Properties

Label 539.2.q.g.312.2
Level 539
Weight 2
Character 539.312
Analytic conductor 4.304
Analytic rank 0
Dimension 32
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 539.q (of order \(15\), degree \(8\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{15})\)
Coefficient ring index: multiple of None
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 312.2
Character \(\chi\) = 539.312
Dual form 539.2.q.g.520.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.116493 + 1.10836i) q^{2} +(-1.91292 - 2.12452i) q^{3} +(0.741401 + 0.157590i) q^{4} +(3.15728 + 1.40571i) q^{5} +(2.57757 - 1.87272i) q^{6} +(-0.949813 + 2.92322i) q^{8} +(-0.540709 + 5.14450i) q^{9} +O(q^{10})\) \(q+(-0.116493 + 1.10836i) q^{2} +(-1.91292 - 2.12452i) q^{3} +(0.741401 + 0.157590i) q^{4} +(3.15728 + 1.40571i) q^{5} +(2.57757 - 1.87272i) q^{6} +(-0.949813 + 2.92322i) q^{8} +(-0.540709 + 5.14450i) q^{9} +(-1.92584 + 3.33566i) q^{10} +(-1.57633 + 2.91808i) q^{11} +(-1.08344 - 1.87657i) q^{12} +(1.66629 + 1.21063i) q^{13} +(-3.05318 - 9.39672i) q^{15} +(-1.74447 - 0.776689i) q^{16} +(-0.202130 - 1.92314i) q^{17} +(-5.63898 - 1.19860i) q^{18} +(-1.58749 + 0.337432i) q^{19} +(2.11929 + 1.53975i) q^{20} +(-3.05065 - 2.08708i) q^{22} +(0.403568 + 0.699000i) q^{23} +(8.02735 - 3.57401i) q^{24} +(4.64676 + 5.16075i) q^{25} +(-1.53593 + 1.70583i) q^{26} +(5.02542 - 3.65118i) q^{27} +(2.46400 + 7.58342i) q^{29} +(10.7706 - 2.28937i) q^{30} +(0.720257 - 0.320679i) q^{31} +(-2.00959 + 3.48071i) q^{32} +(9.21490 - 2.23312i) q^{33} +2.15508 q^{34} +(-1.21160 + 3.72893i) q^{36} +(6.73264 - 7.47735i) q^{37} +(-0.189064 - 1.79883i) q^{38} +(-0.615482 - 5.85592i) q^{39} +(-7.10804 + 7.89428i) q^{40} +(-0.657011 + 2.02207i) q^{41} +3.08043 q^{43} +(-1.62855 + 1.91505i) q^{44} +(-8.93887 + 15.4826i) q^{45} +(-0.821758 + 0.365870i) q^{46} +(-7.40098 + 1.57313i) q^{47} +(1.68695 + 5.19190i) q^{48} +(-6.26129 + 4.54910i) q^{50} +(-3.69907 + 4.10824i) q^{51} +(1.04461 + 1.16016i) q^{52} +(9.88680 - 4.40189i) q^{53} +(3.46140 + 5.99532i) q^{54} +(-9.07891 + 6.99733i) q^{55} +(3.75363 + 2.72717i) q^{57} +(-8.69221 + 1.84759i) q^{58} +(3.22460 + 0.685409i) q^{59} +(-0.782805 - 7.44789i) q^{60} +(-0.983548 - 0.437904i) q^{61} +(0.271523 + 0.835662i) q^{62} +(-6.71351 - 4.87765i) q^{64} +(3.55916 + 6.16465i) q^{65} +(1.40163 + 10.4736i) q^{66} +(-1.20157 + 2.08118i) q^{67} +(0.153207 - 1.45767i) q^{68} +(0.713042 - 2.19452i) q^{69} +(2.57963 - 1.87421i) q^{71} +(-14.5250 - 6.46693i) q^{72} +(-1.19948 - 0.254957i) q^{73} +(7.50330 + 8.33326i) q^{74} +(2.07520 - 19.7442i) q^{75} -1.23015 q^{76} +6.56217 q^{78} +(0.991120 - 9.42988i) q^{79} +(-4.41599 - 4.90445i) q^{80} +(-2.19082 - 0.465673i) q^{81} +(-2.16465 - 0.963764i) q^{82} +(13.0004 - 9.44536i) q^{83} +(2.06520 - 6.35602i) q^{85} +(-0.358850 + 3.41423i) q^{86} +(11.3976 - 19.7413i) q^{87} +(-7.03298 - 7.37959i) q^{88} +(2.21915 + 3.84368i) q^{89} +(-16.1190 - 11.7111i) q^{90} +(0.189050 + 0.581837i) q^{92} +(-2.05908 - 0.916763i) q^{93} +(-0.881427 - 8.38622i) q^{94} +(-5.48650 - 1.16619i) q^{95} +(11.2390 - 2.38892i) q^{96} +(-5.23278 - 3.80184i) q^{97} +(-14.1597 - 9.68727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 3q^{2} + 2q^{3} + 11q^{4} + 5q^{5} + 6q^{6} - 10q^{8} + 12q^{9} + O(q^{10}) \) \( 32q + 3q^{2} + 2q^{3} + 11q^{4} + 5q^{5} + 6q^{6} - 10q^{8} + 12q^{9} - 12q^{10} + 3q^{11} - 18q^{12} - 14q^{13} - 36q^{15} - 17q^{16} + 5q^{17} - 11q^{18} - 19q^{19} + 2q^{20} - 66q^{22} - 32q^{23} + 35q^{24} - 7q^{25} + 27q^{26} + 20q^{27} + 6q^{29} + 2q^{30} + 7q^{31} - 32q^{32} + 26q^{33} - 48q^{34} + 104q^{36} - 4q^{37} + 5q^{38} - 11q^{39} + 10q^{40} - 20q^{41} - 16q^{43} + 38q^{44} - 70q^{45} + 42q^{46} + 23q^{47} - 72q^{48} + 104q^{50} + 29q^{51} - 33q^{52} - 4q^{53} - 60q^{54} - 24q^{55} - 22q^{57} - 20q^{58} - 17q^{59} + 30q^{60} + 7q^{61} + 158q^{62} + 14q^{64} + 8q^{65} - 8q^{66} + 38q^{67} + 2q^{68} + 20q^{69} - 28q^{71} + 35q^{73} + 29q^{74} - 9q^{75} + 104q^{76} - 116q^{78} - 15q^{79} + 87q^{80} + 14q^{81} - 19q^{82} + 10q^{83} + 12q^{85} + 52q^{86} + 72q^{87} - 55q^{88} - 74q^{89} - 28q^{90} - 110q^{92} - 32q^{93} + 24q^{94} - 32q^{95} + 42q^{96} + 40q^{97} + 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.116493 + 1.10836i −0.0823733 + 0.783730i 0.872879 + 0.487937i \(0.162250\pi\)
−0.955252 + 0.295793i \(0.904416\pi\)
\(3\) −1.91292 2.12452i −1.10443 1.22659i −0.971896 0.235411i \(-0.924356\pi\)
−0.132530 0.991179i \(-0.542310\pi\)
\(4\) 0.741401 + 0.157590i 0.370700 + 0.0787948i
\(5\) 3.15728 + 1.40571i 1.41198 + 0.628654i 0.964124 0.265451i \(-0.0855210\pi\)
0.447856 + 0.894106i \(0.352188\pi\)
\(6\) 2.57757 1.87272i 1.05229 0.764534i
\(7\) 0 0
\(8\) −0.949813 + 2.92322i −0.335810 + 1.03352i
\(9\) −0.540709 + 5.14450i −0.180236 + 1.71483i
\(10\) −1.92584 + 3.33566i −0.609005 + 1.05483i
\(11\) −1.57633 + 2.91808i −0.475282 + 0.879834i
\(12\) −1.08344 1.87657i −0.312762 0.541720i
\(13\) 1.66629 + 1.21063i 0.462147 + 0.335769i 0.794373 0.607430i \(-0.207800\pi\)
−0.332226 + 0.943200i \(0.607800\pi\)
\(14\) 0 0
\(15\) −3.05318 9.39672i −0.788328 2.42622i
\(16\) −1.74447 0.776689i −0.436118 0.194172i
\(17\) −0.202130 1.92314i −0.0490237 0.466429i −0.991303 0.131601i \(-0.957988\pi\)
0.942279 0.334828i \(-0.108678\pi\)
\(18\) −5.63898 1.19860i −1.32912 0.282513i
\(19\) −1.58749 + 0.337432i −0.364196 + 0.0774123i −0.386375 0.922342i \(-0.626273\pi\)
0.0221790 + 0.999754i \(0.492940\pi\)
\(20\) 2.11929 + 1.53975i 0.473887 + 0.344299i
\(21\) 0 0
\(22\) −3.05065 2.08708i −0.650401 0.444967i
\(23\) 0.403568 + 0.699000i 0.0841497 + 0.145752i 0.905029 0.425351i \(-0.139849\pi\)
−0.820879 + 0.571102i \(0.806516\pi\)
\(24\) 8.02735 3.57401i 1.63858 0.729541i
\(25\) 4.64676 + 5.16075i 0.929352 + 1.03215i
\(26\) −1.53593 + 1.70583i −0.301221 + 0.334540i
\(27\) 5.02542 3.65118i 0.967142 0.702670i
\(28\) 0 0
\(29\) 2.46400 + 7.58342i 0.457554 + 1.40821i 0.868111 + 0.496371i \(0.165334\pi\)
−0.410557 + 0.911835i \(0.634666\pi\)
\(30\) 10.7706 2.28937i 1.96644 0.417980i
\(31\) 0.720257 0.320679i 0.129362 0.0575957i −0.341035 0.940051i \(-0.610777\pi\)
0.470397 + 0.882455i \(0.344111\pi\)
\(32\) −2.00959 + 3.48071i −0.355248 + 0.615308i
\(33\) 9.21490 2.23312i 1.60411 0.388736i
\(34\) 2.15508 0.369592
\(35\) 0 0
\(36\) −1.21160 + 3.72893i −0.201934 + 0.621488i
\(37\) 6.73264 7.47735i 1.10684 1.22927i 0.135701 0.990750i \(-0.456671\pi\)
0.971138 0.238519i \(-0.0766620\pi\)
\(38\) −0.189064 1.79883i −0.0306703 0.291808i
\(39\) −0.615482 5.85592i −0.0985559 0.937697i
\(40\) −7.10804 + 7.89428i −1.12388 + 1.24820i
\(41\) −0.657011 + 2.02207i −0.102608 + 0.315795i −0.989162 0.146831i \(-0.953093\pi\)
0.886554 + 0.462626i \(0.153093\pi\)
\(42\) 0 0
\(43\) 3.08043 0.469761 0.234880 0.972024i \(-0.424530\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(44\) −1.62855 + 1.91505i −0.245513 + 0.288705i
\(45\) −8.93887 + 15.4826i −1.33253 + 2.30801i
\(46\) −0.821758 + 0.365870i −0.121162 + 0.0539446i
\(47\) −7.40098 + 1.57313i −1.07954 + 0.229464i −0.713161 0.701000i \(-0.752737\pi\)
−0.366382 + 0.930464i \(0.619404\pi\)
\(48\) 1.68695 + 5.19190i 0.243490 + 0.749387i
\(49\) 0 0
\(50\) −6.26129 + 4.54910i −0.885481 + 0.643339i
\(51\) −3.69907 + 4.10824i −0.517974 + 0.575268i
\(52\) 1.04461 + 1.16016i 0.144861 + 0.160885i
\(53\) 9.88680 4.40189i 1.35806 0.604645i 0.406933 0.913458i \(-0.366598\pi\)
0.951123 + 0.308812i \(0.0999316\pi\)
\(54\) 3.46140 + 5.99532i 0.471037 + 0.815859i
\(55\) −9.07891 + 6.99733i −1.22420 + 0.943520i
\(56\) 0 0
\(57\) 3.75363 + 2.72717i 0.497181 + 0.361223i
\(58\) −8.69221 + 1.84759i −1.14134 + 0.242600i
\(59\) 3.22460 + 0.685409i 0.419807 + 0.0892327i 0.412972 0.910744i \(-0.364491\pi\)
0.00683535 + 0.999977i \(0.497824\pi\)
\(60\) −0.782805 7.44789i −0.101060 0.961518i
\(61\) −0.983548 0.437904i −0.125930 0.0560678i 0.342804 0.939407i \(-0.388623\pi\)
−0.468735 + 0.883339i \(0.655290\pi\)
\(62\) 0.271523 + 0.835662i 0.0344835 + 0.106129i
\(63\) 0 0
\(64\) −6.71351 4.87765i −0.839189 0.609707i
\(65\) 3.55916 + 6.16465i 0.441459 + 0.764630i
\(66\) 1.40163 + 10.4736i 0.172528 + 1.28921i
\(67\) −1.20157 + 2.08118i −0.146795 + 0.254257i −0.930041 0.367455i \(-0.880229\pi\)
0.783246 + 0.621712i \(0.213562\pi\)
\(68\) 0.153207 1.45767i 0.0185791 0.176768i
\(69\) 0.713042 2.19452i 0.0858402 0.264189i
\(70\) 0 0
\(71\) 2.57963 1.87421i 0.306145 0.222428i −0.424095 0.905618i \(-0.639408\pi\)
0.730241 + 0.683190i \(0.239408\pi\)
\(72\) −14.5250 6.46693i −1.71178 0.762135i
\(73\) −1.19948 0.254957i −0.140388 0.0298405i 0.137181 0.990546i \(-0.456196\pi\)
−0.277570 + 0.960705i \(0.589529\pi\)
\(74\) 7.50330 + 8.33326i 0.872241 + 0.968722i
\(75\) 2.07520 19.7442i 0.239624 2.27987i
\(76\) −1.23015 −0.141107
\(77\) 0 0
\(78\) 6.56217 0.743020
\(79\) 0.991120 9.42988i 0.111510 1.06094i −0.785478 0.618889i \(-0.787583\pi\)
0.896988 0.442055i \(-0.145750\pi\)
\(80\) −4.41599 4.90445i −0.493723 0.548335i
\(81\) −2.19082 0.465673i −0.243424 0.0517414i
\(82\) −2.16465 0.963764i −0.239046 0.106430i
\(83\) 13.0004 9.44536i 1.42698 1.03676i 0.436412 0.899747i \(-0.356249\pi\)
0.990569 0.137016i \(-0.0437511\pi\)
\(84\) 0 0
\(85\) 2.06520 6.35602i 0.224002 0.689407i
\(86\) −0.358850 + 3.41423i −0.0386958 + 0.368165i
\(87\) 11.3976 19.7413i 1.22196 2.11649i
\(88\) −7.03298 7.37959i −0.749718 0.786667i
\(89\) 2.21915 + 3.84368i 0.235230 + 0.407430i 0.959339 0.282255i \(-0.0910825\pi\)
−0.724110 + 0.689685i \(0.757749\pi\)
\(90\) −16.1190 11.7111i −1.69909 1.23446i
\(91\) 0 0
\(92\) 0.189050 + 0.581837i 0.0197099 + 0.0606607i
\(93\) −2.05908 0.916763i −0.213517 0.0950639i
\(94\) −0.881427 8.38622i −0.0909122 0.864972i
\(95\) −5.48650 1.16619i −0.562903 0.119649i
\(96\) 11.2390 2.38892i 1.14708 0.243819i
\(97\) −5.23278 3.80184i −0.531308 0.386018i 0.289539 0.957166i \(-0.406498\pi\)
−0.820847 + 0.571148i \(0.806498\pi\)
\(98\) 0 0
\(99\) −14.1597 9.68727i −1.42311 0.973607i
\(100\) 2.63183 + 4.55847i 0.263183 + 0.455847i
\(101\) −14.1096 + 6.28201i −1.40396 + 0.625083i −0.962273 0.272086i \(-0.912286\pi\)
−0.441687 + 0.897169i \(0.645620\pi\)
\(102\) −4.12249 4.57849i −0.408188 0.453338i
\(103\) 5.96070 6.62003i 0.587325 0.652291i −0.374090 0.927392i \(-0.622045\pi\)
0.961415 + 0.275102i \(0.0887116\pi\)
\(104\) −5.12162 + 3.72107i −0.502216 + 0.364881i
\(105\) 0 0
\(106\) 3.72713 + 11.4709i 0.362011 + 1.11416i
\(107\) −3.43544 + 0.730225i −0.332117 + 0.0705936i −0.370952 0.928652i \(-0.620969\pi\)
0.0388354 + 0.999246i \(0.487635\pi\)
\(108\) 4.30124 1.91503i 0.413887 0.184274i
\(109\) −1.93827 + 3.35719i −0.185653 + 0.321560i −0.943796 0.330527i \(-0.892773\pi\)
0.758143 + 0.652088i \(0.226107\pi\)
\(110\) −6.69794 10.8779i −0.638624 1.03716i
\(111\) −28.7648 −2.73023
\(112\) 0 0
\(113\) 3.29224 10.1325i 0.309708 0.953183i −0.668170 0.744008i \(-0.732922\pi\)
0.977878 0.209175i \(-0.0670777\pi\)
\(114\) −3.45997 + 3.84269i −0.324056 + 0.359900i
\(115\) 0.291585 + 2.77424i 0.0271904 + 0.258699i
\(116\) 0.631745 + 6.01065i 0.0586561 + 0.558075i
\(117\) −7.12909 + 7.91766i −0.659085 + 0.731987i
\(118\) −1.13533 + 3.49417i −0.104515 + 0.321665i
\(119\) 0 0
\(120\) 30.3687 2.77227
\(121\) −6.03036 9.19971i −0.548215 0.836337i
\(122\) 0.599933 1.03911i 0.0543154 0.0940769i
\(123\) 5.55274 2.47224i 0.500674 0.222914i
\(124\) 0.584535 0.124247i 0.0524928 0.0111577i
\(125\) 2.07667 + 6.39134i 0.185743 + 0.571659i
\(126\) 0 0
\(127\) −15.7361 + 11.4330i −1.39635 + 1.01451i −0.401220 + 0.915982i \(0.631414\pi\)
−0.995134 + 0.0985289i \(0.968586\pi\)
\(128\) 0.809577 0.899127i 0.0715572 0.0794723i
\(129\) −5.89262 6.54442i −0.518816 0.576204i
\(130\) −7.24727 + 3.22669i −0.635628 + 0.283000i
\(131\) −2.55642 4.42785i −0.223355 0.386863i 0.732469 0.680800i \(-0.238368\pi\)
−0.955825 + 0.293937i \(0.905034\pi\)
\(132\) 7.18385 0.203464i 0.625274 0.0177092i
\(133\) 0 0
\(134\) −2.16672 1.57422i −0.187176 0.135992i
\(135\) 20.9992 4.46351i 1.80732 0.384158i
\(136\) 5.81374 + 1.23575i 0.498524 + 0.105965i
\(137\) −0.951263 9.05066i −0.0812719 0.773250i −0.956930 0.290319i \(-0.906239\pi\)
0.875658 0.482932i \(-0.160428\pi\)
\(138\) 2.34926 + 1.04596i 0.199982 + 0.0890377i
\(139\) −4.02234 12.3795i −0.341171 1.05002i −0.963602 0.267341i \(-0.913855\pi\)
0.622431 0.782675i \(-0.286145\pi\)
\(140\) 0 0
\(141\) 17.4996 + 12.7142i 1.47373 + 1.07073i
\(142\) 1.77679 + 3.07749i 0.149105 + 0.258257i
\(143\) −6.15935 + 2.95402i −0.515071 + 0.247027i
\(144\) 4.93893 8.55448i 0.411577 0.712873i
\(145\) −2.88056 + 27.4067i −0.239217 + 2.27600i
\(146\) 0.422316 1.29975i 0.0349511 0.107568i
\(147\) 0 0
\(148\) 6.16994 4.48272i 0.507166 0.368477i
\(149\) −2.87447 1.27980i −0.235486 0.104845i 0.285601 0.958348i \(-0.407807\pi\)
−0.521087 + 0.853504i \(0.674473\pi\)
\(150\) 21.6420 + 4.60015i 1.76706 + 0.375601i
\(151\) 1.91837 + 2.13057i 0.156115 + 0.173383i 0.816128 0.577871i \(-0.196116\pi\)
−0.660014 + 0.751254i \(0.729449\pi\)
\(152\) 0.521432 4.96110i 0.0422938 0.402398i
\(153\) 10.0029 0.808684
\(154\) 0 0
\(155\) 2.72484 0.218864
\(156\) 0.466513 4.43858i 0.0373509 0.355370i
\(157\) −14.3793 15.9698i −1.14759 1.27453i −0.956102 0.293035i \(-0.905335\pi\)
−0.191490 0.981495i \(-0.561332\pi\)
\(158\) 10.3363 + 2.19704i 0.822308 + 0.174787i
\(159\) −28.2646 12.5842i −2.24152 0.997991i
\(160\) −11.2377 + 8.16468i −0.888420 + 0.645475i
\(161\) 0 0
\(162\) 0.771349 2.37397i 0.0606029 0.186517i
\(163\) 0.859480 8.17741i 0.0673197 0.640504i −0.907888 0.419213i \(-0.862306\pi\)
0.975208 0.221291i \(-0.0710272\pi\)
\(164\) −0.805767 + 1.39563i −0.0629198 + 0.108980i
\(165\) 32.2332 + 5.90292i 2.50935 + 0.459542i
\(166\) 8.95440 + 15.5095i 0.694997 + 1.20377i
\(167\) 17.5626 + 12.7600i 1.35904 + 0.987397i 0.998506 + 0.0546489i \(0.0174040\pi\)
0.360529 + 0.932748i \(0.382596\pi\)
\(168\) 0 0
\(169\) −2.70632 8.32919i −0.208178 0.640707i
\(170\) 6.80419 + 3.02942i 0.521857 + 0.232346i
\(171\) −0.877549 8.34932i −0.0671079 0.638489i
\(172\) 2.28383 + 0.485443i 0.174141 + 0.0370147i
\(173\) 7.86982 1.67278i 0.598331 0.127179i 0.101217 0.994864i \(-0.467726\pi\)
0.497114 + 0.867685i \(0.334393\pi\)
\(174\) 20.5527 + 14.9324i 1.55810 + 1.13203i
\(175\) 0 0
\(176\) 5.01630 3.86619i 0.378118 0.291425i
\(177\) −4.71224 8.16184i −0.354194 0.613482i
\(178\) −4.51871 + 2.01186i −0.338691 + 0.150795i
\(179\) −2.42286 2.69086i −0.181093 0.201124i 0.645763 0.763538i \(-0.276540\pi\)
−0.826856 + 0.562414i \(0.809873\pi\)
\(180\) −9.06718 + 10.0701i −0.675828 + 0.750583i
\(181\) −12.7970 + 9.29753i −0.951190 + 0.691080i −0.951088 0.308920i \(-0.900033\pi\)
−0.000102207 1.00000i \(0.500033\pi\)
\(182\) 0 0
\(183\) 0.951118 + 2.92724i 0.0703087 + 0.216388i
\(184\) −2.42665 + 0.515800i −0.178895 + 0.0380253i
\(185\) 31.7679 14.1440i 2.33562 1.03988i
\(186\) 1.25598 2.17541i 0.0920926 0.159509i
\(187\) 5.93048 + 2.44167i 0.433680 + 0.178552i
\(188\) −5.73500 −0.418268
\(189\) 0 0
\(190\) 1.93170 5.94518i 0.140141 0.431308i
\(191\) 0.287111 0.318869i 0.0207746 0.0230726i −0.732668 0.680586i \(-0.761725\pi\)
0.753443 + 0.657514i \(0.228392\pi\)
\(192\) 2.47978 + 23.5935i 0.178963 + 1.70272i
\(193\) 1.58620 + 15.0917i 0.114177 + 1.08632i 0.890185 + 0.455600i \(0.150575\pi\)
−0.776007 + 0.630724i \(0.782758\pi\)
\(194\) 4.82339 5.35692i 0.346299 0.384604i
\(195\) 6.28849 19.3540i 0.450328 1.38597i
\(196\) 0 0
\(197\) −20.8082 −1.48252 −0.741262 0.671216i \(-0.765772\pi\)
−0.741262 + 0.671216i \(0.765772\pi\)
\(198\) 12.3865 14.5656i 0.880271 1.03513i
\(199\) −4.22284 + 7.31417i −0.299349 + 0.518488i −0.975987 0.217828i \(-0.930103\pi\)
0.676638 + 0.736316i \(0.263436\pi\)
\(200\) −19.4996 + 8.68177i −1.37883 + 0.613894i
\(201\) 6.72001 1.42838i 0.473993 0.100750i
\(202\) −5.31906 16.3704i −0.374247 1.15182i
\(203\) 0 0
\(204\) −3.38991 + 2.46292i −0.237341 + 0.172439i
\(205\) −4.91683 + 5.46069i −0.343406 + 0.381391i
\(206\) 6.64300 + 7.37780i 0.462840 + 0.514035i
\(207\) −3.81422 + 1.69820i −0.265107 + 0.118033i
\(208\) −1.96652 3.40611i −0.136353 0.236171i
\(209\) 1.51776 5.16434i 0.104986 0.357225i
\(210\) 0 0
\(211\) 7.97632 + 5.79513i 0.549112 + 0.398953i 0.827458 0.561528i \(-0.189786\pi\)
−0.278346 + 0.960481i \(0.589786\pi\)
\(212\) 8.02377 1.70551i 0.551075 0.117135i
\(213\) −8.91641 1.89524i −0.610943 0.129860i
\(214\) −0.409147 3.89278i −0.0279687 0.266105i
\(215\) 9.72578 + 4.33020i 0.663293 + 0.295317i
\(216\) 5.90001 + 18.1584i 0.401445 + 1.23552i
\(217\) 0 0
\(218\) −3.49518 2.53940i −0.236724 0.171990i
\(219\) 1.75285 + 3.03602i 0.118447 + 0.205156i
\(220\) −7.83382 + 3.75709i −0.528156 + 0.253303i
\(221\) 1.99140 3.44921i 0.133956 0.232019i
\(222\) 3.35091 31.8818i 0.224898 2.13976i
\(223\) 5.37562 16.5445i 0.359978 1.10790i −0.593088 0.805138i \(-0.702091\pi\)
0.953066 0.302762i \(-0.0979087\pi\)
\(224\) 0 0
\(225\) −29.0620 + 21.1148i −1.93747 + 1.40765i
\(226\) 10.8469 + 4.82936i 0.721526 + 0.321244i
\(227\) 12.3555 + 2.62623i 0.820060 + 0.174309i 0.598793 0.800904i \(-0.295647\pi\)
0.221267 + 0.975213i \(0.428981\pi\)
\(228\) 2.35317 + 2.61346i 0.155843 + 0.173081i
\(229\) −0.478052 + 4.54836i −0.0315906 + 0.300564i 0.967306 + 0.253610i \(0.0816181\pi\)
−0.998897 + 0.0469539i \(0.985049\pi\)
\(230\) −3.10883 −0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) −2.49372 + 23.7262i −0.163369 + 1.55436i 0.538855 + 0.842399i \(0.318857\pi\)
−0.702224 + 0.711956i \(0.747809\pi\)
\(234\) −7.94513 8.82396i −0.519389 0.576840i
\(235\) −25.5784 5.43685i −1.66855 0.354661i
\(236\) 2.28271 + 1.01633i 0.148592 + 0.0661572i
\(237\) −21.9299 + 15.9330i −1.42450 + 1.03496i
\(238\) 0 0
\(239\) 2.73114 8.40558i 0.176663 0.543711i −0.823043 0.567979i \(-0.807725\pi\)
0.999705 + 0.0242677i \(0.00772541\pi\)
\(240\) −1.97214 + 18.7637i −0.127301 + 1.21119i
\(241\) −9.47322 + 16.4081i −0.610224 + 1.05694i 0.380978 + 0.924584i \(0.375587\pi\)
−0.991202 + 0.132355i \(0.957746\pi\)
\(242\) 10.8991 5.61212i 0.700621 0.360761i
\(243\) −6.11610 10.5934i −0.392348 0.679567i
\(244\) −0.660194 0.479659i −0.0422646 0.0307070i
\(245\) 0 0
\(246\) 2.09328 + 6.44244i 0.133462 + 0.410755i
\(247\) −3.05374 1.35961i −0.194305 0.0865101i
\(248\) 0.253307 + 2.41006i 0.0160850 + 0.153039i
\(249\) −44.9356 9.55136i −2.84768 0.605293i
\(250\) −7.32584 + 1.55715i −0.463327 + 0.0984831i
\(251\) 2.31938 + 1.68513i 0.146398 + 0.106364i 0.658573 0.752516i \(-0.271160\pi\)
−0.512175 + 0.858881i \(0.671160\pi\)
\(252\) 0 0
\(253\) −2.67589 + 0.0757876i −0.168232 + 0.00476473i
\(254\) −10.8387 18.7732i −0.680080 1.17793i
\(255\) −17.4540 + 7.77104i −1.09301 + 0.486641i
\(256\) −10.2031 11.3317i −0.637695 0.708232i
\(257\) 14.9991 16.6582i 0.935621 1.03911i −0.0635326 0.997980i \(-0.520237\pi\)
0.999154 0.0411328i \(-0.0130967\pi\)
\(258\) 7.94003 5.76877i 0.494325 0.359148i
\(259\) 0 0
\(260\) 1.66728 + 5.13136i 0.103400 + 0.318234i
\(261\) −40.3452 + 8.57564i −2.49731 + 0.530819i
\(262\) 5.20546 2.31762i 0.321594 0.143183i
\(263\) −0.495353 + 0.857976i −0.0305448 + 0.0529051i −0.880894 0.473314i \(-0.843058\pi\)
0.850349 + 0.526219i \(0.176391\pi\)
\(264\) −2.22453 + 29.0583i −0.136910 + 1.78841i
\(265\) 37.4032 2.29766
\(266\) 0 0
\(267\) 3.92090 12.0673i 0.239955 0.738506i
\(268\) −1.21882 + 1.35363i −0.0744511 + 0.0826863i
\(269\) 0.751598 + 7.15098i 0.0458257 + 0.436003i 0.993247 + 0.116015i \(0.0370121\pi\)
−0.947422 + 0.319988i \(0.896321\pi\)
\(270\) 2.50092 + 23.7947i 0.152201 + 1.44810i
\(271\) −18.1765 + 20.1870i −1.10414 + 1.22627i −0.132156 + 0.991229i \(0.542190\pi\)
−0.971985 + 0.235044i \(0.924477\pi\)
\(272\) −1.14107 + 3.51185i −0.0691874 + 0.212937i
\(273\) 0 0
\(274\) 10.1422 0.612714
\(275\) −22.3843 + 5.42456i −1.34982 + 0.327113i
\(276\) 0.874484 1.51465i 0.0526377 0.0911712i
\(277\) 19.1713 8.53561i 1.15189 0.512855i 0.260225 0.965548i \(-0.416203\pi\)
0.891667 + 0.452693i \(0.149536\pi\)
\(278\) 14.1895 3.01608i 0.851032 0.180892i
\(279\) 1.26029 + 3.87876i 0.0754513 + 0.232215i
\(280\) 0 0
\(281\) 22.7803 16.5509i 1.35896 0.987341i 0.360448 0.932779i \(-0.382624\pi\)
0.998510 0.0545621i \(-0.0173763\pi\)
\(282\) −16.1305 + 17.9148i −0.960560 + 1.06681i
\(283\) −17.5257 19.4643i −1.04179 1.15703i −0.987357 0.158512i \(-0.949330\pi\)
−0.0544372 0.998517i \(-0.517336\pi\)
\(284\) 2.20789 0.983018i 0.131014 0.0583314i
\(285\) 8.01766 + 13.8870i 0.474925 + 0.822595i
\(286\) −2.55660 7.17091i −0.151175 0.424025i
\(287\) 0 0
\(288\) −16.8199 12.2204i −0.991123 0.720093i
\(289\) 12.9709 2.75705i 0.762995 0.162180i
\(290\) −30.0410 6.38540i −1.76407 0.374964i
\(291\) 1.93284 + 18.3897i 0.113305 + 1.07803i
\(292\) −0.849116 0.378051i −0.0496907 0.0221237i
\(293\) −1.37941 4.24538i −0.0805858 0.248017i 0.902644 0.430388i \(-0.141623\pi\)
−0.983230 + 0.182370i \(0.941623\pi\)
\(294\) 0 0
\(295\) 9.21748 + 6.69689i 0.536663 + 0.389908i
\(296\) 15.4632 + 26.7831i 0.898782 + 1.55674i
\(297\) 2.73271 + 20.4200i 0.158568 + 1.18489i
\(298\) 1.75333 3.03686i 0.101568 0.175921i
\(299\) −0.173770 + 1.65331i −0.0100494 + 0.0956135i
\(300\) 4.65004 14.3114i 0.268470 0.826267i
\(301\) 0 0
\(302\) −2.58492 + 1.87805i −0.148745 + 0.108070i
\(303\) 40.3368 + 17.9591i 2.31729 + 1.03172i
\(304\) 3.03142 + 0.644348i 0.173864 + 0.0369559i
\(305\) −2.48977 2.76517i −0.142564 0.158333i
\(306\) −1.16527 + 11.0868i −0.0666140 + 0.633790i
\(307\) 12.8841 0.735334 0.367667 0.929957i \(-0.380157\pi\)
0.367667 + 0.929957i \(0.380157\pi\)
\(308\) 0 0
\(309\) −25.4667 −1.44875
\(310\) −0.317426 + 3.02011i −0.0180286 + 0.171531i
\(311\) 17.9460 + 19.9310i 1.01762 + 1.13019i 0.991445 + 0.130528i \(0.0416672\pi\)
0.0261787 + 0.999657i \(0.491666\pi\)
\(312\) 17.7027 + 3.76283i 1.00222 + 0.213029i
\(313\) 3.27843 + 1.45965i 0.185308 + 0.0825043i 0.497293 0.867583i \(-0.334327\pi\)
−0.311985 + 0.950087i \(0.600994\pi\)
\(314\) 19.3754 14.0771i 1.09342 0.794415i
\(315\) 0 0
\(316\) 2.22087 6.83513i 0.124934 0.384506i
\(317\) 1.76842 16.8254i 0.0993243 0.945007i −0.825446 0.564481i \(-0.809076\pi\)
0.924770 0.380526i \(-0.124257\pi\)
\(318\) 17.2405 29.8614i 0.966797 1.67454i
\(319\) −26.0131 4.76382i −1.45645 0.266723i
\(320\) −14.3399 24.8374i −0.801624 1.38845i
\(321\) 8.12311 + 5.90178i 0.453388 + 0.329405i
\(322\) 0 0
\(323\) 0.969808 + 2.98476i 0.0539616 + 0.166077i
\(324\) −1.55089 0.690500i −0.0861605 0.0383611i
\(325\) 1.49509 + 14.2249i 0.0829328 + 0.789053i
\(326\) 8.96340 + 1.90523i 0.496437 + 0.105521i
\(327\) 10.8402 2.30415i 0.599463 0.127420i
\(328\) −5.28693 3.84118i −0.291922 0.212094i
\(329\) 0 0
\(330\) −10.2975 + 35.0384i −0.566860 + 1.92880i
\(331\) 0.619131 + 1.07237i 0.0340305 + 0.0589426i 0.882539 0.470239i \(-0.155832\pi\)
−0.848509 + 0.529182i \(0.822499\pi\)
\(332\) 11.1270 4.95406i 0.610674 0.271890i
\(333\) 34.8269 + 38.6792i 1.90850 + 2.11960i
\(334\) −16.1886 + 17.9793i −0.885801 + 0.983781i
\(335\) −6.71924 + 4.88181i −0.367111 + 0.266722i
\(336\) 0 0
\(337\) −6.32885 19.4782i −0.344754 1.06104i −0.961715 0.274051i \(-0.911636\pi\)
0.616961 0.786994i \(-0.288364\pi\)
\(338\) 9.54702 2.02928i 0.519290 0.110378i
\(339\) −27.8244 + 12.3882i −1.51121 + 0.672836i
\(340\) 2.53278 4.38691i 0.137359 0.237913i
\(341\) −0.199596 + 2.60726i −0.0108088 + 0.141191i
\(342\) 9.35630 0.505931
\(343\) 0 0
\(344\) −2.92583 + 9.00478i −0.157750 + 0.485505i
\(345\) 5.33614 5.92639i 0.287288 0.319066i
\(346\) 0.937264 + 8.91747i 0.0503876 + 0.479406i
\(347\) −2.85048 27.1205i −0.153022 1.45590i −0.754125 0.656731i \(-0.771939\pi\)
0.601103 0.799171i \(-0.294728\pi\)
\(348\) 11.5613 12.8401i 0.619748 0.688300i
\(349\) 2.46730 7.59356i 0.132071 0.406474i −0.863052 0.505116i \(-0.831450\pi\)
0.995123 + 0.0986418i \(0.0314498\pi\)
\(350\) 0 0
\(351\) 12.7941 0.682897
\(352\) −6.98920 11.3509i −0.372526 0.605004i
\(353\) −2.96736 + 5.13961i −0.157937 + 0.273554i −0.934124 0.356948i \(-0.883817\pi\)
0.776188 + 0.630502i \(0.217151\pi\)
\(354\) 9.59522 4.27207i 0.509980 0.227058i
\(355\) 10.7792 2.29119i 0.572102 0.121604i
\(356\) 1.03956 + 3.19942i 0.0550964 + 0.169569i
\(357\) 0 0
\(358\) 3.26469 2.37194i 0.172544 0.125361i
\(359\) 19.0169 21.1204i 1.00367 1.11469i 0.0102773 0.999947i \(-0.496729\pi\)
0.993395 0.114744i \(-0.0366048\pi\)
\(360\) −36.7688 40.8359i −1.93788 2.15224i
\(361\) −14.9511 + 6.65665i −0.786899 + 0.350350i
\(362\) −8.81427 15.2668i −0.463267 0.802403i
\(363\) −8.00931 + 30.4099i −0.420380 + 1.59611i
\(364\) 0 0
\(365\) −3.42870 2.49109i −0.179466 0.130390i
\(366\) −3.35524 + 0.713178i −0.175381 + 0.0372784i
\(367\) 29.7371 + 6.32081i 1.55226 + 0.329944i 0.902668 0.430337i \(-0.141605\pi\)
0.649595 + 0.760281i \(0.274939\pi\)
\(368\) −0.161107 1.53283i −0.00839829 0.0799044i
\(369\) −10.0473 4.47335i −0.523042 0.232873i
\(370\) 11.9759 + 36.8580i 0.622596 + 1.91615i
\(371\) 0 0
\(372\) −1.38213 1.00418i −0.0716603 0.0520643i
\(373\) −7.21128 12.4903i −0.373386 0.646723i 0.616698 0.787200i \(-0.288470\pi\)
−0.990084 + 0.140476i \(0.955137\pi\)
\(374\) −3.39711 + 6.28868i −0.175660 + 0.325180i
\(375\) 9.60599 16.6381i 0.496051 0.859186i
\(376\) 2.43094 23.1289i 0.125366 1.19278i
\(377\) −5.07499 + 15.6192i −0.261375 + 0.804430i
\(378\) 0 0
\(379\) 18.1278 13.1706i 0.931163 0.676529i −0.0151144 0.999886i \(-0.504811\pi\)
0.946277 + 0.323356i \(0.104811\pi\)
\(380\) −3.88392 1.72923i −0.199241 0.0887077i
\(381\) 54.3915 + 11.5613i 2.78656 + 0.592301i
\(382\) 0.319976 + 0.355369i 0.0163714 + 0.0181823i
\(383\) −3.52037 + 33.4940i −0.179882 + 1.71147i 0.416808 + 0.908994i \(0.363149\pi\)
−0.596691 + 0.802471i \(0.703518\pi\)
\(384\) −3.45887 −0.176510
\(385\) 0 0
\(386\) −16.9118 −0.860790
\(387\) −1.66561 + 15.8473i −0.0846680 + 0.805562i
\(388\) −3.28046 3.64332i −0.166540 0.184961i
\(389\) −2.37478 0.504774i −0.120406 0.0255931i 0.147315 0.989090i \(-0.452937\pi\)
−0.267720 + 0.963497i \(0.586270\pi\)
\(390\) 20.7186 + 9.22453i 1.04913 + 0.467102i
\(391\) 1.26270 0.917404i 0.0638574 0.0463951i
\(392\) 0 0
\(393\) −4.51680 + 13.9013i −0.227842 + 0.701227i
\(394\) 2.42402 23.0630i 0.122120 1.16190i
\(395\) 16.3850 28.3796i 0.824417 1.42793i
\(396\) −8.97142 9.41358i −0.450831 0.473050i
\(397\) 2.94848 + 5.10692i 0.147980 + 0.256309i 0.930481 0.366341i \(-0.119390\pi\)
−0.782501 + 0.622650i \(0.786056\pi\)
\(398\) −7.61481 5.53248i −0.381696 0.277318i
\(399\) 0 0
\(400\) −4.09784 12.6119i −0.204892 0.630593i
\(401\) 10.2679 + 4.57155i 0.512753 + 0.228292i 0.646768 0.762687i \(-0.276120\pi\)
−0.134015 + 0.990979i \(0.542787\pi\)
\(402\) 0.800326 + 7.61460i 0.0399166 + 0.379782i
\(403\) 1.58839 + 0.337622i 0.0791231 + 0.0168181i
\(404\) −11.4509 + 2.43396i −0.569702 + 0.121094i
\(405\) −6.26243 4.54992i −0.311183 0.226087i
\(406\) 0 0
\(407\) 11.2066 + 31.4331i 0.555492 + 1.55808i
\(408\) −8.49587 14.7153i −0.420608 0.728515i
\(409\) 26.7983 11.9314i 1.32509 0.589968i 0.382511 0.923951i \(-0.375059\pi\)
0.942579 + 0.333983i \(0.108393\pi\)
\(410\) −5.47964 6.08576i −0.270620 0.300554i
\(411\) −17.4086 + 19.3342i −0.858702 + 0.953685i
\(412\) 5.46251 3.96875i 0.269119 0.195526i
\(413\) 0 0
\(414\) −1.43789 4.42536i −0.0706683 0.217495i
\(415\) 54.3235 11.5468i 2.66663 0.566811i
\(416\) −7.56243 + 3.36701i −0.370778 + 0.165081i
\(417\) −18.6060 + 32.2266i −0.911140 + 1.57814i
\(418\) 5.54714 + 2.28384i 0.271320 + 0.111706i
\(419\) −20.2858 −0.991027 −0.495514 0.868600i \(-0.665020\pi\)
−0.495514 + 0.868600i \(0.665020\pi\)
\(420\) 0 0
\(421\) −0.945600 + 2.91026i −0.0460857 + 0.141837i −0.971452 0.237238i \(-0.923758\pi\)
0.925366 + 0.379075i \(0.123758\pi\)
\(422\) −7.35229 + 8.16555i −0.357904 + 0.397493i
\(423\) −4.09118 38.9250i −0.198920 1.89260i
\(424\) 3.47709 + 33.0823i 0.168862 + 1.60662i
\(425\) 8.98557 9.97949i 0.435864 0.484076i
\(426\) 3.13932 9.66183i 0.152100 0.468117i
\(427\) 0 0
\(428\) −2.66211 −0.128678
\(429\) 18.0582 + 7.43484i 0.871859 + 0.358957i
\(430\) −5.93241 + 10.2752i −0.286086 + 0.495516i
\(431\) 6.88993 3.06759i 0.331876 0.147761i −0.234032 0.972229i \(-0.575192\pi\)
0.565909 + 0.824468i \(0.308526\pi\)
\(432\) −11.6025 + 2.46619i −0.558227 + 0.118655i
\(433\) −9.93848 30.5875i −0.477613 1.46994i −0.842401 0.538851i \(-0.818859\pi\)
0.364788 0.931091i \(-0.381141\pi\)
\(434\) 0 0
\(435\) 63.7362 46.3071i 3.05592 2.22025i
\(436\) −1.96610 + 2.18357i −0.0941589 + 0.104574i
\(437\) −0.876527 0.973482i −0.0419300 0.0465679i
\(438\) −3.56921 + 1.58911i −0.170543 + 0.0759308i
\(439\) 2.33363 + 4.04196i 0.111378 + 0.192912i 0.916326 0.400433i \(-0.131140\pi\)
−0.804948 + 0.593345i \(0.797807\pi\)
\(440\) −11.8315 33.1858i −0.564045 1.58207i
\(441\) 0 0
\(442\) 3.59099 + 2.60901i 0.170806 + 0.124098i
\(443\) −16.8996 + 3.59212i −0.802924 + 0.170667i −0.591055 0.806631i \(-0.701288\pi\)
−0.211869 + 0.977298i \(0.567955\pi\)
\(444\) −21.3262 4.53303i −1.01210 0.215128i
\(445\) 1.60337 + 15.2551i 0.0760072 + 0.723161i
\(446\) 17.7110 + 7.88546i 0.838642 + 0.373387i
\(447\) 2.77969 + 8.55501i 0.131475 + 0.404638i
\(448\) 0 0
\(449\) 13.5430 + 9.83957i 0.639134 + 0.464358i 0.859553 0.511047i \(-0.170742\pi\)
−0.220418 + 0.975405i \(0.570742\pi\)
\(450\) −20.0173 34.6710i −0.943625 1.63441i
\(451\) −4.86490 5.10467i −0.229079 0.240369i
\(452\) 4.03764 6.99340i 0.189915 0.328942i
\(453\) 0.856728 8.15123i 0.0402526 0.382978i
\(454\) −4.35015 + 13.3884i −0.204162 + 0.628347i
\(455\) 0 0
\(456\) −11.5374 + 8.38241i −0.540288 + 0.392542i
\(457\) −19.8216 8.82513i −0.927214 0.412822i −0.113137 0.993579i \(-0.536090\pi\)
−0.814077 + 0.580757i \(0.802757\pi\)
\(458\) −4.98554 1.05971i −0.232959 0.0495169i
\(459\) −8.03750 8.92655i −0.375158 0.416656i
\(460\) −0.221011 + 2.10278i −0.0103047 + 0.0980425i
\(461\) −6.07778 −0.283070 −0.141535 0.989933i \(-0.545204\pi\)
−0.141535 + 0.989933i \(0.545204\pi\)
\(462\) 0 0
\(463\) −5.14719 −0.239210 −0.119605 0.992822i \(-0.538163\pi\)
−0.119605 + 0.992822i \(0.538163\pi\)
\(464\) 1.59157 15.1428i 0.0738870 0.702988i
\(465\) −5.21241 5.78897i −0.241720 0.268457i
\(466\) −26.0067 5.52789i −1.20474 0.256075i
\(467\) −3.58044 1.59411i −0.165683 0.0737667i 0.322219 0.946665i \(-0.395571\pi\)
−0.487902 + 0.872898i \(0.662238\pi\)
\(468\) −6.53325 + 4.74669i −0.302000 + 0.219416i
\(469\) 0 0
\(470\) 9.00570 27.7167i 0.415402 1.27848i
\(471\) −6.42166 + 61.0980i −0.295895 + 2.81525i
\(472\) −5.06637 + 8.77521i −0.233199 + 0.403912i
\(473\) −4.85577 + 8.98893i −0.223269 + 0.413311i
\(474\) −15.1048 26.1623i −0.693787 1.20167i
\(475\) −9.11811 6.62469i −0.418368 0.303962i
\(476\) 0 0
\(477\) 17.2996 + 53.2428i 0.792096 + 2.43782i
\(478\) 8.99826 + 4.00628i 0.411571 + 0.183243i
\(479\) 1.57973 + 15.0301i 0.0721797 + 0.686744i 0.969454 + 0.245271i \(0.0788771\pi\)
−0.897275 + 0.441473i \(0.854456\pi\)
\(480\) 38.8429 + 8.25631i 1.77293 + 0.376847i
\(481\) 20.2709 4.30871i 0.924273 0.196460i
\(482\) −17.0825 12.4112i −0.778088 0.565314i
\(483\) 0 0
\(484\) −3.02114 7.77100i −0.137324 0.353227i
\(485\) −11.1771 19.3593i −0.507525 0.879059i
\(486\) 12.4538 5.54479i 0.564916 0.251517i
\(487\) 16.7797 + 18.6357i 0.760359 + 0.844464i 0.991722 0.128404i \(-0.0409853\pi\)
−0.231363 + 0.972867i \(0.574319\pi\)
\(488\) 2.21428 2.45920i 0.100236 0.111323i
\(489\) −19.0172 + 13.8168i −0.859985 + 0.624816i
\(490\) 0 0
\(491\) 11.5019 + 35.3991i 0.519071 + 1.59754i 0.775750 + 0.631040i \(0.217372\pi\)
−0.256679 + 0.966497i \(0.582628\pi\)
\(492\) 4.50641 0.957866i 0.203164 0.0431839i
\(493\) 14.0859 6.27144i 0.634397 0.282452i
\(494\) 1.86268 3.22626i 0.0838060 0.145156i
\(495\) −31.0888 50.4900i −1.39734 2.26936i
\(496\) −1.50554 −0.0676006
\(497\) 0 0
\(498\) 15.8211 48.6922i 0.708959 2.18195i
\(499\) −21.2873 + 23.6419i −0.952950 + 1.05836i 0.0452852 + 0.998974i \(0.485580\pi\)
−0.998235 + 0.0593841i \(0.981086\pi\)
\(500\) 0.532438 + 5.06581i 0.0238114 + 0.226550i
\(501\) −6.48713 61.7209i −0.289823 2.75749i
\(502\) −2.13792 + 2.37441i −0.0954203 + 0.105975i
\(503\) −5.93493 + 18.2658i −0.264626 + 0.814434i 0.727154 + 0.686474i \(0.240843\pi\)
−0.991779 + 0.127959i \(0.959157\pi\)
\(504\) 0 0
\(505\) −53.3788 −2.37532
\(506\) 0.227724 2.97469i 0.0101236 0.132241i
\(507\) −12.5185 + 21.6827i −0.555967 + 0.962963i
\(508\) −13.4685 + 5.99655i −0.597567 + 0.266054i
\(509\) −2.46052 + 0.522999i −0.109061 + 0.0231815i −0.262119 0.965036i \(-0.584421\pi\)
0.153058 + 0.988217i \(0.451088\pi\)
\(510\) −6.57984 20.2506i −0.291360 0.896714i
\(511\) 0 0
\(512\) 15.7059 11.4110i 0.694109 0.504300i
\(513\) −6.74580 + 7.49196i −0.297834 + 0.330778i
\(514\) 16.7160 + 18.5651i 0.737313 + 0.818869i
\(515\) 28.1255 12.5223i 1.23936 0.551797i
\(516\) −3.33746 5.78065i −0.146924 0.254479i
\(517\) 7.07588 24.0764i 0.311197 1.05888i
\(518\) 0 0
\(519\) −18.6082 13.5196i −0.816809 0.593447i
\(520\) −21.4012 + 4.54896i −0.938504 + 0.199485i
\(521\) −14.5712 3.09721i −0.638377 0.135691i −0.122658 0.992449i \(-0.539142\pi\)
−0.515719 + 0.856758i \(0.672475\pi\)
\(522\) −4.80496 45.7161i −0.210307 2.00094i
\(523\) −9.04869 4.02874i −0.395672 0.176164i 0.199249 0.979949i \(-0.436150\pi\)
−0.594920 + 0.803785i \(0.702816\pi\)
\(524\) −1.19755 3.68567i −0.0523151 0.161009i
\(525\) 0 0
\(526\) −0.893242 0.648979i −0.0389472 0.0282968i
\(527\) −0.762295 1.32033i −0.0332061 0.0575146i
\(528\) −17.8096 3.26150i −0.775062 0.141938i
\(529\) 11.1743 19.3544i 0.485838 0.841496i
\(530\) −4.35723 + 41.4563i −0.189266 + 1.80075i
\(531\) −5.26966 + 16.2183i −0.228684 + 0.703816i
\(532\) 0 0
\(533\) −3.54276 + 2.57397i −0.153454 + 0.111491i
\(534\) 12.9182 + 5.75153i 0.559023 + 0.248893i
\(535\) −11.8731 2.52372i −0.513321 0.109110i
\(536\) −4.94249 5.48919i −0.213483 0.237097i
\(537\) −1.08203 + 10.2948i −0.0466930 + 0.444254i
\(538\) −8.01342 −0.345483
\(539\) 0 0
\(540\) 16.2722 0.700245
\(541\) 2.30050 21.8878i 0.0989063 0.941031i −0.826726 0.562605i \(-0.809799\pi\)
0.925632 0.378425i \(-0.123534\pi\)
\(542\) −20.2571 22.4977i −0.870115 0.966361i
\(543\) 44.2323 + 9.40188i 1.89819 + 0.403473i
\(544\) 7.10007 + 3.16116i 0.304413 + 0.135533i
\(545\) −10.8389 + 7.87494i −0.464289 + 0.337325i
\(546\) 0 0
\(547\) −3.35724 + 10.3325i −0.143545 + 0.441787i −0.996821 0.0796728i \(-0.974612\pi\)
0.853276 + 0.521460i \(0.174612\pi\)
\(548\) 0.721023 6.86008i 0.0308006 0.293048i
\(549\) 2.78461 4.82309i 0.118844 0.205844i
\(550\) −3.40475 25.4418i −0.145179 1.08484i
\(551\) −6.47048 11.2072i −0.275652 0.477443i
\(552\) 5.73781 + 4.16876i 0.244218 + 0.177434i
\(553\) 0 0
\(554\) 7.22721 + 22.2431i 0.307055 + 0.945018i
\(555\) −90.8185 40.4350i −3.85503 1.71637i
\(556\) −1.03129 9.81205i −0.0437364 0.416124i
\(557\) −32.8781 6.98845i −1.39309 0.296110i −0.550575 0.834786i \(-0.685592\pi\)
−0.842513 + 0.538675i \(0.818925\pi\)
\(558\) −4.44588 + 0.945002i −0.188209 + 0.0400051i
\(559\) 5.13290 + 3.72927i 0.217098 + 0.157731i
\(560\) 0 0
\(561\) −6.15720 17.2701i −0.259957 0.729145i
\(562\) 15.6906 + 27.1769i 0.661867 + 1.14639i
\(563\) −1.87595 + 0.835227i −0.0790619 + 0.0352006i −0.445887 0.895089i \(-0.647112\pi\)
0.366825 + 0.930290i \(0.380445\pi\)
\(564\) 10.9706 + 12.1841i 0.461946 + 0.513043i
\(565\) 24.6379 27.3632i 1.03652 1.15118i
\(566\) 23.6151 17.1573i 0.992615 0.721177i
\(567\) 0 0
\(568\) 3.02857 + 9.32098i 0.127076 + 0.391099i
\(569\) −3.20261 + 0.680736i −0.134260 + 0.0285379i −0.274552 0.961572i \(-0.588529\pi\)
0.140291 + 0.990110i \(0.455196\pi\)
\(570\) −16.3258 + 7.26872i −0.683813 + 0.304453i
\(571\) 21.9448 38.0096i 0.918363 1.59065i 0.116462 0.993195i \(-0.462845\pi\)
0.801901 0.597457i \(-0.203822\pi\)
\(572\) −5.03207 + 1.21946i −0.210402 + 0.0509883i
\(573\) −1.22666 −0.0512446
\(574\) 0 0
\(575\) −1.73208 + 5.33080i −0.0722328 + 0.222310i
\(576\) 28.7232 31.9003i 1.19680 1.32918i
\(577\) 4.58780 + 43.6500i 0.190992 + 1.81717i 0.499904 + 0.866081i \(0.333369\pi\)
−0.308912 + 0.951091i \(0.599965\pi\)
\(578\) 1.54478 + 14.6976i 0.0642546 + 0.611341i
\(579\) 29.0283 32.2392i 1.20637 1.33981i
\(580\) −6.45466 + 19.8654i −0.268015 + 0.824866i
\(581\) 0 0
\(582\) −20.6076 −0.854214
\(583\) −2.73981 + 35.7893i −0.113471 + 1.48224i
\(584\) 1.88458 3.26418i 0.0779843 0.135073i
\(585\) −33.6385 + 14.9768i −1.39078 + 0.619216i
\(586\) 4.86610 1.03432i 0.201017 0.0427274i
\(587\) 0.862670 + 2.65503i 0.0356062 + 0.109585i 0.967280 0.253711i \(-0.0816513\pi\)
−0.931674 + 0.363296i \(0.881651\pi\)
\(588\) 0 0
\(589\) −1.03520 + 0.752114i −0.0426545 + 0.0309903i
\(590\) −8.49635 + 9.43616i −0.349789 + 0.388480i
\(591\) 39.8045 + 44.2074i 1.63734 + 1.81845i
\(592\) −17.5525 + 7.81486i −0.721402 + 0.321189i
\(593\) −11.6263 20.1374i −0.477435 0.826942i 0.522230 0.852805i \(-0.325100\pi\)
−0.999666 + 0.0258622i \(0.991767\pi\)
\(594\) −22.9511 + 0.650030i −0.941696 + 0.0266710i
\(595\) 0 0
\(596\) −1.92945 1.40183i −0.0790334 0.0574211i
\(597\) 23.6170 5.01995i 0.966581 0.205453i
\(598\) −1.81222 0.385200i −0.0741074 0.0157520i
\(599\) −1.09331 10.4022i −0.0446715 0.425021i −0.993888 0.110396i \(-0.964788\pi\)
0.949216 0.314624i \(-0.101879\pi\)
\(600\) 55.7457 + 24.8196i 2.27581 + 1.01326i
\(601\) 6.89406 + 21.2177i 0.281215 + 0.865489i 0.987508 + 0.157570i \(0.0503660\pi\)
−0.706293 + 0.707919i \(0.749634\pi\)
\(602\) 0 0
\(603\) −10.0569 7.30679i −0.409550 0.297556i
\(604\) 1.08653 + 1.88192i 0.0442102 + 0.0765743i
\(605\) −6.10741 37.5231i −0.248302 1.52553i
\(606\) −24.6042 + 42.6157i −0.999476 + 1.73114i
\(607\) −1.98483 + 18.8844i −0.0805617 + 0.766494i 0.877431 + 0.479702i \(0.159255\pi\)
−0.957993 + 0.286791i \(0.907411\pi\)
\(608\) 2.01571 6.20370i 0.0817477 0.251593i
\(609\) 0 0
\(610\) 3.35485 2.43744i 0.135834 0.0986892i
\(611\) −14.2367 6.33858i −0.575955 0.256431i
\(612\) 7.41614 + 1.57635i 0.299780 + 0.0637201i
\(613\) 13.4908 + 14.9830i 0.544888 + 0.605160i 0.951200 0.308575i \(-0.0998520\pi\)
−0.406312 + 0.913734i \(0.633185\pi\)
\(614\) −1.50091 + 14.2802i −0.0605719 + 0.576303i
\(615\) 21.0068 0.847077
\(616\) 0 0
\(617\) 7.03919 0.283387 0.141694 0.989911i \(-0.454745\pi\)
0.141694 + 0.989911i \(0.454745\pi\)
\(618\) 2.96670 28.2263i 0.119338 1.13543i
\(619\) −20.7986 23.0992i −0.835968 0.928436i 0.162331 0.986736i \(-0.448099\pi\)
−0.998299 + 0.0582999i \(0.981432\pi\)
\(620\) 2.02020 + 0.429407i 0.0811331 + 0.0172454i
\(621\) 4.58027 + 2.03927i 0.183800 + 0.0818330i
\(622\) −24.1814 + 17.5688i −0.969585 + 0.704445i
\(623\) 0 0
\(624\) −3.47453 + 10.6935i −0.139093 + 0.428083i
\(625\) 1.20173 11.4337i 0.0480691 0.457347i
\(626\) −1.99974 + 3.46364i −0.0799255 + 0.138435i
\(627\) −13.8751 + 6.65447i −0.554117 + 0.265754i
\(628\) −8.14414 14.1061i −0.324986 0.562893i
\(629\) −15.7408 11.4364i −0.627628 0.455998i
\(630\) 0 0
\(631\) 6.78971 + 20.8966i 0.270294 + 0.831880i 0.990426 + 0.138043i \(0.0440812\pi\)
−0.720132 + 0.693837i \(0.755919\pi\)
\(632\) 26.6243 + 11.8539i 1.05906 + 0.471522i
\(633\) −2.94622 28.0314i −0.117102 1.11415i
\(634\) 18.4426 + 3.92009i 0.732449 + 0.155687i
\(635\) −65.7548 + 13.9766i −2.60940 + 0.554645i
\(636\) −18.9722 13.7841i −0.752298 0.546576i
\(637\) 0 0
\(638\) 8.31039 28.2770i 0.329012 1.11950i
\(639\) 8.24705 + 14.2843i 0.326248 + 0.565078i
\(640\) 3.81998 1.70076i 0.150998 0.0672286i
\(641\) −8.89337 9.87709i −0.351267 0.390122i 0.541455 0.840730i \(-0.317874\pi\)
−0.892722 + 0.450608i \(0.851207\pi\)
\(642\) −7.48760 + 8.31582i −0.295512 + 0.328199i
\(643\) −11.8848 + 8.63480i −0.468690 + 0.340523i −0.796930 0.604071i \(-0.793544\pi\)
0.328241 + 0.944594i \(0.393544\pi\)
\(644\) 0 0
\(645\) −9.40510 28.9459i −0.370325 1.13974i
\(646\) −3.42117 + 0.727192i −0.134604 + 0.0286110i
\(647\) −5.61395 + 2.49949i −0.220707 + 0.0982651i −0.514112 0.857723i \(-0.671878\pi\)
0.293405 + 0.955988i \(0.405212\pi\)
\(648\) 3.44213 5.96195i 0.135220 0.234207i
\(649\) −7.08311 + 8.32920i −0.278036 + 0.326950i
\(650\) −15.9404 −0.625236
\(651\) 0 0
\(652\) 1.92589 5.92729i 0.0754238 0.232131i
\(653\) −27.2129 + 30.2230i −1.06492 + 1.18272i −0.0823978 + 0.996600i \(0.526258\pi\)
−0.982527 + 0.186119i \(0.940409\pi\)
\(654\) 1.29102 + 12.2832i 0.0504829 + 0.480313i
\(655\) −1.84706 17.5736i −0.0721704 0.686656i
\(656\) 2.71666 3.01716i 0.106068 0.117800i
\(657\) 1.96020 6.03286i 0.0764745 0.235364i
\(658\) 0 0
\(659\) 18.0090 0.701531 0.350765 0.936463i \(-0.385921\pi\)
0.350765 + 0.936463i \(0.385921\pi\)
\(660\) 22.9675 + 9.45605i 0.894008 + 0.368076i
\(661\) 8.57098 14.8454i 0.333373 0.577418i −0.649798 0.760107i \(-0.725147\pi\)
0.983171 + 0.182689i \(0.0584800\pi\)
\(662\) −1.26069 + 0.561297i −0.0489983 + 0.0218154i
\(663\) −11.1373 + 2.36731i −0.432537 + 0.0919387i
\(664\) 15.2629 + 46.9744i 0.592316 + 1.82296i
\(665\) 0 0
\(666\) −46.9276 + 34.0949i −1.81841 + 1.32115i
\(667\) −4.30642 + 4.78276i −0.166745 + 0.185189i
\(668\) 11.0101 + 12.2279i 0.425993 + 0.473113i
\(669\) −45.4321 + 20.2277i −1.75651 + 0.782048i
\(670\) −4.62807 8.01605i −0.178798 0.309687i
\(671\) 2.82823 2.17979i 0.109183 0.0841498i
\(672\) 0 0
\(673\) 18.7632 + 13.6322i 0.723268 + 0.525485i 0.887426 0.460949i \(-0.152491\pi\)
−0.164159 + 0.986434i \(0.552491\pi\)
\(674\) 22.3261 4.74557i 0.859971 0.182792i
\(675\) 42.1947 + 8.96877i 1.62408 + 0.345208i
\(676\) −0.693873 6.60176i −0.0266874 0.253914i
\(677\) −25.1869 11.2139i −0.968012 0.430987i −0.139046 0.990286i \(-0.544404\pi\)
−0.828966 + 0.559299i \(0.811070\pi\)
\(678\) −10.4893 32.2826i −0.402838 1.23981i
\(679\) 0 0
\(680\) 16.6185 + 12.0741i 0.637291 + 0.463019i
\(681\) −18.0556 31.2731i −0.691890 1.19839i
\(682\) −2.86654 0.524954i −0.109765 0.0201015i
\(683\) −10.9675 + 18.9963i −0.419661 + 0.726874i −0.995905 0.0904032i \(-0.971184\pi\)
0.576244 + 0.817278i \(0.304518\pi\)
\(684\) 0.665151 6.32849i 0.0254327 0.241976i
\(685\) 9.71923 29.9127i 0.371353 1.14291i
\(686\) 0 0
\(687\) 10.5775 7.68503i 0.403558 0.293202i
\(688\) −5.37372 2.39253i −0.204871 0.0912145i
\(689\) 21.8034 + 4.63445i 0.830643 + 0.176559i
\(690\) 5.94695 + 6.60476i 0.226397 + 0.251439i
\(691\) 2.68289 25.5260i 0.102062 0.971055i −0.816919 0.576753i \(-0.804320\pi\)
0.918981 0.394303i \(-0.129014\pi\)
\(692\) 6.09830 0.231823
\(693\) 0 0
\(694\) 30.3913 1.15364
\(695\) 4.70235 44.7399i 0.178370 1.69708i
\(696\) 46.8826 + 52.0684i 1.77708 + 1.97365i
\(697\) 4.02152 + 0.854801i 0.152326 + 0.0323779i
\(698\) 8.12899 + 3.61926i 0.307687 + 0.136991i
\(699\) 55.1770 40.0884i 2.08699 1.51628i
\(700\) 0 0
\(701\) −5.69007 + 17.5122i −0.214911 + 0.661428i 0.784249 + 0.620446i \(0.213049\pi\)
−0.999160 + 0.0409817i \(0.986951\pi\)
\(702\) −1.49042 + 14.1804i −0.0562525 + 0.535206i
\(703\) −8.16492 + 14.1421i −0.307946 + 0.533378i
\(704\) 24.8161 11.9018i 0.935292 0.448565i
\(705\) 37.3787 + 64.7419i 1.40776 + 2.43832i
\(706\) −5.35087 3.88764i −0.201383 0.146313i
\(707\) 0 0
\(708\) −2.20744 6.79380i −0.0829607 0.255327i
\(709\) 21.6164 + 9.62422i 0.811819 + 0.361445i 0.770291 0.637692i \(-0.220111\pi\)
0.0415280 + 0.999137i \(0.486777\pi\)
\(710\) 1.28376 + 12.2142i 0.0481787 + 0.458390i
\(711\) 47.9761 + 10.1976i 1.79925 + 0.382442i
\(712\) −13.3437 + 2.83630i −0.500077 + 0.106295i
\(713\) 0.514827 + 0.374044i 0.0192804 + 0.0140081i
\(714\) 0 0
\(715\) −23.5993 + 0.668389i −0.882565 + 0.0249963i
\(716\) −1.37226 2.37682i −0.0512838 0.0888261i
\(717\) −23.0822 + 10.2769i −0.862022 + 0.383797i
\(718\) 21.1937 + 23.5380i 0.790941 + 0.878429i
\(719\) 7.44223 8.26544i 0.277548 0.308249i −0.588213 0.808706i \(-0.700168\pi\)
0.865761 + 0.500458i \(0.166835\pi\)
\(720\) 27.6187 20.0662i 1.02929 0.747823i
\(721\) 0 0
\(722\) −5.63627 17.3467i −0.209760 0.645576i
\(723\) 52.9808 11.2614i 1.97038 0.418817i
\(724\) −10.9529 + 4.87653i −0.407060 + 0.181235i
\(725\) −27.6865 + 47.9544i −1.02825 + 1.78098i
\(726\) −32.7722 12.4198i −1.21629 0.460941i
\(727\) 42.4803 1.57551 0.787753 0.615991i \(-0.211244\pi\)
0.787753 + 0.615991i \(0.211244\pi\)
\(728\) 0 0
\(729\) −12.8826 + 39.6485i −0.477133 + 1.46846i
\(730\) 3.16045 3.51004i 0.116974 0.129912i
\(731\) −0.622646 5.92408i −0.0230294 0.219110i
\(732\) 0.243857 + 2.32014i 0.00901321 + 0.0857550i
\(733\) 14.8470 16.4892i 0.548385 0.609043i −0.403695 0.914894i \(-0.632274\pi\)
0.952080 + 0.305851i \(0.0989408\pi\)
\(734\) −10.4699 + 32.2231i −0.386452 + 1.18938i
\(735\) 0 0
\(736\) −3.24402 −0.119576
\(737\) −4.17897 6.78690i −0.153935 0.249999i
\(738\) 6.12854 10.6149i 0.225595 0.390741i
\(739\) 26.9022 11.9776i 0.989613 0.440604i 0.152898 0.988242i \(-0.451140\pi\)
0.836715 + 0.547638i \(0.184473\pi\)
\(740\) 25.7817 5.48006i 0.947753 0.201451i
\(741\) 2.95305 + 9.08855i 0.108483 + 0.333876i
\(742\) 0 0
\(743\) −13.6772 + 9.93704i −0.501766 + 0.364555i −0.809691 0.586856i \(-0.800365\pi\)
0.307925 + 0.951411i \(0.400365\pi\)
\(744\) 4.63565 5.14841i 0.169951 0.188750i
\(745\) −7.27649 8.08136i −0.266590 0.296078i
\(746\) 14.6838 6.53767i 0.537613 0.239361i
\(747\) 41.5622 + 71.9879i 1.52068 + 2.63390i
\(748\) 4.01208 + 2.74484i 0.146696 + 0.100361i
\(749\) 0 0
\(750\) 17.3220 + 12.5851i 0.632508 + 0.459544i
\(751\) 1.51756 0.322568i 0.0553766 0.0117707i −0.180140 0.983641i \(-0.557655\pi\)
0.235517 + 0.971870i \(0.424322\pi\)
\(752\) 14.1326 + 3.00398i 0.515364 + 0.109544i
\(753\) −0.856713 8.15108i −0.0312204 0.297042i
\(754\) −16.7205 7.44446i −0.608926 0.271111i
\(755\) 3.06188 + 9.42349i 0.111433 + 0.342956i
\(756\) 0 0
\(757\) −10.1505 7.37474i −0.368925 0.268040i 0.387840 0.921727i \(-0.373221\pi\)
−0.756765 + 0.653687i \(0.773221\pi\)
\(758\) 12.4860 + 21.6265i 0.453513 + 0.785508i
\(759\) 5.27979 + 5.54000i 0.191644 + 0.201089i
\(760\) 8.62019 14.9306i 0.312687 0.541590i
\(761\) 0.944347 8.98487i 0.0342326 0.325701i −0.963982 0.265968i \(-0.914308\pi\)
0.998214 0.0597330i \(-0.0190249\pi\)
\(762\) −19.1503 + 58.9386i −0.693742 + 2.13512i
\(763\) 0 0
\(764\) 0.263115 0.191164i 0.00951916 0.00691608i
\(765\) 31.5819 + 14.0612i 1.14185 + 0.508383i
\(766\) −36.7134 7.80368i −1.32651 0.281958i
\(767\) 4.54335 + 5.04590i 0.164051 + 0.182197i
\(768\) −4.55663 + 43.3534i −0.164423 + 1.56438i
\(769\) −16.1383