Properties

Label 108.6.h.a.35.20
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 35.20
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.20

$q$-expansion

\(f(q)\) \(=\) \(q+(3.75408 - 4.23165i) q^{2} +(-3.81374 - 31.7719i) q^{4} +(52.1793 - 30.1257i) q^{5} +(185.316 + 106.992i) q^{7} +(-148.765 - 103.136i) q^{8} +O(q^{10})\) \(q+(3.75408 - 4.23165i) q^{2} +(-3.81374 - 31.7719i) q^{4} +(52.1793 - 30.1257i) q^{5} +(185.316 + 106.992i) q^{7} +(-148.765 - 103.136i) q^{8} +(68.4038 - 333.899i) q^{10} +(185.570 - 321.417i) q^{11} +(402.759 + 697.599i) q^{13} +(1148.44 - 382.534i) q^{14} +(-994.911 + 242.339i) q^{16} +34.0704i q^{17} -1173.48i q^{19} +(-1156.15 - 1542.95i) q^{20} +(-663.480 - 1991.90i) q^{22} +(-1980.40 - 3430.16i) q^{23} +(252.621 - 437.553i) q^{25} +(4463.99 + 914.509i) q^{26} +(2692.60 - 6295.88i) q^{28} +(382.894 + 221.064i) q^{29} +(1381.28 - 797.481i) q^{31} +(-2709.48 + 5119.88i) q^{32} +(144.174 + 127.903i) q^{34} +12892.9 q^{35} -11057.6 q^{37} +(-4965.76 - 4405.34i) q^{38} +(-10869.5 - 899.918i) q^{40} +(7969.76 - 4601.35i) q^{41} +(-1061.38 - 612.787i) q^{43} +(-10919.8 - 4670.13i) q^{44} +(-21949.8 - 4496.72i) q^{46} +(-1222.66 + 2117.71i) q^{47} +(14491.1 + 25099.3i) q^{49} +(-903.210 - 2711.61i) q^{50} +(20628.1 - 15456.9i) q^{52} +20212.4i q^{53} -22361.8i q^{55} +(-16533.7 - 35029.4i) q^{56} +(2372.88 - 790.381i) q^{58} +(1704.67 + 2952.58i) q^{59} +(-19919.9 + 34502.3i) q^{61} +(1810.77 - 8838.89i) q^{62} +(11493.9 + 30686.0i) q^{64} +(42031.4 + 24266.8i) q^{65} +(-6088.22 + 3515.04i) q^{67} +(1082.48 - 129.935i) q^{68} +(48400.9 - 54558.1i) q^{70} -25694.1 q^{71} +65431.6 q^{73} +(-41511.2 + 46792.0i) q^{74} +(-37283.7 + 4475.34i) q^{76} +(68778.2 - 39709.1i) q^{77} +(41126.9 + 23744.6i) q^{79} +(-44613.1 + 42617.5i) q^{80} +(10447.9 - 50999.1i) q^{82} +(-6605.97 + 11441.9i) q^{83} +(1026.39 + 1777.77i) q^{85} +(-6577.60 + 2190.93i) q^{86} +(-60756.1 + 28676.6i) q^{88} +85682.2i q^{89} +172368. i q^{91} +(-101430. + 76003.0i) q^{92} +(4371.44 + 13123.9i) q^{94} +(-35352.0 - 61231.4i) q^{95} +(-27944.9 + 48402.0i) q^{97} +(160612. + 32903.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.75408 4.23165i 0.663634 0.748057i
\(3\) 0 0
\(4\) −3.81374 31.7719i −0.119179 0.992873i
\(5\) 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 0.997077 0.0764081i \(-0.0243452\pi\)
0.432367 + 0.901698i \(0.357679\pi\)
\(8\) −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 \(-0.680318\pi\)
0.999080 + 0.0428745i \(0.0136516\pi\)
\(12\) 0 0
\(13\) 402.759 + 697.599i 0.660978 + 1.14485i 0.980359 + 0.197221i \(0.0631917\pi\)
−0.319381 + 0.947626i \(0.603475\pi\)
\(14\) 1148.44 382.534i 1.56599 0.521615i
\(15\) 0 0
\(16\) −994.911 + 242.339i −0.971593 + 0.236660i
\(17\) 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 \(-0.878373\pi\)
0.927882 0.372874i \(-0.121627\pi\)
\(20\) −1156.15 1542.95i −0.646308 0.862533i
\(21\) 0 0
\(22\) −663.480 1991.90i −0.292261 0.877425i
\(23\) −1980.40 3430.16i −0.780610 1.35206i −0.931587 0.363519i \(-0.881575\pi\)
0.150977 0.988537i \(1.54824\pi\)
\(24\) 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 −0.365339 0.930875i \(-0.619047\pi\)
0.623492 + 0.781830i \(0.285714\pi\)
\(32\) −2709.48 + 5119.88i −0.467747 + 0.883862i
\(33\) 0 0
\(34\) 144.174 + 127.903i 0.0213889 + 0.0189751i
\(35\) 12892.9 1.77901
\(36\) 0 0
\(37\) −11057.6 −1.32787 −0.663937 0.747788i \(-0.731116\pi\)
−0.663937 + 0.747788i \(0.731116\pi\)
\(38\) −4965.76 4405.34i −0.557861 0.494903i
\(39\) 0 0
\(40\) −10869.5 899.918i −1.07414 0.0889310i
\(41\) 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 0.455592 0.890189i \(-0.349428\pi\)
−0.543130 + 0.839648i \(0.682761\pi\)
\(44\) −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 \(-0.859060\pi\)
0.822831 + 0.568286i \(0.192393\pi\)
\(48\) 0 0
\(49\) 14491.1 + 25099.3i 0.862206 + 1.49338i
\(50\) −903.210 2711.61i −0.0510933 0.153392i
\(51\) 0 0
\(52\) 20628.1 15456.9i 1.05791 0.792709i
\(53\) 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
\(56\) −16533.7 35029.4i −0.704531 1.49266i
\(57\) 0 0
\(58\) 2372.88 790.381i 0.0926202 0.0308508i
\(59\) 1704.67 + 2952.58i 0.0637546 + 0.110426i 0.896141 0.443770i \(-0.146359\pi\)
−0.832386 + 0.554196i \(0.813026\pi\)
\(60\) 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 −0.580553 0.814222i \(-0.697164\pi\)
0.414861 + 0.909885i \(0.363830\pi\)
\(68\) 1082.48 129.935i 0.0283889 0.00340765i
\(69\) 0 0
\(70\) 48400.9 54558.1i 1.18061 1.33080i
\(71\) −25694.1 −0.604905 −0.302453 0.953164i \(-0.597805\pi\)
−0.302453 + 0.953164i \(0.597805\pi\)
\(72\) 0 0
\(73\) 65431.6 1.43708 0.718540 0.695486i \(-0.244811\pi\)
0.718540 + 0.695486i \(0.244811\pi\)
\(74\) −41511.2 + 46792.0i −0.881223 + 0.993326i
\(75\) 0 0
\(76\) −37283.7 + 4475.34i −0.740432 + 0.0888776i
\(77\) 68778.2 39709.1i 1.32198 0.763244i
\(78\) 0 0
\(79\) 41126.9 + 23744.6i 0.741409 + 0.428053i 0.822581 0.568647i \(-0.192533\pi\)
−0.0811725 + 0.996700i \(0.525866\pi\)
\(80\) −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 \(-0.866899\pi\)
0.808588 + 0.588376i \(0.200232\pi\)
\(84\) 0 0
\(85\) 1026.39 + 1777.77i 0.0154087 + 0.0266887i
\(86\) −6577.60 + 2190.93i −0.0959005 + 0.0319435i
\(87\) 0 0
\(88\) −60756.1 + 28676.6i −0.836340 + 0.394749i
\(89\) 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
\(92\) −101430. + 76003.0i −1.24939 + 0.936183i
\(93\) 0 0
\(94\) 4371.44 + 13123.9i 0.0510275 + 0.153195i
\(95\) −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 −0.0108398 0.999941i \(-0.503450\pi\)
0.860555 + 0.509358i \(0.170117\pi\)
\(104\) 12031.2 145317.i 0.109076 1.31745i
\(105\) 0 0
\(106\) 85531.8 + 75879.0i 0.739372 + 0.655929i
\(107\) −3806.62 −0.0321426 −0.0160713 0.999871i \(-0.505116\pi\)
−0.0160713 + 0.999871i \(0.505116\pi\)
\(108\) 0 0
\(109\) −85149.1 −0.686458 −0.343229 0.939252i \(-0.611521\pi\)
−0.343229 + 0.939252i \(0.611521\pi\)
\(110\) −94627.3 83948.0i −0.745649 0.661498i
\(111\) 0 0
\(112\) −210301. 61538.3i −1.58415 0.463554i
\(113\) 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
\(122\) 71220.7 + 213819.i 0.433218 + 1.30061i
\(123\) 0 0
\(124\) −30605.3 40844.5i −0.178749 0.238550i
\(125\) 157844.i 0.903553i
\(126\) 0 0
\(127\) 37078.8i 0.203994i −0.994785 0.101997i \(-0.967477\pi\)
0.994785 0.101997i \(-0.0325232\pi\)
\(128\) 173002. + 66559.6i 0.933309 + 0.359075i
\(129\) 0 0
\(130\) 260478. 86762.5i 1.35180 0.450271i
\(131\) 83730.6 + 145026.i 0.426291 + 0.738357i 0.996540 0.0831144i \(-0.0264867\pi\)
−0.570249 + 0.821472i \(0.693153\pi\)
\(132\) 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 0.127200 0.991877i \(-0.459401\pi\)
0.922591 + 0.385780i \(0.126068\pi\)
\(140\) −49170.0 409631.i −0.212021 1.76633i
\(141\) 0 0
\(142\) −96457.7 + 108728.i −0.401436 + 0.452504i
\(143\) 298961. 1.22257
\(144\) 0 0
\(145\) 26638.8 0.105219
\(146\) 245636. 276884.i 0.953695 1.07502i
\(147\) 0 0
\(148\) 42170.8 + 351322.i 0.158255 + 1.31841i
\(149\) −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 −0.343587 0.939121i \(-0.611642\pi\)
−0.985096 + 0.172006i \(0.944975\pi\)
\(152\) −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 \(-0.536768\pi\)
\(158\) 254872. 84895.3i 0.812232 0.270546i
\(159\) 0 0
\(160\) 12861.2 + 348777.i 0.0397176 + 1.07708i
\(161\) 847550.i 2.57692i
\(162\) 0 0
\(163\) 50545.5i 0.149009i 0.997221 + 0.0745047i \(0.0237376\pi\)
−0.997221 + 0.0745047i \(0.976262\pi\)
\(164\) −176588. 235666.i −0.512687 0.684208i
\(165\) 0 0
\(166\) 23618.7 + 70907.9i 0.0665250 + 0.199721i
\(167\) −155078. 268602.i −0.430287 0.745279i 0.566611 0.823985i \(-0.308254\pi\)
−0.996898 + 0.0787068i \(0.974921\pi\)
\(168\) 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
\(176\) −106734. + 364753.i −0.259729 + 0.887599i
\(177\) 0 0
\(178\) 362577. + 321658.i 0.857729 + 0.760929i
\(179\) −313216. −0.730653 −0.365326 0.930880i \(-0.619043\pi\)
−0.365326 + 0.930880i \(0.619043\pi\)
\(180\) 0 0
\(181\) 241414. 0.547729 0.273865 0.961768i \(-0.411698\pi\)
0.273865 + 0.961768i \(0.411698\pi\)
\(182\) 729402. + 647084.i 1.63226 + 1.44805i
\(183\) 0 0
\(184\) −59158.7 + 714538.i −0.128817 + 1.55590i
\(185\) −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 \(0.436561\pi\)
−0.947874 + 0.318644i \(0.896773\pi\)
\(192\) 0 0
\(193\) −210750. 365029.i −0.407262 0.705398i 0.587320 0.809355i \(-0.300183\pi\)
−0.994582 + 0.103957i \(0.966850\pi\)
\(194\) 99913.0 + 299958.i 0.190598 + 0.572212i
\(195\) 0 0
\(196\) 742188. 556132.i 1.37998 1.03404i
\(197\) 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 \(0.462940\pi\)
−0.116163 + 0.993230i \(0.537060\pi\)
\(200\) −82708.6 + 39038.1i −0.146210 + 0.0690103i
\(201\) 0 0
\(202\) −491669. + 163770.i −0.847803 + 0.282394i
\(203\) 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 \(-0.717889\pi\)
0.354780 + 0.934950i \(0.384556\pi\)
\(212\) 642187. 77084.7i 0.981345 0.117796i
\(213\) 0 0
\(214\) −14290.4 + 16108.3i −0.0213309 + 0.0240445i
\(215\) −73842.6 −0.108946
\(216\) 0 0
\(217\) 341296. 0.492020
\(218\) −319657. + 360321.i −0.455557 + 0.513510i
\(219\) 0 0
\(220\) −710477. + 85282.0i −0.989677 + 0.118796i
\(221\) −23767.5 + 13722.1i −0.0327342 + 0.0188991i
\(222\) 0 0
\(223\) 557586. + 321922.i 0.750844 + 0.433500i 0.825999 0.563672i \(-0.190612\pi\)
−0.0751547 + 0.997172i \(0.523945\pi\)
\(224\) −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 \(-0.554533\pi\)
0.938589 0.345036i \(-0.112133\pi\)
\(228\) 0 0
\(229\) 538232. + 932245.i 0.678236 + 1.17474i 0.975512 + 0.219947i \(0.0705886\pi\)
−0.297276 + 0.954792i \(0.596078\pi\)
\(230\) −1.28079e6 + 426619.i −1.59647 + 0.531766i
\(231\) 0 0
\(232\) −34161.4 72376.6i −0.0416693 0.0882833i
\(233\) 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
\(236\) 87308.1 65421.2i 0.102041 0.0764607i
\(237\) 0 0
\(238\) 13033.1 + 39127.9i 0.0149144 + 0.0447758i
\(239\) 336873. + 583482.i 0.381480 + 0.660743i 0.991274 0.131817i \(-0.0420811\pi\)
−0.609794 + 0.792560i \(0.708748\pi\)
\(240\) 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
\(248\) −287734. 23822.4i −0.297073 0.0245955i
\(249\) 0 0
\(250\) 667942. + 592560.i 0.675910 + 0.599629i
\(251\) −1.32110e6 −1.32358 −0.661789 0.749690i \(-0.730203\pi\)
−0.661789 + 0.749690i \(0.730203\pi\)
\(252\) 0 0
\(253\) −1.47002e6 −1.44385
\(254\) −156905. 139197.i −0.152599 0.135377i
\(255\) 0 0
\(256\) 931119. 482212.i 0.887984 0.459873i
\(257\) 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 −0.994624 0.103556i \(-0.966978\pi\)
0.586994 + 0.809591i \(0.300311\pi\)
\(264\) 0 0
\(265\) 608914. + 1.05467e6i 0.532649 + 0.922575i
\(266\) −448896. 1.34767e6i −0.388993 1.16783i
\(267\) 0 0
\(268\) 134898. + 180029.i 0.114728 + 0.153111i
\(269\) 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 \(-0.931309\pi\)
0.976806 0.214127i \(-0.0686907\pi\)
\(272\) −8256.59 33897.0i −0.00676672 0.0277804i
\(273\) 0 0
\(274\) −1.84693e6 + 615194.i −1.48619 + 0.495035i
\(275\) −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 0.0602971 0.998180i \(-0.480795\pi\)
0.894598 + 0.446871i \(0.147462\pi\)
\(284\) 97990.5 + 816351.i 0.0720921 + 0.600594i
\(285\) 0 0
\(286\) 1.12232e6 1.26510e6i 0.811340 0.914553i
\(287\) 1.96923e6 1.41121
\(288\) 0 0
\(289\) 1.41870e6 0.999182
\(290\) 100004. 112726.i 0.0698271 0.0787100i
\(291\) 0 0
\(292\) −249539. 2.07889e6i −0.171270 1.42684i
\(293\) −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
\(302\) −2.30707e6 + 768461.i −1.45561 + 0.484847i
\(303\) 0 0
\(304\) 284380. + 1.16751e6i 0.176488 + 0.724562i
\(305\) 2.40041e6i 1.47753i
\(306\) 0 0
\(307\) 29930.7i 0.0181247i −0.999959 0.00906235i \(-0.997115\pi\)
0.999959 0.00906235i \(-0.00288467\pi\)
\(308\) −1.52394e6 2.03378e6i −0.915357 1.22159i
\(309\) 0 0
\(310\) −171794. 515758.i −0.101532 0.304819i
\(311\) 828429. + 1.43488e6i 0.485685 + 0.841231i 0.999865 0.0164516i \(-0.00523694\pi\)
−0.514180 + 0.857682i \(0.671904\pi\)
\(312\) 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
\(320\) 1.52418e6 + 1.25491e6i 0.832075 + 0.685076i
\(321\) 0 0
\(322\) −3.58653e6 3.18177e6i −1.92768 1.71013i
\(323\) 39980.9 0.0213229
\(324\) 0 0
\(325\) 406982. 0.213731
\(326\) 213891. + 189752.i 0.111468 + 0.0988877i
\(327\) 0 0
\(328\) −1.66018e6 137452.i −0.852063 0.0705449i
\(329\) −453156. + 261630.i −0.230812 + 0.133259i
\(330\) 0 0
\(331\) −1828.81 1055.86i −0.000917484 0.000529710i 0.499541 0.866290i \(-0.333502\pi\)
−0.500459 + 0.865760i \(0.666835\pi\)
\(332\) 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 \(-0.370224\pi\)
\(338\) 496200. + 1.48969e6i 0.236246 + 0.709257i
\(339\) 0 0
\(340\) 52568.7 39390.5i 0.0246621 0.0184797i
\(341\) 591955.i 0.275679i
\(342\) 0 0
\(343\) 2.60530e6i 1.19570i
\(344\) 94695.2 + 200627.i 0.0431451 + 0.0914100i
\(345\) 0 0
\(346\) 870816. 290060.i 0.391054 0.130256i
\(347\) −1.65555e6 2.86750e6i −0.738106 1.27844i −0.953347 0.301877i \(-0.902387\pi\)
0.215241 0.976561i \(1.56905\pi\)
\(348\) 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
\(356\) 2.72229e6 326769.i 1.13844 0.136652i
\(357\) 0 0
\(358\) −1.17584e6 + 1.32542e6i −0.484886 + 0.546570i
\(359\) −1.46738e6 −0.600905 −0.300453 0.953797i \(-0.597138\pi\)
−0.300453 + 0.953797i \(0.597138\pi\)
\(360\) 0 0
\(361\) 1.09904e6 0.443861
\(362\) 906288. 1.02158e6i 0.363492 0.409733i
\(363\) 0 0
\(364\) 5.47647e6 657366.i 2.16644 0.260048i
\(365\) 3.41418e6 1.97118e6i 1.34139 0.774450i
\(366\) 0 0
\(367\) 1.76458e6 + 1.01878e6i 0.683874 + 0.394835i 0.801313 0.598245i \(-0.204135\pi\)
−0.117439 + 0.993080i \(0.537468\pi\)
\(368\) 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 \(0.758122\pi\)
\(374\) 67864.6 22605.0i 0.0250879 0.00835652i
\(375\) 0 0
\(376\) 400301. 188940.i 0.146021 0.0689215i
\(377\) 356142.i 0.129053i
\(378\) 0 0
\(379\) 3.51959e6i 1.25862i −0.777154 0.629310i \(-0.783338\pi\)
0.777154 0.629310i \(-0.216662\pi\)
\(380\) −1.81062e6 + 1.35672e6i −0.643232 + 0.481982i
\(381\) 0 0
\(382\) 1.35176e6 + 4.05826e6i 0.473960 + 1.42292i
\(383\) −1.45304e6 2.51675e6i −0.506153 0.876683i −0.999975 0.00711941i \(-0.997734\pi\)
0.493822 0.869563i \(1.66440\pi\)
\(384\) 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
\(392\) 432879. 5.22845e6i 0.142282 1.71853i
\(393\) 0 0
\(394\) 3.36841e6 + 2.98826e6i 1.09316 + 0.969791i
\(395\) 2.86130e6 0.922720
\(396\) 0 0
\(397\) −1.37551e6 −0.438012 −0.219006 0.975723i \(-0.570281\pi\)
−0.219006 + 0.975723i \(0.570281\pi\)
\(398\) 4.69594e6 + 4.16597e6i 1.48599 + 1.31828i
\(399\) 0 0
\(400\) −145299. + 496546.i −0.0454060 + 0.155171i
\(401\) −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 \(0.919384\pi\)
\(410\) −991223. 2.97585e6i −0.291214 0.874281i
\(411\) 0 0
\(412\) −2.02713e6 2.70532e6i −0.588355 0.785191i
\(413\) 729546.i 0.210464i
\(414\) 0 0
\(415\) 796039.i 0.226889i
\(416\) −4.66289e6 + 171945.i −1.32106 + 0.0487144i
\(417\) 0 0
\(418\) −2.33745e6 + 778580.i −0.654337 + 0.217953i
\(419\) 926212. + 1.60425e6i 0.257736 + 0.446412i 0.965635 0.259902i \(-0.0836901\pi\)
−0.707899 + 0.706314i \(0.750357\pi\)
\(420\) 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
\(428\) 14517.5 + 120944.i 0.00383073 + 0.0319135i
\(429\) 0 0
\(430\) −277211. + 312476.i −0.0723002 + 0.0814978i
\(431\) −277886. −0.0720565 −0.0360283 0.999351i \(-0.511471\pi\)
−0.0360283 + 0.999351i \(0.511471\pi\)
\(432\) 0 0
\(433\) −2.49224e6 −0.638807 −0.319403 0.947619i \(-0.603482\pi\)
−0.319403 + 0.947619i \(0.603482\pi\)
\(434\) 1.28125e6 1.44425e6i 0.326521 0.368059i
\(435\) 0 0
\(436\) 324736. + 2.70535e6i 0.0818115 + 0.681565i
\(437\) −4.02522e6 + 2.32396e6i −1.00829 + 0.582138i
\(438\) 0 0
\(439\) 1.04465e6 + 603126.i 0.258707 + 0.149364i 0.623744 0.781628i \(-0.285611\pi\)
−0.365038 + 0.930993i \(0.618944\pi\)
\(440\) −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 \(-0.730761\pi\)
0.979796 + 0.200001i \(0.0640946\pi\)
\(444\) 0 0
\(445\) 2.58124e6 + 4.47084e6i 0.617914 + 1.07026i
\(446\) 3.45549e6 1.15099e6i 0.822569 0.273989i
\(447\) 0 0
\(448\) −1.15316e6 + 6.91636e6i −0.271452 + 1.62810i
\(449\) 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
\(452\) −814379. 1.08683e6i −0.187491 0.250217i
\(453\) 0 0
\(454\) −2.13208e6 6.40093e6i −0.485472 1.45748i
\(455\) 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 −0.0360597 0.999350i \(-0.511481\pi\)
0.847432 + 0.530903i \(0.178147\pi\)
\(464\) −434517. 127148.i −0.0936941 0.0274168i
\(465\) 0 0
\(466\) −753940. 668853.i −0.160832 0.142681i
\(467\) −3.41339e6 −0.724258 −0.362129 0.932128i \(-0.617950\pi\)
−0.362129 + 0.932128i \(0.617950\pi\)
\(468\) 0 0
\(469\) −1.50432e6 −0.315798
\(470\) 623466. + 553104.i 0.130187 + 0.115495i
\(471\) 0 0
\(472\) 50922.1 615054.i 0.0105209 0.127074i
\(473\) −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 \(-0.749448\pi\)
0.966373 + 0.257144i \(0.0827814\pi\)
\(480\) 0 0
\(481\) −4.45356e6 7.71378e6i −0.877696 1.52021i
\(482\) 582726. + 1.74946e6i 0.114247 + 0.342994i
\(483\) 0 0
\(484\) 596816. 447203.i 0.115805 0.0867743i
\(485\) 3.36745e6i 0.650050i
\(486\) 0 0
\(487\) 8.58357e6i 1.64001i −0.572359 0.820003i \(-0.693971\pi\)
0.572359 0.820003i \(-0.306029\pi\)
\(488\) 6.52181e6 3.07827e6i 1.23971 0.585136i
\(489\) 0 0
\(490\) 9.37189e6 3.12168e6i 1.76334 0.587351i
\(491\) −4.45187e6 7.71087e6i −0.833372 1.44344i −0.895349 0.445366i \(-0.853074\pi\)
0.0619764 0.998078i \(1.51974\pi\)
\(492\) 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 \(0.717882\pi\)
−0.987084 + 0.160205i \(0.948784\pi\)
\(500\) 5.01502e6 601976.i 0.897114 0.107685i
\(501\) 0 0
\(502\) −4.95950e6 + 5.59041e6i −0.878372 + 0.990113i
\(503\) −3.07909e6 −0.542628 −0.271314 0.962491i \(-0.587458\pi\)
−0.271314 + 0.962491i \(0.587458\pi\)
\(504\) 0 0
\(505\) −5.51967e6 −0.963129
\(506\) −5.51857e6 + 6.22060e6i −0.958186 + 1.08008i
\(507\) 0 0
\(508\) −1.17807e6 + 141409.i −0.202540 + 0.0243118i
\(509\) 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
\(518\) −1.26990e7 + 4.22992e6i −2.07944 + 0.692640i
\(519\) 0 0
\(520\) −3.75001e6 7.94500e6i −0.608168 1.28850i
\(521\) 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 \(-0.973822\pi\)
0.996620 0.0821476i \(-0.0261779\pi\)
\(524\) 4.28842e6 3.21337e6i 0.682290 0.511249i
\(525\) 0 0
\(526\) 1.63483e6 + 4.90809e6i 0.257638 + 0.773479i
\(527\) 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
\(536\) 1.26824e6 + 105001.i 0.190673 + 0.0157864i
\(537\) 0 0
\(538\) −7.88049e6 6.99113e6i −1.17381 1.04134i
\(539\) 1.07565e7 1.59477
\(540\) 0 0
\(541\) 9.97892e6 1.46585 0.732926 0.680308i \(-0.238154\pi\)
0.732926 + 0.680308i \(0.238154\pi\)
\(542\) −2.19096e6 1.94370e6i −0.320359 0.284204i
\(543\) 0 0
\(544\) −174436. 92313.0i −0.0252720 0.0133741i
\(545\) −4.44302e6 + 2.56518e6i −0.640748 + 0.369936i
\(546\) 0 0
\(547\) −6.89166e6 3.97890e6i −0.984817 0.568584i −0.0810959 0.996706i \(-0.525842\pi\)
−0.903721 + 0.428122i \(0.859175\pi\)
\(548\) −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
\(554\) 1.11508e6 + 3.34770e6i 0.154360 + 0.463418i
\(555\) 0 0
\(556\) −5.29854e6 7.07119e6i −0.726891 0.970075i
\(557\) 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
\(560\) −1.28272e7 + 3.12445e6i −1.72848 + 0.421021i
\(561\) 0 0
\(562\) 9.49868e6 3.16391e6i 1.26859 0.422555i
\(563\) −3.58742e6 6.21360e6i −0.476993 0.826176i 0.522660 0.852541i \(-0.324940\pi\)
−0.999652 + 0.0263657i \(0.991607\pi\)
\(564\) 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 0.215970 0.976400i \(-0.430709\pi\)
0.953572 + 0.301165i \(0.0973755\pi\)
\(572\) −1.14016e6 9.49856e6i −0.145705 1.21386i
\(573\) 0 0
\(574\) 7.39265e6 8.33309e6i 0.936527 1.05567i
\(575\) −2.00117e6 −0.252414
\(576\) 0 0
\(577\) 1.46593e6 0.183305 0.0916526 0.995791i \(-0.470785\pi\)
0.0916526 + 0.995791i \(0.470785\pi\)
\(578\) 5.32590e6 6.00343e6i 0.663092 0.747446i
\(579\) 0 0
\(580\) −101593. 846367.i −0.0125400 0.104469i
\(581\) −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 \(-0.853326\pi\)
0.832934 + 0.553372i \(0.186659\pi\)
\(588\) 0 0
\(589\) −935827. 1.62090e6i −0.111150 0.192517i
\(590\) 1.10247e6 367221.i 0.130388 0.0434308i
\(591\) 0 0
\(592\) 1.10013e7 2.67970e6i 1.29015 0.314254i
\(593\) 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
\(596\) 751120. + 1.00241e6i 0.0866151 + 0.115593i
\(597\) 0 0
\(598\) −5.70358e6 1.71233e7i −0.652221 1.95810i
\(599\) 4.39728e6 + 7.61632e6i 0.500746 + 0.867317i 1.00000 0.000861327i \(0.000274169\pi\)
−0.499254 + 0.866456i \(0.666392\pi\)
\(600\) 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 −0.577826 0.816160i \(-0.696099\pi\)
0.417902 + 0.908492i \(0.362765\pi\)
\(608\) 6.00807e6 + 3.17952e6i 0.659138 + 0.348821i
\(609\) 0 0
\(610\) 1.01577e7 + 9.01133e6i 1.10528 + 0.980538i
\(611\) −1.96975e6 −0.213456
\(612\) 0 0
\(613\) 615822. 0.0661918 0.0330959 0.999452i \(-0.489463\pi\)
0.0330959 + 0.999452i \(0.489463\pi\)
\(614\) −126656. 112362.i −0.0135583 0.0120282i
\(615\) 0 0
\(616\) −1.43272e7 1.18619e6i −1.52128 0.125952i
\(617\) 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 \(-0.981679\pi\)
−0.548991 0.835829i \(1.31501\pi\)
\(620\) −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
\(626\) 5.33858e6 + 1.60275e7i 0.544490 + 1.63467i
\(627\) 0 0
\(628\) −1.45194e7 + 1.08796e7i −1.46909 + 1.10081i
\(629\) 376737.i 0.0379674i
\(630\) 0 0
\(631\) 1.01556e7i 1.01539i 0.861538 + 0.507693i \(0.169502\pi\)
−0.861538 + 0.507693i \(0.830498\pi\)
\(632\) −3.66930e6 7.77402e6i −0.365419 0.774200i
\(633\) 0 0
\(634\) −4.63649e6 + 1.54437e6i −0.458107 + 0.152590i
\(635\) −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 −0.592288 0.805726i \(-0.701775\pi\)
0.401635 + 0.915800i \(0.368442\pi\)
\(644\) −2.69283e7 + 3.23233e6i −2.55855 + 0.307115i
\(645\) 0 0
\(646\) 150091. 169185.i 0.0141506 0.0159507i
\(647\) −4.18696e6 −0.393222 −0.196611 0.980482i \(-0.562994\pi\)
−0.196611 + 0.980482i \(0.562994\pi\)
\(648\) 0 0
\(649\) 1.26535e6 0.117923
\(650\) 1.52784e6 1.72221e6i 0.141839 0.159883i
\(651\) 0 0
\(652\) 1.60593e6 192767.i 0.147947 0.0177588i
\(653\) 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 −0.744111 0.668056i \(-0.767127\pi\)
0.950609 + 0.310391i \(0.100460\pi\)
\(660\) 0 0
\(661\) −2.73544e6 4.73792e6i −0.243514 0.421778i 0.718199 0.695838i \(-0.244967\pi\)
−0.961713 + 0.274060i \(0.911633\pi\)
\(662\) −11333.5 + 3775.08i −0.00100513 + 0.000334797i
\(663\) 0 0
\(664\) 2.16280e6 1.02083e6i 0.190369 0.0898535i
\(665\) 1.51295e7i 1.32669i
\(666\) 0 0
\(667\) 1.75118e6i 0.152411i
\(668\) −7.94259e6 + 5.95149e6i −0.688686 + 0.516042i
\(669\) 0 0
\(670\) 757210. + 2.27329e6i 0.0651673 + 0.195645i
\(671\) 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
\(680\) 30660.5 370328.i 0.00254277 0.0307124i
\(681\) 0 0
\(682\) −2.50495e6 2.22225e6i −0.206223 0.182950i
\(683\) −3.24667e6 −0.266310 −0.133155 0.991095i \(-0.542511\pi\)
−0.133155 + 0.991095i \(0.542511\pi\)
\(684\) 0 0
\(685\) −2.07344e7 −1.68836
\(686\) 1.10247e7 + 9.78050e6i 0.894452 + 0.793507i
\(687\) 0 0
\(688\) 1.20448e6 + 352454.i 0.0970125 + 0.0283878i
\(689\) −1.41002e7 + 8.14073e6i −1.13156 + 0.653304i
\(690\) 0 0
\(691\) 1.27793e7 + 7.37815e6i 1.01815 + 0.587831i 0.913568 0.406685i \(-0.133315\pi\)
0.104584 + 0.994516i \(0.466649\pi\)
\(692\) 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
\(698\) 470177. + 1.41156e6i 0.0365277 + 0.109663i
\(699\) 0 0
\(700\) −2.07457e6 2.76863e6i −0.160023 0.213560i
\(701\) 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
\(704\) 1.19960e7 + 2.00007e6i 0.912227 + 0.152095i
\(705\) 0 0
\(706\) −792472. + 263964.i −0.0598374 + 0.0199312i
\(707\) −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
\(716\) 1.19452e6 + 9.95147e6i 0.0870786 + 0.725445i
\(717\) 0 0
\(718\) −5.50866e6 + 6.20943e6i −0.398781 + 0.449511i
\(719\) 7.72155e6 0.557035 0.278517 0.960431i \(-0.410157\pi\)
0.278517 + 0.960431i \(0.410157\pi\)
\(720\) 0 0
\(721\) 2.26057e7 1.61949
\(722\) 4.12590e6 4.65077e6i 0.294562 0.332034i
\(723\) 0 0
\(724\) −920689. 7.67019e6i −0.0652780 0.543825i
\(725\) 193454. 111691.i 0.0136689 0.00789173i
\(726\) 0 0
\(727\) −1.28498e7 7.41886e6i −0.901700 0.520596i −0.0239484 0.999713i \(-0.507624\pi\)
−0.877751 + 0.479117i \(0.840957\pi\)
\(728\) 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 \(0.870914\pi\)
\(734\) 1.09355e7 3.64250e6i 0.749201 0.249551i
\(735\) 0 0
\(736\) 2.29279e7 845471.i 1.56016 0.0575313i
\(737\) 2.60915e6i 0.176942i
\(738\) 0 0
\(739\) 1.26632e7i 0.852970i −0.904495 0.426485i \(-0.859752\pi\)
0.904495 0.426485i \(-0.140248\pi\)
\(740\) 1.27843e7 + 1.70613e7i 0.858216 + 1.14534i
\(741\) 0 0
\(742\) 7.73194e6 + 2.32128e7i 0.515559 + 1.54781i
\(743\) 6.02221e6 + 1.04308e7i 0.400206 + 0.693178i 0.993751 0.111624i \(-0.0356052\pi\)
−0.593544 + 0.804801i \(0.702272\pi\)
\(744\) 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 \(-0.542604\pi\)
0.791558 + 0.611094i \(0.209270\pi\)
\(752\) 703233. 2.40323e6i 0.0453476 0.154971i
\(753\) 0 0
\(754\) 1.50707e6 + 1.33699e6i 0.0965393 + 0.0856443i
\(755\) −2.59001e7 −1.65361
\(756\) 0 0
\(757\) 5.08821e6 0.322719 0.161360 0.986896i \(-0.448412\pi\)
0.161360 + 0.986896i \(0.448412\pi\)
\(758\) −1.48937e7 1.32128e7i −0.941520 0.835263i
\(759\) 0 0
\(760\) −1.05604e6 + 1.27551e7i −0.0663200 + 0.801034i
\(761\) 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 \(0.663009\pi\)
\(770\) −8.55415e6 2.56812e7i −0.519936 1.56095i
\(771\) 0 0
\(772\) −1.07939e7 + 8.08804e6i −0.651833 + 0.488428i
\(773\) 610007.i 0.0367186i −0.999831 0.0183593i \(-0.994156\pi\)
0.999831 0.0183593i \(-0.00584428\pi\)
\(774\) 0 0