Properties

Label 105.3.h.a.76.2
Level 105
Weight 3
Character 105.76
Analytic conductor 2.861
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 76.2
Root \(1.86875 + 3.23677i\) of \(x^{12} - 2 x^{11} + 21 x^{10} - 26 x^{9} + 295 x^{8} - 372 x^{7} + 1704 x^{6} - 1074 x^{5} + 5613 x^{4} - 5472 x^{3} + 4950 x^{2} - 1638 x + 441\)
Character \(\chi\) \(=\) 105.76
Dual form 105.3.h.a.76.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.80460 q^{2} +1.73205i q^{3} +10.4750 q^{4} +2.23607i q^{5} -6.58976i q^{6} +(2.44621 - 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-3.80460 q^{2} +1.73205i q^{3} +10.4750 q^{4} +2.23607i q^{5} -6.58976i q^{6} +(2.44621 - 6.55866i) q^{7} -24.6348 q^{8} -3.00000 q^{9} -8.50735i q^{10} +14.4489 q^{11} +18.1432i q^{12} +16.9427i q^{13} +(-9.30684 + 24.9531i) q^{14} -3.87298 q^{15} +51.8255 q^{16} +13.0093i q^{17} +11.4138 q^{18} +18.6908i q^{19} +23.4228i q^{20} +(11.3599 + 4.23695i) q^{21} -54.9723 q^{22} +10.3861 q^{23} -42.6687i q^{24} -5.00000 q^{25} -64.4602i q^{26} -5.19615i q^{27} +(25.6240 - 68.7020i) q^{28} -13.7269 q^{29} +14.7352 q^{30} +42.4383i q^{31} -98.6363 q^{32} +25.0262i q^{33} -49.4951i q^{34} +(14.6656 + 5.46988i) q^{35} -31.4250 q^{36} +28.7434 q^{37} -71.1112i q^{38} -29.3456 q^{39} -55.0850i q^{40} -28.8060i q^{41} +(-43.2200 - 16.1199i) q^{42} -5.84593 q^{43} +151.352 q^{44} -6.70820i q^{45} -39.5151 q^{46} +10.5013i q^{47} +89.7644i q^{48} +(-37.0322 - 32.0877i) q^{49} +19.0230 q^{50} -22.5327 q^{51} +177.475i q^{52} +81.9074 q^{53} +19.7693i q^{54} +32.3087i q^{55} +(-60.2617 + 161.571i) q^{56} -32.3735 q^{57} +52.2254 q^{58} +35.1680i q^{59} -40.5695 q^{60} -68.4826i q^{61} -161.461i q^{62} +(-7.33862 + 19.6760i) q^{63} +167.970 q^{64} -37.8850 q^{65} -95.2149i q^{66} +47.4637 q^{67} +136.272i q^{68} +17.9893i q^{69} +(-55.7968 - 20.8107i) q^{70} +47.6548 q^{71} +73.9043 q^{72} -125.967i q^{73} -109.357 q^{74} -8.66025i q^{75} +195.786i q^{76} +(35.3450 - 94.7655i) q^{77} +111.648 q^{78} -129.527 q^{79} +115.885i q^{80} +9.00000 q^{81} +109.595i q^{82} -42.6906i q^{83} +(118.995 + 44.3820i) q^{84} -29.0896 q^{85} +22.2414 q^{86} -23.7757i q^{87} -355.945 q^{88} +25.5329i q^{89} +25.5220i q^{90} +(111.122 + 41.4453i) q^{91} +108.795 q^{92} -73.5053 q^{93} -39.9533i q^{94} -41.7940 q^{95} -170.843i q^{96} +28.7310i q^{97} +(140.893 + 122.081i) q^{98} -43.3467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 12q - 4q^{2} + 44q^{4} - 8q^{7} + 4q^{8} - 36q^{9} - 16q^{11} - 40q^{14} + 92q^{16} + 12q^{18} + 36q^{21} - 88q^{22} - 64q^{23} - 60q^{25} + 88q^{28} + 104q^{29} - 228q^{32} + 60q^{35} - 132q^{36} + 32q^{37} - 24q^{39} - 60q^{42} + 152q^{43} + 192q^{44} + 200q^{46} + 60q^{49} + 20q^{50} + 24q^{51} + 176q^{53} - 368q^{56} - 240q^{57} - 400q^{58} + 24q^{63} - 20q^{64} - 240q^{65} + 168q^{67} - 60q^{70} + 32q^{71} - 12q^{72} + 184q^{74} + 8q^{77} + 456q^{78} + 120q^{79} + 108q^{81} + 108q^{84} + 120q^{85} + 400q^{86} - 536q^{88} + 24q^{91} + 192q^{92} + 48q^{93} + 884q^{98} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.80460 −1.90230 −0.951150 0.308728i \(-0.900097\pi\)
−0.951150 + 0.308728i \(0.900097\pi\)
\(3\) 1.73205i 0.577350i
\(4\) 10.4750 2.61875
\(5\) 2.23607i 0.447214i
\(6\) 6.58976i 1.09829i
\(7\) 2.44621 6.55866i 0.349458 0.936952i
\(8\) −24.6348 −3.07935
\(9\) −3.00000 −0.333333
\(10\) 8.50735i 0.850735i
\(11\) 14.4489 1.31354 0.656768 0.754092i \(-0.271923\pi\)
0.656768 + 0.754092i \(0.271923\pi\)
\(12\) 18.1432i 1.51193i
\(13\) 16.9427i 1.30329i 0.758526 + 0.651643i \(0.225920\pi\)
−0.758526 + 0.651643i \(0.774080\pi\)
\(14\) −9.30684 + 24.9531i −0.664774 + 1.78236i
\(15\) −3.87298 −0.258199
\(16\) 51.8255 3.23909
\(17\) 13.0093i 0.765251i 0.923904 + 0.382625i \(0.124980\pi\)
−0.923904 + 0.382625i \(0.875020\pi\)
\(18\) 11.4138 0.634100
\(19\) 18.6908i 0.983729i 0.870672 + 0.491864i \(0.163684\pi\)
−0.870672 + 0.491864i \(0.836316\pi\)
\(20\) 23.4228i 1.17114i
\(21\) 11.3599 + 4.23695i 0.540950 + 0.201760i
\(22\) −54.9723 −2.49874
\(23\) 10.3861 0.451570 0.225785 0.974177i \(-0.427505\pi\)
0.225785 + 0.974177i \(0.427505\pi\)
\(24\) 42.6687i 1.77786i
\(25\) −5.00000 −0.200000
\(26\) 64.4602i 2.47924i
\(27\) 5.19615i 0.192450i
\(28\) 25.6240 68.7020i 0.915142 2.45364i
\(29\) −13.7269 −0.473341 −0.236671 0.971590i \(-0.576056\pi\)
−0.236671 + 0.971590i \(0.576056\pi\)
\(30\) 14.7352 0.491172
\(31\) 42.4383i 1.36898i 0.729024 + 0.684488i \(0.239974\pi\)
−0.729024 + 0.684488i \(0.760026\pi\)
\(32\) −98.6363 −3.08238
\(33\) 25.0262i 0.758371i
\(34\) 49.4951i 1.45574i
\(35\) 14.6656 + 5.46988i 0.419018 + 0.156282i
\(36\) −31.4250 −0.872916
\(37\) 28.7434 0.776850 0.388425 0.921480i \(-0.373019\pi\)
0.388425 + 0.921480i \(0.373019\pi\)
\(38\) 71.1112i 1.87135i
\(39\) −29.3456 −0.752452
\(40\) 55.0850i 1.37713i
\(41\) 28.8060i 0.702585i −0.936266 0.351293i \(-0.885742\pi\)
0.936266 0.351293i \(-0.114258\pi\)
\(42\) −43.2200 16.1199i −1.02905 0.383807i
\(43\) −5.84593 −0.135952 −0.0679759 0.997687i \(-0.521654\pi\)
−0.0679759 + 0.997687i \(0.521654\pi\)
\(44\) 151.352 3.43982
\(45\) 6.70820i 0.149071i
\(46\) −39.5151 −0.859023
\(47\) 10.5013i 0.223432i 0.993740 + 0.111716i \(0.0356347\pi\)
−0.993740 + 0.111716i \(0.964365\pi\)
\(48\) 89.7644i 1.87009i
\(49\) −37.0322 32.0877i −0.755758 0.654851i
\(50\) 19.0230 0.380460
\(51\) −22.5327 −0.441818
\(52\) 177.475i 3.41298i
\(53\) 81.9074 1.54542 0.772712 0.634757i \(-0.218900\pi\)
0.772712 + 0.634757i \(0.218900\pi\)
\(54\) 19.7693i 0.366098i
\(55\) 32.3087i 0.587432i
\(56\) −60.2617 + 161.571i −1.07610 + 2.88520i
\(57\) −32.3735 −0.567956
\(58\) 52.2254 0.900438
\(59\) 35.1680i 0.596067i 0.954555 + 0.298033i \(0.0963307\pi\)
−0.954555 + 0.298033i \(0.903669\pi\)
\(60\) −40.5695 −0.676158
\(61\) 68.4826i 1.12267i −0.827590 0.561333i \(-0.810289\pi\)
0.827590 0.561333i \(-0.189711\pi\)
\(62\) 161.461i 2.60421i
\(63\) −7.33862 + 19.6760i −0.116486 + 0.312317i
\(64\) 167.970 2.62453
\(65\) −37.8850 −0.582847
\(66\) 95.2149i 1.44265i
\(67\) 47.4637 0.708414 0.354207 0.935167i \(-0.384751\pi\)
0.354207 + 0.935167i \(0.384751\pi\)
\(68\) 136.272i 2.00400i
\(69\) 17.9893i 0.260714i
\(70\) −55.7968 20.8107i −0.797098 0.297296i
\(71\) 47.6548 0.671194 0.335597 0.942006i \(-0.391062\pi\)
0.335597 + 0.942006i \(0.391062\pi\)
\(72\) 73.9043 1.02645
\(73\) 125.967i 1.72557i −0.505569 0.862786i \(-0.668717\pi\)
0.505569 0.862786i \(-0.331283\pi\)
\(74\) −109.357 −1.47780
\(75\) 8.66025i 0.115470i
\(76\) 195.786i 2.57614i
\(77\) 35.3450 94.7655i 0.459026 1.23072i
\(78\) 111.648 1.43139
\(79\) −129.527 −1.63958 −0.819790 0.572665i \(-0.805910\pi\)
−0.819790 + 0.572665i \(0.805910\pi\)
\(80\) 115.885i 1.44857i
\(81\) 9.00000 0.111111
\(82\) 109.595i 1.33653i
\(83\) 42.6906i 0.514345i −0.966365 0.257173i \(-0.917209\pi\)
0.966365 0.257173i \(-0.0827909\pi\)
\(84\) 118.995 + 44.3820i 1.41661 + 0.528358i
\(85\) −29.0896 −0.342231
\(86\) 22.2414 0.258621
\(87\) 23.7757i 0.273284i
\(88\) −355.945 −4.04483
\(89\) 25.5329i 0.286886i 0.989659 + 0.143443i \(0.0458174\pi\)
−0.989659 + 0.143443i \(0.954183\pi\)
\(90\) 25.5220i 0.283578i
\(91\) 111.122 + 41.4453i 1.22112 + 0.455443i
\(92\) 108.795 1.18255
\(93\) −73.5053 −0.790379
\(94\) 39.9533i 0.425035i
\(95\) −41.7940 −0.439937
\(96\) 170.843i 1.77961i
\(97\) 28.7310i 0.296196i 0.988973 + 0.148098i \(0.0473151\pi\)
−0.988973 + 0.148098i \(0.952685\pi\)
\(98\) 140.893 + 122.081i 1.43768 + 1.24572i
\(99\) −43.3467 −0.437846
\(100\) −52.3750 −0.523750
\(101\) 12.4609i 0.123375i −0.998096 0.0616875i \(-0.980352\pi\)
0.998096 0.0616875i \(-0.0196482\pi\)
\(102\) 85.7280 0.840470
\(103\) 38.4795i 0.373587i −0.982399 0.186794i \(-0.940190\pi\)
0.982399 0.186794i \(-0.0598096\pi\)
\(104\) 417.380i 4.01326i
\(105\) −9.47411 + 25.4016i −0.0902296 + 0.241920i
\(106\) −311.625 −2.93986
\(107\) −87.7985 −0.820547 −0.410273 0.911963i \(-0.634567\pi\)
−0.410273 + 0.911963i \(0.634567\pi\)
\(108\) 54.4297i 0.503978i
\(109\) 130.012 1.19277 0.596386 0.802698i \(-0.296603\pi\)
0.596386 + 0.802698i \(0.296603\pi\)
\(110\) 122.922i 1.11747i
\(111\) 49.7851i 0.448515i
\(112\) 126.776 339.906i 1.13193 3.03487i
\(113\) −158.597 −1.40351 −0.701757 0.712417i \(-0.747601\pi\)
−0.701757 + 0.712417i \(0.747601\pi\)
\(114\) 123.168 1.08042
\(115\) 23.2241i 0.201948i
\(116\) −143.789 −1.23956
\(117\) 50.8281i 0.434428i
\(118\) 133.800i 1.13390i
\(119\) 85.3234 + 31.8233i 0.717003 + 0.267423i
\(120\) 95.4100 0.795084
\(121\) 87.7709 0.725379
\(122\) 260.549i 2.13565i
\(123\) 49.8934 0.405638
\(124\) 444.541i 3.58501i
\(125\) 11.1803i 0.0894427i
\(126\) 27.9205 74.8593i 0.221591 0.594122i
\(127\) 43.0643 0.339089 0.169545 0.985523i \(-0.445770\pi\)
0.169545 + 0.985523i \(0.445770\pi\)
\(128\) −244.513 −1.91026
\(129\) 10.1254i 0.0784919i
\(130\) 144.137 1.10875
\(131\) 0.686731i 0.00524222i −0.999997 0.00262111i \(-0.999166\pi\)
0.999997 0.00262111i \(-0.000834326\pi\)
\(132\) 262.150i 1.98598i
\(133\) 122.587 + 45.7216i 0.921707 + 0.343772i
\(134\) −180.581 −1.34762
\(135\) 11.6190 0.0860663
\(136\) 320.480i 2.35647i
\(137\) 76.2084 0.556266 0.278133 0.960543i \(-0.410284\pi\)
0.278133 + 0.960543i \(0.410284\pi\)
\(138\) 68.4421i 0.495957i
\(139\) 49.0445i 0.352838i −0.984315 0.176419i \(-0.943549\pi\)
0.984315 0.176419i \(-0.0564514\pi\)
\(140\) 153.622 + 57.2970i 1.09730 + 0.409264i
\(141\) −18.1888 −0.128998
\(142\) −181.307 −1.27681
\(143\) 244.804i 1.71191i
\(144\) −155.476 −1.07970
\(145\) 30.6943i 0.211685i
\(146\) 479.253i 3.28256i
\(147\) 55.5775 64.1416i 0.378078 0.436337i
\(148\) 301.087 2.03437
\(149\) −242.344 −1.62647 −0.813236 0.581934i \(-0.802296\pi\)
−0.813236 + 0.581934i \(0.802296\pi\)
\(150\) 32.9488i 0.219659i
\(151\) 107.704 0.713271 0.356636 0.934244i \(-0.383924\pi\)
0.356636 + 0.934244i \(0.383924\pi\)
\(152\) 460.445i 3.02924i
\(153\) 39.0278i 0.255084i
\(154\) −134.474 + 360.545i −0.873205 + 2.34120i
\(155\) −94.8949 −0.612225
\(156\) −307.395 −1.97048
\(157\) 76.1684i 0.485149i 0.970133 + 0.242575i \(0.0779919\pi\)
−0.970133 + 0.242575i \(0.922008\pi\)
\(158\) 492.798 3.11897
\(159\) 141.868i 0.892250i
\(160\) 220.557i 1.37848i
\(161\) 25.4066 68.1191i 0.157805 0.423100i
\(162\) −34.2414 −0.211367
\(163\) 10.4287 0.0639800 0.0319900 0.999488i \(-0.489816\pi\)
0.0319900 + 0.999488i \(0.489816\pi\)
\(164\) 301.743i 1.83989i
\(165\) −55.9604 −0.339154
\(166\) 162.421i 0.978439i
\(167\) 75.7598i 0.453652i 0.973935 + 0.226826i \(0.0728348\pi\)
−0.973935 + 0.226826i \(0.927165\pi\)
\(168\) −279.849 104.376i −1.66577 0.621287i
\(169\) −118.055 −0.698552
\(170\) 110.674 0.651025
\(171\) 56.0725i 0.327910i
\(172\) −61.2361 −0.356024
\(173\) 325.843i 1.88349i −0.336333 0.941743i \(-0.609187\pi\)
0.336333 0.941743i \(-0.390813\pi\)
\(174\) 90.4570i 0.519868i
\(175\) −12.2310 + 32.7933i −0.0698916 + 0.187390i
\(176\) 748.822 4.25467
\(177\) −60.9127 −0.344139
\(178\) 97.1424i 0.545744i
\(179\) −30.9215 −0.172746 −0.0863728 0.996263i \(-0.527528\pi\)
−0.0863728 + 0.996263i \(0.527528\pi\)
\(180\) 70.2684i 0.390380i
\(181\) 211.403i 1.16797i −0.811764 0.583985i \(-0.801493\pi\)
0.811764 0.583985i \(-0.198507\pi\)
\(182\) −422.773 157.683i −2.32293 0.866390i
\(183\) 118.615 0.648171
\(184\) −255.860 −1.39054
\(185\) 64.2723i 0.347418i
\(186\) 279.658 1.50354
\(187\) 187.970i 1.00519i
\(188\) 110.001i 0.585112i
\(189\) −34.0798 12.7109i −0.180317 0.0672532i
\(190\) 159.010 0.836892
\(191\) 112.093 0.586874 0.293437 0.955978i \(-0.405201\pi\)
0.293437 + 0.955978i \(0.405201\pi\)
\(192\) 290.932i 1.51527i
\(193\) −293.541 −1.52094 −0.760470 0.649373i \(-0.775031\pi\)
−0.760470 + 0.649373i \(0.775031\pi\)
\(194\) 109.310i 0.563453i
\(195\) 65.6188i 0.336507i
\(196\) −387.912 336.118i −1.97914 1.71489i
\(197\) −90.7583 −0.460702 −0.230351 0.973108i \(-0.573987\pi\)
−0.230351 + 0.973108i \(0.573987\pi\)
\(198\) 164.917 0.832914
\(199\) 389.421i 1.95689i −0.206505 0.978445i \(-0.566209\pi\)
0.206505 0.978445i \(-0.433791\pi\)
\(200\) 123.174 0.615869
\(201\) 82.2096i 0.409003i
\(202\) 47.4086i 0.234696i
\(203\) −33.5788 + 90.0301i −0.165413 + 0.443498i
\(204\) −236.030 −1.15701
\(205\) 64.4122 0.314206
\(206\) 146.399i 0.710676i
\(207\) −31.1584 −0.150523
\(208\) 878.064i 4.22146i
\(209\) 270.062i 1.29216i
\(210\) 36.0452 96.6430i 0.171644 0.460205i
\(211\) −21.1049 −0.100023 −0.0500115 0.998749i \(-0.515926\pi\)
−0.0500115 + 0.998749i \(0.515926\pi\)
\(212\) 857.980 4.04707
\(213\) 82.5405i 0.387514i
\(214\) 334.038 1.56093
\(215\) 13.0719i 0.0607995i
\(216\) 128.006i 0.592620i
\(217\) 278.338 + 103.813i 1.28267 + 0.478400i
\(218\) −494.645 −2.26901
\(219\) 218.181 0.996259
\(220\) 338.434i 1.53834i
\(221\) −220.412 −0.997340
\(222\) 189.413i 0.853209i
\(223\) 293.039i 1.31408i 0.753857 + 0.657039i \(0.228191\pi\)
−0.753857 + 0.657039i \(0.771809\pi\)
\(224\) −241.285 + 646.922i −1.07716 + 2.88805i
\(225\) 15.0000 0.0666667
\(226\) 603.398 2.66990
\(227\) 73.9333i 0.325697i 0.986651 + 0.162849i \(0.0520682\pi\)
−0.986651 + 0.162849i \(0.947932\pi\)
\(228\) −339.112 −1.48733
\(229\) 233.516i 1.01972i −0.860257 0.509860i \(-0.829697\pi\)
0.860257 0.509860i \(-0.170303\pi\)
\(230\) 88.3583i 0.384167i
\(231\) 164.139 + 61.2193i 0.710557 + 0.265019i
\(232\) 338.159 1.45758
\(233\) −385.429 −1.65420 −0.827101 0.562054i \(-0.810011\pi\)
−0.827101 + 0.562054i \(0.810011\pi\)
\(234\) 193.381i 0.826413i
\(235\) −23.4816 −0.0999218
\(236\) 368.384i 1.56095i
\(237\) 224.347i 0.946611i
\(238\) −324.621 121.075i −1.36396 0.508719i
\(239\) 407.373 1.70449 0.852244 0.523144i \(-0.175241\pi\)
0.852244 + 0.523144i \(0.175241\pi\)
\(240\) −200.719 −0.836330
\(241\) 271.816i 1.12787i −0.825820 0.563934i \(-0.809287\pi\)
0.825820 0.563934i \(-0.190713\pi\)
\(242\) −333.933 −1.37989
\(243\) 15.5885i 0.0641500i
\(244\) 717.355i 2.93998i
\(245\) 71.7502 82.8064i 0.292858 0.337985i
\(246\) −189.825 −0.771645
\(247\) −316.673 −1.28208
\(248\) 1045.46i 4.21555i
\(249\) 73.9424 0.296957
\(250\) 42.5367i 0.170147i
\(251\) 442.250i 1.76195i −0.473162 0.880976i \(-0.656887\pi\)
0.473162 0.880976i \(-0.343113\pi\)
\(252\) −76.8719 + 206.106i −0.305047 + 0.817880i
\(253\) 150.068 0.593154
\(254\) −163.843 −0.645049
\(255\) 50.3847i 0.197587i
\(256\) 258.395 1.00935
\(257\) 390.436i 1.51921i −0.650386 0.759604i \(-0.725393\pi\)
0.650386 0.759604i \(-0.274607\pi\)
\(258\) 38.5233i 0.149315i
\(259\) 70.3124 188.519i 0.271476 0.727871i
\(260\) −396.846 −1.52633
\(261\) 41.1807 0.157780
\(262\) 2.61274i 0.00997228i
\(263\) −1.63279 −0.00620832 −0.00310416 0.999995i \(-0.500988\pi\)
−0.00310416 + 0.999995i \(0.500988\pi\)
\(264\) 616.515i 2.33529i
\(265\) 183.151i 0.691134i
\(266\) −466.395 173.953i −1.75336 0.653957i
\(267\) −44.2242 −0.165634
\(268\) 497.182 1.85516
\(269\) 410.340i 1.52543i 0.646737 + 0.762713i \(0.276133\pi\)
−0.646737 + 0.762713i \(0.723867\pi\)
\(270\) −44.2055 −0.163724
\(271\) 470.030i 1.73443i 0.497937 + 0.867213i \(0.334091\pi\)
−0.497937 + 0.867213i \(0.665909\pi\)
\(272\) 674.211i 2.47872i
\(273\) −71.7854 + 192.468i −0.262950 + 0.705011i
\(274\) −289.943 −1.05818
\(275\) −72.2445 −0.262707
\(276\) 188.438i 0.682745i
\(277\) 366.582 1.32340 0.661701 0.749768i \(-0.269835\pi\)
0.661701 + 0.749768i \(0.269835\pi\)
\(278\) 186.595i 0.671204i
\(279\) 127.315i 0.456326i
\(280\) −361.284 134.749i −1.29030 0.481247i
\(281\) 10.1164 0.0360015 0.0180008 0.999838i \(-0.494270\pi\)
0.0180008 + 0.999838i \(0.494270\pi\)
\(282\) 69.2011 0.245394
\(283\) 121.896i 0.430729i −0.976534 0.215364i \(-0.930906\pi\)
0.976534 0.215364i \(-0.0690939\pi\)
\(284\) 499.183 1.75769
\(285\) 72.3893i 0.253998i
\(286\) 931.380i 3.25657i
\(287\) −188.929 70.4654i −0.658289 0.245524i
\(288\) 295.909 1.02746
\(289\) 119.759 0.414391
\(290\) 116.780i 0.402688i
\(291\) −49.7635 −0.171009
\(292\) 1319.50i 4.51884i
\(293\) 292.803i 0.999327i 0.866220 + 0.499663i \(0.166543\pi\)
−0.866220 + 0.499663i \(0.833457\pi\)
\(294\) −211.450 + 244.033i −0.719218 + 0.830045i
\(295\) −78.6379 −0.266569
\(296\) −708.088 −2.39219
\(297\) 75.0787i 0.252790i
\(298\) 922.023 3.09404
\(299\) 175.969i 0.588525i
\(300\) 90.7161i 0.302387i
\(301\) −14.3003 + 38.3415i −0.0475095 + 0.127380i
\(302\) −409.771 −1.35686
\(303\) 21.5829 0.0712306
\(304\) 968.662i 3.18639i
\(305\) 153.132 0.502071
\(306\) 148.485i 0.485246i
\(307\) 167.855i 0.546758i 0.961906 + 0.273379i \(0.0881412\pi\)
−0.961906 + 0.273379i \(0.911859\pi\)
\(308\) 370.238 992.668i 1.20207 3.22295i
\(309\) 66.6485 0.215691
\(310\) 361.037 1.16464
\(311\) 303.739i 0.976652i 0.872661 + 0.488326i \(0.162392\pi\)
−0.872661 + 0.488326i \(0.837608\pi\)
\(312\) 722.923 2.31706
\(313\) 17.2151i 0.0550004i 0.999622 + 0.0275002i \(0.00875470\pi\)
−0.999622 + 0.0275002i \(0.991245\pi\)
\(314\) 289.790i 0.922899i
\(315\) −43.9969 16.4096i −0.139673 0.0520941i
\(316\) −1356.79 −4.29364
\(317\) 82.8657 0.261406 0.130703 0.991422i \(-0.458277\pi\)
0.130703 + 0.991422i \(0.458277\pi\)
\(318\) 539.750i 1.69733i
\(319\) −198.339 −0.621751
\(320\) 375.592i 1.17372i
\(321\) 152.071i 0.473743i
\(322\) −96.6619 + 259.166i −0.300192 + 0.804863i
\(323\) −243.154 −0.752799
\(324\) 94.2749 0.290972
\(325\) 84.7135i 0.260657i
\(326\) −39.6772 −0.121709
\(327\) 225.188i 0.688647i
\(328\) 709.629i 2.16350i
\(329\) 68.8745 + 25.6883i 0.209345 + 0.0780800i
\(330\) 212.907 0.645172
\(331\) −451.490 −1.36402 −0.682009 0.731343i \(-0.738894\pi\)
−0.682009 + 0.731343i \(0.738894\pi\)
\(332\) 447.184i 1.34694i
\(333\) −86.2303 −0.258950
\(334\) 288.236i 0.862982i
\(335\) 106.132i 0.316812i
\(336\) 588.734 + 219.582i 1.75219 + 0.653518i
\(337\) 204.157 0.605808 0.302904 0.953021i \(-0.402044\pi\)
0.302904 + 0.953021i \(0.402044\pi\)
\(338\) 449.153 1.32886
\(339\) 274.698i 0.810319i
\(340\) −304.713 −0.896215
\(341\) 613.187i 1.79820i
\(342\) 213.334i 0.623783i
\(343\) −301.041 + 164.388i −0.877669 + 0.479267i
\(344\) 144.013 0.418643
\(345\) −40.2253 −0.116595
\(346\) 1239.70i 3.58296i
\(347\) 146.593 0.422458 0.211229 0.977437i \(-0.432253\pi\)
0.211229 + 0.977437i \(0.432253\pi\)
\(348\) 249.050i 0.715661i
\(349\) 11.4454i 0.0327947i −0.999866 0.0163974i \(-0.994780\pi\)
0.999866 0.0163974i \(-0.00521968\pi\)
\(350\) 46.5342 124.766i 0.132955 0.356473i
\(351\) 88.0369 0.250817
\(352\) −1425.19 −4.04882
\(353\) 177.817i 0.503730i −0.967762 0.251865i \(-0.918956\pi\)
0.967762 0.251865i \(-0.0810439\pi\)
\(354\) 231.748 0.654657
\(355\) 106.559i 0.300167i
\(356\) 267.457i 0.751283i
\(357\) −55.1196 + 147.784i −0.154397 + 0.413962i
\(358\) 117.644 0.328614
\(359\) 653.079 1.81916 0.909581 0.415526i \(-0.136402\pi\)
0.909581 + 0.415526i \(0.136402\pi\)
\(360\) 165.255i 0.459042i
\(361\) 11.6523 0.0322780
\(362\) 804.303i 2.22183i
\(363\) 152.024i 0.418798i
\(364\) 1164.00 + 434.140i 3.19779 + 1.19269i
\(365\) 281.670 0.771699
\(366\) −451.284 −1.23302
\(367\) 466.632i 1.27148i 0.771905 + 0.635738i \(0.219304\pi\)
−0.771905 + 0.635738i \(0.780696\pi\)
\(368\) 538.266 1.46268
\(369\) 86.4180i 0.234195i
\(370\) 244.530i 0.660893i
\(371\) 200.362 537.203i 0.540060 1.44799i
\(372\) −769.967 −2.06980
\(373\) −452.082 −1.21202 −0.606008 0.795459i \(-0.707230\pi\)
−0.606008 + 0.795459i \(0.707230\pi\)
\(374\) 715.149i 1.91216i
\(375\) 19.3649 0.0516398
\(376\) 258.697i 0.688024i
\(377\) 232.571i 0.616899i
\(378\) 129.660 + 48.3597i 0.343016 + 0.127936i
\(379\) 326.478 0.861420 0.430710 0.902490i \(-0.358263\pi\)
0.430710 + 0.902490i \(0.358263\pi\)
\(380\) −437.792 −1.15208
\(381\) 74.5896i 0.195773i
\(382\) −426.469 −1.11641
\(383\) 381.262i 0.995462i −0.867331 0.497731i \(-0.834167\pi\)
0.867331 0.497731i \(-0.165833\pi\)
\(384\) 423.509i 1.10289i
\(385\) 211.902 + 79.0338i 0.550395 + 0.205283i
\(386\) 1116.81 2.89329
\(387\) 17.5378 0.0453173
\(388\) 300.957i 0.775662i
\(389\) −68.8443 −0.176978 −0.0884888 0.996077i \(-0.528204\pi\)
−0.0884888 + 0.996077i \(0.528204\pi\)
\(390\) 249.653i 0.640137i
\(391\) 135.116i 0.345565i
\(392\) 912.278 + 790.472i 2.32724 + 2.01651i
\(393\) 1.18945 0.00302660
\(394\) 345.299 0.876394
\(395\) 289.631i 0.733242i
\(396\) −454.056 −1.14661
\(397\) 370.531i 0.933328i 0.884435 + 0.466664i \(0.154544\pi\)
−0.884435 + 0.466664i \(0.845456\pi\)
\(398\) 1481.59i 3.72259i
\(399\) −79.1922 + 212.327i −0.198477 + 0.532148i
\(400\) −259.127 −0.647819
\(401\) 8.95073 0.0223210 0.0111605 0.999938i \(-0.496447\pi\)
0.0111605 + 0.999938i \(0.496447\pi\)
\(402\) 312.775i 0.778047i
\(403\) −719.019 −1.78417
\(404\) 130.528i 0.323088i
\(405\) 20.1246i 0.0496904i
\(406\) 127.754 342.529i 0.314665 0.843667i
\(407\) 415.311 1.02042
\(408\) 555.088 1.36051
\(409\) 63.1330i 0.154359i −0.997017 0.0771797i \(-0.975408\pi\)
0.997017 0.0771797i \(-0.0245915\pi\)
\(410\) −245.063 −0.597714
\(411\) 131.997i 0.321160i
\(412\) 403.072i 0.978331i
\(413\) 230.655 + 86.0280i 0.558486 + 0.208300i
\(414\) 118.545 0.286341
\(415\) 95.4592 0.230022
\(416\) 1671.17i 4.01722i
\(417\) 84.9475 0.203711
\(418\) 1027.48i 2.45808i
\(419\) 3.58774i 0.00856263i −0.999991 0.00428131i \(-0.998637\pi\)
0.999991 0.00428131i \(-0.00136279\pi\)
\(420\) −99.2412 + 266.082i −0.236289 + 0.633527i
\(421\) 119.594 0.284071 0.142035 0.989862i \(-0.454635\pi\)
0.142035 + 0.989862i \(0.454635\pi\)
\(422\) 80.2956 0.190274
\(423\) 31.5039i 0.0744773i
\(424\) −2017.77 −4.75889
\(425\) 65.0463i 0.153050i
\(426\) 314.034i 0.737168i
\(427\) −449.154 167.523i −1.05188 0.392324i
\(428\) −919.689 −2.14881
\(429\) −424.012 −0.988373
\(430\) 49.7334i 0.115659i
\(431\) −404.488 −0.938488 −0.469244 0.883069i \(-0.655473\pi\)
−0.469244 + 0.883069i \(0.655473\pi\)
\(432\) 269.293i 0.623364i
\(433\) 116.085i 0.268094i −0.990975 0.134047i \(-0.957203\pi\)
0.990975 0.134047i \(-0.0427974\pi\)
\(434\) −1058.97 394.966i −2.44002 0.910060i
\(435\) 53.1641 0.122216
\(436\) 1361.88 3.12357
\(437\) 194.125i 0.444223i
\(438\) −830.091 −1.89519
\(439\) 58.4183i 0.133071i −0.997784 0.0665357i \(-0.978805\pi\)
0.997784 0.0665357i \(-0.0211946\pi\)
\(440\) 795.918i 1.80890i
\(441\) 111.096 + 96.2630i 0.251919 + 0.218284i
\(442\) 838.580 1.89724
\(443\) 267.301 0.603388 0.301694 0.953405i \(-0.402448\pi\)
0.301694 + 0.953405i \(0.402448\pi\)
\(444\) 521.499i 1.17455i
\(445\) −57.0932 −0.128299
\(446\) 1114.90i 2.49977i
\(447\) 419.753i 0.939044i
\(448\) 410.888 1101.66i 0.917162 2.45906i
\(449\) 296.478 0.660307 0.330154 0.943927i \(-0.392899\pi\)
0.330154 + 0.943927i \(0.392899\pi\)
\(450\) −57.0690 −0.126820
\(451\) 416.215i 0.922872i
\(452\) −1661.30 −3.67545
\(453\) 186.549i 0.411807i
\(454\) 281.287i 0.619574i
\(455\) −92.6746 + 248.475i −0.203680 + 0.546100i
\(456\) 797.513 1.74893
\(457\) 12.1251 0.0265320 0.0132660 0.999912i \(-0.495777\pi\)
0.0132660 + 0.999912i \(0.495777\pi\)
\(458\) 888.435i 1.93981i
\(459\) 67.5981 0.147273
\(460\) 243.272i 0.528852i
\(461\) 103.948i 0.225483i 0.993624 + 0.112741i \(0.0359632\pi\)
−0.993624 + 0.112741i \(0.964037\pi\)
\(462\) −624.482 232.915i −1.35169 0.504145i
\(463\) 498.831 1.07739 0.538694 0.842501i \(-0.318918\pi\)
0.538694 + 0.842501i \(0.318918\pi\)
\(464\) −711.403 −1.53320
\(465\) 164.363i 0.353468i
\(466\) 1466.40 3.14679
\(467\) 597.683i 1.27983i −0.768444 0.639917i \(-0.778969\pi\)
0.768444 0.639917i \(-0.221031\pi\)
\(468\) 532.424i 1.13766i
\(469\) 116.106 311.299i 0.247561 0.663750i
\(470\) 89.3382 0.190081
\(471\) −131.928 −0.280101
\(472\) 866.354i 1.83550i
\(473\) −84.4673 −0.178578
\(474\) 853.551i 1.80074i
\(475\) 93.4542i 0.196746i
\(476\) 893.762 + 333.349i 1.87765 + 0.700313i
\(477\) −245.722 −0.515141
\(478\) −1549.89 −3.24245
\(479\) 276.703i 0.577669i 0.957379 + 0.288834i \(0.0932677\pi\)
−0.957379 + 0.288834i \(0.906732\pi\)
\(480\) 382.017 0.795868
\(481\) 486.992i 1.01246i
\(482\) 1034.15i 2.14554i
\(483\) 117.986 + 44.0055i 0.244277 + 0.0911087i
\(484\) 919.399 1.89958
\(485\) −64.2444 −0.132463
\(486\) 59.3079i 0.122033i
\(487\) −542.653 −1.11428 −0.557138 0.830420i \(-0.688101\pi\)
−0.557138 + 0.830420i \(0.688101\pi\)
\(488\) 1687.05i 3.45708i
\(489\) 18.0631i 0.0369389i
\(490\) −272.981 + 315.045i −0.557104 + 0.642950i
\(491\) 574.817 1.17071 0.585353 0.810778i \(-0.300956\pi\)
0.585353 + 0.810778i \(0.300956\pi\)
\(492\) 522.633 1.06226
\(493\) 178.577i 0.362225i
\(494\) 1204.82 2.43890
\(495\) 96.9262i 0.195811i
\(496\) 2199.38i 4.43424i
\(497\) 116.573 312.552i 0.234554 0.628877i
\(498\) −281.321 −0.564902
\(499\) −549.967 −1.10214 −0.551070 0.834459i \(-0.685780\pi\)
−0.551070 + 0.834459i \(0.685780\pi\)
\(500\) 117.114i 0.234228i
\(501\) −131.220 −0.261916
\(502\) 1682.58i 3.35176i
\(503\) 397.053i 0.789369i −0.918817 0.394685i \(-0.870854\pi\)
0.918817 0.394685i \(-0.129146\pi\)
\(504\) 180.785 484.713i 0.358701 0.961733i
\(505\) 27.8634 0.0551750
\(506\) −570.949 −1.12836
\(507\) 204.478i 0.403309i
\(508\) 451.098 0.887989
\(509\) 557.813i 1.09590i −0.836511 0.547950i \(-0.815408\pi\)
0.836511 0.547950i \(-0.184592\pi\)
\(510\) 191.694i 0.375870i
\(511\) −826.174 308.141i −1.61678 0.603015i
\(512\) −5.03806 −0.00983995
\(513\) 97.1205 0.189319
\(514\) 1485.45i 2.88999i
\(515\) 86.0428 0.167073
\(516\) 106.064i 0.205550i
\(517\) 151.732i 0.293486i
\(518\) −267.511 + 717.238i −0.516430 + 1.38463i
\(519\) 564.377 1.08743
\(520\) 933.289 1.79479
\(521\) 287.300i 0.551439i 0.961238 + 0.275719i \(0.0889161\pi\)
−0.961238 + 0.275719i \(0.911084\pi\)
\(522\) −156.676 −0.300146
\(523\) 1012.28i 1.93553i −0.251853 0.967766i \(-0.581040\pi\)
0.251853 0.967766i \(-0.418960\pi\)
\(524\) 7.19350i 0.0137281i
\(525\) −56.7997 21.1848i −0.108190 0.0403519i
\(526\) 6.21211 0.0118101
\(527\) −552.091 −1.04761
\(528\) 1297.00i 2.45643i
\(529\) −421.128 −0.796084
\(530\) 696.815i 1.31475i
\(531\) 105.504i 0.198689i
\(532\) 1284.10 + 478.934i 2.41372 + 0.900252i
\(533\) 488.051 0.915669
\(534\) 168.256 0.315085
\(535\) 196.323i 0.366960i
\(536\) −1169.26 −2.18145
\(537\) 53.5575i 0.0997347i
\(538\) 1561.18i 2.90182i
\(539\) −535.074 463.632i −0.992716 0.860170i
\(540\) 121.708 0.225386
\(541\) 526.853 0.973851 0.486925 0.873444i \(-0.338118\pi\)
0.486925 + 0.873444i \(0.338118\pi\)
\(542\) 1788.28i 3.29940i
\(543\) 366.160 0.674328
\(544\) 1283.19i 2.35880i
\(545\) 290.716i 0.533424i
\(546\) 273.115 732.265i 0.500211 1.34114i
\(547\) −250.549 −0.458042 −0.229021 0.973421i \(-0.573553\pi\)
−0.229021 + 0.973421i \(0.573553\pi\)
\(548\) 798.282 1.45672
\(549\) 205.448i 0.374222i
\(550\) 274.862 0.499748
\(551\) 256.567i 0.465640i
\(552\) 443.162i 0.802829i
\(553\) −316.849 + 849.522i −0.572964 + 1.53621i
\(554\) −1394.70 −2.51751
\(555\) −111.323 −0.200582
\(556\) 513.741i 0.923994i
\(557\) −64.1496 −0.115170 −0.0575849 0.998341i \(-0.518340\pi\)
−0.0575849 + 0.998341i \(0.518340\pi\)
\(558\) 484.382i 0.868069i
\(559\) 99.0459i 0.177184i
\(560\) 760.053 + 283.479i 1.35724 + 0.506213i
\(561\) −325.573 −0.580344
\(562\) −38.4890 −0.0684857
\(563\) 17.3869i 0.0308826i 0.999881 + 0.0154413i \(0.00491531\pi\)
−0.999881 + 0.0154413i \(0.995085\pi\)
\(564\) −190.527 −0.337814
\(565\) 354.634i 0.627670i
\(566\) 463.767i 0.819376i
\(567\) 22.0158 59.0280i 0.0388287 0.104106i
\(568\) −1173.96 −2.06684
\(569\) 174.914 0.307405 0.153703 0.988117i \(-0.450880\pi\)
0.153703 + 0.988117i \(0.450880\pi\)
\(570\) 275.413i 0.483180i
\(571\) −376.637 −0.659609 −0.329805 0.944049i \(-0.606983\pi\)
−0.329805 + 0.944049i \(0.606983\pi\)
\(572\) 2564.32i 4.48307i
\(573\) 194.151i 0.338832i
\(574\) 718.799 + 268.093i 1.25226 + 0.467060i
\(575\) −51.9306 −0.0903141
\(576\) −503.909 −0.874842
\(577\) 448.775i 0.777773i −0.921286 0.388886i \(-0.872860\pi\)
0.921286 0.388886i \(-0.127140\pi\)
\(578\) −455.636 −0.788297
\(579\) 508.429i 0.878115i
\(580\) 321.522i 0.554349i
\(581\) −279.994 104.430i −0.481917 0.179742i
\(582\) 189.330 0.325310
\(583\) 1183.47 2.02997
\(584\) 3103.16i 5.31363i
\(585\) 113.655 0.194282
\(586\) 1114.00i 1.90102i
\(587\) 275.916i 0.470044i −0.971990 0.235022i \(-0.924484\pi\)
0.971990 0.235022i \(-0.0755162\pi\)
\(588\) 582.174 671.883i 0.990091 1.14266i
\(589\) −793.207 −1.34670
\(590\) 299.186 0.507095
\(591\) 157.198i 0.265986i
\(592\) 1489.64 2.51629
\(593\) 893.938i 1.50748i −0.657171 0.753742i \(-0.728247\pi\)
0.657171 0.753742i \(-0.271753\pi\)
\(594\) 285.645i 0.480883i
\(595\) −71.1591 + 190.789i −0.119595 + 0.320654i
\(596\) −2538.55 −4.25932
\(597\) 674.497 1.12981
\(598\) 669.492i 1.11955i
\(599\) −122.407 −0.204352 −0.102176 0.994766i \(-0.532581\pi\)
−0.102176 + 0.994766i \(0.532581\pi\)
\(600\) 213.343i 0.355572i
\(601\) 594.921i 0.989885i 0.868926 + 0.494943i \(0.164811\pi\)
−0.868926 + 0.494943i \(0.835189\pi\)
\(602\) 54.4071 145.874i 0.0903773 0.242316i
\(603\) −142.391 −0.236138
\(604\) 1128.20 1.86788
\(605\) 196.262i 0.324399i
\(606\) −82.1142 −0.135502
\(607\) 539.772i 0.889246i 0.895718 + 0.444623i \(0.146662\pi\)
−0.895718 + 0.444623i \(0.853338\pi\)
\(608\) 1843.60i 3.03223i
\(609\) −155.937 58.1602i −0.256054 0.0955012i
\(610\) −582.605 −0.955091
\(611\) −177.920 −0.291195
\(612\) 408.816i 0.668000i
\(613\) 1180.07 1.92508 0.962540 0.271140i \(-0.0874006\pi\)
0.962540 + 0.271140i \(0.0874006\pi\)
\(614\) 638.620i 1.04010i
\(615\) 111.565i 0.181407i
\(616\) −870.715 + 2334.53i −1.41350 + 3.78982i
\(617\) −777.688 −1.26043 −0.630217 0.776419i \(-0.717034\pi\)
−0.630217 + 0.776419i \(0.717034\pi\)
\(618\) −253.571 −0.410309
\(619\) 285.107i 0.460592i −0.973121 0.230296i \(-0.926030\pi\)
0.973121 0.230296i \(-0.0739695\pi\)
\(620\) −994.023 −1.60326
\(621\) 53.9679i 0.0869048i
\(622\) 1155.60i 1.85789i
\(623\) 167.462 + 62.4586i 0.268799 + 0.100255i
\(624\) −1520.85 −2.43726
\(625\) 25.0000 0.0400000
\(626\) 65.4967i 0.104627i
\(627\) −467.762 −0.746031
\(628\) 797.863i 1.27048i
\(629\) 373.931i 0.594485i
\(630\) 167.391 + 62.4322i 0.265699 + 0.0990987i
\(631\) 506.946 0.803401 0.401700 0.915771i \(-0.368419\pi\)
0.401700 + 0.915771i \(0.368419\pi\)
\(632\) 3190.86 5.04883
\(633\) 36.5547i 0.0577483i
\(634\) −315.271 −0.497273
\(635\) 96.2947i 0.151645i
\(636\) 1486.06i 2.33658i
\(637\) 543.652 627.425i 0.853457 0.984969i
\(638\) 754.600 1.18276
\(639\) −142.964 −0.223731
\(640\) 546.747i 0.854293i
\(641\) 537.896 0.839152 0.419576 0.907720i \(-0.362179\pi\)
0.419576 + 0.907720i \(0.362179\pi\)
\(642\) 578.571i 0.901202i
\(643\) 673.330i 1.04717i 0.851973 + 0.523585i \(0.175406\pi\)
−0.851973 + 0.523585i \(0.824594\pi\)
\(644\) 266.134 713.547i 0.413251 1.10799i
\(645\) 22.6412 0.0351026
\(646\) 925.104 1.43205
\(647\) 1082.21i 1.67266i 0.548224 + 0.836332i \(0.315304\pi\)
−0.548224 + 0.836332i \(0.684696\pi\)
\(648\) −221.713 −0.342149
\(649\) 508.138i 0.782956i
\(650\) 322.301i 0.495848i
\(651\) −179.809 + 482.096i −0.276204 + 0.740547i
\(652\) 109.241 0.167547
\(653\) −491.429 −0.752571 −0.376285 0.926504i \(-0.622799\pi\)
−0.376285 + 0.926504i \(0.622799\pi\)
\(654\) 856.749i 1.31001i
\(655\) 1.53558 0.00234439
\(656\) 1492.88i 2.27574i
\(657\) 377.900i 0.575191i
\(658\) −262.040 97.7339i −0.398237 0.148532i
\(659\) 248.373 0.376893 0.188447 0.982083i \(-0.439655\pi\)
0.188447 + 0.982083i \(0.439655\pi\)
\(660\) −586.184 −0.888158
\(661\) 681.545i 1.03108i −0.856865 0.515541i \(-0.827591\pi\)
0.856865 0.515541i \(-0.172409\pi\)
\(662\) 1717.74 2.59477
\(663\) 381.765i 0.575814i
\(664\) 1051.67i 1.58385i
\(665\) −102.237 + 274.113i −0.153739 + 0.412200i
\(666\) 328.072 0.492601
\(667\) −142.569 −0.213747
\(668\) 793.584i 1.18800i
\(669\) −507.559 −0.758683
\(670\) 403.791i 0.602672i
\(671\) 989.499i 1.47466i
\(672\) −1120.50 417.917i −1.66741 0.621900i
\(673\) 86.1498 0.128009 0.0640043 0.997950i \(-0.479613\pi\)
0.0640043 + 0.997950i \(0.479613\pi\)
\(674\) −776.737 −1.15243
\(675\) 25.9808i 0.0384900i
\(676\) −1236.63 −1.82933
\(677\) 793.846i 1.17259i 0.810096 + 0.586297i \(0.199415\pi\)
−0.810096 + 0.586297i \(0.800585\pi\)
\(678\) 1045.12i 1.54147i
\(679\) 188.437 + 70.2819i 0.277521 + 0.103508i
\(680\) 716.615 1.05385
\(681\) −128.056 −0.188041
\(682\) 2332.93i 3.42072i
\(683\) −186.736 −0.273406 −0.136703 0.990612i \(-0.543651\pi\)
−0.136703 + 0.990612i \(0.543651\pi\)
\(684\) 587.359i 0.858712i
\(685\) 170.407i 0.248770i
\(686\) 1145.34 625.433i 1.66959 0.911709i
\(687\) 404.461 0.588736
\(688\) −302.968 −0.440361
\(689\) 1387.73i 2.01413i
\(690\) 153.041 0.221799
\(691\) 1030.46i 1.49126i 0.666361 + 0.745630i \(0.267851\pi\)
−0.666361 + 0.745630i \(0.732149\pi\)
\(692\) 3413.20i 4.93238i
\(693\) −106.035 + 284.297i −0.153009 + 0.410240i
\(694\) −557.727 −0.803642
\(695\) 109.667 0.157794
\(696\) 585.709i 0.841535i
\(697\) 374.745 0.537654
\(698\) 43.5450i 0.0623854i
\(699\) 667.582i 0.955054i
\(700\) −128.120 + 343.510i −0.183028 + 0.490728i
\(701\) −1143.88 −1.63179 −0.815893 0.578203i \(-0.803754\pi\)
−0.815893 + 0.578203i \(0.803754\pi\)
\(702\) −334.945 −0.477130
\(703\) 537.239i 0.764210i
\(704\) 2426.98 3.44741
\(705\) 40.6714i 0.0576899i
\(706\) 676.521i 0.958246i
\(707\) −81.7267 30.4818i −0.115596 0.0431143i
\(708\) −638.060 −0.901214
\(709\) −316.757 −0.446766 −0.223383 0.974731i \(-0.571710\pi\)
−0.223383 + 0.974731i \(0.571710\pi\)
\(710\) 405.416i 0.571008i
\(711\) 388.580 0.546526
\(712\) 628.996i 0.883422i
\(713\) 440.769i 0.618190i
\(714\) 209.708 562.261i 0.293709 0.787480i
\(715\) −547.397 −0.765591
\(716\) −323.902 −0.452377
\(717\) 705.590i 0.984087i
\(718\) −2484.71 −3.46059
\(719\) 1145.95i 1.59381i 0.604104 + 0.796906i \(0.293531\pi\)
−0.604104 + 0.796906i \(0.706469\pi\)
\(720\) 347.656i 0.482855i
\(721\) −252.374 94.1288i −0.350034 0.130553i
\(722\) −44.3325 −0.0614024
\(723\) 470.799 0.651174
\(724\) 2214.44i 3.05862i
\(725\) 68.6345 0.0946683
\(726\) 578.389i 0.796679i
\(727\) 149.829i 0.206093i 0.994677 + 0.103046i \(0.0328590\pi\)
−0.994677 + 0.103046i \(0.967141\pi\)
\(728\) −2737.45 1021.00i −3.76024 1.40247i
\(729\) −27.0000 −0.0370370
\(730\) −1071.64 −1.46800
\(731\) 76.0512i 0.104037i
\(732\) 1242.49 1.69740
\(733\) 70.3231i 0.0959388i 0.998849 + 0.0479694i \(0.0152750\pi\)
−0.998849 + 0.0479694i \(0.984725\pi\)
\(734\) 1775.35i 2.41873i
\(735\) 143.425 + 124.275i 0.195136 + 0.169082i
\(736\) −1024.45 −1.39191
\(737\) 685.799 0.930528
\(738\) 328.786i 0.445509i
\(739\) 774.145 1.04756 0.523779 0.851854i \(-0.324522\pi\)
0.523779 + 0.851854i \(0.324522\pi\)
\(740\) 673.252i 0.909800i
\(741\) 548.495i 0.740209i
\(742\) −762.299 + 2043.84i −1.02736 + 2.75451i
\(743\) 1071.79 1.44252 0.721260 0.692665i \(-0.243563\pi\)
0.721260 + 0.692665i \(0.243563\pi\)
\(744\) 1810.78 2.43385
\(745\) 541.898i 0.727380i
\(746\) 1719.99 2.30562
\(747\) 128.072i 0.171448i
\(748\) 1968.98i 2.63233i
\(749\) −214.773 + 575.841i −0.286747 + 0.768813i
\(750\) −73.6758 −0.0982344
\(751\) 361.789 0.481742 0.240871 0.970557i \(-0.422567\pi\)
0.240871 + 0.970557i \(0.422567\pi\)
\(752\) 544.235i 0.723717i
\(753\) 765.999 1.01726
\(754\) 884.839i 1.17353i
\(755\) 240.833i 0.318985i
\(756\) −356.986 133.146i −0.472203 0.176119i
\(757\) 812.552 1.07338 0.536692 0.843778i \(-0.319674\pi\)
0.536692 + 0.843778i \(0.319674\pi\)
\(758\) −1242.12 −1.63868
\(759\) 259.926i 0.342458i
\(760\) 1029.59 1.35472
\(761\) 728.812i 0.957703i 0.877896 + 0.478851i \(0.158947\pi\)
−0.877896 + 0.478851i \(0.841053\pi\)
\(762\) 283.784i 0.372419i
\(763\) 318.036 852.706i 0.416824 1.11757i
\(764\) 1174.17 1.53688
\(765\) 87.2688 0.114077
\(766\) 1450.55i 1.89367i
\(767\) −595.840 −0.776845
\(768\) 447.553i 0.582751i
\(769\) 624.378i 0.811935i 0.913888 + 0.405967i \(0.133065\pi\)
−0.913888 + 0.405967i \(0.866935\pi\)
\(770\) −806.203 300.692i −1.04702 0.390509i
\(771\) 676.255 0.877115
\(772\) −3074.84 −3.98296
\(773\) 34.6106i 0.0447744i −0.999749 0.0223872i \(-0.992873\pi\)
0.999749 0.0223872i \(-0.00712666\pi\)
\(774\) −66.7243 −0.0862071
\(775\) 212.191i 0.273795i
\(776\) 707.781i 0.912089i
\(777\) 326.524 + 121.785i 0.420237 + 0.156737i
\(778\) 261.925 0.336665
\(779\) 538.408 0.691153
\(780\) 687.357i 0.881226i
\(781\) 688.559 0.881638
\(782\) 514.062i 0.657368i
\(783\) 71.3271i 0.0910946i
\(784\) −1919.21 1662.96i −2.44797 2.12112i
\(785\) −170.318 −0.216965
\(786\) −4.52539 −0.00575750
\(787\)