Properties

Label 483.3.f.a.22.10
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.10
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.9

$q$-expansion

\(f(q)\) \(=\) \(q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-2.89983 q^{2} +1.73205 q^{3} +4.40899 q^{4} +7.66563i q^{5} -5.02265 q^{6} +2.64575i q^{7} -1.18601 q^{8} +3.00000 q^{9} -22.2290i q^{10} -21.3601i q^{11} +7.63660 q^{12} -24.5575 q^{13} -7.67222i q^{14} +13.2773i q^{15} -14.1967 q^{16} -23.1246i q^{17} -8.69948 q^{18} -14.5030i q^{19} +33.7977i q^{20} +4.58258i q^{21} +61.9405i q^{22} +(19.0162 - 12.9377i) q^{23} -2.05424 q^{24} -33.7618 q^{25} +71.2125 q^{26} +5.19615 q^{27} +11.6651i q^{28} +20.1704 q^{29} -38.5017i q^{30} +48.4690 q^{31} +45.9122 q^{32} -36.9967i q^{33} +67.0573i q^{34} -20.2813 q^{35} +13.2270 q^{36} +36.8319i q^{37} +42.0562i q^{38} -42.5348 q^{39} -9.09154i q^{40} -15.4070 q^{41} -13.2887i q^{42} -55.7126i q^{43} -94.1765i q^{44} +22.9969i q^{45} +(-55.1437 + 37.5170i) q^{46} -60.0964 q^{47} -24.5895 q^{48} -7.00000 q^{49} +97.9035 q^{50} -40.0530i q^{51} -108.274 q^{52} -14.8057i q^{53} -15.0679 q^{54} +163.738 q^{55} -3.13790i q^{56} -25.1199i q^{57} -58.4906 q^{58} +95.6217 q^{59} +58.5393i q^{60} +24.7832i q^{61} -140.552 q^{62} +7.93725i q^{63} -76.3503 q^{64} -188.249i q^{65} +107.284i q^{66} -28.9116i q^{67} -101.956i q^{68} +(32.9371 - 22.4087i) q^{69} +58.8124 q^{70} +38.7353 q^{71} -3.55804 q^{72} -71.3117 q^{73} -106.806i q^{74} -58.4772 q^{75} -63.9436i q^{76} +56.5135 q^{77} +123.344 q^{78} +13.8494i q^{79} -108.827i q^{80} +9.00000 q^{81} +44.6777 q^{82} -9.87591i q^{83} +20.2046i q^{84} +177.265 q^{85} +161.557i q^{86} +34.9361 q^{87} +25.3333i q^{88} -17.9357i q^{89} -66.6870i q^{90} -64.9730i q^{91} +(83.8424 - 57.0421i) q^{92} +83.9507 q^{93} +174.269 q^{94} +111.175 q^{95} +79.5222 q^{96} +43.6587i q^{97} +20.2988 q^{98} -64.0802i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.89983 −1.44991 −0.724957 0.688794i \(-0.758140\pi\)
−0.724957 + 0.688794i \(0.758140\pi\)
\(3\) 1.73205 0.577350
\(4\) 4.40899 1.10225
\(5\) 7.66563i 1.53313i 0.642169 + 0.766563i \(0.278035\pi\)
−0.642169 + 0.766563i \(0.721965\pi\)
\(6\) −5.02265 −0.837108
\(7\) 2.64575i 0.377964i
\(8\) −1.18601 −0.148252
\(9\) 3.00000 0.333333
\(10\) 22.2290i 2.22290i
\(11\) 21.3601i 1.94183i −0.239434 0.970913i \(-0.576962\pi\)
0.239434 0.970913i \(-0.423038\pi\)
\(12\) 7.63660 0.636384
\(13\) −24.5575 −1.88904 −0.944519 0.328458i \(-0.893471\pi\)
−0.944519 + 0.328458i \(0.893471\pi\)
\(14\) 7.67222i 0.548016i
\(15\) 13.2773i 0.885150i
\(16\) −14.1967 −0.887297
\(17\) 23.1246i 1.36027i −0.733087 0.680135i \(-0.761921\pi\)
0.733087 0.680135i \(-0.238079\pi\)
\(18\) −8.69948 −0.483304
\(19\) 14.5030i 0.763316i −0.924304 0.381658i \(-0.875353\pi\)
0.924304 0.381658i \(-0.124647\pi\)
\(20\) 33.7977i 1.68989i
\(21\) 4.58258i 0.218218i
\(22\) 61.9405i 2.81548i
\(23\) 19.0162 12.9377i 0.826792 0.562508i
\(24\) −2.05424 −0.0855932
\(25\) −33.7618 −1.35047
\(26\) 71.2125 2.73894
\(27\) 5.19615 0.192450
\(28\) 11.6651i 0.416611i
\(29\) 20.1704 0.695531 0.347765 0.937582i \(-0.386941\pi\)
0.347765 + 0.937582i \(0.386941\pi\)
\(30\) 38.5017i 1.28339i
\(31\) 48.4690 1.56352 0.781758 0.623582i \(-0.214323\pi\)
0.781758 + 0.623582i \(0.214323\pi\)
\(32\) 45.9122 1.43475
\(33\) 36.9967i 1.12111i
\(34\) 67.0573i 1.97227i
\(35\) −20.2813 −0.579467
\(36\) 13.2270 0.367416
\(37\) 36.8319i 0.995457i 0.867333 + 0.497729i \(0.165832\pi\)
−0.867333 + 0.497729i \(0.834168\pi\)
\(38\) 42.0562i 1.10674i
\(39\) −42.5348 −1.09064
\(40\) 9.09154i 0.227288i
\(41\) −15.4070 −0.375781 −0.187890 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(42\) 13.2887i 0.316397i
\(43\) 55.7126i 1.29564i −0.761792 0.647821i \(-0.775680\pi\)
0.761792 0.647821i \(-0.224320\pi\)
\(44\) 94.1765i 2.14037i
\(45\) 22.9969i 0.511042i
\(46\) −55.1437 + 37.5170i −1.19878 + 0.815587i
\(47\) −60.0964 −1.27865 −0.639324 0.768938i \(-0.720786\pi\)
−0.639324 + 0.768938i \(0.720786\pi\)
\(48\) −24.5895 −0.512281
\(49\) −7.00000 −0.142857
\(50\) 97.9035 1.95807
\(51\) 40.0530i 0.785352i
\(52\) −108.274 −2.08219
\(53\) 14.8057i 0.279353i −0.990197 0.139677i \(-0.955394\pi\)
0.990197 0.139677i \(-0.0446063\pi\)
\(54\) −15.0679 −0.279036
\(55\) 163.738 2.97706
\(56\) 3.13790i 0.0560339i
\(57\) 25.1199i 0.440701i
\(58\) −58.4906 −1.00846
\(59\) 95.6217 1.62071 0.810353 0.585942i \(-0.199275\pi\)
0.810353 + 0.585942i \(0.199275\pi\)
\(60\) 58.5393i 0.975656i
\(61\) 24.7832i 0.406281i 0.979150 + 0.203141i \(0.0651149\pi\)
−0.979150 + 0.203141i \(0.934885\pi\)
\(62\) −140.552 −2.26696
\(63\) 7.93725i 0.125988i
\(64\) −76.3503 −1.19297
\(65\) 188.249i 2.89613i
\(66\) 107.284i 1.62552i
\(67\) 28.9116i 0.431517i −0.976447 0.215758i \(-0.930778\pi\)
0.976447 0.215758i \(-0.0692223\pi\)
\(68\) 101.956i 1.49936i
\(69\) 32.9371 22.4087i 0.477349 0.324764i
\(70\) 58.8124 0.840177
\(71\) 38.7353 0.545567 0.272784 0.962075i \(-0.412056\pi\)
0.272784 + 0.962075i \(0.412056\pi\)
\(72\) −3.55804 −0.0494172
\(73\) −71.3117 −0.976873 −0.488437 0.872599i \(-0.662433\pi\)
−0.488437 + 0.872599i \(0.662433\pi\)
\(74\) 106.806i 1.44333i
\(75\) −58.4772 −0.779696
\(76\) 63.9436i 0.841364i
\(77\) 56.5135 0.733941
\(78\) 123.344 1.58133
\(79\) 13.8494i 0.175309i 0.996151 + 0.0876545i \(0.0279372\pi\)
−0.996151 + 0.0876545i \(0.972063\pi\)
\(80\) 108.827i 1.36034i
\(81\) 9.00000 0.111111
\(82\) 44.6777 0.544850
\(83\) 9.87591i 0.118987i −0.998229 0.0594934i \(-0.981051\pi\)
0.998229 0.0594934i \(-0.0189485\pi\)
\(84\) 20.2046i 0.240530i
\(85\) 177.265 2.08546
\(86\) 161.557i 1.87857i
\(87\) 34.9361 0.401565
\(88\) 25.3333i 0.287879i
\(89\) 17.9357i 0.201525i −0.994911 0.100763i \(-0.967872\pi\)
0.994911 0.100763i \(-0.0321282\pi\)
\(90\) 66.6870i 0.740966i
\(91\) 64.9730i 0.713989i
\(92\) 83.8424 57.0421i 0.911331 0.620023i
\(93\) 83.9507 0.902696
\(94\) 174.269 1.85393
\(95\) 111.175 1.17026
\(96\) 79.5222 0.828356
\(97\) 43.6587i 0.450089i 0.974348 + 0.225045i \(0.0722528\pi\)
−0.974348 + 0.225045i \(0.927747\pi\)
\(98\) 20.2988 0.207130
\(99\) 64.0802i 0.647275i
\(100\) −148.856 −1.48856
\(101\) −30.6066 −0.303036 −0.151518 0.988454i \(-0.548416\pi\)
−0.151518 + 0.988454i \(0.548416\pi\)
\(102\) 116.147i 1.13869i
\(103\) 50.1044i 0.486450i −0.969970 0.243225i \(-0.921795\pi\)
0.969970 0.243225i \(-0.0782054\pi\)
\(104\) 29.1255 0.280053
\(105\) −35.1283 −0.334555
\(106\) 42.9340i 0.405038i
\(107\) 78.8462i 0.736881i −0.929651 0.368440i \(-0.879892\pi\)
0.929651 0.368440i \(-0.120108\pi\)
\(108\) 22.9098 0.212128
\(109\) 149.793i 1.37425i −0.726539 0.687125i \(-0.758872\pi\)
0.726539 0.687125i \(-0.241128\pi\)
\(110\) −474.813 −4.31648
\(111\) 63.7947i 0.574727i
\(112\) 37.5611i 0.335367i
\(113\) 49.6484i 0.439366i 0.975571 + 0.219683i \(0.0705024\pi\)
−0.975571 + 0.219683i \(0.929498\pi\)
\(114\) 72.8434i 0.638978i
\(115\) 99.1754 + 145.771i 0.862395 + 1.26758i
\(116\) 88.9311 0.766648
\(117\) −73.6725 −0.629679
\(118\) −277.286 −2.34988
\(119\) 61.1819 0.514134
\(120\) 15.7470i 0.131225i
\(121\) −335.253 −2.77069
\(122\) 71.8669i 0.589073i
\(123\) −26.6857 −0.216957
\(124\) 213.699 1.72338
\(125\) 67.1650i 0.537320i
\(126\) 23.0167i 0.182672i
\(127\) −22.9804 −0.180948 −0.0904740 0.995899i \(-0.528838\pi\)
−0.0904740 + 0.995899i \(0.528838\pi\)
\(128\) 37.7540 0.294953
\(129\) 96.4971i 0.748039i
\(130\) 545.888i 4.19914i
\(131\) 112.596 0.859509 0.429755 0.902946i \(-0.358600\pi\)
0.429755 + 0.902946i \(0.358600\pi\)
\(132\) 163.118i 1.23575i
\(133\) 38.3713 0.288506
\(134\) 83.8387i 0.625662i
\(135\) 39.8318i 0.295050i
\(136\) 27.4261i 0.201662i
\(137\) 66.0321i 0.481986i −0.970527 0.240993i \(-0.922527\pi\)
0.970527 0.240993i \(-0.0774731\pi\)
\(138\) −95.5118 + 64.9814i −0.692114 + 0.470879i
\(139\) −173.970 −1.25159 −0.625793 0.779989i \(-0.715224\pi\)
−0.625793 + 0.779989i \(0.715224\pi\)
\(140\) −89.4203 −0.638717
\(141\) −104.090 −0.738228
\(142\) −112.326 −0.791025
\(143\) 524.550i 3.66818i
\(144\) −42.5902 −0.295766
\(145\) 154.619i 1.06634i
\(146\) 206.792 1.41638
\(147\) −12.1244 −0.0824786
\(148\) 162.392i 1.09724i
\(149\) 147.220i 0.988054i −0.869446 0.494027i \(-0.835524\pi\)
0.869446 0.494027i \(-0.164476\pi\)
\(150\) 169.574 1.13049
\(151\) −0.584214 −0.00386897 −0.00193448 0.999998i \(-0.500616\pi\)
−0.00193448 + 0.999998i \(0.500616\pi\)
\(152\) 17.2008i 0.113163i
\(153\) 69.3738i 0.453423i
\(154\) −163.879 −1.06415
\(155\) 371.545i 2.39707i
\(156\) −187.536 −1.20215
\(157\) 0.0946435i 0.000602825i −1.00000 0.000301412i \(-0.999904\pi\)
1.00000 0.000301412i \(-9.59425e-5\pi\)
\(158\) 40.1609i 0.254183i
\(159\) 25.6443i 0.161285i
\(160\) 351.945i 2.19966i
\(161\) 34.2299 + 50.3122i 0.212608 + 0.312498i
\(162\) −26.0984 −0.161101
\(163\) 31.6600 0.194233 0.0971167 0.995273i \(-0.469038\pi\)
0.0971167 + 0.995273i \(0.469038\pi\)
\(164\) −67.9294 −0.414204
\(165\) 283.603 1.71881
\(166\) 28.6384i 0.172521i
\(167\) 129.452 0.775159 0.387579 0.921836i \(-0.373311\pi\)
0.387579 + 0.921836i \(0.373311\pi\)
\(168\) 5.43500i 0.0323512i
\(169\) 434.070 2.56846
\(170\) −514.036 −3.02374
\(171\) 43.5090i 0.254439i
\(172\) 245.637i 1.42812i
\(173\) −191.724 −1.10823 −0.554117 0.832439i \(-0.686944\pi\)
−0.554117 + 0.832439i \(0.686944\pi\)
\(174\) −101.309 −0.582234
\(175\) 89.3254i 0.510431i
\(176\) 303.244i 1.72297i
\(177\) 165.622 0.935715
\(178\) 52.0105i 0.292194i
\(179\) 82.4216 0.460456 0.230228 0.973137i \(-0.426053\pi\)
0.230228 + 0.973137i \(0.426053\pi\)
\(180\) 101.393i 0.563295i
\(181\) 198.224i 1.09516i −0.836752 0.547581i \(-0.815549\pi\)
0.836752 0.547581i \(-0.184451\pi\)
\(182\) 188.410i 1.03522i
\(183\) 42.9257i 0.234567i
\(184\) −22.5535 + 15.3443i −0.122573 + 0.0833927i
\(185\) −282.340 −1.52616
\(186\) −243.443 −1.30883
\(187\) −493.943 −2.64141
\(188\) −264.965 −1.40939
\(189\) 13.7477i 0.0727393i
\(190\) −322.387 −1.69677
\(191\) 291.406i 1.52569i −0.646583 0.762843i \(-0.723803\pi\)
0.646583 0.762843i \(-0.276197\pi\)
\(192\) −132.243 −0.688764
\(193\) −141.629 −0.733827 −0.366913 0.930255i \(-0.619585\pi\)
−0.366913 + 0.930255i \(0.619585\pi\)
\(194\) 126.603i 0.652590i
\(195\) 326.056i 1.67208i
\(196\) −30.8630 −0.157464
\(197\) 225.553 1.14494 0.572470 0.819926i \(-0.305985\pi\)
0.572470 + 0.819926i \(0.305985\pi\)
\(198\) 185.822i 0.938493i
\(199\) 76.0047i 0.381933i −0.981597 0.190967i \(-0.938838\pi\)
0.981597 0.190967i \(-0.0611622\pi\)
\(200\) 40.0420 0.200210
\(201\) 50.0764i 0.249136i
\(202\) 88.7540 0.439376
\(203\) 53.3658i 0.262886i
\(204\) 176.593i 0.865654i
\(205\) 118.104i 0.576119i
\(206\) 145.294i 0.705311i
\(207\) 57.0487 38.8130i 0.275597 0.187503i
\(208\) 348.636 1.67614
\(209\) −309.785 −1.48223
\(210\) 101.866 0.485076
\(211\) 64.3162 0.304816 0.152408 0.988318i \(-0.451297\pi\)
0.152408 + 0.988318i \(0.451297\pi\)
\(212\) 65.2783i 0.307917i
\(213\) 67.0915 0.314983
\(214\) 228.640i 1.06841i
\(215\) 427.072 1.98638
\(216\) −6.16271 −0.0285311
\(217\) 128.237i 0.590953i
\(218\) 434.375i 1.99254i
\(219\) −123.516 −0.563998
\(220\) 721.922 3.28146
\(221\) 567.882i 2.56960i
\(222\) 184.994i 0.833305i
\(223\) −206.293 −0.925080 −0.462540 0.886598i \(-0.653062\pi\)
−0.462540 + 0.886598i \(0.653062\pi\)
\(224\) 121.472i 0.542286i
\(225\) −101.286 −0.450158
\(226\) 143.972i 0.637043i
\(227\) 295.776i 1.30298i −0.758659 0.651488i \(-0.774145\pi\)
0.758659 0.651488i \(-0.225855\pi\)
\(228\) 110.754i 0.485762i
\(229\) 35.2342i 0.153861i 0.997036 + 0.0769305i \(0.0245120\pi\)
−0.997036 + 0.0769305i \(0.975488\pi\)
\(230\) −287.591 422.711i −1.25040 1.83788i
\(231\) 97.8842 0.423741
\(232\) −23.9224 −0.103114
\(233\) 99.8965 0.428740 0.214370 0.976752i \(-0.431230\pi\)
0.214370 + 0.976752i \(0.431230\pi\)
\(234\) 213.637 0.912980
\(235\) 460.677i 1.96033i
\(236\) 421.596 1.78642
\(237\) 23.9879i 0.101215i
\(238\) −177.417 −0.745449
\(239\) −352.484 −1.47483 −0.737415 0.675440i \(-0.763954\pi\)
−0.737415 + 0.675440i \(0.763954\pi\)
\(240\) 188.494i 0.785391i
\(241\) 263.827i 1.09472i 0.836898 + 0.547359i \(0.184367\pi\)
−0.836898 + 0.547359i \(0.815633\pi\)
\(242\) 972.175 4.01725
\(243\) 15.5885 0.0641500
\(244\) 109.269i 0.447823i
\(245\) 53.6594i 0.219018i
\(246\) 77.3840 0.314569
\(247\) 356.157i 1.44193i
\(248\) −57.4849 −0.231794
\(249\) 17.1056i 0.0686971i
\(250\) 194.767i 0.779067i
\(251\) 167.791i 0.668492i −0.942486 0.334246i \(-0.891518\pi\)
0.942486 0.334246i \(-0.108482\pi\)
\(252\) 34.9953i 0.138870i
\(253\) −276.350 406.188i −1.09229 1.60549i
\(254\) 66.6391 0.262359
\(255\) 307.031 1.20404
\(256\) 195.921 0.765317
\(257\) −70.2520 −0.273354 −0.136677 0.990616i \(-0.543642\pi\)
−0.136677 + 0.990616i \(0.543642\pi\)
\(258\) 279.825i 1.08459i
\(259\) −97.4481 −0.376247
\(260\) 829.987i 3.19226i
\(261\) 60.5112 0.231844
\(262\) −326.508 −1.24621
\(263\) 35.7078i 0.135771i −0.997693 0.0678855i \(-0.978375\pi\)
0.997693 0.0678855i \(-0.0216253\pi\)
\(264\) 43.8786i 0.166207i
\(265\) 113.495 0.428283
\(266\) −111.270 −0.418309
\(267\) 31.0656i 0.116351i
\(268\) 127.471i 0.475639i
\(269\) −61.0645 −0.227006 −0.113503 0.993538i \(-0.536207\pi\)
−0.113503 + 0.993538i \(0.536207\pi\)
\(270\) 115.505i 0.427797i
\(271\) 79.3467 0.292792 0.146396 0.989226i \(-0.453233\pi\)
0.146396 + 0.989226i \(0.453233\pi\)
\(272\) 328.294i 1.20696i
\(273\) 112.537i 0.412222i
\(274\) 191.482i 0.698838i
\(275\) 721.155i 2.62238i
\(276\) 145.219 98.7999i 0.526157 0.357971i
\(277\) −9.47197 −0.0341948 −0.0170974 0.999854i \(-0.505443\pi\)
−0.0170974 + 0.999854i \(0.505443\pi\)
\(278\) 504.484 1.81469
\(279\) 145.407 0.521172
\(280\) 24.0539 0.0859070
\(281\) 200.842i 0.714741i −0.933963 0.357371i \(-0.883673\pi\)
0.933963 0.357371i \(-0.116327\pi\)
\(282\) 301.843 1.07037
\(283\) 323.221i 1.14212i −0.820907 0.571062i \(-0.806532\pi\)
0.820907 0.571062i \(-0.193468\pi\)
\(284\) 170.784 0.601351
\(285\) 192.560 0.675649
\(286\) 1521.10i 5.31854i
\(287\) 40.7631i 0.142032i
\(288\) 137.736 0.478252
\(289\) −245.747 −0.850335
\(290\) 448.367i 1.54609i
\(291\) 75.6190i 0.259859i
\(292\) −314.413 −1.07676
\(293\) 312.073i 1.06510i 0.846400 + 0.532548i \(0.178765\pi\)
−0.846400 + 0.532548i \(0.821235\pi\)
\(294\) 35.1585 0.119587
\(295\) 733.000i 2.48475i
\(296\) 43.6831i 0.147578i
\(297\) 110.990i 0.373704i
\(298\) 426.913i 1.43259i
\(299\) −466.991 + 317.717i −1.56184 + 1.06260i
\(300\) −257.826 −0.859419
\(301\) 147.402 0.489707
\(302\) 1.69412 0.00560966
\(303\) −53.0123 −0.174958
\(304\) 205.895i 0.677287i
\(305\) −189.979 −0.622880
\(306\) 201.172i 0.657425i
\(307\) 256.912 0.836847 0.418423 0.908252i \(-0.362583\pi\)
0.418423 + 0.908252i \(0.362583\pi\)
\(308\) 249.168 0.808985
\(309\) 86.7833i 0.280852i
\(310\) 1077.42i 3.47554i
\(311\) −302.391 −0.972319 −0.486160 0.873870i \(-0.661603\pi\)
−0.486160 + 0.873870i \(0.661603\pi\)
\(312\) 50.4469 0.161689
\(313\) 443.127i 1.41574i 0.706343 + 0.707870i \(0.250344\pi\)
−0.706343 + 0.707870i \(0.749656\pi\)
\(314\) 0.274450i 0.000874043i
\(315\) −60.8440 −0.193156
\(316\) 61.0620i 0.193234i
\(317\) 29.6095 0.0934053 0.0467027 0.998909i \(-0.485129\pi\)
0.0467027 + 0.998909i \(0.485129\pi\)
\(318\) 74.3639i 0.233849i
\(319\) 430.841i 1.35060i
\(320\) 585.273i 1.82898i
\(321\) 136.566i 0.425438i
\(322\) −99.2607 145.897i −0.308263 0.453095i
\(323\) −335.376 −1.03832
\(324\) 39.6810 0.122472
\(325\) 829.106 2.55110
\(326\) −91.8086 −0.281622
\(327\) 259.450i 0.793424i
\(328\) 18.2729 0.0557101
\(329\) 159.000i 0.483283i
\(330\) −822.400 −2.49212
\(331\) 166.644 0.503455 0.251728 0.967798i \(-0.419001\pi\)
0.251728 + 0.967798i \(0.419001\pi\)
\(332\) 43.5428i 0.131153i
\(333\) 110.496i 0.331819i
\(334\) −375.387 −1.12391
\(335\) 221.626 0.661569
\(336\) 65.0577i 0.193624i
\(337\) 373.572i 1.10852i −0.832342 0.554262i \(-0.813001\pi\)
0.832342 0.554262i \(-0.186999\pi\)
\(338\) −1258.73 −3.72405
\(339\) 85.9936i 0.253668i
\(340\) 781.558 2.29870
\(341\) 1035.30i 3.03607i
\(342\) 126.169i 0.368914i
\(343\) 18.5203i 0.0539949i
\(344\) 66.0759i 0.192081i
\(345\) 171.777 + 252.483i 0.497904 + 0.731835i
\(346\) 555.967 1.60684
\(347\) 247.289 0.712648 0.356324 0.934362i \(-0.384030\pi\)
0.356324 + 0.934362i \(0.384030\pi\)
\(348\) 154.033 0.442624
\(349\) 427.280 1.22430 0.612149 0.790743i \(-0.290305\pi\)
0.612149 + 0.790743i \(0.290305\pi\)
\(350\) 259.028i 0.740081i
\(351\) −127.604 −0.363545
\(352\) 980.687i 2.78604i
\(353\) −461.657 −1.30781 −0.653906 0.756576i \(-0.726871\pi\)
−0.653906 + 0.756576i \(0.726871\pi\)
\(354\) −480.274 −1.35671
\(355\) 296.930i 0.836423i
\(356\) 79.0785i 0.222131i
\(357\) 105.970 0.296835
\(358\) −239.008 −0.667621
\(359\) 280.808i 0.782195i −0.920349 0.391097i \(-0.872096\pi\)
0.920349 0.391097i \(-0.127904\pi\)
\(360\) 27.2746i 0.0757628i
\(361\) 150.663 0.417349
\(362\) 574.816i 1.58789i
\(363\) −580.675 −1.59966
\(364\) 286.466i 0.786993i
\(365\) 546.649i 1.49767i
\(366\) 124.477i 0.340101i
\(367\) 712.423i 1.94121i 0.240681 + 0.970604i \(0.422629\pi\)
−0.240681 + 0.970604i \(0.577371\pi\)
\(368\) −269.968 + 183.673i −0.733610 + 0.499111i
\(369\) −46.2210 −0.125260
\(370\) 818.736 2.21280
\(371\) 39.1722 0.105586
\(372\) 370.138 0.994996
\(373\) 601.055i 1.61141i 0.592319 + 0.805704i \(0.298213\pi\)
−0.592319 + 0.805704i \(0.701787\pi\)
\(374\) 1432.35 3.82981
\(375\) 116.333i 0.310222i
\(376\) 71.2752 0.189562
\(377\) −495.334 −1.31388
\(378\) 39.8660i 0.105466i
\(379\) 495.803i 1.30819i −0.756414 0.654093i \(-0.773050\pi\)
0.756414 0.654093i \(-0.226950\pi\)
\(380\) 490.168 1.28992
\(381\) −39.8032 −0.104470
\(382\) 845.027i 2.21211i
\(383\) 189.048i 0.493599i 0.969067 + 0.246799i \(0.0793789\pi\)
−0.969067 + 0.246799i \(0.920621\pi\)
\(384\) 65.3919 0.170291
\(385\) 433.211i 1.12522i
\(386\) 410.698 1.06399
\(387\) 167.138i 0.431881i
\(388\) 192.491i 0.496110i
\(389\) 187.187i 0.481201i −0.970624 0.240601i \(-0.922656\pi\)
0.970624 0.240601i \(-0.0773444\pi\)
\(390\) 945.506i 2.42437i
\(391\) −299.178 439.742i −0.765162 1.12466i
\(392\) 8.30210 0.0211788
\(393\) 195.021 0.496238
\(394\) −654.065 −1.66006
\(395\) −106.164 −0.268771
\(396\) 282.529i 0.713458i
\(397\) 739.527 1.86279 0.931394 0.364012i \(-0.118593\pi\)
0.931394 + 0.364012i \(0.118593\pi\)
\(398\) 220.401i 0.553770i
\(399\) 66.4611 0.166569
\(400\) 479.308 1.19827
\(401\) 270.705i 0.675076i 0.941312 + 0.337538i \(0.109594\pi\)
−0.941312 + 0.337538i \(0.890406\pi\)
\(402\) 145.213i 0.361226i
\(403\) −1190.28 −2.95354
\(404\) −134.945 −0.334021
\(405\) 68.9906i 0.170347i
\(406\) 154.752i 0.381162i
\(407\) 786.733 1.93300
\(408\) 47.5034i 0.116430i
\(409\) −135.282 −0.330764 −0.165382 0.986230i \(-0.552886\pi\)
−0.165382 + 0.986230i \(0.552886\pi\)
\(410\) 342.482i 0.835323i
\(411\) 114.371i 0.278275i
\(412\) 220.910i 0.536189i
\(413\) 252.991i 0.612570i
\(414\) −165.431 + 112.551i −0.399592 + 0.271862i
\(415\) 75.7050 0.182422
\(416\) −1127.49 −2.71031
\(417\) −301.326 −0.722603
\(418\) 898.323 2.14910
\(419\) 482.244i 1.15094i 0.817823 + 0.575470i \(0.195181\pi\)
−0.817823 + 0.575470i \(0.804819\pi\)
\(420\) −154.881 −0.368763
\(421\) 267.087i 0.634410i −0.948357 0.317205i \(-0.897256\pi\)
0.948357 0.317205i \(-0.102744\pi\)
\(422\) −186.506 −0.441957
\(423\) −180.289 −0.426216
\(424\) 17.5598i 0.0414146i
\(425\) 780.729i 1.83701i
\(426\) −194.554 −0.456699
\(427\) −65.5701 −0.153560
\(428\) 347.633i 0.812226i
\(429\) 908.547i 2.11782i
\(430\) −1238.44 −2.88008
\(431\) 147.922i 0.343207i −0.985166 0.171603i \(-0.945105\pi\)
0.985166 0.171603i \(-0.0548947\pi\)
\(432\) −73.7684 −0.170760
\(433\) 459.179i 1.06046i 0.847854 + 0.530230i \(0.177894\pi\)
−0.847854 + 0.530230i \(0.822106\pi\)
\(434\) 371.865i 0.856831i
\(435\) 267.807i 0.615649i
\(436\) 660.438i 1.51477i
\(437\) −187.635 275.792i −0.429371 0.631103i
\(438\) 358.174 0.817748
\(439\) 496.750 1.13155 0.565775 0.824560i \(-0.308577\pi\)
0.565775 + 0.824560i \(0.308577\pi\)
\(440\) −194.196 −0.441354
\(441\) −21.0000 −0.0476190
\(442\) 1646.76i 3.72570i
\(443\) −658.279 −1.48596 −0.742979 0.669315i \(-0.766588\pi\)
−0.742979 + 0.669315i \(0.766588\pi\)
\(444\) 281.271i 0.633493i
\(445\) 137.489 0.308963
\(446\) 598.214 1.34129
\(447\) 254.993i 0.570453i
\(448\) 202.004i 0.450902i
\(449\) 773.252 1.72216 0.861082 0.508465i \(-0.169787\pi\)
0.861082 + 0.508465i \(0.169787\pi\)
\(450\) 293.710 0.652690
\(451\) 329.095i 0.729701i
\(452\) 218.900i 0.484291i
\(453\) −1.01189 −0.00223375
\(454\) 857.698i 1.88920i
\(455\) 498.059 1.09463
\(456\) 29.7926i 0.0653346i
\(457\) 175.394i 0.383795i −0.981415 0.191898i \(-0.938536\pi\)
0.981415 0.191898i \(-0.0614642\pi\)
\(458\) 102.173i 0.223085i
\(459\) 120.159i 0.261784i
\(460\) 437.264 + 642.705i 0.950573 + 1.39718i
\(461\) −216.139 −0.468848 −0.234424 0.972134i \(-0.575320\pi\)
−0.234424 + 0.972134i \(0.575320\pi\)
\(462\) −283.847 −0.614388
\(463\) −581.314 −1.25554 −0.627769 0.778400i \(-0.716032\pi\)
−0.627769 + 0.778400i \(0.716032\pi\)
\(464\) −286.354 −0.617142
\(465\) 643.535i 1.38395i
\(466\) −289.683 −0.621636
\(467\) 557.888i 1.19462i −0.802010 0.597311i \(-0.796236\pi\)
0.802010 0.597311i \(-0.203764\pi\)
\(468\) −324.821 −0.694063
\(469\) 76.4930 0.163098
\(470\) 1335.88i 2.84230i
\(471\) 0.163927i 0.000348041i
\(472\) −113.409 −0.240273
\(473\) −1190.03 −2.51591
\(474\) 69.5607i 0.146753i
\(475\) 489.648i 1.03084i
\(476\) 269.751 0.566703
\(477\) 44.4172i 0.0931177i
\(478\) 1022.14 2.13838
\(479\) 816.324i 1.70423i 0.523359 + 0.852113i \(0.324679\pi\)
−0.523359 + 0.852113i \(0.675321\pi\)
\(480\) 609.587i 1.26997i
\(481\) 904.499i 1.88046i
\(482\) 765.052i 1.58725i
\(483\) 59.2879 + 87.1433i 0.122749 + 0.180421i
\(484\) −1478.13 −3.05398
\(485\) −334.671 −0.690043
\(486\) −45.2038 −0.0930120
\(487\) −169.233 −0.347501 −0.173751 0.984790i \(-0.555589\pi\)
−0.173751 + 0.984790i \(0.555589\pi\)
\(488\) 29.3932i 0.0602319i
\(489\) 54.8368 0.112141
\(490\) 155.603i 0.317557i
\(491\) −260.741 −0.531041 −0.265521 0.964105i \(-0.585544\pi\)
−0.265521 + 0.964105i \(0.585544\pi\)
\(492\) −117.657 −0.239141
\(493\) 466.432i 0.946109i
\(494\) 1032.79i 2.09068i
\(495\) 491.215 0.992354
\(496\) −688.102 −1.38730
\(497\) 102.484i 0.206205i
\(498\) 49.6032i 0.0996048i
\(499\) 386.813 0.775176 0.387588 0.921833i \(-0.373308\pi\)
0.387588 + 0.921833i \(0.373308\pi\)
\(500\) 296.130i 0.592260i
\(501\) 224.217 0.447538
\(502\) 486.566i 0.969255i
\(503\) 81.2567i 0.161544i 0.996733 + 0.0807720i \(0.0257386\pi\)
−0.996733 + 0.0807720i \(0.974261\pi\)
\(504\) 9.41369i 0.0186780i
\(505\) 234.619i 0.464592i
\(506\) 801.366 + 1177.87i 1.58373 + 2.32782i
\(507\) 751.831 1.48290
\(508\) −101.320 −0.199450
\(509\) 366.298 0.719643 0.359821 0.933021i \(-0.382838\pi\)
0.359821 + 0.933021i \(0.382838\pi\)
\(510\) −890.337 −1.74576
\(511\) 188.673i 0.369223i
\(512\) −719.153 −1.40460
\(513\) 75.3598i 0.146900i
\(514\) 203.719 0.396340
\(515\) 384.081 0.745789
\(516\) 425.455i 0.824525i
\(517\) 1283.66i 2.48291i
\(518\) 282.583 0.545526
\(519\) −332.076 −0.639839
\(520\) 223.265i 0.429356i
\(521\) 207.640i 0.398541i −0.979945 0.199270i \(-0.936143\pi\)
0.979945 0.199270i \(-0.0638572\pi\)
\(522\) −175.472 −0.336153
\(523\) 954.258i 1.82458i 0.409540 + 0.912292i \(0.365689\pi\)
−0.409540 + 0.912292i \(0.634311\pi\)
\(524\) 496.434 0.947393
\(525\) 154.716i 0.294697i
\(526\) 103.546i 0.196856i
\(527\) 1120.83i 2.12680i
\(528\) 525.233i 0.994760i
\(529\) 194.233 492.051i 0.367171 0.930154i
\(530\) −329.116 −0.620974
\(531\) 286.865 0.540236
\(532\) 169.179 0.318006
\(533\) 378.357 0.709864
\(534\) 90.0848i 0.168698i
\(535\) 604.406 1.12973
\(536\) 34.2896i 0.0639731i
\(537\) 142.758 0.265844
\(538\) 177.076 0.329138
\(539\) 149.521i 0.277404i
\(540\) 175.618i 0.325219i
\(541\) −962.141 −1.77845 −0.889225 0.457471i \(-0.848756\pi\)
−0.889225 + 0.457471i \(0.848756\pi\)
\(542\) −230.092 −0.424523
\(543\) 343.335i 0.632292i
\(544\) 1061.70i 1.95165i
\(545\) 1148.26 2.10690
\(546\) 326.336i 0.597686i
\(547\) −948.368 −1.73376 −0.866881 0.498514i \(-0.833879\pi\)
−0.866881 + 0.498514i \(0.833879\pi\)
\(548\) 291.135i 0.531269i
\(549\) 74.3495i 0.135427i
\(550\) 2091.23i 3.80223i
\(551\) 292.531i 0.530909i
\(552\) −39.0638 + 26.5770i −0.0707678 + 0.0481468i
\(553\) −36.6421 −0.0662606
\(554\) 27.4671 0.0495795
\(555\) −489.027 −0.881129
\(556\) −767.035 −1.37956
\(557\) 488.802i 0.877561i 0.898594 + 0.438781i \(0.144589\pi\)
−0.898594 + 0.438781i \(0.855411\pi\)
\(558\) −421.655 −0.755654
\(559\) 1368.16i 2.44752i
\(560\) 287.929 0.514159
\(561\) −855.535 −1.52502
\(562\) 582.408i 1.03631i
\(563\) 634.765i 1.12747i 0.825956 + 0.563734i \(0.190636\pi\)
−0.825956 + 0.563734i \(0.809364\pi\)
\(564\) −458.933 −0.813710
\(565\) −380.586 −0.673604
\(566\) 937.285i 1.65598i
\(567\) 23.8118i 0.0419961i
\(568\) −45.9406 −0.0808813
\(569\) 82.6433i 0.145243i −0.997360 0.0726215i \(-0.976863\pi\)
0.997360 0.0726215i \(-0.0231365\pi\)
\(570\) −558.391 −0.979633
\(571\) 7.06853i 0.0123792i 0.999981 + 0.00618960i \(0.00197022\pi\)
−0.999981 + 0.00618960i \(0.998030\pi\)
\(572\) 2312.74i 4.04325i
\(573\) 504.730i 0.880856i
\(574\) 118.206i 0.205934i
\(575\) −642.023 + 436.800i −1.11656 + 0.759652i
\(576\) −229.051 −0.397658
\(577\) 120.115 0.208171 0.104086 0.994568i \(-0.466808\pi\)
0.104086 + 0.994568i \(0.466808\pi\)
\(578\) 712.623 1.23291
\(579\) −245.308 −0.423675
\(580\) 681.713i 1.17537i
\(581\) 26.1292 0.0449728
\(582\) 219.282i 0.376773i
\(583\) −316.251 −0.542455
\(584\) 84.5767 0.144823
\(585\) 564.746i 0.965377i
\(586\) 904.958i 1.54430i
\(587\) 1063.93 1.81249 0.906247 0.422750i \(-0.138935\pi\)
0.906247 + 0.422750i \(0.138935\pi\)
\(588\) −53.4562 −0.0909119
\(589\) 702.946i 1.19346i
\(590\) 2125.57i 3.60267i
\(591\) 390.669 0.661031
\(592\) 522.893i 0.883266i
\(593\) 358.957 0.605323 0.302661 0.953098i \(-0.402125\pi\)
0.302661 + 0.953098i \(0.402125\pi\)
\(594\) 321.852i 0.541839i
\(595\) 468.998i 0.788232i
\(596\) 649.093i 1.08908i
\(597\) 131.644i 0.220509i
\(598\) 1354.19 921.323i 2.26453 1.54067i
\(599\) −690.887 −1.15340 −0.576700 0.816956i \(-0.695660\pi\)
−0.576700 + 0.816956i \(0.695660\pi\)
\(600\) 69.3548 0.115591
\(601\) 280.146 0.466133 0.233066 0.972461i \(-0.425124\pi\)
0.233066 + 0.972461i \(0.425124\pi\)
\(602\) −427.439 −0.710032
\(603\) 86.7349i 0.143839i
\(604\) −2.57580 −0.00426456
\(605\) 2569.92i 4.24781i
\(606\) 153.726 0.253674
\(607\) −972.078 −1.60145 −0.800723 0.599035i \(-0.795551\pi\)
−0.800723 + 0.599035i \(0.795551\pi\)
\(608\) 665.864i 1.09517i
\(609\) 92.4323i 0.151777i
\(610\) 550.905 0.903123
\(611\) 1475.82 2.41541
\(612\) 305.869i 0.499785i
\(613\) 1043.54i 1.70234i 0.524886 + 0.851172i \(0.324108\pi\)
−0.524886 + 0.851172i \(0.675892\pi\)
\(614\) −745.000 −1.21335
\(615\) 204.563i 0.332622i
\(616\) −67.0257 −0.108808
\(617\) 101.207i 0.164031i −0.996631 0.0820156i \(-0.973864\pi\)
0.996631 0.0820156i \(-0.0261357\pi\)
\(618\) 251.657i 0.407211i
\(619\) 225.172i 0.363767i −0.983320 0.181884i \(-0.941781\pi\)
0.983320 0.181884i \(-0.0582194\pi\)
\(620\) 1638.14i 2.64216i
\(621\) 98.8112 67.2261i 0.159116 0.108255i
\(622\) 876.882 1.40978
\(623\) 47.4535 0.0761693
\(624\) 603.856 0.967718
\(625\) −329.184 −0.526695
\(626\) 1284.99i 2.05270i
\(627\) −536.564 −0.855763
\(628\) 0.417282i 0.000664463i
\(629\) 851.723 1.35409
\(630\) 176.437 0.280059
\(631\) 238.722i 0.378324i −0.981946 0.189162i \(-0.939423\pi\)
0.981946 0.189162i \(-0.0605771\pi\)
\(632\) 16.4256i 0.0259899i
\(633\) 111.399 0.175986
\(634\) −85.8624 −0.135430
\(635\) 176.159i 0.277416i
\(636\) 113.065i 0.177776i
\(637\) 171.902 0.269862
\(638\) 1249.36i 1.95825i
\(639\) 116.206 0.181856
\(640\) 289.408i 0.452201i
\(641\) 13.4831i 0.0210345i −0.999945 0.0105172i \(-0.996652\pi\)
0.999945 0.0105172i \(-0.00334781\pi\)
\(642\) 396.017i 0.616849i
\(643\) 135.190i 0.210249i −0.994459 0.105124i \(-0.966476\pi\)
0.994459 0.105124i \(-0.0335241\pi\)
\(644\) 150.919 + 221.826i 0.234347 + 0.344451i
\(645\) 739.711 1.14684
\(646\) 972.532 1.50547
\(647\) −1028.55 −1.58971 −0.794857 0.606796i \(-0.792454\pi\)
−0.794857 + 0.606796i \(0.792454\pi\)
\(648\) −10.6741 −0.0164724
\(649\) 2042.49i 3.14713i
\(650\) −2404.26 −3.69887
\(651\) 222.113i 0.341187i
\(652\) 139.589 0.214093
\(653\) 217.516 0.333103 0.166552 0.986033i \(-0.446737\pi\)
0.166552 + 0.986033i \(0.446737\pi\)
\(654\) 752.359i 1.15040i
\(655\) 863.117i 1.31774i
\(656\) 218.729 0.333429
\(657\) −213.935 −0.325624
\(658\) 461.073i 0.700719i
\(659\) 793.296i 1.20379i 0.798576 + 0.601894i \(0.205587\pi\)
−0.798576 + 0.601894i \(0.794413\pi\)
\(660\) 1250.41 1.89455
\(661\) 179.910i 0.272179i 0.990697 + 0.136089i \(0.0434534\pi\)
−0.990697 + 0.136089i \(0.956547\pi\)
\(662\) −483.238 −0.729967
\(663\) 983.600i 1.48356i
\(664\) 11.7130i 0.0176400i
\(665\) 294.140i 0.442316i
\(666\) 320.418i 0.481109i
\(667\) 383.564 260.958i 0.575059 0.391241i
\(668\) 570.751 0.854418
\(669\) −357.310 −0.534095
\(670\) −642.676 −0.959218
\(671\) 529.370 0.788928
\(672\) 210.396i 0.313089i
\(673\) 253.556 0.376754 0.188377 0.982097i \(-0.439677\pi\)
0.188377 + 0.982097i \(0.439677\pi\)
\(674\) 1083.30i 1.60726i
\(675\) −175.432 −0.259899
\(676\) 1913.81 2.83108
\(677\) 566.422i 0.836665i −0.908294 0.418332i \(-0.862615\pi\)
0.908294 0.418332i \(-0.137385\pi\)
\(678\) 249.366i 0.367797i
\(679\) −115.510 −0.170118
\(680\) −210.238 −0.309174
\(681\) 512.298i 0.752274i
\(682\) 3002.19i 4.40204i
\(683\) 943.122 1.38085 0.690426 0.723403i \(-0.257423\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(684\) 191.831i 0.280455i
\(685\) 506.177 0.738945
\(686\) 53.7055i 0.0782880i
\(687\) 61.0274i 0.0888317i
\(688\) 790.938i 1.14962i
\(689\) 363.591i 0.527709i
\(690\) −498.123 732.158i −0.721917 1.06110i
\(691\) 444.301 0.642983 0.321492 0.946912i \(-0.395816\pi\)
0.321492 + 0.946912i \(0.395816\pi\)
\(692\) −845.312 −1.22155
\(693\) 169.540 0.244647
\(694\) −717.095 −1.03328
\(695\) 1333.59i 1.91884i
\(696\) −41.4347 −0.0595327
\(697\) 356.281i 0.511163i
\(698\) −1239.04 −1.77513
\(699\) 173.026 0.247533
\(700\) 393.835i 0.562622i
\(701\) 201.877i 0.287984i 0.989579 + 0.143992i \(0.0459939\pi\)
−0.989579 + 0.143992i \(0.954006\pi\)
\(702\) 370.031 0.527109
\(703\) 534.173 0.759848
\(704\) 1630.85i 2.31655i
\(705\) 797.916i 1.13180i
\(706\) 1338.73 1.89621
\(707\) 80.9776i 0.114537i
\(708\) 730.225 1.03139
\(709\) 848.778i 1.19715i 0.801067 + 0.598574i \(0.204266\pi\)
−0.801067 + 0.598574i \(0.795734\pi\)
\(710\) 861.046i 1.21274i
\(711\) 41.5483i 0.0584364i
\(712\) 21.2720i 0.0298764i
\(713\) 921.697 627.076i 1.29270 0.879489i
\(714\) −307.295 −0.430385
\(715\) −4021.00 −5.62378
\(716\) 363.397 0.507537
\(717\) −610.521 −0.851493
\(718\) 814.295i 1.13411i
\(719\) −173.366 −0.241121 −0.120561 0.992706i \(-0.538469\pi\)
−0.120561 + 0.992706i \(0.538469\pi\)
\(720\) 326.481i 0.453446i
\(721\) 132.564 0.183861
\(722\) −436.897 −0.605120
\(723\) 456.962i 0.632036i
\(724\) 873.970i 1.20714i
\(725\) −680.989 −0.939296
\(726\) 1683.86 2.31936
\(727\) 249.279i 0.342887i −0.985194 0.171443i \(-0.945157\pi\)
0.985194 0.171443i \(-0.0548431\pi\)
\(728\) 77.0589i 0.105850i
\(729\) 27.0000 0.0370370
\(730\) 1585.19i 2.17149i
\(731\) −1288.33 −1.76242
\(732\) 189.259i 0.258551i
\(733\) 331.771i 0.452621i −0.974055 0.226310i \(-0.927334\pi\)
0.974055 0.226310i \(-0.0726663\pi\)
\(734\) 2065.90i 2.81458i
\(735\) 92.9408i 0.126450i
\(736\) 873.076 593.996i 1.18624 0.807060i
\(737\) −617.554 −0.837930
\(738\) 134.033 0.181617
\(739\) 671.110 0.908132 0.454066 0.890968i \(-0.349973\pi\)
0.454066 + 0.890968i \(0.349973\pi\)
\(740\) −1244.83 −1.68221
\(741\) 616.882i 0.832500i
\(742\) −113.593 −0.153090
\(743\) 1176.40i 1.58331i −0.610967 0.791656i \(-0.709219\pi\)
0.610967 0.791656i \(-0.290781\pi\)
\(744\) −99.5667 −0.133826
\(745\) 1128.53 1.51481
\(746\) 1742.96i 2.33640i
\(747\) 29.6277i 0.0396623i
\(748\) −2177.79 −2.91149
\(749\) 208.608 0.278515
\(750\) 337.346i 0.449795i
\(751\) 626.464i 0.834173i 0.908867 + 0.417087i \(0.136949\pi\)
−0.908867 + 0.417087i \(0.863051\pi\)
\(752\) 853.174 1.13454
\(753\) 290.623i 0.385954i
\(754\) 1436.38 1.90502
\(755\) 4.47836i 0.00593161i
\(756\) 60.6137i 0.0801768i
\(757\) 589.991i 0.779380i 0.920946 + 0.389690i \(0.127418\pi\)
−0.920946 + 0.389690i \(0.872582\pi\)
\(758\) 1437.74i 1.89676i
\(759\) −478.652 703.538i −0.630635 0.926928i
\(760\) −131.855 −0.173493
\(761\) −371.524 −0.488205 −0.244103 0.969749i \(-0.578493\pi\)
−0.244103 + 0.969749i \(0.578493\pi\)
\(762\) 115.422 0.151473
\(763\) 396.316 0.519418
\(764\) 1284.81i 1.68169i
\(765\) 531.794 0.695155
\(766\) 548.208i 0.715676i
\(767\) −2348.23 −3.06158
\(768\) 339.345 0.441856
\(769\) 1242.64i 1.61591i −0.589241 0.807957i \(-0.700573\pi\)
0.589241 0.807957i \(-0.299427\pi\)
\(770\) 1256.24i 1.63148i
\(771\) −121.680 −0.157821
\(772\) −624.440 −0.808860
\(773\) 1144.15i 1.48014i 0.672531 + 0.740069i \(0.265207\pi\)
−0.672531 + 0.740069i \(0.734793\pi\)
\(774\) 484.671i 0.626190i
\(775\) −1636.40 −2.11149
\(776\) 51.7798i 0.0667265i
\(777\) −168.785 −0.217227
\(778\) 542.811i 0.697700i
\(779\) 223.448i 0.286839i
\(780\) 1437.58i 1.84305i
\(781\) 827.389i 1.05940i
\(782\) 867.566 + 1275.18i 1.10942 + 1.63066i
\(783\) 104.808 0.133855
\(784\) 99.3772 0.126757
\(785\) 0.725501 0.000924206
\(786\) −565.528 −0.719502
\(787\) 637.991i 0.810662i −0.914170 0.405331i \(-0.867156\pi\)
0.914170 0.405331i \(-0.132844\pi\)
\(788\) 994.462 1.26201
\(789\) 61.8477i 0.0783874i
\(790\) 307.859 0.389694
\(791\) −131.357 −0.166065