Properties

Label 177.3.b.a.119.27
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 119.27
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.12

$q$-expansion

\(f(q)\) \(=\) \(q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +O(q^{10})\) \(q+1.89638i q^{2} +(0.180746 + 2.99455i) q^{3} +0.403751 q^{4} -2.43864i q^{5} +(-5.67880 + 0.342762i) q^{6} -8.99368 q^{7} +8.35118i q^{8} +(-8.93466 + 1.08250i) q^{9} +4.62459 q^{10} +9.24832i q^{11} +(0.0729763 + 1.20905i) q^{12} -11.6512 q^{13} -17.0554i q^{14} +(7.30264 - 0.440774i) q^{15} -14.2220 q^{16} +27.6502i q^{17} +(-2.05284 - 16.9435i) q^{18} +29.8253 q^{19} -0.984604i q^{20} +(-1.62557 - 26.9320i) q^{21} -17.5383 q^{22} -29.8868i q^{23} +(-25.0080 + 1.50944i) q^{24} +19.0530 q^{25} -22.0950i q^{26} +(-4.85652 - 26.5596i) q^{27} -3.63121 q^{28} +16.6314i q^{29} +(0.835875 + 13.8486i) q^{30} -11.5203 q^{31} +6.43445i q^{32} +(-27.6946 + 1.67160i) q^{33} -52.4351 q^{34} +21.9324i q^{35} +(-3.60738 + 0.437062i) q^{36} +68.3024 q^{37} +56.5600i q^{38} +(-2.10590 - 34.8900i) q^{39} +20.3655 q^{40} +2.67565i q^{41} +(51.0733 - 3.08269i) q^{42} +14.6822 q^{43} +3.73402i q^{44} +(2.63984 + 21.7884i) q^{45} +56.6767 q^{46} +15.0479i q^{47} +(-2.57056 - 42.5884i) q^{48} +31.8863 q^{49} +36.1317i q^{50} +(-82.7998 + 4.99765i) q^{51} -4.70417 q^{52} +67.2208i q^{53} +(50.3671 - 9.20979i) q^{54} +22.5533 q^{55} -75.1078i q^{56} +(5.39080 + 89.3134i) q^{57} -31.5394 q^{58} -7.68115i q^{59} +(2.94845 - 0.177963i) q^{60} +102.337 q^{61} -21.8468i q^{62} +(80.3555 - 9.73570i) q^{63} -69.0901 q^{64} +28.4130i q^{65} +(-3.16998 - 52.5193i) q^{66} -55.2408 q^{67} +11.1638i q^{68} +(89.4976 - 5.40192i) q^{69} -41.5921 q^{70} -123.624i q^{71} +(-9.04019 - 74.6149i) q^{72} -81.1699 q^{73} +129.527i q^{74} +(3.44375 + 57.0552i) q^{75} +12.0420 q^{76} -83.1764i q^{77} +(66.1646 - 3.99358i) q^{78} -45.7843 q^{79} +34.6823i q^{80} +(78.6564 - 19.3436i) q^{81} -5.07404 q^{82} +144.462i q^{83} +(-0.656325 - 10.8738i) q^{84} +67.4288 q^{85} +27.8430i q^{86} +(-49.8036 + 3.00606i) q^{87} -77.2343 q^{88} +8.00625i q^{89} +(-41.3191 + 5.00614i) q^{90} +104.787 q^{91} -12.0668i q^{92} +(-2.08224 - 34.4980i) q^{93} -28.5365 q^{94} -72.7332i q^{95} +(-19.2683 + 1.16300i) q^{96} -41.6023 q^{97} +60.4684i q^{98} +(-10.0114 - 82.6306i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.89638i 0.948189i 0.880474 + 0.474094i \(0.157224\pi\)
−0.880474 + 0.474094i \(0.842776\pi\)
\(3\) 0.180746 + 2.99455i 0.0602486 + 0.998183i
\(4\) 0.403751 0.100938
\(5\) 2.43864i 0.487728i −0.969809 0.243864i \(-0.921585\pi\)
0.969809 0.243864i \(-0.0784151\pi\)
\(6\) −5.67880 + 0.342762i −0.946466 + 0.0571271i
\(7\) −8.99368 −1.28481 −0.642406 0.766365i \(-0.722064\pi\)
−0.642406 + 0.766365i \(0.722064\pi\)
\(8\) 8.35118i 1.04390i
\(9\) −8.93466 + 1.08250i −0.992740 + 0.120278i
\(10\) 4.62459 0.462459
\(11\) 9.24832i 0.840756i 0.907349 + 0.420378i \(0.138103\pi\)
−0.907349 + 0.420378i \(0.861897\pi\)
\(12\) 0.0729763 + 1.20905i 0.00608136 + 0.100754i
\(13\) −11.6512 −0.896243 −0.448121 0.893973i \(-0.647907\pi\)
−0.448121 + 0.893973i \(0.647907\pi\)
\(14\) 17.0554i 1.21824i
\(15\) 7.30264 0.440774i 0.486842 0.0293850i
\(16\) −14.2220 −0.888874
\(17\) 27.6502i 1.62648i 0.581929 + 0.813240i \(0.302298\pi\)
−0.581929 + 0.813240i \(0.697702\pi\)
\(18\) −2.05284 16.9435i −0.114047 0.941305i
\(19\) 29.8253 1.56975 0.784876 0.619652i \(-0.212726\pi\)
0.784876 + 0.619652i \(0.212726\pi\)
\(20\) 0.984604i 0.0492302i
\(21\) −1.62557 26.9320i −0.0774081 1.28248i
\(22\) −17.5383 −0.797196
\(23\) 29.8868i 1.29943i −0.760179 0.649714i \(-0.774889\pi\)
0.760179 0.649714i \(-0.225111\pi\)
\(24\) −25.0080 + 1.50944i −1.04200 + 0.0628933i
\(25\) 19.0530 0.762121
\(26\) 22.0950i 0.849807i
\(27\) −4.85652 26.5596i −0.179871 0.983690i
\(28\) −3.63121 −0.129686
\(29\) 16.6314i 0.573497i 0.958006 + 0.286748i \(0.0925744\pi\)
−0.958006 + 0.286748i \(0.907426\pi\)
\(30\) 0.835875 + 13.8486i 0.0278625 + 0.461619i
\(31\) −11.5203 −0.371621 −0.185811 0.982586i \(-0.559491\pi\)
−0.185811 + 0.982586i \(0.559491\pi\)
\(32\) 6.43445i 0.201077i
\(33\) −27.6946 + 1.67160i −0.839229 + 0.0506544i
\(34\) −52.4351 −1.54221
\(35\) 21.9324i 0.626639i
\(36\) −3.60738 + 0.437062i −0.100205 + 0.0121406i
\(37\) 68.3024 1.84601 0.923006 0.384786i \(-0.125725\pi\)
0.923006 + 0.384786i \(0.125725\pi\)
\(38\) 56.5600i 1.48842i
\(39\) −2.10590 34.8900i −0.0539974 0.894615i
\(40\) 20.3655 0.509138
\(41\) 2.67565i 0.0652597i 0.999468 + 0.0326299i \(0.0103883\pi\)
−0.999468 + 0.0326299i \(0.989612\pi\)
\(42\) 51.0733 3.08269i 1.21603 0.0733975i
\(43\) 14.6822 0.341447 0.170723 0.985319i \(-0.445390\pi\)
0.170723 + 0.985319i \(0.445390\pi\)
\(44\) 3.73402i 0.0848641i
\(45\) 2.63984 + 21.7884i 0.0586632 + 0.484188i
\(46\) 56.6767 1.23210
\(47\) 15.0479i 0.320169i 0.987103 + 0.160084i \(0.0511766\pi\)
−0.987103 + 0.160084i \(0.948823\pi\)
\(48\) −2.57056 42.5884i −0.0535534 0.887259i
\(49\) 31.8863 0.650740
\(50\) 36.1317i 0.722635i
\(51\) −82.7998 + 4.99765i −1.62353 + 0.0979931i
\(52\) −4.70417 −0.0904647
\(53\) 67.2208i 1.26832i 0.773203 + 0.634159i \(0.218653\pi\)
−0.773203 + 0.634159i \(0.781347\pi\)
\(54\) 50.3671 9.20979i 0.932724 0.170552i
\(55\) 22.5533 0.410061
\(56\) 75.1078i 1.34121i
\(57\) 5.39080 + 89.3134i 0.0945754 + 1.56690i
\(58\) −31.5394 −0.543783
\(59\) 7.68115i 0.130189i
\(60\) 2.94845 0.177963i 0.0491408 0.00296605i
\(61\) 102.337 1.67766 0.838830 0.544393i \(-0.183240\pi\)
0.838830 + 0.544393i \(0.183240\pi\)
\(62\) 21.8468i 0.352367i
\(63\) 80.3555 9.73570i 1.27548 0.154535i
\(64\) −69.0901 −1.07953
\(65\) 28.4130i 0.437123i
\(66\) −3.16998 52.5193i −0.0480299 0.795748i
\(67\) −55.2408 −0.824489 −0.412245 0.911073i \(-0.635255\pi\)
−0.412245 + 0.911073i \(0.635255\pi\)
\(68\) 11.1638i 0.164173i
\(69\) 89.4976 5.40192i 1.29707 0.0782887i
\(70\) −41.5921 −0.594172
\(71\) 123.624i 1.74118i −0.492009 0.870590i \(-0.663737\pi\)
0.492009 0.870590i \(-0.336263\pi\)
\(72\) −9.04019 74.6149i −0.125558 1.03632i
\(73\) −81.1699 −1.11192 −0.555958 0.831210i \(-0.687649\pi\)
−0.555958 + 0.831210i \(0.687649\pi\)
\(74\) 129.527i 1.75037i
\(75\) 3.44375 + 57.0552i 0.0459167 + 0.760736i
\(76\) 12.0420 0.158447
\(77\) 83.1764i 1.08021i
\(78\) 66.1646 3.99358i 0.848264 0.0511997i
\(79\) −45.7843 −0.579549 −0.289774 0.957095i \(-0.593580\pi\)
−0.289774 + 0.957095i \(0.593580\pi\)
\(80\) 34.6823i 0.433529i
\(81\) 78.6564 19.3436i 0.971066 0.238810i
\(82\) −5.07404 −0.0618786
\(83\) 144.462i 1.74051i 0.492606 + 0.870253i \(0.336044\pi\)
−0.492606 + 0.870253i \(0.663956\pi\)
\(84\) −0.656325 10.8738i −0.00781340 0.129450i
\(85\) 67.4288 0.793280
\(86\) 27.8430i 0.323756i
\(87\) −49.8036 + 3.00606i −0.572455 + 0.0345524i
\(88\) −77.2343 −0.877663
\(89\) 8.00625i 0.0899578i 0.998988 + 0.0449789i \(0.0143221\pi\)
−0.998988 + 0.0449789i \(0.985678\pi\)
\(90\) −41.3191 + 5.00614i −0.459101 + 0.0556238i
\(91\) 104.787 1.15150
\(92\) 12.0668i 0.131161i
\(93\) −2.08224 34.4980i −0.0223897 0.370946i
\(94\) −28.5365 −0.303580
\(95\) 72.7332i 0.765613i
\(96\) −19.2683 + 1.16300i −0.200711 + 0.0121146i
\(97\) −41.6023 −0.428890 −0.214445 0.976736i \(-0.568794\pi\)
−0.214445 + 0.976736i \(0.568794\pi\)
\(98\) 60.4684i 0.617024i
\(99\) −10.0114 82.6306i −0.101125 0.834653i
\(100\) 7.69268 0.0769268
\(101\) 10.6631i 0.105575i 0.998606 + 0.0527874i \(0.0168106\pi\)
−0.998606 + 0.0527874i \(0.983189\pi\)
\(102\) −9.47743 157.020i −0.0929160 1.53941i
\(103\) 67.0506 0.650977 0.325488 0.945546i \(-0.394471\pi\)
0.325488 + 0.945546i \(0.394471\pi\)
\(104\) 97.3008i 0.935585i
\(105\) −65.6776 + 3.96418i −0.625501 + 0.0377541i
\(106\) −127.476 −1.20260
\(107\) 52.2979i 0.488765i −0.969679 0.244383i \(-0.921415\pi\)
0.969679 0.244383i \(-0.0785853\pi\)
\(108\) −1.96082 10.7235i −0.0181558 0.0992915i
\(109\) −83.2905 −0.764133 −0.382066 0.924135i \(-0.624787\pi\)
−0.382066 + 0.924135i \(0.624787\pi\)
\(110\) 42.7697i 0.388815i
\(111\) 12.3454 + 204.535i 0.111220 + 1.84266i
\(112\) 127.908 1.14204
\(113\) 105.890i 0.937079i 0.883443 + 0.468539i \(0.155220\pi\)
−0.883443 + 0.468539i \(0.844780\pi\)
\(114\) −169.372 + 10.2230i −1.48572 + 0.0896754i
\(115\) −72.8833 −0.633768
\(116\) 6.71495i 0.0578875i
\(117\) 104.099 12.6124i 0.889736 0.107799i
\(118\) 14.5664 0.123444
\(119\) 248.677i 2.08972i
\(120\) 3.68098 + 60.9856i 0.0306749 + 0.508213i
\(121\) 35.4686 0.293129
\(122\) 194.070i 1.59074i
\(123\) −8.01237 + 0.483612i −0.0651412 + 0.00393181i
\(124\) −4.65132 −0.0375106
\(125\) 107.430i 0.859437i
\(126\) 18.4626 + 152.384i 0.146528 + 1.20940i
\(127\) −127.874 −1.00688 −0.503442 0.864029i \(-0.667933\pi\)
−0.503442 + 0.864029i \(0.667933\pi\)
\(128\) 105.283i 0.822524i
\(129\) 2.65375 + 43.9666i 0.0205717 + 0.340826i
\(130\) −53.8818 −0.414475
\(131\) 135.750i 1.03626i −0.855302 0.518130i \(-0.826628\pi\)
0.855302 0.518130i \(-0.173372\pi\)
\(132\) −11.1817 + 0.674908i −0.0847099 + 0.00511294i
\(133\) −268.239 −2.01684
\(134\) 104.757i 0.781772i
\(135\) −64.7695 + 11.8433i −0.479774 + 0.0877282i
\(136\) −230.911 −1.69788
\(137\) 0.886492i 0.00647074i 0.999995 + 0.00323537i \(0.00102985\pi\)
−0.999995 + 0.00323537i \(0.998970\pi\)
\(138\) 10.2441 + 169.721i 0.0742324 + 1.22986i
\(139\) −28.7731 −0.207001 −0.103500 0.994629i \(-0.533004\pi\)
−0.103500 + 0.994629i \(0.533004\pi\)
\(140\) 8.85522i 0.0632515i
\(141\) −45.0618 + 2.71985i −0.319587 + 0.0192897i
\(142\) 234.437 1.65097
\(143\) 107.754i 0.753522i
\(144\) 127.069 15.3954i 0.882421 0.106912i
\(145\) 40.5581 0.279711
\(146\) 153.929i 1.05431i
\(147\) 5.76331 + 95.4850i 0.0392062 + 0.649558i
\(148\) 27.5772 0.186332
\(149\) 134.861i 0.905106i −0.891737 0.452553i \(-0.850513\pi\)
0.891737 0.452553i \(-0.149487\pi\)
\(150\) −108.198 + 6.53066i −0.721322 + 0.0435377i
\(151\) 265.411 1.75769 0.878843 0.477110i \(-0.158316\pi\)
0.878843 + 0.477110i \(0.158316\pi\)
\(152\) 249.076i 1.63866i
\(153\) −29.9314 247.045i −0.195630 1.61467i
\(154\) 157.734 1.02425
\(155\) 28.0938i 0.181250i
\(156\) −0.850258 14.0869i −0.00545037 0.0903004i
\(157\) 120.706 0.768826 0.384413 0.923161i \(-0.374404\pi\)
0.384413 + 0.923161i \(0.374404\pi\)
\(158\) 86.8244i 0.549522i
\(159\) −201.296 + 12.1499i −1.26601 + 0.0764143i
\(160\) 15.6913 0.0980708
\(161\) 268.792i 1.66952i
\(162\) 36.6828 + 149.162i 0.226437 + 0.920754i
\(163\) 266.809 1.63686 0.818432 0.574603i \(-0.194844\pi\)
0.818432 + 0.574603i \(0.194844\pi\)
\(164\) 1.08030i 0.00658717i
\(165\) 4.07642 + 67.5371i 0.0247056 + 0.409316i
\(166\) −273.954 −1.65033
\(167\) 165.193i 0.989179i 0.869127 + 0.494589i \(0.164682\pi\)
−0.869127 + 0.494589i \(0.835318\pi\)
\(168\) 224.914 13.5754i 1.33877 0.0808061i
\(169\) −33.2506 −0.196749
\(170\) 127.871i 0.752180i
\(171\) −266.479 + 32.2860i −1.55836 + 0.188807i
\(172\) 5.92796 0.0344649
\(173\) 4.59582i 0.0265654i 0.999912 + 0.0132827i \(0.00422814\pi\)
−0.999912 + 0.0132827i \(0.995772\pi\)
\(174\) −5.70062 94.4464i −0.0327622 0.542796i
\(175\) −171.357 −0.979182
\(176\) 131.529i 0.747326i
\(177\) 23.0016 1.38833i 0.129952 0.00784370i
\(178\) −15.1829 −0.0852970
\(179\) 201.860i 1.12771i −0.825875 0.563854i \(-0.809318\pi\)
0.825875 0.563854i \(-0.190682\pi\)
\(180\) 1.06584 + 8.79711i 0.00592133 + 0.0488728i
\(181\) 59.5716 0.329125 0.164562 0.986367i \(-0.447379\pi\)
0.164562 + 0.986367i \(0.447379\pi\)
\(182\) 198.715i 1.09184i
\(183\) 18.4970 + 306.454i 0.101077 + 1.67461i
\(184\) 249.590 1.35647
\(185\) 166.565i 0.900352i
\(186\) 65.4213 3.94871i 0.351727 0.0212296i
\(187\) −255.717 −1.36747
\(188\) 6.07561i 0.0323171i
\(189\) 43.6780 + 238.869i 0.231100 + 1.26386i
\(190\) 137.930 0.725946
\(191\) 224.796i 1.17694i −0.808519 0.588470i \(-0.799730\pi\)
0.808519 0.588470i \(-0.200270\pi\)
\(192\) −12.4877 206.894i −0.0650403 1.07757i
\(193\) 120.501 0.624357 0.312178 0.950024i \(-0.398941\pi\)
0.312178 + 0.950024i \(0.398941\pi\)
\(194\) 78.8937i 0.406669i
\(195\) −85.0842 + 5.13553i −0.436329 + 0.0263361i
\(196\) 12.8741 0.0656842
\(197\) 39.8294i 0.202180i 0.994877 + 0.101090i \(0.0322330\pi\)
−0.994877 + 0.101090i \(0.967767\pi\)
\(198\) 156.699 18.9853i 0.791408 0.0958854i
\(199\) −74.5626 −0.374687 −0.187343 0.982295i \(-0.559988\pi\)
−0.187343 + 0.982295i \(0.559988\pi\)
\(200\) 159.115i 0.795576i
\(201\) −9.98454 165.421i −0.0496743 0.822991i
\(202\) −20.2212 −0.100105
\(203\) 149.578i 0.736835i
\(204\) −33.4305 + 2.01781i −0.163875 + 0.00989121i
\(205\) 6.52495 0.0318290
\(206\) 127.153i 0.617249i
\(207\) 32.3526 + 267.029i 0.156293 + 1.28999i
\(208\) 165.702 0.796647
\(209\) 275.834i 1.31978i
\(210\) −7.51759 124.549i −0.0357980 0.593093i
\(211\) 400.704 1.89907 0.949536 0.313658i \(-0.101555\pi\)
0.949536 + 0.313658i \(0.101555\pi\)
\(212\) 27.1405i 0.128021i
\(213\) 370.198 22.3445i 1.73802 0.104904i
\(214\) 99.1765 0.463442
\(215\) 35.8047i 0.166533i
\(216\) 221.804 40.5576i 1.02687 0.187767i
\(217\) 103.610 0.477463
\(218\) 157.950i 0.724542i
\(219\) −14.6711 243.067i −0.0669914 1.10990i
\(220\) 9.10594 0.0413906
\(221\) 322.156i 1.45772i
\(222\) −387.876 + 23.4115i −1.74719 + 0.105457i
\(223\) −318.939 −1.43022 −0.715110 0.699012i \(-0.753623\pi\)
−0.715110 + 0.699012i \(0.753623\pi\)
\(224\) 57.8694i 0.258346i
\(225\) −170.232 + 20.6250i −0.756588 + 0.0916666i
\(226\) −200.807 −0.888528
\(227\) 13.1790i 0.0580573i 0.999579 + 0.0290287i \(0.00924141\pi\)
−0.999579 + 0.0290287i \(0.990759\pi\)
\(228\) 2.17654 + 36.0604i 0.00954623 + 0.158160i
\(229\) 134.842 0.588832 0.294416 0.955677i \(-0.404875\pi\)
0.294416 + 0.955677i \(0.404875\pi\)
\(230\) 138.214i 0.600931i
\(231\) 249.076 15.0338i 1.07825 0.0650813i
\(232\) −138.892 −0.598672
\(233\) 67.8138i 0.291046i −0.989355 0.145523i \(-0.953513\pi\)
0.989355 0.145523i \(-0.0464865\pi\)
\(234\) 23.9179 + 197.411i 0.102213 + 0.843638i
\(235\) 36.6965 0.156155
\(236\) 3.10127i 0.0131410i
\(237\) −8.27533 137.104i −0.0349170 0.578496i
\(238\) 471.585 1.98145
\(239\) 91.0150i 0.380816i 0.981705 + 0.190408i \(0.0609811\pi\)
−0.981705 + 0.190408i \(0.939019\pi\)
\(240\) −103.858 + 6.26868i −0.432742 + 0.0261195i
\(241\) 212.975 0.883714 0.441857 0.897086i \(-0.354320\pi\)
0.441857 + 0.897086i \(0.354320\pi\)
\(242\) 67.2618i 0.277941i
\(243\) 72.1423 + 232.044i 0.296882 + 0.954914i
\(244\) 41.3188 0.169339
\(245\) 77.7592i 0.317384i
\(246\) −0.917112 15.1945i −0.00372810 0.0617662i
\(247\) −347.499 −1.40688
\(248\) 96.2077i 0.387934i
\(249\) −432.598 + 26.1109i −1.73734 + 0.104863i
\(250\) 203.727 0.814908
\(251\) 198.118i 0.789314i 0.918829 + 0.394657i \(0.129137\pi\)
−0.918829 + 0.394657i \(0.870863\pi\)
\(252\) 32.4436 3.93080i 0.128744 0.0155984i
\(253\) 276.403 1.09250
\(254\) 242.498i 0.954716i
\(255\) 12.1875 + 201.919i 0.0477940 + 0.791839i
\(256\) −76.7038 −0.299624
\(257\) 269.943i 1.05036i 0.850991 + 0.525181i \(0.176002\pi\)
−0.850991 + 0.525181i \(0.823998\pi\)
\(258\) −83.3773 + 5.03251i −0.323168 + 0.0195058i
\(259\) −614.290 −2.37178
\(260\) 11.4718i 0.0441222i
\(261\) −18.0036 148.596i −0.0689792 0.569334i
\(262\) 257.433 0.982570
\(263\) 62.6176i 0.238090i −0.992889 0.119045i \(-0.962017\pi\)
0.992889 0.119045i \(-0.0379833\pi\)
\(264\) −13.9598 231.282i −0.0528780 0.876069i
\(265\) 163.927 0.618594
\(266\) 508.683i 1.91234i
\(267\) −23.9751 + 1.44710i −0.0897944 + 0.00541983i
\(268\) −22.3035 −0.0832221
\(269\) 103.492i 0.384728i 0.981324 + 0.192364i \(0.0616154\pi\)
−0.981324 + 0.192364i \(0.938385\pi\)
\(270\) −22.4594 122.827i −0.0831829 0.454916i
\(271\) −264.533 −0.976137 −0.488069 0.872805i \(-0.662298\pi\)
−0.488069 + 0.872805i \(0.662298\pi\)
\(272\) 393.240i 1.44574i
\(273\) 18.9398 + 313.789i 0.0693764 + 1.14941i
\(274\) −1.68112 −0.00613549
\(275\) 176.208i 0.640758i
\(276\) 36.1347 2.18103i 0.130923 0.00790228i
\(277\) −47.1067 −0.170060 −0.0850301 0.996378i \(-0.527099\pi\)
−0.0850301 + 0.996378i \(0.527099\pi\)
\(278\) 54.5646i 0.196276i
\(279\) 102.930 12.4707i 0.368923 0.0446980i
\(280\) −183.161 −0.654147
\(281\) 202.879i 0.721989i 0.932568 + 0.360995i \(0.117563\pi\)
−0.932568 + 0.360995i \(0.882437\pi\)
\(282\) −5.15786 85.4541i −0.0182903 0.303029i
\(283\) −71.1501 −0.251414 −0.125707 0.992067i \(-0.540120\pi\)
−0.125707 + 0.992067i \(0.540120\pi\)
\(284\) 49.9132i 0.175751i
\(285\) 217.803 13.1462i 0.764222 0.0461271i
\(286\) 204.342 0.714481
\(287\) 24.0639i 0.0838464i
\(288\) −6.96533 57.4897i −0.0241852 0.199617i
\(289\) −475.531 −1.64544
\(290\) 76.9134i 0.265219i
\(291\) −7.51944 124.580i −0.0258400 0.428111i
\(292\) −32.7724 −0.112234
\(293\) 224.865i 0.767458i −0.923446 0.383729i \(-0.874640\pi\)
0.923446 0.383729i \(-0.125360\pi\)
\(294\) −181.076 + 10.9294i −0.615903 + 0.0371749i
\(295\) −18.7316 −0.0634968
\(296\) 570.406i 1.92705i
\(297\) 245.632 44.9146i 0.827044 0.151228i
\(298\) 255.747 0.858212
\(299\) 348.216i 1.16460i
\(300\) 1.39042 + 23.0361i 0.00463473 + 0.0767870i
\(301\) −132.047 −0.438695
\(302\) 503.319i 1.66662i
\(303\) −31.9310 + 1.92730i −0.105383 + 0.00636073i
\(304\) −424.175 −1.39531
\(305\) 249.564i 0.818243i
\(306\) 468.490 56.7613i 1.53101 0.185494i
\(307\) −582.919 −1.89876 −0.949380 0.314130i \(-0.898287\pi\)
−0.949380 + 0.314130i \(0.898287\pi\)
\(308\) 33.5826i 0.109034i
\(309\) 12.1191 + 200.786i 0.0392204 + 0.649794i
\(310\) −53.2765 −0.171860
\(311\) 288.317i 0.927064i 0.886080 + 0.463532i \(0.153418\pi\)
−0.886080 + 0.463532i \(0.846582\pi\)
\(312\) 291.372 17.5867i 0.933885 0.0563677i
\(313\) 45.4385 0.145171 0.0725855 0.997362i \(-0.476875\pi\)
0.0725855 + 0.997362i \(0.476875\pi\)
\(314\) 228.904i 0.728993i
\(315\) −23.7419 195.958i −0.0753711 0.622090i
\(316\) −18.4855 −0.0584983
\(317\) 135.104i 0.426197i −0.977031 0.213099i \(-0.931644\pi\)
0.977031 0.213099i \(-0.0683555\pi\)
\(318\) −23.0408 381.733i −0.0724552 1.20042i
\(319\) −153.813 −0.482171
\(320\) 168.486i 0.526519i
\(321\) 156.609 9.45262i 0.487877 0.0294474i
\(322\) −509.732 −1.58302
\(323\) 824.674i 2.55317i
\(324\) 31.7576 7.81001i 0.0980173 0.0241050i
\(325\) −221.990 −0.683045
\(326\) 505.971i 1.55206i
\(327\) −15.0544 249.418i −0.0460379 0.762745i
\(328\) −22.3448 −0.0681244
\(329\) 135.336i 0.411356i
\(330\) −128.076 + 7.73044i −0.388109 + 0.0234256i
\(331\) 12.7021 0.0383748 0.0191874 0.999816i \(-0.493892\pi\)
0.0191874 + 0.999816i \(0.493892\pi\)
\(332\) 58.3267i 0.175683i
\(333\) −610.259 + 73.9377i −1.83261 + 0.222035i
\(334\) −313.268 −0.937928
\(335\) 134.712i 0.402127i
\(336\) 23.1188 + 383.027i 0.0688060 + 1.13996i
\(337\) 459.719 1.36415 0.682076 0.731281i \(-0.261077\pi\)
0.682076 + 0.731281i \(0.261077\pi\)
\(338\) 63.0557i 0.186555i
\(339\) −317.093 + 19.1392i −0.935377 + 0.0564577i
\(340\) 27.2245 0.0800719
\(341\) 106.543i 0.312443i
\(342\) −61.2265 505.345i −0.179025 1.47762i
\(343\) 153.916 0.448733
\(344\) 122.614i 0.356435i
\(345\) −13.1733 218.253i −0.0381836 0.632616i
\(346\) −8.71540 −0.0251890
\(347\) 77.6938i 0.223901i −0.993714 0.111951i \(-0.964290\pi\)
0.993714 0.111951i \(-0.0357099\pi\)
\(348\) −20.1083 + 1.21370i −0.0577823 + 0.00348764i
\(349\) −263.372 −0.754649 −0.377324 0.926081i \(-0.623156\pi\)
−0.377324 + 0.926081i \(0.623156\pi\)
\(350\) 324.957i 0.928449i
\(351\) 56.5840 + 309.450i 0.161208 + 0.881625i
\(352\) −59.5079 −0.169057
\(353\) 314.961i 0.892242i −0.894973 0.446121i \(-0.852805\pi\)
0.894973 0.446121i \(-0.147195\pi\)
\(354\) 2.63281 + 43.6197i 0.00743731 + 0.123219i
\(355\) −301.474 −0.849223
\(356\) 3.23253i 0.00908014i
\(357\) 744.675 44.9473i 2.08592 0.125903i
\(358\) 382.802 1.06928
\(359\) 373.835i 1.04132i −0.853763 0.520661i \(-0.825685\pi\)
0.853763 0.520661i \(-0.174315\pi\)
\(360\) −181.959 + 22.0458i −0.505442 + 0.0612383i
\(361\) 528.549 1.46412
\(362\) 112.970i 0.312073i
\(363\) 6.41080 + 106.212i 0.0176606 + 0.292596i
\(364\) 42.3078 0.116230
\(365\) 197.944i 0.542313i
\(366\) −581.153 + 35.0774i −1.58785 + 0.0958398i
\(367\) −225.537 −0.614541 −0.307271 0.951622i \(-0.599416\pi\)
−0.307271 + 0.951622i \(0.599416\pi\)
\(368\) 425.050i 1.15503i
\(369\) −2.89640 23.9060i −0.00784933 0.0647860i
\(370\) 315.871 0.853704
\(371\) 604.562i 1.62955i
\(372\) −0.840706 13.9286i −0.00225996 0.0374425i
\(373\) 400.892 1.07478 0.537389 0.843334i \(-0.319411\pi\)
0.537389 + 0.843334i \(0.319411\pi\)
\(374\) 484.937i 1.29662i
\(375\) 321.703 19.4174i 0.857875 0.0517798i
\(376\) −125.668 −0.334223
\(377\) 193.775i 0.513992i
\(378\) −452.986 + 82.8299i −1.19837 + 0.219127i
\(379\) −335.706 −0.885769 −0.442884 0.896579i \(-0.646045\pi\)
−0.442884 + 0.896579i \(0.646045\pi\)
\(380\) 29.3661i 0.0772793i
\(381\) −23.1127 382.926i −0.0606634 1.00506i
\(382\) 426.297 1.11596
\(383\) 599.733i 1.56588i −0.622096 0.782941i \(-0.713719\pi\)
0.622096 0.782941i \(-0.286281\pi\)
\(384\) 315.275 19.0295i 0.821030 0.0495559i
\(385\) −202.838 −0.526851
\(386\) 228.515i 0.592008i
\(387\) −131.181 + 15.8936i −0.338968 + 0.0410686i
\(388\) −16.7970 −0.0432912
\(389\) 107.907i 0.277397i 0.990335 + 0.138698i \(0.0442918\pi\)
−0.990335 + 0.138698i \(0.955708\pi\)
\(390\) −9.73891 161.352i −0.0249716 0.413722i
\(391\) 826.375 2.11349
\(392\) 266.288i 0.679305i
\(393\) 406.510 24.5363i 1.03438 0.0624332i
\(394\) −75.5316 −0.191705
\(395\) 111.652i 0.282662i
\(396\) −4.04209 33.3622i −0.0102073 0.0842480i
\(397\) −178.931 −0.450707 −0.225353 0.974277i \(-0.572354\pi\)
−0.225353 + 0.974277i \(0.572354\pi\)
\(398\) 141.399i 0.355274i
\(399\) −48.4831 803.256i −0.121512 2.01317i
\(400\) −270.972 −0.677429
\(401\) 218.712i 0.545416i −0.962097 0.272708i \(-0.912081\pi\)
0.962097 0.272708i \(-0.0879194\pi\)
\(402\) 313.701 18.9345i 0.780351 0.0471006i
\(403\) 134.224 0.333063
\(404\) 4.30522i 0.0106565i
\(405\) −47.1722 191.815i −0.116475 0.473617i
\(406\) 283.656 0.698659
\(407\) 631.683i 1.55205i
\(408\) −41.7362 691.475i −0.102295 1.69479i
\(409\) −149.540 −0.365623 −0.182812 0.983148i \(-0.558520\pi\)
−0.182812 + 0.983148i \(0.558520\pi\)
\(410\) 12.3738i 0.0301799i
\(411\) −2.65464 + 0.160230i −0.00645899 + 0.000389853i
\(412\) 27.0717 0.0657081
\(413\) 69.0818i 0.167268i
\(414\) −506.387 + 61.3528i −1.22316 + 0.148195i
\(415\) 352.291 0.848894
\(416\) 74.9688i 0.180214i
\(417\) −5.20061 86.1624i −0.0124715 0.206625i
\(418\) −523.085 −1.25140
\(419\) 481.158i 1.14835i −0.818733 0.574174i \(-0.805323\pi\)
0.818733 0.574174i \(-0.194677\pi\)
\(420\) −26.5174 + 1.60054i −0.0631366 + 0.00381082i
\(421\) 433.117 1.02878 0.514391 0.857556i \(-0.328018\pi\)
0.514391 + 0.857556i \(0.328018\pi\)
\(422\) 759.886i 1.80068i
\(423\) −16.2894 134.448i −0.0385093 0.317844i
\(424\) −561.373 −1.32399
\(425\) 526.819i 1.23957i
\(426\) 42.3736 + 702.035i 0.0994685 + 1.64797i
\(427\) −920.389 −2.15548
\(428\) 21.1153i 0.0493349i
\(429\) 322.674 19.4760i 0.752153 0.0453986i
\(430\) 67.8992 0.157905
\(431\) 374.706i 0.869387i −0.900578 0.434693i \(-0.856857\pi\)
0.900578 0.434693i \(-0.143143\pi\)
\(432\) 69.0693 + 377.731i 0.159883 + 0.874376i
\(433\) 77.4189 0.178796 0.0893982 0.995996i \(-0.471506\pi\)
0.0893982 + 0.995996i \(0.471506\pi\)
\(434\) 196.483i 0.452725i
\(435\) 7.33070 + 121.453i 0.0168522 + 0.279203i
\(436\) −33.6286 −0.0771299
\(437\) 891.384i 2.03978i
\(438\) 460.948 27.8220i 1.05239 0.0635205i
\(439\) 770.006 1.75400 0.877000 0.480490i \(-0.159541\pi\)
0.877000 + 0.480490i \(0.159541\pi\)
\(440\) 188.347i 0.428061i
\(441\) −284.893 + 34.5170i −0.646016 + 0.0782699i
\(442\) 610.930 1.38219
\(443\) 139.287i 0.314417i 0.987565 + 0.157208i \(0.0502494\pi\)
−0.987565 + 0.157208i \(0.949751\pi\)
\(444\) 4.98446 + 82.5812i 0.0112263 + 0.185994i
\(445\) 19.5244 0.0438750
\(446\) 604.829i 1.35612i
\(447\) 403.847 24.3755i 0.903462 0.0545314i
\(448\) 621.374 1.38700
\(449\) 667.731i 1.48715i 0.668652 + 0.743576i \(0.266872\pi\)
−0.668652 + 0.743576i \(0.733128\pi\)
\(450\) −39.1128 322.825i −0.0869173 0.717388i
\(451\) −24.7453 −0.0548675
\(452\) 42.7532i 0.0945867i
\(453\) 47.9719 + 794.786i 0.105898 + 1.75449i
\(454\) −24.9924 −0.0550493
\(455\) 255.537i 0.561621i
\(456\) −745.872 + 45.0195i −1.63568 + 0.0987270i
\(457\) 694.295 1.51925 0.759623 0.650364i \(-0.225384\pi\)
0.759623 + 0.650364i \(0.225384\pi\)
\(458\) 255.712i 0.558324i
\(459\) 734.378 134.283i 1.59995 0.292557i
\(460\) −29.4267 −0.0639711
\(461\) 612.964i 1.32964i 0.747004 + 0.664820i \(0.231492\pi\)
−0.747004 + 0.664820i \(0.768508\pi\)
\(462\) 28.5097 + 472.342i 0.0617094 + 1.02239i
\(463\) 189.967 0.410296 0.205148 0.978731i \(-0.434233\pi\)
0.205148 + 0.978731i \(0.434233\pi\)
\(464\) 236.532i 0.509766i
\(465\) −84.1283 + 5.07784i −0.180921 + 0.0109201i
\(466\) 128.601 0.275967
\(467\) 338.134i 0.724056i −0.932167 0.362028i \(-0.882084\pi\)
0.932167 0.362028i \(-0.117916\pi\)
\(468\) 42.0301 5.09228i 0.0898080 0.0108809i
\(469\) 496.818 1.05931
\(470\) 69.5904i 0.148065i
\(471\) 21.8171 + 361.459i 0.0463207 + 0.767430i
\(472\) 64.1466 0.135904
\(473\) 135.786i 0.287074i
\(474\) 260.000 15.6931i 0.548523 0.0331079i
\(475\) 568.262 1.19634
\(476\) 100.403i 0.210932i
\(477\) −72.7668 600.595i −0.152551 1.25911i
\(478\) −172.599 −0.361086
\(479\) 102.071i 0.213092i 0.994308 + 0.106546i \(0.0339791\pi\)
−0.994308 + 0.106546i \(0.966021\pi\)
\(480\) 2.83614 + 46.9885i 0.00590863 + 0.0978927i
\(481\) −795.802 −1.65447
\(482\) 403.881i 0.837927i
\(483\) −804.913 + 48.5831i −1.66649 + 0.100586i
\(484\) 14.3205 0.0295878
\(485\) 101.453i 0.209182i
\(486\) −440.043 + 136.809i −0.905439 + 0.281500i
\(487\) 776.399 1.59425 0.797125 0.603815i \(-0.206353\pi\)
0.797125 + 0.603815i \(0.206353\pi\)
\(488\) 854.637i 1.75130i
\(489\) 48.2246 + 798.973i 0.0986188 + 1.63389i
\(490\) 147.461 0.300940
\(491\) 364.534i 0.742432i 0.928546 + 0.371216i \(0.121059\pi\)
−0.928546 + 0.371216i \(0.878941\pi\)
\(492\) −3.23500 + 0.195259i −0.00657521 + 0.000396868i
\(493\) −459.861 −0.932781
\(494\) 658.990i 1.33399i
\(495\) −201.507 + 24.4141i −0.407084 + 0.0493214i
\(496\) 163.841 0.330324
\(497\) 1111.83i 2.23709i
\(498\) −49.5161 820.370i −0.0994299 1.64733i
\(499\) −323.663 −0.648624 −0.324312 0.945950i \(-0.605133\pi\)
−0.324312 + 0.945950i \(0.605133\pi\)
\(500\) 43.3748i 0.0867496i
\(501\) −494.678 + 29.8579i −0.987382 + 0.0595966i
\(502\) −375.706 −0.748418
\(503\) 241.598i 0.480314i −0.970734 0.240157i \(-0.922801\pi\)
0.970734 0.240157i \(-0.0771990\pi\)
\(504\) 81.3045 + 671.063i 0.161319 + 1.33147i
\(505\) 26.0034 0.0514918
\(506\) 524.164i 1.03590i
\(507\) −6.00991 99.5706i −0.0118539 0.196392i
\(508\) −51.6294 −0.101633
\(509\) 18.3011i 0.0359549i 0.999838 + 0.0179775i \(0.00572271\pi\)
−0.999838 + 0.0179775i \(0.994277\pi\)
\(510\) −382.915 + 23.1121i −0.750813 + 0.0453178i
\(511\) 730.016 1.42860
\(512\) 566.592i 1.10662i
\(513\) −144.847 792.149i −0.282353 1.54415i
\(514\) −511.914 −0.995941
\(515\) 163.512i 0.317500i
\(516\) 1.07145 + 17.7516i 0.00207646 + 0.0344023i
\(517\) −139.168 −0.269184
\(518\) 1164.93i 2.24889i
\(519\) −13.7624 + 0.830674i −0.0265171 + 0.00160053i
\(520\) −237.282 −0.456311
\(521\) 513.675i 0.985941i 0.870046 + 0.492970i \(0.164089\pi\)
−0.870046 + 0.492970i \(0.835911\pi\)
\(522\) 281.794 34.1416i 0.539836 0.0654054i
\(523\) 259.010 0.495239 0.247619 0.968857i \(-0.420352\pi\)
0.247619 + 0.968857i \(0.420352\pi\)
\(524\) 54.8092i 0.104598i
\(525\) −30.9720 513.136i −0.0589943 0.977403i
\(526\) 118.747 0.225754
\(527\) 318.537i 0.604435i
\(528\) 393.871 23.7734i 0.745969 0.0450254i
\(529\) −364.222 −0.688511
\(530\) 310.868i 0.586544i
\(531\) 8.31488 + 68.6284i 0.0156589 + 0.129244i
\(532\) −108.302 −0.203575
\(533\) 31.1744i 0.0584886i
\(534\) −2.74424 45.4659i −0.00513903 0.0851421i
\(535\) −127.536 −0.238385
\(536\) 461.325i 0.860682i
\(537\) 604.479 36.4853i 1.12566 0.0679428i
\(538\) −196.259 −0.364794
\(539\) 294.894i 0.547114i
\(540\) −26.1507 + 4.78175i −0.0484273 + 0.00885509i
\(541\) −314.149 −0.580682 −0.290341 0.956923i \(-0.593769\pi\)
−0.290341 + 0.956923i \(0.593769\pi\)
\(542\) 501.655i 0.925563i
\(543\) 10.7673 + 178.390i 0.0198293 + 0.328527i
\(544\) −177.914 −0.327047
\(545\) 203.116i 0.372689i
\(546\) −595.063 + 35.9169i −1.08986 + 0.0657820i
\(547\) 953.073 1.74236 0.871182 0.490961i \(-0.163354\pi\)
0.871182 + 0.490961i \(0.163354\pi\)
\(548\) 0.357922i 0.000653142i
\(549\) −914.349 + 110.781i −1.66548 + 0.201786i
\(550\) −334.158 −0.607560
\(551\) 496.037i 0.900249i
\(552\) 45.1124 + 747.410i 0.0817253 + 1.35400i
\(553\) 411.770 0.744611
\(554\) 89.3321i 0.161249i
\(555\) 498.788 30.1060i 0.898717 0.0542450i
\(556\) −11.6172 −0.0208942
\(557\) 36.2728i 0.0651217i −0.999470 0.0325608i \(-0.989634\pi\)
0.999470 0.0325608i \(-0.0103663\pi\)
\(558\) 23.6492 + 195.194i 0.0423821 + 0.349809i
\(559\) −171.065 −0.306019
\(560\) 311.922i 0.557003i
\(561\) −46.2199 765.759i −0.0823883 1.36499i
\(562\) −384.735 −0.684582
\(563\) 661.989i 1.17582i 0.808925 + 0.587912i \(0.200050\pi\)
−0.808925 + 0.587912i \(0.799950\pi\)
\(564\) −18.1937 + 1.09814i −0.0322584 + 0.00194706i
\(565\) 258.228 0.457040
\(566\) 134.927i 0.238388i
\(567\) −707.410 + 173.970i −1.24764 + 0.306826i
\(568\) 1032.40 1.81761
\(569\) 303.170i 0.532813i −0.963861 0.266406i \(-0.914164\pi\)
0.963861 0.266406i \(-0.0858363\pi\)
\(570\) 24.9302 + 413.037i 0.0437372 + 0.724627i
\(571\) 144.133 0.252422 0.126211 0.992003i \(-0.459718\pi\)
0.126211 + 0.992003i \(0.459718\pi\)
\(572\) 43.5056i 0.0760588i
\(573\) 673.162 40.6309i 1.17480 0.0709090i
\(574\) 45.6343 0.0795023
\(575\) 569.434i 0.990321i
\(576\) 617.297 74.7903i 1.07170 0.129844i
\(577\) −1009.11 −1.74889 −0.874445 0.485125i \(-0.838774\pi\)
−0.874445 + 0.485125i \(0.838774\pi\)
\(578\) 901.787i 1.56018i
\(579\) 21.7800 + 360.846i 0.0376166 + 0.623222i
\(580\) 16.3754 0.0282334
\(581\) 1299.24i 2.23622i
\(582\) 236.251 14.2597i 0.405930 0.0245012i
\(583\) −621.680 −1.06635
\(584\) 677.864i 1.16073i
\(585\) −30.7572 253.861i −0.0525764 0.433950i
\(586\) 426.429 0.727695
\(587\) 516.896i 0.880573i −0.897857 0.440286i \(-0.854877\pi\)
0.897857 0.440286i \(-0.145123\pi\)
\(588\) 2.32694 + 38.5522i 0.00395738 + 0.0655649i
\(589\) −343.595 −0.583354
\(590\) 35.5221i 0.0602070i
\(591\) −119.271 + 7.19900i −0.201812 + 0.0121810i
\(592\) −971.396 −1.64087
\(593\) 560.953i 0.945957i −0.881074 0.472979i \(-0.843179\pi\)
0.881074 0.472979i \(-0.156821\pi\)
\(594\) 85.1751 + 465.811i 0.143392 + 0.784194i
\(595\) −606.433 −1.01922
\(596\) 54.4502i 0.0913594i
\(597\) −13.4769 223.282i −0.0225743 0.374006i
\(598\) −660.349 −1.10426
\(599\) 736.447i 1.22946i 0.788738 + 0.614730i \(0.210735\pi\)
−0.788738 + 0.614730i \(0.789265\pi\)
\(600\) −476.478 + 28.7594i −0.794131 + 0.0479323i
\(601\) 935.818 1.55710 0.778550 0.627582i \(-0.215955\pi\)
0.778550 + 0.627582i \(0.215955\pi\)
\(602\) 250.411i 0.415965i
\(603\) 493.558 59.7984i 0.818504 0.0991682i
\(604\) 107.160 0.177417
\(605\) 86.4952i 0.142967i
\(606\) −3.65489 60.5533i −0.00603118 0.0999230i
\(607\) −137.313 −0.226216 −0.113108 0.993583i \(-0.536081\pi\)
−0.113108 + 0.993583i \(0.536081\pi\)
\(608\) 191.910i 0.315641i
\(609\) 447.918 27.0355i 0.735497 0.0443933i
\(610\) 473.268 0.775849
\(611\) 175.326i 0.286949i
\(612\) −12.0848 99.7446i −0.0197465 0.162981i
\(613\) −813.877 −1.32770 −0.663848 0.747868i \(-0.731078\pi\)
−0.663848 + 0.747868i \(0.731078\pi\)
\(614\) 1105.44i 1.80038i
\(615\) 1.17936 + 19.5393i 0.00191765 + 0.0317712i
\(616\) 694.621 1.12763
\(617\) 657.088i 1.06497i −0.846439 0.532486i \(-0.821258\pi\)
0.846439 0.532486i \(-0.178742\pi\)
\(618\) −380.767 + 22.9824i −0.616128 + 0.0371884i
\(619\) −775.722 −1.25319 −0.626593 0.779347i \(-0.715551\pi\)
−0.626593 + 0.779347i \(0.715551\pi\)
\(620\) 11.3429i 0.0182950i
\(621\) −793.783 + 145.146i −1.27823 + 0.233729i
\(622\) −546.758 −0.879031
\(623\) 72.0056i 0.115579i
\(624\) 29.9500 + 496.204i 0.0479968 + 0.795199i
\(625\) 214.343 0.342949
\(626\) 86.1686i 0.137650i
\(627\) −825.999 + 49.8558i −1.31738 + 0.0795149i
\(628\) 48.7351 0.0776036
\(629\) 1888.57i 3.00250i
\(630\) 371.611 45.0236i 0.589859 0.0714660i
\(631\) −214.389 −0.339761 −0.169881 0.985465i \(-0.554338\pi\)
−0.169881 + 0.985465i \(0.554338\pi\)
\(632\) 382.353i 0.604989i
\(633\) 72.4256 + 1199.93i 0.114416 + 1.89562i
\(634\) 256.209 0.404115
\(635\) 311.840i 0.491086i
\(636\) −81.2735 + 4.90553i −0.127789 + 0.00771309i
\(637\) −371.512 −0.583221
\(638\) 291.687i 0.457189i
\(639\) 133.823 + 1104.54i 0.209426 + 1.72854i
\(640\) −256.748 −0.401168
\(641\) 832.235i 1.29834i 0.760644 + 0.649169i \(0.224883\pi\)
−0.760644 + 0.649169i \(0.775117\pi\)
\(642\) 17.9257 + 296.989i 0.0279217 + 0.462600i
\(643\) −874.064 −1.35935 −0.679676 0.733512i \(-0.737880\pi\)
−0.679676 + 0.733512i \(0.737880\pi\)
\(644\) 108.525i 0.168517i
\(645\) 107.219 6.47154i 0.166231 0.0100334i
\(646\) −1563.89 −2.42089
\(647\) 505.000i 0.780526i −0.920704 0.390263i \(-0.872384\pi\)
0.920704 0.390263i \(-0.127616\pi\)
\(648\) 161.542 + 656.873i 0.249293 + 1.01369i
\(649\) 71.0377 0.109457
\(650\) 420.976i 0.647656i
\(651\) 18.7270 + 310.264i 0.0287665 + 0.476596i
\(652\) 107.724 0.165221
\(653\) 469.638i 0.719201i 0.933106 + 0.359600i \(0.117087\pi\)
−0.933106 + 0.359600i \(0.882913\pi\)
\(654\) 472.990 28.5488i 0.723226 0.0436527i
\(655\) −331.046 −0.505414
\(656\) 38.0530i 0.0580077i
\(657\) 725.226 87.8668i 1.10384 0.133739i
\(658\) 256.649 0.390043
\(659\) 1147.55i 1.74135i −0.491862 0.870673i \(-0.663683\pi\)
0.491862 0.870673i \(-0.336317\pi\)
\(660\) 1.64586 + 27.2682i 0.00249373 + 0.0413154i
\(661\) 286.508 0.433446 0.216723 0.976233i \(-0.430463\pi\)
0.216723 + 0.976233i \(0.430463\pi\)
\(662\) 24.0879i 0.0363866i
\(663\) 964.713 58.2284i 1.45507 0.0878256i
\(664\) −1206.43 −1.81691
\(665\) 654.139i 0.983668i
\(666\) −140.214 1157.28i −0.210531 1.73766i
\(667\) 497.060 0.745217
\(668\) 66.6968i 0.0998455i
\(669\) −57.6469 955.079i −0.0861687 1.42762i
\(670\) −255.466 −0.381292
\(671\) 946.448i 1.41050i
\(672\) 173.293 10.4597i 0.257876 0.0155650i
\(673\) 614.908 0.913682 0.456841 0.889548i \(-0.348981\pi\)
0.456841 + 0.889548i \(0.348981\pi\)
\(674\) 871.801i 1.29347i
\(675\) −92.5313 506.041i −0.137083 0.749691i
\(676\) −13.4250 −0.0198594
\(677\) 203.554i 0.300671i −0.988635 0.150336i \(-0.951965\pi\)
0.988635 0.150336i \(-0.0480354\pi\)
\(678\) −36.2951 601.328i −0.0535326 0.886914i
\(679\) 374.158 0.551042
\(680\) 563.110i 0.828103i
\(681\) −39.4652 + 2.38205i −0.0579519 + 0.00349787i
\(682\) 202.046 0.296255
\(683\) 1206.46i 1.76641i −0.468990 0.883203i \(-0.655382\pi\)
0.468990 0.883203i \(-0.344618\pi\)
\(684\) −107.591 + 13.0355i −0.157297 + 0.0190578i
\(685\) 2.16184 0.00315597
\(686\) 291.882i 0.425484i
\(687\) 24.3722 + 403.793i 0.0354763 + 0.587762i
\(688\) −208.810 −0.303503
\(689\) 783.200i 1.13672i
\(690\) 413.889 24.9816i 0.599840 0.0362053i
\(691\) −220.368 −0.318911 −0.159456 0.987205i \(-0.550974\pi\)
−0.159456 + 0.987205i \(0.550974\pi\)
\(692\) 1.85557i 0.00268145i
\(693\) 90.0389 + 743.153i 0.129926 + 1.07237i
\(694\) 147.337 0.212301
\(695\) 70.1672i 0.100960i
\(696\) −25.1041 415.919i −0.0360691 0.597584i
\(697\) −73.9821 −0.106144
\(698\) 499.454i 0.715550i
\(699\) 203.072 12.2571i 0.290518 0.0175351i
\(700\) −69.1855 −0.0988364
\(701\) 1139.10i 1.62496i 0.582986 + 0.812482i \(0.301884\pi\)
−0.582986 + 0.812482i \(0.698116\pi\)
\(702\) −586.835 + 107.305i −0.835947 + 0.152856i
\(703\) 2037.14 2.89778
\(704\) 638.967i 0.907624i
\(705\) 6.63274 + 109.890i 0.00940814 + 0.155872i
\(706\) 597.286 0.846014
\(707\) 95.9001i 0.135644i
\(708\) 9.28691 0.560542i 0.0131171 0.000791725i
\(709\) 729.352 1.02870 0.514352 0.857579i \(-0.328032\pi\)
0.514352 + 0.857579i \(0.328032\pi\)
\(710\) 571.709i 0.805224i
\(711\) 409.068 49.5618i 0.575341 0.0697071i
\(712\) −66.8616 −0.0939067
\(713\) 344.304i 0.482895i
\(714\) 85.2370 + 1412.18i 0.119380 + 1.97785i
\(715\) −262.773 −0.367514
\(716\) 81.5010i 0.113828i
\(717\) −272.549 + 16.4506i −0.380124 + 0.0229436i
\(718\) 708.932 0.987370
\(719\) 815.315i 1.13396i 0.823733 + 0.566978i \(0.191888\pi\)
−0.823733 + 0.566978i \(0.808112\pi\)
\(720\) −37.5438 309.875i −0.0521441 0.430382i
\(721\) −603.031 −0.836382
\(722\) 1002.33i 1.38827i
\(723\) 38.4943 + 637.764i 0.0532425 + 0.882108i
\(724\) 24.0521 0.0332211
\(725\) 316.879i 0.437074i
\(726\) −201.419 + 12.1573i −0.277436 + 0.0167456i
\(727\) 244.795 0.336719 0.168359 0.985726i \(-0.446153\pi\)
0.168359 + 0.985726i \(0.446153\pi\)
\(728\) 875.092i 1.20205i
\(729\) −681.828 + 257.975i −0.935293 + 0.353875i
\(730\) −375.377 −0.514215
\(731\) 405.965i 0.555356i
\(732\) 7.46820 + 123.731i 0.0102025 + 0.169032i
\(733\) −1169.54 −1.59556 −0.797779 0.602950i \(-0.793992\pi\)
−0.797779 + 0.602950i \(0.793992\pi\)
\(734\) 427.703i 0.582701i
\(735\) 232.854 14.0546i 0.316808 0.0191220i
\(736\) 192.305 0.261284
\(737\) 510.884i 0.693195i
\(738\) 45.3348 5.49267i 0.0614293 0.00744265i
\(739\) 75.1506 0.101692 0.0508461 0.998706i \(-0.483808\pi\)
0.0508461 + 0.998706i \(0.483808\pi\)
\(740\) 67.2509i 0.0908795i
\(741\) −62.8090 1040.60i −0.0847625 1.40432i
\(742\) 1146.48 1.54512
\(743\) 1357.17i 1.82661i −0.407271 0.913307i \(-0.633520\pi\)
0.407271 0.913307i \(-0.366480\pi\)
\(744\) 288.099 17.3891i 0.387230 0.0233725i
\(745\) −328.877 −0.441446
\(746\) 760.243i 1.01909i
\(747\) −156.381 1290.72i −0.209345 1.72787i
\(748\) −103.246 −0.138030
\(749\) 470.350i 0.627971i
\(750\) 36.8228 + 610.071i 0.0490971 + 0.813428i
\(751\) 524.167 0.697958 0.348979 0.937131i \(-0.386528\pi\)
0.348979 + 0.937131i \(0.386528\pi\)
\(752\) 214.011i 0.284589i
\(753\) −593.273 + 35.8089i −0.787880 + 0.0475550i
\(754\) 367.471 0.487362
\(755\) 647.242i 0.857274i
\(756\) 17.6350 + 96.4435i 0.0233267 + 0.127571i
\(757\) −406.400 −0.536855 −0.268428 0.963300i \(-0.586504\pi\)
−0.268428 + 0.963300i \(0.586504\pi\)
\(758\) 636.626i 0.839876i
\(759\) 49.9587 + 827.702i 0.0658217 + 1.09052i
\(760\) 607.408 0.799221
\(761\) 1447.41i 1.90199i 0.309210 + 0.950994i \(0.399935\pi\)
−0.309210 + 0.950994i \(0.600065\pi\)
\(762\) 726.172 43.8305i 0.952982 0.0575203i
\(763\) 749.088 0.981766
\(764\) 90.7614i 0.118798i
\(765\) −602.454 + 72.9920i −0.787521 + 0.0954144i
\(766\) 1137.32 1.48475
\(767\) 89.4942i 0.116681i
\(768\) −13.8639 229.693i −0.0180519 0.299080i
\(769\) 1021.92 1.32889 0.664447 0.747335i \(-0.268667\pi\)
0.664447 + 0.747335i \(0.268667\pi\)
\(770\) 384.657i 0.499554i
\(771\) −808.357 + 48.7910i −1.04845 + 0.0632828i
\(772\) 48.6523 0.0630211
\(773\) 757.370i 0.979780i 0.871784 + 0.489890i \(0.162963\pi\)
−0.871784 + 0.489890i \(0.837037\pi\)
\(774\) −30.1402 248.768i −0.0389408 0.321406i
\(775\) −219.496 −0.283220
\(776\) 347.428i 0.447717i
\(777\) −111.030 1839.52i −0.142896 2.36747i
\(778\) −204.633 −0.263024
\(779\) 79.8021i 0.102442i
\(780\) −34.3528 + 2.07348i −0.0440421 + 0.00265830i
\(781\) 1143.31 1.46391
\(782\) 1567.12i 2.00399i
\(783\) 441.724 80.7707i 0.564143 0.103155i
\(784\) −453.486 −0.578426
\(785\) 294.358i 0.374978i