Properties

Label 392.3.k.l.275.5
Level 392
Weight 3
Character 392.275
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 275.5
Root \(2.79733 + 1.03769i\) of defining polynomial
Character \(\chi\) \(=\) 392.275
Dual form 392.3.k.l.67.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.51615 - 1.30434i) q^{2} +(0.824388 + 1.42788i) q^{3} +(0.597396 - 3.95514i) q^{4} +(-3.95004 - 2.28056i) q^{5} +(3.11234 + 1.08960i) q^{6} +(-4.25310 - 6.77577i) q^{8} +(3.14077 - 5.43997i) q^{9} +O(q^{10})\) \(q+(1.51615 - 1.30434i) q^{2} +(0.824388 + 1.42788i) q^{3} +(0.597396 - 3.95514i) 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} +(-8.96346 + 1.69454i) q^{10} +(6.18983 + 10.7211i) q^{11} +(6.13996 - 2.40756i) q^{12} -18.3741i q^{13} -7.52026i q^{15} +(-15.2862 - 4.72557i) q^{16} +(-6.51422 - 11.2830i) q^{17} +(-2.33371 - 12.3444i) 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} +(6.16880 - 11.6588i) q^{24} +(-2.09812 - 3.63405i) q^{25} +(-23.9661 - 27.8579i) q^{26} +25.1958 q^{27} -22.7701i q^{29} +(-9.80897 - 11.4018i) q^{30} +(-19.5382 + 11.2804i) q^{31} +(-29.3399 + 12.7738i) 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} +(1.12393 + 5.94517i) q^{38} +(26.2361 - 15.1474i) q^{39} +(1.34740 + 36.4640i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(46.1012 - 18.0769i) q^{44} +(-24.8123 + 14.3254i) q^{45} +(-59.5919 + 11.2658i) 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} +(-72.6723 - 10.9766i) q^{52} +(4.12744 - 2.38298i) q^{53} +(38.2006 - 32.8639i) q^{54} -56.4650i q^{55} -4.98794 q^{57} +(-29.6999 - 34.5228i) q^{58} +(5.86884 + 10.1651i) q^{59} +(-29.7437 - 4.49257i) 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} +(7.58317 + 40.1121i) q^{66} +(39.5997 + 68.5887i) q^{67} +(-48.5172 + 19.0242i) q^{68} -49.9970i q^{69} +12.9952i q^{71} +(-50.2180 + 1.85563i) q^{72} +(-49.2909 - 85.3744i) q^{73} +(27.0797 - 5.11940i) 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} +(49.6043 + 53.5273i) q^{80} +(-7.49577 - 12.9831i) q^{81} +(91.7308 - 78.9160i) q^{82} -28.3732 q^{83} +59.4242i q^{85} +(59.1582 - 50.8938i) q^{86} +(32.5130 - 18.7714i) q^{87} +(46.3177 - 87.5388i) 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} +(39.9642 - 7.55521i) q^{94} +(11.9498 - 6.89923i) q^{95} +(-42.4269 - 31.3634i) 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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.51615 1.30434i 0.758073 0.652170i
\(3\) 0.824388 + 1.42788i 0.274796 + 0.475961i 0.970084 0.242771i \(-0.0780563\pi\)
−0.695288 + 0.718732i \(0.744723\pi\)
\(4\) 0.597396 3.95514i 0.149349 0.988785i
\(5\) −3.95004 2.28056i −0.790008 0.456111i 0.0499573 0.998751i \(-0.484091\pi\)
−0.839965 + 0.542640i \(0.817425\pi\)
\(6\) 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
\(10\) −8.96346 + 1.69454i −0.896346 + 0.169454i
\(11\) 6.18983 + 10.7211i 0.562712 + 0.974645i 0.997259 + 0.0739960i \(0.0235752\pi\)
−0.434547 + 0.900649i \(0.643091\pi\)
\(12\) 6.13996 2.40756i 0.511663 0.200630i
\(13\) 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
\(16\) −15.2862 4.72557i −0.955390 0.295348i
\(17\) −6.51422 11.2830i −0.383189 0.663703i 0.608327 0.793687i \(-0.291841\pi\)
−0.991516 + 0.129983i \(0.958508\pi\)
\(18\) −2.33371 12.3444i −0.129650 0.685801i
\(19\) −1.51262 + 2.61993i −0.0796115 + 0.137891i −0.903082 0.429467i \(-0.858701\pi\)
0.823471 + 0.567359i \(0.192035\pi\)
\(20\) −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 \(-0.562443\pi\)
−0.946873 + 0.321609i \(0.895776\pi\)
\(24\) 6.16880 11.6588i 0.257033 0.485783i
\(25\) −2.09812 3.63405i −0.0839248 0.145362i
\(26\) −23.9661 27.8579i −0.921774 1.07146i
\(27\) 25.1958 0.933179
\(28\) 0 0
\(29\) 22.7701i 0.785176i −0.919714 0.392588i \(-0.871580\pi\)
0.919714 0.392588i \(-0.128420\pi\)
\(30\) −9.80897 11.4018i −0.326966 0.380060i
\(31\) −19.5382 + 11.2804i −0.630264 + 0.363883i −0.780855 0.624713i \(-0.785216\pi\)
0.150590 + 0.988596i \(0.451883\pi\)
\(32\) −29.3399 + 12.7738i −0.916872 + 0.399181i
\(33\) −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 \(-0.273712\pi\)
−0.329991 + 0.943984i \(0.607046\pi\)
\(38\) 1.12393 + 5.94517i 0.0295772 + 0.156452i
\(39\) 26.2361 15.1474i 0.672721 0.388395i
\(40\) 1.34740 + 36.4640i 0.0336849 + 0.911601i
\(41\) 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 \(0.350101\pi\)
\(44\) 46.1012 18.0769i 1.04775 0.410838i
\(45\) −24.8123 + 14.3254i −0.551385 + 0.318342i
\(46\) −59.5919 + 11.2658i −1.29548 + 0.244909i
\(47\) 17.6115 + 10.1680i 0.374713 + 0.216341i 0.675516 0.737346i \(-0.263921\pi\)
−0.300802 + 0.953686i \(0.597254\pi\)
\(48\) −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
\(52\) −72.6723 10.9766i −1.39754 0.211089i
\(53\) 4.12744 2.38298i 0.0778762 0.0449619i −0.460556 0.887631i \(-0.652350\pi\)
0.538432 + 0.842669i \(0.319017\pi\)
\(54\) 38.2006 32.8639i 0.707418 0.608591i
\(55\) 56.4650i 1.02664i
\(56\) 0 0
\(57\) −4.98794 −0.0875077
\(58\) −29.6999 34.5228i −0.512068 0.595221i
\(59\) 5.86884 + 10.1651i 0.0994718 + 0.172290i 0.911466 0.411375i \(-0.134951\pi\)
−0.811994 + 0.583665i \(0.801618\pi\)
\(60\) −29.7437 4.49257i −0.495728 0.0748762i
\(61\) 94.3137 + 54.4520i 1.54613 + 0.892656i 0.998432 + 0.0559779i \(0.0178276\pi\)
0.547694 + 0.836679i \(0.315506\pi\)
\(62\) −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
\(66\) 7.58317 + 40.1121i 0.114896 + 0.607759i
\(67\) 39.5997 + 68.5887i 0.591041 + 1.02371i 0.994093 + 0.108535i \(0.0346160\pi\)
−0.403052 + 0.915177i \(0.632051\pi\)
\(68\) −48.5172 + 19.0242i −0.713488 + 0.279768i
\(69\) 49.9970i 0.724595i
\(70\) 0 0
\(71\) 12.9952i 0.183031i 0.995804 + 0.0915157i \(0.0291712\pi\)
−0.995804 + 0.0915157i \(0.970829\pi\)
\(72\) −50.2180 + 1.85563i −0.697473 + 0.0257726i
\(73\) −49.2909 85.3744i −0.675218 1.16951i −0.976405 0.215947i \(-0.930716\pi\)
0.301187 0.953565i \(-0.402617\pi\)
\(74\) 27.0797 5.11940i 0.365942 0.0691811i
\(75\) 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 \(-0.0213681\pi\)
0.440781 + 0.897615i \(0.354701\pi\)
\(80\) 49.6043 + 53.5273i 0.620054 + 0.669091i
\(81\) −7.49577 12.9831i −0.0925404 0.160285i
\(82\) 91.7308 78.9160i 1.11867 0.962390i
\(83\) −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
\(86\) 59.1582 50.8938i 0.687886 0.591788i
\(87\) 32.5130 18.7714i 0.373713 0.215763i
\(88\) 46.3177 87.5388i 0.526338 0.994759i
\(89\) −78.7090 + 136.328i −0.884371 + 1.53178i −0.0379380 + 0.999280i \(0.512079\pi\)
−0.846433 + 0.532495i \(0.821254\pi\)
\(90\) −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
\(94\) 39.9642 7.55521i 0.425151 0.0803746i
\(95\) 11.9498 6.89923i 0.125788 0.0726235i
\(96\) −42.4269 31.3634i −0.441947 0.326702i
\(97\) 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
\(100\) −15.6266 + 6.12739i −0.156266 + 0.0612739i
\(101\) −37.7745 + 21.8091i −0.374005 + 0.215932i −0.675207 0.737628i \(-0.735946\pi\)
0.301202 + 0.953560i \(0.402612\pi\)
\(102\) −7.98058 42.2142i −0.0782409 0.413865i
\(103\) −54.4748 31.4510i −0.528881 0.305350i 0.211679 0.977339i \(-0.432107\pi\)
−0.740561 + 0.671989i \(0.765440\pi\)
\(104\) −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 −0.950663 0.310227i \(-0.899595\pi\)
0.743996 + 0.668184i \(0.232928\pi\)
\(108\) 15.0519 99.6530i 0.139369 0.922713i
\(109\) 7.63419 4.40760i 0.0700384 0.0404367i −0.464572 0.885535i \(-0.653792\pi\)
0.534610 + 0.845099i \(0.320458\pi\)
\(110\) −73.6496 85.6092i −0.669542 0.778266i
\(111\) 22.7196i 0.204681i
\(112\) 0 0
\(113\) −121.408 −1.07440 −0.537202 0.843454i \(-0.680519\pi\)
−0.537202 + 0.843454i \(0.680519\pi\)
\(114\) −7.56245 + 6.50597i −0.0663373 + 0.0570699i
\(115\) 69.1550 + 119.780i 0.601347 + 1.04156i
\(116\) −90.0589 13.6028i −0.776370 0.117265i
\(117\) −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
\(122\) 214.017 40.4599i 1.75424 0.331638i
\(123\) 49.8776 + 86.3906i 0.405509 + 0.702363i
\(124\) 32.9434 + 84.0151i 0.265673 + 0.677541i
\(125\) 133.167i 1.06534i
\(126\) 0 0
\(127\) 222.845i 1.75468i −0.479868 0.877341i \(-0.659315\pi\)
0.479868 0.877341i \(-0.340685\pi\)
\(128\) 32.9946 + 123.674i 0.257770 + 0.966206i
\(129\) 32.1666 + 55.7143i 0.249354 + 0.431893i
\(130\) 31.1357 + 164.696i 0.239505 + 1.26689i
\(131\) 118.527 205.294i 0.904785 1.56713i 0.0835786 0.996501i \(-0.473365\pi\)
0.821206 0.570632i \(-0.193302\pi\)
\(132\) 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
\(136\) −48.7451 + 92.1264i −0.358420 + 0.677400i
\(137\) 4.83138 + 8.36820i 0.0352656 + 0.0610818i 0.883119 0.469148i \(-0.155439\pi\)
−0.847854 + 0.530230i \(0.822106\pi\)
\(138\) −65.2131 75.8028i −0.472559 0.549295i
\(139\) 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
\(142\) 16.9502 + 19.7027i 0.119368 + 0.138751i
\(143\) 196.991 113.733i 1.37756 0.795334i
\(144\) −73.7175 + 68.3148i −0.511927 + 0.474408i
\(145\) −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 0.996309 + 0.0858343i \(0.0273556\pi\)
0.572489 + 0.819912i \(0.305978\pi\)
\(150\) −2.57041 13.5965i −0.0171361 0.0906432i
\(151\) 93.6846 54.0888i 0.620428 0.358204i −0.156608 0.987661i \(-0.550056\pi\)
0.777036 + 0.629457i \(0.216723\pi\)
\(152\) 24.1854 0.893685i 0.159114 0.00587951i
\(153\) −81.8386 −0.534893
\(154\) 0 0
\(155\) 102.902 0.663885
\(156\) −44.2368 112.816i −0.283569 0.723182i
\(157\) 102.565 59.2159i 0.653280 0.377171i −0.136432 0.990649i \(-0.543563\pi\)
0.789712 + 0.613478i \(0.210230\pi\)
\(158\) 257.881 48.7523i 1.63216 0.308559i
\(159\) 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 −0.712351 0.701823i \(-0.752370\pi\)
0.963972 + 0.266003i \(0.0857031\pi\)
\(164\) 36.1440 239.296i 0.220390 1.45912i
\(165\) 80.6254 46.5491i 0.488639 0.282116i
\(166\) −43.0179 + 37.0083i −0.259144 + 0.222942i
\(167\) 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
\(170\) 77.5093 + 90.0957i 0.455937 + 0.529975i
\(171\) 9.50157 + 16.4572i 0.0555648 + 0.0962410i
\(172\) 23.3097 154.325i 0.135521 0.897237i
\(173\) 95.3611 + 55.0568i 0.551220 + 0.318247i 0.749614 0.661875i \(-0.230239\pi\)
−0.198394 + 0.980122i \(0.563572\pi\)
\(174\) 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
\(178\) 58.4837 + 309.356i 0.328560 + 1.73796i
\(179\) −76.9263 133.240i −0.429756 0.744359i 0.567095 0.823652i \(-0.308067\pi\)
−0.996851 + 0.0792929i \(0.974734\pi\)
\(180\) 41.8362 + 106.694i 0.232423 + 0.592745i
\(181\) 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
\(184\) 8.95792 + 242.424i 0.0486844 + 1.31752i
\(185\) −31.4253 54.4303i −0.169867 0.294218i
\(186\) −73.1005 + 13.8196i −0.393013 + 0.0742990i
\(187\) 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 \(-0.436406\pi\)
−0.749569 + 0.661927i \(0.769739\pi\)
\(192\) −105.234 + 7.78772i −0.548093 + 0.0405610i
\(193\) −42.7276 74.0064i −0.221386 0.383453i 0.733843 0.679319i \(-0.237725\pi\)
−0.955229 + 0.295867i \(0.904392\pi\)
\(194\) 60.0659 51.6747i 0.309618 0.266364i
\(195\) −138.178 −0.708606
\(196\) 0 0
\(197\) 214.100i 1.08680i 0.839474 + 0.543400i \(0.182863\pi\)
−0.839474 + 0.543400i \(0.817137\pi\)
\(198\) 117.900 101.430i 0.595457 0.512271i
\(199\) −214.968 + 124.112i −1.08024 + 0.623677i −0.930961 0.365118i \(-0.881029\pi\)
−0.149279 + 0.988795i \(0.547695\pi\)
\(200\) −15.7000 + 29.6724i −0.0784999 + 0.148362i
\(201\) −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
\(206\) −123.615 + 23.3693i −0.600070 + 0.113443i
\(207\) −164.960 + 95.2398i −0.796909 + 0.460096i
\(208\) −86.8282 + 280.871i −0.417443 + 1.35034i
\(209\) −37.4514 −0.179193
\(210\) 0 0
\(211\) 191.753 0.908783 0.454392 0.890802i \(-0.349857\pi\)
0.454392 + 0.890802i \(0.349857\pi\)
\(212\) −6.95929 17.7482i −0.0328269 0.0837178i
\(213\) −18.5557 + 10.7131i −0.0871157 + 0.0502963i
\(214\) 16.4310 + 86.9139i 0.0767805 + 0.406140i
\(215\) −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
\(220\) −223.327 33.7320i −1.01512 0.153327i
\(221\) −207.315 + 119.693i −0.938075 + 0.541598i
\(222\) 29.6341 + 34.4462i 0.133487 + 0.155163i
\(223\) 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
\(226\) −184.072 + 158.357i −0.814477 + 0.700694i
\(227\) 35.2219 + 61.0060i 0.155162 + 0.268749i 0.933118 0.359570i \(-0.117077\pi\)
−0.777956 + 0.628319i \(0.783743\pi\)
\(228\) −2.97978 + 19.7280i −0.0130692 + 0.0865263i
\(229\) 81.8558 + 47.2595i 0.357449 + 0.206373i 0.667961 0.744196i \(-0.267167\pi\)
−0.310512 + 0.950569i \(0.600501\pi\)
\(230\) 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 −0.681930 0.731417i \(-0.738859\pi\)
0.974391 + 0.224860i \(0.0721925\pi\)
\(234\) −226.818 + 42.8799i −0.969308 + 0.183247i
\(235\) −46.3775 80.3281i −0.197351 0.341822i
\(236\) 43.7105 17.1395i 0.185214 0.0726248i
\(237\) 216.360i 0.912911i
\(238\) 0 0
\(239\) 173.230i 0.724813i 0.932020 + 0.362406i \(0.118045\pi\)
−0.932020 + 0.362406i \(0.881955\pi\)
\(240\) −35.5375 + 114.956i −0.148073 + 0.478985i
\(241\) −164.461 284.856i −0.682413 1.18197i −0.974242 0.225503i \(-0.927597\pi\)
0.291830 0.956470i \(-0.405736\pi\)
\(242\) 11.9837 + 63.3890i 0.0495193 + 0.261938i
\(243\) 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
\(248\) 159.531 + 84.4098i 0.643271 + 0.340362i
\(249\) −23.3905 40.5136i −0.0939379 0.162705i
\(250\) 173.695 + 201.901i 0.694782 + 0.807605i
\(251\) −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
\(254\) −290.665 337.865i −1.14435 1.33018i
\(255\) −84.8507 + 48.9886i −0.332748 + 0.192112i
\(256\) 211.338 + 144.472i 0.825539 + 0.564345i
\(257\) 72.7208 125.956i 0.282960 0.490102i −0.689152 0.724617i \(-0.742017\pi\)
0.972113 + 0.234515i \(0.0753502\pi\)
\(258\) 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
\(262\) −88.0698 465.855i −0.336144 1.77807i
\(263\) −175.617 + 101.392i −0.667745 + 0.385523i −0.795222 0.606319i \(-0.792645\pi\)
0.127477 + 0.991842i \(0.459312\pi\)
\(264\) 163.179 6.02969i 0.618102 0.0228397i
\(265\) −21.7381 −0.0820305
\(266\) 0 0
\(267\) −259.547 −0.972087
\(268\) 294.935 115.648i 1.10050 0.431521i
\(269\) −191.662 + 110.656i −0.712497 + 0.411360i −0.811985 0.583679i \(-0.801613\pi\)
0.0994882 + 0.995039i \(0.468279\pi\)
\(270\) −225.842 + 42.6953i −0.836451 + 0.158131i
\(271\) −101.651 58.6880i −0.375095 0.216561i 0.300587 0.953754i \(-0.402817\pi\)
−0.675682 + 0.737193i \(0.736151\pi\)
\(272\) 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
\(276\) −197.745 29.8680i −0.716468 0.108217i
\(277\) −221.277 + 127.755i −0.798835 + 0.461208i −0.843064 0.537814i \(-0.819250\pi\)
0.0442283 + 0.999021i \(0.485917\pi\)
\(278\) 95.6113 82.2544i 0.343926 0.295879i
\(279\) 141.716i 0.507944i
\(280\) 0 0
\(281\) −278.004 −0.989336 −0.494668 0.869082i \(-0.664710\pi\)
−0.494668 + 0.869082i \(0.664710\pi\)
\(282\) 43.7339 + 50.8357i 0.155085 + 0.180268i
\(283\) 28.3448 + 49.0947i 0.100158 + 0.173479i 0.911750 0.410746i \(-0.134732\pi\)
−0.811591 + 0.584225i \(0.801398\pi\)
\(284\) 51.3979 + 7.76330i 0.180979 + 0.0273356i
\(285\) 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
\(290\) 38.5848 + 204.099i 0.133051 + 0.703789i
\(291\) 32.6602 + 56.5691i 0.112234 + 0.194396i
\(292\) −367.114 + 143.950i −1.25724 + 0.492980i
\(293\) 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
\(296\) −4.07065 110.162i −0.0137522 0.372169i
\(297\) 155.958 + 270.127i 0.525111 + 0.909518i
\(298\) 530.429 100.277i 1.77996 0.336501i
\(299\) −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
\(304\) 35.5029 32.9009i 0.116786 0.108227i
\(305\) −248.362 430.176i −0.814302 1.41041i
\(306\) −124.079 + 106.745i −0.405488 + 0.348841i
\(307\) −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
\(310\) 156.015 134.219i 0.503274 0.432966i
\(311\) −91.0263 + 52.5541i −0.292689 + 0.168984i −0.639154 0.769079i \(-0.720715\pi\)
0.346465 + 0.938063i \(0.387382\pi\)
\(312\) −214.220 113.346i −0.686604 0.363290i
\(313\) 105.245 182.290i 0.336246 0.582395i −0.647477 0.762085i \(-0.724176\pi\)
0.983723 + 0.179690i \(0.0575093\pi\)
\(314\) 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 \(-0.301707\pi\)
−0.411631 + 0.911351i \(0.635041\pi\)
\(318\) 15.4425 2.91939i 0.0485612 0.00918047i
\(319\) 244.120 140.943i 0.765268 0.441828i
\(320\) 241.341 164.215i 0.754192 0.513172i
\(321\) −72.9199 −0.227165
\(322\) 0 0
\(323\) 39.4141 0.122025
\(324\) −55.8277 + 21.8908i −0.172308 + 0.0675641i
\(325\) −66.7725 + 38.5511i −0.205454 + 0.118619i
\(326\) −30.4751 161.201i −0.0934818 0.494483i
\(327\) 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 −0.975436 0.220284i \(-0.929302\pi\)
0.678489 + 0.734610i \(0.262635\pi\)
\(332\) −16.9500 + 112.220i −0.0510544 + 0.338012i
\(333\) 74.9610 43.2787i 0.225108 0.129966i
\(334\) 171.646 + 199.519i 0.513911 + 0.597363i
\(335\) 361.238i 1.07832i
\(336\) 0 0
\(337\) 591.516 1.75524 0.877620 0.479358i \(-0.159130\pi\)
0.877620 + 0.479358i \(0.159130\pi\)
\(338\) −255.636 + 219.923i −0.756319 + 0.650661i
\(339\) −100.087 173.356i −0.295242 0.511374i
\(340\) 235.031 + 35.4998i 0.691267 + 0.104411i
\(341\) −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
\(346\) 216.394 40.9092i 0.625416 0.118235i
\(347\) −123.770 214.376i −0.356685 0.617797i 0.630719 0.776011i \(-0.282760\pi\)
−0.987405 + 0.158214i \(0.949427\pi\)
\(348\) −54.8203 139.807i −0.157530 0.401746i
\(349\) 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
\(352\) −318.558 235.488i −0.904995 0.669001i
\(353\) −0.634830 1.09956i −0.00179839 0.00311490i 0.865125 0.501557i \(-0.167239\pi\)
−0.866923 + 0.498442i \(0.833906\pi\)
\(354\) 7.18992 + 38.0319i 0.0203105 + 0.107435i
\(355\) 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 \(-0.341049\pi\)
−0.520843 + 0.853653i \(0.674382\pi\)
\(360\) 202.595 + 107.195i 0.562764 + 0.297765i
\(361\) 175.924 + 304.709i 0.487324 + 0.844070i
\(362\) −296.752 344.940i −0.819756 0.952873i
\(363\) −53.1828 −0.146509
\(364\) 0 0
\(365\) 449.643i 1.23190i
\(366\) 234.205 + 272.237i 0.639905 + 0.743816i
\(367\) 459.021 265.016i 1.25074 0.722115i 0.279483 0.960151i \(-0.409837\pi\)
0.971256 + 0.238036i \(0.0765036\pi\)
\(368\) 329.785 + 355.866i 0.896155 + 0.967028i
\(369\) 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 \(-0.384160\pi\)
−0.631337 + 0.775509i \(0.717493\pi\)
\(374\) −59.9213 316.961i −0.160217 0.847489i
\(375\) −190.147 + 109.782i −0.507059 + 0.292751i
\(376\) −6.00746 162.577i −0.0159773 0.432386i
\(377\) −418.381 −1.10976
\(378\) 0 0
\(379\) −345.947 −0.912790 −0.456395 0.889777i \(-0.650860\pi\)
−0.456395 + 0.889777i \(0.650860\pi\)
\(380\) −20.1486 51.3847i −0.0530227 0.135223i
\(381\) 318.196 183.710i 0.835160 0.482180i
\(382\) −238.860 + 45.1564i −0.625288 + 0.118210i
\(383\) 350.630 + 202.436i 0.915483 + 0.528555i 0.882191 0.470891i \(-0.156068\pi\)
0.0332920 + 0.999446i \(0.489401\pi\)
\(384\) −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
\(388\) 23.6673 156.693i 0.0609983 0.403847i
\(389\) 116.391 67.1985i 0.299206 0.172747i −0.342880 0.939379i \(-0.611402\pi\)
0.642086 + 0.766632i \(0.278069\pi\)
\(390\) −209.498 + 180.231i −0.537175 + 0.462132i
\(391\) 395.070i 1.01041i
\(392\) 0 0
\(393\) 390.848 0.994525
\(394\) 279.259 + 324.606i 0.708779 + 0.823874i
\(395\) −299.265 518.342i −0.757633 1.31226i
\(396\) 46.4555 307.564i 0.117312 0.776678i
\(397\) −530.424 306.240i −1.33608 0.771386i −0.349857 0.936803i \(-0.613770\pi\)
−0.986224 + 0.165417i \(0.947103\pi\)
\(398\) −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 −0.776521 0.630092i \(-0.783017\pi\)
0.933936 + 0.357441i \(0.116351\pi\)
\(402\) 48.5137 + 256.619i 0.120681 + 0.638355i
\(403\) 207.267 + 358.998i 0.514311 + 0.890813i
\(404\) 63.6918 + 162.432i 0.157653 + 0.402060i
\(405\) 68.3781i 0.168835i
\(406\) 0 0
\(407\) 170.588i 0.419134i
\(408\) −171.731 + 6.34569i −0.420908 + 0.0155532i
\(409\) 171.259 + 296.630i 0.418727 + 0.725257i 0.995812 0.0914275i \(-0.0291430\pi\)
−0.577084 + 0.816685i \(0.695810\pi\)
\(410\) −542.313 + 102.524i −1.32271 + 0.250058i
\(411\) −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
\(416\) 234.708 + 539.096i 0.564201 + 1.29590i
\(417\) 51.9876 + 90.0452i 0.124671 + 0.215936i
\(418\) −56.7818 + 48.8494i −0.135842 + 0.116865i
\(419\) 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 \(0.957864\pi\)
\(422\) 290.726 250.111i 0.688924 0.592681i
\(423\) 110.627 63.8708i 0.261531 0.150995i
\(424\) −33.7010 17.8315i −0.0794834 0.0420555i
\(425\) −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
\(430\) −349.743 + 66.1188i −0.813357 + 0.153765i
\(431\) −35.7481 + 20.6392i −0.0829422 + 0.0478867i −0.540898 0.841089i \(-0.681915\pi\)
0.457955 + 0.888975i \(0.348582\pi\)
\(432\) −385.149 119.065i −0.891550 0.275613i
\(433\) 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
\(436\) −12.8720 32.8273i −0.0295230 0.0752921i
\(437\) 79.4461 45.8682i 0.181799 0.104962i
\(438\) −60.3864 319.421i −0.137868 0.729272i
\(439\) 459.215 + 265.128i 1.04605 + 0.603936i 0.921541 0.388282i \(-0.126931\pi\)
0.124508 + 0.992219i \(0.460265\pi\)
\(440\) −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 −0.990290 0.139015i \(-0.955606\pi\)
0.615535 + 0.788109i \(0.288940\pi\)
\(444\) 89.8591 + 13.5726i 0.202385 + 0.0305689i
\(445\) 621.808 359.001i 1.39732 0.806743i
\(446\) −53.7739 62.5060i −0.120569 0.140148i
\(447\) 445.025i 0.995582i
\(448\) 0 0
\(449\) −19.4200 −0.0432517 −0.0216259 0.999766i \(-0.506884\pi\)
−0.0216259 + 0.999766i \(0.506884\pi\)
\(450\) −39.9638 + 34.3809i −0.0888085 + 0.0764019i
\(451\) 374.501 + 648.654i 0.830379 + 1.43826i
\(452\) −72.5285 + 480.184i −0.160461 + 1.06235i
\(453\) 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 −0.752100 0.659049i \(-0.770959\pi\)
0.946803 + 0.321813i \(0.104292\pi\)
\(458\) 185.748 35.1155i 0.405563 0.0766715i
\(459\) −164.131 284.283i −0.357584 0.619354i
\(460\) 515.059 201.961i 1.11969 0.439047i
\(461\) 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 \(0.816307\pi\)
\(464\) −107.602 + 348.069i −0.231900 + 0.750149i
\(465\) 84.8314 + 146.932i 0.182433 + 0.315983i
\(466\) −50.6330 267.829i −0.108655 0.574741i
\(467\) −325.162 + 563.197i −0.696278 + 1.20599i 0.273470 + 0.961881i \(0.411829\pi\)
−0.969748 + 0.244108i \(0.921505\pi\)
\(468\) −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
\(472\) 43.9158 82.9992i 0.0930419 0.175846i
\(473\) 241.520 + 418.324i 0.510612 + 0.884407i
\(474\) 282.207 + 328.033i 0.595373 + 0.692053i
\(475\) 12.6946 0.0267255
\(476\) 0 0
\(477\) 29.9375i 0.0627621i
\(478\) 225.951 + 262.642i 0.472701 + 0.549461i
\(479\) −572.400 + 330.475i −1.19499 + 0.689928i −0.959434 0.281933i \(-0.909024\pi\)
−0.235556 + 0.971861i \(0.575691\pi\)
\(480\) 96.0622 + 220.644i 0.200130 + 0.459674i
\(481\) 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
\(486\) −93.4295 494.207i −0.192242 1.01689i
\(487\) 334.373 193.050i 0.686597 0.396407i −0.115739 0.993280i \(-0.536924\pi\)
0.802336 + 0.596873i \(0.203590\pi\)
\(488\) −32.1713 870.639i −0.0659248 1.78410i
\(489\) 135.246 0.276578
\(490\) 0 0
\(491\) −898.359 −1.82965 −0.914826 0.403848i \(-0.867672\pi\)
−0.914826 + 0.403848i \(0.867672\pi\)
\(492\) 371.483 145.664i 0.755048 0.296064i
\(493\) −256.914 + 148.329i −0.521124 + 0.300871i
\(494\) 109.237 20.6513i 0.221128 0.0418042i
\(495\) −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 0.131490 + 0.991318i \(0.458024\pi\)
−0.924251 + 0.381785i \(0.875309\pi\)
\(500\) 526.695 + 79.5537i 1.05339 + 0.159107i
\(501\) −187.904 + 108.486i −0.375058 + 0.216540i
\(502\) −242.970 + 209.027i −0.484004 + 0.416389i
\(503\) 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
\(506\) −489.645 569.157i −0.967679 1.12482i
\(507\) −138.999 240.754i −0.274160 0.474860i
\(508\) −881.381 133.126i −1.73500 0.262060i
\(509\) 477.272 + 275.553i 0.937666 + 0.541362i 0.889228 0.457465i \(-0.151242\pi\)
0.0484379 + 0.998826i \(0.484576\pi\)
\(510\) −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
\(514\) −54.0342 285.820i −0.105125 0.556071i
\(515\) 143.452 + 248.466i 0.278547 + 0.482458i
\(516\) 239.574 93.9400i 0.464290 0.182054i
\(517\) 251.753i 0.486950i
\(518\) 0 0
\(519\) 181.553i 0.349812i
\(520\) 669.995 24.7573i 1.28845 0.0476101i
\(521\) 71.3914 + 123.654i 0.137028 + 0.237339i 0.926370 0.376614i \(-0.122912\pi\)
−0.789343 + 0.613953i \(0.789578\pi\)
\(522\) −281.084 + 53.1387i −0.538474 + 0.101798i
\(523\) −416.255 + 720.976i −0.795900 + 1.37854i 0.126367 + 0.991984i \(0.459668\pi\)
−0.922266 + 0.386555i \(0.873665\pi\)
\(524\) −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
\(528\) 239.538 221.983i 0.453671 0.420422i
\(529\) 195.264 + 338.207i 0.369119 + 0.639333i
\(530\) −32.9581 + 28.3538i −0.0621851 + 0.0534978i
\(531\) 73.7306 0.138852
\(532\) 0 0
\(533\) 1111.68i 2.08571i
\(534\) −393.511 + 338.538i −0.736912 + 0.633966i
\(535\) 174.697 100.862i 0.326537 0.188526i
\(536\) 296.320 560.034i 0.552836 1.04484i
\(537\) 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 \(-0.140375\pi\)
0.0825038 + 0.996591i \(0.473708\pi\)
\(542\) −230.666 + 43.6074i −0.425584 + 0.0804564i
\(543\) 324.859 187.557i 0.598267 0.345410i
\(544\) 335.253 + 247.830i 0.616273 + 0.455569i
\(545\) −40.2071 −0.0737746
\(546\) 0 0
\(547\) 577.704 1.05613 0.528065 0.849204i \(-0.322918\pi\)
0.528065 + 0.849204i \(0.322918\pi\)
\(548\) 35.9836 14.1097i 0.0656636 0.0257475i
\(549\) 592.435 342.043i 1.07912 0.623028i
\(550\) −19.2996 102.088i −0.0350903 0.185614i
\(551\) 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
\(556\) 37.6730 249.419i 0.0677573 0.448596i
\(557\) −445.752 + 257.355i −0.800273 + 0.462038i −0.843566 0.537025i \(-0.819548\pi\)
0.0432939 + 0.999062i \(0.486215\pi\)
\(558\) 184.846 + 214.863i 0.331266 + 0.385058i
\(559\) 716.937i 1.28253i
\(560\) 0 0
\(561\) 265.927 0.474023
\(562\) −421.494 + 362.611i −0.749989 + 0.645215i
\(563\) −304.360 527.166i −0.540603 0.936352i −0.998869 0.0475374i \(-0.984863\pi\)
0.458266 0.888815i \(-0.348471\pi\)
\(564\) 132.614 + 20.0304i 0.235131 + 0.0355149i
\(565\) 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 −0.936219 0.351417i \(-0.885700\pi\)
0.772445 + 0.635081i \(0.219033\pi\)
\(570\) 44.7092 8.45226i 0.0784372 0.0148285i
\(571\) −91.8878 159.154i −0.160924 0.278729i 0.774276 0.632848i \(-0.218114\pi\)
−0.935200 + 0.354119i \(0.884781\pi\)
\(572\) −332.147 847.070i −0.580677 1.48089i
\(573\) 200.401i 0.349741i
\(574\) 0 0
\(575\) 127.246i 0.221297i
\(576\) 226.156 + 332.374i 0.392632 + 0.577038i
\(577\) 67.2281 + 116.442i 0.116513 + 0.201807i 0.918384 0.395691i \(-0.129495\pi\)
−0.801870 + 0.597498i \(0.796162\pi\)
\(578\) −44.3073 234.369i −0.0766562 0.405482i
\(579\) 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
\(584\) −368.838 + 697.091i −0.631572 + 1.19365i
\(585\) 263.217 + 455.905i 0.449944 + 0.779325i
\(586\) 375.481 + 436.454i 0.640753 + 0.744802i
\(587\) 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
\(590\) −69.8303 81.1697i −0.118356 0.137576i
\(591\) −305.709 + 176.501i −0.517274 + 0.298648i
\(592\) −149.861 161.712i −0.253143 0.273163i
\(593\) 48.1873 83.4628i 0.0812602 0.140747i −0.822531 0.568720i \(-0.807439\pi\)
0.903791 + 0.427973i \(0.140772\pi\)
\(594\) 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
\(598\) 207.000 + 1094.95i 0.346153 + 1.83102i
\(599\) −144.711 + 83.5489i −0.241587 + 0.139481i −0.615906 0.787820i \(-0.711210\pi\)
0.374319 + 0.927300i \(0.377877\pi\)
\(600\) −55.3115 + 2.04384i −0.0921859 + 0.00340640i
\(601\) −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
\(604\) −157.962 402.848i −0.261526 0.666967i
\(605\) 127.412 73.5614i 0.210598 0.121589i
\(606\) −141.330 + 26.7184i −0.233218 + 0.0440898i
\(607\) −48.1243 27.7846i −0.0792822 0.0457736i 0.459835 0.888004i \(-0.347909\pi\)
−0.539117 + 0.842231i \(0.681242\pi\)
\(608\) 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
\(612\) −48.8900 + 323.683i −0.0798857 + 0.528894i
\(613\) 752.678 434.559i 1.22786 0.708905i 0.261278 0.965264i \(-0.415856\pi\)
0.966582 + 0.256359i \(0.0825229\pi\)
\(614\) −81.3386 + 69.9756i −0.132473 + 0.113967i
\(615\) 454.995i 0.739829i
\(616\) 0 0
\(617\) −249.359 −0.404147 −0.202074 0.979370i \(-0.564768\pi\)
−0.202074 + 0.979370i \(0.564768\pi\)
\(618\) −135.275 157.242i −0.218891 0.254436i
\(619\) −248.837 430.998i −0.401998 0.696280i 0.591969 0.805961i \(-0.298351\pi\)
−0.993967 + 0.109680i \(0.965017\pi\)
\(620\) 61.4734 406.993i 0.0991506 0.656440i
\(621\) −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
\(626\) −78.2009 413.653i −0.124922 0.660787i
\(627\) −30.8745 53.4762i −0.0492416 0.0852890i
\(628\) −172.935 441.034i −0.275374 0.702283i
\(629\) 179.527i 0.285417i
\(630\) 0 0
\(631\) 172.763i 0.273792i −0.990585 0.136896i \(-0.956287\pi\)
0.990585 0.136896i \(-0.0437126\pi\)
\(632\) −38.7650 1049.08i −0.0613370 1.65994i
\(633\) 158.079 + 273.801i 0.249730 + 0.432545i
\(634\) 123.587 23.3641i 0.194932 0.0368518i
\(635\) −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
\(640\) 151.717 563.765i 0.237057 0.880883i
\(641\) 213.949 + 370.570i 0.333774 + 0.578113i 0.983248 0.182270i \(-0.0583446\pi\)
−0.649475 + 0.760383i \(0.725011\pi\)
\(642\) −110.557 + 95.1124i −0.172208 + 0.148150i
\(643\) 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
\(646\) 59.7575 51.4094i 0.0925039 0.0795811i
\(647\) −450.510 + 260.102i −0.696306 + 0.402012i −0.805970 0.591956i \(-0.798356\pi\)
0.109664 + 0.993969i \(0.465022\pi\)
\(648\) −56.0899 + 106.008i −0.0865586 + 0.163592i
\(649\) −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 \(-0.438728\pi\)
−0.754378 + 0.656440i \(0.772061\pi\)
\(654\) 28.5627 5.39976i 0.0436738 0.00825651i
\(655\) −936.371 + 540.614i −1.42957 + 0.825365i
\(656\) −924.857 285.909i −1.40984 0.435837i
\(657\) −619.246 −0.942535
\(658\) 0 0
\(659\) 304.044 0.461372 0.230686 0.973028i \(-0.425903\pi\)
0.230686 + 0.973028i \(0.425903\pi\)
\(660\) −135.943 346.693i −0.205974 0.525292i
\(661\) −155.112 + 89.5542i −0.234663 + 0.135483i −0.612722 0.790299i \(-0.709925\pi\)
0.378058 + 0.925782i \(0.376592\pi\)
\(662\) 73.0326 + 386.315i 0.110321 + 0.583557i
\(663\) −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
\(668\) 520.482 + 78.6151i 0.779164 + 0.117687i
\(669\) 58.8671 33.9870i 0.0879927 0.0508026i
\(670\) −471.177 547.689i −0.703249 0.817446i
\(671\) 1348.20i 2.00923i
\(672\) 0 0
\(673\) 544.352 0.808844 0.404422 0.914573i \(-0.367473\pi\)
0.404422 + 0.914573i \(0.367473\pi\)
\(674\) 896.824 771.537i 1.33060 1.14471i
\(675\) −52.8639 91.5629i −0.0783168 0.135649i
\(676\) −100.726 + 666.872i −0.149004 + 0.986497i
\(677\) 471.416 + 272.172i 0.696330 + 0.402027i 0.805979 0.591944i \(-0.201639\pi\)
−0.109649 + 0.993970i \(0.534973\pi\)
\(678\) −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
\(682\) −548.867 + 103.763i −0.804790 + 0.152145i
\(683\) −443.494 768.154i −0.649332 1.12468i −0.983283 0.182086i \(-0.941715\pi\)
0.333951 0.942591i \(-0.391618\pi\)
\(684\) 70.7667 27.7486i 0.103460 0.0405681i
\(685\) 44.0730i 0.0643401i
\(686\) 0 0
\(687\) 155.841i 0.226842i
\(688\) −596.451 184.386i −0.866934 0.268003i
\(689\) −43.7852 75.8382i −0.0635489 0.110070i
\(690\) 84.7218 + 448.146i 0.122785 + 0.649487i
\(691\) 589.242 1020.60i 0.852738 1.47698i −0.0259906 0.999662i \(-0.508274\pi\)
0.878728 0.477323i \(-0.158393\pi\)
\(692\) 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
\(696\) −265.472 140.464i −0.381425 0.201816i
\(697\) −394.127 682.648i −0.565462 0.979409i
\(698\) −376.627 437.786i −0.539580 0.627200i
\(699\) 224.706 0.321468
\(700\) 0 0
\(701\) 901.601i 1.28616i 0.765797 + 0.643082i \(0.222345\pi\)
−0.765797 + 0.643082i \(0.777655\pi\)
\(702\) −603.846 701.902i −0.860180 0.999861i
\(703\) −36.1018 + 20.8434i −0.0513539 + 0.0296492i
\(704\) −790.137 + 58.4732i −1.12235 + 0.0830586i
\(705\) 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 \(-0.408744\pi\)
−0.689289 + 0.724487i \(0.742077\pi\)
\(710\) −22.0209 116.482i −0.0310154 0.164059i
\(711\) 713.858 412.146i 1.00402 0.579671i
\(712\) 1258.49 46.5028i 1.76754 0.0653129i
\(713\) 684.126 0.959504
\(714\) 0 0
\(715\) −1037.50 −1.45104
\(716\) −572.939 + 224.657i −0.800195 + 0.313767i
\(717\) −247.352 + 142.809i −0.344982 + 0.199176i
\(718\) −34.1985 + 6.46520i −0.0476302 + 0.00900446i
\(719\) 1026.20 + 592.475i 1.42726 + 0.824027i 0.996904 0.0786341i \(-0.0250559\pi\)
0.430353 + 0.902661i \(0.358389\pi\)
\(720\) 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
\(724\) −899.838 135.914i −1.24287 0.187727i
\(725\) −82.7477 + 47.7744i −0.114135 + 0.0658957i
\(726\) −80.6328 + 69.3684i −0.111064 + 0.0955487i
\(727\) 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
\(730\) 586.487 + 681.725i 0.803407 + 0.933869i
\(731\) −254.177 440.247i −0.347711 0.602254i
\(732\) 710.179 + 107.268i 0.970189 + 0.146540i
\(733\) −898.325 518.648i −1.22555 0.707569i −0.259450 0.965756i \(-0.583541\pi\)
−0.966095 + 0.258188i \(0.916875\pi\)
\(734\) 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
\(738\) −141.195 746.869i −0.191322 1.01202i
\(739\) 209.986 + 363.706i 0.284148 + 0.492160i 0.972402 0.233310i \(-0.0749558\pi\)
−0.688254 + 0.725470i \(0.741622\pi\)
\(740\) −234.053 + 91.7751i −0.316287 + 0.124020i
\(741\) 91.6491i 0.123683i
\(742\) 0 0
\(743\) 1241.67i 1.67116i −0.549370 0.835579i \(-0.685132\pi\)
0.549370 0.835579i \(-0.314868\pi\)
\(744\) 10.9886 + 297.378i 0.0147696 + 0.399702i
\(745\) −615.551 1066.17i −0.826243 1.43109i
\(746\) −233.098 + 44.0670i −0.312463 + 0.0590711i
\(747\) −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 \(-0.475275\pi\)
−0.824614 + 0.565695i \(0.808608\pi\)
\(752\) −221.164 238.655i −0.294101 0.317360i
\(753\) −132.112 228.825i −0.175448 0.303885i
\(754\) −634.327 + 545.711i −0.841282 + 0.723755i
\(755\) −493.411 −0.653524
\(756\) 0 0
\(757\) 105.310i 0.139116i −0.997578 0.0695578i \(-0.977841\pi\)
0.997578 0.0695578i \(-0.0221588\pi\)
\(758\) −524.507 + 451.233i −0.691961 + 0.595294i
\(759\) 536.023 309.473i 0.706223 0.407738i
\(760\) −97.5714 51.6261i −0.128383 0.0679291i
\(761\) −210.942 + 365.362i −0.277190 + 0.480108i −0.970685 0.240354i \(-0.922737\pi\)
0.693495 + 0.720461i \(0.256070\pi\)
\(762\) 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
\(766\) 795.652 150.418i 1.03871 0.196368i
\(767\) 186.775 107.835i 0.243514 0.140593i
\(768\) −32.0648 + 420.867i −0.0417511 + 0.548004i
\(769\) 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
\(772\) −318.231 + 124.782i −0.412216 + 0.161635i
\(773\) −729.875 + 421.394i −0.944211 + 0.545141i −0.891278 0.453457i \(-0.850190\pi\)
−0.0529334 + 0.998598i \(0.516857\pi\)
\(774\) −91.0584 481.664i −0.117647 0.622305i
\(775\) 81.9870 + 47.3352i 0.105790 + 0.0610777i
\(776\) −168.497 268.439i −0.217136 0.345927i
\(777\) 0