Properties

Label 108.5.k.a.29.6
Level 108
Weight 5
Character 108.29
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 29.6
Character \(\chi\) \(=\) 108.29
Dual form 108.5.k.a.41.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.21427 - 8.91771i) q^{3} +(-22.3567 - 26.6437i) q^{5} +(80.4961 - 29.2982i) q^{7} +(-78.0511 + 21.6570i) q^{9} +O(q^{10})\) \(q+(-1.21427 - 8.91771i) q^{3} +(-22.3567 - 26.6437i) q^{5} +(80.4961 - 29.2982i) q^{7} +(-78.0511 + 21.6570i) q^{9} +(-32.7869 + 39.0740i) q^{11} +(-24.9815 - 141.677i) q^{13} +(-210.453 + 231.723i) q^{15} +(-462.052 + 266.766i) q^{17} +(16.9961 - 29.4382i) q^{19} +(-359.017 - 682.265i) q^{21} +(7.86326 - 21.6041i) q^{23} +(-101.533 + 575.822i) q^{25} +(287.905 + 669.740i) q^{27} +(890.785 + 157.069i) q^{29} +(-1362.59 - 495.941i) q^{31} +(388.262 + 244.938i) q^{33} +(-2580.24 - 1489.70i) q^{35} +(-500.150 - 866.285i) q^{37} +(-1233.10 + 394.812i) q^{39} +(-316.444 + 55.7976i) q^{41} +(1511.35 + 1268.18i) q^{43} +(2321.98 + 1595.39i) q^{45} +(-1096.53 - 3012.68i) q^{47} +(3781.97 - 3173.45i) q^{49} +(2940.00 + 3796.52i) q^{51} -256.114i q^{53} +1774.08 q^{55} +(-283.159 - 115.821i) q^{57} +(470.340 + 560.529i) q^{59} +(6427.64 - 2339.47i) q^{61} +(-5648.30 + 4030.06i) q^{63} +(-3216.30 + 3833.04i) q^{65} +(-37.1850 - 210.886i) q^{67} +(-202.208 - 43.8891i) q^{69} +(1971.22 - 1138.08i) q^{71} +(-2326.61 + 4029.81i) q^{73} +(5258.31 + 206.240i) q^{75} +(-1494.43 + 4105.90i) q^{77} +(1830.56 - 10381.6i) q^{79} +(5622.95 - 3380.70i) q^{81} +(-2377.57 - 419.230i) q^{83} +(17437.6 + 6346.76i) q^{85} +(319.049 - 8134.48i) q^{87} +(-1223.50 - 706.387i) q^{89} +(-6161.81 - 10672.6i) q^{91} +(-2768.11 + 12753.4i) q^{93} +(-1164.32 + 205.301i) q^{95} +(-9768.43 - 8196.69i) q^{97} +(1712.83 - 3759.83i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q + 9q^{5} - 102q^{9} + O(q^{10}) \) \( 72q + 9q^{5} - 102q^{9} + 18q^{11} - 225q^{15} - 282q^{21} - 1278q^{23} + 441q^{25} + 54q^{27} + 1854q^{29} - 1665q^{31} - 45q^{33} - 2673q^{35} + 6951q^{39} - 5472q^{41} + 1260q^{43} + 5553q^{45} + 5103q^{47} - 5904q^{49} + 1899q^{51} + 1107q^{57} - 10944q^{59} + 8352q^{61} - 11985q^{63} + 8757q^{65} + 378q^{67} + 5607q^{69} - 19764q^{71} + 6111q^{73} - 3453q^{75} - 5679q^{77} - 5652q^{79} - 20466q^{81} - 20061q^{83} + 26100q^{85} + 40545q^{87} + 15633q^{89} - 6039q^{91} + 40179q^{93} + 48024q^{95} - 37530q^{97} + 12177q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) −1.21427 8.91771i −0.134919 0.990857i
\(4\) 0 0
\(5\) −22.3567 26.6437i −0.894267 1.06575i −0.997470 0.0710858i \(-0.977354\pi\)
0.103203 0.994660i \(-0.467091\pi\)
\(6\) 0 0
\(7\) 80.4961 29.2982i 1.64278 0.597922i 0.655256 0.755407i \(-0.272561\pi\)
0.987521 + 0.157485i \(0.0503384\pi\)
\(8\) 0 0
\(9\) −78.0511 + 21.6570i −0.963594 + 0.267370i
\(10\) 0 0
\(11\) −32.7869 + 39.0740i −0.270967 + 0.322925i −0.884318 0.466885i \(-0.845376\pi\)
0.613352 + 0.789810i \(0.289821\pi\)
\(12\) 0 0
\(13\) −24.9815 141.677i −0.147820 0.838328i −0.965060 0.262030i \(-0.915608\pi\)
0.817240 0.576298i \(-0.195503\pi\)
\(14\) 0 0
\(15\) −210.453 + 231.723i −0.935348 + 1.02988i
\(16\) 0 0
\(17\) −462.052 + 266.766i −1.59880 + 0.923065i −0.607077 + 0.794643i \(0.707658\pi\)
−0.991720 + 0.128422i \(0.959009\pi\)
\(18\) 0 0
\(19\) 16.9961 29.4382i 0.0470807 0.0815462i −0.841525 0.540219i \(-0.818342\pi\)
0.888605 + 0.458672i \(0.151675\pi\)
\(20\) 0 0
\(21\) −359.017 682.265i −0.814096 1.54709i
\(22\) 0 0
\(23\) 7.86326 21.6041i 0.0148644 0.0408396i −0.932039 0.362359i \(-0.881971\pi\)
0.946903 + 0.321520i \(0.104194\pi\)
\(24\) 0 0
\(25\) −101.533 + 575.822i −0.162453 + 0.921316i
\(26\) 0 0
\(27\) 287.905 + 669.740i 0.394932 + 0.918710i
\(28\) 0 0
\(29\) 890.785 + 157.069i 1.05920 + 0.186765i 0.676000 0.736902i \(-0.263712\pi\)
0.383197 + 0.923667i \(0.374823\pi\)
\(30\) 0 0
\(31\) −1362.59 495.941i −1.41788 0.516068i −0.484451 0.874819i \(-0.660981\pi\)
−0.933433 + 0.358751i \(0.883203\pi\)
\(32\) 0 0
\(33\) 388.262 + 244.938i 0.356531 + 0.224920i
\(34\) 0 0
\(35\) −2580.24 1489.70i −2.10632 1.21608i
\(36\) 0 0
\(37\) −500.150 866.285i −0.365340 0.632787i 0.623491 0.781831i \(-0.285714\pi\)
−0.988831 + 0.149044i \(0.952380\pi\)
\(38\) 0 0
\(39\) −1233.10 + 394.812i −0.810719 + 0.259574i
\(40\) 0 0
\(41\) −316.444 + 55.7976i −0.188248 + 0.0331931i −0.266977 0.963703i \(-0.586025\pi\)
0.0787295 + 0.996896i \(0.474914\pi\)
\(42\) 0 0
\(43\) 1511.35 + 1268.18i 0.817389 + 0.685871i 0.952359 0.304979i \(-0.0986494\pi\)
−0.134970 + 0.990850i \(0.543094\pi\)
\(44\) 0 0
\(45\) 2321.98 + 1595.39i 1.14666 + 0.787846i
\(46\) 0 0
\(47\) −1096.53 3012.68i −0.496391 1.36382i −0.894739 0.446589i \(-0.852639\pi\)
0.398349 0.917234i \(-0.369583\pi\)
\(48\) 0 0
\(49\) 3781.97 3173.45i 1.57516 1.32172i
\(50\) 0 0
\(51\) 2940.00 + 3796.52i 1.13033 + 1.45964i
\(52\) 0 0
\(53\) 256.114i 0.0911761i −0.998960 0.0455880i \(-0.985484\pi\)
0.998960 0.0455880i \(-0.0145162\pi\)
\(54\) 0 0
\(55\) 1774.08 0.586473
\(56\) 0 0
\(57\) −283.159 115.821i −0.0871526 0.0356481i
\(58\) 0 0
\(59\) 470.340 + 560.529i 0.135116 + 0.161025i 0.829360 0.558715i \(-0.188705\pi\)
−0.694244 + 0.719740i \(0.744261\pi\)
\(60\) 0 0
\(61\) 6427.64 2339.47i 1.72740 0.628721i 0.728956 0.684560i \(-0.240006\pi\)
0.998440 + 0.0558393i \(0.0177835\pi\)
\(62\) 0 0
\(63\) −5648.30 + 4030.06i −1.42310 + 1.01538i
\(64\) 0 0
\(65\) −3216.30 + 3833.04i −0.761254 + 0.907227i
\(66\) 0 0
\(67\) −37.1850 210.886i −0.00828357 0.0469785i 0.980386 0.197088i \(-0.0631485\pi\)
−0.988669 + 0.150110i \(0.952037\pi\)
\(68\) 0 0
\(69\) −202.208 43.8891i −0.0424717 0.00921847i
\(70\) 0 0
\(71\) 1971.22 1138.08i 0.391037 0.225766i −0.291572 0.956549i \(-0.594178\pi\)
0.682610 + 0.730783i \(0.260845\pi\)
\(72\) 0 0
\(73\) −2326.61 + 4029.81i −0.436595 + 0.756204i −0.997424 0.0717270i \(-0.977149\pi\)
0.560830 + 0.827931i \(0.310482\pi\)
\(74\) 0 0
\(75\) 5258.31 + 206.240i 0.934810 + 0.0366649i
\(76\) 0 0
\(77\) −1494.43 + 4105.90i −0.252054 + 0.692511i
\(78\) 0 0
\(79\) 1830.56 10381.6i 0.293311 1.66345i −0.380676 0.924708i \(-0.624309\pi\)
0.673988 0.738743i \(-0.264580\pi\)
\(80\) 0 0
\(81\) 5622.95 3380.70i 0.857027 0.515272i
\(82\) 0 0
\(83\) −2377.57 419.230i −0.345125 0.0608549i −0.00160115 0.999999i \(-0.500510\pi\)
−0.343524 + 0.939144i \(0.611621\pi\)
\(84\) 0 0
\(85\) 17437.6 + 6346.76i 2.41350 + 0.878444i
\(86\) 0 0
\(87\) 319.049 8134.48i 0.0421520 1.07471i
\(88\) 0 0
\(89\) −1223.50 706.387i −0.154463 0.0891790i 0.420777 0.907164i \(-0.361758\pi\)
−0.575239 + 0.817985i \(0.695091\pi\)
\(90\) 0 0
\(91\) −6161.81 10672.6i −0.744090 1.28880i
\(92\) 0 0
\(93\) −2768.11 + 12753.4i −0.320050 + 1.47455i
\(94\) 0 0
\(95\) −1164.32 + 205.301i −0.129010 + 0.0227480i
\(96\) 0 0
\(97\) −9768.43 8196.69i −1.03820 0.871154i −0.0463971 0.998923i \(-0.514774\pi\)
−0.991804 + 0.127769i \(0.959218\pi\)
\(98\) 0 0
\(99\) 1712.83 3759.83i 0.174761 0.383617i
\(100\) 0 0
\(101\) −6645.49 18258.3i −0.651455 1.78986i −0.612301 0.790625i \(-0.709756\pi\)
−0.0391537 0.999233i \(-0.512466\pi\)
\(102\) 0 0
\(103\) −12318.9 + 10336.8i −1.16117 + 0.974338i −0.999921 0.0125753i \(-0.995997\pi\)
−0.161250 + 0.986914i \(0.551553\pi\)
\(104\) 0 0
\(105\) −10151.6 + 24818.7i −0.920782 + 2.25113i
\(106\) 0 0
\(107\) 16995.1i 1.48442i −0.670168 0.742209i \(-0.733778\pi\)
0.670168 0.742209i \(-0.266222\pi\)
\(108\) 0 0
\(109\) 11922.8 1.00352 0.501760 0.865007i \(-0.332686\pi\)
0.501760 + 0.865007i \(0.332686\pi\)
\(110\) 0 0
\(111\) −7117.96 + 5512.09i −0.577710 + 0.447374i
\(112\) 0 0
\(113\) −4315.44 5142.94i −0.337962 0.402768i 0.570119 0.821562i \(-0.306897\pi\)
−0.908081 + 0.418795i \(0.862453\pi\)
\(114\) 0 0
\(115\) −751.410 + 273.491i −0.0568174 + 0.0206798i
\(116\) 0 0
\(117\) 5018.14 + 10517.1i 0.366582 + 0.768285i
\(118\) 0 0
\(119\) −29377.6 + 35010.9i −2.07455 + 2.47235i
\(120\) 0 0
\(121\) 2090.59 + 11856.3i 0.142790 + 0.809804i
\(122\) 0 0
\(123\) 881.835 + 2754.20i 0.0582877 + 0.182048i
\(124\) 0 0
\(125\) −1213.72 + 700.740i −0.0776779 + 0.0448474i
\(126\) 0 0
\(127\) −6544.45 + 11335.3i −0.405757 + 0.702791i −0.994409 0.105595i \(-0.966325\pi\)
0.588652 + 0.808386i \(0.299659\pi\)
\(128\) 0 0
\(129\) 9474.03 15017.7i 0.569319 0.902452i
\(130\) 0 0
\(131\) 5498.71 15107.6i 0.320419 0.880344i −0.670014 0.742348i \(-0.733712\pi\)
0.990433 0.137995i \(-0.0440658\pi\)
\(132\) 0 0
\(133\) 505.638 2867.61i 0.0285849 0.162113i
\(134\) 0 0
\(135\) 11407.7 22644.0i 0.625937 1.24247i
\(136\) 0 0
\(137\) 4073.77 + 718.316i 0.217048 + 0.0382714i 0.281115 0.959674i \(-0.409296\pi\)
−0.0640667 + 0.997946i \(0.520407\pi\)
\(138\) 0 0
\(139\) −19736.9 7183.64i −1.02153 0.371805i −0.223677 0.974663i \(-0.571806\pi\)
−0.797848 + 0.602858i \(0.794028\pi\)
\(140\) 0 0
\(141\) −25534.8 + 13436.7i −1.28438 + 0.675857i
\(142\) 0 0
\(143\) 6354.97 + 3669.04i 0.310772 + 0.179424i
\(144\) 0 0
\(145\) −15730.1 27245.3i −0.748161 1.29585i
\(146\) 0 0
\(147\) −32892.2 29873.1i −1.52215 1.38244i
\(148\) 0 0
\(149\) 36313.4 6403.03i 1.63566 0.288412i 0.721094 0.692837i \(-0.243640\pi\)
0.914571 + 0.404426i \(0.132529\pi\)
\(150\) 0 0
\(151\) 15078.0 + 12651.9i 0.661285 + 0.554884i 0.910472 0.413571i \(-0.135719\pi\)
−0.249186 + 0.968456i \(0.580163\pi\)
\(152\) 0 0
\(153\) 30286.3 30828.0i 1.29379 1.31693i
\(154\) 0 0
\(155\) 17249.2 + 47391.9i 0.717970 + 1.97261i
\(156\) 0 0
\(157\) 4733.09 3971.53i 0.192019 0.161123i −0.541709 0.840566i \(-0.682223\pi\)
0.733729 + 0.679442i \(0.237778\pi\)
\(158\) 0 0
\(159\) −2283.95 + 310.990i −0.0903424 + 0.0123013i
\(160\) 0 0
\(161\) 1969.43i 0.0759781i
\(162\) 0 0
\(163\) −4373.14 −0.164595 −0.0822977 0.996608i \(-0.526226\pi\)
−0.0822977 + 0.996608i \(0.526226\pi\)
\(164\) 0 0
\(165\) −2154.21 15820.7i −0.0791261 0.581111i
\(166\) 0 0
\(167\) 24911.1 + 29687.9i 0.893225 + 1.06450i 0.997550 + 0.0699603i \(0.0222873\pi\)
−0.104325 + 0.994543i \(0.533268\pi\)
\(168\) 0 0
\(169\) 7390.15 2689.80i 0.258750 0.0941772i
\(170\) 0 0
\(171\) −689.026 + 2665.77i −0.0235637 + 0.0911654i
\(172\) 0 0
\(173\) 19067.0 22723.2i 0.637075 0.759236i −0.346830 0.937928i \(-0.612742\pi\)
0.983905 + 0.178692i \(0.0571865\pi\)
\(174\) 0 0
\(175\) 8697.54 + 49326.2i 0.284001 + 1.61065i
\(176\) 0 0
\(177\) 4427.52 4874.99i 0.141323 0.155606i
\(178\) 0 0
\(179\) 14709.6 8492.60i 0.459087 0.265054i −0.252573 0.967578i \(-0.581277\pi\)
0.711660 + 0.702524i \(0.247944\pi\)
\(180\) 0 0
\(181\) −23313.7 + 40380.6i −0.711631 + 1.23258i 0.252614 + 0.967567i \(0.418710\pi\)
−0.964245 + 0.265014i \(0.914624\pi\)
\(182\) 0 0
\(183\) −28667.6 54479.1i −0.856030 1.62678i
\(184\) 0 0
\(185\) −11899.3 + 32693.1i −0.347679 + 0.955240i
\(186\) 0 0
\(187\) 4725.68 26800.6i 0.135139 0.766412i
\(188\) 0 0
\(189\) 42797.4 + 45476.3i 1.19810 + 1.27310i
\(190\) 0 0
\(191\) 1180.85 + 208.216i 0.0323689 + 0.00570751i 0.189809 0.981821i \(-0.439213\pi\)
−0.157440 + 0.987529i \(0.550324\pi\)
\(192\) 0 0
\(193\) 36334.6 + 13224.7i 0.975451 + 0.355035i 0.780070 0.625692i \(-0.215183\pi\)
0.195381 + 0.980727i \(0.437406\pi\)
\(194\) 0 0
\(195\) 38087.4 + 24027.7i 1.00164 + 0.631892i
\(196\) 0 0
\(197\) −47062.9 27171.8i −1.21268 0.700141i −0.249338 0.968417i \(-0.580213\pi\)
−0.963342 + 0.268276i \(0.913546\pi\)
\(198\) 0 0
\(199\) −10298.4 17837.3i −0.260053 0.450425i 0.706203 0.708010i \(-0.250407\pi\)
−0.966256 + 0.257585i \(0.917073\pi\)
\(200\) 0 0
\(201\) −1835.47 + 587.677i −0.0454313 + 0.0145461i
\(202\) 0 0
\(203\) 76306.5 13454.9i 1.85170 0.326504i
\(204\) 0 0
\(205\) 8561.29 + 7183.78i 0.203719 + 0.170941i
\(206\) 0 0
\(207\) −145.856 + 1856.52i −0.00340396 + 0.0433271i
\(208\) 0 0
\(209\) 593.015 + 1629.29i 0.0135760 + 0.0372998i
\(210\) 0 0
\(211\) −12766.1 + 10712.0i −0.286744 + 0.240606i −0.774801 0.632205i \(-0.782150\pi\)
0.488058 + 0.872811i \(0.337706\pi\)
\(212\) 0 0
\(213\) −12542.7 16196.8i −0.276460 0.357002i
\(214\) 0 0
\(215\) 68620.1i 1.48448i
\(216\) 0 0
\(217\) −124213. −2.63784
\(218\) 0 0
\(219\) 38761.8 + 15854.8i 0.808195 + 0.330577i
\(220\) 0 0
\(221\) 49337.5 + 58798.1i 1.01017 + 1.20387i
\(222\) 0 0
\(223\) 34408.3 12523.6i 0.691915 0.251837i 0.0279603 0.999609i \(-0.491099\pi\)
0.663955 + 0.747772i \(0.268877\pi\)
\(224\) 0 0
\(225\) −4545.80 47142.5i −0.0897936 0.931209i
\(226\) 0 0
\(227\) 23831.2 28400.9i 0.462481 0.551163i −0.483517 0.875335i \(-0.660641\pi\)
0.945998 + 0.324171i \(0.105085\pi\)
\(228\) 0 0
\(229\) 2456.01 + 13928.7i 0.0468338 + 0.265608i 0.999229 0.0392581i \(-0.0124995\pi\)
−0.952395 + 0.304866i \(0.901388\pi\)
\(230\) 0 0
\(231\) 38429.9 + 8341.19i 0.720186 + 0.156316i
\(232\) 0 0
\(233\) 52304.4 30198.0i 0.963445 0.556245i 0.0662132 0.997805i \(-0.478908\pi\)
0.897232 + 0.441560i \(0.145575\pi\)
\(234\) 0 0
\(235\) −55754.2 + 96569.1i −1.00958 + 1.74865i
\(236\) 0 0
\(237\) −94802.9 3718.33i −1.68781 0.0661990i
\(238\) 0 0
\(239\) −29500.3 + 81051.3i −0.516452 + 1.41894i 0.357951 + 0.933740i \(0.383475\pi\)
−0.874403 + 0.485200i \(0.838747\pi\)
\(240\) 0 0
\(241\) 4921.28 27910.0i 0.0847314 0.480535i −0.912683 0.408669i \(-0.865993\pi\)
0.997414 0.0718669i \(-0.0228957\pi\)
\(242\) 0 0
\(243\) −36975.9 46038.8i −0.626190 0.779671i
\(244\) 0 0
\(245\) −169104. 29817.7i −2.81723 0.496754i
\(246\) 0 0
\(247\) −4595.31 1672.56i −0.0753219 0.0274149i
\(248\) 0 0
\(249\) −851.564 + 21711.5i −0.0137347 + 0.350180i
\(250\) 0 0
\(251\) 53648.5 + 30973.9i 0.851549 + 0.491642i 0.861173 0.508312i \(-0.169730\pi\)
−0.00962404 + 0.999954i \(0.503063\pi\)
\(252\) 0 0
\(253\) 586.347 + 1015.58i 0.00916038 + 0.0158662i
\(254\) 0 0
\(255\) 35424.7 163210.i 0.544785 2.50996i
\(256\) 0 0
\(257\) 18606.9 3280.89i 0.281713 0.0496736i −0.0310063 0.999519i \(-0.509871\pi\)
0.312719 + 0.949846i \(0.398760\pi\)
\(258\) 0 0
\(259\) −65640.7 55079.1i −0.978529 0.821083i
\(260\) 0 0
\(261\) −72928.4 + 7032.25i −1.07057 + 0.103232i
\(262\) 0 0
\(263\) 25920.2 + 71215.2i 0.374737 + 1.02958i 0.973506 + 0.228660i \(0.0734345\pi\)
−0.598769 + 0.800922i \(0.704343\pi\)
\(264\) 0 0
\(265\) −6823.80 + 5725.85i −0.0971705 + 0.0815358i
\(266\) 0 0
\(267\) −4813.70 + 11768.5i −0.0675238 + 0.165082i
\(268\) 0 0
\(269\) 8594.85i 0.118777i −0.998235 0.0593887i \(-0.981085\pi\)
0.998235 0.0593887i \(-0.0189151\pi\)
\(270\) 0 0
\(271\) −72299.1 −0.984451 −0.492226 0.870468i \(-0.663816\pi\)
−0.492226 + 0.870468i \(0.663816\pi\)
\(272\) 0 0
\(273\) −87692.8 + 67908.6i −1.17663 + 0.911170i
\(274\) 0 0
\(275\) −19170.7 22846.8i −0.253497 0.302106i
\(276\) 0 0
\(277\) 89969.1 32746.1i 1.17256 0.426776i 0.318990 0.947758i \(-0.396656\pi\)
0.853568 + 0.520982i \(0.174434\pi\)
\(278\) 0 0
\(279\) 117092. + 9199.25i 1.50425 + 0.118180i
\(280\) 0 0
\(281\) −64103.4 + 76395.4i −0.811836 + 0.967509i −0.999893 0.0146496i \(-0.995337\pi\)
0.188057 + 0.982158i \(0.439781\pi\)
\(282\) 0 0
\(283\) 9678.71 + 54890.7i 0.120849 + 0.685371i 0.983687 + 0.179889i \(0.0575740\pi\)
−0.862837 + 0.505482i \(0.831315\pi\)
\(284\) 0 0
\(285\) 3244.60 + 10133.8i 0.0399459 + 0.124762i
\(286\) 0 0
\(287\) −23837.7 + 13762.7i −0.289402 + 0.167086i
\(288\) 0 0
\(289\) 100568. 174188.i 1.20410 2.08556i
\(290\) 0 0
\(291\) −61234.2 + 97065.0i −0.723116 + 1.14624i
\(292\) 0 0
\(293\) 1269.57 3488.12i 0.0147884 0.0406309i −0.932079 0.362256i \(-0.882007\pi\)
0.946867 + 0.321625i \(0.104229\pi\)
\(294\) 0 0
\(295\) 4419.31 25063.1i 0.0507821 0.287999i
\(296\) 0 0
\(297\) −35608.9 10709.1i −0.403688 0.121406i
\(298\) 0 0
\(299\) −3257.26 574.342i −0.0364342 0.00642434i
\(300\) 0 0
\(301\) 158813. + 57803.3i 1.75289 + 0.637998i
\(302\) 0 0
\(303\) −154753. + 81433.1i −1.68560 + 0.886984i
\(304\) 0 0
\(305\) −206033. 118953.i −2.21481 1.27872i
\(306\) 0 0
\(307\) 16774.6 + 29054.4i 0.177981 + 0.308273i 0.941189 0.337881i \(-0.109710\pi\)
−0.763208 + 0.646153i \(0.776377\pi\)
\(308\) 0 0
\(309\) 107139. + 97304.5i 1.12209 + 1.01910i
\(310\) 0 0
\(311\) 62429.2 11007.9i 0.645456 0.113811i 0.158669 0.987332i \(-0.449280\pi\)
0.486787 + 0.873520i \(0.338169\pi\)
\(312\) 0 0
\(313\) 31389.0 + 26338.5i 0.320397 + 0.268845i 0.788774 0.614684i \(-0.210716\pi\)
−0.468376 + 0.883529i \(0.655161\pi\)
\(314\) 0 0
\(315\) 233653. + 60392.7i 2.35478 + 0.608644i
\(316\) 0 0
\(317\) 9984.29 + 27431.6i 0.0993571 + 0.272981i 0.979406 0.201902i \(-0.0647124\pi\)
−0.880049 + 0.474884i \(0.842490\pi\)
\(318\) 0 0
\(319\) −35343.4 + 29656.7i −0.347318 + 0.291434i
\(320\) 0 0
\(321\) −151557. + 20636.6i −1.47085 + 0.200276i
\(322\) 0 0
\(323\) 18136.0i 0.173834i
\(324\) 0 0
\(325\) 84117.5 0.796378
\(326\) 0 0
\(327\) −14477.5 106324.i −0.135394 0.994345i
\(328\) 0 0
\(329\) −176532. 210383.i −1.63092 1.94365i
\(330\) 0 0
\(331\) −88966.2 + 32381.0i −0.812024 + 0.295553i −0.714460 0.699677i \(-0.753327\pi\)
−0.0975643 + 0.995229i \(0.531105\pi\)
\(332\) 0 0
\(333\) 57798.4 + 56782.8i 0.521227 + 0.512069i
\(334\) 0 0
\(335\) −4787.45 + 5705.46i −0.0426594 + 0.0508395i
\(336\) 0 0
\(337\) −10184.4 57758.4i −0.0896756 0.508576i −0.996249 0.0865284i \(-0.972423\pi\)
0.906574 0.422047i \(-0.138688\pi\)
\(338\) 0 0
\(339\) −40623.2 + 44728.7i −0.353488 + 0.389213i
\(340\) 0 0
\(341\) 64053.4 36981.3i 0.550850 0.318034i
\(342\) 0 0
\(343\) 108620. 188135.i 0.923254 1.59912i
\(344\) 0 0
\(345\) 3351.32 + 6368.76i 0.0281565 + 0.0535078i
\(346\) 0 0
\(347\) 34392.2 94491.8i 0.285628 0.784757i −0.711037 0.703155i \(-0.751774\pi\)
0.996665 0.0816021i \(-0.0260037\pi\)
\(348\) 0 0
\(349\) 23996.6 136091.i 0.197015 1.11732i −0.712506 0.701666i \(-0.752440\pi\)
0.909521 0.415659i \(-0.136449\pi\)
\(350\) 0 0
\(351\) 87694.7 57520.8i 0.711802 0.466886i
\(352\) 0 0
\(353\) −9968.45 1757.71i −0.0799979 0.0141058i 0.133506 0.991048i \(-0.457376\pi\)
−0.213504 + 0.976942i \(0.568488\pi\)
\(354\) 0 0
\(355\) −74392.7 27076.7i −0.590301 0.214852i
\(356\) 0 0
\(357\) 347889. + 219469.i 2.72964 + 1.72201i
\(358\) 0 0
\(359\) 189855. + 109613.i 1.47311 + 0.850498i 0.999542 0.0302618i \(-0.00963412\pi\)
0.473563 + 0.880760i \(0.342967\pi\)
\(360\) 0 0
\(361\) 64582.8 + 111861.i 0.495567 + 0.858347i
\(362\) 0 0
\(363\) 103193. 33040.1i 0.783135 0.250742i
\(364\) 0 0
\(365\) 159384. 28103.7i 1.19635 0.210950i
\(366\) 0 0
\(367\) 38686.2 + 32461.6i 0.287226 + 0.241012i 0.775004 0.631956i \(-0.217748\pi\)
−0.487778 + 0.872968i \(0.662192\pi\)
\(368\) 0 0
\(369\) 23490.4 11208.3i 0.172519 0.0823164i
\(370\) 0 0
\(371\) −7503.66 20616.1i −0.0545162 0.149782i
\(372\) 0 0
\(373\) −62732.5 + 52638.9i −0.450895 + 0.378346i −0.839768 0.542946i \(-0.817309\pi\)
0.388873 + 0.921291i \(0.372864\pi\)
\(374\) 0 0
\(375\) 7722.77 + 9972.69i 0.0549175 + 0.0709169i
\(376\) 0 0
\(377\) 130128.i 0.915562i
\(378\) 0 0
\(379\) −21554.8 −0.150060 −0.0750302 0.997181i \(-0.523905\pi\)
−0.0750302 + 0.997181i \(0.523905\pi\)
\(380\) 0 0
\(381\) 109032. + 44597.4i 0.751110 + 0.307227i
\(382\) 0 0
\(383\) −55591.7 66251.6i −0.378977 0.451647i 0.542514 0.840047i \(-0.317472\pi\)
−0.921491 + 0.388400i \(0.873028\pi\)
\(384\) 0 0
\(385\) 142807. 51977.3i 0.963445 0.350665i
\(386\) 0 0
\(387\) −145428. 66251.2i −0.971012 0.442356i
\(388\) 0 0
\(389\) −86855.2 + 103510.i −0.573980 + 0.684042i −0.972443 0.233142i \(-0.925099\pi\)
0.398463 + 0.917184i \(0.369544\pi\)
\(390\) 0 0
\(391\) 2130.01 + 12079.9i 0.0139325 + 0.0790150i
\(392\) 0 0
\(393\) −141402. 30691.3i −0.915525 0.198714i
\(394\) 0 0
\(395\) −317529. + 183325.i −2.03512 + 1.17497i
\(396\) 0 0
\(397\) 10887.3 18857.3i 0.0690778 0.119646i −0.829418 0.558629i \(-0.811328\pi\)
0.898496 + 0.438982i \(0.144661\pi\)
\(398\) 0 0
\(399\) −26186.5 1027.08i −0.164487 0.00645147i
\(400\) 0 0
\(401\) −86805.3 + 238496.i −0.539831 + 1.48317i 0.307208 + 0.951642i \(0.400605\pi\)
−0.847039 + 0.531531i \(0.821617\pi\)
\(402\) 0 0
\(403\) −36224.1 + 205437.i −0.223042 + 1.26494i
\(404\) 0 0
\(405\) −215785. 74234.7i −1.31556 0.452582i
\(406\) 0 0
\(407\) 50247.6 + 8860.00i 0.303338 + 0.0534866i
\(408\) 0 0
\(409\) −56993.9 20744.1i −0.340707 0.124007i 0.165999 0.986126i \(-0.446915\pi\)
−0.506707 + 0.862119i \(0.669137\pi\)
\(410\) 0 0
\(411\) 1459.09 37200.9i 0.00863768 0.220227i
\(412\) 0 0
\(413\) 54283.0 + 31340.3i 0.318247 + 0.183740i
\(414\) 0 0
\(415\) 41984.7 + 72719.7i 0.243778 + 0.422237i
\(416\) 0 0
\(417\) −40095.8 + 184731.i −0.230583 + 1.06235i
\(418\) 0 0
\(419\) −65027.1 + 11466.0i −0.370396 + 0.0653109i −0.355748 0.934582i \(-0.615774\pi\)
−0.0146481 + 0.999893i \(0.504663\pi\)
\(420\) 0 0
\(421\) −47220.1 39622.4i −0.266418 0.223551i 0.499786 0.866149i \(-0.333412\pi\)
−0.766203 + 0.642598i \(0.777857\pi\)
\(422\) 0 0
\(423\) 150831. + 211396.i 0.842964 + 1.18145i
\(424\) 0 0
\(425\) −106696. 293146.i −0.590706 1.62295i
\(426\) 0 0
\(427\) 448858. 376636.i 2.46180 2.06570i
\(428\) 0 0
\(429\) 25002.8 61126.9i 0.135855 0.332138i
\(430\) 0 0
\(431\) 43491.4i 0.234125i −0.993125 0.117063i \(-0.962652\pi\)
0.993125 0.117063i \(-0.0373478\pi\)
\(432\) 0 0
\(433\) −19380.2 −0.103367 −0.0516835 0.998664i \(-0.516459\pi\)
−0.0516835 + 0.998664i \(0.516459\pi\)
\(434\) 0 0
\(435\) −223865. + 173359.i −1.18306 + 0.916155i
\(436\) 0 0
\(437\) −502.341 598.667i −0.00263049 0.00313489i
\(438\) 0 0
\(439\) 5089.93 1852.58i 0.0264109 0.00961277i −0.328781 0.944406i \(-0.606638\pi\)
0.355192 + 0.934793i \(0.384416\pi\)
\(440\) 0 0
\(441\) −226459. + 329597.i −1.16443 + 1.69475i
\(442\) 0 0
\(443\) 35044.8 41764.7i 0.178573 0.212815i −0.669332 0.742964i \(-0.733419\pi\)
0.847905 + 0.530149i \(0.177864\pi\)
\(444\) 0 0
\(445\) 8532.63 + 48390.9i 0.0430886 + 0.244368i
\(446\) 0 0
\(447\) −101195. 316057.i −0.506456 1.58180i
\(448\) 0 0
\(449\) 247357. 142811.i 1.22696 0.708386i 0.260568 0.965455i \(-0.416090\pi\)
0.966393 + 0.257069i \(0.0827568\pi\)
\(450\) 0 0
\(451\) 8195.00 14194.2i 0.0402899 0.0697841i
\(452\) 0 0
\(453\) 94517.5 149824.i 0.460591 0.730103i
\(454\) 0 0
\(455\) −146599. + 402776.i −0.708120 + 1.94554i
\(456\) 0 0
\(457\) 29580.8 167761.i 0.141637 0.803264i −0.828369 0.560183i \(-0.810731\pi\)
0.970006 0.243081i \(-0.0781580\pi\)
\(458\) 0 0
\(459\) −311691. 232651.i −1.47945 1.10428i
\(460\) 0 0
\(461\) 250743. + 44212.8i 1.17985 + 0.208040i 0.728971 0.684544i \(-0.239999\pi\)
0.450881 + 0.892584i \(0.351110\pi\)
\(462\) 0 0
\(463\) −232305. 84552.1i −1.08367 0.394423i −0.262397 0.964960i \(-0.584513\pi\)
−0.821272 + 0.570537i \(0.806735\pi\)
\(464\) 0 0
\(465\) 401682. 211370.i 1.85770 0.977547i
\(466\) 0 0
\(467\) −260643. 150482.i −1.19512 0.690003i −0.235658 0.971836i \(-0.575724\pi\)
−0.959464 + 0.281833i \(0.909058\pi\)
\(468\) 0 0
\(469\) −9171.83 15886.1i −0.0416975 0.0722223i
\(470\) 0 0
\(471\) −41164.2 37385.8i −0.185557 0.168525i
\(472\) 0 0
\(473\) −99105.3 + 17474.9i −0.442970 + 0.0781076i
\(474\) 0 0
\(475\) 15225.5 + 12775.7i 0.0674814 + 0.0566236i
\(476\) 0 0
\(477\) 5546.64 + 19989.9i 0.0243777 + 0.0878567i
\(478\) 0 0
\(479\) −114518. 314637.i −0.499120 1.37132i −0.892127 0.451785i \(-0.850788\pi\)
0.393007 0.919535i \(-0.371435\pi\)
\(480\) 0 0
\(481\) −110238. + 92501.1i −0.476478 + 0.399813i
\(482\) 0 0
\(483\) −17562.8 + 2391.41i −0.0752834 + 0.0102509i
\(484\) 0 0
\(485\) 443518.i 1.88550i
\(486\) 0 0
\(487\) −315837. −1.33170 −0.665848 0.746088i \(-0.731930\pi\)
−0.665848 + 0.746088i \(0.731930\pi\)
\(488\) 0 0
\(489\) 5310.16 + 38998.4i 0.0222070 + 0.163091i
\(490\) 0 0
\(491\) −205076. 244400.i −0.850650 1.01377i −0.999689 0.0249339i \(-0.992062\pi\)
0.149039 0.988831i \(-0.452382\pi\)
\(492\) 0 0
\(493\) −453490. + 165057.i −1.86584 + 0.679109i
\(494\) 0 0
\(495\) −138469. + 38421.2i −0.565122 + 0.156805i
\(496\) 0 0
\(497\) 125332. 149365.i 0.507397 0.604693i
\(498\) 0 0
\(499\) −17686.5 100305.i −0.0710299 0.402830i −0.999506 0.0314376i \(-0.989991\pi\)
0.928476 0.371393i \(-0.121120\pi\)
\(500\) 0 0
\(501\) 234500. 258199.i 0.934258 1.02868i
\(502\) 0 0
\(503\) −115666. + 66779.9i −0.457162 + 0.263943i −0.710850 0.703343i \(-0.751690\pi\)
0.253688 + 0.967286i \(0.418356\pi\)
\(504\) 0 0
\(505\) −337898. + 585256.i −1.32496 + 2.29490i
\(506\) 0 0
\(507\) −32960.4 62637.1i −0.128226 0.243678i
\(508\) 0 0
\(509\) −89439.9 + 245734.i −0.345220 + 0.948484i 0.638634 + 0.769511i \(0.279500\pi\)
−0.983854 + 0.178973i \(0.942722\pi\)
\(510\) 0 0
\(511\) −69217.1 + 392550.i −0.265077 + 1.50333i
\(512\) 0 0
\(513\) 24609.2 + 2907.58i 0.0935110 + 0.0110483i
\(514\) 0 0
\(515\) 550818. + 97124.0i 2.07679 + 0.366195i
\(516\) 0 0
\(517\) 153669. + 55931.1i 0.574918 + 0.209253i
\(518\) 0 0
\(519\) −225791. 142442.i −0.838248 0.528815i
\(520\) 0 0
\(521\) 375248. + 216649.i 1.38243 + 0.798145i 0.992447 0.122677i \(-0.0391480\pi\)
0.389982 + 0.920823i \(0.372481\pi\)
\(522\) 0 0
\(523\) −45791.2 79312.7i −0.167409 0.289961i 0.770099 0.637924i \(-0.220207\pi\)
−0.937508 + 0.347963i \(0.886873\pi\)
\(524\) 0 0
\(525\) 429316. 137457.i 1.55761 0.498711i
\(526\) 0 0
\(527\) 761886. 134341.i 2.74327 0.483713i
\(528\) 0 0
\(529\) 213966. + 179539.i 0.764598 + 0.641573i
\(530\) 0 0
\(531\) −48849.9 33563.8i −0.173251 0.119037i
\(532\) 0 0
\(533\) 15810.5 + 43439.1i 0.0556534 + 0.152907i
\(534\) 0 0
\(535\) −452812. + 379954.i −1.58201 + 1.32747i
\(536\) 0 0
\(537\) −93595.9 120864.i −0.324570 0.419129i
\(538\) 0 0
\(539\) 251824.i 0.866802i
\(540\) 0 0
\(541\) 274417. 0.937597 0.468799 0.883305i \(-0.344687\pi\)
0.468799 + 0.883305i \(0.344687\pi\)
\(542\) 0 0
\(543\) 388411. + 158872.i 1.31732 + 0.538826i
\(544\) 0 0
\(545\) −266555. 317668.i −0.897415 1.06950i
\(546\) 0 0
\(547\) −161263. + 58694.9i −0.538964 + 0.196167i −0.597137 0.802140i \(-0.703695\pi\)
0.0581722 + 0.998307i \(0.481473\pi\)
\(548\) 0 0
\(549\) −451019. + 321801.i −1.49641 + 1.06769i
\(550\) 0 0
\(551\) 19763.7 23553.5i 0.0650977 0.0775804i
\(552\) 0 0
\(553\) −156809. 889310.i −0.512769 2.90806i
\(554\) 0 0
\(555\) 305996. + 66416.4i 0.993414 + 0.215620i
\(556\) 0 0
\(557\) 252481. 145770.i 0.813803 0.469849i −0.0344720 0.999406i \(-0.510975\pi\)
0.848275 + 0.529556i \(0.177642\pi\)
\(558\) 0 0
\(559\) 141916. 245805.i 0.454158 0.786625i
\(560\) 0 0
\(561\) −244739. 9599.08i −0.777637 0.0305003i
\(562\) 0 0
\(563\) 66820.2 183587.i 0.210810 0.579196i −0.788550 0.614971i \(-0.789168\pi\)
0.999360 + 0.0357751i \(0.0113900\pi\)
\(564\) 0 0
\(565\) −40547.8 + 229958.i −0.127020 + 0.720364i
\(566\) 0 0
\(567\) 353577. 436876.i 1.09981 1.35891i
\(568\) 0 0
\(569\) 190504. + 33591.0i 0.588410 + 0.103753i 0.459923 0.887959i \(-0.347877\pi\)
0.128487 + 0.991711i \(0.458988\pi\)
\(570\) 0 0
\(571\) −399219. 145304.i −1.22444 0.445661i −0.352753 0.935717i \(-0.614754\pi\)
−0.871691 + 0.490056i \(0.836976\pi\)
\(572\) 0 0
\(573\) 422.940 10783.3i 0.00128816 0.0328430i
\(574\) 0 0
\(575\) 11641.8 + 6721.38i 0.0352114 + 0.0203293i
\(576\) 0 0
\(577\) 164752. + 285358.i 0.494855 + 0.857114i 0.999982 0.00593081i \(-0.00188785\pi\)
−0.505127 + 0.863045i \(0.668555\pi\)
\(578\) 0 0
\(579\) 73814.2 340080.i 0.220182 1.01443i
\(580\) 0 0
\(581\) −203668. + 35912.1i −0.603351 + 0.106387i
\(582\) 0 0
\(583\) 10007.4 + 8397.18i 0.0294431 + 0.0247057i
\(584\) 0 0
\(585\) 168024. 368828.i 0.490975 1.07774i
\(586\) 0 0
\(587\) 193089. + 530508.i 0.560378 + 1.53963i 0.819086 + 0.573671i \(0.194481\pi\)
−0.258708 + 0.965956i \(0.583297\pi\)
\(588\) 0 0
\(589\) −37758.3 + 31683.0i −0.108838 + 0.0913262i
\(590\) 0 0
\(591\) −185163. + 452687.i −0.530126 + 1.29605i
\(592\) 0 0
\(593\) 224726.i 0.639063i 0.947576 + 0.319531i \(0.103525\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(594\) 0 0
\(595\) 1.58960e6 4.49009
\(596\) 0 0
\(597\) −146563. + 113497.i −0.411221 + 0.318446i
\(598\) 0 0
\(599\) −281053. 334946.i −0.783312 0.933515i 0.215766 0.976445i \(-0.430775\pi\)
−0.999078 + 0.0429297i \(0.986331\pi\)
\(600\) 0 0
\(601\) 24667.2 8978.14i 0.0682923 0.0248564i −0.307648 0.951500i \(-0.599542\pi\)
0.375940 + 0.926644i \(0.377320\pi\)
\(602\) 0 0
\(603\) 7469.49 + 15654.6i 0.0205426 + 0.0430534i
\(604\) 0 0
\(605\) 269157. 320769.i 0.735353 0.876359i
\(606\) 0 0
\(607\) 14807.5 + 83977.7i 0.0401888 + 0.227922i 0.998286 0.0585206i \(-0.0186383\pi\)
−0.958097 + 0.286443i \(0.907527\pi\)
\(608\) 0 0
\(609\) −212643. 664142.i −0.573347 1.79071i
\(610\) 0 0
\(611\) −399436. + 230615.i −1.06995 + 0.617738i
\(612\) 0 0
\(613\) 180496. 312628.i 0.480337 0.831968i −0.519408 0.854526i \(-0.673848\pi\)
0.999746 + 0.0225579i \(0.00718100\pi\)
\(614\) 0 0
\(615\) 53667.1 85070.1i 0.141892 0.224919i
\(616\) 0 0
\(617\) −63106.4 + 173383.i −0.165769 + 0.455446i −0.994567 0.104102i \(-0.966803\pi\)
0.828798 + 0.559548i \(0.189025\pi\)
\(618\) 0 0
\(619\) −118484. + 671958.i −0.309228 + 1.75372i 0.293674 + 0.955906i \(0.405122\pi\)
−0.602902 + 0.797815i \(0.705989\pi\)
\(620\) 0 0
\(621\) 16733.0 953.608i 0.0433902 0.00247279i
\(622\) 0 0
\(623\) −119183. 21015.1i −0.307070 0.0541447i
\(624\) 0 0
\(625\) 389207. + 141660.i 0.996370 + 0.362649i
\(626\) 0 0
\(627\) 13809.5 7266.73i 0.0351271 0.0184843i
\(628\) 0 0
\(629\) 462191. + 266846.i 1.16821 + 0.674465i
\(630\) 0 0
\(631\) −290649. 503419.i −0.729979 1.26436i −0.956891 0.290446i \(-0.906196\pi\)
0.226912 0.973915i \(-0.427137\pi\)
\(632\) 0 0
\(633\) 111028. + 100837.i 0.277094 + 0.251660i
\(634\) 0 0
\(635\) 448327. 79052.1i 1.11185 0.196050i
\(636\) 0 0
\(637\) −544085. 456542.i −1.34087 1.12513i
\(638\) 0 0
\(639\) −129208. + 131519.i −0.316438 + 0.322098i
\(640\) 0 0
\(641\) 80269.0 + 220537.i 0.195358 + 0.536743i 0.998234 0.0594038i \(-0.0189200\pi\)
−0.802876 + 0.596146i \(0.796698\pi\)
\(642\) 0 0
\(643\) 67595.6 56719.4i 0.163492 0.137186i −0.557371 0.830263i \(-0.688190\pi\)
0.720863 + 0.693077i \(0.243746\pi\)
\(644\) 0 0
\(645\) −611934. + 83323.2i −1.47091 + 0.200284i
\(646\) 0 0
\(647\) 130796.i 0.312453i 0.987721 + 0.156227i \(0.0499330\pi\)
−0.987721 + 0.156227i \(0.950067\pi\)
\(648\) 0 0
\(649\) −37323.1 −0.0886112
\(650\) 0 0
\(651\) 150828. + 1.10770e6i 0.355893 + 2.61372i
\(652\) 0 0
\(653\) −191857. 228646.i −0.449937 0.536214i 0.492627 0.870241i \(-0.336037\pi\)
−0.942564 + 0.334027i \(0.891592\pi\)
\(654\) 0 0
\(655\) −525454. + 191250.i −1.22476 + 0.445777i
\(656\) 0 0
\(657\) 94321.2 364919.i 0.218514 0.845406i
\(658\) 0 0
\(659\) 338107. 402940.i 0.778545 0.927834i −0.220322 0.975427i \(-0.570711\pi\)
0.998867 + 0.0475937i \(0.0151553\pi\)
\(660\) 0 0
\(661\) 133796. + 758795.i 0.306225 + 1.73669i 0.617683 + 0.786427i \(0.288071\pi\)
−0.311458 + 0.950260i \(0.600817\pi\)
\(662\) 0 0
\(663\) 464436. 511374.i 1.05657 1.16335i
\(664\) 0 0
\(665\) −87708.1 + 50638.3i −0.198334 + 0.114508i
\(666\) 0 0
\(667\) 10397.8 18009.6i 0.0233717 0.0404810i
\(668\) 0 0
\(669\) −153463. 291636.i −0.342886 0.651612i
\(670\) 0 0
\(671\) −119330. + 327858.i −0.265037 + 0.728182i
\(672\) 0 0
\(673\) 45071.9 255616.i 0.0995121 0.564361i −0.893759 0.448548i \(-0.851941\pi\)
0.993271 0.115813i \(-0.0369475\pi\)
\(674\) 0 0
\(675\) −414883. + 97781.7i −0.910580 + 0.214610i
\(676\) 0 0
\(677\) −458739. 80888.0i −1.00089 0.176485i −0.350891 0.936416i \(-0.614121\pi\)
−0.650003 + 0.759932i \(0.725232\pi\)
\(678\) 0 0
\(679\) −1.02647e6 373604.i −2.22642 0.810349i
\(680\) 0 0
\(681\) −282208. 178033.i −0.608521 0.383890i
\(682\) 0 0
\(683\) 22955.6 + 13253.4i 0.0492093 + 0.0284110i 0.524403 0.851470i \(-0.324289\pi\)
−0.475194 + 0.879881i \(0.657622\pi\)
\(684\) 0 0
\(685\) −71937.4 124599.i −0.153311 0.265543i
\(686\) 0 0
\(687\) 121230. 38815.2i 0.256860 0.0822410i
\(688\) 0 0
\(689\) −36285.5 + 6398.11i −0.0764354 + 0.0134776i
\(690\) 0 0
\(691\) 429215. + 360155.i 0.898916 + 0.754280i 0.969978 0.243192i \(-0.0781944\pi\)
−0.0710620 + 0.997472i \(0.522639\pi\)
\(692\) 0 0
\(693\) 27720.2 352835.i 0.0577205 0.734691i
\(694\) 0 0
\(695\) 249853. + 686465.i 0.517267 + 1.42118i
\(696\) 0 0
\(697\) 131329. 110198.i 0.270330 0.226834i
\(698\) 0 0
\(699\) −332808. 429767.i −0.681146 0.879588i
\(700\) 0 0
\(701\) 301499.i 0.613550i 0.951782 + 0.306775i \(0.0992500\pi\)
−0.951782 + 0.306775i \(0.900750\pi\)
\(702\) 0 0
\(703\) −34002.5 −0.0688018
\(704\) 0 0
\(705\) 928876. + 379939.i 1.86887 + 0.764427i
\(706\) 0 0
\(707\) −1.06987e6 1.27502e6i −2.14039 2.55082i
\(708\) 0 0
\(709\) −15586.2 + 5672.93i −0.0310062 + 0.0112853i −0.357477 0.933922i \(-0.616363\pi\)
0.326470 + 0.945207i \(0.394141\pi\)
\(710\) 0 0
\(711\) 81957.0 + 849940.i 0.162124 + 1.68131i
\(712\) 0 0
\(713\) −21428.8 + 25537.8i −0.0421520 + 0.0502348i
\(714\) 0 0
\(715\) −44319.3 251347.i −0.0866923 0.491657i
\(716\) 0 0
\(717\) 758613. + 164657.i 1.47565 + 0.320288i
\(718\) 0 0
\(719\) 599437. 346085.i 1.15954 0.669460i 0.208346 0.978055i \(-0.433192\pi\)
0.951194 + 0.308595i \(0.0998588\pi\)
\(720\) 0 0
\(721\) −688772. + 1.19299e6i −1.32497 + 2.29491i
\(722\) 0 0
\(723\) −254869. 9996.40i −0.487574 0.0191235i
\(724\) 0 0
\(725\) −180888. + 496986.i −0.344139 + 0.945514i
\(726\) 0 0
\(727\) 73451.3 416563.i 0.138973 0.788156i −0.833037 0.553217i \(-0.813400\pi\)
0.972010 0.234939i \(-0.0754889\pi\)
\(728\) 0 0
\(729\) −365662. + 385643.i −0.688057 + 0.725656i
\(730\) 0 0
\(731\) −1.03663e6 182786.i −1.93994 0.342064i
\(732\) 0 0
\(733\) 125203. + 45570.3i 0.233028 + 0.0848152i 0.455895 0.890034i \(-0.349319\pi\)
−0.222867 + 0.974849i \(0.571542\pi\)
\(734\) 0 0
\(735\) −60567.4 + 1.54423e6i −0.112115 + 2.85850i
\(736\) 0 0
\(737\) 9459.35 + 5461.36i 0.0174151 + 0.0100546i
\(738\) 0 0
\(739\) 245668. + 425509.i 0.449841 + 0.779148i 0.998375 0.0569803i \(-0.0181472\pi\)
−0.548534 + 0.836128i \(0.684814\pi\)
\(740\) 0 0
\(741\) −9335.44 + 43010.6i −0.0170019 + 0.0783320i
\(742\) 0 0
\(743\) −481817. + 84957.4i −0.872780 + 0.153895i −0.592059 0.805895i \(-0.701685\pi\)
−0.280721 + 0.959789i \(0.590574\pi\)
\(744\) 0 0
\(745\) −982447. 824371.i −1.77010 1.48529i
\(746\) 0 0
\(747\) 194651. 18769.6i 0.348832 0.0336367i
\(748\) 0 0
\(749\) −497926. 1.36804e6i −0.887566 2.43857i
\(750\) 0 0
\(751\) 818800. 687055.i 1.45177 1.21818i 0.520495 0.853865i \(-0.325747\pi\)
0.931276 0.364315i \(-0.118697\pi\)
\(752\) 0 0
\(753\) 211073. 516032.i 0.372257 0.910095i
\(754\) 0 0
\(755\) 684587.i 1.20098i
\(756\) 0 0
\(757\) −396105. −0.691223 −0.345612 0.938378i \(-0.612328\pi\)
−0.345612 + 0.938378i \(0.612328\pi\)
\(758\) 0 0
\(759\) 8344.69 6462.06i 0.0144853 0.0112173i
\(760\) 0 0
\(761\) 204590. + 243821.i 0.353278 + 0.421020i 0.913191 0.407531i \(-0.133610\pi\)
−0.559914 + 0.828551i \(0.689166\pi\)
\(762\) 0 0
\(763\) 959741. 349317.i 1.64856 0.600027i
\(764\) 0 0
\(765\) −1.49847e6 117727.i −2.56051 0.201165i
\(766\) 0 0
\(767\) 67664.5 80639.4i 0.115019 0.137074i
\(768\) 0 0
\(769\) −51188.2 290303.i −0.0865599 0.490906i −0.997009 0.0772847i \(-0.975375\pi\)
0.910449 0.413621i \(-0.135736\pi\)
\(770\) 0 0
\(771\) −51851.7 161947.i −0.0872277 0.272435i
\(772\) 0 0
\(773\) −805902. + 465288.i −1.34873 + 0.778687i −0.988069 0.154012i \(-0.950781\pi\)
−0.360656 + 0.932699i \(0.617447\pi\)
\(774\) 0 0
\(775\) 423921. 734254.i 0.705801 1.22248i
\(776\) 0 0
\(777\) −411474. + 652245.i −0.681554 + 1.08036i
\(778\) 0 0
\(779\) −3735.75 + 10263.9i −0.00615605 + 0.0169136i
\(780\) 0 0