Properties

Label 570.4.i.h.121.2
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 121.2
Root \(-4.65535 + 8.06331i\) of defining polynomial
Character \(\chi\) \(=\) 570.121
Dual form 570.4.i.h.391.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(2.50000 + 4.33013i) q^{5} +(3.00000 - 5.19615i) q^{6} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(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} +28.6214 q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 - 8.66025i) q^{10} +4.31071 q^{11} -12.0000 q^{12} +(23.0000 - 39.8372i) q^{13} +(-28.6214 - 49.5737i) q^{14} +(-7.50000 + 12.9904i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-40.9661 - 70.9553i) q^{17} +18.0000 q^{18} +(63.4321 - 53.2482i) q^{19} -20.0000 q^{20} +(42.9321 + 74.3606i) q^{21} +(-4.31071 - 7.46637i) q^{22} +(64.4857 - 111.692i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 + 21.6506i) q^{25} -92.0000 q^{26} -27.0000 q^{27} +(-57.2428 + 99.1475i) q^{28} +(-35.3303 + 61.1939i) q^{29} +30.0000 q^{30} +189.486 q^{31} +(-16.0000 + 27.7128i) q^{32} +(6.46606 + 11.1995i) q^{33} +(-81.9321 + 141.911i) q^{34} +(71.5535 + 123.934i) q^{35} +(-18.0000 - 31.1769i) q^{36} -271.379 q^{37} +(-155.661 - 56.6195i) q^{38} +138.000 q^{39} +(20.0000 + 34.6410i) q^{40} +(60.7285 + 105.185i) q^{41} +(85.8643 - 148.721i) q^{42} +(-13.7572 - 23.8281i) q^{43} +(-8.62142 + 14.9327i) q^{44} -45.0000 q^{45} -257.943 q^{46} +(-24.1018 + 41.7456i) q^{47} +(24.0000 - 41.5692i) q^{48} +476.186 q^{49} +50.0000 q^{50} +(122.898 - 212.866i) q^{51} +(92.0000 + 159.349i) q^{52} +(-77.3160 + 133.915i) q^{53} +(27.0000 + 46.7654i) q^{54} +(10.7768 + 18.6659i) q^{55} +228.971 q^{56} +(233.491 + 84.9293i) q^{57} +141.321 q^{58} +(39.6697 + 68.7099i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(256.505 - 444.280i) q^{61} +(-189.486 - 328.199i) q^{62} +(-128.796 + 223.082i) q^{63} +64.0000 q^{64} +230.000 q^{65} +(12.9321 - 22.3991i) q^{66} +(451.243 - 781.576i) q^{67} +327.729 q^{68} +386.914 q^{69} +(143.107 - 247.869i) q^{70} +(-89.0091 - 154.168i) q^{71} +(-36.0000 + 62.3538i) q^{72} +(280.186 + 485.296i) q^{73} +(271.379 + 470.041i) q^{74} -75.0000 q^{75} +(57.5928 + 326.232i) q^{76} +123.379 q^{77} +(-138.000 - 239.023i) q^{78} +(472.069 + 817.648i) q^{79} +(40.0000 - 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(121.457 - 210.370i) q^{82} +107.446 q^{83} -343.457 q^{84} +(204.830 - 354.777i) q^{85} +(-27.5143 + 47.6562i) q^{86} -211.982 q^{87} +34.4857 q^{88} +(-297.612 + 515.480i) q^{89} +(45.0000 + 77.9423i) q^{90} +(658.293 - 1140.20i) q^{91} +(257.943 + 446.770i) q^{92} +(284.229 + 492.298i) q^{93} +96.4072 q^{94} +(389.152 + 141.549i) q^{95} -96.0000 q^{96} +(-331.175 - 573.612i) q^{97} +(-476.186 - 824.777i) q^{98} +(-19.3982 + 33.5986i) 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
\(7\) 28.6214 1.54541 0.772706 0.634765i \(-0.218903\pi\)
0.772706 + 0.634765i \(0.218903\pi\)
\(8\) 8.00000 0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 5.00000 8.66025i 0.158114 0.273861i
\(11\) 4.31071 0.118157 0.0590785 0.998253i \(-0.481184\pi\)
0.0590785 + 0.998253i \(0.481184\pi\)
\(12\) −12.0000 −0.288675
\(13\) 23.0000 39.8372i 0.490696 0.849911i −0.509246 0.860621i \(-0.670076\pi\)
0.999943 + 0.0107098i \(0.00340911\pi\)
\(14\) −28.6214 49.5737i −0.546385 0.946367i
\(15\) −7.50000 + 12.9904i −0.129099 + 0.223607i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −40.9661 70.9553i −0.584455 1.01231i −0.994943 0.100439i \(-0.967975\pi\)
0.410488 0.911866i \(-0.365358\pi\)
\(18\) 18.0000 0.235702
\(19\) 63.4321 53.2482i 0.765912 0.642945i
\(20\) −20.0000 −0.223607
\(21\) 42.9321 + 74.3606i 0.446122 + 0.772706i
\(22\) −4.31071 7.46637i −0.0417748 0.0723561i
\(23\) 64.4857 111.692i 0.584617 1.01259i −0.410306 0.911948i \(-0.634578\pi\)
0.994923 0.100638i \(-0.0320885\pi\)
\(24\) 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
\(28\) −57.2428 + 99.1475i −0.386353 + 0.669183i
\(29\) −35.3303 + 61.1939i −0.226230 + 0.391842i −0.956688 0.291116i \(-0.905973\pi\)
0.730458 + 0.682958i \(0.239307\pi\)
\(30\) 30.0000 0.182574
\(31\) 189.486 1.09783 0.548913 0.835879i \(-0.315042\pi\)
0.548913 + 0.835879i \(0.315042\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 6.46606 + 11.1995i 0.0341090 + 0.0590785i
\(34\) −81.9321 + 141.911i −0.413272 + 0.715808i
\(35\) 71.5535 + 123.934i 0.345564 + 0.598535i
\(36\) −18.0000 31.1769i −0.0833333 0.144338i
\(37\) −271.379 −1.20579 −0.602897 0.797819i \(-0.705987\pi\)
−0.602897 + 0.797819i \(0.705987\pi\)
\(38\) −155.661 56.6195i −0.664513 0.241708i
\(39\) 138.000 0.566607
\(40\) 20.0000 + 34.6410i 0.0790569 + 0.136931i
\(41\) 60.7285 + 105.185i 0.231322 + 0.400661i 0.958197 0.286108i \(-0.0923616\pi\)
−0.726875 + 0.686769i \(0.759028\pi\)
\(42\) 85.8643 148.721i 0.315456 0.546385i
\(43\) −13.7572 23.8281i −0.0487895 0.0845059i 0.840599 0.541657i \(-0.182203\pi\)
−0.889389 + 0.457152i \(0.848870\pi\)
\(44\) −8.62142 + 14.9327i −0.0295393 + 0.0511635i
\(45\) −45.0000 −0.149071
\(46\) −257.943 −0.826773
\(47\) −24.1018 + 41.7456i −0.0748002 + 0.129558i −0.900999 0.433820i \(-0.857165\pi\)
0.826199 + 0.563378i \(0.190499\pi\)
\(48\) 24.0000 41.5692i 0.0721688 0.125000i
\(49\) 476.186 1.38830
\(50\) 50.0000 0.141421
\(51\) 122.898 212.866i 0.337435 0.584455i
\(52\) 92.0000 + 159.349i 0.245348 + 0.424955i
\(53\) −77.3160 + 133.915i −0.200381 + 0.347069i −0.948651 0.316324i \(-0.897551\pi\)
0.748271 + 0.663394i \(0.230885\pi\)
\(54\) 27.0000 + 46.7654i 0.0680414 + 0.117851i
\(55\) 10.7768 + 18.6659i 0.0264207 + 0.0457620i
\(56\) 228.971 0.546385
\(57\) 233.491 + 84.9293i 0.542572 + 0.197354i
\(58\) 141.321 0.319938
\(59\) 39.6697 + 68.7099i 0.0875348 + 0.151615i 0.906469 0.422273i \(-0.138768\pi\)
−0.818934 + 0.573888i \(0.805434\pi\)
\(60\) −30.0000 51.9615i −0.0645497 0.111803i
\(61\) 256.505 444.280i 0.538396 0.932529i −0.460595 0.887610i \(-0.652364\pi\)
0.998991 0.0449182i \(-0.0143027\pi\)
\(62\) −189.486 328.199i −0.388140 0.672279i
\(63\) −128.796 + 223.082i −0.257569 + 0.446122i
\(64\) 64.0000 0.125000
\(65\) 230.000 0.438892
\(66\) 12.9321 22.3991i 0.0241187 0.0417748i
\(67\) 451.243 781.576i 0.822807 1.42514i −0.0807764 0.996732i \(-0.525740\pi\)
0.903584 0.428412i \(-0.140927\pi\)
\(68\) 327.729 0.584455
\(69\) 386.914 0.675058
\(70\) 143.107 247.869i 0.244351 0.423228i
\(71\) −89.0091 154.168i −0.148781 0.257696i 0.781996 0.623283i \(-0.214202\pi\)
−0.930777 + 0.365587i \(0.880868\pi\)
\(72\) −36.0000 + 62.3538i −0.0589256 + 0.102062i
\(73\) 280.186 + 485.296i 0.449222 + 0.778076i 0.998336 0.0576720i \(-0.0183678\pi\)
−0.549113 + 0.835748i \(0.685034\pi\)
\(74\) 271.379 + 470.041i 0.426312 + 0.738395i
\(75\) −75.0000 −0.115470
\(76\) 57.5928 + 326.232i 0.0869255 + 0.492386i
\(77\) 123.379 0.182601
\(78\) −138.000 239.023i −0.200326 0.346975i
\(79\) 472.069 + 817.648i 0.672303 + 1.16446i 0.977249 + 0.212094i \(0.0680282\pi\)
−0.304946 + 0.952370i \(0.598638\pi\)
\(80\) 40.0000 69.2820i 0.0559017 0.0968246i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 121.457 210.370i 0.163569 0.283310i
\(83\) 107.446 0.142094 0.0710469 0.997473i \(-0.477366\pi\)
0.0710469 + 0.997473i \(0.477366\pi\)
\(84\) −343.457 −0.446122
\(85\) 204.830 354.777i 0.261376 0.452717i
\(86\) −27.5143 + 47.6562i −0.0344994 + 0.0597547i
\(87\) −211.982 −0.261228
\(88\) 34.4857 0.0417748
\(89\) −297.612 + 515.480i −0.354459 + 0.613941i −0.987025 0.160565i \(-0.948668\pi\)
0.632566 + 0.774506i \(0.282002\pi\)
\(90\) 45.0000 + 77.9423i 0.0527046 + 0.0912871i
\(91\) 658.293 1140.20i 0.758328 1.31346i
\(92\) 257.943 + 446.770i 0.292309 + 0.506293i
\(93\) 284.229 + 492.298i 0.316915 + 0.548913i
\(94\) 96.4072 0.105783
\(95\) 389.152 + 141.549i 0.420275 + 0.152869i
\(96\) −96.0000 −0.102062
\(97\) −331.175 573.612i −0.346657 0.600427i 0.638996 0.769210i \(-0.279350\pi\)
−0.985653 + 0.168782i \(0.946017\pi\)
\(98\) −476.186 824.777i −0.490837 0.850154i
\(99\) −19.3982 + 33.5986i −0.0196928 + 0.0341090i
\(100\) −50.0000 86.6025i −0.0500000 0.0866025i
\(101\) 390.730 676.764i 0.384941 0.666738i −0.606820 0.794840i \(-0.707555\pi\)
0.991761 + 0.128101i \(0.0408883\pi\)
\(102\) −491.593 −0.477205
\(103\) 852.314 0.815349 0.407675 0.913127i \(-0.366340\pi\)
0.407675 + 0.913127i \(0.366340\pi\)
\(104\) 184.000 318.697i 0.173487 0.300489i
\(105\) −214.661 + 371.803i −0.199512 + 0.345564i
\(106\) 309.264 0.283381
\(107\) 792.903 0.716382 0.358191 0.933648i \(-0.383394\pi\)
0.358191 + 0.933648i \(0.383394\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) 290.918 + 503.884i 0.255641 + 0.442783i 0.965069 0.261994i \(-0.0843802\pi\)
−0.709428 + 0.704778i \(0.751047\pi\)
\(110\) 21.5535 37.3318i 0.0186823 0.0323586i
\(111\) −407.068 705.062i −0.348083 0.602897i
\(112\) −228.971 396.590i −0.193176 0.334591i
\(113\) −682.747 −0.568384 −0.284192 0.958767i \(-0.591725\pi\)
−0.284192 + 0.958767i \(0.591725\pi\)
\(114\) −86.3891 489.347i −0.0709744 0.402031i
\(115\) 644.857 0.522897
\(116\) −141.321 244.776i −0.113115 0.195921i
\(117\) 207.000 + 358.535i 0.163565 + 0.283304i
\(118\) 79.3394 137.420i 0.0618965 0.107208i
\(119\) −1172.51 2030.84i −0.903223 1.56443i
\(120\) −60.0000 + 103.923i −0.0456435 + 0.0790569i
\(121\) −1312.42 −0.986039
\(122\) −1026.02 −0.761406
\(123\) −182.186 + 315.555i −0.133554 + 0.231322i
\(124\) −378.971 + 656.398i −0.274457 + 0.475373i
\(125\) −125.000 −0.0894427
\(126\) 515.186 0.364257
\(127\) 866.293 1500.46i 0.605284 1.04838i −0.386723 0.922196i \(-0.626393\pi\)
0.992007 0.126186i \(-0.0402737\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 41.2715 71.4843i 0.0281686 0.0487895i
\(130\) −230.000 398.372i −0.155172 0.268765i
\(131\) 906.350 + 1569.84i 0.604490 + 1.04701i 0.992132 + 0.125197i \(0.0399563\pi\)
−0.387642 + 0.921810i \(0.626710\pi\)
\(132\) −51.7285 −0.0341090
\(133\) 1815.52 1524.04i 1.18365 0.993615i
\(134\) −1804.97 −1.16363
\(135\) −67.5000 116.913i −0.0430331 0.0745356i
\(136\) −327.729 567.642i −0.206636 0.357904i
\(137\) −971.577 + 1682.82i −0.605894 + 1.04944i 0.386016 + 0.922492i \(0.373851\pi\)
−0.991910 + 0.126946i \(0.959482\pi\)
\(138\) −386.914 670.155i −0.238669 0.413387i
\(139\) −1003.92 + 1738.84i −0.612599 + 1.06105i 0.378201 + 0.925723i \(0.376543\pi\)
−0.990801 + 0.135330i \(0.956791\pi\)
\(140\) −572.428 −0.345564
\(141\) −144.611 −0.0863719
\(142\) −178.018 + 308.336i −0.105204 + 0.182218i
\(143\) 99.1463 171.726i 0.0579792 0.100423i
\(144\) 144.000 0.0833333
\(145\) −353.303 −0.202346
\(146\) 560.371 970.591i 0.317648 0.550183i
\(147\) 714.278 + 1237.17i 0.400767 + 0.694148i
\(148\) 542.757 940.083i 0.301448 0.522124i
\(149\) −1150.17 1992.15i −0.632386 1.09532i −0.987063 0.160336i \(-0.948742\pi\)
0.354677 0.934989i \(-0.384591\pi\)
\(150\) 75.0000 + 129.904i 0.0408248 + 0.0707107i
\(151\) 637.507 0.343573 0.171787 0.985134i \(-0.445046\pi\)
0.171787 + 0.985134i \(0.445046\pi\)
\(152\) 507.457 425.985i 0.270791 0.227316i
\(153\) 737.389 0.389636
\(154\) −123.379 213.698i −0.0645593 0.111820i
\(155\) 473.714 + 820.497i 0.245482 + 0.425186i
\(156\) −276.000 + 478.046i −0.141652 + 0.245348i
\(157\) −527.979 914.486i −0.268390 0.464866i 0.700056 0.714088i \(-0.253158\pi\)
−0.968446 + 0.249222i \(0.919825\pi\)
\(158\) 944.139 1635.30i 0.475390 0.823400i
\(159\) −463.896 −0.231379
\(160\) −160.000 −0.0790569
\(161\) 1845.67 3196.80i 0.903474 1.56486i
\(162\) −81.0000 + 140.296i −0.0392837 + 0.0680414i
\(163\) 3251.73 1.56255 0.781275 0.624188i \(-0.214570\pi\)
0.781275 + 0.624188i \(0.214570\pi\)
\(164\) −485.828 −0.231322
\(165\) −32.3303 + 55.9977i −0.0152540 + 0.0264207i
\(166\) −107.446 186.103i −0.0502377 0.0870143i
\(167\) 820.501 1421.15i 0.380193 0.658514i −0.610896 0.791711i \(-0.709191\pi\)
0.991090 + 0.133196i \(0.0425241\pi\)
\(168\) 343.457 + 594.885i 0.157728 + 0.273193i
\(169\) 40.5000 + 70.1481i 0.0184342 + 0.0319290i
\(170\) −819.321 −0.369642
\(171\) 129.584 + 734.021i 0.0579504 + 0.328257i
\(172\) 110.057 0.0487895
\(173\) 1897.55 + 3286.65i 0.833919 + 1.44439i 0.894908 + 0.446251i \(0.147241\pi\)
−0.0609887 + 0.998138i \(0.519425\pi\)
\(174\) 211.982 + 367.163i 0.0923581 + 0.159969i
\(175\) −357.768 + 619.672i −0.154541 + 0.267673i
\(176\) −34.4857 59.7309i −0.0147696 0.0255818i
\(177\) −119.009 + 206.130i −0.0505382 + 0.0875348i
\(178\) 1190.45 0.501281
\(179\) −1668.07 −0.696520 −0.348260 0.937398i \(-0.613227\pi\)
−0.348260 + 0.937398i \(0.613227\pi\)
\(180\) 90.0000 155.885i 0.0372678 0.0645497i
\(181\) 576.966 999.335i 0.236937 0.410386i −0.722897 0.690956i \(-0.757190\pi\)
0.959834 + 0.280569i \(0.0905233\pi\)
\(182\) −2633.17 −1.07244
\(183\) 1539.03 0.621686
\(184\) 515.885 893.540i 0.206693 0.358003i
\(185\) −678.446 1175.10i −0.269624 0.467002i
\(186\) 568.457 984.596i 0.224093 0.388140i
\(187\) −176.593 305.868i −0.0690574 0.119611i
\(188\) −96.4072 166.982i −0.0374001 0.0647789i
\(189\) −772.778 −0.297415
\(190\) −143.982 815.579i −0.0549765 0.311412i
\(191\) −2740.14 −1.03806 −0.519031 0.854755i \(-0.673707\pi\)
−0.519031 + 0.854755i \(0.673707\pi\)
\(192\) 96.0000 + 166.277i 0.0360844 + 0.0625000i
\(193\) 2578.97 + 4466.91i 0.961858 + 1.66599i 0.717829 + 0.696219i \(0.245136\pi\)
0.244029 + 0.969768i \(0.421531\pi\)
\(194\) −662.350 + 1147.22i −0.245123 + 0.424566i
\(195\) 345.000 + 597.558i 0.126697 + 0.219446i
\(196\) −952.371 + 1649.55i −0.347074 + 0.601150i
\(197\) −3205.90 −1.15945 −0.579723 0.814813i \(-0.696839\pi\)
−0.579723 + 0.814813i \(0.696839\pi\)
\(198\) 77.5928 0.0278499
\(199\) −409.988 + 710.120i −0.146047 + 0.252960i −0.929763 0.368159i \(-0.879988\pi\)
0.783716 + 0.621119i \(0.213322\pi\)
\(200\) −100.000 + 173.205i −0.0353553 + 0.0612372i
\(201\) 2707.46 0.950096
\(202\) −1562.92 −0.544389
\(203\) −1011.20 + 1751.46i −0.349619 + 0.605557i
\(204\) 491.593 + 851.464i 0.168718 + 0.292227i
\(205\) −303.643 + 525.924i −0.103450 + 0.179181i
\(206\) −852.314 1476.25i −0.288269 0.499297i
\(207\) 580.371 + 1005.23i 0.194872 + 0.337529i
\(208\) −736.000 −0.245348
\(209\) 273.437 229.537i 0.0904979 0.0759685i
\(210\) 858.643 0.282152
\(211\) 1263.76 + 2188.90i 0.412327 + 0.714172i 0.995144 0.0984318i \(-0.0313826\pi\)
−0.582816 + 0.812604i \(0.698049\pi\)
\(212\) −309.264 535.661i −0.100190 0.173535i
\(213\) 267.027 462.505i 0.0858986 0.148781i
\(214\) −792.903 1373.35i −0.253279 0.438693i
\(215\) 68.7858 119.141i 0.0218193 0.0377922i
\(216\) −216.000 −0.0680414
\(217\) 5423.35 1.69659
\(218\) 581.836 1007.77i 0.180765 0.313095i
\(219\) −840.557 + 1455.89i −0.259359 + 0.449222i
\(220\) −86.2142 −0.0264207
\(221\) −3768.88 −1.14716
\(222\) −814.136 + 1410.12i −0.246132 + 0.426312i
\(223\) 975.431 + 1689.50i 0.292914 + 0.507341i 0.974497 0.224399i \(-0.0720419\pi\)
−0.681584 + 0.731740i \(0.738709\pi\)
\(224\) −457.943 + 793.180i −0.136596 + 0.236592i
\(225\) −112.500 194.856i −0.0333333 0.0577350i
\(226\) 682.747 + 1182.55i 0.200954 + 0.348063i
\(227\) −3629.36 −1.06119 −0.530593 0.847627i \(-0.678031\pi\)
−0.530593 + 0.847627i \(0.678031\pi\)
\(228\) −761.186 + 638.978i −0.221100 + 0.185602i
\(229\) −145.350 −0.0419432 −0.0209716 0.999780i \(-0.506676\pi\)
−0.0209716 + 0.999780i \(0.506676\pi\)
\(230\) −644.857 1116.92i −0.184872 0.320208i
\(231\) 185.068 + 320.547i 0.0527124 + 0.0913006i
\(232\) −282.643 + 489.551i −0.0799844 + 0.138537i
\(233\) −2093.44 3625.94i −0.588609 1.01950i −0.994415 0.105541i \(-0.966343\pi\)
0.405806 0.913959i \(-0.366991\pi\)
\(234\) 414.000 717.069i 0.115658 0.200326i
\(235\) −241.018 −0.0669034
\(236\) −317.357 −0.0875348
\(237\) −1416.21 + 2452.94i −0.388154 + 0.672303i
\(238\) −2345.01 + 4061.68i −0.638675 + 1.10622i
\(239\) −5470.20 −1.48049 −0.740247 0.672335i \(-0.765291\pi\)
−0.740247 + 0.672335i \(0.765291\pi\)
\(240\) 240.000 0.0645497
\(241\) −2905.25 + 5032.05i −0.776530 + 1.34499i 0.157400 + 0.987535i \(0.449689\pi\)
−0.933930 + 0.357455i \(0.883645\pi\)
\(242\) 1312.42 + 2273.17i 0.348617 + 0.603823i
\(243\) 121.500 210.444i 0.0320750 0.0555556i
\(244\) 1026.02 + 1777.12i 0.269198 + 0.466264i
\(245\) 1190.46 + 2061.94i 0.310432 + 0.537685i
\(246\) 728.742 0.188874
\(247\) −662.317 3751.66i −0.170616 0.966448i
\(248\) 1515.89 0.388140
\(249\) 161.170 + 279.154i 0.0410189 + 0.0710469i
\(250\) 125.000 + 216.506i 0.0316228 + 0.0547723i
\(251\) −1298.77 + 2249.53i −0.326604 + 0.565695i −0.981836 0.189733i \(-0.939238\pi\)
0.655232 + 0.755428i \(0.272571\pi\)
\(252\) −515.186 892.327i −0.128784 0.223061i
\(253\) 277.979 481.474i 0.0690766 0.119644i
\(254\) −3465.17 −0.856000
\(255\) 1228.98 0.301811
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2230.58 + 3863.47i −0.541399 + 0.937731i 0.457425 + 0.889248i \(0.348772\pi\)
−0.998824 + 0.0484827i \(0.984561\pi\)
\(258\) −165.086 −0.0398365
\(259\) −7767.24 −1.86345
\(260\) −460.000 + 796.743i −0.109723 + 0.190046i
\(261\) −317.973 550.745i −0.0754101 0.130614i
\(262\) 1812.70 3139.69i 0.427439 0.740346i
\(263\) −2707.67 4689.83i −0.634838 1.09957i −0.986550 0.163463i \(-0.947734\pi\)
0.351712 0.936108i \(-0.385600\pi\)
\(264\) 51.7285 + 89.5964i 0.0120594 + 0.0208874i
\(265\) −773.160 −0.179226
\(266\) −4455.23 1620.53i −1.02695 0.373538i
\(267\) −1785.67 −0.409294
\(268\) 1804.97 + 3126.30i 0.411404 + 0.712572i
\(269\) 3613.08 + 6258.04i 0.818934 + 1.41844i 0.906468 + 0.422275i \(0.138768\pi\)
−0.0875335 + 0.996162i \(0.527898\pi\)
\(270\) −135.000 + 233.827i −0.0304290 + 0.0527046i
\(271\) 417.557 + 723.231i 0.0935971 + 0.162115i 0.909022 0.416748i \(-0.136830\pi\)
−0.815425 + 0.578863i \(0.803497\pi\)
\(272\) −655.457 + 1135.28i −0.146114 + 0.253076i
\(273\) 3949.76 0.875641
\(274\) 3886.31 0.856863
\(275\) −53.8839 + 93.3296i −0.0118157 + 0.0204654i
\(276\) −773.828 + 1340.31i −0.168764 + 0.292309i
\(277\) −209.858 −0.0455204 −0.0227602 0.999741i \(-0.507245\pi\)
−0.0227602 + 0.999741i \(0.507245\pi\)
\(278\) 4015.68 0.866346
\(279\) −852.686 + 1476.89i −0.182971 + 0.316915i
\(280\) 572.428 + 991.475i 0.122175 + 0.211614i
\(281\) 859.842 1489.29i 0.182540 0.316169i −0.760205 0.649684i \(-0.774901\pi\)
0.942745 + 0.333515i \(0.108235\pi\)
\(282\) 144.611 + 250.473i 0.0305371 + 0.0528917i
\(283\) −147.157 254.883i −0.0309101 0.0535379i 0.850157 0.526530i \(-0.176507\pi\)
−0.881067 + 0.472992i \(0.843174\pi\)
\(284\) 712.072 0.148781
\(285\) 215.973 + 1223.37i 0.0448882 + 0.254267i
\(286\) −396.585 −0.0819950
\(287\) 1738.14 + 3010.54i 0.357487 + 0.619186i
\(288\) −144.000 249.415i −0.0294628 0.0510310i
\(289\) −899.937 + 1558.74i −0.183175 + 0.317268i
\(290\) 353.303 + 611.939i 0.0715403 + 0.123911i
\(291\) 993.525 1720.84i 0.200142 0.346657i
\(292\) −2241.48 −0.449222
\(293\) 6457.02 1.28745 0.643725 0.765257i \(-0.277388\pi\)
0.643725 + 0.765257i \(0.277388\pi\)
\(294\) 1428.56 2474.33i 0.283385 0.490837i
\(295\) −198.348 + 343.550i −0.0391468 + 0.0678042i
\(296\) −2171.03 −0.426312
\(297\) −116.389 −0.0227393
\(298\) −2300.34 + 3984.30i −0.447164 + 0.774511i
\(299\) −2966.34 5137.85i −0.573739 0.993745i
\(300\) 150.000 259.808i 0.0288675 0.0500000i
\(301\) −393.750 681.994i −0.0753998 0.130596i
\(302\) −637.507 1104.19i −0.121471 0.210395i
\(303\) 2344.38 0.444492
\(304\) −1245.29 452.956i −0.234941 0.0854566i
\(305\) 2565.05 0.481556
\(306\) −737.389 1277.20i −0.137757 0.238603i
\(307\) 1926.96 + 3337.59i 0.358232 + 0.620476i 0.987666 0.156578i \(-0.0500464\pi\)
−0.629434 + 0.777054i \(0.716713\pi\)
\(308\) −246.757 + 427.396i −0.0456503 + 0.0790687i
\(309\) 1278.47 + 2214.38i 0.235371 + 0.407675i
\(310\) 947.428 1640.99i 0.173582 0.300652i
\(311\) −8358.72 −1.52405 −0.762025 0.647548i \(-0.775795\pi\)
−0.762025 + 0.647548i \(0.775795\pi\)
\(312\) 1104.00 0.200326
\(313\) −1925.35 + 3334.80i −0.347690 + 0.602218i −0.985839 0.167696i \(-0.946367\pi\)
0.638148 + 0.769913i \(0.279701\pi\)
\(314\) −1055.96 + 1828.97i −0.189781 + 0.328710i
\(315\) −1287.96 −0.230376
\(316\) −3776.55 −0.672303
\(317\) 3892.71 6742.37i 0.689704 1.19460i −0.282229 0.959347i \(-0.591074\pi\)
0.971933 0.235256i \(-0.0755928\pi\)
\(318\) 463.896 + 803.491i 0.0818050 + 0.141690i
\(319\) −152.299 + 263.789i −0.0267307 + 0.0462989i
\(320\) 160.000 + 277.128i 0.0279508 + 0.0484123i
\(321\) 1189.36 + 2060.02i 0.206802 + 0.358191i
\(322\) −7382.68 −1.27770
\(323\) −6376.80 2319.48i −1.09850 0.399564i
\(324\) 324.000 0.0555556
\(325\) 575.000 + 995.929i 0.0981393 + 0.169982i
\(326\) −3251.73 5632.17i −0.552445 0.956862i
\(327\) −872.753 + 1511.65i −0.147594 + 0.255641i
\(328\) 485.828 + 841.479i 0.0817846 + 0.141655i
\(329\) −689.828 + 1194.82i −0.115597 + 0.200220i
\(330\) 129.321 0.0215724
\(331\) −3570.70 −0.592940 −0.296470 0.955042i \(-0.595810\pi\)
−0.296470 + 0.955042i \(0.595810\pi\)
\(332\) −214.893 + 372.205i −0.0355234 + 0.0615284i
\(333\) 1221.20 2115.19i 0.200966 0.348083i
\(334\) −3282.01 −0.537675
\(335\) 4512.43 0.735941
\(336\) 686.914 1189.77i 0.111530 0.193176i
\(337\) −1633.33 2829.01i −0.264015 0.457287i 0.703290 0.710903i \(-0.251713\pi\)
−0.967305 + 0.253616i \(0.918380\pi\)
\(338\) 81.0000 140.296i 0.0130350 0.0225772i
\(339\) −1024.12 1773.83i −0.164078 0.284192i
\(340\) 819.321 + 1419.11i 0.130688 + 0.226358i
\(341\) 816.817 0.129716
\(342\) 1141.78 958.467i 0.180527 0.151544i
\(343\) 3811.96 0.600077
\(344\) −110.057 190.625i −0.0172497 0.0298773i
\(345\) 967.285 + 1675.39i 0.150947 + 0.261449i
\(346\) 3795.10 6573.30i 0.589670 1.02134i
\(347\) 2745.92 + 4756.07i 0.424808 + 0.735790i 0.996403 0.0847468i \(-0.0270081\pi\)
−0.571594 + 0.820537i \(0.693675\pi\)
\(348\) 423.964 734.327i 0.0653070 0.113115i
\(349\) 4375.75 0.671142 0.335571 0.942015i \(-0.391071\pi\)
0.335571 + 0.942015i \(0.391071\pi\)
\(350\) 1431.07 0.218554
\(351\) −621.000 + 1075.60i −0.0944346 + 0.163565i
\(352\) −68.9713 + 119.462i −0.0104437 + 0.0180890i
\(353\) 9525.41 1.43622 0.718111 0.695929i \(-0.245007\pi\)
0.718111 + 0.695929i \(0.245007\pi\)
\(354\) 476.036 0.0714719
\(355\) 445.045 770.841i 0.0665368 0.115245i
\(356\) −1190.45 2061.92i −0.177229 0.306970i
\(357\) 3517.52 6092.52i 0.521476 0.903223i
\(358\) 1668.07 + 2889.18i 0.246257 + 0.426530i
\(359\) 627.576 + 1086.99i 0.0922624 + 0.159803i 0.908463 0.417966i \(-0.137257\pi\)
−0.816200 + 0.577769i \(0.803923\pi\)
\(360\) −360.000 −0.0527046
\(361\) 1188.27 6755.29i 0.173242 0.984879i
\(362\) −2307.86 −0.335079
\(363\) −1968.63 3409.76i −0.284645 0.493019i
\(364\) 2633.17 + 4560.78i 0.379164 + 0.656731i
\(365\) −1400.93 + 2426.48i −0.200898 + 0.347966i
\(366\) −1539.03 2665.68i −0.219799 0.380703i
\(367\) −5243.43 + 9081.88i −0.745789 + 1.29174i 0.204036 + 0.978963i \(0.434594\pi\)
−0.949825 + 0.312781i \(0.898739\pi\)
\(368\) −2063.54 −0.292309
\(369\) −1093.11 −0.154215
\(370\) −1356.89 + 2350.21i −0.190653 + 0.330220i
\(371\) −2212.89 + 3832.84i −0.309670 + 0.536365i
\(372\) −2273.83 −0.316915
\(373\) −7848.84 −1.08954 −0.544769 0.838586i \(-0.683383\pi\)
−0.544769 + 0.838586i \(0.683383\pi\)
\(374\) −353.186 + 611.735i −0.0488310 + 0.0845777i
\(375\) −187.500 324.760i −0.0258199 0.0447214i
\(376\) −192.814 + 333.965i −0.0264459 + 0.0458056i
\(377\) 1625.19 + 2814.92i 0.222021 + 0.384551i
\(378\) 772.778 + 1338.49i 0.105152 + 0.182128i
\(379\) 4137.48 0.560760 0.280380 0.959889i \(-0.409540\pi\)
0.280380 + 0.959889i \(0.409540\pi\)
\(380\) −1268.64 + 1064.96i −0.171263 + 0.143767i
\(381\) 5197.76 0.698921
\(382\) 2740.14 + 4746.07i 0.367010 + 0.635681i
\(383\) −39.5605 68.5207i −0.00527792 0.00914163i 0.863374 0.504564i \(-0.168347\pi\)
−0.868652 + 0.495422i \(0.835013\pi\)
\(384\) 192.000 332.554i 0.0255155 0.0441942i
\(385\) 308.446 + 534.245i 0.0408309 + 0.0707212i
\(386\) 5157.95 8933.83i 0.680136 1.17803i
\(387\) 247.629 0.0325263
\(388\) 2649.40 0.346657
\(389\) 3676.32 6367.58i 0.479170 0.829946i −0.520545 0.853834i \(-0.674271\pi\)
0.999715 + 0.0238880i \(0.00760450\pi\)
\(390\) 690.000 1195.12i 0.0895885 0.155172i
\(391\) −10566.9 −1.36673
\(392\) 3809.48 0.490837
\(393\) −2719.05 + 4709.53i −0.349002 + 0.604490i
\(394\) 3205.90 + 5552.78i 0.409926 + 0.710013i
\(395\) −2360.35 + 4088.24i −0.300663 + 0.520764i
\(396\) −77.5928 134.395i −0.00984642 0.0170545i
\(397\) −5491.24 9511.11i −0.694201 1.20239i −0.970449 0.241305i \(-0.922425\pi\)
0.276249 0.961086i \(-0.410909\pi\)
\(398\) 1639.95 0.206541
\(399\) 6682.84 + 2430.80i 0.838498 + 0.304993i
\(400\) 400.000 0.0500000
\(401\) −1035.41 1793.39i −0.128943 0.223335i 0.794325 0.607494i \(-0.207825\pi\)
−0.923267 + 0.384158i \(0.874492\pi\)
\(402\) −2707.46 4689.45i −0.335910 0.581813i
\(403\) 4358.17 7548.57i 0.538700 0.933055i
\(404\) 1562.92 + 2707.06i 0.192471 + 0.333369i
\(405\) 202.500 350.740i 0.0248452 0.0430331i
\(406\) 4044.81 0.494435
\(407\) −1169.83 −0.142473
\(408\) 983.186 1702.93i 0.119301 0.206636i
\(409\) 4531.55 7848.87i 0.547850 0.948904i −0.450572 0.892740i \(-0.648780\pi\)
0.998422 0.0561638i \(-0.0178869\pi\)
\(410\) 1214.57 0.146301
\(411\) −5829.46 −0.699626
\(412\) −1704.63 + 2952.50i −0.203837 + 0.353057i
\(413\) 1135.40 + 1966.58i 0.135277 + 0.234307i
\(414\) 1160.74 2010.46i 0.137796 0.238669i
\(415\) 268.616 + 465.257i 0.0317731 + 0.0550327i
\(416\) 736.000 + 1274.79i 0.0867437 + 0.150244i
\(417\) −6023.52 −0.707369
\(418\) −671.008 244.070i −0.0785169 0.0285595i
\(419\) −1690.59 −0.197113 −0.0985567 0.995131i \(-0.531423\pi\)
−0.0985567 + 0.995131i \(0.531423\pi\)
\(420\) −858.643 1487.21i −0.0997559 0.172782i
\(421\) −7501.22 12992.5i −0.868378 1.50407i −0.863654 0.504086i \(-0.831830\pi\)
−0.00472430 0.999989i \(-0.501504\pi\)
\(422\) 2527.53 4377.81i 0.291560 0.504996i
\(423\) −216.916 375.710i −0.0249334 0.0431859i
\(424\) −618.528 + 1071.32i −0.0708452 + 0.122707i
\(425\) 2048.30 0.233782
\(426\) −1068.11 −0.121479
\(427\) 7341.54 12715.9i 0.832043 1.44114i
\(428\) −1585.81 + 2746.70i −0.179095 + 0.310202i
\(429\) 594.878 0.0669486
\(430\) −275.143 −0.0308572
\(431\) −6820.70 + 11813.8i −0.762277 + 1.32030i 0.179397 + 0.983777i \(0.442585\pi\)
−0.941674 + 0.336526i \(0.890748\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) 5415.71 9380.29i 0.601068 1.04108i −0.391591 0.920139i \(-0.628075\pi\)
0.992660 0.120942i \(-0.0385914\pi\)
\(434\) −5423.35 9393.51i −0.599837 1.03895i
\(435\) −529.955 917.908i −0.0584124 0.101173i
\(436\) −2327.34 −0.255641
\(437\) −1856.95 10518.6i −0.203273 1.15143i
\(438\) 3362.23 0.366789
\(439\) −6346.96 10993.3i −0.690032 1.19517i −0.971827 0.235695i \(-0.924263\pi\)
0.281795 0.959475i \(-0.409070\pi\)
\(440\) 86.2142 + 149.327i 0.00934113 + 0.0161793i
\(441\) −2142.83 + 3711.50i −0.231383 + 0.400767i
\(442\) 3768.88 + 6527.89i 0.405582 + 0.702489i
\(443\) −1450.82 + 2512.89i −0.155599 + 0.269505i −0.933277 0.359157i \(-0.883064\pi\)
0.777678 + 0.628663i \(0.216397\pi\)
\(444\) 3256.54 0.348083
\(445\) −2976.12 −0.317038
\(446\) 1950.86 3378.99i 0.207121 0.358744i
\(447\) 3450.51 5976.45i 0.365108 0.632386i
\(448\) 1831.77 0.193176
\(449\) −50.5038 −0.00530829 −0.00265414 0.999996i \(-0.500845\pi\)
−0.00265414 + 0.999996i \(0.500845\pi\)
\(450\) −225.000 + 389.711i −0.0235702 + 0.0408248i
\(451\) 261.783 + 453.421i 0.0273323 + 0.0473410i
\(452\) 1365.49 2365.10i 0.142096 0.246118i
\(453\) 956.260 + 1656.29i 0.0991811 + 0.171787i
\(454\) 3629.36 + 6286.24i 0.375186 + 0.649841i
\(455\) 6582.93 0.678269
\(456\) 1867.93 + 679.434i 0.191828 + 0.0697750i
\(457\) −10840.4 −1.10961 −0.554804 0.831981i \(-0.687207\pi\)
−0.554804 + 0.831981i \(0.687207\pi\)
\(458\) 145.350 + 251.753i 0.0148292 + 0.0256849i
\(459\) 1106.08 + 1915.79i 0.112478 + 0.194818i
\(460\) −1289.71 + 2233.85i −0.130724 + 0.226421i
\(461\) −1804.67 3125.77i −0.182325 0.315795i 0.760347 0.649517i \(-0.225029\pi\)
−0.942672 + 0.333721i \(0.891695\pi\)
\(462\) 370.136 641.094i 0.0372733 0.0645593i
\(463\) 9096.20 0.913038 0.456519 0.889714i \(-0.349096\pi\)
0.456519 + 0.889714i \(0.349096\pi\)
\(464\) 1130.57 0.113115
\(465\) −1421.14 + 2461.49i −0.141729 + 0.245482i
\(466\) −4186.88 + 7251.89i −0.416209 + 0.720895i
\(467\) 1927.45 0.190989 0.0954943 0.995430i \(-0.469557\pi\)
0.0954943 + 0.995430i \(0.469557\pi\)
\(468\) −1656.00 −0.163565
\(469\) 12915.2 22369.8i 1.27158 2.20243i
\(470\) 241.018 + 417.456i 0.0236539 + 0.0409698i
\(471\) 1583.94 2743.46i 0.154955 0.268390i
\(472\) 317.357 + 549.679i 0.0309482 + 0.0536039i
\(473\) −59.3031 102.716i −0.00576482 0.00998497i
\(474\) 5664.83 0.548933
\(475\) 359.955 + 2038.95i 0.0347702 + 0.196954i
\(476\) 9380.05 0.903223
\(477\) −695.844 1205.24i −0.0667935 0.115690i
\(478\) 5470.20 + 9474.67i 0.523434 + 0.906613i
\(479\) 9349.27 16193.4i 0.891814 1.54467i 0.0541151 0.998535i \(-0.482766\pi\)
0.837699 0.546132i \(-0.183900\pi\)
\(480\) −240.000 415.692i −0.0228218 0.0395285i
\(481\) −6241.71 + 10811.0i −0.591679 + 1.02482i
\(482\) 11621.0 1.09818
\(483\) 11074.0 1.04324
\(484\) 2624.84 4546.35i 0.246510 0.426967i
\(485\) 1655.87 2868.06i 0.155030 0.268519i
\(486\) −486.000 −0.0453609
\(487\) 9370.36 0.871892 0.435946 0.899973i \(-0.356414\pi\)
0.435946 + 0.899973i \(0.356414\pi\)
\(488\) 2052.04 3554.24i 0.190352 0.329699i
\(489\) 4877.60 + 8448.25i 0.451069 + 0.781275i
\(490\) 2380.93 4123.89i 0.219509 0.380200i
\(491\) −8801.87 15245.3i −0.809008 1.40124i −0.913552 0.406723i \(-0.866671\pi\)
0.104544 0.994520i \(-0.466662\pi\)
\(492\) −728.742 1262.22i −0.0667769 0.115661i
\(493\) 5789.38 0.528885
\(494\) −5835.76 + 4898.83i −0.531504 + 0.446172i
\(495\) −193.982 −0.0176138
\(496\) −1515.89 2625.59i −0.137228 0.237686i
\(497\) −2547.57 4412.51i −0.229927 0.398246i
\(498\) 322.339 558.308i 0.0290048 0.0502377i
\(499\) −9161.02 15867.3i −0.821851 1.42349i −0.904303 0.426892i \(-0.859608\pi\)
0.0824520 0.996595i \(-0.473725\pi\)
\(500\) 250.000 433.013i 0.0223607 0.0387298i
\(501\) 4923.01 0.439010
\(502\) 5195.08 0.461888
\(503\) −5635.20 + 9760.45i −0.499525 + 0.865203i −1.00000 0.000548122i \(-0.999826\pi\)
0.500475 + 0.865751i \(0.333159\pi\)
\(504\) −1030.37 + 1784.65i −0.0910642 + 0.157728i
\(505\) 3907.30 0.344302
\(506\) −1111.92 −0.0976891
\(507\) −121.500 + 210.444i −0.0106430 + 0.0184342i
\(508\) 3465.17 + 6001.85i 0.302642 + 0.524191i
\(509\) −2067.88 + 3581.68i −0.180073 + 0.311896i −0.941905 0.335878i \(-0.890967\pi\)
0.761832 + 0.647775i \(0.224300\pi\)
\(510\) −1228.98 2128.66i −0.106706 0.184821i
\(511\) 8019.31 + 13889.8i 0.694233 + 1.20245i
\(512\) 512.000 0.0441942
\(513\) −1712.67 + 1437.70i −0.147400 + 0.123735i
\(514\) 8922.31 0.765654
\(515\) 2130.78 + 3690.63i 0.182318 + 0.315783i
\(516\) 165.086 + 285.937i 0.0140843 + 0.0243947i
\(517\) −103.896 + 179.953i −0.00883817 + 0.0153082i
\(518\) 7767.24 + 13453.3i 0.658828 + 1.14112i
\(519\) −5692.65 + 9859.95i −0.481463 + 0.833919i
\(520\) 1840.00 0.155172
\(521\) −5893.76 −0.495606 −0.247803 0.968810i \(-0.579709\pi\)
−0.247803 + 0.968810i \(0.579709\pi\)
\(522\) −635.946 + 1101.49i −0.0533230 + 0.0923581i
\(523\) −2513.85 + 4354.11i −0.210178 + 0.364038i −0.951770 0.306812i \(-0.900738\pi\)
0.741592 + 0.670851i \(0.234071\pi\)
\(524\) −7250.80 −0.604490
\(525\) −2146.61 −0.178449
\(526\) −5415.35 + 9379.66i −0.448898 + 0.777514i
\(527\) −7762.48 13445.0i −0.641630 1.11134i
\(528\) 103.457 179.193i 0.00852725 0.0147696i
\(529\) −2233.30 3868.19i −0.183554 0.317925i
\(530\) 773.160 + 1339.15i 0.0633659 + 0.109753i
\(531\) −714.054 −0.0583565
\(532\) 1648.39 + 9337.21i 0.134336 + 0.760939i
\(533\) 5587.02 0.454035
\(534\) 1785.67 + 3092.88i 0.144707 + 0.250640i
\(535\) 1982.26 + 3433.37i 0.160188 + 0.277454i
\(536\) 3609.94 6252.60i 0.290906 0.503864i
\(537\) −2502.10 4333.76i −0.201068 0.348260i
\(538\) 7226.16 12516.1i 0.579074 1.00299i
\(539\) 2052.70 0.164037
\(540\) 540.000 0.0430331
\(541\) −7786.73 + 13487.0i −0.618813 + 1.07181i 0.370890 + 0.928677i \(0.379053\pi\)
−0.989703 + 0.143138i \(0.954281\pi\)
\(542\) 835.115 1446.46i 0.0661831 0.114633i
\(543\) 3461.80 0.273591
\(544\) 2621.83 0.206636
\(545\) −1454.59 + 2519.42i −0.114326 + 0.198019i
\(546\) −3949.76 6841.18i −0.309586 0.536219i
\(547\) −3746.10 + 6488.44i −0.292819 + 0.507177i −0.974475 0.224496i \(-0.927927\pi\)
0.681656 + 0.731672i \(0.261260\pi\)
\(548\) −3886.31 6731.28i −0.302947 0.524719i
\(549\) 2308.55 + 3998.52i 0.179465 + 0.310843i
\(550\) 215.535 0.0167099
\(551\) 1017.38 + 5762.93i 0.0786607 + 0.445570i
\(552\) 3095.31 0.238669
\(553\) 13511.3 + 23402.2i 1.03898 + 1.79957i
\(554\) 209.858 + 363.485i 0.0160939 + 0.0278755i
\(555\) 2035.34 3525.31i 0.155667 0.269624i
\(556\) −4015.68 6955.36i −0.306300 0.530527i
\(557\) 2062.15 3571.75i 0.156869 0.271705i −0.776869 0.629662i \(-0.783193\pi\)
0.933738 + 0.357957i \(0.116527\pi\)
\(558\) 3410.74 0.258760
\(559\) −1265.66 −0.0957633
\(560\) 1144.86 1982.95i 0.0863911 0.149634i
\(561\) 529.778 917.603i 0.0398703 0.0690574i
\(562\) −3439.37 −0.258151
\(563\) 7596.95 0.568691 0.284346 0.958722i \(-0.408224\pi\)
0.284346 + 0.958722i \(0.408224\pi\)
\(564\) 289.222 500.947i 0.0215930 0.0374001i
\(565\) −1706.87 2956.38i −0.127095 0.220134i
\(566\) −294.314 + 509.766i −0.0218568 + 0.0378570i
\(567\) −1159.17 2007.74i −0.0858562 0.148707i
\(568\) −712.072 1233.35i −0.0526019 0.0911092i
\(569\) −25780.6 −1.89943 −0.949717 0.313108i \(-0.898630\pi\)
−0.949717 + 0.313108i \(0.898630\pi\)
\(570\) 1902.96 1597.44i 0.139836 0.117385i
\(571\) −16636.4 −1.21928 −0.609642 0.792677i \(-0.708687\pi\)
−0.609642 + 0.792677i \(0.708687\pi\)
\(572\) 396.585 + 686.906i 0.0289896 + 0.0502115i
\(573\) −4110.22 7119.10i −0.299663 0.519031i
\(574\) 3476.27 6021.08i 0.252782 0.437831i
\(575\) 1612.14 + 2792.31i 0.116923 + 0.202517i
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 1857.95 0.134051 0.0670254 0.997751i \(-0.478649\pi\)
0.0670254 + 0.997751i \(0.478649\pi\)
\(578\) 3599.75 0.259048
\(579\) −7736.92 + 13400.7i −0.555329 + 0.961858i
\(580\) 706.606 1223.88i 0.0505866 0.0876186i
\(581\) 3075.27 0.219593
\(582\) −3974.10 −0.283044
\(583\) −333.287 + 577.269i −0.0236764 + 0.0410087i
\(584\) 2241.48 + 3882.36i 0.158824 + 0.275091i
\(585\) −1035.00 + 1792.67i −0.0731487 + 0.126697i
\(586\) −6457.02 11183.9i −0.455183 0.788399i
\(587\) 12908.6 + 22358.4i 0.907658 + 1.57211i 0.817309 + 0.576199i \(0.195465\pi\)
0.0903484 + 0.995910i \(0.471202\pi\)
\(588\) −5714.23 −0.400767
\(589\) 12019.5 10089.8i 0.840839 0.705843i
\(590\) 793.394 0.0553619
\(591\) −4808.85 8329.18i −0.334704 0.579723i
\(592\) 2171.03 + 3760.33i 0.150724 + 0.261062i
\(593\) −241.613 + 418.486i −0.0167316 + 0.0289801i −0.874270 0.485440i \(-0.838659\pi\)
0.857538 + 0.514420i \(0.171993\pi\)
\(594\) 116.389 + 201.592i 0.00803957 + 0.0139249i
\(595\) 5862.53 10154.2i 0.403934 0.699633i
\(596\) 9201.35 0.632386
\(597\) −2459.93 −0.168640
\(598\) −5932.68 + 10275.7i −0.405695 + 0.702684i
\(599\) −3337.55 + 5780.80i −0.227660 + 0.394319i −0.957114 0.289711i \(-0.906441\pi\)
0.729454 + 0.684030i \(0.239774\pi\)
\(600\) −600.000 −0.0408248
\(601\) −1767.06 −0.119933 −0.0599665 0.998200i \(-0.519099\pi\)
−0.0599665 + 0.998200i \(0.519099\pi\)
\(602\) −787.499 + 1363.99i −0.0533157 + 0.0923456i
\(603\) 4061.19 + 7034.18i 0.274269 + 0.475048i
\(604\) −1275.01 + 2208.39i −0.0858933 + 0.148772i
\(605\) −3281.04 5682.94i −0.220485 0.381891i
\(606\) −2344.38 4060.59i −0.157152 0.272195i
\(607\) −25376.2 −1.69685 −0.848426 0.529314i \(-0.822449\pi\)
−0.848426 + 0.529314i \(0.822449\pi\)
\(608\) 460.742 + 2609.85i 0.0307328 + 0.174085i
\(609\) −6067.22 −0.403705
\(610\) −2565.05 4442.80i −0.170256 0.294891i
\(611\) 1108.68 + 1920.30i 0.0734084 + 0.127147i
\(612\) −1474.78 + 2554.39i −0.0974091 + 0.168718i
\(613\) 10802.8 + 18711.0i 0.711780 + 1.23284i 0.964189 + 0.265218i \(0.0854438\pi\)
−0.252409 + 0.967621i \(0.581223\pi\)
\(614\) 3853.91 6675.17i 0.253308 0.438743i
\(615\) −1821.86 −0.119454
\(616\) 987.029 0.0645593
\(617\) 6471.86 11209.6i 0.422281 0.731412i −0.573881 0.818938i \(-0.694563\pi\)
0.996162 + 0.0875266i \(0.0278963\pi\)
\(618\) 2556.94 4428.75i 0.166432 0.288269i
\(619\) −10134.0 −0.658030 −0.329015 0.944325i \(-0.606717\pi\)
−0.329015 + 0.944325i \(0.606717\pi\)
\(620\) −3789.71 −0.245482
\(621\) −1741.11 + 3015.70i −0.112510 + 0.194872i
\(622\) 8358.72 + 14477.7i 0.538833 + 0.933286i
\(623\) −8518.09 + 14753.8i −0.547785 + 0.948791i
\(624\) −1104.00 1912.18i −0.0708259 0.122674i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 7701.39 0.491709
\(627\) 1006.51 + 366.105i 0.0641088 + 0.0233187i
\(628\) 4223.83 0.268390
\(629\) 11117.3 + 19255.7i 0.704732 + 1.22063i
\(630\) 1287.96 + 2230.82i 0.0814503 + 0.141076i
\(631\) 3914.47 6780.07i 0.246962 0.427750i −0.715720 0.698388i \(-0.753901\pi\)
0.962681 + 0.270638i \(0.0872345\pi\)
\(632\) 3776.55 + 6541.18i 0.237695 + 0.411700i
\(633\) −3791.29 + 6566.71i −0.238057 + 0.412327i
\(634\) −15570.8 −0.975389
\(635\) 8662.93 0.541382
\(636\) 927.792 1606.98i 0.0578449 0.100190i
\(637\) 10952.3 18969.9i 0.681232 1.17993i
\(638\) 609.195 0.0378029
\(639\) 1602.16 0.0991872
\(640\) 320.000 554.256i 0.0197642 0.0342327i
\(641\) −2251.98 3900.55i −0.138764 0.240347i 0.788265 0.615336i \(-0.210980\pi\)
−0.927029 + 0.374989i \(0.877646\pi\)
\(642\) 2378.71 4120.05i 0.146231 0.253279i
\(643\) −8593.07 14883.6i −0.527026 0.912836i −0.999504 0.0314933i \(-0.989974\pi\)
0.472478 0.881342i \(-0.343360\pi\)
\(644\) 7382.68 + 12787.2i 0.451737 + 0.782431i
\(645\) 412.715 0.0251948
\(646\) 2359.35 + 13364.4i 0.143696 + 0.813957i
\(647\) −8654.23 −0.525862 −0.262931 0.964815i \(-0.584689\pi\)
−0.262931 + 0.964815i \(0.584689\pi\)
\(648\) −324.000 561.184i −0.0196419 0.0340207i
\(649\) 171.004 + 296.188i 0.0103429 + 0.0179143i
\(650\) 1150.00 1991.86i 0.0693949 0.120196i
\(651\) 8135.02 + 14090.3i 0.489764 + 0.848297i
\(652\) −6503.47 + 11264.3i −0.390637 + 0.676604i
\(653\) −3442.22 −0.206286 −0.103143 0.994667i \(-0.532890\pi\)
−0.103143 + 0.994667i \(0.532890\pi\)
\(654\) 3491.01 0.208730
\(655\) −4531.75 + 7849.22i −0.270336 + 0.468236i
\(656\) 971.656 1682.96i 0.0578305 0.100165i
\(657\) −5043.34 −0.299482
\(658\) 2759.31 0.163479
\(659\) 607.674 1052.52i 0.0359205 0.0622162i −0.847506 0.530785i \(-0.821897\pi\)
0.883427 + 0.468569i \(0.155230\pi\)
\(660\) −129.321 223.991i −0.00762700 0.0132104i
\(661\) 9794.68 16964.9i 0.576352 0.998271i −0.419541 0.907736i \(-0.637809\pi\)
0.995893 0.0905351i \(-0.0288577\pi\)
\(662\) 3570.70 + 6184.63i 0.209636 + 0.363100i
\(663\) −5653.32 9791.83i −0.331156 0.573580i
\(664\) 859.572 0.0502377
\(665\) 11138.1 + 4051.33i 0.649497 + 0.236246i
\(666\) −4884.81 −0.284208
\(667\) 4556.60 + 7892.26i 0.264516 + 0.458155i
\(668\) 3282.01 + 5684.60i 0.190097 + 0.329257i
\(669\) −2926.29 + 5068.49i −0.169114 + 0.292914i
\(670\) −4512.43 7815.76i −0.260195 0.450670i
\(671\) 1105.72 1915.16i 0.0636152 0.110185i
\(672\) −2747.66 −0.157728
\(673\) 17853.2 1.02257 0.511284 0.859412i \(-0.329170\pi\)
0.511284 + 0.859412i \(0.329170\pi\)
\(674\) −3266.65 + 5658.01i −0.186687 + 0.323351i
\(675\) 337.500 584.567i 0.0192450 0.0333333i
\(676\) −324.000 −0.0184342
\(677\) 20443.0 1.16054 0.580271 0.814423i \(-0.302947\pi\)
0.580271 + 0.814423i \(0.302947\pi\)
\(678\) −2048.24 + 3547.66i −0.116021 + 0.200954i
\(679\) −9478.70 16417.6i −0.535728 0.927907i
\(680\) 1638.64 2838.21i 0.0924104 0.160060i
\(681\) −5444.05 9429.36i −0.306338 0.530593i
\(682\) −816.817 1414.77i −0.0458615 0.0794345i
\(683\) −3882.95 −0.217536 −0.108768 0.994067i \(-0.534691\pi\)
−0.108768 + 0.994067i \(0.534691\pi\)
\(684\) −2801.89 1019.15i −0.156627 0.0569711i
\(685\) −9715.77 −0.541928
\(686\) −3811.96 6602.50i −0.212159 0.367471i
\(687\) −218.025 377.630i −0.0121080 0.0209716i
\(688\) −220.115 + 381.250i −0.0121974 + 0.0211265i
\(689\) 3556.54 + 6160.10i 0.196652 + 0.340611i
\(690\) 1934.57 3350.77i 0.106736 0.184872i
\(691\) 12415.2 0.683496 0.341748 0.939792i \(-0.388981\pi\)
0.341748 + 0.939792i \(0.388981\pi\)
\(692\) −15180.4 −0.833919
\(693\) −555.204 + 961.641i −0.0304335 + 0.0527124i
\(694\) 5491.83 9512.13i 0.300385 0.520282i
\(695\) −10039.2 −0.547926
\(696\) −1695.86 −0.0923581
\(697\) 4975.62 8618.02i 0.270394 0.468337i
\(698\) −4375.75 7579.02i −0.237285 0.410989i
\(699\) 6280.32 10877.8i 0.339833 0.588609i
\(700\) −1431.07 2478.69i −0.0772706 0.133837i
\(701\) 18484.8 + 32016.6i 0.995950 + 1.72504i 0.575839 + 0.817563i \(0.304676\pi\)
0.420111 + 0.907473i \(0.361991\pi\)
\(702\) 2484.00 0.133551
\(703\) −17214.1 + 14450.4i −0.923532 + 0.775260i
\(704\) 275.885 0.0147696
\(705\) −361.527 626.183i −0.0193133 0.0334517i
\(706\) −9525.41 16498.5i −0.507781 0.879503i
\(707\) 11183.2 19369.9i 0.594893 1.03038i
\(708\) −476.036 824.519i −0.0252691 0.0437674i
\(709\) −1299.50 + 2250.80i −0.0688346 + 0.119225i −0.898389 0.439201i \(-0.855261\pi\)
0.829554 + 0.558427i \(0.188595\pi\)
\(710\) −1780.18 −0.0940972
\(711\) −8497.25 −0.448202
\(712\) −2380.90 + 4123.84i −0.125320 + 0.217061i
\(713\) 12219.1 21164.1i 0.641808 1.11164i
\(714\) −14070.1 −0.737478
\(715\) 991.463 0.0518582
\(716\) 3336.13 5778.35i 0.174130 0.301602i
\(717\) −8205.30 14212.0i −0.427382 0.740247i
\(718\) 1255.15 2173.99i 0.0652394 0.112998i
\(719\) 1928.66 + 3340.54i 0.100037 + 0.173270i 0.911700 0.410857i \(-0.134770\pi\)
−0.811662 + 0.584127i \(0.801437\pi\)
\(720\) 360.000 + 623.538i 0.0186339 + 0.0322749i
\(721\) 24394.4 1.26005
\(722\) −12888.8 + 4697.14i −0.664363 + 0.242119i
\(723\) −17431.5 −0.896660
\(724\) 2307.86 + 3997.34i 0.118468 + 0.205193i
\(725\) −883.258 1529.85i −0.0452460 0.0783684i
\(726\) −3937.25 + 6819.52i −0.201274 + 0.348617i
\(727\) −6751.68 11694.2i −0.344437 0.596583i 0.640814 0.767696i \(-0.278597\pi\)
−0.985251 + 0.171113i \(0.945264\pi\)
\(728\) 5266.34 9121.57i 0.268109 0.464379i
\(729\) 729.000 0.0370370
\(730\) 5603.71 0.284113
\(731\) −1127.15 + 1952.29i −0.0570305 + 0.0987797i
\(732\) −3078.06 + 5331.36i −0.155421 + 0.269198i
\(733\) −39035.0 −1.96697 −0.983485 0.180987i \(-0.942071\pi\)
−0.983485 + 0.180987i \(0.942071\pi\)
\(734\) 20973.7 1.05470
\(735\) −3571.39 + 6185.83i −0.179228 + 0.310432i
\(736\) 2063.54 + 3574.16i 0.103347 + 0.179002i
\(737\) 1945.18 3369.14i 0.0972205 0.168391i
\(738\) 1093.11 + 1893.33i 0.0545231 + 0.0944368i
\(739\) −4629.94 8019.30i −0.230467 0.399181i 0.727479 0.686130i \(-0.240692\pi\)
−0.957946 + 0.286950i \(0.907359\pi\)
\(740\) 5427.57 0.269624
\(741\) 8753.63 7348.24i 0.433971 0.364298i
\(742\) 8851.57 0.437940
\(743\) 14970.9 + 25930.4i 0.739205 + 1.28034i 0.952854 + 0.303430i \(0.0981320\pi\)
−0.213648 + 0.976911i \(0.568535\pi\)
\(744\) 2273.83 + 3938.39i 0.112046 + 0.194070i
\(745\) 5750.84 9960.75i 0.282812 0.489844i
\(746\) 7848.84 + 13594.6i 0.385210 + 0.667203i
\(747\) −483.509 + 837.462i −0.0236823 + 0.0410189i
\(748\) 1412.74 0.0690574
\(749\) 22694.0 1.10710
\(750\) −375.000 + 649.519i −0.0182574 + 0.0316228i
\(751\) −14364.7 + 24880.5i −0.697972 + 1.20892i 0.271196 + 0.962524i \(0.412581\pi\)
−0.969168 + 0.246399i \(0.920753\pi\)
\(752\) 771.258 0.0374001
\(753\) −7792.62 −0.377130
\(754\) 3250.39 5629.84i 0.156992 0.271919i
\(755\) 1593.77 + 2760.49i 0.0768253 + 0.133065i
\(756\) 1545.56 2676.98i 0.0743536 0.128784i
\(757\) −16105.9 27896.2i −0.773286 1.33937i −0.935753 0.352656i \(-0.885279\pi\)
0.162468 0.986714i \(-0.448055\pi\)
\(758\) −4137.48 7166.32i −0.198259 0.343394i
\(759\) 1667.87 0.0797628
\(760\) 3113.21 + 1132.39i 0.148590 + 0.0540475i
\(761\) −26848.7 −1.27893 −0.639465 0.768820i \(-0.720844\pi\)
−0.639465 + 0.768820i \(0.720844\pi\)
\(762\) −5197.76 9002.78i −0.247106 0.428000i
\(763\) 8326.48 + 14421.9i 0.395071 + 0.684282i
\(764\) 5480.29 9492.14i 0.259516 0.449494i
\(765\) 1843.47 + 3192.99i 0.0871254 + 0.150906i
\(766\) −79.1209 + 137.041i −0.00373206 + 0.00646411i
\(767\) 3649.61 0.171812
\(768\) −768.000 −0.0360844
\(769\) −752.838 + 1303.95i −0.0353030 + 0.0611467i −0.883137 0.469115i \(-0.844573\pi\)
0.847834 + 0.530262i \(0.177906\pi\)
\(770\) 616.893 1068.49i 0.0288718 0.0500074i
\(771\) −13383.5 −0.625154
\(772\) −20631.8 −0.961858
\(773\) −2065.25 + 3577.12i −0.0960957 + 0.166443i −0.910065 0.414465i \(-0.863969\pi\)
0.813970 + 0.580907i \(0.197302\pi\)
\(774\) −247.629 428.906i −0.0114998 0.0199182i