Properties

Label 637.2.k.h.569.6
Level $637$
Weight $2$
Character 637.569
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.k (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: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
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 569.6
Root \(-1.30089 + 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.h.459.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.10939i q^{2} +(-1.13082 + 1.95864i) q^{3} -2.44952 q^{4} +(-3.11923 - 1.80089i) q^{5} +(-4.13154 - 2.38535i) q^{6} -0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})\) \(q+2.10939i q^{2} +(-1.13082 + 1.95864i) q^{3} -2.44952 q^{4} +(-3.11923 - 1.80089i) 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} +(2.76998 - 4.79774i) q^{12} +(-1.17349 - 3.40924i) q^{13} +(7.05461 - 4.07298i) q^{15} -2.89889 q^{16} +4.96016 q^{17} +(3.86375 - 2.23073i) q^{18} +(-2.06008 + 1.18939i) q^{19} +(7.64062 + 4.41132i) q^{20} +(0.934864 - 1.61923i) q^{22} +3.85851 q^{23} +(1.85721 + 1.07226i) q^{24} +(3.98641 + 6.90466i) q^{25} +(7.19141 - 2.47534i) q^{26} -2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +(-7.33455 + 4.23460i) q^{31} -8.01131i q^{32} +(1.73611 - 1.00234i) q^{33} +10.4629i q^{34} +(2.59043 + 4.48676i) q^{36} -9.63812i q^{37} +(-2.50888 - 4.34551i) q^{38} +(8.00450 + 1.55681i) 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} +7.61796i q^{45} +8.13910i 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} +(2.87448 + 8.35100i) q^{52} +(-2.46016 - 4.26112i) q^{53} -4.22181i q^{54} +(1.59628 + 2.76484i) q^{55} -5.37995i q^{57} +(2.34189 - 1.35209i) q^{58} -7.32746i q^{59} +(-17.2804 + 9.97684i) q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 - 15.4714i) q^{62} +11.1012 q^{64} +(-2.47929 + 12.7475i) q^{65} +(2.11433 + 3.66213i) q^{66} +(-7.29756 - 4.21325i) q^{67} -12.1500 q^{68} +(-4.36330 + 7.55745i) q^{69} +(-5.58490 - 3.22444i) q^{71} +(-1.73683 + 1.00276i) q^{72} +(-6.19086 + 3.57430i) q^{73} +20.3305 q^{74} -18.0317 q^{75} +(5.04621 - 2.91343i) q^{76} +(-3.28391 + 16.8846i) q^{78} +(-0.378775 + 0.656058i) 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} +(-6.65406 - 3.84172i) q^{86} +2.89937 q^{87} +(-0.420240 + 0.727877i) q^{88} +3.61884i q^{89} -16.0692 q^{90} -9.45150 q^{92} -19.1544i q^{93} +(3.14541 - 5.44800i) q^{94} +8.56783 q^{95} +(15.6913 + 9.05939i) q^{96} +(-0.401229 - 0.231650i) q^{97} +1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.10939i 1.49156i 0.666191 + 0.745781i \(0.267924\pi\)
−0.666191 + 0.745781i \(0.732076\pi\)
\(3\) −1.13082 + 1.95864i −0.652882 + 1.13082i 0.329539 + 0.944142i \(0.393107\pi\)
−0.982420 + 0.186682i \(0.940227\pi\)
\(4\) −2.44952 −1.22476
\(5\) −3.11923 1.80089i −1.39496 0.805382i −0.401104 0.916033i \(-0.631373\pi\)
−0.993859 + 0.110650i \(0.964707\pi\)
\(6\) −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 \(-0.375996\pi\)
−0.611241 + 0.791445i \(0.709329\pi\)
\(12\) 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
\(16\) −2.89889 −0.724723
\(17\) 4.96016 1.20302 0.601508 0.798867i \(-0.294567\pi\)
0.601508 + 0.798867i \(0.294567\pi\)
\(18\) 3.86375 2.23073i 0.910694 0.525789i
\(19\) −2.06008 + 1.18939i −0.472615 + 0.272864i −0.717334 0.696730i \(-0.754638\pi\)
0.244719 + 0.969594i \(0.421304\pi\)
\(20\) 7.64062 + 4.41132i 1.70849 + 0.986400i
\(21\) 0 0
\(22\) 0.934864 1.61923i 0.199314 0.345222i
\(23\) 3.85851 0.804555 0.402278 0.915518i \(-0.368219\pi\)
0.402278 + 0.915518i \(0.368219\pi\)
\(24\) 1.85721 + 1.07226i 0.379101 + 0.218874i
\(25\) 3.98641 + 6.90466i 0.797282 + 1.38093i
\(26\) 7.19141 2.47534i 1.41035 0.485454i
\(27\) −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
\(31\) −7.33455 + 4.23460i −1.31732 + 0.760557i −0.983297 0.182006i \(-0.941741\pi\)
−0.334027 + 0.942564i \(0.608408\pi\)
\(32\) 8.01131i 1.41621i
\(33\) 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
\(37\) 9.63812i 1.58450i −0.610198 0.792249i \(-0.708910\pi\)
0.610198 0.792249i \(-0.291090\pi\)
\(38\) −2.50888 4.34551i −0.406994 0.704935i
\(39\) 8.00450 + 1.55681i 1.28175 + 0.249289i
\(40\) −1.70762 + 2.95769i −0.269999 + 0.467652i
\(41\) 10.4652 6.04207i 1.63438 0.943612i 0.651666 0.758506i \(-0.274071\pi\)
0.982719 0.185106i \(-0.0592628\pi\)
\(42\) 0 0
\(43\) −1.82125 + 3.15450i −0.277738 + 0.481056i −0.970822 0.239800i \(-0.922918\pi\)
0.693084 + 0.720856i \(0.256251\pi\)
\(44\) 1.88033 + 1.08561i 0.283470 + 0.163662i
\(45\) 7.61796i 1.13562i
\(46\) 8.13910i 1.20004i
\(47\) −2.58274 1.49115i −0.376731 0.217506i 0.299664 0.954045i \(-0.403126\pi\)
−0.676395 + 0.736539i \(0.736459\pi\)
\(48\) 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
\(52\) 2.87448 + 8.35100i 0.398619 + 1.15808i
\(53\) −2.46016 4.26112i −0.337929 0.585310i 0.646114 0.763241i \(-0.276393\pi\)
−0.984043 + 0.177931i \(0.943060\pi\)
\(54\) 4.22181i 0.574516i
\(55\) 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
\(59\) 7.32746i 0.953954i −0.878916 0.476977i \(-0.841732\pi\)
0.878916 0.476977i \(-0.158268\pi\)
\(60\) −17.2804 + 9.97684i −2.23089 + 1.28800i
\(61\) 0.769632 + 1.33304i 0.0985412 + 0.170678i 0.911081 0.412227i \(-0.135249\pi\)
−0.812540 + 0.582906i \(0.801916\pi\)
\(62\) −8.93242 15.4714i −1.13442 1.96487i
\(63\) 0 0
\(64\) 11.1012 1.38765
\(65\) −2.47929 + 12.7475i −0.307518 + 1.58114i
\(66\) 2.11433 + 3.66213i 0.260257 + 0.450778i
\(67\) −7.29756 4.21325i −0.891539 0.514730i −0.0170931 0.999854i \(-0.505441\pi\)
−0.874445 + 0.485124i \(0.838775\pi\)
\(68\) −12.1500 −1.47341
\(69\) −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
\(73\) −6.19086 + 3.57430i −0.724586 + 0.418340i −0.816438 0.577433i \(-0.804054\pi\)
0.0918526 + 0.995773i \(0.470721\pi\)
\(74\) 20.3305 2.36338
\(75\) −18.0317 −2.08212
\(76\) 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 \(0.180236\pi\)
\(80\) 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 \(0.0842697\pi\)
−0.965160 + 0.261659i \(0.915730\pi\)
\(84\) 0 0
\(85\) −15.4719 8.93270i −1.67816 0.968888i
\(86\) −6.65406 3.84172i −0.717525 0.414263i
\(87\) 2.89937 0.310845
\(88\) −0.420240 + 0.727877i −0.0447977 + 0.0775919i
\(89\) 3.61884i 0.383596i 0.981434 + 0.191798i \(0.0614318\pi\)
−0.981434 + 0.191798i \(0.938568\pi\)
\(90\) −16.0692 −1.69385
\(91\) 0 0
\(92\) −9.45150 −0.985387
\(93\) 19.1544i 1.98622i
\(94\) 3.14541 5.44800i 0.324424 0.561919i
\(95\) 8.56783 0.879040
\(96\) 15.6913 + 9.05939i 1.60149 + 0.924620i
\(97\) −0.401229 0.231650i −0.0407386 0.0235205i 0.479492 0.877546i \(-0.340821\pi\)
−0.520231 + 0.854026i \(0.674154\pi\)
\(98\) 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 \(-0.739776\pi\)
0.973740 + 0.227664i \(0.0731089\pi\)
\(102\) −20.4931 11.8317i −2.02912 1.17151i
\(103\) 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
\(107\) −3.83260 −0.370511 −0.185256 0.982690i \(-0.559311\pi\)
−0.185256 + 0.982690i \(0.559311\pi\)
\(108\) 4.90256 0.471749
\(109\) 9.02229 5.20902i 0.864178 0.498934i −0.00123094 0.999999i \(-0.500392\pi\)
0.865409 + 0.501066i \(0.167058\pi\)
\(110\) −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 \(0.0924826\pi\)
\(114\) 11.3484 1.06288
\(115\) −12.0356 6.94875i −1.12233 0.647975i
\(116\) 1.57011 + 2.71951i 0.145781 + 0.252500i
\(117\) −5.00368 + 5.75483i −0.462590 + 0.532034i
\(118\) 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
\(122\) −2.81190 + 1.62345i −0.254578 + 0.146980i
\(123\) 27.3301i 2.46427i
\(124\) 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 \(-0.350583\pi\)
\(128\) 7.39409i 0.653551i
\(129\) −4.11902 7.13436i −0.362660 0.628145i
\(130\) −26.8895 5.22978i −2.35837 0.458682i
\(131\) 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
\(136\) 4.70328i 0.403303i
\(137\) 7.45555i 0.636971i −0.947928 0.318485i \(-0.896826\pi\)
0.947928 0.318485i \(-0.103174\pi\)
\(138\) −15.9416 9.20389i −1.35704 0.783487i
\(139\) −8.34028 + 14.4458i −0.707413 + 1.22528i 0.258400 + 0.966038i \(0.416805\pi\)
−0.965813 + 0.259238i \(0.916529\pi\)
\(140\) 0 0
\(141\) 5.84125 3.37245i 0.491922 0.284011i
\(142\) 6.80160 11.7807i 0.570778 0.988616i
\(143\) −0.610143 + 3.13712i −0.0510228 + 0.262339i
\(144\) 3.06566 + 5.30987i 0.255471 + 0.442489i
\(145\) 4.61738i 0.383453i
\(146\) −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 \(-0.633730\pi\)
0.586777 + 0.809748i \(0.300396\pi\)
\(150\) 38.0359i 3.10562i
\(151\) −13.7674 + 7.94862i −1.12038 + 0.646849i −0.941497 0.337022i \(-0.890580\pi\)
−0.178879 + 0.983871i \(0.557247\pi\)
\(152\) 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
\(156\) −19.6072 3.81343i −1.56983 0.305319i
\(157\) −6.49155 11.2437i −0.518082 0.897344i −0.999779 0.0210065i \(-0.993313\pi\)
0.481697 0.876338i \(-0.340020\pi\)
\(158\) −1.38388 0.798985i −0.110096 0.0635638i
\(159\) 11.1280 0.882511
\(160\) −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 \(-0.637712\pi\)
0.576601 + 0.817026i \(0.304379\pi\)
\(164\) −25.6346 + 14.8002i −2.00173 + 1.15570i
\(165\) −7.22045 −0.562111
\(166\) −10.0569 −0.780563
\(167\) −11.9441 + 6.89591i −0.924260 + 0.533622i −0.884992 0.465607i \(-0.845836\pi\)
−0.0392682 + 0.999229i \(0.512503\pi\)
\(168\) 0 0
\(169\) −10.2459 + 8.00140i −0.788143 + 0.615493i
\(170\) 18.8425 32.6362i 1.44516 2.50309i
\(171\) 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 \(-0.211395\pi\)
−0.927518 + 0.373779i \(0.878062\pi\)
\(174\) 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
\(178\) −7.63353 −0.572157
\(179\) −2.94638 + 5.10328i −0.220223 + 0.381437i −0.954876 0.297006i \(-0.904012\pi\)
0.734653 + 0.678443i \(0.237345\pi\)
\(180\) 18.6603i 1.39086i
\(181\) −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
\(184\) 3.65869i 0.269722i
\(185\) −17.3572 + 30.0635i −1.27613 + 2.21032i
\(186\) 40.4040 2.96257
\(187\) −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
\(191\) 5.68333 + 9.84381i 0.411231 + 0.712273i 0.995025 0.0996290i \(-0.0317656\pi\)
−0.583794 + 0.811902i \(0.698432\pi\)
\(192\) −12.5535 + 21.7433i −0.905970 + 1.56919i
\(193\) −12.2017 7.04468i −0.878301 0.507087i −0.00820314 0.999966i \(-0.502611\pi\)
−0.870098 + 0.492879i \(0.835945\pi\)
\(194\) 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 −0.995989 0.0894753i \(-0.971481\pi\)
−0.420507 + 0.907289i \(0.638148\pi\)
\(198\) −3.95458 −0.281040
\(199\) 3.14985 0.223287 0.111643 0.993748i \(-0.464389\pi\)
0.111643 + 0.993748i \(0.464389\pi\)
\(200\) 6.54708 3.77996i 0.462949 0.267283i
\(201\) 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
\(205\) −43.5244 −3.03987
\(206\) 15.0507 + 8.68950i 1.04863 + 0.605426i
\(207\) −4.08048 7.06760i −0.283613 0.491232i
\(208\) 3.40181 + 9.88303i 0.235873 + 0.685265i
\(209\) 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
\(213\) 12.6311 7.29255i 0.865467 0.499678i
\(214\) 8.08444i 0.552641i
\(215\) 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
\(219\) 16.1676i 1.09251i
\(220\) −3.91012 6.77253i −0.263620 0.456604i
\(221\) −5.82069 16.9104i −0.391542 1.13752i
\(222\) −22.9903 + 39.8203i −1.54301 + 2.67257i
\(223\) 3.79396 2.19044i 0.254062 0.146683i −0.367561 0.930000i \(-0.619807\pi\)
0.621623 + 0.783317i \(0.286474\pi\)
\(224\) 0 0
\(225\) 8.43147 14.6037i 0.562098 0.973582i
\(226\) 8.96971 + 5.17866i 0.596656 + 0.344480i
\(227\) 13.5663i 0.900428i −0.892921 0.450214i \(-0.851348\pi\)
0.892921 0.450214i \(-0.148652\pi\)
\(228\) 13.1783i 0.872754i
\(229\) −14.3050 8.25900i −0.945302 0.545770i −0.0536833 0.998558i \(-0.517096\pi\)
−0.891618 + 0.452788i \(0.850429\pi\)
\(230\) 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 \(0.984879\pi\)
\(234\) −12.1392 10.5547i −0.793562 0.689983i
\(235\) 5.37078 + 9.30246i 0.350351 + 0.606826i
\(236\) 17.9488i 1.16836i
\(237\) −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
\(241\) 29.5143i 1.90119i 0.310440 + 0.950593i \(0.399524\pi\)
−0.310440 + 0.950593i \(0.600476\pi\)
\(242\) 18.6594 10.7730i 1.19947 0.692514i
\(243\) 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
\(247\) 6.47239 + 5.62758i 0.411828 + 0.358074i
\(248\) 4.01530 + 6.95471i 0.254972 + 0.441624i
\(249\) −9.33816 5.39139i −0.591782 0.341665i
\(250\) 22.5861 1.42847
\(251\) −6.49134 + 11.2433i −0.409730 + 0.709673i −0.994859 0.101267i \(-0.967710\pi\)
0.585130 + 0.810940i \(0.301044\pi\)
\(252\) 0 0
\(253\) −2.96191 1.71006i −0.186214 0.107511i
\(254\) 22.4880 12.9835i 1.41102 0.814654i
\(255\) 34.9920 20.2026i 2.19128 1.26514i
\(256\) 6.60537 0.412836
\(257\) 4.58521 0.286018 0.143009 0.989721i \(-0.454322\pi\)
0.143009 + 0.989721i \(0.454322\pi\)
\(258\) 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
\(262\) 14.9845 + 8.65129i 0.925744 + 0.534479i
\(263\) 1.33250 2.30795i 0.0821652 0.142314i −0.822015 0.569466i \(-0.807150\pi\)
0.904180 + 0.427152i \(0.140483\pi\)
\(264\) −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
\(268\) 17.8755 + 10.3204i 1.09192 + 0.630421i
\(269\) 11.9256 0.727119 0.363559 0.931571i \(-0.381561\pi\)
0.363559 + 0.931571i \(0.381561\pi\)
\(270\) −7.60301 + 13.1688i −0.462705 + 0.801428i
\(271\) 13.0283i 0.791414i −0.918377 0.395707i \(-0.870500\pi\)
0.918377 0.395707i \(-0.129500\pi\)
\(272\) −14.3790 −0.871853
\(273\) 0 0
\(274\) 15.7267 0.950082
\(275\) 7.06698i 0.426155i
\(276\) 10.6880 18.5121i 0.643341 1.11430i
\(277\) −21.3649 −1.28369 −0.641846 0.766833i \(-0.721831\pi\)
−0.641846 + 0.766833i \(0.721831\pi\)
\(278\) −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 \(0.172228\pi\)
−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 0.355987 + 0.934491i \(0.384145\pi\)
−0.987286 + 0.158952i \(0.949189\pi\)
\(284\) 13.6803 + 7.89833i 0.811777 + 0.468680i
\(285\) −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
\(289\) 7.60320 0.447247
\(290\) −9.73985 −0.571944
\(291\) 0.907439 0.523910i 0.0531950 0.0307122i
\(292\) 15.1646 8.75531i 0.887443 0.512366i
\(293\) −0.363782 0.210030i −0.0212524 0.0122701i 0.489336 0.872095i \(-0.337239\pi\)
−0.510589 + 0.859825i \(0.670572\pi\)
\(294\) 0 0
\(295\) −13.1959 + 22.8561i −0.768298 + 1.33073i
\(296\) −9.13898 −0.531192
\(297\) 1.53637 + 0.887022i 0.0891490 + 0.0514702i
\(298\) 2.65955 + 4.60648i 0.154064 + 0.266846i
\(299\) −4.52791 13.1546i −0.261856 0.760750i
\(300\) 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
\(304\) 5.97195 3.44791i 0.342515 0.197751i
\(305\) 5.54409i 0.317453i
\(306\) 19.1648 11.0648i 1.09558 0.632533i
\(307\) 14.0807i 0.803628i −0.915721 0.401814i \(-0.868380\pi\)
0.915721 0.401814i \(-0.131620\pi\)
\(308\) 0 0
\(309\) 9.31673 + 16.1370i 0.530010 + 0.918004i
\(310\) 64.3453i 3.65456i
\(311\) 5.19240 + 8.99349i 0.294434 + 0.509974i 0.974853 0.222849i \(-0.0715356\pi\)
−0.680419 + 0.732823i \(0.738202\pi\)
\(312\) 1.47618 7.58996i 0.0835724 0.429697i
\(313\) −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 0.482848 0.875704i \(-0.339602\pi\)
−0.516958 + 0.856011i \(0.672936\pi\)
\(318\) 23.4734i 1.31632i
\(319\) 1.13632i 0.0636217i
\(320\) −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
\(325\) 18.8617 21.6932i 1.04626 1.20332i
\(326\) 2.44634 + 4.23719i 0.135490 + 0.234676i
\(327\) 23.5619i 1.30298i
\(328\) −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 \(-0.703478\pi\)
0.396730 + 0.917935i \(0.370145\pi\)
\(332\) 11.6785i 0.640940i
\(333\) −17.6541 + 10.1926i −0.967436 + 0.558550i
\(334\) −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 \(0.687813\pi\)
\(338\) −16.8781 21.6125i −0.918046 1.17556i
\(339\) 5.55247 + 9.61716i 0.301569 + 0.522333i
\(340\) 37.8987 + 21.8808i 2.05535 + 1.18665i
\(341\) 7.50697 0.406525
\(342\) −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
\(346\) 6.73045 3.88583i 0.361831 0.208903i
\(347\) 7.97000 0.427852 0.213926 0.976850i \(-0.431375\pi\)
0.213926 + 0.976850i \(0.431375\pi\)
\(348\) −7.10207 −0.380711
\(349\) 18.7038 10.7986i 1.00119 0.578037i 0.0925892 0.995704i \(-0.470486\pi\)
0.908600 + 0.417668i \(0.137152\pi\)
\(350\) 0 0
\(351\) 2.34866 + 6.82338i 0.125362 + 0.364205i
\(352\) −3.55055 + 6.14974i −0.189245 + 0.327782i
\(353\) −18.7214 10.8088i −0.996439 0.575295i −0.0892465 0.996010i \(-0.528446\pi\)
−0.907193 + 0.420715i \(0.861779\pi\)
\(354\) −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
\(359\) −11.8501 6.84168i −0.625426 0.361090i 0.153552 0.988141i \(-0.450929\pi\)
−0.778979 + 0.627051i \(0.784262\pi\)
\(360\) 7.22344 0.380708
\(361\) −6.67071 + 11.5540i −0.351090 + 0.608106i
\(362\) 4.46226i 0.234531i
\(363\) 23.1012 1.21250
\(364\) 0 0
\(365\) 25.7477 1.34769
\(366\) 7.34335i 0.383843i
\(367\) 5.70638 9.88374i 0.297871 0.515927i −0.677778 0.735267i \(-0.737057\pi\)
0.975649 + 0.219339i \(0.0703902\pi\)
\(368\) −11.1854 −0.583080
\(369\) −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
\(373\) 15.6404 + 27.0900i 0.809830 + 1.40267i 0.912981 + 0.408002i \(0.133774\pi\)
−0.103151 + 0.994666i \(0.532892\pi\)
\(374\) 4.63708 8.03166i 0.239778 0.415307i
\(375\) 20.9721 + 12.1082i 1.08299 + 0.625266i
\(376\) −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 0.254729 0.967012i \(-0.418014\pi\)
0.964822 + 0.262904i \(0.0846803\pi\)
\(380\) −20.9871 −1.07661
\(381\) 27.8412 1.42635
\(382\) −20.7644 + 11.9883i −1.06240 + 0.613377i
\(383\) −13.9436 + 8.05032i −0.712483 + 0.411352i −0.811980 0.583686i \(-0.801610\pi\)
0.0994967 + 0.995038i \(0.468277\pi\)
\(384\) −14.4824 8.36142i −0.739052 0.426692i
\(385\) 0 0
\(386\) 14.8600 25.7382i 0.756353 1.31004i
\(387\) 7.70408 0.391620
\(388\) 0.982819 + 0.567431i 0.0498951 + 0.0288069i
\(389\) 10.5690 + 18.3060i 0.535870 + 0.928153i 0.999121 + 0.0419264i \(0.0133495\pi\)
−0.463251 + 0.886227i \(0.653317\pi\)
\(390\) 40.6506 46.7530i 2.05842 2.36743i
\(391\) 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
\(395\) 2.36298 1.36427i 0.118894 0.0686437i
\(396\) 4.59224i 0.230769i
\(397\) −11.3436 + 6.54921i −0.569317 + 0.328695i −0.756876 0.653558i \(-0.773276\pi\)
0.187560 + 0.982253i \(0.439942\pi\)
\(398\) 6.64426i 0.333046i
\(399\) 0 0
\(400\) −11.5562 20.0159i −0.577808 1.00079i
\(401\) 19.4447i 0.971022i 0.874230 + 0.485511i \(0.161367\pi\)
−0.874230 + 0.485511i \(0.838633\pi\)
\(402\) 20.1001 + 34.8144i 1.00250 + 1.73639i
\(403\) 23.0438 + 20.0360i 1.14789 + 0.998064i
\(404\) −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
\(409\) 24.0559i 1.18949i −0.803916 0.594743i \(-0.797254\pi\)
0.803916 0.594743i \(-0.202746\pi\)
\(410\) 91.8098i 4.53416i
\(411\) 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
\(416\) −27.3125 + 9.40118i −1.33911 + 0.460931i
\(417\) −18.8628 32.6713i −0.923714 1.59992i
\(418\) 4.44767i 0.217542i
\(419\) −19.5119 33.7956i −0.953218 1.65102i −0.738394 0.674370i \(-0.764415\pi\)
−0.214825 0.976653i \(-0.568918\pi\)
\(420\) 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
\(423\) 6.30771i 0.306691i
\(424\) −4.04045 + 2.33275i −0.196221 + 0.113289i
\(425\) 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
\(429\) −5.45454 4.74259i −0.263348 0.228974i
\(430\) 13.8370 + 23.9664i 0.667281 + 1.15576i
\(431\) 31.0727 + 17.9398i 1.49672 + 0.864131i 0.999993 0.00377645i \(-0.00120209\pi\)
0.496726 + 0.867907i \(0.334535\pi\)
\(432\) 5.80195 0.279147
\(433\) 6.10678 10.5773i 0.293473 0.508310i −0.681155 0.732139i \(-0.738522\pi\)
0.974629 + 0.223828i \(0.0718555\pi\)
\(434\) 0 0
\(435\) −9.04381 5.22145i −0.433618 0.250349i
\(436\) −22.1003 + 12.7596i −1.05841 + 0.611074i
\(437\) −7.94884 + 4.58927i −0.380245 + 0.219534i
\(438\) 34.1037 1.62954
\(439\) 15.7553 0.751960 0.375980 0.926628i \(-0.377306\pi\)
0.375980 + 0.926628i \(0.377306\pi\)
\(440\) 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 \(0.0501207\pi\)
\(444\) −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 \(0.407877\pi\)
\(450\) 30.8049 + 17.7852i 1.45216 + 0.838404i
\(451\) −10.7112 −0.504370
\(452\) −6.01371 + 10.4160i −0.282861 + 0.489929i
\(453\) 35.9540i 1.68926i
\(454\) 28.6166 1.34304
\(455\) 0 0
\(456\) −5.10133 −0.238892
\(457\) 7.75597i 0.362809i −0.983409 0.181405i \(-0.941936\pi\)
0.983409 0.181405i \(-0.0580643\pi\)
\(458\) 17.4214 30.1748i 0.814050 1.40998i
\(459\) −9.92745 −0.463374
\(460\) 29.4814 + 17.0211i 1.37458 + 0.793613i
\(461\) 1.27498 + 0.736110i 0.0593817 + 0.0342840i 0.529397 0.848374i \(-0.322418\pi\)
−0.470015 + 0.882658i \(0.655752\pi\)
\(462\) 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
\(467\) 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
\(471\) 29.3632 1.35298
\(472\) −6.94798 −0.319807
\(473\) 2.79610 1.61433i 0.128565 0.0742268i
\(474\) 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
\(478\) 64.1698 2.93506
\(479\) −35.6760 20.5975i −1.63008 0.941125i −0.984068 0.177795i \(-0.943104\pi\)
−0.646009 0.763330i \(-0.723563\pi\)
\(480\) −32.6299 56.5167i −1.48935 2.57962i
\(481\) −32.8587 + 11.3102i −1.49823 + 0.515701i
\(482\) −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
\(486\) −33.9484 + 19.6001i −1.53993 + 0.889078i
\(487\) 28.3265i 1.28360i −0.766874 0.641798i \(-0.778189\pi\)
0.766874 0.641798i \(-0.221811\pi\)
\(488\) 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 \(0.546027\pi\)
\(492\) 66.9455i 3.01814i
\(493\) −3.17940 5.50687i −0.143193 0.248017i
\(494\) −11.8707 + 13.6528i −0.534090 + 0.614268i
\(495\) 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 0.501346 0.865247i \(-0.332838\pi\)
−0.498652 + 0.866802i \(0.666172\pi\)
\(500\) 26.2281i 1.17295i
\(501\) 31.1923i 1.39357i
\(502\) −23.7165 13.6928i −1.05852 0.611138i
\(503\) −12.8686 + 22.2891i −0.573782 + 0.993820i 0.422391 + 0.906414i \(0.361191\pi\)
−0.996173 + 0.0874060i \(0.972142\pi\)
\(504\) 0 0
\(505\) −18.1634 + 10.4866i −0.808260 + 0.466649i
\(506\) 3.60719 6.24783i 0.160359 0.277750i
\(507\) −4.08565 29.1162i −0.181450 1.29309i
\(508\) 15.0770 + 26.1141i 0.668933 + 1.15863i
\(509\) 7.04000i 0.312042i −0.987754 0.156021i \(-0.950133\pi\)
0.987754 0.156021i \(-0.0498668\pi\)
\(510\) 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
\(514\) 9.67199i 0.426613i
\(515\) −25.6990 + 14.8373i −1.13243 + 0.653810i
\(516\) 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
\(520\) 12.0874 + 2.35089i 0.530066 + 0.103093i
\(521\) −8.16266 14.1381i −0.357613 0.619403i 0.629949 0.776637i \(-0.283076\pi\)
−0.987561 + 0.157234i \(0.949742\pi\)
\(522\) −4.95322 2.85974i −0.216796 0.125167i
\(523\) −7.08946 −0.310000 −0.155000 0.987914i \(-0.549538\pi\)
−0.155000 + 0.987914i \(0.549538\pi\)
\(524\) −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
\(528\) −5.03280 + 2.90569i −0.219025 + 0.126454i
\(529\) −8.11189 −0.352691
\(530\) −37.3824 −1.62379
\(531\) −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
\(535\) 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
\(541\) 22.0977 + 12.7581i 0.950055 + 0.548515i 0.893098 0.449862i \(-0.148527\pi\)
0.0569571 + 0.998377i \(0.481860\pi\)
\(542\) 27.4818 1.18044
\(543\) 2.39218 4.14338i 0.102658 0.177809i
\(544\) 39.7374i 1.70373i
\(545\) −37.5235 −1.60733
\(546\) 0 0
\(547\) −13.3073 −0.568978 −0.284489 0.958679i \(-0.591824\pi\)
−0.284489 + 0.958679i \(0.591824\pi\)
\(548\) 18.2625i 0.780136i
\(549\) 1.62781 2.81945i 0.0694733 0.120331i
\(550\) 14.9070 0.635637
\(551\) 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
\(555\) −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 \(-0.216006\pi\)
−0.154383 + 0.988011i \(0.549339\pi\)
\(558\) −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
\(562\) −36.4244 −1.53647
\(563\) 24.9193 1.05022 0.525111 0.851034i \(-0.324024\pi\)
0.525111 + 0.851034i \(0.324024\pi\)
\(564\) −14.3083 + 8.26088i −0.602486 + 0.347846i
\(565\) −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
\(569\) −5.88129 −0.246557 −0.123278 0.992372i \(-0.539341\pi\)
−0.123278 + 0.992372i \(0.539341\pi\)
\(570\) −35.3983 20.4372i −1.48267 0.856022i
\(571\) 4.46311 + 7.73034i 0.186775 + 0.323504i 0.944173 0.329449i \(-0.106863\pi\)
−0.757398 + 0.652954i \(0.773530\pi\)
\(572\) 1.49456 7.68444i 0.0624906 0.321303i
\(573\) −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
\(577\) 31.3443 18.0967i 1.30488 0.753374i 0.323645 0.946179i \(-0.395092\pi\)
0.981237 + 0.192804i \(0.0617583\pi\)
\(578\) 16.0381i 0.667097i
\(579\) 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
\(583\) 4.36130i 0.180626i
\(584\) 3.38919 + 5.87025i 0.140246 + 0.242913i
\(585\) 25.9715 8.93958i 1.07379 0.369606i
\(586\) 0.443035 0.767358i 0.0183016 0.0316993i
\(587\) 31.6008 18.2447i 1.30431 0.753041i 0.323166 0.946342i \(-0.395253\pi\)
0.981139 + 0.193301i \(0.0619195\pi\)
\(588\) 0 0
\(589\) 10.0732 17.4472i 0.415058 0.718901i
\(590\) −48.2123 27.8354i −1.98487 1.14596i
\(591\) 51.9210i 2.13574i
\(592\) 27.9399i 1.14832i
\(593\) 30.3048 + 17.4965i 1.24447 + 0.718495i 0.970001 0.243102i \(-0.0781649\pi\)
0.274468 + 0.961596i \(0.411498\pi\)
\(594\) −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
\(598\) 27.7482 9.55113i 1.13471 0.390575i
\(599\) 16.2526 + 28.1503i 0.664062 + 1.15019i 0.979539 + 0.201256i \(0.0645025\pi\)
−0.315476 + 0.948934i \(0.602164\pi\)
\(600\) 17.0979i 0.698018i
\(601\) −10.0390 17.3881i −0.409500 0.709275i 0.585334 0.810792i \(-0.300963\pi\)
−0.994834 + 0.101518i \(0.967630\pi\)
\(602\) 0 0
\(603\) 17.8225i 0.725788i
\(604\) 33.7235 19.4703i 1.37219 0.792235i
\(605\) 36.7897i 1.49572i
\(606\) −24.0581 + 13.8900i −0.977294 + 0.564241i
\(607\) −4.85800 8.41431i −0.197180 0.341526i 0.750433 0.660947i \(-0.229845\pi\)
−0.947613 + 0.319420i \(0.896512\pi\)
\(608\) 9.52856 + 16.5039i 0.386434 + 0.669323i
\(609\) 0 0
\(610\) 11.6946 0.473502
\(611\) −2.05286 + 10.5550i −0.0830500 + 0.427011i
\(612\) 12.8490 + 22.2551i 0.519389 + 0.899607i
\(613\) 10.2898 + 5.94080i 0.415600 + 0.239947i 0.693193 0.720752i \(-0.256203\pi\)
−0.277593 + 0.960699i \(0.589537\pi\)
\(614\) 29.7017 1.19866
\(615\) 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
\(619\) −36.1285 + 20.8588i −1.45213 + 0.838386i −0.998602 0.0528581i \(-0.983167\pi\)
−0.453525 + 0.891244i \(0.649834\pi\)
\(620\) −74.7207 −3.00086
\(621\) −7.72257 −0.309896
\(622\) −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
\(626\) −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 \(0.552458\pi\)
\(632\) 0.622082 + 0.359159i 0.0247451 + 0.0142866i
\(633\) −33.6168 −1.33615
\(634\) 0.739603 1.28103i 0.0293734 0.0508762i
\(635\) 44.3385i 1.75952i
\(636\) −27.2584 −1.08086
\(637\) 0 0
\(638\) −2.39694 −0.0948958
\(639\) 13.6397i 0.539580i
\(640\) 13.3159 23.0639i 0.526359 0.911680i
\(641\) 10.9202 0.431324 0.215662 0.976468i \(-0.430809\pi\)
0.215662 + 0.976468i \(0.430809\pi\)
\(642\) 15.8346 + 9.14208i 0.624940 + 0.360809i
\(643\) 15.2725 + 8.81757i 0.602288 + 0.347731i 0.769941 0.638115i \(-0.220286\pi\)
−0.167653 + 0.985846i \(0.553619\pi\)
\(644\) 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 \(-0.727048\pi\)
0.982062 + 0.188558i \(0.0603815\pi\)
\(648\) −8.92758 5.15434i −0.350708 0.202482i
\(649\) −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
\(653\) −6.77329 −0.265059 −0.132530 0.991179i \(-0.542310\pi\)
−0.132530 + 0.991179i \(0.542310\pi\)
\(654\) −49.7013 −1.94347
\(655\) −25.5860 + 14.7721i −0.999727 + 0.577193i
\(656\) −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 \(0.940097\pi\)
\(660\) 17.6866 0.688451
\(661\) 21.7945 + 12.5830i 0.847707 + 0.489424i 0.859876 0.510502i \(-0.170540\pi\)
−0.0121696 + 0.999926i \(0.503874\pi\)
\(662\) −4.42829 7.67002i −0.172110 0.298104i
\(663\) 39.7036 + 7.72202i 1.54196 + 0.299898i
\(664\) 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
\(668\) 29.2572 16.8917i 1.13200 0.653558i
\(669\) 9.90802i 0.383066i
\(670\) −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 \(0.844714\pi\)
\(674\) 43.0902i 1.65977i
\(675\) −7.97855 13.8193i −0.307094 0.531903i
\(676\) 25.0974 19.5996i 0.965286 0.753831i
\(677\) 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
\(682\) 15.8351i 0.606358i
\(683\) 7.94353i 0.303951i −0.988384 0.151975i \(-0.951437\pi\)
0.988384 0.151975i \(-0.0485634\pi\)
\(684\) −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
\(689\) −11.6402 + 13.3877i −0.443458 + 0.510029i
\(690\) 33.1504 + 57.4182i 1.26201 + 2.18587i
\(691\) 10.2307i 0.389193i 0.980883 + 0.194597i \(0.0623397\pi\)
−0.980883 + 0.194597i \(0.937660\pi\)
\(692\) 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
\(696\) 2.74922i 0.104209i
\(697\) 51.9089 29.9696i 1.96619 1.13518i
\(698\) 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 \(0.601483\pi\)
\(702\) −14.3932 + 4.95424i −0.543235 + 0.186986i
\(703\) 11.4635 + 19.8553i 0.432353 + 0.748857i
\(704\) −8.52162 4.91996i −0.321171 0.185428i
\(705\) −24.2936 −0.914951
\(706\) 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 −0.559242 + 0.829004i \(0.688908\pi\)
−0.997560 + 0.0698158i \(0.977759\pi\)
\(710\) −42.4316 + 24.4979i −1.59243 + 0.919389i
\(711\) 1.60226 0.0600895
\(712\) 3.43142 0.128598
\(713\) −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
\(717\) 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 −0.964744 0.263188i \(-0.915226\pi\)
0.254444 0.967087i \(-0.418107\pi\)
\(720\) 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
\(724\) 5.18179 0.192580
\(725\) 5.11047 8.85159i 0.189798 0.328740i
\(726\) 48.7294i 1.80852i
\(727\) 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
\(730\) 54.3118i 2.01017i
\(731\) −9.03369 + 15.6468i −0.334123 + 0.578718i
\(732\) 8.52744 0.315183
\(733\) 10.0717 + 5.81490i 0.372007 + 0.214778i 0.674335 0.738426i \(-0.264430\pi\)
−0.302328 + 0.953204i \(0.597764\pi\)
\(734\) 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 \(-0.349083\pi\)
−0.542220 + 0.840236i \(0.682416\pi\)
\(740\) 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 −0.538681 0.842510i \(-0.681077\pi\)
0.460295 + 0.887766i \(0.347744\pi\)
\(744\) −18.1624 −0.665866
\(745\) −9.08236 −0.332752
\(746\) −57.1433 + 32.9917i −2.09217 + 1.20791i
\(747\) 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
\(751\) 37.9185 1.38366 0.691832 0.722058i \(-0.256804\pi\)
0.691832 + 0.722058i \(0.256804\pi\)
\(752\) 7.48709 + 4.32267i 0.273026 + 0.157632i
\(753\) −14.6811 25.4285i −0.535010 0.926664i
\(754\) −7.35777 6.39740i −0.267954 0.232980i
\(755\) 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
\(759\) 6.69881 3.86756i 0.243151 0.140384i
\(760\) 8.12411i 0.294692i
\(761\) −19.7969 + 11.4297i −0.717636 + 0.414328i −0.813882 0.581030i \(-0.802650\pi\)
0.0962458 + 0.995358i \(0.469317\pi\)
\(762\) 58.7280i 2.12749i
\(763\) 0 0
\(764\) −13.9214 24.1126i −0.503659 0.872363i
\(765\) 37.7863i 1.36617i
\(766\) −16.9813 29.4124i −0.613558 1.06271i
\(767\) −24.9811 + 8.59868i −0.902015 + 0.310480i
\(768\) −7.46951 + 12.9376i −0.269533 + 0.466844i
\(769\) −44.8839 + 25.9137i −1.61855 + 0.934473i −0.631260 + 0.775571i \(0.717462\pi\)
−0.987294 + 0.158902i \(0.949205\pi\)
\(770\) 0 0
\(771\) −5.18507 + 8.98080i −0.186736 + 0.323436i
\(772\) 29.8884 + 17.2561i 1.07571 + 0.621060i
\(773\) 5.69966i 0.205003i 0.994733 + 0.102501i \(0.0326846\pi\)
−0.994733 + 0.102501i \(0.967315\pi\)
\(774\) 16.2509i 0.584126i
\(775\) −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