Properties

Label 177.5.b.a.119.13
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.13
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.66

$q$-expansion

\(f(q)\) \(=\) \(q-5.74797i q^{2} +(-1.10979 + 8.93131i) q^{3} -17.0392 q^{4} +1.93242i q^{5} +(51.3369 + 6.37903i) q^{6} -31.0983 q^{7} +5.97306i q^{8} +(-78.5367 - 19.8237i) q^{9} +O(q^{10})\) \(q-5.74797i q^{2} +(-1.10979 + 8.93131i) q^{3} -17.0392 q^{4} +1.93242i q^{5} +(51.3369 + 6.37903i) q^{6} -31.0983 q^{7} +5.97306i q^{8} +(-78.5367 - 19.8237i) q^{9} +11.1075 q^{10} -36.5780i q^{11} +(18.9098 - 152.182i) q^{12} +150.671 q^{13} +178.752i q^{14} +(-17.2590 - 2.14458i) q^{15} -238.294 q^{16} +397.713i q^{17} +(-113.946 + 451.427i) q^{18} +641.461 q^{19} -32.9268i q^{20} +(34.5125 - 277.749i) q^{21} -210.249 q^{22} +670.788i q^{23} +(-53.3473 - 6.62883i) q^{24} +621.266 q^{25} -866.051i q^{26} +(264.211 - 679.436i) q^{27} +529.889 q^{28} +1328.66i q^{29} +(-12.3270 + 99.2045i) q^{30} +747.325 q^{31} +1465.27i q^{32} +(326.690 + 40.5939i) q^{33} +2286.04 q^{34} -60.0949i q^{35} +(1338.20 + 337.780i) q^{36} +1452.82 q^{37} -3687.10i q^{38} +(-167.213 + 1345.69i) q^{39} -11.5425 q^{40} +820.955i q^{41} +(-1596.49 - 198.377i) q^{42} -2961.00 q^{43} +623.259i q^{44} +(38.3078 - 151.766i) q^{45} +3855.67 q^{46} +945.968i q^{47} +(264.455 - 2128.27i) q^{48} -1433.90 q^{49} -3571.02i q^{50} +(-3552.10 - 441.376i) q^{51} -2567.30 q^{52} -5310.33i q^{53} +(-3905.38 - 1518.68i) q^{54} +70.6841 q^{55} -185.752i q^{56} +(-711.885 + 5729.09i) q^{57} +7637.10 q^{58} -453.188i q^{59} +(294.080 + 36.5418i) q^{60} +722.307 q^{61} -4295.60i q^{62} +(2442.36 + 616.484i) q^{63} +4609.65 q^{64} +291.159i q^{65} +(233.332 - 1877.80i) q^{66} +7494.48 q^{67} -6776.69i q^{68} +(-5991.02 - 744.433i) q^{69} -345.424 q^{70} +3888.73i q^{71} +(118.408 - 469.105i) q^{72} -8396.06 q^{73} -8350.75i q^{74} +(-689.473 + 5548.72i) q^{75} -10930.0 q^{76} +1137.51i q^{77} +(7734.98 + 961.133i) q^{78} +9517.31 q^{79} -460.483i q^{80} +(5775.04 + 3113.78i) q^{81} +4718.82 q^{82} -432.863i q^{83} +(-588.064 + 4732.60i) q^{84} -768.548 q^{85} +17019.7i q^{86} +(-11866.7 - 1474.53i) q^{87} +218.483 q^{88} +6891.78i q^{89} +(-872.346 - 220.192i) q^{90} -4685.60 q^{91} -11429.7i q^{92} +(-829.372 + 6674.59i) q^{93} +5437.39 q^{94} +1239.57i q^{95} +(-13086.8 - 1626.14i) q^{96} +3927.71 q^{97} +8242.00i q^{98} +(-725.113 + 2872.72i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.74797i 1.43699i −0.695531 0.718496i \(-0.744831\pi\)
0.695531 0.718496i \(-0.255169\pi\)
\(3\) −1.10979 + 8.93131i −0.123310 + 0.992368i
\(4\) −17.0392 −1.06495
\(5\) 1.93242i 0.0772968i 0.999253 + 0.0386484i \(0.0123052\pi\)
−0.999253 + 0.0386484i \(0.987695\pi\)
\(6\) 51.3369 + 6.37903i 1.42603 + 0.177195i
\(7\) −31.0983 −0.634659 −0.317329 0.948315i \(-0.602786\pi\)
−0.317329 + 0.948315i \(0.602786\pi\)
\(8\) 5.97306i 0.0933291i
\(9\) −78.5367 19.8237i −0.969589 0.244737i
\(10\) 11.1075 0.111075
\(11\) 36.5780i 0.302298i −0.988511 0.151149i \(-0.951703\pi\)
0.988511 0.151149i \(-0.0482973\pi\)
\(12\) 18.9098 152.182i 0.131318 1.05682i
\(13\) 150.671 0.891543 0.445772 0.895147i \(-0.352929\pi\)
0.445772 + 0.895147i \(0.352929\pi\)
\(14\) 178.752i 0.912000i
\(15\) −17.2590 2.14458i −0.0767069 0.00953145i
\(16\) −238.294 −0.930834
\(17\) 397.713i 1.37617i 0.725631 + 0.688084i \(0.241548\pi\)
−0.725631 + 0.688084i \(0.758452\pi\)
\(18\) −113.946 + 451.427i −0.351686 + 1.39329i
\(19\) 641.461 1.77690 0.888450 0.458974i \(-0.151783\pi\)
0.888450 + 0.458974i \(0.151783\pi\)
\(20\) 32.9268i 0.0823170i
\(21\) 34.5125 277.749i 0.0782596 0.629815i
\(22\) −210.249 −0.434400
\(23\) 670.788i 1.26803i 0.773320 + 0.634016i \(0.218594\pi\)
−0.773320 + 0.634016i \(0.781406\pi\)
\(24\) −53.3473 6.62883i −0.0926168 0.0115084i
\(25\) 621.266 0.994025
\(26\) 866.051i 1.28114i
\(27\) 264.211 679.436i 0.362429 0.932011i
\(28\) 529.889 0.675878
\(29\) 1328.66i 1.57986i 0.613198 + 0.789929i \(0.289883\pi\)
−0.613198 + 0.789929i \(0.710117\pi\)
\(30\) −12.3270 + 99.2045i −0.0136966 + 0.110227i
\(31\) 747.325 0.777653 0.388827 0.921311i \(-0.372880\pi\)
0.388827 + 0.921311i \(0.372880\pi\)
\(32\) 1465.27i 1.43093i
\(33\) 326.690 + 40.5939i 0.299991 + 0.0372763i
\(34\) 2286.04 1.97754
\(35\) 60.0949i 0.0490571i
\(36\) 1338.20 + 337.780i 1.03256 + 0.260632i
\(37\) 1452.82 1.06123 0.530613 0.847614i \(-0.321962\pi\)
0.530613 + 0.847614i \(0.321962\pi\)
\(38\) 3687.10i 2.55339i
\(39\) −167.213 + 1345.69i −0.109936 + 0.884739i
\(40\) −11.5425 −0.00721404
\(41\) 820.955i 0.488373i 0.969728 + 0.244186i \(0.0785209\pi\)
−0.969728 + 0.244186i \(0.921479\pi\)
\(42\) −1596.49 198.377i −0.905040 0.112458i
\(43\) −2961.00 −1.60141 −0.800703 0.599061i \(-0.795541\pi\)
−0.800703 + 0.599061i \(0.795541\pi\)
\(44\) 623.259i 0.321931i
\(45\) 38.3078 151.766i 0.0189174 0.0749461i
\(46\) 3855.67 1.82215
\(47\) 945.968i 0.428233i 0.976808 + 0.214117i \(0.0686873\pi\)
−0.976808 + 0.214117i \(0.931313\pi\)
\(48\) 264.455 2128.27i 0.114781 0.923730i
\(49\) −1433.90 −0.597208
\(50\) 3571.02i 1.42841i
\(51\) −3552.10 441.376i −1.36567 0.169695i
\(52\) −2567.30 −0.949447
\(53\) 5310.33i 1.89047i −0.326389 0.945236i \(-0.605832\pi\)
0.326389 0.945236i \(-0.394168\pi\)
\(54\) −3905.38 1518.68i −1.33929 0.520808i
\(55\) 70.6841 0.0233667
\(56\) 185.752i 0.0592321i
\(57\) −711.885 + 5729.09i −0.219109 + 1.76334i
\(58\) 7637.10 2.27024
\(59\) 453.188i 0.130189i
\(60\) 294.080 + 36.5418i 0.0816888 + 0.0101505i
\(61\) 722.307 0.194116 0.0970581 0.995279i \(-0.469057\pi\)
0.0970581 + 0.995279i \(0.469057\pi\)
\(62\) 4295.60i 1.11748i
\(63\) 2442.36 + 616.484i 0.615358 + 0.155325i
\(64\) 4609.65 1.12540
\(65\) 291.159i 0.0689134i
\(66\) 233.332 1877.80i 0.0535657 0.431085i
\(67\) 7494.48 1.66952 0.834761 0.550613i \(-0.185606\pi\)
0.834761 + 0.550613i \(0.185606\pi\)
\(68\) 6776.69i 1.46555i
\(69\) −5991.02 744.433i −1.25835 0.156361i
\(70\) −345.424 −0.0704947
\(71\) 3888.73i 0.771420i 0.922620 + 0.385710i \(0.126043\pi\)
−0.922620 + 0.385710i \(0.873957\pi\)
\(72\) 118.408 469.105i 0.0228411 0.0904909i
\(73\) −8396.06 −1.57554 −0.787771 0.615968i \(-0.788765\pi\)
−0.787771 + 0.615968i \(0.788765\pi\)
\(74\) 8350.75i 1.52497i
\(75\) −689.473 + 5548.72i −0.122573 + 0.986439i
\(76\) −10930.0 −1.89230
\(77\) 1137.51i 0.191856i
\(78\) 7734.98 + 961.133i 1.27136 + 0.157977i
\(79\) 9517.31 1.52497 0.762483 0.647009i \(-0.223980\pi\)
0.762483 + 0.647009i \(0.223980\pi\)
\(80\) 460.483i 0.0719505i
\(81\) 5775.04 + 3113.78i 0.880207 + 0.474589i
\(82\) 4718.82 0.701788
\(83\) 432.863i 0.0628340i −0.999506 0.0314170i \(-0.989998\pi\)
0.999506 0.0314170i \(-0.0100020\pi\)
\(84\) −588.064 + 4732.60i −0.0833424 + 0.670720i
\(85\) −768.548 −0.106373
\(86\) 17019.7i 2.30121i
\(87\) −11866.7 1474.53i −1.56780 0.194812i
\(88\) 218.483 0.0282132
\(89\) 6891.78i 0.870064i 0.900415 + 0.435032i \(0.143263\pi\)
−0.900415 + 0.435032i \(0.856737\pi\)
\(90\) −872.346 220.192i −0.107697 0.0271842i
\(91\) −4685.60 −0.565826
\(92\) 11429.7i 1.35039i
\(93\) −829.372 + 6674.59i −0.0958922 + 0.771719i
\(94\) 5437.39 0.615368
\(95\) 1239.57i 0.137349i
\(96\) −13086.8 1626.14i −1.42001 0.176448i
\(97\) 3927.71 0.417442 0.208721 0.977975i \(-0.433070\pi\)
0.208721 + 0.977975i \(0.433070\pi\)
\(98\) 8242.00i 0.858184i
\(99\) −725.113 + 2872.72i −0.0739836 + 0.293105i
\(100\) −10585.8 −1.05858
\(101\) 9292.23i 0.910914i −0.890258 0.455457i \(-0.849476\pi\)
0.890258 0.455457i \(-0.150524\pi\)
\(102\) −2537.02 + 20417.3i −0.243850 + 1.96245i
\(103\) −8180.42 −0.771083 −0.385542 0.922690i \(-0.625985\pi\)
−0.385542 + 0.922690i \(0.625985\pi\)
\(104\) 899.966i 0.0832069i
\(105\) 536.727 + 66.6926i 0.0486827 + 0.00604922i
\(106\) −30523.6 −2.71659
\(107\) 15960.5i 1.39406i 0.717044 + 0.697028i \(0.245495\pi\)
−0.717044 + 0.697028i \(0.754505\pi\)
\(108\) −4501.93 + 11577.0i −0.385968 + 0.992543i
\(109\) −8197.01 −0.689926 −0.344963 0.938616i \(-0.612109\pi\)
−0.344963 + 0.938616i \(0.612109\pi\)
\(110\) 406.290i 0.0335777i
\(111\) −1612.32 + 12975.6i −0.130859 + 1.05313i
\(112\) 7410.52 0.590762
\(113\) 9498.83i 0.743897i 0.928253 + 0.371949i \(0.121310\pi\)
−0.928253 + 0.371949i \(0.878690\pi\)
\(114\) 32930.6 + 4091.89i 2.53390 + 0.314858i
\(115\) −1296.24 −0.0980147
\(116\) 22639.3i 1.68247i
\(117\) −11833.2 2986.86i −0.864431 0.218194i
\(118\) −2604.91 −0.187080
\(119\) 12368.2i 0.873397i
\(120\) 12.8097 103.089i 0.000889561 0.00715898i
\(121\) 13303.0 0.908616
\(122\) 4151.80i 0.278944i
\(123\) −7332.20 911.085i −0.484646 0.0602211i
\(124\) −12733.8 −0.828160
\(125\) 2408.31i 0.154132i
\(126\) 3543.53 14038.6i 0.223200 0.884265i
\(127\) 14304.8 0.886896 0.443448 0.896300i \(-0.353755\pi\)
0.443448 + 0.896300i \(0.353755\pi\)
\(128\) 3051.76i 0.186264i
\(129\) 3286.08 26445.6i 0.197469 1.58918i
\(130\) 1673.57 0.0990281
\(131\) 5681.21i 0.331054i −0.986205 0.165527i \(-0.947068\pi\)
0.986205 0.165527i \(-0.0529324\pi\)
\(132\) −5566.52 691.685i −0.319474 0.0396973i
\(133\) −19948.3 −1.12772
\(134\) 43078.1i 2.39909i
\(135\) 1312.96 + 510.567i 0.0720415 + 0.0280146i
\(136\) −2375.56 −0.128436
\(137\) 2593.21i 0.138165i 0.997611 + 0.0690823i \(0.0220071\pi\)
−0.997611 + 0.0690823i \(0.977993\pi\)
\(138\) −4278.98 + 34436.2i −0.224689 + 1.80824i
\(139\) 17990.6 0.931141 0.465571 0.885011i \(-0.345849\pi\)
0.465571 + 0.885011i \(0.345849\pi\)
\(140\) 1023.97i 0.0522432i
\(141\) −8448.74 1049.82i −0.424965 0.0528054i
\(142\) 22352.3 1.10852
\(143\) 5511.24i 0.269512i
\(144\) 18714.8 + 4723.87i 0.902527 + 0.227810i
\(145\) −2567.53 −0.122118
\(146\) 48260.3i 2.26404i
\(147\) 1591.32 12806.6i 0.0736416 0.592650i
\(148\) −24754.8 −1.13015
\(149\) 31573.3i 1.42216i −0.703112 0.711079i \(-0.748207\pi\)
0.703112 0.711079i \(-0.251793\pi\)
\(150\) 31893.9 + 3963.07i 1.41751 + 0.176136i
\(151\) −37926.7 −1.66338 −0.831689 0.555241i \(-0.812626\pi\)
−0.831689 + 0.555241i \(0.812626\pi\)
\(152\) 3831.48i 0.165836i
\(153\) 7884.14 31235.1i 0.336800 1.33432i
\(154\) 6538.40 0.275696
\(155\) 1444.15i 0.0601101i
\(156\) 2849.16 22929.4i 0.117076 0.942201i
\(157\) −25795.6 −1.04652 −0.523258 0.852174i \(-0.675284\pi\)
−0.523258 + 0.852174i \(0.675284\pi\)
\(158\) 54705.2i 2.19136i
\(159\) 47428.3 + 5893.34i 1.87604 + 0.233113i
\(160\) −2831.52 −0.110606
\(161\) 20860.4i 0.804767i
\(162\) 17897.9 33194.8i 0.681981 1.26485i
\(163\) −20201.6 −0.760343 −0.380172 0.924916i \(-0.624135\pi\)
−0.380172 + 0.924916i \(0.624135\pi\)
\(164\) 13988.4i 0.520091i
\(165\) −78.4444 + 631.302i −0.00288134 + 0.0231883i
\(166\) −2488.09 −0.0902920
\(167\) 22630.0i 0.811432i 0.913999 + 0.405716i \(0.132978\pi\)
−0.913999 + 0.405716i \(0.867022\pi\)
\(168\) 1659.01 + 206.145i 0.0587801 + 0.00730389i
\(169\) −5859.30 −0.205151
\(170\) 4417.59i 0.152858i
\(171\) −50378.2 12716.1i −1.72286 0.434874i
\(172\) 50453.0 1.70541
\(173\) 16695.6i 0.557839i −0.960314 0.278920i \(-0.910024\pi\)
0.960314 0.278920i \(-0.0899763\pi\)
\(174\) −8475.56 + 68209.4i −0.279943 + 2.25292i
\(175\) −19320.3 −0.630867
\(176\) 8716.31i 0.281389i
\(177\) 4047.56 + 502.942i 0.129195 + 0.0160536i
\(178\) 39613.7 1.25028
\(179\) 22555.9i 0.703970i 0.936006 + 0.351985i \(0.114493\pi\)
−0.936006 + 0.351985i \(0.885507\pi\)
\(180\) −652.732 + 2585.96i −0.0201460 + 0.0798137i
\(181\) −27550.6 −0.840958 −0.420479 0.907302i \(-0.638138\pi\)
−0.420479 + 0.907302i \(0.638138\pi\)
\(182\) 26932.7i 0.813087i
\(183\) −801.607 + 6451.15i −0.0239364 + 0.192635i
\(184\) −4006.66 −0.118344
\(185\) 2807.45i 0.0820293i
\(186\) 38365.4 + 4767.21i 1.10895 + 0.137796i
\(187\) 14547.5 0.416013
\(188\) 16118.5i 0.456046i
\(189\) −8216.51 + 21129.3i −0.230019 + 0.591509i
\(190\) 7125.02 0.197369
\(191\) 35316.8i 0.968089i 0.875043 + 0.484044i \(0.160833\pi\)
−0.875043 + 0.484044i \(0.839167\pi\)
\(192\) −5115.73 + 41170.2i −0.138773 + 1.11681i
\(193\) 47333.5 1.27073 0.635366 0.772211i \(-0.280849\pi\)
0.635366 + 0.772211i \(0.280849\pi\)
\(194\) 22576.4i 0.599861i
\(195\) −2600.43 323.125i −0.0683875 0.00849770i
\(196\) 24432.4 0.635995
\(197\) 11513.5i 0.296671i −0.988937 0.148335i \(-0.952609\pi\)
0.988937 0.148335i \(-0.0473915\pi\)
\(198\) 16512.3 + 4167.93i 0.421189 + 0.106314i
\(199\) 61848.9 1.56180 0.780901 0.624655i \(-0.214760\pi\)
0.780901 + 0.624655i \(0.214760\pi\)
\(200\) 3710.86i 0.0927714i
\(201\) −8317.28 + 66935.6i −0.205868 + 1.65678i
\(202\) −53411.5 −1.30898
\(203\) 41319.1i 1.00267i
\(204\) 60524.7 + 7520.68i 1.45436 + 0.180716i
\(205\) −1586.43 −0.0377496
\(206\) 47020.8i 1.10804i
\(207\) 13297.5 52681.5i 0.310335 1.22947i
\(208\) −35903.9 −0.829879
\(209\) 23463.4i 0.537153i
\(210\) 383.347 3085.09i 0.00869268 0.0699567i
\(211\) −15185.7 −0.341090 −0.170545 0.985350i \(-0.554553\pi\)
−0.170545 + 0.985350i \(0.554553\pi\)
\(212\) 90483.6i 2.01325i
\(213\) −34731.5 4315.66i −0.765533 0.0951236i
\(214\) 91740.7 2.00325
\(215\) 5721.89i 0.123784i
\(216\) 4058.31 + 1578.15i 0.0869837 + 0.0338252i
\(217\) −23240.5 −0.493545
\(218\) 47116.2i 0.991419i
\(219\) 9317.85 74987.9i 0.194280 1.56352i
\(220\) −1204.40 −0.0248843
\(221\) 59923.7i 1.22691i
\(222\) 74583.2 + 9267.56i 1.51333 + 0.188044i
\(223\) 4578.23 0.0920636 0.0460318 0.998940i \(-0.485342\pi\)
0.0460318 + 0.998940i \(0.485342\pi\)
\(224\) 45567.5i 0.908153i
\(225\) −48792.2 12315.8i −0.963796 0.243275i
\(226\) 54599.0 1.06898
\(227\) 37276.5i 0.723407i 0.932293 + 0.361704i \(0.117805\pi\)
−0.932293 + 0.361704i \(0.882195\pi\)
\(228\) 12129.9 97618.8i 0.233340 1.87786i
\(229\) 15778.0 0.300871 0.150435 0.988620i \(-0.451932\pi\)
0.150435 + 0.988620i \(0.451932\pi\)
\(230\) 7450.78i 0.140846i
\(231\) −10159.5 1262.40i −0.190392 0.0236577i
\(232\) −7936.17 −0.147447
\(233\) 48712.1i 0.897275i −0.893714 0.448637i \(-0.851910\pi\)
0.893714 0.448637i \(-0.148090\pi\)
\(234\) −17168.4 + 68016.9i −0.313543 + 1.24218i
\(235\) −1828.01 −0.0331011
\(236\) 7721.94i 0.138644i
\(237\) −10562.2 + 85002.1i −0.188043 + 1.51333i
\(238\) −71091.9 −1.25507
\(239\) 84845.2i 1.48536i 0.669647 + 0.742679i \(0.266445\pi\)
−0.669647 + 0.742679i \(0.733555\pi\)
\(240\) 4112.72 + 511.039i 0.0714014 + 0.00887220i
\(241\) −53883.0 −0.927722 −0.463861 0.885908i \(-0.653536\pi\)
−0.463861 + 0.885908i \(0.653536\pi\)
\(242\) 76465.5i 1.30567i
\(243\) −34219.2 + 48123.1i −0.579506 + 0.814968i
\(244\) −12307.5 −0.206724
\(245\) 2770.89i 0.0461623i
\(246\) −5236.89 + 42145.3i −0.0865373 + 0.696432i
\(247\) 96649.4 1.58418
\(248\) 4463.82i 0.0725777i
\(249\) 3866.04 + 480.386i 0.0623545 + 0.00774804i
\(250\) 13842.9 0.221486
\(251\) 77001.2i 1.22222i −0.791545 0.611111i \(-0.790723\pi\)
0.791545 0.611111i \(-0.209277\pi\)
\(252\) −41615.7 10504.4i −0.655324 0.165413i
\(253\) 24536.1 0.383323
\(254\) 82223.3i 1.27446i
\(255\) 852.925 6864.14i 0.0131169 0.105562i
\(256\) 56213.0 0.857742
\(257\) 33402.0i 0.505716i −0.967503 0.252858i \(-0.918630\pi\)
0.967503 0.252858i \(-0.0813705\pi\)
\(258\) −152009. 18888.3i −2.28365 0.283761i
\(259\) −45180.1 −0.673516
\(260\) 4961.11i 0.0733892i
\(261\) 26339.0 104349.i 0.386650 1.53181i
\(262\) −32655.4 −0.475721
\(263\) 86858.5i 1.25574i 0.778317 + 0.627871i \(0.216074\pi\)
−0.778317 + 0.627871i \(0.783926\pi\)
\(264\) −242.470 + 1951.34i −0.00347896 + 0.0279979i
\(265\) 10261.8 0.146127
\(266\) 114662.i 1.62053i
\(267\) −61552.6 7648.41i −0.863424 0.107287i
\(268\) −127700. −1.77795
\(269\) 89268.9i 1.23366i −0.787096 0.616830i \(-0.788417\pi\)
0.787096 0.616830i \(-0.211583\pi\)
\(270\) 2934.72 7546.83i 0.0402568 0.103523i
\(271\) 113447. 1.54474 0.772371 0.635172i \(-0.219071\pi\)
0.772371 + 0.635172i \(0.219071\pi\)
\(272\) 94772.4i 1.28098i
\(273\) 5200.02 41848.6i 0.0697718 0.561508i
\(274\) 14905.7 0.198542
\(275\) 22724.7i 0.300492i
\(276\) 102082. + 12684.5i 1.34008 + 0.166516i
\(277\) −57909.5 −0.754727 −0.377364 0.926065i \(-0.623169\pi\)
−0.377364 + 0.926065i \(0.623169\pi\)
\(278\) 103409.i 1.33804i
\(279\) −58692.5 14814.8i −0.754005 0.190321i
\(280\) 358.951 0.00457845
\(281\) 16277.6i 0.206147i −0.994674 0.103073i \(-0.967132\pi\)
0.994674 0.103073i \(-0.0328677\pi\)
\(282\) −6034.35 + 48563.1i −0.0758809 + 0.610672i
\(283\) 118418. 1.47858 0.739289 0.673388i \(-0.235162\pi\)
0.739289 + 0.673388i \(0.235162\pi\)
\(284\) 66260.7i 0.821522i
\(285\) −11071.0 1375.66i −0.136300 0.0169364i
\(286\) −31678.5 −0.387286
\(287\) 25530.3i 0.309950i
\(288\) 29047.2 115078.i 0.350202 1.38742i
\(289\) −74654.3 −0.893839
\(290\) 14758.1i 0.175483i
\(291\) −4358.92 + 35079.6i −0.0514746 + 0.414256i
\(292\) 143062. 1.67787
\(293\) 146916.i 1.71133i 0.517531 + 0.855665i \(0.326851\pi\)
−0.517531 + 0.855665i \(0.673149\pi\)
\(294\) −73611.9 9146.87i −0.851634 0.105822i
\(295\) 875.749 0.0100632
\(296\) 8677.76i 0.0990431i
\(297\) −24852.4 9664.32i −0.281745 0.109562i
\(298\) −181483. −2.04363
\(299\) 101068.i 1.13050i
\(300\) 11748.0 94545.5i 0.130534 1.05051i
\(301\) 92082.0 1.01635
\(302\) 218002.i 2.39026i
\(303\) 82991.8 + 10312.4i 0.903962 + 0.112325i
\(304\) −152856. −1.65400
\(305\) 1395.80i 0.0150046i
\(306\) −179538. 45317.8i −1.91741 0.483979i
\(307\) 7617.24 0.0808204 0.0404102 0.999183i \(-0.487134\pi\)
0.0404102 + 0.999183i \(0.487134\pi\)
\(308\) 19382.3i 0.204317i
\(309\) 9078.53 73061.9i 0.0950821 0.765198i
\(310\) 8300.91 0.0863778
\(311\) 77684.8i 0.803184i −0.915819 0.401592i \(-0.868457\pi\)
0.915819 0.401592i \(-0.131543\pi\)
\(312\) −8037.88 998.771i −0.0825719 0.0102602i
\(313\) −4590.34 −0.0468551 −0.0234275 0.999726i \(-0.507458\pi\)
−0.0234275 + 0.999726i \(0.507458\pi\)
\(314\) 148272.i 1.50384i
\(315\) −1191.31 + 4719.66i −0.0120061 + 0.0475652i
\(316\) −162167. −1.62401
\(317\) 12717.0i 0.126551i 0.997996 + 0.0632757i \(0.0201548\pi\)
−0.997996 + 0.0632757i \(0.979845\pi\)
\(318\) 33874.8 272616.i 0.334982 2.69586i
\(319\) 48599.8 0.477588
\(320\) 8907.78i 0.0869900i
\(321\) −142549. 17712.8i −1.38342 0.171901i
\(322\) −119905. −1.15644
\(323\) 255117.i 2.44531i
\(324\) −98401.8 53056.2i −0.937375 0.505413i
\(325\) 93606.6 0.886217
\(326\) 116118.i 1.09261i
\(327\) 9096.94 73210.1i 0.0850746 0.684661i
\(328\) −4903.61 −0.0455794
\(329\) 29418.0i 0.271782i
\(330\) 3628.71 + 450.896i 0.0333214 + 0.00414046i
\(331\) −84728.0 −0.773341 −0.386671 0.922218i \(-0.626375\pi\)
−0.386671 + 0.922218i \(0.626375\pi\)
\(332\) 7375.63i 0.0669149i
\(333\) −114100. 28800.2i −1.02895 0.259721i
\(334\) 130077. 1.16602
\(335\) 14482.5i 0.129049i
\(336\) −8224.10 + 66185.7i −0.0728467 + 0.586254i
\(337\) 18359.9 0.161663 0.0808317 0.996728i \(-0.474242\pi\)
0.0808317 + 0.996728i \(0.474242\pi\)
\(338\) 33679.1i 0.294800i
\(339\) −84837.0 10541.7i −0.738220 0.0917298i
\(340\) 13095.4 0.113282
\(341\) 27335.7i 0.235083i
\(342\) −73092.0 + 289573.i −0.624910 + 2.47574i
\(343\) 119259. 1.01368
\(344\) 17686.2i 0.149458i
\(345\) 1438.56 11577.2i 0.0120862 0.0972667i
\(346\) −95965.6 −0.801611
\(347\) 68522.1i 0.569078i 0.958665 + 0.284539i \(0.0918405\pi\)
−0.958665 + 0.284539i \(0.908160\pi\)
\(348\) 202198. + 25124.8i 1.66963 + 0.207464i
\(349\) 9503.69 0.0780264 0.0390132 0.999239i \(-0.487579\pi\)
0.0390132 + 0.999239i \(0.487579\pi\)
\(350\) 111052.i 0.906551i
\(351\) 39808.9 102371.i 0.323121 0.830928i
\(352\) 53596.8 0.432567
\(353\) 157953.i 1.26759i −0.773501 0.633795i \(-0.781496\pi\)
0.773501 0.633795i \(-0.218504\pi\)
\(354\) 2890.90 23265.3i 0.0230688 0.185653i
\(355\) −7514.65 −0.0596283
\(356\) 117430.i 0.926573i
\(357\) 110464. + 13726.1i 0.866732 + 0.107698i
\(358\) 129651. 1.01160
\(359\) 43690.8i 0.339001i −0.985530 0.169500i \(-0.945785\pi\)
0.985530 0.169500i \(-0.0542154\pi\)
\(360\) 906.507 + 228.814i 0.00699465 + 0.00176554i
\(361\) 281151. 2.15737
\(362\) 158360.i 1.20845i
\(363\) −14763.6 + 118814.i −0.112041 + 0.901682i
\(364\) 79838.7 0.602575
\(365\) 16224.7i 0.121784i
\(366\) 37081.0 + 4607.61i 0.276815 + 0.0343965i
\(367\) −209462. −1.55515 −0.777576 0.628789i \(-0.783551\pi\)
−0.777576 + 0.628789i \(0.783551\pi\)
\(368\) 159845.i 1.18033i
\(369\) 16274.4 64475.1i 0.119523 0.473521i
\(370\) 16137.2 0.117875
\(371\) 165142.i 1.19980i
\(372\) 14131.8 113729.i 0.102120 0.821840i
\(373\) 12200.0 0.0876886 0.0438443 0.999038i \(-0.486039\pi\)
0.0438443 + 0.999038i \(0.486039\pi\)
\(374\) 83618.9i 0.597807i
\(375\) −21509.4 2672.71i −0.152955 0.0190059i
\(376\) −5650.32 −0.0399666
\(377\) 200190.i 1.40851i
\(378\) 121451. + 47228.2i 0.849994 + 0.330536i
\(379\) 58846.1 0.409675 0.204838 0.978796i \(-0.434333\pi\)
0.204838 + 0.978796i \(0.434333\pi\)
\(380\) 21121.3i 0.146269i
\(381\) −15875.2 + 127760.i −0.109363 + 0.880128i
\(382\) 203000. 1.39114
\(383\) 96149.7i 0.655466i 0.944770 + 0.327733i \(0.106285\pi\)
−0.944770 + 0.327733i \(0.893715\pi\)
\(384\) 27256.2 + 3386.80i 0.184843 + 0.0229682i
\(385\) −2198.15 −0.0148299
\(386\) 272072.i 1.82603i
\(387\) 232547. + 58698.0i 1.55271 + 0.391924i
\(388\) −66924.9 −0.444554
\(389\) 189303.i 1.25100i 0.780222 + 0.625502i \(0.215106\pi\)
−0.780222 + 0.625502i \(0.784894\pi\)
\(390\) −1857.31 + 14947.2i −0.0122111 + 0.0982723i
\(391\) −266781. −1.74502
\(392\) 8564.75i 0.0557369i
\(393\) 50740.7 + 6304.94i 0.328527 + 0.0408221i
\(394\) −66179.2 −0.426313
\(395\) 18391.4i 0.117875i
\(396\) 12355.3 48948.7i 0.0787886 0.312141i
\(397\) −14667.4 −0.0930619 −0.0465310 0.998917i \(-0.514817\pi\)
−0.0465310 + 0.998917i \(0.514817\pi\)
\(398\) 355506.i 2.24430i
\(399\) 22138.4 178165.i 0.139059 1.11912i
\(400\) −148044. −0.925273
\(401\) 83639.3i 0.520142i 0.965590 + 0.260071i \(0.0837459\pi\)
−0.965590 + 0.260071i \(0.916254\pi\)
\(402\) 384744. + 47807.5i 2.38078 + 0.295831i
\(403\) 112600. 0.693312
\(404\) 158332.i 0.970075i
\(405\) −6017.13 + 11159.8i −0.0366842 + 0.0680372i
\(406\) −237501. −1.44083
\(407\) 53141.2i 0.320806i
\(408\) 2636.37 21216.9i 0.0158375 0.127456i
\(409\) −87346.8 −0.522156 −0.261078 0.965318i \(-0.584078\pi\)
−0.261078 + 0.965318i \(0.584078\pi\)
\(410\) 9118.75i 0.0542460i
\(411\) −23160.8 2877.92i −0.137110 0.0170370i
\(412\) 139388. 0.821163
\(413\) 14093.4i 0.0826255i
\(414\) −302812. 76433.8i −1.76674 0.445948i
\(415\) 836.474 0.00485687
\(416\) 220774.i 1.27574i
\(417\) −19965.7 + 160679.i −0.114819 + 0.924035i
\(418\) −134867. −0.771885
\(419\) 252031.i 1.43558i −0.696261 0.717789i \(-0.745154\pi\)
0.696261 0.717789i \(-0.254846\pi\)
\(420\) −9145.37 1136.39i −0.0518445 0.00644210i
\(421\) 61654.8 0.347859 0.173929 0.984758i \(-0.444354\pi\)
0.173929 + 0.984758i \(0.444354\pi\)
\(422\) 87286.7i 0.490143i
\(423\) 18752.6 74293.2i 0.104805 0.415211i
\(424\) 31718.9 0.176436
\(425\) 247085.i 1.36795i
\(426\) −24806.3 + 199635.i −0.136692 + 1.10006i
\(427\) −22462.5 −0.123198
\(428\) 271954.i 1.48460i
\(429\) 49222.6 + 6116.31i 0.267455 + 0.0332334i
\(430\) −32889.3 −0.177876
\(431\) 278438.i 1.49890i −0.662059 0.749452i \(-0.730317\pi\)
0.662059 0.749452i \(-0.269683\pi\)
\(432\) −62959.8 + 161905.i −0.337362 + 0.867548i
\(433\) −208094. −1.10990 −0.554949 0.831884i \(-0.687262\pi\)
−0.554949 + 0.831884i \(0.687262\pi\)
\(434\) 133586.i 0.709220i
\(435\) 2849.41 22931.4i 0.0150583 0.121186i
\(436\) 139670. 0.734735
\(437\) 430284.i 2.25316i
\(438\) −431028. 53558.7i −2.24676 0.279178i
\(439\) 110262. 0.572132 0.286066 0.958210i \(-0.407652\pi\)
0.286066 + 0.958210i \(0.407652\pi\)
\(440\) 422.200i 0.00218079i
\(441\) 112614. + 28425.2i 0.579047 + 0.146159i
\(442\) 344440. 1.76307
\(443\) 240587.i 1.22593i −0.790112 0.612963i \(-0.789977\pi\)
0.790112 0.612963i \(-0.210023\pi\)
\(444\) 27472.6 221093.i 0.139358 1.12152i
\(445\) −13317.8 −0.0672532
\(446\) 26315.5i 0.132295i
\(447\) 281991. + 35039.7i 1.41130 + 0.175366i
\(448\) −143352. −0.714247
\(449\) 300308.i 1.48962i −0.667279 0.744808i \(-0.732541\pi\)
0.667279 0.744808i \(-0.267459\pi\)
\(450\) −70790.9 + 280456.i −0.349584 + 1.38497i
\(451\) 30028.9 0.147634
\(452\) 161852.i 0.792212i
\(453\) 42090.6 338735.i 0.205111 1.65068i
\(454\) 214264. 1.03953
\(455\) 9054.55i 0.0437365i
\(456\) −34220.2 4252.13i −0.164571 0.0204492i
\(457\) −196362. −0.940213 −0.470106 0.882610i \(-0.655784\pi\)
−0.470106 + 0.882610i \(0.655784\pi\)
\(458\) 90691.3i 0.432349i
\(459\) 270220. + 105080.i 1.28260 + 0.498764i
\(460\) 22086.9 0.104381
\(461\) 236979.i 1.11509i −0.830148 0.557544i \(-0.811744\pi\)
0.830148 0.557544i \(-0.188256\pi\)
\(462\) −7256.23 + 58396.5i −0.0339960 + 0.273592i
\(463\) 91894.9 0.428676 0.214338 0.976760i \(-0.431241\pi\)
0.214338 + 0.976760i \(0.431241\pi\)
\(464\) 316611.i 1.47059i
\(465\) −12898.1 1602.69i −0.0596514 0.00741216i
\(466\) −279996. −1.28938
\(467\) 153481.i 0.703754i 0.936046 + 0.351877i \(0.114456\pi\)
−0.936046 + 0.351877i \(0.885544\pi\)
\(468\) 201628. + 50893.5i 0.920574 + 0.232365i
\(469\) −233065. −1.05958
\(470\) 10507.3i 0.0475660i
\(471\) 28627.6 230388.i 0.129046 1.03853i
\(472\) 2706.92 0.0121504
\(473\) 108308.i 0.484102i
\(474\) 488589. + 60711.2i 2.17464 + 0.270216i
\(475\) 398518. 1.76628
\(476\) 210743.i 0.930122i
\(477\) −105271. + 417056.i −0.462669 + 1.83298i
\(478\) 487688. 2.13445
\(479\) 89639.7i 0.390688i −0.980735 0.195344i \(-0.937418\pi\)
0.980735 0.195344i \(-0.0625823\pi\)
\(480\) 3142.39 25289.2i 0.0136388 0.109762i
\(481\) 218897. 0.946128
\(482\) 309718.i 1.33313i
\(483\) 186310. + 23150.6i 0.798625 + 0.0992356i
\(484\) −226673. −0.967628
\(485\) 7589.98i 0.0322669i
\(486\) 276610. + 196691.i 1.17110 + 0.832745i
\(487\) 44486.3 0.187572 0.0937861 0.995592i \(-0.470103\pi\)
0.0937861 + 0.995592i \(0.470103\pi\)
\(488\) 4314.38i 0.0181167i
\(489\) 22419.4 180427.i 0.0937578 0.754541i
\(490\) −15927.0 −0.0663348
\(491\) 404358.i 1.67727i −0.544695 0.838635i \(-0.683354\pi\)
0.544695 0.838635i \(-0.316646\pi\)
\(492\) 124935. + 15524.1i 0.516122 + 0.0641323i
\(493\) −528425. −2.17415
\(494\) 555538.i 2.27646i
\(495\) −5551.30 1401.22i −0.0226561 0.00571869i
\(496\) −178083. −0.723867
\(497\) 120933.i 0.489588i
\(498\) 2761.25 22221.9i 0.0111339 0.0896029i
\(499\) 187410. 0.752648 0.376324 0.926488i \(-0.377188\pi\)
0.376324 + 0.926488i \(0.377188\pi\)
\(500\) 41035.6i 0.164142i
\(501\) −202116. 25114.5i −0.805240 0.100058i
\(502\) −442601. −1.75632
\(503\) 203611.i 0.804760i 0.915473 + 0.402380i \(0.131817\pi\)
−0.915473 + 0.402380i \(0.868183\pi\)
\(504\) −3682.29 + 14588.3i −0.0144963 + 0.0574308i
\(505\) 17956.5 0.0704107
\(506\) 141033.i 0.550832i
\(507\) 6502.58 52331.3i 0.0252971 0.203585i
\(508\) −243741. −0.944498
\(509\) 95695.5i 0.369365i −0.982798 0.184682i \(-0.940874\pi\)
0.982798 0.184682i \(-0.0591257\pi\)
\(510\) −39454.9 4902.59i −0.151691 0.0188488i
\(511\) 261103. 0.999932
\(512\) 371939.i 1.41883i
\(513\) 169481. 435832.i 0.644001 1.65609i
\(514\) −191994. −0.726710
\(515\) 15808.0i 0.0596022i
\(516\) −55992.1 + 450611.i −0.210294 + 1.69240i
\(517\) 34601.7 0.129454
\(518\) 259694.i 0.967837i
\(519\) 149113. + 18528.5i 0.553582 + 0.0687870i
\(520\) −1739.11 −0.00643163
\(521\) 431600.i 1.59003i 0.606589 + 0.795016i \(0.292537\pi\)
−0.606589 + 0.795016i \(0.707463\pi\)
\(522\) −599793. 151396.i −2.20120 0.555613i
\(523\) 507455. 1.85522 0.927608 0.373555i \(-0.121861\pi\)
0.927608 + 0.373555i \(0.121861\pi\)
\(524\) 96803.0i 0.352555i
\(525\) 21441.4 172556.i 0.0777920 0.626052i
\(526\) 499260. 1.80449
\(527\) 297221.i 1.07018i
\(528\) −77848.1 9673.26i −0.279242 0.0346980i
\(529\) −170116. −0.607903
\(530\) 58984.5i 0.209984i
\(531\) −8983.87 + 35591.9i −0.0318621 + 0.126230i
\(532\) 339903. 1.20097
\(533\) 123694.i 0.435406i
\(534\) −43962.8 + 353803.i −0.154171 + 1.24073i
\(535\) −30842.5 −0.107756
\(536\) 44765.0i 0.155815i
\(537\) −201454. 25032.2i −0.698597 0.0868063i
\(538\) −513115. −1.77276
\(539\) 52449.1i 0.180535i
\(540\) −22371.7 8699.62i −0.0767204 0.0298341i
\(541\) 113361. 0.387320 0.193660 0.981069i \(-0.437964\pi\)
0.193660 + 0.981069i \(0.437964\pi\)
\(542\) 652092.i 2.21978i
\(543\) 30575.3 246063.i 0.103698 0.834540i
\(544\) −582758. −1.96920
\(545\) 15840.1i 0.0533291i
\(546\) −240544. 29889.6i −0.806882 0.100262i
\(547\) −91662.3 −0.306349 −0.153174 0.988199i \(-0.548950\pi\)
−0.153174 + 0.988199i \(0.548950\pi\)
\(548\) 44186.2i 0.147138i
\(549\) −56727.6 14318.8i −0.188213 0.0475075i
\(550\) −130621. −0.431804
\(551\) 852284.i 2.80725i
\(552\) 4446.54 35784.7i 0.0145930 0.117441i
\(553\) −295972. −0.967833
\(554\) 332862.i 1.08454i
\(555\) −25074.2 3115.68i −0.0814033 0.0101150i
\(556\) −306544. −0.991616
\(557\) 145180.i 0.467946i −0.972243 0.233973i \(-0.924827\pi\)
0.972243 0.233973i \(-0.0751727\pi\)
\(558\) −85154.8 + 337363.i −0.273490 + 1.08350i
\(559\) −446136. −1.42772
\(560\) 14320.2i 0.0456640i
\(561\) −16144.7 + 129929.i −0.0512984 + 0.412838i
\(562\) −93563.0 −0.296232
\(563\) 458837.i 1.44758i −0.690023 0.723788i \(-0.742400\pi\)
0.690023 0.723788i \(-0.257600\pi\)
\(564\) 143959. + 17888.1i 0.452566 + 0.0562349i
\(565\) −18355.7 −0.0575009
\(566\) 680663.i 2.12471i
\(567\) −179594. 96833.2i −0.558631 0.301202i
\(568\) −23227.6 −0.0719959
\(569\) 165151.i 0.510101i −0.966928 0.255050i \(-0.917908\pi\)
0.966928 0.255050i \(-0.0820921\pi\)
\(570\) −7907.26 + 63635.8i −0.0243375 + 0.195863i
\(571\) 407820. 1.25082 0.625411 0.780295i \(-0.284931\pi\)
0.625411 + 0.780295i \(0.284931\pi\)
\(572\) 93907.0i 0.287016i
\(573\) −315426. 39194.2i −0.960700 0.119375i
\(574\) −146747. −0.445396
\(575\) 416738.i 1.26045i
\(576\) −362027. 91380.4i −1.09118 0.275428i
\(577\) −364230. −1.09402 −0.547008 0.837127i \(-0.684233\pi\)
−0.547008 + 0.837127i \(0.684233\pi\)
\(578\) 429111.i 1.28444i
\(579\) −52530.2 + 422751.i −0.156694 + 1.26104i
\(580\) 43748.6 0.130049
\(581\) 13461.3i 0.0398781i
\(582\) 201637. + 25055.0i 0.595283 + 0.0739687i
\(583\) −194242. −0.571485
\(584\) 50150.2i 0.147044i
\(585\) 5771.86 22866.7i 0.0168657 0.0668177i
\(586\) 844468. 2.45917
\(587\) 467751.i 1.35750i −0.734371 0.678749i \(-0.762523\pi\)
0.734371 0.678749i \(-0.237477\pi\)
\(588\) −27114.8 + 218213.i −0.0784244 + 0.631142i
\(589\) 479380. 1.38181
\(590\) 5033.78i 0.0144607i
\(591\) 102831. + 12777.5i 0.294406 + 0.0365824i
\(592\) −346197. −0.987825
\(593\) 8445.16i 0.0240159i −0.999928 0.0120079i \(-0.996178\pi\)
0.999928 0.0120079i \(-0.00382234\pi\)
\(594\) −55550.2 + 142851.i −0.157439 + 0.404865i
\(595\) 23900.5 0.0675108
\(596\) 537983.i 1.51452i
\(597\) −68639.2 + 552392.i −0.192585 + 1.54988i
\(598\) 580937. 1.62453
\(599\) 618699.i 1.72435i −0.506609 0.862176i \(-0.669101\pi\)
0.506609 0.862176i \(-0.330899\pi\)
\(600\) −33142.8 4118.26i −0.0920634 0.0114396i
\(601\) −585473. −1.62091 −0.810453 0.585804i \(-0.800779\pi\)
−0.810453 + 0.585804i \(0.800779\pi\)
\(602\) 529285.i 1.46048i
\(603\) −588592. 148569.i −1.61875 0.408594i
\(604\) 646239. 1.77141
\(605\) 25707.1i 0.0702331i
\(606\) 59275.4 477035.i 0.161410 1.29899i
\(607\) 262153. 0.711504 0.355752 0.934580i \(-0.384225\pi\)
0.355752 + 0.934580i \(0.384225\pi\)
\(608\) 939915.i 2.54262i
\(609\) 369034. + 45855.4i 0.995019 + 0.123639i
\(610\) 8023.01 0.0215614
\(611\) 142530.i 0.381789i
\(612\) −134339. + 532219.i −0.358674 + 1.42098i
\(613\) −654490. −1.74174 −0.870868 0.491517i \(-0.836442\pi\)
−0.870868 + 0.491517i \(0.836442\pi\)
\(614\) 43783.7i 0.116138i
\(615\) 1760.60 14168.9i 0.00465490 0.0374616i
\(616\) −6794.44 −0.0179057
\(617\) 370184.i 0.972406i 0.873846 + 0.486203i \(0.161618\pi\)
−0.873846 + 0.486203i \(0.838382\pi\)
\(618\) −419958. 52183.1i −1.09958 0.136632i
\(619\) 215394. 0.562150 0.281075 0.959686i \(-0.409309\pi\)
0.281075 + 0.959686i \(0.409309\pi\)
\(620\) 24607.0i 0.0640141i
\(621\) 455758. + 177230.i 1.18182 + 0.459572i
\(622\) −446530. −1.15417
\(623\) 214322.i 0.552194i
\(624\) 39845.7 320669.i 0.102332 0.823546i
\(625\) 383637. 0.982111
\(626\) 26385.2i 0.0673304i
\(627\) 209559. + 26039.4i 0.533054 + 0.0662362i
\(628\) 439535. 1.11448
\(629\) 577804.i 1.46042i
\(630\) 27128.5 + 6847.59i 0.0683509 + 0.0172527i
\(631\) −547165. −1.37423 −0.687116 0.726548i \(-0.741123\pi\)
−0.687116 + 0.726548i \(0.741123\pi\)
\(632\) 56847.5i 0.142324i
\(633\) 16852.8 135628.i 0.0420597 0.338487i
\(634\) 73097.1 0.181853
\(635\) 27642.8i 0.0685542i
\(636\) −808138. 100418.i −1.99789 0.248254i
\(637\) −216046. −0.532437
\(638\) 279350.i 0.686290i
\(639\) 77089.1 305408.i 0.188795 0.747961i
\(640\) 5897.27 0.0143976
\(641\) 169274.i 0.411978i −0.978554 0.205989i \(-0.933959\pi\)
0.978554 0.205989i \(-0.0660410\pi\)
\(642\) −101813. + 819365.i −0.247020 + 1.98796i
\(643\) −169103. −0.409006 −0.204503 0.978866i \(-0.565558\pi\)
−0.204503 + 0.978866i \(0.565558\pi\)
\(644\) 355443.i 0.857035i
\(645\) 51104.0 + 6350.09i 0.122839 + 0.0152637i
\(646\) 1.46641e6 3.51390
\(647\) 75215.6i 0.179680i −0.995956 0.0898399i \(-0.971364\pi\)
0.995956 0.0898399i \(-0.0286355\pi\)
\(648\) −18598.8 + 34494.7i −0.0442930 + 0.0821489i
\(649\) −16576.7 −0.0393558
\(650\) 538048.i 1.27349i
\(651\) 25792.0 207568.i 0.0608589 0.489778i
\(652\) 344218. 0.809726
\(653\) 221333.i 0.519062i 0.965735 + 0.259531i \(0.0835679\pi\)
−0.965735 + 0.259531i \(0.916432\pi\)
\(654\) −420809. 52289.0i −0.983853 0.122252i
\(655\) 10978.5 0.0255894
\(656\) 195628.i 0.454594i
\(657\) 659400. + 166441.i 1.52763 + 0.385594i
\(658\) −169094. −0.390549
\(659\) 514765.i 1.18533i −0.805450 0.592664i \(-0.798076\pi\)
0.805450 0.592664i \(-0.201924\pi\)
\(660\) 1336.63 10756.9i 0.00306847 0.0246943i
\(661\) 483903. 1.10753 0.553765 0.832673i \(-0.313191\pi\)
0.553765 + 0.832673i \(0.313191\pi\)
\(662\) 487014.i 1.11129i
\(663\) −535197. 66502.6i −1.21755 0.151290i
\(664\) 2585.52 0.00586424
\(665\) 38548.5i 0.0871695i
\(666\) −165543. + 655841.i −0.373218 + 1.47860i
\(667\) −891250. −2.00331
\(668\) 385597.i 0.864133i
\(669\) −5080.86 + 40889.6i −0.0113523 + 0.0913610i
\(670\) 83244.9 0.185442
\(671\) 26420.6i 0.0586809i
\(672\) 406977. + 50570.2i 0.901222 + 0.111984i
\(673\) −321389. −0.709580 −0.354790 0.934946i \(-0.615448\pi\)
−0.354790 + 0.934946i \(0.615448\pi\)
\(674\) 105532.i 0.232309i
\(675\) 164145. 422110.i 0.360264 0.926443i
\(676\) 99837.6 0.218475
\(677\) 13310.7i 0.0290418i 0.999895 + 0.0145209i \(0.00462231\pi\)
−0.999895 + 0.0145209i \(0.995378\pi\)
\(678\) −60593.3 + 487641.i −0.131815 + 1.06082i
\(679\) −122145. −0.264933
\(680\) 4590.58i 0.00992773i
\(681\) −332928. 41369.0i −0.717886 0.0892032i
\(682\) −157125. −0.337813
\(683\) 106249.i 0.227763i −0.993494 0.113881i \(-0.963672\pi\)
0.993494 0.113881i \(-0.0363284\pi\)
\(684\) 858403. + 216672.i 1.83476 + 0.463118i
\(685\) −5011.18 −0.0106797
\(686\) 685495.i 1.45665i
\(687\) −17510.2 + 140918.i −0.0371003 + 0.298575i
\(688\) 705587. 1.49064
\(689\) 800112.i 1.68544i
\(690\) −66545.2 8268.78i −0.139772 0.0173677i
\(691\) 239444. 0.501473 0.250737 0.968055i \(-0.419327\pi\)
0.250737 + 0.968055i \(0.419327\pi\)
\(692\) 284478.i 0.594070i
\(693\) 22549.8 89336.7i 0.0469543 0.186022i
\(694\) 393863. 0.817760
\(695\) 34765.3i 0.0719742i
\(696\) 8807.46 70880.4i 0.0181816 0.146321i
\(697\) −326504. −0.672083
\(698\) 54627.0i 0.112123i
\(699\) 435063. + 54060.1i 0.890427 + 0.110643i
\(700\) 329202. 0.671840
\(701\) 292642.i 0.595526i −0.954640 0.297763i \(-0.903760\pi\)
0.954640 0.297763i \(-0.0962404\pi\)
\(702\) −588427. 228820.i −1.19404 0.464323i
\(703\) 931925. 1.88569
\(704\) 168612.i 0.340207i
\(705\) 2028.70 16326.5i 0.00408168 0.0328485i
\(706\) −907910. −1.82152
\(707\) 288972.i 0.578119i
\(708\) −68967.0 8569.71i −0.137586 0.0170962i
\(709\) 116194. 0.231148 0.115574 0.993299i \(-0.463129\pi\)
0.115574 + 0.993299i \(0.463129\pi\)
\(710\) 43194.0i 0.0856854i
\(711\) −747458. 188669.i −1.47859 0.373216i
\(712\) −41165.0 −0.0812023
\(713\) 501297.i 0.986089i
\(714\) 78896.9 634944.i 0.154762 1.24549i
\(715\) 10650.0 0.0208324
\(716\) 384333.i 0.749691i
\(717\) −757779. 94160.1i −1.47402 0.183159i
\(718\) −251133. −0.487142
\(719\) 586921.i 1.13533i 0.823260 + 0.567665i \(0.192153\pi\)
−0.823260 + 0.567665i \(0.807847\pi\)
\(720\) −9128.49 + 36164.9i −0.0176090 + 0.0697624i
\(721\) 254397. 0.489375
\(722\) 1.61605e6i 3.10013i
\(723\) 59798.7 481246.i 0.114397 0.920642i
\(724\) 469439. 0.895576
\(725\) 825451.i 1.57042i
\(726\) 682938. + 84860.5i 1.29571 + 0.161002i
\(727\) 288584. 0.546014 0.273007 0.962012i \(-0.411982\pi\)
0.273007 + 0.962012i \(0.411982\pi\)
\(728\) 27987.4i 0.0528080i
\(729\) −391826. 359029.i −0.737290 0.675576i
\(730\) −93259.2 −0.175003
\(731\) 1.17763e6i 2.20380i
\(732\) 13658.7 109922.i 0.0254910 0.205146i
\(733\) −907687. −1.68938 −0.844692 0.535253i \(-0.820216\pi\)
−0.844692 + 0.535253i \(0.820216\pi\)
\(734\) 1.20398e6i 2.23474i
\(735\) 24747.7 + 3075.10i 0.0458100 + 0.00569226i
\(736\) −982888. −1.81446
\(737\) 274133.i 0.504693i
\(738\) −370601. 93544.6i −0.680446 0.171754i
\(739\) −476269. −0.872094 −0.436047 0.899924i \(-0.643622\pi\)
−0.436047 + 0.899924i \(0.643622\pi\)
\(740\) 47836.6i 0.0873569i
\(741\) −107260. + 863206.i −0.195345 + 1.57209i
\(742\) 949233. 1.72411
\(743\) 141273.i 0.255906i 0.991780 + 0.127953i \(0.0408407\pi\)
−0.991780 + 0.127953i \(0.959159\pi\)
\(744\) −39867.7 4953.89i −0.0720238 0.00894953i
\(745\) 61012.9 0.109928
\(746\) 70125.4i 0.126008i
\(747\) −8580.96 + 33995.7i −0.0153778 + 0.0609232i
\(748\) −247878. −0.443032
\(749\) 496345.i 0.884750i
\(750\) −15362.7 + 123635.i −0.0273114 + 0.219796i
\(751\) −678092. −1.20229 −0.601144 0.799141i \(-0.705288\pi\)
−0.601144 + 0.799141i \(0.705288\pi\)
\(752\) 225418.i 0.398614i
\(753\) 687722. + 85455.0i 1.21289 + 0.150712i
\(754\) 1.15069e6 2.02402
\(755\) 73290.3i 0.128574i
\(756\) 140002. 360025.i 0.244958 0.629926i
\(757\) 354843. 0.619219 0.309610 0.950864i \(-0.399802\pi\)
0.309610 + 0.950864i \(0.399802\pi\)
\(758\) 338246.i 0.588700i
\(759\) −27229.9 + 219140.i −0.0472675 + 0.380398i
\(760\) −7404.03 −0.0128186
\(761\) 242437.i 0.418629i −0.977848 0.209315i \(-0.932877\pi\)
0.977848 0.209315i \(-0.0671232\pi\)
\(762\) 734362. + 91250.4i 1.26474 + 0.157154i
\(763\) 254913. 0.437868
\(764\) 601769.i 1.03096i
\(765\) 60359.2 + 15235.5i 0.103138 + 0.0260335i
\(766\) 552665. 0.941900
\(767\) 68282.1i 0.116069i
\(768\) −62384.5 + 502056.i −0.105768 + 0.851196i
\(769\) 766824. 1.29671 0.648355 0.761338i \(-0.275457\pi\)
0.648355 + 0.761338i \(0.275457\pi\)
\(770\) 12634.9i 0.0213104i
\(771\) 298324. + 37069.1i 0.501856 + 0.0623597i
\(772\) −806524. −1.35326
\(773\) 277865.i 0.465024i −0.972593 0.232512i \(-0.925305\pi\)
0.972593 0.232512i \(-0.0746945\pi\)
\(774\) 337395. 1.33667e6i 0.563192 2.23123i
\(775\) 464287. 0.773007
\(776\) 23460.4i 0.0389594i
\(777\) 50140.3 403518.i 0.0830511 0.668376i
\(778\) 1.08811e6 1.79768
\(779\) 526610.i 0.867790i
\(780\) 44309.2 + 5505.78i 0.0728291 + 0.00904960i
\(781\) 142242. 0.233199