Properties

Label 392.3.k.l.67.4
Level 392
Weight 3
Character 392.67
Analytic conductor 10.681
Analytic rank 0
Dimension 12
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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} - 116 x^{3} + 60 x^{2} - 20 x + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.4
Root \(-2.29733 + 1.90372i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.l.275.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.371518 + 1.96519i) q^{2} +(0.824388 - 1.42788i) q^{3} +(-3.72395 + 1.46021i) q^{4} +(3.95004 - 2.28056i) q^{5} +(3.11234 + 1.08960i) q^{6} +(-4.25310 - 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +O(q^{10})\) \(q+(0.371518 + 1.96519i) q^{2} +(0.824388 - 1.42788i) q^{3} +(-3.72395 + 1.46021i) q^{4} +(3.95004 - 2.28056i) q^{5} +(3.11234 + 1.08960i) q^{6} +(-4.25310 - 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +(5.94924 + 6.91531i) q^{10} +(6.18983 - 10.7211i) q^{11} +(-0.984972 + 6.52114i) q^{12} -18.3741i q^{13} -7.52026i q^{15} +(11.7356 - 10.8755i) q^{16} +(-6.51422 + 11.2830i) q^{17} +(-9.52373 + 8.19326i) q^{18} +(-1.51262 - 2.61993i) q^{19} +(-11.3797 + 14.2606i) q^{20} +(23.3686 + 8.18111i) q^{22} +(26.2611 - 15.1619i) q^{23} +(-13.1812 + 0.487065i) q^{24} +(-2.09812 + 3.63405i) q^{25} +(36.1087 - 6.82633i) q^{26} +25.1958 q^{27} -22.7701i q^{29} +(14.7787 - 2.79391i) q^{30} +(19.5382 + 11.2804i) q^{31} +(25.7324 + 19.0222i) q^{32} +(-10.2056 - 17.6767i) q^{33} +(-24.5933 - 8.60985i) q^{34} +(-19.6396 - 15.6720i) q^{36} +(-11.9335 + 6.88983i) q^{37} +(4.58670 - 3.94594i) q^{38} +(-26.2361 - 15.1474i) q^{39} +(-32.2525 - 17.0651i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(-7.39556 + 48.9633i) q^{44} +(24.8123 + 14.3254i) q^{45} +(39.5524 + 45.9752i) q^{46} +(-17.6115 + 10.1680i) q^{47} +(-5.85424 - 25.7226i) q^{48} +(-7.92109 - 2.77309i) q^{50} +(10.7405 + 18.6031i) q^{51} +(26.8301 + 68.4243i) q^{52} +(-4.12744 - 2.38298i) q^{53} +(9.36072 + 49.5146i) q^{54} -56.4650i q^{55} -4.98794 q^{57} +(44.7476 - 8.45951i) q^{58} +(5.86884 - 10.1651i) q^{59} +(10.9811 + 28.0050i) q^{60} +(-94.3137 + 54.4520i) q^{61} +(-14.9093 + 42.5872i) q^{62} +(-27.8222 + 57.6361i) q^{64} +(-41.9033 - 72.5786i) q^{65} +(30.9465 - 26.6232i) q^{66} +(39.5997 - 68.5887i) q^{67} +(7.78313 - 51.5293i) q^{68} -49.9970i q^{69} +12.9952i q^{71} +(23.5020 - 44.4179i) q^{72} +(-49.2909 + 85.3744i) q^{73} +(-17.9734 - 20.8920i) q^{74} +(3.45933 + 5.99173i) q^{75} +(9.45857 + 7.54776i) q^{76} +(20.0204 - 57.1865i) q^{78} +(-113.644 + 65.6123i) q^{79} +(21.5539 - 69.7223i) q^{80} +(-7.49577 + 12.9831i) q^{81} +(22.4778 + 118.899i) q^{82} -28.3732 q^{83} +59.4242i q^{85} +(14.4962 + 76.6794i) q^{86} +(-32.5130 - 18.7714i) q^{87} +(-98.9697 + 3.65707i) q^{88} +(-78.7090 - 136.328i) q^{89} +(-18.9339 + 54.0831i) q^{90} +(-75.6555 + 94.8087i) q^{92} +(32.2141 - 18.5988i) q^{93} +(-26.5251 - 30.8324i) q^{94} +(-11.9498 - 6.89923i) q^{95} +(48.3749 - 21.0611i) q^{96} +39.6175 q^{97} +77.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + O(q^{10}) \) \( 12q + 2q^{2} + 6q^{3} - 4q^{4} + 56q^{6} + 8q^{8} - 40q^{9} + 6q^{10} + 30q^{11} - 32q^{12} + 16q^{16} - 30q^{17} - 16q^{18} - 78q^{19} - 48q^{20} + 24q^{22} + 76q^{24} - 92q^{25} + 128q^{26} - 156q^{27} - 16q^{30} + 112q^{32} + 78q^{33} - 76q^{34} - 248q^{36} - 80q^{38} - 44q^{40} + 232q^{41} - 200q^{43} + 132q^{44} - 156q^{46} - 176q^{48} + 48q^{50} + 10q^{51} - 132q^{52} + 36q^{54} + 332q^{57} + 4q^{58} + 110q^{59} + 84q^{60} + 96q^{62} - 160q^{64} - 32q^{65} + 138q^{66} + 434q^{67} - 96q^{68} - 328q^{72} - 102q^{73} - 34q^{74} + 60q^{75} + 168q^{76} + 720q^{78} + 256q^{80} - 82q^{81} + 24q^{82} + 536q^{83} + 240q^{86} - 204q^{88} - 214q^{89} - 440q^{90} + 160q^{92} + 16q^{94} - 48q^{96} + 152q^{97} + 504q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.371518 + 1.96519i 0.185759 + 0.982595i
\(3\) 0.824388 1.42788i 0.274796 0.475961i −0.695288 0.718732i \(-0.744723\pi\)
0.970084 + 0.242771i \(0.0780563\pi\)
\(4\) −3.72395 + 1.46021i −0.930987 + 0.365052i
\(5\) 3.95004 2.28056i 0.790008 0.456111i −0.0499573 0.998751i \(-0.515909\pi\)
0.839965 + 0.542640i \(0.182575\pi\)
\(6\) 3.11234 + 1.08960i 0.518723 + 0.181599i
\(7\) 0 0
\(8\) −4.25310 6.77577i −0.531638 0.846972i
\(9\) 3.14077 + 5.43997i 0.348974 + 0.604441i
\(10\) 5.94924 + 6.91531i 0.594924 + 0.691531i
\(11\) 6.18983 10.7211i 0.562712 0.974645i −0.434547 0.900649i \(-0.643091\pi\)
0.997259 0.0739960i \(-0.0235752\pi\)
\(12\) −0.984972 + 6.52114i −0.0820810 + 0.543428i
\(13\) 18.3741i 1.41340i −0.707516 0.706698i \(-0.750184\pi\)
0.707516 0.706698i \(-0.249816\pi\)
\(14\) 0 0
\(15\) 7.52026i 0.501350i
\(16\) 11.7356 10.8755i 0.733474 0.679718i
\(17\) −6.51422 + 11.2830i −0.383189 + 0.663703i −0.991516 0.129983i \(-0.958508\pi\)
0.608327 + 0.793687i \(0.291841\pi\)
\(18\) −9.52373 + 8.19326i −0.529096 + 0.455181i
\(19\) −1.51262 2.61993i −0.0796115 0.137891i 0.823471 0.567359i \(-0.192035\pi\)
−0.903082 + 0.429467i \(0.858701\pi\)
\(20\) −11.3797 + 14.2606i −0.568983 + 0.713028i
\(21\) 0 0
\(22\) 23.3686 + 8.18111i 1.06221 + 0.371869i
\(23\) 26.2611 15.1619i 1.14179 0.659211i 0.194915 0.980820i \(-0.437557\pi\)
0.946873 + 0.321609i \(0.104224\pi\)
\(24\) −13.1812 + 0.487065i −0.549217 + 0.0202944i
\(25\) −2.09812 + 3.63405i −0.0839248 + 0.145362i
\(26\) 36.1087 6.82633i 1.38880 0.262551i
\(27\) 25.1958 0.933179
\(28\) 0 0
\(29\) 22.7701i 0.785176i −0.919714 0.392588i \(-0.871580\pi\)
0.919714 0.392588i \(-0.128420\pi\)
\(30\) 14.7787 2.79391i 0.492625 0.0931305i
\(31\) 19.5382 + 11.2804i 0.630264 + 0.363883i 0.780855 0.624713i \(-0.214784\pi\)
−0.150590 + 0.988596i \(0.548117\pi\)
\(32\) 25.7324 + 19.0222i 0.804137 + 0.594444i
\(33\) −10.2056 17.6767i −0.309262 0.535657i
\(34\) −24.5933 8.60985i −0.723333 0.253231i
\(35\) 0 0
\(36\) −19.6396 15.6720i −0.545543 0.435333i
\(37\) −11.9335 + 6.88983i −0.322528 + 0.186212i −0.652519 0.757772i \(-0.726288\pi\)
0.329991 + 0.943984i \(0.392954\pi\)
\(38\) 4.58670 3.94594i 0.120703 0.103840i
\(39\) −26.2361 15.1474i −0.672721 0.388395i
\(40\) −32.2525 17.0651i −0.806312 0.426628i
\(41\) 60.5026 1.47567 0.737837 0.674979i \(-0.235847\pi\)
0.737837 + 0.674979i \(0.235847\pi\)
\(42\) 0 0
\(43\) 39.0188 0.907414 0.453707 0.891151i \(-0.350101\pi\)
0.453707 + 0.891151i \(0.350101\pi\)
\(44\) −7.39556 + 48.9633i −0.168081 + 1.11280i
\(45\) 24.8123 + 14.3254i 0.551385 + 0.318342i
\(46\) 39.5524 + 45.9752i 0.859835 + 0.999460i
\(47\) −17.6115 + 10.1680i −0.374713 + 0.216341i −0.675516 0.737346i \(-0.736079\pi\)
0.300802 + 0.953686i \(0.402746\pi\)
\(48\) −5.85424 25.7226i −0.121963 0.535888i
\(49\) 0 0
\(50\) −7.92109 2.77309i −0.158422 0.0554618i
\(51\) 10.7405 + 18.6031i 0.210598 + 0.364766i
\(52\) 26.8301 + 68.4243i 0.515963 + 1.31585i
\(53\) −4.12744 2.38298i −0.0778762 0.0449619i 0.460556 0.887631i \(-0.347650\pi\)
−0.538432 + 0.842669i \(0.680983\pi\)
\(54\) 9.36072 + 49.5146i 0.173347 + 0.916937i
\(55\) 56.4650i 1.02664i
\(56\) 0 0
\(57\) −4.98794 −0.0875077
\(58\) 44.7476 8.45951i 0.771510 0.145854i
\(59\) 5.86884 10.1651i 0.0994718 0.172290i −0.811994 0.583665i \(-0.801618\pi\)
0.911466 + 0.411375i \(0.134951\pi\)
\(60\) 10.9811 + 28.0050i 0.183019 + 0.466751i
\(61\) −94.3137 + 54.4520i −1.54613 + 0.892656i −0.547694 + 0.836679i \(0.684494\pi\)
−0.998432 + 0.0559779i \(0.982172\pi\)
\(62\) −14.9093 + 42.5872i −0.240473 + 0.686890i
\(63\) 0 0
\(64\) −27.8222 + 57.6361i −0.434722 + 0.900565i
\(65\) −41.9033 72.5786i −0.644666 1.11659i
\(66\) 30.9465 26.6232i 0.468886 0.403383i
\(67\) 39.5997 68.5887i 0.591041 1.02371i −0.403052 0.915177i \(-0.632051\pi\)
0.994093 0.108535i \(-0.0346160\pi\)
\(68\) 7.78313 51.5293i 0.114458 0.757783i
\(69\) 49.9970i 0.724595i
\(70\) 0 0
\(71\) 12.9952i 0.183031i 0.995804 + 0.0915157i \(0.0291712\pi\)
−0.995804 + 0.0915157i \(0.970829\pi\)
\(72\) 23.5020 44.4179i 0.326417 0.616915i
\(73\) −49.2909 + 85.3744i −0.675218 + 1.16951i 0.301187 + 0.953565i \(0.402617\pi\)
−0.976405 + 0.215947i \(0.930716\pi\)
\(74\) −17.9734 20.8920i −0.242883 0.282324i
\(75\) 3.45933 + 5.99173i 0.0461244 + 0.0798898i
\(76\) 9.45857 + 7.54776i 0.124455 + 0.0993126i
\(77\) 0 0
\(78\) 20.0204 57.1865i 0.256671 0.733160i
\(79\) −113.644 + 65.6123i −1.43853 + 0.830535i −0.997748 0.0670794i \(-0.978632\pi\)
−0.440781 + 0.897615i \(0.645299\pi\)
\(80\) 21.5539 69.7223i 0.269423 0.871528i
\(81\) −7.49577 + 12.9831i −0.0925404 + 0.160285i
\(82\) 22.4778 + 118.899i 0.274120 + 1.44999i
\(83\) −28.3732 −0.341846 −0.170923 0.985284i \(-0.554675\pi\)
−0.170923 + 0.985284i \(0.554675\pi\)
\(84\) 0 0
\(85\) 59.4242i 0.699108i
\(86\) 14.4962 + 76.6794i 0.168561 + 0.891621i
\(87\) −32.5130 18.7714i −0.373713 0.215763i
\(88\) −98.9697 + 3.65707i −1.12466 + 0.0415576i
\(89\) −78.7090 136.328i −0.884371 1.53178i −0.846433 0.532495i \(-0.821254\pi\)
−0.0379380 0.999280i \(-0.512079\pi\)
\(90\) −18.9339 + 54.0831i −0.210377 + 0.600923i
\(91\) 0 0
\(92\) −75.6555 + 94.8087i −0.822343 + 1.03053i
\(93\) 32.2141 18.5988i 0.346388 0.199987i
\(94\) −26.5251 30.8324i −0.282182 0.328004i
\(95\) −11.9498 6.89923i −0.125788 0.0726235i
\(96\) 48.3749 21.0611i 0.503906 0.219387i
\(97\) 39.6175 0.408428 0.204214 0.978926i \(-0.434536\pi\)
0.204214 + 0.978926i \(0.434536\pi\)
\(98\) 0 0
\(99\) 77.7633 0.785488
\(100\) 2.50682 16.5967i 0.0250682 0.165967i
\(101\) 37.7745 + 21.8091i 0.374005 + 0.215932i 0.675207 0.737628i \(-0.264054\pi\)
−0.301202 + 0.953560i \(0.597388\pi\)
\(102\) −32.5683 + 28.0185i −0.319297 + 0.274691i
\(103\) 54.4748 31.4510i 0.528881 0.305350i −0.211679 0.977339i \(-0.567893\pi\)
0.740561 + 0.671989i \(0.234560\pi\)
\(104\) −124.499 + 78.1471i −1.19711 + 0.751415i
\(105\) 0 0
\(106\) 3.14959 8.99653i 0.0297131 0.0848729i
\(107\) −22.1133 38.3014i −0.206667 0.357957i 0.743996 0.668184i \(-0.232928\pi\)
−0.950663 + 0.310227i \(0.899595\pi\)
\(108\) −93.8280 + 36.7912i −0.868778 + 0.340659i
\(109\) −7.63419 4.40760i −0.0700384 0.0404367i 0.464572 0.885535i \(-0.346208\pi\)
−0.534610 + 0.845099i \(0.679542\pi\)
\(110\) 110.965 20.9778i 1.00877 0.190707i
\(111\) 22.7196i 0.204681i
\(112\) 0 0
\(113\) −121.408 −1.07440 −0.537202 0.843454i \(-0.680519\pi\)
−0.537202 + 0.843454i \(0.680519\pi\)
\(114\) −1.85311 9.80226i −0.0162554 0.0859847i
\(115\) 69.1550 119.780i 0.601347 1.04156i
\(116\) 33.2491 + 84.7947i 0.286630 + 0.730989i
\(117\) 99.9548 57.7089i 0.854314 0.493239i
\(118\) 22.1568 + 7.75685i 0.187769 + 0.0657360i
\(119\) 0 0
\(120\) −50.9556 + 31.9844i −0.424630 + 0.266537i
\(121\) −16.1279 27.9344i −0.133289 0.230863i
\(122\) −142.048 165.114i −1.16433 1.35340i
\(123\) 49.8776 86.3906i 0.405509 0.702363i
\(124\) −89.2310 13.4777i −0.719605 0.108691i
\(125\) 133.167i 1.06534i
\(126\) 0 0
\(127\) 222.845i 1.75468i −0.479868 0.877341i \(-0.659315\pi\)
0.479868 0.877341i \(-0.340685\pi\)
\(128\) −123.602 33.2631i −0.965644 0.259868i
\(129\) 32.1666 55.7143i 0.249354 0.431893i
\(130\) 127.063 109.312i 0.977407 0.840863i
\(131\) 118.527 + 205.294i 0.904785 + 1.56713i 0.821206 + 0.570632i \(0.193302\pi\)
0.0835786 + 0.996501i \(0.473365\pi\)
\(132\) 63.8169 + 50.9247i 0.483462 + 0.385793i
\(133\) 0 0
\(134\) 149.502 + 52.3390i 1.11569 + 0.390590i
\(135\) 99.5246 57.4605i 0.737219 0.425634i
\(136\) 104.156 3.84873i 0.765856 0.0282995i
\(137\) 4.83138 8.36820i 0.0352656 0.0610818i −0.847854 0.530230i \(-0.822106\pi\)
0.883119 + 0.469148i \(0.155439\pi\)
\(138\) 98.2537 18.5748i 0.711983 0.134600i
\(139\) 63.0621 0.453684 0.226842 0.973932i \(-0.427160\pi\)
0.226842 + 0.973932i \(0.427160\pi\)
\(140\) 0 0
\(141\) 33.5296i 0.237798i
\(142\) −25.5381 + 4.82797i −0.179846 + 0.0339998i
\(143\) −196.991 113.733i −1.37756 0.795334i
\(144\) 96.0211 + 29.6838i 0.666813 + 0.206138i
\(145\) −51.9285 89.9428i −0.358128 0.620295i
\(146\) −186.089 65.1479i −1.27459 0.446219i
\(147\) 0 0
\(148\) 34.3793 43.0829i 0.232293 0.291100i
\(149\) −233.751 + 134.956i −1.56880 + 0.905746i −0.572489 + 0.819912i \(0.694022\pi\)
−0.996309 + 0.0858343i \(0.972644\pi\)
\(150\) −10.4897 + 9.02428i −0.0699313 + 0.0601619i
\(151\) −93.6846 54.0888i −0.620428 0.358204i 0.156608 0.987661i \(-0.449944\pi\)
−0.777036 + 0.629457i \(0.783277\pi\)
\(152\) −11.3187 + 21.3920i −0.0744654 + 0.140737i
\(153\) −81.8386 −0.534893
\(154\) 0 0
\(155\) 102.902 0.663885
\(156\) 119.820 + 18.0980i 0.768079 + 0.116013i
\(157\) −102.565 59.2159i −0.653280 0.377171i 0.136432 0.990649i \(-0.456437\pi\)
−0.789712 + 0.613478i \(0.789770\pi\)
\(158\) −171.161 198.956i −1.08330 1.25921i
\(159\) −6.80523 + 3.92900i −0.0428002 + 0.0247107i
\(160\) 145.025 + 16.4543i 0.906407 + 0.102839i
\(161\) 0 0
\(162\) −28.2990 9.90717i −0.174685 0.0611554i
\(163\) 41.0142 + 71.0387i 0.251621 + 0.435820i 0.963972 0.266003i \(-0.0857031\pi\)
−0.712351 + 0.701823i \(0.752370\pi\)
\(164\) −225.309 + 88.3465i −1.37383 + 0.538698i
\(165\) −80.6254 46.5491i −0.488639 0.282116i
\(166\) −10.5412 55.7588i −0.0635011 0.335896i
\(167\) 131.596i 0.788002i 0.919110 + 0.394001i \(0.128909\pi\)
−0.919110 + 0.394001i \(0.871091\pi\)
\(168\) 0 0
\(169\) −168.609 −0.997687
\(170\) −116.780 + 22.0772i −0.686940 + 0.129866i
\(171\) 9.50157 16.4572i 0.0555648 0.0962410i
\(172\) −145.304 + 56.9756i −0.844791 + 0.331254i
\(173\) −95.3611 + 55.0568i −0.551220 + 0.318247i −0.749614 0.661875i \(-0.769761\pi\)
0.198394 + 0.980122i \(0.436428\pi\)
\(174\) 24.8102 70.8682i 0.142587 0.407289i
\(175\) 0 0
\(176\) −43.9559 193.136i −0.249749 1.09736i
\(177\) −9.67640 16.7600i −0.0546689 0.0946893i
\(178\) 238.669 205.327i 1.34084 1.15352i
\(179\) −76.9263 + 133.240i −0.429756 + 0.744359i −0.996851 0.0792929i \(-0.974734\pi\)
0.567095 + 0.823652i \(0.308067\pi\)
\(180\) −113.318 17.1159i −0.629544 0.0950882i
\(181\) 227.511i 1.25697i −0.777823 0.628484i \(-0.783676\pi\)
0.777823 0.628484i \(-0.216324\pi\)
\(182\) 0 0
\(183\) 179.558i 0.981194i
\(184\) −214.425 113.454i −1.16535 0.616600i
\(185\) −31.4253 + 54.4303i −0.169867 + 0.294218i
\(186\) 48.5184 + 56.3971i 0.260852 + 0.303210i
\(187\) 80.6438 + 139.679i 0.431250 + 0.746947i
\(188\) 50.7370 63.5817i 0.269877 0.338200i
\(189\) 0 0
\(190\) 9.11872 26.0469i 0.0479933 0.137089i
\(191\) 105.262 60.7728i 0.551107 0.318182i −0.198461 0.980109i \(-0.563594\pi\)
0.749569 + 0.661927i \(0.230261\pi\)
\(192\) 59.3613 + 87.2414i 0.309174 + 0.454382i
\(193\) −42.7276 + 74.0064i −0.221386 + 0.383453i −0.955229 0.295867i \(-0.904392\pi\)
0.733843 + 0.679319i \(0.237725\pi\)
\(194\) 14.7186 + 77.8560i 0.0758692 + 0.401319i
\(195\) −138.178 −0.708606
\(196\) 0 0
\(197\) 214.100i 1.08680i 0.839474 + 0.543400i \(0.182863\pi\)
−0.839474 + 0.543400i \(0.817137\pi\)
\(198\) 28.8905 + 152.820i 0.145912 + 0.771816i
\(199\) 214.968 + 124.112i 1.08024 + 0.623677i 0.930961 0.365118i \(-0.118971\pi\)
0.149279 + 0.988795i \(0.452305\pi\)
\(200\) 33.5470 1.23961i 0.167735 0.00619805i
\(201\) −65.2911 113.087i −0.324831 0.562624i
\(202\) −28.8252 + 82.3366i −0.142699 + 0.407607i
\(203\) 0 0
\(204\) −67.1614 53.5935i −0.329222 0.262713i
\(205\) 238.988 137.980i 1.16579 0.673071i
\(206\) 82.0456 + 95.3687i 0.398280 + 0.462955i
\(207\) 164.960 + 95.2398i 0.796909 + 0.460096i
\(208\) −199.828 215.631i −0.960710 1.03669i
\(209\) −37.4514 −0.179193
\(210\) 0 0
\(211\) 191.753 0.908783 0.454392 0.890802i \(-0.349857\pi\)
0.454392 + 0.890802i \(0.349857\pi\)
\(212\) 18.8500 + 2.84716i 0.0889152 + 0.0134300i
\(213\) 18.5557 + 10.7131i 0.0871157 + 0.0502963i
\(214\) 67.0541 57.6866i 0.313337 0.269564i
\(215\) 154.126 88.9846i 0.716864 0.413882i
\(216\) −107.161 170.721i −0.496113 0.790376i
\(217\) 0 0
\(218\) 5.82553 16.6401i 0.0267226 0.0763309i
\(219\) 81.2697 + 140.763i 0.371095 + 0.642755i
\(220\) 82.4507 + 210.273i 0.374776 + 0.955786i
\(221\) 207.315 + 119.693i 0.938075 + 0.541598i
\(222\) −44.6483 + 8.44075i −0.201119 + 0.0380214i
\(223\) 41.2269i 0.184874i −0.995719 0.0924370i \(-0.970534\pi\)
0.995719 0.0924370i \(-0.0294657\pi\)
\(224\) 0 0
\(225\) −26.3588 −0.117150
\(226\) −45.1052 238.589i −0.199580 1.05570i
\(227\) 35.2219 61.0060i 0.155162 0.268749i −0.777956 0.628319i \(-0.783743\pi\)
0.933118 + 0.359570i \(0.117077\pi\)
\(228\) 18.5748 7.28344i 0.0814686 0.0319449i
\(229\) −81.8558 + 47.2595i −0.357449 + 0.206373i −0.667961 0.744196i \(-0.732833\pi\)
0.310512 + 0.950569i \(0.399499\pi\)
\(230\) 261.083 + 91.4022i 1.13514 + 0.397401i
\(231\) 0 0
\(232\) −154.285 + 96.8436i −0.665022 + 0.417429i
\(233\) 68.1434 + 118.028i 0.292461 + 0.506557i 0.974391 0.224860i \(-0.0721925\pi\)
−0.681930 + 0.731417i \(0.738859\pi\)
\(234\) 150.544 + 174.990i 0.643351 + 0.747822i
\(235\) −46.3775 + 80.3281i −0.197351 + 0.341822i
\(236\) −7.01204 + 46.4241i −0.0297120 + 0.196712i
\(237\) 216.360i 0.912911i
\(238\) 0 0
\(239\) 173.230i 0.724813i 0.932020 + 0.362406i \(0.118045\pi\)
−0.932020 + 0.362406i \(0.881955\pi\)
\(240\) −81.7864 88.2546i −0.340777 0.367727i
\(241\) −164.461 + 284.856i −0.682413 + 1.18197i 0.291830 + 0.956470i \(0.405736\pi\)
−0.974242 + 0.225503i \(0.927597\pi\)
\(242\) 48.9046 42.0726i 0.202085 0.173854i
\(243\) 125.740 + 217.788i 0.517449 + 0.896248i
\(244\) 271.708 340.494i 1.11356 1.39547i
\(245\) 0 0
\(246\) 188.304 + 65.9234i 0.765465 + 0.267981i
\(247\) −48.1390 + 27.7931i −0.194895 + 0.112523i
\(248\) −6.66467 180.363i −0.0268737 0.727270i
\(249\) −23.3905 + 40.5136i −0.0939379 + 0.162705i
\(250\) −261.699 + 49.4741i −1.04680 + 0.197897i
\(251\) −160.255 −0.638466 −0.319233 0.947676i \(-0.603425\pi\)
−0.319233 + 0.947676i \(0.603425\pi\)
\(252\) 0 0
\(253\) 375.397i 1.48378i
\(254\) 437.932 82.7909i 1.72414 0.325948i
\(255\) 84.8507 + 48.9886i 0.332748 + 0.192112i
\(256\) 19.4476 255.260i 0.0759674 0.997110i
\(257\) 72.7208 + 125.956i 0.282960 + 0.490102i 0.972113 0.234515i \(-0.0753502\pi\)
−0.689152 + 0.724617i \(0.742017\pi\)
\(258\) 121.440 + 42.5147i 0.470696 + 0.164786i
\(259\) 0 0
\(260\) 262.026 + 209.091i 1.00779 + 0.804198i
\(261\) 123.869 71.5156i 0.474593 0.274006i
\(262\) −359.408 + 309.198i −1.37179 + 1.18015i
\(263\) 175.617 + 101.392i 0.667745 + 0.385523i 0.795222 0.606319i \(-0.207355\pi\)
−0.127477 + 0.991842i \(0.540688\pi\)
\(264\) −76.3676 + 144.332i −0.289271 + 0.546712i
\(265\) −21.7381 −0.0820305
\(266\) 0 0
\(267\) −259.547 −0.972087
\(268\) −47.3134 + 313.245i −0.176543 + 1.16882i
\(269\) 191.662 + 110.656i 0.712497 + 0.411360i 0.811985 0.583679i \(-0.198387\pi\)
−0.0994882 + 0.995039i \(0.531721\pi\)
\(270\) 149.896 + 174.237i 0.555171 + 0.645323i
\(271\) 101.651 58.6880i 0.375095 0.216561i −0.300587 0.953754i \(-0.597183\pi\)
0.675682 + 0.737193i \(0.263849\pi\)
\(272\) 46.2595 + 203.257i 0.170072 + 0.747269i
\(273\) 0 0
\(274\) 18.2401 + 6.38565i 0.0665695 + 0.0233053i
\(275\) 25.9740 + 44.9883i 0.0944509 + 0.163594i
\(276\) 73.0061 + 186.186i 0.264515 + 0.674588i
\(277\) 221.277 + 127.755i 0.798835 + 0.461208i 0.843064 0.537814i \(-0.180750\pi\)
−0.0442283 + 0.999021i \(0.514083\pi\)
\(278\) 23.4287 + 123.929i 0.0842760 + 0.445788i
\(279\) 141.716i 0.507944i
\(280\) 0 0
\(281\) −278.004 −0.989336 −0.494668 0.869082i \(-0.664710\pi\)
−0.494668 + 0.869082i \(0.664710\pi\)
\(282\) −65.8920 + 12.4569i −0.233660 + 0.0441732i
\(283\) 28.3448 49.0947i 0.100158 0.173479i −0.811591 0.584225i \(-0.801398\pi\)
0.911750 + 0.410746i \(0.134732\pi\)
\(284\) −18.9757 48.3936i −0.0668160 0.170400i
\(285\) −19.7026 + 11.3753i −0.0691318 + 0.0399133i
\(286\) 150.321 429.379i 0.525597 1.50132i
\(287\) 0 0
\(288\) −22.6608 + 199.728i −0.0786833 + 0.693499i
\(289\) 59.6300 + 103.282i 0.206332 + 0.357378i
\(290\) 157.462 135.465i 0.542974 0.467120i
\(291\) 32.6602 56.5691i 0.112234 0.194396i
\(292\) 58.8924 389.905i 0.201686 1.33529i
\(293\) 287.871i 0.982493i 0.871020 + 0.491247i \(0.163459\pi\)
−0.871020 + 0.491247i \(0.836541\pi\)
\(294\) 0 0
\(295\) 53.5369i 0.181481i
\(296\) 97.4386 + 51.5558i 0.329184 + 0.174175i
\(297\) 155.958 270.127i 0.525111 0.909518i
\(298\) −352.058 409.227i −1.18140 1.37324i
\(299\) −278.586 482.525i −0.931726 1.61380i
\(300\) −21.6315 17.2616i −0.0721052 0.0575385i
\(301\) 0 0
\(302\) 71.4893 204.203i 0.236720 0.676169i
\(303\) 62.2817 35.9584i 0.205550 0.118675i
\(304\) −46.2445 14.2960i −0.152120 0.0470262i
\(305\) −248.362 + 430.176i −0.814302 + 1.41041i
\(306\) −30.4045 160.828i −0.0993612 0.525583i
\(307\) −53.6483 −0.174750 −0.0873750 0.996175i \(-0.527848\pi\)
−0.0873750 + 0.996175i \(0.527848\pi\)
\(308\) 0 0
\(309\) 103.711i 0.335636i
\(310\) 38.2301 + 202.223i 0.123323 + 0.652331i
\(311\) 91.0263 + 52.5541i 0.292689 + 0.168984i 0.639154 0.769079i \(-0.279285\pi\)
−0.346465 + 0.938063i \(0.612618\pi\)
\(312\) 8.94939 + 242.193i 0.0286839 + 0.776261i
\(313\) 105.245 + 182.290i 0.336246 + 0.582395i 0.983723 0.179690i \(-0.0575093\pi\)
−0.647477 + 0.762085i \(0.724176\pi\)
\(314\) 78.2657 223.559i 0.249254 0.711973i
\(315\) 0 0
\(316\) 327.396 410.280i 1.03606 1.29836i
\(317\) −54.4626 + 31.4440i −0.171806 + 0.0991925i −0.583437 0.812158i \(-0.698293\pi\)
0.411631 + 0.911351i \(0.364959\pi\)
\(318\) −10.2495 11.9139i −0.0322311 0.0374650i
\(319\) −244.120 140.943i −0.765268 0.441828i
\(320\) 21.5437 + 291.115i 0.0673239 + 0.909735i
\(321\) −72.9199 −0.227165
\(322\) 0 0
\(323\) 39.4141 0.122025
\(324\) 8.95589 59.2936i 0.0276416 0.183005i
\(325\) 66.7725 + 38.5511i 0.205454 + 0.118619i
\(326\) −124.367 + 106.993i −0.381494 + 0.328199i
\(327\) −12.5871 + 7.26715i −0.0384926 + 0.0222237i
\(328\) −257.324 409.952i −0.784524 1.24985i
\(329\) 0 0
\(330\) 61.5240 175.738i 0.186436 0.532540i
\(331\) −98.2893 170.242i −0.296947 0.514327i 0.678489 0.734610i \(-0.262635\pi\)
−0.975436 + 0.220284i \(0.929302\pi\)
\(332\) 105.660 41.4308i 0.318254 0.124792i
\(333\) −74.9610 43.2787i −0.225108 0.129966i
\(334\) −258.612 + 48.8905i −0.774287 + 0.146379i
\(335\) 361.238i 1.07832i
\(336\) 0 0
\(337\) 591.516 1.75524 0.877620 0.479358i \(-0.159130\pi\)
0.877620 + 0.479358i \(0.159130\pi\)
\(338\) −62.6414 331.349i −0.185329 0.980322i
\(339\) −100.087 + 173.356i −0.295242 + 0.511374i
\(340\) −86.7717 221.293i −0.255211 0.650860i
\(341\) 241.876 139.647i 0.709314 0.409523i
\(342\) 35.8716 + 12.5582i 0.104888 + 0.0367200i
\(343\) 0 0
\(344\) −165.951 264.383i −0.482416 0.768554i
\(345\) −114.021 197.490i −0.330496 0.572436i
\(346\) −143.625 166.948i −0.415102 0.482509i
\(347\) −123.770 + 214.376i −0.356685 + 0.617797i −0.987405 0.158214i \(-0.949427\pi\)
0.630719 + 0.776011i \(0.282760\pi\)
\(348\) 148.487 + 22.4279i 0.426687 + 0.0644480i
\(349\) 288.749i 0.827362i −0.910422 0.413681i \(-0.864243\pi\)
0.910422 0.413681i \(-0.135757\pi\)
\(350\) 0 0
\(351\) 462.952i 1.31895i
\(352\) 363.218 158.135i 1.03187 0.449248i
\(353\) −0.634830 + 1.09956i −0.00179839 + 0.00311490i −0.866923 0.498442i \(-0.833906\pi\)
0.865125 + 0.501557i \(0.167239\pi\)
\(354\) 29.3417 25.2426i 0.0828860 0.0713068i
\(355\) 29.6364 + 51.3317i 0.0834827 + 0.144596i
\(356\) 492.176 + 392.747i 1.38252 + 1.10322i
\(357\) 0 0
\(358\) −290.422 101.674i −0.811235 0.284005i
\(359\) 15.0707 8.70105i 0.0419796 0.0242369i −0.478863 0.877889i \(-0.658951\pi\)
0.520843 + 0.853653i \(0.325618\pi\)
\(360\) −8.46373 229.050i −0.0235104 0.636250i
\(361\) 175.924 304.709i 0.487324 0.844070i
\(362\) 447.103 84.5246i 1.23509 0.233493i
\(363\) −53.1828 −0.146509
\(364\) 0 0
\(365\) 449.643i 1.23190i
\(366\) −352.867 + 66.7093i −0.964116 + 0.182266i
\(367\) −459.021 265.016i −1.25074 0.722115i −0.279483 0.960151i \(-0.590163\pi\)
−0.971256 + 0.238036i \(0.923496\pi\)
\(368\) 143.297 463.535i 0.389393 1.25961i
\(369\) 190.025 + 329.132i 0.514972 + 0.891958i
\(370\) −118.641 41.5349i −0.320651 0.112256i
\(371\) 0 0
\(372\) −92.8055 + 116.300i −0.249477 + 0.312636i
\(373\) 102.722 59.3066i 0.275394 0.158999i −0.355942 0.934508i \(-0.615840\pi\)
0.631337 + 0.775509i \(0.282507\pi\)
\(374\) −244.535 + 210.374i −0.653838 + 0.562497i
\(375\) 190.147 + 109.782i 0.507059 + 0.292751i
\(376\) 143.800 + 76.0860i 0.382446 + 0.202356i
\(377\) −418.381 −1.10976
\(378\) 0 0
\(379\) −345.947 −0.912790 −0.456395 0.889777i \(-0.650860\pi\)
−0.456395 + 0.889777i \(0.650860\pi\)
\(380\) 54.5748 + 8.24314i 0.143618 + 0.0216925i
\(381\) −318.196 183.710i −0.835160 0.482180i
\(382\) 158.537 + 184.281i 0.415017 + 0.482410i
\(383\) −350.630 + 202.436i −0.915483 + 0.528555i −0.882191 0.470891i \(-0.843932\pi\)
−0.0332920 + 0.999446i \(0.510599\pi\)
\(384\) −149.392 + 149.068i −0.389042 + 0.388198i
\(385\) 0 0
\(386\) −161.311 56.4731i −0.417903 0.146303i
\(387\) 122.549 + 212.261i 0.316664 + 0.548478i
\(388\) −147.534 + 57.8498i −0.380241 + 0.149098i
\(389\) −116.391 67.1985i −0.299206 0.172747i 0.342880 0.939379i \(-0.388598\pi\)
−0.642086 + 0.766632i \(0.721931\pi\)
\(390\) −51.3358 271.547i −0.131630 0.696273i
\(391\) 395.070i 1.01041i
\(392\) 0 0
\(393\) 390.848 0.994525
\(394\) −420.747 + 79.5420i −1.06789 + 0.201883i
\(395\) −299.265 + 518.342i −0.757633 + 1.31226i
\(396\) −289.586 + 113.551i −0.731279 + 0.286744i
\(397\) 530.424 306.240i 1.33608 0.771386i 0.349857 0.936803i \(-0.386230\pi\)
0.986224 + 0.165417i \(0.0528969\pi\)
\(398\) −164.039 + 468.563i −0.412158 + 1.17729i
\(399\) 0 0
\(400\) 14.8994 + 65.4657i 0.0372485 + 0.163664i
\(401\) 63.1234 + 109.333i 0.157415 + 0.272651i 0.933936 0.357441i \(-0.116351\pi\)
−0.776521 + 0.630092i \(0.783017\pi\)
\(402\) 197.982 170.323i 0.492491 0.423690i
\(403\) 207.267 358.998i 0.514311 0.890813i
\(404\) −172.516 26.0574i −0.427021 0.0644985i
\(405\) 68.3781i 0.168835i
\(406\) 0 0
\(407\) 170.588i 0.419134i
\(408\) 80.3698 151.896i 0.196985 0.372294i
\(409\) 171.259 296.630i 0.418727 0.725257i −0.577084 0.816685i \(-0.695810\pi\)
0.995812 + 0.0914275i \(0.0291430\pi\)
\(410\) 359.945 + 418.395i 0.877914 + 1.02047i
\(411\) −7.96587 13.7973i −0.0193817 0.0335700i
\(412\) −156.936 + 196.667i −0.380913 + 0.477346i
\(413\) 0 0
\(414\) −125.879 + 359.561i −0.304055 + 0.868506i
\(415\) −112.075 + 64.7068i −0.270061 + 0.155920i
\(416\) 349.517 472.810i 0.840184 1.13656i
\(417\) 51.9876 90.0452i 0.124671 0.215936i
\(418\) −13.9139 73.5992i −0.0332868 0.176075i
\(419\) 376.392 0.898311 0.449155 0.893454i \(-0.351725\pi\)
0.449155 + 0.893454i \(0.351725\pi\)
\(420\) 0 0
\(421\) 111.135i 0.263978i 0.991251 + 0.131989i \(0.0421363\pi\)
−0.991251 + 0.131989i \(0.957864\pi\)
\(422\) 71.2399 + 376.832i 0.168815 + 0.892966i
\(423\) −110.627 63.8708i −0.261531 0.150995i
\(424\) 1.40791 + 38.1017i 0.00332054 + 0.0898624i
\(425\) −27.3352 47.3460i −0.0643181 0.111402i
\(426\) −14.1595 + 40.4455i −0.0332384 + 0.0949425i
\(427\) 0 0
\(428\) 138.277 + 110.342i 0.323077 + 0.257810i
\(429\) −324.794 + 187.520i −0.757096 + 0.437109i
\(430\) 232.132 + 269.827i 0.539843 + 0.627505i
\(431\) 35.7481 + 20.6392i 0.0829422 + 0.0478867i 0.540898 0.841089i \(-0.318085\pi\)
−0.457955 + 0.888975i \(0.651418\pi\)
\(432\) 295.688 274.017i 0.684462 0.634298i
\(433\) 675.176 1.55930 0.779649 0.626217i \(-0.215397\pi\)
0.779649 + 0.626217i \(0.215397\pi\)
\(434\) 0 0
\(435\) −171.237 −0.393648
\(436\) 34.8653 + 5.26616i 0.0799664 + 0.0120784i
\(437\) −79.4461 45.8682i −0.181799 0.104962i
\(438\) −246.434 + 212.007i −0.562634 + 0.484033i
\(439\) −459.215 + 265.128i −1.04605 + 0.603936i −0.921541 0.388282i \(-0.873069\pi\)
−0.124508 + 0.992219i \(0.539735\pi\)
\(440\) −382.594 + 240.152i −0.869532 + 0.545799i
\(441\) 0 0
\(442\) −158.199 + 451.881i −0.357915 + 1.02235i
\(443\) −166.016 287.549i −0.374755 0.649094i 0.615535 0.788109i \(-0.288940\pi\)
−0.990290 + 0.139015i \(0.955606\pi\)
\(444\) −33.1753 84.6066i −0.0747193 0.190555i
\(445\) −621.808 359.001i −1.39732 0.806743i
\(446\) 81.0187 15.3166i 0.181656 0.0343420i
\(447\) 445.025i 0.995582i
\(448\) 0 0
\(449\) −19.4200 −0.0432517 −0.0216259 0.999766i \(-0.506884\pi\)
−0.0216259 + 0.999766i \(0.506884\pi\)
\(450\) −9.79279 51.8001i −0.0217618 0.115111i
\(451\) 374.501 648.654i 0.830379 1.43826i
\(452\) 452.116 177.281i 1.00026 0.392214i
\(453\) −154.465 + 89.1804i −0.340982 + 0.196866i
\(454\) 132.974 + 46.5528i 0.292894 + 0.102539i
\(455\) 0 0
\(456\) 21.2142 + 33.7972i 0.0465224 + 0.0741166i
\(457\) 88.9796 + 154.117i 0.194704 + 0.337237i 0.946803 0.321813i \(-0.104292\pi\)
−0.752100 + 0.659049i \(0.770959\pi\)
\(458\) −123.285 143.305i −0.269181 0.312892i
\(459\) −164.131 + 284.283i −0.357584 + 0.619354i
\(460\) −82.6258 + 547.035i −0.179621 + 1.18921i
\(461\) 299.341i 0.649329i −0.945829 0.324664i \(-0.894749\pi\)
0.945829 0.324664i \(-0.105251\pi\)
\(462\) 0 0
\(463\) 505.213i 1.09117i 0.838055 + 0.545586i \(0.183693\pi\)
−0.838055 + 0.545586i \(0.816307\pi\)
\(464\) −247.636 267.220i −0.533698 0.575906i
\(465\) 84.8314 146.932i 0.182433 0.315983i
\(466\) −206.631 + 177.764i −0.443413 + 0.381468i
\(467\) −325.162 563.197i −0.696278 1.20599i −0.969748 0.244108i \(-0.921505\pi\)
0.273470 0.961881i \(-0.411829\pi\)
\(468\) −287.959 + 360.860i −0.615298 + 0.771068i
\(469\) 0 0
\(470\) −175.090 61.2972i −0.372532 0.130420i
\(471\) −169.107 + 97.6338i −0.359037 + 0.207290i
\(472\) −93.8373 + 3.46742i −0.198808 + 0.00734623i
\(473\) 241.520 418.324i 0.510612 0.884407i
\(474\) −425.188 + 80.3817i −0.897022 + 0.169582i
\(475\) 12.6946 0.0267255
\(476\) 0 0
\(477\) 29.9375i 0.0627621i
\(478\) −340.430 + 64.3582i −0.712198 + 0.134641i
\(479\) 572.400 + 330.475i 1.19499 + 0.689928i 0.959434 0.281933i \(-0.0909755\pi\)
0.235556 + 0.971861i \(0.424309\pi\)
\(480\) 143.052 193.514i 0.298025 0.403154i
\(481\) 126.595 + 219.269i 0.263191 + 0.455860i
\(482\) −620.896 217.369i −1.28817 0.450973i
\(483\) 0 0
\(484\) 100.850 + 80.4762i 0.208367 + 0.166273i
\(485\) 156.491 90.3500i 0.322661 0.186289i
\(486\) −381.281 + 328.016i −0.784528 + 0.674929i
\(487\) −334.373 193.050i −0.686597 0.396407i 0.115739 0.993280i \(-0.463076\pi\)
−0.802336 + 0.596873i \(0.796410\pi\)
\(488\) 770.081 + 407.458i 1.57803 + 0.834955i
\(489\) 135.246 0.276578
\(490\) 0 0
\(491\) −898.359 −1.82965 −0.914826 0.403848i \(-0.867672\pi\)
−0.914826 + 0.403848i \(0.867672\pi\)
\(492\) −59.5934 + 394.546i −0.121125 + 0.801922i
\(493\) 256.914 + 148.329i 0.521124 + 0.300871i
\(494\) −72.5032 84.2767i −0.146768 0.170601i
\(495\) 307.168 177.344i 0.620542 0.358270i
\(496\) 351.972 80.1055i 0.709620 0.161503i
\(497\) 0 0
\(498\) −88.3070 30.9153i −0.177323 0.0620790i
\(499\) −395.588 685.178i −0.792761 1.37310i −0.924251 0.381785i \(-0.875309\pi\)
0.131490 0.991318i \(-0.458024\pi\)
\(500\) −194.452 495.908i −0.388904 0.991817i
\(501\) 187.904 + 108.486i 0.375058 + 0.216540i
\(502\) −59.5377 314.932i −0.118601 0.627354i
\(503\) 798.990i 1.58845i −0.607624 0.794225i \(-0.707877\pi\)
0.607624 0.794225i \(-0.292123\pi\)
\(504\) 0 0
\(505\) 198.948 0.393956
\(506\) 737.727 139.467i 1.45796 0.275626i
\(507\) −138.999 + 240.754i −0.274160 + 0.474860i
\(508\) 325.400 + 829.862i 0.640551 + 1.63359i
\(509\) −477.272 + 275.553i −0.937666 + 0.541362i −0.889228 0.457465i \(-0.848758\pi\)
−0.0484379 + 0.998826i \(0.515424\pi\)
\(510\) −64.7483 + 184.948i −0.126957 + 0.362643i
\(511\) 0 0
\(512\) 508.860 56.6155i 0.993868 0.110577i
\(513\) −38.1117 66.0114i −0.0742918 0.128677i
\(514\) −220.511 + 189.705i −0.429009 + 0.369076i
\(515\) 143.452 248.466i 0.278547 0.482458i
\(516\) −38.4324 + 254.447i −0.0744815 + 0.493114i
\(517\) 251.753i 0.486950i
\(518\) 0 0
\(519\) 181.553i 0.349812i
\(520\) −313.557 + 592.611i −0.602995 + 1.13964i
\(521\) 71.3914 123.654i 0.137028 0.237339i −0.789343 0.613953i \(-0.789578\pi\)
0.926370 + 0.376614i \(0.122912\pi\)
\(522\) 186.561 + 216.856i 0.357397 + 0.415433i
\(523\) −416.255 720.976i −0.795900 1.37854i −0.922266 0.386555i \(-0.873665\pi\)
0.126367 0.991984i \(-0.459668\pi\)
\(524\) −741.160 591.432i −1.41443 1.12869i
\(525\) 0 0
\(526\) −134.011 + 382.790i −0.254773 + 0.727737i
\(527\) −254.552 + 146.966i −0.483021 + 0.278872i
\(528\) −312.012 96.4549i −0.590931 0.182680i
\(529\) 195.264 338.207i 0.369119 0.639333i
\(530\) −8.07610 42.7195i −0.0152379 0.0806028i
\(531\) 73.7306 0.138852
\(532\) 0 0
\(533\) 1111.68i 2.08571i
\(534\) −96.4265 510.060i −0.180574 0.955168i
\(535\) −174.697 100.862i −0.326537 0.188526i
\(536\) −633.163 + 23.3963i −1.18127 + 0.0436498i
\(537\) 126.834 + 219.683i 0.236191 + 0.409094i
\(538\) −146.254 + 417.762i −0.271848 + 0.776510i
\(539\) 0 0
\(540\) −286.720 + 359.307i −0.530963 + 0.665383i
\(541\) −533.874 + 308.232i −0.986829 + 0.569746i −0.904325 0.426845i \(-0.859625\pi\)
−0.0825038 + 0.996591i \(0.526292\pi\)
\(542\) 153.098 + 177.959i 0.282469 + 0.328338i
\(543\) −324.859 187.557i −0.598267 0.345410i
\(544\) −382.253 + 166.423i −0.702671 + 0.305924i
\(545\) −40.2071 −0.0737746
\(546\) 0 0
\(547\) 577.704 1.05613 0.528065 0.849204i \(-0.322918\pi\)
0.528065 + 0.849204i \(0.322918\pi\)
\(548\) −5.77250 + 38.2176i −0.0105338 + 0.0697401i
\(549\) −592.435 342.043i −1.07912 0.623028i
\(550\) −78.7607 + 67.7578i −0.143201 + 0.123196i
\(551\) −59.6562 + 34.4425i −0.108269 + 0.0625091i
\(552\) −338.768 + 212.643i −0.613711 + 0.385222i
\(553\) 0 0
\(554\) −168.853 + 482.316i −0.304790 + 0.870606i
\(555\) 51.8133 + 89.7433i 0.0933573 + 0.161700i
\(556\) −234.840 + 92.0838i −0.422374 + 0.165618i
\(557\) 445.752 + 257.355i 0.800273 + 0.462038i 0.843566 0.537025i \(-0.180452\pi\)
−0.0432939 + 0.999062i \(0.513785\pi\)
\(558\) −278.500 + 52.6502i −0.499103 + 0.0943552i
\(559\) 716.937i 1.28253i
\(560\) 0 0
\(561\) 265.927 0.474023
\(562\) −103.283 546.330i −0.183778 0.972117i
\(563\) −304.360 + 527.166i −0.540603 + 0.936352i 0.458266 + 0.888815i \(0.348471\pi\)
−0.998869 + 0.0475374i \(0.984863\pi\)
\(564\) −48.9602 124.862i −0.0868088 0.221387i
\(565\) −479.565 + 276.877i −0.848788 + 0.490048i
\(566\) 107.011 + 37.4634i 0.189065 + 0.0661897i
\(567\) 0 0
\(568\) 88.0527 55.2701i 0.155022 0.0973064i
\(569\) −93.1872 161.405i −0.163774 0.283664i 0.772445 0.635081i \(-0.219033\pi\)
−0.936219 + 0.351417i \(0.885700\pi\)
\(570\) −29.6745 34.4932i −0.0520605 0.0605144i
\(571\) −91.8878 + 159.154i −0.160924 + 0.278729i −0.935200 0.354119i \(-0.884781\pi\)
0.774276 + 0.632848i \(0.218114\pi\)
\(572\) 899.658 + 135.887i 1.57283 + 0.237565i
\(573\) 200.401i 0.349741i
\(574\) 0 0
\(575\) 127.246i 0.221297i
\(576\) −400.922 + 29.6698i −0.696045 + 0.0515100i
\(577\) 67.2281 116.442i 0.116513 0.201807i −0.801870 0.597498i \(-0.796162\pi\)
0.918384 + 0.395691i \(0.129495\pi\)
\(578\) −180.815 + 155.555i −0.312830 + 0.269127i
\(579\) 70.4482 + 122.020i 0.121672 + 0.210743i
\(580\) 324.714 + 259.116i 0.559852 + 0.446752i
\(581\) 0 0
\(582\) 123.303 + 43.1670i 0.211861 + 0.0741702i
\(583\) −51.0963 + 29.5005i −0.0876437 + 0.0506011i
\(584\) 788.117 29.1220i 1.34952 0.0498665i
\(585\) 263.217 455.905i 0.449944 0.779325i
\(586\) −565.721 + 106.949i −0.965393 + 0.182507i
\(587\) 921.405 1.56968 0.784842 0.619696i \(-0.212744\pi\)
0.784842 + 0.619696i \(0.212744\pi\)
\(588\) 0 0
\(589\) 68.2517i 0.115877i
\(590\) 105.210 19.8899i 0.178322 0.0337117i
\(591\) 305.709 + 176.501i 0.517274 + 0.298648i
\(592\) −65.1168 + 210.639i −0.109995 + 0.355810i
\(593\) 48.1873 + 83.4628i 0.0812602 + 0.140747i 0.903791 0.427973i \(-0.140772\pi\)
−0.822531 + 0.568720i \(0.807439\pi\)
\(594\) 588.792 + 206.130i 0.991233 + 0.347020i
\(595\) 0 0
\(596\) 673.412 843.895i 1.12989 1.41593i
\(597\) 354.434 204.632i 0.593692 0.342768i
\(598\) 844.754 726.742i 1.41263 1.21529i
\(599\) 144.711 + 83.5489i 0.241587 + 0.139481i 0.615906 0.787820i \(-0.288790\pi\)
−0.374319 + 0.927300i \(0.622123\pi\)
\(600\) 25.8857 48.9231i 0.0431429 0.0815385i
\(601\) −88.4635 −0.147194 −0.0735969 0.997288i \(-0.523448\pi\)
−0.0735969 + 0.997288i \(0.523448\pi\)
\(602\) 0 0
\(603\) 497.494 0.825032
\(604\) 427.858 + 64.6249i 0.708373 + 0.106995i
\(605\) −127.412 73.5614i −0.210598 0.121589i
\(606\) 93.8039 + 109.036i 0.154792 + 0.179928i
\(607\) 48.1243 27.7846i 0.0792822 0.0457736i −0.459835 0.888004i \(-0.652091\pi\)
0.539117 + 0.842231i \(0.318758\pi\)
\(608\) 10.9136 96.1905i 0.0179500 0.158208i
\(609\) 0 0
\(610\) −937.648 328.260i −1.53713 0.538132i
\(611\) 186.829 + 323.597i 0.305775 + 0.529618i
\(612\) 304.763 119.501i 0.497978 0.195264i
\(613\) −752.678 434.559i −1.22786 0.708905i −0.261278 0.965264i \(-0.584144\pi\)
−0.966582 + 0.256359i \(0.917477\pi\)
\(614\) −19.9313 105.429i −0.0324614 0.171709i
\(615\) 454.995i 0.739829i
\(616\) 0 0
\(617\) −249.359 −0.404147 −0.202074 0.979370i \(-0.564768\pi\)
−0.202074 + 0.979370i \(0.564768\pi\)
\(618\) 203.813 38.5307i 0.329794 0.0623474i
\(619\) −248.837 + 430.998i −0.401998 + 0.696280i −0.993967 0.109680i \(-0.965017\pi\)
0.591969 + 0.805961i \(0.298351\pi\)
\(620\) −383.203 + 150.259i −0.618069 + 0.242353i
\(621\) 661.671 382.016i 1.06549 0.615162i
\(622\) −69.4608 + 198.409i −0.111673 + 0.318985i
\(623\) 0 0
\(624\) −472.631 + 107.567i −0.757422 + 0.172382i
\(625\) 251.243 + 435.165i 0.401988 + 0.696264i
\(626\) −319.133 + 274.550i −0.509798 + 0.438579i
\(627\) −30.8745 + 53.4762i −0.0492416 + 0.0852890i
\(628\) 468.414 + 70.7507i 0.745882 + 0.112660i
\(629\) 179.527i 0.285417i
\(630\) 0 0
\(631\) 172.763i 0.273792i −0.990585 0.136896i \(-0.956287\pi\)
0.990585 0.136896i \(-0.0437126\pi\)
\(632\) 927.913 + 490.969i 1.46822 + 0.776849i
\(633\) 158.079 273.801i 0.249730 0.432545i
\(634\) −82.0273 95.3474i −0.129381 0.150390i
\(635\) −508.210 880.245i −0.800330 1.38621i
\(636\) 19.6051 24.5684i 0.0308257 0.0386296i
\(637\) 0 0
\(638\) 186.285 532.106i 0.291982 0.834022i
\(639\) −70.6937 + 40.8150i −0.110632 + 0.0638732i
\(640\) −564.093 + 150.492i −0.881395 + 0.235144i
\(641\) 213.949 370.570i 0.333774 0.578113i −0.649475 0.760383i \(-0.725011\pi\)
0.983248 + 0.182270i \(0.0583446\pi\)
\(642\) −27.0911 143.302i −0.0421980 0.223211i
\(643\) 15.9463 0.0247998 0.0123999 0.999923i \(-0.496053\pi\)
0.0123999 + 0.999923i \(0.496053\pi\)
\(644\) 0 0
\(645\) 293.431i 0.454932i
\(646\) 14.6431 + 77.4563i 0.0226673 + 0.119901i
\(647\) 450.510 + 260.102i 0.696306 + 0.402012i 0.805970 0.591956i \(-0.201644\pi\)
−0.109664 + 0.993969i \(0.534978\pi\)
\(648\) 119.851 4.42865i 0.184955 0.00683433i
\(649\) −72.6542 125.841i −0.111948 0.193899i
\(650\) −50.9531 + 145.543i −0.0783894 + 0.223913i
\(651\) 0 0
\(652\) −256.466 204.655i −0.393353 0.313888i
\(653\) 367.687 212.284i 0.563074 0.325091i −0.191305 0.981531i \(-0.561272\pi\)
0.754378 + 0.656440i \(0.227939\pi\)
\(654\) −18.9577 22.0361i −0.0289872 0.0336943i
\(655\) 936.371 + 540.614i 1.42957 + 0.825365i
\(656\) 710.033 657.995i 1.08237 1.00304i
\(657\) −619.246 −0.942535
\(658\) 0 0
\(659\) 304.044 0.461372 0.230686 0.973028i \(-0.425903\pi\)
0.230686 + 0.973028i \(0.425903\pi\)
\(660\) 368.216 + 55.6165i 0.557903 + 0.0842674i
\(661\) 155.112 + 89.5542i 0.234663 + 0.135483i 0.612722 0.790299i \(-0.290075\pi\)
−0.378058 + 0.925782i \(0.623408\pi\)
\(662\) 298.042 256.405i 0.450214 0.387319i
\(663\) 341.815 197.347i 0.515559 0.297658i
\(664\) 120.674 + 192.251i 0.181738 + 0.289534i
\(665\) 0 0
\(666\) 57.2016 163.391i 0.0858883 0.245333i
\(667\) −345.237 597.968i −0.517597 0.896504i
\(668\) −192.158 490.058i −0.287662 0.733620i
\(669\) −58.8671 33.9870i −0.0879927 0.0508026i
\(670\) 709.901 134.206i 1.05955 0.200308i
\(671\) 1348.20i 2.00923i
\(672\) 0 0
\(673\) 544.352 0.808844 0.404422 0.914573i \(-0.367473\pi\)
0.404422 + 0.914573i \(0.367473\pi\)
\(674\) 219.759 + 1162.44i 0.326052 + 1.72469i
\(675\) −52.8639 + 91.5629i −0.0783168 + 0.135649i
\(676\) 627.891 246.204i 0.928833 0.364208i
\(677\) −471.416 + 272.172i −0.696330 + 0.402027i −0.805979 0.591944i \(-0.798361\pi\)
0.109649 + 0.993970i \(0.465027\pi\)
\(678\) −377.861 132.285i −0.557318 0.195111i
\(679\) 0 0
\(680\) 402.645 252.737i 0.592125 0.371672i
\(681\) −58.0730 100.585i −0.0852760 0.147702i
\(682\) 364.295 + 423.451i 0.534157 + 0.620896i
\(683\) −443.494 + 768.154i −0.649332 + 1.12468i 0.333951 + 0.942591i \(0.391618\pi\)
−0.983283 + 0.182086i \(0.941715\pi\)
\(684\) −11.3524 + 75.1601i −0.0165971 + 0.109883i
\(685\) 44.0730i 0.0643401i
\(686\) 0 0
\(687\) 155.841i 0.226842i
\(688\) 457.908 424.348i 0.665564 0.616786i
\(689\) −43.7852 + 75.8382i −0.0635489 + 0.110070i
\(690\) 345.745 297.444i 0.501080 0.431079i
\(691\) 589.242 + 1020.60i 0.852738 + 1.47698i 0.878728 + 0.477323i \(0.158393\pi\)
−0.0259906 + 0.999662i \(0.508274\pi\)
\(692\) 274.725 344.276i 0.397002 0.497508i
\(693\) 0 0
\(694\) −467.272 163.587i −0.673302 0.235716i
\(695\) 249.098 143.817i 0.358414 0.206930i
\(696\) 11.0905 + 300.138i 0.0159346 + 0.431232i
\(697\) −394.127 + 682.648i −0.565462 + 0.979409i
\(698\) 567.447 107.276i 0.812962 0.153690i
\(699\) 224.706 0.321468
\(700\) 0 0
\(701\) 901.601i 1.28616i 0.765797 + 0.643082i \(0.222345\pi\)
−0.765797 + 0.643082i \(0.777655\pi\)
\(702\) 909.789 171.995i 1.29600 0.245007i
\(703\) 36.1018 + 20.8434i 0.0513539 + 0.0296492i
\(704\) 445.708 + 655.042i 0.633108 + 0.930458i
\(705\) 76.4661 + 132.443i 0.108463 + 0.187863i
\(706\) −2.39669 0.839056i −0.00339475 0.00118846i
\(707\) 0 0
\(708\) 60.5075 + 48.2839i 0.0854626 + 0.0681975i
\(709\) 288.215 166.401i 0.406510 0.234698i −0.282779 0.959185i \(-0.591256\pi\)
0.689289 + 0.724487i \(0.257923\pi\)
\(710\) −89.8661 + 77.3118i −0.126572 + 0.108890i
\(711\) −713.858 412.146i −1.00402 0.579671i
\(712\) −588.970 + 1113.13i −0.827205 + 1.56339i
\(713\) 684.126 0.959504
\(714\) 0 0
\(715\) −1037.50 −1.45104
\(716\) 91.9110 608.509i 0.128367 0.849872i
\(717\) 247.352 + 142.809i 0.344982 + 0.199176i
\(718\) 22.6983 + 26.3841i 0.0316132 + 0.0367467i
\(719\) −1026.20 + 592.475i −1.42726 + 0.824027i −0.996904 0.0786341i \(-0.974944\pi\)
−0.430353 + 0.902661i \(0.641611\pi\)
\(720\) 446.983 101.729i 0.620809 0.141291i
\(721\) 0 0
\(722\) 664.171 + 232.519i 0.919904 + 0.322049i
\(723\) 271.160 + 469.663i 0.375049 + 0.649603i
\(724\) 332.214 + 847.240i 0.458859 + 1.17022i
\(725\) 82.7477 + 47.7744i 0.114135 + 0.0658957i
\(726\) −19.7584 104.514i −0.0272154 0.143959i
\(727\) 19.9398i 0.0274275i −0.999906 0.0137138i \(-0.995635\pi\)
0.999906 0.0137138i \(-0.00436536\pi\)
\(728\) 0 0
\(729\) 279.711 0.383691
\(730\) −883.635 + 167.051i −1.21046 + 0.228837i
\(731\) −254.177 + 440.247i −0.347711 + 0.602254i
\(732\) −262.193 668.666i −0.358187 0.913479i
\(733\) 898.325 518.648i 1.22555 0.707569i 0.259450 0.965756i \(-0.416459\pi\)
0.966095 + 0.258188i \(0.0831252\pi\)
\(734\) 350.272 1000.52i 0.477210 1.36311i
\(735\) 0 0
\(736\) 964.173 + 109.393i 1.31002 + 0.148632i
\(737\) −490.231 849.105i −0.665171 1.15211i
\(738\) −576.210 + 495.713i −0.780773 + 0.671699i
\(739\) 209.986 363.706i 0.284148 0.492160i −0.688254 0.725470i \(-0.741622\pi\)
0.972402 + 0.233310i \(0.0749558\pi\)
\(740\) 37.5467 248.583i 0.0507388 0.335923i
\(741\) 91.6491i 0.123683i
\(742\) 0 0
\(743\) 1241.67i 1.67116i −0.549370 0.835579i \(-0.685132\pi\)
0.549370 0.835579i \(-0.314868\pi\)
\(744\) −263.031 139.173i −0.353537 0.187060i
\(745\) −615.551 + 1066.17i −0.826243 + 1.43109i
\(746\) 154.712 + 179.835i 0.207389 + 0.241066i
\(747\) −89.1137 154.349i −0.119295 0.206626i
\(748\) −504.274 402.401i −0.674163 0.537969i
\(749\) 0 0
\(750\) −145.099 + 414.462i −0.193465 + 0.552615i
\(751\) 561.008 323.898i 0.747015 0.431289i −0.0775992 0.996985i \(-0.524725\pi\)
0.824614 + 0.565695i \(0.191392\pi\)
\(752\) −96.0993 + 310.861i −0.127792 + 0.413379i
\(753\) −132.112 + 228.825i −0.175448 + 0.303885i
\(754\) −155.436 822.198i −0.206149 1.09045i
\(755\) −493.411 −0.653524
\(756\) 0 0
\(757\) 105.310i 0.139116i −0.997578 0.0695578i \(-0.977841\pi\)
0.997578 0.0695578i \(-0.0221588\pi\)
\(758\) −128.526 679.852i −0.169559 0.896903i
\(759\) −536.023 309.473i −0.706223 0.407738i
\(760\) 4.07620 + 110.312i 0.00536342 + 0.145148i
\(761\) −210.942 365.362i −0.277190 0.480108i 0.693495 0.720461i \(-0.256070\pi\)
−0.970685 + 0.240354i \(0.922737\pi\)
\(762\) 242.810 693.567i 0.318649 0.910193i
\(763\) 0 0
\(764\) −303.247 + 380.018i −0.396921 + 0.497406i
\(765\) −323.266 + 186.638i −0.422570 + 0.243971i
\(766\) −528.092 613.846i −0.689415 0.801366i
\(767\) −186.775 107.835i −0.243514 0.140593i
\(768\) −348.449 238.202i −0.453710 0.310159i
\(769\) 189.767 0.246772 0.123386 0.992359i \(-0.460625\pi\)
0.123386 + 0.992359i \(0.460625\pi\)
\(770\) 0 0
\(771\) 239.801 0.311025
\(772\) 51.0506 337.987i 0.0661277 0.437807i
\(773\) 729.875 + 421.394i 0.944211 + 0.545141i 0.891278 0.453457i \(-0.149810\pi\)
0.0529334 + 0.998598i \(0.483143\pi\)
\(774\) −371.604 + 319.691i −0.480109 + 0.413038i
\(775\) −81.9870 + 47.3352i −0.105790 + 0.0610777i
\(776\) −168.497 268.439i −0.217136 0.345927i
\(777\) 0