Properties

Label 105.3.n.a.31.3
Level 105
Weight 3
Character 105.31
Analytic conductor 2.861
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.n (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.523596960000.16
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.3
Root \(0.836732 + 1.44926i\) of \(x^{8} - 2 x^{7} + 13 x^{6} - 2 x^{5} + 91 x^{4} - 50 x^{3} + 190 x^{2} + 100 x + 100\)
Character \(\chi\) \(=\) 105.31
Dual form 105.3.n.a.61.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.836732 + 1.44926i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.89852i q^{6} +(4.76104 + 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.836732 + 1.44926i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(0.599760 - 1.03881i) q^{4} +(1.93649 - 1.11803i) q^{5} -2.89852i q^{6} +(4.76104 + 5.13152i) q^{7} +8.70121 q^{8} +(1.50000 + 2.59808i) q^{9} +(3.24065 + 1.87099i) q^{10} +(6.91411 - 11.9756i) q^{11} +(-1.79928 + 1.03881i) q^{12} +6.12052i q^{13} +(-3.45321 + 11.1937i) q^{14} -3.87298 q^{15} +(4.88154 + 8.45507i) q^{16} +(-2.14655 - 1.23931i) q^{17} +(-2.51020 + 4.34779i) q^{18} +(-24.2290 + 13.9886i) q^{19} -2.68221i q^{20} +(-2.69753 - 11.8205i) q^{21} +23.1410 q^{22} +(-6.62020 - 11.4665i) q^{23} +(-13.0518 - 7.53547i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-8.87024 + 5.12123i) q^{26} -5.19615i q^{27} +(8.18618 - 1.86816i) q^{28} -27.6516 q^{29} +(-3.24065 - 5.61297i) q^{30} +(-16.2122 - 9.36010i) q^{31} +(9.23334 - 15.9926i) q^{32} +(-20.7423 + 11.9756i) q^{33} -4.14789i q^{34} +(14.9569 + 4.61414i) q^{35} +3.59856 q^{36} +(20.5067 + 35.5187i) q^{37} +(-40.5463 - 23.4094i) q^{38} +(5.30052 - 9.18078i) q^{39} +(16.8498 - 9.72824i) q^{40} -22.5351i q^{41} +(14.8738 - 13.8000i) q^{42} +7.60485 q^{43} +(-8.29361 - 14.3650i) q^{44} +(5.80948 + 3.35410i) q^{45} +(11.0787 - 19.1888i) q^{46} +(-11.9214 + 6.88283i) q^{47} -16.9101i q^{48} +(-3.66502 + 48.8627i) q^{49} +8.36732 q^{50} +(2.14655 + 3.71794i) q^{51} +(6.35808 + 3.67084i) q^{52} +(-46.2995 + 80.1930i) q^{53} +(7.53059 - 4.34779i) q^{54} -30.9208i q^{55} +(41.4268 + 44.6504i) q^{56} +48.4579 q^{57} +(-23.1370 - 40.0744i) q^{58} +(-61.5680 - 35.5463i) q^{59} +(-2.32286 + 4.02331i) q^{60} +(-100.214 + 57.8584i) q^{61} -31.3276i q^{62} +(-6.19052 + 20.0668i) q^{63} +69.9556 q^{64} +(6.84295 + 11.8523i) q^{65} +(-34.7115 - 20.0407i) q^{66} +(5.70227 - 9.87662i) q^{67} +(-2.57483 + 1.48658i) q^{68} +22.9330i q^{69} +(5.82783 + 25.5373i) q^{70} +99.4924 q^{71} +(13.0518 + 22.6064i) q^{72} +(90.1276 + 52.0352i) q^{73} +(-34.3172 + 59.4392i) q^{74} +(-7.50000 + 4.33013i) q^{75} +33.5592i q^{76} +(94.3714 - 21.5364i) q^{77} +17.7405 q^{78} +(-64.4982 - 111.714i) q^{79} +(18.9061 + 10.9154i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(32.6592 - 18.8558i) q^{82} -30.3382i q^{83} +(-13.8971 - 4.28721i) q^{84} -5.54238 q^{85} +(6.36322 + 11.0214i) q^{86} +(41.4774 + 23.9470i) q^{87} +(60.1611 - 104.202i) q^{88} +(93.9587 - 54.2471i) q^{89} +11.2259i q^{90} +(-31.4076 + 29.1400i) q^{91} -15.8821 q^{92} +(16.2122 + 28.0803i) q^{93} +(-19.9501 - 11.5182i) q^{94} +(-31.2794 + 54.1776i) q^{95} +(-27.7000 + 15.9926i) q^{96} -153.154i q^{97} +(-73.8816 + 35.5734i) q^{98} +41.4847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + O(q^{10}) \) \( 8q + 2q^{2} - 12q^{3} - 6q^{4} - 16q^{7} - 32q^{8} + 12q^{9} + 20q^{11} + 18q^{12} - 16q^{14} - 2q^{16} - 18q^{17} - 6q^{18} + 48q^{21} - 16q^{22} + 62q^{23} + 48q^{24} + 20q^{25} + 120q^{26} - 120q^{28} - 100q^{29} - 126q^{31} + 36q^{32} - 60q^{33} - 36q^{36} - 80q^{37} + 114q^{38} - 12q^{39} + 90q^{40} + 90q^{42} + 352q^{43} - 18q^{44} - 82q^{46} - 72q^{47} + 38q^{49} + 20q^{50} + 18q^{51} - 48q^{52} - 76q^{53} + 18q^{54} + 196q^{56} - 40q^{58} - 54q^{59} - 60q^{60} - 396q^{61} - 96q^{63} - 4q^{64} - 60q^{65} + 24q^{66} + 184q^{67} - 312q^{68} + 164q^{71} - 48q^{72} + 348q^{73} - 140q^{74} - 60q^{75} + 152q^{77} - 240q^{78} - 206q^{79} - 36q^{81} + 204q^{82} + 132q^{84} - 60q^{85} + 178q^{86} + 150q^{87} + 124q^{88} + 282q^{89} - 114q^{91} - 288q^{92} + 126q^{93} + 30q^{94} - 120q^{95} - 108q^{96} - 592q^{98} + 120q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.836732 + 1.44926i 0.418366 + 0.724631i 0.995775 0.0918238i \(-0.0292697\pi\)
−0.577409 + 0.816455i \(0.695936\pi\)
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) 0.599760 1.03881i 0.149940 0.259704i
\(5\) 1.93649 1.11803i 0.387298 0.223607i
\(6\) 2.89852i 0.483087i
\(7\) 4.76104 + 5.13152i 0.680148 + 0.733074i
\(8\) 8.70121 1.08765
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 3.24065 + 1.87099i 0.324065 + 0.187099i
\(11\) 6.91411 11.9756i 0.628556 1.08869i −0.359286 0.933227i \(-0.616980\pi\)
0.987842 0.155463i \(-0.0496869\pi\)
\(12\) −1.79928 + 1.03881i −0.149940 + 0.0865679i
\(13\) 6.12052i 0.470809i 0.971897 + 0.235405i \(0.0756415\pi\)
−0.971897 + 0.235405i \(0.924358\pi\)
\(14\) −3.45321 + 11.1937i −0.246658 + 0.799550i
\(15\) −3.87298 −0.258199
\(16\) 4.88154 + 8.45507i 0.305096 + 0.528442i
\(17\) −2.14655 1.23931i −0.126268 0.0729008i 0.435536 0.900171i \(-0.356559\pi\)
−0.561804 + 0.827271i \(0.689892\pi\)
\(18\) −2.51020 + 4.34779i −0.139455 + 0.241544i
\(19\) −24.2290 + 13.9886i −1.27521 + 0.736242i −0.975963 0.217935i \(-0.930068\pi\)
−0.299245 + 0.954176i \(0.596735\pi\)
\(20\) 2.68221i 0.134110i
\(21\) −2.69753 11.8205i −0.128454 0.562879i
\(22\) 23.1410 1.05186
\(23\) −6.62020 11.4665i −0.287835 0.498544i 0.685458 0.728112i \(-0.259602\pi\)
−0.973293 + 0.229568i \(0.926269\pi\)
\(24\) −13.0518 7.53547i −0.543825 0.313978i
\(25\) 2.50000 4.33013i 0.100000 0.173205i
\(26\) −8.87024 + 5.12123i −0.341163 + 0.196970i
\(27\) 5.19615i 0.192450i
\(28\) 8.18618 1.86816i 0.292364 0.0667199i
\(29\) −27.6516 −0.953503 −0.476751 0.879038i \(-0.658186\pi\)
−0.476751 + 0.879038i \(0.658186\pi\)
\(30\) −3.24065 5.61297i −0.108022 0.187099i
\(31\) −16.2122 9.36010i −0.522973 0.301939i 0.215177 0.976575i \(-0.430967\pi\)
−0.738150 + 0.674636i \(0.764300\pi\)
\(32\) 9.23334 15.9926i 0.288542 0.499769i
\(33\) −20.7423 + 11.9756i −0.628556 + 0.362897i
\(34\) 4.14789i 0.121997i
\(35\) 14.9569 + 4.61414i 0.427341 + 0.131833i
\(36\) 3.59856 0.0999600
\(37\) 20.5067 + 35.5187i 0.554235 + 0.959964i 0.997963 + 0.0638017i \(0.0203225\pi\)
−0.443727 + 0.896162i \(0.646344\pi\)
\(38\) −40.5463 23.4094i −1.06701 0.616037i
\(39\) 5.30052 9.18078i 0.135911 0.235405i
\(40\) 16.8498 9.72824i 0.421245 0.243206i
\(41\) 22.5351i 0.549636i −0.961496 0.274818i \(-0.911382\pi\)
0.961496 0.274818i \(-0.0886176\pi\)
\(42\) 14.8738 13.8000i 0.354139 0.328571i
\(43\) 7.60485 0.176857 0.0884285 0.996083i \(-0.471816\pi\)
0.0884285 + 0.996083i \(0.471816\pi\)
\(44\) −8.29361 14.3650i −0.188491 0.326476i
\(45\) 5.80948 + 3.35410i 0.129099 + 0.0745356i
\(46\) 11.0787 19.1888i 0.240840 0.417148i
\(47\) −11.9214 + 6.88283i −0.253647 + 0.146443i −0.621433 0.783467i \(-0.713449\pi\)
0.367786 + 0.929910i \(0.380116\pi\)
\(48\) 16.9101i 0.352295i
\(49\) −3.66502 + 48.8627i −0.0747963 + 0.997199i
\(50\) 8.36732 0.167346
\(51\) 2.14655 + 3.71794i 0.0420893 + 0.0729008i
\(52\) 6.35808 + 3.67084i 0.122271 + 0.0705931i
\(53\) −46.2995 + 80.1930i −0.873575 + 1.51308i −0.0153016 + 0.999883i \(0.504871\pi\)
−0.858273 + 0.513193i \(0.828463\pi\)
\(54\) 7.53059 4.34779i 0.139455 0.0805146i
\(55\) 30.9208i 0.562197i
\(56\) 41.4268 + 44.6504i 0.739764 + 0.797329i
\(57\) 48.4579 0.850139
\(58\) −23.1370 40.0744i −0.398913 0.690938i
\(59\) −61.5680 35.5463i −1.04352 0.602479i −0.122695 0.992444i \(-0.539154\pi\)
−0.920830 + 0.389965i \(0.872487\pi\)
\(60\) −2.32286 + 4.02331i −0.0387143 + 0.0670552i
\(61\) −100.214 + 57.8584i −1.64285 + 0.948498i −0.663031 + 0.748592i \(0.730730\pi\)
−0.979815 + 0.199906i \(0.935936\pi\)
\(62\) 31.3276i 0.505283i
\(63\) −6.19052 + 20.0668i −0.0982623 + 0.318521i
\(64\) 69.9556 1.09306
\(65\) 6.84295 + 11.8523i 0.105276 + 0.182344i
\(66\) −34.7115 20.0407i −0.525932 0.303647i
\(67\) 5.70227 9.87662i 0.0851085 0.147412i −0.820329 0.571892i \(-0.806210\pi\)
0.905437 + 0.424480i \(0.139543\pi\)
\(68\) −2.57483 + 1.48658i −0.0378652 + 0.0218615i
\(69\) 22.9330i 0.332363i
\(70\) 5.82783 + 25.5373i 0.0832547 + 0.364819i
\(71\) 99.4924 1.40130 0.700651 0.713504i \(-0.252893\pi\)
0.700651 + 0.713504i \(0.252893\pi\)
\(72\) 13.0518 + 22.6064i 0.181275 + 0.313978i
\(73\) 90.1276 + 52.0352i 1.23462 + 0.712811i 0.967991 0.250987i \(-0.0807550\pi\)
0.266634 + 0.963798i \(0.414088\pi\)
\(74\) −34.3172 + 59.4392i −0.463746 + 0.803232i
\(75\) −7.50000 + 4.33013i −0.100000 + 0.0577350i
\(76\) 33.5592i 0.441568i
\(77\) 94.3714 21.5364i 1.22560 0.279693i
\(78\) 17.7405 0.227442
\(79\) −64.4982 111.714i −0.816433 1.41410i −0.908294 0.418331i \(-0.862615\pi\)
0.0918616 0.995772i \(-0.470718\pi\)
\(80\) 18.9061 + 10.9154i 0.236326 + 0.136443i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 32.6592 18.8558i 0.398283 0.229949i
\(83\) 30.3382i 0.365520i −0.983158 0.182760i \(-0.941497\pi\)
0.983158 0.182760i \(-0.0585032\pi\)
\(84\) −13.8971 4.28721i −0.165442 0.0510382i
\(85\) −5.54238 −0.0652045
\(86\) 6.36322 + 11.0214i 0.0739909 + 0.128156i
\(87\) 41.4774 + 23.9470i 0.476751 + 0.275253i
\(88\) 60.1611 104.202i 0.683649 1.18411i
\(89\) 93.9587 54.2471i 1.05572 0.609518i 0.131472 0.991320i \(-0.458030\pi\)
0.924244 + 0.381802i \(0.124696\pi\)
\(90\) 11.2259i 0.124733i
\(91\) −31.4076 + 29.1400i −0.345138 + 0.320220i
\(92\) −15.8821 −0.172632
\(93\) 16.2122 + 28.0803i 0.174324 + 0.301939i
\(94\) −19.9501 11.5182i −0.212235 0.122534i
\(95\) −31.2794 + 54.1776i −0.329257 + 0.570290i
\(96\) −27.7000 + 15.9926i −0.288542 + 0.166590i
\(97\) 153.154i 1.57890i −0.613812 0.789452i \(-0.710365\pi\)
0.613812 0.789452i \(-0.289635\pi\)
\(98\) −73.8816 + 35.5734i −0.753893 + 0.362994i
\(99\) 41.4847 0.419037
\(100\) −2.99880 5.19407i −0.0299880 0.0519407i
\(101\) 98.9544 + 57.1314i 0.979747 + 0.565657i 0.902194 0.431331i \(-0.141956\pi\)
0.0775531 + 0.996988i \(0.475289\pi\)
\(102\) −3.59218 + 6.22184i −0.0352174 + 0.0609984i
\(103\) −48.4794 + 27.9896i −0.470674 + 0.271744i −0.716522 0.697565i \(-0.754267\pi\)
0.245848 + 0.969308i \(0.420934\pi\)
\(104\) 53.2559i 0.512076i
\(105\) −18.4394 19.8743i −0.175614 0.189279i
\(106\) −154.961 −1.46190
\(107\) −49.3529 85.4817i −0.461242 0.798895i 0.537781 0.843085i \(-0.319263\pi\)
−0.999023 + 0.0441897i \(0.985929\pi\)
\(108\) −5.39784 3.11644i −0.0499800 0.0288560i
\(109\) −26.3791 + 45.6900i −0.242010 + 0.419174i −0.961287 0.275550i \(-0.911140\pi\)
0.719276 + 0.694724i \(0.244473\pi\)
\(110\) 44.8124 25.8725i 0.407386 0.235204i
\(111\) 71.0373i 0.639976i
\(112\) −20.1462 + 65.3046i −0.179877 + 0.583077i
\(113\) 106.206 0.939875 0.469937 0.882700i \(-0.344276\pi\)
0.469937 + 0.882700i \(0.344276\pi\)
\(114\) 40.5463 + 70.2282i 0.355669 + 0.616037i
\(115\) −25.6399 14.8032i −0.222956 0.128724i
\(116\) −16.5843 + 28.7249i −0.142968 + 0.247628i
\(117\) −15.9016 + 9.18078i −0.135911 + 0.0784682i
\(118\) 118.971i 1.00823i
\(119\) −3.86026 16.9155i −0.0324392 0.142147i
\(120\) −33.6996 −0.280830
\(121\) −35.1099 60.8121i −0.290164 0.502579i
\(122\) −167.704 96.8239i −1.37462 0.793638i
\(123\) −19.5160 + 33.8026i −0.158666 + 0.274818i
\(124\) −19.4468 + 11.2276i −0.156829 + 0.0905453i
\(125\) 11.1803i 0.0894427i
\(126\) −34.2619 + 7.81886i −0.271920 + 0.0620544i
\(127\) −197.402 −1.55434 −0.777172 0.629288i \(-0.783347\pi\)
−0.777172 + 0.629288i \(0.783347\pi\)
\(128\) 21.6007 + 37.4135i 0.168756 + 0.292293i
\(129\) −11.4073 6.58599i −0.0884285 0.0510542i
\(130\) −11.4514 + 19.8344i −0.0880879 + 0.152573i
\(131\) 127.379 73.5423i 0.972358 0.561391i 0.0724040 0.997375i \(-0.476933\pi\)
0.899954 + 0.435984i \(0.143600\pi\)
\(132\) 28.7299i 0.217651i
\(133\) −187.138 57.7311i −1.40705 0.434069i
\(134\) 19.0851 0.142426
\(135\) −5.80948 10.0623i −0.0430331 0.0745356i
\(136\) −18.6776 10.7835i −0.137335 0.0792906i
\(137\) −124.296 + 215.287i −0.907270 + 1.57144i −0.0894293 + 0.995993i \(0.528504\pi\)
−0.817841 + 0.575445i \(0.804829\pi\)
\(138\) −33.2360 + 19.1888i −0.240840 + 0.139049i
\(139\) 15.7344i 0.113197i −0.998397 0.0565985i \(-0.981974\pi\)
0.998397 0.0565985i \(-0.0180255\pi\)
\(140\) 13.7638 12.7701i 0.0983129 0.0912150i
\(141\) 23.8428 0.169098
\(142\) 83.2485 + 144.191i 0.586257 + 1.01543i
\(143\) 73.2968 + 42.3180i 0.512565 + 0.295930i
\(144\) −14.6446 + 25.3652i −0.101699 + 0.176147i
\(145\) −53.5471 + 30.9154i −0.369290 + 0.213210i
\(146\) 174.158i 1.19286i
\(147\) 47.8139 70.1201i 0.325265 0.477008i
\(148\) 49.1964 0.332408
\(149\) −92.1029 159.527i −0.618140 1.07065i −0.989825 0.142291i \(-0.954553\pi\)
0.371684 0.928359i \(-0.378780\pi\)
\(150\) −12.5510 7.24631i −0.0836732 0.0483087i
\(151\) 131.625 227.982i 0.871690 1.50981i 0.0114426 0.999935i \(-0.496358\pi\)
0.860247 0.509877i \(-0.170309\pi\)
\(152\) −210.821 + 121.718i −1.38698 + 0.800774i
\(153\) 7.43588i 0.0486005i
\(154\) 110.175 + 118.749i 0.715424 + 0.771095i
\(155\) −41.8596 −0.270062
\(156\) −6.35808 11.0125i −0.0407570 0.0705931i
\(157\) 187.600 + 108.311i 1.19490 + 0.689878i 0.959415 0.281999i \(-0.0909975\pi\)
0.235489 + 0.971877i \(0.424331\pi\)
\(158\) 107.935 186.950i 0.683135 1.18323i
\(159\) 138.898 80.1930i 0.873575 0.504359i
\(160\) 41.2928i 0.258080i
\(161\) 27.3217 88.5642i 0.169700 0.550088i
\(162\) −15.0612 −0.0929702
\(163\) 86.2901 + 149.459i 0.529387 + 0.916926i 0.999413 + 0.0342728i \(0.0109115\pi\)
−0.470025 + 0.882653i \(0.655755\pi\)
\(164\) −23.4098 13.5156i −0.142743 0.0824124i
\(165\) −26.7782 + 46.3813i −0.162292 + 0.281099i
\(166\) 43.9680 25.3849i 0.264867 0.152921i
\(167\) 156.923i 0.939658i −0.882758 0.469829i \(-0.844316\pi\)
0.882758 0.469829i \(-0.155684\pi\)
\(168\) −23.4718 102.852i −0.139713 0.612216i
\(169\) 131.539 0.778339
\(170\) −4.63748 8.03236i −0.0272793 0.0472492i
\(171\) −72.6869 41.9658i −0.425069 0.245414i
\(172\) 4.56108 7.90003i 0.0265179 0.0459304i
\(173\) −41.2245 + 23.8010i −0.238292 + 0.137578i −0.614391 0.789001i \(-0.710598\pi\)
0.376100 + 0.926579i \(0.377265\pi\)
\(174\) 80.1488i 0.460625i
\(175\) 34.1227 7.78710i 0.194987 0.0444977i
\(176\) 135.006 0.767079
\(177\) 61.5680 + 106.639i 0.347842 + 0.602479i
\(178\) 157.237 + 90.7805i 0.883351 + 0.510003i
\(179\) −14.7747 + 25.5905i −0.0825402 + 0.142964i −0.904340 0.426812i \(-0.859637\pi\)
0.821800 + 0.569776i \(0.192970\pi\)
\(180\) 6.96858 4.02331i 0.0387143 0.0223517i
\(181\) 10.3249i 0.0570439i −0.999593 0.0285219i \(-0.990920\pi\)
0.999593 0.0285219i \(-0.00908005\pi\)
\(182\) −68.5112 21.1354i −0.376435 0.116129i
\(183\) 200.427 1.09523
\(184\) −57.6037 99.7725i −0.313064 0.542242i
\(185\) 79.4221 + 45.8544i 0.429309 + 0.247862i
\(186\) −27.1305 + 46.9913i −0.145863 + 0.252642i
\(187\) −29.6830 + 17.1375i −0.158733 + 0.0916444i
\(188\) 16.5122i 0.0878308i
\(189\) 26.6642 24.7391i 0.141080 0.130895i
\(190\) −104.690 −0.551000
\(191\) 59.5045 + 103.065i 0.311542 + 0.539607i 0.978696 0.205313i \(-0.0658212\pi\)
−0.667154 + 0.744920i \(0.732488\pi\)
\(192\) −104.933 60.5833i −0.546528 0.315538i
\(193\) −4.95254 + 8.57805i −0.0256608 + 0.0444459i −0.878571 0.477612i \(-0.841502\pi\)
0.852910 + 0.522058i \(0.174836\pi\)
\(194\) 221.960 128.149i 1.14412 0.660560i
\(195\) 23.7047i 0.121562i
\(196\) 48.5612 + 33.1132i 0.247761 + 0.168945i
\(197\) −290.342 −1.47382 −0.736908 0.675994i \(-0.763715\pi\)
−0.736908 + 0.675994i \(0.763715\pi\)
\(198\) 34.7115 + 60.1222i 0.175311 + 0.303647i
\(199\) 294.002 + 169.742i 1.47740 + 0.852977i 0.999674 0.0255322i \(-0.00812803\pi\)
0.477725 + 0.878509i \(0.341461\pi\)
\(200\) 21.7530 37.6773i 0.108765 0.188387i
\(201\) −17.1068 + 9.87662i −0.0851085 + 0.0491374i
\(202\) 191.215i 0.946607i
\(203\) −131.650 141.895i −0.648523 0.698989i
\(204\) 5.14967 0.0252435
\(205\) −25.1950 43.6390i −0.122902 0.212873i
\(206\) −81.1285 46.8396i −0.393828 0.227377i
\(207\) 19.8606 34.3995i 0.0959449 0.166181i
\(208\) −51.7494 + 29.8775i −0.248795 + 0.143642i
\(209\) 386.875i 1.85108i
\(210\) 13.3742 43.3530i 0.0636867 0.206443i
\(211\) 11.1098 0.0526531 0.0263265 0.999653i \(-0.491619\pi\)
0.0263265 + 0.999653i \(0.491619\pi\)
\(212\) 55.5371 + 96.1931i 0.261968 + 0.453741i
\(213\) −149.239 86.1630i −0.700651 0.404521i
\(214\) 82.5903 143.051i 0.385936 0.668461i
\(215\) 14.7267 8.50248i 0.0684964 0.0395464i
\(216\) 45.2128i 0.209319i
\(217\) −29.1552 127.757i −0.134356 0.588741i
\(218\) −88.2890 −0.404996
\(219\) −90.1276 156.106i −0.411542 0.712811i
\(220\) −32.1210 18.5451i −0.146005 0.0842958i
\(221\) 7.58524 13.1380i 0.0343224 0.0594481i
\(222\) 102.952 59.4392i 0.463746 0.267744i
\(223\) 359.376i 1.61155i 0.592220 + 0.805776i \(0.298252\pi\)
−0.592220 + 0.805776i \(0.701748\pi\)
\(224\) 126.027 28.7604i 0.562619 0.128395i
\(225\) 15.0000 0.0666667
\(226\) 88.8658 + 153.920i 0.393212 + 0.681062i
\(227\) −64.3040 37.1259i −0.283277 0.163550i 0.351629 0.936140i \(-0.385628\pi\)
−0.634906 + 0.772589i \(0.718961\pi\)
\(228\) 29.0631 50.3388i 0.127470 0.220784i
\(229\) 288.608 166.628i 1.26030 0.727633i 0.287165 0.957881i \(-0.407287\pi\)
0.973132 + 0.230248i \(0.0739538\pi\)
\(230\) 49.5453i 0.215414i
\(231\) −160.208 49.4235i −0.693541 0.213954i
\(232\) −240.602 −1.03708
\(233\) 132.338 + 229.216i 0.567975 + 0.983761i 0.996766 + 0.0803575i \(0.0256062\pi\)
−0.428791 + 0.903404i \(0.641060\pi\)
\(234\) −26.6107 15.3637i −0.113721 0.0656568i
\(235\) −15.3905 + 26.6571i −0.0654914 + 0.113434i
\(236\) −73.8520 + 42.6385i −0.312932 + 0.180671i
\(237\) 223.428i 0.942735i
\(238\) 21.2850 19.7483i 0.0894328 0.0829759i
\(239\) −266.197 −1.11380 −0.556898 0.830581i \(-0.688009\pi\)
−0.556898 + 0.830581i \(0.688009\pi\)
\(240\) −18.9061 32.7463i −0.0787755 0.136443i
\(241\) −29.4197 16.9855i −0.122074 0.0704792i 0.437720 0.899111i \(-0.355786\pi\)
−0.559793 + 0.828632i \(0.689120\pi\)
\(242\) 58.7551 101.767i 0.242790 0.420524i
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 138.805i 0.568871i
\(245\) 47.5329 + 98.7199i 0.194012 + 0.402938i
\(246\) −65.3185 −0.265522
\(247\) −85.6174 148.294i −0.346629 0.600380i
\(248\) −141.065 81.4441i −0.568812 0.328404i
\(249\) −26.2736 + 45.5073i −0.105517 + 0.182760i
\(250\) 16.2032 9.35495i 0.0648130 0.0374198i
\(251\) 84.6771i 0.337359i −0.985671 0.168680i \(-0.946050\pi\)
0.985671 0.168680i \(-0.0539503\pi\)
\(252\) 17.1329 + 18.4661i 0.0679876 + 0.0732781i
\(253\) −183.091 −0.723680
\(254\) −165.172 286.087i −0.650285 1.12633i
\(255\) 8.31357 + 4.79984i 0.0326022 + 0.0188229i
\(256\) 103.763 179.723i 0.405325 0.702044i
\(257\) 27.6440 15.9603i 0.107564 0.0621022i −0.445253 0.895405i \(-0.646886\pi\)
0.552817 + 0.833303i \(0.313553\pi\)
\(258\) 22.0428i 0.0854374i
\(259\) −84.6315 + 274.336i −0.326763 + 1.05921i
\(260\) 16.4165 0.0631404
\(261\) −41.4774 71.8409i −0.158917 0.275253i
\(262\) 213.164 + 123.070i 0.813603 + 0.469734i
\(263\) 74.0405 128.242i 0.281523 0.487612i −0.690237 0.723583i \(-0.742494\pi\)
0.971760 + 0.235971i \(0.0758272\pi\)
\(264\) −180.483 + 104.202i −0.683649 + 0.394705i
\(265\) 207.057i 0.781349i
\(266\) −72.9165 319.517i −0.274122 1.20119i
\(267\) −187.917 −0.703811
\(268\) −6.83998 11.8472i −0.0255223 0.0442060i
\(269\) −78.8909 45.5477i −0.293275 0.169322i 0.346143 0.938182i \(-0.387491\pi\)
−0.639418 + 0.768859i \(0.720825\pi\)
\(270\) 9.72194 16.8389i 0.0360072 0.0623663i
\(271\) −108.045 + 62.3797i −0.398689 + 0.230183i −0.685918 0.727679i \(-0.740599\pi\)
0.287229 + 0.957862i \(0.407266\pi\)
\(272\) 24.1990i 0.0889670i
\(273\) 72.3474 16.5103i 0.265009 0.0604772i
\(274\) −416.010 −1.51828
\(275\) −34.5706 59.8780i −0.125711 0.217738i
\(276\) 23.8232 + 13.7543i 0.0863158 + 0.0498345i
\(277\) 61.9619 107.321i 0.223689 0.387441i −0.732236 0.681051i \(-0.761523\pi\)
0.955925 + 0.293610i \(0.0948566\pi\)
\(278\) 22.8033 13.1655i 0.0820261 0.0473578i
\(279\) 56.1606i 0.201292i
\(280\) 130.143 + 40.1486i 0.464798 + 0.143388i
\(281\) −17.8049 −0.0633627 −0.0316814 0.999498i \(-0.510086\pi\)
−0.0316814 + 0.999498i \(0.510086\pi\)
\(282\) 19.9501 + 34.5545i 0.0707449 + 0.122534i
\(283\) −96.2623 55.5770i −0.340149 0.196385i 0.320189 0.947354i \(-0.396254\pi\)
−0.660338 + 0.750968i \(0.729587\pi\)
\(284\) 59.6716 103.354i 0.210111 0.363923i
\(285\) 93.8383 54.1776i 0.329257 0.190097i
\(286\) 141.635i 0.495228i
\(287\) 115.639 107.290i 0.402924 0.373834i
\(288\) 55.4000 0.192361
\(289\) −141.428 244.961i −0.489371 0.847615i
\(290\) −89.6091 51.7358i −0.308997 0.178399i
\(291\) −132.635 + 229.731i −0.455791 + 0.789452i
\(292\) 108.110 62.4173i 0.370239 0.213758i
\(293\) 76.6488i 0.261600i −0.991409 0.130800i \(-0.958245\pi\)
0.991409 0.130800i \(-0.0417546\pi\)
\(294\) 141.630 + 10.6231i 0.481734 + 0.0361332i
\(295\) −158.968 −0.538874
\(296\) 178.433 + 309.055i 0.602814 + 1.04411i
\(297\) −62.2270 35.9268i −0.209519 0.120966i
\(298\) 154.131 266.963i 0.517218 0.895847i
\(299\) 70.1810 40.5190i 0.234719 0.135515i
\(300\) 10.3881i 0.0346272i
\(301\) 36.2070 + 39.0244i 0.120289 + 0.129649i
\(302\) 440.540 1.45874
\(303\) −98.9544 171.394i −0.326582 0.565657i
\(304\) −236.549 136.572i −0.778122 0.449249i
\(305\) −129.375 + 224.084i −0.424181 + 0.734703i
\(306\) 10.7765 6.22184i 0.0352174 0.0203328i
\(307\) 357.562i 1.16470i −0.812939 0.582349i \(-0.802134\pi\)
0.812939 0.582349i \(-0.197866\pi\)
\(308\) 34.2279 110.951i 0.111129 0.360230i
\(309\) 96.9588 0.313783
\(310\) −35.0253 60.6656i −0.112985 0.195695i
\(311\) 272.856 + 157.533i 0.877349 + 0.506538i 0.869784 0.493434i \(-0.164258\pi\)
0.00756579 + 0.999971i \(0.497592\pi\)
\(312\) 46.1210 79.8839i 0.147824 0.256038i
\(313\) −227.260 + 131.209i −0.726070 + 0.419197i −0.816983 0.576662i \(-0.804355\pi\)
0.0909126 + 0.995859i \(0.471022\pi\)
\(314\) 362.508i 1.15449i
\(315\) 10.4475 + 45.7805i 0.0331666 + 0.145335i
\(316\) −154.734 −0.489664
\(317\) 154.797 + 268.117i 0.488320 + 0.845795i 0.999910 0.0134349i \(-0.00427658\pi\)
−0.511590 + 0.859230i \(0.670943\pi\)
\(318\) 232.441 + 134.200i 0.730948 + 0.422013i
\(319\) −191.186 + 331.144i −0.599330 + 1.03807i
\(320\) 135.468 78.2127i 0.423339 0.244415i
\(321\) 170.963i 0.532597i
\(322\) 151.214 34.5082i 0.469607 0.107168i
\(323\) 69.3450 0.214690
\(324\) 5.39784 + 9.34933i 0.0166600 + 0.0288560i
\(325\) 26.5026 + 15.3013i 0.0815465 + 0.0470809i
\(326\) −144.403 + 250.114i −0.442955 + 0.767221i
\(327\) 79.1374 45.6900i 0.242010 0.139725i
\(328\) 196.082i 0.597812i
\(329\) −92.0778 28.4056i −0.279872 0.0863391i
\(330\) −89.6248 −0.271590
\(331\) 43.4062 + 75.1818i 0.131137 + 0.227135i 0.924115 0.382115i \(-0.124804\pi\)
−0.792978 + 0.609250i \(0.791471\pi\)
\(332\) −31.5157 18.1956i −0.0949269 0.0548061i
\(333\) −61.5201 + 106.556i −0.184745 + 0.319988i
\(334\) 227.422 131.302i 0.680905 0.393121i
\(335\) 25.5013i 0.0761233i
\(336\) 86.7747 80.5098i 0.258258 0.239613i
\(337\) 373.915 1.10954 0.554770 0.832004i \(-0.312806\pi\)
0.554770 + 0.832004i \(0.312806\pi\)
\(338\) 110.063 + 190.635i 0.325630 + 0.564008i
\(339\) −159.309 91.9770i −0.469937 0.271318i
\(340\) −3.32410 + 5.75750i −0.00977675 + 0.0169338i
\(341\) −224.185 + 129.433i −0.657435 + 0.379570i
\(342\) 140.456i 0.410691i
\(343\) −268.190 + 213.830i −0.781894 + 0.623412i
\(344\) 66.1714 0.192359
\(345\) 25.6399 + 44.4096i 0.0743186 + 0.128724i
\(346\) −68.9877 39.8301i −0.199386 0.115116i
\(347\) 165.439 286.549i 0.476770 0.825790i −0.522875 0.852409i \(-0.675141\pi\)
0.999646 + 0.0266188i \(0.00847401\pi\)
\(348\) 49.7529 28.7249i 0.142968 0.0825427i
\(349\) 250.907i 0.718932i −0.933158 0.359466i \(-0.882959\pi\)
0.933158 0.359466i \(-0.117041\pi\)
\(350\) 39.8371 + 42.9371i 0.113820 + 0.122677i
\(351\) 31.8031 0.0906073
\(352\) −127.681 221.149i −0.362729 0.628265i
\(353\) −108.875 62.8589i −0.308427 0.178071i 0.337795 0.941220i \(-0.390319\pi\)
−0.646222 + 0.763149i \(0.723652\pi\)
\(354\) −103.032 + 178.456i −0.291050 + 0.504114i
\(355\) 192.666 111.236i 0.542722 0.313341i
\(356\) 130.141i 0.365564i
\(357\) −8.85886 + 28.7163i −0.0248147 + 0.0804379i
\(358\) −49.4498 −0.138128
\(359\) 178.790 + 309.674i 0.498023 + 0.862601i 0.999997 0.00228149i \(-0.000726221\pi\)
−0.501975 + 0.864882i \(0.667393\pi\)
\(360\) 50.5494 + 29.1847i 0.140415 + 0.0810687i
\(361\) 210.861 365.223i 0.584103 1.01170i
\(362\) 14.9636 8.63921i 0.0413358 0.0238652i
\(363\) 121.624i 0.335053i
\(364\) 11.4341 + 50.1037i 0.0314123 + 0.137647i
\(365\) 232.709 0.637558
\(366\) 167.704 + 290.472i 0.458207 + 0.793638i
\(367\) 603.879 + 348.650i 1.64545 + 0.949999i 0.978850 + 0.204582i \(0.0655834\pi\)
0.666598 + 0.745418i \(0.267750\pi\)
\(368\) 64.6334 111.948i 0.175634 0.304208i
\(369\) 58.5479 33.8026i 0.158666 0.0916060i
\(370\) 153.471i 0.414787i
\(371\) −631.946 + 144.215i −1.70336 + 0.388721i
\(372\) 38.8936 0.104553
\(373\) 72.6433 + 125.822i 0.194754 + 0.337324i 0.946820 0.321764i \(-0.104276\pi\)
−0.752066 + 0.659088i \(0.770942\pi\)
\(374\) −49.6735 28.6790i −0.132817 0.0766818i
\(375\) −9.68246 + 16.7705i −0.0258199 + 0.0447214i
\(376\) −103.731 + 59.8890i −0.275880 + 0.159279i
\(377\) 169.242i 0.448918i
\(378\) 58.1642 + 17.9434i 0.153873 + 0.0474693i
\(379\) −222.630 −0.587415 −0.293708 0.955895i \(-0.594889\pi\)
−0.293708 + 0.955895i \(0.594889\pi\)
\(380\) 37.5203 + 64.9871i 0.0987377 + 0.171019i
\(381\) 296.103 + 170.955i 0.777172 + 0.448701i
\(382\) −99.5787 + 172.475i −0.260677 + 0.451506i
\(383\) −30.1012 + 17.3789i −0.0785932 + 0.0453758i −0.538782 0.842445i \(-0.681115\pi\)
0.460188 + 0.887821i \(0.347782\pi\)
\(384\) 74.8271i 0.194862i
\(385\) 158.671 147.215i 0.412132 0.382378i
\(386\) −16.5758 −0.0429425
\(387\) 11.4073 + 19.7580i 0.0294762 + 0.0510542i
\(388\) −159.098 91.8555i −0.410047 0.236741i
\(389\) −276.283 + 478.537i −0.710240 + 1.23017i 0.254528 + 0.967066i \(0.418080\pi\)
−0.964767 + 0.263105i \(0.915253\pi\)
\(390\) 34.3543 19.8344i 0.0880879 0.0508576i
\(391\) 32.8180i 0.0839335i
\(392\) −31.8901 + 425.165i −0.0813523 + 1.08460i
\(393\) −254.758 −0.648239
\(394\) −242.938 420.781i −0.616594 1.06797i
\(395\) −249.800 144.222i −0.632406 0.365120i
\(396\) 24.8808 43.0949i 0.0628304 0.108825i
\(397\) 49.9274 28.8256i 0.125762 0.0726085i −0.435799 0.900044i \(-0.643534\pi\)
0.561561 + 0.827435i \(0.310201\pi\)
\(398\) 568.115i 1.42743i
\(399\) 230.710 + 248.663i 0.578220 + 0.623215i
\(400\) 48.8154 0.122038
\(401\) −281.160 486.983i −0.701146 1.21442i −0.968064 0.250701i \(-0.919339\pi\)
0.266918 0.963719i \(-0.413995\pi\)
\(402\) −28.6276 16.5282i −0.0712130 0.0411148i
\(403\) 57.2886 99.2268i 0.142155 0.246220i
\(404\) 118.698 68.5302i 0.293806 0.169629i
\(405\) 20.1246i 0.0496904i
\(406\) 95.4866 309.524i 0.235189 0.762373i
\(407\) 567.143 1.39347
\(408\) 18.6776 + 32.3506i 0.0457785 + 0.0792906i
\(409\) −174.709 100.869i −0.427163 0.246622i 0.270975 0.962587i \(-0.412654\pi\)
−0.698137 + 0.715964i \(0.745987\pi\)
\(410\) 42.1629 73.0283i 0.102836 0.178118i
\(411\) 372.888 215.287i 0.907270 0.523813i
\(412\) 67.1482i 0.162981i
\(413\) −110.721 485.175i −0.268090 1.17476i
\(414\) 66.4719 0.160560
\(415\) −33.9191 58.7496i −0.0817328 0.141565i
\(416\) 97.8831 + 56.5128i 0.235296 + 0.135848i
\(417\) −13.6264 + 23.6016i −0.0326772 + 0.0565985i
\(418\) −560.683 + 323.710i −1.34135 + 0.774427i
\(419\) 304.381i 0.726447i −0.931702 0.363223i \(-0.881676\pi\)
0.931702 0.363223i \(-0.118324\pi\)
\(420\) −31.7049 + 7.23534i −0.0754879 + 0.0172270i
\(421\) 556.622 1.32214 0.661071 0.750323i \(-0.270102\pi\)
0.661071 + 0.750323i \(0.270102\pi\)
\(422\) 9.29592 + 16.1010i 0.0220283 + 0.0381541i
\(423\) −35.7643 20.6485i −0.0845491 0.0488144i
\(424\) −402.861 + 697.776i −0.950144 + 1.64570i
\(425\) −10.7328 + 6.19657i −0.0252536 + 0.0145802i
\(426\) 288.381i 0.676951i
\(427\) −774.022 238.782i −1.81270 0.559209i
\(428\) −118.400 −0.276635
\(429\) −73.2968 126.954i −0.170855 0.295930i
\(430\) 24.6446 + 14.2286i 0.0573131 + 0.0330897i
\(431\) 90.2225 156.270i 0.209333 0.362575i −0.742172 0.670210i \(-0.766204\pi\)
0.951505 + 0.307634i \(0.0995374\pi\)
\(432\) 43.9338 25.3652i 0.101699 0.0587158i
\(433\) 724.048i 1.67217i −0.548603 0.836083i \(-0.684840\pi\)
0.548603 0.836083i \(-0.315160\pi\)
\(434\) 160.758 149.152i 0.370410 0.343668i
\(435\) 107.094 0.246193
\(436\) 31.6423 + 54.8061i 0.0725741 + 0.125702i
\(437\) 320.801 + 185.214i 0.734098 + 0.423832i
\(438\) 150.825 261.237i 0.344350 0.596432i
\(439\) 354.272 204.539i 0.806997 0.465920i −0.0389147 0.999243i \(-0.512390\pi\)
0.845912 + 0.533322i \(0.179057\pi\)
\(440\) 269.049i 0.611474i
\(441\) −132.447 + 63.7721i −0.300333 + 0.144608i
\(442\) 25.3873 0.0574372
\(443\) 199.400 + 345.370i 0.450112 + 0.779617i 0.998393 0.0566775i \(-0.0180507\pi\)
−0.548280 + 0.836295i \(0.684717\pi\)
\(444\) −73.7946 42.6053i −0.166204 0.0959579i
\(445\) 121.300 210.098i 0.272585 0.472131i
\(446\) −520.830 + 300.702i −1.16778 + 0.674219i
\(447\) 319.054i 0.713767i
\(448\) 333.061 + 358.979i 0.743441 + 0.801292i
\(449\) −519.843 −1.15778 −0.578889 0.815406i \(-0.696514\pi\)
−0.578889 + 0.815406i \(0.696514\pi\)
\(450\) 12.5510 + 21.7389i 0.0278911 + 0.0483087i
\(451\) −269.871 155.810i −0.598384 0.345477i
\(452\) 63.6980 110.328i 0.140925 0.244089i
\(453\) −394.876 + 227.982i −0.871690 + 0.503270i
\(454\) 124.258i 0.273695i
\(455\) −28.2410 + 91.5442i −0.0620680 + 0.201196i
\(456\) 421.642 0.924654
\(457\) −116.891 202.462i −0.255780 0.443024i 0.709327 0.704880i \(-0.248999\pi\)
−0.965107 + 0.261856i \(0.915666\pi\)
\(458\) 482.975 + 278.846i 1.05453 + 0.608834i
\(459\) −6.43966 + 11.1538i −0.0140298 + 0.0243003i
\(460\) −30.7556 + 17.7567i −0.0668599 + 0.0386016i
\(461\) 745.085i 1.61624i −0.589021 0.808118i \(-0.700486\pi\)
0.589021 0.808118i \(-0.299514\pi\)
\(462\) −62.4236 273.538i −0.135116 0.592073i
\(463\) 742.448 1.60356 0.801779 0.597620i \(-0.203887\pi\)
0.801779 + 0.597620i \(0.203887\pi\)
\(464\) −134.982 233.796i −0.290910 0.503871i
\(465\) 62.7894 + 36.2515i 0.135031 + 0.0779602i
\(466\) −221.463 + 383.585i −0.475242 + 0.823144i
\(467\) −524.404 + 302.765i −1.12292 + 0.648318i −0.942145 0.335206i \(-0.891194\pi\)
−0.180776 + 0.983524i \(0.557861\pi\)
\(468\) 22.0251i 0.0470621i
\(469\) 77.8308 17.7617i 0.165951 0.0378713i
\(470\) −51.5108 −0.109598
\(471\) −187.600 324.933i −0.398301 0.689878i
\(472\) −535.716 309.296i −1.13499 0.655287i
\(473\) 52.5808 91.0726i 0.111164 0.192542i
\(474\) −323.806 + 186.950i −0.683135 + 0.394408i
\(475\) 139.886i 0.294497i
\(476\) −19.8873 6.13515i −0.0417801 0.0128890i
\(477\) −277.797 −0.582383
\(478\) −222.736 385.790i −0.465974 0.807091i
\(479\) 260.542 + 150.424i 0.543930 + 0.314038i 0.746670 0.665194i \(-0.231651\pi\)
−0.202740 + 0.979233i \(0.564985\pi\)
\(480\) −35.7606 + 61.9391i −0.0745012 + 0.129040i
\(481\) −217.393 + 125.512i −0.451960 + 0.260939i
\(482\) 56.8492i 0.117944i
\(483\) −117.681 + 109.185i −0.243647 + 0.226056i
\(484\) −84.2300 −0.174029
\(485\) −171.231 296.581i −0.353054 0.611507i
\(486\) 22.5918 + 13.0434i 0.0464851 + 0.0268382i
\(487\) −295.602 + 511.998i −0.606986 + 1.05133i 0.384748 + 0.923021i \(0.374288\pi\)
−0.991734 + 0.128309i \(0.959045\pi\)
\(488\) −871.979 + 503.438i −1.78684 + 1.03163i
\(489\) 298.918i 0.611284i
\(490\) −103.299 + 151.490i −0.210814 + 0.309163i
\(491\) −308.637 −0.628589 −0.314295 0.949325i \(-0.601768\pi\)
−0.314295 + 0.949325i \(0.601768\pi\)
\(492\) 23.4098 + 40.5469i 0.0475808 + 0.0824124i
\(493\) 59.3556 + 34.2690i 0.120397 + 0.0695111i
\(494\) 143.278 248.164i 0.290036 0.502357i
\(495\) 80.3347 46.3813i 0.162292 0.0936995i
\(496\) 182.767i 0.368481i
\(497\) 473.687 + 510.548i 0.953093 + 1.02726i
\(498\) −87.9359 −0.176578
\(499\) 447.344 + 774.822i 0.896480 + 1.55275i 0.831962 + 0.554833i \(0.187218\pi\)
0.0645183 + 0.997917i \(0.479449\pi\)
\(500\) −11.6143 6.70552i −0.0232286 0.0134110i
\(501\) −135.899 + 235.384i −0.271256 + 0.469829i
\(502\) 122.719 70.8520i 0.244461 0.141140i
\(503\) 609.546i 1.21182i −0.795533 0.605911i \(-0.792809\pi\)
0.795533 0.605911i \(-0.207191\pi\)
\(504\) −53.8650 + 174.606i −0.106875 + 0.346440i
\(505\) 255.499 0.505939
\(506\) −153.198 265.347i −0.302763 0.524401i
\(507\) −197.309 113.916i −0.389169 0.224687i
\(508\) −118.394 + 205.064i −0.233058 + 0.403669i
\(509\) 205.570 118.686i 0.403871 0.233175i −0.284282 0.958741i \(-0.591755\pi\)
0.688153 + 0.725566i \(0.258422\pi\)
\(510\) 16.0647i 0.0314994i
\(511\) 162.081 + 710.233i 0.317185 + 1.38989i
\(512\) 520.094 1.01581
\(513\) 72.6869 + 125.897i 0.141690 + 0.245414i
\(514\) 46.2612 + 26.7089i 0.0900023 + 0.0519629i
\(515\) −62.5867 + 108.403i −0.121527 + 0.210492i
\(516\) −13.6833 + 7.90003i −0.0265179 + 0.0153101i
\(517\) 190.355i 0.368191i
\(518\) −468.399 + 106.893i −0.904245 + 0.206356i
\(519\) 82.4490 0.158861
\(520\) 59.5419 + 103.130i 0.114504 + 0.198326i
\(521\) −32.6670 18.8603i −0.0627006 0.0362002i 0.468322 0.883558i \(-0.344859\pi\)
−0.531023 + 0.847358i \(0.678192\pi\)
\(522\) 69.4109 120.223i 0.132971 0.230313i
\(523\) 40.5068 23.3866i 0.0774509 0.0447163i −0.460774 0.887517i \(-0.652428\pi\)
0.538225 + 0.842801i \(0.319095\pi\)
\(524\) 176.431i 0.336700i
\(525\) −57.9279 17.8705i −0.110339 0.0340391i
\(526\) 247.808 0.471118
\(527\) 23.2002 + 40.1839i 0.0440231 + 0.0762503i
\(528\) −202.509 116.919i −0.383540 0.221437i
\(529\) 176.846 306.306i 0.334303 0.579029i
\(530\) −300.081 + 173.252i −0.566190 + 0.326890i
\(531\) 213.278i 0.401653i
\(532\) −172.210 + 159.777i −0.323702 + 0.300332i
\(533\) 137.926 0.258774
\(534\) −157.237 272.342i −0.294450 0.510003i
\(535\) −191.143 110.356i −0.357277 0.206274i
\(536\) 49.6166 85.9385i 0.0925683 0.160333i
\(537\) 44.3241 25.5905i 0.0825402 0.0476546i
\(538\) 152.445i 0.283355i
\(539\) 559.820 + 381.733i 1.03863 + 0.708225i
\(540\) −13.9372 −0.0258096
\(541\) 195.629 + 338.839i 0.361606 + 0.626320i 0.988225 0.153005i \(-0.0488951\pi\)
−0.626619 + 0.779326i \(0.715562\pi\)
\(542\) −180.809 104.390i −0.333596 0.192602i
\(543\) −8.94167 + 15.4874i −0.0164672 + 0.0285219i
\(544\) −39.6397 + 22.8860i −0.0728671 + 0.0420699i
\(545\) 117.971i 0.216461i
\(546\) 84.4631 + 91.0356i 0.154694 + 0.166732i
\(547\) −389.827 −0.712664 −0.356332 0.934359i \(-0.615973\pi\)
−0.356332 + 0.934359i \(0.615973\pi\)
\(548\) 149.096 + 258.241i 0.272072 + 0.471243i
\(549\) −300.641 173.575i −0.547615 0.316166i
\(550\) 57.8526 100.204i 0.105186 0.182188i
\(551\) 669.969 386.807i 1.21591 0.702009i
\(552\) 199.545i 0.361495i
\(553\) 266.185 862.849i 0.481347 1.56031i
\(554\) 207.382 0.374336
\(555\) −79.4221 137.563i −0.143103 0.247862i
\(556\) −16.3451 9.43686i −0.0293977 0.0169728i
\(557\) −89.4085 + 154.860i −0.160518 + 0.278025i −0.935055 0.354504i \(-0.884650\pi\)
0.774537 + 0.632529i \(0.217983\pi\)
\(558\) 81.3914 46.9913i 0.145863 0.0842139i
\(559\) 46.5456i 0.0832659i
\(560\) 33.9999 + 148.986i 0.0607141 + 0.266046i
\(561\) 59.3661 0.105822
\(562\) −14.8979 25.8040i −0.0265088 0.0459146i
\(563\) −139.571 80.5815i −0.247906 0.143129i 0.370899 0.928673i \(-0.379050\pi\)
−0.618805 + 0.785545i \(0.712383\pi\)
\(564\) 14.3000 24.7683i 0.0253546 0.0439154i
\(565\) 205.667 118.742i 0.364012 0.210162i
\(566\) 186.012i 0.328644i
\(567\) −61.4209 + 14.0168i −0.108326 + 0.0247210i
\(568\) 865.704 1.52413
\(569\) −6.24946 10.8244i −0.0109832 0.0190235i 0.860482 0.509482i \(-0.170163\pi\)
−0.871465 + 0.490458i \(0.836829\pi\)
\(570\) 157.035 + 90.6642i 0.275500 + 0.159060i
\(571\) −61.6982 + 106.864i −0.108053 + 0.187153i −0.914981 0.403496i \(-0.867795\pi\)
0.806929 + 0.590649i \(0.201128\pi\)
\(572\) 87.9210 50.7612i 0.153708 0.0887434i
\(573\) 206.130i 0.359738i
\(574\) 252.251 + 77.8183i 0.439462 + 0.135572i
\(575\) −66.2020 −0.115134
\(576\) 104.933 + 181.750i 0.182176 + 0.315538i
\(577\) −143.692 82.9608i −0.249033 0.143779i 0.370288 0.928917i \(-0.379259\pi\)
−0.619322 + 0.785137i \(0.712592\pi\)
\(578\) 236.675 409.933i 0.409472 0.709227i
\(579\) 14.8576 8.57805i 0.0256608 0.0148153i
\(580\) 74.1673i 0.127875i
\(581\) 155.681 144.441i 0.267954 0.248608i
\(582\) −443.920 −0.762749
\(583\) 640.239 + 1108.93i 1.09818 + 1.90210i
\(584\) 784.219 + 452.769i 1.34284 + 0.775290i
\(585\) −20.5288 + 35.5570i −0.0350920 + 0.0607812i
\(586\) 111.084 64.1345i 0.189564 0.109445i
\(587\) 186.037i 0.316929i −0.987365 0.158465i \(-0.949346\pi\)
0.987365 0.158465i \(-0.0506544\pi\)
\(588\) −44.1649 91.7250i −0.0751104 0.155995i
\(589\) 523.738 0.889199
\(590\) −133.013 230.386i −0.225446 0.390485i
\(591\) 435.512 + 251.443i 0.736908 + 0.425454i
\(592\) −200.208 + 346.771i −0.338190 + 0.585762i
\(593\) 494.838 285.695i 0.834465 0.481779i −0.0209140 0.999781i \(-0.506658\pi\)
0.855379 + 0.518003i \(0.173324\pi\)
\(594\) 120.244i 0.202431i
\(595\) −26.3875 28.4408i −0.0443487 0.0477997i
\(596\) −220.959 −0.370736
\(597\) −294.002 509.227i −0.492466 0.852977i
\(598\) 117.445 + 67.8071i 0.196397 + 0.113390i
\(599\) −87.2619 + 151.142i −0.145679 + 0.252324i −0.929626 0.368504i \(-0.879870\pi\)
0.783947 + 0.620828i \(0.213203\pi\)
\(600\) −65.2591 + 37.6773i −0.108765 + 0.0627956i
\(601\) 667.415i 1.11051i 0.831681 + 0.555254i \(0.187379\pi\)
−0.831681 + 0.555254i \(0.812621\pi\)
\(602\) −26.2611 + 85.1264i −0.0436231 + 0.141406i
\(603\) 34.2136 0.0567390
\(604\) −157.887 273.468i −0.261402 0.452762i
\(605\) −135.980 78.5081i −0.224760 0.129765i
\(606\) 165.597 286.822i 0.273262 0.473303i
\(607\) 23.3123 13.4594i 0.0384057 0.0221736i −0.480674 0.876899i \(-0.659608\pi\)
0.519080 + 0.854726i \(0.326275\pi\)
\(608\) 516.646i 0.849746i
\(609\) 74.5910 + 326.855i 0.122481 + 0.536707i
\(610\) −433.009 −0.709852
\(611\) −42.1265 72.9653i −0.0689468 0.119419i
\(612\) −7.72450 4.45974i −0.0126217 0.00728716i
\(613\) 32.7197 56.6723i 0.0533764 0.0924507i −0.838103 0.545513i \(-0.816335\pi\)
0.891479 + 0.453062i \(0.149668\pi\)
\(614\) 518.201 299.183i 0.843976 0.487270i
\(615\) 87.2780i 0.141915i
\(616\) 821.145 187.392i 1.33303 0.304208i
\(617\) 1059.51 1.71720 0.858601 0.512644i \(-0.171334\pi\)
0.858601 + 0.512644i \(0.171334\pi\)
\(618\) 81.1285 + 140.519i 0.131276 + 0.227377i
\(619\) 139.355 + 80.4565i 0.225129 + 0.129978i 0.608323 0.793690i \(-0.291843\pi\)
−0.383194 + 0.923668i \(0.625176\pi\)
\(620\) −25.1057 + 43.4844i −0.0404931 + 0.0701361i
\(621\) −59.5818 + 34.3995i −0.0959449 + 0.0553938i
\(622\) 527.252i 0.847673i
\(623\) 725.711 + 223.879i 1.16487 + 0.359356i
\(624\) 103.499 0.165863
\(625\) −12.5000 21.6506i −0.0200000 0.0346410i
\(626\) −380.311 219.573i −0.607526 0.350755i
\(627\) 335.043 580.312i 0.534359 0.925538i
\(628\) 225.030 129.921i 0.358328 0.206881i
\(629\) 101.657i 0.161617i
\(630\) −57.6061 + 53.4471i −0.0914383 + 0.0848367i
\(631\) −45.2151 −0.0716562 −0.0358281 0.999358i \(-0.511407\pi\)
−0.0358281 + 0.999358i \(0.511407\pi\)
\(632\) −561.212 972.048i −0.887994 1.53805i
\(633\) −16.6647 9.62137i −0.0263265 0.0151996i
\(634\) −259.048 + 448.684i −0.408593 + 0.707703i
\(635\) −382.267 + 220.702i −0.601995 + 0.347562i
\(636\) 192.386i 0.302494i
\(637\) −299.065 22.4318i −0.469490 0.0352148i
\(638\) −639.886 −1.00296
\(639\) 149.239 + 258.489i 0.233550 + 0.404521i
\(640\) 83.6592 + 48.3007i 0.130718 + 0.0754698i
\(641\) −161.675 + 280.030i −0.252224 + 0.436865i −0.964138 0.265402i \(-0.914495\pi\)
0.711914 + 0.702267i \(0.247829\pi\)
\(642\) −247.771 + 143.051i −0.385936 + 0.222820i
\(643\) 363.744i 0.565698i −0.959164 0.282849i \(-0.908720\pi\)
0.959164 0.282849i \(-0.0912795\pi\)
\(644\) −75.6153 81.4994i −0.117415 0.126552i
\(645\) −29.4535 −0.0456643
\(646\) 58.0232 + 100.499i 0.0898191 + 0.155571i
\(647\) −1114.98 643.737i −1.72331 0.994956i −0.911812 0.410608i \(-0.865317\pi\)
−0.811503 0.584348i \(-0.801350\pi\)
\(648\) −39.1554 + 67.8192i −0.0604250 + 0.104659i
\(649\) −851.376 + 491.542i −1.31183 + 0.757384i
\(650\) 51.2123i 0.0787882i
\(651\) −66.9079 + 216.884i −0.102777 + 0.333156i
\(652\) 207.013 0.317505
\(653\) −308.886 535.007i −0.473026 0.819306i 0.526497 0.850177i \(-0.323505\pi\)
−0.999523 + 0.0308714i \(0.990172\pi\)
\(654\) 132.434 + 76.4606i 0.202498 + 0.116912i
\(655\) 164.446 284.828i 0.251062 0.434852i
\(656\) 190.536 110.006i 0.290451 0.167692i
\(657\) 312.211i 0.475207i
\(658\) −35.8773 157.213i −0.0545247 0.238925i
\(659\) −1229.62 −1.86589 −0.932945 0.360019i \(-0.882770\pi\)
−0.932945 + 0.360019i \(0.882770\pi\)
\(660\) 32.1210 + 55.6353i 0.0486682 + 0.0842958i
\(661\) −606.437 350.127i −0.917454 0.529692i −0.0346322 0.999400i \(-0.511026\pi\)
−0.882822 + 0.469708i \(0.844359\pi\)
\(662\) −72.6387 + 125.814i −0.109726 + 0.190051i
\(663\) −22.7557 + 13.1380i −0.0343224 + 0.0198160i
\(664\) 263.979i 0.397558i
\(665\) −426.936 + 97.4304i −0.642009 + 0.146512i
\(666\) −205.903 −0.309164
\(667\) 183.059 + 317.067i 0.274451 + 0.475363i
\(668\) −163.014 94.1160i −0.244032 0.140892i
\(669\) 311.229 539.064i 0.465215 0.805776i
\(670\) 36.9581 21.3378i 0.0551613 0.0318474i
\(671\) 1600.16i 2.38473i
\(672\) −213.947 66.0018i −0.318374 0.0982169i
\(673\) −121.032 −0.179840 −0.0899201 0.995949i \(-0.528661\pi\)
−0.0899201 + 0.995949i \(0.528661\pi\)
\(674\) 312.867 + 541.901i 0.464194 + 0.804007i
\(675\) −22.5000 12.9904i −0.0333333 0.0192450i
\(676\) 78.8920 136.645i 0.116704 0.202137i
\(677\) −851.854 + 491.818i −1.25828 + 0.726467i −0.972739 0.231901i \(-0.925506\pi\)
−0.285538 + 0.958367i \(0.592172\pi\)
\(678\) 307.840i 0.454042i
\(679\) 785.912 729.171i 1.15745 1.07389i
\(680\) −48.2254 −0.0709197
\(681\) 64.3040 + 111.378i 0.0944258 + 0.163550i
\(682\) −375.166 216.602i −0.550097 0.317599i
\(683\) −56.5263 + 97.9064i −0.0827618 + 0.143348i −0.904435 0.426611i \(-0.859707\pi\)
0.821674 + 0.569958i \(0.193041\pi\)
\(684\) −87.1893 + 50.3388i −0.127470 + 0.0735947i
\(685\) 555.869i 0.811487i
\(686\) −534.299 209.758i −0.778861 0.305770i
\(687\) −577.216 −0.840198
\(688\) 37.1234 + 64.2995i 0.0539584 + 0.0934586i
\(689\) −490.823 283.377i −0.712370 0.411287i
\(690\) −42.9074 + 74.3179i −0.0621847 + 0.107707i
\(691\) −771.062 + 445.173i −1.11586 + 0.644244i −0.940342 0.340231i \(-0.889495\pi\)
−0.175522 + 0.984475i \(0.556161\pi\)
\(692\) 57.0995i 0.0825137i
\(693\) 197.510 + 212.879i 0.285007 + 0.307185i
\(694\) 553.713 0.797858
\(695\) −17.5916 30.4695i −0.0253116 0.0438410i
\(696\) 360.903 + 208.368i 0.518539 + 0.299379i
\(697\) −27.9280 + 48.3728i −0.0400689 + 0.0694014i
\(698\) 363.630 209.942i 0.520960 0.300776i
\(699\) 458.433i 0.655841i
\(700\) 12.3761 40.1176i 0.0176801 0.0573108i
\(701\) −730.892 −1.04264 −0.521321 0.853361i \(-0.674560\pi\)
−0.521321 + 0.853361i \(0.674560\pi\)
\(702\) 26.6107 + 46.0911i 0.0379070 + 0.0656568i
\(703\) −993.712 573.720i −1.41353 0.816102i
\(704\) 483.681 837.760i 0.687047 1.19000i
\(705\) 46.1715 26.6571i 0.0654914 0.0378115i
\(706\) 210.384i 0.297995i
\(707\) 177.955 + 779.791i 0.251704 + 1.10296i
\(708\) 147.704 0.208621
\(709\) −576.325 998.224i −0.812870 1.40793i −0.910847 0.412744i \(-0.864570\pi\)
0.0979765 0.995189i \(-0.468763\pi\)
\(710\) 322.420 + 186.149i 0.454113 + 0.262182i
\(711\) 193.495 335.142i 0.272144 0.471368i
\(712\) 817.554 472.015i 1.14825 0.662943i
\(713\) 247.863i 0.347633i
\(714\) −49.0300 + 11.1891i −0.0686695 + 0.0156710i
\(715\) 189.252 0.264688
\(716\) 17.7225 + 30.6963i 0.0247521 + 0.0428720i
\(717\) 399.296 + 230.534i 0.556898 + 0.321525i
\(718\) −299.199 + 518.228i −0.416712 + 0.721766i
\(719\) 688.275 397.376i 0.957267 0.552678i 0.0619361 0.998080i \(-0.480273\pi\)
0.895331 + 0.445402i \(0.146939\pi\)
\(720\) 65.4927i 0.0909621i
\(721\) −374.442 115.514i −0.519336 0.160213i
\(722\) 705.738 0.977476
\(723\) 29.4197 + 50.9565i 0.0406912 + 0.0704792i
\(724\) −10.7257 6.19249i −0.0148145 0.00855316i
\(725\) −69.1290 + 119.735i −0.0953503 + 0.165152i
\(726\) −176.265 + 101.767i −0.242790 + 0.140175i
\(727\) 312.108i 0.429310i −0.976690 0.214655i \(-0.931137\pi\)
0.976690 0.214655i \(-0.0688626\pi\)
\(728\) −273.284 + 253.553i −0.375390 + 0.348288i
\(729\) −27.0000 −0.0370370
\(730\) 194.715 + 337.256i 0.266732 + 0.461994i
\(731\) −16.3242 9.42479i −0.0223314 0.0128930i
\(732\) 120.208 208.207i 0.164219 0.284435i
\(733\) 215.629 124.493i 0.294173 0.169841i −0.345649 0.938364i \(-0.612341\pi\)
0.639822 + 0.768523i \(0.279008\pi\)
\(734\) 1166.91i 1.58979i
\(735\) 14.1946 189.245i 0.0193123 0.257476i
\(736\) −244.506 −0.332209
\(737\) −78.8522 136.576i −0.106991 0.185314i
\(738\) 97.9777 + 56.5675i 0.132761 + 0.0766497i
\(739\) −152.219 + 263.652i −0.205980 + 0.356768i −0.950445 0.310894i \(-0.899372\pi\)
0.744464 + 0.667662i \(0.232705\pi\)
\(740\) 95.2684 55.0032i 0.128741 0.0743287i
\(741\) 296.588i 0.400253i
\(742\) −737.775 795.185i −0.994306 1.07168i
\(743\) −235.455 −0.316898 −0.158449 0.987367i \(-0.550649\pi\)
−0.158449 + 0.987367i \(0.550649\pi\)
\(744\) 141.065 + 244.332i 0.189604 + 0.328404i
\(745\) −356.713 205.948i −0.478810 0.276441i
\(746\) −121.566 + 210.558i −0.162957 + 0.282250i
\(747\) 78.8209 45.5073i 0.105517 0.0609200i
\(748\) 41.1136i 0.0549646i
\(749\) 203.680 660.237i 0.271936 0.881492i
\(750\) −32.4065 −0.0432086
\(751\) 387.921 + 671.900i 0.516540 + 0.894673i 0.999816 + 0.0192050i \(0.00611351\pi\)
−0.483276 + 0.875468i \(0.660553\pi\)
\(752\) −116.390 67.1976i −0.154774 0.0893585i
\(753\) −73.3325 + 127.016i −0.0973872 + 0.168680i
\(754\) 245.276 141.610i 0.325300 0.187812i
\(755\) 588.646i 0.779663i
\(756\) −9.70722 42.5366i −0.0128402 0.0562654i
\(757\) −194.342 −0.256727 −0.128363 0.991727i \(-0.540972\pi\)
−0.128363 + 0.991727i \(0.540972\pi\)
\(758\) −186.282 322.650i −0.245755 0.425659i
\(759\) 274.637 + 158.562i 0.361840 + 0.208908i
\(760\) −272.169 + 471.410i −0.358117 + 0.620277i
\(761\) −441.278 + 254.772i −0.579866 + 0.334786i −0.761080 0.648658i \(-0.775331\pi\)
0.181214 + 0.983444i \(0.441997\pi\)
\(762\) 572.174i 0.750884i
\(763\) −360.051 + 82.1668i −0.471889 + 0.107689i
\(764\) 142.754 0.186850
\(765\) −8.31357 14.3995i −0.0108674 0.0188229i
\(766\) −50.3732 29.0830i −0.0657614 0.0379674i
\(767\) 217.562 376.828i 0.283653 0.491301i
\(768\) −311.290 + 179.723i −0.405325 + 0.234015i
\(769\) 1174.80i 1.52769i −0.645398 0.763846i \(-0.723308\pi\)
0.645398 0.763846i \(-0.276692\pi\)
\(770\) 346.119 + 106.776i 0.449505 + 0.138670i
\(771\) −55.2880 −0.0717094
\(772\) 5.94067 + 10.2895i 0.00769517 + 0.0133284i
\(773\) 996.623 + 575.401i 1.28929 + 0.744373i 0.978528 0.206114i \(-0.0660817\pi\)
0.310764 + 0.950487i \(0.399415\pi\)
\(774\) −19.0897 + 33.0643i −0.0246636 + 0.0427187i
\(775\) −81.0608 + 46.8005i −0.104595 + 0.0603877i