Properties

Label 12.4.b.a.11.2
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 11.2
Root \(-0.866025 + 1.11803i\)
Character \(\chi\) = 12.11
Dual form 12.4.b.a.11.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) q^{6} -7.74597i q^{7} +(20.7846 + 8.94427i) q^{8} +(-3.00000 + 26.8328i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 2.23607i) q^{2} +(3.46410 + 3.87298i) q^{3} +(-2.00000 - 7.74597i) q^{4} -8.94427i q^{5} +(-14.6603 + 1.03776i) 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} +(23.0718 - 34.5788i) 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} +(-54.8038 - 53.1840i) 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} +(37.3590 + 111.482i) 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} +(9.28203 + 131.125i) 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} +(213.846 - 30.4277i) 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} +(8.03848 + 113.558i) 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} +(-313.990 - 109.556i) 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} +(16.1347 - 396.489i) 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} +(-309.282 - 206.360i) 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} +(507.846 - 35.9492i) 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} +(-302.354 + 530.877i) 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} +(146.603 - 10.3776i) 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} +(-267.846 - 178.713i) 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} +(-475.692 + 490.181i) 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} +(788.820 - 512.346i) 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 \(-0.869010\pi\)
0.916515 0.400000i \(-0.130990\pi\)
\(6\) −14.6603 + 1.03776i −0.997504 + 0.0706108i
\(7\) 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 \(-0.657464\pi\)
−0.474757 + 0.880117i \(0.657464\pi\)
\(12\) 23.0718 34.5788i 0.555021 0.831836i
\(13\) −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 \(-0.917855\pi\)
0.966885 0.255212i \(-0.0821454\pi\)
\(18\) −54.8038 53.1840i −0.717633 0.696422i
\(19\) 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 \(-0.355095\pi\)
0.439670 + 0.898159i \(0.355095\pi\)
\(24\) 37.3590 + 111.482i 0.317745 + 0.948176i
\(25\) 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 \(0.161843\pi\)
−0.873503 + 0.486818i \(0.838157\pi\)
\(30\) 9.28203 + 131.125i 0.0564886 + 0.798003i
\(31\) 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
\(36\) 213.846 30.4277i 0.990028 0.140869i
\(37\) −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 \(0.0766519\pi\)
−0.971145 + 0.238488i \(0.923348\pi\)
\(42\) 8.03848 + 113.558i 0.0295325 + 0.417199i
\(43\) 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 \(-0.402671\pi\)
0.301025 + 0.953616i \(0.402671\pi\)
\(48\) −313.990 109.556i −0.944177 0.329438i
\(49\) 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 \(-0.750040\pi\)
0.707195 0.707019i \(-0.249960\pi\)
\(54\) 16.1347 396.489i 0.0406602 0.999173i
\(55\) 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 \(-0.561204\pi\)
−0.191096 + 0.981571i \(0.561204\pi\)
\(60\) −309.282 206.360i −0.665469 0.444017i
\(61\) −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
\(66\) 507.846 35.9492i 0.947144 0.0670460i
\(67\) 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 \(-0.834947\pi\)
−0.868549 + 0.495603i \(0.834947\pi\)
\(72\) −302.354 + 530.877i −0.494899 + 0.868950i
\(73\) 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
\(78\) 146.603 10.3776i 0.212814 0.0150646i
\(79\) 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 \(-0.188804\pi\)
0.829186 + 0.558973i \(0.188804\pi\)
\(84\) −267.846 178.713i −0.347910 0.232134i
\(85\) −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 \(-0.833084\pi\)
0.865634 0.500677i \(-0.166916\pi\)
\(90\) −475.692 + 490.181i −0.557137 + 0.574106i
\(91\) 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
\(96\) 788.820 512.346i 0.838632 0.544699i
\(97\) 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 \(0.263185\pi\)
−0.677218 + 0.735782i \(0.736815\pi\)
\(102\) 37.1281 + 524.501i 0.0360415 + 0.509151i
\(103\) 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 \(-0.594011\pi\)
−0.291070 + 0.956702i \(0.594011\pi\)
\(108\) 858.631 + 722.818i 0.765016 + 0.644011i
\(109\) −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 \(0.142147\pi\)
−0.901935 + 0.431872i \(0.857853\pi\)
\(114\) −72.3463 1022.02i −0.0594373 0.839658i
\(115\) 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
\(120\) 997.128 334.149i 0.758541 0.254196i
\(121\) −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
\(126\) −411.962 + 424.509i −0.291273 + 0.300145i
\(127\) 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 \(-0.452016\pi\)
0.150175 + 0.988659i \(0.452016\pi\)
\(132\) −799.230 + 1197.84i −0.527001 + 0.789841i
\(133\) 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 \(-0.991121\pi\)
0.999611 0.0278891i \(-0.00887852\pi\)
\(138\) −1421.97 + 100.658i −0.877145 + 0.0620909i
\(139\) 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
\(144\) −663.384 1595.59i −0.383903 0.923373i
\(145\) 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 \(-0.853184\pi\)
0.895503 0.445055i \(-0.146816\pi\)
\(150\) −659.711 + 46.6993i −0.359101 + 0.0254199i
\(151\) 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
\(156\) −230.718 + 345.788i −0.118412 + 0.177469i
\(157\) −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
\(162\) 1591.49 1310.99i 0.771846 0.635809i
\(163\) 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 \(-0.498978\pi\)
0.00321030 + 0.999995i \(0.498978\pi\)
\(168\) 863.538 289.381i 0.396568 0.132894i
\(169\) −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 \(0.0790086\pi\)
−0.969353 + 0.245672i \(0.920991\pi\)
\(174\) −157.795 2229.13i −0.0687493 0.971206i
\(175\) 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 \(-0.591019\pi\)
−0.282063 + 0.959396i \(0.591019\pi\)
\(180\) −272.154 1912.70i −0.112695 0.792023i
\(181\) 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
\(186\) 233.116 + 3293.18i 0.0918972 + 1.29821i
\(187\) 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 \(-0.324092\pi\)
0.524929 + 0.851146i \(0.324092\pi\)
\(192\) −220.636 + 2651.27i −0.0829325 + 0.996555i
\(193\) −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 \(0.126336\pi\)
−0.922266 + 0.386557i \(0.873664\pi\)
\(198\) 1898.46 + 1842.35i 0.681403 + 0.661262i
\(199\) 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
\(204\) −1237.13 825.442i −0.424590 0.283296i
\(205\) 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
\(210\) 1015.69 71.8983i 0.333759 0.0236260i
\(211\) 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
\(216\) −3103.46 + 668.000i −0.977610 + 0.210424i
\(217\) −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
\(222\) 1905.83 134.909i 0.576176 0.0407861i
\(223\) 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 \(-0.476443\pi\)
0.0739392 + 0.997263i \(0.476443\pi\)
\(228\) 2410.61 + 1608.42i 0.700206 + 0.467194i
\(229\) 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 \(0.266065\pi\)
−0.670534 + 0.741879i \(0.733935\pi\)
\(234\) 548.038 + 531.840i 0.153104 + 0.148579i
\(235\) 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 \(-0.779141\pi\)
−0.768790 + 0.639502i \(0.779141\pi\)
\(240\) −979.897 + 2808.41i −0.263550 + 0.755342i
\(241\) −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
\(246\) −129.948 1835.75i −0.0336797 0.475786i
\(247\) 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 \(-0.320032\pi\)
0.535741 + 0.844382i \(0.320032\pi\)
\(252\) −235.692 1656.44i −0.0589175 0.414072i
\(253\) −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 \(-0.875207\pi\)
0.924128 0.382083i \(-0.124793\pi\)
\(258\) −233.116 3293.18i −0.0562525 0.794668i
\(259\) 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 \(-0.666183\pi\)
−0.498684 + 0.866784i \(0.666183\pi\)
\(264\) −1294.15 3861.86i −0.301703 0.900307i
\(265\) −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 \(0.00161328\pi\)
−0.999987 + 0.00506823i \(0.998387\pi\)
\(270\) −3546.31 144.313i −0.799338 0.0325281i
\(271\) 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
\(276\) 2237.85 3353.96i 0.488052 0.731467i
\(277\) 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 \(-0.798917\pi\)
0.807012 0.590535i \(-0.201083\pi\)
\(282\) −2843.94 + 201.315i −0.600546 + 0.0425112i
\(283\) 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
\(288\) 4716.86 + 1280.27i 0.965082 + 0.261946i
\(289\) 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 \(-0.979265\pi\)
0.997879 0.0650933i \(-0.0207345\pi\)
\(294\) −4148.85 + 293.687i −0.823013 + 0.0582591i
\(295\) 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
\(300\) 1038.23 1556.05i 0.199808 0.299461i
\(301\) 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
\(306\) −1902.77 + 1960.72i −0.355471 + 0.366297i
\(307\) 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 \(-0.404061\pi\)
0.296857 + 0.954922i \(0.404061\pi\)
\(312\) −373.590 1114.82i −0.0677896 0.202290i
\(313\) −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 \(-0.986124\pi\)
0.999050 0.0435802i \(-0.0138764\pi\)
\(318\) 566.204 + 7998.64i 0.0998464 + 1.41051i
\(319\) 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
\(324\) 174.923 + 5829.38i 0.0299937 + 0.999550i
\(325\) −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
\(330\) −321.539 4542.31i −0.0536368 0.757716i
\(331\) 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
\(336\) −848.616 + 2432.15i −0.137785 + 0.394895i
\(337\) 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
\(342\) 3707.65 3820.58i 0.586219 0.604074i
\(343\) 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 \(-0.450846\pi\)
0.153808 + 0.988101i \(0.450846\pi\)
\(348\) 5257.79 + 3508.13i 0.809906 + 0.540389i
\(349\) −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 \(0.226373\pi\)
−0.757597 + 0.652722i \(0.773627\pi\)
\(354\) 2539.23 179.746i 0.381239 0.0269870i
\(355\) 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 \(-0.296816\pi\)
0.595847 + 0.803098i \(0.296816\pi\)
\(360\) 4748.31 + 2704.33i 0.695160 + 0.395919i
\(361\) 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
\(366\) 6479.83 458.691i 0.925427 0.0655087i
\(367\) 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
\(372\) −7767.54 5182.69i −1.08260 0.722338i
\(373\) 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
\(378\) −3071.19 124.979i −0.417897 0.0170058i
\(379\) 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 \(-0.364098\pi\)
0.414095 + 0.910233i \(0.364098\pi\)
\(384\) −5546.26 5085.48i −0.737060 0.675827i
\(385\) 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 \(-0.788703\pi\)
0.787652 0.616120i \(-0.211297\pi\)
\(390\) −92.8203 1311.25i −0.0120516 0.170251i
\(391\) 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
\(396\) −7407.85 + 1054.05i −0.940046 + 0.133757i
\(397\) −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 \(0.0333890\pi\)
−0.994504 + 0.104702i \(0.966611\pi\)
\(402\) 763.655 + 10788.0i 0.0947454 + 1.33845i
\(403\) 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
\(408\) 3988.51 1336.60i 0.483973 0.162185i
\(409\) −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
\(414\) −5315.69 5158.57i −0.631043 0.612392i
\(415\) 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 \(-0.852561\pi\)
−0.894630 + 0.446808i \(0.852561\pi\)
\(420\) −1598.46 + 2395.69i −0.185707 + 0.278328i
\(421\) 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
\(426\) 15235.4 1078.47i 1.73276 0.122658i
\(427\) 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 \(-0.755900\pi\)
−0.720091 + 0.693879i \(0.755900\pi\)
\(432\) 3881.66 8096.56i 0.432307 0.901727i
\(433\) 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
\(438\) −6010.70 + 425.483i −0.655714 + 0.0464163i
\(439\) 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 \(-0.447851\pi\)
0.163098 + 0.986610i \(0.447851\pi\)
\(444\) −2999.33 + 4495.24i −0.320590 + 0.480484i
\(445\) −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 \(-0.729049\pi\)
0.659069 0.752082i \(-0.270951\pi\)
\(450\) −2466.17 2393.28i −0.258348 0.250712i
\(451\) 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
\(456\) −7771.84 + 2604.43i −0.798136 + 0.267464i
\(457\) −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 \(0.0632642\pi\)
−0.980314 + 0.197445i \(0.936736\pi\)
\(462\) −278.461 3933.76i −0.0280415 0.396136i
\(463\) 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 \(-0.529214\pi\)
−0.0916488 + 0.995791i \(0.529214\pi\)
\(468\) −2138.46 + 304.277i −0.211219 + 0.0300539i
\(469\) −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
\(474\) −88.4232 1249.14i −0.00856838 0.121044i
\(475\) 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 \(-0.240933\pi\)
0.726959 + 0.686681i \(0.240933\pi\)
\(480\) −4582.56 7055.42i −0.435759 0.670905i
\(481\) 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
\(486\) 10590.5 + 1622.41i 0.988468 + 0.151428i
\(487\) 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 \(-0.397390\pi\)
0.316805 + 0.948491i \(0.397390\pi\)
\(492\) 4329.95 + 2889.05i 0.396767 + 0.264732i
\(493\) 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
\(498\) −18384.0 + 1301.36i −1.65423 + 0.117099i
\(499\) 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 \(-0.614465\pi\)
−0.351903 + 0.936036i \(0.614465\pi\)
\(504\) 4112.15 + 2342.02i 0.363432 + 0.206988i
\(505\) 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 \(0.218110\pi\)
−0.774285 + 0.632837i \(0.781890\pi\)
\(510\) 4691.28 332.084i 0.407320 0.0288332i
\(511\) 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
\(516\) 7767.54 + 5182.69i 0.662687 + 0.442161i
\(517\) −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 \(0.128687\pi\)
−0.919385 + 0.393360i \(0.871313\pi\)
\(522\) 8086.77 8333.07i 0.678062 0.698714i
\(523\) 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
\(528\) 10876.9 + 3795.12i 0.896510 + 0.312806i
\(529\) −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
\(534\) 872.511 + 12325.8i 0.0707065 + 0.998855i
\(535\) 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
\(540\) 6465.08 7679.83i 0.515209 0.612013i
\(541\) −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
\(546\) −80.3848 1135.58i −0.00630064 0.0890078i
\(547\) 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
\(552\) 3623.63 + 10813.2i 0.279406 + 0.833770i
\(553\) 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 \(-0.790906\pi\)
0.791896 0.610656i \(-0.209094\pi\)
\(558\) −11946.9 + 12310.8i −0.906365 + 0.933971i
\(559\) 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 \(-0.109836\pi\)
0.941055 + 0.338254i \(0.109836\pi\)
\(564\) 4475.69 6707.93i 0.334150 0.500806i
\(565\) 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 \(0.331174\pi\)
−0.505864 + 0.862613i \(0.668826\pi\)
\(570\) −9141.23 + 647.085i −0.671726 + 0.0475498i
\(571\) 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
\(576\) −11032.6 + 8329.73i −0.798077 + 0.602556i
\(577\) 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
\(582\) −11288.4 + 799.077i −0.803985 + 0.0569121i
\(583\) 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 \(-0.515280\pi\)
−0.0479844 + 0.998848i \(0.515280\pi\)
\(588\) 6529.32 9785.80i 0.457933 0.686326i
\(589\) 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 \(-0.648485\pi\)
0.449743 0.893158i \(-0.351515\pi\)
\(594\) −558.921 + 13734.8i −0.0386074 + 0.948729i
\(595\) 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 \(-0.473645\pi\)
0.0827025 + 0.996574i \(0.473645\pi\)
\(600\) 1681.15 + 5016.70i 0.114388 + 0.341343i
\(601\) −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
\(606\) −1550.10 21897.9i −0.103908 1.46789i
\(607\) 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
\(612\) −1088.62 7650.79i −0.0719031 0.505335i
\(613\) −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 \(-0.910976\pi\)
0.961145 0.276044i \(-0.0890236\pi\)
\(618\) −1406.73 19872.6i −0.0915649 1.29352i
\(619\) 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
\(624\) 3139.90 + 1095.56i 0.201437 + 0.0702843i
\(625\) −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
\(630\) 3796.92 + 3684.70i 0.240116 + 0.233019i
\(631\) 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
\(636\) −18866.2 12588.0i −1.17625 0.784821i
\(637\) −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 \(-0.930684\pi\)
0.976383 0.216045i \(-0.0693158\pi\)
\(642\) 9445.94 668.654i 0.580688 0.0411054i
\(643\) 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 \(-0.684176\pi\)
−0.546856 + 0.837226i \(0.684176\pi\)
\(648\) −13337.9 9705.63i −0.808581 0.588385i
\(649\) 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 \(0.0497671\pi\)
−0.987803 + 0.155712i \(0.950233\pi\)
\(654\) 15627.8 1106.26i 0.934398 0.0661437i
\(655\) 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 \(-0.557342\pi\)
−0.179172 + 0.983818i \(0.557342\pi\)
\(660\) 10713.8 + 7148.53i 0.631872 + 0.421601i
\(661\) 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
\(666\) 7124.50 + 6913.92i 0.414518 + 0.402266i
\(667\) 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
\(672\) −3968.62 6110.18i −0.227816 0.350752i
\(673\) −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 \(0.201181\pi\)
−0.806830 + 0.590784i \(0.798819\pi\)
\(678\) −1076.72 15210.5i −0.0609897 0.861589i
\(679\) 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 \(-0.614975\pi\)
−0.353402 + 0.935471i \(0.614975\pi\)
\(684\) 2121.23 + 14908.0i 0.118578 + 0.833365i
\(685\) −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
\(690\) 900.309 + 12718.5i 0.0496727 + 0.701716i
\(691\) 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
\(696\) −16951.2 + 5680.53i −0.923179 + 0.309368i
\(697\) 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 \(-0.842127\pi\)
0.879506 0.475888i \(-0.157873\pi\)
\(702\) −161.347 + 3964.89i −0.00867470 + 0.213170i
\(703\) 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
\(708\) −3996.15 + 5989.22i −0.212125 + 0.317922i
\(709\) 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
\(714\) 4062.77 287.593i 0.212949 0.0150741i
\(715\) 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 \(-0.175585\pi\)
0.851678 + 0.524065i \(0.175585\pi\)
\(720\) −14271.4 + 5933.49i −0.738699 + 0.307122i
\(721\) 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
\(726\) 1920.49 135.947i 0.0981766 0.00694967i
\(727\) 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
\(732\) −10197.7 + 15283.8i −0.514917 + 0.771730i
\(733\) 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
\(738\) 6659.69 6862.53i 0.332177 0.342294i
\(739\) 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 \(-0.717698\pi\)
−0.631836 + 0.775102i \(0.717698\pi\)
\(744\) 25042.6 8392.06i 1.23401 0.413532i
\(745\) −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
\(750\) 1577.95 + 22291.3i 0.0768246 + 1.08528i
\(751\) 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
\(756\) 5598.92 6650.92i 0.269353 0.319963i
\(757\) −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 \(0.132495\pi\)
−0.914614 + 0.404328i \(0.867505\pi\)
\(762\) 1905.12 + 26913.2i 0.0905711 + 1.27948i
\(763\) 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
\(768\) 20977.9 3593.49i 0.985644 0.168840i
\(769\) −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 \(0.166373\pi\)
−0.866486 + 0.499202i \(0.833627\pi\)
\(774\) 11946.9 12310.8i 0.554809 0.571707i
\(775\) 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
\(780\) 3092.82 + 2063.60i 0.141975 + 0.0947293i
\(781\) 36000.0 1.64940
\(782\) 7759.59 + 6010.55i 0.354837 + 0.274855i
\(783\) −12366.8 17381.9i −0.564438