Properties

Label 324.5.d.e.163.5
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 163.5
Character \(\chi\) \(=\) 324.163
Dual form 324.5.d.e.163.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.82463 - 2.83222i) q^{2} +(-0.0429591 + 15.9999i) q^{4} -11.7888 q^{5} -58.3756i q^{7} +(45.4367 - 45.0722i) q^{8} +O(q^{10})\) \(q+(-2.82463 - 2.83222i) q^{2} +(-0.0429591 + 15.9999i) q^{4} -11.7888 q^{5} -58.3756i q^{7} +(45.4367 - 45.0722i) q^{8} +(33.2988 + 33.3884i) q^{10} +100.429i q^{11} -170.636 q^{13} +(-165.333 + 164.889i) q^{14} +(-255.996 - 1.37469i) q^{16} +398.571 q^{17} -404.608i q^{19} +(0.506434 - 188.619i) q^{20} +(284.438 - 283.675i) q^{22} -336.123i q^{23} -486.025 q^{25} +(481.982 + 483.278i) q^{26} +(934.007 + 2.50777i) q^{28} +655.342 q^{29} -635.277i q^{31} +(719.201 + 728.921i) q^{32} +(-1125.81 - 1128.84i) q^{34} +688.176i q^{35} -1599.91 q^{37} +(-1145.94 + 1142.87i) q^{38} +(-535.642 + 531.345i) q^{40} -2463.27 q^{41} +2232.48i q^{43} +(-1606.86 - 4.31435i) q^{44} +(-951.976 + 949.423i) q^{46} +2903.56i q^{47} -1006.72 q^{49} +(1372.84 + 1376.53i) q^{50} +(7.33036 - 2730.16i) q^{52} -1291.73 q^{53} -1183.94i q^{55} +(-2631.12 - 2652.40i) q^{56} +(-1851.10 - 1856.07i) q^{58} +1157.28i q^{59} +5921.62 q^{61} +(-1799.24 + 1794.42i) q^{62} +(32.9923 - 4095.87i) q^{64} +2011.58 q^{65} +3563.26i q^{67} +(-17.1222 + 6377.11i) q^{68} +(1949.07 - 1943.84i) q^{70} +5639.73i q^{71} -5496.39 q^{73} +(4519.16 + 4531.31i) q^{74} +(6473.71 + 17.3816i) q^{76} +5862.62 q^{77} +3220.39i q^{79} +(3017.88 + 16.2058i) q^{80} +(6957.81 + 6976.52i) q^{82} +8156.71i q^{83} -4698.65 q^{85} +(6322.88 - 6305.92i) q^{86} +(4526.57 + 4563.17i) q^{88} -910.873 q^{89} +9960.97i q^{91} +(5377.95 + 14.4396i) q^{92} +(8223.52 - 8201.47i) q^{94} +4769.83i q^{95} -17608.9 q^{97} +(2843.60 + 2851.24i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + O(q^{10}) \) \( 22q - q^{2} + q^{4} - 2q^{5} - 61q^{8} + 14q^{10} + 2q^{13} + 252q^{14} + q^{16} + 28q^{17} - 140q^{20} + 33q^{22} + 1752q^{25} - 548q^{26} - 258q^{28} + 526q^{29} - 121q^{32} - 385q^{34} - 4q^{37} + 1395q^{38} + 2276q^{40} - 2762q^{41} - 3357q^{44} + 1788q^{46} - 3428q^{49} + 6375q^{50} - 1438q^{52} + 5044q^{53} - 7506q^{56} + 4064q^{58} + 2q^{61} + 9162q^{62} + 4513q^{64} - 2014q^{65} - 11405q^{68} - 3666q^{70} - 1708q^{73} + 14620q^{74} - 1581q^{76} - 3942q^{77} - 22760q^{80} - 4243q^{82} + 1252q^{85} + 22113q^{86} - 1995q^{88} - 6524q^{89} - 30294q^{92} - 7524q^{94} - 5638q^{97} + 46469q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.82463 2.83222i −0.706157 0.708055i
\(3\) 0 0
\(4\) −0.0429591 + 15.9999i −0.00268494 + 0.999996i
\(5\) −11.7888 −0.471550 −0.235775 0.971808i \(-0.575763\pi\)
−0.235775 + 0.971808i \(0.575763\pi\)
\(6\) 0 0
\(7\) 58.3756i 1.19134i −0.803229 0.595670i \(-0.796887\pi\)
0.803229 0.595670i \(-0.203113\pi\)
\(8\) 45.4367 45.0722i 0.709949 0.704253i
\(9\) 0 0
\(10\) 33.2988 + 33.3884i 0.332988 + 0.333884i
\(11\) 100.429i 0.829993i 0.909823 + 0.414997i \(0.136217\pi\)
−0.909823 + 0.414997i \(0.863783\pi\)
\(12\) 0 0
\(13\) −170.636 −1.00968 −0.504839 0.863213i \(-0.668448\pi\)
−0.504839 + 0.863213i \(0.668448\pi\)
\(14\) −165.333 + 164.889i −0.843535 + 0.841273i
\(15\) 0 0
\(16\) −255.996 1.37469i −0.999986 0.00536987i
\(17\) 398.571 1.37914 0.689569 0.724220i \(-0.257800\pi\)
0.689569 + 0.724220i \(0.257800\pi\)
\(18\) 0 0
\(19\) 404.608i 1.12080i −0.828223 0.560399i \(-0.810648\pi\)
0.828223 0.560399i \(-0.189352\pi\)
\(20\) 0.506434 188.619i 0.00126609 0.471549i
\(21\) 0 0
\(22\) 284.438 283.675i 0.587681 0.586105i
\(23\) 336.123i 0.635394i −0.948192 0.317697i \(-0.897091\pi\)
0.948192 0.317697i \(-0.102909\pi\)
\(24\) 0 0
\(25\) −486.025 −0.777640
\(26\) 481.982 + 483.278i 0.712991 + 0.714908i
\(27\) 0 0
\(28\) 934.007 + 2.50777i 1.19134 + 0.00319868i
\(29\) 655.342 0.779241 0.389621 0.920975i \(-0.372606\pi\)
0.389621 + 0.920975i \(0.372606\pi\)
\(30\) 0 0
\(31\) 635.277i 0.661058i −0.943796 0.330529i \(-0.892773\pi\)
0.943796 0.330529i \(-0.107227\pi\)
\(32\) 719.201 + 728.921i 0.702345 + 0.711837i
\(33\) 0 0
\(34\) −1125.81 1128.84i −0.973888 0.976506i
\(35\) 688.176i 0.561776i
\(36\) 0 0
\(37\) −1599.91 −1.16867 −0.584336 0.811512i \(-0.698645\pi\)
−0.584336 + 0.811512i \(0.698645\pi\)
\(38\) −1145.94 + 1142.87i −0.793587 + 0.791459i
\(39\) 0 0
\(40\) −535.642 + 531.345i −0.334777 + 0.332091i
\(41\) −2463.27 −1.46536 −0.732679 0.680574i \(-0.761730\pi\)
−0.732679 + 0.680574i \(0.761730\pi\)
\(42\) 0 0
\(43\) 2232.48i 1.20740i 0.797212 + 0.603699i \(0.206307\pi\)
−0.797212 + 0.603699i \(0.793693\pi\)
\(44\) −1606.86 4.31435i −0.829990 0.00222849i
\(45\) 0 0
\(46\) −951.976 + 949.423i −0.449894 + 0.448688i
\(47\) 2903.56i 1.31442i 0.753707 + 0.657211i \(0.228264\pi\)
−0.753707 + 0.657211i \(0.771736\pi\)
\(48\) 0 0
\(49\) −1006.72 −0.419290
\(50\) 1372.84 + 1376.53i 0.549136 + 0.550613i
\(51\) 0 0
\(52\) 7.33036 2730.16i 0.00271093 1.00967i
\(53\) −1291.73 −0.459852 −0.229926 0.973208i \(-0.573848\pi\)
−0.229926 + 0.973208i \(0.573848\pi\)
\(54\) 0 0
\(55\) 1183.94i 0.391384i
\(56\) −2631.12 2652.40i −0.839005 0.845790i
\(57\) 0 0
\(58\) −1851.10 1856.07i −0.550267 0.551746i
\(59\) 1157.28i 0.332457i 0.986087 + 0.166229i \(0.0531590\pi\)
−0.986087 + 0.166229i \(0.946841\pi\)
\(60\) 0 0
\(61\) 5921.62 1.59141 0.795703 0.605687i \(-0.207101\pi\)
0.795703 + 0.605687i \(0.207101\pi\)
\(62\) −1799.24 + 1794.42i −0.468066 + 0.466811i
\(63\) 0 0
\(64\) 32.9923 4095.87i 0.00805476 0.999968i
\(65\) 2011.58 0.476114
\(66\) 0 0
\(67\) 3563.26i 0.793775i 0.917867 + 0.396888i \(0.129910\pi\)
−0.917867 + 0.396888i \(0.870090\pi\)
\(68\) −17.1222 + 6377.11i −0.00370291 + 1.37913i
\(69\) 0 0
\(70\) 1949.07 1943.84i 0.397769 0.396702i
\(71\) 5639.73i 1.11877i 0.828907 + 0.559386i \(0.188963\pi\)
−0.828907 + 0.559386i \(0.811037\pi\)
\(72\) 0 0
\(73\) −5496.39 −1.03141 −0.515705 0.856766i \(-0.672470\pi\)
−0.515705 + 0.856766i \(0.672470\pi\)
\(74\) 4519.16 + 4531.31i 0.825266 + 0.827485i
\(75\) 0 0
\(76\) 6473.71 + 17.3816i 1.12079 + 0.00300928i
\(77\) 5862.62 0.988804
\(78\) 0 0
\(79\) 3220.39i 0.516006i 0.966144 + 0.258003i \(0.0830645\pi\)
−0.966144 + 0.258003i \(0.916936\pi\)
\(80\) 3017.88 + 16.2058i 0.471543 + 0.00253216i
\(81\) 0 0
\(82\) 6957.81 + 6976.52i 1.03477 + 1.03755i
\(83\) 8156.71i 1.18402i 0.805931 + 0.592010i \(0.201665\pi\)
−0.805931 + 0.592010i \(0.798335\pi\)
\(84\) 0 0
\(85\) −4698.65 −0.650333
\(86\) 6322.88 6305.92i 0.854905 0.852612i
\(87\) 0 0
\(88\) 4526.57 + 4563.17i 0.584525 + 0.589253i
\(89\) −910.873 −0.114995 −0.0574974 0.998346i \(-0.518312\pi\)
−0.0574974 + 0.998346i \(0.518312\pi\)
\(90\) 0 0
\(91\) 9960.97i 1.20287i
\(92\) 5377.95 + 14.4396i 0.635391 + 0.00170600i
\(93\) 0 0
\(94\) 8223.52 8201.47i 0.930683 0.928188i
\(95\) 4769.83i 0.528513i
\(96\) 0 0
\(97\) −17608.9 −1.87149 −0.935747 0.352673i \(-0.885273\pi\)
−0.935747 + 0.352673i \(0.885273\pi\)
\(98\) 2843.60 + 2851.24i 0.296085 + 0.296881i
\(99\) 0 0
\(100\) 20.8792 7776.38i 0.00208792 0.777638i
\(101\) −6660.82 −0.652957 −0.326479 0.945205i \(-0.605862\pi\)
−0.326479 + 0.945205i \(0.605862\pi\)
\(102\) 0 0
\(103\) 6753.50i 0.636582i 0.947993 + 0.318291i \(0.103109\pi\)
−0.947993 + 0.318291i \(0.896891\pi\)
\(104\) −7753.12 + 7690.92i −0.716820 + 0.711069i
\(105\) 0 0
\(106\) 3648.64 + 3658.45i 0.324728 + 0.325601i
\(107\) 30.7569i 0.00268643i 0.999999 + 0.00134321i \(0.000427558\pi\)
−0.999999 + 0.00134321i \(0.999572\pi\)
\(108\) 0 0
\(109\) 10691.4 0.899872 0.449936 0.893061i \(-0.351447\pi\)
0.449936 + 0.893061i \(0.351447\pi\)
\(110\) −3353.17 + 3344.18i −0.277121 + 0.276378i
\(111\) 0 0
\(112\) −80.2482 + 14943.9i −0.00639734 + 1.19132i
\(113\) −10016.2 −0.784414 −0.392207 0.919877i \(-0.628288\pi\)
−0.392207 + 0.919877i \(0.628288\pi\)
\(114\) 0 0
\(115\) 3962.47i 0.299620i
\(116\) −28.1529 + 10485.4i −0.00209222 + 0.779238i
\(117\) 0 0
\(118\) 3277.69 3268.90i 0.235398 0.234767i
\(119\) 23266.8i 1.64302i
\(120\) 0 0
\(121\) 4554.98 0.311111
\(122\) −16726.4 16771.4i −1.12378 1.12680i
\(123\) 0 0
\(124\) 10164.4 + 27.2909i 0.661056 + 0.00177490i
\(125\) 13097.6 0.838247
\(126\) 0 0
\(127\) 16087.8i 0.997444i 0.866762 + 0.498722i \(0.166197\pi\)
−0.866762 + 0.498722i \(0.833803\pi\)
\(128\) −11693.6 + 11475.9i −0.713720 + 0.700431i
\(129\) 0 0
\(130\) −5681.97 5697.25i −0.336211 0.337115i
\(131\) 20906.5i 1.21825i 0.793073 + 0.609127i \(0.208480\pi\)
−0.793073 + 0.609127i \(0.791520\pi\)
\(132\) 0 0
\(133\) −23619.3 −1.33525
\(134\) 10091.9 10064.9i 0.562037 0.560530i
\(135\) 0 0
\(136\) 18109.8 17964.5i 0.979117 0.971262i
\(137\) −4676.05 −0.249137 −0.124568 0.992211i \(-0.539755\pi\)
−0.124568 + 0.992211i \(0.539755\pi\)
\(138\) 0 0
\(139\) 9305.07i 0.481604i 0.970574 + 0.240802i \(0.0774104\pi\)
−0.970574 + 0.240802i \(0.922590\pi\)
\(140\) −11010.8 29.5634i −0.561774 0.00150834i
\(141\) 0 0
\(142\) 15973.0 15930.1i 0.792152 0.790028i
\(143\) 17136.8i 0.838026i
\(144\) 0 0
\(145\) −7725.67 −0.367451
\(146\) 15525.3 + 15567.0i 0.728338 + 0.730296i
\(147\) 0 0
\(148\) 68.7308 25598.5i 0.00313782 1.16867i
\(149\) 24771.6 1.11579 0.557893 0.829913i \(-0.311610\pi\)
0.557893 + 0.829913i \(0.311610\pi\)
\(150\) 0 0
\(151\) 10209.5i 0.447767i −0.974616 0.223884i \(-0.928126\pi\)
0.974616 0.223884i \(-0.0718735\pi\)
\(152\) −18236.6 18384.1i −0.789326 0.795709i
\(153\) 0 0
\(154\) −16559.7 16604.2i −0.698251 0.700128i
\(155\) 7489.12i 0.311722i
\(156\) 0 0
\(157\) −28973.0 −1.17542 −0.587712 0.809070i \(-0.699971\pi\)
−0.587712 + 0.809070i \(0.699971\pi\)
\(158\) 9120.87 9096.41i 0.365361 0.364381i
\(159\) 0 0
\(160\) −8478.48 8593.07i −0.331191 0.335667i
\(161\) −19621.4 −0.756970
\(162\) 0 0
\(163\) 17736.4i 0.667560i 0.942651 + 0.333780i \(0.108324\pi\)
−0.942651 + 0.333780i \(0.891676\pi\)
\(164\) 105.820 39412.1i 0.00393441 1.46535i
\(165\) 0 0
\(166\) 23101.6 23039.7i 0.838352 0.836104i
\(167\) 41063.6i 1.47239i −0.676767 0.736197i \(-0.736620\pi\)
0.676767 0.736197i \(-0.263380\pi\)
\(168\) 0 0
\(169\) 555.522 0.0194504
\(170\) 13271.9 + 13307.6i 0.459237 + 0.460472i
\(171\) 0 0
\(172\) −35719.5 95.9053i −1.20739 0.00324180i
\(173\) −6955.73 −0.232408 −0.116204 0.993225i \(-0.537073\pi\)
−0.116204 + 0.993225i \(0.537073\pi\)
\(174\) 0 0
\(175\) 28372.0i 0.926434i
\(176\) 138.059 25709.5i 0.00445696 0.829981i
\(177\) 0 0
\(178\) 2572.88 + 2579.80i 0.0812043 + 0.0814227i
\(179\) 1754.50i 0.0547580i 0.999625 + 0.0273790i \(0.00871609\pi\)
−0.999625 + 0.0273790i \(0.991284\pi\)
\(180\) 0 0
\(181\) −43787.9 −1.33659 −0.668293 0.743898i \(-0.732975\pi\)
−0.668293 + 0.743898i \(0.732975\pi\)
\(182\) 28211.7 28136.0i 0.851699 0.849415i
\(183\) 0 0
\(184\) −15149.8 15272.3i −0.447478 0.451097i
\(185\) 18861.0 0.551088
\(186\) 0 0
\(187\) 40028.1i 1.14468i
\(188\) −46456.8 124.734i −1.31442 0.00352915i
\(189\) 0 0
\(190\) 13509.2 13473.0i 0.374216 0.373213i
\(191\) 39725.3i 1.08893i −0.838783 0.544466i \(-0.816732\pi\)
0.838783 0.544466i \(-0.183268\pi\)
\(192\) 0 0
\(193\) −21094.4 −0.566308 −0.283154 0.959074i \(-0.591381\pi\)
−0.283154 + 0.959074i \(0.591381\pi\)
\(194\) 49738.5 + 49872.3i 1.32157 + 1.32512i
\(195\) 0 0
\(196\) 43.2476 16107.4i 0.00112577 0.419289i
\(197\) −28256.1 −0.728080 −0.364040 0.931383i \(-0.618603\pi\)
−0.364040 + 0.931383i \(0.618603\pi\)
\(198\) 0 0
\(199\) 24063.5i 0.607650i −0.952728 0.303825i \(-0.901736\pi\)
0.952728 0.303825i \(-0.0982638\pi\)
\(200\) −22083.4 + 21906.2i −0.552085 + 0.547656i
\(201\) 0 0
\(202\) 18814.3 + 18864.9i 0.461090 + 0.462330i
\(203\) 38256.0i 0.928341i
\(204\) 0 0
\(205\) 29038.9 0.690990
\(206\) 19127.4 19076.1i 0.450735 0.449527i
\(207\) 0 0
\(208\) 43682.1 + 234.571i 1.00966 + 0.00542184i
\(209\) 40634.5 0.930255
\(210\) 0 0
\(211\) 58079.8i 1.30455i −0.757983 0.652274i \(-0.773815\pi\)
0.757983 0.652274i \(-0.226185\pi\)
\(212\) 55.4914 20667.5i 0.00123468 0.459851i
\(213\) 0 0
\(214\) 87.1104 86.8768i 0.00190214 0.00189704i
\(215\) 26318.1i 0.569349i
\(216\) 0 0
\(217\) −37084.7 −0.787545
\(218\) −30199.2 30280.4i −0.635451 0.637159i
\(219\) 0 0
\(220\) 18942.9 + 50.8608i 0.391382 + 0.00105084i
\(221\) −68010.4 −1.39249
\(222\) 0 0
\(223\) 16661.8i 0.335053i −0.985868 0.167526i \(-0.946422\pi\)
0.985868 0.167526i \(-0.0535779\pi\)
\(224\) 42551.3 41983.8i 0.848040 0.836731i
\(225\) 0 0
\(226\) 28292.0 + 28368.0i 0.553919 + 0.555409i
\(227\) 56258.7i 1.09179i 0.837855 + 0.545894i \(0.183810\pi\)
−0.837855 + 0.545894i \(0.816190\pi\)
\(228\) 0 0
\(229\) 2447.82 0.0466775 0.0233388 0.999728i \(-0.492570\pi\)
0.0233388 + 0.999728i \(0.492570\pi\)
\(230\) 11222.6 11192.5i 0.212148 0.211579i
\(231\) 0 0
\(232\) 29776.6 29537.7i 0.553221 0.548783i
\(233\) 76971.2 1.41781 0.708903 0.705306i \(-0.249191\pi\)
0.708903 + 0.705306i \(0.249191\pi\)
\(234\) 0 0
\(235\) 34229.3i 0.619816i
\(236\) −18516.5 49.7159i −0.332456 0.000892630i
\(237\) 0 0
\(238\) −65896.8 + 65720.1i −1.16335 + 1.16023i
\(239\) 26058.7i 0.456202i 0.973637 + 0.228101i \(0.0732517\pi\)
−0.973637 + 0.228101i \(0.926748\pi\)
\(240\) 0 0
\(241\) −27999.6 −0.482079 −0.241039 0.970515i \(-0.577488\pi\)
−0.241039 + 0.970515i \(0.577488\pi\)
\(242\) −12866.1 12900.7i −0.219693 0.220284i
\(243\) 0 0
\(244\) −254.388 + 94745.6i −0.00427284 + 1.59140i
\(245\) 11867.9 0.197716
\(246\) 0 0
\(247\) 69040.6i 1.13165i
\(248\) −28633.3 28864.9i −0.465552 0.469317i
\(249\) 0 0
\(250\) −36995.9 37095.3i −0.591934 0.593525i
\(251\) 19782.5i 0.314003i −0.987598 0.157001i \(-0.949817\pi\)
0.987598 0.157001i \(-0.0501827\pi\)
\(252\) 0 0
\(253\) 33756.6 0.527373
\(254\) 45564.1 45442.0i 0.706246 0.704352i
\(255\) 0 0
\(256\) 65532.2 + 703.829i 0.999942 + 0.0107396i
\(257\) −77273.9 −1.16995 −0.584974 0.811052i \(-0.698895\pi\)
−0.584974 + 0.811052i \(0.698895\pi\)
\(258\) 0 0
\(259\) 93395.9i 1.39229i
\(260\) −86.4158 + 32185.2i −0.00127834 + 0.476112i
\(261\) 0 0
\(262\) 59211.7 59053.0i 0.862592 0.860279i
\(263\) 21212.4i 0.306675i −0.988174 0.153337i \(-0.950998\pi\)
0.988174 0.153337i \(-0.0490021\pi\)
\(264\) 0 0
\(265\) 15227.8 0.216844
\(266\) 66715.6 + 66895.0i 0.942897 + 0.945432i
\(267\) 0 0
\(268\) −57011.9 153.074i −0.793772 0.00213124i
\(269\) −1106.24 −0.0152878 −0.00764389 0.999971i \(-0.502433\pi\)
−0.00764389 + 0.999971i \(0.502433\pi\)
\(270\) 0 0
\(271\) 33038.3i 0.449861i 0.974375 + 0.224931i \(0.0722155\pi\)
−0.974375 + 0.224931i \(0.927784\pi\)
\(272\) −102033. 547.910i −1.37912 0.00740579i
\(273\) 0 0
\(274\) 13208.1 + 13243.6i 0.175930 + 0.176403i
\(275\) 48811.1i 0.645436i
\(276\) 0 0
\(277\) 28842.5 0.375901 0.187951 0.982178i \(-0.439816\pi\)
0.187951 + 0.982178i \(0.439816\pi\)
\(278\) 26354.0 26283.3i 0.341002 0.340088i
\(279\) 0 0
\(280\) 31017.6 + 31268.5i 0.395633 + 0.398833i
\(281\) −32125.8 −0.406856 −0.203428 0.979090i \(-0.565208\pi\)
−0.203428 + 0.979090i \(0.565208\pi\)
\(282\) 0 0
\(283\) 71340.3i 0.890763i −0.895341 0.445382i \(-0.853068\pi\)
0.895341 0.445382i \(-0.146932\pi\)
\(284\) −90235.3 242.278i −1.11877 0.00300384i
\(285\) 0 0
\(286\) −48535.2 + 48405.1i −0.593369 + 0.591778i
\(287\) 143795.i 1.74574i
\(288\) 0 0
\(289\) 75337.7 0.902021
\(290\) 21822.1 + 21880.8i 0.259478 + 0.260176i
\(291\) 0 0
\(292\) 236.120 87941.9i 0.00276928 1.03141i
\(293\) 36641.5 0.426813 0.213407 0.976963i \(-0.431544\pi\)
0.213407 + 0.976963i \(0.431544\pi\)
\(294\) 0 0
\(295\) 13642.9i 0.156770i
\(296\) −72694.8 + 72111.6i −0.829698 + 0.823041i
\(297\) 0 0
\(298\) −69970.4 70158.5i −0.787920 0.790038i
\(299\) 57354.6i 0.641543i
\(300\) 0 0
\(301\) 130322. 1.43842
\(302\) −28915.7 + 28838.1i −0.317044 + 0.316194i
\(303\) 0 0
\(304\) −556.209 + 103578.i −0.00601854 + 1.12078i
\(305\) −69808.6 −0.750428
\(306\) 0 0
\(307\) 11668.1i 0.123801i 0.998082 + 0.0619005i \(0.0197161\pi\)
−0.998082 + 0.0619005i \(0.980284\pi\)
\(308\) −251.853 + 93801.6i −0.00265488 + 0.988800i
\(309\) 0 0
\(310\) 21210.8 21154.0i 0.220716 0.220125i
\(311\) 4336.03i 0.0448303i 0.999749 + 0.0224151i \(0.00713556\pi\)
−0.999749 + 0.0224151i \(0.992864\pi\)
\(312\) 0 0
\(313\) 86498.6 0.882918 0.441459 0.897282i \(-0.354461\pi\)
0.441459 + 0.897282i \(0.354461\pi\)
\(314\) 81838.0 + 82058.1i 0.830034 + 0.832266i
\(315\) 0 0
\(316\) −51526.1 138.345i −0.516004 0.00138545i
\(317\) 24632.2 0.245124 0.122562 0.992461i \(-0.460889\pi\)
0.122562 + 0.992461i \(0.460889\pi\)
\(318\) 0 0
\(319\) 65815.5i 0.646765i
\(320\) −388.938 + 48285.2i −0.00379822 + 0.471535i
\(321\) 0 0
\(322\) 55423.2 + 55572.2i 0.534539 + 0.535977i
\(323\) 161265.i 1.54573i
\(324\) 0 0
\(325\) 82933.2 0.785167
\(326\) 50233.4 50098.7i 0.472669 0.471402i
\(327\) 0 0
\(328\) −111923. + 111025.i −1.04033 + 1.03198i
\(329\) 169497. 1.56592
\(330\) 0 0
\(331\) 187265.i 1.70923i −0.519265 0.854614i \(-0.673794\pi\)
0.519265 0.854614i \(-0.326206\pi\)
\(332\) −130507. 350.405i −1.18402 0.00317903i
\(333\) 0 0
\(334\) −116301. + 115989.i −1.04254 + 1.03974i
\(335\) 42006.4i 0.374305i
\(336\) 0 0
\(337\) −100959. −0.888967 −0.444484 0.895787i \(-0.646613\pi\)
−0.444484 + 0.895787i \(0.646613\pi\)
\(338\) −1569.14 1573.36i −0.0137350 0.0137719i
\(339\) 0 0
\(340\) 201.850 75178.2i 0.00174611 0.650330i
\(341\) 63800.3 0.548674
\(342\) 0 0
\(343\) 81392.2i 0.691823i
\(344\) 100623. + 101437.i 0.850314 + 0.857191i
\(345\) 0 0
\(346\) 19647.4 + 19700.2i 0.164116 + 0.164558i
\(347\) 174903.i 1.45257i 0.687392 + 0.726287i \(0.258756\pi\)
−0.687392 + 0.726287i \(0.741244\pi\)
\(348\) 0 0
\(349\) 43896.9 0.360399 0.180199 0.983630i \(-0.442326\pi\)
0.180199 + 0.983630i \(0.442326\pi\)
\(350\) 80355.9 80140.4i 0.655967 0.654208i
\(351\) 0 0
\(352\) −73205.0 + 72228.8i −0.590820 + 0.582941i
\(353\) −155579. −1.24854 −0.624270 0.781209i \(-0.714603\pi\)
−0.624270 + 0.781209i \(0.714603\pi\)
\(354\) 0 0
\(355\) 66485.4i 0.527557i
\(356\) 39.1303 14573.9i 0.000308755 0.114994i
\(357\) 0 0
\(358\) 4969.13 4955.81i 0.0387717 0.0386677i
\(359\) 184004.i 1.42771i 0.700295 + 0.713853i \(0.253052\pi\)
−0.700295 + 0.713853i \(0.746948\pi\)
\(360\) 0 0
\(361\) −33386.7 −0.256188
\(362\) 123685. + 124017.i 0.943840 + 0.946377i
\(363\) 0 0
\(364\) −159375. 427.914i −1.20287 0.00322964i
\(365\) 64795.6 0.486362
\(366\) 0 0
\(367\) 165901.i 1.23173i −0.787851 0.615866i \(-0.788806\pi\)
0.787851 0.615866i \(-0.211194\pi\)
\(368\) −462.064 + 86046.3i −0.00341198 + 0.635385i
\(369\) 0 0
\(370\) −53275.2 53418.5i −0.389154 0.390201i
\(371\) 75405.3i 0.547841i
\(372\) 0 0
\(373\) 130320. 0.936685 0.468343 0.883547i \(-0.344851\pi\)
0.468343 + 0.883547i \(0.344851\pi\)
\(374\) 113369. 113065.i 0.810493 0.808320i
\(375\) 0 0
\(376\) 130870. + 131928.i 0.925686 + 0.933172i
\(377\) −111825. −0.786783
\(378\) 0 0
\(379\) 43645.6i 0.303852i 0.988392 + 0.151926i \(0.0485475\pi\)
−0.988392 + 0.151926i \(0.951453\pi\)
\(380\) −76316.9 204.907i −0.528511 0.00141903i
\(381\) 0 0
\(382\) −112511. + 112209.i −0.771024 + 0.768957i
\(383\) 273879.i 1.86707i 0.358485 + 0.933535i \(0.383293\pi\)
−0.358485 + 0.933535i \(0.616707\pi\)
\(384\) 0 0
\(385\) −69113.0 −0.466271
\(386\) 59583.9 + 59744.1i 0.399902 + 0.400978i
\(387\) 0 0
\(388\) 756.462 281741.i 0.00502486 1.87149i
\(389\) 245188. 1.62032 0.810159 0.586211i \(-0.199381\pi\)
0.810159 + 0.586211i \(0.199381\pi\)
\(390\) 0 0
\(391\) 133969.i 0.876295i
\(392\) −45741.9 + 45374.9i −0.297675 + 0.295287i
\(393\) 0 0
\(394\) 79812.9 + 80027.4i 0.514139 + 0.515521i
\(395\) 37964.4i 0.243323i
\(396\) 0 0
\(397\) −4252.39 −0.0269806 −0.0134903 0.999909i \(-0.504294\pi\)
−0.0134903 + 0.999909i \(0.504294\pi\)
\(398\) −68153.3 + 67970.6i −0.430250 + 0.429096i
\(399\) 0 0
\(400\) 124421. + 668.132i 0.777629 + 0.00417583i
\(401\) −7331.22 −0.0455919 −0.0227959 0.999740i \(-0.507257\pi\)
−0.0227959 + 0.999740i \(0.507257\pi\)
\(402\) 0 0
\(403\) 108401.i 0.667456i
\(404\) 286.143 106573.i 0.00175315 0.652955i
\(405\) 0 0
\(406\) −108349. + 108059.i −0.657317 + 0.655554i
\(407\) 160678.i 0.969990i
\(408\) 0 0
\(409\) −28414.0 −0.169858 −0.0849289 0.996387i \(-0.527066\pi\)
−0.0849289 + 0.996387i \(0.527066\pi\)
\(410\) −82023.9 82244.5i −0.487947 0.489259i
\(411\) 0 0
\(412\) −108056. 290.124i −0.636580 0.00170919i
\(413\) 67557.2 0.396070
\(414\) 0 0
\(415\) 96157.5i 0.558325i
\(416\) −122721. 124380.i −0.709142 0.718727i
\(417\) 0 0
\(418\) −114777. 115086.i −0.656906 0.658672i
\(419\) 158490.i 0.902763i −0.892331 0.451382i \(-0.850931\pi\)
0.892331 0.451382i \(-0.149069\pi\)
\(420\) 0 0
\(421\) −285592. −1.61132 −0.805659 0.592379i \(-0.798189\pi\)
−0.805659 + 0.592379i \(0.798189\pi\)
\(422\) −164495. + 164054.i −0.923693 + 0.921216i
\(423\) 0 0
\(424\) −58691.8 + 58220.9i −0.326472 + 0.323853i
\(425\) −193715. −1.07247
\(426\) 0 0
\(427\) 345679.i 1.89591i
\(428\) −492.109 1.32129i −0.00268642 7.21291e-6i
\(429\) 0 0
\(430\) −74538.8 + 74339.0i −0.403130 + 0.402050i
\(431\) 115124.i 0.619741i 0.950779 + 0.309870i \(0.100286\pi\)
−0.950779 + 0.309870i \(0.899714\pi\)
\(432\) 0 0
\(433\) 95600.5 0.509899 0.254950 0.966954i \(-0.417941\pi\)
0.254950 + 0.966954i \(0.417941\pi\)
\(434\) 104750. + 105032.i 0.556130 + 0.557625i
\(435\) 0 0
\(436\) −459.292 + 171061.i −0.00241611 + 0.899869i
\(437\) −135998. −0.712148
\(438\) 0 0
\(439\) 371524.i 1.92778i −0.266300 0.963890i \(-0.585801\pi\)
0.266300 0.963890i \(-0.414199\pi\)
\(440\) −53362.6 53794.1i −0.275633 0.277862i
\(441\) 0 0
\(442\) 192104. + 192620.i 0.983313 + 0.985957i
\(443\) 138264.i 0.704536i 0.935899 + 0.352268i \(0.114589\pi\)
−0.935899 + 0.352268i \(0.885411\pi\)
\(444\) 0 0
\(445\) 10738.1 0.0542258
\(446\) −47190.0 + 47063.5i −0.237236 + 0.236600i
\(447\) 0 0
\(448\) −239099. 1925.95i −1.19130 0.00959595i
\(449\) −128427. −0.637035 −0.318518 0.947917i \(-0.603185\pi\)
−0.318518 + 0.947917i \(0.603185\pi\)
\(450\) 0 0
\(451\) 247384.i 1.21624i
\(452\) 430.286 160258.i 0.00210611 0.784411i
\(453\) 0 0
\(454\) 159337. 158910.i 0.773046 0.770973i
\(455\) 117427.i 0.567214i
\(456\) 0 0
\(457\) 293085. 1.40334 0.701668 0.712504i \(-0.252439\pi\)
0.701668 + 0.712504i \(0.252439\pi\)
\(458\) −6914.17 6932.76i −0.0329617 0.0330503i
\(459\) 0 0
\(460\) −63399.4 170.224i −0.299619 0.000804463i
\(461\) −296134. −1.39343 −0.696717 0.717346i \(-0.745357\pi\)
−0.696717 + 0.717346i \(0.745357\pi\)
\(462\) 0 0
\(463\) 354683.i 1.65455i 0.561801 + 0.827273i \(0.310109\pi\)
−0.561801 + 0.827273i \(0.689891\pi\)
\(464\) −167765. 900.890i −0.779230 0.00418442i
\(465\) 0 0
\(466\) −217415. 218000.i −1.00119 1.00388i
\(467\) 116644.i 0.534848i −0.963579 0.267424i \(-0.913828\pi\)
0.963579 0.267424i \(-0.0861724\pi\)
\(468\) 0 0
\(469\) 208007. 0.945656
\(470\) −96945.0 + 96685.1i −0.438864 + 0.437687i
\(471\) 0 0
\(472\) 52161.4 + 52583.2i 0.234134 + 0.236028i
\(473\) −224206. −1.00213
\(474\) 0 0
\(475\) 196650.i 0.871578i
\(476\) 372268. + 999.522i 1.64302 + 0.00441142i
\(477\) 0 0
\(478\) 73804.1 73606.2i 0.323017 0.322151i
\(479\) 104079.i 0.453618i 0.973939 + 0.226809i \(0.0728293\pi\)
−0.973939 + 0.226809i \(0.927171\pi\)
\(480\) 0 0
\(481\) 273002. 1.17998
\(482\) 79088.5 + 79301.1i 0.340423 + 0.341338i
\(483\) 0 0
\(484\) −195.678 + 72879.4i −0.000835316 + 0.311110i
\(485\) 207587. 0.882503
\(486\) 0 0
\(487\) 101284.i 0.427055i 0.976937 + 0.213527i \(0.0684953\pi\)
−0.976937 + 0.213527i \(0.931505\pi\)
\(488\) 269059. 266901.i 1.12982 1.12075i
\(489\) 0 0
\(490\) −33522.5 33612.6i −0.139619 0.139994i
\(491\) 175225.i 0.726831i −0.931627 0.363416i \(-0.881611\pi\)
0.931627 0.363416i \(-0.118389\pi\)
\(492\) 0 0
\(493\) 261200. 1.07468
\(494\) 195538. 195014.i 0.801268 0.799119i
\(495\) 0 0
\(496\) −873.306 + 162628.i −0.00354979 + 0.661048i
\(497\) 329223. 1.33284
\(498\) 0 0
\(499\) 96102.5i 0.385952i 0.981203 + 0.192976i \(0.0618140\pi\)
−0.981203 + 0.192976i \(0.938186\pi\)
\(500\) −562.661 + 209561.i −0.00225065 + 0.838244i
\(501\) 0 0
\(502\) −56028.4 + 55878.2i −0.222331 + 0.221735i
\(503\) 164729.i 0.651080i −0.945528 0.325540i \(-0.894454\pi\)
0.945528 0.325540i \(-0.105546\pi\)
\(504\) 0 0
\(505\) 78522.7 0.307902
\(506\) −95349.8 95606.1i −0.372408 0.373409i
\(507\) 0 0
\(508\) −257403. 691.117i −0.997440 0.00267808i
\(509\) 85940.1 0.331711 0.165856 0.986150i \(-0.446961\pi\)
0.165856 + 0.986150i \(0.446961\pi\)
\(510\) 0 0
\(511\) 320855.i 1.22876i
\(512\) −183111. 187590.i −0.698512 0.715598i
\(513\) 0 0
\(514\) 218270. + 218857.i 0.826166 + 0.828388i
\(515\) 79615.3i 0.300180i
\(516\) 0 0
\(517\) −291602. −1.09096
\(518\) 264518. 263809.i 0.985815 0.983172i
\(519\) 0 0
\(520\) 91399.7 90666.4i 0.338017 0.335305i
\(521\) 173047. 0.637514 0.318757 0.947836i \(-0.396735\pi\)
0.318757 + 0.947836i \(0.396735\pi\)
\(522\) 0 0
\(523\) 252188.i 0.921978i 0.887406 + 0.460989i \(0.152505\pi\)
−0.887406 + 0.460989i \(0.847495\pi\)
\(524\) −334502. 898.123i −1.21825 0.00327095i
\(525\) 0 0
\(526\) −60078.2 + 59917.1i −0.217143 + 0.216560i
\(527\) 253203.i 0.911690i
\(528\) 0 0
\(529\) 166862. 0.596275
\(530\) −43013.0 43128.6i −0.153126 0.153537i
\(531\) 0 0
\(532\) 1014.66 377907.i 0.00358508 1.33525i
\(533\) 420321. 1.47954
\(534\) 0 0
\(535\) 362.586i 0.00126679i
\(536\) 160604. + 161903.i 0.559019 + 0.563540i
\(537\) 0 0
\(538\) 3124.71 + 3133.11i 0.0107956 + 0.0108246i
\(539\) 101104.i 0.348008i
\(540\) 0 0
\(541\) −472358. −1.61390 −0.806950 0.590620i \(-0.798883\pi\)
−0.806950 + 0.590620i \(0.798883\pi\)
\(542\) 93571.7 93320.8i 0.318527 0.317673i
\(543\) 0 0
\(544\) 286652. + 290527.i 0.968630 + 0.981721i
\(545\) −126038. −0.424335
\(546\) 0 0
\(547\) 384377.i 1.28465i 0.766434 + 0.642323i \(0.222029\pi\)
−0.766434 + 0.642323i \(0.777971\pi\)
\(548\) 200.879 74816.5i 0.000668918 0.249136i
\(549\) 0 0
\(550\) −138244. + 137873.i −0.457005 + 0.455779i
\(551\) 265157.i 0.873372i
\(552\) 0 0
\(553\) 187993. 0.614739
\(554\) −81469.4 81688.4i −0.265445 0.266159i
\(555\) 0 0
\(556\) −148881. 399.737i −0.481602 0.00129308i
\(557\) 19803.1 0.0638297 0.0319148 0.999491i \(-0.489839\pi\)
0.0319148 + 0.999491i \(0.489839\pi\)
\(558\) 0 0
\(559\) 380940.i 1.21908i
\(560\) 946.027 176171.i 0.00301667 0.561768i
\(561\) 0 0
\(562\) 90743.4 + 90987.4i 0.287304 + 0.288077i
\(563\) 153074.i 0.482929i −0.970410 0.241465i \(-0.922372\pi\)
0.970410 0.241465i \(-0.0776278\pi\)
\(564\) 0 0
\(565\) 118078. 0.369891
\(566\) −202052. + 201510.i −0.630710 + 0.629019i
\(567\) 0 0
\(568\) 254195. + 256251.i 0.787898 + 0.794271i
\(569\) 51911.0 0.160337 0.0801687 0.996781i \(-0.474454\pi\)
0.0801687 + 0.996781i \(0.474454\pi\)
\(570\) 0 0
\(571\) 107343.i 0.329232i 0.986358 + 0.164616i \(0.0526385\pi\)
−0.986358 + 0.164616i \(0.947361\pi\)
\(572\) 274188. + 736.182i 0.838023 + 0.00225005i
\(573\) 0 0
\(574\) 407259. 406167.i 1.23608 1.23277i
\(575\) 163364.i 0.494108i
\(576\) 0 0
\(577\) −114098. −0.342710 −0.171355 0.985209i \(-0.554814\pi\)
−0.171355 + 0.985209i \(0.554814\pi\)
\(578\) −212801. 213373.i −0.636968 0.638681i
\(579\) 0 0
\(580\) 331.888 123610.i 0.000986587 0.367450i
\(581\) 476153. 1.41057
\(582\) 0 0
\(583\) 129727.i 0.381674i
\(584\) −249738. + 247734.i −0.732249 + 0.726374i
\(585\) 0 0
\(586\) −103499. 103777.i −0.301397 0.302208i
\(587\) 52235.3i 0.151596i 0.997123 + 0.0757980i \(0.0241504\pi\)
−0.997123 + 0.0757980i \(0.975850\pi\)
\(588\) 0 0
\(589\) −257038. −0.740912
\(590\) −38639.8 + 38536.2i −0.111002 + 0.110704i
\(591\) 0 0
\(592\) 409572. + 2199.38i 1.16866 + 0.00627562i
\(593\) −277354. −0.788724 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(594\) 0 0
\(595\) 274287.i 0.774767i
\(596\) −1064.16 + 396343.i −0.00299582 + 1.11578i
\(597\) 0 0
\(598\) 162441. 162005.i 0.454248 0.453030i
\(599\) 19107.2i 0.0532528i 0.999645 + 0.0266264i \(0.00847645\pi\)
−0.999645 + 0.0266264i \(0.991524\pi\)
\(600\) 0 0
\(601\) −418892. −1.15972 −0.579861 0.814716i \(-0.696893\pi\)
−0.579861 + 0.814716i \(0.696893\pi\)
\(602\) −368112. 369102.i −1.01575 1.01848i
\(603\) 0 0
\(604\) 163352. + 438.593i 0.447765 + 0.00120223i
\(605\) −53697.5 −0.146704
\(606\) 0 0
\(607\) 382383.i 1.03782i −0.854830 0.518909i \(-0.826338\pi\)
0.854830 0.518909i \(-0.173662\pi\)
\(608\) 294927. 290994.i 0.797826 0.787186i
\(609\) 0 0
\(610\) 197183. + 197713.i 0.529920 + 0.531345i
\(611\) 495450.i 1.32714i
\(612\) 0 0
\(613\) −210852. −0.561121 −0.280560 0.959836i \(-0.590520\pi\)
−0.280560 + 0.959836i \(0.590520\pi\)
\(614\) 33046.7 32958.1i 0.0876579 0.0874229i
\(615\) 0 0
\(616\) 266378. 264241.i 0.702000 0.696368i
\(617\) −626580. −1.64591 −0.822955 0.568106i \(-0.807676\pi\)
−0.822955 + 0.568106i \(0.807676\pi\)
\(618\) 0 0
\(619\) 41204.9i 0.107539i 0.998553 + 0.0537697i \(0.0171237\pi\)
−0.998553 + 0.0537697i \(0.982876\pi\)
\(620\) −119825. 321.726i −0.311721 0.000836956i
\(621\) 0 0
\(622\) 12280.6 12247.7i 0.0317423 0.0316572i
\(623\) 53172.8i 0.136998i
\(624\) 0 0
\(625\) 149361. 0.382365
\(626\) −244326. 244983.i −0.623478 0.625155i
\(627\) 0 0
\(628\) 1244.66 463567.i 0.00315595 1.17542i
\(629\) −637678. −1.61176
\(630\) 0 0
\(631\) 150814.i 0.378777i 0.981902 + 0.189389i \(0.0606506\pi\)
−0.981902 + 0.189389i \(0.939349\pi\)
\(632\) 145150. + 146324.i 0.363399 + 0.366338i
\(633\) 0 0
\(634\) −69576.9 69764.0i −0.173096 0.173561i
\(635\) 189655.i 0.470345i
\(636\) 0 0
\(637\) 171782. 0.423348
\(638\) 186404. 185904.i 0.457946 0.456718i
\(639\) 0 0
\(640\) 137853. 135286.i 0.336555 0.330288i
\(641\) −428379. −1.04259 −0.521293 0.853378i \(-0.674550\pi\)
−0.521293 + 0.853378i \(0.674550\pi\)
\(642\) 0 0
\(643\) 85771.0i 0.207452i −0.994606 0.103726i \(-0.966923\pi\)
0.994606 0.103726i \(-0.0330766\pi\)
\(644\) 842.919 313941.i 0.00203242 0.756967i
\(645\) 0 0
\(646\) −456738. + 455513.i −1.09447 + 1.09153i
\(647\) 128368.i 0.306653i 0.988176 + 0.153327i \(0.0489986\pi\)
−0.988176 + 0.153327i \(0.951001\pi\)
\(648\) 0 0
\(649\) −116225. −0.275937
\(650\) −234255. 234885.i −0.554451 0.555942i
\(651\) 0 0
\(652\) −283781. 761.940i −0.667557 0.00179236i
\(653\) 465879. 1.09256 0.546282 0.837601i \(-0.316043\pi\)
0.546282 + 0.837601i \(0.316043\pi\)
\(654\) 0 0
\(655\) 246461.i 0.574468i
\(656\) 630587. + 3386.22i 1.46534 + 0.00786878i
\(657\) 0 0
\(658\) −478766. 480053.i −1.10579 1.10876i
\(659\) 351017.i 0.808271i −0.914699 0.404135i \(-0.867573\pi\)
0.914699 0.404135i \(-0.132427\pi\)
\(660\) 0 0
\(661\) −282262. −0.646026 −0.323013 0.946395i \(-0.604696\pi\)
−0.323013 + 0.946395i \(0.604696\pi\)
\(662\) −530375. + 528953.i −1.21023 + 1.20698i
\(663\) 0 0
\(664\) 367641. + 370614.i 0.833850 + 0.840594i
\(665\) 278442. 0.629638
\(666\) 0 0
\(667\) 220276.i 0.495125i
\(668\) 657015. + 1764.06i 1.47239 + 0.00395330i
\(669\) 0 0
\(670\) −118971. + 118652.i −0.265029 + 0.264318i
\(671\) 594704.i 1.32086i
\(672\) 0 0
\(673\) −797180. −1.76006 −0.880028 0.474922i \(-0.842476\pi\)
−0.880028 + 0.474922i \(0.842476\pi\)
\(674\) 285172. + 285939.i 0.627751 + 0.629438i
\(675\) 0 0
\(676\) −23.8647 + 8888.32i −5.22231e−5 + 0.0194503i
\(677\) −281346. −0.613852 −0.306926 0.951733i \(-0.599300\pi\)
−0.306926 + 0.951733i \(0.599300\pi\)
\(678\) 0 0
\(679\) 1.02793e6i 2.22958i
\(680\) −213491. + 211779.i −0.461703 + 0.457999i
\(681\) 0 0
\(682\) −180212. 180697.i −0.387450 0.388491i
\(683\) 687094.i 1.47291i 0.676489 + 0.736453i \(0.263501\pi\)
−0.676489 + 0.736453i \(0.736499\pi\)
\(684\) 0 0
\(685\) 55124.8 0.117480
\(686\) −230521. + 229903.i −0.489849 + 0.488535i
\(687\) 0 0
\(688\) 3068.96 571506.i 0.00648357 1.20738i
\(689\) 220414. 0.464303
\(690\) 0 0
\(691\) 329040.i 0.689116i −0.938765 0.344558i \(-0.888029\pi\)
0.938765 0.344558i \(-0.111971\pi\)
\(692\) 298.812 111291.i 0.000624002 0.232407i
\(693\) 0 0
\(694\) 495364. 494036.i 1.02850 1.02574i
\(695\) 109695.i 0.227100i
\(696\) 0 0
\(697\) −981786. −2.02093
\(698\) −123992. 124326.i −0.254498 0.255182i
\(699\) 0 0
\(700\) −453951. 1218.84i −0.926431 0.00248742i
\(701\) 961471. 1.95659 0.978296 0.207214i \(-0.0664395\pi\)
0.978296 + 0.207214i \(0.0664395\pi\)
\(702\) 0 0
\(703\) 647338.i 1.30985i
\(704\) 411345. + 3313.39i 0.829966 + 0.00668539i
\(705\) 0 0
\(706\) 439453. + 440635.i 0.881665 + 0.884035i
\(707\) 388830.i 0.777894i
\(708\) 0 0
\(709\) −598276. −1.19017 −0.595085 0.803663i \(-0.702882\pi\)
−0.595085 + 0.803663i \(0.702882\pi\)
\(710\) −188301. + 187796.i −0.373540 + 0.372538i
\(711\) 0 0
\(712\) −41387.1 + 41055.1i −0.0816404 + 0.0809854i
\(713\) −213531. −0.420032
\(714\) 0 0
\(715\) 202022.i 0.395171i
\(716\) −28071.9 75.3717i −0.0547578 0.000147022i
\(717\) 0 0
\(718\) 521141. 519744.i 1.01090 1.00819i
\(719\) 608601.i 1.17727i −0.808400 0.588633i \(-0.799666\pi\)
0.808400 0.588633i \(-0.200334\pi\)
\(720\) 0 0
\(721\) 394240. 0.758385
\(722\) 94305.1 + 94558.6i 0.180909 + 0.181396i
\(723\) 0 0
\(724\) 1881.09 700604.i 0.00358866 1.33658i
\(725\) −318513. −0.605970
\(726\) 0 0
\(727\) 458391.i 0.867296i 0.901082 + 0.433648i \(0.142774\pi\)
−0.901082 + 0.433648i \(0.857226\pi\)
\(728\) 448963. + 452594.i 0.847125 + 0.853976i
\(729\) 0 0
\(730\) −183023. 183515.i −0.343448 0.344371i
\(731\) 889801.i 1.66517i
\(732\) 0 0
\(733\) 70695.6 0.131578 0.0657892 0.997834i \(-0.479044\pi\)
0.0657892 + 0.997834i \(0.479044\pi\)
\(734\) −469868. + 468608.i −0.872135 + 0.869796i
\(735\) 0 0
\(736\) 245007. 241740.i 0.452297 0.446265i
\(737\) −357855. −0.658828
\(738\) 0 0
\(739\) 476430.i 0.872390i 0.899852 + 0.436195i \(0.143674\pi\)
−0.899852 + 0.436195i \(0.856326\pi\)
\(740\) −810.251 + 301775.i −0.00147964 + 0.551086i
\(741\) 0 0
\(742\) 213565. 212992.i 0.387901 0.386861i
\(743\) 126020.i 0.228277i −0.993465 0.114139i \(-0.963589\pi\)
0.993465 0.114139i \(-0.0364108\pi\)
\(744\) 0 0
\(745\) −292026. −0.526149
\(746\) −368106. 369095.i −0.661447 0.663225i
\(747\) 0 0
\(748\) −640448. 1719.57i −1.14467 0.00307339i
\(749\) 1795.45 0.00320045
\(750\) 0 0
\(751\) 204276.i 0.362191i −0.983465 0.181096i \(-0.942036\pi\)
0.983465 0.181096i \(-0.0579644\pi\)
\(752\) 3991.48 743300.i 0.00705827 1.31440i
\(753\) 0 0
\(754\) 315863. + 316712.i 0.555592 + 0.557086i
\(755\) 120358.i 0.211145i
\(756\) 0 0
\(757\) 588244. 1.02652 0.513258 0.858235i \(-0.328438\pi\)
0.513258 + 0.858235i \(0.328438\pi\)
\(758\) 123614. 123282.i 0.215144 0.214567i
\(759\) 0 0
\(760\) 214987. + 216725.i 0.372207 + 0.375217i
\(761\) 50737.5 0.0876113 0.0438056 0.999040i \(-0.486052\pi\)
0.0438056 + 0.999040i \(0.486052\pi\)
\(762\) 0 0
\(763\) 624116.i 1.07205i
\(764\) 635603. + 1706.56i 1.08893 + 0.00292372i
\(765\) 0 0
\(766\) 775685. 773605.i 1.32199 1.31844i
\(767\) 197474.i 0.335675i
\(768\) 0 0
\(769\) 882679. 1.49262 0.746312 0.665597i \(-0.231823\pi\)
0.746312 + 0.665597i \(0.231823\pi\)
\(770\) 195218. + 195743.i 0.329260 + 0.330146i
\(771\) 0 0
\(772\) 906.197 337509.i 0.00152051 0.566306i
\(773\) 100820. 0.168728 0.0843642 0.996435i \(-0.473114\pi\)
0.0843642 + 0.996435i \(0.473114\pi\)
\(774\) 0 0
\(775\) 308760.i 0.514065i
\(776\) −800090. + 793671.i −1.32866 + 1.31801i
\(777\) 0 0
\(778\) −692565. 694427.i −1.14420 1.14727i
\(779\) 996658.i 1.64237i
\(780\) 0 0
\(781\) −566393. −0.928573
\(782\) −379430. + 378412.i −0.620466 + 0.618802i
\(783\) 0 0
\(784\) 257716. + 1383.92i 0.419284 + 0.00225153i
\(785\) 341556. 0.554272
\(786\) 0 0