Properties

Label 177.3.b.a.119.11
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.11
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.28

$q$-expansion

\(f(q)\) \(=\) \(q-1.90736i q^{2} +(-2.89185 + 0.798268i) q^{3} +0.361959 q^{4} +0.0951742i q^{5} +(1.52259 + 5.51580i) q^{6} -10.1724 q^{7} -8.31985i q^{8} +(7.72554 - 4.61693i) q^{9} +O(q^{10})\) \(q-1.90736i q^{2} +(-2.89185 + 0.798268i) q^{3} +0.361959 q^{4} +0.0951742i q^{5} +(1.52259 + 5.51580i) q^{6} -10.1724 q^{7} -8.31985i q^{8} +(7.72554 - 4.61693i) q^{9} +0.181532 q^{10} +21.4541i q^{11} +(-1.04673 + 0.288940i) q^{12} -18.5391 q^{13} +19.4024i q^{14} +(-0.0759745 - 0.275229i) q^{15} -14.4211 q^{16} +11.7919i q^{17} +(-8.80618 - 14.7354i) q^{18} -16.0947 q^{19} +0.0344492i q^{20} +(29.4169 - 8.12026i) q^{21} +40.9207 q^{22} +4.05406i q^{23} +(6.64147 + 24.0597i) q^{24} +24.9909 q^{25} +35.3609i q^{26} +(-18.6555 + 19.5185i) q^{27} -3.68198 q^{28} +13.2543i q^{29} +(-0.524962 + 0.144911i) q^{30} -10.0374 q^{31} -5.77300i q^{32} +(-17.1261 - 62.0418i) q^{33} +22.4915 q^{34} -0.968146i q^{35} +(2.79633 - 1.67114i) q^{36} -26.6736 q^{37} +30.6984i q^{38} +(53.6123 - 14.7992i) q^{39} +0.791835 q^{40} -42.3187i q^{41} +(-15.4883 - 56.1087i) q^{42} -55.1187 q^{43} +7.76549i q^{44} +(0.439413 + 0.735272i) q^{45} +7.73258 q^{46} -37.5402i q^{47} +(41.7037 - 11.5119i) q^{48} +54.4767 q^{49} -47.6668i q^{50} +(-9.41312 - 34.1005i) q^{51} -6.71041 q^{52} -72.8845i q^{53} +(37.2289 + 35.5829i) q^{54} -2.04187 q^{55} +84.6324i q^{56} +(46.5433 - 12.8478i) q^{57} +25.2809 q^{58} -7.68115i q^{59} +(-0.0274997 - 0.0996217i) q^{60} -69.0450 q^{61} +19.1451i q^{62} +(-78.5869 + 46.9651i) q^{63} -68.6958 q^{64} -1.76445i q^{65} +(-118.336 + 32.6657i) q^{66} +60.8758 q^{67} +4.26820i q^{68} +(-3.23623 - 11.7237i) q^{69} -1.84661 q^{70} +50.2583i q^{71} +(-38.4122 - 64.2753i) q^{72} +29.1706 q^{73} +50.8763i q^{74} +(-72.2699 + 19.9495i) q^{75} -5.82561 q^{76} -218.238i q^{77} +(-28.2275 - 102.258i) q^{78} +59.8769 q^{79} -1.37252i q^{80} +(38.3679 - 71.3366i) q^{81} -80.7172 q^{82} +92.7342i q^{83} +(10.6477 - 2.93920i) q^{84} -1.12229 q^{85} +105.131i q^{86} +(-10.5805 - 38.3295i) q^{87} +178.494 q^{88} +130.792i q^{89} +(1.40243 - 0.838121i) q^{90} +188.587 q^{91} +1.46741i q^{92} +(29.0267 - 8.01257i) q^{93} -71.6028 q^{94} -1.53180i q^{95} +(4.60840 + 16.6946i) q^{96} +68.0654 q^{97} -103.907i q^{98} +(99.0519 + 165.744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90736i 0.953682i −0.878989 0.476841i \(-0.841782\pi\)
0.878989 0.476841i \(-0.158218\pi\)
\(3\) −2.89185 + 0.798268i −0.963948 + 0.266089i
\(4\) 0.361959 0.0904898
\(5\) 0.0951742i 0.0190348i 0.999955 + 0.00951742i \(0.00302954\pi\)
−0.999955 + 0.00951742i \(0.996970\pi\)
\(6\) 1.52259 + 5.51580i 0.253765 + 0.919301i
\(7\) −10.1724 −1.45319 −0.726596 0.687064i \(-0.758899\pi\)
−0.726596 + 0.687064i \(0.758899\pi\)
\(8\) 8.31985i 1.03998i
\(9\) 7.72554 4.61693i 0.858393 0.512993i
\(10\) 0.181532 0.0181532
\(11\) 21.4541i 1.95037i 0.221395 + 0.975184i \(0.428939\pi\)
−0.221395 + 0.975184i \(0.571061\pi\)
\(12\) −1.04673 + 0.288940i −0.0872275 + 0.0240784i
\(13\) −18.5391 −1.42609 −0.713043 0.701120i \(-0.752684\pi\)
−0.713043 + 0.701120i \(0.752684\pi\)
\(14\) 19.4024i 1.38588i
\(15\) −0.0759745 0.275229i −0.00506497 0.0183486i
\(16\) −14.4211 −0.901322
\(17\) 11.7919i 0.693643i 0.937931 + 0.346822i \(0.112739\pi\)
−0.937931 + 0.346822i \(0.887261\pi\)
\(18\) −8.80618 14.7354i −0.489232 0.818634i
\(19\) −16.0947 −0.847087 −0.423544 0.905876i \(-0.639214\pi\)
−0.423544 + 0.905876i \(0.639214\pi\)
\(20\) 0.0344492i 0.00172246i
\(21\) 29.4169 8.12026i 1.40080 0.386679i
\(22\) 40.9207 1.86003
\(23\) 4.05406i 0.176264i 0.996109 + 0.0881318i \(0.0280897\pi\)
−0.996109 + 0.0881318i \(0.971910\pi\)
\(24\) 6.64147 + 24.0597i 0.276728 + 1.00249i
\(25\) 24.9909 0.999638
\(26\) 35.3609i 1.36003i
\(27\) −18.6555 + 19.5185i −0.690945 + 0.722907i
\(28\) −3.68198 −0.131499
\(29\) 13.2543i 0.457046i 0.973538 + 0.228523i \(0.0733896\pi\)
−0.973538 + 0.228523i \(0.926610\pi\)
\(30\) −0.524962 + 0.144911i −0.0174987 + 0.00483037i
\(31\) −10.0374 −0.323789 −0.161894 0.986808i \(-0.551760\pi\)
−0.161894 + 0.986808i \(0.551760\pi\)
\(32\) 5.77300i 0.180406i
\(33\) −17.1261 62.0418i −0.518972 1.88005i
\(34\) 22.4915 0.661516
\(35\) 0.968146i 0.0276613i
\(36\) 2.79633 1.67114i 0.0776758 0.0464206i
\(37\) −26.6736 −0.720908 −0.360454 0.932777i \(-0.617378\pi\)
−0.360454 + 0.932777i \(0.617378\pi\)
\(38\) 30.6984i 0.807852i
\(39\) 53.6123 14.7992i 1.37467 0.379466i
\(40\) 0.791835 0.0197959
\(41\) 42.3187i 1.03216i −0.856539 0.516082i \(-0.827390\pi\)
0.856539 0.516082i \(-0.172610\pi\)
\(42\) −15.4883 56.1087i −0.368769 1.33592i
\(43\) −55.1187 −1.28183 −0.640915 0.767612i \(-0.721445\pi\)
−0.640915 + 0.767612i \(0.721445\pi\)
\(44\) 7.76549i 0.176488i
\(45\) 0.439413 + 0.735272i 0.00976474 + 0.0163394i
\(46\) 7.73258 0.168100
\(47\) 37.5402i 0.798727i −0.916793 0.399364i \(-0.869231\pi\)
0.916793 0.399364i \(-0.130769\pi\)
\(48\) 41.7037 11.5119i 0.868828 0.239832i
\(49\) 54.4767 1.11177
\(50\) 47.6668i 0.953337i
\(51\) −9.41312 34.1005i −0.184571 0.668637i
\(52\) −6.71041 −0.129046
\(53\) 72.8845i 1.37518i −0.726099 0.687590i \(-0.758669\pi\)
0.726099 0.687590i \(-0.241331\pi\)
\(54\) 37.2289 + 35.5829i 0.689424 + 0.658942i
\(55\) −2.04187 −0.0371250
\(56\) 84.6324i 1.51129i
\(57\) 46.5433 12.8478i 0.816549 0.225401i
\(58\) 25.2809 0.435877
\(59\) 7.68115i 0.130189i
\(60\) −0.0274997 0.0996217i −0.000458328 0.00166036i
\(61\) −69.0450 −1.13188 −0.565942 0.824445i \(-0.691488\pi\)
−0.565942 + 0.824445i \(0.691488\pi\)
\(62\) 19.1451i 0.308792i
\(63\) −78.5869 + 46.9651i −1.24741 + 0.745477i
\(64\) −68.6958 −1.07337
\(65\) 1.76445i 0.0271453i
\(66\) −118.336 + 32.6657i −1.79298 + 0.494935i
\(67\) 60.8758 0.908594 0.454297 0.890850i \(-0.349890\pi\)
0.454297 + 0.890850i \(0.349890\pi\)
\(68\) 4.26820i 0.0627676i
\(69\) −3.23623 11.7237i −0.0469019 0.169909i
\(70\) −1.84661 −0.0263801
\(71\) 50.2583i 0.707864i 0.935271 + 0.353932i \(0.115156\pi\)
−0.935271 + 0.353932i \(0.884844\pi\)
\(72\) −38.4122 64.2753i −0.533502 0.892712i
\(73\) 29.1706 0.399597 0.199799 0.979837i \(-0.435971\pi\)
0.199799 + 0.979837i \(0.435971\pi\)
\(74\) 50.8763i 0.687518i
\(75\) −72.2699 + 19.9495i −0.963599 + 0.265993i
\(76\) −5.82561 −0.0766528
\(77\) 218.238i 2.83426i
\(78\) −28.2275 102.258i −0.361890 1.31100i
\(79\) 59.8769 0.757936 0.378968 0.925410i \(-0.376279\pi\)
0.378968 + 0.925410i \(0.376279\pi\)
\(80\) 1.37252i 0.0171565i
\(81\) 38.3679 71.3366i 0.473677 0.880698i
\(82\) −80.7172 −0.984356
\(83\) 92.7342i 1.11728i 0.829411 + 0.558640i \(0.188676\pi\)
−0.829411 + 0.558640i \(0.811324\pi\)
\(84\) 10.6477 2.93920i 0.126758 0.0349905i
\(85\) −1.12229 −0.0132034
\(86\) 105.131i 1.22246i
\(87\) −10.5805 38.3295i −0.121615 0.440569i
\(88\) 178.494 2.02835
\(89\) 130.792i 1.46957i 0.678298 + 0.734787i \(0.262718\pi\)
−0.678298 + 0.734787i \(0.737282\pi\)
\(90\) 1.40243 0.838121i 0.0155826 0.00931246i
\(91\) 188.587 2.07238
\(92\) 1.46741i 0.0159501i
\(93\) 29.0267 8.01257i 0.312116 0.0861567i
\(94\) −71.6028 −0.761732
\(95\) 1.53180i 0.0161242i
\(96\) 4.60840 + 16.6946i 0.0480041 + 0.173902i
\(97\) 68.0654 0.701705 0.350852 0.936431i \(-0.385892\pi\)
0.350852 + 0.936431i \(0.385892\pi\)
\(98\) 103.907i 1.06028i
\(99\) 99.0519 + 165.744i 1.00052 + 1.67418i
\(100\) 9.04570 0.0904570
\(101\) 132.603i 1.31290i −0.754371 0.656449i \(-0.772058\pi\)
0.754371 0.656449i \(-0.227942\pi\)
\(102\) −65.0420 + 17.9543i −0.637667 + 0.176022i
\(103\) −15.8984 −0.154353 −0.0771767 0.997017i \(-0.524591\pi\)
−0.0771767 + 0.997017i \(0.524591\pi\)
\(104\) 154.243i 1.48310i
\(105\) 0.772839 + 2.79973i 0.00736038 + 0.0266641i
\(106\) −139.017 −1.31148
\(107\) 118.559i 1.10803i 0.832508 + 0.554013i \(0.186904\pi\)
−0.832508 + 0.554013i \(0.813096\pi\)
\(108\) −6.75253 + 7.06490i −0.0625234 + 0.0654157i
\(109\) 71.1676 0.652914 0.326457 0.945212i \(-0.394145\pi\)
0.326457 + 0.945212i \(0.394145\pi\)
\(110\) 3.89460i 0.0354054i
\(111\) 77.1359 21.2927i 0.694918 0.191826i
\(112\) 146.697 1.30979
\(113\) 13.6200i 0.120531i −0.998182 0.0602654i \(-0.980805\pi\)
0.998182 0.0602654i \(-0.0191947\pi\)
\(114\) −24.5055 88.7750i −0.214961 0.778728i
\(115\) −0.385842 −0.00335515
\(116\) 4.79753i 0.0413580i
\(117\) −143.225 + 85.5939i −1.22414 + 0.731572i
\(118\) −14.6507 −0.124159
\(119\) 119.952i 1.00800i
\(120\) −2.28986 + 0.632096i −0.0190822 + 0.00526747i
\(121\) −339.276 −2.80394
\(122\) 131.694i 1.07946i
\(123\) 33.7817 + 122.379i 0.274648 + 0.994953i
\(124\) −3.63315 −0.0292996
\(125\) 4.75785i 0.0380628i
\(126\) 89.5795 + 149.894i 0.710948 + 1.18963i
\(127\) −120.467 −0.948557 −0.474279 0.880375i \(-0.657291\pi\)
−0.474279 + 0.880375i \(0.657291\pi\)
\(128\) 107.936i 0.843250i
\(129\) 159.395 43.9995i 1.23562 0.341081i
\(130\) −3.36545 −0.0258880
\(131\) 210.339i 1.60564i −0.596221 0.802820i \(-0.703332\pi\)
0.596221 0.802820i \(-0.296668\pi\)
\(132\) −6.19894 22.4566i −0.0469617 0.170126i
\(133\) 163.721 1.23098
\(134\) 116.112i 0.866511i
\(135\) −1.85766 1.77552i −0.0137604 0.0131520i
\(136\) 98.1071 0.721376
\(137\) 228.804i 1.67010i 0.550170 + 0.835052i \(0.314563\pi\)
−0.550170 + 0.835052i \(0.685437\pi\)
\(138\) −22.3614 + 6.17267i −0.162039 + 0.0447295i
\(139\) −235.370 −1.69331 −0.846655 0.532142i \(-0.821387\pi\)
−0.846655 + 0.532142i \(0.821387\pi\)
\(140\) 0.350429i 0.00250307i
\(141\) 29.9671 + 108.560i 0.212533 + 0.769932i
\(142\) 95.8609 0.675077
\(143\) 397.739i 2.78140i
\(144\) −111.411 + 66.5815i −0.773688 + 0.462371i
\(145\) −1.26147 −0.00869981
\(146\) 55.6390i 0.381089i
\(147\) −157.538 + 43.4870i −1.07169 + 0.295830i
\(148\) −9.65476 −0.0652348
\(149\) 52.3287i 0.351200i 0.984462 + 0.175600i \(0.0561865\pi\)
−0.984462 + 0.175600i \(0.943814\pi\)
\(150\) 38.0509 + 137.845i 0.253673 + 0.918968i
\(151\) 182.444 1.20824 0.604121 0.796893i \(-0.293525\pi\)
0.604121 + 0.796893i \(0.293525\pi\)
\(152\) 133.905i 0.880955i
\(153\) 54.4426 + 91.0991i 0.355834 + 0.595419i
\(154\) −416.260 −2.70299
\(155\) 0.955307i 0.00616327i
\(156\) 19.4055 5.35670i 0.124394 0.0343378i
\(157\) −274.716 −1.74978 −0.874891 0.484320i \(-0.839067\pi\)
−0.874891 + 0.484320i \(0.839067\pi\)
\(158\) 114.207i 0.722830i
\(159\) 58.1814 + 210.771i 0.365920 + 1.32560i
\(160\) 0.549441 0.00343400
\(161\) 41.2394i 0.256145i
\(162\) −136.065 73.1815i −0.839907 0.451738i
\(163\) 94.9693 0.582634 0.291317 0.956627i \(-0.405907\pi\)
0.291317 + 0.956627i \(0.405907\pi\)
\(164\) 15.3176i 0.0934003i
\(165\) 5.90478 1.62996i 0.0357866 0.00987855i
\(166\) 176.878 1.06553
\(167\) 195.343i 1.16972i 0.811136 + 0.584858i \(0.198850\pi\)
−0.811136 + 0.584858i \(0.801150\pi\)
\(168\) −67.5593 244.744i −0.402139 1.45681i
\(169\) 174.699 1.03372
\(170\) 2.14061i 0.0125918i
\(171\) −124.340 + 74.3080i −0.727134 + 0.434550i
\(172\) −19.9507 −0.115993
\(173\) 188.675i 1.09061i 0.838238 + 0.545304i \(0.183586\pi\)
−0.838238 + 0.545304i \(0.816414\pi\)
\(174\) −73.1083 + 20.1809i −0.420163 + 0.115982i
\(175\) −254.217 −1.45267
\(176\) 309.392i 1.75791i
\(177\) 6.13161 + 22.2127i 0.0346419 + 0.125495i
\(178\) 249.468 1.40151
\(179\) 196.729i 1.09904i 0.835479 + 0.549522i \(0.185190\pi\)
−0.835479 + 0.549522i \(0.814810\pi\)
\(180\) 0.159050 + 0.266138i 0.000883609 + 0.00147855i
\(181\) 14.7951 0.0817407 0.0408704 0.999164i \(-0.486987\pi\)
0.0408704 + 0.999164i \(0.486987\pi\)
\(182\) 359.703i 1.97639i
\(183\) 199.667 55.1164i 1.09108 0.301182i
\(184\) 33.7292 0.183311
\(185\) 2.53864i 0.0137224i
\(186\) −15.2829 55.3646i −0.0821661 0.297659i
\(187\) −252.985 −1.35286
\(188\) 13.5880i 0.0722766i
\(189\) 189.770 198.549i 1.00408 1.05052i
\(190\) −2.92170 −0.0153773
\(191\) 122.673i 0.642268i 0.947034 + 0.321134i \(0.104064\pi\)
−0.947034 + 0.321134i \(0.895936\pi\)
\(192\) 198.658 54.8376i 1.03468 0.285613i
\(193\) 201.864 1.04593 0.522963 0.852355i \(-0.324827\pi\)
0.522963 + 0.852355i \(0.324827\pi\)
\(194\) 129.826i 0.669204i
\(195\) 1.40850 + 5.10251i 0.00722308 + 0.0261667i
\(196\) 19.7183 0.100604
\(197\) 123.704i 0.627938i −0.949433 0.313969i \(-0.898341\pi\)
0.949433 0.313969i \(-0.101659\pi\)
\(198\) 316.134 188.928i 1.59664 0.954183i
\(199\) −111.272 −0.559158 −0.279579 0.960123i \(-0.590195\pi\)
−0.279579 + 0.960123i \(0.590195\pi\)
\(200\) 207.921i 1.03960i
\(201\) −176.043 + 48.5952i −0.875838 + 0.241767i
\(202\) −252.922 −1.25209
\(203\) 134.828i 0.664176i
\(204\) −3.40717 12.3430i −0.0167018 0.0605048i
\(205\) 4.02765 0.0196471
\(206\) 30.3241i 0.147204i
\(207\) 18.7173 + 31.3198i 0.0904219 + 0.151303i
\(208\) 267.356 1.28536
\(209\) 345.296i 1.65213i
\(210\) 5.34010 1.47409i 0.0254291 0.00701946i
\(211\) −209.476 −0.992777 −0.496388 0.868101i \(-0.665341\pi\)
−0.496388 + 0.868101i \(0.665341\pi\)
\(212\) 26.3812i 0.124440i
\(213\) −40.1196 145.339i −0.188355 0.682344i
\(214\) 226.135 1.05671
\(215\) 5.24588i 0.0243994i
\(216\) 162.391 + 155.211i 0.751810 + 0.718569i
\(217\) 102.104 0.470527
\(218\) 135.743i 0.622673i
\(219\) −84.3569 + 23.2860i −0.385191 + 0.106329i
\(220\) −0.739075 −0.00335943
\(221\) 218.612i 0.989196i
\(222\) −40.6129 147.126i −0.182941 0.662732i
\(223\) −98.8711 −0.443368 −0.221684 0.975119i \(-0.571155\pi\)
−0.221684 + 0.975119i \(0.571155\pi\)
\(224\) 58.7250i 0.262165i
\(225\) 193.068 115.382i 0.858082 0.512807i
\(226\) −25.9783 −0.114948
\(227\) 266.082i 1.17217i 0.810251 + 0.586083i \(0.199331\pi\)
−0.810251 + 0.586083i \(0.800669\pi\)
\(228\) 16.8468 4.65040i 0.0738893 0.0203965i
\(229\) 94.9380 0.414577 0.207288 0.978280i \(-0.433536\pi\)
0.207288 + 0.978280i \(0.433536\pi\)
\(230\) 0.735942i 0.00319975i
\(231\) 174.212 + 631.111i 0.754167 + 2.73208i
\(232\) 110.274 0.475319
\(233\) 11.1408i 0.0478147i 0.999714 + 0.0239073i \(0.00761067\pi\)
−0.999714 + 0.0239073i \(0.992389\pi\)
\(234\) 163.259 + 273.182i 0.697687 + 1.16744i
\(235\) 3.57286 0.0152036
\(236\) 2.78026i 0.0117808i
\(237\) −173.155 + 47.7978i −0.730611 + 0.201679i
\(238\) −228.792 −0.961310
\(239\) 102.629i 0.429410i −0.976679 0.214705i \(-0.931121\pi\)
0.976679 0.214705i \(-0.0688791\pi\)
\(240\) 1.09564 + 3.96912i 0.00456517 + 0.0165380i
\(241\) 135.675 0.562968 0.281484 0.959566i \(-0.409173\pi\)
0.281484 + 0.959566i \(0.409173\pi\)
\(242\) 647.124i 2.67407i
\(243\) −54.0082 + 236.922i −0.222256 + 0.974988i
\(244\) −24.9915 −0.102424
\(245\) 5.18478i 0.0211624i
\(246\) 233.422 64.4339i 0.948869 0.261927i
\(247\) 298.381 1.20802
\(248\) 83.5100i 0.336734i
\(249\) −74.0267 268.173i −0.297296 1.07700i
\(250\) 9.07496 0.0362998
\(251\) 209.115i 0.833129i −0.909106 0.416564i \(-0.863234\pi\)
0.909106 0.416564i \(-0.136766\pi\)
\(252\) −28.4452 + 16.9994i −0.112878 + 0.0674581i
\(253\) −86.9761 −0.343779
\(254\) 229.774i 0.904622i
\(255\) 3.24549 0.895887i 0.0127274 0.00351328i
\(256\) −68.9099 −0.269179
\(257\) 280.472i 1.09133i −0.838003 0.545665i \(-0.816277\pi\)
0.838003 0.545665i \(-0.183723\pi\)
\(258\) −83.9231 304.024i −0.325283 1.17839i
\(259\) 271.333 1.04762
\(260\) 0.638658i 0.00245638i
\(261\) 61.1944 + 102.397i 0.234461 + 0.392325i
\(262\) −401.193 −1.53127
\(263\) 488.477i 1.85733i −0.370925 0.928663i \(-0.620959\pi\)
0.370925 0.928663i \(-0.379041\pi\)
\(264\) −516.178 + 142.486i −1.95522 + 0.539721i
\(265\) 6.93673 0.0261763
\(266\) 312.275i 1.17397i
\(267\) −104.407 378.231i −0.391038 1.41659i
\(268\) 22.0346 0.0822185
\(269\) 289.117i 1.07479i 0.843332 + 0.537393i \(0.180591\pi\)
−0.843332 + 0.537393i \(0.819409\pi\)
\(270\) −3.38657 + 3.54323i −0.0125429 + 0.0131231i
\(271\) −173.151 −0.638934 −0.319467 0.947597i \(-0.603504\pi\)
−0.319467 + 0.947597i \(0.603504\pi\)
\(272\) 170.053i 0.625196i
\(273\) −545.363 + 150.543i −1.99767 + 0.551438i
\(274\) 436.413 1.59275
\(275\) 536.157i 1.94966i
\(276\) −1.17138 4.24351i −0.00424414 0.0153750i
\(277\) −27.0948 −0.0978152 −0.0489076 0.998803i \(-0.515574\pi\)
−0.0489076 + 0.998803i \(0.515574\pi\)
\(278\) 448.937i 1.61488i
\(279\) −77.5447 + 46.3422i −0.277938 + 0.166101i
\(280\) −8.05483 −0.0287672
\(281\) 39.5691i 0.140815i 0.997518 + 0.0704076i \(0.0224300\pi\)
−0.997518 + 0.0704076i \(0.977570\pi\)
\(282\) 207.064 57.1582i 0.734270 0.202689i
\(283\) −25.8831 −0.0914599 −0.0457299 0.998954i \(-0.514561\pi\)
−0.0457299 + 0.998954i \(0.514561\pi\)
\(284\) 18.1915i 0.0640544i
\(285\) 1.22278 + 4.42972i 0.00429047 + 0.0155429i
\(286\) −758.634 −2.65257
\(287\) 430.481i 1.49993i
\(288\) −26.6535 44.5995i −0.0925470 0.154859i
\(289\) 149.950 0.518859
\(290\) 2.40609i 0.00829685i
\(291\) −196.835 + 54.3344i −0.676407 + 0.186716i
\(292\) 10.5586 0.0361595
\(293\) 344.114i 1.17445i −0.809424 0.587225i \(-0.800220\pi\)
0.809424 0.587225i \(-0.199780\pi\)
\(294\) 82.9456 + 300.483i 0.282128 + 1.02205i
\(295\) 0.731047 0.00247813
\(296\) 221.920i 0.749731i
\(297\) −418.751 400.236i −1.40994 1.34760i
\(298\) 99.8100 0.334933
\(299\) 75.1588i 0.251367i
\(300\) −26.1588 + 7.22089i −0.0871959 + 0.0240696i
\(301\) 560.687 1.86275
\(302\) 347.988i 1.15228i
\(303\) 105.852 + 383.466i 0.349348 + 1.26557i
\(304\) 232.103 0.763498
\(305\) 6.57130i 0.0215453i
\(306\) 173.759 103.842i 0.567840 0.339353i
\(307\) 398.833 1.29913 0.649565 0.760306i \(-0.274951\pi\)
0.649565 + 0.760306i \(0.274951\pi\)
\(308\) 78.9933i 0.256472i
\(309\) 45.9757 12.6912i 0.148789 0.0410718i
\(310\) −1.82212 −0.00587780
\(311\) 369.284i 1.18741i 0.804684 + 0.593704i \(0.202335\pi\)
−0.804684 + 0.593704i \(0.797665\pi\)
\(312\) −123.127 446.046i −0.394638 1.42964i
\(313\) −132.228 −0.422455 −0.211228 0.977437i \(-0.567746\pi\)
−0.211228 + 0.977437i \(0.567746\pi\)
\(314\) 523.983i 1.66874i
\(315\) −4.46986 7.47945i −0.0141900 0.0237443i
\(316\) 21.6730 0.0685854
\(317\) 321.344i 1.01370i 0.862033 + 0.506852i \(0.169191\pi\)
−0.862033 + 0.506852i \(0.830809\pi\)
\(318\) 402.017 110.973i 1.26420 0.348972i
\(319\) −284.359 −0.891409
\(320\) 6.53807i 0.0204315i
\(321\) −94.6417 342.854i −0.294834 1.06808i
\(322\) −78.6585 −0.244281
\(323\) 189.787i 0.587577i
\(324\) 13.8876 25.8209i 0.0428630 0.0796942i
\(325\) −463.310 −1.42557
\(326\) 181.141i 0.555647i
\(327\) −205.806 + 56.8108i −0.629376 + 0.173733i
\(328\) −352.085 −1.07343
\(329\) 381.872i 1.16070i
\(330\) −3.10893 11.2626i −0.00942100 0.0341290i
\(331\) 2.24571 0.00678462 0.00339231 0.999994i \(-0.498920\pi\)
0.00339231 + 0.999994i \(0.498920\pi\)
\(332\) 33.5660i 0.101102i
\(333\) −206.068 + 123.150i −0.618823 + 0.369821i
\(334\) 372.590 1.11554
\(335\) 5.79381i 0.0172950i
\(336\) −424.225 + 117.103i −1.26257 + 0.348522i
\(337\) −336.616 −0.998860 −0.499430 0.866354i \(-0.666457\pi\)
−0.499430 + 0.866354i \(0.666457\pi\)
\(338\) 333.215i 0.985844i
\(339\) 10.8724 + 39.3869i 0.0320720 + 0.116186i
\(340\) −0.406223 −0.00119477
\(341\) 215.344i 0.631507i
\(342\) 141.732 + 237.162i 0.414422 + 0.693455i
\(343\) −55.7111 −0.162423
\(344\) 458.579i 1.33308i
\(345\) 1.11580 0.308006i 0.00323419 0.000892770i
\(346\) 359.873 1.04009
\(347\) 84.3858i 0.243187i −0.992580 0.121593i \(-0.961200\pi\)
0.992580 0.121593i \(-0.0388004\pi\)
\(348\) −3.82971 13.8737i −0.0110049 0.0398670i
\(349\) −300.424 −0.860814 −0.430407 0.902635i \(-0.641630\pi\)
−0.430407 + 0.902635i \(0.641630\pi\)
\(350\) 484.884i 1.38538i
\(351\) 345.857 361.856i 0.985347 1.03093i
\(352\) 123.854 0.351858
\(353\) 541.944i 1.53525i 0.640898 + 0.767626i \(0.278562\pi\)
−0.640898 + 0.767626i \(0.721438\pi\)
\(354\) 42.3677 11.6952i 0.119683 0.0330373i
\(355\) −4.78330 −0.0134741
\(356\) 47.3414i 0.132981i
\(357\) 95.7536 + 346.882i 0.268217 + 0.971658i
\(358\) 375.234 1.04814
\(359\) 247.949i 0.690666i −0.938480 0.345333i \(-0.887766\pi\)
0.938480 0.345333i \(-0.112234\pi\)
\(360\) 6.11735 3.65585i 0.0169926 0.0101551i
\(361\) −101.962 −0.282443
\(362\) 28.2196i 0.0779547i
\(363\) 981.135 270.833i 2.70285 0.746098i
\(364\) 68.2606 0.187529
\(365\) 2.77629i 0.00760628i
\(366\) −105.127 380.839i −0.287232 1.04054i
\(367\) 368.950 1.00531 0.502656 0.864486i \(-0.332356\pi\)
0.502656 + 0.864486i \(0.332356\pi\)
\(368\) 58.4643i 0.158870i
\(369\) −195.383 326.935i −0.529492 0.886002i
\(370\) −4.84211 −0.0130868
\(371\) 741.407i 1.99840i
\(372\) 10.5065 2.90022i 0.0282433 0.00779630i
\(373\) −16.6190 −0.0445549 −0.0222775 0.999752i \(-0.507092\pi\)
−0.0222775 + 0.999752i \(0.507092\pi\)
\(374\) 482.534i 1.29020i
\(375\) −3.79804 13.7590i −0.0101281 0.0366906i
\(376\) −312.329 −0.830661
\(377\) 245.724i 0.651788i
\(378\) −378.705 361.961i −1.00187 0.957570i
\(379\) 181.804 0.479694 0.239847 0.970811i \(-0.422903\pi\)
0.239847 + 0.970811i \(0.422903\pi\)
\(380\) 0.554448i 0.00145907i
\(381\) 348.371 96.1647i 0.914360 0.252401i
\(382\) 233.982 0.612520
\(383\) 254.866i 0.665445i −0.943025 0.332723i \(-0.892033\pi\)
0.943025 0.332723i \(-0.107967\pi\)
\(384\) −86.1618 312.134i −0.224380 0.812849i
\(385\) 20.7707 0.0539497
\(386\) 385.028i 0.997481i
\(387\) −425.822 + 254.479i −1.10031 + 0.657569i
\(388\) 24.6369 0.0634971
\(389\) 613.478i 1.57706i 0.614993 + 0.788532i \(0.289159\pi\)
−0.614993 + 0.788532i \(0.710841\pi\)
\(390\) 9.73235 2.68653i 0.0249547 0.00688853i
\(391\) −47.8053 −0.122264
\(392\) 453.238i 1.15622i
\(393\) 167.907 + 608.268i 0.427244 + 1.54775i
\(394\) −235.948 −0.598854
\(395\) 5.69874i 0.0144272i
\(396\) 35.8527 + 59.9926i 0.0905372 + 0.151496i
\(397\) 534.070 1.34526 0.672632 0.739977i \(-0.265164\pi\)
0.672632 + 0.739977i \(0.265164\pi\)
\(398\) 212.237i 0.533259i
\(399\) −473.454 + 130.693i −1.18660 + 0.327551i
\(400\) −360.398 −0.900995
\(401\) 674.374i 1.68173i −0.541245 0.840865i \(-0.682047\pi\)
0.541245 0.840865i \(-0.317953\pi\)
\(402\) 92.6888 + 335.779i 0.230569 + 0.835272i
\(403\) 186.086 0.461751
\(404\) 47.9967i 0.118804i
\(405\) 6.78940 + 3.65163i 0.0167640 + 0.00901637i
\(406\) −257.166 −0.633413
\(407\) 572.257i 1.40604i
\(408\) −283.711 + 78.3158i −0.695369 + 0.191950i
\(409\) 592.660 1.44905 0.724523 0.689251i \(-0.242060\pi\)
0.724523 + 0.689251i \(0.242060\pi\)
\(410\) 7.68220i 0.0187371i
\(411\) −182.647 661.667i −0.444397 1.60989i
\(412\) −5.75457 −0.0139674
\(413\) 78.1353i 0.189190i
\(414\) 59.7383 35.7008i 0.144295 0.0862338i
\(415\) −8.82590 −0.0212672
\(416\) 107.026i 0.257275i
\(417\) 680.654 187.888i 1.63226 0.450571i
\(418\) −658.605 −1.57561
\(419\) 218.340i 0.521098i 0.965461 + 0.260549i \(0.0839036\pi\)
−0.965461 + 0.260549i \(0.916096\pi\)
\(420\) 0.279736 + 1.01339i 0.000666039 + 0.00241283i
\(421\) 262.667 0.623913 0.311957 0.950096i \(-0.399016\pi\)
0.311957 + 0.950096i \(0.399016\pi\)
\(422\) 399.547i 0.946794i
\(423\) −173.320 290.018i −0.409741 0.685622i
\(424\) −606.388 −1.43016
\(425\) 294.692i 0.693392i
\(426\) −277.215 + 76.5227i −0.650739 + 0.179631i
\(427\) 702.350 1.64485
\(428\) 42.9134i 0.100265i
\(429\) 317.503 + 1150.20i 0.740099 + 2.68112i
\(430\) −10.0058 −0.0232693
\(431\) 139.875i 0.324536i −0.986747 0.162268i \(-0.948119\pi\)
0.986747 0.162268i \(-0.0518809\pi\)
\(432\) 269.034 281.479i 0.622764 0.651572i
\(433\) −41.8624 −0.0966799 −0.0483399 0.998831i \(-0.515393\pi\)
−0.0483399 + 0.998831i \(0.515393\pi\)
\(434\) 194.750i 0.448734i
\(435\) 3.64798 1.00699i 0.00838616 0.00231492i
\(436\) 25.7598 0.0590821
\(437\) 65.2488i 0.149311i
\(438\) 44.4148 + 160.899i 0.101404 + 0.367350i
\(439\) −453.852 −1.03383 −0.516916 0.856036i \(-0.672920\pi\)
−0.516916 + 0.856036i \(0.672920\pi\)
\(440\) 16.9881i 0.0386093i
\(441\) 420.862 251.515i 0.954335 0.570330i
\(442\) −416.973 −0.943379
\(443\) 247.987i 0.559789i −0.960031 0.279895i \(-0.909700\pi\)
0.960031 0.279895i \(-0.0902995\pi\)
\(444\) 27.9201 7.70708i 0.0628830 0.0173583i
\(445\) −12.4480 −0.0279731
\(446\) 188.583i 0.422832i
\(447\) −41.7723 151.327i −0.0934504 0.338538i
\(448\) 698.798 1.55982
\(449\) 682.664i 1.52041i −0.649683 0.760205i \(-0.725098\pi\)
0.649683 0.760205i \(-0.274902\pi\)
\(450\) −220.075 368.252i −0.489055 0.818338i
\(451\) 907.908 2.01310
\(452\) 4.92988i 0.0109068i
\(453\) −527.601 + 145.639i −1.16468 + 0.321500i
\(454\) 507.515 1.11787
\(455\) 17.9486i 0.0394474i
\(456\) −106.892 387.233i −0.234413 0.849195i
\(457\) −379.628 −0.830696 −0.415348 0.909662i \(-0.636340\pi\)
−0.415348 + 0.909662i \(0.636340\pi\)
\(458\) 181.081i 0.395374i
\(459\) −230.161 219.985i −0.501440 0.479269i
\(460\) −0.139659 −0.000303607
\(461\) 419.873i 0.910788i 0.890290 + 0.455394i \(0.150502\pi\)
−0.890290 + 0.455394i \(0.849498\pi\)
\(462\) 1203.76 332.287i 2.60554 0.719235i
\(463\) −885.854 −1.91329 −0.956646 0.291253i \(-0.905928\pi\)
−0.956646 + 0.291253i \(0.905928\pi\)
\(464\) 191.143i 0.411946i
\(465\) 0.762590 + 2.76260i 0.00163998 + 0.00594107i
\(466\) 21.2496 0.0456000
\(467\) 393.302i 0.842188i −0.907017 0.421094i \(-0.861646\pi\)
0.907017 0.421094i \(-0.138354\pi\)
\(468\) −51.8415 + 30.9815i −0.110772 + 0.0661998i
\(469\) −619.250 −1.32036
\(470\) 6.81474i 0.0144995i
\(471\) 794.435 219.297i 1.68670 0.465598i
\(472\) −63.9060 −0.135394
\(473\) 1182.52i 2.50004i
\(474\) 91.1679 + 330.269i 0.192337 + 0.696771i
\(475\) −402.221 −0.846780
\(476\) 43.4176i 0.0912135i
\(477\) −336.503 563.072i −0.705457 1.18044i
\(478\) −195.751 −0.409521
\(479\) 32.5927i 0.0680432i 0.999421 + 0.0340216i \(0.0108315\pi\)
−0.999421 + 0.0340216i \(0.989168\pi\)
\(480\) −1.58890 + 0.438601i −0.00331020 + 0.000913751i
\(481\) 494.506 1.02808
\(482\) 258.782i 0.536892i
\(483\) 32.9200 + 119.258i 0.0681574 + 0.246911i
\(484\) −122.804 −0.253728
\(485\) 6.47807i 0.0133568i
\(486\) 451.897 + 103.013i 0.929829 + 0.211962i
\(487\) 12.9619 0.0266157 0.0133079 0.999911i \(-0.495764\pi\)
0.0133079 + 0.999911i \(0.495764\pi\)
\(488\) 574.444i 1.17714i
\(489\) −274.636 + 75.8109i −0.561629 + 0.155033i
\(490\) 9.88927 0.0201822
\(491\) 70.7457i 0.144085i −0.997402 0.0720425i \(-0.977048\pi\)
0.997402 0.0720425i \(-0.0229517\pi\)
\(492\) 12.2276 + 44.2963i 0.0248528 + 0.0900330i
\(493\) −156.294 −0.317027
\(494\) 569.121i 1.15207i
\(495\) −15.7746 + 9.42719i −0.0318678 + 0.0190448i
\(496\) 144.752 0.291838
\(497\) 511.245i 1.02866i
\(498\) −511.504 + 141.196i −1.02712 + 0.283526i
\(499\) −497.143 −0.996279 −0.498140 0.867097i \(-0.665983\pi\)
−0.498140 + 0.867097i \(0.665983\pi\)
\(500\) 1.72215i 0.00344429i
\(501\) −155.936 564.901i −0.311249 1.12755i
\(502\) −398.859 −0.794540
\(503\) 302.588i 0.601567i 0.953692 + 0.300783i \(0.0972481\pi\)
−0.953692 + 0.300783i \(0.902752\pi\)
\(504\) 390.742 + 653.831i 0.775282 + 1.29728i
\(505\) 12.6204 0.0249908
\(506\) 165.895i 0.327856i
\(507\) −505.203 + 139.457i −0.996457 + 0.275063i
\(508\) −43.6040 −0.0858347
\(509\) 44.8634i 0.0881402i 0.999028 + 0.0440701i \(0.0140325\pi\)
−0.999028 + 0.0440701i \(0.985968\pi\)
\(510\) −1.70878 6.19033i −0.00335056 0.0121379i
\(511\) −296.734 −0.580692
\(512\) 563.180i 1.09996i
\(513\) 300.254 314.144i 0.585291 0.612366i
\(514\) −534.963 −1.04078
\(515\) 1.51312i 0.00293809i
\(516\) 57.6944 15.9260i 0.111811 0.0308644i
\(517\) 805.389 1.55781
\(518\) 517.532i 0.999096i
\(519\) −150.613 545.620i −0.290199 1.05129i
\(520\) −14.6799 −0.0282306
\(521\) 57.9774i 0.111281i 0.998451 + 0.0556405i \(0.0177201\pi\)
−0.998451 + 0.0556405i \(0.982280\pi\)
\(522\) 195.308 116.720i 0.374154 0.223602i
\(523\) −681.136 −1.30236 −0.651182 0.758922i \(-0.725726\pi\)
−0.651182 + 0.758922i \(0.725726\pi\)
\(524\) 76.1341i 0.145294i
\(525\) 735.155 202.933i 1.40030 0.386539i
\(526\) −931.703 −1.77130
\(527\) 118.361i 0.224594i
\(528\) 246.978 + 894.714i 0.467761 + 1.69453i
\(529\) 512.565 0.968931
\(530\) 13.2309i 0.0249639i
\(531\) −35.4633 59.3410i −0.0667859 0.111753i
\(532\) 59.2601 0.111391
\(533\) 784.552i 1.47196i
\(534\) −721.424 + 199.142i −1.35098 + 0.372926i
\(535\) −11.2837 −0.0210911
\(536\) 506.478i 0.944921i
\(537\) −157.042 568.910i −0.292444 1.05942i
\(538\) 551.452 1.02500
\(539\) 1168.75i 2.16836i
\(540\) −0.672396 0.642667i −0.00124518 0.00119012i
\(541\) −449.122 −0.830170 −0.415085 0.909783i \(-0.636248\pi\)
−0.415085 + 0.909783i \(0.636248\pi\)
\(542\) 330.263i 0.609340i
\(543\) −42.7851 + 11.8104i −0.0787939 + 0.0217503i
\(544\) 68.0748 0.125138
\(545\) 6.77333i 0.0124281i
\(546\) 287.140 + 1040.21i 0.525897 + 1.90514i
\(547\) −161.571 −0.295377 −0.147689 0.989034i \(-0.547183\pi\)
−0.147689 + 0.989034i \(0.547183\pi\)
\(548\) 82.8178i 0.151127i
\(549\) −533.410 + 318.776i −0.971602 + 0.580649i
\(550\) 1022.65 1.85936
\(551\) 213.324i 0.387158i
\(552\) −97.5396 + 26.9249i −0.176702 + 0.0487770i
\(553\) −609.089 −1.10143
\(554\) 51.6797i 0.0932846i
\(555\) 2.02651 + 7.34136i 0.00365138 + 0.0132277i
\(556\) −85.1943 −0.153227
\(557\) 1097.79i 1.97090i 0.169975 + 0.985448i \(0.445631\pi\)
−0.169975 + 0.985448i \(0.554369\pi\)
\(558\) 88.3915 + 147.906i 0.158408 + 0.265065i
\(559\) 1021.85 1.82800
\(560\) 13.9618i 0.0249317i
\(561\) 731.593 201.950i 1.30409 0.359982i
\(562\) 75.4727 0.134293
\(563\) 310.918i 0.552252i 0.961121 + 0.276126i \(0.0890507\pi\)
−0.961121 + 0.276126i \(0.910949\pi\)
\(564\) 10.8469 + 39.2944i 0.0192320 + 0.0696710i
\(565\) 1.29627 0.00229429
\(566\) 49.3686i 0.0872237i
\(567\) −390.291 + 725.661i −0.688344 + 1.27982i
\(568\) 418.142 0.736165
\(569\) 465.717i 0.818484i 0.912426 + 0.409242i \(0.134207\pi\)
−0.912426 + 0.409242i \(0.865793\pi\)
\(570\) 8.44909 2.33230i 0.0148230 0.00409175i
\(571\) 208.273 0.364752 0.182376 0.983229i \(-0.441621\pi\)
0.182376 + 0.983229i \(0.441621\pi\)
\(572\) 143.965i 0.251688i
\(573\) −97.9260 354.752i −0.170901 0.619113i
\(574\) 821.084 1.43046
\(575\) 101.315i 0.176200i
\(576\) −530.712 + 317.164i −0.921375 + 0.550632i
\(577\) −893.615 −1.54873 −0.774363 0.632742i \(-0.781929\pi\)
−0.774363 + 0.632742i \(0.781929\pi\)
\(578\) 286.010i 0.494826i
\(579\) −583.759 + 161.141i −1.00822 + 0.278310i
\(580\) −0.456601 −0.000787243
\(581\) 943.325i 1.62362i
\(582\) 103.636 + 375.435i 0.178068 + 0.645078i
\(583\) 1563.67 2.68211
\(584\) 242.695i 0.415574i
\(585\) −8.14634 13.6313i −0.0139254 0.0233014i
\(586\) −656.350 −1.12005
\(587\) 625.531i 1.06564i 0.846228 + 0.532821i \(0.178868\pi\)
−0.846228 + 0.532821i \(0.821132\pi\)
\(588\) −57.0224 + 15.7405i −0.0969769 + 0.0267696i
\(589\) 161.549 0.274277
\(590\) 1.39437i 0.00236335i
\(591\) 98.7488 + 357.732i 0.167088 + 0.605300i
\(592\) 384.664 0.649770
\(593\) 361.671i 0.609901i 0.952368 + 0.304951i \(0.0986400\pi\)
−0.952368 + 0.304951i \(0.901360\pi\)
\(594\) −763.397 + 798.711i −1.28518 + 1.34463i
\(595\) 11.4163 0.0191871
\(596\) 18.9409i 0.0317800i
\(597\) 321.783 88.8252i 0.538999 0.148786i
\(598\) −143.355 −0.239725
\(599\) 824.494i 1.37645i −0.725497 0.688225i \(-0.758390\pi\)
0.725497 0.688225i \(-0.241610\pi\)
\(600\) 165.976 + 601.275i 0.276627 + 1.00212i
\(601\) 98.4169 0.163755 0.0818776 0.996642i \(-0.473908\pi\)
0.0818776 + 0.996642i \(0.473908\pi\)
\(602\) 1069.43i 1.77647i
\(603\) 470.299 281.060i 0.779931 0.466102i
\(604\) 66.0374 0.109333
\(605\) 32.2904i 0.0533725i
\(606\) 731.410 201.899i 1.20695 0.333167i
\(607\) −310.874 −0.512149 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(608\) 92.9144i 0.152820i
\(609\) 107.629 + 389.901i 0.176730 + 0.640232i
\(610\) −12.5339 −0.0205473
\(611\) 695.962i 1.13905i
\(612\) 19.7060 + 32.9741i 0.0321993 + 0.0538793i
\(613\) −925.306 −1.50947 −0.754735 0.656029i \(-0.772235\pi\)
−0.754735 + 0.656029i \(0.772235\pi\)
\(614\) 760.719i 1.23896i
\(615\) −11.6473 + 3.21514i −0.0189388 + 0.00522788i
\(616\) −1815.71 −2.94758
\(617\) 88.8400i 0.143987i −0.997405 0.0719935i \(-0.977064\pi\)
0.997405 0.0719935i \(-0.0229361\pi\)
\(618\) −24.2067 87.6925i −0.0391694 0.141897i
\(619\) −572.406 −0.924727 −0.462364 0.886690i \(-0.652999\pi\)
−0.462364 + 0.886690i \(0.652999\pi\)
\(620\) 0.345782i 0.000557713i
\(621\) −79.1293 75.6306i −0.127422 0.121788i
\(622\) 704.359 1.13241
\(623\) 1330.46i 2.13557i
\(624\) −773.151 + 213.421i −1.23902 + 0.342021i
\(625\) 624.321 0.998913
\(626\) 252.208i 0.402888i
\(627\) 275.638 + 998.542i 0.439615 + 1.59257i
\(628\) −99.4359 −0.158337
\(629\) 314.534i 0.500053i
\(630\) −14.2660 + 8.52566i −0.0226445 + 0.0135328i
\(631\) 688.994 1.09191 0.545954 0.837815i \(-0.316167\pi\)
0.545954 + 0.837815i \(0.316167\pi\)
\(632\) 498.167i 0.788239i
\(633\) 605.772 167.218i 0.956985 0.264167i
\(634\) 612.921 0.966752
\(635\) 11.4653i 0.0180556i
\(636\) 21.0593 + 76.2904i 0.0331121 + 0.119953i
\(637\) −1009.95 −1.58548
\(638\) 542.377i 0.850121i
\(639\) 232.039 + 388.272i 0.363129 + 0.607625i
\(640\) −10.2727 −0.0160511
\(641\) 607.078i 0.947080i 0.880772 + 0.473540i \(0.157024\pi\)
−0.880772 + 0.473540i \(0.842976\pi\)
\(642\) −653.947 + 180.516i −1.01861 + 0.281178i
\(643\) 545.922 0.849024 0.424512 0.905422i \(-0.360446\pi\)
0.424512 + 0.905422i \(0.360446\pi\)
\(644\) 14.9270i 0.0231785i
\(645\) 4.18762 + 15.1703i 0.00649243 + 0.0235198i
\(646\) −361.994 −0.560362
\(647\) 595.240i 0.920000i −0.887919 0.460000i \(-0.847849\pi\)
0.887919 0.460000i \(-0.152151\pi\)
\(648\) −593.509 319.215i −0.915910 0.492615i
\(649\) 164.792 0.253916
\(650\) 883.702i 1.35954i
\(651\) −295.270 + 81.5067i −0.453564 + 0.125202i
\(652\) 34.3750 0.0527224
\(653\) 572.686i 0.877008i −0.898729 0.438504i \(-0.855508\pi\)
0.898729 0.438504i \(-0.144492\pi\)
\(654\) 108.359 + 392.547i 0.165687 + 0.600224i
\(655\) 20.0188 0.0305631
\(656\) 610.284i 0.930312i
\(657\) 225.359 134.679i 0.343012 0.204991i
\(658\) 728.369 1.10694
\(659\) 601.131i 0.912187i −0.889932 0.456094i \(-0.849248\pi\)
0.889932 0.456094i \(-0.150752\pi\)
\(660\) 2.13729 0.589979i 0.00323832 0.000893908i
\(661\) 1210.51 1.83132 0.915662 0.401949i \(-0.131667\pi\)
0.915662 + 0.401949i \(0.131667\pi\)
\(662\) 4.28339i 0.00647037i
\(663\) 174.511 + 632.193i 0.263214 + 0.953534i
\(664\) 771.534 1.16195
\(665\) 15.5820i 0.0234315i
\(666\) 234.892 + 393.047i 0.352691 + 0.590160i
\(667\) −53.7339 −0.0805606
\(668\) 70.7061i 0.105847i
\(669\) 285.920 78.9256i 0.427384 0.117975i
\(670\) 11.0509 0.0164939
\(671\) 1481.29i 2.20759i
\(672\) −46.8782 169.823i −0.0697593 0.252713i
\(673\) −1136.89 −1.68928 −0.844641 0.535334i \(-0.820186\pi\)
−0.844641 + 0.535334i \(0.820186\pi\)
\(674\) 642.049i 0.952596i
\(675\) −466.219 + 487.786i −0.690694 + 0.722646i
\(676\) 63.2340 0.0935415
\(677\) 250.404i 0.369872i 0.982751 + 0.184936i \(0.0592078\pi\)
−0.982751 + 0.184936i \(0.940792\pi\)
\(678\) 75.1252 20.7376i 0.110804 0.0305865i
\(679\) −692.385 −1.01971
\(680\) 9.33727i 0.0137313i
\(681\) −212.405 769.467i −0.311901 1.12991i
\(682\) −410.740 −0.602257
\(683\) 375.307i 0.549497i −0.961516 0.274749i \(-0.911405\pi\)
0.961516 0.274749i \(-0.0885946\pi\)
\(684\) −45.0060 + 26.8964i −0.0657982 + 0.0393223i
\(685\) −21.7763 −0.0317902
\(686\) 106.261i 0.154900i
\(687\) −274.546 + 75.7860i −0.399630 + 0.110314i
\(688\) 794.875 1.15534
\(689\) 1351.22i 1.96113i
\(690\) −0.587479 2.12823i −0.000851419 0.00308439i
\(691\) −897.005 −1.29813 −0.649063 0.760734i \(-0.724839\pi\)
−0.649063 + 0.760734i \(0.724839\pi\)
\(692\) 68.2928i 0.0986890i
\(693\) −1007.59 1686.01i −1.45396 2.43291i
\(694\) −160.954 −0.231923
\(695\) 22.4012i 0.0322319i
\(696\) −318.896 + 88.0282i −0.458183 + 0.126477i
\(697\) 499.020 0.715954
\(698\) 573.019i 0.820943i
\(699\) −8.89336 32.2175i −0.0127230 0.0460909i
\(700\) −92.0160 −0.131451
\(701\) 27.9883i 0.0399263i 0.999801 + 0.0199631i \(0.00635489\pi\)
−0.999801 + 0.0199631i \(0.993645\pi\)
\(702\) −690.192 659.675i −0.983179 0.939709i
\(703\) 429.303 0.610672
\(704\) 1473.80i 2.09347i
\(705\) −10.3322 + 2.85210i −0.0146555 + 0.00404553i
\(706\) 1033.69 1.46414
\(707\) 1348.88i 1.90789i
\(708\) 2.21939 + 8.04008i 0.00313473 + 0.0113561i
\(709\) −193.636 −0.273112 −0.136556 0.990632i \(-0.543603\pi\)
−0.136556 + 0.990632i \(0.543603\pi\)
\(710\) 9.12349i 0.0128500i
\(711\) 462.581 276.448i 0.650607 0.388815i
\(712\) 1088.17 1.52833
\(713\) 40.6925i 0.0570722i
\(714\) 661.630 182.637i 0.926653 0.255794i
\(715\) 37.8546 0.0529434
\(716\) 71.2079i 0.0994523i
\(717\) 81.9255 + 296.787i 0.114261 + 0.413929i
\(718\) −472.929 −0.658676
\(719\) 40.3715i 0.0561495i −0.999606 0.0280748i \(-0.991062\pi\)
0.999606 0.0280748i \(-0.00893765\pi\)
\(720\) −6.33684 10.6035i −0.00880117 0.0147270i
\(721\) 161.724 0.224305
\(722\) 194.479i 0.269361i
\(723\) −392.352 + 108.305i −0.542672 + 0.149800i
\(724\) 5.35521 0.00739670
\(725\) 331.238i 0.456881i
\(726\) −516.578 1871.38i −0.711540 2.57766i
\(727\) 155.577 0.213998 0.106999 0.994259i \(-0.465876\pi\)
0.106999 + 0.994259i \(0.465876\pi\)
\(728\) 1569.01i 2.15524i
\(729\) −32.9439 728.255i −0.0451905 0.998978i
\(730\) 5.29540 0.00725397
\(731\) 649.956i 0.889133i
\(732\) 72.2714 19.9499i 0.0987315 0.0272539i
\(733\) −314.245 −0.428711 −0.214356 0.976756i \(-0.568765\pi\)
−0.214356 + 0.976756i \(0.568765\pi\)
\(734\) 703.722i 0.958749i
\(735\) −4.13884 14.9936i −0.00563108 0.0203994i
\(736\) 23.4041 0.0317990
\(737\) 1306.03i 1.77209i
\(738\) −623.584 + 372.666i −0.844965 + 0.504967i
\(739\) −388.040 −0.525088 −0.262544 0.964920i \(-0.584562\pi\)
−0.262544 + 0.964920i \(0.584562\pi\)
\(740\) 0.918884i 0.00124174i
\(741\) −862.872 + 238.188i −1.16447 + 0.321441i
\(742\) 1414.13 1.90584
\(743\) 972.982i 1.30953i −0.755832 0.654766i \(-0.772767\pi\)
0.755832 0.654766i \(-0.227233\pi\)
\(744\) −66.6634 241.498i −0.0896013 0.324594i
\(745\) −4.98035 −0.00668503
\(746\) 31.6985i 0.0424913i
\(747\) 428.147 + 716.421i 0.573156 + 0.959065i
\(748\) −91.5702 −0.122420
\(749\) 1206.02i 1.61018i
\(750\) −26.2434 + 7.24424i −0.0349912 + 0.00965899i
\(751\) −1188.98 −1.58319 −0.791596 0.611044i \(-0.790750\pi\)
−0.791596 + 0.611044i \(0.790750\pi\)
\(752\) 541.372i 0.719910i
\(753\) 166.930 + 604.729i 0.221687 + 0.803093i
\(754\) −468.685 −0.621598
\(755\) 17.3640i 0.0229987i
\(756\) 68.6891 71.8666i 0.0908586 0.0950617i
\(757\) 378.178 0.499575 0.249787 0.968301i \(-0.419639\pi\)
0.249787 + 0.968301i \(0.419639\pi\)
\(758\) 346.767i 0.457476i
\(759\) 251.521 69.4302i 0.331385 0.0914759i
\(760\) −12.7443 −0.0167688
\(761\) 584.274i 0.767771i −0.923381 0.383886i \(-0.874586\pi\)
0.923381 0.383886i \(-0.125414\pi\)
\(762\) −183.421 664.471i −0.240710 0.872009i
\(763\) −723.942 −0.948810
\(764\) 44.4027i 0.0581187i
\(765\) −8.67028 + 5.18153i −0.0113337 + 0.00677324i
\(766\) −486.122 −0.634623
\(767\) 142.402i 0.185661i
\(768\) 199.277 55.0086i 0.259475 0.0716257i
\(769\) −827.160 −1.07563 −0.537815 0.843063i \(-0.680750\pi\)
−0.537815 + 0.843063i \(0.680750\pi\)
\(770\) 39.6172i 0.0514509i
\(771\) 223.892 + 811.082i 0.290391 + 1.05199i
\(772\) 73.0664 0.0946456
\(773\) 39.7974i 0.0514843i 0.999669 + 0.0257422i \(0.00819489\pi\)
−0.999669 + 0.0257422i \(0.991805\pi\)
\(774\) 485.385 + 812.197i 0.627112 + 1.04935i
\(775\) −250.845 −0.323671
\(776\) 566.294i 0.729760i
\(777\) −784.654 + 216.597i −1.00985 + 0.278760i
\(778\) 1170.13 1.50402
\(779\) 681.105i 0.874333i
\(780\) 0.509820 + 1.84690i 0.000653615 + 0.00236782i
\(781\) −1078.24 −1.38059
\(782\) 91.1821i 0.116601i
\(783\) −258.705 247.266i −0.330402 0.315794i
\(784\) −785.617 −1.00206
\(785\) 26.1459i 0.0333068i
\(786\) 1160.19