Properties

Label 147.4.c.b.146.24
Level $147$
Weight $4$
Character 147.146
Analytic conductor $8.673$
Analytic rank $0$
Dimension $24$
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: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.24
Character \(\chi\) \(=\) 147.146
Dual form 147.4.c.b.146.2

$q$-expansion

\(f(q)\) \(=\) \(q+5.37572i q^{2} +(2.08523 - 4.75939i) q^{3} -20.8984 q^{4} -2.78815 q^{5} +(25.5852 + 11.2096i) q^{6} -69.3382i q^{8} +(-18.3036 - 19.8488i) q^{9} +O(q^{10})\) \(q+5.37572i q^{2} +(2.08523 - 4.75939i) q^{3} -20.8984 q^{4} -2.78815 q^{5} +(25.5852 + 11.2096i) q^{6} -69.3382i q^{8} +(-18.3036 - 19.8488i) q^{9} -14.9883i q^{10} -17.5600i q^{11} +(-43.5779 + 99.4637i) q^{12} -47.8755i q^{13} +(-5.81394 + 13.2699i) q^{15} +205.556 q^{16} +89.4402 q^{17} +(106.702 - 98.3954i) q^{18} -42.2598i q^{19} +58.2680 q^{20} +94.3978 q^{22} -87.6734i q^{23} +(-330.008 - 144.586i) q^{24} -117.226 q^{25} +257.365 q^{26} +(-132.636 + 45.7249i) q^{27} +40.8422i q^{29} +(-71.3354 - 31.2541i) q^{30} -95.6222i q^{31} +550.306i q^{32} +(-83.5751 - 36.6167i) q^{33} +480.806i q^{34} +(382.517 + 414.809i) q^{36} -64.5502 q^{37} +227.177 q^{38} +(-227.858 - 99.8313i) q^{39} +193.326i q^{40} -403.003 q^{41} -230.669 q^{43} +366.976i q^{44} +(51.0334 + 55.3416i) q^{45} +471.308 q^{46} +365.410 q^{47} +(428.631 - 978.321i) q^{48} -630.176i q^{50} +(186.503 - 425.681i) q^{51} +1000.52i q^{52} -598.298i q^{53} +(-245.805 - 713.013i) q^{54} +48.9601i q^{55} +(-201.131 - 88.1213i) q^{57} -219.556 q^{58} +236.679 q^{59} +(121.502 - 277.320i) q^{60} +430.942i q^{61} +514.039 q^{62} -1313.84 q^{64} +133.484i q^{65} +(196.841 - 449.276i) q^{66} -428.035 q^{67} -1869.16 q^{68} +(-417.272 - 182.819i) q^{69} +519.586i q^{71} +(-1376.28 + 1269.14i) q^{72} -764.579i q^{73} -347.004i q^{74} +(-244.443 + 557.926i) q^{75} +883.162i q^{76} +(536.665 - 1224.90i) q^{78} -227.679 q^{79} -573.121 q^{80} +(-58.9528 + 726.612i) q^{81} -2166.43i q^{82} +1136.62 q^{83} -249.373 q^{85} -1240.01i q^{86} +(194.384 + 85.1652i) q^{87} -1217.58 q^{88} +1130.48 q^{89} +(-297.501 + 274.341i) q^{90} +1832.23i q^{92} +(-455.104 - 199.394i) q^{93} +1964.34i q^{94} +117.827i q^{95} +(2619.12 + 1147.51i) q^{96} -1480.50i q^{97} +(-348.546 + 321.413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.37572i 1.90061i 0.311328 + 0.950303i \(0.399226\pi\)
−0.311328 + 0.950303i \(0.600774\pi\)
\(3\) 2.08523 4.75939i 0.401302 0.915946i
\(4\) −20.8984 −2.61230
\(5\) −2.78815 −0.249380 −0.124690 0.992196i \(-0.539794\pi\)
−0.124690 + 0.992196i \(0.539794\pi\)
\(6\) 25.5852 + 11.2096i 1.74085 + 0.762717i
\(7\) 0 0
\(8\) 69.3382i 3.06435i
\(9\) −18.3036 19.8488i −0.677913 0.735142i
\(10\) 14.9883i 0.473973i
\(11\) 17.5600i 0.481322i −0.970609 0.240661i \(-0.922636\pi\)
0.970609 0.240661i \(-0.0773643\pi\)
\(12\) −43.5779 + 99.4637i −1.04832 + 2.39272i
\(13\) 47.8755i 1.02140i −0.859758 0.510702i \(-0.829385\pi\)
0.859758 0.510702i \(-0.170615\pi\)
\(14\) 0 0
\(15\) −5.81394 + 13.2699i −0.100077 + 0.228419i
\(16\) 205.556 3.21181
\(17\) 89.4402 1.27603 0.638013 0.770026i \(-0.279757\pi\)
0.638013 + 0.770026i \(0.279757\pi\)
\(18\) 106.702 98.3954i 1.39721 1.28844i
\(19\) 42.2598i 0.510267i −0.966906 0.255133i \(-0.917881\pi\)
0.966906 0.255133i \(-0.0821194\pi\)
\(20\) 58.2680 0.651456
\(21\) 0 0
\(22\) 94.3978 0.914804
\(23\) 87.6734i 0.794833i −0.917638 0.397417i \(-0.869907\pi\)
0.917638 0.397417i \(-0.130093\pi\)
\(24\) −330.008 144.586i −2.80677 1.22973i
\(25\) −117.226 −0.937810
\(26\) 257.365 1.94129
\(27\) −132.636 + 45.7249i −0.945398 + 0.325917i
\(28\) 0 0
\(29\) 40.8422i 0.261524i 0.991414 + 0.130762i \(0.0417424\pi\)
−0.991414 + 0.130762i \(0.958258\pi\)
\(30\) −71.3354 31.2541i −0.434134 0.190206i
\(31\) 95.6222i 0.554008i −0.960869 0.277004i \(-0.910658\pi\)
0.960869 0.277004i \(-0.0893416\pi\)
\(32\) 550.306i 3.04004i
\(33\) −83.5751 36.6167i −0.440865 0.193156i
\(34\) 480.806i 2.42522i
\(35\) 0 0
\(36\) 382.517 + 414.809i 1.77091 + 1.92041i
\(37\) −64.5502 −0.286810 −0.143405 0.989664i \(-0.545805\pi\)
−0.143405 + 0.989664i \(0.545805\pi\)
\(38\) 227.177 0.969815
\(39\) −227.858 99.8313i −0.935551 0.409892i
\(40\) 193.326i 0.764187i
\(41\) −403.003 −1.53509 −0.767543 0.640997i \(-0.778521\pi\)
−0.767543 + 0.640997i \(0.778521\pi\)
\(42\) 0 0
\(43\) −230.669 −0.818061 −0.409031 0.912521i \(-0.634133\pi\)
−0.409031 + 0.912521i \(0.634133\pi\)
\(44\) 366.976i 1.25736i
\(45\) 51.0334 + 55.3416i 0.169058 + 0.183330i
\(46\) 471.308 1.51066
\(47\) 365.410 1.13405 0.567027 0.823699i \(-0.308094\pi\)
0.567027 + 0.823699i \(0.308094\pi\)
\(48\) 428.631 978.321i 1.28891 2.94184i
\(49\) 0 0
\(50\) 630.176i 1.78241i
\(51\) 186.503 425.681i 0.512072 1.16877i
\(52\) 1000.52i 2.66822i
\(53\) 598.298i 1.55061i −0.631585 0.775307i \(-0.717595\pi\)
0.631585 0.775307i \(-0.282405\pi\)
\(54\) −245.805 713.013i −0.619440 1.79683i
\(55\) 48.9601i 0.120032i
\(56\) 0 0
\(57\) −201.131 88.1213i −0.467377 0.204771i
\(58\) −219.556 −0.497054
\(59\) 236.679 0.522254 0.261127 0.965304i \(-0.415906\pi\)
0.261127 + 0.965304i \(0.415906\pi\)
\(60\) 121.502 277.320i 0.261431 0.596698i
\(61\) 430.942i 0.904532i 0.891883 + 0.452266i \(0.149384\pi\)
−0.891883 + 0.452266i \(0.850616\pi\)
\(62\) 514.039 1.05295
\(63\) 0 0
\(64\) −1313.84 −2.56610
\(65\) 133.484i 0.254718i
\(66\) 196.841 449.276i 0.367113 0.837911i
\(67\) −428.035 −0.780490 −0.390245 0.920711i \(-0.627610\pi\)
−0.390245 + 0.920711i \(0.627610\pi\)
\(68\) −1869.16 −3.33336
\(69\) −417.272 182.819i −0.728024 0.318968i
\(70\) 0 0
\(71\) 519.586i 0.868500i 0.900792 + 0.434250i \(0.142987\pi\)
−0.900792 + 0.434250i \(0.857013\pi\)
\(72\) −1376.28 + 1269.14i −2.25273 + 2.07736i
\(73\) 764.579i 1.22585i −0.790140 0.612926i \(-0.789992\pi\)
0.790140 0.612926i \(-0.210008\pi\)
\(74\) 347.004i 0.545113i
\(75\) −244.443 + 557.926i −0.376345 + 0.858983i
\(76\) 883.162i 1.33297i
\(77\) 0 0
\(78\) 536.665 1224.90i 0.779043 1.77811i
\(79\) −227.679 −0.324252 −0.162126 0.986770i \(-0.551835\pi\)
−0.162126 + 0.986770i \(0.551835\pi\)
\(80\) −573.121 −0.800962
\(81\) −58.9528 + 726.612i −0.0808680 + 0.996725i
\(82\) 2166.43i 2.91759i
\(83\) 1136.62 1.50313 0.751565 0.659659i \(-0.229299\pi\)
0.751565 + 0.659659i \(0.229299\pi\)
\(84\) 0 0
\(85\) −249.373 −0.318215
\(86\) 1240.01i 1.55481i
\(87\) 194.384 + 85.1652i 0.239542 + 0.104950i
\(88\) −1217.58 −1.47494
\(89\) 1130.48 1.34641 0.673205 0.739455i \(-0.264917\pi\)
0.673205 + 0.739455i \(0.264917\pi\)
\(90\) −297.501 + 274.341i −0.348438 + 0.321312i
\(91\) 0 0
\(92\) 1832.23i 2.07634i
\(93\) −455.104 199.394i −0.507442 0.222325i
\(94\) 1964.34i 2.15539i
\(95\) 117.827i 0.127250i
\(96\) 2619.12 + 1147.51i 2.78451 + 1.21997i
\(97\) 1480.50i 1.54971i −0.632136 0.774857i \(-0.717822\pi\)
0.632136 0.774857i \(-0.282178\pi\)
\(98\) 0 0
\(99\) −348.546 + 321.413i −0.353840 + 0.326295i
\(100\) 2449.84 2.44984
\(101\) −1162.07 −1.14486 −0.572429 0.819954i \(-0.693999\pi\)
−0.572429 + 0.819954i \(0.693999\pi\)
\(102\) 2288.34 + 1002.59i 2.22137 + 0.973246i
\(103\) 91.5428i 0.0875726i 0.999041 + 0.0437863i \(0.0139421\pi\)
−0.999041 + 0.0437863i \(0.986058\pi\)
\(104\) −3319.60 −3.12994
\(105\) 0 0
\(106\) 3216.28 2.94710
\(107\) 1499.33i 1.35463i 0.735693 + 0.677315i \(0.236857\pi\)
−0.735693 + 0.677315i \(0.763143\pi\)
\(108\) 2771.87 955.578i 2.46966 0.851393i
\(109\) 1244.48 1.09357 0.546785 0.837273i \(-0.315851\pi\)
0.546785 + 0.837273i \(0.315851\pi\)
\(110\) −263.196 −0.228134
\(111\) −134.602 + 307.220i −0.115098 + 0.262703i
\(112\) 0 0
\(113\) 470.193i 0.391434i 0.980660 + 0.195717i \(0.0627034\pi\)
−0.980660 + 0.195717i \(0.937297\pi\)
\(114\) 473.716 1081.23i 0.389189 0.888298i
\(115\) 244.447i 0.198216i
\(116\) 853.536i 0.683179i
\(117\) −950.272 + 876.296i −0.750878 + 0.692424i
\(118\) 1272.32i 0.992599i
\(119\) 0 0
\(120\) 920.113 + 403.128i 0.699953 + 0.306670i
\(121\) 1022.65 0.768329
\(122\) −2316.62 −1.71916
\(123\) −840.353 + 1918.05i −0.616033 + 1.40606i
\(124\) 1998.35i 1.44724i
\(125\) 675.364 0.483251
\(126\) 0 0
\(127\) −2329.37 −1.62754 −0.813772 0.581185i \(-0.802589\pi\)
−0.813772 + 0.581185i \(0.802589\pi\)
\(128\) 2660.42i 1.83711i
\(129\) −480.997 + 1097.84i −0.328290 + 0.749300i
\(130\) −717.574 −0.484118
\(131\) 588.971 0.392814 0.196407 0.980522i \(-0.437073\pi\)
0.196407 + 0.980522i \(0.437073\pi\)
\(132\) 1746.59 + 765.229i 1.15167 + 0.504581i
\(133\) 0 0
\(134\) 2301.00i 1.48340i
\(135\) 369.809 127.488i 0.235763 0.0812773i
\(136\) 6201.62i 3.91018i
\(137\) 529.151i 0.329989i 0.986295 + 0.164994i \(0.0527606\pi\)
−0.986295 + 0.164994i \(0.947239\pi\)
\(138\) 982.784 2243.14i 0.606233 1.38369i
\(139\) 1043.90i 0.636997i 0.947923 + 0.318499i \(0.103179\pi\)
−0.947923 + 0.318499i \(0.896821\pi\)
\(140\) 0 0
\(141\) 761.963 1739.13i 0.455098 1.03873i
\(142\) −2793.15 −1.65068
\(143\) −840.694 −0.491625
\(144\) −3762.42 4080.05i −2.17733 2.36114i
\(145\) 113.874i 0.0652189i
\(146\) 4110.17 2.32986
\(147\) 0 0
\(148\) 1349.00 0.749235
\(149\) 2065.04i 1.13540i 0.823235 + 0.567701i \(0.192167\pi\)
−0.823235 + 0.567701i \(0.807833\pi\)
\(150\) −2999.25 1314.06i −1.63259 0.715283i
\(151\) −540.261 −0.291164 −0.145582 0.989346i \(-0.546506\pi\)
−0.145582 + 0.989346i \(0.546506\pi\)
\(152\) −2930.22 −1.56363
\(153\) −1637.08 1775.28i −0.865034 0.938060i
\(154\) 0 0
\(155\) 266.610i 0.138159i
\(156\) 4761.87 + 2086.31i 2.44394 + 1.07076i
\(157\) 658.650i 0.334815i 0.985888 + 0.167408i \(0.0535396\pi\)
−0.985888 + 0.167408i \(0.946460\pi\)
\(158\) 1223.94i 0.616274i
\(159\) −2847.53 1247.59i −1.42028 0.622265i
\(160\) 1534.34i 0.758125i
\(161\) 0 0
\(162\) −3906.07 316.914i −1.89438 0.153698i
\(163\) 403.947 0.194108 0.0970540 0.995279i \(-0.469058\pi\)
0.0970540 + 0.995279i \(0.469058\pi\)
\(164\) 8422.12 4.01010
\(165\) 233.020 + 102.093i 0.109943 + 0.0481692i
\(166\) 6110.13i 2.85686i
\(167\) 2046.40 0.948237 0.474118 0.880461i \(-0.342767\pi\)
0.474118 + 0.880461i \(0.342767\pi\)
\(168\) 0 0
\(169\) −95.0602 −0.0432682
\(170\) 1340.56i 0.604802i
\(171\) −838.808 + 773.509i −0.375119 + 0.345916i
\(172\) 4820.61 2.13702
\(173\) 705.271 0.309947 0.154973 0.987919i \(-0.450471\pi\)
0.154973 + 0.987919i \(0.450471\pi\)
\(174\) −457.825 + 1044.95i −0.199469 + 0.455274i
\(175\) 0 0
\(176\) 3609.57i 1.54592i
\(177\) 493.530 1126.45i 0.209582 0.478357i
\(178\) 6077.14i 2.55900i
\(179\) 740.849i 0.309350i 0.987965 + 0.154675i \(0.0494331\pi\)
−0.987965 + 0.154675i \(0.950567\pi\)
\(180\) −1066.52 1156.55i −0.441630 0.478912i
\(181\) 1339.29i 0.549993i −0.961445 0.274997i \(-0.911323\pi\)
0.961445 0.274997i \(-0.0886768\pi\)
\(182\) 0 0
\(183\) 2051.02 + 898.612i 0.828502 + 0.362991i
\(184\) −6079.12 −2.43564
\(185\) 179.976 0.0715248
\(186\) 1071.89 2446.51i 0.422552 0.964446i
\(187\) 1570.57i 0.614180i
\(188\) −7636.48 −2.96249
\(189\) 0 0
\(190\) −633.405 −0.241853
\(191\) 1863.68i 0.706027i −0.935618 0.353014i \(-0.885157\pi\)
0.935618 0.353014i \(-0.114843\pi\)
\(192\) −2739.66 + 6253.10i −1.02978 + 2.35041i
\(193\) 2190.72 0.817055 0.408528 0.912746i \(-0.366042\pi\)
0.408528 + 0.912746i \(0.366042\pi\)
\(194\) 7958.77 2.94539
\(195\) 635.304 + 278.345i 0.233308 + 0.102219i
\(196\) 0 0
\(197\) 1173.24i 0.424315i −0.977236 0.212157i \(-0.931951\pi\)
0.977236 0.212157i \(-0.0680489\pi\)
\(198\) −1727.82 1873.69i −0.620157 0.672511i
\(199\) 4835.99i 1.72268i −0.508025 0.861342i \(-0.669624\pi\)
0.508025 0.861342i \(-0.330376\pi\)
\(200\) 8128.26i 2.87377i
\(201\) −892.551 + 2037.19i −0.313213 + 0.714887i
\(202\) 6246.99i 2.17592i
\(203\) 0 0
\(204\) −3897.62 + 8896.05i −1.33769 + 3.05318i
\(205\) 1123.63 0.382820
\(206\) −492.109 −0.166441
\(207\) −1740.21 + 1604.74i −0.584315 + 0.538828i
\(208\) 9841.08i 3.28056i
\(209\) −742.083 −0.245603
\(210\) 0 0
\(211\) 2930.01 0.955972 0.477986 0.878368i \(-0.341367\pi\)
0.477986 + 0.878368i \(0.341367\pi\)
\(212\) 12503.5i 4.05067i
\(213\) 2472.91 + 1083.46i 0.795499 + 0.348531i
\(214\) −8059.97 −2.57462
\(215\) 643.140 0.204008
\(216\) 3170.48 + 9196.72i 0.998723 + 2.89703i
\(217\) 0 0
\(218\) 6689.96i 2.07845i
\(219\) −3638.93 1594.32i −1.12281 0.491937i
\(220\) 1023.19i 0.313560i
\(221\) 4281.99i 1.30334i
\(222\) −1651.53 723.582i −0.499294 0.218755i
\(223\) 4874.38i 1.46373i 0.681447 + 0.731867i \(0.261351\pi\)
−0.681447 + 0.731867i \(0.738649\pi\)
\(224\) 0 0
\(225\) 2145.67 + 2326.80i 0.635753 + 0.689423i
\(226\) −2527.63 −0.743962
\(227\) 2439.53 0.713293 0.356647 0.934239i \(-0.383920\pi\)
0.356647 + 0.934239i \(0.383920\pi\)
\(228\) 4203.32 + 1841.59i 1.22093 + 0.534924i
\(229\) 4723.32i 1.36299i −0.731820 0.681497i \(-0.761329\pi\)
0.731820 0.681497i \(-0.238671\pi\)
\(230\) −1314.08 −0.376730
\(231\) 0 0
\(232\) 2831.92 0.801400
\(233\) 1768.83i 0.497339i −0.968588 0.248670i \(-0.920007\pi\)
0.968588 0.248670i \(-0.0799933\pi\)
\(234\) −4710.72 5108.40i −1.31602 1.42712i
\(235\) −1018.82 −0.282810
\(236\) −4946.22 −1.36428
\(237\) −474.762 + 1083.61i −0.130123 + 0.296997i
\(238\) 0 0
\(239\) 1527.40i 0.413386i −0.978406 0.206693i \(-0.933730\pi\)
0.978406 0.206693i \(-0.0662701\pi\)
\(240\) −1195.09 + 2727.71i −0.321428 + 0.733637i
\(241\) 1418.76i 0.379214i 0.981860 + 0.189607i \(0.0607214\pi\)
−0.981860 + 0.189607i \(0.939279\pi\)
\(242\) 5497.46i 1.46029i
\(243\) 3335.30 + 1795.73i 0.880493 + 0.474059i
\(244\) 9005.99i 2.36291i
\(245\) 0 0
\(246\) −10310.9 4517.51i −2.67236 1.17084i
\(247\) −2023.21 −0.521189
\(248\) −6630.28 −1.69767
\(249\) 2370.10 5409.60i 0.603209 1.37678i
\(250\) 3630.57i 0.918469i
\(251\) −2152.91 −0.541396 −0.270698 0.962664i \(-0.587255\pi\)
−0.270698 + 0.962664i \(0.587255\pi\)
\(252\) 0 0
\(253\) −1539.55 −0.382571
\(254\) 12522.0i 3.09332i
\(255\) −520.000 + 1186.86i −0.127701 + 0.291468i
\(256\) 3790.91 0.925515
\(257\) 665.100 0.161431 0.0807156 0.996737i \(-0.474279\pi\)
0.0807156 + 0.996737i \(0.474279\pi\)
\(258\) −5901.70 2585.70i −1.42412 0.623949i
\(259\) 0 0
\(260\) 2789.61i 0.665400i
\(261\) 810.669 747.561i 0.192257 0.177291i
\(262\) 3166.14i 0.746584i
\(263\) 5133.87i 1.20368i −0.798617 0.601840i \(-0.794434\pi\)
0.798617 0.601840i \(-0.205566\pi\)
\(264\) −2538.93 + 5794.95i −0.591896 + 1.35096i
\(265\) 1668.15i 0.386692i
\(266\) 0 0
\(267\) 2357.31 5380.40i 0.540318 1.23324i
\(268\) 8945.26 2.03887
\(269\) 5975.29 1.35435 0.677174 0.735823i \(-0.263204\pi\)
0.677174 + 0.735823i \(0.263204\pi\)
\(270\) 685.341 + 1987.99i 0.154476 + 0.448093i
\(271\) 1496.60i 0.335469i −0.985832 0.167734i \(-0.946355\pi\)
0.985832 0.167734i \(-0.0536451\pi\)
\(272\) 18385.0 4.09835
\(273\) 0 0
\(274\) −2844.57 −0.627178
\(275\) 2058.49i 0.451389i
\(276\) 8720.32 + 3820.62i 1.90182 + 0.833241i
\(277\) 6515.07 1.41319 0.706593 0.707620i \(-0.250231\pi\)
0.706593 + 0.707620i \(0.250231\pi\)
\(278\) −5611.73 −1.21068
\(279\) −1897.99 + 1750.24i −0.407275 + 0.375569i
\(280\) 0 0
\(281\) 2236.41i 0.474780i 0.971414 + 0.237390i \(0.0762920\pi\)
−0.971414 + 0.237390i \(0.923708\pi\)
\(282\) 9349.08 + 4096.10i 1.97422 + 0.864962i
\(283\) 3959.25i 0.831636i −0.909448 0.415818i \(-0.863495\pi\)
0.909448 0.415818i \(-0.136505\pi\)
\(284\) 10858.5i 2.26878i
\(285\) 560.784 + 245.696i 0.116554 + 0.0510659i
\(286\) 4519.34i 0.934385i
\(287\) 0 0
\(288\) 10922.9 10072.6i 2.23486 2.06088i
\(289\) 3086.55 0.628241
\(290\) 612.156 0.123955
\(291\) −7046.30 3087.19i −1.41945 0.621904i
\(292\) 15978.5i 3.20229i
\(293\) −3668.54 −0.731461 −0.365731 0.930721i \(-0.619181\pi\)
−0.365731 + 0.930721i \(0.619181\pi\)
\(294\) 0 0
\(295\) −659.898 −0.130240
\(296\) 4475.80i 0.878886i
\(297\) 802.931 + 2329.09i 0.156871 + 0.455041i
\(298\) −11101.1 −2.15795
\(299\) −4197.40 −0.811847
\(300\) 5108.47 11659.8i 0.983126 2.24392i
\(301\) 0 0
\(302\) 2904.29i 0.553388i
\(303\) −2423.19 + 5530.77i −0.459434 + 1.04863i
\(304\) 8686.75i 1.63888i
\(305\) 1201.53i 0.225572i
\(306\) 9543.43 8800.50i 1.78288 1.64409i
\(307\) 6704.82i 1.24646i 0.782037 + 0.623231i \(0.214181\pi\)
−0.782037 + 0.623231i \(0.785819\pi\)
\(308\) 0 0
\(309\) 435.688 + 190.888i 0.0802117 + 0.0351431i
\(310\) −1433.22 −0.262585
\(311\) −8012.92 −1.46100 −0.730500 0.682913i \(-0.760713\pi\)
−0.730500 + 0.682913i \(0.760713\pi\)
\(312\) −6922.12 + 15799.3i −1.25605 + 2.86685i
\(313\) 177.232i 0.0320056i −0.999872 0.0160028i \(-0.994906\pi\)
0.999872 0.0160028i \(-0.00509407\pi\)
\(314\) −3540.72 −0.636352
\(315\) 0 0
\(316\) 4758.12 0.847042
\(317\) 6088.73i 1.07879i −0.842052 0.539396i \(-0.818653\pi\)
0.842052 0.539396i \(-0.181347\pi\)
\(318\) 6706.68 15307.6i 1.18268 2.69939i
\(319\) 717.189 0.125877
\(320\) 3663.20 0.639935
\(321\) 7135.89 + 3126.44i 1.24077 + 0.543616i
\(322\) 0 0
\(323\) 3779.73i 0.651113i
\(324\) 1232.02 15185.0i 0.211252 2.60374i
\(325\) 5612.26i 0.957883i
\(326\) 2171.51i 0.368923i
\(327\) 2595.02 5922.95i 0.438852 1.00165i
\(328\) 27943.5i 4.70403i
\(329\) 0 0
\(330\) −548.823 + 1252.65i −0.0915506 + 0.208958i
\(331\) −10388.3 −1.72505 −0.862526 0.506013i \(-0.831119\pi\)
−0.862526 + 0.506013i \(0.831119\pi\)
\(332\) −23753.4 −3.92662
\(333\) 1181.50 + 1281.25i 0.194433 + 0.210846i
\(334\) 11000.9i 1.80222i
\(335\) 1193.43 0.194639
\(336\) 0 0
\(337\) −565.857 −0.0914664 −0.0457332 0.998954i \(-0.514562\pi\)
−0.0457332 + 0.998954i \(0.514562\pi\)
\(338\) 511.017i 0.0822357i
\(339\) 2237.83 + 980.460i 0.358532 + 0.157083i
\(340\) 5211.50 0.831274
\(341\) −1679.13 −0.266657
\(342\) −4158.17 4509.20i −0.657450 0.712952i
\(343\) 0 0
\(344\) 15994.2i 2.50682i
\(345\) 1163.42 + 509.727i 0.181555 + 0.0795444i
\(346\) 3791.34i 0.589086i
\(347\) 10179.1i 1.57476i 0.616465 + 0.787382i \(0.288564\pi\)
−0.616465 + 0.787382i \(0.711436\pi\)
\(348\) −4062.31 1779.82i −0.625755 0.274161i
\(349\) 6924.54i 1.06207i −0.847350 0.531034i \(-0.821804\pi\)
0.847350 0.531034i \(-0.178196\pi\)
\(350\) 0 0
\(351\) 2189.10 + 6350.00i 0.332893 + 0.965635i
\(352\) 9663.38 1.46324
\(353\) 2975.74 0.448677 0.224338 0.974511i \(-0.427978\pi\)
0.224338 + 0.974511i \(0.427978\pi\)
\(354\) 6055.48 + 2653.08i 0.909167 + 0.398332i
\(355\) 1448.69i 0.216587i
\(356\) −23625.2 −3.51723
\(357\) 0 0
\(358\) −3982.60 −0.587952
\(359\) 2753.05i 0.404736i 0.979310 + 0.202368i \(0.0648637\pi\)
−0.979310 + 0.202368i \(0.935136\pi\)
\(360\) 3837.29 3538.56i 0.561786 0.518052i
\(361\) 5073.11 0.739628
\(362\) 7199.66 1.04532
\(363\) 2132.45 4867.17i 0.308332 0.703747i
\(364\) 0 0
\(365\) 2131.76i 0.305703i
\(366\) −4830.69 + 11025.7i −0.689902 + 1.57466i
\(367\) 12658.1i 1.80040i −0.435482 0.900198i \(-0.643422\pi\)
0.435482 0.900198i \(-0.356578\pi\)
\(368\) 18021.8i 2.55285i
\(369\) 7376.43 + 7999.15i 1.04065 + 1.12851i
\(370\) 967.501i 0.135940i
\(371\) 0 0
\(372\) 9510.94 + 4167.02i 1.32559 + 0.580779i
\(373\) 10810.6 1.50068 0.750339 0.661054i \(-0.229890\pi\)
0.750339 + 0.661054i \(0.229890\pi\)
\(374\) 8442.96 1.16731
\(375\) 1408.29 3214.32i 0.193930 0.442632i
\(376\) 25336.9i 3.47513i
\(377\) 1955.34 0.267122
\(378\) 0 0
\(379\) 5489.38 0.743985 0.371993 0.928236i \(-0.378675\pi\)
0.371993 + 0.928236i \(0.378675\pi\)
\(380\) 2462.39i 0.332416i
\(381\) −4857.26 + 11086.4i −0.653137 + 1.49074i
\(382\) 10018.6 1.34188
\(383\) −12465.9 −1.66313 −0.831566 0.555426i \(-0.812555\pi\)
−0.831566 + 0.555426i \(0.812555\pi\)
\(384\) −12662.0 5547.57i −1.68269 0.737236i
\(385\) 0 0
\(386\) 11776.7i 1.55290i
\(387\) 4222.08 + 4578.50i 0.554574 + 0.601391i
\(388\) 30940.1i 4.04832i
\(389\) 7252.37i 0.945269i 0.881259 + 0.472634i \(0.156697\pi\)
−0.881259 + 0.472634i \(0.843303\pi\)
\(390\) −1496.31 + 3415.22i −0.194278 + 0.443426i
\(391\) 7841.52i 1.01423i
\(392\) 0 0
\(393\) 1228.14 2803.14i 0.157637 0.359796i
\(394\) 6307.02 0.806454
\(395\) 634.804 0.0808619
\(396\) 7284.06 6717.01i 0.924337 0.852380i
\(397\) 1114.55i 0.140900i −0.997515 0.0704502i \(-0.977556\pi\)
0.997515 0.0704502i \(-0.0224436\pi\)
\(398\) 25996.9 3.27414
\(399\) 0 0
\(400\) −24096.5 −3.01207
\(401\) 10183.0i 1.26811i −0.773287 0.634056i \(-0.781389\pi\)
0.773287 0.634056i \(-0.218611\pi\)
\(402\) −10951.4 4798.11i −1.35872 0.595293i
\(403\) −4577.96 −0.565867
\(404\) 24285.5 2.99071
\(405\) 164.369 2025.91i 0.0201669 0.248563i
\(406\) 0 0
\(407\) 1133.50i 0.138048i
\(408\) −29516.0 12931.8i −3.58151 1.56917i
\(409\) 756.556i 0.0914653i −0.998954 0.0457327i \(-0.985438\pi\)
0.998954 0.0457327i \(-0.0145622\pi\)
\(410\) 6040.35i 0.727589i
\(411\) 2518.44 + 1103.40i 0.302252 + 0.132425i
\(412\) 1913.10i 0.228766i
\(413\) 0 0
\(414\) −8626.65 9354.91i −1.02410 1.11055i
\(415\) −3169.06 −0.374851
\(416\) 26346.1 3.10511
\(417\) 4968.34 + 2176.77i 0.583455 + 0.255628i
\(418\) 3989.23i 0.466794i
\(419\) −1348.55 −0.157234 −0.0786169 0.996905i \(-0.525050\pi\)
−0.0786169 + 0.996905i \(0.525050\pi\)
\(420\) 0 0
\(421\) −5570.16 −0.644829 −0.322415 0.946599i \(-0.604495\pi\)
−0.322415 + 0.946599i \(0.604495\pi\)
\(422\) 15750.9i 1.81692i
\(423\) −6688.33 7252.96i −0.768789 0.833690i
\(424\) −41484.9 −4.75161
\(425\) −10484.7 −1.19667
\(426\) −5824.36 + 13293.7i −0.662420 + 1.51193i
\(427\) 0 0
\(428\) 31333.5i 3.53870i
\(429\) −1753.04 + 4001.20i −0.197290 + 0.450302i
\(430\) 3457.34i 0.387739i
\(431\) 15192.0i 1.69785i 0.528514 + 0.848924i \(0.322749\pi\)
−0.528514 + 0.848924i \(0.677251\pi\)
\(432\) −27264.1 + 9399.03i −3.03644 + 1.04678i
\(433\) 6207.85i 0.688984i −0.938789 0.344492i \(-0.888051\pi\)
0.938789 0.344492i \(-0.111949\pi\)
\(434\) 0 0
\(435\) −541.972 237.454i −0.0597370 0.0261725i
\(436\) −26007.6 −2.85673
\(437\) −3705.06 −0.405577
\(438\) 8570.63 19561.9i 0.934979 2.13403i
\(439\) 1123.90i 0.122189i −0.998132 0.0610945i \(-0.980541\pi\)
0.998132 0.0610945i \(-0.0194591\pi\)
\(440\) 3394.80 0.367820
\(441\) 0 0
\(442\) 23018.8 2.47713
\(443\) 8246.58i 0.884440i 0.896907 + 0.442220i \(0.145809\pi\)
−0.896907 + 0.442220i \(0.854191\pi\)
\(444\) 2812.96 6420.40i 0.300670 0.686259i
\(445\) −3151.95 −0.335768
\(446\) −26203.3 −2.78198
\(447\) 9828.35 + 4306.08i 1.03997 + 0.455639i
\(448\) 0 0
\(449\) 11803.3i 1.24060i −0.784364 0.620301i \(-0.787011\pi\)
0.784364 0.620301i \(-0.212989\pi\)
\(450\) −12508.3 + 11534.5i −1.31032 + 1.20832i
\(451\) 7076.75i 0.738871i
\(452\) 9826.29i 1.02254i
\(453\) −1126.57 + 2571.31i −0.116845 + 0.266691i
\(454\) 13114.3i 1.35569i
\(455\) 0 0
\(456\) −6110.18 + 13946.1i −0.627490 + 1.43220i
\(457\) 16386.5 1.67731 0.838653 0.544666i \(-0.183343\pi\)
0.838653 + 0.544666i \(0.183343\pi\)
\(458\) 25391.3 2.59052
\(459\) −11863.0 + 4089.65i −1.20635 + 0.415879i
\(460\) 5108.55i 0.517798i
\(461\) −3268.14 −0.330179 −0.165089 0.986279i \(-0.552791\pi\)
−0.165089 + 0.986279i \(0.552791\pi\)
\(462\) 0 0
\(463\) −12241.9 −1.22879 −0.614395 0.788999i \(-0.710600\pi\)
−0.614395 + 0.788999i \(0.710600\pi\)
\(464\) 8395.35i 0.839966i
\(465\) 1268.90 + 555.942i 0.126546 + 0.0554434i
\(466\) 9508.75 0.945245
\(467\) 10989.3 1.08892 0.544459 0.838788i \(-0.316735\pi\)
0.544459 + 0.838788i \(0.316735\pi\)
\(468\) 19859.2 18313.2i 1.96152 1.80882i
\(469\) 0 0
\(470\) 5476.89i 0.537511i
\(471\) 3134.78 + 1373.44i 0.306673 + 0.134362i
\(472\) 16410.9i 1.60037i
\(473\) 4050.55i 0.393751i
\(474\) −5825.20 2552.19i −0.564474 0.247312i
\(475\) 4953.96i 0.478533i
\(476\) 0 0
\(477\) −11875.5 + 10951.0i −1.13992 + 1.05118i
\(478\) 8210.87 0.785683
\(479\) −14237.8 −1.35812 −0.679062 0.734081i \(-0.737613\pi\)
−0.679062 + 0.734081i \(0.737613\pi\)
\(480\) −7302.51 3199.44i −0.694401 0.304237i
\(481\) 3090.37i 0.292950i
\(482\) −7626.88 −0.720736
\(483\) 0 0
\(484\) −21371.7 −2.00710
\(485\) 4127.87i 0.386468i
\(486\) −9653.36 + 17929.7i −0.900998 + 1.67347i
\(487\) −1229.45 −0.114398 −0.0571988 0.998363i \(-0.518217\pi\)
−0.0571988 + 0.998363i \(0.518217\pi\)
\(488\) 29880.7 2.77180
\(489\) 842.322 1922.54i 0.0778960 0.177792i
\(490\) 0 0
\(491\) 4755.37i 0.437081i −0.975828 0.218540i \(-0.929870\pi\)
0.975828 0.218540i \(-0.0701296\pi\)
\(492\) 17562.0 40084.2i 1.60926 3.67304i
\(493\) 3652.93i 0.333711i
\(494\) 10876.2i 0.990574i
\(495\) 971.800 896.148i 0.0882407 0.0813714i
\(496\) 19655.7i 1.77937i
\(497\) 0 0
\(498\) 29080.5 + 12741.0i 2.61672 + 1.14646i
\(499\) −6041.14 −0.541961 −0.270980 0.962585i \(-0.587348\pi\)
−0.270980 + 0.962585i \(0.587348\pi\)
\(500\) −14114.0 −1.26240
\(501\) 4267.22 9739.65i 0.380530 0.868534i
\(502\) 11573.5i 1.02898i
\(503\) −9730.02 −0.862505 −0.431253 0.902231i \(-0.641928\pi\)
−0.431253 + 0.902231i \(0.641928\pi\)
\(504\) 0 0
\(505\) 3240.04 0.285505
\(506\) 8276.18i 0.727117i
\(507\) −198.222 + 452.429i −0.0173636 + 0.0396313i
\(508\) 48680.1 4.25163
\(509\) 3117.41 0.271467 0.135733 0.990745i \(-0.456661\pi\)
0.135733 + 0.990745i \(0.456661\pi\)
\(510\) −6380.25 2795.37i −0.553965 0.242708i
\(511\) 0 0
\(512\) 904.452i 0.0780694i
\(513\) 1932.33 + 5605.16i 0.166305 + 0.482405i
\(514\) 3575.39i 0.306817i
\(515\) 255.235i 0.0218389i
\(516\) 10052.1 22943.2i 0.857592 1.95740i
\(517\) 6416.61i 0.545845i
\(518\) 0 0
\(519\) 1470.65 3356.66i 0.124382 0.283894i
\(520\) 9255.55 0.780544
\(521\) 6598.64 0.554879 0.277439 0.960743i \(-0.410514\pi\)
0.277439 + 0.960743i \(0.410514\pi\)
\(522\) 4018.68 + 4357.93i 0.336959 + 0.365405i
\(523\) 20339.3i 1.70052i 0.526360 + 0.850262i \(0.323556\pi\)
−0.526360 + 0.850262i \(0.676444\pi\)
\(524\) −12308.5 −1.02615
\(525\) 0 0
\(526\) 27598.3 2.28772
\(527\) 8552.47i 0.706929i
\(528\) −17179.3 7526.77i −1.41598 0.620380i
\(529\) 4480.38 0.368240
\(530\) −8967.49 −0.734949
\(531\) −4332.09 4697.81i −0.354043 0.383931i
\(532\) 0 0
\(533\) 19294.0i 1.56794i
\(534\) 28923.5 + 12672.2i 2.34390 + 1.02693i
\(535\) 4180.35i 0.337818i
\(536\) 29679.2i 2.39169i
\(537\) 3525.99 + 1544.84i 0.283348 + 0.124143i
\(538\) 32121.5i 2.57408i
\(539\) 0 0
\(540\) −7728.41 + 2664.30i −0.615885 + 0.212321i
\(541\) −14425.4 −1.14639 −0.573193 0.819420i \(-0.694295\pi\)
−0.573193 + 0.819420i \(0.694295\pi\)
\(542\) 8045.31 0.637594
\(543\) −6374.22 2792.73i −0.503764 0.220714i
\(544\) 49219.4i 3.87917i
\(545\) −3469.79 −0.272715
\(546\) 0 0
\(547\) −4720.80 −0.369007 −0.184503 0.982832i \(-0.559068\pi\)
−0.184503 + 0.982832i \(0.559068\pi\)
\(548\) 11058.4i 0.862030i
\(549\) 8553.69 7887.81i 0.664960 0.613194i
\(550\) −11065.9 −0.857912
\(551\) 1725.98 0.133447
\(552\) −12676.3 + 28932.9i −0.977429 + 2.23092i
\(553\) 0 0
\(554\) 35023.2i 2.68591i
\(555\) 375.291 856.576i 0.0287031 0.0655128i
\(556\) 21815.9i 1.66403i
\(557\) 5248.72i 0.399273i −0.979870 0.199637i \(-0.936024\pi\)
0.979870 0.199637i \(-0.0639762\pi\)
\(558\) −9408.78 10203.1i −0.713809 0.774069i
\(559\) 11043.4i 0.835572i
\(560\) 0 0
\(561\) −7474.97 3275.00i −0.562555 0.246472i
\(562\) −12022.3 −0.902370
\(563\) 15779.6 1.18122 0.590612 0.806955i \(-0.298886\pi\)
0.590612 + 0.806955i \(0.298886\pi\)
\(564\) −15923.8 + 36345.0i −1.18885 + 2.71348i
\(565\) 1310.97i 0.0976159i
\(566\) 21283.8 1.58061
\(567\) 0 0
\(568\) 36027.2 2.66139
\(569\) 2878.32i 0.212066i −0.994363 0.106033i \(-0.966185\pi\)
0.994363 0.106033i \(-0.0338149\pi\)
\(570\) −1320.79 + 3014.62i −0.0970560 + 0.221524i
\(571\) −8287.48 −0.607391 −0.303696 0.952769i \(-0.598221\pi\)
−0.303696 + 0.952769i \(0.598221\pi\)
\(572\) 17569.2 1.28427
\(573\) −8869.99 3886.20i −0.646683 0.283330i
\(574\) 0 0
\(575\) 10277.6i 0.745402i
\(576\) 24048.1 + 26078.3i 1.73959 + 1.88645i
\(577\) 3726.07i 0.268836i −0.990925 0.134418i \(-0.957083\pi\)
0.990925 0.134418i \(-0.0429165\pi\)
\(578\) 16592.4i 1.19404i
\(579\) 4568.16 10426.5i 0.327886 0.748378i
\(580\) 2379.79i 0.170371i
\(581\) 0 0
\(582\) 16595.9 37878.9i 1.18199 2.69782i
\(583\) −10506.1 −0.746345
\(584\) −53014.6 −3.75644
\(585\) 2649.51 2443.25i 0.187254 0.172677i
\(586\) 19721.0i 1.39022i
\(587\) 10108.9 0.710799 0.355399 0.934715i \(-0.384345\pi\)
0.355399 + 0.934715i \(0.384345\pi\)
\(588\) 0 0
\(589\) −4040.98 −0.282692
\(590\) 3547.43i 0.247534i
\(591\) −5583.92 2446.47i −0.388649 0.170278i
\(592\) −13268.7 −0.921181
\(593\) 7119.62 0.493032 0.246516 0.969139i \(-0.420714\pi\)
0.246516 + 0.969139i \(0.420714\pi\)
\(594\) −12520.5 + 4316.33i −0.864854 + 0.298150i
\(595\) 0 0
\(596\) 43156.1i 2.96601i
\(597\) −23016.4 10084.1i −1.57789 0.691317i
\(598\) 22564.1i 1.54300i
\(599\) 25732.9i 1.75529i −0.479311 0.877645i \(-0.659113\pi\)
0.479311 0.877645i \(-0.340887\pi\)
\(600\) 38685.6 + 16949.3i 2.63222 + 1.15325i
\(601\) 13381.0i 0.908193i −0.890952 0.454097i \(-0.849962\pi\)
0.890952 0.454097i \(-0.150038\pi\)
\(602\) 0 0
\(603\) 7834.61 + 8496.01i 0.529105 + 0.573771i
\(604\) 11290.6 0.760608
\(605\) −2851.29 −0.191606
\(606\) −29731.9 13026.4i −1.99303 0.873203i
\(607\) 1107.28i 0.0740412i 0.999315 + 0.0370206i \(0.0117867\pi\)
−0.999315 + 0.0370206i \(0.988213\pi\)
\(608\) 23255.8 1.55123
\(609\) 0 0
\(610\) 6459.10 0.428724
\(611\) 17494.2i 1.15833i
\(612\) 34212.4 + 37100.6i 2.25973 + 2.45049i
\(613\) −13454.7 −0.886509 −0.443255 0.896396i \(-0.646176\pi\)
−0.443255 + 0.896396i \(0.646176\pi\)
\(614\) −36043.2 −2.36903
\(615\) 2343.03 5347.82i 0.153626 0.350642i
\(616\) 0 0
\(617\) 1025.37i 0.0669043i 0.999440 + 0.0334521i \(0.0106501\pi\)
−0.999440 + 0.0334521i \(0.989350\pi\)
\(618\) −1026.16 + 2342.14i −0.0667931 + 0.152451i
\(619\) 165.513i 0.0107472i −0.999986 0.00537360i \(-0.998290\pi\)
0.999986 0.00537360i \(-0.00171048\pi\)
\(620\) 5571.71i 0.360912i
\(621\) 4008.86 + 11628.6i 0.259050 + 0.751434i
\(622\) 43075.2i 2.77678i
\(623\) 0 0
\(624\) −46837.6 20520.9i −3.00481 1.31650i
\(625\) 12770.3 0.817296
\(626\) 952.751 0.0608300
\(627\) −1547.41 + 3531.87i −0.0985610 + 0.224959i
\(628\) 13764.7i 0.874638i
\(629\) −5773.38 −0.365977
\(630\) 0 0
\(631\) −8462.41 −0.533888 −0.266944 0.963712i \(-0.586014\pi\)
−0.266944 + 0.963712i \(0.586014\pi\)
\(632\) 15786.8i 0.993619i
\(633\) 6109.73 13945.1i 0.383634 0.875618i
\(634\) 32731.3 2.05036
\(635\) 6494.64 0.405877
\(636\) 59508.9 + 26072.6i 3.71019 + 1.62554i
\(637\) 0 0
\(638\) 3855.41i 0.239243i
\(639\) 10313.2 9510.32i 0.638471 0.588768i
\(640\) 7417.65i 0.458138i
\(641\) 25724.2i 1.58510i −0.609810 0.792548i \(-0.708754\pi\)
0.609810 0.792548i \(-0.291246\pi\)
\(642\) −16806.9 + 38360.5i −1.03320 + 2.35821i
\(643\) 13662.8i 0.837961i 0.907995 + 0.418980i \(0.137612\pi\)
−0.907995 + 0.418980i \(0.862388\pi\)
\(644\) 0 0
\(645\) 1341.09 3060.95i 0.0818690 0.186860i
\(646\) 20318.8 1.23751
\(647\) 26101.8 1.58604 0.793021 0.609194i \(-0.208507\pi\)
0.793021 + 0.609194i \(0.208507\pi\)
\(648\) 50382.0 + 4087.68i 3.05431 + 0.247808i
\(649\) 4156.09i 0.251373i
\(650\) −30169.9 −1.82056
\(651\) 0 0
\(652\) −8441.85 −0.507068
\(653\) 22257.9i 1.33387i 0.745114 + 0.666937i \(0.232395\pi\)
−0.745114 + 0.666937i \(0.767605\pi\)
\(654\) 31840.1 + 13950.1i 1.90374 + 0.834085i
\(655\) −1642.14 −0.0979599
\(656\) −82839.7 −4.93041
\(657\) −15176.0 + 13994.6i −0.901176 + 0.831021i
\(658\) 0 0
\(659\) 1866.04i 0.110304i −0.998478 0.0551521i \(-0.982436\pi\)
0.998478 0.0551521i \(-0.0175644\pi\)
\(660\) −4869.75 2133.58i −0.287204 0.125832i
\(661\) 15987.1i 0.940737i 0.882470 + 0.470369i \(0.155879\pi\)
−0.882470 + 0.470369i \(0.844121\pi\)
\(662\) 55844.6i 3.27864i
\(663\) −20379.7 8928.93i −1.19379 0.523033i
\(664\) 78810.9i 4.60611i
\(665\) 0 0
\(666\) −6887.63 + 6351.44i −0.400736 + 0.369539i
\(667\) 3580.77 0.207868
\(668\) −42766.6 −2.47708
\(669\) 23199.1 + 10164.2i 1.34070 + 0.587400i
\(670\) 6415.54i 0.369931i
\(671\) 7567.35 0.435372
\(672\) 0 0
\(673\) 28696.0 1.64361 0.821805 0.569768i \(-0.192967\pi\)
0.821805 + 0.569768i \(0.192967\pi\)
\(674\) 3041.89i 0.173842i
\(675\) 15548.4 5360.16i 0.886604 0.305648i
\(676\) 1986.60 0.113029
\(677\) 3352.98 0.190348 0.0951740 0.995461i \(-0.469659\pi\)
0.0951740 + 0.995461i \(0.469659\pi\)
\(678\) −5270.68 + 12030.0i −0.298554 + 0.681429i
\(679\) 0 0
\(680\) 17291.1i 0.975122i
\(681\) 5086.98 11610.7i 0.286246 0.653338i
\(682\) 9026.53i 0.506809i
\(683\) 12564.9i 0.703925i 0.936014 + 0.351963i \(0.114486\pi\)
−0.936014 + 0.351963i \(0.885514\pi\)
\(684\) 17529.7 16165.1i 0.979922 0.903637i
\(685\) 1475.36i 0.0822926i
\(686\) 0 0
\(687\) −22480.1 9849.20i −1.24843 0.546973i
\(688\) −47415.3 −2.62746
\(689\) −28643.8 −1.58380
\(690\) −2740.15 + 6254.22i −0.151182 + 0.345064i
\(691\) 12429.0i 0.684255i 0.939654 + 0.342127i \(0.111147\pi\)
−0.939654 + 0.342127i \(0.888853\pi\)
\(692\) −14739.0 −0.809673
\(693\) 0 0
\(694\) −54720.1 −2.99301
\(695\) 2910.56i 0.158854i
\(696\) 5905.20 13478.2i 0.321604 0.734039i
\(697\) −36044.7 −1.95881
\(698\) 37224.4 2.01857
\(699\) −8418.57 3688.42i −0.455536 0.199583i
\(700\) 0 0
\(701\) 28195.4i 1.51915i −0.650420 0.759575i \(-0.725407\pi\)
0.650420 0.759575i \(-0.274593\pi\)
\(702\) −34135.8 + 11768.0i −1.83529 + 0.632699i
\(703\) 2727.88i 0.146350i
\(704\) 23071.1i 1.23512i
\(705\) −2124.47 + 4848.96i −0.113492 + 0.259039i
\(706\) 15996.8i 0.852757i
\(707\) 0 0
\(708\) −10314.0 + 23541.0i −0.547491 + 1.24961i
\(709\) −15169.6 −0.803535 −0.401767 0.915742i \(-0.631604\pi\)
−0.401767 + 0.915742i \(0.631604\pi\)
\(710\) 7787.73 0.411646
\(711\) 4167.35 + 4519.16i 0.219814 + 0.238371i
\(712\) 78385.4i 4.12587i
\(713\) −8383.52 −0.440344
\(714\) 0 0
\(715\) 2343.99 0.122602
\(716\) 15482.6i 0.808115i
\(717\) −7269.49 3184.98i −0.378639 0.165893i
\(718\) −14799.6 −0.769243
\(719\) 10512.1 0.545250 0.272625 0.962120i \(-0.412108\pi\)
0.272625 + 0.962120i \(0.412108\pi\)
\(720\) 10490.2 + 11375.8i 0.542982 + 0.588821i
\(721\) 0 0
\(722\) 27271.6i 1.40574i
\(723\) 6752.45 + 2958.44i 0.347339 + 0.152179i
\(724\) 27989.1i 1.43675i
\(725\) 4787.77i 0.245260i
\(726\) 26164.6 + 11463.5i 1.33755 + 0.586018i
\(727\) 14866.0i 0.758390i 0.925317 + 0.379195i \(0.123799\pi\)
−0.925317 + 0.379195i \(0.876201\pi\)
\(728\) 0 0
\(729\) 15501.5 12129.5i 0.787556 0.616243i
\(730\) −11459.8 −0.581021
\(731\) −20631.0 −1.04387
\(732\) −42863.1 18779.5i −2.16430 0.948241i
\(733\) 27332.1i 1.37726i −0.725111 0.688632i \(-0.758211\pi\)
0.725111 0.688632i \(-0.241789\pi\)
\(734\) 68046.2 3.42184
\(735\) 0 0
\(736\) 48247.2 2.41632
\(737\) 7516.31i 0.375667i
\(738\) −43001.2 + 39653.6i −2.14485 + 1.97787i
\(739\) 17041.0 0.848257 0.424128 0.905602i \(-0.360581\pi\)
0.424128 + 0.905602i \(0.360581\pi\)
\(740\) −3761.21 −0.186844
\(741\) −4218.85 + 9629.24i −0.209154 + 0.477381i
\(742\) 0 0
\(743\) 31844.1i 1.57234i 0.618012 + 0.786169i \(0.287938\pi\)
−0.618012 + 0.786169i \(0.712062\pi\)
\(744\) −13825.6 + 31556.1i −0.681280 + 1.55498i
\(745\) 5757.66i 0.283147i
\(746\) 58114.9i 2.85219i
\(747\) −20804.2 22560.5i −1.01899 1.10501i
\(748\) 32822.4i 1.60442i
\(749\) 0 0
\(750\) 17279.3 + 7570.56i 0.841268 + 0.368584i
\(751\) 14506.4 0.704854 0.352427 0.935839i \(-0.385356\pi\)
0.352427 + 0.935839i \(0.385356\pi\)
\(752\) 75112.1 3.64236
\(753\) −4489.31 + 10246.5i −0.217264 + 0.495890i
\(754\) 10511.4i 0.507693i
\(755\) 1506.33 0.0726106
\(756\) 0 0
\(757\) −1811.69 −0.0869843 −0.0434921 0.999054i \(-0.513848\pi\)
−0.0434921 + 0.999054i \(0.513848\pi\)
\(758\) 29509.4i 1.41402i
\(759\) −3210.31 + 7327.31i −0.153527 + 0.350414i
\(760\) 8169.91 0.389939
\(761\) 12464.2 0.593726 0.296863 0.954920i \(-0.404060\pi\)
0.296863 + 0.954920i \(0.404060\pi\)
\(762\) −59597.3 26111.3i −2.83331 1.24136i
\(763\) 0 0
\(764\) 38947.9i 1.84435i
\(765\) 4564.44 + 4949.76i 0.215722 + 0.233933i
\(766\) 67013.4i 3.16096i
\(767\) 11331.1i 0.533433i
\(768\) 7904.91 18042.4i 0.371411 0.847721i
\(769\) 216.728i 0.0101631i 0.999987 + 0.00508155i \(0.00161751\pi\)
−0.999987 + 0.00508155i \(0.998382\pi\)
\(770\) 0 0
\(771\) 1386.88 3165.47i 0.0647827 0.147862i
\(772\) −45782.6 −2.13439
\(773\) 32130.7 1.49503 0.747517 0.664243i \(-0.231246\pi\)
0.747517 + 0.664243i \(0.231246\pi\)
\(774\) −24612.8 + 22696.7i −1.14301 + 1.05403i
\(775\) 11209.4i 0.519554i
\(776\) −102655. −4.74886
\(777\) 0 0
\(778\) −38986.7 −1.79658
\(779\) 17030.8i 0.783303i
\(780\) −13276.8 5816.96i −0.609470 0.267027i
\(781\) 9123.94 0.418029
\(782\) 42153.9 1.92765
\(783\) −1867.50 5417.13i −0.0852352 0.247244i
\(784\) 0 0
\(785\) 1836.42i 0.0834963i
\(786\) 15068.9 + 6602.13i 0.683830 + 0.299606i </