385201\pi\)
\(548\) 11.7430i 0.501635i
\(549\) 13.6120 + 32.8623i 0.580947 + 1.40253i
\(550\) −1.59083 0.658944i −0.0678333 0.0280975i
\(551\) 3.93732 9.50553i 0.167735 0.404949i
\(552\) −2.73995 + 2.73995i −0.116620 + 0.116620i
\(553\) −0.429902 + 0.429902i −0.0182813 + 0.0182813i
\(554\) 3.94374 9.52103i 0.167553 0.404510i
\(555\) 65.3546 + 27.0708i 2.77415 + 1.14909i
\(556\) −6.18170 14.9239i −0.262162 0.632916i
\(557\) 4.01932i 0.170304i 0.996368 + 0.0851520i \(0.0271376\pi\)
−0.996368 + 0.0851520i \(0.972862\pi\)
\(558\) −14.3914 + 5.96112i −0.609237 + 0.252354i
\(559\) 3.06062 + 3.06062i 0.129450 + 0.129450i
\(560\) −33.2239 −1.40397
\(561\) −56.1066 + 49.4344i −2.36882 + 2.08712i
\(562\) −0.462480 −0.0195085
\(563\) −0.295624 0.295624i −0.0124590 0.0124590i 0.700850 0.713309i \(-0.252804\pi\)
−0.713309 + 0.700850i \(0.752804\pi\)
\(564\) −47.5398 + 19.6916i −2.00179 + 0.829167i
\(565\) 19.3453i 0.813863i
\(566\) 2.52985 + 6.10759i 0.106337 + 0.256721i
\(567\) 104.982 + 43.4848i 4.40881 + 1.82619i
\(568\) 0.425906 1.02823i 0.0178706 0.0431435i
\(569\) 1.37231 1.37231i 0.0575303 0.0575303i −0.677756 0.735287i \(-0.737048\pi\)
0.735287 + 0.677756i \(0.237048\pi\)
\(570\) −3.70418 + 3.70418i −0.155151 + 0.155151i
\(571\) −12.0521 + 29.0964i −0.504366 + 1.21765i 0.442717 + 0.896661i \(0.354015\pi\)
−0.947084 + 0.320987i \(0.895985\pi\)
\(572\) 41.0501 + 17.0035i 1.71639 + 0.710953i
\(573\) −0.102087 0.246461i −0.00426476 0.0102960i
\(574\) 6.22492i 0.259823i
\(575\) 0.539004 0.223263i 0.0224780 0.00931070i
\(576\) 22.9639 + 22.9639i 0.956827 + 0.956827i
\(577\) −46.3934 −1.93138 −0.965690 0.259696i \(-0.916378\pi\)
−0.965690 + 0.259696i \(0.916378\pi\)
\(578\) −5.44904 + 4.22142i −0.226650 + 0.175588i
\(579\) 24.0236 0.998387
\(580\) −19.3062 19.3062i −0.801648 0.801648i
\(581\) 15.9576 6.60986i 0.662033 0.274223i
\(582\) 16.9210i 0.701398i
\(583\) −12.0044 28.9813i −0.497173 1.20028i
\(584\) 15.8829 + 6.57891i 0.657238 + 0.272237i
\(585\) −29.8821 + 72.1417i −1.23547 + 2.98269i
\(586\) 9.01231 9.01231i 0.372295 0.372295i
\(587\) 15.4552 15.4552i 0.637904 0.637904i −0.312134 0.950038i \(-0.601044\pi\)
0.950038 + 0.312134i \(0.101044\pi\)
\(588\) 31.2784 75.5128i 1.28990 3.11410i
\(589\) −7.83797 3.24659i −0.322958 0.133774i
\(590\) 1.26565 + 3.05555i 0.0521060 + 0.125795i
\(591\) 6.91113i 0.284286i
\(592\) −25.5328 + 10.5760i −1.04939 + 0.434672i
\(593\) −13.1313 13.1313i −0.539237 0.539237i 0.384068 0.923305i \(-0.374523\pi\)
−0.923305 + 0.384068i \(0.874523\pi\)
\(594\) −33.2182 −1.36296
\(595\) −33.8030 + 29.7832i −1.38579 + 1.22099i
\(596\) 26.1092 1.06948
\(597\) −24.2126 24.2126i −0.990957 0.990957i
\(598\) 1.24570 0.515986i 0.0509405 0.0211002i
\(599\) 4.75635i 0.194339i −0.995268 0.0971696i \(-0.969021\pi\)
0.995268 0.0971696i \(-0.0309789\pi\)
\(600\) 1.46567 + 3.53843i 0.0598356 + 0.144456i
\(601\) 28.0904 + 11.6354i 1.14583 + 0.474618i 0.873133 0.487482i \(-0.162085\pi\)
0.272696 + 0.962100i \(0.412085\pi\)
\(602\) −0.706474 + 1.70558i −0.0287937 + 0.0695142i
\(603\) 50.6113 50.6113i 2.06105 2.06105i
\(604\) −9.50789 + 9.50789i −0.386871 + 0.386871i
\(605\) 18.6202 44.9530i 0.757017 1.82760i
\(606\) −6.25669 2.59161i −0.254161 0.105277i
\(607\) 1.05182 + 2.53933i 0.0426922 + 0.103068i 0.943787 0.330554i \(-0.107235\pi\)
−0.901095 + 0.433622i \(0.857235\pi\)
\(608\) 7.20993i 0.292401i
\(609\) 84.5504 35.0219i 3.42615 1.41916i
\(610\) −3.25576 3.25576i −0.131822 0.131822i
\(611\) 37.4143 1.51362
\(612\) 56.7799 + 3.58958i 2.29519 + 0.145100i
\(613\) 18.6755 0.754295 0.377147 0.926153i \(-0.376905\pi\)
0.377147 + 0.926153i \(0.376905\pi\)
\(614\) −3.21193 3.21193i −0.129623 0.129623i
\(615\) −24.2455 + 10.0428i −0.977674 + 0.404966i
\(616\) 39.5992i 1.59550i
\(617\) 16.8537 + 40.6885i 0.678506 + 1.63806i 0.766740 + 0.641958i \(0.221878\pi\)
−0.0882345 + 0.996100i \(0.528122\pi\)
\(618\) −5.68085 2.35309i −0.228517 0.0946550i
\(619\) −4.44398 + 10.7287i −0.178619 + 0.431223i −0.987677 0.156505i \(-0.949977\pi\)
0.809059 + 0.587728i \(0.199977\pi\)
\(620\) −15.9193 + 15.9193i −0.639336 + 0.639336i
\(621\) 7.95845 7.95845i 0.319362 0.319362i
\(622\) 0.662821 1.60019i 0.0265767 0.0641619i
\(623\) −35.6022 14.7469i −1.42637 0.590823i
\(624\) −16.3334 39.4323i −0.653859 1.57855i
\(625\) 28.2202i 1.12881i
\(626\) 8.66734 3.59013i 0.346417 0.143491i
\(627\) −21.2886 21.2886i −0.850184 0.850184i
\(628\) 6.05363 0.241566
\(629\) −16.4971 + 33.6490i −0.657783 + 1.34167i
\(630\) −33.3045 −1.32688
\(631\) 24.0194 + 24.0194i 0.956198 + 0.956198i 0.999080 0.0428817i \(-0.0136539\pi\)
−0.0428817 + 0.999080i \(0.513654\pi\)
\(632\) −0.191861 + 0.0794713i −0.00763181 + 0.00316120i
\(633\) 53.1617i 2.11299i
\(634\) −2.83668 6.84835i −0.112659 0.271983i
\(635\) 19.5086 + 8.08075i 0.774177 + 0.320675i
\(636\) −12.7783 + 30.8495i −0.506692 + 1.22326i
\(637\) −42.0229 + 42.0229i −1.66501 + 1.66501i
\(638\) −9.93765 + 9.93765i −0.393436 + 0.393436i
\(639\) −2.05866 + 4.97005i −0.0814394 + 0.196612i
\(640\) −23.1436 9.58637i −0.914829 0.378935i
\(641\) −2.44130 5.89381i −0.0964254 0.232791i 0.868305 0.496030i \(-0.165209\pi\)
−0.964731 + 0.263238i \(0.915209\pi\)
\(642\) 10.8827i 0.429504i
\(643\) −28.9428 + 11.9885i −1.14139 + 0.472780i −0.871639 0.490149i \(-0.836942\pi\)
−0.269754 + 0.962929i \(0.586942\pi\)
\(644\) −4.54029 4.54029i −0.178912 0.178912i
\(645\) −7.78285 −0.306449
\(646\) −1.83463 2.08226i −0.0721827 0.0819253i
\(647\) 0.962636 0.0378451 0.0189226 0.999821i \(-0.493976\pi\)
0.0189226 + 0.999821i \(0.493976\pi\)
\(648\) 27.4453 + 27.4453i 1.07816 + 1.07816i
\(649\) −17.5608 + 7.27392i −0.689322 + 0.285526i
\(650\) 1.33271i 0.0522733i
\(651\) −28.8780 69.7177i −1.13182 2.73245i
\(652\) 18.3892 + 7.61705i 0.720176 + 0.298307i
\(653\) 0.0448775 0.108344i 0.00175619 0.00423982i −0.922999 0.384802i \(-0.874270\pi\)
0.924755 + 0.380563i \(0.124270\pi\)
\(654\) 12.9773 12.9773i 0.507454 0.507454i
\(655\) −14.2709 + 14.2709i −0.557610 + 0.557610i
\(656\) 3.92354 9.47227i 0.153189 0.369830i
\(657\) −76.7716 31.7998i −2.99515 1.24063i
\(658\) 6.10674 + 14.7430i 0.238065 + 0.574741i
\(659\) 21.7602i 0.847657i 0.905742 + 0.423828i \(0.139314\pi\)
−0.905742 + 0.423828i \(0.860686\pi\)
\(660\) −73.8123 + 30.5740i −2.87314 + 1.19009i
\(661\) −7.94582 7.94582i −0.309057 0.309057i 0.535487 0.844544i \(-0.320128\pi\)
−0.844544 + 0.535487i \(0.820128\pi\)
\(662\) −12.2698 −0.476881
\(663\) −51.9667 25.4778i −2.01822 0.989475i
\(664\) 5.89981 0.228957
\(665\) −12.8259 12.8259i −0.497367 0.497367i
\(666\) −25.5947 + 10.6017i −0.991776 + 0.410807i
\(667\) 4.76175i 0.184376i
\(668\) 2.44316 + 5.89831i 0.0945287 + 0.228212i
\(669\) −30.0067 12.4292i −1.16013 0.480540i
\(670\) −3.54556 + 8.55975i −0.136977 + 0.330692i
\(671\) 18.7114 18.7114i 0.722346 0.722346i
\(672\) 45.3477 45.3477i 1.74932 1.74932i
\(673\) 9.52856 23.0040i 0.367299 0.886739i −0.626892 0.779106i \(-0.715673\pi\)
0.994191 0.107632i \(-0.0343269\pi\)
\(674\) −0.157924 0.0654141i −0.00608299 0.00251966i
\(675\) −4.25717 10.2777i −0.163859 0.395590i
\(676\) 10.5268i 0.404876i
\(677\) −3.69983 + 1.53252i −0.142196 + 0.0588995i −0.452647 0.891690i \(-0.649520\pi\)
0.310451 + 0.950590i \(0.399520\pi\)
\(678\) 7.49511 + 7.49511i 0.287848 + 0.287848i
\(679\) −58.5898 −2.24847
\(680\) −14.5605 + 4.98023i −0.558368 + 0.190983i
\(681\) 77.3705 2.96484
\(682\) 8.19429 + 8.19429i 0.313776 + 0.313776i
\(683\) 31.5247 13.0580i 1.20626 0.499649i 0.313243 0.949673i \(-0.398585\pi\)
0.893016 + 0.450024i \(0.148585\pi\)
\(684\) 22.9060i 0.875834i
\(685\) 5.87527 + 14.1842i 0.224483 + 0.541949i
\(686\) −11.4789 4.75471i −0.438266 0.181536i
\(687\) 19.5418 47.1780i 0.745564 1.79995i
\(688\) 2.15004 2.15004i 0.0819694 0.0819694i
\(689\) 17.1678 17.1678i 0.654041 0.654041i
\(690\) −0.927795 + 2.23990i −0.0353205 + 0.0852713i
\(691\) 36.6646 + 15.1870i 1.39479 + 0.577740i 0.948393 0.317097i \(-0.102708\pi\)
0.446394 + 0.894837i \(0.352708\pi\)
\(692\) 3.41465 + 8.24370i 0.129806 + 0.313378i
\(693\) 191.407i 7.27094i
\(694\) −1.19694 + 0.495787i −0.0454350 + 0.0188198i
\(695\) −14.9336 14.9336i −0.566462 0.566462i
\(696\) 31.2598 1.18490
\(697\) −4.49937 13.1546i −0.170426 0.498266i
\(698\) 5.19494 0.196632
\(699\) 51.4735 + 51.4735i 1.94691 + 1.94691i
\(700\) −5.86343 + 2.42871i −0.221617 + 0.0917967i
\(701\) 45.7695i 1.72869i −0.502899 0.864345i \(-0.667733\pi\)
0.502899 0.864345i \(-0.332267\pi\)
\(702\) −9.83882 23.7530i −0.371342 0.896500i
\(703\) −13.9396 5.77398i −0.525743 0.217770i
\(704\) 9.24566 22.3210i 0.348459 0.841254i
\(705\) −47.5704 + 47.5704i −1.79161 + 1.79161i
\(706\) 0.413163 0.413163i 0.0155496 0.0155496i
\(707\) 8.97358 21.6641i 0.337486 0.814763i
\(708\) 18.6929 + 7.74284i 0.702521 + 0.290994i
\(709\) −2.39392 5.77943i −0.0899054 0.217051i 0.872531 0.488559i \(-0.162477\pi\)
−0.962436 + 0.271509i \(0.912477\pi\)
\(710\) 0.696352i 0.0261336i
\(711\) 0.927378 0.384133i 0.0347794 0.0144061i
\(712\) −9.30749 9.30749i −0.348813 0.348813i
\(713\) −3.92639 −0.147045
\(714\) 1.55745 24.6357i 0.0582862 0.921969i
\(715\) 58.0911 2.17248
\(716\) −24.4124 24.4124i −0.912333 0.912333i
\(717\) −74.6653 + 30.9274i −2.78843 + 1.15500i
\(718\) 3.48035i 0.129886i
\(719\) 15.4347 + 37.2628i 0.575619 + 1.38967i 0.896710 + 0.442618i \(0.145950\pi\)
−0.321091 + 0.947048i \(0.604050\pi\)
\(720\) 50.6784 + 20.9917i 1.88867 + 0.782313i
\(721\) 8.14769 19.6703i 0.303436 0.732559i
\(722\) −4.65738 + 4.65738i −0.173330 + 0.173330i
\(723\) 6.65464 6.65464i 0.247489 0.247489i
\(724\) 5.85974 14.1467i 0.217775 0.525756i
\(725\) −4.34831 1.80113i −0.161492 0.0668922i
\(726\) 10.2024 + 24.6307i 0.378645 + 0.914131i
\(727\) 18.0827i 0.670651i −0.942102 0.335325i \(-0.891154\pi\)
0.942102 0.335325i \(-0.108846\pi\)
\(728\) −28.3158 + 11.7288i −1.04945 + 0.434698i
\(729\) −31.8783 31.8783i −1.18068 1.18068i
\(730\) 10.7564 0.398114
\(731\) 0.260140 4.11489i 0.00962163 0.152195i
\(732\) −28.1678 −1.04111
\(733\) 3.16884 + 3.16884i 0.117044 + 0.117044i 0.763203 0.646159i \(-0.223626\pi\)
−0.646159 + 0.763203i \(0.723626\pi\)
\(734\) 2.99588 1.24093i 0.110580 0.0458037i
\(735\) 106.860i 3.94159i
\(736\) −1.27696 3.08284i −0.0470692 0.113635i
\(737\) −49.1944 20.3770i −1.81210 0.750596i
\(738\) 3.93306 9.49525i 0.144778 0.349525i
\(739\) −33.2526 + 33.2526i −1.22322 + 1.22322i −0.256733 + 0.966482i \(0.582646\pi\)
−0.966482 + 0.256733i \(0.917354\pi\)
\(740\) −28.3121 + 28.3121i −1.04077 + 1.04077i
\(741\) 8.91721 21.5280i 0.327582 0.790852i
\(742\) 9.56701 + 3.96279i 0.351216 + 0.145478i
\(743\) −5.20311 12.5614i −0.190883 0.460833i 0.799243 0.601007i \(-0.205234\pi\)
−0.990127 + 0.140174i \(0.955234\pi\)
\(744\) 25.7759i 0.944989i
\(745\) 31.5370 13.0630i 1.15542 0.478593i
\(746\) −4.82825 4.82825i −0.176775 0.176775i
\(747\) −28.5173 −1.04340
\(748\) −13.6977 40.0474i −0.500838 1.46428i
\(749\) 37.6818 1.37686
\(750\) −9.46254 9.46254i −0.345523 0.345523i
\(751\) −25.2323 + 10.4516i −0.920739 + 0.381383i −0.792158 0.610316i \(-0.791042\pi\)
−0.128581 + 0.991699i \(0.541042\pi\)
\(752\) 26.2830i 0.958441i
\(753\) −1.03240 2.49243i −0.0376227 0.0908291i
\(754\) −10.0494 4.16261i −0.365979 0.151593i
\(755\) −6.72743 + 16.2415i −0.244836 + 0.591087i
\(756\) −86.5742 + 86.5742i −3.14867 + 3.14867i
\(757\) 32.4574 32.4574i 1.17969 1.17969i 0.199861 0.979824i \(-0.435951\pi\)
0.979824 0.199861i \(-0.0640492\pi\)
\(758\) −5.22637 + 12.6176i −0.189830 + 0.458290i
\(759\) −12.8731 5.33220i −0.467263 0.193547i
\(760\) −2.37098 5.72406i −0.0860046 0.207634i
\(761\) 5.50581i