Properties

Label 539.2.f.e.344.2
Level 539
Weight 2
Character 539.344
Analytic conductor 4.304
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 539 = 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 539.f (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.30393666895\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 344.2
Root \(0.901622 - 0.655067i\)
Character \(\chi\) = 539.344
Dual form 539.2.f.e.246.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.901622 + 0.655067i) q^{2} +(0.883423 + 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(2.79603 + 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} +O(q^{10})\) \(q+(-0.901622 + 0.655067i) q^{2} +(0.883423 + 2.71890i) q^{3} +(-0.234224 + 0.720867i) q^{4} +(2.79603 + 2.03143i) q^{5} +(-2.57757 - 1.87272i) q^{6} +(-0.949813 - 2.92322i) q^{8} +(-4.18492 + 3.04052i) q^{9} -3.85168 q^{10} +(3.31530 + 0.0938970i) q^{11} -2.16688 q^{12} +(-1.66629 + 1.21063i) q^{13} +(-3.05318 + 9.39672i) q^{15} +(1.54487 + 1.12241i) q^{16} +(1.56442 + 1.13662i) q^{17} +(1.78147 - 5.48280i) q^{18} +(-0.501522 - 1.54353i) q^{19} +(-2.11929 + 1.53975i) q^{20} +(-3.05065 + 2.08708i) q^{22} -0.807136 q^{23} +(7.10886 - 5.16489i) q^{24} +(2.14596 + 6.60459i) q^{25} +(0.709322 - 2.18307i) q^{26} +(-5.02542 - 3.65118i) q^{27} +(2.46400 - 7.58342i) q^{29} +(-3.40267 - 10.4723i) q^{30} +(0.637845 - 0.463421i) q^{31} +4.01918 q^{32} +(2.67351 + 9.09690i) q^{33} -2.15508 q^{34} +(-1.21160 - 3.72893i) q^{36} +(3.10926 - 9.56931i) q^{37} +(1.46330 + 1.06315i) q^{38} +(-4.76363 - 3.46098i) q^{39} +(3.28263 - 10.1029i) q^{40} +(0.657011 + 2.02207i) q^{41} +3.08043 q^{43} +(-0.844208 + 2.36789i) q^{44} -17.8777 q^{45} +(0.727732 - 0.528728i) q^{46} +(-2.33812 - 7.19600i) q^{47} +(-1.68695 + 5.19190i) q^{48} +(-6.26129 - 4.54910i) q^{50} +(-1.70830 + 5.25761i) q^{51} +(-0.482420 - 1.48474i) q^{52} +(-8.75554 + 6.36127i) q^{53} +6.92280 q^{54} +(9.07891 + 6.99733i) q^{55} +(3.75363 - 2.72717i) q^{57} +(2.74605 + 8.45147i) q^{58} +(1.01872 - 3.13529i) q^{59} +(-6.05866 - 4.40187i) q^{60} +(-0.871010 - 0.632826i) q^{61} +(-0.271523 + 0.835662i) q^{62} +(-6.71351 + 4.87765i) q^{64} -7.11832 q^{65} +(-8.36958 - 6.45064i) q^{66} +2.40314 q^{67} +(-1.18577 + 0.861515i) q^{68} +(-0.713042 - 2.19452i) q^{69} +(2.57963 + 1.87421i) q^{71} +(12.8630 + 9.34552i) q^{72} +(-0.378940 + 1.16626i) q^{73} +(3.46516 + 10.6647i) q^{74} +(-16.0614 + 11.6693i) q^{75} +1.23015 q^{76} +6.56217 q^{78} +(7.67096 - 5.57328i) q^{79} +(2.03939 + 6.27659i) q^{80} +(0.692124 - 2.13014i) q^{81} +(-1.91697 - 1.39276i) q^{82} +(-13.0004 - 9.44536i) q^{83} +(2.06520 + 6.35602i) q^{85} +(-2.77738 + 2.01789i) q^{86} +22.7953 q^{87} +(-2.87443 - 9.78053i) q^{88} +4.43830 q^{89} +(16.1190 - 11.7111i) q^{90} +(0.189050 - 0.581837i) q^{92} +(1.82348 + 1.32484i) q^{93} +(6.82196 + 4.95645i) q^{94} +(1.73330 - 5.33455i) q^{95} +(3.55063 + 10.9277i) q^{96} +(5.23278 - 3.80184i) q^{97} +(-14.1597 + 9.68727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 3q^{2} + 2q^{3} - 11q^{4} + 5q^{5} - 3q^{6} - 5q^{8} - 12q^{9} + O(q^{10}) \) \( 16q - 3q^{2} + 2q^{3} - 11q^{4} + 5q^{5} - 3q^{6} - 5q^{8} - 12q^{9} - 12q^{10} - 3q^{11} - 18q^{12} + 7q^{13} - 18q^{15} + 17q^{16} + 5q^{17} + 11q^{18} - 19q^{19} - q^{20} - 33q^{22} + 32q^{23} + 35q^{24} + 7q^{25} + 27q^{26} - 10q^{27} + 3q^{29} - 2q^{30} + 7q^{31} + 32q^{32} + 26q^{33} + 24q^{34} + 52q^{36} + 4q^{37} + 5q^{38} + 11q^{39} + 10q^{40} + 10q^{41} - 8q^{43} - 38q^{44} - 70q^{45} - 42q^{46} + 23q^{47} + 36q^{48} + 52q^{50} - 29q^{51} - 33q^{52} + 4q^{53} - 60q^{54} + 12q^{55} - 11q^{57} + 20q^{58} - 17q^{59} - 30q^{60} + 7q^{61} - 79q^{62} + 7q^{64} - 8q^{65} - 8q^{66} - 38q^{67} + 2q^{68} - 10q^{69} - 14q^{71} + 35q^{73} - 29q^{74} - 9q^{75} - 52q^{76} - 58q^{78} + 15q^{79} + 87q^{80} - 14q^{81} - 19q^{82} - 5q^{83} + 6q^{85} - 52q^{86} + 72q^{87} + 55q^{88} - 74q^{89} + 14q^{90} - 55q^{92} + 32q^{93} + 24q^{94} + 32q^{95} + 42q^{96} - 20q^{97} + 16q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.901622 + 0.655067i −0.637543 + 0.463202i −0.859005 0.511967i \(-0.828917\pi\)
0.221462 + 0.975169i \(0.428917\pi\)
\(3\) 0.883423 + 2.71890i 0.510045 + 1.56976i 0.792121 + 0.610364i \(0.208977\pi\)
−0.282076 + 0.959392i \(0.591023\pi\)
\(4\) −0.234224 + 0.720867i −0.117112 + 0.360433i
\(5\) 2.79603 + 2.03143i 1.25042 + 0.908484i 0.998246 0.0591979i \(-0.0188543\pi\)
0.252174 + 0.967682i \(0.418854\pi\)
\(6\) −2.57757 1.87272i −1.05229 0.764534i
\(7\) 0 0
\(8\) −0.949813 2.92322i −0.335810 1.03352i
\(9\) −4.18492 + 3.04052i −1.39497 + 1.01351i
\(10\) −3.85168 −1.21801
\(11\) 3.31530 + 0.0938970i 0.999599 + 0.0283110i
\(12\) −2.16688 −0.625525
\(13\) −1.66629 + 1.21063i −0.462147 + 0.335769i −0.794373 0.607430i \(-0.792200\pi\)
0.332226 + 0.943200i \(0.392200\pi\)
\(14\) 0 0
\(15\) −3.05318 + 9.39672i −0.788328 + 2.42622i
\(16\) 1.54487 + 1.12241i 0.386217 + 0.280603i
\(17\) 1.56442 + 1.13662i 0.379427 + 0.275670i 0.761109 0.648624i \(-0.224655\pi\)
−0.381682 + 0.924294i \(0.624655\pi\)
\(18\) 1.78147 5.48280i 0.419897 1.29231i
\(19\) −0.501522 1.54353i −0.115057 0.354109i 0.876902 0.480669i \(-0.159606\pi\)
−0.991959 + 0.126560i \(0.959606\pi\)
\(20\) −2.11929 + 1.53975i −0.473887 + 0.344299i
\(21\) 0 0
\(22\) −3.05065 + 2.08708i −0.650401 + 0.444967i
\(23\) −0.807136 −0.168299 −0.0841497 0.996453i \(-0.526817\pi\)
−0.0841497 + 0.996453i \(0.526817\pi\)
\(24\) 7.10886 5.16489i 1.45109 1.05428i
\(25\) 2.14596 + 6.60459i 0.429192 + 1.32092i
\(26\) 0.709322 2.18307i 0.139109 0.428135i
\(27\) −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 \(-0.165334\pi\)
\(30\) −3.40267 10.4723i −0.621239 1.91198i
\(31\) 0.637845 0.463421i 0.114560 0.0832330i −0.529030 0.848603i \(-0.677444\pi\)
0.643590 + 0.765370i \(0.277444\pi\)
\(32\) 4.01918 0.710497
\(33\) 2.67351 + 9.09690i 0.465399 + 1.58357i
\(34\) −2.15508 −0.369592
\(35\) 0 0
\(36\) −1.21160 3.72893i −0.201934 0.621488i
\(37\) 3.10926 9.56931i 0.511159 1.57318i −0.279005 0.960290i \(-0.590005\pi\)
0.790164 0.612895i \(-0.209995\pi\)
\(38\) 1.46330 + 1.06315i 0.237378 + 0.172465i
\(39\) −4.76363 3.46098i −0.762792 0.554200i
\(40\) 3.28263 10.1029i 0.519029 1.59741i
\(41\) 0.657011 + 2.02207i 0.102608 + 0.315795i 0.989162 0.146831i \(-0.0469074\pi\)
−0.886554 + 0.462626i \(0.846907\pi\)
\(42\) 0 0
\(43\) 3.08043 0.469761 0.234880 0.972024i \(-0.424530\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(44\) −0.844208 + 2.36789i −0.127269 + 0.356973i
\(45\) −17.8777 −2.66506
\(46\) 0.727732 0.528728i 0.107298 0.0779567i
\(47\) −2.33812 7.19600i −0.341050 1.04964i −0.963665 0.267115i \(-0.913930\pi\)
0.622615 0.782529i \(-0.286070\pi\)
\(48\) −1.68695 + 5.19190i −0.243490 + 0.749387i
\(49\) 0 0
\(50\) −6.26129 4.54910i −0.885481 0.643339i
\(51\) −1.70830 + 5.25761i −0.239210 + 0.736213i
\(52\) −0.482420 1.48474i −0.0668996 0.205896i
\(53\) −8.75554 + 6.36127i −1.20267 + 0.873788i −0.994544 0.104315i \(-0.966735\pi\)
−0.208122 + 0.978103i \(0.566735\pi\)
\(54\) 6.92280 0.942073
\(55\) 9.07891 + 6.99733i 1.22420 + 0.943520i
\(56\) 0 0
\(57\) 3.75363 2.72717i 0.497181 0.361223i
\(58\) 2.74605 + 8.45147i 0.360574 + 1.10973i
\(59\) 1.01872 3.13529i 0.132626 0.408180i −0.862587 0.505908i \(-0.831158\pi\)
0.995213 + 0.0977281i \(0.0311576\pi\)
\(60\) −6.05866 4.40187i −0.782169 0.568279i
\(61\) −0.871010 0.632826i −0.111521 0.0810250i 0.530627 0.847606i \(-0.321957\pi\)
−0.642148 + 0.766581i \(0.721957\pi\)
\(62\) −0.271523 + 0.835662i −0.0344835 + 0.106129i
\(63\) 0 0
\(64\) −6.71351 + 4.87765i −0.839189 + 0.609707i
\(65\) −7.11832 −0.882919
\(66\) −8.36958 6.45064i −1.03022 0.794019i
\(67\) 2.40314 0.293590 0.146795 0.989167i \(-0.453104\pi\)
0.146795 + 0.989167i \(0.453104\pi\)
\(68\) −1.18577 + 0.861515i −0.143796 + 0.104474i
\(69\) −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 \(0.639408\pi\)
\(72\) 12.8630 + 9.34552i 1.51592 + 1.10138i
\(73\) −0.378940 + 1.16626i −0.0443516 + 0.136500i −0.970780 0.239970i \(-0.922862\pi\)
0.926429 + 0.376470i \(0.122862\pi\)
\(74\) 3.46516 + 10.6647i 0.402817 + 1.23974i
\(75\) −16.0614 + 11.6693i −1.85461 + 1.34745i
\(76\) 1.23015 0.141107
\(77\) 0 0
\(78\) 6.56217 0.743020
\(79\) 7.67096 5.57328i 0.863050 0.627043i −0.0656630 0.997842i \(-0.520916\pi\)
0.928713 + 0.370799i \(0.120916\pi\)
\(80\) 2.03939 + 6.27659i 0.228010 + 0.701744i
\(81\) 0.692124 2.13014i 0.0769027 0.236682i
\(82\) −1.91697 1.39276i −0.211694 0.153805i
\(83\) −13.0004 9.44536i −1.42698 1.03676i −0.990569 0.137016i \(-0.956249\pi\)
−0.436412 0.899747i \(-0.643751\pi\)
\(84\) 0 0
\(85\) 2.06520 + 6.35602i 0.224002 + 0.689407i
\(86\) −2.77738 + 2.01789i −0.299493 + 0.217594i
\(87\) 22.7953 2.44391
\(88\) −2.87443 9.78053i −0.306415 1.04261i
\(89\) 4.43830 0.470459 0.235230 0.971940i \(-0.424416\pi\)
0.235230 + 0.971940i \(0.424416\pi\)
\(90\) 16.1190 11.7111i 1.69909 1.23446i
\(91\) 0 0
\(92\) 0.189050 0.581837i 0.0197099 0.0606607i
\(93\) 1.82348 + 1.32484i 0.189086 + 0.137379i
\(94\) 6.82196 + 4.95645i 0.703632 + 0.511218i
\(95\) 1.73330 5.33455i 0.177833 0.547313i
\(96\) 3.55063 + 10.9277i 0.362385 + 1.11531i
\(97\) 5.23278 3.80184i 0.531308 0.386018i −0.289539 0.957166i \(-0.593502\pi\)
0.820847 + 0.571148i \(0.193502\pi\)
\(98\) 0 0
\(99\) −14.1597 + 9.68727i −1.42311 + 0.973607i
\(100\) −5.26366 −0.526366
\(101\) −12.4952 + 9.07828i −1.24332 + 0.903323i −0.997815 0.0660728i \(-0.978953\pi\)
−0.245503 + 0.969396i \(0.578953\pi\)
\(102\) −1.90384 5.85943i −0.188509 0.580170i
\(103\) −2.75276 + 8.47213i −0.271238 + 0.834784i 0.718953 + 0.695059i \(0.244622\pi\)
−0.990190 + 0.139725i \(0.955378\pi\)
\(104\) 5.12162 + 3.72107i 0.502216 + 0.364881i
\(105\) 0 0
\(106\) 3.72713 11.4709i 0.362011 1.11416i
\(107\) 1.08533 + 3.34029i 0.104922 + 0.322918i 0.989712 0.143072i \(-0.0456981\pi\)
−0.884790 + 0.465990i \(0.845698\pi\)
\(108\) 3.80909 2.76746i 0.366530 0.266299i
\(109\) 3.87655 0.371306 0.185653 0.982615i \(-0.440560\pi\)
0.185653 + 0.982615i \(0.440560\pi\)
\(110\) −12.7695 0.361662i −1.21752 0.0344831i
\(111\) 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 \(0.732922\pi\)
\(114\) −1.59788 + 4.91776i −0.149655 + 0.460591i
\(115\) −2.25677 1.63964i −0.210445 0.152897i
\(116\) 4.88951 + 3.55243i 0.453979 + 0.329835i
\(117\) 3.29235 10.1328i 0.304378 0.936778i
\(118\) 1.13533 + 3.49417i 0.104515 + 0.321665i
\(119\) 0 0
\(120\) 30.3687 2.77227
\(121\) 10.9824 + 0.622593i 0.998397 + 0.0565993i
\(122\) 1.19987 0.108631
\(123\) −4.91739 + 3.57269i −0.443386 + 0.322139i
\(124\) 0.184667 + 0.568346i 0.0165836 + 0.0510389i
\(125\) −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 \(-0.631414\pi\)
\(128\) 0.373878 1.15068i 0.0330464 0.101706i
\(129\) 2.72132 + 8.37537i 0.239599 + 0.737410i
\(130\) 6.41804 4.66298i 0.562899 0.408970i
\(131\) −5.11284 −0.446711 −0.223355 0.974737i \(-0.571701\pi\)
−0.223355 + 0.974737i \(0.571701\pi\)
\(132\) −7.18385 0.203464i −0.625274 0.0177092i
\(133\) 0 0
\(134\) −2.16672 + 1.57422i −0.187176 + 0.135992i
\(135\) −6.63407 20.4176i −0.570970 1.75727i
\(136\) 1.83668 5.65272i 0.157494 0.484717i
\(137\) −7.36247 5.34915i −0.629019 0.457009i 0.227042 0.973885i \(-0.427095\pi\)
−0.856060 + 0.516876i \(0.827095\pi\)
\(138\) 2.08045 + 1.51154i 0.177100 + 0.128671i
\(139\) 4.02234 12.3795i 0.341171 1.05002i −0.622431 0.782675i \(-0.713855\pi\)
0.963602 0.267341i \(-0.0861450\pi\)
\(140\) 0 0
\(141\) 17.4996 12.7142i 1.47373 1.07073i
\(142\) −3.55358 −0.298210
\(143\) −5.63793 + 3.85715i −0.471468 + 0.322551i
\(144\) −9.87786 −0.823155
\(145\) 22.2946 16.1980i 1.85147 1.34517i
\(146\) −0.422316 1.29975i −0.0349511 0.107568i
\(147\) 0 0
\(148\) 6.16994 + 4.48272i 0.507166 + 0.368477i
\(149\) 2.54557 + 1.84947i 0.208541 + 0.151514i 0.687153 0.726512i \(-0.258860\pi\)
−0.478612 + 0.878026i \(0.658860\pi\)
\(150\) 6.83715 21.0426i 0.558251 1.71812i
\(151\) 0.885940 + 2.72664i 0.0720968 + 0.221891i 0.980612 0.195962i \(-0.0627828\pi\)
−0.908515 + 0.417853i \(0.862783\pi\)
\(152\) −4.03572 + 2.93212i −0.327340 + 0.237827i
\(153\) −10.0029 −0.808684
\(154\) 0 0
\(155\) 2.72484 0.218864
\(156\) 3.61066 2.62330i 0.289084 0.210032i
\(157\) 6.64062 + 20.4377i 0.529979 + 1.63111i 0.754254 + 0.656582i \(0.227999\pi\)
−0.224275 + 0.974526i \(0.572001\pi\)
\(158\) −3.26544 + 10.0500i −0.259784 + 0.799534i
\(159\) −25.0305 18.1857i −1.98505 1.44222i
\(160\) 11.2377 + 8.16468i 0.888420 + 0.645475i
\(161\) 0 0
\(162\) 0.771349 + 2.37397i 0.0606029 + 0.186517i
\(163\) 6.65210 4.83304i 0.521033 0.378553i −0.295960 0.955200i \(-0.595639\pi\)
0.816993 + 0.576648i \(0.195639\pi\)
\(164\) −1.61153 −0.125840
\(165\) −11.0045 + 30.8662i −0.856701 + 2.40293i
\(166\) 17.9088 1.38999
\(167\) −17.5626 + 12.7600i −1.35904 + 0.987397i −0.360529 + 0.932748i \(0.617404\pi\)
−0.998506 + 0.0546489i \(0.982596\pi\)
\(168\) 0 0
\(169\) −2.70632 + 8.32919i −0.208178 + 0.640707i
\(170\) −6.02565 4.37789i −0.462146 0.335769i
\(171\) 6.79195 + 4.93464i 0.519393 + 0.377361i
\(172\) −0.721509 + 2.22058i −0.0550146 + 0.169317i
\(173\) 2.48624 + 7.65185i 0.189025 + 0.581760i 0.999994 0.00332915i \(-0.00105970\pi\)
−0.810969 + 0.585089i \(0.801060\pi\)
\(174\) −20.5527 + 14.9324i −1.55810 + 1.13203i
\(175\) 0 0
\(176\) 5.01630 + 3.86619i 0.378118 + 0.291425i
\(177\) 9.42449 0.708388
\(178\) −4.00167 + 2.90739i −0.299938 + 0.217918i
\(179\) −1.11892 3.44369i −0.0836322 0.257393i 0.900493 0.434871i \(-0.143206\pi\)
−0.984125 + 0.177478i \(0.943206\pi\)
\(180\) 4.18739 12.8875i 0.312110 0.960575i
\(181\) 12.7970 + 9.29753i 0.951190 + 0.691080i 0.951088 0.308920i \(-0.0999675\pi\)
0.000102207 1.00000i \(0.499967\pi\)
\(182\) 0 0
\(183\) 0.951118 2.92724i 0.0703087 0.216388i
\(184\) 0.766628 + 2.35944i 0.0565165 + 0.173940i
\(185\) 28.1330 20.4398i 2.06838 1.50276i
\(186\) −2.51195 −0.184185
\(187\) 5.07979 + 3.91512i 0.371471 + 0.286302i
\(188\) 5.73500 0.418268
\(189\) 0 0
\(190\) 1.93170 + 5.94518i 0.140141 + 0.431308i
\(191\) 0.132593 0.408080i 0.00959411 0.0295276i −0.946145 0.323744i \(-0.895058\pi\)
0.955739 + 0.294216i \(0.0950585\pi\)
\(192\) −19.1927 13.9443i −1.38511 1.00634i
\(193\) 12.2767 + 8.91954i 0.883696 + 0.642042i 0.934227 0.356680i \(-0.116091\pi\)
−0.0505310 + 0.998722i \(0.516091\pi\)
\(194\) −2.22753 + 6.85564i −0.159927 + 0.492206i
\(195\) −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 \(0.765772\pi\)
\(198\) 6.42092 18.0098i 0.456315 1.27990i
\(199\) −8.44567 −0.598698 −0.299349 0.954144i \(-0.596769\pi\)
−0.299349 + 0.954144i \(0.596769\pi\)
\(200\) 17.2684 12.5462i 1.22106 0.887153i
\(201\) 2.12299 + 6.53389i 0.149744 + 0.460865i
\(202\) 5.31906 16.3704i 0.374247 1.15182i
\(203\) 0 0
\(204\) −3.38991 2.46292i −0.237341 0.172439i
\(205\) −2.27068 + 6.98844i −0.158591 + 0.488094i
\(206\) −3.06786 9.44190i −0.213748 0.657849i
\(207\) 3.37779 2.45411i 0.234773 0.170573i
\(208\) −3.93303 −0.272707
\(209\) −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 \(0.189786\pi\)
\(212\) −2.53487 7.80154i −0.174096 0.535812i
\(213\) −2.81688 + 8.66946i −0.193009 + 0.594022i
\(214\) −3.16667 2.30072i −0.216469 0.157274i
\(215\) 8.61295 + 6.25768i 0.587399 + 0.426770i
\(216\) −5.90001 + 18.1584i −0.401445 + 1.23552i
\(217\) 0 0
\(218\) −3.49518 + 2.53940i −0.236724 + 0.171990i
\(219\) −3.50570 −0.236893
\(220\) −7.17064 + 4.90574i −0.483445 + 0.330745i
\(221\) −3.98281 −0.267913
\(222\) −25.9350 + 18.8429i −1.74064 + 1.26465i
\(223\) −5.37562 16.5445i −0.359978 1.10790i −0.953066 0.302762i \(-0.902091\pi\)
0.593088 0.805138i \(-0.297909\pi\)
\(224\) 0 0
\(225\) −29.0620 21.1148i −1.93747 1.40765i
\(226\) −9.60581 6.97903i −0.638969 0.464238i
\(227\) 3.90334 12.0133i 0.259074 0.797348i −0.733926 0.679230i \(-0.762314\pi\)
0.993000 0.118118i \(-0.0376861\pi\)
\(228\) 1.08674 + 3.34464i 0.0719711 + 0.221504i
\(229\) 3.69997 2.68819i 0.244501 0.177640i −0.458785 0.888547i \(-0.651715\pi\)
0.703286 + 0.710907i \(0.251715\pi\)
\(230\) 3.10883 0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) −19.3006 + 14.0227i −1.26443 + 0.918659i −0.998966 0.0454624i \(-0.985524\pi\)
−0.265460 + 0.964122i \(0.585524\pi\)
\(234\) 3.66921 + 11.2927i 0.239864 + 0.738225i
\(235\) 8.08073 24.8699i 0.527129 1.62234i
\(236\) 2.02152 + 1.46872i 0.131590 + 0.0956054i
\(237\) 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 \(0.807725\pi\)
\(240\) −15.2638 + 11.0898i −0.985271 + 0.715841i
\(241\) −18.9464 −1.22045 −0.610224 0.792229i \(-0.708921\pi\)
−0.610224 + 0.792229i \(0.708921\pi\)
\(242\) −10.3098 + 6.63284i −0.662738 + 0.426375i
\(243\) −12.2322 −0.784696
\(244\) 0.660194 0.479659i 0.0422646 0.0307070i
\(245\) 0 0
\(246\) 2.09328 6.44244i 0.133462 0.410755i
\(247\) 2.70433 + 1.96481i 0.172072 + 0.125018i
\(248\) −1.96052 1.42440i −0.124493 0.0904495i
\(249\) 14.1961 43.6911i 0.899640 2.76881i
\(250\) −2.31438 7.12294i −0.146374 0.450494i
\(251\) −2.31938 + 1.68513i −0.146398 + 0.106364i −0.658573 0.752516i \(-0.728840\pi\)
0.512175 + 0.858881i \(0.328840\pi\)
\(252\) 0 0
\(253\) −2.67589 0.0757876i −0.168232 0.00476473i
\(254\) 21.6774 1.36016
\(255\) −15.4569 + 11.2301i −0.967950 + 0.703257i
\(256\) −4.71199 14.5020i −0.294500 0.906377i
\(257\) −6.92689 + 21.3188i −0.432087 + 1.32983i 0.463955 + 0.885859i \(0.346430\pi\)
−0.896042 + 0.443969i \(0.853570\pi\)
\(258\) −7.94003 5.76877i −0.494325 0.359148i
\(259\) 0 0
\(260\) 1.66728 5.13136i 0.103400 0.318234i
\(261\) 12.7459 + 39.2278i 0.788951 + 2.42814i
\(262\) 4.60985 3.34925i 0.284797 0.206917i
\(263\) 0.990706 0.0610895 0.0305448 0.999533i \(-0.490276\pi\)
0.0305448 + 0.999533i \(0.490276\pi\)
\(264\) 24.0529 16.4556i 1.48036 1.01277i
\(265\) −37.4032 −2.29766
\(266\) 0 0
\(267\) 3.92090 + 12.0673i 0.239955 + 0.738506i
\(268\) −0.562873 + 1.73234i −0.0343829 + 0.105820i
\(269\) −5.81713 4.22639i −0.354677 0.257688i 0.396152 0.918185i \(-0.370345\pi\)
−0.750828 + 0.660497i \(0.770345\pi\)
\(270\) 19.3563 + 14.0632i 1.17799 + 0.855858i
\(271\) 8.39423 25.8348i 0.509913 1.56935i −0.282438 0.959285i \(-0.591143\pi\)
0.792351 0.610065i \(-0.208857\pi\)
\(272\) 1.14107 + 3.51185i 0.0691874 + 0.212937i
\(273\) 0 0
\(274\) 10.1422 0.612714
\(275\) 6.49434 + 22.0977i 0.391624 + 1.33254i
\(276\) 1.74897 0.105275
\(277\) −16.9777 + 12.3350i −1.02009 + 0.741140i −0.966302 0.257412i \(-0.917130\pi\)
−0.0537900 + 0.998552i \(0.517130\pi\)
\(278\) 4.48277 + 13.7965i 0.268859 + 0.827462i
\(279\) −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 \(0.382624\pi\)
\(282\) −7.44939 + 22.9269i −0.443605 + 1.36527i
\(283\) 8.09369 + 24.9098i 0.481120 + 1.48074i 0.837523 + 0.546403i \(0.184003\pi\)
−0.356403 + 0.934332i \(0.615997\pi\)
\(284\) −1.95527 + 1.42058i −0.116024 + 0.0842961i
\(285\) 16.0353 0.949851
\(286\) 2.55660 7.17091i 0.151175 0.424025i
\(287\) 0 0
\(288\) −16.8199 + 12.2204i −0.991123 + 0.720093i
\(289\) −4.09778 12.6117i −0.241046 0.741863i
\(290\) −9.49056 + 29.2089i −0.557305 + 1.71521i
\(291\) 14.9596 + 10.8688i 0.876945 + 0.637138i
\(292\) −0.751959 0.546331i −0.0440051 0.0319716i
\(293\) 1.37941 4.24538i 0.0805858 0.248017i −0.902644 0.430388i \(-0.858377\pi\)
0.983230 + 0.182370i \(0.0583769\pi\)
\(294\) 0 0
\(295\) 9.21748 6.69689i 0.536663 0.389908i
\(296\) −30.9264 −1.79756
\(297\) −16.3179 12.5766i −0.946861 0.729769i
\(298\) −3.50667 −0.203136
\(299\) 1.34493 0.977145i 0.0777790 0.0565098i
\(300\) −4.65004 14.3114i −0.268470 0.826267i
\(301\) 0 0
\(302\) −2.58492 1.87805i −0.148745 0.108070i
\(303\) −35.7215 25.9532i −2.05214 1.49097i
\(304\) 0.957688 2.94746i 0.0549271 0.169048i
\(305\) −1.14982 3.53879i −0.0658387 0.202631i
\(306\) 9.01881 6.55255i 0.515571 0.374584i
\(307\) −12.8841 −0.735334 −0.367667 0.929957i \(-0.619843\pi\)
−0.367667 + 0.929957i \(0.619843\pi\)
\(308\) 0 0
\(309\) −25.4667 −1.44875
\(310\) −2.45678 + 1.78495i −0.139536 + 0.101379i
\(311\) −8.28779 25.5072i −0.469957 1.44638i −0.852639 0.522500i \(-0.824999\pi\)
0.382682 0.923880i \(-0.375001\pi\)
\(312\) −5.59266 + 17.2124i −0.316622 + 0.974463i
\(313\) 2.90331 + 2.10938i 0.164105 + 0.119229i 0.666807 0.745231i \(-0.267661\pi\)
−0.502702 + 0.864460i \(0.667661\pi\)
\(314\) −19.3754 14.0771i −1.09342 0.794415i
\(315\) 0 0
\(316\) 2.22087 + 6.83513i 0.124934 + 0.384506i
\(317\) 13.6870 9.94418i 0.768738 0.558521i −0.132840 0.991138i \(-0.542410\pi\)
0.901578 + 0.432617i \(0.142410\pi\)
\(318\) 34.4809 1.93359
\(319\) 8.88095 24.9099i 0.497238 1.39469i
\(320\) −28.6798 −1.60325
\(321\) −8.12311 + 5.90178i −0.453388 + 0.329405i
\(322\) 0 0
\(323\) 0.969808 2.98476i 0.0539616 0.166077i
\(324\) 1.37343 + 0.997859i 0.0763019 + 0.0554366i
\(325\) −11.5715 8.40721i −0.641873 0.466348i
\(326\) −2.83172 + 8.71515i −0.156835 + 0.482687i
\(327\) 3.42463 + 10.5399i 0.189383 + 0.582860i
\(328\) 5.28693 3.84118i 0.291922 0.212094i
\(329\) 0 0
\(330\) −10.2975 35.0384i −0.566860 1.92880i
\(331\) −1.23826 −0.0680610 −0.0340305 0.999421i \(-0.510834\pi\)
−0.0340305 + 0.999421i \(0.510834\pi\)
\(332\) 9.85385 7.15924i 0.540800 0.392914i
\(333\) 16.0837 + 49.5005i 0.881381 + 2.71261i
\(334\) 7.47620 23.0094i 0.409079 1.25902i
\(335\) 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 \(0.911636\pi\)
\(338\) −3.01610 9.28261i −0.164054 0.504907i
\(339\) −24.6407 + 17.9025i −1.33830 + 0.972332i
\(340\) −5.06556 −0.274719
\(341\) 2.15816 1.47649i 0.116871 0.0799563i
\(342\) −9.35630 −0.505931
\(343\) 0 0
\(344\) −2.92583 9.00478i −0.157750 0.485505i
\(345\) 2.46433 7.58443i 0.132675 0.408332i
\(346\) −7.25412 5.27043i −0.389984 0.283340i
\(347\) −22.0618 16.0288i −1.18434 0.860472i −0.191684 0.981457i \(-0.561395\pi\)
−0.992654 + 0.120985i \(0.961395\pi\)
\(348\) −5.33920 + 16.4324i −0.286211 + 0.880868i
\(349\) −2.46730 7.59356i −0.132071 0.406474i 0.863052 0.505116i \(-0.168550\pi\)
−0.995123 + 0.0986418i \(0.968550\pi\)
\(350\) 0 0
\(351\) 12.7941 0.682897
\(352\) 13.3248 + 0.377388i 0.710212 + 0.0201149i
\(353\) −5.93472 −0.315873 −0.157937 0.987449i \(-0.550484\pi\)
−0.157937 + 0.987449i \(0.550484\pi\)
\(354\) −8.49733 + 6.17367i −0.451628 + 0.328127i
\(355\) 3.40538 + 10.4807i 0.180739 + 0.556256i
\(356\) −1.03956 + 3.19942i −0.0550964 + 0.169569i
\(357\) 0 0
\(358\) 3.26469 + 2.37194i 0.172544 + 0.125361i
\(359\) 8.78235 27.0293i 0.463515 1.42655i −0.397326 0.917677i \(-0.630062\pi\)
0.860841 0.508874i \(-0.169938\pi\)
\(360\) 16.9805 + 52.2606i 0.894951 + 2.75438i
\(361\) 13.2404 9.61969i 0.696862 0.506300i
\(362\) −17.6285 −0.926535
\(363\) 8.00931 + 30.4099i 0.420380 + 1.59611i
\(364\) 0 0
\(365\) −3.42870 + 2.49109i −0.179466 + 0.130390i
\(366\) 1.05999 + 3.26231i 0.0554065 + 0.170524i
\(367\) 9.39456 28.9135i 0.490392 1.50927i −0.333625 0.942706i \(-0.608272\pi\)
0.824017 0.566565i \(-0.191728\pi\)
\(368\) −1.24692 0.905939i −0.0650001 0.0472253i
\(369\) −8.89769 6.46455i −0.463195 0.336531i
\(370\) −11.9759 + 36.8580i −0.622596 + 1.91615i
\(371\) 0 0
\(372\) −1.38213 + 1.00418i −0.0716603 + 0.0520643i
\(373\) 14.4226 0.746772 0.373386 0.927676i \(-0.378197\pi\)
0.373386 + 0.927676i \(0.378197\pi\)
\(374\) −7.14471 0.202355i −0.369444 0.0104635i
\(375\) −19.2120 −0.992103
\(376\) −18.8147 + 13.6697i −0.970296 + 0.704961i
\(377\) 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 \(0.504811\pi\)
\(380\) 3.43952 + 2.49896i 0.176444 + 0.128194i
\(381\) 17.1834 52.8850i 0.880331 2.70938i
\(382\) 0.147771 + 0.454792i 0.00756061 + 0.0232692i
\(383\) 27.2465 19.7957i 1.39223 1.01152i 0.396615 0.917985i \(-0.370185\pi\)
0.995616 0.0935305i \(-0.0298153\pi\)
\(384\) 3.45887 0.176510
\(385\) 0 0
\(386\) −16.9118 −0.860790
\(387\) −12.8913 + 9.36610i −0.655303 + 0.476106i
\(388\) 1.51498 + 4.66262i 0.0769112 + 0.236708i
\(389\) 0.750241 2.30900i 0.0380387 0.117071i −0.930234 0.366967i \(-0.880396\pi\)
0.968273 + 0.249896i \(0.0803963\pi\)
\(390\) 18.3480 + 13.3306i 0.929087 + 0.675021i
\(391\) −1.26270 0.917404i −0.0638574 0.0463951i
\(392\) 0 0
\(393\) −4.51680 13.9013i −0.227842 0.701227i
\(394\) 18.7611 13.6308i 0.945173 0.686708i
\(395\) 32.7699 1.64883
\(396\) −3.66669 12.4763i −0.184258 0.626956i
\(397\) 5.89696 0.295960 0.147980 0.988990i \(-0.452723\pi\)
0.147980 + 0.988990i \(0.452723\pi\)
\(398\) 7.61481 5.53248i 0.381696 0.277318i
\(399\) 0 0
\(400\) −4.09784 + 12.6119i −0.204892 + 0.630593i
\(401\) −9.09302 6.60646i −0.454084 0.329911i 0.337122 0.941461i \(-0.390546\pi\)
−0.791206 + 0.611550i \(0.790546\pi\)
\(402\) −6.19427 4.50040i −0.308942 0.224460i
\(403\) −0.501804 + 1.54439i −0.0249966 + 0.0769317i
\(404\) −3.61756 11.1337i −0.179981 0.553923i
\(405\) 6.26243 4.54992i 0.311183 0.226087i
\(406\) 0 0
\(407\) 11.2066 31.4331i 0.555492 1.55808i
\(408\) 16.9917 0.841216
\(409\) 23.7320 17.2423i 1.17347 0.852578i 0.182052 0.983289i \(-0.441726\pi\)
0.991421 + 0.130711i \(0.0417260\pi\)
\(410\) −2.53060 7.78839i −0.124977 0.384641i
\(411\) 8.03961 24.7434i 0.396565 1.22050i
\(412\) −5.46251 3.96875i −0.269119 0.195526i
\(413\) 0 0
\(414\) −1.43789 + 4.42536i −0.0706683 + 0.217495i
\(415\) −17.1619 52.8189i −0.842445 2.59278i
\(416\) −6.69713 + 4.86575i −0.328354 + 0.238563i
\(417\) 37.2120 1.82228
\(418\) 4.75144 + 3.66205i 0.232400 + 0.179117i
\(419\) 20.2858 0.991027 0.495514 0.868600i \(-0.334980\pi\)
0.495514 + 0.868600i \(0.334980\pi\)
\(420\) 0 0
\(421\) −0.945600 2.91026i −0.0460857 0.141837i 0.925366 0.379075i \(-0.123758\pi\)
−0.971452 + 0.237238i \(0.923758\pi\)
\(422\) −3.39542 + 10.4500i −0.165287 + 0.508700i
\(423\) 31.6644 + 23.0055i 1.53958 + 1.11857i
\(424\) 26.9116 + 19.5524i 1.30694 + 0.949548i
\(425\) −4.14971 + 12.7715i −0.201290 + 0.619508i
\(426\) −3.13932 9.66183i −0.152100 0.468117i
\(427\) 0 0
\(428\) −2.66211 −0.128678
\(429\) −15.4679 11.9215i −0.746796 0.575574i
\(430\) −11.8648 −0.572173
\(431\) −6.10158 + 4.43306i −0.293903 + 0.213533i −0.724959 0.688792i \(-0.758141\pi\)
0.431056 + 0.902325i \(0.358141\pi\)
\(432\) −3.66548 11.2812i −0.176355 0.542766i
\(433\) 9.93848 30.5875i 0.477613 1.46994i −0.364788 0.931091i \(-0.618859\pi\)
0.842401 0.538851i \(-0.181141\pi\)
\(434\) 0 0
\(435\) 63.7362 + 46.3071i 3.05592 + 2.22025i
\(436\) −0.907980 + 2.79447i −0.0434844 + 0.133831i
\(437\) 0.404796 + 1.24584i 0.0193640 + 0.0595964i
\(438\) 3.16082 2.29647i 0.151030 0.109729i
\(439\) 4.66725 0.222756 0.111378 0.993778i \(-0.464474\pi\)
0.111378 + 0.993778i \(0.464474\pi\)
\(440\) 11.8315 33.1858i 0.564045 1.58207i
\(441\) 0 0
\(442\) 3.59099 2.60901i 0.170806 0.124098i
\(443\) 5.33893 + 16.4315i 0.253660 + 0.780686i 0.994091 + 0.108553i \(0.0346218\pi\)
−0.740430 + 0.672133i \(0.765378\pi\)
\(444\) −6.73739 + 20.7356i −0.319743 + 0.984066i
\(445\) 12.4096 + 9.01611i 0.588272 + 0.427404i
\(446\) 15.6845 + 11.3955i 0.742684 + 0.539591i
\(447\) −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 \(0.170742\pi\)
\(450\) 40.0346 1.88725
\(451\) 1.98832 + 6.76546i 0.0936264 + 0.318573i
\(452\) −8.07529 −0.379829
\(453\) −6.63080 + 4.81756i −0.311542 + 0.226349i
\(454\) 4.35015 + 13.3884i 0.204162 + 0.628347i
\(455\) 0 0
\(456\) −11.5374 8.38241i −0.540288 0.392542i
\(457\) 17.5536 + 12.7534i 0.821121 + 0.596580i 0.917033 0.398810i \(-0.130577\pi\)
−0.0959121 + 0.995390i \(0.530577\pi\)
\(458\) −1.57503 + 4.84746i −0.0735965 + 0.226507i
\(459\) −3.71187 11.4240i −0.173255 0.533224i
\(460\) 1.71055 1.24279i 0.0797549 0.0579453i
\(461\) 6.07778 0.283070 0.141535 0.989933i \(-0.454796\pi\)
0.141535 + 0.989933i \(0.454796\pi\)
\(462\) 0 0
\(463\) −5.14719 −0.239210 −0.119605 0.992822i \(-0.538163\pi\)
−0.119605 + 0.992822i \(0.538163\pi\)
\(464\) 12.3183 8.94975i 0.571862 0.415482i
\(465\) 2.40719 + 7.40856i 0.111631 + 0.343564i
\(466\) 8.21605 25.2864i 0.380601 1.17137i
\(467\) −3.17076 2.30369i −0.146725 0.106602i 0.512001 0.858985i \(-0.328904\pi\)
−0.658726 + 0.752383i \(0.728904\pi\)
\(468\) 6.53325 + 4.74669i 0.302000 + 0.219416i
\(469\) 0 0
\(470\) 9.00570 + 27.7167i 0.415402 + 1.27848i
\(471\) −49.7016 + 36.1103i −2.29013 + 1.66388i
\(472\) −10.1327 −0.466397
\(473\) 10.2125 + 0.289243i 0.469572 + 0.0132994i
\(474\) −30.2096 −1.38757
\(475\) 9.11811 6.62469i 0.418368 0.303962i
\(476\) 0 0
\(477\) 17.2996 53.2428i 0.792096 2.43782i
\(478\) −7.96867 5.78958i −0.364478 0.264809i
\(479\) −12.2266 8.88315i −0.558648 0.405882i 0.272316 0.962208i \(-0.412210\pi\)
−0.830964 + 0.556326i \(0.812210\pi\)
\(480\) −12.2713 + 37.7671i −0.560104 + 1.72382i
\(481\) 6.40399 + 19.7095i 0.291997 + 0.898674i
\(482\) 17.0825 12.4112i 0.778088 0.565314i
\(483\) 0 0
\(484\) −3.02114 + 7.77100i −0.137324 + 0.353227i
\(485\) 22.3541 1.01505
\(486\) 11.0288 8.01291i 0.500278 0.363473i
\(487\) 7.74916 + 23.8495i 0.351148 + 1.08072i 0.958210 + 0.286067i \(0.0923480\pi\)
−0.607062 + 0.794655i \(0.707652\pi\)
\(488\) −1.02259 + 3.14722i −0.0462907 + 0.142468i
\(489\) 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 \(-0.217372\pi\)
\(492\) −1.42367 4.38159i −0.0641838 0.197538i
\(493\) 12.4742 9.06302i 0.561809 0.408178i
\(494\) −3.72536 −0.167612
\(495\) −59.2700 1.67867i −2.66399 0.0754504i
\(496\) 1.50554 0.0676006
\(497\) 0 0
\(498\) 15.8211 + 48.6922i 0.708959 + 2.18195i
\(499\) −9.83087 + 30.2563i −0.440090 + 1.35446i 0.447689 + 0.894189i \(0.352247\pi\)
−0.887780 + 0.460269i \(0.847753\pi\)
\(500\) −4.12090 2.99401i −0.184292 0.133896i
\(501\) −50.2083 36.4785i −2.24314 1.62974i
\(502\) 0.987334 3.03870i 0.0440669 0.135624i
\(503\) 5.93493 + 18.2658i 0.264626 + 0.814434i 0.991779 + 0.127959i \(0.0408426\pi\)
−0.727154 + 0.686474i \(0.759157\pi\)
\(504\) 0 0
\(505\) −53.3788 −2.37532
\(506\) 2.46229 1.68456i 0.109462 0.0748877i
\(507\) −25.0370 −1.11193
\(508\) 11.9274 8.66577i 0.529193 0.384481i
\(509\) −0.777328 2.39237i −0.0344545 0.106040i 0.932350 0.361556i \(-0.117754\pi\)
−0.966805 + 0.255516i \(0.917754\pi\)
\(510\) 6.57984 20.2506i 0.291360 0.896714i
\(511\) 0 0
\(512\) 15.7059 + 11.4110i 0.694109 + 0.504300i
\(513\) −3.11533 + 9.58801i −0.137545 + 0.423321i
\(514\) −7.71978 23.7590i −0.340505 1.04797i
\(515\) −24.9073 + 18.0962i −1.09755 + 0.797416i
\(516\) −6.67492 −0.293847
\(517\) −7.07588 24.0764i −0.311197 1.05888i
\(518\) 0 0
\(519\) −18.6082 + 13.5196i −0.816809 + 0.593447i
\(520\) 6.76107 + 20.8084i 0.296493 + 0.912510i
\(521\) −4.60335 + 14.1677i −0.201677 + 0.620697i 0.798157 + 0.602450i \(0.205809\pi\)
−0.999834 + 0.0182471i \(0.994191\pi\)
\(522\) −37.1888 27.0193i −1.62771 1.18260i
\(523\) −8.01333 5.82203i −0.350399 0.254579i 0.398638 0.917109i \(-0.369483\pi\)
−0.749036 + 0.662529i \(0.769483\pi\)
\(524\) 1.19755 3.68567i 0.0523151 0.161009i
\(525\) 0 0
\(526\) −0.893242 + 0.648979i −0.0389472 + 0.0282968i
\(527\) 1.52459 0.0664122
\(528\) −6.08025 + 17.0543i −0.264609 + 0.742193i
\(529\) −22.3485 −0.971675
\(530\) 33.7236 24.5016i 1.46486 1.06428i
\(531\) 5.26966 + 16.2183i 0.228684 + 0.703816i
\(532\) 0 0
\(533\) −3.54276 2.57397i −0.153454 0.111491i
\(534\) −11.4401 8.31169i −0.495060 0.359682i
\(535\) −3.75097 + 11.5443i −0.162169 + 0.499104i
\(536\) −2.28253 7.02491i −0.0985904 0.303430i
\(537\) 8.37456 6.08447i 0.361389 0.262564i
\(538\) 8.01342 0.345483
\(539\) 0 0
\(540\) 16.2722 0.700245
\(541\) 17.8052 12.9362i 0.765503 0.556171i −0.135090 0.990833i \(-0.543132\pi\)
0.900593 + 0.434663i \(0.143132\pi\)
\(542\) 9.35508 + 28.7920i 0.401835 + 1.23672i
\(543\) −13.9739 + 43.0073i −0.599678 + 1.84562i
\(544\) 6.28768 + 4.56826i 0.269582 + 0.195863i
\(545\) 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 \(0.974612\pi\)
\(548\) 5.58049 4.05446i 0.238387 0.173198i
\(549\) 5.56922 0.237689
\(550\) −20.3309 15.6695i −0.866912 0.668150i
\(551\) −12.9410 −0.551303
\(552\) −5.73781 + 4.16876i −0.244218 + 0.177434i
\(553\) 0 0
\(554\) 7.22721 22.2431i 0.307055 0.945018i
\(555\) 80.4270 + 58.4337i 3.41394 + 2.48037i
\(556\) 7.98184 + 5.79915i 0.338506 + 0.245939i
\(557\) 10.3869 31.9675i 0.440105 1.35451i −0.447658 0.894205i \(-0.647742\pi\)
0.887763 0.460300i \(-0.152258\pi\)
\(558\) −1.40455 4.32275i −0.0594592 0.182997i
\(559\) −5.13290 + 3.72927i −0.217098 + 0.157731i
\(560\) 0 0
\(561\) −6.15720 + 17.2701i −0.259957 + 0.729145i
\(562\) −31.3811 −1.32373
\(563\) −1.66130 + 1.20701i −0.0700155 + 0.0508693i −0.622242 0.782825i \(-0.713778\pi\)
0.552227 + 0.833694i \(0.313778\pi\)
\(564\) 5.06643 + 15.5929i 0.213335 + 0.656578i
\(565\) −11.3782 + 35.0186i −0.478686 + 1.47324i
\(566\) −23.6151 17.1573i −0.992615 0.721177i
\(567\) 0 0
\(568\) 3.02857 9.32098i 0.127076 0.391099i
\(569\) 1.01177 + 3.11391i 0.0424156 + 0.130542i 0.970022 0.243017i \(-0.0781372\pi\)
−0.927606 + 0.373559i \(0.878137\pi\)
\(570\) −14.4578 + 10.5042i −0.605571 + 0.439973i
\(571\) −43.8897 −1.83673 −0.918363 0.395738i \(-0.870489\pi\)
−0.918363 + 0.395738i \(0.870489\pi\)
\(572\) −1.45995 4.96763i −0.0610437 0.207707i
\(573\) 1.22666 0.0512446
\(574\) 0 0
\(575\) −1.73208 5.33080i −0.0722328 0.222310i
\(576\) 13.2649 40.8251i 0.552704 1.70105i
\(577\) −35.5081 25.7981i −1.47822 1.07399i −0.978125 0.208020i \(-0.933298\pi\)
−0.500096 0.865970i \(-0.666702\pi\)
\(578\) 11.9561 + 8.68664i 0.497310 + 0.361317i
\(579\) −13.4058 + 41.2588i −0.557126 + 1.71466i
\(580\) 6.45466 + 19.8654i 0.268015 + 0.824866i
\(581\) 0 0
\(582\) −20.6076 −0.854214
\(583\) −29.6245 + 20.2674i −1.22692 + 0.839389i
\(584\) 3.76915 0.155969
\(585\) 29.7896 21.6434i 1.23165 0.894844i
\(586\) 1.53730 + 4.73133i 0.0635054 + 0.195449i
\(587\) −0.862670 + 2.65503i −0.0356062 + 0.109585i −0.967280 0.253711i \(-0.918349\pi\)
0.931674 + 0.363296i \(0.118349\pi\)
\(588\) 0 0
\(589\) −1.03520 0.752114i −0.0426545 0.0309903i
\(590\) −3.92378 + 12.0761i −0.161539 + 0.497167i
\(591\) −18.3825 56.5754i −0.756153 2.32720i
\(592\) 15.5441 11.2935i 0.638859 0.464158i
\(593\) −23.2526 −0.954871 −0.477435 0.878667i \(-0.658434\pi\)
−0.477435 + 0.878667i \(0.658434\pi\)
\(594\) 22.9511 + 0.650030i 0.941696 + 0.0266710i
\(595\) 0 0
\(596\) −1.92945 + 1.40183i −0.0790334 + 0.0574211i
\(597\) −7.46111 22.9629i −0.305363 0.939810i
\(598\) −0.572519 + 1.76203i −0.0234120 + 0.0720549i
\(599\) −8.46187 6.14791i −0.345743 0.251197i 0.401338 0.915930i \(-0.368545\pi\)
−0.747081 + 0.664733i \(0.768545\pi\)
\(600\) 49.3673 + 35.8674i 2.01541 + 1.46428i
\(601\) −6.89406 + 21.2177i −0.281215 + 0.865489i 0.706293 + 0.707919i \(0.250366\pi\)
−0.987508 + 0.157570i \(0.949634\pi\)
\(602\) 0 0
\(603\) −10.0569 + 7.30679i −0.409550 + 0.297556i
\(604\) −2.17306 −0.0884204
\(605\) 29.4422 + 24.0507i 1.19700 + 0.977800i
\(606\) 49.2083 1.99895
\(607\) 15.3619 11.1611i 0.623522 0.453015i −0.230628 0.973042i \(-0.574078\pi\)
0.854150 + 0.520027i \(0.174078\pi\)
\(608\) −2.01571 6.20370i −0.0817477 0.251593i
\(609\) 0 0
\(610\) 3.35485 + 2.43744i 0.135834 + 0.0986892i
\(611\) 12.6077 + 9.16004i 0.510053 + 0.370576i
\(612\) 2.34291 7.21074i 0.0947066 0.291477i
\(613\) 6.23030 + 19.1749i 0.251639 + 0.774467i 0.994473 + 0.104991i \(0.0334813\pi\)
−0.742834 + 0.669476i \(0.766519\pi\)
\(614\) 11.6166 8.43995i 0.468807 0.340608i
\(615\) −21.0068 −0.847077
\(616\) 0 0
\(617\) 7.03919 0.283387 0.141694 0.989911i \(-0.454745\pi\)
0.141694 + 0.989911i \(0.454745\pi\)
\(618\) 22.9614 16.6824i 0.923641 0.671064i
\(619\) 9.60520 + 29.5618i 0.386066 + 1.18819i 0.935704 + 0.352785i \(0.114765\pi\)
−0.549639 + 0.835402i \(0.685235\pi\)
\(620\) −0.638222 + 1.96425i −0.0256316 + 0.0788860i
\(621\) 4.05619 + 2.94700i 0.162769 + 0.118259i
\(622\) 24.1814 + 17.5688i 0.969585 + 0.704445i
\(623\) 0 0
\(624\) −3.47453 10.6935i −0.139093 0.428083i
\(625\) 9.30098 6.75756i 0.372039 0.270302i
\(626\) −3.99947 −0.159851
\(627\) 12.7005 8.68894i 0.507208 0.347003i
\(628\) −16.2883 −0.649973
\(629\) 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 \(-0.0440812\pi\)
\(632\) −23.5779 17.1303i −0.937879 0.681409i
\(633\) 22.8028 + 16.5672i 0.906331 + 0.658488i
\(634\) −5.82639 + 17.9318i −0.231396 + 0.712163i
\(635\) −20.7733 63.9337i −0.824364 2.53713i
\(636\) 18.9722 13.7841i 0.752298 0.546576i
\(637\) 0 0
\(638\) 8.31039 + 28.2770i 0.329012 + 1.11950i
\(639\) −16.4941 −0.652496
\(640\) 3.38290 2.45782i 0.133721 0.0971538i
\(641\) −4.10713 12.6404i −0.162222 0.499267i 0.836599 0.547816i \(-0.184540\pi\)
−0.998821 + 0.0485485i \(0.984540\pi\)
\(642\) 3.45791 10.6424i 0.136473 0.420020i
\(643\) 11.8848 + 8.63480i 0.468690 + 0.340523i 0.796930 0.604071i \(-0.206456\pi\)
−0.328241 + 0.944594i \(0.606456\pi\)
\(644\) 0 0
\(645\) −9.40510 + 28.9459i −0.370325 + 1.13974i
\(646\) 1.08082 + 3.32642i 0.0425242 + 0.130876i
\(647\) −4.97160 + 3.61208i −0.195454 + 0.142005i −0.681208 0.732090i \(-0.738545\pi\)
0.485754 + 0.874095i \(0.338545\pi\)
\(648\) −6.88426 −0.270439
\(649\) 3.67174 10.2988i 0.144128 0.404261i
\(650\) 15.9404 0.625236
\(651\) 0 0
\(652\) 1.92589 + 5.92729i 0.0754238 + 0.232131i
\(653\) −12.5674 + 38.6786i −0.491802 + 1.51361i 0.330079 + 0.943953i \(0.392924\pi\)
−0.821882 + 0.569658i \(0.807076\pi\)
\(654\) −9.99209 7.25968i −0.390722 0.283876i
\(655\) −14.2956 10.3864i −0.558576 0.405829i
\(656\) −1.25460 + 3.86127i −0.0489841 + 0.150757i
\(657\) −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 \(0.385921\pi\)
\(660\) −19.6729 15.1624i −0.765767 0.590196i
\(661\) 17.1420 0.666745 0.333373 0.942795i \(-0.391813\pi\)
0.333373 + 0.942795i \(0.391813\pi\)
\(662\) 1.11644 0.811145i 0.0433919 0.0315260i
\(663\) −3.51851 10.8289i −0.136647 0.420558i
\(664\) −15.2629 + 46.9744i −0.592316 + 1.82296i
\(665\) 0 0
\(666\) −46.9276 34.0949i −1.81841 1.32115i
\(667\) −1.98878 + 6.12085i −0.0770060 + 0.237000i
\(668\) −5.08466 15.6490i −0.196732 0.605478i
\(669\) 40.2338 29.2315i 1.55553 1.13016i
\(670\) −9.25613 −0.357596
\(671\) −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 \(0.152491\pi\)
\(674\) −7.05329 21.7078i −0.271683 0.836153i
\(675\) 13.3302 41.0261i 0.513079 1.57910i
\(676\) −5.37035 3.90179i −0.206552 0.150069i
\(677\) −22.3050 16.2056i −0.857252 0.622830i 0.0698841 0.997555i \(-0.477737\pi\)
−0.927136 + 0.374725i \(0.877737\pi\)
\(678\) 10.4893 32.2826i 0.402838 1.23981i
\(679\) 0 0
\(680\) 16.6185 12.0741i 0.637291 0.463019i
\(681\) 36.1111 1.38378
\(682\) −0.978646 + 2.74497i −0.0374743 + 0.105110i
\(683\) 21.9351 0.839322 0.419661 0.907681i \(-0.362149\pi\)
0.419661 + 0.907681i \(0.362149\pi\)
\(684\) −5.14806 + 3.74028i −0.196841 + 0.143013i
\(685\) −9.71923 29.9127i −0.371353 1.14291i
\(686\) 0 0
\(687\) 10.5775 + 7.68503i 0.403558 + 0.293202i
\(688\) 4.75885 + 3.45751i 0.181430 + 0.131816i
\(689\) 6.88814 21.1995i 0.262417 0.807637i
\(690\) 2.74641 + 8.45259i 0.104554 + 0.321785i
\(691\) −20.7647 + 15.0865i −0.789928 + 0.573916i −0.907942 0.419096i \(-0.862347\pi\)
0.118014 + 0.993012i \(0.462347\pi\)
\(692\) −6.09830 −0.231823
\(693\) 0 0
\(694\) 30.3913 1.15364
\(695\) 36.3947 26.4423i 1.38053 1.00301i
\(696\) −21.6513 66.6357i −0.820689 2.52582i
\(697\) −1.27048 + 3.91014i −0.0481229 + 0.148107i
\(698\) 7.19886 + 5.23028i 0.272481 + 0.197969i
\(699\) −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 \(-0.213049\pi\)
\(702\) −11.5354 + 8.38097i −0.435376 + 0.316319i
\(703\) −16.3298 −0.615892
\(704\) −22.7153 + 15.5405i −0.856114 + 0.585704i
\(705\) 74.7575 2.81553
\(706\) 5.35087 3.88764i 0.201383 0.146313i
\(707\) 0 0
\(708\) −2.20744 + 6.79380i −0.0829607 + 0.255327i
\(709\) −19.1430 13.9082i −0.718930 0.522334i 0.167112 0.985938i \(-0.446556\pi\)
−0.886042 + 0.463604i \(0.846556\pi\)
\(710\) −9.93591 7.21886i −0.372888 0.270919i
\(711\) −15.1567 + 46.6474i −0.568419 + 1.74941i
\(712\) −4.21556 12.9741i −0.157985 0.486227i
\(713\) −0.514827 + 0.374044i −0.0192804 + 0.0140081i
\(714\) 0 0
\(715\) −23.5993 0.668389i −0.882565 0.0249963i
\(716\) 2.74452 0.102568
\(717\) −20.4411 + 14.8514i −0.763389 + 0.554634i
\(718\) 9.78763 + 30.1232i 0.365271 + 1.12419i
\(719\) −3.43696 + 10.5779i −0.128177 + 0.394488i −0.994467 0.105054i \(-0.966498\pi\)
0.866289 + 0.499542i \(0.166498\pi\)
\(720\) −27.6187 20.0662i −1.02929 0.747823i
\(721\) 0 0
\(722\) −5.63627 + 17.3467i −0.209760 + 0.645576i
\(723\) −16.7377 51.5135i −0.622483 1.91581i
\(724\) −9.69964 + 7.04720i −0.360484 + 0.261907i
\(725\) 55.3730 2.05650
\(726\) −27.1419 22.1716i −1.00733 0.822867i
\(727\) −42.4803 −1.57551 −0.787753 0.615991i \(-0.788756\pi\)
−0.787753 + 0.615991i \(0.788756\pi\)
\(728\) 0 0
\(729\) −12.8826 39.6485i −0.477133 1.46846i
\(730\) 1.45956 4.49205i 0.0540206 0.166258i
\(731\) 4.81908 + 3.50127i 0.178240 + 0.129499i
\(732\) 1.88738 + 1.37126i 0.0697594 + 0.0506832i
\(733\) −6.85660 + 21.1025i −0.253254 + 0.779437i 0.740914 + 0.671600i \(0.234393\pi\)
−0.994169 + 0.107837i \(0.965607\pi\)
\(734\) 10.4699 + 32.2231i 0.386452 + 1.18938i
\(735\) 0 0
\(736\) −3.24402 −0.119576
\(737\) 7.96712 + 0.225648i 0.293473 + 0.00831184i
\(738\) 12.2571 0.451189
\(739\) −23.8240 + 17.3092i −0.876381 + 0.636728i −0.932292 0.361708i \(-0.882194\pi\)
0.0559106 + 0.998436i \(0.482194\pi\)
\(740\) 8.14496 + 25.0676i 0.299415 + 0.921504i
\(741\) −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 \(0.800365\pi\)
\(744\) 2.14083 6.58879i 0.0784866 0.241557i
\(745\) 3.36042 + 10.3423i 0.123116 + 0.378913i
\(746\) −13.0037 + 9.44774i −0.476099 + 0.345906i
\(747\) 83.1244 3.04136
\(748\) −4.01208 + 2.74484i −0.146696 + 0.100361i
\(749\) 0 0
\(750\) 17.3220 12.5851i 0.632508 0.459544i
\(751\) −0.479429 1.47553i −0.0174946 0.0538429i 0.941928 0.335815i \(-0.109012\pi\)
−0.959423 + 0.281972i \(0.909012\pi\)
\(752\) 4.46479 13.7412i 0.162814 0.501090i
\(753\) −6.63069 4.81748i −0.241636 0.175559i
\(754\) −14.8074 10.7582i −0.539252 0.391789i
\(755\) −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 \(0.373221\pi\)
\(758\) −24.9721 −0.907027
\(759\) −2.15789 7.34243i −0.0783264 0.266513i
\(760\) −17.2404 −0.625375
\(761\) −7.30895 + 5.31026i −0.264949 + 0.192497i −0.712326 0.701849i \(-0.752358\pi\)
0.447377 + 0.894346i \(0.352358\pi\)
\(762\) 19.1503 + 58.9386i 0.693742 + 2.13512i
\(763\) 0 0
\(764\) 0.263115 + 0.191164i 0.00951916 + 0.00691608i
\(765\) −27.9683 20.3201i −1.01120 0.734677i
\(766\) −11.5985 + 35.6966i −0.419072 + 1.28977i
\(767\) 2.09820 + 6.45761i 0.0757617 + 0.233171i
\(768\) 35.2668 25.6229i 1.27258 0.924585i
\(769\) 16.1383 0.581963 0.290981 0.956729i \(-0.406018\pi\)
0.290981 + 0.956729i \(0.406018\pi\)
\(770\) 0 0
\(771\) −64.0829 −2.30789
\(772\) −9.30529 + 6.76069i −0.334905 + 0.243323i
\(773\) 5.69007 + 17.5122i 0.204657 + 0.629871i 0.999727 + 0.0233530i \(0.00743416\pi\)
−0.795070 + 0.606518i \(0.792566\pi\)
\(774\) 5.48769 16.8894i 0.197251 0.607076i