Properties

Label 847.2.f.v.148.2
Level 847
Weight 2
Character 847.148
Analytic conductor 6.763
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 847.f (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.76332905120\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 77)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 148.2
Root \(0.901622 - 0.655067i\)
Character \(\chi\) = 847.148
Dual form 847.2.f.v.372.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.344389 - 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(0.984546 - 3.03012i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.48664 - 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} +O(q^{10})\) \(q+(-0.344389 - 1.05992i) q^{2} +(2.31283 + 1.68037i) q^{3} +(0.613206 - 0.445520i) q^{4} +(1.06799 - 3.28693i) q^{5} +(0.984546 - 3.03012i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-2.48664 - 1.80665i) q^{8} +(1.59850 + 4.91966i) q^{9} -3.85168 q^{10} +2.16688 q^{12} +(0.636468 + 1.95885i) q^{13} +(-0.901622 - 0.655067i) q^{14} +(7.99333 - 5.80749i) q^{15} +(-0.590087 + 1.81610i) q^{16} +(-0.597555 + 1.83909i) q^{17} +(4.66395 - 3.38856i) q^{18} +(1.31300 + 0.953952i) q^{19} +(-0.809496 - 2.49137i) q^{20} +2.85882 q^{21} -0.807136 q^{23} +(-2.71534 - 8.35696i) q^{24} +(-5.61820 - 4.08186i) q^{25} +(1.85703 - 1.34921i) q^{26} +(-1.91954 + 5.90773i) q^{27} +(0.234224 - 0.720867i) q^{28} +(6.45084 - 4.68681i) q^{29} +(-8.90830 - 6.47226i) q^{30} +(0.243635 + 0.749832i) q^{31} -4.01918 q^{32} +2.15508 q^{34} +(-1.06799 - 3.28693i) q^{35} +(3.17202 + 2.30461i) q^{36} +(-8.14014 + 5.91416i) q^{37} +(0.558930 - 1.72021i) q^{38} +(-1.81955 + 5.59998i) q^{39} +(-8.59403 + 6.24393i) q^{40} +(-1.72008 - 1.24971i) q^{41} +(-0.984546 - 3.03012i) q^{42} -3.08043 q^{43} +17.8777 q^{45} +(0.277969 + 0.855500i) q^{46} +(-6.12128 - 4.44737i) q^{47} +(-4.41650 + 3.20877i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-2.39160 + 7.36059i) q^{50} +(-4.47239 + 3.24938i) q^{51} +(1.26299 + 0.917617i) q^{52} +(3.34432 + 10.2928i) q^{53} +6.92280 q^{54} -3.07366 q^{56} +(1.43376 + 4.41266i) q^{57} +(-7.18925 - 5.22329i) q^{58} +(2.66704 - 1.93771i) q^{59} +(2.31420 - 7.12238i) q^{60} +(0.332696 - 1.02393i) q^{61} +(0.710857 - 0.516468i) q^{62} +(4.18492 + 3.04052i) q^{63} +(2.56433 + 7.89221i) q^{64} +7.11832 q^{65} +2.40314 q^{67} +(0.452925 + 1.39396i) q^{68} +(-1.86677 - 1.35629i) q^{69} +(-3.11608 + 2.26396i) q^{70} +(-0.985330 + 3.03253i) q^{71} +(4.91323 - 15.1214i) q^{72} +(0.992078 - 0.720787i) q^{73} +(9.07192 + 6.59113i) q^{74} +(-6.13491 - 18.8813i) q^{75} +1.23015 q^{76} +6.56217 q^{78} +(2.93004 + 9.01775i) q^{79} +(5.33918 + 3.87914i) q^{80} +(-1.81200 + 1.31650i) q^{81} +(-0.732217 + 2.25353i) q^{82} +(4.96572 - 15.2829i) q^{83} +(1.75304 - 1.27366i) q^{84} +(5.40676 + 3.92824i) q^{85} +(1.06087 + 3.26501i) q^{86} +22.7953 q^{87} -4.43830 q^{89} +(-6.15690 - 18.9490i) q^{90} +(1.66629 + 1.21063i) q^{91} +(-0.494940 + 0.359595i) q^{92} +(-0.696508 + 2.14363i) q^{93} +(-2.60576 + 8.01970i) q^{94} +(4.53784 - 3.29693i) q^{95} +(-9.29568 - 6.75371i) q^{96} +(1.99874 + 6.15150i) q^{97} -1.11447 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 2q^{2} - 2q^{3} + 4q^{4} - 5q^{5} + 2q^{6} + 4q^{7} - 5q^{8} - 2q^{9} + O(q^{10}) \) \( 16q - 2q^{2} - 2q^{3} + 4q^{4} - 5q^{5} + 2q^{6} + 4q^{7} - 5q^{8} - 2q^{9} - 12q^{10} + 18q^{12} - 13q^{13} - 3q^{14} + 7q^{15} - 18q^{16} - 10q^{17} + 19q^{18} + 6q^{19} - 24q^{20} - 8q^{21} + 32q^{23} - 45q^{24} - 23q^{25} + 33q^{26} - 20q^{27} + 11q^{28} + 12q^{29} - 38q^{30} - 2q^{31} - 32q^{32} - 24q^{34} + 5q^{35} - 38q^{36} - 11q^{37} + 15q^{38} + 24q^{39} - 5q^{40} - 20q^{41} - 2q^{42} + 8q^{43} + 70q^{45} - 38q^{46} + 7q^{47} + 39q^{48} - 4q^{49} + 58q^{50} - 16q^{51} - 8q^{52} - 41q^{53} - 60q^{54} - 9q^{57} - 5q^{58} - 18q^{59} + 25q^{60} + 12q^{61} + 61q^{62} + 12q^{63} - 3q^{64} + 8q^{65} - 38q^{67} + 7q^{68} - 30q^{69} + 12q^{70} + q^{71} - 35q^{72} - 60q^{73} + 4q^{74} + 4q^{75} - 52q^{76} - 58q^{78} + 15q^{79} + 83q^{80} + 6q^{81} - 6q^{82} - 20q^{83} + 17q^{84} + 9q^{85} + 48q^{86} + 72q^{87} + 74q^{89} - 16q^{90} - 7q^{91} + 20q^{92} - 53q^{93} - 66q^{94} + 53q^{95} - 48q^{96} - 35q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.344389 1.05992i −0.243520 0.749477i −0.995876 0.0907209i \(-0.971083\pi\)
0.752356 0.658756i \(-0.228917\pi\)
\(3\) 2.31283 + 1.68037i 1.33531 + 0.970163i 0.999602 + 0.0281981i \(0.00897692\pi\)
0.335712 + 0.941965i \(0.391023\pi\)
\(4\) 0.613206 0.445520i 0.306603 0.222760i
\(5\) 1.06799 3.28693i 0.477618 1.46996i −0.364776 0.931095i \(-0.618854\pi\)
0.842394 0.538862i \(-0.181146\pi\)
\(6\) 0.984546 3.03012i 0.401939 1.23704i
\(7\) 0.809017 0.587785i 0.305780 0.222162i
\(8\) −2.48664 1.80665i −0.879161 0.638748i
\(9\) 1.59850 + 4.91966i 0.532832 + 1.63989i
\(10\) −3.85168 −1.21801
\(11\) 0 0
\(12\) 2.16688 0.625525
\(13\) 0.636468 + 1.95885i 0.176524 + 0.543286i 0.999700 0.0245009i \(-0.00779967\pi\)
−0.823175 + 0.567787i \(0.807800\pi\)
\(14\) −0.901622 0.655067i −0.240969 0.175074i
\(15\) 7.99333 5.80749i 2.06387 1.49949i
\(16\) −0.590087 + 1.81610i −0.147522 + 0.454025i
\(17\) −0.597555 + 1.83909i −0.144928 + 0.446044i −0.997002 0.0773786i \(-0.975345\pi\)
0.852073 + 0.523422i \(0.175345\pi\)
\(18\) 4.66395 3.38856i 1.09930 0.798691i
\(19\) 1.31300 + 0.953952i 0.301223 + 0.218852i 0.728121 0.685448i \(-0.240394\pi\)
−0.426898 + 0.904300i \(0.640394\pi\)
\(20\) −0.809496 2.49137i −0.181009 0.557088i
\(21\) 2.85882 0.623845
\(22\) 0 0
\(23\) −0.807136 −0.168299 −0.0841497 0.996453i \(-0.526817\pi\)
−0.0841497 + 0.996453i \(0.526817\pi\)
\(24\) −2.71534 8.35696i −0.554267 1.70586i
\(25\) −5.61820 4.08186i −1.12364 0.816372i
\(26\) 1.85703 1.34921i 0.364193 0.264602i
\(27\) −1.91954 + 5.90773i −0.369415 + 1.13694i
\(28\) 0.234224 0.720867i 0.0442641 0.136231i
\(29\) 6.45084 4.68681i 1.19789 0.870319i 0.203815 0.979009i \(-0.434666\pi\)
0.994076 + 0.108690i \(0.0346657\pi\)
\(30\) −8.90830 6.47226i −1.62643 1.18167i
\(31\) 0.243635 + 0.749832i 0.0437582 + 0.134674i 0.970549 0.240905i \(-0.0774441\pi\)
−0.926791 + 0.375578i \(0.877444\pi\)
\(32\) −4.01918 −0.710497
\(33\) 0 0
\(34\) 2.15508 0.369592
\(35\) −1.06799 3.28693i −0.180523 0.555592i
\(36\) 3.17202 + 2.30461i 0.528669 + 0.384101i
\(37\) −8.14014 + 5.91416i −1.33823 + 0.972282i −0.338724 + 0.940886i \(0.609995\pi\)
−0.999507 + 0.0313960i \(0.990005\pi\)
\(38\) 0.558930 1.72021i 0.0906704 0.279055i
\(39\) −1.81955 + 5.59998i −0.291360 + 0.896715i
\(40\) −8.59403 + 6.24393i −1.35884 + 0.987252i
\(41\) −1.72008 1.24971i −0.268631 0.195172i 0.445312 0.895375i \(-0.353093\pi\)
−0.713943 + 0.700203i \(0.753093\pi\)
\(42\) −0.984546 3.03012i −0.151919 0.467558i
\(43\) −3.08043 −0.469761 −0.234880 0.972024i \(-0.575470\pi\)
−0.234880 + 0.972024i \(0.575470\pi\)
\(44\) 0 0
\(45\) 17.8777 2.66506
\(46\) 0.277969 + 0.855500i 0.0409842 + 0.126137i
\(47\) −6.12128 4.44737i −0.892881 0.648716i 0.0437469 0.999043i \(-0.486070\pi\)
−0.936627 + 0.350327i \(0.886070\pi\)
\(48\) −4.41650 + 3.20877i −0.637466 + 0.463146i
\(49\) 0.309017 0.951057i 0.0441453 0.135865i
\(50\) −2.39160 + 7.36059i −0.338224 + 1.04094i
\(51\) −4.47239 + 3.24938i −0.626260 + 0.455004i
\(52\) 1.26299 + 0.917617i 0.175145 + 0.127251i
\(53\) 3.34432 + 10.2928i 0.459378 + 1.41382i 0.865918 + 0.500186i \(0.166735\pi\)
−0.406540 + 0.913633i \(0.633265\pi\)
\(54\) 6.92280 0.942073
\(55\) 0 0
\(56\) −3.07366 −0.410735
\(57\) 1.43376 + 4.41266i 0.189906 + 0.584471i
\(58\) −7.18925 5.22329i −0.943994 0.685852i
\(59\) 2.66704 1.93771i 0.347218 0.252269i −0.400483 0.916304i \(-0.631158\pi\)
0.747701 + 0.664035i \(0.231158\pi\)
\(60\) 2.31420 7.12238i 0.298762 0.919495i
\(61\) 0.332696 1.02393i 0.0425974 0.131101i −0.927496 0.373833i \(-0.878043\pi\)
0.970094 + 0.242731i \(0.0780434\pi\)
\(62\) 0.710857 0.516468i 0.0902789 0.0655915i
\(63\) 4.18492 + 3.04052i 0.527250 + 0.383069i
\(64\) 2.56433 + 7.89221i 0.320542 + 0.986526i
\(65\) 7.11832 0.882919
\(66\) 0 0
\(67\) 2.40314 0.293590 0.146795 0.989167i \(-0.453104\pi\)
0.146795 + 0.989167i \(0.453104\pi\)
\(68\) 0.452925 + 1.39396i 0.0549253 + 0.169043i
\(69\) −1.86677 1.35629i −0.224733 0.163278i
\(70\) −3.11608 + 2.26396i −0.372442 + 0.270595i
\(71\) −0.985330 + 3.03253i −0.116937 + 0.359896i −0.992346 0.123487i \(-0.960592\pi\)
0.875409 + 0.483383i \(0.160592\pi\)
\(72\) 4.91323 15.1214i 0.579030 1.78207i
\(73\) 0.992078 0.720787i 0.116114 0.0843617i −0.528213 0.849112i \(-0.677138\pi\)
0.644327 + 0.764750i \(0.277138\pi\)
\(74\) 9.07192 + 6.59113i 1.05459 + 0.766204i
\(75\) −6.13491 18.8813i −0.708399 2.18023i
\(76\) 1.23015 0.141107
\(77\) 0 0
\(78\) 6.56217 0.743020
\(79\) 2.93004 + 9.01775i 0.329656 + 1.01458i 0.969295 + 0.245901i \(0.0790838\pi\)
−0.639639 + 0.768675i \(0.720916\pi\)
\(80\) 5.33918 + 3.87914i 0.596939 + 0.433701i
\(81\) −1.81200 + 1.31650i −0.201334 + 0.146278i
\(82\) −0.732217 + 2.25353i −0.0808599 + 0.248861i
\(83\) 4.96572 15.2829i 0.545058 1.67752i −0.175793 0.984427i \(-0.556249\pi\)
0.720851 0.693090i \(-0.243751\pi\)
\(84\) 1.75304 1.27366i 0.191273 0.138968i
\(85\) 5.40676 + 3.92824i 0.586445 + 0.426077i
\(86\) 1.06087 + 3.26501i 0.114396 + 0.352075i
\(87\) 22.7953 2.44391
\(88\) 0 0
\(89\) −4.43830 −0.470459 −0.235230 0.971940i \(-0.575584\pi\)
−0.235230 + 0.971940i \(0.575584\pi\)
\(90\) −6.15690 18.9490i −0.648994 1.99740i
\(91\) 1.66629 + 1.21063i 0.174675 + 0.126909i
\(92\) −0.494940 + 0.359595i −0.0516011 + 0.0374904i
\(93\) −0.696508 + 2.14363i −0.0722246 + 0.222284i
\(94\) −2.60576 + 8.01970i −0.268763 + 0.827169i
\(95\) 4.53784 3.29693i 0.465572 0.338258i
\(96\) −9.29568 6.75371i −0.948736 0.689297i
\(97\) 1.99874 + 6.15150i 0.202942 + 0.624590i 0.999792 + 0.0204129i \(0.00649807\pi\)
−0.796850 + 0.604177i \(0.793502\pi\)
\(98\) −1.11447 −0.112578
\(99\) 0 0
\(100\) −5.26366 −0.526366
\(101\) 4.77274 + 14.6890i 0.474905 + 1.46161i 0.846086 + 0.533047i \(0.178953\pi\)
−0.371181 + 0.928561i \(0.621047\pi\)
\(102\) 4.98433 + 3.62133i 0.493522 + 0.358565i
\(103\) −7.20682 + 5.23606i −0.710109 + 0.515925i −0.883209 0.468980i \(-0.844622\pi\)
0.173100 + 0.984904i \(0.444622\pi\)
\(104\) 1.95628 6.02083i 0.191829 0.590390i
\(105\) 3.05318 9.39672i 0.297960 0.917026i
\(106\) 9.75776 7.08943i 0.947757 0.688586i
\(107\) 2.84142 + 2.06441i 0.274691 + 0.199574i 0.716598 0.697486i \(-0.245698\pi\)
−0.441908 + 0.897061i \(0.645698\pi\)
\(108\) 1.45494 + 4.47785i 0.140002 + 0.430881i
\(109\) −3.87655 −0.371306 −0.185653 0.982615i \(-0.559440\pi\)
−0.185653 + 0.982615i \(0.559440\pi\)
\(110\) 0 0
\(111\) −28.7648 −2.73023
\(112\) 0.590087 + 1.81610i 0.0557580 + 0.171605i
\(113\) −8.61920 6.26221i −0.810826 0.589099i 0.103244 0.994656i \(-0.467078\pi\)
−0.914070 + 0.405557i \(0.867078\pi\)
\(114\) 4.18330 3.03935i 0.391802 0.284661i
\(115\) −0.862010 + 2.65299i −0.0803829 + 0.247393i
\(116\) 1.86763 5.74796i 0.173405 0.533685i
\(117\) −8.61947 + 6.26241i −0.796871 + 0.578960i
\(118\) −2.97232 2.15952i −0.273624 0.198800i
\(119\) 0.597555 + 1.83909i 0.0547778 + 0.168589i
\(120\) −30.3687 −2.77227
\(121\) 0 0
\(122\) −1.19987 −0.108631
\(123\) −1.87828 5.78074i −0.169358 0.521232i
\(124\) 0.483464 + 0.351257i 0.0434163 + 0.0315438i
\(125\) −5.43680 + 3.95007i −0.486282 + 0.353305i
\(126\) 1.78147 5.48280i 0.158706 0.488447i
\(127\) −6.01066 + 18.4989i −0.533360 + 1.64151i 0.213807 + 0.976876i \(0.431414\pi\)
−0.747167 + 0.664637i \(0.768586\pi\)
\(128\) 0.978825 0.711158i 0.0865167 0.0628581i
\(129\) −7.12451 5.17626i −0.627278 0.455744i
\(130\) −2.45147 7.54486i −0.215008 0.661728i
\(131\) −5.11284 −0.446711 −0.223355 0.974737i \(-0.571701\pi\)
−0.223355 + 0.974737i \(0.571701\pi\)
\(132\) 0 0
\(133\) 1.62296 0.140728
\(134\) −0.827615 2.54714i −0.0714951 0.220039i
\(135\) 17.3682 + 12.6188i 1.49482 + 1.08605i
\(136\) 4.80849 3.49357i 0.412325 0.299571i
\(137\) 2.81221 8.65511i 0.240264 0.739456i −0.756116 0.654438i \(-0.772905\pi\)
0.996379 0.0850177i \(-0.0270947\pi\)
\(138\) −0.794662 + 2.44572i −0.0676461 + 0.208193i
\(139\) −10.5306 + 7.65095i −0.893197 + 0.648945i −0.936710 0.350108i \(-0.886145\pi\)
0.0435129 + 0.999053i \(0.486145\pi\)
\(140\) −2.11929 1.53975i −0.179112 0.130133i
\(141\) −6.68426 20.5720i −0.562916 1.73248i
\(142\) 3.55358 0.298210
\(143\) 0 0
\(144\) −9.87786 −0.823155
\(145\) −8.51578 26.2089i −0.707197 2.17653i
\(146\) −1.10564 0.803293i −0.0915032 0.0664810i
\(147\) 2.31283 1.68037i 0.190759 0.138595i
\(148\) −2.35671 + 7.25320i −0.193720 + 0.596209i
\(149\) 0.972321 2.99250i 0.0796557 0.245155i −0.903296 0.429017i \(-0.858860\pi\)
0.982952 + 0.183862i \(0.0588600\pi\)
\(150\) −17.8999 + 13.0050i −1.46152 + 1.06186i
\(151\) 2.31942 + 1.68516i 0.188752 + 0.137136i 0.678148 0.734925i \(-0.262783\pi\)
−0.489396 + 0.872062i \(0.662783\pi\)
\(152\) −1.54151 4.74427i −0.125033 0.384811i
\(153\) −10.0029 −0.808684
\(154\) 0 0
\(155\) 2.72484 0.218864
\(156\) 1.37915 + 4.24459i 0.110420 + 0.339839i
\(157\) 17.3854 + 12.6312i 1.38750 + 1.00808i 0.996134 + 0.0878468i \(0.0279986\pi\)
0.391370 + 0.920234i \(0.372001\pi\)
\(158\) 8.54902 6.21123i 0.680124 0.494139i
\(159\) −9.56080 + 29.4251i −0.758221 + 2.33356i
\(160\) −4.29243 + 13.2107i −0.339346 + 1.04440i
\(161\) −0.652986 + 0.474422i −0.0514625 + 0.0373897i
\(162\) 2.01942 + 1.46719i 0.158661 + 0.115274i
\(163\) −2.54088 7.82002i −0.199017 0.612511i −0.999906 0.0136985i \(-0.995639\pi\)
0.800889 0.598812i \(-0.204361\pi\)
\(164\) −1.61153 −0.125840
\(165\) 0 0
\(166\) −17.9088 −1.38999
\(167\) 6.70832 + 20.6461i 0.519105 + 1.59764i 0.775686 + 0.631119i \(0.217404\pi\)
−0.256581 + 0.966523i \(0.582596\pi\)
\(168\) −7.10886 5.16489i −0.548460 0.398480i
\(169\) 7.08523 5.14772i 0.545018 0.395979i
\(170\) 2.30159 7.08357i 0.176524 0.543285i
\(171\) −2.59429 + 7.98442i −0.198391 + 0.610584i
\(172\) −1.88894 + 1.37239i −0.144030 + 0.104644i
\(173\) −6.50905 4.72910i −0.494874 0.359547i 0.312181 0.950022i \(-0.398940\pi\)
−0.807056 + 0.590475i \(0.798940\pi\)
\(174\) −7.85045 24.1612i −0.595141 1.83166i
\(175\) −6.94447 −0.524953
\(176\) 0 0
\(177\) 9.42449 0.708388
\(178\) 1.52850 + 4.70425i 0.114566 + 0.352598i
\(179\) 2.92938 + 2.12832i 0.218952 + 0.159078i 0.691855 0.722037i \(-0.256794\pi\)
−0.472903 + 0.881115i \(0.656794\pi\)
\(180\) 10.9627 7.96490i 0.817114 0.593668i
\(181\) 4.88800 15.0437i 0.363322 1.11819i −0.587703 0.809077i \(-0.699967\pi\)
0.951025 0.309114i \(-0.100033\pi\)
\(182\) 0.709322 2.18307i 0.0525784 0.161820i
\(183\) 2.49006 1.80913i 0.184070 0.133735i
\(184\) 2.00706 + 1.45821i 0.147962 + 0.107501i
\(185\) 10.7458 + 33.0723i 0.790050 + 2.43152i
\(186\) 2.51195 0.184185
\(187\) 0 0
\(188\) −5.73500 −0.418268
\(189\) 1.91954 + 5.90773i 0.139626 + 0.429724i
\(190\) −5.05727 3.67432i −0.366893 0.266563i
\(191\) −0.347134 + 0.252207i −0.0251177 + 0.0182491i −0.600273 0.799795i \(-0.704942\pi\)
0.575156 + 0.818044i \(0.304942\pi\)
\(192\) −7.33097 + 22.5624i −0.529067 + 1.62830i
\(193\) 4.68928 14.4321i 0.337542 1.03885i −0.627915 0.778282i \(-0.716091\pi\)
0.965456 0.260564i \(-0.0839086\pi\)
\(194\) 5.83176 4.23702i 0.418696 0.304200i
\(195\) 16.4635 + 11.9614i 1.17897 + 0.856575i
\(196\) −0.234224 0.720867i −0.0167303 0.0514905i
\(197\) 20.8082 1.48252 0.741262 0.671216i \(-0.234228\pi\)
0.741262 + 0.671216i \(0.234228\pi\)
\(198\) 0 0
\(199\) 8.44567 0.598698 0.299349 0.954144i \(-0.403231\pi\)
0.299349 + 0.954144i \(0.403231\pi\)
\(200\) 6.59595 + 20.3003i 0.466404 + 1.43544i
\(201\) 5.55806 + 4.03817i 0.392035 + 0.284830i
\(202\) 13.9255 10.1174i 0.979792 0.711861i
\(203\) 2.46400 7.58342i 0.172939 0.532252i
\(204\) −1.29483 + 3.98508i −0.0906563 + 0.279011i
\(205\) −5.94472 + 4.31910i −0.415198 + 0.301659i
\(206\) 8.03176 + 5.83542i 0.559599 + 0.406573i
\(207\) −1.29020 3.97084i −0.0896753 0.275992i
\(208\) −3.93303 −0.272707
\(209\) 0 0
\(210\) −11.0113 −0.759849
\(211\) 3.04668 + 9.37672i 0.209742 + 0.645520i 0.999485 + 0.0320823i \(0.0102139\pi\)
−0.789743 + 0.613438i \(0.789786\pi\)
\(212\) 6.63639 + 4.82162i 0.455789 + 0.331150i
\(213\) −7.37469 + 5.35802i −0.505305 + 0.367126i
\(214\) 1.20956 3.72264i 0.0826838 0.254475i
\(215\) −3.28986 + 10.1251i −0.224366 + 0.690528i
\(216\) 15.4464 11.2225i 1.05100 0.763593i
\(217\) 0.637845 + 0.463421i 0.0432997 + 0.0314591i
\(218\) 1.33504 + 4.10883i 0.0904204 + 0.278285i
\(219\) 3.50570 0.236893
\(220\) 0 0
\(221\) −3.98281 −0.267913
\(222\) 9.90627 + 30.4884i 0.664865 + 2.04625i
\(223\) −14.0736 10.2250i −0.942436 0.684720i 0.00656992 0.999978i \(-0.497909\pi\)
−0.949006 + 0.315259i \(0.897909\pi\)
\(224\) −3.25158 + 2.36241i −0.217255 + 0.157845i
\(225\) 11.1007 34.1645i 0.740048 2.27763i
\(226\) −3.66909 + 11.2923i −0.244064 + 0.751153i
\(227\) −10.2191 + 7.42460i −0.678264 + 0.492788i −0.872781 0.488111i \(-0.837686\pi\)
0.194517 + 0.980899i \(0.437686\pi\)
\(228\) 2.84512 + 2.06710i 0.188423 + 0.136897i
\(229\) 1.41326 + 4.34958i 0.0933910 + 0.287428i 0.986831 0.161755i \(-0.0517153\pi\)
−0.893440 + 0.449183i \(0.851715\pi\)
\(230\) 3.10883 0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) −7.37218 22.6893i −0.482968 1.48642i −0.834903 0.550398i \(-0.814476\pi\)
0.351935 0.936025i \(-0.385524\pi\)
\(234\) 9.60612 + 6.97925i 0.627971 + 0.456248i
\(235\) −21.1556 + 15.3705i −1.38004 + 1.00266i
\(236\) 0.772151 2.37644i 0.0502628 0.154693i
\(237\) −8.37646 + 25.7801i −0.544110 + 1.67460i
\(238\) 1.74349 1.26672i 0.113014 0.0821094i
\(239\) 7.15021 + 5.19493i 0.462509 + 0.336032i 0.794515 0.607245i \(-0.207725\pi\)
−0.332006 + 0.943277i \(0.607725\pi\)
\(240\) 5.83024 + 17.9436i 0.376340 + 1.15826i
\(241\) −18.9464 −1.22045 −0.610224 0.792229i \(-0.708921\pi\)
−0.610224 + 0.792229i \(0.708921\pi\)
\(242\) 0 0
\(243\) 12.2322 0.784696
\(244\) −0.252172 0.776105i −0.0161436 0.0496850i
\(245\) −2.79603 2.03143i −0.178632 0.129783i
\(246\) −5.48027 + 3.98165i −0.349409 + 0.253861i
\(247\) −1.03296 + 3.17913i −0.0657258 + 0.202283i
\(248\) 0.748851 2.30473i 0.0475521 0.146350i
\(249\) 37.1658 27.0026i 2.35529 1.71122i
\(250\) 6.05913 + 4.40222i 0.383213 + 0.278421i
\(251\) −0.885925 2.72660i −0.0559191 0.172101i 0.919196 0.393800i \(-0.128840\pi\)
−0.975115 + 0.221699i \(0.928840\pi\)
\(252\) 3.92083 0.246989
\(253\) 0 0
\(254\) 21.6774 1.36016
\(255\) 5.90402 + 18.1707i 0.369724 + 1.13789i
\(256\) 12.3362 + 8.96275i 0.771010 + 0.560172i
\(257\) −18.1348 + 13.1757i −1.13122 + 0.821879i −0.985872 0.167502i \(-0.946430\pi\)
−0.145347 + 0.989381i \(0.546430\pi\)
\(258\) −3.03282 + 9.33406i −0.188815 + 0.581113i
\(259\) −3.10926 + 9.56931i −0.193200 + 0.594608i
\(260\) 4.36500 3.17136i 0.270706 0.196679i
\(261\) 33.3692 + 24.2441i 2.06550 + 1.50067i
\(262\) 1.76080 + 5.41920i 0.108783 + 0.334799i
\(263\) −0.990706 −0.0610895 −0.0305448 0.999533i \(-0.509724\pi\)
−0.0305448 + 0.999533i \(0.509724\pi\)
\(264\) 0 0
\(265\) 37.4032 2.29766
\(266\) −0.558930 1.72021i −0.0342702 0.105473i
\(267\) −10.2650 7.45800i −0.628211 0.456422i
\(268\) 1.47362 1.07065i 0.0900156 0.0654002i
\(269\) −2.22194 + 6.83844i −0.135474 + 0.416947i −0.995664 0.0930279i \(-0.970345\pi\)
0.860189 + 0.509975i \(0.170345\pi\)
\(270\) 7.39345 22.7547i 0.449951 1.38481i
\(271\) −21.9764 + 15.9668i −1.33497 + 0.969912i −0.335356 + 0.942091i \(0.608857\pi\)
−0.999613 + 0.0278207i \(0.991143\pi\)
\(272\) −2.98736 2.17044i −0.181135 0.131602i
\(273\) 1.81955 + 5.59998i 0.110124 + 0.338927i
\(274\) −10.1422 −0.612714
\(275\) 0 0
\(276\) −1.74897 −0.105275
\(277\) −6.48491 19.9585i −0.389640 1.19919i −0.933058 0.359727i \(-0.882870\pi\)
0.543417 0.839463i \(-0.317130\pi\)
\(278\) 11.7360 + 8.52673i 0.703881 + 0.511399i
\(279\) −3.29947 + 2.39721i −0.197534 + 0.143517i
\(280\) −3.28263 + 10.1029i −0.196174 + 0.603763i
\(281\) 8.70130 26.7798i 0.519076 1.59755i −0.256665 0.966500i \(-0.582624\pi\)
0.775741 0.631051i \(-0.217376\pi\)
\(282\) −19.5027 + 14.1696i −1.16137 + 0.843786i
\(283\) −21.1896 15.3951i −1.25959 0.915145i −0.260851 0.965379i \(-0.584003\pi\)
−0.998737 + 0.0502344i \(0.984003\pi\)
\(284\) 0.746845 + 2.29855i 0.0443171 + 0.136394i
\(285\) 16.0353 0.949851
\(286\) 0 0
\(287\) −2.12613 −0.125502
\(288\) −6.42463 19.7730i −0.378575 1.16513i
\(289\) 10.7281 + 7.79444i 0.631066 + 0.458496i
\(290\) −24.8466 + 18.0521i −1.45904 + 1.06006i
\(291\) −5.71404 + 17.5860i −0.334963 + 1.03091i
\(292\) 0.287223 0.883981i 0.0168085 0.0517311i
\(293\) −3.61133 + 2.62379i −0.210976 + 0.153283i −0.688255 0.725469i \(-0.741623\pi\)
0.477279 + 0.878752i \(0.341623\pi\)
\(294\) −2.57757 1.87272i −0.150327 0.109219i
\(295\) −3.52077 10.8358i −0.204987 0.630885i
\(296\) 30.9264 1.79756
\(297\) 0 0
\(298\) −3.50667 −0.203136
\(299\) −0.513716 1.58105i −0.0297089 0.0914347i
\(300\) −12.1740 8.84491i −0.702865 0.510661i
\(301\) −2.49212 + 1.81063i −0.143643 + 0.104363i
\(302\) 0.987351 3.03875i 0.0568157 0.174861i
\(303\) −13.6444 + 41.9931i −0.783849 + 2.41244i
\(304\) −2.50726 + 1.82163i −0.143801 + 0.104478i
\(305\) −3.01028 2.18710i −0.172368 0.125233i
\(306\) 3.44488 + 10.6023i 0.196931 + 0.606090i
\(307\) −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
\(310\) −0.938405 2.88811i −0.0532978 0.164034i
\(311\) −21.6977 15.7643i −1.23036 0.893912i −0.233447 0.972370i \(-0.575001\pi\)
−0.996917 + 0.0784574i \(0.975001\pi\)
\(312\) 14.6418 10.6379i 0.828928 0.602251i
\(313\) 1.10896 3.41304i 0.0626824 0.192917i −0.914811 0.403882i \(-0.867661\pi\)
0.977494 + 0.210965i \(0.0676607\pi\)
\(314\) 7.40075 22.7772i 0.417648 1.28539i
\(315\) 14.4634 10.5083i 0.814920 0.592074i
\(316\) 5.81431 + 4.22434i 0.327081 + 0.237638i
\(317\) −5.22797 16.0900i −0.293632 0.903706i −0.983678 0.179940i \(-0.942410\pi\)
0.690046 0.723766i \(-0.257590\pi\)
\(318\) 34.4809 1.93359
\(319\) 0 0
\(320\) 28.6798 1.60325
\(321\) 3.10275 + 9.54929i 0.173179 + 0.532989i
\(322\) 0.727732 + 0.528728i 0.0405549 + 0.0294649i
\(323\) −2.53899 + 1.84468i −0.141273 + 0.102641i
\(324\) −0.524605 + 1.61457i −0.0291447 + 0.0896983i
\(325\) 4.41993 13.6032i 0.245174 0.754567i
\(326\) −7.41355 + 5.38626i −0.410598 + 0.298317i
\(327\) −8.96581 6.51404i −0.495810 0.360227i
\(328\) 2.01943 + 6.21516i 0.111504 + 0.343175i
\(329\) −7.56632 −0.417145
\(330\) 0 0
\(331\) −1.23826 −0.0680610 −0.0340305 0.999421i \(-0.510834\pi\)
−0.0340305 + 0.999421i \(0.510834\pi\)
\(332\) −3.76384 11.5839i −0.206567 0.635749i
\(333\) −42.1077 30.5930i −2.30749 1.67649i
\(334\) 19.5729 14.2206i 1.07098 0.778115i
\(335\) 2.56652 7.89894i 0.140224 0.431565i
\(336\) −1.68695 + 5.19190i −0.0920307 + 0.283242i
\(337\) −16.5691 + 12.0382i −0.902579 + 0.655762i −0.939127 0.343570i \(-0.888364\pi\)
0.0365484 + 0.999332i \(0.488364\pi\)
\(338\) −7.89626 5.73697i −0.429500 0.312050i
\(339\) −9.41192 28.9669i −0.511185 1.57327i
\(340\) 5.06556 0.274719
\(341\) 0 0
\(342\) 9.35630 0.505931
\(343\) −0.309017 0.951057i −0.0166853 0.0513522i
\(344\) 7.65992 + 5.56526i 0.412995 + 0.300059i
\(345\) −6.45170 + 4.68743i −0.347348 + 0.252363i
\(346\) −2.77083 + 8.52773i −0.148961 + 0.458454i
\(347\) −8.42685 + 25.9352i −0.452377 + 1.39227i 0.421810 + 0.906684i \(0.361395\pi\)
−0.874187 + 0.485589i \(0.838605\pi\)
\(348\) 13.9782 10.1558i 0.749311 0.544406i
\(349\) 6.45947 + 4.69308i 0.345767 + 0.251215i 0.747091 0.664721i \(-0.231450\pi\)
−0.401324 + 0.915936i \(0.631450\pi\)
\(350\) 2.39160 + 7.36059i 0.127836 + 0.393440i
\(351\) −12.7941 −0.682897
\(352\) 0 0
\(353\) 5.93472 0.315873 0.157937 0.987449i \(-0.449516\pi\)
0.157937 + 0.987449i \(0.449516\pi\)
\(354\) −3.24569 9.98921i −0.172507 0.530920i
\(355\) 8.91539 + 6.47741i 0.473180 + 0.343785i
\(356\) −2.72159 + 1.97735i −0.144244 + 0.104800i
\(357\) −1.70830 + 5.25761i −0.0904129 + 0.278262i
\(358\) 1.24700 3.83788i 0.0659061 0.202838i
\(359\) 22.9925 16.7050i 1.21350 0.881657i 0.217953 0.975959i \(-0.430062\pi\)
0.995544 + 0.0943020i \(0.0300619\pi\)
\(360\) −44.4555 32.2988i −2.34301 1.70230i
\(361\) −5.05737 15.5650i −0.266178 0.819210i
\(362\) −17.6285 −0.926535
\(363\) 0 0
\(364\) 1.56114 0.0818261
\(365\) −1.30965 4.03068i −0.0685500 0.210975i
\(366\) −2.77509 2.01622i −0.145056 0.105389i
\(367\) 24.5953 17.8695i 1.28386 0.932781i 0.284200 0.958765i \(-0.408272\pi\)
0.999662 + 0.0259840i \(0.00827188\pi\)
\(368\) 0.476280 1.46584i 0.0248278 0.0764122i
\(369\) 3.39862 10.4599i 0.176925 0.544519i
\(370\) 31.3532 22.7795i 1.62998 1.18425i
\(371\) 8.75554 + 6.36127i 0.454565 + 0.330261i
\(372\) 0.527928 + 1.62480i 0.0273718 + 0.0842418i
\(373\) −14.4226 −0.746772 −0.373386 0.927676i \(-0.621803\pi\)
−0.373386 + 0.927676i \(0.621803\pi\)
\(374\) 0 0
\(375\) −19.2120 −0.992103
\(376\) 7.18659 + 22.1180i 0.370620 + 1.14065i
\(377\) 13.2865 + 9.65320i 0.684289 + 0.497165i
\(378\) 5.60066 4.06912i 0.288067 0.209293i
\(379\) −6.92421 + 21.3105i −0.355673 + 1.09465i 0.599946 + 0.800041i \(0.295189\pi\)
−0.955618 + 0.294607i \(0.904811\pi\)
\(380\) 1.31378 4.04340i 0.0673955 0.207422i
\(381\) −44.9867 + 32.6847i −2.30474 + 1.67449i
\(382\) 0.386869 + 0.281077i 0.0197939 + 0.0143811i
\(383\) 10.4072 + 32.0302i 0.531785 + 1.63667i 0.750495 + 0.660876i \(0.229815\pi\)
−0.218710 + 0.975790i \(0.570185\pi\)
\(384\) 3.45887 0.176510
\(385\) 0 0
\(386\) −16.9118 −0.860790
\(387\) −4.92405 15.1547i −0.250304 0.770355i
\(388\) 3.96626 + 2.88166i 0.201356 + 0.146294i
\(389\) −1.96416 + 1.42704i −0.0995866 + 0.0723539i −0.636464 0.771306i \(-0.719604\pi\)
0.536878 + 0.843660i \(0.319604\pi\)
\(390\) 7.00831 21.5694i 0.354880 1.09221i
\(391\) 0.482308 1.48439i 0.0243914 0.0750689i
\(392\) −2.48664 + 1.80665i −0.125594 + 0.0912497i
\(393\) −11.8251 8.59146i −0.596499 0.433382i
\(394\) −7.16612 22.0550i −0.361024 1.11112i
\(395\) 32.7699 1.64883
\(396\) 0 0
\(397\) −5.89696 −0.295960 −0.147980 0.988990i \(-0.547277\pi\)
−0.147980 + 0.988990i \(0.547277\pi\)
\(398\) −2.90860 8.95175i −0.145795 0.448710i
\(399\) 3.75363 + 2.72717i 0.187917 + 0.136530i
\(400\) 10.7283 7.79456i 0.536415 0.389728i
\(401\) 3.47322 10.6895i 0.173445 0.533807i −0.826114 0.563502i \(-0.809454\pi\)
0.999559 + 0.0296950i \(0.00945359\pi\)
\(402\) 2.36600 7.28180i 0.118005 0.363183i
\(403\) −1.31374 + 0.954487i −0.0654420 + 0.0475464i
\(404\) 9.47090 + 6.88102i 0.471195 + 0.342343i
\(405\) 2.39204 + 7.36193i 0.118861 + 0.365817i
\(406\) −8.88640 −0.441025
\(407\) 0 0
\(408\) 16.9917 0.841216
\(409\) −9.06482 27.8987i −0.448227 1.37950i −0.878906 0.476995i \(-0.841726\pi\)
0.430679 0.902505i \(-0.358274\pi\)
\(410\) 6.62520 + 4.81349i 0.327195 + 0.237721i
\(411\) 21.0480 15.2922i 1.03822 0.754311i
\(412\) −2.08649 + 6.42157i −0.102794 + 0.316368i
\(413\) 1.01872 3.13529i 0.0501278 0.154277i
\(414\) −3.76444 + 2.73503i −0.185012 + 0.134419i
\(415\) −44.9305 32.6439i −2.20555 1.60243i
\(416\) −2.55808 7.87295i −0.125420 0.386003i
\(417\) −37.2120 −1.82228
\(418\) 0 0
\(419\) −20.2858 −0.991027 −0.495514 0.868600i \(-0.665020\pi\)
−0.495514 + 0.868600i \(0.665020\pi\)
\(420\) −2.31420 7.12238i −0.112921 0.347537i
\(421\) 2.47561 + 1.79864i 0.120654 + 0.0876603i 0.646476 0.762934i \(-0.276242\pi\)
−0.525822 + 0.850595i \(0.676242\pi\)
\(422\) 8.88934 6.45848i 0.432726 0.314394i
\(423\) 12.0947 37.2237i 0.588066 1.80988i
\(424\) 10.2793 31.6364i 0.499207 1.53640i
\(425\) 10.8641 7.89321i 0.526985 0.382877i
\(426\) 8.21884 + 5.97134i 0.398204 + 0.289312i
\(427\) −0.332696 1.02393i −0.0161003 0.0495516i
\(428\) 2.66211 0.128678
\(429\) 0 0
\(430\) 11.8648 0.572173
\(431\) −2.33060 7.17284i −0.112261 0.345503i 0.879105 0.476628i \(-0.158141\pi\)
−0.991366 + 0.131125i \(0.958141\pi\)
\(432\) −9.59634 6.97215i −0.461704 0.335448i
\(433\) 26.0193 18.9041i 1.25041 0.908474i 0.252161 0.967685i \(-0.418859\pi\)
0.998245 + 0.0592114i \(0.0188586\pi\)
\(434\) 0.271523 0.835662i 0.0130335 0.0401131i
\(435\) 24.3451 74.9264i 1.16726 3.59245i
\(436\) −2.37712 + 1.72708i −0.113844 + 0.0827122i
\(437\) −1.05977 0.769968i −0.0506957 0.0368326i
\(438\) −1.20732 3.71576i −0.0576882 0.177546i
\(439\) 4.66725 0.222756 0.111378 0.993778i \(-0.464474\pi\)
0.111378 + 0.993778i \(0.464474\pi\)
\(440\) 0 0
\(441\) 5.17284 0.246326
\(442\) 1.37164 + 4.22146i 0.0652421 + 0.200794i
\(443\) −13.9775 10.1553i −0.664091 0.482491i 0.203951 0.978981i \(-0.434622\pi\)
−0.868042 + 0.496490i \(0.834622\pi\)
\(444\) −17.6387 + 12.8153i −0.837097 + 0.608187i
\(445\) −4.74005 + 14.5884i −0.224700 + 0.691555i
\(446\) −5.99095 + 18.4383i −0.283680 + 0.873077i
\(447\) 7.27732 5.28728i 0.344206 0.250080i
\(448\) 6.71351 + 4.87765i 0.317184 + 0.230447i
\(449\) −5.17297 15.9208i −0.244128 0.751347i −0.995779 0.0917865i \(-0.970742\pi\)
0.751651 0.659561i \(-0.229258\pi\)
\(450\) −40.0346 −1.88725
\(451\) 0 0
\(452\) −8.07529 −0.379829
\(453\) 2.53274 + 7.79498i 0.118999 + 0.366240i
\(454\) 11.3888 + 8.27447i 0.534504 + 0.388340i
\(455\) 5.75884 4.18404i 0.269979 0.196151i
\(456\) 4.40689 13.5630i 0.206372 0.635146i
\(457\) 6.70487 20.6355i 0.313640 0.965286i −0.662670 0.748912i \(-0.730577\pi\)
0.976310 0.216375i \(-0.0694232\pi\)
\(458\) 4.12349 2.99589i 0.192678 0.139989i
\(459\) −9.71779 7.06039i −0.453588 0.329551i
\(460\) 0.653373 + 2.01087i 0.0304637 + 0.0937575i
\(461\) 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 \(0.538163\pi\)
\(464\) 4.70516 + 14.4810i 0.218432 + 0.672264i
\(465\) 6.30210 + 4.57874i 0.292253 + 0.212334i
\(466\) −21.5099 + 15.6279i −0.996427 + 0.723947i
\(467\) −1.21112 + 3.72745i −0.0560441 + 0.172486i −0.975160 0.221501i \(-0.928904\pi\)
0.919116 + 0.393987i \(0.128904\pi\)
\(468\) −2.49548 + 7.68030i −0.115354 + 0.355022i
\(469\) 1.94418 1.41253i 0.0897739 0.0652246i
\(470\) 23.5772 + 17.1299i 1.08754 + 0.790142i
\(471\) 18.9843 + 58.4277i 0.874752 + 2.69221i
\(472\) −10.1327 −0.466397
\(473\) 0 0
\(474\) 30.2096 1.38757
\(475\) −3.48281 10.7190i −0.159802 0.491821i
\(476\) 1.18577 + 0.861515i 0.0543499 + 0.0394875i
\(477\) −45.2910 + 32.9059i −2.07373 + 1.50666i
\(478\) 3.04376 9.36773i 0.139218 0.428470i
\(479\) 4.67015 14.3732i 0.213385 0.656730i −0.785880 0.618379i \(-0.787790\pi\)
0.999264 0.0383508i \(-0.0122104\pi\)
\(480\) −32.1266 + 23.3413i −1.46637 + 1.06538i
\(481\) −16.7659 12.1811i −0.764458 0.555411i
\(482\) 6.52495 + 20.0817i 0.297203 + 0.914698i
\(483\) −2.30745 −0.104993
\(484\) 0 0
\(485\) 22.3541 1.01505
\(486\) −4.21264 12.9652i −0.191089 0.588112i
\(487\) −20.2876 14.7398i −0.919317 0.667923i 0.0240370 0.999711i \(-0.492348\pi\)
−0.943354 + 0.331788i \(0.892348\pi\)
\(488\) −2.67719 + 1.94509i −0.121191 + 0.0880501i
\(489\) 7.26391 22.3560i 0.328485 1.01097i
\(490\) −1.19024 + 3.66317i −0.0537694 + 0.165485i
\(491\) 30.1122 21.8778i 1.35895 0.987332i 0.360435 0.932784i \(-0.382628\pi\)
0.998511 0.0545479i \(-0.0173718\pi\)
\(492\) −3.72721 2.70797i −0.168035 0.122085i
\(493\) 4.76471 + 14.6643i 0.214592 + 0.660446i
\(494\) 3.72536 0.167612
\(495\) 0 0
\(496\) −1.50554 −0.0676006
\(497\) 0.985330 + 3.03253i 0.0441981 + 0.136028i
\(498\) −41.4201 30.0934i −1.85608 1.34852i
\(499\) 25.7375 18.6994i 1.15217 0.837101i 0.163403 0.986559i \(-0.447753\pi\)
0.988768 + 0.149458i \(0.0477530\pi\)
\(500\) −1.57404 + 4.84441i −0.0703934 + 0.216649i
\(501\) −19.1779 + 59.0234i −0.856804 + 2.63697i
\(502\) −2.58487 + 1.87802i −0.115369 + 0.0838201i
\(503\) −15.5379 11.2889i −0.692799 0.503348i 0.184780 0.982780i \(-0.440843\pi\)
−0.877579 + 0.479432i \(0.840843\pi\)
\(504\) −4.91323 15.1214i −0.218853 0.673559i
\(505\) 53.3788 2.37532
\(506\) 0 0
\(507\) 25.0370 1.11193
\(508\) 4.55587 + 14.0215i 0.202134 + 0.622104i
\(509\) −2.03507 1.47857i −0.0902029 0.0655363i 0.541770 0.840527i \(-0.317754\pi\)
−0.631973 + 0.774991i \(0.717754\pi\)
\(510\) 17.2262 12.5156i 0.762790 0.554200i
\(511\) 0.378940 1.16626i 0.0167633 0.0515922i
\(512\) 5.99912 18.4634i 0.265126 0.815974i
\(513\) −8.15605 + 5.92572i −0.360098 + 0.261627i
\(514\) 20.2107 + 14.6839i 0.891454 + 0.647679i
\(515\) 9.51376 + 29.2803i 0.419226 + 1.29025i
\(516\) −6.67492 −0.293847
\(517\) 0 0
\(518\) 11.2135 0.492693
\(519\) −7.10770 21.8753i −0.311993 0.960217i
\(520\) −17.7007 12.8603i −0.776228 0.563962i
\(521\) −12.0517 + 8.75610i −0.527996 + 0.383612i −0.819608 0.572925i \(-0.805809\pi\)
0.291612 + 0.956537i \(0.405809\pi\)
\(522\) 14.2049 43.7181i 0.621730 1.91349i
\(523\) 3.06082 9.42024i 0.133840 0.411918i −0.861567 0.507643i \(-0.830517\pi\)
0.995408 + 0.0957248i \(0.0305169\pi\)
\(524\) −3.13522 + 2.27787i −0.136963 + 0.0995093i
\(525\) −16.0614 11.6693i −0.700977 0.509290i
\(526\) 0.341188 + 1.05007i 0.0148765 + 0.0457852i
\(527\) −1.52459 −0.0664122
\(528\) 0 0
\(529\) −22.3485 −0.971675
\(530\) −12.8813 39.6444i −0.559526 1.72204i
\(531\) 13.7962 + 10.0235i 0.598702 + 0.434982i
\(532\) 0.995209 0.723061i 0.0431478 0.0313487i
\(533\) 1.35322 4.16477i 0.0586143 0.180396i
\(534\) −4.36971 + 13.4486i −0.189096 + 0.581977i
\(535\) 9.82017 7.13477i 0.424563 0.308463i
\(536\) −5.97575 4.34164i −0.258113 0.187530i
\(537\) 3.19880 + 9.84488i 0.138038 + 0.424838i
\(538\) 8.01342 0.345483
\(539\) 0 0
\(540\) 16.2722 0.700245
\(541\) 6.80096 + 20.9312i 0.292396 + 0.899903i 0.984084 + 0.177706i \(0.0568676\pi\)
−0.691687 + 0.722197i \(0.743132\pi\)
\(542\) 24.4919 + 17.7944i 1.05202 + 0.764336i
\(543\) 36.5842 26.5800i 1.56998 1.14066i
\(544\) 2.40168 7.39161i 0.102971 0.316912i
\(545\) −4.14010 + 12.7419i −0.177342 + 0.545804i
\(546\) 5.30891 3.85715i 0.227200 0.165071i
\(547\) −8.78938 6.38586i −0.375807 0.273040i 0.383808 0.923413i \(-0.374612\pi\)
−0.759615 + 0.650373i \(0.774612\pi\)
\(548\) −2.13156 6.56026i −0.0910557 0.280240i
\(549\) 5.56922 0.237689
\(550\) 0 0
\(551\) 12.9410 0.551303
\(552\) 2.19165 + 6.74520i 0.0932828 + 0.287095i
\(553\) 7.67096 + 5.57328i 0.326202 + 0.237000i
\(554\) −18.9211 + 13.7470i −0.803880 + 0.584053i
\(555\) −30.7204 + 94.5476i −1.30401 + 4.01332i
\(556\) −3.04879 + 9.38322i −0.129298 + 0.397937i
\(557\) 27.1932 19.7570i 1.15221 0.837130i 0.163438 0.986554i \(-0.447742\pi\)
0.988773 + 0.149423i \(0.0477418\pi\)
\(558\) 3.67715 + 2.67161i 0.155666 + 0.113098i
\(559\) −1.96059 6.03408i −0.0829242 0.255214i
\(560\) 6.59959 0.278884
\(561\) 0 0
\(562\) −31.3811 −1.32373
\(563\) 0.634561 + 1.95298i 0.0267436 + 0.0823082i 0.963537 0.267573i \(-0.0862218\pi\)
−0.936794 + 0.349882i \(0.886222\pi\)
\(564\) −13.2641 9.63693i −0.558519 0.405788i
\(565\) −29.7886 + 21.6427i −1.25322 + 0.910515i
\(566\) −9.02015 + 27.7612i −0.379145 + 1.16689i
\(567\) −0.692124 + 2.13014i −0.0290665 + 0.0894575i
\(568\) 7.92890 5.76068i 0.332689 0.241713i
\(569\) 2.64885 + 1.92450i 0.111046 + 0.0806793i 0.641922 0.766770i \(-0.278137\pi\)
−0.530877 + 0.847449i \(0.678137\pi\)
\(570\) −5.52239 16.9962i −0.231308 0.711891i
\(571\) 43.8897 1.83673 0.918363 0.395738i \(-0.129511\pi\)
0.918363 + 0.395738i \(0.129511\pi\)
\(572\) 0 0
\(573\) −1.22666 −0.0512446
\(574\) 0.732217 + 2.25353i 0.0305622 + 0.0940607i
\(575\) 4.53465 + 3.29461i 0.189108 + 0.137395i
\(576\) −34.7279 + 25.2313i −1.44700 + 1.05131i
\(577\) −13.5629 + 41.7422i −0.564630 + 1.73775i 0.104418 + 0.994533i \(0.466702\pi\)
−0.669048 + 0.743219i \(0.733298\pi\)
\(578\) 4.56684 14.0553i 0.189955 0.584623i
\(579\) 35.0968 25.4993i 1.45857 1.05972i
\(580\) −16.8985 12.2775i −0.701673 0.509795i
\(581\) −4.96572 15.2829i −0.206013 0.634042i
\(582\) 20.6076 0.854214
\(583\) 0 0
\(584\) −3.76915 −0.155969
\(585\) 11.3786 + 35.0197i 0.470447 + 1.44789i
\(586\) 4.02471 + 2.92412i 0.166259 + 0.120794i
\(587\) −2.25850 + 1.64090i −0.0932183 + 0.0677271i −0.633418 0.773810i \(-0.718349\pi\)
0.540200 + 0.841537i \(0.318349\pi\)
\(588\) 0.669603 2.06083i 0.0276140 0.0849871i
\(589\) −0.395410 + 1.21695i −0.0162926 + 0.0501434i
\(590\) −10.2726 + 7.46346i −0.422915 + 0.307266i
\(591\) 48.1259 + 34.9655i 1.97963 + 1.43829i
\(592\) −5.93732 18.2732i −0.244022 0.751023i
\(593\) −23.2526 −0.954871 −0.477435 0.878667i \(-0.658434\pi\)
−0.477435 + 0.878667i \(0.658434\pi\)
\(594\) 0 0
\(595\) 6.68312 0.273981
\(596\) −0.736985 2.26821i −0.0301881 0.0929093i
\(597\) 19.5334 + 14.1919i 0.799450 + 0.580835i
\(598\) −1.49887 + 1.08900i −0.0612935 + 0.0445324i
\(599\) 3.23215 9.94753i 0.132062 0.406445i −0.863059 0.505102i \(-0.831455\pi\)
0.995121 + 0.0986573i \(0.0314547\pi\)
\(600\) −18.8566 + 58.0347i −0.769818 + 2.36926i
\(601\) 18.0489 13.1133i 0.736229 0.534902i −0.155299 0.987868i \(-0.549634\pi\)
0.891528 + 0.452966i \(0.149634\pi\)
\(602\) 2.77738 + 2.01789i 0.113198 + 0.0822429i
\(603\) 3.84141 + 11.8226i 0.156434 + 0.481455i
\(604\) 2.17306 0.0884204
\(605\) 0 0
\(606\) 49.2083 1.99895
\(607\) −5.86774 18.0591i −0.238164 0.732994i −0.996686 0.0813464i \(-0.974078\pi\)
0.758522 0.651648i \(-0.225922\pi\)
\(608\) −5.27719 3.83410i −0.214018 0.155493i
\(609\) 18.4418 13.3987i 0.747299 0.542944i
\(610\) −1.28144 + 3.94387i −0.0518840 + 0.159683i
\(611\) 4.81572 14.8213i 0.194823 0.599604i
\(612\) −6.13382 + 4.45648i −0.247945 + 0.180143i
\(613\) 16.3111 + 11.8507i 0.658801 + 0.478647i 0.866258 0.499597i \(-0.166519\pi\)
−0.207457 + 0.978244i \(0.566519\pi\)
\(614\) 4.43714 + 13.6561i 0.179068 + 0.551116i
\(615\) −21.0068 −0.847077
\(616\) 0 0
\(617\) 7.03919 0.283387 0.141694 0.989911i \(-0.454745\pi\)
0.141694 + 0.989911i \(0.454745\pi\)
\(618\) 8.77046 + 26.9927i 0.352799 + 1.08581i
\(619\) 25.1467 + 18.2702i 1.01073 + 0.734340i 0.964363 0.264584i \(-0.0852346\pi\)
0.0463701 + 0.998924i \(0.485235\pi\)
\(620\) 1.67089 1.21397i 0.0671045 0.0487543i
\(621\) 1.54933 4.76834i 0.0621724 0.191347i
\(622\) −9.23646 + 28.4269i −0.370348 + 1.13982i
\(623\) −3.59066 + 2.60877i −0.143857 + 0.104518i
\(624\) −9.09645 6.60896i −0.364149 0.264570i
\(625\) −3.55266 10.9340i −0.142106 0.437358i
\(626\) −3.99947 −0.159851
\(627\) 0 0
\(628\) 16.2883 0.649973
\(629\) −6.01246 18.5045i −0.239733 0.737821i
\(630\) −16.1190 11.7111i −0.642195 0.466582i
\(631\) −17.7757 + 12.9148i −0.707639 + 0.514130i −0.882411 0.470479i \(-0.844081\pi\)
0.174772 + 0.984609i \(0.444081\pi\)
\(632\) 9.00596 27.7175i 0.358238 1.10254i
\(633\) −8.70991 + 26.8063i −0.346188 + 1.06546i
\(634\) −15.2537 + 11.0825i −0.605802 + 0.440141i
\(635\) 54.3852 + 39.5132i 2.15821 + 1.56803i
\(636\) 7.24675 + 22.3032i 0.287352 + 0.884379i
\(637\) 2.05965 0.0816064
\(638\) 0 0
\(639\) −16.4941 −0.652496
\(640\) −1.29215 3.97683i −0.0510768 0.157198i
\(641\) 10.7526 + 7.81222i 0.424702 + 0.308564i 0.779527 0.626369i \(-0.215460\pi\)
−0.354825 + 0.934933i \(0.615460\pi\)
\(642\) 9.05293 6.57734i 0.357291 0.259587i
\(643\) 4.53958 13.9714i 0.179024 0.550978i −0.820771 0.571258i \(-0.806456\pi\)
0.999794 + 0.0202797i \(0.00645568\pi\)
\(644\) −0.189050 + 0.581837i −0.00744963 + 0.0229276i
\(645\) −24.6229 + 17.8896i −0.969524 + 0.704401i
\(646\) 2.82962 + 2.05584i 0.111330 + 0.0808859i
\(647\) −1.89898 5.84446i −0.0746566 0.229770i 0.906764 0.421639i \(-0.138545\pi\)
−0.981420 + 0.191869i \(0.938545\pi\)
\(648\) 6.88426 0.270439
\(649\) 0 0
\(650\) −15.9404 −0.625236
\(651\) 0.696508 + 2.14363i 0.0272983 + 0.0840156i
\(652\) −5.04206 3.66327i −0.197462 0.143465i
\(653\) 32.9020 23.9047i 1.28755 0.935463i 0.287802 0.957690i \(-0.407076\pi\)
0.999753 + 0.0222266i \(0.00707554\pi\)
\(654\) −3.81664 + 11.7464i −0.149242 + 0.459321i
\(655\) −5.46044 + 16.8055i −0.213357 + 0.656646i
\(656\) 3.28460 2.38640i 0.128242 0.0931732i
\(657\) 5.13186 + 3.72852i 0.200213 + 0.145463i
\(658\) 2.60576 + 8.01970i 0.101583 + 0.312640i
\(659\) −18.0090 −0.701531 −0.350765 0.936463i \(-0.614079\pi\)
−0.350765 + 0.936463i \(0.614079\pi\)
\(660\) 0 0
\(661\) −17.1420 −0.666745 −0.333373 0.942795i \(-0.608187\pi\)
−0.333373 + 0.942795i \(0.608187\pi\)
\(662\) 0.426444 + 1.31246i 0.0165742 + 0.0510102i
\(663\) −9.21157 6.69260i −0.357748 0.259919i
\(664\) −39.9588 + 29.0318i −1.55070 + 1.12665i
\(665\) 1.73330 5.33455i 0.0672145 0.206865i
\(666\) −17.9247 + 55.1667i −0.694570 + 2.13767i
\(667\) −5.20670 + 3.78289i −0.201604 + 0.146474i
\(668\) 13.3118 + 9.67161i 0.515050 + 0.374206i
\(669\) −15.3679 47.2976i −0.594159 1.82863i
\(670\) −9.25613 −0.357596
\(671\) 0 0
\(672\) −11.4901 −0.443240
\(673\) 7.16690 + 22.0574i 0.276264 + 0.850252i 0.988882 + 0.148700i \(0.0475090\pi\)
−0.712619 + 0.701552i \(0.752491\pi\)
\(674\) 18.4658 + 13.4162i 0.711274 + 0.516771i
\(675\) 34.8989 25.3555i 1.34326 0.975934i
\(676\) 2.05129 6.31323i 0.0788959 0.242817i
\(677\) 8.51976 26.2211i 0.327441 1.00776i −0.642886 0.765962i \(-0.722263\pi\)
0.970327 0.241798i \(-0.0777371\pi\)
\(678\) −27.4613 + 19.9518i −1.05464 + 0.766243i
\(679\) 5.23278 + 3.80184i 0.200816 + 0.145901i
\(680\) −6.34771 19.5362i −0.243424 0.749181i
\(681\) −36.1111 −1.38378
\(682\) 0 0
\(683\) 21.9351 0.839322 0.419661 0.907681i \(-0.362149\pi\)
0.419661 + 0.907681i \(0.362149\pi\)
\(684\) 1.96638 + 6.05190i 0.0751865 + 0.231400i
\(685\) −25.4453 18.4871i −0.972214 0.706355i
\(686\) −0.901622 + 0.655067i −0.0344241 + 0.0250106i
\(687\) −4.04026 + 12.4346i −0.154146 + 0.474411i
\(688\) 1.81772 5.59437i 0.0692999 0.213283i
\(689\) −18.0334 + 13.1020i −0.687017 + 0.499147i
\(690\) 7.19020 + 5.22399i 0.273726 + 0.198874i
\(691\) −7.93142 24.4104i −0.301726 0.928616i −0.980879 0.194619i \(-0.937653\pi\)
0.679153 0.733996i \(-0.262347\pi\)
\(692\) −6.09830 −0.231823
\(693\) 0 0
\(694\) 30.3913 1.15364
\(695\) 13.9015 + 42.7845i 0.527315 + 1.62291i
\(696\) −56.6837 41.1832i −2.14859 1.56104i
\(697\) 3.32616 2.41660i 0.125987 0.0915353i
\(698\) 2.74972 8.46277i 0.104078 0.320321i
\(699\) 21.0757 64.8644i 0.797157 2.45340i
\(700\) −4.25839 + 3.09390i −0.160952 + 0.116939i
\(701\) −14.8968 10.8232i −0.562644 0.408785i 0.269781 0.962922i \(-0.413049\pi\)
−0.832426 + 0.554137i \(0.813049\pi\)
\(702\) 4.40614 + 13.5607i 0.166299 + 0.511815i
\(703\) −16.3298 −0.615892
\(704\) 0 0
\(705\) −74.7575 −2.81553
\(706\) −2.04385 6.29033i −0.0769214 0.236740i
\(707\) 12.4952 + 9.07828i 0.469930 + 0.341424i
\(708\) 5.77915 4.19880i 0.217194 0.157801i
\(709\) 7.31198 22.5039i 0.274607 0.845153i −0.714716 0.699415i \(-0.753444\pi\)
0.989323 0.145739i \(-0.0465559\pi\)
\(710\) 3.79518 11.6804i 0.142431 0.438356i
\(711\) −39.6806 + 28.8297i −1.48814 + 1.08120i
\(712\) 11.0365 + 8.01847i 0.413609 + 0.300505i
\(713\) −0.196647 0.605216i −0.00736447 0.0226655i
\(714\) 6.16097 0.230569
\(715\) 0 0
\(716\) 2.74452 0.102568
\(717\) 7.80782 + 24.0300i 0.291589 + 0.897417i
\(718\) −25.6244 18.6172i −0.956293 0.694787i
\(719\) −8.99808 + 6.53749i −0.335572 + 0.243807i −0.742791 0.669523i \(-0.766498\pi\)
0.407219 + 0.913330i \(0.366498\pi\)
\(720\) −10.5494 + 32.4678i −0.393154 + 1.21000i
\(721\) −2.75276 + 8.47213i −0.102518 + 0.315519i
\(722\) −14.7560 + 10.7208i −0.549160 + 0.398988i
\(723\) −43.8200 31.8371i −1.62968 1.18403i
\(724\) −3.70493 11.4026i −0.137693 0.423775i
\(725\) −55.3730 −2.05650
\(726\) 0 0
\(727\) 42.4803 1.57551 0.787753 0.615991i \(-0.211244\pi\)
0.787753 + 0.615991i \(0.211244\pi\)
\(728\) −1.95628 6.02083i −0.0725047 0.223147i
\(729\) 33.7270 + 24.5041i 1.24915 + 0.907561i
\(730\) −3.82117 + 2.77624i −0.141428 + 0.102753i
\(731\) 1.84072 5.66517i 0.0680817 0.209534i
\(732\) 0.720913 2.21874i 0.0266457 0.0820071i
\(733\) 17.9508 13.0420i 0.663029 0.481719i −0.204656 0.978834i \(-0.565607\pi\)
0.867684 + 0.497116i \(0.165607\pi\)
\(734\) −27.4106 19.9150i −1.01174 0.735075i
\(735\) −3.05318 9.39672i −0.112618 0.346603i
\(736\) 3.24402 0.119576
\(737\) 0 0
\(738\) −12.2571 −0.451189
\(739\) −9.09997 28.0068i −0.334748 1.03025i −0.966846 0.255359i \(-0.917806\pi\)
0.632098 0.774888i \(-0.282194\pi\)
\(740\) 21.3238 + 15.4926i 0.783878 + 0.569521i
\(741\) −7.73118 + 5.61703i −0.284012 + 0.206347i
\(742\) 3.72713 11.4709i 0.136827 0.421111i
\(743\) −5.22421 + 16.0785i −0.191658 + 0.589862i 0.808342 + 0.588714i \(0.200365\pi\)
−0.999999 + 0.00114815i \(0.999635\pi\)
\(744\) 5.60476 4.07210i 0.205481 0.149290i
\(745\) −8.79769 6.39190i −0.322322 0.234181i
\(746\) 4.96697 + 15.2868i 0.181854 + 0.559688i
\(747\) 83.1244 3.04136
\(748\) 0 0
\(749\) 3.51219 0.128333
\(750\) 6.61640 + 20.3632i 0.241597 + 0.743558i
\(751\) 1.25516 + 0.911929i 0.0458015 + 0.0332767i 0.610450 0.792054i \(-0.290988\pi\)
−0.564649 + 0.825331i \(0.690988\pi\)
\(752\) 11.6890 8.49253i 0.426253 0.309691i
\(753\) 2.53270 7.79484i 0.0922966 0.284060i
\(754\) 5.65591 17.4071i 0.205976 0.633929i
\(755\) 8.01610 5.82404i 0.291736 0.211958i
\(756\) 3.80909 + 2.76746i 0.138535 + 0.100652i
\(757\) 3.87713 + 11.9326i 0.140917 + 0.433697i 0.996463 0.0840286i \(-0.0267787\pi\)
−0.855547 + 0.517726i \(0.826779\pi\)
\(758\) 24.9721 0.907027
\(759\) 0 0
\(760\) −17.2404 −0.625375
\(761\) 2.79177 + 8.59218i 0.101202 + 0.311466i 0.988820 0.149113i \(-0.0476417\pi\)
−0.887619 + 0.460579i \(0.847642\pi\)
\(762\) 50.1362 + 36.4260i 1.81624 + 1.31958i
\(763\) −3.13619 + 2.27858i −0.113538 + 0.0824901i
\(764\) −0.100501 + 0.309310i −0.00363600 + 0.0111904i
\(765\) −10.6829 + 32.8787i −0.386242 + 1.18873i
\(766\) 30.3653 22.0617i 1.09714 0.797122i
\(767\) 5.49317 + 3.99102i 0.198347 + 0.144107i
\(768\) 13.4707 + 41.4587i 0.486083 + 1.49601i
\(769\) 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
\(772\) −3.55431 10.9390i −0.127922 0.393704i
\(773\) 14.8968 + 10.8231i 0.535800 + 0.389282i 0.822523 0.568732i \(-0.192566\pi\)
−0.286723 + 0.958014i \(0.592566\pi\)