Properties

Label 847.2.f.w.372.3
Level 847
Weight 2
Character 847.372
Analytic conductor 6.763
Analytic rank 0
Dimension 16
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 372.3
Root \(0.901622 + 0.655067i\)
Character \(\chi\) = 847.372
Dual form 847.2.f.w.148.3

$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(365\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.752356 0.658756i \(-0.771083\pi\)
0.995876 0.0907209i \(-0.0289171\pi\)
\(3\) 2.31283 1.68037i 1.33531 0.970163i 0.335712 0.941965i \(-0.391023\pi\)
0.999602 0.0281981i \(-0.00897692\pi\)
\(4\) 0.613206 + 0.445520i 0.306603 + 0.222760i
\(5\) 1.06799 + 3.28693i 0.477618 + 1.46996i 0.842394 + 0.538862i \(0.181146\pi\)
−0.364776 + 0.931095i \(0.618854\pi\)
\(6\) −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 \(-0.992200\pi\)
0.823175 + 0.567787i \(0.192200\pi\)
\(14\) −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 \(-0.0246550\pi\)
−0.852073 + 0.523422i \(0.824655\pi\)
\(18\) −4.66395 3.38856i −1.09930 0.798691i
\(19\) −1.31300 + 0.953952i −0.301223 + 0.218852i −0.728121 0.685448i \(-0.759606\pi\)
0.426898 + 0.904300i \(0.359606\pi\)
\(20\) −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 \(-0.565334\pi\)
−0.994076 + 0.108690i \(0.965334\pi\)
\(30\) 8.90830 6.47226i 1.62643 1.18167i
\(31\) 0.243635 0.749832i 0.0437582 0.134674i −0.926791 0.375578i \(-0.877444\pi\)
0.970549 + 0.240905i \(0.0774441\pi\)
\(32\) 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 −0.999507 0.0313960i \(-0.990005\pi\)
−0.338724 0.940886i \(-0.609995\pi\)
\(38\) 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 \(-0.646907\pi\)
0.713943 + 0.700203i \(0.246907\pi\)
\(42\) −0.984546 + 3.03012i −0.151919 + 0.467558i
\(43\) 3.08043 0.469761 0.234880 0.972024i \(-0.424530\pi\)
0.234880 + 0.972024i \(0.424530\pi\)
\(44\) 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 −0.936627 0.350327i \(-0.886070\pi\)
0.0437469 + 0.999043i \(0.486070\pi\)
\(48\) −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 −0.406540 0.913633i \(-0.633265\pi\)
0.865918 0.500186i \(-0.166735\pi\)
\(54\) −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 0.747701 0.664035i \(-0.231158\pi\)
−0.400483 + 0.916304i \(0.631158\pi\)
\(60\) 2.31420 + 7.12238i 0.298762 + 0.919495i
\(61\) −0.332696 1.02393i −0.0425974 0.131101i 0.927496 0.373833i \(-0.121957\pi\)
−0.970094 + 0.242731i \(0.921957\pi\)
\(62\) −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 0.875409 0.483383i \(-0.160592\pi\)
−0.992346 + 0.123487i \(0.960592\pi\)
\(72\) −4.91323 15.1214i −0.579030 1.78207i
\(73\) −0.992078 0.720787i −0.116114 0.0843617i 0.528213 0.849112i \(-0.322862\pi\)
−0.644327 + 0.764750i \(0.722862\pi\)
\(74\) −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 0.639639 + 0.768675i \(0.279084\pi\)
−0.969295 + 0.245901i \(0.920916\pi\)
\(80\) 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 −0.720851 0.693090i \(-0.756249\pi\)
0.175793 0.984427i \(-0.443751\pi\)
\(84\) −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 −0.796850 0.604177i \(-0.793502\pi\)
0.999792 0.0204129i \(-0.00649807\pi\)
\(98\) 1.11447 0.112578
\(99\) 0 0
\(100\) −5.26366 −0.526366
\(101\) −4.77274 + 14.6890i −0.474905 + 1.46161i 0.371181 + 0.928561i \(0.378953\pi\)
−0.846086 + 0.533047i \(0.821047\pi\)
\(102\) 4.98433 3.62133i 0.493522 0.358565i
\(103\) −7.20682 5.23606i −0.710109 0.515925i 0.173100 0.984904i \(-0.444622\pi\)
−0.883209 + 0.468980i \(0.844622\pi\)
\(104\) 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 \(-0.754302\pi\)
0.441908 + 0.897061i \(0.354302\pi\)
\(108\) 1.45494 4.47785i 0.140002 0.430881i
\(109\) 3.87655 0.371306 0.185653 0.982615i \(-0.440560\pi\)
0.185653 + 0.982615i \(0.440560\pi\)
\(110\) 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 −0.914070 0.405557i \(-0.867078\pi\)
0.103244 + 0.994656i \(0.467078\pi\)
\(114\) 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 0.747167 + 0.664637i \(0.231414\pi\)
−0.213807 + 0.976876i \(0.568586\pi\)
\(128\) −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 \(-0.428299\pi\)
0.223355 + 0.974737i \(0.428299\pi\)
\(132\) 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 0.996379 + 0.0850177i \(0.0270947\pi\)
−0.756116 + 0.654438i \(0.772905\pi\)
\(138\) 0.794662 + 2.44572i 0.0676461 + 0.208193i
\(139\) 10.5306 + 7.65095i 0.893197 + 0.648945i 0.936710 0.350108i \(-0.113855\pi\)
−0.0435129 + 0.999053i \(0.513855\pi\)
\(140\) 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 \(-0.141140\pi\)
−0.982952 + 0.183862i \(0.941140\pi\)
\(150\) 17.8999 + 13.0050i 1.46152 + 1.06186i
\(151\) −2.31942 + 1.68516i −0.188752 + 0.137136i −0.678148 0.734925i \(-0.737217\pi\)
0.489396 + 0.872062i \(0.337217\pi\)
\(152\) −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 0.391370 0.920234i \(-0.372001\pi\)
0.996134 0.0878468i \(-0.0279986\pi\)
\(158\) 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 0.800889 + 0.598812i \(0.204361\pi\)
−0.999906 + 0.0136985i \(0.995639\pi\)
\(164\) 1.61153 0.125840
\(165\) 0 0
\(166\) −17.9088 −1.38999
\(167\) −6.70832 + 20.6461i −0.519105 + 1.59764i 0.256581 + 0.966523i \(0.417404\pi\)
−0.775686 + 0.631119i \(0.782596\pi\)
\(168\) −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 \(-0.601060\pi\)
0.807056 + 0.590475i \(0.201060\pi\)
\(174\) −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 −0.472903 0.881115i \(-0.656794\pi\)
0.691855 + 0.722037i \(0.256794\pi\)
\(180\) 10.9627 + 7.96490i 0.817114 + 0.593668i
\(181\) 4.88800 + 15.0437i 0.363322 + 1.11819i 0.951025 + 0.309114i \(0.100033\pi\)
−0.587703 + 0.809077i \(0.699967\pi\)
\(182\) −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 0.575156 0.818044i \(-0.304942\pi\)
−0.600273 + 0.799795i \(0.704942\pi\)
\(192\) −7.33097 22.5624i −0.529067 1.62830i
\(193\) −4.68928 14.4321i −0.337542 1.03885i −0.965456 0.260564i \(-0.916091\pi\)
0.627915 0.778282i \(-0.283909\pi\)
\(194\) −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 \(-0.765772\pi\)
−0.741262 + 0.671216i \(0.765772\pi\)
\(198\) 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 0.789743 + 0.613438i \(0.210214\pi\)
−0.999485 + 0.0320823i \(0.989786\pi\)
\(212\) 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 −0.949006 0.315259i \(-0.897909\pi\)
0.00656992 + 0.999978i \(0.497909\pi\)
\(224\) −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 \(-0.162314\pi\)
−0.194517 + 0.980899i \(0.562314\pi\)
\(228\) −2.84512 + 2.06710i −0.188423 + 0.136897i
\(229\) 1.41326 4.34958i 0.0933910 0.287428i −0.893440 0.449183i \(-0.851715\pi\)
0.986831 + 0.161755i \(0.0517153\pi\)
\(230\) −3.10883 −0.204990
\(231\) 0 0
\(232\) −24.5084 −1.60905
\(233\) 7.37218 22.6893i 0.482968 1.48642i −0.351935 0.936025i \(-0.614476\pi\)
0.834903 0.550398i \(-0.185524\pi\)
\(234\) 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 \(-0.792275\pi\)
0.332006 + 0.943277i \(0.392275\pi\)
\(240\) 5.83024 17.9436i 0.376340 1.15826i
\(241\) 18.9464 1.22045 0.610224 0.792229i \(-0.291079\pi\)
0.610224 + 0.792229i \(0.291079\pi\)
\(242\) 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 −0.975115 0.221699i \(-0.928840\pi\)
0.919196 + 0.393800i \(0.128840\pi\)
\(252\) −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 −0.145347 0.989381i \(-0.546430\pi\)
−0.985872 + 0.167502i \(0.946430\pi\)
\(258\) −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 \(-0.490276\pi\)
0.0305448 + 0.999533i \(0.490276\pi\)
\(264\) 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 0.860189 0.509975i \(-0.170345\pi\)
−0.995664 + 0.0930279i \(0.970345\pi\)
\(270\) −7.39345 22.7547i −0.449951 1.38481i
\(271\) 21.9764 + 15.9668i 1.33497 + 0.969912i 0.999613 + 0.0278207i \(0.00885676\pi\)
0.335356 + 0.942091i \(0.391143\pi\)
\(272\) 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 −0.543417 0.839463i \(-0.682870\pi\)
0.933058 0.359727i \(-0.117130\pi\)
\(278\) 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 −0.775741 0.631051i \(-0.782624\pi\)
0.256665 0.966500i \(-0.417376\pi\)
\(282\) 19.5027 + 14.1696i 1.16137 + 0.843786i
\(283\) 21.1896 15.3951i 1.25959 0.915145i 0.260851 0.965379i \(-0.415997\pi\)
0.998737 + 0.0502344i \(0.0159969\pi\)
\(284\) 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 \(-0.258377\pi\)
−0.477279 + 0.878752i \(0.658377\pi\)
\(294\) 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 \(-0.380157\pi\)
0.367667 + 0.929957i \(0.380157\pi\)
\(308\) 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 −0.996917 0.0784574i \(-0.975001\pi\)
−0.233447 + 0.972370i \(0.575001\pi\)
\(312\) 14.6418 + 10.6379i 0.828928 + 0.602251i
\(313\) 1.10896 + 3.41304i 0.0626824 + 0.192917i 0.977494 0.210965i \(-0.0676607\pi\)
−0.914811 + 0.403882i \(0.867661\pi\)
\(314\) −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 0.690046 + 0.723766i \(0.257590\pi\)
−0.983678 + 0.179940i \(0.942410\pi\)
\(318\) −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 \(-0.111636\pi\)
−0.0365484 + 0.999332i \(0.511636\pi\)
\(338\) 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 0.874187 + 0.485589i \(0.161395\pi\)
−0.421810 + 0.906684i \(0.638605\pi\)
\(348\) −13.9782 10.1558i −0.749311 0.544406i
\(349\) −6.45947 + 4.69308i −0.345767 + 0.251215i −0.747091 0.664721i \(-0.768550\pi\)
0.401324 + 0.915936i \(0.368550\pi\)
\(350\) 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 \(-0.569938\pi\)
−0.995544 + 0.0943020i \(0.969938\pi\)
\(360\) 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 0.999662 0.0259840i \(-0.00827188\pi\)
0.284200 + 0.958765i \(0.408272\pi\)
\(368\) 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 \(-0.378197\pi\)
0.373386 + 0.927676i \(0.378197\pi\)
\(374\) 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 −0.955618 0.294607i \(-0.904811\pi\)
0.599946 0.800041i \(-0.295189\pi\)
\(380\) −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 −0.218710 0.975790i \(-0.570185\pi\)
0.750495 0.660876i \(-0.229815\pi\)
\(384\) −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 0.536878 0.843660i \(-0.319604\pi\)
−0.636464 + 0.771306i \(0.719604\pi\)
\(390\) 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 0.999559 0.0296950i \(-0.00945359\pi\)
−0.826114 + 0.563502i \(0.809454\pi\)
\(402\) −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 −0.430679 0.902505i \(-0.641726\pi\)
0.878906 0.476995i \(-0.158274\pi\)
\(410\) 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 −0.525822 0.850595i \(-0.676242\pi\)
0.646476 + 0.762934i \(0.276242\pi\)
\(422\) 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 \(-0.841859\pi\)
0.991366 + 0.131125i \(0.0418588\pi\)
\(432\) −9.59634 + 6.97215i −0.461704 + 0.335448i
\(433\) 26.0193 + 18.9041i 1.25041 + 0.908474i 0.998245 0.0592114i \(-0.0188586\pi\)
0.252161 + 0.967685i \(0.418859\pi\)
\(434\) 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 \(-0.535526\pi\)
−0.111378 + 0.993778i \(0.535526\pi\)
\(440\) 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 −0.868042 0.496490i \(-0.834622\pi\)
0.203951 + 0.978981i \(0.434622\pi\)
\(444\) −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 0.751651 + 0.659561i \(0.229258\pi\)
−0.995779 + 0.0917865i \(0.970742\pi\)
\(450\) 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 −0.976310 0.216375i \(-0.930577\pi\)
0.662670 0.748912i \(-0.269423\pi\)
\(458\) −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 \(-0.545204\pi\)
−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 \(0.538163\pi\)
\(464\) −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 0.919116 0.393987i \(-0.128904\pi\)
−0.975160 + 0.221501i \(0.928904\pi\)
\(468\) 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 −0.999264 0.0383508i \(-0.987790\pi\)
0.785880 0.618379i \(-0.212210\pi\)
\(480\) 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 −0.943354 0.331788i \(-0.892348\pi\)
0.0240370 + 0.999711i \(0.492348\pi\)
\(488\) −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 −0.998511 0.0545479i \(-0.982628\pi\)
−0.360435 0.932784i \(-0.617372\pi\)
\(492\) 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 0.988768 0.149458i \(-0.0477530\pi\)
0.163403 + 0.986559i \(0.447753\pi\)
\(500\) −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 \(-0.559157\pi\)
0.877579 + 0.479432i \(0.159157\pi\)
\(504\) −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 −0.631973 0.774991i \(-0.717754\pi\)
0.541770 + 0.840527i \(0.317754\pi\)
\(510\) 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 0.291612 0.956537i \(-0.405809\pi\)
−0.819608 + 0.572925i \(0.805809\pi\)
\(522\) 14.2049 + 43.7181i 0.621730 + 1.91349i
\(523\) −3.06082 9.42024i −0.133840 0.411918i 0.861567 0.507643i \(-0.169483\pi\)
−0.995408 + 0.0957248i \(0.969483\pi\)
\(524\) 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 0.691687 + 0.722197i \(0.256868\pi\)
−0.984084 + 0.177706i \(0.943132\pi\)
\(542\) 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 \(-0.625388\pi\)
0.759615 + 0.650373i \(0.225388\pi\)
\(548\) −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 \(-0.552258\pi\)
−0.988773 + 0.149423i \(0.952258\pi\)
\(558\) −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 \(-0.913778\pi\)
0.936794 + 0.349882i \(0.113778\pi\)
\(564\) −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 \(-0.721863\pi\)
0.530877 + 0.847449i \(0.321863\pi\)
\(570\) −5.52239 + 16.9962i −0.231308 + 0.711891i
\(571\) −43.8897 −1.83673 −0.918363 0.395738i \(-0.870489\pi\)
−0.918363 + 0.395738i \(0.870489\pi\)
\(572\) 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 −0.669048 0.743219i \(-0.733298\pi\)
0.104418 0.994533i \(-0.466702\pi\)
\(578\) −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 0.540200 0.841537i \(-0.318349\pi\)
−0.633418 + 0.773810i \(0.718349\pi\)
\(588\) 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 \(-0.341566\pi\)
0.477435 + 0.878667i \(0.341566\pi\)
\(594\) 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 0.995121 0.0986573i \(-0.0314547\pi\)
−0.863059 + 0.505102i \(0.831455\pi\)
\(600\) 18.8566 + 58.0347i 0.769818 + 2.36926i
\(601\) −18.0489 13.1133i −0.736229 0.534902i 0.155299 0.987868i \(-0.450366\pi\)
−0.891528 + 0.452966i \(0.850366\pi\)
\(602\) −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 −0.758522 0.651648i \(-0.774078\pi\)
0.996686 0.0813464i \(-0.0259220\pi\)
\(608\) −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 \(-0.833481\pi\)
0.207457 + 0.978244i \(0.433481\pi\)
\(614\) 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 0.0463701 0.998924i \(-0.485235\pi\)
0.964363 + 0.264584i \(0.0852346\pi\)
\(620\) 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 0.174772 0.984609i \(-0.444081\pi\)
−0.882411 + 0.470479i \(0.844081\pi\)
\(632\) 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 −0.354825 0.934933i \(-0.615460\pi\)
0.779527 + 0.626369i \(0.215460\pi\)
\(642\) 9.05293 + 6.57734i 0.357291 + 0.259587i
\(643\) 4.53958 + 13.9714i 0.179024 + 0.550978i 0.999794 0.0202797i \(-0.00645568\pi\)
−0.820771 + 0.571258i \(0.806456\pi\)
\(644\) 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 −0.981420 0.191869i \(-0.938545\pi\)
0.906764 + 0.421639i \(0.138545\pi\)
\(648\) −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 0.999753 0.0222266i \(-0.00707554\pi\)
0.287802 + 0.957690i \(0.407076\pi\)
\(654\) −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 \(-0.385921\pi\)
0.350765 + 0.936463i \(0.385921\pi\)
\(660\) 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 0.712619 + 0.701552i \(0.247509\pi\)
−0.988882 + 0.148700i \(0.952491\pi\)
\(674\) 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 −0.970327 0.241798i \(-0.922263\pi\)
0.642886 0.765962i \(-0.277737\pi\)
\(678\) 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 0.679153 + 0.733996i \(0.262347\pi\)
−0.980879 + 0.194619i \(0.937653\pi\)
\(692\) 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 \(-0.586951\pi\)
0.832426 + 0.554137i \(0.186951\pi\)
\(702\) 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 0.989323 + 0.145739i \(0.0465559\pi\)
−0.714716 + 0.699415i \(0.753444\pi\)
\(710\) −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 0.407219 0.913330i \(-0.366498\pi\)
−0.742791 + 0.669523i \(0.766498\pi\)
\(720\) −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 \(-0.434393\pi\)
−0.867684 + 0.497116i \(0.834393\pi\)
\(734\) 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 −0.632098 0.774888i \(-0.717806\pi\)
0.966846 0.255359i \(-0.0821938\pi\)
\(740\) 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 0.999999 + 0.00114815i \(0.000365467\pi\)
−0.808342 + 0.588714i \(0.799635\pi\)
\(744\) −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 −0.564649 0.825331i \(-0.690988\pi\)
0.610450 + 0.792054i \(0.290988\pi\)
\(752\) 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 −0.855547 0.517726i \(-0.826779\pi\)
0.996463 + 0.0840286i \(0.0267787\pi\)
\(758\) −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 \(-0.952358\pi\)
0.887619 + 0.460579i \(0.152358\pi\)
\(762\) 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 \(-0.593982\pi\)
−0.290981 + 0.956729i \(0.593982\pi\)
\(770\) 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 −0.286723 0.958014i \(-0.592566\pi\)
0.822523 + 0.568732i \(0.192566\pi\)