Properties

Label 147.6.c.c.146.1
Level $147$
Weight $6$
Character 147.146
Analytic conductor $23.576$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + 7244325760 x^{4} - 29387167488 x^{2} + 90230547456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{8}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 146.1
Root \(8.95007 + 5.16733i\) of defining polynomial
Character \(\chi\) \(=\) 147.146
Dual form 147.6.c.c.146.15

$q$-expansion

\(f(q)\) \(=\) \(q-10.3347i q^{2} +(-12.5210 - 9.28579i) q^{3} -74.8050 q^{4} -31.7408 q^{5} +(-95.9654 + 129.400i) q^{6} +442.375i q^{8} +(70.5484 + 232.534i) q^{9} +O(q^{10})\) \(q-10.3347i q^{2} +(-12.5210 - 9.28579i) q^{3} -74.8050 q^{4} -31.7408 q^{5} +(-95.9654 + 129.400i) q^{6} +442.375i q^{8} +(70.5484 + 232.534i) q^{9} +328.031i q^{10} -453.489i q^{11} +(936.630 + 694.623i) q^{12} +551.786i q^{13} +(397.426 + 294.739i) q^{15} +2178.03 q^{16} -538.161 q^{17} +(2403.15 - 729.093i) q^{18} +1366.77i q^{19} +2374.38 q^{20} -4686.65 q^{22} -3237.97i q^{23} +(4107.80 - 5538.96i) q^{24} -2117.52 q^{25} +5702.52 q^{26} +(1275.93 - 3566.64i) q^{27} -1604.88i q^{29} +(3046.02 - 4107.25i) q^{30} +7069.92i q^{31} -8353.19i q^{32} +(-4211.00 + 5678.11i) q^{33} +5561.71i q^{34} +(-5277.37 - 17394.7i) q^{36} -1951.06 q^{37} +14125.1 q^{38} +(5123.77 - 6908.89i) q^{39} -14041.4i q^{40} -1800.47 q^{41} +7882.36 q^{43} +33923.2i q^{44} +(-2239.27 - 7380.82i) q^{45} -33463.3 q^{46} +6090.22 q^{47} +(-27271.0 - 20224.7i) q^{48} +21883.8i q^{50} +(6738.29 + 4997.25i) q^{51} -41276.4i q^{52} +14177.9i q^{53} +(-36860.0 - 13186.2i) q^{54} +14394.1i q^{55} +(12691.6 - 17113.3i) q^{57} -16585.9 q^{58} -16918.9 q^{59} +(-29729.4 - 22047.9i) q^{60} -29718.9i q^{61} +73065.1 q^{62} -16630.3 q^{64} -17514.2i q^{65} +(58681.3 + 43519.2i) q^{66} +13614.3 q^{67} +40257.1 q^{68} +(-30067.1 + 40542.4i) q^{69} -31338.5i q^{71} +(-102867. + 31208.8i) q^{72} -9821.33i q^{73} +20163.6i q^{74} +(26513.3 + 19662.8i) q^{75} -102242. i q^{76} +(-71401.0 - 52952.4i) q^{78} +99798.2 q^{79} -69132.6 q^{80} +(-49094.8 + 32809.8i) q^{81} +18607.2i q^{82} +79557.4 q^{83} +17081.7 q^{85} -81461.4i q^{86} +(-14902.6 + 20094.6i) q^{87} +200612. q^{88} -953.735 q^{89} +(-76278.2 + 23142.0i) q^{90} +242216. i q^{92} +(65649.7 - 88522.1i) q^{93} -62940.3i q^{94} -43382.6i q^{95} +(-77566.0 + 104590. i) q^{96} +115552. i q^{97} +(105451. - 31992.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 172 q^{4} + 1212 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 172 q^{4} + 1212 q^{9} + 1188 q^{15} + 5716 q^{16} + 876 q^{18} - 21900 q^{22} + 13156 q^{25} - 900 q^{30} - 15132 q^{36} + 20932 q^{37} + 34836 q^{39} + 111052 q^{43} - 163392 q^{46} - 63192 q^{51} - 31368 q^{57} + 83412 q^{58} - 120132 q^{60} - 158884 q^{64} + 204404 q^{67} - 661728 q^{72} - 277512 q^{78} + 502616 q^{79} - 358524 q^{81} + 205152 q^{85} + 719028 q^{88} - 35352 q^{93} + 215472 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.3347i 1.82693i −0.406922 0.913463i \(-0.633398\pi\)
0.406922 0.913463i \(-0.366602\pi\)
\(3\) −12.5210 9.28579i −0.803219 0.595683i
\(4\) −74.8050 −2.33766
\(5\) −31.7408 −0.567798 −0.283899 0.958854i \(-0.591628\pi\)
−0.283899 + 0.958854i \(0.591628\pi\)
\(6\) −95.9654 + 129.400i −1.08827 + 1.46742i
\(7\) 0 0
\(8\) 442.375i 2.44380i
\(9\) 70.5484 + 232.534i 0.290323 + 0.956929i
\(10\) 328.031i 1.03732i
\(11\) 453.489i 1.13002i −0.825085 0.565008i \(-0.808873\pi\)
0.825085 0.565008i \(-0.191127\pi\)
\(12\) 936.630 + 694.623i 1.87765 + 1.39250i
\(13\) 551.786i 0.905550i 0.891625 + 0.452775i \(0.149566\pi\)
−0.891625 + 0.452775i \(0.850434\pi\)
\(14\) 0 0
\(15\) 397.426 + 294.739i 0.456066 + 0.338228i
\(16\) 2178.03 2.12698
\(17\) −538.161 −0.451637 −0.225819 0.974169i \(-0.572506\pi\)
−0.225819 + 0.974169i \(0.572506\pi\)
\(18\) 2403.15 729.093i 1.74824 0.530398i
\(19\) 1366.77i 0.868586i 0.900772 + 0.434293i \(0.143002\pi\)
−0.900772 + 0.434293i \(0.856998\pi\)
\(20\) 2374.38 1.32732
\(21\) 0 0
\(22\) −4686.65 −2.06446
\(23\) 3237.97i 1.27630i −0.769912 0.638150i \(-0.779700\pi\)
0.769912 0.638150i \(-0.220300\pi\)
\(24\) 4107.80 5538.96i 1.45573 1.96291i
\(25\) −2117.52 −0.677606
\(26\) 5702.52 1.65437
\(27\) 1275.93 3566.64i 0.336834 0.941564i
\(28\) 0 0
\(29\) 1604.88i 0.354363i −0.984178 0.177181i \(-0.943302\pi\)
0.984178 0.177181i \(-0.0566979\pi\)
\(30\) 3046.02 4107.25i 0.617917 0.833199i
\(31\) 7069.92i 1.32133i 0.750683 + 0.660663i \(0.229725\pi\)
−0.750683 + 0.660663i \(0.770275\pi\)
\(32\) 8353.19i 1.44204i
\(33\) −4211.00 + 5678.11i −0.673132 + 0.907651i
\(34\) 5561.71i 0.825108i
\(35\) 0 0
\(36\) −5277.37 17394.7i −0.678675 2.23697i
\(37\) −1951.06 −0.234297 −0.117149 0.993114i \(-0.537375\pi\)
−0.117149 + 0.993114i \(0.537375\pi\)
\(38\) 14125.1 1.58684
\(39\) 5123.77 6908.89i 0.539421 0.727355i
\(40\) 14041.4i 1.38758i
\(41\) −1800.47 −0.167273 −0.0836365 0.996496i \(-0.526653\pi\)
−0.0836365 + 0.996496i \(0.526653\pi\)
\(42\) 0 0
\(43\) 7882.36 0.650107 0.325054 0.945696i \(-0.394618\pi\)
0.325054 + 0.945696i \(0.394618\pi\)
\(44\) 33923.2i 2.64159i
\(45\) −2239.27 7380.82i −0.164844 0.543342i
\(46\) −33463.3 −2.33170
\(47\) 6090.22 0.402150 0.201075 0.979576i \(-0.435556\pi\)
0.201075 + 0.979576i \(0.435556\pi\)
\(48\) −27271.0 20224.7i −1.70843 1.26701i
\(49\) 0 0
\(50\) 21883.8i 1.23794i
\(51\) 6738.29 + 4997.25i 0.362764 + 0.269033i
\(52\) 41276.4i 2.11687i
\(53\) 14177.9i 0.693302i 0.937994 + 0.346651i \(0.112681\pi\)
−0.937994 + 0.346651i \(0.887319\pi\)
\(54\) −36860.0 13186.2i −1.72017 0.615370i
\(55\) 14394.1i 0.641621i
\(56\) 0 0
\(57\) 12691.6 17113.3i 0.517402 0.697665i
\(58\) −16585.9 −0.647394
\(59\) −16918.9 −0.632764 −0.316382 0.948632i \(-0.602468\pi\)
−0.316382 + 0.948632i \(0.602468\pi\)
\(60\) −29729.4 22047.9i −1.06613 0.790660i
\(61\) 29718.9i 1.02261i −0.859401 0.511303i \(-0.829163\pi\)
0.859401 0.511303i \(-0.170837\pi\)
\(62\) 73065.1 2.41396
\(63\) 0 0
\(64\) −16630.3 −0.507518
\(65\) 17514.2i 0.514169i
\(66\) 58681.3 + 43519.2i 1.65821 + 1.22976i
\(67\) 13614.3 0.370516 0.185258 0.982690i \(-0.440688\pi\)
0.185258 + 0.982690i \(0.440688\pi\)
\(68\) 40257.1 1.05577
\(69\) −30067.1 + 40542.4i −0.760271 + 1.02515i
\(70\) 0 0
\(71\) 31338.5i 0.737790i −0.929471 0.368895i \(-0.879736\pi\)
0.929471 0.368895i \(-0.120264\pi\)
\(72\) −102867. + 31208.8i −2.33854 + 0.709490i
\(73\) 9821.33i 0.215707i −0.994167 0.107853i \(-0.965602\pi\)
0.994167 0.107853i \(-0.0343977\pi\)
\(74\) 20163.6i 0.428044i
\(75\) 26513.3 + 19662.8i 0.544266 + 0.403639i
\(76\) 102242.i 2.03046i
\(77\) 0 0
\(78\) −71401.0 52952.4i −1.32882 0.985482i
\(79\) 99798.2 1.79910 0.899550 0.436818i \(-0.143895\pi\)
0.899550 + 0.436818i \(0.143895\pi\)
\(80\) −69132.6 −1.20770
\(81\) −49094.8 + 32809.8i −0.831426 + 0.555636i
\(82\) 18607.2i 0.305595i
\(83\) 79557.4 1.26761 0.633804 0.773493i \(-0.281492\pi\)
0.633804 + 0.773493i \(0.281492\pi\)
\(84\) 0 0
\(85\) 17081.7 0.256439
\(86\) 81461.4i 1.18770i
\(87\) −14902.6 + 20094.6i −0.211088 + 0.284631i
\(88\) 200612. 2.76154
\(89\) −953.735 −0.0127630 −0.00638150 0.999980i \(-0.502031\pi\)
−0.00638150 + 0.999980i \(0.502031\pi\)
\(90\) −76278.2 + 23142.0i −0.992645 + 0.301159i
\(91\) 0 0
\(92\) 242216.i 2.98355i
\(93\) 65649.7 88522.1i 0.787092 1.06131i
\(94\) 62940.3i 0.734699i
\(95\) 43382.6i 0.493181i
\(96\) −77566.0 + 104590.i −0.859000 + 1.15828i
\(97\) 115552.i 1.24695i 0.781842 + 0.623476i \(0.214280\pi\)
−0.781842 + 0.623476i \(0.785720\pi\)
\(98\) 0 0
\(99\) 105451. 31992.9i 1.08135 0.328069i
\(100\) 158401. 1.58401
\(101\) 89983.4 0.877726 0.438863 0.898554i \(-0.355381\pi\)
0.438863 + 0.898554i \(0.355381\pi\)
\(102\) 51644.8 69637.9i 0.491503 0.662743i
\(103\) 156663.i 1.45503i 0.686089 + 0.727517i \(0.259326\pi\)
−0.686089 + 0.727517i \(0.740674\pi\)
\(104\) −244096. −2.21298
\(105\) 0 0
\(106\) 146524. 1.26661
\(107\) 139107.i 1.17460i 0.809370 + 0.587299i \(0.199809\pi\)
−0.809370 + 0.587299i \(0.800191\pi\)
\(108\) −95445.6 + 266803.i −0.787402 + 2.20105i
\(109\) 24226.4 0.195309 0.0976547 0.995220i \(-0.468866\pi\)
0.0976547 + 0.995220i \(0.468866\pi\)
\(110\) 148758. 1.17219
\(111\) 24429.2 + 18117.2i 0.188192 + 0.139567i
\(112\) 0 0
\(113\) 38230.9i 0.281655i −0.990034 0.140828i \(-0.955024\pi\)
0.990034 0.140828i \(-0.0449763\pi\)
\(114\) −176860. 131163.i −1.27458 0.945255i
\(115\) 102776.i 0.724680i
\(116\) 120053.i 0.828378i
\(117\) −128309. + 38927.6i −0.866547 + 0.262902i
\(118\) 174851.i 1.15601i
\(119\) 0 0
\(120\) −130385. + 175811.i −0.826561 + 1.11453i
\(121\) −44601.2 −0.276938
\(122\) −307135. −1.86822
\(123\) 22543.6 + 16718.8i 0.134357 + 0.0996417i
\(124\) 528865.i 3.08881i
\(125\) 166402. 0.952541
\(126\) 0 0
\(127\) −65650.6 −0.361184 −0.180592 0.983558i \(-0.557801\pi\)
−0.180592 + 0.983558i \(0.557801\pi\)
\(128\) 95433.4i 0.514844i
\(129\) −98694.6 73193.9i −0.522179 0.387258i
\(130\) −181003. −0.939349
\(131\) −205595. −1.04673 −0.523364 0.852109i \(-0.675323\pi\)
−0.523364 + 0.852109i \(0.675323\pi\)
\(132\) 315004. 424751.i 1.57355 2.12178i
\(133\) 0 0
\(134\) 140699.i 0.676905i
\(135\) −40498.9 + 113208.i −0.191253 + 0.534618i
\(136\) 238069.i 1.10371i
\(137\) 410472.i 1.86845i 0.356683 + 0.934225i \(0.383908\pi\)
−0.356683 + 0.934225i \(0.616092\pi\)
\(138\) 418992. + 310733.i 1.87287 + 1.38896i
\(139\) 73875.8i 0.324314i −0.986765 0.162157i \(-0.948155\pi\)
0.986765 0.162157i \(-0.0518450\pi\)
\(140\) 0 0
\(141\) −76255.4 56552.5i −0.323015 0.239554i
\(142\) −323873. −1.34789
\(143\) 250229. 1.02329
\(144\) 153657. + 506466.i 0.617511 + 2.03537i
\(145\) 50940.3i 0.201206i
\(146\) −101500. −0.394080
\(147\) 0 0
\(148\) 145949. 0.547707
\(149\) 57972.3i 0.213922i −0.994263 0.106961i \(-0.965888\pi\)
0.994263 0.106961i \(-0.0341119\pi\)
\(150\) 203208. 274006.i 0.737418 0.994334i
\(151\) −172435. −0.615435 −0.307718 0.951478i \(-0.599565\pi\)
−0.307718 + 0.951478i \(0.599565\pi\)
\(152\) −604627. −2.12265
\(153\) −37966.4 125141.i −0.131121 0.432185i
\(154\) 0 0
\(155\) 224405.i 0.750246i
\(156\) −383284. + 516820.i −1.26098 + 1.70031i
\(157\) 239287.i 0.774764i 0.921919 + 0.387382i \(0.126620\pi\)
−0.921919 + 0.387382i \(0.873380\pi\)
\(158\) 1.03138e6i 3.28682i
\(159\) 131653. 177521.i 0.412989 0.556874i
\(160\) 265137.i 0.818787i
\(161\) 0 0
\(162\) 339077. + 507378.i 1.01511 + 1.51895i
\(163\) 148378. 0.437422 0.218711 0.975790i \(-0.429815\pi\)
0.218711 + 0.975790i \(0.429815\pi\)
\(164\) 134684. 0.391027
\(165\) 133661. 180228.i 0.382203 0.515362i
\(166\) 822198.i 2.31583i
\(167\) −549931. −1.52587 −0.762934 0.646476i \(-0.776242\pi\)
−0.762934 + 0.646476i \(0.776242\pi\)
\(168\) 0 0
\(169\) 66825.0 0.179979
\(170\) 176533.i 0.468494i
\(171\) −317821. + 96423.7i −0.831175 + 0.252170i
\(172\) −589640. −1.51973
\(173\) −316273. −0.803428 −0.401714 0.915765i \(-0.631585\pi\)
−0.401714 + 0.915765i \(0.631585\pi\)
\(174\) 207671. + 154013.i 0.520000 + 0.385642i
\(175\) 0 0
\(176\) 987713.i 2.40353i
\(177\) 211840. + 157105.i 0.508248 + 0.376927i
\(178\) 9856.52i 0.0233170i
\(179\) 563606.i 1.31475i 0.753564 + 0.657374i \(0.228333\pi\)
−0.753564 + 0.657374i \(0.771667\pi\)
\(180\) 167508. + 552122.i 0.385350 + 1.27015i
\(181\) 329274.i 0.747069i 0.927616 + 0.373535i \(0.121854\pi\)
−0.927616 + 0.373535i \(0.878146\pi\)
\(182\) 0 0
\(183\) −275963. + 372109.i −0.609149 + 0.821377i
\(184\) 1.43240e6 3.11902
\(185\) 61928.4 0.133033
\(186\) −914845. 678467.i −1.93894 1.43796i
\(187\) 244050.i 0.510358i
\(188\) −455579. −0.940090
\(189\) 0 0
\(190\) −448344. −0.901004
\(191\) 805475.i 1.59760i 0.601595 + 0.798801i \(0.294532\pi\)
−0.601595 + 0.798801i \(0.705468\pi\)
\(192\) 208228. + 154426.i 0.407648 + 0.302320i
\(193\) 635701. 1.22846 0.614228 0.789128i \(-0.289467\pi\)
0.614228 + 0.789128i \(0.289467\pi\)
\(194\) 1.19419e6 2.27809
\(195\) −162633. + 219294.i −0.306282 + 0.412991i
\(196\) 0 0
\(197\) 137701.i 0.252796i 0.991980 + 0.126398i \(0.0403417\pi\)
−0.991980 + 0.126398i \(0.959658\pi\)
\(198\) −330636. 1.08980e6i −0.599358 1.97554i
\(199\) 895559.i 1.60310i −0.597926 0.801552i \(-0.704008\pi\)
0.597926 0.801552i \(-0.295992\pi\)
\(200\) 936737.i 1.65593i
\(201\) −170463. 126419.i −0.297606 0.220710i
\(202\) 929947.i 1.60354i
\(203\) 0 0
\(204\) −504058. 373819.i −0.848018 0.628907i
\(205\) 57148.4 0.0949772
\(206\) 1.61906e6 2.65824
\(207\) 752936. 228433.i 1.22133 0.370539i
\(208\) 1.20181e6i 1.92609i
\(209\) 619817. 0.981516
\(210\) 0 0
\(211\) −392533. −0.606974 −0.303487 0.952836i \(-0.598151\pi\)
−0.303487 + 0.952836i \(0.598151\pi\)
\(212\) 1.06058e6i 1.62070i
\(213\) −291003. + 392388.i −0.439489 + 0.592607i
\(214\) 1.43762e6 2.14590
\(215\) −250193. −0.369129
\(216\) 1.57779e6 + 564437.i 2.30099 + 0.823155i
\(217\) 0 0
\(218\) 250372.i 0.356816i
\(219\) −91198.8 + 122972.i −0.128493 + 0.173260i
\(220\) 1.07675e6i 1.49989i
\(221\) 296950.i 0.408980i
\(222\) 187235. 252467.i 0.254979 0.343813i
\(223\) 1.01457e6i 1.36622i −0.730317 0.683109i \(-0.760628\pi\)
0.730317 0.683109i \(-0.239372\pi\)
\(224\) 0 0
\(225\) −149388. 492394.i −0.196724 0.648421i
\(226\) −395103. −0.514563
\(227\) 313370. 0.403639 0.201820 0.979423i \(-0.435315\pi\)
0.201820 + 0.979423i \(0.435315\pi\)
\(228\) −949393. + 1.28016e6i −1.20951 + 1.63090i
\(229\) 450743.i 0.567990i 0.958826 + 0.283995i \(0.0916599\pi\)
−0.958826 + 0.283995i \(0.908340\pi\)
\(230\) 1.06215e6 1.32394
\(231\) 0 0
\(232\) 709960. 0.865992
\(233\) 134459.i 0.162255i 0.996704 + 0.0811276i \(0.0258521\pi\)
−0.996704 + 0.0811276i \(0.974148\pi\)
\(234\) 402303. + 1.32603e6i 0.480302 + 1.58312i
\(235\) −193309. −0.228340
\(236\) 1.26562e6 1.47918
\(237\) −1.24957e6 926705.i −1.44507 1.07169i
\(238\) 0 0
\(239\) 1.26368e6i 1.43101i 0.698605 + 0.715507i \(0.253804\pi\)
−0.698605 + 0.715507i \(0.746196\pi\)
\(240\) 865605. + 641950.i 0.970045 + 0.719405i
\(241\) 486586.i 0.539656i −0.962909 0.269828i \(-0.913033\pi\)
0.962909 0.269828i \(-0.0869668\pi\)
\(242\) 460938.i 0.505945i
\(243\) 919379. + 45074.9i 0.998800 + 0.0489687i
\(244\) 2.22312e6i 2.39050i
\(245\) 0 0
\(246\) 172783. 232980.i 0.182038 0.245460i
\(247\) −754167. −0.786548
\(248\) −3.12755e6 −3.22906
\(249\) −996134. 738753.i −1.01817 0.755093i
\(250\) 1.71971e6i 1.74022i
\(251\) −453648. −0.454501 −0.227250 0.973836i \(-0.572974\pi\)
−0.227250 + 0.973836i \(0.572974\pi\)
\(252\) 0 0
\(253\) −1.46838e6 −1.44224
\(254\) 678476.i 0.659857i
\(255\) −213879. 158617.i −0.205976 0.152756i
\(256\) −1.51844e6 −1.44810
\(257\) −1.98345e6 −1.87322 −0.936610 0.350373i \(-0.886055\pi\)
−0.936610 + 0.350373i \(0.886055\pi\)
\(258\) −756433. + 1.01997e6i −0.707492 + 0.953982i
\(259\) 0 0
\(260\) 1.31015e6i 1.20195i
\(261\) 373189. 113222.i 0.339100 0.102879i
\(262\) 2.12475e6i 1.91229i
\(263\) 782254.i 0.697363i 0.937241 + 0.348681i \(0.113370\pi\)
−0.937241 + 0.348681i \(0.886630\pi\)
\(264\) −2.51186e6 1.86284e6i −2.21812 1.64500i
\(265\) 450019.i 0.393655i
\(266\) 0 0
\(267\) 11941.7 + 8856.17i 0.0102515 + 0.00760270i
\(268\) −1.01841e6 −0.866139
\(269\) −1.68301e6 −1.41809 −0.709047 0.705161i \(-0.750875\pi\)
−0.709047 + 0.705161i \(0.750875\pi\)
\(270\) 1.16997e6 + 418543.i 0.976707 + 0.349406i
\(271\) 813635.i 0.672986i 0.941686 + 0.336493i \(0.109241\pi\)
−0.941686 + 0.336493i \(0.890759\pi\)
\(272\) −1.17213e6 −0.960625
\(273\) 0 0
\(274\) 4.24208e6 3.41352
\(275\) 960271.i 0.765706i
\(276\) 2.24917e6 3.03278e6i 1.77725 2.39645i
\(277\) 375524. 0.294062 0.147031 0.989132i \(-0.453028\pi\)
0.147031 + 0.989132i \(0.453028\pi\)
\(278\) −763481. −0.592497
\(279\) −1.64399e6 + 498771.i −1.26441 + 0.383611i
\(280\) 0 0
\(281\) 264282.i 0.199665i −0.995004 0.0998326i \(-0.968169\pi\)
0.995004 0.0998326i \(-0.0318307\pi\)
\(282\) −584450. + 788073.i −0.437648 + 0.590124i
\(283\) 1.84525e6i 1.36959i 0.728738 + 0.684793i \(0.240107\pi\)
−0.728738 + 0.684793i \(0.759893\pi\)
\(284\) 2.34428e6i 1.72470i
\(285\) −402841. + 543191.i −0.293780 + 0.396132i
\(286\) 2.58603e6i 1.86947i
\(287\) 0 0
\(288\) 1.94240e6 589304.i 1.37993 0.418657i
\(289\) −1.13024e6 −0.796024
\(290\) 526450. 0.367589
\(291\) 1.07300e6 1.44683e6i 0.742789 1.00158i
\(292\) 734685.i 0.504248i
\(293\) 1.96922e6 1.34006 0.670032 0.742332i \(-0.266280\pi\)
0.670032 + 0.742332i \(0.266280\pi\)
\(294\) 0 0
\(295\) 537020. 0.359282
\(296\) 863102.i 0.572576i
\(297\) −1.61743e6 578618.i −1.06398 0.380628i
\(298\) −599123. −0.390819
\(299\) 1.78667e6 1.15575
\(300\) −1.98333e6 1.47088e6i −1.27231 0.943569i
\(301\) 0 0
\(302\) 1.78205e6i 1.12435i
\(303\) −1.12668e6 835566.i −0.705006 0.522847i
\(304\) 2.97688e6i 1.84747i
\(305\) 943303.i 0.580633i
\(306\) −1.29328e6 + 392369.i −0.789570 + 0.239547i
\(307\) 2.38073e6i 1.44166i 0.693110 + 0.720832i \(0.256240\pi\)
−0.693110 + 0.720832i \(0.743760\pi\)
\(308\) 0 0
\(309\) 1.45474e6 1.96157e6i 0.866740 1.16871i
\(310\) −2.31915e6 −1.37064
\(311\) 3.37378e6 1.97795 0.988976 0.148078i \(-0.0473088\pi\)
0.988976 + 0.148078i \(0.0473088\pi\)
\(312\) 3.05632e6 + 2.26663e6i 1.77751 + 1.31824i
\(313\) 2.68664e6i 1.55006i −0.631923 0.775031i \(-0.717734\pi\)
0.631923 0.775031i \(-0.282266\pi\)
\(314\) 2.47294e6 1.41544
\(315\) 0 0
\(316\) −7.46541e6 −4.20568
\(317\) 690592.i 0.385988i −0.981200 0.192994i \(-0.938180\pi\)
0.981200 0.192994i \(-0.0618197\pi\)
\(318\) −1.83462e6 1.36059e6i −1.01737 0.754500i
\(319\) −727796. −0.400436
\(320\) 527861. 0.288167
\(321\) 1.29172e6 1.74175e6i 0.699689 0.943460i
\(322\) 0 0
\(323\) 735544.i 0.392286i
\(324\) 3.67254e6 2.45433e6i 1.94359 1.29889i
\(325\) 1.16842e6i 0.613606i
\(326\) 1.53344e6i 0.799138i
\(327\) −303338. 224961.i −0.156876 0.116343i
\(328\) 796482.i 0.408782i
\(329\) 0 0
\(330\) −1.86259e6 1.38134e6i −0.941528 0.698256i
\(331\) 3.23377e6 1.62233 0.811164 0.584819i \(-0.198834\pi\)
0.811164 + 0.584819i \(0.198834\pi\)
\(332\) −5.95129e6 −2.96323
\(333\) −137644. 453688.i −0.0680218 0.224206i
\(334\) 5.68335e6i 2.78765i
\(335\) −432128. −0.210378
\(336\) 0 0
\(337\) −751164. −0.360296 −0.180148 0.983639i \(-0.557658\pi\)
−0.180148 + 0.983639i \(0.557658\pi\)
\(338\) 690613.i 0.328808i
\(339\) −355003. + 478687.i −0.167777 + 0.226231i
\(340\) −1.27780e6 −0.599466
\(341\) 3.20613e6 1.49312
\(342\) 996505. + 3.28457e6i 0.460696 + 1.51849i
\(343\) 0 0
\(344\) 3.48696e6i 1.58873i
\(345\) 954354. 1.28685e6i 0.431680 0.582077i
\(346\) 3.26857e6i 1.46780i
\(347\) 2.12687e6i 0.948236i 0.880461 + 0.474118i \(0.157233\pi\)
−0.880461 + 0.474118i \(0.842767\pi\)
\(348\) 1.11479e6 1.50318e6i 0.493451 0.665370i
\(349\) 1.87399e6i 0.823575i 0.911280 + 0.411787i \(0.135095\pi\)
−0.911280 + 0.411787i \(0.864905\pi\)
\(350\) 0 0
\(351\) 1.96802e6 + 704038.i 0.852633 + 0.305020i
\(352\) −3.78808e6 −1.62953
\(353\) 3.19891e6 1.36636 0.683180 0.730250i \(-0.260597\pi\)
0.683180 + 0.730250i \(0.260597\pi\)
\(354\) 1.62363e6 2.18930e6i 0.688617 0.928531i
\(355\) 994711.i 0.418915i
\(356\) 71344.1 0.0298355
\(357\) 0 0
\(358\) 5.82467e6 2.40195
\(359\) 246921.i 0.101117i −0.998721 0.0505583i \(-0.983900\pi\)
0.998721 0.0505583i \(-0.0161001\pi\)
\(360\) 3.26509e6 990595.i 1.32782 0.402847i
\(361\) 608029. 0.245559
\(362\) 3.40293e6 1.36484
\(363\) 558449. + 414157.i 0.222442 + 0.164967i
\(364\) 0 0
\(365\) 311737.i 0.122478i
\(366\) 3.84562e6 + 2.85199e6i 1.50059 + 1.11287i
\(367\) 454308.i 0.176070i 0.996117 + 0.0880349i \(0.0280587\pi\)
−0.996117 + 0.0880349i \(0.971941\pi\)
\(368\) 7.05239e6i 2.71467i
\(369\) −127020. 418670.i −0.0485631 0.160068i
\(370\) 640009.i 0.243042i
\(371\) 0 0
\(372\) −4.91093e6 + 6.62189e6i −1.83995 + 2.48099i
\(373\) 2.35605e6 0.876825 0.438412 0.898774i \(-0.355541\pi\)
0.438412 + 0.898774i \(0.355541\pi\)
\(374\) 2.52217e6 0.932386
\(375\) −2.08351e6 1.54517e6i −0.765099 0.567413i
\(376\) 2.69416e6i 0.982775i
\(377\) 885551. 0.320893
\(378\) 0 0
\(379\) 1.39242e6 0.497935 0.248968 0.968512i \(-0.419909\pi\)
0.248968 + 0.968512i \(0.419909\pi\)
\(380\) 3.24523e6i 1.15289i
\(381\) 822007. + 609617.i 0.290110 + 0.215152i
\(382\) 8.32431e6 2.91870
\(383\) −4.55786e6 −1.58768 −0.793841 0.608125i \(-0.791922\pi\)
−0.793841 + 0.608125i \(0.791922\pi\)
\(384\) −886174. + 1.19492e6i −0.306684 + 0.413532i
\(385\) 0 0
\(386\) 6.56975e6i 2.24430i
\(387\) 556088. + 1.83291e6i 0.188741 + 0.622106i
\(388\) 8.64391e6i 2.91495i
\(389\) 1.66786e6i 0.558839i 0.960169 + 0.279420i \(0.0901420\pi\)
−0.960169 + 0.279420i \(0.909858\pi\)
\(390\) 2.26633e6 + 1.68075e6i 0.754503 + 0.559554i
\(391\) 1.74255e6i 0.576425i
\(392\) 0 0
\(393\) 2.57424e6 + 1.90911e6i 0.840752 + 0.623518i
\(394\) 1.42309e6 0.461840
\(395\) −3.16768e6 −1.02152
\(396\) −7.88830e6 + 2.39323e6i −2.52782 + 0.766914i
\(397\) 1.72340e6i 0.548793i 0.961617 + 0.274397i \(0.0884781\pi\)
−0.961617 + 0.274397i \(0.911522\pi\)
\(398\) −9.25529e6 −2.92875
\(399\) 0 0
\(400\) −4.61202e6 −1.44126
\(401\) 5.66032e6i 1.75784i −0.476966 0.878922i \(-0.658263\pi\)
0.476966 0.878922i \(-0.341737\pi\)
\(402\) −1.30650e6 + 1.76168e6i −0.403221 + 0.543703i
\(403\) −3.90108e6 −1.19653
\(404\) −6.73121e6 −2.05182
\(405\) 1.55831e6 1.04141e6i 0.472081 0.315489i
\(406\) 0 0
\(407\) 884786.i 0.264760i
\(408\) −2.21066e6 + 2.98085e6i −0.657463 + 0.886522i
\(409\) 2.24354e6i 0.663170i −0.943425 0.331585i \(-0.892417\pi\)
0.943425 0.331585i \(-0.107583\pi\)
\(410\) 590609.i 0.173516i
\(411\) 3.81155e6 5.13949e6i 1.11301 1.50078i
\(412\) 1.17192e7i 3.40137i
\(413\) 0 0
\(414\) −2.36078e6 7.78133e6i −0.676947 2.23128i
\(415\) −2.52522e6 −0.719745
\(416\) 4.60918e6 1.30584
\(417\) −685995. + 924995.i −0.193188 + 0.260495i
\(418\) 6.40559e6i 1.79316i
\(419\) 6.62738e6 1.84419 0.922097 0.386959i \(-0.126474\pi\)
0.922097 + 0.386959i \(0.126474\pi\)
\(420\) 0 0
\(421\) −633684. −0.174248 −0.0871240 0.996197i \(-0.527768\pi\)
−0.0871240 + 0.996197i \(0.527768\pi\)
\(422\) 4.05669e6i 1.10890i
\(423\) 429655. + 1.41618e6i 0.116753 + 0.384829i
\(424\) −6.27196e6 −1.69429
\(425\) 1.13957e6 0.306032
\(426\) 4.05519e6 + 3.00741e6i 1.08265 + 0.802914i
\(427\) 0 0
\(428\) 1.04059e7i 2.74581i
\(429\) −3.13310e6 2.32357e6i −0.821924 0.609555i
\(430\) 2.58565e6i 0.674372i
\(431\) 3.73993e6i 0.969772i −0.874577 0.484886i \(-0.838861\pi\)
0.874577 0.484886i \(-0.161139\pi\)
\(432\) 2.77901e6 7.76825e6i 0.716440 2.00269i
\(433\) 3.36951e6i 0.863668i 0.901953 + 0.431834i \(0.142133\pi\)
−0.901953 + 0.431834i \(0.857867\pi\)
\(434\) 0 0
\(435\) 473021. 637821.i 0.119855 0.161613i
\(436\) −1.81226e6 −0.456566
\(437\) 4.42557e6 1.10858
\(438\) 1.27088e6 + 942508.i 0.316533 + 0.234747i
\(439\) 1.28182e6i 0.317443i 0.987323 + 0.158722i \(0.0507372\pi\)
−0.987323 + 0.158722i \(0.949263\pi\)
\(440\) −6.36760e6 −1.56799
\(441\) 0 0
\(442\) −3.06887e6 −0.747177
\(443\) 4.24150e6i 1.02686i 0.858132 + 0.513428i \(0.171625\pi\)
−0.858132 + 0.513428i \(0.828375\pi\)
\(444\) −1.82743e6 1.35525e6i −0.439929 0.326260i
\(445\) 30272.3 0.00724680
\(446\) −1.04852e7 −2.49598
\(447\) −538318. + 725868.i −0.127430 + 0.171826i
\(448\) 0 0
\(449\) 5.30045e6i 1.24079i −0.784291 0.620393i \(-0.786973\pi\)
0.784291 0.620393i \(-0.213027\pi\)
\(450\) −5.08873e6 + 1.54387e6i −1.18462 + 0.359401i
\(451\) 816492.i 0.189021i
\(452\) 2.85986e6i 0.658413i
\(453\) 2.15905e6 + 1.60119e6i 0.494330 + 0.366605i
\(454\) 3.23857e6i 0.737419i
\(455\) 0 0
\(456\) 7.57050e6 + 5.61443e6i 1.70495 + 1.26443i
\(457\) −7.00723e6 −1.56948 −0.784741 0.619824i \(-0.787204\pi\)
−0.784741 + 0.619824i \(0.787204\pi\)
\(458\) 4.65827e6 1.03768
\(459\) −686653. + 1.91943e6i −0.152127 + 0.425246i
\(460\) 7.68815e6i 1.69405i
\(461\) −640032. −0.140265 −0.0701325 0.997538i \(-0.522342\pi\)
−0.0701325 + 0.997538i \(0.522342\pi\)
\(462\) 0 0
\(463\) 3.47378e6 0.753096 0.376548 0.926397i \(-0.377111\pi\)
0.376548 + 0.926397i \(0.377111\pi\)
\(464\) 3.49548e6i 0.753724i
\(465\) −2.08378e6 + 2.80977e6i −0.446909 + 0.602612i
\(466\) 1.38958e6 0.296428
\(467\) 1.23565e6 0.262182 0.131091 0.991370i \(-0.458152\pi\)
0.131091 + 0.991370i \(0.458152\pi\)
\(468\) 9.59815e6 2.91198e6i 2.02569 0.614574i
\(469\) 0 0
\(470\) 1.99778e6i 0.417160i
\(471\) 2.22196e6 2.99610e6i 0.461514 0.622305i
\(472\) 7.48449e6i 1.54635i
\(473\) 3.57456e6i 0.734632i
\(474\) −9.57717e6 + 1.29139e7i −1.95790 + 2.64004i
\(475\) 2.89417e6i 0.588559i
\(476\) 0 0
\(477\) −3.29684e6 + 1.00023e6i −0.663441 + 0.201281i
\(478\) 1.30597e7 2.61436
\(479\) −1.56481e6 −0.311618 −0.155809 0.987787i \(-0.549799\pi\)
−0.155809 + 0.987787i \(0.549799\pi\)
\(480\) 2.46201e6 3.31977e6i 0.487738 0.657666i
\(481\) 1.07657e6i 0.212168i
\(482\) −5.02870e6 −0.985911
\(483\) 0 0
\(484\) 3.33639e6 0.647387
\(485\) 3.66773e6i 0.708017i
\(486\) 465833. 9.50146e6i 0.0894623 1.82473i
\(487\) −2.89980e6 −0.554045 −0.277023 0.960863i \(-0.589348\pi\)
−0.277023 + 0.960863i \(0.589348\pi\)
\(488\) 1.31469e7 2.49904
\(489\) −1.85784e6 1.37781e6i −0.351346 0.260565i
\(490\) 0 0
\(491\) 4.46273e6i 0.835405i 0.908584 + 0.417702i \(0.137165\pi\)
−0.908584 + 0.417702i \(0.862835\pi\)
\(492\) −1.68637e6 1.25065e6i −0.314080 0.232928i
\(493\) 863685.i 0.160043i
\(494\) 7.79405e6i 1.43696i
\(495\) −3.34712e6 + 1.01548e6i −0.613985 + 0.186277i
\(496\) 1.53985e7i 2.81044i
\(497\) 0 0
\(498\) −7.63475e6 + 1.02947e7i −1.37950 + 1.86012i
\(499\) 2.66828e6 0.479711 0.239855 0.970809i \(-0.422900\pi\)
0.239855 + 0.970809i \(0.422900\pi\)
\(500\) −1.24477e7 −2.22671
\(501\) 6.88566e6 + 5.10654e6i 1.22561 + 0.908935i
\(502\) 4.68830e6i 0.830339i
\(503\) −6.90952e6 −1.21767 −0.608833 0.793299i \(-0.708362\pi\)
−0.608833 + 0.793299i \(0.708362\pi\)
\(504\) 0 0
\(505\) −2.85615e6 −0.498370
\(506\) 1.51752e7i 2.63487i
\(507\) −836712. 620522.i −0.144563 0.107211i
\(508\) 4.91099e6 0.844326
\(509\) 4.56189e6 0.780460 0.390230 0.920717i \(-0.372396\pi\)
0.390230 + 0.920717i \(0.372396\pi\)
\(510\) −1.63925e6 + 2.21036e6i −0.279074 + 0.376304i
\(511\) 0 0
\(512\) 1.26387e7i 2.13073i
\(513\) 4.87479e6 + 1.74390e6i 0.817829 + 0.292569i
\(514\) 2.04983e7i 3.42224i
\(515\) 4.97262e6i 0.826165i
\(516\) 7.38285e6 + 5.47527e6i 1.22067 + 0.905277i
\(517\) 2.76185e6i 0.454437i
\(518\) 0 0
\(519\) 3.96004e6 + 2.93684e6i 0.645329 + 0.478589i
\(520\) 7.74783e6 1.25653
\(521\) −532535. −0.0859515 −0.0429758 0.999076i \(-0.513684\pi\)
−0.0429758 + 0.999076i \(0.513684\pi\)
\(522\) −1.17011e6 3.85678e6i −0.187953 0.619510i
\(523\) 1.32596e6i 0.211971i 0.994368 + 0.105985i \(0.0337996\pi\)
−0.994368 + 0.105985i \(0.966200\pi\)
\(524\) 1.53795e7 2.44689
\(525\) 0 0
\(526\) 8.08433e6 1.27403
\(527\) 3.80475e6i 0.596760i
\(528\) −9.17169e6 + 1.23671e7i −1.43174 + 1.93056i
\(529\) −4.04808e6 −0.628941
\(530\) −4.65079e6 −0.719179
\(531\) −1.19360e6 3.93421e6i −0.183706 0.605510i
\(532\) 0 0
\(533\) 993473.i 0.151474i
\(534\) 91525.5 123413.i 0.0138896 0.0187287i
\(535\) 4.41537e6i 0.666934i
\(536\) 6.02261e6i 0.905467i
\(537\) 5.23352e6 7.05688e6i 0.783174 1.05603i
\(538\) 1.73933e7i 2.59075i
\(539\) 0 0
\(540\) 3.02952e6 8.46854e6i 0.447085 1.24975i
\(541\) −1.12979e7 −1.65961 −0.829804 0.558055i \(-0.811548\pi\)
−0.829804 + 0.558055i \(0.811548\pi\)
\(542\) 8.40863e6 1.22950
\(543\) 3.05757e6 4.12282e6i 0.445017 0.600060i
\(544\) 4.49536e6i 0.651280i
\(545\) −768967. −0.110896
\(546\) 0 0
\(547\) −1.17217e7 −1.67503 −0.837516 0.546413i \(-0.815993\pi\)
−0.837516 + 0.546413i \(0.815993\pi\)
\(548\) 3.07053e7i 4.36780i
\(549\) 6.91065e6 2.09662e6i 0.978561 0.296886i
\(550\) 9.92407e6 1.39889
\(551\) 2.19351e6 0.307794
\(552\) −1.79350e7 1.33009e7i −2.50526 1.85795i
\(553\) 0 0
\(554\) 3.88091e6i 0.537229i
\(555\) −775403. 575054.i −0.106855 0.0792458i
\(556\) 5.52628e6i 0.758134i
\(557\) 5.47372e6i 0.747558i −0.927518 0.373779i \(-0.878062\pi\)
0.927518 0.373779i \(-0.121938\pi\)
\(558\) 5.15463e6 + 1.69901e7i 0.700828 + 2.30999i
\(559\) 4.34938e6i 0.588705i
\(560\) 0 0
\(561\) 2.26620e6 3.05574e6i 0.304012 0.409929i
\(562\) −2.73127e6 −0.364773
\(563\) −1.44586e7 −1.92245 −0.961224 0.275769i \(-0.911067\pi\)
−0.961224 + 0.275769i \(0.911067\pi\)
\(564\) 5.70428e6 + 4.23041e6i 0.755098 + 0.559996i
\(565\) 1.21348e6i 0.159923i
\(566\) 1.90700e7 2.50213
\(567\) 0 0
\(568\) 1.38634e7 1.80301
\(569\) 4.69732e6i 0.608233i 0.952635 + 0.304116i \(0.0983612\pi\)
−0.952635 + 0.304116i \(0.901639\pi\)
\(570\) 5.61369e6 + 4.16322e6i 0.723704 + 0.536713i
\(571\) 5.07275e6 0.651108 0.325554 0.945523i \(-0.394449\pi\)
0.325554 + 0.945523i \(0.394449\pi\)
\(572\) −1.87184e7 −2.39209
\(573\) 7.47947e6 1.00853e7i 0.951665 1.28323i
\(574\) 0 0
\(575\) 6.85645e6i 0.864828i
\(576\) −1.17324e6 3.86712e6i −0.147344 0.485659i
\(577\) 7.54076e6i 0.942922i −0.881887 0.471461i \(-0.843727\pi\)
0.881887 0.471461i \(-0.156273\pi\)
\(578\) 1.16806e7i 1.45428i
\(579\) −7.95959e6 5.90299e6i −0.986720 0.731771i
\(580\) 3.81059e6i 0.470351i
\(581\) 0 0
\(582\) −1.49525e7 1.10890e7i −1.82981 1.35702i
\(583\) 6.42953e6 0.783443
\(584\) 4.34471e6 0.527144
\(585\) 4.07263e6 1.23560e6i 0.492023 0.149275i
\(586\) 2.03512e7i 2.44820i
\(587\) −1.49725e7 −1.79349 −0.896743 0.442551i \(-0.854074\pi\)
−0.896743 + 0.442551i \(0.854074\pi\)
\(588\) 0 0
\(589\) −9.66297e6 −1.14768
\(590\) 5.54991e6i 0.656381i
\(591\) 1.27866e6 1.72414e6i 0.150586 0.203051i
\(592\) −4.24948e6 −0.498347
\(593\) 3.02527e6 0.353287 0.176644 0.984275i \(-0.443476\pi\)
0.176644 + 0.984275i \(0.443476\pi\)
\(594\) −5.97981e6 + 1.67156e7i −0.695379 + 1.94382i
\(595\) 0 0
\(596\) 4.33662e6i 0.500075i
\(597\) −8.31597e6 + 1.12132e7i −0.954942 + 1.28764i
\(598\) 1.84646e7i 2.11148i
\(599\) 5.80456e6i 0.661001i −0.943806 0.330501i \(-0.892782\pi\)
0.943806 0.330501i \(-0.107218\pi\)
\(600\) −8.69834e6 + 1.17288e7i −0.986412 + 1.33008i
\(601\) 8.90296e6i 1.00542i −0.864455 0.502711i \(-0.832336\pi\)
0.864455 0.502711i \(-0.167664\pi\)
\(602\) 0 0
\(603\) 960464. + 3.16577e6i 0.107569 + 0.354557i
\(604\) 1.28990e7 1.43868
\(605\) 1.41568e6 0.157245
\(606\) −8.63528e6 + 1.16438e7i −0.955202 + 1.28799i
\(607\) 344344.i 0.0379333i −0.999820 0.0189667i \(-0.993962\pi\)
0.999820 0.0189667i \(-0.00603764\pi\)
\(608\) 1.14169e7 1.25254
\(609\) 0 0
\(610\) 9.74871e6 1.06077
\(611\) 3.36050e6i 0.364167i
\(612\) 2.84008e6 + 9.36114e6i 0.306515 + 1.01030i
\(613\) −40196.2 −0.00432050 −0.00216025 0.999998i \(-0.500688\pi\)
−0.00216025 + 0.999998i \(0.500688\pi\)
\(614\) 2.46040e7 2.63381
\(615\) −715552. 530668.i −0.0762875 0.0565763i
\(616\) 0 0
\(617\) 4.04424e6i 0.427685i −0.976868 0.213843i \(-0.931402\pi\)
0.976868 0.213843i \(-0.0685980\pi\)
\(618\) −2.02721e7 1.50342e7i −2.13515 1.58347i
\(619\) 7.68259e6i 0.805900i −0.915222 0.402950i \(-0.867985\pi\)
0.915222 0.402950i \(-0.132015\pi\)
\(620\) 1.67866e7i 1.75382i
\(621\) −1.15487e7 4.13140e6i −1.20172 0.429901i
\(622\) 3.48668e7i 3.61357i
\(623\) 0 0
\(624\) 1.11597e7 1.50478e7i 1.14734 1.54707i
\(625\) 1.33551e6 0.136756
\(626\) −2.77655e7 −2.83185
\(627\) −7.76069e6 5.75548e6i −0.788373 0.584673i
\(628\) 1.78998e7i 1.81113i
\(629\) 1.04999e6 0.105817
\(630\) 0 0
\(631\) 1.42740e7 1.42716 0.713582 0.700572i \(-0.247072\pi\)
0.713582 + 0.700572i \(0.247072\pi\)
\(632\) 4.41483e7i 4.39664i
\(633\) 4.91488e6 + 3.64498e6i 0.487533 + 0.361564i
\(634\) −7.13703e6 −0.705171
\(635\) 2.08380e6 0.205080
\(636\) −9.84831e6 + 1.32795e7i −0.965426 + 1.30178i
\(637\) 0 0
\(638\) 7.52152e6i 0.731566i
\(639\) 7.28726e6 2.21088e6i 0.706012 0.214197i
\(640\) 3.02914e6i 0.292327i
\(641\) 7.73472e6i 0.743532i 0.928326 + 0.371766i \(0.121248\pi\)
−0.928326 + 0.371766i \(0.878752\pi\)
\(642\) −1.80004e7 1.33494e7i −1.72363 1.27828i
\(643\) 1.41911e7i 1.35360i 0.736168 + 0.676799i \(0.236633\pi\)
−0.736168 + 0.676799i \(0.763367\pi\)
\(644\) 0 0
\(645\) 3.13265e6 + 2.32324e6i 0.296492 + 0.219884i
\(646\) −7.60159e6 −0.716677
\(647\) 678952. 0.0637644 0.0318822 0.999492i \(-0.489850\pi\)
0.0318822 + 0.999492i \(0.489850\pi\)
\(648\) −1.45142e7 2.17183e7i −1.35786 2.03184i
\(649\) 7.67252e6i 0.715034i
\(650\) −1.20752e7 −1.12101
\(651\) 0 0
\(652\) −1.10994e7 −1.02254
\(653\) 2.65332e6i 0.243505i 0.992561 + 0.121752i \(0.0388514\pi\)
−0.992561 + 0.121752i \(0.961149\pi\)
\(654\) −2.32490e6 + 3.13489e6i −0.212549 + 0.286601i
\(655\) 6.52575e6 0.594329
\(656\) −3.92148e6 −0.355787
\(657\) 2.28379e6 692879.i 0.206416 0.0626245i
\(658\) 0 0
\(659\) 1.07933e7i 0.968149i 0.875027 + 0.484074i \(0.160844\pi\)
−0.875027 + 0.484074i \(0.839156\pi\)
\(660\) −9.99849e6 + 1.34820e7i −0.893459 + 1.20474i
\(661\) 2.05761e7i 1.83172i 0.401496 + 0.915861i \(0.368490\pi\)
−0.401496 + 0.915861i \(0.631510\pi\)
\(662\) 3.34198e7i 2.96387i
\(663\) −2.75741e6 + 3.71809e6i −0.243623 + 0.328501i
\(664\) 3.51942e7i 3.09778i
\(665\) 0 0
\(666\) −4.68871e6 + 1.42251e6i −0.409607 + 0.124271i
\(667\) −5.19655e6 −0.452273
\(668\) 4.11376e7 3.56696
\(669\) −9.42108e6 + 1.27034e7i −0.813833 + 1.09737i
\(670\) 4.46589e6i 0.384345i
\(671\) −1.34772e7 −1.15556
\(672\) 0 0
\(673\) −1.73039e7 −1.47268 −0.736338 0.676614i \(-0.763447\pi\)
−0.736338 + 0.676614i \(0.763447\pi\)
\(674\) 7.76302e6i 0.658235i
\(675\) −2.70180e6 + 7.55243e6i −0.228241 + 0.638009i
\(676\) −4.99884e6 −0.420729
\(677\) 2.14664e6 0.180006 0.0900031 0.995941i \(-0.471312\pi\)
0.0900031 + 0.995941i \(0.471312\pi\)
\(678\) 4.94706e6 + 3.66884e6i 0.413307 + 0.306517i
\(679\) 0 0
\(680\) 7.55651e6i 0.626685i
\(681\) −3.92369e6 2.90989e6i −0.324211 0.240441i
\(682\) 3.31342e7i 2.72782i
\(683\) 2.60907e6i 0.214010i 0.994258 + 0.107005i \(0.0341260\pi\)
−0.994258 + 0.107005i \(0.965874\pi\)
\(684\) 2.37746e7 7.21298e6i 1.94300 0.589487i
\(685\) 1.30287e7i 1.06090i
\(686\) 0 0
\(687\) 4.18550e6 5.64373e6i 0.338342 0.456220i
\(688\) 1.71680e7 1.38277
\(689\) −7.82318e6 −0.627820
\(690\) −1.32992e7 9.86292e6i −1.06341 0.788647i
\(691\) 8.38905e6i 0.668371i 0.942507 + 0.334185i \(0.108461\pi\)
−0.942507 + 0.334185i \(0.891539\pi\)
\(692\) 2.36588e7 1.87814
\(693\) 0 0
\(694\) 2.19804e7 1.73236
\(695\) 2.34488e6i 0.184144i
\(696\) −8.88937e6 6.59253e6i −0.695581 0.515857i
\(697\) 968942. 0.0755467
\(698\) 1.93670e7 1.50461
\(699\) 1.24855e6 1.68355e6i 0.0966527 0.130327i
\(700\) 0 0
\(701\) 1.05701e6i 0.0812425i −0.999175 0.0406213i \(-0.987066\pi\)
0.999175 0.0406213i \(-0.0129337\pi\)
\(702\) 7.27599e6 2.03388e7i 0.557249 1.55770i
\(703\) 2.66666e6i 0.203507i
\(704\) 7.54168e6i 0.573504i
\(705\) 2.42041e6 + 1.79502e6i 0.183407 + 0.136018i
\(706\) 3.30596e7i 2.49624i
\(707\) 0 0
\(708\) −1.58467e7 1.17523e7i −1.18811 0.881126i
\(709\) 8.71222e6 0.650898 0.325449 0.945560i \(-0.394485\pi\)
0.325449 + 0.945560i \(0.394485\pi\)
\(710\) 1.02800e7 0.765327
\(711\) 7.04061e6 + 2.32065e7i 0.522319 + 1.72161i
\(712\) 421908.i 0.0311902i
\(713\) 2.28921e7 1.68641
\(714\) 0 0
\(715\) −7.94248e6 −0.581020
\(716\) 4.21605e7i 3.07343i
\(717\) 1.17343e7 1.58225e7i 0.852431 1.14942i
\(718\) −2.55185e6 −0.184732
\(719\) −2.34094e7 −1.68876 −0.844380 0.535744i \(-0.820031\pi\)
−0.844380 + 0.535744i \(0.820031\pi\)
\(720\) −4.87719e6 1.60757e7i −0.350621 1.15568i
\(721\) 0 0
\(722\) 6.28377e6i 0.448618i
\(723\) −4.51833e6 + 6.09252e6i −0.321464 + 0.433462i
\(724\) 2.46313e7i 1.74639i
\(725\) 3.39837e6i 0.240118i
\(726\) 4.28017e6 5.77138e6i 0.301383 0.406385i
\(727\) 1.80153e7i 1.26417i 0.774899 + 0.632085i \(0.217801\pi\)
−0.774899 + 0.632085i \(0.782199\pi\)
\(728\) 0 0
\(729\) −1.10929e7 9.10153e6i −0.773086 0.634301i
\(730\) 3.22170e6 0.223758
\(731\) −4.24198e6 −0.293613
\(732\) 2.06434e7 2.78356e7i 1.42398 1.92010i
\(733\) 7.02971e6i 0.483256i 0.970369 + 0.241628i \(0.0776814\pi\)
−0.970369 + 0.241628i \(0.922319\pi\)
\(734\) 4.69511e6 0.321667
\(735\) 0 0
\(736\) −2.70474e7 −1.84048
\(737\) 6.17391e6i 0.418689i
\(738\) −4.32680e6 + 1.31271e6i −0.292433 + 0.0887212i
\(739\) 1.59687e7 1.07562 0.537810 0.843066i \(-0.319252\pi\)
0.537810 + 0.843066i \(0.319252\pi\)
\(740\) −4.63256e6 −0.310987
\(741\) 9.44289e6 + 7.00303e6i 0.631770 + 0.468533i
\(742\) 0 0
\(743\) 2.50742e7i 1.66630i −0.553044 0.833152i \(-0.686534\pi\)
0.553044 0.833152i \(-0.313466\pi\)
\(744\) 3.91600e7 + 2.90418e7i 2.59364 + 1.92350i
\(745\) 1.84009e6i 0.121464i
\(746\) 2.43490e7i 1.60189i
\(747\) 5.61264e6 + 1.84998e7i 0.368015 + 1.21301i
\(748\) 1.82562e7i 1.19304i
\(749\) 0 0
\(750\) −1.59688e7 + 2.15324e7i −1.03662 + 1.39778i
\(751\) −2.18908e6 −0.141632 −0.0708159 0.997489i \(-0.522560\pi\)
−0.0708159 + 0.997489i \(0.522560\pi\)
\(752\) 1.32647e7 0.855367
\(753\) 5.68011e6 + 4.21248e6i 0.365064 + 0.270739i
\(754\) 9.15187e6i 0.586248i
\(755\) 5.47323e6 0.349443
\(756\) 0 0
\(757\) −1.44147e6 −0.0914251 −0.0457126 0.998955i \(-0.514556\pi\)
−0.0457126 + 0.998955i \(0.514556\pi\)
\(758\) 1.43902e7i 0.909691i
\(759\) 1.83855e7 + 1.36351e7i 1.15844 + 0.859119i
\(760\) 1.91914e7 1.20524
\(761\) 1.36473e6 0.0854253 0.0427126 0.999087i \(-0.486400\pi\)
0.0427126 + 0.999087i \(0.486400\pi\)
\(762\) 6.30018e6 8.49516e6i 0.393066 0.530010i
\(763\) 0 0
\(764\) 6.02536e7i 3.73465i
\(765\) 1.20509e6 + 3.97207e6i 0.0744499 + 0.245394i
\(766\) 4.71038e7i 2.90058i
\(767\) 9.33561e6i 0.572999i
\(768\) 1.90123e7 + 1.40999e7i 1.16314 + 0.862608i
\(769\) 1.59541e7i 0.972875i 0.873715 + 0.486437i \(0.161704\pi\)
−0.873715 + 0.486437i \(0.838296\pi\)
\(770\) 0 0
\(771\) 2.48347e7 + 1.84179e7i 1.50461 + 1.11585i
\(772\) −4.75537e7 −2.87171
\(773\) −1.72753e7 −1.03986 −0.519931 0.854208i \(-0.674042\pi\)
−0.519931 + 0.854208i \(0.674042\pi\)
\(774\) 1.89425e7 5.74697e6i 1.13654 0.344815i
\(775\) 1.49707e7i 0.895338i
\(776\) −5.11175e7 −3.04730
\(777\) 0 0
\(778\) 1.72368e7 1.02096
\(779\) 2.46083e6i 0.145291i
\(780\) 1.21657e7