Properties

Label 147.4.c.a.146.12
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} - 29 x^{9} + 6 x^{8} - 49 x^{7} + 1564 x^{6} - 441 x^{5} + 486 x^{4} - 21141 x^{3} - 59049 x + 531441\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{3} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.12
Root \(2.70662 - 1.29391i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.a.146.2

$q$-expansion

\(f(q)\) \(=\) \(q+4.54551i q^{2} +(2.93937 + 4.28487i) q^{3} -12.6617 q^{4} -11.6039 q^{5} +(-19.4769 + 13.3609i) q^{6} -21.1897i q^{8} +(-9.72022 + 25.1896i) q^{9} +O(q^{10})\) \(q+4.54551i q^{2} +(2.93937 + 4.28487i) q^{3} -12.6617 q^{4} -11.6039 q^{5} +(-19.4769 + 13.3609i) q^{6} -21.1897i q^{8} +(-9.72022 + 25.1896i) q^{9} -52.7455i q^{10} +17.9160i q^{11} +(-37.2174 - 54.2537i) q^{12} -62.4185i q^{13} +(-34.1081 - 49.7211i) q^{15} -4.97524 q^{16} +21.4164 q^{17} +(-114.500 - 44.1834i) q^{18} +10.9783i q^{19} +146.925 q^{20} -81.4374 q^{22} +69.0934i q^{23} +(90.7953 - 62.2845i) q^{24} +9.64979 q^{25} +283.724 q^{26} +(-136.506 + 32.3918i) q^{27} +265.583i q^{29} +(226.008 - 155.039i) q^{30} -10.2283i q^{31} -192.133i q^{32} +(-76.7677 + 52.6617i) q^{33} +97.3486i q^{34} +(123.074 - 318.943i) q^{36} +41.6514 q^{37} -49.9019 q^{38} +(267.455 - 183.471i) q^{39} +245.883i q^{40} +31.0035 q^{41} -224.550 q^{43} -226.847i q^{44} +(112.792 - 292.297i) q^{45} -314.065 q^{46} -163.719 q^{47} +(-14.6241 - 21.3182i) q^{48} +43.8633i q^{50} +(62.9508 + 91.7665i) q^{51} +790.323i q^{52} +527.220i q^{53} +(-147.237 - 620.488i) q^{54} -207.895i q^{55} +(-47.0405 + 32.2692i) q^{57} -1207.21 q^{58} -411.956 q^{59} +(431.865 + 629.552i) q^{60} +258.431i q^{61} +46.4928 q^{62} +833.541 q^{64} +724.296i q^{65} +(-239.375 - 348.949i) q^{66} +323.474 q^{67} -271.168 q^{68} +(-296.056 + 203.091i) q^{69} -45.4199i q^{71} +(533.762 + 205.969i) q^{72} +562.199i q^{73} +189.327i q^{74} +(28.3643 + 41.3481i) q^{75} -139.004i q^{76} +(833.969 + 1215.72i) q^{78} +289.221 q^{79} +57.7320 q^{80} +(-540.035 - 489.697i) q^{81} +140.927i q^{82} -448.767 q^{83} -248.513 q^{85} -1020.70i q^{86} +(-1137.99 + 780.647i) q^{87} +379.635 q^{88} -561.628 q^{89} +(1328.64 + 512.698i) q^{90} -874.839i q^{92} +(43.8268 - 30.0647i) q^{93} -744.187i q^{94} -127.391i q^{95} +(823.265 - 564.750i) q^{96} +214.364i q^{97} +(-451.297 - 174.147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 28 q^{4} + 6 q^{9} + O(q^{10}) \) \( 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.54551i 1.60708i 0.595250 + 0.803541i \(0.297053\pi\)
−0.595250 + 0.803541i \(0.702947\pi\)
\(3\) 2.93937 + 4.28487i 0.565682 + 0.824624i
\(4\) −12.6617 −1.58271
\(5\) −11.6039 −1.03788 −0.518941 0.854810i \(-0.673674\pi\)
−0.518941 + 0.854810i \(0.673674\pi\)
\(6\) −19.4769 + 13.3609i −1.32524 + 0.909097i
\(7\) 0 0
\(8\) 21.1897i 0.936463i
\(9\) −9.72022 + 25.1896i −0.360008 + 0.932949i
\(10\) 52.7455i 1.66796i
\(11\) 17.9160i 0.491080i 0.969387 + 0.245540i \(0.0789652\pi\)
−0.969387 + 0.245540i \(0.921035\pi\)
\(12\) −37.2174 54.2537i −0.895311 1.30514i
\(13\) 62.4185i 1.33167i −0.746097 0.665837i \(-0.768075\pi\)
0.746097 0.665837i \(-0.231925\pi\)
\(14\) 0 0
\(15\) −34.1081 49.7211i −0.587111 0.855862i
\(16\) −4.97524 −0.0777381
\(17\) 21.4164 0.305544 0.152772 0.988261i \(-0.451180\pi\)
0.152772 + 0.988261i \(0.451180\pi\)
\(18\) −114.500 44.1834i −1.49933 0.578562i
\(19\) 10.9783i 0.132557i 0.997801 + 0.0662787i \(0.0211126\pi\)
−0.997801 + 0.0662787i \(0.978887\pi\)
\(20\) 146.925 1.64267
\(21\) 0 0
\(22\) −81.4374 −0.789205
\(23\) 69.0934i 0.626390i 0.949689 + 0.313195i \(0.101399\pi\)
−0.949689 + 0.313195i \(0.898601\pi\)
\(24\) 90.7953 62.2845i 0.772230 0.529740i
\(25\) 9.64979 0.0771983
\(26\) 283.724 2.14011
\(27\) −136.506 + 32.3918i −0.972982 + 0.230881i
\(28\) 0 0
\(29\) 265.583i 1.70061i 0.526294 + 0.850303i \(0.323581\pi\)
−0.526294 + 0.850303i \(0.676419\pi\)
\(30\) 226.008 155.039i 1.37544 0.943535i
\(31\) 10.2283i 0.0592598i −0.999561 0.0296299i \(-0.990567\pi\)
0.999561 0.0296299i \(-0.00943286\pi\)
\(32\) 192.133i 1.06139i
\(33\) −76.7677 + 52.6617i −0.404956 + 0.277795i
\(34\) 97.3486i 0.491034i
\(35\) 0 0
\(36\) 123.074 318.943i 0.569788 1.47659i
\(37\) 41.6514 0.185066 0.0925331 0.995710i \(-0.470504\pi\)
0.0925331 + 0.995710i \(0.470504\pi\)
\(38\) −49.9019 −0.213031
\(39\) 267.455 183.471i 1.09813 0.753304i
\(40\) 245.883i 0.971938i
\(41\) 31.0035 0.118096 0.0590480 0.998255i \(-0.481193\pi\)
0.0590480 + 0.998255i \(0.481193\pi\)
\(42\) 0 0
\(43\) −224.550 −0.796363 −0.398181 0.917307i \(-0.630359\pi\)
−0.398181 + 0.917307i \(0.630359\pi\)
\(44\) 226.847i 0.777237i
\(45\) 112.792 292.297i 0.373646 0.968291i
\(46\) −314.065 −1.00666
\(47\) −163.719 −0.508103 −0.254052 0.967191i \(-0.581763\pi\)
−0.254052 + 0.967191i \(0.581763\pi\)
\(48\) −14.6241 21.3182i −0.0439750 0.0641046i
\(49\) 0 0
\(50\) 43.8633i 0.124064i
\(51\) 62.9508 + 91.7665i 0.172841 + 0.251959i
\(52\) 790.323i 2.10765i
\(53\) 527.220i 1.36640i 0.730231 + 0.683200i \(0.239412\pi\)
−0.730231 + 0.683200i \(0.760588\pi\)
\(54\) −147.237 620.488i −0.371045 1.56366i
\(55\) 207.895i 0.509682i
\(56\) 0 0
\(57\) −47.0405 + 32.2692i −0.109310 + 0.0749853i
\(58\) −1207.21 −2.73301
\(59\) −411.956 −0.909020 −0.454510 0.890742i \(-0.650186\pi\)
−0.454510 + 0.890742i \(0.650186\pi\)
\(60\) 431.865 + 629.552i 0.929227 + 1.35458i
\(61\) 258.431i 0.542437i 0.962518 + 0.271218i \(0.0874266\pi\)
−0.962518 + 0.271218i \(0.912573\pi\)
\(62\) 46.4928 0.0952352
\(63\) 0 0
\(64\) 833.541 1.62801
\(65\) 724.296i 1.38212i
\(66\) −239.375 348.949i −0.446439 0.650797i
\(67\) 323.474 0.589831 0.294915 0.955523i \(-0.404709\pi\)
0.294915 + 0.955523i \(0.404709\pi\)
\(68\) −271.168 −0.483587
\(69\) −296.056 + 203.091i −0.516536 + 0.354338i
\(70\) 0 0
\(71\) 45.4199i 0.0759205i −0.999279 0.0379603i \(-0.987914\pi\)
0.999279 0.0379603i \(-0.0120860\pi\)
\(72\) 533.762 + 205.969i 0.873673 + 0.337134i
\(73\) 562.199i 0.901376i 0.892682 + 0.450688i \(0.148821\pi\)
−0.892682 + 0.450688i \(0.851179\pi\)
\(74\) 189.327i 0.297416i
\(75\) 28.3643 + 41.3481i 0.0436697 + 0.0636596i
\(76\) 139.004i 0.209800i
\(77\) 0 0
\(78\) 833.969 + 1215.72i 1.21062 + 1.76478i
\(79\) 289.221 0.411898 0.205949 0.978563i \(-0.433972\pi\)
0.205949 + 0.978563i \(0.433972\pi\)
\(80\) 57.7320 0.0806829
\(81\) −540.035 489.697i −0.740789 0.671738i
\(82\) 140.927i 0.189790i
\(83\) −448.767 −0.593477 −0.296738 0.954959i \(-0.595899\pi\)
−0.296738 + 0.954959i \(0.595899\pi\)
\(84\) 0 0
\(85\) −248.513 −0.317118
\(86\) 1020.70i 1.27982i
\(87\) −1137.99 + 780.647i −1.40236 + 0.962002i
\(88\) 379.635 0.459878
\(89\) −561.628 −0.668904 −0.334452 0.942413i \(-0.608551\pi\)
−0.334452 + 0.942413i \(0.608551\pi\)
\(90\) 1328.64 + 512.698i 1.55612 + 0.600479i
\(91\) 0 0
\(92\) 874.839i 0.991394i
\(93\) 43.8268 30.0647i 0.0488670 0.0335222i
\(94\) 744.187i 0.816564i
\(95\) 127.391i 0.137579i
\(96\) 823.265 564.750i 0.875251 0.600412i
\(97\) 214.364i 0.224385i 0.993686 + 0.112192i \(0.0357873\pi\)
−0.993686 + 0.112192i \(0.964213\pi\)
\(98\) 0 0
\(99\) −451.297 174.147i −0.458152 0.176793i
\(100\) −122.183 −0.122183
\(101\) 1717.69 1.69224 0.846122 0.532990i \(-0.178932\pi\)
0.846122 + 0.532990i \(0.178932\pi\)
\(102\) −417.126 + 286.143i −0.404918 + 0.277769i
\(103\) 1157.71i 1.10750i 0.832683 + 0.553750i \(0.186804\pi\)
−0.832683 + 0.553750i \(0.813196\pi\)
\(104\) −1322.63 −1.24706
\(105\) 0 0
\(106\) −2396.48 −2.19592
\(107\) 1217.79i 1.10027i −0.835077 0.550134i \(-0.814577\pi\)
0.835077 0.550134i \(-0.185423\pi\)
\(108\) 1728.39 410.134i 1.53995 0.365418i
\(109\) 1298.26 1.14084 0.570418 0.821355i \(-0.306781\pi\)
0.570418 + 0.821355i \(0.306781\pi\)
\(110\) 944.989 0.819101
\(111\) 122.429 + 178.471i 0.104689 + 0.152610i
\(112\) 0 0
\(113\) 1437.86i 1.19701i −0.801118 0.598506i \(-0.795761\pi\)
0.801118 0.598506i \(-0.204239\pi\)
\(114\) −146.680 213.823i −0.120508 0.175670i
\(115\) 801.751i 0.650119i
\(116\) 3362.73i 2.69157i
\(117\) 1572.30 + 606.721i 1.24238 + 0.479413i
\(118\) 1872.55i 1.46087i
\(119\) 0 0
\(120\) −1053.58 + 722.741i −0.801483 + 0.549808i
\(121\) 1010.02 0.758841
\(122\) −1174.70 −0.871740
\(123\) 91.1308 + 132.846i 0.0668048 + 0.0973848i
\(124\) 129.507i 0.0937910i
\(125\) 1338.51 0.957759
\(126\) 0 0
\(127\) 2686.32 1.87695 0.938475 0.345347i \(-0.112239\pi\)
0.938475 + 0.345347i \(0.112239\pi\)
\(128\) 2251.81i 1.55495i
\(129\) −660.036 962.169i −0.450488 0.656699i
\(130\) −3292.29 −2.22118
\(131\) −1603.27 −1.06930 −0.534651 0.845073i \(-0.679557\pi\)
−0.534651 + 0.845073i \(0.679557\pi\)
\(132\) 972.008 666.786i 0.640928 0.439669i
\(133\) 0 0
\(134\) 1470.36i 0.947906i
\(135\) 1583.99 375.870i 1.00984 0.239628i
\(136\) 453.808i 0.286130i
\(137\) 2318.52i 1.44588i 0.690913 + 0.722938i \(0.257209\pi\)
−0.690913 + 0.722938i \(0.742791\pi\)
\(138\) −923.153 1345.73i −0.569449 0.830116i
\(139\) 1841.57i 1.12374i 0.827225 + 0.561871i \(0.189918\pi\)
−0.827225 + 0.561871i \(0.810082\pi\)
\(140\) 0 0
\(141\) −481.230 701.514i −0.287425 0.418994i
\(142\) 206.457 0.122010
\(143\) 1118.29 0.653958
\(144\) 48.3604 125.324i 0.0279863 0.0725257i
\(145\) 3081.79i 1.76503i
\(146\) −2555.48 −1.44858
\(147\) 0 0
\(148\) −527.377 −0.292906
\(149\) 1300.98i 0.715302i 0.933855 + 0.357651i \(0.116422\pi\)
−0.933855 + 0.357651i \(0.883578\pi\)
\(150\) −187.948 + 128.930i −0.102306 + 0.0701808i
\(151\) −2616.49 −1.41011 −0.705055 0.709152i \(-0.749078\pi\)
−0.705055 + 0.709152i \(0.749078\pi\)
\(152\) 232.627 0.124135
\(153\) −208.172 + 539.472i −0.109998 + 0.285057i
\(154\) 0 0
\(155\) 118.688i 0.0615046i
\(156\) −3386.43 + 2323.05i −1.73802 + 1.19226i
\(157\) 935.164i 0.475377i 0.971341 + 0.237689i \(0.0763898\pi\)
−0.971341 + 0.237689i \(0.923610\pi\)
\(158\) 1314.66i 0.661953i
\(159\) −2259.07 + 1549.69i −1.12677 + 0.772948i
\(160\) 2229.49i 1.10160i
\(161\) 0 0
\(162\) 2225.92 2454.74i 1.07954 1.19051i
\(163\) −518.158 −0.248989 −0.124495 0.992220i \(-0.539731\pi\)
−0.124495 + 0.992220i \(0.539731\pi\)
\(164\) −392.557 −0.186912
\(165\) 890.802 611.080i 0.420296 0.288318i
\(166\) 2039.88i 0.953765i
\(167\) 3767.97 1.74595 0.872977 0.487761i \(-0.162186\pi\)
0.872977 + 0.487761i \(0.162186\pi\)
\(168\) 0 0
\(169\) −1699.06 −0.773356
\(170\) 1129.62i 0.509635i
\(171\) −276.539 106.711i −0.123669 0.0477217i
\(172\) 2843.18 1.26041
\(173\) 2393.06 1.05168 0.525841 0.850583i \(-0.323751\pi\)
0.525841 + 0.850583i \(0.323751\pi\)
\(174\) −3548.44 5172.74i −1.54602 2.25371i
\(175\) 0 0
\(176\) 89.1363i 0.0381756i
\(177\) −1210.89 1765.18i −0.514216 0.749599i
\(178\) 2552.89i 1.07498i
\(179\) 640.144i 0.267299i 0.991029 + 0.133650i \(0.0426697\pi\)
−0.991029 + 0.133650i \(0.957330\pi\)
\(180\) −1428.14 + 3700.97i −0.591373 + 1.53252i
\(181\) 4204.05i 1.72643i −0.504833 0.863217i \(-0.668446\pi\)
0.504833 0.863217i \(-0.331554\pi\)
\(182\) 0 0
\(183\) −1107.34 + 759.623i −0.447306 + 0.306847i
\(184\) 1464.07 0.586591
\(185\) −483.318 −0.192077
\(186\) 136.659 + 199.215i 0.0538729 + 0.0785332i
\(187\) 383.696i 0.150046i
\(188\) 2072.96 0.804181
\(189\) 0 0
\(190\) 579.056 0.221101
\(191\) 1457.06i 0.551985i 0.961160 + 0.275993i \(0.0890066\pi\)
−0.961160 + 0.275993i \(0.910993\pi\)
\(192\) 2450.08 + 3571.61i 0.920935 + 1.34249i
\(193\) 1829.27 0.682246 0.341123 0.940019i \(-0.389193\pi\)
0.341123 + 0.940019i \(0.389193\pi\)
\(194\) −974.393 −0.360605
\(195\) −3103.51 + 2128.97i −1.13973 + 0.781840i
\(196\) 0 0
\(197\) 661.168i 0.239118i 0.992827 + 0.119559i \(0.0381481\pi\)
−0.992827 + 0.119559i \(0.961852\pi\)
\(198\) 791.589 2051.38i 0.284120 0.736288i
\(199\) 1949.13i 0.694322i 0.937806 + 0.347161i \(0.112854\pi\)
−0.937806 + 0.347161i \(0.887146\pi\)
\(200\) 204.477i 0.0722934i
\(201\) 950.810 + 1386.04i 0.333657 + 0.486388i
\(202\) 7807.78i 2.71957i
\(203\) 0 0
\(204\) −797.063 1161.92i −0.273557 0.398777i
\(205\) −359.761 −0.122570
\(206\) −5262.38 −1.77984
\(207\) −1740.44 671.603i −0.584390 0.225505i
\(208\) 310.547i 0.103522i
\(209\) −196.687 −0.0650963
\(210\) 0 0
\(211\) 3341.96 1.09038 0.545189 0.838313i \(-0.316458\pi\)
0.545189 + 0.838313i \(0.316458\pi\)
\(212\) 6675.49i 2.16262i
\(213\) 194.619 133.506i 0.0626058 0.0429469i
\(214\) 5535.50 1.76822
\(215\) 2605.65 0.826530
\(216\) 686.373 + 2892.52i 0.216212 + 0.911162i
\(217\) 0 0
\(218\) 5901.27i 1.83342i
\(219\) −2408.95 + 1652.51i −0.743296 + 0.509892i
\(220\) 2632.30i 0.806680i
\(221\) 1336.78i 0.406885i
\(222\) −811.242 + 556.502i −0.245257 + 0.168243i
\(223\) 2143.28i 0.643608i −0.946806 0.321804i \(-0.895711\pi\)
0.946806 0.321804i \(-0.104289\pi\)
\(224\) 0 0
\(225\) −93.7981 + 243.075i −0.0277920 + 0.0720221i
\(226\) 6535.80 1.92370
\(227\) 2569.11 0.751178 0.375589 0.926786i \(-0.377440\pi\)
0.375589 + 0.926786i \(0.377440\pi\)
\(228\) 595.612 408.583i 0.173006 0.118680i
\(229\) 105.173i 0.0303495i 0.999885 + 0.0151748i \(0.00483046\pi\)
−0.999885 + 0.0151748i \(0.995170\pi\)
\(230\) 3644.37 1.04479
\(231\) 0 0
\(232\) 5627.64 1.59255
\(233\) 2625.72i 0.738270i −0.929376 0.369135i \(-0.879654\pi\)
0.929376 0.369135i \(-0.120346\pi\)
\(234\) −2757.86 + 7146.90i −0.770456 + 1.99661i
\(235\) 1899.77 0.527351
\(236\) 5216.06 1.43872
\(237\) 850.127 + 1239.27i 0.233003 + 0.339660i
\(238\) 0 0
\(239\) 6080.85i 1.64576i 0.568212 + 0.822882i \(0.307635\pi\)
−0.568212 + 0.822882i \(0.692365\pi\)
\(240\) 169.696 + 247.374i 0.0456409 + 0.0665330i
\(241\) 4628.89i 1.23723i −0.785693 0.618616i \(-0.787694\pi\)
0.785693 0.618616i \(-0.212306\pi\)
\(242\) 4591.05i 1.21952i
\(243\) 510.927 3753.38i 0.134881 0.990862i
\(244\) 3272.17i 0.858521i
\(245\) 0 0
\(246\) −603.853 + 414.236i −0.156505 + 0.107361i
\(247\) 685.248 0.176523
\(248\) −216.735 −0.0554946
\(249\) −1319.09 1922.91i −0.335719 0.489395i
\(250\) 6084.21i 1.53920i
\(251\) −5967.85 −1.50075 −0.750373 0.661015i \(-0.770126\pi\)
−0.750373 + 0.661015i \(0.770126\pi\)
\(252\) 0 0
\(253\) −1237.88 −0.307607
\(254\) 12210.7i 3.01641i
\(255\) −730.472 1064.85i −0.179388 0.261503i
\(256\) −3567.29 −0.870920
\(257\) −5639.40 −1.36878 −0.684389 0.729117i \(-0.739931\pi\)
−0.684389 + 0.729117i \(0.739931\pi\)
\(258\) 4373.55 3000.20i 1.05537 0.723971i
\(259\) 0 0
\(260\) 9170.80i 2.18750i
\(261\) −6689.94 2581.53i −1.58658 0.612232i
\(262\) 7287.70i 1.71846i
\(263\) 3485.62i 0.817234i −0.912706 0.408617i \(-0.866011\pi\)
0.912706 0.408617i \(-0.133989\pi\)
\(264\) 1115.89 + 1626.69i 0.260145 + 0.379226i
\(265\) 6117.79i 1.41816i
\(266\) 0 0
\(267\) −1650.83 2406.50i −0.378387 0.551594i
\(268\) −4095.73 −0.933531
\(269\) −3794.55 −0.860066 −0.430033 0.902813i \(-0.641498\pi\)
−0.430033 + 0.902813i \(0.641498\pi\)
\(270\) 1708.52 + 7200.06i 0.385101 + 1.62290i
\(271\) 7457.62i 1.67165i −0.548993 0.835827i \(-0.684989\pi\)
0.548993 0.835827i \(-0.315011\pi\)
\(272\) −106.552 −0.0237524
\(273\) 0 0
\(274\) −10538.9 −2.32364
\(275\) 172.886i 0.0379105i
\(276\) 3748.57 2571.48i 0.817527 0.560814i
\(277\) −3415.49 −0.740856 −0.370428 0.928861i \(-0.620789\pi\)
−0.370428 + 0.928861i \(0.620789\pi\)
\(278\) −8370.89 −1.80595
\(279\) 257.646 + 99.4210i 0.0552863 + 0.0213340i
\(280\) 0 0
\(281\) 2762.14i 0.586390i −0.956053 0.293195i \(-0.905281\pi\)
0.956053 0.293195i \(-0.0947185\pi\)
\(282\) 3188.74 2187.44i 0.673358 0.461915i
\(283\) 5505.20i 1.15636i 0.815909 + 0.578181i \(0.196237\pi\)
−0.815909 + 0.578181i \(0.803763\pi\)
\(284\) 575.093i 0.120160i
\(285\) 545.852 374.448i 0.113451 0.0778259i
\(286\) 5083.19i 1.05096i
\(287\) 0 0
\(288\) 4839.76 + 1867.57i 0.990227 + 0.382110i
\(289\) −4454.34 −0.906643
\(290\) 14008.3 2.83654
\(291\) −918.520 + 630.094i −0.185033 + 0.126930i
\(292\) 7118.39i 1.42662i
\(293\) −4101.08 −0.817705 −0.408853 0.912600i \(-0.634071\pi\)
−0.408853 + 0.912600i \(0.634071\pi\)
\(294\) 0 0
\(295\) 4780.29 0.943455
\(296\) 882.583i 0.173308i
\(297\) −580.331 2445.63i −0.113381 0.477812i
\(298\) −5913.60 −1.14955
\(299\) 4312.70 0.834148
\(300\) −359.140 523.537i −0.0691165 0.100755i
\(301\) 0 0
\(302\) 11893.3i 2.26616i
\(303\) 5048.93 + 7360.08i 0.957271 + 1.39546i
\(304\) 54.6196i 0.0103048i
\(305\) 2998.80i 0.562985i
\(306\) −2452.17 946.249i −0.458109 0.176776i
\(307\) 8281.42i 1.53956i 0.638308 + 0.769781i \(0.279635\pi\)
−0.638308 + 0.769781i \(0.720365\pi\)
\(308\) 0 0
\(309\) −4960.63 + 3402.94i −0.913270 + 0.626493i
\(310\) −539.496 −0.0988429
\(311\) −6871.05 −1.25280 −0.626401 0.779501i \(-0.715473\pi\)
−0.626401 + 0.779501i \(0.715473\pi\)
\(312\) −3887.70 5667.30i −0.705441 1.02836i
\(313\) 3374.49i 0.609386i −0.952451 0.304693i \(-0.901446\pi\)
0.952451 0.304693i \(-0.0985538\pi\)
\(314\) −4250.80 −0.763970
\(315\) 0 0
\(316\) −3662.02 −0.651914
\(317\) 2369.77i 0.419872i −0.977715 0.209936i \(-0.932674\pi\)
0.977715 0.209936i \(-0.0673255\pi\)
\(318\) −7044.15 10268.6i −1.24219 1.81080i
\(319\) −4758.19 −0.835133
\(320\) −9672.30 −1.68968
\(321\) 5218.09 3579.55i 0.907306 0.622401i
\(322\) 0 0
\(323\) 235.116i 0.0405021i
\(324\) 6837.75 + 6200.39i 1.17245 + 1.06317i
\(325\) 602.325i 0.102803i
\(326\) 2355.29i 0.400146i
\(327\) 3816.08 + 5562.89i 0.645350 + 0.940760i
\(328\) 656.957i 0.110593i
\(329\) 0 0
\(330\) 2777.67 + 4049.15i 0.463351 + 0.675450i
\(331\) 3803.61 0.631617 0.315808 0.948823i \(-0.397724\pi\)
0.315808 + 0.948823i \(0.397724\pi\)
\(332\) 5682.14 0.939302
\(333\) −404.861 + 1049.18i −0.0666253 + 0.172657i
\(334\) 17127.4i 2.80589i
\(335\) −3753.55 −0.612175
\(336\) 0 0
\(337\) −592.955 −0.0958466 −0.0479233 0.998851i \(-0.515260\pi\)
−0.0479233 + 0.998851i \(0.515260\pi\)
\(338\) 7723.11i 1.24285i
\(339\) 6161.04 4226.40i 0.987084 0.677128i
\(340\) 3146.60 0.501906
\(341\) 183.250 0.0291013
\(342\) 485.058 1257.01i 0.0766927 0.198747i
\(343\) 0 0
\(344\) 4758.16i 0.745764i
\(345\) 3435.40 2356.64i 0.536103 0.367760i
\(346\) 10877.7i 1.69014i
\(347\) 4777.16i 0.739054i −0.929220 0.369527i \(-0.879520\pi\)
0.929220 0.369527i \(-0.120480\pi\)
\(348\) 14408.9 9884.31i 2.21953 1.52257i
\(349\) 7358.26i 1.12859i −0.825573 0.564296i \(-0.809148\pi\)
0.825573 0.564296i \(-0.190852\pi\)
\(350\) 0 0
\(351\) 2021.84 + 8520.47i 0.307459 + 1.29569i
\(352\) 3442.25 0.521229
\(353\) 3305.55 0.498405 0.249202 0.968451i \(-0.419832\pi\)
0.249202 + 0.968451i \(0.419832\pi\)
\(354\) 8023.65 5504.13i 1.20467 0.826387i
\(355\) 527.047i 0.0787965i
\(356\) 7111.16 1.05868
\(357\) 0 0
\(358\) −2909.78 −0.429572
\(359\) 414.716i 0.0609689i 0.999535 + 0.0304845i \(0.00970501\pi\)
−0.999535 + 0.0304845i \(0.990295\pi\)
\(360\) −6193.70 2390.04i −0.906769 0.349905i
\(361\) 6738.48 0.982429
\(362\) 19109.6 2.77452
\(363\) 2968.81 + 4327.79i 0.429263 + 0.625758i
\(364\) 0 0
\(365\) 6523.69i 0.935522i
\(366\) −3452.88 5033.43i −0.493128 0.718858i
\(367\) 76.1227i 0.0108272i 0.999985 + 0.00541359i \(0.00172321\pi\)
−0.999985 + 0.00541359i \(0.998277\pi\)
\(368\) 343.756i 0.0486944i
\(369\) −301.361 + 780.967i −0.0425155 + 0.110178i
\(370\) 2196.93i 0.308683i
\(371\) 0 0
\(372\) −554.921 + 380.669i −0.0773423 + 0.0530559i
\(373\) −12301.0 −1.70756 −0.853781 0.520632i \(-0.825696\pi\)
−0.853781 + 0.520632i \(0.825696\pi\)
\(374\) −1744.10 −0.241137
\(375\) 3934.37 + 5735.34i 0.541787 + 0.789791i
\(376\) 3469.16i 0.475820i
\(377\) 16577.3 2.26465
\(378\) 0 0
\(379\) −1429.02 −0.193678 −0.0968389 0.995300i \(-0.530873\pi\)
−0.0968389 + 0.995300i \(0.530873\pi\)
\(380\) 1612.98i 0.217748i
\(381\) 7896.10 + 11510.5i 1.06176 + 1.54778i
\(382\) −6623.09 −0.887086
\(383\) 5110.90 0.681866 0.340933 0.940088i \(-0.389257\pi\)
0.340933 + 0.940088i \(0.389257\pi\)
\(384\) −9648.70 + 6618.89i −1.28225 + 0.879606i
\(385\) 0 0
\(386\) 8314.95i 1.09642i
\(387\) 2182.68 5656.34i 0.286697 0.742966i
\(388\) 2714.20i 0.355136i
\(389\) 7320.62i 0.954165i 0.878858 + 0.477083i \(0.158306\pi\)
−0.878858 + 0.477083i \(0.841694\pi\)
\(390\) −9677.27 14107.1i −1.25648 1.83164i
\(391\) 1479.73i 0.191390i
\(392\) 0 0
\(393\) −4712.61 6869.82i −0.604885 0.881772i
\(394\) −3005.35 −0.384283
\(395\) −3356.08 −0.427501
\(396\) 5714.18 + 2205.00i 0.725122 + 0.279811i
\(397\) 8679.44i 1.09725i 0.836068 + 0.548625i \(0.184849\pi\)
−0.836068 + 0.548625i \(0.815151\pi\)
\(398\) −8859.79 −1.11583
\(399\) 0 0
\(400\) −48.0100 −0.00600125
\(401\) 9754.54i 1.21476i −0.794412 0.607379i \(-0.792221\pi\)
0.794412 0.607379i \(-0.207779\pi\)
\(402\) −6300.28 + 4321.92i −0.781666 + 0.536213i
\(403\) −638.433 −0.0789147
\(404\) −21748.9 −2.67833
\(405\) 6266.49 + 5682.38i 0.768851 + 0.697185i
\(406\) 0 0
\(407\) 746.226i 0.0908822i
\(408\) 1944.51 1333.91i 0.235950 0.161859i
\(409\) 3389.41i 0.409769i −0.978786 0.204885i \(-0.934318\pi\)
0.978786 0.204885i \(-0.0656819\pi\)
\(410\) 1635.30i 0.196979i
\(411\) −9934.58 + 6815.00i −1.19230 + 0.817906i
\(412\) 14658.5i 1.75285i
\(413\) 0 0
\(414\) 3052.78 7911.18i 0.362406 0.939163i
\(415\) 5207.43 0.615959
\(416\) −11992.6 −1.41343
\(417\) −7890.90 + 5413.06i −0.926664 + 0.635681i
\(418\) 894.043i 0.104615i
\(419\) −12777.4 −1.48977 −0.744887 0.667191i \(-0.767496\pi\)
−0.744887 + 0.667191i \(0.767496\pi\)
\(420\) 0 0
\(421\) 11005.4 1.27404 0.637020 0.770848i \(-0.280167\pi\)
0.637020 + 0.770848i \(0.280167\pi\)
\(422\) 15190.9i 1.75233i
\(423\) 1591.38 4124.02i 0.182921 0.474035i
\(424\) 11171.6 1.27958
\(425\) 206.664 0.0235875
\(426\) 606.853 + 884.641i 0.0690191 + 0.100613i
\(427\) 0 0
\(428\) 15419.3i 1.74140i
\(429\) 3287.06 + 4791.72i 0.369932 + 0.539269i
\(430\) 11844.0i 1.32830i
\(431\) 3786.41i 0.423167i 0.977360 + 0.211584i \(0.0678621\pi\)
−0.977360 + 0.211584i \(0.932138\pi\)
\(432\) 679.147 161.157i 0.0756377 0.0179483i
\(433\) 3191.67i 0.354230i 0.984190 + 0.177115i \(0.0566765\pi\)
−0.984190 + 0.177115i \(0.943323\pi\)
\(434\) 0 0
\(435\) 13205.1 9058.53i 1.45548 0.998444i
\(436\) −16438.2 −1.80561
\(437\) −758.527 −0.0830327
\(438\) −7511.51 10949.9i −0.819438 1.19454i
\(439\) 3317.34i 0.360656i −0.983607 0.180328i \(-0.942284\pi\)
0.983607 0.180328i \(-0.0577159\pi\)
\(440\) −4405.24 −0.477299
\(441\) 0 0
\(442\) 6076.35 0.653897
\(443\) 10700.5i 1.14763i 0.818986 + 0.573813i \(0.194536\pi\)
−0.818986 + 0.573813i \(0.805464\pi\)
\(444\) −1550.16 2259.74i −0.165692 0.241537i
\(445\) 6517.06 0.694243
\(446\) 9742.29 1.03433
\(447\) −5574.51 + 3824.05i −0.589855 + 0.404634i
\(448\) 0 0
\(449\) 4017.92i 0.422310i −0.977453 0.211155i \(-0.932278\pi\)
0.977453 0.211155i \(-0.0677225\pi\)
\(450\) −1104.90 426.360i −0.115745 0.0446640i
\(451\) 555.459i 0.0579945i
\(452\) 18205.7i 1.89452i
\(453\) −7690.82 11211.3i −0.797674 1.16281i
\(454\) 11677.9i 1.20720i
\(455\) 0 0
\(456\) 683.777 + 996.777i 0.0702210 + 0.102365i
\(457\) 9169.65 0.938596 0.469298 0.883040i \(-0.344507\pi\)
0.469298 + 0.883040i \(0.344507\pi\)
\(458\) −478.066 −0.0487742
\(459\) −2923.46 + 693.716i −0.297289 + 0.0705444i
\(460\) 10151.5i 1.02895i
\(461\) 1289.80 0.130308 0.0651542 0.997875i \(-0.479246\pi\)
0.0651542 + 0.997875i \(0.479246\pi\)
\(462\) 0 0
\(463\) 6976.52 0.700273 0.350137 0.936699i \(-0.386135\pi\)
0.350137 + 0.936699i \(0.386135\pi\)
\(464\) 1321.34i 0.132202i
\(465\) −508.561 + 348.867i −0.0507182 + 0.0347920i
\(466\) 11935.3 1.18646
\(467\) −7863.66 −0.779201 −0.389600 0.920984i \(-0.627387\pi\)
−0.389600 + 0.920984i \(0.627387\pi\)
\(468\) −19907.9 7682.11i −1.96633 0.758772i
\(469\) 0 0
\(470\) 8635.44i 0.847496i
\(471\) −4007.06 + 2748.79i −0.392007 + 0.268912i
\(472\) 8729.25i 0.851263i
\(473\) 4023.04i 0.391077i
\(474\) −5633.14 + 3864.26i −0.545862 + 0.374455i
\(475\) 105.938i 0.0102332i
\(476\) 0 0
\(477\) −13280.5 5124.69i −1.27478 0.491915i
\(478\) −27640.6 −2.64488
\(479\) 3694.27 0.352391 0.176196 0.984355i \(-0.443621\pi\)
0.176196 + 0.984355i \(0.443621\pi\)
\(480\) −9553.05 + 6553.28i −0.908407 + 0.623156i
\(481\) 2599.82i 0.246448i
\(482\) 21040.7 1.98833
\(483\) 0 0
\(484\) −12788.5 −1.20103
\(485\) 2487.45i 0.232885i
\(486\) 17061.0 + 2322.42i 1.59240 + 0.216764i
\(487\) −1052.72 −0.0979533 −0.0489766 0.998800i \(-0.515596\pi\)
−0.0489766 + 0.998800i \(0.515596\pi\)
\(488\) 5476.08 0.507972
\(489\) −1523.06 2220.24i −0.140849 0.205322i
\(490\) 0 0
\(491\) 2378.40i 0.218607i 0.994008 + 0.109303i \(0.0348620\pi\)
−0.994008 + 0.109303i \(0.965138\pi\)
\(492\) −1153.87 1682.05i −0.105733 0.154132i
\(493\) 5687.84i 0.519609i
\(494\) 3114.80i 0.283687i
\(495\) 5236.79 + 2020.78i 0.475508 + 0.183490i
\(496\) 50.8881i 0.00460674i
\(497\) 0 0
\(498\) 8740.60 5995.95i 0.786497 0.539528i
\(499\) 18771.5 1.68402 0.842011 0.539461i \(-0.181372\pi\)
0.842011 + 0.539461i \(0.181372\pi\)
\(500\) −16947.8 −1.51586
\(501\) 11075.5 + 16145.3i 0.987655 + 1.43975i
\(502\) 27126.9i 2.41182i
\(503\) 16095.2 1.42674 0.713370 0.700788i \(-0.247168\pi\)
0.713370 + 0.700788i \(0.247168\pi\)
\(504\) 0 0
\(505\) −19931.9 −1.75635
\(506\) 5626.79i 0.494350i
\(507\) −4994.17 7280.26i −0.437473 0.637728i
\(508\) −34013.4 −2.97067
\(509\) 3150.63 0.274360 0.137180 0.990546i \(-0.456196\pi\)
0.137180 + 0.990546i \(0.456196\pi\)
\(510\) 4840.28 3320.37i 0.420257 0.288291i
\(511\) 0 0
\(512\) 1799.30i 0.155310i
\(513\) −355.606 1498.60i −0.0306051 0.128976i
\(514\) 25633.9i 2.19974i
\(515\) 13433.9i 1.14945i
\(516\) 8357.17 + 12182.7i 0.712992 + 1.03937i
\(517\) 2933.19i 0.249519i
\(518\) 0 0
\(519\) 7034.08 + 10253.9i 0.594917 + 0.867241i
\(520\) 15347.6 1.29430
\(521\) −4979.20 −0.418700 −0.209350 0.977841i \(-0.567135\pi\)
−0.209350 + 0.977841i \(0.567135\pi\)
\(522\) 11734.4 30409.2i 0.983906 2.54976i
\(523\) 13829.8i 1.15628i 0.815936 + 0.578142i \(0.196222\pi\)
−0.815936 + 0.578142i \(0.803778\pi\)
\(524\) 20300.1 1.69240
\(525\) 0 0
\(526\) 15843.9 1.31336
\(527\) 219.053i 0.0181064i
\(528\) 381.937 262.005i 0.0314805 0.0215952i
\(529\) 7393.10 0.607635
\(530\) 27808.5 2.27910
\(531\) 4004.31 10377.0i 0.327254 0.848069i
\(532\) 0 0
\(533\) 1935.19i 0.157265i
\(534\) 10938.8 7503.88i 0.886456 0.608098i
\(535\) 14131.1i 1.14195i
\(536\) 6854.33i 0.552355i
\(537\) −2742.93 + 1881.62i −0.220421 + 0.151206i
\(538\) 17248.2i 1.38220i
\(539\) 0 0
\(540\) −20056.0 + 4759.15i −1.59828 + 0.379261i
\(541\) 5317.95 0.422618 0.211309 0.977419i \(-0.432227\pi\)
0.211309 + 0.977419i \(0.432227\pi\)
\(542\) 33898.7 2.68648
\(543\) 18013.8 12357.3i 1.42366 0.976613i
\(544\) 4114.80i 0.324302i
\(545\) −15064.9 −1.18405
\(546\) 0 0
\(547\) −9266.96 −0.724363 −0.362181 0.932108i \(-0.617968\pi\)
−0.362181 + 0.932108i \(0.617968\pi\)
\(548\) 29356.4i 2.28840i
\(549\) −6509.77 2512.00i −0.506066 0.195282i
\(550\) −785.854 −0.0609253
\(551\) −2915.65 −0.225428
\(552\) 4303.45 + 6273.36i 0.331824 + 0.483717i
\(553\) 0 0
\(554\) 15525.2i 1.19062i
\(555\) −1420.65 2070.95i −0.108654 0.158391i
\(556\) 23317.4i 1.77856i
\(557\) 145.400i 0.0110607i −0.999985 0.00553033i \(-0.998240\pi\)
0.999985 0.00553033i \(-0.00176037\pi\)
\(558\) −451.920 + 1171.14i −0.0342854 + 0.0888497i
\(559\) 14016.1i 1.06050i
\(560\) 0 0
\(561\) −1644.09 + 1127.83i −0.123732 + 0.0848785i
\(562\) 12555.4 0.942376
\(563\) 3916.24 0.293161 0.146581 0.989199i \(-0.453173\pi\)
0.146581 + 0.989199i \(0.453173\pi\)
\(564\) 6093.19 + 8882.35i 0.454910 + 0.663146i
\(565\) 16684.7i 1.24236i
\(566\) −25024.0 −1.85837
\(567\) 0 0
\(568\) −962.437 −0.0710968
\(569\) 8550.53i 0.629977i 0.949096 + 0.314988i \(0.102001\pi\)
−0.949096 + 0.314988i \(0.897999\pi\)
\(570\) 1702.06 + 2481.18i 0.125073 + 0.182325i
\(571\) −23913.7 −1.75264 −0.876318 0.481733i \(-0.840007\pi\)
−0.876318 + 0.481733i \(0.840007\pi\)
\(572\) −14159.4 −1.03503
\(573\) −6243.32 + 4282.84i −0.455180 + 0.312248i
\(574\) 0 0
\(575\) 666.737i 0.0483563i
\(576\) −8102.20 + 20996.6i −0.586096 + 1.51885i
\(577\) 13103.3i 0.945405i −0.881222 0.472703i \(-0.843279\pi\)
0.881222 0.472703i \(-0.156721\pi\)
\(578\) 20247.2i 1.45705i
\(579\) 5376.89 + 7838.16i 0.385934 + 0.562596i
\(580\) 39020.7i 2.79353i
\(581\) 0 0
\(582\) −2864.10 4175.15i −0.203988 0.297363i
\(583\) −9445.66 −0.671011
\(584\) 11912.9 0.844106
\(585\) −18244.7 7040.31i −1.28945 0.497574i
\(586\) 18641.5i 1.31412i
\(587\) −18034.7 −1.26809 −0.634047 0.773294i \(-0.718608\pi\)
−0.634047 + 0.773294i \(0.718608\pi\)
\(588\) 0 0
\(589\) 112.289 0.00785532
\(590\) 21728.9i 1.51621i
\(591\) −2833.02 + 1943.42i −0.197183 + 0.135265i
\(592\) −207.226 −0.0143867
\(593\) 22716.2 1.57309 0.786547 0.617531i \(-0.211867\pi\)
0.786547 + 0.617531i \(0.211867\pi\)
\(594\) 11116.7 2637.90i 0.767882 0.182213i
\(595\) 0 0
\(596\) 16472.5i 1.13212i
\(597\) −8351.76 + 5729.21i −0.572554 + 0.392765i
\(598\) 19603.5i 1.34054i
\(599\) 13533.6i 0.923149i 0.887101 + 0.461575i \(0.152715\pi\)
−0.887101 + 0.461575i \(0.847285\pi\)
\(600\) 876.156 601.032i 0.0596148 0.0408951i
\(601\) 3667.98i 0.248952i −0.992223 0.124476i \(-0.960275\pi\)
0.992223 0.124476i \(-0.0397250\pi\)
\(602\) 0 0
\(603\) −3144.24 + 8148.20i −0.212344 + 0.550282i
\(604\) 33129.1 2.23180
\(605\) −11720.1 −0.787587
\(606\) −33455.3 + 22950.0i −2.24262 + 1.53841i
\(607\) 8017.00i 0.536079i −0.963408 0.268039i \(-0.913624\pi\)
0.963408 0.268039i \(-0.0863758\pi\)
\(608\) 2109.29 0.140696
\(609\) 0 0
\(610\) 13631.1 0.904763
\(611\) 10219.1i 0.676628i
\(612\) 2635.81 6830.62i 0.174095 0.451162i
\(613\) 9396.52 0.619122 0.309561 0.950880i \(-0.399818\pi\)
0.309561 + 0.950880i \(0.399818\pi\)
\(614\) −37643.3 −2.47420
\(615\) −1057.47 1541.53i −0.0693355 0.101074i
\(616\) 0 0
\(617\) 8906.76i 0.581155i 0.956851 + 0.290578i \(0.0938474\pi\)
−0.956851 + 0.290578i \(0.906153\pi\)
\(618\) −15468.1 22548.6i −1.00682 1.46770i
\(619\) 7034.12i 0.456745i 0.973574 + 0.228373i \(0.0733404\pi\)
−0.973574 + 0.228373i \(0.926660\pi\)
\(620\) 1502.78i 0.0973440i
\(621\) −2238.06 9431.64i −0.144622 0.609466i
\(622\) 31232.4i 2.01335i
\(623\) 0 0
\(624\) −1330.65 + 912.811i −0.0853665 + 0.0585604i
\(625\) −16738.1 −1.07124
\(626\) 15338.8 0.979332
\(627\) −578.135 842.778i −0.0368238 0.0536799i
\(628\) 11840.8i 0.752385i
\(629\) 892.024 0.0565458
\(630\) 0 0
\(631\) −12628.6 −0.796728 −0.398364 0.917227i \(-0.630422\pi\)
−0.398364 + 0.917227i \(0.630422\pi\)
\(632\) 6128.52i 0.385727i
\(633\) 9823.25 + 14319.9i 0.616808 + 0.899152i
\(634\) 10771.8 0.674768
\(635\) −31171.8 −1.94805
\(636\) 28603.6 19621.7i 1.78334 1.22335i
\(637\) 0 0
\(638\) 21628.4i 1.34213i
\(639\) 1144.11 + 441.492i 0.0708300 + 0.0273320i
\(640\) 26129.7i 1.61385i
\(641\) 9923.02i 0.611444i −0.952121 0.305722i \(-0.901102\pi\)
0.952121 0.305722i \(-0.0988978\pi\)
\(642\) 16270.9 + 23718.9i 1.00025 + 1.45811i
\(643\) 294.191i 0.0180432i 0.999959 + 0.00902160i \(0.00287170\pi\)
−0.999959 + 0.00902160i \(0.997128\pi\)
\(644\) 0 0
\(645\) 7658.97 + 11164.9i 0.467553 + 0.681576i
\(646\) −1068.72 −0.0650902
\(647\) −7718.79 −0.469021 −0.234511 0.972114i \(-0.575349\pi\)
−0.234511 + 0.972114i \(0.575349\pi\)
\(648\) −10376.6 + 11443.2i −0.629058 + 0.693721i
\(649\) 7380.61i 0.446401i
\(650\) 2737.88 0.165213
\(651\) 0 0
\(652\) 6560.75 0.394078
\(653\) 11370.2i 0.681395i 0.940173 + 0.340697i \(0.110663\pi\)
−0.940173 + 0.340697i \(0.889337\pi\)
\(654\) −25286.2 + 17346.0i −1.51188 + 1.03713i
\(655\) 18604.2 1.10981
\(656\) −154.250 −0.00918056
\(657\) −14161.6 5464.70i −0.840938 0.324503i
\(658\) 0 0
\(659\) 19795.1i 1.17012i −0.810990 0.585060i \(-0.801071\pi\)
0.810990 0.585060i \(-0.198929\pi\)
\(660\) −11279.1 + 7737.30i −0.665207 + 0.456324i
\(661\) 31057.5i 1.82753i −0.406247 0.913763i \(-0.633163\pi\)
0.406247 0.913763i \(-0.366837\pi\)
\(662\) 17289.3i 1.01506i
\(663\) 5727.93 3929.29i 0.335527 0.230167i
\(664\) 9509.25i 0.555769i
\(665\) 0 0
\(666\) −4769.08 1840.30i −0.277474 0.107072i
\(667\) −18350.1 −1.06524
\(668\) −47708.9 −2.76334
\(669\) 9183.66 6299.88i 0.530734 0.364077i
\(670\) 17061.8i 0.983814i
\(671\) −4630.04 −0.266380
\(672\) 0 0
\(673\) 5340.26 0.305872 0.152936 0.988236i \(-0.451127\pi\)
0.152936 + 0.988236i \(0.451127\pi\)
\(674\) 2695.28i 0.154033i
\(675\) −1317.25 + 312.574i −0.0751126 + 0.0178237i
\(676\) 21513.0 1.22400
\(677\) −24956.6 −1.41678 −0.708389 0.705822i \(-0.750578\pi\)
−0.708389 + 0.705822i \(0.750578\pi\)
\(678\) 19211.1 + 28005.1i 1.08820 + 1.58632i
\(679\) 0 0
\(680\) 5265.93i 0.296970i
\(681\) 7551.55 + 11008.3i 0.424928 + 0.619439i
\(682\) 832.964i 0.0467681i
\(683\) 11208.5i 0.627937i 0.949433 + 0.313968i \(0.101659\pi\)
−0.949433 + 0.313968i \(0.898341\pi\)
\(684\) 3501.45 + 1351.14i 0.195733 + 0.0755297i
\(685\) 26903.9i 1.50065i
\(686\) 0 0
\(687\) −450.654 + 309.143i −0.0250269 + 0.0171682i
\(688\) 1117.19 0.0619077
\(689\) 32908.2 1.81960
\(690\) 10712.1 + 15615.6i 0.591021 + 0.861562i
\(691\) 10937.8i 0.602159i −0.953599 0.301079i \(-0.902653\pi\)
0.953599 0.301079i \(-0.0973469\pi\)
\(692\) −30300.2 −1.66451
\(693\) 0 0
\(694\) 21714.7 1.18772
\(695\) 21369.4i 1.16631i
\(696\) 16541.7 + 24113.7i 0.900879 + 1.31326i
\(697\) 663.984 0.0360835
\(698\) 33447.1 1.81374
\(699\) 11250.9 7717.97i 0.608795 0.417626i
\(700\) 0 0
\(701\) 27949.3i 1.50589i 0.658082 + 0.752947i \(0.271368\pi\)
−0.658082 + 0.752947i \(0.728632\pi\)
\(702\) −38729.9 + 9190.32i −2.08229 + 0.494111i
\(703\) 457.261i 0.0245319i
\(704\) 14933.7i 0.799482i
\(705\) 5584.14 + 8140.28i 0.298313 + 0.434866i
\(706\) 15025.4i 0.800977i
\(707\) 0 0
\(708\) 15331.9 + 22350.1i 0.813855 + 1.18640i
\(709\) 20945.4 1.10948 0.554741 0.832023i \(-0.312817\pi\)
0.554741 + 0.832023i \(0.312817\pi\)
\(710\) −2395.70 −0.126632
\(711\) −2811.29 + 7285.37i −0.148286 + 0.384279i
\(712\) 11900.8i 0.626404i
\(713\) 706.707 0.0371197
\(714\) 0 0
\(715\) −12976.5 −0.678731
\(716\) 8105.30i 0.423058i
\(717\) −26055.7 + 17873.9i −1.35714 + 0.930979i
\(718\) −1885.09 −0.0979820
\(719\) 8300.21 0.430522 0.215261 0.976557i \(-0.430940\pi\)
0.215261 + 0.976557i \(0.430940\pi\)
\(720\) −561.167 + 1454.25i −0.0290465 + 0.0752731i
\(721\) 0 0
\(722\) 30629.8i 1.57884i
\(723\) 19834.2 13606.0i 1.02025 0.699880i
\(724\) 53230.4i 2.73245i
\(725\) 2562.82i 0.131284i
\(726\) −19672.0 + 13494.8i −1.00564 + 0.689860i
\(727\) 20951.5i 1.06884i 0.845218 + 0.534421i \(0.179470\pi\)
−0.845218 + 0.534421i \(0.820530\pi\)
\(728\) 0 0
\(729\) 17584.5 8843.31i 0.893388 0.449287i
\(730\) 29653.5 1.50346
\(731\) −4809.06 −0.243324
\(732\) 14020.8 9618.11i 0.707956 0.485650i
\(733\) 5641.56i 0.284278i 0.989847 + 0.142139i \(0.0453980\pi\)
−0.989847 + 0.142139i \(0.954602\pi\)
\(734\) −346.017 −0.0174001
\(735\) 0 0
\(736\) 13275.1 0.664847
\(737\) 5795.36i 0.289654i
\(738\) −3549.90 1369.84i −0.177064 0.0683259i
\(739\) −11382.2 −0.566576 −0.283288 0.959035i \(-0.591425\pi\)
−0.283288 + 0.959035i \(0.591425\pi\)
\(740\) 6119.61 0.304002
\(741\) 2014.20 + 2936.20i 0.0998560 + 0.145565i
\(742\) 0 0
\(743\) 4665.46i 0.230362i −0.993345 0.115181i \(-0.963255\pi\)
0.993345 0.115181i \(-0.0367449\pi\)
\(744\) −637.063 928.679i −0.0313923 0.0457621i
\(745\) 15096.3i 0.742399i
\(746\) 55914.3i 2.74419i
\(747\) 4362.11 11304.3i 0.213656 0.553684i
\(748\) 4858.24i 0.237480i
\(749\) 0 0
\(750\) −26070.0 + 17883.7i −1.26926 + 0.870696i
\(751\) −9560.86 −0.464555 −0.232277 0.972650i \(-0.574618\pi\)
−0.232277 + 0.972650i \(0.574618\pi\)
\(752\) 814.540 0.0394990
\(753\) −17541.7 25571.5i −0.848945 1.23755i
\(754\) 75352.3i 3.63948i
\(755\) 30361.4 1.46353
\(756\) 0 0
\(757\) 31574.1 1.51596 0.757979 0.652279i \(-0.226187\pi\)
0.757979 + 0.652279i \(0.226187\pi\)
\(758\) 6495.63i 0.311256i
\(759\) −3638.58 5304.14i −0.174008 0.253660i
\(760\) −2699.37 −0.128838
\(761\) 22429.9 1.06844 0.534221 0.845345i \(-0.320605\pi\)
0.534221 + 0.845345i \(0.320605\pi\)
\(762\) −52321.3 + 35891.8i −2.48740 + 1.70633i
\(763\) 0 0
\(764\) 18448.8i 0.873633i
\(765\) 2415.60 6259.96i 0.114165 0.295855i
\(766\) 23231.6i 1.09581i
\(767\) 25713.7i 1.21052i
\(768\) −10485.6 15285.4i −0.492664 0.718181i
\(769\) 26887.4i 1.26084i 0.776254 + 0.630420i \(0.217117\pi\)
−0.776254 + 0.630420i \(0.782883\pi\)
\(770\) 0 0
\(771\) −16576.3 24164.1i −0.774293 1.12873i
\(772\) −23161.6 −1.07980
\(773\) 22209.1 1.03339 0.516693 0.856171i \(-0.327163\pi\)
0.516693 + 0.856171i \(0.327163\pi\)
\(774\) 25711.0 + 9921.39i 1.19401 + 0.460745i
\(775\) 98.7007i 0.00457476i
\(776\) 4542.31 0.210128
\(777\) 0 0
\(778\) −33276.0 −1.53342
\(779\) 340.366i 0.0156545i
\(780\) 39295.7 26956.4i 1.80386 1.23743i
\(781\) 813.743 0.0372830
\(782\) −6726.15 −0.307579
\(783\) −8602.71 36253.6i −0.392638 1.65466i
\(784\) 0 0
\(785\) 10851.5i 0.493385i
\(786\) 31226.8 21421.2i 1.41708 0.972100i
\(787\) 20095.5i