Properties

Label 363.3.b.m.122.2
Level $363$
Weight $3$
Character 363.122
Analytic conductor $9.891$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 363.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89103359628\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 33)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 122.2
Root \(-3.06025i\) of defining polynomial
Character \(\chi\) \(=\) 363.122
Dual form 363.3.b.m.122.7

$q$-expansion

\(f(q)\) \(=\) \(q-3.06025i q^{2} +(0.126437 - 2.99733i) q^{3} -5.36516 q^{4} -6.63932i q^{5} +(-9.17261 - 0.386930i) q^{6} -3.06298 q^{7} +4.17774i q^{8} +(-8.96803 - 0.757950i) q^{9} +O(q^{10})\) \(q-3.06025i q^{2} +(0.126437 - 2.99733i) q^{3} -5.36516 q^{4} -6.63932i q^{5} +(-9.17261 - 0.386930i) q^{6} -3.06298 q^{7} +4.17774i q^{8} +(-8.96803 - 0.757950i) q^{9} -20.3180 q^{10} +(-0.678356 + 16.0812i) q^{12} +16.2447 q^{13} +9.37349i q^{14} +(-19.9003 - 0.839458i) q^{15} -8.67570 q^{16} +0.805648i q^{17} +(-2.31952 + 27.4444i) q^{18} +20.7018 q^{19} +35.6210i q^{20} +(-0.387274 + 9.18076i) q^{21} -27.3224i q^{23} +(12.5221 + 0.528222i) q^{24} -19.0806 q^{25} -49.7128i q^{26} +(-3.40572 + 26.7843i) q^{27} +16.4334 q^{28} +3.78268i q^{29} +(-2.56896 + 60.8999i) q^{30} -20.7800 q^{31} +43.2608i q^{32} +2.46549 q^{34} +20.3361i q^{35} +(48.1149 + 4.06652i) q^{36} +38.5536 q^{37} -63.3527i q^{38} +(2.05393 - 48.6907i) q^{39} +27.7373 q^{40} +13.3726i q^{41} +(28.0955 + 1.18516i) q^{42} +43.4125 q^{43} +(-5.03227 + 59.5416i) q^{45} -83.6135 q^{46} -19.8903i q^{47} +(-1.09693 + 26.0040i) q^{48} -39.6182 q^{49} +58.3915i q^{50} +(2.41480 + 0.101864i) q^{51} -87.1552 q^{52} +17.6754i q^{53} +(81.9669 + 10.4224i) q^{54} -12.7963i q^{56} +(2.61748 - 62.0502i) q^{57} +11.5760 q^{58} -43.5255i q^{59} +(106.768 + 4.50383i) q^{60} +10.6547 q^{61} +63.5921i q^{62} +(27.4689 + 2.32158i) q^{63} +97.6863 q^{64} -107.854i q^{65} +72.2963 q^{67} -4.32243i q^{68} +(-81.8944 - 3.45457i) q^{69} +62.2336 q^{70} -2.56990i q^{71} +(3.16651 - 37.4660i) q^{72} -45.4788 q^{73} -117.984i q^{74} +(-2.41250 + 57.1910i) q^{75} -111.068 q^{76} +(-149.006 - 6.28555i) q^{78} -98.2423 q^{79} +57.6008i q^{80} +(79.8510 + 13.5946i) q^{81} +40.9237 q^{82} +31.9006i q^{83} +(2.07779 - 49.2563i) q^{84} +5.34895 q^{85} -132.853i q^{86} +(11.3380 + 0.478272i) q^{87} -18.5409i q^{89} +(182.213 + 15.4000i) q^{90} -49.7570 q^{91} +146.589i q^{92} +(-2.62737 + 62.2846i) q^{93} -60.8693 q^{94} -137.446i q^{95} +(129.667 + 5.46978i) q^{96} -63.3019 q^{97} +121.242i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 5 q^{3} - 26 q^{4} + q^{6} + 28 q^{7} + 11 q^{9} - 6 q^{10} + 53 q^{12} + 44 q^{13} - 54 q^{15} - 14 q^{16} + q^{18} + 68 q^{19} - 6 q^{21} + 33 q^{24} + 42 q^{25} - 25 q^{27} - 118 q^{28} + 10 q^{30} + 2 q^{31} - 66 q^{34} - 7 q^{36} + 140 q^{37} + 38 q^{39} + 58 q^{40} + 174 q^{42} - 78 q^{43} - 36 q^{45} - 286 q^{46} - 285 q^{48} - 140 q^{49} + 58 q^{51} - 102 q^{52} + 523 q^{54} - 22 q^{57} - 68 q^{58} + 262 q^{60} + 22 q^{61} + 246 q^{63} - 52 q^{64} + 184 q^{67} - 176 q^{69} + 374 q^{70} + 489 q^{72} - 378 q^{73} - 33 q^{75} - 450 q^{76} - 246 q^{78} - 252 q^{79} + 11 q^{81} - 200 q^{82} + 450 q^{84} - 156 q^{85} + 66 q^{87} + 598 q^{90} - 148 q^{91} + 380 q^{93} - 460 q^{94} + 399 q^{96} - 324 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(244\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.06025i 1.53013i −0.643955 0.765064i \(-0.722707\pi\)
0.643955 0.765064i \(-0.277293\pi\)
\(3\) 0.126437 2.99733i 0.0421458 0.999111i
\(4\) −5.36516 −1.34129
\(5\) 6.63932i 1.32786i −0.747793 0.663932i \(-0.768886\pi\)
0.747793 0.663932i \(-0.231114\pi\)
\(6\) −9.17261 0.386930i −1.52877 0.0644884i
\(7\) −3.06298 −0.437568 −0.218784 0.975773i \(-0.570209\pi\)
−0.218784 + 0.975773i \(0.570209\pi\)
\(8\) 4.17774i 0.522217i
\(9\) −8.96803 0.757950i −0.996447 0.0842166i
\(10\) −20.3180 −2.03180
\(11\) 0 0
\(12\) −0.678356 + 16.0812i −0.0565297 + 1.34010i
\(13\) 16.2447 1.24959 0.624795 0.780789i \(-0.285183\pi\)
0.624795 + 0.780789i \(0.285183\pi\)
\(14\) 9.37349i 0.669535i
\(15\) −19.9003 0.839458i −1.32668 0.0559639i
\(16\) −8.67570 −0.542231
\(17\) 0.805648i 0.0473910i 0.999719 + 0.0236955i \(0.00754322\pi\)
−0.999719 + 0.0236955i \(0.992457\pi\)
\(18\) −2.31952 + 27.4444i −0.128862 + 1.52469i
\(19\) 20.7018 1.08957 0.544784 0.838577i \(-0.316612\pi\)
0.544784 + 0.838577i \(0.316612\pi\)
\(20\) 35.6210i 1.78105i
\(21\) −0.387274 + 9.18076i −0.0184416 + 0.437179i
\(22\) 0 0
\(23\) 27.3224i 1.18793i −0.804491 0.593965i \(-0.797562\pi\)
0.804491 0.593965i \(-0.202438\pi\)
\(24\) 12.5221 + 0.528222i 0.521753 + 0.0220092i
\(25\) −19.0806 −0.763224
\(26\) 49.7128i 1.91203i
\(27\) −3.40572 + 26.7843i −0.126138 + 0.992013i
\(28\) 16.4334 0.586906
\(29\) 3.78268i 0.130437i 0.997871 + 0.0652187i \(0.0207745\pi\)
−0.997871 + 0.0652187i \(0.979226\pi\)
\(30\) −2.56896 + 60.8999i −0.0856318 + 2.03000i
\(31\) −20.7800 −0.670323 −0.335161 0.942161i \(-0.608791\pi\)
−0.335161 + 0.942161i \(0.608791\pi\)
\(32\) 43.2608i 1.35190i
\(33\) 0 0
\(34\) 2.46549 0.0725143
\(35\) 20.3361i 0.581031i
\(36\) 48.1149 + 4.06652i 1.33652 + 0.112959i
\(37\) 38.5536 1.04199 0.520995 0.853560i \(-0.325561\pi\)
0.520995 + 0.853560i \(0.325561\pi\)
\(38\) 63.3527i 1.66718i
\(39\) 2.05393 48.6907i 0.0526649 1.24848i
\(40\) 27.7373 0.693433
\(41\) 13.3726i 0.326162i 0.986613 + 0.163081i \(0.0521432\pi\)
−0.986613 + 0.163081i \(0.947857\pi\)
\(42\) 28.0955 + 1.18516i 0.668940 + 0.0282181i
\(43\) 43.4125 1.00959 0.504797 0.863238i \(-0.331567\pi\)
0.504797 + 0.863238i \(0.331567\pi\)
\(44\) 0 0
\(45\) −5.03227 + 59.5416i −0.111828 + 1.32315i
\(46\) −83.6135 −1.81768
\(47\) 19.8903i 0.423198i −0.977357 0.211599i \(-0.932133\pi\)
0.977357 0.211599i \(-0.0678670\pi\)
\(48\) −1.09693 + 26.0040i −0.0228528 + 0.541750i
\(49\) −39.6182 −0.808534
\(50\) 58.3915i 1.16783i
\(51\) 2.41480 + 0.101864i 0.0473489 + 0.00199733i
\(52\) −87.1552 −1.67606
\(53\) 17.6754i 0.333499i 0.985999 + 0.166750i \(0.0533271\pi\)
−0.985999 + 0.166750i \(0.946673\pi\)
\(54\) 81.9669 + 10.4224i 1.51791 + 0.193007i
\(55\) 0 0
\(56\) 12.7963i 0.228505i
\(57\) 2.61748 62.0502i 0.0459207 1.08860i
\(58\) 11.5760 0.199586
\(59\) 43.5255i 0.737721i −0.929485 0.368860i \(-0.879748\pi\)
0.929485 0.368860i \(-0.120252\pi\)
\(60\) 106.768 + 4.50383i 1.77947 + 0.0750638i
\(61\) 10.6547 0.174668 0.0873339 0.996179i \(-0.472165\pi\)
0.0873339 + 0.996179i \(0.472165\pi\)
\(62\) 63.5921i 1.02568i
\(63\) 27.4689 + 2.32158i 0.436014 + 0.0368505i
\(64\) 97.6863 1.52635
\(65\) 107.854i 1.65929i
\(66\) 0 0
\(67\) 72.2963 1.07905 0.539525 0.841970i \(-0.318604\pi\)
0.539525 + 0.841970i \(0.318604\pi\)
\(68\) 4.32243i 0.0635651i
\(69\) −81.8944 3.45457i −1.18687 0.0500662i
\(70\) 62.2336 0.889052
\(71\) 2.56990i 0.0361957i −0.999836 0.0180979i \(-0.994239\pi\)
0.999836 0.0180979i \(-0.00576105\pi\)
\(72\) 3.16651 37.4660i 0.0439793 0.520362i
\(73\) −45.4788 −0.622997 −0.311499 0.950247i \(-0.600831\pi\)
−0.311499 + 0.950247i \(0.600831\pi\)
\(74\) 117.984i 1.59438i
\(75\) −2.41250 + 57.1910i −0.0321667 + 0.762546i
\(76\) −111.068 −1.46143
\(77\) 0 0
\(78\) −149.006 6.28555i −1.91033 0.0805840i
\(79\) −98.2423 −1.24357 −0.621786 0.783187i \(-0.713593\pi\)
−0.621786 + 0.783187i \(0.713593\pi\)
\(80\) 57.6008i 0.720010i
\(81\) 79.8510 + 13.5946i 0.985815 + 0.167835i
\(82\) 40.9237 0.499069
\(83\) 31.9006i 0.384345i 0.981361 + 0.192172i \(0.0615533\pi\)
−0.981361 + 0.192172i \(0.938447\pi\)
\(84\) 2.07779 49.2563i 0.0247356 0.586384i
\(85\) 5.34895 0.0629289
\(86\) 132.853i 1.54481i
\(87\) 11.3380 + 0.478272i 0.130321 + 0.00549738i
\(88\) 0 0
\(89\) 18.5409i 0.208325i −0.994560 0.104162i \(-0.966784\pi\)
0.994560 0.104162i \(-0.0332161\pi\)
\(90\) 182.213 + 15.4000i 2.02458 + 0.171112i
\(91\) −49.7570 −0.546780
\(92\) 146.589i 1.59336i
\(93\) −2.62737 + 62.2846i −0.0282513 + 0.669727i
\(94\) −60.8693 −0.647546
\(95\) 137.446i 1.44680i
\(96\) 129.667 + 5.46978i 1.35070 + 0.0569769i
\(97\) −63.3019 −0.652597 −0.326298 0.945267i \(-0.605801\pi\)
−0.326298 + 0.945267i \(0.605801\pi\)
\(98\) 121.242i 1.23716i
\(99\) 0 0
\(100\) 102.371 1.02371
\(101\) 150.359i 1.48870i 0.667790 + 0.744350i \(0.267241\pi\)
−0.667790 + 0.744350i \(0.732759\pi\)
\(102\) 0.311729 7.38989i 0.00305617 0.0724499i
\(103\) −149.767 −1.45405 −0.727026 0.686610i \(-0.759098\pi\)
−0.727026 + 0.686610i \(0.759098\pi\)
\(104\) 67.8659i 0.652557i
\(105\) 60.9541 + 2.57124i 0.580515 + 0.0244880i
\(106\) 54.0914 0.510296
\(107\) 20.7515i 0.193939i 0.995287 + 0.0969696i \(0.0309150\pi\)
−0.995287 + 0.0969696i \(0.969085\pi\)
\(108\) 18.2722 143.702i 0.169187 1.33058i
\(109\) −105.794 −0.970583 −0.485291 0.874352i \(-0.661286\pi\)
−0.485291 + 0.874352i \(0.661286\pi\)
\(110\) 0 0
\(111\) 4.87462 115.558i 0.0439155 1.04106i
\(112\) 26.5735 0.237263
\(113\) 132.769i 1.17495i −0.809244 0.587473i \(-0.800123\pi\)
0.809244 0.587473i \(-0.199877\pi\)
\(114\) −189.889 8.01015i −1.66570 0.0702644i
\(115\) −181.402 −1.57741
\(116\) 20.2947i 0.174954i
\(117\) −145.683 12.3126i −1.24515 0.105236i
\(118\) −133.199 −1.12881
\(119\) 2.46768i 0.0207368i
\(120\) 3.50703 83.1381i 0.0292253 0.692817i
\(121\) 0 0
\(122\) 32.6062i 0.267264i
\(123\) 40.0823 + 1.69080i 0.325872 + 0.0137463i
\(124\) 111.488 0.899097
\(125\) 39.3007i 0.314406i
\(126\) 7.10463 84.0617i 0.0563860 0.667156i
\(127\) −146.655 −1.15477 −0.577384 0.816473i \(-0.695926\pi\)
−0.577384 + 0.816473i \(0.695926\pi\)
\(128\) 125.902i 0.983607i
\(129\) 5.48896 130.122i 0.0425501 1.00870i
\(130\) −330.059 −2.53892
\(131\) 149.467i 1.14097i −0.821309 0.570484i \(-0.806756\pi\)
0.821309 0.570484i \(-0.193244\pi\)
\(132\) 0 0
\(133\) −63.4091 −0.476760
\(134\) 221.245i 1.65108i
\(135\) 177.830 + 22.6117i 1.31726 + 0.167494i
\(136\) −3.36578 −0.0247484
\(137\) 152.207i 1.11100i 0.831517 + 0.555500i \(0.187473\pi\)
−0.831517 + 0.555500i \(0.812527\pi\)
\(138\) −10.5719 + 250.618i −0.0766077 + 1.81607i
\(139\) 111.836 0.804573 0.402286 0.915514i \(-0.368216\pi\)
0.402286 + 0.915514i \(0.368216\pi\)
\(140\) 109.106i 0.779331i
\(141\) −59.6178 2.51487i −0.422822 0.0178360i
\(142\) −7.86454 −0.0553841
\(143\) 0 0
\(144\) 77.8039 + 6.57574i 0.540305 + 0.0456649i
\(145\) 25.1145 0.173203
\(146\) 139.177i 0.953265i
\(147\) −5.00921 + 118.749i −0.0340763 + 0.807816i
\(148\) −206.846 −1.39761
\(149\) 259.695i 1.74292i −0.490465 0.871461i \(-0.663173\pi\)
0.490465 0.871461i \(-0.336827\pi\)
\(150\) 175.019 + 7.38287i 1.16679 + 0.0492191i
\(151\) 88.0177 0.582899 0.291449 0.956586i \(-0.405863\pi\)
0.291449 + 0.956586i \(0.405863\pi\)
\(152\) 86.4866i 0.568991i
\(153\) 0.610640 7.22507i 0.00399111 0.0472227i
\(154\) 0 0
\(155\) 137.965i 0.890098i
\(156\) −11.0197 + 261.233i −0.0706389 + 1.67457i
\(157\) −7.65530 −0.0487598 −0.0243799 0.999703i \(-0.507761\pi\)
−0.0243799 + 0.999703i \(0.507761\pi\)
\(158\) 300.646i 1.90282i
\(159\) 52.9792 + 2.23484i 0.333203 + 0.0140556i
\(160\) 287.222 1.79514
\(161\) 83.6879i 0.519800i
\(162\) 41.6030 244.364i 0.256809 1.50842i
\(163\) 262.547 1.61072 0.805359 0.592788i \(-0.201973\pi\)
0.805359 + 0.592788i \(0.201973\pi\)
\(164\) 71.7464i 0.437478i
\(165\) 0 0
\(166\) 97.6240 0.588096
\(167\) 160.006i 0.958122i −0.877782 0.479061i \(-0.840977\pi\)
0.877782 0.479061i \(-0.159023\pi\)
\(168\) −38.3548 1.61793i −0.228302 0.00963054i
\(169\) 94.8889 0.561473
\(170\) 16.3692i 0.0962892i
\(171\) −185.654 15.6909i −1.08570 0.0917597i
\(172\) −232.915 −1.35416
\(173\) 165.524i 0.956785i 0.878146 + 0.478392i \(0.158780\pi\)
−0.878146 + 0.478392i \(0.841220\pi\)
\(174\) 1.46363 34.6971i 0.00841169 0.199408i
\(175\) 58.4435 0.333963
\(176\) 0 0
\(177\) −130.461 5.50325i −0.737065 0.0310918i
\(178\) −56.7398 −0.318763
\(179\) 58.5371i 0.327023i −0.986541 0.163511i \(-0.947718\pi\)
0.986541 0.163511i \(-0.0522820\pi\)
\(180\) 26.9989 319.450i 0.149994 1.77472i
\(181\) 284.678 1.57281 0.786403 0.617713i \(-0.211941\pi\)
0.786403 + 0.617713i \(0.211941\pi\)
\(182\) 152.269i 0.836643i
\(183\) 1.34716 31.9358i 0.00736151 0.174513i
\(184\) 114.146 0.620357
\(185\) 255.970i 1.38362i
\(186\) 190.607 + 8.04041i 1.02477 + 0.0432280i
\(187\) 0 0
\(188\) 106.715i 0.567631i
\(189\) 10.4316 82.0398i 0.0551939 0.434073i
\(190\) −420.619 −2.21379
\(191\) 137.443i 0.719595i −0.933031 0.359797i \(-0.882846\pi\)
0.933031 0.359797i \(-0.117154\pi\)
\(192\) 12.3512 292.798i 0.0643291 1.52499i
\(193\) 298.094 1.54453 0.772265 0.635300i \(-0.219124\pi\)
0.772265 + 0.635300i \(0.219124\pi\)
\(194\) 193.720i 0.998556i
\(195\) −323.273 13.6367i −1.65781 0.0699318i
\(196\) 212.558 1.08448
\(197\) 58.1375i 0.295114i 0.989054 + 0.147557i \(0.0471410\pi\)
−0.989054 + 0.147557i \(0.952859\pi\)
\(198\) 0 0
\(199\) −125.049 −0.628385 −0.314193 0.949359i \(-0.601734\pi\)
−0.314193 + 0.949359i \(0.601734\pi\)
\(200\) 79.7138i 0.398569i
\(201\) 9.14095 216.696i 0.0454774 1.07809i
\(202\) 460.136 2.27790
\(203\) 11.5863i 0.0570752i
\(204\) −12.9558 0.546516i −0.0635086 0.00267900i
\(205\) 88.7853 0.433099
\(206\) 458.326i 2.22489i
\(207\) −20.7090 + 245.028i −0.100043 + 1.18371i
\(208\) −140.934 −0.677566
\(209\) 0 0
\(210\) 7.86865 186.535i 0.0374698 0.888262i
\(211\) −48.3927 −0.229349 −0.114675 0.993403i \(-0.536583\pi\)
−0.114675 + 0.993403i \(0.536583\pi\)
\(212\) 94.8316i 0.447319i
\(213\) −7.70284 0.324931i −0.0361636 0.00152550i
\(214\) 63.5048 0.296752
\(215\) 288.230i 1.34060i
\(216\) −111.898 14.2282i −0.518046 0.0658713i
\(217\) 63.6486 0.293312
\(218\) 323.755i 1.48512i
\(219\) −5.75021 + 136.315i −0.0262567 + 0.622444i
\(220\) 0 0
\(221\) 13.0875i 0.0592193i
\(222\) −353.637 14.9176i −1.59296 0.0671962i
\(223\) 211.716 0.949401 0.474701 0.880147i \(-0.342556\pi\)
0.474701 + 0.880147i \(0.342556\pi\)
\(224\) 132.507i 0.591548i
\(225\) 171.115 + 14.4621i 0.760513 + 0.0642762i
\(226\) −406.307 −1.79782
\(227\) 121.385i 0.534736i −0.963594 0.267368i \(-0.913846\pi\)
0.963594 0.267368i \(-0.0861540\pi\)
\(228\) −14.0432 + 332.909i −0.0615929 + 1.46013i
\(229\) 322.944 1.41023 0.705117 0.709091i \(-0.250894\pi\)
0.705117 + 0.709091i \(0.250894\pi\)
\(230\) 555.137i 2.41364i
\(231\) 0 0
\(232\) −15.8030 −0.0681166
\(233\) 402.409i 1.72708i 0.504282 + 0.863539i \(0.331757\pi\)
−0.504282 + 0.863539i \(0.668243\pi\)
\(234\) −37.6798 + 445.826i −0.161025 + 1.90524i
\(235\) −132.058 −0.561949
\(236\) 233.521i 0.989497i
\(237\) −12.4215 + 294.465i −0.0524113 + 1.24247i
\(238\) −7.55173 −0.0317299
\(239\) 0.321443i 0.00134495i −1.00000 0.000672476i \(-0.999786\pi\)
1.00000 0.000672476i \(-0.000214056\pi\)
\(240\) 172.649 + 7.28289i 0.719370 + 0.0303454i
\(241\) 290.799 1.20664 0.603318 0.797500i \(-0.293845\pi\)
0.603318 + 0.797500i \(0.293845\pi\)
\(242\) 0 0
\(243\) 50.8438 237.621i 0.209234 0.977866i
\(244\) −57.1643 −0.234280
\(245\) 263.038i 1.07362i
\(246\) 5.17428 122.662i 0.0210337 0.498626i
\(247\) 336.293 1.36151
\(248\) 86.8133i 0.350054i
\(249\) 95.6168 + 4.03343i 0.384003 + 0.0161985i
\(250\) −120.270 −0.481081
\(251\) 112.621i 0.448691i 0.974510 + 0.224345i \(0.0720244\pi\)
−0.974510 + 0.224345i \(0.927976\pi\)
\(252\) −147.375 12.4557i −0.584821 0.0494272i
\(253\) 0 0
\(254\) 448.803i 1.76694i
\(255\) 0.676307 16.0326i 0.00265219 0.0628730i
\(256\) 5.45390 0.0213043
\(257\) 196.568i 0.764858i −0.923985 0.382429i \(-0.875088\pi\)
0.923985 0.382429i \(-0.124912\pi\)
\(258\) −398.206 16.7976i −1.54343 0.0651071i
\(259\) −118.089 −0.455942
\(260\) 578.651i 2.22558i
\(261\) 2.86708 33.9232i 0.0109850 0.129974i
\(262\) −457.407 −1.74583
\(263\) 378.327i 1.43850i −0.694749 0.719252i \(-0.744485\pi\)
0.694749 0.719252i \(-0.255515\pi\)
\(264\) 0 0
\(265\) 117.353 0.442842
\(266\) 194.048i 0.729503i
\(267\) −55.5732 2.34426i −0.208139 0.00877999i
\(268\) −387.881 −1.44732
\(269\) 201.154i 0.747785i −0.927472 0.373892i \(-0.878023\pi\)
0.927472 0.373892i \(-0.121977\pi\)
\(270\) 69.1975 544.205i 0.256287 2.01557i
\(271\) 80.2146 0.295995 0.147997 0.988988i \(-0.452717\pi\)
0.147997 + 0.988988i \(0.452717\pi\)
\(272\) 6.98956i 0.0256969i
\(273\) −6.29114 + 149.138i −0.0230445 + 0.546294i
\(274\) 465.792 1.69997
\(275\) 0 0
\(276\) 439.376 + 18.5343i 1.59194 + 0.0671533i
\(277\) 218.915 0.790306 0.395153 0.918615i \(-0.370692\pi\)
0.395153 + 0.918615i \(0.370692\pi\)
\(278\) 342.245i 1.23110i
\(279\) 186.356 + 15.7502i 0.667941 + 0.0564523i
\(280\) −84.9588 −0.303424
\(281\) 496.437i 1.76668i 0.468733 + 0.883340i \(0.344711\pi\)
−0.468733 + 0.883340i \(0.655289\pi\)
\(282\) −7.69615 + 182.446i −0.0272913 + 0.646971i
\(283\) −307.702 −1.08729 −0.543643 0.839317i \(-0.682955\pi\)
−0.543643 + 0.839317i \(0.682955\pi\)
\(284\) 13.7879i 0.0485490i
\(285\) −411.971 17.3783i −1.44551 0.0609764i
\(286\) 0 0
\(287\) 40.9601i 0.142718i
\(288\) 32.7895 387.964i 0.113852 1.34710i
\(289\) 288.351 0.997754
\(290\) 76.8566i 0.265023i
\(291\) −8.00372 + 189.737i −0.0275042 + 0.652017i
\(292\) 244.001 0.835620
\(293\) 339.698i 1.15938i 0.814837 + 0.579690i \(0.196826\pi\)
−0.814837 + 0.579690i \(0.803174\pi\)
\(294\) 363.402 + 15.3295i 1.23606 + 0.0521411i
\(295\) −288.980 −0.979593
\(296\) 161.067i 0.544145i
\(297\) 0 0
\(298\) −794.734 −2.66689
\(299\) 443.843i 1.48442i
\(300\) 12.9435 306.839i 0.0431448 1.02280i
\(301\) −132.972 −0.441766
\(302\) 269.357i 0.891909i
\(303\) 450.675 + 19.0109i 1.48738 + 0.0627424i
\(304\) −179.603 −0.590798
\(305\) 70.7402i 0.231935i
\(306\) −22.1106 1.86871i −0.0722567 0.00610691i
\(307\) −396.129 −1.29032 −0.645161 0.764047i \(-0.723210\pi\)
−0.645161 + 0.764047i \(0.723210\pi\)
\(308\) 0 0
\(309\) −18.9362 + 448.903i −0.0612821 + 1.45276i
\(310\) 422.208 1.36196
\(311\) 87.0358i 0.279858i 0.990162 + 0.139929i \(0.0446874\pi\)
−0.990162 + 0.139929i \(0.955313\pi\)
\(312\) 203.417 + 8.58078i 0.651977 + 0.0275025i
\(313\) −598.914 −1.91346 −0.956731 0.290973i \(-0.906021\pi\)
−0.956731 + 0.290973i \(0.906021\pi\)
\(314\) 23.4272i 0.0746088i
\(315\) 15.4137 182.375i 0.0489325 0.578967i
\(316\) 527.085 1.66799
\(317\) 2.45490i 0.00774416i 0.999993 + 0.00387208i \(0.00123252\pi\)
−0.999993 + 0.00387208i \(0.998767\pi\)
\(318\) 6.83917 162.130i 0.0215068 0.509843i
\(319\) 0 0
\(320\) 648.571i 2.02678i
\(321\) 62.1992 + 2.62376i 0.193767 + 0.00817371i
\(322\) 256.106 0.795361
\(323\) 16.6783i 0.0516357i
\(324\) −428.413 72.9373i −1.32226 0.225115i
\(325\) −309.958 −0.953717
\(326\) 803.461i 2.46460i
\(327\) −13.3762 + 317.099i −0.0409059 + 0.969720i
\(328\) −55.8674 −0.170327
\(329\) 60.9235i 0.185178i
\(330\) 0 0
\(331\) 368.074 1.11200 0.556002 0.831181i \(-0.312335\pi\)
0.556002 + 0.831181i \(0.312335\pi\)
\(332\) 171.152i 0.515518i
\(333\) −345.750 29.2217i −1.03829 0.0877529i
\(334\) −489.660 −1.46605
\(335\) 479.999i 1.43283i
\(336\) 3.35988 79.6496i 0.00999963 0.237052i
\(337\) 591.880 1.75632 0.878160 0.478368i \(-0.158771\pi\)
0.878160 + 0.478368i \(0.158771\pi\)
\(338\) 290.384i 0.859125i
\(339\) −397.953 16.7869i −1.17390 0.0495190i
\(340\) −28.6980 −0.0844059
\(341\) 0 0
\(342\) −48.0182 + 568.149i −0.140404 + 1.66125i
\(343\) 271.435 0.791357
\(344\) 181.366i 0.527227i
\(345\) −22.9360 + 543.723i −0.0664812 + 1.57601i
\(346\) 506.545 1.46400
\(347\) 294.601i 0.848994i −0.905429 0.424497i \(-0.860451\pi\)
0.905429 0.424497i \(-0.139549\pi\)
\(348\) −60.8300 2.56601i −0.174799 0.00737358i
\(349\) 412.008 1.18054 0.590269 0.807206i \(-0.299021\pi\)
0.590269 + 0.807206i \(0.299021\pi\)
\(350\) 178.852i 0.511005i
\(351\) −55.3248 + 435.102i −0.157620 + 1.23961i
\(352\) 0 0
\(353\) 135.577i 0.384070i 0.981388 + 0.192035i \(0.0615086\pi\)
−0.981388 + 0.192035i \(0.938491\pi\)
\(354\) −16.8413 + 399.242i −0.0475744 + 1.12780i
\(355\) −17.0624 −0.0480630
\(356\) 99.4748i 0.279424i
\(357\) −7.39646 0.312007i −0.0207184 0.000873968i
\(358\) −179.138 −0.500386
\(359\) 278.775i 0.776533i −0.921547 0.388267i \(-0.873074\pi\)
0.921547 0.388267i \(-0.126926\pi\)
\(360\) −248.749 21.0235i −0.690970 0.0583986i
\(361\) 67.5639 0.187158
\(362\) 871.187i 2.40659i
\(363\) 0 0
\(364\) 266.954 0.733391
\(365\) 301.948i 0.827256i
\(366\) −97.7317 4.12264i −0.267026 0.0112640i
\(367\) −176.388 −0.480620 −0.240310 0.970696i \(-0.577249\pi\)
−0.240310 + 0.970696i \(0.577249\pi\)
\(368\) 237.041i 0.644133i
\(369\) 10.1358 119.926i 0.0274683 0.325003i
\(370\) −783.333 −2.11712
\(371\) 54.1395i 0.145929i
\(372\) 14.0962 334.167i 0.0378931 0.898298i
\(373\) 163.109 0.437289 0.218645 0.975805i \(-0.429836\pi\)
0.218645 + 0.975805i \(0.429836\pi\)
\(374\) 0 0
\(375\) −117.797 4.96908i −0.314126 0.0132509i
\(376\) 83.0964 0.221001
\(377\) 61.4484i 0.162993i
\(378\) −251.063 31.9235i −0.664187 0.0844537i
\(379\) 53.2306 0.140450 0.0702250 0.997531i \(-0.477628\pi\)
0.0702250 + 0.997531i \(0.477628\pi\)
\(380\) 737.419i 1.94058i
\(381\) −18.5427 + 439.575i −0.0486685 + 1.15374i
\(382\) −420.609 −1.10107
\(383\) 89.6653i 0.234113i −0.993125 0.117057i \(-0.962654\pi\)
0.993125 0.117057i \(-0.0373459\pi\)
\(384\) −377.369 15.9187i −0.982733 0.0414549i
\(385\) 0 0
\(386\) 912.245i 2.36333i
\(387\) −389.325 32.9045i −1.00601 0.0850246i
\(388\) 339.625 0.875322
\(389\) 269.601i 0.693062i −0.938038 0.346531i \(-0.887360\pi\)
0.938038 0.346531i \(-0.112640\pi\)
\(390\) −41.7318 + 989.298i −0.107005 + 2.53666i
\(391\) 22.0122 0.0562972
\(392\) 165.514i 0.422230i
\(393\) −448.002 18.8982i −1.13995 0.0480870i
\(394\) 177.916 0.451562
\(395\) 652.262i 1.65130i
\(396\) 0 0
\(397\) 211.490 0.532720 0.266360 0.963874i \(-0.414179\pi\)
0.266360 + 0.963874i \(0.414179\pi\)
\(398\) 382.681i 0.961509i
\(399\) −8.01727 + 190.058i −0.0200934 + 0.476336i
\(400\) 165.538 0.413844
\(401\) 449.798i 1.12169i 0.827920 + 0.560846i \(0.189524\pi\)
−0.827920 + 0.560846i \(0.810476\pi\)
\(402\) −663.146 27.9736i −1.64962 0.0695861i
\(403\) −337.564 −0.837628
\(404\) 806.698i 1.99678i
\(405\) 90.2591 530.157i 0.222862 1.30903i
\(406\) −35.4569 −0.0873323
\(407\) 0 0
\(408\) −0.425560 + 10.0884i −0.00104304 + 0.0247264i
\(409\) −154.294 −0.377247 −0.188623 0.982049i \(-0.560403\pi\)
−0.188623 + 0.982049i \(0.560403\pi\)
\(410\) 271.706i 0.662697i
\(411\) 456.215 + 19.2446i 1.11001 + 0.0468239i
\(412\) 803.526 1.95031
\(413\) 133.318i 0.322803i
\(414\) 749.848 + 63.3748i 1.81123 + 0.153079i
\(415\) 211.798 0.510358
\(416\) 702.757i 1.68932i
\(417\) 14.1402 335.209i 0.0339093 0.803858i
\(418\) 0 0
\(419\) 755.530i 1.80317i −0.432599 0.901587i \(-0.642403\pi\)
0.432599 0.901587i \(-0.357597\pi\)
\(420\) −327.028 13.7951i −0.778639 0.0328455i
\(421\) −436.890 −1.03774 −0.518872 0.854852i \(-0.673648\pi\)
−0.518872 + 0.854852i \(0.673648\pi\)
\(422\) 148.094i 0.350933i
\(423\) −15.0758 + 178.377i −0.0356403 + 0.421694i
\(424\) −73.8433 −0.174159
\(425\) 15.3722i 0.0361700i
\(426\) −0.994371 + 23.5727i −0.00233420 + 0.0553349i
\(427\) −32.6352 −0.0764290
\(428\) 111.335i 0.260129i
\(429\) 0 0
\(430\) −882.057 −2.05129
\(431\) 9.73407i 0.0225849i −0.999936 0.0112924i \(-0.996405\pi\)
0.999936 0.0112924i \(-0.00359457\pi\)
\(432\) 29.5470 232.373i 0.0683959 0.537900i
\(433\) −59.2747 −0.136893 −0.0684466 0.997655i \(-0.521804\pi\)
−0.0684466 + 0.997655i \(0.521804\pi\)
\(434\) 194.781i 0.448804i
\(435\) 3.17540 75.2764i 0.00729978 0.173049i
\(436\) 567.599 1.30183
\(437\) 565.622i 1.29433i
\(438\) 417.159 + 17.5971i 0.952418 + 0.0401761i
\(439\) 444.724 1.01304 0.506519 0.862229i \(-0.330932\pi\)
0.506519 + 0.862229i \(0.330932\pi\)
\(440\) 0 0
\(441\) 355.297 + 30.0286i 0.805662 + 0.0680920i
\(442\) 40.0510 0.0906131
\(443\) 535.351i 1.20847i 0.796807 + 0.604234i \(0.206521\pi\)
−0.796807 + 0.604234i \(0.793479\pi\)
\(444\) −26.1531 + 619.988i −0.0589034 + 1.39637i
\(445\) −123.099 −0.276627
\(446\) 647.906i 1.45270i
\(447\) −778.394 32.8352i −1.74137 0.0734568i
\(448\) −299.211 −0.667881
\(449\) 769.414i 1.71362i −0.515635 0.856809i \(-0.672444\pi\)
0.515635 0.856809i \(-0.327556\pi\)
\(450\) 44.2578 523.657i 0.0983508 1.16368i
\(451\) 0 0
\(452\) 712.327i 1.57594i
\(453\) 11.1287 263.818i 0.0245667 0.582381i
\(454\) −371.470 −0.818215
\(455\) 330.353i 0.726050i
\(456\) 259.229 + 10.9351i 0.568485 + 0.0239805i
\(457\) 169.655 0.371236 0.185618 0.982622i \(-0.440571\pi\)
0.185618 + 0.982622i \(0.440571\pi\)
\(458\) 988.290i 2.15784i
\(459\) −21.5787 2.74381i −0.0470125 0.00597780i
\(460\) 973.252 2.11577
\(461\) 266.355i 0.577777i 0.957363 + 0.288888i \(0.0932857\pi\)
−0.957363 + 0.288888i \(0.906714\pi\)
\(462\) 0 0
\(463\) −704.848 −1.52235 −0.761175 0.648547i \(-0.775377\pi\)
−0.761175 + 0.648547i \(0.775377\pi\)
\(464\) 32.8174i 0.0707272i
\(465\) 413.528 + 17.4439i 0.889307 + 0.0375138i
\(466\) 1231.47 2.64265
\(467\) 675.178i 1.44578i −0.690965 0.722888i \(-0.742814\pi\)
0.690965 0.722888i \(-0.257186\pi\)
\(468\) 781.610 + 66.0592i 1.67011 + 0.141152i
\(469\) −221.442 −0.472158
\(470\) 404.131i 0.859854i
\(471\) −0.967915 + 22.9455i −0.00205502 + 0.0487165i
\(472\) 181.838 0.385250
\(473\) 0 0
\(474\) 901.138 + 38.0129i 1.90113 + 0.0801960i
\(475\) −395.003 −0.831585
\(476\) 13.2395i 0.0278141i
\(477\) 13.3971 158.514i 0.0280862 0.332314i
\(478\) −0.983699 −0.00205795
\(479\) 699.807i 1.46098i 0.682926 + 0.730488i \(0.260707\pi\)
−0.682926 + 0.730488i \(0.739293\pi\)
\(480\) 36.3156 860.902i 0.0756575 1.79355i
\(481\) 626.291 1.30206
\(482\) 889.920i 1.84631i
\(483\) 250.841 + 10.5813i 0.519339 + 0.0219074i
\(484\) 0 0
\(485\) 420.282i 0.866560i
\(486\) −727.182 155.595i −1.49626 0.320154i
\(487\) −653.347 −1.34157 −0.670787 0.741650i \(-0.734044\pi\)
−0.670787 + 0.741650i \(0.734044\pi\)
\(488\) 44.5127i 0.0912145i
\(489\) 33.1957 786.941i 0.0678849 1.60929i
\(490\) 804.963 1.64278
\(491\) 61.8372i 0.125941i 0.998015 + 0.0629707i \(0.0200575\pi\)
−0.998015 + 0.0629707i \(0.979943\pi\)
\(492\) −215.048 9.07141i −0.437089 0.0184378i
\(493\) −3.04751 −0.00618156
\(494\) 1029.14i 2.08329i
\(495\) 0 0
\(496\) 180.281 0.363470
\(497\) 7.87154i 0.0158381i
\(498\) 12.3433 292.612i 0.0247858 0.587574i
\(499\) 329.993 0.661309 0.330654 0.943752i \(-0.392731\pi\)
0.330654 + 0.943752i \(0.392731\pi\)
\(500\) 210.855i 0.421709i
\(501\) −479.592 20.2308i −0.957270 0.0403808i
\(502\) 344.650 0.686554
\(503\) 347.179i 0.690217i −0.938563 0.345109i \(-0.887842\pi\)
0.938563 0.345109i \(-0.112158\pi\)
\(504\) −9.69895 + 114.758i −0.0192440 + 0.227694i
\(505\) 998.280 1.97679
\(506\) 0 0
\(507\) 11.9975 284.414i 0.0236637 0.560974i
\(508\) 786.830 1.54888
\(509\) 856.194i 1.68211i −0.540950 0.841055i \(-0.681935\pi\)
0.540950 0.841055i \(-0.318065\pi\)
\(510\) −49.0639 2.06967i −0.0962036 0.00405818i
\(511\) 139.300 0.272604
\(512\) 520.297i 1.01621i
\(513\) −70.5045 + 554.484i −0.137436 + 1.08086i
\(514\) −601.549 −1.17033
\(515\) 994.354i 1.93078i
\(516\) −29.4492 + 698.125i −0.0570720 + 1.35295i
\(517\) 0 0
\(518\) 361.382i 0.697649i
\(519\) 496.130 + 20.9284i 0.955935 + 0.0403244i
\(520\) 450.584 0.866507
\(521\) 712.659i 1.36787i 0.729544 + 0.683934i \(0.239732\pi\)
−0.729544 + 0.683934i \(0.760268\pi\)
\(522\) −103.814 8.77400i −0.198877 0.0168084i
\(523\) 503.925 0.963527 0.481764 0.876301i \(-0.339996\pi\)
0.481764 + 0.876301i \(0.339996\pi\)
\(524\) 801.914i 1.53037i
\(525\) 7.38943 175.175i 0.0140751 0.333666i
\(526\) −1157.78 −2.20109
\(527\) 16.7414i 0.0317673i
\(528\) 0 0
\(529\) −217.513 −0.411179
\(530\) 359.130i 0.677604i
\(531\) −32.9901 + 390.338i −0.0621283 + 0.735100i
\(532\) 340.200 0.639473
\(533\) 217.234i 0.407568i
\(534\) −7.17403 + 170.068i −0.0134345 + 0.318480i
\(535\) 137.776 0.257525
\(536\) 302.035i 0.563498i
\(537\) −175.455 7.40127i −0.326732 0.0137826i
\(538\) −615.583 −1.14421
\(539\) 0 0
\(540\) −954.086 121.315i −1.76683 0.224658i
\(541\) −586.637 −1.08436 −0.542179 0.840263i \(-0.682400\pi\)
−0.542179 + 0.840263i \(0.682400\pi\)
\(542\) 245.477i 0.452910i
\(543\) 35.9939 853.275i 0.0662871 1.57141i
\(544\) −34.8530 −0.0640679
\(545\) 702.397i 1.28880i
\(546\) 456.401 + 19.2525i 0.835900 + 0.0352610i
\(547\) 688.847 1.25932 0.629659 0.776872i \(-0.283195\pi\)
0.629659 + 0.776872i \(0.283195\pi\)
\(548\) 816.614i 1.49017i
\(549\) −95.5519 8.07575i −0.174047 0.0147099i
\(550\) 0 0
\(551\) 78.3083i 0.142120i
\(552\) 14.4323 342.133i 0.0261454 0.619806i
\(553\) 300.914 0.544148
\(554\) 669.935i 1.20927i
\(555\) −767.228 32.3642i −1.38239 0.0583138i
\(556\) −600.016 −1.07917
\(557\) 618.806i 1.11096i 0.831529 + 0.555481i \(0.187466\pi\)
−0.831529 + 0.555481i \(0.812534\pi\)
\(558\) 48.1996 570.296i 0.0863792 1.02204i
\(559\) 705.222 1.26158
\(560\) 176.430i 0.315053i
\(561\) 0 0
\(562\) 1519.22 2.70325
\(563\) 569.270i 1.01114i −0.862787 0.505568i \(-0.831283\pi\)
0.862787 0.505568i \(-0.168717\pi\)
\(564\) 319.859 + 13.4927i 0.567126 + 0.0239232i
\(565\) −881.496 −1.56017
\(566\) 941.645i 1.66368i
\(567\) −244.582 41.6400i −0.431361 0.0734392i
\(568\) 10.7364 0.0189020
\(569\) 901.528i 1.58441i 0.610256 + 0.792204i \(0.291066\pi\)
−0.610256 + 0.792204i \(0.708934\pi\)
\(570\) −53.1820 + 1260.74i −0.0933017 + 2.21182i
\(571\) −804.182 −1.40837 −0.704187 0.710014i \(-0.748688\pi\)
−0.704187 + 0.710014i \(0.748688\pi\)
\(572\) 0 0
\(573\) −411.961 17.3779i −0.718955 0.0303279i
\(574\) −125.348 −0.218377
\(575\) 521.328i 0.906658i
\(576\) −876.053 74.0413i −1.52093 0.128544i
\(577\) −787.100 −1.36412 −0.682062 0.731294i \(-0.738917\pi\)
−0.682062 + 0.731294i \(0.738917\pi\)
\(578\) 882.427i 1.52669i
\(579\) 37.6902 893.489i 0.0650954 1.54316i
\(580\) −134.743 −0.232316
\(581\) 97.7108i 0.168177i
\(582\) 580.643 + 24.4934i 0.997669 + 0.0420849i
\(583\) 0 0
\(584\) 189.998i 0.325340i
\(585\) −81.7475 + 967.233i −0.139739 + 1.65339i
\(586\) 1039.56 1.77400
\(587\) 182.527i 0.310948i 0.987840 + 0.155474i \(0.0496906\pi\)
−0.987840 + 0.155474i \(0.950309\pi\)
\(588\) 26.8752 637.107i 0.0457062 1.08352i
\(589\) −430.183 −0.730362
\(590\) 884.352i 1.49890i
\(591\) 174.258 + 7.35075i 0.294852 + 0.0124378i
\(592\) −334.480 −0.565000
\(593\) 685.071i 1.15526i 0.816297 + 0.577632i \(0.196023\pi\)
−0.816297 + 0.577632i \(0.803977\pi\)
\(594\) 0 0
\(595\) −16.3837 −0.0275357
\(596\) 1393.31i 2.33776i
\(597\) −15.8108 + 374.813i −0.0264838 + 0.627827i
\(598\) −1358.27 −2.27136
\(599\) 360.876i 0.602463i 0.953551 + 0.301232i \(0.0973978\pi\)
−0.953551 + 0.301232i \(0.902602\pi\)
\(600\) −238.929 10.0788i −0.398215 0.0167980i
\(601\) −419.487 −0.697982 −0.348991 0.937126i \(-0.613476\pi\)
−0.348991 + 0.937126i \(0.613476\pi\)
\(602\) 406.927i 0.675958i
\(603\) −648.355 54.7970i −1.07522 0.0908739i
\(604\) −472.229 −0.781836
\(605\) 0 0
\(606\) 58.1783 1379.18i 0.0960039 2.27588i
\(607\) 1007.72 1.66017 0.830084 0.557639i \(-0.188293\pi\)
0.830084 + 0.557639i \(0.188293\pi\)
\(608\) 895.576i 1.47299i
\(609\) −34.7279 1.46494i −0.0570245 0.00240548i
\(610\) −216.483 −0.354890
\(611\) 323.111i 0.528823i
\(612\) −3.27618 + 38.7636i −0.00535324 + 0.0633393i
\(613\) −552.248 −0.900893 −0.450447 0.892803i \(-0.648735\pi\)
−0.450447 + 0.892803i \(0.648735\pi\)
\(614\) 1212.26i 1.97436i
\(615\) 11.2258 266.119i 0.0182533 0.432714i
\(616\) 0 0
\(617\) 675.556i 1.09490i 0.836837 + 0.547452i \(0.184402\pi\)
−0.836837 + 0.547452i \(0.815598\pi\)
\(618\) 1373.76 + 57.9495i 2.22291 + 0.0937695i
\(619\) −269.119 −0.434765 −0.217382 0.976087i \(-0.569752\pi\)
−0.217382 + 0.976087i \(0.569752\pi\)
\(620\) 740.205i 1.19388i
\(621\) 731.813 + 93.0525i 1.17844 + 0.149843i
\(622\) 266.352 0.428218
\(623\) 56.7903i 0.0911562i
\(624\) −17.8193 + 422.426i −0.0285565 + 0.676964i
\(625\) −737.946 −1.18071
\(626\) 1832.83i 2.92784i
\(627\) 0 0
\(628\) 41.0719 0.0654011
\(629\) 31.0606i 0.0493810i
\(630\) −558.113 47.1699i −0.885893 0.0748729i
\(631\) 93.3489 0.147938 0.0739690 0.997261i \(-0.476433\pi\)
0.0739690 + 0.997261i \(0.476433\pi\)
\(632\) 410.430i 0.649415i
\(633\) −6.11864 + 145.049i −0.00966609 + 0.229145i
\(634\) 7.51261 0.0118495
\(635\) 973.693i 1.53337i
\(636\) −284.242 11.9902i −0.446921 0.0188526i
\(637\) −643.584 −1.01034
\(638\) 0 0
\(639\) −1.94785 + 23.0469i −0.00304828 + 0.0360672i
\(640\) −835.902 −1.30610
\(641\) 14.7703i 0.0230425i 0.999934 + 0.0115213i \(0.00366741\pi\)
−0.999934 + 0.0115213i \(0.996333\pi\)
\(642\) 8.02938 190.345i 0.0125068 0.296488i
\(643\) −436.040 −0.678133 −0.339067 0.940762i \(-0.610111\pi\)
−0.339067 + 0.940762i \(0.610111\pi\)
\(644\) 448.999i 0.697203i
\(645\) −863.921 36.4430i −1.33941 0.0565008i
\(646\) 51.0400 0.0790092
\(647\) 314.372i 0.485892i 0.970040 + 0.242946i \(0.0781137\pi\)
−0.970040 + 0.242946i \(0.921886\pi\)
\(648\) −56.7948 + 333.596i −0.0876462 + 0.514809i
\(649\) 0 0
\(650\) 948.550i 1.45931i
\(651\) 8.04756 190.776i 0.0123618 0.293051i
\(652\) −1408.61 −2.16044
\(653\) 191.919i 0.293904i 0.989144 + 0.146952i \(0.0469463\pi\)
−0.989144 + 0.146952i \(0.953054\pi\)
\(654\) 970.402 + 40.9347i 1.48380 + 0.0625913i
\(655\) −992.359 −1.51505
\(656\) 116.017i 0.176855i
\(657\) 407.855 + 34.4706i 0.620784 + 0.0524667i
\(658\) 186.441 0.283346
\(659\) 127.678i 0.193745i −0.995297 0.0968724i \(-0.969116\pi\)
0.995297 0.0968724i \(-0.0308839\pi\)
\(660\) 0 0
\(661\) 580.599 0.878364 0.439182 0.898398i \(-0.355268\pi\)
0.439182 + 0.898398i \(0.355268\pi\)
\(662\) 1126.40i 1.70151i
\(663\) 39.2275 + 1.65474i 0.0591667 + 0.00249584i
\(664\) −133.272 −0.200711
\(665\) 420.993i 0.633073i
\(666\) −89.4259 + 1058.08i −0.134273 + 1.58871i
\(667\) 103.352 0.154950
\(668\) 858.459i 1.28512i
\(669\) 26.7689 634.585i 0.0400132 0.948558i
\(670\) −1468.92 −2.19241
\(671\) 0 0
\(672\) −397.167 16.7538i −0.591023 0.0249313i
\(673\) −546.461 −0.811977 −0.405989 0.913878i \(-0.633073\pi\)
−0.405989 + 0.913878i \(0.633073\pi\)
\(674\) 1811.30i 2.68739i
\(675\) 64.9832 511.062i 0.0962715 0.757128i
\(676\) −509.094 −0.753098
\(677\) 29.1664i 0.0430819i −0.999768 0.0215409i \(-0.993143\pi\)
0.999768 0.0215409i \(-0.00685722\pi\)
\(678\) −51.3723 + 1217.84i −0.0757704 + 1.79622i
\(679\) 193.892 0.285556
\(680\) 22.3465i 0.0328625i
\(681\) −363.832 15.3476i −0.534261 0.0225369i
\(682\) 0 0
\(683\) 82.4506i 0.120718i 0.998177 + 0.0603592i \(0.0192246\pi\)
−0.998177 + 0.0603592i \(0.980775\pi\)
\(684\) 996.064 + 84.1842i 1.45623 + 0.123076i
\(685\) 1010.55 1.47526
\(686\) 830.661i 1.21088i
\(687\) 40.8321 967.970i 0.0594354 1.40898i
\(688\) −376.634 −0.547433
\(689\) 287.132i 0.416737i
\(690\) 1663.93 + 70.1900i 2.41149 + 0.101725i
\(691\) 967.715 1.40046 0.700228 0.713919i \(-0.253082\pi\)
0.700228 + 0.713919i \(0.253082\pi\)
\(692\) 888.061i 1.28333i
\(693\) 0 0
\(694\) −901.554 −1.29907
\(695\) 742.513i 1.06836i
\(696\) −1.99809 + 47.3670i −0.00287083 + 0.0680561i
\(697\) −10.7736 −0.0154572
\(698\) 1260.85i 1.80638i
\(699\) 1206.16 + 50.8795i 1.72554 + 0.0727890i
\(700\) −313.558 −0.447941
\(701\) 314.100i 0.448075i −0.974581 0.224037i \(-0.928076\pi\)
0.974581 0.224037i \(-0.0719237\pi\)
\(702\) 1331.52 + 169.308i 1.89676 + 0.241179i
\(703\) 798.129 1.13532
\(704\) 0 0
\(705\) −16.6971 + 395.822i −0.0236838 + 0.561450i
\(706\) 414.899 0.587675
\(707\) 460.545i 0.651408i
\(708\) 699.941 + 29.5258i 0.988618 + 0.0417031i
\(709\) 327.352 0.461709 0.230855 0.972988i \(-0.425848\pi\)
0.230855 + 0.972988i \(0.425848\pi\)
\(710\) 52.2152i 0.0735426i
\(711\) 881.039 + 74.4627i 1.23916 + 0.104730i
\(712\) 77.4589 0.108791
\(713\) 567.759i 0.796297i
\(714\) −0.954820 + 22.6351i −0.00133728 + 0.0317018i
\(715\) 0 0
\(716\) 314.061i 0.438632i
\(717\) −0.963473 0.0406424i −0.00134376 5.66840e-5i
\(718\) −853.124 −1.18820
\(719\) 1106.21i 1.53853i 0.638928 + 0.769266i \(0.279378\pi\)
−0.638928 + 0.769266i \(0.720622\pi\)
\(720\) 43.6585 516.565i 0.0606368 0.717452i
\(721\) 458.734 0.636247
\(722\) 206.763i 0.286375i
\(723\) 36.7679 871.623i 0.0508546 1.20556i
\(724\) −1527.34 −2.10959
\(725\) 72.1759i 0.0995530i
\(726\) 0 0
\(727\) 577.040 0.793727 0.396864 0.917878i \(-0.370099\pi\)
0.396864 + 0.917878i \(0.370099\pi\)
\(728\) 207.872i 0.285538i
\(729\) −705.802 182.440i −0.968178 0.250261i
\(730\) 924.039 1.26581
\(731\) 34.9752i 0.0478457i
\(732\) −7.22770 + 171.341i −0.00987391 + 0.234072i
\(733\) 619.302 0.844886 0.422443 0.906389i \(-0.361173\pi\)
0.422443 + 0.906389i \(0.361173\pi\)
\(734\) 539.791i 0.735410i
\(735\) 788.412 + 33.2578i 1.07267 + 0.0452487i
\(736\) 1181.99 1.60596
\(737\) 0 0
\(738\) −367.005 31.0181i −0.497297 0.0420299i
\(739\) −1119.31 −1.51462 −0.757311 0.653055i \(-0.773487\pi\)
−0.757311 + 0.653055i \(0.773487\pi\)
\(740\) 1373.32i 1.85584i
\(741\) 42.5200 1007.98i 0.0573819 1.36030i
\(742\) −165.681 −0.223289
\(743\) 1148.58i 1.54586i −0.634489 0.772932i \(-0.718790\pi\)
0.634489 0.772932i \(-0.281210\pi\)
\(744\) −260.209 10.9764i −0.349743 0.0147533i
\(745\) −1724.20 −2.31436
\(746\) 499.155i 0.669108i
\(747\) 24.1791 286.086i 0.0323682 0.382979i
\(748\) 0 0
\(749\) 63.5613i 0.0848616i
\(750\) −15.2066 + 360.490i −0.0202755 + 0.480654i
\(751\) −273.658 −0.364391 −0.182196 0.983262i \(-0.558320\pi\)
−0.182196 + 0.983262i \(0.558320\pi\)
\(752\) 172.562i 0.229471i
\(753\) 337.564 + 14.2395i 0.448292 + 0.0189104i
\(754\) 188.048 0.249400
\(755\) 584.378i 0.774011i
\(756\) −55.9674 + 440.157i −0.0740310 + 0.582218i
\(757\) −558.006 −0.737128 −0.368564 0.929602i \(-0.620150\pi\)
−0.368564 + 0.929602i \(0.620150\pi\)
\(758\) 162.899i 0.214906i
\(759\) 0 0
\(760\) 574.212 0.755543
\(761\) 421.755i 0.554211i 0.960839 + 0.277106i \(0.0893752\pi\)
−0.960839 + 0.277106i \(0.910625\pi\)
\(762\) 1345.21 + 56.7454i 1.76537 + 0.0744691i
\(763\) 324.043 0.424696
\(764\) 737.401i 0.965185i
\(765\) −47.9696 4.05424i −0.0627053 0.00529966i
\(766\) −274.399 −0.358223
\(767\) 707.057i 0.921847i
\(768\) 0.689576 16.3472i 0.000897886 0.0212854i
\(769\) −108.997 −0.141738 −0.0708692 0.997486i \(-0.522577\pi\)
−0.0708692 + 0.997486i \(0.522577\pi\)
\(770\) 0 0
\(771\) −589.181 24.8536i −0.764178 0.0322355i
\(772\) −1599.32 −2.07166
\(773\) 1031.61i 1.33456i 0.744808 + 0.667279i \(0.232541\pi\)
−0.744808 + 0.667279i \(0.767459\pi\)
\(774\) −100.696 + 1191.43i −0.130098 + 1.53932i
\(775\) 396.495 0.511607
\(776\) 264.459i 0.340797i
\(777\) −14.9308 + 353.952i −0.0192160 + 0.455536i
\(778\) −825.048 −1.06047
\(779\) 276.838i 0.355376i
\(780\) 1734.41 + 73.1631i 2.22360 + 0.0937988i
\(781\) 0 0
\(782\) 67.3630i 0.0861420i