Properties

Label 882.4.g.l.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.l.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +8.00000 q^{8} +(15.0000 - 25.9808i) q^{10} +(-4.50000 + 7.79423i) q^{11} +88.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(42.0000 - 72.7461i) q^{17} +(52.0000 + 90.0666i) q^{19} -60.0000 q^{20} +18.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(-50.0000 + 86.6025i) q^{25} +(-88.0000 - 152.420i) q^{26} -51.0000 q^{29} +(92.5000 - 160.215i) q^{31} +(-16.0000 + 27.7128i) q^{32} -168.000 q^{34} +(-22.0000 - 38.1051i) q^{37} +(104.000 - 180.133i) q^{38} +(60.0000 + 103.923i) q^{40} -168.000 q^{41} +326.000 q^{43} +(-18.0000 - 31.1769i) q^{44} +(-84.0000 + 145.492i) q^{46} +(69.0000 + 119.512i) q^{47} +200.000 q^{50} +(-176.000 + 304.841i) q^{52} +(319.500 - 553.390i) q^{53} -135.000 q^{55} +(51.0000 + 88.3346i) q^{58} +(-79.5000 + 137.698i) q^{59} +(361.000 + 625.270i) q^{61} -370.000 q^{62} +64.0000 q^{64} +(660.000 + 1143.15i) q^{65} +(83.0000 - 143.760i) q^{67} +(168.000 + 290.985i) q^{68} -1086.00 q^{71} +(109.000 - 188.794i) q^{73} +(-44.0000 + 76.2102i) q^{74} -416.000 q^{76} +(291.500 + 504.893i) q^{79} +(120.000 - 207.846i) q^{80} +(168.000 + 290.985i) q^{82} -597.000 q^{83} +1260.00 q^{85} +(-326.000 - 564.649i) q^{86} +(-36.0000 + 62.3538i) q^{88} +(519.000 + 898.934i) q^{89} +336.000 q^{92} +(138.000 - 239.023i) q^{94} +(-780.000 + 1351.00i) q^{95} +169.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 15q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 15q^{5} + 16q^{8} + 30q^{10} - 9q^{11} + 176q^{13} - 16q^{16} + 84q^{17} + 104q^{19} - 120q^{20} + 36q^{22} - 84q^{23} - 100q^{25} - 176q^{26} - 102q^{29} + 185q^{31} - 32q^{32} - 336q^{34} - 44q^{37} + 208q^{38} + 120q^{40} - 336q^{41} + 652q^{43} - 36q^{44} - 168q^{46} + 138q^{47} + 400q^{50} - 352q^{52} + 639q^{53} - 270q^{55} + 102q^{58} - 159q^{59} + 722q^{61} - 740q^{62} + 128q^{64} + 1320q^{65} + 166q^{67} + 336q^{68} - 2172q^{71} + 218q^{73} - 88q^{74} - 832q^{76} + 583q^{79} + 240q^{80} + 336q^{82} - 1194q^{83} + 2520q^{85} - 652q^{86} - 72q^{88} + 1038q^{89} + 672q^{92} + 276q^{94} - 1560q^{95} + 338q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 7.50000 + 12.9904i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 15.0000 25.9808i 0.474342 0.821584i
\(11\) −4.50000 + 7.79423i −0.123346 + 0.213641i −0.921085 0.389362i \(-0.872696\pi\)
0.797739 + 0.603002i \(0.206029\pi\)
\(12\) 0 0
\(13\) 88.0000 1.87745 0.938723 0.344671i \(-0.112010\pi\)
0.938723 + 0.344671i \(0.112010\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 42.0000 72.7461i 0.599206 1.03785i −0.393733 0.919225i \(-0.628817\pi\)
0.992939 0.118630i \(-0.0378502\pi\)
\(18\) 0 0
\(19\) 52.0000 + 90.0666i 0.627875 + 1.08751i 0.987977 + 0.154598i \(0.0494083\pi\)
−0.360103 + 0.932913i \(0.617258\pi\)
\(20\) −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 \(-0.291006\pi\)
−0.991172 + 0.132583i \(0.957673\pi\)
\(24\) 0 0
\(25\) −50.0000 + 86.6025i −0.400000 + 0.692820i
\(26\) −88.0000 152.420i −0.663778 1.14970i
\(27\) 0 0
\(28\) 0 0
\(29\) −51.0000 −0.326568 −0.163284 0.986579i \(-0.552209\pi\)
−0.163284 + 0.986579i \(0.552209\pi\)
\(30\) 0 0
\(31\) 92.5000 160.215i 0.535919 0.928239i −0.463199 0.886254i \(-0.653299\pi\)
0.999118 0.0419848i \(-0.0133681\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −168.000 −0.847405
\(35\) 0 0
\(36\) 0 0
\(37\) −22.0000 38.1051i −0.0977507 0.169309i 0.813003 0.582260i \(-0.197831\pi\)
−0.910753 + 0.412951i \(0.864498\pi\)
\(38\) 104.000 180.133i 0.443974 0.768986i
\(39\) 0 0
\(40\) 60.0000 + 103.923i 0.237171 + 0.410792i
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 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
\(45\) 0 0
\(46\) −84.0000 + 145.492i −0.269242 + 0.466341i
\(47\) 69.0000 + 119.512i 0.214142 + 0.370905i 0.953007 0.302949i \(-0.0979711\pi\)
−0.738865 + 0.673854i \(0.764638\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 200.000 0.565685
\(51\) 0 0
\(52\) −176.000 + 304.841i −0.469362 + 0.812958i
\(53\) 319.500 553.390i 0.828051 1.43423i −0.0715141 0.997440i \(-0.522783\pi\)
0.899565 0.436787i \(-0.143884\pi\)
\(54\) 0 0
\(55\) −135.000 −0.330971
\(56\) 0 0
\(57\) 0 0
\(58\) 51.0000 + 88.3346i 0.115459 + 0.199981i
\(59\) −79.5000 + 137.698i −0.175424 + 0.303843i −0.940308 0.340325i \(-0.889463\pi\)
0.764884 + 0.644168i \(0.222796\pi\)
\(60\) 0 0
\(61\) 361.000 + 625.270i 0.757726 + 1.31242i 0.944007 + 0.329924i \(0.107023\pi\)
−0.186281 + 0.982497i \(0.559643\pi\)
\(62\) −370.000 −0.757904
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 660.000 + 1143.15i 1.25943 + 2.18140i
\(66\) 0 0
\(67\) 83.0000 143.760i 0.151344 0.262136i −0.780378 0.625309i \(-0.784973\pi\)
0.931722 + 0.363173i \(0.118306\pi\)
\(68\) 168.000 + 290.985i 0.299603 + 0.518927i
\(69\) 0 0
\(70\) 0 0
\(71\) −1086.00 −1.81527 −0.907637 0.419755i \(-0.862116\pi\)
−0.907637 + 0.419755i \(0.862116\pi\)
\(72\) 0 0
\(73\) 109.000 188.794i 0.174760 0.302693i −0.765318 0.643652i \(-0.777418\pi\)
0.940078 + 0.340959i \(0.110752\pi\)
\(74\) −44.0000 + 76.2102i −0.0691202 + 0.119720i
\(75\) 0 0
\(76\) −416.000 −0.627875
\(77\) 0 0
\(78\) 0 0
\(79\) 291.500 + 504.893i 0.415143 + 0.719049i 0.995443 0.0953535i \(-0.0303981\pi\)
−0.580300 + 0.814403i \(0.697065\pi\)
\(80\) 120.000 207.846i 0.167705 0.290474i
\(81\) 0 0
\(82\) 168.000 + 290.985i 0.226250 + 0.391876i
\(83\) −597.000 −0.789509 −0.394755 0.918787i \(-0.629170\pi\)
−0.394755 + 0.918787i \(0.629170\pi\)
\(84\) 0 0
\(85\) 1260.00 1.60784
\(86\) −326.000 564.649i −0.408761 0.707996i
\(87\) 0 0
\(88\) −36.0000 + 62.3538i −0.0436092 + 0.0755334i
\(89\) 519.000 + 898.934i 0.618134 + 1.07064i 0.989826 + 0.142283i \(0.0454443\pi\)
−0.371692 + 0.928356i \(0.621222\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 336.000 0.380765
\(93\) 0 0
\(94\) 138.000 239.023i 0.151421 0.262270i
\(95\) −780.000 + 1351.00i −0.842382 + 1.45905i
\(96\) 0 0
\(97\) 169.000 0.176901 0.0884503 0.996081i \(-0.471809\pi\)
0.0884503 + 0.996081i \(0.471809\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −200.000 346.410i −0.200000 0.346410i
\(101\) −321.000 + 555.988i −0.316244 + 0.547752i −0.979701 0.200463i \(-0.935755\pi\)
0.663457 + 0.748215i \(0.269089\pi\)
\(102\) 0 0
\(103\) 232.000 + 401.836i 0.221938 + 0.384408i 0.955396 0.295326i \(-0.0954283\pi\)
−0.733458 + 0.679735i \(0.762095\pi\)
\(104\) 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 \(-0.109854\pi\)
−0.763500 + 0.645808i \(0.776521\pi\)
\(108\) 0 0
\(109\) −7.00000 + 12.1244i −0.00615118 + 0.0106542i −0.869085 0.494663i \(-0.835291\pi\)
0.862933 + 0.505318i \(0.168625\pi\)
\(110\) 135.000 + 233.827i 0.117016 + 0.202677i
\(111\) 0 0
\(112\) 0 0
\(113\) 2184.00 1.81817 0.909086 0.416608i \(-0.136781\pi\)
0.909086 + 0.416608i \(0.136781\pi\)
\(114\) 0 0
\(115\) 630.000 1091.19i 0.510850 0.884819i
\(116\) 102.000 176.669i 0.0816419 0.141408i
\(117\) 0 0
\(118\) 318.000 0.248087
\(119\) 0 0
\(120\) 0 0
\(121\) 625.000 + 1082.53i 0.469572 + 0.813322i
\(122\) 722.000 1250.54i 0.535794 0.928022i
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 1320.00 2286.31i 0.890551 1.54248i
\(131\) 586.500 + 1015.85i 0.391166 + 0.677519i 0.992604 0.121400i \(-0.0387385\pi\)
−0.601438 + 0.798920i \(0.705405\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −332.000 −0.214033
\(135\) 0 0
\(136\) 336.000 581.969i 0.211851 0.366937i
\(137\) 15.0000 25.9808i 0.00935428 0.0162021i −0.861310 0.508079i \(-0.830356\pi\)
0.870665 + 0.491877i \(0.163689\pi\)
\(138\) 0 0
\(139\) 82.0000 0.0500370 0.0250185 0.999687i \(-0.492036\pi\)
0.0250185 + 0.999687i \(0.492036\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1086.00 + 1881.01i 0.641796 + 1.11162i
\(143\) −396.000 + 685.892i −0.231575 + 0.401099i
\(144\) 0 0
\(145\) −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 \(-0.295652\pi\)
−0.993001 + 0.118102i \(0.962319\pi\)
\(150\) 0 0
\(151\) 1335.50 2313.15i 0.719745 1.24663i −0.241356 0.970437i \(-0.577592\pi\)
0.961101 0.276198i \(-0.0890745\pi\)
\(152\) 416.000 + 720.533i 0.221987 + 0.384493i
\(153\) 0 0
\(154\) 0 0
\(155\) 2775.00 1.43802
\(156\) 0 0
\(157\) 1126.00 1950.29i 0.572386 0.991401i −0.423934 0.905693i \(-0.639351\pi\)
0.996320 0.0857085i \(-0.0273154\pi\)
\(158\) 583.000 1009.79i 0.293551 0.508444i
\(159\) 0 0
\(160\) −480.000 −0.237171
\(161\) 0 0
\(162\) 0 0
\(163\) −838.000 1451.46i −0.402682 0.697466i 0.591366 0.806403i \(-0.298589\pi\)
−0.994049 + 0.108937i \(0.965255\pi\)
\(164\) 336.000 581.969i 0.159983 0.277098i
\(165\) 0 0
\(166\) 597.000 + 1034.03i 0.279134 + 0.483474i
\(167\) 3030.00 1.40400 0.702001 0.712176i \(-0.252290\pi\)
0.702001 + 0.712176i \(0.252290\pi\)
\(168\) 0 0
\(169\) 5547.00 2.52481
\(170\) −1260.00 2182.38i −0.568456 0.984595i
\(171\) 0 0
\(172\) −652.000 + 1129.30i −0.289038 + 0.500628i
\(173\) −1719.00 2977.40i −0.755452 1.30848i −0.945149 0.326638i \(-0.894084\pi\)
0.189698 0.981843i \(-0.439249\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 144.000 0.0616728
\(177\) 0 0
\(178\) 1038.00 1797.87i 0.437086 0.757056i
\(179\) −606.000 + 1049.62i −0.253042 + 0.438282i −0.964362 0.264587i \(-0.914765\pi\)
0.711320 + 0.702869i \(0.248098\pi\)
\(180\) 0 0
\(181\) −3032.00 −1.24512 −0.622560 0.782572i \(-0.713907\pi\)
−0.622560 + 0.782572i \(0.713907\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −336.000 581.969i −0.134621 0.233170i
\(185\) 330.000 571.577i 0.131146 0.227152i
\(186\) 0 0
\(187\) 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 \(-0.00827060\pi\)
−0.522331 + 0.852743i \(0.674937\pi\)
\(192\) 0 0
\(193\) −182.500 + 316.099i −0.0680655 + 0.117893i −0.898050 0.439894i \(-0.855016\pi\)
0.829984 + 0.557787i \(0.188349\pi\)
\(194\) −169.000 292.717i −0.0625438 0.108329i
\(195\) 0 0
\(196\) 0 0
\(197\) 1590.00 0.575040 0.287520 0.957775i \(-0.407169\pi\)
0.287520 + 0.957775i \(0.407169\pi\)
\(198\) 0 0
\(199\) −2690.00 + 4659.22i −0.958236 + 1.65971i −0.231455 + 0.972846i \(0.574348\pi\)
−0.726782 + 0.686868i \(0.758985\pi\)
\(200\) −400.000 + 692.820i −0.141421 + 0.244949i
\(201\) 0 0
\(202\) 1284.00 0.447237
\(203\) 0 0
\(204\) 0 0
\(205\) −1260.00 2182.38i −0.429279 0.743533i
\(206\) 464.000 803.672i 0.156934 0.271818i
\(207\) 0 0
\(208\) −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
\(213\) 0 0
\(214\) 393.000 680.696i 0.125537 0.217437i
\(215\) 2445.00 + 4234.86i 0.775570 + 1.34333i
\(216\) 0 0
\(217\) 0 0
\(218\) 28.0000 0.00869908
\(219\) 0 0
\(220\) 270.000 467.654i 0.0827427 0.143315i
\(221\) 3696.00 6401.66i 1.12498 1.94852i
\(222\) 0 0
\(223\) 1573.00 0.472358 0.236179 0.971710i \(-0.424105\pi\)
0.236179 + 0.971710i \(0.424105\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −2184.00 3782.80i −0.642821 1.11340i
\(227\) −460.500 + 797.609i −0.134645 + 0.233212i −0.925462 0.378841i \(-0.876323\pi\)
0.790817 + 0.612053i \(0.209656\pi\)
\(228\) 0 0
\(229\) 2026.00 + 3509.13i 0.584637 + 1.01262i 0.994921 + 0.100663i \(0.0320963\pi\)
−0.410284 + 0.911958i \(0.634570\pi\)
\(230\) −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 \(-0.187624\pi\)
−0.897046 + 0.441938i \(0.854291\pi\)
\(234\) 0 0
\(235\) −1035.00 + 1792.67i −0.287302 + 0.497622i
\(236\) −318.000 550.792i −0.0877120 0.151922i
\(237\) 0 0
\(238\) 0 0
\(239\) −4932.00 −1.33483 −0.667415 0.744686i \(-0.732599\pi\)
−0.667415 + 0.744686i \(0.732599\pi\)
\(240\) 0 0
\(241\) −768.500 + 1331.08i −0.205408 + 0.355778i −0.950263 0.311449i \(-0.899186\pi\)
0.744854 + 0.667227i \(0.232519\pi\)
\(242\) 1250.00 2165.06i 0.332037 0.575106i
\(243\) 0 0
\(244\) −2888.00 −0.757726
\(245\) 0 0
\(246\) 0 0
\(247\) 4576.00 + 7925.86i 1.17880 + 2.04174i
\(248\) 740.000 1281.72i 0.189476 0.328182i
\(249\) 0 0
\(250\) −375.000 649.519i −0.0948683 0.164317i
\(251\) 5319.00 1.33758 0.668789 0.743452i \(-0.266813\pi\)
0.668789 + 0.743452i \(0.266813\pi\)
\(252\) 0 0
\(253\) 756.000 0.187863
\(254\) 373.000 + 646.055i 0.0921421 + 0.159595i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2673.00 4629.77i −0.648783 1.12372i −0.983414 0.181375i \(-0.941945\pi\)
0.334631 0.942349i \(-0.391388\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −5280.00 −1.25943
\(261\) 0 0
\(262\) 1173.00 2031.70i 0.276596 0.479079i
\(263\) 387.000 670.304i 0.0907355 0.157159i −0.817085 0.576517i \(-0.804412\pi\)
0.907821 + 0.419358i \(0.137745\pi\)
\(264\) 0 0
\(265\) 9585.00 2.22189
\(266\) 0 0
\(267\) 0 0
\(268\) 332.000 + 575.041i 0.0756721 + 0.131068i
\(269\) −1207.50 + 2091.45i −0.273690 + 0.474045i −0.969804 0.243887i \(-0.921578\pi\)
0.696114 + 0.717931i \(0.254911\pi\)
\(270\) 0 0
\(271\) −237.500 411.362i −0.0532365 0.0922084i 0.838179 0.545395i \(-0.183620\pi\)
−0.891416 + 0.453187i \(0.850287\pi\)
\(272\) −1344.00 −0.299603
\(273\) 0 0
\(274\) −60.0000 −0.0132290
\(275\) −450.000 779.423i −0.0986764 0.170913i
\(276\) 0 0
\(277\) −1864.00 + 3228.54i −0.404321 + 0.700304i −0.994242 0.107156i \(-0.965825\pi\)
0.589921 + 0.807461i \(0.299159\pi\)
\(278\) −82.0000 142.028i −0.0176908 0.0306413i
\(279\) 0 0
\(280\) 0 0
\(281\) −1602.00 −0.340097 −0.170049 0.985436i \(-0.554392\pi\)
−0.170049 + 0.985436i \(0.554392\pi\)
\(282\) 0 0
\(283\) 343.000 594.093i 0.0720468 0.124789i −0.827751 0.561095i \(-0.810380\pi\)
0.899798 + 0.436306i \(0.143714\pi\)
\(284\) 2172.00 3762.01i 0.453819 0.786037i
\(285\) 0 0
\(286\) 1584.00 0.327496
\(287\) 0 0
\(288\) 0 0
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) −765.000 + 1325.02i −0.154905 + 0.268303i
\(291\) 0 0
\(292\) 436.000 + 755.174i 0.0873800 + 0.151347i
\(293\) −1101.00 −0.219526 −0.109763 0.993958i \(-0.535009\pi\)
−0.109763 + 0.993958i \(0.535009\pi\)
\(294\) 0 0
\(295\) −2385.00 −0.470712
\(296\) −176.000 304.841i −0.0345601 0.0598599i
\(297\) 0 0
\(298\) −1434.00 + 2483.76i −0.278756 + 0.482820i
\(299\) −3696.00 6401.66i −0.714867 1.23819i
\(300\) 0 0
\(301\) 0 0
\(302\) −5342.00 −1.01787
\(303\) 0 0
\(304\) 832.000 1441.07i 0.156969 0.271878i
\(305\) −5415.00 + 9379.06i −1.01660 + 1.76080i
\(306\) 0 0
\(307\) −2780.00 −0.516818 −0.258409 0.966036i \(-0.583198\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2775.00 4806.44i −0.508417 0.880605i
\(311\) −2148.00 + 3720.45i −0.391646 + 0.678351i −0.992667 0.120883i \(-0.961428\pi\)
0.601021 + 0.799233i \(0.294761\pi\)
\(312\) 0 0
\(313\) 2744.50 + 4753.61i 0.495618 + 0.858435i 0.999987 0.00505298i \(-0.00160842\pi\)
−0.504370 + 0.863488i \(0.668275\pi\)
\(314\) −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 \(-0.0364216\pi\)
−0.595607 + 0.803276i \(0.703088\pi\)
\(318\) 0 0
\(319\) 229.500 397.506i 0.0402807 0.0697682i
\(320\) 480.000 + 831.384i 0.0838525 + 0.145237i
\(321\) 0 0
\(322\) 0 0
\(323\) 8736.00 1.50490
\(324\) 0 0
\(325\) −4400.00 + 7621.02i −0.750979 + 1.30073i
\(326\) −1676.00 + 2902.92i −0.284739 + 0.493183i
\(327\) 0 0
\(328\) −1344.00 −0.226250
\(329\) 0 0
\(330\) 0 0
\(331\) 1982.00 + 3432.92i 0.329126 + 0.570062i 0.982339 0.187112i \(-0.0599127\pi\)
−0.653213 + 0.757174i \(0.726579\pi\)
\(332\) 1194.00 2068.07i 0.197377 0.341868i
\(333\) 0 0
\(334\) −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
\(339\) 0 0
\(340\) −2520.00 + 4364.77i −0.401959 + 0.696214i
\(341\) 832.500 + 1441.93i 0.132206 + 0.228988i
\(342\) 0 0
\(343\) 0 0
\(344\) 2608.00 0.408761
\(345\) 0 0
\(346\) −3438.00 + 5954.79i −0.534185 + 0.925236i
\(347\) −2958.00 + 5123.41i −0.457619 + 0.792619i −0.998835 0.0482646i \(-0.984631\pi\)
0.541216 + 0.840884i \(0.317964\pi\)
\(348\) 0 0
\(349\) 142.000 0.0217796 0.0108898 0.999941i \(-0.496534\pi\)
0.0108898 + 0.999941i \(0.496534\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −144.000 249.415i −0.0218046 0.0377667i
\(353\) 2220.00 3845.15i 0.334727 0.579764i −0.648705 0.761040i \(-0.724689\pi\)
0.983432 + 0.181275i \(0.0580225\pi\)
\(354\) 0 0
\(355\) −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 \(-0.112924\pi\)
−0.769693 + 0.638415i \(0.779591\pi\)
\(360\) 0 0
\(361\) −1978.50 + 3426.86i −0.288453 + 0.499615i
\(362\) 3032.00 + 5251.58i 0.440217 + 0.762477i
\(363\) 0 0
\(364\) 0 0
\(365\) 3270.00 0.468930
\(366\) 0 0
\(367\) −1434.50 + 2484.63i −0.204033 + 0.353396i −0.949824 0.312784i \(-0.898738\pi\)
0.745791 + 0.666180i \(0.232072\pi\)
\(368\) −672.000 + 1163.94i −0.0951914 + 0.164876i
\(369\) 0 0
\(370\) −1320.00 −0.185469
\(371\) 0 0
\(372\) 0 0
\(373\) 1532.00 + 2653.50i 0.212665 + 0.368346i 0.952548 0.304390i \(-0.0984524\pi\)
−0.739883 + 0.672736i \(0.765119\pi\)
\(374\) 756.000 1309.43i 0.104524 0.181040i
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) 2520.00 4364.77i 0.337525 0.584610i
\(383\) −921.000 1595.22i −0.122874 0.212825i 0.798026 0.602623i \(-0.205878\pi\)
−0.920900 + 0.389799i \(0.872545\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 730.000 0.0962591
\(387\) 0 0
\(388\) −338.000 + 585.433i −0.0442251 + 0.0766002i
\(389\) 3915.00 6780.98i 0.510279 0.883828i −0.489650 0.871919i \(-0.662876\pi\)
0.999929 0.0119097i \(-0.00379105\pi\)
\(390\) 0 0
\(391\) −7056.00 −0.912627
\(392\) 0 0
\(393\) 0 0
\(394\) −1590.00 2753.96i −0.203307 0.352138i
\(395\) −4372.50 + 7573.39i −0.556973 + 0.964706i
\(396\) 0 0
\(397\) −7382.00 12786.0i −0.933229 1.61640i −0.777762 0.628559i \(-0.783645\pi\)
−0.155467 0.987841i \(-0.549688\pi\)
\(398\) 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 \(-0.0391291\pi\)
−0.602417 + 0.798181i \(0.705796\pi\)
\(402\) 0 0
\(403\) 8140.00 14098.9i 1.00616 1.74272i
\(404\) −1284.00 2223.95i −0.158122 0.273876i
\(405\) 0 0
\(406\) 0 0
\(407\) 396.000 0.0482285
\(408\) 0 0
\(409\) 2375.50 4114.49i 0.287191 0.497429i −0.685948 0.727651i \(-0.740612\pi\)
0.973138 + 0.230222i \(0.0739454\pi\)
\(410\) −2520.00 + 4364.77i −0.303546 + 0.525757i
\(411\) 0 0
\(412\) −1856.00 −0.221938
\(413\) 0 0
\(414\) 0 0
\(415\) −4477.50 7755.26i −0.529619 0.917327i
\(416\) −1408.00 + 2438.73i −0.165944 + 0.287424i
\(417\) 0 0
\(418\) 936.000 + 1621.20i 0.109525 + 0.189702i
\(419\) −4704.00 −0.548462 −0.274231 0.961664i \(-0.588423\pi\)
−0.274231 + 0.961664i \(0.588423\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 2556.00 4427.12i 0.292760 0.507076i
\(425\) 4200.00 + 7274.61i 0.479365 + 0.830284i
\(426\) 0 0
\(427\) 0 0
\(428\) −1572.00 −0.177536
\(429\) 0 0
\(430\) 4890.00 8469.73i 0.548411 0.949876i
\(431\) −6402.00 + 11088.6i −0.715484 + 1.23925i 0.247289 + 0.968942i \(0.420460\pi\)
−0.962773 + 0.270312i \(0.912873\pi\)
\(432\) 0 0
\(433\) 5074.00 0.563143 0.281571 0.959540i \(-0.409144\pi\)
0.281571 + 0.959540i \(0.409144\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −28.0000 48.4974i −0.00307559 0.00532708i
\(437\) 4368.00 7565.60i 0.478146 0.828173i
\(438\) 0 0
\(439\) −633.500 1097.25i −0.0688731 0.119292i 0.829532 0.558459i \(-0.188607\pi\)
−0.898406 + 0.439167i \(0.855274\pi\)
\(440\) −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 \(-0.287919\pi\)
−0.989839 + 0.142190i \(0.954586\pi\)
\(444\) 0 0
\(445\) −7785.00 + 13484.0i −0.829313 + 1.43641i
\(446\) −1573.00 2724.52i −0.167004 0.289259i
\(447\) 0 0
\(448\) 0 0
\(449\) −11688.0 −1.22849 −0.614244 0.789116i \(-0.710539\pi\)
−0.614244 + 0.789116i \(0.710539\pi\)
\(450\) 0 0
\(451\) 756.000 1309.43i 0.0789327 0.136715i
\(452\) −4368.00 + 7565.60i −0.454543 + 0.787292i
\(453\) 0 0
\(454\) 1842.00 0.190417
\(455\) 0 0
\(456\) 0 0
\(457\) −275.500 477.180i −0.0281999 0.0488436i 0.851581 0.524223i \(-0.175644\pi\)
−0.879781 + 0.475379i \(0.842311\pi\)
\(458\) 4052.00 7018.27i 0.413401 0.716031i
\(459\) 0 0
\(460\) 2520.00 + 4364.77i 0.255425 + 0.442409i
\(461\) 13386.0 1.35238 0.676191 0.736726i \(-0.263629\pi\)
0.676191 + 0.736726i \(0.263629\pi\)
\(462\) 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
\(465\) 0 0
\(466\) −468.000 + 810.600i −0.0465229 + 0.0805801i
\(467\) −2850.00 4936.34i −0.282403 0.489137i 0.689573 0.724216i \(-0.257798\pi\)
−0.971976 + 0.235080i \(0.924465\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 4140.00 0.406306
\(471\) 0 0
\(472\) −636.000 + 1101.58i −0.0620218 + 0.107425i
\(473\) −1467.00 + 2540.92i −0.142606 + 0.247001i
\(474\) 0 0
\(475\) −10400.0 −1.00460
\(476\) 0 0
\(477\) 0 0
\(478\) 4932.00 + 8542.47i 0.471934 + 0.817414i
\(479\) −9897.00 + 17142.1i −0.944062 + 1.63516i −0.186442 + 0.982466i \(0.559696\pi\)
−0.757619 + 0.652697i \(0.773638\pi\)
\(480\) 0 0
\(481\) −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
\(486\) 0 0
\(487\) −7967.50 + 13800.1i −0.741359 + 1.28407i 0.210517 + 0.977590i \(0.432485\pi\)
−0.951877 + 0.306482i \(0.900848\pi\)
\(488\) 2888.00 + 5002.16i 0.267897 + 0.464011i
\(489\) 0 0
\(490\) 0 0
\(491\) −9963.00 −0.915731 −0.457865 0.889021i \(-0.651386\pi\)
−0.457865 + 0.889021i \(0.651386\pi\)
\(492\) 0 0
\(493\) −2142.00 + 3710.05i −0.195681 + 0.338930i
\(494\) 9152.00 15851.7i 0.833538 1.44373i
\(495\) 0 0
\(496\) −2960.00 −0.267960
\(497\) 0 0
\(498\) 0 0
\(499\) −9571.00 16577.5i −0.858631 1.48719i −0.873235 0.487299i \(-0.837982\pi\)
0.0146043 0.999893i \(-0.495351\pi\)
\(500\) −750.000 + 1299.04i −0.0670820 + 0.116190i
\(501\) 0 0
\(502\) −5319.00 9212.78i −0.472906 0.819096i
\(503\) −12192.0 −1.08074 −0.540372 0.841426i \(-0.681717\pi\)
−0.540372 + 0.841426i \(0.681717\pi\)
\(504\) 0 0
\(505\) −9630.00 −0.848573
\(506\) −756.000 1309.43i −0.0664196 0.115042i
\(507\) 0 0
\(508\) 746.000 1292.11i 0.0651543 0.112851i
\(509\) 9904.50 + 17155.1i 0.862494 + 1.49388i 0.869515 + 0.493907i \(0.164432\pi\)
−0.00702091 + 0.999975i \(0.502235\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −5346.00 + 9259.54i −0.458759 + 0.794593i
\(515\) −3480.00 + 6027.54i −0.297761 + 0.515738i
\(516\) 0 0
\(517\) −1242.00 −0.105654
\(518\) 0 0
\(519\) 0 0
\(520\) 5280.00 + 9145.23i 0.445276 + 0.771240i
\(521\) 897.000 1553.65i 0.0754286 0.130646i −0.825844 0.563899i \(-0.809301\pi\)
0.901273 + 0.433253i \(0.142634\pi\)
\(522\) 0 0
\(523\) −3224.00 5584.13i −0.269552 0.466878i 0.699194 0.714932i \(-0.253542\pi\)
−0.968746 + 0.248054i \(0.920209\pi\)
\(524\) −4692.00 −0.391166
\(525\) 0 0
\(526\) −1548.00 −0.128319
\(527\) −7770.00 13458.0i −0.642251 1.11241i
\(528\) 0 0
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) −9585.00 16601.7i −0.785558 1.36063i
\(531\) 0 0
\(532\) 0 0
\(533\) −14784.0 −1.20144
\(534\) 0 0
\(535\) −2947.50 + 5105.22i −0.238190 + 0.412557i
\(536\) 664.000 1150.08i 0.0535083 0.0926790i
\(537\) 0 0
\(538\) 4830.00 0.387056
\(539\) 0 0
\(540\) 0 0
\(541\) −3631.00 6289.08i −0.288556 0.499794i 0.684909 0.728628i \(-0.259842\pi\)
−0.973465 + 0.228835i \(0.926509\pi\)
\(542\) −475.000 + 822.724i −0.0376439 + 0.0652012i
\(543\) 0 0
\(544\) 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
\(549\) 0 0
\(550\) −900.000 + 1558.85i −0.0697748 + 0.120853i
\(551\) −2652.00 4593.40i −0.205044 0.355146i
\(552\) 0 0
\(553\) 0 0
\(554\) 7456.00 0.571796
\(555\) 0 0
\(556\) −164.000 + 284.056i −0.0125093 + 0.0216667i
\(557\) 7912.50 13704.9i 0.601909 1.04254i −0.390623 0.920551i \(-0.627740\pi\)
0.992532 0.121986i \(-0.0389264\pi\)
\(558\) 0 0
\(559\) 28688.0 2.17061
\(560\) 0 0
\(561\) 0 0
\(562\) 1602.00 + 2774.75i 0.120243 + 0.208266i
\(563\) −529.500 + 917.121i −0.0396372 + 0.0686537i −0.885163 0.465280i \(-0.845954\pi\)
0.845526 + 0.533934i \(0.179287\pi\)
\(564\) 0 0
\(565\) 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 \(-0.120065\pi\)
−0.783821 + 0.620987i \(0.786732\pi\)
\(570\) 0 0
\(571\) 1265.00 2191.04i 0.0927121 0.160582i −0.815939 0.578138i \(-0.803780\pi\)
0.908651 + 0.417555i \(0.137113\pi\)
\(572\) −1584.00 2743.57i −0.115787 0.200550i
\(573\) 0 0
\(574\) 0 0
\(575\) 8400.00 0.609225
\(576\) 0 0
\(577\) 5915.50 10245.9i 0.426803 0.739245i −0.569784 0.821795i \(-0.692973\pi\)
0.996587 + 0.0825498i \(0.0263063\pi\)
\(578\) −2143.00 + 3711.78i −0.154216 + 0.267111i
\(579\) 0 0
\(580\) 3060.00 0.219068
\(581\) 0 0
\(582\) 0 0
\(583\) 2875.50 + 4980.51i 0.204273 + 0.353811i
\(584\) 872.000 1510.35i 0.0617870 0.107018i
\(585\) 0 0
\(586\) 1101.00 + 1906.99i 0.0776141 + 0.134432i
\(587\) 4809.00 0.338141 0.169070 0.985604i \(-0.445923\pi\)
0.169070 + 0.985604i \(0.445923\pi\)
\(588\) 0 0
\(589\) 19240.0 1.34596
\(590\) 2385.00 + 4130.94i 0.166422 + 0.288251i
\(591\) 0 0
\(592\) −352.000 + 609.682i −0.0244377 + 0.0423273i
\(593\) −10902.0 18882.8i −0.754960 1.30763i −0.945394 0.325930i \(-0.894323\pi\)
0.190434 0.981700i \(-0.439011\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5736.00 0.394221
\(597\) 0 0
\(598\) −7392.00 + 12803.3i −0.505487 + 0.875530i
\(599\) 7083.00 12268.1i 0.483144 0.836831i −0.516668 0.856186i \(-0.672828\pi\)
0.999813 + 0.0193549i \(0.00616125\pi\)
\(600\) 0 0
\(601\) −5891.00 −0.399832 −0.199916 0.979813i \(-0.564067\pi\)
−0.199916 + 0.979813i \(0.564067\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 5342.00 + 9252.62i 0.359872 + 0.623317i
\(605\) −9375.00 + 16238.0i −0.629997 + 1.09119i
\(606\) 0 0
\(607\) −1368.50 2370.31i −0.0915086 0.158497i 0.816638 0.577151i \(-0.195836\pi\)
−0.908146 + 0.418653i \(0.862502\pi\)
\(608\) −3328.00 −0.221987
\(609\) 0 0
\(610\) 21660.0 1.43768
\(611\) 6072.00 + 10517.0i 0.402041 + 0.696355i
\(612\) 0 0
\(613\) 13094.0 22679.5i 0.862743 1.49432i −0.00652719 0.999979i \(-0.502078\pi\)
0.869271 0.494337i \(-0.164589\pi\)
\(614\) 2780.00 + 4815.10i 0.182723 + 0.316485i
\(615\) 0 0
\(616\) 0 0
\(617\) 2358.00 0.153857 0.0769283 0.997037i \(-0.475489\pi\)
0.0769283 + 0.997037i \(0.475489\pi\)
\(618\) 0 0
\(619\) 6883.00 11921.7i 0.446932 0.774110i −0.551252 0.834339i \(-0.685850\pi\)
0.998185 + 0.0602291i \(0.0191831\pi\)
\(620\) −5550.00 + 9612.88i −0.359505 + 0.622682i
\(621\) 0 0
\(622\) 8592.00 0.553871
\(623\) 0 0
\(624\) 0 0
\(625\) 9062.50 + 15696.7i 0.580000 + 1.00459i
\(626\) 5489.00 9507.23i 0.350455 0.607005i
\(627\) 0 0
\(628\) 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
\(633\) 0 0
\(634\) 4491.00 7778.64i 0.281326 0.487270i
\(635\) −2797.50 4845.41i −0.174827 0.302810i
\(636\) 0 0
\(637\) 0 0
\(638\) −918.000 −0.0569655
\(639\) 0 0
\(640\) 960.000 1662.77i 0.0592927 0.102698i
\(641\) 10713.0 18555.5i 0.660122 1.14336i −0.320462 0.947262i \(-0.603838\pi\)
0.980583 0.196103i \(-0.0628287\pi\)
\(642\) 0 0
\(643\) −9962.00 −0.610984 −0.305492 0.952195i \(-0.598821\pi\)
−0.305492 + 0.952195i \(0.598821\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −8736.00 15131.2i −0.532064 0.921562i
\(647\) 9087.00 15739.1i 0.552159 0.956367i −0.445960 0.895053i \(-0.647137\pi\)
0.998119 0.0613142i \(-0.0195292\pi\)
\(648\) 0 0
\(649\) −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 −0.996115 0.0880610i \(-0.971933\pi\)
0.421795 0.906691i \(-0.361400\pi\)
\(654\) 0 0
\(655\) −8797.50 + 15237.7i −0.524804 + 0.908988i
\(656\) 1344.00 + 2327.88i 0.0799914 + 0.138549i
\(657\) 0 0
\(658\) 0 0
\(659\) −13080.0 −0.773178 −0.386589 0.922252i \(-0.626347\pi\)
−0.386589 + 0.922252i \(0.626347\pi\)
\(660\) 0 0
\(661\) −7595.00 + 13154.9i −0.446916 + 0.774081i −0.998183 0.0602477i \(-0.980811\pi\)
0.551268 + 0.834328i \(0.314144\pi\)
\(662\) 3964.00 6865.85i 0.232727 0.403095i
\(663\) 0 0
\(664\) −4776.00 −0.279134
\(665\) 0 0
\(666\) 0 0
\(667\) 2142.00 + 3710.05i 0.124346 + 0.215373i
\(668\) −6060.00 + 10496.2i −0.351001 + 0.607951i
\(669\) 0 0
\(670\) −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
\(675\) 0 0
\(676\) −11094.0 + 19215.4i −0.631202 + 1.09327i
\(677\) −2014.50 3489.22i −0.114363 0.198082i 0.803162 0.595761i \(-0.203149\pi\)
−0.917525 + 0.397679i \(0.869816\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 10080.0 0.568456
\(681\) 0 0
\(682\) 1665.00 2883.86i 0.0934841 0.161919i
\(683\) 7510.50 13008.6i 0.420763 0.728783i −0.575251 0.817977i \(-0.695096\pi\)
0.996014 + 0.0891936i \(0.0284290\pi\)
\(684\) 0 0
\(685\) 450.000 0.0251002
\(686\) 0 0
\(687\) 0 0
\(688\) −2608.00 4517.19i −0.144519 0.250314i
\(689\) 28116.0 48698.3i 1.55462 2.69268i
\(690\) 0 0
\(691\) −6992.00 12110.5i −0.384932 0.666722i 0.606828 0.794834i \(-0.292442\pi\)
−0.991760 + 0.128111i \(0.959109\pi\)
\(692\) 13752.0 0.755452
\(693\) 0 0
\(694\) 11832.0 0.647171
\(695\) 615.000 + 1065.21i 0.0335659 + 0.0581378i
\(696\) 0 0
\(697\) −7056.00 + 12221.4i −0.383451 + 0.664156i
\(698\) −142.000 245.951i −0.00770026 0.0133372i
\(699\) 0 0
\(700\) 0 0
\(701\) 31053.0 1.67312 0.836559 0.547877i \(-0.184564\pi\)
0.836559 + 0.547877i \(0.184564\pi\)
\(702\) 0 0
\(703\) 2288.00 3962.93i 0.122750 0.212610i
\(704\) −288.000 + 498.831i −0.0154182 + 0.0267051i
\(705\) 0 0
\(706\) −8880.00 −0.473376
\(707\) 0 0
\(708\) 0 0
\(709\) −7543.00 13064.9i −0.399553 0.692047i 0.594117 0.804378i \(-0.297501\pi\)
−0.993671 + 0.112332i \(0.964168\pi\)
\(710\) −16290.0 + 28215.1i −0.861060 + 1.49140i
\(711\) 0 0
\(712\) 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
\(717\) 0 0
\(718\) 2286.00 3959.47i 0.118820 0.205802i
\(719\) 3189.00 + 5523.51i 0.165410 + 0.286498i 0.936801 0.349863i \(-0.113772\pi\)
−0.771391 + 0.636362i \(0.780439\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7914.00 0.407934
\(723\) 0 0
\(724\) 6064.00 10503.2i 0.311280 0.539153i
\(725\) 2550.00 4416.73i 0.130627 0.226253i
\(726\) 0 0
\(727\) 7363.00 0.375624 0.187812 0.982205i \(-0.439860\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −3270.00 5663.81i −0.165792 0.287160i
\(731\) 13692.0 23715.2i 0.692773 1.19992i
\(732\) 0 0
\(733\) 16405.0 + 28414.3i 0.826647 + 1.43180i 0.900654 + 0.434537i \(0.143088\pi\)
−0.0740064 + 0.997258i \(0.523579\pi\)
\(734\) 5738.00 0.288547
\(735\) 0 0
\(736\) 2688.00 0.134621
\(737\) 747.000 + 1293.84i 0.0373353 + 0.0646666i
\(738\) 0 0
\(739\) 12017.0 20814.1i 0.598177 1.03607i −0.394914 0.918718i \(-0.629225\pi\)
0.993090 0.117354i \(-0.0374412\pi\)
\(740\) 1320.00 + 2286.31i 0.0655732 + 0.113576i
\(741\) 0 0
\(742\) 0 0
\(743\) 8022.00 0.396095 0.198048 0.980192i \(-0.436540\pi\)
0.198048 + 0.980192i \(0.436540\pi\)
\(744\) 0 0
\(745\) 10755.0 18628.2i 0.528903 0.916087i
\(746\) 3064.00 5307.00i 0.150377 0.260460i
\(747\) 0 0
\(748\) −3024.00 −0.147819
\(749\) 0 0
\(750\) 0 0
\(751\) −14759.5 25564.2i −0.717153 1.24215i −0.962123 0.272615i \(-0.912112\pi\)
0.244970 0.969531i \(-0.421222\pi\)
\(752\) 1104.00 1912.18i 0.0535356 0.0927263i
\(753\) 0 0
\(754\) 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
\(759\) 0 0
\(760\) −6240.00 + 10808.0i −0.297827 + 0.515852i
\(761\) 5448.00 + 9436.21i 0.259514 + 0.449491i 0.966112 0.258124i \(-0.0831044\pi\)
−0.706598 + 0.707615i \(0.749771\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −10080.0 −0.477332
\(765\) 0 0
\(766\) −1842.00 + 3190.44i −0.0868853 + 0.150490i
\(767\) −6996.00 + 12117.4i −0.329349 + 0.570450i
\(768\) 0 0
\(769\) −17285.0 −0.810550 −0.405275 0.914195i \(-0.632824\pi\)
−0.405275 + 0.914195i \(0.632824\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −730.000 1264.40i −0.0340327 0.0589464i
\(773\) −5913.00 + 10241.6i −0.275130 + 0.476540i −0.970168 0.242434i \(-0.922054\pi\)
0.695038 + 0.718973i \(0.255388\pi\)
\(774\) 0 0
\(775\) 9250.00 + 16021.5i 0.428735 + 0.742591i
\(776\) 1352.00 0.0625438
\(777\) 0 0
\(778\) −15660.0 −0.721643
\(779\) −8736.00 15131.2i −0.401797 0.695932i
\(780\) 0 0
\(781\) 4887.00 8464.53i 0.223906 0.387817i
\(782\) 7056.00 + 12221.4i 0.322662 + 0.558868i
\(783\) 0 0
\(784\) 0 0
\(785\) 33780.0 1.53587
\(786\) 0 0
\(787\) 8857.00 15340.8i 0.401166 0.694841i −0.592701 0.805423i \(-0.701938\pi\)
0.993867 + 0.110582i \(0.0352716\pi\)
\(788\) −3180.00 + 5507.92i −0.143760 + 0.248999i
\(789\) 0 0
\(790\)