Properties

Label 637.2.q.h.491.6
Level $637$
Weight $2$
Character 637.491
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.q (of order \(6\), degree \(2\), 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: \(\Z[a_1, \ldots, a_{5}]\)
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 491.6
Root \(-1.30089 + 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.h.589.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 + 1.83169i) q^{9} +O(q^{10})\) \(q+(1.82678 - 1.05469i) q^{2} +(1.13082 + 1.95864i) q^{3} +(1.22476 - 2.12135i) q^{4} -3.60178i q^{5} +(4.13154 + 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 + 1.83169i) q^{9} +(-3.79878 - 6.57967i) q^{10} +(0.767631 - 0.443192i) q^{11} +5.53995 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} +4.46147i q^{18} +(-2.06008 - 1.18939i) q^{19} +(-7.64062 - 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +(-1.92926 - 3.34157i) q^{23} +(1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(5.73942 + 4.99028i) q^{26} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 - 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 + 4.00566i) q^{32} +(1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} +(-8.34686 + 4.81906i) q^{37} -5.01776 q^{38} +(-5.35049 + 6.15370i) q^{39} -3.41525 q^{40} +(-10.4652 + 6.04207i) q^{41} +(-1.82125 + 3.15450i) q^{43} -2.17122i q^{44} +(6.59734 + 3.80898i) q^{45} +(-7.04867 - 4.06955i) q^{46} -2.98229i q^{47} +(-3.27814 + 5.67790i) q^{48} +(-14.5646 + 8.40888i) q^{50} +11.2181 q^{51} +(8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(3.65619 - 2.11090i) q^{54} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +(-2.34189 - 1.35209i) q^{58} +(-6.34577 - 3.66373i) q^{59} -19.9537i q^{60} +(-0.769632 + 1.33304i) q^{61} +(8.93242 + 15.4714i) q^{62} +11.1012 q^{64} +(12.2793 - 4.22664i) q^{65} +4.22867 q^{66} +(7.29756 - 4.21325i) q^{67} +(-6.07501 - 10.5222i) q^{68} +(4.36330 - 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(1.73683 + 1.00276i) q^{72} +7.14859i 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} +0.757551 q^{79} +(9.04232 - 5.22059i) q^{80} +(5.43585 + 9.41518i) q^{81} +(-12.7451 + 22.0751i) q^{82} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +7.68344i q^{86} +(1.44969 - 2.51093i) q^{87} +(-0.420240 - 0.727877i) q^{88} +(-3.13400 + 1.80942i) q^{89} +16.0692 q^{90} -9.45150 q^{92} +(-16.5882 + 9.57719i) q^{93} +(-3.14541 - 5.44800i) q^{94} +(-4.28391 + 7.41995i) q^{95} +18.1188i q^{96} +(0.401229 + 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.82678 1.05469i 1.29173 0.745781i 0.312770 0.949829i \(-0.398743\pi\)
0.978961 + 0.204047i \(0.0654097\pi\)
\(3\) 1.13082 + 1.95864i 0.652882 + 1.13082i 0.982420 + 0.186682i \(0.0597734\pi\)
−0.329539 + 0.944142i \(0.606893\pi\)
\(4\) 1.22476 2.12135i 0.612380 1.06067i
\(5\) 3.60178i 1.61076i −0.592756 0.805382i \(-0.701960\pi\)
0.592756 0.805382i \(-0.298040\pi\)
\(6\) 4.13154 + 2.38535i 1.68670 + 0.973814i
\(7\) 0 0
\(8\) 0.948212i 0.335243i
\(9\) −1.05753 + 1.83169i −0.352509 + 0.610563i
\(10\) −3.79878 6.57967i −1.20128 2.08068i
\(11\) 0.767631 0.443192i 0.231450 0.133627i −0.379791 0.925072i \(-0.624004\pi\)
0.611241 + 0.791445i \(0.290671\pi\)
\(12\) 5.53995 1.59925
\(13\) 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 \(-0.627900\pi\)
0.992593 0.121488i \(-0.0387665\pi\)
\(18\) 4.46147i 1.05158i
\(19\) −2.06008 1.18939i −0.472615 0.272864i 0.244719 0.969594i \(-0.421304\pi\)
−0.717334 + 0.696730i \(0.754638\pi\)
\(20\) −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 \(0.965115\pi\)
\(24\) 1.85721 1.07226i 0.379101 0.218874i
\(25\) −7.97282 −1.59456
\(26\) 5.73942 + 4.99028i 1.12559 + 0.978674i
\(27\) 2.00144 0.385177
\(28\) 0 0
\(29\) −0.640986 1.11022i −0.119028 0.206163i 0.800355 0.599527i \(-0.204645\pi\)
−0.919383 + 0.393364i \(0.871311\pi\)
\(30\) 8.59150 14.8809i 1.56859 2.71687i
\(31\) 8.46921i 1.52111i 0.649271 + 0.760557i \(0.275074\pi\)
−0.649271 + 0.760557i \(0.724926\pi\)
\(32\) 6.93800 + 4.00566i 1.22648 + 0.708107i
\(33\) 1.73611 + 1.00234i 0.302218 + 0.174486i
\(34\) 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 −0.991207 0.132323i \(-0.957757\pi\)
−0.381009 + 0.924571i \(0.624423\pi\)
\(38\) −5.01776 −0.813988
\(39\) −5.35049 + 6.15370i −0.856763 + 0.985380i
\(40\) −3.41525 −0.539998
\(41\) −10.4652 + 6.04207i −1.63438 + 0.943612i −0.651666 + 0.758506i \(0.725929\pi\)
−0.982719 + 0.185106i \(0.940737\pi\)
\(42\) 0 0
\(43\) −1.82125 + 3.15450i −0.277738 + 0.481056i −0.970822 0.239800i \(-0.922918\pi\)
0.693084 + 0.720856i \(0.256251\pi\)
\(44\) 2.17122i 0.327323i
\(45\) 6.59734 + 3.80898i 0.983474 + 0.567809i
\(46\) −7.04867 4.06955i −1.03927 0.600022i
\(47\) 2.98229i 0.435012i −0.976059 0.217506i \(-0.930208\pi\)
0.976059 0.217506i \(-0.0697922\pi\)
\(48\) −3.27814 + 5.67790i −0.473158 + 0.819535i
\(49\) 0 0
\(50\) −14.5646 + 8.40888i −2.05975 + 1.18920i
\(51\) 11.2181 1.57085
\(52\) 8.66942 + 1.68613i 1.20223 + 0.233824i
\(53\) 4.92032 0.675858 0.337929 0.941172i \(-0.390274\pi\)
0.337929 + 0.941172i \(0.390274\pi\)
\(54\) 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
\(58\) −2.34189 1.35209i −0.307505 0.177538i
\(59\) −6.34577 3.66373i −0.826148 0.476977i 0.0263837 0.999652i \(-0.491601\pi\)
−0.852532 + 0.522675i \(0.824934\pi\)
\(60\) 19.9537i 2.57601i
\(61\) −0.769632 + 1.33304i −0.0985412 + 0.170678i −0.911081 0.412227i \(-0.864751\pi\)
0.812540 + 0.582906i \(0.198084\pi\)
\(62\) 8.93242 + 15.4714i 1.13442 + 1.96487i
\(63\) 0 0
\(64\) 11.1012 1.38765
\(65\) 12.2793 4.22664i 1.52306 0.524250i
\(66\) 4.22867 0.520513
\(67\) 7.29756 4.21325i 0.891539 0.514730i 0.0170931 0.999854i \(-0.494559\pi\)
0.874445 + 0.485124i \(0.161225\pi\)
\(68\) −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 0.130540 0.991443i \(-0.458329\pi\)
−0.793345 + 0.608772i \(0.791662\pi\)
\(72\) 1.73683 + 1.00276i 0.204687 + 0.118176i
\(73\) 7.14859i 0.836679i 0.908291 + 0.418340i \(0.137388\pi\)
−0.908291 + 0.418340i \(0.862612\pi\)
\(74\) −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
\(79\) 0.757551 0.0852311 0.0426156 0.999092i \(-0.486431\pi\)
0.0426156 + 0.999092i \(0.486431\pi\)
\(80\) 9.04232 5.22059i 1.01096 0.583679i
\(81\) 5.43585 + 9.41518i 0.603984 + 1.04613i
\(82\) −12.7451 + 22.0751i −1.40746 + 2.43779i
\(83\) 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
\(86\) 7.68344i 0.828527i
\(87\) 1.44969 2.51093i 0.155423 0.269200i
\(88\) −0.420240 0.727877i −0.0447977 0.0775919i
\(89\) −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
\(94\) −3.14541 5.44800i −0.324424 0.561919i
\(95\) −4.28391 + 7.41995i −0.439520 + 0.761271i
\(96\) 18.1188i 1.84924i
\(97\) 0.401229 + 0.231650i 0.0407386 + 0.0235205i 0.520231 0.854026i \(-0.325846\pi\)
−0.479492 + 0.877546i \(0.659179\pi\)
\(98\) 0 0
\(99\) 1.87475i 0.188419i
\(100\) −9.76479 + 16.9131i −0.976479 + 1.69131i
\(101\) −2.91152 5.04289i −0.289707 0.501787i 0.684033 0.729451i \(-0.260224\pi\)
−0.973740 + 0.227664i \(0.926891\pi\)
\(102\) 20.4931 11.8317i 2.02912 1.17151i
\(103\) 8.23888 0.811801 0.405901 0.913917i \(-0.366958\pi\)
0.405901 + 0.913917i \(0.366958\pi\)
\(104\) 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
\(109\) 10.4180i 0.997867i 0.866640 + 0.498934i \(0.166275\pi\)
−0.866640 + 0.498934i \(0.833725\pi\)
\(110\) −5.83212 3.36718i −0.556071 0.321048i
\(111\) −18.8777 10.8990i −1.79179 1.03449i
\(112\) 0 0
\(113\) 2.45505 4.25228i 0.230952 0.400021i −0.727136 0.686493i \(-0.759149\pi\)
0.958089 + 0.286472i \(0.0924826\pi\)
\(114\) −5.67421 9.82801i −0.531438 0.920478i
\(115\) −12.0356 + 6.94875i −1.12233 + 0.647975i
\(116\) −3.14022 −0.291562
\(117\) −7.48567 1.45590i −0.692050 0.134598i
\(118\) −15.4565 −1.42288
\(119\) 0 0
\(120\) −3.86205 6.68926i −0.352555 0.610643i
\(121\) −5.10716 + 8.84586i −0.464287 + 0.804169i
\(122\) 3.24690i 0.293961i
\(123\) −23.6685 13.6650i −2.13412 1.23213i
\(124\) 17.9661 + 10.3727i 1.61341 + 0.931500i
\(125\) 10.7074i 0.957702i
\(126\) 0 0
\(127\) −6.15508 10.6609i −0.546175 0.946003i −0.998532 0.0541658i \(-0.982750\pi\)
0.452357 0.891837i \(-0.350583\pi\)
\(128\) 6.40347 3.69704i 0.565992 0.326776i
\(129\) −8.23805 −0.725320
\(130\) 17.9739 20.6721i 1.57641 1.81306i
\(131\) 8.20265 0.716669 0.358335 0.933593i \(-0.383345\pi\)
0.358335 + 0.933593i \(0.383345\pi\)
\(132\) 4.25264 2.45526i 0.370145 0.213703i
\(133\) 0 0
\(134\) 8.88737 15.3934i 0.767752 1.32979i
\(135\) 7.20874i 0.620429i
\(136\) −4.07316 2.35164i −0.349271 0.201652i
\(137\) 6.45670 + 3.72778i 0.551633 + 0.318485i 0.749780 0.661687i \(-0.230159\pi\)
−0.198147 + 0.980172i \(0.563492\pi\)
\(138\) 18.4078i 1.56697i
\(139\) 8.34028 14.4458i 0.707413 1.22528i −0.258400 0.966038i \(-0.583195\pi\)
0.965813 0.259238i \(-0.0834714\pi\)
\(140\) 0 0
\(141\) 5.84125 3.37245i 0.491922 0.284011i
\(142\) −13.6032 −1.14156
\(143\) 2.41175 + 2.09696i 0.201681 + 0.175357i
\(144\) −6.13131 −0.510943
\(145\) −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
\(149\) −2.18380 1.26082i −0.178904 0.103290i 0.407874 0.913038i \(-0.366270\pi\)
−0.586777 + 0.809748i \(0.699604\pi\)
\(150\) −32.9400 19.0179i −2.68954 1.55281i
\(151\) 15.8972i 1.29370i −0.762618 0.646849i \(-0.776086\pi\)
0.762618 0.646849i \(-0.223914\pi\)
\(152\) −1.12779 + 1.95339i −0.0914760 + 0.158441i
\(153\) 5.24550 + 9.08548i 0.424074 + 0.734517i
\(154\) 0 0
\(155\) 30.5042 2.45016
\(156\) 6.50106 + 18.8870i 0.520502 + 1.51217i
\(157\) −12.9831 −1.03616 −0.518082 0.855331i \(-0.673354\pi\)
−0.518082 + 0.855331i \(0.673354\pi\)
\(158\) 1.38388 0.798985i 0.110096 0.0635638i
\(159\) 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
\(163\) −2.00873 1.15974i −0.157336 0.0908378i 0.419265 0.907864i \(-0.362288\pi\)
−0.576601 + 0.817026i \(0.695621\pi\)
\(164\) 29.6003i 2.31140i
\(165\) 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 \(-0.487497\pi\)
0.884992 + 0.465607i \(0.154164\pi\)
\(168\) 0 0
\(169\) −10.2459 + 8.00140i −0.788143 + 0.615493i
\(170\) −37.6851 −2.89031
\(171\) 4.35718 2.51562i 0.333202 0.192374i
\(172\) 4.46118 + 7.72700i 0.340162 + 0.589178i
\(173\) 1.84216 3.19071i 0.140057 0.242585i −0.787461 0.616364i \(-0.788605\pi\)
0.927518 + 0.373779i \(0.121938\pi\)
\(174\) 6.11590i 0.463645i
\(175\) 0 0
\(176\) 2.22528 + 1.28477i 0.167737 + 0.0968429i
\(177\) 16.5721i 1.24564i
\(178\) −3.81677 + 6.61083i −0.286079 + 0.495503i
\(179\) −2.94638 5.10328i −0.220223 0.381437i 0.734653 0.678443i \(-0.237345\pi\)
−0.954876 + 0.297006i \(0.904012\pi\)
\(180\) 16.1603 9.33017i 1.20452 0.695430i
\(181\) 2.11543 0.157239 0.0786193 0.996905i \(-0.474949\pi\)
0.0786193 + 0.996905i \(0.474949\pi\)
\(182\) 0 0
\(183\) −3.48127 −0.257343
\(184\) −3.16851 + 1.82934i −0.233586 + 0.134861i
\(185\) 17.3572 + 30.0635i 1.27613 + 2.21032i
\(186\) −20.2020 + 34.9909i −1.48128 + 2.56566i
\(187\) 4.39661i 0.321512i
\(188\) −6.32647 3.65259i −0.461406 0.266393i
\(189\) 0 0
\(190\) 18.0729i 1.31114i
\(191\) 5.68333 9.84381i 0.411231 0.712273i −0.583794 0.811902i \(-0.698432\pi\)
0.995025 + 0.0996290i \(0.0317656\pi\)
\(192\) 12.5535 + 21.7433i 0.905970 + 1.56919i
\(193\) 12.2017 7.04468i 0.878301 0.507087i 0.00820314 0.999966i \(-0.497389\pi\)
0.870098 + 0.492879i \(0.164055\pi\)
\(194\) 0.977279 0.0701645
\(195\) 22.1643 + 19.2713i 1.58722 + 1.38004i
\(196\) 0 0
\(197\) −19.8815 + 11.4786i −1.41650 + 0.817814i −0.995989 0.0894753i \(-0.971481\pi\)
−0.420507 + 0.907289i \(0.638148\pi\)
\(198\) 1.97729 + 3.42476i 0.140520 + 0.243387i
\(199\) 1.57492 2.72785i 0.111643 0.193372i −0.804790 0.593560i \(-0.797722\pi\)
0.916433 + 0.400188i \(0.131055\pi\)
\(200\) 7.55992i 0.534567i
\(201\) 16.5045 + 9.52888i 1.16414 + 0.672116i
\(202\) −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
\(206\) 15.0507 8.68950i 1.04863 0.605426i
\(207\) 8.16096 0.567226
\(208\) −6.85804 + 7.88757i −0.475520 + 0.546905i
\(209\) −2.10851 −0.145849
\(210\) 0 0
\(211\) 7.43191 + 12.8725i 0.511634 + 0.886176i 0.999909 + 0.0134864i \(0.00429298\pi\)
−0.488275 + 0.872690i \(0.662374\pi\)
\(212\) 6.02621 10.4377i 0.413882 0.716865i
\(213\) 14.5851i 0.999355i
\(214\) 7.00133 + 4.04222i 0.478601 + 0.276321i
\(215\) 11.3618 + 6.55974i 0.774868 + 0.447370i
\(216\) 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
\(220\) −7.82024 −0.527241
\(221\) 17.5552 + 3.41433i 1.18089 + 0.229673i
\(222\) −45.9805 −3.08601
\(223\) −3.79396 + 2.19044i −0.254062 + 0.146683i −0.621623 0.783317i \(-0.713526\pi\)
0.367561 + 0.930000i \(0.380193\pi\)
\(224\) 0 0
\(225\) 8.43147 14.6037i 0.562098 0.973582i
\(226\) 10.3573i 0.688959i
\(227\) −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
\(229\) 16.5180i 1.09154i −0.837935 0.545770i \(-0.816237\pi\)
0.837935 0.545770i \(-0.183763\pi\)
\(230\) −14.6576 + 25.3877i −0.966495 + 1.67402i
\(231\) 0 0
\(232\) −1.05272 + 0.607791i −0.0691147 + 0.0399034i
\(233\) 16.5026 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(234\) −15.2102 + 5.23548i −0.994324 + 0.342254i
\(235\) −10.7416 −0.700702
\(236\) −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 \(-0.557220\pi\)
0.178796 0.983886i \(-0.442780\pi\)
\(240\) 20.4506 + 11.8071i 1.32008 + 0.762147i
\(241\) 25.5602 + 14.7572i 1.64648 + 0.950593i 0.978458 + 0.206448i \(0.0661904\pi\)
0.668018 + 0.744145i \(0.267143\pi\)
\(242\) 21.5460i 1.38503i
\(243\) −9.29184 + 16.0939i −0.596072 + 1.03243i
\(244\) 1.88523 + 3.26531i 0.120689 + 0.209040i
\(245\) 0 0
\(246\) −57.6497 −3.67561
\(247\) 1.63743 8.41904i 0.104187 0.535691i
\(248\) 8.03060 0.509944
\(249\) 9.33816 5.39139i 0.591782 0.341665i
\(250\) 11.2931 + 19.5602i 0.714236 + 1.23709i
\(251\) 6.49134 11.2433i 0.409730 0.709673i −0.585130 0.810940i \(-0.698956\pi\)
0.994859 + 0.101267i \(0.0322897\pi\)
\(252\) 0 0
\(253\) −2.96191 1.71006i −0.186214 0.107511i
\(254\) −22.4880 12.9835i −1.41102 0.814654i
\(255\) 40.4053i 2.53028i
\(256\) −3.30268 + 5.72042i −0.206418 + 0.357526i
\(257\) 2.29261 + 3.97091i 0.143009 + 0.247698i 0.928628 0.371011i \(-0.120989\pi\)
−0.785620 + 0.618710i \(0.787656\pi\)
\(258\) −15.0491 + 8.68862i −0.936918 + 0.540930i
\(259\) 0 0
\(260\) 6.07307 31.2253i 0.376636 1.93651i
\(261\) 2.71144 0.167834
\(262\) 14.9845 8.65129i 0.925744 0.534479i
\(263\) 1.33250 + 2.30795i 0.0821652 + 0.142314i 0.904180 0.427152i \(-0.140483\pi\)
−0.822015 + 0.569466i \(0.807150\pi\)
\(264\) 0.950435 1.64620i 0.0584952 0.101317i
\(265\) 17.7219i 1.08865i
\(266\) 0 0
\(267\) −7.08801 4.09227i −0.433779 0.250443i
\(268\) 20.6409i 1.26084i
\(269\) 5.96282 10.3279i 0.363559 0.629703i −0.624984 0.780637i \(-0.714895\pi\)
0.988544 + 0.150934i \(0.0482280\pi\)
\(270\) −7.60301 13.1688i −0.462705 0.801428i
\(271\) 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
\(276\) −10.6880 18.5121i −0.643341 1.11430i
\(277\) 10.6824 18.5025i 0.641846 1.11171i −0.343174 0.939272i \(-0.611502\pi\)
0.985020 0.172438i \(-0.0551646\pi\)
\(278\) 35.1858i 2.11030i
\(279\) −15.5130 8.95641i −0.928737 0.536206i
\(280\) 0 0
\(281\) 17.2678i 1.03011i 0.857158 + 0.515054i \(0.172228\pi\)
−0.857158 + 0.515054i \(0.827772\pi\)
\(282\) 7.11380 12.3215i 0.423621 0.733733i
\(283\) 10.6201 + 18.3946i 0.631299 + 1.09344i 0.987286 + 0.158952i \(0.0508114\pi\)
−0.355987 + 0.934491i \(0.615855\pi\)
\(284\) −13.6803 + 7.89833i −0.811777 + 0.468680i
\(285\) −19.3774 −1.14782
\(286\) 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
\(291\) 1.04782i 0.0614243i
\(292\) 15.1646 + 8.75531i 0.887443 + 0.512366i
\(293\) 0.363782 + 0.210030i 0.0212524 + 0.0122701i 0.510589 0.859825i \(-0.329428\pi\)
−0.489336 + 0.872095i \(0.662761\pi\)
\(294\) 0 0
\(295\) −13.1959 + 22.8561i −0.768298 + 1.33073i
\(296\) 4.56949 + 7.91459i 0.265596 + 0.460026i
\(297\) 1.53637 0.887022i 0.0891490 0.0514702i
\(298\) −5.31910 −0.308127
\(299\) 9.12826 10.4986i 0.527901 0.607149i
\(300\) −44.1690 −2.55010
\(301\) 0 0
\(302\) −16.7667 29.0408i −0.964817 1.67111i
\(303\) 6.58482 11.4053i 0.378288 0.655215i
\(304\) 6.89581i 0.395502i
\(305\) 4.80132 + 2.77204i 0.274923 + 0.158727i
\(306\) 19.1648 + 11.0648i 1.09558 + 0.632533i
\(307\) 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
\(311\) 10.3848 0.588867 0.294434 0.955672i \(-0.404869\pi\)
0.294434 + 0.955672i \(0.404869\pi\)
\(312\) 5.83501 + 5.07339i 0.330342 + 0.287224i
\(313\) −6.84759 −0.387048 −0.193524 0.981096i \(-0.561992\pi\)
−0.193524 + 0.981096i \(0.561992\pi\)
\(314\) −23.7173 + 13.6932i −1.33845 + 0.772752i
\(315\) 0 0
\(316\) 0.927818 1.60703i 0.0521938 0.0904024i
\(317\) 0.701249i 0.0393861i 0.999806 + 0.0196930i \(0.00626889\pi\)
−0.999806 + 0.0196930i \(0.993731\pi\)
\(318\) 20.3285 + 11.7367i 1.13997 + 0.658160i
\(319\) −0.984082 0.568160i −0.0550980 0.0318109i
\(320\) 39.9840i 2.23518i
\(321\) −4.33400 + 7.50670i −0.241900 + 0.418983i
\(322\) 0 0
\(323\) −10.2183 + 5.89956i −0.568563 + 0.328260i
\(324\) 26.6305 1.47947
\(325\) −9.35600 27.1813i −0.518977 1.50774i
\(326\) −4.89268 −0.270980
\(327\) −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
\(331\) 3.63613 + 2.09932i 0.199860 + 0.115389i 0.596590 0.802546i \(-0.296522\pi\)
−0.396730 + 0.917935i \(0.629855\pi\)
\(332\) −10.1139 5.83924i −0.555070 0.320470i
\(333\) 20.3851i 1.11710i
\(334\) 14.5462 25.1947i 0.795930 1.37859i
\(335\) −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 \(0.687813\pi\)
\(338\) −10.2779 + 25.4231i −0.559046 + 1.38283i
\(339\) 11.1049 0.603138
\(340\) −37.8987 + 21.8808i −2.05535 + 1.18665i
\(341\) 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
\(345\) −27.2203 15.7156i −1.46549 0.846102i
\(346\) 7.77165i 0.417807i
\(347\) −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 \(-0.862848\pi\)
−0.0925892 + 0.995704i \(0.529514\pi\)
\(350\) 0 0
\(351\) 2.34866 + 6.82338i 0.125362 + 0.364205i
\(352\) 7.10110 0.378490
\(353\) −18.7214 + 10.8088i −0.996439 + 0.575295i −0.907193 0.420715i \(-0.861779\pi\)
−0.0892465 + 0.996010i \(0.528446\pi\)
\(354\) −17.4785 30.2737i −0.928974 1.60903i
\(355\) −11.6137 + 20.1156i −0.616393 + 1.06762i
\(356\) 8.86441i 0.469813i
\(357\) 0 0
\(358\) −10.7648 6.21507i −0.568938 0.328476i
\(359\) 13.6834i 0.722180i 0.932531 + 0.361090i \(0.117595\pi\)
−0.932531 + 0.361090i \(0.882405\pi\)
\(360\) 3.61172 6.25568i 0.190354 0.329703i
\(361\) −6.67071 11.5540i −0.351090 0.608106i
\(362\) 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
\(367\) −5.70638 9.88374i −0.297871 0.515927i 0.677778 0.735267i \(-0.262943\pi\)
−0.975649 + 0.219339i \(0.929610\pi\)
\(368\) 5.59271 9.68685i 0.291540 0.504962i
\(369\) 25.5586i 1.33053i
\(370\) 63.4157 + 36.6131i 3.29683 + 1.90342i
\(371\) 0 0
\(372\) 46.9190i 2.43264i
\(373\) 15.6404 27.0900i 0.809830 1.40267i −0.103151 0.994666i \(-0.532892\pi\)
0.912981 0.408002i \(-0.133774\pi\)
\(374\) −4.63708 8.03166i −0.239778 0.415307i
\(375\) −20.9721 + 12.1082i −1.08299 + 0.625266i
\(376\) −2.82784 −0.145835
\(377\) 3.03282 3.48811i 0.156198 0.179647i
\(378\) 0 0
\(379\) 23.7421 13.7075i 1.21955 0.704108i 0.254729 0.967012i \(-0.418014\pi\)
0.964822 + 0.262904i \(0.0846803\pi\)
\(380\) 10.4935 + 18.1753i 0.538307 + 0.932374i
\(381\) 13.9206 24.1112i 0.713175 1.23526i
\(382\) 23.9767i 1.22675i
\(383\) −13.9436 8.05032i −0.712483 0.411352i 0.0994967 0.995038i \(-0.468277\pi\)
−0.811980 + 0.583686i \(0.801610\pi\)
\(384\) 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
\(388\) 0.982819 0.567431i 0.0498951 0.0288069i
\(389\) −21.1380 −1.07174 −0.535870 0.844301i \(-0.680016\pi\)
−0.535870 + 0.844301i \(0.680016\pi\)
\(390\) 60.8146 + 11.8279i 3.07947 + 0.598930i
\(391\) −19.1388 −0.967893
\(392\) 0 0
\(393\) 9.27576 + 16.0661i 0.467900 + 0.810427i
\(394\) −24.2128 + 41.9377i −1.21982 + 2.11279i
\(395\) 2.72853i 0.137287i
\(396\) 3.97699 + 2.29612i 0.199851 + 0.115384i
\(397\) −11.3436 6.54921i −0.569317 0.328695i 0.187560 0.982253i \(-0.439942\pi\)
−0.756876 + 0.653558i \(0.773276\pi\)
\(398\) 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 −0.0166501 0.999861i \(-0.505300\pi\)
0.857580 + 0.514350i \(0.171967\pi\)
\(402\) 40.2002 2.00501
\(403\) −28.8736 + 9.93851i −1.43830 + 0.495072i
\(404\) −14.2636 −0.709642
\(405\) 33.9114 19.5788i 1.68507 0.972876i
\(406\) 0 0
\(407\) −4.27154 + 7.39853i −0.211732 + 0.366731i
\(408\) 10.6372i 0.526618i
\(409\) −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
\(411\) 16.8618i 0.831733i
\(412\) 10.0907 17.4775i 0.497131 0.861056i
\(413\) 0 0
\(414\) 14.9083 8.60732i 0.732703 0.423026i
\(415\) −17.1721 −0.842944
\(416\) −5.51460 + 28.3539i −0.270375 + 1.39016i
\(417\) 37.7256 1.84743
\(418\) −3.85179 + 2.22383i −0.188397 + 0.108771i
\(419\) 19.5119 + 33.7956i 0.953218 + 1.65102i 0.738394 + 0.674370i \(0.235585\pi\)
0.214825 + 0.976653i \(0.431082\pi\)
\(420\) 0 0
\(421\) 22.0284i 1.07360i −0.843710 0.536799i \(-0.819633\pi\)
0.843710 0.536799i \(-0.180367\pi\)
\(422\) 27.1530 + 15.6768i 1.32179 + 0.763134i
\(423\) 5.46263 + 3.15385i 0.265602 + 0.153346i
\(424\) 4.66551i 0.226577i
\(425\) −19.7732 + 34.2482i −0.959142 + 1.66128i
\(426\) −15.3828 26.6438i −0.745301 1.29090i
\(427\) 0 0
\(428\) 9.38803 0.453787
\(429\) −1.37993 + 7.09506i −0.0666237 + 0.342553i
\(430\) 27.6741 1.33456
\(431\) −31.0727 + 17.9398i −1.49672 + 0.864131i −0.999993 0.00377645i \(-0.998798\pi\)
−0.496726 + 0.867907i \(0.665465\pi\)
\(432\) 2.90098 + 5.02464i 0.139573 + 0.241748i
\(433\) −6.10678 + 10.5773i −0.293473 + 0.508310i −0.974629 0.223828i \(-0.928144\pi\)
0.681155 + 0.732139i \(0.261478\pi\)
\(434\) 0 0
\(435\) −9.04381 5.22145i −0.433618 0.250349i
\(436\) 22.1003 + 12.7596i 1.05841 + 0.611074i
\(437\) 9.17853i 0.439069i
\(438\) −17.0519 + 29.5347i −0.814770 + 1.41122i
\(439\) 7.87765 + 13.6445i 0.375980 + 0.651216i 0.990473 0.137706i \(-0.0439728\pi\)
−0.614493 + 0.788922i \(0.710639\pi\)
\(440\) −2.62165 + 1.51361i −0.124982 + 0.0721586i
\(441\) 0 0
\(442\) 35.6706 12.2781i 1.69668 0.584009i
\(443\) −15.0706 −0.716028 −0.358014 0.933716i \(-0.616546\pi\)
−0.358014 + 0.933716i \(0.616546\pi\)
\(444\) −46.2412 + 26.6974i −2.19451 + 1.26700i
\(445\) 6.51712 + 11.2880i 0.308941 + 0.535102i
\(446\) −4.62050 + 8.00293i −0.218787 + 0.378950i
\(447\) 5.70305i 0.269745i
\(448\) 0 0
\(449\) 26.6585 + 15.3913i 1.25809 + 0.726360i 0.972703 0.232052i \(-0.0745441\pi\)
0.285388 + 0.958412i \(0.407877\pi\)
\(450\) 35.5705i 1.67681i
\(451\) −5.35559 + 9.27616i −0.252185 + 0.436797i
\(452\) −6.01371 10.4160i −0.282861 0.489929i
\(453\) 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 −0.648805 0.760955i \(-0.724731\pi\)
0.334603 + 0.942359i \(0.391398\pi\)
\(458\) −17.4214 30.1748i −0.814050 1.40998i
\(459\) 4.96373 8.59743i 0.231687 0.401294i
\(460\) 34.0422i 1.58723i
\(461\) −1.27498 0.736110i −0.0593817 0.0342840i 0.470015 0.882658i \(-0.344248\pi\)
−0.529397 + 0.848374i \(0.677582\pi\)
\(462\) 0 0
\(463\) 14.0366i 0.652335i −0.945312 0.326168i \(-0.894243\pi\)
0.945312 0.326168i \(-0.105757\pi\)
\(464\) 1.85815 3.21841i 0.0862625 0.149411i
\(465\) 34.4949 + 59.7469i 1.59966 + 2.77070i
\(466\) 30.1467 17.4052i 1.39652 0.806281i
\(467\) 31.3806 1.45212 0.726060 0.687631i \(-0.241349\pi\)
0.726060 + 0.687631i \(0.241349\pi\)
\(468\) −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
\(473\) 3.22865i 0.148454i
\(474\) 3.12985 + 1.80702i 0.143759 + 0.0829993i
\(475\) 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
\(479\) −35.6760 + 20.5975i −1.63008 + 0.941125i −0.646009 + 0.763330i \(0.723563\pi\)
−0.984068 + 0.177795i \(0.943104\pi\)
\(480\) 65.2598 2.97869
\(481\) −26.2243 22.8014i −1.19572 1.03965i
\(482\) 62.2572 2.83574
\(483\) 0 0
\(484\) 12.5101 + 21.6681i 0.568641 + 0.984914i
\(485\) 0.834351 1.44514i 0.0378859 0.0656204i
\(486\) 39.2002i 1.77816i
\(487\) 24.5314 + 14.1632i 1.11163 + 0.641798i 0.939250 0.343234i \(-0.111522\pi\)
0.172376 + 0.985031i \(0.444856\pi\)
\(488\) 1.26400 + 0.729774i 0.0572188 + 0.0330353i
\(489\) 5.24584i 0.237225i
\(490\) 0 0
\(491\) 17.3931 + 30.1258i 0.784941 + 1.35956i 0.929034 + 0.369993i \(0.120640\pi\)
−0.144094 + 0.989564i \(0.546027\pi\)
\(492\) −57.9765 + 33.4728i −2.61378 + 1.50907i
\(493\) −6.35879 −0.286386
\(494\) −5.88828 17.1068i −0.264926 0.769670i
\(495\) 6.75244 0.303499
\(496\) −21.2621 + 12.2757i −0.954695 + 0.551194i
\(497\) 0 0
\(498\) 11.3725 19.6978i 0.509615 0.882680i
\(499\) 0.0694885i 0.00311073i −0.999999 0.00155537i \(-0.999505\pi\)
0.999999 0.00155537i \(-0.000495089\pi\)
\(500\) 22.7142 + 13.1140i 1.01581 + 0.586477i
\(501\) 27.0133 + 15.5961i 1.20686 + 0.696783i
\(502\) 27.3855i 1.22228i
\(503\) 12.8686 22.2891i 0.573782 0.993820i −0.422391 0.906414i \(-0.638809\pi\)
0.996173 0.0874060i \(-0.0278578\pi\)
\(504\) 0 0
\(505\) −18.1634 + 10.4866i −0.808260 + 0.466649i
\(506\) −7.21437 −0.320718
\(507\) −27.2582 11.0198i −1.21058 0.489407i
\(508\) −30.1540 −1.33787
\(509\) 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
\(513\) −4.12312 2.38049i −0.182040 0.105101i
\(514\) 8.37619 + 4.83599i 0.369458 + 0.213307i
\(515\) 29.6746i 1.30762i
\(516\) −10.0896 + 17.4758i −0.444171 + 0.769327i
\(517\) −1.32173 2.28930i −0.0581295 0.100683i
\(518\) 0 0
\(519\) 8.33263 0.365762
\(520\) −4.00775 11.6434i −0.175752 0.510597i
\(521\) −16.3253 −0.715225 −0.357613 0.933870i \(-0.616409\pi\)
−0.357613 + 0.933870i \(0.616409\pi\)
\(522\) 4.95322 2.85974i 0.216796 0.125167i
\(523\) −3.54473 6.13965i −0.155000 0.268468i 0.778059 0.628191i \(-0.216204\pi\)
−0.933059 + 0.359723i \(0.882871\pi\)
\(524\) 10.0463 17.4007i 0.438874 0.760152i
\(525\) 0 0
\(526\) 4.86836 + 2.81075i 0.212271 + 0.122555i
\(527\) 36.3805 + 21.0043i 1.58476 + 0.914963i
\(528\) 5.81138i 0.252908i
\(529\) 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
\(534\) −17.2644 −0.747102
\(535\) 11.9548 6.90209i 0.516850 0.298403i
\(536\) −3.99505 6.91963i −0.172560 0.298882i
\(537\) 6.66368 11.5418i 0.287559 0.498067i
\(538\) 25.1558i 1.08454i
\(539\) 0 0
\(540\) −15.2922 8.82897i −0.658073 0.379938i
\(541\) 25.5162i 1.09703i −0.836141 0.548515i \(-0.815194\pi\)
0.836141 0.548515i \(-0.184806\pi\)
\(542\) 13.7409 23.7999i 0.590222 1.02229i
\(543\) 2.39218 + 4.14338i 0.102658 + 0.177809i
\(544\) 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
\(549\) −1.62781 2.81945i −0.0694733 0.120331i
\(550\) −7.45350 + 12.9098i −0.317818 + 0.550478i
\(551\) 3.04952i 0.129914i
\(552\) −7.16607 4.13733i −0.305008 0.176096i
\(553\) 0 0
\(554\) 45.0669i 1.91471i
\(555\) −39.2559 + 67.9932i −1.66632 + 2.88615i
\(556\) −20.4297 35.3852i −0.866412 1.50067i
\(557\) −14.7285 + 8.50353i −0.624069 + 0.360306i −0.778451 0.627705i \(-0.783994\pi\)
0.154383 + 0.988011i \(0.450661\pi\)
\(558\) −37.7851 −1.59957
\(559\) −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 \(-0.657357\pi\)
0.999572 0.0292428i \(-0.00930961\pi\)
\(564\) 16.5218i 0.695691i
\(565\) −15.3158 8.84257i −0.644340 0.372010i
\(566\) 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 \(0.793993\pi\)
\(570\) −35.3983 + 20.4372i −1.48267 + 0.856022i
\(571\) −8.92622 −0.373551 −0.186775 0.982403i \(-0.559804\pi\)
−0.186775 + 0.982403i \(0.559804\pi\)
\(572\) 7.40220 2.54789i 0.309501 0.106533i
\(573\) 25.7074 1.07394
\(574\) 0 0
\(575\) 15.3816 + 26.6417i 0.641457 + 1.11104i
\(576\) −11.7398 + 20.3339i −0.489158 + 0.847247i
\(577\) 36.1933i 1.50675i −0.657592 0.753374i \(-0.728425\pi\)
0.657592 0.753374i \(-0.271575\pi\)
\(578\) −13.8894 8.01905i −0.577723 0.333549i
\(579\) 27.5961 + 15.9326i 1.14685 + 0.662136i
\(580\) 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
\(584\) 6.77838 0.280491
\(585\) −5.24383 + 26.9617i −0.216806 + 1.11473i
\(586\) 0.886069 0.0366032
\(587\) −31.6008 + 18.2447i −1.30431 + 0.753041i −0.981139 0.193301i \(-0.938080\pi\)
−0.323166 + 0.946342i \(0.604747\pi\)
\(588\) 0 0
\(589\) 10.0732 17.4472i 0.415058 0.718901i
\(590\) 55.6708i 2.29193i
\(591\) −44.9649 25.9605i −1.84961 1.06787i
\(592\) −24.1967 13.9699i −0.994476 0.574161i
\(593\) 34.9930i 1.43699i 0.695533 + 0.718495i \(0.255168\pi\)
−0.695533 + 0.718495i \(0.744832\pi\)
\(594\) 1.87107 3.24079i 0.0767711 0.132971i
\(595\) 0 0
\(596\) −5.34926 + 3.08839i −0.219114 + 0.126506i
\(597\) 7.12385 0.291560
\(598\) 5.60256 28.8062i 0.229106 1.17797i
\(599\) −32.5052 −1.32812 −0.664062 0.747677i \(-0.731169\pi\)
−0.664062 + 0.747677i \(0.731169\pi\)
\(600\) −14.8072 + 8.54894i −0.604501 + 0.349009i
\(601\) 10.0390 + 17.3881i 0.409500 + 0.709275i 0.994834 0.101518i \(-0.0323699\pi\)
−0.585334 + 0.810792i \(0.699037\pi\)
\(602\) 0 0
\(603\) 17.8225i 0.725788i
\(604\) −33.7235 19.4703i −1.37219 0.792235i
\(605\) 31.8608 + 18.3949i 1.29533 + 0.747858i
\(606\) 27.7799i 1.12848i
\(607\) 4.85800 8.41431i 0.197180 0.341526i −0.750433 0.660947i \(-0.770155\pi\)
0.947613 + 0.319420i \(0.103488\pi\)
\(608\) −9.52856 16.5039i −0.386434 0.669323i
\(609\) 0 0
\(610\) 11.6946 0.473502
\(611\) 10.1674 3.49968i 0.411327 0.141582i
\(612\) 25.6979 1.03878
\(613\) −10.2898 + 5.94080i −0.415600 + 0.239947i −0.693193 0.720752i \(-0.743797\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(614\) 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 0.109295 0.994009i \(-0.465141\pi\)
−0.806190 + 0.591657i \(0.798474\pi\)
\(618\) 34.0393 + 19.6526i 1.36926 + 0.790543i
\(619\) 41.7176i 1.67677i 0.545078 + 0.838386i \(0.316500\pi\)
−0.545078 + 0.838386i \(0.683500\pi\)
\(620\) 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
\(625\) −1.29828 −0.0519312
\(626\) −12.5091 + 7.22211i −0.499963 + 0.288654i
\(627\) −2.38435 4.12982i −0.0952219 0.164929i
\(628\) −15.9012 + 27.5416i −0.634526 + 1.09903i
\(629\) 47.8066i 1.90618i
\(630\) 0 0
\(631\) 15.2780 + 8.82074i 0.608206 + 0.351148i 0.772263 0.635303i \(-0.219125\pi\)
−0.164057 + 0.986451i \(0.552458\pi\)
\(632\) 0.718319i 0.0285732i
\(633\) −16.8084 + 29.1130i −0.668073 + 1.15714i
\(634\) 0.739603 + 1.28103i 0.0293734 + 0.0508762i
\(635\) −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
\(640\) −13.3159 23.0639i −0.526359 0.911680i
\(641\) −5.46012 + 9.45721i −0.215662 + 0.373537i −0.953477 0.301465i \(-0.902524\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(642\) 18.2842i 0.721618i
\(643\) −15.2725 8.81757i −0.602288 0.347731i 0.167653 0.985846i \(-0.446381\pi\)
−0.769941 + 0.638115i \(0.779714\pi\)
\(644\) 0 0
\(645\) 29.6716i 1.16832i
\(646\) −12.4445 + 21.5544i −0.489620 + 0.848048i
\(647\) −8.33632 14.4389i −0.327735 0.567653i 0.654327 0.756211i \(-0.272952\pi\)
−0.982062 + 0.188558i \(0.939619\pi\)
\(648\) 8.92758 5.15434i 0.350708 0.202482i
\(649\) −6.49495 −0.254949
\(650\) −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
\(655\) 29.5441i 1.15439i
\(656\) −30.3374 17.5153i −1.18448 0.683858i
\(657\) −13.0940 7.55983i −0.510846 0.294937i
\(658\) 0 0
\(659\) −16.7680 + 29.0431i −0.653190 + 1.13136i 0.329154 + 0.944276i \(0.393236\pi\)
−0.982344 + 0.187082i \(0.940097\pi\)
\(660\) −8.84332 15.3171i −0.344226 0.596216i
\(661\) 21.7945 12.5830i 0.847707 0.489424i −0.0121696 0.999926i \(-0.503874\pi\)
0.859876 + 0.510502i \(0.170540\pi\)
\(662\) 8.85657 0.344221
\(663\) 13.1643 + 38.2454i 0.511261 + 1.48533i
\(664\) −4.52075 −0.175439
\(665\) 0 0
\(666\) −21.5001 37.2393i −0.833112 1.44299i
\(667\) −2.47325 + 4.28380i −0.0957647 + 0.165869i
\(668\) 33.7833i 1.30712i
\(669\) −8.58060 4.95401i −0.331745 0.191533i
\(670\) −55.4436 32.0104i −2.14197 1.23667i
\(671\) 1.36438i 0.0526713i
\(672\) 0 0
\(673\) −0.927341 1.60620i −0.0357464 0.0619145i 0.847599 0.530638i \(-0.178048\pi\)
−0.883345 + 0.468723i \(0.844714\pi\)
\(674\) −37.3172 + 21.5451i −1.43741 + 0.829887i
\(675\) −15.9571 −0.614189
\(676\) 4.42503 + 31.5348i 0.170194 + 1.21288i
\(677\) 14.7209 0.565770 0.282885 0.959154i \(-0.408709\pi\)
0.282885 + 0.959154i \(0.408709\pi\)
\(678\) 20.2863 11.7123i 0.779092 0.449809i
\(679\) 0 0
\(680\) −8.47009 + 14.6706i −0.324813 + 0.562593i
\(681\) 30.6822i 1.17575i
\(682\) 13.7136 + 7.91756i 0.525122 + 0.303179i
\(683\) 6.87930 + 3.97177i 0.263229 + 0.151975i 0.625807 0.779978i \(-0.284770\pi\)
−0.362578 + 0.931954i \(0.618103\pi\)
\(684\) 12.3241i 0.471224i
\(685\) 13.4266 23.2556i 0.513005 0.888551i
\(686\) 0 0
\(687\) 32.3529 18.6790i 1.23434 0.712647i
\(688\) −10.5592 −0.402566
\(689\) 5.77394 + 16.7746i 0.219969 + 0.639060i
\(690\) −66.3008 −2.52403
\(691\) −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
\(695\) −52.0306 30.0399i −1.97363 1.13948i
\(696\) −2.38089 1.37461i −0.0902475 0.0521044i
\(697\) 59.9392i 2.27036i
\(698\) −22.7785 + 39.4535i −0.862178 + 1.49334i
\(699\) 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 \(0.601483\pi\)
\(702\) 11.4871 + 9.98773i 0.433552 + 0.376963i
\(703\) 22.9269 0.864706
\(704\) 8.52162 4.91996i 0.321171 0.185428i
\(705\) −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
\(709\) 41.4531 + 23.9329i 1.55680 + 0.898820i 0.997560 + 0.0698158i \(0.0222412\pi\)
0.559242 + 0.829004i \(0.311092\pi\)
\(710\) 48.9957i 1.83878i
\(711\) −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
\(716\) −14.4344 −0.539441
\(717\) 59.5840 34.4008i 2.22520 1.28472i
\(718\) 14.4318 + 24.9965i 0.538588 + 0.932862i
\(719\) 19.0461 32.9888i 0.710300 1.23028i −0.254444 0.967087i \(-0.581893\pi\)
0.964744 0.263188i \(-0.0847741\pi\)
\(720\) 22.0836i 0.823009i
\(721\) 0 0
\(722\) −24.3719 14.0711i −0.907028 0.523673i
\(723\) 66.7511i 2.48250i
\(724\) 2.59089 4.48756i 0.0962898 0.166779i
\(725\) 5.11047 + 8.85159i 0.189798 + 0.328740i
\(726\) −42.2009 + 24.3647i −1.56622 + 0.904259i
\(727\) −15.4059 −0.571374 −0.285687 0.958323i \(-0.592222\pi\)
−0.285687 + 0.958323i \(0.592222\pi\)
\(728\) 0 0
\(729\) −9.41460 −0.348689
\(730\) 47.0354 27.1559i 1.74086 1.00508i
\(731\) 9.03369 + 15.6468i 0.334123 + 0.578718i
\(732\) −4.26372 + 7.38498i −0.157592 + 0.272957i
\(733\) 11.6298i 0.429557i 0.976663 + 0.214778i \(0.0689029\pi\)
−0.976663 + 0.214778i \(0.931097\pi\)
\(734\) −20.8487 12.0370i −0.769538 0.444293i
\(735\) 0 0
\(736\) 30.9117i 1.13942i
\(737\) 3.73456 6.46844i 0.137564 0.238268i
\(738\) −26.9565 46.6900i −0.992282 1.71868i
\(739\) 2.32875 1.34451i 0.0856645 0.0494584i −0.456556 0.889695i \(-0.650917\pi\)
0.542220 + 0.840236i \(0.317584\pi\)
\(740\) 85.0336 3.12590
\(741\) 18.3416 6.31331i 0.673794 0.231925i
\(742\) 0 0
\(743\) −2.13665 + 1.23360i −0.0783862 + 0.0452563i −0.538681 0.842510i \(-0.681077\pi\)
0.460295 + 0.887766i \(0.347744\pi\)
\(744\) 9.08120 + 15.7291i 0.332933 + 0.576657i
\(745\) −4.54118 + 7.86556i −0.166376 + 0.288172i
\(746\) 65.9835i 2.41583i
\(747\) 8.73288 + 5.04193i 0.319519 + 0.184475i
\(748\) −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 \(-0.409863\pi\)
\(752\) 7.48709 4.32267i 0.273026 0.157632i
\(753\) 29.3623 1.07002
\(754\) 1.86142 9.57072i 0.0677890 0.348545i
\(755\) −57.2583 −2.08384
\(756\) 0 0
\(757\) −17.3225 30.0035i −0.629598 1.09050i −0.987632 0.156788i \(-0.949886\pi\)
0.358034 0.933709i \(-0.383447\pi\)
\(758\) 28.9145 50.0814i 1.05022 1.81904i
\(759\) 7.73512i 0.280767i
\(760\) 7.03569 + 4.06206i 0.255211 + 0.147346i
\(761\) −19.7969 11.4297i −0.717636 0.414328i 0.0962458 0.995358i \(-0.469317\pi\)
−0.813882 + 0.581030i \(0.802650\pi\)
\(762\) 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
\(766\) −33.9625 −1.22712
\(767\) 5.04386 25.9336i 0.182123 0.936408i
\(768\) −14.9390 −0.539065
\(769\) 44.8839 25.9137i 1.61855 0.934473i 0.631260 0.775571i \(-0.282538\pi\)
0.987294 0.158902i \(-0.0507953\pi\)
\(770\) 0 0
\(771\) −5.18507 + 8.98080i −0.186736 + 0.323436i
\(772\) 34.5122i 1.24212i
\(773\) 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
\(775\) 67.5234i 2.42551i
\(776\) 0.219653 0.380450i 0.00788508 0.0136574i
\(777\) 0 0
\(778\) −38.6146 + 22.2941i −1.38440 + 0.799283i
\(779\) 28.7454 1.02991
\(780\) 68.0269 23.4154i 2.43576 0.838406i
\(781\) −5.71619