Properties

Label 12.4.b.a.11.3
Level 12
Weight 4
Character 12.11
Analytic conductor 0.708
Analytic rank 0
Dimension 4
CM No
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(0.708022920069\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{3}, \sqrt{-5})\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.3
Root \(0.866025 - 1.11803i\)
Character \(\chi\) = 12.11
Dual form 12.4.b.a.11.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 - 2.23607i) q^{2} +(-3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} +8.94427i q^{5} +(2.66025 + 14.4542i) q^{6} -7.74597i q^{7} +(-20.7846 - 8.94427i) q^{8} +(-3.00000 - 26.8328i) q^{9} +O(q^{10})\) \(q+(1.73205 - 2.23607i) q^{2} +(-3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} +8.94427i q^{5} +(2.66025 + 14.4542i) q^{6} -7.74597i q^{7} +(-20.7846 - 8.94427i) q^{8} +(-3.00000 - 26.8328i) q^{9} +(20.0000 + 15.4919i) q^{10} +34.6410 q^{11} +(36.9282 + 19.0868i) q^{12} -10.0000 q^{13} +(-17.3205 - 13.4164i) q^{14} +(-34.6410 - 30.9839i) q^{15} +(-56.0000 + 30.9839i) q^{16} +35.7771i q^{17} +(-65.1962 - 39.7676i) q^{18} +69.7137i q^{19} +(69.2820 - 17.8885i) q^{20} +(30.0000 + 26.8328i) q^{21} +(60.0000 - 77.4597i) q^{22} -96.9948 q^{23} +(106.641 - 49.5146i) q^{24} +45.0000 q^{25} +(-17.3205 + 22.3607i) q^{26} +(114.315 + 81.3327i) q^{27} +(-60.0000 + 15.4919i) q^{28} -152.053i q^{29} +(-129.282 + 23.7940i) q^{30} -224.633i q^{31} +(-27.7128 + 178.885i) q^{32} +(-120.000 + 134.164i) q^{33} +(80.0000 + 61.9677i) q^{34} +69.2820 q^{35} +(-201.846 + 76.9035i) q^{36} -130.000 q^{37} +(155.885 + 120.748i) q^{38} +(34.6410 - 38.7298i) q^{39} +(80.0000 - 185.903i) q^{40} -125.220i q^{41} +(111.962 - 20.6062i) q^{42} +224.633i q^{43} +(-69.2820 - 268.328i) q^{44} +(240.000 - 26.8328i) q^{45} +(-168.000 + 216.887i) q^{46} -193.990 q^{47} +(73.9897 - 324.218i) q^{48} +283.000 q^{49} +(77.9423 - 100.623i) q^{50} +(-138.564 - 123.935i) q^{51} +(20.0000 + 77.4597i) q^{52} +545.601i q^{53} +(379.865 - 114.745i) q^{54} +309.839i q^{55} +(-69.2820 + 160.997i) q^{56} +(-270.000 - 241.495i) q^{57} +(-340.000 - 263.363i) q^{58} +173.205 q^{59} +(-170.718 + 330.296i) q^{60} -442.000 q^{61} +(-502.295 - 389.076i) q^{62} +(-207.846 + 23.2379i) q^{63} +(352.000 + 371.806i) q^{64} -89.4427i q^{65} +(92.1539 + 500.707i) q^{66} -735.867i q^{67} +(277.128 - 71.5542i) q^{68} +(336.000 - 375.659i) q^{69} +(120.000 - 154.919i) q^{70} +1039.23 q^{71} +(-177.646 + 584.542i) q^{72} +410.000 q^{73} +(-225.167 + 290.689i) q^{74} +(-155.885 + 174.284i) q^{75} +(540.000 - 139.427i) q^{76} -268.328i q^{77} +(-26.6025 - 144.542i) q^{78} +85.2056i q^{79} +(-277.128 - 500.879i) q^{80} +(-711.000 + 160.997i) q^{81} +(-280.000 - 216.887i) q^{82} -1254.00 q^{83} +(147.846 - 286.045i) q^{84} -320.000 q^{85} +(502.295 + 389.076i) q^{86} +(588.897 + 526.726i) q^{87} +(-720.000 - 309.839i) q^{88} +840.762i q^{89} +(355.692 - 583.132i) q^{90} +77.4597i q^{91} +(193.990 + 751.319i) q^{92} +(870.000 + 778.152i) q^{93} +(-336.000 + 433.774i) q^{94} -623.538 q^{95} +(-596.820 - 727.009i) q^{96} +770.000 q^{97} +(490.170 - 632.807i) q^{98} +(-103.923 - 929.516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 8q^{4} - 24q^{6} - 12q^{9} + O(q^{10}) \) \( 4q - 8q^{4} - 24q^{6} - 12q^{9} + 80q^{10} + 120q^{12} - 40q^{13} - 224q^{16} - 240q^{18} + 120q^{21} + 240q^{22} + 288q^{24} + 180q^{25} - 240q^{28} - 240q^{30} - 480q^{33} + 320q^{34} + 24q^{36} - 520q^{37} + 320q^{40} + 240q^{42} + 960q^{45} - 672q^{46} - 480q^{48} + 1132q^{49} + 80q^{52} + 792q^{54} - 1080q^{57} - 1360q^{58} - 960q^{60} - 1768q^{61} + 1408q^{64} + 1200q^{66} + 1344q^{69} + 480q^{70} - 960q^{72} + 1640q^{73} + 2160q^{76} + 240q^{78} - 2844q^{81} - 1120q^{82} - 240q^{84} - 1280q^{85} - 2880q^{88} - 240q^{90} + 3480q^{93} - 1344q^{94} + 384q^{96} + 3080q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 2.23607i 0.612372 0.790569i
\(3\) −3.46410 + 3.87298i −0.666667 + 0.745356i
\(4\) −2.00000 7.74597i −0.250000 0.968246i
\(5\) 8.94427i 0.800000i 0.916515 + 0.400000i \(0.130990\pi\)
−0.916515 + 0.400000i \(0.869010\pi\)
\(6\) 2.66025 + 14.4542i 0.181007 + 0.983482i
\(7\) 7.74597i 0.418243i −0.977890 0.209121i \(-0.932940\pi\)
0.977890 0.209121i \(-0.0670604\pi\)
\(8\) −20.7846 8.94427i −0.918559 0.395285i
\(9\) −3.00000 26.8328i −0.111111 0.993808i
\(10\) 20.0000 + 15.4919i 0.632456 + 0.489898i
\(11\) 34.6410 0.949514 0.474757 0.880117i \(-0.342536\pi\)
0.474757 + 0.880117i \(0.342536\pi\)
\(12\) 36.9282 + 19.0868i 0.888355 + 0.459158i
\(13\) −10.0000 −0.213346 −0.106673 0.994294i \(-0.534020\pi\)
−0.106673 + 0.994294i \(0.534020\pi\)
\(14\) −17.3205 13.4164i −0.330650 0.256120i
\(15\) −34.6410 30.9839i −0.596285 0.533333i
\(16\) −56.0000 + 30.9839i −0.875000 + 0.484123i
\(17\) 35.7771i 0.510425i 0.966885 + 0.255212i \(0.0821454\pi\)
−0.966885 + 0.255212i \(0.917855\pi\)
\(18\) −65.1962 39.7676i −0.853716 0.520740i
\(19\) 69.7137i 0.841759i 0.907117 + 0.420879i \(0.138278\pi\)
−0.907117 + 0.420879i \(0.861722\pi\)
\(20\) 69.2820 17.8885i 0.774597 0.200000i
\(21\) 30.0000 + 26.8328i 0.311740 + 0.278829i
\(22\) 60.0000 77.4597i 0.581456 0.750657i
\(23\) −96.9948 −0.879340 −0.439670 0.898159i \(-0.644905\pi\)
−0.439670 + 0.898159i \(0.644905\pi\)
\(24\) 106.641 49.5146i 0.907000 0.421130i
\(25\) 45.0000 0.360000
\(26\) −17.3205 + 22.3607i −0.130647 + 0.168665i
\(27\) 114.315 + 81.3327i 0.814815 + 0.579721i
\(28\) −60.0000 + 15.4919i −0.404962 + 0.104561i
\(29\) 152.053i 0.973637i −0.873503 0.486818i \(-0.838157\pi\)
0.873503 0.486818i \(-0.161843\pi\)
\(30\) −129.282 + 23.7940i −0.786785 + 0.144806i
\(31\) 224.633i 1.30146i −0.759309 0.650730i \(-0.774463\pi\)
0.759309 0.650730i \(-0.225537\pi\)
\(32\) −27.7128 + 178.885i −0.153093 + 0.988212i
\(33\) −120.000 + 134.164i −0.633010 + 0.707726i
\(34\) 80.0000 + 61.9677i 0.403526 + 0.312570i
\(35\) 69.2820 0.334594
\(36\) −201.846 + 76.9035i −0.934473 + 0.356035i
\(37\) −130.000 −0.577618 −0.288809 0.957387i \(-0.593259\pi\)
−0.288809 + 0.957387i \(0.593259\pi\)
\(38\) 155.885 + 120.748i 0.665469 + 0.515470i
\(39\) 34.6410 38.7298i 0.142231 0.159019i
\(40\) 80.0000 185.903i 0.316228 0.734847i
\(41\) 125.220i 0.476977i −0.971145 0.238488i \(-0.923348\pi\)
0.971145 0.238488i \(-0.0766519\pi\)
\(42\) 111.962 20.6062i 0.411334 0.0757050i
\(43\) 224.633i 0.796656i 0.917243 + 0.398328i \(0.130409\pi\)
−0.917243 + 0.398328i \(0.869591\pi\)
\(44\) −69.2820 268.328i −0.237379 0.919363i
\(45\) 240.000 26.8328i 0.795046 0.0888889i
\(46\) −168.000 + 216.887i −0.538484 + 0.695179i
\(47\) −193.990 −0.602049 −0.301025 0.953616i \(-0.597329\pi\)
−0.301025 + 0.953616i \(0.597329\pi\)
\(48\) 73.9897 324.218i 0.222489 0.974935i
\(49\) 283.000 0.825073
\(50\) 77.9423 100.623i 0.220454 0.284605i
\(51\) −138.564 123.935i −0.380448 0.340283i
\(52\) 20.0000 + 77.4597i 0.0533366 + 0.206572i
\(53\) 545.601i 1.41404i 0.707195 + 0.707019i \(0.249960\pi\)
−0.707195 + 0.707019i \(0.750040\pi\)
\(54\) 379.865 114.745i 0.957280 0.289162i
\(55\) 309.839i 0.759612i
\(56\) −69.2820 + 160.997i −0.165325 + 0.384181i
\(57\) −270.000 241.495i −0.627410 0.561173i
\(58\) −340.000 263.363i −0.769727 0.596228i
\(59\) 173.205 0.382193 0.191096 0.981571i \(-0.438796\pi\)
0.191096 + 0.981571i \(0.438796\pi\)
\(60\) −170.718 + 330.296i −0.367327 + 0.710684i
\(61\) −442.000 −0.927743 −0.463871 0.885903i \(-0.653540\pi\)
−0.463871 + 0.885903i \(0.653540\pi\)
\(62\) −502.295 389.076i −1.02890 0.796979i
\(63\) −207.846 + 23.2379i −0.415653 + 0.0464714i
\(64\) 352.000 + 371.806i 0.687500 + 0.726184i
\(65\) 89.4427i 0.170677i
\(66\) 92.1539 + 500.707i 0.171869 + 0.933830i
\(67\) 735.867i 1.34180i −0.741549 0.670899i \(-0.765908\pi\)
0.741549 0.670899i \(-0.234092\pi\)
\(68\) 277.128 71.5542i 0.494217 0.127606i
\(69\) 336.000 375.659i 0.586227 0.655421i
\(70\) 120.000 154.919i 0.204896 0.264520i
\(71\) 1039.23 1.73710 0.868549 0.495603i \(-0.165053\pi\)
0.868549 + 0.495603i \(0.165053\pi\)
\(72\) −177.646 + 584.542i −0.290775 + 0.956791i
\(73\) 410.000 0.657354 0.328677 0.944442i \(-0.393397\pi\)
0.328677 + 0.944442i \(0.393397\pi\)
\(74\) −225.167 + 290.689i −0.353717 + 0.456647i
\(75\) −155.885 + 174.284i −0.240000 + 0.268328i
\(76\) 540.000 139.427i 0.815030 0.210440i
\(77\) 268.328i 0.397128i
\(78\) −26.6025 144.542i −0.0386172 0.209822i
\(79\) 85.2056i 0.121347i 0.998158 + 0.0606733i \(0.0193248\pi\)
−0.998158 + 0.0606733i \(0.980675\pi\)
\(80\) −277.128 500.879i −0.387298 0.700000i
\(81\) −711.000 + 160.997i −0.975309 + 0.220846i
\(82\) −280.000 216.887i −0.377083 0.292087i
\(83\) −1254.00 −1.65837 −0.829186 0.558973i \(-0.811196\pi\)
−0.829186 + 0.558973i \(0.811196\pi\)
\(84\) 147.846 286.045i 0.192040 0.371548i
\(85\) −320.000 −0.408340
\(86\) 502.295 + 389.076i 0.629812 + 0.487850i
\(87\) 588.897 + 526.726i 0.725706 + 0.649091i
\(88\) −720.000 309.839i −0.872185 0.375329i
\(89\) 840.762i 1.00135i 0.865634 + 0.500677i \(0.166916\pi\)
−0.865634 + 0.500677i \(0.833084\pi\)
\(90\) 355.692 583.132i 0.416592 0.682972i
\(91\) 77.4597i 0.0892305i
\(92\) 193.990 + 751.319i 0.219835 + 0.851417i
\(93\) 870.000 + 778.152i 0.970052 + 0.867641i
\(94\) −336.000 + 433.774i −0.368678 + 0.475962i
\(95\) −623.538 −0.673407
\(96\) −596.820 727.009i −0.634507 0.772917i
\(97\) 770.000 0.805996 0.402998 0.915201i \(-0.367968\pi\)
0.402998 + 0.915201i \(0.367968\pi\)
\(98\) 490.170 632.807i 0.505252 0.652277i
\(99\) −103.923 929.516i −0.105502 0.943635i
\(100\) −90.0000 348.569i −0.0900000 0.348569i
\(101\) 1493.69i 1.47156i −0.677218 0.735782i \(-0.736815\pi\)
0.677218 0.735782i \(-0.263185\pi\)
\(102\) −517.128 + 95.1761i −0.501993 + 0.0923906i
\(103\) 1355.54i 1.29675i 0.761319 + 0.648377i \(0.224552\pi\)
−0.761319 + 0.648377i \(0.775448\pi\)
\(104\) 207.846 + 89.4427i 0.195971 + 0.0843325i
\(105\) −240.000 + 268.328i −0.223063 + 0.249392i
\(106\) 1220.00 + 945.008i 1.11790 + 0.865918i
\(107\) 644.323 0.582141 0.291070 0.956702i \(-0.405989\pi\)
0.291070 + 0.956702i \(0.405989\pi\)
\(108\) 401.369 1048.15i 0.357609 0.933871i
\(109\) −1066.00 −0.936737 −0.468368 0.883533i \(-0.655158\pi\)
−0.468368 + 0.883533i \(0.655158\pi\)
\(110\) 692.820 + 536.656i 0.600526 + 0.465165i
\(111\) 450.333 503.488i 0.385079 0.430531i
\(112\) 240.000 + 433.774i 0.202481 + 0.365963i
\(113\) 1037.54i 0.863745i −0.901935 0.431872i \(-0.857853\pi\)
0.901935 0.431872i \(-0.142147\pi\)
\(114\) −1007.65 + 185.456i −0.827855 + 0.152365i
\(115\) 867.548i 0.703472i
\(116\) −1177.79 + 304.105i −0.942720 + 0.243409i
\(117\) 30.0000 + 268.328i 0.0237051 + 0.212025i
\(118\) 300.000 387.298i 0.234044 0.302150i
\(119\) 277.128 0.213481
\(120\) 442.872 + 953.826i 0.336904 + 0.725600i
\(121\) −131.000 −0.0984222
\(122\) −765.566 + 988.342i −0.568124 + 0.733445i
\(123\) 484.974 + 433.774i 0.355518 + 0.317985i
\(124\) −1740.00 + 449.266i −1.26013 + 0.325365i
\(125\) 1520.53i 1.08800i
\(126\) −308.038 + 505.007i −0.217796 + 0.357060i
\(127\) 1835.79i 1.28268i −0.767257 0.641340i \(-0.778379\pi\)
0.767257 0.641340i \(-0.221621\pi\)
\(128\) 1441.07 143.108i 0.995105 0.0988212i
\(129\) −870.000 778.152i −0.593792 0.531104i
\(130\) −200.000 154.919i −0.134932 0.104518i
\(131\) −450.333 −0.300350 −0.150175 0.988659i \(-0.547984\pi\)
−0.150175 + 0.988659i \(0.547984\pi\)
\(132\) 1279.23 + 661.188i 0.843505 + 0.435977i
\(133\) 540.000 0.352060
\(134\) −1645.45 1274.56i −1.06078 0.821680i
\(135\) −727.461 + 1022.47i −0.463777 + 0.651852i
\(136\) 320.000 743.613i 0.201763 0.468855i
\(137\) 89.4427i 0.0557782i 0.999611 + 0.0278891i \(0.00887852\pi\)
−0.999611 + 0.0278891i \(0.991121\pi\)
\(138\) −258.031 1401.98i −0.159167 0.864815i
\(139\) 1959.73i 1.19584i 0.801555 + 0.597921i \(0.204006\pi\)
−0.801555 + 0.597921i \(0.795994\pi\)
\(140\) −138.564 536.656i −0.0836486 0.323970i
\(141\) 672.000 751.319i 0.401366 0.448741i
\(142\) 1800.00 2323.79i 1.06375 1.37330i
\(143\) −346.410 −0.202575
\(144\) 999.384 + 1409.69i 0.578347 + 0.815791i
\(145\) 1360.00 0.778909
\(146\) 710.141 916.788i 0.402546 0.519684i
\(147\) −980.341 + 1096.05i −0.550049 + 0.614973i
\(148\) 260.000 + 1006.98i 0.144405 + 0.559276i
\(149\) 1618.91i 0.890111i 0.895503 + 0.445055i \(0.146816\pi\)
−0.895503 + 0.445055i \(0.853184\pi\)
\(150\) 119.711 + 650.438i 0.0651626 + 0.354053i
\(151\) 565.456i 0.304743i −0.988323 0.152371i \(-0.951309\pi\)
0.988323 0.152371i \(-0.0486909\pi\)
\(152\) 623.538 1448.97i 0.332734 0.773205i
\(153\) 960.000 107.331i 0.507264 0.0567138i
\(154\) −600.000 464.758i −0.313957 0.243190i
\(155\) 2009.18 1.04117
\(156\) −369.282 190.868i −0.189527 0.0979597i
\(157\) −730.000 −0.371085 −0.185542 0.982636i \(-0.559404\pi\)
−0.185542 + 0.982636i \(0.559404\pi\)
\(158\) 190.526 + 147.580i 0.0959329 + 0.0743093i
\(159\) −2113.10 1890.02i −1.05396 0.942692i
\(160\) −1600.00 247.871i −0.790569 0.122474i
\(161\) 751.319i 0.367778i
\(162\) −871.488 + 1868.70i −0.422658 + 0.906289i
\(163\) 255.617i 0.122831i 0.998112 + 0.0614155i \(0.0195615\pi\)
−0.998112 + 0.0614155i \(0.980439\pi\)
\(164\) −969.948 + 250.440i −0.461831 + 0.119244i
\(165\) −1200.00 1073.31i −0.566181 0.506408i
\(166\) −2172.00 + 2804.04i −1.01554 + 1.31106i
\(167\) −13.8564 −0.00642060 −0.00321030 0.999995i \(-0.501022\pi\)
−0.00321030 + 0.999995i \(0.501022\pi\)
\(168\) −383.538 826.038i −0.176135 0.379346i
\(169\) −2097.00 −0.954483
\(170\) −554.256 + 715.542i −0.250056 + 0.322821i
\(171\) 1870.61 209.141i 0.836547 0.0935288i
\(172\) 1740.00 449.266i 0.771359 0.199164i
\(173\) 1118.03i 0.491344i −0.969353 0.245672i \(-0.920991\pi\)
0.969353 0.245672i \(-0.0790086\pi\)
\(174\) 2197.79 404.499i 0.957554 0.176235i
\(175\) 348.569i 0.150567i
\(176\) −1939.90 + 1073.31i −0.830825 + 0.459682i
\(177\) −600.000 + 670.820i −0.254795 + 0.284870i
\(178\) 1880.00 + 1456.24i 0.791640 + 0.613202i
\(179\) 1351.00 0.564125 0.282063 0.959396i \(-0.408981\pi\)
0.282063 + 0.959396i \(0.408981\pi\)
\(180\) −687.846 1805.37i −0.284828 0.747578i
\(181\) 1262.00 0.518253 0.259126 0.965843i \(-0.416565\pi\)
0.259126 + 0.965843i \(0.416565\pi\)
\(182\) 173.205 + 134.164i 0.0705429 + 0.0546423i
\(183\) 1531.13 1711.86i 0.618495 0.691499i
\(184\) 2016.00 + 867.548i 0.807725 + 0.347590i
\(185\) 1162.76i 0.462094i
\(186\) 3246.88 597.581i 1.27996 0.235574i
\(187\) 1239.35i 0.484656i
\(188\) 387.979 + 1502.64i 0.150512 + 0.582931i
\(189\) 630.000 885.483i 0.242464 0.340791i
\(190\) −1080.00 + 1394.27i −0.412376 + 0.532375i
\(191\) −2771.28 −1.04986 −0.524929 0.851146i \(-0.675908\pi\)
−0.524929 + 0.851146i \(0.675908\pi\)
\(192\) −2659.36 + 75.3150i −0.999599 + 0.0283093i
\(193\) −190.000 −0.0708627 −0.0354313 0.999372i \(-0.511281\pi\)
−0.0354313 + 0.999372i \(0.511281\pi\)
\(194\) 1333.68 1721.77i 0.493570 0.637196i
\(195\) 346.410 + 309.839i 0.127215 + 0.113785i
\(196\) −566.000 2192.11i −0.206268 0.798873i
\(197\) 2137.68i 0.773114i −0.922266 0.386557i \(-0.873664\pi\)
0.922266 0.386557i \(-0.126336\pi\)
\(198\) −2258.46 1377.59i −0.810615 0.494450i
\(199\) 255.617i 0.0910563i −0.998963 0.0455281i \(-0.985503\pi\)
0.998963 0.0455281i \(-0.0144971\pi\)
\(200\) −935.307 402.492i −0.330681 0.142302i
\(201\) 2850.00 + 2549.12i 1.00012 + 0.894532i
\(202\) −3340.00 2587.15i −1.16337 0.901146i
\(203\) −1177.79 −0.407217
\(204\) −682.872 + 1321.18i −0.234366 + 0.453438i
\(205\) 1120.00 0.381581
\(206\) 3031.09 + 2347.87i 1.02517 + 0.794097i
\(207\) 290.985 + 2602.64i 0.0977045 + 0.873895i
\(208\) 560.000 309.839i 0.186678 0.103286i
\(209\) 2414.95i 0.799262i
\(210\) 184.308 + 1001.41i 0.0605640 + 0.329067i
\(211\) 549.964i 0.179436i −0.995967 0.0897181i \(-0.971403\pi\)
0.995967 0.0897181i \(-0.0285966\pi\)
\(212\) 4226.20 1091.20i 1.36914 0.353509i
\(213\) −3600.00 + 4024.92i −1.15807 + 1.29476i
\(214\) 1116.00 1440.75i 0.356487 0.460223i
\(215\) −2009.18 −0.637325
\(216\) −1648.54 2712.93i −0.519300 0.854592i
\(217\) −1740.00 −0.544327
\(218\) −1846.37 + 2383.65i −0.573632 + 0.740555i
\(219\) −1420.28 + 1587.92i −0.438236 + 0.489963i
\(220\) 2400.00 619.677i 0.735491 0.189903i
\(221\) 357.771i 0.108897i
\(222\) −345.833 1879.04i −0.104553 0.568077i
\(223\) 472.504i 0.141889i −0.997480 0.0709444i \(-0.977399\pi\)
0.997480 0.0709444i \(-0.0226013\pi\)
\(224\) 1385.64 + 214.663i 0.413313 + 0.0640301i
\(225\) −135.000 1207.48i −0.0400000 0.357771i
\(226\) −2320.00 1797.06i −0.682850 0.528933i
\(227\) −505.759 −0.147878 −0.0739392 0.997263i \(-0.523557\pi\)
−0.0739392 + 0.997263i \(0.523557\pi\)
\(228\) −1330.61 + 2574.40i −0.386501 + 0.747780i
\(229\) 4094.00 1.18139 0.590697 0.806894i \(-0.298853\pi\)
0.590697 + 0.806894i \(0.298853\pi\)
\(230\) −1939.90 1502.64i −0.556144 0.430787i
\(231\) 1039.23 + 929.516i 0.296001 + 0.264752i
\(232\) −1360.00 + 3160.35i −0.384864 + 0.894342i
\(233\) 5277.12i 1.48376i −0.670534 0.741879i \(-0.733935\pi\)
0.670534 0.741879i \(-0.266065\pi\)
\(234\) 651.962 + 397.676i 0.182137 + 0.111098i
\(235\) 1735.10i 0.481639i
\(236\) −346.410 1341.64i −0.0955482 0.370057i
\(237\) −330.000 295.161i −0.0904464 0.0808977i
\(238\) 480.000 619.677i 0.130730 0.168772i
\(239\) 5681.13 1.53758 0.768790 0.639502i \(-0.220859\pi\)
0.768790 + 0.639502i \(0.220859\pi\)
\(240\) 2899.90 + 661.784i 0.779948 + 0.177992i
\(241\) −1198.00 −0.320207 −0.160104 0.987100i \(-0.551183\pi\)
−0.160104 + 0.987100i \(0.551183\pi\)
\(242\) −226.899 + 292.925i −0.0602711 + 0.0778096i
\(243\) 1839.44 3311.40i 0.485597 0.874183i
\(244\) 884.000 + 3423.72i 0.231936 + 0.898283i
\(245\) 2531.23i 0.660058i
\(246\) 1809.95 333.116i 0.469098 0.0863363i
\(247\) 697.137i 0.179586i
\(248\) −2009.18 + 4668.91i −0.514448 + 1.19547i
\(249\) 4344.00 4856.74i 1.10558 1.23608i
\(250\) 3400.00 + 2633.63i 0.860140 + 0.666261i
\(251\) −4260.84 −1.07148 −0.535741 0.844382i \(-0.679968\pi\)
−0.535741 + 0.844382i \(0.679968\pi\)
\(252\) 595.692 + 1563.49i 0.148909 + 0.390837i
\(253\) −3360.00 −0.834946
\(254\) −4104.96 3179.69i −1.01405 0.785478i
\(255\) 1108.51 1239.35i 0.272226 0.304358i
\(256\) 2176.00 3470.19i 0.531250 0.847215i
\(257\) 3148.38i 0.764166i 0.924128 + 0.382083i \(0.124793\pi\)
−0.924128 + 0.382083i \(0.875207\pi\)
\(258\) −3246.88 + 597.581i −0.783497 + 0.144201i
\(259\) 1006.98i 0.241585i
\(260\) −692.820 + 178.885i −0.165257 + 0.0426692i
\(261\) −4080.00 + 456.158i −0.967608 + 0.108182i
\(262\) −780.000 + 1006.98i −0.183926 + 0.237447i
\(263\) 4253.92 0.997368 0.498684 0.866784i \(-0.333817\pi\)
0.498684 + 0.866784i \(0.333817\pi\)
\(264\) 3694.15 1715.24i 0.861210 0.399869i
\(265\) −4880.00 −1.13123
\(266\) 935.307 1207.48i 0.215592 0.278328i
\(267\) −3256.26 2912.48i −0.746366 0.667570i
\(268\) −5700.00 + 1471.73i −1.29919 + 0.335449i
\(269\) 44.7214i 0.0101365i −0.999987 0.00506823i \(-0.998387\pi\)
0.999987 0.00506823i \(-0.00161328\pi\)
\(270\) 1026.31 + 3397.62i 0.231330 + 0.765824i
\(271\) 8760.69i 1.96374i 0.189552 + 0.981871i \(0.439296\pi\)
−0.189552 + 0.981871i \(0.560704\pi\)
\(272\) −1108.51 2003.52i −0.247108 0.446622i
\(273\) −300.000 268.328i −0.0665085 0.0594870i
\(274\) 200.000 + 154.919i 0.0440965 + 0.0341570i
\(275\) 1558.85 0.341825
\(276\) −3581.85 1851.33i −0.781166 0.403756i
\(277\) 6350.00 1.37738 0.688690 0.725055i \(-0.258186\pi\)
0.688690 + 0.725055i \(0.258186\pi\)
\(278\) 4382.09 + 3394.35i 0.945396 + 0.732301i
\(279\) −6027.54 + 673.899i −1.29340 + 0.144607i
\(280\) −1440.00 619.677i −0.307344 0.132260i
\(281\) 5563.34i 1.18107i 0.807012 + 0.590535i \(0.201083\pi\)
−0.807012 + 0.590535i \(0.798917\pi\)
\(282\) −516.062 2803.96i −0.108975 0.592104i
\(283\) 6777.72i 1.42365i −0.702356 0.711826i \(-0.747868\pi\)
0.702356 0.711826i \(-0.252132\pi\)
\(284\) −2078.46 8049.84i −0.434275 1.68194i
\(285\) 2160.00 2414.95i 0.448938 0.501928i
\(286\) −600.000 + 774.597i −0.124052 + 0.160150i
\(287\) −969.948 −0.199492
\(288\) 4883.14 + 206.956i 0.999103 + 0.0423438i
\(289\) 3633.00 0.739467
\(290\) 2355.59 3041.05i 0.476983 0.615782i
\(291\) −2667.36 + 2982.20i −0.537331 + 0.600754i
\(292\) −820.000 3175.85i −0.164339 0.636481i
\(293\) 652.932i 0.130187i 0.997879 + 0.0650933i \(0.0207345\pi\)
−0.997879 + 0.0650933i \(0.979265\pi\)
\(294\) 752.852 + 4090.53i 0.149344 + 0.811444i
\(295\) 1549.19i 0.305754i
\(296\) 2702.00 + 1162.76i 0.530576 + 0.228324i
\(297\) 3960.00 + 2817.45i 0.773678 + 0.550454i
\(298\) 3620.00 + 2804.04i 0.703695 + 0.545079i
\(299\) 969.948 0.187604
\(300\) 1661.77 + 858.908i 0.319808 + 0.165297i
\(301\) 1740.00 0.333196
\(302\) −1264.40 979.398i −0.240920 0.186616i
\(303\) 5785.05 + 5174.31i 1.09684 + 0.981043i
\(304\) −2160.00 3903.97i −0.407515 0.736539i
\(305\) 3953.37i 0.742194i
\(306\) 1422.77 2332.53i 0.265798 0.435757i
\(307\) 1556.94i 0.289444i 0.989472 + 0.144722i \(0.0462287\pi\)
−0.989472 + 0.144722i \(0.953771\pi\)
\(308\) −2078.46 + 536.656i −0.384517 + 0.0992819i
\(309\) −5250.00 4695.74i −0.966544 0.864503i
\(310\) 3480.00 4492.66i 0.637583 0.823116i
\(311\) −3256.26 −0.593715 −0.296857 0.954922i \(-0.595939\pi\)
−0.296857 + 0.954922i \(0.595939\pi\)
\(312\) −1066.41 + 495.146i −0.193505 + 0.0898465i
\(313\) −7030.00 −1.26952 −0.634759 0.772710i \(-0.718901\pi\)
−0.634759 + 0.772710i \(0.718901\pi\)
\(314\) −1264.40 + 1632.33i −0.227242 + 0.293368i
\(315\) −207.846 1859.03i −0.0371771 0.332522i
\(316\) 660.000 170.411i 0.117493 0.0303367i
\(317\) 491.935i 0.0871603i 0.999050 + 0.0435802i \(0.0138764\pi\)
−0.999050 + 0.0435802i \(0.986124\pi\)
\(318\) −7886.20 + 1451.44i −1.39068 + 0.255951i
\(319\) 5267.26i 0.924482i
\(320\) −3325.54 + 3148.38i −0.580948 + 0.550000i
\(321\) −2232.00 + 2495.45i −0.388094 + 0.433902i
\(322\) 1680.00 + 1301.32i 0.290754 + 0.225217i
\(323\) −2494.15 −0.429654
\(324\) 2669.08 + 5185.39i 0.457661 + 0.889127i
\(325\) −450.000 −0.0768046
\(326\) 571.577 + 442.741i 0.0971065 + 0.0752183i
\(327\) 3692.73 4128.60i 0.624491 0.698202i
\(328\) −1120.00 + 2602.64i −0.188542 + 0.438131i
\(329\) 1502.64i 0.251803i
\(330\) −4478.46 + 824.250i −0.747064 + 0.137495i
\(331\) 4237.04i 0.703592i −0.936077 0.351796i \(-0.885571\pi\)
0.936077 0.351796i \(-0.114429\pi\)
\(332\) 2508.01 + 9713.48i 0.414593 + 1.60571i
\(333\) 390.000 + 3488.27i 0.0641798 + 0.574041i
\(334\) −24.0000 + 30.9839i −0.00393180 + 0.00507593i
\(335\) 6581.79 1.07344
\(336\) −2511.38 573.122i −0.407760 0.0930546i
\(337\) 1490.00 0.240847 0.120424 0.992723i \(-0.461575\pi\)
0.120424 + 0.992723i \(0.461575\pi\)
\(338\) −3632.11 + 4689.03i −0.584499 + 0.754585i
\(339\) 4018.36 + 3594.13i 0.643797 + 0.575830i
\(340\) 640.000 + 2478.71i 0.102085 + 0.395373i
\(341\) 7781.52i 1.23576i
\(342\) 2772.35 4545.07i 0.438337 0.718623i
\(343\) 4848.98i 0.763324i
\(344\) 2009.18 4668.91i 0.314906 0.731775i
\(345\) 3360.00 + 3005.28i 0.524337 + 0.468981i
\(346\) −2500.00 1936.49i −0.388442 0.300886i
\(347\) −1988.39 −0.307616 −0.153808 0.988101i \(-0.549154\pi\)
−0.153808 + 0.988101i \(0.549154\pi\)
\(348\) 2902.21 5615.03i 0.447053 0.864935i
\(349\) −2074.00 −0.318105 −0.159053 0.987270i \(-0.550844\pi\)
−0.159053 + 0.987270i \(0.550844\pi\)
\(350\) −779.423 603.738i −0.119034 0.0922033i
\(351\) −1143.15 813.327i −0.173838 0.123681i
\(352\) −960.000 + 6196.77i −0.145364 + 0.938321i
\(353\) 8658.06i 1.30544i −0.757597 0.652722i \(-0.773627\pi\)
0.757597 0.652722i \(-0.226373\pi\)
\(354\) 460.770 + 2503.54i 0.0691797 + 0.375880i
\(355\) 9295.16i 1.38968i
\(356\) 6512.51 1681.52i 0.969557 0.250339i
\(357\) −960.000 + 1073.31i −0.142321 + 0.159120i
\(358\) 2340.00 3020.93i 0.345455 0.445980i
\(359\) −8106.00 −1.19169 −0.595847 0.803098i \(-0.703184\pi\)
−0.595847 + 0.803098i \(0.703184\pi\)
\(360\) −5228.31 1588.92i −0.765433 0.232620i
\(361\) 1999.00 0.291442
\(362\) 2185.85 2821.92i 0.317364 0.409715i
\(363\) 453.797 507.361i 0.0656148 0.0733596i
\(364\) 600.000 154.919i 0.0863971 0.0223076i
\(365\) 3667.15i 0.525884i
\(366\) −1175.83 6388.74i −0.167928 0.912418i
\(367\) 7893.14i 1.12267i 0.827590 + 0.561333i \(0.189711\pi\)
−0.827590 + 0.561333i \(0.810289\pi\)
\(368\) 5431.71 3005.28i 0.769423 0.425709i
\(369\) −3360.00 + 375.659i −0.474023 + 0.0529974i
\(370\) −2600.00 2013.95i −0.365318 0.282974i
\(371\) 4226.20 0.591411
\(372\) 4287.54 8295.29i 0.597576 1.15616i
\(373\) 4910.00 0.681582 0.340791 0.940139i \(-0.389305\pi\)
0.340791 + 0.940139i \(0.389305\pi\)
\(374\) 2771.28 + 2146.63i 0.383154 + 0.296790i
\(375\) −5888.97 5267.26i −0.810947 0.725333i
\(376\) 4032.00 + 1735.10i 0.553017 + 0.237981i
\(377\) 1520.53i 0.207722i
\(378\) −888.808 2942.42i −0.120940 0.400376i
\(379\) 3137.12i 0.425179i 0.977142 + 0.212590i \(0.0681897\pi\)
−0.977142 + 0.212590i \(0.931810\pi\)
\(380\) 1247.08 + 4829.91i 0.168352 + 0.652024i
\(381\) 7110.00 + 6359.38i 0.956053 + 0.855120i
\(382\) −4800.00 + 6196.77i −0.642904 + 0.829986i
\(383\) −6207.67 −0.828191 −0.414095 0.910233i \(-0.635902\pi\)
−0.414095 + 0.910233i \(0.635902\pi\)
\(384\) −4437.74 + 6076.97i −0.589747 + 0.807588i
\(385\) 2400.00 0.317702
\(386\) −329.090 + 424.853i −0.0433944 + 0.0560219i
\(387\) 6027.54 673.899i 0.791723 0.0885174i
\(388\) −1540.00 5964.39i −0.201499 0.780403i
\(389\) 9454.10i 1.23224i 0.787652 + 0.616120i \(0.211297\pi\)
−0.787652 + 0.616120i \(0.788703\pi\)
\(390\) 1292.82 237.940i 0.167858 0.0308938i
\(391\) 3470.19i 0.448837i
\(392\) −5882.04 2531.23i −0.757878 0.326139i
\(393\) 1560.00 1744.13i 0.200233 0.223867i
\(394\) −4780.00 3702.57i −0.611200 0.473434i
\(395\) −762.102 −0.0970773
\(396\) −6992.15 + 2664.02i −0.887295 + 0.338060i
\(397\) −10570.0 −1.33625 −0.668127 0.744047i \(-0.732904\pi\)
−0.668127 + 0.744047i \(0.732904\pi\)
\(398\) −571.577 442.741i −0.0719863 0.0557604i
\(399\) −1870.61 + 2091.41i −0.234706 + 0.262410i
\(400\) −2520.00 + 1394.27i −0.315000 + 0.174284i
\(401\) 1681.52i 0.209405i −0.994504 0.104702i \(-0.966611\pi\)
0.994504 0.104702i \(-0.0333890\pi\)
\(402\) 10636.3 1957.59i 1.31963 0.242875i
\(403\) 2246.33i 0.277662i
\(404\) −11570.1 + 2987.39i −1.42484 + 0.367891i
\(405\) −1440.00 6359.38i −0.176677 0.780247i
\(406\) −2040.00 + 2633.63i −0.249368 + 0.321933i
\(407\) −4503.33 −0.548457
\(408\) 1771.49 + 3815.30i 0.214955 + 0.462955i
\(409\) −3574.00 −0.432085 −0.216043 0.976384i \(-0.569315\pi\)
−0.216043 + 0.976384i \(0.569315\pi\)
\(410\) 1939.90 2504.40i 0.233670 0.301667i
\(411\) −346.410 309.839i −0.0415746 0.0371854i
\(412\) 10500.0 2711.09i 1.25558 0.324189i
\(413\) 1341.64i 0.159849i
\(414\) 6323.69 + 3857.25i 0.750706 + 0.457907i
\(415\) 11216.2i 1.32670i
\(416\) 277.128 1788.85i 0.0326618 0.210831i
\(417\) −7590.00 6788.70i −0.891328 0.797228i
\(418\) 5400.00 + 4182.82i 0.631872 + 0.489446i
\(419\) 15346.0 1.78926 0.894630 0.446808i \(-0.147439\pi\)
0.894630 + 0.446808i \(0.147439\pi\)
\(420\) 2558.46 + 1322.38i 0.297238 + 0.153632i
\(421\) 3518.00 0.407261 0.203630 0.979048i \(-0.434726\pi\)
0.203630 + 0.979048i \(0.434726\pi\)
\(422\) −1229.76 952.565i −0.141857 0.109882i
\(423\) 581.969 + 5205.29i 0.0668943 + 0.598321i
\(424\) 4880.00 11340.1i 0.558948 1.29888i
\(425\) 1609.97i 0.183753i
\(426\) 2764.62 + 15021.2i 0.314428 + 1.70840i
\(427\) 3423.72i 0.388022i
\(428\) −1288.65 4990.90i −0.145535 0.563655i
\(429\) 1200.00 1341.64i 0.135050 0.150991i
\(430\) −3480.00 + 4492.66i −0.390280 + 0.503850i
\(431\) 12886.5 1.44018 0.720091 0.693879i \(-0.244100\pi\)
0.720091 + 0.693879i \(0.244100\pi\)
\(432\) −8921.66 1012.70i −0.993619 0.112786i
\(433\) 14450.0 1.60375 0.801874 0.597493i \(-0.203837\pi\)
0.801874 + 0.597493i \(0.203837\pi\)
\(434\) −3013.77 + 3890.76i −0.333331 + 0.430328i
\(435\) −4711.18 + 5267.26i −0.519273 + 0.580565i
\(436\) 2132.00 + 8257.20i 0.234184 + 0.906991i
\(437\) 6761.87i 0.740192i
\(438\) 1090.70 + 5926.21i 0.118986 + 0.646496i
\(439\) 15065.9i 1.63794i −0.573835 0.818971i \(-0.694545\pi\)
0.573835 0.818971i \(-0.305455\pi\)
\(440\) 2771.28 6439.88i 0.300263 0.697748i
\(441\) −849.000 7593.69i −0.0916748 0.819964i
\(442\) −800.000 619.677i −0.0860908 0.0666856i
\(443\) −3041.48 −0.326197 −0.163098 0.986610i \(-0.552149\pi\)
−0.163098 + 0.986610i \(0.552149\pi\)
\(444\) −4800.67 2481.29i −0.513130 0.265218i
\(445\) −7520.00 −0.801084
\(446\) −1056.55 818.401i −0.112173 0.0868888i
\(447\) −6270.02 5608.08i −0.663450 0.593407i
\(448\) 2880.00 2726.58i 0.303721 0.287542i
\(449\) 14310.8i 1.50416i 0.659069 + 0.752082i \(0.270951\pi\)
−0.659069 + 0.752082i \(0.729049\pi\)
\(450\) −2933.83 1789.54i −0.307338 0.187466i
\(451\) 4337.74i 0.452896i
\(452\) −8036.72 + 2075.07i −0.836317 + 0.215936i
\(453\) 2190.00 + 1958.80i 0.227142 + 0.203162i
\(454\) −876.000 + 1130.91i −0.0905566 + 0.116908i
\(455\) −692.820 −0.0713844
\(456\) 3451.84 + 7434.34i 0.354490 + 0.763476i
\(457\) −3430.00 −0.351091 −0.175546 0.984471i \(-0.556169\pi\)
−0.175546 + 0.984471i \(0.556169\pi\)
\(458\) 7091.02 9154.46i 0.723453 0.933974i
\(459\) −2909.85 + 4089.87i −0.295904 + 0.415902i
\(460\) −6720.00 + 1735.10i −0.681134 + 0.175868i
\(461\) 3908.65i 0.394889i −0.980314 0.197445i \(-0.936736\pi\)
0.980314 0.197445i \(-0.0632642\pi\)
\(462\) 3878.46 713.821i 0.390568 0.0718830i
\(463\) 18179.8i 1.82481i 0.409291 + 0.912404i \(0.365776\pi\)
−0.409291 + 0.912404i \(0.634224\pi\)
\(464\) 4711.18 + 8514.95i 0.471360 + 0.851932i
\(465\) −6960.00 + 7781.52i −0.694112 + 0.776041i
\(466\) −11800.0 9140.24i −1.17301 0.908613i
\(467\) 1849.83 0.183298 0.0916488 0.995791i \(-0.470786\pi\)
0.0916488 + 0.995791i \(0.470786\pi\)
\(468\) 2018.46 769.035i 0.199366 0.0759587i
\(469\) −5700.00 −0.561197
\(470\) −3879.79 3005.28i −0.380769 0.294943i
\(471\) 2528.79 2827.28i 0.247390 0.276590i
\(472\) −3600.00 1549.19i −0.351067 0.151075i
\(473\) 7781.52i 0.756437i
\(474\) −1231.58 + 226.669i −0.119342 + 0.0219646i
\(475\) 3137.12i 0.303033i
\(476\) −554.256 2146.63i −0.0533704 0.206703i
\(477\) 14640.0 1636.80i 1.40528 0.157115i
\(478\) 9840.00 12703.4i 0.941571 1.21556i
\(479\) −15242.0 −1.45392 −0.726959 0.686681i \(-0.759067\pi\)
−0.726959 + 0.686681i \(0.759067\pi\)
\(480\) 6502.56 5338.12i 0.618333 0.507606i
\(481\) 1300.00 0.123233
\(482\) −2075.00 + 2678.81i −0.196086 + 0.253146i
\(483\) −2909.85 2602.64i −0.274125 0.245185i
\(484\) 262.000 + 1014.72i 0.0246056 + 0.0952969i
\(485\) 6887.09i 0.644797i
\(486\) −4218.52 9848.62i −0.393736 0.919223i
\(487\) 9783.16i 0.910302i 0.890414 + 0.455151i \(0.150415\pi\)
−0.890414 + 0.455151i \(0.849585\pi\)
\(488\) 9186.80 + 3953.37i 0.852186 + 0.366722i
\(489\) −990.000 885.483i −0.0915529 0.0818874i
\(490\) 5660.00 + 4384.22i 0.521822 + 0.404202i
\(491\) −6893.56 −0.633609 −0.316805 0.948491i \(-0.602610\pi\)
−0.316805 + 0.948491i \(0.602610\pi\)
\(492\) 2390.05 4624.14i 0.219008 0.423724i
\(493\) 5440.00 0.496968
\(494\) −1558.85 1207.48i −0.141975 0.109974i
\(495\) 8313.84 929.516i 0.754908 0.0844013i
\(496\) 6960.00 + 12579.4i 0.630067 + 1.13878i
\(497\) 8049.84i 0.726529i
\(498\) −3335.97 18125.6i −0.300178 1.63098i
\(499\) 1309.07i 0.117439i 0.998275 + 0.0587194i \(0.0187017\pi\)
−0.998275 + 0.0587194i \(0.981298\pi\)
\(500\) 11777.9 3041.05i 1.05345 0.272000i
\(501\) 48.0000 53.6656i 0.00428040 0.00478564i
\(502\) −7380.00 + 9527.54i −0.656146 + 0.847081i
\(503\) 7939.72 0.703806 0.351903 0.936036i \(-0.385535\pi\)
0.351903 + 0.936036i \(0.385535\pi\)
\(504\) 4527.85 + 1376.04i 0.400171 + 0.121615i
\(505\) 13360.0 1.17725
\(506\) −5819.69 + 7513.19i −0.511298 + 0.660083i
\(507\) 7264.22 8121.65i 0.636322 0.711430i
\(508\) −14220.0 + 3671.59i −1.24195 + 0.320670i
\(509\) 14534.4i 1.26567i −0.774285 0.632837i \(-0.781890\pi\)
0.774285 0.632837i \(-0.218110\pi\)
\(510\) −851.281 4625.33i −0.0739125 0.401595i
\(511\) 3175.85i 0.274934i
\(512\) −3990.65 10876.2i −0.344459 0.938801i
\(513\) −5670.00 + 7969.35i −0.487986 + 0.685878i
\(514\) 7040.00 + 5453.16i 0.604127 + 0.467954i
\(515\) −12124.4 −1.03740
\(516\) −4287.54 + 8295.29i −0.365791 + 0.707713i
\(517\) −6720.00 −0.571654
\(518\) 2251.67 + 1744.13i 0.190989 + 0.147940i
\(519\) 4330.13 + 3872.98i 0.366226 + 0.327563i
\(520\) −800.000 + 1859.03i −0.0674660 + 0.156777i
\(521\) 9355.71i 0.786720i −0.919385 0.393360i \(-0.871313\pi\)
0.919385 0.393360i \(-0.128687\pi\)
\(522\) −6046.77 + 9913.25i −0.507011 + 0.831209i
\(523\) 10062.0i 0.841264i −0.907231 0.420632i \(-0.861808\pi\)
0.907231 0.420632i \(-0.138192\pi\)
\(524\) 900.666 + 3488.27i 0.0750874 + 0.290812i
\(525\) 1350.00 + 1207.48i 0.112226 + 0.100378i
\(526\) 7368.00 9512.05i 0.610761 0.788489i
\(527\) 8036.72 0.664298
\(528\) 2563.08 11231.3i 0.211257 0.925715i
\(529\) −2759.00 −0.226761
\(530\) −8452.41 + 10912.0i −0.692734 + 0.894316i
\(531\) −519.615 4647.58i −0.0424659 0.379826i
\(532\) −1080.00 4182.82i −0.0880149 0.340880i
\(533\) 1252.20i 0.101761i
\(534\) −12152.5 + 2236.64i −0.984814 + 0.181253i
\(535\) 5763.00i 0.465712i
\(536\) −6581.79 + 15294.7i −0.530392 + 1.23252i
\(537\) −4680.00 + 5232.40i −0.376084 + 0.420474i
\(538\) −100.000 77.4597i −0.00801358 0.00620729i
\(539\) 9803.41 0.783419
\(540\) 9374.92 + 3589.96i 0.747097 + 0.286087i
\(541\) −23962.0 −1.90426 −0.952132 0.305687i \(-0.901114\pi\)
−0.952132 + 0.305687i \(0.901114\pi\)
\(542\) 19589.5 + 15174.0i 1.55247 + 1.20254i
\(543\) −4371.70 + 4887.70i −0.345502 + 0.386283i
\(544\) −6400.00 991.484i −0.504408 0.0781425i
\(545\) 9534.59i 0.749389i
\(546\) −1119.62 + 206.062i −0.0877566 + 0.0161514i
\(547\) 15112.4i 1.18128i −0.806936 0.590639i \(-0.798876\pi\)
0.806936 0.590639i \(-0.201124\pi\)
\(548\) 692.820 178.885i 0.0540070 0.0139445i
\(549\) 1326.00 + 11860.1i 0.103083 + 0.921998i
\(550\) 2700.00 3485.69i 0.209324 0.270237i
\(551\) 10600.2 0.819567
\(552\) −10343.6 + 4802.66i −0.797562 + 0.370317i
\(553\) 660.000 0.0507524
\(554\) 10998.5 14199.0i 0.843470 1.08892i
\(555\) 4503.33 + 4027.90i 0.344425 + 0.308063i
\(556\) 15180.0 3919.46i 1.15787 0.298961i
\(557\) 16055.0i 1.22131i 0.791896 + 0.610656i \(0.209094\pi\)
−0.791896 + 0.610656i \(0.790906\pi\)
\(558\) −8933.12 + 14645.2i −0.677722 + 1.11108i
\(559\) 2246.33i 0.169964i
\(560\) −3879.79 + 2146.63i −0.292770 + 0.161985i
\(561\) −4800.00 4293.25i −0.361241 0.323104i
\(562\) 12440.0 + 9635.98i 0.933718 + 0.723255i
\(563\) −25142.4 −1.88211 −0.941055 0.338254i \(-0.890164\pi\)
−0.941055 + 0.338254i \(0.890164\pi\)
\(564\) −7163.69 3702.65i −0.534833 0.276436i
\(565\) 9280.00 0.690996
\(566\) −15155.4 11739.4i −1.12550 0.871806i
\(567\) 1247.08 + 5507.38i 0.0923674 + 0.407916i
\(568\) −21600.0 9295.16i −1.59563 0.686648i
\(569\) 23416.1i 1.72523i −0.505864 0.862613i \(-0.668826\pi\)
0.505864 0.862613i \(-0.331174\pi\)
\(570\) −1658.77 9012.73i −0.121892 0.662284i
\(571\) 4918.69i 0.360492i −0.983622 0.180246i \(-0.942311\pi\)
0.983622 0.180246i \(-0.0576893\pi\)
\(572\) 692.820 + 2683.28i 0.0506438 + 0.196143i
\(573\) 9600.00 10733.1i 0.699905 0.782518i
\(574\) −1680.00 + 2168.87i −0.122163 + 0.157712i
\(575\) −4364.77 −0.316562
\(576\) 8920.61 10560.6i 0.645299 0.763930i
\(577\) 19490.0 1.40620 0.703102 0.711089i \(-0.251798\pi\)
0.703102 + 0.711089i \(0.251798\pi\)
\(578\) 6292.54 8123.63i 0.452829 0.584600i
\(579\) 658.179 735.867i 0.0472418 0.0528179i
\(580\) −2720.00 10534.5i −0.194727 0.754176i
\(581\) 9713.48i 0.693602i
\(582\) 2048.40 + 11129.7i 0.145891 + 0.792683i
\(583\) 18900.2i 1.34265i
\(584\) −8521.69 3667.15i −0.603819 0.259842i
\(585\) −2400.00 + 268.328i −0.169620 + 0.0189641i
\(586\) 1460.00 + 1130.91i 0.102922 + 0.0797227i
\(587\) 1364.86 0.0959687 0.0479844 0.998848i \(-0.484720\pi\)
0.0479844 + 0.998848i \(0.484720\pi\)
\(588\) 10450.7 + 5401.58i 0.732957 + 0.378839i
\(589\) 15660.0 1.09552
\(590\) 3464.10 + 2683.28i 0.241720 + 0.187236i
\(591\) 8279.20 + 7405.14i 0.576245 + 0.515409i
\(592\) 7280.00 4027.90i 0.505416 0.279638i
\(593\) 25795.3i 1.78632i 0.449743 + 0.893158i \(0.351515\pi\)
−0.449743 + 0.893158i \(0.648485\pi\)
\(594\) 13158.9 3974.87i 0.908951 0.274564i
\(595\) 2478.71i 0.170785i
\(596\) 12540.0 3237.83i 0.861846 0.222528i
\(597\) 990.000 + 885.483i 0.0678694 + 0.0607042i
\(598\) 1680.00 2168.87i 0.114883 0.148314i
\(599\) −2424.87 −0.165405 −0.0827025 0.996574i \(-0.526355\pi\)
−0.0827025 + 0.996574i \(0.526355\pi\)
\(600\) 4798.85 2228.16i 0.326520 0.151607i
\(601\) −8758.00 −0.594420 −0.297210 0.954812i \(-0.596056\pi\)
−0.297210 + 0.954812i \(0.596056\pi\)
\(602\) 3013.77 3890.76i 0.204040 0.263414i
\(603\) −19745.4 + 2207.60i −1.33349 + 0.149089i
\(604\) −4380.00 + 1130.91i −0.295066 + 0.0761856i
\(605\) 1171.70i 0.0787378i
\(606\) 21590.1 3973.60i 1.44726 0.266364i
\(607\) 19558.6i 1.30784i −0.756565 0.653919i \(-0.773124\pi\)
0.756565 0.653919i \(-0.226876\pi\)
\(608\) −12470.8 1931.96i −0.831836 0.128867i
\(609\) 4080.00 4561.58i 0.271478 0.303521i
\(610\) −8840.00 6847.43i −0.586756 0.454499i
\(611\) 1939.90 0.128445
\(612\) −2751.38 7221.47i −0.181729 0.476978i
\(613\) −16450.0 −1.08386 −0.541932 0.840422i \(-0.682307\pi\)
−0.541932 + 0.840422i \(0.682307\pi\)
\(614\) 3481.42 + 2696.70i 0.228825 + 0.177247i
\(615\) −3879.79 + 4337.74i −0.254388 + 0.284414i
\(616\) −2400.00 + 5577.10i −0.156978 + 0.364785i
\(617\) 8461.28i 0.552088i 0.961145 + 0.276044i \(0.0890236\pi\)
−0.961145 + 0.276044i \(0.910976\pi\)
\(618\) −19593.3 + 3606.09i −1.27533 + 0.234722i
\(619\) 19930.4i 1.29413i 0.762433 + 0.647067i \(0.224005\pi\)
−0.762433 + 0.647067i \(0.775995\pi\)
\(620\) −4018.36 15563.0i −0.260292 1.00811i
\(621\) −11088.0 7888.85i −0.716499 0.509772i
\(622\) −5640.00 + 7281.21i −0.363575 + 0.469373i
\(623\) 6512.51 0.418809
\(624\) −739.897 + 3242.18i −0.0474673 + 0.207999i
\(625\) −7975.00 −0.510400
\(626\) −12176.3 + 15719.6i −0.777418 + 1.00364i
\(627\) −9353.07 8365.64i −0.595735 0.532842i
\(628\) 1460.00 + 5654.56i 0.0927712 + 0.359301i
\(629\) 4651.02i 0.294830i
\(630\) −4516.92 2755.18i −0.285648 0.174236i
\(631\) 12199.9i 0.769683i 0.922983 + 0.384842i \(0.125744\pi\)
−0.922983 + 0.384842i \(0.874256\pi\)
\(632\) 762.102 1770.97i 0.0479665 0.111464i
\(633\) 2130.00 + 1905.13i 0.133744 + 0.119624i
\(634\) 1100.00 + 852.056i 0.0689063 + 0.0533746i
\(635\) 16419.8 1.02614
\(636\) −10413.8 + 20148.0i −0.649267 + 1.25617i
\(637\) −2830.00 −0.176026
\(638\) −11777.9 9123.16i −0.730867 0.566127i
\(639\) −3117.69 27885.5i −0.193011 1.72634i
\(640\) 1280.00 + 12889.3i 0.0790569 + 0.796084i
\(641\) 7012.31i 0.432090i 0.976383 + 0.216045i \(0.0693158\pi\)
−0.976383 + 0.216045i \(0.930684\pi\)
\(642\) 1714.06 + 9313.15i 0.105372 + 0.572525i
\(643\) 15979.9i 0.980073i −0.871702 0.490036i \(-0.836983\pi\)
0.871702 0.490036i \(-0.163017\pi\)
\(644\) 5819.69 1502.64i 0.356099 0.0919444i
\(645\) 6960.00 7781.52i 0.424883 0.475034i
\(646\) −4320.00 + 5577.10i −0.263109 + 0.339672i
\(647\) 17999.5 1.09371 0.546856 0.837226i \(-0.315824\pi\)
0.546856 + 0.837226i \(0.315824\pi\)
\(648\) 16217.9 + 3013.12i 0.983175 + 0.182664i
\(649\) 6000.00 0.362898
\(650\) −779.423 + 1006.23i −0.0470330 + 0.0607194i
\(651\) 6027.54 6738.99i 0.362884 0.405717i
\(652\) 1980.00 511.234i 0.118931 0.0307078i
\(653\) 5196.62i 0.311423i −0.987803 0.155712i \(-0.950233\pi\)
0.987803 0.155712i \(-0.0497671\pi\)
\(654\) −2835.83 15408.1i −0.169556 0.921263i
\(655\) 4027.90i 0.240280i
\(656\) 3879.79 + 7012.31i 0.230915 + 0.417355i
\(657\) −1230.00 11001.5i −0.0730394 0.653284i
\(658\) 3360.00 + 2602.64i 0.199068 + 0.154197i
\(659\) 6062.18 0.358344 0.179172 0.983818i \(-0.442658\pi\)
0.179172 + 0.983818i \(0.442658\pi\)
\(660\) −5913.84 + 11441.8i −0.348782 + 0.674804i
\(661\) 9422.00 0.554423 0.277211 0.960809i \(-0.410590\pi\)
0.277211 + 0.960809i \(0.410590\pi\)
\(662\) −9474.32 7338.78i −0.556238 0.430860i
\(663\) 1385.64 + 1239.35i 0.0811672 + 0.0725981i
\(664\) 26064.0 + 11216.2i 1.52331 + 0.655529i
\(665\) 4829.91i 0.281648i
\(666\) 8475.50 + 5169.79i 0.493122 + 0.300789i
\(667\) 14748.3i 0.856158i
\(668\) 27.7128 + 107.331i 0.00160515 + 0.00621672i
\(669\) 1830.00 + 1636.80i 0.105758 + 0.0945925i
\(670\) 11400.0 14717.3i 0.657344 0.848627i
\(671\) −15311.3 −0.880905
\(672\) −5631.38 + 4622.95i −0.323267 + 0.265378i
\(673\) −17470.0 −1.00062 −0.500311 0.865846i \(-0.666781\pi\)
−0.500311 + 0.865846i \(0.666781\pi\)
\(674\) 2580.76 3331.74i 0.147488 0.190406i
\(675\) 5144.19 + 3659.97i 0.293333 + 0.208700i
\(676\) 4194.00 + 16243.3i 0.238621 + 0.924175i
\(677\) 20813.3i 1.18157i −0.806830 0.590784i \(-0.798819\pi\)
0.806830 0.590784i \(-0.201181\pi\)
\(678\) 14996.7 2760.11i 0.849477 0.156344i
\(679\) 5964.39i 0.337102i
\(680\) 6651.08 + 2862.17i 0.375084 + 0.161410i
\(681\) 1752.00 1958.80i 0.0985856 0.110222i
\(682\) −17400.0 13478.0i −0.976951 0.756743i
\(683\) 12616.3 0.706805 0.353402 0.935471i \(-0.385025\pi\)
0.353402 + 0.935471i \(0.385025\pi\)
\(684\) −5361.23 14071.4i −0.299696 0.786601i
\(685\) −800.000 −0.0446225
\(686\) −10842.6 8398.67i −0.603460 0.467438i
\(687\) −14182.0 + 15856.0i −0.787596 + 0.880559i
\(688\) −6960.00 12579.4i −0.385680 0.697074i
\(689\) 5456.01i 0.301680i
\(690\) 12539.7 2307.90i 0.691852 0.127334i
\(691\) 3028.67i 0.166738i −0.996519 0.0833691i \(-0.973432\pi\)
0.996519 0.0833691i \(-0.0265681\pi\)
\(692\) −8660.25 + 2236.07i −0.475742 + 0.122836i
\(693\) −7200.00 + 804.984i −0.394669 + 0.0441253i
\(694\) −3444.00 + 4446.18i −0.188375 + 0.243191i
\(695\) −17528.4 −0.956674
\(696\) −7528.82 16215.0i −0.410028 0.883089i
\(697\) 4480.00 0.243461
\(698\) −3592.27 + 4637.60i −0.194799 + 0.251484i
\(699\) 20438.2 + 18280.5i 1.10593 + 0.989172i
\(700\) −2700.00 + 697.137i −0.145786 + 0.0376419i
\(701\) 17664.9i 0.951777i 0.879506 + 0.475888i \(0.157873\pi\)
−0.879506 + 0.475888i \(0.842127\pi\)
\(702\) −3798.65 + 1147.45i −0.204232 + 0.0616917i
\(703\) 9062.78i 0.486215i
\(704\) 12193.6 + 12879.8i 0.652791 + 0.689523i
\(705\) 6720.00 + 6010.55i 0.358993 + 0.321093i
\(706\) −19360.0 14996.2i −1.03204 0.799418i
\(707\) −11570.1 −0.615472
\(708\) 6396.15 + 3305.94i 0.339523 + 0.175487i
\(709\) 14174.0 0.750798 0.375399 0.926863i \(-0.377506\pi\)
0.375399 + 0.926863i \(0.377506\pi\)
\(710\) 20784.6 + 16099.7i 1.09864 + 0.851001i
\(711\) 2286.31 255.617i 0.120595 0.0134830i
\(712\) 7520.00 17474.9i 0.395820 0.919803i
\(713\) 21788.2i 1.14443i
\(714\) 737.231 + 4005.66i 0.0386417 + 0.209955i
\(715\) 3098.39i 0.162060i
\(716\) −2702.00 10464.8i −0.141031 0.546212i
\(717\) −19680.0 + 22002.9i −1.02505 + 1.14604i
\(718\) −14040.0 + 18125.6i −0.729761 + 0.942117i
\(719\) −32839.7 −1.70336 −0.851678 0.524065i \(-0.824415\pi\)
−0.851678 + 0.524065i \(0.824415\pi\)
\(720\) −12608.6 + 8938.77i −0.652632 + 0.462678i
\(721\) 10500.0 0.542358
\(722\) 3462.37 4469.90i 0.178471 0.230405i
\(723\) 4149.99 4639.83i 0.213472 0.238668i
\(724\) −2524.00 9775.41i −0.129563 0.501796i
\(725\) 6842.37i 0.350509i
\(726\) −348.493 1893.50i −0.0178151 0.0967965i
\(727\) 8001.58i 0.408201i −0.978950 0.204101i \(-0.934573\pi\)
0.978950 0.204101i \(-0.0654270\pi\)
\(728\) 692.820 1609.97i 0.0352715 0.0819635i
\(729\) 6453.00 + 18595.1i 0.327846 + 0.944731i
\(730\) 8200.00 + 6351.69i 0.415747 + 0.322037i
\(731\) −8036.72 −0.406633
\(732\) −16322.3 8436.39i −0.824164 0.425981i
\(733\) 11750.0 0.592082 0.296041 0.955175i \(-0.404333\pi\)
0.296041 + 0.955175i \(0.404333\pi\)
\(734\) 17649.6 + 13671.3i 0.887546 + 0.687490i
\(735\) −9803.41 8768.43i −0.491978 0.440039i
\(736\) 2688.00 17351.0i 0.134621 0.868974i
\(737\) 25491.2i 1.27406i
\(738\) −4979.69 + 8163.85i −0.248381 + 0.407203i
\(739\) 19961.4i 0.993627i 0.867857 + 0.496814i \(0.165497\pi\)
−0.867857 + 0.496814i \(0.834503\pi\)
\(740\) −9006.66 + 2325.51i −0.447421 + 0.115524i
\(741\) 2700.00 + 2414.95i 0.133856 + 0.119724i
\(742\) 7320.00 9450.08i 0.362164 0.467552i
\(743\) 25592.8 1.26367 0.631836 0.775102i \(-0.282302\pi\)
0.631836 + 0.775102i \(0.282302\pi\)
\(744\) −11122.6 23955.1i −0.548084 1.18043i
\(745\) −14480.0 −0.712089
\(746\) 8504.37 10979.1i 0.417382 0.538838i
\(747\) 3762.01 + 33648.5i 0.184264 + 1.64810i
\(748\) 9600.00 2478.71i 0.469266 0.121164i
\(749\) 4990.90i 0.243476i
\(750\) −21977.9 + 4044.99i −1.07003 + 0.196936i
\(751\) 5244.02i 0.254803i −0.991851 0.127401i \(-0.959336\pi\)
0.991851 0.127401i \(-0.0406637\pi\)
\(752\) 10863.4 6010.55i 0.526793 0.291466i
\(753\) 14760.0 16502.2i 0.714322 0.798636i
\(754\) 3400.00 + 2633.63i 0.164218 + 0.127203i
\(755\) 5057.59 0.243794
\(756\) −8118.92 3108.99i −0.390585 0.149567i
\(757\) −14290.0 −0.686102 −0.343051 0.939317i \(-0.611460\pi\)
−0.343051 + 0.939317i \(0.611460\pi\)
\(758\) 7014.81 + 5433.65i 0.336134 + 0.260368i
\(759\) 11639.4 13013.2i 0.556631 0.622332i
\(760\) 12960.0 + 5577.10i 0.618564 + 0.266188i
\(761\) 16976.2i 0.808657i −0.914614 0.404328i \(-0.867505\pi\)
0.914614 0.404328i \(-0.132495\pi\)
\(762\) 26534.9 4883.68i 1.26149 0.232175i
\(763\) 8257.20i 0.391783i
\(764\) 5542.56 + 21466.3i 0.262464 + 1.01652i
\(765\) 960.000 + 8586.50i 0.0453711 + 0.405811i
\(766\) −10752.0 + 13880.8i −0.507161 + 0.654742i
\(767\) −1732.05 −0.0815394
\(768\) 5902.11 + 20448.7i 0.277310 + 0.960780i
\(769\) −29566.0 −1.38645 −0.693223 0.720723i \(-0.743810\pi\)
−0.693223 + 0.720723i \(0.743810\pi\)
\(770\) 4156.92 5366.56i 0.194552 0.251166i
\(771\) −12193.6 10906.3i −0.569576 0.509444i
\(772\) 380.000 + 1471.73i 0.0177157 + 0.0686125i
\(773\) 21457.3i 0.998403i −0.866486 0.499202i \(-0.833627\pi\)
0.866486 0.499202i \(-0.166373\pi\)
\(774\) 8933.12 14645.2i 0.414850 0.680118i
\(775\) 10108.5i 0.468526i
\(776\) −16004.1 6887.09i −0.740355 0.318598i
\(777\) −3900.00 3488.27i −0.180067 0.161056i
\(778\) 21140.0 + 16375.0i 0.974172 + 0.754590i
\(779\) 8729.54 0.401499
\(780\) 1707.18 3302.96i 0.0783677 0.151622i
\(781\) 36000.0 1.64940
\(782\) −7759.59 6010.55i −0.354837 0.274855i
\(783\) 12366.8 17381.9i 0.564438