Properties

Label 729.2.i.a.685.19
Level $729$
Weight $2$
Character 729.685
Analytic conductor $5.821$
Analytic rank $0$
Dimension $1404$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.i (of order \(81\), degree \(54\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(1404\)
Relative dimension: \(26\) over \(\Q(\zeta_{81})\)
Twist minimal: no (minimal twist has level 243)
Sato-Tate group: $\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label 685.19
Character \(\chi\) \(=\) 729.685
Dual form 729.2.i.a.613.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36720 + 0.380585i) q^{2} +(0.0120479 + 0.00727097i) q^{4} +(2.11465 - 0.0820581i) q^{5} +(1.64831 + 0.257791i) q^{7} +(-1.93410 - 2.05002i) q^{8} +O(q^{10})\) \(q+(1.36720 + 0.380585i) q^{2} +(0.0120479 + 0.00727097i) q^{4} +(2.11465 - 0.0820581i) q^{5} +(1.64831 + 0.257791i) q^{7} +(-1.93410 - 2.05002i) q^{8} +(2.92238 + 0.692616i) q^{10} +(0.699652 + 5.12236i) q^{11} +(3.44321 - 5.02032i) q^{13} +(2.15545 + 0.979773i) q^{14} +(-1.87720 - 3.56377i) q^{16} +(1.16391 - 0.584539i) q^{17} +(0.0591164 + 1.01499i) q^{19} +(0.0260739 + 0.0143869i) q^{20} +(-0.992932 + 7.26955i) q^{22} +(0.0433815 - 0.112361i) q^{23} +(-0.519946 + 0.0404134i) q^{25} +(6.61820 - 5.55333i) q^{26} +(0.0179844 + 0.0150907i) q^{28} +(2.48271 + 1.77454i) q^{29} +(2.39439 - 2.74366i) q^{31} +(-0.0168520 - 0.0777973i) q^{32} +(1.81376 - 0.356212i) q^{34} +(3.50675 + 0.409881i) q^{35} +(4.61774 + 6.20270i) q^{37} +(-0.305466 + 1.41019i) q^{38} +(-4.25816 - 4.17637i) q^{40} +(0.596270 - 2.31486i) q^{41} +(3.38429 + 3.07108i) q^{43} +(-0.0288152 + 0.0668011i) q^{44} +(0.102074 - 0.137109i) q^{46} +(-7.20444 - 8.25537i) q^{47} +(-4.01527 - 1.28744i) q^{49} +(-0.726249 - 0.142631i) q^{50} +(0.0779862 - 0.0354491i) q^{52} +(0.302416 - 1.71509i) q^{53} +(1.89985 + 10.7746i) q^{55} +(-2.65951 - 3.87766i) q^{56} +(2.71899 + 3.37102i) q^{58} +(-8.73103 + 3.56702i) q^{59} +(1.96222 - 1.18420i) q^{61} +(4.31780 - 2.83986i) q^{62} +(-0.461840 + 7.92948i) q^{64} +(6.86923 - 10.8988i) q^{65} +(-9.88876 + 7.06806i) q^{67} +(0.0182729 + 0.00142028i) q^{68} +(4.63843 + 1.89501i) q^{70} +(-1.31428 - 4.38998i) q^{71} +(-4.13087 + 0.979034i) q^{73} +(3.95270 + 10.2377i) q^{74} +(-0.00666773 + 0.0126584i) q^{76} +(-0.167255 + 8.62360i) q^{77} +(-10.9439 + 10.7337i) q^{79} +(-4.26206 - 7.38210i) q^{80} +(1.69622 - 2.93794i) q^{82} +(3.80074 + 14.7554i) q^{83} +(2.41330 - 1.33160i) q^{85} +(3.45818 + 5.48678i) q^{86} +(9.14776 - 11.3414i) q^{88} +(3.04886 - 10.1839i) q^{89} +(6.96967 - 7.38742i) q^{91} +(0.00133963 - 0.00103829i) q^{92} +(-6.70801 - 14.0286i) q^{94} +(0.208299 + 2.14150i) q^{95} +(-11.8871 - 0.461274i) q^{97} +(-4.99968 - 3.28834i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{81}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36720 + 0.380585i 0.966754 + 0.269114i 0.715349 0.698768i \(-0.246268\pi\)
0.251405 + 0.967882i \(0.419107\pi\)
\(3\) 0 0
\(4\) 0.0120479 + 0.00727097i 0.00602397 + 0.00363549i
\(5\) 2.11465 0.0820581i 0.945701 0.0366975i 0.438691 0.898638i \(-0.355442\pi\)
0.507010 + 0.861940i \(0.330751\pi\)
\(6\) 0 0
\(7\) 1.64831 + 0.257791i 0.623002 + 0.0974358i 0.458139 0.888881i \(-0.348516\pi\)
0.164863 + 0.986316i \(0.447282\pi\)
\(8\) −1.93410 2.05002i −0.683806 0.724792i
\(9\) 0 0
\(10\) 2.92238 + 0.692616i 0.924136 + 0.219024i
\(11\) 0.699652 + 5.12236i 0.210953 + 1.54445i 0.726246 + 0.687435i \(0.241264\pi\)
−0.515292 + 0.857014i \(0.672317\pi\)
\(12\) 0 0
\(13\) 3.44321 5.02032i 0.954974 1.39239i 0.0354424 0.999372i \(-0.488716\pi\)
0.919532 0.393015i \(-0.128568\pi\)
\(14\) 2.15545 + 0.979773i 0.576069 + 0.261855i
\(15\) 0 0
\(16\) −1.87720 3.56377i −0.469300 0.890943i
\(17\) 1.16391 0.584539i 0.282290 0.141771i −0.302021 0.953301i \(-0.597661\pi\)
0.584311 + 0.811530i \(0.301365\pi\)
\(18\) 0 0
\(19\) 0.0591164 + 1.01499i 0.0135622 + 0.232855i 0.998277 + 0.0586793i \(0.0186889\pi\)
−0.984715 + 0.174175i \(0.944274\pi\)
\(20\) 0.0260739 + 0.0143869i 0.00583029 + 0.00321702i
\(21\) 0 0
\(22\) −0.992932 + 7.26955i −0.211694 + 1.54987i
\(23\) 0.0433815 0.112361i 0.00904566 0.0234289i −0.928287 0.371864i \(-0.878719\pi\)
0.937333 + 0.348435i \(0.113287\pi\)
\(24\) 0 0
\(25\) −0.519946 + 0.0404134i −0.103989 + 0.00808268i
\(26\) 6.61820 5.55333i 1.29794 1.08910i
\(27\) 0 0
\(28\) 0.0179844 + 0.0150907i 0.00339872 + 0.00285187i
\(29\) 2.48271 + 1.77454i 0.461028 + 0.329523i 0.788176 0.615450i \(-0.211026\pi\)
−0.327148 + 0.944973i \(0.606088\pi\)
\(30\) 0 0
\(31\) 2.39439 2.74366i 0.430045 0.492777i −0.496988 0.867758i \(-0.665561\pi\)
0.927033 + 0.374981i \(0.122351\pi\)
\(32\) −0.0168520 0.0777973i −0.00297903 0.0137528i
\(33\) 0 0
\(34\) 1.81376 0.356212i 0.311058 0.0610898i
\(35\) 3.50675 + 0.409881i 0.592750 + 0.0692825i
\(36\) 0 0
\(37\) 4.61774 + 6.20270i 0.759151 + 1.01972i 0.998806 + 0.0488587i \(0.0155584\pi\)
−0.239655 + 0.970858i \(0.577034\pi\)
\(38\) −0.305466 + 1.41019i −0.0495532 + 0.228763i
\(39\) 0 0
\(40\) −4.25816 4.17637i −0.673274 0.660343i
\(41\) 0.596270 2.31486i 0.0931217 0.361521i −0.904809 0.425817i \(-0.859987\pi\)
0.997931 + 0.0642967i \(0.0204804\pi\)
\(42\) 0 0
\(43\) 3.38429 + 3.07108i 0.516100 + 0.468335i 0.887939 0.459962i \(-0.152137\pi\)
−0.371839 + 0.928297i \(0.621273\pi\)
\(44\) −0.0288152 + 0.0668011i −0.00434405 + 0.0100706i
\(45\) 0 0
\(46\) 0.102074 0.137109i 0.0150500 0.0202156i
\(47\) −7.20444 8.25537i −1.05087 1.20417i −0.978383 0.206800i \(-0.933695\pi\)
−0.0724917 0.997369i \(-0.523095\pi\)
\(48\) 0 0
\(49\) −4.01527 1.28744i −0.573610 0.183921i
\(50\) −0.726249 0.142631i −0.102707 0.0201710i
\(51\) 0 0
\(52\) 0.0779862 0.0354491i 0.0108147 0.00491591i
\(53\) 0.302416 1.71509i 0.0415400 0.235585i −0.956968 0.290194i \(-0.906280\pi\)
0.998508 + 0.0546090i \(0.0173912\pi\)
\(54\) 0 0
\(55\) 1.89985 + 10.7746i 0.256176 + 1.45285i
\(56\) −2.65951 3.87766i −0.355392 0.518175i
\(57\) 0 0
\(58\) 2.71899 + 3.37102i 0.357021 + 0.442637i
\(59\) −8.73103 + 3.56702i −1.13668 + 0.464386i −0.866874 0.498528i \(-0.833874\pi\)
−0.269809 + 0.962914i \(0.586961\pi\)
\(60\) 0 0
\(61\) 1.96222 1.18420i 0.251236 0.151622i −0.385489 0.922712i \(-0.625967\pi\)
0.636726 + 0.771090i \(0.280288\pi\)
\(62\) 4.31780 2.83986i 0.548361 0.360663i
\(63\) 0 0
\(64\) −0.461840 + 7.92948i −0.0577300 + 0.991186i
\(65\) 6.86923 10.8988i 0.852023 1.35183i
\(66\) 0 0
\(67\) −9.88876 + 7.06806i −1.20810 + 0.863501i −0.993570 0.113216i \(-0.963885\pi\)
−0.214534 + 0.976717i \(0.568823\pi\)
\(68\) 0.0182729 + 0.00142028i 0.00221592 + 0.000172235i
\(69\) 0 0
\(70\) 4.63843 + 1.89501i 0.554398 + 0.226497i
\(71\) −1.31428 4.38998i −0.155976 0.520995i 0.843904 0.536494i \(-0.180252\pi\)
−0.999880 + 0.0154987i \(0.995066\pi\)
\(72\) 0 0
\(73\) −4.13087 + 0.979034i −0.483482 + 0.114587i −0.465126 0.885244i \(-0.653991\pi\)
−0.0183553 + 0.999832i \(0.505843\pi\)
\(74\) 3.95270 + 10.2377i 0.459492 + 1.19011i
\(75\) 0 0
\(76\) −0.00666773 + 0.0126584i −0.000764841 + 0.00145202i
\(77\) −0.167255 + 8.62360i −0.0190604 + 0.982750i
\(78\) 0 0
\(79\) −10.9439 + 10.7337i −1.23128 + 1.20763i −0.261087 + 0.965315i \(0.584081\pi\)
−0.970197 + 0.242319i \(0.922092\pi\)
\(80\) −4.26206 7.38210i −0.476512 0.825344i
\(81\) 0 0
\(82\) 1.69622 2.93794i 0.187316 0.324441i
\(83\) 3.80074 + 14.7554i 0.417186 + 1.61961i 0.739622 + 0.673023i \(0.235004\pi\)
−0.322436 + 0.946591i \(0.604502\pi\)
\(84\) 0 0
\(85\) 2.41330 1.33160i 0.261759 0.144433i
\(86\) 3.45818 + 5.48678i 0.372906 + 0.591655i
\(87\) 0 0
\(88\) 9.14776 11.3414i 0.975154 1.20900i
\(89\) 3.04886 10.1839i 0.323179 1.07949i −0.629877 0.776695i \(-0.716895\pi\)
0.953055 0.302796i \(-0.0979202\pi\)
\(90\) 0 0
\(91\) 6.96967 7.38742i 0.730620 0.774412i
\(92\) 0.00133963 0.00103829i 0.000139666 0.000108249i
\(93\) 0 0
\(94\) −6.70801 14.0286i −0.691878 1.44694i
\(95\) 0.208299 + 2.14150i 0.0213710 + 0.219713i
\(96\) 0 0
\(97\) −11.8871 0.461274i −1.20695 0.0468352i −0.572571 0.819855i \(-0.694054\pi\)
−0.634381 + 0.773020i \(0.718745\pi\)
\(98\) −4.99968 3.28834i −0.505044 0.332173i
\(99\) 0 0
\(100\) −0.00655813 0.00329361i −0.000655813 0.000329361i
\(101\) −0.314783 16.2301i −0.0313221 1.61496i −0.605239 0.796044i \(-0.706922\pi\)
0.573917 0.818914i \(-0.305423\pi\)
\(102\) 0 0
\(103\) −5.39414 4.18077i −0.531500 0.411944i 0.311186 0.950349i \(-0.399274\pi\)
−0.842686 + 0.538405i \(0.819027\pi\)
\(104\) −16.9513 + 2.65113i −1.66221 + 0.259965i
\(105\) 0 0
\(106\) 1.06620 2.22976i 0.103558 0.216574i
\(107\) 1.03937 + 0.378301i 0.100480 + 0.0365717i 0.391771 0.920063i \(-0.371863\pi\)
−0.291291 + 0.956634i \(0.594085\pi\)
\(108\) 0 0
\(109\) 16.6084 6.04495i 1.59079 0.579002i 0.613279 0.789867i \(-0.289850\pi\)
0.977515 + 0.210865i \(0.0676280\pi\)
\(110\) −1.50318 + 15.4540i −0.143323 + 1.47349i
\(111\) 0 0
\(112\) −2.17550 6.35812i −0.205565 0.600786i
\(113\) −7.55180 + 6.85290i −0.710414 + 0.644666i −0.944864 0.327462i \(-0.893807\pi\)
0.234451 + 0.972128i \(0.424671\pi\)
\(114\) 0 0
\(115\) 0.0825166 0.241164i 0.00769471 0.0224886i
\(116\) 0.0170090 + 0.0394312i 0.00157924 + 0.00366110i
\(117\) 0 0
\(118\) −13.2946 + 1.55391i −1.22387 + 0.143049i
\(119\) 2.06918 0.663455i 0.189681 0.0608188i
\(120\) 0 0
\(121\) −15.1520 + 4.21784i −1.37745 + 0.383440i
\(122\) 3.13343 0.872250i 0.283687 0.0789698i
\(123\) 0 0
\(124\) 0.0487966 0.0156460i 0.00438206 0.00140505i
\(125\) −11.6059 + 1.35653i −1.03806 + 0.121332i
\(126\) 0 0
\(127\) 2.24490 + 5.20427i 0.199203 + 0.461804i 0.988311 0.152450i \(-0.0487163\pi\)
−0.789108 + 0.614254i \(0.789457\pi\)
\(128\) −3.70081 + 10.8160i −0.327108 + 0.956011i
\(129\) 0 0
\(130\) 13.5395 12.2864i 1.18749 1.07759i
\(131\) −4.12091 12.0438i −0.360046 1.05227i −0.966392 0.257073i \(-0.917242\pi\)
0.606346 0.795201i \(-0.292635\pi\)
\(132\) 0 0
\(133\) −0.164213 + 1.68826i −0.0142391 + 0.146390i
\(134\) −16.2099 + 5.89991i −1.40032 + 0.509675i
\(135\) 0 0
\(136\) −3.44944 1.25549i −0.295787 0.107658i
\(137\) −10.0033 + 20.9201i −0.854640 + 1.78733i −0.303747 + 0.952753i \(0.598238\pi\)
−0.550893 + 0.834576i \(0.685713\pi\)
\(138\) 0 0
\(139\) −16.6551 + 2.60481i −1.41267 + 0.220937i −0.814374 0.580341i \(-0.802919\pi\)
−0.598292 + 0.801278i \(0.704154\pi\)
\(140\) 0.0392690 + 0.0304357i 0.00331883 + 0.00257229i
\(141\) 0 0
\(142\) −0.126109 6.50217i −0.0105829 0.545650i
\(143\) 28.1249 + 14.1249i 2.35193 + 1.18118i
\(144\) 0 0
\(145\) 5.39568 + 3.54880i 0.448087 + 0.294712i
\(146\) −6.02032 0.233616i −0.498245 0.0193342i
\(147\) 0 0
\(148\) 0.0105346 + 0.108305i 0.000865939 + 0.00890263i
\(149\) −4.02502 8.41762i −0.329743 0.689598i 0.668807 0.743436i \(-0.266805\pi\)
−0.998550 + 0.0538379i \(0.982855\pi\)
\(150\) 0 0
\(151\) 6.37590 4.94169i 0.518863 0.402149i −0.319229 0.947678i \(-0.603424\pi\)
0.838092 + 0.545528i \(0.183671\pi\)
\(152\) 1.96641 2.08428i 0.159497 0.169057i
\(153\) 0 0
\(154\) −3.51068 + 11.7265i −0.282899 + 0.944948i
\(155\) 4.83816 5.99837i 0.388610 0.481801i
\(156\) 0 0
\(157\) 0.839314 + 1.33166i 0.0669846 + 0.106278i 0.877808 0.479012i \(-0.159005\pi\)
−0.810824 + 0.585291i \(0.800980\pi\)
\(158\) −19.0475 + 10.5100i −1.51534 + 0.836129i
\(159\) 0 0
\(160\) −0.0420199 0.163131i −0.00332197 0.0128967i
\(161\) 0.100472 0.174022i 0.00791828 0.0137149i
\(162\) 0 0
\(163\) −3.29213 5.70214i −0.257860 0.446626i 0.707808 0.706404i \(-0.249684\pi\)
−0.965668 + 0.259778i \(0.916351\pi\)
\(164\) 0.0240151 0.0235539i 0.00187527 0.00183925i
\(165\) 0 0
\(166\) −0.419320 + 21.6200i −0.0325455 + 1.67804i
\(167\) 6.73795 12.7917i 0.521398 0.989850i −0.472685 0.881231i \(-0.656715\pi\)
0.994083 0.108619i \(-0.0346428\pi\)
\(168\) 0 0
\(169\) −8.66563 22.4446i −0.666587 1.72650i
\(170\) 3.80625 0.902098i 0.291926 0.0691877i
\(171\) 0 0
\(172\) 0.0184440 + 0.0616073i 0.00140634 + 0.00469751i
\(173\) −9.77211 3.99235i −0.742960 0.303533i −0.0250668 0.999686i \(-0.507980\pi\)
−0.717893 + 0.696153i \(0.754893\pi\)
\(174\) 0 0
\(175\) −0.867450 0.0674235i −0.0655731 0.00509674i
\(176\) 16.9415 12.1091i 1.27702 0.912757i
\(177\) 0 0
\(178\) 8.04424 12.7630i 0.602941 0.956631i
\(179\) −0.116577 + 2.00154i −0.00871335 + 0.149602i 0.991145 + 0.132783i \(0.0423912\pi\)
−0.999859 + 0.0168198i \(0.994646\pi\)
\(180\) 0 0
\(181\) −5.53808 + 3.64245i −0.411642 + 0.270741i −0.738395 0.674368i \(-0.764416\pi\)
0.326753 + 0.945110i \(0.394046\pi\)
\(182\) 12.3404 7.44750i 0.914735 0.552045i
\(183\) 0 0
\(184\) −0.314246 + 0.128384i −0.0231665 + 0.00946457i
\(185\) 10.2739 + 12.7376i 0.755351 + 0.936488i
\(186\) 0 0
\(187\) 3.80855 + 5.55300i 0.278509 + 0.406076i
\(188\) −0.0267741 0.151844i −0.00195270 0.0110743i
\(189\) 0 0
\(190\) −0.530237 + 3.00713i −0.0384675 + 0.218160i
\(191\) 19.2903 8.76853i 1.39580 0.634468i 0.432189 0.901783i \(-0.357741\pi\)
0.963609 + 0.267315i \(0.0861363\pi\)
\(192\) 0 0
\(193\) 10.9658 + 2.15360i 0.789333 + 0.155020i 0.571104 0.820878i \(-0.306515\pi\)
0.218229 + 0.975898i \(0.429972\pi\)
\(194\) −16.0764 5.15471i −1.15422 0.370086i
\(195\) 0 0
\(196\) −0.0390148 0.0447060i −0.00278677 0.00319328i
\(197\) −9.25641 + 12.4335i −0.659492 + 0.885852i −0.998490 0.0549355i \(-0.982505\pi\)
0.338998 + 0.940787i \(0.389912\pi\)
\(198\) 0 0
\(199\) 7.90454 18.3248i 0.560338 1.29901i −0.368879 0.929477i \(-0.620258\pi\)
0.929218 0.369533i \(-0.120482\pi\)
\(200\) 1.08847 + 0.987737i 0.0769667 + 0.0698436i
\(201\) 0 0
\(202\) 5.74657 22.3096i 0.404328 1.56970i
\(203\) 3.63482 + 3.56500i 0.255114 + 0.250214i
\(204\) 0 0
\(205\) 1.07095 4.94406i 0.0747984 0.345308i
\(206\) −5.78371 7.76887i −0.402970 0.541283i
\(207\) 0 0
\(208\) −24.3549 2.84668i −1.68871 0.197381i
\(209\) −5.15778 + 1.01296i −0.356771 + 0.0700676i
\(210\) 0 0
\(211\) 5.85071 + 27.0099i 0.402780 + 1.85944i 0.502728 + 0.864445i \(0.332330\pi\)
−0.0999485 + 0.994993i \(0.531868\pi\)
\(212\) 0.0161138 0.0184644i 0.00110670 0.00126814i
\(213\) 0 0
\(214\) 1.27705 + 0.912781i 0.0872974 + 0.0623964i
\(215\) 7.40860 + 6.21656i 0.505263 + 0.423966i
\(216\) 0 0
\(217\) 4.65399 3.90516i 0.315933 0.265099i
\(218\) 25.0075 1.94374i 1.69372 0.131647i
\(219\) 0 0
\(220\) −0.0554525 + 0.143626i −0.00373861 + 0.00968323i
\(221\) 1.07302 7.85590i 0.0721792 0.528445i
\(222\) 0 0
\(223\) 13.7856 + 7.60659i 0.923155 + 0.509375i 0.872104 0.489321i \(-0.162755\pi\)
0.0510509 + 0.998696i \(0.483743\pi\)
\(224\) −0.00772181 0.132578i −0.000515935 0.00885826i
\(225\) 0 0
\(226\) −12.9329 + 6.49515i −0.860284 + 0.432051i
\(227\) 0.340802 + 0.646996i 0.0226198 + 0.0429427i 0.895811 0.444435i \(-0.146596\pi\)
−0.873191 + 0.487378i \(0.837954\pi\)
\(228\) 0 0
\(229\) 13.3632 + 6.07430i 0.883063 + 0.401401i 0.803413 0.595422i \(-0.203015\pi\)
0.0796494 + 0.996823i \(0.474620\pi\)
\(230\) 0.204600 0.298314i 0.0134909 0.0196702i
\(231\) 0 0
\(232\) −1.16397 8.52173i −0.0764181 0.559479i
\(233\) −6.64226 1.57424i −0.435149 0.103132i 0.00720234 0.999974i \(-0.497707\pi\)
−0.442351 + 0.896842i \(0.645856\pi\)
\(234\) 0 0
\(235\) −15.9123 16.8660i −1.03800 1.10022i
\(236\) −0.131127 0.0205078i −0.00853562 0.00133495i
\(237\) 0 0
\(238\) 3.08147 0.119575i 0.199742 0.00775091i
\(239\) −0.574409 0.346657i −0.0371554 0.0224234i 0.498000 0.867177i \(-0.334068\pi\)
−0.535155 + 0.844754i \(0.679747\pi\)
\(240\) 0 0
\(241\) 5.63552 + 1.56876i 0.363016 + 0.101052i 0.444878 0.895591i \(-0.353247\pi\)
−0.0818618 + 0.996644i \(0.526087\pi\)
\(242\) −22.3210 −1.43485
\(243\) 0 0
\(244\) 0.0322510 0.00206466
\(245\) −8.59654 2.39301i −0.549213 0.152884i
\(246\) 0 0
\(247\) 5.29913 + 3.19804i 0.337175 + 0.203486i
\(248\) −10.2556 + 0.397962i −0.651228 + 0.0252706i
\(249\) 0 0
\(250\) −16.3838 2.56237i −1.03620 0.162059i
\(251\) 20.4900 + 21.7182i 1.29332 + 1.37084i 0.890120 + 0.455727i \(0.150620\pi\)
0.403200 + 0.915112i \(0.367898\pi\)
\(252\) 0 0
\(253\) 0.605905 + 0.143602i 0.0380929 + 0.00902818i
\(254\) 1.08856 + 7.96963i 0.0683020 + 0.500059i
\(255\) 0 0
\(256\) −0.191011 + 0.278501i −0.0119382 + 0.0174063i
\(257\) 0.245890 + 0.111771i 0.0153382 + 0.00697207i 0.421465 0.906845i \(-0.361516\pi\)
−0.406127 + 0.913817i \(0.633121\pi\)
\(258\) 0 0
\(259\) 6.01246 + 11.4144i 0.373596 + 0.709255i
\(260\) 0.162005 0.0813619i 0.0100471 0.00504585i
\(261\) 0 0
\(262\) −1.05040 18.0346i −0.0648938 1.11418i
\(263\) 12.0256 + 6.63547i 0.741532 + 0.409160i 0.808424 0.588600i \(-0.200321\pi\)
−0.0668920 + 0.997760i \(0.521308\pi\)
\(264\) 0 0
\(265\) 0.498768 3.65162i 0.0306390 0.224317i
\(266\) −0.867037 + 2.24568i −0.0531615 + 0.137692i
\(267\) 0 0
\(268\) −0.170531 + 0.0132547i −0.0104168 + 0.000809660i
\(269\) −5.01650 + 4.20934i −0.305861 + 0.256648i −0.782779 0.622300i \(-0.786198\pi\)
0.476918 + 0.878948i \(0.341754\pi\)
\(270\) 0 0
\(271\) 17.5181 + 14.6994i 1.06415 + 0.892927i 0.994510 0.104645i \(-0.0333706\pi\)
0.0696395 + 0.997572i \(0.477815\pi\)
\(272\) −4.26806 3.05062i −0.258789 0.184971i
\(273\) 0 0
\(274\) −21.6384 + 24.7948i −1.30722 + 1.49791i
\(275\) −0.570793 2.63508i −0.0344201 0.158901i
\(276\) 0 0
\(277\) 10.8775 2.13627i 0.653564 0.128356i 0.145070 0.989421i \(-0.453659\pi\)
0.508494 + 0.861065i \(0.330202\pi\)
\(278\) −23.7621 2.77739i −1.42516 0.166577i
\(279\) 0 0
\(280\) −5.94214 7.98167i −0.355111 0.476996i
\(281\) 1.21382 5.60362i 0.0724105 0.334284i −0.926730 0.375727i \(-0.877393\pi\)
0.999141 + 0.0414430i \(0.0131955\pi\)
\(282\) 0 0
\(283\) −9.33718 9.15784i −0.555038 0.544377i 0.367631 0.929972i \(-0.380169\pi\)
−0.922668 + 0.385595i \(0.873996\pi\)
\(284\) 0.0160851 0.0624464i 0.000954478 0.00370551i
\(285\) 0 0
\(286\) 33.0766 + 30.0154i 1.95586 + 1.77485i
\(287\) 1.57959 3.66190i 0.0932401 0.216155i
\(288\) 0 0
\(289\) −9.13869 + 12.2754i −0.537570 + 0.722082i
\(290\) 6.02634 + 6.90542i 0.353879 + 0.405500i
\(291\) 0 0
\(292\) −0.0568870 0.0182401i −0.00332906 0.00106742i
\(293\) 4.66855 + 0.916874i 0.272740 + 0.0535643i 0.327212 0.944951i \(-0.393891\pi\)
−0.0544723 + 0.998515i \(0.517348\pi\)
\(294\) 0 0
\(295\) −18.1704 + 8.25945i −1.05792 + 0.480884i
\(296\) 3.78452 21.4631i 0.219971 1.24752i
\(297\) 0 0
\(298\) −2.29937 13.0404i −0.133199 0.755410i
\(299\) −0.414716 0.604671i −0.0239836 0.0349690i
\(300\) 0 0
\(301\) 4.78666 + 5.93453i 0.275899 + 0.342061i
\(302\) 10.5978 4.32970i 0.609837 0.249146i
\(303\) 0 0
\(304\) 3.50622 2.11601i 0.201095 0.121362i
\(305\) 4.05223 2.66520i 0.232030 0.152609i
\(306\) 0 0
\(307\) −1.44851 + 24.8699i −0.0826706 + 1.41940i 0.660766 + 0.750592i \(0.270232\pi\)
−0.743436 + 0.668807i \(0.766805\pi\)
\(308\) −0.0647170 + 0.102681i −0.00368760 + 0.00585077i
\(309\) 0 0
\(310\) 8.89761 6.35963i 0.505350 0.361203i
\(311\) 4.46835 + 0.347308i 0.253377 + 0.0196940i 0.203553 0.979064i \(-0.434751\pi\)
0.0498243 + 0.998758i \(0.484134\pi\)
\(312\) 0 0
\(313\) −22.2506 9.09038i −1.25768 0.513819i −0.351292 0.936266i \(-0.614258\pi\)
−0.906387 + 0.422447i \(0.861171\pi\)
\(314\) 0.640697 + 2.14008i 0.0361566 + 0.120771i
\(315\) 0 0
\(316\) −0.209896 + 0.0497462i −0.0118076 + 0.00279844i
\(317\) −6.70925 17.3774i −0.376829 0.976012i −0.983476 0.181040i \(-0.942054\pi\)
0.606646 0.794972i \(-0.292514\pi\)
\(318\) 0 0
\(319\) −7.35277 + 13.9589i −0.411676 + 0.781548i
\(320\) −0.325952 + 16.8060i −0.0182213 + 0.939484i
\(321\) 0 0
\(322\) 0.203595 0.199684i 0.0113459 0.0111280i
\(323\) 0.662107 + 1.14680i 0.0368406 + 0.0638098i
\(324\) 0 0
\(325\) −1.58739 + 2.74945i −0.0880528 + 0.152512i
\(326\) −2.33084 9.04889i −0.129093 0.501172i
\(327\) 0 0
\(328\) −5.89876 + 3.25480i −0.325705 + 0.179716i
\(329\) −9.74698 15.4646i −0.537368 0.852593i
\(330\) 0 0
\(331\) 6.99440 8.67169i 0.384447 0.476639i −0.548759 0.835980i \(-0.684900\pi\)
0.933206 + 0.359341i \(0.116998\pi\)
\(332\) −0.0614949 + 0.205407i −0.00337497 + 0.0112732i
\(333\) 0 0
\(334\) 14.0804 14.9244i 0.770447 0.816626i
\(335\) −20.3313 + 15.7579i −1.11082 + 0.860948i
\(336\) 0 0
\(337\) 2.90961 + 6.08494i 0.158497 + 0.331468i 0.966062 0.258311i \(-0.0831658\pi\)
−0.807565 + 0.589778i \(0.799215\pi\)
\(338\) −3.30556 33.9841i −0.179799 1.84849i
\(339\) 0 0
\(340\) 0.0387574 + 0.00150396i 0.00210192 + 8.15639e-5i
\(341\) 15.7293 + 10.3453i 0.851788 + 0.560230i
\(342\) 0 0
\(343\) −16.7227 8.39847i −0.902943 0.453475i
\(344\) −0.249761 12.8776i −0.0134662 0.694316i
\(345\) 0 0
\(346\) −11.8410 9.17745i −0.636575 0.493383i
\(347\) 24.4142 3.81831i 1.31062 0.204978i 0.539674 0.841874i \(-0.318547\pi\)
0.770950 + 0.636896i \(0.219782\pi\)
\(348\) 0 0
\(349\) 3.56087 7.44692i 0.190609 0.398625i −0.784571 0.620039i \(-0.787117\pi\)
0.975180 + 0.221414i \(0.0710673\pi\)
\(350\) −1.16031 0.422320i −0.0620214 0.0225739i
\(351\) 0 0
\(352\) 0.386715 0.140753i 0.0206120 0.00750215i
\(353\) 1.77750 18.2743i 0.0946067 0.972642i −0.821097 0.570789i \(-0.806638\pi\)
0.915704 0.401854i \(-0.131634\pi\)
\(354\) 0 0
\(355\) −3.13947 9.17544i −0.166626 0.486982i
\(356\) 0.110779 0.100527i 0.00587130 0.00532792i
\(357\) 0 0
\(358\) −0.921141 + 2.69214i −0.0486838 + 0.142284i
\(359\) −3.94087 9.13597i −0.207991 0.482178i 0.782005 0.623272i \(-0.214197\pi\)
−0.989996 + 0.141094i \(0.954938\pi\)
\(360\) 0 0
\(361\) 17.8448 2.08576i 0.939201 0.109777i
\(362\) −8.95791 + 2.87224i −0.470817 + 0.150962i
\(363\) 0 0
\(364\) 0.137684 0.0383269i 0.00721660 0.00200888i
\(365\) −8.65501 + 2.40929i −0.453024 + 0.126108i
\(366\) 0 0
\(367\) 2.19651 0.704281i 0.114657 0.0367632i −0.247444 0.968902i \(-0.579591\pi\)
0.362101 + 0.932139i \(0.382060\pi\)
\(368\) −0.481864 + 0.0563218i −0.0251189 + 0.00293598i
\(369\) 0 0
\(370\) 9.19867 + 21.3249i 0.478216 + 1.10863i
\(371\) 0.940608 2.74903i 0.0488339 0.142723i
\(372\) 0 0
\(373\) 24.7965 22.5016i 1.28391 1.16509i 0.306942 0.951728i \(-0.400694\pi\)
0.976973 0.213362i \(-0.0684415\pi\)
\(374\) 3.09365 + 9.04153i 0.159969 + 0.467526i
\(375\) 0 0
\(376\) −2.98961 + 30.7359i −0.154178 + 1.58508i
\(377\) 17.4572 6.35391i 0.899093 0.327243i
\(378\) 0 0
\(379\) 8.16389 + 2.97141i 0.419351 + 0.152631i 0.543073 0.839686i \(-0.317261\pi\)
−0.123722 + 0.992317i \(0.539483\pi\)
\(380\) −0.0130612 + 0.0273152i −0.000670026 + 0.00140124i
\(381\) 0 0
\(382\) 29.7108 4.64669i 1.52014 0.237745i
\(383\) 17.6671 + 13.6930i 0.902747 + 0.699682i 0.954256 0.298990i \(-0.0966499\pi\)
−0.0515086 + 0.998673i \(0.516403\pi\)
\(384\) 0 0
\(385\) 0.353951 + 18.2496i 0.0180390 + 0.930087i
\(386\) 14.1727 + 7.11781i 0.721372 + 0.362287i
\(387\) 0 0
\(388\) −0.139861 0.0919882i −0.00710038 0.00466999i
\(389\) 11.0329 + 0.428125i 0.559388 + 0.0217068i 0.316919 0.948452i \(-0.397352\pi\)
0.242468 + 0.970159i \(0.422043\pi\)
\(390\) 0 0
\(391\) −0.0151870 0.156136i −0.000768041 0.00789615i
\(392\) 5.12663 + 10.7214i 0.258934 + 0.541514i
\(393\) 0 0
\(394\) −17.3874 + 13.4762i −0.875962 + 0.678922i
\(395\) −22.2617 + 23.5961i −1.12011 + 1.18725i
\(396\) 0 0
\(397\) 7.67558 25.6382i 0.385226 1.28675i −0.517186 0.855873i \(-0.673021\pi\)
0.902413 0.430873i \(-0.141794\pi\)
\(398\) 17.7812 22.0452i 0.891292 1.10503i
\(399\) 0 0
\(400\) 1.12007 + 1.77711i 0.0560033 + 0.0888553i
\(401\) −25.7931 + 14.2320i −1.28805 + 0.710713i −0.971314 0.237802i \(-0.923573\pi\)
−0.316732 + 0.948515i \(0.602585\pi\)
\(402\) 0 0
\(403\) −5.52970 21.4676i −0.275454 1.06938i
\(404\) 0.114216 0.197828i 0.00568247 0.00984233i
\(405\) 0 0
\(406\) 3.61272 + 6.25742i 0.179296 + 0.310550i
\(407\) −28.5416 + 27.9934i −1.41476 + 1.38758i
\(408\) 0 0
\(409\) −0.570957 + 29.4384i −0.0282320 + 1.45564i 0.671380 + 0.741113i \(0.265702\pi\)
−0.699612 + 0.714523i \(0.746644\pi\)
\(410\) 3.34583 6.35191i 0.165239 0.313698i
\(411\) 0 0
\(412\) −0.0345900 0.0895904i −0.00170413 0.00441380i
\(413\) −15.3110 + 3.62877i −0.753404 + 0.178560i
\(414\) 0 0
\(415\) 9.24804 + 30.8906i 0.453969 + 1.51636i
\(416\) −0.448592 0.183270i −0.0219940 0.00898556i
\(417\) 0 0
\(418\) −7.43722 0.578066i −0.363766 0.0282742i
\(419\) 19.6641 14.0550i 0.960653 0.686634i 0.0110011 0.999939i \(-0.496498\pi\)
0.949652 + 0.313306i \(0.101436\pi\)
\(420\) 0 0
\(421\) −7.59737 + 12.0541i −0.370273 + 0.587479i −0.978490 0.206292i \(-0.933860\pi\)
0.608217 + 0.793771i \(0.291885\pi\)
\(422\) −2.28049 + 39.1545i −0.111013 + 1.90601i
\(423\) 0 0
\(424\) −4.10086 + 2.69718i −0.199156 + 0.130987i
\(425\) −0.581548 + 0.350966i −0.0282092 + 0.0170244i
\(426\) 0 0
\(427\) 3.53962 1.44609i 0.171294 0.0699814i
\(428\) 0.00977169 + 0.0121150i 0.000472333 + 0.000585600i
\(429\) 0 0
\(430\) 7.76309 + 11.3189i 0.374369 + 0.545844i
\(431\) 0.0302866 + 0.171764i 0.00145886 + 0.00827358i 0.985528 0.169510i \(-0.0542185\pi\)
−0.984070 + 0.177783i \(0.943107\pi\)
\(432\) 0 0
\(433\) 5.54783 31.4633i 0.266612 1.51203i −0.497795 0.867295i \(-0.665857\pi\)
0.764407 0.644734i \(-0.223032\pi\)
\(434\) 7.84916 3.56788i 0.376772 0.171264i
\(435\) 0 0
\(436\) 0.244050 + 0.0479298i 0.0116879 + 0.00229542i
\(437\) 0.116610 + 0.0373894i 0.00557820 + 0.00178858i
\(438\) 0 0
\(439\) −8.01086 9.17943i −0.382337 0.438110i 0.529720 0.848173i \(-0.322297\pi\)
−0.912057 + 0.410062i \(0.865507\pi\)
\(440\) 18.4137 24.7338i 0.877837 1.17914i
\(441\) 0 0
\(442\) 4.45687 10.3322i 0.211992 0.491452i
\(443\) −9.74151 8.83995i −0.462833 0.419999i 0.406937 0.913456i \(-0.366597\pi\)
−0.869770 + 0.493458i \(0.835733\pi\)
\(444\) 0 0
\(445\) 5.61161 21.7856i 0.266016 1.03274i
\(446\) 15.9527 + 15.6463i 0.755383 + 0.740875i
\(447\) 0 0
\(448\) −2.80540 + 12.9512i −0.132543 + 0.611886i
\(449\) 5.28833 + 7.10346i 0.249572 + 0.335233i 0.909201 0.416358i \(-0.136694\pi\)
−0.659629 + 0.751592i \(0.729286\pi\)
\(450\) 0 0
\(451\) 12.2747 + 1.43471i 0.577995 + 0.0675579i
\(452\) −0.140811 + 0.0276544i −0.00662319 + 0.00130075i
\(453\) 0 0
\(454\) 0.219706 + 1.01428i 0.0103113 + 0.0476023i
\(455\) 14.1322 16.1937i 0.662529 0.759174i
\(456\) 0 0
\(457\) −23.9224 17.0987i −1.11904 0.799842i −0.137388 0.990517i \(-0.543871\pi\)
−0.981653 + 0.190675i \(0.938932\pi\)
\(458\) 15.9583 + 13.3906i 0.745682 + 0.625701i
\(459\) 0 0
\(460\) 0.00274765 0.00230555i 0.000128110 0.000107497i
\(461\) −0.133810 + 0.0104006i −0.00623216 + 0.000484402i −0.0806081 0.996746i \(-0.525686\pi\)
0.0743760 + 0.997230i \(0.476304\pi\)
\(462\) 0 0
\(463\) 4.00599 10.3758i 0.186174 0.482203i −0.808102 0.589042i \(-0.799505\pi\)
0.994276 + 0.106839i \(0.0340730\pi\)
\(464\) 1.66350 12.1790i 0.0772260 0.565395i
\(465\) 0 0
\(466\) −8.48214 4.68025i −0.392928 0.216808i
\(467\) 0.776947 + 13.3397i 0.0359528 + 0.617286i 0.967375 + 0.253347i \(0.0815314\pi\)
−0.931423 + 0.363939i \(0.881432\pi\)
\(468\) 0 0
\(469\) −18.1218 + 9.10112i −0.836788 + 0.420251i
\(470\) −15.3363 29.1152i −0.707409 1.34298i
\(471\) 0 0
\(472\) 24.1991 + 10.9998i 1.11385 + 0.506309i
\(473\) −13.3634 + 19.4842i −0.614448 + 0.895887i
\(474\) 0 0
\(475\) −0.0717565 0.525351i −0.00329242 0.0241047i
\(476\) 0.0297533 + 0.00705166i 0.00136374 + 0.000323212i
\(477\) 0 0
\(478\) −0.653397 0.692560i −0.0298857 0.0316770i
\(479\) −8.34732 1.30550i −0.381399 0.0596497i −0.0390863 0.999236i \(-0.512445\pi\)
−0.342313 + 0.939586i \(0.611210\pi\)
\(480\) 0 0
\(481\) 47.0394 1.82534i 2.14481 0.0832284i
\(482\) 7.10783 + 4.28959i 0.323753 + 0.195386i
\(483\) 0 0
\(484\) −0.213218 0.0593533i −0.00969173 0.00269788i
\(485\) −25.1749 −1.14313
\(486\) 0 0
\(487\) −24.3215 −1.10211 −0.551056 0.834469i \(-0.685775\pi\)
−0.551056 + 0.834469i \(0.685775\pi\)
\(488\) −6.22276 1.73222i −0.281691 0.0784141i
\(489\) 0 0
\(490\) −10.8424 6.54343i −0.489810 0.295602i
\(491\) 12.0409 0.467243i 0.543400 0.0210864i 0.234385 0.972144i \(-0.424692\pi\)
0.309014 + 0.951057i \(0.400001\pi\)
\(492\) 0 0
\(493\) 3.92694 + 0.614163i 0.176861 + 0.0276605i
\(494\) 6.02782 + 6.38912i 0.271205 + 0.287460i
\(495\) 0 0
\(496\) −14.2725 3.38265i −0.640856 0.151886i
\(497\) −1.03463 7.57486i −0.0464097 0.339779i
\(498\) 0 0
\(499\) −7.32513 + 10.6803i −0.327918 + 0.478116i −0.953224 0.302263i \(-0.902258\pi\)
0.625307 + 0.780379i \(0.284974\pi\)
\(500\) −0.149690 0.0680425i −0.00669434 0.00304295i
\(501\) 0 0
\(502\) 19.7483 + 37.4912i 0.881409 + 1.67331i
\(503\) 16.3324 8.20243i 0.728225 0.365728i −0.0457431 0.998953i \(-0.514566\pi\)
0.773968 + 0.633225i \(0.218269\pi\)
\(504\) 0 0
\(505\) −1.99747 34.2952i −0.0888862 1.52612i
\(506\) 0.773738 + 0.426931i 0.0343968 + 0.0189794i
\(507\) 0 0
\(508\) −0.0107936 + 0.0790234i −0.000478890 + 0.00350610i
\(509\) 9.18573 23.7916i 0.407150 1.05455i −0.566006 0.824401i \(-0.691512\pi\)
0.973156 0.230144i \(-0.0739199\pi\)
\(510\) 0 0
\(511\) −7.06134 + 0.548851i −0.312375 + 0.0242797i
\(512\) 17.1471 14.3882i 0.757804 0.635873i
\(513\) 0 0
\(514\) 0.293642 + 0.246395i 0.0129520 + 0.0108680i
\(515\) −11.7498 8.39825i −0.517758 0.370071i
\(516\) 0 0
\(517\) 37.2464 42.6796i 1.63809 1.87705i
\(518\) 3.87607 + 17.8939i 0.170305 + 0.786215i
\(519\) 0 0
\(520\) −35.6285 + 6.99721i −1.56241 + 0.306848i
\(521\) 3.63665 + 0.425063i 0.159324 + 0.0186224i 0.195381 0.980727i \(-0.437406\pi\)
−0.0360567 + 0.999350i \(0.511480\pi\)
\(522\) 0 0
\(523\) 16.7111 + 22.4470i 0.730727 + 0.981537i 0.999830 + 0.0184255i \(0.00586537\pi\)
−0.269103 + 0.963111i \(0.586727\pi\)
\(524\) 0.0379218 0.175066i 0.00165662 0.00764781i
\(525\) 0 0
\(526\) 13.9161 + 13.6488i 0.606769 + 0.595114i
\(527\) 1.18308 4.59300i 0.0515358 0.200074i
\(528\) 0 0
\(529\) 17.0218 + 15.4464i 0.740077 + 0.671584i
\(530\) 2.07167 4.80266i 0.0899875 0.208614i
\(531\) 0 0
\(532\) −0.0142537 + 0.0191460i −0.000617976 + 0.000830086i
\(533\) −9.56827 10.9640i −0.414448 0.474904i
\(534\) 0 0
\(535\) 2.22895 + 0.714685i 0.0963661 + 0.0308985i
\(536\) 33.6155 + 6.60187i 1.45197 + 0.285157i
\(537\) 0 0
\(538\) −8.46055 + 3.84579i −0.364760 + 0.165804i
\(539\) 3.78546 21.4684i 0.163051 0.924710i
\(540\) 0 0
\(541\) −7.53251 42.7190i −0.323848 1.83663i −0.517649 0.855593i \(-0.673193\pi\)
0.193801 0.981041i \(-0.437918\pi\)
\(542\) 18.3563 + 26.7642i 0.788471 + 1.14962i
\(543\) 0 0
\(544\) −0.0650897 0.0806986i −0.00279070 0.00345992i
\(545\) 34.6249 14.1458i 1.48317 0.605941i
\(546\) 0 0
\(547\) −17.6080 + 10.6265i −0.752864 + 0.454356i −0.840510 0.541796i \(-0.817745\pi\)
0.0876460 + 0.996152i \(0.472066\pi\)
\(548\) −0.272629 + 0.179311i −0.0116461 + 0.00765979i
\(549\) 0 0
\(550\) 0.222484 3.81990i 0.00948675 0.162881i
\(551\) −1.65437 + 2.62483i −0.0704784 + 0.111822i
\(552\) 0 0
\(553\) −20.8060 + 14.8712i −0.884760 + 0.632388i
\(554\) 15.6847 + 1.21911i 0.666379 + 0.0517950i
\(555\) 0 0
\(556\) −0.219599 0.0897161i −0.00931308 0.00380481i
\(557\) −7.95449 26.5699i −0.337043 1.12580i −0.943690 0.330830i \(-0.892671\pi\)
0.606648 0.794971i \(-0.292514\pi\)
\(558\) 0 0
\(559\) 27.0706 6.41586i 1.14497 0.271362i
\(560\) −5.12215 13.2667i −0.216450 0.560621i
\(561\) 0 0
\(562\) 3.79219 7.19929i 0.159964 0.303684i
\(563\) 0.272184 14.0338i 0.0114712 0.591452i −0.949340 0.314250i \(-0.898247\pi\)
0.960812 0.277202i \(-0.0894073\pi\)
\(564\) 0 0
\(565\) −15.4071 + 15.1112i −0.648182 + 0.635732i
\(566\) −9.28042 16.0742i −0.390085 0.675647i
\(567\) 0 0
\(568\) −6.45763 + 11.1849i −0.270956 + 0.469310i
\(569\) −0.195839 0.760292i −0.00820998 0.0318731i 0.964154 0.265344i \(-0.0854855\pi\)
−0.972364 + 0.233471i \(0.924992\pi\)
\(570\) 0 0
\(571\) −20.9112 + 11.5383i −0.875108 + 0.482864i −0.856014 0.516953i \(-0.827066\pi\)
−0.0190948 + 0.999818i \(0.506078\pi\)
\(572\) 0.236146 + 0.374672i 0.00987377 + 0.0156658i
\(573\) 0 0
\(574\) 3.55327 4.40536i 0.148311 0.183876i
\(575\) −0.0180151 + 0.0601747i −0.000751283 + 0.00250946i
\(576\) 0 0
\(577\) 10.4078 11.0317i 0.433284 0.459254i −0.473535 0.880775i \(-0.657022\pi\)
0.906819 + 0.421521i \(0.138504\pi\)
\(578\) −17.1662 + 13.3048i −0.714021 + 0.553408i
\(579\) 0 0
\(580\) 0.0392037 + 0.0819876i 0.00162785 + 0.00340435i
\(581\) 2.46099 + 25.3012i 0.102099 + 1.04967i
\(582\) 0 0
\(583\) 8.99687 + 0.349120i 0.372612 + 0.0144591i
\(584\) 9.99654 + 6.57483i 0.413660 + 0.272068i
\(585\) 0 0
\(586\) 6.03388 + 3.03033i 0.249257 + 0.125182i
\(587\) −0.0184781 0.952729i −0.000762675 0.0393233i −1.00000 0.000274076i \(-0.999913\pi\)
0.999237 0.0390492i \(-0.0124329\pi\)
\(588\) 0 0
\(589\) 2.92634 + 2.26808i 0.120578 + 0.0934548i
\(590\) −27.9859 + 4.37692i −1.15216 + 0.180195i
\(591\) 0 0
\(592\) 13.4366 28.1002i 0.552241 1.15491i
\(593\) 6.95908 + 2.53290i 0.285775 + 0.104014i 0.480931 0.876759i \(-0.340299\pi\)
−0.195155 + 0.980772i \(0.562521\pi\)
\(594\) 0 0
\(595\) 4.32115 1.57277i 0.177150 0.0644772i
\(596\) 0.0127110 0.130681i 0.000520664 0.00535290i
\(597\) 0 0
\(598\) −0.336870 0.984539i −0.0137756 0.0402608i
\(599\) −33.3372 + 30.2519i −1.36212 + 1.23606i −0.417180 + 0.908824i \(0.636982\pi\)
−0.944942 + 0.327237i \(0.893883\pi\)
\(600\) 0 0
\(601\) −1.31772 + 3.85118i −0.0537509 + 0.157093i −0.969758 0.244070i \(-0.921517\pi\)
0.916007 + 0.401163i \(0.131394\pi\)
\(602\) 4.28571 + 9.93540i 0.174673 + 0.404937i
\(603\) 0 0
\(604\) 0.112747 0.0131783i 0.00458763 0.000536217i
\(605\) −31.6951 + 10.1626i −1.28859 + 0.413169i
\(606\) 0 0
\(607\) −34.3775 + 9.56964i −1.39534 + 0.388420i −0.882600 0.470124i \(-0.844209\pi\)
−0.512741 + 0.858544i \(0.671370\pi\)
\(608\) 0.0779672 0.0217037i 0.00316199 0.000880200i
\(609\) 0 0
\(610\) 6.55454 2.10163i 0.265385 0.0850924i
\(611\) −66.2510 + 7.74363i −2.68023 + 0.313274i
\(612\) 0 0
\(613\) 11.2484 + 26.0768i 0.454321 + 1.05323i 0.979354 + 0.202152i \(0.0647935\pi\)
−0.525034 + 0.851081i \(0.675947\pi\)
\(614\) −11.4455 + 33.4507i −0.461903 + 1.34996i
\(615\) 0 0
\(616\) 18.0021 16.3360i 0.725323 0.658196i
\(617\) 3.21416 + 9.39374i 0.129397 + 0.378178i 0.991759 0.128114i \(-0.0408924\pi\)
−0.862362 + 0.506292i \(0.831016\pi\)
\(618\) 0 0
\(619\) −1.71009 + 17.5813i −0.0687345 + 0.706652i 0.896110 + 0.443832i \(0.146381\pi\)
−0.964845 + 0.262821i \(0.915347\pi\)
\(620\) 0.101904 0.0370900i 0.00409256 0.00148957i
\(621\) 0 0
\(622\) 5.97694 + 2.17543i 0.239653 + 0.0872267i
\(623\) 7.65078 16.0003i 0.306522 0.641037i
\(624\) 0 0
\(625\) −21.8548 + 3.41803i −0.874191 + 0.136721i
\(626\) −26.9613 20.8966i −1.07759 0.835196i
\(627\) 0 0
\(628\) 0.000429530 0.0221464i 1.71401e−5 0.000883739i
\(629\) 9.00035 + 4.52015i 0.358868 + 0.180230i
\(630\) 0 0
\(631\) −7.73755 5.08907i −0.308027 0.202593i 0.386078 0.922466i \(-0.373829\pi\)
−0.694105 + 0.719873i \(0.744200\pi\)
\(632\) 43.1708 + 1.67523i 1.71724 + 0.0666369i
\(633\) 0 0
\(634\) −2.55929 26.3118i −0.101642 1.04497i
\(635\) 5.17424 + 10.8210i 0.205333 + 0.429418i
\(636\) 0 0
\(637\) −20.2888 + 15.7250i −0.803871 + 0.623047i
\(638\) −15.3652 + 16.2862i −0.608316 + 0.644777i
\(639\) 0 0
\(640\) −6.93838 + 23.1758i −0.274264 + 0.916104i
\(641\) −4.34687 + 5.38927i −0.171691 + 0.212864i −0.856899 0.515484i \(-0.827612\pi\)
0.685208 + 0.728347i \(0.259711\pi\)
\(642\) 0 0
\(643\) −5.84829 9.27894i −0.230634 0.365926i 0.710648 0.703548i \(-0.248402\pi\)
−0.941282 + 0.337622i \(0.890377\pi\)
\(644\) 0.00247579 0.00136608i 9.75597e−5 5.38312e-5i
\(645\) 0 0
\(646\) 0.468774 + 1.81989i 0.0184437 + 0.0716028i
\(647\) 9.56019 16.5587i 0.375850 0.650991i −0.614604 0.788836i \(-0.710684\pi\)
0.990454 + 0.137845i \(0.0440175\pi\)
\(648\) 0 0
\(649\) −24.3802 42.2278i −0.957008 1.65759i
\(650\) −3.21668 + 3.15490i −0.126169 + 0.123745i
\(651\) 0 0
\(652\) 0.00179668 0.0926362i 7.03633e−5 0.00362791i
\(653\) −5.11057 + 9.70217i −0.199992 + 0.379675i −0.964152 0.265352i \(-0.914512\pi\)
0.764160 + 0.645027i \(0.223154\pi\)
\(654\) 0 0
\(655\) −9.70259 25.1303i −0.379112 0.981924i
\(656\) −9.36896 + 2.22048i −0.365796 + 0.0866953i
\(657\) 0 0
\(658\) −7.44043 24.8528i −0.290058 0.968861i
\(659\) −12.3833 5.05915i −0.482386 0.197076i 0.123944 0.992289i \(-0.460446\pi\)
−0.606331 + 0.795213i \(0.707359\pi\)
\(660\) 0 0
\(661\) −37.7345 2.93295i −1.46770 0.114079i −0.681394 0.731916i \(-0.738626\pi\)
−0.786306 + 0.617838i \(0.788009\pi\)
\(662\) 12.8630 9.19394i 0.499936 0.357333i
\(663\) 0 0
\(664\) 22.8979 36.3299i 0.888609 1.40987i
\(665\) −0.208718 + 3.58355i −0.00809374 + 0.138964i
\(666\) 0 0
\(667\) 0.307092 0.201977i 0.0118906 0.00782060i
\(668\) 0.174187 0.105122i 0.00673948 0.00406730i
\(669\) 0 0
\(670\) −33.7941 + 13.8064i −1.30558 + 0.533388i
\(671\) 7.43879 + 9.22266i 0.287171 + 0.356037i
\(672\) 0 0
\(673\) −5.49939 8.01831i −0.211986 0.309083i 0.704072 0.710128i \(-0.251363\pi\)
−0.916058 + 0.401045i \(0.868647\pi\)
\(674\) 1.66218 + 9.42666i 0.0640246 + 0.363102i
\(675\) 0 0
\(676\) 0.0587907 0.333418i 0.00226118 0.0128238i
\(677\) 14.2107 6.45956i 0.546162 0.248261i −0.121673 0.992570i \(-0.538826\pi\)
0.667835 + 0.744309i \(0.267221\pi\)
\(678\) 0 0
\(679\) −19.4747 3.82471i −0.747371 0.146779i
\(680\) −7.39738 2.37187i −0.283676 0.0909572i
\(681\) 0 0
\(682\) 17.5677 + 20.1304i 0.672704 + 0.770833i
\(683\) −20.6634 + 27.7558i −0.790664 + 1.06205i 0.205847 + 0.978584i \(0.434005\pi\)
−0.996511 + 0.0834614i \(0.973402\pi\)
\(684\) 0 0
\(685\) −19.4368 + 45.0597i −0.742644 + 1.72164i
\(686\) −19.6669 17.8468i −0.750887 0.681394i
\(687\) 0 0
\(688\) 4.59165 17.8259i 0.175055 0.679605i
\(689\) −7.56900 7.42362i −0.288356 0.282818i
\(690\) 0 0
\(691\) 9.50091 43.8611i 0.361432 1.66855i −0.328365 0.944551i \(-0.606498\pi\)
0.689797 0.724003i \(-0.257700\pi\)
\(692\) −0.0887057 0.119152i −0.00337208 0.00452949i
\(693\) 0 0
\(694\) 34.8322 + 4.07130i 1.32221 + 0.154545i
\(695\) −35.0060 + 6.87495i −1.32785 + 0.260782i
\(696\) 0 0
\(697\) −0.659120 3.04284i −0.0249660 0.115256i
\(698\) 7.70260 8.82620i 0.291548 0.334076i
\(699\) 0 0
\(700\) −0.00996076 0.00711952i −0.000376481 0.000269093i
\(701\) 27.3151 + 22.9201i 1.03168 + 0.865681i 0.991050 0.133494i \(-0.0426195\pi\)
0.0406285 + 0.999174i \(0.487064\pi\)
\(702\) 0 0
\(703\) −6.02269 + 5.05364i −0.227150 + 0.190602i
\(704\) −40.9408 + 3.18217i −1.54301 + 0.119933i
\(705\) 0 0
\(706\) 9.38512 24.3081i 0.353213 0.914846i
\(707\) 3.66512 26.8334i 0.137841 1.00917i
\(708\) 0 0
\(709\) −8.97279 4.95097i −0.336980 0.185938i 0.305593 0.952162i \(-0.401145\pi\)
−0.642573 + 0.766225i \(0.722133\pi\)
\(710\) −0.800233 13.7395i −0.0300322 0.515633i
\(711\) 0 0
\(712\) −26.7740 + 13.4464i −1.00340 + 0.503926i
\(713\) −0.204408 0.388060i −0.00765515 0.0145329i
\(714\) 0 0
\(715\) 60.6335 + 27.5613i 2.26757 + 1.03074i
\(716\) −0.0159577 + 0.0232669i −0.000596367 + 0.000869524i
\(717\) 0 0
\(718\) −1.91093 13.9905i −0.0713154 0.522121i
\(719\) −1.86091 0.441044i −0.0694003 0.0164482i 0.195769 0.980650i \(-0.437280\pi\)
−0.265169 + 0.964202i \(0.585428\pi\)
\(720\) 0 0
\(721\) −7.81344 8.28177i −0.290988 0.308429i
\(722\) 25.1912 + 3.93983i 0.937519 + 0.146625i
\(723\) 0 0
\(724\) −0.0932067 + 0.00361684i −0.00346400 + 0.000134419i
\(725\) −1.36259 0.822328i −0.0506053 0.0305405i
\(726\) 0 0
\(727\) −30.3075 8.43666i −1.12404 0.312898i −0.344213 0.938891i \(-0.611854\pi\)
−0.779829 + 0.625993i \(0.784694\pi\)
\(728\) −28.6244 −1.06089
\(729\) 0 0
\(730\) −12.7500 −0.471900
\(731\) 5.73418 + 1.59622i 0.212086 + 0.0590383i
\(732\) 0 0
\(733\) 11.3002 + 6.81971i 0.417383 + 0.251892i 0.709806 0.704397i \(-0.248783\pi\)
−0.292423 + 0.956289i \(0.594462\pi\)
\(734\) 3.27109 0.126933i 0.120738 0.00468520i
\(735\) 0 0
\(736\) −0.00947243 0.00148146i −0.000349158 5.46074e-5i
\(737\) −43.1238 45.7086i −1.58849 1.68370i
\(738\) 0 0
\(739\) −6.13893 1.45495i −0.225824 0.0535213i 0.116146 0.993232i \(-0.462946\pi\)
−0.341970 + 0.939711i \(0.611094\pi\)
\(740\) 0.0311643 + 0.228163i 0.00114562 + 0.00838745i
\(741\) 0 0
\(742\) 2.33224 3.40049i 0.0856191 0.124836i
\(743\) 20.2298 + 9.19555i 0.742158 + 0.337352i 0.748952 0.662625i \(-0.230558\pi\)
−0.00679364 + 0.999977i \(0.502162\pi\)
\(744\) 0 0
\(745\) −9.20225 17.4700i −0.337144 0.640053i
\(746\) 42.4655 21.3270i 1.55477 0.780836i
\(747\) 0 0
\(748\) 0.00550948 + 0.0945942i 0.000201447 + 0.00345871i
\(749\) 1.61569 + 0.891497i 0.0590358 + 0.0325746i
\(750\) 0 0
\(751\) 4.81180 35.2286i 0.175585 1.28551i −0.666231 0.745745i \(-0.732094\pi\)
0.841816 0.539764i \(-0.181487\pi\)
\(752\) −15.8961 + 41.1719i −0.579671 + 1.50139i
\(753\) 0 0
\(754\) 26.2857 2.04308i 0.957268 0.0744047i
\(755\) 13.0773 10.9732i 0.475932 0.399354i
\(756\) 0 0
\(757\) 0.911680 + 0.764990i 0.0331356 + 0.0278040i 0.659205 0.751963i \(-0.270893\pi\)
−0.626069 + 0.779767i \(0.715337\pi\)
\(758\) 10.0308 + 7.16956i 0.364334 + 0.260410i
\(759\) 0 0
\(760\) 3.98725 4.56888i 0.144633 0.165731i
\(761\) 1.59301 + 7.35413i 0.0577464 + 0.266587i 0.997075 0.0764321i \(-0.0243529\pi\)
−0.939328 + 0.343019i \(0.888550\pi\)
\(762\) 0 0
\(763\) 28.9341 5.68247i 1.04748 0.205719i
\(764\) 0.296164 + 0.0346167i 0.0107149 + 0.00125239i
\(765\) 0 0
\(766\) 18.9431 + 25.4449i 0.684440 + 0.919363i
\(767\) −12.1552 + 56.1146i −0.438898 + 2.02618i
\(768\) 0 0
\(769\) 19.0485 + 18.6826i 0.686905 + 0.673711i 0.957319 0.289033i \(-0.0933336\pi\)
−0.270415 + 0.962744i \(0.587161\pi\)
\(770\) −6.46162 + 25.0855i −0.232861 + 0.904020i
\(771\) 0 0
\(772\) 0.116456 + 0.105678i 0.00419135 + 0.00380344i
\(773\) −12.9741 + 30.0774i −0.466647 + 1.08181i 0.508662 + 0.860966i \(0.330140\pi\)
−0.975309 + 0.220844i \(0.929119\pi\)
\(774\) 0 0
\(775\) −1.13407 + 1.52332i −0.0407371 + 0.0547194i
\(776\) 22.0452 + 25.2610i 0.791376 + 0.906816i
\(777\) 0 0
\(778\) 14.9211 + 4.78427i 0.534949 + 0.171524i
\(779\) 2.38481 + 0.468362i 0.0854447 + 0.0167808i
\(780\) 0 0
\(781\) 21.5675 9.80365i 0.771748 0.350802i
\(782\) 0.0386595 0.219249i 0.00138246 0.00784033i
\(783\) 0 0
\(784\) 2.94930 + 16.7263i 0.105332 + 0.597367i
\(785\) 1.88413 + 2.74713i 0.0672475 + 0.0980493i
\(786\) 0 0