Properties

Label 731.2.j.a.135.9
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 135.9
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.9

$q$-expansion

\(f(q)\) \(=\) \(q-2.09187 q^{2} +(-0.414315 - 0.239205i) q^{3} +2.37591 q^{4} +(1.22310 + 0.706158i) q^{5} +(0.866692 + 0.500385i) q^{6} +(-2.02420 + 1.16867i) q^{7} -0.786343 q^{8} +(-1.38556 - 2.39986i) q^{9} +O(q^{10})\) \(q-2.09187 q^{2} +(-0.414315 - 0.239205i) q^{3} +2.37591 q^{4} +(1.22310 + 0.706158i) q^{5} +(0.866692 + 0.500385i) q^{6} +(-2.02420 + 1.16867i) q^{7} -0.786343 q^{8} +(-1.38556 - 2.39986i) q^{9} +(-2.55857 - 1.47719i) q^{10} -2.22029i q^{11} +(-0.984374 - 0.568328i) q^{12} +(3.44285 + 5.96319i) q^{13} +(4.23436 - 2.44471i) q^{14} +(-0.337833 - 0.585144i) q^{15} -3.10688 q^{16} +(-3.88327 + 1.38573i) q^{17} +(2.89841 + 5.02019i) q^{18} +(0.0342440 - 0.0593123i) q^{19} +(2.90597 + 1.67777i) q^{20} +1.11821 q^{21} +4.64456i q^{22} +(3.19208 + 1.84295i) q^{23} +(0.325794 + 0.188097i) q^{24} +(-1.50268 - 2.60272i) q^{25} +(-7.20199 - 12.4742i) q^{26} +2.76096i q^{27} +(-4.80932 + 2.77666i) q^{28} +(1.97503 - 1.14028i) q^{29} +(0.706702 + 1.22404i) q^{30} +(-4.10408 - 2.36949i) q^{31} +8.07188 q^{32} +(-0.531105 + 0.919901i) q^{33} +(8.12328 - 2.89875i) q^{34} -3.30108 q^{35} +(-3.29196 - 5.70185i) q^{36} +(-6.36747 - 3.67626i) q^{37} +(-0.0716338 + 0.124073i) q^{38} -3.29419i q^{39} +(-0.961778 - 0.555283i) q^{40} +11.1475i q^{41} -2.33915 q^{42} +(5.40537 - 3.71241i) q^{43} -5.27521i q^{44} -3.91370i q^{45} +(-6.67740 - 3.85520i) q^{46} -0.393738 q^{47} +(1.28723 + 0.743182i) q^{48} +(-0.768401 + 1.33091i) q^{49} +(3.14341 + 5.44454i) q^{50} +(1.94037 + 0.354770i) q^{51} +(8.17989 + 14.1680i) q^{52} +(-3.16119 + 5.47535i) q^{53} -5.77557i q^{54} +(1.56788 - 2.71565i) q^{55} +(1.59172 - 0.918979i) q^{56} +(-0.0283756 + 0.0163827i) q^{57} +(-4.13150 + 2.38532i) q^{58} +4.31625 q^{59} +(-0.802660 - 1.39025i) q^{60} +(-11.8063 + 6.81636i) q^{61} +(8.58519 + 4.95666i) q^{62} +(5.60932 + 3.23854i) q^{63} -10.6715 q^{64} +9.72479i q^{65} +(1.11100 - 1.92431i) q^{66} +(-4.37635 + 7.58006i) q^{67} +(-9.22627 + 3.29235i) q^{68} +(-0.881684 - 1.52712i) q^{69} +6.90541 q^{70} +(-8.52881 + 4.92411i) q^{71} +(1.08953 + 1.88712i) q^{72} +(-7.29754 + 4.21323i) q^{73} +(13.3199 + 7.69024i) q^{74} +1.43780i q^{75} +(0.0813605 - 0.140920i) q^{76} +(2.59480 + 4.49433i) q^{77} +6.89100i q^{78} +(-10.7762 + 6.22164i) q^{79} +(-3.80004 - 2.19395i) q^{80} +(-3.49625 + 6.05568i) q^{81} -23.3190i q^{82} +(6.32858 - 10.9614i) q^{83} +2.65676 q^{84} +(-5.72817 - 1.04732i) q^{85} +(-11.3073 + 7.76587i) q^{86} -1.09105 q^{87} +1.74591i q^{88} +(-2.28162 + 3.95188i) q^{89} +8.18695i q^{90} +(-13.9381 - 8.04714i) q^{91} +(7.58407 + 4.37867i) q^{92} +(1.13359 + 1.96343i) q^{93} +0.823647 q^{94} +(0.0837678 - 0.0483633i) q^{95} +(-3.34430 - 1.93083i) q^{96} +10.0986i q^{97} +(1.60739 - 2.78408i) q^{98} +(-5.32840 + 3.07635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.09187 −1.47917 −0.739586 0.673062i \(-0.764979\pi\)
−0.739586 + 0.673062i \(0.764979\pi\)
\(3\) −0.414315 0.239205i −0.239205 0.138105i 0.375606 0.926779i \(-0.377434\pi\)
−0.614811 + 0.788674i \(0.710768\pi\)
\(4\) 2.37591 1.18795
\(5\) 1.22310 + 0.706158i 0.546988 + 0.315804i 0.747906 0.663804i \(-0.231059\pi\)
−0.200918 + 0.979608i \(0.564393\pi\)
\(6\) 0.866692 + 0.500385i 0.353826 + 0.204281i
\(7\) −2.02420 + 1.16867i −0.765077 + 0.441717i −0.831116 0.556100i \(-0.812297\pi\)
0.0660387 + 0.997817i \(0.478964\pi\)
\(8\) −0.786343 −0.278014
\(9\) −1.38556 2.39986i −0.461854 0.799955i
\(10\) −2.55857 1.47719i −0.809090 0.467128i
\(11\) 2.22029i 0.669444i −0.942317 0.334722i \(-0.891358\pi\)
0.942317 0.334722i \(-0.108642\pi\)
\(12\) −0.984374 0.568328i −0.284164 0.164062i
\(13\) 3.44285 + 5.96319i 0.954875 + 1.65389i 0.734653 + 0.678443i \(0.237345\pi\)
0.220222 + 0.975450i \(0.429322\pi\)
\(14\) 4.23436 2.44471i 1.13168 0.653376i
\(15\) −0.337833 0.585144i −0.0872281 0.151084i
\(16\) −3.10688 −0.776721
\(17\) −3.88327 + 1.38573i −0.941831 + 0.336088i
\(18\) 2.89841 + 5.02019i 0.683162 + 1.18327i
\(19\) 0.0342440 0.0593123i 0.00785611 0.0136072i −0.862071 0.506788i \(-0.830833\pi\)
0.869927 + 0.493181i \(0.164166\pi\)
\(20\) 2.90597 + 1.67777i 0.649796 + 0.375160i
\(21\) 1.11821 0.244014
\(22\) 4.64456i 0.990223i
\(23\) 3.19208 + 1.84295i 0.665594 + 0.384281i 0.794405 0.607388i \(-0.207783\pi\)
−0.128811 + 0.991669i \(0.541116\pi\)
\(24\) 0.325794 + 0.188097i 0.0665024 + 0.0383952i
\(25\) −1.50268 2.60272i −0.300536 0.520544i
\(26\) −7.20199 12.4742i −1.41243 2.44639i
\(27\) 2.76096i 0.531348i
\(28\) −4.80932 + 2.77666i −0.908875 + 0.524739i
\(29\) 1.97503 1.14028i 0.366754 0.211745i −0.305286 0.952261i \(-0.598752\pi\)
0.672039 + 0.740516i \(0.265419\pi\)
\(30\) 0.706702 + 1.22404i 0.129026 + 0.223479i
\(31\) −4.10408 2.36949i −0.737115 0.425574i 0.0839043 0.996474i \(-0.473261\pi\)
−0.821019 + 0.570900i \(0.806594\pi\)
\(32\) 8.07188 1.42692
\(33\) −0.531105 + 0.919901i −0.0924536 + 0.160134i
\(34\) 8.12328 2.89875i 1.39313 0.497132i
\(35\) −3.30108 −0.557984
\(36\) −3.29196 5.70185i −0.548661 0.950308i
\(37\) −6.36747 3.67626i −1.04680 0.604373i −0.125052 0.992150i \(-0.539910\pi\)
−0.921753 + 0.387777i \(0.873243\pi\)
\(38\) −0.0716338 + 0.124073i −0.0116205 + 0.0201274i
\(39\) 3.29419i 0.527492i
\(40\) −0.961778 0.555283i −0.152070 0.0877979i
\(41\) 11.1475i 1.74094i 0.492221 + 0.870470i \(0.336185\pi\)
−0.492221 + 0.870470i \(0.663815\pi\)
\(42\) −2.33915 −0.360938
\(43\) 5.40537 3.71241i 0.824311 0.566138i
\(44\) 5.27521i 0.795268i
\(45\) 3.91370i 0.583421i
\(46\) −6.67740 3.85520i −0.984529 0.568418i
\(47\) −0.393738 −0.0574326 −0.0287163 0.999588i \(-0.509142\pi\)
−0.0287163 + 0.999588i \(0.509142\pi\)
\(48\) 1.28723 + 0.743182i 0.185796 + 0.107269i
\(49\) −0.768401 + 1.33091i −0.109772 + 0.190130i
\(50\) 3.14341 + 5.44454i 0.444545 + 0.769975i
\(51\) 1.94037 + 0.354770i 0.271706 + 0.0496777i
\(52\) 8.17989 + 14.1680i 1.13435 + 1.96475i
\(53\) −3.16119 + 5.47535i −0.434223 + 0.752097i −0.997232 0.0743542i \(-0.976310\pi\)
0.563009 + 0.826451i \(0.309644\pi\)
\(54\) 5.77557i 0.785955i
\(55\) 1.56788 2.71565i 0.211413 0.366178i
\(56\) 1.59172 0.918979i 0.212702 0.122804i
\(57\) −0.0283756 + 0.0163827i −0.00375844 + 0.00216994i
\(58\) −4.13150 + 2.38532i −0.542492 + 0.313208i
\(59\) 4.31625 0.561928 0.280964 0.959718i \(-0.409346\pi\)
0.280964 + 0.959718i \(0.409346\pi\)
\(60\) −0.802660 1.39025i −0.103623 0.179480i
\(61\) −11.8063 + 6.81636i −1.51164 + 0.872746i −0.511733 + 0.859145i \(0.670996\pi\)
−0.999908 + 0.0136011i \(0.995671\pi\)
\(62\) 8.58519 + 4.95666i 1.09032 + 0.629497i
\(63\) 5.60932 + 3.23854i 0.706708 + 0.408018i
\(64\) −10.6715 −1.33394
\(65\) 9.72479i 1.20621i
\(66\) 1.11100 1.92431i 0.136755 0.236866i
\(67\) −4.37635 + 7.58006i −0.534656 + 0.926052i 0.464523 + 0.885561i \(0.346226\pi\)
−0.999180 + 0.0404913i \(0.987108\pi\)
\(68\) −9.22627 + 3.29235i −1.11885 + 0.399256i
\(69\) −0.881684 1.52712i −0.106142 0.183844i
\(70\) 6.90541 0.825354
\(71\) −8.52881 + 4.92411i −1.01218 + 0.584385i −0.911830 0.410567i \(-0.865331\pi\)
−0.100354 + 0.994952i \(0.531997\pi\)
\(72\) 1.08953 + 1.88712i 0.128402 + 0.222399i
\(73\) −7.29754 + 4.21323i −0.854112 + 0.493122i −0.862036 0.506847i \(-0.830811\pi\)
0.00792416 + 0.999969i \(0.497478\pi\)
\(74\) 13.3199 + 7.69024i 1.54841 + 0.893972i
\(75\) 1.43780i 0.166022i
\(76\) 0.0813605 0.140920i 0.00933269 0.0161647i
\(77\) 2.59480 + 4.49433i 0.295705 + 0.512176i
\(78\) 6.89100i 0.780252i
\(79\) −10.7762 + 6.22164i −1.21242 + 0.699989i −0.963285 0.268481i \(-0.913478\pi\)
−0.249131 + 0.968470i \(0.580145\pi\)
\(80\) −3.80004 2.19395i −0.424857 0.245291i
\(81\) −3.49625 + 6.05568i −0.388472 + 0.672854i
\(82\) 23.3190i 2.57515i
\(83\) 6.32858 10.9614i 0.694652 1.20317i −0.275645 0.961259i \(-0.588892\pi\)
0.970298 0.241914i \(-0.0777751\pi\)
\(84\) 2.65676 0.289877
\(85\) −5.72817 1.04732i −0.621308 0.113598i
\(86\) −11.3073 + 7.76587i −1.21930 + 0.837415i
\(87\) −1.09105 −0.116972
\(88\) 1.74591i 0.186115i
\(89\) −2.28162 + 3.95188i −0.241851 + 0.418898i −0.961242 0.275708i \(-0.911088\pi\)
0.719391 + 0.694606i \(0.244421\pi\)
\(90\) 8.18695i 0.862980i
\(91\) −13.9381 8.04714i −1.46111 0.843570i
\(92\) 7.58407 + 4.37867i 0.790694 + 0.456507i
\(93\) 1.13359 + 1.96343i 0.117548 + 0.203599i
\(94\) 0.823647 0.0849527
\(95\) 0.0837678 0.0483633i 0.00859439 0.00496197i
\(96\) −3.34430 1.93083i −0.341326 0.197065i
\(97\) 10.0986i 1.02535i 0.858581 + 0.512677i \(0.171346\pi\)
−0.858581 + 0.512677i \(0.828654\pi\)
\(98\) 1.60739 2.78408i 0.162371 0.281235i
\(99\) −5.32840 + 3.07635i −0.535525 + 0.309185i
\(100\) −3.57023 6.18382i −0.357023 0.618382i
\(101\) 3.47315 + 6.01567i 0.345591 + 0.598581i 0.985461 0.169902i \(-0.0543451\pi\)
−0.639870 + 0.768483i \(0.721012\pi\)
\(102\) −4.05899 0.742131i −0.401900 0.0734819i
\(103\) −2.71805 4.70780i −0.267817 0.463873i 0.700480 0.713672i \(-0.252969\pi\)
−0.968298 + 0.249798i \(0.919636\pi\)
\(104\) −2.70726 4.68912i −0.265469 0.459806i
\(105\) 1.36769 + 0.789634i 0.133472 + 0.0770604i
\(106\) 6.61280 11.4537i 0.642291 1.11248i
\(107\) 16.2298i 1.56899i 0.620133 + 0.784497i \(0.287079\pi\)
−0.620133 + 0.784497i \(0.712921\pi\)
\(108\) 6.55979i 0.631216i
\(109\) −9.50914 5.49010i −0.910810 0.525856i −0.0301184 0.999546i \(-0.509588\pi\)
−0.880692 + 0.473690i \(0.842922\pi\)
\(110\) −3.27979 + 5.68077i −0.312716 + 0.541640i
\(111\) 1.75876 + 3.04626i 0.166934 + 0.289138i
\(112\) 6.28897 3.63094i 0.594251 0.343091i
\(113\) 4.33057i 0.407386i 0.979035 + 0.203693i \(0.0652944\pi\)
−0.979035 + 0.203693i \(0.934706\pi\)
\(114\) 0.0593580 0.0342703i 0.00555938 0.00320971i
\(115\) 2.60282 + 4.50822i 0.242715 + 0.420394i
\(116\) 4.69248 2.70920i 0.435686 0.251543i
\(117\) 9.54057 16.5247i 0.882026 1.52771i
\(118\) −9.02902 −0.831189
\(119\) 6.24106 7.34327i 0.572117 0.673156i
\(120\) 0.265653 + 0.460124i 0.0242507 + 0.0420034i
\(121\) 6.07029 0.551845
\(122\) 24.6972 14.2589i 2.23598 1.29094i
\(123\) 2.66653 4.61856i 0.240433 0.416442i
\(124\) −9.75091 5.62969i −0.875658 0.505561i
\(125\) 11.3061i 1.01125i
\(126\) −11.7339 6.77460i −1.04534 0.603529i
\(127\) −1.42931 −0.126830 −0.0634152 0.997987i \(-0.520199\pi\)
−0.0634152 + 0.997987i \(0.520199\pi\)
\(128\) 6.17963 0.546208
\(129\) −3.12755 + 0.245118i −0.275366 + 0.0215814i
\(130\) 20.3430i 1.78420i
\(131\) 14.6724i 1.28193i −0.767570 0.640966i \(-0.778534\pi\)
0.767570 0.640966i \(-0.221466\pi\)
\(132\) −1.26186 + 2.18560i −0.109830 + 0.190232i
\(133\) 0.160080i 0.0138807i
\(134\) 9.15474 15.8565i 0.790849 1.36979i
\(135\) −1.94968 + 3.37694i −0.167801 + 0.290641i
\(136\) 3.05358 1.08966i 0.261842 0.0934373i
\(137\) 0.277081 0.0236726 0.0118363 0.999930i \(-0.496232\pi\)
0.0118363 + 0.999930i \(0.496232\pi\)
\(138\) 1.84436 + 3.19453i 0.157003 + 0.271937i
\(139\) 16.9041 + 9.75957i 1.43379 + 0.827796i 0.997407 0.0719672i \(-0.0229277\pi\)
0.436378 + 0.899763i \(0.356261\pi\)
\(140\) −7.84304 −0.662858
\(141\) 0.163132 + 0.0941841i 0.0137382 + 0.00793173i
\(142\) 17.8411 10.3006i 1.49720 0.864406i
\(143\) 13.2400 7.64414i 1.10719 0.639235i
\(144\) 4.30478 + 7.45610i 0.358732 + 0.621342i
\(145\) 3.22088 0.267480
\(146\) 15.2655 8.81352i 1.26338 0.729412i
\(147\) 0.636720 0.367611i 0.0525158 0.0303200i
\(148\) −15.1285 8.73444i −1.24355 0.717967i
\(149\) −6.63371 + 11.4899i −0.543455 + 0.941291i 0.455248 + 0.890365i \(0.349551\pi\)
−0.998702 + 0.0509262i \(0.983783\pi\)
\(150\) 3.00768i 0.245576i
\(151\) −3.41425 −0.277848 −0.138924 0.990303i \(-0.544364\pi\)
−0.138924 + 0.990303i \(0.544364\pi\)
\(152\) −0.0269275 + 0.0466399i −0.00218411 + 0.00378299i
\(153\) 8.70606 + 7.39930i 0.703843 + 0.598198i
\(154\) −5.42798 9.40153i −0.437399 0.757597i
\(155\) −3.34648 5.79626i −0.268795 0.465567i
\(156\) 7.82668i 0.626636i
\(157\) −6.96443 12.0627i −0.555822 0.962712i −0.997839 0.0657053i \(-0.979070\pi\)
0.442017 0.897007i \(-0.354263\pi\)
\(158\) 22.5423 13.0148i 1.79337 1.03540i
\(159\) 2.61946 1.51235i 0.207737 0.119937i
\(160\) 9.87273 + 5.70002i 0.780508 + 0.450626i
\(161\) −8.61522 −0.678974
\(162\) 7.31369 12.6677i 0.574618 0.995267i
\(163\) 1.09914 0.634589i 0.0860913 0.0497048i −0.456336 0.889807i \(-0.650839\pi\)
0.542428 + 0.840103i \(0.317505\pi\)
\(164\) 26.4853i 2.06815i
\(165\) −1.29919 + 0.750089i −0.101142 + 0.0583943i
\(166\) −13.2386 + 22.9298i −1.02751 + 1.77970i
\(167\) −3.35841 1.93898i −0.259881 0.150042i 0.364399 0.931243i \(-0.381274\pi\)
−0.624280 + 0.781200i \(0.714608\pi\)
\(168\) −0.879298 −0.0678393
\(169\) −17.2065 + 29.8025i −1.32357 + 2.29250i
\(170\) 11.9826 + 2.19085i 0.919021 + 0.168030i
\(171\) −0.189789 −0.0145135
\(172\) 12.8426 8.82034i 0.979242 0.672545i
\(173\) 2.89906i 0.220411i −0.993909 0.110206i \(-0.964849\pi\)
0.993909 0.110206i \(-0.0351510\pi\)
\(174\) 2.28232 0.173022
\(175\) 6.08346 + 3.51229i 0.459867 + 0.265504i
\(176\) 6.89820i 0.519971i
\(177\) −1.78829 1.03247i −0.134416 0.0776051i
\(178\) 4.77284 8.26680i 0.357740 0.619623i
\(179\) 3.05948 + 5.29917i 0.228676 + 0.396079i 0.957416 0.288712i \(-0.0932270\pi\)
−0.728740 + 0.684791i \(0.759894\pi\)
\(180\) 9.29859i 0.693076i
\(181\) −1.40681 + 0.812223i −0.104567 + 0.0603720i −0.551372 0.834260i \(-0.685895\pi\)
0.446804 + 0.894632i \(0.352562\pi\)
\(182\) 29.1566 + 16.8336i 2.16123 + 1.24779i
\(183\) 6.52203 0.482122
\(184\) −2.51007 1.44919i −0.185045 0.106836i
\(185\) −5.19204 8.99288i −0.381726 0.661169i
\(186\) −2.37132 4.10724i −0.173873 0.301158i
\(187\) 3.07672 + 8.62199i 0.224992 + 0.630503i
\(188\) −0.935484 −0.0682272
\(189\) −3.22667 5.58875i −0.234705 0.406522i
\(190\) −0.175231 + 0.101170i −0.0127126 + 0.00733962i
\(191\) 9.52317 16.4946i 0.689072 1.19351i −0.283066 0.959100i \(-0.591352\pi\)
0.972138 0.234408i \(-0.0753151\pi\)
\(192\) 4.42137 + 2.55268i 0.319085 + 0.184224i
\(193\) 5.47315i 0.393966i 0.980407 + 0.196983i \(0.0631143\pi\)
−0.980407 + 0.196983i \(0.936886\pi\)
\(194\) 21.1249i 1.51668i
\(195\) 2.32622 4.02913i 0.166584 0.288532i
\(196\) −1.82565 + 3.16211i −0.130403 + 0.225865i
\(197\) 19.4863 11.2504i 1.38834 0.801560i 0.395214 0.918589i \(-0.370670\pi\)
0.993128 + 0.117029i \(0.0373371\pi\)
\(198\) 11.1463 6.43532i 0.792134 0.457339i
\(199\) 3.33136i 0.236154i −0.993004 0.118077i \(-0.962327\pi\)
0.993004 0.118077i \(-0.0376729\pi\)
\(200\) 1.18162 + 2.04663i 0.0835534 + 0.144719i
\(201\) 3.62638 2.09369i 0.255785 0.147678i
\(202\) −7.26536 12.5840i −0.511189 0.885405i
\(203\) −2.66524 + 4.61633i −0.187063 + 0.324003i
\(204\) 4.61013 + 0.842899i 0.322774 + 0.0590147i
\(205\) −7.87187 + 13.6345i −0.549795 + 0.952273i
\(206\) 5.68580 + 9.84809i 0.396148 + 0.686149i
\(207\) 10.2141i 0.709927i
\(208\) −10.6965 18.5270i −0.741672 1.28461i
\(209\) −0.131691 0.0760317i −0.00910924 0.00525922i
\(210\) −2.86102 1.65181i −0.197429 0.113986i
\(211\) 24.3773i 1.67820i −0.543976 0.839101i \(-0.683082\pi\)
0.543976 0.839101i \(-0.316918\pi\)
\(212\) −7.51070 + 13.0089i −0.515837 + 0.893455i
\(213\) 4.71149 0.322826
\(214\) 33.9506i 2.32081i
\(215\) 9.23287 0.723614i 0.629676 0.0493501i
\(216\) 2.17107i 0.147722i
\(217\) 11.0767 0.751933
\(218\) 19.8918 + 11.4846i 1.34725 + 0.777833i
\(219\) 4.03131 0.272410
\(220\) 3.72513 6.45212i 0.251148 0.435002i
\(221\) −21.6329 18.3858i −1.45518 1.23676i
\(222\) −3.67909 6.37237i −0.246924 0.427685i
\(223\) −14.6482 −0.980913 −0.490457 0.871466i \(-0.663170\pi\)
−0.490457 + 0.871466i \(0.663170\pi\)
\(224\) −16.3391 + 9.43339i −1.09170 + 0.630295i
\(225\) −4.16412 + 7.21246i −0.277608 + 0.480831i
\(226\) 9.05898i 0.602594i
\(227\) 6.77044 + 3.90891i 0.449370 + 0.259444i 0.707564 0.706649i \(-0.249794\pi\)
−0.258194 + 0.966093i \(0.583127\pi\)
\(228\) −0.0674177 + 0.0389237i −0.00446485 + 0.00257778i
\(229\) −11.8722 20.5632i −0.784536 1.35886i −0.929276 0.369386i \(-0.879568\pi\)
0.144740 0.989470i \(-0.453765\pi\)
\(230\) −5.44476 9.43060i −0.359017 0.621835i
\(231\) 2.48276i 0.163353i
\(232\) −1.55305 + 0.896654i −0.101963 + 0.0588682i
\(233\) 6.74257 3.89282i 0.441720 0.255027i −0.262607 0.964903i \(-0.584582\pi\)
0.704327 + 0.709876i \(0.251249\pi\)
\(234\) −19.9576 + 34.5676i −1.30467 + 2.25975i
\(235\) −0.481582 0.278041i −0.0314149 0.0181374i
\(236\) 10.2550 0.667544
\(237\) 5.95299 0.386688
\(238\) −13.0555 + 15.3611i −0.846260 + 0.995714i
\(239\) 2.32961 4.03500i 0.150690 0.261003i −0.780791 0.624792i \(-0.785184\pi\)
0.931481 + 0.363789i \(0.118517\pi\)
\(240\) 1.04961 + 1.81798i 0.0677520 + 0.117350i
\(241\) −6.99062 + 4.03603i −0.450305 + 0.259984i −0.707959 0.706253i \(-0.750384\pi\)
0.257654 + 0.966237i \(0.417051\pi\)
\(242\) −12.6982 −0.816274
\(243\) 10.0703 5.81409i 0.646009 0.372974i
\(244\) −28.0506 + 16.1950i −1.79576 + 1.03678i
\(245\) −1.87967 + 1.08523i −0.120087 + 0.0693325i
\(246\) −5.57802 + 9.66141i −0.355642 + 0.615989i
\(247\) 0.471588 0.0300064
\(248\) 3.22722 + 1.86324i 0.204929 + 0.118316i
\(249\) −5.24406 + 3.02766i −0.332329 + 0.191870i
\(250\) 23.6509i 1.49581i
\(251\) 1.02603 + 1.77714i 0.0647626 + 0.112172i 0.896589 0.442864i \(-0.146038\pi\)
−0.831826 + 0.555036i \(0.812704\pi\)
\(252\) 13.3272 + 7.69447i 0.839535 + 0.484706i
\(253\) 4.09188 7.08735i 0.257254 0.445578i
\(254\) 2.98992 0.187604
\(255\) 2.12275 + 1.80413i 0.132931 + 0.112979i
\(256\) 8.41606 0.526004
\(257\) 19.3353 1.20610 0.603052 0.797702i \(-0.293951\pi\)
0.603052 + 0.797702i \(0.293951\pi\)
\(258\) 6.54242 0.512754i 0.407313 0.0319227i
\(259\) 17.1854 1.06785
\(260\) 23.1052i 1.43292i
\(261\) −5.47305 3.15987i −0.338773 0.195591i
\(262\) 30.6926i 1.89620i
\(263\) −14.8042 + 25.6416i −0.912866 + 1.58113i −0.102871 + 0.994695i \(0.532803\pi\)
−0.809996 + 0.586436i \(0.800531\pi\)
\(264\) 0.417631 0.723359i 0.0257034 0.0445196i
\(265\) −7.73292 + 4.46461i −0.475030 + 0.274259i
\(266\) 0.334867i 0.0205320i
\(267\) 1.89062 1.09155i 0.115704 0.0668017i
\(268\) −10.3978 + 18.0095i −0.635147 + 1.10011i
\(269\) 7.66238i 0.467184i −0.972335 0.233592i \(-0.924952\pi\)
0.972335 0.233592i \(-0.0750479\pi\)
\(270\) 4.07846 7.06411i 0.248207 0.429908i
\(271\) −0.166203 0.287873i −0.0100961 0.0174870i 0.860933 0.508718i \(-0.169880\pi\)
−0.871029 + 0.491231i \(0.836547\pi\)
\(272\) 12.0649 4.30529i 0.731540 0.261047i
\(273\) 3.84983 + 6.66811i 0.233003 + 0.403572i
\(274\) −0.579616 −0.0350159
\(275\) −5.77880 + 3.33639i −0.348475 + 0.201192i
\(276\) −2.09480 3.62830i −0.126092 0.218398i
\(277\) −20.8620 12.0447i −1.25348 0.723696i −0.281680 0.959508i \(-0.590892\pi\)
−0.971799 + 0.235812i \(0.924225\pi\)
\(278\) −35.3611 20.4157i −2.12082 1.22445i
\(279\) 13.1323i 0.786212i
\(280\) 2.59578 0.155128
\(281\) −1.00936 + 1.74827i −0.0602136 + 0.104293i −0.894561 0.446946i \(-0.852512\pi\)
0.834347 + 0.551239i \(0.185845\pi\)
\(282\) −0.341249 0.197020i −0.0203211 0.0117324i
\(283\) 27.1554 15.6782i 1.61422 0.931972i 0.625846 0.779947i \(-0.284754\pi\)
0.988377 0.152025i \(-0.0485795\pi\)
\(284\) −20.2637 + 11.6992i −1.20243 + 0.694221i
\(285\) −0.0462750 −0.00274110
\(286\) −27.6964 + 15.9905i −1.63772 + 0.945540i
\(287\) −13.0277 22.5647i −0.769004 1.33195i
\(288\) −11.1841 19.3714i −0.659028 1.14147i
\(289\) 13.1595 10.7623i 0.774090 0.633076i
\(290\) −6.73765 −0.395649
\(291\) 2.41563 4.18399i 0.141607 0.245270i
\(292\) −17.3383 + 10.0102i −1.01464 + 0.585805i
\(293\) 24.7675 1.44693 0.723466 0.690361i \(-0.242548\pi\)
0.723466 + 0.690361i \(0.242548\pi\)
\(294\) −1.33193 + 0.768992i −0.0776799 + 0.0448485i
\(295\) 5.27922 + 3.04796i 0.307368 + 0.177459i
\(296\) 5.00701 + 2.89080i 0.291027 + 0.168024i
\(297\) 6.13015 0.355707
\(298\) 13.8768 24.0354i 0.803863 1.39233i
\(299\) 25.3800i 1.46776i
\(300\) 3.41606i 0.197227i
\(301\) −6.60296 + 13.8318i −0.380588 + 0.797251i
\(302\) 7.14216 0.410985
\(303\) 3.32318i 0.190911i
\(304\) −0.106392 + 0.184277i −0.00610201 + 0.0105690i
\(305\) −19.2537 −1.10247
\(306\) −18.2119 15.4784i −1.04111 0.884839i
\(307\) −11.8204 + 20.4735i −0.674626 + 1.16849i 0.301952 + 0.953323i \(0.402362\pi\)
−0.976578 + 0.215164i \(0.930971\pi\)
\(308\) 6.16500 + 10.6781i 0.351283 + 0.608441i
\(309\) 2.60068i 0.147948i
\(310\) 7.00038 + 12.1250i 0.397595 + 0.688654i
\(311\) 2.58148 + 1.49042i 0.146382 + 0.0845139i 0.571402 0.820670i \(-0.306400\pi\)
−0.425020 + 0.905184i \(0.639733\pi\)
\(312\) 2.59036i 0.146650i
\(313\) 15.4125 + 8.89839i 0.871164 + 0.502967i 0.867735 0.497027i \(-0.165575\pi\)
0.00342923 + 0.999994i \(0.498908\pi\)
\(314\) 14.5687 + 25.2337i 0.822157 + 1.42402i
\(315\) 4.57385 + 7.92213i 0.257707 + 0.446362i
\(316\) −25.6032 + 14.7820i −1.44029 + 0.831553i
\(317\) 26.6216i 1.49522i 0.664138 + 0.747610i \(0.268799\pi\)
−0.664138 + 0.747610i \(0.731201\pi\)
\(318\) −5.47956 + 3.16363i −0.307279 + 0.177407i
\(319\) −2.53176 4.38514i −0.141752 0.245521i
\(320\) −13.0524 7.53578i −0.729649 0.421263i
\(321\) 3.88225 6.72425i 0.216686 0.375311i
\(322\) 18.0219 1.00432
\(323\) −0.0507879 + 0.277778i −0.00282592 + 0.0154560i
\(324\) −8.30676 + 14.3877i −0.461487 + 0.799318i
\(325\) 10.3470 17.9216i 0.573949 0.994109i
\(326\) −2.29925 + 1.32747i −0.127344 + 0.0735220i
\(327\) 2.62652 + 4.54927i 0.145247 + 0.251575i
\(328\) 8.76573i 0.484007i
\(329\) 0.797006 0.460151i 0.0439403 0.0253690i
\(330\) 2.71774 1.56909i 0.149606 0.0863753i
\(331\) 15.2357 + 26.3891i 0.837431 + 1.45047i 0.892035 + 0.451966i \(0.149277\pi\)
−0.0546040 + 0.998508i \(0.517390\pi\)
\(332\) 15.0361 26.0433i 0.825214 1.42931i
\(333\) 20.3747i 1.11653i
\(334\) 7.02534 + 4.05608i 0.384409 + 0.221939i
\(335\) −10.7054 + 6.18079i −0.584901 + 0.337693i
\(336\) −3.47415 −0.189531
\(337\) −24.3595 + 14.0639i −1.32695 + 0.766112i −0.984826 0.173544i \(-0.944478\pi\)
−0.342119 + 0.939657i \(0.611145\pi\)
\(338\) 35.9936 62.3428i 1.95779 3.39100i
\(339\) 1.03589 1.79422i 0.0562621 0.0974488i
\(340\) −13.6096 2.48833i −0.738084 0.134948i
\(341\) −5.26097 + 9.11227i −0.284898 + 0.493457i
\(342\) 0.397013 0.0214680
\(343\) 19.9535i 1.07739i
\(344\) −4.25048 + 2.91923i −0.229170 + 0.157394i
\(345\) 2.49043i 0.134080i
\(346\) 6.06445i 0.326027i
\(347\) −8.62537 4.97986i −0.463034 0.267333i 0.250285 0.968172i \(-0.419476\pi\)
−0.713319 + 0.700839i \(0.752809\pi\)
\(348\) −2.59222 −0.138958
\(349\) 4.68512 8.11486i 0.250789 0.434379i −0.712955 0.701210i \(-0.752643\pi\)
0.963743 + 0.266832i \(0.0859768\pi\)
\(350\) −12.7258 7.34724i −0.680222 0.392726i
\(351\) −16.4642 + 9.50559i −0.878792 + 0.507371i
\(352\) 17.9219i 0.955242i
\(353\) 1.82960 + 3.16895i 0.0973796 + 0.168666i 0.910599 0.413290i \(-0.135621\pi\)
−0.813220 + 0.581957i \(0.802287\pi\)
\(354\) 3.74086 + 2.15979i 0.198825 + 0.114791i
\(355\) −13.9088 −0.738203
\(356\) −5.42091 + 9.38929i −0.287308 + 0.497631i
\(357\) −4.34231 + 1.54953i −0.229819 + 0.0820100i
\(358\) −6.40002 11.0852i −0.338251 0.585869i
\(359\) −15.9122 27.5607i −0.839813 1.45460i −0.890051 0.455861i \(-0.849331\pi\)
0.0502382 0.998737i \(-0.484002\pi\)
\(360\) 3.07752i 0.162199i
\(361\) 9.49765 + 16.4504i 0.499877 + 0.865812i
\(362\) 2.94286 1.69906i 0.154673 0.0893007i
\(363\) −2.51502 1.45204i −0.132004 0.0762126i
\(364\) −33.1155 19.1193i −1.73572 1.00212i
\(365\) −11.9008 −0.622919
\(366\) −13.6432 −0.713142
\(367\) 15.6397 + 9.02961i 0.816388 + 0.471342i 0.849169 0.528121i \(-0.177103\pi\)
−0.0327813 + 0.999463i \(0.510436\pi\)
\(368\) −9.91741 5.72582i −0.516981 0.298479i
\(369\) 26.7524 15.4455i 1.39267 0.804060i
\(370\) 10.8611 + 18.8119i 0.564639 + 0.977984i
\(371\) 14.7776i 0.767216i
\(372\) 2.69330 + 4.66493i 0.139641 + 0.241866i
\(373\) 10.0533 + 17.4128i 0.520538 + 0.901599i 0.999715 + 0.0238801i \(0.00760200\pi\)
−0.479177 + 0.877718i \(0.659065\pi\)
\(374\) −6.43608 18.0361i −0.332802 0.932623i
\(375\) −2.70448 + 4.68429i −0.139659 + 0.241896i
\(376\) 0.309613 0.0159671
\(377\) 13.5995 + 7.85165i 0.700408 + 0.404381i
\(378\) 6.74976 + 11.6909i 0.347170 + 0.601316i
\(379\) 13.0425i 0.669946i 0.942228 + 0.334973i \(0.108727\pi\)
−0.942228 + 0.334973i \(0.891273\pi\)
\(380\) 0.199024 0.114907i 0.0102097 0.00589459i
\(381\) 0.592183 + 0.341897i 0.0303385 + 0.0175159i
\(382\) −19.9212 + 34.5045i −1.01926 + 1.76541i
\(383\) −14.5726 −0.744625 −0.372312 0.928107i \(-0.621435\pi\)
−0.372312 + 0.928107i \(0.621435\pi\)
\(384\) −2.56032 1.47820i −0.130656 0.0754340i
\(385\) 7.32936i 0.373539i
\(386\) 11.4491i 0.582744i
\(387\) −16.3988 7.82837i −0.833596 0.397938i
\(388\) 23.9932i 1.21807i
\(389\) −4.15122 −0.210475 −0.105237 0.994447i \(-0.533560\pi\)
−0.105237 + 0.994447i \(0.533560\pi\)
\(390\) −4.86614 + 8.42840i −0.246407 + 0.426789i
\(391\) −14.9495 2.73331i −0.756029 0.138229i
\(392\) 0.604227 1.04655i 0.0305181 0.0528588i
\(393\) −3.50971 + 6.07899i −0.177041 + 0.306644i
\(394\) −40.7628 + 23.5344i −2.05360 + 1.18565i
\(395\) −17.5738 −0.884236
\(396\) −12.6598 + 7.30913i −0.636178 + 0.367297i
\(397\) 17.0926 + 9.86843i 0.857854 + 0.495282i 0.863293 0.504703i \(-0.168398\pi\)
−0.00543911 + 0.999985i \(0.501731\pi\)
\(398\) 6.96875i 0.349312i
\(399\) 0.0382920 0.0663237i 0.00191700 0.00332034i
\(400\) 4.66866 + 8.08635i 0.233433 + 0.404318i
\(401\) −3.36538 + 1.94300i −0.168059 + 0.0970288i −0.581670 0.813425i \(-0.697601\pi\)
0.413611 + 0.910454i \(0.364267\pi\)
\(402\) −7.58590 + 4.37972i −0.378350 + 0.218441i
\(403\) 32.6313i 1.62548i
\(404\) 8.25187 + 14.2927i 0.410546 + 0.711086i
\(405\) −8.55254 + 4.93781i −0.424979 + 0.245362i
\(406\) 5.57532 9.65675i 0.276699 0.479256i
\(407\) −8.16237 + 14.1376i −0.404594 + 0.700777i
\(408\) −1.52580 0.278971i −0.0755382 0.0138111i
\(409\) 31.9239 1.57854 0.789268 0.614049i \(-0.210460\pi\)
0.789268 + 0.614049i \(0.210460\pi\)
\(410\) 16.4669 28.5215i 0.813242 1.40858i
\(411\) −0.114799 0.0662791i −0.00566261 0.00326931i
\(412\) −6.45783 11.1853i −0.318154 0.551060i
\(413\) −8.73697 + 5.04429i −0.429918 + 0.248213i
\(414\) 21.3665i 1.05010i
\(415\) 15.4810 8.93796i 0.759933 0.438747i
\(416\) 27.7903 + 48.1342i 1.36253 + 2.35997i
\(417\) −4.66908 8.08708i −0.228646 0.396026i
\(418\) 0.275480 + 0.159048i 0.0134741 + 0.00777930i
\(419\) 29.0309i 1.41825i −0.705081 0.709127i \(-0.749089\pi\)
0.705081 0.709127i \(-0.250911\pi\)
\(420\) 3.24949 + 1.87610i 0.158559 + 0.0915441i
\(421\) −15.2581 26.4278i −0.743633 1.28801i −0.950831 0.309711i \(-0.899768\pi\)
0.207197 0.978299i \(-0.433566\pi\)
\(422\) 50.9940i 2.48235i
\(423\) 0.545548 + 0.944917i 0.0265255 + 0.0459434i
\(424\) 2.48578 4.30550i 0.120720 0.209094i
\(425\) 9.44197 + 8.02475i 0.458003 + 0.389258i
\(426\) −9.85581 −0.477515
\(427\) 15.9322 27.5954i 0.771014 1.33544i
\(428\) 38.5604i 1.86389i
\(429\) −7.31407 −0.353127
\(430\) −19.3139 + 1.51370i −0.931400 + 0.0729973i
\(431\) 25.0984i 1.20895i −0.796624 0.604475i \(-0.793383\pi\)
0.796624 0.604475i \(-0.206617\pi\)
\(432\) 8.57799i 0.412709i
\(433\) −8.90733 + 15.4280i −0.428059 + 0.741420i −0.996701 0.0811653i \(-0.974136\pi\)
0.568642 + 0.822585i \(0.307469\pi\)
\(434\) −23.1709 −1.11224
\(435\) −1.33446 0.770451i −0.0639825 0.0369403i
\(436\) −22.5928 13.0440i −1.08200 0.624693i
\(437\) 0.218619 0.126220i 0.0104580 0.00603790i
\(438\) −8.43295 −0.402942
\(439\) 30.7231 17.7380i 1.46633 0.846588i 0.467042 0.884235i \(-0.345320\pi\)
0.999291 + 0.0376478i \(0.0119865\pi\)
\(440\) −1.23289 + 2.13543i −0.0587758 + 0.101803i
\(441\) 4.25867 0.202794
\(442\) 45.2531 + 38.4607i 2.15247 + 1.82939i
\(443\) −7.37973 12.7821i −0.350622 0.607294i 0.635737 0.771906i \(-0.280696\pi\)
−0.986359 + 0.164611i \(0.947363\pi\)
\(444\) 4.17864 + 7.23762i 0.198310 + 0.343482i
\(445\) −5.58130 + 3.22237i −0.264579 + 0.152755i
\(446\) 30.6420 1.45094
\(447\) 5.49689 3.17363i 0.259994 0.150108i
\(448\) 21.6013 12.4715i 1.02057 0.589224i
\(449\) 5.05540 + 2.91874i 0.238579 + 0.137744i 0.614524 0.788898i \(-0.289348\pi\)
−0.375944 + 0.926642i \(0.622682\pi\)
\(450\) 8.71077 15.0875i 0.410630 0.711232i
\(451\) 24.7506 1.16546
\(452\) 10.2890i 0.483955i
\(453\) 1.41458 + 0.816706i 0.0664626 + 0.0383722i
\(454\) −14.1628 8.17692i −0.664695 0.383762i
\(455\) −11.3651 19.6850i −0.532805 0.922845i
\(456\) 0.0223130 0.0128824i 0.00104490 0.000603274i
\(457\) −3.15958 −0.147799 −0.0738994 0.997266i \(-0.523544\pi\)
−0.0738994 + 0.997266i \(0.523544\pi\)
\(458\) 24.8350 + 43.0155i 1.16046 + 2.00998i
\(459\) −3.82594 10.7216i −0.178579 0.500439i
\(460\) 6.18406 + 10.7111i 0.288333 + 0.499408i
\(461\) 2.59970 4.50282i 0.121080 0.209717i −0.799114 0.601180i \(-0.794697\pi\)
0.920194 + 0.391463i \(0.128031\pi\)
\(462\) 5.19360i 0.241628i
\(463\) −13.6282 + 23.6047i −0.633355 + 1.09700i 0.353507 + 0.935432i \(0.384989\pi\)
−0.986861 + 0.161570i \(0.948344\pi\)
\(464\) −6.13619 + 3.54273i −0.284865 + 0.164467i
\(465\) 3.20197i 0.148488i
\(466\) −14.1046 + 8.14327i −0.653381 + 0.377230i
\(467\) −18.1466 + 31.4308i −0.839723 + 1.45444i 0.0504034 + 0.998729i \(0.483949\pi\)
−0.890126 + 0.455714i \(0.849384\pi\)
\(468\) 22.6675 39.2612i 1.04780 1.81485i
\(469\) 20.4581i 0.944668i
\(470\) 1.00740 + 0.581625i 0.0464681 + 0.0268284i
\(471\) 6.66370i 0.307047i
\(472\) −3.39406 −0.156224
\(473\) −8.24265 12.0015i −0.378997 0.551830i
\(474\) −12.4528 −0.571978
\(475\) −0.205831 −0.00944418
\(476\) 14.8282 17.4469i 0.679648 0.799677i
\(477\) 17.5201 0.802191
\(478\) −4.87323 + 8.44069i −0.222897 + 0.386068i
\(479\) −15.1252 8.73253i −0.691087 0.398999i 0.112932 0.993603i \(-0.463976\pi\)
−0.804019 + 0.594603i \(0.797309\pi\)
\(480\) −2.72695 4.72321i −0.124468 0.215584i
\(481\) 50.6272i 2.30840i
\(482\) 14.6234 8.44285i 0.666079 0.384561i
\(483\) 3.56941 + 2.06080i 0.162414 + 0.0937698i
\(484\) 14.4224 0.655566
\(485\) −7.13119 + 12.3516i −0.323811 + 0.560856i
\(486\) −21.0657 + 12.1623i −0.955560 + 0.551693i
\(487\) 15.0905 8.71253i 0.683818 0.394803i −0.117474 0.993076i \(-0.537480\pi\)
0.801292 + 0.598273i \(0.204146\pi\)
\(488\) 9.28380 5.36000i 0.420258 0.242636i
\(489\) −0.607187 −0.0274580
\(490\) 3.93201 2.27015i 0.177630 0.102555i
\(491\) 10.8611 + 18.8120i 0.490156 + 0.848975i 0.999936 0.0113296i \(-0.00360639\pi\)
−0.509780 + 0.860305i \(0.670273\pi\)
\(492\) 6.33542 10.9733i 0.285623 0.494713i
\(493\) −6.08944 + 7.16487i −0.274255 + 0.322690i
\(494\) −0.986499 −0.0443847
\(495\) −8.68957 −0.390567
\(496\) 12.7509 + 7.36174i 0.572533 + 0.330552i
\(497\) 11.5094 19.9348i 0.516266 0.894199i
\(498\) 10.9699 6.33346i 0.491571 0.283809i
\(499\) 25.6943 14.8346i 1.15024 0.664089i 0.201291 0.979532i \(-0.435486\pi\)
0.948945 + 0.315443i \(0.102153\pi\)
\(500\) 26.8622i 1.20132i
\(501\) 0.927626 + 1.60669i 0.0414433 + 0.0717818i
\(502\) −2.14632 3.71754i −0.0957951 0.165922i
\(503\) −14.6729 + 8.47138i −0.654230 + 0.377720i −0.790075 0.613010i \(-0.789959\pi\)
0.135845 + 0.990730i \(0.456625\pi\)
\(504\) −4.41085 2.54661i −0.196475 0.113435i
\(505\) 9.81036i 0.436555i
\(506\) −8.55967 + 14.8258i −0.380524 + 0.659087i
\(507\) 14.2578 8.23174i 0.633211 0.365584i
\(508\) −3.39589 −0.150668
\(509\) 17.6288 + 30.5339i 0.781382 + 1.35339i 0.931137 + 0.364670i \(0.118818\pi\)
−0.149755 + 0.988723i \(0.547848\pi\)
\(510\) −4.44050 3.77399i −0.196629 0.167115i
\(511\) 9.84780 17.0569i 0.435641 0.754552i
\(512\) −29.9645 −1.32426
\(513\) 0.163759 + 0.0945464i 0.00723014 + 0.00417432i
\(514\) −40.4469 −1.78404
\(515\) 7.67749i 0.338311i
\(516\) −7.43077 + 0.582377i −0.327121 + 0.0256377i
\(517\) 0.874214i 0.0384479i
\(518\) −35.9495 −1.57953
\(519\) −0.693470 + 1.20112i −0.0304399 + 0.0527235i
\(520\) 7.64703i 0.335344i
\(521\) −23.7548 13.7149i −1.04072 0.600859i −0.120682 0.992691i \(-0.538508\pi\)
−0.920037 + 0.391832i \(0.871841\pi\)
\(522\) 11.4489 + 6.61002i 0.501104 + 0.289313i
\(523\) −19.3735 33.5558i −0.847143 1.46729i −0.883747 0.467964i \(-0.844988\pi\)
0.0366048 0.999330i \(-0.488346\pi\)
\(524\) 34.8602i 1.52287i
\(525\) −1.68031 2.91039i −0.0733349 0.127020i
\(526\) 30.9684 53.6389i 1.35029 2.33877i
\(527\) 19.2207 + 3.51424i 0.837268 + 0.153083i
\(528\) 1.65008 2.85803i 0.0718107 0.124380i
\(529\) −4.70710 8.15293i −0.204656 0.354475i
\(530\) 16.1762 9.33936i 0.702651 0.405676i
\(531\) −5.98044 10.3584i −0.259529 0.449517i
\(532\) 0.380336i 0.0164896i
\(533\) −66.4745 + 38.3790i −2.87933 + 1.66238i
\(534\) −3.95492 + 2.28337i −0.171146 + 0.0988113i
\(535\) −11.4608 + 19.8507i −0.495494 + 0.858220i
\(536\) 3.44132 5.96053i 0.148642 0.257456i
\(537\) 2.92737i 0.126325i
\(538\) 16.0287i 0.691045i
\(539\) 2.95501 + 1.70608i 0.127281 + 0.0734859i
\(540\) −4.63225 + 8.02329i −0.199340 + 0.345267i
\(541\) −2.81781 + 1.62686i −0.121147 + 0.0699442i −0.559349 0.828932i \(-0.688949\pi\)
0.438202 + 0.898877i \(0.355615\pi\)
\(542\) 0.347675 + 0.602191i 0.0149339 + 0.0258663i
\(543\) 0.777151 0.0333507
\(544\) −31.3452 + 11.1854i −1.34392 + 0.479570i
\(545\) −7.75376 13.4299i −0.332135 0.575274i
\(546\) −8.05334 13.9488i −0.344651 0.596953i
\(547\) 24.8186 + 14.3290i 1.06116 + 0.612664i 0.925754 0.378126i \(-0.123431\pi\)
0.135410 + 0.990790i \(0.456765\pi\)
\(548\) 0.658318 0.0281220
\(549\) 32.7167 + 18.8890i 1.39631 + 0.806162i
\(550\) 12.0885 6.97929i 0.515455 0.297598i
\(551\) 0.156191i 0.00665398i
\(552\) 0.693306 + 1.20084i 0.0295091 + 0.0511112i
\(553\) 14.5421 25.1877i 0.618394 1.07109i
\(554\) 43.6406 + 25.1959i 1.85411 + 1.07047i
\(555\) 4.96785i 0.210873i
\(556\) 40.1625 + 23.1878i 1.70327 + 0.983383i
\(557\) 16.6322 0.704730 0.352365 0.935863i \(-0.385378\pi\)
0.352365 + 0.935863i \(0.385378\pi\)
\(558\) 27.4711i 1.16294i
\(559\) 40.7477 + 19.4520i 1.72344 + 0.822731i
\(560\) 10.2561 0.433398
\(561\) 0.787693 4.30819i 0.0332564 0.181892i
\(562\) 2.11146 3.65715i 0.0890664 0.154268i
\(563\) 0.477067 0.0201060 0.0100530 0.999949i \(-0.496800\pi\)
0.0100530 + 0.999949i \(0.496800\pi\)
\(564\) 0.387585 + 0.223772i 0.0163203 + 0.00942252i
\(565\) −3.05807 + 5.29673i −0.128654 + 0.222835i
\(566\) −56.8055 + 32.7967i −2.38771 + 1.37855i
\(567\) 16.3439i 0.686380i
\(568\) 6.70658 3.87204i 0.281402 0.162467i
\(569\) 3.01473 5.22166i 0.126384 0.218904i −0.795889 0.605442i \(-0.792996\pi\)
0.922273 + 0.386539i \(0.126330\pi\)
\(570\) 0.0968011 0.00405455
\(571\) 5.59583 + 3.23075i 0.234178 + 0.135203i 0.612498 0.790472i \(-0.290165\pi\)
−0.378320 + 0.925675i \(0.623498\pi\)
\(572\) 31.4571 18.1618i 1.31529 0.759381i
\(573\) −7.89119 + 4.55598i −0.329659 + 0.190329i
\(574\) 27.2523 + 47.2024i 1.13749 + 1.97019i
\(575\) 11.0774i 0.461961i
\(576\) 14.7860 + 25.6102i 0.616085 + 1.06709i
\(577\) 3.09141 + 5.35448i 0.128697 + 0.222910i 0.923172 0.384387i \(-0.125587\pi\)
−0.794475 + 0.607297i \(0.792254\pi\)
\(578\) −27.5280 + 22.5133i −1.14501 + 0.936428i
\(579\) 1.30920 2.26761i 0.0544087 0.0942386i
\(580\) 7.65251 0.317753
\(581\) 29.5842i 1.22736i
\(582\) −5.05317 + 8.75235i −0.209461 + 0.362797i
\(583\) 12.1569 + 7.01878i 0.503487 + 0.290688i
\(584\) 5.73837 3.31305i 0.237455 0.137095i
\(585\) 23.3382 13.4743i 0.964915 0.557094i
\(586\) −51.8102 −2.14026
\(587\) −8.37099 14.4990i −0.345508 0.598437i 0.639938 0.768426i \(-0.278960\pi\)
−0.985446 + 0.169990i \(0.945627\pi\)
\(588\) 1.51279 0.873408i 0.0623863 0.0360187i
\(589\) −0.281080 + 0.162282i −0.0115817 + 0.00668671i
\(590\) −11.0434 6.37592i −0.454650 0.262492i
\(591\) −10.7646 −0.442798
\(592\) 19.7830 + 11.4217i 0.813076 + 0.469429i
\(593\) −1.80975 3.13457i −0.0743174 0.128722i 0.826472 0.562978i \(-0.190344\pi\)
−0.900789 + 0.434257i \(0.857011\pi\)
\(594\) −12.8235 −0.526153
\(595\) 12.8190 4.57439i 0.525526 0.187532i
\(596\) −15.7611 + 27.2990i −0.645598 + 1.11821i
\(597\) −0.796877 + 1.38023i −0.0326140 + 0.0564891i
\(598\) 53.0915i 2.17107i
\(599\) 4.53821 7.86042i 0.185426 0.321168i −0.758294 0.651913i \(-0.773967\pi\)
0.943720 + 0.330745i \(0.107300\pi\)
\(600\) 1.13060i 0.0461566i
\(601\) 4.36936i 0.178230i −0.996021 0.0891149i \(-0.971596\pi\)
0.996021 0.0891149i \(-0.0284038\pi\)
\(602\) 13.8125 28.9343i 0.562956 1.17927i
\(603\) 24.2548 0.987733
\(604\) −8.11194 −0.330070
\(605\) 7.42459 + 4.28659i 0.301852 + 0.174275i
\(606\) 6.95164i 0.282391i
\(607\) −13.6107 7.85813i −0.552441 0.318952i 0.197665 0.980270i \(-0.436664\pi\)
−0.750106 + 0.661318i \(0.769997\pi\)
\(608\) 0.276413 0.478762i 0.0112100 0.0194163i
\(609\) 2.20850 1.27508i 0.0894929 0.0516687i
\(610\) 40.2762 1.63074
\(611\) −1.35558 2.34794i −0.0548409 0.0949873i
\(612\) 20.6848 + 17.5800i 0.836132 + 0.710631i
\(613\) 16.8481 0.680487 0.340243 0.940337i \(-0.389491\pi\)
0.340243 + 0.940337i \(0.389491\pi\)
\(614\) 24.7267 42.8279i 0.997889 1.72839i
\(615\) 6.52287 3.76598i 0.263028 0.151859i
\(616\) −2.04040 3.53408i −0.0822102 0.142392i
\(617\) 10.3860 5.99638i 0.418126 0.241405i −0.276149 0.961115i \(-0.589058\pi\)
0.694275 + 0.719710i \(0.255725\pi\)
\(618\) 5.44028i 0.218840i
\(619\) −14.3957 + 8.31137i −0.578612 + 0.334062i −0.760582 0.649242i \(-0.775086\pi\)
0.181969 + 0.983304i \(0.441753\pi\)
\(620\) −7.95091 13.7714i −0.319316 0.553072i
\(621\) −5.08831 + 8.81321i −0.204187 + 0.353662i
\(622\) −5.40011 3.11776i −0.216525 0.125011i
\(623\) 10.6659i 0.427319i
\(624\) 10.2347i 0.409715i
\(625\) 0.470495 0.814921i 0.0188198 0.0325969i
\(626\) −32.2408 18.6142i −1.28860 0.743975i
\(627\) 0.0363743 + 0.0630022i 0.00145265 + 0.00251606i
\(628\) −16.5468 28.6599i −0.660290 1.14366i
\(629\) 29.8209 + 5.45233i 1.18904 + 0.217399i
\(630\) −9.56787 16.5720i −0.381193 0.660246i
\(631\) −11.0399 19.1217i −0.439493 0.761224i 0.558157 0.829735i \(-0.311508\pi\)
−0.997650 + 0.0685111i \(0.978175\pi\)
\(632\) 8.47379 4.89234i 0.337069 0.194607i
\(633\) −5.83117 + 10.0999i −0.231768 + 0.401434i
\(634\) 55.6889i 2.21169i
\(635\) −1.74819 1.00932i −0.0693747 0.0400535i
\(636\) 6.22359 3.59319i 0.246781 0.142479i
\(637\) −10.5820 −0.419273
\(638\) 5.29611 + 9.17314i 0.209675 + 0.363168i
\(639\) 23.6344 + 13.6453i 0.934962 + 0.539801i
\(640\) 7.55832 + 4.36380i 0.298769 + 0.172494i
\(641\) 48.0967i 1.89970i −0.312699 0.949852i \(-0.601233\pi\)
0.312699 0.949852i \(-0.398767\pi\)
\(642\) −8.12114 + 14.0662i −0.320516 + 0.555150i
\(643\) 23.2841i 0.918234i 0.888376 + 0.459117i \(0.151834\pi\)
−0.888376 + 0.459117i \(0.848166\pi\)
\(644\) −20.4689 −0.806589
\(645\) −3.99841 1.90874i −0.157437 0.0751567i
\(646\) 0.106242 0.581075i 0.00418002 0.0228621i
\(647\) 24.0207 0.944351 0.472176 0.881504i \(-0.343469\pi\)
0.472176 + 0.881504i \(0.343469\pi\)
\(648\) 2.74925 4.76185i 0.108001 0.187063i
\(649\) 9.58335i 0.376179i
\(650\) −21.6446 + 37.4895i −0.848970 + 1.47046i
\(651\) −4.58923 2.64959i −0.179866 0.103846i
\(652\) 2.61145 1.50772i 0.102272 0.0590470i
\(653\) 5.82310i 0.227876i −0.993488 0.113938i \(-0.963654\pi\)
0.993488 0.113938i \(-0.0363465\pi\)
\(654\) −5.49433 9.51646i −0.214845 0.372123i
\(655\) 10.3610 17.9458i 0.404839 0.701201i
\(656\) 34.6339i 1.35223i
\(657\) 20.2224 + 11.6754i 0.788950 + 0.455501i
\(658\) −1.66723 + 0.962575i −0.0649954 + 0.0375251i
\(659\) −0.115319 0.199738i −0.00449219 0.00778069i 0.863771 0.503885i \(-0.168097\pi\)
−0.868263 + 0.496105i \(0.834763\pi\)
\(660\) −3.08676 + 1.78214i −0.120152 + 0.0693697i
\(661\) −49.3436 −1.91924 −0.959622 0.281292i \(-0.909237\pi\)
−0.959622 + 0.281292i \(0.909237\pi\)
\(662\) −31.8711 55.2024i −1.23871 2.14550i
\(663\) 4.56484 + 12.7922i 0.177284 + 0.496809i
\(664\) −4.97644 + 8.61945i −0.193123 + 0.334499i
\(665\) −0.113042 + 0.195794i −0.00438358 + 0.00759258i
\(666\) 42.6212i 1.65154i
\(667\) 8.40592 0.325479
\(668\) −7.97925 4.60682i −0.308727 0.178243i
\(669\) 6.06896 + 3.50391i 0.234639 + 0.135469i
\(670\) 22.3944 12.9294i 0.865170 0.499506i
\(671\) 15.1343 + 26.2134i 0.584254 + 1.01196i
\(672\) 9.02606 0.348188
\(673\) −29.3143 + 16.9246i −1.12998 + 0.652397i −0.943931 0.330143i \(-0.892903\pi\)
−0.186053 + 0.982540i \(0.559570\pi\)
\(674\) 50.9568 29.4199i 1.96278 1.13321i
\(675\) 7.18601 4.14885i 0.276590 0.159689i
\(676\) −40.8809 + 70.8078i −1.57234 + 2.72338i
\(677\) 20.1020i 0.772581i −0.922377 0.386290i \(-0.873756\pi\)
0.922377 0.386290i \(-0.126244\pi\)
\(678\) −2.16695 + 3.75327i −0.0832213 + 0.144144i
\(679\) −11.8019 20.4416i −0.452917 0.784475i
\(680\) 4.50431 + 0.823551i 0.172732 + 0.0315817i
\(681\) −1.87006 3.23904i −0.0716610 0.124120i
\(682\) 11.0053 19.0617i 0.421413 0.729909i
\(683\) 11.8653 + 6.85041i 0.454011 + 0.262124i 0.709523 0.704682i \(-0.248911\pi\)
−0.255511 + 0.966806i \(0.582244\pi\)
\(684\) −0.450920 −0.0172414
\(685\) 0.338898 + 0.195663i 0.0129486 + 0.00747590i
\(686\) 41.7400i 1.59364i
\(687\) 11.3595i 0.433393i
\(688\) −16.7939 + 11.5340i −0.640260 + 0.439731i
\(689\) −43.5341 −1.65852
\(690\) 5.20965i 0.198328i
\(691\) −24.4463 14.1141i −0.929982 0.536925i −0.0431761 0.999067i \(-0.513748\pi\)
−0.886806 + 0.462142i \(0.847081\pi\)
\(692\) 6.88789i 0.261838i
\(693\) 7.19051 12.4543i 0.273145 0.473101i
\(694\) 18.0431 + 10.4172i 0.684907 + 0.395431i
\(695\) 13.7836 + 23.8739i 0.522842 + 0.905589i
\(696\) 0.857937 0.0325200
\(697\) −15.4473 43.2886i −0.585109 1.63967i
\(698\) −9.80064 + 16.9752i −0.370960 + 0.642521i
\(699\) −3.72473 −0.140882
\(700\) 14.4537 + 8.34487i 0.546300 + 0.315406i
\(701\) 2.16688 + 3.75314i 0.0818417 + 0.141754i 0.904041 0.427446i \(-0.140586\pi\)
−0.822199 + 0.569200i \(0.807253\pi\)
\(702\) 34.4408 19.8844i 1.29989 0.750489i
\(703\) −0.436095 + 0.251779i −0.0164476 + 0.00949604i
\(704\) 23.6939i 0.892997i
\(705\) 0.133018 + 0.230393i 0.00500974 + 0.00867712i
\(706\) −3.82727 6.62903i −0.144041 0.249487i
\(707\) −14.0607 8.11795i −0.528807 0.305307i
\(708\) −4.24881 2.45305i −0.159680 0.0921912i
\(709\) 40.7023i 1.52861i 0.644858 + 0.764303i \(0.276917\pi\)
−0.644858 + 0.764303i \(0.723083\pi\)
\(710\) 29.0954 1.09193
\(711\) 29.8622 + 17.2409i 1.11992 + 0.646585i
\(712\) 1.79414 3.10753i 0.0672381 0.116460i
\(713\) −8.73370 15.1272i −0.327080 0.566518i
\(714\) 9.08354 3.24142i 0.339943 0.121307i
\(715\) 21.5919 0.807491
\(716\) 7.26903 + 12.5903i 0.271656 + 0.470523i
\(717\) −1.93039 + 1.11451i −0.0720916 + 0.0416221i
\(718\) 33.2862 + 57.6533i 1.24223 + 2.15160i
\(719\) −19.4818 11.2478i −0.726547 0.419472i 0.0906108 0.995886i \(-0.471118\pi\)
−0.817158 + 0.576414i \(0.804451\pi\)
\(720\) 12.1594i 0.453155i
\(721\) 11.0038 + 6.35303i 0.409802 + 0.236599i
\(722\) −19.8678 34.4121i −0.739404 1.28069i
\(723\) 3.86176 0.143620
\(724\) −3.34245 + 1.92976i −0.124221 + 0.0717191i
\(725\) −5.93568 3.42696i −0.220445 0.127274i
\(726\) 5.26108 + 3.03748i 0.195257 + 0.112732i
\(727\) 31.9930 1.18656 0.593278 0.804998i \(-0.297833\pi\)
0.593278 + 0.804998i \(0.297833\pi\)
\(728\) 10.9601 + 6.32782i 0.406209 + 0.234525i
\(729\) 15.4145 0.570906
\(730\) 24.8950 0.921404
\(731\) −15.8461 + 21.9066i −0.586089 + 0.810247i
\(732\) 15.4957 0.572739
\(733\) 23.4670 0.866775 0.433387 0.901208i \(-0.357318\pi\)
0.433387 + 0.901208i \(0.357318\pi\)
\(734\) −32.7163 18.8887i −1.20758 0.697196i
\(735\) 1.03837 0.0383007
\(736\) 25.7660 + 14.8760i 0.949749 + 0.548338i
\(737\) 16.8300 + 9.71679i 0.619940 + 0.357922i
\(738\) −55.9624 + 32.3099i −2.06000 + 1.18934i
\(739\) −34.9374 −1.28519 −0.642596 0.766205i \(-0.722143\pi\)
−0.642596 + 0.766205i \(0.722143\pi\)
\(740\) −12.3358 21.3662i −0.453473 0.785438i
\(741\) −0.195386 0.112806i −0.00717768 0.00414404i
\(742\) 30.9128i 1.13485i
\(743\) 11.5112 + 6.64601i 0.422306 + 0.243818i 0.696063 0.717980i \(-0.254933\pi\)
−0.273757 + 0.961799i \(0.588267\pi\)
\(744\) −0.891391 1.54393i −0.0326800 0.0566034i
\(745\) −16.2274 + 9.36890i −0.594526 + 0.343250i
\(746\) −21.0301 36.4252i −0.769966 1.33362i
\(747\) −35.0746 −1.28331
\(748\) 7.30999 + 20.4850i 0.267280 + 0.749007i
\(749\) −18.9673 32.8524i −0.693052 1.20040i
\(750\) 5.65740 9.79891i 0.206579 0.357806i
\(751\) 8.10092 + 4.67707i 0.295607 + 0.170669i 0.640468 0.767985i \(-0.278741\pi\)
−0.344861 + 0.938654i \(0.612074\pi\)
\(752\) 1.22330 0.0446091
\(753\) 0.981729i 0.0357762i
\(754\) −28.4483 16.4246i −1.03602 0.598149i
\(755\) −4.17598 2.41100i −0.151979 0.0877454i
\(756\) −7.66625 13.2783i −0.278819 0.482929i
\(757\) −17.4901 30.2938i −0.635689 1.10105i −0.986369 0.164550i \(-0.947383\pi\)
0.350680 0.936495i \(-0.385951\pi\)
\(758\) 27.2831i 0.990967i
\(759\) −3.39066 + 1.95760i −0.123073 + 0.0710563i
\(760\) −0.0658702 + 0.0380302i −0.00238936 + 0.00137950i
\(761\) 6.43433 + 11.1446i 0.233244 + 0.403991i 0.958761 0.284213i \(-0.0917324\pi\)
−0.725517 + 0.688205i \(0.758399\pi\)
\(762\) −1.23877 0.715203i −0.0448758