Properties

Label 108.5.d.a.55.3
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 55.3
Root \(-1.81633 + 0.757118i\) 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.55.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.36416 - 2.16389i) q^{2} +(6.63513 + 14.5594i) q^{4} +43.0579 q^{5} +14.1139i q^{7} +(9.18328 - 63.3377i) q^{8} +O(q^{10})\) \(q+(-3.36416 - 2.16389i) q^{2} +(6.63513 + 14.5594i) q^{4} +43.0579 q^{5} +14.1139i q^{7} +(9.18328 - 63.3377i) q^{8} +(-144.853 - 93.1726i) q^{10} +209.481i q^{11} -195.703 q^{13} +(30.5409 - 47.4813i) q^{14} +(-167.950 + 193.207i) q^{16} +303.688 q^{17} +274.792i q^{19} +(285.694 + 626.895i) q^{20} +(453.296 - 704.729i) q^{22} -466.347i q^{23} +1228.98 q^{25} +(658.376 + 423.480i) q^{26} +(-205.489 + 93.6473i) q^{28} +439.835 q^{29} +1220.96i q^{31} +(983.089 - 286.551i) q^{32} +(-1021.65 - 657.148i) q^{34} +607.713i q^{35} +624.147 q^{37} +(594.620 - 924.443i) q^{38} +(395.412 - 2727.19i) q^{40} +203.592 q^{41} +419.418i q^{43} +(-3049.92 + 1389.94i) q^{44} +(-1009.12 + 1568.86i) q^{46} +1995.53i q^{47} +2201.80 q^{49} +(-4134.48 - 2659.38i) q^{50} +(-1298.51 - 2849.31i) q^{52} +206.451 q^{53} +9019.82i q^{55} +(893.940 + 129.612i) q^{56} +(-1479.67 - 951.756i) q^{58} -2321.87i q^{59} -1392.10 q^{61} +(2642.02 - 4107.49i) q^{62} +(-3927.33 - 1163.30i) q^{64} -8426.55 q^{65} -7348.27i q^{67} +(2015.01 + 4421.50i) q^{68} +(1315.03 - 2044.44i) q^{70} -8546.65i q^{71} -3245.43 q^{73} +(-2099.73 - 1350.59i) q^{74} +(-4000.79 + 1823.28i) q^{76} -2956.59 q^{77} +6157.41i q^{79} +(-7231.57 + 8319.06i) q^{80} +(-684.915 - 440.551i) q^{82} +213.990i q^{83} +13076.2 q^{85} +(907.576 - 1410.99i) q^{86} +(13268.1 + 1923.73i) q^{88} +8439.35 q^{89} -2762.12i q^{91} +(6789.71 - 3094.27i) q^{92} +(4318.11 - 6713.28i) q^{94} +11831.9i q^{95} -1022.49 q^{97} +(-7407.20 - 4764.46i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 14q^{4} + O(q^{10}) \) \( 16q - 14q^{4} - 202q^{10} - 352q^{13} - 206q^{16} + 738q^{22} + 1632q^{25} + 342q^{28} - 2536q^{34} + 3200q^{37} - 2854q^{40} + 36q^{46} - 896q^{49} + 2288q^{52} + 2492q^{58} - 2752q^{61} + 682q^{64} - 14166q^{70} + 8240q^{73} - 33084q^{76} + 68q^{82} + 8800q^{85} + 48294q^{88} + 52596q^{94} - 6928q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.36416 2.16389i −0.841040 0.540973i
\(3\) 0 0
\(4\) 6.63513 + 14.5594i 0.414696 + 0.909960i
\(5\) 43.0579 1.72231 0.861157 0.508339i \(-0.169740\pi\)
0.861157 + 0.508339i \(0.169740\pi\)
\(6\) 0 0
\(7\) 14.1139i 0.288038i 0.989575 + 0.144019i \(0.0460027\pi\)
−0.989575 + 0.144019i \(0.953997\pi\)
\(8\) 9.18328 63.3377i 0.143489 0.989652i
\(9\) 0 0
\(10\) −144.853 93.1726i −1.44853 0.931726i
\(11\) 209.481i 1.73125i 0.500691 + 0.865626i \(0.333079\pi\)
−0.500691 + 0.865626i \(0.666921\pi\)
\(12\) 0 0
\(13\) −195.703 −1.15801 −0.579003 0.815326i \(-0.696558\pi\)
−0.579003 + 0.815326i \(0.696558\pi\)
\(14\) 30.5409 47.4813i 0.155821 0.242252i
\(15\) 0 0
\(16\) −167.950 + 193.207i −0.656055 + 0.754713i
\(17\) 303.688 1.05082 0.525412 0.850848i \(-0.323911\pi\)
0.525412 + 0.850848i \(0.323911\pi\)
\(18\) 0 0
\(19\) 274.792i 0.761196i 0.924741 + 0.380598i \(0.124282\pi\)
−0.924741 + 0.380598i \(0.875718\pi\)
\(20\) 285.694 + 626.895i 0.714236 + 1.56724i
\(21\) 0 0
\(22\) 453.296 704.729i 0.936561 1.45605i
\(23\) 466.347i 0.881563i −0.897614 0.440782i \(-0.854701\pi\)
0.897614 0.440782i \(-0.145299\pi\)
\(24\) 0 0
\(25\) 1228.98 1.96637
\(26\) 658.376 + 423.480i 0.973928 + 0.626450i
\(27\) 0 0
\(28\) −205.489 + 93.6473i −0.262103 + 0.119448i
\(29\) 439.835 0.522990 0.261495 0.965205i \(-0.415784\pi\)
0.261495 + 0.965205i \(0.415784\pi\)
\(30\) 0 0
\(31\) 1220.96i 1.27051i 0.772304 + 0.635253i \(0.219104\pi\)
−0.772304 + 0.635253i \(0.780896\pi\)
\(32\) 983.089 286.551i 0.960048 0.279835i
\(33\) 0 0
\(34\) −1021.65 657.148i −0.883784 0.568467i
\(35\) 607.713i 0.496092i
\(36\) 0 0
\(37\) 624.147 0.455914 0.227957 0.973671i \(-0.426795\pi\)
0.227957 + 0.973671i \(0.426795\pi\)
\(38\) 594.620 924.443i 0.411787 0.640196i
\(39\) 0 0
\(40\) 395.412 2727.19i 0.247133 1.70449i
\(41\) 203.592 0.121114 0.0605568 0.998165i \(-0.480712\pi\)
0.0605568 + 0.998165i \(0.480712\pi\)
\(42\) 0 0
\(43\) 419.418i 0.226835i 0.993547 + 0.113418i \(0.0361798\pi\)
−0.993547 + 0.113418i \(0.963820\pi\)
\(44\) −3049.92 + 1389.94i −1.57537 + 0.717943i
\(45\) 0 0
\(46\) −1009.12 + 1568.86i −0.476902 + 0.741430i
\(47\) 1995.53i 0.903364i 0.892179 + 0.451682i \(0.149176\pi\)
−0.892179 + 0.451682i \(0.850824\pi\)
\(48\) 0 0
\(49\) 2201.80 0.917034
\(50\) −4134.48 2659.38i −1.65379 1.06375i
\(51\) 0 0
\(52\) −1298.51 2849.31i −0.480220 1.05374i
\(53\) 206.451 0.0734962 0.0367481 0.999325i \(-0.488300\pi\)
0.0367481 + 0.999325i \(0.488300\pi\)
\(54\) 0 0
\(55\) 9019.82i 2.98176i
\(56\) 893.940 + 129.612i 0.285057 + 0.0413302i
\(57\) 0 0
\(58\) −1479.67 951.756i −0.439856 0.282924i
\(59\) 2321.87i 0.667011i −0.942748 0.333505i \(-0.891768\pi\)
0.942748 0.333505i \(-0.108232\pi\)
\(60\) 0 0
\(61\) −1392.10 −0.374120 −0.187060 0.982349i \(-0.559896\pi\)
−0.187060 + 0.982349i \(0.559896\pi\)
\(62\) 2642.02 4107.49i 0.687310 1.06855i
\(63\) 0 0
\(64\) −3927.33 1163.30i −0.958822 0.284008i
\(65\) −8426.55 −1.99445
\(66\) 0 0
\(67\) 7348.27i 1.63695i −0.574542 0.818475i \(-0.694820\pi\)
0.574542 0.818475i \(-0.305180\pi\)
\(68\) 2015.01 + 4421.50i 0.435772 + 0.956207i
\(69\) 0 0
\(70\) 1315.03 2044.44i 0.268373 0.417233i
\(71\) 8546.65i 1.69543i −0.530453 0.847714i \(-0.677978\pi\)
0.530453 0.847714i \(-0.322022\pi\)
\(72\) 0 0
\(73\) −3245.43 −0.609012 −0.304506 0.952510i \(-0.598491\pi\)
−0.304506 + 0.952510i \(0.598491\pi\)
\(74\) −2099.73 1350.59i −0.383442 0.246638i
\(75\) 0 0
\(76\) −4000.79 + 1823.28i −0.692658 + 0.315665i
\(77\) −2956.59 −0.498667
\(78\) 0 0
\(79\) 6157.41i 0.986606i 0.869858 + 0.493303i \(0.164211\pi\)
−0.869858 + 0.493303i \(0.835789\pi\)
\(80\) −7231.57 + 8319.06i −1.12993 + 1.29985i
\(81\) 0 0
\(82\) −684.915 440.551i −0.101861 0.0655192i
\(83\) 213.990i 0.0310626i 0.999879 + 0.0155313i \(0.00494397\pi\)
−0.999879 + 0.0155313i \(0.995056\pi\)
\(84\) 0 0
\(85\) 13076.2 1.80985
\(86\) 907.576 1410.99i 0.122712 0.190777i
\(87\) 0 0
\(88\) 13268.1 + 1923.73i 1.71334 + 0.248415i
\(89\) 8439.35 1.06544 0.532720 0.846292i \(-0.321170\pi\)
0.532720 + 0.846292i \(0.321170\pi\)
\(90\) 0 0
\(91\) 2762.12i 0.333550i
\(92\) 6789.71 3094.27i 0.802187 0.365580i
\(93\) 0 0
\(94\) 4318.11 6713.28i 0.488696 0.759765i
\(95\) 11831.9i 1.31102i
\(96\) 0 0
\(97\) −1022.49 −0.108672 −0.0543358 0.998523i \(-0.517304\pi\)
−0.0543358 + 0.998523i \(0.517304\pi\)
\(98\) −7407.20 4764.46i −0.771262 0.496091i
\(99\) 0 0
\(100\) 8154.44 + 17893.2i 0.815444 + 1.78932i
\(101\) −2374.52 −0.232773 −0.116387 0.993204i \(-0.537131\pi\)
−0.116387 + 0.993204i \(0.537131\pi\)
\(102\) 0 0
\(103\) 8481.02i 0.799418i −0.916642 0.399709i \(-0.869111\pi\)
0.916642 0.399709i \(-0.130889\pi\)
\(104\) −1797.19 + 12395.4i −0.166161 + 1.14602i
\(105\) 0 0
\(106\) −694.533 446.738i −0.0618132 0.0397595i
\(107\) 9579.93i 0.836748i 0.908275 + 0.418374i \(0.137400\pi\)
−0.908275 + 0.418374i \(0.862600\pi\)
\(108\) 0 0
\(109\) −11549.9 −0.972130 −0.486065 0.873923i \(-0.661568\pi\)
−0.486065 + 0.873923i \(0.661568\pi\)
\(110\) 19517.9 30344.1i 1.61305 2.50778i
\(111\) 0 0
\(112\) −2726.89 2370.43i −0.217386 0.188969i
\(113\) 21853.8 1.71147 0.855735 0.517414i \(-0.173105\pi\)
0.855735 + 0.517414i \(0.173105\pi\)
\(114\) 0 0
\(115\) 20079.9i 1.51833i
\(116\) 2918.36 + 6403.71i 0.216882 + 0.475900i
\(117\) 0 0
\(118\) −5024.27 + 7811.12i −0.360835 + 0.560983i
\(119\) 4286.21i 0.302677i
\(120\) 0 0
\(121\) −29241.5 −1.99723
\(122\) 4683.25 + 3012.36i 0.314650 + 0.202389i
\(123\) 0 0
\(124\) −17776.4 + 8101.21i −1.15611 + 0.526874i
\(125\) 26006.0 1.66439
\(126\) 0 0
\(127\) 7358.63i 0.456236i −0.973634 0.228118i \(-0.926743\pi\)
0.973634 0.228118i \(-0.0732572\pi\)
\(128\) 10694.9 + 12411.8i 0.652767 + 0.757559i
\(129\) 0 0
\(130\) 28348.2 + 18234.2i 1.67741 + 1.07894i
\(131\) 8567.97i 0.499270i −0.968340 0.249635i \(-0.919689\pi\)
0.968340 0.249635i \(-0.0803106\pi\)
\(132\) 0 0
\(133\) −3878.37 −0.219253
\(134\) −15900.9 + 24720.7i −0.885546 + 1.37674i
\(135\) 0 0
\(136\) 2788.85 19234.9i 0.150781 1.03995i
\(137\) −33585.2 −1.78940 −0.894699 0.446669i \(-0.852610\pi\)
−0.894699 + 0.446669i \(0.852610\pi\)
\(138\) 0 0
\(139\) 8638.51i 0.447104i 0.974692 + 0.223552i \(0.0717653\pi\)
−0.974692 + 0.223552i \(0.928235\pi\)
\(140\) −8847.91 + 4032.25i −0.451424 + 0.205727i
\(141\) 0 0
\(142\) −18494.1 + 28752.3i −0.917182 + 1.42592i
\(143\) 40996.1i 2.00480i
\(144\) 0 0
\(145\) 18938.3 0.900754
\(146\) 10918.1 + 7022.75i 0.512203 + 0.329459i
\(147\) 0 0
\(148\) 4141.29 + 9087.18i 0.189066 + 0.414864i
\(149\) −24096.5 −1.08538 −0.542689 0.839934i \(-0.682594\pi\)
−0.542689 + 0.839934i \(0.682594\pi\)
\(150\) 0 0
\(151\) 26512.7i 1.16279i −0.813623 0.581393i \(-0.802508\pi\)
0.813623 0.581393i \(-0.197492\pi\)
\(152\) 17404.7 + 2523.49i 0.753319 + 0.109223i
\(153\) 0 0
\(154\) 9946.45 + 6397.75i 0.419398 + 0.269765i
\(155\) 52571.8i 2.18821i
\(156\) 0 0
\(157\) −33191.1 −1.34655 −0.673274 0.739393i \(-0.735113\pi\)
−0.673274 + 0.739393i \(0.735113\pi\)
\(158\) 13324.0 20714.5i 0.533727 0.829775i
\(159\) 0 0
\(160\) 42329.7 12338.3i 1.65350 0.481964i
\(161\) 6581.96 0.253924
\(162\) 0 0
\(163\) 22135.9i 0.833146i −0.909102 0.416573i \(-0.863231\pi\)
0.909102 0.416573i \(-0.136769\pi\)
\(164\) 1350.86 + 2964.17i 0.0502252 + 0.110208i
\(165\) 0 0
\(166\) 463.052 719.897i 0.0168040 0.0261249i
\(167\) 31233.9i 1.11993i −0.828515 0.559967i \(-0.810814\pi\)
0.828515 0.559967i \(-0.189186\pi\)
\(168\) 0 0
\(169\) 9738.62 0.340976
\(170\) −43990.3 28295.4i −1.52215 0.979080i
\(171\) 0 0
\(172\) −6106.46 + 2782.89i −0.206411 + 0.0940675i
\(173\) −19702.2 −0.658298 −0.329149 0.944278i \(-0.606762\pi\)
−0.329149 + 0.944278i \(0.606762\pi\)
\(174\) 0 0
\(175\) 17345.6i 0.566388i
\(176\) −40473.2 35182.4i −1.30660 1.13580i
\(177\) 0 0
\(178\) −28391.3 18261.9i −0.896077 0.576375i
\(179\) 931.868i 0.0290836i 0.999894 + 0.0145418i \(0.00462896\pi\)
−0.999894 + 0.0145418i \(0.995371\pi\)
\(180\) 0 0
\(181\) 8201.99 0.250358 0.125179 0.992134i \(-0.460049\pi\)
0.125179 + 0.992134i \(0.460049\pi\)
\(182\) −5976.94 + 9292.23i −0.180441 + 0.280529i
\(183\) 0 0
\(184\) −29537.3 4282.59i −0.872441 0.126494i
\(185\) 26874.4 0.785228
\(186\) 0 0
\(187\) 63617.0i 1.81924i
\(188\) −29053.6 + 13240.6i −0.822025 + 0.374621i
\(189\) 0 0
\(190\) 25603.1 39804.5i 0.709226 1.10262i
\(191\) 3283.65i 0.0900099i 0.998987 + 0.0450049i \(0.0143304\pi\)
−0.998987 + 0.0450049i \(0.985670\pi\)
\(192\) 0 0
\(193\) 70666.2 1.89713 0.948565 0.316583i \(-0.102536\pi\)
0.948565 + 0.316583i \(0.102536\pi\)
\(194\) 3439.82 + 2212.56i 0.0913971 + 0.0587884i
\(195\) 0 0
\(196\) 14609.2 + 32056.8i 0.380290 + 0.834464i
\(197\) 14865.2 0.383034 0.191517 0.981489i \(-0.438659\pi\)
0.191517 + 0.981489i \(0.438659\pi\)
\(198\) 0 0
\(199\) 63878.1i 1.61304i −0.591205 0.806521i \(-0.701348\pi\)
0.591205 0.806521i \(-0.298652\pi\)
\(200\) 11286.1 77840.7i 0.282151 1.94602i
\(201\) 0 0
\(202\) 7988.26 + 5138.21i 0.195771 + 0.125924i
\(203\) 6207.77i 0.150641i
\(204\) 0 0
\(205\) 8766.23 0.208596
\(206\) −18352.0 + 28531.5i −0.432464 + 0.672342i
\(207\) 0 0
\(208\) 32868.3 37811.1i 0.759715 0.873962i
\(209\) −57563.8 −1.31782
\(210\) 0 0
\(211\) 66608.9i 1.49612i 0.663629 + 0.748062i \(0.269015\pi\)
−0.663629 + 0.748062i \(0.730985\pi\)
\(212\) 1369.83 + 3005.79i 0.0304786 + 0.0668786i
\(213\) 0 0
\(214\) 20729.9 32228.4i 0.452658 0.703738i
\(215\) 18059.2i 0.390681i
\(216\) 0 0
\(217\) −17232.4 −0.365954
\(218\) 38855.6 + 24992.7i 0.817600 + 0.525896i
\(219\) 0 0
\(220\) −131323. + 59847.7i −2.71328 + 1.23652i
\(221\) −59432.6 −1.21686
\(222\) 0 0
\(223\) 48074.2i 0.966723i 0.875421 + 0.483361i \(0.160584\pi\)
−0.875421 + 0.483361i \(0.839416\pi\)
\(224\) 4044.35 + 13875.2i 0.0806032 + 0.276530i
\(225\) 0 0
\(226\) −73519.5 47289.2i −1.43941 0.925860i
\(227\) 18940.2i 0.367564i −0.982967 0.183782i \(-0.941166\pi\)
0.982967 0.183782i \(-0.0588341\pi\)
\(228\) 0 0
\(229\) 349.738 0.00666917 0.00333458 0.999994i \(-0.498939\pi\)
0.00333458 + 0.999994i \(0.498939\pi\)
\(230\) −43450.8 + 67552.0i −0.821375 + 1.27697i
\(231\) 0 0
\(232\) 4039.13 27858.1i 0.0750432 0.517578i
\(233\) −7529.14 −0.138686 −0.0693432 0.997593i \(-0.522090\pi\)
−0.0693432 + 0.997593i \(0.522090\pi\)
\(234\) 0 0
\(235\) 85923.3i 1.55588i
\(236\) 33804.9 15405.9i 0.606953 0.276607i
\(237\) 0 0
\(238\) 9274.91 14419.5i 0.163740 0.254564i
\(239\) 53394.8i 0.934766i −0.884055 0.467383i \(-0.845197\pi\)
0.884055 0.467383i \(-0.154803\pi\)
\(240\) 0 0
\(241\) −88157.7 −1.51784 −0.758920 0.651184i \(-0.774273\pi\)
−0.758920 + 0.651184i \(0.774273\pi\)
\(242\) 98373.0 + 63275.5i 1.67975 + 1.08045i
\(243\) 0 0
\(244\) −9236.76 20268.1i −0.155146 0.340434i
\(245\) 94804.7 1.57942
\(246\) 0 0
\(247\) 53777.5i 0.881469i
\(248\) 77332.6 + 11212.4i 1.25736 + 0.182303i
\(249\) 0 0
\(250\) −87488.4 56274.3i −1.39982 0.900389i
\(251\) 23284.3i 0.369587i −0.982777 0.184793i \(-0.940838\pi\)
0.982777 0.184793i \(-0.0591616\pi\)
\(252\) 0 0
\(253\) 97691.0 1.52621
\(254\) −15923.3 + 24755.6i −0.246811 + 0.383712i
\(255\) 0 0
\(256\) −9121.53 64898.1i −0.139183 0.990267i
\(257\) 118409. 1.79274 0.896369 0.443308i \(-0.146195\pi\)
0.896369 + 0.443308i \(0.146195\pi\)
\(258\) 0 0
\(259\) 8809.12i 0.131321i
\(260\) −55911.2 122685.i −0.827089 1.81487i
\(261\) 0 0
\(262\) −18540.2 + 28824.0i −0.270092 + 0.419906i
\(263\) 44424.6i 0.642262i −0.947035 0.321131i \(-0.895937\pi\)
0.947035 0.321131i \(-0.104063\pi\)
\(264\) 0 0
\(265\) 8889.33 0.126584
\(266\) 13047.5 + 8392.39i 0.184401 + 0.118610i
\(267\) 0 0
\(268\) 106986. 48756.7i 1.48956 0.678836i
\(269\) 55818.5 0.771390 0.385695 0.922626i \(-0.373962\pi\)
0.385695 + 0.922626i \(0.373962\pi\)
\(270\) 0 0
\(271\) 98301.7i 1.33851i 0.743032 + 0.669256i \(0.233387\pi\)
−0.743032 + 0.669256i \(0.766613\pi\)
\(272\) −51004.4 + 58674.5i −0.689398 + 0.793070i
\(273\) 0 0
\(274\) 112986. + 72674.8i 1.50496 + 0.968017i
\(275\) 257448.i 3.40428i
\(276\) 0 0
\(277\) 111306. 1.45063 0.725317 0.688415i \(-0.241693\pi\)
0.725317 + 0.688415i \(0.241693\pi\)
\(278\) 18692.8 29061.3i 0.241872 0.376033i
\(279\) 0 0
\(280\) 38491.2 + 5580.80i 0.490959 + 0.0711836i
\(281\) −24996.7 −0.316571 −0.158285 0.987393i \(-0.550597\pi\)
−0.158285 + 0.987393i \(0.550597\pi\)
\(282\) 0 0
\(283\) 30559.7i 0.381571i 0.981632 + 0.190786i \(0.0611035\pi\)
−0.981632 + 0.190786i \(0.938896\pi\)
\(284\) 124434. 56708.2i 1.54277 0.703087i
\(285\) 0 0
\(286\) −88711.3 + 137917.i −1.08454 + 1.68612i
\(287\) 2873.47i 0.0348853i
\(288\) 0 0
\(289\) 8705.37 0.104230
\(290\) −63711.6 40980.6i −0.757570 0.487284i
\(291\) 0 0
\(292\) −21533.8 47251.3i −0.252555 0.554177i
\(293\) −49225.1 −0.573392 −0.286696 0.958022i \(-0.592557\pi\)
−0.286696 + 0.958022i \(0.592557\pi\)
\(294\) 0 0
\(295\) 99974.5i 1.14880i
\(296\) 5731.71 39532.0i 0.0654186 0.451197i
\(297\) 0 0
\(298\) 81064.4 + 52142.2i 0.912846 + 0.587160i
\(299\) 91265.4i 1.02085i
\(300\) 0 0
\(301\) −5919.61 −0.0653372
\(302\) −57370.7 + 89192.9i −0.629037 + 0.977950i
\(303\) 0 0
\(304\) −53091.5 46151.3i −0.574484 0.499386i
\(305\) −59940.8 −0.644352
\(306\) 0 0
\(307\) 143871.i 1.52650i −0.646105 0.763249i \(-0.723603\pi\)
0.646105 0.763249i \(-0.276397\pi\)
\(308\) −19617.4 43046.1i −0.206795 0.453767i
\(309\) 0 0
\(310\) 113760. 176860.i 1.18376 1.84037i
\(311\) 144670.i 1.49575i −0.663842 0.747873i \(-0.731075\pi\)
0.663842 0.747873i \(-0.268925\pi\)
\(312\) 0 0
\(313\) 80345.4 0.820111 0.410055 0.912061i \(-0.365509\pi\)
0.410055 + 0.912061i \(0.365509\pi\)
\(314\) 111660. + 71821.9i 1.13250 + 0.728447i
\(315\) 0 0
\(316\) −89647.9 + 40855.2i −0.897772 + 0.409141i
\(317\) 144593. 1.43889 0.719445 0.694549i \(-0.244396\pi\)
0.719445 + 0.694549i \(0.244396\pi\)
\(318\) 0 0
\(319\) 92137.2i 0.905428i
\(320\) −169103. 50089.0i −1.65139 0.489151i
\(321\) 0 0
\(322\) −22142.8 14242.7i −0.213560 0.137366i
\(323\) 83450.9i 0.799882i
\(324\) 0 0
\(325\) −240515. −2.27706
\(326\) −47899.6 + 74468.5i −0.450710 + 0.700709i
\(327\) 0 0
\(328\) 1869.64 12895.0i 0.0173784 0.119860i
\(329\) −28164.7 −0.260203
\(330\) 0 0
\(331\) 89506.7i 0.816957i −0.912768 0.408479i \(-0.866059\pi\)
0.912768 0.408479i \(-0.133941\pi\)
\(332\) −3115.56 + 1419.85i −0.0282657 + 0.0128815i
\(333\) 0 0
\(334\) −67586.8 + 105076.i −0.605855 + 0.941910i
\(335\) 316401.i 2.81934i
\(336\) 0 0
\(337\) −134427. −1.18366 −0.591830 0.806062i \(-0.701595\pi\)
−0.591830 + 0.806062i \(0.701595\pi\)
\(338\) −32762.3 21073.3i −0.286775 0.184459i
\(339\) 0 0
\(340\) 86762.0 + 190380.i 0.750536 + 1.64689i
\(341\) −255768. −2.19957
\(342\) 0 0
\(343\) 64963.3i 0.552179i
\(344\) 26565.0 + 3851.63i 0.224488 + 0.0325483i
\(345\) 0 0
\(346\) 66281.3 + 42633.4i 0.553654 + 0.356121i
\(347\) 73087.9i 0.606997i −0.952832 0.303499i \(-0.901845\pi\)
0.952832 0.303499i \(-0.0981547\pi\)
\(348\) 0 0
\(349\) −54237.0 −0.445292 −0.222646 0.974899i \(-0.571469\pi\)
−0.222646 + 0.974899i \(0.571469\pi\)
\(350\) 37534.1 58353.5i 0.306401 0.476355i
\(351\) 0 0
\(352\) 60027.2 + 205939.i 0.484465 + 1.66208i
\(353\) −29031.6 −0.232982 −0.116491 0.993192i \(-0.537165\pi\)
−0.116491 + 0.993192i \(0.537165\pi\)
\(354\) 0 0
\(355\) 368001.i 2.92006i
\(356\) 55996.2 + 122872.i 0.441833 + 0.969508i
\(357\) 0 0
\(358\) 2016.46 3134.95i 0.0157335 0.0244605i
\(359\) 9197.54i 0.0713646i −0.999363 0.0356823i \(-0.988640\pi\)
0.999363 0.0356823i \(-0.0113604\pi\)
\(360\) 0 0
\(361\) 54810.5 0.420581
\(362\) −27592.8 17748.2i −0.210561 0.135437i
\(363\) 0 0
\(364\) 40214.8 18327.1i 0.303517 0.138322i
\(365\) −139741. −1.04891
\(366\) 0 0
\(367\) 96131.3i 0.713728i 0.934156 + 0.356864i \(0.116154\pi\)
−0.934156 + 0.356864i \(0.883846\pi\)
\(368\) 90101.3 + 78323.0i 0.665327 + 0.578354i
\(369\) 0 0
\(370\) −90409.8 58153.4i −0.660408 0.424787i
\(371\) 2913.82i 0.0211697i
\(372\) 0 0
\(373\) −27728.8 −0.199303 −0.0996513 0.995022i \(-0.531773\pi\)
−0.0996513 + 0.995022i \(0.531773\pi\)
\(374\) 137660. 214018.i 0.984160 1.53005i
\(375\) 0 0
\(376\) 126392. + 18325.5i 0.894016 + 0.129623i
\(377\) −86076.9 −0.605626
\(378\) 0 0
\(379\) 101903.i 0.709432i 0.934974 + 0.354716i \(0.115422\pi\)
−0.934974 + 0.354716i \(0.884578\pi\)
\(380\) −172266. + 78506.5i −1.19297 + 0.543674i
\(381\) 0 0
\(382\) 7105.47 11046.7i 0.0486930 0.0757019i
\(383\) 6261.76i 0.0426873i 0.999772 + 0.0213437i \(0.00679442\pi\)
−0.999772 + 0.0213437i \(0.993206\pi\)
\(384\) 0 0
\(385\) −127305. −0.858860
\(386\) −237732. 152914.i −1.59556 1.02630i
\(387\) 0 0
\(388\) −6784.36 14886.8i −0.0450656 0.0988867i
\(389\) 147789. 0.976658 0.488329 0.872660i \(-0.337607\pi\)
0.488329 + 0.872660i \(0.337607\pi\)
\(390\) 0 0
\(391\) 141624.i 0.926367i
\(392\) 20219.7 139457.i 0.131584 0.907545i
\(393\) 0 0
\(394\) −50008.8 32166.6i −0.322147 0.207211i
\(395\) 265125.i 1.69924i
\(396\) 0 0
\(397\) −142937. −0.906912 −0.453456 0.891279i \(-0.649809\pi\)
−0.453456 + 0.891279i \(0.649809\pi\)
\(398\) −138225. + 214896.i −0.872613 + 1.35663i
\(399\) 0 0
\(400\) −206407. + 237447.i −1.29004 + 1.48404i
\(401\) −18071.6 −0.112385 −0.0561923 0.998420i \(-0.517896\pi\)
−0.0561923 + 0.998420i \(0.517896\pi\)
\(402\) 0 0
\(403\) 238945.i 1.47125i
\(404\) −15755.2 34571.5i −0.0965300 0.211814i
\(405\) 0 0
\(406\) 13433.0 20883.9i 0.0814928 0.126695i
\(407\) 130747.i 0.789303i
\(408\) 0 0
\(409\) 166751. 0.996831 0.498416 0.866938i \(-0.333915\pi\)
0.498416 + 0.866938i \(0.333915\pi\)
\(410\) −29491.0 18969.2i −0.175437 0.112845i
\(411\) 0 0
\(412\) 123478. 56272.7i 0.727438 0.331515i
\(413\) 32770.5 0.192125
\(414\) 0 0
\(415\) 9213.96i 0.0534996i
\(416\) −192393. + 56078.9i −1.11174 + 0.324051i
\(417\) 0 0
\(418\) 193654. + 124562.i 1.10834 + 0.712906i
\(419\) 24068.3i 0.137094i −0.997648 0.0685469i \(-0.978164\pi\)
0.997648 0.0685469i \(-0.0218363\pi\)
\(420\) 0 0
\(421\) −113463. −0.640162 −0.320081 0.947390i \(-0.603710\pi\)
−0.320081 + 0.947390i \(0.603710\pi\)
\(422\) 144135. 224083.i 0.809363 1.25830i
\(423\) 0 0
\(424\) 1895.90 13076.1i 0.0105459 0.0727357i
\(425\) 373226. 2.06630
\(426\) 0 0
\(427\) 19647.9i 0.107761i
\(428\) −139478. + 63564.1i −0.761407 + 0.346996i
\(429\) 0 0
\(430\) 39078.3 60754.2i 0.211348 0.328579i
\(431\) 154439.i 0.831388i −0.909505 0.415694i \(-0.863539\pi\)
0.909505 0.415694i \(-0.136461\pi\)
\(432\) 0 0
\(433\) 124462. 0.663836 0.331918 0.943308i \(-0.392304\pi\)
0.331918 + 0.943308i \(0.392304\pi\)
\(434\) 57972.6 + 37289.1i 0.307782 + 0.197972i
\(435\) 0 0
\(436\) −76634.9 168159.i −0.403138 0.884600i
\(437\) 128148. 0.671042
\(438\) 0 0
\(439\) 100585.i 0.521921i 0.965349 + 0.260960i \(0.0840392\pi\)
−0.965349 + 0.260960i \(0.915961\pi\)
\(440\) 571295. + 82831.5i 2.95090 + 0.427849i
\(441\) 0 0
\(442\) 199941. + 128606.i 1.02343 + 0.658288i
\(443\) 195614.i 0.996764i 0.866957 + 0.498382i \(0.166072\pi\)
−0.866957 + 0.498382i \(0.833928\pi\)
\(444\) 0 0
\(445\) 363380. 1.83502
\(446\) 104027. 161729.i 0.522971 0.813052i
\(447\) 0 0
\(448\) 16418.6 55429.9i 0.0818051 0.276177i
\(449\) 47139.5 0.233826 0.116913 0.993142i \(-0.462700\pi\)
0.116913 + 0.993142i \(0.462700\pi\)
\(450\) 0 0
\(451\) 42648.7i 0.209678i
\(452\) 145003. + 318177.i 0.709739 + 1.55737i
\(453\) 0 0
\(454\) −40984.6 + 63717.9i −0.198842 + 0.309136i
\(455\) 118931.i 0.574477i
\(456\) 0 0
\(457\) −44420.0 −0.212690 −0.106345 0.994329i \(-0.533915\pi\)
−0.106345 + 0.994329i \(0.533915\pi\)
\(458\) −1176.57 756.796i −0.00560904 0.00360784i
\(459\) 0 0
\(460\) 292350. 133233.i 1.38162 0.629644i
\(461\) −189396. −0.891187 −0.445594 0.895235i \(-0.647007\pi\)
−0.445594 + 0.895235i \(0.647007\pi\)
\(462\) 0 0
\(463\) 146188.i 0.681944i 0.940073 + 0.340972i \(0.110756\pi\)
−0.940073 + 0.340972i \(0.889244\pi\)
\(464\) −73870.3 + 84979.0i −0.343110 + 0.394708i
\(465\) 0 0
\(466\) 25329.2 + 16292.3i 0.116641 + 0.0750256i
\(467\) 145806.i 0.668563i 0.942473 + 0.334281i \(0.108494\pi\)
−0.942473 + 0.334281i \(0.891506\pi\)
\(468\) 0 0
\(469\) 103712. 0.471504
\(470\) 185929. 289059.i 0.841687 1.30855i
\(471\) 0 0
\(472\) −147062. 21322.3i −0.660109 0.0957086i
\(473\) −87860.3 −0.392709
\(474\) 0 0
\(475\) 337713.i 1.49679i
\(476\) −62404.5 + 28439.6i −0.275424 + 0.125519i
\(477\) 0 0
\(478\) −115541. + 179629.i −0.505684 + 0.786175i
\(479\) 366733.i 1.59838i −0.601081 0.799188i \(-0.705263\pi\)
0.601081 0.799188i \(-0.294737\pi\)
\(480\) 0 0
\(481\) −122147. −0.527951
\(482\) 296576. + 190764.i 1.27656 + 0.821111i
\(483\) 0 0
\(484\) −194021. 425737.i −0.828244 1.81740i
\(485\) −44026.2 −0.187166
\(486\) 0 0
\(487\) 202033.i 0.851851i −0.904758 0.425926i \(-0.859949\pi\)
0.904758 0.425926i \(-0.140051\pi\)
\(488\) −12784.0 + 88172.4i −0.0536820 + 0.370248i
\(489\) 0 0
\(490\) −318938. 205147.i −1.32836 0.854425i
\(491\) 229449.i 0.951750i 0.879513 + 0.475875i \(0.157869\pi\)
−0.879513 + 0.475875i \(0.842131\pi\)
\(492\) 0 0
\(493\) 133573. 0.549570
\(494\) −116369. + 180916.i −0.476851 + 0.741350i
\(495\) 0 0
\(496\) −235897. 205060.i −0.958868 0.833523i
\(497\) 120626. 0.488348
\(498\) 0 0
\(499\) 353378.i 1.41918i 0.704613 + 0.709592i \(0.251121\pi\)
−0.704613 + 0.709592i \(0.748879\pi\)
\(500\) 172553. + 378631.i 0.690214 + 1.51453i
\(501\) 0 0
\(502\) −50384.8 + 78332.2i −0.199937 + 0.310837i
\(503\) 173765.i 0.686793i −0.939190 0.343397i \(-0.888422\pi\)
0.939190 0.343397i \(-0.111578\pi\)
\(504\) 0 0
\(505\) −102242. −0.400908
\(506\) −328648. 211393.i −1.28360 0.825638i
\(507\) 0 0
\(508\) 107137. 48825.4i 0.415156 0.189199i
\(509\) 427247. 1.64909 0.824543 0.565800i \(-0.191432\pi\)
0.824543 + 0.565800i \(0.191432\pi\)
\(510\) 0 0
\(511\) 45805.5i 0.175419i
\(512\) −109746. + 238066.i −0.418649 + 0.908148i
\(513\) 0 0
\(514\) −398345. 256224.i −1.50776 0.969824i
\(515\) 365175.i 1.37685i
\(516\) 0 0
\(517\) −418027. −1.56395
\(518\) 19062.0 29635.3i 0.0710410 0.110446i
\(519\) 0 0
\(520\) −77383.3 + 533718.i −0.286181 + 1.97381i
\(521\) −238355. −0.878111 −0.439056 0.898460i \(-0.644687\pi\)
−0.439056 + 0.898460i \(0.644687\pi\)
\(522\) 0 0
\(523\) 65331.4i 0.238846i −0.992843 0.119423i \(-0.961895\pi\)
0.992843 0.119423i \(-0.0381045\pi\)
\(524\) 124744. 56849.6i 0.454315 0.207045i
\(525\) 0 0
\(526\) −96130.1 + 149451.i −0.347446 + 0.540168i
\(527\) 370790.i 1.33508i
\(528\) 0 0
\(529\) 62361.6 0.222847
\(530\) −29905.1 19235.6i −0.106462 0.0684783i
\(531\) 0 0
\(532\) −25733.5 56466.6i −0.0909234 0.199512i
\(533\) −39843.5 −0.140250
\(534\) 0 0
\(535\) 412491.i 1.44114i
\(536\) −465423. 67481.2i −1.62001 0.234884i
\(537\) 0 0
\(538\) −187782. 120785.i −0.648769 0.417301i
\(539\) 461236.i 1.58762i
\(540\) 0 0
\(541\) 343182. 1.17255 0.586273 0.810113i \(-0.300595\pi\)
0.586273 + 0.810113i \(0.300595\pi\)
\(542\) 212714. 330703.i 0.724100 1.12574i
\(543\) 0 0
\(544\) 298552. 87022.2i 1.00884 0.294057i
\(545\) −497313. −1.67431
\(546\) 0 0
\(547\) 135514.i 0.452908i 0.974022 + 0.226454i \(0.0727133\pi\)
−0.974022 + 0.226454i \(0.927287\pi\)
\(548\) −222842. 488979.i −0.742056 1.62828i
\(549\) 0 0
\(550\) 557091. 866097.i 1.84162 2.86313i
\(551\) 120863.i 0.398098i
\(552\) 0 0
\(553\) −86904.8 −0.284180
\(554\) −374450. 240854.i −1.22004 0.784755i
\(555\) 0 0
\(556\) −125771. + 57317.6i −0.406847 + 0.185412i
\(557\) 64031.9 0.206389 0.103194 0.994661i \(-0.467094\pi\)
0.103194 + 0.994661i \(0.467094\pi\)
\(558\) 0 0
\(559\) 82081.3i 0.262676i
\(560\) −117414. 102065.i −0.374407 0.325464i
\(561\) 0 0
\(562\) 84093.0 + 54090.3i 0.266248 + 0.171256i
\(563\) 53438.7i 0.168593i 0.996441 + 0.0842964i \(0.0268643\pi\)
−0.996441 + 0.0842964i \(0.973136\pi\)
\(564\) 0 0
\(565\) 940976. 2.94769
\(566\) 66127.9 102808.i 0.206420 0.320917i
\(567\) 0 0
\(568\) −541326. 78486.3i −1.67788 0.243275i
\(569\) 225959. 0.697919 0.348960 0.937138i \(-0.386535\pi\)
0.348960 + 0.937138i \(0.386535\pi\)
\(570\) 0 0
\(571\) 472292.i 1.44857i 0.689502 + 0.724284i \(0.257829\pi\)
−0.689502 + 0.724284i \(0.742171\pi\)
\(572\) 596878. 272015.i 1.82429 0.831381i
\(573\) 0 0
\(574\) 6217.88 9666.80i 0.0188720 0.0293399i
\(575\) 573130.i 1.73348i
\(576\) 0 0
\(577\) 376338. 1.13038 0.565192 0.824959i \(-0.308802\pi\)
0.565192 + 0.824959i \(0.308802\pi\)
\(578\) −29286.2 18837.5i −0.0876613 0.0563855i
\(579\) 0 0
\(580\) 125658. + 275730.i 0.373539 + 0.819650i
\(581\) −3020.23 −0.00894722
\(582\) 0 0
\(583\) 43247.6i 0.127240i
\(584\) −29803.6 + 205558.i −0.0873864 + 0.602710i
\(585\) 0 0
\(586\) 165601. + 106518.i 0.482245 + 0.310190i
\(587\) 282756.i 0.820608i 0.911949 + 0.410304i \(0.134577\pi\)
−0.911949 + 0.410304i \(0.865423\pi\)
\(588\) 0 0
\(589\) −335509. −0.967104
\(590\) −216334. + 336330.i −0.621472 + 0.966189i
\(591\) 0 0
\(592\) −104826. + 120589.i −0.299105 + 0.344085i
\(593\) 439919. 1.25102 0.625508 0.780217i \(-0.284892\pi\)
0.625508 + 0.780217i \(0.284892\pi\)
\(594\) 0 0
\(595\) 184555.i 0.521305i
\(596\) −159883. 350829.i −0.450101 0.987651i
\(597\) 0 0
\(598\) 197489. 307031.i 0.552255 0.858579i
\(599\) 384400.i 1.07135i −0.844425 0.535673i \(-0.820058\pi\)
0.844425 0.535673i \(-0.179942\pi\)
\(600\) 0 0
\(601\) −495470. −1.37173 −0.685864 0.727730i \(-0.740576\pi\)
−0.685864 + 0.727730i \(0.740576\pi\)
\(602\) 19914.5 + 12809.4i 0.0549512 + 0.0353457i
\(603\) 0 0
\(604\) 386008. 175915.i 1.05809 0.482203i
\(605\) −1.25908e6 −3.43986
\(606\) 0 0
\(607\) 630975.i 1.71252i −0.516549 0.856258i \(-0.672784\pi\)
0.516549 0.856258i \(-0.327216\pi\)
\(608\) 78741.9 + 270145.i 0.213009 + 0.730784i
\(609\) 0 0
\(610\) 201651. + 129706.i 0.541926 + 0.348577i
\(611\) 390531.i 1.04610i
\(612\) 0 0
\(613\) −256888. −0.683634 −0.341817 0.939767i \(-0.611042\pi\)
−0.341817 + 0.939767i \(0.611042\pi\)
\(614\) −311321. + 484004.i −0.825794 + 1.28384i
\(615\) 0 0
\(616\) −27151.2 + 187264.i −0.0715530 + 0.493506i
\(617\) −115496. −0.303387 −0.151694 0.988428i \(-0.548473\pi\)
−0.151694 + 0.988428i \(0.548473\pi\)
\(618\) 0 0
\(619\) 229059.i 0.597814i −0.954282 0.298907i \(-0.903378\pi\)
0.954282 0.298907i \(-0.0966221\pi\)
\(620\) −765412. + 348821.i −1.99119 + 0.907442i
\(621\) 0 0
\(622\) −313051. + 486693.i −0.809159 + 1.25798i
\(623\) 119112.i 0.306887i
\(624\) 0 0
\(625\) 351652. 0.900230
\(626\) −270295. 173859.i −0.689746 0.443658i
\(627\) 0 0
\(628\) −220227. 483241.i −0.558408 1.22531i
\(629\) 189546. 0.479085
\(630\) 0 0
\(631\) 481121.i 1.20836i −0.796849 0.604178i \(-0.793501\pi\)
0.796849 0.604178i \(-0.206499\pi\)
\(632\) 389996. + 56545.2i 0.976396 + 0.141567i
\(633\) 0 0
\(634\) −486433. 312883.i −1.21016 0.778402i
\(635\) 316847.i 0.785781i
\(636\) 0 0
\(637\) −430898. −1.06193
\(638\) 199375. 309964.i 0.489812 0.761501i
\(639\) 0 0
\(640\) 460501. + 534428.i 1.12427 + 1.30475i
\(641\) −476453. −1.15959 −0.579794 0.814763i \(-0.696867\pi\)
−0.579794 + 0.814763i \(0.696867\pi\)
\(642\) 0 0
\(643\) 416293.i 1.00688i 0.864030 + 0.503440i \(0.167932\pi\)
−0.864030 + 0.503440i \(0.832068\pi\)
\(644\) 43672.1 + 95829.1i 0.105301 + 0.231061i
\(645\) 0 0
\(646\) 180579. 280742.i 0.432715 0.672733i
\(647\) 18567.6i 0.0443554i −0.999754 0.0221777i \(-0.992940\pi\)
0.999754 0.0221777i \(-0.00705996\pi\)
\(648\) 0 0
\(649\) 486388. 1.15476
\(650\) 809130. + 520448.i 1.91510 + 1.23183i
\(651\) 0 0
\(652\) 322284. 146874.i 0.758130 0.345502i
\(653\) 462788. 1.08531 0.542657 0.839954i \(-0.317418\pi\)
0.542657 + 0.839954i \(0.317418\pi\)
\(654\) 0 0
\(655\) 368918.i 0.859899i
\(656\) −34193.3 + 39335.3i −0.0794571 + 0.0914059i
\(657\) 0 0
\(658\) 94750.4 + 60945.3i 0.218841 + 0.140763i
\(659\) 602985.i 1.38847i 0.719749 + 0.694234i \(0.244257\pi\)
−0.719749 + 0.694234i \(0.755743\pi\)
\(660\) 0 0
\(661\) 412862. 0.944935 0.472468 0.881348i \(-0.343363\pi\)
0.472468 + 0.881348i \(0.343363\pi\)
\(662\) −193683. + 301115.i −0.441952 + 0.687094i
\(663\) 0 0
\(664\) 13553.7 + 1965.13i 0.0307412 + 0.00445713i
\(665\) −166994. −0.377623
\(666\) 0 0
\(667\) 205116.i 0.461049i
\(668\) 454745. 207241.i 1.01910 0.464432i
\(669\) 0 0
\(670\) −684657. + 1.06442e6i −1.52519 + 2.37118i
\(671\) 291619.i 0.647696i
\(672\) 0 0
\(673\) −372998. −0.823525 −0.411763 0.911291i \(-0.635087\pi\)
−0.411763 + 0.911291i \(0.635087\pi\)
\(674\) 452234. + 290886.i 0.995506 + 0.640329i
\(675\) 0 0
\(676\) 64617.0 + 141788.i 0.141401 + 0.310275i
\(677\) 359783. 0.784989 0.392494 0.919754i \(-0.371612\pi\)
0.392494 + 0.919754i \(0.371612\pi\)
\(678\) 0 0
\(679\) 14431.3i 0.0313015i
\(680\) 120082. 828214.i 0.259693 1.79112i
\(681\) 0 0
\(682\) 860444. + 553454.i 1.84992 + 1.18991i
\(683\) 107389.i 0.230206i −0.993354 0.115103i \(-0.963280\pi\)
0.993354 0.115103i \(-0.0367199\pi\)
\(684\) 0 0
\(685\) −1.44611e6 −3.08191
\(686\) 140574. 218547.i 0.298714 0.464404i
\(687\) 0 0
\(688\) −81034.3 70441.3i −0.171195 0.148816i
\(689\) −40403.0 −0.0851090
\(690\) 0 0
\(691\) 617454.i 1.29315i 0.762851 + 0.646574i \(0.223799\pi\)
−0.762851 + 0.646574i \(0.776201\pi\)
\(692\) −130727. 286851.i −0.272993 0.599025i
\(693\) 0 0
\(694\) −158154. + 245879.i −0.328369 + 0.510509i
\(695\) 371956.i 0.770054i
\(696\) 0 0
\(697\) 61828.4 0.127269
\(698\) 182462. + 117363.i 0.374508 + 0.240891i
\(699\) 0 0
\(700\) −252542. + 115091.i −0.515391 + 0.234879i
\(701\) 486515. 0.990057 0.495028 0.868877i \(-0.335158\pi\)
0.495028 + 0.868877i \(0.335158\pi\)
\(702\) 0 0
\(703\) 171510.i 0.347040i
\(704\) 243689. 822704.i 0.491689 1.65996i
\(705\) 0 0
\(706\) 97667.0 + 62821.3i 0.195947 + 0.126037i
\(707\) 33513.6i 0.0670475i
\(708\) 0 0
\(709\) −144205. −0.286872 −0.143436 0.989660i \(-0.545815\pi\)
−0.143436 + 0.989660i \(0.545815\pi\)
\(710\) −796314. + 1.23801e6i −1.57967 + 2.45589i
\(711\) 0 0
\(712\) 77500.9 534529.i 0.152879 1.05441i
\(713\) 569390. 1.12003
\(714\) 0 0
\(715\) 1.76521e6i 3.45289i
\(716\) −13567.4 + 6183.06i −0.0264649 + 0.0120608i
\(717\) 0 0
\(718\) −19902.5 + 30942.0i −0.0386063 + 0.0600204i
\(719\) 978439.i 1.89268i 0.323179 + 0.946338i \(0.395248\pi\)
−0.323179 + 0.946338i \(0.604752\pi\)
\(720\) 0 0
\(721\) 119700. 0.230263
\(722\) −184391. 118604.i −0.353725 0.227523i
\(723\) 0 0
\(724\) 54421.3 + 119416.i 0.103822 + 0.227816i
\(725\) 540548. 1.02839
\(726\) 0 0
\(727\) 650971.i 1.23166i −0.787877 0.615832i \(-0.788820\pi\)
0.787877 0.615832i \(-0.211180\pi\)
\(728\) −174947. 25365.4i −0.330098 0.0478606i
\(729\) 0 0
\(730\) 470111. + 302385.i 0.882175 + 0.567432i
\(731\) 127372.i 0.238364i
\(732\) 0 0
\(733\) −502166. −0.934629 −0.467315 0.884091i \(-0.654778\pi\)
−0.467315 + 0.884091i \(0.654778\pi\)
\(734\) 208018. 323401.i 0.386108 0.600274i
\(735\) 0 0
\(736\) −133632. 458461.i −0.246692 0.846343i
\(737\) 1.53933e6 2.83397
\(738\) 0 0
\(739\) 143898.i 0.263491i 0.991284 + 0.131745i \(0.0420581\pi\)
−0.991284 + 0.131745i \(0.957942\pi\)
\(740\) 178315. + 391274.i 0.325631 + 0.714526i
\(741\) 0 0
\(742\) 6305.20 9802.55i 0.0114522 0.0178046i
\(743\) 639135.i 1.15775i 0.815416 + 0.578876i \(0.196508\pi\)
−0.815416 + 0.578876i \(0.803492\pi\)
\(744\) 0 0
\(745\) −1.03754e6 −1.86936
\(746\) 93284.0 + 60002.1i 0.167621 + 0.107817i
\(747\) 0 0
\(748\) −926223. + 422107.i −1.65544 + 0.754431i
\(749\) −135210. −0.241015
\(750\) 0 0
\(751\) 494004.i 0.875892i −0.899001 0.437946i \(-0.855706\pi\)
0.899001 0.437946i \(-0.144294\pi\)
\(752\) −385549. 335150.i −0.681780 0.592656i
\(753\) 0 0
\(754\) 289577. + 186261.i 0.509355 + 0.327627i
\(755\) 1.14158e6i 2.00268i
\(756\) 0 0
\(757\) −207090. −0.361382 −0.180691 0.983540i \(-0.557833\pi\)
−0.180691 + 0.983540i \(0.557833\pi\)
\(758\) 220508. 342819.i 0.383784 0.596660i
\(759\) 0 0
\(760\) 749408. + 108656.i 1.29745 + 0.188116i
\(761\) −584487. −1.00927 −0.504633 0.863334i \(-0.668372\pi\)
−0.504633 + 0.863334i \(0.668372\pi\)
\(762\) 0 0
\(763\) 163013.i 0.280011i
\(764\) −47807.9 + 21787.4i −0.0819054 + 0.0373267i
\(765\) 0 0
\(766\) 13549.8 21065.6i 0.0230927 0.0359017i
\(767\) 454396.i 0.772402i
\(768\) 0 0
\(769\) 521698. 0.882200 0.441100 0.897458i \(-0.354588\pi\)
0.441100 + 0.897458i \(0.354588\pi\)
\(770\) 428273. + 275474.i 0.722336 + 0.464621i
\(771\) 0 0
\(772\) 468879. + 1.02885e6i 0.786731 + 1.72631i
\(773\) −810366. −1.35620 −0.678098 0.734971i \(-0.737196\pi\)
−0.678098 + 0.734971i \(0.737196\pi\)
\(774\) 0 0
\(775\) 1.50053e6i 2.49828i
\(776\) −9389.81 + 64762.2i −0.0155931 + 0.107547i
\(777\) 0 0
\(778\) −497185. 319799.i −0.821408 0.528346i
\(779\) 55945.3i 0.0921911i
\(780\) 0 0
\(781\) 1.79037e6 2.93521
\(782\) −306459. + 476445.i −0.501140 + 0.779111i
\(783\) 0 0
\(784\) −369792. + 425402.i −0.601625 + 0.692098i
\(785\) −1.42914e6 −2.31918
\(786\) 0 0
\(787\) 380693.i 0.614646i −0.951605 0.307323i \(-0.900567\pi\)
0.951605 0.307323i \(-0.0994332\pi\)