Properties

Label 1183.2.e.i.508.3
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 11 x^{14} + 85 x^{12} + 334 x^{10} + 952 x^{8} + 1050 x^{6} + 853 x^{4} + 93 x^{2} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.3
Root \(-0.536527 + 0.929293i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.i.170.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +O(q^{10})\) \(q+(-0.536527 - 0.929293i) q^{2} +(1.21570 - 2.10566i) q^{3} +(0.424277 - 0.734868i) q^{4} +(0.312716 + 0.541640i) q^{5} -2.60903 q^{6} +(-1.21561 - 2.34996i) q^{7} -3.05665 q^{8} +(-1.45586 - 2.52163i) q^{9} +(0.335561 - 0.581209i) q^{10} +(-0.354260 + 0.613597i) q^{11} +(-1.03159 - 1.78676i) q^{12} +(-1.53159 + 2.39047i) q^{14} +1.52068 q^{15} +(0.791426 + 1.37079i) q^{16} +(1.67157 - 2.89524i) q^{17} +(-1.56222 + 2.70585i) q^{18} +(-2.60138 - 4.50573i) q^{19} +0.530712 q^{20} +(-6.42602 - 0.297185i) q^{21} +0.760282 q^{22} +(2.21570 + 3.83771i) q^{23} +(-3.71598 + 6.43627i) q^{24} +(2.30442 - 3.99137i) q^{25} +0.214623 q^{27} +(-2.24266 - 0.103717i) q^{28} -6.59711 q^{29} +(-0.815886 - 1.41316i) q^{30} +(-2.19530 + 3.80238i) q^{31} +(-2.20741 + 3.82335i) q^{32} +(0.861351 + 1.49190i) q^{33} -3.58737 q^{34} +(0.892689 - 1.39329i) q^{35} -2.47076 q^{36} +(0.211704 + 0.366683i) q^{37} +(-2.79143 + 4.83489i) q^{38} +(-0.955864 - 1.65561i) q^{40} +5.01604 q^{41} +(3.17157 + 6.13111i) q^{42} -11.2059 q^{43} +(0.300609 + 0.520670i) q^{44} +(0.910544 - 1.57711i) q^{45} +(2.37757 - 4.11807i) q^{46} +(4.03635 + 6.99116i) q^{47} +3.84855 q^{48} +(-4.04458 + 5.71326i) q^{49} -4.94553 q^{50} +(-4.06426 - 7.03950i) q^{51} +(0.348553 - 0.603712i) q^{53} +(-0.115151 - 0.199447i) q^{54} -0.443132 q^{55} +(3.71570 + 7.18300i) q^{56} -12.6500 q^{57} +(3.53953 + 6.13065i) q^{58} +(4.93159 - 8.54177i) q^{59} +(0.645188 - 1.11750i) q^{60} +(-2.34855 - 4.06781i) q^{61} +4.71136 q^{62} +(-4.15596 + 6.48654i) q^{63} +7.90305 q^{64} +(0.924277 - 1.60089i) q^{66} +(5.21041 - 9.02470i) q^{67} +(-1.41841 - 2.45676i) q^{68} +10.7745 q^{69} +(-1.77373 - 0.0820297i) q^{70} +14.0876 q^{71} +(4.45007 + 7.70775i) q^{72} +(-2.54191 + 4.40273i) q^{73} +(0.227170 - 0.393471i) q^{74} +(-5.60297 - 9.70463i) q^{75} -4.41482 q^{76} +(1.87257 + 0.0866008i) q^{77} +(1.95586 + 3.38766i) q^{79} +(-0.494983 + 0.857336i) q^{80} +(4.62851 - 8.01682i) q^{81} +(-2.69124 - 4.66137i) q^{82} -10.2035 q^{83} +(-2.94480 + 4.59619i) q^{84} +2.09090 q^{85} +(6.01230 + 10.4136i) q^{86} +(-8.02012 + 13.8913i) q^{87} +(1.08285 - 1.87555i) q^{88} +(-6.68955 - 11.5866i) q^{89} -1.95413 q^{90} +3.76028 q^{92} +(5.33767 + 9.24512i) q^{93} +(4.33122 - 7.50190i) q^{94} +(1.62699 - 2.81802i) q^{95} +(5.36711 + 9.29610i) q^{96} +0.202023 q^{97} +(7.47932 + 0.693276i) q^{98} +2.06302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + O(q^{10}) \) \( 16q - 4q^{3} - 6q^{4} - 12q^{9} + 6q^{10} - 18q^{12} - 26q^{14} + 2q^{16} - 8q^{17} - 36q^{22} + 12q^{23} + 32q^{27} - 16q^{29} - 38q^{30} + 56q^{36} - 34q^{38} - 4q^{40} + 16q^{42} - 16q^{43} + 36q^{48} - 40q^{49} - 16q^{51} - 20q^{53} + 24q^{55} + 36q^{56} - 12q^{61} - 44q^{62} - 88q^{64} + 2q^{66} - 2q^{68} + 56q^{69} + 42q^{74} - 8q^{75} + 76q^{77} + 20q^{79} - 24q^{81} + 16q^{82} - 68q^{87} - 4q^{88} + 216q^{90} + 12q^{92} - 26q^{94} + 16q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.536527 0.929293i −0.379382 0.657109i 0.611590 0.791175i \(-0.290530\pi\)
−0.990972 + 0.134065i \(0.957197\pi\)
\(3\) 1.21570 2.10566i 0.701886 1.21570i −0.265918 0.963996i \(-0.585675\pi\)
0.967804 0.251707i \(-0.0809918\pi\)
\(4\) 0.424277 0.734868i 0.212138 0.367434i
\(5\) 0.312716 + 0.541640i 0.139851 + 0.242229i 0.927440 0.373972i \(-0.122004\pi\)
−0.787589 + 0.616201i \(0.788671\pi\)
\(6\) −2.60903 −1.06513
\(7\) −1.21561 2.34996i −0.459458 0.888200i
\(8\) −3.05665 −1.08069
\(9\) −1.45586 2.52163i −0.485288 0.840544i
\(10\) 0.335561 0.581209i 0.106114 0.183795i
\(11\) −0.354260 + 0.613597i −0.106814 + 0.185006i −0.914478 0.404636i \(-0.867398\pi\)
0.807664 + 0.589643i \(0.200731\pi\)
\(12\) −1.03159 1.78676i −0.297794 0.515794i
\(13\) 0 0
\(14\) −1.53159 + 2.39047i −0.409334 + 0.638881i
\(15\) 1.52068 0.392637
\(16\) 0.791426 + 1.37079i 0.197856 + 0.342697i
\(17\) 1.67157 2.89524i 0.405414 0.702199i −0.588955 0.808166i \(-0.700461\pi\)
0.994370 + 0.105967i \(0.0337939\pi\)
\(18\) −1.56222 + 2.70585i −0.368219 + 0.637775i
\(19\) −2.60138 4.50573i −0.596798 1.03368i −0.993290 0.115646i \(-0.963106\pi\)
0.396492 0.918038i \(-0.370227\pi\)
\(20\) 0.530712 0.118671
\(21\) −6.42602 0.297185i −1.40227 0.0648510i
\(22\) 0.760282 0.162093
\(23\) 2.21570 + 3.83771i 0.462006 + 0.800218i 0.999061 0.0433296i \(-0.0137966\pi\)
−0.537055 + 0.843547i \(0.680463\pi\)
\(24\) −3.71598 + 6.43627i −0.758522 + 1.31380i
\(25\) 2.30442 3.99137i 0.460883 0.798274i
\(26\) 0 0
\(27\) 0.214623 0.0413042
\(28\) −2.24266 0.103717i −0.423824 0.0196006i
\(29\) −6.59711 −1.22505 −0.612526 0.790450i \(-0.709847\pi\)
−0.612526 + 0.790450i \(0.709847\pi\)
\(30\) −0.815886 1.41316i −0.148960 0.258006i
\(31\) −2.19530 + 3.80238i −0.394288 + 0.682927i −0.993010 0.118030i \(-0.962342\pi\)
0.598722 + 0.800957i \(0.295675\pi\)
\(32\) −2.20741 + 3.82335i −0.390219 + 0.675879i
\(33\) 0.861351 + 1.49190i 0.149942 + 0.259707i
\(34\) −3.58737 −0.615228
\(35\) 0.892689 1.39329i 0.150892 0.235509i
\(36\) −2.47076 −0.411793
\(37\) 0.211704 + 0.366683i 0.0348040 + 0.0602823i 0.882903 0.469556i \(-0.155586\pi\)
−0.848099 + 0.529838i \(0.822253\pi\)
\(38\) −2.79143 + 4.83489i −0.452829 + 0.784323i
\(39\) 0 0
\(40\) −0.955864 1.65561i −0.151135 0.261774i
\(41\) 5.01604 0.783374 0.391687 0.920099i \(-0.371892\pi\)
0.391687 + 0.920099i \(0.371892\pi\)
\(42\) 3.17157 + 6.13111i 0.489383 + 0.946050i
\(43\) −11.2059 −1.70889 −0.854445 0.519542i \(-0.826103\pi\)
−0.854445 + 0.519542i \(0.826103\pi\)
\(44\) 0.300609 + 0.520670i 0.0453185 + 0.0784939i
\(45\) 0.910544 1.57711i 0.135736 0.235101i
\(46\) 2.37757 4.11807i 0.350554 0.607177i
\(47\) 4.03635 + 6.99116i 0.588762 + 1.01977i 0.994395 + 0.105729i \(0.0337177\pi\)
−0.405633 + 0.914036i \(0.632949\pi\)
\(48\) 3.84855 0.555491
\(49\) −4.04458 + 5.71326i −0.577797 + 0.816180i
\(50\) −4.94553 −0.699404
\(51\) −4.06426 7.03950i −0.569110 0.985727i
\(52\) 0 0
\(53\) 0.348553 0.603712i 0.0478774 0.0829262i −0.841094 0.540890i \(-0.818088\pi\)
0.888971 + 0.457964i \(0.151421\pi\)
\(54\) −0.115151 0.199447i −0.0156701 0.0271414i
\(55\) −0.443132 −0.0597519
\(56\) 3.71570 + 7.18300i 0.496532 + 0.959869i
\(57\) −12.6500 −1.67554
\(58\) 3.53953 + 6.13065i 0.464763 + 0.804993i
\(59\) 4.93159 8.54177i 0.642039 1.11204i −0.342938 0.939358i \(-0.611422\pi\)
0.984977 0.172686i \(-0.0552445\pi\)
\(60\) 0.645188 1.11750i 0.0832934 0.144268i
\(61\) −2.34855 4.06781i −0.300701 0.520830i 0.675594 0.737274i \(-0.263887\pi\)
−0.976295 + 0.216444i \(0.930554\pi\)
\(62\) 4.71136 0.598344
\(63\) −4.15596 + 6.48654i −0.523601 + 0.817227i
\(64\) 7.90305 0.987881
\(65\) 0 0
\(66\) 0.924277 1.60089i 0.113771 0.197056i
\(67\) 5.21041 9.02470i 0.636553 1.10254i −0.349631 0.936888i \(-0.613693\pi\)
0.986184 0.165655i \(-0.0529738\pi\)
\(68\) −1.41841 2.45676i −0.172008 0.297926i
\(69\) 10.7745 1.29710
\(70\) −1.77373 0.0820297i −0.212001 0.00980443i
\(71\) 14.0876 1.67189 0.835946 0.548812i \(-0.184920\pi\)
0.835946 + 0.548812i \(0.184920\pi\)
\(72\) 4.45007 + 7.70775i 0.524446 + 0.908368i
\(73\) −2.54191 + 4.40273i −0.297509 + 0.515300i −0.975565 0.219710i \(-0.929489\pi\)
0.678057 + 0.735010i \(0.262822\pi\)
\(74\) 0.227170 0.393471i 0.0264080 0.0457400i
\(75\) −5.60297 9.70463i −0.646975 1.12059i
\(76\) −4.41482 −0.506415
\(77\) 1.87257 + 0.0866008i 0.213399 + 0.00986908i
\(78\) 0 0
\(79\) 1.95586 + 3.38766i 0.220052 + 0.381141i 0.954823 0.297174i \(-0.0960440\pi\)
−0.734772 + 0.678315i \(0.762711\pi\)
\(80\) −0.494983 + 0.857336i −0.0553408 + 0.0958530i
\(81\) 4.62851 8.01682i 0.514279 0.890757i
\(82\) −2.69124 4.66137i −0.297198 0.514762i
\(83\) −10.2035 −1.11998 −0.559990 0.828499i \(-0.689195\pi\)
−0.559990 + 0.828499i \(0.689195\pi\)
\(84\) −2.94480 + 4.59619i −0.321304 + 0.501486i
\(85\) 2.09090 0.226790
\(86\) 6.01230 + 10.4136i 0.648323 + 1.12293i
\(87\) −8.02012 + 13.8913i −0.859847 + 1.48930i
\(88\) 1.08285 1.87555i 0.115432 0.199935i
\(89\) −6.68955 11.5866i −0.709090 1.22818i −0.965195 0.261532i \(-0.915772\pi\)
0.256104 0.966649i \(-0.417561\pi\)
\(90\) −1.95413 −0.205983
\(91\) 0 0
\(92\) 3.76028 0.392036
\(93\) 5.33767 + 9.24512i 0.553491 + 0.958674i
\(94\) 4.33122 7.50190i 0.446731 0.773761i
\(95\) 1.62699 2.81802i 0.166925 0.289123i
\(96\) 5.36711 + 9.29610i 0.547778 + 0.948780i
\(97\) 0.202023 0.0205123 0.0102562 0.999947i \(-0.496735\pi\)
0.0102562 + 0.999947i \(0.496735\pi\)
\(98\) 7.47932 + 0.693276i 0.755526 + 0.0700315i
\(99\) 2.06302 0.207341
\(100\) −1.95542 3.38689i −0.195542 0.338689i
\(101\) 8.66723 15.0121i 0.862421 1.49376i −0.00716374 0.999974i \(-0.502280\pi\)
0.869585 0.493783i \(-0.164386\pi\)
\(102\) −4.36117 + 7.55377i −0.431820 + 0.747934i
\(103\) 5.40739 + 9.36587i 0.532806 + 0.922847i 0.999266 + 0.0383047i \(0.0121957\pi\)
−0.466460 + 0.884542i \(0.654471\pi\)
\(104\) 0 0
\(105\) −1.84855 3.57353i −0.180400 0.348740i
\(106\) −0.748033 −0.0726554
\(107\) 3.05839 + 5.29729i 0.295666 + 0.512108i 0.975140 0.221592i \(-0.0711252\pi\)
−0.679474 + 0.733700i \(0.737792\pi\)
\(108\) 0.0910594 0.157720i 0.00876220 0.0151766i
\(109\) 5.69958 9.87196i 0.545921 0.945563i −0.452628 0.891700i \(-0.649513\pi\)
0.998548 0.0538629i \(-0.0171534\pi\)
\(110\) 0.237752 + 0.411799i 0.0226688 + 0.0392635i
\(111\) 1.02948 0.0977137
\(112\) 2.25923 3.52616i 0.213477 0.333191i
\(113\) −0.923456 −0.0868714 −0.0434357 0.999056i \(-0.513830\pi\)
−0.0434357 + 0.999056i \(0.513830\pi\)
\(114\) 6.78709 + 11.7556i 0.635669 + 1.10101i
\(115\) −1.38577 + 2.40023i −0.129224 + 0.223822i
\(116\) −2.79900 + 4.84801i −0.259880 + 0.450126i
\(117\) 0 0
\(118\) −10.5837 −0.974312
\(119\) −8.83566 0.408623i −0.809963 0.0374584i
\(120\) −4.64819 −0.424319
\(121\) 5.24900 + 9.09153i 0.477182 + 0.826503i
\(122\) −2.52013 + 4.36499i −0.228162 + 0.395187i
\(123\) 6.09801 10.5621i 0.549839 0.952349i
\(124\) 1.86283 + 3.22652i 0.167287 + 0.289750i
\(125\) 6.00967 0.537521
\(126\) 8.25768 + 0.381893i 0.735652 + 0.0340218i
\(127\) −8.50972 −0.755116 −0.377558 0.925986i \(-0.623236\pi\)
−0.377558 + 0.925986i \(0.623236\pi\)
\(128\) 0.174618 + 0.302447i 0.0154342 + 0.0267328i
\(129\) −13.6231 + 23.5959i −1.19945 + 2.07750i
\(130\) 0 0
\(131\) 3.50152 + 6.06482i 0.305930 + 0.529885i 0.977468 0.211084i \(-0.0676995\pi\)
−0.671538 + 0.740970i \(0.734366\pi\)
\(132\) 1.46180 0.127234
\(133\) −7.42599 + 11.5903i −0.643915 + 1.00501i
\(134\) −11.1821 −0.965988
\(135\) 0.0671160 + 0.116248i 0.00577642 + 0.0100051i
\(136\) −5.10940 + 8.84974i −0.438128 + 0.758859i
\(137\) −3.10847 + 5.38403i −0.265575 + 0.459989i −0.967714 0.252051i \(-0.918895\pi\)
0.702139 + 0.712040i \(0.252228\pi\)
\(138\) −5.78084 10.0127i −0.492097 0.852338i
\(139\) 6.53140 0.553986 0.276993 0.960872i \(-0.410662\pi\)
0.276993 + 0.960872i \(0.410662\pi\)
\(140\) −0.645140 1.24715i −0.0545242 0.105403i
\(141\) 19.6280 1.65297
\(142\) −7.55839 13.0915i −0.634286 1.09862i
\(143\) 0 0
\(144\) 2.30442 3.99137i 0.192035 0.332614i
\(145\) −2.06302 3.57326i −0.171325 0.296743i
\(146\) 5.45523 0.451478
\(147\) 7.11317 + 15.4621i 0.586685 + 1.27529i
\(148\) 0.359285 0.0295330
\(149\) −1.84869 3.20203i −0.151451 0.262320i 0.780310 0.625393i \(-0.215061\pi\)
−0.931761 + 0.363072i \(0.881728\pi\)
\(150\) −6.01230 + 10.4136i −0.490902 + 0.850267i
\(151\) −2.43887 + 4.22425i −0.198473 + 0.343764i −0.948033 0.318171i \(-0.896931\pi\)
0.749561 + 0.661935i \(0.230265\pi\)
\(152\) 7.95152 + 13.7724i 0.644954 + 1.11709i
\(153\) −9.73430 −0.786971
\(154\) −0.924207 1.78663i −0.0744747 0.143971i
\(155\) −2.74603 −0.220566
\(156\) 0 0
\(157\) 4.75984 8.24428i 0.379876 0.657965i −0.611168 0.791501i \(-0.709300\pi\)
0.991044 + 0.133536i \(0.0426332\pi\)
\(158\) 2.09875 3.63514i 0.166968 0.289196i
\(159\) −0.847473 1.46787i −0.0672090 0.116409i
\(160\) −2.76117 −0.218290
\(161\) 6.32501 9.87196i 0.498481 0.778020i
\(162\) −9.93329 −0.780433
\(163\) −11.8544 20.5325i −0.928511 1.60823i −0.785815 0.618461i \(-0.787756\pi\)
−0.142696 0.989767i \(-0.545577\pi\)
\(164\) 2.12819 3.68613i 0.166184 0.287838i
\(165\) −0.538716 + 0.933084i −0.0419390 + 0.0726405i
\(166\) 5.47446 + 9.48204i 0.424901 + 0.735949i
\(167\) −1.13193 −0.0875914 −0.0437957 0.999041i \(-0.513945\pi\)
−0.0437957 + 0.999041i \(0.513945\pi\)
\(168\) 19.6421 + 0.908391i 1.51542 + 0.0700839i
\(169\) 0 0
\(170\) −1.12183 1.94306i −0.0860402 0.149026i
\(171\) −7.57452 + 13.1195i −0.579238 + 1.00327i
\(172\) −4.75442 + 8.23489i −0.362521 + 0.627905i
\(173\) −5.99458 10.3829i −0.455760 0.789399i 0.542972 0.839751i \(-0.317299\pi\)
−0.998732 + 0.0503522i \(0.983966\pi\)
\(174\) 17.2121 1.30484
\(175\) −12.1808 0.563327i −0.920783 0.0425835i
\(176\) −1.12148 −0.0845350
\(177\) −11.9907 20.7685i −0.901276 1.56106i
\(178\) −7.17825 + 12.4331i −0.538033 + 0.931900i
\(179\) −4.73538 + 8.20192i −0.353939 + 0.613040i −0.986936 0.161114i \(-0.948491\pi\)
0.632997 + 0.774154i \(0.281825\pi\)
\(180\) −0.772645 1.33826i −0.0575896 0.0997480i
\(181\) 11.4314 0.849690 0.424845 0.905266i \(-0.360329\pi\)
0.424845 + 0.905266i \(0.360329\pi\)
\(182\) 0 0
\(183\) −11.4206 −0.844233
\(184\) −6.77264 11.7305i −0.499285 0.864788i
\(185\) −0.132407 + 0.229335i −0.00973473 + 0.0168611i
\(186\) 5.72761 9.92052i 0.419969 0.727408i
\(187\) 1.18434 + 2.05134i 0.0866075 + 0.150009i
\(188\) 6.85011 0.499595
\(189\) −0.260898 0.504354i −0.0189775 0.0366864i
\(190\) −3.49169 −0.253314
\(191\) −7.84377 13.5858i −0.567555 0.983034i −0.996807 0.0798496i \(-0.974556\pi\)
0.429252 0.903185i \(-0.358777\pi\)
\(192\) 9.60776 16.6411i 0.693380 1.20097i
\(193\) 11.5036 19.9248i 0.828045 1.43422i −0.0715256 0.997439i \(-0.522787\pi\)
0.899570 0.436776i \(-0.143880\pi\)
\(194\) −0.108391 0.187739i −0.00778202 0.0134788i
\(195\) 0 0
\(196\) 2.48248 + 5.39624i 0.177320 + 0.385446i
\(197\) 10.2035 0.726970 0.363485 0.931600i \(-0.381587\pi\)
0.363485 + 0.931600i \(0.381587\pi\)
\(198\) −1.10687 1.91715i −0.0786616 0.136246i
\(199\) −5.96173 + 10.3260i −0.422616 + 0.731992i −0.996194 0.0871586i \(-0.972221\pi\)
0.573579 + 0.819150i \(0.305555\pi\)
\(200\) −7.04381 + 12.2002i −0.498072 + 0.862687i
\(201\) −12.6686 21.9427i −0.893576 1.54772i
\(202\) −18.6008 −1.30875
\(203\) 8.01952 + 15.5029i 0.562860 + 1.08809i
\(204\) −6.89747 −0.482920
\(205\) 1.56860 + 2.71689i 0.109555 + 0.189756i
\(206\) 5.80243 10.0501i 0.404274 0.700223i
\(207\) 6.45152 11.1744i 0.448412 0.776672i
\(208\) 0 0
\(209\) 3.68627 0.254984
\(210\) −2.32905 + 3.63514i −0.160720 + 0.250849i
\(211\) −15.5893 −1.07321 −0.536606 0.843833i \(-0.680294\pi\)
−0.536606 + 0.843833i \(0.680294\pi\)
\(212\) −0.295766 0.512281i −0.0203133 0.0351836i
\(213\) 17.1263 29.6637i 1.17348 2.03252i
\(214\) 3.28182 5.68428i 0.224341 0.388570i
\(215\) −3.50428 6.06959i −0.238990 0.413942i
\(216\) −0.656028 −0.0446370
\(217\) 11.6041 + 0.536653i 0.787734 + 0.0364304i
\(218\) −12.2319 −0.828451
\(219\) 6.18042 + 10.7048i 0.417634 + 0.723364i
\(220\) −0.188010 + 0.325643i −0.0126757 + 0.0219549i
\(221\) 0 0
\(222\) −0.552343 0.956687i −0.0370709 0.0642086i
\(223\) −6.76662 −0.453126 −0.226563 0.973996i \(-0.572749\pi\)
−0.226563 + 0.973996i \(0.572749\pi\)
\(224\) 11.6680 + 0.539613i 0.779604 + 0.0360544i
\(225\) −13.4197 −0.894645
\(226\) 0.495459 + 0.858161i 0.0329575 + 0.0570840i
\(227\) −8.41225 + 14.5704i −0.558340 + 0.967074i 0.439295 + 0.898343i \(0.355228\pi\)
−0.997635 + 0.0687311i \(0.978105\pi\)
\(228\) −5.36711 + 9.29610i −0.355445 + 0.615650i
\(229\) −5.51286 9.54855i −0.364300 0.630986i 0.624364 0.781134i \(-0.285358\pi\)
−0.988664 + 0.150148i \(0.952025\pi\)
\(230\) 2.97402 0.196101
\(231\) 2.45884 3.83771i 0.161780 0.252503i
\(232\) 20.1651 1.32390
\(233\) −8.67743 15.0298i −0.568477 0.984632i −0.996717 0.0809664i \(-0.974199\pi\)
0.428239 0.903665i \(-0.359134\pi\)
\(234\) 0 0
\(235\) −2.52446 + 4.37249i −0.164678 + 0.285230i
\(236\) −4.18472 7.24814i −0.272402 0.471814i
\(237\) 9.51100 0.617806
\(238\) 4.36084 + 8.43015i 0.282671 + 0.546445i
\(239\) 19.7223 1.27573 0.637865 0.770148i \(-0.279818\pi\)
0.637865 + 0.770148i \(0.279818\pi\)
\(240\) 1.20350 + 2.08453i 0.0776858 + 0.134556i
\(241\) −1.39206 + 2.41112i −0.0896706 + 0.155314i −0.907372 0.420329i \(-0.861915\pi\)
0.817701 + 0.575643i \(0.195248\pi\)
\(242\) 5.63246 9.75571i 0.362069 0.627121i
\(243\) −10.9318 18.9345i −0.701278 1.21465i
\(244\) −3.98574 −0.255161
\(245\) −4.35934 0.404077i −0.278508 0.0258155i
\(246\) −13.0870 −0.834397
\(247\) 0 0
\(248\) 6.71028 11.6226i 0.426103 0.738033i
\(249\) −12.4044 + 21.4851i −0.786098 + 1.36156i
\(250\) −3.22435 5.58475i −0.203926 0.353210i
\(251\) 23.5608 1.48714 0.743572 0.668655i \(-0.233130\pi\)
0.743572 + 0.668655i \(0.233130\pi\)
\(252\) 3.00348 + 5.80617i 0.189201 + 0.365754i
\(253\) −3.13974 −0.197394
\(254\) 4.56570 + 7.90803i 0.286478 + 0.496194i
\(255\) 2.54191 4.40273i 0.159181 0.275709i
\(256\) 8.09042 14.0130i 0.505651 0.875814i
\(257\) 1.71615 + 2.97245i 0.107050 + 0.185417i 0.914574 0.404419i \(-0.132526\pi\)
−0.807524 + 0.589835i \(0.799193\pi\)
\(258\) 29.2367 1.82019
\(259\) 0.604338 0.943239i 0.0375517 0.0586100i
\(260\) 0 0
\(261\) 9.60450 + 16.6355i 0.594503 + 1.02971i
\(262\) 3.75733 6.50788i 0.232128 0.402058i
\(263\) 10.7245 18.5754i 0.661303 1.14541i −0.318970 0.947765i \(-0.603337\pi\)
0.980273 0.197646i \(-0.0633298\pi\)
\(264\) −2.63285 4.56023i −0.162041 0.280663i
\(265\) 0.435992 0.0267828
\(266\) 14.7551 + 0.682378i 0.904691 + 0.0418393i
\(267\) −32.5300 −1.99080
\(268\) −4.42131 7.65794i −0.270075 0.467783i
\(269\) −7.32843 + 12.6932i −0.446822 + 0.773919i −0.998177 0.0603517i \(-0.980778\pi\)
0.551355 + 0.834271i \(0.314111\pi\)
\(270\) 0.0720191 0.124741i 0.00438294 0.00759148i
\(271\) 1.02183 + 1.76986i 0.0620717 + 0.107511i 0.895391 0.445280i \(-0.146896\pi\)
−0.833320 + 0.552792i \(0.813563\pi\)
\(272\) 5.29168 0.320856
\(273\) 0 0
\(274\) 6.67112 0.403017
\(275\) 1.63273 + 2.82797i 0.0984572 + 0.170533i
\(276\) 4.57138 7.91787i 0.275165 0.476600i
\(277\) 2.71678 4.70560i 0.163236 0.282732i −0.772792 0.634660i \(-0.781140\pi\)
0.936027 + 0.351927i \(0.114474\pi\)
\(278\) −3.50428 6.06959i −0.210173 0.364030i
\(279\) 12.7843 0.765373
\(280\) −2.72864 + 4.25881i −0.163067 + 0.254513i
\(281\) 20.2356 1.20715 0.603577 0.797305i \(-0.293742\pi\)
0.603577 + 0.797305i \(0.293742\pi\)
\(282\) −10.5310 18.2401i −0.627109 1.08618i
\(283\) −0.867593 + 1.50272i −0.0515731 + 0.0893272i −0.890659 0.454671i \(-0.849757\pi\)
0.839086 + 0.543998i \(0.183090\pi\)
\(284\) 5.97704 10.3525i 0.354672 0.614310i
\(285\) −3.95586 6.85176i −0.234325 0.405863i
\(286\) 0 0
\(287\) −6.09755 11.7875i −0.359927 0.695792i
\(288\) 12.8548 0.757474
\(289\) 2.91173 + 5.04326i 0.171278 + 0.296662i
\(290\) −2.21373 + 3.83430i −0.129995 + 0.225158i
\(291\) 0.245600 0.425392i 0.0143973 0.0249369i
\(292\) 2.15695 + 3.73595i 0.126226 + 0.218630i
\(293\) 27.2441 1.59162 0.795810 0.605547i \(-0.207046\pi\)
0.795810 + 0.605547i \(0.207046\pi\)
\(294\) 10.5524 14.9061i 0.615430 0.869340i
\(295\) 6.16875 0.359159
\(296\) −0.647107 1.12082i −0.0376123 0.0651465i
\(297\) −0.0760324 + 0.131692i −0.00441185 + 0.00764154i
\(298\) −1.98375 + 3.43595i −0.114915 + 0.199039i
\(299\) 0 0
\(300\) −9.50884 −0.548993
\(301\) 13.6221 + 26.3335i 0.785163 + 1.51784i
\(302\) 5.23409 0.301188
\(303\) −21.0735 36.5004i −1.21064 2.09690i
\(304\) 4.11760 7.13190i 0.236161 0.409042i
\(305\) 1.46886 2.54414i 0.0841067 0.145677i
\(306\) 5.22272 + 9.04601i 0.298563 + 0.517126i
\(307\) 12.7138 0.725612 0.362806 0.931865i \(-0.381819\pi\)
0.362806 + 0.931865i \(0.381819\pi\)
\(308\) 0.858127 1.33935i 0.0488963 0.0763165i
\(309\) 26.2951 1.49588
\(310\) 1.47332 + 2.55186i 0.0836788 + 0.144936i
\(311\) −4.80939 + 8.33011i −0.272716 + 0.472357i −0.969556 0.244869i \(-0.921255\pi\)
0.696841 + 0.717226i \(0.254588\pi\)
\(312\) 0 0
\(313\) 4.51273 + 7.81628i 0.255075 + 0.441802i 0.964916 0.262559i \(-0.0845666\pi\)
−0.709841 + 0.704362i \(0.751233\pi\)
\(314\) −10.2151 −0.576473
\(315\) −4.81300 0.222587i −0.271182 0.0125414i
\(316\) 3.31931 0.186726
\(317\) −12.3131 21.3269i −0.691572 1.19784i −0.971323 0.237766i \(-0.923585\pi\)
0.279750 0.960073i \(-0.409748\pi\)
\(318\) −0.909386 + 1.57510i −0.0509958 + 0.0883273i
\(319\) 2.33709 4.04797i 0.130852 0.226643i
\(320\) 2.47141 + 4.28061i 0.138156 + 0.239293i
\(321\) 14.8724 0.830095
\(322\) −12.5675 0.581209i −0.700359 0.0323895i
\(323\) −17.3935 −0.967802
\(324\) −3.92754 6.80269i −0.218196 0.377927i
\(325\) 0 0
\(326\) −12.7205 + 22.0325i −0.704521 + 1.22027i
\(327\) −13.8580 24.0027i −0.766348 1.32735i
\(328\) −15.3323 −0.846584
\(329\) 11.5223 17.9838i 0.635244 0.991477i
\(330\) 1.15614 0.0636436
\(331\) −6.58591 11.4071i −0.361994 0.626993i 0.626295 0.779586i \(-0.284571\pi\)
−0.988289 + 0.152594i \(0.951237\pi\)
\(332\) −4.32911 + 7.49823i −0.237591 + 0.411519i
\(333\) 0.616426 1.06768i 0.0337799 0.0585085i
\(334\) 0.607311 + 1.05189i 0.0332306 + 0.0575571i
\(335\) 6.51752 0.356090
\(336\) −4.67834 9.04393i −0.255225 0.493387i
\(337\) −17.0307 −0.927720 −0.463860 0.885909i \(-0.653536\pi\)
−0.463860 + 0.885909i \(0.653536\pi\)
\(338\) 0 0
\(339\) −1.12265 + 1.94448i −0.0609738 + 0.105610i
\(340\) 0.887121 1.53654i 0.0481109 0.0833305i
\(341\) −1.55542 2.69406i −0.0842306 0.145892i
\(342\) 16.2558 0.879010
\(343\) 18.3425 + 2.55948i 0.990405 + 0.138199i
\(344\) 34.2527 1.84678
\(345\) 3.36937 + 5.83592i 0.181401 + 0.314195i
\(346\) −6.43251 + 11.1414i −0.345814 + 0.598968i
\(347\) −0.229959 + 0.398300i −0.0123448 + 0.0213819i −0.872132 0.489271i \(-0.837263\pi\)
0.859787 + 0.510653i \(0.170596\pi\)
\(348\) 6.80550 + 11.7875i 0.364813 + 0.631875i
\(349\) −6.87822 −0.368183 −0.184091 0.982909i \(-0.558934\pi\)
−0.184091 + 0.982909i \(0.558934\pi\)
\(350\) 6.01184 + 11.6218i 0.321347 + 0.621210i
\(351\) 0 0
\(352\) −1.56400 2.70892i −0.0833613 0.144386i
\(353\) −0.766631 + 1.32784i −0.0408036 + 0.0706740i −0.885706 0.464247i \(-0.846325\pi\)
0.844902 + 0.534921i \(0.179658\pi\)
\(354\) −12.8667 + 22.2857i −0.683856 + 1.18447i
\(355\) 4.40542 + 7.63041i 0.233815 + 0.404980i
\(356\) −11.3529 −0.601701
\(357\) −11.6019 + 18.1081i −0.614040 + 0.958383i
\(358\) 10.1626 0.537112
\(359\) 13.6034 + 23.5617i 0.717959 + 1.24354i 0.961807 + 0.273728i \(0.0882568\pi\)
−0.243848 + 0.969813i \(0.578410\pi\)
\(360\) −2.78322 + 4.82068i −0.146688 + 0.254072i
\(361\) −4.03438 + 6.98774i −0.212336 + 0.367776i
\(362\) −6.13326 10.6231i −0.322357 0.558339i
\(363\) 25.5249 1.33971
\(364\) 0 0
\(365\) −3.17959 −0.166427
\(366\) 6.12745 + 10.6131i 0.320287 + 0.554753i
\(367\) −13.4907 + 23.3666i −0.704208 + 1.21972i 0.262769 + 0.964859i \(0.415364\pi\)
−0.966977 + 0.254865i \(0.917969\pi\)
\(368\) −3.50713 + 6.07452i −0.182822 + 0.316656i
\(369\) −7.30267 12.6486i −0.380162 0.658460i
\(370\) 0.284159 0.0147727
\(371\) −1.84240 0.0852056i −0.0956526 0.00442365i
\(372\) 9.05859 0.469666
\(373\) −1.98619 3.44018i −0.102841 0.178126i 0.810013 0.586412i \(-0.199460\pi\)
−0.912854 + 0.408286i \(0.866127\pi\)
\(374\) 1.27086 2.20120i 0.0657147 0.113821i
\(375\) 7.30597 12.6543i 0.377279 0.653466i
\(376\) −12.3377 21.3695i −0.636269 1.10205i
\(377\) 0 0
\(378\) −0.328714 + 0.513050i −0.0169072 + 0.0263885i
\(379\) −11.4059 −0.585884 −0.292942 0.956130i \(-0.594634\pi\)
−0.292942 + 0.956130i \(0.594634\pi\)
\(380\) −1.38058 2.39124i −0.0708225 0.122668i
\(381\) −10.3453 + 17.9186i −0.530005 + 0.917996i
\(382\) −8.41680 + 14.5783i −0.430641 + 0.745892i
\(383\) 11.8960 + 20.6044i 0.607856 + 1.05284i 0.991593 + 0.129395i \(0.0413036\pi\)
−0.383737 + 0.923442i \(0.625363\pi\)
\(384\) 0.849134 0.0433322
\(385\) 0.538676 + 1.04134i 0.0274535 + 0.0530716i
\(386\) −24.6879 −1.25658
\(387\) 16.3143 + 28.2573i 0.829304 + 1.43640i
\(388\) 0.0857137 0.148460i 0.00435145 0.00753694i
\(389\) 14.2055 24.6046i 0.720247 1.24751i −0.240653 0.970611i \(-0.577362\pi\)
0.960901 0.276894i \(-0.0893051\pi\)
\(390\) 0 0
\(391\) 14.8148 0.749216
\(392\) 12.3629 17.4635i 0.624420 0.882038i
\(393\) 17.0272 0.858911
\(394\) −5.47446 9.48204i −0.275799 0.477698i
\(395\) −1.22326 + 2.11875i −0.0615489 + 0.106606i
\(396\) 0.875291 1.51605i 0.0439850 0.0761843i
\(397\) 4.92956 + 8.53825i 0.247408 + 0.428522i 0.962806 0.270195i \(-0.0870880\pi\)
−0.715398 + 0.698717i \(0.753755\pi\)
\(398\) 12.7945 0.641332
\(399\) 15.3775 + 29.7270i 0.769838 + 1.48821i
\(400\) 7.29510 0.364755
\(401\) −6.30971 10.9287i −0.315092 0.545756i 0.664365 0.747408i \(-0.268702\pi\)
−0.979457 + 0.201653i \(0.935369\pi\)
\(402\) −13.5941 + 23.5457i −0.678013 + 1.17435i
\(403\) 0 0
\(404\) −7.35460 12.7385i −0.365905 0.633766i
\(405\) 5.78964 0.287689
\(406\) 10.1041 15.7702i 0.501456 0.782663i
\(407\) −0.299994 −0.0148701
\(408\) 12.4230 + 21.5173i 0.615031 + 1.06527i
\(409\) 9.02867 15.6381i 0.446439 0.773255i −0.551712 0.834035i \(-0.686025\pi\)
0.998151 + 0.0607793i \(0.0193586\pi\)
\(410\) 1.68319 2.91537i 0.0831268 0.143980i
\(411\) 7.55795 + 13.0908i 0.372806 + 0.645720i
\(412\) 9.17691 0.452114
\(413\) −26.0677 1.20555i −1.28271 0.0593214i
\(414\) −13.8457 −0.680478
\(415\) −3.19080 5.52663i −0.156630 0.271291i
\(416\) 0 0
\(417\) 7.94024 13.7529i 0.388835 0.673483i
\(418\) −1.97778 3.42562i −0.0967366 0.167553i
\(419\) 14.2805 0.697647 0.348823 0.937188i \(-0.386581\pi\)
0.348823 + 0.937188i \(0.386581\pi\)
\(420\) −3.41037 0.157720i −0.166409 0.00769593i
\(421\) 4.27439 0.208321 0.104160 0.994561i \(-0.466784\pi\)
0.104160 + 0.994561i \(0.466784\pi\)
\(422\) 8.36410 + 14.4870i 0.407158 + 0.705218i
\(423\) 11.7527 20.3564i 0.571438 0.989760i
\(424\) −1.06541 + 1.84534i −0.0517407 + 0.0896175i
\(425\) −7.70398 13.3437i −0.373698 0.647263i
\(426\) −36.7550 −1.78079
\(427\) −6.70425 + 10.4639i −0.324441 + 0.506382i
\(428\) 5.19042 0.250888
\(429\) 0 0
\(430\) −3.76028 + 6.51300i −0.181337 + 0.314085i
\(431\) −7.30335 + 12.6498i −0.351790 + 0.609318i −0.986563 0.163381i \(-0.947760\pi\)
0.634773 + 0.772698i \(0.281094\pi\)
\(432\) 0.169858 + 0.294203i 0.00817230 + 0.0141548i
\(433\) −28.0099 −1.34607 −0.673035 0.739611i \(-0.735009\pi\)
−0.673035 + 0.739611i \(0.735009\pi\)
\(434\) −5.72718 11.0715i −0.274914 0.531449i
\(435\) −10.0321 −0.481001
\(436\) −4.83640 8.37688i −0.231621 0.401180i
\(437\) 11.5278 19.9667i 0.551448 0.955137i
\(438\) 6.63193 11.4868i 0.316886 0.548863i
\(439\) −8.53872 14.7895i −0.407531 0.705864i 0.587082 0.809528i \(-0.300277\pi\)
−0.994612 + 0.103664i \(0.966943\pi\)
\(440\) 1.35450 0.0645733
\(441\) 20.2951 + 1.88120i 0.966433 + 0.0895810i
\(442\) 0 0
\(443\) −6.90783 11.9647i −0.328201 0.568461i 0.653954 0.756534i \(-0.273109\pi\)
−0.982155 + 0.188073i \(0.939776\pi\)
\(444\) 0.436783 0.756531i 0.0207288 0.0359034i
\(445\) 4.18386 7.24665i 0.198334 0.343524i
\(446\) 3.63048 + 6.28817i 0.171908 + 0.297754i
\(447\) −8.98984 −0.425205
\(448\) −9.60703 18.5718i −0.453890 0.877436i
\(449\) 32.6410 1.54042 0.770211 0.637789i \(-0.220151\pi\)
0.770211 + 0.637789i \(0.220151\pi\)
\(450\) 7.20003 + 12.4708i 0.339412 + 0.587880i
\(451\) −1.77698 + 3.07783i −0.0836749 + 0.144929i
\(452\) −0.391801 + 0.678619i −0.0184287 + 0.0319195i
\(453\) 5.92988 + 10.2709i 0.278610 + 0.482567i
\(454\) 18.0536 0.847298
\(455\) 0 0
\(456\) 38.6667 1.81074
\(457\) 1.58517 + 2.74559i 0.0741511 + 0.128433i 0.900717 0.434407i \(-0.143042\pi\)
−0.826566 + 0.562840i \(0.809709\pi\)
\(458\) −5.91560 + 10.2461i −0.276418 + 0.478769i
\(459\) 0.358756 0.621384i 0.0167453 0.0290037i
\(460\) 1.17590 + 2.03672i 0.0548266 + 0.0949625i
\(461\) −0.202023 −0.00940915 −0.00470458 0.999989i \(-0.501498\pi\)
−0.00470458 + 0.999989i \(0.501498\pi\)
\(462\) −4.88559 0.225944i −0.227298 0.0105119i
\(463\) −17.2121 −0.799912 −0.399956 0.916534i \(-0.630975\pi\)
−0.399956 + 0.916534i \(0.630975\pi\)
\(464\) −5.22112 9.04325i −0.242384 0.419822i
\(465\) −3.33835 + 5.78219i −0.154812 + 0.268143i
\(466\) −9.31136 + 16.1277i −0.431340 + 0.747103i
\(467\) 0.0955845 + 0.165557i 0.00442312 + 0.00766108i 0.868228 0.496165i \(-0.165259\pi\)
−0.863805 + 0.503826i \(0.831925\pi\)
\(468\) 0 0
\(469\) −27.5415 1.27371i −1.27175 0.0588146i
\(470\) 5.41777 0.249903
\(471\) −11.5731 20.0452i −0.533260 0.923633i
\(472\) −15.0742 + 26.1092i −0.693845 + 1.20177i
\(473\) 3.96982 6.87593i 0.182533 0.316156i
\(474\) −5.10291 8.83850i −0.234384 0.405966i
\(475\) −23.9787 −1.10022
\(476\) −4.04905 + 6.31968i −0.185588 + 0.289662i
\(477\) −2.02978 −0.0929374
\(478\) −10.5816 18.3278i −0.483989 0.838294i
\(479\) −10.7392 + 18.6009i −0.490688 + 0.849897i −0.999943 0.0107189i \(-0.996588\pi\)
0.509254 + 0.860616i \(0.329921\pi\)
\(480\) −3.35676 + 5.81408i −0.153214 + 0.265375i
\(481\) 0 0
\(482\) 2.98752 0.136078
\(483\) −13.0976 25.3197i −0.595964 1.15209i
\(484\) 8.90811 0.404914
\(485\) 0.0631758 + 0.109424i 0.00286867 + 0.00496868i
\(486\) −11.7305 + 20.3178i −0.532105 + 0.921633i
\(487\) −9.52422 + 16.4964i −0.431584 + 0.747525i −0.997010 0.0772740i \(-0.975378\pi\)
0.565426 + 0.824799i \(0.308712\pi\)
\(488\) 7.17871 + 12.4339i 0.324965 + 0.562856i
\(489\) −57.6458 −2.60684
\(490\) 1.96340 + 4.26790i 0.0886973 + 0.192804i
\(491\) 35.7559 1.61364 0.806821 0.590796i \(-0.201186\pi\)
0.806821 + 0.590796i \(0.201186\pi\)
\(492\) −5.17448 8.96247i −0.233284 0.404059i
\(493\) −11.0275 + 19.1002i −0.496654 + 0.860230i
\(494\) 0 0
\(495\) 0.645140 + 1.11741i 0.0289969 + 0.0502240i
\(496\) −6.94968 −0.312050
\(497\) −17.1251 33.1053i −0.768164 1.48497i
\(498\) 26.6213 1.19293
\(499\) −8.84457 15.3192i −0.395937 0.685784i 0.597283 0.802031i \(-0.296247\pi\)
−0.993220 + 0.116247i \(0.962914\pi\)
\(500\) 2.54976 4.41632i 0.114029 0.197504i
\(501\) −1.37609 + 2.38346i −0.0614792 + 0.106485i
\(502\) −12.6410 21.8949i −0.564196 0.977217i
\(503\) 11.3305 0.505203 0.252601 0.967570i \(-0.418714\pi\)
0.252601 + 0.967570i \(0.418714\pi\)
\(504\) 12.7033 19.8271i 0.565851 0.883169i
\(505\) 10.8415 0.482441
\(506\) 1.68456 + 2.91774i 0.0748878 + 0.129709i
\(507\) 0 0
\(508\) −3.61048 + 6.25353i −0.160189 + 0.277455i
\(509\) 9.67569 + 16.7588i 0.428868 + 0.742821i 0.996773 0.0802734i \(-0.0255793\pi\)
−0.567905 + 0.823094i \(0.692246\pi\)
\(510\) −5.45523 −0.241562
\(511\) 13.4362 + 0.621384i 0.594382 + 0.0274884i
\(512\) −16.6645 −0.736472
\(513\) −0.558316 0.967032i −0.0246502 0.0426955i
\(514\) 1.84152 3.18961i 0.0812259 0.140687i
\(515\) −3.38195 + 5.85772i −0.149027 + 0.258122i
\(516\) 11.5599 + 20.0224i 0.508897 + 0.881435i
\(517\) −5.71967 −0.251551
\(518\) −1.20079 0.0555330i −0.0527597 0.00243998i
\(519\) −29.1505 −1.27957
\(520\) 0 0
\(521\) 3.85550 6.67791i 0.168912 0.292565i −0.769125 0.639098i \(-0.779308\pi\)
0.938038 + 0.346533i \(0.112641\pi\)
\(522\) 10.3062 17.8508i 0.451088 0.781307i
\(523\) 17.5251 + 30.3543i 0.766317 + 1.32730i 0.939547 + 0.342419i \(0.111246\pi\)
−0.173230 + 0.984881i \(0.555420\pi\)
\(524\) 5.94246 0.259597
\(525\) −15.9944 + 24.9638i −0.698054 + 1.08951i
\(526\) −23.0160 −1.00355
\(527\) 7.33919 + 12.7119i 0.319700 + 0.553737i
\(528\) −1.36339 + 2.36146i −0.0593339 + 0.102769i
\(529\) 1.68133 2.91214i 0.0731011 0.126615i
\(530\) −0.233922 0.405165i −0.0101609 0.0175992i
\(531\) −28.7189 −1.24630
\(532\) 5.36671 + 10.3746i 0.232676 + 0.449797i
\(533\) 0 0
\(534\) 17.4532 + 30.2299i 0.755275 + 1.30818i
\(535\) −1.91282 + 3.31309i −0.0826982 + 0.143238i
\(536\) −15.9264 + 27.5854i −0.687917 + 1.19151i
\(537\) 11.5136 + 19.9422i 0.496849 + 0.860568i
\(538\) 15.7276 0.678066
\(539\) −2.07281 4.50573i −0.0892821 0.194075i
\(540\) 0.113903 0.00490160
\(541\) −6.06674 10.5079i −0.260829 0.451770i 0.705633 0.708577i \(-0.250663\pi\)
−0.966463 + 0.256807i \(0.917329\pi\)
\(542\) 1.09648 1.89916i 0.0470978 0.0815758i
\(543\) 13.8972 24.0706i 0.596385 1.03297i
\(544\) 7.37967 + 12.7820i 0.316401 + 0.548022i
\(545\) 7.12940 0.305390
\(546\) 0 0
\(547\) −5.12546 −0.219149 −0.109575 0.993979i \(-0.534949\pi\)
−0.109575 + 0.993979i \(0.534949\pi\)
\(548\) 2.63770 + 4.56864i 0.112677 + 0.195162i
\(549\) −6.83835 + 11.8444i −0.291854 + 0.505505i
\(550\) 1.75201 3.03457i 0.0747058 0.129394i
\(551\) 17.1616 + 29.7248i 0.731109 + 1.26632i
\(552\) −32.9340 −1.40177
\(553\) 5.58327 8.71427i 0.237425 0.370568i
\(554\) −5.83051 −0.247715
\(555\) 0.321934 + 0.557606i 0.0136653 + 0.0236691i
\(556\) 2.77112 4.79972i 0.117522 0.203554i
\(557\) −18.7793 + 32.5267i −0.795705 + 1.37820i 0.126686 + 0.991943i \(0.459566\pi\)
−0.922391 + 0.386258i \(0.873767\pi\)
\(558\) −6.85911 11.8803i −0.290369 0.502934i
\(559\) 0 0
\(560\) 2.61641 + 0.121001i 0.110563 + 0.00511323i
\(561\) 5.75922 0.243154
\(562\) −10.8569 18.8048i −0.457973 0.793232i
\(563\) −14.3504 + 24.8557i −0.604799 + 1.04754i 0.387284 + 0.921960i \(0.373413\pi\)
−0.992083 + 0.125583i \(0.959920\pi\)
\(564\) 8.32769 14.4240i 0.350659 0.607359i
\(565\) −0.288779 0.500180i −0.0121490 0.0210428i
\(566\) 1.86195 0.0782636
\(567\) −24.4656 1.13146i −1.02746 0.0475170i
\(568\) −43.0610 −1.80680
\(569\) −8.97417 15.5437i −0.376217 0.651627i 0.614291 0.789079i \(-0.289442\pi\)
−0.990508 + 0.137452i \(0.956109\pi\)
\(570\) −4.24486 + 7.35231i −0.177798 + 0.307955i
\(571\) −8.91370 + 15.4390i −0.373027 + 0.646101i −0.990030 0.140860i \(-0.955013\pi\)
0.617003 + 0.786961i \(0.288347\pi\)
\(572\) 0 0
\(573\) −38.1428 −1.59344
\(574\) −7.68250 + 11.9907i −0.320662 + 0.500483i
\(575\) 20.4236 0.851724
\(576\) −11.5058 19.9286i −0.479407 0.830357i
\(577\) −16.5285 + 28.6282i −0.688091 + 1.19181i 0.284363 + 0.958717i \(0.408218\pi\)
−0.972455 + 0.233092i \(0.925116\pi\)
\(578\) 3.12445 5.41170i 0.129960 0.225097i
\(579\) −27.9698 48.4451i −1.16239 2.01331i
\(580\) −3.50117 −0.145378
\(581\) 12.4035 + 23.9778i 0.514584 + 0.994766i
\(582\) −0.527085 −0.0218484
\(583\) 0.246957 + 0.427742i 0.0102279 + 0.0177153i
\(584\) 7.76975 13.4576i 0.321515 0.556880i
\(585\) 0 0
\(586\) −14.6172 25.3178i −0.603832 1.04587i
\(587\) 14.7295 0.607953 0.303976 0.952680i \(-0.401686\pi\)
0.303976 + 0.952680i \(0.401686\pi\)
\(588\) 14.3806 + 1.33297i 0.593045 + 0.0549708i
\(589\) 22.8433 0.941241
\(590\) −3.30970 5.73258i −0.136258 0.236006i
\(591\) 12.4044 21.4851i 0.510250 0.883779i
\(592\) −0.335097 + 0.580404i −0.0137724 + 0.0238545i
\(593\) 4.60494 + 7.97598i 0.189102 + 0.327534i 0.944951 0.327212i \(-0.106109\pi\)
−0.755849 + 0.654746i \(0.772776\pi\)
\(594\) 0.163174 0.00669510
\(595\) −2.54172 4.91353i −0.104201 0.201435i
\(596\) −3.13743 −0.128514
\(597\) 14.4954 + 25.1067i 0.593256 + 1.02755i
\(598\) 0 0
\(599\) 5.28727 9.15782i 0.216032 0.374178i −0.737559 0.675282i \(-0.764022\pi\)
0.953591 + 0.301104i \(0.0973551\pi\)
\(600\) 17.1263 + 29.6637i 0.699180 + 1.21102i
\(601\) 4.08916 0.166800 0.0834001 0.996516i \(-0.473422\pi\)
0.0834001 + 0.996516i \(0.473422\pi\)
\(602\) 17.1629 26.7875i 0.699507 1.09178i
\(603\) −30.3426 −1.23565
\(604\) 2.06951 + 3.58450i 0.0842072 + 0.145851i
\(605\) −3.28289 + 5.68613i −0.133469 + 0.231174i
\(606\) −22.6131 + 39.1670i −0.918593 + 1.59105i
\(607\) −1.80353 3.12380i −0.0732030 0.126791i 0.827100 0.562054i \(-0.189989\pi\)
−0.900303 + 0.435263i \(0.856655\pi\)
\(608\) 22.9693 0.931527
\(609\) 42.3932 + 1.96056i 1.71786 + 0.0794459i
\(610\) −3.15233 −0.127634
\(611\) 0 0
\(612\) −4.13003 + 7.15343i −0.166947 + 0.289160i
\(613\) 19.2422 33.3285i 0.777186 1.34613i −0.156371 0.987698i \(-0.549980\pi\)
0.933557 0.358428i \(-0.116687\pi\)
\(614\) −6.82128 11.8148i −0.275284 0.476806i
\(615\) 7.62778 0.307582
\(616\) −5.72379 0.264709i −0.230618 0.0106654i
\(617\) −3.09503 −0.124601 −0.0623007 0.998057i \(-0.519844\pi\)
−0.0623007 + 0.998057i \(0.519844\pi\)
\(618\) −14.1080 24.4359i −0.567509 0.982954i
\(619\) −6.13462 + 10.6255i −0.246571 + 0.427074i −0.962572 0.271025i \(-0.912637\pi\)
0.716001 + 0.698099i \(0.245971\pi\)
\(620\) −1.16507 + 2.01797i −0.0467905 + 0.0810435i
\(621\) 0.475540 + 0.823660i 0.0190828 + 0.0330523i
\(622\) 10.3215 0.413854
\(623\) −19.0962 + 29.8050i −0.765073 + 1.19411i
\(624\) 0 0
\(625\) −9.64277 16.7018i −0.385711 0.668071i
\(626\) 4.84241 8.38730i 0.193542 0.335224i
\(627\) 4.48140 7.76202i 0.178970 0.309985i
\(628\) −4.03897 6.99571i −0.161173 0.279159i
\(629\) 1.41551 0.0564402
\(630\) 2.37546 + 4.59211i 0.0946406 + 0.182954i
\(631\) −5.31780 −0.211698 −0.105849 0.994382i \(-0.533756\pi\)
−0.105849 + 0.994382i \(0.533756\pi\)
\(632\) −5.97840 10.3549i −0.237808 0.411896i
\(633\) −18.9520 + 32.8258i −0.753273 + 1.30471i
\(634\) −13.2126 + 22.8849i −0.524740 + 0.908877i
\(635\) −2.66113 4.60921i −0.105604 0.182911i
\(636\) −1.43825 −0.0570304
\(637\) 0 0
\(638\) −5.01566 −0.198572
\(639\) −20.5097 35.5238i −0.811349 1.40530i
\(640\) −0.109212 + 0.189160i −0.00431697 + 0.00747721i
\(641\) −6.09521 + 10.5572i −0.240746 + 0.416985i −0.960927 0.276801i \(-0.910726\pi\)
0.720181 + 0.693787i \(0.244059\pi\)
\(642\) −7.97944 13.8208i −0.314923 0.545463i
\(643\) −18.9733 −0.748235 −0.374117 0.927381i \(-0.622054\pi\)
−0.374117 + 0.927381i \(0.622054\pi\)
\(644\) −4.57104 8.83649i −0.180124 0.348207i
\(645\) −17.0406 −0.670974
\(646\) 9.33211 + 16.1637i 0.367167 + 0.635952i
\(647\) −9.85587 + 17.0709i −0.387474 + 0.671125i −0.992109 0.125378i \(-0.959986\pi\)
0.604635 + 0.796503i \(0.293319\pi\)
\(648\) −14.1478 + 24.5046i −0.555776 + 0.962633i
\(649\) 3.49414 + 6.05202i 0.137157 + 0.237563i
\(650\) 0 0
\(651\) 15.2371 23.7818i 0.597188 0.932080i
\(652\) −20.1182 −0.787891
\(653\) 10.1986 + 17.6645i 0.399103 + 0.691267i 0.993616 0.112819i \(-0.0359882\pi\)
−0.594512 + 0.804087i \(0.702655\pi\)
\(654\) −14.8704 + 25.7563i −0.581478 + 1.00715i
\(655\) −2.18996 + 3.79313i −0.0855690 + 0.148210i
\(656\) 3.96982 + 6.87593i 0.154996 + 0.268460i
\(657\) 14.8027 0.577510
\(658\) −22.8942 1.05879i −0.892509 0.0412759i
\(659\) 32.6628 1.27236 0.636181 0.771540i \(-0.280513\pi\)
0.636181 + 0.771540i \(0.280513\pi\)
\(660\) 0.457129 + 0.791771i 0.0177937 + 0.0308196i
\(661\) 4.86846 8.43242i 0.189361 0.327983i −0.755676 0.654945i \(-0.772692\pi\)
0.945037 + 0.326962i \(0.106025\pi\)
\(662\) −7.06704 + 12.2405i −0.274668 + 0.475740i
\(663\) 0 0
\(664\) 31.1886 1.21035
\(665\) −8.60002 0.397725i −0.333494 0.0154231i
\(666\) −1.32292 −0.0512620
\(667\) −14.6172 25.3178i −0.565981 0.980308i
\(668\) −0.480251 + 0.831819i −0.0185815 + 0.0321841i
\(669\) −8.22620 + 14.2482i −0.318043 + 0.550867i
\(670\) −3.49683 6.05668i −0.135094 0.233990i
\(671\) 3.32800 0.128476
\(672\) 15.3211 23.9129i 0.591025 0.922461i
\(673\) 39.4512 1.52073 0.760367 0.649494i \(-0.225019\pi\)
0.760367 + 0.649494i \(0.225019\pi\)
\(674\) 9.13742 + 15.8265i 0.351960 + 0.609613i
\(675\) 0.494581 0.856639i 0.0190364 0.0329720i
\(676\) 0 0
\(677\) 24.3169 + 42.1182i 0.934576 + 1.61873i 0.775389 + 0.631484i \(0.217554\pi\)
0.159187 + 0.987248i \(0.449113\pi\)
\(678\) 2.40932 0.0925296
\(679\) −0.245582 0.474745i −0.00942455 0.0182191i
\(680\) −6.39117 −0.245090
\(681\) 20.4536 + 35.4266i 0.783783 + 1.35755i
\(682\) −1.66905 + 2.89088i −0.0639112 + 0.110697i
\(683\) −2.85387 + 4.94304i −0.109200 + 0.189140i −0.915446 0.402440i \(-0.868162\pi\)
0.806246 + 0.591580i \(0.201496\pi\)
\(684\) 6.42738 + 11.1326i 0.245757 + 0.425664i
\(685\) −3.88828 −0.148563
\(686\) −7.46278 18.4188i −0.284930 0.703234i
\(687\) −26.8080 −1.02279
\(688\) −8.86867 15.3610i −0.338115 0.585632i
\(689\) 0 0
\(690\) 3.61552 6.26226i 0.137640 0.238400i
\(691\) 20.8866 + 36.1766i 0.794563 + 1.37622i 0.923116 + 0.384521i \(0.125633\pi\)
−0.128553 + 0.991703i \(0.541033\pi\)
\(692\) −10.1734 −0.386736
\(693\) −2.50783 4.84801i −0.0952646 0.184161i
\(694\) 0.493517 0.0187336
\(695\) 2.04247 + 3.53767i 0.0774754 + 0.134191i
\(696\) 24.5147 42.4608i 0.929228 1.60947i
\(697\) 8.38464 14.5226i 0.317591 0.550084i
\(698\) 3.69035 + 6.39188i 0.139682 + 0.241936i
\(699\) −42.1967 −1.59603
\(700\) −5.58200 + 8.71229i −0.210980 + 0.329294i
\(701\) −22.4361 −0.847399 −0.423700 0.905803i \(-0.639269\pi\)
−0.423700 + 0.905803i \(0.639269\pi\)
\(702\) 0 0
\(703\) 1.10145 1.90776i 0.0415419 0.0719527i
\(704\) −2.79974 + 4.84929i −0.105519 + 0.182764i
\(705\) 6.13798 + 10.6313i 0.231170 + 0.400398i
\(706\) 1.64527 0.0619207
\(707\) −45.8137 2.11875i −1.72300 0.0796837i
\(708\) −20.3495 −0.764780
\(709\) 14.3734 + 24.8955i 0.539804 + 0.934969i 0.998914 + 0.0465891i \(0.0148351\pi\)
−0.459110 + 0.888380i \(0.651832\pi\)
\(710\) 4.72726 8.18785i 0.177411 0.307285i
\(711\) 5.69495 9.86394i 0.213577 0.369927i
\(712\) 20.4476 + 35.4163i 0.766307 + 1.32728i
\(713\) −19.4566 −0.728654
\(714\) 23.0525 + 1.06611i 0.862718 + 0.0398982i
\(715\) 0 0
\(716\) 4.01822 + 6.95976i 0.150168 + 0.260098i
\(717\) 23.9765 41.5284i 0.895417 1.55091i
\(718\) 14.5972 25.2830i 0.544762 0.943555i
\(719\) 2.10450 + 3.64509i 0.0784844 + 0.135939i 0.902596 0.430488i \(-0.141659\pi\)
−0.824112 + 0.566427i \(0.808325\pi\)
\(720\) 2.88251 0.107425
\(721\) 15.4361 24.0924i 0.574870 0.897247i
\(722\) 8.65821 0.322225
\(723\) 3.38467 + 5.86242i 0.125877 + 0.218026i
\(724\) 4.85008 8.40058i 0.180252 0.312205i
\(725\) −15.2025 + 26.3315i −0.564606 + 0.977927i
\(726\) −13.6948 23.7201i −0.508262 0.880335i
\(727\) 43.4680 1.61214 0.806070 0.591820i \(-0.201591\pi\)
0.806070 + 0.591820i \(0.201591\pi\)
\(728\) 0 0
\(729\) −25.3884 −0.940312
\(730\) 1.70594 + 2.95477i 0.0631396 + 0.109361i
\(731\) −18.7315 + 32.4439i −0.692809 + 1.19998i
\(732\) −4.84548 + 8.39261i −0.179094 + 0.310200i
\(733\) 4.54710 + 7.87581i 0.167951 + 0.290900i 0.937699 0.347448i \(-0.112952\pi\)
−0.769748 + 0.638348i \(0.779618\pi\)
\(734\) 28.9525 1.06866
\(735\) −6.15050 + 8.68803i −0.226865 + 0.320463i
\(736\) −19.5639 −0.721133
\(737\) 3.69169 + 6.39419i 0.135985 + 0.235533i
\(738\) −7.83617 + 13.5726i −0.288453 + 0.499616i
\(739\) 4.80433 8.32135i 0.176730 0.306106i −0.764028 0.645183i \(-0.776781\pi\)
0.940759 + 0.339077i \(0.110115\pi\)
\(740\) 0.112354 + 0.194603i 0.00413022 + 0.00715375i
\(741\) 0 0
\(742\) 0.909317 + 1.75784i 0.0333821 + 0.0645325i
\(743\) −32.1771 −1.18046 −0.590231 0.807234i \(-0.700964\pi\)
−0.590231 + 0.807234i \(0.700964\pi\)
\(744\) −16.3154 28.2591i −0.598152 1.03603i
\(745\) 1.15623 2.00265i 0.0423610 0.0733714i
\(746\) −2.13129 + 3.69150i −0.0780320 + 0.135155i
\(747\) 14.8549 + 25.7295i 0.543513 + 0.941392i
\(748\) 2.00995 0.0734911
\(749\) 8.73058 13.6265i 0.319008 0.497903i
\(750\) −15.6794 −0.572531
\(751\) −3.89892 6.75313i −0.142274 0.246425i 0.786079 0.618126i \(-0.212108\pi\)
−0.928352 + 0.371701i \(0.878775\pi\)
\(752\) −6.38894 + 11.0660i −0.232981 + 0.403534i
\(753\) 28.6429 49.6110i 1.04381 1.80793i
\(754\) 0 0
\(755\) −3.05070 −0.111026
\(756\) −0.481327 0.0222599i −0.0175057 0.000809586i
\(757\) 17.9970 0.654110 0.327055 0.945005i \(-0.393944\pi\)
0.327055 + 0.945005i \(0.393944\pi\)
\(758\) 6.11960 + 10.5995i 0.222274 + 0.384990i
\(759\) −3.81699 + 6.61123i −0.138548 + 0.239972i
\(760\) −4.97314 + 8.61373i −0.180395 + 0.312453i
\(761\) 20.3395 + 35.2290i 0.737306 + 1.27705i 0.953704 + 0.300746i \(0.0972358\pi\)
−0.216398 + 0.976305i \(0.569431\pi\)
\(762\) 22.2021 0.804299
\(763\) −30.1271 1.39329i −1.09068 0.0504406i
\(764\) −13.3117 −0.481601
\(765\) −3.04407 5.27248i −0.110059 0.190627i
\(766\) 12.7650 22.1097i 0.461220 0.798856i
\(767\) 0 0
\(768\) −19.6711 34.0713i −0.709819 1.22944i
\(769\) 39.3098 1.41755 0.708774 0.705435i \(-0.249248\pi\)
0.708774 + 0.705435i \(0.249248\pi\)
\(770\) 0.678695 1.05929i 0.0244585 0.0381743i
\(771\) 8.34529 0.300548
\(772\) −9.76138 16.9072i −0.351320 0.608504i
\(773\) −6.73679 + 11.6685i −0.242306 + 0.419685i −0.961371 0.275257i \(-0.911237\pi\)
0.719065 + 0.694943i \(0.244570\pi\)
\(774\) 17.5062 30.3216i 0.629247 1.08989i
\(775\) 10.1178 + 17.5245i 0.363442 + 0.629500i
\(776\) −0.617515 −0.0221675
\(777\) −1.25144 2.41923i −0.0448953 0.0867893i
\(778\) −30.4866 −1.09300
\(779\) −13.0486 22.6009i −0.467516 0.809761i
\(780\) 0 0