Properties

Label 392.3.k.j.67.1
Level 392
Weight 3
Character 392.67
Analytic conductor 10.681
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.796594176.2
Defining polynomial: \(x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.1
Root \(-0.207107 - 2.54762i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.j.275.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.97374 + 0.323042i) q^{2} +(1.70711 - 2.95680i) q^{3} +(3.79129 - 1.27520i) q^{4} +(-1.34221 + 0.774923i) q^{5} +(-2.41421 + 6.38741i) q^{6} +(-7.07107 + 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +O(q^{10})\) \(q+(-1.97374 + 0.323042i) q^{2} +(1.70711 - 2.95680i) q^{3} +(3.79129 - 1.27520i) q^{4} +(-1.34221 + 0.774923i) q^{5} +(-2.41421 + 6.38741i) q^{6} +(-7.07107 + 3.74166i) q^{8} +(-1.32843 - 2.30090i) q^{9} +(2.39883 - 1.96308i) q^{10} +(2.24264 - 3.88437i) q^{11} +(2.70163 - 13.3870i) q^{12} +1.54985i q^{13} +5.29150i q^{15} +(12.7477 - 9.66930i) q^{16} +(11.8284 - 20.4874i) q^{17} +(3.36526 + 4.11224i) q^{18} +(-12.4350 - 21.5381i) q^{19} +(-4.10051 + 4.64954i) q^{20} +(-3.17157 + 8.39119i) q^{22} +(30.5055 - 17.6124i) q^{23} +(-1.00775 + 27.2951i) q^{24} +(-11.2990 + 19.5704i) q^{25} +(-0.500665 - 3.05899i) q^{26} +21.6569 q^{27} -22.4499i q^{29} +(-1.70938 - 10.4440i) q^{30} +(-40.4569 - 23.3578i) q^{31} +(-22.0371 + 23.2027i) q^{32} +(-7.65685 - 13.2621i) q^{33} +(-16.7279 + 44.2579i) q^{34} +(-7.97056 - 7.02938i) q^{36} +(-50.7340 + 29.2913i) q^{37} +(31.5012 + 38.4935i) q^{38} +(4.58258 + 2.64575i) q^{39} +(6.59133 - 10.5016i) q^{40} +26.9706 q^{41} -17.1716 q^{43} +(3.54915 - 17.5866i) q^{44} +(3.56604 + 2.05886i) q^{45} +(-54.5204 + 44.6168i) q^{46} +(31.2918 - 18.0663i) q^{47} +(-6.82843 - 54.1990i) q^{48} +(15.9792 - 42.2769i) q^{50} +(-40.3848 - 69.9485i) q^{51} +(1.97636 + 5.87591i) q^{52} +(-84.7102 - 48.9075i) q^{53} +(-42.7450 + 6.99607i) q^{54} +6.95149i q^{55} -84.9117 q^{57} +(7.25227 + 44.3103i) q^{58} +(30.7782 - 53.3094i) q^{59} +(6.74773 + 20.0616i) q^{60} +(32.6340 - 18.8412i) q^{61} +(87.3970 + 33.0329i) q^{62} +(36.0000 - 52.9150i) q^{64} +(-1.20101 - 2.08021i) q^{65} +(19.3968 + 23.7024i) q^{66} +(16.6863 - 28.9015i) q^{67} +(18.7194 - 92.7574i) q^{68} -120.265i q^{69} +102.199i q^{71} +(18.0026 + 11.2993i) q^{72} +(34.6569 - 60.0274i) q^{73} +(90.6733 - 74.2026i) q^{74} +(38.5772 + 66.8176i) q^{75} +(-74.6102 - 65.8000i) q^{76} +(-9.89949 - 3.74166i) q^{78} +(33.5156 - 19.3503i) q^{79} +(-9.61710 + 22.8567i) q^{80} +(48.9264 - 84.7430i) q^{81} +(-53.2328 + 8.71262i) q^{82} -3.61522 q^{83} +36.6645i q^{85} +(33.8922 - 5.54714i) q^{86} +(-66.3799 - 38.3245i) q^{87} +(-1.32389 + 35.8578i) q^{88} +(22.0294 + 38.1561i) q^{89} +(-7.70354 - 2.91166i) q^{90} +(93.1960 - 105.674i) q^{92} +(-138.129 + 79.7486i) q^{93} +(-55.9256 + 45.7668i) q^{94} +(33.3807 + 19.2724i) q^{95} +(30.9861 + 104.769i) q^{96} -96.1076 q^{97} -11.9167 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} + O(q^{10}) \) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} - 28q^{10} - 16q^{11} - 24q^{12} - 8q^{16} + 72q^{17} - 16q^{18} + 8q^{19} - 112q^{20} - 48q^{22} - 40q^{24} + 68q^{25} + 28q^{26} + 128q^{27} - 16q^{33} - 32q^{34} + 72q^{36} - 76q^{38} + 56q^{40} + 80q^{41} - 160q^{43} + 48q^{44} - 224q^{46} - 32q^{48} + 224q^{50} - 176q^{51} - 56q^{52} - 16q^{54} - 272q^{57} + 168q^{58} + 184q^{59} - 56q^{60} + 224q^{62} + 288q^{64} - 168q^{65} - 32q^{66} + 224q^{67} - 216q^{68} + 160q^{72} + 232q^{73} + 280q^{74} + 88q^{75} + 48q^{76} - 336q^{80} + 52q^{81} - 48q^{82} - 176q^{83} - 8q^{86} - 240q^{88} + 312q^{89} - 616q^{90} + 112q^{92} - 112q^{94} + 176q^{96} + 272q^{97} - 480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.97374 + 0.323042i −0.986869 + 0.161521i
\(3\) 1.70711 2.95680i 0.569036 0.985599i −0.427626 0.903956i \(-0.640650\pi\)
0.996662 0.0816428i \(-0.0260167\pi\)
\(4\) 3.79129 1.27520i 0.947822 0.318800i
\(5\) −1.34221 + 0.774923i −0.268441 + 0.154985i −0.628179 0.778069i \(-0.716199\pi\)
0.359738 + 0.933053i \(0.382866\pi\)
\(6\) −2.41421 + 6.38741i −0.402369 + 1.06457i
\(7\) 0 0
\(8\) −7.07107 + 3.74166i −0.883883 + 0.467707i
\(9\) −1.32843 2.30090i −0.147603 0.255656i
\(10\) 2.39883 1.96308i 0.239883 0.196308i
\(11\) 2.24264 3.88437i 0.203876 0.353124i −0.745898 0.666060i \(-0.767979\pi\)
0.949774 + 0.312936i \(0.101313\pi\)
\(12\) 2.70163 13.3870i 0.225135 1.11558i
\(13\) 1.54985i 0.119219i 0.998222 + 0.0596094i \(0.0189855\pi\)
−0.998222 + 0.0596094i \(0.981014\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) 12.7477 9.66930i 0.796733 0.604332i
\(17\) 11.8284 20.4874i 0.695790 1.20514i −0.274124 0.961694i \(-0.588388\pi\)
0.969914 0.243449i \(-0.0782788\pi\)
\(18\) 3.36526 + 4.11224i 0.186959 + 0.228458i
\(19\) −12.4350 21.5381i −0.654475 1.13358i −0.982025 0.188750i \(-0.939556\pi\)
0.327550 0.944834i \(-0.393777\pi\)
\(20\) −4.10051 + 4.64954i −0.205025 + 0.232477i
\(21\) 0 0
\(22\) −3.17157 + 8.39119i −0.144162 + 0.381418i
\(23\) 30.5055 17.6124i 1.32633 0.765756i 0.341598 0.939846i \(-0.389032\pi\)
0.984730 + 0.174090i \(0.0556985\pi\)
\(24\) −1.00775 + 27.2951i −0.0419896 + 1.13730i
\(25\) −11.2990 + 19.5704i −0.451960 + 0.782817i
\(26\) −0.500665 3.05899i −0.0192563 0.117653i
\(27\) 21.6569 0.802106
\(28\) 0 0
\(29\) 22.4499i 0.774136i −0.922051 0.387068i \(-0.873488\pi\)
0.922051 0.387068i \(-0.126512\pi\)
\(30\) −1.70938 10.4440i −0.0569792 0.348135i
\(31\) −40.4569 23.3578i −1.30506 0.753478i −0.323795 0.946127i \(-0.604959\pi\)
−0.981268 + 0.192649i \(0.938292\pi\)
\(32\) −22.0371 + 23.2027i −0.688659 + 0.725085i
\(33\) −7.65685 13.2621i −0.232026 0.401881i
\(34\) −16.7279 + 44.2579i −0.491998 + 1.30170i
\(35\) 0 0
\(36\) −7.97056 7.02938i −0.221405 0.195260i
\(37\) −50.7340 + 29.2913i −1.37119 + 0.791657i −0.991078 0.133284i \(-0.957448\pi\)
−0.380111 + 0.924941i \(0.624114\pi\)
\(38\) 31.5012 + 38.4935i 0.828979 + 1.01299i
\(39\) 4.58258 + 2.64575i 0.117502 + 0.0678398i
\(40\) 6.59133 10.5016i 0.164783 0.262540i
\(41\) 26.9706 0.657819 0.328909 0.944362i \(-0.393319\pi\)
0.328909 + 0.944362i \(0.393319\pi\)
\(42\) 0 0
\(43\) −17.1716 −0.399339 −0.199669 0.979863i \(-0.563987\pi\)
−0.199669 + 0.979863i \(0.563987\pi\)
\(44\) 3.54915 17.5866i 0.0806625 0.399695i
\(45\) 3.56604 + 2.05886i 0.0792454 + 0.0457524i
\(46\) −54.5204 + 44.6168i −1.18523 + 0.969930i
\(47\) 31.2918 18.0663i 0.665783 0.384390i −0.128694 0.991684i \(-0.541079\pi\)
0.794477 + 0.607295i \(0.207745\pi\)
\(48\) −6.82843 54.1990i −0.142259 1.12915i
\(49\) 0 0
\(50\) 15.9792 42.2769i 0.319584 0.845539i
\(51\) −40.3848 69.9485i −0.791858 1.37154i
\(52\) 1.97636 + 5.87591i 0.0380070 + 0.112998i
\(53\) −84.7102 48.9075i −1.59831 0.922782i −0.991814 0.127693i \(-0.959243\pi\)
−0.606492 0.795090i \(1.29258\pi\)
\(54\) −42.7450 + 6.99607i −0.791573 + 0.129557i
\(55\) 6.95149i 0.126391i
\(56\) 0 0
\(57\) −84.9117 −1.48968
\(58\) 7.25227 + 44.3103i 0.125039 + 0.763971i
\(59\) 30.7782 53.3094i 0.521664 0.903549i −0.478018 0.878350i \(-0.658645\pi\)
0.999682 0.0251987i \(-0.00802186\pi\)
\(60\) 6.74773 + 20.0616i 0.112462 + 0.334360i
\(61\) 32.6340 18.8412i 0.534983 0.308873i −0.208060 0.978116i \(-0.566715\pi\)
0.743043 + 0.669243i \(0.233382\pi\)
\(62\) 87.3970 + 33.0329i 1.40963 + 0.532790i
\(63\) 0 0
\(64\) 36.0000 52.9150i 0.562500 0.826797i
\(65\) −1.20101 2.08021i −0.0184771 0.0320032i
\(66\) 19.3968 + 23.7024i 0.293891 + 0.359127i
\(67\) 16.6863 28.9015i 0.249049 0.431366i −0.714213 0.699928i \(-0.753215\pi\)
0.963262 + 0.268563i \(0.0865486\pi\)
\(68\) 18.7194 92.7574i 0.275285 1.36408i
\(69\) 120.265i 1.74297i
\(70\) 0 0
\(71\) 102.199i 1.43942i 0.694277 + 0.719708i \(0.255724\pi\)
−0.694277 + 0.719708i \(0.744276\pi\)
\(72\) 18.0026 + 11.2993i 0.250036 + 0.156935i
\(73\) 34.6569 60.0274i 0.474751 0.822294i −0.524830 0.851207i \(-0.675871\pi\)
0.999582 + 0.0289132i \(0.00920463\pi\)
\(74\) 90.6733 74.2026i 1.22532 1.00274i
\(75\) 38.5772 + 66.8176i 0.514362 + 0.890901i
\(76\) −74.6102 65.8000i −0.981713 0.865789i
\(77\) 0 0
\(78\) −9.89949 3.74166i −0.126917 0.0479700i
\(79\) 33.5156 19.3503i 0.424248 0.244940i −0.272645 0.962115i \(-0.587898\pi\)
0.696893 + 0.717175i \(0.254565\pi\)
\(80\) −9.61710 + 22.8567i −0.120214 + 0.285709i
\(81\) 48.9264 84.7430i 0.604030 1.04621i
\(82\) −53.2328 + 8.71262i −0.649181 + 0.106251i
\(83\) −3.61522 −0.0435569 −0.0217785 0.999763i \(-0.506933\pi\)
−0.0217785 + 0.999763i \(0.506933\pi\)
\(84\) 0 0
\(85\) 36.6645i 0.431347i
\(86\) 33.8922 5.54714i 0.394095 0.0645016i
\(87\) −66.3799 38.3245i −0.762987 0.440511i
\(88\) −1.32389 + 35.8578i −0.0150442 + 0.407475i
\(89\) 22.0294 + 38.1561i 0.247522 + 0.428720i 0.962838 0.270081i \(-0.0870505\pi\)
−0.715316 + 0.698801i \(0.753717\pi\)
\(90\) −7.70354 2.91166i −0.0855948 0.0323518i
\(91\) 0 0
\(92\) 93.1960 105.674i 1.01300 1.14863i
\(93\) −138.129 + 79.7486i −1.48525 + 0.857512i
\(94\) −55.9256 + 45.7668i −0.594953 + 0.486880i
\(95\) 33.3807 + 19.2724i 0.351376 + 0.202867i
\(96\) 30.9861 + 104.769i 0.322772 + 1.09134i
\(97\) −96.1076 −0.990800 −0.495400 0.868665i \(-0.664979\pi\)
−0.495400 + 0.868665i \(0.664979\pi\)
\(98\) 0 0
\(99\) −11.9167 −0.120371
\(100\) −17.8815 + 88.6056i −0.178815 + 0.886056i
\(101\) 16.9881 + 9.80808i 0.168199 + 0.0971097i 0.581736 0.813377i \(-0.302374\pi\)
−0.413537 + 0.910487i \(0.635707\pi\)
\(102\) 102.305 + 125.014i 1.00299 + 1.22563i
\(103\) −37.3120 + 21.5421i −0.362252 + 0.209146i −0.670068 0.742300i \(-0.733735\pi\)
0.307816 + 0.951446i \(0.400402\pi\)
\(104\) −5.79899 10.9591i −0.0557595 0.105376i
\(105\) 0 0
\(106\) 182.995 + 69.1656i 1.72637 + 0.652506i
\(107\) −7.79899 13.5082i −0.0728878 0.126245i 0.827278 0.561793i \(-0.189888\pi\)
−0.900166 + 0.435547i \(0.856555\pi\)
\(108\) 82.1074 27.6168i 0.760253 0.255711i
\(109\) −3.33576 1.92590i −0.0306033 0.0176688i 0.484620 0.874725i \(-0.338958\pi\)
−0.515224 + 0.857056i \(0.672291\pi\)
\(110\) −2.24562 13.7204i −0.0204148 0.124731i
\(111\) 200.013i 1.80192i
\(112\) 0 0
\(113\) −13.7746 −0.121899 −0.0609496 0.998141i \(-0.519413\pi\)
−0.0609496 + 0.998141i \(0.519413\pi\)
\(114\) 167.593 27.4300i 1.47012 0.240614i
\(115\) −27.2965 + 47.2789i −0.237361 + 0.411121i
\(116\) −28.6282 85.1142i −0.246795 0.733743i
\(117\) 3.56604 2.05886i 0.0304790 0.0175971i
\(118\) −43.5269 + 115.161i −0.368872 + 0.975944i
\(119\) 0 0
\(120\) −19.7990 37.4166i −0.164992 0.311805i
\(121\) 50.4411 + 87.3666i 0.416869 + 0.722038i
\(122\) −58.3245 + 47.7298i −0.478069 + 0.391228i
\(123\) 46.0416 79.7464i 0.374322 0.648345i
\(124\) −183.170 36.9655i −1.47718 0.298109i
\(125\) 73.7695i 0.590156i
\(126\) 0 0
\(127\) 125.025i 0.984445i 0.870469 + 0.492223i \(0.163815\pi\)
−0.870469 + 0.492223i \(0.836185\pi\)
\(128\) −53.9608 + 116.070i −0.421569 + 0.906796i
\(129\) −29.3137 + 50.7728i −0.227238 + 0.393588i
\(130\) 3.04248 + 3.71782i 0.0234037 + 0.0285986i
\(131\) 50.1751 + 86.9059i 0.383016 + 0.663404i 0.991492 0.130169i \(-0.0415519\pi\)
−0.608475 + 0.793573i \(0.708219\pi\)
\(132\) −45.9411 40.5163i −0.348039 0.306941i
\(133\) 0 0
\(134\) −23.5980 + 62.4344i −0.176104 + 0.465928i
\(135\) −29.0679 + 16.7824i −0.215318 + 0.124314i
\(136\) −6.98264 + 189.126i −0.0513430 + 1.39063i
\(137\) −28.6569 + 49.6351i −0.209174 + 0.362300i −0.951455 0.307789i \(-0.900411\pi\)
0.742280 + 0.670089i \(0.233744\pi\)
\(138\) 38.8506 + 237.371i 0.281526 + 1.72008i
\(139\) 183.664 1.32132 0.660662 0.750684i \(-0.270276\pi\)
0.660662 + 0.750684i \(0.270276\pi\)
\(140\) 0 0
\(141\) 123.365i 0.874926i
\(142\) −33.0144 201.713i −0.232496 1.42052i
\(143\) 6.02017 + 3.47575i 0.0420991 + 0.0243059i
\(144\) −39.1826 16.4863i −0.272101 0.114488i
\(145\) 17.3970 + 30.1324i 0.119979 + 0.207810i
\(146\) −49.0122 + 129.674i −0.335700 + 0.888179i
\(147\) 0 0
\(148\) −154.995 + 175.748i −1.04726 + 1.18748i
\(149\) 166.545 96.1549i 1.11775 0.645335i 0.176927 0.984224i \(-0.443384\pi\)
0.940826 + 0.338889i \(0.110051\pi\)
\(150\) −97.7261 119.418i −0.651508 0.796123i
\(151\) 99.3791 + 57.3765i 0.658140 + 0.379977i 0.791568 0.611081i \(-0.209265\pi\)
−0.133428 + 0.991058i \(0.542599\pi\)
\(152\) 168.517 + 105.770i 1.10867 + 0.695854i
\(153\) −62.8528 −0.410803
\(154\) 0 0
\(155\) 72.4020 0.467110
\(156\) 20.7477 + 4.18710i 0.132998 + 0.0268404i
\(157\) −183.724 106.073i −1.17022 0.675625i −0.216486 0.976286i \(-0.569460\pi\)
−0.953731 + 0.300661i \(0.902793\pi\)
\(158\) −59.9001 + 49.0193i −0.379115 + 0.310249i
\(159\) −289.219 + 166.981i −1.81899 + 1.05019i
\(160\) 11.5980 48.2199i 0.0724874 0.301374i
\(161\) 0 0
\(162\) −69.1924 + 183.066i −0.427114 + 1.13004i
\(163\) 120.267 + 208.309i 0.737835 + 1.27797i 0.953469 + 0.301493i \(0.0974849\pi\)
−0.215634 + 0.976474i \(0.569182\pi\)
\(164\) 102.253 34.3929i 0.623495 0.209713i
\(165\) 20.5541 + 11.8669i 0.124571 + 0.0719208i
\(166\) 7.13551 1.16787i 0.0429850 0.00703535i
\(167\) 212.101i 1.27006i 0.772486 + 0.635032i \(0.219013\pi\)
−0.772486 + 0.635032i \(0.780987\pi\)
\(168\) 0 0
\(169\) 166.598 0.985787
\(170\) −11.8442 72.3661i −0.0696715 0.425683i
\(171\) −33.0381 + 57.2236i −0.193205 + 0.334641i
\(172\) −65.1024 + 21.8972i −0.378502 + 0.127309i
\(173\) 157.801 91.1065i 0.912145 0.526627i 0.0310245 0.999519i \(-0.490123\pi\)
0.881121 + 0.472891i \(0.156790\pi\)
\(174\) 143.397 + 54.1990i 0.824121 + 0.311488i
\(175\) 0 0
\(176\) −8.97056 71.2016i −0.0509691 0.404555i
\(177\) −105.083 182.010i −0.593691 1.02830i
\(178\) −55.8064 68.1937i −0.313519 0.383111i
\(179\) −28.6030 + 49.5419i −0.159793 + 0.276770i −0.934794 0.355190i \(-0.884416\pi\)
0.775001 + 0.631960i \(0.217749\pi\)
\(180\) 16.1454 + 3.25830i 0.0896964 + 0.0181016i
\(181\) 326.212i 1.80228i −0.433533 0.901138i \(-0.642733\pi\)
0.433533 0.901138i \(-0.357267\pi\)
\(182\) 0 0
\(183\) 128.656i 0.703039i
\(184\) −149.807 + 238.680i −0.814170 + 1.29717i
\(185\) 45.3970 78.6299i 0.245389 0.425026i
\(186\) 246.868 202.024i 1.32725 1.08615i
\(187\) −53.0538 91.8919i −0.283710 0.491401i
\(188\) 95.5980 108.398i 0.508500 0.576585i
\(189\) 0 0
\(190\) −72.1106 27.2552i −0.379530 0.143449i
\(191\) 84.0589 48.5314i 0.440099 0.254091i −0.263541 0.964648i \(-0.584890\pi\)
0.703639 + 0.710557i \(0.251557\pi\)
\(192\) −95.0031 196.776i −0.494808 1.02488i
\(193\) −78.6518 + 136.229i −0.407522 + 0.705849i −0.994611 0.103673i \(-0.966940\pi\)
0.587089 + 0.809522i \(0.300274\pi\)
\(194\) 189.691 31.0468i 0.977791 0.160035i
\(195\) −8.20101 −0.0420565
\(196\) 0 0
\(197\) 124.117i 0.630034i −0.949086 0.315017i \(-0.897990\pi\)
0.949086 0.315017i \(-0.102010\pi\)
\(198\) 23.5205 3.84961i 0.118791 0.0194425i
\(199\) 156.729 + 90.4874i 0.787581 + 0.454710i 0.839110 0.543961i \(-0.183076\pi\)
−0.0515289 + 0.998672i \(0.516409\pi\)
\(200\) 6.67010 180.661i 0.0333505 0.903304i
\(201\) −56.9706 98.6759i −0.283436 0.490925i
\(202\) −36.6985 13.8707i −0.181676 0.0686669i
\(203\) 0 0
\(204\) −242.309 213.696i −1.18779 1.04753i
\(205\) −36.2000 + 20.9001i −0.176586 + 0.101952i
\(206\) 66.6851 54.5717i 0.323714 0.264911i
\(207\) −81.0488 46.7935i −0.391540 0.226056i
\(208\) 14.9859 + 19.7570i 0.0720477 + 0.0949856i
\(209\) −111.549 −0.533728
\(210\) 0 0
\(211\) 164.049 0.777482 0.388741 0.921347i \(-0.372910\pi\)
0.388741 + 0.921347i \(0.372910\pi\)
\(212\) −383.528 77.3998i −1.80909 0.365093i
\(213\) 302.180 + 174.464i 1.41869 + 0.819079i
\(214\) 19.7569 + 24.1423i 0.0923219 + 0.112815i
\(215\) 23.0478 13.3066i 0.107199 0.0618913i
\(216\) −153.137 + 81.0325i −0.708968 + 0.375151i
\(217\) 0 0
\(218\) 7.20606 + 2.72363i 0.0330553 + 0.0124937i
\(219\) −118.326 204.946i −0.540301 0.935829i
\(220\) 8.86455 + 26.3551i 0.0402934 + 0.119796i
\(221\) 31.7524 + 18.3322i 0.143676 + 0.0829513i
\(222\) −64.6127 394.774i −0.291048 1.77826i
\(223\) 10.5830i 0.0474574i −0.999718 0.0237287i \(-0.992446\pi\)
0.999718 0.0237287i \(-0.00755379\pi\)
\(224\) 0 0
\(225\) 60.0395 0.266842
\(226\) 27.1875 4.44977i 0.120299 0.0196893i
\(227\) 52.9031 91.6308i 0.233053 0.403660i −0.725652 0.688062i \(-0.758462\pi\)
0.958705 + 0.284402i \(0.0917951\pi\)
\(228\) −321.925 + 108.279i −1.41195 + 0.474910i
\(229\) −64.8469 + 37.4394i −0.283174 + 0.163491i −0.634860 0.772628i \(-0.718942\pi\)
0.351685 + 0.936118i \(0.385609\pi\)
\(230\) 38.6030 102.134i 0.167839 0.444061i
\(231\) 0 0
\(232\) 84.0000 + 158.745i 0.362069 + 0.684246i
\(233\) 209.569 + 362.983i 0.899436 + 1.55787i 0.828217 + 0.560408i \(0.189356\pi\)
0.0712190 + 0.997461i \(0.477311\pi\)
\(234\) −6.37334 + 5.21563i −0.0272365 + 0.0222890i
\(235\) −28.0000 + 48.4974i −0.119149 + 0.206372i
\(236\) 48.7088 241.359i 0.206393 1.02271i
\(237\) 132.132i 0.557518i
\(238\) 0 0
\(239\) 148.318i 0.620577i −0.950642 0.310288i \(-0.899574\pi\)
0.950642 0.310288i \(-0.100426\pi\)
\(240\) 51.1652 + 67.4546i 0.213188 + 0.281061i
\(241\) −229.936 + 398.261i −0.954092 + 1.65254i −0.217658 + 0.976025i \(0.569842\pi\)
−0.736433 + 0.676510i \(0.763492\pi\)
\(242\) −127.781 156.144i −0.528019 0.645224i
\(243\) −69.5894 120.532i −0.286376 0.496018i
\(244\) 99.6985 113.047i 0.408600 0.463309i
\(245\) 0 0
\(246\) −65.1127 + 172.272i −0.264686 + 0.700293i
\(247\) 33.3807 19.2724i 0.135145 0.0780258i
\(248\) 373.471 + 13.7888i 1.50593 + 0.0555998i
\(249\) −6.17157 + 10.6895i −0.0247854 + 0.0429296i
\(250\) 23.8306 + 145.602i 0.0953226 + 0.582407i
\(251\) −124.919 −0.497685 −0.248842 0.968544i \(-0.580050\pi\)
−0.248842 + 0.968544i \(0.580050\pi\)
\(252\) 0 0
\(253\) 157.993i 0.624478i
\(254\) −40.3882 246.766i −0.159009 0.971519i
\(255\) 108.409 + 62.5902i 0.425135 + 0.245452i
\(256\) 69.0091 246.523i 0.269567 0.962982i
\(257\) −213.676 370.098i −0.831425 1.44007i −0.896908 0.442216i \(-0.854192\pi\)
0.0654835 0.997854i \(-0.479141\pi\)
\(258\) 41.4558 109.682i 0.160682 0.425123i
\(259\) 0 0
\(260\) −7.20606 6.35515i −0.0277156 0.0244429i
\(261\) −51.6552 + 29.8231i −0.197912 + 0.114265i
\(262\) −127.107 155.321i −0.485141 0.592828i
\(263\) 223.109 + 128.812i 0.848322 + 0.489779i 0.860084 0.510152i \(-0.170411\pi\)
−0.0117625 + 0.999931i \(0.503744\pi\)
\(264\) 103.764 + 65.1276i 0.393046 + 0.246695i
\(265\) 151.598 0.572068
\(266\) 0 0
\(267\) 150.426 0.563395
\(268\) 26.4073 130.852i 0.0985348 0.488255i
\(269\) 186.408 + 107.623i 0.692968 + 0.400085i 0.804723 0.593650i \(-0.202314\pi\)
−0.111755 + 0.993736i \(0.535647\pi\)
\(270\) 51.9511 42.5142i 0.192412 0.157460i
\(271\) 327.833 189.275i 1.20972 0.698431i 0.247020 0.969010i \(-0.420549\pi\)
0.962698 + 0.270580i \(0.0872154\pi\)
\(272\) −47.3137 375.541i −0.173947 1.38067i
\(273\) 0 0
\(274\) 40.5269 107.224i 0.147908 0.391329i
\(275\) 50.6791 + 87.7789i 0.184288 + 0.319196i
\(276\) −153.362 455.959i −0.555659 1.65202i
\(277\) −144.149 83.2243i −0.520393 0.300449i 0.216703 0.976238i \(-0.430470\pi\)
−0.737095 + 0.675789i \(0.763803\pi\)
\(278\) −362.505 + 59.3312i −1.30397 + 0.213421i
\(279\) 124.117i 0.444863i
\(280\) 0 0
\(281\) −421.765 −1.50094 −0.750471 0.660904i \(-0.770173\pi\)
−0.750471 + 0.660904i \(0.770173\pi\)
\(282\) 39.8519 + 243.489i 0.141319 + 0.863437i
\(283\) −172.719 + 299.159i −0.610316 + 1.05710i 0.380872 + 0.924628i \(0.375624\pi\)
−0.991187 + 0.132470i \(0.957709\pi\)
\(284\) 130.324 + 387.464i 0.458886 + 1.36431i
\(285\) 113.969 65.8000i 0.399891 0.230877i
\(286\) −13.0051 4.91545i −0.0454722 0.0171869i
\(287\) 0 0
\(288\) 82.6619 + 19.8821i 0.287021 + 0.0690350i
\(289\) −135.323 234.387i −0.468247 0.811028i
\(290\) −44.0711 53.8536i −0.151969 0.185702i
\(291\) −164.066 + 284.171i −0.563801 + 0.976532i
\(292\) 54.8471 271.776i 0.187833 0.930739i
\(293\) 511.038i 1.74416i 0.489365 + 0.872079i \(0.337229\pi\)
−0.489365 + 0.872079i \(0.662771\pi\)
\(294\) 0 0
\(295\) 95.4028i 0.323399i
\(296\) 249.146 396.950i 0.841708 1.34105i
\(297\) 48.5685 84.1232i 0.163530 0.283243i
\(298\) −297.655 + 243.586i −0.998841 + 0.817402i
\(299\) 27.2965 + 47.2789i 0.0912925 + 0.158123i
\(300\) 231.463 + 204.131i 0.771543 + 0.680437i
\(301\) 0 0
\(302\) −214.683 81.1427i −0.710872 0.268684i
\(303\) 58.0010 33.4869i 0.191422 0.110518i
\(304\) −366.777 154.324i −1.20650 0.507644i
\(305\) −29.2010 + 50.5776i −0.0957410 + 0.165828i
\(306\) 124.055 20.3041i 0.405409 0.0663532i
\(307\) −223.331 −0.727462 −0.363731 0.931504i \(-0.618497\pi\)
−0.363731 + 0.931504i \(0.618497\pi\)
\(308\) 0 0
\(309\) 147.098i 0.476047i
\(310\) −142.903 + 23.3889i −0.460976 + 0.0754480i
\(311\) 10.7376 + 6.19938i 0.0345262 + 0.0199337i 0.517164 0.855886i \(-0.326988\pi\)
−0.482638 + 0.875820i \(0.660321\pi\)
\(312\) −42.3032 1.56186i −0.135587 0.00500596i
\(313\) 205.024 + 355.113i 0.655030 + 1.13455i 0.981886 + 0.189471i \(0.0606774\pi\)
−0.326856 + 0.945074i \(0.605989\pi\)
\(314\) 396.889 + 150.010i 1.26398 + 0.477739i
\(315\) 0 0
\(316\) 102.392 116.102i 0.324025 0.367410i
\(317\) 112.857 65.1580i 0.356016 0.205546i −0.311316 0.950306i \(-0.600770\pi\)
0.667332 + 0.744761i \(0.267436\pi\)
\(318\) 516.900 423.006i 1.62547 1.33021i
\(319\) −87.2038 50.3472i −0.273366 0.157828i
\(320\) −7.31434 + 98.9200i −0.0228573 + 0.309125i
\(321\) −53.2548 −0.165903
\(322\) 0 0
\(323\) −588.347 −1.82151
\(324\) 77.4297 383.676i 0.238981 1.18419i
\(325\) −30.3311 17.5117i −0.0933266 0.0538821i
\(326\) −304.668 372.295i −0.934565 1.14201i
\(327\) −11.3890 + 6.57544i −0.0348287 + 0.0201084i
\(328\) −190.711 + 100.915i −0.581435 + 0.307666i
\(329\) 0 0
\(330\) −44.4020 16.7824i −0.134552 0.0508557i
\(331\) −107.130 185.555i −0.323655 0.560588i 0.657584 0.753381i \(-0.271579\pi\)
−0.981239 + 0.192794i \(0.938245\pi\)
\(332\) −13.7064 + 4.61014i −0.0412842 + 0.0138859i
\(333\) 134.793 + 77.8227i 0.404783 + 0.233702i
\(334\) −68.5174 418.631i −0.205142 1.25339i
\(335\) 51.7223i 0.154395i
\(336\) 0 0
\(337\) 164.049 0.486792 0.243396 0.969927i \(-0.421739\pi\)
0.243396 + 0.969927i \(0.421739\pi\)
\(338\) −328.821 + 53.8181i −0.972843 + 0.159225i
\(339\) −23.5147 + 40.7287i −0.0693650 + 0.120144i
\(340\) 46.7545 + 139.006i 0.137513 + 0.408840i
\(341\) −181.461 + 104.766i −0.532143 + 0.307233i
\(342\) 46.7229 123.617i 0.136617 0.361454i
\(343\) 0 0
\(344\) 121.421 64.2501i 0.352969 0.186774i
\(345\) 93.1960 + 161.420i 0.270133 + 0.467884i
\(346\) −282.027 + 230.797i −0.815107 + 0.667043i
\(347\) 54.8457 94.9955i 0.158057 0.273762i −0.776111 0.630596i \(-0.782810\pi\)
0.934168 + 0.356834i \(0.116144\pi\)
\(348\) −300.537 60.6513i −0.863611 0.174285i
\(349\) 463.479i 1.32802i 0.747723 + 0.664010i \(0.231147\pi\)
−0.747723 + 0.664010i \(0.768853\pi\)
\(350\) 0 0
\(351\) 33.5648i 0.0956261i
\(352\) 40.7067 + 137.636i 0.115644 + 0.391010i
\(353\) 39.0488 67.6345i 0.110620 0.191599i −0.805401 0.592731i \(-0.798050\pi\)
0.916020 + 0.401132i \(0.131383\pi\)
\(354\) 266.204 + 325.293i 0.751988 + 0.918907i
\(355\) −79.1960 137.171i −0.223087 0.386398i
\(356\) 132.177 + 116.569i 0.371283 + 0.327441i
\(357\) 0 0
\(358\) 40.4508 107.023i 0.112991 0.298946i
\(359\) 316.198 182.557i 0.880774 0.508515i 0.00986020 0.999951i \(-0.496861\pi\)
0.870913 + 0.491437i \(0.163528\pi\)
\(360\) −32.9193 1.21540i −0.0914424 0.00337611i
\(361\) −128.760 + 223.019i −0.356676 + 0.617780i
\(362\) 105.380 + 643.857i 0.291105 + 1.77861i
\(363\) 344.434 0.948853
\(364\) 0 0
\(365\) 107.426i 0.294316i
\(366\) 41.5613 + 253.933i 0.113555 + 0.693807i
\(367\) −191.165 110.369i −0.520887 0.300734i 0.216411 0.976302i \(-0.430565\pi\)
−0.737297 + 0.675568i \(0.763898\pi\)
\(368\) 218.577 519.485i 0.593959 1.41164i
\(369\) −35.8284 62.0567i −0.0970960 0.168175i
\(370\) −64.2010 + 169.860i −0.173516 + 0.459081i
\(371\) 0 0
\(372\) −421.990 + 478.492i −1.13438 + 1.28627i
\(373\) −217.852 + 125.777i −0.584052 + 0.337203i −0.762742 0.646703i \(-0.776147\pi\)
0.178690 + 0.983905i \(0.442814\pi\)
\(374\) 134.399 + 164.232i 0.359356 + 0.439123i
\(375\) −218.121 125.932i −0.581657 0.335820i
\(376\) −153.668 + 244.831i −0.408692 + 0.651147i
\(377\) 34.7939 0.0922916
\(378\) 0 0
\(379\) 286.024 0.754682 0.377341 0.926074i \(-0.376839\pi\)
0.377341 + 0.926074i \(0.376839\pi\)
\(380\) 151.132 + 30.5000i 0.397716 + 0.0802631i
\(381\) 369.672 + 213.430i 0.970268 + 0.560184i
\(382\) −150.233 + 122.943i −0.393279 + 0.321840i
\(383\) −92.5727 + 53.4468i −0.241704 + 0.139548i −0.615960 0.787778i \(-0.711232\pi\)
0.374256 + 0.927326i \(0.377898\pi\)
\(384\) 251.078 + 357.695i 0.653850 + 0.931497i
\(385\) 0 0
\(386\) 111.230 294.288i 0.288162 0.762404i
\(387\) 22.8112 + 39.5101i 0.0589436 + 0.102093i
\(388\) −364.372 + 122.557i −0.939102 + 0.315867i
\(389\) 66.8405 + 38.5904i 0.171826 + 0.0992040i 0.583447 0.812151i \(-0.301704\pi\)
−0.411620 + 0.911355i \(0.635037\pi\)
\(390\) 16.1866 2.64927i 0.0415042 0.00679300i
\(391\) 833.307i 2.13122i
\(392\) 0 0
\(393\) 342.617 0.871800
\(394\) 40.0949 + 244.974i 0.101764 + 0.621761i
\(395\) −29.9899 + 51.9440i −0.0759238 + 0.131504i
\(396\) −45.1798 + 15.1962i −0.114090 + 0.0383743i
\(397\) −569.424 + 328.757i −1.43432 + 0.828103i −0.997446 0.0714218i \(-0.977246\pi\)
−0.436870 + 0.899525i \(0.643913\pi\)
\(398\) −338.573 127.968i −0.850685 0.321529i
\(399\) 0 0
\(400\) 45.1960 + 358.732i 0.112990 + 0.896830i
\(401\) −159.397 276.084i −0.397499 0.688488i 0.595918 0.803045i \(-0.296788\pi\)
−0.993417 + 0.114557i \(0.963455\pi\)
\(402\) 144.321 + 176.357i 0.359009 + 0.438698i
\(403\) 36.2010 62.7020i 0.0898288 0.155588i
\(404\) 76.9140 + 15.5220i 0.190381 + 0.0384209i
\(405\) 151.657i 0.374461i
\(406\) 0 0
\(407\) 262.759i 0.645600i
\(408\) 547.287 + 343.504i 1.34139 + 0.841923i
\(409\) 72.6325 125.803i 0.177585 0.307587i −0.763468 0.645846i \(-0.776505\pi\)
0.941053 + 0.338259i \(0.109838\pi\)
\(410\) 64.6978 52.9455i 0.157799 0.129135i
\(411\) 97.8406 + 169.465i 0.238055 + 0.412323i
\(412\) −113.990 + 129.252i −0.276675 + 0.313719i
\(413\) 0 0
\(414\) 175.085 + 66.1760i 0.422911 + 0.159846i
\(415\) 4.85237 2.80152i 0.0116925 0.00675065i
\(416\) −35.9606 34.1541i −0.0864438 0.0821012i
\(417\) 313.534 543.057i 0.751880 1.30229i
\(418\) 220.169 36.0351i 0.526720 0.0862083i
\(419\) −707.012 −1.68738 −0.843690 0.536831i \(-0.819621\pi\)
−0.843690 + 0.536831i \(0.819621\pi\)
\(420\) 0 0
\(421\) 121.989i 0.289761i 0.989449 + 0.144880i \(0.0462798\pi\)
−0.989449 + 0.144880i \(0.953720\pi\)
\(422\) −323.789 + 52.9946i −0.767273 + 0.125580i
\(423\) −83.1377 47.9996i −0.196543 0.113474i
\(424\) 781.987 + 28.8714i 1.84431 + 0.0680929i
\(425\) 267.299 + 462.975i 0.628938 + 1.08935i
\(426\) −652.784 246.729i −1.53236 0.579176i
\(427\) 0 0
\(428\) −46.7939 41.2684i −0.109332 0.0964214i
\(429\) 20.5541 11.8669i 0.0479118 0.0276619i
\(430\) −41.1917 + 33.7092i −0.0957946 + 0.0783936i
\(431\) 509.969 + 294.431i 1.18322 + 0.683133i 0.956758 0.290886i \(-0.0939501\pi\)
0.226464 + 0.974020i \(0.427283\pi\)
\(432\) 276.076 209.407i 0.639064 0.484738i
\(433\) −137.696 −0.318004 −0.159002 0.987278i \(-0.550828\pi\)
−0.159002 + 0.987278i \(0.550828\pi\)
\(434\) 0 0
\(435\) 118.794 0.273090
\(436\) −15.1027 3.04788i −0.0346393 0.00699056i
\(437\) −758.675 438.021i −1.73610 1.00234i
\(438\) 299.751 + 366.287i 0.684362 + 0.836271i
\(439\) 381.522 220.272i 0.869070 0.501758i 0.00203069 0.999998i \(-0.499354\pi\)
0.867039 + 0.498240i \(0.166020\pi\)
\(440\) −26.0101 49.1545i −0.0591139 0.111715i
\(441\) 0 0
\(442\) −68.5929 25.9257i −0.155188 0.0586554i
\(443\) 243.529 + 421.805i 0.549727 + 0.952155i 0.998293 + 0.0584052i \(0.0186015\pi\)
−0.448566 + 0.893750i \(0.648065\pi\)
\(444\) 255.057 + 758.309i 0.574453 + 1.70790i
\(445\) −59.1361 34.1422i −0.132890 0.0767241i
\(446\) 3.41875 + 20.8881i 0.00766537 + 0.0468343i
\(447\) 656.587i 1.46887i
\(448\) 0 0
\(449\) 264.039 0.588059 0.294030 0.955796i \(-0.405004\pi\)
0.294030 + 0.955796i \(0.405004\pi\)
\(450\) −118.502 + 19.3953i −0.263339 + 0.0431006i
\(451\) 60.4853 104.764i 0.134114 0.232292i
\(452\) −52.2235 + 17.5654i −0.115539 + 0.0388615i
\(453\) 339.301 195.896i 0.749010 0.432441i
\(454\) −74.8162 + 197.945i −0.164793 + 0.436003i
\(455\) 0 0
\(456\) 600.416 317.710i 1.31670 0.696733i
\(457\) 257.161 + 445.417i 0.562717 + 0.974654i 0.997258 + 0.0740019i \(0.0235771\pi\)
−0.434542 + 0.900652i \(0.643090\pi\)
\(458\) 115.896 94.8438i 0.253049 0.207083i
\(459\) 256.167 443.693i 0.558097 0.966652i
\(460\) −43.1987 + 214.056i −0.0939103 + 0.465340i
\(461\) 202.224i 0.438664i 0.975650 + 0.219332i \(0.0703878\pi\)
−0.975650 + 0.219332i \(0.929612\pi\)
\(462\) 0 0
\(463\) 722.653i 1.56081i −0.625277 0.780403i \(-0.715014\pi\)
0.625277 0.780403i \(-0.284986\pi\)
\(464\) −217.075 286.186i −0.467835 0.616780i
\(465\) 123.598 214.078i 0.265802 0.460383i
\(466\) −530.892 648.735i −1.13925 1.39213i
\(467\) −173.641 300.755i −0.371822 0.644015i 0.618023 0.786160i \(-0.287934\pi\)
−0.989846 + 0.142144i \(0.954600\pi\)
\(468\) 10.8944 12.3531i 0.0232787 0.0263956i
\(469\) 0 0
\(470\) 39.5980 104.766i 0.0842510 0.222907i
\(471\) −627.273 + 362.156i −1.33179 + 0.768910i
\(472\) −18.1692 + 492.115i −0.0384940 + 1.04262i
\(473\) −38.5097 + 66.7007i −0.0814158 + 0.141016i
\(474\) 42.6841 + 260.794i 0.0900509 + 0.550198i
\(475\) 562.013 1.18319
\(476\) 0 0
\(477\) 259.880i 0.544822i
\(478\) 47.9129 + 292.741i 0.100236 + 0.612428i
\(479\) 25.2716 + 14.5906i 0.0527591 + 0.0304605i 0.526148 0.850393i \(-0.323636\pi\)
−0.473388 + 0.880854i \(0.656969\pi\)
\(480\) −122.777 116.609i −0.255786 0.242936i
\(481\) −45.3970 78.6299i −0.0943804 0.163472i
\(482\) 325.179 860.342i 0.674645 1.78494i
\(483\) 0 0
\(484\) 302.647 + 266.909i 0.625303 + 0.551466i
\(485\) 128.996 74.4760i 0.265972 0.153559i
\(486\) 176.288 + 215.419i 0.362733 + 0.443249i
\(487\) −607.640 350.821i −1.24772 0.720372i −0.277067 0.960851i \(-0.589362\pi\)
−0.970654 + 0.240478i \(0.922696\pi\)
\(488\) −160.260 + 255.333i −0.328401 + 0.523223i
\(489\) 821.235 1.67942
\(490\) 0 0
\(491\) −59.9512 −0.122100 −0.0610501 0.998135i \(-0.519445\pi\)
−0.0610501 + 0.998135i \(0.519445\pi\)
\(492\) 72.8644 361.054i 0.148098 0.733850i
\(493\) −459.942 265.548i −0.932945 0.538636i
\(494\) −59.6590 + 48.8220i −0.120767 + 0.0988299i
\(495\) 15.9947 9.23455i 0.0323125 0.0186557i
\(496\) −741.588 + 93.4313i −1.49514 + 0.188370i
\(497\) 0 0
\(498\) 8.72792 23.0919i 0.0175259 0.0463693i
\(499\) 42.1421 + 72.9923i 0.0844532 + 0.146277i 0.905158 0.425075i \(-0.139752\pi\)
−0.820705 + 0.571352i \(0.806419\pi\)
\(500\) −94.0709 279.681i −0.188142 0.559363i
\(501\) 627.138 + 362.079i 1.25177 + 0.722712i
\(502\) 246.557 40.3540i 0.491150 0.0803865i
\(503\) 409.987i 0.815083i −0.913187 0.407542i \(-0.866386\pi\)
0.913187 0.407542i \(-0.133614\pi\)
\(504\) 0 0
\(505\) −30.4020 −0.0602020
\(506\) 51.0384 + 311.837i 0.100866 + 0.616278i
\(507\) 284.401 492.596i 0.560948 0.971590i
\(508\) 159.431 + 474.004i 0.313841 + 0.933079i
\(509\) −413.123 + 238.516i −0.811636 + 0.468598i −0.847524 0.530758i \(-0.821907\pi\)
0.0358878 + 0.999356i \(0.488574\pi\)
\(510\) −234.191 88.5158i −0.459198 0.173560i
\(511\) 0 0
\(512\) −56.5685 + 508.865i −0.110485 + 0.993878i
\(513\) −269.304 466.448i −0.524958 0.909254i
\(514\) 541.298 + 661.450i 1.05311 + 1.28687i
\(515\) 33.3869 57.8278i 0.0648289 0.112287i
\(516\) −46.3912 + 229.875i −0.0899054 + 0.445495i
\(517\) 162.065i 0.313472i
\(518\) 0 0
\(519\) 622.114i 1.19868i
\(520\) 16.2759 + 10.2155i 0.0312997 + 0.0196453i
\(521\) 105.437 182.621i 0.202373 0.350521i −0.746919 0.664915i \(-0.768468\pi\)
0.949293 + 0.314394i \(0.101801\pi\)
\(522\) 92.3196 75.5498i 0.176858 0.144731i
\(523\) 255.783 + 443.030i 0.489069 + 0.847093i 0.999921 0.0125761i \(-0.00400319\pi\)
−0.510852 + 0.859669i \(0.670670\pi\)
\(524\) 301.051 + 265.502i 0.574525 + 0.506683i
\(525\) 0 0
\(526\) −481.970 182.167i −0.916292 0.346326i
\(527\) −957.084 + 552.573i −1.81610 + 1.04852i
\(528\) −225.842 95.0247i −0.427732 0.179971i
\(529\) 355.892 616.423i 0.672764 1.16526i
\(530\) −299.215 + 48.9725i −0.564556 + 0.0924009i
\(531\) −163.546 −0.307997
\(532\) 0 0
\(533\) 41.8002i 0.0784244i
\(534\) −296.902 + 48.5940i −0.555997 + 0.0910001i
\(535\) 20.9357 + 12.0872i 0.0391321 + 0.0225929i
\(536\) −9.85037 + 266.799i −0.0183776 + 0.497759i
\(537\) 97.6569 + 169.147i 0.181856 + 0.314984i
\(538\) −402.688 152.202i −0.748491 0.282903i
\(539\) 0 0
\(540\) −88.8040 + 100.694i −0.164452 + 0.186471i
\(541\) 296.542 171.208i 0.548136 0.316466i −0.200234 0.979748i \(-0.564170\pi\)
0.748370 + 0.663282i \(0.230837\pi\)
\(542\) −585.914 + 479.483i −1.08102 + 0.884654i
\(543\) −964.542 556.878i −1.77632 1.02556i
\(544\) 214.700 + 725.935i 0.394670 + 1.33444i
\(545\) 5.96970 0.0109536
\(546\) 0 0
\(547\) −441.976 −0.807999 −0.404000 0.914759i \(-0.632380\pi\)
−0.404000 + 0.914759i \(0.632380\pi\)
\(548\) −45.3516 + 224.724i −0.0827585 + 0.410081i
\(549\) −86.7038 50.0584i −0.157930 0.0911811i
\(550\) −128.384 156.881i −0.233425 0.285238i
\(551\) −483.529 + 279.166i −0.877548 + 0.506653i
\(552\) 449.990 + 850.401i 0.815199 + 1.54058i
\(553\) 0 0
\(554\) 311.397 + 117.697i 0.562088 + 0.212449i
\(555\) −154.995 268.459i −0.279270 0.483710i
\(556\) 696.323 234.208i 1.25238 0.421238i
\(557\) −316.714 182.855i −0.568607 0.328285i 0.187986 0.982172i \(-0.439804\pi\)
−0.756593 + 0.653886i \(0.773137\pi\)
\(558\) −40.0949 244.974i −0.0718546 0.439021i
\(559\) 26.6133i 0.0476087i
\(560\) 0 0
\(561\) −362.274 −0.645765
\(562\) 832.453 136.248i 1.48123 0.242433i
\(563\) 403.194 698.353i 0.716154 1.24041i −0.246359 0.969179i \(-0.579234\pi\)
0.962513 0.271236i \(-0.0874323\pi\)
\(564\) −157.315 467.711i −0.278926 0.829274i
\(565\) 18.4883 10.6743i 0.0327227 0.0188925i
\(566\) 244.262 646.256i 0.431558 1.14180i
\(567\) 0 0
\(568\) −382.392 722.653i −0.673225 1.27228i
\(569\) −111.446 193.030i −0.195862 0.339244i 0.751320 0.659938i \(-0.229417\pi\)
−0.947183 + 0.320694i \(0.896084\pi\)
\(570\) −203.689 + 166.689i −0.357349 + 0.292436i
\(571\) −286.541 + 496.304i −0.501823 + 0.869184i 0.498174 + 0.867077i \(0.334004\pi\)
−0.999998 + 0.00210683i \(0.999329\pi\)
\(572\) 27.2565 + 5.50063i 0.0476512 + 0.00961649i
\(573\) 331.393i 0.578348i
\(574\) 0 0
\(575\) 796.008i 1.38436i
\(576\) −169.576 12.5388i −0.294402 0.0217687i
\(577\) −361.950 + 626.916i −0.627297 + 1.08651i 0.360795 + 0.932645i \(0.382505\pi\)
−0.988092 + 0.153865i \(0.950828\pi\)
\(578\) 342.810 + 418.903i 0.593097 + 0.724746i
\(579\) 268.534 + 465.115i 0.463789 + 0.803307i
\(580\) 104.382 + 92.0561i 0.179969 + 0.158717i
\(581\) 0 0
\(582\) 232.024 613.879i 0.398667 1.05477i
\(583\) −379.949 + 219.364i −0.651714 + 0.376267i
\(584\) −20.4589 + 554.132i −0.0350323 + 0.948856i
\(585\) −3.19091 + 5.52682i −0.00545455 + 0.00944755i
\(586\) −165.087 1008.66i −0.281718 1.72126i
\(587\) −21.1198 −0.0359793 −0.0179896 0.999838i \(-0.505727\pi\)
−0.0179896 + 0.999838i \(0.505727\pi\)
\(588\) 0 0
\(589\) 1161.82i 1.97253i
\(590\) −30.8191 188.300i −0.0522358 0.319153i
\(591\) −366.988 211.880i −0.620960 0.358512i
\(592\) −363.517 + 863.960i −0.614049 + 1.45939i
\(593\) −64.3726 111.497i −0.108554 0.188021i 0.806631 0.591056i \(-0.201289\pi\)
−0.915185 + 0.403035i \(0.867955\pi\)
\(594\) −68.6863 + 181.727i −0.115633 + 0.305937i
\(595\) 0 0
\(596\) 508.804 576.930i 0.853698 0.968003i
\(597\) 535.105 308.943i 0.896324 0.517493i
\(598\) −69.1491 84.4982i −0.115634 0.141301i
\(599\) 280.705 + 162.065i 0.468623 + 0.270559i 0.715663 0.698446i \(-0.246125\pi\)
−0.247040 + 0.969005i \(0.579458\pi\)
\(600\) −522.790 328.129i −0.871317 0.546882i
\(601\) 721.862 1.20110 0.600551 0.799587i \(-0.294948\pi\)
0.600551 + 0.799587i \(0.294948\pi\)
\(602\) 0 0
\(603\) −88.6661 −0.147042
\(604\) 449.941 + 90.8027i 0.744936 + 0.150336i
\(605\) −135.405 78.1759i −0.223809 0.129216i
\(606\) −103.661 + 84.8311i −0.171058 + 0.139985i
\(607\) 611.413 353.000i 1.00727 0.581548i 0.0968795 0.995296i \(-0.469114\pi\)
0.910391 + 0.413748i \(0.135781\pi\)
\(608\) 773.775 + 186.110i 1.27266 + 0.306103i
\(609\) 0 0
\(610\) 41.2965 109.260i 0.0676991 0.179115i
\(611\) 28.0000 + 48.4974i 0.0458265 + 0.0793739i
\(612\) −238.293 + 80.1499i −0.389368 + 0.130964i
\(613\) 18.9026 + 10.9134i 0.0308363 + 0.0178033i 0.515339 0.856986i \(-0.327666\pi\)
−0.484503 + 0.874790i \(0.660999\pi\)
\(614\) 440.797 72.1453i 0.717910 0.117500i
\(615\) 142.715i 0.232057i
\(616\) 0 0
\(617\) −699.578 −1.13384 −0.566919 0.823774i \(-0.691865\pi\)
−0.566919 + 0.823774i \(0.691865\pi\)
\(618\) −47.5190 290.334i −0.0768915 0.469796i
\(619\) 48.0990 83.3100i 0.0777044 0.134588i −0.824555 0.565782i \(-0.808574\pi\)
0.902259 + 0.431194i \(0.141908\pi\)
\(620\) 274.497 92.3271i 0.442737 0.148915i
\(621\) 660.654 381.429i 1.06386 0.614217i
\(622\) −23.1960 8.76725i −0.0372925 0.0140953i
\(623\) 0 0
\(624\) 84.0000 10.5830i 0.134615 0.0169599i
\(625\) −225.309 390.247i −0.360495 0.624395i
\(626\) −519.381 634.668i −0.829682 1.01385i
\(627\) −190.426 + 329.828i −0.303710 + 0.526042i
\(628\) −831.815 167.869i −1.32455 0.267307i
\(629\) 1385.88i 2.20331i
\(630\) 0 0
\(631\) 269.399i 0.426940i −0.976950 0.213470i \(-0.931523\pi\)
0.976950 0.213470i \(-0.0684766\pi\)
\(632\) −164.589 + 262.231i −0.260426 + 0.414922i
\(633\) 280.049 485.059i 0.442415 0.766285i
\(634\) −201.701 + 165.062i −0.318141 + 0.260351i
\(635\) −96.8843 167.809i −0.152574 0.264266i
\(636\) −883.578 + 1001.88i −1.38927 + 1.57529i
\(637\) 0 0
\(638\) 188.382 + 71.2016i 0.295269 + 0.111601i
\(639\) 235.149 135.763i 0.367995 0.212462i
\(640\) −17.5187 197.605i −0.0273730 0.308758i
\(641\) −317.907 + 550.630i −0.495954 + 0.859018i −0.999989 0.00466541i \(-0.998515\pi\)
0.504035 + 0.863683i \(0.331848\pi\)
\(642\) 105.111 17.2035i 0.163724 0.0267968i
\(643\) −1281.70 −1.99332 −0.996658 0.0816828i \(-0.973971\pi\)
−0.996658 + 0.0816828i \(0.973971\pi\)
\(644\) 0 0
\(645\) 90.8634i 0.140874i
\(646\) 1161.24 190.061i 1.79759 0.294212i
\(647\) 225.826 + 130.381i 0.349035 + 0.201516i 0.664260 0.747501i \(-0.268747\pi\)
−0.315225 + 0.949017i \(0.602080\pi\)
\(648\) −28.8826 + 782.290i −0.0445719 + 1.20724i
\(649\) −138.049 239.107i −0.212710 0.368424i
\(650\) 65.5227 + 24.7653i 0.100804 + 0.0381004i
\(651\) 0 0
\(652\) 721.602 + 636.393i 1.10675 + 0.976063i
\(653\) 944.471 545.291i 1.44636 0.835055i 0.448095 0.893986i \(-0.352103\pi\)
0.998262 + 0.0589313i \(0.0187693\pi\)
\(654\) 20.3547 16.6573i 0.0311235 0.0254699i
\(655\) −134.691 77.7637i −0.205635 0.118723i
\(656\) 343.813 260.787i 0.524106 0.397541i
\(657\) −184.156 −0.280299
\(658\) 0 0
\(659\) −362.780 −0.550500 −0.275250 0.961373i \(-0.588761\pi\)
−0.275250 + 0.961373i \(0.588761\pi\)
\(660\) 93.0594 + 18.7803i 0.140999 + 0.0284550i
\(661\) −102.047 58.9169i −0.154383 0.0891330i 0.420818 0.907145i \(-0.361743\pi\)
−0.575201 + 0.818012i \(0.695076\pi\)
\(662\) 271.388 + 331.629i 0.409952 + 0.500950i
\(663\) 108.409 62.5902i 0.163513 0.0944045i
\(664\) 25.5635 13.5269i 0.0384992 0.0203719i
\(665\) 0 0
\(666\) −291.186 110.058i −0.437216 0.165252i
\(667\) −395.397 684.848i −0.592799 1.02676i
\(668\) 270.471 + 804.135i 0.404897 + 1.20379i
\(669\) −31.2918 18.0663i −0.0467740 0.0270050i
\(670\) −16.7085 102.086i −0.0249380 0.152368i
\(671\) 169.017i 0.251888i
\(672\) 0 0
\(673\) −6.56854 −0.00976009 −0.00488005 0.999988i \(-0.501553\pi\)
−0.00488005 + 0.999988i \(0.501553\pi\)
\(674\) −323.789 + 52.9946i −0.480400 + 0.0786270i
\(675\) −244.701 + 423.834i −0.362519 + 0.627902i
\(676\) 631.621 212.446i 0.934350 0.314269i
\(677\) 108.942 62.8978i 0.160919 0.0929066i −0.417378 0.908733i \(-0.637051\pi\)
0.578297 + 0.815826i \(0.303718\pi\)
\(678\) 33.2548 87.9840i 0.0490484 0.129770i
\(679\) 0 0
\(680\) −137.186 259.257i −0.201744 0.381260i
\(681\) −180.622 312.847i −0.265231 0.459394i
\(682\) 324.312 265.401i 0.475531 0.389151i
\(683\) 276.887 479.583i 0.405399 0.702171i −0.588969 0.808156i \(-0.700466\pi\)
0.994368 + 0.105984i \(0.0337994\pi\)
\(684\) −52.2852 + 259.081i −0.0764404 + 0.378774i
\(685\) 88.8274i 0.129675i
\(686\) 0 0
\(687\) 255.652i 0.372128i
\(688\) −218.899 + 166.037i −0.318166 + 0.241333i
\(689\) 75.7990 131.288i 0.110013 0.190548i
\(690\) −236.090 288.495i −0.342159 0.418109i
\(691\) −523.413 906.577i −0.757471 1.31198i −0.944136 0.329555i \(-0.893101\pi\)
0.186665 0.982424i \(-0.440232\pi\)
\(692\) 482.090 546.639i 0.696662 0.789941i
\(693\) 0 0
\(694\) −77.5635 + 205.214i −0.111763 + 0.295697i
\(695\) −246.515 + 142.325i −0.354698 + 0.204785i
\(696\) 612.774 + 22.6240i 0.880422 + 0.0325057i
\(697\) 319.019 552.558i 0.457703 0.792766i
\(698\) −149.723 914.787i −0.214503 1.31058i
\(699\) 1431.02 2.04724
\(700\) 0 0
\(701\) 625.993i 0.893000i 0.894784 + 0.446500i \(0.147330\pi\)
−0.894784 + 0.446500i \(0.852670\pi\)
\(702\) −10.8428 66.2481i −0.0154456 0.0943705i
\(703\) 1261.76 + 728.476i 1.79482 + 1.03624i
\(704\) −124.806 258.507i −0.177282 0.367197i
\(705\) 95.5980 + 165.581i 0.135600 + 0.234866i
\(706\) −55.2233 + 146.107i −0.0782200 + 0.206951i
\(707\) 0 0
\(708\) −630.500 556.048i −0.890536 0.785379i
\(709\) −513.979 + 296.746i −0.724935 + 0.418541i −0.816566 0.577252i \(-0.804125\pi\)
0.0916314 + 0.995793i \(0.470792\pi\)
\(710\) 200.624 + 245.157i 0.282569 + 0.345291i
\(711\) −89.0461 51.4108i −0.125241 0.0723077i
\(712\) −298.539 187.378i −0.419296 0.263171i
\(713\) −1645.55 −2.30792
\(714\) 0 0
\(715\) −10.7737 −0.0150682
\(716\) −45.2665 + 224.302i −0.0632213 + 0.313271i
\(717\) −438.546 253.194i −0.611640 0.353130i
\(718\) −565.118 + 462.465i −0.787073 + 0.644101i
\(719\) −529.578 + 305.752i −0.736549 + 0.425247i −0.820813 0.571197i \(-0.806479\pi\)
0.0842645 + 0.996443i \(0.473146\pi\)
\(720\) 65.3667 8.23543i 0.0907870 0.0114381i
\(721\) 0 0
\(722\) 182.094 481.775i 0.252208 0.667279i
\(723\) 785.051 + 1359.75i 1.08582 + 1.88070i
\(724\) −415.985 1236.76i −0.574566 1.70824i
\(725\) 439.355 + 253.662i 0.606007 + 0.349878i
\(726\) −679.822 + 111.266i −0.936394 + 0.153260i
\(727\) 944.144i 1.29868i 0.760496 + 0.649342i \(0.224956\pi\)
−0.760496 + 0.649342i \(0.775044\pi\)
\(728\) 0 0
\(729\) 405.489 0.556227
\(730\) −34.7029 212.030i −0.0475383 0.290452i
\(731\) −203.113 + 351.802i −0.277856 + 0.481261i
\(732\) −164.062 487.772i −0.224129 0.666355i
\(733\) −189.014 + 109.127i −0.257863 + 0.148878i −0.623360 0.781935i \(-0.714233\pi\)
0.365496 + 0.930813i \(0.380899\pi\)
\(734\) 412.965 + 156.086i 0.562622 + 0.212651i
\(735\) 0 0
\(736\) −263.598 + 1095.94i −0.358149 + 1.48905i
\(737\) −74.8427 129.631i −0.101550 0.175891i
\(738\) 90.7628 + 110.910i 0.122985 + 0.150284i
\(739\) 3.64971 6.32149i 0.00493872 0.00855411i −0.863545 0.504271i \(-0.831761\pi\)
0.868484 + 0.495717i \(0.165095\pi\)
\(740\) 71.8441 355.999i 0.0970867 0.481079i
\(741\) 131.600i 0.177598i
\(742\) 0 0
\(743\) 106.867i 0.143832i 0.997411 + 0.0719159i \(0.0229113\pi\)
−0.997411 + 0.0719159i \(0.977089\pi\)
\(744\) 678.325 1080.74i 0.911727 1.45260i
\(745\) −149.025 + 258.119i −0.200034 + 0.346469i
\(746\) 389.351 318.625i 0.521918 0.427112i
\(747\) 4.80256 + 8.31828i 0.00642913 + 0.0111356i
\(748\) −318.323 280.734i −0.425565 0.375313i
\(749\) 0 0
\(750\) 471.196 + 178.095i 0.628261 + 0.237460i
\(751\) −110.387 + 63.7317i −0.146986 + 0.0848624i −0.571689 0.820470i \(-0.693712\pi\)
0.424703 + 0.905333i \(0.360378\pi\)
\(752\) 224.210 532.874i 0.298152 0.708609i
\(753\) −213.250 + 369.359i −0.283200 + 0.490517i
\(754\) −68.6741 + 11.2399i −0.0910798 + 0.0149070i
\(755\) −177.849 −0.235562
\(756\) 0 0
\(757\) 704.275i 0.930350i −0.885219 0.465175i \(-0.845991\pi\)
0.885219 0.465175i \(-0.154009\pi\)
\(758\) −564.537 + 92.3979i −0.744772 + 0.121897i
\(759\) −467.153 269.711i −0.615485 0.355350i
\(760\) −308.148 11.3770i −0.405458 0.0149697i
\(761\) −501.465 868.563i −0.658955 1.14134i −0.980886 0.194581i \(-0.937665\pi\)
0.321931 0.946763i \(-0.395668\pi\)
\(762\) −798.583 301.836i −1.04801 0.396110i
\(763\) 0 0
\(764\) 256.804 291.188i 0.336131 0.381137i
\(765\) 84.3614 48.7061i 0.110276 0.0636681i
\(766\) 165.449 135.395i 0.215990 0.176756i
\(767\) 82.6213 + 47.7014i 0.107720 + 0.0621922i
\(768\) −611.113 624.887i −0.795720 0.813655i
\(769\) 646.950 0.841288 0.420644 0.907226i \(-0.361804\pi\)
0.420644 + 0.907226i \(0.361804\pi\)
\(770\) 0 0
\(771\) −1459.07 −1.89244
\(772\) −124.472 + 616.780i −0.161234 + 0.798938i
\(773\) 488.668 + 282.132i 0.632170 + 0.364984i 0.781592 0.623790i \(-0.214408\pi\)
−0.149422 + 0.988774i \(0.547741\pi\)
\(774\) −57.7867 70.6137i −0.0746599 0.0912322i
\(775\) 914.245 527.840i 1.17967 0.681083i
\(776\) 679.584 359.602i 0.875752 0.463404i
\(777\) 0 0
\(778\) −144.392 54.5750i −0.185594 0.0701478i
\(779\) −335.380 580.895i −0.430526 0.745693i
\(780\) −31.0924 + 10.4579i