Properties

Label 42.4.e.c.25.2
Level $42$
Weight $4$
Character 42.25
Analytic conductor $2.478$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.47808022024\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{1345})\)
Defining polynomial: \(x^{4} - x^{3} + 337 x^{2} + 336 x + 112896\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.2
Root \(9.41856 + 16.3134i\) of defining polynomial
Character \(\chi\) \(=\) 42.25
Dual form 42.4.e.c.37.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.91856 + 13.7153i) q^{5} +6.00000 q^{6} +(18.3371 - 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-1.50000 + 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.91856 + 13.7153i) q^{5} +6.00000 q^{6} +(18.3371 - 2.59808i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(15.8371 - 27.4307i) q^{10} +(-25.9186 + 44.8923i) q^{11} +(-6.00000 - 10.3923i) q^{12} +38.8371 q^{13} +(-22.8371 - 29.1627i) q^{14} -47.5114 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.6742 + 23.6845i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-38.2557 - 66.2608i) q^{19} -63.3485 q^{20} +(-20.7557 + 51.5384i) q^{21} +103.674 q^{22} +(-73.6742 - 127.608i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-62.9072 + 108.958i) q^{25} +(-38.8371 - 67.2679i) q^{26} +27.0000 q^{27} +(-27.6742 + 68.7178i) q^{28} +240.208 q^{29} +(47.5114 + 82.2921i) q^{30} +(148.337 - 256.927i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-77.7557 - 134.677i) q^{33} +54.6970 q^{34} +(180.837 + 230.927i) q^{35} +36.0000 q^{36} +(80.7670 + 139.893i) q^{37} +(-76.5114 + 132.522i) q^{38} +(-58.2557 + 100.902i) q^{39} +(63.3485 + 109.723i) q^{40} -102.977 q^{41} +(110.023 - 15.5885i) q^{42} -328.557 q^{43} +(-103.674 - 179.569i) q^{44} +(71.2670 - 123.438i) q^{45} +(-147.348 + 255.215i) q^{46} +(-33.9773 - 58.8504i) q^{47} +48.0000 q^{48} +(329.500 - 95.2825i) q^{49} +251.629 q^{50} +(-41.0227 - 71.0534i) q^{51} +(-77.6742 + 134.536i) q^{52} +(33.2443 - 57.5808i) q^{53} +(-27.0000 - 46.7654i) q^{54} -820.951 q^{55} +(146.697 - 20.7846i) q^{56} +229.534 q^{57} +(-240.208 - 416.053i) q^{58} +(230.964 - 400.041i) q^{59} +(95.0227 - 164.584i) q^{60} +(-92.6742 - 160.516i) q^{61} -593.348 q^{62} +(-102.767 - 131.232i) q^{63} +64.0000 q^{64} +(307.534 + 532.665i) q^{65} +(-155.511 + 269.354i) q^{66} +(-272.604 + 472.164i) q^{67} +(-54.6970 - 94.7379i) q^{68} +442.045 q^{69} +(219.140 - 544.146i) q^{70} -130.742 q^{71} +(-36.0000 - 62.3538i) q^{72} +(-90.6496 + 157.010i) q^{73} +(161.534 - 279.785i) q^{74} +(-188.722 - 326.875i) q^{75} +306.045 q^{76} +(-358.638 + 890.533i) q^{77} +233.023 q^{78} +(204.848 + 354.808i) q^{79} +(126.697 - 219.446i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(102.977 + 178.362i) q^{82} +347.928 q^{83} +(-137.023 - 174.976i) q^{84} -433.121 q^{85} +(328.557 + 569.077i) q^{86} +(-360.312 + 624.080i) q^{87} +(-207.348 + 359.138i) q^{88} +(-578.580 - 1002.13i) q^{89} -285.068 q^{90} +(712.161 - 100.902i) q^{91} +589.394 q^{92} +(445.011 + 770.782i) q^{93} +(-67.9546 + 117.701i) q^{94} +(605.860 - 1049.38i) q^{95} +(-48.0000 - 83.1384i) q^{96} +1618.30 q^{97} +(-494.534 - 475.428i) q^{98} +466.534 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{2} - 6 q^{3} - 8 q^{4} - 5 q^{5} + 24 q^{6} + 32 q^{8} - 18 q^{9} - 10 q^{10} - 67 q^{11} - 24 q^{12} + 82 q^{13} - 18 q^{14} + 30 q^{15} - 32 q^{16} + 92 q^{17} - 36 q^{18} - 43 q^{19} + 40 q^{20} + 27 q^{21} + 268 q^{22} - 148 q^{23} - 48 q^{24} - 435 q^{25} - 82 q^{26} + 108 q^{27} + 36 q^{28} + 154 q^{29} - 30 q^{30} + 520 q^{31} - 64 q^{32} - 201 q^{33} - 368 q^{34} + 650 q^{35} + 144 q^{36} - 7 q^{37} - 86 q^{38} - 123 q^{39} - 40 q^{40} - 852 q^{41} - 214 q^{43} - 268 q^{44} - 45 q^{45} - 296 q^{46} - 576 q^{47} + 192 q^{48} + 1318 q^{49} + 1740 q^{50} + 276 q^{51} - 164 q^{52} + 243 q^{53} - 108 q^{54} - 1010 q^{55} + 258 q^{57} - 154 q^{58} + 7 q^{59} - 60 q^{60} - 224 q^{61} - 2080 q^{62} - 81 q^{63} + 256 q^{64} + 570 q^{65} - 402 q^{66} - 687 q^{67} + 368 q^{68} + 888 q^{69} + 1390 q^{70} + 944 q^{71} - 144 q^{72} + 921 q^{73} - 14 q^{74} - 1305 q^{75} + 344 q^{76} - 371 q^{77} + 492 q^{78} + 526 q^{79} - 80 q^{80} - 162 q^{81} + 852 q^{82} - 442 q^{83} - 108 q^{84} - 5840 q^{85} + 214 q^{86} - 231 q^{87} - 536 q^{88} - 774 q^{89} + 180 q^{90} + 1345 q^{91} + 1184 q^{92} + 1560 q^{93} - 1152 q^{94} + 1910 q^{95} - 192 q^{96} + 3906 q^{97} - 1318 q^{98} + 1206 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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
\(5\) 7.91856 + 13.7153i 0.708258 + 1.22674i 0.965503 + 0.260392i \(0.0838518\pi\)
−0.257245 + 0.966346i \(0.582815\pi\)
\(6\) 6.00000 0.408248
\(7\) 18.3371 2.59808i 0.990111 0.140283i
\(8\) 8.00000 0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) 15.8371 27.4307i 0.500814 0.867435i
\(11\) −25.9186 + 44.8923i −0.710431 + 1.23050i 0.254265 + 0.967135i \(0.418167\pi\)
−0.964696 + 0.263368i \(0.915167\pi\)
\(12\) −6.00000 10.3923i −0.144338 0.250000i
\(13\) 38.8371 0.828575 0.414288 0.910146i \(-0.364031\pi\)
0.414288 + 0.910146i \(0.364031\pi\)
\(14\) −22.8371 29.1627i −0.435963 0.556719i
\(15\) −47.5114 −0.817825
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −13.6742 + 23.6845i −0.195088 + 0.337902i −0.946929 0.321442i \(-0.895832\pi\)
0.751842 + 0.659344i \(0.229166\pi\)
\(18\) −9.00000 + 15.5885i −0.117851 + 0.204124i
\(19\) −38.2557 66.2608i −0.461919 0.800067i 0.537138 0.843494i \(-0.319505\pi\)
−0.999057 + 0.0434278i \(0.986172\pi\)
\(20\) −63.3485 −0.708258
\(21\) −20.7557 + 51.5384i −0.215679 + 0.535552i
\(22\) 103.674 1.00470
\(23\) −73.6742 127.608i −0.667919 1.15687i −0.978485 0.206318i \(-0.933852\pi\)
0.310566 0.950552i \(-0.399481\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) −62.9072 + 108.958i −0.503258 + 0.871668i
\(26\) −38.8371 67.2679i −0.292946 0.507397i
\(27\) 27.0000 0.192450
\(28\) −27.6742 + 68.7178i −0.186784 + 0.463802i
\(29\) 240.208 1.53812 0.769061 0.639175i \(-0.220724\pi\)
0.769061 + 0.639175i \(0.220724\pi\)
\(30\) 47.5114 + 82.2921i 0.289145 + 0.500814i
\(31\) 148.337 256.927i 0.859424 1.48857i −0.0130559 0.999915i \(-0.504156\pi\)
0.872480 0.488651i \(-0.162511\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) −77.7557 134.677i −0.410167 0.710431i
\(34\) 54.6970 0.275896
\(35\) 180.837 + 230.927i 0.873344 + 1.11525i
\(36\) 36.0000 0.166667
\(37\) 80.7670 + 139.893i 0.358865 + 0.621573i 0.987772 0.155908i \(-0.0498304\pi\)
−0.628906 + 0.777481i \(0.716497\pi\)
\(38\) −76.5114 + 132.522i −0.326626 + 0.565733i
\(39\) −58.2557 + 100.902i −0.239189 + 0.414288i
\(40\) 63.3485 + 109.723i 0.250407 + 0.433717i
\(41\) −102.977 −0.392252 −0.196126 0.980579i \(-0.562836\pi\)
−0.196126 + 0.980579i \(0.562836\pi\)
\(42\) 110.023 15.5885i 0.404211 0.0572703i
\(43\) −328.557 −1.16522 −0.582610 0.812752i \(-0.697968\pi\)
−0.582610 + 0.812752i \(0.697968\pi\)
\(44\) −103.674 179.569i −0.355215 0.615251i
\(45\) 71.2670 123.438i 0.236086 0.408913i
\(46\) −147.348 + 255.215i −0.472290 + 0.818031i
\(47\) −33.9773 58.8504i −0.105449 0.182643i 0.808473 0.588534i \(-0.200295\pi\)
−0.913921 + 0.405891i \(0.866961\pi\)
\(48\) 48.0000 0.144338
\(49\) 329.500 95.2825i 0.960641 0.277791i
\(50\) 251.629 0.711714
\(51\) −41.0227 71.0534i −0.112634 0.195088i
\(52\) −77.6742 + 134.536i −0.207144 + 0.358784i
\(53\) 33.2443 57.5808i 0.0861596 0.149233i −0.819725 0.572757i \(-0.805874\pi\)
0.905885 + 0.423524i \(0.139207\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) −820.951 −2.01267
\(56\) 146.697 20.7846i 0.350057 0.0495975i
\(57\) 229.534 0.533378
\(58\) −240.208 416.053i −0.543809 0.941904i
\(59\) 230.964 400.041i 0.509643 0.882728i −0.490294 0.871557i \(-0.663111\pi\)
0.999938 0.0111711i \(-0.00355595\pi\)
\(60\) 95.0227 164.584i 0.204456 0.354129i
\(61\) −92.6742 160.516i −0.194520 0.336919i 0.752223 0.658909i \(-0.228982\pi\)
−0.946743 + 0.321990i \(0.895648\pi\)
\(62\) −593.348 −1.21541
\(63\) −102.767 131.232i −0.205515 0.262440i
\(64\) 64.0000 0.125000
\(65\) 307.534 + 532.665i 0.586845 + 1.01644i
\(66\) −155.511 + 269.354i −0.290032 + 0.502351i
\(67\) −272.604 + 472.164i −0.497073 + 0.860956i −0.999994 0.00337637i \(-0.998925\pi\)
0.502921 + 0.864332i \(0.332259\pi\)
\(68\) −54.6970 94.7379i −0.0975438 0.168951i
\(69\) 442.045 0.771247
\(70\) 219.140 544.146i 0.374175 0.929113i
\(71\) −130.742 −0.218539 −0.109270 0.994012i \(-0.534851\pi\)
−0.109270 + 0.994012i \(0.534851\pi\)
\(72\) −36.0000 62.3538i −0.0589256 0.102062i
\(73\) −90.6496 + 157.010i −0.145339 + 0.251734i −0.929499 0.368824i \(-0.879761\pi\)
0.784160 + 0.620558i \(0.213094\pi\)
\(74\) 161.534 279.785i 0.253756 0.439519i
\(75\) −188.722 326.875i −0.290556 0.503258i
\(76\) 306.045 0.461919
\(77\) −358.638 + 890.533i −0.530787 + 1.31800i
\(78\) 233.023 0.338264
\(79\) 204.848 + 354.808i 0.291737 + 0.505304i 0.974221 0.225597i \(-0.0724333\pi\)
−0.682483 + 0.730901i \(0.739100\pi\)
\(80\) 126.697 219.446i 0.177064 0.306685i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) 102.977 + 178.362i 0.138682 + 0.240205i
\(83\) 347.928 0.460121 0.230061 0.973176i \(-0.426108\pi\)
0.230061 + 0.973176i \(0.426108\pi\)
\(84\) −137.023 174.976i −0.177981 0.227280i
\(85\) −433.121 −0.552689
\(86\) 328.557 + 569.077i 0.411967 + 0.713548i
\(87\) −360.312 + 624.080i −0.444018 + 0.769061i
\(88\) −207.348 + 359.138i −0.251175 + 0.435048i
\(89\) −578.580 1002.13i −0.689093 1.19354i −0.972132 0.234436i \(-0.924676\pi\)
0.283038 0.959109i \(-0.408658\pi\)
\(90\) −285.068 −0.333876
\(91\) 712.161 100.902i 0.820382 0.116235i
\(92\) 589.394 0.667919
\(93\) 445.011 + 770.782i 0.496188 + 0.859424i
\(94\) −67.9546 + 117.701i −0.0745636 + 0.129148i
\(95\) 605.860 1049.38i 0.654315 1.13331i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) 1618.30 1.69395 0.846976 0.531631i \(-0.178421\pi\)
0.846976 + 0.531631i \(0.178421\pi\)
\(98\) −494.534 475.428i −0.509750 0.490056i
\(99\) 466.534 0.473621
\(100\) −251.629 435.834i −0.251629 0.435834i
\(101\) −359.371 + 622.449i −0.354047 + 0.613228i −0.986954 0.161000i \(-0.948528\pi\)
0.632907 + 0.774228i \(0.281861\pi\)
\(102\) −82.0454 + 142.107i −0.0796442 + 0.137948i
\(103\) 805.790 + 1395.67i 0.770843 + 1.33514i 0.937102 + 0.349057i \(0.113498\pi\)
−0.166259 + 0.986082i \(0.553169\pi\)
\(104\) 310.697 0.292946
\(105\) −871.222 + 123.438i −0.809738 + 0.114727i
\(106\) −132.977 −0.121848
\(107\) −467.335 809.448i −0.422234 0.731330i 0.573924 0.818909i \(-0.305420\pi\)
−0.996158 + 0.0875784i \(0.972087\pi\)
\(108\) −54.0000 + 93.5307i −0.0481125 + 0.0833333i
\(109\) 598.509 1036.65i 0.525934 0.910944i −0.473610 0.880735i \(-0.657049\pi\)
0.999544 0.0302095i \(-0.00961746\pi\)
\(110\) 820.951 + 1421.93i 0.711587 + 1.23251i
\(111\) −484.602 −0.414382
\(112\) −182.697 233.302i −0.154136 0.196830i
\(113\) −2384.64 −1.98521 −0.992604 0.121400i \(-0.961262\pi\)
−0.992604 + 0.121400i \(0.961262\pi\)
\(114\) −229.534 397.565i −0.188578 0.326626i
\(115\) 1166.79 2020.94i 0.946118 1.63872i
\(116\) −480.417 + 832.106i −0.384531 + 0.666027i
\(117\) −174.767 302.705i −0.138096 0.239189i
\(118\) −923.856 −0.720744
\(119\) −189.212 + 469.832i −0.145757 + 0.361928i
\(120\) −380.091 −0.289145
\(121\) −678.044 1174.41i −0.509424 0.882349i
\(122\) −185.348 + 321.033i −0.137546 + 0.238237i
\(123\) 154.466 267.543i 0.113234 0.196126i
\(124\) 593.348 + 1027.71i 0.429712 + 0.744283i
\(125\) −12.8977 −0.00922883
\(126\) −124.534 + 309.230i −0.0880506 + 0.218638i
\(127\) −2673.92 −1.86829 −0.934143 0.356898i \(-0.883834\pi\)
−0.934143 + 0.356898i \(0.883834\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 492.835 853.616i 0.336370 0.582610i
\(130\) 615.068 1065.33i 0.414962 0.718735i
\(131\) 19.4299 + 33.6536i 0.0129588 + 0.0224453i 0.872432 0.488735i \(-0.162542\pi\)
−0.859473 + 0.511181i \(0.829208\pi\)
\(132\) 622.045 0.410167
\(133\) −873.650 1115.64i −0.569587 0.727356i
\(134\) 1090.42 0.702968
\(135\) 213.801 + 370.314i 0.136304 + 0.236086i
\(136\) −109.394 + 189.476i −0.0689739 + 0.119466i
\(137\) 384.072 665.232i 0.239514 0.414851i −0.721061 0.692872i \(-0.756345\pi\)
0.960575 + 0.278021i \(0.0896784\pi\)
\(138\) −442.045 765.645i −0.272677 0.472290i
\(139\) 1052.55 0.642274 0.321137 0.947033i \(-0.395935\pi\)
0.321137 + 0.947033i \(0.395935\pi\)
\(140\) −1161.63 + 164.584i −0.701254 + 0.0993564i
\(141\) 203.864 0.121762
\(142\) 130.742 + 226.453i 0.0772652 + 0.133827i
\(143\) −1006.60 + 1743.49i −0.588646 + 1.01956i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) 1902.10 + 3294.54i 1.08939 + 1.88687i
\(146\) 362.598 0.205540
\(147\) −246.699 + 998.990i −0.138418 + 0.560512i
\(148\) −646.136 −0.358865
\(149\) −180.489 312.615i −0.0992363 0.171882i 0.812132 0.583473i \(-0.198307\pi\)
−0.911369 + 0.411591i \(0.864973\pi\)
\(150\) −377.443 + 653.751i −0.205454 + 0.355857i
\(151\) −774.195 + 1340.95i −0.417239 + 0.722679i −0.995661 0.0930587i \(-0.970336\pi\)
0.578422 + 0.815738i \(0.303669\pi\)
\(152\) −306.045 530.086i −0.163313 0.282866i
\(153\) 246.136 0.130058
\(154\) 1901.09 269.354i 0.994766 0.140942i
\(155\) 4698.47 2.43477
\(156\) −233.023 403.607i −0.119595 0.207144i
\(157\) 483.534 837.506i 0.245798 0.425734i −0.716558 0.697528i \(-0.754283\pi\)
0.962356 + 0.271794i \(0.0876168\pi\)
\(158\) 409.697 709.616i 0.206289 0.357304i
\(159\) 99.7330 + 172.743i 0.0497443 + 0.0861596i
\(160\) −506.788 −0.250407
\(161\) −1682.51 2148.54i −0.823604 1.05173i
\(162\) 162.000 0.0785674
\(163\) 663.250 + 1148.78i 0.318710 + 0.552022i 0.980219 0.197915i \(-0.0634170\pi\)
−0.661509 + 0.749937i \(0.730084\pi\)
\(164\) 205.955 356.724i 0.0980631 0.169850i
\(165\) 1231.43 2132.89i 0.581008 1.00634i
\(166\) −347.928 602.629i −0.162677 0.281766i
\(167\) 1416.70 0.656451 0.328225 0.944599i \(-0.393549\pi\)
0.328225 + 0.944599i \(0.393549\pi\)
\(168\) −166.045 + 412.307i −0.0762541 + 0.189346i
\(169\) −688.678 −0.313463
\(170\) 433.121 + 750.188i 0.195405 + 0.338452i
\(171\) −344.301 + 596.347i −0.153973 + 0.266689i
\(172\) 657.114 1138.15i 0.291305 0.504555i
\(173\) 518.299 + 897.721i 0.227778 + 0.394523i 0.957149 0.289595i \(-0.0935207\pi\)
−0.729371 + 0.684118i \(0.760187\pi\)
\(174\) 1441.25 0.627936
\(175\) −870.454 + 2161.42i −0.376001 + 0.933647i
\(176\) 829.394 0.355215
\(177\) 692.892 + 1200.12i 0.294243 + 0.509643i
\(178\) −1157.16 + 2004.26i −0.487263 + 0.843964i
\(179\) 383.716 664.615i 0.160225 0.277518i −0.774724 0.632299i \(-0.782111\pi\)
0.934949 + 0.354781i \(0.115445\pi\)
\(180\) 285.068 + 493.753i 0.118043 + 0.204456i
\(181\) −3957.71 −1.62527 −0.812636 0.582772i \(-0.801968\pi\)
−0.812636 + 0.582772i \(0.801968\pi\)
\(182\) −886.928 1132.60i −0.361228 0.461284i
\(183\) 556.045 0.224612
\(184\) −589.394 1020.86i −0.236145 0.409015i
\(185\) −1279.12 + 2215.50i −0.508338 + 0.880468i
\(186\) 890.023 1541.56i 0.350858 0.607704i
\(187\) −708.833 1227.74i −0.277193 0.480112i
\(188\) 271.818 0.105449
\(189\) 495.102 70.1481i 0.190547 0.0269975i
\(190\) −2423.44 −0.925341
\(191\) 902.648 + 1563.43i 0.341954 + 0.592282i 0.984796 0.173717i \(-0.0555778\pi\)
−0.642841 + 0.765999i \(0.722244\pi\)
\(192\) −96.0000 + 166.277i −0.0360844 + 0.0625000i
\(193\) −1685.42 + 2919.23i −0.628597 + 1.08876i 0.359237 + 0.933247i \(0.383037\pi\)
−0.987833 + 0.155515i \(0.950296\pi\)
\(194\) −1618.30 2802.98i −0.598903 1.03733i
\(195\) −1845.20 −0.677630
\(196\) −328.932 + 1331.99i −0.119873 + 0.485418i
\(197\) −4612.31 −1.66809 −0.834044 0.551697i \(-0.813980\pi\)
−0.834044 + 0.551697i \(0.813980\pi\)
\(198\) −466.534 808.061i −0.167450 0.290032i
\(199\) 1114.93 1931.12i 0.397163 0.687906i −0.596212 0.802827i \(-0.703328\pi\)
0.993375 + 0.114921i \(0.0366615\pi\)
\(200\) −503.258 + 871.668i −0.177928 + 0.308181i
\(201\) −817.812 1416.49i −0.286985 0.497073i
\(202\) 1437.48 0.500698
\(203\) 4404.73 624.080i 1.52291 0.215772i
\(204\) 328.182 0.112634
\(205\) −815.432 1412.37i −0.277816 0.481191i
\(206\) 1611.58 2791.34i 0.545068 0.944086i
\(207\) −663.068 + 1148.47i −0.222640 + 0.385623i
\(208\) −310.697 538.143i −0.103572 0.179392i
\(209\) 3966.13 1.31265
\(210\) 1085.02 + 1385.56i 0.356541 + 0.455299i
\(211\) 912.614 0.297758 0.148879 0.988855i \(-0.452434\pi\)
0.148879 + 0.988855i \(0.452434\pi\)
\(212\) 132.977 + 230.323i 0.0430798 + 0.0746164i
\(213\) 196.114 339.679i 0.0630868 0.109270i
\(214\) −934.670 + 1618.90i −0.298564 + 0.517129i
\(215\) −2601.70 4506.27i −0.825276 1.42942i
\(216\) 216.000 0.0680414
\(217\) 2052.56 5096.70i 0.642105 1.59441i
\(218\) −2394.04 −0.743783
\(219\) −271.949 471.029i −0.0839114 0.145339i
\(220\) 1641.90 2843.86i 0.503168 0.871513i
\(221\) −531.068 + 919.837i −0.161645 + 0.279977i
\(222\) 484.602 + 839.356i 0.146506 + 0.253756i
\(223\) −4319.47 −1.29710 −0.648549 0.761173i \(-0.724624\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(224\) −221.394 + 549.742i −0.0660380 + 0.163979i
\(225\) 1132.33 0.335505
\(226\) 2384.64 + 4130.32i 0.701877 + 1.21569i
\(227\) −1030.64 + 1785.12i −0.301349 + 0.521951i −0.976442 0.215782i \(-0.930770\pi\)
0.675093 + 0.737733i \(0.264103\pi\)
\(228\) −459.068 + 795.129i −0.133344 + 0.230959i
\(229\) 1737.32 + 3009.12i 0.501332 + 0.868333i 0.999999 + 0.00153905i \(0.000489896\pi\)
−0.498667 + 0.866794i \(0.666177\pi\)
\(230\) −4667.15 −1.33801
\(231\) −1775.72 2267.57i −0.505773 0.645866i
\(232\) 1921.67 0.543809
\(233\) −388.049 672.121i −0.109107 0.188979i 0.806302 0.591505i \(-0.201466\pi\)
−0.915409 + 0.402525i \(0.868132\pi\)
\(234\) −349.534 + 605.411i −0.0976485 + 0.169132i
\(235\) 538.102 932.020i 0.149370 0.258716i
\(236\) 923.856 + 1600.17i 0.254822 + 0.441364i
\(237\) −1229.09 −0.336869
\(238\) 1002.98 142.107i 0.273167 0.0387035i
\(239\) 2006.80 0.543133 0.271567 0.962420i \(-0.412458\pi\)
0.271567 + 0.962420i \(0.412458\pi\)
\(240\) 380.091 + 658.337i 0.102228 + 0.177064i
\(241\) −402.824 + 697.711i −0.107669 + 0.186488i −0.914825 0.403850i \(-0.867672\pi\)
0.807157 + 0.590337i \(0.201005\pi\)
\(242\) −1356.09 + 2348.81i −0.360217 + 0.623915i
\(243\) −121.500 210.444i −0.0320750 0.0555556i
\(244\) 741.394 0.194520
\(245\) 3916.00 + 3764.71i 1.02116 + 0.981707i
\(246\) −617.864 −0.160136
\(247\) −1485.74 2573.38i −0.382734 0.662915i
\(248\) 1186.70 2055.42i 0.303852 0.526287i
\(249\) −521.892 + 903.944i −0.132826 + 0.230061i
\(250\) 12.8977 + 22.3394i 0.00326289 + 0.00565148i
\(251\) 1421.78 0.357539 0.178769 0.983891i \(-0.442788\pi\)
0.178769 + 0.983891i \(0.442788\pi\)
\(252\) 660.136 93.5307i 0.165019 0.0233805i
\(253\) 7638.12 1.89804
\(254\) 2673.92 + 4631.37i 0.660539 + 1.14409i
\(255\) 649.682 1125.28i 0.159548 0.276345i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 732.909 + 1269.44i 0.177890 + 0.308114i 0.941157 0.337968i \(-0.109740\pi\)
−0.763268 + 0.646082i \(0.776406\pi\)
\(258\) −1971.34 −0.475699
\(259\) 1844.49 + 2355.39i 0.442513 + 0.565084i
\(260\) −2460.27 −0.586845
\(261\) −1080.94 1872.24i −0.256354 0.444018i
\(262\) 38.8598 67.3072i 0.00916324 0.0158712i
\(263\) −3495.69 + 6054.72i −0.819596 + 1.41958i 0.0863847 + 0.996262i \(0.472469\pi\)
−0.905980 + 0.423320i \(0.860865\pi\)
\(264\) −622.045 1077.41i −0.145016 0.251175i
\(265\) 1052.99 0.244093
\(266\) −1058.70 + 2628.85i −0.244033 + 0.605958i
\(267\) 3471.48 0.795696
\(268\) −1090.42 1888.66i −0.248537 0.430478i
\(269\) −404.479 + 700.578i −0.0916786 + 0.158792i −0.908218 0.418498i \(-0.862557\pi\)
0.816539 + 0.577290i \(0.195890\pi\)
\(270\) 427.602 740.629i 0.0963816 0.166938i
\(271\) −3330.88 5769.26i −0.746630 1.29320i −0.949429 0.313981i \(-0.898337\pi\)
0.202799 0.979220i \(-0.434996\pi\)
\(272\) 437.576 0.0975438
\(273\) −806.091 + 2001.60i −0.178706 + 0.443745i
\(274\) −1536.29 −0.338725
\(275\) −3260.93 5648.09i −0.715059 1.23852i
\(276\) −884.091 + 1531.29i −0.192812 + 0.333960i
\(277\) 3765.73 6522.44i 0.816827 1.41479i −0.0911823 0.995834i \(-0.529065\pi\)
0.908009 0.418951i \(-0.137602\pi\)
\(278\) −1052.55 1823.07i −0.227078 0.393311i
\(279\) −2670.07 −0.572949
\(280\) 1446.70 + 1847.42i 0.308774 + 0.394301i
\(281\) 1690.19 0.358819 0.179410 0.983774i \(-0.442581\pi\)
0.179410 + 0.983774i \(0.442581\pi\)
\(282\) −203.864 353.102i −0.0430493 0.0745636i
\(283\) −1589.12 + 2752.43i −0.333792 + 0.578145i −0.983252 0.182251i \(-0.941662\pi\)
0.649460 + 0.760396i \(0.274995\pi\)
\(284\) 261.485 452.905i 0.0546348 0.0946302i
\(285\) 1817.58 + 3148.14i 0.377769 + 0.654315i
\(286\) 4026.41 0.832470
\(287\) −1888.31 + 267.543i −0.388374 + 0.0550263i
\(288\) 288.000 0.0589256
\(289\) 2082.53 + 3607.05i 0.423882 + 0.734184i
\(290\) 3804.21 6589.08i 0.770313 1.33422i
\(291\) −2427.45 + 4204.46i −0.489002 + 0.846976i
\(292\) −362.598 628.039i −0.0726694 0.125867i
\(293\) −2176.53 −0.433974 −0.216987 0.976174i \(-0.569623\pi\)
−0.216987 + 0.976174i \(0.569623\pi\)
\(294\) 1977.00 571.695i 0.392180 0.113408i
\(295\) 7315.61 1.44383
\(296\) 646.136 + 1119.14i 0.126878 + 0.219759i
\(297\) −699.801 + 1212.09i −0.136722 + 0.236810i
\(298\) −360.977 + 625.231i −0.0701706 + 0.121539i
\(299\) −2861.30 4955.91i −0.553421 0.958554i
\(300\) 1509.77 0.290556
\(301\) −6024.79 + 853.616i −1.15370 + 0.163460i
\(302\) 3096.78 0.590065
\(303\) −1078.11 1867.35i −0.204409 0.354047i
\(304\) −612.091 + 1060.17i −0.115480 + 0.200017i
\(305\) 1467.69 2542.12i 0.275541 0.477250i
\(306\) −246.136 426.321i −0.0459826 0.0796442i
\(307\) 623.504 0.115913 0.0579564 0.998319i \(-0.481542\pi\)
0.0579564 + 0.998319i \(0.481542\pi\)
\(308\) −2367.62 3023.43i −0.438012 0.559337i
\(309\) −4834.74 −0.890093
\(310\) −4698.47 8137.98i −0.860822 1.49099i
\(311\) −233.996 + 405.293i −0.0426647 + 0.0738973i −0.886569 0.462596i \(-0.846918\pi\)
0.843905 + 0.536493i \(0.180251\pi\)
\(312\) −466.045 + 807.214i −0.0845661 + 0.146473i
\(313\) −1806.41 3128.79i −0.326211 0.565014i 0.655546 0.755156i \(-0.272439\pi\)
−0.981757 + 0.190141i \(0.939105\pi\)
\(314\) −1934.14 −0.347610
\(315\) 986.131 2448.66i 0.176388 0.437988i
\(316\) −1638.79 −0.291737
\(317\) −2265.87 3924.60i −0.401463 0.695355i 0.592439 0.805615i \(-0.298165\pi\)
−0.993903 + 0.110260i \(0.964832\pi\)
\(318\) 199.466 345.485i 0.0351745 0.0609240i
\(319\) −6225.85 + 10783.5i −1.09273 + 1.89266i
\(320\) 506.788 + 877.782i 0.0885322 + 0.153342i
\(321\) 2804.01 0.487553
\(322\) −2038.88 + 5062.73i −0.352864 + 0.876196i
\(323\) 2092.47 0.360459
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) −2443.13 + 4231.63i −0.416987 + 0.722242i
\(326\) 1326.50 2297.57i 0.225362 0.390339i
\(327\) 1795.53 + 3109.95i 0.303648 + 0.525934i
\(328\) −823.818 −0.138682
\(329\) −775.943 990.871i −0.130028 0.166044i
\(330\) −4925.70 −0.821670
\(331\) 618.528 + 1071.32i 0.102711 + 0.177901i 0.912801 0.408405i \(-0.133915\pi\)
−0.810090 + 0.586306i \(0.800582\pi\)
\(332\) −695.856 + 1205.26i −0.115030 + 0.199238i
\(333\) 726.903 1259.03i 0.119622 0.207191i
\(334\) −1416.70 2453.79i −0.232090 0.401992i
\(335\) −8634.53 −1.40822
\(336\) 880.182 124.708i 0.142910 0.0202481i
\(337\) −1867.83 −0.301921 −0.150960 0.988540i \(-0.548237\pi\)
−0.150960 + 0.988540i \(0.548237\pi\)
\(338\) 688.678 + 1192.83i 0.110826 + 0.191956i
\(339\) 3576.97 6195.49i 0.573080 0.992604i
\(340\) 866.242 1500.38i 0.138172 0.239322i
\(341\) 7689.37 + 13318.4i 1.22112 + 2.11505i
\(342\) 1377.20 0.217751
\(343\) 5794.53 2603.27i 0.912173 0.409806i
\(344\) −2628.45 −0.411967
\(345\) 3500.36 + 6062.81i 0.546241 + 0.946118i
\(346\) 1036.60 1795.44i 0.161063 0.278970i
\(347\) 31.6819 54.8746i 0.00490136 0.00848940i −0.863564 0.504239i \(-0.831773\pi\)
0.868466 + 0.495749i \(0.165107\pi\)
\(348\) −1441.25 2496.32i −0.222009 0.384531i
\(349\) 1223.79 0.187702 0.0938508 0.995586i \(-0.470082\pi\)
0.0938508 + 0.995586i \(0.470082\pi\)
\(350\) 4614.15 653.751i 0.704676 0.0998413i
\(351\) 1048.60 0.159459
\(352\) −829.394 1436.55i −0.125588 0.217524i
\(353\) 2257.81 3910.64i 0.340428 0.589638i −0.644085 0.764954i \(-0.722762\pi\)
0.984512 + 0.175316i \(0.0560949\pi\)
\(354\) 1385.78 2400.25i 0.208061 0.360372i
\(355\) −1035.29 1793.18i −0.154782 0.268090i
\(356\) 4628.64 0.689093
\(357\) −936.841 1196.34i −0.138888 0.177358i
\(358\) −1534.86 −0.226592
\(359\) −1114.25 1929.93i −0.163810 0.283727i 0.772422 0.635109i \(-0.219045\pi\)
−0.936232 + 0.351383i \(0.885712\pi\)
\(360\) 570.136 987.505i 0.0834690 0.144572i
\(361\) 502.506 870.365i 0.0732622 0.126894i
\(362\) 3957.71 + 6854.95i 0.574620 + 0.995271i
\(363\) 4068.26 0.588232
\(364\) −1074.79 + 2668.80i −0.154764 + 0.384295i
\(365\) −2871.26 −0.411749
\(366\) −556.045 963.099i −0.0794125 0.137546i
\(367\) 718.670 1244.77i 0.102219 0.177048i −0.810380 0.585905i \(-0.800739\pi\)
0.912598 + 0.408857i \(0.134072\pi\)
\(368\) −1178.79 + 2041.72i −0.166980 + 0.289217i
\(369\) 463.398 + 802.628i 0.0653754 + 0.113234i
\(370\) 5116.47 0.718899
\(371\) 460.006 1142.24i 0.0643728 0.159844i
\(372\) −3560.09 −0.496188
\(373\) 6118.71 + 10597.9i 0.849370 + 1.47115i 0.881771 + 0.471677i \(0.156351\pi\)
−0.0324014 + 0.999475i \(0.510315\pi\)
\(374\) −1417.67 + 2455.47i −0.196005 + 0.339490i
\(375\) 19.3465 33.5092i 0.00266413 0.00461442i
\(376\) −271.818 470.803i −0.0372818 0.0645740i
\(377\) 9329.00 1.27445
\(378\) −616.602 787.394i −0.0839011 0.107141i
\(379\) −10647.0 −1.44301 −0.721503 0.692411i \(-0.756549\pi\)
−0.721503 + 0.692411i \(0.756549\pi\)
\(380\) 2423.44 + 4197.52i 0.327157 + 0.566653i
\(381\) 4010.89 6947.06i 0.539328 0.934143i
\(382\) 1805.30 3126.86i 0.241798 0.418807i
\(383\) 3357.41 + 5815.20i 0.447925 + 0.775829i 0.998251 0.0591208i \(-0.0188297\pi\)
−0.550326 + 0.834950i \(0.685496\pi\)
\(384\) 384.000 0.0510310
\(385\) −15053.9 + 2132.89i −1.99277 + 0.282344i
\(386\) 6741.68 0.888970
\(387\) 1478.51 + 2560.85i 0.194203 + 0.336370i
\(388\) −3236.60 + 5605.95i −0.423488 + 0.733503i
\(389\) 5326.54 9225.83i 0.694258 1.20249i −0.276173 0.961108i \(-0.589066\pi\)
0.970430 0.241381i \(-0.0776005\pi\)
\(390\) 1845.20 + 3195.99i 0.239578 + 0.414962i
\(391\) 4029.76 0.521211
\(392\) 2636.00 762.260i 0.339638 0.0982141i
\(393\) −116.580 −0.0149635
\(394\) 4612.31 + 7988.76i 0.589758 + 1.02149i
\(395\) −3244.21 + 5619.14i −0.413250 + 0.715771i
\(396\) −933.068 + 1616.12i −0.118405 + 0.205084i
\(397\) −1610.52 2789.50i −0.203601 0.352648i 0.746085 0.665851i \(-0.231931\pi\)
−0.949686 + 0.313203i \(0.898598\pi\)
\(398\) −4459.73 −0.561673
\(399\) 4208.99 596.347i 0.528103 0.0748238i
\(400\) 2013.03 0.251629
\(401\) −6242.50 10812.3i −0.777395 1.34649i −0.933438 0.358738i \(-0.883207\pi\)
0.156043 0.987750i \(-0.450126\pi\)
\(402\) −1635.62 + 2832.99i −0.202929 + 0.351484i
\(403\) 5760.99 9978.32i 0.712097 1.23339i
\(404\) −1437.48 2489.80i −0.177024 0.306614i
\(405\) −1282.81 −0.157391
\(406\) −5485.67 7005.14i −0.670564 0.856303i
\(407\) −8373.46 −1.01980
\(408\) −328.182 568.428i −0.0398221 0.0689739i
\(409\) −3518.69 + 6094.56i −0.425399 + 0.736813i −0.996458 0.0840967i \(-0.973200\pi\)
0.571059 + 0.820909i \(0.306533\pi\)
\(410\) −1630.86 + 2824.74i −0.196445 + 0.340253i
\(411\) 1152.22 + 1995.70i 0.138284 + 0.239514i
\(412\) −6446.32 −0.770843
\(413\) 3195.88 7935.67i 0.380772 0.945493i
\(414\) 2652.27 0.314860
\(415\) 2755.09 + 4771.95i 0.325884 + 0.564448i
\(416\) −621.394 + 1076.29i −0.0732364 + 0.126849i
\(417\) −1578.82 + 2734.60i −0.185408 + 0.321137i
\(418\) −3966.13 6869.54i −0.464090 0.803828i
\(419\) −1549.66 −0.180682 −0.0903410 0.995911i \(-0.528796\pi\)
−0.0903410 + 0.995911i \(0.528796\pi\)
\(420\) 1314.84 3264.88i 0.152756 0.379309i
\(421\) 5531.63 0.640369 0.320184 0.947355i \(-0.396255\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(422\) −912.614 1580.69i −0.105273 0.182339i
\(423\) −305.795 + 529.653i −0.0351496 + 0.0608809i
\(424\) 265.955 460.647i 0.0304620 0.0527618i
\(425\) −1720.42 2979.85i −0.196359 0.340103i
\(426\) −784.454 −0.0892182
\(427\) −2116.41 2702.64i −0.239860 0.306299i
\(428\) 3738.68 0.422234
\(429\) −3019.81 5230.46i −0.339855 0.588646i
\(430\) −5203.39 + 9012.54i −0.583558 + 1.01075i
\(431\) 1014.97 1757.97i 0.113432 0.196470i −0.803720 0.595008i \(-0.797149\pi\)
0.917152 + 0.398538i \(0.130482\pi\)
\(432\) −216.000 374.123i −0.0240563 0.0416667i
\(433\) −327.739 −0.0363744 −0.0181872 0.999835i \(-0.505789\pi\)
−0.0181872 + 0.999835i \(0.505789\pi\)
\(434\) −10880.3 + 1541.56i −1.20339 + 0.170501i
\(435\) −11412.6 −1.25792
\(436\) 2394.04 + 4146.60i 0.262967 + 0.455472i
\(437\) −5636.92 + 9763.43i −0.617049 + 1.06876i
\(438\) −543.898 + 942.058i −0.0593343 + 0.102770i
\(439\) −3954.34 6849.12i −0.429910 0.744625i 0.566955 0.823749i \(-0.308121\pi\)
−0.996865 + 0.0791234i \(0.974788\pi\)
\(440\) −6567.61 −0.711587
\(441\) −2225.40 2139.43i −0.240298 0.231015i
\(442\) 2124.27 0.228600
\(443\) 1460.41 + 2529.51i 0.156628 + 0.271288i 0.933651 0.358185i \(-0.116604\pi\)
−0.777023 + 0.629473i \(0.783271\pi\)
\(444\) 969.205 1678.71i 0.103596 0.179433i
\(445\) 9163.03 15870.8i 0.976111 1.69067i
\(446\) 4319.47 + 7481.53i 0.458593 + 0.794307i
\(447\) 1082.93 0.114588
\(448\) 1173.58 166.277i 0.123764 0.0175354i
\(449\) −10240.2 −1.07631 −0.538156 0.842845i \(-0.680879\pi\)
−0.538156 + 0.842845i \(0.680879\pi\)
\(450\) −1132.33 1961.25i −0.118619 0.205454i
\(451\) 2669.02 4622.88i 0.278668 0.482668i
\(452\) 4769.29 8260.65i 0.496302 0.859620i
\(453\) −2322.59 4022.84i −0.240893 0.417239i
\(454\) 4122.57 0.426171
\(455\) 7023.19 + 8968.54i 0.723632 + 0.924069i
\(456\) 1836.27 0.188578
\(457\) −2946.31 5103.17i −0.301582 0.522355i 0.674913 0.737897i \(-0.264181\pi\)
−0.976494 + 0.215543i \(0.930848\pi\)
\(458\) 3474.63 6018.24i 0.354495 0.614004i
\(459\) −369.205 + 639.481i −0.0375446 + 0.0650292i
\(460\) 4667.15 + 8083.74i 0.473059 + 0.819362i
\(461\) −12643.4 −1.27735 −0.638677 0.769475i \(-0.720518\pi\)
−0.638677 + 0.769475i \(0.720518\pi\)
\(462\) −2151.83 + 5343.20i −0.216693 + 0.538070i
\(463\) 15093.2 1.51499 0.757494 0.652842i \(-0.226423\pi\)
0.757494 + 0.652842i \(0.226423\pi\)
\(464\) −1921.67 3328.42i −0.192265 0.333013i
\(465\) −7047.70 + 12207.0i −0.702858 + 1.21739i
\(466\) −776.099 + 1344.24i −0.0771504 + 0.133628i
\(467\) 1410.12 + 2442.39i 0.139727 + 0.242014i 0.927393 0.374088i \(-0.122044\pi\)
−0.787666 + 0.616102i \(0.788711\pi\)
\(468\) 1398.14 0.138096
\(469\) −3772.06 + 9366.38i −0.371380 + 0.922173i
\(470\) −2152.41 −0.211241
\(471\) 1450.60 + 2512.52i 0.141911 + 0.245798i
\(472\) 1847.71 3200.33i 0.180186 0.312091i
\(473\) 8515.72 14749.7i 0.827808 1.43381i
\(474\) 1229.09 + 2128.85i 0.119101 + 0.206289i
\(475\) 9626.23 0.929856
\(476\) −1249.12 1595.11i −0.120280 0.153596i
\(477\) −598.398 −0.0574397
\(478\) −2006.80 3475.87i −0.192027 0.332600i
\(479\) 8224.25 14244.8i 0.784500 1.35879i −0.144798 0.989461i \(-0.546253\pi\)
0.929297 0.369332i \(-0.120414\pi\)
\(480\) 760.182 1316.67i 0.0722862 0.125203i
\(481\) 3136.76 + 5433.03i 0.297347 + 0.515020i
\(482\) 1611.30 0.152267
\(483\) 8105.84 1148.47i 0.763620 0.108193i
\(484\) 5424.35 0.509424
\(485\) 12814.6 + 22195.5i 1.19975 + 2.07804i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) −3165.53 + 5482.87i −0.294546 + 0.510169i −0.974879 0.222734i \(-0.928502\pi\)
0.680333 + 0.732903i \(0.261835\pi\)
\(488\) −741.394 1284.13i −0.0687732 0.119119i
\(489\) −3979.50 −0.368015
\(490\) 2604.67 10547.4i 0.240136 0.972416i
\(491\) −9286.90 −0.853588 −0.426794 0.904349i \(-0.640357\pi\)
−0.426794 + 0.904349i \(0.640357\pi\)
\(492\) 617.864 + 1070.17i 0.0566168 + 0.0980631i
\(493\) −3284.67 + 5689.21i −0.300069 + 0.519735i
\(494\) −2971.48 + 5146.76i −0.270634 + 0.468752i
\(495\) 3694.28 + 6398.68i 0.335445 + 0.581008i
\(496\) −4746.79 −0.429712
\(497\) −2397.44 + 339.679i −0.216378 + 0.0306573i
\(498\) 2087.57 0.187844
\(499\) 121.725 + 210.835i 0.0109202 + 0.0189143i 0.871434 0.490513i \(-0.163191\pi\)
−0.860514 + 0.509427i \(0.829857\pi\)
\(500\) 25.7954 44.6789i 0.00230721 0.00399620i
\(501\) −2125.05 + 3680.69i −0.189501 + 0.328225i
\(502\) −1421.78 2462.60i −0.126409 0.218947i
\(503\) 8499.30 0.753409 0.376705 0.926333i \(-0.377057\pi\)
0.376705 + 0.926333i \(0.377057\pi\)
\(504\) −822.136 1049.86i −0.0726604 0.0927866i
\(505\) −11382.8 −1.00303
\(506\) −7638.12 13229.6i −0.671059 1.16231i
\(507\) 1033.02 1789.24i 0.0904890 0.156731i
\(508\) 5347.85 9262.75i 0.467072 0.808992i
\(509\) 3841.55 + 6653.76i 0.334526 + 0.579416i 0.983394 0.181485i \(-0.0580904\pi\)
−0.648868 + 0.760901i \(0.724757\pi\)
\(510\) −2598.73 −0.225634
\(511\) −1254.33 + 3114.62i −0.108588 + 0.269634i
\(512\) 512.000 0.0441942
\(513\) −1032.90 1789.04i −0.0888963 0.153973i
\(514\) 1465.82 2538.87i 0.125787 0.217869i
\(515\) −12761.4 + 22103.4i −1.09191 + 1.89124i
\(516\) 1971.34 + 3414.46i 0.168185 + 0.291305i
\(517\) 3522.57 0.299656
\(518\) 2235.17 5550.13i 0.189590 0.470770i
\(519\) −3109.80 −0.263015
\(520\) 2460.27 + 4261.32i 0.207481 + 0.359368i
\(521\) 10765.3 18646.1i 0.905253 1.56794i 0.0846750 0.996409i \(-0.473015\pi\)
0.820578 0.571535i \(-0.193652\pi\)
\(522\) −2161.87 + 3744.48i −0.181270 + 0.313968i
\(523\) 8423.53 + 14590.0i 0.704274 + 1.21984i 0.966953 + 0.254955i \(0.0820606\pi\)
−0.262679 + 0.964883i \(0.584606\pi\)
\(524\) −155.439 −0.0129588
\(525\) −4309.86 5503.64i −0.358281 0.457521i
\(526\) 13982.8 1.15908
\(527\) 4056.80 + 7026.58i 0.335326 + 0.580802i
\(528\) −1244.09 + 2154.83i −0.102542 + 0.177608i
\(529\) −4772.29 + 8265.84i −0.392232 + 0.679366i
\(530\) −1052.99 1823.83i −0.0862998 0.149476i
\(531\) −4157.35 −0.339762
\(532\) 5611.99 795.129i 0.457351 0.0647993i
\(533\) −3999.34 −0.325011
\(534\) −3471.48 6012.77i −0.281321 0.487263i
\(535\) 7401.24 12819.3i 0.598100 1.03594i
\(536\) −2180.83 + 3777.31i −0.175742 + 0.304394i
\(537\) 1151.15 + 1993.85i 0.0925059 + 0.160225i
\(538\) 1617.92 0.129653
\(539\) −4262.72 + 17261.6i −0.340646 + 1.37942i
\(540\) −1710.41 −0.136304
\(541\) −8720.02 15103.5i −0.692981 1.20028i −0.970856 0.239662i \(-0.922963\pi\)
0.277875 0.960617i \(-0.410370\pi\)
\(542\) −6661.77 + 11538.5i −0.527947 + 0.914432i
\(543\) 5936.56 10282.4i 0.469175 0.812636i
\(544\) −437.576 757.903i −0.0344870 0.0597332i
\(545\) 18957.3 1.48999
\(546\) 4272.97 605.411i 0.334920 0.0474527i
\(547\) 11520.7 0.900530 0.450265 0.892895i \(-0.351329\pi\)
0.450265 + 0.892895i \(0.351329\pi\)
\(548\) 1536.29 + 2660.93i 0.119757 + 0.207426i
\(549\) −834.068 + 1444.65i −0.0648400 + 0.112306i
\(550\) −6521.86 + 11296.2i −0.505623 + 0.875765i
\(551\) −9189.33 15916.4i −0.710488 1.23060i
\(552\) 3536.36 0.272677
\(553\) 4678.15 + 5973.94i 0.359738 + 0.459382i
\(554\) −15062.9 −1.15517
\(555\) −3837.35 6646.49i −0.293489 0.508338i
\(556\) −2105.10 + 3646.14i −0.160568 + 0.278113i
\(557\) −5746.51 + 9953.25i −0.437141 + 0.757151i −0.997468 0.0711212i \(-0.977342\pi\)
0.560327 + 0.828272i \(0.310676\pi\)
\(558\) 2670.07 + 4624.69i 0.202568 + 0.350858i
\(559\) −12760.2 −0.965472
\(560\) 1753.12 4353.17i 0.132291 0.328491i
\(561\) 4253.00 0.320075
\(562\) −1690.19 2927.49i −0.126862 0.219731i
\(563\) −9055.65 + 15684.8i −0.677886 + 1.17413i 0.297730 + 0.954650i \(0.403770\pi\)
−0.975616 + 0.219483i \(0.929563\pi\)
\(564\) −407.727 + 706.204i −0.0304405 + 0.0527244i
\(565\) −18882.9 32706.2i −1.40604 2.43533i
\(566\) 6356.46 0.472053
\(567\) −560.403 + 1391.54i −0.0415075 + 0.103067i
\(568\) −1045.94 −0.0772652
\(569\) −2208.81 3825.77i −0.162738 0.281871i 0.773112 0.634270i \(-0.218699\pi\)
−0.935850 + 0.352399i \(0.885366\pi\)
\(570\) 3635.16 6296.28i 0.267123 0.462670i
\(571\) −6609.87 + 11448.6i −0.484439 + 0.839073i −0.999840 0.0178762i \(-0.994310\pi\)
0.515401 + 0.856949i \(0.327643\pi\)
\(572\) −4026.41 6973.95i −0.294323 0.509782i
\(573\) −5415.89 −0.394855
\(574\) 2351.70 + 3003.10i 0.171007 + 0.218375i
\(575\) 18538.6 1.34454
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) 8748.20 15152.3i 0.631182 1.09324i −0.356128 0.934437i \(-0.615903\pi\)
0.987310 0.158803i \(-0.0507634\pi\)
\(578\) 4165.06 7214.10i 0.299730 0.519147i
\(579\) −5056.26 8757.70i −0.362921 0.628597i
\(580\) −15216.8 −1.08939
\(581\) 6380.00 903.944i 0.455571 0.0645472i
\(582\) 9709.80 0.691553
\(583\) 1723.29 + 2984.83i 0.122421 + 0.212039i
\(584\) −725.197 + 1256.08i −0.0513850 + 0.0890015i
\(585\) 2767.81 4793.98i 0.195615 0.338815i
\(586\) 2176.53 + 3769.87i 0.153433 + 0.265754i
\(587\) −4280.53 −0.300982 −0.150491 0.988611i \(-0.548085\pi\)
−0.150491 + 0.988611i \(0.548085\pi\)
\(588\) −2967.20 2852.57i −0.208105 0.200065i
\(589\) −22699.0 −1.58794
\(590\) −7315.61 12671.0i −0.510473 0.884165i
\(591\) 6918.47 11983.1i 0.481536 0.834044i
\(592\) 1292.27 2238.28i 0.0897164 0.155393i
\(593\) 795.466 + 1377.79i 0.0550858 + 0.0954114i 0.892253 0.451535i \(-0.149123\pi\)
−0.837168 + 0.546946i \(0.815790\pi\)
\(594\) 2799.20 0.193355
\(595\) −7942.20 + 1125.28i −0.547224 + 0.0775329i
\(596\) 1443.91 0.0992363
\(597\) 3344.80 + 5793.36i 0.229302 + 0.397163i
\(598\) −5722.59 + 9911.82i −0.391328 + 0.677800i
\(599\) 6961.42 12057.5i 0.474851 0.822467i −0.524734 0.851266i \(-0.675835\pi\)
0.999585 + 0.0287997i \(0.00916851\pi\)
\(600\) −1509.77 2615.00i −0.102727 0.177928i
\(601\) 12559.7 0.852446 0.426223 0.904618i \(-0.359844\pi\)
0.426223 + 0.904618i \(0.359844\pi\)
\(602\) 7503.29 + 9581.62i 0.507992 + 0.648700i
\(603\) 4906.87 0.331382
\(604\) −3096.78 5363.78i −0.208620 0.361340i
\(605\) 10738.3 18599.2i 0.721607 1.24986i
\(606\) −2156.23 + 3734.70i −0.144539 + 0.250349i
\(607\) −3839.19 6649.66i −0.256718 0.444648i 0.708643 0.705567i \(-0.249308\pi\)
−0.965361 + 0.260919i \(0.915974\pi\)
\(608\) 2448.36 0.163313
\(609\) −4985.69 + 12379.9i −0.331741 + 0.823745i
\(610\) −5870.77 −0.389673
\(611\) −1319.58 2285.58i −0.0873723 0.151333i
\(612\) −492.273 + 852.641i −0.0325146 + 0.0563170i
\(613\) −3079.19 + 5333.31i −0.202883 + 0.351403i −0.949456 0.313900i \(-0.898364\pi\)
0.746573 + 0.665303i \(0.231698\pi\)
\(614\) −623.504 1079.94i −0.0409814 0.0709818i
\(615\) 4892.59 0.320794
\(616\) −2869.11 + 7124.27i −0.187662 + 0.465982i
\(617\) 8813.12 0.575045 0.287523 0.957774i \(-0.407168\pi\)
0.287523 + 0.957774i \(0.407168\pi\)
\(618\) 4834.74 + 8374.01i 0.314695 + 0.545068i
\(619\) −11595.0 + 20083.1i −0.752894 + 1.30405i 0.193521 + 0.981096i \(0.438009\pi\)
−0.946415 + 0.322954i \(0.895324\pi\)
\(620\) −9396.93 + 16276.0i −0.608693 + 1.05429i
\(621\) −1989.20 3445.40i −0.128541 0.222640i
\(622\) 935.985 0.0603369
\(623\) −13213.1 16873.0i −0.849713 1.08507i
\(624\) 1864.18 0.119595
\(625\) 7761.27 + 13442.9i 0.496721 + 0.860346i
\(626\) −3612.81 + 6257.57i −0.230666 + 0.399525i
\(627\) −5949.19 + 10304.3i −0.378928 + 0.656323i
\(628\) 1934.14 + 3350.02i 0.122899 + 0.212867i
\(629\) −4417.71 −0.280041
\(630\) −5227.33 + 740.629i −0.330574 + 0.0468371i
\(631\) 7936.94 0.500736 0.250368 0.968151i \(-0.419448\pi\)
0.250368 + 0.968151i \(0.419448\pi\)
\(632\) 1638.79 + 2838.46i 0.103145 + 0.178652i
\(633\) −1368.92 + 2371.04i −0.0859553 + 0.148879i
\(634\) −4531.74 + 7849.20i −0.283877 + 0.491690i
\(635\) −21173.6 36673.8i −1.32323 2.29190i
\(636\) −797.864 −0.0497443
\(637\) 12796.8 3700.50i 0.795964 0.230171i
\(638\) 24903.4 1.54535
\(639\) 588.341 + 1019.04i 0.0364232 + 0.0630868i
\(640\) 1013.58 1755.56i 0.0626017 0.108429i
\(641\) −16057.3 + 27812.1i −0.989432 + 1.71375i −0.369146 + 0.929371i \(0.620350\pi\)
−0.620286 + 0.784376i \(0.712984\pi\)
\(642\) −2804.01 4856.69i −0.172376 0.298564i
\(643\) −24786.7 −1.52021 −0.760104 0.649802i \(-0.774852\pi\)
−0.760104 + 0.649802i \(0.774852\pi\)
\(644\) 10807.8 1531.29i 0.661314 0.0936977i
\(645\) 15610.2 0.952946
\(646\) −2092.47 3624.26i −0.127441 0.220735i
\(647\) −3772.80 + 6534.67i −0.229249 + 0.397070i −0.957586 0.288149i \(-0.906960\pi\)
0.728337 + 0.685219i \(0.240294\pi\)
\(648\) −324.000 + 561.184i −0.0196419 + 0.0340207i
\(649\) 11972.5 + 20737.0i 0.724133 + 1.25423i
\(650\) 9772.54 0.589708
\(651\) 10162.8 + 12977.8i 0.611844 + 0.781318i
\(652\) −5306.00 −0.318710
\(653\) 2444.49 + 4233.99i 0.146494 + 0.253735i 0.929929 0.367738i \(-0.119868\pi\)
−0.783435 + 0.621473i \(0.786534\pi\)
\(654\) 3591.06 6219.89i 0.214712 0.371892i
\(655\) −307.714 + 532.976i −0.0183563 + 0.0317941i
\(656\) 823.818 + 1426.89i 0.0490316 + 0.0849251i
\(657\) 1631.69 0.0968926
\(658\) −940.295 + 2334.84i −0.0557090 + 0.138331i
\(659\) 25895.9 1.53075 0.765374 0.643586i \(-0.222554\pi\)
0.765374 + 0.643586i \(0.222554\pi\)
\(660\) 4925.70 + 8531.57i 0.290504 + 0.503168i
\(661\) −4091.68 + 7087.00i −0.240769 + 0.417023i −0.960933 0.276780i \(-0.910733\pi\)
0.720165 + 0.693803i \(0.244066\pi\)
\(662\) 1237.06 2142.65i 0.0726278 0.125795i
\(663\) −1593.20 2759.51i −0.0933257 0.161645i
\(664\) 2783.42 0.162677
\(665\) 8383.36 20816.7i 0.488861 1.21389i
\(666\) −2907.61 −0.169171
\(667\) −17697.2 30652.4i −1.02734 1.77941i
\(668\) −2833.39 + 4907.58i −0.164113 + 0.284252i
\(669\) 6479.20 11222.3i 0.374440 0.648549i
\(670\) 8634.53 + 14955.4i 0.497882 + 0.862357i
\(671\) 9607.93 0.552772
\(672\) −1096.18 1399.81i −0.0629258 0.0803555i
\(673\) −4635.02 −0.265478 −0.132739 0.991151i \(-0.542377\pi\)
−0.132739 + 0.991151i \(0.542377\pi\)
\(674\) 1867.83 + 3235.18i 0.106745 + 0.184888i
\(675\) −1698.49 + 2941.88i −0.0968520 + 0.167753i
\(676\) 1377.36 2385.65i 0.0783657 0.135733i
\(677\) 12192.9 + 21118.7i 0.692187 + 1.19890i 0.971120 + 0.238593i \(0.0766862\pi\)
−0.278932 + 0.960311i \(0.589980\pi\)
\(678\) −14307.9 −0.810458
\(679\) 29674.9 4204.46i 1.67720 0.237633i
\(680\) −3464.97 −0.195405
\(681\) −3091.93 5355.37i −0.173984 0.301349i
\(682\) 15378.7 26636.8i 0.863464 1.49556i
\(683\) 9196.71 15929.2i 0.515230 0.892405i −0.484613 0.874728i \(-0.661040\pi\)
0.999844 0.0176767i \(-0.00562697\pi\)
\(684\) −1377.20 2385.39i −0.0769864 0.133344i
\(685\) 12165.2 0.678552
\(686\) −10303.5 7433.15i −0.573456 0.413701i
\(687\) −10423.9 −0.578889
\(688\) 2628.45 + 4552.62i 0.145652 + 0.252277i
\(689\) 1291.11 2236.27i 0.0713897 0.123651i
\(690\) 7000.73 12125.6i 0.386251 0.669006i
\(691\) 7449.44 + 12902.8i 0.410116 + 0.710341i 0.994902 0.100846i \(-0.0321550\pi\)
−0.584786 + 0.811187i \(0.698822\pi\)
\(692\) −4146.39 −0.227778
\(693\) 8554.89 1212.09i 0.468937 0.0664409i
\(694\) −126.727 −0.00693157
\(695\) 8334.67 + 14436.1i 0.454895 + 0.787902i
\(696\) −2882.50 + 4992.64i −0.156984 + 0.271904i
\(697\) 1408.14 2438.96i 0.0765236 0.132543i
\(698\) −1223.79 2119.66i −0.0663625 0.114943i
\(699\) 2328.30 0.125986
\(700\) −5746.48 7338.19i −0.310281 0.396225i
\(701\) −5725.70 −0.308497 −0.154249 0.988032i \(-0.549296\pi\)
−0.154249 + 0.988032i \(0.549296\pi\)
\(702\) −1048.60 1816.23i −0.0563774 0.0976485i
\(703\) 6179.60 10703.4i 0.331533 0.574232i
\(704\) −1658.79 + 2873.10i −0.0888039 + 0.153813i
\(705\) 1614.31 + 2796.06i 0.0862387 + 0.149370i
\(706\) −9031.23 −0.481437
\(707\) −4972.66 + 12347.6i −0.264521 + 0.656831i
\(708\) −5543.14 −0.294243
\(709\) 11728.4 + 20314.2i 0.621255 + 1.07604i 0.989252 + 0.146218i \(0.0467101\pi\)
−0.367998 + 0.929827i \(0.619957\pi\)
\(710\) −2070.58 + 3586.36i −0.109447 + 0.189568i
\(711\) 1843.64 3193.27i 0.0972458 0.168435i
\(712\) −4628.64 8017.03i −0.243631 0.421982i
\(713\) −43714.5 −2.29610
\(714\) −1135.27 + 2818.99i −0.0595049 + 0.147756i
\(715\) −31883.4 −1.66765
\(716\) 1534.86 + 2658.46i 0.0801125 + 0.138759i
\(717\) −3010.19 + 5213.81i −0.156789 + 0.271567i
\(718\) −2228.49 + 3859.86i −0.115831 + 0.200625i
\(719\) 4229.50 + 7325.71i 0.219379 + 0.379976i 0.954618 0.297832i \(-0.0962634\pi\)
−0.735239 + 0.677808i \(0.762930\pi\)
\(720\) −2280.55 −0.118043
\(721\) 18401.9 + 23499.0i 0.950518 + 1.21380i
\(722\) −2010.02 −0.103608
\(723\) −1208.47 2093.13i −0.0621626 0.107669i
\(724\) 7915.42 13709.9i 0.406318 0.703763i
\(725\) −15110.8 + 26172.7i −0.774072 + 1.34073i
\(726\) −4068.26 7046.44i −0.207972 0.360217i
\(727\) −11822.2 −0.603111 −0.301555 0.953449i \(-0.597506\pi\)
−0.301555 + 0.953449i \(0.597506\pi\)
\(728\) 5697.29 807.214i 0.290049 0.0410953i
\(729\) 729.000 0.0370370
\(730\) 2871.26 + 4973.16i 0.145575 + 0.252144i
\(731\) 4492.77 7781.70i 0.227320 0.393730i
\(732\) −1112.09 + 1926.20i −0.0561531 + 0.0972600i
\(733\) −2514.48 4355.20i −0.126704 0.219458i 0.795694 0.605699i \(-0.207107\pi\)
−0.922398 + 0.386241i \(0.873773\pi\)
\(734\) −2874.68 −0.144559
\(735\) −15655.0 + 4527.00i −0.785637 + 0.227185i
\(736\) 4715.15 0.236145
\(737\) −14131.0 24475.6i −0.706272 1.22330i
\(738\) 926.795 1605.26i 0.0462274 0.0800682i
\(739\) 8871.95 15366.7i 0.441624 0.764914i −0.556187 0.831057i \(-0.687736\pi\)
0.997810 + 0.0661431i \(0.0210694\pi\)
\(740\) −5116.47 8861.99i −0.254169 0.440234i
\(741\) 8914.44 0.441944
\(742\) −2438.42 + 345.485i −0.120643 + 0.0170932i
\(743\) −13202.3 −0.651877 −0.325938 0.945391i \(-0.605680\pi\)
−0.325938 + 0.945391i \(0.605680\pi\)
\(744\) 3560.09 + 6166.26i 0.175429 + 0.303852i
\(745\) 2858.42 4950.93i 0.140570 0.243474i
\(746\) 12237.4 21195.8i 0.600595 1.04026i
\(747\) −1565.68 2711.83i −0.0766869 0.132826i
\(748\) 5670.67 0.277193
\(749\) −10672.6 13628.8i −0.520652 0.664866i
\(750\) −77.3861 −0.00376766
\(751\) −7800.49 13510.8i −0.379020 0.656482i 0.611900 0.790935i \(-0.290406\pi\)
−0.990920 + 0.134453i \(0.957072\pi\)
\(752\) −543.636 + 941.606i −0.0263622 + 0.0456607i
\(753\) −2132.68 + 3693.90i −0.103213 + 0.178769i
\(754\) −9329.00 16158.3i −0.450586 0.780439i
\(755\) −24522.0 −1.18205
\(756\) −747.205 + 1855.38i −0.0359465 + 0.0892587i
\(757\) 2948.08 0.141545 0.0707725 0.997492i \(-0.477454\pi\)
0.0707725 + 0.997492i \(0.477454\pi\)
\(758\) 10647.0 + 18441.1i 0.510180 + 0.883657i
\(759\) −11457.2 + 19844.4i −0.547917 + 0.949021i
\(760\) 4846.88 8395.04i 0.231335 0.400684i
\(761\) −848.515 1469.67i −0.0404187 0.0700073i 0.845108 0.534595i \(-0.179536\pi\)
−0.885527 + 0.464588i \(0.846203\pi\)
\(762\) −16043.5 −0.762725
\(763\) 8281.65 20564.1i 0.392943 0.975716i
\(764\) −7221.18 −0.341954
\(765\) 1949.05 + 3375.85i 0.0921149 + 0.159548i
\(766\) 6714.81 11630.4i 0.316731 0.548594i
\(767\) 8969.98 15536.5i 0.422278 0.731407i
\(768\) −384.000 665.108i −0.0180422 0.0312500i
\(769\) −96.7799 −0.00453833 −0.00226916 0.999997i \(-0.500722\pi\)
−0.00226916 + 0.999997i \(0.500722\pi\)
\(770\) 18748.2 + 23941.2i 0.877450 + 1.12049i
\(771\) −4397.45 −0.205409
\(772\) −6741.68 11676.9i −0.314298 0.544381i
\(773\) −18163.4 +