Properties

Label 108.6.h.a.35.11
Level 108
Weight 6
Character 108.35
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 35.11
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.11

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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 0.0455230 0.998963i \(-0.485505\pi\)
0.887889 + 0.460058i \(0.152171\pi\)
\(6\) 0 0
\(7\) −185.316 106.992i −1.42944 0.825290i −0.432367 0.901698i \(-0.642321\pi\)
−0.997077 + 0.0764081i \(0.975655\pi\)
\(8\) 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 −0.999080 0.0428745i \(-0.986348\pi\)
0.536671 + 0.843792i \(0.319682\pi\)
\(12\) 0 0
\(13\) 402.759 + 697.599i 0.660978 + 1.14485i 0.980359 + 0.197221i \(0.0631917\pi\)
−0.319381 + 0.947626i \(0.603475\pi\)
\(14\) 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 \(0.00455082\pi\)
−0.999898 + 0.0142963i \(0.995449\pi\)
\(18\) 0 0
\(19\) 1173.48i 0.745747i 0.927882 + 0.372874i \(0.121627\pi\)
−0.927882 + 0.372874i \(0.878373\pi\)
\(20\) −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 0.931587 + 0.363519i \(0.118425\pi\)
−0.150977 + 0.988537i \(0.548242\pi\)
\(24\) 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 0.541676 0.840587i \(-0.317790\pi\)
−0.457132 + 0.889399i \(0.651123\pi\)
\(30\) 0 0
\(31\) −1381.28 + 797.481i −0.258153 + 0.149045i −0.623492 0.781830i \(-0.714286\pi\)
0.365339 + 0.930875i \(0.380953\pi\)
\(32\) −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 −0.0817937 0.996649i \(-0.526065\pi\)
0.822227 + 0.569160i \(0.192732\pi\)
\(42\) 0 0
\(43\) 1061.38 + 612.787i 0.0875384 + 0.0505403i 0.543130 0.839648i \(-0.317239\pi\)
−0.455592 + 0.890189i \(0.650572\pi\)
\(44\) 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 −0.822831 0.568286i \(-0.807607\pi\)
0.903566 + 0.428449i \(0.140940\pi\)
\(48\) 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 \(0.164537\pi\)
−0.869351 + 0.494195i \(0.835463\pi\)
\(54\) 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 0.832386 0.554196i \(-0.186974\pi\)
−0.896141 + 0.443770i \(0.853641\pi\)
\(60\) 0 0
\(61\) −19919.9 + 34502.3i −0.685430 + 1.18720i 0.287872 + 0.957669i \(0.407052\pi\)
−0.973302 + 0.229530i \(0.926281\pi\)
\(62\) −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 −0.414861 0.909885i \(-0.636170\pi\)
0.580553 + 0.814222i \(0.302836\pi\)
\(68\) 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 0.0811725 0.996700i \(-0.474134\pi\)
−0.822581 + 0.568647i \(0.807467\pi\)
\(80\) 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 −0.808588 0.588376i \(-0.799768\pi\)
0.913842 + 0.406069i \(0.133101\pi\)
\(84\) 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 \(0.194339\pi\)
−0.819342 + 0.573305i \(0.805661\pi\)
\(90\) 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 −0.976490 0.215565i \(-0.930841\pi\)
0.674929 + 0.737882i \(0.264174\pi\)
\(98\) −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 0.0603784 0.998176i \(-0.480769\pi\)
−0.834256 + 0.551377i \(0.814103\pi\)
\(102\) 0 0
\(103\) −91488.4 + 52820.9i −0.849715 + 0.490583i −0.860555 0.509358i \(-0.829883\pi\)
0.0108398 + 0.999941i \(0.496550\pi\)
\(104\) 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 −0.358463 0.933544i \(-0.616699\pi\)
0.629241 + 0.777210i \(0.283366\pi\)
\(114\) 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 \(0.0325232\pi\)
−0.994785 + 0.101997i \(0.967477\pi\)
\(128\) 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 0.570249 0.821472i \(-0.306847\pi\)
−0.996540 + 0.0831144i \(0.973513\pi\)
\(132\) 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 −0.367438 0.930048i \(-0.619765\pi\)
−0.989164 + 0.146814i \(0.953098\pi\)
\(138\) 0 0
\(139\) −239133. + 138064.i −1.04979 + 0.606097i −0.922591 0.385780i \(-0.873932\pi\)
−0.127200 + 0.991877i \(0.540599\pi\)
\(140\) 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 −0.561240 0.827653i \(-0.689676\pi\)
0.436149 + 0.899875i \(0.356342\pi\)
\(150\) 0 0
\(151\) 372275. + 214933.i 1.32868 + 0.767115i 0.985096 0.172006i \(-0.0550247\pi\)
0.343587 + 0.939121i \(0.388358\pi\)
\(152\) 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 −0.802628 0.596479i \(-0.796566\pi\)
−0.115252 0.993336i \(-0.536768\pi\)
\(158\) 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 \(-0.976262\pi\)
0.997221 0.0745047i \(-0.0237376\pi\)
\(164\) −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 0.996898 0.0787068i \(-0.0250791\pi\)
−0.566611 + 0.823985i \(0.691746\pi\)
\(168\) 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 0.667744 0.744391i \(-0.267260\pi\)
−0.310789 + 0.950479i \(0.600593\pi\)
\(174\) 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 −0.197983 0.980205i \(-0.563439\pi\)
0.947874 0.318644i \(-0.103227\pi\)
\(192\) 0 0
\(193\) −210750. 365029.i −0.407262 0.705398i 0.587320 0.809355i \(-0.300183\pi\)
−0.994582 + 0.103957i \(0.966850\pi\)
\(194\) −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 \(0.260791\pi\)
−0.682734 + 0.730667i \(0.739209\pi\)
\(198\) 0 0
\(199\) 1.10972e6i 1.98646i −0.116163 0.993230i \(-0.537060\pi\)
0.116163 0.993230i \(-0.462940\pi\)
\(200\) −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 −0.354780 0.934950i \(-0.615444\pi\)
0.632300 + 0.774724i \(0.282111\pi\)
\(212\) 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 0.0751547 0.997172i \(-0.476055\pi\)
−0.825999 + 0.563672i \(0.809388\pi\)
\(224\) 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 0.170485 + 0.985360i \(0.445467\pi\)
−0.938589 + 0.345036i \(0.887867\pi\)
\(228\) 0 0
\(229\) 538232. + 932245.i 0.678236 + 1.17474i 0.975512 + 0.219947i \(0.0705886\pi\)
−0.297276 + 0.954792i \(0.596078\pi\)
\(230\) −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 \(-0.965716\pi\)
0.994205 0.107500i \(-0.0342845\pi\)
\(234\) 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 0.609794 0.792560i \(-0.291252\pi\)
−0.991274 + 0.131817i \(0.957919\pi\)
\(240\) 0 0
\(241\) −162984. + 282297.i −0.180760 + 0.313086i −0.942140 0.335221i \(-0.891189\pi\)
0.761379 + 0.648307i \(0.224522\pi\)
\(242\) −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 0.157744 0.987480i \(-0.449578\pi\)
0.934055 + 0.357130i \(0.116245\pi\)
\(258\) 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 −0.586994 0.809591i \(-0.699689\pi\)
0.994624 + 0.103556i \(0.0330222\pi\)
\(264\) 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 \(-0.712883\pi\)
0.620038 0.784572i \(-0.287117\pi\)
\(270\) 0 0
\(271\) 517756.i 0.428254i 0.976806 + 0.214127i \(0.0686907\pi\)
−0.976806 + 0.214127i \(0.931309\pi\)
\(272\) −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 −0.961913 0.273354i \(-0.911867\pi\)
0.717689 + 0.696364i \(0.245200\pi\)
\(278\) −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 0.950818 0.309749i \(-0.100245\pi\)
0.207159 + 0.978307i \(0.433578\pi\)
\(282\) 0 0
\(283\) −1.28654e6 + 742782.i −0.954895 + 0.551309i −0.894598 0.446871i \(-0.852538\pi\)
−0.0602971 + 0.998180i \(0.519205\pi\)
\(284\) −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 −0.895597 0.444867i \(-0.853251\pi\)
−0.0625325 + 0.998043i \(0.519918\pi\)
\(294\) 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 \(0.00288467\pi\)
−0.999959 + 0.00906235i \(0.997115\pi\)
\(308\) −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 0.514180 0.857682i \(-0.328096\pi\)
−0.999865 + 0.0164516i \(0.994763\pi\)
\(312\) 0 0
\(313\) −1.49316e6 + 2.58623e6i −0.861482 + 1.49213i 0.00901652 + 0.999959i \(0.497130\pi\)
−0.870498 + 0.492171i \(0.836203\pi\)
\(314\) 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 0.276129 0.961121i \(-0.410948\pi\)
−0.694290 + 0.719695i \(0.744282\pi\)
\(318\) 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 0.500459 0.865760i \(-0.333165\pi\)
−0.499541 + 0.866290i \(0.666498\pi\)
\(332\) −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 −0.993292 0.115637i \(-0.963109\pi\)
0.396501 0.918034i \(-0.370224\pi\)
\(338\) −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 0.953347 + 0.301877i \(0.0976131\pi\)
−0.215241 + 0.976561i \(0.569054\pi\)
\(348\) 0 0
\(349\) −131505. + 227773.i −0.0577934 + 0.100101i −0.893475 0.449114i \(-0.851740\pi\)
0.835681 + 0.549215i \(0.185073\pi\)
\(350\) −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 0.472441 0.881362i \(-0.343373\pi\)
−0.527061 + 0.849827i \(0.676706\pi\)
\(354\) 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 0.117439 0.993080i \(-0.462532\pi\)
−0.801313 + 0.598245i \(0.795865\pi\)
\(368\) −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 0.959008 0.283378i \(-0.0914551\pi\)
−0.724917 + 0.688837i \(0.758122\pi\)
\(374\) 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 \(0.216662\pi\)
−0.777154 + 0.629310i \(0.783338\pi\)
\(380\) 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 0.999975 + 0.00711941i \(0.00226620\pi\)
−0.493822 + 0.869563i \(0.664400\pi\)
\(384\) 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 −0.350660 0.936503i \(-0.614043\pi\)
−0.986365 + 0.164570i \(0.947376\pi\)
\(390\) 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 −0.514482 0.857501i \(-0.672016\pi\)
0.485377 + 0.874305i \(0.338682\pi\)
\(402\) 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 0.701046 0.713116i \(-0.252717\pi\)
−0.968100 + 0.250565i \(0.919384\pi\)
\(410\) 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 0.707899 0.706314i \(-0.249643\pi\)
−0.965635 + 0.259902i \(0.916310\pi\)
\(420\) 0 0
\(421\) 1.85582e6 3.21437e6i 0.510305 0.883874i −0.489624 0.871934i \(-0.662866\pi\)
0.999929 0.0119403i \(-0.00380082\pi\)
\(422\) 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 0.365038 0.930993i \(-0.381056\pi\)
−0.623744 + 0.781628i \(0.714389\pi\)
\(440\) 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 −0.979796 0.200001i \(-0.935905\pi\)
0.663104 + 0.748527i \(0.269239\pi\)
\(444\) 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 \(0.0130029\pi\)
−0.999166 + 0.0408385i \(0.986997\pi\)
\(450\) 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 −0.608171 0.793806i \(-0.708096\pi\)
0.991542 + 0.129788i \(0.0414297\pi\)
\(458\) −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 −0.113251 0.993566i \(-0.536126\pi\)
−0.917079 + 0.398705i \(0.869460\pi\)
\(462\) 0 0
\(463\) −3.74259e6 + 2.16079e6i −0.811373 + 0.468446i −0.847432 0.530903i \(-0.821853\pi\)
0.0360597 + 0.999350i \(0.488519\pi\)
\(464\) −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 −0.966373 0.257144i \(-0.917219\pi\)
0.705880 + 0.708332i \(0.250552\pi\)
\(480\) 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 \(0.306029\pi\)
−0.572359 + 0.820003i \(0.693971\pi\)
\(488\) 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 0.895349 + 0.445366i \(0.146926\pi\)
−0.0619764 + 0.998078i \(0.519740\pi\)
\(492\) 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 0.632284 0.774737i \(-0.282118\pi\)
0.987084 0.160205i \(-0.0512156\pi\)
\(500\) 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 0.438172 0.898891i \(-0.355626\pi\)
0.997549 + 0.0699775i \(0.0222928\pi\)
\(510\) 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 \(-0.786851\pi\)
0.784053 0.620694i \(-0.213149\pi\)
\(522\) 0 0
\(523\) 1.02773e6i 0.164295i 0.996620 + 0.0821476i \(0.0261779\pi\)
−0.996620 + 0.0821476i \(0.973822\pi\)
\(524\) −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 0.903721 0.428122i \(-0.140825\pi\)
0.0810959 + 0.996706i \(0.474158\pi\)
\(548\) 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 \(0.0210590\pi\)
−0.997812 + 0.0661107i \(0.978941\pi\)
\(558\) 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 0.999652 0.0263657i \(-0.00839345\pi\)
−0.522660 + 0.852541i \(0.675060\pi\)
\(564\) 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 0.983400 0.181448i \(-0.0580785\pi\)
0.334561 + 0.942374i \(0.391412\pi\)
\(570\) 0 0
\(571\) −9.11184e6 + 5.26072e6i −1.16954 + 0.675235i −0.953572 0.301165i \(-0.902625\pi\)
−0.215970 + 0.976400i \(0.569291\pi\)
\(572\) 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 −0.832934 0.553372i \(-0.813341\pi\)
0.895701 + 0.444656i \(0.146674\pi\)
\(588\) 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 \(0.165473\pi\)
−0.867894 + 0.496750i \(0.834527\pi\)
\(594\) 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 −1.00000 0.000861327i \(-0.999726\pi\)
0.499254 0.866456i \(1.66639\pi\)
\(600\) 0 0
\(601\) −2.32237e6 + 4.02246e6i −0.262268 + 0.454261i −0.966844 0.255367i \(-0.917804\pi\)
0.704576 + 0.709628i \(0.251137\pi\)
\(602\) 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 −0.417902 0.908492i \(-0.637235\pi\)
0.577826 + 0.816160i \(0.303901\pi\)
\(608\) 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 −0.294070 0.955784i \(-0.595010\pi\)
0.680698 + 0.732564i \(0.261676\pi\)
\(618\) 0 0
\(619\) 1.47506e7 + 8.51629e6i 1.54733 + 0.893354i 0.998344 + 0.0575254i \(0.0183210\pi\)
0.548991 + 0.835829i \(0.315012\pi\)
\(620\) 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 \(-0.830498\pi\)
0.861538 0.507693i \(-0.169502\pi\)
\(632\) −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 0.941735 + 0.336355i \(0.109194\pi\)
0.762160 + 0.647389i \(0.224139\pi\)
\(642\) 0 0
\(643\) 1.99881e6 1.15401e6i 0.190653 0.110074i −0.401635 0.915800i \(-0.631558\pi\)
0.592288 + 0.805726i \(0.298225\pi\)
\(644\) −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 −0.419879 0.907580i \(-0.637928\pi\)
0.576048 + 0.817416i \(0.304594\pi\)
\(654\) 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 −0.950609 0.310391i \(-0.899540\pi\)
0.744111 + 0.668056i \(0.232873\pi\)
\(660\) 0 0
\(661\) −2.73544e6 4.73792e6i −0.243514 0.421778i 0.718199 0.695838i \(-0.244967\pi\)
−0.961713 + 0.274060i \(0.911633\pi\)
\(662\) −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 0.0233415 0.999728i \(-0.492569\pi\)
0.854119 0.520078i \(-0.174097\pi\)
\(674\) 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 0.387184 0.922003i \(-0.373448\pi\)
−0.604886 + 0.796312i \(0.706781\pi\)
\(678\) 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 −0.104584 0.994516i \(-0.533351\pi\)
−0.913568 + 0.406685i \(0.866685\pi\)
\(692\) −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 \(0.00698656\pi\)
−0.999759 + 0.0219472i \(0.993013\pi\)
\(702\) 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 −0.273651 0.961829i \(-0.588231\pi\)
0.969794 0.243926i \(-0.0784354\pi\)
\(710\) 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 0.877751 0.479117i \(-0.159043\pi\)
0.0239484 + 0.999713i \(0.492376\pi\)
\(728\) −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 0.801102 0.598528i \(-0.204248\pi\)
−0.918891 + 0.394510i \(0.870914\pi\)
\(734\) 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 \(0.140248\pi\)
−0.904495 + 0.426485i \(0.859752\pi\)
\(740\) 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 0.593544 0.804801i \(-0.297728\pi\)
−0.993751 + 0.111624i \(0.964395\pi\)
\(744\) 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 −0.791558 0.611094i \(-0.790730\pi\)
0.133444 + 0.991056i \(0.457396\pi\)
\(752\) 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 −0.278867 0.960330i \(-0.589959\pi\)
0.692237 + 0.721671i \(0.256625\pi\)
\(762\) 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 0.999934 + 0.0114909i \(0.00365776\pi\)
−0.490016 + 0.871714i \(0.663009\pi\)
\(770\) 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 \(-0.994156\pi\)
0.999831 0.0183593i \(-0.00584428\pi\)
\(774\) 0 0
\(775\) 805843.i 0.0481943i
\(776\) 834773. + 1