Properties

Label 324.5.d.e.163.15
Level 324
Weight 5
Character 324.163
Analytic conductor 33.492
Analytic rank 0
Dimension 22
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.15
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.e.163.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +O(q^{10})\) \(q+(1.75474 - 3.59457i) q^{2} +(-9.84180 - 12.6150i) q^{4} -46.6931 q^{5} +60.5483i q^{7} +(-62.6153 + 13.2409i) q^{8} +(-81.9341 + 167.841i) q^{10} -73.6273i q^{11} -31.1848 q^{13} +(217.645 + 106.246i) q^{14} +(-62.2781 + 248.309i) q^{16} -53.8013 q^{17} -54.9619i q^{19} +(459.544 + 589.035i) q^{20} +(-264.658 - 129.197i) q^{22} -281.589i q^{23} +1555.25 q^{25} +(-54.7210 + 112.096i) q^{26} +(763.818 - 595.904i) q^{28} +447.195 q^{29} +277.802i q^{31} +(783.282 + 659.580i) q^{32} +(-94.4072 + 193.392i) q^{34} -2827.19i q^{35} +1016.51 q^{37} +(-197.564 - 96.4437i) q^{38} +(2923.70 - 618.259i) q^{40} -1892.32 q^{41} -769.338i q^{43} +(-928.811 + 724.625i) q^{44} +(-1012.19 - 494.115i) q^{46} -2742.20i q^{47} -1265.09 q^{49} +(2729.05 - 5590.44i) q^{50} +(306.914 + 393.397i) q^{52} +4647.69 q^{53} +3437.89i q^{55} +(-801.714 - 3791.25i) q^{56} +(784.709 - 1607.47i) q^{58} -303.446i q^{59} +956.348 q^{61} +(998.577 + 487.469i) q^{62} +(3745.36 - 1658.17i) q^{64} +1456.11 q^{65} +6940.86i q^{67} +(529.502 + 678.706i) q^{68} +(-10162.5 - 4960.97i) q^{70} +5971.60i q^{71} -4339.17 q^{73} +(1783.71 - 3653.92i) q^{74} +(-693.346 + 540.924i) q^{76} +4458.01 q^{77} +3803.76i q^{79} +(2907.96 - 11594.3i) q^{80} +(-3320.52 + 6802.05i) q^{82} +3153.07i q^{83} +2512.15 q^{85} +(-2765.44 - 1349.99i) q^{86} +(974.892 + 4610.20i) q^{88} +7132.44 q^{89} -1888.18i q^{91} +(-3552.26 + 2771.34i) q^{92} +(-9857.00 - 4811.83i) q^{94} +2566.34i q^{95} -1960.81 q^{97} +(-2219.91 + 4547.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + O(q^{10}) \) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + 14q^{10} + 2q^{13} + 252q^{14} + q^{16} + 28q^{17} - 140q^{20} + 33q^{22} + 1752q^{25} - 548q^{26} - 258q^{28} + 526q^{29} - 121q^{32} - 385q^{34} - 4q^{37} + 1395q^{38} + 2276q^{40} - 2762q^{41} - 3357q^{44} + 1788q^{46} - 3428q^{49} + 6375q^{50} - 1438q^{52} + 5044q^{53} - 7506q^{56} + 4064q^{58} + 2q^{61} + 9162q^{62} + 4513q^{64} - 2014q^{65} - 11405q^{68} - 3666q^{70} - 1708q^{73} + 14620q^{74} - 1581q^{76} - 3942q^{77} - 22760q^{80} - 4243q^{82} + 1252q^{85} + 22113q^{86} - 1995q^{88} - 6524q^{89} - 30294q^{92} - 7524q^{94} - 5638q^{97} + 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.75474 3.59457i 0.438684 0.898641i
\(3\) 0 0
\(4\) −9.84180 12.6150i −0.615112 0.788440i
\(5\) −46.6931 −1.86772 −0.933862 0.357633i \(-0.883584\pi\)
−0.933862 + 0.357633i \(0.883584\pi\)
\(6\) 0 0
\(7\) 60.5483i 1.23568i 0.786304 + 0.617839i \(0.211992\pi\)
−0.786304 + 0.617839i \(0.788008\pi\)
\(8\) −62.6153 + 13.2409i −0.978364 + 0.206889i
\(9\) 0 0
\(10\) −81.9341 + 167.841i −0.819341 + 1.67841i
\(11\) 73.6273i 0.608490i −0.952594 0.304245i \(-0.901596\pi\)
0.952594 0.304245i \(-0.0984042\pi\)
\(12\) 0 0
\(13\) −31.1848 −0.184525 −0.0922626 0.995735i \(-0.529410\pi\)
−0.0922626 + 0.995735i \(0.529410\pi\)
\(14\) 217.645 + 106.246i 1.11043 + 0.542073i
\(15\) 0 0
\(16\) −62.2781 + 248.309i −0.243274 + 0.969958i
\(17\) −53.8013 −0.186164 −0.0930819 0.995658i \(-0.529672\pi\)
−0.0930819 + 0.995658i \(0.529672\pi\)
\(18\) 0 0
\(19\) 54.9619i 0.152249i −0.997098 0.0761245i \(-0.975745\pi\)
0.997098 0.0761245i \(-0.0242546\pi\)
\(20\) 459.544 + 589.035i 1.14886 + 1.47259i
\(21\) 0 0
\(22\) −264.658 129.197i −0.546814 0.266935i
\(23\) 281.589i 0.532305i −0.963931 0.266152i \(-0.914248\pi\)
0.963931 0.266152i \(-0.0857525\pi\)
\(24\) 0 0
\(25\) 1555.25 2.48840
\(26\) −54.7210 + 112.096i −0.0809483 + 0.165822i
\(27\) 0 0
\(28\) 763.818 595.904i 0.974258 0.760081i
\(29\) 447.195 0.531742 0.265871 0.964009i \(-0.414341\pi\)
0.265871 + 0.964009i \(0.414341\pi\)
\(30\) 0 0
\(31\) 277.802i 0.289076i 0.989499 + 0.144538i \(0.0461696\pi\)
−0.989499 + 0.144538i \(0.953830\pi\)
\(32\) 783.282 + 659.580i 0.764923 + 0.644121i
\(33\) 0 0
\(34\) −94.4072 + 193.392i −0.0816671 + 0.167294i
\(35\) 2827.19i 2.30791i
\(36\) 0 0
\(37\) 1016.51 0.742522 0.371261 0.928528i \(-0.378925\pi\)
0.371261 + 0.928528i \(0.378925\pi\)
\(38\) −197.564 96.4437i −0.136817 0.0667892i
\(39\) 0 0
\(40\) 2923.70 618.259i 1.82732 0.386412i
\(41\) −1892.32 −1.12571 −0.562854 0.826556i \(-0.690297\pi\)
−0.562854 + 0.826556i \(0.690297\pi\)
\(42\) 0 0
\(43\) 769.338i 0.416083i −0.978120 0.208042i \(-0.933291\pi\)
0.978120 0.208042i \(-0.0667090\pi\)
\(44\) −928.811 + 724.625i −0.479758 + 0.374290i
\(45\) 0 0
\(46\) −1012.19 494.115i −0.478351 0.233514i
\(47\) 2742.20i 1.24137i −0.784058 0.620687i \(-0.786854\pi\)
0.784058 0.620687i \(-0.213146\pi\)
\(48\) 0 0
\(49\) −1265.09 −0.526902
\(50\) 2729.05 5590.44i 1.09162 2.23617i
\(51\) 0 0
\(52\) 306.914 + 393.397i 0.113504 + 0.145487i
\(53\) 4647.69 1.65457 0.827286 0.561780i \(-0.189883\pi\)
0.827286 + 0.561780i \(0.189883\pi\)
\(54\) 0 0
\(55\) 3437.89i 1.13649i
\(56\) −801.714 3791.25i −0.255649 1.20894i
\(57\) 0 0
\(58\) 784.709 1607.47i 0.233267 0.477845i
\(59\) 303.446i 0.0871722i −0.999050 0.0435861i \(-0.986122\pi\)
0.999050 0.0435861i \(-0.0138783\pi\)
\(60\) 0 0
\(61\) 956.348 0.257014 0.128507 0.991709i \(-0.458982\pi\)
0.128507 + 0.991709i \(0.458982\pi\)
\(62\) 998.577 + 487.469i 0.259776 + 0.126813i
\(63\) 0 0
\(64\) 3745.36 1658.17i 0.914394 0.404826i
\(65\) 1456.11 0.344642
\(66\) 0 0
\(67\) 6940.86i 1.54619i 0.634289 + 0.773096i \(0.281293\pi\)
−0.634289 + 0.773096i \(0.718707\pi\)
\(68\) 529.502 + 678.706i 0.114512 + 0.146779i
\(69\) 0 0
\(70\) −10162.5 4960.97i −2.07398 1.01244i
\(71\) 5971.60i 1.18461i 0.805715 + 0.592303i \(0.201781\pi\)
−0.805715 + 0.592303i \(0.798219\pi\)
\(72\) 0 0
\(73\) −4339.17 −0.814257 −0.407128 0.913371i \(-0.633470\pi\)
−0.407128 + 0.913371i \(0.633470\pi\)
\(74\) 1783.71 3653.92i 0.325733 0.667261i
\(75\) 0 0
\(76\) −693.346 + 540.924i −0.120039 + 0.0936502i
\(77\) 4458.01 0.751898
\(78\) 0 0
\(79\) 3803.76i 0.609479i 0.952436 + 0.304740i \(0.0985694\pi\)
−0.952436 + 0.304740i \(0.901431\pi\)
\(80\) 2907.96 11594.3i 0.454369 1.81161i
\(81\) 0 0
\(82\) −3320.52 + 6802.05i −0.493831 + 1.01161i
\(83\) 3153.07i 0.457696i 0.973462 + 0.228848i \(0.0734958\pi\)
−0.973462 + 0.228848i \(0.926504\pi\)
\(84\) 0 0
\(85\) 2512.15 0.347703
\(86\) −2765.44 1349.99i −0.373910 0.182529i
\(87\) 0 0
\(88\) 974.892 + 4610.20i 0.125890 + 0.595325i
\(89\) 7132.44 0.900447 0.450224 0.892916i \(-0.351344\pi\)
0.450224 + 0.892916i \(0.351344\pi\)
\(90\) 0 0
\(91\) 1888.18i 0.228014i
\(92\) −3552.26 + 2771.34i −0.419690 + 0.327427i
\(93\) 0 0
\(94\) −9857.00 4811.83i −1.11555 0.544571i
\(95\) 2566.34i 0.284359i
\(96\) 0 0
\(97\) −1960.81 −0.208397 −0.104199 0.994557i \(-0.533228\pi\)
−0.104199 + 0.994557i \(0.533228\pi\)
\(98\) −2219.91 + 4547.46i −0.231144 + 0.473496i
\(99\) 0 0
\(100\) −15306.4 19619.5i −1.53064 1.96195i
\(101\) 7699.91 0.754820 0.377410 0.926046i \(-0.376815\pi\)
0.377410 + 0.926046i \(0.376815\pi\)
\(102\) 0 0
\(103\) 3689.52i 0.347772i −0.984766 0.173886i \(-0.944367\pi\)
0.984766 0.173886i \(-0.0556325\pi\)
\(104\) 1952.64 412.914i 0.180533 0.0381763i
\(105\) 0 0
\(106\) 8155.48 16706.4i 0.725835 1.48687i
\(107\) 13741.5i 1.20024i −0.799911 0.600118i \(-0.795120\pi\)
0.799911 0.600118i \(-0.204880\pi\)
\(108\) 0 0
\(109\) 18709.9 1.57478 0.787388 0.616458i \(-0.211433\pi\)
0.787388 + 0.616458i \(0.211433\pi\)
\(110\) 12357.7 + 6032.59i 1.02130 + 0.498561i
\(111\) 0 0
\(112\) −15034.7 3770.83i −1.19856 0.300608i
\(113\) 10001.0 0.783225 0.391613 0.920130i \(-0.371917\pi\)
0.391613 + 0.920130i \(0.371917\pi\)
\(114\) 0 0
\(115\) 13148.3i 0.994199i
\(116\) −4401.20 5641.38i −0.327081 0.419246i
\(117\) 0 0
\(118\) −1090.76 532.469i −0.0783366 0.0382411i
\(119\) 3257.58i 0.230039i
\(120\) 0 0
\(121\) 9220.02 0.629740
\(122\) 1678.14 3437.66i 0.112748 0.230963i
\(123\) 0 0
\(124\) 3504.48 2734.07i 0.227919 0.177814i
\(125\) −43436.1 −2.77991
\(126\) 0 0
\(127\) 18883.8i 1.17080i 0.810745 + 0.585400i \(0.199063\pi\)
−0.810745 + 0.585400i \(0.800937\pi\)
\(128\) 611.727 16372.6i 0.0373369 0.999303i
\(129\) 0 0
\(130\) 2555.10 5234.09i 0.151189 0.309710i
\(131\) 29676.9i 1.72932i −0.502358 0.864660i \(-0.667534\pi\)
0.502358 0.864660i \(-0.332466\pi\)
\(132\) 0 0
\(133\) 3327.85 0.188131
\(134\) 24949.4 + 12179.4i 1.38947 + 0.678290i
\(135\) 0 0
\(136\) 3368.79 712.379i 0.182136 0.0385153i
\(137\) −16665.6 −0.887931 −0.443965 0.896044i \(-0.646429\pi\)
−0.443965 + 0.896044i \(0.646429\pi\)
\(138\) 0 0
\(139\) 4094.51i 0.211920i −0.994370 0.105960i \(-0.966208\pi\)
0.994370 0.105960i \(-0.0337915\pi\)
\(140\) −35665.1 + 27824.6i −1.81965 + 1.41962i
\(141\) 0 0
\(142\) 21465.3 + 10478.6i 1.06454 + 0.519668i
\(143\) 2296.05i 0.112282i
\(144\) 0 0
\(145\) −20880.9 −0.993147
\(146\) −7614.11 + 15597.4i −0.357202 + 0.731725i
\(147\) 0 0
\(148\) −10004.3 12823.3i −0.456735 0.585434i
\(149\) 5869.18 0.264365 0.132183 0.991225i \(-0.457801\pi\)
0.132183 + 0.991225i \(0.457801\pi\)
\(150\) 0 0
\(151\) 33169.5i 1.45474i 0.686246 + 0.727369i \(0.259257\pi\)
−0.686246 + 0.727369i \(0.740743\pi\)
\(152\) 727.745 + 3441.46i 0.0314987 + 0.148955i
\(153\) 0 0
\(154\) 7822.63 16024.6i 0.329846 0.675687i
\(155\) 12971.4i 0.539914i
\(156\) 0 0
\(157\) 22178.5 0.899772 0.449886 0.893086i \(-0.351465\pi\)
0.449886 + 0.893086i \(0.351465\pi\)
\(158\) 13672.9 + 6674.60i 0.547703 + 0.267369i
\(159\) 0 0
\(160\) −36573.9 30797.8i −1.42867 1.20304i
\(161\) 17049.7 0.657758
\(162\) 0 0
\(163\) 31303.8i 1.17821i 0.808057 + 0.589104i \(0.200519\pi\)
−0.808057 + 0.589104i \(0.799481\pi\)
\(164\) 18623.8 + 23871.6i 0.692437 + 0.887553i
\(165\) 0 0
\(166\) 11333.9 + 5532.80i 0.411304 + 0.200784i
\(167\) 26040.4i 0.933717i 0.884332 + 0.466858i \(0.154614\pi\)
−0.884332 + 0.466858i \(0.845386\pi\)
\(168\) 0 0
\(169\) −27588.5 −0.965950
\(170\) 4408.17 9030.10i 0.152532 0.312460i
\(171\) 0 0
\(172\) −9705.23 + 7571.67i −0.328057 + 0.255938i
\(173\) −15660.8 −0.523264 −0.261632 0.965168i \(-0.584261\pi\)
−0.261632 + 0.965168i \(0.584261\pi\)
\(174\) 0 0
\(175\) 94167.5i 3.07486i
\(176\) 18282.3 + 4585.37i 0.590210 + 0.148030i
\(177\) 0 0
\(178\) 12515.6 25638.0i 0.395012 0.809179i
\(179\) 36836.7i 1.14967i 0.818268 + 0.574837i \(0.194935\pi\)
−0.818268 + 0.574837i \(0.805065\pi\)
\(180\) 0 0
\(181\) 56961.0 1.73868 0.869342 0.494211i \(-0.164543\pi\)
0.869342 + 0.494211i \(0.164543\pi\)
\(182\) −6787.20 3313.26i −0.204903 0.100026i
\(183\) 0 0
\(184\) 3728.50 + 17631.8i 0.110128 + 0.520788i
\(185\) −47464.2 −1.38683
\(186\) 0 0
\(187\) 3961.25i 0.113279i
\(188\) −34592.9 + 26988.1i −0.978749 + 0.763584i
\(189\) 0 0
\(190\) 9224.88 + 4503.26i 0.255537 + 0.124744i
\(191\) 39071.7i 1.07102i 0.844530 + 0.535508i \(0.179880\pi\)
−0.844530 + 0.535508i \(0.820120\pi\)
\(192\) 0 0
\(193\) 4051.93 0.108780 0.0543898 0.998520i \(-0.482679\pi\)
0.0543898 + 0.998520i \(0.482679\pi\)
\(194\) −3440.71 + 7048.26i −0.0914206 + 0.187274i
\(195\) 0 0
\(196\) 12450.8 + 15959.2i 0.324104 + 0.415431i
\(197\) 44869.6 1.15617 0.578083 0.815978i \(-0.303801\pi\)
0.578083 + 0.815978i \(0.303801\pi\)
\(198\) 0 0
\(199\) 56256.7i 1.42059i −0.703905 0.710294i \(-0.748562\pi\)
0.703905 0.710294i \(-0.251438\pi\)
\(200\) −97382.3 + 20592.9i −2.43456 + 0.514822i
\(201\) 0 0
\(202\) 13511.3 27677.8i 0.331127 0.678312i
\(203\) 27076.9i 0.657062i
\(204\) 0 0
\(205\) 88358.1 2.10251
\(206\) −13262.2 6474.13i −0.312523 0.152562i
\(207\) 0 0
\(208\) 1942.13 7743.46i 0.0448902 0.178982i
\(209\) −4046.70 −0.0926420
\(210\) 0 0
\(211\) 73103.9i 1.64201i −0.570921 0.821005i \(-0.693414\pi\)
0.570921 0.821005i \(-0.306586\pi\)
\(212\) −45741.7 58630.8i −1.01775 1.30453i
\(213\) 0 0
\(214\) −49394.7 24112.7i −1.07858 0.526525i
\(215\) 35922.8i 0.777129i
\(216\) 0 0
\(217\) −16820.4 −0.357205
\(218\) 32831.0 67254.0i 0.690829 1.41516i
\(219\) 0 0
\(220\) 43369.1 33835.0i 0.896055 0.699070i
\(221\) 1677.78 0.0343519
\(222\) 0 0
\(223\) 75906.6i 1.52641i −0.646159 0.763203i \(-0.723626\pi\)
0.646159 0.763203i \(-0.276374\pi\)
\(224\) −39936.4 + 47426.3i −0.795927 + 0.945200i
\(225\) 0 0
\(226\) 17549.1 35949.3i 0.343589 0.703839i
\(227\) 41237.3i 0.800273i 0.916456 + 0.400136i \(0.131037\pi\)
−0.916456 + 0.400136i \(0.868963\pi\)
\(228\) 0 0
\(229\) 27584.3 0.526005 0.263003 0.964795i \(-0.415287\pi\)
0.263003 + 0.964795i \(0.415287\pi\)
\(230\) 47262.4 + 23071.8i 0.893428 + 0.436139i
\(231\) 0 0
\(232\) −28001.2 + 5921.26i −0.520237 + 0.110012i
\(233\) −49430.2 −0.910502 −0.455251 0.890363i \(-0.650450\pi\)
−0.455251 + 0.890363i \(0.650450\pi\)
\(234\) 0 0
\(235\) 128042.i 2.31855i
\(236\) −3827.99 + 2986.46i −0.0687300 + 0.0536207i
\(237\) 0 0
\(238\) −11709.6 5716.19i −0.206722 0.100914i
\(239\) 112055.i 1.96172i 0.194717 + 0.980859i \(0.437621\pi\)
−0.194717 + 0.980859i \(0.562379\pi\)
\(240\) 0 0
\(241\) 41096.6 0.707573 0.353787 0.935326i \(-0.384894\pi\)
0.353787 + 0.935326i \(0.384894\pi\)
\(242\) 16178.7 33142.0i 0.276257 0.565910i
\(243\) 0 0
\(244\) −9412.18 12064.4i −0.158092 0.202640i
\(245\) 59071.1 0.984109
\(246\) 0 0
\(247\) 1713.97i 0.0280938i
\(248\) −3678.35 17394.7i −0.0598067 0.282822i
\(249\) 0 0
\(250\) −76219.0 + 156134.i −1.21950 + 2.49814i
\(251\) 50848.1i 0.807099i −0.914958 0.403550i \(-0.867776\pi\)
0.914958 0.403550i \(-0.132224\pi\)
\(252\) 0 0
\(253\) −20732.7 −0.323902
\(254\) 67879.2 + 33136.2i 1.05213 + 0.513612i
\(255\) 0 0
\(256\) −57778.9 30928.5i −0.881636 0.471931i
\(257\) −12810.0 −0.193948 −0.0969738 0.995287i \(-0.530916\pi\)
−0.0969738 + 0.995287i \(0.530916\pi\)
\(258\) 0 0
\(259\) 61548.1i 0.917519i
\(260\) −14330.8 18368.9i −0.211994 0.271730i
\(261\) 0 0
\(262\) −106675. 52075.1i −1.55404 0.758625i
\(263\) 31691.3i 0.458172i −0.973406 0.229086i \(-0.926426\pi\)
0.973406 0.229086i \(-0.0735737\pi\)
\(264\) 0 0
\(265\) −217015. −3.09029
\(266\) 5839.50 11962.2i 0.0825301 0.169062i
\(267\) 0 0
\(268\) 87559.1 68310.5i 1.21908 0.951082i
\(269\) 54892.9 0.758598 0.379299 0.925274i \(-0.376165\pi\)
0.379299 + 0.925274i \(0.376165\pi\)
\(270\) 0 0
\(271\) 106332.i 1.44785i −0.689877 0.723927i \(-0.742335\pi\)
0.689877 0.723927i \(-0.257665\pi\)
\(272\) 3350.65 13359.4i 0.0452888 0.180571i
\(273\) 0 0
\(274\) −29243.7 + 59905.5i −0.389521 + 0.797931i
\(275\) 114509.i 1.51416i
\(276\) 0 0
\(277\) −50333.1 −0.655986 −0.327993 0.944680i \(-0.606372\pi\)
−0.327993 + 0.944680i \(0.606372\pi\)
\(278\) −14718.0 7184.78i −0.190440 0.0929660i
\(279\) 0 0
\(280\) 37434.5 + 177025.i 0.477481 + 2.25797i
\(281\) 6096.41 0.0772078 0.0386039 0.999255i \(-0.487709\pi\)
0.0386039 + 0.999255i \(0.487709\pi\)
\(282\) 0 0
\(283\) 51378.2i 0.641513i 0.947162 + 0.320757i \(0.103937\pi\)
−0.947162 + 0.320757i \(0.896063\pi\)
\(284\) 75331.9 58771.3i 0.933990 0.728666i
\(285\) 0 0
\(286\) 8253.30 + 4028.96i 0.100901 + 0.0492562i
\(287\) 114576.i 1.39101i
\(288\) 0 0
\(289\) −80626.4 −0.965343
\(290\) −36640.5 + 75057.8i −0.435678 + 0.892483i
\(291\) 0 0
\(292\) 42705.3 + 54738.8i 0.500859 + 0.641992i
\(293\) −91281.3 −1.06328 −0.531639 0.846971i \(-0.678424\pi\)
−0.531639 + 0.846971i \(0.678424\pi\)
\(294\) 0 0
\(295\) 14168.9i 0.162814i
\(296\) −63649.3 + 13459.6i −0.726457 + 0.153620i
\(297\) 0 0
\(298\) 10298.9 21097.1i 0.115973 0.237570i
\(299\) 8781.29i 0.0982236i
\(300\) 0 0
\(301\) 46582.1 0.514145
\(302\) 119230. + 58203.8i 1.30729 + 0.638171i
\(303\) 0 0
\(304\) 13647.5 + 3422.92i 0.147675 + 0.0370382i
\(305\) −44654.9 −0.480031
\(306\) 0 0
\(307\) 108180.i 1.14781i −0.818923 0.573904i \(-0.805428\pi\)
0.818923 0.573904i \(-0.194572\pi\)
\(308\) −43874.8 56237.9i −0.462502 0.592826i
\(309\) 0 0
\(310\) −46626.7 22761.5i −0.485189 0.236852i
\(311\) 100082.i 1.03475i −0.855760 0.517373i \(-0.826910\pi\)
0.855760 0.517373i \(-0.173090\pi\)
\(312\) 0 0
\(313\) −151791. −1.54937 −0.774687 0.632345i \(-0.782093\pi\)
−0.774687 + 0.632345i \(0.782093\pi\)
\(314\) 38917.4 79722.0i 0.394716 0.808572i
\(315\) 0 0
\(316\) 47984.5 37435.8i 0.480537 0.374898i
\(317\) −112404. −1.11857 −0.559285 0.828976i \(-0.688924\pi\)
−0.559285 + 0.828976i \(0.688924\pi\)
\(318\) 0 0
\(319\) 32925.7i 0.323560i
\(320\) −174882. + 77425.0i −1.70784 + 0.756103i
\(321\) 0 0
\(322\) 29917.8 61286.4i 0.288548 0.591088i
\(323\) 2957.02i 0.0283433i
\(324\) 0 0
\(325\) −48500.0 −0.459172
\(326\) 112524. + 54929.9i 1.05879 + 0.516861i
\(327\) 0 0
\(328\) 118488. 25056.0i 1.10135 0.232897i
\(329\) 166035. 1.53394
\(330\) 0 0
\(331\) 114926.i 1.04897i −0.851420 0.524484i \(-0.824258\pi\)
0.851420 0.524484i \(-0.175742\pi\)
\(332\) 39776.0 31031.8i 0.360865 0.281534i
\(333\) 0 0
\(334\) 93604.0 + 45694.1i 0.839076 + 0.409607i
\(335\) 324090.i 2.88786i
\(336\) 0 0
\(337\) 123292. 1.08562 0.542808 0.839857i \(-0.317361\pi\)
0.542808 + 0.839857i \(0.317361\pi\)
\(338\) −48410.6 + 99168.7i −0.423747 + 0.868043i
\(339\) 0 0
\(340\) −24724.1 31690.9i −0.213876 0.274143i
\(341\) 20453.8 0.175900
\(342\) 0 0
\(343\) 68777.2i 0.584597i
\(344\) 10186.7 + 48172.4i 0.0860831 + 0.407081i
\(345\) 0 0
\(346\) −27480.5 + 56293.6i −0.229548 + 0.470227i
\(347\) 95659.4i 0.794454i −0.917720 0.397227i \(-0.869973\pi\)
0.917720 0.397227i \(-0.130027\pi\)
\(348\) 0 0
\(349\) 43087.1 0.353750 0.176875 0.984233i \(-0.443401\pi\)
0.176875 + 0.984233i \(0.443401\pi\)
\(350\) 338491. + 165239.i 2.76319 + 1.34889i
\(351\) 0 0
\(352\) 48563.1 57670.9i 0.391941 0.465448i
\(353\) 112874. 0.905825 0.452912 0.891555i \(-0.350385\pi\)
0.452912 + 0.891555i \(0.350385\pi\)
\(354\) 0 0
\(355\) 278833.i 2.21252i
\(356\) −70196.1 89976.0i −0.553876 0.709948i
\(357\) 0 0
\(358\) 132412. + 64638.8i 1.03315 + 0.504344i
\(359\) 223134.i 1.73132i 0.500632 + 0.865660i \(0.333101\pi\)
−0.500632 + 0.865660i \(0.666899\pi\)
\(360\) 0 0
\(361\) 127300. 0.976820
\(362\) 99951.6 204750.i 0.762733 1.56245i
\(363\) 0 0
\(364\) −23819.5 + 18583.1i −0.179775 + 0.140254i
\(365\) 202610. 1.52081
\(366\) 0 0
\(367\) 106530.i 0.790933i −0.918481 0.395466i \(-0.870583\pi\)
0.918481 0.395466i \(-0.129417\pi\)
\(368\) 69921.2 + 17536.9i 0.516313 + 0.129496i
\(369\) 0 0
\(370\) −83287.1 + 170613.i −0.608379 + 1.24626i
\(371\) 281410.i 2.04452i
\(372\) 0 0
\(373\) 142881. 1.02697 0.513484 0.858099i \(-0.328355\pi\)
0.513484 + 0.858099i \(0.328355\pi\)
\(374\) 14239.0 + 6950.95i 0.101797 + 0.0496936i
\(375\) 0 0
\(376\) 36309.2 + 171703.i 0.256827 + 1.21452i
\(377\) −13945.7 −0.0981197
\(378\) 0 0
\(379\) 95242.7i 0.663061i −0.943445 0.331530i \(-0.892435\pi\)
0.943445 0.331530i \(-0.107565\pi\)
\(380\) 32374.5 25257.4i 0.224200 0.174913i
\(381\) 0 0
\(382\) 140446. + 68560.6i 0.962459 + 0.469838i
\(383\) 54154.9i 0.369182i 0.982815 + 0.184591i \(0.0590960\pi\)
−0.982815 + 0.184591i \(0.940904\pi\)
\(384\) 0 0
\(385\) −208158. −1.40434
\(386\) 7110.07 14564.9i 0.0477199 0.0977538i
\(387\) 0 0
\(388\) 19297.9 + 24735.7i 0.128188 + 0.164309i
\(389\) −13026.5 −0.0860850 −0.0430425 0.999073i \(-0.513705\pi\)
−0.0430425 + 0.999073i \(0.513705\pi\)
\(390\) 0 0
\(391\) 15149.9i 0.0990959i
\(392\) 79214.2 16751.0i 0.515503 0.109010i
\(393\) 0 0
\(394\) 78734.4 161287.i 0.507191 1.03898i
\(395\) 177609.i 1.13834i
\(396\) 0 0
\(397\) 54407.2 0.345204 0.172602 0.984992i \(-0.444783\pi\)
0.172602 + 0.984992i \(0.444783\pi\)
\(398\) −202218. 98715.7i −1.27660 0.623190i
\(399\) 0 0
\(400\) −96857.9 + 386182.i −0.605362 + 2.41364i
\(401\) −50422.4 −0.313570 −0.156785 0.987633i \(-0.550113\pi\)
−0.156785 + 0.987633i \(0.550113\pi\)
\(402\) 0 0
\(403\) 8663.19i 0.0533418i
\(404\) −75781.0 97134.7i −0.464299 0.595130i
\(405\) 0 0
\(406\) 97329.6 + 47512.8i 0.590463 + 0.288243i
\(407\) 74843.1i 0.451817i
\(408\) 0 0
\(409\) 40833.8 0.244103 0.122052 0.992524i \(-0.461053\pi\)
0.122052 + 0.992524i \(0.461053\pi\)
\(410\) 155045. 317609.i 0.922340 1.88941i
\(411\) 0 0
\(412\) −46543.4 + 36311.5i −0.274198 + 0.213919i
\(413\) 18373.2 0.107717
\(414\) 0 0
\(415\) 147226.i 0.854850i
\(416\) −24426.4 20568.8i −0.141148 0.118857i
\(417\) 0 0
\(418\) −7100.89 + 14546.1i −0.0406406 + 0.0832519i
\(419\) 33332.6i 0.189864i 0.995484 + 0.0949318i \(0.0302633\pi\)
−0.995484 + 0.0949318i \(0.969737\pi\)
\(420\) 0 0
\(421\) 8360.62 0.0471709 0.0235855 0.999722i \(-0.492492\pi\)
0.0235855 + 0.999722i \(0.492492\pi\)
\(422\) −262777. 128278.i −1.47558 0.720324i
\(423\) 0 0
\(424\) −291017. + 61539.7i −1.61877 + 0.342313i
\(425\) −83674.4 −0.463249
\(426\) 0 0
\(427\) 57905.2i 0.317586i
\(428\) −173350. + 135241.i −0.946314 + 0.738280i
\(429\) 0 0
\(430\) 129127. + 63035.1i 0.698360 + 0.340914i
\(431\) 88445.3i 0.476124i −0.971250 0.238062i \(-0.923488\pi\)
0.971250 0.238062i \(-0.0765122\pi\)
\(432\) 0 0
\(433\) 119092. 0.635195 0.317598 0.948226i \(-0.397124\pi\)
0.317598 + 0.948226i \(0.397124\pi\)
\(434\) −29515.4 + 60462.1i −0.156700 + 0.320999i
\(435\) 0 0
\(436\) −184139. 236026.i −0.968664 1.24162i
\(437\) −15476.7 −0.0810429
\(438\) 0 0
\(439\) 119492.i 0.620028i 0.950732 + 0.310014i \(0.100334\pi\)
−0.950732 + 0.310014i \(0.899666\pi\)
\(440\) −45520.7 215264.i −0.235128 1.11190i
\(441\) 0 0
\(442\) 2944.07 6030.90i 0.0150696 0.0308700i
\(443\) 203706.i 1.03800i 0.854776 + 0.518998i \(0.173695\pi\)
−0.854776 + 0.518998i \(0.826305\pi\)
\(444\) 0 0
\(445\) −333036. −1.68179
\(446\) −272851. 133196.i −1.37169 0.669610i
\(447\) 0 0
\(448\) 100399. + 226775.i 0.500235 + 1.12990i
\(449\) −77156.2 −0.382717 −0.191359 0.981520i \(-0.561289\pi\)
−0.191359 + 0.981520i \(0.561289\pi\)
\(450\) 0 0
\(451\) 139326.i 0.684982i
\(452\) −98427.8 126163.i −0.481771 0.617526i
\(453\) 0 0
\(454\) 148230. + 72360.5i 0.719158 + 0.351067i
\(455\) 88165.1i 0.425867i
\(456\) 0 0
\(457\) 280840. 1.34471 0.672353 0.740231i \(-0.265284\pi\)
0.672353 + 0.740231i \(0.265284\pi\)
\(458\) 48403.1 99153.4i 0.230750 0.472690i
\(459\) 0 0
\(460\) 165866. 129403.i 0.783866 0.611544i
\(461\) 401621. 1.88980 0.944898 0.327365i \(-0.106161\pi\)
0.944898 + 0.327365i \(0.106161\pi\)
\(462\) 0 0
\(463\) 59820.5i 0.279054i −0.990218 0.139527i \(-0.955442\pi\)
0.990218 0.139527i \(-0.0445582\pi\)
\(464\) −27850.5 + 111043.i −0.129359 + 0.515767i
\(465\) 0 0
\(466\) −86737.1 + 177680.i −0.399423 + 0.818215i
\(467\) 208473.i 0.955909i 0.878385 + 0.477955i \(0.158622\pi\)
−0.878385 + 0.477955i \(0.841378\pi\)
\(468\) 0 0
\(469\) −420257. −1.91060
\(470\) 460254. + 224679.i 2.08354 + 1.01711i
\(471\) 0 0
\(472\) 4017.91 + 19000.4i 0.0180350 + 0.0852862i
\(473\) −56644.3 −0.253183
\(474\) 0 0
\(475\) 85479.3i 0.378856i
\(476\) −41094.5 + 32060.4i −0.181372 + 0.141500i
\(477\) 0 0
\(478\) 402790. + 196628.i 1.76288 + 0.860575i
\(479\) 160119.i 0.697864i −0.937148 0.348932i \(-0.886544\pi\)
0.937148 0.348932i \(-0.113456\pi\)
\(480\) 0 0
\(481\) −31699.7 −0.137014
\(482\) 72113.7 147724.i 0.310401 0.635855i
\(483\) 0 0
\(484\) −90741.6 116311.i −0.387361 0.496512i
\(485\) 91556.4 0.389229
\(486\) 0 0
\(487\) 371960.i 1.56834i −0.620549 0.784168i \(-0.713090\pi\)
0.620549 0.784168i \(-0.286910\pi\)
\(488\) −59882.0 + 12662.9i −0.251453 + 0.0531734i
\(489\) 0 0
\(490\) 103654. 212335.i 0.431713 0.884361i
\(491\) 66814.9i 0.277147i 0.990352 + 0.138574i \(0.0442517\pi\)
−0.990352 + 0.138574i \(0.955748\pi\)
\(492\) 0 0
\(493\) −24059.7 −0.0989911
\(494\) 6160.99 + 3007.57i 0.0252462 + 0.0123243i
\(495\) 0 0
\(496\) −68980.8 17301.0i −0.280391 0.0703246i
\(497\) −361570. −1.46379
\(498\) 0 0
\(499\) 332728.i 1.33625i −0.744048 0.668127i \(-0.767096\pi\)
0.744048 0.668127i \(-0.232904\pi\)
\(500\) 427490. + 547948.i 1.70996 + 2.19179i
\(501\) 0 0
\(502\) −182777. 89225.0i −0.725293 0.354062i
\(503\) 12673.0i 0.0500892i 0.999686 + 0.0250446i \(0.00797278\pi\)
−0.999686 + 0.0250446i \(0.992027\pi\)
\(504\) 0 0
\(505\) −359533. −1.40980
\(506\) −36380.4 + 74524.9i −0.142091 + 0.291072i
\(507\) 0 0
\(508\) 238220. 185851.i 0.923105 0.720174i
\(509\) 38905.4 0.150167 0.0750834 0.997177i \(-0.476078\pi\)
0.0750834 + 0.997177i \(0.476078\pi\)
\(510\) 0 0
\(511\) 262729.i 1.00616i
\(512\) −212561. + 153419.i −0.810856 + 0.585245i
\(513\) 0 0
\(514\) −22478.3 + 46046.5i −0.0850817 + 0.174289i
\(515\) 172275.i 0.649543i
\(516\) 0 0
\(517\) −201900. −0.755364
\(518\) 221239. + 108001.i 0.824521 + 0.402501i
\(519\) 0 0
\(520\) −91175.0 + 19280.3i −0.337186 + 0.0713027i
\(521\) −28001.3 −0.103158 −0.0515790 0.998669i \(-0.516425\pi\)
−0.0515790 + 0.998669i \(0.516425\pi\)
\(522\) 0 0
\(523\) 306435.i 1.12030i 0.828391 + 0.560151i \(0.189257\pi\)
−0.828391 + 0.560151i \(0.810743\pi\)
\(524\) −374375. + 292074.i −1.36346 + 1.06373i
\(525\) 0 0
\(526\) −113916. 55609.9i −0.411732 0.200993i
\(527\) 14946.1i 0.0538155i
\(528\) 0 0
\(529\) 200548. 0.716652
\(530\) −380805. + 780076.i −1.35566 + 2.77706i
\(531\) 0 0
\(532\) −32752.0 41980.9i −0.115722 0.148330i
\(533\) 59011.4 0.207722
\(534\) 0 0
\(535\) 641634.i 2.24171i
\(536\) −91903.2 434604.i −0.319890 1.51274i
\(537\) 0 0
\(538\) 96322.6 197316.i 0.332785 0.681707i
\(539\) 93145.3i 0.320615i
\(540\) 0 0
\(541\) 387269. 1.32318 0.661590 0.749866i \(-0.269882\pi\)
0.661590 + 0.749866i \(0.269882\pi\)
\(542\) −382217. 186584.i −1.30110 0.635151i
\(543\) 0 0
\(544\) −42141.6 35486.3i −0.142401 0.119912i
\(545\) −873624. −2.94125
\(546\) 0 0
\(547\) 254245.i 0.849724i 0.905258 + 0.424862i \(0.139677\pi\)
−0.905258 + 0.424862i \(0.860323\pi\)
\(548\) 164019. + 210237.i 0.546177 + 0.700080i
\(549\) 0 0
\(550\) −411609. 200933.i −1.36069 0.664240i
\(551\) 24578.7i 0.0809571i
\(552\) 0 0
\(553\) −230311. −0.753120
\(554\) −88321.4 + 180926.i −0.287771 + 0.589496i
\(555\) 0 0
\(556\) −51652.3 + 40297.3i −0.167086 + 0.130355i
\(557\) 154243. 0.497159 0.248580 0.968611i \(-0.420036\pi\)
0.248580 + 0.968611i \(0.420036\pi\)
\(558\) 0 0
\(559\) 23991.6i 0.0767779i
\(560\) 702016. + 176072.i 2.23857 + 0.561454i
\(561\) 0 0
\(562\) 10697.6 21913.9i 0.0338699 0.0693822i
\(563\) 217837.i 0.687251i 0.939107 + 0.343626i \(0.111655\pi\)
−0.939107 + 0.343626i \(0.888345\pi\)
\(564\) 0 0
\(565\) −466978. −1.46285
\(566\) 184682. + 90155.2i 0.576490 + 0.281422i
\(567\) 0 0
\(568\) −79069.4 373914.i −0.245082 1.15898i
\(569\) −224329. −0.692886 −0.346443 0.938071i \(-0.612611\pi\)
−0.346443 + 0.938071i \(0.612611\pi\)
\(570\) 0 0
\(571\) 262311.i 0.804535i −0.915522 0.402268i \(-0.868222\pi\)
0.915522 0.402268i \(-0.131778\pi\)
\(572\) 28964.7 22597.2i 0.0885274 0.0690659i
\(573\) 0 0
\(574\) −411852. 201052.i −1.25002 0.610216i
\(575\) 437941.i 1.32458i
\(576\) 0 0
\(577\) 450994. 1.35462 0.677312 0.735696i \(-0.263145\pi\)
0.677312 + 0.735696i \(0.263145\pi\)
\(578\) −141478. + 289817.i −0.423481 + 0.867497i
\(579\) 0 0
\(580\) 205506. + 263413.i 0.610897 + 0.783036i
\(581\) −190913. −0.565565
\(582\) 0 0
\(583\) 342197.i 1.00679i
\(584\) 271699. 57454.6i 0.796640 0.168461i
\(585\) 0 0
\(586\) −160175. + 328117.i −0.466443 + 0.955505i
\(587\) 355346.i 1.03128i −0.856807 0.515638i \(-0.827555\pi\)
0.856807 0.515638i \(-0.172445\pi\)
\(588\) 0 0
\(589\) 15268.5 0.0440115
\(590\) 50930.9 + 24862.6i 0.146311 + 0.0714238i
\(591\) 0 0
\(592\) −63306.5 + 252409.i −0.180636 + 0.720215i
\(593\) −89819.5 −0.255424 −0.127712 0.991811i \(-0.540763\pi\)
−0.127712 + 0.991811i \(0.540763\pi\)
\(594\) 0 0
\(595\) 152106.i 0.429649i
\(596\) −57763.2 74039.9i −0.162614 0.208436i
\(597\) 0 0
\(598\) 31564.9 + 15408.9i 0.0882678 + 0.0430892i
\(599\) 413022.i 1.15112i 0.817761 + 0.575558i \(0.195215\pi\)
−0.817761 + 0.575558i \(0.804785\pi\)
\(600\) 0 0
\(601\) 258635. 0.716041 0.358020 0.933714i \(-0.383452\pi\)
0.358020 + 0.933714i \(0.383452\pi\)
\(602\) 81739.3 167442.i 0.225548 0.462032i
\(603\) 0 0
\(604\) 418434. 326447.i 1.14697 0.894828i
\(605\) −430512. −1.17618
\(606\) 0 0
\(607\) 308801.i 0.838111i 0.907961 + 0.419055i \(0.137639\pi\)
−0.907961 + 0.419055i \(0.862361\pi\)
\(608\) 36251.8 43050.6i 0.0980668 0.116459i
\(609\) 0 0
\(610\) −78357.6 + 160515.i −0.210582 + 0.431376i
\(611\) 85514.7i 0.229065i
\(612\) 0 0
\(613\) −464349. −1.23573 −0.617865 0.786284i \(-0.712002\pi\)
−0.617865 + 0.786284i \(0.712002\pi\)
\(614\) −388859. 189827.i −1.03147 0.503525i
\(615\) 0 0
\(616\) −279139. + 59028.0i −0.735631 + 0.155560i
\(617\) 507377. 1.33278 0.666392 0.745601i \(-0.267838\pi\)
0.666392 + 0.745601i \(0.267838\pi\)
\(618\) 0 0
\(619\) 282768.i 0.737986i −0.929432 0.368993i \(-0.879703\pi\)
0.929432 0.368993i \(-0.120297\pi\)
\(620\) −163635. + 127662.i −0.425690 + 0.332108i
\(621\) 0 0
\(622\) −359750. 175617.i −0.929865 0.453927i
\(623\) 431857.i 1.11266i
\(624\) 0 0
\(625\) 1.05614e6 2.70372
\(626\) −266353. + 545621.i −0.679686 + 1.39233i
\(627\) 0 0
\(628\) −218276. 279782.i −0.553461 0.709416i
\(629\) −54689.8 −0.138231
\(630\) 0 0
\(631\) 403620.i 1.01371i 0.862031 + 0.506855i \(0.169192\pi\)
−0.862031 + 0.506855i \(0.830808\pi\)
\(632\) −50365.2 238174.i −0.126095 0.596293i
\(633\) 0 0
\(634\) −197239. + 404043.i −0.490699 + 1.00519i
\(635\) 881745.i 2.18673i
\(636\) 0 0
\(637\) 39451.6 0.0972267
\(638\) −118354. 57776.0i −0.290764 0.141940i
\(639\) 0 0
\(640\) −28563.4 + 764487.i −0.0697350 + 1.86642i
\(641\) 362055. 0.881168 0.440584 0.897711i \(-0.354771\pi\)
0.440584 + 0.897711i \(0.354771\pi\)
\(642\) 0 0
\(643\) 400278.i 0.968144i 0.875028 + 0.484072i \(0.160843\pi\)
−0.875028 + 0.484072i \(0.839157\pi\)
\(644\) −167800. 215083.i −0.404595 0.518602i
\(645\) 0 0
\(646\) 10629.2 + 5188.80i 0.0254704 + 0.0124337i
\(647\) 98990.1i 0.236474i 0.992985 + 0.118237i \(0.0377242\pi\)
−0.992985 + 0.118237i \(0.962276\pi\)
\(648\) 0 0
\(649\) −22341.9 −0.0530434
\(650\) −85104.7 + 174336.i −0.201431 + 0.412630i
\(651\) 0 0
\(652\) 394898. 308086.i 0.928945 0.724730i
\(653\) 538330. 1.26247 0.631237 0.775590i \(-0.282547\pi\)
0.631237 + 0.775590i \(0.282547\pi\)
\(654\) 0 0
\(655\) 1.38570e6i 3.22989i
\(656\) 117850. 469879.i 0.273856 1.09189i
\(657\) 0 0
\(658\) 291348. 596824.i 0.672915 1.37846i
\(659\) 145745.i 0.335601i −0.985821 0.167801i \(-0.946334\pi\)
0.985821 0.167801i \(-0.0536665\pi\)
\(660\) 0 0
\(661\) −252352. −0.577568 −0.288784 0.957394i \(-0.593251\pi\)
−0.288784 + 0.957394i \(0.593251\pi\)
\(662\) −413109. 201665.i −0.942646 0.460166i
\(663\) 0 0
\(664\) −41749.4 197430.i −0.0946923 0.447793i
\(665\) −155388. −0.351377
\(666\) 0 0
\(667\) 125925.i 0.283049i
\(668\) 328501. 256285.i 0.736179 0.574341i
\(669\) 0 0
\(670\) −1.16496e6 568693.i −2.59515 1.26686i
\(671\) 70413.3i 0.156390i
\(672\) 0 0
\(673\) 654664. 1.44540 0.722701 0.691161i \(-0.242901\pi\)
0.722701 + 0.691161i \(0.242901\pi\)
\(674\) 216346. 443182.i 0.476243 0.975580i
\(675\) 0 0
\(676\) 271520. + 348030.i 0.594168 + 0.761594i
\(677\) 213512. 0.465849 0.232924 0.972495i \(-0.425171\pi\)
0.232924 + 0.972495i \(0.425171\pi\)
\(678\) 0 0
\(679\) 118724.i 0.257512i
\(680\) −157299. + 33263.2i −0.340180 + 0.0719359i
\(681\) 0 0
\(682\) 35891.1 73522.5i 0.0771645 0.158071i
\(683\) 885039.i 1.89724i 0.316425 + 0.948618i \(0.397517\pi\)
−0.316425 + 0.948618i \(0.602483\pi\)
\(684\) 0 0
\(685\) 778168. 1.65841
\(686\) 247224. + 120686.i 0.525343 + 0.256453i
\(687\) 0 0
\(688\) 191034. + 47912.9i 0.403583 + 0.101222i
\(689\) −144937. −0.305310
\(690\) 0 0
\(691\) 441853.i 0.925384i 0.886519 + 0.462692i \(0.153116\pi\)
−0.886519 + 0.462692i \(0.846884\pi\)
\(692\) 154130. + 197561.i 0.321866 + 0.412562i
\(693\) 0 0
\(694\) −343854. 167857.i −0.713929 0.348514i
\(695\) 191185.i 0.395808i
\(696\) 0 0
\(697\) 101809. 0.209566
\(698\) 75606.6 154879.i 0.155185 0.317894i
\(699\) 0 0
\(700\) 1.18793e6 926777.i 2.42434 1.89138i
\(701\) −340679. −0.693281 −0.346640 0.937998i \(-0.612678\pi\)
−0.346640 + 0.937998i \(0.612678\pi\)
\(702\) 0 0
\(703\) 55869.5i 0.113048i
\(704\) −122086. 275760.i −0.246333 0.556399i
\(705\) 0 0
\(706\) 198064. 405733.i 0.397371 0.814011i
\(707\) 466216.i 0.932715i
\(708\) 0 0
\(709\) −585440. −1.16464 −0.582318 0.812961i \(-0.697854\pi\)
−0.582318 + 0.812961i \(0.697854\pi\)
\(710\) −1.00228e6 489278.i −1.98826 0.970597i
\(711\) 0 0
\(712\) −446600. + 94440.0i −0.880966 + 0.186293i
\(713\) 78226.1 0.153877
\(714\) 0 0
\(715\) 107210.i 0.209711i
\(716\) 464697. 362540.i 0.906449 0.707179i
\(717\) 0 0
\(718\) 802071. + 391542.i 1.55584 + 0.759503i
\(719\) 306988.i 0.593832i 0.954904 + 0.296916i \(0.0959581\pi\)
−0.954904 + 0.296916i \(0.904042\pi\)
\(720\) 0 0
\(721\) 223394. 0.429735
\(722\) 223378. 457589.i 0.428516 0.877811i
\(723\) 0 0
\(724\) −560599. 718565.i −1.06949 1.37085i
\(725\) 695498. 1.32318
\(726\) 0 0
\(727\) 564049.i 1.06721i −0.845735 0.533603i \(-0.820838\pi\)
0.845735 0.533603i \(-0.179162\pi\)
\(728\) 25001.2 + 118229.i 0.0471736 + 0.223081i
\(729\) 0 0
\(730\) 355526. 728293.i 0.667154 1.36666i
\(731\) 41391.4i 0.0774597i
\(732\) 0 0
\(733\) 581920. 1.08307 0.541533 0.840679i \(-0.317844\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(734\) −382929. 186932.i −0.710765 0.346970i
\(735\) 0 0
\(736\) 185731. 220564.i 0.342869 0.407173i
\(737\) 511037. 0.940843
\(738\) 0 0
\(739\) 193774.i 0.354818i 0.984137 + 0.177409i \(0.0567715\pi\)
−0.984137 + 0.177409i \(0.943228\pi\)
\(740\) 467133. + 598762.i 0.853054 + 1.09343i
\(741\) 0 0
\(742\) 1.01155e6 + 493800.i 1.83729 + 0.896899i
\(743\) 88312.5i 0.159972i 0.996796 + 0.0799861i \(0.0254876\pi\)
−0.996796 + 0.0799861i \(0.974512\pi\)
\(744\) 0 0
\(745\) −274050. −0.493762
\(746\) 250719. 513595.i 0.450514 0.922875i
\(747\) 0 0
\(748\) 49971.3 38985.8i 0.0893135 0.0696792i
\(749\) 832024. 1.48311
\(750\) 0 0
\(751\) 547536.i 0.970806i −0.874290 0.485403i \(-0.838673\pi\)
0.874290 0.485403i \(-0.161327\pi\)
\(752\) 680912. + 170779.i 1.20408 + 0.301994i
\(753\) 0 0
\(754\) −24471.0 + 50128.6i −0.0430436 + 0.0881744i
\(755\) 1.54879e6i 2.71705i
\(756\) 0 0
\(757\) −45164.0 −0.0788135 −0.0394068 0.999223i \(-0.512547\pi\)
−0.0394068 + 0.999223i \(0.512547\pi\)
\(758\) −342356. 167126.i −0.595854 0.290874i
\(759\) 0 0
\(760\) −33980.7 160692.i −0.0588308 0.278207i
\(761\) 200370. 0.345989 0.172995 0.984923i \(-0.444656\pi\)
0.172995 + 0.984923i \(0.444656\pi\)
\(762\) 0 0
\(763\) 1.13285e6i 1.94592i
\(764\) 492891. 384536.i 0.844432 0.658795i
\(765\) 0 0
\(766\) 194663. + 95027.7i 0.331762 + 0.161954i
\(767\) 9462.90i 0.0160855i
\(768\) 0 0
\(769\) 425668. 0.719810 0.359905 0.932989i \(-0.382809\pi\)
0.359905 + 0.932989i \(0.382809\pi\)
\(770\) −365263. + 748238.i −0.616061 + 1.26200i
\(771\) 0 0
\(772\) −39878.3 51115.2i −0.0669117 0.0857661i
\(773\) −199528. −0.333922 −0.166961 0.985964i \(-0.553395\pi\)
−0.166961 + 0.985964i \(0.553395\pi\)
\(774\) 0 0
\(775\) 432051.i 0.719335i
\(776\) 122777. 25962.9i 0.203889 0.0431152i
\(777\) 0 0
\(778\) −22858.0 + 46824.5i −0.0377641 + 0.0773595i
\(779\) 104005.i 0.171388i
\(780\) 0 0
\(781\) 439673. 0.720821
\(782\) 54457.2 + 26584.1i 0.0890517 + 0.0434718i
\(783\) 0 0
\(784\) 78787.6 314134.i 0.128182 0.511073i
\(785\) −1.03558e6 −1.68053
\(786\) 0 0
\(787\) 1.03914e6i