Properties

Label 324.5.d.f.163.21
Level $324$
Weight $5$
Character 324.163
Analytic conductor $33.492$
Analytic rank $0$
Dimension $22$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 324.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(33.4918680392\)
Analytic rank: \(0\)
Dimension: \(22\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 163.21
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.f.163.22

$q$-expansion

\(f(q)\) \(=\) \(q+(3.99662 - 0.164298i) q^{2} +(15.9460 - 1.31328i) q^{4} +29.7694 q^{5} +59.8988i q^{7} +(63.5145 - 7.86857i) q^{8} +O(q^{10})\) \(q+(3.99662 - 0.164298i) q^{2} +(15.9460 - 1.31328i) q^{4} +29.7694 q^{5} +59.8988i q^{7} +(63.5145 - 7.86857i) q^{8} +(118.977 - 4.89106i) q^{10} -225.488i q^{11} +171.765 q^{13} +(9.84126 + 239.393i) q^{14} +(252.551 - 41.8830i) q^{16} -99.0725 q^{17} +169.267i q^{19} +(474.703 - 39.0954i) q^{20} +(-37.0472 - 901.189i) q^{22} +358.855i q^{23} +261.217 q^{25} +(686.480 - 28.2206i) q^{26} +(78.6636 + 955.147i) q^{28} -18.0327 q^{29} +775.841i q^{31} +(1002.47 - 208.884i) q^{32} +(-395.956 + 16.2774i) q^{34} +1783.15i q^{35} +609.762 q^{37} +(27.8102 + 676.496i) q^{38} +(1890.79 - 234.243i) q^{40} -413.091 q^{41} -306.571i q^{43} +(-296.127 - 3595.63i) q^{44} +(58.9591 + 1434.21i) q^{46} -2621.85i q^{47} -1186.86 q^{49} +(1043.99 - 42.9175i) q^{50} +(2738.96 - 225.575i) q^{52} +2034.30 q^{53} -6712.63i q^{55} +(471.318 + 3804.44i) q^{56} +(-72.0699 + 2.96274i) q^{58} -2598.63i q^{59} -1417.36 q^{61} +(127.469 + 3100.74i) q^{62} +(3972.17 - 999.536i) q^{64} +5113.34 q^{65} +5995.13i q^{67} +(-1579.81 + 130.110i) q^{68} +(292.968 + 7126.58i) q^{70} +1239.44i q^{71} -5060.60 q^{73} +(2436.99 - 100.183i) q^{74} +(222.294 + 2699.13i) q^{76} +13506.4 q^{77} -1889.08i q^{79} +(7518.28 - 1246.83i) q^{80} +(-1650.97 + 67.8700i) q^{82} +6733.68i q^{83} -2949.33 q^{85} +(-50.3691 - 1225.25i) q^{86} +(-1774.27 - 14321.7i) q^{88} +9436.67 q^{89} +10288.5i q^{91} +(471.275 + 5722.30i) q^{92} +(-430.765 - 10478.6i) q^{94} +5038.98i q^{95} -14595.8 q^{97} +(-4743.45 + 195.000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + O(q^{10}) \) \( 22q + q^{2} + q^{4} + 2q^{5} + 61q^{8} + 14q^{10} + 2q^{13} - 252q^{14} + q^{16} - 28q^{17} + 140q^{20} + 33q^{22} + 1752q^{25} + 548q^{26} - 258q^{28} - 526q^{29} + 121q^{32} - 385q^{34} - 4q^{37} - 1395q^{38} + 2276q^{40} + 2762q^{41} + 3357q^{44} + 1788q^{46} - 3428q^{49} - 6375q^{50} - 1438q^{52} - 5044q^{53} + 7506q^{56} + 4064q^{58} + 2q^{61} - 9162q^{62} + 4513q^{64} + 2014q^{65} + 11405q^{68} - 3666q^{70} - 1708q^{73} - 14620q^{74} - 1581q^{76} + 3942q^{77} + 22760q^{80} - 4243q^{82} + 1252q^{85} - 22113q^{86} - 1995q^{88} + 6524q^{89} + 30294q^{92} - 7524q^{94} - 5638q^{97} - 46469q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.99662 0.164298i 0.999156 0.0410745i
\(3\) 0 0
\(4\) 15.9460 1.31328i 0.996626 0.0820797i
\(5\) 29.7694 1.19078 0.595388 0.803438i \(-0.296998\pi\)
0.595388 + 0.803438i \(0.296998\pi\)
\(6\) 0 0
\(7\) 59.8988i 1.22242i 0.791467 + 0.611212i \(0.209318\pi\)
−0.791467 + 0.611212i \(0.790682\pi\)
\(8\) 63.5145 7.86857i 0.992413 0.122946i
\(9\) 0 0
\(10\) 118.977 4.89106i 1.18977 0.0489106i
\(11\) 225.488i 1.86353i −0.363057 0.931767i \(-0.618267\pi\)
0.363057 0.931767i \(-0.381733\pi\)
\(12\) 0 0
\(13\) 171.765 1.01636 0.508180 0.861251i \(-0.330318\pi\)
0.508180 + 0.861251i \(0.330318\pi\)
\(14\) 9.84126 + 239.393i 0.0502105 + 1.22139i
\(15\) 0 0
\(16\) 252.551 41.8830i 0.986526 0.163606i
\(17\) −99.0725 −0.342812 −0.171406 0.985201i \(-0.554831\pi\)
−0.171406 + 0.985201i \(0.554831\pi\)
\(18\) 0 0
\(19\) 169.267i 0.468884i 0.972130 + 0.234442i \(0.0753262\pi\)
−0.972130 + 0.234442i \(0.924674\pi\)
\(20\) 474.703 39.0954i 1.18676 0.0977386i
\(21\) 0 0
\(22\) −37.0472 901.189i −0.0765438 1.86196i
\(23\) 358.855i 0.678364i 0.940721 + 0.339182i \(0.110150\pi\)
−0.940721 + 0.339182i \(0.889850\pi\)
\(24\) 0 0
\(25\) 261.217 0.417948
\(26\) 686.480 28.2206i 1.01550 0.0417465i
\(27\) 0 0
\(28\) 78.6636 + 955.147i 0.100336 + 1.21830i
\(29\) −18.0327 −0.0214420 −0.0107210 0.999943i \(-0.503413\pi\)
−0.0107210 + 0.999943i \(0.503413\pi\)
\(30\) 0 0
\(31\) 775.841i 0.807326i 0.914908 + 0.403663i \(0.132263\pi\)
−0.914908 + 0.403663i \(0.867737\pi\)
\(32\) 1002.47 208.884i 0.978973 0.203989i
\(33\) 0 0
\(34\) −395.956 + 16.2774i −0.342522 + 0.0140808i
\(35\) 1783.15i 1.45563i
\(36\) 0 0
\(37\) 609.762 0.445407 0.222703 0.974886i \(-0.428512\pi\)
0.222703 + 0.974886i \(0.428512\pi\)
\(38\) 27.8102 + 676.496i 0.0192592 + 0.468488i
\(39\) 0 0
\(40\) 1890.79 234.243i 1.18174 0.146402i
\(41\) −413.091 −0.245741 −0.122871 0.992423i \(-0.539210\pi\)
−0.122871 + 0.992423i \(0.539210\pi\)
\(42\) 0 0
\(43\) 306.571i 0.165804i −0.996558 0.0829019i \(-0.973581\pi\)
0.996558 0.0829019i \(-0.0264188\pi\)
\(44\) −296.127 3595.63i −0.152958 1.85725i
\(45\) 0 0
\(46\) 58.9591 + 1434.21i 0.0278635 + 0.677791i
\(47\) 2621.85i 1.18689i −0.804873 0.593447i \(-0.797767\pi\)
0.804873 0.593447i \(-0.202233\pi\)
\(48\) 0 0
\(49\) −1186.86 −0.494321
\(50\) 1043.99 42.9175i 0.417595 0.0171670i
\(51\) 0 0
\(52\) 2738.96 225.575i 1.01293 0.0834226i
\(53\) 2034.30 0.724209 0.362104 0.932138i \(-0.382058\pi\)
0.362104 + 0.932138i \(0.382058\pi\)
\(54\) 0 0
\(55\) 6712.63i 2.21905i
\(56\) 471.318 + 3804.44i 0.150293 + 1.21315i
\(57\) 0 0
\(58\) −72.0699 + 2.96274i −0.0214239 + 0.000880719i
\(59\) 2598.63i 0.746520i −0.927727 0.373260i \(-0.878240\pi\)
0.927727 0.373260i \(-0.121760\pi\)
\(60\) 0 0
\(61\) −1417.36 −0.380909 −0.190455 0.981696i \(-0.560996\pi\)
−0.190455 + 0.981696i \(0.560996\pi\)
\(62\) 127.469 + 3100.74i 0.0331606 + 0.806645i
\(63\) 0 0
\(64\) 3972.17 999.536i 0.969768 0.244027i
\(65\) 5113.34 1.21026
\(66\) 0 0
\(67\) 5995.13i 1.33552i 0.744379 + 0.667758i \(0.232746\pi\)
−0.744379 + 0.667758i \(0.767254\pi\)
\(68\) −1579.81 + 130.110i −0.341655 + 0.0281379i
\(69\) 0 0
\(70\) 292.968 + 7126.58i 0.0597895 + 1.45441i
\(71\) 1239.44i 0.245872i 0.992415 + 0.122936i \(0.0392310\pi\)
−0.992415 + 0.122936i \(0.960769\pi\)
\(72\) 0 0
\(73\) −5060.60 −0.949633 −0.474817 0.880085i \(-0.657486\pi\)
−0.474817 + 0.880085i \(0.657486\pi\)
\(74\) 2436.99 100.183i 0.445031 0.0182949i
\(75\) 0 0
\(76\) 222.294 + 2699.13i 0.0384858 + 0.467301i
\(77\) 13506.4 2.27803
\(78\) 0 0
\(79\) 1889.08i 0.302688i −0.988481 0.151344i \(-0.951640\pi\)
0.988481 0.151344i \(-0.0483601\pi\)
\(80\) 7518.28 1246.83i 1.17473 0.194818i
\(81\) 0 0
\(82\) −1650.97 + 67.8700i −0.245534 + 0.0100937i
\(83\) 6733.68i 0.977455i 0.872437 + 0.488727i \(0.162539\pi\)
−0.872437 + 0.488727i \(0.837461\pi\)
\(84\) 0 0
\(85\) −2949.33 −0.408212
\(86\) −50.3691 1225.25i −0.00681031 0.165664i
\(87\) 0 0
\(88\) −1774.27 14321.7i −0.229115 1.84940i
\(89\) 9436.67 1.19135 0.595674 0.803226i \(-0.296885\pi\)
0.595674 + 0.803226i \(0.296885\pi\)
\(90\) 0 0
\(91\) 10288.5i 1.24242i
\(92\) 471.275 + 5722.30i 0.0556799 + 0.676075i
\(93\) 0 0
\(94\) −430.765 10478.6i −0.0487511 1.18589i
\(95\) 5038.98i 0.558335i
\(96\) 0 0
\(97\) −14595.8 −1.55126 −0.775631 0.631186i \(-0.782568\pi\)
−0.775631 + 0.631186i \(0.782568\pi\)
\(98\) −4743.45 + 195.000i −0.493904 + 0.0203040i
\(99\) 0 0
\(100\) 4165.37 343.050i 0.416537 0.0343050i
\(101\) 6461.42 0.633411 0.316705 0.948524i \(-0.397423\pi\)
0.316705 + 0.948524i \(0.397423\pi\)
\(102\) 0 0
\(103\) 16156.1i 1.52286i −0.648244 0.761432i \(-0.724496\pi\)
0.648244 0.761432i \(-0.275504\pi\)
\(104\) 10909.6 1351.54i 1.00865 0.124958i
\(105\) 0 0
\(106\) 8130.34 334.232i 0.723597 0.0297465i
\(107\) 3065.27i 0.267732i −0.990999 0.133866i \(-0.957261\pi\)
0.990999 0.133866i \(-0.0427392\pi\)
\(108\) 0 0
\(109\) −17728.8 −1.49220 −0.746098 0.665836i \(-0.768075\pi\)
−0.746098 + 0.665836i \(0.768075\pi\)
\(110\) −1102.87 26827.9i −0.0911465 2.21718i
\(111\) 0 0
\(112\) 2508.74 + 15127.5i 0.199995 + 1.20595i
\(113\) −14793.1 −1.15852 −0.579259 0.815143i \(-0.696658\pi\)
−0.579259 + 0.815143i \(0.696658\pi\)
\(114\) 0 0
\(115\) 10682.9i 0.807780i
\(116\) −287.550 + 23.6819i −0.0213696 + 0.00175995i
\(117\) 0 0
\(118\) −426.951 10385.8i −0.0306629 0.745890i
\(119\) 5934.32i 0.419061i
\(120\) 0 0
\(121\) −36203.7 −2.47276
\(122\) −5664.67 + 232.870i −0.380588 + 0.0156457i
\(123\) 0 0
\(124\) 1018.89 + 12371.6i 0.0662651 + 0.804602i
\(125\) −10829.6 −0.693094
\(126\) 0 0
\(127\) 18478.7i 1.14568i 0.819667 + 0.572841i \(0.194159\pi\)
−0.819667 + 0.572841i \(0.805841\pi\)
\(128\) 15711.1 4647.39i 0.958927 0.283654i
\(129\) 0 0
\(130\) 20436.1 840.112i 1.20924 0.0497108i
\(131\) 8320.71i 0.484862i 0.970169 + 0.242431i \(0.0779447\pi\)
−0.970169 + 0.242431i \(0.922055\pi\)
\(132\) 0 0
\(133\) −10138.9 −0.573175
\(134\) 984.989 + 23960.3i 0.0548557 + 1.33439i
\(135\) 0 0
\(136\) −6292.54 + 779.559i −0.340211 + 0.0421474i
\(137\) −21406.7 −1.14054 −0.570268 0.821459i \(-0.693160\pi\)
−0.570268 + 0.821459i \(0.693160\pi\)
\(138\) 0 0
\(139\) 18225.3i 0.943292i −0.881788 0.471646i \(-0.843660\pi\)
0.881788 0.471646i \(-0.156340\pi\)
\(140\) 2341.77 + 28434.1i 0.119478 + 1.45072i
\(141\) 0 0
\(142\) 203.638 + 4953.59i 0.0100991 + 0.245665i
\(143\) 38730.8i 1.89402i
\(144\) 0 0
\(145\) −536.823 −0.0255326
\(146\) −20225.3 + 831.446i −0.948832 + 0.0390057i
\(147\) 0 0
\(148\) 9723.27 800.785i 0.443904 0.0365589i
\(149\) −16239.4 −0.731473 −0.365736 0.930718i \(-0.619183\pi\)
−0.365736 + 0.930718i \(0.619183\pi\)
\(150\) 0 0
\(151\) 24526.3i 1.07567i −0.843050 0.537835i \(-0.819242\pi\)
0.843050 0.537835i \(-0.180758\pi\)
\(152\) 1331.89 + 10750.9i 0.0576476 + 0.465326i
\(153\) 0 0
\(154\) 53980.1 2219.08i 2.27611 0.0935690i
\(155\) 23096.3i 0.961345i
\(156\) 0 0
\(157\) 39654.1 1.60875 0.804375 0.594122i \(-0.202500\pi\)
0.804375 + 0.594122i \(0.202500\pi\)
\(158\) −310.372 7549.92i −0.0124328 0.302432i
\(159\) 0 0
\(160\) 29842.9 6218.36i 1.16574 0.242905i
\(161\) −21494.9 −0.829248
\(162\) 0 0
\(163\) 25324.6i 0.953162i −0.879130 0.476581i \(-0.841876\pi\)
0.879130 0.476581i \(-0.158124\pi\)
\(164\) −6587.15 + 542.502i −0.244912 + 0.0201704i
\(165\) 0 0
\(166\) 1106.33 + 26912.0i 0.0401485 + 0.976630i
\(167\) 27839.5i 0.998226i −0.866537 0.499113i \(-0.833659\pi\)
0.866537 0.499113i \(-0.166341\pi\)
\(168\) 0 0
\(169\) 942.163 0.0329877
\(170\) −11787.4 + 484.569i −0.407867 + 0.0167671i
\(171\) 0 0
\(172\) −402.612 4888.59i −0.0136091 0.165244i
\(173\) −22054.5 −0.736895 −0.368448 0.929648i \(-0.620111\pi\)
−0.368448 + 0.929648i \(0.620111\pi\)
\(174\) 0 0
\(175\) 15646.6i 0.510909i
\(176\) −9444.10 56947.0i −0.304885 1.83842i
\(177\) 0 0
\(178\) 37714.8 1550.43i 1.19034 0.0489341i
\(179\) 52513.4i 1.63895i 0.573118 + 0.819473i \(0.305734\pi\)
−0.573118 + 0.819473i \(0.694266\pi\)
\(180\) 0 0
\(181\) −7223.25 −0.220483 −0.110242 0.993905i \(-0.535162\pi\)
−0.110242 + 0.993905i \(0.535162\pi\)
\(182\) 1690.38 + 41119.3i 0.0510319 + 1.24137i
\(183\) 0 0
\(184\) 2823.67 + 22792.4i 0.0834024 + 0.673217i
\(185\) 18152.2 0.530380
\(186\) 0 0
\(187\) 22339.6i 0.638841i
\(188\) −3443.21 41808.1i −0.0974200 1.18289i
\(189\) 0 0
\(190\) 827.894 + 20138.9i 0.0229334 + 0.557864i
\(191\) 10582.8i 0.290090i 0.989425 + 0.145045i \(0.0463326\pi\)
−0.989425 + 0.145045i \(0.953667\pi\)
\(192\) 0 0
\(193\) −39086.5 −1.04933 −0.524665 0.851309i \(-0.675809\pi\)
−0.524665 + 0.851309i \(0.675809\pi\)
\(194\) −58334.0 + 2398.07i −1.54995 + 0.0637174i
\(195\) 0 0
\(196\) −18925.7 + 1558.68i −0.492653 + 0.0405737i
\(197\) −10820.0 −0.278802 −0.139401 0.990236i \(-0.544518\pi\)
−0.139401 + 0.990236i \(0.544518\pi\)
\(198\) 0 0
\(199\) 807.389i 0.0203881i 0.999948 + 0.0101940i \(0.00324492\pi\)
−0.999948 + 0.0101940i \(0.996755\pi\)
\(200\) 16591.1 2055.41i 0.414777 0.0513852i
\(201\) 0 0
\(202\) 25823.9 1061.60i 0.632876 0.0260171i
\(203\) 1080.14i 0.0262112i
\(204\) 0 0
\(205\) −12297.5 −0.292623
\(206\) −2654.41 64569.8i −0.0625510 1.52158i
\(207\) 0 0
\(208\) 43379.3 7194.03i 1.00267 0.166282i
\(209\) 38167.6 0.873780
\(210\) 0 0
\(211\) 60834.1i 1.36641i 0.730225 + 0.683207i \(0.239415\pi\)
−0.730225 + 0.683207i \(0.760585\pi\)
\(212\) 32439.0 2671.60i 0.721765 0.0594429i
\(213\) 0 0
\(214\) −503.618 12250.7i −0.0109970 0.267506i
\(215\) 9126.44i 0.197435i
\(216\) 0 0
\(217\) −46471.9 −0.986895
\(218\) −70855.3 + 2912.81i −1.49094 + 0.0612913i
\(219\) 0 0
\(220\) −8815.54 107040.i −0.182139 2.21156i
\(221\) −17017.2 −0.348420
\(222\) 0 0
\(223\) 10729.6i 0.215762i −0.994164 0.107881i \(-0.965594\pi\)
0.994164 0.107881i \(-0.0344065\pi\)
\(224\) 12511.9 + 60046.6i 0.249361 + 1.19672i
\(225\) 0 0
\(226\) −59122.5 + 2430.48i −1.15754 + 0.0475856i
\(227\) 75731.3i 1.46968i −0.678239 0.734842i \(-0.737256\pi\)
0.678239 0.734842i \(-0.262744\pi\)
\(228\) 0 0
\(229\) −53366.6 −1.01765 −0.508825 0.860870i \(-0.669920\pi\)
−0.508825 + 0.860870i \(0.669920\pi\)
\(230\) 1755.18 + 42695.5i 0.0331792 + 0.807098i
\(231\) 0 0
\(232\) −1145.34 + 141.892i −0.0212793 + 0.00263621i
\(233\) 56485.5 1.04046 0.520230 0.854026i \(-0.325846\pi\)
0.520230 + 0.854026i \(0.325846\pi\)
\(234\) 0 0
\(235\) 78050.9i 1.41333i
\(236\) −3412.72 41437.9i −0.0612741 0.744001i
\(237\) 0 0
\(238\) −974.998 23717.3i −0.0172127 0.418707i
\(239\) 47991.4i 0.840171i 0.907484 + 0.420086i \(0.138000\pi\)
−0.907484 + 0.420086i \(0.862000\pi\)
\(240\) 0 0
\(241\) −64150.1 −1.10449 −0.552247 0.833681i \(-0.686229\pi\)
−0.552247 + 0.833681i \(0.686229\pi\)
\(242\) −144692. + 5948.19i −2.47067 + 0.101567i
\(243\) 0 0
\(244\) −22601.3 + 1861.39i −0.379624 + 0.0312649i
\(245\) −35332.2 −0.588625
\(246\) 0 0
\(247\) 29074.1i 0.476555i
\(248\) 6104.76 + 49277.1i 0.0992579 + 0.801201i
\(249\) 0 0
\(250\) −43281.8 + 1779.28i −0.692509 + 0.0284685i
\(251\) 65230.8i 1.03539i 0.855564 + 0.517696i \(0.173210\pi\)
−0.855564 + 0.517696i \(0.826790\pi\)
\(252\) 0 0
\(253\) 80917.3 1.26415
\(254\) 3036.02 + 73852.4i 0.0470583 + 1.14471i
\(255\) 0 0
\(256\) 62027.6 21155.2i 0.946466 0.322802i
\(257\) −43315.8 −0.655813 −0.327907 0.944710i \(-0.606343\pi\)
−0.327907 + 0.944710i \(0.606343\pi\)
\(258\) 0 0
\(259\) 36524.0i 0.544476i
\(260\) 81537.3 6715.22i 1.20617 0.0993376i
\(261\) 0 0
\(262\) 1367.08 + 33254.7i 0.0199155 + 0.484452i
\(263\) 84805.2i 1.22606i −0.790061 0.613029i \(-0.789951\pi\)
0.790061 0.613029i \(-0.210049\pi\)
\(264\) 0 0
\(265\) 60560.0 0.862370
\(266\) −40521.3 + 1665.80i −0.572691 + 0.0235429i
\(267\) 0 0
\(268\) 7873.26 + 95598.4i 0.109619 + 1.33101i
\(269\) −66685.5 −0.921567 −0.460784 0.887513i \(-0.652432\pi\)
−0.460784 + 0.887513i \(0.652432\pi\)
\(270\) 0 0
\(271\) 122426.i 1.66700i 0.552516 + 0.833502i \(0.313668\pi\)
−0.552516 + 0.833502i \(0.686332\pi\)
\(272\) −25020.8 + 4149.46i −0.338192 + 0.0560859i
\(273\) 0 0
\(274\) −85554.5 + 3517.08i −1.13957 + 0.0468469i
\(275\) 58901.3i 0.778860i
\(276\) 0 0
\(277\) 137452. 1.79140 0.895699 0.444661i \(-0.146676\pi\)
0.895699 + 0.444661i \(0.146676\pi\)
\(278\) −2994.39 72839.8i −0.0387453 0.942496i
\(279\) 0 0
\(280\) 14030.8 + 113256.i 0.178965 + 1.44459i
\(281\) 14003.2 0.177344 0.0886718 0.996061i \(-0.471738\pi\)
0.0886718 + 0.996061i \(0.471738\pi\)
\(282\) 0 0
\(283\) 115048.i 1.43650i −0.695786 0.718249i \(-0.744944\pi\)
0.695786 0.718249i \(-0.255056\pi\)
\(284\) 1627.73 + 19764.2i 0.0201811 + 0.245043i
\(285\) 0 0
\(286\) −6363.41 154793.i −0.0777961 1.89242i
\(287\) 24743.6i 0.300400i
\(288\) 0 0
\(289\) −73705.6 −0.882480
\(290\) −2145.48 + 88.1990i −0.0255110 + 0.00104874i
\(291\) 0 0
\(292\) −80696.3 + 6645.96i −0.946429 + 0.0779457i
\(293\) 28518.6 0.332195 0.166097 0.986109i \(-0.446883\pi\)
0.166097 + 0.986109i \(0.446883\pi\)
\(294\) 0 0
\(295\) 77359.8i 0.888938i
\(296\) 38728.7 4797.95i 0.442027 0.0547611i
\(297\) 0 0
\(298\) −64902.9 + 2668.11i −0.730856 + 0.0300449i
\(299\) 61638.6i 0.689462i
\(300\) 0 0
\(301\) 18363.2 0.202682
\(302\) −4029.63 98022.5i −0.0441826 1.07476i
\(303\) 0 0
\(304\) 7089.41 + 42748.5i 0.0767120 + 0.462566i
\(305\) −42194.0 −0.453577
\(306\) 0 0
\(307\) 115338.i 1.22376i −0.790952 0.611879i \(-0.790414\pi\)
0.790952 0.611879i \(-0.209586\pi\)
\(308\) 215374. 17737.7i 2.27034 0.186980i
\(309\) 0 0
\(310\) 3794.68 + 92307.3i 0.0394868 + 0.960534i
\(311\) 98803.8i 1.02153i 0.859719 + 0.510767i \(0.170639\pi\)
−0.859719 + 0.510767i \(0.829361\pi\)
\(312\) 0 0
\(313\) −74132.1 −0.756690 −0.378345 0.925665i \(-0.623507\pi\)
−0.378345 + 0.925665i \(0.623507\pi\)
\(314\) 158482. 6515.09i 1.60739 0.0660786i
\(315\) 0 0
\(316\) −2480.88 30123.2i −0.0248445 0.301667i
\(317\) −2114.59 −0.0210430 −0.0105215 0.999945i \(-0.503349\pi\)
−0.0105215 + 0.999945i \(0.503349\pi\)
\(318\) 0 0
\(319\) 4066.15i 0.0399579i
\(320\) 118249. 29755.6i 1.15478 0.290582i
\(321\) 0 0
\(322\) −85907.2 + 3531.58i −0.828549 + 0.0340610i
\(323\) 16769.7i 0.160739i
\(324\) 0 0
\(325\) 44868.0 0.424785
\(326\) −4160.78 101213.i −0.0391507 0.952358i
\(327\) 0 0
\(328\) −26237.2 + 3250.43i −0.243877 + 0.0302130i
\(329\) 157046. 1.45089
\(330\) 0 0
\(331\) 14242.0i 0.129992i −0.997886 0.0649960i \(-0.979297\pi\)
0.997886 0.0649960i \(-0.0207034\pi\)
\(332\) 8843.19 + 107375.i 0.0802292 + 0.974156i
\(333\) 0 0
\(334\) −4573.98 111264.i −0.0410017 0.997384i
\(335\) 178471.i 1.59030i
\(336\) 0 0
\(337\) 75423.6 0.664121 0.332061 0.943258i \(-0.392256\pi\)
0.332061 + 0.943258i \(0.392256\pi\)
\(338\) 3765.47 154.796i 0.0329599 0.00135496i
\(339\) 0 0
\(340\) −47030.1 + 3873.28i −0.406834 + 0.0335059i
\(341\) 174942. 1.50448
\(342\) 0 0
\(343\) 72725.3i 0.618155i
\(344\) −2412.28 19471.7i −0.0203850 0.164546i
\(345\) 0 0
\(346\) −88143.7 + 3623.52i −0.736274 + 0.0302676i
\(347\) 148440.i 1.23280i −0.787432 0.616401i \(-0.788590\pi\)
0.787432 0.616401i \(-0.211410\pi\)
\(348\) 0 0
\(349\) −23330.9 −0.191549 −0.0957745 0.995403i \(-0.530533\pi\)
−0.0957745 + 0.995403i \(0.530533\pi\)
\(350\) 2570.71 + 62533.6i 0.0209854 + 0.510478i
\(351\) 0 0
\(352\) −47100.8 226044.i −0.380140 1.82435i
\(353\) 19374.4 0.155482 0.0777409 0.996974i \(-0.475229\pi\)
0.0777409 + 0.996974i \(0.475229\pi\)
\(354\) 0 0
\(355\) 36897.5i 0.292779i
\(356\) 150477. 12393.0i 1.18733 0.0977856i
\(357\) 0 0
\(358\) 8627.86 + 209877.i 0.0673189 + 1.63756i
\(359\) 139927.i 1.08571i −0.839827 0.542854i \(-0.817344\pi\)
0.839827 0.542854i \(-0.182656\pi\)
\(360\) 0 0
\(361\) 101670. 0.780148
\(362\) −28868.6 + 1186.77i −0.220297 + 0.00905625i
\(363\) 0 0
\(364\) 13511.6 + 164061.i 0.101978 + 1.23823i
\(365\) −150651. −1.13080
\(366\) 0 0
\(367\) 91572.9i 0.679884i 0.940446 + 0.339942i \(0.110407\pi\)
−0.940446 + 0.339942i \(0.889593\pi\)
\(368\) 15029.9 + 90628.9i 0.110984 + 0.669224i
\(369\) 0 0
\(370\) 72547.7 2982.38i 0.529932 0.0217851i
\(371\) 121852.i 0.885290i
\(372\) 0 0
\(373\) 85580.8 0.615118 0.307559 0.951529i \(-0.400488\pi\)
0.307559 + 0.951529i \(0.400488\pi\)
\(374\) 3670.36 + 89283.1i 0.0262401 + 0.638302i
\(375\) 0 0
\(376\) −20630.2 166525.i −0.145924 1.17789i
\(377\) −3097.38 −0.0217928
\(378\) 0 0
\(379\) 39838.1i 0.277345i 0.990338 + 0.138672i \(0.0442835\pi\)
−0.990338 + 0.138672i \(0.955716\pi\)
\(380\) 6617.57 + 80351.6i 0.0458280 + 0.556451i
\(381\) 0 0
\(382\) 1738.73 + 42295.3i 0.0119153 + 0.289845i
\(383\) 170684.i 1.16357i 0.813341 + 0.581787i \(0.197646\pi\)
−0.813341 + 0.581787i \(0.802354\pi\)
\(384\) 0 0
\(385\) 402078. 2.71262
\(386\) −156214. + 6421.84i −1.04844 + 0.0431007i
\(387\) 0 0
\(388\) −232745. + 19168.3i −1.54603 + 0.127327i
\(389\) 215815. 1.42621 0.713103 0.701059i \(-0.247289\pi\)
0.713103 + 0.701059i \(0.247289\pi\)
\(390\) 0 0
\(391\) 35552.6i 0.232551i
\(392\) −75383.0 + 9338.92i −0.490570 + 0.0607750i
\(393\) 0 0
\(394\) −43243.6 + 1777.71i −0.278567 + 0.0114517i
\(395\) 56236.6i 0.360434i
\(396\) 0 0
\(397\) 292553. 1.85620 0.928098 0.372336i \(-0.121443\pi\)
0.928098 + 0.372336i \(0.121443\pi\)
\(398\) 132.652 + 3226.83i 0.000837431 + 0.0203709i
\(399\) 0 0
\(400\) 65970.6 10940.6i 0.412316 0.0683786i
\(401\) 204314. 1.27060 0.635300 0.772266i \(-0.280877\pi\)
0.635300 + 0.772266i \(0.280877\pi\)
\(402\) 0 0
\(403\) 133262.i 0.820534i
\(404\) 103034. 8485.63i 0.631274 0.0519902i
\(405\) 0 0
\(406\) −177.464 4316.90i −0.00107661 0.0261891i
\(407\) 137494.i 0.830030i
\(408\) 0 0
\(409\) 34728.8 0.207607 0.103804 0.994598i \(-0.466899\pi\)
0.103804 + 0.994598i \(0.466899\pi\)
\(410\) −49148.3 + 2020.45i −0.292376 + 0.0120193i
\(411\) 0 0
\(412\) −21217.4 257625.i −0.124996 1.51773i
\(413\) 155655. 0.912564
\(414\) 0 0
\(415\) 200458.i 1.16393i
\(416\) 172189. 35879.0i 0.994989 0.207326i
\(417\) 0 0
\(418\) 152542. 6270.87i 0.873043 0.0358901i
\(419\) 320640.i 1.82637i −0.407541 0.913187i \(-0.633614\pi\)
0.407541 0.913187i \(-0.366386\pi\)
\(420\) 0 0
\(421\) 135771. 0.766028 0.383014 0.923743i \(-0.374886\pi\)
0.383014 + 0.923743i \(0.374886\pi\)
\(422\) 9994.93 + 243131.i 0.0561248 + 1.36526i
\(423\) 0 0
\(424\) 129208. 16007.0i 0.718714 0.0890388i
\(425\) −25879.5 −0.143277
\(426\) 0 0
\(427\) 84898.3i 0.465632i
\(428\) −4025.54 48878.8i −0.0219754 0.266829i
\(429\) 0 0
\(430\) −1499.46 36474.9i −0.00810955 0.197268i
\(431\) 31343.0i 0.168728i −0.996435 0.0843638i \(-0.973114\pi\)
0.996435 0.0843638i \(-0.0268858\pi\)
\(432\) 0 0
\(433\) 101022. 0.538815 0.269407 0.963026i \(-0.413172\pi\)
0.269407 + 0.963026i \(0.413172\pi\)
\(434\) −185731. + 7635.25i −0.986062 + 0.0405363i
\(435\) 0 0
\(436\) −282704. + 23282.8i −1.48716 + 0.122479i
\(437\) −60742.2 −0.318074
\(438\) 0 0
\(439\) 181972.i 0.944227i −0.881538 0.472113i \(-0.843491\pi\)
0.881538 0.472113i \(-0.156509\pi\)
\(440\) −52818.8 426349.i −0.272824 2.20222i
\(441\) 0 0
\(442\) −68011.3 + 2795.89i −0.348126 + 0.0143112i
\(443\) 37188.8i 0.189498i −0.995501 0.0947490i \(-0.969795\pi\)
0.995501 0.0947490i \(-0.0302049\pi\)
\(444\) 0 0
\(445\) 280924. 1.41863
\(446\) −1762.85 42882.2i −0.00886231 0.215580i
\(447\) 0 0
\(448\) 59871.0 + 237928.i 0.298305 + 1.18547i
\(449\) −20385.0 −0.101115 −0.0505577 0.998721i \(-0.516100\pi\)
−0.0505577 + 0.998721i \(0.516100\pi\)
\(450\) 0 0
\(451\) 93146.9i 0.457947i
\(452\) −235891. + 19427.4i −1.15461 + 0.0950909i
\(453\) 0 0
\(454\) −12442.5 302670.i −0.0603666 1.46844i
\(455\) 306283.i 1.47945i
\(456\) 0 0
\(457\) −279658. −1.33904 −0.669521 0.742793i \(-0.733501\pi\)
−0.669521 + 0.742793i \(0.733501\pi\)
\(458\) −213286. + 8768.03i −1.01679 + 0.0417995i
\(459\) 0 0
\(460\) 14029.6 + 170349.i 0.0663023 + 0.805054i
\(461\) −160597. −0.755675 −0.377838 0.925872i \(-0.623332\pi\)
−0.377838 + 0.925872i \(0.623332\pi\)
\(462\) 0 0
\(463\) 99153.6i 0.462537i −0.972890 0.231268i \(-0.925712\pi\)
0.972890 0.231268i \(-0.0742876\pi\)
\(464\) −4554.17 + 755.264i −0.0211531 + 0.00350803i
\(465\) 0 0
\(466\) 225752. 9280.47i 1.03958 0.0427364i
\(467\) 278790.i 1.27833i 0.769068 + 0.639167i \(0.220721\pi\)
−0.769068 + 0.639167i \(0.779279\pi\)
\(468\) 0 0
\(469\) −359101. −1.63257
\(470\) −12823.6 311940.i −0.0580517 1.41213i
\(471\) 0 0
\(472\) −20447.5 165051.i −0.0917819 0.740856i
\(473\) −69128.0 −0.308981
\(474\) 0 0
\(475\) 44215.5i 0.195969i
\(476\) −7793.40 94628.8i −0.0343964 0.417647i
\(477\) 0 0
\(478\) 7884.90 + 191804.i 0.0345096 + 0.839462i
\(479\) 31991.6i 0.139433i 0.997567 + 0.0697163i \(0.0222094\pi\)
−0.997567 + 0.0697163i \(0.977791\pi\)
\(480\) 0 0
\(481\) 104736. 0.452693
\(482\) −256384. + 10539.7i −1.10356 + 0.0453666i
\(483\) 0 0
\(484\) −577304. + 47545.4i −2.46442 + 0.202963i
\(485\) −434509. −1.84721
\(486\) 0 0
\(487\) 346823.i 1.46235i −0.682192 0.731173i \(-0.738973\pi\)
0.682192 0.731173i \(-0.261027\pi\)
\(488\) −90023.0 + 11152.6i −0.378019 + 0.0468314i
\(489\) 0 0
\(490\) −141210. + 5805.02i −0.588129 + 0.0241775i
\(491\) 239982.i 0.995440i 0.867338 + 0.497720i \(0.165829\pi\)
−0.867338 + 0.497720i \(0.834171\pi\)
\(492\) 0 0
\(493\) 1786.55 0.00735056
\(494\) 4776.82 + 116198.i 0.0195743 + 0.476152i
\(495\) 0 0
\(496\) 32494.6 + 195939.i 0.132083 + 0.796448i
\(497\) −74241.1 −0.300560
\(498\) 0 0
\(499\) 341046.i 1.36966i 0.728705 + 0.684828i \(0.240123\pi\)
−0.728705 + 0.684828i \(0.759877\pi\)
\(500\) −172689. + 14222.2i −0.690755 + 0.0568890i
\(501\) 0 0
\(502\) 10717.3 + 260703.i 0.0425283 + 1.03452i
\(503\) 3886.22i 0.0153600i −0.999971 0.00768001i \(-0.997555\pi\)
0.999971 0.00768001i \(-0.00244465\pi\)
\(504\) 0 0
\(505\) 192353. 0.754250
\(506\) 323396. 13294.6i 1.26309 0.0519245i
\(507\) 0 0
\(508\) 24267.6 + 294662.i 0.0940373 + 1.14182i
\(509\) 197346. 0.761717 0.380858 0.924633i \(-0.375629\pi\)
0.380858 + 0.924633i \(0.375629\pi\)
\(510\) 0 0
\(511\) 303124.i 1.16085i
\(512\) 244425. 94740.3i 0.932409 0.361405i
\(513\) 0 0
\(514\) −173117. + 7116.71i −0.655260 + 0.0269372i
\(515\) 480957.i 1.81339i
\(516\) 0 0
\(517\) −591195. −2.21182
\(518\) 6000.82 + 145973.i 0.0223641 + 0.544016i
\(519\) 0 0
\(520\) 324771. 40234.7i 1.20108 0.148797i
\(521\) 229165. 0.844255 0.422127 0.906536i \(-0.361283\pi\)
0.422127 + 0.906536i \(0.361283\pi\)
\(522\) 0 0
\(523\) 346673.i 1.26741i −0.773575 0.633705i \(-0.781533\pi\)
0.773575 0.633705i \(-0.218467\pi\)
\(524\) 10927.4 + 132682.i 0.0397973 + 0.483226i
\(525\) 0 0
\(526\) −13933.3 338934.i −0.0503597 1.22502i
\(527\) 76864.5i 0.276761i
\(528\) 0 0
\(529\) 151064. 0.539822
\(530\) 242035. 9949.89i 0.861642 0.0354215i
\(531\) 0 0
\(532\) −161675. + 13315.2i −0.571241 + 0.0470460i
\(533\) −70954.5 −0.249761
\(534\) 0 0
\(535\) 91251.2i 0.318809i
\(536\) 47173.1 + 380777.i 0.164197 + 1.32538i
\(537\) 0 0
\(538\) −266517. + 10956.3i −0.920789 + 0.0378529i
\(539\) 267623.i 0.921184i
\(540\) 0 0
\(541\) −287354. −0.981799 −0.490900 0.871216i \(-0.663332\pi\)
−0.490900 + 0.871216i \(0.663332\pi\)
\(542\) 20114.4 + 489293.i 0.0684714 + 1.66560i
\(543\) 0 0
\(544\) −99317.1 + 20694.7i −0.335603 + 0.0699296i
\(545\) −527776. −1.77687
\(546\) 0 0
\(547\) 561865.i 1.87783i 0.344144 + 0.938917i \(0.388169\pi\)
−0.344144 + 0.938917i \(0.611831\pi\)
\(548\) −341352. + 28112.9i −1.13669 + 0.0936148i
\(549\) 0 0
\(550\) −9677.37 235406.i −0.0319913 0.778203i
\(551\) 3052.34i 0.0100538i
\(552\) 0 0
\(553\) 113153. 0.370013
\(554\) 549345. 22583.1i 1.78989 0.0735808i
\(555\) 0 0
\(556\) −23934.9 290621.i −0.0774251 0.940109i
\(557\) −393303. −1.26770 −0.633850 0.773456i \(-0.718526\pi\)
−0.633850 + 0.773456i \(0.718526\pi\)
\(558\) 0 0
\(559\) 52658.1i 0.168516i
\(560\) 74683.8 + 450336.i 0.238150 + 1.43602i
\(561\) 0 0
\(562\) 55965.6 2300.70i 0.177194 0.00728431i
\(563\) 556412.i 1.75541i −0.479198 0.877707i \(-0.659072\pi\)
0.479198 0.877707i \(-0.340928\pi\)
\(564\) 0 0
\(565\) −440382. −1.37954
\(566\) −18902.1 459802.i −0.0590035 1.43529i
\(567\) 0 0
\(568\) 9752.64 + 78722.5i 0.0302291 + 0.244007i
\(569\) 182062. 0.562333 0.281167 0.959659i \(-0.409279\pi\)
0.281167 + 0.959659i \(0.409279\pi\)
\(570\) 0 0
\(571\) 219715.i 0.673888i 0.941525 + 0.336944i \(0.109393\pi\)
−0.941525 + 0.336944i \(0.890607\pi\)
\(572\) −50864.3 617603.i −0.155461 1.88763i
\(573\) 0 0
\(574\) −4065.33 98891.0i −0.0123388 0.300146i
\(575\) 93739.0i 0.283521i
\(576\) 0 0
\(577\) 9527.81 0.0286181 0.0143091 0.999898i \(-0.495445\pi\)
0.0143091 + 0.999898i \(0.495445\pi\)
\(578\) −294574. + 12109.7i −0.881736 + 0.0362475i
\(579\) 0 0
\(580\) −8560.18 + 704.996i −0.0254464 + 0.00209571i
\(581\) −403339. −1.19486
\(582\) 0 0
\(583\) 458710.i 1.34959i
\(584\) −321421. + 39819.7i −0.942429 + 0.116754i
\(585\) 0 0
\(586\) 113978. 4685.55i 0.331914 0.0136447i
\(587\) 10333.0i 0.0299882i −0.999888 0.0149941i \(-0.995227\pi\)
0.999888 0.0149941i \(-0.00477294\pi\)
\(588\) 0 0
\(589\) −131324. −0.378542
\(590\) −12710.1 309178.i −0.0365127 0.888188i
\(591\) 0 0
\(592\) 153996. 25538.7i 0.439405 0.0728710i
\(593\) 143639. 0.408473 0.204236 0.978922i \(-0.434529\pi\)
0.204236 + 0.978922i \(0.434529\pi\)
\(594\) 0 0
\(595\) 176661.i 0.499008i
\(596\) −258954. + 21326.9i −0.729005 + 0.0600391i
\(597\) 0 0
\(598\) 10127.1 + 246346.i 0.0283193 + 0.688880i
\(599\) 352934.i 0.983649i −0.870694 0.491824i \(-0.836330\pi\)
0.870694 0.491824i \(-0.163670\pi\)
\(600\) 0 0
\(601\) 35467.7 0.0981937 0.0490969 0.998794i \(-0.484366\pi\)
0.0490969 + 0.998794i \(0.484366\pi\)
\(602\) 73390.9 3017.04i 0.202511 0.00832509i
\(603\) 0 0
\(604\) −32209.8 391097.i −0.0882907 1.07204i
\(605\) −1.07776e6 −2.94450
\(606\) 0 0
\(607\) 489950.i 1.32976i 0.746949 + 0.664881i \(0.231518\pi\)
−0.746949 + 0.664881i \(0.768482\pi\)
\(608\) 35357.2 + 169685.i 0.0956469 + 0.459024i
\(609\) 0 0
\(610\) −168634. + 6932.40i −0.453195 + 0.0186305i
\(611\) 450342.i 1.20631i
\(612\) 0 0
\(613\) 284390. 0.756821 0.378410 0.925638i \(-0.376471\pi\)
0.378410 + 0.925638i \(0.376471\pi\)
\(614\) −18949.8 460962.i −0.0502653 1.22272i
\(615\) 0 0
\(616\) 857854. 106276.i 2.26075 0.280075i
\(617\) 196475. 0.516103 0.258052 0.966131i \(-0.416920\pi\)
0.258052 + 0.966131i \(0.416920\pi\)
\(618\) 0 0
\(619\) 67817.0i 0.176993i 0.996076 + 0.0884967i \(0.0282063\pi\)
−0.996076 + 0.0884967i \(0.971794\pi\)
\(620\) 30331.8 + 368294.i 0.0789069 + 0.958101i
\(621\) 0 0
\(622\) 16233.3 + 394882.i 0.0419590 + 1.02067i
\(623\) 565245.i 1.45633i
\(624\) 0 0
\(625\) −485651. −1.24327
\(626\) −296278. + 12179.8i −0.756051 + 0.0310807i
\(627\) 0 0
\(628\) 632324. 52076.7i 1.60332 0.132046i
\(629\) −60410.6 −0.152691
\(630\) 0 0
\(631\) 716972.i 1.80071i 0.435158 + 0.900354i \(0.356692\pi\)
−0.435158 + 0.900354i \(0.643308\pi\)
\(632\) −14864.3 119984.i −0.0372144 0.300392i
\(633\) 0 0
\(634\) −8451.23 + 347.423i −0.0210253 + 0.000864332i
\(635\) 550100.i 1.36425i
\(636\) 0 0
\(637\) −203862. −0.502408
\(638\) 668.061 + 16250.9i 0.00164125 + 0.0399241i
\(639\) 0 0
\(640\) 467709. 138350.i 1.14187 0.337769i
\(641\) 642891. 1.56466 0.782332 0.622861i \(-0.214030\pi\)
0.782332 + 0.622861i \(0.214030\pi\)
\(642\) 0 0
\(643\) 1531.82i 0.00370498i 0.999998 + 0.00185249i \(0.000589666\pi\)
−0.999998 + 0.00185249i \(0.999410\pi\)
\(644\) −342759. + 28228.8i −0.826450 + 0.0680645i
\(645\) 0 0
\(646\) −2755.23 67022.2i −0.00660227 0.160603i
\(647\) 106720.i 0.254938i −0.991843 0.127469i \(-0.959315\pi\)
0.991843 0.127469i \(-0.0406854\pi\)
\(648\) 0 0
\(649\) −585960. −1.39116
\(650\) 179320. 7371.72i 0.424427 0.0174479i
\(651\) 0 0
\(652\) −33258.1 403826.i −0.0782353 0.949946i
\(653\) 229665. 0.538603 0.269301 0.963056i \(-0.413207\pi\)
0.269301 + 0.963056i \(0.413207\pi\)
\(654\) 0 0
\(655\) 247703.i 0.577362i
\(656\) −104326. + 17301.5i −0.242430 + 0.0402046i
\(657\) 0 0
\(658\) 627652. 25802.3i 1.44966 0.0595946i
\(659\) 390184.i 0.898460i 0.893416 + 0.449230i \(0.148302\pi\)
−0.893416 + 0.449230i \(0.851698\pi\)
\(660\) 0 0
\(661\) 446886. 1.02281 0.511403 0.859341i \(-0.329126\pi\)
0.511403 + 0.859341i \(0.329126\pi\)
\(662\) −2339.94 56920.1i −0.00533936 0.129882i
\(663\) 0 0
\(664\) 52984.5 + 427686.i 0.120175 + 0.970039i
\(665\) −301829. −0.682523
\(666\) 0 0
\(667\) 6471.12i 0.0145455i
\(668\) −36561.0 443930.i −0.0819342 0.994858i
\(669\) 0 0
\(670\) 29322.5 + 713283.i 0.0653208 + 1.58896i
\(671\) 319598.i 0.709837i
\(672\) 0 0
\(673\) 339492. 0.749548 0.374774 0.927116i \(-0.377720\pi\)
0.374774 + 0.927116i \(0.377720\pi\)
\(674\) 301440. 12392.0i 0.663561 0.0272785i
\(675\) 0 0
\(676\) 15023.7 1237.32i 0.0328764 0.00270762i
\(677\) 533403. 1.16380 0.581900 0.813260i \(-0.302310\pi\)
0.581900 + 0.813260i \(0.302310\pi\)
\(678\) 0 0
\(679\) 874272.i 1.89630i
\(680\) −187325. + 23207.0i −0.405115 + 0.0501882i
\(681\) 0 0
\(682\) 699179. 28742.7i 1.50321 0.0617958i
\(683\) 175866.i 0.376999i 0.982073 + 0.188500i \(0.0603624\pi\)
−0.982073 + 0.188500i \(0.939638\pi\)
\(684\) 0 0
\(685\) −637265. −1.35812
\(686\) 11948.6 + 290656.i 0.0253904 + 0.617633i
\(687\) 0 0
\(688\) −12840.1 77424.7i −0.0271264 0.163570i
\(689\) 349422. 0.736057
\(690\) 0 0
\(691\) 234536.i 0.491194i −0.969372 0.245597i \(-0.921016\pi\)
0.969372 0.245597i \(-0.0789840\pi\)
\(692\) −351682. + 28963.7i −0.734409 + 0.0604842i
\(693\) 0 0
\(694\) −24388.5 593261.i −0.0506368 1.23176i
\(695\) 542557.i 1.12325i
\(696\) 0 0
\(697\) 40925.9 0.0842429
\(698\) −93244.6 + 3833.22i −0.191387 + 0.00786778i
\(699\) 0 0
\(700\) 20548.3 + 249501.i 0.0419353 + 0.509185i
\(701\) 192485. 0.391707 0.195853 0.980633i \(-0.437252\pi\)
0.195853 + 0.980633i \(0.437252\pi\)
\(702\) 0 0
\(703\) 103213.i 0.208844i
\(704\) −225383. 895675.i −0.454753 1.80720i
\(705\) 0 0
\(706\) 77432.3 3183.18i 0.155351 0.00638634i
\(707\) 387031.i 0.774297i
\(708\) 0 0
\(709\) −600879. −1.19535 −0.597674 0.801739i \(-0.703908\pi\)
−0.597674 + 0.801739i \(0.703908\pi\)
\(710\) 6062.18 + 147465.i 0.0120258 + 0.292532i
\(711\) 0 0
\(712\) 599365. 74253.1i 1.18231 0.146472i
\(713\) −278414. −0.547661
\(714\) 0 0
\(715\) 1.15299e6i 2.25536i
\(716\) 68964.6 + 837380.i 0.134524 + 1.63342i
\(717\) 0 0
\(718\) −22989.8 559236.i −0.0445950 1.08479i
\(719\) 37302.4i 0.0721571i −0.999349 0.0360786i \(-0.988513\pi\)
0.999349 0.0360786i \(-0.0114867\pi\)
\(720\) 0 0
\(721\) 967729. 1.86159
\(722\) 406336. 16704.1i 0.779490 0.0320442i
\(723\) 0 0
\(724\) −115182. + 9486.12i −0.219739 + 0.0180972i
\(725\) −4710.45 −0.00896163
\(726\) 0 0
\(727\) 748065.i 1.41537i 0.706527 + 0.707686i \(0.250261\pi\)
−0.706527 + 0.707686i \(0.749739\pi\)
\(728\) 80955.8 + 653469.i 0.152751 + 1.23300i
\(729\) 0 0
\(730\) −602095. + 24751.7i −1.12985 + 0.0464471i
\(731\) 30372.8i 0.0568394i
\(732\) 0 0
\(733\) −263418. −0.490272 −0.245136 0.969489i \(-0.578833\pi\)
−0.245136 + 0.969489i \(0.578833\pi\)
\(734\) 15045.3 + 365983.i 0.0279259 + 0.679310i
\(735\) 0 0
\(736\) 74959.1 + 359740.i 0.138379 + 0.664100i
\(737\) 1.35183e6 2.48878
\(738\) 0 0
\(739\) 288908.i 0.529018i 0.964383 + 0.264509i \(0.0852099\pi\)
−0.964383 + 0.264509i \(0.914790\pi\)
\(740\) 289456. 23838.9i 0.528590 0.0435334i
\(741\) 0 0
\(742\) 20020.1 + 486997.i 0.0363629 + 0.884543i
\(743\) 313404.i 0.567710i −0.958867 0.283855i \(-0.908387\pi\)
0.958867 0.283855i \(-0.0916134\pi\)
\(744\) 0 0
\(745\) −483438. −0.871020
\(746\) 342034. 14060.8i 0.614599 0.0252657i
\(747\) 0 0
\(748\) 29338.1 + 356228.i 0.0524359 + 0.636685i
\(749\) 183606. 0.327282
\(750\) 0 0
\(751\) 236182.i 0.418761i 0.977834 + 0.209381i \(0.0671447\pi\)
−0.977834 + 0.209381i \(0.932855\pi\)
\(752\) −109811. 662150.i −0.194183 1.17090i
\(753\) 0 0
\(754\) −12379.1 + 508.894i −0.0217744 + 0.000895128i
\(755\) 730134.i 1.28088i
\(756\) 0 0
\(757\) −1.00219e6 −1.74888 −0.874438 0.485137i \(-0.838770\pi\)
−0.874438 + 0.485137i \(0.838770\pi\)
\(758\) 6545.33 + 159218.i 0.0113918 + 0.277111i
\(759\) 0 0
\(760\) 39649.5 + 320048.i 0.0686453 + 0.554099i
\(761\) 912825. 1.57622 0.788112 0.615532i \(-0.211059\pi\)
0.788112 + 0.615532i \(0.211059\pi\)
\(762\) 0 0
\(763\) 1.06193e6i 1.82410i
\(764\) 13898.1 + 168753.i 0.0238105 + 0.289111i
\(765\) 0 0
\(766\) 28043.0 + 682158.i 0.0477933 + 1.16259i
\(767\) 446354.i 0.758733i
\(768\) 0 0
\(769\) −208651. −0.352831 −0.176416 0.984316i \(-0.556450\pi\)
−0.176416 + 0.984316i \(0.556450\pi\)
\(770\) 1.60696e6 66060.7i 2.71033 0.111420i
\(771\) 0 0
\(772\) −623274. + 51331.3i −1.04579 + 0.0861287i
\(773\) −661279. −1.10669 −0.553345 0.832952i \(-0.686649\pi\)
−0.553345 + 0.832952i \(0.686649\pi\)
\(774\) 0 0
\(775\) 202663.i 0.337420i
\(776\) −927046. + 114848.i −1.53949 + 0.190722i
\(777\) 0 0
\(778\) 862531. 35458.0i 1.42500 0.0585808i
\(779\) 69922.6i 0.115224i
\(780\) 0 0
\(781\) 279479. 0.458191
\(782\) −5841.23 142090.i −0.00955192 0.232355i
\(783\) 0 0
\(784\) −299743. + 49709.5i −0.487660 + 0.0808736i
\(785\) 1.18048e6 1.91566
\(786\) 0 0
\(787\) 38862.8i 0.0627459i −0.999508 0.0313729i \(-0.990012\pi\)
0.999508 0.0313729i \(-0.00998795\pi\)