Properties

Label 108.5.k.a.5.9
Level 108
Weight 5
Character 108.5
Analytic conductor 11.164
Analytic rank 0
Dimension 72
CM no
Inner twists 2

Related objects

Downloads

Learn more about

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 5.9
Character \(\chi\) \(=\) 108.5
Dual form 108.5.k.a.65.9

$q$-expansion

\(f(q)\) \(=\) \(q+(5.44219 - 7.16816i) q^{3} +(4.60350 + 12.6480i) q^{5} +(-6.68463 - 37.9104i) q^{7} +(-21.7651 - 78.0210i) q^{9} +O(q^{10})\) \(q+(5.44219 - 7.16816i) q^{3} +(4.60350 + 12.6480i) q^{5} +(-6.68463 - 37.9104i) q^{7} +(-21.7651 - 78.0210i) q^{9} +(53.6284 - 147.343i) q^{11} +(218.794 + 183.590i) q^{13} +(115.716 + 35.8343i) q^{15} +(-358.304 - 206.867i) q^{17} +(-263.726 - 456.787i) q^{19} +(-308.127 - 158.399i) q^{21} +(72.8639 + 12.8479i) q^{23} +(339.998 - 285.292i) q^{25} +(-677.717 - 268.590i) q^{27} +(749.617 + 893.359i) q^{29} +(216.262 - 1226.48i) q^{31} +(-764.321 - 1186.29i) q^{33} +(448.719 - 259.068i) q^{35} +(-292.196 + 506.099i) q^{37} +(2506.72 - 569.218i) q^{39} +(-255.514 + 304.510i) q^{41} +(1657.55 + 603.297i) q^{43} +(886.615 - 634.454i) q^{45} +(-3421.41 + 603.286i) q^{47} +(863.684 - 314.355i) q^{49} +(-3432.82 + 1442.57i) q^{51} +2453.33i q^{53} +2110.47 q^{55} +(-4709.57 - 595.492i) q^{57} +(1740.39 + 4781.69i) q^{59} +(-86.2656 - 489.236i) q^{61} +(-2812.32 + 1346.67i) q^{63} +(-1314.83 + 3612.46i) q^{65} +(5153.66 + 4324.44i) q^{67} +(488.635 - 452.380i) q^{69} +(4493.20 + 2594.15i) q^{71} +(216.646 + 375.242i) q^{73} +(-194.685 - 3989.78i) q^{75} +(-5944.32 - 1048.14i) q^{77} +(-143.418 + 120.342i) q^{79} +(-5613.56 + 3396.26i) q^{81} +(4632.45 + 5520.74i) q^{83} +(967.002 - 5484.14i) q^{85} +(10483.3 - 511.544i) q^{87} +(-4640.51 + 2679.20i) q^{89} +(5497.42 - 9521.81i) q^{91} +(-7614.68 - 8224.95i) q^{93} +(4563.38 - 5438.42i) q^{95} +(8556.61 + 3114.35i) q^{97} +(-12663.1 - 977.219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

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
\(3\) 5.44219 7.16816i 0.604688 0.796462i
\(4\) 0 0
\(5\) 4.60350 + 12.6480i 0.184140 + 0.505920i 0.997075 0.0764347i \(-0.0243537\pi\)
−0.812935 + 0.582355i \(0.802131\pi\)
\(6\) 0 0
\(7\) −6.68463 37.9104i −0.136421 0.773683i −0.973860 0.227151i \(-0.927059\pi\)
0.837438 0.546532i \(-0.184052\pi\)
\(8\) 0 0
\(9\) −21.7651 78.0210i −0.268704 0.963223i
\(10\) 0 0
\(11\) 53.6284 147.343i 0.443210 1.21771i −0.494159 0.869372i \(-0.664524\pi\)
0.937369 0.348338i \(-0.113254\pi\)
\(12\) 0 0
\(13\) 218.794 + 183.590i 1.29464 + 1.08633i 0.991045 + 0.133529i \(0.0426310\pi\)
0.303594 + 0.952802i \(0.401813\pi\)
\(14\) 0 0
\(15\) 115.716 + 35.8343i 0.514293 + 0.159263i
\(16\) 0 0
\(17\) −358.304 206.867i −1.23981 0.715803i −0.270752 0.962649i \(-0.587272\pi\)
−0.969055 + 0.246846i \(0.920606\pi\)
\(18\) 0 0
\(19\) −263.726 456.787i −0.730543 1.26534i −0.956651 0.291235i \(-0.905934\pi\)
0.226109 0.974102i \(-0.427400\pi\)
\(20\) 0 0
\(21\) −308.127 158.399i −0.698701 0.359182i
\(22\) 0 0
\(23\) 72.8639 + 12.8479i 0.137739 + 0.0242871i 0.242093 0.970253i \(-0.422166\pi\)
−0.104354 + 0.994540i \(0.533277\pi\)
\(24\) 0 0
\(25\) 339.998 285.292i 0.543997 0.456468i
\(26\) 0 0
\(27\) −677.717 268.590i −0.929653 0.368436i
\(28\) 0 0
\(29\) 749.617 + 893.359i 0.891340 + 1.06226i 0.997690 + 0.0679289i \(0.0216391\pi\)
−0.106350 + 0.994329i \(0.533916\pi\)
\(30\) 0 0
\(31\) 216.262 1226.48i 0.225038 1.27626i −0.637574 0.770389i \(-0.720062\pi\)
0.862612 0.505866i \(-0.168827\pi\)
\(32\) 0 0
\(33\) −764.321 1186.29i −0.701856 1.08933i
\(34\) 0 0
\(35\) 448.719 259.068i 0.366301 0.211484i
\(36\) 0 0
\(37\) −292.196 + 506.099i −0.213438 + 0.369685i −0.952788 0.303636i \(-0.901799\pi\)
0.739350 + 0.673321i \(0.235133\pi\)
\(38\) 0 0
\(39\) 2506.72 569.218i 1.64807 0.374239i
\(40\) 0 0
\(41\) −255.514 + 304.510i −0.152001 + 0.181148i −0.836672 0.547705i \(-0.815502\pi\)
0.684670 + 0.728853i \(0.259946\pi\)
\(42\) 0 0
\(43\) 1657.55 + 603.297i 0.896455 + 0.326283i 0.748831 0.662761i \(-0.230615\pi\)
0.147624 + 0.989044i \(0.452838\pi\)
\(44\) 0 0
\(45\) 886.615 634.454i 0.437835 0.313311i
\(46\) 0 0
\(47\) −3421.41 + 603.286i −1.54885 + 0.273104i −0.881696 0.471817i \(-0.843598\pi\)
−0.667153 + 0.744921i \(0.732487\pi\)
\(48\) 0 0
\(49\) 863.684 314.355i 0.359719 0.130927i
\(50\) 0 0
\(51\) −3432.82 + 1442.57i −1.31981 + 0.554622i
\(52\) 0 0
\(53\) 2453.33i 0.873384i 0.899611 + 0.436692i \(0.143850\pi\)
−0.899611 + 0.436692i \(0.856150\pi\)
\(54\) 0 0
\(55\) 2110.47 0.697676
\(56\) 0 0
\(57\) −4709.57 595.492i −1.44954 0.183285i
\(58\) 0 0
\(59\) 1740.39 + 4781.69i 0.499969 + 1.37365i 0.891304 + 0.453405i \(0.149791\pi\)
−0.391336 + 0.920248i \(0.627987\pi\)
\(60\) 0 0
\(61\) −86.2656 489.236i −0.0231834 0.131480i 0.971019 0.239001i \(-0.0768198\pi\)
−0.994203 + 0.107521i \(0.965709\pi\)
\(62\) 0 0
\(63\) −2812.32 + 1346.67i −0.708572 + 0.339296i
\(64\) 0 0
\(65\) −1314.83 + 3612.46i −0.311202 + 0.855020i
\(66\) 0 0
\(67\) 5153.66 + 4324.44i 1.14807 + 0.963341i 0.999673 0.0255875i \(-0.00814565\pi\)
0.148393 + 0.988929i \(0.452590\pi\)
\(68\) 0 0
\(69\) 488.635 452.380i 0.102633 0.0950178i
\(70\) 0 0
\(71\) 4493.20 + 2594.15i 0.891331 + 0.514610i 0.874378 0.485246i \(-0.161270\pi\)
0.0169537 + 0.999856i \(0.494603\pi\)
\(72\) 0 0
\(73\) 216.646 + 375.242i 0.0406542 + 0.0704151i 0.885637 0.464379i \(-0.153722\pi\)
−0.844982 + 0.534794i \(0.820389\pi\)
\(74\) 0 0
\(75\) −194.685 3989.78i −0.0346107 0.709293i
\(76\) 0 0
\(77\) −5944.32 1048.14i −1.00258 0.176783i
\(78\) 0 0
\(79\) −143.418 + 120.342i −0.0229800 + 0.0192825i −0.654205 0.756317i \(-0.726997\pi\)
0.631225 + 0.775600i \(0.282552\pi\)
\(80\) 0 0
\(81\) −5613.56 + 3396.26i −0.855596 + 0.517644i
\(82\) 0 0
\(83\) 4632.45 + 5520.74i 0.672442 + 0.801385i 0.989114 0.147150i \(-0.0470101\pi\)
−0.316673 + 0.948535i \(0.602566\pi\)
\(84\) 0 0
\(85\) 967.002 5484.14i 0.133841 0.759051i
\(86\) 0 0
\(87\) 10483.3 511.544i 1.38503 0.0675840i
\(88\) 0 0
\(89\) −4640.51 + 2679.20i −0.585849 + 0.338240i −0.763454 0.645862i \(-0.776498\pi\)
0.177605 + 0.984102i \(0.443165\pi\)
\(90\) 0 0
\(91\) 5497.42 9521.81i 0.663859 1.14984i
\(92\) 0 0
\(93\) −7614.68 8224.95i −0.880411 0.950971i
\(94\) 0 0
\(95\) 4563.38 5438.42i 0.505638 0.602595i
\(96\) 0 0
\(97\) 8556.61 + 3114.35i 0.909407 + 0.330997i 0.754016 0.656856i \(-0.228114\pi\)
0.155391 + 0.987853i \(0.450336\pi\)
\(98\) 0 0
\(99\) −12663.1 977.219i −1.29202 0.0997061i
\(100\) 0 0
\(101\) −2321.64 + 409.367i −0.227589 + 0.0401301i −0.286280 0.958146i \(-0.592419\pi\)
0.0586904 + 0.998276i \(0.481308\pi\)
\(102\) 0 0
\(103\) 7180.63 2613.53i 0.676843 0.246351i 0.0193515 0.999813i \(-0.493840\pi\)
0.657491 + 0.753462i \(0.271618\pi\)
\(104\) 0 0
\(105\) 584.974 4626.39i 0.0530589 0.419627i
\(106\) 0 0
\(107\) 4807.21i 0.419881i 0.977714 + 0.209940i \(0.0673270\pi\)
−0.977714 + 0.209940i \(0.932673\pi\)
\(108\) 0 0
\(109\) −9508.49 −0.800311 −0.400155 0.916447i \(-0.631044\pi\)
−0.400155 + 0.916447i \(0.631044\pi\)
\(110\) 0 0
\(111\) 2037.61 + 4848.80i 0.165377 + 0.393540i
\(112\) 0 0
\(113\) −4933.89 13555.7i −0.386396 1.06161i −0.968612 0.248579i \(-0.920036\pi\)
0.582216 0.813034i \(-0.302186\pi\)
\(114\) 0 0
\(115\) 172.929 + 980.728i 0.0130759 + 0.0741571i
\(116\) 0 0
\(117\) 9561.81 21066.4i 0.698503 1.53893i
\(118\) 0 0
\(119\) −5447.29 + 14966.3i −0.384668 + 1.05687i
\(120\) 0 0
\(121\) −7618.26 6392.48i −0.520337 0.436615i
\(122\) 0 0
\(123\) 792.218 + 3488.77i 0.0523642 + 0.230601i
\(124\) 0 0
\(125\) 12458.8 + 7193.12i 0.797366 + 0.460359i
\(126\) 0 0
\(127\) −3484.81 6035.87i −0.216059 0.374224i 0.737541 0.675302i \(-0.235987\pi\)
−0.953600 + 0.301078i \(0.902654\pi\)
\(128\) 0 0
\(129\) 13345.2 8598.29i 0.801948 0.516693i
\(130\) 0 0
\(131\) −13968.4 2463.00i −0.813959 0.143523i −0.248853 0.968541i \(-0.580054\pi\)
−0.565106 + 0.825018i \(0.691165\pi\)
\(132\) 0 0
\(133\) −15554.1 + 13051.4i −0.879308 + 0.737827i
\(134\) 0 0
\(135\) 277.262 9808.22i 0.0152133 0.538174i
\(136\) 0 0
\(137\) −19227.5 22914.5i −1.02443 1.22087i −0.975026 0.222091i \(-0.928712\pi\)
−0.0494051 0.998779i \(-0.515733\pi\)
\(138\) 0 0
\(139\) 2829.19 16045.1i 0.146431 0.830450i −0.819777 0.572683i \(-0.805902\pi\)
0.966207 0.257766i \(-0.0829864\pi\)
\(140\) 0 0
\(141\) −14295.5 + 27808.4i −0.719054 + 1.39874i
\(142\) 0 0
\(143\) 38784.2 22392.1i 1.89663 1.09502i
\(144\) 0 0
\(145\) −7848.34 + 13593.7i −0.373286 + 0.646551i
\(146\) 0 0
\(147\) 2446.99 7901.81i 0.113239 0.365672i
\(148\) 0 0
\(149\) 2233.89 2662.24i 0.100621 0.119915i −0.713384 0.700773i \(-0.752838\pi\)
0.814005 + 0.580858i \(0.197283\pi\)
\(150\) 0 0
\(151\) 10231.2 + 3723.85i 0.448717 + 0.163320i 0.556487 0.830856i \(-0.312149\pi\)
−0.107770 + 0.994176i \(0.534371\pi\)
\(152\) 0 0
\(153\) −8341.47 + 32457.7i −0.356336 + 1.38655i
\(154\) 0 0
\(155\) 16508.1 2910.82i 0.687122 0.121158i
\(156\) 0 0
\(157\) 38822.4 14130.2i 1.57501 0.573257i 0.600898 0.799326i \(-0.294810\pi\)
0.974111 + 0.226069i \(0.0725875\pi\)
\(158\) 0 0
\(159\) 17585.9 + 13351.5i 0.695617 + 0.528125i
\(160\) 0 0
\(161\) 2848.19i 0.109879i
\(162\) 0 0
\(163\) −29474.8 −1.10937 −0.554684 0.832061i \(-0.687161\pi\)
−0.554684 + 0.832061i \(0.687161\pi\)
\(164\) 0 0
\(165\) 11485.6 15128.2i 0.421877 0.555673i
\(166\) 0 0
\(167\) −4422.16 12149.8i −0.158563 0.435648i 0.834816 0.550528i \(-0.185574\pi\)
−0.993379 + 0.114880i \(0.963351\pi\)
\(168\) 0 0
\(169\) 9205.96 + 52209.6i 0.322326 + 1.82800i
\(170\) 0 0
\(171\) −29899.0 + 30518.2i −1.02250 + 1.04368i
\(172\) 0 0
\(173\) −8360.34 + 22969.8i −0.279339 + 0.767478i 0.718099 + 0.695941i \(0.245013\pi\)
−0.997438 + 0.0715366i \(0.977210\pi\)
\(174\) 0 0
\(175\) −13088.3 10982.4i −0.427374 0.358609i
\(176\) 0 0
\(177\) 43747.5 + 13547.5i 1.39639 + 0.432426i
\(178\) 0 0
\(179\) −27156.0 15678.5i −0.847540 0.489327i 0.0122803 0.999925i \(-0.496091\pi\)
−0.859820 + 0.510597i \(0.829424\pi\)
\(180\) 0 0
\(181\) −26117.4 45236.7i −0.797211 1.38081i −0.921426 0.388554i \(-0.872975\pi\)
0.124215 0.992255i \(-0.460359\pi\)
\(182\) 0 0
\(183\) −3976.40 2044.15i −0.118737 0.0610396i
\(184\) 0 0
\(185\) −7746.27 1365.88i −0.226334 0.0399087i
\(186\) 0 0
\(187\) −49695.7 + 41699.6i −1.42113 + 1.19247i
\(188\) 0 0
\(189\) −5652.08 + 27488.0i −0.158229 + 0.769519i
\(190\) 0 0
\(191\) 26863.4 + 32014.6i 0.736367 + 0.877568i 0.996111 0.0881093i \(-0.0280825\pi\)
−0.259744 + 0.965678i \(0.583638\pi\)
\(192\) 0 0
\(193\) −10887.1 + 61744.0i −0.292280 + 1.65760i 0.385777 + 0.922592i \(0.373934\pi\)
−0.678057 + 0.735010i \(0.737178\pi\)
\(194\) 0 0
\(195\) 18739.2 + 29084.6i 0.492811 + 0.764881i
\(196\) 0 0
\(197\) 28224.2 16295.3i 0.727260 0.419884i −0.0901589 0.995927i \(-0.528737\pi\)
0.817419 + 0.576044i \(0.195404\pi\)
\(198\) 0 0
\(199\) −22285.7 + 38599.9i −0.562756 + 0.974721i 0.434499 + 0.900672i \(0.356925\pi\)
−0.997255 + 0.0740490i \(0.976408\pi\)
\(200\) 0 0
\(201\) 59045.5 13407.9i 1.46149 0.331870i
\(202\) 0 0
\(203\) 28856.7 34390.1i 0.700253 0.834529i
\(204\) 0 0
\(205\) −5027.70 1829.93i −0.119636 0.0435439i
\(206\) 0 0
\(207\) −583.482 5964.55i −0.0136172 0.139199i
\(208\) 0 0
\(209\) −81447.5 + 14361.4i −1.86460 + 0.328779i
\(210\) 0 0
\(211\) −49.4728 + 18.0066i −0.00111122 + 0.000404452i −0.342576 0.939490i \(-0.611299\pi\)
0.341464 + 0.939895i \(0.389077\pi\)
\(212\) 0 0
\(213\) 43048.2 18090.1i 0.948845 0.398733i
\(214\) 0 0
\(215\) 23741.9i 0.513616i
\(216\) 0 0
\(217\) −47942.1 −1.01812
\(218\) 0 0
\(219\) 3868.83 + 489.186i 0.0806661 + 0.0101997i
\(220\) 0 0
\(221\) −40416.1 111042.i −0.827503 2.27355i
\(222\) 0 0
\(223\) −5603.41 31778.5i −0.112679 0.639034i −0.987873 0.155262i \(-0.950378\pi\)
0.875194 0.483771i \(-0.160733\pi\)
\(224\) 0 0
\(225\) −29658.9 20317.6i −0.585854 0.401335i
\(226\) 0 0
\(227\) 5268.18 14474.2i 0.102237 0.280894i −0.878019 0.478626i \(-0.841135\pi\)
0.980256 + 0.197731i \(0.0633574\pi\)
\(228\) 0 0
\(229\) 50139.2 + 42071.8i 0.956106 + 0.802269i 0.980315 0.197438i \(-0.0632622\pi\)
−0.0242088 + 0.999707i \(0.507707\pi\)
\(230\) 0 0
\(231\) −39863.4 + 36905.6i −0.747051 + 0.691622i
\(232\) 0 0
\(233\) 70026.3 + 40429.7i 1.28988 + 0.744713i 0.978633 0.205616i \(-0.0659198\pi\)
0.311248 + 0.950329i \(0.399253\pi\)
\(234\) 0 0
\(235\) −23380.8 40496.7i −0.423374 0.733305i
\(236\) 0 0
\(237\) 82.1221 + 1682.97i 0.00146205 + 0.0299625i
\(238\) 0 0
\(239\) 26236.1 + 4626.14i 0.459308 + 0.0809884i 0.398515 0.917162i \(-0.369526\pi\)
0.0607935 + 0.998150i \(0.480637\pi\)
\(240\) 0 0
\(241\) 42998.4 36079.9i 0.740318 0.621200i −0.192605 0.981276i \(-0.561694\pi\)
0.932923 + 0.360076i \(0.117249\pi\)
\(242\) 0 0
\(243\) −6205.14 + 58722.1i −0.105085 + 0.994463i
\(244\) 0 0
\(245\) 7951.94 + 9476.75i 0.132477 + 0.157880i
\(246\) 0 0
\(247\) 26159.8 148360.i 0.428786 2.43177i
\(248\) 0 0
\(249\) 64784.2 3161.21i 1.04489 0.0509865i
\(250\) 0 0
\(251\) 79884.8 46121.5i 1.26799 0.732076i 0.293385 0.955994i \(-0.405218\pi\)
0.974608 + 0.223919i \(0.0718850\pi\)
\(252\) 0 0
\(253\) 5800.62 10047.0i 0.0906219 0.156962i
\(254\) 0 0
\(255\) −34048.6 36777.4i −0.523623 0.565589i
\(256\) 0 0
\(257\) 8885.03 10588.8i 0.134522 0.160317i −0.694578 0.719417i \(-0.744409\pi\)
0.829100 + 0.559100i \(0.188853\pi\)
\(258\) 0 0
\(259\) 21139.7 + 7694.21i 0.315136 + 0.114700i
\(260\) 0 0
\(261\) 53385.3 77929.9i 0.783684 1.14399i
\(262\) 0 0
\(263\) −97792.6 + 17243.5i −1.41382 + 0.249295i −0.827810 0.561008i \(-0.810414\pi\)
−0.586011 + 0.810303i \(0.699303\pi\)
\(264\) 0 0
\(265\) −31029.8 + 11293.9i −0.441862 + 0.160825i
\(266\) 0 0
\(267\) −6049.62 + 47844.7i −0.0848605 + 0.671137i
\(268\) 0 0
\(269\) 47534.8i 0.656912i −0.944519 0.328456i \(-0.893472\pi\)
0.944519 0.328456i \(-0.106528\pi\)
\(270\) 0 0
\(271\) −80043.5 −1.08990 −0.544951 0.838468i \(-0.683452\pi\)
−0.544951 + 0.838468i \(0.683452\pi\)
\(272\) 0 0
\(273\) −38335.8 91225.9i −0.514375 1.22403i
\(274\) 0 0
\(275\) −23802.2 65396.0i −0.314740 0.864741i
\(276\) 0 0
\(277\) 21523.8 + 122068.i 0.280518 + 1.59089i 0.720870 + 0.693070i \(0.243742\pi\)
−0.440353 + 0.897825i \(0.645147\pi\)
\(278\) 0 0
\(279\) −100398. + 9821.47i −1.28979 + 0.126173i
\(280\) 0 0
\(281\) −13652.0 + 37508.6i −0.172896 + 0.475027i −0.995629 0.0934011i \(-0.970226\pi\)
0.822733 + 0.568428i \(0.192448\pi\)
\(282\) 0 0
\(283\) −1984.59 1665.27i −0.0247798 0.0207927i 0.630314 0.776341i \(-0.282926\pi\)
−0.655093 + 0.755548i \(0.727371\pi\)
\(284\) 0 0
\(285\) −14148.7 62308.0i −0.174191 0.767104i
\(286\) 0 0
\(287\) 13252.1 + 7651.12i 0.160887 + 0.0928883i
\(288\) 0 0
\(289\) 43827.4 + 75911.3i 0.524747 + 0.908888i
\(290\) 0 0
\(291\) 68890.9 44386.2i 0.813534 0.524158i
\(292\) 0 0
\(293\) −65805.0 11603.2i −0.766520 0.135158i −0.223302 0.974749i \(-0.571683\pi\)
−0.543219 + 0.839591i \(0.682795\pi\)
\(294\) 0 0
\(295\) −52466.9 + 44025.0i −0.602895 + 0.505889i
\(296\) 0 0
\(297\) −75919.7 + 85452.7i −0.860680 + 0.968753i
\(298\) 0 0
\(299\) 13583.4 + 16188.1i 0.151938 + 0.181073i
\(300\) 0 0
\(301\) 11791.2 66871.1i 0.130144 0.738084i
\(302\) 0 0
\(303\) −9700.39 + 18869.7i −0.105658 + 0.205532i
\(304\) 0 0
\(305\) 5790.74 3343.29i 0.0622493 0.0359396i
\(306\) 0 0
\(307\) 88454.5 153208.i 0.938520 1.62556i 0.170285 0.985395i \(-0.445531\pi\)
0.768234 0.640169i \(-0.221136\pi\)
\(308\) 0 0
\(309\) 20344.1 65695.2i 0.213070 0.688045i
\(310\) 0 0
\(311\) −85840.5 + 102301.i −0.887506 + 1.05769i 0.110456 + 0.993881i \(0.464769\pi\)
−0.997962 + 0.0638078i \(0.979676\pi\)
\(312\) 0 0
\(313\) −32851.6 11957.0i −0.335327 0.122049i 0.168869 0.985639i \(-0.445989\pi\)
−0.504195 + 0.863590i \(0.668211\pi\)
\(314\) 0 0
\(315\) −29979.1 29370.9i −0.302133 0.296003i
\(316\) 0 0
\(317\) 120383. 21226.8i 1.19797 0.211235i 0.461151 0.887321i \(-0.347437\pi\)
0.736822 + 0.676086i \(0.236325\pi\)
\(318\) 0 0
\(319\) 171831. 62541.3i 1.68857 0.614590i
\(320\) 0 0
\(321\) 34458.9 + 26161.8i 0.334419 + 0.253897i
\(322\) 0 0
\(323\) 218225.i 2.09170i
\(324\) 0 0
\(325\) 126766. 1.20015
\(326\) 0 0
\(327\) −51747.1 + 68158.4i −0.483939 + 0.637417i
\(328\) 0 0
\(329\) 45741.7 + 125674.i 0.422591 + 1.16106i
\(330\) 0 0
\(331\) 16667.3 + 94525.1i 0.152128 + 0.862762i 0.961364 + 0.275279i \(0.0887701\pi\)
−0.809236 + 0.587483i \(0.800119\pi\)
\(332\) 0 0
\(333\) 45846.0 + 11782.2i 0.413441 + 0.106252i
\(334\) 0 0
\(335\) −30970.6 + 85091.1i −0.275969 + 0.758219i
\(336\) 0 0
\(337\) 47572.9 + 39918.4i 0.418890 + 0.351490i 0.827741 0.561111i \(-0.189626\pi\)
−0.408851 + 0.912601i \(0.634070\pi\)
\(338\) 0 0
\(339\) −124021. 38406.1i −1.07918 0.334196i
\(340\) 0 0
\(341\) −169115. 97638.9i −1.45437 0.839680i
\(342\) 0 0
\(343\) −63904.3 110686.i −0.543178 0.940812i
\(344\) 0 0
\(345\) 7971.13 + 4097.73i 0.0669702 + 0.0344275i
\(346\) 0 0
\(347\) 72408.5 + 12767.6i 0.601354 + 0.106035i 0.466034 0.884767i \(-0.345683\pi\)
0.135320 + 0.990802i \(0.456794\pi\)
\(348\) 0 0
\(349\) 28998.6 24332.7i 0.238082 0.199775i −0.515938 0.856626i \(-0.672557\pi\)
0.754020 + 0.656851i \(0.228112\pi\)
\(350\) 0 0
\(351\) −98969.9 183188.i −0.803321 1.48690i
\(352\) 0 0
\(353\) −14388.4 17147.4i −0.115468 0.137610i 0.705214 0.708994i \(-0.250851\pi\)
−0.820682 + 0.571385i \(0.806406\pi\)
\(354\) 0 0
\(355\) −12126.4 + 68772.2i −0.0962221 + 0.545703i
\(356\) 0 0
\(357\) 77635.6 + 120497.i 0.609151 + 0.945449i
\(358\) 0 0
\(359\) 62766.1 36238.0i 0.487008 0.281174i −0.236324 0.971674i \(-0.575943\pi\)
0.723332 + 0.690500i \(0.242609\pi\)
\(360\) 0 0
\(361\) −73942.3 + 128072.i −0.567386 + 0.982741i
\(362\) 0 0
\(363\) −87282.3 + 19819.8i −0.662389 + 0.150413i
\(364\) 0 0
\(365\) −3748.73 + 4467.57i −0.0281384 + 0.0335340i
\(366\) 0 0
\(367\) 98300.8 + 35778.6i 0.729835 + 0.265638i 0.680095 0.733124i \(-0.261938\pi\)
0.0497401 + 0.998762i \(0.484161\pi\)
\(368\) 0 0
\(369\) 29319.5 + 13307.8i 0.215329 + 0.0977358i
\(370\) 0 0
\(371\) 93007.0 16399.6i 0.675722 0.119148i
\(372\) 0 0
\(373\) −29291.1 + 10661.1i −0.210532 + 0.0766274i −0.445133 0.895464i \(-0.646844\pi\)
0.234601 + 0.972092i \(0.424622\pi\)
\(374\) 0 0
\(375\) 119365. 50160.7i 0.848817 0.356698i
\(376\) 0 0
\(377\) 333084.i 2.34353i
\(378\) 0 0
\(379\) −102137. −0.711056 −0.355528 0.934666i \(-0.615699\pi\)
−0.355528 + 0.934666i \(0.615699\pi\)
\(380\) 0 0
\(381\) −62231.1 7868.68i −0.428704 0.0542066i
\(382\) 0 0
\(383\) 26507.4 + 72828.4i 0.180704 + 0.496481i 0.996663 0.0816293i \(-0.0260124\pi\)
−0.815958 + 0.578111i \(0.803790\pi\)
\(384\) 0 0
\(385\) −14107.7 80008.9i −0.0951778 0.539780i
\(386\) 0 0
\(387\) 10993.3 142454.i 0.0734018 0.951159i
\(388\) 0 0
\(389\) −75326.6 + 206958.i −0.497794 + 1.36768i 0.395609 + 0.918419i \(0.370534\pi\)
−0.893402 + 0.449257i \(0.851689\pi\)
\(390\) 0 0
\(391\) −23449.6 19676.6i −0.153385 0.128705i
\(392\) 0 0
\(393\) −93673.6 + 86723.3i −0.606502 + 0.561501i
\(394\) 0 0
\(395\) −2182.31 1259.96i −0.0139869 0.00807535i
\(396\) 0 0
\(397\) 35865.7 + 62121.2i 0.227561 + 0.394148i 0.957085 0.289808i \(-0.0935915\pi\)
−0.729524 + 0.683956i \(0.760258\pi\)
\(398\) 0 0
\(399\) 8906.38 + 182523.i 0.0559442 + 1.14649i
\(400\) 0 0
\(401\) −217196. 38297.4i −1.35071 0.238167i −0.548971 0.835841i \(-0.684980\pi\)
−0.801739 + 0.597675i \(0.796091\pi\)
\(402\) 0 0
\(403\) 272486. 228643.i 1.67778 1.40782i
\(404\) 0 0
\(405\) −68798.0 55365.7i −0.419436 0.337544i
\(406\) 0 0
\(407\) 58900.1 + 70194.4i 0.355571 + 0.423754i
\(408\) 0 0
\(409\) 4932.61 27974.2i 0.0294870 0.167229i −0.966508 0.256636i \(-0.917386\pi\)
0.995995 + 0.0894067i \(0.0284971\pi\)
\(410\) 0 0
\(411\) −268895. + 13121.0i −1.59184 + 0.0776754i
\(412\) 0 0
\(413\) 169642. 97942.9i 0.994565 0.574213i
\(414\) 0 0
\(415\) −48500.8 + 84005.9i −0.281613 + 0.487769i
\(416\) 0 0
\(417\) −99617.0 107601.i −0.572877 0.618790i
\(418\) 0 0
\(419\) 72788.9 86746.4i 0.414608 0.494110i −0.517809 0.855497i \(-0.673252\pi\)
0.932416 + 0.361386i \(0.117696\pi\)
\(420\) 0 0
\(421\) −38555.7 14033.1i −0.217533 0.0791754i 0.230955 0.972964i \(-0.425815\pi\)
−0.448488 + 0.893789i \(0.648037\pi\)
\(422\) 0 0
\(423\) 121536. + 253811.i 0.679242 + 1.41850i
\(424\) 0 0
\(425\) −180840. + 31887.0i −1.00119 + 0.176537i
\(426\) 0 0
\(427\) −17970.5 + 6540.73i −0.0985609 + 0.0358732i
\(428\) 0 0
\(429\) 50561.2 399874.i 0.274728 2.17274i
\(430\) 0 0
\(431\) 146523.i 0.788770i −0.918945 0.394385i \(-0.870958\pi\)
0.918945 0.394385i \(-0.129042\pi\)
\(432\) 0 0
\(433\) 348349. 1.85797 0.928984 0.370120i \(-0.120683\pi\)
0.928984 + 0.370120i \(0.120683\pi\)
\(434\) 0 0
\(435\) 54729.8 + 130238.i 0.289232 + 0.688270i
\(436\) 0 0
\(437\) −13347.4 36671.6i −0.0698928 0.192029i
\(438\) 0 0
\(439\) −5535.98 31396.1i −0.0287254 0.162910i 0.967071 0.254508i \(-0.0819135\pi\)
−0.995796 + 0.0915983i \(0.970802\pi\)
\(440\) 0 0
\(441\) −43324.5 60543.6i −0.222770 0.311309i
\(442\) 0 0
\(443\) 98890.6 271700.i 0.503904 1.38446i −0.383530 0.923528i \(-0.625292\pi\)
0.887434 0.460936i \(-0.152486\pi\)
\(444\) 0 0
\(445\) −55249.1 46359.5i −0.279001 0.234109i
\(446\) 0 0
\(447\) −6926.14 30501.3i −0.0346638 0.152652i
\(448\) 0 0
\(449\) −297866. 171973.i −1.47750 0.853038i −0.477828 0.878453i \(-0.658576\pi\)
−0.999677 + 0.0254156i \(0.991909\pi\)
\(450\) 0 0
\(451\) 31164.5 + 53978.6i 0.153217 + 0.265380i
\(452\) 0 0
\(453\) 82373.3 53072.9i 0.401412 0.258629i
\(454\) 0 0
\(455\) 145739. + 25697.7i 0.703969 + 0.124129i
\(456\) 0 0
\(457\) −201132. + 168770.i −0.963049 + 0.808094i −0.981446 0.191736i \(-0.938588\pi\)
0.0183970 + 0.999831i \(0.494144\pi\)
\(458\) 0 0
\(459\) 187266. + 236434.i 0.888862 + 1.12224i
\(460\) 0 0
\(461\) −228609. 272445.i −1.07570 1.28197i −0.957329 0.288999i \(-0.906677\pi\)
−0.118370 0.992970i \(-0.537767\pi\)
\(462\) 0 0
\(463\) −32179.6 + 182500.i −0.150113 + 0.851335i 0.813005 + 0.582257i \(0.197830\pi\)
−0.963118 + 0.269078i \(0.913281\pi\)
\(464\) 0 0
\(465\) 68975.0 134174.i 0.318997 0.620529i
\(466\) 0 0
\(467\) −28902.8 + 16687.0i −0.132527 + 0.0765147i −0.564798 0.825229i \(-0.691046\pi\)
0.432271 + 0.901744i \(0.357713\pi\)
\(468\) 0 0
\(469\) 129491. 224285.i 0.588700 1.01966i
\(470\) 0 0
\(471\) 109992. 355185.i 0.495812 1.60108i
\(472\) 0 0
\(473\) 177783. 211874.i 0.794636 0.947010i
\(474\) 0 0
\(475\) −219984. 80067.6i −0.974998 0.354870i
\(476\) 0 0
\(477\) 191412. 53397.0i 0.841263 0.234682i
\(478\) 0 0
\(479\) 282964. 49894.1i 1.23327 0.217459i 0.481243 0.876587i \(-0.340185\pi\)
0.752031 + 0.659128i \(0.229074\pi\)
\(480\) 0 0
\(481\) −156845. + 57087.1i −0.677925 + 0.246745i
\(482\) 0 0
\(483\) −20416.3 15500.4i −0.0875149 0.0664428i
\(484\) 0 0
\(485\) 122561.i 0.521037i
\(486\) 0 0
\(487\) 56772.7 0.239376 0.119688 0.992812i \(-0.461811\pi\)
0.119688 + 0.992812i \(0.461811\pi\)
\(488\) 0 0
\(489\) −160408. + 211280.i −0.670822 + 0.883570i
\(490\) 0 0
\(491\) 153157. + 420796.i 0.635293 + 1.74545i 0.666028 + 0.745927i \(0.267993\pi\)
−0.0307346 + 0.999528i \(0.509785\pi\)
\(492\) 0 0
\(493\) −83784.4 475165.i −0.344722 1.95502i
\(494\) 0 0
\(495\) −45934.5 164661.i −0.187469 0.672018i
\(496\) 0 0
\(497\) 68310.0 187680.i 0.276549 0.759811i
\(498\) 0 0
\(499\) −209763. 176012.i −0.842417 0.706871i 0.115689 0.993285i \(-0.463092\pi\)
−0.958106 + 0.286414i \(0.907537\pi\)
\(500\) 0 0
\(501\) −111158. 34422.7i −0.442858 0.137142i
\(502\) 0 0
\(503\) −334005. 192838.i −1.32013 0.762179i −0.336382 0.941725i \(-0.609203\pi\)
−0.983749 + 0.179547i \(0.942537\pi\)
\(504\) 0 0
\(505\) −15865.3 27479.6i −0.0622109 0.107752i
\(506\) 0 0
\(507\) 424348. + 218145.i 1.65084 + 0.848652i
\(508\) 0 0
\(509\) 310960. + 54830.7i 1.20024 + 0.211635i 0.737804 0.675015i \(-0.235863\pi\)
0.462440 + 0.886651i \(0.346974\pi\)
\(510\) 0 0
\(511\) 12777.4 10721.5i 0.0489329 0.0410595i
\(512\) 0 0
\(513\) 56043.1 + 380406.i 0.212955 + 1.44548i
\(514\) 0 0
\(515\) 66112.0 + 78789.2i 0.249267 + 0.297065i
\(516\) 0 0
\(517\) −94594.7 + 536473.i −0.353904 + 2.00709i
\(518\) 0 0
\(519\) 119153. + 184935.i 0.442354 + 0.686568i
\(520\) 0 0
\(521\) 182293. 105247.i 0.671573 0.387733i −0.125099 0.992144i \(-0.539925\pi\)
0.796673 + 0.604411i \(0.206592\pi\)
\(522\) 0 0
\(523\) −60943.8 + 105558.i −0.222806 + 0.385911i −0.955659 0.294476i \(-0.904855\pi\)
0.732853 + 0.680387i \(0.238188\pi\)
\(524\) 0 0
\(525\) −149953. + 34050.8i −0.544046 + 0.123540i
\(526\) 0 0
\(527\) −331206. + 394716.i −1.19255 + 1.42123i
\(528\) 0 0
\(529\) −257820. 93839.0i −0.921310 0.335330i
\(530\) 0 0
\(531\) 335192. 239861.i 1.18879 0.850688i
\(532\) 0 0
\(533\) −111810. + 19715.1i −0.393573 + 0.0693976i
\(534\) 0 0
\(535\) −60801.6 + 22130.0i −0.212426 + 0.0773168i
\(536\) 0 0
\(537\) −260175. + 109333.i −0.902228 + 0.379143i
\(538\) 0 0
\(539\) 144116.i 0.496061i
\(540\) 0 0
\(541\) −308626. −1.05448 −0.527239 0.849717i \(-0.676773\pi\)
−0.527239 + 0.849717i \(0.676773\pi\)
\(542\) 0 0
\(543\) −466400. 58973.0i −1.58183 0.200011i
\(544\) 0 0
\(545\) −43772.3 120263.i −0.147369 0.404893i
\(546\) 0 0
\(547\) 22670.6 + 128572.i 0.0757686 + 0.429705i 0.998969 + 0.0453872i \(0.0144522\pi\)
−0.923201 + 0.384318i \(0.874437\pi\)
\(548\) 0 0
\(549\) −36293.2 + 17378.8i −0.120415 + 0.0576600i
\(550\) 0 0
\(551\) 210381. 578017.i 0.692952 1.90387i
\(552\) 0 0
\(553\) 5520.91 + 4632.59i 0.0180535 + 0.0151487i
\(554\) 0 0
\(555\) −51947.5 + 48093.1i −0.168647 + 0.156134i
\(556\) 0 0
\(557\) −175247. 101179.i −0.564859 0.326121i 0.190235 0.981739i \(-0.439075\pi\)
−0.755093 + 0.655617i \(0.772408\pi\)
\(558\) 0 0
\(559\) 251902. + 436306.i 0.806134 + 1.39627i
\(560\) 0 0
\(561\) 28456.1 + 583164.i 0.0904169 + 1.85295i
\(562\) 0 0
\(563\) −309219. 54523.7i −0.975551 0.172016i −0.336924 0.941532i \(-0.609386\pi\)
−0.638628 + 0.769516i \(0.720498\pi\)
\(564\) 0 0
\(565\) 148740. 124808.i 0.465941 0.390971i
\(566\) 0 0
\(567\) 166279. + 190110.i 0.517214 + 0.591342i
\(568\) 0 0
\(569\) 137484. + 163846.i 0.424645 + 0.506072i 0.935369 0.353672i \(-0.115067\pi\)
−0.510724 + 0.859745i \(0.670623\pi\)
\(570\) 0 0
\(571\) 26314.4 149236.i 0.0807088 0.457722i −0.917492 0.397755i \(-0.869789\pi\)
0.998200 0.0599671i \(-0.0190996\pi\)
\(572\) 0 0
\(573\) 375681. 18331.8i 1.14422 0.0558335i
\(574\) 0 0
\(575\) 28439.0 16419.3i 0.0860158 0.0496613i
\(576\) 0 0
\(577\) −197733. + 342484.i −0.593920 + 1.02870i 0.399778 + 0.916612i \(0.369087\pi\)
−0.993698 + 0.112088i \(0.964246\pi\)
\(578\) 0 0
\(579\) 383341. + 414064.i 1.14348 + 1.23512i
\(580\) 0 0
\(581\) 178327. 212522.i 0.528282 0.629582i
\(582\) 0 0
\(583\) 361481. + 131568.i 1.06353 + 0.387092i
\(584\) 0 0
\(585\) 310465. + 23958.9i 0.907196 + 0.0700091i
\(586\) 0 0
\(587\) 144861. 25542.9i 0.420412 0.0741299i 0.0405594 0.999177i \(-0.487086\pi\)
0.379852 + 0.925047i \(0.375975\pi\)
\(588\) 0 0
\(589\) −617274. + 224669.i −1.77929 + 0.647610i
\(590\) 0 0
\(591\) 36794.7 290998.i 0.105344 0.833134i
\(592\) 0 0
\(593\) 580736.i 1.65147i 0.564061 + 0.825733i \(0.309238\pi\)
−0.564061 + 0.825733i \(0.690762\pi\)
\(594\) 0 0
\(595\) −214370. −0.605523
\(596\) 0 0
\(597\) 155408. + 369816.i 0.436037 + 1.03762i
\(598\) 0 0
\(599\) −14952.8 41082.5i −0.0416743 0.114499i 0.917110 0.398634i \(-0.130516\pi\)
−0.958784 + 0.284135i \(0.908294\pi\)
\(600\) 0 0
\(601\) −37245.3 211228.i −0.103115 0.584794i −0.991956 0.126580i \(-0.959600\pi\)
0.888841 0.458215i \(-0.151511\pi\)
\(602\) 0 0
\(603\) 225227. 496216.i 0.619422 1.36470i
\(604\) 0 0
\(605\) 45781.4 125783.i 0.125077 0.343647i
\(606\) 0 0
\(607\) 190213. + 159608.i 0.516254 + 0.433188i 0.863323 0.504651i \(-0.168379\pi\)
−0.347070 + 0.937839i \(0.612823\pi\)
\(608\) 0 0
\(609\) −89469.9 394007.i −0.241236 1.06235i
\(610\) 0 0
\(611\) −859341. 496140.i −2.30188 1.32899i
\(612\) 0 0
\(613\) 99795.7 + 172851.i 0.265577 + 0.459993i 0.967715 0.252048i \(-0.0811041\pi\)
−0.702137 + 0.712041i \(0.747771\pi\)
\(614\) 0 0
\(615\) −40479.0 + 26080.5i −0.107024 + 0.0689550i
\(616\) 0 0
\(617\) 378464. + 66733.4i 0.994156 + 0.175296i 0.646983 0.762505i \(-0.276031\pi\)
0.347173 + 0.937801i \(0.387142\pi\)
\(618\) 0 0
\(619\) −320380. + 268831.i −0.836151 + 0.701614i −0.956694 0.291094i \(-0.905981\pi\)
0.120544 + 0.992708i \(0.461536\pi\)
\(620\) 0 0
\(621\) −45930.3 28277.8i −0.119101 0.0733266i
\(622\) 0 0
\(623\) 132590. + 158014.i 0.341613 + 0.407118i
\(624\) 0 0
\(625\) 14545.2 82490.2i 0.0372358 0.211175i
\(626\) 0 0
\(627\) −340308. + 661986.i −0.865640 + 1.68389i
\(628\) 0 0
\(629\) 209390. 120892.i 0.529243 0.305559i
\(630\) 0 0
\(631\) 161548. 279809.i 0.405735 0.702753i −0.588672 0.808372i \(-0.700349\pi\)
0.994407 + 0.105619i \(0.0336824\pi\)
\(632\) 0 0
\(633\) −140.166 + 452.624i −0.000349813 + 0.00112961i
\(634\) 0 0
\(635\) 60299.3 71862.0i 0.149543 0.178218i
\(636\) 0 0
\(637\) 246681. + 89784.7i 0.607936 + 0.221270i
\(638\) 0 0
\(639\) 104604. 407026.i 0.256180 0.996829i
\(640\) 0 0
\(641\) 328831. 57981.8i 0.800307 0.141116i 0.241486 0.970404i \(-0.422365\pi\)
0.558821 + 0.829288i \(0.311254\pi\)
\(642\) 0 0
\(643\) −551393. + 200691.i −1.33364 + 0.485406i −0.907805 0.419394i \(-0.862243\pi\)
−0.425838 + 0.904800i \(0.640021\pi\)
\(644\) 0 0
\(645\) 170186. + 129208.i 0.409076 + 0.310578i
\(646\) 0 0
\(647\) 406198.i 0.970351i 0.874417 + 0.485175i \(0.161244\pi\)
−0.874417 + 0.485175i \(0.838756\pi\)
\(648\) 0 0
\(649\) 797882. 1.89430
\(650\) 0 0
\(651\) −260910. + 343657.i −0.615643 + 0.810891i
\(652\) 0 0
\(653\) 127919. + 351455.i 0.299992 + 0.824221i 0.994500 + 0.104736i \(0.0333999\pi\)
−0.694508 + 0.719485i \(0.744378\pi\)
\(654\) 0 0
\(655\) −33151.3 188010.i −0.0772712 0.438227i
\(656\) 0 0
\(657\) 24561.5 25070.1i 0.0569015 0.0580799i
\(658\) 0 0
\(659\) 86619.0 237984.i 0.199454 0.547995i −0.799132 0.601155i \(-0.794707\pi\)
0.998586 + 0.0531605i \(0.0169295\pi\)
\(660\) 0 0
\(661\) −231121. 193933.i −0.528976 0.443863i 0.338772 0.940869i \(-0.389989\pi\)
−0.867748 + 0.497005i \(0.834433\pi\)
\(662\) 0 0
\(663\) −1.01592e6 314605.i −2.31117 0.715711i
\(664\) 0 0
\(665\) −236678. 136646.i −0.535197 0.308996i
\(666\) 0 0
\(667\) 43142.3 + 74724.6i 0.0969731 + 0.167962i
\(668\) 0 0
\(669\) −258288. 132779.i −0.577102 0.296672i
\(670\) 0 0
\(671\) −76711.8 13526.4i −0.170379 0.0300425i
\(672\) 0 0
\(673\) 74645.5 62635.0i 0.164806 0.138289i −0.556655 0.830744i \(-0.687915\pi\)
0.721461 + 0.692455i \(0.243471\pi\)
\(674\) 0 0
\(675\) −307049. + 102027.i −0.673908 + 0.223928i
\(676\) 0 0
\(677\) −369317. 440135.i −0.805790 0.960303i 0.193996 0.981002i \(-0.437855\pi\)
−0.999786 + 0.0206997i \(0.993411\pi\)
\(678\) 0 0
\(679\) 60868.6 345203.i 0.132024 0.748747i
\(680\) 0 0
\(681\) −75083.0 116535.i −0.161900 0.251281i
\(682\) 0 0
\(683\) 161270. 93109.1i 0.345709 0.199595i −0.317084 0.948397i \(-0.602704\pi\)
0.662794 + 0.748802i \(0.269371\pi\)
\(684\) 0 0
\(685\) 201309. 348677.i 0.429024 0.743091i
\(686\) 0 0
\(687\) 574444. 130443.i 1.21712 0.276380i
\(688\) 0 0
\(689\) −450407. + 536775.i −0.948783 + 1.13072i
\(690\) 0 0
\(691\) −756814. 275458.i −1.58501 0.576898i −0.608728 0.793379i \(-0.708320\pi\)
−0.976287 + 0.216481i \(0.930542\pi\)
\(692\) 0 0
\(693\) 47601.2 + 486595.i 0.0991177 + 1.01321i
\(694\) 0 0
\(695\) 215963. 38080.1i 0.447105 0.0788366i
\(696\) 0 0
\(697\) 154545. 56249.7i 0.318118 0.115786i
\(698\) 0 0
\(699\) 670904. 281934.i 1.37311 0.577022i
\(700\) 0 0
\(701\) 603002.i 1.22711i 0.789653 + 0.613554i \(0.210261\pi\)
−0.789653 + 0.613554i \(0.789739\pi\)
\(702\) 0 0
\(703\) 308239. 0.623702
\(704\) 0 0
\(705\) −417530. 52793.8i −0.840058 0.106220i
\(706\) 0 0
\(707\) 31038.6 + 85277.9i 0.0620960 + 0.170607i
\(708\) 0 0
\(709\) −109788. 622641.i −0.218406 1.23864i −0.874898 0.484308i \(-0.839072\pi\)
0.656492 0.754333i \(-0.272040\pi\)
\(710\) 0 0
\(711\) 12510.7 + 8570.36i 0.0247481 + 0.0169535i
\(712\) 0 0
\(713\) 31515.3 86587.7i 0.0619931 0.170325i
\(714\) 0 0
\(715\) 461758. + 387461.i 0.903239 + 0.757907i
\(716\) 0 0
\(717\) 175943. 162889.i 0.342243 0.316849i
\(718\) 0 0
\(719\) −621112. 358599.i −1.20147 0.693668i −0.240586 0.970628i \(-0.577340\pi\)
−0.960881 + 0.276960i \(0.910673\pi\)
\(720\) 0 0
\(721\) −147080. 254750.i −0.282933 0.490054i
\(722\) 0 0
\(723\) −24621.2 504573.i −0.0471012 0.965268i
\(724\) 0 0
\(725\) 509737. + 89880.3i 0.969772 + 0.170997i
\(726\) 0 0
\(727\) 36455.9 30590.1i 0.0689761 0.0578778i −0.607648 0.794207i \(-0.707887\pi\)
0.676624 + 0.736329i \(0.263442\pi\)
\(728\) 0 0
\(729\) 387160. + 364056.i 0.728509 + 0.685036i
\(730\) 0 0
\(731\) −469103. 559055.i −0.877877 1.04621i
\(732\) 0 0
\(733\) 1543.89 8755.82i 0.00287348 0.0162963i −0.983337 0.181790i \(-0.941811\pi\)
0.986211 + 0.165494i \(0.0529219\pi\)
\(734\) 0 0
\(735\) 111207. 5426.45i 0.205853 0.0100448i
\(736\) 0 0
\(737\) 913558. 527443.i 1.68190 0.971047i
\(738\) 0 0
\(739\) −191027. + 330869.i −0.349789 + 0.605852i −0.986212 0.165488i \(-0.947080\pi\)
0.636423 + 0.771340i \(0.280413\pi\)
\(740\) 0 0
\(741\) −921099. 994919.i −1.67753 1.81197i
\(742\) 0 0
\(743\) −530396. + 632101.i −0.960777 + 1.14501i 0.0285936 + 0.999591i \(0.490897\pi\)
−0.989370 + 0.145418i \(0.953547\pi\)
\(744\) 0 0
\(745\) 43955.7 + 15998.6i 0.0791960 + 0.0288250i
\(746\) 0 0
\(747\) 329908. 481588.i 0.591224 0.863047i
\(748\) 0 0
\(749\) 182244. 32134.5i 0.324854 0.0572806i
\(750\) 0 0
\(751\) 560057. 203844.i 0.993006 0.361425i 0.206123 0.978526i \(-0.433915\pi\)
0.786884 + 0.617101i \(0.211693\pi\)
\(752\) 0 0
\(753\) 104142. 823629.i 0.183669 1.45259i
\(754\) 0 0
\(755\) 146547.i 0.257089i
\(756\) 0 0
\(757\) 801472. 1.39861 0.699305 0.714824i \(-0.253493\pi\)
0.699305 + 0.714824i \(0.253493\pi\)
\(758\) 0 0
\(759\) −40450.2 96257.3i −0.0702161 0.167090i
\(760\) 0 0
\(761\) −71741.4 197108.i −0.123880 0.340357i 0.862215 0.506543i \(-0.169077\pi\)
−0.986094 + 0.166186i \(0.946855\pi\)
\(762\) 0 0
\(763\) 63560.8 + 360471.i 0.109179 + 0.619187i
\(764\) 0 0
\(765\) −448925. + 43916.1i −0.767099 + 0.0750415i
\(766\) 0 0
\(767\) −497082. + 1.36572e6i −0.844963 + 2.32152i
\(768\) 0 0
\(769\) −290461. 243726.i −0.491174 0.412144i 0.363273 0.931683i \(-0.381659\pi\)
−0.854447 + 0.519539i \(0.826104\pi\)
\(770\) 0 0
\(771\) −27547.9 121315.i −0.0463426 0.204083i
\(772\) 0 0
\(773\) 577429. + 333379.i 0.966361 + 0.557929i 0.898125 0.439740i \(-0.144930\pi\)
0.0682362 + 0.997669i \(0.478263\pi\)
\(774\) 0 0
\(775\) −276377. 478699.i −0.460149 0.797001i
\(776\) 0 0
\(777\) 170200. 109659.i 0.281914 0.181636i
\(778\) 0 0
\(779\) 206482. + 36408.3i 0.340257 + 0.0599965i
\(780\) 0 0