Properties

Label 539.2.q.g.520.2
Level 539
Weight 2
Character 539.520
Analytic conductor 4.304
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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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 520.2
Character \(\chi\) = 539.520
Dual form 539.2.q.g.312.2

$q$-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 \(\left(\mathbb{Z}/539\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{5}\right)\)

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 −0.955252 0.295793i \(-0.904416\pi\)
0.872879 0.487937i \(-0.162250\pi\)
\(3\) −1.91292 + 2.12452i −1.10443 + 1.22659i −0.132530 + 0.991179i \(0.542310\pi\)
−0.971896 + 0.235411i \(0.924356\pi\)
\(4\) 0.741401 0.157590i 0.370700 0.0787948i
\(5\) 3.15728 1.40571i 1.41198 0.628654i 0.447856 0.894106i \(-0.352188\pi\)
0.964124 + 0.265451i \(0.0855210\pi\)
\(6\) 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 −0.332226 0.943200i \(-0.607800\pi\)
0.794373 + 0.607430i \(0.207800\pi\)
\(14\) 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 0.942279 + 0.334828i \(0.108678\pi\)
−0.991303 + 0.131601i \(0.957988\pi\)
\(18\) −5.63898 + 1.19860i −1.32912 + 0.282513i
\(19\) −1.58749 0.337432i −0.364196 0.0774123i 0.0221790 0.999754i \(-0.492940\pi\)
−0.386375 + 0.922342i \(0.626273\pi\)
\(20\) 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 −0.820879 0.571102i \(-0.806516\pi\)
0.905029 + 0.425351i \(0.139849\pi\)
\(24\) 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 −0.410557 0.911835i \(-0.634666\pi\)
0.868111 0.496371i \(-0.165334\pi\)
\(30\) 10.7706 + 2.28937i 1.96644 + 0.417980i
\(31\) 0.720257 + 0.320679i 0.129362 + 0.0575957i 0.470397 0.882455i \(-0.344111\pi\)
−0.341035 + 0.940051i \(0.610777\pi\)
\(32\) −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 0.971138 + 0.238519i \(0.0766620\pi\)
0.135701 + 0.990750i \(0.456671\pi\)
\(38\) −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 0.886554 0.462626i \(-0.153093\pi\)
−0.989162 + 0.146831i \(0.953093\pi\)
\(42\) 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 −0.366382 0.930464i \(-0.619404\pi\)
−0.713161 + 0.701000i \(0.752737\pi\)
\(48\) 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 0.951123 0.308812i \(-0.0999316\pi\)
0.406933 + 0.913458i \(0.366598\pi\)
\(54\) 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 0.00683535 0.999977i \(-0.497824\pi\)
0.412972 + 0.910744i \(0.364491\pi\)
\(60\) −0.782805 + 7.44789i −0.101060 + 0.961518i
\(61\) −0.983548 + 0.437904i −0.125930 + 0.0560678i −0.468735 0.883339i \(-0.655290\pi\)
0.342804 + 0.939407i \(0.388623\pi\)
\(62\) 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 0.783246 0.621712i \(-0.213562\pi\)
−0.930041 + 0.367455i \(0.880229\pi\)
\(68\) 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 0.730241 0.683190i \(-0.239408\pi\)
−0.424095 + 0.905618i \(0.639408\pi\)
\(72\) −14.5250 + 6.46693i −1.71178 + 0.762135i
\(73\) −1.19948 + 0.254957i −0.140388 + 0.0298405i −0.277570 0.960705i \(-0.589529\pi\)
0.137181 + 0.990546i \(0.456196\pi\)
\(74\) 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 0.896988 + 0.442055i \(0.145750\pi\)
−0.785478 + 0.618889i \(0.787583\pi\)
\(80\) −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 0.990569 + 0.137016i \(0.0437511\pi\)
0.436412 + 0.899747i \(0.356249\pi\)
\(84\) 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 −0.724110 0.689685i \(-0.757749\pi\)
0.959339 + 0.282255i \(0.0910825\pi\)
\(90\) −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 −0.820847 0.571148i \(-0.806498\pi\)
0.289539 + 0.957166i \(0.406498\pi\)
\(98\) 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 −0.441687 0.897169i \(-0.645620\pi\)
−0.962273 + 0.272086i \(0.912286\pi\)
\(102\) −4.12249 + 4.57849i −0.408188 + 0.453338i
\(103\) 5.96070 + 6.62003i 0.587325 + 0.652291i 0.961415 0.275102i \(-0.0887116\pi\)
−0.374090 + 0.927392i \(0.622045\pi\)
\(104\) −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 0.0388354 0.999246i \(-0.487635\pi\)
−0.370952 + 0.928652i \(0.620969\pi\)
\(108\) 4.30124 + 1.91503i 0.413887 + 0.184274i
\(109\) −1.93827 3.35719i −0.185653 0.321560i 0.758143 0.652088i \(-0.226107\pi\)
−0.943796 + 0.330527i \(0.892773\pi\)
\(110\) −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 0.977878 + 0.209175i \(0.0670777\pi\)
−0.668170 + 0.744008i \(0.732922\pi\)
\(114\) −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 −0.995134 0.0985289i \(-0.968586\pi\)
−0.401220 0.915982i \(-0.631414\pi\)
\(128\) 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 −0.955825 0.293937i \(-0.905034\pi\)
0.732469 + 0.680800i \(0.238368\pi\)
\(132\) 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 0.875658 + 0.482932i \(0.160428\pi\)
−0.956930 + 0.290319i \(0.906239\pi\)
\(138\) 2.34926 1.04596i 0.199982 0.0890377i
\(139\) −4.02234 + 12.3795i −0.341171 + 1.05002i 0.622431 + 0.782675i \(0.286145\pi\)
−0.963602 + 0.267341i \(0.913855\pi\)
\(140\) 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 −0.521087 0.853504i \(-0.674473\pi\)
0.285601 + 0.958348i \(0.407807\pi\)
\(150\) 21.6420 4.60015i 1.76706 0.375601i
\(151\) 1.91837 2.13057i 0.156115 0.173383i −0.660014 0.751254i \(-0.729449\pi\)
0.816128 + 0.577871i \(0.196116\pi\)
\(152\) 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 −0.191490 + 0.981495i \(0.561332\pi\)
−0.956102 + 0.293035i \(0.905335\pi\)
\(158\) 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 0.975208 + 0.221291i \(0.0710272\pi\)
−0.907888 + 0.419213i \(0.862306\pi\)
\(164\) −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 0.360529 0.932748i \(-0.382596\pi\)
0.998506 0.0546489i \(-0.0174040\pi\)
\(168\) 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 0.497114 0.867685i \(-0.334393\pi\)
0.101217 + 0.994864i \(0.467726\pi\)
\(174\) 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 −0.826856 0.562414i \(-0.809873\pi\)
0.645763 + 0.763538i \(0.276540\pi\)
\(180\) −9.06718 10.0701i −0.675828 0.750583i
\(181\) −12.7970 9.29753i −0.951190 0.691080i −0.000102207 1.00000i \(-0.500033\pi\)
−0.951088 + 0.308920i \(0.900033\pi\)
\(182\) 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 0.753443 0.657514i \(-0.228392\pi\)
−0.732668 + 0.680586i \(0.761725\pi\)
\(192\) 2.47978 23.5935i 0.178963 1.70272i
\(193\) 1.58620 15.0917i 0.114177 1.08632i −0.776007 0.630724i \(-0.782758\pi\)
0.890185 0.455600i \(-0.150575\pi\)
\(194\) 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 0.676638 0.736316i \(-0.263436\pi\)
−0.975987 + 0.217828i \(0.930103\pi\)
\(200\) −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 −0.278346 0.960481i \(-0.589786\pi\)
0.827458 + 0.561528i \(0.189786\pi\)
\(212\) 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 0.953066 + 0.302762i \(0.0979087\pi\)
−0.593088 + 0.805138i \(0.702091\pi\)
\(224\) 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 0.221267 0.975213i \(-0.428981\pi\)
0.598793 + 0.800904i \(0.295647\pi\)
\(228\) 2.35317 2.61346i 0.155843 0.173081i
\(229\) −0.478052 4.54836i −0.0315906 0.300564i −0.998897 0.0469539i \(-0.985049\pi\)
0.967306 0.253610i \(-0.0816181\pi\)
\(230\) −3.10883 −0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) −2.49372 23.7262i −0.163369 1.55436i −0.702224 0.711956i \(-0.747809\pi\)
0.538855 0.842399i \(-0.318857\pi\)
\(234\) −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 0.999705 0.0242677i \(-0.00772541\pi\)
−0.823043 + 0.567979i \(0.807725\pi\)
\(240\) −1.97214 18.7637i −0.127301 1.21119i
\(241\) −9.47322 16.4081i −0.610224 1.05694i −0.991202 0.132355i \(-0.957746\pi\)
0.380978 0.924584i \(-0.375587\pi\)
\(242\) 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 −0.512175 0.858881i \(-0.671160\pi\)
0.658573 + 0.752516i \(0.271160\pi\)
\(252\) 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 0.999154 + 0.0411328i \(0.0130967\pi\)
−0.0635326 + 0.997980i \(0.520237\pi\)
\(258\) 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 0.850349 0.526219i \(-0.176391\pi\)
−0.880894 + 0.473314i \(0.843058\pi\)
\(264\) −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 −0.947422 0.319988i \(-0.896321\pi\)
0.993247 0.116015i \(-0.0370121\pi\)
\(270\) 2.50092 23.7947i 0.152201 1.44810i
\(271\) −18.1765 20.1870i −1.10414 1.22627i −0.971985 0.235044i \(-0.924477\pi\)
−0.132156 0.991229i \(-0.542190\pi\)
\(272\) −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 0.891667 0.452693i \(-0.149536\pi\)
0.260225 + 0.965548i \(0.416203\pi\)
\(278\) 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 0.998510 + 0.0545621i \(0.0173763\pi\)
0.360448 + 0.932779i \(0.382624\pi\)
\(282\) −16.1305 17.9148i −0.960560 1.06681i
\(283\) −17.5257 + 19.4643i −1.04179 + 1.15703i −0.0544372 + 0.998517i \(0.517336\pi\)
−0.987357 + 0.158512i \(0.949330\pi\)
\(284\) 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 −0.983230 0.182370i \(-0.941623\pi\)
0.902644 + 0.430388i \(0.141623\pi\)
\(294\) 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 0.0261787 0.999657i \(-0.491666\pi\)
0.991445 0.130528i \(-0.0416672\pi\)
\(312\) 17.7027 3.76283i 1.00222 0.213029i
\(313\) 3.27843 1.45965i 0.185308 0.0825043i −0.311985 0.950087i \(-0.600994\pi\)
0.497293 + 0.867583i \(0.334327\pi\)
\(314\) 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 0.924770 + 0.380526i \(0.124257\pi\)
−0.825446 + 0.564481i \(0.809076\pi\)
\(318\) 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 −0.848509 0.529182i \(-0.822499\pi\)
0.882539 + 0.470239i \(0.155832\pi\)
\(332\) 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 0.616961 + 0.786994i \(0.288364\pi\)
−0.961715 + 0.274051i \(0.911636\pi\)
\(338\) 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 0.601103 + 0.799171i \(0.294728\pi\)
−0.754125 + 0.656731i \(0.771939\pi\)
\(348\) 11.5613 + 12.8401i 0.619748 + 0.688300i
\(349\) 2.46730 + 7.59356i 0.132071 + 0.406474i 0.995123 0.0986418i \(-0.0314498\pi\)
−0.863052 + 0.505116i \(0.831450\pi\)
\(350\) 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 0.776188 0.630502i \(-0.217151\pi\)
−0.934124 + 0.356948i \(0.883817\pi\)
\(354\) 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 0.993395 + 0.114744i \(0.0366048\pi\)
0.0102773 + 0.999947i \(0.496729\pi\)
\(360\) −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 0.649595 0.760281i \(-0.274939\pi\)
0.902668 + 0.430337i \(0.141605\pi\)
\(368\) −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 −0.990084 0.140476i \(-0.955137\pi\)
0.616698 + 0.787200i \(0.288470\pi\)
\(374\) −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 0.946277 0.323356i \(-0.104811\pi\)
−0.0151144 + 0.999886i \(0.504811\pi\)
\(380\) −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 −0.596691 0.802471i \(-0.703518\pi\)
0.416808 0.908994i \(-0.363149\pi\)
\(384\) −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 −0.267720 0.963497i \(-0.586270\pi\)
0.147315 + 0.989090i \(0.452937\pi\)
\(390\) 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 −0.782501 0.622650i \(-0.786056\pi\)
0.930481 + 0.366341i \(0.119390\pi\)
\(398\) −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 −0.134015 0.990979i \(-0.542787\pi\)
0.646768 + 0.762687i \(0.276120\pi\)
\(402\) 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 0.942579 0.333983i \(-0.108393\pi\)
0.382511 + 0.923951i \(0.375059\pi\)
\(410\) −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 0.925366 0.379075i \(-0.123758\pi\)
−0.971452 + 0.237238i \(0.923758\pi\)
\(422\) −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 0.565909 0.824468i \(-0.308526\pi\)
−0.234032 + 0.972229i \(0.575192\pi\)
\(432\) −11.6025 2.46619i −0.558227 0.118655i
\(433\) −9.93848 + 30.5875i −0.477613 + 1.46994i 0.364788 + 0.931091i \(0.381141\pi\)
−0.842401 + 0.538851i \(0.818859\pi\)
\(434\) 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 −0.804948 0.593345i \(-0.797807\pi\)
0.916326 + 0.400433i \(0.131140\pi\)
\(440\) −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 −0.211869 0.977298i \(-0.567955\pi\)
−0.591055 + 0.806631i \(0.701288\pi\)
\(444\) −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 −0.220418 0.975405i \(-0.570742\pi\)
0.859553 + 0.511047i \(0.170742\pi\)
\(450\) −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 −0.814077 0.580757i \(-0.802757\pi\)
−0.113137 + 0.993579i \(0.536090\pi\)
\(458\) −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 −0.487902 0.872898i \(-0.662238\pi\)
0.322219 + 0.946665i \(0.395571\pi\)
\(468\) −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 −0.897275 0.441473i \(-0.854456\pi\)
0.969454 0.245271i \(-0.0788771\pi\)
\(480\) 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 −0.231363 0.972867i \(-0.574319\pi\)
0.991722 + 0.128404i \(0.0409853\pi\)
\(488\) 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 −0.256679 0.966497i \(-0.582628\pi\)
0.775750 0.631040i \(-0.217372\pi\)
\(492\) 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 −0.998235 0.0593841i \(-0.981086\pi\)
0.0452852 0.998974i \(-0.485580\pi\)
\(500\) 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 −0.991779 0.127959i \(-0.959157\pi\)
0.727154 0.686474i \(-0.240843\pi\)
\(504\) 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 0.153058 0.988217i \(-0.451088\pi\)
−0.262119 + 0.965036i \(0.584421\pi\)
\(510\) −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 −0.515719 0.856758i \(-0.672475\pi\)
−0.122658 + 0.992449i \(0.539142\pi\)
\(522\) −4.80496 + 45.7161i −0.210307 + 2.00094i
\(523\) −9.04869 + 4.02874i −0.395672 + 0.176164i −0.594920 0.803785i \(-0.702816\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(524\) −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 0.925632 + 0.378425i \(0.123534\pi\)
−0.826726 + 0.562605i \(0.809799\pi\)
\(542\) −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 0.853276 0.521460i \(-0.174612\pi\)
−0.996821 + 0.0796728i \(0.974612\pi\)
\(548\) 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 −0.842513 0.538675i \(-0.818925\pi\)
−0.550575 + 0.834786i \(0.685592\pi\)
\(558\) −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 0.366825 0.930290i \(-0.380445\pi\)
−0.445887 + 0.895089i \(0.647112\pi\)
\(564\) 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 0.140291 0.990110i \(-0.455196\pi\)
−0.274552 + 0.961572i \(0.588529\pi\)
\(570\) −16.3258 7.26872i −0.683813 0.304453i
\(571\) 21.9448 + 38.0096i 0.918363 + 1.59065i 0.801901 + 0.597457i \(0.203822\pi\)
0.116462 + 0.993195i \(0.462845\pi\)
\(572\) −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 −0.308912 0.951091i \(-0.599965\pi\)
0.499904 0.866081i \(-0.333369\pi\)
\(578\) 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 −0.931674 0.363296i \(-0.881651\pi\)
0.967280 + 0.253711i \(0.0816513\pi\)
\(588\) 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 −0.999666 0.0258622i \(-0.991767\pi\)
0.522230 + 0.852805i \(0.325100\pi\)
\(594\) −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 0.949216 + 0.314624i \(0.101879\pi\)
−0.993888 + 0.110396i \(0.964788\pi\)
\(600\) 55.7457 24.8196i 2.27581 1.01326i
\(601\) 6.89406 21.2177i 0.281215 0.865489i −0.706293 0.707919i \(-0.749634\pi\)
0.987508 0.157570i \(-0.0503660\pi\)
\(602\) 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 −0.957993 0.286791i \(-0.907411\pi\)
0.877431 0.479702i \(-0.159255\pi\)
\(608\) 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 −0.406312 0.913734i \(-0.633185\pi\)
0.951200 + 0.308575i \(0.0998520\pi\)
\(614\) −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 −0.998299 0.0582999i \(-0.981432\pi\)
0.162331 + 0.986736i \(0.448099\pi\)
\(620\) 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 −0.720132 0.693837i \(-0.755919\pi\)
0.990426 0.138043i \(-0.0440812\pi\)
\(632\) 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 −0.892722 0.450608i \(-0.851207\pi\)
0.541455 + 0.840730i \(0.317874\pi\)
\(642\) −7.48760 8.31582i −0.295512 0.328199i
\(643\) −11.8848 8.63480i −0.468690 0.340523i 0.328241 0.944594i \(-0.393544\pi\)
−0.796930 + 0.604071i \(0.793544\pi\)
\(644\) 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 0.293405 0.955988i \(-0.405212\pi\)
−0.514112 + 0.857723i \(0.671878\pi\)
\(648\) 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 −0.982527 0.186119i \(-0.940409\pi\)
−0.0823978 0.996600i \(-0.526258\pi\)
\(654\) 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 0.983171 0.182689i \(-0.0584800\pi\)
−0.649798 + 0.760107i \(0.725147\pi\)
\(662\) −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 −0.164159 0.986434i \(-0.552491\pi\)
0.887426 + 0.460949i \(0.152491\pi\)
\(674\) 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 −0.828966 0.559299i \(-0.811070\pi\)
−0.139046 + 0.990286i \(0.544404\pi\)
\(678\) −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 0.576244 0.817278i \(-0.304518\pi\)
−0.995905 + 0.0904032i \(0.971184\pi\)
\(684\) 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 0.918981 + 0.394303i \(0.129014\pi\)
−0.816919 + 0.576753i \(0.804320\pi\)
\(692\) 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 −0.999160 0.0409817i \(-0.986951\pi\)
0.784249 0.620446i \(-0.213049\pi\)
\(702\) −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 0.0415280 0.999137i \(-0.486777\pi\)
0.770291 + 0.637692i \(0.220111\pi\)
\(710\) 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 0.865761 0.500458i \(-0.166835\pi\)
−0.588213 + 0.808706i \(0.700168\pi\)
\(720\) 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 0.952080 0.305851i \(-0.0989408\pi\)
−0.403695 + 0.914894i \(0.632274\pi\)
\(734\) −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 0.836715 0.547638i \(-0.184473\pi\)
0.152898 + 0.988242i \(0.451140\pi\)
\(740\) 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 0.307925 0.951411i \(-0.400365\pi\)
−0.809691 + 0.586856i \(0.800365\pi\)
\(744\) 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 0.235517 0.971870i \(-0.424322\pi\)
−0.180140 + 0.983641i \(0.557655\pi\)
\(752\) 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 −0.756765 0.653687i \(-0.773221\pi\)
0.387840 + 0.921727i \(0.373221\pi\)
\(758\) 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 0.998214 + 0.0597330i \(0.0190249\pi\)
−0.963982 + 0.265968i \(0.914308\pi\)
\(762\) −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
\(769\)