Properties

Label 147.4.e.j.79.2
Level $147$
Weight $4$
Character 147.79
Analytic conductor $8.673$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.67328077084\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.4.e.j.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.207107 - 0.358719i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.91421 + 6.77962i) q^{4} +(0.0502525 - 0.0870399i) q^{5} -1.24264 q^{6} +6.55635 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(0.207107 - 0.358719i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(3.91421 + 6.77962i) q^{4} +(0.0502525 - 0.0870399i) q^{5} -1.24264 q^{6} +6.55635 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-0.0208153 - 0.0360531i) q^{10} +(21.9706 + 38.0541i) q^{11} +(11.7426 - 20.3389i) q^{12} -16.6447 q^{13} -0.301515 q^{15} +(-29.9558 + 51.8850i) q^{16} +(60.8198 + 105.343i) q^{17} +(1.86396 + 3.22848i) q^{18} +(63.5563 - 110.083i) q^{19} +0.786797 q^{20} +18.2010 q^{22} +(-26.7990 + 46.4172i) q^{23} +(-9.83452 - 17.0339i) q^{24} +(62.4949 + 108.244i) q^{25} +(-3.44722 + 5.97076i) q^{26} +27.0000 q^{27} +235.681 q^{29} +(-0.0624458 + 0.108159i) q^{30} +(9.35534 + 16.2039i) q^{31} +(38.6335 + 66.9152i) q^{32} +(65.9117 - 114.162i) q^{33} +50.3848 q^{34} -70.4558 q^{36} +(95.9411 - 166.175i) q^{37} +(-26.3259 - 45.5978i) q^{38} +(24.9670 + 43.2441i) q^{39} +(0.329473 - 0.570664i) q^{40} -319.713 q^{41} -218.579 q^{43} +(-171.995 + 297.904i) q^{44} +(0.452273 + 0.783359i) q^{45} +(11.1005 + 19.2266i) q^{46} +(-200.777 + 347.755i) q^{47} +179.735 q^{48} +51.7725 q^{50} +(182.459 - 316.029i) q^{51} +(-65.1508 - 112.844i) q^{52} +(-321.558 - 556.956i) q^{53} +(5.59188 - 9.68543i) q^{54} +4.41631 q^{55} -381.338 q^{57} +(48.8112 - 84.5434i) q^{58} +(5.80613 + 10.0565i) q^{59} +(-1.18019 - 2.04416i) q^{60} +(6.12132 - 10.6024i) q^{61} +7.75022 q^{62} -447.288 q^{64} +(-0.836436 + 1.44875i) q^{65} +(-27.3015 - 47.2876i) q^{66} +(-334.524 - 579.412i) q^{67} +(-476.123 + 824.670i) q^{68} +160.794 q^{69} +822.098 q^{71} +(-29.5036 + 51.1017i) q^{72} +(-257.550 - 446.089i) q^{73} +(-39.7401 - 68.8319i) q^{74} +(187.485 - 324.733i) q^{75} +995.092 q^{76} +20.6833 q^{78} +(402.877 - 697.804i) q^{79} +(3.01071 + 5.21471i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-66.2147 + 114.687i) q^{82} -394.863 q^{83} +12.2254 q^{85} +(-45.2691 + 78.4084i) q^{86} +(-353.522 - 612.318i) q^{87} +(144.047 + 249.496i) q^{88} +(-336.709 + 583.197i) q^{89} +0.374675 q^{90} -419.588 q^{92} +(28.0660 - 48.6118i) q^{93} +(83.1644 + 144.045i) q^{94} +(-6.38773 - 11.0639i) q^{95} +(115.901 - 200.746i) q^{96} -1091.11 q^{97} -395.470 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{3} + 10q^{4} + 20q^{5} + 12q^{6} - 36q^{8} - 18q^{9} + 48q^{10} + 20q^{11} + 30q^{12} - 208q^{13} - 120q^{15} - 18q^{16} + 116q^{17} - 18q^{18} + 192q^{19} + 88q^{20} + 152q^{22} - 28q^{23} + 54q^{24} - 146q^{25} + 204q^{26} + 108q^{27} + 592q^{29} + 144q^{30} - 104q^{31} - 18q^{32} + 60q^{33} + 128q^{34} - 180q^{36} + 248q^{37} + 104q^{38} + 312q^{39} - 488q^{40} - 40q^{41} - 1440q^{43} - 292q^{44} + 180q^{45} + 84q^{46} - 96q^{47} + 108q^{48} + 1412q^{50} + 348q^{51} - 320q^{52} - 268q^{53} - 54q^{54} - 944q^{55} - 1152q^{57} - 48q^{58} - 616q^{59} - 132q^{60} + 16q^{61} + 608q^{62} + 236q^{64} - 1740q^{65} - 228q^{66} + 144q^{67} - 940q^{68} + 168q^{69} + 1976q^{71} + 162q^{72} + 104q^{73} + 56q^{74} - 438q^{75} + 2272q^{76} - 1224q^{78} + 944q^{79} - 828q^{80} - 162q^{81} - 856q^{82} - 2032q^{83} - 200q^{85} + 1120q^{86} - 888q^{87} + 876q^{88} - 388q^{89} - 864q^{90} - 728q^{92} - 312q^{93} + 904q^{94} - 1304q^{95} - 54q^{96} - 976q^{97} - 360q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.207107 0.358719i 0.0732233 0.126826i −0.827089 0.562071i \(-0.810005\pi\)
0.900312 + 0.435245i \(0.143338\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) 3.91421 + 6.77962i 0.489277 + 0.847452i
\(5\) 0.0502525 0.0870399i 0.00449472 0.00778509i −0.863769 0.503887i \(-0.831903\pi\)
0.868264 + 0.496102i \(0.165236\pi\)
\(6\) −1.24264 −0.0845510
\(7\) 0 0
\(8\) 6.55635 0.289752
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −0.0208153 0.0360531i −0.000658237 0.00114010i
\(11\) 21.9706 + 38.0541i 0.602216 + 1.04307i 0.992485 + 0.122368i \(0.0390487\pi\)
−0.390269 + 0.920701i \(0.627618\pi\)
\(12\) 11.7426 20.3389i 0.282484 0.489277i
\(13\) −16.6447 −0.355108 −0.177554 0.984111i \(-0.556818\pi\)
−0.177554 + 0.984111i \(0.556818\pi\)
\(14\) 0 0
\(15\) −0.301515 −0.00519006
\(16\) −29.9558 + 51.8850i −0.468060 + 0.810704i
\(17\) 60.8198 + 105.343i 0.867704 + 1.50291i 0.864337 + 0.502913i \(0.167738\pi\)
0.00336718 + 0.999994i \(0.498928\pi\)
\(18\) 1.86396 + 3.22848i 0.0244078 + 0.0422755i
\(19\) 63.5563 110.083i 0.767412 1.32920i −0.171550 0.985175i \(-0.554878\pi\)
0.938962 0.344021i \(-0.111789\pi\)
\(20\) 0.786797 0.00879665
\(21\) 0 0
\(22\) 18.2010 0.176385
\(23\) −26.7990 + 46.4172i −0.242955 + 0.420811i −0.961555 0.274613i \(-0.911450\pi\)
0.718599 + 0.695424i \(0.244784\pi\)
\(24\) −9.83452 17.0339i −0.0836443 0.144876i
\(25\) 62.4949 + 108.244i 0.499960 + 0.865955i
\(26\) −3.44722 + 5.97076i −0.0260021 + 0.0450370i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 235.681 1.50913 0.754567 0.656223i \(-0.227847\pi\)
0.754567 + 0.656223i \(0.227847\pi\)
\(30\) −0.0624458 + 0.108159i −0.000380033 + 0.000658237i
\(31\) 9.35534 + 16.2039i 0.0542022 + 0.0938810i 0.891853 0.452324i \(-0.149405\pi\)
−0.837651 + 0.546205i \(0.816072\pi\)
\(32\) 38.6335 + 66.9152i 0.213422 + 0.369658i
\(33\) 65.9117 114.162i 0.347689 0.602216i
\(34\) 50.3848 0.254145
\(35\) 0 0
\(36\) −70.4558 −0.326184
\(37\) 95.9411 166.175i 0.426287 0.738351i −0.570253 0.821469i \(-0.693155\pi\)
0.996540 + 0.0831185i \(0.0264880\pi\)
\(38\) −26.3259 45.5978i −0.112385 0.194656i
\(39\) 24.9670 + 43.2441i 0.102511 + 0.177554i
\(40\) 0.329473 0.570664i 0.00130236 0.00225575i
\(41\) −319.713 −1.21782 −0.608912 0.793238i \(-0.708394\pi\)
−0.608912 + 0.793238i \(0.708394\pi\)
\(42\) 0 0
\(43\) −218.579 −0.775184 −0.387592 0.921831i \(-0.626693\pi\)
−0.387592 + 0.921831i \(0.626693\pi\)
\(44\) −171.995 + 297.904i −0.589300 + 1.02070i
\(45\) 0.452273 + 0.783359i 0.00149824 + 0.00259503i
\(46\) 11.1005 + 19.2266i 0.0355800 + 0.0616264i
\(47\) −200.777 + 347.755i −0.623113 + 1.07926i 0.365790 + 0.930697i \(0.380799\pi\)
−0.988903 + 0.148565i \(0.952535\pi\)
\(48\) 179.735 0.540469
\(49\) 0 0
\(50\) 51.7725 0.146435
\(51\) 182.459 316.029i 0.500969 0.867704i
\(52\) −65.1508 112.844i −0.173746 0.300937i
\(53\) −321.558 556.956i −0.833386 1.44347i −0.895338 0.445387i \(-0.853066\pi\)
0.0619521 0.998079i \(-0.480267\pi\)
\(54\) 5.59188 9.68543i 0.0140918 0.0244078i
\(55\) 4.41631 0.0108272
\(56\) 0 0
\(57\) −381.338 −0.886131
\(58\) 48.8112 84.5434i 0.110504 0.191398i
\(59\) 5.80613 + 10.0565i 0.0128118 + 0.0221906i 0.872360 0.488864i \(-0.162588\pi\)
−0.859548 + 0.511054i \(0.829255\pi\)
\(60\) −1.18019 2.04416i −0.00253937 0.00439833i
\(61\) 6.12132 10.6024i 0.0128484 0.0222541i −0.859530 0.511086i \(-0.829243\pi\)
0.872378 + 0.488832i \(0.162577\pi\)
\(62\) 7.75022 0.0158755
\(63\) 0 0
\(64\) −447.288 −0.873610
\(65\) −0.836436 + 1.44875i −0.00159611 + 0.00276454i
\(66\) −27.3015 47.2876i −0.0509179 0.0881925i
\(67\) −334.524 579.412i −0.609979 1.05651i −0.991243 0.132049i \(-0.957844\pi\)
0.381264 0.924466i \(-0.375489\pi\)
\(68\) −476.123 + 824.670i −0.849095 + 1.47068i
\(69\) 160.794 0.280541
\(70\) 0 0
\(71\) 822.098 1.37416 0.687078 0.726584i \(-0.258893\pi\)
0.687078 + 0.726584i \(0.258893\pi\)
\(72\) −29.5036 + 51.1017i −0.0482921 + 0.0836443i
\(73\) −257.550 446.089i −0.412930 0.715217i 0.582278 0.812990i \(-0.302161\pi\)
−0.995209 + 0.0977730i \(0.968828\pi\)
\(74\) −39.7401 68.8319i −0.0624283 0.108129i
\(75\) 187.485 324.733i 0.288652 0.499960i
\(76\) 995.092 1.50191
\(77\) 0 0
\(78\) 20.6833 0.0300247
\(79\) 402.877 697.804i 0.573762 0.993786i −0.422413 0.906404i \(-0.638817\pi\)
0.996175 0.0873819i \(-0.0278500\pi\)
\(80\) 3.01071 + 5.21471i 0.00420760 + 0.00728778i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −66.2147 + 114.687i −0.0891730 + 0.154452i
\(83\) −394.863 −0.522191 −0.261095 0.965313i \(-0.584084\pi\)
−0.261095 + 0.965313i \(0.584084\pi\)
\(84\) 0 0
\(85\) 12.2254 0.0156004
\(86\) −45.2691 + 78.4084i −0.0567616 + 0.0983139i
\(87\) −353.522 612.318i −0.435650 0.754567i
\(88\) 144.047 + 249.496i 0.174493 + 0.302232i
\(89\) −336.709 + 583.197i −0.401024 + 0.694593i −0.993850 0.110737i \(-0.964679\pi\)
0.592826 + 0.805331i \(0.298012\pi\)
\(90\) 0.374675 0.000438825
\(91\) 0 0
\(92\) −419.588 −0.475490
\(93\) 28.0660 48.6118i 0.0312937 0.0542022i
\(94\) 83.1644 + 144.045i 0.0912527 + 0.158054i
\(95\) −6.38773 11.0639i −0.00689861 0.0119487i
\(96\) 115.901 200.746i 0.123219 0.213422i
\(97\) −1091.11 −1.14212 −0.571061 0.820908i \(-0.693468\pi\)
−0.571061 + 0.820908i \(0.693468\pi\)
\(98\) 0 0
\(99\) −395.470 −0.401477
\(100\) −489.237 + 847.384i −0.489237 + 0.847384i
\(101\) 685.395 + 1187.14i 0.675242 + 1.16955i 0.976398 + 0.215978i \(0.0692940\pi\)
−0.301157 + 0.953575i \(0.597373\pi\)
\(102\) −75.5772 130.903i −0.0733652 0.127072i
\(103\) 706.978 1224.52i 0.676316 1.17141i −0.299766 0.954013i \(-0.596909\pi\)
0.976082 0.217401i \(-0.0697581\pi\)
\(104\) −109.128 −0.102893
\(105\) 0 0
\(106\) −266.388 −0.244093
\(107\) 171.770 297.514i 0.155192 0.268801i −0.777937 0.628343i \(-0.783734\pi\)
0.933129 + 0.359542i \(0.117067\pi\)
\(108\) 105.684 + 183.050i 0.0941613 + 0.163092i
\(109\) 158.828 + 275.099i 0.139569 + 0.241740i 0.927333 0.374236i \(-0.122095\pi\)
−0.787765 + 0.615976i \(0.788762\pi\)
\(110\) 0.914647 1.58421i 0.000792801 0.00137317i
\(111\) −575.647 −0.492234
\(112\) 0 0
\(113\) 798.373 0.664643 0.332321 0.943166i \(-0.392168\pi\)
0.332321 + 0.943166i \(0.392168\pi\)
\(114\) −78.9777 + 136.793i −0.0648854 + 0.112385i
\(115\) 2.69343 + 4.66516i 0.00218404 + 0.00378286i
\(116\) 922.507 + 1597.83i 0.738384 + 1.27892i
\(117\) 74.9010 129.732i 0.0591846 0.102511i
\(118\) 4.80996 0.00375248
\(119\) 0 0
\(120\) −1.97684 −0.00150383
\(121\) −299.911 + 519.462i −0.225328 + 0.390279i
\(122\) −2.53553 4.39167i −0.00188161 0.00325904i
\(123\) 479.569 + 830.638i 0.351555 + 0.608912i
\(124\) −73.2376 + 126.851i −0.0530398 + 0.0918676i
\(125\) 25.1253 0.0179782
\(126\) 0 0
\(127\) 1071.40 0.748593 0.374297 0.927309i \(-0.377884\pi\)
0.374297 + 0.927309i \(0.377884\pi\)
\(128\) −401.705 + 695.773i −0.277391 + 0.480455i
\(129\) 327.868 + 567.884i 0.223776 + 0.387592i
\(130\) 0.346463 + 0.600092i 0.000233745 + 0.000404858i
\(131\) 1257.51 2178.07i 0.838695 1.45266i −0.0522910 0.998632i \(-0.516652\pi\)
0.890986 0.454031i \(-0.150014\pi\)
\(132\) 1031.97 0.680465
\(133\) 0 0
\(134\) −277.129 −0.178659
\(135\) 1.35682 2.35008i 0.000865010 0.00149824i
\(136\) 398.756 + 690.665i 0.251419 + 0.435471i
\(137\) −125.532 217.428i −0.0782841 0.135592i 0.824226 0.566262i \(-0.191611\pi\)
−0.902510 + 0.430670i \(0.858277\pi\)
\(138\) 33.3015 57.6799i 0.0205421 0.0355800i
\(139\) 886.067 0.540685 0.270343 0.962764i \(-0.412863\pi\)
0.270343 + 0.962764i \(0.412863\pi\)
\(140\) 0 0
\(141\) 1204.66 0.719508
\(142\) 170.262 294.902i 0.100620 0.174279i
\(143\) −365.693 633.398i −0.213851 0.370401i
\(144\) −269.603 466.965i −0.156020 0.270235i
\(145\) 11.8436 20.5137i 0.00678314 0.0117487i
\(146\) −213.361 −0.120945
\(147\) 0 0
\(148\) 1502.14 0.834289
\(149\) −291.313 + 504.569i −0.160170 + 0.277422i −0.934929 0.354834i \(-0.884537\pi\)
0.774760 + 0.632256i \(0.217871\pi\)
\(150\) −77.6588 134.509i −0.0422721 0.0732174i
\(151\) 1405.88 + 2435.06i 0.757676 + 1.31233i 0.944033 + 0.329851i \(0.106999\pi\)
−0.186357 + 0.982482i \(0.559668\pi\)
\(152\) 416.698 721.741i 0.222359 0.385138i
\(153\) −1094.76 −0.578469
\(154\) 0 0
\(155\) 1.88052 0.000974496
\(156\) −195.452 + 338.533i −0.100312 + 0.173746i
\(157\) 845.672 + 1464.75i 0.429885 + 0.744583i 0.996863 0.0791504i \(-0.0252207\pi\)
−0.566978 + 0.823733i \(0.691887\pi\)
\(158\) −166.877 289.040i −0.0840256 0.145537i
\(159\) −964.675 + 1670.87i −0.481156 + 0.833386i
\(160\) 7.76573 0.00383709
\(161\) 0 0
\(162\) −33.5513 −0.0162718
\(163\) 20.3616 35.2674i 0.00978432 0.0169469i −0.861092 0.508450i \(-0.830219\pi\)
0.870876 + 0.491503i \(0.163552\pi\)
\(164\) −1251.42 2167.53i −0.595852 1.03205i
\(165\) −6.62446 11.4739i −0.00312554 0.00541359i
\(166\) −81.7788 + 141.645i −0.0382365 + 0.0662276i
\(167\) 2900.47 1.34398 0.671990 0.740560i \(-0.265440\pi\)
0.671990 + 0.740560i \(0.265440\pi\)
\(168\) 0 0
\(169\) −1919.96 −0.873899
\(170\) 2.53196 4.38549i 0.00114231 0.00197854i
\(171\) 572.007 + 990.745i 0.255804 + 0.443065i
\(172\) −855.563 1481.88i −0.379280 0.656932i
\(173\) 1073.07 1858.62i 0.471585 0.816810i −0.527886 0.849315i \(-0.677015\pi\)
0.999472 + 0.0325052i \(0.0103485\pi\)
\(174\) −292.867 −0.127599
\(175\) 0 0
\(176\) −2632.59 −1.12749
\(177\) 17.4184 30.1695i 0.00739688 0.0128118i
\(178\) 139.470 + 241.568i 0.0587286 + 0.101721i
\(179\) −601.770 1042.30i −0.251276 0.435222i 0.712602 0.701569i \(-0.247517\pi\)
−0.963877 + 0.266347i \(0.914183\pi\)
\(180\) −3.54058 + 6.13247i −0.00146611 + 0.00253937i
\(181\) −2990.47 −1.22807 −0.614033 0.789280i \(-0.710454\pi\)
−0.614033 + 0.789280i \(0.710454\pi\)
\(182\) 0 0
\(183\) −36.7279 −0.0148361
\(184\) −175.704 + 304.327i −0.0703969 + 0.121931i
\(185\) −9.64257 16.7014i −0.00383209 0.00663737i
\(186\) −11.6253 20.1357i −0.00458285 0.00793773i
\(187\) −2672.49 + 4628.89i −1.04509 + 1.81015i
\(188\) −3143.53 −1.21950
\(189\) 0 0
\(190\) −5.29177 −0.00202056
\(191\) 1403.70 2431.29i 0.531772 0.921057i −0.467540 0.883972i \(-0.654860\pi\)
0.999312 0.0370847i \(-0.0118071\pi\)
\(192\) 670.933 + 1162.09i 0.252190 + 0.436805i
\(193\) −1668.18 2889.38i −0.622169 1.07763i −0.989081 0.147372i \(-0.952919\pi\)
0.366913 0.930255i \(-0.380415\pi\)
\(194\) −225.977 + 391.404i −0.0836299 + 0.144851i
\(195\) 5.01862 0.00184303
\(196\) 0 0
\(197\) −4226.65 −1.52861 −0.764305 0.644855i \(-0.776918\pi\)
−0.764305 + 0.644855i \(0.776918\pi\)
\(198\) −81.9045 + 141.863i −0.0293975 + 0.0509179i
\(199\) −2192.85 3798.12i −0.781140 1.35297i −0.931278 0.364309i \(-0.881305\pi\)
0.150139 0.988665i \(-0.452028\pi\)
\(200\) 409.739 + 709.688i 0.144865 + 0.250913i
\(201\) −1003.57 + 1738.24i −0.352172 + 0.609979i
\(202\) 567.800 0.197774
\(203\) 0 0
\(204\) 2856.74 0.980450
\(205\) −16.0664 + 27.8278i −0.00547378 + 0.00948086i
\(206\) −292.840 507.213i −0.0990442 0.171550i
\(207\) −241.191 417.755i −0.0809852 0.140270i
\(208\) 498.605 863.609i 0.166212 0.287887i
\(209\) 5585.48 1.84859
\(210\) 0 0
\(211\) 2291.56 0.747665 0.373833 0.927496i \(-0.378043\pi\)
0.373833 + 0.927496i \(0.378043\pi\)
\(212\) 2517.30 4360.09i 0.815513 1.41251i
\(213\) −1233.15 2135.87i −0.396684 0.687078i
\(214\) −71.1493 123.234i −0.0227274 0.0393650i
\(215\) −10.9841 + 19.0251i −0.00348424 + 0.00603488i
\(216\) 177.021 0.0557629
\(217\) 0 0
\(218\) 131.578 0.0408788
\(219\) −772.649 + 1338.27i −0.238406 + 0.412930i
\(220\) 17.2864 + 29.9409i 0.00529748 + 0.00917551i
\(221\) −1012.33 1753.40i −0.308128 0.533694i
\(222\) −119.220 + 206.496i −0.0360430 + 0.0624283i
\(223\) −217.970 −0.0654544 −0.0327272 0.999464i \(-0.510419\pi\)
−0.0327272 + 0.999464i \(0.510419\pi\)
\(224\) 0 0
\(225\) −1124.91 −0.333306
\(226\) 165.349 286.392i 0.0486674 0.0842943i
\(227\) −917.680 1589.47i −0.268320 0.464743i 0.700108 0.714037i \(-0.253135\pi\)
−0.968428 + 0.249293i \(0.919802\pi\)
\(228\) −1492.64 2585.33i −0.433563 0.750954i
\(229\) −1387.00 + 2402.36i −0.400244 + 0.693243i −0.993755 0.111583i \(-0.964408\pi\)
0.593511 + 0.804826i \(0.297741\pi\)
\(230\) 2.23131 0.000639689
\(231\) 0 0
\(232\) 1545.21 0.437275
\(233\) 494.356 856.250i 0.138997 0.240750i −0.788120 0.615522i \(-0.788945\pi\)
0.927117 + 0.374771i \(0.122279\pi\)
\(234\) −31.0250 53.7369i −0.00866738 0.0150123i
\(235\) 20.1791 + 34.9512i 0.00560144 + 0.00970197i
\(236\) −45.4529 + 78.7267i −0.0125370 + 0.0217147i
\(237\) −2417.26 −0.662524
\(238\) 0 0
\(239\) −837.928 −0.226783 −0.113391 0.993550i \(-0.536171\pi\)
−0.113391 + 0.993550i \(0.536171\pi\)
\(240\) 9.03214 15.6441i 0.00242926 0.00420760i
\(241\) 1727.49 + 2992.11i 0.461733 + 0.799745i 0.999047 0.0436371i \(-0.0138945\pi\)
−0.537315 + 0.843382i \(0.680561\pi\)
\(242\) 124.227 + 215.168i 0.0329985 + 0.0571551i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 95.8406 0.0251458
\(245\) 0 0
\(246\) 397.288 0.102968
\(247\) −1057.87 + 1832.29i −0.272514 + 0.472008i
\(248\) 61.3369 + 106.239i 0.0157052 + 0.0272022i
\(249\) 592.294 + 1025.88i 0.150743 + 0.261095i
\(250\) 5.20361 9.01292i 0.00131642 0.00228011i
\(251\) 5635.01 1.41705 0.708523 0.705688i \(-0.249362\pi\)
0.708523 + 0.705688i \(0.249362\pi\)
\(252\) 0 0
\(253\) −2355.16 −0.585246
\(254\) 221.894 384.332i 0.0548145 0.0949414i
\(255\) −18.3381 31.7625i −0.00450344 0.00780018i
\(256\) −1622.76 2810.71i −0.396182 0.686208i
\(257\) 1135.58 1966.88i 0.275624 0.477395i −0.694668 0.719330i \(-0.744449\pi\)
0.970292 + 0.241935i \(0.0777821\pi\)
\(258\) 271.615 0.0655426
\(259\) 0 0
\(260\) −13.0960 −0.00312376
\(261\) −1060.57 + 1836.95i −0.251522 + 0.435650i
\(262\) −520.877 902.186i −0.122824 0.212737i
\(263\) −81.9336 141.913i −0.0192101 0.0332728i 0.856261 0.516544i \(-0.172782\pi\)
−0.875471 + 0.483271i \(0.839448\pi\)
\(264\) 432.140 748.489i 0.100744 0.174493i
\(265\) −64.6365 −0.0149834
\(266\) 0 0
\(267\) 2020.26 0.463062
\(268\) 2618.80 4535.89i 0.596897 1.03386i
\(269\) 2583.55 + 4474.84i 0.585582 + 1.01426i 0.994803 + 0.101823i \(0.0324675\pi\)
−0.409220 + 0.912436i \(0.634199\pi\)
\(270\) −0.562013 0.973434i −0.000126678 0.000219412i
\(271\) 811.136 1404.93i 0.181819 0.314920i −0.760681 0.649126i \(-0.775135\pi\)
0.942500 + 0.334206i \(0.108468\pi\)
\(272\) −7287.63 −1.62455
\(273\) 0 0
\(274\) −103.994 −0.0229289
\(275\) −2746.10 + 4756.38i −0.602167 + 1.04298i
\(276\) 629.382 + 1090.12i 0.137262 + 0.237745i
\(277\) 2306.18 + 3994.43i 0.500235 + 0.866433i 1.00000 0.000271708i \(8.64874e-5\pi\)
−0.499765 + 0.866161i \(0.666580\pi\)
\(278\) 183.511 317.850i 0.0395908 0.0685732i
\(279\) −168.396 −0.0361348
\(280\) 0 0
\(281\) −2125.22 −0.451174 −0.225587 0.974223i \(-0.572430\pi\)
−0.225587 + 0.974223i \(0.572430\pi\)
\(282\) 249.493 432.135i 0.0526848 0.0912527i
\(283\) −1285.77 2227.02i −0.270075 0.467783i 0.698806 0.715311i \(-0.253715\pi\)
−0.968881 + 0.247528i \(0.920382\pi\)
\(284\) 3217.87 + 5573.51i 0.672342 + 1.16453i
\(285\) −19.1632 + 33.1916i −0.00398291 + 0.00689861i
\(286\) −302.950 −0.0626356
\(287\) 0 0
\(288\) −695.403 −0.142281
\(289\) −4941.60 + 8559.10i −1.00582 + 1.74213i
\(290\) −4.90577 8.49704i −0.000993368 0.00172056i
\(291\) 1636.67 + 2834.80i 0.329702 + 0.571061i
\(292\) 2016.21 3492.18i 0.404075 0.699878i
\(293\) −3324.96 −0.662957 −0.331478 0.943463i \(-0.607547\pi\)
−0.331478 + 0.943463i \(0.607547\pi\)
\(294\) 0 0
\(295\) 1.16709 0.000230341
\(296\) 629.024 1089.50i 0.123518 0.213939i
\(297\) 593.205 + 1027.46i 0.115896 + 0.200739i
\(298\) 120.666 + 208.999i 0.0234563 + 0.0406275i
\(299\) 446.060 772.599i 0.0862753 0.149433i
\(300\) 2935.42 0.564922
\(301\) 0 0
\(302\) 1164.67 0.221918
\(303\) 2056.19 3561.42i 0.389851 0.675242i
\(304\) 3807.77 + 6595.25i 0.718390 + 1.24429i
\(305\) −0.615224 1.06560i −0.000115500 0.000200052i
\(306\) −226.731 + 392.710i −0.0423574 + 0.0733652i
\(307\) 887.096 0.164916 0.0824580 0.996595i \(-0.473723\pi\)
0.0824580 + 0.996595i \(0.473723\pi\)
\(308\) 0 0
\(309\) −4241.87 −0.780943
\(310\) 0.389468 0.674578i 7.13558e−5 0.000123592i
\(311\) −2255.41 3906.48i −0.411230 0.712271i 0.583794 0.811902i \(-0.301567\pi\)
−0.995025 + 0.0996300i \(0.968234\pi\)
\(312\) 163.692 + 283.523i 0.0297027 + 0.0514466i
\(313\) 1857.89 3217.96i 0.335509 0.581118i −0.648074 0.761578i \(-0.724425\pi\)
0.983582 + 0.180459i \(0.0577584\pi\)
\(314\) 700.577 0.125910
\(315\) 0 0
\(316\) 6307.79 1.12291
\(317\) −3477.26 + 6022.79i −0.616096 + 1.06711i 0.374095 + 0.927390i \(0.377953\pi\)
−0.990191 + 0.139719i \(0.955380\pi\)
\(318\) 399.582 + 692.096i 0.0704636 + 0.122047i
\(319\) 5178.05 + 8968.64i 0.908825 + 1.57413i
\(320\) −22.4774 + 38.9320i −0.00392664 + 0.00680113i
\(321\) −1030.62 −0.179201
\(322\) 0 0
\(323\) 15461.9 2.66355
\(324\) 317.051 549.149i 0.0543641 0.0941613i
\(325\) −1040.21 1801.69i −0.177539 0.307507i
\(326\) −8.43406 14.6082i −0.00143288 0.00248182i
\(327\) 476.485 825.297i 0.0805801 0.139569i
\(328\) −2096.15 −0.352867
\(329\) 0 0
\(330\) −5.48788 −0.000915448
\(331\) 4931.59 8541.76i 0.818926 1.41842i −0.0875478 0.996160i \(-0.527903\pi\)
0.906474 0.422262i \(-0.138764\pi\)
\(332\) −1545.58 2677.02i −0.255496 0.442532i
\(333\) 863.470 + 1495.57i 0.142096 + 0.246117i
\(334\) 600.706 1040.45i 0.0984107 0.170452i
\(335\) −67.2427 −0.0109668
\(336\) 0 0
\(337\) −5945.06 −0.960974 −0.480487 0.877002i \(-0.659540\pi\)
−0.480487 + 0.877002i \(0.659540\pi\)
\(338\) −397.636 + 688.725i −0.0639897 + 0.110833i
\(339\) −1197.56 2074.24i −0.191866 0.332321i
\(340\) 47.8528 + 82.8835i 0.00763289 + 0.0132206i
\(341\) −411.084 + 712.019i −0.0652829 + 0.113073i
\(342\) 473.866 0.0749232
\(343\) 0 0
\(344\) −1433.08 −0.224612
\(345\) 8.08030 13.9955i 0.00126095 0.00218404i
\(346\) −444.482 769.865i −0.0690621 0.119619i
\(347\) −584.786 1012.88i −0.0904697 0.156698i 0.817239 0.576299i \(-0.195503\pi\)
−0.907709 + 0.419601i \(0.862170\pi\)
\(348\) 2767.52 4793.49i 0.426306 0.738384i
\(349\) 9176.66 1.40749 0.703747 0.710451i \(-0.251509\pi\)
0.703747 + 0.710451i \(0.251509\pi\)
\(350\) 0 0
\(351\) −449.406 −0.0683405
\(352\) −1697.60 + 2940.33i −0.257052 + 0.445228i
\(353\) 5293.60 + 9168.78i 0.798158 + 1.38245i 0.920814 + 0.390001i \(0.127526\pi\)
−0.122656 + 0.992449i \(0.539141\pi\)
\(354\) −7.21494 12.4966i −0.00108325 0.00187624i
\(355\) 41.3125 71.5553i 0.00617645 0.0106979i
\(356\) −5271.81 −0.784846
\(357\) 0 0
\(358\) −498.522 −0.0735970
\(359\) −4307.61 + 7460.99i −0.633278 + 1.09687i 0.353599 + 0.935397i \(0.384958\pi\)
−0.986877 + 0.161472i \(0.948376\pi\)
\(360\) 2.96526 + 5.13598i 0.000434119 + 0.000751916i
\(361\) −4649.32 8052.86i −0.677842 1.17406i
\(362\) −619.347 + 1072.74i −0.0899230 + 0.155751i
\(363\) 1799.47 0.260186
\(364\) 0 0
\(365\) −51.7701 −0.00742403
\(366\) −7.60660 + 13.1750i −0.00108635 + 0.00188161i
\(367\) 4148.89 + 7186.10i 0.590110 + 1.02210i 0.994217 + 0.107389i \(0.0342492\pi\)
−0.404107 + 0.914712i \(0.632418\pi\)
\(368\) −1605.57 2780.93i −0.227436 0.393930i
\(369\) 1438.71 2491.91i 0.202971 0.351555i
\(370\) −7.98817 −0.00112239
\(371\) 0 0
\(372\) 439.426 0.0612450
\(373\) 2561.93 4437.39i 0.355634 0.615977i −0.631592 0.775301i \(-0.717598\pi\)
0.987226 + 0.159324i \(0.0509315\pi\)
\(374\) 1106.98 + 1917.35i 0.153050 + 0.265090i
\(375\) −37.6879 65.2773i −0.00518985 0.00898908i
\(376\) −1316.36 + 2280.01i −0.180548 + 0.312719i
\(377\) −3922.83 −0.535905
\(378\) 0 0
\(379\) −1502.49 −0.203635 −0.101817 0.994803i \(-0.532466\pi\)
−0.101817 + 0.994803i \(0.532466\pi\)
\(380\) 50.0059 86.6128i 0.00675066 0.0116925i
\(381\) −1607.10 2783.58i −0.216100 0.374297i
\(382\) −581.434 1007.07i −0.0778763 0.134886i
\(383\) −5436.47 + 9416.24i −0.725301 + 1.25626i 0.233548 + 0.972345i \(0.424966\pi\)
−0.958850 + 0.283914i \(0.908367\pi\)
\(384\) 2410.23 0.320303
\(385\) 0 0
\(386\) −1381.97 −0.182229
\(387\) 983.604 1703.65i 0.129197 0.223776i
\(388\) −4270.85 7397.33i −0.558814 0.967894i
\(389\) −2309.50 4000.16i −0.301018 0.521379i 0.675349 0.737499i \(-0.263993\pi\)
−0.976367 + 0.216120i \(0.930660\pi\)
\(390\) 1.03939 1.80028i 0.000134953 0.000233745i
\(391\) −6519.64 −0.843254
\(392\) 0 0
\(393\) −7545.05 −0.968442
\(394\) −875.367 + 1516.18i −0.111930 + 0.193868i
\(395\) −40.4912 70.1328i −0.00515781 0.00893358i
\(396\) −1547.95 2681.14i −0.196433 0.340233i
\(397\) 4803.48 8319.86i 0.607253 1.05179i −0.384438 0.923151i \(-0.625605\pi\)
0.991691 0.128642i \(-0.0410620\pi\)
\(398\) −1816.61 −0.228791
\(399\) 0 0
\(400\) −7488.36 −0.936044
\(401\) 5250.52 9094.17i 0.653862 1.13252i −0.328316 0.944568i \(-0.606481\pi\)
0.982178 0.187954i \(-0.0601857\pi\)
\(402\) 415.693 + 720.002i 0.0515743 + 0.0893294i
\(403\) −155.716 269.709i −0.0192476 0.0333378i
\(404\) −5365.57 + 9293.44i −0.660760 + 1.14447i
\(405\) −8.14091 −0.000998827
\(406\) 0 0
\(407\) 8431.52 1.02687
\(408\) 1196.27 2072.00i 0.145157 0.251419i
\(409\) −6033.47 10450.3i −0.729427 1.26340i −0.957126 0.289673i \(-0.906453\pi\)
0.227699 0.973732i \(-0.426880\pi\)
\(410\) 6.65491 + 11.5266i 0.000801616 + 0.00138844i
\(411\) −376.596 + 652.283i −0.0451973 + 0.0782841i
\(412\) 11069.0 1.32362
\(413\) 0 0
\(414\) −199.809 −0.0237200
\(415\) −19.8429 + 34.3688i −0.00234710 + 0.00406530i
\(416\) −643.042 1113.78i −0.0757878 0.131268i
\(417\) −1329.10 2302.07i −0.156082 0.270343i
\(418\) 1156.79 2003.62i 0.135360 0.234450i
\(419\) 6366.31 0.742278 0.371139 0.928577i \(-0.378967\pi\)
0.371139 + 0.928577i \(0.378967\pi\)
\(420\) 0 0
\(421\) −4731.84 −0.547781 −0.273890 0.961761i \(-0.588311\pi\)
−0.273890 + 0.961761i \(0.588311\pi\)
\(422\) 474.597 822.026i 0.0547465 0.0948237i
\(423\) −1806.99 3129.80i −0.207704 0.359754i
\(424\) −2108.25 3651.60i −0.241476 0.418248i
\(425\) −7601.86 + 13166.8i −0.867634 + 1.50279i
\(426\) −1021.57 −0.116186
\(427\) 0 0
\(428\) 2689.37 0.303728
\(429\) −1097.08 + 1900.19i −0.123467 + 0.213851i
\(430\) 4.54978 + 7.88044i 0.000510255 + 0.000883788i
\(431\) −1876.39 3250.01i −0.209704 0.363219i 0.741917 0.670492i \(-0.233917\pi\)
−0.951621 + 0.307273i \(0.900584\pi\)
\(432\) −808.808 + 1400.90i −0.0900782 + 0.156020i
\(433\) −11709.2 −1.29956 −0.649780 0.760122i \(-0.725139\pi\)
−0.649780 + 0.760122i \(0.725139\pi\)
\(434\) 0 0
\(435\) −71.0615 −0.00783250
\(436\) −1243.38 + 2153.59i −0.136576 + 0.236556i
\(437\) 3406.49 + 5900.22i 0.372894 + 0.645871i
\(438\) 320.042 + 554.329i 0.0349137 + 0.0604723i
\(439\) −7462.36 + 12925.2i −0.811296 + 1.40521i 0.100661 + 0.994921i \(0.467904\pi\)
−0.911957 + 0.410285i \(0.865429\pi\)
\(440\) 28.9548 0.00313720
\(441\) 0 0
\(442\) −838.638 −0.0902487
\(443\) 4258.83 7376.51i 0.456756 0.791125i −0.542031 0.840359i \(-0.682344\pi\)
0.998787 + 0.0492333i \(0.0156778\pi\)
\(444\) −2253.20 3902.66i −0.240839 0.417145i
\(445\) 33.8410 + 58.6143i 0.00360498 + 0.00624401i
\(446\) −45.1430 + 78.1900i −0.00479279 + 0.00830135i
\(447\) 1747.88 0.184948
\(448\) 0 0
\(449\) −5965.73 −0.627038 −0.313519 0.949582i \(-0.601508\pi\)
−0.313519 + 0.949582i \(0.601508\pi\)
\(450\) −232.976 + 403.527i −0.0244058 + 0.0422721i
\(451\) −7024.27 12166.4i −0.733392 1.27027i
\(452\) 3125.00 + 5412.67i 0.325194 + 0.563253i
\(453\) 4217.65 7305.18i 0.437444 0.757676i
\(454\) −760.231 −0.0785890
\(455\) 0 0
\(456\) −2500.19 −0.256759
\(457\) 6930.28 12003.6i 0.709376 1.22868i −0.255712 0.966753i \(-0.582310\pi\)
0.965089 0.261923i \(-0.0843567\pi\)
\(458\) 574.516 + 995.091i 0.0586143 + 0.101523i
\(459\) 1642.13 + 2844.26i 0.166990 + 0.289235i
\(460\) −21.0854 + 36.5209i −0.00213719 + 0.00370173i
\(461\) 149.312 0.0150850 0.00754249 0.999972i \(-0.497599\pi\)
0.00754249 + 0.999972i \(0.497599\pi\)
\(462\) 0 0
\(463\) 5403.95 0.542425 0.271213 0.962519i \(-0.412575\pi\)
0.271213 + 0.962519i \(0.412575\pi\)
\(464\) −7060.03 + 12228.3i −0.706366 + 1.22346i
\(465\) −2.82078 4.88573i −0.000281313 0.000487248i
\(466\) −204.769 354.670i −0.0203557 0.0352571i
\(467\) 1852.33 3208.33i 0.183545 0.317909i −0.759540 0.650460i \(-0.774576\pi\)
0.943085 + 0.332551i \(0.107909\pi\)
\(468\) 1172.71 0.115831
\(469\) 0 0
\(470\) 16.7169 0.00164062
\(471\) 2537.02 4394.24i 0.248194 0.429885i
\(472\) 38.0670 + 65.9340i 0.00371224 + 0.00642979i
\(473\) −4802.30 8317.82i −0.466828 0.808570i
\(474\) −500.632 + 867.119i −0.0485122 + 0.0840256i
\(475\) 15887.8 1.53470
\(476\) 0 0
\(477\) 5788.05 0.555591
\(478\) −173.540 + 300.581i −0.0166058 + 0.0287620i
\(479\) −5335.88 9242.02i −0.508982 0.881583i −0.999946 0.0104033i \(-0.996688\pi\)
0.490963 0.871180i \(-0.336645\pi\)
\(480\) −11.6486 20.1760i −0.00110767 0.00191855i
\(481\) −1596.91 + 2765.92i −0.151378 + 0.262194i
\(482\) 1431.10 0.135238
\(483\) 0 0
\(484\) −4695.67 −0.440990
\(485\) −54.8312 + 94.9705i −0.00513352 + 0.00889152i
\(486\) 50.3269 + 87.1688i 0.00469728 + 0.00813592i
\(487\) −2926.96 5069.65i −0.272348 0.471720i 0.697115 0.716959i \(-0.254467\pi\)
−0.969463 + 0.245239i \(0.921133\pi\)
\(488\) 40.1335 69.5133i 0.00372287 0.00644819i
\(489\) −122.170 −0.0112980
\(490\) 0 0
\(491\) 4065.31 0.373656 0.186828 0.982393i \(-0.440179\pi\)
0.186828 + 0.982393i \(0.440179\pi\)
\(492\) −3754.27 + 6502.59i −0.344016 + 0.595852i
\(493\) 14334.1 + 24827.4i 1.30948 + 2.26809i
\(494\) 438.186 + 758.960i 0.0399087 + 0.0691239i
\(495\) −19.8734 + 34.4217i −0.00180453 + 0.00312554i
\(496\) −1120.99 −0.101480
\(497\) 0 0
\(498\) 490.673 0.0441517
\(499\) −2405.59 + 4166.61i −0.215810 + 0.373794i −0.953523 0.301321i \(-0.902572\pi\)
0.737713 + 0.675115i \(0.235906\pi\)
\(500\) 98.3456 + 170.340i 0.00879630 + 0.0152356i
\(501\) −4350.70 7535.63i −0.387974 0.671990i
\(502\) 1167.05 2021.39i 0.103761 0.179719i
\(503\) −17001.2 −1.50705 −0.753526 0.657418i \(-0.771649\pi\)
−0.753526 + 0.657418i \(0.771649\pi\)
\(504\) 0 0
\(505\) 137.771 0.0121401
\(506\) −487.769 + 844.840i −0.0428537 + 0.0742248i
\(507\) 2879.93 + 4988.19i 0.252273 + 0.436949i
\(508\) 4193.69 + 7263.68i 0.366269 + 0.634397i
\(509\) 6898.61 11948.7i 0.600738 1.04051i −0.391972 0.919977i \(-0.628207\pi\)
0.992710 0.120531i \(-0.0384597\pi\)
\(510\) −15.1918 −0.00131903
\(511\) 0 0
\(512\) −7771.61 −0.670820
\(513\) 1716.02 2972.24i 0.147688 0.255804i
\(514\) −470.372 814.708i −0.0403642 0.0699129i
\(515\) −71.0548 123.071i −0.00607971 0.0105304i
\(516\) −2566.69 + 4445.64i −0.218977 + 0.379280i
\(517\) −17644.7 −1.50099
\(518\) 0 0
\(519\) −6438.44 −0.544540
\(520\) −5.48397 + 9.49851i −0.000462477 + 0.000801033i
\(521\) 1968.31 + 3409.21i 0.165515 + 0.286680i 0.936838 0.349764i \(-0.113738\pi\)
−0.771323 + 0.636443i \(0.780405\pi\)
\(522\) 439.301 + 760.891i 0.0368346 + 0.0637994i
\(523\) 8729.63 15120.2i 0.729866 1.26417i −0.227073 0.973878i \(-0.572916\pi\)
0.956939 0.290288i \(-0.0937510\pi\)
\(524\) 19688.6 1.64142
\(525\) 0 0
\(526\) −67.8760 −0.00562649
\(527\) −1137.98 + 1971.04i −0.0940630 + 0.162922i
\(528\) 3948.88 + 6839.66i 0.325479 + 0.563746i
\(529\) 4647.13 + 8049.06i 0.381945 + 0.661549i
\(530\) −13.3867 + 23.1864i −0.00109713 + 0.00190029i
\(531\) −104.510 −0.00854118
\(532\) 0 0
\(533\) 5321.51 0.432458
\(534\) 418.409 724.705i 0.0339069 0.0587286i
\(535\) −17.2637 29.9016i −0.00139509 0.00241637i
\(536\) −2193.26 3798.83i −0.176743 0.306128i
\(537\) −1805.31 + 3126.89i −0.145074 + 0.251276i
\(538\) 2140.28 0.171513
\(539\) 0 0
\(540\) 21.2435 0.00169292
\(541\) −9550.66 + 16542.2i −0.758992 + 1.31461i 0.184373 + 0.982856i \(0.440975\pi\)
−0.943365 + 0.331757i \(0.892359\pi\)
\(542\) −335.983 581.940i −0.0266268 0.0461190i
\(543\) 4485.71 + 7769.47i 0.354512 + 0.614033i
\(544\) −4699.37 + 8139.54i −0.370374 + 0.641507i
\(545\) 31.9261 0.00250929
\(546\) 0 0
\(547\) 15413.5 1.20481 0.602407 0.798189i \(-0.294208\pi\)
0.602407 + 0.798189i \(0.294208\pi\)
\(548\) 982.718 1702.12i 0.0766052 0.132684i
\(549\) 55.0919 + 95.4219i 0.00428281 + 0.00741805i
\(550\) 1137.47 + 1970.16i 0.0881853 + 0.152741i
\(551\) 14979.0 25944.5i 1.15813 2.00594i
\(552\) 1054.22 0.0812874
\(553\) 0 0
\(554\) 1910.51 0.146516
\(555\) −28.9277 + 50.1043i −0.00221246 + 0.00383209i
\(556\) 3468.26 + 6007.20i 0.264545 + 0.458205i
\(557\) 10246.4 + 17747.3i 0.779453 + 1.35005i 0.932257 + 0.361796i \(0.117836\pi\)
−0.152804 + 0.988257i \(0.548830\pi\)
\(558\) −34.8760 + 60.4070i −0.00264591 + 0.00458285i
\(559\) 3638.17 0.275274
\(560\) 0 0
\(561\) 16034.9 1.20677
\(562\) −440.147 + 762.357i −0.0330364 + 0.0572208i
\(563\) −3571.24 6185.57i −0.267336 0.463039i 0.700837 0.713321i \(-0.252810\pi\)
−0.968173 + 0.250282i \(0.919477\pi\)
\(564\) 4715.30 + 8167.13i 0.352039 + 0.609749i
\(565\) 40.1203 69.4904i 0.00298739 0.00517430i
\(566\) −1065.17 −0.0791030
\(567\) 0 0
\(568\) 5389.96 0.398165
\(569\) −2048.96 + 3548.90i −0.150961 + 0.261472i −0.931581 0.363534i \(-0.881570\pi\)
0.780620 + 0.625006i \(0.214903\pi\)
\(570\) 7.93766 + 13.7484i 0.000583284 + 0.00101028i
\(571\) 1419.24 + 2458.20i 0.104016 + 0.180162i 0.913336 0.407207i \(-0.133497\pi\)
−0.809320 + 0.587369i \(0.800164\pi\)
\(572\) 2862.80 4958.51i 0.209265 0.362458i
\(573\) −8422.23 −0.614038
\(574\) 0 0
\(575\) −6699.21 −0.485872
\(576\) 2012.80 3486.27i 0.145602 0.252190i
\(577\) −7732.23 13392.6i −0.557881 0.966277i −0.997673 0.0681781i \(-0.978281\pi\)
0.439793 0.898099i \(-0.355052\pi\)
\(578\) 2046.88 + 3545.29i 0.147299 + 0.255129i
\(579\) −5004.55 + 8668.14i −0.359209 + 0.622169i
\(580\) 185.433 0.0132753
\(581\) 0 0
\(582\) 1355.86 0.0965675
\(583\) 14129.6 24473.3i 1.00376 1.73856i
\(584\) −1688.59 2924.72i −0.119648 0.207236i
\(585\) −7.52793 13.0388i −0.000532037 0.000921515i
\(586\) −688.622 + 1192.73i −0.0485439 + 0.0840805i
\(587\) −14003.6 −0.984652 −0.492326 0.870411i \(-0.663853\pi\)
−0.492326 + 0.870411i \(0.663853\pi\)
\(588\) 0 0
\(589\) 2378.36 0.166382
\(590\) 0.241713 0.418658i 1.68664e−5 2.92134e-5i
\(591\) 6339.97 + 10981.1i 0.441272 + 0.764305i
\(592\) 5747.99 + 9955.82i 0.399056 + 0.691185i
\(593\) 3252.25 5633.06i 0.225217 0.390088i −0.731167 0.682198i \(-0.761024\pi\)
0.956385 + 0.292110i \(0.0943574\pi\)
\(594\) 491.427 0.0339453
\(595\) 0 0
\(596\) −4561.04 −0.313469
\(597\) −6578.54 + 11394.4i −0.450991 + 0.781140i
\(598\) −184.764 320.021i −0.0126347 0.0218840i
\(599\) 6308.05 + 10925.9i 0.430284 + 0.745273i 0.996898 0.0787104i \(-0.0250802\pi\)
−0.566614 + 0.823983i \(0.691747\pi\)
\(600\) 1229.22 2129.06i 0.0836376 0.144865i
\(601\) −8270.87 −0.561358 −0.280679 0.959802i \(-0.590560\pi\)
−0.280679 + 0.959802i \(0.590560\pi\)
\(602\) 0 0
\(603\) 6021.43 0.406653
\(604\) −11005.8 + 19062.7i −0.741426 + 1.28419i
\(605\) 30.1426 + 52.2085i 0.00202557 + 0.00350839i
\(606\) −851.700 1475.19i −0.0570923 0.0988868i
\(607\) 1905.92 3301.15i 0.127445 0.220740i −0.795241 0.606293i \(-0.792656\pi\)
0.922686 + 0.385553i \(0.125989\pi\)
\(608\) 9821.62 0.655130
\(609\) 0 0
\(610\) −0.509668 −3.38293e−5
\(611\) 3341.86 5788.27i 0.221272 0.383254i
\(612\) −4285.11 7422.03i −0.283032 0.490225i
\(613\) −5679.63 9837.42i −0.374222 0.648172i 0.615988 0.787756i \(-0.288757\pi\)
−0.990210 + 0.139583i \(0.955424\pi\)
\(614\) 183.724 318.219i 0.0120757 0.0209157i
\(615\) 96.3983 0.00632057
\(616\) 0 0
\(617\) −18272.2 −1.19224 −0.596118 0.802896i \(-0.703291\pi\)
−0.596118 + 0.802896i \(0.703291\pi\)
\(618\) −878.519 + 1521.64i −0.0571832 + 0.0990442i
\(619\) 14800.1 + 25634.6i 0.961013 + 1.66452i 0.719965 + 0.694010i \(0.244158\pi\)
0.241048 + 0.970513i \(0.422509\pi\)
\(620\) 7.36075 + 12.7492i 0.000476798 + 0.000825838i
\(621\) −723.573 + 1253.26i −0.0467568 + 0.0809852i
\(622\) −1868.44 −0.120447
\(623\) 0 0
\(624\) −2991.63 −0.191925
\(625\) −7810.61 + 13528.4i −0.499879 + 0.865815i
\(626\) −769.564 1332.92i −0.0491341 0.0851028i
\(627\) −8378.21 14511.5i −0.533642 0.924295i
\(628\) −6620.28 + 11466.7i −0.420665 + 0.728614i
\(629\) 23340.5 1.47956
\(630\) 0 0
\(631\) 7185.41 0.453322 0.226661 0.973974i \(-0.427219\pi\)
0.226661 + 0.973974i \(0.427219\pi\)
\(632\) 2641.40 4575.05i 0.166249 0.287952i
\(633\) −3437.34 5953.64i −0.215832 0.373833i
\(634\) 1440.33 + 2494.72i 0.0902252 + 0.156275i
\(635\) 53.8405 93.2545i 0.00336472 0.00582786i
\(636\) −15103.8 −0.941673
\(637\) 0 0
\(638\) 4289.64 0.266189
\(639\) −3699.44 + 6407.62i −0.229026 + 0.396684i
\(640\) 40.3733 + 69.9287i 0.00249359 + 0.00431902i
\(641\) 116.491 + 201.768i 0.00717803 + 0.0124327i 0.869592 0.493771i \(-0.164382\pi\)
−0.862414 + 0.506203i \(0.831048\pi\)
\(642\) −213.448 + 369.702i −0.0131217 + 0.0227274i
\(643\) 1837.96 0.112725 0.0563624 0.998410i \(-0.482050\pi\)
0.0563624 + 0.998410i \(0.482050\pi\)
\(644\) 0 0
\(645\) 65.9048 0.00402325
\(646\) 3202.27 5546.50i 0.195034 0.337808i
\(647\) −9297.35 16103.5i −0.564941 0.978506i −0.997055 0.0766874i \(-0.975566\pi\)
0.432114 0.901819i \(-0.357768\pi\)
\(648\) −265.532 459.915i −0.0160974 0.0278814i
\(649\) −255.128 + 441.895i −0.0154309 + 0.0267271i
\(650\) −861.736 −0.0520001
\(651\) 0 0
\(652\) 318.799 0.0191490
\(653\) 14432.3 24997.6i 0.864902 1.49805i −0.00224162 0.999997i \(-0.500714\pi\)
0.867144 0.498057i \(-0.165953\pi\)
\(654\) −197.367 341.849i −0.0118007 0.0204394i
\(655\) −126.386 218.907i −0.00753940 0.0130586i
\(656\) 9577.27 16588.3i 0.570014 0.987294i
\(657\) 4635.90 0.275287
\(658\) 0 0
\(659\) −29066.3 −1.71815 −0.859076 0.511847i \(-0.828961\pi\)
−0.859076 + 0.511847i \(0.828961\pi\)
\(660\) 51.8591 89.8226i 0.00305850 0.00529748i
\(661\) −1989.75 3446.36i −0.117084 0.202795i 0.801527 0.597959i \(-0.204021\pi\)
−0.918611 + 0.395163i \(0.870688\pi\)
\(662\) −2042.73 3538.11i −0.119929 0.207723i
\(663\) −3036.98 + 5260.20i −0.177898 + 0.308128i
\(664\) −2588.86 −0.151306
\(665\) 0 0
\(666\) 715.322 0.0416189
\(667\) −6316.02 + 10939.7i −0.366653 + 0.635061i
\(668\) 11353.0 + 19664.0i 0.657578 + 1.13896i
\(669\) 326.955 + 566.302i 0.0188951 + 0.0327272i
\(670\) −13.9264 + 24.1213i −0.000803022 + 0.00139087i
\(671\) 537.955 0.0309501
\(672\) 0 0
\(673\) −184.229 −0.0105520 −0.00527601 0.999986i \(-0.501679\pi\)
−0.00527601 + 0.999986i \(0.501679\pi\)
\(674\) −1231.26 + 2132.61i −0.0703657 + 0.121877i
\(675\) 1687.36 + 2922.60i 0.0962173 + 0.166653i
\(676\) −7515.11 13016.6i −0.427578 0.740587i
\(677\) −8341.73 + 14448.3i −0.473558 + 0.820227i −0.999542 0.0302680i \(-0.990364\pi\)
0.525984 + 0.850495i \(0.323697\pi\)
\(678\) −992.091 −0.0561962
\(679\) 0 0
\(680\) 80.1540 0.00452024
\(681\) −2753.04 + 4768.41i −0.154914 + 0.268320i
\(682\) 170.277 + 294.928i 0.00956045 + 0.0165592i
\(683\) −8904.11 15422.4i −0.498838 0.864013i 0.501161 0.865354i \(-0.332906\pi\)
−0.999999 + 0.00134107i \(0.999573\pi\)
\(684\) −4477.92 + 7755.98i −0.250318 + 0.433563i
\(685\) −25.2332 −0.00140746
\(686\) 0 0
\(687\) 8322.03 0.462162
\(688\) 6547.71 11341.0i 0.362833 0.628445i
\(689\) 5352.23 + 9270.34i 0.295942 + 0.512586i
\(690\) −3.34697 5.79712i −0.000184662 0.000319845i
\(691\) −10072.8 + 17446.7i −0.554542 + 0.960495i 0.443397 + 0.896325i \(0.353773\pi\)
−0.997939 + 0.0641695i \(0.979560\pi\)
\(692\) 16801.0 0.922943
\(693\) 0 0
\(694\) −484.453 −0.0264980
\(695\) 44.5271 77.1232i 0.00243023 0.00420928i
\(696\) −2317.81 4014.57i −0.126231 0.218638i
\(697\) −19444.9 33679.5i −1.05671 1.83028i
\(698\) 1900.55 3291.85i 0.103061 0.178507i
\(699\) −2966.14 −0.160500
\(700\) 0 0
\(701\) −2719.67 −0.146534 −0.0732672 0.997312i \(-0.523343\pi\)
−0.0732672 + 0.997312i \(0.523343\pi\)
\(702\) −93.0750 + 161.211i −0.00500412 + 0.00866738i
\(703\) −12195.3 21122.9i −0.654276 1.13324i
\(704\) −9827.18 17021.2i −0.526102 0.911235i
\(705\) 60.5372 104.854i 0.00323399 0.00560144i
\(706\) 4385.36 0.233775
\(707\) 0 0
\(708\) 272.717 0.0144765
\(709\) 312.854 541.879i 0.0165719 0.0287034i −0.857621 0.514283i \(-0.828058\pi\)
0.874192 + 0.485580i \(0.161391\pi\)
\(710\) −17.1122 29.6392i −0.000904520 0.00156667i
\(711\) 3625.89 + 6280.23i 0.191254 + 0.331262i
\(712\) −2207.58 + 3823.65i −0.116198 + 0.201260i
\(713\) −1002.85 −0.0526749
\(714\) 0 0
\(715\) −73.5079 −0.00384481
\(716\) 4710.91 8159.53i 0.245887 0.425888i
\(717\) 1256.89 + 2177.00i 0.0654665 + 0.113391i
\(718\) 1784.27 + 3090.44i 0.0927414 + 0.160633i
\(719\) −4788.77 + 8294.39i −0.248388 + 0.430221i −0.963079 0.269220i \(-0.913234\pi\)
0.714691 + 0.699441i \(0.246567\pi\)
\(720\) −54.1929 −0.00280507
\(721\) 0 0
\(722\) −3851.62 −0.198535
\(723\) 5182.48 8976.32i 0.266582 0.461733i
\(724\) −11705.3 20274.2i −0.600864 1.04073i
\(725\) 14728.9 + 25511.2i 0.754506 + 1.30684i
\(726\) 372.682 645.504i 0.0190517 0.0329985i
\(727\) 16741.2 0.854053 0.427027 0.904239i \(-0.359561\pi\)
0.427027 + 0.904239i \(0.359561\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −10.7219 + 18.5710i −0.000543612 + 0.000941564i
\(731\) −13293.9 23025.7i −0.672631 1.16503i
\(732\) −143.761 249.001i −0.00725896 0.0125729i
\(733\) −3248.02 + 5625.74i −0.163668 + 0.283481i −0.936181 0.351517i \(-0.885666\pi\)
0.772514 + 0.634998i \(0.218999\pi\)
\(734\) 3437.06 0.172839
\(735\) 0 0
\(736\) −4141.36 −0.207408
\(737\) 14699.4 25460.0i 0.734678 1.27250i
\(738\) −595.932 1032.18i −0.0297243 0.0514841i
\(739\) −249.640 432.389i −0.0124265 0.0215233i 0.859745 0.510723i \(-0.170622\pi\)
−0.872172 + 0.489200i \(0.837289\pi\)
\(740\) 75.4861 130.746i 0.00374990 0.00649502i
\(741\) 6347.24 0.314672
\(742\) 0 0
\(743\) −6367.30 −0.314393 −0.157196 0.987567i \(-0.550246\pi\)
−0.157196 + 0.987567i \(0.550246\pi\)
\(744\) 184.011 318.716i 0.00906741 0.0157052i
\(745\) 29.2784 + 50.7117i 0.00143984 + 0.00249387i
\(746\) −1061.19 1838.03i −0.0520814 0.0902077i
\(747\) 1776.88 3077.65i 0.0870318 0.150743i
\(748\) −41842.8 −2.04535
\(749\) 0 0
\(750\) −31.2217 −0.00152007
\(751\) −248.049 + 429.634i −0.0120525 + 0.0208756i −0.871989 0.489526i \(-0.837170\pi\)
0.859936 + 0.510401i \(0.170503\pi\)
\(752\) −12028.9 20834.6i −0.583308 1.01032i
\(753\) −8452.51 14640.2i −0.409066 0.708523i
\(754\) −812.446 + 1407.20i −0.0392407 + 0.0679670i
\(755\) 282.597 0.0136222
\(756\) 0 0
\(757\) 13025.9 0.625408 0.312704 0.949851i \(-0.398765\pi\)
0.312704 + 0.949851i \(0.398765\pi\)
\(758\) −311.175 + 538.971i −0.0149108 + 0.0258263i
\(759\) 3532.73 + 6118.87i 0.168946 + 0.292623i
\(760\) −41.8802 72.5387i −0.00199889 0.00346218i
\(761\) −12737.3 + 22061.6i −0.606736 + 1.05090i 0.385039 + 0.922900i \(0.374188\pi\)
−0.991775 + 0.127997i \(0.959145\pi\)
\(762\) −1331.36 −0.0632943
\(763\) 0 0
\(764\) 21977.6 1.04074
\(765\) −55.0143 + 95.2875i −0.00260006 + 0.00450344i
\(766\) 2251.86 + 3900.33i 0.106218 + 0.183975i
\(767\) −96.6411 167.387i −0.00454955 0.00788006i
\(768\) −4868.29 + 8432.12i −0.228736 + 0.396182i
\(769\) 29054.0 1.36244 0.681218 0.732080i \(-0.261450\pi\)
0.681218 + 0.732080i \(0.261450\pi\)
\(770\) 0 0
\(771\) −6813.47 −0.318263
\(772\) 13059.3 22619.3i 0.608825 1.05452i
\(773\) 948.677 + 1643.16i 0.0441417 + 0.0764557i 0.887252 0.461285i \(-0.152611\pi\)
−0.843110 + 0.537740i \(0.819278\pi\)
\(774\) −407.422 705.676i −0.0189205 0.0327713i
\(775\) −1169.32 + 2025.33i −0.0541978 + 0.0938734i
\(776\) −7153.72 −0.330933
\(777\) 0 0
\(778\) −1913.25 −0.0881662
\(779\) −20319.8 +