Properties

Label 108.5.k.a.5.3
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.74246 + 4.58850i) q^{3} +(-2.39469 - 6.57935i) q^{5} +(-4.62159 - 26.2104i) q^{7} +(38.8914 - 71.0525i) q^{9} +O(q^{10})\) \(q+(-7.74246 + 4.58850i) q^{3} +(-2.39469 - 6.57935i) q^{5} +(-4.62159 - 26.2104i) q^{7} +(38.8914 - 71.0525i) q^{9} +(-16.9285 + 46.5107i) q^{11} +(94.6619 + 79.4308i) q^{13} +(48.7301 + 39.9523i) q^{15} +(285.051 + 164.574i) q^{17} +(116.459 + 201.713i) q^{19} +(156.049 + 181.727i) q^{21} +(392.366 + 69.1848i) q^{23} +(441.224 - 370.231i) q^{25} +(24.9088 + 728.574i) q^{27} +(555.504 + 662.024i) q^{29} +(-8.30835 + 47.1190i) q^{31} +(-82.3458 - 437.784i) q^{33} +(-161.380 + 93.1727i) q^{35} +(822.095 - 1423.91i) q^{37} +(-1097.38 - 180.634i) q^{39} +(242.838 - 289.403i) q^{41} +(-807.328 - 293.843i) q^{43} +(-560.612 - 85.7317i) q^{45} +(-579.809 + 102.236i) q^{47} +(1590.58 - 578.923i) q^{49} +(-2962.14 + 33.7453i) q^{51} +1451.91i q^{53} +346.549 q^{55} +(-1827.24 - 1027.38i) q^{57} +(1907.08 + 5239.66i) q^{59} +(-744.330 - 4221.31i) q^{61} +(-2042.05 - 690.982i) q^{63} +(295.917 - 813.026i) q^{65} +(-2803.64 - 2352.53i) q^{67} +(-3355.34 + 1264.71i) q^{69} +(68.5308 + 39.5663i) q^{71} +(-1304.49 - 2259.43i) q^{73} +(-1717.36 + 4891.06i) q^{75} +(1297.30 + 228.749i) q^{77} +(4203.68 - 3527.30i) q^{79} +(-3535.92 - 5526.66i) q^{81} +(2372.59 + 2827.55i) q^{83} +(400.183 - 2269.55i) q^{85} +(-7338.66 - 2576.77i) q^{87} +(-3207.30 + 1851.74i) q^{89} +(1644.42 - 2848.22i) q^{91} +(-151.878 - 402.940i) q^{93} +(1048.25 - 1249.26i) q^{95} +(-1634.86 - 595.041i) q^{97} +(2646.33 + 3011.68i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −7.74246 + 4.58850i −0.860273 + 0.509833i
\(4\) 0 0
\(5\) −2.39469 6.57935i −0.0957875 0.263174i 0.882540 0.470237i \(-0.155832\pi\)
−0.978328 + 0.207063i \(0.933609\pi\)
\(6\) 0 0
\(7\) −4.62159 26.2104i −0.0943182 0.534905i −0.994954 0.100331i \(-0.968010\pi\)
0.900636 0.434574i \(-0.143101\pi\)
\(8\) 0 0
\(9\) 38.8914 71.0525i 0.480141 0.877191i
\(10\) 0 0
\(11\) −16.9285 + 46.5107i −0.139905 + 0.384386i −0.989781 0.142597i \(-0.954455\pi\)
0.849876 + 0.526983i \(0.176677\pi\)
\(12\) 0 0
\(13\) 94.6619 + 79.4308i 0.560130 + 0.470005i 0.878354 0.478011i \(-0.158642\pi\)
−0.318224 + 0.948015i \(0.603086\pi\)
\(14\) 0 0
\(15\) 48.7301 + 39.9523i 0.216578 + 0.177566i
\(16\) 0 0
\(17\) 285.051 + 164.574i 0.986335 + 0.569461i 0.904177 0.427158i \(-0.140485\pi\)
0.0821585 + 0.996619i \(0.473819\pi\)
\(18\) 0 0
\(19\) 116.459 + 201.713i 0.322601 + 0.558761i 0.981024 0.193887i \(-0.0621096\pi\)
−0.658423 + 0.752648i \(0.728776\pi\)
\(20\) 0 0
\(21\) 156.049 + 181.727i 0.353852 + 0.412078i
\(22\) 0 0
\(23\) 392.366 + 69.1848i 0.741713 + 0.130784i 0.531722 0.846919i \(-0.321545\pi\)
0.209992 + 0.977703i \(0.432656\pi\)
\(24\) 0 0
\(25\) 441.224 370.231i 0.705959 0.592370i
\(26\) 0 0
\(27\) 24.9088 + 728.574i 0.0341684 + 0.999416i
\(28\) 0 0
\(29\) 555.504 + 662.024i 0.660528 + 0.787187i 0.987461 0.157861i \(-0.0504597\pi\)
−0.326933 + 0.945047i \(0.606015\pi\)
\(30\) 0 0
\(31\) −8.30835 + 47.1190i −0.00864552 + 0.0490312i −0.988825 0.149079i \(-0.952369\pi\)
0.980180 + 0.198110i \(0.0634803\pi\)
\(32\) 0 0
\(33\) −82.3458 437.784i −0.0756160 0.402005i
\(34\) 0 0
\(35\) −161.380 + 93.1727i −0.131739 + 0.0760593i
\(36\) 0 0
\(37\) 822.095 1423.91i 0.600508 1.04011i −0.392236 0.919864i \(-0.628298\pi\)
0.992744 0.120246i \(-0.0383682\pi\)
\(38\) 0 0
\(39\) −1097.38 180.634i −0.721488 0.118760i
\(40\) 0 0
\(41\) 242.838 289.403i 0.144460 0.172161i −0.688962 0.724797i \(-0.741934\pi\)
0.833423 + 0.552636i \(0.186378\pi\)
\(42\) 0 0
\(43\) −807.328 293.843i −0.436629 0.158920i 0.114347 0.993441i \(-0.463522\pi\)
−0.550976 + 0.834521i \(0.685745\pi\)
\(44\) 0 0
\(45\) −560.612 85.7317i −0.276845 0.0423366i
\(46\) 0 0
\(47\) −579.809 + 102.236i −0.262476 + 0.0462815i −0.303337 0.952883i \(-0.598101\pi\)
0.0408616 + 0.999165i \(0.486990\pi\)
\(48\) 0 0
\(49\) 1590.58 578.923i 0.662465 0.241118i
\(50\) 0 0
\(51\) −2962.14 + 33.7453i −1.13885 + 0.0129740i
\(52\) 0 0
\(53\) 1451.91i 0.516880i 0.966027 + 0.258440i \(0.0832084\pi\)
−0.966027 + 0.258440i \(0.916792\pi\)
\(54\) 0 0
\(55\) 346.549 0.114562
\(56\) 0 0
\(57\) −1827.24 1027.38i −0.562399 0.316215i
\(58\) 0 0
\(59\) 1907.08 + 5239.66i 0.547854 + 1.50522i 0.836601 + 0.547812i \(0.184539\pi\)
−0.288747 + 0.957405i \(0.593239\pi\)
\(60\) 0 0
\(61\) −744.330 4221.31i −0.200035 1.13445i −0.905064 0.425276i \(-0.860177\pi\)
0.705029 0.709179i \(-0.250934\pi\)
\(62\) 0 0
\(63\) −2042.05 690.982i −0.514500 0.174095i
\(64\) 0 0
\(65\) 295.917 813.026i 0.0700396 0.192432i
\(66\) 0 0
\(67\) −2803.64 2352.53i −0.624557 0.524066i 0.274675 0.961537i \(-0.411430\pi\)
−0.899232 + 0.437471i \(0.855874\pi\)
\(68\) 0 0
\(69\) −3355.34 + 1264.71i −0.704754 + 0.265640i
\(70\) 0 0
\(71\) 68.5308 + 39.5663i 0.0135947 + 0.00784889i 0.506782 0.862074i \(-0.330835\pi\)
−0.493187 + 0.869923i \(0.664168\pi\)
\(72\) 0 0
\(73\) −1304.49 2259.43i −0.244790 0.423988i 0.717283 0.696782i \(-0.245386\pi\)
−0.962073 + 0.272794i \(0.912052\pi\)
\(74\) 0 0
\(75\) −1717.36 + 4891.06i −0.305308 + 0.869521i
\(76\) 0 0
\(77\) 1297.30 + 228.749i 0.218806 + 0.0385814i
\(78\) 0 0
\(79\) 4203.68 3527.30i 0.673558 0.565182i −0.240558 0.970635i \(-0.577330\pi\)
0.914116 + 0.405452i \(0.132886\pi\)
\(80\) 0 0
\(81\) −3535.92 5526.66i −0.538929 0.842351i
\(82\) 0 0
\(83\) 2372.59 + 2827.55i 0.344403 + 0.410444i 0.910245 0.414070i \(-0.135893\pi\)
−0.565842 + 0.824514i \(0.691449\pi\)
\(84\) 0 0
\(85\) 400.183 2269.55i 0.0553887 0.314125i
\(86\) 0 0
\(87\) −7338.66 2576.77i −0.969569 0.340437i
\(88\) 0 0
\(89\) −3207.30 + 1851.74i −0.404911 + 0.233776i −0.688601 0.725140i \(-0.741775\pi\)
0.283690 + 0.958916i \(0.408441\pi\)
\(90\) 0 0
\(91\) 1644.42 2848.22i 0.198577 0.343946i
\(92\) 0 0
\(93\) −151.878 402.940i −0.0175602 0.0465880i
\(94\) 0 0
\(95\) 1048.25 1249.26i 0.116150 0.138422i
\(96\) 0 0
\(97\) −1634.86 595.041i −0.173755 0.0632417i 0.253678 0.967289i \(-0.418360\pi\)
−0.427433 + 0.904047i \(0.640582\pi\)
\(98\) 0 0
\(99\) 2646.33 + 3011.68i 0.270006 + 0.307283i
\(100\) 0 0
\(101\) 11040.4 1946.73i 1.08229 0.190837i 0.396062 0.918224i \(-0.370377\pi\)
0.686227 + 0.727387i \(0.259265\pi\)
\(102\) 0 0
\(103\) −3421.96 + 1245.49i −0.322553 + 0.117400i −0.498222 0.867050i \(-0.666013\pi\)
0.175669 + 0.984449i \(0.443791\pi\)
\(104\) 0 0
\(105\) 821.954 1461.88i 0.0745537 0.132596i
\(106\) 0 0
\(107\) 12263.4i 1.07113i 0.844493 + 0.535566i \(0.179902\pi\)
−0.844493 + 0.535566i \(0.820098\pi\)
\(108\) 0 0
\(109\) 20211.4 1.70115 0.850575 0.525854i \(-0.176254\pi\)
0.850575 + 0.525854i \(0.176254\pi\)
\(110\) 0 0
\(111\) 168.567 + 14796.8i 0.0136813 + 1.20094i
\(112\) 0 0
\(113\) 5651.59 + 15527.6i 0.442602 + 1.21604i 0.937774 + 0.347245i \(0.112883\pi\)
−0.495172 + 0.868795i \(0.664895\pi\)
\(114\) 0 0
\(115\) −484.404 2747.19i −0.0366279 0.207727i
\(116\) 0 0
\(117\) 9325.29 3636.79i 0.681225 0.265672i
\(118\) 0 0
\(119\) 2996.16 8231.88i 0.211578 0.581306i
\(120\) 0 0
\(121\) 9338.98 + 7836.34i 0.637865 + 0.535232i
\(122\) 0 0
\(123\) −552.239 + 3354.95i −0.0365020 + 0.221756i
\(124\) 0 0
\(125\) −7282.20 4204.38i −0.466061 0.269080i
\(126\) 0 0
\(127\) 3442.74 + 5963.01i 0.213451 + 0.369707i 0.952792 0.303623i \(-0.0981964\pi\)
−0.739342 + 0.673331i \(0.764863\pi\)
\(128\) 0 0
\(129\) 7599.00 1429.35i 0.456643 0.0858932i
\(130\) 0 0
\(131\) 15623.6 + 2754.87i 0.910415 + 0.160531i 0.609192 0.793023i \(-0.291494\pi\)
0.301223 + 0.953554i \(0.402605\pi\)
\(132\) 0 0
\(133\) 4748.73 3984.66i 0.268457 0.225262i
\(134\) 0 0
\(135\) 4733.90 1908.59i 0.259747 0.104724i
\(136\) 0 0
\(137\) −16763.9 19978.5i −0.893170 1.06444i −0.997554 0.0699017i \(-0.977731\pi\)
0.104384 0.994537i \(-0.466713\pi\)
\(138\) 0 0
\(139\) −3919.05 + 22226.1i −0.202839 + 1.15036i 0.697965 + 0.716132i \(0.254089\pi\)
−0.900804 + 0.434226i \(0.857022\pi\)
\(140\) 0 0
\(141\) 4020.04 3452.01i 0.202205 0.173633i
\(142\) 0 0
\(143\) −5296.87 + 3058.15i −0.259028 + 0.149550i
\(144\) 0 0
\(145\) 3025.43 5240.20i 0.143897 0.249236i
\(146\) 0 0
\(147\) −9658.60 + 11780.7i −0.446971 + 0.545173i
\(148\) 0 0
\(149\) −2520.68 + 3004.02i −0.113539 + 0.135310i −0.819820 0.572621i \(-0.805927\pi\)
0.706282 + 0.707931i \(0.250371\pi\)
\(150\) 0 0
\(151\) −35103.6 12776.7i −1.53957 0.560356i −0.573625 0.819118i \(-0.694463\pi\)
−0.965941 + 0.258762i \(0.916686\pi\)
\(152\) 0 0
\(153\) 22779.4 13853.1i 0.973106 0.591783i
\(154\) 0 0
\(155\) 329.908 58.1717i 0.0137319 0.00242130i
\(156\) 0 0
\(157\) −35398.4 + 12884.0i −1.43610 + 0.522697i −0.938672 0.344810i \(-0.887943\pi\)
−0.497425 + 0.867507i \(0.665721\pi\)
\(158\) 0 0
\(159\) −6662.10 11241.4i −0.263522 0.444658i
\(160\) 0 0
\(161\) 10603.8i 0.409082i
\(162\) 0 0
\(163\) 5722.24 0.215373 0.107686 0.994185i \(-0.465656\pi\)
0.107686 + 0.994185i \(0.465656\pi\)
\(164\) 0 0
\(165\) −2683.14 + 1590.14i −0.0985543 + 0.0584072i
\(166\) 0 0
\(167\) −3814.37 10479.9i −0.136770 0.375772i 0.852333 0.523000i \(-0.175187\pi\)
−0.989103 + 0.147228i \(0.952965\pi\)
\(168\) 0 0
\(169\) −2307.94 13089.0i −0.0808073 0.458281i
\(170\) 0 0
\(171\) 18861.4 429.802i 0.645034 0.0146986i
\(172\) 0 0
\(173\) 9145.34 25126.6i 0.305568 0.839541i −0.687939 0.725769i \(-0.741484\pi\)
0.993507 0.113772i \(-0.0362934\pi\)
\(174\) 0 0
\(175\) −11743.1 9853.59i −0.383447 0.321750i
\(176\) 0 0
\(177\) −38807.7 31817.2i −1.23871 1.01558i
\(178\) 0 0
\(179\) −40225.0 23223.9i −1.25542 0.724819i −0.283242 0.959049i \(-0.591410\pi\)
−0.972181 + 0.234230i \(0.924743\pi\)
\(180\) 0 0
\(181\) 24531.3 + 42489.5i 0.748797 + 1.29695i 0.948400 + 0.317077i \(0.102701\pi\)
−0.199603 + 0.979877i \(0.563965\pi\)
\(182\) 0 0
\(183\) 25132.4 + 29267.9i 0.750467 + 0.873957i
\(184\) 0 0
\(185\) −11337.1 1999.03i −0.331251 0.0584085i
\(186\) 0 0
\(187\) −12480.0 + 10471.9i −0.356886 + 0.299463i
\(188\) 0 0
\(189\) 18981.1 4020.04i 0.531370 0.112540i
\(190\) 0 0
\(191\) −22885.6 27273.9i −0.627328 0.747621i 0.354984 0.934872i \(-0.384486\pi\)
−0.982312 + 0.187252i \(0.940042\pi\)
\(192\) 0 0
\(193\) −9753.90 + 55317.1i −0.261857 + 1.48506i 0.515982 + 0.856599i \(0.327427\pi\)
−0.777839 + 0.628464i \(0.783684\pi\)
\(194\) 0 0
\(195\) 1439.44 + 7652.63i 0.0378550 + 0.201253i
\(196\) 0 0
\(197\) −54922.0 + 31709.2i −1.41519 + 0.817059i −0.995871 0.0907812i \(-0.971064\pi\)
−0.419317 + 0.907840i \(0.637730\pi\)
\(198\) 0 0
\(199\) 1739.17 3012.33i 0.0439172 0.0760669i −0.843231 0.537551i \(-0.819350\pi\)
0.887148 + 0.461484i \(0.152683\pi\)
\(200\) 0 0
\(201\) 32501.6 + 5349.90i 0.804476 + 0.132420i
\(202\) 0 0
\(203\) 14784.6 17619.6i 0.358770 0.427566i
\(204\) 0 0
\(205\) −2485.60 904.686i −0.0591458 0.0215273i
\(206\) 0 0
\(207\) 20175.4 25187.9i 0.470850 0.587830i
\(208\) 0 0
\(209\) −11353.3 + 2001.89i −0.259913 + 0.0458297i
\(210\) 0 0
\(211\) −41197.3 + 14994.6i −0.925346 + 0.336799i −0.760363 0.649498i \(-0.774979\pi\)
−0.164983 + 0.986296i \(0.552757\pi\)
\(212\) 0 0
\(213\) −712.146 + 8.11291i −0.0156968 + 0.000178820i
\(214\) 0 0
\(215\) 6015.35i 0.130132i
\(216\) 0 0
\(217\) 1273.40 0.0270425
\(218\) 0 0
\(219\) 20467.3 + 11508.0i 0.426749 + 0.239944i
\(220\) 0 0
\(221\) 13911.2 + 38220.7i 0.284826 + 0.782554i
\(222\) 0 0
\(223\) −9275.03 52601.3i −0.186512 1.05776i −0.923998 0.382397i \(-0.875099\pi\)
0.737486 0.675362i \(-0.236013\pi\)
\(224\) 0 0
\(225\) −9146.01 45748.9i −0.180662 0.903682i
\(226\) 0 0
\(227\) 31965.3 87823.9i 0.620336 1.70436i −0.0858271 0.996310i \(-0.527353\pi\)
0.706163 0.708049i \(-0.250425\pi\)
\(228\) 0 0
\(229\) 45556.5 + 38226.5i 0.868720 + 0.728942i 0.963828 0.266525i \(-0.0858753\pi\)
−0.0951084 + 0.995467i \(0.530320\pi\)
\(230\) 0 0
\(231\) −11093.9 + 4181.57i −0.207903 + 0.0783638i
\(232\) 0 0
\(233\) −90002.3 51962.9i −1.65784 0.957153i −0.973710 0.227790i \(-0.926850\pi\)
−0.684127 0.729363i \(-0.739817\pi\)
\(234\) 0 0
\(235\) 2061.11 + 3569.94i 0.0373220 + 0.0646435i
\(236\) 0 0
\(237\) −16361.8 + 46598.6i −0.291296 + 0.829614i
\(238\) 0 0
\(239\) 94510.7 + 16664.8i 1.65457 + 0.291745i 0.921491 0.388399i \(-0.126972\pi\)
0.733079 + 0.680144i \(0.238083\pi\)
\(240\) 0 0
\(241\) 4706.66 3949.36i 0.0810362 0.0679975i −0.601370 0.798971i \(-0.705378\pi\)
0.682406 + 0.730973i \(0.260934\pi\)
\(242\) 0 0
\(243\) 52735.8 + 26565.5i 0.893085 + 0.449888i
\(244\) 0 0
\(245\) −7617.87 9078.63i −0.126912 0.151247i
\(246\) 0 0
\(247\) −4997.97 + 28344.9i −0.0819219 + 0.464602i
\(248\) 0 0
\(249\) −31343.9 11005.5i −0.505539 0.177506i
\(250\) 0 0
\(251\) 56184.4 32438.1i 0.891802 0.514882i 0.0172704 0.999851i \(-0.494502\pi\)
0.874531 + 0.484969i \(0.161169\pi\)
\(252\) 0 0
\(253\) −9860.01 + 17078.0i −0.154041 + 0.266807i
\(254\) 0 0
\(255\) 7315.43 + 19408.2i 0.112502 + 0.298472i
\(256\) 0 0
\(257\) −54498.0 + 64948.2i −0.825115 + 0.983334i −0.999999 0.00125545i \(-0.999600\pi\)
0.174884 + 0.984589i \(0.444045\pi\)
\(258\) 0 0
\(259\) −41120.6 14966.7i −0.612999 0.223113i
\(260\) 0 0
\(261\) 68642.8 13722.9i 1.00766 0.201449i
\(262\) 0 0
\(263\) 58941.3 10392.9i 0.852134 0.150254i 0.269512 0.962997i \(-0.413138\pi\)
0.582622 + 0.812743i \(0.302027\pi\)
\(264\) 0 0
\(265\) 9552.65 3476.88i 0.136029 0.0495106i
\(266\) 0 0
\(267\) 16335.7 29053.7i 0.229148 0.407548i
\(268\) 0 0
\(269\) 112684.i 1.55725i 0.627491 + 0.778624i \(0.284082\pi\)
−0.627491 + 0.778624i \(0.715918\pi\)
\(270\) 0 0
\(271\) 124765. 1.69885 0.849423 0.527712i \(-0.176950\pi\)
0.849423 + 0.527712i \(0.176950\pi\)
\(272\) 0 0
\(273\) 337.182 + 29597.6i 0.00452417 + 0.397129i
\(274\) 0 0
\(275\) 9750.45 + 26789.1i 0.128932 + 0.354236i
\(276\) 0 0
\(277\) 2480.76 + 14069.1i 0.0323314 + 0.183361i 0.996697 0.0812137i \(-0.0258796\pi\)
−0.964365 + 0.264574i \(0.914769\pi\)
\(278\) 0 0
\(279\) 3024.80 + 2422.85i 0.0388587 + 0.0311257i
\(280\) 0 0
\(281\) 2564.76 7046.62i 0.0324813 0.0892417i −0.922392 0.386255i \(-0.873768\pi\)
0.954873 + 0.297013i \(0.0959906\pi\)
\(282\) 0 0
\(283\) −35218.1 29551.5i −0.439737 0.368983i 0.395874 0.918305i \(-0.370442\pi\)
−0.835611 + 0.549322i \(0.814886\pi\)
\(284\) 0 0
\(285\) −2383.84 + 14482.3i −0.0293486 + 0.178298i
\(286\) 0 0
\(287\) −8707.65 5027.37i −0.105715 0.0610347i
\(288\) 0 0
\(289\) 12408.8 + 21492.7i 0.148572 + 0.257333i
\(290\) 0 0
\(291\) 15388.2 2894.48i 0.181720 0.0341809i
\(292\) 0 0
\(293\) 76504.6 + 13489.8i 0.891153 + 0.157134i 0.600434 0.799674i \(-0.294994\pi\)
0.290719 + 0.956808i \(0.406106\pi\)
\(294\) 0 0
\(295\) 29906.7 25094.7i 0.343656 0.288362i
\(296\) 0 0
\(297\) −34308.2 11175.2i −0.388942 0.126690i
\(298\) 0 0
\(299\) 31646.8 + 37715.1i 0.353987 + 0.421865i
\(300\) 0 0
\(301\) −3970.60 + 22518.4i −0.0438251 + 0.248544i
\(302\) 0 0
\(303\) −76547.6 + 65731.4i −0.833770 + 0.715958i
\(304\) 0 0
\(305\) −25991.0 + 15005.9i −0.279398 + 0.161311i
\(306\) 0 0
\(307\) 39030.5 67602.8i 0.414121 0.717279i −0.581215 0.813750i \(-0.697422\pi\)
0.995336 + 0.0964716i \(0.0307557\pi\)
\(308\) 0 0
\(309\) 20779.5 25344.9i 0.217630 0.265444i
\(310\) 0 0
\(311\) 22796.0 27167.3i 0.235689 0.280883i −0.635216 0.772334i \(-0.719089\pi\)
0.870905 + 0.491451i \(0.163533\pi\)
\(312\) 0 0
\(313\) 39308.2 + 14307.0i 0.401231 + 0.146036i 0.534750 0.845010i \(-0.320406\pi\)
−0.133519 + 0.991046i \(0.542628\pi\)
\(314\) 0 0
\(315\) 343.862 + 15090.1i 0.00346548 + 0.152079i
\(316\) 0 0
\(317\) −28243.0 + 4980.00i −0.281055 + 0.0495576i −0.312399 0.949951i \(-0.601133\pi\)
0.0313435 + 0.999509i \(0.490021\pi\)
\(318\) 0 0
\(319\) −40195.1 + 14629.8i −0.394995 + 0.143766i
\(320\) 0 0
\(321\) −56270.5 94948.8i −0.546098 0.921466i
\(322\) 0 0
\(323\) 76664.5i 0.734834i
\(324\) 0 0
\(325\) 71174.9 0.673845
\(326\) 0 0
\(327\) −156486. + 92739.8i −1.46345 + 0.867302i
\(328\) 0 0
\(329\) 5359.28 + 14724.5i 0.0495125 + 0.136034i
\(330\) 0 0
\(331\) −30145.6 170964.i −0.275149 1.56045i −0.738489 0.674266i \(-0.764460\pi\)
0.463340 0.886181i \(-0.346651\pi\)
\(332\) 0 0
\(333\) −69200.0 113790.i −0.624047 1.02616i
\(334\) 0 0
\(335\) −8764.29 + 24079.7i −0.0780957 + 0.214566i
\(336\) 0 0
\(337\) −82889.8 69552.8i −0.729863 0.612428i 0.200231 0.979749i \(-0.435831\pi\)
−0.930094 + 0.367321i \(0.880275\pi\)
\(338\) 0 0
\(339\) −115006. 94289.6i −1.00074 0.820474i
\(340\) 0 0
\(341\) −2050.89 1184.08i −0.0176374 0.0101829i
\(342\) 0 0
\(343\) −54475.7 94354.7i −0.463036 0.802002i
\(344\) 0 0
\(345\) 16356.0 + 19047.3i 0.137416 + 0.160028i
\(346\) 0 0
\(347\) −65651.3 11576.1i −0.545236 0.0961398i −0.105756 0.994392i \(-0.533726\pi\)
−0.439480 + 0.898252i \(0.644837\pi\)
\(348\) 0 0
\(349\) 17393.2 14594.6i 0.142800 0.119823i −0.568589 0.822621i \(-0.692511\pi\)
0.711389 + 0.702798i \(0.248066\pi\)
\(350\) 0 0
\(351\) −55513.3 + 70946.8i −0.450591 + 0.575862i
\(352\) 0 0
\(353\) −46885.1 55875.5i −0.376258 0.448407i 0.544371 0.838844i \(-0.316768\pi\)
−0.920629 + 0.390437i \(0.872324\pi\)
\(354\) 0 0
\(355\) 96.2104 545.637i 0.000763424 0.00432959i
\(356\) 0 0
\(357\) 14574.3 + 77482.9i 0.114354 + 0.607952i
\(358\) 0 0
\(359\) 90021.6 51974.0i 0.698487 0.403271i −0.108297 0.994119i \(-0.534540\pi\)
0.806783 + 0.590847i \(0.201206\pi\)
\(360\) 0 0
\(361\) 38035.2 65878.9i 0.291858 0.505512i
\(362\) 0 0
\(363\) −108264. 17820.7i −0.821618 0.135242i
\(364\) 0 0
\(365\) −11741.8 + 13993.3i −0.0881349 + 0.105035i
\(366\) 0 0
\(367\) −142673. 51928.7i −1.05928 0.385545i −0.247120 0.968985i \(-0.579484\pi\)
−0.812156 + 0.583440i \(0.801706\pi\)
\(368\) 0 0
\(369\) −11118.5 28509.5i −0.0816570 0.209381i
\(370\) 0 0
\(371\) 38055.2 6710.16i 0.276482 0.0487512i
\(372\) 0 0
\(373\) 128474. 46760.5i 0.923413 0.336095i 0.163818 0.986491i \(-0.447619\pi\)
0.759596 + 0.650396i \(0.225397\pi\)
\(374\) 0 0
\(375\) 75673.9 862.092i 0.538126 0.00613043i
\(376\) 0 0
\(377\) 106793.i 0.751378i
\(378\) 0 0
\(379\) −102503. −0.713606 −0.356803 0.934180i \(-0.616133\pi\)
−0.356803 + 0.934180i \(0.616133\pi\)
\(380\) 0 0
\(381\) −54016.5 30371.3i −0.372115 0.209225i
\(382\) 0 0
\(383\) 32174.5 + 88398.6i 0.219338 + 0.602626i 0.999744 0.0226476i \(-0.00720957\pi\)
−0.780406 + 0.625274i \(0.784987\pi\)
\(384\) 0 0
\(385\) −1601.61 9083.16i −0.0108052 0.0612796i
\(386\) 0 0
\(387\) −52276.4 + 45934.7i −0.349047 + 0.306703i
\(388\) 0 0
\(389\) −36200.3 + 99459.6i −0.239229 + 0.657276i 0.760737 + 0.649060i \(0.224837\pi\)
−0.999966 + 0.00821594i \(0.997385\pi\)
\(390\) 0 0
\(391\) 100458. + 84294.6i 0.657102 + 0.551374i
\(392\) 0 0
\(393\) −133606. + 50359.5i −0.865050 + 0.326059i
\(394\) 0 0
\(395\) −33273.8 19210.7i −0.213260 0.123126i
\(396\) 0 0
\(397\) 31794.5 + 55069.7i 0.201730 + 0.349407i 0.949086 0.315017i \(-0.102010\pi\)
−0.747356 + 0.664424i \(0.768677\pi\)
\(398\) 0 0
\(399\) −18483.3 + 52640.6i −0.116100 + 0.330655i
\(400\) 0 0
\(401\) −46597.3 8216.37i −0.289783 0.0510965i 0.0268672 0.999639i \(-0.491447\pi\)
−0.316650 + 0.948543i \(0.602558\pi\)
\(402\) 0 0
\(403\) −4529.18 + 3800.43i −0.0278875 + 0.0234004i
\(404\) 0 0
\(405\) −27894.4 + 36498.7i −0.170062 + 0.222519i
\(406\) 0 0
\(407\) 52310.3 + 62340.9i 0.315790 + 0.376344i
\(408\) 0 0
\(409\) 39403.7 223470.i 0.235554 1.33589i −0.605890 0.795549i \(-0.707183\pi\)
0.841444 0.540345i \(-0.181706\pi\)
\(410\) 0 0
\(411\) 221465. + 77761.3i 1.31106 + 0.460341i
\(412\) 0 0
\(413\) 128520. 74200.9i 0.753476 0.435020i
\(414\) 0 0
\(415\) 12921.8 22381.2i 0.0750286 0.129953i
\(416\) 0 0
\(417\) −71641.0 190067.i −0.411993 1.09304i
\(418\) 0 0
\(419\) 55767.8 66461.5i 0.317655 0.378566i −0.583464 0.812139i \(-0.698303\pi\)
0.901118 + 0.433573i \(0.142747\pi\)
\(420\) 0 0
\(421\) 283952. + 103350.i 1.60207 + 0.583105i 0.979849 0.199739i \(-0.0640095\pi\)
0.622218 + 0.782844i \(0.286232\pi\)
\(422\) 0 0
\(423\) −15285.5 + 45173.0i −0.0854275 + 0.252463i
\(424\) 0 0
\(425\) 186702. 32920.6i 1.03364 0.182259i
\(426\) 0 0
\(427\) −107202. + 39018.3i −0.587959 + 0.213999i
\(428\) 0 0
\(429\) 26978.5 47982.2i 0.146590 0.260715i
\(430\) 0 0
\(431\) 203554.i 1.09579i 0.836549 + 0.547893i \(0.184570\pi\)
−0.836549 + 0.547893i \(0.815430\pi\)
\(432\) 0 0
\(433\) −172649. −0.920846 −0.460423 0.887700i \(-0.652302\pi\)
−0.460423 + 0.887700i \(0.652302\pi\)
\(434\) 0 0
\(435\) 620.352 + 54454.2i 0.00327838 + 0.287775i
\(436\) 0 0
\(437\) 31739.1 + 87202.4i 0.166200 + 0.456631i
\(438\) 0 0
\(439\) 20306.1 + 115162.i 0.105365 + 0.597557i 0.991074 + 0.133315i \(0.0425622\pi\)
−0.885708 + 0.464242i \(0.846327\pi\)
\(440\) 0 0
\(441\) 20725.9 135530.i 0.106570 0.696879i
\(442\) 0 0
\(443\) −27746.3 + 76232.3i −0.141383 + 0.388447i −0.990093 0.140411i \(-0.955157\pi\)
0.848710 + 0.528858i \(0.177380\pi\)
\(444\) 0 0
\(445\) 19863.7 + 16667.6i 0.100309 + 0.0841693i
\(446\) 0 0
\(447\) 5732.28 34824.7i 0.0286888 0.174290i
\(448\) 0 0
\(449\) −284164. 164062.i −1.40954 0.813796i −0.414193 0.910189i \(-0.635936\pi\)
−0.995343 + 0.0963929i \(0.969269\pi\)
\(450\) 0 0
\(451\) 9349.45 + 16193.7i 0.0459656 + 0.0796148i
\(452\) 0 0
\(453\) 330414. 62150.0i 1.61014 0.302862i
\(454\) 0 0
\(455\) −22677.3 3998.62i −0.109539 0.0193147i
\(456\) 0 0
\(457\) −77985.4 + 65437.5i −0.373406 + 0.313325i −0.810107 0.586282i \(-0.800591\pi\)
0.436701 + 0.899607i \(0.356147\pi\)
\(458\) 0 0
\(459\) −112804. + 211780.i −0.535427 + 1.00522i
\(460\) 0 0
\(461\) 78911.8 + 94043.5i 0.371313 + 0.442514i 0.919052 0.394135i \(-0.128956\pi\)
−0.547739 + 0.836649i \(0.684511\pi\)
\(462\) 0 0
\(463\) 7079.25 40148.4i 0.0330237 0.187287i −0.963834 0.266505i \(-0.914131\pi\)
0.996857 + 0.0792181i \(0.0252423\pi\)
\(464\) 0 0
\(465\) −2287.38 + 1964.17i −0.0105787 + 0.00908393i
\(466\) 0 0
\(467\) 333060. 192292.i 1.52718 0.881715i 0.527697 0.849433i \(-0.323056\pi\)
0.999479 0.0322828i \(-0.0102777\pi\)
\(468\) 0 0
\(469\) −48703.4 + 84356.8i −0.221418 + 0.383508i
\(470\) 0 0
\(471\) 214953. 262179.i 0.968949 1.18183i
\(472\) 0 0
\(473\) 27333.7 32575.1i 0.122173 0.145600i
\(474\) 0 0
\(475\) 126065. + 45883.8i 0.558736 + 0.203363i
\(476\) 0 0
\(477\) 103162. + 56467.0i 0.453402 + 0.248175i
\(478\) 0 0
\(479\) −403511. + 71149.9i −1.75867 + 0.310101i −0.957521 0.288363i \(-0.906889\pi\)
−0.801150 + 0.598464i \(0.795778\pi\)
\(480\) 0 0
\(481\) 190923. 69490.5i 0.825219 0.300355i
\(482\) 0 0
\(483\) 48655.5 + 82099.6i 0.208563 + 0.351922i
\(484\) 0 0
\(485\) 12181.3i 0.0517856i
\(486\) 0 0
\(487\) −10720.1 −0.0452001 −0.0226001 0.999745i \(-0.507194\pi\)
−0.0226001 + 0.999745i \(0.507194\pi\)
\(488\) 0 0
\(489\) −44304.2 + 26256.5i −0.185279 + 0.109804i
\(490\) 0 0
\(491\) −142217. 390738.i −0.589913 1.62077i −0.770662 0.637244i \(-0.780074\pi\)
0.180749 0.983529i \(-0.442148\pi\)
\(492\) 0 0
\(493\) 49394.9 + 280132.i 0.203230 + 1.15258i
\(494\) 0 0
\(495\) 13477.8 24623.1i 0.0550057 0.100492i
\(496\) 0 0
\(497\) 720.324 1979.07i 0.00291619 0.00801216i
\(498\) 0 0
\(499\) 26084.9 + 21887.9i 0.104758 + 0.0879027i 0.693662 0.720300i \(-0.255996\pi\)
−0.588904 + 0.808203i \(0.700440\pi\)
\(500\) 0 0
\(501\) 77619.5 + 63637.9i 0.309240 + 0.253537i
\(502\) 0 0
\(503\) 92901.4 + 53636.6i 0.367186 + 0.211995i 0.672228 0.740344i \(-0.265337\pi\)
−0.305042 + 0.952339i \(0.598671\pi\)
\(504\) 0 0
\(505\) −39246.6 67977.0i −0.153893 0.266551i
\(506\) 0 0
\(507\) 77927.7 + 90750.8i 0.303163 + 0.353049i
\(508\) 0 0
\(509\) −188545. 33245.5i −0.727744 0.128321i −0.202512 0.979280i \(-0.564910\pi\)
−0.525232 + 0.850959i \(0.676022\pi\)
\(510\) 0 0
\(511\) −53191.8 + 44633.2i −0.203706 + 0.170929i
\(512\) 0 0
\(513\) −144062. + 89873.3i −0.547412 + 0.341504i
\(514\) 0 0
\(515\) 16389.1 + 19531.7i 0.0617931 + 0.0736421i
\(516\) 0 0
\(517\) 5060.23 28698.0i 0.0189317 0.107367i
\(518\) 0 0
\(519\) 44485.9 + 236505.i 0.165154 + 0.878023i
\(520\) 0 0
\(521\) 412944. 238413.i 1.52130 0.878324i 0.521618 0.853179i \(-0.325329\pi\)
0.999684 0.0251453i \(-0.00800483\pi\)
\(522\) 0 0
\(523\) −190822. + 330513.i −0.697629 + 1.20833i 0.271658 + 0.962394i \(0.412428\pi\)
−0.969286 + 0.245934i \(0.920905\pi\)
\(524\) 0 0
\(525\) 136133. + 22408.1i 0.493908 + 0.0812993i
\(526\) 0 0
\(527\) −10122.9 + 12064.0i −0.0364487 + 0.0434379i
\(528\) 0 0
\(529\) −113800. 41419.7i −0.406658 0.148011i
\(530\) 0 0
\(531\) 446460. + 68275.0i 1.58341 + 0.242143i
\(532\) 0 0
\(533\) 45975.0 8106.63i 0.161833 0.0285355i
\(534\) 0 0
\(535\) 80685.1 29367.0i 0.281894 0.102601i
\(536\) 0 0
\(537\) 418003. 4761.97i 1.44954 0.0165135i
\(538\) 0 0
\(539\) 83779.2i 0.288376i
\(540\) 0 0
\(541\) −360726. −1.23249 −0.616244 0.787555i \(-0.711346\pi\)
−0.616244 + 0.787555i \(0.711346\pi\)
\(542\) 0 0
\(543\) −384896. 216411.i −1.30540 0.733974i
\(544\) 0 0
\(545\) −48399.9 132978.i −0.162949 0.447698i
\(546\) 0 0
\(547\) 51311.5 + 291002.i 0.171490 + 0.972571i 0.942117 + 0.335284i \(0.108832\pi\)
−0.770627 + 0.637287i \(0.780057\pi\)
\(548\) 0 0
\(549\) −328882. 111286.i −1.09118 0.369229i
\(550\) 0 0
\(551\) −68845.2 + 189151.i −0.226762 + 0.623024i
\(552\) 0 0
\(553\) −111880. 93878.1i −0.365848 0.306983i
\(554\) 0 0
\(555\) 96949.3 36542.7i 0.314745 0.118635i
\(556\) 0 0
\(557\) −504904. 291507.i −1.62742 0.939589i −0.984860 0.173350i \(-0.944541\pi\)
−0.642556 0.766239i \(-0.722126\pi\)
\(558\) 0 0
\(559\) −53083.0 91942.4i −0.169876 0.294234i
\(560\) 0 0
\(561\) 48575.2 138343.i 0.154344 0.439572i
\(562\) 0 0
\(563\) −445514. 78556.2i −1.40555 0.247836i −0.581125 0.813814i \(-0.697387\pi\)
−0.824420 + 0.565978i \(0.808499\pi\)
\(564\) 0 0
\(565\) 88627.8 74367.5i 0.277634 0.232963i
\(566\) 0 0
\(567\) −128514. + 118220.i −0.399747 + 0.367725i
\(568\) 0 0
\(569\) −84329.0 100499.i −0.260467 0.310412i 0.619923 0.784662i \(-0.287164\pi\)
−0.880390 + 0.474250i \(0.842719\pi\)
\(570\) 0 0
\(571\) −22878.3 + 129749.i −0.0701700 + 0.397954i 0.929412 + 0.369044i \(0.120315\pi\)
−0.999582 + 0.0289101i \(0.990796\pi\)
\(572\) 0 0
\(573\) 302337. + 106157.i 0.920835 + 0.323326i
\(574\) 0 0
\(575\) 198736. 114740.i 0.601092 0.347041i
\(576\) 0 0
\(577\) −195982. + 339451.i −0.588661 + 1.01959i 0.405747 + 0.913985i \(0.367011\pi\)
−0.994408 + 0.105605i \(0.966322\pi\)
\(578\) 0 0
\(579\) −178303. 473046.i −0.531866 1.41106i
\(580\) 0 0
\(581\) 63145.8 75254.3i 0.187065 0.222935i
\(582\) 0 0
\(583\) −67529.6 24578.8i −0.198681 0.0723141i
\(584\) 0 0
\(585\) −46258.9 52645.4i −0.135171 0.153833i
\(586\) 0 0
\(587\) −483459. + 85246.9i −1.40308 + 0.247401i −0.823410 0.567447i \(-0.807931\pi\)
−0.579674 + 0.814849i \(0.696820\pi\)
\(588\) 0 0
\(589\) −10472.1 + 3811.52i −0.0301858 + 0.0109867i
\(590\) 0 0
\(591\) 279734. 497517.i 0.800885 1.42440i
\(592\) 0 0
\(593\) 126196.i 0.358870i 0.983770 + 0.179435i \(0.0574269\pi\)
−0.983770 + 0.179435i \(0.942573\pi\)
\(594\) 0 0
\(595\) −61335.3 −0.173251
\(596\) 0 0
\(597\) 356.609 + 31303.0i 0.00100056 + 0.0878288i
\(598\) 0 0
\(599\) −214012. 587994.i −0.596465 1.63878i −0.758261 0.651951i \(-0.773951\pi\)
0.161796 0.986824i \(-0.448271\pi\)
\(600\) 0 0
\(601\) 64146.8 + 363795.i 0.177593 + 1.00718i 0.935108 + 0.354363i \(0.115302\pi\)
−0.757515 + 0.652818i \(0.773587\pi\)
\(602\) 0 0
\(603\) −276191. + 107712.i −0.759581 + 0.296231i
\(604\) 0 0
\(605\) 29194.1 80210.0i 0.0797597 0.219138i
\(606\) 0 0
\(607\) 16151.0 + 13552.3i 0.0438350 + 0.0367819i 0.664442 0.747340i \(-0.268669\pi\)
−0.620607 + 0.784122i \(0.713114\pi\)
\(608\) 0 0
\(609\) −33621.7 + 204258.i −0.0906535 + 0.550737i
\(610\) 0 0
\(611\) −63006.5 36376.8i −0.168773 0.0974411i
\(612\) 0 0
\(613\) −234797. 406680.i −0.624844 1.08226i −0.988571 0.150756i \(-0.951829\pi\)
0.363727 0.931506i \(-0.381504\pi\)
\(614\) 0 0
\(615\) 23395.8 4400.69i 0.0618569 0.0116351i
\(616\) 0 0
\(617\) −329956. 58180.1i −0.866734 0.152829i −0.277436 0.960744i \(-0.589485\pi\)
−0.589298 + 0.807916i \(0.700596\pi\)
\(618\) 0 0
\(619\) −391964. + 328896.i −1.02297 + 0.858377i −0.989998 0.141080i \(-0.954943\pi\)
−0.0329751 + 0.999456i \(0.510498\pi\)
\(620\) 0 0
\(621\) −40632.9 + 287591.i −0.105365 + 0.745749i
\(622\) 0 0
\(623\) 63357.5 + 75506.6i 0.163238 + 0.194540i
\(624\) 0 0
\(625\) 52287.4 296537.i 0.133856 0.759134i
\(626\) 0 0
\(627\) 78716.6 67594.0i 0.200231 0.171938i
\(628\) 0 0
\(629\) 468678. 270591.i 1.18460 0.683932i
\(630\) 0 0
\(631\) 213064. 369037.i 0.535120 0.926854i −0.464038 0.885815i \(-0.653600\pi\)
0.999158 0.0410389i \(-0.0130668\pi\)
\(632\) 0 0
\(633\) 250166. 305129.i 0.624340 0.761511i
\(634\) 0 0
\(635\) 30988.4 36930.5i 0.0768514 0.0915879i
\(636\) 0 0
\(637\) 196552. + 71538.9i 0.484393 + 0.176304i
\(638\) 0 0
\(639\) 5476.54 3330.49i 0.0134123 0.00815656i
\(640\) 0 0
\(641\) 161675. 28507.7i 0.393484 0.0693819i 0.0265944 0.999646i \(-0.491534\pi\)
0.366890 + 0.930264i \(0.380423\pi\)
\(642\) 0 0
\(643\) 135755. 49410.8i 0.328348 0.119509i −0.172586 0.984994i \(-0.555212\pi\)
0.500934 + 0.865486i \(0.332990\pi\)
\(644\) 0 0
\(645\) −27601.4 46573.6i −0.0663456 0.111949i
\(646\) 0 0
\(647\) 517527.i 1.23630i 0.786059 + 0.618151i \(0.212118\pi\)
−0.786059 + 0.618151i \(0.787882\pi\)
\(648\) 0 0
\(649\) −275984. −0.655232
\(650\) 0 0
\(651\) −9859.27 + 5843.00i −0.0232639 + 0.0137871i
\(652\) 0 0
\(653\) 56327.0 + 154757.i 0.132096 + 0.362931i 0.988053 0.154116i \(-0.0492531\pi\)
−0.855956 + 0.517048i \(0.827031\pi\)
\(654\) 0 0
\(655\) −19288.5 109390.i −0.0449589 0.254974i
\(656\) 0 0
\(657\) −211272. + 4814.32i −0.489453 + 0.0111533i
\(658\) 0 0
\(659\) −159820. + 439101.i −0.368010 + 1.01110i 0.608107 + 0.793855i \(0.291929\pi\)
−0.976117 + 0.217244i \(0.930293\pi\)
\(660\) 0 0
\(661\) −68881.5 57798.4i −0.157652 0.132286i 0.560550 0.828121i \(-0.310590\pi\)
−0.718201 + 0.695835i \(0.755034\pi\)
\(662\) 0 0
\(663\) −283083. 232091.i −0.644000 0.527997i
\(664\) 0 0
\(665\) −37588.2 21701.6i −0.0849979 0.0490736i
\(666\) 0 0
\(667\) 172159. + 298188.i 0.386971 + 0.670254i
\(668\) 0 0
\(669\) 313172. + 364705.i 0.699731 + 0.814873i
\(670\) 0 0
\(671\) 208936. + 36841.1i 0.464054 + 0.0818253i
\(672\) 0 0
\(673\) −12569.7 + 10547.2i −0.0277521 + 0.0232867i −0.656558 0.754275i \(-0.727988\pi\)
0.628806 + 0.777562i \(0.283544\pi\)
\(674\) 0 0
\(675\) 280731. + 312243.i 0.616146 + 0.685307i
\(676\) 0 0
\(677\) 282969. + 337229.i 0.617393 + 0.735780i 0.980620 0.195920i \(-0.0627694\pi\)
−0.363227 + 0.931701i \(0.618325\pi\)
\(678\) 0 0
\(679\) −8040.58 + 45600.4i −0.0174400 + 0.0989074i
\(680\) 0 0
\(681\) 155490. + 826646.i 0.335280 + 1.78248i
\(682\) 0 0
\(683\) 586826. 338804.i 1.25796 0.726285i 0.285285 0.958443i \(-0.407912\pi\)
0.972678 + 0.232158i \(0.0745785\pi\)
\(684\) 0 0
\(685\) −91300.9 + 158138.i −0.194578 + 0.337019i
\(686\) 0 0
\(687\) −528122. 86931.0i −1.11898 0.184188i
\(688\) 0 0
\(689\) −115327. + 137441.i −0.242936 + 0.289520i
\(690\) 0 0
\(691\) 405109. + 147448.i 0.848430 + 0.308803i 0.729400 0.684087i \(-0.239799\pi\)
0.119030 + 0.992891i \(0.462022\pi\)
\(692\) 0 0
\(693\) 66707.0 83280.0i 0.138901 0.173410i
\(694\) 0 0
\(695\) 155618. 27439.6i 0.322173 0.0568079i
\(696\) 0 0
\(697\) 116849. 42529.7i 0.240525 0.0875441i
\(698\) 0 0
\(699\) 935271. 10654.8i 1.91418 0.0218067i
\(700\) 0 0
\(701\) 267426.i 0.544211i 0.962267 + 0.272105i \(0.0877199\pi\)
−0.962267 + 0.272105i \(0.912280\pi\)
\(702\) 0 0
\(703\) 382961. 0.774897
\(704\) 0 0
\(705\) −32338.7 18182.7i −0.0650645 0.0365832i
\(706\) 0 0
\(707\) −102049. 280377.i −0.204159 0.560923i
\(708\) 0 0
\(709\) 80759.1 + 458008.i 0.160657 + 0.911130i 0.953430 + 0.301613i \(0.0975252\pi\)
−0.792774 + 0.609516i \(0.791364\pi\)
\(710\) 0 0
\(711\) −87136.8 435864.i −0.172370 0.862207i
\(712\) 0 0
\(713\) −6519.83 + 17913.1i −0.0128250 + 0.0352364i
\(714\) 0 0
\(715\) 32805.0 + 27526.6i 0.0641693 + 0.0538445i
\(716\) 0 0
\(717\) −808212. + 304635.i −1.57212 + 0.592573i
\(718\) 0 0
\(719\) 166203. + 95957.6i 0.321501 + 0.185619i 0.652061 0.758166i \(-0.273904\pi\)
−0.330560 + 0.943785i \(0.607238\pi\)
\(720\) 0 0
\(721\) 48459.7 + 83934.7i 0.0932203 + 0.161462i
\(722\) 0 0
\(723\) −18319.5 + 52174.3i −0.0350460 + 0.0998113i
\(724\) 0 0
\(725\) 490204. + 86436.2i 0.932612 + 0.164445i
\(726\) 0 0
\(727\) 646158. 542191.i 1.22256 1.02585i 0.223873 0.974618i \(-0.428130\pi\)
0.998687 0.0512314i \(-0.0163146\pi\)
\(728\) 0 0
\(729\) −530200. + 36295.8i −0.997665 + 0.0682970i
\(730\) 0 0
\(731\) −181770. 216626.i −0.340164 0.405392i
\(732\) 0 0
\(733\) 169815. 963071.i 0.316060 1.79246i −0.250154 0.968206i \(-0.580481\pi\)
0.566214 0.824258i \(-0.308408\pi\)
\(734\) 0 0
\(735\) 100638. + 35336.4i 0.186290 + 0.0654104i
\(736\) 0 0
\(737\) 156879. 90574.3i 0.288822 0.166752i
\(738\) 0 0
\(739\) 101513. 175825.i 0.185880 0.321953i −0.757993 0.652263i \(-0.773820\pi\)
0.943873 + 0.330310i \(0.107153\pi\)
\(740\) 0 0
\(741\) −91363.9 242393.i −0.166394 0.441451i
\(742\) 0 0
\(743\) −231095. + 275408.i −0.418613 + 0.498883i −0.933601 0.358314i \(-0.883352\pi\)
0.514988 + 0.857197i \(0.327796\pi\)
\(744\) 0 0
\(745\) 25800.8 + 9390.71i 0.0464857 + 0.0169194i
\(746\) 0 0
\(747\) 293178. 58611.4i 0.525400 0.105037i
\(748\) 0 0
\(749\) 321428. 56676.4i 0.572954 0.101027i
\(750\) 0 0
\(751\) 679048. 247153.i 1.20398 0.438214i 0.339370 0.940653i \(-0.389786\pi\)
0.864613 + 0.502439i \(0.167564\pi\)
\(752\) 0 0
\(753\) −286164. + 508952.i −0.504690 + 0.897609i
\(754\) 0 0
\(755\) 261555.i 0.458849i
\(756\) 0 0
\(757\) −916562. −1.59945 −0.799724 0.600367i \(-0.795021\pi\)
−0.799724 + 0.600367i \(0.795021\pi\)
\(758\) 0 0
\(759\) −2021.76 177469.i −0.00350950 0.308062i
\(760\) 0 0
\(761\) 231376. + 635700.i 0.399529 + 1.09770i 0.962514 + 0.271231i \(0.0874306\pi\)
−0.562985 + 0.826467i \(0.690347\pi\)
\(762\) 0 0
\(763\) −93408.7 529747.i −0.160449 0.909954i
\(764\) 0 0
\(765\) −145694. 116700.i −0.248953 0.199411i
\(766\) 0 0
\(767\) −235662. + 647477.i −0.400590 + 1.10061i
\(768\) 0 0
\(769\) −179399. 150534.i −0.303366 0.254555i 0.478377 0.878154i \(-0.341225\pi\)
−0.781744 + 0.623600i \(0.785670\pi\)
\(770\) 0 0
\(771\) 123934. 752923.i 0.208489 1.26661i
\(772\) 0 0
\(773\) −208696. 120491.i −0.349266 0.201649i 0.315096 0.949060i \(-0.397963\pi\)
−0.664362 + 0.747411i \(0.731297\pi\)
\(774\) 0 0
\(775\) 13779.1 + 23866.1i 0.0229412 + 0.0397354i
\(776\) 0 0
\(777\) 387049. 72802.8i 0.641098 0.120589i
\(778\) 0 0
\(779\) 86656.8 + 15279.9i 0.142800 + 0.0251795i
\(780\) 0 0