Properties

Label 288.3.u.a.163.4
Level $288$
Weight $3$
Character 288.163
Analytic conductor $7.847$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 288.u (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.84743161358\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 32)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 163.4
Character \(\chi\) \(=\) 288.163
Dual form 288.3.u.a.235.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +O(q^{10})\) \(q+(0.658450 - 1.88850i) q^{2} +(-3.13289 - 2.48697i) q^{4} +(0.659338 + 1.59178i) q^{5} +(9.54718 + 9.54718i) q^{7} +(-6.75950 + 4.27892i) q^{8} +(3.44023 - 0.197052i) q^{10} +(3.96481 + 9.57189i) q^{11} +(1.91784 - 4.63007i) q^{13} +(24.3162 - 11.7435i) q^{14} +(3.62996 + 15.5828i) q^{16} +15.3143i q^{17} +(0.827335 + 0.342693i) q^{19} +(1.89308 - 6.62663i) q^{20} +(20.6872 - 1.18494i) q^{22} +(12.9230 - 12.9230i) q^{23} +(15.5786 - 15.5786i) q^{25} +(-7.48110 - 6.67051i) q^{26} +(-6.16668 - 53.6538i) q^{28} +(-23.7905 - 9.85436i) q^{29} -25.1562i q^{31} +(31.8183 + 3.40530i) q^{32} +(28.9211 + 10.0837i) q^{34} +(-8.90221 + 21.4918i) q^{35} +(13.6161 + 32.8721i) q^{37} +(1.19194 - 1.33678i) q^{38} +(-11.2679 - 7.93840i) q^{40} +(32.9116 + 32.9116i) q^{41} +(-17.9473 - 43.3286i) q^{43} +(11.3837 - 39.8480i) q^{44} +(-15.8960 - 32.9143i) q^{46} -20.1127 q^{47} +133.297i q^{49} +(-19.1625 - 39.6780i) q^{50} +(-17.5232 + 9.73588i) q^{52} +(-35.0503 + 14.5183i) q^{53} +(-12.6222 + 12.6222i) q^{55} +(-105.386 - 23.6825i) q^{56} +(-34.2749 + 38.4399i) q^{58} +(60.6706 - 25.1306i) q^{59} +(-27.9825 - 11.5907i) q^{61} +(-47.5076 - 16.5641i) q^{62} +(27.3817 - 57.8467i) q^{64} +8.63457 q^{65} +(1.13412 - 2.73801i) q^{67} +(38.0862 - 47.9780i) q^{68} +(34.7257 + 30.9632i) q^{70} +(45.6144 + 45.6144i) q^{71} +(-29.1727 - 29.1727i) q^{73} +(71.0445 - 4.06934i) q^{74} +(-1.73968 - 3.13118i) q^{76} +(-53.5318 + 129.237i) q^{77} +3.27983 q^{79} +(-22.4110 + 16.0524i) q^{80} +(83.8242 - 40.4830i) q^{82} +(-56.7834 - 23.5205i) q^{83} +(-24.3770 + 10.0973i) q^{85} +(-93.6436 + 5.36380i) q^{86} +(-67.7575 - 47.7361i) q^{88} +(44.5059 - 44.5059i) q^{89} +(62.5140 - 25.8942i) q^{91} +(-72.6256 + 8.34720i) q^{92} +(-13.2432 + 37.9829i) q^{94} +1.54289i q^{95} -106.417 q^{97} +(251.732 + 87.7695i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 28q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 44q^{10} + 4q^{11} - 4q^{13} + 20q^{14} + 16q^{16} - 4q^{19} - 76q^{20} + 144q^{22} + 68q^{23} - 4q^{25} - 96q^{26} + 56q^{28} + 4q^{29} + 24q^{32} - 48q^{34} - 92q^{35} - 4q^{37} + 396q^{38} - 408q^{40} + 4q^{41} + 92q^{43} + 188q^{44} - 36q^{46} + 8q^{47} - 308q^{50} + 420q^{52} + 164q^{53} + 252q^{55} - 552q^{56} + 528q^{58} - 124q^{59} - 68q^{61} - 216q^{62} - 232q^{64} + 8q^{65} - 164q^{67} + 368q^{68} - 664q^{70} + 260q^{71} - 4q^{73} + 532q^{74} - 516q^{76} - 220q^{77} - 520q^{79} - 312q^{80} + 636q^{82} + 484q^{83} + 96q^{85} - 688q^{86} + 672q^{88} + 4q^{89} - 196q^{91} - 616q^{92} + 40q^{94} - 8q^{97} + 328q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.658450 1.88850i 0.329225 0.944251i
\(3\) 0 0
\(4\) −3.13289 2.48697i −0.783222 0.621742i
\(5\) 0.659338 + 1.59178i 0.131868 + 0.318356i 0.975997 0.217782i \(-0.0698823\pi\)
−0.844130 + 0.536139i \(0.819882\pi\)
\(6\) 0 0
\(7\) 9.54718 + 9.54718i 1.36388 + 1.36388i 0.868907 + 0.494975i \(0.164823\pi\)
0.494975 + 0.868907i \(0.335177\pi\)
\(8\) −6.75950 + 4.27892i −0.844937 + 0.534865i
\(9\) 0 0
\(10\) 3.44023 0.197052i 0.344023 0.0197052i
\(11\) 3.96481 + 9.57189i 0.360437 + 0.870172i 0.995236 + 0.0974947i \(0.0310829\pi\)
−0.634799 + 0.772677i \(0.718917\pi\)
\(12\) 0 0
\(13\) 1.91784 4.63007i 0.147526 0.356159i −0.832792 0.553587i \(-0.813259\pi\)
0.980317 + 0.197428i \(0.0632587\pi\)
\(14\) 24.3162 11.7435i 1.73687 0.838824i
\(15\) 0 0
\(16\) 3.62996 + 15.5828i 0.226873 + 0.973924i
\(17\) 15.3143i 0.900842i 0.892816 + 0.450421i \(0.148726\pi\)
−0.892816 + 0.450421i \(0.851274\pi\)
\(18\) 0 0
\(19\) 0.827335 + 0.342693i 0.0435439 + 0.0180365i 0.404349 0.914605i \(-0.367498\pi\)
−0.360805 + 0.932641i \(0.617498\pi\)
\(20\) 1.89308 6.62663i 0.0946542 0.331331i
\(21\) 0 0
\(22\) 20.6872 1.18494i 0.940326 0.0538608i
\(23\) 12.9230 12.9230i 0.561871 0.561871i −0.367968 0.929839i \(-0.619946\pi\)
0.929839 + 0.367968i \(0.119946\pi\)
\(24\) 0 0
\(25\) 15.5786 15.5786i 0.623145 0.623145i
\(26\) −7.48110 6.67051i −0.287735 0.256558i
\(27\) 0 0
\(28\) −6.16668 53.6538i −0.220239 1.91621i
\(29\) −23.7905 9.85436i −0.820363 0.339805i −0.0672825 0.997734i \(-0.521433\pi\)
−0.753080 + 0.657929i \(0.771433\pi\)
\(30\) 0 0
\(31\) 25.1562i 0.811491i −0.913986 0.405746i \(-0.867012\pi\)
0.913986 0.405746i \(-0.132988\pi\)
\(32\) 31.8183 + 3.40530i 0.994322 + 0.106416i
\(33\) 0 0
\(34\) 28.9211 + 10.0837i 0.850621 + 0.296580i
\(35\) −8.90221 + 21.4918i −0.254349 + 0.614053i
\(36\) 0 0
\(37\) 13.6161 + 32.8721i 0.368001 + 0.888434i 0.994078 + 0.108672i \(0.0346599\pi\)
−0.626076 + 0.779762i \(0.715340\pi\)
\(38\) 1.19194 1.33678i 0.0313667 0.0351784i
\(39\) 0 0
\(40\) −11.2679 7.93840i −0.281698 0.198460i
\(41\) 32.9116 + 32.9116i 0.802721 + 0.802721i 0.983520 0.180799i \(-0.0578684\pi\)
−0.180799 + 0.983520i \(0.557868\pi\)
\(42\) 0 0
\(43\) −17.9473 43.3286i −0.417379 1.00764i −0.983104 0.183048i \(-0.941404\pi\)
0.565725 0.824594i \(-0.308596\pi\)
\(44\) 11.3837 39.8480i 0.258721 0.905637i
\(45\) 0 0
\(46\) −15.8960 32.9143i −0.345565 0.715529i
\(47\) −20.1127 −0.427930 −0.213965 0.976841i \(-0.568638\pi\)
−0.213965 + 0.976841i \(0.568638\pi\)
\(48\) 0 0
\(49\) 133.297i 2.72035i
\(50\) −19.1625 39.6780i −0.383251 0.793561i
\(51\) 0 0
\(52\) −17.5232 + 9.73588i −0.336985 + 0.187228i
\(53\) −35.0503 + 14.5183i −0.661327 + 0.273931i −0.687997 0.725714i \(-0.741510\pi\)
0.0266698 + 0.999644i \(0.491510\pi\)
\(54\) 0 0
\(55\) −12.6222 + 12.6222i −0.229495 + 0.229495i
\(56\) −105.386 23.6825i −1.88189 0.422902i
\(57\) 0 0
\(58\) −34.2749 + 38.4399i −0.590946 + 0.662756i
\(59\) 60.6706 25.1306i 1.02832 0.425942i 0.196212 0.980562i \(-0.437136\pi\)
0.832104 + 0.554619i \(0.187136\pi\)
\(60\) 0 0
\(61\) −27.9825 11.5907i −0.458730 0.190012i 0.141338 0.989961i \(-0.454860\pi\)
−0.600067 + 0.799949i \(0.704860\pi\)
\(62\) −47.5076 16.5641i −0.766252 0.267163i
\(63\) 0 0
\(64\) 27.3817 57.8467i 0.427839 0.903855i
\(65\) 8.63457 0.132839
\(66\) 0 0
\(67\) 1.13412 2.73801i 0.0169272 0.0408659i −0.915190 0.403023i \(-0.867960\pi\)
0.932117 + 0.362157i \(0.117960\pi\)
\(68\) 38.0862 47.9780i 0.560092 0.705559i
\(69\) 0 0
\(70\) 34.7257 + 30.9632i 0.496082 + 0.442331i
\(71\) 45.6144 + 45.6144i 0.642456 + 0.642456i 0.951159 0.308702i \(-0.0998947\pi\)
−0.308702 + 0.951159i \(0.599895\pi\)
\(72\) 0 0
\(73\) −29.1727 29.1727i −0.399626 0.399626i 0.478475 0.878101i \(-0.341190\pi\)
−0.878101 + 0.478475i \(0.841190\pi\)
\(74\) 71.0445 4.06934i 0.960060 0.0549911i
\(75\) 0 0
\(76\) −1.73968 3.13118i −0.0228905 0.0411997i
\(77\) −53.5318 + 129.237i −0.695219 + 1.67841i
\(78\) 0 0
\(79\) 3.27983 0.0415169 0.0207584 0.999785i \(-0.493392\pi\)
0.0207584 + 0.999785i \(0.493392\pi\)
\(80\) −22.4110 + 16.0524i −0.280138 + 0.200655i
\(81\) 0 0
\(82\) 83.8242 40.4830i 1.02225 0.493695i
\(83\) −56.7834 23.5205i −0.684138 0.283379i 0.0134176 0.999910i \(-0.495729\pi\)
−0.697555 + 0.716531i \(0.745729\pi\)
\(84\) 0 0
\(85\) −24.3770 + 10.0973i −0.286789 + 0.118792i
\(86\) −93.6436 + 5.36380i −1.08888 + 0.0623697i
\(87\) 0 0
\(88\) −67.7575 47.7361i −0.769971 0.542456i
\(89\) 44.5059 44.5059i 0.500066 0.500066i −0.411392 0.911458i \(-0.634957\pi\)
0.911458 + 0.411392i \(0.134957\pi\)
\(90\) 0 0
\(91\) 62.5140 25.8942i 0.686967 0.284551i
\(92\) −72.6256 + 8.34720i −0.789408 + 0.0907305i
\(93\) 0 0
\(94\) −13.2432 + 37.9829i −0.140885 + 0.404074i
\(95\) 1.54289i 0.0162409i
\(96\) 0 0
\(97\) −106.417 −1.09708 −0.548542 0.836123i \(-0.684817\pi\)
−0.548542 + 0.836123i \(0.684817\pi\)
\(98\) 251.732 + 87.7695i 2.56869 + 0.895607i
\(99\) 0 0
\(100\) −87.5496 + 10.0625i −0.875496 + 0.100625i
\(101\) −3.62243 8.74531i −0.0358656 0.0865872i 0.904932 0.425557i \(-0.139922\pi\)
−0.940797 + 0.338969i \(0.889922\pi\)
\(102\) 0 0
\(103\) 26.0911 + 26.0911i 0.253312 + 0.253312i 0.822327 0.569015i \(-0.192675\pi\)
−0.569015 + 0.822327i \(0.692675\pi\)
\(104\) 6.84808 + 39.5032i 0.0658469 + 0.379839i
\(105\) 0 0
\(106\) 4.33900 + 75.7523i 0.0409340 + 0.714644i
\(107\) −32.1753 77.6781i −0.300704 0.725963i −0.999939 0.0110713i \(-0.996476\pi\)
0.699235 0.714892i \(-0.253524\pi\)
\(108\) 0 0
\(109\) −36.0541 + 87.0422i −0.330771 + 0.798553i 0.667760 + 0.744377i \(0.267253\pi\)
−0.998531 + 0.0541760i \(0.982747\pi\)
\(110\) 15.5260 + 32.1482i 0.141145 + 0.292256i
\(111\) 0 0
\(112\) −114.116 + 183.428i −1.01889 + 1.63775i
\(113\) 6.32445i 0.0559686i 0.999608 + 0.0279843i \(0.00890884\pi\)
−0.999608 + 0.0279843i \(0.991091\pi\)
\(114\) 0 0
\(115\) 29.0913 + 12.0500i 0.252968 + 0.104783i
\(116\) 50.0255 + 90.0389i 0.431255 + 0.776197i
\(117\) 0 0
\(118\) −7.51063 131.124i −0.0636494 1.11122i
\(119\) −146.208 + 146.208i −1.22864 + 1.22864i
\(120\) 0 0
\(121\) 9.65850 9.65850i 0.0798223 0.0798223i
\(122\) −40.3142 + 45.2131i −0.330444 + 0.370599i
\(123\) 0 0
\(124\) −62.5628 + 78.8116i −0.504539 + 0.635577i
\(125\) 74.8639 + 31.0096i 0.598911 + 0.248077i
\(126\) 0 0
\(127\) 34.6015i 0.272453i 0.990678 + 0.136226i \(0.0434975\pi\)
−0.990678 + 0.136226i \(0.956503\pi\)
\(128\) −91.2142 89.7996i −0.712611 0.701559i
\(129\) 0 0
\(130\) 5.68543 16.3064i 0.0437341 0.125434i
\(131\) 68.0051 164.179i 0.519123 1.25327i −0.419320 0.907838i \(-0.637732\pi\)
0.938443 0.345434i \(-0.112268\pi\)
\(132\) 0 0
\(133\) 4.62696 + 11.1705i 0.0347892 + 0.0839885i
\(134\) −4.42398 3.94464i −0.0330148 0.0294376i
\(135\) 0 0
\(136\) −65.5287 103.517i −0.481829 0.761155i
\(137\) −71.5748 71.5748i −0.522444 0.522444i 0.395865 0.918309i \(-0.370445\pi\)
−0.918309 + 0.395865i \(0.870445\pi\)
\(138\) 0 0
\(139\) −75.1916 181.529i −0.540947 1.30596i −0.924056 0.382258i \(-0.875147\pi\)
0.383109 0.923703i \(-0.374853\pi\)
\(140\) 81.3392 45.1920i 0.580994 0.322800i
\(141\) 0 0
\(142\) 116.178 56.1081i 0.818153 0.395128i
\(143\) 51.9224 0.363094
\(144\) 0 0
\(145\) 44.3667i 0.305977i
\(146\) −74.3015 + 35.8840i −0.508915 + 0.245781i
\(147\) 0 0
\(148\) 39.0943 136.847i 0.264150 0.924643i
\(149\) −211.685 + 87.6826i −1.42070 + 0.588474i −0.955037 0.296487i \(-0.904185\pi\)
−0.465665 + 0.884961i \(0.654185\pi\)
\(150\) 0 0
\(151\) 10.5820 10.5820i 0.0700794 0.0700794i −0.671198 0.741278i \(-0.734220\pi\)
0.741278 + 0.671198i \(0.234220\pi\)
\(152\) −7.05873 + 1.22366i −0.0464390 + 0.00805043i
\(153\) 0 0
\(154\) 208.817 + 186.191i 1.35595 + 1.20903i
\(155\) 40.0432 16.5864i 0.258343 0.107009i
\(156\) 0 0
\(157\) 26.9641 + 11.1689i 0.171746 + 0.0711394i 0.466900 0.884310i \(-0.345371\pi\)
−0.295154 + 0.955450i \(0.595371\pi\)
\(158\) 2.15961 6.19398i 0.0136684 0.0392024i
\(159\) 0 0
\(160\) 15.5585 + 52.8930i 0.0972407 + 0.330581i
\(161\) 246.757 1.53265
\(162\) 0 0
\(163\) 111.743 269.771i 0.685540 1.65504i −0.0680396 0.997683i \(-0.521674\pi\)
0.753579 0.657357i \(-0.228326\pi\)
\(164\) −21.2581 184.958i −0.129623 1.12779i
\(165\) 0 0
\(166\) −81.8075 + 91.7486i −0.492816 + 0.552703i
\(167\) 10.3664 + 10.3664i 0.0620741 + 0.0620741i 0.737462 0.675388i \(-0.236024\pi\)
−0.675388 + 0.737462i \(0.736024\pi\)
\(168\) 0 0
\(169\) 101.742 + 101.742i 0.602021 + 0.602021i
\(170\) 3.01772 + 52.6847i 0.0177513 + 0.309910i
\(171\) 0 0
\(172\) −51.5301 + 180.378i −0.299594 + 1.04871i
\(173\) 88.6518 214.024i 0.512438 1.23714i −0.430022 0.902818i \(-0.641494\pi\)
0.942461 0.334317i \(-0.108506\pi\)
\(174\) 0 0
\(175\) 297.464 1.69979
\(176\) −134.765 + 96.5284i −0.765709 + 0.548457i
\(177\) 0 0
\(178\) −54.7446 113.354i −0.307554 0.636822i
\(179\) −2.58312 1.06996i −0.0144308 0.00597744i 0.375456 0.926840i \(-0.377486\pi\)
−0.389887 + 0.920863i \(0.627486\pi\)
\(180\) 0 0
\(181\) −184.394 + 76.3786i −1.01875 + 0.421981i −0.828640 0.559781i \(-0.810885\pi\)
−0.190112 + 0.981762i \(0.560885\pi\)
\(182\) −7.73883 135.108i −0.0425210 0.742351i
\(183\) 0 0
\(184\) −32.0566 + 142.650i −0.174221 + 0.775271i
\(185\) −43.3476 + 43.3476i −0.234311 + 0.234311i
\(186\) 0 0
\(187\) −146.587 + 60.7183i −0.783887 + 0.324697i
\(188\) 63.0109 + 50.0197i 0.335164 + 0.266062i
\(189\) 0 0
\(190\) 2.91375 + 1.01591i 0.0153355 + 0.00534692i
\(191\) 185.771i 0.972625i −0.873785 0.486313i \(-0.838342\pi\)
0.873785 0.486313i \(-0.161658\pi\)
\(192\) 0 0
\(193\) 208.055 1.07800 0.539002 0.842305i \(-0.318802\pi\)
0.539002 + 0.842305i \(0.318802\pi\)
\(194\) −70.0704 + 200.969i −0.361188 + 1.03592i
\(195\) 0 0
\(196\) 331.506 417.605i 1.69136 2.13064i
\(197\) −123.852 299.006i −0.628691 1.51780i −0.841250 0.540647i \(-0.818180\pi\)
0.212558 0.977148i \(-0.431820\pi\)
\(198\) 0 0
\(199\) −253.762 253.762i −1.27519 1.27519i −0.943329 0.331858i \(-0.892324\pi\)
−0.331858 0.943329i \(-0.607676\pi\)
\(200\) −38.6440 + 171.963i −0.193220 + 0.859817i
\(201\) 0 0
\(202\) −18.9007 + 1.08261i −0.0935680 + 0.00535946i
\(203\) −133.051 321.214i −0.655424 1.58233i
\(204\) 0 0
\(205\) −30.6882 + 74.0879i −0.149699 + 0.361404i
\(206\) 66.4529 32.0935i 0.322587 0.155794i
\(207\) 0 0
\(208\) 79.1111 + 13.0783i 0.380342 + 0.0628764i
\(209\) 9.27787i 0.0443917i
\(210\) 0 0
\(211\) 102.533 + 42.4705i 0.485938 + 0.201282i 0.612182 0.790717i \(-0.290292\pi\)
−0.126244 + 0.991999i \(0.540292\pi\)
\(212\) 145.915 + 41.6849i 0.688280 + 0.196627i
\(213\) 0 0
\(214\) −167.881 + 9.61603i −0.784491 + 0.0449347i
\(215\) 57.1364 57.1364i 0.265751 0.265751i
\(216\) 0 0
\(217\) 240.171 240.171i 1.10678 1.10678i
\(218\) 140.640 + 125.401i 0.645136 + 0.575235i
\(219\) 0 0
\(220\) 70.9351 8.15291i 0.322432 0.0370587i
\(221\) 70.9063 + 29.3704i 0.320843 + 0.132898i
\(222\) 0 0
\(223\) 187.153i 0.839252i 0.907697 + 0.419626i \(0.137839\pi\)
−0.907697 + 0.419626i \(0.862161\pi\)
\(224\) 271.264 + 336.286i 1.21100 + 1.50128i
\(225\) 0 0
\(226\) 11.9437 + 4.16433i 0.0528484 + 0.0184263i
\(227\) 2.72348 6.57507i 0.0119977 0.0289650i −0.917767 0.397119i \(-0.870010\pi\)
0.929765 + 0.368154i \(0.120010\pi\)
\(228\) 0 0
\(229\) −124.655 300.944i −0.544345 1.31416i −0.921631 0.388068i \(-0.873143\pi\)
0.377286 0.926097i \(-0.376857\pi\)
\(230\) 41.9116 47.0047i 0.182225 0.204368i
\(231\) 0 0
\(232\) 202.978 35.1872i 0.874905 0.151669i
\(233\) 208.047 + 208.047i 0.892904 + 0.892904i 0.994796 0.101891i \(-0.0324894\pi\)
−0.101891 + 0.994796i \(0.532489\pi\)
\(234\) 0 0
\(235\) −13.2611 32.0151i −0.0564301 0.136234i
\(236\) −252.573 72.1547i −1.07023 0.305740i
\(237\) 0 0
\(238\) 179.844 + 372.386i 0.755647 + 1.56465i
\(239\) 277.832 1.16248 0.581239 0.813733i \(-0.302568\pi\)
0.581239 + 0.813733i \(0.302568\pi\)
\(240\) 0 0
\(241\) 63.2696i 0.262529i 0.991347 + 0.131265i \(0.0419038\pi\)
−0.991347 + 0.131265i \(0.958096\pi\)
\(242\) −11.8805 24.5997i −0.0490928 0.101652i
\(243\) 0 0
\(244\) 58.8402 + 105.904i 0.241148 + 0.434033i
\(245\) −212.180 + 87.8879i −0.866041 + 0.358726i
\(246\) 0 0
\(247\) 3.17339 3.17339i 0.0128477 0.0128477i
\(248\) 107.641 + 170.043i 0.434038 + 0.685659i
\(249\) 0 0
\(250\) 107.856 120.962i 0.431424 0.483850i
\(251\) −161.948 + 67.0812i −0.645212 + 0.267256i −0.681201 0.732097i \(-0.738542\pi\)
0.0359886 + 0.999352i \(0.488542\pi\)
\(252\) 0 0
\(253\) 174.935 + 72.4605i 0.691443 + 0.286405i
\(254\) 65.3451 + 22.7834i 0.257264 + 0.0896983i
\(255\) 0 0
\(256\) −229.647 + 113.130i −0.897058 + 0.441913i
\(257\) 82.9690 0.322836 0.161418 0.986886i \(-0.448393\pi\)
0.161418 + 0.986886i \(0.448393\pi\)
\(258\) 0 0
\(259\) −183.840 + 443.830i −0.709809 + 1.71363i
\(260\) −27.0511 21.4739i −0.104043 0.0825919i
\(261\) 0 0
\(262\) −265.274 236.531i −1.01250 0.902791i
\(263\) 148.394 + 148.394i 0.564235 + 0.564235i 0.930508 0.366272i \(-0.119366\pi\)
−0.366272 + 0.930508i \(0.619366\pi\)
\(264\) 0 0
\(265\) −46.2200 46.2200i −0.174415 0.174415i
\(266\) 24.1421 1.38283i 0.0907597 0.00519861i
\(267\) 0 0
\(268\) −10.3624 + 5.75736i −0.0386658 + 0.0214827i
\(269\) −78.7117 + 190.027i −0.292609 + 0.706420i −1.00000 0.000402393i \(-0.999872\pi\)
0.707391 + 0.706822i \(0.249872\pi\)
\(270\) 0 0
\(271\) −29.7996 −0.109962 −0.0549809 0.998487i \(-0.517510\pi\)
−0.0549809 + 0.998487i \(0.517510\pi\)
\(272\) −238.640 + 55.5903i −0.877352 + 0.204376i
\(273\) 0 0
\(274\) −182.298 + 88.0408i −0.665320 + 0.321317i
\(275\) 210.883 + 87.3507i 0.766848 + 0.317639i
\(276\) 0 0
\(277\) −368.831 + 152.775i −1.33152 + 0.551534i −0.931089 0.364793i \(-0.881140\pi\)
−0.400431 + 0.916327i \(0.631140\pi\)
\(278\) −392.327 + 22.4721i −1.41125 + 0.0808347i
\(279\) 0 0
\(280\) −31.7874 183.366i −0.113526 0.654878i
\(281\) 280.258 280.258i 0.997358 0.997358i −0.00263807 0.999997i \(-0.500840\pi\)
0.999997 + 0.00263807i \(0.000839724\pi\)
\(282\) 0 0
\(283\) −176.650 + 73.1708i −0.624204 + 0.258554i −0.672288 0.740289i \(-0.734688\pi\)
0.0480840 + 0.998843i \(0.484688\pi\)
\(284\) −29.4631 256.346i −0.103743 0.902628i
\(285\) 0 0
\(286\) 34.1883 98.0556i 0.119540 0.342852i
\(287\) 628.425i 2.18963i
\(288\) 0 0
\(289\) 54.4719 0.188484
\(290\) −83.7866 29.2132i −0.288919 0.100735i
\(291\) 0 0
\(292\) 18.8432 + 163.946i 0.0645313 + 0.561461i
\(293\) −11.3590 27.4231i −0.0387679 0.0935940i 0.903310 0.428989i \(-0.141130\pi\)
−0.942078 + 0.335395i \(0.891130\pi\)
\(294\) 0 0
\(295\) 80.0049 + 80.0049i 0.271203 + 0.271203i
\(296\) −232.695 163.937i −0.786130 0.553840i
\(297\) 0 0
\(298\) 26.2052 + 457.502i 0.0879368 + 1.53524i
\(299\) −35.0503 84.6188i −0.117225 0.283006i
\(300\) 0 0
\(301\) 242.320 585.012i 0.805049 1.94356i
\(302\) −13.0164 26.9518i −0.0431007 0.0892444i
\(303\) 0 0
\(304\) −2.33693 + 14.1362i −0.00768726 + 0.0465005i
\(305\) 52.1843i 0.171096i
\(306\) 0 0
\(307\) 463.833 + 192.126i 1.51086 + 0.625817i 0.975734 0.218957i \(-0.0702655\pi\)
0.535122 + 0.844775i \(0.320266\pi\)
\(308\) 489.118 271.754i 1.58805 0.882317i
\(309\) 0 0
\(310\) −4.95709 86.5431i −0.0159906 0.279171i
\(311\) −230.516 + 230.516i −0.741210 + 0.741210i −0.972811 0.231601i \(-0.925604\pi\)
0.231601 + 0.972811i \(0.425604\pi\)
\(312\) 0 0
\(313\) 2.89884 2.89884i 0.00926146 0.00926146i −0.702461 0.711722i \(-0.747915\pi\)
0.711722 + 0.702461i \(0.247915\pi\)
\(314\) 38.8469 43.5676i 0.123716 0.138750i
\(315\) 0 0
\(316\) −10.2753 8.15685i −0.0325169 0.0258128i
\(317\) −510.087 211.285i −1.60911 0.666514i −0.616441 0.787401i \(-0.711426\pi\)
−0.992666 + 0.120887i \(0.961426\pi\)
\(318\) 0 0
\(319\) 266.791i 0.836335i
\(320\) 110.133 + 5.44514i 0.344166 + 0.0170161i
\(321\) 0 0
\(322\) 162.477 466.001i 0.504587 1.44721i
\(323\) −5.24811 + 12.6701i −0.0162480 + 0.0392262i
\(324\) 0 0
\(325\) −42.2528 102.007i −0.130009 0.313869i
\(326\) −435.887 388.658i −1.33708 1.19220i
\(327\) 0 0
\(328\) −363.292 81.6397i −1.10760 0.248902i
\(329\) −192.020 192.020i −0.583647 0.583647i
\(330\) 0 0
\(331\) −95.3030 230.082i −0.287924 0.695111i 0.712051 0.702128i \(-0.247766\pi\)
−0.999975 + 0.00701670i \(0.997766\pi\)
\(332\) 119.401 + 214.906i 0.359643 + 0.647306i
\(333\) 0 0
\(334\) 26.4027 12.7512i 0.0790499 0.0381772i
\(335\) 5.10609 0.0152421
\(336\) 0 0
\(337\) 203.997i 0.605334i 0.953096 + 0.302667i \(0.0978769\pi\)
−0.953096 + 0.302667i \(0.902123\pi\)
\(338\) 259.131 125.148i 0.766660 0.370259i
\(339\) 0 0
\(340\) 101.482 + 28.9913i 0.298477 + 0.0852684i
\(341\) 240.793 99.7396i 0.706137 0.292491i
\(342\) 0 0
\(343\) −804.800 + 804.800i −2.34636 + 2.34636i
\(344\) 306.714 + 216.085i 0.891612 + 0.628153i
\(345\) 0 0
\(346\) −345.813 308.344i −0.999459 0.891167i
\(347\) 120.709 49.9993i 0.347865 0.144090i −0.201908 0.979404i \(-0.564714\pi\)
0.549773 + 0.835314i \(0.314714\pi\)
\(348\) 0 0
\(349\) 279.116 + 115.614i 0.799759 + 0.331271i 0.744860 0.667221i \(-0.232516\pi\)
0.0548993 + 0.998492i \(0.482516\pi\)
\(350\) 195.865 561.761i 0.559614 1.60503i
\(351\) 0 0
\(352\) 93.5583 + 318.063i 0.265791 + 0.903587i
\(353\) −608.156 −1.72282 −0.861410 0.507910i \(-0.830418\pi\)
−0.861410 + 0.507910i \(0.830418\pi\)
\(354\) 0 0
\(355\) −42.5329 + 102.683i −0.119811 + 0.289249i
\(356\) −250.117 + 28.7471i −0.702575 + 0.0807503i
\(357\) 0 0
\(358\) −3.72148 + 4.17371i −0.0103952 + 0.0116584i
\(359\) −196.029 196.029i −0.546041 0.546041i 0.379252 0.925293i \(-0.376181\pi\)
−0.925293 + 0.379252i \(0.876181\pi\)
\(360\) 0 0
\(361\) −254.699 254.699i −0.705536 0.705536i
\(362\) 22.8268 + 398.521i 0.0630574 + 1.10089i
\(363\) 0 0
\(364\) −260.247 74.3470i −0.714965 0.204250i
\(365\) 27.2019 65.6713i 0.0745259 0.179921i
\(366\) 0 0
\(367\) −33.0375 −0.0900203 −0.0450102 0.998987i \(-0.514332\pi\)
−0.0450102 + 0.998987i \(0.514332\pi\)
\(368\) 248.287 + 154.467i 0.674693 + 0.419747i
\(369\) 0 0
\(370\) 53.3198 + 110.404i 0.144108 + 0.298390i
\(371\) −473.241 196.023i −1.27558 0.528363i
\(372\) 0 0
\(373\) 115.583 47.8760i 0.309874 0.128354i −0.222327 0.974972i \(-0.571365\pi\)
0.532201 + 0.846618i \(0.321365\pi\)
\(374\) 18.1465 + 316.810i 0.0485200 + 0.847085i
\(375\) 0 0
\(376\) 135.952 86.0608i 0.361574 0.228885i
\(377\) −91.2527 + 91.2527i −0.242050 + 0.242050i
\(378\) 0 0
\(379\) 164.874 68.2930i 0.435024 0.180193i −0.154415 0.988006i \(-0.549349\pi\)
0.589438 + 0.807813i \(0.299349\pi\)
\(380\) 3.83712 4.83369i 0.0100977 0.0127202i
\(381\) 0 0
\(382\) −350.830 122.321i −0.918403 0.320213i
\(383\) 307.309i 0.802373i 0.915996 + 0.401186i \(0.131402\pi\)
−0.915996 + 0.401186i \(0.868598\pi\)
\(384\) 0 0
\(385\) −241.013 −0.626008
\(386\) 136.994 392.912i 0.354906 1.01791i
\(387\) 0 0
\(388\) 333.393 + 264.656i 0.859261 + 0.682104i
\(389\) 204.874 + 494.611i 0.526669 + 1.27149i 0.933693 + 0.358075i \(0.116567\pi\)
−0.407024 + 0.913418i \(0.633433\pi\)
\(390\) 0 0
\(391\) 197.907 + 197.907i 0.506157 + 0.506157i
\(392\) −570.368 901.022i −1.45502 2.29853i
\(393\) 0 0
\(394\) −646.224 + 37.0149i −1.64016 + 0.0939465i
\(395\) 2.16252 + 5.22078i 0.00547473 + 0.0132172i
\(396\) 0 0
\(397\) −224.796 + 542.706i −0.566237 + 1.36702i 0.338467 + 0.940978i \(0.390092\pi\)
−0.904705 + 0.426040i \(0.859908\pi\)
\(398\) −646.321 + 312.141i −1.62392 + 0.784274i
\(399\) 0 0
\(400\) 299.308 + 186.209i 0.748271 + 0.465522i
\(401\) 125.790i 0.313691i 0.987623 + 0.156846i \(0.0501325\pi\)
−0.987623 + 0.156846i \(0.949868\pi\)
\(402\) 0 0
\(403\) −116.475 48.2456i −0.289020 0.119716i
\(404\) −10.4007 + 36.4069i −0.0257442 + 0.0901162i
\(405\) 0 0
\(406\) −694.220 + 39.7641i −1.70990 + 0.0979412i
\(407\) −260.663 + 260.663i −0.640449 + 0.640449i
\(408\) 0 0
\(409\) 492.952 492.952i 1.20526 1.20526i 0.232717 0.972544i \(-0.425238\pi\)
0.972544 0.232717i \(-0.0747617\pi\)
\(410\) 119.708 + 106.738i 0.291972 + 0.260336i
\(411\) 0 0
\(412\) −16.8527 146.628i −0.0409046 0.355894i
\(413\) 819.159 + 339.307i 1.98344 + 0.821567i
\(414\) 0 0
\(415\) 105.895i 0.255168i
\(416\) 76.7891 140.790i 0.184589 0.338438i
\(417\) 0 0
\(418\) 17.5213 + 6.10902i 0.0419170 + 0.0146149i
\(419\) −203.456 + 491.187i −0.485576 + 1.17228i 0.471349 + 0.881947i \(0.343767\pi\)
−0.956925 + 0.290336i \(0.906233\pi\)
\(420\) 0 0
\(421\) −0.995616 2.40363i −0.00236488 0.00570934i 0.922693 0.385536i \(-0.125984\pi\)
−0.925058 + 0.379827i \(0.875984\pi\)
\(422\) 147.718 165.669i 0.350044 0.392580i
\(423\) 0 0
\(424\) 174.800 248.114i 0.412264 0.585175i
\(425\) 238.576 + 238.576i 0.561355 + 0.561355i
\(426\) 0 0
\(427\) −156.495 377.813i −0.366499 0.884807i
\(428\) −92.3814 + 323.376i −0.215844 + 0.755551i
\(429\) 0 0
\(430\) −70.2808 145.524i −0.163444 0.338427i
\(431\) −404.244 −0.937920 −0.468960 0.883219i \(-0.655371\pi\)
−0.468960 + 0.883219i \(0.655371\pi\)
\(432\) 0 0
\(433\) 446.431i 1.03102i 0.856884 + 0.515509i \(0.172397\pi\)
−0.856884 + 0.515509i \(0.827603\pi\)
\(434\) −295.423 611.704i −0.680698 1.40946i
\(435\) 0 0
\(436\) 329.425 183.028i 0.755561 0.419789i
\(437\) 15.1203 6.26304i 0.0346003 0.0143319i
\(438\) 0 0
\(439\) −203.077 + 203.077i −0.462590 + 0.462590i −0.899503 0.436914i \(-0.856072\pi\)
0.436914 + 0.899503i \(0.356072\pi\)
\(440\) 31.3104 139.329i 0.0711600 0.316658i
\(441\) 0 0
\(442\) 102.154 114.568i 0.231118 0.259203i
\(443\) 440.203 182.338i 0.993685 0.411598i 0.174207 0.984709i \(-0.444264\pi\)
0.819478 + 0.573111i \(0.194264\pi\)
\(444\) 0 0
\(445\) 100.188 + 41.4993i 0.225142 + 0.0932568i
\(446\) 353.439 + 123.231i 0.792465 + 0.276303i
\(447\) 0 0
\(448\) 813.691 290.855i 1.81627 0.649230i
\(449\) 636.256 1.41705 0.708526 0.705685i \(-0.249361\pi\)
0.708526 + 0.705685i \(0.249361\pi\)
\(450\) 0 0
\(451\) −184.538 + 445.514i −0.409175 + 0.987836i
\(452\) 15.7287 19.8138i 0.0347980 0.0438358i
\(453\) 0 0
\(454\) −10.6238 9.47266i −0.0234003 0.0208649i
\(455\) 82.4357 + 82.4357i 0.181177 + 0.181177i
\(456\) 0 0
\(457\) −359.285 359.285i −0.786181 0.786181i 0.194685 0.980866i \(-0.437632\pi\)
−0.980866 + 0.194685i \(0.937632\pi\)
\(458\) −650.412 + 37.2549i −1.42011 + 0.0813425i
\(459\) 0 0
\(460\) −61.1717 110.100i −0.132982 0.239349i
\(461\) −68.2156 + 164.687i −0.147973 + 0.357239i −0.980435 0.196844i \(-0.936931\pi\)
0.832462 + 0.554083i \(0.186931\pi\)
\(462\) 0 0
\(463\) 662.155 1.43014 0.715070 0.699053i \(-0.246395\pi\)
0.715070 + 0.699053i \(0.246395\pi\)
\(464\) 67.1997 406.494i 0.144827 0.876064i
\(465\) 0 0
\(466\) 529.885 255.908i 1.13709 0.549160i
\(467\) 854.762 + 354.054i 1.83033 + 0.758146i 0.967607 + 0.252461i \(0.0812399\pi\)
0.862718 + 0.505685i \(0.168760\pi\)
\(468\) 0 0
\(469\) 36.9680 15.3126i 0.0788229 0.0326495i
\(470\) −69.1923 + 3.96326i −0.147218 + 0.00843246i
\(471\) 0 0
\(472\) −302.571 + 429.475i −0.641041 + 0.909905i
\(473\) 343.579 343.579i 0.726383 0.726383i
\(474\) 0 0
\(475\) 18.2274 7.55005i 0.0383735 0.0158948i
\(476\) 821.670 94.4385i 1.72620 0.198400i
\(477\) 0 0
\(478\) 182.939 524.687i 0.382717 1.09767i
\(479\) 926.802i 1.93487i −0.253122 0.967434i \(-0.581458\pi\)
0.253122 0.967434i \(-0.418542\pi\)
\(480\) 0 0
\(481\) 178.313 0.370714
\(482\) 119.485 + 41.6599i 0.247894 + 0.0864312i
\(483\) 0 0
\(484\) −54.2794 + 6.23859i −0.112147 + 0.0128896i
\(485\) −70.1649 169.393i −0.144670 0.349264i
\(486\) 0 0
\(487\) 586.001 + 586.001i 1.20329 + 1.20329i 0.973161 + 0.230127i \(0.0739141\pi\)
0.230127 + 0.973161i \(0.426086\pi\)
\(488\) 238.744 41.3874i 0.489229 0.0848102i
\(489\) 0 0
\(490\) 26.2665 + 458.572i 0.0536051 + 0.935862i
\(491\) 17.1543 + 41.4142i 0.0349375 + 0.0843466i 0.940385 0.340111i \(-0.110465\pi\)
−0.905448 + 0.424458i \(0.860465\pi\)
\(492\) 0 0
\(493\) 150.913 364.335i 0.306111 0.739017i
\(494\) −3.90344 8.08247i −0.00790169 0.0163613i
\(495\) 0 0
\(496\) 392.004 91.3161i 0.790331 0.184105i
\(497\) 870.977i 1.75247i
\(498\) 0 0
\(499\) −143.291 59.3531i −0.287156 0.118944i 0.234456 0.972127i \(-0.424669\pi\)
−0.521612 + 0.853183i \(0.674669\pi\)
\(500\) −157.420 283.334i −0.314840 0.566668i
\(501\) 0 0
\(502\) 20.0481 + 350.009i 0.0399365 + 0.697230i
\(503\) −74.0929 + 74.0929i −0.147302 + 0.147302i −0.776912 0.629610i \(-0.783215\pi\)
0.629610 + 0.776912i \(0.283215\pi\)
\(504\) 0 0
\(505\) 11.5322 11.5322i 0.0228361 0.0228361i
\(506\) 252.028 282.654i 0.498079 0.558605i
\(507\) 0 0
\(508\) 86.0529 108.403i 0.169396 0.213391i
\(509\) −467.540 193.661i −0.918546 0.380474i −0.127224 0.991874i \(-0.540607\pi\)
−0.791322 + 0.611400i \(0.790607\pi\)
\(510\) 0 0
\(511\) 557.034i 1.09009i
\(512\) 62.4351 + 508.179i 0.121944 + 0.992537i
\(513\) 0 0
\(514\) 54.6309 156.687i 0.106286 0.304839i
\(515\) −24.3285 + 58.7343i −0.0472399 + 0.114047i
\(516\) 0 0
\(517\) −79.7431 192.517i −0.154242 0.372373i
\(518\) 717.125 + 639.423i 1.38441 + 1.23441i
\(519\) 0 0
\(520\) −58.3653 + 36.9466i −0.112241 + 0.0710512i
\(521\) −694.307 694.307i −1.33264 1.33264i −0.902998 0.429644i \(-0.858639\pi\)
−0.429644 0.902998i \(-0.641361\pi\)
\(522\) 0 0
\(523\) 67.4311 + 162.793i 0.128931 + 0.311268i 0.975142 0.221581i \(-0.0711216\pi\)
−0.846211 + 0.532848i \(0.821122\pi\)
\(524\) −621.360 + 345.227i −1.18580 + 0.658830i
\(525\) 0 0
\(526\) 377.952 182.532i 0.718540 0.347020i
\(527\) 385.250 0.731025
\(528\) 0 0
\(529\) 194.991i 0.368602i
\(530\) −117.720 + 56.8531i −0.222114 + 0.107270i
\(531\) 0 0
\(532\) 13.2849 46.5029i 0.0249716 0.0874115i
\(533\) 215.502 89.2638i 0.404319 0.167474i
\(534\) 0 0
\(535\) 102.432 102.432i 0.191462 0.191462i
\(536\) 4.04964 + 23.3604i 0.00755530 + 0.0435829i
\(537\) 0 0
\(538\) 307.039 + 273.771i 0.570704 + 0.508867i
\(539\) −1275.91 + 528.498i −2.36717 + 0.980515i
\(540\) 0 0
\(541\) 125.547 + 52.0035i 0.232066 + 0.0961247i 0.495686 0.868502i \(-0.334917\pi\)
−0.263620 + 0.964626i \(0.584917\pi\)
\(542\) −19.6216 + 56.2767i −0.0362022 + 0.103832i
\(543\) 0 0
\(544\) −52.1498 + 487.275i −0.0958636 + 0.895727i
\(545\) −162.324 −0.297842
\(546\) 0 0
\(547\) −278.945 + 673.432i −0.509954 + 1.23114i 0.433956 + 0.900934i \(0.357117\pi\)
−0.943910 + 0.330204i \(0.892883\pi\)
\(548\) 46.2314 + 402.240i 0.0843638 + 0.734015i
\(549\) 0 0
\(550\) 303.818 340.737i 0.552396 0.619523i
\(551\) −16.3057 16.3057i −0.0295929 0.0295929i
\(552\) 0 0
\(553\) 31.3132 + 31.3132i 0.0566241 + 0.0566241i
\(554\) 45.6589 + 797.133i 0.0824167 + 1.43887i
\(555\) 0 0
\(556\) −215.889 + 755.708i −0.388290 + 1.35919i
\(557\) 228.207 550.942i 0.409708 0.989123i −0.575506 0.817797i \(-0.695195\pi\)
0.985214 0.171326i \(-0.0548051\pi\)
\(558\) 0 0
\(559\) −235.035 −0.420455
\(560\) −367.218 60.7068i −0.655746 0.108405i
\(561\) 0 0
\(562\) −344.732 713.803i −0.613402 1.27011i
\(563\) 236.899 + 98.1268i 0.420780 + 0.174293i 0.583019 0.812459i \(-0.301871\pi\)
−0.162239 + 0.986752i \(0.551871\pi\)
\(564\) 0 0
\(565\) −10.0671 + 4.16995i −0.0178180 + 0.00738044i
\(566\) 21.8681 + 381.783i 0.0386362 + 0.674528i
\(567\) 0 0
\(568\) −503.511 113.150i −0.886463 0.199208i
\(569\) 289.568 289.568i 0.508907 0.508907i −0.405284 0.914191i \(-0.632827\pi\)
0.914191 + 0.405284i \(0.132827\pi\)
\(570\) 0 0
\(571\) 801.877 332.148i 1.40434 0.581695i 0.453464 0.891275i \(-0.350188\pi\)
0.950874 + 0.309579i \(0.100188\pi\)
\(572\) −162.667 129.129i −0.284383 0.225751i
\(573\) 0 0
\(574\) 1186.78 + 413.786i 2.06756 + 0.720882i
\(575\) 402.646i 0.700254i
\(576\) 0 0
\(577\) −107.872 −0.186953 −0.0934767 0.995621i \(-0.529798\pi\)
−0.0934767 + 0.995621i \(0.529798\pi\)
\(578\) 35.8670 102.870i 0.0620537 0.177976i
\(579\) 0 0
\(580\) −110.339 + 138.996i −0.190239 + 0.239648i
\(581\) −317.567 766.676i −0.546588 1.31958i
\(582\) 0 0
\(583\) −277.936 277.936i −0.476734 0.476734i
\(584\) 322.021 + 72.3652i 0.551405 + 0.123913i
\(585\) 0 0
\(586\) −59.2679 + 3.39479i −0.101140 + 0.00579316i
\(587\) 292.393 + 705.899i 0.498114 + 1.20255i 0.950498 + 0.310730i \(0.100574\pi\)
−0.452384 + 0.891823i \(0.649426\pi\)
\(588\) 0 0
\(589\) 8.62087 20.8126i 0.0146365 0.0353355i
\(590\) 203.769 98.4102i 0.345371 0.166797i
\(591\) 0 0
\(592\) −462.813 + 331.500i −0.781778 + 0.559967i
\(593\) 247.178i 0.416826i −0.978041 0.208413i \(-0.933170\pi\)
0.978041 0.208413i \(-0.0668298\pi\)
\(594\) 0 0
\(595\) −329.133 136.331i −0.553164 0.229128i
\(596\) 881.248 + 251.753i 1.47860 + 0.422405i
\(597\) 0 0
\(598\) −182.882 + 10.4753i −0.305822 + 0.0175171i
\(599\) 633.115 633.115i 1.05695 1.05695i 0.0586768 0.998277i \(-0.481312\pi\)
0.998277 0.0586768i \(-0.0186881\pi\)
\(600\) 0 0
\(601\) −147.019 + 147.019i −0.244624 + 0.244624i −0.818760 0.574136i \(-0.805338\pi\)
0.574136 + 0.818760i \(0.305338\pi\)
\(602\) −945.241 842.823i −1.57017 1.40004i
\(603\) 0 0
\(604\) −59.4692 + 6.83508i −0.0984590 + 0.0113164i
\(605\) 21.7424 + 9.00601i 0.0359379 + 0.0148860i
\(606\) 0 0
\(607\) 52.6594i 0.0867536i −0.999059 0.0433768i \(-0.986188\pi\)
0.999059 0.0433768i \(-0.0138116\pi\)
\(608\) 25.1574 + 13.7212i 0.0413773 + 0.0225678i
\(609\) 0 0
\(610\) −98.5501 34.3607i −0.161558 0.0563291i
\(611\) −38.5729 + 93.1233i −0.0631308 + 0.152411i
\(612\) 0 0
\(613\) −336.988 813.562i −0.549737 1.32718i −0.917675 0.397331i \(-0.869936\pi\)
0.367939 0.929850i \(-0.380064\pi\)
\(614\) 668.241 749.445i 1.08834 1.22059i
\(615\) 0 0
\(616\) −191.148 1102.64i −0.310305 1.79000i
\(617\) 150.269 + 150.269i 0.243547 + 0.243547i 0.818316 0.574769i \(-0.194908\pi\)
−0.574769 + 0.818316i \(0.694908\pi\)
\(618\) 0 0
\(619\) 4.34083 + 10.4797i 0.00701265 + 0.0169300i 0.927347 0.374202i \(-0.122083\pi\)
−0.920334 + 0.391132i \(0.872083\pi\)
\(620\) −166.701 47.6228i −0.268872 0.0768110i
\(621\) 0 0
\(622\) 283.547 + 587.114i 0.455864 + 0.943914i
\(623\) 849.811 1.36406
\(624\) 0 0
\(625\) 411.175i 0.657880i
\(626\) −3.56572 7.38320i −0.00569604 0.0117942i
\(627\) 0 0
\(628\) −56.6987 102.050i −0.0902845 0.162499i
\(629\) −503.413 + 208.520i −0.800338 + 0.331511i
\(630\) 0 0
\(631\) 356.485 356.485i 0.564952 0.564952i −0.365758 0.930710i \(-0.619190\pi\)
0.930710 + 0.365758i \(0.119190\pi\)
\(632\) −22.1700 + 14.0341i −0.0350792 + 0.0222059i
\(633\) 0 0
\(634\) −734.879 + 824.180i −1.15912 + 1.29997i
\(635\) −55.0781 + 22.8141i −0.0867371 + 0.0359277i
\(636\) 0 0
\(637\) 617.175 + 255.642i 0.968878 + 0.401322i
\(638\) −503.835 175.669i −0.789711 0.275343i
\(639\) 0 0
\(640\) 82.8004 204.401i 0.129376 0.319377i
\(641\) −741.748 −1.15717 −0.578587 0.815621i \(-0.696396\pi\)
−0.578587 + 0.815621i \(0.696396\pi\)
\(642\) 0 0
\(643\) 181.837 438.994i 0.282795 0.682729i −0.717103 0.696967i \(-0.754532\pi\)
0.999899 + 0.0142385i \(0.00453240\pi\)
\(644\) −773.061 613.677i −1.20041 0.952915i
\(645\) 0 0
\(646\) 20.4718 + 18.2537i 0.0316901 + 0.0282565i
\(647\) −520.304 520.304i −0.804180 0.804180i 0.179566 0.983746i \(-0.442531\pi\)
−0.983746 + 0.179566i \(0.942531\pi\)
\(648\) 0 0
\(649\) 481.095 + 481.095i 0.741286 + 0.741286i
\(650\) −220.463 + 12.6278i −0.339173 + 0.0194275i
\(651\) 0 0
\(652\) −1020.99 + 567.262i −1.56594 + 0.870034i
\(653\) −161.753 + 390.507i −0.247708 + 0.598019i −0.998009 0.0630771i \(-0.979909\pi\)
0.750301 + 0.661096i \(0.229909\pi\)
\(654\) 0 0
\(655\) 306.175 0.467443
\(656\) −393.386 + 632.322i −0.599674 + 0.963905i
\(657\) 0 0
\(658\) −489.065 + 236.194i −0.743260 + 0.358958i
\(659\) −70.1853 29.0717i −0.106503 0.0441149i 0.328796 0.944401i \(-0.393357\pi\)
−0.435299 + 0.900286i \(0.643357\pi\)
\(660\) 0 0
\(661\) −81.1193 + 33.6007i −0.122722 + 0.0508331i −0.443199 0.896423i \(-0.646157\pi\)
0.320477 + 0.947256i \(0.396157\pi\)
\(662\) −497.262 + 28.4826i −0.751152 + 0.0430251i
\(663\) 0 0
\(664\) 484.470 83.9852i 0.729623 0.126484i
\(665\) −14.7302 + 14.7302i −0.0221507 + 0.0221507i
\(666\) 0 0
\(667\) −434.794 + 180.097i −0.651865 + 0.270011i
\(668\) −6.69582 58.2575i −0.0100237 0.0872119i
\(669\) 0 0
\(670\) 3.36210 9.64286i 0.00501807 0.0143923i
\(671\) 313.801i 0.467661i
\(672\) 0 0
\(673\) −851.239 −1.26484 −0.632421 0.774625i \(-0.717939\pi\)
−0.632421 + 0.774625i \(0.717939\pi\)
\(674\) 385.250 + 134.322i 0.571587 + 0.199291i
\(675\) 0 0
\(676\) −65.7166 571.773i −0.0972139 0.845818i
\(677\) 380.410 + 918.390i 0.561905 + 1.35656i 0.908241 + 0.418448i \(0.137426\pi\)
−0.346335 + 0.938111i \(0.612574\pi\)
\(678\) 0 0
\(679\) −1015.98 1015.98i −1.49629 1.49629i
\(680\) 121.571 172.560i 0.178781 0.253765i
\(681\) 0 0
\(682\) −29.8086 520.411i −0.0437076 0.763066i
\(683\) −425.467 1027.17i −0.622939 1.50391i −0.848236 0.529618i \(-0.822335\pi\)
0.225297 0.974290i \(-0.427665\pi\)
\(684\) 0 0
\(685\) 66.7395 161.123i 0.0974299 0.235217i
\(686\) 989.946 + 2049.79i 1.44307 + 2.98803i
\(687\) 0 0
\(688\) 610.033 436.950i 0.886675 0.635102i
\(689\) 190.129i 0.275950i
\(690\) 0 0
\(691\) 260.940 + 108.085i 0.377627 + 0.156418i 0.563420 0.826171i \(-0.309485\pi\)
−0.185793 + 0.982589i \(0.559485\pi\)
\(692\) −810.008 + 450.040i −1.17053 + 0.650347i
\(693\) 0 0
\(694\) −14.9430 260.881i −0.0215317 0.375910i
\(695\) 239.377 239.377i 0.344428 0.344428i
\(696\) 0 0
\(697\) −504.018 + 504.018i −0.723124 + 0.723124i
\(698\) 402.121 450.986i 0.576104 0.646111i
\(699\) 0 0
\(700\) −931.920 739.783i −1.33131 1.05683i
\(701\) 727.192 + 301.213i 1.03736 + 0.429690i 0.835365 0.549695i \(-0.185256\pi\)
0.201999 + 0.979386i \(0.435256\pi\)
\(702\) 0 0
\(703\) 31.8623i 0.0453234i
\(704\) 662.266 + 32.7433i 0.940718 + 0.0465104i
\(705\) 0 0
\(706\) −400.440 + 1148.50i −0.567196 + 1.62678i
\(707\) 48.9091 118.077i 0.0691783 0.167011i
\(708\) 0 0
\(709\) 259.577 + 626.675i 0.366118 + 0.883886i 0.994379 + 0.105883i \(0.0337670\pi\)
−0.628261 + 0.778003i \(0.716233\pi\)
\(710\) 165.912 + 147.935i 0.233679 + 0.208360i
\(711\) 0 0
\(712\) −110.400 + 491.275i −0.155057 + 0.689992i
\(713\) −325.095 325.095i −0.455953 0.455953i
\(714\) 0 0
\(715\) 34.2344 + 82.6491i 0.0478803 + 0.115593i
\(716\) 5.43165 + 9.77621i 0.00758611 + 0.0136539i
\(717\) 0 0
\(718\) −499.276 + 241.126i −0.695370 + 0.335830i
\(719\) −1034.71 −1.43910 −0.719549 0.694442i \(-0.755651\pi\)
−0.719549 + 0.694442i \(0.755651\pi\)
\(720\) 0 0
\(721\) 498.193i 0.690975i
\(722\) −648.705 + 313.293i −0.898484 + 0.433923i
\(723\) 0 0
\(724\) 767.638 + 219.297i 1.06027 + 0.302897i
\(725\) −524.141 + 217.106i −0.722953 + 0.299457i
\(726\) 0 0
\(727\) 227.066 227.066i 0.312332 0.312332i −0.533480 0.845813i \(-0.679116\pi\)
0.845813 + 0.533480i \(0.179116\pi\)
\(728\) −311.765 + 442.524i −0.428248 + 0.607863i
\(729\) 0 0
\(730\) −106.109 94.6122i −0.145355 0.129606i
\(731\) 663.548 274.850i 0.907726 0.375992i
\(732\) 0 0
\(733\) 973.386 + 403.190i 1.32795 + 0.550054i 0.930070 0.367384i \(-0.119746\pi\)
0.397879 + 0.917438i \(0.369746\pi\)
\(734\) −21.7535 + 62.3913i −0.0296369 + 0.0850018i
\(735\) 0 0
\(736\) 455.196 367.182i 0.618472 0.498889i
\(737\) 30.7045 0.0416615
\(738\) 0 0
\(739\) 387.131 934.616i 0.523857 1.26470i −0.411632 0.911350i \(-0.635041\pi\)
0.935490 0.353354i \(-0.114959\pi\)
\(740\) 243.607 27.9989i 0.329199 0.0378364i
\(741\) 0 0
\(742\) −681.795 + 764.645i −0.918861 + 1.03052i
\(743\) −528.819 528.819i −0.711735 0.711735i 0.255163 0.966898i \(-0.417871\pi\)
−0.966898 + 0.255163i \(0.917871\pi\)
\(744\) 0 0
\(745\) −279.143 279.143i −0.374689 0.374689i
\(746\) −14.3084 249.803i −0.0191802 0.334856i
\(747\) 0 0
\(748\) 610.245 + 174.334i 0.815835 + 0.233066i
\(749\) 434.423 1048.79i 0.580004 1.40025i
\(750\) 0 0
\(751\) −176.760 −0.235366 −0.117683 0.993051i \(-0.537547\pi\)
−0.117683 + 0.993051i \(0.537547\pi\)
\(752\) −73.0084 313.412i −0.0970856 0.416772i
\(753\) 0 0
\(754\) 112.246 + 232.416i 0.148867 + 0.308245i
\(755\) 23.8213 + 9.86711i 0.0315514 + 0.0130690i
\(756\) 0 0
\(757\) −59.8575 + 24.7938i −0.0790720 + 0.0327527i −0.421869 0.906657i \(-0.638626\pi\)
0.342797 + 0.939410i \(0.388626\pi\)
\(758\) −20.4103 356.333i −0.0269265 0.470096i
\(759\) 0 0
\(760\) −6.60189 10.4292i −0.00868670 0.0137226i
\(761\) −713.497 + 713.497i −0.937579 + 0.937579i −0.998163 0.0605844i \(-0.980704\pi\)
0.0605844 + 0.998163i \(0.480704\pi\)
\(762\) 0 0
\(763\) −1175.22 + 486.793i −1.54026 + 0.637999i
\(764\) −462.008 + 582.001i −0.604722 + 0.761781i
\(765\) 0 0
\(766\) 580.354 + 202.348i 0.757642 + 0.264161i
\(767\) 329.106i 0.429082i
\(768\) 0 0
\(769\) −147.511 −0.191821 −0.0959107 0.995390i \(-0.530576\pi\)
−0.0959107 + 0.995390i \(0.530576\pi\)
\(770\) −158.695 + 455.154i −0.206098 + 0.591109i
\(771\) 0 0
\(772\) −651.811 517.426i −0.844315 0.670240i
\(773\) −104.027 251.144i −0.134576 0.324896i 0.842198 0.539169i \(-0.181262\pi\)
−0.976774 + 0.214273i \(0.931262\pi\)
\(774\) 0 0
\(775\) −391.899 391.899i −0.505677 0.505677i
\(776\) 719.327 455.351i 0.926968 0.586792i
\(777\) 0 0
\(778\) 1068.97 61.2295i 1.37400 0.0787012i
\(779\) 15.9503 + 38.5075i 0.0204754 + 0.0494319i
\(780\) 0 0
\(781\) −255.764 + 617.468i −0.327482 + 0.790612i
\(782\) 504.061 243.436i 0.644579 0.311300i
\(783\) 0 0
\(784\) −2077.14 + 483.863i −2.64942 + 0.617173i
\(785\) 50.2850i 0.0640573i
\(786\) 0 0
\(787\) 999.730 + 414.102i 1.27031 + 0.526178i 0.913057 0.407832i \(-0.133715\pi\)
0.357248 + 0.934010i \(0.383715\pi\)