Properties

Label 405.4.e.w.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(2.93142 - 2.93142i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.w.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.61668 - 4.53223i) q^{2} +(-9.69405 + 16.7906i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.5090 - 28.5945i) q^{7} +59.5981 q^{8} +O(q^{10})\) \(q+(-2.61668 - 4.53223i) q^{2} +(-9.69405 + 16.7906i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(-16.5090 - 28.5945i) q^{7} +59.5981 q^{8} +26.1668 q^{10} +(-3.04155 - 5.26813i) q^{11} +(32.2254 - 55.8160i) q^{13} +(-86.3977 + 149.645i) q^{14} +(-78.3969 - 135.787i) q^{16} -76.9845 q^{17} -118.716 q^{19} +(-48.4703 - 83.9529i) q^{20} +(-15.9176 + 27.5700i) q^{22} +(-38.8002 + 67.2039i) q^{23} +(-12.5000 - 21.6506i) q^{25} -337.294 q^{26} +640.157 q^{28} +(-31.4075 - 54.3993i) q^{29} +(53.4569 - 92.5901i) q^{31} +(-171.887 + 297.717i) q^{32} +(201.444 + 348.911i) q^{34} +165.090 q^{35} +108.268 q^{37} +(310.642 + 538.048i) q^{38} +(-148.995 + 258.067i) q^{40} +(-71.3830 + 123.639i) q^{41} +(-169.784 - 294.075i) q^{43} +117.940 q^{44} +406.111 q^{46} +(299.173 + 518.182i) q^{47} +(-373.595 + 647.086i) q^{49} +(-65.4171 + 113.306i) q^{50} +(624.789 + 1082.17i) q^{52} +488.041 q^{53} +30.4155 q^{55} +(-983.906 - 1704.18i) q^{56} +(-164.367 + 284.691i) q^{58} +(-121.413 + 210.294i) q^{59} +(249.669 + 432.440i) q^{61} -559.519 q^{62} +544.744 q^{64} +(161.127 + 279.080i) q^{65} +(460.817 - 798.159i) q^{67} +(746.292 - 1292.62i) q^{68} +(-431.989 - 748.226i) q^{70} -60.6882 q^{71} -338.439 q^{73} +(-283.303 - 490.695i) q^{74} +(1150.84 - 1993.31i) q^{76} +(-100.426 + 173.943i) q^{77} +(278.155 + 481.779i) q^{79} +783.969 q^{80} +747.147 q^{82} +(32.4210 + 56.1548i) q^{83} +(192.461 - 333.353i) q^{85} +(-888.542 + 1539.00i) q^{86} +(-181.271 - 313.970i) q^{88} +941.159 q^{89} -2128.04 q^{91} +(-752.262 - 1302.96i) q^{92} +(1565.68 - 2711.84i) q^{94} +(296.790 - 514.056i) q^{95} +(521.085 + 902.546i) q^{97} +3910.32 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{2} - 34 q^{4} - 30 q^{5} - 40 q^{7} + 132 q^{8} + 40 q^{10} - 88 q^{11} - 20 q^{13} - 180 q^{14} - 58 q^{16} + 248 q^{17} - 92 q^{19} - 170 q^{20} + 74 q^{22} - 210 q^{23} - 150 q^{25} + 8 q^{26} + 704 q^{28} - 296 q^{29} + 104 q^{31} - 722 q^{32} + 428 q^{34} + 400 q^{35} - 408 q^{37} + 20 q^{38} - 330 q^{40} - 344 q^{41} - 512 q^{43} + 1432 q^{44} - 372 q^{46} - 238 q^{47} - 68 q^{49} - 100 q^{50} + 468 q^{52} + 1700 q^{53} + 880 q^{55} - 2316 q^{56} - 890 q^{58} - 1840 q^{59} + 364 q^{61} + 2076 q^{62} - 1980 q^{64} - 100 q^{65} - 88 q^{67} - 236 q^{68} - 900 q^{70} + 2728 q^{71} + 1672 q^{73} - 1316 q^{74} + 2106 q^{76} - 840 q^{77} + 680 q^{79} + 580 q^{80} + 3484 q^{82} - 2148 q^{83} - 620 q^{85} - 2872 q^{86} - 1296 q^{88} + 6000 q^{89} - 6116 q^{91} - 1002 q^{92} + 3662 q^{94} + 230 q^{95} + 612 q^{97} + 3964 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61668 4.53223i −0.925137 1.60238i −0.791341 0.611375i \(-0.790617\pi\)
−0.133796 0.991009i \(-0.542717\pi\)
\(3\) 0 0
\(4\) −9.69405 + 16.7906i −1.21176 + 2.09882i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −16.5090 28.5945i −0.891403 1.54396i −0.838194 0.545372i \(-0.816388\pi\)
−0.0532095 0.998583i \(-0.516945\pi\)
\(8\) 59.5981 2.63389
\(9\) 0 0
\(10\) 26.1668 0.827468
\(11\) −3.04155 5.26813i −0.0833694 0.144400i 0.821326 0.570459i \(-0.193235\pi\)
−0.904695 + 0.426059i \(0.859901\pi\)
\(12\) 0 0
\(13\) 32.2254 55.8160i 0.687516 1.19081i −0.285123 0.958491i \(-0.592034\pi\)
0.972639 0.232322i \(-0.0746322\pi\)
\(14\) −86.3977 + 149.645i −1.64934 + 2.85674i
\(15\) 0 0
\(16\) −78.3969 135.787i −1.22495 2.12168i
\(17\) −76.9845 −1.09832 −0.549162 0.835716i \(-0.685053\pi\)
−0.549162 + 0.835716i \(0.685053\pi\)
\(18\) 0 0
\(19\) −118.716 −1.43344 −0.716720 0.697361i \(-0.754357\pi\)
−0.716720 + 0.697361i \(0.754357\pi\)
\(20\) −48.4703 83.9529i −0.541914 0.938623i
\(21\) 0 0
\(22\) −15.9176 + 27.5700i −0.154256 + 0.267179i
\(23\) −38.8002 + 67.2039i −0.351757 + 0.609260i −0.986557 0.163416i \(-0.947749\pi\)
0.634801 + 0.772676i \(0.281082\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −337.294 −2.54419
\(27\) 0 0
\(28\) 640.157 4.32065
\(29\) −31.4075 54.3993i −0.201111 0.348334i 0.747776 0.663951i \(-0.231122\pi\)
−0.948887 + 0.315617i \(0.897789\pi\)
\(30\) 0 0
\(31\) 53.4569 92.5901i 0.309714 0.536441i −0.668585 0.743635i \(-0.733100\pi\)
0.978300 + 0.207194i \(0.0664332\pi\)
\(32\) −171.887 + 297.717i −0.949550 + 1.64467i
\(33\) 0 0
\(34\) 201.444 + 348.911i 1.01610 + 1.75994i
\(35\) 165.090 0.797295
\(36\) 0 0
\(37\) 108.268 0.481058 0.240529 0.970642i \(-0.422679\pi\)
0.240529 + 0.970642i \(0.422679\pi\)
\(38\) 310.642 + 538.048i 1.32613 + 2.29692i
\(39\) 0 0
\(40\) −148.995 + 258.067i −0.588955 + 1.02010i
\(41\) −71.3830 + 123.639i −0.271906 + 0.470955i −0.969350 0.245684i \(-0.920987\pi\)
0.697444 + 0.716640i \(0.254321\pi\)
\(42\) 0 0
\(43\) −169.784 294.075i −0.602136 1.04293i −0.992497 0.122268i \(-0.960983\pi\)
0.390361 0.920662i \(-0.372350\pi\)
\(44\) 117.940 0.404093
\(45\) 0 0
\(46\) 406.111 1.30169
\(47\) 299.173 + 518.182i 0.928486 + 1.60818i 0.785857 + 0.618408i \(0.212222\pi\)
0.142629 + 0.989776i \(0.454445\pi\)
\(48\) 0 0
\(49\) −373.595 + 647.086i −1.08920 + 1.88655i
\(50\) −65.4171 + 113.306i −0.185027 + 0.320477i
\(51\) 0 0
\(52\) 624.789 + 1082.17i 1.66620 + 2.88595i
\(53\) 488.041 1.26486 0.632431 0.774617i \(-0.282057\pi\)
0.632431 + 0.774617i \(0.282057\pi\)
\(54\) 0 0
\(55\) 30.4155 0.0745678
\(56\) −983.906 1704.18i −2.34786 4.06661i
\(57\) 0 0
\(58\) −164.367 + 284.691i −0.372110 + 0.644514i
\(59\) −121.413 + 210.294i −0.267909 + 0.464033i −0.968322 0.249706i \(-0.919666\pi\)
0.700412 + 0.713738i \(0.252999\pi\)
\(60\) 0 0
\(61\) 249.669 + 432.440i 0.524047 + 0.907676i 0.999608 + 0.0279936i \(0.00891181\pi\)
−0.475561 + 0.879683i \(0.657755\pi\)
\(62\) −559.519 −1.14611
\(63\) 0 0
\(64\) 544.744 1.06395
\(65\) 161.127 + 279.080i 0.307466 + 0.532548i
\(66\) 0 0
\(67\) 460.817 798.159i 0.840266 1.45538i −0.0494046 0.998779i \(-0.515732\pi\)
0.889670 0.456604i \(-0.150934\pi\)
\(68\) 746.292 1292.62i 1.33090 2.30519i
\(69\) 0 0
\(70\) −431.989 748.226i −0.737607 1.27757i
\(71\) −60.6882 −0.101442 −0.0507209 0.998713i \(-0.516152\pi\)
−0.0507209 + 0.998713i \(0.516152\pi\)
\(72\) 0 0
\(73\) −338.439 −0.542621 −0.271311 0.962492i \(-0.587457\pi\)
−0.271311 + 0.962492i \(0.587457\pi\)
\(74\) −283.303 490.695i −0.445045 0.770840i
\(75\) 0 0
\(76\) 1150.84 1993.31i 1.73698 3.00854i
\(77\) −100.426 + 173.943i −0.148631 + 0.257437i
\(78\) 0 0
\(79\) 278.155 + 481.779i 0.396138 + 0.686131i 0.993246 0.116030i \(-0.0370168\pi\)
−0.597108 + 0.802161i \(0.703683\pi\)
\(80\) 783.969 1.09563
\(81\) 0 0
\(82\) 747.147 1.00620
\(83\) 32.4210 + 56.1548i 0.0428755 + 0.0742625i 0.886667 0.462409i \(-0.153015\pi\)
−0.843791 + 0.536671i \(0.819681\pi\)
\(84\) 0 0
\(85\) 192.461 333.353i 0.245592 0.425379i
\(86\) −888.542 + 1539.00i −1.11412 + 1.92971i
\(87\) 0 0
\(88\) −181.271 313.970i −0.219586 0.380333i
\(89\) 941.159 1.12093 0.560465 0.828178i \(-0.310623\pi\)
0.560465 + 0.828178i \(0.310623\pi\)
\(90\) 0 0
\(91\) −2128.04 −2.45142
\(92\) −752.262 1302.96i −0.852487 1.47655i
\(93\) 0 0
\(94\) 1565.68 2711.84i 1.71795 2.97558i
\(95\) 296.790 514.056i 0.320527 0.555169i
\(96\) 0 0
\(97\) 521.085 + 902.546i 0.545445 + 0.944738i 0.998579 + 0.0532958i \(0.0169726\pi\)
−0.453134 + 0.891442i \(0.649694\pi\)
\(98\) 3910.32 4.03064
\(99\) 0 0
\(100\) 484.703 0.484703
\(101\) −341.121 590.840i −0.336068 0.582086i 0.647622 0.761962i \(-0.275764\pi\)
−0.983689 + 0.179876i \(0.942430\pi\)
\(102\) 0 0
\(103\) −606.832 + 1051.06i −0.580514 + 1.00548i 0.414905 + 0.909865i \(0.363815\pi\)
−0.995418 + 0.0956144i \(0.969518\pi\)
\(104\) 1920.57 3326.52i 1.81084 3.13647i
\(105\) 0 0
\(106\) −1277.05 2211.91i −1.17017 2.02679i
\(107\) −1311.93 −1.18532 −0.592658 0.805454i \(-0.701921\pi\)
−0.592658 + 0.805454i \(0.701921\pi\)
\(108\) 0 0
\(109\) −294.780 −0.259035 −0.129518 0.991577i \(-0.541343\pi\)
−0.129518 + 0.991577i \(0.541343\pi\)
\(110\) −79.5878 137.850i −0.0689854 0.119486i
\(111\) 0 0
\(112\) −2588.51 + 4483.43i −2.18385 + 3.78254i
\(113\) −792.562 + 1372.76i −0.659805 + 1.14282i 0.320861 + 0.947126i \(0.396028\pi\)
−0.980666 + 0.195689i \(0.937306\pi\)
\(114\) 0 0
\(115\) −194.001 336.020i −0.157310 0.272469i
\(116\) 1217.86 0.974790
\(117\) 0 0
\(118\) 1270.80 0.991412
\(119\) 1270.94 + 2201.33i 0.979049 + 1.69576i
\(120\) 0 0
\(121\) 646.998 1120.63i 0.486099 0.841948i
\(122\) 1306.61 2263.12i 0.969631 1.67945i
\(123\) 0 0
\(124\) 1036.43 + 1795.15i 0.750597 + 1.30007i
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −149.176 −0.104230 −0.0521149 0.998641i \(-0.516596\pi\)
−0.0521149 + 0.998641i \(0.516596\pi\)
\(128\) −50.3275 87.1698i −0.0347528 0.0601937i
\(129\) 0 0
\(130\) 843.235 1460.53i 0.568897 0.985359i
\(131\) −585.886 + 1014.78i −0.390757 + 0.676810i −0.992550 0.121842i \(-0.961120\pi\)
0.601793 + 0.798652i \(0.294453\pi\)
\(132\) 0 0
\(133\) 1959.89 + 3394.62i 1.27777 + 2.21317i
\(134\) −4823.25 −3.10944
\(135\) 0 0
\(136\) −4588.13 −2.89286
\(137\) 579.313 + 1003.40i 0.361270 + 0.625739i 0.988170 0.153361i \(-0.0490098\pi\)
−0.626900 + 0.779100i \(0.715676\pi\)
\(138\) 0 0
\(139\) −793.262 + 1373.97i −0.484055 + 0.838408i −0.999832 0.0183149i \(-0.994170\pi\)
0.515777 + 0.856723i \(0.327503\pi\)
\(140\) −1600.39 + 2771.96i −0.966128 + 1.67338i
\(141\) 0 0
\(142\) 158.802 + 275.053i 0.0938475 + 0.162549i
\(143\) −392.061 −0.229271
\(144\) 0 0
\(145\) 314.075 0.179879
\(146\) 885.588 + 1533.88i 0.501999 + 0.869487i
\(147\) 0 0
\(148\) −1049.56 + 1817.88i −0.582925 + 1.00966i
\(149\) −258.555 + 447.830i −0.142158 + 0.246226i −0.928309 0.371809i \(-0.878738\pi\)
0.786151 + 0.618035i \(0.212071\pi\)
\(150\) 0 0
\(151\) −277.793 481.151i −0.149712 0.259308i 0.781409 0.624019i \(-0.214501\pi\)
−0.931121 + 0.364711i \(0.881168\pi\)
\(152\) −7075.25 −3.77552
\(153\) 0 0
\(154\) 1051.13 0.550018
\(155\) 267.285 + 462.950i 0.138508 + 0.239904i
\(156\) 0 0
\(157\) −527.016 + 912.818i −0.267901 + 0.464018i −0.968320 0.249714i \(-0.919663\pi\)
0.700419 + 0.713732i \(0.252997\pi\)
\(158\) 1455.69 2521.33i 0.732964 1.26953i
\(159\) 0 0
\(160\) −859.435 1488.58i −0.424652 0.735519i
\(161\) 2562.21 1.25423
\(162\) 0 0
\(163\) −635.916 −0.305575 −0.152788 0.988259i \(-0.548825\pi\)
−0.152788 + 0.988259i \(0.548825\pi\)
\(164\) −1383.98 2397.13i −0.658968 1.14137i
\(165\) 0 0
\(166\) 169.671 293.879i 0.0793314 0.137406i
\(167\) −682.557 + 1182.22i −0.316274 + 0.547803i −0.979708 0.200432i \(-0.935765\pi\)
0.663433 + 0.748236i \(0.269099\pi\)
\(168\) 0 0
\(169\) −978.448 1694.72i −0.445356 0.771380i
\(170\) −2014.44 −0.908827
\(171\) 0 0
\(172\) 6583.59 2.91857
\(173\) −567.465 982.878i −0.249385 0.431947i 0.713970 0.700176i \(-0.246895\pi\)
−0.963355 + 0.268229i \(0.913562\pi\)
\(174\) 0 0
\(175\) −412.726 + 714.862i −0.178281 + 0.308791i
\(176\) −476.897 + 826.009i −0.204247 + 0.353766i
\(177\) 0 0
\(178\) −2462.72 4265.55i −1.03701 1.79616i
\(179\) 1813.33 0.757179 0.378589 0.925565i \(-0.376409\pi\)
0.378589 + 0.925565i \(0.376409\pi\)
\(180\) 0 0
\(181\) 2334.37 0.958634 0.479317 0.877642i \(-0.340884\pi\)
0.479317 + 0.877642i \(0.340884\pi\)
\(182\) 5568.40 + 9644.74i 2.26790 + 3.92811i
\(183\) 0 0
\(184\) −2312.42 + 4005.23i −0.926488 + 1.60472i
\(185\) −270.670 + 468.814i −0.107568 + 0.186313i
\(186\) 0 0
\(187\) 234.153 + 405.564i 0.0915665 + 0.158598i
\(188\) −11600.8 −4.50039
\(189\) 0 0
\(190\) −3106.42 −1.18612
\(191\) −221.322 383.341i −0.0838444 0.145223i 0.821054 0.570851i \(-0.193387\pi\)
−0.904898 + 0.425628i \(0.860053\pi\)
\(192\) 0 0
\(193\) 1851.27 3206.49i 0.690452 1.19590i −0.281237 0.959638i \(-0.590745\pi\)
0.971690 0.236261i \(-0.0759219\pi\)
\(194\) 2727.03 4723.35i 1.00922 1.74802i
\(195\) 0 0
\(196\) −7243.31 12545.8i −2.63969 4.57208i
\(197\) 4491.92 1.62455 0.812274 0.583276i \(-0.198229\pi\)
0.812274 + 0.583276i \(0.198229\pi\)
\(198\) 0 0
\(199\) −2934.08 −1.04518 −0.522591 0.852584i \(-0.675034\pi\)
−0.522591 + 0.852584i \(0.675034\pi\)
\(200\) −744.976 1290.34i −0.263389 0.456203i
\(201\) 0 0
\(202\) −1785.21 + 3092.08i −0.621817 + 1.07702i
\(203\) −1037.01 + 1796.16i −0.358542 + 0.621013i
\(204\) 0 0
\(205\) −356.915 618.195i −0.121600 0.210618i
\(206\) 6351.54 2.14822
\(207\) 0 0
\(208\) −10105.5 −3.36869
\(209\) 361.082 + 625.412i 0.119505 + 0.206989i
\(210\) 0 0
\(211\) 336.970 583.649i 0.109943 0.190427i −0.805804 0.592182i \(-0.798267\pi\)
0.915747 + 0.401756i \(0.131600\pi\)
\(212\) −4731.10 + 8194.50i −1.53270 + 2.65472i
\(213\) 0 0
\(214\) 3432.90 + 5945.95i 1.09658 + 1.89933i
\(215\) 1697.84 0.538567
\(216\) 0 0
\(217\) −3530.08 −1.10432
\(218\) 771.347 + 1336.01i 0.239643 + 0.415074i
\(219\) 0 0
\(220\) −294.850 + 510.695i −0.0903580 + 0.156505i
\(221\) −2480.85 + 4296.97i −0.755115 + 1.30790i
\(222\) 0 0
\(223\) −89.2581 154.599i −0.0268034 0.0464249i 0.852313 0.523033i \(-0.175199\pi\)
−0.879116 + 0.476608i \(0.841866\pi\)
\(224\) 11350.7 3.38573
\(225\) 0 0
\(226\) 8295.53 2.44164
\(227\) −2526.05 4375.25i −0.738590 1.27928i −0.953130 0.302561i \(-0.902158\pi\)
0.214540 0.976715i \(-0.431175\pi\)
\(228\) 0 0
\(229\) −654.484 + 1133.60i −0.188863 + 0.327120i −0.944871 0.327442i \(-0.893813\pi\)
0.756009 + 0.654562i \(0.227147\pi\)
\(230\) −1015.28 + 1758.51i −0.291067 + 0.504143i
\(231\) 0 0
\(232\) −1871.82 3242.10i −0.529704 0.917474i
\(233\) −6591.30 −1.85326 −0.926632 0.375970i \(-0.877309\pi\)
−0.926632 + 0.375970i \(0.877309\pi\)
\(234\) 0 0
\(235\) −2991.73 −0.830463
\(236\) −2353.97 4077.20i −0.649282 1.12459i
\(237\) 0 0
\(238\) 6651.29 11520.4i 1.81151 3.13762i
\(239\) −792.252 + 1372.22i −0.214421 + 0.371387i −0.953093 0.302677i \(-0.902120\pi\)
0.738673 + 0.674064i \(0.235453\pi\)
\(240\) 0 0
\(241\) 837.234 + 1450.13i 0.223780 + 0.387598i 0.955953 0.293521i \(-0.0948269\pi\)
−0.732173 + 0.681119i \(0.761494\pi\)
\(242\) −6771.95 −1.79883
\(243\) 0 0
\(244\) −9681.23 −2.54007
\(245\) −1867.98 3235.43i −0.487105 0.843690i
\(246\) 0 0
\(247\) −3825.67 + 6626.25i −0.985512 + 1.70696i
\(248\) 3185.93 5518.19i 0.815753 1.41293i
\(249\) 0 0
\(250\) −327.085 566.528i −0.0827468 0.143322i
\(251\) −1200.75 −0.301955 −0.150978 0.988537i \(-0.548242\pi\)
−0.150978 + 0.988537i \(0.548242\pi\)
\(252\) 0 0
\(253\) 472.052 0.117303
\(254\) 390.345 + 676.098i 0.0964269 + 0.167016i
\(255\) 0 0
\(256\) 1915.60 3317.91i 0.467675 0.810036i
\(257\) 2603.34 4509.12i 0.631876 1.09444i −0.355292 0.934755i \(-0.615619\pi\)
0.987168 0.159686i \(-0.0510481\pi\)
\(258\) 0 0
\(259\) −1787.40 3095.87i −0.428817 0.742733i
\(260\) −6247.89 −1.49030
\(261\) 0 0
\(262\) 6132.31 1.44601
\(263\) −3841.78 6654.16i −0.900739 1.56012i −0.826537 0.562882i \(-0.809693\pi\)
−0.0742011 0.997243i \(-0.523641\pi\)
\(264\) 0 0
\(265\) −1220.10 + 2113.28i −0.282832 + 0.489879i
\(266\) 10256.8 17765.3i 2.36423 4.09496i
\(267\) 0 0
\(268\) 8934.37 + 15474.8i 2.03639 + 3.52714i
\(269\) −624.277 −0.141497 −0.0707487 0.997494i \(-0.522539\pi\)
−0.0707487 + 0.997494i \(0.522539\pi\)
\(270\) 0 0
\(271\) −1462.51 −0.327828 −0.163914 0.986475i \(-0.552412\pi\)
−0.163914 + 0.986475i \(0.552412\pi\)
\(272\) 6035.35 + 10453.5i 1.34539 + 2.33029i
\(273\) 0 0
\(274\) 3031.76 5251.15i 0.668449 1.15779i
\(275\) −76.0388 + 131.703i −0.0166739 + 0.0288800i
\(276\) 0 0
\(277\) 2949.02 + 5107.85i 0.639673 + 1.10795i 0.985505 + 0.169649i \(0.0542635\pi\)
−0.345832 + 0.938297i \(0.612403\pi\)
\(278\) 8302.86 1.79127
\(279\) 0 0
\(280\) 9839.06 2.09999
\(281\) 2636.45 + 4566.47i 0.559707 + 0.969441i 0.997521 + 0.0703753i \(0.0224197\pi\)
−0.437813 + 0.899066i \(0.644247\pi\)
\(282\) 0 0
\(283\) 559.632 969.311i 0.117550 0.203603i −0.801246 0.598335i \(-0.795829\pi\)
0.918796 + 0.394732i \(0.129163\pi\)
\(284\) 588.315 1018.99i 0.122923 0.212908i
\(285\) 0 0
\(286\) 1025.90 + 1776.91i 0.212107 + 0.367380i
\(287\) 4713.86 0.969513
\(288\) 0 0
\(289\) 1013.62 0.206313
\(290\) −821.833 1423.46i −0.166413 0.288235i
\(291\) 0 0
\(292\) 3280.85 5682.60i 0.657525 1.13887i
\(293\) 470.370 814.705i 0.0937860 0.162442i −0.815315 0.579017i \(-0.803436\pi\)
0.909101 + 0.416575i \(0.136770\pi\)
\(294\) 0 0
\(295\) −607.066 1051.47i −0.119813 0.207522i
\(296\) 6452.57 1.26705
\(297\) 0 0
\(298\) 2706.22 0.526064
\(299\) 2500.70 + 4331.34i 0.483676 + 0.837752i
\(300\) 0 0
\(301\) −5605.94 + 9709.77i −1.07349 + 1.85934i
\(302\) −1453.79 + 2518.04i −0.277008 + 0.479791i
\(303\) 0 0
\(304\) 9306.97 + 16120.1i 1.75589 + 3.04130i
\(305\) −2496.69 −0.468722
\(306\) 0 0
\(307\) 1931.88 0.359148 0.179574 0.983744i \(-0.442528\pi\)
0.179574 + 0.983744i \(0.442528\pi\)
\(308\) −1947.07 3372.43i −0.360210 0.623902i
\(309\) 0 0
\(310\) 1398.80 2422.79i 0.256279 0.443888i
\(311\) 3149.08 5454.37i 0.574174 0.994498i −0.421957 0.906616i \(-0.638657\pi\)
0.996131 0.0878821i \(-0.0280099\pi\)
\(312\) 0 0
\(313\) 909.403 + 1575.13i 0.164225 + 0.284446i 0.936380 0.350988i \(-0.114154\pi\)
−0.772155 + 0.635435i \(0.780821\pi\)
\(314\) 5516.13 0.991380
\(315\) 0 0
\(316\) −10785.8 −1.92009
\(317\) −1579.32 2735.46i −0.279821 0.484665i 0.691519 0.722358i \(-0.256942\pi\)
−0.971340 + 0.237694i \(0.923609\pi\)
\(318\) 0 0
\(319\) −191.055 + 330.917i −0.0335330 + 0.0580808i
\(320\) −1361.86 + 2358.81i −0.237907 + 0.412068i
\(321\) 0 0
\(322\) −6704.50 11612.5i −1.16033 2.00975i
\(323\) 9139.31 1.57438
\(324\) 0 0
\(325\) −1611.27 −0.275006
\(326\) 1663.99 + 2882.12i 0.282699 + 0.489649i
\(327\) 0 0
\(328\) −4254.29 + 7368.65i −0.716171 + 1.24044i
\(329\) 9878.10 17109.4i 1.65531 2.86708i
\(330\) 0 0
\(331\) 476.545 + 825.400i 0.0791338 + 0.137064i 0.902876 0.429900i \(-0.141451\pi\)
−0.823743 + 0.566964i \(0.808118\pi\)
\(332\) −1257.16 −0.207819
\(333\) 0 0
\(334\) 7144.14 1.17039
\(335\) 2304.09 + 3990.79i 0.375778 + 0.650867i
\(336\) 0 0
\(337\) 284.447 492.676i 0.0459786 0.0796373i −0.842120 0.539290i \(-0.818693\pi\)
0.888099 + 0.459653i \(0.152026\pi\)
\(338\) −5120.57 + 8869.09i −0.824031 + 1.42726i
\(339\) 0 0
\(340\) 3731.46 + 6463.08i 0.595197 + 1.03091i
\(341\) −650.368 −0.103283
\(342\) 0 0
\(343\) 13345.6 2.10086
\(344\) −10118.8 17526.3i −1.58596 2.74696i
\(345\) 0 0
\(346\) −2969.75 + 5143.76i −0.461430 + 0.799220i
\(347\) −4213.28 + 7297.61i −0.651817 + 1.12898i 0.330864 + 0.943678i \(0.392660\pi\)
−0.982682 + 0.185302i \(0.940674\pi\)
\(348\) 0 0
\(349\) −3571.98 6186.85i −0.547861 0.948924i −0.998421 0.0561773i \(-0.982109\pi\)
0.450559 0.892746i \(-0.351225\pi\)
\(350\) 4319.89 0.659736
\(351\) 0 0
\(352\) 2091.21 0.316654
\(353\) −2650.35 4590.54i −0.399614 0.692152i 0.594064 0.804418i \(-0.297522\pi\)
−0.993678 + 0.112266i \(0.964189\pi\)
\(354\) 0 0
\(355\) 151.720 262.788i 0.0226831 0.0392882i
\(356\) −9123.65 + 15802.6i −1.35829 + 2.35263i
\(357\) 0 0
\(358\) −4744.92 8218.44i −0.700494 1.21329i
\(359\) −9536.35 −1.40198 −0.700988 0.713173i \(-0.747257\pi\)
−0.700988 + 0.713173i \(0.747257\pi\)
\(360\) 0 0
\(361\) 7234.52 1.05475
\(362\) −6108.32 10579.9i −0.886867 1.53610i
\(363\) 0 0
\(364\) 20629.3 35731.0i 2.97052 5.14509i
\(365\) 846.098 1465.49i 0.121334 0.210156i
\(366\) 0 0
\(367\) 365.104 + 632.379i 0.0519299 + 0.0899453i 0.890822 0.454353i \(-0.150129\pi\)
−0.838892 + 0.544298i \(0.816796\pi\)
\(368\) 12167.3 1.72354
\(369\) 0 0
\(370\) 2833.03 0.398060
\(371\) −8057.09 13955.3i −1.12750 1.95289i
\(372\) 0 0
\(373\) −6434.47 + 11144.8i −0.893201 + 1.54707i −0.0571863 + 0.998364i \(0.518213\pi\)
−0.836015 + 0.548707i \(0.815120\pi\)
\(374\) 1225.41 2122.47i 0.169423 0.293449i
\(375\) 0 0
\(376\) 17830.1 + 30882.7i 2.44553 + 4.23578i
\(377\) −4048.47 −0.553068
\(378\) 0 0
\(379\) −4000.88 −0.542246 −0.271123 0.962545i \(-0.587395\pi\)
−0.271123 + 0.962545i \(0.587395\pi\)
\(380\) 5754.20 + 9966.57i 0.776801 + 1.34546i
\(381\) 0 0
\(382\) −1158.26 + 2006.16i −0.155135 + 0.268702i
\(383\) 32.6599 56.5687i 0.00435730 0.00754706i −0.863839 0.503769i \(-0.831946\pi\)
0.868196 + 0.496222i \(0.165280\pi\)
\(384\) 0 0
\(385\) −502.131 869.716i −0.0664700 0.115129i
\(386\) −19376.7 −2.55505
\(387\) 0 0
\(388\) −20205.7 −2.64379
\(389\) −2959.89 5126.67i −0.385790 0.668207i 0.606089 0.795397i \(-0.292738\pi\)
−0.991878 + 0.127190i \(0.959404\pi\)
\(390\) 0 0
\(391\) 2987.02 5173.66i 0.386342 0.669165i
\(392\) −22265.6 + 38565.1i −2.86883 + 4.96896i
\(393\) 0 0
\(394\) −11753.9 20358.4i −1.50293 2.60315i
\(395\) −2781.55 −0.354317
\(396\) 0 0
\(397\) −10228.7 −1.29310 −0.646551 0.762871i \(-0.723789\pi\)
−0.646551 + 0.762871i \(0.723789\pi\)
\(398\) 7677.54 + 13297.9i 0.966936 + 1.67478i
\(399\) 0 0
\(400\) −1959.92 + 3394.68i −0.244990 + 0.424335i
\(401\) −6122.56 + 10604.6i −0.762460 + 1.32062i 0.179120 + 0.983827i \(0.442675\pi\)
−0.941579 + 0.336791i \(0.890658\pi\)
\(402\) 0 0
\(403\) −3445.34 5967.50i −0.425867 0.737623i
\(404\) 13227.4 1.62893
\(405\) 0 0
\(406\) 10854.1 1.32680
\(407\) −329.303 570.370i −0.0401055 0.0694648i
\(408\) 0 0
\(409\) −4916.47 + 8515.58i −0.594386 + 1.02951i 0.399247 + 0.916843i \(0.369272\pi\)
−0.993633 + 0.112664i \(0.964062\pi\)
\(410\) −1867.87 + 3235.24i −0.224994 + 0.389700i
\(411\) 0 0
\(412\) −11765.3 20378.1i −1.40688 2.43679i
\(413\) 8017.65 0.955262
\(414\) 0 0
\(415\) −324.210 −0.0383490
\(416\) 11078.2 + 19188.1i 1.30566 + 2.26147i
\(417\) 0 0
\(418\) 1889.67 3273.01i 0.221117 0.382986i
\(419\) −6157.57 + 10665.2i −0.717941 + 1.24351i 0.243873 + 0.969807i \(0.421582\pi\)
−0.961814 + 0.273703i \(0.911751\pi\)
\(420\) 0 0
\(421\) 2159.21 + 3739.86i 0.249961 + 0.432945i 0.963515 0.267656i \(-0.0862489\pi\)
−0.713554 + 0.700600i \(0.752916\pi\)
\(422\) −3526.97 −0.406849
\(423\) 0 0
\(424\) 29086.3 3.33150
\(425\) 962.307 + 1666.76i 0.109832 + 0.190235i
\(426\) 0 0
\(427\) 8243.59 14278.3i 0.934275 1.61821i
\(428\) 12717.9 22028.0i 1.43631 2.48777i
\(429\) 0 0
\(430\) −4442.71 7695.00i −0.498248 0.862991i
\(431\) 5265.39 0.588457 0.294228 0.955735i \(-0.404937\pi\)
0.294228 + 0.955735i \(0.404937\pi\)
\(432\) 0 0
\(433\) 5855.07 0.649831 0.324916 0.945743i \(-0.394664\pi\)
0.324916 + 0.945743i \(0.394664\pi\)
\(434\) 9237.11 + 15999.1i 1.02165 + 1.76955i
\(435\) 0 0
\(436\) 2857.62 4949.54i 0.313888 0.543669i
\(437\) 4606.21 7978.19i 0.504222 0.873338i
\(438\) 0 0
\(439\) −2011.35 3483.76i −0.218671 0.378748i 0.735731 0.677274i \(-0.236839\pi\)
−0.954402 + 0.298525i \(0.903505\pi\)
\(440\) 1812.71 0.196403
\(441\) 0 0
\(442\) 25966.4 2.79434
\(443\) −3751.11 6497.12i −0.402304 0.696811i 0.591699 0.806159i \(-0.298457\pi\)
−0.994004 + 0.109347i \(0.965124\pi\)
\(444\) 0 0
\(445\) −2352.90 + 4075.34i −0.250647 + 0.434134i
\(446\) −467.120 + 809.076i −0.0495937 + 0.0858987i
\(447\) 0 0
\(448\) −8993.20 15576.7i −0.948412 1.64270i
\(449\) −18574.2 −1.95227 −0.976135 0.217166i \(-0.930319\pi\)
−0.976135 + 0.217166i \(0.930319\pi\)
\(450\) 0 0
\(451\) 868.461 0.0906746
\(452\) −15366.3 26615.2i −1.59905 2.76963i
\(453\) 0 0
\(454\) −13219.8 + 22897.3i −1.36659 + 2.36701i
\(455\) 5320.09 9214.67i 0.548153 0.949429i
\(456\) 0 0
\(457\) −7072.78 12250.4i −0.723962 1.25394i −0.959400 0.282049i \(-0.908986\pi\)
0.235438 0.971889i \(-0.424347\pi\)
\(458\) 6850.31 0.698895
\(459\) 0 0
\(460\) 7522.62 0.762487
\(461\) 2455.37 + 4252.83i 0.248066 + 0.429662i 0.962989 0.269541i \(-0.0868718\pi\)
−0.714923 + 0.699203i \(0.753538\pi\)
\(462\) 0 0
\(463\) −4627.72 + 8015.45i −0.464511 + 0.804557i −0.999179 0.0405054i \(-0.987103\pi\)
0.534668 + 0.845062i \(0.320437\pi\)
\(464\) −4924.49 + 8529.47i −0.492702 + 0.853385i
\(465\) 0 0
\(466\) 17247.3 + 29873.3i 1.71452 + 2.96964i
\(467\) −2825.10 −0.279936 −0.139968 0.990156i \(-0.544700\pi\)
−0.139968 + 0.990156i \(0.544700\pi\)
\(468\) 0 0
\(469\) −30430.6 −2.99606
\(470\) 7828.40 + 13559.2i 0.768292 + 1.33072i
\(471\) 0 0
\(472\) −7236.00 + 12533.1i −0.705644 + 1.22221i
\(473\) −1032.82 + 1788.89i −0.100399 + 0.173897i
\(474\) 0 0
\(475\) 1483.95 + 2570.28i 0.143344 + 0.248279i
\(476\) −49282.2 −4.74547
\(477\) 0 0
\(478\) 8292.29 0.793474
\(479\) −4586.74 7944.47i −0.437523 0.757812i 0.559975 0.828510i \(-0.310811\pi\)
−0.997498 + 0.0706977i \(0.977477\pi\)
\(480\) 0 0
\(481\) 3488.98 6043.08i 0.330735 0.572850i
\(482\) 4381.55 7589.07i 0.414054 0.717163i
\(483\) 0 0
\(484\) 12544.1 + 21727.0i 1.17807 + 2.04047i
\(485\) −5210.85 −0.487861
\(486\) 0 0
\(487\) 13663.7 1.27138 0.635690 0.771945i \(-0.280716\pi\)
0.635690 + 0.771945i \(0.280716\pi\)
\(488\) 14879.8 + 25772.6i 1.38028 + 2.39072i
\(489\) 0 0
\(490\) −9775.81 + 16932.2i −0.901277 + 1.56106i
\(491\) 2925.16 5066.52i 0.268860 0.465680i −0.699707 0.714430i \(-0.746686\pi\)
0.968568 + 0.248750i \(0.0800196\pi\)
\(492\) 0 0
\(493\) 2417.89 + 4187.91i 0.220885 + 0.382584i
\(494\) 40042.2 3.64694
\(495\) 0 0
\(496\) −16763.4 −1.51754
\(497\) 1001.90 + 1735.35i 0.0904255 + 0.156622i
\(498\) 0 0
\(499\) −1921.49 + 3328.11i −0.172380 + 0.298571i −0.939251 0.343230i \(-0.888479\pi\)
0.766872 + 0.641801i \(0.221812\pi\)
\(500\) −1211.76 + 2098.82i −0.108383 + 0.187725i
\(501\) 0 0
\(502\) 3141.98 + 5442.08i 0.279350 + 0.483848i
\(503\) 4242.88 0.376104 0.188052 0.982159i \(-0.439783\pi\)
0.188052 + 0.982159i \(0.439783\pi\)
\(504\) 0 0
\(505\) 3411.21 0.300588
\(506\) −1235.21 2139.44i −0.108521 0.187964i
\(507\) 0 0
\(508\) 1446.12 2504.75i 0.126301 0.218760i
\(509\) −3682.80 + 6378.80i −0.320702 + 0.555472i −0.980633 0.195854i \(-0.937252\pi\)
0.659931 + 0.751326i \(0.270585\pi\)
\(510\) 0 0
\(511\) 5587.30 + 9677.49i 0.483694 + 0.837783i
\(512\) −20855.3 −1.80016
\(513\) 0 0
\(514\) −27248.5 −2.33829
\(515\) −3034.16 5255.32i −0.259614 0.449664i
\(516\) 0 0
\(517\) 1819.90 3152.16i 0.154815 0.268147i
\(518\) −9354.11 + 16201.8i −0.793429 + 1.37426i
\(519\) 0 0
\(520\) 9602.85 + 16632.6i 0.809832 + 1.40267i
\(521\) −8717.87 −0.733084 −0.366542 0.930401i \(-0.619458\pi\)
−0.366542 + 0.930401i \(0.619458\pi\)
\(522\) 0 0
\(523\) 23515.4 1.96607 0.983037 0.183407i \(-0.0587127\pi\)
0.983037 + 0.183407i \(0.0587127\pi\)
\(524\) −11359.2 19674.7i −0.947004 1.64026i
\(525\) 0 0
\(526\) −20105.4 + 34823.6i −1.66661 + 2.88666i
\(527\) −4115.36 + 7128.00i −0.340166 + 0.589185i
\(528\) 0 0
\(529\) 3072.59 + 5321.88i 0.252535 + 0.437403i
\(530\) 12770.5 1.04663
\(531\) 0 0
\(532\) −75997.0 −6.19340
\(533\) 4600.69 + 7968.63i 0.373880 + 0.647579i
\(534\) 0 0
\(535\) 3279.82 5680.81i 0.265045 0.459071i
\(536\) 27463.8 47568.8i 2.21317 3.83332i
\(537\) 0 0
\(538\) 1633.53 + 2829.36i 0.130905 + 0.226733i
\(539\) 4545.24 0.363224
\(540\) 0 0
\(541\) 3803.94 0.302300 0.151150 0.988511i \(-0.451702\pi\)
0.151150 + 0.988511i \(0.451702\pi\)
\(542\) 3826.94 + 6628.45i 0.303286 + 0.525307i
\(543\) 0 0
\(544\) 13232.6 22919.6i 1.04291 1.80638i
\(545\) 736.951 1276.44i 0.0579221 0.100324i
\(546\) 0 0
\(547\) −8667.95 15013.3i −0.677540 1.17353i −0.975719 0.219024i \(-0.929713\pi\)
0.298179 0.954510i \(-0.403621\pi\)
\(548\) −22463.6 −1.75109
\(549\) 0 0
\(550\) 795.878 0.0617025
\(551\) 3728.57 + 6458.07i 0.288280 + 0.499316i
\(552\) 0 0
\(553\) 9184.14 15907.4i 0.706238 1.22324i
\(554\) 15433.3 26731.2i 1.18357 2.05000i
\(555\) 0 0
\(556\) −15379.9 26638.7i −1.17311 2.03189i
\(557\) 7797.62 0.593170 0.296585 0.955006i \(-0.404152\pi\)
0.296585 + 0.955006i \(0.404152\pi\)
\(558\) 0 0
\(559\) −21885.4 −1.65591
\(560\) −12942.6 22417.2i −0.976648 1.69160i
\(561\) 0 0
\(562\) 13797.5 23898.0i 1.03561 1.79373i
\(563\) 5767.81 9990.14i 0.431766 0.747840i −0.565260 0.824913i \(-0.691224\pi\)
0.997025 + 0.0770727i \(0.0245574\pi\)
\(564\) 0 0
\(565\) −3962.81 6863.79i −0.295074 0.511083i
\(566\) −5857.52 −0.435000
\(567\) 0 0
\(568\) −3616.90 −0.267186
\(569\) 5038.86 + 8727.56i 0.371248 + 0.643020i 0.989758 0.142757i \(-0.0455967\pi\)
−0.618510 + 0.785777i \(0.712263\pi\)
\(570\) 0 0
\(571\) 8169.66 14150.3i 0.598756 1.03708i −0.394249 0.919004i \(-0.628995\pi\)
0.993005 0.118072i \(-0.0376714\pi\)
\(572\) 3800.66 6582.93i 0.277821 0.481200i
\(573\) 0 0
\(574\) −12334.7 21364.3i −0.896932 1.55353i
\(575\) 1940.01 0.140703
\(576\) 0 0
\(577\) 18648.6 1.34550 0.672748 0.739871i \(-0.265114\pi\)
0.672748 + 0.739871i \(0.265114\pi\)
\(578\) −2652.32 4593.95i −0.190868 0.330593i
\(579\) 0 0
\(580\) −3044.65 + 5273.50i −0.217970 + 0.377535i
\(581\) 1070.48 1854.12i 0.0764387 0.132396i
\(582\) 0 0
\(583\) −1484.40 2571.06i −0.105451 0.182646i
\(584\) −20170.3 −1.42920
\(585\) 0 0
\(586\) −4923.24 −0.347060
\(587\) 9048.54 + 15672.5i 0.636241 + 1.10200i 0.986251 + 0.165255i \(0.0528449\pi\)
−0.350010 + 0.936746i \(0.613822\pi\)
\(588\) 0 0
\(589\) −6346.20 + 10991.9i −0.443957 + 0.768956i
\(590\) −3177.00 + 5502.72i −0.221686 + 0.383972i
\(591\) 0 0
\(592\) −8487.87 14701.4i −0.589273 1.02065i
\(593\) 27154.1 1.88041 0.940207 0.340602i \(-0.110631\pi\)
0.940207 + 0.340602i \(0.110631\pi\)
\(594\) 0 0
\(595\) −12709.4 −0.875688
\(596\) −5012.88 8682.57i −0.344523 0.596731i
\(597\) 0 0
\(598\) 13087.1 22667.5i 0.894934 1.55007i
\(599\) −1728.73 + 2994.25i −0.117920 + 0.204243i −0.918943 0.394390i \(-0.870956\pi\)
0.801023 + 0.598633i \(0.204289\pi\)
\(600\) 0 0
\(601\) 1469.21 + 2544.75i 0.0997179 + 0.172717i 0.911568 0.411150i \(-0.134873\pi\)
−0.811850 + 0.583866i \(0.801539\pi\)
\(602\) 58675.9 3.97251
\(603\) 0 0
\(604\) 10771.8 0.725656
\(605\) 3234.99 + 5603.17i 0.217390 + 0.376531i
\(606\) 0 0
\(607\) 3892.97 6742.82i 0.260314 0.450877i −0.706011 0.708201i \(-0.749507\pi\)
0.966325 + 0.257323i \(0.0828405\pi\)
\(608\) 20405.8 35343.8i 1.36112 2.35753i
\(609\) 0 0
\(610\) 6533.05 + 11315.6i 0.433632 + 0.751073i
\(611\) 38563.8 2.55339
\(612\) 0 0
\(613\) 23893.4 1.57430 0.787151 0.616760i \(-0.211555\pi\)
0.787151 + 0.616760i \(0.211555\pi\)
\(614\) −5055.13 8755.74i −0.332261 0.575493i
\(615\) 0 0
\(616\) −5985.21 + 10366.7i −0.391479 + 0.678061i
\(617\) 2440.23 4226.60i 0.159222 0.275781i −0.775366 0.631512i \(-0.782435\pi\)
0.934588 + 0.355731i \(0.115768\pi\)
\(618\) 0 0
\(619\) −7941.77 13755.6i −0.515681 0.893186i −0.999834 0.0182030i \(-0.994205\pi\)
0.484153 0.874983i \(-0.339128\pi\)
\(620\) −10364.3 −0.671354
\(621\) 0 0
\(622\) −32960.6 −2.12476
\(623\) −15537.6 26911.9i −0.999200 1.73067i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 4759.24 8243.24i 0.303862 0.526304i
\(627\) 0 0
\(628\) −10217.8 17697.8i −0.649261 1.12455i
\(629\) −8334.96 −0.528357
\(630\) 0 0
\(631\) −12862.4 −0.811479 −0.405740 0.913989i \(-0.632986\pi\)
−0.405740 + 0.913989i \(0.632986\pi\)
\(632\) 16577.5 + 28713.1i 1.04338 + 1.80719i
\(633\) 0 0
\(634\) −8265.15 + 14315.7i −0.517746 + 0.896763i
\(635\) 372.939 645.949i 0.0233065 0.0403680i
\(636\) 0 0
\(637\) 24078.5 + 41705.2i 1.49768 + 2.59407i
\(638\) 1999.72 0.124090
\(639\) 0 0
\(640\) 503.275 0.0310839
\(641\) 14742.8 + 25535.3i 0.908435 + 1.57346i 0.816238 + 0.577715i \(0.196056\pi\)
0.0921970 + 0.995741i \(0.470611\pi\)
\(642\) 0 0
\(643\) 7057.32 12223.6i 0.432836 0.749694i −0.564280 0.825583i \(-0.690846\pi\)
0.997116 + 0.0758891i \(0.0241795\pi\)
\(644\) −24838.2 + 43021.1i −1.51982 + 2.63240i
\(645\) 0 0
\(646\) −23914.7 41421.4i −1.45652 2.52276i
\(647\) −13313.3 −0.808962 −0.404481 0.914546i \(-0.632548\pi\)
−0.404481 + 0.914546i \(0.632548\pi\)
\(648\) 0 0
\(649\) 1477.14 0.0893418
\(650\) 4216.18 + 7302.63i 0.254419 + 0.440666i
\(651\) 0 0
\(652\) 6164.60 10677.4i 0.370283 0.641349i
\(653\) −5753.08 + 9964.62i −0.344771 + 0.597160i −0.985312 0.170763i \(-0.945377\pi\)
0.640541 + 0.767924i \(0.278710\pi\)
\(654\) 0 0
\(655\) −2929.43 5073.92i −0.174752 0.302679i
\(656\) 22384.8 1.33229
\(657\) 0 0
\(658\) −103391. −6.12556
\(659\) 12885.8 + 22318.9i 0.761699 + 1.31930i 0.941974 + 0.335686i \(0.108968\pi\)
−0.180275 + 0.983616i \(0.557699\pi\)
\(660\) 0 0
\(661\) −3941.44 + 6826.77i −0.231928 + 0.401710i −0.958375 0.285511i \(-0.907837\pi\)
0.726448 + 0.687222i \(0.241170\pi\)
\(662\) 2493.93 4319.62i 0.146419 0.253605i
\(663\) 0 0
\(664\) 1932.23 + 3346.72i 0.112929 + 0.195599i
\(665\) −19598.9 −1.14287
\(666\) 0 0
\(667\) 4874.46 0.282968
\(668\) −13233.5 22921.1i −0.766495 1.32761i
\(669\) 0 0
\(670\) 12058.1 20885.3i 0.695292 1.20428i
\(671\) 1518.77 2630.58i 0.0873790 0.151345i
\(672\) 0 0
\(673\) 9815.64 + 17001.2i 0.562207 + 0.973771i 0.997304 + 0.0733871i \(0.0233808\pi\)
−0.435097 + 0.900384i \(0.643286\pi\)
\(674\) −2977.23 −0.170146
\(675\) 0 0
\(676\) 37940.5 2.15865
\(677\) −299.163 518.166i −0.0169834 0.0294161i 0.857409 0.514636i \(-0.172073\pi\)
−0.874392 + 0.485220i \(0.838740\pi\)
\(678\) 0 0
\(679\) 17205.2 29800.3i 0.972423 1.68429i
\(680\) 11470.3 19867.2i 0.646863 1.12040i
\(681\) 0 0
\(682\) 1701.81 + 2947.62i 0.0955507 + 0.165499i
\(683\) −19041.9 −1.06679 −0.533394 0.845867i \(-0.679084\pi\)
−0.533394 + 0.845867i \(0.679084\pi\)
\(684\) 0 0
\(685\) −5793.13 −0.323130
\(686\) −34921.2 60485.3i −1.94358 3.36638i
\(687\) 0 0
\(688\) −26621.1 + 46109.1i −1.47517 + 2.55508i
\(689\) 15727.3 27240.5i 0.869612 1.50621i
\(690\) 0 0
\(691\) 13585.4 + 23530.6i 0.747921 + 1.29544i 0.948817 + 0.315825i \(0.102281\pi\)
−0.200896 + 0.979613i \(0.564385\pi\)
\(692\) 22004.1 1.20877
\(693\) 0 0
\(694\) 44099.2 2.41208
\(695\) −3966.31 6869.85i −0.216476 0.374947i
\(696\) 0 0
\(697\) 5495.39 9518.29i 0.298641 0.517261i
\(698\) −18693.5 + 32378.0i −1.01369 + 1.75577i
\(699\) 0 0
\(700\) −8001.96 13859.8i −0.432065 0.748359i
\(701\) −27091.0 −1.45965 −0.729824 0.683635i \(-0.760398\pi\)
−0.729824 + 0.683635i \(0.760398\pi\)
\(702\) 0 0
\(703\) −12853.2 −0.689568
\(704\) −1656.87 2869.78i −0.0887012 0.153635i
\(705\) 0 0
\(706\) −13870.2 + 24023.9i −0.739395 + 1.28067i
\(707\) −11263.2 + 19508.4i −0.599144 + 1.03775i
\(708\) 0 0
\(709\) 2477.30 + 4290.81i 0.131223 + 0.227284i 0.924148 0.382034i \(-0.124776\pi\)
−0.792925 + 0.609319i \(0.791443\pi\)
\(710\) −1588.02 −0.0839398
\(711\) 0 0
\(712\) 56091.3 2.95240
\(713\) 4148.28 + 7185.03i 0.217888 + 0.377393i
\(714\) 0 0
\(715\) 980.152 1697.67i 0.0512666 0.0887963i
\(716\) −17578.6 + 30447.0i −0.917516 + 1.58918i
\(717\) 0 0
\(718\) 24953.6 + 43220.9i 1.29702 + 2.24650i
\(719\) −23414.3 −1.21447 −0.607235 0.794522i \(-0.707721\pi\)
−0.607235 + 0.794522i \(0.707721\pi\)
\(720\) 0 0
\(721\) 40072.8 2.06989
\(722\) −18930.4 32788.5i −0.975787 1.69011i
\(723\) 0 0
\(724\) −22629.5 + 39195.5i −1.16163 + 2.01200i
\(725\) −785.186 + 1359.98i −0.0402222 + 0.0696669i
\(726\) 0 0
\(727\) −15477.8 26808.4i −0.789603 1.36763i −0.926210 0.377007i \(-0.876953\pi\)
0.136607 0.990625i \(-0.456380\pi\)
\(728\) −126827. −6.45676
\(729\) 0 0
\(730\) −8855.88 −0.449001
\(731\) 13070.8 + 22639.2i 0.661340 + 1.14547i
\(732\) 0 0
\(733\) −7786.36 + 13486.4i −0.392354 + 0.679578i −0.992760 0.120118i \(-0.961673\pi\)
0.600405 + 0.799696i \(0.295006\pi\)
\(734\) 1910.72 3309.47i 0.0960846 0.166423i
\(735\) 0 0
\(736\) −13338.5 23103.0i −0.668021 1.15705i
\(737\) −5606.40 −0.280210
\(738\) 0 0
\(739\) −30909.9 −1.53862 −0.769310 0.638876i \(-0.779400\pi\)
−0.769310 + 0.638876i \(0.779400\pi\)
\(740\) −5247.78 9089.42i −0.260692 0.451532i
\(741\) 0 0
\(742\) −42165.7 + 73033.1i −2.08619 + 3.61338i
\(743\) −17511.6 + 30331.0i −0.864656 + 1.49763i 0.00273301 + 0.999996i \(0.499130\pi\)
−0.867389 + 0.497631i \(0.834203\pi\)
\(744\) 0 0
\(745\) −1292.77 2239.15i −0.0635752 0.110115i
\(746\) 67347.8 3.30533
\(747\) 0 0
\(748\) −9079.55 −0.443825
\(749\) 21658.6 + 37513.8i 1.05659 + 1.83007i
\(750\) 0 0
\(751\) 1805.39 3127.03i 0.0877226 0.151940i −0.818826 0.574043i \(-0.805374\pi\)
0.906548 + 0.422102i \(0.138708\pi\)
\(752\) 46908.4 81247.7i 2.27470 3.93989i
\(753\) 0 0
\(754\) 10593.5 + 18348.6i 0.511664 + 0.886227i
\(755\) 2777.93 0.133906
\(756\) 0 0
\(757\) −19982.2 −0.959399 −0.479700 0.877433i \(-0.659254\pi\)
−0.479700 + 0.877433i \(0.659254\pi\)
\(758\) 10469.0 + 18132.9i 0.501652 + 0.868887i
\(759\) 0 0
\(760\) 17688.1 30636.8i 0.844232 1.46225i
\(761\) −17578.7 + 30447.1i −0.837354 + 1.45034i 0.0547461 + 0.998500i \(0.482565\pi\)
−0.892100 + 0.451839i \(0.850768\pi\)
\(762\) 0 0
\(763\) 4866.54 + 8429.09i 0.230905 + 0.399939i
\(764\) 8582.02 0.406396
\(765\) 0 0
\(766\) −341.843 −0.0161244
\(767\) 7825.17 + 13553.6i 0.368384 + 0.638060i
\(768\) 0 0
\(769\) 19520.6 33810.6i 0.915384 1.58549i 0.109045 0.994037i \(-0.465221\pi\)
0.806339 0.591454i \(-0.201446\pi\)
\(770\) −2627.83 + 4551.54i −0.122988 + 0.213021i
\(771\) 0 0
\(772\) 35892.6 + 62167.8i 1.67332 + 2.89828i
\(773\) −18244.4 −0.848907 −0.424453 0.905450i \(-0.639534\pi\)
−0.424453 + 0.905450i \(0.639534\pi\)
\(774\) 0 0
\(775\) −2672.85 −0.123886
\(776\) 31055.7 + 53790.0i 1.43664 + 2.48834i
\(777\) 0 0
\(778\) −15490.2 + 26829.7i −0.713816 + 1.23637i
\(779\) 8474.32 14677.9i 0.389761 0.675086i
\(780\) 0 0
\(781\) 184.586 + 319.713i 0.00845713 + 0.0146482i
\(782\) −31264.3 −1.42968
\(783\) 0 0
\(784\) 117155. 5.33686
\(785\)