Properties

Label 108.3.f.c.19.3
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 19.3
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 \(\chi\) \(=\) 108.19
Dual form 108.3.f.c.91.3

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.697956 0.716140i \(-0.254093\pi\)
−0.969174 + 0.246378i \(0.920760\pi\)
\(6\) 0 0
\(7\) −10.0431 5.79837i −1.43473 0.828339i −0.437249 0.899340i \(-0.644047\pi\)
−0.997476 + 0.0710013i \(0.977381\pi\)
\(8\) 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 0.0582943 0.998299i \(-0.481434\pi\)
−0.835406 + 0.549634i \(0.814767\pi\)
\(12\) 0 0
\(13\) 0.296185 + 0.513008i 0.0227835 + 0.0394622i 0.877192 0.480139i \(-0.159414\pi\)
−0.854409 + 0.519601i \(0.826080\pi\)
\(14\) 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 \(-0.879007\pi\)
0.928624 0.371023i \(-0.120993\pi\)
\(20\) −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 −0.841574 0.540142i \(-0.818370\pi\)
0.0469902 + 0.998895i \(0.485037\pi\)
\(24\) 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 −0.713070 0.701093i \(-0.752696\pi\)
0.250629 + 0.968083i \(0.419362\pi\)
\(32\) −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 −0.999793 0.0203330i \(-0.993527\pi\)
0.482288 0.876013i \(-0.339806\pi\)
\(42\) 0 0
\(43\) 32.2385 + 18.6129i 0.749732 + 0.432858i 0.825597 0.564260i \(-0.190838\pi\)
−0.0758649 + 0.997118i \(0.524172\pi\)
\(44\) 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 0.516623 0.856213i \(-0.327189\pi\)
−0.483191 + 0.875515i \(0.660522\pi\)
\(48\) 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 0.319427 0.947611i \(-0.396510\pi\)
0.980369 + 0.197174i \(0.0631764\pi\)
\(60\) 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 −0.186064 0.982538i \(-0.559573\pi\)
0.757871 + 0.652405i \(0.226240\pi\)
\(68\) −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 \(-0.711473\pi\)
0.616557 0.787310i \(-0.288527\pi\)
\(72\) 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 0.551637 0.834084i \(-0.314003\pi\)
−0.446519 + 0.894774i \(0.647337\pi\)
\(80\) 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 0.872973 0.487768i \(-0.162189\pi\)
0.0140672 + 0.999901i \(0.495522\pi\)
\(84\) 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 −0.883944 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 −0.833924 0.551879i \(-0.813911\pi\)
0.0609793 + 0.998139i \(0.480578\pi\)
\(104\) 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 \(0.167942\pi\)
−0.864016 + 0.503465i \(0.832058\pi\)
\(108\) 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 0.876245 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
\(122\) 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 \(-0.989507\pi\)
0.999457 0.0329574i \(-0.0104926\pi\)
\(128\) 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 −0.870121 0.492837i \(-0.835960\pi\)
−0.00825098 + 0.999966i \(0.502626\pi\)
\(132\) 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 0.0504522 0.998726i \(-0.483934\pi\)
0.890149 + 0.455670i \(0.150600\pi\)
\(140\) 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 0.520577 0.853815i \(-0.325717\pi\)
−0.999714 + 0.0239255i \(0.992384\pi\)
\(150\) 0 0
\(151\) −220.027 127.033i −1.45713 0.841276i −0.458263 0.888817i \(-0.651528\pi\)
−0.998869 + 0.0475407i \(0.984862\pi\)
\(152\) −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 \(0.827953\pi\)
\(158\) −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 \(-0.941523\pi\)
0.983173 0.182679i \(-0.0584770\pi\)
\(164\) −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 −0.734244 0.678886i \(-0.762463\pi\)
0.220810 + 0.975317i \(0.429130\pi\)
\(168\) 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
\(176\) 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 \(0.0324441\pi\)
−0.994810 + 0.101750i \(0.967556\pi\)
\(180\) 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 −0.305260 0.952269i \(-0.598743\pi\)
−0.977319 + 0.211772i \(0.932077\pi\)
\(192\) 0 0
\(193\) −151.542 262.479i −0.785193 1.35999i −0.928884 0.370372i \(-0.879230\pi\)
0.143691 0.989623i \(-0.454103\pi\)
\(194\) −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 \(-0.991014\pi\)
0.999602 0.0282253i \(-0.00898558\pi\)
\(200\) 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 −0.210492 0.977595i \(-0.567507\pi\)
0.741376 + 0.671090i \(0.234173\pi\)
\(212\) −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 0.889383 0.457163i \(-0.151134\pi\)
0.0487765 + 0.998810i \(0.484468\pi\)
\(224\) 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 0.998856 0.0478181i \(-0.0152268\pi\)
0.458016 + 0.888944i \(0.348560\pi\)
\(228\) 0 0
\(229\) 74.6642 + 129.322i 0.326044 + 0.564725i 0.981723 0.190315i \(-0.0609508\pi\)
−0.655679 + 0.755040i \(0.727617\pi\)
\(230\) −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 0.0317388 0.999496i \(-0.489896\pi\)
0.881458 + 0.472262i \(0.156562\pi\)
\(240\) 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
\(248\) −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 \(-0.910413\pi\)
0.960655 0.277746i \(-0.0895874\pi\)
\(252\) 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 −0.806029 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 0.541616 0.840626i \(-0.317813\pi\)
−0.457195 + 0.889366i \(0.651146\pi\)
\(264\) 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 \(0.265961\pi\)
−0.670777 + 0.741659i \(0.734039\pi\)
\(272\) 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 −0.746565 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 −0.268104 0.963390i \(-0.586397\pi\)
0.700268 + 0.713880i \(0.253064\pi\)
\(284\) −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 0.928415 + 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
\(302\) 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 \(0.111289\pi\)
−0.939502 + 0.342545i \(0.888711\pi\)
\(308\) 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 −0.310824 0.950467i \(-0.600605\pi\)
0.667717 + 0.744416i \(0.267272\pi\)
\(312\) 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
\(320\) −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 −0.177845 0.984058i \(-0.556913\pi\)
−0.941142 + 0.338011i \(0.890246\pi\)
\(332\) −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 \(0.683919\pi\)
\(338\) 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 −0.695898 0.718140i \(-0.744994\pi\)
0.273979 + 0.961736i \(0.411660\pi\)
\(348\) 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
\(356\) 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 \(-0.718885\pi\)
0.634721 0.772741i \(-0.281115\pi\)
\(360\) 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 0.288277 0.957547i \(-0.406918\pi\)
−0.685122 + 0.728429i \(0.740251\pi\)
\(368\) −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 \(0.681069\pi\)
\(374\) 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 \(-0.707621\pi\)
0.606986 0.794713i \(-0.292379\pi\)
\(380\) 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 −0.851946 0.523630i \(-0.824578\pi\)
0.0275035 + 0.999622i \(0.491244\pi\)
\(384\) 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
\(392\) 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 0.722577 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 \(0.680448\pi\)
\(410\) −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 −0.783847 0.620954i \(-0.786745\pi\)
0.145838 + 0.989308i \(0.453412\pi\)
\(420\) 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
\(428\) 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 \(0.184787\pi\)
−0.836174 + 0.548465i \(0.815213\pi\)
\(432\) 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 0.845972 0.533228i \(-0.179021\pi\)
−0.0388030 + 0.999247i \(0.512354\pi\)
\(440\) 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 \(-0.996392\pi\)
−0.509785 0.860302i \(1.32972\pi\)
\(444\) 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 −0.674332 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 0.463677 0.886004i \(-0.346530\pi\)
0.999141 + 0.0414459i \(0.0131964\pi\)
\(464\) −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 \(0.251336\pi\)
−0.704133 + 0.710068i \(0.748664\pi\)
\(468\) 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 0.954459 0.298344i \(-0.0964341\pi\)
0.218856 + 0.975757i \(0.429767\pi\)
\(480\) 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 \(0.0935338\pi\)
−0.957137 + 0.289635i \(0.906466\pi\)
\(488\) 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 0.344534 0.938774i \(-0.388037\pi\)
0.985269 + 0.171012i \(0.0547036\pi\)
\(492\) 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 0.0188362 0.999823i \(-0.494004\pi\)
0.875290 + 0.483599i \(0.160671\pi\)
\(500\) 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 \(-0.825732\pi\)
0.853839 0.520537i \(-0.174268\pi\)
\(504\) 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 0.999545 + 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
\(518\) −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 \(0.139610\pi\)
−0.905347 + 0.424672i \(0.860390\pi\)
\(524\) 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 0.366664 0.930353i \(-0.380500\pi\)
−0.622377 + 0.782717i \(0.713833\pi\)
\(548\) 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 −0.260725 0.965413i \(-0.583962\pi\)
0.705710 + 0.708501i \(0.250628\pi\)
\(564\) 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 −0.789285 0.614027i \(-0.789549\pi\)
0.137121 + 0.990554i \(0.456215\pi\)
\(572\) −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 −0.161358 0.986896i \(-0.551587\pi\)
−0.935356 + 0.353708i \(0.884921\pi\)
\(588\) 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 0.432384 0.901689i \(-0.357672\pi\)
0.997078 + 0.0763888i \(0.0243390\pi\)
\(600\) 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 −0.821141 0.570726i \(-0.806662\pi\)
0.0836928 + 0.996492i \(0.473329\pi\)
\(608\) −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 0.812429 0.583060i \(-0.198145\pi\)
−0.911160 + 0.412054i \(0.864812\pi\)
\(618\) 0 0
\(619\) −265.675 153.388i −0.429200 0.247799i 0.269806 0.962915i \(-0.413041\pi\)
−0.699006 + 0.715116i \(0.746374\pi\)
\(620\) −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 \(-0.677360\pi\)
0.528805 0.848744i \(-0.322640\pi\)
\(632\) 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 0.0812143 + 0.996697i \(0.474120\pi\)
−0.903772 + 0.428015i \(0.859213\pi\)
\(642\) 0 0
\(643\) 42.0680 24.2880i 0.0654246 0.0377729i −0.466931 0.884294i \(-0.654640\pi\)
0.532355 + 0.846521i \(0.321307\pi\)
\(644\) −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 \(0.136858\pi\)
−0.908986 + 0.416826i \(0.863142\pi\)
\(648\) 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 0.996266 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 −0.174178 0.984714i \(-0.555727\pi\)
−0.939877 + 0.341514i \(0.889060\pi\)
\(660\) 0 0
\(661\) −359.447 622.580i −0.543792 0.941876i −0.998682 0.0513280i \(-0.983655\pi\)
0.454890 0.890548i \(-0.349679\pi\)
\(662\) 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 −0.568095 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
\(680\) −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 \(-0.863433\pi\)
0.909367 0.415995i \(-0.136567\pi\)
\(684\) 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 0.732218 0.681070i \(-0.238485\pi\)
−0.223714 + 0.974655i \(0.571818\pi\)
\(692\) 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 −0.962212 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
\(716\) 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 \(0.121648\pi\)
−0.927858 + 0.372933i \(0.878352\pi\)
\(720\) 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 −0.179435 0.983770i \(-0.557427\pi\)
−0.941687 + 0.336490i \(0.890760\pi\)
\(728\) −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 \(0.693829\pi\)
\(734\) 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 \(0.0972213\pi\)
−0.953718 + 0.300703i \(0.902779\pi\)
\(740\) 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 −0.543905 0.839147i \(-0.683055\pi\)
0.454770 + 0.890609i \(0.349721\pi\)
\(744\) 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 0.289897 0.957058i \(-0.406379\pi\)
0.973785 + 0.227471i \(0.0730457\pi\)
\(752\) −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 0.927509 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 \(0.947875\pi\)
\(770\) 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