Properties

Label 570.4.i.h.121.1
Level $570$
Weight $4$
Character 570.121
Analytic conductor $33.631$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.6310887033\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{385})\)
Defining polynomial: \(x^{4} - x^{3} + 97 x^{2} + 96 x + 9216\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 121.1
Root \(5.15535 - 8.92934i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.4.i.h.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} -10.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} -10.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 - 8.66025i) q^{10} -15.3107 q^{11} -12.0000 q^{12} +(23.0000 - 39.8372i) q^{13} +(10.6214 + 18.3968i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-11.5339 - 19.9774i) q^{17} +18.0000 q^{18} +(4.56787 + 82.6930i) q^{19} -20.0000 q^{20} +(-15.9321 - 27.5953i) q^{21} +(15.3107 + 26.5189i) q^{22} +(-92.4857 + 160.190i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -92.0000 q^{26} -27.0000 q^{27} +(21.2428 - 36.7937i) q^{28} +(111.830 - 193.696i) q^{29} +30.0000 q^{30} +32.5143 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-22.9661 - 39.7784i) q^{33} +(-23.0679 + 39.9547i) q^{34} +(-26.5535 - 45.9921i) q^{35} +(-18.0000 - 31.1769i) q^{36} -310.621 q^{37} +(138.661 - 90.6048i) q^{38} +138.000 q^{39} +(20.0000 + 34.6410i) q^{40} +(-174.729 - 302.639i) q^{41} +(-31.8643 + 55.1905i) q^{42} +(-92.2428 - 159.769i) q^{43} +(30.6214 - 53.0378i) q^{44} -45.0000 q^{45} +369.943 q^{46} +(-112.398 + 194.679i) q^{47} +(24.0000 - 41.5692i) q^{48} -230.186 q^{49} +50.0000 q^{50} +(34.6018 - 59.9321i) q^{51} +(92.0000 + 159.349i) q^{52} +(226.816 - 392.857i) q^{53} +(27.0000 + 46.7654i) q^{54} +(-38.2768 - 66.2973i) q^{55} -84.9713 q^{56} +(-207.991 + 135.907i) q^{57} -447.321 q^{58} +(186.830 + 323.600i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(-28.0053 + 48.5066i) q^{61} +(-32.5143 - 56.3165i) q^{62} +(47.7964 - 82.7858i) q^{63} +64.0000 q^{64} +230.000 q^{65} +(-45.9321 + 79.5568i) q^{66} +(372.757 - 645.634i) q^{67} +92.2715 q^{68} -554.914 q^{69} +(-53.1071 + 91.9842i) q^{70} +(-530.491 - 918.837i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(-426.186 - 738.175i) q^{73} +(310.621 + 538.012i) q^{74} -75.0000 q^{75} +(-295.593 - 149.562i) q^{76} +162.621 q^{77} +(-138.000 - 239.023i) q^{78} +(-479.569 - 830.638i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-349.457 + 605.277i) q^{82} +205.554 q^{83} +127.457 q^{84} +(57.6697 - 99.8868i) q^{85} +(-184.486 + 319.539i) q^{86} +670.982 q^{87} -122.486 q^{88} +(183.112 - 317.160i) q^{89} +(45.0000 + 77.9423i) q^{90} +(-244.293 + 423.127i) q^{91} +(-369.943 - 640.760i) q^{92} +(48.7715 + 84.4747i) q^{93} +449.593 q^{94} +(-346.652 + 226.512i) q^{95} -96.0000 q^{96} +(-193.825 - 335.715i) q^{97} +(230.186 + 398.693i) q^{98} +(68.8982 - 119.335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} + 6q^{3} - 8q^{4} + 10q^{5} + 12q^{6} + 36q^{7} + 32q^{8} - 18q^{9} + O(q^{10}) \) \( 4q - 4q^{2} + 6q^{3} - 8q^{4} + 10q^{5} + 12q^{6} + 36q^{7} + 32q^{8} - 18q^{9} + 20q^{10} - 22q^{11} - 48q^{12} + 92q^{13} - 36q^{14} - 30q^{15} - 32q^{16} - 105q^{17} + 72q^{18} + 136q^{19} - 80q^{20} + 54q^{21} + 22q^{22} - 56q^{23} + 48q^{24} - 50q^{25} - 368q^{26} - 108q^{27} - 72q^{28} + 153q^{29} + 120q^{30} + 444q^{31} - 64q^{32} - 33q^{33} - 210q^{34} + 90q^{35} - 72q^{36} - 1164q^{37} - 34q^{38} + 552q^{39} + 80q^{40} - 228q^{41} + 108q^{42} - 212q^{43} + 44q^{44} - 180q^{45} + 224q^{46} - 273q^{47} + 96q^{48} + 492q^{49} + 200q^{50} + 315q^{51} + 368q^{52} + 299q^{53} + 108q^{54} - 55q^{55} + 288q^{56} + 51q^{57} - 612q^{58} + 453q^{59} - 120q^{60} + 457q^{61} - 444q^{62} - 162q^{63} + 256q^{64} + 920q^{65} - 66q^{66} + 1648q^{67} + 840q^{68} - 336q^{69} + 180q^{70} - 1239q^{71} - 144q^{72} - 292q^{73} + 1164q^{74} - 300q^{75} - 476q^{76} + 572q^{77} - 552q^{78} - 15q^{79} + 160q^{80} - 162q^{81} - 456q^{82} + 626q^{83} - 432q^{84} + 525q^{85} - 424q^{86} + 918q^{87} - 176q^{88} - 229q^{89} + 180q^{90} + 828q^{91} - 224q^{92} + 666q^{93} + 1092q^{94} + 85q^{95} - 384q^{96} - 1050q^{97} - 492q^{98} + 99q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 1.50000 + 2.59808i 0.288675 + 0.500000i
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 3.00000 5.19615i 0.204124 0.353553i
\(7\) −10.6214 −0.573503 −0.286751 0.958005i \(-0.592575\pi\)
−0.286751 + 0.958005i \(0.592575\pi\)
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 5.00000 8.66025i 0.158114 0.273861i
\(11\) −15.3107 −0.419668 −0.209834 0.977737i \(-0.567292\pi\)
−0.209834 + 0.977737i \(0.567292\pi\)
\(12\) −12.0000 −0.288675
\(13\) 23.0000 39.8372i 0.490696 0.849911i −0.509246 0.860621i \(-0.670076\pi\)
0.999943 + 0.0107098i \(0.00340911\pi\)
\(14\) 10.6214 + 18.3968i 0.202764 + 0.351197i
\(15\) −7.50000 + 12.9904i −0.129099 + 0.223607i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −11.5339 19.9774i −0.164552 0.285013i 0.771944 0.635691i \(-0.219285\pi\)
−0.936496 + 0.350678i \(0.885951\pi\)
\(18\) 18.0000 0.235702
\(19\) 4.56787 + 82.6930i 0.0551549 + 0.998478i
\(20\) −20.0000 −0.223607
\(21\) −15.9321 27.5953i −0.165556 0.286751i
\(22\) 15.3107 + 26.5189i 0.148375 + 0.256993i
\(23\) −92.4857 + 160.190i −0.838461 + 1.45226i 0.0527208 + 0.998609i \(0.483211\pi\)
−0.891181 + 0.453647i \(0.850123\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −92.0000 −0.693949
\(27\) −27.0000 −0.192450
\(28\) 21.2428 36.7937i 0.143376 0.248334i
\(29\) 111.830 193.696i 0.716082 1.24029i −0.246459 0.969153i \(-0.579267\pi\)
0.962541 0.271137i \(-0.0873995\pi\)
\(30\) 30.0000 0.182574
\(31\) 32.5143 0.188379 0.0941895 0.995554i \(-0.469974\pi\)
0.0941895 + 0.995554i \(0.469974\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) −22.9661 39.7784i −0.121148 0.209834i
\(34\) −23.0679 + 39.9547i −0.116356 + 0.201535i
\(35\) −26.5535 45.9921i −0.128239 0.222117i
\(36\) −18.0000 31.1769i −0.0833333 0.144338i
\(37\) −310.621 −1.38016 −0.690079 0.723734i \(-0.742424\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(38\) 138.661 90.6048i 0.591940 0.386791i
\(39\) 138.000 0.566607
\(40\) 20.0000 + 34.6410i 0.0790569 + 0.136931i
\(41\) −174.729 302.639i −0.665561 1.15279i −0.979133 0.203221i \(-0.934859\pi\)
0.313572 0.949565i \(-0.398474\pi\)
\(42\) −31.8643 + 55.1905i −0.117066 + 0.202764i
\(43\) −92.2428 159.769i −0.327137 0.566618i 0.654805 0.755798i \(-0.272751\pi\)
−0.981943 + 0.189179i \(0.939417\pi\)
\(44\) 30.6214 53.0378i 0.104917 0.181722i
\(45\) −45.0000 −0.149071
\(46\) 369.943 1.18576
\(47\) −112.398 + 194.679i −0.348829 + 0.604189i −0.986042 0.166498i \(-0.946754\pi\)
0.637213 + 0.770688i \(0.280087\pi\)
\(48\) 24.0000 41.5692i 0.0721688 0.125000i
\(49\) −230.186 −0.671095
\(50\) 50.0000 0.141421
\(51\) 34.6018 59.9321i 0.0950044 0.164552i
\(52\) 92.0000 + 159.349i 0.245348 + 0.424955i
\(53\) 226.816 392.857i 0.587841 1.01817i −0.406674 0.913573i \(-0.633311\pi\)
0.994515 0.104597i \(-0.0333553\pi\)
\(54\) 27.0000 + 46.7654i 0.0680414 + 0.117851i
\(55\) −38.2768 66.2973i −0.0938407 0.162537i
\(56\) −84.9713 −0.202764
\(57\) −207.991 + 135.907i −0.483317 + 0.315813i
\(58\) −447.321 −1.01269
\(59\) 186.830 + 323.600i 0.412258 + 0.714052i 0.995136 0.0985074i \(-0.0314068\pi\)
−0.582878 + 0.812560i \(0.698073\pi\)
\(60\) −30.0000 51.9615i −0.0645497 0.111803i
\(61\) −28.0053 + 48.5066i −0.0587821 + 0.101814i −0.893919 0.448229i \(-0.852055\pi\)
0.835137 + 0.550042i \(0.185388\pi\)
\(62\) −32.5143 56.3165i −0.0666020 0.115358i
\(63\) 47.7964 82.7858i 0.0955838 0.165556i
\(64\) 64.0000 0.125000
\(65\) 230.000 0.438892
\(66\) −45.9321 + 79.5568i −0.0856645 + 0.148375i
\(67\) 372.757 645.634i 0.679695 1.17727i −0.295378 0.955380i \(-0.595446\pi\)
0.975073 0.221885i \(-0.0712210\pi\)
\(68\) 92.2715 0.164552
\(69\) −554.914 −0.968171
\(70\) −53.1071 + 91.9842i −0.0906787 + 0.157060i
\(71\) −530.491 918.837i −0.886728 1.53586i −0.843720 0.536783i \(-0.819639\pi\)
−0.0430079 0.999075i \(-0.513694\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) −426.186 738.175i −0.683305 1.18352i −0.973966 0.226693i \(-0.927209\pi\)
0.290662 0.956826i \(-0.406125\pi\)
\(74\) 310.621 + 538.012i 0.487960 + 0.845171i
\(75\) −75.0000 −0.115470
\(76\) −295.593 149.562i −0.446142 0.225737i
\(77\) 162.621 0.240681
\(78\) −138.000 239.023i −0.200326 0.346975i
\(79\) −479.569 830.638i −0.682984 1.18296i −0.974066 0.226265i \(-0.927348\pi\)
0.291081 0.956698i \(-0.405985\pi\)
\(80\) 40.0000 69.2820i 0.0559017 0.0968246i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −349.457 + 605.277i −0.470623 + 0.815143i
\(83\) 205.554 0.271837 0.135918 0.990720i \(-0.456602\pi\)
0.135918 + 0.990720i \(0.456602\pi\)
\(84\) 127.457 0.165556
\(85\) 57.6697 99.8868i 0.0735901 0.127462i
\(86\) −184.486 + 319.539i −0.231321 + 0.400660i
\(87\) 670.982 0.826860
\(88\) −122.486 −0.148375
\(89\) 183.112 317.160i 0.218088 0.377740i −0.736135 0.676835i \(-0.763351\pi\)
0.954224 + 0.299094i \(0.0966845\pi\)
\(90\) 45.0000 + 77.9423i 0.0527046 + 0.0912871i
\(91\) −244.293 + 423.127i −0.281416 + 0.487426i
\(92\) −369.943 640.760i −0.419230 0.726128i
\(93\) 48.7715 + 84.4747i 0.0543803 + 0.0941895i
\(94\) 449.593 0.493319
\(95\) −346.652 + 226.512i −0.374376 + 0.244628i
\(96\) −96.0000 −0.102062
\(97\) −193.825 335.715i −0.202886 0.351409i 0.746571 0.665306i \(-0.231699\pi\)
−0.949457 + 0.313897i \(0.898365\pi\)
\(98\) 230.186 + 398.693i 0.237268 + 0.410960i
\(99\) 68.8982 119.335i 0.0699447 0.121148i
\(100\) −50.0000 86.6025i −0.0500000 0.0866025i
\(101\) −855.230 + 1481.30i −0.842560 + 1.45936i 0.0451634 + 0.998980i \(0.485619\pi\)
−0.887723 + 0.460377i \(0.847714\pi\)
\(102\) −138.407 −0.134356
\(103\) −1188.31 −1.13678 −0.568388 0.822760i \(-0.692433\pi\)
−0.568388 + 0.822760i \(0.692433\pi\)
\(104\) 184.000 318.697i 0.173487 0.300489i
\(105\) 79.6606 137.976i 0.0740389 0.128239i
\(106\) −907.264 −0.831333
\(107\) 420.097 0.379554 0.189777 0.981827i \(-0.439224\pi\)
0.189777 + 0.981827i \(0.439224\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) 75.0822 + 130.046i 0.0659777 + 0.114277i 0.897127 0.441772i \(-0.145650\pi\)
−0.831150 + 0.556049i \(0.812317\pi\)
\(110\) −76.5535 + 132.595i −0.0663554 + 0.114931i
\(111\) −465.932 807.018i −0.398417 0.690079i
\(112\) 84.9713 + 147.175i 0.0716878 + 0.124167i
\(113\) −1330.25 −1.10743 −0.553716 0.832706i \(-0.686790\pi\)
−0.553716 + 0.832706i \(0.686790\pi\)
\(114\) 443.389 + 224.344i 0.364274 + 0.184313i
\(115\) −924.857 −0.749942
\(116\) 447.321 + 774.783i 0.358041 + 0.620145i
\(117\) 207.000 + 358.535i 0.163565 + 0.283304i
\(118\) 373.661 647.199i 0.291511 0.504911i
\(119\) 122.507 + 212.188i 0.0943712 + 0.163456i
\(120\) −60.0000 + 103.923i −0.0456435 + 0.0790569i
\(121\) −1096.58 −0.823878
\(122\) 112.021 0.0831304
\(123\) 524.186 907.916i 0.384262 0.665561i
\(124\) −65.0287 + 112.633i −0.0470947 + 0.0815705i
\(125\) −125.000 −0.0894427
\(126\) −191.186 −0.135176
\(127\) −36.2926 + 62.8606i −0.0253578 + 0.0439211i −0.878426 0.477879i \(-0.841406\pi\)
0.853068 + 0.521800i \(0.174739\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 276.729 479.308i 0.188873 0.327137i
\(130\) −230.000 398.372i −0.155172 0.268765i
\(131\) 631.650 + 1094.05i 0.421279 + 0.729676i 0.996065 0.0886274i \(-0.0282481\pi\)
−0.574786 + 0.818304i \(0.694915\pi\)
\(132\) 183.729 0.121148
\(133\) −48.5173 878.317i −0.0316315 0.572630i
\(134\) −1491.03 −0.961233
\(135\) −67.5000 116.913i −0.0430331 0.0745356i
\(136\) −92.2715 159.819i −0.0581781 0.100767i
\(137\) −1471.92 + 2549.45i −0.917919 + 1.58988i −0.115348 + 0.993325i \(0.536798\pi\)
−0.802571 + 0.596557i \(0.796535\pi\)
\(138\) 554.914 + 961.139i 0.342300 + 0.592881i
\(139\) 222.419 385.241i 0.135722 0.235077i −0.790151 0.612912i \(-0.789998\pi\)
0.925873 + 0.377835i \(0.123331\pi\)
\(140\) 212.428 0.128239
\(141\) −674.389 −0.402793
\(142\) −1060.98 + 1837.67i −0.627011 + 1.08602i
\(143\) −352.146 + 609.935i −0.205930 + 0.356681i
\(144\) 144.000 0.0833333
\(145\) 1118.30 0.640483
\(146\) −852.371 + 1476.35i −0.483169 + 0.836874i
\(147\) −345.278 598.039i −0.193728 0.335547i
\(148\) 621.243 1076.02i 0.345040 0.597626i
\(149\) 1449.67 + 2510.90i 0.797057 + 1.38054i 0.921525 + 0.388320i \(0.126944\pi\)
−0.124468 + 0.992224i \(0.539722\pi\)
\(150\) 75.0000 + 129.904i 0.0408248 + 0.0707107i
\(151\) −657.507 −0.354352 −0.177176 0.984179i \(-0.556696\pi\)
−0.177176 + 0.984179i \(0.556696\pi\)
\(152\) 36.5430 + 661.544i 0.0195002 + 0.353015i
\(153\) 207.611 0.109702
\(154\) −162.621 281.669i −0.0850936 0.147386i
\(155\) 81.2858 + 140.791i 0.0421228 + 0.0729588i
\(156\) −276.000 + 478.046i −0.141652 + 0.245348i
\(157\) −1666.02 2885.63i −0.846898 1.46687i −0.883963 0.467557i \(-0.845134\pi\)
0.0370650 0.999313i \(-0.488199\pi\)
\(158\) −959.139 + 1661.28i −0.482943 + 0.836482i
\(159\) 1360.90 0.678780
\(160\) −160.000 −0.0790569
\(161\) 982.329 1701.44i 0.480859 0.832873i
\(162\) −81.0000 + 140.296i −0.0392837 + 0.0680414i
\(163\) −1025.73 −0.492894 −0.246447 0.969156i \(-0.579263\pi\)
−0.246447 + 0.969156i \(0.579263\pi\)
\(164\) 1397.83 0.665561
\(165\) 114.830 198.892i 0.0541790 0.0938407i
\(166\) −205.554 356.029i −0.0961087 0.166465i
\(167\) −190.001 + 329.092i −0.0880405 + 0.152491i −0.906683 0.421813i \(-0.861394\pi\)
0.818642 + 0.574304i \(0.194727\pi\)
\(168\) −127.457 220.762i −0.0585329 0.101382i
\(169\) 40.5000 + 70.1481i 0.0184342 + 0.0319290i
\(170\) −230.679 −0.104072
\(171\) −665.084 336.516i −0.297428 0.150491i
\(172\) 737.943 0.327137
\(173\) −1673.55 2898.67i −0.735477 1.27388i −0.954514 0.298167i \(-0.903625\pi\)
0.219036 0.975717i \(-0.429709\pi\)
\(174\) −670.982 1162.17i −0.292339 0.506346i
\(175\) 132.768 229.960i 0.0573503 0.0993336i
\(176\) 122.486 + 212.151i 0.0524585 + 0.0908609i
\(177\) −560.491 + 970.799i −0.238017 + 0.412258i
\(178\) −732.449 −0.308424
\(179\) 3767.07 1.57298 0.786491 0.617602i \(-0.211896\pi\)
0.786491 + 0.617602i \(0.211896\pi\)
\(180\) 90.0000 155.885i 0.0372678 0.0645497i
\(181\) 547.534 948.357i 0.224850 0.389452i −0.731424 0.681923i \(-0.761144\pi\)
0.956274 + 0.292471i \(0.0944774\pi\)
\(182\) 977.170 0.397982
\(183\) −168.032 −0.0678757
\(184\) −739.885 + 1281.52i −0.296441 + 0.513450i
\(185\) −776.554 1345.03i −0.308613 0.534533i
\(186\) 97.5430 168.949i 0.0384527 0.0666020i
\(187\) 176.593 + 305.868i 0.0690574 + 0.119611i
\(188\) −449.593 778.717i −0.174414 0.302095i
\(189\) 286.778 0.110371
\(190\) 738.982 + 373.906i 0.282165 + 0.142768i
\(191\) 3205.14 1.21422 0.607110 0.794618i \(-0.292329\pi\)
0.607110 + 0.794618i \(0.292329\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) 244.026 + 422.665i 0.0910122 + 0.157638i 0.907937 0.419106i \(-0.137656\pi\)
−0.816925 + 0.576744i \(0.804323\pi\)
\(194\) −387.650 + 671.430i −0.143462 + 0.248484i
\(195\) 345.000 + 597.558i 0.126697 + 0.219446i
\(196\) 460.371 797.386i 0.167774 0.290593i
\(197\) 2660.90 0.962342 0.481171 0.876627i \(-0.340212\pi\)
0.481171 + 0.876627i \(0.340212\pi\)
\(198\) −275.593 −0.0989168
\(199\) −1989.51 + 3445.94i −0.708707 + 1.22752i 0.256629 + 0.966510i \(0.417388\pi\)
−0.965337 + 0.261007i \(0.915945\pi\)
\(200\) −100.000 + 173.205i −0.0353553 + 0.0612372i
\(201\) 2236.54 0.784844
\(202\) 3420.92 1.19156
\(203\) −1187.80 + 2057.32i −0.410675 + 0.711309i
\(204\) 138.407 + 239.728i 0.0475022 + 0.0822762i
\(205\) 873.643 1513.19i 0.297648 0.515541i
\(206\) 1188.31 + 2058.22i 0.401911 + 0.696131i
\(207\) −832.371 1441.71i −0.279487 0.484085i
\(208\) −736.000 −0.245348
\(209\) −69.9374 1266.09i −0.0231468 0.419030i
\(210\) −318.643 −0.104707
\(211\) 47.2361 + 81.8153i 0.0154117 + 0.0266938i 0.873628 0.486594i \(-0.161761\pi\)
−0.858217 + 0.513288i \(0.828427\pi\)
\(212\) 907.264 + 1571.43i 0.293920 + 0.509085i
\(213\) 1591.47 2756.51i 0.511953 0.886728i
\(214\) −420.097 727.629i −0.134193 0.232428i
\(215\) 461.214 798.846i 0.146300 0.253399i
\(216\) −216.000 −0.0680414
\(217\) −345.348 −0.108036
\(218\) 150.164 260.092i 0.0466533 0.0808059i
\(219\) 1278.56 2214.52i 0.394506 0.683305i
\(220\) 306.214 0.0938407
\(221\) −1061.12 −0.322981
\(222\) −931.864 + 1614.04i −0.281724 + 0.487960i
\(223\) −1830.43 3170.40i −0.549663 0.952043i −0.998297 0.0583283i \(-0.981423\pi\)
0.448635 0.893715i \(-0.351910\pi\)
\(224\) 169.943 294.349i 0.0506909 0.0877993i
\(225\) −112.500 194.856i −0.0333333 0.0577350i
\(226\) 1330.25 + 2304.07i 0.391536 + 0.678160i
\(227\) −764.637 −0.223571 −0.111786 0.993732i \(-0.535657\pi\)
−0.111786 + 0.993732i \(0.535657\pi\)
\(228\) −54.8145 992.316i −0.0159218 0.288236i
\(229\) 129.350 0.0373261 0.0186631 0.999826i \(-0.494059\pi\)
0.0186631 + 0.999826i \(0.494059\pi\)
\(230\) 924.857 + 1601.90i 0.265145 + 0.459244i
\(231\) 243.932 + 422.503i 0.0694786 + 0.120340i
\(232\) 894.643 1549.57i 0.253173 0.438509i
\(233\) 3017.94 + 5227.22i 0.848548 + 1.46973i 0.882504 + 0.470306i \(0.155856\pi\)
−0.0339551 + 0.999423i \(0.510810\pi\)
\(234\) 414.000 717.069i 0.115658 0.200326i
\(235\) −1123.98 −0.312002
\(236\) −1494.64 −0.412258
\(237\) 1438.71 2491.92i 0.394321 0.682984i
\(238\) 245.014 424.376i 0.0667305 0.115581i
\(239\) −152.798 −0.0413543 −0.0206772 0.999786i \(-0.506582\pi\)
−0.0206772 + 0.999786i \(0.506582\pi\)
\(240\) 240.000 0.0645497
\(241\) 489.253 847.410i 0.130770 0.226500i −0.793204 0.608956i \(-0.791588\pi\)
0.923974 + 0.382456i \(0.124922\pi\)
\(242\) 1096.58 + 1899.34i 0.291285 + 0.504520i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) −112.021 194.026i −0.0293910 0.0509068i
\(245\) −575.464 996.732i −0.150061 0.259914i
\(246\) −2096.74 −0.543428
\(247\) 3399.32 + 1719.97i 0.875682 + 0.443073i
\(248\) 260.115 0.0666020
\(249\) 308.330 + 534.044i 0.0784724 + 0.135918i
\(250\) 125.000 + 216.506i 0.0316228 + 0.0547723i
\(251\) 202.269 350.341i 0.0508650 0.0881008i −0.839472 0.543403i \(-0.817136\pi\)
0.890337 + 0.455302i \(0.150469\pi\)
\(252\) 191.186 + 331.143i 0.0477919 + 0.0827780i
\(253\) 1416.02 2452.62i 0.351875 0.609466i
\(254\) 145.170 0.0358614
\(255\) 346.018 0.0849745
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1026.58 1778.08i 0.249168 0.431571i −0.714127 0.700016i \(-0.753176\pi\)
0.963295 + 0.268444i \(0.0865096\pi\)
\(258\) −1106.91 −0.267106
\(259\) 3299.24 0.791524
\(260\) −460.000 + 796.743i −0.109723 + 0.190046i
\(261\) 1006.47 + 1743.26i 0.238694 + 0.413430i
\(262\) 1263.30 2188.10i 0.297889 0.515959i
\(263\) −3580.83 6202.17i −0.839556 1.45415i −0.890266 0.455440i \(-0.849482\pi\)
0.0507104 0.998713i \(-0.483851\pi\)
\(264\) −183.729 318.227i −0.0428322 0.0741876i
\(265\) 2268.16 0.525781
\(266\) −1472.77 + 962.351i −0.339479 + 0.221825i
\(267\) 1098.67 0.251827
\(268\) 1491.03 + 2582.54i 0.339847 + 0.588633i
\(269\) 2092.42 + 3624.18i 0.474264 + 0.821450i 0.999566 0.0294663i \(-0.00938077\pi\)
−0.525301 + 0.850916i \(0.676047\pi\)
\(270\) −135.000 + 233.827i −0.0304290 + 0.0527046i
\(271\) 1045.44 + 1810.76i 0.234340 + 0.405889i 0.959081 0.283133i \(-0.0913738\pi\)
−0.724741 + 0.689022i \(0.758040\pi\)
\(272\) −184.543 + 319.638i −0.0411381 + 0.0712533i
\(273\) −1465.76 −0.324951
\(274\) 5887.69 1.29813
\(275\) 191.384 331.487i 0.0419668 0.0726887i
\(276\) 1109.83 1922.28i 0.242043 0.419230i
\(277\) −4134.14 −0.896738 −0.448369 0.893848i \(-0.647995\pi\)
−0.448369 + 0.893848i \(0.647995\pi\)
\(278\) −889.677 −0.191940
\(279\) −146.314 + 253.424i −0.0313965 + 0.0543803i
\(280\) −212.428 367.937i −0.0453394 0.0785301i
\(281\) −3613.84 + 6259.36i −0.767202 + 1.32883i 0.171873 + 0.985119i \(0.445018\pi\)
−0.939075 + 0.343713i \(0.888315\pi\)
\(282\) 674.389 + 1168.08i 0.142409 + 0.246659i
\(283\) 873.157 + 1512.35i 0.183406 + 0.317668i 0.943038 0.332685i \(-0.107955\pi\)
−0.759632 + 0.650353i \(0.774621\pi\)
\(284\) 4243.93 0.886728
\(285\) −1108.47 560.859i −0.230387 0.116570i
\(286\) 1408.59 0.291229
\(287\) 1855.86 + 3214.45i 0.381701 + 0.661126i
\(288\) −144.000 249.415i −0.0294628 0.0510310i
\(289\) 2190.44 3793.95i 0.445845 0.772226i
\(290\) −1118.30 1936.96i −0.226445 0.392214i
\(291\) 581.475 1007.14i 0.117136 0.202886i
\(292\) 3409.48 0.683305
\(293\) 7339.98 1.46350 0.731751 0.681572i \(-0.238703\pi\)
0.731751 + 0.681572i \(0.238703\pi\)
\(294\) −690.557 + 1196.08i −0.136987 + 0.237268i
\(295\) −934.152 + 1618.00i −0.184367 + 0.319334i
\(296\) −2484.97 −0.487960
\(297\) 413.389 0.0807652
\(298\) 2899.34 5021.80i 0.563604 0.976192i
\(299\) 4254.34 + 7368.73i 0.822859 + 1.42523i
\(300\) 150.000 259.808i 0.0288675 0.0500000i
\(301\) 979.750 + 1696.98i 0.187614 + 0.324957i
\(302\) 657.507 + 1138.84i 0.125282 + 0.216995i
\(303\) −5131.38 −0.972905
\(304\) 1109.29 724.838i 0.209282 0.136751i
\(305\) −280.053 −0.0525763
\(306\) −207.611 359.593i −0.0387854 0.0671782i
\(307\) −1290.96 2236.00i −0.239996 0.415685i 0.720717 0.693230i \(-0.243813\pi\)
−0.960713 + 0.277544i \(0.910479\pi\)
\(308\) −325.243 + 563.337i −0.0601702 + 0.104218i
\(309\) −1782.47 3087.33i −0.328159 0.568388i
\(310\) 162.572 281.582i 0.0297853 0.0515897i
\(311\) 4316.72 0.787069 0.393535 0.919310i \(-0.371252\pi\)
0.393535 + 0.919310i \(0.371252\pi\)
\(312\) 1104.00 0.200326
\(313\) 3843.35 6656.87i 0.694054 1.20214i −0.276445 0.961030i \(-0.589156\pi\)
0.970499 0.241107i \(-0.0775104\pi\)
\(314\) −3332.04 + 5771.27i −0.598847 + 1.03723i
\(315\) 477.964 0.0854927
\(316\) 3836.55 0.682984
\(317\) 1037.79 1797.51i 0.183874 0.318480i −0.759322 0.650715i \(-0.774469\pi\)
0.943197 + 0.332235i \(0.107803\pi\)
\(318\) −1360.90 2357.14i −0.239985 0.415666i
\(319\) −1712.20 + 2965.62i −0.300517 + 0.520510i
\(320\) 160.000 + 277.128i 0.0279508 + 0.0484123i
\(321\) 630.145 + 1091.44i 0.109568 + 0.189777i
\(322\) −3929.32 −0.680038
\(323\) 1599.30 1045.03i 0.275503 0.180022i
\(324\) 324.000 0.0555556
\(325\) 575.000 + 995.929i 0.0981393 + 0.169982i
\(326\) 1025.73 + 1776.62i 0.174264 + 0.301835i
\(327\) −225.247 + 390.139i −0.0380923 + 0.0659777i
\(328\) −1397.83 2421.11i −0.235311 0.407571i
\(329\) 1193.83 2067.77i 0.200054 0.346504i
\(330\) −459.321 −0.0766206
\(331\) 7966.70 1.32293 0.661464 0.749977i \(-0.269935\pi\)
0.661464 + 0.749977i \(0.269935\pi\)
\(332\) −411.107 + 712.058i −0.0679591 + 0.117709i
\(333\) 1397.80 2421.05i 0.230026 0.398417i
\(334\) 760.006 0.124508
\(335\) 3727.57 0.607937
\(336\) −254.914 + 441.524i −0.0413890 + 0.0716878i
\(337\) 2997.33 + 5191.52i 0.484495 + 0.839170i 0.999841 0.0178120i \(-0.00567005\pi\)
−0.515346 + 0.856982i \(0.672337\pi\)
\(338\) 81.0000 140.296i 0.0130350 0.0225772i
\(339\) −1995.38 3456.10i −0.319688 0.553716i
\(340\) 230.679 + 399.547i 0.0367950 + 0.0637309i
\(341\) −497.817 −0.0790567
\(342\) 82.2217 + 1488.47i 0.0130001 + 0.235343i
\(343\) 6088.04 0.958377
\(344\) −737.943 1278.15i −0.115660 0.200330i
\(345\) −1387.29 2402.85i −0.216490 0.374971i
\(346\) −3347.10 + 5797.34i −0.520061 + 0.900772i
\(347\) 3540.58 + 6132.47i 0.547748 + 0.948727i 0.998428 + 0.0560418i \(0.0178480\pi\)
−0.450681 + 0.892685i \(0.648819\pi\)
\(348\) −1341.96 + 2324.35i −0.206715 + 0.358041i
\(349\) −4512.75 −0.692155 −0.346077 0.938206i \(-0.612487\pi\)
−0.346077 + 0.938206i \(0.612487\pi\)
\(350\) −531.071 −0.0811055
\(351\) −621.000 + 1075.60i −0.0944346 + 0.163565i
\(352\) 244.971 424.303i 0.0370938 0.0642483i
\(353\) −10645.4 −1.60509 −0.802547 0.596589i \(-0.796522\pi\)
−0.802547 + 0.596589i \(0.796522\pi\)
\(354\) 2241.96 0.336607
\(355\) 2652.45 4594.19i 0.396557 0.686857i
\(356\) 732.449 + 1268.64i 0.109044 + 0.188870i
\(357\) −367.520 + 636.564i −0.0544853 + 0.0943712i
\(358\) −3767.07 6524.75i −0.556133 0.963251i
\(359\) 4885.42 + 8461.80i 0.718225 + 1.24400i 0.961702 + 0.274096i \(0.0883785\pi\)
−0.243477 + 0.969907i \(0.578288\pi\)
\(360\) −360.000 −0.0527046
\(361\) −6817.27 + 755.463i −0.993916 + 0.110142i
\(362\) −2190.14 −0.317986
\(363\) −1644.87 2849.00i −0.237833 0.411939i
\(364\) −977.170 1692.51i −0.140708 0.243713i
\(365\) 2130.93 3690.87i 0.305583 0.529286i
\(366\) 168.032 + 291.039i 0.0239977 + 0.0415652i
\(367\) −6479.57 + 11223.0i −0.921610 + 1.59628i −0.124687 + 0.992196i \(0.539793\pi\)
−0.796924 + 0.604080i \(0.793541\pi\)
\(368\) 2959.54 0.419230
\(369\) 3145.11 0.443707
\(370\) −1553.11 + 2690.06i −0.218222 + 0.377972i
\(371\) −2409.11 + 4172.70i −0.337128 + 0.583923i
\(372\) −390.172 −0.0543803
\(373\) −14363.2 −1.99382 −0.996912 0.0785331i \(-0.974976\pi\)
−0.996912 + 0.0785331i \(0.974976\pi\)
\(374\) 353.186 611.735i 0.0488310 0.0845777i
\(375\) −187.500 324.760i −0.0258199 0.0447214i
\(376\) −899.186 + 1557.43i −0.123330 + 0.213613i
\(377\) −5144.19 8910.01i −0.702757 1.21721i
\(378\) −286.778 496.715i −0.0390219 0.0675879i
\(379\) −10480.5 −1.42044 −0.710219 0.703981i \(-0.751404\pi\)
−0.710219 + 0.703981i \(0.751404\pi\)
\(380\) −91.3575 1653.86i −0.0123330 0.223266i
\(381\) −217.756 −0.0292807
\(382\) −3205.14 5551.47i −0.429292 0.743555i
\(383\) −5150.94 8921.69i −0.687208 1.19028i −0.972737 0.231909i \(-0.925503\pi\)
0.285529 0.958370i \(-0.407831\pi\)
\(384\) 192.000 332.554i 0.0255155 0.0441942i
\(385\) 406.554 + 704.171i 0.0538179 + 0.0932153i
\(386\) 488.051 845.330i 0.0643553 0.111467i
\(387\) 1660.37 0.218091
\(388\) 1550.60 0.202886
\(389\) −5437.82 + 9418.59i −0.708763 + 1.22761i 0.256554 + 0.966530i \(0.417413\pi\)
−0.965316 + 0.261083i \(0.915920\pi\)
\(390\) 690.000 1195.12i 0.0895885 0.155172i
\(391\) 4266.90 0.551883
\(392\) −1841.48 −0.237268
\(393\) −1894.95 + 3282.15i −0.243225 + 0.421279i
\(394\) −2660.90 4608.82i −0.340239 0.589312i
\(395\) 2397.85 4153.19i 0.305440 0.529037i
\(396\) 275.593 + 477.341i 0.0349724 + 0.0605739i
\(397\) 2102.24 + 3641.19i 0.265765 + 0.460318i 0.967764 0.251860i \(-0.0810422\pi\)
−0.701999 + 0.712178i \(0.747709\pi\)
\(398\) 7958.05 1.00226
\(399\) 2209.16 1443.53i 0.277184 0.181120i
\(400\) 400.000 0.0500000
\(401\) 1642.91 + 2845.61i 0.204596 + 0.354371i 0.950004 0.312238i \(-0.101079\pi\)
−0.745408 + 0.666609i \(0.767745\pi\)
\(402\) −2236.54 3873.81i −0.277484 0.480617i
\(403\) 747.830 1295.28i 0.0924368 0.160105i
\(404\) −3420.92 5925.21i −0.421280 0.729678i
\(405\) 202.500 350.740i 0.0248452 0.0430331i
\(406\) 4751.19 0.580782
\(407\) 4755.83 0.579209
\(408\) 276.814 479.457i 0.0335891 0.0581781i
\(409\) −5544.05 + 9602.57i −0.670258 + 1.16092i 0.307573 + 0.951525i \(0.400483\pi\)
−0.977831 + 0.209397i \(0.932850\pi\)
\(410\) −3494.57 −0.420938
\(411\) −8831.54 −1.05992
\(412\) 2376.63 4116.44i 0.284194 0.492239i
\(413\) −1984.40 3437.09i −0.236431 0.409511i
\(414\) −1664.74 + 2883.42i −0.197627 + 0.342300i
\(415\) 513.884 + 890.073i 0.0607845 + 0.105282i
\(416\) 736.000 + 1274.79i 0.0867437 + 0.150244i
\(417\) 1334.52 0.156718
\(418\) −2122.99 + 1387.22i −0.248419 + 0.162324i
\(419\) −12894.4 −1.50342 −0.751710 0.659493i \(-0.770771\pi\)
−0.751710 + 0.659493i \(0.770771\pi\)
\(420\) 318.643 + 551.905i 0.0370194 + 0.0641195i
\(421\) 3437.72 + 5954.31i 0.397967 + 0.689300i 0.993475 0.114050i \(-0.0363824\pi\)
−0.595508 + 0.803350i \(0.703049\pi\)
\(422\) 94.4722 163.631i 0.0108977 0.0188754i
\(423\) −1011.58 1752.11i −0.116276 0.201396i
\(424\) 1814.53 3142.85i 0.207833 0.359978i
\(425\) 576.697 0.0658210
\(426\) −6365.89 −0.724010
\(427\) 297.456 515.208i 0.0337117 0.0583903i
\(428\) −840.193 + 1455.26i −0.0948885 + 0.164352i
\(429\) −2112.88 −0.237787
\(430\) −1844.86 −0.206900
\(431\) −1787.80 + 3096.57i −0.199804 + 0.346070i −0.948465 0.316883i \(-0.897364\pi\)
0.748661 + 0.662953i \(0.230697\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) 7770.29 13458.5i 0.862393 1.49371i −0.00722013 0.999974i \(-0.502298\pi\)
0.869613 0.493734i \(-0.164368\pi\)
\(434\) 345.348 + 598.161i 0.0381964 + 0.0661581i
\(435\) 1677.45 + 2905.44i 0.184891 + 0.320241i
\(436\) −600.658 −0.0659777
\(437\) −13669.0 6916.19i −1.49629 0.757085i
\(438\) −5114.23 −0.557916
\(439\) 3659.96 + 6339.24i 0.397905 + 0.689192i 0.993467 0.114117i \(-0.0364039\pi\)
−0.595562 + 0.803309i \(0.703071\pi\)
\(440\) −306.214 530.378i −0.0331777 0.0574655i
\(441\) 1035.83 1794.12i 0.111849 0.193728i
\(442\) 1061.12 + 1837.92i 0.114191 + 0.197785i
\(443\) −3893.68 + 6744.06i −0.417595 + 0.723295i −0.995697 0.0926690i \(-0.970460\pi\)
0.578102 + 0.815964i \(0.303793\pi\)
\(444\) 3727.46 0.398417
\(445\) 1831.12 0.195064
\(446\) −3660.86 + 6340.80i −0.388670 + 0.673196i
\(447\) −4349.01 + 7532.70i −0.460181 + 0.797057i
\(448\) −679.771 −0.0716878
\(449\) −776.496 −0.0816150 −0.0408075 0.999167i \(-0.512993\pi\)
−0.0408075 + 0.999167i \(0.512993\pi\)
\(450\) −225.000 + 389.711i −0.0235702 + 0.0408248i
\(451\) 2675.22 + 4633.61i 0.279315 + 0.483788i
\(452\) 2660.51 4608.13i 0.276858 0.479532i
\(453\) −986.260 1708.25i −0.102293 0.177176i
\(454\) 764.637 + 1324.39i 0.0790444 + 0.136909i
\(455\) −2442.93 −0.251706
\(456\) −1663.93 + 1087.26i −0.170878 + 0.111657i
\(457\) −6523.64 −0.667753 −0.333877 0.942617i \(-0.608357\pi\)
−0.333877 + 0.942617i \(0.608357\pi\)
\(458\) −129.350 224.041i −0.0131968 0.0228575i
\(459\) 311.416 + 539.389i 0.0316681 + 0.0548508i
\(460\) 1849.71 3203.80i 0.187485 0.324734i
\(461\) 1521.17 + 2634.74i 0.153683 + 0.266186i 0.932579 0.360967i \(-0.117553\pi\)
−0.778896 + 0.627153i \(0.784220\pi\)
\(462\) 487.864 845.006i 0.0491288 0.0850936i
\(463\) 1757.80 0.176440 0.0882199 0.996101i \(-0.471882\pi\)
0.0882199 + 0.996101i \(0.471882\pi\)
\(464\) −3578.57 −0.358041
\(465\) −243.857 + 422.374i −0.0243196 + 0.0421228i
\(466\) 6035.88 10454.4i 0.600014 1.03926i
\(467\) −13004.4 −1.28860 −0.644298 0.764775i \(-0.722850\pi\)
−0.644298 + 0.764775i \(0.722850\pi\)
\(468\) −1656.00 −0.163565
\(469\) −3959.21 + 6857.55i −0.389807 + 0.675165i
\(470\) 1123.98 + 1946.79i 0.110309 + 0.191061i
\(471\) 4998.06 8656.90i 0.488957 0.846898i
\(472\) 1494.64 + 2588.80i 0.145755 + 0.252456i
\(473\) 1412.30 + 2446.18i 0.137289 + 0.237792i
\(474\) −5754.83 −0.557654
\(475\) −1847.45 934.765i −0.178457 0.0902947i
\(476\) −980.054 −0.0943712
\(477\) 2041.34 + 3535.71i 0.195947 + 0.339390i
\(478\) 152.798 + 264.654i 0.0146210 + 0.0253242i
\(479\) −392.767 + 680.292i −0.0374655 + 0.0648921i −0.884150 0.467203i \(-0.845262\pi\)
0.846685 + 0.532095i \(0.178595\pi\)
\(480\) −240.000 415.692i −0.0228218 0.0395285i
\(481\) −7144.29 + 12374.3i −0.677238 + 1.17301i
\(482\) −1957.01 −0.184936
\(483\) 5893.97 0.555249
\(484\) 2193.16 3798.67i 0.205970 0.356750i
\(485\) 969.125 1678.57i 0.0907334 0.157155i
\(486\) −486.000 −0.0453609
\(487\) −9976.36 −0.928279 −0.464140 0.885762i \(-0.653636\pi\)
−0.464140 + 0.885762i \(0.653636\pi\)
\(488\) −224.042 + 388.052i −0.0207826 + 0.0359965i
\(489\) −1538.60 2664.94i −0.142286 0.246447i
\(490\) −1150.93 + 1993.46i −0.106109 + 0.183787i
\(491\) 3883.37 + 6726.20i 0.356933 + 0.618226i 0.987447 0.157952i \(-0.0504891\pi\)
−0.630514 + 0.776178i \(0.717156\pi\)
\(492\) 2096.74 + 3631.66i 0.192131 + 0.332781i
\(493\) −5159.38 −0.471332
\(494\) −420.244 7607.76i −0.0382747 0.692893i
\(495\) 688.982 0.0625605
\(496\) −260.115 450.532i −0.0235474 0.0407852i
\(497\) 5634.57 + 9759.35i 0.508541 + 0.880819i
\(498\) 616.661 1068.09i 0.0554884 0.0961087i
\(499\) −792.483 1372.62i −0.0710950 0.123140i 0.828286 0.560305i \(-0.189316\pi\)
−0.899381 + 0.437165i \(0.855983\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) −1140.01 −0.101660
\(502\) −809.077 −0.0719340
\(503\) 8933.70 15473.6i 0.791917 1.37164i −0.132862 0.991135i \(-0.542417\pi\)
0.924779 0.380505i \(-0.124250\pi\)
\(504\) 382.371 662.286i 0.0337940 0.0585329i
\(505\) −8552.30 −0.753609
\(506\) −5664.08 −0.497627
\(507\) −121.500 + 210.444i −0.0106430 + 0.0184342i
\(508\) −145.170 251.442i −0.0126789 0.0219605i
\(509\) 4681.88 8109.26i 0.407703 0.706162i −0.586929 0.809638i \(-0.699663\pi\)
0.994632 + 0.103476i \(0.0329965\pi\)
\(510\) −346.018 599.321i −0.0300430 0.0520360i
\(511\) 4526.69 + 7840.46i 0.391877 + 0.678751i
\(512\) 512.000 0.0441942
\(513\) −123.333 2232.71i −0.0106146 0.192157i
\(514\) −4106.31 −0.352377
\(515\) −2970.78 5145.55i −0.254191 0.440272i
\(516\) 1106.91 + 1917.23i 0.0944364 + 0.163569i
\(517\) 1720.90 2980.68i 0.146392 0.253559i
\(518\) −3299.24 5714.45i −0.279846 0.484708i
\(519\) 5020.65 8696.02i 0.424628 0.735477i
\(520\) 1840.00 0.155172
\(521\) 5584.76 0.469622 0.234811 0.972041i \(-0.424553\pi\)
0.234811 + 0.972041i \(0.424553\pi\)
\(522\) 2012.95 3486.52i 0.168782 0.292339i
\(523\) 6001.85 10395.5i 0.501802 0.869147i −0.498196 0.867065i \(-0.666004\pi\)
0.999998 0.00208206i \(-0.000662742\pi\)
\(524\) −5053.20 −0.421279
\(525\) 796.606 0.0662224
\(526\) −7161.65 + 12404.3i −0.593656 + 1.02824i
\(527\) −375.018 649.551i −0.0309982 0.0536905i
\(528\) −367.457 + 636.454i −0.0302870 + 0.0524585i
\(529\) −11023.7 19093.6i −0.906032 1.56929i
\(530\) −2268.16 3928.57i −0.185892 0.321974i
\(531\) −3362.95 −0.274839
\(532\) 3139.61 + 1588.57i 0.255864 + 0.129461i
\(533\) −16075.0 −1.30635
\(534\) −1098.67 1902.96i −0.0890342 0.154212i
\(535\) 1050.24 + 1819.07i 0.0848708 + 0.147001i
\(536\) 2982.06 5165.07i 0.240308 0.416226i
\(537\) 5650.60 + 9787.13i 0.454081 + 0.786491i
\(538\) 4184.84 7248.36i 0.335356 0.580853i
\(539\) 3524.30 0.281637
\(540\) 540.000 0.0430331
\(541\) 2710.73 4695.12i 0.215422 0.373122i −0.737981 0.674822i \(-0.764221\pi\)
0.953403 + 0.301700i \(0.0975539\pi\)
\(542\) 2090.89 3621.52i 0.165703 0.287007i
\(543\) 3285.20 0.259635
\(544\) 738.172 0.0581781
\(545\) −375.411 + 650.231i −0.0295061 + 0.0511061i
\(546\) 1465.76 + 2538.76i 0.114887 + 0.198991i
\(547\) −5570.90 + 9649.07i −0.435456 + 0.754232i −0.997333 0.0729893i \(-0.976746\pi\)
0.561877 + 0.827221i \(0.310079\pi\)
\(548\) −5887.69 10197.8i −0.458959 0.794941i
\(549\) −252.047 436.559i −0.0195940 0.0339379i
\(550\) −765.535 −0.0593501
\(551\) 16528.1 + 8362.81i 1.27790 + 0.646584i
\(552\) −4439.31 −0.342300
\(553\) 5093.71 + 8822.56i 0.391693 + 0.678433i
\(554\) 4134.14 + 7160.54i 0.317045 + 0.549138i
\(555\) 2329.66 4035.09i 0.178178 0.308613i
\(556\) 889.677 + 1540.97i 0.0678610 + 0.117539i
\(557\) 12598.9 21821.8i 0.958403 1.66000i 0.232022 0.972711i \(-0.425466\pi\)
0.726381 0.687292i \(-0.241201\pi\)
\(558\) 585.258 0.0444013
\(559\) −8486.34 −0.642100
\(560\) −424.857 + 735.873i −0.0320598 + 0.0555292i
\(561\) −529.778 + 917.603i −0.0398703 + 0.0690574i
\(562\) 14455.4 1.08499
\(563\) 15936.1 1.19294 0.596469 0.802636i \(-0.296570\pi\)
0.596469 + 0.802636i \(0.296570\pi\)
\(564\) 1348.78 2336.15i 0.100698 0.174414i
\(565\) −3325.63 5760.17i −0.247629 0.428906i
\(566\) 1746.31 3024.70i 0.129687 0.224625i
\(567\) 430.167 + 745.072i 0.0318613 + 0.0551853i
\(568\) −4243.93 7350.70i −0.313506 0.543008i
\(569\) 4063.59 0.299393 0.149696 0.988732i \(-0.452170\pi\)
0.149696 + 0.988732i \(0.452170\pi\)
\(570\) 137.036 + 2480.79i 0.0100699 + 0.182296i
\(571\) 24372.4 1.78626 0.893128 0.449802i \(-0.148506\pi\)
0.893128 + 0.449802i \(0.148506\pi\)
\(572\) −1408.59 2439.74i −0.102965 0.178340i
\(573\) 4807.72 + 8327.21i 0.350515 + 0.607110i
\(574\) 3711.73 6428.90i 0.269903 0.467486i
\(575\) −2312.14 4004.75i −0.167692 0.290451i
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) −13799.9 −0.995666 −0.497833 0.867273i \(-0.665871\pi\)
−0.497833 + 0.867273i \(0.665871\pi\)
\(578\) −8761.75 −0.630520
\(579\) −732.077 + 1267.99i −0.0525459 + 0.0910122i
\(580\) −2236.61 + 3873.92i −0.160121 + 0.277337i
\(581\) −2183.27 −0.155899
\(582\) −2325.90 −0.165656
\(583\) −3472.71 + 6014.92i −0.246698 + 0.427294i
\(584\) −3409.48 5905.40i −0.241585 0.418437i
\(585\) −1035.00 + 1792.67i −0.0731487 + 0.126697i
\(586\) −7339.98 12713.2i −0.517426 0.896209i
\(587\) −4780.10 8279.38i −0.336109 0.582158i 0.647588 0.761990i \(-0.275778\pi\)
−0.983697 + 0.179833i \(0.942444\pi\)
\(588\) 2762.23 0.193728
\(589\) 148.521 + 2688.71i 0.0103900 + 0.188092i
\(590\) 3736.61 0.260735
\(591\) 3991.35 + 6913.23i 0.277804 + 0.481171i
\(592\) 2484.97 + 4304.10i 0.172520 + 0.298813i
\(593\) −2507.89 + 4343.79i −0.173670 + 0.300806i −0.939700 0.341999i \(-0.888896\pi\)
0.766030 + 0.642805i \(0.222229\pi\)
\(594\) −413.389 716.011i −0.0285548 0.0494584i
\(595\) −612.534 + 1060.94i −0.0422041 + 0.0730996i
\(596\) −11597.4 −0.797057
\(597\) −11937.1 −0.818345
\(598\) 8508.68 14737.5i 0.581849 1.00779i
\(599\) −1787.45 + 3095.96i −0.121926 + 0.211181i −0.920527 0.390679i \(-0.872240\pi\)
0.798601 + 0.601860i \(0.205574\pi\)
\(600\) −600.000 −0.0408248
\(601\) −9909.94 −0.672604 −0.336302 0.941754i \(-0.609176\pi\)
−0.336302 + 0.941754i \(0.609176\pi\)
\(602\) 1959.50 3393.95i 0.132663 0.229779i
\(603\) 3354.81 + 5810.71i 0.226565 + 0.392422i
\(604\) 1315.01 2277.67i 0.0885880 0.153439i
\(605\) −2741.46 4748.34i −0.184225 0.319087i
\(606\) 5131.38 + 8887.81i 0.343974 + 0.595780i
\(607\) −1869.77 −0.125027 −0.0625137 0.998044i \(-0.519912\pi\)
−0.0625137 + 0.998044i \(0.519912\pi\)
\(608\) −2364.74 1196.50i −0.157735 0.0798100i
\(609\) −7126.78 −0.474206
\(610\) 280.053 + 485.066i 0.0185885 + 0.0321963i
\(611\) 5170.32 + 8955.25i 0.342338 + 0.592947i
\(612\) −415.222 + 719.185i −0.0274254 + 0.0475022i
\(613\) 3111.20 + 5388.76i 0.204992 + 0.355057i 0.950130 0.311853i \(-0.100950\pi\)
−0.745138 + 0.666910i \(0.767616\pi\)
\(614\) −2581.91 + 4472.00i −0.169703 + 0.293934i
\(615\) 5241.86 0.343694
\(616\) 1300.97 0.0850936
\(617\) −13885.4 + 24050.1i −0.906003 + 1.56924i −0.0864367 + 0.996257i \(0.527548\pi\)
−0.819566 + 0.572985i \(0.805785\pi\)
\(618\) −3564.94 + 6174.66i −0.232044 + 0.401911i
\(619\) −9564.99 −0.621081 −0.310541 0.950560i \(-0.600510\pi\)
−0.310541 + 0.950560i \(0.600510\pi\)
\(620\) −650.287 −0.0421228
\(621\) 2497.11 4325.13i 0.161362 0.279487i
\(622\) −4316.72 7476.77i −0.278271 0.481980i
\(623\) −1944.91 + 3368.69i −0.125074 + 0.216635i
\(624\) −1104.00 1912.18i −0.0708259 0.122674i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −15373.4 −0.981541
\(627\) 3184.49 2080.84i 0.202833 0.132537i
\(628\) 13328.2 0.846898
\(629\) 3582.69 + 6205.40i 0.227108 + 0.393363i
\(630\) −477.964 827.858i −0.0302262 0.0523534i
\(631\) 9094.53 15752.2i 0.573768 0.993795i −0.422407 0.906406i \(-0.638815\pi\)
0.996174 0.0873883i \(-0.0278521\pi\)
\(632\) −3836.55 6645.11i −0.241471 0.418241i
\(633\) −141.708 + 245.446i −0.00889794 + 0.0154117i
\(634\) −4151.17 −0.260038
\(635\) −362.926 −0.0226807
\(636\) −2721.79 + 4714.28i −0.169695 + 0.293920i
\(637\) −5294.27 + 9169.94i −0.329304 + 0.570371i
\(638\) 6848.81 0.424995
\(639\) 9548.84 0.591152
\(640\) 320.000 554.256i 0.0197642 0.0342327i
\(641\) −358.517 620.969i −0.0220914 0.0382633i 0.854768 0.519010i \(-0.173699\pi\)
−0.876860 + 0.480746i \(0.840366\pi\)
\(642\) 1260.29 2182.89i 0.0774761 0.134193i
\(643\) 884.072 + 1531.26i 0.0542215 + 0.0939143i 0.891862 0.452307i \(-0.149399\pi\)
−0.837641 + 0.546222i \(0.816066\pi\)
\(644\) 3929.32 + 6805.77i 0.240430 + 0.416436i
\(645\) 2767.29 0.168933
\(646\) −3409.35 1725.04i −0.207646 0.105063i
\(647\) 22367.2 1.35911 0.679557 0.733623i \(-0.262172\pi\)
0.679557 + 0.733623i \(0.262172\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) −2860.50 4954.54i −0.173012 0.299665i
\(650\) 1150.00 1991.86i 0.0693949 0.120196i
\(651\) −518.022 897.241i −0.0311872 0.0540179i
\(652\) 2051.47 3553.25i 0.123223 0.213429i
\(653\) 16022.2 0.960181 0.480090 0.877219i \(-0.340604\pi\)
0.480090 + 0.877219i \(0.340604\pi\)
\(654\) 900.986 0.0538706
\(655\) −3158.25 + 5470.25i −0.188402 + 0.326321i
\(656\) −2795.66 + 4842.22i −0.166390 + 0.288196i
\(657\) 7671.34 0.455536
\(658\) −4775.31 −0.282920
\(659\) 10732.3 18588.9i 0.634404 1.09882i −0.352237 0.935911i \(-0.614579\pi\)
0.986641 0.162909i \(-0.0520876\pi\)
\(660\) 459.321 + 795.568i 0.0270895 + 0.0469204i
\(661\) 13130.3 22742.4i 0.772633 1.33824i −0.163483 0.986546i \(-0.552273\pi\)
0.936115 0.351693i \(-0.114394\pi\)
\(662\) −7966.70 13798.7i −0.467726 0.810125i
\(663\) −1591.68 2756.88i −0.0932366 0.161491i
\(664\) 1644.43 0.0961087
\(665\) 3681.93 2405.88i 0.214705 0.140295i
\(666\) −5591.19 −0.325306
\(667\) 20685.4 + 35828.2i 1.20081 + 2.07987i
\(668\) −760.006 1316.37i −0.0440202 0.0762453i
\(669\) 5491.29 9511.20i 0.317348 0.549663i
\(670\) −3727.57 6456.34i −0.214938 0.372284i
\(671\) 428.781 742.670i 0.0246690 0.0427279i
\(672\) 1019.66 0.0585329
\(673\) −14679.2 −0.840772 −0.420386 0.907345i \(-0.638105\pi\)
−0.420386 + 0.907345i \(0.638105\pi\)
\(674\) 5994.65 10383.0i 0.342590 0.593383i
\(675\) 337.500 584.567i 0.0192450 0.0333333i
\(676\) −324.000 −0.0184342
\(677\) −20350.0 −1.15526 −0.577631 0.816298i \(-0.696023\pi\)
−0.577631 + 0.816298i \(0.696023\pi\)
\(678\) −3990.76 + 6912.20i −0.226053 + 0.391536i
\(679\) 2058.70 + 3565.77i 0.116356 + 0.201534i
\(680\) 461.357 799.095i 0.0260180 0.0450645i
\(681\) −1146.95 1986.58i −0.0645395 0.111786i
\(682\) 497.817 + 862.245i 0.0279508 + 0.0484121i
\(683\) −12222.1 −0.684720 −0.342360 0.939569i \(-0.611226\pi\)
−0.342360 + 0.939569i \(0.611226\pi\)
\(684\) 2495.89 1630.89i 0.139522 0.0911674i
\(685\) −14719.2 −0.821012
\(686\) −6088.04 10544.8i −0.338838 0.586884i
\(687\) 194.025 + 336.061i 0.0107751 + 0.0186631i
\(688\) −1475.89 + 2556.31i −0.0817843 + 0.141655i
\(689\) −10433.5 18071.4i −0.576903 0.999225i
\(690\) −2774.57 + 4805.70i −0.153081 + 0.265145i
\(691\) −731.175 −0.0402535 −0.0201268 0.999797i \(-0.506407\pi\)
−0.0201268 + 0.999797i \(0.506407\pi\)
\(692\) 13388.4 0.735477
\(693\) −731.796 + 1267.51i −0.0401135 + 0.0694786i
\(694\) 7081.17 12264.9i 0.387316 0.670851i
\(695\) 2224.19 0.121393
\(696\) 5367.86 0.292339
\(697\) −4030.62 + 6981.23i −0.219039 + 0.379387i
\(698\) 4512.75 + 7816.31i 0.244714 + 0.423857i
\(699\) −9053.82 + 15681.7i −0.489910 + 0.848548i
\(700\) 531.071 + 919.842i 0.0286751 + 0.0496668i
\(701\) −11182.8 19369.2i −0.602522 1.04360i −0.992438 0.122749i \(-0.960829\pi\)
0.389915 0.920851i \(-0.372504\pi\)
\(702\) 2484.00 0.133551
\(703\) −1418.88 25686.2i −0.0761224 1.37806i
\(704\) −979.885 −0.0524585
\(705\) −1685.97 2920.19i −0.0900672 0.156001i
\(706\) 10645.4 + 18438.4i 0.567486 + 0.982915i
\(707\) 9083.75 15733.5i 0.483210 0.836945i
\(708\) −2241.96 3883.20i −0.119009 0.206129i
\(709\) −14308.5 + 24783.0i −0.757922 + 1.31276i 0.185986 + 0.982552i \(0.440452\pi\)
−0.943908 + 0.330208i \(0.892881\pi\)
\(710\) −10609.8 −0.560816
\(711\) 8632.25 0.455323
\(712\) 1464.90 2537.28i 0.0771059 0.133551i
\(713\) −3007.11 + 5208.47i −0.157948 + 0.273574i
\(714\) 1470.08 0.0770538
\(715\) −3521.46 −0.184189
\(716\) −7534.13 + 13049.5i −0.393245 + 0.681121i
\(717\) −229.197 396.981i −0.0119380 0.0206772i
\(718\) 9770.85 16923.6i 0.507862 0.879642i
\(719\) −4870.16 8435.37i −0.252610 0.437533i 0.711634 0.702551i \(-0.247956\pi\)
−0.964244 + 0.265018i \(0.914622\pi\)
\(720\) 360.000 + 623.538i 0.0186339 + 0.0322749i
\(721\) 12621.6 0.651945
\(722\) 8125.77 + 11052.4i 0.418850 + 0.569706i
\(723\) 2935.52 0.151000
\(724\) 2190.14 + 3793.43i 0.112425 + 0.194726i
\(725\) 2795.76 + 4842.39i 0.143216 + 0.248058i
\(726\) −3289.75 + 5698.01i −0.168173 + 0.291285i
\(727\) 18677.7 + 32350.7i 0.952843 + 1.65037i 0.739229 + 0.673454i \(0.235190\pi\)
0.213614 + 0.976918i \(0.431477\pi\)
\(728\) −1954.34 + 3385.02i −0.0994954 + 0.172331i
\(729\) 729.000 0.0370370
\(730\) −8523.71 −0.432160
\(731\) −2127.85 + 3685.54i −0.107662 + 0.186477i
\(732\) 336.063 582.079i 0.0169689 0.0293910i
\(733\) 28345.0 1.42830 0.714151 0.699992i \(-0.246813\pi\)
0.714151 + 0.699992i \(0.246813\pi\)
\(734\) 25918.3 1.30335
\(735\) 1726.39 2990.20i 0.0866380 0.150061i
\(736\) −2959.54 5126.08i −0.148220 0.256725i
\(737\) −5707.18 + 9885.12i −0.285246 + 0.494061i
\(738\) −3145.11 5447.50i −0.156874 0.271714i
\(739\) 6259.94 + 10842.5i 0.311605 + 0.539715i 0.978710 0.205249i \(-0.0658003\pi\)
−0.667105 + 0.744963i \(0.732467\pi\)
\(740\) 6212.43 0.308613
\(741\) 630.367 + 11411.6i 0.0312511 + 0.565745i
\(742\) 9636.43 0.476771
\(743\) −716.411 1240.86i −0.0353736 0.0612689i 0.847797 0.530322i \(-0.177929\pi\)
−0.883170 + 0.469053i \(0.844595\pi\)
\(744\) 390.172 + 675.798i 0.0192263 + 0.0333010i
\(745\) −7248.34 + 12554.5i −0.356455 + 0.617398i
\(746\) 14363.2 + 24877.7i 0.704923 + 1.22096i
\(747\) −924.991 + 1602.13i −0.0453061 + 0.0784724i
\(748\) −1412.74 −0.0690574
\(749\) −4462.02 −0.217675
\(750\) −375.000 + 649.519i −0.0182574 + 0.0316228i
\(751\) −17759.3 + 30759.9i −0.862909 + 1.49460i 0.00620039 + 0.999981i \(0.498026\pi\)
−0.869109 + 0.494621i \(0.835307\pi\)
\(752\) 3596.74 0.174414
\(753\) 1213.62 0.0587339
\(754\) −10288.4 + 17820.0i −0.496924 + 0.860698i
\(755\) −1643.77 2847.09i −0.0792355 0.137240i
\(756\) −573.557 + 993.429i −0.0275927 + 0.0477919i
\(757\) −11063.1 19161.9i −0.531172 0.920016i −0.999338 0.0363760i \(-0.988419\pi\)
0.468167 0.883640i \(-0.344915\pi\)
\(758\) 10480.5 + 18152.7i 0.502201 + 0.869837i
\(759\) 8496.13 0.406311
\(760\) −2773.21 + 1812.10i −0.132362 + 0.0864890i
\(761\) −13035.3 −0.620930 −0.310465 0.950585i \(-0.600485\pi\)
−0.310465 + 0.950585i \(0.600485\pi\)
\(762\) 217.756 + 377.164i 0.0103523 + 0.0179307i
\(763\) −797.479 1381.27i −0.0378384 0.0655380i
\(764\) −6410.29 + 11102.9i −0.303555 + 0.525773i
\(765\) 519.027 + 898.981i 0.0245300 + 0.0424872i
\(766\) −10301.9 + 17843.4i −0.485930 + 0.841655i
\(767\) 17188.4 0.809174
\(768\) −768.000 −0.0360844
\(769\) −8562.16 + 14830.1i −0.401508 + 0.695432i −0.993908 0.110212i \(-0.964847\pi\)
0.592400 + 0.805644i \(0.298180\pi\)
\(770\) 813.107 1408.34i 0.0380550 0.0659132i
\(771\) 6159.47 0.287714
\(772\) −1952.21 −0.0910122
\(773\) −1417.75 + 2455.61i −0.0659674 + 0.114259i −0.897123 0.441781i \(-0.854347\pi\)
0.831155 + 0.556040i \(0.187680\pi\)
\(774\) −1660.37 2875.85i −0.0771070 0.133553i