Properties

Label 76.5.j.a.13.7
Level $76$
Weight $5$
Character 76.13
Analytic conductor $7.856$
Analytic rank $0$
Dimension $42$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.j (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.85611719437\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 13.7
Character \(\chi\) \(=\) 76.13
Dual form 76.5.j.a.41.7

$q$-expansion

\(f(q)\) \(=\) \(q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +O(q^{10})\) \(q+(5.33930 - 14.6696i) q^{3} +(-7.24101 - 41.0658i) q^{5} +(-15.7120 + 27.2140i) q^{7} +(-124.640 - 104.585i) q^{9} +(89.7471 + 155.447i) q^{11} +(34.6560 + 95.2165i) q^{13} +(-641.081 - 113.040i) q^{15} +(-2.64161 + 2.21657i) q^{17} +(145.418 - 330.416i) q^{19} +(315.328 + 375.793i) q^{21} +(179.219 - 1016.40i) q^{23} +(-1046.66 + 380.953i) q^{25} +(-1104.62 + 637.755i) q^{27} +(545.399 - 649.981i) q^{29} +(-974.956 - 562.891i) q^{31} +(2759.53 - 486.579i) q^{33} +(1231.34 + 448.170i) q^{35} -89.0040i q^{37} +1581.83 q^{39} +(-344.404 + 946.243i) q^{41} +(-83.5286 - 473.714i) q^{43} +(-3392.35 + 5875.73i) q^{45} +(2550.07 + 2139.76i) q^{47} +(706.764 + 1224.15i) q^{49} +(18.4119 + 50.5863i) q^{51} +(819.014 + 144.414i) q^{53} +(5733.68 - 4811.13i) q^{55} +(-4070.64 - 3897.42i) q^{57} +(-1606.04 - 1914.01i) q^{59} +(-369.330 + 2094.57i) q^{61} +(4804.53 - 1748.70i) q^{63} +(3659.20 - 2112.64i) q^{65} +(1209.96 - 1441.98i) q^{67} +(-13953.3 - 8055.95i) q^{69} +(-1305.86 + 230.258i) q^{71} +(278.093 + 101.218i) q^{73} +17388.1i q^{75} -5640.44 q^{77} +(3934.97 - 10811.2i) q^{79} +(1169.16 + 6630.64i) q^{81} +(-4761.55 + 8247.25i) q^{83} +(110.153 + 92.4296i) q^{85} +(-6622.92 - 11471.2i) q^{87} +(3530.74 + 9700.62i) q^{89} +(-3135.74 - 552.916i) q^{91} +(-13463.0 + 11296.8i) q^{93} +(-14621.8 - 3579.18i) q^{95} +(2269.14 + 2704.25i) q^{97} +(5071.34 - 28761.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} + O(q^{10}) \) \( 42q + 12q^{3} - 45q^{7} - 84q^{9} - 45q^{11} + 33q^{13} - 393q^{15} + 909q^{17} + 1242q^{19} + 1107q^{21} - 360q^{23} - 810q^{25} - 7056q^{27} - 2889q^{29} + 2808q^{31} + 10875q^{33} + 6741q^{35} - 3480q^{39} - 3060q^{41} - 8079q^{43} - 4320q^{45} - 2655q^{47} - 474q^{49} - 12222q^{51} - 6705q^{53} + 4623q^{55} - 8022q^{57} + 24309q^{59} + 7104q^{61} + 12063q^{63} + 25245q^{65} + 15573q^{67} - 10881q^{69} - 25506q^{71} + 3036q^{73} + 12924q^{77} - 16839q^{79} - 2208q^{81} - 6363q^{83} - 37890q^{85} - 21924q^{87} - 22644q^{89} + 17418q^{91} + 8184q^{93} - 82413q^{95} + 13383q^{97} + 23565q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 5.33930 14.6696i 0.593256 1.62996i −0.171168 0.985242i \(-0.554754\pi\)
0.764423 0.644714i \(-0.223024\pi\)
\(4\) 0 0
\(5\) −7.24101 41.0658i −0.289640 1.64263i −0.688223 0.725499i \(-0.741609\pi\)
0.398583 0.917132i \(-0.369502\pi\)
\(6\) 0 0
\(7\) −15.7120 + 27.2140i −0.320654 + 0.555389i −0.980623 0.195904i \(-0.937236\pi\)
0.659969 + 0.751293i \(0.270569\pi\)
\(8\) 0 0
\(9\) −124.640 104.585i −1.53876 1.29117i
\(10\) 0 0
\(11\) 89.7471 + 155.447i 0.741712 + 1.28468i 0.951715 + 0.306982i \(0.0993190\pi\)
−0.210004 + 0.977701i \(0.567348\pi\)
\(12\) 0 0
\(13\) 34.6560 + 95.2165i 0.205065 + 0.563411i 0.999006 0.0445838i \(-0.0141962\pi\)
−0.793941 + 0.607995i \(0.791974\pi\)
\(14\) 0 0
\(15\) −641.081 113.040i −2.84925 0.502399i
\(16\) 0 0
\(17\) −2.64161 + 2.21657i −0.00914052 + 0.00766981i −0.647346 0.762196i \(-0.724121\pi\)
0.638206 + 0.769866i \(0.279677\pi\)
\(18\) 0 0
\(19\) 145.418 330.416i 0.402821 0.915279i
\(20\) 0 0
\(21\) 315.328 + 375.793i 0.715030 + 0.852139i
\(22\) 0 0
\(23\) 179.219 1016.40i 0.338788 1.92137i −0.0472516 0.998883i \(-0.515046\pi\)
0.386040 0.922482i \(-0.373843\pi\)
\(24\) 0 0
\(25\) −1046.66 + 380.953i −1.67465 + 0.609525i
\(26\) 0 0
\(27\) −1104.62 + 637.755i −1.51526 + 0.874835i
\(28\) 0 0
\(29\) 545.399 649.981i 0.648512 0.772867i −0.337177 0.941441i \(-0.609472\pi\)
0.985689 + 0.168575i \(0.0539164\pi\)
\(30\) 0 0
\(31\) −974.956 562.891i −1.01452 0.585735i −0.102010 0.994783i \(-0.532527\pi\)
−0.912513 + 0.409048i \(0.865861\pi\)
\(32\) 0 0
\(33\) 2759.53 486.579i 2.53400 0.446813i
\(34\) 0 0
\(35\) 1231.34 + 448.170i 1.00517 + 0.365853i
\(36\) 0 0
\(37\) 89.0040i 0.0650139i −0.999472 0.0325069i \(-0.989651\pi\)
0.999472 0.0325069i \(-0.0103491\pi\)
\(38\) 0 0
\(39\) 1581.83 1.03999
\(40\) 0 0
\(41\) −344.404 + 946.243i −0.204881 + 0.562905i −0.998993 0.0448660i \(-0.985714\pi\)
0.794112 + 0.607771i \(0.207936\pi\)
\(42\) 0 0
\(43\) −83.5286 473.714i −0.0451750 0.256200i 0.953853 0.300273i \(-0.0970778\pi\)
−0.999028 + 0.0440728i \(0.985967\pi\)
\(44\) 0 0
\(45\) −3392.35 + 5875.73i −1.67524 + 2.90159i
\(46\) 0 0
\(47\) 2550.07 + 2139.76i 1.15440 + 0.968656i 0.999813 0.0193232i \(-0.00615114\pi\)
0.154586 + 0.987979i \(0.450596\pi\)
\(48\) 0 0
\(49\) 706.764 + 1224.15i 0.294362 + 0.509850i
\(50\) 0 0
\(51\) 18.4119 + 50.5863i 0.00707879 + 0.0194488i
\(52\) 0 0
\(53\) 819.014 + 144.414i 0.291568 + 0.0514113i 0.317519 0.948252i \(-0.397150\pi\)
−0.0259511 + 0.999663i \(0.508261\pi\)
\(54\) 0 0
\(55\) 5733.68 4811.13i 1.89543 1.59045i
\(56\) 0 0
\(57\) −4070.64 3897.42i −1.25289 1.19957i
\(58\) 0 0
\(59\) −1606.04 1914.01i −0.461374 0.549844i 0.484325 0.874888i \(-0.339065\pi\)
−0.945699 + 0.325044i \(0.894621\pi\)
\(60\) 0 0
\(61\) −369.330 + 2094.57i −0.0992555 + 0.562906i 0.894104 + 0.447859i \(0.147813\pi\)
−0.993360 + 0.115048i \(0.963298\pi\)
\(62\) 0 0
\(63\) 4804.53 1748.70i 1.21051 0.440591i
\(64\) 0 0
\(65\) 3659.20 2112.64i 0.866082 0.500033i
\(66\) 0 0
\(67\) 1209.96 1441.98i 0.269540 0.321225i −0.614248 0.789113i \(-0.710541\pi\)
0.883788 + 0.467888i \(0.154985\pi\)
\(68\) 0 0
\(69\) −13953.3 8055.95i −2.93075 1.69207i
\(70\) 0 0
\(71\) −1305.86 + 230.258i −0.259048 + 0.0456771i −0.301664 0.953414i \(-0.597542\pi\)
0.0426159 + 0.999092i \(0.486431\pi\)
\(72\) 0 0
\(73\) 278.093 + 101.218i 0.0521849 + 0.0189937i 0.367981 0.929833i \(-0.380049\pi\)
−0.315796 + 0.948827i \(0.602271\pi\)
\(74\) 0 0
\(75\) 17388.1i 3.09122i
\(76\) 0 0
\(77\) −5640.44 −0.951330
\(78\) 0 0
\(79\) 3934.97 10811.2i 0.630503 1.73229i −0.0491834 0.998790i \(-0.515662\pi\)
0.679686 0.733503i \(-0.262116\pi\)
\(80\) 0 0
\(81\) 1169.16 + 6630.64i 0.178199 + 1.01061i
\(82\) 0 0
\(83\) −4761.55 + 8247.25i −0.691182 + 1.19716i 0.280269 + 0.959921i \(0.409576\pi\)
−0.971451 + 0.237241i \(0.923757\pi\)
\(84\) 0 0
\(85\) 110.153 + 92.4296i 0.0152461 + 0.0127930i
\(86\) 0 0
\(87\) −6622.92 11471.2i −0.875006 1.51555i
\(88\) 0 0
\(89\) 3530.74 + 9700.62i 0.445744 + 1.22467i 0.935661 + 0.352901i \(0.114805\pi\)
−0.489917 + 0.871769i \(0.662973\pi\)
\(90\) 0 0
\(91\) −3135.74 552.916i −0.378667 0.0667692i
\(92\) 0 0
\(93\) −13463.0 + 11296.8i −1.55659 + 1.30614i
\(94\) 0 0
\(95\) −14621.8 3579.18i −1.62014 0.396585i
\(96\) 0 0
\(97\) 2269.14 + 2704.25i 0.241167 + 0.287411i 0.873028 0.487670i \(-0.162153\pi\)
−0.631861 + 0.775082i \(0.717709\pi\)
\(98\) 0 0
\(99\) 5071.34 28761.0i 0.517431 2.93450i
\(100\) 0 0
\(101\) 13748.2 5003.95i 1.34773 0.490535i 0.435495 0.900191i \(-0.356573\pi\)
0.912240 + 0.409656i \(0.134351\pi\)
\(102\) 0 0
\(103\) 4736.29 2734.50i 0.446441 0.257753i −0.259885 0.965640i \(-0.583685\pi\)
0.706326 + 0.707887i \(0.250351\pi\)
\(104\) 0 0
\(105\) 13149.0 15670.3i 1.19265 1.42134i
\(106\) 0 0
\(107\) 18084.6 + 10441.2i 1.57958 + 0.911972i 0.994917 + 0.100697i \(0.0321072\pi\)
0.584665 + 0.811275i \(0.301226\pi\)
\(108\) 0 0
\(109\) 11960.7 2109.00i 1.00671 0.177510i 0.354103 0.935206i \(-0.384786\pi\)
0.652607 + 0.757696i \(0.273675\pi\)
\(110\) 0 0
\(111\) −1305.65 475.219i −0.105970 0.0385698i
\(112\) 0 0
\(113\) 12893.0i 1.00971i 0.863205 + 0.504854i \(0.168454\pi\)
−0.863205 + 0.504854i \(0.831546\pi\)
\(114\) 0 0
\(115\) −43037.1 −3.25422
\(116\) 0 0
\(117\) 5638.72 15492.3i 0.411916 1.13173i
\(118\) 0 0
\(119\) −18.8169 106.716i −0.00132878 0.00753590i
\(120\) 0 0
\(121\) −8788.58 + 15222.3i −0.600272 + 1.03970i
\(122\) 0 0
\(123\) 12042.1 + 10104.6i 0.795964 + 0.667893i
\(124\) 0 0
\(125\) 10192.0 + 17653.0i 0.652286 + 1.12979i
\(126\) 0 0
\(127\) 1344.04 + 3692.72i 0.0833306 + 0.228949i 0.974359 0.224998i \(-0.0722377\pi\)
−0.891029 + 0.453947i \(0.850015\pi\)
\(128\) 0 0
\(129\) −7395.18 1303.97i −0.444395 0.0783589i
\(130\) 0 0
\(131\) 12566.9 10544.8i 0.732292 0.614466i −0.198464 0.980108i \(-0.563595\pi\)
0.930755 + 0.365643i \(0.119151\pi\)
\(132\) 0 0
\(133\) 6707.13 + 9148.92i 0.379169 + 0.517210i
\(134\) 0 0
\(135\) 34188.5 + 40744.3i 1.87591 + 2.23563i
\(136\) 0 0
\(137\) −2132.93 + 12096.4i −0.113641 + 0.644490i 0.873773 + 0.486334i \(0.161666\pi\)
−0.987414 + 0.158156i \(0.949445\pi\)
\(138\) 0 0
\(139\) −10258.7 + 3733.87i −0.530963 + 0.193255i −0.593568 0.804784i \(-0.702281\pi\)
0.0626054 + 0.998038i \(0.480059\pi\)
\(140\) 0 0
\(141\) 45005.0 25983.7i 2.26372 1.30696i
\(142\) 0 0
\(143\) −11690.8 + 13932.6i −0.571706 + 0.681332i
\(144\) 0 0
\(145\) −30641.2 17690.7i −1.45737 0.841413i
\(146\) 0 0
\(147\) 21731.4 3831.84i 1.00567 0.177326i
\(148\) 0 0
\(149\) −16333.5 5944.92i −0.735711 0.267777i −0.0531308 0.998588i \(-0.516920\pi\)
−0.682580 + 0.730811i \(0.739142\pi\)
\(150\) 0 0
\(151\) 21119.7i 0.926262i −0.886290 0.463131i \(-0.846726\pi\)
0.886290 0.463131i \(-0.153274\pi\)
\(152\) 0 0
\(153\) 561.070 0.0239681
\(154\) 0 0
\(155\) −16055.9 + 44113.3i −0.668300 + 1.83614i
\(156\) 0 0
\(157\) −2180.35 12365.4i −0.0884561 0.501659i −0.996557 0.0829083i \(-0.973579\pi\)
0.908101 0.418751i \(-0.137532\pi\)
\(158\) 0 0
\(159\) 6491.46 11243.5i 0.256772 0.444743i
\(160\) 0 0
\(161\) 24844.5 + 20847.0i 0.958470 + 0.804252i
\(162\) 0 0
\(163\) 7477.22 + 12950.9i 0.281426 + 0.487445i 0.971736 0.236069i \(-0.0758591\pi\)
−0.690310 + 0.723514i \(0.742526\pi\)
\(164\) 0 0
\(165\) −39963.5 109799.i −1.46790 4.03301i
\(166\) 0 0
\(167\) −22290.5 3930.42i −0.799258 0.140931i −0.240921 0.970545i \(-0.577449\pi\)
−0.558337 + 0.829614i \(0.688560\pi\)
\(168\) 0 0
\(169\) 14013.8 11759.0i 0.490664 0.411716i
\(170\) 0 0
\(171\) −52681.4 + 25974.3i −1.80163 + 0.888283i
\(172\) 0 0
\(173\) 4516.54 + 5382.60i 0.150908 + 0.179846i 0.836203 0.548421i \(-0.184771\pi\)
−0.685294 + 0.728266i \(0.740326\pi\)
\(174\) 0 0
\(175\) 6077.88 34469.4i 0.198461 1.12553i
\(176\) 0 0
\(177\) −36652.9 + 13340.6i −1.16994 + 0.425822i
\(178\) 0 0
\(179\) 34046.8 19656.9i 1.06260 0.613493i 0.136451 0.990647i \(-0.456431\pi\)
0.926151 + 0.377154i \(0.123097\pi\)
\(180\) 0 0
\(181\) −40789.7 + 48611.3i −1.24507 + 1.48382i −0.431755 + 0.901991i \(0.642106\pi\)
−0.813314 + 0.581825i \(0.802339\pi\)
\(182\) 0 0
\(183\) 28754.6 + 16601.5i 0.858629 + 0.495729i
\(184\) 0 0
\(185\) −3655.02 + 644.478i −0.106794 + 0.0188306i
\(186\) 0 0
\(187\) −581.636 211.698i −0.0166329 0.00605388i
\(188\) 0 0
\(189\) 40081.7i 1.12208i
\(190\) 0 0
\(191\) 22006.1 0.603220 0.301610 0.953431i \(-0.402476\pi\)
0.301610 + 0.953431i \(0.402476\pi\)
\(192\) 0 0
\(193\) −3866.00 + 10621.8i −0.103788 + 0.285155i −0.980707 0.195483i \(-0.937373\pi\)
0.876919 + 0.480638i \(0.159595\pi\)
\(194\) 0 0
\(195\) −11454.0 64959.0i −0.301224 1.70832i
\(196\) 0 0
\(197\) −21154.9 + 36641.4i −0.545103 + 0.944146i 0.453497 + 0.891258i \(0.350176\pi\)
−0.998600 + 0.0528886i \(0.983157\pi\)
\(198\) 0 0
\(199\) −20672.4 17346.2i −0.522018 0.438025i 0.343316 0.939220i \(-0.388450\pi\)
−0.865335 + 0.501194i \(0.832894\pi\)
\(200\) 0 0
\(201\) −14692.9 25448.9i −0.363677 0.629907i
\(202\) 0 0
\(203\) 9119.28 + 25055.0i 0.221294 + 0.607999i
\(204\) 0 0
\(205\) 41352.1 + 7291.48i 0.983987 + 0.173503i
\(206\) 0 0
\(207\) −128638. + 107940.i −3.00213 + 2.51909i
\(208\) 0 0
\(209\) 64412.8 7049.07i 1.47462 0.161376i
\(210\) 0 0
\(211\) −21018.7 25049.1i −0.472107 0.562635i 0.476466 0.879193i \(-0.341917\pi\)
−0.948573 + 0.316558i \(0.897473\pi\)
\(212\) 0 0
\(213\) −3594.58 + 20385.9i −0.0792298 + 0.449335i
\(214\) 0 0
\(215\) −18848.6 + 6860.33i −0.407758 + 0.148412i
\(216\) 0 0
\(217\) 30637.1 17688.3i 0.650621 0.375636i
\(218\) 0 0
\(219\) 2969.65 3539.09i 0.0619179 0.0737909i
\(220\) 0 0
\(221\) −302.602 174.707i −0.00619566 0.00357707i
\(222\) 0 0
\(223\) 24173.3 4262.40i 0.486100 0.0857126i 0.0747734 0.997201i \(-0.476177\pi\)
0.411327 + 0.911488i \(0.365066\pi\)
\(224\) 0 0
\(225\) 170297. + 61983.1i 3.36390 + 1.22436i
\(226\) 0 0
\(227\) 72453.9i 1.40608i 0.711150 + 0.703040i \(0.248175\pi\)
−0.711150 + 0.703040i \(0.751825\pi\)
\(228\) 0 0
\(229\) −59643.4 −1.13734 −0.568671 0.822565i \(-0.692542\pi\)
−0.568671 + 0.822565i \(0.692542\pi\)
\(230\) 0 0
\(231\) −30116.0 + 82743.0i −0.564382 + 1.55063i
\(232\) 0 0
\(233\) −11025.2 62527.0i −0.203083 1.15174i −0.900427 0.435007i \(-0.856746\pi\)
0.697344 0.716737i \(-0.254365\pi\)
\(234\) 0 0
\(235\) 69405.9 120215.i 1.25678 2.17682i
\(236\) 0 0
\(237\) −137587. 115449.i −2.44951 2.05538i
\(238\) 0 0
\(239\) −32898.7 56982.2i −0.575947 0.997570i −0.995938 0.0900414i \(-0.971300\pi\)
0.419991 0.907528i \(-0.362033\pi\)
\(240\) 0 0
\(241\) 19008.1 + 52224.2i 0.327268 + 0.899161i 0.988800 + 0.149245i \(0.0476842\pi\)
−0.661532 + 0.749917i \(0.730094\pi\)
\(242\) 0 0
\(243\) 1764.73 + 311.170i 0.0298859 + 0.00526968i
\(244\) 0 0
\(245\) 45153.0 37887.9i 0.752237 0.631202i
\(246\) 0 0
\(247\) 36500.7 + 2395.35i 0.598283 + 0.0392623i
\(248\) 0 0
\(249\) 95560.5 + 113885.i 1.54127 + 1.83682i
\(250\) 0 0
\(251\) 4921.92 27913.6i 0.0781244 0.443066i −0.920505 0.390730i \(-0.872222\pi\)
0.998630 0.0523352i \(-0.0166664\pi\)
\(252\) 0 0
\(253\) 174081. 63360.1i 2.71963 0.989863i
\(254\) 0 0
\(255\) 1944.05 1122.40i 0.0298969 0.0172610i
\(256\) 0 0
\(257\) 2843.15 3388.34i 0.0430461 0.0513004i −0.744092 0.668077i \(-0.767118\pi\)
0.787138 + 0.616777i \(0.211562\pi\)
\(258\) 0 0
\(259\) 2422.16 + 1398.43i 0.0361080 + 0.0208469i
\(260\) 0 0
\(261\) −135957. + 23972.8i −1.99581 + 0.351915i
\(262\) 0 0
\(263\) 37875.5 + 13785.5i 0.547579 + 0.199302i 0.600970 0.799271i \(-0.294781\pi\)
−0.0533918 + 0.998574i \(0.517003\pi\)
\(264\) 0 0
\(265\) 34679.2i 0.493829i
\(266\) 0 0
\(267\) 161156. 2.26060
\(268\) 0 0
\(269\) −23225.6 + 63811.9i −0.320969 + 0.881854i 0.669338 + 0.742958i \(0.266578\pi\)
−0.990307 + 0.138896i \(0.955644\pi\)
\(270\) 0 0
\(271\) 9398.41 + 53301.1i 0.127972 + 0.725767i 0.979498 + 0.201454i \(0.0645667\pi\)
−0.851526 + 0.524313i \(0.824322\pi\)
\(272\) 0 0
\(273\) −24853.7 + 43047.9i −0.333477 + 0.577600i
\(274\) 0 0
\(275\) −153152. 128510.i −2.02516 1.69931i
\(276\) 0 0
\(277\) −11644.8 20169.4i −0.151766 0.262866i 0.780111 0.625641i \(-0.215163\pi\)
−0.931877 + 0.362775i \(0.881829\pi\)
\(278\) 0 0
\(279\) 62648.2 + 172124.i 0.804822 + 2.21123i
\(280\) 0 0
\(281\) 134068. + 23639.8i 1.69790 + 0.299385i 0.936959 0.349438i \(-0.113628\pi\)
0.760939 + 0.648824i \(0.224739\pi\)
\(282\) 0 0
\(283\) −71245.6 + 59782.1i −0.889580 + 0.746446i −0.968126 0.250464i \(-0.919417\pi\)
0.0785460 + 0.996910i \(0.474972\pi\)
\(284\) 0 0
\(285\) −130575. + 195385.i −1.60757 + 2.40548i
\(286\) 0 0
\(287\) −20339.8 24240.0i −0.246935 0.294286i
\(288\) 0 0
\(289\) −14501.2 + 82240.4i −0.173623 + 0.984668i
\(290\) 0 0
\(291\) 51785.9 18848.5i 0.611542 0.222583i
\(292\) 0 0
\(293\) −66295.4 + 38275.7i −0.772233 + 0.445849i −0.833670 0.552262i \(-0.813765\pi\)
0.0614379 + 0.998111i \(0.480431\pi\)
\(294\) 0 0
\(295\) −66970.9 + 79812.8i −0.769559 + 0.917125i
\(296\) 0 0
\(297\) −198274. 114473.i −2.24777 1.29775i
\(298\) 0 0
\(299\) 102989. 18159.8i 1.15199 0.203127i
\(300\) 0 0
\(301\) 14204.1 + 5169.86i 0.156776 + 0.0570619i
\(302\) 0 0
\(303\) 228399.i 2.48776i
\(304\) 0 0
\(305\) 88689.7 0.953396
\(306\) 0 0
\(307\) 8430.56 23162.8i 0.0894499 0.245762i −0.886899 0.461964i \(-0.847145\pi\)
0.976349 + 0.216202i \(0.0693671\pi\)
\(308\) 0 0
\(309\) −14825.5 84079.9i −0.155272 0.880593i
\(310\) 0 0
\(311\) −42271.8 + 73217.0i −0.437049 + 0.756992i −0.997460 0.0712230i \(-0.977310\pi\)
0.560411 + 0.828215i \(0.310643\pi\)
\(312\) 0 0
\(313\) −71271.8 59804.1i −0.727493 0.610439i 0.201954 0.979395i \(-0.435271\pi\)
−0.929447 + 0.368956i \(0.879715\pi\)
\(314\) 0 0
\(315\) −106602. 184639.i −1.07434 1.86081i
\(316\) 0 0
\(317\) 3915.26 + 10757.1i 0.0389621 + 0.107047i 0.957648 0.287941i \(-0.0929708\pi\)
−0.918686 + 0.394989i \(0.870749\pi\)
\(318\) 0 0
\(319\) 149985. + 26446.4i 1.47390 + 0.259888i
\(320\) 0 0
\(321\) 249727. 209546.i 2.42357 2.03362i
\(322\) 0 0
\(323\) 348.252 + 1195.16i 0.00333802 + 0.0114557i
\(324\) 0 0
\(325\) −72546.0 86457.0i −0.686826 0.818528i
\(326\) 0 0
\(327\) 32923.7 186720.i 0.307903 1.74620i
\(328\) 0 0
\(329\) −98298.3 + 35777.7i −0.908143 + 0.330537i
\(330\) 0 0
\(331\) −15831.7 + 9140.42i −0.144501 + 0.0834277i −0.570507 0.821292i \(-0.693253\pi\)
0.426006 + 0.904720i \(0.359920\pi\)
\(332\) 0 0
\(333\) −9308.49 + 11093.4i −0.0839442 + 0.100041i
\(334\) 0 0
\(335\) −67977.4 39246.8i −0.605724 0.349715i
\(336\) 0 0
\(337\) −221765. + 39103.2i −1.95269 + 0.344313i −0.953633 + 0.300972i \(0.902689\pi\)
−0.999060 + 0.0433406i \(0.986200\pi\)
\(338\) 0 0
\(339\) 189135. + 68839.4i 1.64578 + 0.599015i
\(340\) 0 0
\(341\) 202071.i 1.73779i
\(342\) 0 0
\(343\) −119868. −1.01886
\(344\) 0 0
\(345\) −229788. + 631337.i −1.93059 + 5.30424i
\(346\) 0 0
\(347\) −18415.0 104437.i −0.152937 0.867349i −0.960648 0.277770i \(-0.910405\pi\)
0.807711 0.589579i \(-0.200706\pi\)
\(348\) 0 0
\(349\) −22498.0 + 38967.7i −0.184711 + 0.319929i −0.943479 0.331432i \(-0.892468\pi\)
0.758768 + 0.651361i \(0.225802\pi\)
\(350\) 0 0
\(351\) −99006.7 83076.5i −0.803619 0.674316i
\(352\) 0 0
\(353\) 4393.73 + 7610.16i 0.0352601 + 0.0610724i 0.883117 0.469153i \(-0.155441\pi\)
−0.847857 + 0.530225i \(0.822107\pi\)
\(354\) 0 0
\(355\) 18911.5 + 51958.8i 0.150061 + 0.412290i
\(356\) 0 0
\(357\) −1665.95 293.752i −0.0130715 0.00230486i
\(358\) 0 0
\(359\) 993.881 833.965i 0.00771162 0.00647081i −0.638924 0.769270i \(-0.720620\pi\)
0.646635 + 0.762799i \(0.276176\pi\)
\(360\) 0 0
\(361\) −88028.0 96097.0i −0.675471 0.737387i
\(362\) 0 0
\(363\) 176380. + 210201.i 1.33855 + 1.59523i
\(364\) 0 0
\(365\) 2142.91 12153.0i 0.0160849 0.0912219i
\(366\) 0 0
\(367\) −46474.5 + 16915.3i −0.345051 + 0.125588i −0.508732 0.860925i \(-0.669885\pi\)
0.163681 + 0.986513i \(0.447663\pi\)
\(368\) 0 0
\(369\) 141889. 81919.9i 1.04207 0.601640i
\(370\) 0 0
\(371\) −16798.5 + 20019.6i −0.122046 + 0.145448i
\(372\) 0 0
\(373\) 91944.6 + 53084.2i 0.660858 + 0.381547i 0.792604 0.609737i \(-0.208725\pi\)
−0.131746 + 0.991284i \(0.542058\pi\)
\(374\) 0 0
\(375\) 313381. 55257.5i 2.22848 0.392942i
\(376\) 0 0
\(377\) 80790.3 + 29405.3i 0.568429 + 0.206891i
\(378\) 0 0
\(379\) 217444.i 1.51380i 0.653531 + 0.756900i \(0.273287\pi\)
−0.653531 + 0.756900i \(0.726713\pi\)
\(380\) 0 0
\(381\) 61346.9 0.422613
\(382\) 0 0
\(383\) 22149.4 60855.1i 0.150996 0.414858i −0.841015 0.541012i \(-0.818041\pi\)
0.992011 + 0.126154i \(0.0402635\pi\)
\(384\) 0 0
\(385\) 40842.5 + 231629.i 0.275544 + 1.56269i
\(386\) 0 0
\(387\) −39132.4 + 67779.4i −0.261285 + 0.452560i
\(388\) 0 0
\(389\) −37654.1 31595.5i −0.248836 0.208798i 0.509835 0.860272i \(-0.329706\pi\)
−0.758671 + 0.651474i \(0.774151\pi\)
\(390\) 0 0
\(391\) 1779.50 + 3082.19i 0.0116398 + 0.0201607i
\(392\) 0 0
\(393\) −87590.5 240653.i −0.567116 1.55814i
\(394\) 0 0
\(395\) −472465. 83308.4i −3.02814 0.533942i
\(396\) 0 0
\(397\) −139900. + 117390.i −0.887641 + 0.744819i −0.967736 0.251968i \(-0.918922\pi\)
0.0800945 + 0.996787i \(0.474478\pi\)
\(398\) 0 0
\(399\) 170022. 49542.1i 1.06797 0.311192i
\(400\) 0 0
\(401\) 48668.5 + 58000.9i 0.302663 + 0.360700i 0.895843 0.444370i \(-0.146572\pi\)
−0.593180 + 0.805070i \(0.702128\pi\)
\(402\) 0 0
\(403\) 19808.5 112340.i 0.121967 0.691708i
\(404\) 0 0
\(405\) 263827. 96025.1i 1.60845 0.585430i
\(406\) 0 0
\(407\) 13835.4 7987.85i 0.0835221 0.0482215i
\(408\) 0 0
\(409\) 9286.85 11067.6i 0.0555164 0.0661619i −0.737572 0.675269i \(-0.764028\pi\)
0.793088 + 0.609107i \(0.208472\pi\)
\(410\) 0 0
\(411\) 166062. + 95875.7i 0.983072 + 0.567577i
\(412\) 0 0
\(413\) 77322.1 13634.0i 0.453319 0.0799323i
\(414\) 0 0
\(415\) 373158. + 135819.i 2.16669 + 0.788611i
\(416\) 0 0
\(417\) 170428.i 0.980096i
\(418\) 0 0
\(419\) 216261. 1.23183 0.615915 0.787813i \(-0.288787\pi\)
0.615915 + 0.787813i \(0.288787\pi\)
\(420\) 0 0
\(421\) 70218.5 192924.i 0.396175 1.08848i −0.567956 0.823059i \(-0.692266\pi\)
0.964132 0.265424i \(-0.0855121\pi\)
\(422\) 0 0
\(423\) −94052.5 533398.i −0.525641 2.98106i
\(424\) 0 0
\(425\) 1920.46 3326.33i 0.0106323 0.0184157i
\(426\) 0 0
\(427\) −51198.9 42961.0i −0.280805 0.235623i
\(428\) 0 0
\(429\) 141964. + 245890.i 0.771374 + 1.33606i
\(430\) 0 0
\(431\) −43386.3 119203.i −0.233560 0.641700i 0.766440 0.642316i \(-0.222026\pi\)
−1.00000 0.000615630i \(0.999804\pi\)
\(432\) 0 0
\(433\) 193290. + 34082.3i 1.03094 + 0.181783i 0.663432 0.748237i \(-0.269099\pi\)
0.367510 + 0.930020i \(0.380210\pi\)
\(434\) 0 0
\(435\) −423119. + 355039.i −2.23606 + 1.87628i
\(436\) 0 0
\(437\) −309773. 207020.i −1.62211 1.08405i
\(438\) 0 0
\(439\) 225781. + 269075.i 1.17154 + 1.39619i 0.901189 + 0.433427i \(0.142696\pi\)
0.270352 + 0.962762i \(0.412860\pi\)
\(440\) 0 0
\(441\) 39937.1 226495.i 0.205352 1.16461i
\(442\) 0 0
\(443\) −244865. + 89123.5i −1.24773 + 0.454135i −0.879632 0.475654i \(-0.842211\pi\)
−0.368093 + 0.929789i \(0.619989\pi\)
\(444\) 0 0
\(445\) 372797. 215235.i 1.88258 1.08691i
\(446\) 0 0
\(447\) −174419. + 207865.i −0.872929 + 1.04032i
\(448\) 0 0
\(449\) −96621.1 55784.2i −0.479269 0.276706i 0.240843 0.970564i \(-0.422576\pi\)
−0.720112 + 0.693858i \(0.755909\pi\)
\(450\) 0 0
\(451\) −178000. + 31386.1i −0.875116 + 0.154307i
\(452\) 0 0
\(453\) −309818. 112764.i −1.50977 0.549510i
\(454\) 0 0
\(455\) 132775.i 0.641350i
\(456\) 0 0
\(457\) −170845. −0.818032 −0.409016 0.912527i \(-0.634128\pi\)
−0.409016 + 0.912527i \(0.634128\pi\)
\(458\) 0 0
\(459\) 1504.36 4133.18i 0.00714044 0.0196182i
\(460\) 0 0
\(461\) 18165.3 + 103020.i 0.0854752 + 0.484754i 0.997253 + 0.0740701i \(0.0235989\pi\)
−0.911778 + 0.410684i \(0.865290\pi\)
\(462\) 0 0
\(463\) 94892.9 164359.i 0.442661 0.766712i −0.555225 0.831700i \(-0.687368\pi\)
0.997886 + 0.0649884i \(0.0207011\pi\)
\(464\) 0 0
\(465\) 561397. + 471068.i 2.59635 + 2.17860i
\(466\) 0 0
\(467\) −33851.6 58632.8i −0.155219 0.268848i 0.777919 0.628364i \(-0.216275\pi\)
−0.933139 + 0.359516i \(0.882942\pi\)
\(468\) 0 0
\(469\) 20231.1 + 55584.4i 0.0919758 + 0.252701i
\(470\) 0 0
\(471\) −193037. 34037.7i −0.870160 0.153433i
\(472\) 0 0
\(473\) 66140.8 55498.7i 0.295629 0.248062i
\(474\) 0 0
\(475\) −26330.7 + 401230.i −0.116701 + 1.77831i
\(476\) 0 0
\(477\) −86978.0 103656.i −0.382272 0.455574i
\(478\) 0 0
\(479\) 25878.7 146765.i 0.112790 0.639664i −0.875031 0.484068i \(-0.839159\pi\)
0.987821 0.155597i \(-0.0497300\pi\)
\(480\) 0 0
\(481\) 8474.65 3084.52i 0.0366296 0.0133321i
\(482\) 0 0
\(483\) 438470. 253151.i 1.87951 1.08514i
\(484\) 0 0
\(485\) 94621.5 112765.i 0.402259 0.479394i
\(486\) 0 0
\(487\) −118254. 68274.0i −0.498606 0.287871i 0.229531 0.973301i \(-0.426281\pi\)
−0.728138 + 0.685431i \(0.759614\pi\)
\(488\) 0 0
\(489\) 229908. 40539.0i 0.961472 0.169533i
\(490\) 0 0
\(491\) −73321.2 26686.7i −0.304135 0.110696i 0.185445 0.982655i \(-0.440627\pi\)
−0.489580 + 0.871959i \(0.662850\pi\)
\(492\) 0 0
\(493\) 2925.91i 0.0120384i
\(494\) 0 0
\(495\) −1.21782e6 −4.97017
\(496\) 0 0
\(497\) 14251.4 39155.5i 0.0576961 0.158519i
\(498\) 0 0
\(499\) 12863.5 + 72952.8i 0.0516606 + 0.292982i 0.999682 0.0252254i \(-0.00803034\pi\)
−0.948021 + 0.318207i \(0.896919\pi\)
\(500\) 0 0
\(501\) −176673. + 306007.i −0.703875 + 1.21915i
\(502\) 0 0
\(503\) 75126.9 + 63039.0i 0.296934 + 0.249157i 0.779067 0.626941i \(-0.215693\pi\)
−0.482133 + 0.876098i \(0.660138\pi\)
\(504\) 0 0
\(505\) −305042. 528349.i −1.19613 2.07175i
\(506\) 0 0
\(507\) −97676.0 268362.i −0.379990 1.04401i
\(508\) 0 0
\(509\) 349030. + 61543.4i 1.34719 + 0.237545i 0.800269 0.599642i \(-0.204690\pi\)
0.546917 + 0.837187i \(0.315801\pi\)
\(510\) 0 0
\(511\) −7123.95 + 5977.70i −0.0272822 + 0.0228925i
\(512\) 0 0
\(513\) 50091.6 + 457726.i 0.190340 + 1.73929i
\(514\) 0 0
\(515\) −146590. 174699.i −0.552700 0.658683i
\(516\) 0 0
\(517\) −103757. + 588437.i −0.388184 + 2.20150i
\(518\) 0 0
\(519\) 103076. 37516.5i 0.382668 0.139280i
\(520\) 0 0
\(521\) 166490. 96123.3i 0.613358 0.354122i −0.160921 0.986967i \(-0.551446\pi\)
0.774278 + 0.632845i \(0.218113\pi\)
\(522\) 0 0
\(523\) 174605. 208086.i 0.638341 0.760745i −0.345766 0.938321i \(-0.612381\pi\)
0.984107 + 0.177576i \(0.0568255\pi\)
\(524\) 0 0
\(525\) −473201. 273202.i −1.71683 0.991211i
\(526\) 0 0
\(527\) 3823.15 674.124i 0.0137657 0.00242727i
\(528\) 0 0
\(529\) −737989. 268606.i −2.63717 0.959853i
\(530\) 0 0
\(531\) 406530.i 1.44179i
\(532\) 0 0
\(533\) −102034. −0.359161
\(534\) 0 0
\(535\) 297824. 818264.i 1.04052 2.85881i
\(536\) 0 0
\(537\) −106573. 604408.i −0.369573 2.09595i
\(538\) 0 0
\(539\) −126860. + 219728.i −0.436664 + 0.756324i
\(540\) 0 0
\(541\) −159088. 133491.i −0.543554 0.456096i 0.329197 0.944261i \(-0.393222\pi\)
−0.872751 + 0.488165i \(0.837666\pi\)
\(542\) 0 0
\(543\) 495320. + 857919.i 1.67991 + 2.90969i
\(544\) 0 0
\(545\) −173215. 475905.i −0.583168 1.60224i
\(546\) 0 0
\(547\) 482139. + 85014.1i 1.61138 + 0.284130i 0.905546 0.424248i \(-0.139462\pi\)
0.705833 + 0.708378i \(0.250573\pi\)
\(548\) 0 0
\(549\) 265094. 222441.i 0.879540 0.738022i
\(550\) 0 0
\(551\) −135453. 274727.i −0.446154 0.904896i
\(552\) 0 0
\(553\) 232391. + 276953.i 0.759922 + 0.905640i
\(554\) 0 0
\(555\) −10061.0 + 57058.8i −0.0326629 + 0.185241i
\(556\) 0 0
\(557\) 224269. 81627.3i 0.722869 0.263103i 0.0457256 0.998954i \(-0.485440\pi\)
0.677143 + 0.735851i \(0.263218\pi\)
\(558\) 0 0
\(559\) 42210.6 24370.3i 0.135082 0.0779898i
\(560\) 0 0
\(561\) −6211.06 + 7402.05i −0.0197351 + 0.0235194i
\(562\) 0 0
\(563\) 385339. + 222476.i 1.21570 + 0.701884i 0.963995 0.265920i \(-0.0856756\pi\)
0.251704 + 0.967804i \(0.419009\pi\)
\(564\) 0 0
\(565\) 529460. 93358.0i 1.65858 0.292452i
\(566\) 0 0
\(567\) −198817. 72363.3i −0.618424 0.225088i
\(568\) 0 0
\(569\) 366070.i 1.13068i −0.824859 0.565339i \(-0.808745\pi\)
0.824859 0.565339i \(-0.191255\pi\)
\(570\) 0 0
\(571\) −144578. −0.443435 −0.221718 0.975111i \(-0.571166\pi\)
−0.221718 + 0.975111i \(0.571166\pi\)
\(572\) 0 0
\(573\) 117497. 322820.i 0.357864 0.983222i
\(574\) 0 0
\(575\) 199620. + 1.13210e6i 0.603765 + 3.42412i
\(576\) 0 0
\(577\) −199149. + 344937.i −0.598174 + 1.03607i 0.394917 + 0.918717i \(0.370774\pi\)
−0.993091 + 0.117351i \(0.962560\pi\)
\(578\) 0 0
\(579\) 135175. + 113426.i 0.403218 + 0.338340i
\(580\) 0 0
\(581\) −149627. 259162.i −0.443260 0.767749i
\(582\) 0 0
\(583\) 51055.4 + 140274.i 0.150212 + 0.412704i
\(584\) 0 0
\(585\) −677032. 119379.i −1.97832 0.348832i
\(586\) 0 0
\(587\) −126273. + 105955.i −0.366465 + 0.307501i −0.807361 0.590057i \(-0.799105\pi\)
0.440896 + 0.897558i \(0.354661\pi\)
\(588\) 0 0
\(589\) −327765. + 240286.i −0.944782 + 0.692625i
\(590\) 0 0
\(591\) 424562. + 505973.i 1.21553 + 1.44861i
\(592\) 0 0
\(593\) 52420.3 297290.i 0.149070 0.845417i −0.814939 0.579547i \(-0.803230\pi\)
0.964009 0.265870i \(-0.0856593\pi\)
\(594\) 0 0
\(595\) −4246.12 + 1545.46i −0.0119938 + 0.00436540i
\(596\) 0 0
\(597\) −364839. + 210640.i −1.02365 + 0.591006i
\(598\) 0 0
\(599\) −28443.5 + 33897.6i −0.0792736 + 0.0944747i −0.804223 0.594327i \(-0.797418\pi\)
0.724950 + 0.688802i \(0.241863\pi\)
\(600\) 0 0
\(601\) 157578. + 90977.5i 0.436260 + 0.251875i 0.702010 0.712167i \(-0.252286\pi\)
−0.265750 + 0.964042i \(0.585620\pi\)
\(602\) 0 0
\(603\) −301619. + 53183.6i −0.829515 + 0.146266i
\(604\) 0 0
\(605\) 688753. + 250686.i 1.88171 + 0.684886i
\(606\) 0 0
\(607\) 300602.i 0.815859i 0.913013 + 0.407929i \(0.133749\pi\)
−0.913013 + 0.407929i \(0.866251\pi\)
\(608\) 0 0
\(609\) 416238. 1.12230
\(610\) 0 0
\(611\) −115366. + 316964.i −0.309025 + 0.849039i
\(612\) 0 0
\(613\) 50234.3 + 284893.i 0.133684 + 0.758159i 0.975767 + 0.218812i \(0.0702180\pi\)
−0.842083 + 0.539348i \(0.818671\pi\)
\(614\) 0 0
\(615\) 327754. 567687.i 0.866559 1.50092i
\(616\) 0 0
\(617\) 341235. + 286330.i 0.896362 + 0.752137i 0.969476 0.245186i \(-0.0788492\pi\)
−0.0731138 + 0.997324i \(0.523294\pi\)
\(618\) 0 0
\(619\) 7560.10 + 13094.5i 0.0197309 + 0.0341749i 0.875722 0.482815i \(-0.160386\pi\)
−0.855991 + 0.516990i \(0.827052\pi\)
\(620\) 0 0
\(621\) 450246. + 1.23704e6i 1.16753 + 3.20775i
\(622\) 0 0
\(623\) −319468. 56330.8i −0.823097 0.145134i
\(624\) 0 0
\(625\) 117857. 98893.6i 0.301713 0.253168i
\(626\) 0 0
\(627\) 240512. 982548.i 0.611790 2.49930i
\(628\) 0 0
\(629\) 197.284 + 235.114i 0.000498644 + 0.000594261i
\(630\) 0 0
\(631\) 96573.5 547695.i 0.242549 1.37556i −0.583568 0.812064i \(-0.698344\pi\)
0.826117 0.563498i \(-0.190545\pi\)
\(632\) 0 0
\(633\) −479685. + 174591.i −1.19715 + 0.435727i
\(634\) 0 0
\(635\) 141912. 81933.0i 0.351943 0.203194i
\(636\) 0 0
\(637\) −92065.8 + 109720.i −0.226892 + 0.270400i
\(638\) 0 0
\(639\) 186843. + 107874.i 0.457589 + 0.264189i
\(640\) 0 0
\(641\) 404284. 71286.3i 0.983945 0.173496i 0.341545 0.939865i \(-0.389050\pi\)
0.642400 + 0.766369i \(0.277939\pi\)
\(642\) 0 0
\(643\) −536898. 195415.i −1.29858 0.472646i −0.402048 0.915619i \(-0.631702\pi\)
−0.896535 + 0.442973i \(0.853924\pi\)
\(644\) 0 0
\(645\) 313131.i 0.752674i
\(646\) 0 0
\(647\) 256568. 0.612907 0.306453 0.951886i \(-0.400858\pi\)
0.306453 + 0.951886i \(0.400858\pi\)
\(648\) 0 0
\(649\) 153388. 421431.i 0.364169 1.00055i
\(650\) 0 0
\(651\) −95900.3 543878.i −0.226286 1.28333i
\(652\) 0 0
\(653\) −25726.1 + 44559.0i −0.0603321 + 0.104498i −0.894614 0.446840i \(-0.852549\pi\)
0.834282 + 0.551338i \(0.185883\pi\)
\(654\) 0 0
\(655\) −524029. 439713.i −1.22144 1.02491i
\(656\) 0 0
\(657\) −24075.6 41700.1i −0.0557758 0.0966066i
\(658\) 0 0
\(659\) −85016.0 233580.i −0.195763 0.537854i 0.802508 0.596642i \(-0.203499\pi\)
−0.998270 + 0.0587880i \(0.981276\pi\)
\(660\) 0 0
\(661\) 46683.4 + 8231.55i 0.106846 + 0.0188399i 0.226816 0.973938i \(-0.427169\pi\)
−0.119969 + 0.992778i \(0.538280\pi\)
\(662\) 0 0
\(663\) −4178.57 + 3506.24i −0.00950607 + 0.00797654i
\(664\) 0 0
\(665\) 327141. 341681.i 0.739762 0.772640i
\(666\) 0 0
\(667\) −562896. 670833.i −1.26525 1.50787i
\(668\) 0 0
\(669\) 66540.6 377371.i 0.148674 0.843171i
\(670\) 0 0
\(671\) −358740. + 130571.i −0.796774 + 0.290002i
\(672\) 0 0
\(673\) −483380. + 279079.i −1.06723 + 0.616166i −0.927424 0.374013i \(-0.877982\pi\)
−0.139807 + 0.990179i \(0.544648\pi\)
\(674\) 0 0
\(675\) 913211. 1.08832e6i 2.00430 2.38864i
\(676\) 0 0
\(677\) −473966. 273645.i −1.03412 0.597049i −0.115957 0.993254i \(-0.536993\pi\)
−0.918162 + 0.396206i \(0.870327\pi\)
\(678\) 0 0
\(679\) −109246. + 19263.1i −0.236956 + 0.0417817i
\(680\) 0 0
\(681\) 1.06287e6 + 386853.i 2.29185 + 0.834165i
\(682\) 0 0
\(683\) 223188.i 0.478442i 0.970965 + 0.239221i \(0.0768921\pi\)
−0.970965 + 0.239221i \(0.923108\pi\)
\(684\) 0 0
\(685\) 512194. 1.09157
\(686\) 0 0
\(687\) −318454. + 874945.i −0.674735 + 1.85382i
\(688\) 0 0
\(689\) 14633.1 + 82988.5i 0.0308246 + 0.174815i
\(690\) 0 0
\(691\) −67543.4 + 116989.i −0.141458 + 0.245012i −0.928046 0.372466i \(-0.878512\pi\)
0.786588 + 0.617478i \(0.211846\pi\)
\(692\) 0 0
\(693\) 703022. + 589906.i 1.46387 + 1.22833i
\(694\) 0 0
\(695\) 227618. + 394246.i 0.471235 + 0.816202i
\(696\) 0 0
\(697\) −1187.64 3263.00i −0.00244466 0.00671664i
\(698\) 0 0
\(699\) −976113. 172115.i −1.99777 0.352261i
\(700\) 0 0
\(701\) 318263. 267054.i 0.647664 0.543455i −0.258697 0.965959i \(-0.583293\pi\)
0.906361 + 0.422504i \(0.138849\pi\)
\(702\) 0 0
\(703\) −29408.3 12942.8i −0.0595058 0.0261889i
\(704\) 0 0
\(705\) −1.39292e6 1.66002e6i −2.80252 3.33991i
\(706\) 0 0
\(707\) −79835.1 + 452768.i −0.159719 + 0.905809i
\(708\) 0 0
\(709\) 25063.6 9122.40i 0.0498599 0.0181475i −0.316970 0.948436i \(-0.602665\pi\)
0.366830 + 0.930288i \(0.380443\pi\)
\(710\) 0 0
\(711\) −1.62115e6 + 935970.i −3.20688 + 1.85150i
\(712\) 0 0
\(713\) −746855. + 890067.i −1.46912 + 1.75083i
\(714\) 0 0
\(715\) 656805. + 379206.i 1.28477 + 0.741760i
\(716\) 0 0
\(717\) −1.01156e6 + 178366.i −1.96768 + 0.346955i
\(718\) 0 0
\(719\) −195167. 71035.1i −0.377528 0.137409i 0.146285 0.989243i \(-0.453269\pi\)
−0.523812 + 0.851834i \(0.675491\pi\)
\(720\) 0 0
\(721\) 171858.i 0.330598i
\(722\) 0 0
\(723\) 867598. 1.65975
\(724\) 0 0
\(725\) −323235. + 888080.i −0.614953 + 1.68957i
\(726\) 0 0
\(727\) 92752.4 + 526025.i 0.175492 + 0.995262i 0.937575 + 0.347783i \(0.113065\pi\)
−0.762083 + 0.647479i \(0.775823\pi\)
\(728\) 0 0
\(729\) −258697. + 448076.i −0.486783 + 0.843133i
\(730\) 0 0
\(731\) 1270.67 + 1066.22i 0.00237793 + 0.00199532i
\(732\) 0 0
\(733\) −229907. 398210.i −0.427901 0.741147i 0.568785 0.822486i \(-0.307414\pi\)
−0.996686 + 0.0813395i \(0.974080\pi\)
\(734\) 0 0
\(735\) −314715. 864672.i −0.582563 1.60058i
\(736\) 0 0
\(737\) 332741. + 58671.3i 0.612593 + 0.108017i
\(738\) 0 0
\(739\) 560912. 470661.i 1.02708 0.861826i 0.0365835 0.999331i \(-0.488353\pi\)
0.990501 + 0.137504i \(0.0439081\pi\)
\(740\) 0 0
\(741\) 230027. 522661.i 0.418931 0.951883i
\(742\) 0 0
\(743\) 291541. + 347445.i 0.528107 + 0.629373i 0.962478 0.271361i \(-0.0874737\pi\)
−0.434371 + 0.900734i \(0.643029\pi\)
\(744\) 0 0
\(745\) −125862. + 713796.i −0.226767 + 1.28606i
\(746\) 0 0
\(747\) 1.45602e6 529947.i 2.60931 0.949710i
\(748\) 0 0
\(749\) −568293. + 328104.i −1.01300 + 0.584854i
\(750\) 0 0
\(751\) 165853. 197656.i 0.294065 0.350453i −0.598702 0.800972i \(-0.704317\pi\)
0.892767 + 0.450519i \(0.148761\pi\)
\(752\) 0 0
\(753\) −383202. 221242.i −0.675830 0.390191i
\(754\) 0 0
\(755\) −867298. + 152928.i −1.52151 + 0.268283i
\(756\) 0 0
\(757\) −630471. 229473.i −1.10020 0.400442i −0.272813 0.962067i \(-0.587954\pi\)
−0.827392 + 0.561625i \(0.810176\pi\)
\(758\) 0 0
\(759\) 2.89199e6i 5.02011i
\(760\) 0 0
\(761\) 723766. 1.24977 0.624884 0.780718i \(-0.285146\pi\)
0.624884 + 0.780718i \(0.285146\pi\)
\(762\) 0 0
\(763\) −130533. + 358636.i −0.224218 + 0.616035i
\(764\) 0 0
\(765\) −4062.71 23040.8i −0.00694214 0.0393708i
\(766\) 0 0
\(767\) 126586. 219254.i 0.215177 0.372697i
\(768\) 0 0
\(769\) −717195. 601798.i −1.21279 1.01765i −0.999170 0.0407312i \(-0.987031\pi\)
−0.213616 0.976918i \(-0.568524\pi\)
\(770\) 0 0
\(771\) −34525.2 59799.3i −0.0580800 0.100598i
\(772\) 0 0
\(773\) 199327. + 547647.i 0.333586 + 0.916519i 0.987171 + 0.159666i \(0.0510418\pi\)
−0.653586 + 0.756853i \(0.726736\pi\)
\(774\) 0 0
\(775\) 1.23488e6 + 217743.i 2.05600 + 0.362527i
\(776\) 0 0
\(777\) 33447.1 28065.5i 0.0554009 0.0464868i
\(778\) 0 0
\(779\) 262571. + 251398.i 0.432685 + 0.414273i
\(780\) 0 0
\(781\) −152990. 182326.i −0.250819 0.298915i
\(782\) 0 0
\(783\) −187932. + 1.06582e6i −0.306533 + 1.73844i
\(784\) 0 0
\(785\) −492007. + 179076.i −0.798421 + 0.290602i
\(786\) 0 0
\(787\) 908658. 524614.i 1.46707 0.847013i 0.467749 0.883861i \(-0.345065\pi\)
0.999321 + 0.0368482i \(0.0117318\pi\)
\(788\) 0 0
\(789\) 404457. 482013.i 0.649708 0.774292i
\(790\) 0 0
\(791\) −350870. 202575.i −0.560780 0.323767i
\(792\) 0 0