Properties

Label 108.6.h.a.71.11
Level 108
Weight 6
Character 108.71
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 108.h (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 71.11
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.78768 - 5.36696i) q^{2} +(-25.6084 + 19.1888i) q^{4} +(52.1793 + 30.1257i) q^{5} +(-185.316 + 106.992i) q^{7} +(148.765 + 103.136i) q^{8} +O(q^{10})\) \(q+(-1.78768 - 5.36696i) q^{2} +(-25.6084 + 19.1888i) q^{4} +(52.1793 + 30.1257i) q^{5} +(-185.316 + 106.992i) q^{7} +(148.765 + 103.136i) q^{8} +(68.4038 - 333.899i) q^{10} +(-185.570 - 321.417i) q^{11} +(402.759 - 697.599i) q^{13} +(905.506 + 803.314i) q^{14} +(287.583 - 982.788i) q^{16} -34.0704i q^{17} -1173.48i q^{19} +(-1914.31 + 229.783i) q^{20} +(-1393.29 + 1570.54i) q^{22} +(1980.40 - 3430.16i) q^{23} +(252.621 + 437.553i) q^{25} +(-4463.99 - 914.509i) q^{26} +(2692.60 - 6295.88i) q^{28} +(382.894 - 221.064i) q^{29} +(-1381.28 - 797.481i) q^{31} +(-5788.68 + 213.459i) q^{32} +(-182.854 + 60.9068i) q^{34} -12892.9 q^{35} -11057.6 q^{37} +(-6298.01 + 2097.80i) q^{38} +(4655.40 + 9863.22i) q^{40} +(7969.76 + 4601.35i) q^{41} +(1061.38 - 612.787i) q^{43} +(10919.8 + 4670.13i) q^{44} +(-21949.8 - 4496.72i) q^{46} +(1222.66 + 2117.71i) q^{47} +(14491.1 - 25099.3i) q^{49} +(1896.72 - 2138.01i) q^{50} +(3072.03 + 25592.9i) q^{52} -20212.4i q^{53} -22361.8i q^{55} +(-38603.2 - 3196.07i) q^{56} +(-1870.93 - 1659.78i) q^{58} +(-1704.67 + 2952.58i) q^{59} +(-19919.9 - 34502.3i) q^{61} +(-1810.77 + 8838.89i) q^{62} +(11493.9 + 30686.0i) q^{64} +(42031.4 - 24266.8i) q^{65} +(6088.22 + 3515.04i) q^{67} +(653.768 + 872.488i) q^{68} +(23048.3 + 69195.4i) q^{70} +25694.1 q^{71} +65431.6 q^{73} +(19767.4 + 59345.7i) q^{74} +(22517.6 + 30051.0i) q^{76} +(68778.2 + 39709.1i) q^{77} +(-41126.9 + 23744.6i) q^{79} +(44613.1 - 42617.5i) q^{80} +(10447.9 - 50999.1i) q^{82} +(6605.97 + 11441.9i) q^{83} +(1026.39 - 1777.77i) q^{85} +(-5186.20 - 4600.90i) q^{86} +(5543.37 - 66954.6i) q^{88} -85682.2i q^{89} +172368. i q^{91} +(15105.5 + 125842. i) q^{92} +(9179.93 - 10347.7i) q^{94} +(35352.0 - 61231.4i) q^{95} +(-27944.9 - 48402.0i) q^{97} +(-160612. - 32903.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.78768 5.36696i −0.316019 0.948753i
\(3\) 0 0
\(4\) −25.6084 + 19.1888i −0.800263 + 0.599649i
\(5\) 52.1793 + 30.1257i 0.933412 + 0.538906i 0.887889 0.460058i \(-0.152171\pi\)
0.0455230 + 0.998963i \(0.485505\pi\)
\(6\) 0 0
\(7\) −185.316 + 106.992i −1.42944 + 0.825290i −0.997077 0.0764081i \(-0.975655\pi\)
−0.432367 + 0.901698i \(0.642321\pi\)
\(8\) 148.765 + 103.136i 0.821817 + 0.569751i
\(9\) 0 0
\(10\) 68.4038 333.899i 0.216312 1.05588i
\(11\) −185.570 321.417i −0.462410 0.800917i 0.536671 0.843792i \(-0.319682\pi\)
−0.999080 + 0.0428745i \(0.986348\pi\)
\(12\) 0 0
\(13\) 402.759 697.599i 0.660978 1.14485i −0.319381 0.947626i \(-0.603475\pi\)
0.980359 0.197221i \(-0.0631917\pi\)
\(14\) 905.506 + 803.314i 1.23473 + 1.09538i
\(15\) 0 0
\(16\) 287.583 982.788i 0.280843 0.959754i
\(17\) 34.0704i 0.0285926i −0.999898 0.0142963i \(-0.995449\pi\)
0.999898 0.0142963i \(-0.00455082\pi\)
\(18\) 0 0
\(19\) 1173.48i 0.745747i −0.927882 0.372874i \(-0.878373\pi\)
0.927882 0.372874i \(-0.121627\pi\)
\(20\) −1914.31 + 229.783i −1.07013 + 0.128453i
\(21\) 0 0
\(22\) −1393.29 + 1570.54i −0.613742 + 0.691818i
\(23\) 1980.40 3430.16i 0.780610 1.35206i −0.150977 0.988537i \(-0.548242\pi\)
0.931587 0.363519i \(-0.118425\pi\)
\(24\) 0 0
\(25\) 252.621 + 437.553i 0.0808388 + 0.140017i
\(26\) −4463.99 914.509i −1.29506 0.265311i
\(27\) 0 0
\(28\) 2692.60 6295.88i 0.649048 1.51761i
\(29\) 382.894 221.064i 0.0845441 0.0488115i −0.457132 0.889399i \(-0.651123\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(30\) 0 0
\(31\) −1381.28 797.481i −0.258153 0.149045i 0.365339 0.930875i \(-0.380953\pi\)
−0.623492 + 0.781830i \(0.714286\pi\)
\(32\) −5788.68 + 213.459i −0.999321 + 0.0368502i
\(33\) 0 0
\(34\) −182.854 + 60.9068i −0.0271274 + 0.00903583i
\(35\) −12892.9 −1.77901
\(36\) 0 0
\(37\) −11057.6 −1.32787 −0.663937 0.747788i \(-0.731116\pi\)
−0.663937 + 0.747788i \(0.731116\pi\)
\(38\) −6298.01 + 2097.80i −0.707530 + 0.235671i
\(39\) 0 0
\(40\) 4655.40 + 9863.22i 0.460052 + 0.974695i
\(41\) 7969.76 + 4601.35i 0.740433 + 0.427489i 0.822227 0.569160i \(-0.192732\pi\)
−0.0817937 + 0.996649i \(0.526065\pi\)
\(42\) 0 0
\(43\) 1061.38 612.787i 0.0875384 0.0505403i −0.455592 0.890189i \(-0.650572\pi\)
0.543130 + 0.839648i \(0.317239\pi\)
\(44\) 10919.8 + 4670.13i 0.850319 + 0.363661i
\(45\) 0 0
\(46\) −21949.8 4496.72i −1.52945 0.313330i
\(47\) 1222.66 + 2117.71i 0.0807348 + 0.139837i 0.903566 0.428449i \(-0.140940\pi\)
−0.822831 + 0.568286i \(0.807607\pi\)
\(48\) 0 0
\(49\) 14491.1 25099.3i 0.862206 1.49338i
\(50\) 1896.72 2138.01i 0.107295 0.120944i
\(51\) 0 0
\(52\) 3072.03 + 25592.9i 0.157550 + 1.31253i
\(53\) 20212.4i 0.988390i −0.869351 0.494195i \(-0.835463\pi\)
0.869351 0.494195i \(-0.164537\pi\)
\(54\) 0 0
\(55\) 22361.8i 0.996781i
\(56\) −38603.2 3196.07i −1.64495 0.136190i
\(57\) 0 0
\(58\) −1870.93 1659.78i −0.0730276 0.0647860i
\(59\) −1704.67 + 2952.58i −0.0637546 + 0.110426i −0.896141 0.443770i \(-0.853641\pi\)
0.832386 + 0.554196i \(0.186974\pi\)
\(60\) 0 0
\(61\) −19919.9 34502.3i −0.685430 1.18720i −0.973302 0.229530i \(-0.926281\pi\)
0.287872 0.957669i \(-0.407052\pi\)
\(62\) −1810.77 + 8838.89i −0.0598251 + 0.292024i
\(63\) 0 0
\(64\) 11493.9 + 30686.0i 0.350767 + 0.936463i
\(65\) 42031.4 24266.8i 1.23393 0.712410i
\(66\) 0 0
\(67\) 6088.22 + 3515.04i 0.165693 + 0.0956627i 0.580553 0.814222i \(-0.302836\pi\)
−0.414861 + 0.909885i \(0.636170\pi\)
\(68\) 653.768 + 872.488i 0.0171455 + 0.0228816i
\(69\) 0 0
\(70\) 23048.3 + 69195.4i 0.562203 + 1.68784i
\(71\) 25694.1 0.604905 0.302453 0.953164i \(-0.402195\pi\)
0.302453 + 0.953164i \(0.402195\pi\)
\(72\) 0 0
\(73\) 65431.6 1.43708 0.718540 0.695486i \(-0.244811\pi\)
0.718540 + 0.695486i \(0.244811\pi\)
\(74\) 19767.4 + 59345.7i 0.419634 + 1.25982i
\(75\) 0 0
\(76\) 22517.6 + 30051.0i 0.447186 + 0.596794i
\(77\) 68778.2 + 39709.1i 1.32198 + 0.763244i
\(78\) 0 0
\(79\) −41126.9 + 23744.6i −0.741409 + 0.428053i −0.822581 0.568647i \(-0.807467\pi\)
0.0811725 + 0.996700i \(0.474134\pi\)
\(80\) 44613.1 42617.5i 0.779359 0.744498i
\(81\) 0 0
\(82\) 10447.9 50999.1i 0.171590 0.837583i
\(83\) 6605.97 + 11441.9i 0.105255 + 0.182306i 0.913842 0.406069i \(-0.133101\pi\)
−0.808588 + 0.588376i \(0.799768\pi\)
\(84\) 0 0
\(85\) 1026.39 1777.77i 0.0154087 0.0266887i
\(86\) −5186.20 4600.90i −0.0756141 0.0670806i
\(87\) 0 0
\(88\) 5543.37 66954.6i 0.0763075 0.921666i
\(89\) 85682.2i 1.14661i −0.819342 0.573305i \(-0.805661\pi\)
0.819342 0.573305i \(-0.194339\pi\)
\(90\) 0 0
\(91\) 172368.i 2.18199i
\(92\) 15105.5 + 125842.i 0.186065 + 1.55009i
\(93\) 0 0
\(94\) 9179.93 10347.7i 0.107157 0.120789i
\(95\) 35352.0 61231.4i 0.401887 0.696089i
\(96\) 0 0
\(97\) −27944.9 48402.0i −0.301560 0.522317i 0.674929 0.737882i \(-0.264174\pi\)
−0.976490 + 0.215565i \(0.930841\pi\)
\(98\) −160612. 32903.6i −1.68933 0.346082i
\(99\) 0 0
\(100\) −14865.3 6357.56i −0.148653 0.0635756i
\(101\) −79337.0 + 45805.2i −0.773878 + 0.446799i −0.834256 0.551377i \(-0.814103\pi\)
0.0603784 + 0.998176i \(0.480769\pi\)
\(102\) 0 0
\(103\) −91488.4 52820.9i −0.849715 0.490583i 0.0108398 0.999941i \(-0.496550\pi\)
−0.860555 + 0.509358i \(0.829883\pi\)
\(104\) 131864. 62239.2i 1.19548 0.564262i
\(105\) 0 0
\(106\) −108479. + 36133.2i −0.937737 + 0.312350i
\(107\) 3806.62 0.0321426 0.0160713 0.999871i \(-0.494884\pi\)
0.0160713 + 0.999871i \(0.494884\pi\)
\(108\) 0 0
\(109\) −85149.1 −0.686458 −0.343229 0.939252i \(-0.611521\pi\)
−0.343229 + 0.939252i \(0.611521\pi\)
\(110\) −120015. + 39975.6i −0.945699 + 0.315002i
\(111\) 0 0
\(112\) 51856.8 + 212895.i 0.390625 + 1.60369i
\(113\) 36754.5 + 21220.2i 0.270778 + 0.156334i 0.629241 0.777210i \(-0.283366\pi\)
−0.358463 + 0.933544i \(0.616699\pi\)
\(114\) 0 0
\(115\) 206672. 119322.i 1.45726 0.841350i
\(116\) −5563.37 + 13008.3i −0.0383877 + 0.0897588i
\(117\) 0 0
\(118\) 18893.8 + 3870.65i 0.124915 + 0.0255905i
\(119\) 3645.26 + 6313.77i 0.0235972 + 0.0408716i
\(120\) 0 0
\(121\) 11652.7 20183.1i 0.0723543 0.125321i
\(122\) −149562. + 168588.i −0.909749 + 1.02548i
\(123\) 0 0
\(124\) 50675.0 6082.76i 0.295964 0.0355260i
\(125\) 157844.i 0.903553i
\(126\) 0 0
\(127\) 37078.8i 0.203994i −0.994785 0.101997i \(-0.967477\pi\)
0.994785 0.101997i \(-0.0325232\pi\)
\(128\) 144143. 116544.i 0.777623 0.628731i
\(129\) 0 0
\(130\) −205378. 182199.i −1.06585 0.945559i
\(131\) −83730.6 + 145026.i −0.426291 + 0.738357i −0.996540 0.0831144i \(-0.973513\pi\)
0.570249 + 0.821472i \(0.306847\pi\)
\(132\) 0 0
\(133\) 125553. + 217464.i 0.615457 + 1.06600i
\(134\) 7981.28 38959.0i 0.0383982 0.187433i
\(135\) 0 0
\(136\) 3513.88 5068.47i 0.0162907 0.0234979i
\(137\) −298026. + 172065.i −1.35660 + 0.783234i −0.989164 0.146814i \(-0.953098\pi\)
−0.367438 + 0.930048i \(0.619765\pi\)
\(138\) 0 0
\(139\) −239133. 138064.i −1.04979 0.606097i −0.127200 0.991877i \(-0.540599\pi\)
−0.922591 + 0.385780i \(0.873932\pi\)
\(140\) 330166. 247398.i 1.42368 1.06678i
\(141\) 0 0
\(142\) −45932.7 137899.i −0.191162 0.573906i
\(143\) −298961. −1.22257
\(144\) 0 0
\(145\) 26638.8 0.105219
\(146\) −116971. 351169.i −0.454145 1.36343i
\(147\) 0 0
\(148\) 283168. 212182.i 1.06265 0.796258i
\(149\) −33899.5 19571.9i −0.125091 0.0722216i 0.436149 0.899875i \(-0.356342\pi\)
−0.561240 + 0.827653i \(0.689676\pi\)
\(150\) 0 0
\(151\) 372275. 214933.i 1.32868 0.767115i 0.343587 0.939121i \(-0.388358\pi\)
0.985096 + 0.172006i \(0.0550247\pi\)
\(152\) 121028. 174572.i 0.424890 0.612868i
\(153\) 0 0
\(154\) 90163.9 440117.i 0.306359 1.49543i
\(155\) −48049.4 83224.0i −0.160642 0.278240i
\(156\) 0 0
\(157\) −283488. + 491016.i −0.917881 + 1.58982i −0.115252 + 0.993336i \(0.536768\pi\)
−0.802628 + 0.596479i \(0.796566\pi\)
\(158\) 200958. + 178278.i 0.640416 + 0.568141i
\(159\) 0 0
\(160\) −308480. 163250.i −0.952637 0.504143i
\(161\) 847550.i 2.57692i
\(162\) 0 0
\(163\) 50545.5i 0.149009i 0.997221 + 0.0745047i \(0.0237376\pi\)
−0.997221 + 0.0745047i \(0.976262\pi\)
\(164\) −292387. + 35096.6i −0.848885 + 0.101896i
\(165\) 0 0
\(166\) 49598.7 55908.3i 0.139701 0.157473i
\(167\) 155078. 268602.i 0.430287 0.745279i −0.566611 0.823985i \(-0.691746\pi\)
0.996898 + 0.0787068i \(0.0250791\pi\)
\(168\) 0 0
\(169\) −138783. 240380.i −0.373784 0.647413i
\(170\) −11376.1 2330.54i −0.0301905 0.00618493i
\(171\) 0 0
\(172\) −15421.6 + 36059.0i −0.0397474 + 0.0929379i
\(173\) 140517. 81127.6i 0.356955 0.206088i −0.310789 0.950479i \(-0.600593\pi\)
0.667744 + 0.744391i \(0.267260\pi\)
\(174\) 0 0
\(175\) −93629.4 54056.9i −0.231109 0.133431i
\(176\) −369252. + 89942.1i −0.898548 + 0.218867i
\(177\) 0 0
\(178\) −459852. + 153172.i −1.08785 + 0.362351i
\(179\) 313216. 0.730653 0.365326 0.930880i \(-0.380957\pi\)
0.365326 + 0.930880i \(0.380957\pi\)
\(180\) 0 0
\(181\) 241414. 0.547729 0.273865 0.961768i \(-0.411698\pi\)
0.273865 + 0.961768i \(0.411698\pi\)
\(182\) 925092. 308138.i 2.07017 0.689552i
\(183\) 0 0
\(184\) 648387. 306036.i 1.41185 0.666389i
\(185\) −576979. 333119.i −1.23945 0.715599i
\(186\) 0 0
\(187\) −10950.8 + 6322.45i −0.0229003 + 0.0132215i
\(188\) −71946.6 30769.9i −0.148462 0.0634938i
\(189\) 0 0
\(190\) −391824. 80270.5i −0.787421 0.161314i
\(191\) 378078. + 654851.i 0.749891 + 1.29885i 0.947874 + 0.318644i \(0.103227\pi\)
−0.197983 + 0.980205i \(0.563439\pi\)
\(192\) 0 0
\(193\) −210750. + 365029.i −0.407262 + 0.705398i −0.994582 0.103957i \(-0.966850\pi\)
0.587320 + 0.809355i \(0.300183\pi\)
\(194\) −209815. + 236506.i −0.400251 + 0.451168i
\(195\) 0 0
\(196\) 110530. + 920820.i 0.205514 + 1.71212i
\(197\) 796004.i 1.46133i −0.682734 0.730667i \(-0.739209\pi\)
0.682734 0.730667i \(-0.260791\pi\)
\(198\) 0 0
\(199\) 1.10972e6i 1.98646i 0.116163 + 0.993230i \(0.462940\pi\)
−0.116163 + 0.993230i \(0.537060\pi\)
\(200\) −7546.32 + 91146.8i −0.0133401 + 0.161126i
\(201\) 0 0
\(202\) 387664. + 343913.i 0.668462 + 0.593022i
\(203\) −47304.1 + 81933.1i −0.0805673 + 0.139547i
\(204\) 0 0
\(205\) 277238. + 480190.i 0.460753 + 0.798047i
\(206\) −119936. + 585441.i −0.196916 + 0.961203i
\(207\) 0 0
\(208\) −569765. 596445.i −0.913141 0.955899i
\(209\) −377177. + 217763.i −0.597282 + 0.344841i
\(210\) 0 0
\(211\) 179473. + 103619.i 0.277520 + 0.160226i 0.632300 0.774724i \(-0.282111\pi\)
−0.354780 + 0.934950i \(0.615444\pi\)
\(212\) 387851. + 517608.i 0.592687 + 0.790972i
\(213\) 0 0
\(214\) −6805.01 20430.0i −0.0101577 0.0304953i
\(215\) 73842.6 0.108946
\(216\) 0 0
\(217\) 341296. 0.492020
\(218\) 152219. + 456991.i 0.216934 + 0.651278i
\(219\) 0 0
\(220\) 429095. + 572650.i 0.597719 + 0.797688i
\(221\) −23767.5 13722.1i −0.0327342 0.0188991i
\(222\) 0 0
\(223\) −557586. + 321922.i −0.750844 + 0.433500i −0.825999 0.563672i \(-0.809388\pi\)
0.0751547 + 0.997172i \(0.476055\pi\)
\(224\) 1.04990e6 658901.i 1.39806 0.877404i
\(225\) 0 0
\(226\) 48182.8 235194.i 0.0627511 0.306306i
\(227\) −596328. 1.03287e6i −0.768105 1.33040i −0.938589 0.345036i \(-0.887867\pi\)
0.170485 0.985360i \(1.55453\pi\)
\(228\) 0 0
\(229\) 538232. 932245.i 0.678236 1.17474i −0.297276 0.954792i \(-0.596078\pi\)
0.975512 0.219947i \(-0.0705886\pi\)
\(230\) −1.00986e6 895891.i −1.25876 1.11670i
\(231\) 0 0
\(232\) 79760.7 + 6603.63i 0.0972902 + 0.00805495i
\(233\) 178167.i 0.214999i 0.994205 + 0.107500i \(0.0342845\pi\)
−0.994205 + 0.107500i \(0.965716\pi\)
\(234\) 0 0
\(235\) 147334.i 0.174034i
\(236\) −13002.4 108322.i −0.0151964 0.126600i
\(237\) 0 0
\(238\) 27369.2 30850.9i 0.0313198 0.0353041i
\(239\) −336873. + 583482.i −0.381480 + 0.660743i −0.991274 0.131817i \(-0.957919\pi\)
0.609794 + 0.792560i \(0.291252\pi\)
\(240\) 0 0
\(241\) −162984. 282297.i −0.180760 0.313086i 0.761379 0.648307i \(-0.224522\pi\)
−0.942140 + 0.335221i \(0.891189\pi\)
\(242\) −129153. 26458.8i −0.141764 0.0290424i
\(243\) 0 0
\(244\) 1.17217e6 + 501311.i 1.26043 + 0.539055i
\(245\) 1.51227e6 873110.i 1.60959 0.929296i
\(246\) 0 0
\(247\) −818619. 472630.i −0.853767 0.492922i
\(248\) −123236. 261096.i −0.127236 0.269570i
\(249\) 0 0
\(250\) −847143. + 282174.i −0.857249 + 0.285540i
\(251\) 1.32110e6 1.32358 0.661789 0.749690i \(-0.269797\pi\)
0.661789 + 0.749690i \(0.269797\pi\)
\(252\) 0 0
\(253\) −1.47002e6 −1.44385
\(254\) −199000. + 66284.9i −0.193540 + 0.0644660i
\(255\) 0 0
\(256\) −883168. 565267.i −0.842254 0.539080i
\(257\) 1.15605e6 + 667444.i 1.09180 + 0.630350i 0.934055 0.357130i \(-0.116245\pi\)
0.157744 + 0.987480i \(0.449578\pi\)
\(258\) 0 0
\(259\) 2.04915e6 1.18308e6i 1.89812 1.09588i
\(260\) −610708. + 1.42797e6i −0.560273 + 1.31004i
\(261\) 0 0
\(262\) 928030. + 190120.i 0.835235 + 0.171109i
\(263\) 457251. + 791982.i 0.407629 + 0.706035i 0.994624 0.103556i \(-0.0330222\pi\)
−0.586994 + 0.809591i \(0.699689\pi\)
\(264\) 0 0
\(265\) 608914. 1.05467e6i 0.532649 0.922575i
\(266\) 942672. 1.06259e6i 0.816877 0.920795i
\(267\) 0 0
\(268\) −223359. + 26810.8i −0.189962 + 0.0228020i
\(269\) 1.86227e6i 1.56914i 0.620038 + 0.784572i \(0.287117\pi\)
−0.620038 + 0.784572i \(0.712883\pi\)
\(270\) 0 0
\(271\) 517756.i 0.428254i −0.976806 0.214127i \(-0.931309\pi\)
0.976806 0.214127i \(-0.0686907\pi\)
\(272\) −33483.9 9798.07i −0.0274419 0.00803005i
\(273\) 0 0
\(274\) 1.45624e6 + 1.29189e6i 1.17181 + 1.03956i
\(275\) 93758.1 162394.i 0.0747613 0.129490i
\(276\) 0 0
\(277\) −311881. 540194.i −0.244225 0.423010i 0.717689 0.696364i \(-0.245200\pi\)
−0.961913 + 0.273354i \(0.911867\pi\)
\(278\) −313489. + 1.53023e6i −0.243282 + 1.18753i
\(279\) 0 0
\(280\) −1.91800e6 1.32972e6i −1.46202 1.01360i
\(281\) 1.53273e6 884922.i 1.15798 0.668558i 0.207159 0.978307i \(-0.433578\pi\)
0.950818 + 0.309749i \(0.100245\pi\)
\(282\) 0 0
\(283\) −1.28654e6 742782.i −0.954895 0.551309i −0.0602971 0.998180i \(-0.519205\pi\)
−0.894598 + 0.446871i \(0.852538\pi\)
\(284\) −657985. + 493038.i −0.484084 + 0.362731i
\(285\) 0 0
\(286\) 534445. + 1.60451e6i 0.386356 + 1.15992i
\(287\) −1.96923e6 −1.41121
\(288\) 0 0
\(289\) 1.41870e6 0.999182
\(290\) −47621.6 142969.i −0.0332513 0.0998271i
\(291\) 0 0
\(292\) −1.67560e6 + 1.25555e6i −1.15004 + 0.861742i
\(293\) −1.40797e6 812891.i −0.958129 0.553176i −0.0625325 0.998043i \(-0.519918\pi\)
−0.895597 + 0.444867i \(0.853251\pi\)
\(294\) 0 0
\(295\) −177898. + 102709.i −0.119019 + 0.0687154i
\(296\) −1.64498e6 1.14044e6i −1.09127 0.756559i
\(297\) 0 0
\(298\) −44440.1 + 216925.i −0.0289891 + 0.141504i
\(299\) −1.59525e6 2.76306e6i −1.03193 1.78736i
\(300\) 0 0
\(301\) −131127. + 227118.i −0.0834208 + 0.144489i
\(302\) −1.81904e6 1.61375e6i −1.14769 1.01817i
\(303\) 0 0
\(304\) −1.15328e6 337473.i −0.715734 0.209438i
\(305\) 2.40041e6i 1.47753i
\(306\) 0 0
\(307\) 29930.7i 0.0181247i −0.999959 0.00906235i \(-0.997115\pi\)
0.999959 0.00906235i \(-0.00288467\pi\)
\(308\) −2.52327e6 + 302880.i −1.51561 + 0.181926i
\(309\) 0 0
\(310\) −360763. + 406657.i −0.213215 + 0.240339i
\(311\) −828429. + 1.43488e6i −0.485685 + 0.841231i −0.999865 0.0164516i \(-0.994763\pi\)
0.514180 + 0.857682i \(0.328096\pi\)
\(312\) 0 0
\(313\) −1.49316e6 2.58623e6i −0.861482 1.49213i −0.870498 0.492171i \(-0.836203\pi\)
0.00901652 0.999959i \(-0.497130\pi\)
\(314\) 3.14205e6 + 643692.i 1.79841 + 0.368429i
\(315\) 0 0
\(316\) 597565. 1.39724e6i 0.336641 0.787140i
\(317\) −748156. + 431948.i −0.418162 + 0.241426i −0.694290 0.719695i \(-0.744282\pi\)
0.276129 + 0.961121i \(0.410948\pi\)
\(318\) 0 0
\(319\) −142107. 82045.8i −0.0781880 0.0451419i
\(320\) −324694. + 1.94744e6i −0.177256 + 1.06314i
\(321\) 0 0
\(322\) 4.54876e6 1.51514e6i 2.44486 0.814356i
\(323\) −39980.9 −0.0213229
\(324\) 0 0
\(325\) 406982. 0.213731
\(326\) 271276. 90359.0i 0.141373 0.0470899i
\(327\) 0 0
\(328\) 711056. + 1.50649e6i 0.364938 + 0.773181i
\(329\) −453156. 261630.i −0.230812 0.133259i
\(330\) 0 0
\(331\) 1828.81 1055.86i 0.000917484 0.000529710i −0.499541 0.866290i \(-0.666498\pi\)
0.500459 + 0.865760i \(0.333165\pi\)
\(332\) −388724. 166248.i −0.193551 0.0827773i
\(333\) 0 0
\(334\) −1.71881e6 352121.i −0.843064 0.172713i
\(335\) 211786. + 366824.i 0.103106 + 0.178586i
\(336\) 0 0
\(337\) −1.24422e6 + 2.15505e6i −0.596790 + 1.03367i 0.396501 + 0.918034i \(0.370224\pi\)
−0.993292 + 0.115637i \(0.963109\pi\)
\(338\) −1.04201e6 + 1.17457e6i −0.496112 + 0.559224i
\(339\) 0 0
\(340\) 7828.80 + 65221.1i 0.00367280 + 0.0305978i
\(341\) 591955.i 0.275679i
\(342\) 0 0
\(343\) 2.60530e6i 1.19570i
\(344\) 221096. + 18305.2i 0.100736 + 0.00834024i
\(345\) 0 0
\(346\) −686607. 609119.i −0.308332 0.273534i
\(347\) 1.65555e6 2.86750e6i 0.738106 1.27844i −0.215241 0.976561i \(-0.569054\pi\)
0.953347 0.301877i \(-0.0976131\pi\)
\(348\) 0 0
\(349\) −131505. 227773.i −0.0577934 0.100101i 0.835681 0.549215i \(-0.185073\pi\)
−0.893475 + 0.449114i \(0.851740\pi\)
\(350\) −122742. + 599141.i −0.0535580 + 0.261432i
\(351\) 0 0
\(352\) 1.14282e6 + 1.82097e6i 0.491610 + 0.783333i
\(353\) −127875. + 73828.9i −0.0546198 + 0.0315347i −0.527061 0.849827i \(-0.676706\pi\)
0.472441 + 0.881362i \(0.343373\pi\)
\(354\) 0 0
\(355\) 1.34070e6 + 774054.i 0.564626 + 0.325987i
\(356\) 1.64413e6 + 2.19419e6i 0.687563 + 0.917590i
\(357\) 0 0
\(358\) −559928. 1.68102e6i −0.230900 0.693209i
\(359\) 1.46738e6 0.600905 0.300453 0.953797i \(-0.402862\pi\)
0.300453 + 0.953797i \(0.402862\pi\)
\(360\) 0 0
\(361\) 1.09904e6 0.443861
\(362\) −431570. 1.29566e6i −0.173093 0.519660i
\(363\) 0 0
\(364\) −3.30753e6 4.41408e6i −1.30843 1.74617i
\(365\) 3.41418e6 + 1.97118e6i 1.34139 + 0.774450i
\(366\) 0 0
\(367\) −1.76458e6 + 1.01878e6i −0.683874 + 0.394835i −0.801313 0.598245i \(-0.795865\pi\)
0.117439 + 0.993080i \(0.462532\pi\)
\(368\) −2.80159e6 2.93277e6i −1.07841 1.12891i
\(369\) 0 0
\(370\) −756383. + 3.69213e6i −0.287235 + 1.40208i
\(371\) 2.16257e6 + 3.74567e6i 0.815708 + 1.41285i
\(372\) 0 0
\(373\) 629011. 1.08948e6i 0.234092 0.405459i −0.724917 0.688837i \(-0.758122\pi\)
0.959008 + 0.283378i \(0.0914551\pi\)
\(374\) 53508.8 + 47470.0i 0.0197809 + 0.0175485i
\(375\) 0 0
\(376\) −36523.4 + 441141.i −0.0133230 + 0.160919i
\(377\) 356142.i 0.129053i
\(378\) 0 0
\(379\) 3.51959e6i 1.25862i −0.777154 0.629310i \(-0.783338\pi\)
0.777154 0.629310i \(-0.216662\pi\)
\(380\) 269646. + 2.24640e6i 0.0957933 + 0.798046i
\(381\) 0 0
\(382\) 2.83867e6 3.19979e6i 0.995307 1.12192i
\(383\) 1.45304e6 2.51675e6i 0.506153 0.876683i −0.493822 0.869563i \(-0.664400\pi\)
0.999975 0.00711941i \(-0.00226620\pi\)
\(384\) 0 0
\(385\) 2.39253e6 + 4.14399e6i 0.822633 + 1.42484i
\(386\) 2.33585e6 + 478530.i 0.797951 + 0.163471i
\(387\) 0 0
\(388\) 1.64440e6 + 703272.i 0.554534 + 0.237161i
\(389\) −3.99038e6 + 2.30384e6i −1.33703 + 0.771932i −0.986365 0.164570i \(-0.947376\pi\)
−0.350660 + 0.936503i \(0.614043\pi\)
\(390\) 0 0
\(391\) −116867. 67473.0i −0.0386589 0.0223197i
\(392\) 4.74441e6 2.23934e6i 1.55943 0.736046i
\(393\) 0 0
\(394\) −4.27212e6 + 1.42300e6i −1.38644 + 0.461810i
\(395\) −2.86130e6 −0.922720
\(396\) 0 0
\(397\) −1.37551e6 −0.438012 −0.219006 0.975723i \(-0.570281\pi\)
−0.219006 + 0.975723i \(0.570281\pi\)
\(398\) 5.95581e6 1.98382e6i 1.88466 0.627760i
\(399\) 0 0
\(400\) 502671. 122440.i 0.157085 0.0382626i
\(401\) −93720.9 54109.8i −0.0291055 0.0168041i 0.485377 0.874305i \(-0.338682\pi\)
−0.514482 + 0.857501i \(0.672016\pi\)
\(402\) 0 0
\(403\) −1.11264e6 + 642385.i −0.341266 + 0.197030i
\(404\) 1.15275e6 2.69538e6i 0.351384 0.821611i
\(405\) 0 0
\(406\) 524296. + 107409.i 0.157856 + 0.0323390i
\(407\) 2.05197e6 + 3.55411e6i 0.614022 + 1.06352i
\(408\) 0 0
\(409\) −903457. + 1.56483e6i −0.267054 + 0.462551i −0.968100 0.250565i \(-0.919384\pi\)
0.701046 + 0.713116i \(0.252717\pi\)
\(410\) 2.08155e6 2.34635e6i 0.611543 0.689339i
\(411\) 0 0
\(412\) 3.35644e6 402890.i 0.974173 0.116935i
\(413\) 729546.i 0.210464i
\(414\) 0 0
\(415\) 796039.i 0.226889i
\(416\) −2.18254e6 + 4.12416e6i −0.618341 + 1.16843i
\(417\) 0 0
\(418\) 1.84299e6 + 1.63500e6i 0.515921 + 0.457696i
\(419\) −926212. + 1.60425e6i −0.257736 + 0.446412i −0.965635 0.259902i \(-0.916310\pi\)
0.707899 + 0.706314i \(0.249643\pi\)
\(420\) 0 0
\(421\) 1.85582e6 + 3.21437e6i 0.510305 + 0.883874i 0.999929 + 0.0119403i \(0.00380082\pi\)
−0.489624 + 0.871934i \(0.662866\pi\)
\(422\) 235278. 1.14846e6i 0.0643133 0.313932i
\(423\) 0 0
\(424\) 2.08463e6 3.00689e6i 0.563137 0.812276i
\(425\) 14907.6 8606.90i 0.00400346 0.00231140i
\(426\) 0 0
\(427\) 7.38295e6 + 4.26255e6i 1.95957 + 1.13136i
\(428\) −97481.6 + 73044.4i −0.0257225 + 0.0192742i
\(429\) 0 0
\(430\) −132007. 396310.i −0.0344290 0.103363i
\(431\) 277886. 0.0720565 0.0360283 0.999351i \(-0.488529\pi\)
0.0360283 + 0.999351i \(0.488529\pi\)
\(432\) 0 0
\(433\) −2.49224e6 −0.638807 −0.319403 0.947619i \(-0.603482\pi\)
−0.319403 + 0.947619i \(0.603482\pi\)
\(434\) −610127. 1.83172e6i −0.155488 0.466805i
\(435\) 0 0
\(436\) 2.18053e6 1.63390e6i 0.549347 0.411633i
\(437\) −4.02522e6 2.32396e6i −1.00829 0.582138i
\(438\) 0 0
\(439\) −1.04465e6 + 603126.i −0.258707 + 0.149364i −0.623744 0.781628i \(-0.714389\pi\)
0.365038 + 0.930993i \(0.381056\pi\)
\(440\) 2.30631e6 3.32665e6i 0.567918 0.819172i
\(441\) 0 0
\(442\) −31157.6 + 152090.i −0.00758593 + 0.0370292i
\(443\) −1.30812e6 2.26572e6i −0.316692 0.548526i 0.663104 0.748527i \(-0.269239\pi\)
−0.979796 + 0.200001i \(0.935905\pi\)
\(444\) 0 0
\(445\) 2.58124e6 4.47084e6i 0.617914 1.07026i
\(446\) 2.72453e6 + 2.41705e6i 0.648566 + 0.575371i
\(447\) 0 0
\(448\) −5.41316e6 4.45684e6i −1.27425 1.04914i
\(449\) 348912.i 0.0816770i −0.999166 0.0408385i \(-0.986997\pi\)
0.999166 0.0408385i \(-0.0130029\pi\)
\(450\) 0 0
\(451\) 3.41549e6i 0.790701i
\(452\) −1.34841e6 + 161856.i −0.310440 + 0.0372635i
\(453\) 0 0
\(454\) −4.47733e6 + 5.04690e6i −1.01948 + 1.14917i
\(455\) −5.19272e6 + 8.99405e6i −1.17589 + 2.03670i
\(456\) 0 0
\(457\) 1.71163e6 + 2.96463e6i 0.383371 + 0.664018i 0.991542 0.129788i \(-0.0414297\pi\)
−0.608171 + 0.793806i \(0.708096\pi\)
\(458\) −5.96550e6 1.22211e6i −1.32887 0.272238i
\(459\) 0 0
\(460\) −3.00291e6 + 7.02144e6i −0.661679 + 1.54715i
\(461\) −4.70141e6 + 2.71436e6i −1.03033 + 0.594861i −0.917079 0.398705i \(-0.869460\pi\)
−0.113251 + 0.993566i \(0.536126\pi\)
\(462\) 0 0
\(463\) −3.74259e6 2.16079e6i −0.811373 0.468446i 0.0360597 0.999350i \(-0.488519\pi\)
−0.847432 + 0.530903i \(0.821853\pi\)
\(464\) −107145. 439877.i −0.0231034 0.0948499i
\(465\) 0 0
\(466\) 956214. 318505.i 0.203981 0.0679440i
\(467\) 3.41339e6 0.724258 0.362129 0.932128i \(-0.382050\pi\)
0.362129 + 0.932128i \(0.382050\pi\)
\(468\) 0 0
\(469\) −1.50432e6 −0.315798
\(470\) 790736. 263386.i 0.165115 0.0549981i
\(471\) 0 0
\(472\) −558113. + 263427.i −0.115310 + 0.0544258i
\(473\) −393921. 227430.i −0.0809572 0.0467407i
\(474\) 0 0
\(475\) 513459. 296446.i 0.104417 0.0602853i
\(476\) −214503. 91737.8i −0.0433926 0.0185580i
\(477\) 0 0
\(478\) 3.73374e6 + 764908.i 0.747437 + 0.153123i
\(479\) −1.30808e6 2.26567e6i −0.260493 0.451188i 0.705880 0.708332i \(-0.250552\pi\)
−0.966373 + 0.257144i \(0.917219\pi\)
\(480\) 0 0
\(481\) −4.45356e6 + 7.71378e6i −0.877696 + 1.52021i
\(482\) −1.22371e6 + 1.37938e6i −0.239917 + 0.270438i
\(483\) 0 0
\(484\) 88880.9 + 740460.i 0.0172463 + 0.143677i
\(485\) 3.36745e6i 0.650050i
\(486\) 0 0
\(487\) 8.58357e6i 1.64001i −0.572359 0.820003i \(-0.693971\pi\)
0.572359 0.820003i \(-0.306029\pi\)
\(488\) 595049. 7.18719e6i 0.113111 1.36619i
\(489\) 0 0
\(490\) −7.38940e6 6.55546e6i −1.39033 1.23342i
\(491\) 4.45187e6 7.71087e6i 0.833372 1.44344i −0.0619764 0.998078i \(-0.519740\pi\)
0.895349 0.445366i \(-0.146926\pi\)
\(492\) 0 0
\(493\) −7531.72 13045.3i −0.00139565 0.00241734i
\(494\) −1.07316e6 + 5.23840e6i −0.197855 + 0.965787i
\(495\) 0 0
\(496\) −1.18099e6 + 1.12816e6i −0.215546 + 0.205905i
\(497\) −4.76152e6 + 2.74906e6i −0.864678 + 0.499222i
\(498\) 0 0
\(499\) 9.00734e6 + 5.20039e6i 1.61937 + 0.934942i 0.987084 + 0.160205i \(0.0512156\pi\)
0.632284 + 0.774737i \(0.282118\pi\)
\(500\) 3.02884e6 + 4.04214e6i 0.541815 + 0.723081i
\(501\) 0 0
\(502\) −2.36169e6 7.09026e6i −0.418277 1.25575i
\(503\) 3.07909e6 0.542628 0.271314 0.962491i \(-0.412542\pi\)
0.271314 + 0.962491i \(0.412542\pi\)
\(504\) 0 0
\(505\) −5.51967e6 −0.963129
\(506\) 2.62791e6 + 7.88952e6i 0.456284 + 1.36985i
\(507\) 0 0
\(508\) 711497. + 949531.i 0.122325 + 0.163249i
\(509\) 8.39198e6 + 4.84511e6i 1.43572 + 0.828914i 0.997549 0.0699775i \(-0.0222928\pi\)
0.438172 + 0.898891i \(0.355626\pi\)
\(510\) 0 0
\(511\) −1.21255e7 + 7.00067e6i −2.05422 + 1.18601i
\(512\) −1.45494e6 + 5.75044e6i −0.245285 + 0.969451i
\(513\) 0 0
\(514\) 1.51550e6 7.39762e6i 0.253017 1.23505i
\(515\) −3.18254e6 5.51232e6i −0.528756 0.915832i
\(516\) 0 0
\(517\) 453779. 785968.i 0.0746651 0.129324i
\(518\) −1.00127e7 8.88273e6i −1.63956 1.45453i
\(519\) 0 0
\(520\) 8.75558e6 + 724901.i 1.41996 + 0.117563i
\(521\) 7.69134e6i 1.24139i 0.784053 + 0.620694i \(0.213149\pi\)
−0.784053 + 0.620694i \(0.786851\pi\)
\(522\) 0 0
\(523\) 1.02773e6i 0.164295i −0.996620 0.0821476i \(-0.973822\pi\)
0.996620 0.0821476i \(-0.0261779\pi\)
\(524\) −638653. 5.32057e6i −0.101610 0.846505i
\(525\) 0 0
\(526\) 3.43312e6 3.86985e6i 0.541034 0.609860i
\(527\) −27170.5 + 47060.6i −0.00426158 + 0.00738127i
\(528\) 0 0
\(529\) −4.62582e6 8.01216e6i −0.718704 1.24483i
\(530\) −6.74890e6 1.38261e6i −1.04362 0.213800i
\(531\) 0 0
\(532\) −7.38808e6 3.15971e6i −1.13176 0.484025i
\(533\) 6.41979e6 3.70647e6i 0.978820 0.565122i
\(534\) 0 0
\(535\) 198627. + 114677.i 0.0300023 + 0.0173218i
\(536\) 543186. + 1.15083e6i 0.0816651 + 0.173021i
\(537\) 0 0
\(538\) 9.99474e6 3.32914e6i 1.48873 0.495880i
\(539\) −1.07565e7 −1.59477
\(540\) 0 0
\(541\) 9.97892e6 1.46585 0.732926 0.680308i \(-0.238154\pi\)
0.732926 + 0.680308i \(0.238154\pi\)
\(542\) −2.77877e6 + 925579.i −0.406307 + 0.135337i
\(543\) 0 0
\(544\) 7272.63 + 197223.i 0.00105365 + 0.0285732i
\(545\) −4.44302e6 2.56518e6i −0.640748 0.369936i
\(546\) 0 0
\(547\) 6.89166e6 3.97890e6i 0.984817 0.568584i 0.0810959 0.996706i \(-0.474158\pi\)
0.903721 + 0.428122i \(0.140825\pi\)
\(548\) 4.33025e6 1.01251e7i 0.615973 1.44028i
\(549\) 0 0
\(550\) −1.03917e6 212888.i −0.146480 0.0300085i
\(551\) −259414. 449318.i −0.0364011 0.0630485i
\(552\) 0 0
\(553\) 5.08097e6 8.80049e6i 0.706535 1.22375i
\(554\) −2.34165e6 + 2.63954e6i −0.324152 + 0.365388i
\(555\) 0 0
\(556\) 8.77310e6 1.05308e6i 1.20355 0.144468i
\(557\) 968143.i 0.132221i −0.997812 0.0661107i \(-0.978941\pi\)
0.997812 0.0661107i \(-0.0210590\pi\)
\(558\) 0 0
\(559\) 987222.i 0.133624i
\(560\) −3.70777e6 + 1.26709e7i −0.499624 + 1.70741i
\(561\) 0 0
\(562\) −7.48936e6 6.64414e6i −1.00024 0.887356i
\(563\) 3.58742e6 6.21360e6i 0.476993 0.826176i −0.522660 0.852541i \(-0.675060\pi\)
0.999652 + 0.0263657i \(0.00839345\pi\)
\(564\) 0 0
\(565\) 1.27855e6 + 2.21451e6i 0.168499 + 0.291848i
\(566\) −1.68657e6 + 8.23263e6i −0.221290 + 1.08018i
\(567\) 0 0
\(568\) 3.82238e6 + 2.64999e6i 0.497121 + 0.344646i
\(569\) 1.01785e7 5.87656e6i 1.31796 0.760926i 0.334561 0.942374i \(-0.391412\pi\)
0.983400 + 0.181448i \(0.0580785\pi\)
\(570\) 0 0
\(571\) −9.11184e6 5.26072e6i −1.16954 0.675235i −0.215970 0.976400i \(-0.569291\pi\)
−0.953572 + 0.301165i \(0.902625\pi\)
\(572\) 7.65592e6 5.73669e6i 0.978379 0.733113i
\(573\) 0 0
\(574\) 3.52034e6 + 1.05688e7i 0.445970 + 1.33889i
\(575\) 2.00117e6 0.252414
\(576\) 0 0
\(577\) 1.46593e6 0.183305 0.0916526 0.995791i \(-0.470785\pi\)
0.0916526 + 0.995791i \(0.470785\pi\)
\(578\) −2.53617e6 7.61408e6i −0.315761 0.947977i
\(579\) 0 0
\(580\) −682179. + 511166.i −0.0842031 + 0.0630946i
\(581\) −2.44838e6 1.41357e6i −0.300911 0.173731i
\(582\) 0 0
\(583\) −6.49662e6 + 3.75082e6i −0.791618 + 0.457041i
\(584\) 9.73392e6 + 6.74836e6i 1.18102 + 0.818778i
\(585\) 0 0
\(586\) −1.84576e6 + 9.00970e6i −0.222040 + 1.08384i
\(587\) 523994. + 907585.i 0.0627670 + 0.108716i 0.895701 0.444656i \(-0.146674\pi\)
−0.832934 + 0.553372i \(0.813341\pi\)
\(588\) 0 0
\(589\) −935827. + 1.62090e6i −0.111150 + 0.192517i
\(590\) 869259. + 771157.i 0.102806 + 0.0912038i
\(591\) 0 0
\(592\) −3.17998e6 + 1.08673e7i −0.372924 + 1.27443i
\(593\) 8.50755e6i 0.993500i −0.867894 0.496750i \(-0.834527\pi\)
0.867894 0.496750i \(-0.165473\pi\)
\(594\) 0 0
\(595\) 439264.i 0.0508667i
\(596\) 1.24367e6 149284.i 0.143414 0.0172146i
\(597\) 0 0
\(598\) −1.19774e7 + 1.35011e7i −1.36965 + 1.54389i
\(599\) −4.39728e6 + 7.61632e6i −0.500746 + 0.867317i 0.499254 + 0.866456i \(0.333608\pi\)
−1.00000 0.000861327i \(0.999726\pi\)
\(600\) 0 0
\(601\) −2.32237e6 4.02246e6i −0.262268 0.454261i 0.704576 0.709628i \(-0.251137\pi\)
−0.966844 + 0.255367i \(0.917804\pi\)
\(602\) 1.45334e6 + 297737.i 0.163447 + 0.0334844i
\(603\) 0 0
\(604\) −5.40908e6 + 1.26476e7i −0.603297 + 1.41064i
\(605\) 1.21606e6 702095.i 0.135073 0.0779843i
\(606\) 0 0
\(607\) 1.45173e6 + 838155.i 0.159924 + 0.0923320i 0.577826 0.816160i \(-0.303901\pi\)
−0.417902 + 0.908492i \(0.637235\pi\)
\(608\) 250490. + 6.79290e6i 0.0274809 + 0.745241i
\(609\) 0 0
\(610\) −1.28829e7 + 4.29115e6i −1.40181 + 0.466928i
\(611\) 1.96975e6 0.213456
\(612\) 0 0
\(613\) 615822. 0.0661918 0.0330959 0.999452i \(-0.489463\pi\)
0.0330959 + 0.999452i \(0.489463\pi\)
\(614\) −160637. + 53506.4i −0.0171959 + 0.00572776i
\(615\) 0 0
\(616\) 6.13633e6 + 1.30008e7i 0.651564 + 1.38045i
\(617\) 3.65601e6 + 2.11080e6i 0.386629 + 0.223220i 0.680698 0.732564i \(-0.261676\pi\)
−0.294070 + 0.955784i \(0.595010\pi\)
\(618\) 0 0
\(619\) 1.47506e7 8.51629e6i 1.54733 0.893354i 0.548991 0.835829i \(-0.315012\pi\)
0.998344 0.0575254i \(-0.0183210\pi\)
\(620\) 2.82744e6 + 1.20923e6i 0.295402 + 0.126337i
\(621\) 0 0
\(622\) 9.18191e6 + 1.88104e6i 0.951606 + 0.194950i
\(623\) 9.16731e6 + 1.58782e7i 0.946285 + 1.63901i
\(624\) 0 0
\(625\) 5.54462e6 9.60356e6i 0.567769 0.983405i
\(626\) −1.12109e7 + 1.26371e7i −1.14342 + 1.28888i
\(627\) 0 0
\(628\) −2.16230e6 1.80139e7i −0.218785 1.82268i
\(629\) 376737.i 0.0379674i
\(630\) 0 0
\(631\) 1.01556e7i 1.01539i 0.861538 + 0.507693i \(0.169502\pi\)
−0.861538 + 0.507693i \(0.830498\pi\)
\(632\) −8.56715e6 709300.i −0.853186 0.0706378i
\(633\) 0 0
\(634\) 3.65571e6 + 3.24314e6i 0.361200 + 0.320437i
\(635\) 1.11703e6 1.93475e6i 0.109933 0.190410i
\(636\) 0 0
\(637\) −1.16728e7 2.02180e7i −1.13980 1.97419i
\(638\) −186294. + 909356.i −0.0181195 + 0.0884468i
\(639\) 0 0
\(640\) 1.10323e7 1.73877e6i 1.06467 0.167800i
\(641\) 1.77251e7 1.02336e7i 1.70389 0.983744i 0.762160 0.647389i \(-0.224139\pi\)
0.941735 0.336355i \(-0.109194\pi\)
\(642\) 0 0
\(643\) 1.99881e6 + 1.15401e6i 0.190653 + 0.110074i 0.592288 0.805726i \(-0.298225\pi\)
−0.401635 + 0.915800i \(0.631558\pi\)
\(644\) −1.62634e7 2.17044e7i −1.54524 2.06221i
\(645\) 0 0
\(646\) 71472.8 + 214576.i 0.00673845 + 0.0202301i
\(647\) 4.18696e6 0.393222 0.196611 0.980482i \(-0.437006\pi\)
0.196611 + 0.980482i \(0.437006\pi\)
\(648\) 0 0
\(649\) 1.26535e6 0.117923
\(650\) −727552. 2.18426e6i −0.0675431 0.202778i
\(651\) 0 0
\(652\) −969906. 1.29439e6i −0.0893533 0.119247i
\(653\) 1.70167e6 + 982460.i 0.156168 + 0.0901638i 0.576048 0.817416i \(-0.304594\pi\)
−0.419879 + 0.907580i \(0.637928\pi\)
\(654\) 0 0
\(655\) −8.73801e6 + 5.04489e6i −0.795810 + 0.459461i
\(656\) 6.81412e6 6.50932e6i 0.618230 0.590576i
\(657\) 0 0
\(658\) −594059. + 2.89978e6i −0.0534890 + 0.261096i
\(659\) −2.30212e6 3.98739e6i −0.206497 0.357664i 0.744111 0.668056i \(-0.232873\pi\)
−0.950609 + 0.310391i \(0.899540\pi\)
\(660\) 0 0
\(661\) −2.73544e6 + 4.73792e6i −0.243514 + 0.421778i −0.961713 0.274060i \(-0.911633\pi\)
0.718199 + 0.695838i \(0.244967\pi\)
\(662\) −8936.09 7927.60i −0.000792506 0.000703067i
\(663\) 0 0
\(664\) −197334. + 2.38346e6i −0.0173693 + 0.209791i
\(665\) 1.51295e7i 1.32669i
\(666\) 0 0
\(667\) 1.75118e6i 0.152411i
\(668\) 1.18285e6 + 9.85423e6i 0.102562 + 0.854440i
\(669\) 0 0
\(670\) 1.59013e6 1.79241e6i 0.136850 0.154259i
\(671\) −7.39309e6 + 1.28052e7i −0.633899 + 1.09795i
\(672\) 0 0
\(673\) 1.03102e7 + 1.78577e7i 0.877460 + 1.51981i 0.854119 + 0.520078i \(0.174097\pi\)
0.0233415 + 0.999728i \(0.492569\pi\)
\(674\) 1.37903e7 + 2.82513e6i 1.16930 + 0.239546i
\(675\) 0 0
\(676\) 8.16662e6 + 3.49267e6i 0.687346 + 0.293962i
\(677\) −2.59618e6 + 1.49891e6i −0.217702 + 0.125691i −0.604886 0.796312i \(-0.706781\pi\)
0.387184 + 0.922003i \(0.373448\pi\)
\(678\) 0 0
\(679\) 1.03573e7 + 5.97977e6i 0.862126 + 0.497749i
\(680\) 336043. 158611.i 0.0278691 0.0131541i
\(681\) 0 0
\(682\) 3.17700e6 1.05822e6i 0.261551 0.0871198i
\(683\) 3.24667e6 0.266310 0.133155 0.991095i \(-0.457489\pi\)
0.133155 + 0.991095i \(0.457489\pi\)
\(684\) 0 0
\(685\) −2.07344e7 −1.68836
\(686\) 1.39825e7 4.65743e6i 1.13442 0.377864i
\(687\) 0 0
\(688\) −297005. 1.21934e6i −0.0239217 0.0982092i
\(689\) −1.41002e7 8.14073e6i −1.13156 0.653304i
\(690\) 0 0
\(691\) −1.27793e7 + 7.37815e6i −1.01815 + 0.587831i −0.913568 0.406685i \(-0.866685\pi\)
−0.104584 + 0.994516i \(0.533351\pi\)
\(692\) −2.04169e6 + 4.77390e6i −0.162078 + 0.378973i
\(693\) 0 0
\(694\) −1.83493e7 3.75911e6i −1.44618 0.296269i
\(695\) −8.31854e6 1.44081e7i −0.653259 1.13148i
\(696\) 0 0
\(697\) 156769. 271533.i 0.0122230 0.0211709i
\(698\) −987361. + 1.11297e6i −0.0767074 + 0.0864656i
\(699\) 0 0
\(700\) 3.43499e6 412318.i 0.264960 0.0318044i
\(701\) 571089.i 0.0438944i −0.999759 0.0219472i \(-0.993013\pi\)
0.999759 0.0219472i \(-0.00698656\pi\)
\(702\) 0 0
\(703\) 1.29759e7i 0.990259i
\(704\) 7.73009e6 9.38876e6i 0.587831 0.713965i
\(705\) 0 0
\(706\) 624836. + 554319.i 0.0471796 + 0.0418551i
\(707\) 9.80159e6 1.69769e7i 0.737476 1.27735i
\(708\) 0 0
\(709\) 9.31781e6 + 1.61389e7i 0.696143 + 1.20576i 0.969794 + 0.243926i \(0.0784354\pi\)
−0.273651 + 0.961829i \(0.588231\pi\)
\(710\) 1.75757e6 8.57924e6i 0.130848 0.638709i
\(711\) 0 0
\(712\) 8.83692e6 1.27465e7i 0.653282 0.942303i
\(713\) −5.47097e6 + 3.15867e6i −0.403033 + 0.232691i
\(714\) 0 0
\(715\) −1.55996e7 9.00642e6i −1.14116 0.658851i
\(716\) −8.02096e6 + 6.01022e6i −0.584715 + 0.438135i
\(717\) 0 0
\(718\) −2.62320e6 7.87535e6i −0.189898 0.570110i
\(719\) −7.72155e6 −0.557035 −0.278517 0.960431i \(-0.589843\pi\)
−0.278517 + 0.960431i \(0.589843\pi\)
\(720\) 0 0
\(721\) 2.26057e7 1.61949
\(722\) −1.96474e6 5.89852e6i −0.140269 0.421115i
\(723\) 0 0
\(724\) −6.18223e6 + 4.63243e6i −0.438328 + 0.328445i
\(725\) 193454. + 111691.i 0.0136689 + 0.00789173i
\(726\) 0 0
\(727\) 1.28498e7 7.41886e6i 0.901700 0.520596i 0.0239484 0.999713i \(-0.492376\pi\)
0.877751 + 0.479117i \(0.159043\pi\)
\(728\) −1.77774e7 + 2.56423e7i −1.24319 + 1.79320i
\(729\) 0 0
\(730\) 4.47577e6 2.18476e7i 0.310857 1.51739i
\(731\) −20877.9 36161.5i −0.00144508 0.00250296i
\(732\) 0 0
\(733\) −1.71343e6 + 2.96776e6i −0.117790 + 0.204018i −0.918891 0.394510i \(-0.870914\pi\)
0.801102 + 0.598528i \(0.204248\pi\)
\(734\) 8.62225e6 + 7.64917e6i 0.590718 + 0.524052i
\(735\) 0 0
\(736\) −1.07317e7 + 2.02788e7i −0.730256 + 1.37990i
\(737\) 2.60915e6i 0.176942i
\(738\) 0 0
\(739\) 1.26632e7i 0.852970i −0.904495 0.426485i \(-0.859752\pi\)
0.904495 0.426485i \(-0.140248\pi\)
\(740\) 2.11677e7 2.54085e6i 1.42100 0.170569i
\(741\) 0 0
\(742\) 1.62369e7 1.83025e7i 1.08266 1.22039i
\(743\) −6.02221e6 + 1.04308e7i −0.400206 + 0.693178i −0.993751 0.111624i \(-0.964395\pi\)
0.593544 + 0.804801i \(0.297728\pi\)
\(744\) 0 0
\(745\) −1.17924e6 2.04250e6i −0.0778413 0.134825i
\(746\) −6.97165e6 1.42824e6i −0.458658 0.0939623i
\(747\) 0 0
\(748\) 159113. 372040.i 0.0103980 0.0243129i
\(749\) −705427. + 407278.i −0.0459460 + 0.0265269i
\(750\) 0 0
\(751\) −1.01719e7 5.87273e6i −0.658114 0.379962i 0.133444 0.991056i \(-0.457396\pi\)
−0.791558 + 0.611094i \(0.790730\pi\)
\(752\) 2.43287e6 592597.i 0.156883 0.0382133i
\(753\) 0 0
\(754\) −1.91140e6 + 636666.i −0.122440 + 0.0407834i
\(755\) 2.59001e7 1.65361
\(756\) 0 0
\(757\) 5.08821e6 0.322719 0.161360 0.986896i \(-0.448412\pi\)
0.161360 + 0.986896i \(0.448412\pi\)
\(758\) −1.88895e7 + 6.29189e6i −1.19412 + 0.397748i
\(759\) 0 0
\(760\) 1.15743e7 5.46301e6i 0.726876 0.343082i
\(761\) 6.60390e6 + 3.81276e6i 0.413370 + 0.238659i 0.692237 0.721671i \(-0.256625\pi\)
−0.278867 + 0.960330i \(0.589959\pi\)
\(762\) 0 0
\(763\) 1.57795e7 9.11027e6i 0.981252 0.566526i
\(764\) −2.22478e7 9.51485e6i −1.37896 0.589751i
\(765\) 0 0
\(766\) −1.61048e7 3.29930e6i −0.991709 0.203165i
\(767\) 1.37315e6 + 2.37836e6i 0.0842808 + 0.145979i
\(768\) 0 0
\(769\) 8.36212e6 1.44836e7i 0.509918 0.883205i −0.490016 0.871714i \(-0.663009\pi\)
0.999934 0.0114909i \(-0.00365776\pi\)
\(770\) 1.79635e7 2.02487e7i 1.09186 1.23075i
\(771\) 0 0
\(772\) −1.60749e6 1.33918e7i −0.0970742 0.808718i
\(773\) 610007.i 0.0367186i 0.999831 + 0.0183593i \(0.00584428\pi\)
−0.999831 + 0.0183593i \(0.994156\pi\)
\(774\) 0 0
\(775\) 805843.i 0.0481943i