Properties

Label 177.3.b.a.119.1
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 119.1
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.38

$q$-expansion

\(f(q)\) \(=\) \(q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} +O(q^{10})\) \(q-3.77988i q^{2} +(2.45428 - 1.72526i) q^{3} -10.2875 q^{4} -1.62741i q^{5} +(-6.52128 - 9.27688i) q^{6} -7.78423 q^{7} +23.7661i q^{8} +(3.04695 - 8.46854i) q^{9} -6.15142 q^{10} +2.72883i q^{11} +(-25.2484 + 17.7486i) q^{12} +9.61474 q^{13} +29.4235i q^{14} +(-2.80771 - 3.99412i) q^{15} +48.6829 q^{16} -27.3790i q^{17} +(-32.0101 - 11.5171i) q^{18} -27.7110 q^{19} +16.7420i q^{20} +(-19.1047 + 13.4298i) q^{21} +10.3146 q^{22} -3.53027i q^{23} +(41.0027 + 58.3285i) q^{24} +22.3515 q^{25} -36.3426i q^{26} +(-7.13238 - 26.0409i) q^{27} +80.0804 q^{28} -6.30381i q^{29} +(-15.0973 + 10.6128i) q^{30} +39.9365 q^{31} -88.9515i q^{32} +(4.70794 + 6.69729i) q^{33} -103.489 q^{34} +12.6681i q^{35} +(-31.3455 + 87.1202i) q^{36} +44.2391 q^{37} +104.744i q^{38} +(23.5972 - 16.5879i) q^{39} +38.6772 q^{40} -50.1258i q^{41} +(50.7632 + 72.2134i) q^{42} -53.9729 q^{43} -28.0728i q^{44} +(-13.7818 - 4.95864i) q^{45} -13.3440 q^{46} +47.0156i q^{47} +(119.481 - 83.9907i) q^{48} +11.5943 q^{49} -84.4862i q^{50} +(-47.2359 - 67.1957i) q^{51} -98.9118 q^{52} -9.97840i q^{53} +(-98.4316 + 26.9595i) q^{54} +4.44092 q^{55} -185.001i q^{56} +(-68.0104 + 47.8086i) q^{57} -23.8277 q^{58} +7.68115i q^{59} +(28.8843 + 41.0895i) q^{60} -71.5942 q^{61} -150.955i q^{62} +(-23.7182 + 65.9211i) q^{63} -141.494 q^{64} -15.6471i q^{65} +(25.3150 - 17.7955i) q^{66} +86.8469 q^{67} +281.662i q^{68} +(-6.09063 - 8.66425i) q^{69} +47.8841 q^{70} -119.483i q^{71} +(201.264 + 72.4140i) q^{72} +16.4375 q^{73} -167.219i q^{74} +(54.8569 - 38.5622i) q^{75} +285.077 q^{76} -21.2418i q^{77} +(-62.7005 - 89.1948i) q^{78} +127.483 q^{79} -79.2271i q^{80} +(-62.4322 - 51.6064i) q^{81} -189.470 q^{82} +125.458i q^{83} +(196.540 - 138.160i) q^{84} -44.5569 q^{85} +204.011i q^{86} +(-10.8757 - 15.4713i) q^{87} -64.8535 q^{88} +137.168i q^{89} +(-18.7431 + 52.0935i) q^{90} -74.8434 q^{91} +36.3177i q^{92} +(98.0153 - 68.9009i) q^{93} +177.714 q^{94} +45.0971i q^{95} +(-153.464 - 218.312i) q^{96} +0.0640655 q^{97} -43.8251i q^{98} +(23.1092 + 8.31459i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.77988i 1.88994i −0.327155 0.944971i \(-0.606090\pi\)
0.327155 0.944971i \(-0.393910\pi\)
\(3\) 2.45428 1.72526i 0.818092 0.575087i
\(4\) −10.2875 −2.57188
\(5\) 1.62741i 0.325482i −0.986669 0.162741i \(-0.947966\pi\)
0.986669 0.162741i \(-0.0520335\pi\)
\(6\) −6.52128 9.27688i −1.08688 1.54615i
\(7\) −7.78423 −1.11203 −0.556017 0.831171i \(-0.687671\pi\)
−0.556017 + 0.831171i \(0.687671\pi\)
\(8\) 23.7661i 2.97076i
\(9\) 3.04695 8.46854i 0.338550 0.940948i
\(10\) −6.15142 −0.615142
\(11\) 2.72883i 0.248075i 0.992278 + 0.124038i \(0.0395843\pi\)
−0.992278 + 0.124038i \(0.960416\pi\)
\(12\) −25.2484 + 17.7486i −2.10403 + 1.47905i
\(13\) 9.61474 0.739595 0.369798 0.929112i \(-0.379427\pi\)
0.369798 + 0.929112i \(0.379427\pi\)
\(14\) 29.4235i 2.10168i
\(15\) −2.80771 3.99412i −0.187181 0.266274i
\(16\) 48.6829 3.04268
\(17\) 27.3790i 1.61053i −0.592915 0.805265i \(-0.702023\pi\)
0.592915 0.805265i \(-0.297977\pi\)
\(18\) −32.0101 11.5171i −1.77834 0.639840i
\(19\) −27.7110 −1.45847 −0.729236 0.684262i \(-0.760124\pi\)
−0.729236 + 0.684262i \(0.760124\pi\)
\(20\) 16.7420i 0.837101i
\(21\) −19.1047 + 13.4298i −0.909746 + 0.639516i
\(22\) 10.3146 0.468847
\(23\) 3.53027i 0.153490i −0.997051 0.0767449i \(-0.975547\pi\)
0.997051 0.0767449i \(-0.0244527\pi\)
\(24\) 41.0027 + 58.3285i 1.70845 + 2.43036i
\(25\) 22.3515 0.894061
\(26\) 36.3426i 1.39779i
\(27\) −7.13238 26.0409i −0.264162 0.964478i
\(28\) 80.0804 2.86002
\(29\) 6.30381i 0.217373i −0.994076 0.108686i \(-0.965336\pi\)
0.994076 0.108686i \(-0.0346644\pi\)
\(30\) −15.0973 + 10.6128i −0.503243 + 0.353760i
\(31\) 39.9365 1.28828 0.644138 0.764910i \(-0.277216\pi\)
0.644138 + 0.764910i \(0.277216\pi\)
\(32\) 88.9515i 2.77973i
\(33\) 4.70794 + 6.69729i 0.142665 + 0.202948i
\(34\) −103.489 −3.04381
\(35\) 12.6681i 0.361947i
\(36\) −31.3455 + 87.1202i −0.870710 + 2.42001i
\(37\) 44.2391 1.19565 0.597825 0.801626i \(-0.296032\pi\)
0.597825 + 0.801626i \(0.296032\pi\)
\(38\) 104.744i 2.75643i
\(39\) 23.5972 16.5879i 0.605057 0.425332i
\(40\) 38.6772 0.966929
\(41\) 50.1258i 1.22258i −0.791406 0.611290i \(-0.790651\pi\)
0.791406 0.611290i \(-0.209349\pi\)
\(42\) 50.7632 + 72.2134i 1.20865 + 1.71937i
\(43\) −53.9729 −1.25518 −0.627591 0.778543i \(-0.715959\pi\)
−0.627591 + 0.778543i \(0.715959\pi\)
\(44\) 28.0728i 0.638019i
\(45\) −13.7818 4.95864i −0.306262 0.110192i
\(46\) −13.3440 −0.290087
\(47\) 47.0156i 1.00033i 0.865929 + 0.500166i \(0.166728\pi\)
−0.865929 + 0.500166i \(0.833272\pi\)
\(48\) 119.481 83.9907i 2.48920 1.74981i
\(49\) 11.5943 0.236618
\(50\) 84.4862i 1.68972i
\(51\) −47.2359 67.1957i −0.926195 1.31756i
\(52\) −98.9118 −1.90215
\(53\) 9.97840i 0.188272i −0.995559 0.0941358i \(-0.969991\pi\)
0.995559 0.0941358i \(-0.0300088\pi\)
\(54\) −98.4316 + 26.9595i −1.82281 + 0.499251i
\(55\) 4.44092 0.0807440
\(56\) 185.001i 3.30358i
\(57\) −68.0104 + 47.8086i −1.19316 + 0.838748i
\(58\) −23.8277 −0.410822
\(59\) 7.68115i 0.130189i
\(60\) 28.8843 + 41.0895i 0.481406 + 0.684826i
\(61\) −71.5942 −1.17368 −0.586838 0.809705i \(-0.699627\pi\)
−0.586838 + 0.809705i \(0.699627\pi\)
\(62\) 150.955i 2.43477i
\(63\) −23.7182 + 65.9211i −0.376479 + 1.04637i
\(64\) −141.494 −2.21085
\(65\) 15.6471i 0.240725i
\(66\) 25.3150 17.7955i 0.383560 0.269628i
\(67\) 86.8469 1.29622 0.648111 0.761546i \(-0.275559\pi\)
0.648111 + 0.761546i \(0.275559\pi\)
\(68\) 281.662i 4.14209i
\(69\) −6.09063 8.66425i −0.0882700 0.125569i
\(70\) 47.8841 0.684059
\(71\) 119.483i 1.68285i −0.540372 0.841426i \(-0.681717\pi\)
0.540372 0.841426i \(-0.318283\pi\)
\(72\) 201.264 + 72.4140i 2.79533 + 1.00575i
\(73\) 16.4375 0.225172 0.112586 0.993642i \(-0.464087\pi\)
0.112586 + 0.993642i \(0.464087\pi\)
\(74\) 167.219i 2.25971i
\(75\) 54.8569 38.5622i 0.731425 0.514163i
\(76\) 285.077 3.75101
\(77\) 21.2418i 0.275868i
\(78\) −62.7005 89.1948i −0.803852 1.14352i
\(79\) 127.483 1.61371 0.806854 0.590751i \(-0.201169\pi\)
0.806854 + 0.590751i \(0.201169\pi\)
\(80\) 79.2271i 0.990339i
\(81\) −62.4322 51.6064i −0.770768 0.637116i
\(82\) −189.470 −2.31061
\(83\) 125.458i 1.51155i 0.654833 + 0.755774i \(0.272739\pi\)
−0.654833 + 0.755774i \(0.727261\pi\)
\(84\) 196.540 138.160i 2.33976 1.64476i
\(85\) −44.5569 −0.524199
\(86\) 204.011i 2.37222i
\(87\) −10.8757 15.4713i −0.125008 0.177831i
\(88\) −64.8535 −0.736971
\(89\) 137.168i 1.54121i 0.637313 + 0.770605i \(0.280046\pi\)
−0.637313 + 0.770605i \(0.719954\pi\)
\(90\) −18.7431 + 52.0935i −0.208256 + 0.578817i
\(91\) −74.8434 −0.822455
\(92\) 36.3177i 0.394757i
\(93\) 98.0153 68.9009i 1.05393 0.740870i
\(94\) 177.714 1.89057
\(95\) 45.0971i 0.474707i
\(96\) −153.464 218.312i −1.59859 2.27408i
\(97\) 0.0640655 0.000660469 0.000330234 1.00000i \(-0.499895\pi\)
0.000330234 1.00000i \(0.499895\pi\)
\(98\) 43.8251i 0.447195i
\(99\) 23.1092 + 8.31459i 0.233426 + 0.0839858i
\(100\) −229.942 −2.29942
\(101\) 131.783i 1.30478i −0.757881 0.652392i \(-0.773765\pi\)
0.757881 0.652392i \(-0.226235\pi\)
\(102\) −253.992 + 178.546i −2.49012 + 1.75045i
\(103\) 55.5732 0.539546 0.269773 0.962924i \(-0.413051\pi\)
0.269773 + 0.962924i \(0.413051\pi\)
\(104\) 228.505i 2.19716i
\(105\) 21.8559 + 31.0911i 0.208151 + 0.296106i
\(106\) −37.7172 −0.355822
\(107\) 9.15117i 0.0855250i −0.999085 0.0427625i \(-0.986384\pi\)
0.999085 0.0427625i \(-0.0136159\pi\)
\(108\) 73.3744 + 267.896i 0.679393 + 2.48052i
\(109\) 40.4952 0.371516 0.185758 0.982596i \(-0.440526\pi\)
0.185758 + 0.982596i \(0.440526\pi\)
\(110\) 16.7862i 0.152601i
\(111\) 108.575 76.3240i 0.978153 0.687603i
\(112\) −378.959 −3.38356
\(113\) 116.150i 1.02787i 0.857828 + 0.513937i \(0.171813\pi\)
−0.857828 + 0.513937i \(0.828187\pi\)
\(114\) 180.711 + 257.071i 1.58518 + 2.25501i
\(115\) −5.74519 −0.0499582
\(116\) 64.8505i 0.559056i
\(117\) 29.2956 81.4228i 0.250390 0.695921i
\(118\) 29.0338 0.246049
\(119\) 213.125i 1.79096i
\(120\) 94.9245 66.7282i 0.791037 0.556068i
\(121\) 113.554 0.938459
\(122\) 270.618i 2.21818i
\(123\) −86.4801 123.023i −0.703090 1.00018i
\(124\) −410.848 −3.31329
\(125\) 77.0604i 0.616483i
\(126\) 249.174 + 89.6519i 1.97757 + 0.711523i
\(127\) −66.5716 −0.524186 −0.262093 0.965043i \(-0.584413\pi\)
−0.262093 + 0.965043i \(0.584413\pi\)
\(128\) 179.027i 1.39864i
\(129\) −132.464 + 93.1173i −1.02686 + 0.721839i
\(130\) −59.1443 −0.454956
\(131\) 66.2829i 0.505976i 0.967469 + 0.252988i \(0.0814133\pi\)
−0.967469 + 0.252988i \(0.918587\pi\)
\(132\) −48.4330 68.8985i −0.366916 0.521959i
\(133\) 215.709 1.62187
\(134\) 328.271i 2.44978i
\(135\) −42.3793 + 11.6073i −0.313921 + 0.0859800i
\(136\) 650.692 4.78450
\(137\) 49.1043i 0.358425i 0.983810 + 0.179213i \(0.0573550\pi\)
−0.983810 + 0.179213i \(0.942645\pi\)
\(138\) −32.7498 + 23.0219i −0.237318 + 0.166825i
\(139\) 227.787 1.63875 0.819377 0.573254i \(-0.194319\pi\)
0.819377 + 0.573254i \(0.194319\pi\)
\(140\) 130.324i 0.930884i
\(141\) 81.1142 + 115.389i 0.575278 + 0.818364i
\(142\) −451.630 −3.18049
\(143\) 26.2370i 0.183475i
\(144\) 148.334 412.273i 1.03010 2.86301i
\(145\) −10.2589 −0.0707509
\(146\) 62.1319i 0.425561i
\(147\) 28.4556 20.0032i 0.193576 0.136076i
\(148\) −455.110 −3.07507
\(149\) 23.3606i 0.156783i 0.996923 + 0.0783914i \(0.0249784\pi\)
−0.996923 + 0.0783914i \(0.975022\pi\)
\(150\) −145.761 207.352i −0.971738 1.38235i
\(151\) 133.696 0.885406 0.442703 0.896668i \(-0.354020\pi\)
0.442703 + 0.896668i \(0.354020\pi\)
\(152\) 658.581i 4.33277i
\(153\) −231.860 83.4225i −1.51543 0.545245i
\(154\) −80.2916 −0.521374
\(155\) 64.9932i 0.419311i
\(156\) −242.757 + 170.649i −1.55613 + 1.09390i
\(157\) 194.685 1.24003 0.620016 0.784589i \(-0.287126\pi\)
0.620016 + 0.784589i \(0.287126\pi\)
\(158\) 481.870i 3.04981i
\(159\) −17.2153 24.4897i −0.108273 0.154024i
\(160\) −144.761 −0.904754
\(161\) 27.4804i 0.170686i
\(162\) −195.066 + 235.986i −1.20411 + 1.45671i
\(163\) 27.5035 0.168733 0.0843665 0.996435i \(-0.473113\pi\)
0.0843665 + 0.996435i \(0.473113\pi\)
\(164\) 515.670i 3.14433i
\(165\) 10.8992 7.66175i 0.0660561 0.0464348i
\(166\) 474.218 2.85674
\(167\) 83.9120i 0.502467i −0.967927 0.251233i \(-0.919164\pi\)
0.967927 0.251233i \(-0.0808362\pi\)
\(168\) −319.174 454.043i −1.89985 2.70264i
\(169\) −76.5567 −0.452999
\(170\) 168.420i 0.990705i
\(171\) −84.4339 + 234.671i −0.493766 + 1.37235i
\(172\) 555.247 3.22818
\(173\) 237.213i 1.37118i −0.727990 0.685588i \(-0.759545\pi\)
0.727990 0.685588i \(-0.240455\pi\)
\(174\) −58.4797 + 41.1089i −0.336090 + 0.236258i
\(175\) −173.990 −0.994226
\(176\) 132.847i 0.754814i
\(177\) 13.2520 + 18.8517i 0.0748699 + 0.106507i
\(178\) 518.478 2.91280
\(179\) 226.853i 1.26733i 0.773606 + 0.633667i \(0.218451\pi\)
−0.773606 + 0.633667i \(0.781549\pi\)
\(180\) 141.780 + 51.0121i 0.787669 + 0.283400i
\(181\) −108.540 −0.599666 −0.299833 0.953992i \(-0.596931\pi\)
−0.299833 + 0.953992i \(0.596931\pi\)
\(182\) 282.899i 1.55439i
\(183\) −175.712 + 123.519i −0.960175 + 0.674966i
\(184\) 83.9005 0.455981
\(185\) 71.9952i 0.389163i
\(186\) −260.438 370.486i −1.40020 1.99186i
\(187\) 74.7126 0.399532
\(188\) 483.674i 2.57273i
\(189\) 55.5201 + 202.709i 0.293757 + 1.07253i
\(190\) 170.462 0.897168
\(191\) 0.101903i 0.000533522i 1.00000 0.000266761i \(8.49127e-5\pi\)
−1.00000 0.000266761i \(0.999915\pi\)
\(192\) −347.266 + 244.115i −1.80868 + 1.27143i
\(193\) −162.720 −0.843108 −0.421554 0.906803i \(-0.638515\pi\)
−0.421554 + 0.906803i \(0.638515\pi\)
\(194\) 0.242160i 0.00124825i
\(195\) −26.9954 38.4024i −0.138438 0.196935i
\(196\) −119.276 −0.608553
\(197\) 208.516i 1.05846i 0.848479 + 0.529230i \(0.177519\pi\)
−0.848479 + 0.529230i \(0.822481\pi\)
\(198\) 31.4282 87.3499i 0.158728 0.441161i
\(199\) −43.8940 −0.220573 −0.110286 0.993900i \(-0.535177\pi\)
−0.110286 + 0.993900i \(0.535177\pi\)
\(200\) 531.208i 2.65604i
\(201\) 213.146 149.834i 1.06043 0.745441i
\(202\) −498.125 −2.46597
\(203\) 49.0703i 0.241726i
\(204\) 485.941 + 691.277i 2.38206 + 3.38861i
\(205\) −81.5753 −0.397928
\(206\) 210.060i 1.01971i
\(207\) −29.8962 10.7565i −0.144426 0.0519640i
\(208\) 468.074 2.25035
\(209\) 75.6184i 0.361811i
\(210\) 117.521 82.6126i 0.559623 0.393393i
\(211\) −297.742 −1.41110 −0.705550 0.708660i \(-0.749300\pi\)
−0.705550 + 0.708660i \(0.749300\pi\)
\(212\) 102.653i 0.484212i
\(213\) −206.139 293.243i −0.967786 1.37673i
\(214\) −34.5904 −0.161637
\(215\) 87.8360i 0.408540i
\(216\) 618.890 169.509i 2.86523 0.784762i
\(217\) −310.875 −1.43261
\(218\) 153.067i 0.702143i
\(219\) 40.3422 28.3590i 0.184211 0.129493i
\(220\) −45.6860 −0.207664
\(221\) 263.242i 1.19114i
\(222\) −288.496 410.401i −1.29953 1.84865i
\(223\) −297.595 −1.33451 −0.667254 0.744830i \(-0.732530\pi\)
−0.667254 + 0.744830i \(0.732530\pi\)
\(224\) 692.419i 3.09116i
\(225\) 68.1040 189.285i 0.302684 0.841266i
\(226\) 439.032 1.94262
\(227\) 66.8134i 0.294332i 0.989112 + 0.147166i \(0.0470152\pi\)
−0.989112 + 0.147166i \(0.952985\pi\)
\(228\) 699.658 491.832i 3.06867 2.15716i
\(229\) 92.6270 0.404485 0.202242 0.979336i \(-0.435177\pi\)
0.202242 + 0.979336i \(0.435177\pi\)
\(230\) 21.7162i 0.0944181i
\(231\) −36.6477 52.1333i −0.158648 0.225685i
\(232\) 149.817 0.645762
\(233\) 31.5019i 0.135201i 0.997712 + 0.0676007i \(0.0215344\pi\)
−0.997712 + 0.0676007i \(0.978466\pi\)
\(234\) −307.769 110.734i −1.31525 0.473222i
\(235\) 76.5138 0.325590
\(236\) 79.0199i 0.334830i
\(237\) 312.878 219.941i 1.32016 0.928022i
\(238\) 805.586 3.38482
\(239\) 208.641i 0.872973i −0.899711 0.436487i \(-0.856223\pi\)
0.899711 0.436487i \(-0.143777\pi\)
\(240\) −136.687 194.445i −0.569531 0.810189i
\(241\) 368.093 1.52736 0.763679 0.645596i \(-0.223391\pi\)
0.763679 + 0.645596i \(0.223391\pi\)
\(242\) 429.219i 1.77363i
\(243\) −242.260 18.9446i −0.996956 0.0779612i
\(244\) 736.527 3.01855
\(245\) 18.8687i 0.0770150i
\(246\) −465.011 + 326.885i −1.89029 + 1.32880i
\(247\) −266.434 −1.07868
\(248\) 949.135i 3.82716i
\(249\) 216.449 + 307.910i 0.869272 + 1.23659i
\(250\) −291.279 −1.16512
\(251\) 262.798i 1.04701i 0.852024 + 0.523503i \(0.175375\pi\)
−0.852024 + 0.523503i \(0.824625\pi\)
\(252\) 244.001 678.164i 0.968258 2.69113i
\(253\) 9.63348 0.0380770
\(254\) 251.633i 0.990680i
\(255\) −109.355 + 76.8723i −0.428843 + 0.301460i
\(256\) 110.722 0.432506
\(257\) 86.3269i 0.335902i 0.985795 + 0.167951i \(0.0537151\pi\)
−0.985795 + 0.167951i \(0.946285\pi\)
\(258\) 351.972 + 500.700i 1.36423 + 1.94070i
\(259\) −344.367 −1.32960
\(260\) 160.970i 0.619116i
\(261\) −53.3840 19.2074i −0.204536 0.0735915i
\(262\) 250.541 0.956265
\(263\) 198.233i 0.753737i 0.926267 + 0.376868i \(0.122999\pi\)
−0.926267 + 0.376868i \(0.877001\pi\)
\(264\) −159.168 + 111.889i −0.602911 + 0.423823i
\(265\) −16.2390 −0.0612791
\(266\) 815.353i 3.06524i
\(267\) 236.650 + 336.647i 0.886330 + 1.26085i
\(268\) −893.439 −3.33373
\(269\) 265.983i 0.988784i −0.869239 0.494392i \(-0.835391\pi\)
0.869239 0.494392i \(-0.164609\pi\)
\(270\) 43.8743 + 160.189i 0.162497 + 0.593291i
\(271\) −55.0011 −0.202956 −0.101478 0.994838i \(-0.532357\pi\)
−0.101478 + 0.994838i \(0.532357\pi\)
\(272\) 1332.89i 4.90033i
\(273\) −183.686 + 129.124i −0.672844 + 0.472983i
\(274\) 185.608 0.677403
\(275\) 60.9934i 0.221794i
\(276\) 62.6574 + 89.1336i 0.227020 + 0.322948i
\(277\) 57.8384 0.208803 0.104401 0.994535i \(-0.466707\pi\)
0.104401 + 0.994535i \(0.466707\pi\)
\(278\) 861.008i 3.09715i
\(279\) 121.685 338.204i 0.436146 1.21220i
\(280\) −301.072 −1.07526
\(281\) 204.730i 0.728578i −0.931286 0.364289i \(-0.881312\pi\)
0.931286 0.364289i \(-0.118688\pi\)
\(282\) 436.158 306.602i 1.54666 1.08724i
\(283\) −245.355 −0.866980 −0.433490 0.901158i \(-0.642718\pi\)
−0.433490 + 0.901158i \(0.642718\pi\)
\(284\) 1229.18i 4.32809i
\(285\) 77.8043 + 110.681i 0.272998 + 0.388354i
\(286\) 99.1726 0.346757
\(287\) 390.191i 1.35955i
\(288\) −753.289 271.031i −2.61559 0.941078i
\(289\) −460.611 −1.59381
\(290\) 38.7774i 0.133715i
\(291\) 0.157234 0.110530i 0.000540324 0.000379827i
\(292\) −169.101 −0.579114
\(293\) 444.473i 1.51697i 0.651690 + 0.758486i \(0.274060\pi\)
−0.651690 + 0.758486i \(0.725940\pi\)
\(294\) −75.6097 107.559i −0.257176 0.365846i
\(295\) 12.5004 0.0423742
\(296\) 1051.39i 3.55199i
\(297\) 71.0611 19.4630i 0.239263 0.0655320i
\(298\) 88.3005 0.296310
\(299\) 33.9426i 0.113520i
\(300\) −564.341 + 396.710i −1.88114 + 1.32237i
\(301\) 420.137 1.39581
\(302\) 505.356i 1.67337i
\(303\) −227.361 323.433i −0.750365 1.06743i
\(304\) −1349.05 −4.43767
\(305\) 116.513i 0.382010i
\(306\) −315.327 + 876.404i −1.03048 + 2.86407i
\(307\) −383.922 −1.25056 −0.625281 0.780400i \(-0.715015\pi\)
−0.625281 + 0.780400i \(0.715015\pi\)
\(308\) 218.526i 0.709499i
\(309\) 136.392 95.8783i 0.441398 0.310286i
\(310\) −245.667 −0.792473
\(311\) 99.6589i 0.320447i 0.987081 + 0.160223i \(0.0512214\pi\)
−0.987081 + 0.160223i \(0.948779\pi\)
\(312\) 394.230 + 560.814i 1.26356 + 1.79748i
\(313\) −230.288 −0.735743 −0.367872 0.929877i \(-0.619913\pi\)
−0.367872 + 0.929877i \(0.619913\pi\)
\(314\) 735.887i 2.34359i
\(315\) 107.281 + 38.5992i 0.340574 + 0.122537i
\(316\) −1311.48 −4.15026
\(317\) 455.975i 1.43841i −0.694799 0.719204i \(-0.744507\pi\)
0.694799 0.719204i \(-0.255493\pi\)
\(318\) −92.5684 + 65.0720i −0.291096 + 0.204629i
\(319\) 17.2020 0.0539247
\(320\) 230.270i 0.719592i
\(321\) −15.7882 22.4595i −0.0491843 0.0699673i
\(322\) 103.873 0.322586
\(323\) 758.699i 2.34891i
\(324\) 642.272 + 530.902i 1.98232 + 1.63859i
\(325\) 214.904 0.661244
\(326\) 103.960i 0.318895i
\(327\) 99.3864 69.8648i 0.303934 0.213654i
\(328\) 1191.29 3.63199
\(329\) 365.981i 1.11240i
\(330\) −28.9605 41.1979i −0.0877591 0.124842i
\(331\) −578.942 −1.74907 −0.874535 0.484963i \(-0.838833\pi\)
−0.874535 + 0.484963i \(0.838833\pi\)
\(332\) 1290.66i 3.88752i
\(333\) 134.794 374.640i 0.404788 1.12505i
\(334\) −317.177 −0.949633
\(335\) 141.336i 0.421897i
\(336\) −930.071 + 653.804i −2.76807 + 1.94584i
\(337\) 161.282 0.478581 0.239291 0.970948i \(-0.423085\pi\)
0.239291 + 0.970948i \(0.423085\pi\)
\(338\) 289.376i 0.856141i
\(339\) 200.389 + 285.064i 0.591117 + 0.840895i
\(340\) 458.380 1.34818
\(341\) 108.980i 0.319589i
\(342\) 887.030 + 319.150i 2.59366 + 0.933188i
\(343\) 291.175 0.848906
\(344\) 1282.72i 3.72885i
\(345\) −14.1003 + 9.91196i −0.0408704 + 0.0287303i
\(346\) −896.639 −2.59144
\(347\) 332.681i 0.958735i 0.877614 + 0.479367i \(0.159134\pi\)
−0.877614 + 0.479367i \(0.840866\pi\)
\(348\) 111.884 + 159.161i 0.321506 + 0.457360i
\(349\) 135.069 0.387018 0.193509 0.981099i \(-0.438013\pi\)
0.193509 + 0.981099i \(0.438013\pi\)
\(350\) 657.660i 1.87903i
\(351\) −68.5760 250.377i −0.195373 0.713324i
\(352\) 242.733 0.689583
\(353\) 286.915i 0.812789i −0.913698 0.406395i \(-0.866786\pi\)
0.913698 0.406395i \(-0.133214\pi\)
\(354\) 71.2571 50.0909i 0.201291 0.141500i
\(355\) −194.447 −0.547738
\(356\) 1411.11i 3.96380i
\(357\) 367.696 + 523.067i 1.02996 + 1.46517i
\(358\) 857.478 2.39519
\(359\) 376.147i 1.04776i −0.851791 0.523881i \(-0.824483\pi\)
0.851791 0.523881i \(-0.175517\pi\)
\(360\) 117.847 327.539i 0.327354 0.909831i
\(361\) 406.897 1.12714
\(362\) 410.267i 1.13333i
\(363\) 278.692 195.909i 0.767746 0.539695i
\(364\) 769.953 2.11525
\(365\) 26.7506i 0.0732893i
\(366\) 466.886 + 664.171i 1.27565 + 1.81467i
\(367\) −226.341 −0.616732 −0.308366 0.951268i \(-0.599782\pi\)
−0.308366 + 0.951268i \(0.599782\pi\)
\(368\) 171.864i 0.467021i
\(369\) −424.492 152.731i −1.15039 0.413905i
\(370\) −272.133 −0.735495
\(371\) 77.6742i 0.209364i
\(372\) −1008.33 + 708.820i −2.71058 + 1.90543i
\(373\) 5.23611 0.0140378 0.00701891 0.999975i \(-0.497766\pi\)
0.00701891 + 0.999975i \(0.497766\pi\)
\(374\) 282.405i 0.755093i
\(375\) −132.949 189.128i −0.354531 0.504340i
\(376\) −1117.38 −2.97175
\(377\) 60.6095i 0.160768i
\(378\) 766.215 209.859i 2.02702 0.555184i
\(379\) 99.8976 0.263582 0.131791 0.991278i \(-0.457927\pi\)
0.131791 + 0.991278i \(0.457927\pi\)
\(380\) 463.937i 1.22089i
\(381\) −163.385 + 114.853i −0.428832 + 0.301452i
\(382\) 0.385180 0.00100833
\(383\) 526.256i 1.37404i 0.726641 + 0.687018i \(0.241081\pi\)
−0.726641 + 0.687018i \(0.758919\pi\)
\(384\) 308.867 + 439.381i 0.804342 + 1.14422i
\(385\) −34.5692 −0.0897900
\(386\) 615.062i 1.59342i
\(387\) −164.453 + 457.071i −0.424942 + 1.18106i
\(388\) −0.659074 −0.00169865
\(389\) 12.8702i 0.0330854i −0.999863 0.0165427i \(-0.994734\pi\)
0.999863 0.0165427i \(-0.00526595\pi\)
\(390\) −145.157 + 102.039i −0.372196 + 0.261640i
\(391\) −96.6552 −0.247200
\(392\) 275.551i 0.702936i
\(393\) 114.355 + 162.676i 0.290980 + 0.413935i
\(394\) 788.168 2.00043
\(395\) 207.467i 0.525233i
\(396\) −237.736 85.5365i −0.600343 0.216001i
\(397\) −197.743 −0.498092 −0.249046 0.968492i \(-0.580117\pi\)
−0.249046 + 0.968492i \(0.580117\pi\)
\(398\) 165.914i 0.416870i
\(399\) 529.409 372.154i 1.32684 0.932716i
\(400\) 1088.14 2.72035
\(401\) 37.8334i 0.0943475i 0.998887 + 0.0471738i \(0.0150214\pi\)
−0.998887 + 0.0471738i \(0.984979\pi\)
\(402\) −566.353 805.668i −1.40884 2.00415i
\(403\) 383.979 0.952803
\(404\) 1355.72i 3.35575i
\(405\) −83.9848 + 101.603i −0.207370 + 0.250871i
\(406\) 185.480 0.456847
\(407\) 120.721i 0.296611i
\(408\) 1596.98 1122.61i 3.91416 2.75150i
\(409\) 201.720 0.493203 0.246601 0.969117i \(-0.420686\pi\)
0.246601 + 0.969117i \(0.420686\pi\)
\(410\) 308.345i 0.752061i
\(411\) 84.7177 + 120.515i 0.206126 + 0.293225i
\(412\) −571.711 −1.38765
\(413\) 59.7918i 0.144774i
\(414\) −40.6585 + 113.004i −0.0982088 + 0.272957i
\(415\) 204.172 0.491982
\(416\) 855.245i 2.05588i
\(417\) 559.052 392.992i 1.34065 0.942427i
\(418\) −285.829 −0.683801
\(419\) 362.156i 0.864335i −0.901793 0.432168i \(-0.857749\pi\)
0.901793 0.432168i \(-0.142251\pi\)
\(420\) −224.842 319.851i −0.535339 0.761549i
\(421\) 459.569 1.09161 0.545806 0.837911i \(-0.316223\pi\)
0.545806 + 0.837911i \(0.316223\pi\)
\(422\) 1125.43i 2.66690i
\(423\) 398.154 + 143.254i 0.941262 + 0.338663i
\(424\) 237.147 0.559310
\(425\) 611.963i 1.43991i
\(426\) −1108.42 + 779.179i −2.60194 + 1.82906i
\(427\) 557.306 1.30517
\(428\) 94.1428i 0.219960i
\(429\) 45.2656 + 64.3928i 0.105514 + 0.150100i
\(430\) 332.010 0.772116
\(431\) 290.802i 0.674714i 0.941377 + 0.337357i \(0.109533\pi\)
−0.941377 + 0.337357i \(0.890467\pi\)
\(432\) −347.225 1267.75i −0.803761 2.93460i
\(433\) −687.774 −1.58839 −0.794196 0.607662i \(-0.792108\pi\)
−0.794196 + 0.607662i \(0.792108\pi\)
\(434\) 1175.07i 2.70754i
\(435\) −25.1781 + 17.6993i −0.0578808 + 0.0406879i
\(436\) −416.595 −0.955493
\(437\) 97.8270i 0.223861i
\(438\) −107.194 152.489i −0.244735 0.348148i
\(439\) 335.293 0.763765 0.381882 0.924211i \(-0.375276\pi\)
0.381882 + 0.924211i \(0.375276\pi\)
\(440\) 105.543i 0.239871i
\(441\) 35.3272 98.1867i 0.0801071 0.222646i
\(442\) −995.025 −2.25119
\(443\) 303.866i 0.685928i −0.939348 0.342964i \(-0.888569\pi\)
0.939348 0.342964i \(-0.111431\pi\)
\(444\) −1116.97 + 785.184i −2.51569 + 1.76843i
\(445\) 223.228 0.501636
\(446\) 1124.87i 2.52214i
\(447\) 40.3032 + 57.3335i 0.0901637 + 0.128263i
\(448\) 1101.43 2.45854
\(449\) 144.114i 0.320967i 0.987039 + 0.160483i \(0.0513053\pi\)
−0.987039 + 0.160483i \(0.948695\pi\)
\(450\) −715.474 257.425i −1.58994 0.572056i
\(451\) 136.785 0.303292
\(452\) 1194.89i 2.64357i
\(453\) 328.128 230.661i 0.724344 0.509185i
\(454\) 252.547 0.556271
\(455\) 121.801i 0.267694i
\(456\) −1136.22 1616.34i −2.49172 3.54460i
\(457\) 463.300 1.01379 0.506893 0.862009i \(-0.330794\pi\)
0.506893 + 0.862009i \(0.330794\pi\)
\(458\) 350.119i 0.764452i
\(459\) −712.975 + 195.277i −1.55332 + 0.425441i
\(460\) 59.1038 0.128486
\(461\) 390.113i 0.846232i 0.906076 + 0.423116i \(0.139064\pi\)
−0.906076 + 0.423116i \(0.860936\pi\)
\(462\) −197.058 + 138.524i −0.426532 + 0.299835i
\(463\) 335.403 0.724413 0.362207 0.932098i \(-0.382023\pi\)
0.362207 + 0.932098i \(0.382023\pi\)
\(464\) 306.888i 0.661396i
\(465\) −112.130 159.511i −0.241140 0.343035i
\(466\) 119.074 0.255523
\(467\) 434.067i 0.929481i −0.885447 0.464740i \(-0.846148\pi\)
0.885447 0.464740i \(-0.153852\pi\)
\(468\) −301.379 + 837.638i −0.643973 + 1.78983i
\(469\) −676.037 −1.44144
\(470\) 289.213i 0.615347i
\(471\) 477.811 335.883i 1.01446 0.713126i
\(472\) −182.551 −0.386760
\(473\) 147.283i 0.311380i
\(474\) −831.352 1182.64i −1.75391 2.49503i
\(475\) −619.383 −1.30396
\(476\) 2192.52i 4.60614i
\(477\) −84.5024 30.4037i −0.177154 0.0637394i
\(478\) −788.637 −1.64987
\(479\) 627.445i 1.30991i 0.755669 + 0.654953i \(0.227312\pi\)
−0.755669 + 0.654953i \(0.772688\pi\)
\(480\) −355.283 + 249.750i −0.740172 + 0.520312i
\(481\) 425.347 0.884298
\(482\) 1391.35i 2.88662i
\(483\) 47.4109 + 67.4445i 0.0981592 + 0.139637i
\(484\) −1168.18 −2.41360
\(485\) 0.104261i 0.000214971i
\(486\) −71.6083 + 915.716i −0.147342 + 1.88419i
\(487\) 199.609 0.409875 0.204938 0.978775i \(-0.434301\pi\)
0.204938 + 0.978775i \(0.434301\pi\)
\(488\) 1701.51i 3.48671i
\(489\) 67.5011 47.4507i 0.138039 0.0970361i
\(490\) −71.3214 −0.145554
\(491\) 681.187i 1.38735i −0.720290 0.693674i \(-0.755991\pi\)
0.720290 0.693674i \(-0.244009\pi\)
\(492\) 889.665 + 1265.60i 1.80826 + 2.57235i
\(493\) −172.592 −0.350085
\(494\) 1007.09i 2.03864i
\(495\) 13.5313 37.6081i 0.0273359 0.0759760i
\(496\) 1944.23 3.91981
\(497\) 930.080i 1.87139i
\(498\) 1163.86 818.150i 2.33707 1.64287i
\(499\) 844.498 1.69238 0.846190 0.532881i \(-0.178891\pi\)
0.846190 + 0.532881i \(0.178891\pi\)
\(500\) 792.760i 1.58552i
\(501\) −144.770 205.943i −0.288962 0.411064i
\(502\) 993.347 1.97878
\(503\) 306.629i 0.609600i −0.952416 0.304800i \(-0.901410\pi\)
0.952416 0.304800i \(-0.0985896\pi\)
\(504\) −1566.68 563.688i −3.10850 1.11843i
\(505\) −214.466 −0.424684
\(506\) 36.4134i 0.0719633i
\(507\) −187.891 + 132.080i −0.370595 + 0.260514i
\(508\) 684.856 1.34814
\(509\) 509.953i 1.00187i 0.865484 + 0.500936i \(0.167011\pi\)
−0.865484 + 0.500936i \(0.832989\pi\)
\(510\) 290.568 + 413.349i 0.569742 + 0.810488i
\(511\) −127.954 −0.250398
\(512\) 297.591i 0.581233i
\(513\) 197.645 + 721.619i 0.385273 + 1.40666i
\(514\) 326.306 0.634836
\(515\) 90.4405i 0.175613i
\(516\) 1362.73 957.945i 2.64095 1.85648i
\(517\) −128.297 −0.248158
\(518\) 1301.67i 2.51287i
\(519\) −409.255 582.187i −0.788545 1.12175i
\(520\) 371.871 0.715137
\(521\) 55.1618i 0.105877i 0.998598 + 0.0529384i \(0.0168587\pi\)
−0.998598 + 0.0529384i \(0.983141\pi\)
\(522\) −72.6017 + 201.785i −0.139084 + 0.386562i
\(523\) −855.419 −1.63560 −0.817801 0.575502i \(-0.804807\pi\)
−0.817801 + 0.575502i \(0.804807\pi\)
\(524\) 681.886i 1.30131i
\(525\) −427.019 + 300.177i −0.813369 + 0.571766i
\(526\) 749.297 1.42452
\(527\) 1093.42i 2.07481i
\(528\) 229.196 + 326.044i 0.434084 + 0.617507i
\(529\) 516.537 0.976441
\(530\) 61.3813i 0.115814i
\(531\) 65.0481 + 23.4041i 0.122501 + 0.0440754i
\(532\) −2219.11 −4.17125
\(533\) 481.947i 0.904215i
\(534\) 1272.49 894.509i 2.38294 1.67511i
\(535\) −14.8927 −0.0278369
\(536\) 2064.01i 3.85077i
\(537\) 391.381 + 556.760i 0.728828 + 1.03680i
\(538\) −1005.38 −1.86874
\(539\) 31.6388i 0.0586991i
\(540\) 435.977 119.410i 0.807366 0.221130i
\(541\) 436.832 0.807452 0.403726 0.914880i \(-0.367715\pi\)
0.403726 + 0.914880i \(0.367715\pi\)
\(542\) 207.898i 0.383575i
\(543\) −266.386 + 187.259i −0.490582 + 0.344860i
\(544\) −2435.40 −4.47684
\(545\) 65.9023i 0.120922i
\(546\) 488.075 + 694.313i 0.893910 + 1.27164i
\(547\) 515.478 0.942372 0.471186 0.882034i \(-0.343826\pi\)
0.471186 + 0.882034i \(0.343826\pi\)
\(548\) 505.161i 0.921826i
\(549\) −218.144 + 606.298i −0.397348 + 1.10437i
\(550\) 230.548 0.419178
\(551\) 174.685i 0.317032i
\(552\) 205.915 144.750i 0.373035 0.262229i
\(553\) −992.357 −1.79450
\(554\) 218.622i 0.394625i
\(555\) −124.210 176.696i −0.223803 0.318371i
\(556\) −2343.36 −4.21468
\(557\) 79.9557i 0.143547i 0.997421 + 0.0717735i \(0.0228659\pi\)
−0.997421 + 0.0717735i \(0.977134\pi\)
\(558\) −1278.37 459.954i −2.29099 0.824290i
\(559\) −518.935 −0.928328
\(560\) 616.722i 1.10129i
\(561\) 183.365 128.899i 0.326854 0.229766i
\(562\) −773.857 −1.37697
\(563\) 83.9743i 0.149155i −0.997215 0.0745775i \(-0.976239\pi\)
0.997215 0.0745775i \(-0.0237608\pi\)
\(564\) −834.464 1187.07i −1.47955 2.10473i
\(565\) 189.023 0.334555
\(566\) 927.415i 1.63854i
\(567\) 485.987 + 401.716i 0.857120 + 0.708494i
\(568\) 2839.63 4.99935
\(569\) 269.476i 0.473596i −0.971559 0.236798i \(-0.923902\pi\)
0.971559 0.236798i \(-0.0760980\pi\)
\(570\) 418.361 294.091i 0.733966 0.515949i
\(571\) −301.627 −0.528243 −0.264122 0.964489i \(-0.585082\pi\)
−0.264122 + 0.964489i \(0.585082\pi\)
\(572\) 269.913i 0.471876i
\(573\) 0.175809 + 0.250098i 0.000306822 + 0.000436470i
\(574\) 1474.88 2.56947
\(575\) 78.9068i 0.137229i
\(576\) −431.126 + 1198.25i −0.748483 + 2.08030i
\(577\) −31.1811 −0.0540400 −0.0270200 0.999635i \(-0.508602\pi\)
−0.0270200 + 0.999635i \(0.508602\pi\)
\(578\) 1741.05i 3.01220i
\(579\) −399.359 + 280.734i −0.689740 + 0.484860i
\(580\) 105.538 0.181963
\(581\) 976.598i 1.68089i
\(582\) −0.417789 0.594327i −0.000717851 0.00102118i
\(583\) 27.2293 0.0467055
\(584\) 390.656i 0.668931i
\(585\) −132.508 47.6760i −0.226510 0.0814975i
\(586\) 1680.05 2.86699
\(587\) 250.764i 0.427196i −0.976922 0.213598i \(-0.931482\pi\)
0.976922 0.213598i \(-0.0685183\pi\)
\(588\) −292.737 + 205.783i −0.497853 + 0.349971i
\(589\) −1106.68 −1.87891
\(590\) 47.2500i 0.0800847i
\(591\) 359.745 + 511.757i 0.608706 + 0.865917i
\(592\) 2153.69 3.63799
\(593\) 517.385i 0.872488i −0.899828 0.436244i \(-0.856308\pi\)
0.899828 0.436244i \(-0.143692\pi\)
\(594\) −73.5679 268.603i −0.123852 0.452193i
\(595\) 346.841 0.582927
\(596\) 240.323i 0.403226i
\(597\) −107.728 + 75.7286i −0.180449 + 0.126849i
\(598\) −128.299 −0.214547
\(599\) 716.875i 1.19679i 0.801202 + 0.598393i \(0.204194\pi\)
−0.801202 + 0.598393i \(0.795806\pi\)
\(600\) 916.473 + 1303.73i 1.52745 + 2.17289i
\(601\) −459.122 −0.763931 −0.381965 0.924177i \(-0.624753\pi\)
−0.381965 + 0.924177i \(0.624753\pi\)
\(602\) 1588.07i 2.63799i
\(603\) 264.618 735.466i 0.438836 1.21968i
\(604\) −1375.40 −2.27716
\(605\) 184.798i 0.305452i
\(606\) −1222.54 + 859.396i −2.01739 + 1.41815i
\(607\) −226.409 −0.372996 −0.186498 0.982455i \(-0.559714\pi\)
−0.186498 + 0.982455i \(0.559714\pi\)
\(608\) 2464.93i 4.05416i
\(609\) 84.6591 + 120.432i 0.139013 + 0.197754i
\(610\) 440.406 0.721977
\(611\) 452.043i 0.739842i
\(612\) 2385.27 + 858.210i 3.89749 + 1.40230i
\(613\) 397.612 0.648634 0.324317 0.945949i \(-0.394866\pi\)
0.324317 + 0.945949i \(0.394866\pi\)
\(614\) 1451.18i 2.36349i
\(615\) −200.208 + 140.739i −0.325542 + 0.228843i
\(616\) 504.835 0.819537
\(617\) 872.102i 1.41346i −0.707486 0.706728i \(-0.750171\pi\)
0.707486 0.706728i \(-0.249829\pi\)
\(618\) −362.409 515.546i −0.586422 0.834217i
\(619\) 784.482 1.26734 0.633669 0.773605i \(-0.281548\pi\)
0.633669 + 0.773605i \(0.281548\pi\)
\(620\) 668.618i 1.07842i
\(621\) −91.9313 + 25.1792i −0.148038 + 0.0405462i
\(622\) 376.699 0.605625
\(623\) 1067.75i 1.71388i
\(624\) 1148.78 807.549i 1.84100 1.29415i
\(625\) 433.379 0.693407
\(626\) 870.460i 1.39051i
\(627\) −130.461 185.588i −0.208073 0.295994i
\(628\) −2002.83 −3.18921
\(629\) 1211.22i 1.92563i
\(630\) 145.900 405.508i 0.231588 0.643664i
\(631\) 969.299 1.53613 0.768066 0.640371i \(-0.221219\pi\)
0.768066 + 0.640371i \(0.221219\pi\)
\(632\) 3029.77i 4.79394i
\(633\) −730.742 + 513.683i −1.15441 + 0.811506i
\(634\) −1723.53 −2.71851
\(635\) 108.339i 0.170613i
\(636\) 177.103 + 251.939i 0.278464 + 0.396130i
\(637\) 111.476 0.175002
\(638\) 65.0215i 0.101915i
\(639\) −1011.84 364.057i −1.58348 0.569730i
\(640\) 291.350 0.455234
\(641\) 690.806i 1.07770i 0.842402 + 0.538850i \(0.181141\pi\)
−0.842402 + 0.538850i \(0.818859\pi\)
\(642\) −84.8943 + 59.6774i −0.132234 + 0.0929555i
\(643\) −237.937 −0.370043 −0.185021 0.982735i \(-0.559235\pi\)
−0.185021 + 0.982735i \(0.559235\pi\)
\(644\) 282.705i 0.438983i
\(645\) 151.540 + 215.574i 0.234946 + 0.334223i
\(646\) 2867.79 4.43931
\(647\) 509.640i 0.787698i −0.919175 0.393849i \(-0.871143\pi\)
0.919175 0.393849i \(-0.128857\pi\)
\(648\) 1226.48 1483.77i 1.89272 2.28977i
\(649\) −20.9605 −0.0322966
\(650\) 812.313i 1.24971i
\(651\) −762.974 + 536.341i −1.17200 + 0.823873i
\(652\) −282.942 −0.433961
\(653\) 529.277i 0.810531i 0.914199 + 0.405265i \(0.132821\pi\)
−0.914199 + 0.405265i \(0.867179\pi\)
\(654\) −264.081 375.669i −0.403793 0.574418i
\(655\) 107.869 0.164686
\(656\) 2440.27i 3.71992i
\(657\) 50.0843 139.202i 0.0762318 0.211875i
\(658\) −1383.36 −2.10238
\(659\) 132.453i 0.200991i −0.994938 0.100495i \(-0.967957\pi\)
0.994938 0.100495i \(-0.0320427\pi\)
\(660\) −112.126 + 78.8204i −0.169888 + 0.119425i
\(661\) 310.745 0.470114 0.235057 0.971982i \(-0.424472\pi\)
0.235057 + 0.971982i \(0.424472\pi\)
\(662\) 2188.33i 3.30564i
\(663\) −454.161 646.069i −0.685010 0.974463i
\(664\) −2981.66 −4.49045
\(665\) 351.047i 0.527890i
\(666\) −1416.10 509.506i −2.12627 0.765025i
\(667\) −22.2541 −0.0333645
\(668\) 863.246i 1.29228i
\(669\) −730.381 + 513.429i −1.09175 + 0.767458i
\(670\) −534.232 −0.797361
\(671\) 195.368i 0.291160i
\(672\) 1194.60 + 1699.39i 1.77768 + 2.52885i
\(673\) −722.988 −1.07428 −0.537138 0.843494i \(-0.680495\pi\)
−0.537138 + 0.843494i \(0.680495\pi\)
\(674\) 609.627i 0.904491i
\(675\) −159.420 582.054i −0.236177 0.862303i
\(676\) 787.579 1.16506
\(677\) 619.452i 0.914995i −0.889211 0.457498i \(-0.848746\pi\)
0.889211 0.457498i \(-0.151254\pi\)
\(678\) 1077.51 757.445i 1.58924 1.11718i
\(679\) −0.498700 −0.000734463
\(680\) 1058.94i 1.55727i
\(681\) 115.271 + 163.979i 0.169267 + 0.240791i
\(682\) 411.931 0.604005
\(683\) 329.882i 0.482989i −0.970402 0.241495i \(-0.922362\pi\)
0.970402 0.241495i \(-0.0776376\pi\)
\(684\) 868.615 2414.18i 1.26991 3.52951i
\(685\) 79.9128 0.116661
\(686\) 1100.61i 1.60438i
\(687\) 227.332 159.806i 0.330906 0.232614i
\(688\) −2627.56 −3.81912
\(689\) 95.9397i 0.139245i
\(690\) 37.4660 + 53.2975i 0.0542986 + 0.0772427i
\(691\) 1065.98 1.54266 0.771331 0.636435i \(-0.219591\pi\)
0.771331 + 0.636435i \(0.219591\pi\)
\(692\) 2440.34i 3.52650i
\(693\) −179.887 64.7227i −0.259577 0.0933950i
\(694\) 1257.50 1.81195
\(695\) 370.703i 0.533386i
\(696\) 367.692 258.473i 0.528293 0.371369i
\(697\) −1372.40 −1.96900
\(698\) 510.546i 0.731441i
\(699\) 54.3490 + 77.3144i 0.0777525 + 0.110607i
\(700\) 1789.92 2.55703
\(701\) 716.616i 1.02228i 0.859498 + 0.511138i \(0.170776\pi\)
−0.859498 + 0.511138i \(0.829224\pi\)
\(702\) −946.394 + 259.209i −1.34814 + 0.369244i
\(703\) −1225.91 −1.74382
\(704\) 386.114i 0.548457i
\(705\) 187.786 132.006i 0.266363 0.187243i
\(706\) −1084.50 −1.53612
\(707\) 1025.83i 1.45096i
\(708\) −136.330 193.937i −0.192556 0.273922i
\(709\) −271.634 −0.383123 −0.191561 0.981481i \(-0.561355\pi\)
−0.191561 + 0.981481i \(0.561355\pi\)
\(710\) 734.987i 1.03519i
\(711\) 388.434 1079.59i 0.546321 1.51842i
\(712\) −3259.94 −4.57856
\(713\) 140.987i 0.197737i
\(714\) 1977.13 1389.85i 2.76909 1.94656i
\(715\) 42.6983 0.0597179
\(716\) 2333.75i 3.25943i
\(717\) −359.959 512.062i −0.502035 0.714172i
\(718\) −1421.79 −1.98021
\(719\) 810.340i 1.12704i 0.826103 + 0.563519i \(0.190553\pi\)
−0.826103 + 0.563519i \(0.809447\pi\)
\(720\) −670.938 241.401i −0.931858 0.335279i
\(721\) −432.595 −0.599993
\(722\) 1538.02i 2.13023i
\(723\) 903.403 635.057i 1.24952 0.878364i
\(724\) 1116.60 1.54227
\(725\) 140.900i 0.194345i
\(726\) −740.515 1053.42i −1.01999 1.45099i
\(727\) 1389.13 1.91078 0.955388 0.295354i \(-0.0954375\pi\)
0.955388 + 0.295354i \(0.0954375\pi\)
\(728\) 1778.73i 2.44332i
\(729\) −627.258 + 371.467i −0.860437 + 0.509557i
\(730\) −101.114 −0.138513
\(731\) 1477.72i 2.02151i
\(732\) 1807.64 1270.70i 2.46945 1.73593i
\(733\) 426.964 0.582489 0.291244 0.956649i \(-0.405931\pi\)
0.291244 + 0.956649i \(0.405931\pi\)
\(734\) 855.541i 1.16559i
\(735\) −32.5534 46.3090i −0.0442903 0.0630054i
\(736\) −314.022 −0.426661
\(737\) 236.990i 0.321560i
\(738\) −577.305 + 1604.53i −0.782255 + 2.17416i
\(739\) −637.653 −0.862859 −0.431430 0.902147i \(-0.641991\pi\)
−0.431430 + 0.902147i \(0.641991\pi\)
\(740\) 740.651i 1.00088i
\(741\) −653.902 + 459.668i −0.882459 + 0.620334i
\(742\) 293.599 0.395686
\(743\) 824.103i 1.10916i 0.832132 + 0.554578i \(0.187120\pi\)
−0.832132 + 0.554578i \(0.812880\pi\)
\(744\) 1637.51 + 2329.44i 2.20095 + 3.13097i
\(745\) 38.0174 0.0510300
\(746\) 19.7919i 0.0265307i
\(747\) 1062.45 + 382.266i 1.42229 + 0.511734i
\(748\) −768.607 −1.02755
\(749\) 71.2349i 0.0951066i
\(750\) −714.880 + 502.533i −0.953173 + 0.670044i
\(751\) 313.749 0.417775 0.208888 0.977940i \(-0.433016\pi\)
0.208888 + 0.977940i \(0.433016\pi\)
\(752\) 2288.86i 3.04370i
\(753\) 453.396 + 644.980i 0.602119 + 0.856547i
\(754\) −229.097 −0.303842
\(755\) 217.579i 0.288184i
\(756\) −571.164 2085.37i −0.755508 2.75842i
\(757\) −681.004 −0.899608 −0.449804 0.893127i \(-0.648506\pi\)
−0.449804 + 0.893127i \(0.648506\pi\)
\(758\) 377.601i 0.498155i
\(759\) 23.6432 16.6203i 0.0311505 0.0218976i
\(760\) −1071.78 −1.41024
\(761\) 1057.16i 1.38918i −0.719408 0.694588i \(-0.755587\pi\)
0.719408 0.694588i \(-0.244413\pi\)
\(762\) 434.132 + 617.576i 0.569727 + 0.810468i
\(763\) −315.224 −0.413138
\(764\) 1.04833i 0.00137215i
\(765\) −135.763 + 377.332i −0.177468 + 0.493244i
\(766\) 1989.18 2.59685
\(767\) 73.8522i 0.0962871i
\(768\) 271.742 191.024i 0.353830 0.248729i
\(769\) −50.4233 −0.0655700 −0.0327850 0.999462i \(-0.510438\pi\)
−0.0327850 + 0.999462i \(0.510438\pi\)
\(770\) 130.667i 0.169698i
\(771\) 148.936 + 211.870i 0.193173 + 0.274799i
\(772\) 1673.98 2.16837
\(773\) 750.635i 0.971068i 0.874218 + 0.485534i \(0.161375\pi\)
−0.874218 + 0.485534i \(0.838625\pi\)
\(774\) 1727.68 + 621.612i 2.23214 + 0.803116i
\(775\) 892.643 1.15180
\(776\) 1.52258i 0.00196209i
\(777\) −845.173 + 594.123i −1.08774 + 0.764638i
\(778\) −48.6480 −0.0625295
\(779\) 1389.03i 1.78310i
\(780\) 277.716 + 395.065i 0.356046 + 0.506494i
\(781\) 326.047 0.417474
\(782\) 365.345i 0.467193i
\(783\) −164.157 + 44.9611i −0.209651 + 0.0574216i
\(784\) 564.444 0.719954
\(785\) 316.833i 0.403608i
\(786\) 614.898 432.249i