Properties

Label 147.4.e.k.67.2
Level $147$
Weight $4$
Character 147.67
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 67.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 147.67
Dual form 147.4.e.k.79.2

$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.900312 0.435245i \(-0.143338\pi\)
−0.827089 + 0.562071i \(0.810005\pi\)
\(3\) 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 \(-0.168097\pi\)
−0.868264 + 0.496102i \(0.834764\pi\)
\(6\) 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 −0.390269 0.920701i \(-0.627618\pi\)
0.992485 0.122368i \(-0.0390487\pi\)
\(12\) −11.7426 20.3389i −0.282484 0.489277i
\(13\) 16.6447 0.355108 0.177554 0.984111i \(-0.443182\pi\)
0.177554 + 0.984111i \(0.443182\pi\)
\(14\) 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 −0.00336718 + 0.999994i \(0.501072\pi\)
−0.864337 + 0.502913i \(0.832262\pi\)
\(18\) 1.86396 3.22848i 0.0244078 0.0422755i
\(19\) −63.5563 110.083i −0.767412 1.32920i −0.938962 0.344021i \(-0.888211\pi\)
0.171550 0.985175i \(-0.445122\pi\)
\(20\) −0.786797 −0.00879665
\(21\) 0 0
\(22\) 18.2010 0.176385
\(23\) −26.7990 46.4172i −0.242955 0.420811i 0.718599 0.695424i \(-0.244784\pi\)
−0.961555 + 0.274613i \(0.911450\pi\)
\(24\) 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 \(-0.850595\pi\)
0.837651 + 0.546205i \(0.183928\pi\)
\(32\) 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 0.996540 0.0831185i \(-0.0264880\pi\)
−0.570253 + 0.821469i \(0.693155\pi\)
\(38\) 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 \(-0.291606\pi\)
0.608912 + 0.793238i \(0.291606\pi\)
\(42\) 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 0.988903 + 0.148565i \(0.0474655\pi\)
−0.365790 + 0.930697i \(0.619201\pi\)
\(48\) −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 0.0619521 + 0.998079i \(0.480267\pi\)
−0.895338 + 0.445387i \(0.853066\pi\)
\(54\) −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 \(-0.837412\pi\)
0.859548 + 0.511054i \(0.170745\pi\)
\(60\) −1.18019 + 2.04416i −0.00253937 + 0.00439833i
\(61\) −6.12132 10.6024i −0.0128484 0.0222541i 0.859530 0.511086i \(-0.170757\pi\)
−0.872378 + 0.488832i \(0.837423\pi\)
\(62\) −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 0.381264 + 0.924466i \(0.375489\pi\)
−0.991243 + 0.132049i \(0.957844\pi\)
\(68\) 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 \(-0.697839\pi\)
0.995209 + 0.0977730i \(0.0311719\pi\)
\(74\) −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 0.996175 + 0.0873819i \(0.0278500\pi\)
−0.422413 + 0.906404i \(0.638817\pi\)
\(80\) −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 \(-0.415916\pi\)
0.261095 + 0.965313i \(0.415916\pi\)
\(84\) 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 \(-0.0353212\pi\)
−0.592826 + 0.805331i \(0.701988\pi\)
\(90\) −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 \(-0.306532\pi\)
0.571061 + 0.820908i \(0.306532\pi\)
\(98\) 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 0.301157 + 0.953575i \(0.402627\pi\)
−0.976398 + 0.215978i \(0.930706\pi\)
\(102\) −75.5772 + 130.903i −0.0733652 + 0.127072i
\(103\) −706.978 1224.52i −0.676316 1.17141i −0.976082 0.217401i \(-0.930242\pi\)
0.299766 0.954013i \(-0.403091\pi\)
\(104\) 109.128 0.102893
\(105\) 0 0
\(106\) −266.388 −0.244093
\(107\) 171.770 + 297.514i 0.155192 + 0.268801i 0.933129 0.359542i \(-0.117067\pi\)
−0.777937 + 0.628343i \(0.783734\pi\)
\(108\) −105.684 + 183.050i −0.0941613 + 0.163092i
\(109\) 158.828 275.099i 0.139569 0.241740i −0.787765 0.615976i \(-0.788762\pi\)
0.927333 + 0.374236i \(0.122095\pi\)
\(110\) −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 −0.890986 0.454031i \(-0.849986\pi\)
0.0522910 0.998632i \(-0.483348\pi\)
\(132\) −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 −0.902510 0.430670i \(-0.858277\pi\)
0.824226 + 0.566262i \(0.191611\pi\)
\(138\) −33.3015 57.6799i −0.0205421 0.0355800i
\(139\) −886.067 −0.540685 −0.270343 0.962764i \(-0.587137\pi\)
−0.270343 + 0.962764i \(0.587137\pi\)
\(140\) 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 0.774760 0.632256i \(-0.217871\pi\)
−0.934929 + 0.354834i \(0.884537\pi\)
\(150\) 77.6588 134.509i 0.0422721 0.0732174i
\(151\) 1405.88 2435.06i 0.757676 1.31233i −0.186357 0.982482i \(-0.559668\pi\)
0.944033 0.329851i \(-0.106999\pi\)
\(152\) −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 \(-0.974779\pi\)
0.566978 + 0.823733i \(0.308113\pi\)
\(158\) −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 0.870876 0.491503i \(-0.163552\pi\)
−0.861092 + 0.508450i \(0.830219\pi\)
\(164\) 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 \(-0.734560\pi\)
−0.671990 + 0.740560i \(0.734560\pi\)
\(168\) 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 \(-0.322985\pi\)
−0.999472 + 0.0325052i \(0.989651\pi\)
\(174\) 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 −0.963877 0.266347i \(-0.914183\pi\)
0.712602 + 0.701569i \(0.247517\pi\)
\(180\) 3.54058 + 6.13247i 0.00146611 + 0.00253937i
\(181\) 2990.47 1.22807 0.614033 0.789280i \(-0.289546\pi\)
0.614033 + 0.789280i \(0.289546\pi\)
\(182\) 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 0.999312 + 0.0370847i \(0.0118071\pi\)
−0.467540 + 0.883972i \(0.654860\pi\)
\(192\) −670.933 + 1162.09i −0.252190 + 0.436805i
\(193\) −1668.18 + 2889.38i −0.622169 + 1.07763i 0.366913 + 0.930255i \(0.380415\pi\)
−0.989081 + 0.147372i \(0.952919\pi\)
\(194\) 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 −0.150139 0.988665i \(-0.547972\pi\)
0.931278 0.364309i \(-0.118695\pi\)
\(200\) 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 \(-0.489581\pi\)
0.0327272 + 0.999464i \(0.489581\pi\)
\(224\) 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 \(-0.746865\pi\)
0.968428 + 0.249293i \(0.0801983\pi\)
\(228\) −1492.64 + 2585.33i −0.433563 + 0.750954i
\(229\) 1387.00 + 2402.36i 0.400244 + 0.693243i 0.993755 0.111583i \(-0.0355921\pi\)
−0.593511 + 0.804826i \(0.702259\pi\)
\(230\) −2.23131 −0.000639689
\(231\) 0 0
\(232\) 1545.21 0.437275
\(233\) 494.356 + 856.250i 0.138997 + 0.240750i 0.927117 0.374771i \(-0.122279\pi\)
−0.788120 + 0.615522i \(0.788945\pi\)
\(234\) 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 \(-0.986105\pi\)
0.537315 + 0.843382i \(0.319439\pi\)
\(242\) 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 \(-0.750638\pi\)
−0.708523 + 0.705688i \(0.750638\pi\)
\(252\) 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 \(-0.255551\pi\)
−0.970292 + 0.241935i \(0.922218\pi\)
\(258\) −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 −0.875471 0.483271i \(-0.839448\pi\)
0.856261 + 0.516544i \(0.172782\pi\)
\(264\) −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 0.409220 + 0.912436i \(0.365801\pi\)
−0.994803 + 0.101823i \(0.967533\pi\)
\(270\) −0.562013 + 0.973434i −0.000126678 + 0.000219412i
\(271\) −811.136 1404.93i −0.181819 0.314920i 0.760681 0.649126i \(-0.224865\pi\)
−0.942500 + 0.334206i \(0.891532\pi\)
\(272\) 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 −0.499765 0.866161i \(-0.666580\pi\)
1.00000 0.000271708i \(-8.64874e-5\pi\)
\(278\) −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 \(-0.746285\pi\)
0.968881 + 0.247528i \(0.0796183\pi\)
\(284\) 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 \(-0.392453\pi\)
0.331478 + 0.943463i \(0.392453\pi\)
\(294\) 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 \(-0.526277\pi\)
−0.0824580 + 0.996595i \(0.526277\pi\)
\(308\) 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 \(-0.698433\pi\)
0.995025 + 0.0996300i \(0.0317659\pi\)
\(312\) 163.692 283.523i 0.0297027 0.0514466i
\(313\) −1857.89 3217.96i −0.335509 0.581118i 0.648074 0.761578i \(-0.275575\pi\)
−0.983582 + 0.180459i \(0.942242\pi\)
\(314\) −700.577 −0.125910
\(315\) 0 0
\(316\) 6307.79 1.12291
\(317\) −3477.26 6022.79i −0.616096 1.06711i −0.990191 0.139719i \(-0.955380\pi\)
0.374095 0.927390i \(-0.377953\pi\)
\(318\) −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 0.906474 + 0.422262i \(0.138764\pi\)
−0.0875478 + 0.996160i \(0.527903\pi\)
\(332\) 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 −0.907709 0.419601i \(-0.862170\pi\)
0.817239 + 0.576299i \(0.195503\pi\)
\(348\) −2767.52 4793.49i −0.426306 0.738384i
\(349\) −9176.66 −1.40749 −0.703747 0.710451i \(-0.748491\pi\)
−0.703747 + 0.710451i \(0.748491\pi\)
\(350\) 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 0.122656 + 0.992449i \(0.460859\pi\)
−0.920814 + 0.390001i \(0.872474\pi\)
\(354\) −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 −0.986877 0.161472i \(-0.948376\pi\)
0.353599 0.935397i \(-0.384958\pi\)
\(360\) −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 0.404107 + 0.914712i \(0.367582\pi\)
−0.994217 + 0.107389i \(0.965751\pi\)
\(368\) −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 0.987226 0.159324i \(-0.0509315\pi\)
−0.631592 + 0.775301i \(0.717598\pi\)
\(374\) −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 0.958850 + 0.283914i \(0.0916330\pi\)
−0.233548 + 0.972345i \(0.575034\pi\)
\(384\) −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 −0.976367 0.216120i \(-0.930660\pi\)
0.675349 + 0.737499i \(0.263993\pi\)
\(390\) −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 −0.991691 0.128642i \(-0.958938\pi\)
0.384438 0.923151i \(-0.374395\pi\)
\(398\) 1816.61 0.228791
\(399\) 0 0
\(400\) −7488.36 −0.936044
\(401\) 5250.52 + 9094.17i 0.653862 + 1.13252i 0.982178 + 0.187954i \(0.0601857\pi\)
−0.328316 + 0.944568i \(0.606481\pi\)
\(402\) −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 −0.227699 0.973732i \(-0.573120\pi\)
0.957126 0.289673i \(-0.0935466\pi\)
\(410\) 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 \(-0.621033\pi\)
−0.371139 + 0.928577i \(0.621033\pi\)
\(420\) 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 −0.951621 0.307273i \(-0.900584\pi\)
0.741917 + 0.670492i \(0.233917\pi\)
\(432\) 808.808 + 1400.90i 0.0900782 + 0.156020i
\(433\) 11709.2 1.29956 0.649780 0.760122i \(-0.274861\pi\)
0.649780 + 0.760122i \(0.274861\pi\)
\(434\) 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 0.911957 + 0.410285i \(0.134571\pi\)
−0.100661 + 0.994921i \(0.532096\pi\)
\(440\) −28.9548 −0.00313720
\(441\) 0 0
\(442\) −838.638 −0.0902487
\(443\) 4258.83 + 7376.51i 0.456756 + 0.791125i 0.998787 0.0492333i \(-0.0156778\pi\)
−0.542031 + 0.840359i \(0.682344\pi\)
\(444\) 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 0.965089 + 0.261923i \(0.0843567\pi\)
−0.255712 + 0.966753i \(0.582310\pi\)
\(458\) −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 \(-0.502401\pi\)
−0.00754249 + 0.999972i \(0.502401\pi\)
\(462\) 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 \(-0.225424\pi\)
−0.943085 + 0.332551i \(0.892091\pi\)
\(468\) −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 −0.490963 0.871180i \(-0.663355\pi\)
0.999946 0.0104033i \(-0.00331152\pi\)
\(480\) −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 −0.969463 0.245239i \(-0.921133\pi\)
0.697115 + 0.716959i \(0.254467\pi\)
\(488\) −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 0.737713 0.675115i \(-0.235906\pi\)
−0.953523 + 0.301321i \(0.902572\pi\)
\(500\) −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 \(-0.228351\pi\)
0.753526 + 0.657418i \(0.228351\pi\)
\(504\) 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 −0.992710 0.120531i \(-0.961540\pi\)
0.391972 0.919977i \(-0.371793\pi\)
\(510\) 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 \(-0.886262\pi\)
0.771323 + 0.636443i \(0.219595\pi\)
\(522\) 439.301 760.891i 0.0368346 0.0637994i
\(523\) −8729.63 15120.2i −0.729866 1.26417i −0.956939 0.290288i \(-0.906249\pi\)
0.227073 0.973878i \(-0.427084\pi\)
\(524\) −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 −0.943365 0.331757i \(-0.892359\pi\)
0.184373 0.982856i \(-0.440975\pi\)
\(542\) 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 −0.152804 0.988257i \(-0.548830\pi\)
0.932257 0.361796i \(-0.117836\pi\)
\(558\) 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 \(-0.747190\pi\)
0.968173 + 0.250282i \(0.0805234\pi\)
\(564\) 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 0.780620 0.625006i \(-0.214903\pi\)
−0.931581 + 0.363534i \(0.881570\pi\)
\(570\) −7.93766 + 13.7484i −0.000583284 + 0.00101028i
\(571\) 1419.24 2458.20i 0.104016 0.180162i −0.809320 0.587369i \(-0.800164\pi\)
0.913336 + 0.407207i \(0.133497\pi\)
\(572\) −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 −0.439793 0.898099i \(-0.644948\pi\)
0.997673 0.0681781i \(-0.0217186\pi\)
\(578\) 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 \(-0.336147\pi\)
0.492326 + 0.870411i \(0.336147\pi\)
\(588\) 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 \(-0.238976\pi\)
−0.956385 + 0.292110i \(0.905643\pi\)
\(594\) −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 −0.566614 0.823983i \(-0.691747\pi\)
0.996898 + 0.0787104i \(0.0250802\pi\)
\(600\) −1229.22 2129.06i −0.0836376 0.144865i
\(601\) 8270.87 0.561358 0.280679 0.959802i \(-0.409440\pi\)
0.280679 + 0.959802i \(0.409440\pi\)
\(602\) 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 \(-0.207344\pi\)
−0.922686 + 0.385553i \(0.874011\pi\)
\(608\) −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 −0.990210 0.139583i \(-0.955424\pi\)
0.615988 + 0.787756i \(0.288757\pi\)
\(614\) −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 −0.241048 + 0.970513i \(0.577491\pi\)
−0.719965 + 0.694010i \(0.755842\pi\)
\(620\) 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 −0.862414 0.506203i \(-0.831048\pi\)
0.869592 + 0.493771i \(0.164382\pi\)
\(642\) 213.448 + 369.702i 0.0131217 + 0.0227274i
\(643\) −1837.96 −0.112725 −0.0563624 0.998410i \(-0.517950\pi\)
−0.0563624 + 0.998410i \(0.517950\pi\)
\(644\) 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 −0.432114 0.901819i \(-0.642232\pi\)
0.997055 0.0766874i \(-0.0244343\pi\)
\(648\) −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 0.867144 + 0.498057i \(0.165953\pi\)
−0.00224162 + 0.999997i \(0.500714\pi\)
\(654\) 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 \(-0.795979\pi\)
0.918611 + 0.395163i \(0.129312\pi\)
\(662\) −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 \(-0.00963607\pi\)
−0.525984 + 0.850495i \(0.676303\pi\)
\(678\) 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 −0.999999 0.00134107i \(-0.999573\pi\)
0.501161 + 0.865354i \(0.332906\pi\)
\(684\) 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 0.997939 + 0.0641695i \(0.0204398\pi\)
−0.443397 + 0.896325i \(0.646227\pi\)
\(692\) −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 0.874192 0.485580i \(-0.161391\pi\)
−0.857621 + 0.514283i \(0.828058\pi\)
\(710\) 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 \(-0.0867659\pi\)
−0.714691 + 0.699441i \(0.753433\pi\)
\(720\) 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 \(-0.640439\pi\)
−0.427027 + 0.904239i \(0.640439\pi\)
\(728\) 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 \(-0.114334\pi\)
−0.772514 + 0.634998i \(0.781001\pi\)
\(734\) −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 −0.872172 0.489200i \(-0.837289\pi\)
0.859745 + 0.510723i \(0.170622\pi\)
\(740\) −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 0.859936 0.510401i \(-0.170503\pi\)
−0.871989 + 0.489526i \(0.837170\pi\)
\(752\) 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 0.991775 + 0.127997i \(0.0408548\pi\)
−0.385039 + 0.922900i \(0.625812\pi\)
\(762\) 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 \(-0.738550\pi\)
−0.681218 + 0.732080i \(0.738550\pi\)
\(770\) 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 \(-0.847389\pi\)
0.843110 + 0.537740i \(0.180722\pi\)
\(774\) −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