Properties

Label 108.5.d.a.55.1
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{26} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.1
Root \(-1.64756 - 0.974628i\) of \(x^{16} - 2 x^{15} + 6 x^{14} - 22 x^{13} + 19 x^{12} + 18 x^{11} + 1423 x^{10} + 660 x^{9} - 7353 x^{8} - 22934 x^{7} - 36353 x^{6} - 16248 x^{5} + 360646 x^{4} + 1077384 x^{3} + 2005641 x^{2} + 2990790 x + 2924100\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.a.55.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +O(q^{10})\) \(q+(-3.81409 - 1.20528i) q^{2} +(13.0946 + 9.19411i) q^{4} -13.3855 q^{5} +25.4062i q^{7} +(-38.8625 - 50.8499i) q^{8} +(51.0536 + 16.1333i) q^{10} -34.7583i q^{11} +116.909 q^{13} +(30.6216 - 96.9015i) q^{14} +(86.9367 + 240.786i) q^{16} -109.608 q^{17} -264.951i q^{19} +(-175.278 - 123.068i) q^{20} +(-41.8936 + 132.571i) q^{22} -890.392i q^{23} -445.828 q^{25} +(-445.900 - 140.908i) q^{26} +(-233.587 + 332.683i) q^{28} -1116.85 q^{29} -1661.48i q^{31} +(-41.3691 - 1023.16i) q^{32} +(418.055 + 132.108i) q^{34} -340.075i q^{35} -1989.22 q^{37} +(-319.341 + 1010.55i) q^{38} +(520.194 + 680.652i) q^{40} +1229.27 q^{41} -3144.02i q^{43} +(319.572 - 455.146i) q^{44} +(-1073.17 + 3396.04i) q^{46} +2361.16i q^{47} +1755.53 q^{49} +(1700.43 + 537.348i) q^{50} +(1530.87 + 1074.87i) q^{52} +2187.65 q^{53} +465.258i q^{55} +(1291.90 - 987.347i) q^{56} +(4259.76 + 1346.12i) q^{58} +1808.52i q^{59} +1510.52 q^{61} +(-2002.56 + 6337.06i) q^{62} +(-1075.42 + 3952.30i) q^{64} -1564.88 q^{65} -5254.33i q^{67} +(-1435.27 - 1007.75i) q^{68} +(-409.886 + 1297.08i) q^{70} +1129.85i q^{71} -6351.81 q^{73} +(7587.07 + 2397.57i) q^{74} +(2435.99 - 3469.43i) q^{76} +883.075 q^{77} +445.921i q^{79} +(-1163.69 - 3223.05i) q^{80} +(-4688.55 - 1481.62i) q^{82} -1116.30i q^{83} +1467.16 q^{85} +(-3789.43 + 11991.6i) q^{86} +(-1767.45 + 1350.79i) q^{88} +10384.7 q^{89} +2970.20i q^{91} +(8186.36 - 11659.3i) q^{92} +(2845.86 - 9005.67i) q^{94} +3546.51i q^{95} +474.819 q^{97} +(-6695.74 - 2115.90i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 14q^{4} + O(q^{10}) \) \( 16q - 14q^{4} - 202q^{10} - 352q^{13} - 206q^{16} + 738q^{22} + 1632q^{25} + 342q^{28} - 2536q^{34} + 3200q^{37} - 2854q^{40} + 36q^{46} - 896q^{49} + 2288q^{52} + 2492q^{58} - 2752q^{61} + 682q^{64} - 14166q^{70} + 8240q^{73} - 33084q^{76} + 68q^{82} + 8800q^{85} + 48294q^{88} + 52596q^{94} - 6928q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.81409 1.20528i −0.953523 0.301320i
\(3\) 0 0
\(4\) 13.0946 + 9.19411i 0.818412 + 0.574632i
\(5\) −13.3855 −0.535421 −0.267710 0.963499i \(-0.586267\pi\)
−0.267710 + 0.963499i \(0.586267\pi\)
\(6\) 0 0
\(7\) 25.4062i 0.518493i 0.965811 + 0.259247i \(0.0834742\pi\)
−0.965811 + 0.259247i \(0.916526\pi\)
\(8\) −38.8625 50.8499i −0.607226 0.794529i
\(9\) 0 0
\(10\) 51.0536 + 16.1333i 0.510536 + 0.161333i
\(11\) 34.7583i 0.287259i −0.989632 0.143629i \(-0.954123\pi\)
0.989632 0.143629i \(-0.0458773\pi\)
\(12\) 0 0
\(13\) 116.909 0.691767 0.345883 0.938278i \(-0.387579\pi\)
0.345883 + 0.938278i \(0.387579\pi\)
\(14\) 30.6216 96.9015i 0.156233 0.494395i
\(15\) 0 0
\(16\) 86.9367 + 240.786i 0.339596 + 0.940571i
\(17\) −109.608 −0.379266 −0.189633 0.981855i \(-0.560730\pi\)
−0.189633 + 0.981855i \(0.560730\pi\)
\(18\) 0 0
\(19\) 264.951i 0.733937i −0.930233 0.366968i \(-0.880396\pi\)
0.930233 0.366968i \(-0.119604\pi\)
\(20\) −175.278 123.068i −0.438195 0.307670i
\(21\) 0 0
\(22\) −41.8936 + 132.571i −0.0865569 + 0.273908i
\(23\) 890.392i 1.68316i −0.540132 0.841580i \(-0.681626\pi\)
0.540132 0.841580i \(-0.318374\pi\)
\(24\) 0 0
\(25\) −445.828 −0.713325
\(26\) −445.900 140.908i −0.659615 0.208443i
\(27\) 0 0
\(28\) −233.587 + 332.683i −0.297943 + 0.424341i
\(29\) −1116.85 −1.32800 −0.664000 0.747733i \(-0.731143\pi\)
−0.664000 + 0.747733i \(0.731143\pi\)
\(30\) 0 0
\(31\) 1661.48i 1.72891i −0.502708 0.864456i \(-0.667663\pi\)
0.502708 0.864456i \(-0.332337\pi\)
\(32\) −41.3691 1023.16i −0.0403995 0.999184i
\(33\) 0 0
\(34\) 418.055 + 132.108i 0.361639 + 0.114281i
\(35\) 340.075i 0.277612i
\(36\) 0 0
\(37\) −1989.22 −1.45305 −0.726523 0.687142i \(-0.758865\pi\)
−0.726523 + 0.687142i \(0.758865\pi\)
\(38\) −319.341 + 1010.55i −0.221150 + 0.699826i
\(39\) 0 0
\(40\) 520.194 + 680.652i 0.325121 + 0.425407i
\(41\) 1229.27 0.731274 0.365637 0.930758i \(-0.380851\pi\)
0.365637 + 0.930758i \(0.380851\pi\)
\(42\) 0 0
\(43\) 3144.02i 1.70039i −0.526469 0.850194i \(-0.676484\pi\)
0.526469 0.850194i \(-0.323516\pi\)
\(44\) 319.572 455.146i 0.165068 0.235096i
\(45\) 0 0
\(46\) −1073.17 + 3396.04i −0.507171 + 1.60493i
\(47\) 2361.16i 1.06888i 0.845206 + 0.534440i \(0.179478\pi\)
−0.845206 + 0.534440i \(0.820522\pi\)
\(48\) 0 0
\(49\) 1755.53 0.731165
\(50\) 1700.43 + 537.348i 0.680172 + 0.214939i
\(51\) 0 0
\(52\) 1530.87 + 1074.87i 0.566150 + 0.397511i
\(53\) 2187.65 0.778800 0.389400 0.921069i \(-0.372682\pi\)
0.389400 + 0.921069i \(0.372682\pi\)
\(54\) 0 0
\(55\) 465.258i 0.153804i
\(56\) 1291.90 987.347i 0.411958 0.314843i
\(57\) 0 0
\(58\) 4259.76 + 1346.12i 1.26628 + 0.400154i
\(59\) 1808.52i 0.519540i 0.965671 + 0.259770i \(0.0836467\pi\)
−0.965671 + 0.259770i \(0.916353\pi\)
\(60\) 0 0
\(61\) 1510.52 0.405943 0.202972 0.979185i \(-0.434940\pi\)
0.202972 + 0.979185i \(0.434940\pi\)
\(62\) −2002.56 + 6337.06i −0.520957 + 1.64856i
\(63\) 0 0
\(64\) −1075.42 + 3952.30i −0.262553 + 0.964918i
\(65\) −1564.88 −0.370386
\(66\) 0 0
\(67\) 5254.33i 1.17049i −0.810856 0.585245i \(-0.800998\pi\)
0.810856 0.585245i \(-0.199002\pi\)
\(68\) −1435.27 1007.75i −0.310396 0.217938i
\(69\) 0 0
\(70\) −409.886 + 1297.08i −0.0836502 + 0.264709i
\(71\) 1129.85i 0.224133i 0.993701 + 0.112067i \(0.0357470\pi\)
−0.993701 + 0.112067i \(0.964253\pi\)
\(72\) 0 0
\(73\) −6351.81 −1.19193 −0.595966 0.803010i \(-0.703231\pi\)
−0.595966 + 0.803010i \(0.703231\pi\)
\(74\) 7587.07 + 2397.57i 1.38551 + 0.437833i
\(75\) 0 0
\(76\) 2435.99 3469.43i 0.421744 0.600663i
\(77\) 883.075 0.148942
\(78\) 0 0
\(79\) 445.921i 0.0714502i 0.999362 + 0.0357251i \(0.0113741\pi\)
−0.999362 + 0.0357251i \(0.988626\pi\)
\(80\) −1163.69 3223.05i −0.181827 0.503601i
\(81\) 0 0
\(82\) −4688.55 1481.62i −0.697286 0.220348i
\(83\) 1116.30i 0.162040i −0.996712 0.0810202i \(-0.974182\pi\)
0.996712 0.0810202i \(-0.0258178\pi\)
\(84\) 0 0
\(85\) 1467.16 0.203067
\(86\) −3789.43 + 11991.6i −0.512362 + 1.62136i
\(87\) 0 0
\(88\) −1767.45 + 1350.79i −0.228235 + 0.174431i
\(89\) 10384.7 1.31104 0.655520 0.755178i \(-0.272450\pi\)
0.655520 + 0.755178i \(0.272450\pi\)
\(90\) 0 0
\(91\) 2970.20i 0.358676i
\(92\) 8186.36 11659.3i 0.967198 1.37752i
\(93\) 0 0
\(94\) 2845.86 9005.67i 0.322075 1.01920i
\(95\) 3546.51i 0.392965i
\(96\) 0 0
\(97\) 474.819 0.0504643 0.0252321 0.999682i \(-0.491968\pi\)
0.0252321 + 0.999682i \(0.491968\pi\)
\(98\) −6695.74 2115.90i −0.697182 0.220315i
\(99\) 0 0
\(100\) −5837.94 4098.99i −0.583794 0.409899i
\(101\) −15785.2 −1.54742 −0.773709 0.633542i \(-0.781601\pi\)
−0.773709 + 0.633542i \(0.781601\pi\)
\(102\) 0 0
\(103\) 3784.74i 0.356748i 0.983963 + 0.178374i \(0.0570837\pi\)
−0.983963 + 0.178374i \(0.942916\pi\)
\(104\) −4543.36 5944.78i −0.420059 0.549629i
\(105\) 0 0
\(106\) −8343.89 2636.73i −0.742603 0.234668i
\(107\) 12301.5i 1.07446i −0.843435 0.537231i \(-0.819470\pi\)
0.843435 0.537231i \(-0.180530\pi\)
\(108\) 0 0
\(109\) 530.931 0.0446874 0.0223437 0.999750i \(-0.492887\pi\)
0.0223437 + 0.999750i \(0.492887\pi\)
\(110\) 560.767 1774.54i 0.0463444 0.146656i
\(111\) 0 0
\(112\) −6117.46 + 2208.73i −0.487680 + 0.176078i
\(113\) −11047.5 −0.865183 −0.432591 0.901590i \(-0.642401\pi\)
−0.432591 + 0.901590i \(0.642401\pi\)
\(114\) 0 0
\(115\) 11918.4i 0.901199i
\(116\) −14624.7 10268.4i −1.08685 0.763111i
\(117\) 0 0
\(118\) 2179.77 6897.85i 0.156548 0.495393i
\(119\) 2784.72i 0.196647i
\(120\) 0 0
\(121\) 13432.9 0.917482
\(122\) −5761.24 1820.60i −0.387076 0.122319i
\(123\) 0 0
\(124\) 15275.9 21756.5i 0.993488 1.41496i
\(125\) 14333.6 0.917349
\(126\) 0 0
\(127\) 25919.1i 1.60699i 0.595314 + 0.803493i \(0.297028\pi\)
−0.595314 + 0.803493i \(0.702972\pi\)
\(128\) 8865.37 13778.3i 0.541099 0.840959i
\(129\) 0 0
\(130\) 5968.60 + 1886.12i 0.353172 + 0.111605i
\(131\) 15334.4i 0.893559i −0.894644 0.446779i \(-0.852571\pi\)
0.894644 0.446779i \(-0.147429\pi\)
\(132\) 0 0
\(133\) 6731.40 0.380541
\(134\) −6332.95 + 20040.5i −0.352693 + 1.11609i
\(135\) 0 0
\(136\) 4259.63 + 5573.54i 0.230300 + 0.301338i
\(137\) −29216.9 −1.55666 −0.778329 0.627856i \(-0.783933\pi\)
−0.778329 + 0.627856i \(0.783933\pi\)
\(138\) 0 0
\(139\) 27071.9i 1.40116i 0.713571 + 0.700582i \(0.247076\pi\)
−0.713571 + 0.700582i \(0.752924\pi\)
\(140\) 3126.68 4453.14i 0.159525 0.227201i
\(141\) 0 0
\(142\) 1361.79 4309.37i 0.0675359 0.213716i
\(143\) 4063.54i 0.198716i
\(144\) 0 0
\(145\) 14949.6 0.711039
\(146\) 24226.4 + 7655.72i 1.13653 + 0.359154i
\(147\) 0 0
\(148\) −26048.0 18289.1i −1.18919 0.834967i
\(149\) 27443.5 1.23614 0.618068 0.786125i \(-0.287916\pi\)
0.618068 + 0.786125i \(0.287916\pi\)
\(150\) 0 0
\(151\) 5044.14i 0.221225i 0.993864 + 0.110612i \(0.0352812\pi\)
−0.993864 + 0.110612i \(0.964719\pi\)
\(152\) −13472.7 + 10296.7i −0.583134 + 0.445666i
\(153\) 0 0
\(154\) −3368.13 1064.35i −0.142019 0.0448792i
\(155\) 22239.8i 0.925695i
\(156\) 0 0
\(157\) −11939.3 −0.484374 −0.242187 0.970230i \(-0.577865\pi\)
−0.242187 + 0.970230i \(0.577865\pi\)
\(158\) 537.460 1700.78i 0.0215294 0.0681294i
\(159\) 0 0
\(160\) 553.747 + 13695.6i 0.0216307 + 0.534984i
\(161\) 22621.4 0.872707
\(162\) 0 0
\(163\) 24289.6i 0.914207i −0.889414 0.457103i \(-0.848887\pi\)
0.889414 0.457103i \(-0.151113\pi\)
\(164\) 16096.8 + 11302.1i 0.598483 + 0.420213i
\(165\) 0 0
\(166\) −1345.45 + 4257.66i −0.0488261 + 0.154509i
\(167\) 14400.8i 0.516363i 0.966096 + 0.258181i \(0.0831232\pi\)
−0.966096 + 0.258181i \(0.916877\pi\)
\(168\) 0 0
\(169\) −14893.4 −0.521459
\(170\) −5595.88 1768.34i −0.193629 0.0611882i
\(171\) 0 0
\(172\) 28906.5 41169.6i 0.977098 1.39162i
\(173\) −35985.6 −1.20237 −0.601183 0.799111i \(-0.705304\pi\)
−0.601183 + 0.799111i \(0.705304\pi\)
\(174\) 0 0
\(175\) 11326.8i 0.369854i
\(176\) 8369.32 3021.77i 0.270187 0.0975520i
\(177\) 0 0
\(178\) −39608.4 12516.5i −1.25011 0.395043i
\(179\) 4221.93i 0.131766i −0.997827 0.0658832i \(-0.979014\pi\)
0.997827 0.0658832i \(-0.0209865\pi\)
\(180\) 0 0
\(181\) 18881.9 0.576353 0.288176 0.957577i \(-0.406951\pi\)
0.288176 + 0.957577i \(0.406951\pi\)
\(182\) 3579.93 11328.6i 0.108077 0.342006i
\(183\) 0 0
\(184\) −45276.3 + 34602.8i −1.33732 + 1.02206i
\(185\) 26626.7 0.777991
\(186\) 0 0
\(187\) 3809.78i 0.108947i
\(188\) −21708.7 + 30918.4i −0.614213 + 0.874784i
\(189\) 0 0
\(190\) 4274.54 13526.7i 0.118408 0.374701i
\(191\) 67734.8i 1.85671i 0.371689 + 0.928357i \(0.378779\pi\)
−0.371689 + 0.928357i \(0.621221\pi\)
\(192\) 0 0
\(193\) −52984.0 −1.42243 −0.711213 0.702976i \(-0.751854\pi\)
−0.711213 + 0.702976i \(0.751854\pi\)
\(194\) −1811.00 572.290i −0.0481189 0.0152059i
\(195\) 0 0
\(196\) 22987.9 + 16140.5i 0.598394 + 0.420151i
\(197\) 39007.1 1.00511 0.502553 0.864547i \(-0.332394\pi\)
0.502553 + 0.864547i \(0.332394\pi\)
\(198\) 0 0
\(199\) 58823.4i 1.48540i −0.669623 0.742701i \(-0.733544\pi\)
0.669623 0.742701i \(-0.266456\pi\)
\(200\) 17326.0 + 22670.3i 0.433150 + 0.566757i
\(201\) 0 0
\(202\) 60206.2 + 19025.6i 1.47550 + 0.466268i
\(203\) 28374.8i 0.688559i
\(204\) 0 0
\(205\) −16454.4 −0.391539
\(206\) 4561.68 14435.3i 0.107495 0.340167i
\(207\) 0 0
\(208\) 10163.6 + 28150.0i 0.234921 + 0.650656i
\(209\) −9209.25 −0.210830
\(210\) 0 0
\(211\) 8214.89i 0.184517i 0.995735 + 0.0922586i \(0.0294087\pi\)
−0.995735 + 0.0922586i \(0.970591\pi\)
\(212\) 28646.4 + 20113.5i 0.637379 + 0.447523i
\(213\) 0 0
\(214\) −14826.8 + 46919.1i −0.323758 + 1.02452i
\(215\) 42084.3i 0.910423i
\(216\) 0 0
\(217\) 42212.0 0.896429
\(218\) −2025.02 639.921i −0.0426105 0.0134652i
\(219\) 0 0
\(220\) −4277.63 + 6092.36i −0.0883808 + 0.125875i
\(221\) −12814.1 −0.262364
\(222\) 0 0
\(223\) 36518.9i 0.734357i −0.930150 0.367179i \(-0.880324\pi\)
0.930150 0.367179i \(-0.119676\pi\)
\(224\) 25994.7 1051.03i 0.518070 0.0209469i
\(225\) 0 0
\(226\) 42136.2 + 13315.4i 0.824972 + 0.260697i
\(227\) 83547.6i 1.62137i −0.585483 0.810685i \(-0.699095\pi\)
0.585483 0.810685i \(-0.300905\pi\)
\(228\) 0 0
\(229\) −8882.43 −0.169379 −0.0846897 0.996407i \(-0.526990\pi\)
−0.0846897 + 0.996407i \(0.526990\pi\)
\(230\) 14365.0 45457.7i 0.271550 0.859314i
\(231\) 0 0
\(232\) 43403.5 + 56791.6i 0.806396 + 1.05513i
\(233\) 5239.47 0.0965108 0.0482554 0.998835i \(-0.484634\pi\)
0.0482554 + 0.998835i \(0.484634\pi\)
\(234\) 0 0
\(235\) 31605.3i 0.572301i
\(236\) −16627.7 + 23681.8i −0.298544 + 0.425197i
\(237\) 0 0
\(238\) −3356.37 + 10621.2i −0.0592537 + 0.187507i
\(239\) 5031.54i 0.0880856i 0.999030 + 0.0440428i \(0.0140238\pi\)
−0.999030 + 0.0440428i \(0.985976\pi\)
\(240\) 0 0
\(241\) 37868.6 0.651996 0.325998 0.945370i \(-0.394300\pi\)
0.325998 + 0.945370i \(0.394300\pi\)
\(242\) −51234.2 16190.4i −0.874841 0.276456i
\(243\) 0 0
\(244\) 19779.6 + 13887.8i 0.332229 + 0.233268i
\(245\) −23498.6 −0.391481
\(246\) 0 0
\(247\) 30975.1i 0.507713i
\(248\) −84486.3 + 64569.4i −1.37367 + 1.04984i
\(249\) 0 0
\(250\) −54669.6 17276.0i −0.874714 0.276416i
\(251\) 91242.6i 1.44827i −0.689657 0.724136i \(-0.742239\pi\)
0.689657 0.724136i \(-0.257761\pi\)
\(252\) 0 0
\(253\) −30948.5 −0.483502
\(254\) 31239.8 98857.8i 0.484218 1.53230i
\(255\) 0 0
\(256\) −50420.0 + 41866.3i −0.769349 + 0.638829i
\(257\) −73598.9 −1.11431 −0.557154 0.830409i \(-0.688107\pi\)
−0.557154 + 0.830409i \(0.688107\pi\)
\(258\) 0 0
\(259\) 50538.5i 0.753395i
\(260\) −20491.5 14387.7i −0.303128 0.212836i
\(261\) 0 0
\(262\) −18482.2 + 58486.7i −0.269247 + 0.852029i
\(263\) 5368.69i 0.0776170i −0.999247 0.0388085i \(-0.987644\pi\)
0.999247 0.0388085i \(-0.0123562\pi\)
\(264\) 0 0
\(265\) −29282.8 −0.416985
\(266\) −25674.2 8113.23i −0.362855 0.114665i
\(267\) 0 0
\(268\) 48308.9 68803.3i 0.672601 0.957943i
\(269\) −90206.5 −1.24662 −0.623308 0.781976i \(-0.714212\pi\)
−0.623308 + 0.781976i \(0.714212\pi\)
\(270\) 0 0
\(271\) 13029.5i 0.177415i 0.996058 + 0.0887073i \(0.0282736\pi\)
−0.996058 + 0.0887073i \(0.971726\pi\)
\(272\) −9528.94 26392.1i −0.128797 0.356727i
\(273\) 0 0
\(274\) 111436. + 35214.6i 1.48431 + 0.469053i
\(275\) 15496.2i 0.204909i
\(276\) 0 0
\(277\) −21241.5 −0.276837 −0.138419 0.990374i \(-0.544202\pi\)
−0.138419 + 0.990374i \(0.544202\pi\)
\(278\) 32629.3 103255.i 0.422200 1.33604i
\(279\) 0 0
\(280\) −17292.7 + 13216.1i −0.220571 + 0.168573i
\(281\) 110158. 1.39510 0.697549 0.716537i \(-0.254274\pi\)
0.697549 + 0.716537i \(0.254274\pi\)
\(282\) 0 0
\(283\) 51723.9i 0.645830i −0.946428 0.322915i \(-0.895337\pi\)
0.946428 0.322915i \(-0.104663\pi\)
\(284\) −10388.0 + 14795.0i −0.128794 + 0.183433i
\(285\) 0 0
\(286\) −4897.72 + 15498.7i −0.0598772 + 0.189480i
\(287\) 31231.1i 0.379161i
\(288\) 0 0
\(289\) −71507.1 −0.856157
\(290\) −57019.1 18018.5i −0.677992 0.214250i
\(291\) 0 0
\(292\) −83174.3 58399.2i −0.975492 0.684922i
\(293\) 20425.2 0.237920 0.118960 0.992899i \(-0.462044\pi\)
0.118960 + 0.992899i \(0.462044\pi\)
\(294\) 0 0
\(295\) 24207.9i 0.278172i
\(296\) 77306.1 + 101152.i 0.882328 + 1.15449i
\(297\) 0 0
\(298\) −104672. 33077.1i −1.17868 0.372473i
\(299\) 104094.i 1.16435i
\(300\) 0 0
\(301\) 79877.5 0.881640
\(302\) 6079.61 19238.8i 0.0666595 0.210943i
\(303\) 0 0
\(304\) 63796.6 23034.0i 0.690320 0.249242i
\(305\) −20219.0 −0.217350
\(306\) 0 0
\(307\) 70255.6i 0.745426i 0.927947 + 0.372713i \(0.121572\pi\)
−0.927947 + 0.372713i \(0.878428\pi\)
\(308\) 11563.5 + 8119.09i 0.121896 + 0.0855867i
\(309\) 0 0
\(310\) 26805.3 84824.8i 0.278931 0.882672i
\(311\) 132510.i 1.37002i 0.728532 + 0.685012i \(0.240203\pi\)
−0.728532 + 0.685012i \(0.759797\pi\)
\(312\) 0 0
\(313\) −95836.7 −0.978234 −0.489117 0.872218i \(-0.662681\pi\)
−0.489117 + 0.872218i \(0.662681\pi\)
\(314\) 45537.7 + 14390.3i 0.461861 + 0.145952i
\(315\) 0 0
\(316\) −4099.84 + 5839.15i −0.0410576 + 0.0584757i
\(317\) 91986.8 0.915392 0.457696 0.889109i \(-0.348675\pi\)
0.457696 + 0.889109i \(0.348675\pi\)
\(318\) 0 0
\(319\) 38819.7i 0.381480i
\(320\) 14395.0 52903.6i 0.140576 0.516637i
\(321\) 0 0
\(322\) −86280.3 27265.2i −0.832146 0.262965i
\(323\) 29040.7i 0.278357i
\(324\) 0 0
\(325\) −52121.1 −0.493454
\(326\) −29275.8 + 92642.6i −0.275469 + 0.871717i
\(327\) 0 0
\(328\) −47772.5 62508.3i −0.444049 0.581018i
\(329\) −59987.9 −0.554207
\(330\) 0 0
\(331\) 109298.i 0.997602i 0.866717 + 0.498801i \(0.166226\pi\)
−0.866717 + 0.498801i \(0.833774\pi\)
\(332\) 10263.4 14617.5i 0.0931136 0.132616i
\(333\) 0 0
\(334\) 17357.1 54926.1i 0.155591 0.492364i
\(335\) 70331.9i 0.626705i
\(336\) 0 0
\(337\) 198743. 1.74998 0.874989 0.484144i \(-0.160869\pi\)
0.874989 + 0.484144i \(0.160869\pi\)
\(338\) 56804.7 + 17950.7i 0.497223 + 0.157126i
\(339\) 0 0
\(340\) 19211.8 + 13489.2i 0.166192 + 0.116689i
\(341\) −57750.4 −0.496645
\(342\) 0 0
\(343\) 105601.i 0.897597i
\(344\) −159873. + 122184.i −1.35101 + 1.03252i
\(345\) 0 0
\(346\) 137252. + 43372.8i 1.14648 + 0.362297i
\(347\) 167328.i 1.38966i −0.719174 0.694830i \(-0.755480\pi\)
0.719174 0.694830i \(-0.244520\pi\)
\(348\) 0 0
\(349\) 188371. 1.54655 0.773274 0.634072i \(-0.218618\pi\)
0.773274 + 0.634072i \(0.218618\pi\)
\(350\) −13652.0 + 43201.4i −0.111445 + 0.352664i
\(351\) 0 0
\(352\) −35563.4 + 1437.92i −0.287024 + 0.0116051i
\(353\) 115038. 0.923189 0.461594 0.887091i \(-0.347278\pi\)
0.461594 + 0.887091i \(0.347278\pi\)
\(354\) 0 0
\(355\) 15123.7i 0.120005i
\(356\) 135984. + 95478.5i 1.07297 + 0.753365i
\(357\) 0 0
\(358\) −5088.61 + 16102.8i −0.0397039 + 0.125642i
\(359\) 117266.i 0.909882i 0.890522 + 0.454941i \(0.150340\pi\)
−0.890522 + 0.454941i \(0.849660\pi\)
\(360\) 0 0
\(361\) 60121.9 0.461337
\(362\) −72017.3 22758.0i −0.549566 0.173667i
\(363\) 0 0
\(364\) −27308.3 + 38893.5i −0.206107 + 0.293545i
\(365\) 85022.2 0.638185
\(366\) 0 0
\(367\) 263083.i 1.95326i 0.214929 + 0.976630i \(0.431048\pi\)
−0.214929 + 0.976630i \(0.568952\pi\)
\(368\) 214394. 77407.7i 1.58313 0.571595i
\(369\) 0 0
\(370\) −101557. 32092.7i −0.741832 0.234425i
\(371\) 55579.8i 0.403802i
\(372\) 0 0
\(373\) −34514.3 −0.248074 −0.124037 0.992278i \(-0.539584\pi\)
−0.124037 + 0.992278i \(0.539584\pi\)
\(374\) 4591.86 14530.9i 0.0328281 0.103884i
\(375\) 0 0
\(376\) 120064. 91760.4i 0.849256 0.649052i
\(377\) −130569. −0.918666
\(378\) 0 0
\(379\) 152446.i 1.06130i 0.847591 + 0.530650i \(0.178052\pi\)
−0.847591 + 0.530650i \(0.821948\pi\)
\(380\) −32607.0 + 46440.1i −0.225810 + 0.321607i
\(381\) 0 0
\(382\) 81639.5 258347.i 0.559466 1.77042i
\(383\) 154427.i 1.05275i 0.850253 + 0.526375i \(0.176449\pi\)
−0.850253 + 0.526375i \(0.823551\pi\)
\(384\) 0 0
\(385\) −11820.4 −0.0797465
\(386\) 202086. + 63860.6i 1.35632 + 0.428606i
\(387\) 0 0
\(388\) 6217.56 + 4365.53i 0.0413006 + 0.0289984i
\(389\) 109925. 0.726435 0.363217 0.931704i \(-0.381678\pi\)
0.363217 + 0.931704i \(0.381678\pi\)
\(390\) 0 0
\(391\) 97593.9i 0.638365i
\(392\) −68224.1 89268.3i −0.443982 0.580932i
\(393\) 0 0
\(394\) −148777. 47014.6i −0.958391 0.302859i
\(395\) 5968.88i 0.0382559i
\(396\) 0 0
\(397\) −148277. −0.940789 −0.470394 0.882456i \(-0.655888\pi\)
−0.470394 + 0.882456i \(0.655888\pi\)
\(398\) −70898.8 + 224358.i −0.447582 + 1.41636i
\(399\) 0 0
\(400\) −38758.8 107349.i −0.242242 0.670933i
\(401\) 144225. 0.896913 0.448457 0.893805i \(-0.351974\pi\)
0.448457 + 0.893805i \(0.351974\pi\)
\(402\) 0 0
\(403\) 194242.i 1.19600i
\(404\) −206701. 145131.i −1.26642 0.889195i
\(405\) 0 0
\(406\) −34199.7 + 108224.i −0.207477 + 0.656557i
\(407\) 69141.9i 0.417400i
\(408\) 0 0
\(409\) 54102.7 0.323424 0.161712 0.986838i \(-0.448298\pi\)
0.161712 + 0.986838i \(0.448298\pi\)
\(410\) 62758.7 + 19832.2i 0.373342 + 0.117979i
\(411\) 0 0
\(412\) −34797.3 + 49559.6i −0.204999 + 0.291967i
\(413\) −45947.5 −0.269378
\(414\) 0 0
\(415\) 14942.2i 0.0867598i
\(416\) −4836.40 119617.i −0.0279470 0.691202i
\(417\) 0 0
\(418\) 35124.9 + 11099.7i 0.201031 + 0.0635273i
\(419\) 283173.i 1.61296i −0.591261 0.806480i \(-0.701370\pi\)
0.591261 0.806480i \(-0.298630\pi\)
\(420\) 0 0
\(421\) 2339.30 0.0131984 0.00659920 0.999978i \(-0.497899\pi\)
0.00659920 + 0.999978i \(0.497899\pi\)
\(422\) 9901.26 31332.4i 0.0555988 0.175941i
\(423\) 0 0
\(424\) −85017.4 111242.i −0.472908 0.618779i
\(425\) 48866.3 0.270540
\(426\) 0 0
\(427\) 38376.4i 0.210479i
\(428\) 113102. 161083.i 0.617420 0.879353i
\(429\) 0 0
\(430\) 50723.5 160513.i 0.274329 0.868109i
\(431\) 250884.i 1.35057i 0.737555 + 0.675287i \(0.235980\pi\)
−0.737555 + 0.675287i \(0.764020\pi\)
\(432\) 0 0
\(433\) −28542.2 −0.152234 −0.0761169 0.997099i \(-0.524252\pi\)
−0.0761169 + 0.997099i \(0.524252\pi\)
\(434\) −161000. 50877.3i −0.854766 0.270112i
\(435\) 0 0
\(436\) 6952.32 + 4881.44i 0.0365727 + 0.0256788i
\(437\) −235910. −1.23533
\(438\) 0 0
\(439\) 204222.i 1.05968i −0.848099 0.529838i \(-0.822253\pi\)
0.848099 0.529838i \(-0.177747\pi\)
\(440\) 23658.3 18081.1i 0.122202 0.0933940i
\(441\) 0 0
\(442\) 48874.2 + 15444.6i 0.250170 + 0.0790555i
\(443\) 319736.i 1.62924i −0.579997 0.814619i \(-0.696946\pi\)
0.579997 0.814619i \(-0.303054\pi\)
\(444\) 0 0
\(445\) −139005. −0.701958
\(446\) −44015.5 + 139286.i −0.221277 + 0.700227i
\(447\) 0 0
\(448\) −100413. 27322.2i −0.500303 0.136132i
\(449\) −325480. −1.61448 −0.807239 0.590225i \(-0.799039\pi\)
−0.807239 + 0.590225i \(0.799039\pi\)
\(450\) 0 0
\(451\) 42727.4i 0.210065i
\(452\) −144663. 101572.i −0.708076 0.497162i
\(453\) 0 0
\(454\) −100698. + 318658.i −0.488552 + 1.54601i
\(455\) 39757.6i 0.192043i
\(456\) 0 0
\(457\) 1088.11 0.00521003 0.00260501 0.999997i \(-0.499171\pi\)
0.00260501 + 0.999997i \(0.499171\pi\)
\(458\) 33878.4 + 10705.8i 0.161507 + 0.0510375i
\(459\) 0 0
\(460\) −109579. + 156066.i −0.517858 + 0.737552i
\(461\) 127607. 0.600445 0.300222 0.953869i \(-0.402939\pi\)
0.300222 + 0.953869i \(0.402939\pi\)
\(462\) 0 0
\(463\) 119526.i 0.557572i −0.960353 0.278786i \(-0.910068\pi\)
0.960353 0.278786i \(-0.0899320\pi\)
\(464\) −97095.0 268922.i −0.450984 1.24908i
\(465\) 0 0
\(466\) −19983.8 6315.04i −0.0920252 0.0290807i
\(467\) 351752.i 1.61288i −0.591314 0.806442i \(-0.701391\pi\)
0.591314 0.806442i \(-0.298609\pi\)
\(468\) 0 0
\(469\) 133492. 0.606891
\(470\) −38093.3 + 120546.i −0.172446 + 0.545702i
\(471\) 0 0
\(472\) 91962.8 70283.5i 0.412789 0.315478i
\(473\) −109281. −0.488451
\(474\) 0 0
\(475\) 118123.i 0.523535i
\(476\) 25603.0 36464.7i 0.113000 0.160938i
\(477\) 0 0
\(478\) 6064.42 19190.8i 0.0265420 0.0839917i
\(479\) 44703.0i 0.194835i −0.995244 0.0974173i \(-0.968942\pi\)
0.995244 0.0974173i \(-0.0310581\pi\)
\(480\) 0 0
\(481\) −232557. −1.00517
\(482\) −144434. 45642.3i −0.621693 0.196460i
\(483\) 0 0
\(484\) 175898. + 123503.i 0.750879 + 0.527215i
\(485\) −6355.69 −0.0270196
\(486\) 0 0
\(487\) 171347.i 0.722469i −0.932475 0.361235i \(-0.882355\pi\)
0.932475 0.361235i \(-0.117645\pi\)
\(488\) −58702.4 76809.5i −0.246499 0.322534i
\(489\) 0 0
\(490\) 89625.9 + 28322.5i 0.373286 + 0.117961i
\(491\) 198915.i 0.825095i 0.910936 + 0.412548i \(0.135361\pi\)
−0.910936 + 0.412548i \(0.864639\pi\)
\(492\) 0 0
\(493\) 122415. 0.503665
\(494\) −37333.7 + 118142.i −0.152984 + 0.484116i
\(495\) 0 0
\(496\) 400063. 144444.i 1.62617 0.587132i
\(497\) −28705.3 −0.116211
\(498\) 0 0
\(499\) 114935.i 0.461585i −0.973003 0.230793i \(-0.925868\pi\)
0.973003 0.230793i \(-0.0741319\pi\)
\(500\) 187692. + 131785.i 0.750770 + 0.527138i
\(501\) 0 0
\(502\) −109973. + 348008.i −0.436394 + 1.38096i
\(503\) 95086.4i 0.375822i −0.982186 0.187911i \(-0.939828\pi\)
0.982186 0.187911i \(-0.0601717\pi\)
\(504\) 0 0
\(505\) 211293. 0.828519
\(506\) 118040. + 37301.7i 0.461031 + 0.145689i
\(507\) 0 0
\(508\) −238303. + 339400.i −0.923426 + 1.31518i
\(509\) 23238.2 0.0896947 0.0448474 0.998994i \(-0.485720\pi\)
0.0448474 + 0.998994i \(0.485720\pi\)
\(510\) 0 0
\(511\) 161375.i 0.618009i
\(512\) 242767. 98911.6i 0.926084 0.377318i
\(513\) 0 0
\(514\) 280713. + 88707.4i 1.06252 + 0.335764i
\(515\) 50660.7i 0.191010i
\(516\) 0 0
\(517\) 82069.8 0.307045
\(518\) −60913.1 + 192758.i −0.227013 + 0.718379i
\(519\) 0 0
\(520\) 60815.2 + 79574.0i 0.224908 + 0.294283i
\(521\) 292204. 1.07649 0.538245 0.842788i \(-0.319087\pi\)
0.538245 + 0.842788i \(0.319087\pi\)
\(522\) 0 0
\(523\) 415479.i 1.51896i −0.650532 0.759479i \(-0.725454\pi\)
0.650532 0.759479i \(-0.274546\pi\)
\(524\) 140986. 200797.i 0.513467 0.731299i
\(525\) 0 0
\(526\) −6470.79 + 20476.7i −0.0233876 + 0.0740096i
\(527\) 182112.i 0.655718i
\(528\) 0 0
\(529\) −512956. −1.83303
\(530\) 111687. + 35294.0i 0.397605 + 0.125646i
\(531\) 0 0
\(532\) 88144.9 + 61889.2i 0.311440 + 0.218671i
\(533\) 143712. 0.505871
\(534\) 0 0
\(535\) 164662.i 0.575289i
\(536\) −267182. + 204196.i −0.929989 + 0.710753i
\(537\) 0 0
\(538\) 344056. + 108724.i 1.18868 + 0.375631i
\(539\) 61019.1i 0.210033i
\(540\) 0 0
\(541\) −90006.8 −0.307525 −0.153763 0.988108i \(-0.549139\pi\)
−0.153763 + 0.988108i \(0.549139\pi\)
\(542\) 15704.2 49695.7i 0.0534587 0.169169i
\(543\) 0 0
\(544\) 4534.38 + 112147.i 0.0153222 + 0.378956i
\(545\) −7106.78 −0.0239266
\(546\) 0 0
\(547\) 159823.i 0.534153i 0.963675 + 0.267077i \(0.0860577\pi\)
−0.963675 + 0.267077i \(0.913942\pi\)
\(548\) −382584. 268624.i −1.27399 0.894506i
\(549\) 0 0
\(550\) 18677.3 59104.0i 0.0617432 0.195385i
\(551\) 295910.i 0.974668i
\(552\) 0 0
\(553\) −11329.1 −0.0370464
\(554\) 81016.9 + 25601.9i 0.263971 + 0.0834168i
\(555\) 0 0
\(556\) −248902. + 354496.i −0.805154 + 1.14673i
\(557\) −91192.2 −0.293932 −0.146966 0.989142i \(-0.546951\pi\)
−0.146966 + 0.989142i \(0.546951\pi\)
\(558\) 0 0
\(559\) 367563.i 1.17627i
\(560\) 81885.3 29565.0i 0.261114 0.0942760i
\(561\) 0 0
\(562\) −420154. 132772.i −1.33026 0.420371i
\(563\) 287297.i 0.906390i 0.891412 + 0.453195i \(0.149716\pi\)
−0.891412 + 0.453195i \(0.850284\pi\)
\(564\) 0 0
\(565\) 147877. 0.463237
\(566\) −62341.8 + 197280.i −0.194602 + 0.615814i
\(567\) 0 0
\(568\) 57453.0 43909.0i 0.178080 0.136099i
\(569\) −248591. −0.767824 −0.383912 0.923370i \(-0.625423\pi\)
−0.383912 + 0.923370i \(0.625423\pi\)
\(570\) 0 0
\(571\) 237006.i 0.726921i −0.931610 0.363461i \(-0.881595\pi\)
0.931610 0.363461i \(-0.118405\pi\)
\(572\) 37360.7 53210.4i 0.114189 0.162632i
\(573\) 0 0
\(574\) 37642.2 119118.i 0.114249 0.361538i
\(575\) 396962.i 1.20064i
\(576\) 0 0
\(577\) 567965. 1.70596 0.852982 0.521940i \(-0.174792\pi\)
0.852982 + 0.521940i \(0.174792\pi\)
\(578\) 272735. + 86186.2i 0.816366 + 0.257978i
\(579\) 0 0
\(580\) 195759. + 137448.i 0.581922 + 0.408585i
\(581\) 28360.8 0.0840169
\(582\) 0 0
\(583\) 76038.9i 0.223717i
\(584\) 246847. + 322988.i 0.723773 + 0.947025i
\(585\) 0 0
\(586\) −77903.4 24618.1i −0.226862 0.0716900i
\(587\) 254380.i 0.738256i −0.929379 0.369128i \(-0.879656\pi\)
0.929379 0.369128i \(-0.120344\pi\)
\(588\) 0 0
\(589\) −440212. −1.26891
\(590\) −29177.4 + 92331.3i −0.0838190 + 0.265244i
\(591\) 0 0
\(592\) −172936. 478977.i −0.493449 1.36669i
\(593\) 522460. 1.48574 0.742871 0.669434i \(-0.233463\pi\)
0.742871 + 0.669434i \(0.233463\pi\)
\(594\) 0 0
\(595\) 37274.9i 0.105289i
\(596\) 359361. + 252318.i 1.01167 + 0.710323i
\(597\) 0 0
\(598\) −125463. + 397026.i −0.350844 + 1.11024i
\(599\) 160888.i 0.448406i −0.974543 0.224203i \(-0.928022\pi\)
0.974543 0.224203i \(-0.0719778\pi\)
\(600\) 0 0
\(601\) −305068. −0.844594 −0.422297 0.906458i \(-0.638776\pi\)
−0.422297 + 0.906458i \(0.638776\pi\)
\(602\) −304660. 96274.9i −0.840664 0.265656i
\(603\) 0 0
\(604\) −46376.4 + 66051.0i −0.127123 + 0.181053i
\(605\) −179806. −0.491239
\(606\) 0 0
\(607\) 68932.7i 0.187089i −0.995615 0.0935444i \(-0.970180\pi\)
0.995615 0.0935444i \(-0.0298197\pi\)
\(608\) −271089. + 10960.8i −0.733338 + 0.0296507i
\(609\) 0 0
\(610\) 77117.2 + 24369.6i 0.207249 + 0.0654921i
\(611\) 276039.i 0.739416i
\(612\) 0 0
\(613\) −504419. −1.34237 −0.671183 0.741292i \(-0.734213\pi\)
−0.671183 + 0.741292i \(0.734213\pi\)
\(614\) 84677.8 267961.i 0.224612 0.710780i
\(615\) 0 0
\(616\) −34318.5 44904.3i −0.0904413 0.118338i
\(617\) 348479. 0.915391 0.457696 0.889109i \(-0.348675\pi\)
0.457696 + 0.889109i \(0.348675\pi\)
\(618\) 0 0
\(619\) 311340.i 0.812557i −0.913749 0.406278i \(-0.866826\pi\)
0.913749 0.406278i \(-0.133174\pi\)
\(620\) −204475. + 291221.i −0.531934 + 0.757600i
\(621\) 0 0
\(622\) 159712. 505406.i 0.412816 1.30635i
\(623\) 263837.i 0.679765i
\(624\) 0 0
\(625\) 86780.1 0.222157
\(626\) 365530. + 115510.i 0.932769 + 0.294762i
\(627\) 0 0
\(628\) −156341. 109771.i −0.396417 0.278337i
\(629\) 218034. 0.551091
\(630\) 0 0
\(631\) 58353.5i 0.146558i −0.997311 0.0732788i \(-0.976654\pi\)
0.997311 0.0732788i \(-0.0233463\pi\)
\(632\) 22675.0 17329.6i 0.0567692 0.0433864i
\(633\) 0 0
\(634\) −350846. 110870.i −0.872847 0.275826i
\(635\) 346940.i 0.860414i
\(636\) 0 0
\(637\) 205236. 0.505795
\(638\) 46788.7 148062.i 0.114948 0.363750i
\(639\) 0 0
\(640\) −118668. + 184429.i −0.289716 + 0.450267i
\(641\) 42450.2 0.103315 0.0516575 0.998665i \(-0.483550\pi\)
0.0516575 + 0.998665i \(0.483550\pi\)
\(642\) 0 0
\(643\) 670263.i 1.62115i 0.585634 + 0.810575i \(0.300846\pi\)
−0.585634 + 0.810575i \(0.699154\pi\)
\(644\) 296219. + 207984.i 0.714234 + 0.501485i
\(645\) 0 0
\(646\) 35002.3 110764.i 0.0838748 0.265420i
\(647\) 524487.i 1.25293i −0.779450 0.626465i \(-0.784501\pi\)
0.779450 0.626465i \(-0.215499\pi\)
\(648\) 0 0
\(649\) 62861.0 0.149242
\(650\) 198795. + 62820.6i 0.470520 + 0.148688i
\(651\) 0 0
\(652\) 223321. 318062.i 0.525332 0.748198i
\(653\) −308366. −0.723169 −0.361584 0.932339i \(-0.617764\pi\)
−0.361584 + 0.932339i \(0.617764\pi\)
\(654\) 0 0
\(655\) 205258.i 0.478430i
\(656\) 106869. + 295992.i 0.248338 + 0.687815i
\(657\) 0 0
\(658\) 228800. + 72302.4i 0.528449 + 0.166994i
\(659\) 569201.i 1.31068i 0.755336 + 0.655338i \(0.227474\pi\)
−0.755336 + 0.655338i \(0.772526\pi\)
\(660\) 0 0
\(661\) 218315. 0.499667 0.249833 0.968289i \(-0.419624\pi\)
0.249833 + 0.968289i \(0.419624\pi\)
\(662\) 131735. 416874.i 0.300598 0.951236i
\(663\) 0 0
\(664\) −56763.5 + 43382.1i −0.128746 + 0.0983952i
\(665\) −90103.2 −0.203750
\(666\) 0 0
\(667\) 994432.i 2.23524i
\(668\) −132403. + 188573.i −0.296719 + 0.422598i
\(669\) 0 0
\(670\) 84769.8 268252.i 0.188839 0.597577i
\(671\) 52503.0i 0.116611i
\(672\) 0 0
\(673\) 417495. 0.921768 0.460884 0.887460i \(-0.347532\pi\)
0.460884 + 0.887460i \(0.347532\pi\)
\(674\) −758025. 239541.i −1.66864 0.527304i
\(675\) 0 0
\(676\) −195023. 136931.i −0.426768 0.299647i
\(677\) −904642. −1.97378 −0.986891 0.161385i \(-0.948404\pi\)
−0.986891 + 0.161385i \(0.948404\pi\)
\(678\) 0 0
\(679\) 12063.3i 0.0261654i
\(680\) −57017.4 74604.8i −0.123308 0.161342i
\(681\) 0 0
\(682\) 220265. + 69605.5i 0.473563 + 0.149649i
\(683\) 382473.i 0.819897i −0.912109 0.409948i \(-0.865547\pi\)
0.912109 0.409948i \(-0.134453\pi\)
\(684\) 0 0
\(685\) 391084. 0.833467
\(686\) 127279. 402773.i 0.270464 0.855880i
\(687\) 0 0
\(688\) 757036. 273330.i 1.59934 0.577446i
\(689\) 255755. 0.538748
\(690\) 0 0
\(691\) 248456.i 0.520348i 0.965562 + 0.260174i \(0.0837799\pi\)
−0.965562 + 0.260174i \(0.916220\pi\)
\(692\) −471217. 330856.i −0.984031 0.690918i
\(693\) 0 0
\(694\) −201677. + 638202.i −0.418733 + 1.32507i
\(695\) 362371.i 0.750213i
\(696\) 0 0
\(697\) −134738. −0.277347
\(698\) −718465. 227040.i −1.47467 0.466007i
\(699\) 0 0
\(700\) 104140. 148320.i 0.212530 0.302693i
\(701\) 689676. 1.40349 0.701744 0.712429i \(-0.252405\pi\)
0.701744 + 0.712429i \(0.252405\pi\)
\(702\) 0 0
\(703\) 527046.i 1.06644i
\(704\) 137375. + 37379.6i 0.277181 + 0.0754205i
\(705\) 0 0
\(706\) −438764. 138653.i −0.880281 0.278176i
\(707\) 401041.i 0.802325i
\(708\) 0 0
\(709\) 511438. 1.01742 0.508711 0.860938i \(-0.330122\pi\)
0.508711 + 0.860938i \(0.330122\pi\)
\(710\) −18228.3 + 57683.1i −0.0361601 + 0.114428i
\(711\) 0 0
\(712\) −403577. 528063.i −0.796098 1.04166i
\(713\) −1.47937e6 −2.91004
\(714\) 0 0
\(715\) 54392.6i 0.106397i
\(716\) 38816.9 55284.4i 0.0757172 0.107839i
\(717\) 0 0
\(718\) 141339. 447265.i 0.274166 0.867593i
\(719\) 84661.7i 0.163768i −0.996642 0.0818841i \(-0.973906\pi\)
0.996642 0.0818841i \(-0.0260937\pi\)
\(720\) 0 0
\(721\) −96155.7 −0.184971
\(722\) −229310. 72463.8i −0.439895 0.139010i
\(723\) 0 0
\(724\) 247251. + 173602.i 0.471694 + 0.331191i
\(725\) 497922. 0.947295
\(726\) 0 0
\(727\) 677593.i 1.28203i 0.767526 + 0.641017i \(0.221487\pi\)
−0.767526 + 0.641017i \(0.778513\pi\)
\(728\) 151034. 115429.i 0.284979 0.217798i
\(729\) 0 0
\(730\) −324283. 102476.i −0.608524 0.192298i
\(731\) 344609.i 0.644900i
\(732\) 0 0
\(733\) 523901. 0.975083 0.487542 0.873100i \(-0.337894\pi\)
0.487542 + 0.873100i \(0.337894\pi\)
\(734\) 317089. 1.00342e6i 0.588557 1.86248i
\(735\) 0 0
\(736\) −911017. + 36834.7i −1.68179 + 0.0679989i
\(737\) −182632. −0.336234
\(738\) 0 0
\(739\) 603562.i 1.10518i −0.833453 0.552590i \(-0.813640\pi\)
0.833453 0.552590i \(-0.186360\pi\)
\(740\) 348666. + 244809.i 0.636717 + 0.447059i
\(741\) 0 0
\(742\) 66989.3 211986.i 0.121674 0.385035i
\(743\) 55911.8i 0.101280i −0.998717 0.0506402i \(-0.983874\pi\)
0.998717 0.0506402i \(-0.0161262\pi\)
\(744\) 0 0
\(745\) −367345. −0.661853
\(746\) 131641. + 41599.4i 0.236544 + 0.0747498i
\(747\) 0 0
\(748\) −35027.6 + 49887.6i −0.0626047 + 0.0891639i
\(749\) 312535. 0.557102
\(750\) 0 0
\(751\) 55305.5i 0.0980593i −0.998797 0.0490297i \(-0.984387\pi\)
0.998797 0.0490297i \(-0.0156129\pi\)
\(752\) −568534. + 205271.i −1.00536 + 0.362988i
\(753\) 0 0
\(754\) 498003. + 157373.i 0.875969 + 0.276813i
\(755\) 67518.4i 0.118448i
\(756\) 0 0
\(757\) −813185. −1.41905 −0.709525 0.704680i \(-0.751090\pi\)
−0.709525 + 0.704680i \(0.751090\pi\)
\(758\) 183741. 581444.i 0.319791 1.01197i
\(759\) 0 0
\(760\) 180339. 137826.i 0.312222 0.238619i
\(761\) 84610.9 0.146102 0.0730512 0.997328i \(-0.476726\pi\)
0.0730512 + 0.997328i \(0.476726\pi\)
\(762\) 0 0
\(763\) 13488.9i 0.0231701i
\(764\) −622761. + 886959.i −1.06693 + 1.51956i
\(765\) 0 0
\(766\) 186128. 588998.i 0.317215 1.00382i
\(767\) 211431.i 0.359400i
\(768\) 0 0
\(769\) 499058. 0.843914 0.421957 0.906616i \(-0.361343\pi\)
0.421957 + 0.906616i \(0.361343\pi\)
\(770\) 45084.2 + 14246.9i 0.0760401 + 0.0240292i
\(771\) 0 0
\(772\) −693803. 487140.i −1.16413 0.817372i
\(773\) 149060. 0.249460 0.124730 0.992191i \(-0.460194\pi\)
0.124730 + 0.992191i \(0.460194\pi\)
\(774\) 0 0
\(775\) 740736.i 1.23328i
\(776\) −18452.6 24144.5i −0.0306432 0.0400953i
\(777\) 0 0
\(778\) −419263. 132490.i −0.692672 0.218890i
\(779\) 325697.i 0.536709i
\(780\) 0 0
\(781\) 39271.8 0.0643842
\(782\) 117628. 372232.i 0.192353 0.608696i
\(783\) 0 0
\(784\) 152620. + 422707.i 0.248301 + 0.687713i
\(785\) 159814. 0.259344
\(786\) 0 0
\(787\) 217138.i 0.350579i 0.984517 + 0.175289i \(0.0560861\pi\)
−0.984517 + 0.175289i \(0.943914\pi\)