Properties

Label 882.4.g.u.361.1
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.u.667.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.50000 + 7.79423i) q^{5} -8.00000 q^{8} +(-9.00000 + 15.5885i) q^{10} +(-28.5000 + 49.3634i) q^{11} +70.0000 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-25.5000 + 44.1673i) q^{17} +(2.50000 + 4.33013i) q^{19} -36.0000 q^{20} -114.000 q^{22} +(34.5000 + 59.7558i) q^{23} +(22.0000 - 38.1051i) q^{25} +(70.0000 + 121.244i) q^{26} -114.000 q^{29} +(11.5000 - 19.9186i) q^{31} +(16.0000 - 27.7128i) q^{32} -102.000 q^{34} +(126.500 + 219.104i) q^{37} +(-5.00000 + 8.66025i) q^{38} +(-36.0000 - 62.3538i) q^{40} -42.0000 q^{41} -124.000 q^{43} +(-114.000 - 197.454i) q^{44} +(-69.0000 + 119.512i) q^{46} +(-100.500 - 174.071i) q^{47} +88.0000 q^{50} +(-140.000 + 242.487i) q^{52} +(-196.500 + 340.348i) q^{53} -513.000 q^{55} +(-114.000 - 197.454i) q^{58} +(-109.500 + 189.660i) q^{59} +(-354.500 - 614.012i) q^{61} +46.0000 q^{62} +64.0000 q^{64} +(315.000 + 545.596i) q^{65} +(-209.500 + 362.865i) q^{67} +(-102.000 - 176.669i) q^{68} +96.0000 q^{71} +(-156.500 + 271.066i) q^{73} +(-253.000 + 438.209i) q^{74} -20.0000 q^{76} +(-230.500 - 399.238i) q^{79} +(72.0000 - 124.708i) q^{80} +(-42.0000 - 72.7461i) q^{82} -588.000 q^{83} -459.000 q^{85} +(-124.000 - 214.774i) q^{86} +(228.000 - 394.908i) q^{88} +(508.500 + 880.748i) q^{89} -276.000 q^{92} +(201.000 - 348.142i) q^{94} +(-22.5000 + 38.9711i) q^{95} +1834.00 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 9q^{5} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 9q^{5} - 16q^{8} - 18q^{10} - 57q^{11} + 140q^{13} - 16q^{16} - 51q^{17} + 5q^{19} - 72q^{20} - 228q^{22} + 69q^{23} + 44q^{25} + 140q^{26} - 228q^{29} + 23q^{31} + 32q^{32} - 204q^{34} + 253q^{37} - 10q^{38} - 72q^{40} - 84q^{41} - 248q^{43} - 228q^{44} - 138q^{46} - 201q^{47} + 176q^{50} - 280q^{52} - 393q^{53} - 1026q^{55} - 228q^{58} - 219q^{59} - 709q^{61} + 92q^{62} + 128q^{64} + 630q^{65} - 419q^{67} - 204q^{68} + 192q^{71} - 313q^{73} - 506q^{74} - 40q^{76} - 461q^{79} + 144q^{80} - 84q^{82} - 1176q^{83} - 918q^{85} - 248q^{86} + 456q^{88} + 1017q^{89} - 552q^{92} + 402q^{94} - 45q^{95} + 3668q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 4.50000 + 7.79423i 0.402492 + 0.697137i 0.994026 0.109143i \(-0.0348107\pi\)
−0.591534 + 0.806280i \(0.701477\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −9.00000 + 15.5885i −0.284605 + 0.492950i
\(11\) −28.5000 + 49.3634i −0.781188 + 1.35306i 0.150061 + 0.988677i \(0.452053\pi\)
−0.931250 + 0.364381i \(0.881280\pi\)
\(12\) 0 0
\(13\) 70.0000 1.49342 0.746712 0.665148i \(-0.231631\pi\)
0.746712 + 0.665148i \(0.231631\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) −25.5000 + 44.1673i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) 2.50000 + 4.33013i 0.0301863 + 0.0522842i 0.880724 0.473630i \(-0.157057\pi\)
−0.850538 + 0.525914i \(0.823723\pi\)
\(20\) −36.0000 −0.402492
\(21\) 0 0
\(22\) −114.000 −1.10477
\(23\) 34.5000 + 59.7558i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) 22.0000 38.1051i 0.176000 0.304841i
\(26\) 70.0000 + 121.244i 0.528005 + 0.914531i
\(27\) 0 0
\(28\) 0 0
\(29\) −114.000 −0.729975 −0.364987 0.931012i \(-0.618927\pi\)
−0.364987 + 0.931012i \(0.618927\pi\)
\(30\) 0 0
\(31\) 11.5000 19.9186i 0.0666278 0.115403i −0.830787 0.556590i \(-0.812109\pi\)
0.897415 + 0.441188i \(0.145443\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −102.000 −0.514496
\(35\) 0 0
\(36\) 0 0
\(37\) 126.500 + 219.104i 0.562067 + 0.973528i 0.997316 + 0.0732182i \(0.0233270\pi\)
−0.435249 + 0.900310i \(0.643340\pi\)
\(38\) −5.00000 + 8.66025i −0.0213449 + 0.0369705i
\(39\) 0 0
\(40\) −36.0000 62.3538i −0.142302 0.246475i
\(41\) −42.0000 −0.159983 −0.0799914 0.996796i \(-0.525489\pi\)
−0.0799914 + 0.996796i \(0.525489\pi\)
\(42\) 0 0
\(43\) −124.000 −0.439763 −0.219882 0.975527i \(-0.570567\pi\)
−0.219882 + 0.975527i \(0.570567\pi\)
\(44\) −114.000 197.454i −0.390594 0.676529i
\(45\) 0 0
\(46\) −69.0000 + 119.512i −0.221163 + 0.383065i
\(47\) −100.500 174.071i −0.311903 0.540231i 0.666871 0.745173i \(-0.267633\pi\)
−0.978774 + 0.204941i \(0.934300\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 88.0000 0.248902
\(51\) 0 0
\(52\) −140.000 + 242.487i −0.373356 + 0.646671i
\(53\) −196.500 + 340.348i −0.509271 + 0.882083i 0.490672 + 0.871345i \(0.336751\pi\)
−0.999942 + 0.0107383i \(0.996582\pi\)
\(54\) 0 0
\(55\) −513.000 −1.25769
\(56\) 0 0
\(57\) 0 0
\(58\) −114.000 197.454i −0.258085 0.447016i
\(59\) −109.500 + 189.660i −0.241622 + 0.418501i −0.961176 0.275935i \(-0.911013\pi\)
0.719555 + 0.694436i \(0.244346\pi\)
\(60\) 0 0
\(61\) −354.500 614.012i −0.744083 1.28879i −0.950622 0.310351i \(-0.899553\pi\)
0.206539 0.978438i \(-0.433780\pi\)
\(62\) 46.0000 0.0942259
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 315.000 + 545.596i 0.601091 + 1.04112i
\(66\) 0 0
\(67\) −209.500 + 362.865i −0.382007 + 0.661656i −0.991349 0.131251i \(-0.958100\pi\)
0.609342 + 0.792908i \(0.291434\pi\)
\(68\) −102.000 176.669i −0.181902 0.315063i
\(69\) 0 0
\(70\) 0 0
\(71\) 96.0000 0.160466 0.0802331 0.996776i \(-0.474434\pi\)
0.0802331 + 0.996776i \(0.474434\pi\)
\(72\) 0 0
\(73\) −156.500 + 271.066i −0.250917 + 0.434601i −0.963779 0.266704i \(-0.914065\pi\)
0.712862 + 0.701305i \(0.247399\pi\)
\(74\) −253.000 + 438.209i −0.397441 + 0.688388i
\(75\) 0 0
\(76\) −20.0000 −0.0301863
\(77\) 0 0
\(78\) 0 0
\(79\) −230.500 399.238i −0.328269 0.568579i 0.653899 0.756582i \(-0.273132\pi\)
−0.982169 + 0.188003i \(0.939799\pi\)
\(80\) 72.0000 124.708i 0.100623 0.174284i
\(81\) 0 0
\(82\) −42.0000 72.7461i −0.0565625 0.0979691i
\(83\) −588.000 −0.777607 −0.388804 0.921321i \(-0.627112\pi\)
−0.388804 + 0.921321i \(0.627112\pi\)
\(84\) 0 0
\(85\) −459.000 −0.585712
\(86\) −124.000 214.774i −0.155480 0.269299i
\(87\) 0 0
\(88\) 228.000 394.908i 0.276192 0.478378i
\(89\) 508.500 + 880.748i 0.605628 + 1.04898i 0.991952 + 0.126615i \(0.0404114\pi\)
−0.386324 + 0.922363i \(0.626255\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −276.000 −0.312772
\(93\) 0 0
\(94\) 201.000 348.142i 0.220549 0.382001i
\(95\) −22.5000 + 38.9711i −0.0242995 + 0.0420879i
\(96\) 0 0
\(97\) 1834.00 1.91974 0.959868 0.280451i \(-0.0904839\pi\)
0.959868 + 0.280451i \(0.0904839\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 88.0000 + 152.420i 0.0880000 + 0.152420i
\(101\) 142.500 246.817i 0.140389 0.243161i −0.787254 0.616629i \(-0.788498\pi\)
0.927643 + 0.373468i \(0.121831\pi\)
\(102\) 0 0
\(103\) −249.500 432.147i −0.238679 0.413405i 0.721656 0.692252i \(-0.243381\pi\)
−0.960336 + 0.278847i \(0.910048\pi\)
\(104\) −560.000 −0.528005
\(105\) 0 0
\(106\) −786.000 −0.720218
\(107\) −553.500 958.690i −0.500083 0.866169i −1.00000 9.56665e-5i \(-0.999970\pi\)
0.499917 0.866073i \(-0.333364\pi\)
\(108\) 0 0
\(109\) −461.500 + 799.341i −0.405538 + 0.702413i −0.994384 0.105832i \(-0.966249\pi\)
0.588846 + 0.808246i \(0.299583\pi\)
\(110\) −513.000 888.542i −0.444660 0.770174i
\(111\) 0 0
\(112\) 0 0
\(113\) −1542.00 −1.28371 −0.641855 0.766826i \(-0.721835\pi\)
−0.641855 + 0.766826i \(0.721835\pi\)
\(114\) 0 0
\(115\) −310.500 + 537.802i −0.251776 + 0.436089i
\(116\) 228.000 394.908i 0.182494 0.316088i
\(117\) 0 0
\(118\) −438.000 −0.341705
\(119\) 0 0
\(120\) 0 0
\(121\) −959.000 1661.04i −0.720511 1.24796i
\(122\) 709.000 1228.02i 0.526146 0.911312i
\(123\) 0 0
\(124\) 46.0000 + 79.6743i 0.0333139 + 0.0577013i
\(125\) 1521.00 1.08834
\(126\) 0 0
\(127\) −2056.00 −1.43654 −0.718270 0.695765i \(-0.755066\pi\)
−0.718270 + 0.695765i \(0.755066\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −630.000 + 1091.19i −0.425036 + 0.736184i
\(131\) −1024.50 1774.49i −0.683290 1.18349i −0.973971 0.226673i \(-0.927215\pi\)
0.290681 0.956820i \(-0.406118\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −838.000 −0.540240
\(135\) 0 0
\(136\) 204.000 353.338i 0.128624 0.222783i
\(137\) −70.5000 + 122.110i −0.0439651 + 0.0761498i −0.887171 0.461442i \(-0.847332\pi\)
0.843205 + 0.537591i \(0.180666\pi\)
\(138\) 0 0
\(139\) −1484.00 −0.905548 −0.452774 0.891625i \(-0.649566\pi\)
−0.452774 + 0.891625i \(0.649566\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 96.0000 + 166.277i 0.0567334 + 0.0982651i
\(143\) −1995.00 + 3455.44i −1.16665 + 2.02069i
\(144\) 0 0
\(145\) −513.000 888.542i −0.293809 0.508892i
\(146\) −626.000 −0.354850
\(147\) 0 0
\(148\) −1012.00 −0.562067
\(149\) −28.5000 49.3634i −0.0156699 0.0271410i 0.858084 0.513509i \(-0.171655\pi\)
−0.873754 + 0.486368i \(0.838321\pi\)
\(150\) 0 0
\(151\) −419.500 + 726.595i −0.226082 + 0.391586i −0.956644 0.291261i \(-0.905925\pi\)
0.730561 + 0.682847i \(0.239258\pi\)
\(152\) −20.0000 34.6410i −0.0106725 0.0184852i
\(153\) 0 0
\(154\) 0 0
\(155\) 207.000 0.107269
\(156\) 0 0
\(157\) −1416.50 + 2453.45i −0.720057 + 1.24718i 0.240919 + 0.970545i \(0.422551\pi\)
−0.960976 + 0.276631i \(0.910782\pi\)
\(158\) 461.000 798.475i 0.232121 0.402046i
\(159\) 0 0
\(160\) 288.000 0.142302
\(161\) 0 0
\(162\) 0 0
\(163\) 1155.50 + 2001.38i 0.555250 + 0.961721i 0.997884 + 0.0650188i \(0.0207107\pi\)
−0.442634 + 0.896702i \(0.645956\pi\)
\(164\) 84.0000 145.492i 0.0399957 0.0692746i
\(165\) 0 0
\(166\) −588.000 1018.45i −0.274926 0.476185i
\(167\) 1260.00 0.583843 0.291921 0.956442i \(-0.405705\pi\)
0.291921 + 0.956442i \(0.405705\pi\)
\(168\) 0 0
\(169\) 2703.00 1.23031
\(170\) −459.000 795.011i −0.207081 0.358674i
\(171\) 0 0
\(172\) 248.000 429.549i 0.109941 0.190423i
\(173\) −1633.50 2829.30i −0.717877 1.24340i −0.961839 0.273615i \(-0.911781\pi\)
0.243962 0.969785i \(-0.421553\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 912.000 0.390594
\(177\) 0 0
\(178\) −1017.00 + 1761.50i −0.428244 + 0.741740i
\(179\) 643.500 1114.57i 0.268701 0.465403i −0.699826 0.714314i \(-0.746739\pi\)
0.968527 + 0.248910i \(0.0800724\pi\)
\(180\) 0 0
\(181\) 2674.00 1.09810 0.549052 0.835788i \(-0.314989\pi\)
0.549052 + 0.835788i \(0.314989\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −276.000 478.046i −0.110581 0.191533i
\(185\) −1138.50 + 1971.94i −0.452455 + 0.783675i
\(186\) 0 0
\(187\) −1453.50 2517.54i −0.568398 0.984494i
\(188\) 804.000 0.311903
\(189\) 0 0
\(190\) −90.0000 −0.0343647
\(191\) 2092.50 + 3624.32i 0.792712 + 1.37302i 0.924282 + 0.381711i \(0.124665\pi\)
−0.131570 + 0.991307i \(0.542002\pi\)
\(192\) 0 0
\(193\) 42.5000 73.6122i 0.0158509 0.0274545i −0.857991 0.513664i \(-0.828288\pi\)
0.873842 + 0.486210i \(0.161621\pi\)
\(194\) 1834.00 + 3176.58i 0.678730 + 1.17559i
\(195\) 0 0
\(196\) 0 0
\(197\) 390.000 0.141047 0.0705237 0.997510i \(-0.477533\pi\)
0.0705237 + 0.997510i \(0.477533\pi\)
\(198\) 0 0
\(199\) −1416.50 + 2453.45i −0.504588 + 0.873972i 0.495398 + 0.868666i \(0.335022\pi\)
−0.999986 + 0.00530596i \(0.998311\pi\)
\(200\) −176.000 + 304.841i −0.0622254 + 0.107778i
\(201\) 0 0
\(202\) 570.000 0.198540
\(203\) 0 0
\(204\) 0 0
\(205\) −189.000 327.358i −0.0643919 0.111530i
\(206\) 499.000 864.293i 0.168772 0.292321i
\(207\) 0 0
\(208\) −560.000 969.948i −0.186678 0.323336i
\(209\) −285.000 −0.0943247
\(210\) 0 0
\(211\) −124.000 −0.0404574 −0.0202287 0.999795i \(-0.506439\pi\)
−0.0202287 + 0.999795i \(0.506439\pi\)
\(212\) −786.000 1361.39i −0.254635 0.441041i
\(213\) 0 0
\(214\) 1107.00 1917.38i 0.353612 0.612474i
\(215\) −558.000 966.484i −0.177001 0.306575i
\(216\) 0 0
\(217\) 0 0
\(218\) −1846.00 −0.573518
\(219\) 0 0
\(220\) 1026.00 1777.08i 0.314422 0.544595i
\(221\) −1785.00 + 3091.71i −0.543313 + 0.941045i
\(222\) 0 0
\(223\) −56.0000 −0.0168163 −0.00840816 0.999965i \(-0.502676\pi\)
−0.00840816 + 0.999965i \(0.502676\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1542.00 2670.82i −0.453860 0.786108i
\(227\) 1528.50 2647.44i 0.446917 0.774083i −0.551267 0.834329i \(-0.685855\pi\)
0.998184 + 0.0602465i \(0.0191887\pi\)
\(228\) 0 0
\(229\) −480.500 832.250i −0.138656 0.240160i 0.788332 0.615250i \(-0.210945\pi\)
−0.926988 + 0.375090i \(0.877612\pi\)
\(230\) −1242.00 −0.356065
\(231\) 0 0
\(232\) 912.000 0.258085
\(233\) −1414.50 2449.99i −0.397712 0.688858i 0.595731 0.803184i \(-0.296862\pi\)
−0.993443 + 0.114326i \(0.963529\pi\)
\(234\) 0 0
\(235\) 904.500 1566.64i 0.251077 0.434878i
\(236\) −438.000 758.638i −0.120811 0.209251i
\(237\) 0 0
\(238\) 0 0
\(239\) 3540.00 0.958090 0.479045 0.877790i \(-0.340983\pi\)
0.479045 + 0.877790i \(0.340983\pi\)
\(240\) 0 0
\(241\) 2615.50 4530.18i 0.699084 1.21085i −0.269701 0.962944i \(-0.586925\pi\)
0.968785 0.247904i \(-0.0797419\pi\)
\(242\) 1918.00 3322.07i 0.509478 0.882442i
\(243\) 0 0
\(244\) 2836.00 0.744083
\(245\) 0 0
\(246\) 0 0
\(247\) 175.000 + 303.109i 0.0450809 + 0.0780824i
\(248\) −92.0000 + 159.349i −0.0235565 + 0.0408010i
\(249\) 0 0
\(250\) 1521.00 + 2634.45i 0.384786 + 0.666469i
\(251\) 5040.00 1.26742 0.633709 0.773571i \(-0.281532\pi\)
0.633709 + 0.773571i \(0.281532\pi\)
\(252\) 0 0
\(253\) −3933.00 −0.977334
\(254\) −2056.00 3561.10i −0.507893 0.879697i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 718.500 + 1244.48i 0.174392 + 0.302056i 0.939951 0.341310i \(-0.110871\pi\)
−0.765559 + 0.643366i \(0.777537\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2520.00 −0.601091
\(261\) 0 0
\(262\) 2049.00 3548.97i 0.483159 0.836856i
\(263\) −1162.50 + 2013.51i −0.272558 + 0.472085i −0.969516 0.245027i \(-0.921203\pi\)
0.696958 + 0.717112i \(0.254536\pi\)
\(264\) 0 0
\(265\) −3537.00 −0.819910
\(266\) 0 0
\(267\) 0 0
\(268\) −838.000 1451.46i −0.191004 0.330828i
\(269\) 1192.50 2065.47i 0.270290 0.468156i −0.698646 0.715467i \(-0.746214\pi\)
0.968936 + 0.247311i \(0.0795471\pi\)
\(270\) 0 0
\(271\) −165.500 286.654i −0.0370975 0.0642547i 0.846881 0.531783i \(-0.178478\pi\)
−0.883978 + 0.467528i \(0.845145\pi\)
\(272\) 816.000 0.181902
\(273\) 0 0
\(274\) −282.000 −0.0621761
\(275\) 1254.00 + 2171.99i 0.274978 + 0.476276i
\(276\) 0 0
\(277\) −2435.50 + 4218.41i −0.528285 + 0.915017i 0.471171 + 0.882042i \(0.343831\pi\)
−0.999456 + 0.0329750i \(0.989502\pi\)
\(278\) −1484.00 2570.36i −0.320160 0.554533i
\(279\) 0 0
\(280\) 0 0
\(281\) 7026.00 1.49159 0.745794 0.666177i \(-0.232070\pi\)
0.745794 + 0.666177i \(0.232070\pi\)
\(282\) 0 0
\(283\) −2676.50 + 4635.83i −0.562196 + 0.973752i 0.435109 + 0.900378i \(0.356710\pi\)
−0.997305 + 0.0733738i \(0.976623\pi\)
\(284\) −192.000 + 332.554i −0.0401166 + 0.0694839i
\(285\) 0 0
\(286\) −7980.00 −1.64989
\(287\) 0 0
\(288\) 0 0
\(289\) 1156.00 + 2002.25i 0.235294 + 0.407541i
\(290\) 1026.00 1777.08i 0.207754 0.359841i
\(291\) 0 0
\(292\) −626.000 1084.26i −0.125458 0.217300i
\(293\) 4158.00 0.829054 0.414527 0.910037i \(-0.363947\pi\)
0.414527 + 0.910037i \(0.363947\pi\)
\(294\) 0 0
\(295\) −1971.00 −0.389004
\(296\) −1012.00 1752.84i −0.198721 0.344194i
\(297\) 0 0
\(298\) 57.0000 98.7269i 0.0110803 0.0191916i
\(299\) 2415.00 + 4182.90i 0.467101 + 0.809042i
\(300\) 0 0
\(301\) 0 0
\(302\) −1678.00 −0.319729
\(303\) 0 0
\(304\) 40.0000 69.2820i 0.00754657 0.0130710i
\(305\) 3190.50 5526.11i 0.598975 1.03746i
\(306\) 0 0
\(307\) 9604.00 1.78544 0.892719 0.450615i \(-0.148795\pi\)
0.892719 + 0.450615i \(0.148795\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 207.000 + 358.535i 0.0379252 + 0.0656884i
\(311\) −5065.50 + 8773.70i −0.923595 + 1.59971i −0.129791 + 0.991541i \(0.541430\pi\)
−0.793805 + 0.608173i \(0.791903\pi\)
\(312\) 0 0
\(313\) 5399.50 + 9352.21i 0.975073 + 1.68888i 0.679695 + 0.733495i \(0.262112\pi\)
0.295378 + 0.955380i \(0.404554\pi\)
\(314\) −5666.00 −1.01831
\(315\) 0 0
\(316\) 1844.00 0.328269
\(317\) 265.500 + 459.859i 0.0470409 + 0.0814772i 0.888587 0.458708i \(-0.151688\pi\)
−0.841546 + 0.540185i \(0.818354\pi\)
\(318\) 0 0
\(319\) 3249.00 5627.43i 0.570248 0.987698i
\(320\) 288.000 + 498.831i 0.0503115 + 0.0871421i
\(321\) 0 0
\(322\) 0 0
\(323\) −255.000 −0.0439275
\(324\) 0 0
\(325\) 1540.00 2667.36i 0.262843 0.455257i
\(326\) −2311.00 + 4002.77i −0.392621 + 0.680040i
\(327\) 0 0
\(328\) 336.000 0.0565625
\(329\) 0 0
\(330\) 0 0
\(331\) 3507.50 + 6075.17i 0.582446 + 1.00883i 0.995189 + 0.0979784i \(0.0312376\pi\)
−0.412743 + 0.910848i \(0.635429\pi\)
\(332\) 1176.00 2036.89i 0.194402 0.336714i
\(333\) 0 0
\(334\) 1260.00 + 2182.38i 0.206420 + 0.357529i
\(335\) −3771.00 −0.615020
\(336\) 0 0
\(337\) 8990.00 1.45316 0.726582 0.687079i \(-0.241108\pi\)
0.726582 + 0.687079i \(0.241108\pi\)
\(338\) 2703.00 + 4681.73i 0.434982 + 0.753410i
\(339\) 0 0
\(340\) 918.000 1590.02i 0.146428 0.253621i
\(341\) 655.500 + 1135.36i 0.104098 + 0.180303i
\(342\) 0 0
\(343\) 0 0
\(344\) 992.000 0.155480
\(345\) 0 0
\(346\) 3267.00 5658.61i 0.507616 0.879216i
\(347\) −4354.50 + 7542.22i −0.673665 + 1.16682i 0.303192 + 0.952929i \(0.401948\pi\)
−0.976857 + 0.213893i \(0.931386\pi\)
\(348\) 0 0
\(349\) −6482.00 −0.994193 −0.497097 0.867695i \(-0.665601\pi\)
−0.497097 + 0.867695i \(0.665601\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 912.000 + 1579.63i 0.138096 + 0.239189i
\(353\) 1066.50 1847.23i 0.160805 0.278522i −0.774353 0.632754i \(-0.781924\pi\)
0.935158 + 0.354232i \(0.115258\pi\)
\(354\) 0 0
\(355\) 432.000 + 748.246i 0.0645864 + 0.111867i
\(356\) −4068.00 −0.605628
\(357\) 0 0
\(358\) 2574.00 0.380000
\(359\) 1924.50 + 3333.33i 0.282928 + 0.490046i 0.972105 0.234548i \(-0.0753608\pi\)
−0.689176 + 0.724594i \(0.742028\pi\)
\(360\) 0 0
\(361\) 3417.00 5918.42i 0.498178 0.862869i
\(362\) 2674.00 + 4631.50i 0.388238 + 0.672449i
\(363\) 0 0
\(364\) 0 0
\(365\) −2817.00 −0.403969
\(366\) 0 0
\(367\) 3245.50 5621.37i 0.461618 0.799545i −0.537424 0.843312i \(-0.680603\pi\)
0.999042 + 0.0437668i \(0.0139358\pi\)
\(368\) 552.000 956.092i 0.0781929 0.135434i
\(369\) 0 0
\(370\) −4554.00 −0.639868
\(371\) 0 0
\(372\) 0 0
\(373\) −461.500 799.341i −0.0640632 0.110961i 0.832215 0.554453i \(-0.187073\pi\)
−0.896278 + 0.443493i \(0.853739\pi\)
\(374\) 2907.00 5035.07i 0.401918 0.696143i
\(375\) 0 0
\(376\) 804.000 + 1392.57i 0.110274 + 0.191001i
\(377\) −7980.00 −1.09016
\(378\) 0 0
\(379\) 6344.00 0.859814 0.429907 0.902873i \(-0.358546\pi\)
0.429907 + 0.902873i \(0.358546\pi\)
\(380\) −90.0000 155.885i −0.0121497 0.0210440i
\(381\) 0 0
\(382\) −4185.00 + 7248.63i −0.560532 + 0.970870i
\(383\) 2503.50 + 4336.19i 0.334002 + 0.578509i 0.983293 0.182032i \(-0.0582673\pi\)
−0.649290 + 0.760541i \(0.724934\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 170.000 0.0224165
\(387\) 0 0
\(388\) −3668.00 + 6353.16i −0.479934 + 0.831270i
\(389\) 6145.50 10644.3i 0.801001 1.38737i −0.117958 0.993019i \(-0.537635\pi\)
0.918958 0.394355i \(-0.129032\pi\)
\(390\) 0 0
\(391\) −3519.00 −0.455150
\(392\) 0 0
\(393\) 0 0
\(394\) 390.000 + 675.500i 0.0498678 + 0.0863736i
\(395\) 2074.50 3593.14i 0.264252 0.457697i
\(396\) 0 0
\(397\) 443.500 + 768.165i 0.0560671 + 0.0971110i 0.892697 0.450658i \(-0.148811\pi\)
−0.836630 + 0.547769i \(0.815477\pi\)
\(398\) −5666.00 −0.713595
\(399\) 0 0
\(400\) −704.000 −0.0880000
\(401\) 5977.50 + 10353.3i 0.744394 + 1.28933i 0.950477 + 0.310794i \(0.100595\pi\)
−0.206083 + 0.978535i \(0.566072\pi\)
\(402\) 0 0
\(403\) 805.000 1394.30i 0.0995035 0.172345i
\(404\) 570.000 + 987.269i 0.0701945 + 0.121580i
\(405\) 0 0
\(406\) 0 0
\(407\) −14421.0 −1.75632
\(408\) 0 0
\(409\) −1710.50 + 2962.67i −0.206794 + 0.358178i −0.950703 0.310103i \(-0.899636\pi\)
0.743909 + 0.668281i \(0.232970\pi\)
\(410\) 378.000 654.715i 0.0455319 0.0788636i
\(411\) 0 0
\(412\) 1996.00 0.238679
\(413\) 0 0
\(414\) 0 0
\(415\) −2646.00 4583.01i −0.312981 0.542099i
\(416\) 1120.00 1939.90i 0.132001 0.228633i
\(417\) 0 0
\(418\) −285.000 493.634i −0.0333488 0.0577618i
\(419\) −5460.00 −0.636607 −0.318304 0.947989i \(-0.603113\pi\)
−0.318304 + 0.947989i \(0.603113\pi\)
\(420\) 0 0
\(421\) 7730.00 0.894863 0.447431 0.894318i \(-0.352339\pi\)
0.447431 + 0.894318i \(0.352339\pi\)
\(422\) −124.000 214.774i −0.0143039 0.0247750i
\(423\) 0 0
\(424\) 1572.00 2722.78i 0.180054 0.311863i
\(425\) 1122.00 + 1943.36i 0.128059 + 0.221804i
\(426\) 0 0
\(427\) 0 0
\(428\) 4428.00 0.500083
\(429\) 0 0
\(430\) 1116.00 1932.97i 0.125159 0.216781i
\(431\) −5656.50 + 9797.35i −0.632167 + 1.09495i 0.354941 + 0.934889i \(0.384501\pi\)
−0.987108 + 0.160057i \(0.948832\pi\)
\(432\) 0 0
\(433\) −4214.00 −0.467695 −0.233847 0.972273i \(-0.575132\pi\)
−0.233847 + 0.972273i \(0.575132\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1846.00 3197.37i −0.202769 0.351207i
\(437\) −172.500 + 298.779i −0.0188828 + 0.0327060i
\(438\) 0 0
\(439\) 8276.50 + 14335.3i 0.899808 + 1.55851i 0.827739 + 0.561114i \(0.189627\pi\)
0.0720696 + 0.997400i \(0.477040\pi\)
\(440\) 4104.00 0.444660
\(441\) 0 0
\(442\) −7140.00 −0.768360
\(443\) −8197.50 14198.5i −0.879176 1.52278i −0.852247 0.523140i \(-0.824760\pi\)
−0.0269294 0.999637i \(-0.508573\pi\)
\(444\) 0 0
\(445\) −4576.50 + 7926.73i −0.487521 + 0.844411i
\(446\) −56.0000 96.9948i −0.00594546 0.0102978i
\(447\) 0 0
\(448\) 0 0
\(449\) 15090.0 1.58606 0.793030 0.609182i \(-0.208502\pi\)
0.793030 + 0.609182i \(0.208502\pi\)
\(450\) 0 0
\(451\) 1197.00 2073.26i 0.124977 0.216466i
\(452\) 3084.00 5341.64i 0.320927 0.555862i
\(453\) 0 0
\(454\) 6114.00 0.632036
\(455\) 0 0
\(456\) 0 0
\(457\) 7392.50 + 12804.2i 0.756688 + 1.31062i 0.944531 + 0.328423i \(0.106517\pi\)
−0.187842 + 0.982199i \(0.560149\pi\)
\(458\) 961.000 1664.50i 0.0980449 0.169819i
\(459\) 0 0
\(460\) −1242.00 2151.21i −0.125888 0.218045i
\(461\) 2898.00 0.292784 0.146392 0.989227i \(-0.453234\pi\)
0.146392 + 0.989227i \(0.453234\pi\)
\(462\) 0 0
\(463\) 464.000 0.0465743 0.0232872 0.999729i \(-0.492587\pi\)
0.0232872 + 0.999729i \(0.492587\pi\)
\(464\) 912.000 + 1579.63i 0.0912468 + 0.158044i
\(465\) 0 0
\(466\) 2829.00 4899.97i 0.281225 0.487096i
\(467\) −2116.50 3665.89i −0.209721 0.363248i 0.741905 0.670505i \(-0.233922\pi\)
−0.951627 + 0.307256i \(0.900589\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 3618.00 0.355076
\(471\) 0 0
\(472\) 876.000 1517.28i 0.0854262 0.147963i
\(473\) 3534.00 6121.07i 0.343538 0.595025i
\(474\) 0 0
\(475\) 220.000 0.0212511
\(476\) 0 0
\(477\) 0 0
\(478\) 3540.00 + 6131.46i 0.338736 + 0.586708i
\(479\) −1369.50 + 2372.04i −0.130635 + 0.226266i −0.923921 0.382582i \(-0.875035\pi\)
0.793287 + 0.608848i \(0.208368\pi\)
\(480\) 0 0
\(481\) 8855.00 + 15337.3i 0.839404 + 1.45389i
\(482\) 10462.0 0.988654
\(483\) 0 0
\(484\) 7672.00 0.720511
\(485\) 8253.00 + 14294.6i 0.772679 + 1.33832i
\(486\) 0 0
\(487\) −8525.50 + 14766.6i −0.793280 + 1.37400i 0.130646 + 0.991429i \(0.458295\pi\)
−0.923926 + 0.382572i \(0.875038\pi\)
\(488\) 2836.00 + 4912.10i 0.263073 + 0.455656i
\(489\) 0 0
\(490\) 0 0
\(491\) 4296.00 0.394859 0.197429 0.980317i \(-0.436741\pi\)
0.197429 + 0.980317i \(0.436741\pi\)
\(492\) 0 0
\(493\) 2907.00 5035.07i 0.265567 0.459976i
\(494\) −350.000 + 606.218i −0.0318770 + 0.0552126i
\(495\) 0 0
\(496\) −368.000 −0.0333139
\(497\) 0 0
\(498\) 0 0
\(499\) −1700.50 2945.35i −0.152555 0.264233i 0.779611 0.626264i \(-0.215417\pi\)
−0.932166 + 0.362031i \(0.882083\pi\)
\(500\) −3042.00 + 5268.90i −0.272085 + 0.471265i
\(501\) 0 0
\(502\) 5040.00 + 8729.54i 0.448100 + 0.776132i
\(503\) 16800.0 1.48921 0.744607 0.667503i \(-0.232637\pi\)
0.744607 + 0.667503i \(0.232637\pi\)
\(504\) 0 0
\(505\) 2565.00 0.226022
\(506\) −3933.00 6812.16i −0.345540 0.598493i
\(507\) 0 0
\(508\) 4112.00 7122.19i 0.359135 0.622040i
\(509\) −919.500 1592.62i −0.0800710 0.138687i 0.823209 0.567738i \(-0.192181\pi\)
−0.903280 + 0.429051i \(0.858848\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) −1437.00 + 2488.96i −0.123314 + 0.213586i
\(515\) 2245.50 3889.32i 0.192133 0.332784i
\(516\) 0 0
\(517\) 11457.0 0.974620
\(518\) 0 0
\(519\) 0 0
\(520\) −2520.00 4364.77i −0.212518 0.368092i
\(521\) −151.500 + 262.406i −0.0127396 + 0.0220656i −0.872325 0.488927i \(-0.837389\pi\)
0.859585 + 0.510992i \(0.170722\pi\)
\(522\) 0 0
\(523\) −10833.5 18764.2i −0.905767 1.56883i −0.819885 0.572528i \(-0.805963\pi\)
−0.0858815 0.996305i \(-0.527371\pi\)
\(524\) 8196.00 0.683290
\(525\) 0 0
\(526\) −4650.00 −0.385456
\(527\) 586.500 + 1015.85i 0.0484788 + 0.0839678i
\(528\) 0 0
\(529\) 3703.00 6413.78i 0.304348 0.527146i
\(530\) −3537.00 6126.26i −0.289882 0.502090i
\(531\) 0 0
\(532\) 0 0
\(533\) −2940.00 −0.238922
\(534\) 0 0
\(535\) 4981.50 8628.21i 0.402559 0.697253i
\(536\) 1676.00 2902.92i 0.135060 0.233931i
\(537\) 0 0
\(538\) 4770.00 0.382248
\(539\) 0 0
\(540\) 0 0
\(541\) −2519.50 4363.90i −0.200225 0.346800i 0.748376 0.663275i \(-0.230834\pi\)
−0.948601 + 0.316475i \(0.897501\pi\)
\(542\) 331.000 573.309i 0.0262319 0.0454349i
\(543\) 0 0
\(544\) 816.000 + 1413.35i 0.0643120 + 0.111392i
\(545\) −8307.00 −0.652904
\(546\) 0 0
\(547\) −2392.00 −0.186974 −0.0934868 0.995621i \(-0.529801\pi\)
−0.0934868 + 0.995621i \(0.529801\pi\)
\(548\) −282.000 488.438i −0.0219826 0.0380749i
\(549\) 0 0
\(550\) −2508.00 + 4343.98i −0.194439 + 0.336778i
\(551\) −285.000 493.634i −0.0220352 0.0381661i
\(552\) 0 0
\(553\) 0 0
\(554\) −9742.00 −0.747108
\(555\) 0 0
\(556\) 2968.00 5140.73i 0.226387 0.392114i
\(557\) −11074.5 + 19181.6i −0.842445 + 1.45916i 0.0453775 + 0.998970i \(0.485551\pi\)
−0.887822 + 0.460187i \(0.847782\pi\)
\(558\) 0 0
\(559\) −8680.00 −0.656753
\(560\) 0 0
\(561\) 0 0
\(562\) 7026.00 + 12169.4i 0.527356 + 0.913407i
\(563\) 4174.50 7230.45i 0.312494 0.541256i −0.666408 0.745588i \(-0.732169\pi\)
0.978902 + 0.204332i \(0.0655022\pi\)
\(564\) 0 0
\(565\) −6939.00 12018.7i −0.516683 0.894921i
\(566\) −10706.0 −0.795065
\(567\) 0 0
\(568\) −768.000 −0.0567334
\(569\) −7672.50 13289.2i −0.565286 0.979105i −0.997023 0.0771050i \(-0.975432\pi\)
0.431737 0.902000i \(-0.357901\pi\)
\(570\) 0 0
\(571\) 5796.50 10039.8i 0.424827 0.735821i −0.571578 0.820548i \(-0.693668\pi\)
0.996404 + 0.0847268i \(0.0270017\pi\)
\(572\) −7980.00 13821.8i −0.583323 1.01034i
\(573\) 0 0
\(574\) 0 0
\(575\) 3036.00 0.220191
\(576\) 0 0
\(577\) −7296.50 + 12637.9i −0.526442 + 0.911825i 0.473083 + 0.881018i \(0.343141\pi\)
−0.999525 + 0.0308071i \(0.990192\pi\)
\(578\) −2312.00 + 4004.50i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) 4104.00 0.293809
\(581\) 0 0
\(582\) 0 0
\(583\) −11200.5 19399.8i −0.795673 1.37815i
\(584\) 1252.00 2168.53i 0.0887125 0.153655i
\(585\) 0 0
\(586\) 4158.00 + 7201.87i 0.293115 + 0.507690i
\(587\) −15372.0 −1.08087 −0.540435 0.841386i \(-0.681740\pi\)
−0.540435 + 0.841386i \(0.681740\pi\)
\(588\) 0 0
\(589\) 115.000 0.00804498
\(590\) −1971.00 3413.87i −0.137534 0.238215i
\(591\) 0 0
\(592\) 2024.00 3505.67i 0.140517 0.243382i
\(593\) 7186.50 + 12447.4i 0.497663 + 0.861978i 0.999996 0.00269639i \(-0.000858288\pi\)
−0.502333 + 0.864674i \(0.667525\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 228.000 0.0156699
\(597\) 0 0
\(598\) −4830.00 + 8365.81i −0.330290 + 0.572079i
\(599\) 1273.50 2205.77i 0.0868678 0.150459i −0.819318 0.573340i \(-0.805648\pi\)
0.906186 + 0.422880i \(0.138981\pi\)
\(600\) 0 0
\(601\) 7042.00 0.477952 0.238976 0.971025i \(-0.423188\pi\)
0.238976 + 0.971025i \(0.423188\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1678.00 2906.38i −0.113041 0.195793i
\(605\) 8631.00 14949.3i 0.580000 1.00459i
\(606\) 0 0
\(607\) −11295.5 19564.4i −0.755305 1.30823i −0.945223 0.326427i \(-0.894155\pi\)
0.189917 0.981800i \(-0.439178\pi\)
\(608\) 160.000 0.0106725
\(609\) 0 0
\(610\) 12762.0 0.847079
\(611\) −7035.00 12185.0i −0.465803 0.806794i
\(612\) 0 0
\(613\) 4242.50 7348.23i 0.279532 0.484163i −0.691737 0.722150i \(-0.743154\pi\)
0.971268 + 0.237987i \(0.0764874\pi\)
\(614\) 9604.00 + 16634.6i 0.631247 + 1.09335i
\(615\) 0 0
\(616\) 0 0
\(617\) 18282.0 1.19288 0.596439 0.802658i \(-0.296582\pi\)
0.596439 + 0.802658i \(0.296582\pi\)
\(618\) 0 0
\(619\) 1145.50 1984.06i 0.0743805 0.128831i −0.826436 0.563030i \(-0.809635\pi\)
0.900817 + 0.434200i \(0.142969\pi\)
\(620\) −414.000 + 717.069i −0.0268172 + 0.0464487i
\(621\) 0 0
\(622\) −20262.0 −1.30616
\(623\) 0 0
\(624\) 0 0
\(625\) 4094.50 + 7091.88i 0.262048 + 0.453880i
\(626\) −10799.0 + 18704.4i −0.689481 + 1.19422i
\(627\) 0 0
\(628\) −5666.00 9813.80i −0.360029 0.623588i
\(629\) −12903.0 −0.817927
\(630\) 0 0
\(631\) −6928.00 −0.437083 −0.218541 0.975828i \(-0.570130\pi\)
−0.218541 + 0.975828i \(0.570130\pi\)
\(632\) 1844.00 + 3193.90i 0.116061 + 0.201023i
\(633\) 0 0
\(634\) −531.000 + 919.719i −0.0332629 + 0.0576131i
\(635\) −9252.00 16024.9i −0.578196 1.00146i
\(636\) 0 0
\(637\) 0 0
\(638\) 12996.0 0.806452
\(639\) 0 0
\(640\) −576.000 + 997.661i −0.0355756 + 0.0616188i
\(641\) 12487.5 21629.0i 0.769464 1.33275i −0.168390 0.985721i \(-0.553857\pi\)
0.937854 0.347031i \(-0.112810\pi\)
\(642\) 0 0
\(643\) −9548.00 −0.585593 −0.292797 0.956175i \(-0.594586\pi\)
−0.292797 + 0.956175i \(0.594586\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −255.000 441.673i −0.0155307 0.0269000i
\(647\) −5065.50 + 8773.70i −0.307798 + 0.533122i −0.977880 0.209165i \(-0.932925\pi\)
0.670082 + 0.742287i \(0.266259\pi\)
\(648\) 0 0
\(649\) −6241.50 10810.6i −0.377504 0.653857i
\(650\) 6160.00 0.371716
\(651\) 0 0
\(652\) −9244.00 −0.555250
\(653\) 8329.50 + 14427.1i 0.499171 + 0.864589i 1.00000 0.000957229i \(-0.000304695\pi\)
−0.500829 + 0.865546i \(0.666971\pi\)
\(654\) 0 0
\(655\) 9220.50 15970.4i 0.550038 0.952693i
\(656\) 336.000 + 581.969i 0.0199979 + 0.0346373i
\(657\) 0 0
\(658\) 0 0
\(659\) −29556.0 −1.74710 −0.873550 0.486735i \(-0.838188\pi\)
−0.873550 + 0.486735i \(0.838188\pi\)
\(660\) 0 0
\(661\) 95.5000 165.411i 0.00561955 0.00973334i −0.863202 0.504859i \(-0.831545\pi\)
0.868822 + 0.495125i \(0.164878\pi\)
\(662\) −7015.00 + 12150.3i −0.411852 + 0.713348i
\(663\) 0 0
\(664\) 4704.00 0.274926
\(665\) 0 0
\(666\) 0 0
\(667\) −3933.00 6812.16i −0.228315 0.395454i
\(668\) −2520.00 + 4364.77i −0.145961 + 0.252811i
\(669\) 0 0
\(670\) −3771.00 6531.56i −0.217442 0.376621i
\(671\) 40413.0 2.32508
\(672\) 0 0
\(673\) 2606.00 0.149263 0.0746314 0.997211i \(-0.476222\pi\)
0.0746314 + 0.997211i \(0.476222\pi\)
\(674\) 8990.00 + 15571.1i 0.513771 + 0.889878i
\(675\) 0 0
\(676\) −5406.00 + 9363.47i −0.307579 + 0.532742i
\(677\) 2104.50 + 3645.10i 0.119472 + 0.206931i 0.919559 0.392953i \(-0.128547\pi\)
−0.800087 + 0.599885i \(0.795213\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 3672.00 0.207081
\(681\) 0 0
\(682\) −1311.00 + 2270.72i −0.0736082 + 0.127493i
\(683\) 12151.5 21047.0i 0.680768 1.17912i −0.293979 0.955812i \(-0.594980\pi\)
0.974747 0.223312i \(-0.0716869\pi\)
\(684\) 0 0
\(685\) −1269.00 −0.0707825
\(686\) 0 0
\(687\) 0 0
\(688\) 992.000 + 1718.19i 0.0549704 + 0.0952116i
\(689\) −13755.0 + 23824.4i −0.760557 + 1.31732i
\(690\) 0 0
\(691\) 7520.50 + 13025.9i 0.414028 + 0.717117i 0.995326 0.0965734i \(-0.0307882\pi\)
−0.581298 + 0.813691i \(0.697455\pi\)
\(692\) 13068.0 0.717877
\(693\) 0 0
\(694\) −17418.0 −0.952706
\(695\) −6678.00 11566.6i −0.364476 0.631291i
\(696\) 0 0
\(697\) 1071.00 1855.03i 0.0582023 0.100809i
\(698\) −6482.00 11227.2i −0.351500 0.608817i
\(699\) 0 0
\(700\) 0 0
\(701\) −24726.0 −1.33222 −0.666111 0.745852i \(-0.732042\pi\)
−0.666111 + 0.745852i \(0.732042\pi\)
\(702\) 0 0
\(703\) −632.500 + 1095.52i −0.0339334 + 0.0587744i
\(704\) −1824.00 + 3159.26i −0.0976486 + 0.169132i
\(705\) 0 0
\(706\) 4266.00 0.227412
\(707\) 0 0
\(708\) 0 0
\(709\) 2478.50 + 4292.89i 0.131286 + 0.227395i 0.924173 0.381975i \(-0.124756\pi\)
−0.792886 + 0.609370i \(0.791423\pi\)
\(710\) −864.000 + 1496.49i −0.0456695 + 0.0791019i
\(711\) 0 0
\(712\) −4068.00 7045.98i −0.214122 0.370870i
\(713\) 1587.00 0.0833571
\(714\) 0 0
\(715\) −35910.0 −1.87826
\(716\) 2574.00 + 4458.30i 0.134350 + 0.232702i
\(717\) 0 0
\(718\) −3849.00 + 6666.66i −0.200060 + 0.346515i
\(719\) −13834.5 23962.1i −0.717580 1.24288i −0.961956 0.273204i \(-0.911917\pi\)
0.244376 0.969680i \(-0.421417\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13668.0 0.704529
\(723\) 0 0
\(724\) −5348.00 + 9263.01i −0.274526 + 0.475493i
\(725\) −2508.00 + 4343.98i −0.128476 + 0.222526i
\(726\) 0 0
\(727\) 13888.0 0.708497 0.354249 0.935151i \(-0.384737\pi\)
0.354249 + 0.935151i \(0.384737\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2817.00 4879.19i −0.142824 0.247379i
\(731\) 3162.00 5476.74i 0.159987 0.277106i
\(732\) 0 0
\(733\) 7121.50 + 12334.8i 0.358852 + 0.621550i 0.987769 0.155922i \(-0.0498349\pi\)
−0.628917 + 0.777472i \(0.716502\pi\)
\(734\) 12982.0 0.652826
\(735\) 0 0
\(736\) 2208.00 0.110581
\(737\) −11941.5 20683.3i −0.596840 1.03376i
\(738\) 0 0
\(739\) −18479.5 + 32007.4i −0.919864 + 1.59325i −0.120244 + 0.992744i \(0.538368\pi\)
−0.799620 + 0.600507i \(0.794966\pi\)
\(740\) −4554.00 7887.76i −0.226228 0.391838i
\(741\) 0 0
\(742\) 0 0
\(743\) 12528.0 0.618584 0.309292 0.950967i \(-0.399908\pi\)
0.309292 + 0.950967i \(0.399908\pi\)
\(744\) 0 0
\(745\) 256.500 444.271i 0.0126140 0.0218481i
\(746\) 923.000 1598.68i 0.0452995 0.0784610i
\(747\) 0 0
\(748\) 11628.0 0.568398
\(749\) 0 0
\(750\) 0 0
\(751\) 8883.50 + 15386.7i 0.431643 + 0.747627i 0.997015 0.0772090i \(-0.0246009\pi\)
−0.565372 + 0.824836i \(0.691268\pi\)
\(752\) −1608.00 + 2785.14i −0.0779757 + 0.135058i
\(753\) 0 0
\(754\) −7980.00 13821.8i −0.385430 0.667585i
\(755\) −7551.00 −0.363985
\(756\) 0 0
\(757\) −28726.0 −1.37921 −0.689606 0.724184i \(-0.742216\pi\)
−0.689606 + 0.724184i \(0.742216\pi\)
\(758\) 6344.00 + 10988.1i 0.303990 + 0.526526i
\(759\) 0 0
\(760\) 180.000 311.769i 0.00859117 0.0148803i
\(761\) 13234.5 + 22922.8i 0.630421 + 1.09192i 0.987466 + 0.157834i \(0.0504510\pi\)
−0.357045 + 0.934087i \(0.616216\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16740.0 −0.792712
\(765\) 0 0
\(766\) −5007.00 + 8672.38i −0.236175 + 0.409068i
\(767\) −7665.00 + 13276.2i −0.360844 + 0.625000i
\(768\) 0 0
\(769\) −5054.00 −0.236999 −0.118499 0.992954i \(-0.537808\pi\)
−0.118499 + 0.992954i \(0.537808\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 170.000 + 294.449i 0.00792543 + 0.0137273i
\(773\) 17782.5 30800.2i 0.827415 1.43313i −0.0726439 0.997358i \(-0.523144\pi\)
0.900059 0.435767i \(-0.143523\pi\)
\(774\) 0 0
\(775\) −506.000 876.418i −0.0234530 0.0406217i
\(776\) −14672.0 −0.678730
\(777\) 0 0
\(778\) 24582.0 1.13279
\(779\) −105.000 181.865i −0.00482929 0.00836457i
\(780\) 0 0
\(781\) −2736.00 + 4738.89i −0.125354 + 0.217120i
\(782\) −3519.00 6095.09i −0.160920 0.278721i
\(783\) 0 0
\(784\) 0 0
\(785\) −25497.0 −1.15927
\(786\) 0 0
\(787\) −4314.50 + 7472.93i −0.195420 + 0.338477i −0.947038 0.321121i \(-0.895940\pi\)
0.751618 + 0.659598i \(0.229274\pi\)
\(788\) −780.000 + 1351.00i −0.0352619 + 0.0610753i
\(789\) 0 0
\(790\) 8298.00 0.373708