Properties

Label 731.2.j.a.135.10
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 135.10
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.10

$q$-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} +(3.14171 - 2.67015i) 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} +(-6.57203 + 5.58559i) 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} +(7.46440 - 6.34401i) 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 0.614811 0.788674i \(-0.289232\pi\)
−0.375606 + 0.926779i \(0.622566\pi\)
\(4\) 2.37591 1.18795
\(5\) −1.22310 0.706158i −0.546988 0.315804i 0.200918 0.979608i \(-0.435607\pi\)
−0.747906 + 0.663804i \(0.768941\pi\)
\(6\) −0.866692 0.500385i −0.353826 0.204281i
\(7\) 2.02420 1.16867i 0.765077 0.441717i −0.0660387 0.997817i \(-0.521036\pi\)
0.831116 + 0.556100i \(0.187703\pi\)
\(8\) −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 \(0.108642\pi\)
−0.942317 + 0.334722i \(0.891358\pi\)
\(12\) 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
\(17\) 3.14171 2.67015i 0.761976 0.647605i
\(18\) 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 0.128811 0.991669i \(-0.458884\pi\)
−0.794405 + 0.607388i \(0.792217\pi\)
\(24\) −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 −0.672039 0.740516i \(-0.734581\pi\)
0.305286 + 0.952261i \(0.401248\pi\)
\(30\) 0.706702 + 1.22404i 0.129026 + 0.223479i
\(31\) 4.10408 + 2.36949i 0.737115 + 0.425574i 0.821019 0.570900i \(-0.193406\pi\)
−0.0839043 + 0.996474i \(0.526739\pi\)
\(32\) 8.07188 1.42692
\(33\) −0.531105 + 0.919901i −0.0924536 + 0.160134i
\(34\) −6.57203 + 5.58559i −1.12709 + 0.957920i
\(35\) −3.30108 −0.557984
\(36\) −3.29196 5.70185i −0.548661 0.950308i
\(37\) 6.36747 + 3.67626i 1.04680 + 0.604373i 0.921753 0.387777i \(-0.126757\pi\)
0.125052 + 0.992150i \(0.460090\pi\)
\(38\) −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 \(-0.663815\pi\)
0.492221 0.870470i \(-0.336185\pi\)
\(42\) −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 \(-0.329004\pi\)
0.999908 0.0136011i \(-0.00432948\pi\)
\(62\) −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 \(0.987108\pi\)
\(68\) 7.46440 6.34401i 0.905191 0.769324i
\(69\) −0.881684 1.52712i −0.106142 0.183844i
\(70\) 6.90541 0.825354
\(71\) 8.52881 4.92411i 1.01218 0.584385i 0.100354 0.994952i \(-0.468003\pi\)
0.911830 + 0.410567i \(0.134669\pi\)
\(72\) 1.08953 + 1.88712i 0.128402 + 0.222399i
\(73\) 7.29754 4.21323i 0.854112 0.493122i −0.00792416 0.999969i \(-0.502522\pi\)
0.862036 + 0.506847i \(0.169189\pi\)
\(74\) −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 0.249131 0.968470i \(-0.419855\pi\)
0.963285 + 0.268481i \(0.0865217\pi\)
\(80\) 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 \(-0.828654\pi\)
0.858581 0.512677i \(-0.171346\pi\)
\(98\) 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 \(-0.712921\pi\)
0.620133 0.784497i \(-0.287079\pi\)
\(108\) 6.55979i 0.631216i
\(109\) 9.50914 + 5.49010i 0.910810 + 0.525856i 0.880692 0.473690i \(-0.157078\pi\)
0.0301184 + 0.999546i \(0.490412\pi\)
\(110\) −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 \(-0.934706\pi\)
0.979035 0.203693i \(-0.0652944\pi\)
\(114\) −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
\(119\) 3.23892 9.07655i 0.296912 0.832046i
\(120\) 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 \(0.221466\pi\)
−0.767570 + 0.640966i \(0.778534\pi\)
\(132\) −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
\(136\) −2.47046 + 2.09965i −0.211840 + 0.180044i
\(137\) 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 −0.436378 0.899763i \(-0.643739\pi\)
−0.997407 + 0.0719672i \(0.977072\pi\)
\(140\) −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
\(153\) −10.7610 3.84002i −0.869976 0.310447i
\(154\) −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 −0.542428 0.840103i \(-0.682495\pi\)
0.456336 + 0.889807i \(0.349161\pi\)
\(164\) 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 0.624280 0.781200i \(-0.285392\pi\)
−0.364399 + 0.931243i \(0.618726\pi\)
\(168\) −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 \(0.0351510\pi\)
−0.993909 + 0.110206i \(0.964849\pi\)
\(174\) 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 −0.446804 0.894632i \(-0.647438\pi\)
0.551372 + 0.834260i \(0.314105\pi\)
\(182\) −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
\(187\) 5.92851 + 6.97551i 0.433535 + 0.510100i
\(188\) −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 \(-0.936886\pi\)
0.980407 0.196983i \(-0.0631143\pi\)
\(194\) 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 −0.993128 0.117029i \(-0.962663\pi\)
−0.395214 + 0.918589i \(0.629330\pi\)
\(198\) −11.1463 + 6.43532i −0.792134 + 0.457339i
\(199\) 3.33136i 0.236154i 0.993004 + 0.118077i \(0.0376729\pi\)
−0.993004 + 0.118077i \(0.962327\pi\)
\(200\) 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 \(0.316918\pi\)
−0.543976 + 0.839101i \(0.683082\pi\)
\(212\) −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
\(221\) 26.7390 + 9.54170i 1.79866 + 0.641844i
\(222\) −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 0.258194 0.966093i \(-0.416873\pi\)
−0.707564 + 0.706649i \(0.750206\pi\)
\(228\) 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 −0.704327 0.709876i \(-0.748751\pi\)
0.262607 + 0.964903i \(0.415418\pi\)
\(234\) −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
\(238\) −6.77540 + 18.9869i −0.439184 + 1.23074i
\(239\) 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 −0.257654 0.966237i \(-0.582949\pi\)
0.707959 + 0.706253i \(0.249616\pi\)
\(242\) −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
\(255\) −2.62379 0.936288i −0.164308 0.0586326i
\(256\) 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 \(0.0750479\pi\)
−0.972335 + 0.233592i \(0.924952\pi\)
\(270\) 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 \(0.836547\pi\)
\(272\) −9.76092 + 8.29583i −0.591843 + 0.503009i
\(273\) 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 0.971799 0.235812i \(-0.0757749\pi\)
0.281680 + 0.959508i \(0.409108\pi\)
\(278\) 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 \(0.715246\pi\)
−0.988377 + 0.152025i \(0.951421\pi\)
\(284\) 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
\(289\) 2.74065 16.7776i 0.161215 0.986919i
\(290\) −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
\(306\) 22.5106 + 8.03280i 1.28685 + 0.459205i
\(307\) −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 0.425020 0.905184i \(-0.360267\pi\)
−0.571402 + 0.820670i \(0.693600\pi\)
\(312\) 2.59036i 0.146650i
\(313\) −15.4125 8.89839i −0.871164 0.502967i −0.00342923 0.999994i \(-0.501092\pi\)
−0.867735 + 0.497027i \(0.834425\pi\)
\(314\) 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 \(-0.731201\pi\)
0.664138 0.747610i \(-0.268799\pi\)
\(318\) 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 0.342119 0.939657i \(-0.388855\pi\)
0.984826 + 0.173544i \(0.0555220\pi\)
\(338\) 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 0.713319 0.700839i \(-0.247191\pi\)
−0.250285 + 0.968172i \(0.580524\pi\)
\(348\) −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
\(357\) 3.51309 2.98579i 0.185933 0.158025i
\(358\) −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 0.0327813 0.999463i \(-0.489564\pi\)
−0.849169 + 0.528121i \(0.822897\pi\)
\(368\) 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 \(0.659065\pi\)
\(374\) −12.4016 14.5918i −0.641274 0.754526i
\(375\) −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 \(-0.891273\pi\)
0.942228 0.334973i \(-0.108727\pi\)
\(380\) −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 0.00543911 0.999985i \(-0.498269\pi\)
−0.863293 + 0.504703i \(0.831602\pi\)
\(398\) 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 −0.413611 0.910454i \(-0.635733\pi\)
0.581670 + 0.813425i \(0.302399\pi\)
\(402\) 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 \(0.250911\pi\)
−0.705081 + 0.709127i \(0.749089\pi\)
\(420\) −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
\(425\) −11.6706 4.16461i −0.566108 0.202013i
\(426\) −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 \(0.206617\pi\)
−0.796624 + 0.604475i \(0.793383\pi\)
\(432\) 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 −0.999291 0.0376478i \(-0.988014\pi\)
−0.467042 + 0.884235i \(0.654680\pi\)
\(440\) −1.23289 + 2.13543i −0.0587758 + 0.101803i
\(441\) 4.25867 0.202794
\(442\) −55.9345 19.9600i −2.66053 0.949398i
\(443\) −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 0.375944 0.926642i \(-0.377318\pi\)
−0.614524 + 0.788898i \(0.710652\pi\)
\(450\) 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
\(459\) −7.37217 8.67414i −0.344104 0.404874i
\(460\) 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
\(476\) 7.69538 21.5650i 0.352717 0.988431i
\(477\) 17.5201 0.802191
\(478\) −4.87323 + 8.44069i −0.222897 + 0.386068i
\(479\) 15.1252 + 8.73253i 0.691087 + 0.398999i 0.804019 0.594603i \(-0.202691\pi\)
−0.112932 + 0.993603i \(0.536024\pi\)
\(480\) −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 −0.801292 0.598273i \(-0.795854\pi\)
0.117474 + 0.993076i \(0.462520\pi\)
\(488\) −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
\(493\) −3.16024 + 8.85605i −0.142330 + 0.398856i
\(494\) −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 −0.948945 0.315443i \(-0.897847\pi\)
−0.201291 + 0.979532i \(0.564514\pi\)
\(500\) 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 −0.135845 0.990730i \(-0.543375\pi\)
0.790075 + 0.613010i \(0.210041\pi\)
\(504\) 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 \(0.547848\pi\)
\(510\) 5.48862 + 1.95859i 0.243040 + 0.0867278i
\(511\) 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 0.920037 0.391832i \(-0.128159\pi\)
0.120682 + 0.992691i \(0.461492\pi\)
\(522\) −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 −0.438202 0.898877i \(-0.644385\pi\)
0.559349 + 0.828932i \(0.311051\pi\)
\(542\) 0.347675 + 0.602191i 0.0149339 + 0.0258663i
\(543\) 0.777151 0.0333507
\(544\) 25.3595 21.5531i 1.08728 0.924081i
\(545\) −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 −0.135410 0.990790i \(-0.543235\pi\)
−0.925754 + 0.378126i \(0.876569\pi\)
\(548\) 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 0.378320 0.925675i \(-0.376502\pi\)
−0.612498 + 0.790472i \(0.709835\pi\)
\(572\) −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 \(0.792254\pi\)
\(578\) −5.73307 + 35.0966i −0.238464 + 1.45982i
\(579\) 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
\(595\) −10.3710 + 8.81435i −0.425170 + 0.361353i
\(596\) −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 \(0.0284038\pi\)
−0.996021 + 0.0891149i \(0.971596\pi\)
\(602\) −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 0.750106 0.661318i \(-0.230003\pi\)
−0.197665 + 0.980270i \(0.563336\pi\)
\(608\) 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
\(612\) −25.5672 9.12352i −1.03349 0.368796i
\(613\) 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 −0.694275 0.719710i \(-0.744275\pi\)
0.276149 + 0.961115i \(0.410942\pi\)
\(618\) 5.44028i 0.218840i
\(619\) 14.3957 8.31137i 0.578612 0.334062i −0.181969 0.983304i \(-0.558247\pi\)
0.760582 + 0.649242i \(0.224914\pi\)
\(620\) −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 \(0.398767\pi\)
−0.312699 + 0.949852i \(0.601233\pi\)
\(642\) −8.12114 + 14.0662i −0.320516 + 0.555150i
\(643\) 23.2841i 0.918234i −0.888376 0.459117i \(-0.848166\pi\)
0.888376 0.459117i \(-0.151834\pi\)
\(644\) −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 \(0.0363465\pi\)
−0.993488 + 0.113938i \(0.963654\pi\)
\(654\) −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
\(663\) 8.79596 + 10.3494i 0.341607 + 0.401937i
\(664\) −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 0.186053 0.982540i \(-0.440430\pi\)
0.943931 + 0.330143i \(0.107097\pi\)
\(674\) −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 \(0.126244\pi\)
−0.922377 + 0.386290i \(0.873756\pi\)
\(678\) −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 0.255511 0.966806i \(-0.417756\pi\)
−0.709523 + 0.704682i \(0.751089\pi\)
\(684\) −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 0.886806 0.462142i \(-0.152919\pi\)
0.0431761 + 0.999067i \(0.486252\pi\)
\(692\) 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
\(697\) −29.7653 35.0221i −1.12744 1.32655i
\(698\) −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 \(-0.723083\pi\)
0.644858 0.764303i \(-0.276917\pi\)
\(710\) 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
\(714\) −7.34892 + 6.24586i −0.275026 + 0.233746i
\(715\) 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 0.817158 0.576414i \(-0.195549\pi\)
−0.0906108 + 0.995886i \(0.528882\pi\)
\(720\) 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
\(731\) 7.06940 26.0964i 0.261471 0.965211i
\(732\) 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 0.273757 0.961799i \(-0.411733\pi\)
−0.696063 + 0.717980i \(0.745067\pi\)
\(744\) −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
\(748\) 14.0856 + 16.5732i 0.515019 + 0.605975i
\(749\) −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 0.344861 0.938654i \(-0.387926\pi\)
−0.640468 + 0.767985i \(0.721259\pi\)
\(752\) 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 +