Properties

Label 1183.2.e.i.170.6
Level $1183$
Weight $2$
Character 1183.170
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 170.6
Root \(0.536527 + 0.929293i\) of defining polynomial
Character \(\chi\) \(=\) 1183.170
Dual form 1183.2.e.i.508.6

$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

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

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 \(-0.709470\pi\)
0.990972 + 0.134065i \(0.0428032\pi\)
\(3\) 1.21570 + 2.10566i 0.701886 + 1.21570i 0.967804 + 0.251707i \(0.0809918\pi\)
−0.265918 + 0.963996i \(0.585675\pi\)
\(4\) 0.424277 + 0.734868i 0.212138 + 0.367434i
\(5\) −0.312716 + 0.541640i −0.139851 + 0.242229i −0.927440 0.373972i \(-0.877996\pi\)
0.787589 + 0.616201i \(0.211329\pi\)
\(6\) 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 \(-0.132602\pi\)
−0.807664 + 0.589643i \(0.799269\pi\)
\(12\) −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 0.994370 0.105967i \(-0.0337939\pi\)
−0.588955 + 0.808166i \(0.700461\pi\)
\(18\) 1.56222 + 2.70585i 0.368219 + 0.637775i
\(19\) 2.60138 4.50573i 0.596798 1.03368i −0.396492 0.918038i \(-0.629773\pi\)
0.993290 0.115646i \(-0.0368939\pi\)
\(20\) −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 −0.537055 0.843547i \(-0.680463\pi\)
0.999061 + 0.0433296i \(0.0137966\pi\)
\(24\) 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 \(-0.0376579\pi\)
−0.598722 + 0.800957i \(0.704325\pi\)
\(32\) 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 \(-0.844414\pi\)
0.848099 + 0.529838i \(0.177747\pi\)
\(38\) −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 \(-0.628108\pi\)
−0.391687 + 0.920099i \(0.628108\pi\)
\(42\) 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 0.405633 + 0.914036i \(0.367051\pi\)
−0.994395 + 0.105729i \(0.966282\pi\)
\(48\) 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 0.888971 0.457964i \(-0.151421\pi\)
−0.841094 + 0.540890i \(0.818088\pi\)
\(54\) 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 −0.984977 0.172686i \(-0.944756\pi\)
0.342938 0.939358i \(-0.388578\pi\)
\(60\) −0.645188 1.11750i −0.0832934 0.144268i
\(61\) −2.34855 + 4.06781i −0.300701 + 0.520830i −0.976295 0.216444i \(-0.930554\pi\)
0.675594 + 0.737274i \(0.263887\pi\)
\(62\) 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 −0.986184 0.165655i \(-0.947026\pi\)
0.349631 0.936888i \(-0.386307\pi\)
\(68\) −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 \(-0.815080\pi\)
−0.835946 + 0.548812i \(0.815080\pi\)
\(72\) −4.45007 + 7.70775i −0.524446 + 0.908368i
\(73\) 2.54191 + 4.40273i 0.297509 + 0.515300i 0.975565 0.219710i \(-0.0705110\pi\)
−0.678057 + 0.735010i \(0.737178\pi\)
\(74\) 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 −0.734772 0.678315i \(-0.762711\pi\)
0.954823 + 0.297174i \(0.0960440\pi\)
\(80\) 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 \(-0.310805\pi\)
0.559990 + 0.828499i \(0.310805\pi\)
\(84\) 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 −0.256104 0.966649i \(-0.582439\pi\)
0.965195 0.261532i \(-0.0842276\pi\)
\(90\) −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 \(-0.503265\pi\)
−0.0102562 + 0.999947i \(0.503265\pi\)
\(98\) −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 0.869585 + 0.493783i \(0.164386\pi\)
−0.00716374 + 0.999974i \(0.502280\pi\)
\(102\) 4.36117 + 7.55377i 0.431820 + 0.747934i
\(103\) 5.40739 9.36587i 0.532806 0.922847i −0.466460 0.884542i \(-0.654471\pi\)
0.999266 0.0383047i \(-0.0121957\pi\)
\(104\) 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 −0.679474 0.733700i \(-0.737792\pi\)
0.975140 + 0.221592i \(0.0711252\pi\)
\(108\) 0.0910594 + 0.157720i 0.00876220 + 0.0151766i
\(109\) −5.69958 9.87196i −0.545921 0.945563i −0.998548 0.0538629i \(-0.982847\pi\)
0.452628 0.891700i \(-0.350487\pi\)
\(110\) −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 −0.671538 0.740970i \(-0.734366\pi\)
0.977468 + 0.211084i \(0.0676995\pi\)
\(132\) −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 \(-0.0811050\pi\)
−0.702139 + 0.712040i \(0.747772\pi\)
\(138\) 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 \(-0.784939\pi\)
0.931761 + 0.363072i \(0.118272\pi\)
\(150\) 6.01230 + 10.4136i 0.490902 + 0.850267i
\(151\) 2.43887 + 4.22425i 0.198473 + 0.343764i 0.948033 0.318171i \(-0.103069\pi\)
−0.749561 + 0.661935i \(0.769735\pi\)
\(152\) 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 0.991044 0.133536i \(-0.0426332\pi\)
−0.611168 + 0.791501i \(0.709300\pi\)
\(158\) −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 0.142696 0.989767i \(-0.454423\pi\)
0.785815 0.618461i \(-0.212244\pi\)
\(164\) −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 \(-0.486055\pi\)
0.0437957 + 0.999041i \(0.486055\pi\)
\(168\) 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 −0.998732 0.0503522i \(-0.983966\pi\)
0.542972 + 0.839751i \(0.317299\pi\)
\(174\) −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 0.632997 0.774154i \(-0.281825\pi\)
−0.986936 + 0.161114i \(0.948491\pi\)
\(180\) 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 0.429252 + 0.903185i \(0.358777\pi\)
−0.996807 + 0.0798496i \(0.974556\pi\)
\(192\) 9.60776 + 16.6411i 0.693380 + 1.20097i
\(193\) −11.5036 19.9248i −0.828045 1.43422i −0.899570 0.436776i \(-0.856120\pi\)
0.0715256 0.997439i \(-0.477213\pi\)
\(194\) −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 \(-0.618413\pi\)
−0.363485 + 0.931600i \(0.618413\pi\)
\(198\) −1.10687 + 1.91715i −0.0786616 + 0.136246i
\(199\) −5.96173 10.3260i −0.422616 0.731992i 0.573579 0.819150i \(-0.305555\pi\)
−0.996194 + 0.0871586i \(0.972221\pi\)
\(200\) 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 \(-0.427251\pi\)
0.226563 + 0.973996i \(0.427251\pi\)
\(224\) 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 0.997635 + 0.0687311i \(0.0218950\pi\)
−0.439295 + 0.898343i \(0.644772\pi\)
\(228\) 5.36711 + 9.29610i 0.355445 + 0.615650i
\(229\) 5.51286 9.54855i 0.364300 0.630986i −0.624364 0.781134i \(-0.714642\pi\)
0.988664 + 0.150148i \(0.0479750\pi\)
\(230\) 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 0.428239 + 0.903665i \(0.359134\pi\)
−0.996717 + 0.0809664i \(0.974199\pi\)
\(234\) 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 \(-0.720182\pi\)
−0.637865 + 0.770148i \(0.720182\pi\)
\(240\) −1.20350 + 2.08453i −0.0776858 + 0.134556i
\(241\) 1.39206 + 2.41112i 0.0896706 + 0.155314i 0.907372 0.420329i \(-0.138085\pi\)
−0.817701 + 0.575643i \(0.804752\pi\)
\(242\) −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 −0.807524 0.589835i \(-0.799193\pi\)
0.914574 + 0.404419i \(0.132526\pi\)
\(258\) −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 0.980273 + 0.197646i \(0.0633298\pi\)
−0.318970 + 0.947765i \(0.603337\pi\)
\(264\) −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 0.551355 0.834271i \(-0.314111\pi\)
−0.998177 + 0.0603517i \(0.980778\pi\)
\(270\) 0.0720191 + 0.124741i 0.00438294 + 0.00759148i
\(271\) −1.02183 + 1.76986i −0.0620717 + 0.107511i −0.895391 0.445280i \(-0.853104\pi\)
0.833320 + 0.552792i \(0.186437\pi\)
\(272\) 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 0.936027 0.351927i \(-0.114474\pi\)
−0.772792 + 0.634660i \(0.781140\pi\)
\(278\) 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 \(-0.706258\pi\)
−0.603577 + 0.797305i \(0.706258\pi\)
\(282\) −10.5310 + 18.2401i −0.627109 + 1.08618i
\(283\) −0.867593 1.50272i −0.0515731 0.0893272i 0.839086 0.543998i \(-0.183090\pi\)
−0.890659 + 0.454671i \(0.849757\pi\)
\(284\) −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 \(-0.792954\pi\)
−0.795810 + 0.605547i \(0.792954\pi\)
\(294\) −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 \(-0.618181\pi\)
−0.362806 + 0.931865i \(0.618181\pi\)
\(308\) 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 0.696841 0.717226i \(-0.254588\pi\)
−0.969556 + 0.244869i \(0.921255\pi\)
\(312\) 0 0
\(313\) 4.51273 7.81628i 0.255075 0.441802i −0.709841 0.704362i \(-0.751233\pi\)
0.964916 + 0.262559i \(0.0845666\pi\)
\(314\) 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 −0.279750 0.960073i \(-0.590252\pi\)
0.971323 0.237766i \(-0.0764150\pi\)
\(318\) 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 \(-0.715429\pi\)
0.988289 + 0.152594i \(0.0487626\pi\)
\(332\) 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 0.859787 0.510653i \(-0.170596\pi\)
−0.872132 + 0.489271i \(0.837263\pi\)
\(348\) 6.80550 11.7875i 0.364813 0.631875i
\(349\) 6.87822 0.368183 0.184091 0.982909i \(-0.441066\pi\)
0.184091 + 0.982909i \(0.441066\pi\)
\(350\) 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 \(-0.153675\pi\)
−0.844902 + 0.534921i \(0.820342\pi\)
\(354\) −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 0.243848 + 0.969813i \(0.421590\pi\)
−0.961807 + 0.273728i \(0.911743\pi\)
\(360\) −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 −0.966977 0.254865i \(-0.917969\pi\)
0.262769 0.964859i \(-0.415364\pi\)
\(368\) −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 −0.912854 0.408286i \(-0.866127\pi\)
0.810013 + 0.586412i \(0.199460\pi\)
\(374\) 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 \(-0.405366\pi\)
0.292942 + 0.956130i \(0.405366\pi\)
\(380\) −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 0.383737 + 0.923442i \(0.374637\pi\)
−0.991593 + 0.129395i \(0.958696\pi\)
\(384\) −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 0.960901 + 0.276894i \(0.0893051\pi\)
−0.240653 + 0.970611i \(0.577362\pi\)
\(390\) 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 \(-0.912912\pi\)
0.715398 + 0.698717i \(0.246245\pi\)
\(398\) −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 \(-0.731298\pi\)
0.979457 + 0.201653i \(0.0646313\pi\)
\(402\) −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 \(-0.313975\pi\)
−0.998151 + 0.0607793i \(0.980641\pi\)
\(410\) −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 \(-0.533216\pi\)
−0.104160 + 0.994561i \(0.533216\pi\)
\(422\) −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 \(-0.0522398\pi\)
−0.634773 + 0.772698i \(0.718906\pi\)
\(432\) 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 −0.994612 0.103664i \(-0.966943\pi\)
0.587082 + 0.809528i \(0.300277\pi\)
\(440\) −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 −0.982155 0.188073i \(-0.939776\pi\)
0.653954 + 0.756534i \(0.273109\pi\)
\(444\) −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 \(-0.779849\pi\)
−0.770211 + 0.637789i \(0.779849\pi\)
\(450\) −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 \(-0.856958\pi\)
0.826566 + 0.562840i \(0.190291\pi\)
\(458\) −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 \(-0.498502\pi\)
0.00470458 + 0.999989i \(0.498502\pi\)
\(462\) 4.88559 0.225944i 0.227298 0.0105119i
\(463\) 17.2121 0.799912 0.399956 0.916534i \(-0.369025\pi\)
0.399956 + 0.916534i \(0.369025\pi\)
\(464\) −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 −0.863805 0.503826i \(-0.831925\pi\)
0.868228 + 0.496165i \(0.165259\pi\)
\(468\) 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 \(-0.00341199\pi\)
−0.509254 + 0.860616i \(0.670079\pi\)
\(480\) −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 \(-0.0246216\pi\)
−0.565426 + 0.824799i \(0.691288\pi\)
\(488\) −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 \(-0.703753\pi\)
0.993220 + 0.116247i \(0.0370864\pi\)
\(500\) −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 \(-0.974421\pi\)
0.567905 + 0.823094i \(0.307754\pi\)
\(510\) −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 0.938038 0.346533i \(-0.112641\pi\)
−0.769125 + 0.639098i \(0.779308\pi\)
\(522\) −10.3062 17.8508i −0.451088 0.781307i
\(523\) 17.5251 30.3543i 0.766317 1.32730i −0.173230 0.984881i \(-0.555420\pi\)
0.939547 0.342419i \(-0.111246\pi\)
\(524\) 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 \(-0.749337\pi\)
0.966463 + 0.256807i \(0.0826706\pi\)
\(542\) 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 0.922391 + 0.386258i \(0.126233\pi\)
−0.126686 + 0.991943i \(0.540434\pi\)
\(558\) −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 −0.992083 0.125583i \(-0.959920\pi\)
0.387284 0.921960i \(-0.373413\pi\)
\(564\) −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 −0.990508 0.137452i \(-0.956109\pi\)
0.614291 + 0.789079i \(0.289442\pi\)
\(570\) 4.24486 + 7.35231i 0.177798 + 0.307955i
\(571\) −8.91370 15.4390i −0.373027 0.646101i 0.617003 0.786961i \(-0.288347\pi\)
−0.990030 + 0.140860i \(0.955013\pi\)
\(572\) 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 0.972455 + 0.233092i \(0.0748844\pi\)
−0.284363 + 0.958717i \(0.591782\pi\)
\(578\) −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 \(-0.598314\pi\)
−0.303976 + 0.952680i \(0.598314\pi\)
\(588\) 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 \(-0.893891\pi\)
0.755849 + 0.654746i \(0.227224\pi\)
\(594\) 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 0.953591 0.301104i \(-0.0973551\pi\)
−0.737559 + 0.675282i \(0.764022\pi\)
\(600\) −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 −0.900303 0.435263i \(-0.856655\pi\)
0.827100 + 0.562054i \(0.189989\pi\)
\(608\) 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 −0.933557 0.358428i \(-0.883313\pi\)
0.156371 0.987698i \(-0.450020\pi\)
\(614\) −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 \(-0.480156\pi\)
0.0623007 + 0.998057i \(0.480156\pi\)
\(618\) 14.1080 24.4359i 0.567509 0.982954i
\(619\) 6.13462 + 10.6255i 0.246571 + 0.427074i 0.962572 0.271025i \(-0.0873627\pi\)
−0.716001 + 0.698099i \(0.754029\pi\)
\(620\) −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 \(-0.466244\pi\)
0.105849 + 0.994382i \(0.466244\pi\)
\(632\) 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 0.720181 0.693787i \(-0.244059\pi\)
−0.960927 + 0.276801i \(0.910726\pi\)
\(642\) 7.97944 13.8208i 0.314923 0.545463i
\(643\) 18.9733 0.748235 0.374117 0.927381i \(-0.377946\pi\)
0.374117 + 0.927381i \(0.377946\pi\)
\(644\) 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 0.604635 0.796503i \(-0.293319\pi\)
−0.992109 + 0.125378i \(0.959986\pi\)
\(648\) 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 −0.594512 0.804087i \(-0.702655\pi\)
0.993616 + 0.112819i \(0.0359882\pi\)
\(654\) −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 \(-0.227308\pi\)
−0.945037 + 0.326962i \(0.893975\pi\)
\(662\) −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 0.159187 0.987248i \(-0.449113\pi\)
0.775389 0.631484i \(-0.217554\pi\)
\(678\) −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 \(-0.131838\pi\)
−0.806246 + 0.591580i \(0.798504\pi\)
\(684\) −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 0.128553 + 0.991703i \(0.458967\pi\)
−0.923116 + 0.384521i \(0.874367\pi\)
\(692\) −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 0.459110 + 0.888380i \(0.348168\pi\)
−0.998914 + 0.0465891i \(0.985165\pi\)
\(710\) −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 −0.824112 0.566427i \(-0.808325\pi\)
0.902596 + 0.430488i \(0.141659\pi\)
\(720\) −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 \(-0.887048\pi\)
0.769748 + 0.638348i \(0.220382\pi\)
\(734\) −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 \(-0.223219\pi\)
−0.940759 + 0.339077i \(0.889885\pi\)
\(740\) 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 \(-0.299036\pi\)
0.590231 + 0.807234i \(0.299036\pi\)
\(744\) −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 −0.928352 0.371701i \(-0.878775\pi\)
0.786079 + 0.618126i \(0.212108\pi\)
\(752\) 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 0.216398 + 0.976305i \(0.430569\pi\)
−0.953704 + 0.300746i \(0.902764\pi\)
\(762\) −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 \(-0.750752\pi\)
−0.708774 + 0.705435i \(0.750752\pi\)
\(770\) 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 \(-0.0887630\pi\)
−0.719065 + 0.694943i \(0.755430\pi\)
\(774\) −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
\(781\) −4.99068