Properties

Label 294.4.e.e.79.1
Level $294$
Weight $4$
Character 294.79
Analytic conductor $17.347$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3465615417\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.4.e.e.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-7.50000 + 12.9904i) q^{5} -6.00000 q^{6} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(15.0000 + 25.9808i) q^{10} +(4.50000 + 7.79423i) q^{11} +(-6.00000 + 10.3923i) q^{12} +88.0000 q^{13} +45.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-42.0000 - 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(52.0000 - 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(42.0000 - 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-50.0000 - 86.6025i) q^{25} +(88.0000 - 152.420i) q^{26} +27.0000 q^{27} +51.0000 q^{29} +(45.0000 - 77.9423i) q^{30} +(92.5000 + 160.215i) q^{31} +(16.0000 + 27.7128i) q^{32} +(13.5000 - 23.3827i) q^{33} -168.000 q^{34} +36.0000 q^{36} +(-22.0000 + 38.1051i) q^{37} +(-104.000 - 180.133i) q^{38} +(-132.000 - 228.631i) q^{39} +(60.0000 - 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(18.0000 - 31.1769i) q^{44} +(-67.5000 - 116.913i) q^{45} +(-84.0000 - 145.492i) q^{46} +(-69.0000 + 119.512i) q^{47} +48.0000 q^{48} -200.000 q^{50} +(-126.000 + 218.238i) q^{51} +(-176.000 - 304.841i) q^{52} +(-319.500 - 553.390i) q^{53} +(27.0000 - 46.7654i) q^{54} -135.000 q^{55} -312.000 q^{57} +(51.0000 - 88.3346i) q^{58} +(79.5000 + 137.698i) q^{59} +(-90.0000 - 155.885i) q^{60} +(361.000 - 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(-660.000 + 1143.15i) q^{65} +(-27.0000 - 46.7654i) q^{66} +(83.0000 + 143.760i) q^{67} +(-168.000 + 290.985i) q^{68} -252.000 q^{69} +1086.00 q^{71} +(36.0000 - 62.3538i) q^{72} +(109.000 + 188.794i) q^{73} +(44.0000 + 76.2102i) q^{74} +(-150.000 + 259.808i) q^{75} -416.000 q^{76} -528.000 q^{78} +(291.500 - 504.893i) q^{79} +(-120.000 - 207.846i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(168.000 - 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(326.000 - 564.649i) q^{86} +(-76.5000 - 132.502i) q^{87} +(-36.0000 - 62.3538i) q^{88} +(-519.000 + 898.934i) q^{89} -270.000 q^{90} -336.000 q^{92} +(277.500 - 480.644i) q^{93} +(138.000 + 239.023i) q^{94} +(780.000 + 1351.00i) q^{95} +(48.0000 - 83.1384i) q^{96} +169.000 q^{97} -81.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 3q^{3} - 4q^{4} - 15q^{5} - 12q^{6} - 16q^{8} - 9q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 3q^{3} - 4q^{4} - 15q^{5} - 12q^{6} - 16q^{8} - 9q^{9} + 30q^{10} + 9q^{11} - 12q^{12} + 176q^{13} + 90q^{15} - 16q^{16} - 84q^{17} + 18q^{18} + 104q^{19} + 120q^{20} + 36q^{22} + 84q^{23} + 24q^{24} - 100q^{25} + 176q^{26} + 54q^{27} + 102q^{29} + 90q^{30} + 185q^{31} + 32q^{32} + 27q^{33} - 336q^{34} + 72q^{36} - 44q^{37} - 208q^{38} - 264q^{39} + 120q^{40} + 336q^{41} + 652q^{43} + 36q^{44} - 135q^{45} - 168q^{46} - 138q^{47} + 96q^{48} - 400q^{50} - 252q^{51} - 352q^{52} - 639q^{53} + 54q^{54} - 270q^{55} - 624q^{57} + 102q^{58} + 159q^{59} - 180q^{60} + 722q^{61} + 740q^{62} + 128q^{64} - 1320q^{65} - 54q^{66} + 166q^{67} - 336q^{68} - 504q^{69} + 2172q^{71} + 72q^{72} + 218q^{73} + 88q^{74} - 300q^{75} - 832q^{76} - 1056q^{78} + 583q^{79} - 240q^{80} - 81q^{81} + 336q^{82} + 1194q^{83} + 2520q^{85} + 652q^{86} - 153q^{87} - 72q^{88} - 1038q^{89} - 540q^{90} - 672q^{92} + 555q^{93} + 276q^{94} + 1560q^{95} + 96q^{96} + 338q^{97} - 162q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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
\(5\) −7.50000 + 12.9904i −0.670820 + 1.16190i 0.306851 + 0.951757i \(0.400725\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) −6.00000 −0.408248
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 15.0000 + 25.9808i 0.474342 + 0.821584i
\(11\) 4.50000 + 7.79423i 0.123346 + 0.213641i 0.921085 0.389362i \(-0.127304\pi\)
−0.797739 + 0.603002i \(0.793971\pi\)
\(12\) −6.00000 + 10.3923i −0.144338 + 0.250000i
\(13\) 88.0000 1.87745 0.938723 0.344671i \(-0.112010\pi\)
0.938723 + 0.344671i \(0.112010\pi\)
\(14\) 0 0
\(15\) 45.0000 0.774597
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) −42.0000 72.7461i −0.599206 1.03785i −0.992939 0.118630i \(-0.962150\pi\)
0.393733 0.919225i \(-0.371183\pi\)
\(18\) 9.00000 + 15.5885i 0.117851 + 0.204124i
\(19\) 52.0000 90.0666i 0.627875 1.08751i −0.360103 0.932913i \(-0.617258\pi\)
0.987977 0.154598i \(-0.0494083\pi\)
\(20\) 60.0000 0.670820
\(21\) 0 0
\(22\) 18.0000 0.174437
\(23\) 42.0000 72.7461i 0.380765 0.659505i −0.610406 0.792088i \(-0.708994\pi\)
0.991172 + 0.132583i \(0.0423272\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) −50.0000 86.6025i −0.400000 0.692820i
\(26\) 88.0000 152.420i 0.663778 1.14970i
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 51.0000 0.326568 0.163284 0.986579i \(-0.447791\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(30\) 45.0000 77.9423i 0.273861 0.474342i
\(31\) 92.5000 + 160.215i 0.535919 + 0.928239i 0.999118 + 0.0419848i \(0.0133681\pi\)
−0.463199 + 0.886254i \(0.653299\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 13.5000 23.3827i 0.0712136 0.123346i
\(34\) −168.000 −0.847405
\(35\) 0 0
\(36\) 36.0000 0.166667
\(37\) −22.0000 + 38.1051i −0.0977507 + 0.169309i −0.910753 0.412951i \(-0.864498\pi\)
0.813003 + 0.582260i \(0.197831\pi\)
\(38\) −104.000 180.133i −0.443974 0.768986i
\(39\) −132.000 228.631i −0.541972 0.938723i
\(40\) 60.0000 103.923i 0.237171 0.410792i
\(41\) 168.000 0.639932 0.319966 0.947429i \(-0.396329\pi\)
0.319966 + 0.947429i \(0.396329\pi\)
\(42\) 0 0
\(43\) 326.000 1.15615 0.578076 0.815983i \(-0.303804\pi\)
0.578076 + 0.815983i \(0.303804\pi\)
\(44\) 18.0000 31.1769i 0.0616728 0.106820i
\(45\) −67.5000 116.913i −0.223607 0.387298i
\(46\) −84.0000 145.492i −0.269242 0.466341i
\(47\) −69.0000 + 119.512i −0.214142 + 0.370905i −0.953007 0.302949i \(-0.902029\pi\)
0.738865 + 0.673854i \(0.235362\pi\)
\(48\) 48.0000 0.144338
\(49\) 0 0
\(50\) −200.000 −0.565685
\(51\) −126.000 + 218.238i −0.345952 + 0.599206i
\(52\) −176.000 304.841i −0.469362 0.812958i
\(53\) −319.500 553.390i −0.828051 1.43423i −0.899565 0.436787i \(-0.856116\pi\)
0.0715141 0.997440i \(-0.477217\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) −135.000 −0.330971
\(56\) 0 0
\(57\) −312.000 −0.725007
\(58\) 51.0000 88.3346i 0.115459 0.199981i
\(59\) 79.5000 + 137.698i 0.175424 + 0.303843i 0.940308 0.340325i \(-0.110537\pi\)
−0.764884 + 0.644168i \(0.777204\pi\)
\(60\) −90.0000 155.885i −0.193649 0.335410i
\(61\) 361.000 625.270i 0.757726 1.31242i −0.186281 0.982497i \(-0.559643\pi\)
0.944007 0.329924i \(-0.107023\pi\)
\(62\) 370.000 0.757904
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −660.000 + 1143.15i −1.25943 + 2.18140i
\(66\) −27.0000 46.7654i −0.0503556 0.0872185i
\(67\) 83.0000 + 143.760i 0.151344 + 0.262136i 0.931722 0.363173i \(-0.118306\pi\)
−0.780378 + 0.625309i \(0.784973\pi\)
\(68\) −168.000 + 290.985i −0.299603 + 0.518927i
\(69\) −252.000 −0.439670
\(70\) 0 0
\(71\) 1086.00 1.81527 0.907637 0.419755i \(-0.137884\pi\)
0.907637 + 0.419755i \(0.137884\pi\)
\(72\) 36.0000 62.3538i 0.0589256 0.102062i
\(73\) 109.000 + 188.794i 0.174760 + 0.302693i 0.940078 0.340959i \(-0.110752\pi\)
−0.765318 + 0.643652i \(0.777418\pi\)
\(74\) 44.0000 + 76.2102i 0.0691202 + 0.119720i
\(75\) −150.000 + 259.808i −0.230940 + 0.400000i
\(76\) −416.000 −0.627875
\(77\) 0 0
\(78\) −528.000 −0.766464
\(79\) 291.500 504.893i 0.415143 0.719049i −0.580300 0.814403i \(-0.697065\pi\)
0.995443 + 0.0953535i \(0.0303981\pi\)
\(80\) −120.000 207.846i −0.167705 0.290474i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 168.000 290.985i 0.226250 0.391876i
\(83\) 597.000 0.789509 0.394755 0.918787i \(-0.370830\pi\)
0.394755 + 0.918787i \(0.370830\pi\)
\(84\) 0 0
\(85\) 1260.00 1.60784
\(86\) 326.000 564.649i 0.408761 0.707996i
\(87\) −76.5000 132.502i −0.0942720 0.163284i
\(88\) −36.0000 62.3538i −0.0436092 0.0755334i
\(89\) −519.000 + 898.934i −0.618134 + 1.07064i 0.371692 + 0.928356i \(0.378778\pi\)
−0.989826 + 0.142283i \(0.954556\pi\)
\(90\) −270.000 −0.316228
\(91\) 0 0
\(92\) −336.000 −0.380765
\(93\) 277.500 480.644i 0.309413 0.535919i
\(94\) 138.000 + 239.023i 0.151421 + 0.262270i
\(95\) 780.000 + 1351.00i 0.842382 + 1.45905i
\(96\) 48.0000 83.1384i 0.0510310 0.0883883i
\(97\) 169.000 0.176901 0.0884503 0.996081i \(-0.471809\pi\)
0.0884503 + 0.996081i \(0.471809\pi\)
\(98\) 0 0
\(99\) −81.0000 −0.0822304
\(100\) −200.000 + 346.410i −0.200000 + 0.346410i
\(101\) 321.000 + 555.988i 0.316244 + 0.547752i 0.979701 0.200463i \(-0.0642447\pi\)
−0.663457 + 0.748215i \(0.730911\pi\)
\(102\) 252.000 + 436.477i 0.244625 + 0.423702i
\(103\) 232.000 401.836i 0.221938 0.384408i −0.733458 0.679735i \(-0.762095\pi\)
0.955396 + 0.295326i \(0.0954283\pi\)
\(104\) −704.000 −0.663778
\(105\) 0 0
\(106\) −1278.00 −1.17104
\(107\) −196.500 + 340.348i −0.177536 + 0.307502i −0.941036 0.338306i \(-0.890146\pi\)
0.763500 + 0.645808i \(0.223479\pi\)
\(108\) −54.0000 93.5307i −0.0481125 0.0833333i
\(109\) −7.00000 12.1244i −0.00615118 0.0106542i 0.862933 0.505318i \(-0.168625\pi\)
−0.869085 + 0.494663i \(0.835291\pi\)
\(110\) −135.000 + 233.827i −0.117016 + 0.202677i
\(111\) 132.000 0.112873
\(112\) 0 0
\(113\) −2184.00 −1.81817 −0.909086 0.416608i \(-0.863219\pi\)
−0.909086 + 0.416608i \(0.863219\pi\)
\(114\) −312.000 + 540.400i −0.256329 + 0.443974i
\(115\) 630.000 + 1091.19i 0.510850 + 0.884819i
\(116\) −102.000 176.669i −0.0816419 0.141408i
\(117\) −396.000 + 685.892i −0.312908 + 0.541972i
\(118\) 318.000 0.248087
\(119\) 0 0
\(120\) −360.000 −0.273861
\(121\) 625.000 1082.53i 0.469572 0.813322i
\(122\) −722.000 1250.54i −0.535794 0.928022i
\(123\) −252.000 436.477i −0.184732 0.319966i
\(124\) 370.000 640.859i 0.267960 0.464120i
\(125\) −375.000 −0.268328
\(126\) 0 0
\(127\) −373.000 −0.260617 −0.130309 0.991473i \(-0.541597\pi\)
−0.130309 + 0.991473i \(0.541597\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) −489.000 846.973i −0.333752 0.578076i
\(130\) 1320.00 + 2286.31i 0.890551 + 1.54248i
\(131\) −586.500 + 1015.85i −0.391166 + 0.677519i −0.992604 0.121400i \(-0.961261\pi\)
0.601438 + 0.798920i \(0.294595\pi\)
\(132\) −108.000 −0.0712136
\(133\) 0 0
\(134\) 332.000 0.214033
\(135\) −202.500 + 350.740i −0.129099 + 0.223607i
\(136\) 336.000 + 581.969i 0.211851 + 0.366937i
\(137\) −15.0000 25.9808i −0.00935428 0.0162021i 0.861310 0.508079i \(-0.169644\pi\)
−0.870665 + 0.491877i \(0.836311\pi\)
\(138\) −252.000 + 436.477i −0.155447 + 0.269242i
\(139\) 82.0000 0.0500370 0.0250185 0.999687i \(-0.492036\pi\)
0.0250185 + 0.999687i \(0.492036\pi\)
\(140\) 0 0
\(141\) 414.000 0.247270
\(142\) 1086.00 1881.01i 0.641796 1.11162i
\(143\) 396.000 + 685.892i 0.231575 + 0.401099i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) −382.500 + 662.509i −0.219068 + 0.379437i
\(146\) 436.000 0.247148
\(147\) 0 0
\(148\) 176.000 0.0977507
\(149\) 717.000 1241.88i 0.394221 0.682811i −0.598780 0.800913i \(-0.704348\pi\)
0.993001 + 0.118102i \(0.0376811\pi\)
\(150\) 300.000 + 519.615i 0.163299 + 0.282843i
\(151\) 1335.50 + 2313.15i 0.719745 + 1.24663i 0.961101 + 0.276198i \(0.0890745\pi\)
−0.241356 + 0.970437i \(0.577592\pi\)
\(152\) −416.000 + 720.533i −0.221987 + 0.384493i
\(153\) 756.000 0.399470
\(154\) 0 0
\(155\) −2775.00 −1.43802
\(156\) −528.000 + 914.523i −0.270986 + 0.469362i
\(157\) 1126.00 + 1950.29i 0.572386 + 0.991401i 0.996320 + 0.0857085i \(0.0273154\pi\)
−0.423934 + 0.905693i \(0.639351\pi\)
\(158\) −583.000 1009.79i −0.293551 0.508444i
\(159\) −958.500 + 1660.17i −0.478075 + 0.828051i
\(160\) −480.000 −0.237171
\(161\) 0 0
\(162\) −162.000 −0.0785674
\(163\) −838.000 + 1451.46i −0.402682 + 0.697466i −0.994049 0.108937i \(-0.965255\pi\)
0.591366 + 0.806403i \(0.298589\pi\)
\(164\) −336.000 581.969i −0.159983 0.277098i
\(165\) 202.500 + 350.740i 0.0955431 + 0.165485i
\(166\) 597.000 1034.03i 0.279134 0.483474i
\(167\) −3030.00 −1.40400 −0.702001 0.712176i \(-0.747710\pi\)
−0.702001 + 0.712176i \(0.747710\pi\)
\(168\) 0 0
\(169\) 5547.00 2.52481
\(170\) 1260.00 2182.38i 0.568456 0.984595i
\(171\) 468.000 + 810.600i 0.209292 + 0.362504i
\(172\) −652.000 1129.30i −0.289038 0.500628i
\(173\) 1719.00 2977.40i 0.755452 1.30848i −0.189698 0.981843i \(-0.560751\pi\)
0.945149 0.326638i \(-0.105916\pi\)
\(174\) −306.000 −0.133321
\(175\) 0 0
\(176\) −144.000 −0.0616728
\(177\) 238.500 413.094i 0.101281 0.175424i
\(178\) 1038.00 + 1797.87i 0.437086 + 0.757056i
\(179\) 606.000 + 1049.62i 0.253042 + 0.438282i 0.964362 0.264587i \(-0.0852355\pi\)
−0.711320 + 0.702869i \(0.751902\pi\)
\(180\) −270.000 + 467.654i −0.111803 + 0.193649i
\(181\) −3032.00 −1.24512 −0.622560 0.782572i \(-0.713907\pi\)
−0.622560 + 0.782572i \(0.713907\pi\)
\(182\) 0 0
\(183\) −2166.00 −0.874947
\(184\) −336.000 + 581.969i −0.134621 + 0.233170i
\(185\) −330.000 571.577i −0.131146 0.227152i
\(186\) −555.000 961.288i −0.218788 0.378952i
\(187\) 378.000 654.715i 0.147819 0.256030i
\(188\) 552.000 0.214142
\(189\) 0 0
\(190\) 3120.00 1.19131
\(191\) −1260.00 + 2182.38i −0.477332 + 0.826763i −0.999662 0.0259799i \(-0.991729\pi\)
0.522331 + 0.852743i \(0.325063\pi\)
\(192\) −96.0000 166.277i −0.0360844 0.0625000i
\(193\) −182.500 316.099i −0.0680655 0.117893i 0.829984 0.557787i \(-0.188349\pi\)
−0.898050 + 0.439894i \(0.855016\pi\)
\(194\) 169.000 292.717i 0.0625438 0.108329i
\(195\) 3960.00 1.45426
\(196\) 0 0
\(197\) −1590.00 −0.575040 −0.287520 0.957775i \(-0.592831\pi\)
−0.287520 + 0.957775i \(0.592831\pi\)
\(198\) −81.0000 + 140.296i −0.0290728 + 0.0503556i
\(199\) −2690.00 4659.22i −0.958236 1.65971i −0.726782 0.686868i \(-0.758985\pi\)
−0.231455 0.972846i \(-0.574348\pi\)
\(200\) 400.000 + 692.820i 0.141421 + 0.244949i
\(201\) 249.000 431.281i 0.0873786 0.151344i
\(202\) 1284.00 0.447237
\(203\) 0 0
\(204\) 1008.00 0.345952
\(205\) −1260.00 + 2182.38i −0.429279 + 0.743533i
\(206\) −464.000 803.672i −0.156934 0.271818i
\(207\) 378.000 + 654.715i 0.126922 + 0.219835i
\(208\) −704.000 + 1219.36i −0.234681 + 0.406479i
\(209\) 936.000 0.309782
\(210\) 0 0
\(211\) −5362.00 −1.74946 −0.874728 0.484614i \(-0.838960\pi\)
−0.874728 + 0.484614i \(0.838960\pi\)
\(212\) −1278.00 + 2213.56i −0.414025 + 0.717113i
\(213\) −1629.00 2821.51i −0.524025 0.907637i
\(214\) 393.000 + 680.696i 0.125537 + 0.217437i
\(215\) −2445.00 + 4234.86i −0.775570 + 1.34333i
\(216\) −216.000 −0.0680414
\(217\) 0 0
\(218\) −28.0000 −0.00869908
\(219\) 327.000 566.381i 0.100898 0.174760i
\(220\) 270.000 + 467.654i 0.0827427 + 0.143315i
\(221\) −3696.00 6401.66i −1.12498 1.94852i
\(222\) 132.000 228.631i 0.0399066 0.0691202i
\(223\) 1573.00 0.472358 0.236179 0.971710i \(-0.424105\pi\)
0.236179 + 0.971710i \(0.424105\pi\)
\(224\) 0 0
\(225\) 900.000 0.266667
\(226\) −2184.00 + 3782.80i −0.642821 + 1.11340i
\(227\) 460.500 + 797.609i 0.134645 + 0.233212i 0.925462 0.378841i \(-0.123677\pi\)
−0.790817 + 0.612053i \(0.790344\pi\)
\(228\) 624.000 + 1080.80i 0.181252 + 0.313937i
\(229\) 2026.00 3509.13i 0.584637 1.01262i −0.410284 0.911958i \(-0.634570\pi\)
0.994921 0.100663i \(-0.0320963\pi\)
\(230\) 2520.00 0.722452
\(231\) 0 0
\(232\) −408.000 −0.115459
\(233\) 234.000 405.300i 0.0657933 0.113957i −0.831252 0.555895i \(-0.812376\pi\)
0.897046 + 0.441938i \(0.145709\pi\)
\(234\) 792.000 + 1371.78i 0.221259 + 0.383232i
\(235\) −1035.00 1792.67i −0.287302 0.497622i
\(236\) 318.000 550.792i 0.0877120 0.151922i
\(237\) −1749.00 −0.479366
\(238\) 0 0
\(239\) 4932.00 1.33483 0.667415 0.744686i \(-0.267401\pi\)
0.667415 + 0.744686i \(0.267401\pi\)
\(240\) −360.000 + 623.538i −0.0968246 + 0.167705i
\(241\) −768.500 1331.08i −0.205408 0.355778i 0.744854 0.667227i \(-0.232519\pi\)
−0.950263 + 0.311449i \(0.899186\pi\)
\(242\) −1250.00 2165.06i −0.332037 0.575106i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) −2888.00 −0.757726
\(245\) 0 0
\(246\) −1008.00 −0.261251
\(247\) 4576.00 7925.86i 1.17880 2.04174i
\(248\) −740.000 1281.72i −0.189476 0.328182i
\(249\) −895.500 1551.05i −0.227912 0.394755i
\(250\) −375.000 + 649.519i −0.0948683 + 0.164317i
\(251\) −5319.00 −1.33758 −0.668789 0.743452i \(-0.733187\pi\)
−0.668789 + 0.743452i \(0.733187\pi\)
\(252\) 0 0
\(253\) 756.000 0.187863
\(254\) −373.000 + 646.055i −0.0921421 + 0.159595i
\(255\) −1890.00 3273.58i −0.464143 0.803919i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 2673.00 4629.77i 0.648783 1.12372i −0.334631 0.942349i \(-0.608612\pi\)
0.983414 0.181375i \(-0.0580549\pi\)
\(258\) −1956.00 −0.471997
\(259\) 0 0
\(260\) 5280.00 1.25943
\(261\) −229.500 + 397.506i −0.0544279 + 0.0942720i
\(262\) 1173.00 + 2031.70i 0.276596 + 0.479079i
\(263\) −387.000 670.304i −0.0907355 0.157159i 0.817085 0.576517i \(-0.195588\pi\)
−0.907821 + 0.419358i \(0.862255\pi\)
\(264\) −108.000 + 187.061i −0.0251778 + 0.0436092i
\(265\) 9585.00 2.22189
\(266\) 0 0
\(267\) 3114.00 0.713759
\(268\) 332.000 575.041i 0.0756721 0.131068i
\(269\) 1207.50 + 2091.45i 0.273690 + 0.474045i 0.969804 0.243887i \(-0.0784225\pi\)
−0.696114 + 0.717931i \(0.745089\pi\)
\(270\) 405.000 + 701.481i 0.0912871 + 0.158114i
\(271\) −237.500 + 411.362i −0.0532365 + 0.0922084i −0.891416 0.453187i \(-0.850287\pi\)
0.838179 + 0.545395i \(0.183620\pi\)
\(272\) 1344.00 0.299603
\(273\) 0 0
\(274\) −60.0000 −0.0132290
\(275\) 450.000 779.423i 0.0986764 0.170913i
\(276\) 504.000 + 872.954i 0.109918 + 0.190383i
\(277\) −1864.00 3228.54i −0.404321 0.700304i 0.589921 0.807461i \(-0.299159\pi\)
−0.994242 + 0.107156i \(0.965825\pi\)
\(278\) 82.0000 142.028i 0.0176908 0.0306413i
\(279\) −1665.00 −0.357279
\(280\) 0 0
\(281\) 1602.00 0.340097 0.170049 0.985436i \(-0.445608\pi\)
0.170049 + 0.985436i \(0.445608\pi\)
\(282\) 414.000 717.069i 0.0874232 0.151421i
\(283\) 343.000 + 594.093i 0.0720468 + 0.124789i 0.899798 0.436306i \(-0.143714\pi\)
−0.827751 + 0.561095i \(0.810380\pi\)
\(284\) −2172.00 3762.01i −0.453819 0.786037i
\(285\) 2340.00 4053.00i 0.486350 0.842382i
\(286\) 1584.00 0.327496
\(287\) 0 0
\(288\) −288.000 −0.0589256
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) 765.000 + 1325.02i 0.154905 + 0.268303i
\(291\) −253.500 439.075i −0.0510668 0.0884503i
\(292\) 436.000 755.174i 0.0873800 0.151347i
\(293\) 1101.00 0.219526 0.109763 0.993958i \(-0.464991\pi\)
0.109763 + 0.993958i \(0.464991\pi\)
\(294\) 0 0
\(295\) −2385.00 −0.470712
\(296\) 176.000 304.841i 0.0345601 0.0598599i
\(297\) 121.500 + 210.444i 0.0237379 + 0.0411152i
\(298\) −1434.00 2483.76i −0.278756 0.482820i
\(299\) 3696.00 6401.66i 0.714867 1.23819i
\(300\) 1200.00 0.230940
\(301\) 0 0
\(302\) 5342.00 1.01787
\(303\) 963.000 1667.96i 0.182584 0.316244i
\(304\) 832.000 + 1441.07i 0.156969 + 0.271878i
\(305\) 5415.00 + 9379.06i 1.01660 + 1.76080i
\(306\) 756.000 1309.43i 0.141234 0.244625i
\(307\) −2780.00 −0.516818 −0.258409 0.966036i \(-0.583198\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(308\) 0 0
\(309\) −1392.00 −0.256272
\(310\) −2775.00 + 4806.44i −0.508417 + 0.880605i
\(311\) 2148.00 + 3720.45i 0.391646 + 0.678351i 0.992667 0.120883i \(-0.0385725\pi\)
−0.601021 + 0.799233i \(0.705239\pi\)
\(312\) 1056.00 + 1829.05i 0.191616 + 0.331889i
\(313\) 2744.50 4753.61i 0.495618 0.858435i −0.504370 0.863488i \(-0.668275\pi\)
0.999987 + 0.00505298i \(0.00160842\pi\)
\(314\) 4504.00 0.809476
\(315\) 0 0
\(316\) −2332.00 −0.415143
\(317\) −2245.50 + 3889.32i −0.397854 + 0.689104i −0.993461 0.114172i \(-0.963578\pi\)
0.595607 + 0.803276i \(0.296912\pi\)
\(318\) 1917.00 + 3320.34i 0.338050 + 0.585520i
\(319\) 229.500 + 397.506i 0.0402807 + 0.0697682i
\(320\) −480.000 + 831.384i −0.0838525 + 0.145237i
\(321\) 1179.00 0.205001
\(322\) 0 0
\(323\) −8736.00 −1.50490
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) −4400.00 7621.02i −0.750979 1.30073i
\(326\) 1676.00 + 2902.92i 0.284739 + 0.493183i
\(327\) −21.0000 + 36.3731i −0.00355138 + 0.00615118i
\(328\) −1344.00 −0.226250
\(329\) 0 0
\(330\) 810.000 0.135118
\(331\) 1982.00 3432.92i 0.329126 0.570062i −0.653213 0.757174i \(-0.726579\pi\)
0.982339 + 0.187112i \(0.0599127\pi\)
\(332\) −1194.00 2068.07i −0.197377 0.341868i
\(333\) −198.000 342.946i −0.0325836 0.0564364i
\(334\) −3030.00 + 5248.11i −0.496390 + 0.859773i
\(335\) −2490.00 −0.406099
\(336\) 0 0
\(337\) 161.000 0.0260244 0.0130122 0.999915i \(-0.495858\pi\)
0.0130122 + 0.999915i \(0.495858\pi\)
\(338\) 5547.00 9607.69i 0.892654 1.54612i
\(339\) 3276.00 + 5674.20i 0.524861 + 0.909086i
\(340\) −2520.00 4364.77i −0.401959 0.696214i
\(341\) −832.500 + 1441.93i −0.132206 + 0.228988i
\(342\) 1872.00 0.295983
\(343\) 0 0
\(344\) −2608.00 −0.408761
\(345\) 1890.00 3273.58i 0.294940 0.510850i
\(346\) −3438.00 5954.79i −0.534185 0.925236i
\(347\) 2958.00 + 5123.41i 0.457619 + 0.792619i 0.998835 0.0482646i \(-0.0153691\pi\)
−0.541216 + 0.840884i \(0.682036\pi\)
\(348\) −306.000 + 530.008i −0.0471360 + 0.0816419i
\(349\) 142.000 0.0217796 0.0108898 0.999941i \(-0.496534\pi\)
0.0108898 + 0.999941i \(0.496534\pi\)
\(350\) 0 0
\(351\) 2376.00 0.361315
\(352\) −144.000 + 249.415i −0.0218046 + 0.0377667i
\(353\) −2220.00 3845.15i −0.334727 0.579764i 0.648705 0.761040i \(-0.275311\pi\)
−0.983432 + 0.181275i \(0.941977\pi\)
\(354\) −477.000 826.188i −0.0716166 0.124044i
\(355\) −8145.00 + 14107.6i −1.21772 + 2.10916i
\(356\) 4152.00 0.618134
\(357\) 0 0
\(358\) 2424.00 0.357856
\(359\) −1143.00 + 1979.73i −0.168037 + 0.291048i −0.937730 0.347366i \(-0.887076\pi\)
0.769693 + 0.638415i \(0.220409\pi\)
\(360\) 540.000 + 935.307i 0.0790569 + 0.136931i
\(361\) −1978.50 3426.86i −0.288453 0.499615i
\(362\) −3032.00 + 5251.58i −0.440217 + 0.762477i
\(363\) −3750.00 −0.542215
\(364\) 0 0
\(365\) −3270.00 −0.468930
\(366\) −2166.00 + 3751.62i −0.309341 + 0.535794i
\(367\) −1434.50 2484.63i −0.204033 0.353396i 0.745791 0.666180i \(-0.232072\pi\)
−0.949824 + 0.312784i \(0.898738\pi\)
\(368\) 672.000 + 1163.94i 0.0951914 + 0.164876i
\(369\) −756.000 + 1309.43i −0.106655 + 0.184732i
\(370\) −1320.00 −0.185469
\(371\) 0 0
\(372\) −2220.00 −0.309413
\(373\) 1532.00 2653.50i 0.212665 0.368346i −0.739883 0.672736i \(-0.765119\pi\)
0.952548 + 0.304390i \(0.0984524\pi\)
\(374\) −756.000 1309.43i −0.104524 0.181040i
\(375\) 562.500 + 974.279i 0.0774597 + 0.134164i
\(376\) 552.000 956.092i 0.0757107 0.131135i
\(377\) 4488.00 0.613113
\(378\) 0 0
\(379\) −6040.00 −0.818612 −0.409306 0.912397i \(-0.634229\pi\)
−0.409306 + 0.912397i \(0.634229\pi\)
\(380\) 3120.00 5404.00i 0.421191 0.729524i
\(381\) 559.500 + 969.082i 0.0752337 + 0.130309i
\(382\) 2520.00 + 4364.77i 0.337525 + 0.584610i
\(383\) 921.000 1595.22i 0.122874 0.212825i −0.798026 0.602623i \(-0.794122\pi\)
0.920900 + 0.389799i \(0.127455\pi\)
\(384\) −384.000 −0.0510310
\(385\) 0 0
\(386\) −730.000 −0.0962591
\(387\) −1467.00 + 2540.92i −0.192692 + 0.333752i
\(388\) −338.000 585.433i −0.0442251 0.0766002i
\(389\) −3915.00 6780.98i −0.510279 0.883828i −0.999929 0.0119097i \(-0.996209\pi\)
0.489650 0.871919i \(-0.337124\pi\)
\(390\) 3960.00 6858.92i 0.514160 0.890551i
\(391\) −7056.00 −0.912627
\(392\) 0 0
\(393\) 3519.00 0.451680
\(394\) −1590.00 + 2753.96i −0.203307 + 0.352138i
\(395\) 4372.50 + 7573.39i 0.556973 + 0.964706i
\(396\) 162.000 + 280.592i 0.0205576 + 0.0356068i
\(397\) −7382.00 + 12786.0i −0.933229 + 1.61640i −0.155467 + 0.987841i \(0.549688\pi\)
−0.777762 + 0.628559i \(0.783645\pi\)
\(398\) −10760.0 −1.35515
\(399\) 0 0
\(400\) 1600.00 0.200000
\(401\) −3132.00 + 5424.78i −0.390036 + 0.675563i −0.992454 0.122618i \(-0.960871\pi\)
0.602417 + 0.798181i \(0.294204\pi\)
\(402\) −498.000 862.561i −0.0617860 0.107017i
\(403\) 8140.00 + 14098.9i 1.00616 + 1.74272i
\(404\) 1284.00 2223.95i 0.158122 0.273876i
\(405\) 1215.00 0.149071
\(406\) 0 0
\(407\) −396.000 −0.0482285
\(408\) 1008.00 1745.91i 0.122312 0.211851i
\(409\) 2375.50 + 4114.49i 0.287191 + 0.497429i 0.973138 0.230222i \(-0.0739454\pi\)
−0.685948 + 0.727651i \(0.740612\pi\)
\(410\) 2520.00 + 4364.77i 0.303546 + 0.525757i
\(411\) −45.0000 + 77.9423i −0.00540070 + 0.00935428i
\(412\) −1856.00 −0.221938
\(413\) 0 0
\(414\) 1512.00 0.179495
\(415\) −4477.50 + 7755.26i −0.529619 + 0.917327i
\(416\) 1408.00 + 2438.73i 0.165944 + 0.287424i
\(417\) −123.000 213.042i −0.0144445 0.0250185i
\(418\) 936.000 1621.20i 0.109525 0.189702i
\(419\) 4704.00 0.548462 0.274231 0.961664i \(-0.411577\pi\)
0.274231 + 0.961664i \(0.411577\pi\)
\(420\) 0 0
\(421\) −4474.00 −0.517932 −0.258966 0.965886i \(-0.583382\pi\)
−0.258966 + 0.965886i \(0.583382\pi\)
\(422\) −5362.00 + 9287.26i −0.618526 + 1.07132i
\(423\) −621.000 1075.60i −0.0713807 0.123635i
\(424\) 2556.00 + 4427.12i 0.292760 + 0.507076i
\(425\) −4200.00 + 7274.61i −0.479365 + 0.830284i
\(426\) −6516.00 −0.741083
\(427\) 0 0
\(428\) 1572.00 0.177536
\(429\) 1188.00 2057.68i 0.133700 0.231575i
\(430\) 4890.00 + 8469.73i 0.548411 + 0.949876i
\(431\) 6402.00 + 11088.6i 0.715484 + 1.23925i 0.962773 + 0.270312i \(0.0871270\pi\)
−0.247289 + 0.968942i \(0.579540\pi\)
\(432\) −216.000 + 374.123i −0.0240563 + 0.0416667i
\(433\) 5074.00 0.563143 0.281571 0.959540i \(-0.409144\pi\)
0.281571 + 0.959540i \(0.409144\pi\)
\(434\) 0 0
\(435\) 2295.00 0.252958
\(436\) −28.0000 + 48.4974i −0.00307559 + 0.00532708i
\(437\) −4368.00 7565.60i −0.478146 0.828173i
\(438\) −654.000 1132.76i −0.0713455 0.123574i
\(439\) −633.500 + 1097.25i −0.0688731 + 0.119292i −0.898406 0.439167i \(-0.855274\pi\)
0.829532 + 0.558459i \(0.188607\pi\)
\(440\) 1080.00 0.117016
\(441\) 0 0
\(442\) −14784.0 −1.59096
\(443\) 3466.50 6004.15i 0.371780 0.643941i −0.618060 0.786131i \(-0.712081\pi\)
0.989839 + 0.142190i \(0.0454144\pi\)
\(444\) −264.000 457.261i −0.0282182 0.0488754i
\(445\) −7785.00 13484.0i −0.829313 1.43641i
\(446\) 1573.00 2724.52i 0.167004 0.289259i
\(447\) −4302.00 −0.455207
\(448\) 0 0
\(449\) 11688.0 1.22849 0.614244 0.789116i \(-0.289461\pi\)
0.614244 + 0.789116i \(0.289461\pi\)
\(450\) 900.000 1558.85i 0.0942809 0.163299i
\(451\) 756.000 + 1309.43i 0.0789327 + 0.136715i
\(452\) 4368.00 + 7565.60i 0.454543 + 0.787292i
\(453\) 4006.50 6939.46i 0.415545 0.719745i
\(454\) 1842.00 0.190417
\(455\) 0 0
\(456\) 2496.00 0.256329
\(457\) −275.500 + 477.180i −0.0281999 + 0.0488436i −0.879781 0.475379i \(-0.842311\pi\)
0.851581 + 0.524223i \(0.175644\pi\)
\(458\) −4052.00 7018.27i −0.413401 0.716031i
\(459\) −1134.00 1964.15i −0.115317 0.199735i
\(460\) 2520.00 4364.77i 0.255425 0.442409i
\(461\) −13386.0 −1.35238 −0.676191 0.736726i \(-0.736371\pi\)
−0.676191 + 0.736726i \(0.736371\pi\)
\(462\) 0 0
\(463\) −6376.00 −0.639995 −0.319998 0.947418i \(-0.603682\pi\)
−0.319998 + 0.947418i \(0.603682\pi\)
\(464\) −408.000 + 706.677i −0.0408210 + 0.0707040i
\(465\) 4162.50 + 7209.66i 0.415121 + 0.719011i
\(466\) −468.000 810.600i −0.0465229 0.0805801i
\(467\) 2850.00 4936.34i 0.282403 0.489137i −0.689573 0.724216i \(-0.742202\pi\)
0.971976 + 0.235080i \(0.0755351\pi\)
\(468\) 3168.00 0.312908
\(469\) 0 0
\(470\) −4140.00 −0.406306
\(471\) 3378.00 5850.87i 0.330467 0.572386i
\(472\) −636.000 1101.58i −0.0620218 0.107425i
\(473\) 1467.00 + 2540.92i 0.142606 + 0.247001i
\(474\) −1749.00 + 3029.36i −0.169481 + 0.293551i
\(475\) −10400.0 −1.00460
\(476\) 0 0
\(477\) 5751.00 0.552034
\(478\) 4932.00 8542.47i 0.471934 0.817414i
\(479\) 9897.00 + 17142.1i 0.944062 + 1.63516i 0.757619 + 0.652697i \(0.226362\pi\)
0.186442 + 0.982466i \(0.440304\pi\)
\(480\) 720.000 + 1247.08i 0.0684653 + 0.118585i
\(481\) −1936.00 + 3353.25i −0.183522 + 0.317869i
\(482\) −3074.00 −0.290491
\(483\) 0 0
\(484\) −5000.00 −0.469572
\(485\) −1267.50 + 2195.37i −0.118668 + 0.205540i
\(486\) 243.000 + 420.888i 0.0226805 + 0.0392837i
\(487\) −7967.50 13800.1i −0.741359 1.28407i −0.951877 0.306482i \(-0.900848\pi\)
0.210517 0.977590i \(-0.432485\pi\)
\(488\) −2888.00 + 5002.16i −0.267897 + 0.464011i
\(489\) 5028.00 0.464978
\(490\) 0 0
\(491\) 9963.00 0.915731 0.457865 0.889021i \(-0.348614\pi\)
0.457865 + 0.889021i \(0.348614\pi\)
\(492\) −1008.00 + 1745.91i −0.0923662 + 0.159983i
\(493\) −2142.00 3710.05i −0.195681 0.338930i
\(494\) −9152.00 15851.7i −0.833538 1.44373i
\(495\) 607.500 1052.22i 0.0551618 0.0955431i
\(496\) −2960.00 −0.267960
\(497\) 0 0
\(498\) −3582.00 −0.322316
\(499\) −9571.00 + 16577.5i −0.858631 + 1.48719i 0.0146043 + 0.999893i \(0.495351\pi\)
−0.873235 + 0.487299i \(0.837982\pi\)
\(500\) 750.000 + 1299.04i 0.0670820 + 0.116190i
\(501\) 4545.00 + 7872.17i 0.405301 + 0.702001i
\(502\) −5319.00 + 9212.78i −0.472906 + 0.819096i
\(503\) 12192.0 1.08074 0.540372 0.841426i \(-0.318283\pi\)
0.540372 + 0.841426i \(0.318283\pi\)
\(504\) 0 0
\(505\) −9630.00 −0.848573
\(506\) 756.000 1309.43i 0.0664196 0.115042i
\(507\) −8320.50 14411.5i −0.728849 1.26240i
\(508\) 746.000 + 1292.11i 0.0651543 + 0.112851i
\(509\) −9904.50 + 17155.1i −0.862494 + 1.49388i 0.00702091 + 0.999975i \(0.497765\pi\)
−0.869515 + 0.493907i \(0.835568\pi\)
\(510\) −7560.00 −0.656397
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 1404.00 2431.80i 0.120835 0.209292i
\(514\) −5346.00 9259.54i −0.458759 0.794593i
\(515\) 3480.00 + 6027.54i 0.297761 + 0.515738i
\(516\) −1956.00 + 3387.89i −0.166876 + 0.289038i
\(517\) −1242.00 −0.105654
\(518\) 0 0
\(519\) −10314.0 −0.872321
\(520\) 5280.00 9145.23i 0.445276 0.771240i
\(521\) −897.000 1553.65i −0.0754286 0.130646i 0.825844 0.563899i \(-0.190699\pi\)
−0.901273 + 0.433253i \(0.857366\pi\)
\(522\) 459.000 + 795.011i 0.0384864 + 0.0666603i
\(523\) −3224.00 + 5584.13i −0.269552 + 0.466878i −0.968746 0.248054i \(-0.920209\pi\)
0.699194 + 0.714932i \(0.253542\pi\)
\(524\) 4692.00 0.391166
\(525\) 0 0
\(526\) −1548.00 −0.128319
\(527\) 7770.00 13458.0i 0.642251 1.11241i
\(528\) 216.000 + 374.123i 0.0178034 + 0.0308364i
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) 9585.00 16601.7i 0.785558 1.36063i
\(531\) −1431.00 −0.116949
\(532\) 0 0
\(533\) 14784.0 1.20144
\(534\) 3114.00 5393.61i 0.252352 0.437086i
\(535\) −2947.50 5105.22i −0.238190 0.412557i
\(536\) −664.000 1150.08i −0.0535083 0.0926790i
\(537\) 1818.00 3148.87i 0.146094 0.253042i
\(538\) 4830.00 0.387056
\(539\) 0 0
\(540\) 1620.00 0.129099
\(541\) −3631.00 + 6289.08i −0.288556 + 0.499794i −0.973465 0.228835i \(-0.926509\pi\)
0.684909 + 0.728628i \(0.259842\pi\)
\(542\) 475.000 + 822.724i 0.0376439 + 0.0652012i
\(543\) 4548.00 + 7877.37i 0.359435 + 0.622560i
\(544\) 1344.00 2327.88i 0.105926 0.183469i
\(545\) 210.000 0.0165053
\(546\) 0 0
\(547\) 14204.0 1.11027 0.555136 0.831759i \(-0.312666\pi\)
0.555136 + 0.831759i \(0.312666\pi\)
\(548\) −60.0000 + 103.923i −0.00467714 + 0.00810104i
\(549\) 3249.00 + 5627.43i 0.252575 + 0.437474i
\(550\) −900.000 1558.85i −0.0697748 0.120853i
\(551\) 2652.00 4593.40i 0.205044 0.355146i
\(552\) 2016.00 0.155447
\(553\) 0 0
\(554\) −7456.00 −0.571796
\(555\) −990.000 + 1714.73i −0.0757174 + 0.131146i
\(556\) −164.000 284.056i −0.0125093 0.0216667i
\(557\) −7912.50 13704.9i −0.601909 1.04254i −0.992532 0.121986i \(-0.961074\pi\)
0.390623 0.920551i \(-0.372260\pi\)
\(558\) −1665.00 + 2883.86i −0.126317 + 0.218788i
\(559\) 28688.0 2.17061
\(560\) 0 0
\(561\) −2268.00 −0.170686
\(562\) 1602.00 2774.75i 0.120243 0.208266i
\(563\) 529.500 + 917.121i 0.0396372 + 0.0686537i 0.885163 0.465280i \(-0.154046\pi\)
−0.845526 + 0.533934i \(0.820713\pi\)
\(564\) −828.000 1434.14i −0.0618175 0.107071i
\(565\) 16380.0 28371.0i 1.21967 2.11252i
\(566\) 1372.00 0.101890
\(567\) 0 0
\(568\) −8688.00 −0.641796
\(569\) −1980.00 + 3429.46i −0.145880 + 0.252672i −0.929701 0.368315i \(-0.879935\pi\)
0.783821 + 0.620987i \(0.213268\pi\)
\(570\) −4680.00 8106.00i −0.343901 0.595654i
\(571\) 1265.00 + 2191.04i 0.0927121 + 0.160582i 0.908651 0.417555i \(-0.137113\pi\)
−0.815939 + 0.578138i \(0.803780\pi\)
\(572\) 1584.00 2743.57i 0.115787 0.200550i
\(573\) 7560.00 0.551175
\(574\) 0 0
\(575\) −8400.00 −0.609225
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 5915.50 + 10245.9i 0.426803 + 0.739245i 0.996587 0.0825498i \(-0.0263063\pi\)
−0.569784 + 0.821795i \(0.692973\pi\)
\(578\) 2143.00 + 3711.78i 0.154216 + 0.267111i
\(579\) −547.500 + 948.298i −0.0392976 + 0.0680655i
\(580\) 3060.00 0.219068
\(581\) 0 0
\(582\) −1014.00 −0.0722193
\(583\) 2875.50 4980.51i 0.204273 0.353811i
\(584\) −872.000 1510.35i −0.0617870 0.107018i
\(585\) −5940.00 10288.4i −0.419810 0.727132i
\(586\) 1101.00 1906.99i 0.0776141 0.134432i
\(587\) −4809.00 −0.338141 −0.169070 0.985604i \(-0.554077\pi\)
−0.169070 + 0.985604i \(0.554077\pi\)
\(588\) 0 0
\(589\) 19240.0 1.34596
\(590\) −2385.00 + 4130.94i −0.166422 + 0.288251i
\(591\) 2385.00 + 4130.94i 0.166000 + 0.287520i
\(592\) −352.000 609.682i −0.0244377 0.0423273i
\(593\) 10902.0 18882.8i 0.754960 1.30763i −0.190434 0.981700i \(-0.560989\pi\)
0.945394 0.325930i \(-0.105677\pi\)
\(594\) 486.000 0.0335704
\(595\) 0 0
\(596\) −5736.00 −0.394221
\(597\) −8070.00 + 13977.7i −0.553238 + 0.958236i
\(598\) −7392.00 12803.3i −0.505487 0.875530i
\(599\) −7083.00 12268.1i −0.483144 0.836831i 0.516668 0.856186i \(-0.327172\pi\)
−0.999813 + 0.0193549i \(0.993839\pi\)
\(600\) 1200.00 2078.46i 0.0816497 0.141421i
\(601\) −5891.00 −0.399832 −0.199916 0.979813i \(-0.564067\pi\)
−0.199916 + 0.979813i \(0.564067\pi\)
\(602\) 0 0
\(603\) −1494.00 −0.100896
\(604\) 5342.00 9252.62i 0.359872 0.623317i
\(605\) 9375.00 + 16238.0i 0.629997 + 1.09119i
\(606\) −1926.00 3335.93i −0.129106 0.223619i
\(607\) −1368.50 + 2370.31i −0.0915086 + 0.158497i −0.908146 0.418653i \(-0.862502\pi\)
0.816638 + 0.577151i \(0.195836\pi\)
\(608\) 3328.00 0.221987
\(609\) 0 0
\(610\) 21660.0 1.43768
\(611\) −6072.00 + 10517.0i −0.402041 + 0.696355i
\(612\) −1512.00 2618.86i −0.0998676 0.172976i
\(613\) 13094.0 + 22679.5i 0.862743 + 1.49432i 0.869271 + 0.494337i \(0.164589\pi\)
−0.00652719 + 0.999979i \(0.502078\pi\)
\(614\) −2780.00 + 4815.10i −0.182723 + 0.316485i
\(615\) 7560.00 0.495689
\(616\) 0 0
\(617\) −2358.00 −0.153857 −0.0769283 0.997037i \(-0.524511\pi\)
−0.0769283 + 0.997037i \(0.524511\pi\)
\(618\) −1392.00 + 2411.01i −0.0906059 + 0.156934i
\(619\) 6883.00 + 11921.7i 0.446932 + 0.774110i 0.998185 0.0602291i \(-0.0191831\pi\)
−0.551252 + 0.834339i \(0.685850\pi\)
\(620\) 5550.00 + 9612.88i 0.359505 + 0.622682i
\(621\) 1134.00 1964.15i 0.0732783 0.126922i
\(622\) 8592.00 0.553871
\(623\) 0 0
\(624\) 4224.00 0.270986
\(625\) 9062.50 15696.7i 0.580000 1.00459i
\(626\) −5489.00 9507.23i −0.350455 0.607005i
\(627\) −1404.00 2431.80i −0.0894264 0.154891i
\(628\) 4504.00 7801.16i 0.286193 0.495701i
\(629\) 3696.00 0.234291
\(630\) 0 0
\(631\) 21287.0 1.34298 0.671491 0.741012i \(-0.265654\pi\)
0.671491 + 0.741012i \(0.265654\pi\)
\(632\) −2332.00 + 4039.14i −0.146775 + 0.254222i
\(633\) 8043.00 + 13930.9i 0.505025 + 0.874728i
\(634\) 4491.00 + 7778.64i 0.281326 + 0.487270i
\(635\) 2797.50 4845.41i 0.174827 0.302810i
\(636\) 7668.00 0.478075
\(637\) 0 0
\(638\) 918.000 0.0569655
\(639\) −4887.00 + 8464.53i −0.302546 + 0.524025i
\(640\) 960.000 + 1662.77i 0.0592927 + 0.102698i
\(641\) −10713.0 18555.5i −0.660122 1.14336i −0.980583 0.196103i \(-0.937171\pi\)
0.320462 0.947262i \(-0.396162\pi\)
\(642\) 1179.00 2042.09i 0.0724788 0.125537i
\(643\) −9962.00 −0.610984 −0.305492 0.952195i \(-0.598821\pi\)
−0.305492 + 0.952195i \(0.598821\pi\)
\(644\) 0 0
\(645\) 14670.0 0.895551
\(646\) −8736.00 + 15131.2i −0.532064 + 0.921562i
\(647\) −9087.00 15739.1i −0.552159 0.956367i −0.998119 0.0613142i \(-0.980471\pi\)
0.445960 0.895053i \(-0.352863\pi\)
\(648\) 324.000 + 561.184i 0.0196419 + 0.0340207i
\(649\) −715.500 + 1239.28i −0.0432755 + 0.0749555i
\(650\) −17600.0 −1.06204
\(651\) 0 0
\(652\) 6704.00 0.402682
\(653\) 9583.50 16599.1i 0.574321 0.994752i −0.421795 0.906691i \(-0.638600\pi\)
0.996115 0.0880610i \(-0.0280670\pi\)
\(654\) 42.0000 + 72.7461i 0.00251121 + 0.00434954i
\(655\) −8797.50 15237.7i −0.524804 0.908988i
\(656\) −1344.00 + 2327.88i −0.0799914 + 0.138549i
\(657\) −1962.00 −0.116507
\(658\) 0 0
\(659\) 13080.0 0.773178 0.386589 0.922252i \(-0.373653\pi\)
0.386589 + 0.922252i \(0.373653\pi\)
\(660\) 810.000 1402.96i 0.0477715 0.0827427i
\(661\) −7595.00 13154.9i −0.446916 0.774081i 0.551268 0.834328i \(-0.314144\pi\)
−0.998183 + 0.0602477i \(0.980811\pi\)
\(662\) −3964.00 6865.85i −0.232727 0.403095i
\(663\) −11088.0 + 19205.0i −0.649506 + 1.12498i
\(664\) −4776.00 −0.279134
\(665\) 0 0
\(666\) −792.000 −0.0460801
\(667\) 2142.00 3710.05i 0.124346 0.215373i
\(668\) 6060.00 + 10496.2i 0.351001 + 0.607951i
\(669\) −2359.50 4086.77i −0.136358 0.236179i
\(670\) −2490.00 + 4312.81i −0.143578 + 0.248684i
\(671\) 6498.00 0.373849
\(672\) 0 0
\(673\) 4397.00 0.251845 0.125923 0.992040i \(-0.459811\pi\)
0.125923 + 0.992040i \(0.459811\pi\)
\(674\) 161.000 278.860i 0.00920102 0.0159366i
\(675\) −1350.00 2338.27i −0.0769800 0.133333i
\(676\) −11094.0 19215.4i −0.631202 1.09327i
\(677\) 2014.50 3489.22i 0.114363 0.198082i −0.803162 0.595761i \(-0.796851\pi\)
0.917525 + 0.397679i \(0.130184\pi\)
\(678\) 13104.0 0.742266
\(679\) 0 0
\(680\) −10080.0 −0.568456
\(681\) 1381.50 2392.83i 0.0777374 0.134645i
\(682\) 1665.00 + 2883.86i 0.0934841 + 0.161919i
\(683\) −7510.50 13008.6i −0.420763 0.728783i 0.575251 0.817977i \(-0.304904\pi\)
−0.996014 + 0.0891936i \(0.971571\pi\)
\(684\) 1872.00 3242.40i 0.104646 0.181252i
\(685\) 450.000 0.0251002
\(686\) 0 0
\(687\) −12156.0 −0.675081
\(688\) −2608.00 + 4517.19i −0.144519 + 0.250314i
\(689\) −28116.0 48698.3i −1.55462 2.69268i
\(690\) −3780.00 6547.15i −0.208554 0.361226i
\(691\) −6992.00 + 12110.5i −0.384932 + 0.666722i −0.991760 0.128111i \(-0.959109\pi\)
0.606828 + 0.794834i \(0.292442\pi\)
\(692\) −13752.0 −0.755452
\(693\) 0 0
\(694\) 11832.0 0.647171
\(695\) −615.000 + 1065.21i −0.0335659 + 0.0581378i
\(696\) 612.000 + 1060.02i 0.0333302 + 0.0577296i
\(697\) −7056.00 12221.4i −0.383451 0.664156i
\(698\) 142.000 245.951i 0.00770026 0.0133372i
\(699\) −1404.00 −0.0759716
\(700\) 0 0
\(701\) −31053.0 −1.67312 −0.836559 0.547877i \(-0.815436\pi\)
−0.836559 + 0.547877i \(0.815436\pi\)
\(702\) 2376.00 4115.35i 0.127744 0.221259i
\(703\) 2288.00 + 3962.93i 0.122750 + 0.212610i
\(704\) 288.000 + 498.831i 0.0154182 + 0.0267051i
\(705\) −3105.00 + 5378.02i −0.165874 + 0.287302i
\(706\) −8880.00 −0.473376
\(707\) 0 0
\(708\) −1908.00 −0.101281
\(709\) −7543.00 + 13064.9i −0.399553 + 0.692047i −0.993671 0.112332i \(-0.964168\pi\)
0.594117 + 0.804378i \(0.297501\pi\)
\(710\) 16290.0 + 28215.1i 0.861060 + 1.49140i
\(711\) 2623.50 + 4544.04i 0.138381 + 0.239683i
\(712\) 4152.00 7191.47i 0.218543 0.378528i
\(713\) 15540.0 0.816238
\(714\) 0 0
\(715\) −11880.0 −0.621380
\(716\) 2424.00 4198.49i 0.126521 0.219141i
\(717\) −7398.00 12813.7i −0.385332 0.667415i
\(718\) 2286.00 + 3959.47i 0.118820 + 0.205802i
\(719\) −3189.00 + 5523.51i −0.165410 + 0.286498i −0.936801 0.349863i \(-0.886228\pi\)
0.771391 + 0.636362i \(0.219561\pi\)
\(720\) 2160.00 0.111803
\(721\) 0 0
\(722\) −7914.00 −0.407934
\(723\) −2305.50 + 3993.24i −0.118593 + 0.205408i
\(724\) 6064.00 + 10503.2i 0.311280 + 0.539153i
\(725\) −2550.00 4416.73i −0.130627 0.226253i
\(726\) −3750.00 + 6495.19i −0.191702 + 0.332037i
\(727\) 7363.00 0.375624 0.187812 0.982205i \(-0.439860\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) −3270.00 + 5663.81i −0.165792 + 0.287160i
\(731\) −13692.0 23715.2i −0.692773 1.19992i
\(732\) 4332.00 + 7503.24i 0.218737 + 0.378863i
\(733\) 16405.0 28414.3i 0.826647 1.43180i −0.0740064 0.997258i \(-0.523579\pi\)
0.900654 0.434537i \(-0.143088\pi\)
\(734\) −5738.00 −0.288547
\(735\) 0 0
\(736\) 2688.00 0.134621
\(737\) −747.000 + 1293.84i −0.0373353 + 0.0646666i
\(738\) 1512.00 + 2618.86i 0.0754167 + 0.130625i
\(739\) 12017.0 + 20814.1i 0.598177 + 1.03607i 0.993090 + 0.117354i \(0.0374412\pi\)
−0.394914 + 0.918718i \(0.629225\pi\)
\(740\) −1320.00 + 2286.31i −0.0655732 + 0.113576i
\(741\) −27456.0 −1.36116
\(742\) 0 0
\(743\) −8022.00 −0.396095 −0.198048 0.980192i \(-0.563460\pi\)
−0.198048 + 0.980192i \(0.563460\pi\)
\(744\) −2220.00 + 3845.15i −0.109394 + 0.189476i
\(745\) 10755.0 + 18628.2i 0.528903 + 0.916087i
\(746\) −3064.00 5307.00i −0.150377 0.260460i
\(747\) −2686.50 + 4653.15i −0.131585 + 0.227912i
\(748\) −3024.00 −0.147819
\(749\) 0 0
\(750\) 2250.00 0.109545
\(751\) −14759.5 + 25564.2i −0.717153 + 1.24215i 0.244970 + 0.969531i \(0.421222\pi\)
−0.962123 + 0.272615i \(0.912112\pi\)
\(752\) −1104.00 1912.18i −0.0535356 0.0927263i
\(753\) 7978.50 + 13819.2i 0.386126 + 0.668789i
\(754\) 4488.00 7773.44i 0.216768 0.375454i
\(755\) −40065.0 −1.93128
\(756\) 0 0
\(757\) −3742.00 −0.179664 −0.0898318 0.995957i \(-0.528633\pi\)
−0.0898318 + 0.995957i \(0.528633\pi\)
\(758\) −6040.00 + 10461.6i −0.289423 + 0.501295i
\(759\) −1134.00 1964.15i −0.0542313 0.0939314i
\(760\) −6240.00 10808.0i −0.297827 0.515852i
\(761\) −5448.00 + 9436.21i −0.259514 + 0.449491i −0.966112 0.258124i \(-0.916896\pi\)
0.706598 + 0.707615i \(0.250229\pi\)
\(762\) 2238.00 0.106397
\(763\) 0 0
\(764\) 10080.0 0.477332
\(765\) −5670.00 + 9820.73i −0.267973 + 0.464143i
\(766\) −1842.00 3190.44i −0.0868853 0.150490i
\(767\) 6996.00 + 12117.4i 0.329349 + 0.570450i
\(768\) −384.000 + 665.108i −0.0180422 + 0.0312500i
\(769\) −17285.0 −0.810550 −0.405275 0.914195i \(-0.632824\pi\)
−0.405275 + 0.914195i \(0.632824\pi\)
\(770\) 0 0
\(771\) −16038.0 −0.749150
\(772\) −730.000 + 1264.40i −0.0340327 + 0.0589464i
\(773\) 5913.00 + 10241.6i 0.275130 + 0.476540i 0.970168 0.242434i \(-0.0779456\pi\)
−0.695038 + 0.718973i \(0.744612\pi\)
\(774\) 2934.00 + 5081.84i 0.136254 + 0.235999i
\(775\) 9250.00 16021.5i 0.428735 0.742591i
\(776\) −1352.00 −0.0625438
\(777\) 0 0
\(778\) −15660.0 −0.721643
\(779\) 8736.00