Properties

Label 108.3.f.c.19.2
Level 108
Weight 3
Character 108.19
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(-1.26364 + 1.55023i\) of \(x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + 28672 x^{2} - 49152 x + 65536\)
Character \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})\) \(q+(-1.26364 + 1.55023i) q^{2} +(-0.806428 - 3.91787i) q^{4} +(-1.35609 - 2.34881i) q^{5} +(10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(8.54822 + 4.93532i) q^{11} +(0.296185 + 0.513008i) q^{13} +(-21.6796 + 8.24203i) q^{14} +(-14.6993 + 6.31895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-8.10875 + 7.20712i) q^{20} +(-18.4528 + 7.01525i) q^{22} +(18.2754 - 10.5513i) q^{23} +(8.82205 - 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 + 17.6260i) q^{29} +(14.3357 - 8.27670i) q^{31} +(8.77885 - 30.7723i) q^{32} +(-11.2207 + 13.7655i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(-21.8565 - 17.8159i) q^{38} +(-0.926156 - 21.6776i) q^{40} +(-21.2177 - 36.7502i) q^{41} +(-32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(-1.57134 - 0.907211i) q^{47} +(42.7423 + 74.0318i) q^{49} +(12.5400 + 32.9849i) q^{50} +(1.77105 - 1.57412i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(49.7742 + 78.2914i) q^{56} +(-14.4651 - 38.0487i) q^{58} +(-76.6879 + 44.2758i) q^{59} +(36.4925 - 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 - 1.39137i) q^{65} +(-38.3110 + 22.1189i) q^{67} +(-7.16082 - 34.7894i) q^{68} +(48.7585 + 39.7446i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(51.3742 - 63.0257i) q^{74} +(55.2375 - 11.3697i) q^{76} +(57.2337 + 99.1316i) q^{77} +(-8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(-73.6244 - 42.5070i) q^{83} +(-12.0416 - 20.8567i) q^{85} +(69.5921 - 26.4571i) q^{86} +(42.3656 + 66.6381i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(-56.0765 - 63.0918i) q^{92} +(3.39199 - 1.28954i) q^{94} +(33.1157 - 19.1193i) q^{95} +(-3.59139 + 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.26364 + 1.55023i −0.631820 + 0.775115i
\(3\) 0 0
\(4\) −0.806428 3.91787i −0.201607 0.979467i
\(5\) −1.35609 2.34881i −0.271218 0.469763i 0.697956 0.716140i \(-0.254093\pi\)
−0.969174 + 0.246378i \(0.920760\pi\)
\(6\) 0 0
\(7\) 10.0431 + 5.79837i 1.43473 + 0.828339i 0.997476 0.0710013i \(-0.0226195\pi\)
0.437249 + 0.899340i \(0.355953\pi\)
\(8\) 7.09263 + 3.70062i 0.886579 + 0.462578i
\(9\) 0 0
\(10\) 5.35481 + 0.865806i 0.535481 + 0.0865806i
\(11\) 8.54822 + 4.93532i 0.777111 + 0.448665i 0.835406 0.549634i \(-0.185233\pi\)
−0.0582943 + 0.998299i \(0.518566\pi\)
\(12\) 0 0
\(13\) 0.296185 + 0.513008i 0.0227835 + 0.0394622i 0.877192 0.480139i \(-0.159414\pi\)
−0.854409 + 0.519601i \(0.826080\pi\)
\(14\) −21.6796 + 8.24203i −1.54855 + 0.588716i
\(15\) 0 0
\(16\) −14.6993 + 6.31895i −0.918709 + 0.394935i
\(17\) 8.87968 0.522334 0.261167 0.965294i \(-0.415893\pi\)
0.261167 + 0.965294i \(0.415893\pi\)
\(18\) 0 0
\(19\) 14.0989i 0.742046i 0.928624 + 0.371023i \(0.120993\pi\)
−0.928624 + 0.371023i \(0.879007\pi\)
\(20\) −8.10875 + 7.20712i −0.405438 + 0.360356i
\(21\) 0 0
\(22\) −18.4528 + 7.01525i −0.838762 + 0.318875i
\(23\) 18.2754 10.5513i 0.794583 0.458753i −0.0469902 0.998895i \(-0.514963\pi\)
0.841574 + 0.540142i \(0.181630\pi\)
\(24\) 0 0
\(25\) 8.82205 15.2802i 0.352882 0.611209i
\(26\) −1.16955 0.189102i −0.0449828 0.00727316i
\(27\) 0 0
\(28\) 14.6182 44.0234i 0.522080 1.57226i
\(29\) −10.1764 + 17.6260i −0.350910 + 0.607793i −0.986409 0.164308i \(-0.947461\pi\)
0.635499 + 0.772101i \(0.280794\pi\)
\(30\) 0 0
\(31\) 14.3357 8.27670i 0.462441 0.266990i −0.250629 0.968083i \(-0.580638\pi\)
0.713070 + 0.701093i \(0.247304\pi\)
\(32\) 8.77885 30.7723i 0.274339 0.961633i
\(33\) 0 0
\(34\) −11.2207 + 13.7655i −0.330021 + 0.404869i
\(35\) 31.4524i 0.898641i
\(36\) 0 0
\(37\) −40.6557 −1.09880 −0.549401 0.835559i \(-0.685144\pi\)
−0.549401 + 0.835559i \(0.685144\pi\)
\(38\) −21.8565 17.8159i −0.575171 0.468840i
\(39\) 0 0
\(40\) −0.926156 21.6776i −0.0231539 0.541941i
\(41\) −21.2177 36.7502i −0.517506 0.896346i −0.999793 0.0203330i \(-0.993527\pi\)
0.482288 0.876013i \(-0.339806\pi\)
\(42\) 0 0
\(43\) −32.2385 18.6129i −0.749732 0.432858i 0.0758649 0.997118i \(-0.475828\pi\)
−0.825597 + 0.564260i \(0.809162\pi\)
\(44\) 12.4424 37.4708i 0.282782 0.851609i
\(45\) 0 0
\(46\) −6.73658 + 41.6642i −0.146447 + 0.905743i
\(47\) −1.57134 0.907211i −0.0334327 0.0193024i 0.483191 0.875515i \(-0.339478\pi\)
−0.516623 + 0.856213i \(0.672811\pi\)
\(48\) 0 0
\(49\) 42.7423 + 74.0318i 0.872291 + 1.51085i
\(50\) 12.5400 + 32.9849i 0.250800 + 0.659698i
\(51\) 0 0
\(52\) 1.77105 1.57412i 0.0340586 0.0302715i
\(53\) 21.1005 0.398122 0.199061 0.979987i \(-0.436211\pi\)
0.199061 + 0.979987i \(0.436211\pi\)
\(54\) 0 0
\(55\) 26.7709i 0.486744i
\(56\) 49.7742 + 78.2914i 0.888826 + 1.39806i
\(57\) 0 0
\(58\) −14.4651 38.0487i −0.249398 0.656011i
\(59\) −76.6879 + 44.2758i −1.29980 + 0.750437i −0.980369 0.197174i \(-0.936824\pi\)
−0.319427 + 0.947611i \(0.603490\pi\)
\(60\) 0 0
\(61\) 36.4925 63.2069i 0.598238 1.03618i −0.394843 0.918749i \(-0.629201\pi\)
0.993081 0.117431i \(-0.0374657\pi\)
\(62\) −5.28433 + 32.6823i −0.0852311 + 0.527134i
\(63\) 0 0
\(64\) 36.6108 + 52.4943i 0.572043 + 0.820223i
\(65\) 0.803307 1.39137i 0.0123586 0.0214057i
\(66\) 0 0
\(67\) −38.3110 + 22.1189i −0.571807 + 0.330133i −0.757871 0.652405i \(-0.773760\pi\)
0.186064 + 0.982538i \(0.440427\pi\)
\(68\) −7.16082 34.7894i −0.105306 0.511609i
\(69\) 0 0
\(70\) 48.7585 + 39.7446i 0.696550 + 0.567779i
\(71\) 111.798i 1.57462i 0.616557 + 0.787310i \(0.288527\pi\)
−0.616557 + 0.787310i \(0.711473\pi\)
\(72\) 0 0
\(73\) −76.2003 −1.04384 −0.521920 0.852995i \(-0.674784\pi\)
−0.521920 + 0.852995i \(0.674784\pi\)
\(74\) 51.3742 63.0257i 0.694246 0.851699i
\(75\) 0 0
\(76\) 55.2375 11.3697i 0.726810 0.149602i
\(77\) 57.2337 + 99.1316i 0.743294 + 1.28742i
\(78\) 0 0
\(79\) −8.30434 4.79451i −0.105118 0.0606901i 0.446519 0.894774i \(-0.352663\pi\)
−0.551637 + 0.834084i \(0.685997\pi\)
\(80\) 34.7757 + 25.9570i 0.434696 + 0.324462i
\(81\) 0 0
\(82\) 83.7828 + 13.5466i 1.02174 + 0.165203i
\(83\) −73.6244 42.5070i −0.887041 0.512133i −0.0140672 0.999901i \(-0.504478\pi\)
−0.872973 + 0.487768i \(0.837811\pi\)
\(84\) 0 0
\(85\) −12.0416 20.8567i −0.141666 0.245373i
\(86\) 69.5921 26.4571i 0.809211 0.307640i
\(87\) 0 0
\(88\) 42.3656 + 66.6381i 0.481428 + 0.757252i
\(89\) −64.7845 −0.727916 −0.363958 0.931415i \(-0.618575\pi\)
−0.363958 + 0.931415i \(0.618575\pi\)
\(90\) 0 0
\(91\) 6.86958i 0.0754898i
\(92\) −56.0765 63.0918i −0.609527 0.685780i
\(93\) 0 0
\(94\) 3.39199 1.28954i 0.0360850 0.0137186i
\(95\) 33.1157 19.1193i 0.348586 0.201256i
\(96\) 0 0
\(97\) −3.59139 + 6.22047i −0.0370246 + 0.0641285i −0.883944 0.467593i \(-0.845121\pi\)
0.846919 + 0.531721i \(0.178455\pi\)
\(98\) −168.777 27.2892i −1.72222 0.278461i
\(99\) 0 0
\(100\) −66.9803 22.2412i −0.669803 0.222412i
\(101\) 55.5037 96.1353i 0.549542 0.951834i −0.448764 0.893650i \(-0.648136\pi\)
0.998306 0.0581840i \(-0.0185310\pi\)
\(102\) 0 0
\(103\) 79.6133 45.9648i 0.772945 0.446260i −0.0609793 0.998139i \(-0.519422\pi\)
0.833924 + 0.551879i \(0.186089\pi\)
\(104\) 0.202283 + 4.73465i 0.00194503 + 0.0455255i
\(105\) 0 0
\(106\) −26.6634 + 32.7106i −0.251541 + 0.308590i
\(107\) 107.741i 1.00693i −0.864016 0.503465i \(-0.832058\pi\)
0.864016 0.503465i \(-0.167942\pi\)
\(108\) 0 0
\(109\) 86.5562 0.794093 0.397047 0.917798i \(-0.370035\pi\)
0.397047 + 0.917798i \(0.370035\pi\)
\(110\) 41.5011 + 33.8288i 0.377283 + 0.307535i
\(111\) 0 0
\(112\) −184.266 21.7706i −1.64524 0.194380i
\(113\) 2.35198 + 4.07376i 0.0208140 + 0.0360509i 0.876245 0.481866i \(-0.160041\pi\)
−0.855431 + 0.517917i \(0.826708\pi\)
\(114\) 0 0
\(115\) −49.5662 28.6170i −0.431010 0.248844i
\(116\) 77.2628 + 25.6556i 0.666059 + 0.221169i
\(117\) 0 0
\(118\) 28.2682 174.833i 0.239561 1.48163i
\(119\) 89.1793 + 51.4877i 0.749406 + 0.432670i
\(120\) 0 0
\(121\) −11.7852 20.4126i −0.0973987 0.168700i
\(122\) 51.8719 + 136.443i 0.425179 + 1.11838i
\(123\) 0 0
\(124\) −43.9877 49.4906i −0.354739 0.399118i
\(125\) −115.658 −0.925267
\(126\) 0 0
\(127\) 8.37118i 0.0659148i 0.999457 + 0.0329574i \(0.0104926\pi\)
−0.999457 + 0.0329574i \(0.989507\pi\)
\(128\) −127.641 9.57876i −0.997196 0.0748341i
\(129\) 0 0
\(130\) 1.14185 + 3.00350i 0.00878347 + 0.0231039i
\(131\) 115.067 66.4338i 0.878372 0.507129i 0.00825098 0.999966i \(-0.497374\pi\)
0.870121 + 0.492837i \(0.164040\pi\)
\(132\) 0 0
\(133\) −81.7506 + 141.596i −0.614666 + 1.06463i
\(134\) 14.1220 87.3413i 0.105388 0.651800i
\(135\) 0 0
\(136\) 62.9803 + 32.8603i 0.463090 + 0.241620i
\(137\) −22.5579 + 39.0715i −0.164656 + 0.285193i −0.936533 0.350579i \(-0.885985\pi\)
0.771877 + 0.635772i \(0.219318\pi\)
\(138\) 0 0
\(139\) −130.744 + 75.4848i −0.940601 + 0.543056i −0.890149 0.455670i \(-0.849400\pi\)
−0.0504522 + 0.998726i \(0.516066\pi\)
\(140\) −123.226 + 25.3641i −0.880189 + 0.181172i
\(141\) 0 0
\(142\) −173.313 141.273i −1.22051 0.994877i
\(143\) 5.84708i 0.0408887i
\(144\) 0 0
\(145\) 55.2003 0.380692
\(146\) 96.2897 118.128i 0.659519 0.809096i
\(147\) 0 0
\(148\) 32.7859 + 159.284i 0.221526 + 1.07624i
\(149\) −71.3914 123.653i −0.479137 0.829889i 0.520577 0.853815i \(-0.325717\pi\)
−0.999714 + 0.0239255i \(0.992384\pi\)
\(150\) 0 0
\(151\) 220.027 + 127.033i 1.45713 + 0.841276i 0.998869 0.0475407i \(-0.0151384\pi\)
0.458263 + 0.888817i \(0.348472\pi\)
\(152\) −52.1746 + 99.9981i −0.343254 + 0.657882i
\(153\) 0 0
\(154\) −226.000 36.5413i −1.46753 0.237281i
\(155\) −38.8808 22.4479i −0.250844 0.144825i
\(156\) 0 0
\(157\) 2.65361 + 4.59618i 0.0169020 + 0.0292751i 0.874353 0.485291i \(-0.161286\pi\)
−0.857451 + 0.514566i \(0.827953\pi\)
\(158\) 17.9263 6.81510i 0.113458 0.0431336i
\(159\) 0 0
\(160\) −84.1832 + 21.1100i −0.526145 + 0.131938i
\(161\) 244.722 1.52001
\(162\) 0 0
\(163\) 59.5534i 0.365359i 0.983173 + 0.182679i \(0.0584770\pi\)
−0.983173 + 0.182679i \(0.941523\pi\)
\(164\) −126.872 + 112.765i −0.773608 + 0.687589i
\(165\) 0 0
\(166\) 158.930 60.4211i 0.957412 0.363983i
\(167\) 85.7434 49.5040i 0.513434 0.296431i −0.220810 0.975317i \(-0.570870\pi\)
0.734244 + 0.678886i \(0.237537\pi\)
\(168\) 0 0
\(169\) 84.3245 146.054i 0.498962 0.864227i
\(170\) 47.5490 + 7.68808i 0.279700 + 0.0452240i
\(171\) 0 0
\(172\) −46.9248 + 141.316i −0.272819 + 0.821605i
\(173\) −19.2965 + 33.4225i −0.111540 + 0.193193i −0.916391 0.400283i \(-0.868912\pi\)
0.804851 + 0.593477i \(0.202245\pi\)
\(174\) 0 0
\(175\) 177.201 102.307i 1.01258 0.584612i
\(176\) −156.839 18.5302i −0.891133 0.105285i
\(177\) 0 0
\(178\) 81.8643 100.431i 0.459912 0.564219i
\(179\) 36.4264i 0.203499i −0.994810 0.101750i \(-0.967556\pi\)
0.994810 0.101750i \(-0.0324441\pi\)
\(180\) 0 0
\(181\) −18.5921 −0.102719 −0.0513594 0.998680i \(-0.516355\pi\)
−0.0513594 + 0.998680i \(0.516355\pi\)
\(182\) −10.6494 8.68067i −0.0585133 0.0476960i
\(183\) 0 0
\(184\) 168.667 7.20614i 0.916670 0.0391638i
\(185\) 55.1327 + 95.4927i 0.298015 + 0.516177i
\(186\) 0 0
\(187\) 75.9055 + 43.8240i 0.405912 + 0.234353i
\(188\) −2.28716 + 6.88788i −0.0121658 + 0.0366377i
\(189\) 0 0
\(190\) −12.2069 + 75.4968i −0.0642468 + 0.397352i
\(191\) 244.973 + 141.435i 1.28258 + 0.740497i 0.977319 0.211772i \(-0.0679233\pi\)
0.305260 + 0.952269i \(0.401257\pi\)
\(192\) 0 0
\(193\) −151.542 262.479i −0.785193 1.35999i −0.928884 0.370372i \(-0.879230\pi\)
0.143691 0.989623i \(-0.454103\pi\)
\(194\) −5.10493 13.4279i −0.0263141 0.0692160i
\(195\) 0 0
\(196\) 255.578 227.160i 1.30397 1.15898i
\(197\) −139.184 −0.706520 −0.353260 0.935525i \(-0.614927\pi\)
−0.353260 + 0.935525i \(0.614927\pi\)
\(198\) 0 0
\(199\) 11.2337i 0.0564505i 0.999602 + 0.0282253i \(0.00898558\pi\)
−0.999602 + 0.0282253i \(0.991014\pi\)
\(200\) 119.118 75.7300i 0.595590 0.378650i
\(201\) 0 0
\(202\) 78.8951 + 207.524i 0.390570 + 1.02735i
\(203\) −204.404 + 118.013i −1.00692 + 0.581344i
\(204\) 0 0
\(205\) −57.5462 + 99.6730i −0.280713 + 0.486210i
\(206\) −29.3466 + 181.502i −0.142459 + 0.881077i
\(207\) 0 0
\(208\) −7.59541 5.66930i −0.0365164 0.0272563i
\(209\) −69.5825 + 120.520i −0.332931 + 0.576653i
\(210\) 0 0
\(211\) −112.017 + 64.6728i −0.530884 + 0.306506i −0.741376 0.671090i \(-0.765827\pi\)
0.210492 + 0.977595i \(0.432493\pi\)
\(212\) −17.0160 82.6687i −0.0802641 0.389947i
\(213\) 0 0
\(214\) 167.024 + 136.146i 0.780486 + 0.636198i
\(215\) 100.963i 0.469595i
\(216\) 0 0
\(217\) 191.966 0.884634
\(218\) −109.376 + 134.182i −0.501724 + 0.615514i
\(219\) 0 0
\(220\) −104.885 + 21.5888i −0.476749 + 0.0981310i
\(221\) 2.63003 + 4.55535i 0.0119006 + 0.0206124i
\(222\) 0 0
\(223\) −209.210 120.787i −0.938159 0.541647i −0.0487765 0.998810i \(-0.515532\pi\)
−0.889383 + 0.457163i \(0.848866\pi\)
\(224\) 266.596 258.145i 1.19016 1.15243i
\(225\) 0 0
\(226\) −9.28732 1.50164i −0.0410943 0.00664444i
\(227\) −330.710 190.936i −1.45687 0.841126i −0.458016 0.888944i \(-0.651440\pi\)
−0.998856 + 0.0478181i \(0.984773\pi\)
\(228\) 0 0
\(229\) 74.6642 + 129.322i 0.326044 + 0.564725i 0.981723 0.190315i \(-0.0609508\pi\)
−0.655679 + 0.755040i \(0.727617\pi\)
\(230\) 106.997 40.6773i 0.465204 0.176858i
\(231\) 0 0
\(232\) −137.404 + 87.3558i −0.592261 + 0.376534i
\(233\) 218.934 0.939631 0.469816 0.882765i \(-0.344320\pi\)
0.469816 + 0.882765i \(0.344320\pi\)
\(234\) 0 0
\(235\) 4.92103i 0.0209406i
\(236\) 235.310 + 264.748i 0.997076 + 1.12181i
\(237\) 0 0
\(238\) −192.508 + 73.1865i −0.808858 + 0.307506i
\(239\) −218.254 + 126.009i −0.913197 + 0.527235i −0.881458 0.472262i \(-0.843438\pi\)
−0.0317388 + 0.999496i \(0.510104\pi\)
\(240\) 0 0
\(241\) −226.014 + 391.467i −0.937816 + 1.62435i −0.168282 + 0.985739i \(0.553822\pi\)
−0.769534 + 0.638606i \(0.779511\pi\)
\(242\) 46.5366 + 7.52439i 0.192300 + 0.0310925i
\(243\) 0 0
\(244\) −277.065 92.0011i −1.13551 0.377053i
\(245\) 115.925 200.787i 0.473162 0.819540i
\(246\) 0 0
\(247\) −7.23284 + 4.17588i −0.0292828 + 0.0169064i
\(248\) 132.306 5.65266i 0.533494 0.0227930i
\(249\) 0 0
\(250\) 146.151 179.297i 0.584602 0.717188i
\(251\) 139.429i 0.555492i 0.960655 + 0.277746i \(0.0895874\pi\)
−0.960655 + 0.277746i \(0.910413\pi\)
\(252\) 0 0
\(253\) 208.297 0.823306
\(254\) −12.9773 10.5782i −0.0510916 0.0416463i
\(255\) 0 0
\(256\) 176.142 185.769i 0.688053 0.725660i
\(257\) −235.308 407.565i −0.915594 1.58586i −0.806029 0.591875i \(-0.798388\pi\)
−0.109564 0.993980i \(-0.534946\pi\)
\(258\) 0 0
\(259\) −408.308 235.737i −1.57648 0.910181i
\(260\) −6.09901 2.02521i −0.0234577 0.00778928i
\(261\) 0 0
\(262\) −42.4152 + 262.328i −0.161890 + 1.00125i
\(263\) −22.2028 12.8188i −0.0844214 0.0487407i 0.457195 0.889366i \(-0.348854\pi\)
−0.541616 + 0.840626i \(0.682187\pi\)
\(264\) 0 0
\(265\) −28.6141 49.5610i −0.107978 0.187023i
\(266\) −116.203 305.659i −0.436855 1.14909i
\(267\) 0 0
\(268\) 117.554 + 132.260i 0.438634 + 0.493508i
\(269\) −8.15075 −0.0303002 −0.0151501 0.999885i \(-0.504823\pi\)
−0.0151501 + 0.999885i \(0.504823\pi\)
\(270\) 0 0
\(271\) 401.979i 1.48332i −0.670777 0.741659i \(-0.734039\pi\)
0.670777 0.741659i \(-0.265961\pi\)
\(272\) −130.525 + 56.1103i −0.479873 + 0.206288i
\(273\) 0 0
\(274\) −32.0647 84.3423i −0.117024 0.307819i
\(275\) 150.826 87.0792i 0.548457 0.316652i
\(276\) 0 0
\(277\) 56.2021 97.3449i 0.202896 0.351426i −0.746565 0.665313i \(-0.768298\pi\)
0.949460 + 0.313887i \(0.101631\pi\)
\(278\) 48.1939 298.068i 0.173359 1.07219i
\(279\) 0 0
\(280\) 116.394 223.080i 0.415691 0.796716i
\(281\) −268.867 + 465.692i −0.956823 + 1.65727i −0.226681 + 0.973969i \(0.572788\pi\)
−0.730141 + 0.683296i \(0.760546\pi\)
\(282\) 0 0
\(283\) −122.303 + 70.6114i −0.432164 + 0.249510i −0.700268 0.713880i \(-0.746936\pi\)
0.268104 + 0.963390i \(0.413603\pi\)
\(284\) 438.010 90.1571i 1.54229 0.317454i
\(285\) 0 0
\(286\) −9.06432 7.38860i −0.0316934 0.0258343i
\(287\) 492.113i 1.71468i
\(288\) 0 0
\(289\) −210.151 −0.727167
\(290\) −69.7533 + 85.5732i −0.240529 + 0.295080i
\(291\) 0 0
\(292\) 61.4500 + 298.543i 0.210445 + 1.02241i
\(293\) 230.291 + 398.875i 0.785975 + 1.36135i 0.928415 + 0.371545i \(0.121172\pi\)
−0.142440 + 0.989803i \(0.545495\pi\)
\(294\) 0 0
\(295\) 207.991 + 120.084i 0.705055 + 0.407064i
\(296\) −288.356 150.451i −0.974175 0.508282i
\(297\) 0 0
\(298\) 281.904 + 45.5804i 0.945988 + 0.152954i
\(299\) 10.8258 + 6.25029i 0.0362068 + 0.0209040i
\(300\) 0 0
\(301\) −215.849 373.862i −0.717107 1.24206i
\(302\) −474.965 + 180.569i −1.57273 + 0.597911i
\(303\) 0 0
\(304\) −89.0902 207.244i −0.293060 0.681725i
\(305\) −197.948 −0.649011
\(306\) 0 0
\(307\) 210.322i 0.685089i −0.939502 0.342545i \(-0.888711\pi\)
0.939502 0.342545i \(-0.111289\pi\)
\(308\) 342.229 304.176i 1.11113 0.987585i
\(309\) 0 0
\(310\) 83.9308 31.9082i 0.270744 0.102930i
\(311\) −110.993 + 64.0821i −0.356892 + 0.206052i −0.667717 0.744416i \(-0.732728\pi\)
0.310824 + 0.950467i \(0.399395\pi\)
\(312\) 0 0
\(313\) −3.62140 + 6.27245i −0.0115700 + 0.0200398i −0.871752 0.489947i \(-0.837016\pi\)
0.860182 + 0.509986i \(0.170350\pi\)
\(314\) −10.4784 1.69422i −0.0333705 0.00539560i
\(315\) 0 0
\(316\) −12.0874 + 36.4017i −0.0382513 + 0.115195i
\(317\) 120.145 208.098i 0.379007 0.656460i −0.611911 0.790927i \(-0.709599\pi\)
0.990918 + 0.134467i \(0.0429322\pi\)
\(318\) 0 0
\(319\) −173.980 + 100.447i −0.545392 + 0.314882i
\(320\) 73.6519 157.179i 0.230162 0.491184i
\(321\) 0 0
\(322\) −309.240 + 379.375i −0.960374 + 1.17818i
\(323\) 125.194i 0.387596i
\(324\) 0 0
\(325\) 10.4518 0.0321595
\(326\) −92.3216 75.2541i −0.283195 0.230841i
\(327\) 0 0
\(328\) −14.4909 339.174i −0.0441795 1.03407i
\(329\) −10.5207 18.2224i −0.0319778 0.0553872i
\(330\) 0 0
\(331\) 370.385 + 213.842i 1.11899 + 0.646048i 0.941142 0.338011i \(-0.109754\pi\)
0.177845 + 0.984058i \(0.443087\pi\)
\(332\) −107.164 + 322.729i −0.322784 + 0.972076i
\(333\) 0 0
\(334\) −31.6062 + 195.477i −0.0946295 + 0.585261i
\(335\) 103.906 + 59.9904i 0.310168 + 0.179076i
\(336\) 0 0
\(337\) 152.442 + 264.037i 0.452349 + 0.783492i 0.998531 0.0541746i \(-0.0172528\pi\)
−0.546182 + 0.837666i \(0.683919\pi\)
\(338\) 119.862 + 315.283i 0.354622 + 0.932789i
\(339\) 0 0
\(340\) −72.0031 + 63.9969i −0.211774 + 0.188226i
\(341\) 163.393 0.479157
\(342\) 0 0
\(343\) 423.102i 1.23353i
\(344\) −159.776 251.317i −0.464466 0.730572i
\(345\) 0 0
\(346\) −27.4287 72.1480i −0.0792738 0.208520i
\(347\) 146.406 84.5276i 0.421919 0.243595i −0.273979 0.961736i \(-0.588340\pi\)
0.695898 + 0.718140i \(0.255006\pi\)
\(348\) 0 0
\(349\) 107.298 185.846i 0.307444 0.532509i −0.670358 0.742037i \(-0.733860\pi\)
0.977802 + 0.209529i \(0.0671930\pi\)
\(350\) −65.3188 + 403.982i −0.186625 + 1.15423i
\(351\) 0 0
\(352\) 226.915 219.722i 0.644644 0.624209i
\(353\) 275.895 477.865i 0.781574 1.35373i −0.149451 0.988769i \(-0.547751\pi\)
0.931025 0.364956i \(-0.118916\pi\)
\(354\) 0 0
\(355\) 262.593 151.608i 0.739698 0.427065i
\(356\) 52.2441 + 253.817i 0.146753 + 0.712970i
\(357\) 0 0
\(358\) 56.4693 + 46.0299i 0.157736 + 0.128575i
\(359\) 554.828i 1.54548i 0.634721 + 0.772741i \(0.281115\pi\)
−0.634721 + 0.772741i \(0.718885\pi\)
\(360\) 0 0
\(361\) 162.222 0.449367
\(362\) 23.4937 28.8220i 0.0648998 0.0796189i
\(363\) 0 0
\(364\) 26.9141 5.53982i 0.0739398 0.0152193i
\(365\) 103.334 + 178.980i 0.283108 + 0.490357i
\(366\) 0 0
\(367\) 145.642 + 84.0864i 0.396845 + 0.229118i 0.685122 0.728429i \(-0.259749\pi\)
−0.288277 + 0.957547i \(0.593082\pi\)
\(368\) −201.963 + 270.579i −0.548814 + 0.735269i
\(369\) 0 0
\(370\) −217.704 35.2000i −0.588388 0.0951350i
\(371\) 211.913 + 122.348i 0.571195 + 0.329780i
\(372\) 0 0
\(373\) 171.699 + 297.391i 0.460318 + 0.797295i 0.998977 0.0452296i \(-0.0144020\pi\)
−0.538658 + 0.842524i \(0.681069\pi\)
\(374\) −163.855 + 62.2931i −0.438114 + 0.166559i
\(375\) 0 0
\(376\) −7.78765 12.2494i −0.0207118 0.0325783i
\(377\) −12.0564 −0.0319798
\(378\) 0 0
\(379\) 602.392i 1.58943i 0.606986 + 0.794713i \(0.292379\pi\)
−0.606986 + 0.794713i \(0.707621\pi\)
\(380\) −101.612 114.324i −0.267401 0.300854i
\(381\) 0 0
\(382\) −528.814 + 201.041i −1.38433 + 0.526285i
\(383\) 315.762 182.305i 0.824443 0.475992i −0.0275035 0.999622i \(-0.508756\pi\)
0.851946 + 0.523630i \(0.175422\pi\)
\(384\) 0 0
\(385\) 155.228 268.862i 0.403189 0.698344i
\(386\) 598.398 + 96.7534i 1.55025 + 0.250657i
\(387\) 0 0
\(388\) 27.2672 + 9.05422i 0.0702762 + 0.0233356i
\(389\) −107.326 + 185.893i −0.275901 + 0.477875i −0.970362 0.241656i \(-0.922310\pi\)
0.694461 + 0.719530i \(0.255643\pi\)
\(390\) 0 0
\(391\) 162.280 93.6923i 0.415038 0.239622i
\(392\) 29.1913 + 683.253i 0.0744677 + 1.74299i
\(393\) 0 0
\(394\) 175.879 215.768i 0.446393 0.547634i
\(395\) 26.0071i 0.0658409i
\(396\) 0 0
\(397\) −684.628 −1.72450 −0.862251 0.506480i \(-0.830946\pi\)
−0.862251 + 0.506480i \(0.830946\pi\)
\(398\) −17.4148 14.1953i −0.0437557 0.0356666i
\(399\) 0 0
\(400\) −33.1233 + 280.356i −0.0828082 + 0.700889i
\(401\) −95.1918 164.877i −0.237386 0.411164i 0.722577 0.691290i \(-0.242957\pi\)
−0.959963 + 0.280125i \(0.909624\pi\)
\(402\) 0 0
\(403\) 8.49203 + 4.90287i 0.0210720 + 0.0121659i
\(404\) −421.405 139.930i −1.04308 0.346361i
\(405\) 0 0
\(406\) 75.3463 466.000i 0.185582 1.14778i
\(407\) −347.534 200.649i −0.853892 0.492995i
\(408\) 0 0
\(409\) 188.978 + 327.320i 0.462049 + 0.800293i 0.999063 0.0432806i \(-0.0137809\pi\)
−0.537014 + 0.843574i \(0.680448\pi\)
\(410\) −81.7984 215.161i −0.199508 0.524782i
\(411\) 0 0
\(412\) −244.286 274.847i −0.592928 0.667104i
\(413\) −1026.91 −2.48647
\(414\) 0 0
\(415\) 230.573i 0.555598i
\(416\) 18.3866 4.61067i 0.0441985 0.0110833i
\(417\) 0 0
\(418\) −98.9072 260.163i −0.236620 0.622400i
\(419\) 267.326 154.341i 0.638009 0.368355i −0.145838 0.989308i \(-0.546588\pi\)
0.783847 + 0.620954i \(0.213255\pi\)
\(420\) 0 0
\(421\) 176.834 306.286i 0.420034 0.727521i −0.575908 0.817514i \(-0.695351\pi\)
0.995942 + 0.0899938i \(0.0286847\pi\)
\(422\) 41.2909 255.374i 0.0978457 0.605153i
\(423\) 0 0
\(424\) 149.658 + 78.0848i 0.352966 + 0.184162i
\(425\) 78.3369 135.684i 0.184322 0.319255i
\(426\) 0 0
\(427\) 732.995 423.195i 1.71662 0.991088i
\(428\) −422.117 + 86.8857i −0.986254 + 0.203004i
\(429\) 0 0
\(430\) −156.516 127.581i −0.363990 0.296700i
\(431\) 472.777i 1.09693i −0.836174 0.548465i \(-0.815213\pi\)
0.836174 0.548465i \(-0.184787\pi\)
\(432\) 0 0
\(433\) 61.4188 0.141845 0.0709224 0.997482i \(-0.477406\pi\)
0.0709224 + 0.997482i \(0.477406\pi\)
\(434\) −242.575 + 297.591i −0.558929 + 0.685693i
\(435\) 0 0
\(436\) −69.8013 339.116i −0.160095 0.777788i
\(437\) 148.762 + 257.663i 0.340416 + 0.589618i
\(438\) 0 0
\(439\) −354.347 204.582i −0.807169 0.466019i 0.0388030 0.999247i \(-0.487646\pi\)
−0.845972 + 0.533228i \(0.820979\pi\)
\(440\) 99.0691 189.876i 0.225157 0.431537i
\(441\) 0 0
\(442\) −10.3853 1.67917i −0.0234960 0.00379902i
\(443\) 668.806 + 386.136i 1.50972 + 0.871638i 0.999936 + 0.0113360i \(0.00360844\pi\)
0.509785 + 0.860302i \(0.329725\pi\)
\(444\) 0 0
\(445\) 87.8536 + 152.167i 0.197424 + 0.341948i
\(446\) 451.613 171.691i 1.01259 0.384958i
\(447\) 0 0
\(448\) 63.3033 + 739.487i 0.141302 + 1.65064i
\(449\) 789.037 1.75732 0.878660 0.477448i \(-0.158438\pi\)
0.878660 + 0.477448i \(0.158438\pi\)
\(450\) 0 0
\(451\) 418.865i 0.928747i
\(452\) 14.0637 12.4999i 0.0311144 0.0276548i
\(453\) 0 0
\(454\) 713.892 271.403i 1.57245 0.597804i
\(455\) 16.1354 9.31575i 0.0354623 0.0204742i
\(456\) 0 0
\(457\) 138.165 239.309i 0.302331 0.523653i −0.674332 0.738428i \(-0.735568\pi\)
0.976664 + 0.214775i \(0.0689018\pi\)
\(458\) −294.828 47.6700i −0.643728 0.104083i
\(459\) 0 0
\(460\) −72.1462 + 217.271i −0.156840 + 0.472329i
\(461\) 294.041 509.295i 0.637834 1.10476i −0.348073 0.937467i \(-0.613164\pi\)
0.985907 0.167293i \(-0.0535027\pi\)
\(462\) 0 0
\(463\) −677.285 + 391.031i −1.46282 + 0.844558i −0.999141 0.0414459i \(-0.986804\pi\)
−0.463677 + 0.886004i \(0.653470\pi\)
\(464\) 38.2082 323.395i 0.0823454 0.696972i
\(465\) 0 0
\(466\) −276.654 + 339.398i −0.593678 + 0.728322i
\(467\) 663.203i 1.42014i −0.704133 0.710068i \(-0.748664\pi\)
0.704133 0.710068i \(-0.251336\pi\)
\(468\) 0 0
\(469\) −513.014 −1.09385
\(470\) −7.62874 6.21842i −0.0162314 0.0132307i
\(471\) 0 0
\(472\) −707.767 + 30.2387i −1.49951 + 0.0640649i
\(473\) −183.721 318.214i −0.388417 0.672758i
\(474\) 0 0
\(475\) 215.434 + 124.381i 0.453546 + 0.261855i
\(476\) 129.805 390.914i 0.272700 0.821247i
\(477\) 0 0
\(478\) 80.4516 497.574i 0.168309 1.04095i
\(479\) −562.018 324.481i −1.17331 0.677414i −0.218856 0.975757i \(-0.570233\pi\)
−0.954459 + 0.298344i \(0.903566\pi\)
\(480\) 0 0
\(481\) −12.0416 20.8567i −0.0250346 0.0433611i
\(482\) −321.264 845.047i −0.666524 1.75321i
\(483\) 0 0
\(484\) −70.4700 + 62.6343i −0.145599 + 0.129410i
\(485\) 19.4810 0.0401669
\(486\) 0 0
\(487\) 282.104i 0.579269i −0.957137 0.289635i \(-0.906466\pi\)
0.957137 0.289635i \(-0.0935338\pi\)
\(488\) 492.733 313.258i 1.00970 0.641923i
\(489\) 0 0
\(490\) 164.780 + 433.433i 0.336285 + 0.884557i
\(491\) −652.933 + 376.971i −1.32980 + 0.767762i −0.985269 0.171012i \(-0.945296\pi\)
−0.344534 + 0.938774i \(0.611963\pi\)
\(492\) 0 0
\(493\) −90.3630 + 156.513i −0.183292 + 0.317471i
\(494\) 2.66613 16.4894i 0.00539702 0.0333793i
\(495\) 0 0
\(496\) −158.425 + 212.248i −0.319405 + 0.427920i
\(497\) −648.247 + 1122.80i −1.30432 + 2.25915i
\(498\) 0 0
\(499\) −446.169 + 257.596i −0.894126 + 0.516224i −0.875290 0.483599i \(-0.839329\pi\)
−0.0188362 + 0.999823i \(0.505996\pi\)
\(500\) 93.2701 + 453.134i 0.186540 + 0.906268i
\(501\) 0 0
\(502\) −216.146 176.187i −0.430570 0.350971i
\(503\) 523.660i 1.04107i 0.853839 + 0.520537i \(0.174268\pi\)
−0.853839 + 0.520537i \(0.825732\pi\)
\(504\) 0 0
\(505\) −301.072 −0.596182
\(506\) −263.212 + 322.908i −0.520181 + 0.638157i
\(507\) 0 0
\(508\) 32.7972 6.75075i 0.0645613 0.0132889i
\(509\) 267.685 + 463.645i 0.525905 + 0.910893i 0.999545 + 0.0301749i \(0.00960643\pi\)
−0.473640 + 0.880719i \(0.657060\pi\)
\(510\) 0 0
\(511\) −765.285 441.838i −1.49762 0.864653i
\(512\) 65.4050 + 507.805i 0.127744 + 0.991807i
\(513\) 0 0
\(514\) 929.163 + 150.234i 1.80771 + 0.292284i
\(515\) −215.925 124.665i −0.419273 0.242067i
\(516\) 0 0
\(517\) −8.95475 15.5101i −0.0173206 0.0300002i
\(518\) 881.402 335.085i 1.70155 0.646883i
\(519\) 0 0
\(520\) 10.8465 6.89573i 0.0208586 0.0132610i
\(521\) −177.268 −0.340246 −0.170123 0.985423i \(-0.554416\pi\)
−0.170123 + 0.985423i \(0.554416\pi\)
\(522\) 0 0
\(523\) 444.206i 0.849343i −0.905347 0.424672i \(-0.860390\pi\)
0.905347 0.424672i \(-0.139610\pi\)
\(524\) −353.072 397.242i −0.673801 0.758096i
\(525\) 0 0
\(526\) 47.9285 18.2211i 0.0911188 0.0346409i
\(527\) 127.296 73.4944i 0.241548 0.139458i
\(528\) 0 0
\(529\) −41.8394 + 72.4679i −0.0790914 + 0.136990i
\(530\) 112.989 + 18.2689i 0.213187 + 0.0344696i
\(531\) 0 0
\(532\) 620.681 + 206.101i 1.16669 + 0.387407i
\(533\) 12.5688 21.7697i 0.0235812 0.0408438i
\(534\) 0 0
\(535\) −253.065 + 146.107i −0.473018 + 0.273097i
\(536\) −353.580 + 15.1064i −0.659664 + 0.0281835i
\(537\) 0 0
\(538\) 10.2996 12.6355i 0.0191443 0.0234861i
\(539\) 843.787i 1.56547i
\(540\) 0 0
\(541\) 571.163 1.05575 0.527877 0.849321i \(-0.322988\pi\)
0.527877 + 0.849321i \(0.322988\pi\)
\(542\) 623.160 + 507.957i 1.14974 + 0.937190i
\(543\) 0 0
\(544\) 77.9534 273.248i 0.143297 0.502294i
\(545\) −117.378 203.304i −0.215372 0.373036i
\(546\) 0 0
\(547\) 139.875 + 80.7569i 0.255713 + 0.147636i 0.622377 0.782717i \(-0.286167\pi\)
−0.366664 + 0.930353i \(0.619500\pi\)
\(548\) 171.268 + 56.8706i 0.312533 + 0.103779i
\(549\) 0 0
\(550\) −55.5965 + 343.851i −0.101085 + 0.625184i
\(551\) −248.507 143.476i −0.451011 0.260391i
\(552\) 0 0
\(553\) −55.6008 96.3034i −0.100544 0.174147i
\(554\) 79.8878 + 210.135i 0.144202 + 0.379305i
\(555\) 0 0
\(556\) 401.175 + 451.363i 0.721537 + 0.811803i
\(557\) 568.917 1.02139 0.510697 0.859761i \(-0.329387\pi\)
0.510697 + 0.859761i \(0.329387\pi\)
\(558\) 0 0
\(559\) 22.0515i 0.0394481i
\(560\) 198.746 + 462.330i 0.354904 + 0.825590i
\(561\) 0 0
\(562\) −382.178 1005.27i −0.680032 1.78874i
\(563\) −250.527 + 144.642i −0.444985 + 0.256912i −0.705710 0.708501i \(-0.749372\pi\)
0.260725 + 0.965413i \(0.416038\pi\)
\(564\) 0 0
\(565\) 6.37900 11.0487i 0.0112903 0.0195553i
\(566\) 45.0824 278.824i 0.0796510 0.492623i
\(567\) 0 0
\(568\) −413.723 + 792.942i −0.728385 + 1.39603i
\(569\) 223.117 386.450i 0.392121 0.679174i −0.600608 0.799544i \(-0.705075\pi\)
0.992729 + 0.120370i \(0.0384079\pi\)
\(570\) 0 0
\(571\) 372.386 214.997i 0.652164 0.376527i −0.137121 0.990554i \(-0.543785\pi\)
0.789285 + 0.614027i \(0.210451\pi\)
\(572\) 22.9081 4.71525i 0.0400491 0.00824344i
\(573\) 0 0
\(574\) 762.889 + 621.854i 1.32907 + 1.08337i
\(575\) 372.337i 0.647542i
\(576\) 0 0
\(577\) 50.9694 0.0883353 0.0441676 0.999024i \(-0.485936\pi\)
0.0441676 + 0.999024i \(0.485936\pi\)
\(578\) 265.556 325.783i 0.459439 0.563638i
\(579\) 0 0
\(580\) −44.5150 216.267i −0.0767501 0.372875i
\(581\) −492.943 853.803i −0.848440 1.46954i
\(582\) 0 0
\(583\) 180.371 + 104.137i 0.309385 + 0.178623i
\(584\) −540.460 281.989i −0.925446 0.482857i
\(585\) 0 0
\(586\) −909.353 147.031i −1.55180 0.250906i
\(587\) 643.771 + 371.681i 1.09671 + 0.633188i 0.935356 0.353708i \(-0.115079\pi\)
0.161358 + 0.986896i \(0.448413\pi\)
\(588\) 0 0
\(589\) 116.692 + 202.117i 0.198119 + 0.343152i
\(590\) −448.983 + 170.692i −0.760989 + 0.289308i
\(591\) 0 0
\(592\) 597.612 256.902i 1.00948 0.433955i
\(593\) 382.547 0.645104 0.322552 0.946552i \(-0.395459\pi\)
0.322552 + 0.946552i \(0.395459\pi\)
\(594\) 0 0
\(595\) 279.287i 0.469391i
\(596\) −426.886 + 379.419i −0.716251 + 0.636610i
\(597\) 0 0
\(598\) −23.3693 + 8.88440i −0.0390792 + 0.0148569i
\(599\) −856.248 + 494.355i −1.42946 + 0.825301i −0.997078 0.0763888i \(-0.975661\pi\)
−0.432384 + 0.901689i \(0.642328\pi\)
\(600\) 0 0
\(601\) −263.280 + 456.015i −0.438070 + 0.758760i −0.997541 0.0700905i \(-0.977671\pi\)
0.559470 + 0.828850i \(0.311005\pi\)
\(602\) 852.327 + 137.811i 1.41583 + 0.228921i
\(603\) 0 0
\(604\) 320.261 964.479i 0.530233 1.59682i
\(605\) −31.9637 + 55.3627i −0.0528325 + 0.0915086i
\(606\) 0 0
\(607\) 447.631 258.440i 0.737448 0.425766i −0.0836928 0.996492i \(-0.526671\pi\)
0.821141 + 0.570726i \(0.193338\pi\)
\(608\) 433.854 + 123.772i 0.713576 + 0.203572i
\(609\) 0 0
\(610\) 250.136 306.866i 0.410058 0.503059i
\(611\) 1.07481i 0.00175910i
\(612\) 0 0
\(613\) 762.957 1.24463 0.622314 0.782768i \(-0.286193\pi\)
0.622314 + 0.782768i \(0.286193\pi\)
\(614\) 326.048 + 265.772i 0.531023 + 0.432853i
\(615\) 0 0
\(616\) 39.0884 + 914.904i 0.0634552 + 1.48523i
\(617\) −60.9168 105.511i −0.0987307 0.171007i 0.812429 0.583060i \(-0.198145\pi\)
−0.911160 + 0.412054i \(0.864812\pi\)
\(618\) 0 0
\(619\) 265.675 + 153.388i 0.429200 + 0.247799i 0.699006 0.715116i \(-0.253626\pi\)
−0.269806 + 0.962915i \(0.586959\pi\)
\(620\) −56.5931 + 170.433i −0.0912793 + 0.274891i
\(621\) 0 0
\(622\) 40.9138 253.042i 0.0657778 0.406820i
\(623\) −650.636 375.645i −1.04436 0.602961i
\(624\) 0 0
\(625\) −63.7082 110.346i −0.101933 0.176553i
\(626\) −5.14760 13.5401i −0.00822300 0.0216296i
\(627\) 0 0
\(628\) 15.8673 14.1030i 0.0252664 0.0224570i
\(629\) −361.010 −0.573942
\(630\) 0 0
\(631\) 1071.11i 1.69749i 0.528805 + 0.848744i \(0.322640\pi\)
−0.528805 + 0.848744i \(0.677360\pi\)
\(632\) −41.1569 64.7370i −0.0651217 0.102432i
\(633\) 0 0
\(634\) 170.779 + 449.214i 0.269368 + 0.708539i
\(635\) 19.6623 11.3521i 0.0309643 0.0178773i
\(636\) 0 0
\(637\) −25.3193 + 43.8543i −0.0397477 + 0.0688450i
\(638\) 64.1315 396.638i 0.100520 0.621690i
\(639\) 0 0
\(640\) 150.594 + 312.795i 0.235303 + 0.488742i
\(641\) −527.259 + 913.240i −0.822557 + 1.42471i 0.0812143 + 0.996697i \(0.474120\pi\)
−0.903772 + 0.428015i \(0.859213\pi\)
\(642\) 0 0
\(643\) −42.0680 + 24.2880i −0.0654246 + 0.0377729i −0.532355 0.846521i \(-0.678693\pi\)
0.466931 + 0.884294i \(0.345360\pi\)
\(644\) −197.351 958.788i −0.306445 1.48880i
\(645\) 0 0
\(646\) −194.079 158.200i −0.300432 0.244891i
\(647\) 539.373i 0.833653i −0.908986 0.416826i \(-0.863142\pi\)
0.908986 0.416826i \(-0.136858\pi\)
\(648\) 0 0
\(649\) −874.061 −1.34678
\(650\) −13.2074 + 16.2028i −0.0203190 + 0.0249273i
\(651\) 0 0
\(652\) 233.322 48.0256i 0.357856 0.0736588i
\(653\) 276.457 + 478.838i 0.423365 + 0.733290i 0.996266 0.0863348i \(-0.0275155\pi\)
−0.572901 + 0.819624i \(0.694182\pi\)
\(654\) 0 0
\(655\) −312.081 180.180i −0.476460 0.275084i
\(656\) 544.109 + 406.130i 0.829435 + 0.619100i
\(657\) 0 0
\(658\) 41.5433 + 6.71703i 0.0631357 + 0.0102082i
\(659\) 734.162 + 423.869i 1.11406 + 0.643200i 0.939877 0.341514i \(-0.110940\pi\)
0.174178 + 0.984714i \(0.444273\pi\)
\(660\) 0 0
\(661\) −359.447 622.580i −0.543792 0.941876i −0.998682 0.0513280i \(-0.983655\pi\)
0.454890 0.890548i \(-0.349679\pi\)
\(662\) −799.537 + 303.963i −1.20776 + 0.459158i
\(663\) 0 0
\(664\) −364.888 573.943i −0.549530 0.864372i
\(665\) 443.444 0.666833
\(666\) 0 0
\(667\) 429.497i 0.643923i
\(668\) −263.096 296.010i −0.393856 0.443129i
\(669\) 0 0
\(670\) −224.299 + 85.2725i −0.334775 + 0.127272i
\(671\) 623.893 360.205i 0.929796 0.536818i
\(672\) 0 0
\(673\) 288.488 499.675i 0.428659 0.742460i −0.568095 0.822963i \(-0.692319\pi\)
0.996754 + 0.0805033i \(0.0256528\pi\)
\(674\) −601.949 97.3277i −0.893100 0.144403i
\(675\) 0 0
\(676\) −640.223 212.590i −0.947076 0.314482i
\(677\) 101.021 174.974i 0.149219 0.258454i −0.781720 0.623629i \(-0.785657\pi\)
0.930939 + 0.365175i \(0.118991\pi\)
\(678\) 0 0
\(679\) −72.1372 + 41.6484i −0.106240 + 0.0613379i
\(680\) −8.22397 192.490i −0.0120941 0.283074i
\(681\) 0 0
\(682\) −206.469 + 253.296i −0.302741 + 0.371402i
\(683\) 568.249i 0.831990i 0.909367 + 0.415995i \(0.136567\pi\)
−0.909367 + 0.415995i \(0.863433\pi\)
\(684\) 0 0
\(685\) 122.362 0.178631
\(686\) −655.906 534.649i −0.956131 0.779371i
\(687\) 0 0
\(688\) 591.499 + 69.8840i 0.859737 + 0.101576i
\(689\) 6.24965 + 10.8247i 0.00907060 + 0.0157107i
\(690\) 0 0
\(691\) −351.376 202.867i −0.508504 0.293585i 0.223714 0.974655i \(-0.428182\pi\)
−0.732218 + 0.681070i \(0.761515\pi\)
\(692\) 146.506 + 48.6482i 0.211714 + 0.0703008i
\(693\) 0 0
\(694\) −53.9673 + 333.775i −0.0777627 + 0.480945i
\(695\) 354.600 + 204.728i 0.510215 + 0.294573i
\(696\) 0 0
\(697\) −188.407 326.330i −0.270311 0.468192i
\(698\) 152.517 + 401.178i 0.218506 + 0.574754i
\(699\) 0 0
\(700\) −543.725 611.747i −0.776750 0.873924i
\(701\) −83.5164 −0.119139 −0.0595695 0.998224i \(-0.518973\pi\)
−0.0595695 + 0.998224i \(0.518973\pi\)
\(702\) 0 0
\(703\) 573.200i 0.815363i
\(704\) 53.8810 + 629.419i 0.0765355 + 0.894061i
\(705\) 0 0
\(706\) 392.168 + 1031.55i 0.555479 + 1.46112i
\(707\) 1114.86 643.663i 1.57688 0.910414i
\(708\) 0 0
\(709\) −173.908 + 301.217i −0.245286 + 0.424848i −0.962212 0.272302i \(-0.912215\pi\)
0.716926 + 0.697149i \(0.245548\pi\)
\(710\) −96.7955 + 598.657i −0.136332 + 0.843180i
\(711\) 0 0
\(712\) −459.493 239.743i −0.645355 0.336718i
\(713\) 174.660 302.520i 0.244965 0.424292i
\(714\) 0 0
\(715\) 13.7337 7.92916i 0.0192080 0.0110897i
\(716\) −142.714 + 29.3753i −0.199321 + 0.0410269i
\(717\) 0 0
\(718\) −860.112 701.103i −1.19793 0.976467i
\(719\) 536.277i 0.745865i −0.927858 0.372933i \(-0.878352\pi\)
0.927858 0.372933i \(-0.121648\pi\)
\(720\) 0 0
\(721\) 1066.08 1.47862
\(722\) −204.990 + 251.481i −0.283919 + 0.348311i
\(723\) 0 0
\(724\) 14.9932 + 72.8414i 0.0207088 + 0.100610i
\(725\) 179.553 + 310.995i 0.247659 + 0.428959i
\(726\) 0 0
\(727\) 815.055 + 470.573i 1.12112 + 0.647280i 0.941687 0.336490i \(-0.109240\pi\)
0.179435 + 0.983770i \(0.442573\pi\)
\(728\) −25.4217 + 48.7233i −0.0349199 + 0.0669277i
\(729\) 0 0
\(730\) −408.038 65.9747i −0.558956 0.0903763i
\(731\) −286.267 165.277i −0.391611 0.226096i
\(732\) 0 0
\(733\) 311.063 + 538.777i 0.424370 + 0.735030i 0.996361 0.0852294i \(-0.0271623\pi\)
−0.571991 + 0.820260i \(0.693829\pi\)
\(734\) −314.392 + 119.524i −0.428327 + 0.162839i
\(735\) 0 0
\(736\) −164.251 655.004i −0.223167 0.889952i
\(737\) −436.655 −0.592477
\(738\) 0 0
\(739\) 444.439i 0.601406i −0.953718 0.300703i \(-0.902779\pi\)
0.953718 0.300703i \(-0.0972213\pi\)
\(740\) 329.667 293.011i 0.445496 0.395960i
\(741\) 0 0
\(742\) −457.450 + 173.910i −0.616510 + 0.234381i
\(743\) 66.2270 38.2362i 0.0891346 0.0514619i −0.454770 0.890609i \(-0.650279\pi\)
0.543905 + 0.839147i \(0.316945\pi\)
\(744\) 0 0
\(745\) −193.626 + 335.370i −0.259901 + 0.450161i
\(746\) −677.990 109.622i −0.908833 0.146947i
\(747\) 0 0
\(748\) 110.484 332.728i 0.147706 0.444824i
\(749\) 624.725 1082.06i 0.834079 1.44467i
\(750\) 0 0
\(751\) −949.025 + 547.920i −1.26368 + 0.729587i −0.973785 0.227471i \(-0.926954\pi\)
−0.289897 + 0.957058i \(0.593621\pi\)
\(752\) 28.8302 + 3.40622i 0.0383381 + 0.00452954i
\(753\) 0 0
\(754\) 15.2349 18.6902i 0.0202055 0.0247880i
\(755\) 689.070i 0.912676i
\(756\) 0 0
\(757\) −346.346 −0.457525 −0.228762 0.973482i \(-0.573468\pi\)
−0.228762 + 0.973482i \(0.573468\pi\)
\(758\) −933.847 761.207i −1.23199 1.00423i
\(759\) 0 0
\(760\) 305.630 13.0578i 0.402145 0.0171813i
\(761\) 106.565 + 184.576i 0.140033 + 0.242544i 0.927509 0.373802i \(-0.121946\pi\)
−0.787476 + 0.616345i \(0.788613\pi\)
\(762\) 0 0
\(763\) 869.291 + 501.885i 1.13931 + 0.657779i
\(764\) 356.571 1073.83i 0.466715 1.40553i
\(765\) 0 0
\(766\) −116.394 + 719.871i −0.151951 + 0.939779i
\(767\) −45.4277 26.2277i −0.0592277 0.0341952i
\(768\) 0 0
\(769\) −270.786 469.015i −0.352127 0.609902i 0.634495 0.772927i \(-0.281208\pi\)
−0.986622 + 0.163025i \(0.947875\pi\)
\(770\) 220.647 + 580.384i 0.286554 + 0.753746i
\(771\) 0 0
\(772\) −906.149 + 805.393i −1.17377 + 1.04325i
\(773\) −1255.73 −1.62449 −0.812245 0.583317i \(-0.801755\pi\)
−0.812245 + 0.583317i \(0.801755\pi\)
\(774\) 0 0
\(775\) 292.070i 0.376864i
\(776\) −48.4920 + 30.8291i −0.0624897 + 0.0397282i
\(777\) 0 0
\(778\) −152.557 401.281i −0.196088 0.515786i
\(779\) 518.136 299.146i 0.665130 0.384013i
\(780\) 0 0
\(781\) −551.759 + 955.675i −0.706478 + 1.22366i
\(782\) −59.8186 + 369.964i