Properties

Label 108.5.d.a.55.5
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.5
Root \(2.91300 + 0.609585i\) of \(x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + 1077384 x^{3} + 2005641 x^{2} + 2990790 x + 2924100\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.a.55.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.59266 - 3.66925i) q^{2} +(-10.9268 + 11.6878i) q^{4} -29.4580 q^{5} +32.9098i q^{7} +(60.2882 + 21.4787i) q^{8} +O(q^{10})\) \(q+(-1.59266 - 3.66925i) q^{2} +(-10.9268 + 11.6878i) q^{4} -29.4580 q^{5} +32.9098i q^{7} +(60.2882 + 21.4787i) q^{8} +(46.9167 + 108.089i) q^{10} -136.639i q^{11} +164.522 q^{13} +(120.754 - 52.4142i) q^{14} +(-17.2082 - 255.421i) q^{16} +380.756 q^{17} +439.574i q^{19} +(321.883 - 344.298i) q^{20} +(-501.364 + 217.620i) q^{22} -171.733i q^{23} +242.773 q^{25} +(-262.028 - 603.673i) q^{26} +(-384.642 - 359.600i) q^{28} +1041.21 q^{29} -1181.17i q^{31} +(-909.798 + 469.941i) q^{32} +(-606.417 - 1397.09i) q^{34} -969.456i q^{35} +2700.79 q^{37} +(1612.91 - 700.094i) q^{38} +(-1775.97 - 632.718i) q^{40} -1556.42 q^{41} +2218.02i q^{43} +(1597.01 + 1493.04i) q^{44} +(-630.130 + 273.512i) q^{46} +1292.12i q^{47} +1317.95 q^{49} +(-386.655 - 890.794i) q^{50} +(-1797.71 + 1922.90i) q^{52} -1015.00 q^{53} +4025.12i q^{55} +(-706.858 + 1984.07i) q^{56} +(-1658.29 - 3820.45i) q^{58} +2434.15i q^{59} +3839.98 q^{61} +(-4334.02 + 1881.21i) q^{62} +(3173.33 + 2589.82i) q^{64} -4846.48 q^{65} +2352.60i q^{67} +(-4160.46 + 4450.19i) q^{68} +(-3557.18 + 1544.02i) q^{70} -884.064i q^{71} +6921.45 q^{73} +(-4301.45 - 9909.89i) q^{74} +(-5137.65 - 4803.16i) q^{76} +4496.77 q^{77} -10308.0i q^{79} +(506.918 + 7524.19i) q^{80} +(2478.85 + 5710.89i) q^{82} +12322.0i q^{83} -11216.3 q^{85} +(8138.47 - 3532.56i) q^{86} +(2934.83 - 8237.73i) q^{88} +5751.10 q^{89} +5414.38i q^{91} +(2007.17 + 1876.49i) q^{92} +(4741.11 - 2057.91i) q^{94} -12949.0i q^{95} -8159.93 q^{97} +(-2099.04 - 4835.88i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 14q^{4} + O(q^{10}) \) \( 16q - 14q^{4} - 202q^{10} - 352q^{13} - 206q^{16} + 738q^{22} + 1632q^{25} + 342q^{28} - 2536q^{34} + 3200q^{37} - 2854q^{40} + 36q^{46} - 896q^{49} + 2288q^{52} + 2492q^{58} - 2752q^{61} + 682q^{64} - 14166q^{70} + 8240q^{73} - 33084q^{76} + 68q^{82} + 8800q^{85} + 48294q^{88} + 52596q^{94} - 6928q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.59266 3.66925i −0.398166 0.917313i
\(3\) 0 0
\(4\) −10.9268 + 11.6878i −0.682928 + 0.730486i
\(5\) −29.4580 −1.17832 −0.589160 0.808017i \(-0.700541\pi\)
−0.589160 + 0.808017i \(0.700541\pi\)
\(6\) 0 0
\(7\) 32.9098i 0.671628i 0.941928 + 0.335814i \(0.109011\pi\)
−0.941928 + 0.335814i \(0.890989\pi\)
\(8\) 60.2882 + 21.4787i 0.942003 + 0.335604i
\(9\) 0 0
\(10\) 46.9167 + 108.089i 0.469167 + 1.08089i
\(11\) 136.639i 1.12925i −0.825348 0.564625i \(-0.809021\pi\)
0.825348 0.564625i \(-0.190979\pi\)
\(12\) 0 0
\(13\) 164.522 0.973503 0.486751 0.873541i \(-0.338182\pi\)
0.486751 + 0.873541i \(0.338182\pi\)
\(14\) 120.754 52.4142i 0.616094 0.267420i
\(15\) 0 0
\(16\) −17.2082 255.421i −0.0672195 0.997738i
\(17\) 380.756 1.31750 0.658748 0.752364i \(-0.271086\pi\)
0.658748 + 0.752364i \(0.271086\pi\)
\(18\) 0 0
\(19\) 439.574i 1.21766i 0.793302 + 0.608829i \(0.208360\pi\)
−0.793302 + 0.608829i \(0.791640\pi\)
\(20\) 321.883 344.298i 0.804707 0.860746i
\(21\) 0 0
\(22\) −501.364 + 217.620i −1.03588 + 0.449629i
\(23\) 171.733i 0.324636i −0.986738 0.162318i \(-0.948103\pi\)
0.986738 0.162318i \(-0.0518971\pi\)
\(24\) 0 0
\(25\) 242.773 0.388436
\(26\) −262.028 603.673i −0.387616 0.893007i
\(27\) 0 0
\(28\) −384.642 359.600i −0.490615 0.458674i
\(29\) 1041.21 1.23806 0.619029 0.785368i \(-0.287526\pi\)
0.619029 + 0.785368i \(0.287526\pi\)
\(30\) 0 0
\(31\) 1181.17i 1.22911i −0.788876 0.614553i \(-0.789336\pi\)
0.788876 0.614553i \(-0.210664\pi\)
\(32\) −909.798 + 469.941i −0.888474 + 0.458927i
\(33\) 0 0
\(34\) −606.417 1397.09i −0.524582 1.20856i
\(35\) 969.456i 0.791393i
\(36\) 0 0
\(37\) 2700.79 1.97282 0.986410 0.164301i \(-0.0525370\pi\)
0.986410 + 0.164301i \(0.0525370\pi\)
\(38\) 1612.91 700.094i 1.11697 0.484830i
\(39\) 0 0
\(40\) −1775.97 632.718i −1.10998 0.395449i
\(41\) −1556.42 −0.925887 −0.462944 0.886388i \(-0.653207\pi\)
−0.462944 + 0.886388i \(0.653207\pi\)
\(42\) 0 0
\(43\) 2218.02i 1.19958i 0.800158 + 0.599789i \(0.204749\pi\)
−0.800158 + 0.599789i \(0.795251\pi\)
\(44\) 1597.01 + 1493.04i 0.824901 + 0.771196i
\(45\) 0 0
\(46\) −630.130 + 273.512i −0.297793 + 0.129259i
\(47\) 1292.12i 0.584934i 0.956276 + 0.292467i \(0.0944761\pi\)
−0.956276 + 0.292467i \(0.905524\pi\)
\(48\) 0 0
\(49\) 1317.95 0.548915
\(50\) −386.655 890.794i −0.154662 0.356318i
\(51\) 0 0
\(52\) −1797.71 + 1922.90i −0.664832 + 0.711130i
\(53\) −1015.00 −0.361337 −0.180669 0.983544i \(-0.557826\pi\)
−0.180669 + 0.983544i \(0.557826\pi\)
\(54\) 0 0
\(55\) 4025.12i 1.33062i
\(56\) −706.858 + 1984.07i −0.225401 + 0.632676i
\(57\) 0 0
\(58\) −1658.29 3820.45i −0.492952 1.13569i
\(59\) 2434.15i 0.699268i 0.936886 + 0.349634i \(0.113694\pi\)
−0.936886 + 0.349634i \(0.886306\pi\)
\(60\) 0 0
\(61\) 3839.98 1.03198 0.515988 0.856596i \(-0.327425\pi\)
0.515988 + 0.856596i \(0.327425\pi\)
\(62\) −4334.02 + 1881.21i −1.12748 + 0.489388i
\(63\) 0 0
\(64\) 3173.33 + 2589.82i 0.774740 + 0.632280i
\(65\) −4846.48 −1.14710
\(66\) 0 0
\(67\) 2352.60i 0.524081i 0.965057 + 0.262040i \(0.0843954\pi\)
−0.965057 + 0.262040i \(0.915605\pi\)
\(68\) −4160.46 + 4450.19i −0.899754 + 0.962412i
\(69\) 0 0
\(70\) −3557.18 + 1544.02i −0.725955 + 0.315106i
\(71\) 884.064i 0.175375i −0.996148 0.0876874i \(-0.972052\pi\)
0.996148 0.0876874i \(-0.0279476\pi\)
\(72\) 0 0
\(73\) 6921.45 1.29883 0.649413 0.760436i \(-0.275014\pi\)
0.649413 + 0.760436i \(0.275014\pi\)
\(74\) −4301.45 9909.89i −0.785510 1.80969i
\(75\) 0 0
\(76\) −5137.65 4803.16i −0.889482 0.831572i
\(77\) 4496.77 0.758436
\(78\) 0 0
\(79\) 10308.0i 1.65165i −0.563924 0.825826i \(-0.690709\pi\)
0.563924 0.825826i \(-0.309291\pi\)
\(80\) 506.918 + 7524.19i 0.0792060 + 1.17565i
\(81\) 0 0
\(82\) 2478.85 + 5710.89i 0.368657 + 0.849329i
\(83\) 12322.0i 1.78865i 0.447417 + 0.894326i \(0.352344\pi\)
−0.447417 + 0.894326i \(0.647656\pi\)
\(84\) 0 0
\(85\) −11216.3 −1.55243
\(86\) 8138.47 3532.56i 1.10039 0.477631i
\(87\) 0 0
\(88\) 2934.83 8237.73i 0.378981 1.06376i
\(89\) 5751.10 0.726057 0.363028 0.931778i \(-0.381743\pi\)
0.363028 + 0.931778i \(0.381743\pi\)
\(90\) 0 0
\(91\) 5414.38i 0.653832i
\(92\) 2007.17 + 1876.49i 0.237142 + 0.221703i
\(93\) 0 0
\(94\) 4741.11 2057.91i 0.536568 0.232901i
\(95\) 12949.0i 1.43479i
\(96\) 0 0
\(97\) −8159.93 −0.867247 −0.433624 0.901094i \(-0.642765\pi\)
−0.433624 + 0.901094i \(0.642765\pi\)
\(98\) −2099.04 4835.88i −0.218559 0.503527i
\(99\) 0 0
\(100\) −2652.74 + 2837.47i −0.265274 + 0.283747i
\(101\) −11440.4 −1.12150 −0.560749 0.827986i \(-0.689487\pi\)
−0.560749 + 0.827986i \(0.689487\pi\)
\(102\) 0 0
\(103\) 11724.0i 1.10510i −0.833479 0.552552i \(-0.813654\pi\)
0.833479 0.552552i \(-0.186346\pi\)
\(104\) 9918.73 + 3533.71i 0.917043 + 0.326711i
\(105\) 0 0
\(106\) 1616.55 + 3724.28i 0.143872 + 0.331460i
\(107\) 21224.4i 1.85382i −0.375286 0.926909i \(-0.622456\pi\)
0.375286 0.926909i \(-0.377544\pi\)
\(108\) 0 0
\(109\) −5752.64 −0.484188 −0.242094 0.970253i \(-0.577834\pi\)
−0.242094 + 0.970253i \(0.577834\pi\)
\(110\) 14769.2 6410.66i 1.22059 0.529806i
\(111\) 0 0
\(112\) 8405.85 566.318i 0.670109 0.0451465i
\(113\) 6018.68 0.471351 0.235675 0.971832i \(-0.424270\pi\)
0.235675 + 0.971832i \(0.424270\pi\)
\(114\) 0 0
\(115\) 5058.90i 0.382525i
\(116\) −11377.1 + 12169.4i −0.845504 + 0.904384i
\(117\) 0 0
\(118\) 8931.52 3876.79i 0.641448 0.278425i
\(119\) 12530.6i 0.884868i
\(120\) 0 0
\(121\) −4029.28 −0.275205
\(122\) −6115.80 14089.9i −0.410898 0.946646i
\(123\) 0 0
\(124\) 13805.3 + 12906.5i 0.897845 + 0.839391i
\(125\) 11259.6 0.720617
\(126\) 0 0
\(127\) 7591.93i 0.470700i −0.971911 0.235350i \(-0.924376\pi\)
0.971911 0.235350i \(-0.0756237\pi\)
\(128\) 4448.65 15768.5i 0.271524 0.962432i
\(129\) 0 0
\(130\) 7718.82 + 17783.0i 0.456735 + 1.05225i
\(131\) 3334.49i 0.194306i 0.995269 + 0.0971532i \(0.0309737\pi\)
−0.995269 + 0.0971532i \(0.969026\pi\)
\(132\) 0 0
\(133\) −14466.3 −0.817813
\(134\) 8632.28 3746.90i 0.480746 0.208671i
\(135\) 0 0
\(136\) 22955.1 + 8178.14i 1.24109 + 0.442157i
\(137\) 11823.7 0.629960 0.314980 0.949098i \(-0.398002\pi\)
0.314980 + 0.949098i \(0.398002\pi\)
\(138\) 0 0
\(139\) 5544.34i 0.286959i −0.989653 0.143480i \(-0.954171\pi\)
0.989653 0.143480i \(-0.0458292\pi\)
\(140\) 11330.8 + 10593.1i 0.578101 + 0.540464i
\(141\) 0 0
\(142\) −3243.85 + 1408.02i −0.160874 + 0.0698282i
\(143\) 22480.2i 1.09933i
\(144\) 0 0
\(145\) −30671.8 −1.45883
\(146\) −11023.5 25396.5i −0.517149 1.19143i
\(147\) 0 0
\(148\) −29511.1 + 31566.2i −1.34729 + 1.44112i
\(149\) 11073.6 0.498790 0.249395 0.968402i \(-0.419768\pi\)
0.249395 + 0.968402i \(0.419768\pi\)
\(150\) 0 0
\(151\) 27450.4i 1.20391i 0.798529 + 0.601956i \(0.205612\pi\)
−0.798529 + 0.601956i \(0.794388\pi\)
\(152\) −9441.47 + 26501.1i −0.408651 + 1.14704i
\(153\) 0 0
\(154\) −7161.84 16499.8i −0.301984 0.695724i
\(155\) 34794.9i 1.44828i
\(156\) 0 0
\(157\) 14606.6 0.592583 0.296291 0.955098i \(-0.404250\pi\)
0.296291 + 0.955098i \(0.404250\pi\)
\(158\) −37822.5 + 16417.1i −1.51508 + 0.657632i
\(159\) 0 0
\(160\) 26800.8 13843.5i 1.04691 0.540762i
\(161\) 5651.68 0.218035
\(162\) 0 0
\(163\) 39065.5i 1.47034i −0.677883 0.735170i \(-0.737102\pi\)
0.677883 0.735170i \(-0.262898\pi\)
\(164\) 17006.7 18191.1i 0.632314 0.676348i
\(165\) 0 0
\(166\) 45212.6 19624.8i 1.64075 0.712180i
\(167\) 3123.15i 0.111985i −0.998431 0.0559926i \(-0.982168\pi\)
0.998431 0.0559926i \(-0.0178323\pi\)
\(168\) 0 0
\(169\) −1493.53 −0.0522925
\(170\) 17863.8 + 41155.5i 0.618125 + 1.42407i
\(171\) 0 0
\(172\) −25923.7 24235.9i −0.876274 0.819225i
\(173\) −50749.6 −1.69567 −0.847834 0.530262i \(-0.822093\pi\)
−0.847834 + 0.530262i \(0.822093\pi\)
\(174\) 0 0
\(175\) 7989.60i 0.260885i
\(176\) −34900.5 + 2351.31i −1.12670 + 0.0759076i
\(177\) 0 0
\(178\) −9159.56 21102.2i −0.289091 0.666022i
\(179\) 4456.66i 0.139092i 0.997579 + 0.0695462i \(0.0221551\pi\)
−0.997579 + 0.0695462i \(0.977845\pi\)
\(180\) 0 0
\(181\) −8462.68 −0.258316 −0.129158 0.991624i \(-0.541227\pi\)
−0.129158 + 0.991624i \(0.541227\pi\)
\(182\) 19866.7 8623.29i 0.599769 0.260334i
\(183\) 0 0
\(184\) 3688.59 10353.4i 0.108949 0.305808i
\(185\) −79559.9 −2.32461
\(186\) 0 0
\(187\) 52026.2i 1.48778i
\(188\) −15102.0 14118.8i −0.427286 0.399467i
\(189\) 0 0
\(190\) −47513.1 + 20623.4i −1.31615 + 0.571284i
\(191\) 17699.2i 0.485163i 0.970131 + 0.242582i \(0.0779942\pi\)
−0.970131 + 0.242582i \(0.922006\pi\)
\(192\) 0 0
\(193\) 10944.5 0.293820 0.146910 0.989150i \(-0.453067\pi\)
0.146910 + 0.989150i \(0.453067\pi\)
\(194\) 12996.0 + 29940.9i 0.345308 + 0.795538i
\(195\) 0 0
\(196\) −14401.0 + 15403.9i −0.374869 + 0.400975i
\(197\) −10101.3 −0.260284 −0.130142 0.991495i \(-0.541543\pi\)
−0.130142 + 0.991495i \(0.541543\pi\)
\(198\) 0 0
\(199\) 31394.8i 0.792777i 0.918083 + 0.396388i \(0.129737\pi\)
−0.918083 + 0.396388i \(0.870263\pi\)
\(200\) 14636.3 + 5214.43i 0.365908 + 0.130361i
\(201\) 0 0
\(202\) 18220.7 + 41977.8i 0.446543 + 1.02877i
\(203\) 34265.9i 0.831515i
\(204\) 0 0
\(205\) 45848.9 1.09099
\(206\) −43018.5 + 18672.5i −1.01373 + 0.440015i
\(207\) 0 0
\(208\) −2831.12 42022.4i −0.0654383 0.971301i
\(209\) 60063.1 1.37504
\(210\) 0 0
\(211\) 83361.8i 1.87241i 0.351448 + 0.936207i \(0.385689\pi\)
−0.351448 + 0.936207i \(0.614311\pi\)
\(212\) 11090.7 11863.1i 0.246767 0.263952i
\(213\) 0 0
\(214\) −77877.6 + 33803.3i −1.70053 + 0.738127i
\(215\) 65338.3i 1.41349i
\(216\) 0 0
\(217\) 38872.1 0.825503
\(218\) 9162.02 + 21107.9i 0.192787 + 0.444152i
\(219\) 0 0
\(220\) −47044.7 43981.8i −0.971997 0.908715i
\(221\) 62642.8 1.28259
\(222\) 0 0
\(223\) 13301.4i 0.267478i 0.991017 + 0.133739i \(0.0426983\pi\)
−0.991017 + 0.133739i \(0.957302\pi\)
\(224\) −15465.7 29941.2i −0.308228 0.596724i
\(225\) 0 0
\(226\) −9585.73 22084.1i −0.187676 0.432377i
\(227\) 50075.5i 0.971792i 0.874017 + 0.485896i \(0.161507\pi\)
−0.874017 + 0.485896i \(0.838493\pi\)
\(228\) 0 0
\(229\) 60039.8 1.14490 0.572451 0.819939i \(-0.305993\pi\)
0.572451 + 0.819939i \(0.305993\pi\)
\(230\) 18562.4 8057.12i 0.350895 0.152308i
\(231\) 0 0
\(232\) 62772.5 + 22363.7i 1.16625 + 0.415497i
\(233\) 31252.0 0.575659 0.287830 0.957682i \(-0.407066\pi\)
0.287830 + 0.957682i \(0.407066\pi\)
\(234\) 0 0
\(235\) 38063.2i 0.689239i
\(236\) −28449.8 26597.6i −0.510805 0.477549i
\(237\) 0 0
\(238\) 45978.0 19957.0i 0.811701 0.352324i
\(239\) 62883.1i 1.10087i −0.834876 0.550437i \(-0.814461\pi\)
0.834876 0.550437i \(-0.185539\pi\)
\(240\) 0 0
\(241\) 64613.0 1.11246 0.556232 0.831027i \(-0.312247\pi\)
0.556232 + 0.831027i \(0.312247\pi\)
\(242\) 6417.29 + 14784.5i 0.109577 + 0.252450i
\(243\) 0 0
\(244\) −41958.9 + 44880.9i −0.704765 + 0.753844i
\(245\) −38824.0 −0.646797
\(246\) 0 0
\(247\) 72319.6i 1.18539i
\(248\) 25370.0 71210.7i 0.412493 1.15782i
\(249\) 0 0
\(250\) −17932.8 41314.5i −0.286925 0.661032i
\(251\) 78853.1i 1.25162i 0.779977 + 0.625808i \(0.215231\pi\)
−0.779977 + 0.625808i \(0.784769\pi\)
\(252\) 0 0
\(253\) −23465.4 −0.366595
\(254\) −27856.7 + 12091.4i −0.431780 + 0.187417i
\(255\) 0 0
\(256\) −64943.8 + 8790.66i −0.990963 + 0.134135i
\(257\) 25571.1 0.387153 0.193576 0.981085i \(-0.437991\pi\)
0.193576 + 0.981085i \(0.437991\pi\)
\(258\) 0 0
\(259\) 88882.5i 1.32500i
\(260\) 52956.8 56644.6i 0.783384 0.837938i
\(261\) 0 0
\(262\) 12235.1 5310.73i 0.178240 0.0773662i
\(263\) 110011.i 1.59046i −0.606305 0.795232i \(-0.707349\pi\)
0.606305 0.795232i \(-0.292651\pi\)
\(264\) 0 0
\(265\) 29899.8 0.425771
\(266\) 23040.0 + 53080.5i 0.325625 + 0.750191i
\(267\) 0 0
\(268\) −27496.6 25706.5i −0.382834 0.357909i
\(269\) 39818.1 0.550270 0.275135 0.961406i \(-0.411277\pi\)
0.275135 + 0.961406i \(0.411277\pi\)
\(270\) 0 0
\(271\) 14054.7i 0.191375i −0.995411 0.0956873i \(-0.969495\pi\)
0.995411 0.0956873i \(-0.0305049\pi\)
\(272\) −6552.12 97253.1i −0.0885614 1.31452i
\(273\) 0 0
\(274\) −18831.2 43384.2i −0.250829 0.577871i
\(275\) 33172.3i 0.438642i
\(276\) 0 0
\(277\) −31583.7 −0.411627 −0.205813 0.978591i \(-0.565984\pi\)
−0.205813 + 0.978591i \(0.565984\pi\)
\(278\) −20343.6 + 8830.27i −0.263232 + 0.114257i
\(279\) 0 0
\(280\) 20822.6 58446.8i 0.265595 0.745494i
\(281\) −66899.3 −0.847244 −0.423622 0.905839i \(-0.639242\pi\)
−0.423622 + 0.905839i \(0.639242\pi\)
\(282\) 0 0
\(283\) 160099.i 1.99901i −0.0314612 0.999505i \(-0.510016\pi\)
0.0314612 0.999505i \(-0.489984\pi\)
\(284\) 10332.7 + 9660.03i 0.128109 + 0.119768i
\(285\) 0 0
\(286\) −82485.4 + 35803.3i −1.00843 + 0.437715i
\(287\) 51221.4i 0.621852i
\(288\) 0 0
\(289\) 61454.3 0.735795
\(290\) 48849.9 + 112543.i 0.580855 + 1.33820i
\(291\) 0 0
\(292\) −75629.6 + 80896.3i −0.887005 + 0.948775i
\(293\) 92671.2 1.07947 0.539734 0.841836i \(-0.318525\pi\)
0.539734 + 0.841836i \(0.318525\pi\)
\(294\) 0 0
\(295\) 71705.2i 0.823961i
\(296\) 162826. + 58009.4i 1.85840 + 0.662087i
\(297\) 0 0
\(298\) −17636.6 40631.9i −0.198601 0.457546i
\(299\) 28253.8i 0.316034i
\(300\) 0 0
\(301\) −72994.5 −0.805670
\(302\) 100722. 43719.3i 1.10436 0.479357i
\(303\) 0 0
\(304\) 112277. 7564.28i 1.21490 0.0818503i
\(305\) −113118. −1.21600
\(306\) 0 0
\(307\) 86852.2i 0.921518i 0.887525 + 0.460759i \(0.152423\pi\)
−0.887525 + 0.460759i \(0.847577\pi\)
\(308\) −49135.5 + 52557.2i −0.517957 + 0.554027i
\(309\) 0 0
\(310\) 127671. 55416.6i 1.32853 0.576656i
\(311\) 43940.9i 0.454306i 0.973859 + 0.227153i \(0.0729417\pi\)
−0.973859 + 0.227153i \(0.927058\pi\)
\(312\) 0 0
\(313\) −100801. −1.02890 −0.514452 0.857519i \(-0.672005\pi\)
−0.514452 + 0.857519i \(0.672005\pi\)
\(314\) −23263.4 53595.2i −0.235946 0.543584i
\(315\) 0 0
\(316\) 120477. + 112634.i 1.20651 + 1.12796i
\(317\) 101986. 1.01490 0.507449 0.861682i \(-0.330589\pi\)
0.507449 + 0.861682i \(0.330589\pi\)
\(318\) 0 0
\(319\) 142270.i 1.39808i
\(320\) −93480.0 76290.9i −0.912891 0.745028i
\(321\) 0 0
\(322\) −9001.23 20737.5i −0.0868141 0.200006i
\(323\) 167371.i 1.60426i
\(324\) 0 0
\(325\) 39941.4 0.378144
\(326\) −143341. + 62218.2i −1.34876 + 0.585439i
\(327\) 0 0
\(328\) −93833.6 33429.8i −0.872189 0.310732i
\(329\) −42523.4 −0.392858
\(330\) 0 0
\(331\) 39677.8i 0.362153i 0.983469 + 0.181076i \(0.0579581\pi\)
−0.983469 + 0.181076i \(0.942042\pi\)
\(332\) −144017. 134641.i −1.30658 1.22152i
\(333\) 0 0
\(334\) −11459.6 + 4974.13i −0.102725 + 0.0445887i
\(335\) 69302.8i 0.617534i
\(336\) 0 0
\(337\) −129324. −1.13873 −0.569364 0.822086i \(-0.692810\pi\)
−0.569364 + 0.822086i \(0.692810\pi\)
\(338\) 2378.68 + 5480.12i 0.0208211 + 0.0479686i
\(339\) 0 0
\(340\) 122559. 131094.i 1.06020 1.13403i
\(341\) −161394. −1.38797
\(342\) 0 0
\(343\) 122390.i 1.04030i
\(344\) −47640.1 + 133720.i −0.402583 + 1.13001i
\(345\) 0 0
\(346\) 80827.1 + 186213.i 0.675157 + 1.55546i
\(347\) 174482.i 1.44908i 0.689233 + 0.724540i \(0.257948\pi\)
−0.689233 + 0.724540i \(0.742052\pi\)
\(348\) 0 0
\(349\) −39421.3 −0.323654 −0.161827 0.986819i \(-0.551739\pi\)
−0.161827 + 0.986819i \(0.551739\pi\)
\(350\) 29315.9 12724.7i 0.239313 0.103875i
\(351\) 0 0
\(352\) 64212.4 + 124314.i 0.518243 + 1.00331i
\(353\) 123080. 0.987733 0.493866 0.869538i \(-0.335583\pi\)
0.493866 + 0.869538i \(0.335583\pi\)
\(354\) 0 0
\(355\) 26042.7i 0.206647i
\(356\) −62841.3 + 67217.5i −0.495844 + 0.530374i
\(357\) 0 0
\(358\) 16352.6 7097.96i 0.127591 0.0553818i
\(359\) 20967.0i 0.162685i 0.996686 + 0.0813424i \(0.0259207\pi\)
−0.996686 + 0.0813424i \(0.974079\pi\)
\(360\) 0 0
\(361\) −62904.6 −0.482690
\(362\) 13478.2 + 31051.7i 0.102852 + 0.236956i
\(363\) 0 0
\(364\) −63282.1 59162.1i −0.477615 0.446520i
\(365\) −203892. −1.53043
\(366\) 0 0
\(367\) 58300.8i 0.432855i −0.976299 0.216427i \(-0.930560\pi\)
0.976299 0.216427i \(-0.0694405\pi\)
\(368\) −43864.1 + 2955.21i −0.323902 + 0.0218219i
\(369\) 0 0
\(370\) 126712. + 291925.i 0.925581 + 2.13240i
\(371\) 33403.3i 0.242684i
\(372\) 0 0
\(373\) −79775.3 −0.573391 −0.286695 0.958022i \(-0.592557\pi\)
−0.286695 + 0.958022i \(0.592557\pi\)
\(374\) −190897. + 82860.3i −1.36476 + 0.592384i
\(375\) 0 0
\(376\) −27753.0 + 77899.5i −0.196306 + 0.551009i
\(377\) 171301. 1.20525
\(378\) 0 0
\(379\) 80878.2i 0.563058i 0.959553 + 0.281529i \(0.0908415\pi\)
−0.959553 + 0.281529i \(0.909159\pi\)
\(380\) 151345. + 141491.i 1.04809 + 0.979857i
\(381\) 0 0
\(382\) 64943.0 28188.9i 0.445047 0.193176i
\(383\) 99819.8i 0.680486i −0.940338 0.340243i \(-0.889491\pi\)
0.940338 0.340243i \(-0.110509\pi\)
\(384\) 0 0
\(385\) −132466. −0.893680
\(386\) −17430.9 40158.1i −0.116989 0.269525i
\(387\) 0 0
\(388\) 89162.3 95371.4i 0.592267 0.633512i
\(389\) −15583.1 −0.102981 −0.0514903 0.998673i \(-0.516397\pi\)
−0.0514903 + 0.998673i \(0.516397\pi\)
\(390\) 0 0
\(391\) 65388.3i 0.427707i
\(392\) 79456.6 + 28307.7i 0.517080 + 0.184218i
\(393\) 0 0
\(394\) 16088.0 + 37064.4i 0.103636 + 0.238762i
\(395\) 303652.i 1.94617i
\(396\) 0 0
\(397\) −67256.6 −0.426730 −0.213365 0.976973i \(-0.568442\pi\)
−0.213365 + 0.976973i \(0.568442\pi\)
\(398\) 115195. 50001.3i 0.727225 0.315657i
\(399\) 0 0
\(400\) −4177.68 62009.2i −0.0261105 0.387558i
\(401\) −151843. −0.944288 −0.472144 0.881521i \(-0.656520\pi\)
−0.472144 + 0.881521i \(0.656520\pi\)
\(402\) 0 0
\(403\) 194329.i 1.19654i
\(404\) 125008. 133713.i 0.765903 0.819239i
\(405\) 0 0
\(406\) 125730. 54574.0i 0.762760 0.331081i
\(407\) 369034.i 2.22781i
\(408\) 0 0
\(409\) −64170.7 −0.383610 −0.191805 0.981433i \(-0.561434\pi\)
−0.191805 + 0.981433i \(0.561434\pi\)
\(410\) −73021.9 168231.i −0.434396 1.00078i
\(411\) 0 0
\(412\) 137028. + 128107.i 0.807262 + 0.754706i
\(413\) −80107.4 −0.469648
\(414\) 0 0
\(415\) 362982.i 2.10760i
\(416\) −149682. + 77315.6i −0.864932 + 0.446766i
\(417\) 0 0
\(418\) −95660.3 220387.i −0.547494 1.26134i
\(419\) 85171.9i 0.485142i 0.970134 + 0.242571i \(0.0779907\pi\)
−0.970134 + 0.242571i \(0.922009\pi\)
\(420\) 0 0
\(421\) 214896. 1.21245 0.606224 0.795294i \(-0.292683\pi\)
0.606224 + 0.795294i \(0.292683\pi\)
\(422\) 305875. 132767.i 1.71759 0.745532i
\(423\) 0 0
\(424\) −61192.3 21800.8i −0.340381 0.121266i
\(425\) 92437.2 0.511763
\(426\) 0 0
\(427\) 126373.i 0.693105i
\(428\) 248066. + 231915.i 1.35419 + 1.26602i
\(429\) 0 0
\(430\) −239743. + 104062.i −1.29661 + 0.562802i
\(431\) 19885.9i 0.107051i −0.998566 0.0535254i \(-0.982954\pi\)
0.998566 0.0535254i \(-0.0170458\pi\)
\(432\) 0 0
\(433\) 103996. 0.554679 0.277339 0.960772i \(-0.410547\pi\)
0.277339 + 0.960772i \(0.410547\pi\)
\(434\) −61910.2 142632.i −0.328687 0.757244i
\(435\) 0 0
\(436\) 62858.2 67235.6i 0.330666 0.353693i
\(437\) 75489.2 0.395296
\(438\) 0 0
\(439\) 55956.4i 0.290349i 0.989406 + 0.145175i \(0.0463744\pi\)
−0.989406 + 0.145175i \(0.953626\pi\)
\(440\) −86454.1 + 242667.i −0.446561 + 1.25345i
\(441\) 0 0
\(442\) −99768.9 229852.i −0.510682 1.17653i
\(443\) 22607.4i 0.115198i −0.998340 0.0575988i \(-0.981656\pi\)
0.998340 0.0575988i \(-0.0183444\pi\)
\(444\) 0 0
\(445\) −169416. −0.855527
\(446\) 48806.2 21184.7i 0.245361 0.106501i
\(447\) 0 0
\(448\) −85230.4 + 104434.i −0.424657 + 0.520337i
\(449\) −77577.5 −0.384807 −0.192404 0.981316i \(-0.561628\pi\)
−0.192404 + 0.981316i \(0.561628\pi\)
\(450\) 0 0
\(451\) 212668.i 1.04556i
\(452\) −65765.2 + 70345.0i −0.321899 + 0.344315i
\(453\) 0 0
\(454\) 183740. 79753.4i 0.891438 0.386934i
\(455\) 159497.i 0.770423i
\(456\) 0 0
\(457\) −242860. −1.16285 −0.581425 0.813600i \(-0.697505\pi\)
−0.581425 + 0.813600i \(0.697505\pi\)
\(458\) −95623.2 220301.i −0.455861 1.05023i
\(459\) 0 0
\(460\) −59127.2 55277.8i −0.279429 0.261237i
\(461\) 199640. 0.939391 0.469696 0.882828i \(-0.344364\pi\)
0.469696 + 0.882828i \(0.344364\pi\)
\(462\) 0 0
\(463\) 63490.8i 0.296175i 0.988974 + 0.148088i \(0.0473118\pi\)
−0.988974 + 0.148088i \(0.952688\pi\)
\(464\) −17917.3 265946.i −0.0832216 1.23526i
\(465\) 0 0
\(466\) −49773.9 114671.i −0.229208 0.528060i
\(467\) 112982.i 0.518053i −0.965870 0.259026i \(-0.916598\pi\)
0.965870 0.259026i \(-0.0834017\pi\)
\(468\) 0 0
\(469\) −77423.5 −0.351987
\(470\) −139664. + 60621.9i −0.632248 + 0.274431i
\(471\) 0 0
\(472\) −52282.3 + 146751.i −0.234677 + 0.658713i
\(473\) 303068. 1.35462
\(474\) 0 0
\(475\) 106717.i 0.472982i
\(476\) −146455. 136920.i −0.646383 0.604301i
\(477\) 0 0
\(478\) −230734. + 100152.i −1.00985 + 0.438331i
\(479\) 313437.i 1.36609i −0.730376 0.683045i \(-0.760655\pi\)
0.730376 0.683045i \(-0.239345\pi\)
\(480\) 0 0
\(481\) 444339. 1.92055
\(482\) −102907. 237081.i −0.442945 1.02048i
\(483\) 0 0
\(484\) 44027.3 47093.4i 0.187945 0.201034i
\(485\) 240375. 1.02189
\(486\) 0 0
\(487\) 64950.6i 0.273858i −0.990581 0.136929i \(-0.956277\pi\)
0.990581 0.136929i \(-0.0437232\pi\)
\(488\) 231506. + 82477.7i 0.972125 + 0.346336i
\(489\) 0 0
\(490\) 61833.6 + 142455.i 0.257533 + 0.593316i
\(491\) 358585.i 1.48741i 0.668510 + 0.743703i \(0.266932\pi\)
−0.668510 + 0.743703i \(0.733068\pi\)
\(492\) 0 0
\(493\) 396446. 1.63114
\(494\) 265359. 115181.i 1.08738 0.471983i
\(495\) 0 0
\(496\) −301696. + 20325.8i −1.22633 + 0.0826198i
\(497\) 29094.4 0.117787
\(498\) 0 0
\(499\) 12696.3i 0.0509890i −0.999675 0.0254945i \(-0.991884\pi\)
0.999675 0.0254945i \(-0.00811603\pi\)
\(500\) −123032. + 131600.i −0.492130 + 0.526401i
\(501\) 0 0
\(502\) 289332. 125586.i 1.14812 0.498351i
\(503\) 114739.i 0.453498i 0.973953 + 0.226749i \(0.0728097\pi\)
−0.973953 + 0.226749i \(0.927190\pi\)
\(504\) 0 0
\(505\) 337011. 1.32148
\(506\) 37372.5 + 86100.5i 0.145966 + 0.336283i
\(507\) 0 0
\(508\) 88732.8 + 82955.8i 0.343840 + 0.321454i
\(509\) 44847.2 0.173101 0.0865505 0.996247i \(-0.472416\pi\)
0.0865505 + 0.996247i \(0.472416\pi\)
\(510\) 0 0
\(511\) 227783.i 0.872329i
\(512\) 135689. + 224295.i 0.517611 + 0.855616i
\(513\) 0 0
\(514\) −40726.1 93826.7i −0.154151 0.355141i
\(515\) 345367.i 1.30216i
\(516\) 0 0
\(517\) 176554. 0.660536
\(518\) 326132. 141560.i 1.21544 0.527571i
\(519\) 0 0
\(520\) −292186. 104096.i −1.08057 0.384970i
\(521\) −285591. −1.05213 −0.526065 0.850444i \(-0.676333\pi\)
−0.526065 + 0.850444i \(0.676333\pi\)
\(522\) 0 0
\(523\) 164178.i 0.600220i −0.953905 0.300110i \(-0.902977\pi\)
0.953905 0.300110i \(-0.0970234\pi\)
\(524\) −38972.8 36435.5i −0.141938 0.132697i
\(525\) 0 0
\(526\) −403658. + 175210.i −1.45895 + 0.633269i
\(527\) 449738.i 1.61934i
\(528\) 0 0
\(529\) 250349. 0.894611
\(530\) −47620.3 109710.i −0.169527 0.390565i
\(531\) 0 0
\(532\) 158071. 169079.i 0.558507 0.597401i
\(533\) −256065. −0.901354
\(534\) 0 0
\(535\) 625227.i 2.18439i
\(536\) −50530.7 + 141834.i −0.175884 + 0.493686i
\(537\) 0 0
\(538\) −63416.9 146103.i −0.219099 0.504770i
\(539\) 180083.i 0.619863i
\(540\) 0 0
\(541\) −300448. −1.02654 −0.513269 0.858228i \(-0.671566\pi\)
−0.513269 + 0.858228i \(0.671566\pi\)
\(542\) −51570.4 + 22384.5i −0.175551 + 0.0761989i
\(543\) 0 0
\(544\) −346411. + 178933.i −1.17056 + 0.604634i
\(545\) 169461. 0.570528
\(546\) 0 0
\(547\) 74251.6i 0.248160i −0.992272 0.124080i \(-0.960402\pi\)
0.992272 0.124080i \(-0.0395979\pi\)
\(548\) −129196. + 138193.i −0.430217 + 0.460177i
\(549\) 0 0
\(550\) −121717. + 52832.3i −0.402372 + 0.174652i
\(551\) 457688.i 1.50753i
\(552\) 0 0
\(553\) 339233. 1.10930
\(554\) 50302.2 + 115889.i 0.163896 + 0.377591i
\(555\) 0 0
\(556\) 64801.0 + 60582.1i 0.209620 + 0.195972i
\(557\) −193413. −0.623411 −0.311705 0.950179i \(-0.600900\pi\)
−0.311705 + 0.950179i \(0.600900\pi\)
\(558\) 0 0
\(559\) 364913.i 1.16779i
\(560\) −247619. + 16682.6i −0.789603 + 0.0531970i
\(561\) 0 0
\(562\) 106548. + 245470.i 0.337344 + 0.777188i
\(563\) 177354.i 0.559530i −0.960068 0.279765i \(-0.909743\pi\)
0.960068 0.279765i \(-0.0902566\pi\)
\(564\) 0 0
\(565\) −177298. −0.555402
\(566\) −587443. + 254983.i −1.83372 + 0.795938i
\(567\) 0 0
\(568\) 18988.5 53298.6i 0.0588565 0.165204i
\(569\) −590091. −1.82261 −0.911306 0.411730i \(-0.864925\pi\)
−0.911306 + 0.411730i \(0.864925\pi\)
\(570\) 0 0
\(571\) 524012.i 1.60720i −0.595172 0.803598i \(-0.702916\pi\)
0.595172 0.803598i \(-0.297084\pi\)
\(572\) 262743. + 245637.i 0.803044 + 0.750761i
\(573\) 0 0
\(574\) −187944. + 81578.4i −0.570433 + 0.247600i
\(575\) 41692.0i 0.126100i
\(576\) 0 0
\(577\) −337273. −1.01305 −0.506523 0.862226i \(-0.669070\pi\)
−0.506523 + 0.862226i \(0.669070\pi\)
\(578\) −97876.1 225492.i −0.292969 0.674955i
\(579\) 0 0
\(580\) 335146. 358486.i 0.996273 1.06565i
\(581\) −405515. −1.20131
\(582\) 0 0
\(583\) 138688.i 0.408040i
\(584\) 417282. + 148663.i 1.22350 + 0.435892i
\(585\) 0 0
\(586\) −147594. 340034.i −0.429807 0.990210i
\(587\) 4289.71i 0.0124495i 0.999981 + 0.00622475i \(0.00198141\pi\)
−0.999981 + 0.00622475i \(0.998019\pi\)
\(588\) 0 0
\(589\) 519212. 1.49663
\(590\) −263105. + 114202.i −0.755830 + 0.328073i
\(591\) 0 0
\(592\) −46475.7 689839.i −0.132612 1.96836i
\(593\) −150227. −0.427207 −0.213604 0.976920i \(-0.568520\pi\)
−0.213604 + 0.976920i \(0.568520\pi\)
\(594\) 0 0
\(595\) 369126.i 1.04266i
\(596\) −121000. + 129426.i −0.340637 + 0.364359i
\(597\) 0 0
\(598\) −103670. + 44998.8i −0.289902 + 0.125834i
\(599\) 473108.i 1.31858i 0.751888 + 0.659290i \(0.229143\pi\)
−0.751888 + 0.659290i \(0.770857\pi\)
\(600\) 0 0
\(601\) −83320.1 −0.230675 −0.115338 0.993326i \(-0.536795\pi\)
−0.115338 + 0.993326i \(0.536795\pi\)
\(602\) 116256. + 267835.i 0.320790 + 0.739052i
\(603\) 0 0
\(604\) −320834. 299946.i −0.879441 0.822185i
\(605\) 118695. 0.324280
\(606\) 0 0
\(607\) 143905.i 0.390570i −0.980747 0.195285i \(-0.937437\pi\)
0.980747 0.195285i \(-0.0625632\pi\)
\(608\) −206574. 399924.i −0.558816 1.08186i
\(609\) 0 0
\(610\) 180159. + 415059.i 0.484169 + 1.11545i
\(611\) 212582.i 0.569435i
\(612\) 0 0
\(613\) −5563.04 −0.0148044 −0.00740221 0.999973i \(-0.502356\pi\)
−0.00740221 + 0.999973i \(0.502356\pi\)
\(614\) 318683. 138326.i 0.845321 0.366917i
\(615\) 0 0
\(616\) 271102. + 96584.6i 0.714449 + 0.254534i
\(617\) 300749. 0.790012 0.395006 0.918679i \(-0.370743\pi\)
0.395006 + 0.918679i \(0.370743\pi\)
\(618\) 0 0
\(619\) 158539.i 0.413767i 0.978366 + 0.206883i \(0.0663321\pi\)
−0.978366 + 0.206883i \(0.933668\pi\)
\(620\) −406675. 380199.i −1.05795 0.989070i
\(621\) 0 0
\(622\) 161230. 69983.1i 0.416741 0.180889i
\(623\) 189267.i 0.487640i
\(624\) 0 0
\(625\) −483419. −1.23755
\(626\) 160542. + 369863.i 0.409675 + 0.943828i
\(627\) 0 0
\(628\) −159604. + 170718.i −0.404691 + 0.432873i
\(629\) 1.02834e6 2.59918
\(630\) 0 0
\(631\) 557374.i 1.39987i −0.714206 0.699936i \(-0.753212\pi\)
0.714206 0.699936i \(-0.246788\pi\)
\(632\) 221401. 621449.i 0.554301 1.55586i
\(633\) 0 0
\(634\) −162429. 374213.i −0.404098 0.930979i
\(635\) 223643.i 0.554635i
\(636\) 0 0
\(637\) 216831. 0.534370
\(638\) −522023. + 226588.i −1.28247 + 0.556667i
\(639\) 0 0
\(640\) −131048. + 464508.i −0.319942 + 1.13405i
\(641\) −101106. −0.246071 −0.123036 0.992402i \(-0.539263\pi\)
−0.123036 + 0.992402i \(0.539263\pi\)
\(642\) 0 0
\(643\) 406950.i 0.984281i 0.870516 + 0.492141i \(0.163785\pi\)
−0.870516 + 0.492141i \(0.836215\pi\)
\(644\) −61755.1 + 66055.6i −0.148902 + 0.159271i
\(645\) 0 0
\(646\) 614126. 266565.i 1.47161 0.638761i
\(647\) 427706.i 1.02173i −0.859660 0.510866i \(-0.829325\pi\)
0.859660 0.510866i \(-0.170675\pi\)
\(648\) 0 0
\(649\) 332601. 0.789648
\(650\) −63613.3 146555.i −0.150564 0.346876i
\(651\) 0 0
\(652\) 456588. + 426862.i 1.07406 + 1.00414i
\(653\) −430055. −1.00855 −0.504275 0.863543i \(-0.668240\pi\)
−0.504275 + 0.863543i \(0.668240\pi\)
\(654\) 0 0
\(655\) 98227.4i 0.228955i
\(656\) 26783.1 + 397542.i 0.0622377 + 0.923793i
\(657\) 0 0
\(658\) 67725.4 + 156029.i 0.156423 + 0.360374i
\(659\) 179686.i 0.413755i 0.978367 + 0.206878i \(0.0663302\pi\)
−0.978367 + 0.206878i \(0.933670\pi\)
\(660\) 0 0
\(661\) −539348. −1.23443 −0.617214 0.786795i \(-0.711739\pi\)
−0.617214 + 0.786795i \(0.711739\pi\)
\(662\) 145588. 63193.4i 0.332208 0.144197i
\(663\) 0 0
\(664\) −264660. + 742872.i −0.600279 + 1.68492i
\(665\) 426148. 0.963645
\(666\) 0 0
\(667\) 178809.i 0.401918i
\(668\) 36502.7 + 34126.2i 0.0818036 + 0.0764777i
\(669\) 0 0
\(670\) −254290. + 110376.i −0.566473 + 0.245881i
\(671\) 524693.i 1.16536i
\(672\) 0 0
\(673\) −758520. −1.67470 −0.837350 0.546667i \(-0.815896\pi\)
−0.837350 + 0.546667i \(0.815896\pi\)
\(674\) 205970. + 474523.i 0.453403 + 1.04457i
\(675\) 0 0
\(676\) 16319.5 17456.0i 0.0357120 0.0381989i
\(677\) 394155. 0.859982 0.429991 0.902833i \(-0.358517\pi\)
0.429991 + 0.902833i \(0.358517\pi\)
\(678\) 0 0
\(679\) 268542.i 0.582468i
\(680\) −676211. 240911.i −1.46239 0.521002i
\(681\) 0 0
\(682\) 257047. + 592197.i 0.552642 + 1.27320i
\(683\) 483705.i 1.03691i −0.855106 0.518453i \(-0.826508\pi\)
0.855106 0.518453i \(-0.173492\pi\)
\(684\) 0 0
\(685\) −348303. −0.742294
\(686\) 449079. 194926.i 0.954277 0.414210i
\(687\) 0 0
\(688\) 566528. 38168.1i 1.19686 0.0806349i
\(689\) −166989. −0.351763
\(690\) 0 0
\(691\) 136607.i 0.286098i −0.989716 0.143049i \(-0.954309\pi\)
0.989716 0.143049i \(-0.0456907\pi\)
\(692\) 554533. 593150.i 1.15802 1.23866i
\(693\) 0 0
\(694\) 640219. 277891.i 1.32926 0.576974i
\(695\) 163325.i 0.338130i
\(696\) 0 0
\(697\) −592615. −1.21985
\(698\) 62784.9 + 144647.i 0.128868 + 0.296892i
\(699\) 0 0
\(700\) −93380.6 87301.1i −0.190573 0.178165i
\(701\) −878847. −1.78845 −0.894226 0.447617i \(-0.852273\pi\)
−0.894226 + 0.447617i \(0.852273\pi\)
\(702\) 0 0
\(703\) 1.18720e6i 2.40222i
\(704\) 353871. 433602.i 0.714002 0.874875i
\(705\) 0 0
\(706\) −196026. 451613.i −0.393282 0.906061i
\(707\) 376502.i 0.753231i
\(708\) 0 0
\(709\) 445304. 0.885857 0.442929 0.896557i \(-0.353939\pi\)
0.442929 + 0.896557i \(0.353939\pi\)
\(710\) 95557.4 41477.3i 0.189560 0.0822800i
\(711\) 0 0
\(712\) 346723. + 123526.i 0.683948 + 0.243668i
\(713\) −202846. −0.399012
\(714\) 0 0
\(715\) 662220.i 1.29536i
\(716\) −52088.4 48697.2i −0.101605 0.0949900i
\(717\) 0 0
\(718\) 76933.2 33393.4i 0.149233 0.0647756i
\(719\) 731078.i 1.41418i −0.707121 0.707092i \(-0.750007\pi\)
0.707121 0.707092i \(-0.249993\pi\)
\(720\) 0 0
\(721\) 385836. 0.742219
\(722\) 100186. + 230813.i 0.192191 + 0.442778i
\(723\) 0 0
\(724\) 92470.3 98909.8i 0.176411 0.188696i
\(725\) 252776. 0.480906
\(726\) 0 0
\(727\) 992100.i 1.87710i −0.345147 0.938549i \(-0.612171\pi\)
0.345147 0.938549i \(-0.387829\pi\)
\(728\) −116294. + 326423.i −0.219429 + 0.615912i
\(729\) 0 0
\(730\) 324731. + 748131.i 0.609366 + 1.40389i
\(731\) 844524.i 1.58044i
\(732\) 0 0
\(733\) −121286. −0.225737 −0.112868 0.993610i \(-0.536004\pi\)
−0.112868 + 0.993610i \(0.536004\pi\)
\(734\) −213920. + 92853.6i −0.397064 + 0.172348i
\(735\) 0 0
\(736\) 80704.2 + 156242.i 0.148984 + 0.288431i
\(737\) 321457. 0.591818
\(738\) 0 0
\(739\) 273800.i 0.501355i −0.968071 0.250677i \(-0.919347\pi\)
0.968071 0.250677i \(-0.0806534\pi\)
\(740\) 869338. 929878.i 1.58754 1.69810i
\(741\) 0 0
\(742\) −122565. + 53200.3i −0.222618 + 0.0966287i
\(743\) 389402.i 0.705376i 0.935741 + 0.352688i \(0.114732\pi\)
−0.935741 + 0.352688i \(0.885268\pi\)
\(744\) 0 0
\(745\) −326207. −0.587733
\(746\) 127055. + 292716.i 0.228305 + 0.525979i
\(747\) 0 0
\(748\) 608071. + 568483.i 1.08680 + 1.01605i
\(749\) 698489. 1.24508
\(750\) 0 0
\(751\) 430569.i 0.763419i −0.924282 0.381710i \(-0.875335\pi\)
0.924282 0.381710i \(-0.124665\pi\)
\(752\) 330034. 22235.0i 0.583611 0.0393189i
\(753\) 0 0
\(754\) −272825. 628548.i −0.479891 1.10559i
\(755\) 808633.i 1.41859i
\(756\) 0 0
\(757\) −1.04226e6 −1.81880 −0.909401 0.415920i \(-0.863460\pi\)
−0.909401 + 0.415920i \(0.863460\pi\)
\(758\) 296762. 128812.i 0.516500 0.224190i
\(759\) 0 0
\(760\) 278127. 780670.i 0.481521 1.35158i
\(761\) 117139. 0.202271 0.101135 0.994873i \(-0.467752\pi\)
0.101135 + 0.994873i \(0.467752\pi\)
\(762\) 0 0
\(763\) 189318.i 0.325195i
\(764\) −206865. 193397.i −0.354405 0.331331i
\(765\) 0 0
\(766\) −366264. + 158979.i −0.624219 + 0.270946i
\(767\) 400471.i 0.680739i
\(768\) 0 0
\(769\) −104458. −0.176639 −0.0883197 0.996092i \(-0.528150\pi\)
−0.0883197 + 0.996092i \(0.528150\pi\)
\(770\) 210973. + 486050.i 0.355833 + 0.819785i
\(771\) 0 0
\(772\) −119589. + 127917.i −0.200658 + 0.214631i
\(773\) −34677.2 −0.0580343 −0.0290172 0.999579i \(-0.509238\pi\)
−0.0290172 + 0.999579i \(0.509238\pi\)
\(774\) 0 0
\(775\) 286756.i 0.477429i
\(776\) −491948. 175264.i −0.816950 0.291052i
\(777\) 0 0
\(778\) 24818.7 + 57178.4i 0.0410034 + 0.0944654i
\(779\) 684161.i 1.12741i
\(780\) 0 0
\(781\) −120798. −0.198042
\(782\) −239926. + 104142.i −0.392341 + 0.170298i
\(783\) 0 0
\(784\) −22679.4 336631.i −0.0368978 0.547674i
\(785\) −430280. −0.698252
\(786\) 0 0
\(787\) 1.08172e6i 1.74649i −0.487285 0.873243i \(-0.662013\pi\)
0.487285 0.873243i \(-0.337987\pi\)