Properties

Label 637.2.u.h.30.1
Level $637$
Weight $2$
Character 637.30
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.1
Root \(-1.30089 + 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.h.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.82678 + 1.05469i) q^{2} +2.26165 q^{3} +(1.22476 - 2.12135i) q^{4} +(3.11923 + 1.80089i) q^{5} +(-4.13154 + 2.38535i) q^{6} +0.948212i q^{8} +2.11505 q^{9} +O(q^{10})\) \(q+(-1.82678 + 1.05469i) q^{2} +2.26165 q^{3} +(1.22476 - 2.12135i) q^{4} +(3.11923 + 1.80089i) q^{5} +(-4.13154 + 2.38535i) q^{6} +0.948212i q^{8} +2.11505 q^{9} -7.59755 q^{10} -0.886384i q^{11} +(2.76998 - 4.79774i) q^{12} +(-1.17349 + 3.40924i) q^{13} +(7.05461 + 4.07298i) q^{15} +(1.44945 + 2.51051i) q^{16} +(-2.48008 + 4.29563i) q^{17} +(-3.86375 + 2.23073i) q^{18} +2.37878i q^{19} +(7.64062 - 4.41132i) q^{20} +(0.934864 + 1.61923i) q^{22} +(-1.92926 - 3.34157i) q^{23} +2.14452i q^{24} +(3.98641 + 6.90466i) q^{25} +(-1.45200 - 7.46562i) q^{26} -2.00144 q^{27} +(-0.640986 + 1.11022i) q^{29} -17.1830 q^{30} +(7.33455 - 4.23460i) q^{31} +(-6.93800 - 4.00566i) q^{32} -2.00469i q^{33} -10.4629i q^{34} +(2.59043 - 4.48676i) q^{36} +(8.34686 - 4.81906i) q^{37} +(-2.50888 - 4.34551i) q^{38} +(-2.65402 + 7.71051i) q^{39} +(-1.70762 + 2.95769i) q^{40} +(10.4652 + 6.04207i) q^{41} +(-1.82125 - 3.15450i) q^{43} +(-1.88033 - 1.08561i) q^{44} +(6.59734 + 3.80898i) q^{45} +(7.04867 + 4.06955i) q^{46} +(2.58274 + 1.49115i) q^{47} +(3.27814 + 5.67790i) q^{48} +(-14.5646 - 8.40888i) q^{50} +(-5.60907 + 9.71520i) q^{51} +(5.79494 + 6.66487i) q^{52} +(-2.46016 - 4.26112i) q^{53} +(3.65619 - 2.11090i) q^{54} +(1.59628 - 2.76484i) q^{55} +5.37995i q^{57} -2.70418i q^{58} +(-6.34577 - 3.66373i) q^{59} +(17.2804 - 9.97684i) q^{60} -1.53926 q^{61} +(-8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(-9.80005 + 8.52090i) q^{65} +(2.11433 + 3.66213i) q^{66} -8.42649i q^{67} +(6.07501 + 10.5222i) q^{68} +(-4.36330 - 7.55745i) q^{69} +(-5.58490 + 3.22444i) q^{71} +2.00552i q^{72} +(6.19086 - 3.57430i) q^{73} +(-10.1653 + 17.6068i) q^{74} +(9.01585 + 15.6159i) q^{75} +(5.04621 + 2.91343i) q^{76} +(-3.28391 - 16.8846i) q^{78} +(-0.378775 + 0.656058i) q^{79} +10.4412i q^{80} -10.8717 q^{81} -25.4901 q^{82} -4.76766i q^{83} +(-15.4719 + 8.93270i) q^{85} +(6.65406 + 3.84172i) q^{86} +(-1.44969 + 2.51093i) q^{87} +0.840480 q^{88} +(-3.13400 + 1.80942i) q^{89} -16.0692 q^{90} -9.45150 q^{92} +(16.5882 - 9.57719i) q^{93} -6.29081 q^{94} +(-4.28391 + 7.41995i) q^{95} +(-15.6913 - 9.05939i) q^{96} +(-0.401229 + 0.231650i) q^{97} -1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82678 + 1.05469i −1.29173 + 0.745781i −0.978961 0.204047i \(-0.934590\pi\)
−0.312770 + 0.949829i \(0.601257\pi\)
\(3\) 2.26165 1.30576 0.652882 0.757460i \(-0.273560\pi\)
0.652882 + 0.757460i \(0.273560\pi\)
\(4\) 1.22476 2.12135i 0.612380 1.06067i
\(5\) 3.11923 + 1.80089i 1.39496 + 0.805382i 0.993859 0.110650i \(-0.0352933\pi\)
0.401104 + 0.916033i \(0.368627\pi\)
\(6\) −4.13154 + 2.38535i −1.68670 + 0.973814i
\(7\) 0 0
\(8\) 0.948212i 0.335243i
\(9\) 2.11505 0.705018
\(10\) −7.59755 −2.40256
\(11\) 0.886384i 0.267255i −0.991032 0.133627i \(-0.957337\pi\)
0.991032 0.133627i \(-0.0426626\pi\)
\(12\) 2.76998 4.79774i 0.799623 1.38499i
\(13\) −1.17349 + 3.40924i −0.325467 + 0.945553i
\(14\) 0 0
\(15\) 7.05461 + 4.07298i 1.82149 + 1.05164i
\(16\) 1.44945 + 2.51051i 0.362362 + 0.627629i
\(17\) −2.48008 + 4.29563i −0.601508 + 1.04184i 0.391085 + 0.920355i \(0.372100\pi\)
−0.992593 + 0.121488i \(0.961233\pi\)
\(18\) −3.86375 + 2.23073i −0.910694 + 0.525789i
\(19\) 2.37878i 0.545729i 0.962053 + 0.272864i \(0.0879710\pi\)
−0.962053 + 0.272864i \(0.912029\pi\)
\(20\) 7.64062 4.41132i 1.70849 0.986400i
\(21\) 0 0
\(22\) 0.934864 + 1.61923i 0.199314 + 0.345222i
\(23\) −1.92926 3.34157i −0.402278 0.696765i 0.591723 0.806142i \(-0.298448\pi\)
−0.994000 + 0.109376i \(0.965115\pi\)
\(24\) 2.14452i 0.437749i
\(25\) 3.98641 + 6.90466i 0.797282 + 1.38093i
\(26\) −1.45200 7.46562i −0.284761 1.46413i
\(27\) −2.00144 −0.385177
\(28\) 0 0
\(29\) −0.640986 + 1.11022i −0.119028 + 0.206163i −0.919383 0.393364i \(-0.871311\pi\)
0.800355 + 0.599527i \(0.204645\pi\)
\(30\) −17.1830 −3.13717
\(31\) 7.33455 4.23460i 1.31732 0.760557i 0.334027 0.942564i \(-0.391592\pi\)
0.983297 + 0.182006i \(0.0582591\pi\)
\(32\) −6.93800 4.00566i −1.22648 0.708107i
\(33\) 2.00469i 0.348972i
\(34\) 10.4629i 1.79437i
\(35\) 0 0
\(36\) 2.59043 4.48676i 0.431739 0.747793i
\(37\) 8.34686 4.81906i 1.37222 0.792249i 0.381009 0.924571i \(-0.375577\pi\)
0.991207 + 0.132323i \(0.0422435\pi\)
\(38\) −2.50888 4.34551i −0.406994 0.704935i
\(39\) −2.65402 + 7.71051i −0.424983 + 1.23467i
\(40\) −1.70762 + 2.95769i −0.269999 + 0.467652i
\(41\) 10.4652 + 6.04207i 1.63438 + 0.943612i 0.982719 + 0.185106i \(0.0592628\pi\)
0.651666 + 0.758506i \(0.274071\pi\)
\(42\) 0 0
\(43\) −1.82125 3.15450i −0.277738 0.481056i 0.693084 0.720856i \(-0.256251\pi\)
−0.970822 + 0.239800i \(0.922918\pi\)
\(44\) −1.88033 1.08561i −0.283470 0.163662i
\(45\) 6.59734 + 3.80898i 0.983474 + 0.567809i
\(46\) 7.04867 + 4.06955i 1.03927 + 0.600022i
\(47\) 2.58274 + 1.49115i 0.376731 + 0.217506i 0.676395 0.736539i \(-0.263541\pi\)
−0.299664 + 0.954045i \(0.596874\pi\)
\(48\) 3.27814 + 5.67790i 0.473158 + 0.819535i
\(49\) 0 0
\(50\) −14.5646 8.40888i −2.05975 1.18920i
\(51\) −5.60907 + 9.71520i −0.785427 + 1.36040i
\(52\) 5.79494 + 6.66487i 0.803614 + 0.924252i
\(53\) −2.46016 4.26112i −0.337929 0.585310i 0.646114 0.763241i \(-0.276393\pi\)
−0.984043 + 0.177931i \(0.943060\pi\)
\(54\) 3.65619 2.11090i 0.497545 0.287258i
\(55\) 1.59628 2.76484i 0.215242 0.372811i
\(56\) 0 0
\(57\) 5.37995i 0.712592i
\(58\) 2.70418i 0.355076i
\(59\) −6.34577 3.66373i −0.826148 0.476977i 0.0263837 0.999652i \(-0.491601\pi\)
−0.852532 + 0.522675i \(0.824934\pi\)
\(60\) 17.2804 9.97684i 2.23089 1.28800i
\(61\) −1.53926 −0.197082 −0.0985412 0.995133i \(-0.531418\pi\)
−0.0985412 + 0.995133i \(0.531418\pi\)
\(62\) −8.93242 + 15.4714i −1.13442 + 1.96487i
\(63\) 0 0
\(64\) 11.1012 1.38765
\(65\) −9.80005 + 8.52090i −1.21555 + 1.05689i
\(66\) 2.11433 + 3.66213i 0.260257 + 0.450778i
\(67\) 8.42649i 1.02946i −0.857352 0.514730i \(-0.827892\pi\)
0.857352 0.514730i \(-0.172108\pi\)
\(68\) 6.07501 + 10.5222i 0.736703 + 1.27601i
\(69\) −4.36330 7.55745i −0.525279 0.909811i
\(70\) 0 0
\(71\) −5.58490 + 3.22444i −0.662805 + 0.382671i −0.793345 0.608772i \(-0.791662\pi\)
0.130540 + 0.991443i \(0.458329\pi\)
\(72\) 2.00552i 0.236353i
\(73\) 6.19086 3.57430i 0.724586 0.418340i −0.0918526 0.995773i \(-0.529279\pi\)
0.816438 + 0.577433i \(0.195946\pi\)
\(74\) −10.1653 + 17.6068i −1.18169 + 2.04675i
\(75\) 9.01585 + 15.6159i 1.04106 + 1.80317i
\(76\) 5.04621 + 2.91343i 0.578840 + 0.334193i
\(77\) 0 0
\(78\) −3.28391 16.8846i −0.371830 1.91180i
\(79\) −0.378775 + 0.656058i −0.0426156 + 0.0738123i −0.886546 0.462640i \(-0.846902\pi\)
0.843931 + 0.536452i \(0.180236\pi\)
\(80\) 10.4412i 1.16736i
\(81\) −10.8717 −1.20797
\(82\) −25.4901 −2.81491
\(83\) 4.76766i 0.523319i −0.965160 0.261659i \(-0.915730\pi\)
0.965160 0.261659i \(-0.0842697\pi\)
\(84\) 0 0
\(85\) −15.4719 + 8.93270i −1.67816 + 0.968888i
\(86\) 6.65406 + 3.84172i 0.717525 + 0.414263i
\(87\) −1.44969 + 2.51093i −0.155423 + 0.269200i
\(88\) 0.840480 0.0895955
\(89\) −3.13400 + 1.80942i −0.332204 + 0.191798i −0.656819 0.754048i \(-0.728098\pi\)
0.324615 + 0.945846i \(0.394765\pi\)
\(90\) −16.0692 −1.69385
\(91\) 0 0
\(92\) −9.45150 −0.985387
\(93\) 16.5882 9.57719i 1.72011 0.993108i
\(94\) −6.29081 −0.648848
\(95\) −4.28391 + 7.41995i −0.439520 + 0.761271i
\(96\) −15.6913 9.05939i −1.60149 0.924620i
\(97\) −0.401229 + 0.231650i −0.0407386 + 0.0235205i −0.520231 0.854026i \(-0.674154\pi\)
0.479492 + 0.877546i \(0.340821\pi\)
\(98\) 0 0
\(99\) 1.87475i 0.188419i
\(100\) 19.5296 1.95296
\(101\) −5.82303 −0.579413 −0.289707 0.957115i \(-0.593558\pi\)
−0.289707 + 0.957115i \(0.593558\pi\)
\(102\) 23.6634i 2.34303i
\(103\) 4.11944 7.13508i 0.405901 0.703040i −0.588525 0.808479i \(-0.700291\pi\)
0.994426 + 0.105438i \(0.0336246\pi\)
\(104\) −3.23268 1.11271i −0.316991 0.109111i
\(105\) 0 0
\(106\) 8.98837 + 5.18944i 0.873027 + 0.504043i
\(107\) 1.91630 + 3.31913i 0.185256 + 0.320872i 0.943663 0.330909i \(-0.107355\pi\)
−0.758407 + 0.651781i \(0.774022\pi\)
\(108\) −2.45128 + 4.24574i −0.235875 + 0.408547i
\(109\) −9.02229 + 5.20902i −0.864178 + 0.498934i −0.865409 0.501066i \(-0.832942\pi\)
0.00123094 + 0.999999i \(0.499608\pi\)
\(110\) 6.73435i 0.642095i
\(111\) 18.8777 10.8990i 1.79179 1.03449i
\(112\) 0 0
\(113\) 2.45505 + 4.25228i 0.230952 + 0.400021i 0.958089 0.286472i \(-0.0924826\pi\)
−0.727136 + 0.686493i \(0.759149\pi\)
\(114\) −5.67421 9.82801i −0.531438 0.920478i
\(115\) 13.8975i 1.29595i
\(116\) 1.57011 + 2.71951i 0.145781 + 0.252500i
\(117\) −2.48199 + 7.21073i −0.229460 + 0.666632i
\(118\) 15.4565 1.42288
\(119\) 0 0
\(120\) −3.86205 + 6.68926i −0.352555 + 0.610643i
\(121\) 10.2143 0.928575
\(122\) 2.81190 1.62345i 0.254578 0.146980i
\(123\) 23.6685 + 13.6650i 2.13412 + 1.23213i
\(124\) 20.7455i 1.86300i
\(125\) 10.7074i 0.957702i
\(126\) 0 0
\(127\) −6.15508 + 10.6609i −0.546175 + 0.946003i 0.452357 + 0.891837i \(0.350583\pi\)
−0.998532 + 0.0541658i \(0.982750\pi\)
\(128\) −6.40347 + 3.69704i −0.565992 + 0.326776i
\(129\) −4.11902 7.13436i −0.362660 0.628145i
\(130\) 8.91563 25.9019i 0.781953 2.27175i
\(131\) 4.10133 7.10371i 0.358335 0.620654i −0.629348 0.777123i \(-0.716678\pi\)
0.987683 + 0.156470i \(0.0500114\pi\)
\(132\) −4.25264 2.45526i −0.370145 0.213703i
\(133\) 0 0
\(134\) 8.88737 + 15.3934i 0.767752 + 1.32979i
\(135\) −6.24295 3.60437i −0.537308 0.310215i
\(136\) −4.07316 2.35164i −0.349271 0.201652i
\(137\) −6.45670 3.72778i −0.551633 0.318485i 0.198147 0.980172i \(-0.436508\pi\)
−0.749780 + 0.661687i \(0.769841\pi\)
\(138\) 15.9416 + 9.20389i 1.35704 + 0.783487i
\(139\) −8.34028 14.4458i −0.707413 1.22528i −0.965813 0.259238i \(-0.916529\pi\)
0.258400 0.966038i \(-0.416805\pi\)
\(140\) 0 0
\(141\) 5.84125 + 3.37245i 0.491922 + 0.284011i
\(142\) 6.80160 11.7807i 0.570778 0.988616i
\(143\) 3.02190 + 1.04016i 0.252704 + 0.0869826i
\(144\) 3.06566 + 5.30987i 0.255471 + 0.442489i
\(145\) −3.99877 + 2.30869i −0.332080 + 0.191726i
\(146\) −7.53958 + 13.0589i −0.623980 + 1.08076i
\(147\) 0 0
\(148\) 23.6088i 1.94063i
\(149\) 2.52163i 0.206580i −0.994651 0.103290i \(-0.967063\pi\)
0.994651 0.103290i \(-0.0329370\pi\)
\(150\) −32.9400 19.0179i −2.68954 1.55281i
\(151\) 13.7674 7.94862i 1.12038 0.646849i 0.178879 0.983871i \(-0.442753\pi\)
0.941497 + 0.337022i \(0.109420\pi\)
\(152\) −2.25558 −0.182952
\(153\) −5.24550 + 9.08548i −0.424074 + 0.734517i
\(154\) 0 0
\(155\) 30.5042 2.45016
\(156\) 13.1061 + 15.0736i 1.04933 + 1.20685i
\(157\) −6.49155 11.2437i −0.518082 0.897344i −0.999779 0.0210065i \(-0.993313\pi\)
0.481697 0.876338i \(-0.340020\pi\)
\(158\) 1.59797i 0.127128i
\(159\) −5.56402 9.63717i −0.441256 0.764277i
\(160\) −14.4275 24.9892i −1.14059 1.97557i
\(161\) 0 0
\(162\) 19.8603 11.4663i 1.56037 0.900880i
\(163\) 2.31948i 0.181676i −0.995866 0.0908378i \(-0.971046\pi\)
0.995866 0.0908378i \(-0.0289545\pi\)
\(164\) 25.6346 14.8002i 2.00173 1.15570i
\(165\) 3.61023 6.25309i 0.281056 0.486803i
\(166\) 5.02843 + 8.70949i 0.390282 + 0.675987i
\(167\) −11.9441 6.89591i −0.924260 0.533622i −0.0392682 0.999229i \(-0.512503\pi\)
−0.884992 + 0.465607i \(0.845836\pi\)
\(168\) 0 0
\(169\) −10.2459 8.00140i −0.788143 0.615493i
\(170\) 18.8425 32.6362i 1.44516 2.50309i
\(171\) 5.03124i 0.384748i
\(172\) −8.92237 −0.680324
\(173\) 3.68432 0.280113 0.140057 0.990143i \(-0.455272\pi\)
0.140057 + 0.990143i \(0.455272\pi\)
\(174\) 6.11590i 0.463645i
\(175\) 0 0
\(176\) 2.22528 1.28477i 0.167737 0.0968429i
\(177\) −14.3519 8.28607i −1.07875 0.622819i
\(178\) 3.81677 6.61083i 0.286079 0.495503i
\(179\) 5.89277 0.440446 0.220223 0.975450i \(-0.429322\pi\)
0.220223 + 0.975450i \(0.429322\pi\)
\(180\) 16.1603 9.33017i 1.20452 0.695430i
\(181\) −2.11543 −0.157239 −0.0786193 0.996905i \(-0.525051\pi\)
−0.0786193 + 0.996905i \(0.525051\pi\)
\(182\) 0 0
\(183\) −3.48127 −0.257343
\(184\) 3.16851 1.82934i 0.233586 0.134861i
\(185\) 34.7144 2.55225
\(186\) −20.2020 + 34.9909i −1.48128 + 2.56566i
\(187\) 3.80758 + 2.19830i 0.278437 + 0.160756i
\(188\) 6.32647 3.65259i 0.461406 0.266393i
\(189\) 0 0
\(190\) 18.0729i 1.31114i
\(191\) −11.3667 −0.822462 −0.411231 0.911531i \(-0.634901\pi\)
−0.411231 + 0.911531i \(0.634901\pi\)
\(192\) 25.1070 1.81194
\(193\) 14.0894i 1.01417i −0.861895 0.507087i \(-0.830722\pi\)
0.861895 0.507087i \(-0.169278\pi\)
\(194\) 0.488639 0.846348i 0.0350823 0.0607643i
\(195\) −22.1643 + 19.2713i −1.58722 + 1.38004i
\(196\) 0 0
\(197\) −19.8815 11.4786i −1.41650 0.817814i −0.420507 0.907289i \(-0.638148\pi\)
−0.995989 + 0.0894753i \(0.971481\pi\)
\(198\) 1.97729 + 3.42476i 0.140520 + 0.243387i
\(199\) −1.57492 + 2.72785i −0.111643 + 0.193372i −0.916433 0.400188i \(-0.868945\pi\)
0.804790 + 0.593560i \(0.202278\pi\)
\(200\) −6.54708 + 3.77996i −0.462949 + 0.267283i
\(201\) 19.0578i 1.34423i
\(202\) 10.6374 6.14152i 0.748446 0.432116i
\(203\) 0 0
\(204\) 13.7395 + 23.7976i 0.961959 + 1.66616i
\(205\) 21.7622 + 37.6932i 1.51994 + 2.63261i
\(206\) 17.3790i 1.21085i
\(207\) −4.08048 7.06760i −0.283613 0.491232i
\(208\) −10.2599 + 1.99546i −0.711393 + 0.138360i
\(209\) 2.10851 0.145849
\(210\) 0 0
\(211\) 7.43191 12.8725i 0.511634 0.886176i −0.488275 0.872690i \(-0.662374\pi\)
0.999909 0.0134864i \(-0.00429298\pi\)
\(212\) −12.0524 −0.827764
\(213\) −12.6311 + 7.29255i −0.865467 + 0.499678i
\(214\) −7.00133 4.04222i −0.478601 0.276321i
\(215\) 13.1195i 0.894741i
\(216\) 1.89779i 0.129128i
\(217\) 0 0
\(218\) 10.9878 19.0315i 0.744191 1.28898i
\(219\) 14.0016 8.08380i 0.946137 0.546253i
\(220\) −3.91012 6.77253i −0.263620 0.456604i
\(221\) −11.7345 13.4961i −0.789347 0.907843i
\(222\) −22.9903 + 39.8203i −1.54301 + 2.67257i
\(223\) 3.79396 + 2.19044i 0.254062 + 0.146683i 0.621623 0.783317i \(-0.286474\pi\)
−0.367561 + 0.930000i \(0.619807\pi\)
\(224\) 0 0
\(225\) 8.43147 + 14.6037i 0.562098 + 0.973582i
\(226\) −8.96971 5.17866i −0.596656 0.344480i
\(227\) −11.7488 6.78316i −0.779793 0.450214i 0.0565636 0.998399i \(-0.481986\pi\)
−0.836357 + 0.548185i \(0.815319\pi\)
\(228\) 11.4127 + 6.58915i 0.755827 + 0.436377i
\(229\) 14.3050 + 8.25900i 0.945302 + 0.545770i 0.891618 0.452788i \(-0.149571\pi\)
0.0536833 + 0.998558i \(0.482904\pi\)
\(230\) 14.6576 + 25.3877i 0.966495 + 1.67402i
\(231\) 0 0
\(232\) −1.05272 0.607791i −0.0691147 0.0399034i
\(233\) −8.25131 + 14.2917i −0.540561 + 0.936279i 0.458311 + 0.888792i \(0.348455\pi\)
−0.998872 + 0.0474874i \(0.984879\pi\)
\(234\) −3.07106 15.7902i −0.200761 1.03224i
\(235\) 5.37078 + 9.30246i 0.350351 + 0.606826i
\(236\) −15.5441 + 8.97438i −1.01183 + 0.584182i
\(237\) −0.856657 + 1.48377i −0.0556458 + 0.0963814i
\(238\) 0 0
\(239\) 30.4210i 1.96777i 0.178796 + 0.983886i \(0.442780\pi\)
−0.178796 + 0.983886i \(0.557220\pi\)
\(240\) 23.6143i 1.52429i
\(241\) 25.5602 + 14.7572i 1.64648 + 0.950593i 0.978458 + 0.206448i \(0.0661904\pi\)
0.668018 + 0.744145i \(0.267143\pi\)
\(242\) −18.6594 + 10.7730i −1.19947 + 0.692514i
\(243\) −18.5837 −1.19214
\(244\) −1.88523 + 3.26531i −0.120689 + 0.209040i
\(245\) 0 0
\(246\) −57.6497 −3.67561
\(247\) −8.10982 2.79146i −0.516015 0.177617i
\(248\) 4.01530 + 6.95471i 0.254972 + 0.441624i
\(249\) 10.7828i 0.683331i
\(250\) −11.2931 19.5602i −0.714236 1.23709i
\(251\) −6.49134 11.2433i −0.409730 0.709673i 0.585130 0.810940i \(-0.301044\pi\)
−0.994859 + 0.101267i \(0.967710\pi\)
\(252\) 0 0
\(253\) −2.96191 + 1.71006i −0.186214 + 0.107511i
\(254\) 25.9669i 1.62931i
\(255\) −34.9920 + 20.2026i −2.19128 + 1.26514i
\(256\) −3.30268 + 5.72042i −0.206418 + 0.357526i
\(257\) −2.29261 3.97091i −0.143009 0.247698i 0.785620 0.618710i \(-0.212344\pi\)
−0.928628 + 0.371011i \(0.879011\pi\)
\(258\) 15.0491 + 8.68862i 0.936918 + 0.540930i
\(259\) 0 0
\(260\) 6.07307 + 31.2253i 0.376636 + 1.93651i
\(261\) −1.35572 + 2.34818i −0.0839170 + 0.145348i
\(262\) 17.3026i 1.06896i
\(263\) −2.66499 −0.164330 −0.0821652 0.996619i \(-0.526184\pi\)
−0.0821652 + 0.996619i \(0.526184\pi\)
\(264\) 1.90087 0.116990
\(265\) 17.7219i 1.08865i
\(266\) 0 0
\(267\) −7.08801 + 4.09227i −0.433779 + 0.250443i
\(268\) −17.8755 10.3204i −1.09192 0.630421i
\(269\) −5.96282 + 10.3279i −0.363559 + 0.629703i −0.988544 0.150934i \(-0.951772\pi\)
0.624984 + 0.780637i \(0.285105\pi\)
\(270\) 15.2060 0.925409
\(271\) 11.2828 6.51416i 0.685384 0.395707i −0.116496 0.993191i \(-0.537166\pi\)
0.801881 + 0.597484i \(0.203833\pi\)
\(272\) −14.3790 −0.871853
\(273\) 0 0
\(274\) 15.7267 0.950082
\(275\) 6.12018 3.53349i 0.369061 0.213077i
\(276\) −21.3760 −1.28668
\(277\) 10.6824 18.5025i 0.641846 1.11171i −0.343174 0.939272i \(-0.611502\pi\)
0.985020 0.172438i \(-0.0551646\pi\)
\(278\) 30.4718 + 17.5929i 1.82758 + 1.05515i
\(279\) 15.5130 8.95641i 0.928737 0.536206i
\(280\) 0 0
\(281\) 17.2678i 1.03011i −0.857158 0.515054i \(-0.827772\pi\)
0.857158 0.515054i \(-0.172228\pi\)
\(282\) −14.2276 −0.847242
\(283\) 21.2402 1.26260 0.631299 0.775539i \(-0.282522\pi\)
0.631299 + 0.775539i \(0.282522\pi\)
\(284\) 15.7967i 0.937360i
\(285\) −9.68870 + 16.7813i −0.573909 + 0.994040i
\(286\) −6.61741 + 1.28703i −0.391295 + 0.0761037i
\(287\) 0 0
\(288\) −14.6742 8.47218i −0.864688 0.499228i
\(289\) −3.80160 6.58457i −0.223624 0.387327i
\(290\) 4.86993 8.43496i 0.285972 0.495318i
\(291\) −0.907439 + 0.523910i −0.0531950 + 0.0307122i
\(292\) 17.5106i 1.02473i
\(293\) −0.363782 + 0.210030i −0.0212524 + 0.0122701i −0.510589 0.859825i \(-0.670572\pi\)
0.489336 + 0.872095i \(0.337239\pi\)
\(294\) 0 0
\(295\) −13.1959 22.8561i −0.768298 1.33073i
\(296\) 4.56949 + 7.91459i 0.265596 + 0.460026i
\(297\) 1.77404i 0.102940i
\(298\) 2.65955 + 4.60648i 0.154064 + 0.266846i
\(299\) 13.6562 2.65601i 0.789757 0.153601i
\(300\) 44.1690 2.55010
\(301\) 0 0
\(302\) −16.7667 + 29.0408i −0.964817 + 1.67111i
\(303\) −13.1696 −0.756577
\(304\) −5.97195 + 3.44791i −0.342515 + 0.197751i
\(305\) −4.80132 2.77204i −0.274923 0.158727i
\(306\) 22.1296i 1.26507i
\(307\) 14.0807i 0.803628i 0.915721 + 0.401814i \(0.131620\pi\)
−0.915721 + 0.401814i \(0.868380\pi\)
\(308\) 0 0
\(309\) 9.31673 16.1370i 0.530010 0.918004i
\(310\) −55.7246 + 32.1726i −3.16495 + 1.82728i
\(311\) 5.19240 + 8.99349i 0.294434 + 0.509974i 0.974853 0.222849i \(-0.0715356\pi\)
−0.680419 + 0.732823i \(0.738202\pi\)
\(312\) −7.31119 2.51657i −0.413915 0.142473i
\(313\) −3.42379 + 5.93018i −0.193524 + 0.335194i −0.946416 0.322951i \(-0.895325\pi\)
0.752892 + 0.658145i \(0.228658\pi\)
\(314\) 23.7173 + 13.6932i 1.33845 + 0.772752i
\(315\) 0 0
\(316\) 0.927818 + 1.60703i 0.0521938 + 0.0904024i
\(317\) 0.607299 + 0.350624i 0.0341093 + 0.0196930i 0.516958 0.856011i \(-0.327064\pi\)
−0.482848 + 0.875704i \(0.660398\pi\)
\(318\) 20.3285 + 11.7367i 1.13997 + 0.658160i
\(319\) 0.984082 + 0.568160i 0.0550980 + 0.0318109i
\(320\) 34.6272 + 19.9920i 1.93572 + 1.11759i
\(321\) 4.33400 + 7.50670i 0.241900 + 0.418983i
\(322\) 0 0
\(323\) −10.2183 5.89956i −0.568563 0.328260i
\(324\) −13.3152 + 23.0627i −0.739735 + 1.28126i
\(325\) −28.2177 + 5.48810i −1.56523 + 0.304425i
\(326\) 2.44634 + 4.23719i 0.135490 + 0.234676i
\(327\) −20.4052 + 11.7810i −1.12841 + 0.651489i
\(328\) −5.72916 + 9.92319i −0.316340 + 0.547917i
\(329\) 0 0
\(330\) 15.2307i 0.838424i
\(331\) 4.19865i 0.230778i 0.993320 + 0.115389i \(0.0368115\pi\)
−0.993320 + 0.115389i \(0.963188\pi\)
\(332\) −10.1139 5.83924i −0.555070 0.320470i
\(333\) 17.6541 10.1926i 0.967436 0.558550i
\(334\) 29.0923 1.59186
\(335\) 15.1752 26.2842i 0.829109 1.43606i
\(336\) 0 0
\(337\) −20.4278 −1.11278 −0.556388 0.830923i \(-0.687813\pi\)
−0.556388 + 0.830923i \(0.687813\pi\)
\(338\) 27.1560 + 3.81059i 1.47709 + 0.207269i
\(339\) 5.55247 + 9.61716i 0.301569 + 0.522333i
\(340\) 43.7617i 2.37331i
\(341\) −3.75349 6.50123i −0.203263 0.352061i
\(342\) −5.30642 9.19098i −0.286938 0.496991i
\(343\) 0 0
\(344\) 2.99113 1.72693i 0.161271 0.0931098i
\(345\) 31.4313i 1.69220i
\(346\) −6.73045 + 3.88583i −0.361831 + 0.208903i
\(347\) −3.98500 + 6.90222i −0.213926 + 0.370531i −0.952940 0.303160i \(-0.901959\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(348\) 3.55103 + 6.15057i 0.190355 + 0.329705i
\(349\) 18.7038 + 10.7986i 1.00119 + 0.578037i 0.908600 0.417668i \(-0.137152\pi\)
0.0925892 + 0.995704i \(0.470486\pi\)
\(350\) 0 0
\(351\) 2.34866 6.82338i 0.125362 0.364205i
\(352\) −3.55055 + 6.14974i −0.189245 + 0.327782i
\(353\) 21.6176i 1.15059i −0.817946 0.575295i \(-0.804887\pi\)
0.817946 0.575295i \(-0.195113\pi\)
\(354\) 34.9571 1.85795
\(355\) −23.2275 −1.23279
\(356\) 8.86441i 0.469813i
\(357\) 0 0
\(358\) −10.7648 + 6.21507i −0.568938 + 0.328476i
\(359\) 11.8501 + 6.84168i 0.625426 + 0.361090i 0.778979 0.627051i \(-0.215738\pi\)
−0.153552 + 0.988141i \(0.549071\pi\)
\(360\) −3.61172 + 6.25568i −0.190354 + 0.329703i
\(361\) 13.3414 0.702180
\(362\) 3.86443 2.23113i 0.203110 0.117266i
\(363\) 23.1012 1.21250
\(364\) 0 0
\(365\) 25.7477 1.34769
\(366\) 6.35953 3.67168i 0.332418 0.191922i
\(367\) −11.4128 −0.595741 −0.297871 0.954606i \(-0.596276\pi\)
−0.297871 + 0.954606i \(0.596276\pi\)
\(368\) 5.59271 9.68685i 0.291540 0.504962i
\(369\) 22.1344 + 12.7793i 1.15227 + 0.665263i
\(370\) −63.4157 + 36.6131i −3.29683 + 1.90342i
\(371\) 0 0
\(372\) 46.9190i 2.43264i
\(373\) −31.2808 −1.61966 −0.809830 0.586664i \(-0.800441\pi\)
−0.809830 + 0.586664i \(0.800441\pi\)
\(374\) −9.27416 −0.479555
\(375\) 24.2164i 1.25053i
\(376\) −1.41392 + 2.44898i −0.0729175 + 0.126297i
\(377\) −3.03282 3.48811i −0.156198 0.179647i
\(378\) 0 0
\(379\) 23.7421 + 13.7075i 1.21955 + 0.704108i 0.964822 0.262904i \(-0.0846803\pi\)
0.254729 + 0.967012i \(0.418014\pi\)
\(380\) 10.4935 + 18.1753i 0.538307 + 0.932374i
\(381\) −13.9206 + 24.1112i −0.713175 + 1.23526i
\(382\) 20.7644 11.9883i 1.06240 0.613377i
\(383\) 16.1006i 0.822705i 0.911476 + 0.411352i \(0.134943\pi\)
−0.911476 + 0.411352i \(0.865057\pi\)
\(384\) −14.4824 + 8.36142i −0.739052 + 0.426692i
\(385\) 0 0
\(386\) 14.8600 + 25.7382i 0.756353 + 1.31004i
\(387\) −3.85204 6.67193i −0.195810 0.339153i
\(388\) 1.13486i 0.0576139i
\(389\) 10.5690 + 18.3060i 0.535870 + 0.928153i 0.999121 + 0.0419264i \(0.0133495\pi\)
−0.463251 + 0.886227i \(0.653317\pi\)
\(390\) 20.1640 58.5810i 1.02104 2.96636i
\(391\) 19.1388 0.967893
\(392\) 0 0
\(393\) 9.27576 16.0661i 0.467900 0.810427i
\(394\) 48.4255 2.43964
\(395\) −2.36298 + 1.36427i −0.118894 + 0.0686437i
\(396\) −3.97699 2.29612i −0.199851 0.115384i
\(397\) 13.0984i 0.657390i 0.944436 + 0.328695i \(0.106609\pi\)
−0.944436 + 0.328695i \(0.893391\pi\)
\(398\) 6.64426i 0.333046i
\(399\) 0 0
\(400\) −11.5562 + 20.0159i −0.577808 + 1.00079i
\(401\) −16.8396 + 9.72236i −0.840930 + 0.485511i −0.857580 0.514350i \(-0.828033\pi\)
0.0166501 + 0.999861i \(0.494700\pi\)
\(402\) 20.1001 + 34.8144i 1.00250 + 1.73639i
\(403\) 5.82979 + 29.9745i 0.290402 + 1.49314i
\(404\) −7.13182 + 12.3527i −0.354821 + 0.614568i
\(405\) −33.9114 19.5788i −1.68507 0.972876i
\(406\) 0 0
\(407\) −4.27154 7.39853i −0.211732 0.366731i
\(408\) −9.21206 5.31859i −0.456065 0.263309i
\(409\) −20.8330 12.0279i −1.03013 0.594743i −0.113105 0.993583i \(-0.536079\pi\)
−0.917020 + 0.398840i \(0.869413\pi\)
\(410\) −79.5096 45.9049i −3.92670 2.26708i
\(411\) −14.6028 8.43092i −0.720302 0.415867i
\(412\) −10.0907 17.4775i −0.497131 0.861056i
\(413\) 0 0
\(414\) 14.9083 + 8.60732i 0.732703 + 0.423026i
\(415\) 8.58603 14.8714i 0.421472 0.730011i
\(416\) 21.7979 18.9527i 1.06873 0.929234i
\(417\) −18.8628 32.6713i −0.923714 1.59992i
\(418\) −3.85179 + 2.22383i −0.188397 + 0.108771i
\(419\) −19.5119 + 33.7956i −0.953218 + 1.65102i −0.214825 + 0.976653i \(0.568918\pi\)
−0.738394 + 0.674370i \(0.764415\pi\)
\(420\) 0 0
\(421\) 22.0284i 1.07360i 0.843710 + 0.536799i \(0.180367\pi\)
−0.843710 + 0.536799i \(0.819633\pi\)
\(422\) 31.3536i 1.52627i
\(423\) 5.46263 + 3.15385i 0.265602 + 0.153346i
\(424\) 4.04045 2.33275i 0.196221 0.113289i
\(425\) −39.5465 −1.91828
\(426\) 15.3828 26.6438i 0.745301 1.29090i
\(427\) 0 0
\(428\) 9.38803 0.453787
\(429\) 6.83447 + 2.35248i 0.329971 + 0.113579i
\(430\) 13.8370 + 23.9664i 0.667281 + 1.15576i
\(431\) 35.8797i 1.72826i 0.503267 + 0.864131i \(0.332131\pi\)
−0.503267 + 0.864131i \(0.667869\pi\)
\(432\) −2.90098 5.02464i −0.139573 0.241748i
\(433\) 6.10678 + 10.5773i 0.293473 + 0.508310i 0.974629 0.223828i \(-0.0718555\pi\)
−0.681155 + 0.732139i \(0.738522\pi\)
\(434\) 0 0
\(435\) −9.04381 + 5.22145i −0.433618 + 0.250349i
\(436\) 25.5192i 1.22215i
\(437\) 7.94884 4.58927i 0.380245 0.219534i
\(438\) −17.0519 + 29.5347i −0.814770 + 1.41122i
\(439\) −7.87765 13.6445i −0.375980 0.651216i 0.614493 0.788922i \(-0.289361\pi\)
−0.990473 + 0.137706i \(0.956027\pi\)
\(440\) 2.62165 + 1.51361i 0.124982 + 0.0721586i
\(441\) 0 0
\(442\) 35.6706 + 12.2781i 1.69668 + 0.584009i
\(443\) 7.53532 13.0516i 0.358014 0.620099i −0.629615 0.776907i \(-0.716787\pi\)
0.987629 + 0.156809i \(0.0501207\pi\)
\(444\) 53.3947i 2.53400i
\(445\) −13.0342 −0.617883
\(446\) −9.24099 −0.437574
\(447\) 5.70305i 0.269745i
\(448\) 0 0
\(449\) 26.6585 15.3913i 1.25809 0.726360i 0.285388 0.958412i \(-0.407877\pi\)
0.972703 + 0.232052i \(0.0745441\pi\)
\(450\) −30.8049 17.7852i −1.45216 0.838404i
\(451\) 5.35559 9.27616i 0.252185 0.436797i
\(452\) 12.0274 0.565722
\(453\) 31.1370 17.9770i 1.46295 0.844632i
\(454\) 28.6166 1.34304
\(455\) 0 0
\(456\) −5.10133 −0.238892
\(457\) 6.71687 3.87799i 0.314202 0.181405i −0.334603 0.942359i \(-0.608602\pi\)
0.648805 + 0.760955i \(0.275269\pi\)
\(458\) −34.8429 −1.62810
\(459\) 4.96373 8.59743i 0.231687 0.401294i
\(460\) −29.4814 17.0211i −1.37458 0.793613i
\(461\) 1.27498 0.736110i 0.0593817 0.0342840i −0.470015 0.882658i \(-0.655752\pi\)
0.529397 + 0.848374i \(0.322418\pi\)
\(462\) 0 0
\(463\) 14.0366i 0.652335i 0.945312 + 0.326168i \(0.105757\pi\)
−0.945312 + 0.326168i \(0.894243\pi\)
\(464\) −3.71630 −0.172525
\(465\) 68.9898 3.19933
\(466\) 34.8104i 1.61256i
\(467\) 15.6903 27.1764i 0.726060 1.25757i −0.232476 0.972602i \(-0.574683\pi\)
0.958536 0.284971i \(-0.0919841\pi\)
\(468\) 12.2566 + 14.0966i 0.566562 + 0.651614i
\(469\) 0 0
\(470\) −19.6225 11.3291i −0.905119 0.522571i
\(471\) −14.6816 25.4293i −0.676492 1.17172i
\(472\) 3.47399 6.01713i 0.159903 0.276961i
\(473\) −2.79610 + 1.61433i −0.128565 + 0.0742268i
\(474\) 3.61404i 0.165999i
\(475\) −16.4246 + 9.48277i −0.753614 + 0.435099i
\(476\) 0 0
\(477\) −5.20337 9.01251i −0.238246 0.412654i
\(478\) −32.0849 55.5726i −1.46753 2.54183i
\(479\) 41.1951i 1.88225i −0.338059 0.941125i \(-0.609770\pi\)
0.338059 0.941125i \(-0.390230\pi\)
\(480\) −32.6299 56.5167i −1.48935 2.57962i
\(481\) 6.63441 + 34.1116i 0.302503 + 1.55535i
\(482\) −62.2572 −2.83574
\(483\) 0 0
\(484\) 12.5101 21.6681i 0.568641 0.984914i
\(485\) −1.66870 −0.0757719
\(486\) 33.9484 19.6001i 1.53993 0.889078i
\(487\) −24.5314 14.1632i −1.11163 0.641798i −0.172376 0.985031i \(-0.555144\pi\)
−0.939250 + 0.343234i \(0.888478\pi\)
\(488\) 1.45955i 0.0660706i
\(489\) 5.24584i 0.237225i
\(490\) 0 0
\(491\) 17.3931 30.1258i 0.784941 1.35956i −0.144094 0.989564i \(-0.546027\pi\)
0.929034 0.369993i \(-0.120640\pi\)
\(492\) 57.9765 33.4728i 2.61378 1.50907i
\(493\) −3.17940 5.50687i −0.143193 0.248017i
\(494\) 17.7590 3.45398i 0.799016 0.155402i
\(495\) 3.37622 5.84778i 0.151750 0.262838i
\(496\) 21.2621 + 12.2757i 0.954695 + 0.551194i
\(497\) 0 0
\(498\) 11.3725 + 19.6978i 0.509615 + 0.882680i
\(499\) −0.0601788 0.0347442i −0.00269397 0.00155537i 0.498652 0.866802i \(-0.333828\pi\)
−0.501346 + 0.865247i \(0.667162\pi\)
\(500\) 22.7142 + 13.1140i 1.01581 + 0.586477i
\(501\) −27.0133 15.5961i −1.20686 0.696783i
\(502\) 23.7165 + 13.6928i 1.05852 + 0.611138i
\(503\) −12.8686 22.2891i −0.573782 0.993820i −0.996173 0.0874060i \(-0.972142\pi\)
0.422391 0.906414i \(-0.361191\pi\)
\(504\) 0 0
\(505\) −18.1634 10.4866i −0.808260 0.466649i
\(506\) 3.60719 6.24783i 0.160359 0.277750i
\(507\) −23.1725 18.0964i −1.02913 0.803688i
\(508\) 15.0770 + 26.1141i 0.668933 + 1.15863i
\(509\) 6.09682 3.52000i 0.270237 0.156021i −0.358759 0.933430i \(-0.616800\pi\)
0.628995 + 0.777409i \(0.283467\pi\)
\(510\) 42.6152 73.8117i 1.88703 3.26844i
\(511\) 0 0
\(512\) 28.7215i 1.26932i
\(513\) 4.76097i 0.210202i
\(514\) 8.37619 + 4.83599i 0.369458 + 0.213307i
\(515\) 25.6990 14.8373i 1.13243 0.653810i
\(516\) −20.1793 −0.888342
\(517\) 1.32173 2.28930i 0.0581295 0.100683i
\(518\) 0 0
\(519\) 8.33263 0.365762
\(520\) −8.07961 9.29252i −0.354314 0.407504i
\(521\) −8.16266 14.1381i −0.357613 0.619403i 0.629949 0.776637i \(-0.283076\pi\)
−0.987561 + 0.157234i \(0.949742\pi\)
\(522\) 5.71948i 0.250335i
\(523\) 3.54473 + 6.13965i 0.155000 + 0.268468i 0.933059 0.359723i \(-0.117129\pi\)
−0.778059 + 0.628191i \(0.783796\pi\)
\(524\) −10.0463 17.4007i −0.438874 0.760152i
\(525\) 0 0
\(526\) 4.86836 2.81075i 0.212271 0.122555i
\(527\) 42.0086i 1.82993i
\(528\) 5.03280 2.90569i 0.219025 0.126454i
\(529\) 4.05594 7.02510i 0.176345 0.305439i
\(530\) 18.6912 + 32.3741i 0.811894 + 1.40624i
\(531\) −13.4216 7.74899i −0.582449 0.336277i
\(532\) 0 0
\(533\) −32.8796 + 28.5880i −1.42417 + 1.23828i
\(534\) 8.63218 14.9514i 0.373551 0.647009i
\(535\) 13.8042i 0.596807i
\(536\) 7.99010 0.345120
\(537\) 13.3274 0.575118
\(538\) 25.1558i 1.08454i
\(539\) 0 0
\(540\) −15.2922 + 8.82897i −0.658073 + 0.379938i
\(541\) −22.0977 12.7581i −0.950055 0.548515i −0.0569571 0.998377i \(-0.518140\pi\)
−0.893098 + 0.449862i \(0.851473\pi\)
\(542\) −13.7409 + 23.7999i −0.590222 + 1.02229i
\(543\) −4.78436 −0.205316
\(544\) 34.4136 19.8687i 1.47547 0.851864i
\(545\) −37.5235 −1.60733
\(546\) 0 0
\(547\) −13.3073 −0.568978 −0.284489 0.958679i \(-0.591824\pi\)
−0.284489 + 0.958679i \(0.591824\pi\)
\(548\) −15.8158 + 9.13126i −0.675618 + 0.390068i
\(549\) −3.25562 −0.138947
\(550\) −7.45350 + 12.9098i −0.317818 + 0.550478i
\(551\) −2.64097 1.52476i −0.112509 0.0649571i
\(552\) 7.16607 4.13733i 0.305008 0.176096i
\(553\) 0 0
\(554\) 45.0669i 1.91471i
\(555\) 78.5118 3.33264
\(556\) −40.8594 −1.73282
\(557\) 17.0071i 0.720612i 0.932834 + 0.360306i \(0.117328\pi\)
−0.932834 + 0.360306i \(0.882672\pi\)
\(558\) −18.8926 + 32.7229i −0.799786 + 1.38527i
\(559\) 12.8916 2.50732i 0.545259 0.106048i
\(560\) 0 0
\(561\) 8.61140 + 4.97179i 0.363573 + 0.209909i
\(562\) 18.2122 + 31.5445i 0.768235 + 1.33062i
\(563\) −12.4596 + 21.5807i −0.525111 + 0.909519i 0.474461 + 0.880276i \(0.342643\pi\)
−0.999572 + 0.0292428i \(0.990690\pi\)
\(564\) 14.3083 8.26088i 0.602486 0.347846i
\(565\) 17.6851i 0.744019i
\(566\) −38.8013 + 22.4019i −1.63094 + 0.941623i
\(567\) 0 0
\(568\) −3.05745 5.29566i −0.128288 0.222201i
\(569\) 2.94065 + 5.09335i 0.123278 + 0.213524i 0.921059 0.389424i \(-0.127326\pi\)
−0.797780 + 0.602948i \(0.793993\pi\)
\(570\) 40.8745i 1.71204i
\(571\) 4.46311 + 7.73034i 0.186775 + 0.323504i 0.944173 0.329449i \(-0.106863\pi\)
−0.757398 + 0.652954i \(0.773530\pi\)
\(572\) 5.90764 5.13655i 0.247011 0.214770i
\(573\) −25.7074 −1.07394
\(574\) 0 0
\(575\) 15.3816 26.6417i 0.641457 1.11104i
\(576\) 23.4796 0.978317
\(577\) −31.3443 + 18.0967i −1.30488 + 0.753374i −0.981237 0.192804i \(-0.938242\pi\)
−0.323645 + 0.946179i \(0.604908\pi\)
\(578\) 13.8894 + 8.01905i 0.577723 + 0.333549i
\(579\) 31.8652i 1.32427i
\(580\) 11.3104i 0.469638i
\(581\) 0 0
\(582\) 1.10513 1.91414i 0.0458091 0.0793437i
\(583\) −3.77699 + 2.18065i −0.156427 + 0.0903132i
\(584\) 3.38919 + 5.87025i 0.140246 + 0.242913i
\(585\) −20.7276 + 18.0222i −0.856982 + 0.745124i
\(586\) 0.443035 0.767358i 0.0183016 0.0316993i
\(587\) 31.6008 + 18.2447i 1.30431 + 0.753041i 0.981139 0.193301i \(-0.0619195\pi\)
0.323166 + 0.946342i \(0.395253\pi\)
\(588\) 0 0
\(589\) 10.0732 + 17.4472i 0.415058 + 0.718901i
\(590\) 48.2123 + 27.8354i 1.98487 + 1.14596i
\(591\) −44.9649 25.9605i −1.84961 1.06787i
\(592\) 24.1967 + 13.9699i 0.994476 + 0.574161i
\(593\) −30.3048 17.4965i −1.24447 0.718495i −0.274468 0.961596i \(-0.588502\pi\)
−0.970001 + 0.243102i \(0.921835\pi\)
\(594\) −1.87107 3.24079i −0.0767711 0.132971i
\(595\) 0 0
\(596\) −5.34926 3.08839i −0.219114 0.126506i
\(597\) −3.56193 + 6.16944i −0.145780 + 0.252498i
\(598\) −22.1456 + 19.2550i −0.905601 + 0.787397i
\(599\) 16.2526 + 28.1503i 0.664062 + 1.15019i 0.979539 + 0.201256i \(0.0645025\pi\)
−0.315476 + 0.948934i \(0.602164\pi\)
\(600\) −14.8072 + 8.54894i −0.604501 + 0.349009i
\(601\) −10.0390 + 17.3881i −0.409500 + 0.709275i −0.994834 0.101518i \(-0.967630\pi\)
0.585334 + 0.810792i \(0.300963\pi\)
\(602\) 0 0
\(603\) 17.8225i 0.725788i
\(604\) 38.9406i 1.58447i
\(605\) 31.8608 + 18.3949i 1.29533 + 0.747858i
\(606\) 24.0581 13.8900i 0.977294 0.564241i
\(607\) 9.71601 0.394361 0.197180 0.980367i \(-0.436822\pi\)
0.197180 + 0.980367i \(0.436822\pi\)
\(608\) 9.52856 16.5039i 0.386434 0.669323i
\(609\) 0 0
\(610\) 11.6946 0.473502
\(611\) −8.11449 + 7.05535i −0.328277 + 0.285429i
\(612\) 12.8490 + 22.2551i 0.519389 + 0.899607i
\(613\) 11.8816i 0.479893i 0.970786 + 0.239947i \(0.0771299\pi\)
−0.970786 + 0.239947i \(0.922870\pi\)
\(614\) −14.8508 25.7224i −0.599331 1.03807i
\(615\) 49.2184 + 85.2488i 1.98468 + 3.43756i
\(616\) 0 0
\(617\) −17.3105 + 9.99422i −0.696895 + 0.402352i −0.806190 0.591657i \(-0.798474\pi\)
0.109295 + 0.994009i \(0.465141\pi\)
\(618\) 39.3052i 1.58109i
\(619\) 36.1285 20.8588i 1.45213 0.838386i 0.453525 0.891244i \(-0.350166\pi\)
0.998602 + 0.0528581i \(0.0168331\pi\)
\(620\) 37.3603 64.7100i 1.50043 2.59882i
\(621\) 3.86129 + 6.68794i 0.154948 + 0.268378i
\(622\) −18.9708 10.9528i −0.760659 0.439166i
\(623\) 0 0
\(624\) −23.2042 + 4.51302i −0.928911 + 0.180665i
\(625\) 0.649140 1.12434i 0.0259656 0.0449737i
\(626\) 14.4442i 0.577307i
\(627\) 4.76871 0.190444
\(628\) −31.8023 −1.26905
\(629\) 47.8066i 1.90618i
\(630\) 0 0
\(631\) 15.2780 8.82074i 0.608206 0.351148i −0.164057 0.986451i \(-0.552458\pi\)
0.772263 + 0.635303i \(0.219125\pi\)
\(632\) −0.622082 0.359159i −0.0247451 0.0142866i
\(633\) 16.8084 29.1130i 0.668073 1.15714i
\(634\) −1.47921 −0.0587468
\(635\) −38.3982 + 22.1692i −1.52379 + 0.879759i
\(636\) −27.2584 −1.08086
\(637\) 0 0
\(638\) −2.39694 −0.0948958
\(639\) −11.8124 + 6.81987i −0.467290 + 0.269790i
\(640\) −26.6319 −1.05272
\(641\) −5.46012 + 9.45721i −0.215662 + 0.373537i −0.953477 0.301465i \(-0.902524\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(642\) −15.8346 9.14208i −0.624940 0.360809i
\(643\) 15.2725 8.81757i 0.602288 0.347731i −0.167653 0.985846i \(-0.553619\pi\)
0.769941 + 0.638115i \(0.220286\pi\)
\(644\) 0 0
\(645\) 29.6716i 1.16832i
\(646\) 24.8889 0.979241
\(647\) −16.6726 −0.655469 −0.327735 0.944770i \(-0.606285\pi\)
−0.327735 + 0.944770i \(0.606285\pi\)
\(648\) 10.3087i 0.404963i
\(649\) −3.24747 + 5.62479i −0.127474 + 0.220792i
\(650\) 45.7593 39.7866i 1.79483 1.56056i
\(651\) 0 0
\(652\) −4.92042 2.84080i −0.192698 0.111254i
\(653\) 3.38664 + 5.86584i 0.132530 + 0.229548i 0.924651 0.380816i \(-0.124357\pi\)
−0.792121 + 0.610364i \(0.791023\pi\)
\(654\) 24.8506 43.0426i 0.971737 1.68310i
\(655\) 25.5860 14.7721i 0.999727 0.577193i
\(656\) 35.0306i 1.36772i
\(657\) 13.0940 7.55983i 0.510846 0.294937i
\(658\) 0 0
\(659\) −16.7680 29.0431i −0.653190 1.13136i −0.982344 0.187082i \(-0.940097\pi\)
0.329154 0.944276i \(-0.393236\pi\)
\(660\) −8.84332 15.3171i −0.344226 0.596216i
\(661\) 25.1661i 0.978848i 0.872046 + 0.489424i \(0.162793\pi\)
−0.872046 + 0.489424i \(0.837207\pi\)
\(662\) −4.42829 7.67002i −0.172110 0.298104i
\(663\) −26.5393 30.5233i −1.03070 1.18543i
\(664\) 4.52075 0.175439
\(665\) 0 0
\(666\) −21.5001 + 37.2393i −0.833112 + 1.44299i
\(667\) 4.94651 0.191529
\(668\) −29.2572 + 16.8917i −1.13200 + 0.653558i
\(669\) 8.58060 + 4.95401i 0.331745 + 0.191533i
\(670\) 64.0207i 2.47334i
\(671\) 1.36438i 0.0526713i
\(672\) 0 0
\(673\) −0.927341 + 1.60620i −0.0357464 + 0.0619145i −0.883345 0.468723i \(-0.844714\pi\)
0.847599 + 0.530638i \(0.178048\pi\)
\(674\) 37.3172 21.5451i 1.43741 0.829887i
\(675\) −7.97855 13.8193i −0.307094 0.531903i
\(676\) −29.5225 + 11.9352i −1.13548 + 0.459047i
\(677\) 7.36044 12.7487i 0.282885 0.489971i −0.689209 0.724562i \(-0.742042\pi\)
0.972094 + 0.234592i \(0.0753753\pi\)
\(678\) −20.2863 11.7123i −0.779092 0.449809i
\(679\) 0 0
\(680\) −8.47009 14.6706i −0.324813 0.562593i
\(681\) −26.5716 15.3411i −1.01823 0.587873i
\(682\) 13.7136 + 7.91756i 0.525122 + 0.303179i
\(683\) −6.87930 3.97177i −0.263229 0.151975i 0.362578 0.931954i \(-0.381897\pi\)
−0.625807 + 0.779978i \(0.715230\pi\)
\(684\) 10.6730 + 6.16206i 0.408092 + 0.235612i
\(685\) −13.4266 23.2556i −0.513005 0.888551i
\(686\) 0 0
\(687\) 32.3529 + 18.6790i 1.23434 + 0.712647i
\(688\) 5.27960 9.14454i 0.201283 0.348632i
\(689\) 17.4142 3.38691i 0.663427 0.129031i
\(690\) 33.1504 + 57.4182i 1.26201 + 2.18587i
\(691\) −8.86002 + 5.11534i −0.337051 + 0.194597i −0.658967 0.752172i \(-0.729006\pi\)
0.321916 + 0.946768i \(0.395673\pi\)
\(692\) 4.51240 7.81571i 0.171536 0.297109i
\(693\) 0 0
\(694\) 16.8118i 0.638168i
\(695\) 60.0797i 2.27895i
\(696\) −2.38089 1.37461i −0.0902475 0.0521044i
\(697\) −51.9089 + 29.9696i −1.96619 + 1.13518i
\(698\) −45.5570 −1.72436
\(699\) −18.6616 + 32.3228i −0.705845 + 1.22256i
\(700\) 0 0
\(701\) −16.5978 −0.626891 −0.313445 0.949606i \(-0.601483\pi\)
−0.313445 + 0.949606i \(0.601483\pi\)
\(702\) 2.90609 + 14.9420i 0.109683 + 0.563948i
\(703\) 11.4635 + 19.8553i 0.432353 + 0.748857i
\(704\) 9.83992i 0.370856i
\(705\) 12.1468 + 21.0389i 0.457475 + 0.792371i
\(706\) 22.8000 + 39.4907i 0.858088 + 1.48625i
\(707\) 0 0
\(708\) −35.1552 + 20.2969i −1.32121 + 0.762804i
\(709\) 47.8659i 1.79764i 0.438318 + 0.898820i \(0.355574\pi\)
−0.438318 + 0.898820i \(0.644426\pi\)
\(710\) 42.4316 24.4979i 1.59243 0.919389i
\(711\) −0.801130 + 1.38760i −0.0300447 + 0.0520390i
\(712\) −1.71571 2.97170i −0.0642990 0.111369i
\(713\) −28.3004 16.3393i −1.05986 0.611910i
\(714\) 0 0
\(715\) 7.55279 + 8.68661i 0.282458 + 0.324861i
\(716\) 7.21722 12.5006i 0.269720 0.467169i
\(717\) 68.8017i 2.56944i
\(718\) −28.8635 −1.07718
\(719\) 38.0922 1.42060 0.710300 0.703899i \(-0.248559\pi\)
0.710300 + 0.703899i \(0.248559\pi\)
\(720\) 22.0836i 0.823009i
\(721\) 0 0
\(722\) −24.3719 + 14.0711i −0.907028 + 0.523673i
\(723\) 57.8081 + 33.3755i 2.14991 + 1.24125i
\(724\) −2.59089 + 4.48756i −0.0962898 + 0.166779i
\(725\) −10.2209 −0.379596
\(726\) −42.2009 + 24.3647i −1.56622 + 0.904259i
\(727\) 15.4059 0.571374 0.285687 0.958323i \(-0.407778\pi\)
0.285687 + 0.958323i \(0.407778\pi\)
\(728\) 0 0
\(729\) −9.41460 −0.348689
\(730\) −47.0354 + 27.1559i −1.74086 + 1.00508i
\(731\) 18.0674 0.668246
\(732\) −4.26372 + 7.38498i −0.157592 + 0.272957i
\(733\) −10.0717 5.81490i −0.372007 0.214778i 0.302328 0.953204i \(-0.402236\pi\)
−0.674335 + 0.738426i \(0.735570\pi\)
\(734\) 20.8487 12.0370i 0.769538 0.444293i
\(735\) 0 0
\(736\) 30.9117i 1.13942i
\(737\) −7.46911 −0.275128
\(738\) −53.9130 −1.98456
\(739\) 2.68901i 0.0989168i −0.998776 0.0494584i \(-0.984250\pi\)
0.998776 0.0494584i \(-0.0157495\pi\)
\(740\) 42.5168 73.6413i 1.56295 2.70711i
\(741\) −18.3416 6.31331i −0.673794 0.231925i
\(742\) 0 0
\(743\) −2.13665 1.23360i −0.0783862 0.0452563i 0.460295 0.887766i \(-0.347744\pi\)
−0.538681 + 0.842510i \(0.681077\pi\)
\(744\) 9.08120 + 15.7291i 0.332933 + 0.576657i
\(745\) 4.54118 7.86556i 0.166376 0.288172i
\(746\) 57.1433 32.9917i 2.09217 1.20791i
\(747\) 10.0839i 0.368949i
\(748\) 9.32673 5.38479i 0.341019 0.196887i
\(749\) 0 0
\(750\) −25.5409 44.2382i −0.932623 1.61535i
\(751\) −18.9592 32.8383i −0.691832 1.19829i −0.971237 0.238115i \(-0.923471\pi\)
0.279405 0.960173i \(-0.409863\pi\)
\(752\) 8.64534i 0.315263i
\(753\) −14.6811 25.4285i −0.535010 0.926664i
\(754\) 9.21920 + 3.17332i 0.335743 + 0.115565i
\(755\) 57.2583 2.08384
\(756\) 0 0
\(757\) −17.3225 + 30.0035i −0.629598 + 1.09050i 0.358034 + 0.933709i \(0.383447\pi\)
−0.987632 + 0.156788i \(0.949886\pi\)
\(758\) −57.8290 −2.10044
\(759\) −6.69881 + 3.86756i −0.243151 + 0.140384i
\(760\) −7.03569 4.06206i −0.255211 0.147346i
\(761\) 22.8595i 0.828655i 0.910128 + 0.414328i \(0.135983\pi\)
−0.910128 + 0.414328i \(0.864017\pi\)
\(762\) 58.7280i 2.12749i
\(763\) 0 0
\(764\) −13.9214 + 24.1126i −0.503659 + 0.872363i
\(765\) −32.7239 + 18.8931i −1.18313 + 0.683083i
\(766\) −16.9813 29.4124i −0.613558 1.06271i
\(767\) 19.9372 17.3349i 0.719891 0.625927i
\(768\) −7.46951 + 12.9376i −0.269533 + 0.466844i
\(769\) −44.8839 25.9137i −1.61855 0.934473i −0.987294 0.158902i \(-0.949205\pi\)
−0.631260 0.775571i \(-0.717462\pi\)
\(770\) 0 0
\(771\) −5.18507 8.98080i −0.186736 0.323436i
\(772\) −29.8884 17.2561i −1.07571 0.621060i
\(773\) 4.93605 + 2.84983i 0.177538 + 0.102501i 0.586135 0.810213i \(-0.300649\pi\)
−0.408598 + 0.912715i \(0.633982\pi\)
\(774\) 14.0737 + 8.12545i 0.505868 + 0.292063i
\(775\) 58.4770 + 33.7617i 2.10056 + 1.21276i
\(776\) −0.219653 0.380450i −0.00788508 0.0136574i
\(777\) 0 0
\(778\) −38.6146 22.2941i −1.38440 0.799283i
\(779\) −14.3727 + 24.8943i −0.514956 + 0.891930i
\(780\) 13.7351 + 70.6208i 0.491797 + 2.52863i
\(781\) 2.85809 + 4.950