Properties

Label 108.3.f.c.91.3
Level 108
Weight 3
Character 108.91
Analytic conductor 2.943
Analytic rank 0
Dimension 16
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 91.3
Root \(-0.710719 - 1.86946i\) 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 \(\chi\) \(=\) 108.91
Dual form 108.3.f.c.19.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +O(q^{10})\) \(q+(-0.710719 - 1.86946i) q^{2} +(-2.98976 + 2.65732i) q^{4} +(-1.35609 + 2.34881i) q^{5} +(-10.0431 + 5.79837i) q^{7} +(7.09263 + 3.70062i) q^{8} +(5.35481 + 0.865806i) q^{10} +(-8.54822 + 4.93532i) q^{11} +(0.296185 - 0.513008i) q^{13} +(17.9776 + 14.6541i) q^{14} +(1.87730 - 15.8895i) q^{16} +8.87968 q^{17} +14.0989i q^{19} +(-2.18718 - 10.6259i) q^{20} +(15.3018 + 12.4729i) q^{22} +(-18.2754 - 10.5513i) q^{23} +(8.82205 + 15.2802i) q^{25} +(-1.16955 - 0.189102i) q^{26} +(14.6182 - 44.0234i) q^{28} +(-10.1764 - 17.6260i) q^{29} +(-14.3357 - 8.27670i) q^{31} +(-31.0390 + 7.78342i) q^{32} +(-6.31095 - 16.6002i) q^{34} -31.4524i q^{35} -40.6557 q^{37} +(26.3573 - 10.0203i) q^{38} +(-18.3103 + 11.6409i) q^{40} +(-21.2177 + 36.7502i) q^{41} +(32.2385 - 18.6129i) q^{43} +(12.4424 - 37.4708i) q^{44} +(-6.73658 + 41.6642i) q^{46} +(1.57134 - 0.907211i) q^{47} +(42.7423 - 74.0318i) q^{49} +(22.2958 - 27.3524i) q^{50} +(0.477704 + 2.32083i) q^{52} +21.1005 q^{53} -26.7709i q^{55} +(-92.6894 + 3.96007i) q^{56} +(-25.7186 + 31.5515i) q^{58} +(76.6879 + 44.2758i) q^{59} +(36.4925 + 63.2069i) q^{61} +(-5.28433 + 32.6823i) q^{62} +(36.6108 + 52.4943i) q^{64} +(0.803307 + 1.39137i) q^{65} +(38.3110 + 22.1189i) q^{67} +(-26.5481 + 23.5961i) q^{68} +(-58.7990 + 22.3538i) q^{70} +111.798i q^{71} -76.2003 q^{73} +(28.8948 + 76.0042i) q^{74} +(-37.4652 - 42.1522i) q^{76} +(57.2337 - 99.1316i) q^{77} +(8.30434 - 4.79451i) q^{79} +(34.7757 + 25.9570i) q^{80} +(83.7828 + 13.5466i) q^{82} +(73.6244 - 42.5070i) q^{83} +(-12.0416 + 20.8567i) q^{85} +(-57.7086 - 47.0400i) q^{86} +(-78.8931 + 3.37063i) q^{88} -64.7845 q^{89} +6.86958i q^{91} +(82.6773 - 17.0178i) q^{92} +(-2.81277 - 2.29278i) q^{94} +(-33.1157 - 19.1193i) q^{95} +(-3.59139 - 6.22047i) q^{97} +(-168.777 - 27.2892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + O(q^{10}) \) \( 16q + 3q^{2} - 5q^{4} - 6q^{5} + 54q^{8} + 20q^{10} - 46q^{13} + 12q^{14} - 17q^{16} - 12q^{17} - 36q^{20} + 33q^{22} - 30q^{25} - 72q^{26} + 12q^{28} - 42q^{29} - 87q^{32} + 11q^{34} + 56q^{37} + 99q^{38} + 68q^{40} - 84q^{41} + 222q^{44} - 264q^{46} + 58q^{49} + 219q^{50} + 110q^{52} + 72q^{53} - 270q^{56} - 16q^{58} - 34q^{61} - 516q^{62} - 254q^{64} + 30q^{65} - 375q^{68} + 150q^{70} + 116q^{73} + 372q^{74} - 15q^{76} + 330q^{77} + 720q^{80} + 254q^{82} - 140q^{85} + 273q^{86} + 75q^{88} + 384q^{89} - 258q^{92} + 36q^{94} - 148q^{97} - 1170q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.710719 1.86946i −0.355359 0.934730i
\(3\) 0 0
\(4\) −2.98976 + 2.65732i −0.747439 + 0.664330i
\(5\) −1.35609 + 2.34881i −0.271218 + 0.469763i −0.969174 0.246378i \(-0.920760\pi\)
0.697956 + 0.716140i \(0.254093\pi\)
\(6\) 0 0
\(7\) −10.0431 + 5.79837i −1.43473 + 0.828339i −0.997476 0.0710013i \(-0.977381\pi\)
−0.437249 + 0.899340i \(0.644047\pi\)
\(8\) 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 \(-0.814767\pi\)
0.0582943 + 0.998299i \(0.481434\pi\)
\(12\) 0 0
\(13\) 0.296185 0.513008i 0.0227835 0.0394622i −0.854409 0.519601i \(-0.826080\pi\)
0.877192 + 0.480139i \(0.159414\pi\)
\(14\) 17.9776 + 14.6541i 1.28412 + 1.04672i
\(15\) 0 0
\(16\) 1.87730 15.8895i 0.117331 0.993093i
\(17\) 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 \(0.879007\pi\)
\(20\) −2.18718 10.6259i −0.109359 0.531297i
\(21\) 0 0
\(22\) 15.3018 + 12.4729i 0.695535 + 0.566952i
\(23\) −18.2754 10.5513i −0.794583 0.458753i 0.0469902 0.998895i \(-0.485037\pi\)
−0.841574 + 0.540142i \(0.818370\pi\)
\(24\) 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 0.635499 0.772101i \(-0.280794\pi\)
−0.986409 + 0.164308i \(0.947461\pi\)
\(30\) 0 0
\(31\) −14.3357 8.27670i −0.462441 0.266990i 0.250629 0.968083i \(-0.419362\pi\)
−0.713070 + 0.701093i \(0.752696\pi\)
\(32\) −31.0390 + 7.78342i −0.969968 + 0.243232i
\(33\) 0 0
\(34\) −6.31095 16.6002i −0.185616 0.488241i
\(35\) 31.4524i 0.898641i
\(36\) 0 0
\(37\) −40.6557 −1.09880 −0.549401 0.835559i \(-0.685144\pi\)
−0.549401 + 0.835559i \(0.685144\pi\)
\(38\) 26.3573 10.0203i 0.693613 0.263693i
\(39\) 0 0
\(40\) −18.3103 + 11.6409i −0.457758 + 0.291022i
\(41\) −21.2177 + 36.7502i −0.517506 + 0.896346i 0.482288 + 0.876013i \(0.339806\pi\)
−0.999793 + 0.0203330i \(0.993527\pi\)
\(42\) 0 0
\(43\) 32.2385 18.6129i 0.749732 0.432858i −0.0758649 0.997118i \(-0.524172\pi\)
0.825597 + 0.564260i \(0.190838\pi\)
\(44\) 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 \(-0.660522\pi\)
0.516623 + 0.856213i \(0.327189\pi\)
\(48\) 0 0
\(49\) 42.7423 74.0318i 0.872291 1.51085i
\(50\) 22.2958 27.3524i 0.445916 0.547048i
\(51\) 0 0
\(52\) 0.477704 + 2.32083i 0.00918662 + 0.0446313i
\(53\) 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
\(56\) −92.6894 + 3.96007i −1.65517 + 0.0707155i
\(57\) 0 0
\(58\) −25.7186 + 31.5515i −0.443423 + 0.543991i
\(59\) 76.6879 + 44.2758i 1.29980 + 0.750437i 0.980369 0.197174i \(-0.0631764\pi\)
0.319427 + 0.947611i \(0.396510\pi\)
\(60\) 0 0
\(61\) 36.4925 + 63.2069i 0.598238 + 1.03618i 0.993081 + 0.117431i \(0.0374657\pi\)
−0.394843 + 0.918749i \(0.629201\pi\)
\(62\) −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 \(-0.226240\pi\)
−0.186064 + 0.982538i \(0.559573\pi\)
\(68\) −26.5481 + 23.5961i −0.390413 + 0.347002i
\(69\) 0 0
\(70\) −58.7990 + 22.3538i −0.839986 + 0.319341i
\(71\) 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 \(0.674784\pi\)
\(74\) 28.8948 + 76.0042i 0.390470 + 1.02708i
\(75\) 0 0
\(76\) −37.4652 42.1522i −0.492964 0.554635i
\(77\) 57.2337 99.1316i 0.743294 1.28742i
\(78\) 0 0
\(79\) 8.30434 4.79451i 0.105118 0.0606901i −0.446519 0.894774i \(-0.647337\pi\)
0.551637 + 0.834084i \(0.314003\pi\)
\(80\) 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 \(-0.495522\pi\)
0.872973 + 0.487768i \(0.162189\pi\)
\(84\) 0 0
\(85\) −12.0416 + 20.8567i −0.141666 + 0.245373i
\(86\) −57.7086 47.0400i −0.671030 0.546977i
\(87\) 0 0
\(88\) −78.8931 + 3.37063i −0.896513 + 0.0383026i
\(89\) −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
\(92\) 82.6773 17.0178i 0.898666 0.184976i
\(93\) 0 0
\(94\) −2.81277 2.29278i −0.0299231 0.0243912i
\(95\) −33.1157 19.1193i −0.348586 0.201256i
\(96\) 0 0
\(97\) −3.59139 6.22047i −0.0370246 0.0641285i 0.846919 0.531721i \(-0.178455\pi\)
−0.883944 + 0.467593i \(0.845121\pi\)
\(98\) −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 0.998306 + 0.0581840i \(0.0185310\pi\)
−0.448764 + 0.893650i \(0.648136\pi\)
\(102\) 0 0
\(103\) −79.6133 45.9648i −0.772945 0.446260i 0.0609793 0.998139i \(-0.480578\pi\)
−0.833924 + 0.551879i \(0.813911\pi\)
\(104\) 3.99918 2.54251i 0.0384537 0.0244472i
\(105\) 0 0
\(106\) −14.9965 39.4464i −0.141476 0.372136i
\(107\) 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 \(0.370035\pi\)
\(110\) −50.0472 + 19.0266i −0.454974 + 0.172969i
\(111\) 0 0
\(112\) 73.2793 + 170.465i 0.654279 + 1.52201i
\(113\) 2.35198 4.07376i 0.0208140 0.0360509i −0.855431 0.517917i \(-0.826708\pi\)
0.876245 + 0.481866i \(0.160041\pi\)
\(114\) 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
\(122\) 92.2269 113.144i 0.755958 0.927407i
\(123\) 0 0
\(124\) 64.8540 13.3491i 0.523016 0.107654i
\(125\) −115.658 −0.925267
\(126\) 0 0
\(127\) 8.37118i 0.0659148i 0.999457 + 0.0329574i \(0.0104926\pi\)
−0.999457 + 0.0329574i \(0.989507\pi\)
\(128\) 72.1160 105.751i 0.563406 0.826180i
\(129\) 0 0
\(130\) 2.03018 2.49062i 0.0156168 0.0191586i
\(131\) −115.067 66.4338i −0.878372 0.507129i −0.00825098 0.999966i \(-0.502626\pi\)
−0.870121 + 0.492837i \(0.835960\pi\)
\(132\) 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 0.771877 0.635772i \(-0.219318\pi\)
−0.936533 + 0.350579i \(0.885985\pi\)
\(138\) 0 0
\(139\) 130.744 + 75.4848i 0.940601 + 0.543056i 0.890149 0.455670i \(-0.150600\pi\)
0.0504522 + 0.998726i \(0.483934\pi\)
\(140\) 83.5792 + 94.0351i 0.596994 + 0.671680i
\(141\) 0 0
\(142\) 209.002 79.4570i 1.47184 0.559556i
\(143\) 5.84708i 0.0408887i
\(144\) 0 0
\(145\) 55.2003 0.380692
\(146\) 54.1570 + 142.453i 0.370938 + 0.975708i
\(147\) 0 0
\(148\) 121.551 108.035i 0.821289 0.729968i
\(149\) −71.3914 + 123.653i −0.479137 + 0.829889i −0.999714 0.0239255i \(-0.992384\pi\)
0.520577 + 0.853815i \(0.325717\pi\)
\(150\) 0 0
\(151\) −220.027 + 127.033i −1.45713 + 0.841276i −0.998869 0.0475407i \(-0.984862\pi\)
−0.458263 + 0.888817i \(0.651528\pi\)
\(152\) −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 −0.857451 0.514566i \(-0.827953\pi\)
0.874353 + 0.485291i \(0.161286\pi\)
\(158\) −14.8652 12.1171i −0.0940836 0.0766904i
\(159\) 0 0
\(160\) 23.8098 83.4598i 0.148811 0.521624i
\(161\) 244.722 1.52001
\(162\) 0 0
\(163\) 59.5534i 0.365359i 0.983173 + 0.182679i \(0.0584770\pi\)
−0.983173 + 0.182679i \(0.941523\pi\)
\(164\) −34.2211 166.256i −0.208665 1.01376i
\(165\) 0 0
\(166\) −131.791 107.427i −0.793924 0.647152i
\(167\) −85.7434 49.5040i −0.513434 0.296431i 0.220810 0.975317i \(-0.429130\pi\)
−0.734244 + 0.678886i \(0.762463\pi\)
\(168\) 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 0.804851 0.593477i \(-0.202245\pi\)
−0.916391 + 0.400283i \(0.868912\pi\)
\(174\) 0 0
\(175\) −177.201 102.307i −1.01258 0.584612i
\(176\) 62.3721 + 145.092i 0.354387 + 0.824386i
\(177\) 0 0
\(178\) 46.0436 + 121.112i 0.258672 + 0.680405i
\(179\) 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 \(0.516355\pi\)
\(182\) 12.8424 4.88234i 0.0705626 0.0268260i
\(183\) 0 0
\(184\) −90.5743 142.467i −0.492252 0.774277i
\(185\) 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 \(-0.932077\pi\)
−0.305260 + 0.952269i \(0.598743\pi\)
\(192\) 0 0
\(193\) −151.542 + 262.479i −0.785193 + 1.35999i 0.143691 + 0.989623i \(0.454103\pi\)
−0.928884 + 0.370372i \(0.879230\pi\)
\(194\) −9.07644 + 11.1350i −0.0467858 + 0.0573967i
\(195\) 0 0
\(196\) 68.9371 + 334.917i 0.351720 + 1.70876i
\(197\) −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 \(0.991014\pi\)
\(200\) 6.02512 + 141.024i 0.0301256 + 0.705121i
\(201\) 0 0
\(202\) 140.273 172.087i 0.694423 0.851916i
\(203\) 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 \(-0.234173\pi\)
−0.210492 + 0.977595i \(0.567507\pi\)
\(212\) −63.0852 + 56.0707i −0.297572 + 0.264484i
\(213\) 0 0
\(214\) −201.418 + 76.5739i −0.941207 + 0.357822i
\(215\) 100.963i 0.469595i
\(216\) 0 0
\(217\) 191.966 0.884634
\(218\) −61.5171 161.813i −0.282189 0.742263i
\(219\) 0 0
\(220\) 71.1389 + 80.0386i 0.323359 + 0.363812i
\(221\) 2.63003 4.55535i 0.0119006 0.0206124i
\(222\) 0 0
\(223\) 209.210 120.787i 0.938159 0.541647i 0.0487765 0.998810i \(-0.484468\pi\)
0.889383 + 0.457163i \(0.151134\pi\)
\(224\) 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 \(-0.348560\pi\)
0.998856 + 0.0478181i \(0.0152268\pi\)
\(228\) 0 0
\(229\) 74.6642 129.322i 0.326044 0.564725i −0.655679 0.755040i \(-0.727617\pi\)
0.981723 + 0.190315i \(0.0609508\pi\)
\(230\) −88.7260 72.3233i −0.385765 0.314449i
\(231\) 0 0
\(232\) −6.95007 162.674i −0.0299572 0.701180i
\(233\) 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
\(236\) −346.933 + 71.4105i −1.47006 + 0.302587i
\(237\) 0 0
\(238\) 159.636 + 130.124i 0.670738 + 0.546739i
\(239\) 218.254 + 126.009i 0.913197 + 0.527235i 0.881458 0.472262i \(-0.156562\pi\)
0.0317388 + 0.999496i \(0.489896\pi\)
\(240\) 0 0
\(241\) −226.014 391.467i −0.937816 1.62435i −0.769534 0.638606i \(-0.779511\pi\)
−0.168282 0.985739i \(-0.553822\pi\)
\(242\) 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
\(248\) −71.0486 111.754i −0.286486 0.450623i
\(249\) 0 0
\(250\) 82.2006 + 216.219i 0.328802 + 0.864874i
\(251\) 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
\(254\) 15.6496 5.94955i 0.0616125 0.0234234i
\(255\) 0 0
\(256\) −248.951 59.6587i −0.972467 0.233042i
\(257\) −235.308 + 407.565i −0.915594 + 1.58586i −0.109564 + 0.993980i \(0.534946\pi\)
−0.806029 + 0.591875i \(0.798388\pi\)
\(258\) 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 \(-0.651146\pi\)
0.541616 + 0.840626i \(0.317813\pi\)
\(264\) 0 0
\(265\) −28.6141 + 49.5610i −0.107978 + 0.187023i
\(266\) −206.607 + 253.464i −0.776717 + 0.952874i
\(267\) 0 0
\(268\) −173.318 + 35.6746i −0.646708 + 0.133114i
\(269\) −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 \(-0.265961\pi\)
\(272\) 16.6698 141.094i 0.0612861 0.518726i
\(273\) 0 0
\(274\) −57.0102 + 69.9400i −0.208067 + 0.255255i
\(275\) −150.826 87.0792i −0.548457 0.316652i
\(276\) 0 0
\(277\) 56.2021 + 97.3449i 0.202896 + 0.351426i 0.949460 0.313887i \(-0.101631\pi\)
−0.746565 + 0.665313i \(0.768298\pi\)
\(278\) 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 −0.730141 0.683296i \(-0.760546\pi\)
−0.226681 0.973969i \(-0.572788\pi\)
\(282\) 0 0
\(283\) 122.303 + 70.6114i 0.432164 + 0.249510i 0.700268 0.713880i \(-0.253064\pi\)
−0.268104 + 0.963390i \(0.586397\pi\)
\(284\) −297.083 334.249i −1.04607 1.17693i
\(285\) 0 0
\(286\) 10.9309 4.15563i 0.0382199 0.0145302i
\(287\) 492.113i 1.71468i
\(288\) 0 0
\(289\) −210.151 −0.727167
\(290\) −39.2319 103.195i −0.135282 0.355844i
\(291\) 0 0
\(292\) 227.820 202.489i 0.780207 0.693454i
\(293\) 230.291 398.875i 0.785975 1.36135i −0.142440 0.989803i \(-0.545495\pi\)
0.928415 0.371545i \(-0.121172\pi\)
\(294\) 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
\(302\) 393.860 + 321.047i 1.30417 + 1.06307i
\(303\) 0 0
\(304\) 224.024 + 26.4678i 0.736921 + 0.0870653i
\(305\) −197.948 −0.649011
\(306\) 0 0
\(307\) 210.322i 0.685089i −0.939502 0.342545i \(-0.888711\pi\)
0.939502 0.342545i \(-0.111289\pi\)
\(308\) 92.3096 + 448.468i 0.299707 + 1.45606i
\(309\) 0 0
\(310\) −69.5987 56.7320i −0.224512 0.183007i
\(311\) 110.993 + 64.0821i 0.356892 + 0.206052i 0.667717 0.744416i \(-0.267272\pi\)
−0.310824 + 0.950467i \(0.600605\pi\)
\(312\) 0 0
\(313\) −3.62140 6.27245i −0.0115700 0.0200398i 0.860182 0.509986i \(-0.170350\pi\)
−0.871752 + 0.489947i \(0.837016\pi\)
\(314\) −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 0.990918 0.134467i \(-0.0429322\pi\)
−0.611911 + 0.790927i \(0.709599\pi\)
\(318\) 0 0
\(319\) 173.980 + 100.447i 0.545392 + 0.314882i
\(320\) −172.947 + 14.8050i −0.540459 + 0.0462656i
\(321\) 0 0
\(322\) −173.928 457.498i −0.540151 1.42080i
\(323\) 125.194i 0.387596i
\(324\) 0 0
\(325\) 10.4518 0.0321595
\(326\) 111.333 42.3258i 0.341512 0.129834i
\(327\) 0 0
\(328\) −286.488 + 182.137i −0.873439 + 0.555294i
\(329\) −10.5207 + 18.2224i −0.0319778 + 0.0553872i
\(330\) 0 0
\(331\) −370.385 + 213.842i −1.11899 + 0.646048i −0.941142 0.338011i \(-0.890246\pi\)
−0.177845 + 0.984058i \(0.556913\pi\)
\(332\) −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 −0.546182 0.837666i \(-0.683919\pi\)
0.998531 + 0.0541746i \(0.0172528\pi\)
\(338\) 213.112 261.445i 0.630508 0.773506i
\(339\) 0 0
\(340\) −19.4214 94.3550i −0.0571218 0.277515i
\(341\) 163.393 0.479157
\(342\) 0 0
\(343\) 423.102i 1.23353i
\(344\) 297.535 12.7119i 0.864927 0.0369532i
\(345\) 0 0
\(346\) −48.7676 + 59.8280i −0.140947 + 0.172913i
\(347\) −146.406 84.5276i −0.421919 0.243595i 0.273979 0.961736i \(-0.411660\pi\)
−0.695898 + 0.718140i \(0.744994\pi\)
\(348\) 0 0
\(349\) 107.298 + 185.846i 0.307444 + 0.532509i 0.977802 0.209529i \(-0.0671930\pi\)
−0.670358 + 0.742037i \(0.733860\pi\)
\(350\) −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 0.931025 + 0.364956i \(0.118916\pi\)
−0.149451 + 0.988769i \(0.547751\pi\)
\(354\) 0 0
\(355\) −262.593 151.608i −0.739698 0.427065i
\(356\) 193.690 172.153i 0.544073 0.483577i
\(357\) 0 0
\(358\) −68.0977 + 25.8889i −0.190217 + 0.0723155i
\(359\) 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
\(362\) 13.2138 + 34.7572i 0.0365021 + 0.0960143i
\(363\) 0 0
\(364\) −18.2547 20.5384i −0.0501502 0.0564241i
\(365\) 103.334 178.980i 0.283108 0.490357i
\(366\) 0 0
\(367\) −145.642 + 84.0864i −0.396845 + 0.229118i −0.685122 0.728429i \(-0.740251\pi\)
0.288277 + 0.957547i \(0.406918\pi\)
\(368\) −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 −0.538658 0.842524i \(-0.681069\pi\)
0.998977 + 0.0452296i \(0.0144020\pi\)
\(374\) 135.875 + 110.756i 0.363301 + 0.296138i
\(375\) 0 0
\(376\) 14.5021 0.619590i 0.0385695 0.00164785i
\(377\) −12.0564 −0.0319798
\(378\) 0 0
\(379\) 602.392i 1.58943i 0.606986 + 0.794713i \(0.292379\pi\)
−0.606986 + 0.794713i \(0.707621\pi\)
\(380\) 149.814 30.8367i 0.394247 0.0811493i
\(381\) 0 0
\(382\) 438.514 + 357.446i 1.14794 + 0.935722i
\(383\) −315.762 182.305i −0.824443 0.475992i 0.0275035 0.999622i \(-0.491244\pi\)
−0.851946 + 0.523630i \(0.824578\pi\)
\(384\) 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 0.694461 0.719530i \(-0.255643\pi\)
−0.970362 + 0.241656i \(0.922310\pi\)
\(390\) 0 0
\(391\) −162.280 93.6923i −0.415038 0.239622i
\(392\) 577.119 366.907i 1.47224 0.935987i
\(393\) 0 0
\(394\) 98.9209 + 260.200i 0.251068 + 0.660405i
\(395\) 26.0071i 0.0658409i
\(396\) 0 0
\(397\) −684.628 −1.72450 −0.862251 0.506480i \(-0.830946\pi\)
−0.862251 + 0.506480i \(0.830946\pi\)
\(398\) 21.0009 7.98397i 0.0527660 0.0200602i
\(399\) 0 0
\(400\) 259.357 111.492i 0.648392 0.278731i
\(401\) −95.1918 + 164.877i −0.237386 + 0.411164i −0.959963 0.280125i \(-0.909624\pi\)
0.722577 + 0.691290i \(0.242957\pi\)
\(402\) 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 −0.537014 0.843574i \(-0.680448\pi\)
0.999063 + 0.0432806i \(0.0137809\pi\)
\(410\) −145.435 + 178.420i −0.354721 + 0.435170i
\(411\) 0 0
\(412\) 360.168 74.1345i 0.874193 0.179938i
\(413\) −1026.91 −2.48647
\(414\) 0 0
\(415\) 230.573i 0.555598i
\(416\) −5.20034 + 18.2286i −0.0125008 + 0.0438187i
\(417\) 0 0
\(418\) −175.854 + 215.738i −0.420704 + 0.516119i
\(419\) −267.326 154.341i −0.638009 0.368355i 0.145838 0.989308i \(-0.453412\pi\)
−0.783847 + 0.620954i \(0.786745\pi\)
\(420\) 0 0
\(421\) 176.834 + 306.286i 0.420034 + 0.727521i 0.995942 0.0899938i \(-0.0286847\pi\)
−0.575908 + 0.817514i \(0.695351\pi\)
\(422\) 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
\(428\) 286.304 + 322.121i 0.668934 + 0.752619i
\(429\) 0 0
\(430\) 188.746 71.7563i 0.438945 0.166875i
\(431\) 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 \(0.477406\pi\)
\(434\) −136.434 358.872i −0.314363 0.826893i
\(435\) 0 0
\(436\) −258.782 + 230.007i −0.593537 + 0.527540i
\(437\) 148.762 257.663i 0.340416 0.589618i
\(438\) 0 0
\(439\) 354.347 204.582i 0.807169 0.466019i −0.0388030 0.999247i \(-0.512354\pi\)
0.845972 + 0.533228i \(0.179021\pi\)
\(440\) 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 −0.509785 + 0.860302i \(0.670275\pi\)
−0.999936 + 0.0113360i \(0.996392\pi\)
\(444\) 0 0
\(445\) 87.8536 152.167i 0.197424 0.341948i
\(446\) −374.496 305.263i −0.839677 0.684446i
\(447\) 0 0
\(448\) −672.066 314.921i −1.50015 0.702949i
\(449\) 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
\(452\) 3.79341 + 18.4295i 0.00839250 + 0.0407733i
\(453\) 0 0
\(454\) −591.988 482.548i −1.30394 1.06288i
\(455\) −16.1354 9.31575i −0.0354623 0.0204742i
\(456\) 0 0
\(457\) 138.165 + 239.309i 0.302331 + 0.523653i 0.976664 0.214775i \(-0.0689018\pi\)
−0.674332 + 0.738428i \(0.735568\pi\)
\(458\) −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 0.985907 + 0.167293i \(0.0535027\pi\)
−0.348073 + 0.937467i \(0.613164\pi\)
\(462\) 0 0
\(463\) 677.285 + 391.031i 1.46282 + 0.844558i 0.999141 0.0414459i \(-0.0131964\pi\)
0.463677 + 0.886004i \(0.346530\pi\)
\(464\) −299.172 + 128.608i −0.644768 + 0.277173i
\(465\) 0 0
\(466\) −155.601 409.288i −0.333907 0.878301i
\(467\) 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
\(470\) 9.19967 3.49747i 0.0195738 0.00744143i
\(471\) 0 0
\(472\) 380.071 + 597.825i 0.805235 + 1.26658i
\(473\) −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 \(-0.429767\pi\)
0.954459 + 0.298344i \(0.0964341\pi\)
\(480\) 0 0
\(481\) −12.0416 + 20.8567i −0.0250346 + 0.0433611i
\(482\) −571.200 + 700.746i −1.18506 + 1.45383i
\(483\) 0 0
\(484\) −19.0079 92.3460i −0.0392725 0.190798i
\(485\) 19.4810 0.0401669
\(486\) 0 0
\(487\) 282.104i 0.579269i −0.957137 0.289635i \(-0.906466\pi\)
0.957137 0.289635i \(-0.0935338\pi\)
\(488\) 24.9230 + 583.348i 0.0510717 + 1.19539i
\(489\) 0 0
\(490\) 292.974 359.420i 0.597906 0.733510i
\(491\) 652.933 + 376.971i 1.32980 + 0.767762i 0.985269 0.171012i \(-0.0547036\pi\)
0.344534 + 0.938774i \(0.388037\pi\)
\(492\) 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 \(-0.160671\pi\)
0.0188362 + 0.999823i \(0.494004\pi\)
\(500\) 345.790 307.341i 0.691581 0.614682i
\(501\) 0 0
\(502\) 260.656 99.0945i 0.519235 0.197399i
\(503\) 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
\(506\) −148.040 389.402i −0.292570 0.769569i
\(507\) 0 0
\(508\) −22.2449 25.0278i −0.0437892 0.0492673i
\(509\) 267.685 463.645i 0.525905 0.910893i −0.473640 0.880719i \(-0.657060\pi\)
0.999545 0.0301749i \(-0.00960643\pi\)
\(510\) 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
\(518\) −730.893 595.773i −1.41099 1.15014i
\(519\) 0 0
\(520\) 0.548628 + 12.8412i 0.00105505 + 0.0246946i
\(521\) −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 \(-0.139610\pi\)
\(524\) 520.558 107.148i 0.993431 0.204481i
\(525\) 0 0
\(526\) −39.7442 32.3967i −0.0755593 0.0615907i
\(527\) −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
\(536\) 189.872 + 298.656i 0.354239 + 0.557194i
\(537\) 0 0
\(538\) 5.79289 + 15.2375i 0.0107675 + 0.0283225i
\(539\) 843.787i 1.56547i
\(540\) 0 0
\(541\) 571.163 1.05575 0.527877 0.849321i \(-0.322988\pi\)
0.527877 + 0.849321i \(0.322988\pi\)
\(542\) −751.484 + 285.694i −1.38650 + 0.527111i
\(543\) 0 0
\(544\) −275.616 + 69.1142i −0.506647 + 0.127048i
\(545\) −117.378 + 203.304i −0.215372 + 0.373036i
\(546\) 0 0
\(547\) −139.875 + 80.7569i −0.255713 + 0.147636i −0.622377 0.782717i \(-0.713833\pi\)
0.366664 + 0.930353i \(0.380500\pi\)
\(548\) 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
\(554\) 142.038 174.252i 0.256387 0.314535i
\(555\) 0 0
\(556\) −591.479 + 121.746i −1.06381 + 0.218968i
\(557\) 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
\(560\) −499.763 59.0457i −0.892434 0.105439i
\(561\) 0 0
\(562\) −679.503 + 833.612i −1.20908 + 1.48330i
\(563\) 250.527 + 144.642i 0.444985 + 0.256912i 0.705710 0.708501i \(-0.250628\pi\)
−0.260725 + 0.965413i \(0.583962\pi\)
\(564\) 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 0.992729 0.120370i \(-0.0384079\pi\)
−0.600608 + 0.799544i \(0.705075\pi\)
\(570\) 0 0
\(571\) −372.386 214.997i −0.652164 0.376527i 0.137121 0.990554i \(-0.456215\pi\)
−0.789285 + 0.614027i \(0.789549\pi\)
\(572\) −15.5376 17.4813i −0.0271636 0.0305618i
\(573\) 0 0
\(574\) −919.986 + 349.754i −1.60276 + 0.609328i
\(575\) 372.337i 0.647542i
\(576\) 0 0
\(577\) 50.9694 0.0883353 0.0441676 0.999024i \(-0.485936\pi\)
0.0441676 + 0.999024i \(0.485936\pi\)
\(578\) 149.359 + 392.869i 0.258406 + 0.679705i
\(579\) 0 0
\(580\) −165.035 + 146.685i −0.284544 + 0.252905i
\(581\) −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 \(-0.884921\pi\)
−0.161358 + 0.986896i \(0.551587\pi\)
\(588\) 0 0
\(589\) 116.692 202.117i 0.198119 0.343152i
\(590\) 372.315 + 303.485i 0.631042 + 0.514382i
\(591\) 0 0
\(592\) −76.3230 + 645.998i −0.128924 + 1.09121i
\(593\) 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
\(596\) −115.144 559.404i −0.193195 0.938597i
\(597\) 0 0
\(598\) 19.3788 + 15.7962i 0.0324060 + 0.0264151i
\(599\) 856.248 + 494.355i 1.42946 + 0.825301i 0.997078 0.0763888i \(-0.0243390\pi\)
0.432384 + 0.901689i \(0.357672\pi\)
\(600\) 0 0
\(601\) −263.280 456.015i −0.438070 0.758760i 0.559470 0.828850i \(-0.311005\pi\)
−0.997541 + 0.0700905i \(0.977671\pi\)
\(602\) 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 \(-0.473329\pi\)
−0.821141 + 0.570726i \(0.806662\pi\)
\(608\) −109.737 437.615i −0.180489 0.719761i
\(609\) 0 0
\(610\) 140.686 + 370.057i 0.230632 + 0.606650i
\(611\) 1.07481i 0.00175910i
\(612\) 0 0
\(613\) 762.957 1.24463 0.622314 0.782768i \(-0.286193\pi\)
0.622314 + 0.782768i \(0.286193\pi\)
\(614\) −393.189 + 149.480i −0.640373 + 0.243453i
\(615\) 0 0
\(616\) 772.786 491.303i 1.25452 0.797571i
\(617\) −60.9168 + 105.511i −0.0987307 + 0.171007i −0.911160 0.412054i \(-0.864812\pi\)
0.812429 + 0.583060i \(0.198145\pi\)
\(618\) 0 0
\(619\) −265.675 + 153.388i −0.429200 + 0.247799i −0.699006 0.715116i \(-0.746374\pi\)
0.269806 + 0.962915i \(0.413041\pi\)
\(620\) −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
\(626\) −9.15230 + 11.2280i −0.0146203 + 0.0179361i
\(627\) 0 0
\(628\) 4.27989 + 20.7930i 0.00681511 + 0.0331098i
\(629\) −361.010 −0.573942
\(630\) 0 0
\(631\) 1071.11i 1.69749i 0.528805 + 0.848744i \(0.322640\pi\)
−0.528805 + 0.848744i \(0.677360\pi\)
\(632\) 76.6423 3.27447i 0.121269 0.00518112i
\(633\) 0 0
\(634\) 303.641 372.506i 0.478929 0.587549i
\(635\) −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 −0.903772 0.428015i \(-0.859213\pi\)
0.0812143 0.996697i \(-0.474120\pi\)
\(642\) 0 0
\(643\) 42.0680 + 24.2880i 0.0654246 + 0.0377729i 0.532355 0.846521i \(-0.321307\pi\)
−0.466931 + 0.884294i \(0.654640\pi\)
\(644\) −731.659 + 650.305i −1.13612 + 1.00979i
\(645\) 0 0
\(646\) 234.044 88.9774i 0.362298 0.137736i
\(647\) 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
\(650\) −7.42832 19.5393i −0.0114282 0.0300605i
\(651\) 0 0
\(652\) −158.253 178.050i −0.242719 0.273083i
\(653\) 276.457 478.838i 0.423365 0.733290i −0.572901 0.819624i \(-0.694182\pi\)
0.996266 + 0.0863348i \(0.0275155\pi\)
\(654\) 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 \(-0.889060\pi\)
−0.174178 + 0.984714i \(0.555727\pi\)
\(660\) 0 0
\(661\) −359.447 + 622.580i −0.543792 + 0.941876i 0.454890 + 0.890548i \(0.349679\pi\)
−0.998682 + 0.0513280i \(0.983655\pi\)
\(662\) 663.008 + 540.438i 1.00152 + 0.816372i
\(663\) 0 0
\(664\) 679.493 29.0307i 1.02333 0.0437209i
\(665\) 443.444 0.666833
\(666\) 0 0
\(667\) 429.497i 0.643923i
\(668\) 387.900 79.8428i 0.580689 0.119525i
\(669\) 0 0
\(670\) 185.998 + 151.612i 0.277609 + 0.226287i
\(671\) −623.893 360.205i −0.929796 0.536818i
\(672\) 0 0
\(673\) 288.488 + 499.675i 0.428659 + 0.742460i 0.996754 0.0805033i \(-0.0256528\pi\)
−0.568095 + 0.822963i \(0.692319\pi\)
\(674\) −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 0.930939 0.365175i \(-0.118991\pi\)
−0.781720 + 0.623629i \(0.785657\pi\)
\(678\) 0 0
\(679\) 72.1372 + 41.6484i 0.106240 + 0.0613379i
\(680\) −162.590 + 103.367i −0.239102 + 0.152011i
\(681\) 0 0
\(682\) −116.126 305.456i −0.170273 0.447882i
\(683\) 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
\(686\) 790.972 300.707i 1.15302 0.438348i
\(687\) 0 0
\(688\) −235.228 547.195i −0.341901 0.795341i
\(689\) 6.24965 10.8247i 0.00907060 0.0157107i
\(690\) 0 0
\(691\) 351.376 202.867i 0.508504 0.293585i −0.223714 0.974655i \(-0.571818\pi\)
0.732218 + 0.681070i \(0.238485\pi\)
\(692\) 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
\(698\) 271.172 332.673i 0.388499 0.476609i
\(699\) 0 0
\(700\) 801.651 165.007i 1.14522 0.235724i
\(701\) −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
\(704\) −572.033 268.047i −0.812547 0.380749i
\(705\) 0 0
\(706\) 697.265 855.403i 0.987628 1.21162i
\(707\) −1114.86 643.663i −1.57688 0.910414i
\(708\) 0 0
\(709\) −173.908 301.217i −0.245286 0.424848i 0.716926 0.697149i \(-0.245548\pi\)
−0.962212 + 0.272302i \(0.912215\pi\)
\(710\) −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
\(716\) 96.7966 + 108.906i 0.135191 + 0.152104i
\(717\) 0 0
\(718\) 1037.23 394.327i 1.44461 0.549202i
\(719\) 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
\(722\) −115.294 303.267i −0.159687 0.420037i
\(723\) 0 0
\(724\) 55.5859 49.4052i 0.0767761 0.0682392i
\(725\) 179.553 310.995i 0.247659 0.428959i
\(726\) 0 0
\(727\) −815.055 + 470.573i −1.12112 + 0.647280i −0.941687 0.336490i \(-0.890760\pi\)
−0.179435 + 0.983770i \(0.557427\pi\)
\(728\) −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 −0.571991 0.820260i \(-0.693829\pi\)
0.996361 + 0.0852294i \(0.0271623\pi\)
\(734\) 260.707 + 212.510i 0.355186 + 0.289523i
\(735\) 0 0
\(736\) 649.376 + 185.257i 0.882304 + 0.251708i
\(737\) −436.655 −0.592477
\(738\) 0 0
\(739\) 444.439i 0.601406i −0.953718 0.300703i \(-0.902779\pi\)
0.953718 0.300703i \(-0.0972213\pi\)
\(740\) 88.9212 + 432.005i 0.120164 + 0.583791i
\(741\) 0 0
\(742\) 379.336 + 309.208i 0.511235 + 0.416723i
\(743\) −66.2270 38.2362i −0.0891346 0.0514619i 0.454770 0.890609i \(-0.349721\pi\)
−0.543905 + 0.839147i \(0.683055\pi\)
\(744\) 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 \(-0.0730457\pi\)
0.289897 + 0.957058i \(0.406379\pi\)
\(752\) −11.4652 26.6708i −0.0152463 0.0354665i
\(753\) 0 0
\(754\) 8.56870 + 22.5389i 0.0113643 + 0.0298925i
\(755\) 689.070i 0.912676i
\(756\) 0 0
\(757\) −346.346 −0.457525 −0.228762 0.973482i \(-0.573468\pi\)
−0.228762 + 0.973482i \(0.573468\pi\)
\(758\) 1126.15 428.132i 1.48568 0.564817i
\(759\) 0 0
\(760\) −164.124 258.155i −0.215952 0.339677i
\(761\) 106.565 184.576i 0.140033 0.242544i −0.787476 0.616345i \(-0.788613\pi\)
0.927509 + 0.373802i \(0.121946\pi\)
\(762\) 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 −0.986622 0.163025i \(-0.947875\pi\)
0.634495 + 0.772927i \(0.281208\pi\)
\(770\) 392.304 481.278i 0.509486 0.625036i
\(771\) 0 0
\(772\) −244.416 1187.44i −0.316601 1.53814i
\(773\) −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
\(776\) −2.45278 57.4098i −0.00316080 0.0739818i
\(777\) 0 0
\(778\) −271.242 + 332.759i −0.348640 + 0.427710i
\(779\) −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 −0.0764944