Properties

Label 7098.2.a.cr.1.6
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.48406561.1
Defining polynomial: \(x^{6} - 3 x^{5} - 17 x^{4} + 39 x^{3} + 111 x^{2} - 131 x - 281\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(-2.41496\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.41496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.41496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.41496 q^{10} -3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} +2.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} -1.00000 q^{18} +2.73858 q^{19} +2.41496 q^{20} -1.00000 q^{21} +3.24698 q^{22} -6.58012 q^{23} -1.00000 q^{24} +0.832022 q^{25} +1.00000 q^{27} -1.00000 q^{28} +6.22322 q^{29} -2.41496 q^{30} -2.72294 q^{31} -1.00000 q^{32} -3.24698 q^{33} -1.80194 q^{34} -2.41496 q^{35} +1.00000 q^{36} -8.93878 q^{37} -2.73858 q^{38} -2.41496 q^{40} -9.15862 q^{41} +1.00000 q^{42} -3.95322 q^{43} -3.24698 q^{44} +2.41496 q^{45} +6.58012 q^{46} -9.77289 q^{47} +1.00000 q^{48} +1.00000 q^{49} -0.832022 q^{50} +1.80194 q^{51} -10.3747 q^{53} -1.00000 q^{54} -7.84132 q^{55} +1.00000 q^{56} +2.73858 q^{57} -6.22322 q^{58} +4.50007 q^{59} +2.41496 q^{60} +6.94297 q^{61} +2.72294 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} +2.54486 q^{67} +1.80194 q^{68} -6.58012 q^{69} +2.41496 q^{70} +1.50961 q^{71} -1.00000 q^{72} +0.786291 q^{73} +8.93878 q^{74} +0.832022 q^{75} +2.73858 q^{76} +3.24698 q^{77} -2.41753 q^{79} +2.41496 q^{80} +1.00000 q^{81} +9.15862 q^{82} +3.51468 q^{83} -1.00000 q^{84} +4.35160 q^{85} +3.95322 q^{86} +6.22322 q^{87} +3.24698 q^{88} -10.9361 q^{89} -2.41496 q^{90} -6.58012 q^{92} -2.72294 q^{93} +9.77289 q^{94} +6.61356 q^{95} -1.00000 q^{96} -12.2904 q^{97} -1.00000 q^{98} -3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + 3q^{10} - 10q^{11} + 6q^{12} + 6q^{14} - 3q^{15} + 6q^{16} + 2q^{17} - 6q^{18} - 2q^{19} - 3q^{20} - 6q^{21} + 10q^{22} + 4q^{23} - 6q^{24} + 13q^{25} + 6q^{27} - 6q^{28} + 2q^{29} + 3q^{30} - 9q^{31} - 6q^{32} - 10q^{33} - 2q^{34} + 3q^{35} + 6q^{36} - 7q^{37} + 2q^{38} + 3q^{40} - 11q^{41} + 6q^{42} - 5q^{43} - 10q^{44} - 3q^{45} - 4q^{46} - 5q^{47} + 6q^{48} + 6q^{49} - 13q^{50} + 2q^{51} - 6q^{53} - 6q^{54} + 5q^{55} + 6q^{56} - 2q^{57} - 2q^{58} - 28q^{59} - 3q^{60} + 23q^{61} + 9q^{62} - 6q^{63} + 6q^{64} + 10q^{66} + 10q^{67} + 2q^{68} + 4q^{69} - 3q^{70} - 21q^{71} - 6q^{72} + 7q^{73} + 7q^{74} + 13q^{75} - 2q^{76} + 10q^{77} - 14q^{79} - 3q^{80} + 6q^{81} + 11q^{82} - 17q^{83} - 6q^{84} - q^{85} + 5q^{86} + 2q^{87} + 10q^{88} - 17q^{89} + 3q^{90} + 4q^{92} - 9q^{93} + 5q^{94} - 22q^{95} - 6q^{96} - 6q^{98} - 10q^{99} + O(q^{100}) \)

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 −0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 2.41496 1.08000 0.540001 0.841664i \(-0.318424\pi\)
0.540001 + 0.841664i \(0.318424\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.41496 −0.763677
\(11\) −3.24698 −0.979001 −0.489501 0.872003i \(-0.662821\pi\)
−0.489501 + 0.872003i \(0.662821\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) 2.41496 0.623539
\(16\) 1.00000 0.250000
\(17\) 1.80194 0.437034 0.218517 0.975833i \(-0.429878\pi\)
0.218517 + 0.975833i \(0.429878\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.73858 0.628274 0.314137 0.949378i \(-0.398285\pi\)
0.314137 + 0.949378i \(0.398285\pi\)
\(20\) 2.41496 0.540001
\(21\) −1.00000 −0.218218
\(22\) 3.24698 0.692258
\(23\) −6.58012 −1.37205 −0.686025 0.727578i \(-0.740646\pi\)
−0.686025 + 0.727578i \(0.740646\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0.832022 0.166404
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 6.22322 1.15562 0.577812 0.816170i \(-0.303907\pi\)
0.577812 + 0.816170i \(0.303907\pi\)
\(30\) −2.41496 −0.440909
\(31\) −2.72294 −0.489054 −0.244527 0.969643i \(-0.578633\pi\)
−0.244527 + 0.969643i \(0.578633\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.24698 −0.565227
\(34\) −1.80194 −0.309030
\(35\) −2.41496 −0.408202
\(36\) 1.00000 0.166667
\(37\) −8.93878 −1.46953 −0.734764 0.678323i \(-0.762707\pi\)
−0.734764 + 0.678323i \(0.762707\pi\)
\(38\) −2.73858 −0.444257
\(39\) 0 0
\(40\) −2.41496 −0.381838
\(41\) −9.15862 −1.43034 −0.715168 0.698953i \(-0.753650\pi\)
−0.715168 + 0.698953i \(0.753650\pi\)
\(42\) 1.00000 0.154303
\(43\) −3.95322 −0.602861 −0.301430 0.953488i \(-0.597464\pi\)
−0.301430 + 0.953488i \(0.597464\pi\)
\(44\) −3.24698 −0.489501
\(45\) 2.41496 0.360001
\(46\) 6.58012 0.970186
\(47\) −9.77289 −1.42552 −0.712761 0.701407i \(-0.752556\pi\)
−0.712761 + 0.701407i \(0.752556\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −0.832022 −0.117666
\(51\) 1.80194 0.252322
\(52\) 0 0
\(53\) −10.3747 −1.42507 −0.712536 0.701636i \(-0.752453\pi\)
−0.712536 + 0.701636i \(0.752453\pi\)
\(54\) −1.00000 −0.136083
\(55\) −7.84132 −1.05732
\(56\) 1.00000 0.133631
\(57\) 2.73858 0.362734
\(58\) −6.22322 −0.817149
\(59\) 4.50007 0.585859 0.292930 0.956134i \(-0.405370\pi\)
0.292930 + 0.956134i \(0.405370\pi\)
\(60\) 2.41496 0.311770
\(61\) 6.94297 0.888957 0.444478 0.895790i \(-0.353389\pi\)
0.444478 + 0.895790i \(0.353389\pi\)
\(62\) 2.72294 0.345813
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.24698 0.399676
\(67\) 2.54486 0.310904 0.155452 0.987843i \(-0.450317\pi\)
0.155452 + 0.987843i \(0.450317\pi\)
\(68\) 1.80194 0.218517
\(69\) −6.58012 −0.792153
\(70\) 2.41496 0.288643
\(71\) 1.50961 0.179157 0.0895787 0.995980i \(-0.471448\pi\)
0.0895787 + 0.995980i \(0.471448\pi\)
\(72\) −1.00000 −0.117851
\(73\) 0.786291 0.0920283 0.0460142 0.998941i \(-0.485348\pi\)
0.0460142 + 0.998941i \(0.485348\pi\)
\(74\) 8.93878 1.03911
\(75\) 0.832022 0.0960736
\(76\) 2.73858 0.314137
\(77\) 3.24698 0.370028
\(78\) 0 0
\(79\) −2.41753 −0.271993 −0.135997 0.990709i \(-0.543424\pi\)
−0.135997 + 0.990709i \(0.543424\pi\)
\(80\) 2.41496 0.270001
\(81\) 1.00000 0.111111
\(82\) 9.15862 1.01140
\(83\) 3.51468 0.385786 0.192893 0.981220i \(-0.438213\pi\)
0.192893 + 0.981220i \(0.438213\pi\)
\(84\) −1.00000 −0.109109
\(85\) 4.35160 0.471998
\(86\) 3.95322 0.426287
\(87\) 6.22322 0.667200
\(88\) 3.24698 0.346129
\(89\) −10.9361 −1.15922 −0.579610 0.814894i \(-0.696795\pi\)
−0.579610 + 0.814894i \(0.696795\pi\)
\(90\) −2.41496 −0.254559
\(91\) 0 0
\(92\) −6.58012 −0.686025
\(93\) −2.72294 −0.282355
\(94\) 9.77289 1.00800
\(95\) 6.61356 0.678537
\(96\) −1.00000 −0.102062
\(97\) −12.2904 −1.24790 −0.623950 0.781464i \(-0.714473\pi\)
−0.623950 + 0.781464i \(0.714473\pi\)
\(98\) −1.00000 −0.101015
\(99\) −3.24698 −0.326334
\(100\) 0.832022 0.0832022
\(101\) 15.5746 1.54973 0.774866 0.632126i \(-0.217817\pi\)
0.774866 + 0.632126i \(0.217817\pi\)
\(102\) −1.80194 −0.178418
\(103\) 3.71813 0.366358 0.183179 0.983080i \(-0.441361\pi\)
0.183179 + 0.983080i \(0.441361\pi\)
\(104\) 0 0
\(105\) −2.41496 −0.235676
\(106\) 10.3747 1.00768
\(107\) −0.125781 −0.0121597 −0.00607983 0.999982i \(-0.501935\pi\)
−0.00607983 + 0.999982i \(0.501935\pi\)
\(108\) 1.00000 0.0962250
\(109\) −3.84276 −0.368070 −0.184035 0.982920i \(-0.558916\pi\)
−0.184035 + 0.982920i \(0.558916\pi\)
\(110\) 7.84132 0.747640
\(111\) −8.93878 −0.848432
\(112\) −1.00000 −0.0944911
\(113\) 12.7648 1.20082 0.600408 0.799694i \(-0.295005\pi\)
0.600408 + 0.799694i \(0.295005\pi\)
\(114\) −2.73858 −0.256492
\(115\) −15.8907 −1.48182
\(116\) 6.22322 0.577812
\(117\) 0 0
\(118\) −4.50007 −0.414265
\(119\) −1.80194 −0.165183
\(120\) −2.41496 −0.220454
\(121\) −0.457123 −0.0415567
\(122\) −6.94297 −0.628587
\(123\) −9.15862 −0.825805
\(124\) −2.72294 −0.244527
\(125\) −10.0655 −0.900285
\(126\) 1.00000 0.0890871
\(127\) −11.7970 −1.04682 −0.523408 0.852082i \(-0.675340\pi\)
−0.523408 + 0.852082i \(0.675340\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.95322 −0.348062
\(130\) 0 0
\(131\) −16.5193 −1.44330 −0.721649 0.692259i \(-0.756615\pi\)
−0.721649 + 0.692259i \(0.756615\pi\)
\(132\) −3.24698 −0.282613
\(133\) −2.73858 −0.237465
\(134\) −2.54486 −0.219843
\(135\) 2.41496 0.207846
\(136\) −1.80194 −0.154515
\(137\) −11.5650 −0.988068 −0.494034 0.869443i \(-0.664478\pi\)
−0.494034 + 0.869443i \(0.664478\pi\)
\(138\) 6.58012 0.560137
\(139\) −2.63433 −0.223441 −0.111720 0.993740i \(-0.535636\pi\)
−0.111720 + 0.993740i \(0.535636\pi\)
\(140\) −2.41496 −0.204101
\(141\) −9.77289 −0.823026
\(142\) −1.50961 −0.126683
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 15.0288 1.24808
\(146\) −0.786291 −0.0650739
\(147\) 1.00000 0.0824786
\(148\) −8.93878 −0.734764
\(149\) 19.3553 1.58565 0.792825 0.609450i \(-0.208609\pi\)
0.792825 + 0.609450i \(0.208609\pi\)
\(150\) −0.832022 −0.0679343
\(151\) −9.50760 −0.773717 −0.386859 0.922139i \(-0.626440\pi\)
−0.386859 + 0.922139i \(0.626440\pi\)
\(152\) −2.73858 −0.222128
\(153\) 1.80194 0.145678
\(154\) −3.24698 −0.261649
\(155\) −6.57578 −0.528179
\(156\) 0 0
\(157\) 2.70530 0.215907 0.107953 0.994156i \(-0.465570\pi\)
0.107953 + 0.994156i \(0.465570\pi\)
\(158\) 2.41753 0.192328
\(159\) −10.3747 −0.822766
\(160\) −2.41496 −0.190919
\(161\) 6.58012 0.518586
\(162\) −1.00000 −0.0785674
\(163\) 6.79361 0.532117 0.266058 0.963957i \(-0.414279\pi\)
0.266058 + 0.963957i \(0.414279\pi\)
\(164\) −9.15862 −0.715168
\(165\) −7.84132 −0.610446
\(166\) −3.51468 −0.272792
\(167\) −17.9654 −1.39020 −0.695101 0.718912i \(-0.744640\pi\)
−0.695101 + 0.718912i \(0.744640\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) −4.35160 −0.333753
\(171\) 2.73858 0.209425
\(172\) −3.95322 −0.301430
\(173\) −7.21332 −0.548418 −0.274209 0.961670i \(-0.588416\pi\)
−0.274209 + 0.961670i \(0.588416\pi\)
\(174\) −6.22322 −0.471781
\(175\) −0.832022 −0.0628949
\(176\) −3.24698 −0.244750
\(177\) 4.50007 0.338246
\(178\) 10.9361 0.819693
\(179\) 3.27893 0.245079 0.122539 0.992464i \(-0.460896\pi\)
0.122539 + 0.992464i \(0.460896\pi\)
\(180\) 2.41496 0.180000
\(181\) 21.0091 1.56160 0.780798 0.624783i \(-0.214813\pi\)
0.780798 + 0.624783i \(0.214813\pi\)
\(182\) 0 0
\(183\) 6.94297 0.513239
\(184\) 6.58012 0.485093
\(185\) −21.5868 −1.58709
\(186\) 2.72294 0.199655
\(187\) −5.85086 −0.427857
\(188\) −9.77289 −0.712761
\(189\) −1.00000 −0.0727393
\(190\) −6.61356 −0.479798
\(191\) −6.15290 −0.445208 −0.222604 0.974909i \(-0.571456\pi\)
−0.222604 + 0.974909i \(0.571456\pi\)
\(192\) 1.00000 0.0721688
\(193\) 18.6232 1.34053 0.670265 0.742122i \(-0.266181\pi\)
0.670265 + 0.742122i \(0.266181\pi\)
\(194\) 12.2904 0.882398
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −16.8553 −1.20089 −0.600443 0.799667i \(-0.705009\pi\)
−0.600443 + 0.799667i \(0.705009\pi\)
\(198\) 3.24698 0.230753
\(199\) 12.3376 0.874589 0.437295 0.899318i \(-0.355937\pi\)
0.437295 + 0.899318i \(0.355937\pi\)
\(200\) −0.832022 −0.0588328
\(201\) 2.54486 0.179501
\(202\) −15.5746 −1.09583
\(203\) −6.22322 −0.436785
\(204\) 1.80194 0.126161
\(205\) −22.1177 −1.54477
\(206\) −3.71813 −0.259055
\(207\) −6.58012 −0.457350
\(208\) 0 0
\(209\) −8.89213 −0.615081
\(210\) 2.41496 0.166648
\(211\) −15.6160 −1.07505 −0.537525 0.843248i \(-0.680641\pi\)
−0.537525 + 0.843248i \(0.680641\pi\)
\(212\) −10.3747 −0.712536
\(213\) 1.50961 0.103437
\(214\) 0.125781 0.00859818
\(215\) −9.54686 −0.651091
\(216\) −1.00000 −0.0680414
\(217\) 2.72294 0.184845
\(218\) 3.84276 0.260264
\(219\) 0.786291 0.0531326
\(220\) −7.84132 −0.528662
\(221\) 0 0
\(222\) 8.93878 0.599932
\(223\) −5.53203 −0.370452 −0.185226 0.982696i \(-0.559302\pi\)
−0.185226 + 0.982696i \(0.559302\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0.832022 0.0554681
\(226\) −12.7648 −0.849105
\(227\) −20.4532 −1.35753 −0.678763 0.734357i \(-0.737484\pi\)
−0.678763 + 0.734357i \(0.737484\pi\)
\(228\) 2.73858 0.181367
\(229\) 29.0317 1.91847 0.959234 0.282612i \(-0.0912010\pi\)
0.959234 + 0.282612i \(0.0912010\pi\)
\(230\) 15.8907 1.04780
\(231\) 3.24698 0.213636
\(232\) −6.22322 −0.408575
\(233\) 12.4742 0.817211 0.408605 0.912711i \(-0.366015\pi\)
0.408605 + 0.912711i \(0.366015\pi\)
\(234\) 0 0
\(235\) −23.6011 −1.53957
\(236\) 4.50007 0.292930
\(237\) −2.41753 −0.157035
\(238\) 1.80194 0.116802
\(239\) 23.3225 1.50861 0.754303 0.656527i \(-0.227975\pi\)
0.754303 + 0.656527i \(0.227975\pi\)
\(240\) 2.41496 0.155885
\(241\) −28.8105 −1.85584 −0.927922 0.372773i \(-0.878407\pi\)
−0.927922 + 0.372773i \(0.878407\pi\)
\(242\) 0.457123 0.0293850
\(243\) 1.00000 0.0641500
\(244\) 6.94297 0.444478
\(245\) 2.41496 0.154286
\(246\) 9.15862 0.583932
\(247\) 0 0
\(248\) 2.72294 0.172907
\(249\) 3.51468 0.222734
\(250\) 10.0655 0.636598
\(251\) 1.56870 0.0990152 0.0495076 0.998774i \(-0.484235\pi\)
0.0495076 + 0.998774i \(0.484235\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 21.3655 1.34324
\(254\) 11.7970 0.740211
\(255\) 4.35160 0.272508
\(256\) 1.00000 0.0625000
\(257\) −14.0911 −0.878981 −0.439491 0.898247i \(-0.644841\pi\)
−0.439491 + 0.898247i \(0.644841\pi\)
\(258\) 3.95322 0.246117
\(259\) 8.93878 0.555429
\(260\) 0 0
\(261\) 6.22322 0.385208
\(262\) 16.5193 1.02057
\(263\) −6.63837 −0.409339 −0.204670 0.978831i \(-0.565612\pi\)
−0.204670 + 0.978831i \(0.565612\pi\)
\(264\) 3.24698 0.199838
\(265\) −25.0544 −1.53908
\(266\) 2.73858 0.167913
\(267\) −10.9361 −0.669276
\(268\) 2.54486 0.155452
\(269\) 18.0426 1.10007 0.550037 0.835140i \(-0.314614\pi\)
0.550037 + 0.835140i \(0.314614\pi\)
\(270\) −2.41496 −0.146970
\(271\) −12.0877 −0.734277 −0.367139 0.930166i \(-0.619663\pi\)
−0.367139 + 0.930166i \(0.619663\pi\)
\(272\) 1.80194 0.109259
\(273\) 0 0
\(274\) 11.5650 0.698670
\(275\) −2.70156 −0.162910
\(276\) −6.58012 −0.396077
\(277\) 30.1936 1.81416 0.907080 0.420958i \(-0.138306\pi\)
0.907080 + 0.420958i \(0.138306\pi\)
\(278\) 2.63433 0.157997
\(279\) −2.72294 −0.163018
\(280\) 2.41496 0.144321
\(281\) −20.4356 −1.21909 −0.609543 0.792753i \(-0.708647\pi\)
−0.609543 + 0.792753i \(0.708647\pi\)
\(282\) 9.77289 0.581967
\(283\) −4.01876 −0.238890 −0.119445 0.992841i \(-0.538112\pi\)
−0.119445 + 0.992841i \(0.538112\pi\)
\(284\) 1.50961 0.0895787
\(285\) 6.61356 0.391754
\(286\) 0 0
\(287\) 9.15862 0.540616
\(288\) −1.00000 −0.0589256
\(289\) −13.7530 −0.809001
\(290\) −15.0288 −0.882523
\(291\) −12.2904 −0.720475
\(292\) 0.786291 0.0460142
\(293\) −19.3490 −1.13038 −0.565191 0.824960i \(-0.691198\pi\)
−0.565191 + 0.824960i \(0.691198\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 10.8675 0.632729
\(296\) 8.93878 0.519556
\(297\) −3.24698 −0.188409
\(298\) −19.3553 −1.12122
\(299\) 0 0
\(300\) 0.832022 0.0480368
\(301\) 3.95322 0.227860
\(302\) 9.50760 0.547101
\(303\) 15.5746 0.894738
\(304\) 2.73858 0.157069
\(305\) 16.7670 0.960075
\(306\) −1.80194 −0.103010
\(307\) −5.04050 −0.287677 −0.143838 0.989601i \(-0.545945\pi\)
−0.143838 + 0.989601i \(0.545945\pi\)
\(308\) 3.24698 0.185014
\(309\) 3.71813 0.211517
\(310\) 6.57578 0.373479
\(311\) −16.2638 −0.922235 −0.461117 0.887339i \(-0.652551\pi\)
−0.461117 + 0.887339i \(0.652551\pi\)
\(312\) 0 0
\(313\) −8.80560 −0.497722 −0.248861 0.968539i \(-0.580056\pi\)
−0.248861 + 0.968539i \(0.580056\pi\)
\(314\) −2.70530 −0.152669
\(315\) −2.41496 −0.136067
\(316\) −2.41753 −0.135997
\(317\) −20.0495 −1.12609 −0.563047 0.826425i \(-0.690371\pi\)
−0.563047 + 0.826425i \(0.690371\pi\)
\(318\) 10.3747 0.581783
\(319\) −20.2067 −1.13136
\(320\) 2.41496 0.135000
\(321\) −0.125781 −0.00702039
\(322\) −6.58012 −0.366696
\(323\) 4.93476 0.274577
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.79361 −0.376263
\(327\) −3.84276 −0.212505
\(328\) 9.15862 0.505700
\(329\) 9.77289 0.538797
\(330\) 7.84132 0.431650
\(331\) 19.0732 1.04836 0.524180 0.851607i \(-0.324372\pi\)
0.524180 + 0.851607i \(0.324372\pi\)
\(332\) 3.51468 0.192893
\(333\) −8.93878 −0.489842
\(334\) 17.9654 0.983021
\(335\) 6.14573 0.335777
\(336\) −1.00000 −0.0545545
\(337\) 14.8542 0.809159 0.404580 0.914503i \(-0.367418\pi\)
0.404580 + 0.914503i \(0.367418\pi\)
\(338\) 0 0
\(339\) 12.7648 0.693291
\(340\) 4.35160 0.235999
\(341\) 8.84132 0.478784
\(342\) −2.73858 −0.148086
\(343\) −1.00000 −0.0539949
\(344\) 3.95322 0.213143
\(345\) −15.8907 −0.855527
\(346\) 7.21332 0.387790
\(347\) 26.6896 1.43277 0.716386 0.697704i \(-0.245795\pi\)
0.716386 + 0.697704i \(0.245795\pi\)
\(348\) 6.22322 0.333600
\(349\) 31.8560 1.70521 0.852607 0.522552i \(-0.175020\pi\)
0.852607 + 0.522552i \(0.175020\pi\)
\(350\) 0.832022 0.0444734
\(351\) 0 0
\(352\) 3.24698 0.173065
\(353\) 3.52242 0.187480 0.0937398 0.995597i \(-0.470118\pi\)
0.0937398 + 0.995597i \(0.470118\pi\)
\(354\) −4.50007 −0.239176
\(355\) 3.64564 0.193490
\(356\) −10.9361 −0.579610
\(357\) −1.80194 −0.0953687
\(358\) −3.27893 −0.173297
\(359\) −24.0153 −1.26748 −0.633740 0.773546i \(-0.718481\pi\)
−0.633740 + 0.773546i \(0.718481\pi\)
\(360\) −2.41496 −0.127279
\(361\) −11.5002 −0.605272
\(362\) −21.0091 −1.10422
\(363\) −0.457123 −0.0239928
\(364\) 0 0
\(365\) 1.89886 0.0993908
\(366\) −6.94297 −0.362915
\(367\) −5.01103 −0.261574 −0.130787 0.991411i \(-0.541750\pi\)
−0.130787 + 0.991411i \(0.541750\pi\)
\(368\) −6.58012 −0.343012
\(369\) −9.15862 −0.476779
\(370\) 21.5868 1.12224
\(371\) 10.3747 0.538627
\(372\) −2.72294 −0.141178
\(373\) −12.2463 −0.634092 −0.317046 0.948410i \(-0.602691\pi\)
−0.317046 + 0.948410i \(0.602691\pi\)
\(374\) 5.85086 0.302541
\(375\) −10.0655 −0.519780
\(376\) 9.77289 0.503998
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 15.3669 0.789343 0.394672 0.918822i \(-0.370858\pi\)
0.394672 + 0.918822i \(0.370858\pi\)
\(380\) 6.61356 0.339269
\(381\) −11.7970 −0.604379
\(382\) 6.15290 0.314810
\(383\) −13.7125 −0.700675 −0.350338 0.936623i \(-0.613933\pi\)
−0.350338 + 0.936623i \(0.613933\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 7.84132 0.399631
\(386\) −18.6232 −0.947897
\(387\) −3.95322 −0.200954
\(388\) −12.2904 −0.623950
\(389\) 9.05551 0.459133 0.229566 0.973293i \(-0.426269\pi\)
0.229566 + 0.973293i \(0.426269\pi\)
\(390\) 0 0
\(391\) −11.8570 −0.599633
\(392\) −1.00000 −0.0505076
\(393\) −16.5193 −0.833288
\(394\) 16.8553 0.849155
\(395\) −5.83823 −0.293753
\(396\) −3.24698 −0.163167
\(397\) 20.8502 1.04644 0.523220 0.852198i \(-0.324731\pi\)
0.523220 + 0.852198i \(0.324731\pi\)
\(398\) −12.3376 −0.618428
\(399\) −2.73858 −0.137101
\(400\) 0.832022 0.0416011
\(401\) 19.6443 0.980988 0.490494 0.871445i \(-0.336816\pi\)
0.490494 + 0.871445i \(0.336816\pi\)
\(402\) −2.54486 −0.126926
\(403\) 0 0
\(404\) 15.5746 0.774866
\(405\) 2.41496 0.120000
\(406\) 6.22322 0.308853
\(407\) 29.0240 1.43867
\(408\) −1.80194 −0.0892092
\(409\) 2.96748 0.146733 0.0733663 0.997305i \(-0.476626\pi\)
0.0733663 + 0.997305i \(0.476626\pi\)
\(410\) 22.1177 1.09231
\(411\) −11.5650 −0.570461
\(412\) 3.71813 0.183179
\(413\) −4.50007 −0.221434
\(414\) 6.58012 0.323395
\(415\) 8.48781 0.416650
\(416\) 0 0
\(417\) −2.63433 −0.129004
\(418\) 8.89213 0.434928
\(419\) −0.255356 −0.0124750 −0.00623748 0.999981i \(-0.501985\pi\)
−0.00623748 + 0.999981i \(0.501985\pi\)
\(420\) −2.41496 −0.117838
\(421\) 36.2298 1.76573 0.882867 0.469623i \(-0.155610\pi\)
0.882867 + 0.469623i \(0.155610\pi\)
\(422\) 15.6160 0.760176
\(423\) −9.77289 −0.475174
\(424\) 10.3747 0.503839
\(425\) 1.49925 0.0727244
\(426\) −1.50961 −0.0731407
\(427\) −6.94297 −0.335994
\(428\) −0.125781 −0.00607983
\(429\) 0 0
\(430\) 9.54686 0.460391
\(431\) −26.6462 −1.28350 −0.641752 0.766913i \(-0.721792\pi\)
−0.641752 + 0.766913i \(0.721792\pi\)
\(432\) 1.00000 0.0481125
\(433\) −30.6061 −1.47083 −0.735417 0.677615i \(-0.763014\pi\)
−0.735417 + 0.677615i \(0.763014\pi\)
\(434\) −2.72294 −0.130705
\(435\) 15.0288 0.720577
\(436\) −3.84276 −0.184035
\(437\) −18.0202 −0.862023
\(438\) −0.786291 −0.0375704
\(439\) −11.4091 −0.544525 −0.272262 0.962223i \(-0.587772\pi\)
−0.272262 + 0.962223i \(0.587772\pi\)
\(440\) 7.84132 0.373820
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 38.5387 1.83103 0.915515 0.402283i \(-0.131783\pi\)
0.915515 + 0.402283i \(0.131783\pi\)
\(444\) −8.93878 −0.424216
\(445\) −26.4101 −1.25196
\(446\) 5.53203 0.261949
\(447\) 19.3553 0.915475
\(448\) −1.00000 −0.0472456
\(449\) 2.16519 0.102182 0.0510908 0.998694i \(-0.483730\pi\)
0.0510908 + 0.998694i \(0.483730\pi\)
\(450\) −0.832022 −0.0392219
\(451\) 29.7378 1.40030
\(452\) 12.7648 0.600408
\(453\) −9.50760 −0.446706
\(454\) 20.4532 0.959917
\(455\) 0 0
\(456\) −2.73858 −0.128246
\(457\) 31.4845 1.47278 0.736392 0.676555i \(-0.236528\pi\)
0.736392 + 0.676555i \(0.236528\pi\)
\(458\) −29.0317 −1.35656
\(459\) 1.80194 0.0841073
\(460\) −15.8907 −0.740908
\(461\) −7.94726 −0.370141 −0.185070 0.982725i \(-0.559251\pi\)
−0.185070 + 0.982725i \(0.559251\pi\)
\(462\) −3.24698 −0.151063
\(463\) −12.1131 −0.562943 −0.281471 0.959570i \(-0.590822\pi\)
−0.281471 + 0.959570i \(0.590822\pi\)
\(464\) 6.22322 0.288906
\(465\) −6.57578 −0.304944
\(466\) −12.4742 −0.577855
\(467\) −1.69520 −0.0784446 −0.0392223 0.999231i \(-0.512488\pi\)
−0.0392223 + 0.999231i \(0.512488\pi\)
\(468\) 0 0
\(469\) −2.54486 −0.117511
\(470\) 23.6011 1.08864
\(471\) 2.70530 0.124654
\(472\) −4.50007 −0.207133
\(473\) 12.8360 0.590201
\(474\) 2.41753 0.111041
\(475\) 2.27856 0.104548
\(476\) −1.80194 −0.0825917
\(477\) −10.3747 −0.475024
\(478\) −23.3225 −1.06675
\(479\) −3.59340 −0.164187 −0.0820933 0.996625i \(-0.526161\pi\)
−0.0820933 + 0.996625i \(0.526161\pi\)
\(480\) −2.41496 −0.110227
\(481\) 0 0
\(482\) 28.8105 1.31228
\(483\) 6.58012 0.299406
\(484\) −0.457123 −0.0207783
\(485\) −29.6808 −1.34773
\(486\) −1.00000 −0.0453609
\(487\) 4.79109 0.217105 0.108552 0.994091i \(-0.465378\pi\)
0.108552 + 0.994091i \(0.465378\pi\)
\(488\) −6.94297 −0.314294
\(489\) 6.79361 0.307218
\(490\) −2.41496 −0.109097
\(491\) −42.3139 −1.90960 −0.954800 0.297250i \(-0.903931\pi\)
−0.954800 + 0.297250i \(0.903931\pi\)
\(492\) −9.15862 −0.412902
\(493\) 11.2139 0.505047
\(494\) 0 0
\(495\) −7.84132 −0.352441
\(496\) −2.72294 −0.122263
\(497\) −1.50961 −0.0677151
\(498\) −3.51468 −0.157497
\(499\) −26.4820 −1.18550 −0.592749 0.805387i \(-0.701958\pi\)
−0.592749 + 0.805387i \(0.701958\pi\)
\(500\) −10.0655 −0.450142
\(501\) −17.9654 −0.802633
\(502\) −1.56870 −0.0700143
\(503\) 16.9580 0.756121 0.378060 0.925781i \(-0.376591\pi\)
0.378060 + 0.925781i \(0.376591\pi\)
\(504\) 1.00000 0.0445435
\(505\) 37.6120 1.67371
\(506\) −21.3655 −0.949813
\(507\) 0 0
\(508\) −11.7970 −0.523408
\(509\) 3.29901 0.146226 0.0731129 0.997324i \(-0.476707\pi\)
0.0731129 + 0.997324i \(0.476707\pi\)
\(510\) −4.35160 −0.192692
\(511\) −0.786291 −0.0347834
\(512\) −1.00000 −0.0441942
\(513\) 2.73858 0.120911
\(514\) 14.0911 0.621534
\(515\) 8.97913 0.395668
\(516\) −3.95322 −0.174031
\(517\) 31.7324 1.39559
\(518\) −8.93878 −0.392748
\(519\) −7.21332 −0.316630
\(520\) 0 0
\(521\) −3.85188 −0.168754 −0.0843770 0.996434i \(-0.526890\pi\)
−0.0843770 + 0.996434i \(0.526890\pi\)
\(522\) −6.22322 −0.272383
\(523\) −13.8862 −0.607201 −0.303601 0.952799i \(-0.598189\pi\)
−0.303601 + 0.952799i \(0.598189\pi\)
\(524\) −16.5193 −0.721649
\(525\) −0.832022 −0.0363124
\(526\) 6.63837 0.289447
\(527\) −4.90656 −0.213733
\(528\) −3.24698 −0.141307
\(529\) 20.2980 0.882521
\(530\) 25.0544 1.08829
\(531\) 4.50007 0.195286
\(532\) −2.73858 −0.118733
\(533\) 0 0
\(534\) 10.9361 0.473250
\(535\) −0.303755 −0.0131325
\(536\) −2.54486 −0.109921
\(537\) 3.27893 0.141496
\(538\) −18.0426 −0.777870
\(539\) −3.24698 −0.139857
\(540\) 2.41496 0.103923
\(541\) −5.36925 −0.230842 −0.115421 0.993317i \(-0.536822\pi\)
−0.115421 + 0.993317i \(0.536822\pi\)
\(542\) 12.0877 0.519212
\(543\) 21.0091 0.901588
\(544\) −1.80194 −0.0772574
\(545\) −9.28010 −0.397516
\(546\) 0 0
\(547\) −46.0980 −1.97101 −0.985504 0.169653i \(-0.945735\pi\)
−0.985504 + 0.169653i \(0.945735\pi\)
\(548\) −11.5650 −0.494034
\(549\) 6.94297 0.296319
\(550\) 2.70156 0.115195
\(551\) 17.0428 0.726049
\(552\) 6.58012 0.280068
\(553\) 2.41753 0.102804
\(554\) −30.1936 −1.28281
\(555\) −21.5868 −0.916308
\(556\) −2.63433 −0.111720
\(557\) −15.3154 −0.648936 −0.324468 0.945897i \(-0.605185\pi\)
−0.324468 + 0.945897i \(0.605185\pi\)
\(558\) 2.72294 0.115271
\(559\) 0 0
\(560\) −2.41496 −0.102051
\(561\) −5.85086 −0.247023
\(562\) 20.4356 0.862023
\(563\) −8.13781 −0.342968 −0.171484 0.985187i \(-0.554856\pi\)
−0.171484 + 0.985187i \(0.554856\pi\)
\(564\) −9.77289 −0.411513
\(565\) 30.8266 1.29688
\(566\) 4.01876 0.168921
\(567\) −1.00000 −0.0419961
\(568\) −1.50961 −0.0633417
\(569\) −15.9128 −0.667099 −0.333550 0.942733i \(-0.608246\pi\)
−0.333550 + 0.942733i \(0.608246\pi\)
\(570\) −6.61356 −0.277012
\(571\) 29.3918 1.23001 0.615004 0.788524i \(-0.289154\pi\)
0.615004 + 0.788524i \(0.289154\pi\)
\(572\) 0 0
\(573\) −6.15290 −0.257041
\(574\) −9.15862 −0.382273
\(575\) −5.47480 −0.228315
\(576\) 1.00000 0.0416667
\(577\) 22.0602 0.918377 0.459188 0.888339i \(-0.348140\pi\)
0.459188 + 0.888339i \(0.348140\pi\)
\(578\) 13.7530 0.572050
\(579\) 18.6232 0.773955
\(580\) 15.0288 0.624038
\(581\) −3.51468 −0.145814
\(582\) 12.2904 0.509453
\(583\) 33.6864 1.39515
\(584\) −0.786291 −0.0325369
\(585\) 0 0
\(586\) 19.3490 0.799301
\(587\) −42.3330 −1.74727 −0.873634 0.486583i \(-0.838243\pi\)
−0.873634 + 0.486583i \(0.838243\pi\)
\(588\) 1.00000 0.0412393
\(589\) −7.45699 −0.307260
\(590\) −10.8675 −0.447407
\(591\) −16.8553 −0.693332
\(592\) −8.93878 −0.367382
\(593\) 13.0257 0.534903 0.267451 0.963571i \(-0.413818\pi\)
0.267451 + 0.963571i \(0.413818\pi\)
\(594\) 3.24698 0.133225
\(595\) −4.35160 −0.178398
\(596\) 19.3553 0.792825
\(597\) 12.3376 0.504944
\(598\) 0 0
\(599\) −28.1604 −1.15060 −0.575301 0.817941i \(-0.695115\pi\)
−0.575301 + 0.817941i \(0.695115\pi\)
\(600\) −0.832022 −0.0339671
\(601\) 26.9245 1.09827 0.549136 0.835733i \(-0.314957\pi\)
0.549136 + 0.835733i \(0.314957\pi\)
\(602\) −3.95322 −0.161121
\(603\) 2.54486 0.103635
\(604\) −9.50760 −0.386859
\(605\) −1.10393 −0.0448813
\(606\) −15.5746 −0.632675
\(607\) 19.1584 0.777617 0.388808 0.921319i \(-0.372887\pi\)
0.388808 + 0.921319i \(0.372887\pi\)
\(608\) −2.73858 −0.111064
\(609\) −6.22322 −0.252178
\(610\) −16.7670 −0.678876
\(611\) 0 0
\(612\) 1.80194 0.0728390
\(613\) 3.78753 0.152977 0.0764884 0.997070i \(-0.475629\pi\)
0.0764884 + 0.997070i \(0.475629\pi\)
\(614\) 5.04050 0.203418
\(615\) −22.1177 −0.891871
\(616\) −3.24698 −0.130825
\(617\) 24.0329 0.967527 0.483764 0.875199i \(-0.339269\pi\)
0.483764 + 0.875199i \(0.339269\pi\)
\(618\) −3.71813 −0.149565
\(619\) 44.5020 1.78869 0.894344 0.447381i \(-0.147643\pi\)
0.894344 + 0.447381i \(0.147643\pi\)
\(620\) −6.57578 −0.264090
\(621\) −6.58012 −0.264051
\(622\) 16.2638 0.652118
\(623\) 10.9361 0.438144
\(624\) 0 0
\(625\) −28.4678 −1.13871
\(626\) 8.80560 0.351943
\(627\) −8.89213 −0.355117
\(628\) 2.70530 0.107953
\(629\) −16.1071 −0.642233
\(630\) 2.41496 0.0962142
\(631\) 26.0186 1.03579 0.517893 0.855446i \(-0.326717\pi\)
0.517893 + 0.855446i \(0.326717\pi\)
\(632\) 2.41753 0.0961642
\(633\) −15.6160 −0.620681
\(634\) 20.0495 0.796269
\(635\) −28.4893 −1.13056
\(636\) −10.3747 −0.411383
\(637\) 0 0
\(638\) 20.2067 0.799990
\(639\) 1.50961 0.0597191
\(640\) −2.41496 −0.0954596
\(641\) −37.8504 −1.49500 −0.747500 0.664261i \(-0.768746\pi\)
−0.747500 + 0.664261i \(0.768746\pi\)
\(642\) 0.125781 0.00496416
\(643\) −26.4910 −1.04470 −0.522351 0.852731i \(-0.674945\pi\)
−0.522351 + 0.852731i \(0.674945\pi\)
\(644\) 6.58012 0.259293
\(645\) −9.54686 −0.375907
\(646\) −4.93476 −0.194155
\(647\) −34.8792 −1.37124 −0.685621 0.727959i \(-0.740469\pi\)
−0.685621 + 0.727959i \(0.740469\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −14.6116 −0.573557
\(650\) 0 0
\(651\) 2.72294 0.106720
\(652\) 6.79361 0.266058
\(653\) 0.351211 0.0137439 0.00687197 0.999976i \(-0.497813\pi\)
0.00687197 + 0.999976i \(0.497813\pi\)
\(654\) 3.84276 0.150264
\(655\) −39.8934 −1.55876
\(656\) −9.15862 −0.357584
\(657\) 0.786291 0.0306761
\(658\) −9.77289 −0.380987
\(659\) 10.6161 0.413545 0.206773 0.978389i \(-0.433704\pi\)
0.206773 + 0.978389i \(0.433704\pi\)
\(660\) −7.84132 −0.305223
\(661\) 45.2269 1.75912 0.879561 0.475786i \(-0.157836\pi\)
0.879561 + 0.475786i \(0.157836\pi\)
\(662\) −19.0732 −0.741303
\(663\) 0 0
\(664\) −3.51468 −0.136396
\(665\) −6.61356 −0.256463
\(666\) 8.93878 0.346371
\(667\) −40.9496 −1.58557
\(668\) −17.9654 −0.695101
\(669\) −5.53203 −0.213881
\(670\) −6.14573 −0.237430
\(671\) −22.5437 −0.870290
\(672\) 1.00000 0.0385758
\(673\) 16.2910 0.627973 0.313986 0.949428i \(-0.398335\pi\)
0.313986 + 0.949428i \(0.398335\pi\)
\(674\) −14.8542 −0.572162
\(675\) 0.832022 0.0320245
\(676\) 0 0
\(677\) −29.8672 −1.14789 −0.573946 0.818893i \(-0.694588\pi\)
−0.573946 + 0.818893i \(0.694588\pi\)
\(678\) −12.7648 −0.490231
\(679\) 12.2904 0.471662
\(680\) −4.35160 −0.166876
\(681\) −20.4532 −0.783769
\(682\) −8.84132 −0.338552
\(683\) 3.26490 0.124928 0.0624640 0.998047i \(-0.480104\pi\)
0.0624640 + 0.998047i \(0.480104\pi\)
\(684\) 2.73858 0.104712
\(685\) −27.9291 −1.06712
\(686\) 1.00000 0.0381802
\(687\) 29.0317 1.10763
\(688\) −3.95322 −0.150715
\(689\) 0 0
\(690\) 15.8907 0.604949
\(691\) −38.2216 −1.45402 −0.727010 0.686627i \(-0.759090\pi\)
−0.727010 + 0.686627i \(0.759090\pi\)
\(692\) −7.21332 −0.274209
\(693\) 3.24698 0.123343
\(694\) −26.6896 −1.01312
\(695\) −6.36179 −0.241317
\(696\) −6.22322 −0.235891
\(697\) −16.5033 −0.625105
\(698\) −31.8560 −1.20577
\(699\) 12.4742 0.471817
\(700\) −0.832022 −0.0314475
\(701\) −16.1383 −0.609535 −0.304767 0.952427i \(-0.598579\pi\)
−0.304767 + 0.952427i \(0.598579\pi\)
\(702\) 0 0
\(703\) −24.4796 −0.923266
\(704\) −3.24698 −0.122375
\(705\) −23.6011 −0.888870
\(706\) −3.52242 −0.132568
\(707\) −15.5746 −0.585744
\(708\) 4.50007 0.169123
\(709\) −17.2856 −0.649176 −0.324588 0.945856i \(-0.605226\pi\)
−0.324588 + 0.945856i \(0.605226\pi\)
\(710\) −3.64564 −0.136818
\(711\) −2.41753 −0.0906645
\(712\) 10.9361 0.409846
\(713\) 17.9172 0.671006
\(714\) 1.80194 0.0674358
\(715\) 0 0
\(716\) 3.27893 0.122539
\(717\) 23.3225 0.870994
\(718\) 24.0153 0.896244
\(719\) −32.0469 −1.19515 −0.597574 0.801814i \(-0.703868\pi\)
−0.597574 + 0.801814i \(0.703868\pi\)
\(720\) 2.41496 0.0900002
\(721\) −3.71813 −0.138470
\(722\) 11.5002 0.427992
\(723\) −28.8105 −1.07147
\(724\) 21.0091 0.780798
\(725\) 5.17786 0.192301
\(726\) 0.457123 0.0169654
\(727\) −9.14186 −0.339053 −0.169526 0.985526i \(-0.554224\pi\)
−0.169526 + 0.985526i \(0.554224\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.89886 −0.0702799
\(731\) −7.12346 −0.263471
\(732\) 6.94297 0.256620
\(733\) 0.298008 0.0110072 0.00550359 0.999985i \(-0.498248\pi\)
0.00550359 + 0.999985i \(0.498248\pi\)
\(734\) 5.01103 0.184961
\(735\) 2.41496 0.0890771
\(736\) 6.58012 0.242546
\(737\) −8.26311 −0.304376
\(738\) 9.15862 0.337133
\(739\) 20.7127 0.761931 0.380965 0.924589i \(-0.375592\pi\)
0.380965 + 0.924589i \(0.375592\pi\)
\(740\) −21.5868 −0.793546
\(741\) 0 0
\(742\) −10.3747 −0.380867
\(743\) 43.7005 1.60322 0.801608 0.597849i \(-0.203978\pi\)
0.801608 + 0.597849i \(0.203978\pi\)
\(744\) 2.72294 0.0998277
\(745\) 46.7423 1.71250
\(746\) 12.2463 0.448371
\(747\) 3.51468 0.128595
\(748\) −5.85086 −0.213928
\(749\) 0.125781 0.00459592
\(750\) 10.0655 0.367540
\(751\) −51.8962 −1.89372 −0.946860 0.321646i \(-0.895764\pi\)
−0.946860 + 0.321646i \(0.895764\pi\)
\(752\) −9.77289 −0.356381
\(753\) 1.56870 0.0571664
\(754\) 0 0
\(755\) −22.9604 −0.835616
\(756\) −1.00000 −0.0363696
\(757\) 47.3170 1.71977 0.859883 0.510491i \(-0.170536\pi\)
0.859883 + 0.510491i \(0.170536\pi\)
\(758\) −15.3669 −0.558150
\(759\) 21.3655 0.775519
\(760\) −6.61356 −0.239899
\(761\) −13.5638 −0.491687 −0.245844 0.969310i \(-0.579065\pi\)
−0.245844 + 0.969310i \(0.579065\pi\)
\(762\) 11.7970 0.427361
\(763\) 3.84276 0.139117
\(764\) −6.15290 −0.222604
\(765\) 4.35160 0.157333
\(766\) 13.7125 0.495452
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 32.6689 1.17807 0.589036 0.808107i \(-0.299508\pi\)
0.589036 + 0.808107i \(0.299508\pi\)
\(770\) −7.84132 −0.282582
\(771\) −14.0911 −0.507480
\(772\) 18.6232 0.670265
\(773\) −31.1438 −1.12016 −0.560082 0.828437i \(-0.689230\pi\)
−0.560082 + 0.828437i \(0.689230\pi\)
\(774\) 3.95322 0.142096
\(775\) −2.26554 −0.0813807
\(776\) 12.2904 0.441199
\(777\) 8.93878 0.320677
\(778\) −9.05551 −0.324656
\(779\) −25.0816 −0.898643
\(780\) 0 0
\(781\) −4.90166 −0.175395
\(782\) 11.8570 0.424004
\(783\) 6.22322 0.222400
\(784\) 1.00000 0.0357143
\(785\) 6.53320 0.233180
\(786\) 16.5193 0.589224
\(787\) 32.0019 1.14075 0.570373 0.821386i \(-0.306799\pi\)
0.570373 + 0.821386i \(0.306799\pi\)
\(788\) −16.8553 −0.600443
\(789\) −6.63837 −0.236332
\(790\) 5.83823 0.207715
\(791\) −12.7648 −0.453866
\(792\) 3.24698 0.115376
\(793\) 0 0
\(794\) −20.8502 −0.739944
\(795\) −25.0544 −0.888589
\(796\) 12.3376 0.437295
\(797\) −23.5034 −0.832532 −0.416266 0.909243i \(-0.636661\pi\)
−0.416266 + 0.909243i \(0.636661\pi\)
\(798\) 2.73858 0.0969448
\(799\) −17.6101 −0.623002
\(800\) −0.832022 −0.0294164
\(801\) −10.9361 −0.386407
\(802\) −19.6443 −0.693663
\(803\) −2.55307 −0.0900959
\(804\) 2.54486 0.0897504
\(805\) 15.8907 0.560074
\(806\) 0 0
\(807\) 18.0426 0.635128
\(808\) −15.5746 −0.547913
\(809\) 0.626708 0.0220339 0.0110169 0.999939i \(-0.496493\pi\)
0.0110169 + 0.999939i \(0.496493\pi\)
\(810\) −2.41496 −0.0848530
\(811\) 2.31714 0.0813656 0.0406828 0.999172i \(-0.487047\pi\)
0.0406828 + 0.999172i \(0.487047\pi\)
\(812\) −6.22322 −0.218392
\(813\) −12.0877 −0.423935
\(814\) −29.0240 −1.01729
\(815\) 16.4063 0.574687
\(816\) 1.80194 0.0630804
\(817\) −10.8262 −0.378762
\(818\) −2.96748 −0.103756
\(819\) 0 0
\(820\) −22.1177 −0.772383
\(821\) −45.6066 −1.59168 −0.795841 0.605505i \(-0.792971\pi\)
−0.795841 + 0.605505i \(0.792971\pi\)
\(822\) 11.5650 0.403377
\(823\) 54.7826 1.90960 0.954801 0.297246i \(-0.0960680\pi\)
0.954801 + 0.297246i \(0.0960680\pi\)
\(824\) −3.71813 −0.129527
\(825\) −2.70156 −0.0940562
\(826\) 4.50007 0.156577
\(827\) −5.65372 −0.196599 −0.0982995 0.995157i \(-0.531340\pi\)
−0.0982995 + 0.995157i \(0.531340\pi\)
\(828\) −6.58012 −0.228675
\(829\) −8.87143 −0.308117 −0.154059 0.988062i \(-0.549235\pi\)
−0.154059 + 0.988062i \(0.549235\pi\)
\(830\) −8.48781 −0.294616
\(831\) 30.1936 1.04741
\(832\) 0 0
\(833\) 1.80194 0.0624334
\(834\) 2.63433 0.0912194
\(835\) −43.3856 −1.50142
\(836\) −8.89213 −0.307541
\(837\) −2.72294 −0.0941185
\(838\) 0.255356 0.00882112
\(839\) −1.78656 −0.0616789 −0.0308394 0.999524i \(-0.509818\pi\)
−0.0308394 + 0.999524i \(0.509818\pi\)
\(840\) 2.41496 0.0833240
\(841\) 9.72852 0.335466
\(842\) −36.2298 −1.24856
\(843\) −20.4356 −0.703839
\(844\) −15.6160 −0.537525
\(845\) 0 0
\(846\) 9.77289 0.335999
\(847\) 0.457123 0.0157069
\(848\) −10.3747 −0.356268
\(849\) −4.01876 −0.137923
\(850\) −1.49925 −0.0514239
\(851\) 58.8183 2.01626
\(852\) 1.50961 0.0517183
\(853\) 33.5043 1.14716 0.573582 0.819148i \(-0.305553\pi\)
0.573582 + 0.819148i \(0.305553\pi\)
\(854\) 6.94297 0.237584
\(855\) 6.61356 0.226179
\(856\) 0.125781 0.00429909
\(857\) −1.66717 −0.0569496 −0.0284748 0.999595i \(-0.509065\pi\)
−0.0284748 + 0.999595i \(0.509065\pi\)
\(858\) 0 0
\(859\) 2.42584 0.0827685 0.0413842 0.999143i \(-0.486823\pi\)
0.0413842 + 0.999143i \(0.486823\pi\)
\(860\) −9.54686 −0.325545
\(861\) 9.15862 0.312125
\(862\) 26.6462 0.907574
\(863\) 25.5617 0.870132 0.435066 0.900399i \(-0.356725\pi\)
0.435066 + 0.900399i \(0.356725\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −17.4199 −0.592293
\(866\) 30.6061 1.04004
\(867\) −13.7530 −0.467077
\(868\) 2.72294 0.0924225
\(869\) 7.84967 0.266282
\(870\) −15.0288 −0.509525
\(871\) 0 0
\(872\) 3.84276 0.130132
\(873\) −12.2904 −0.415967
\(874\) 18.0202 0.609543
\(875\) 10.0655 0.340276
\(876\) 0.786291 0.0265663
\(877\) 5.50129 0.185765 0.0928827 0.995677i \(-0.470392\pi\)
0.0928827 + 0.995677i \(0.470392\pi\)
\(878\) 11.4091 0.385037
\(879\) −19.3490 −0.652627
\(880\) −7.84132 −0.264331
\(881\) −54.5279 −1.83709 −0.918546 0.395313i \(-0.870636\pi\)
−0.918546 + 0.395313i \(0.870636\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −29.0931 −0.979062 −0.489531 0.871986i \(-0.662832\pi\)
−0.489531 + 0.871986i \(0.662832\pi\)
\(884\) 0 0
\(885\) 10.8675 0.365306
\(886\) −38.5387 −1.29473
\(887\) 0.0869906 0.00292086 0.00146043 0.999999i \(-0.499535\pi\)
0.00146043 + 0.999999i \(0.499535\pi\)
\(888\) 8.93878 0.299966
\(889\) 11.7970 0.395659
\(890\) 26.4101 0.885270
\(891\) −3.24698 −0.108778
\(892\) −5.53203 −0.185226
\(893\) −26.7639 −0.895619
\(894\) −19.3553 −0.647339
\(895\) 7.91848 0.264686
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −2.16519 −0.0722533
\(899\) −16.9454 −0.565162
\(900\) 0.832022 0.0277341
\(901\) −18.6945 −0.622805
\(902\) −29.7378 −0.990162
\(903\) 3.95322 0.131555
\(904\) −12.7648 −0.424552
\(905\) 50.7362 1.68653
\(906\) 9.50760 0.315869
\(907\) 20.4983 0.680634 0.340317 0.940311i \(-0.389466\pi\)
0.340317 + 0.940311i \(0.389466\pi\)
\(908\) −20.4532 −0.678763
\(909\) 15.5746 0.516577
\(910\) 0 0
\(911\) 31.1649 1.03254 0.516269 0.856426i \(-0.327320\pi\)
0.516269 + 0.856426i \(0.327320\pi\)
\(912\) 2.73858 0.0906836
\(913\) −11.4121 −0.377685
\(914\) −31.4845 −1.04142
\(915\) 16.7670 0.554300
\(916\) 29.0317 0.959234
\(917\) 16.5193 0.545515
\(918\) −1.80194 −0.0594728
\(919\) −39.9574 −1.31807 −0.659037 0.752110i \(-0.729036\pi\)
−0.659037 + 0.752110i \(0.729036\pi\)
\(920\) 15.8907 0.523901
\(921\) −5.04050 −0.166090
\(922\) 7.94726 0.261729
\(923\) 0 0
\(924\) 3.24698 0.106818
\(925\) −7.43726 −0.244536
\(926\) 12.1131 0.398061
\(927\) 3.71813 0.122119
\(928\) −6.22322 −0.204287
\(929\) −12.8743 −0.422393 −0.211196 0.977444i \(-0.567736\pi\)
−0.211196 + 0.977444i \(0.567736\pi\)
\(930\) 6.57578 0.215628
\(931\) 2.73858 0.0897535
\(932\) 12.4742 0.408605
\(933\) −16.2638 −0.532452
\(934\) 1.69520 0.0554687
\(935\) −14.1296 −0.462086
\(936\) 0 0
\(937\) −14.9053 −0.486936 −0.243468 0.969909i \(-0.578285\pi\)
−0.243468 + 0.969909i \(0.578285\pi\)
\(938\) 2.54486 0.0830927
\(939\) −8.80560 −0.287360
\(940\) −23.6011 −0.769784
\(941\) 41.7852 1.36216 0.681080 0.732209i \(-0.261511\pi\)
0.681080 + 0.732209i \(0.261511\pi\)
\(942\) −2.70530 −0.0881436
\(943\) 60.2648 1.96249
\(944\) 4.50007 0.146465
\(945\) −2.41496 −0.0785586
\(946\) −12.8360 −0.417335
\(947\) 21.9153 0.712151 0.356076 0.934457i \(-0.384115\pi\)
0.356076 + 0.934457i \(0.384115\pi\)
\(948\) −2.41753 −0.0785177
\(949\) 0 0
\(950\) −2.27856 −0.0739263
\(951\) −20.0495 −0.650151
\(952\) 1.80194 0.0584011
\(953\) 31.7129 1.02728 0.513641 0.858005i \(-0.328296\pi\)
0.513641 + 0.858005i \(0.328296\pi\)
\(954\) 10.3747 0.335893
\(955\) −14.8590 −0.480826
\(956\) 23.3225 0.754303
\(957\) −20.2067 −0.653189
\(958\) 3.59340 0.116097
\(959\) 11.5650 0.373455
\(960\) 2.41496 0.0779424
\(961\) −23.5856 −0.760826
\(962\) 0 0
\(963\) −0.125781 −0.00405322
\(964\) −28.8105 −0.927922
\(965\) 44.9743 1.44777
\(966\) −6.58012 −0.211712
\(967\) −9.95706 −0.320198 −0.160099 0.987101i \(-0.551181\pi\)
−0.160099 + 0.987101i \(0.551181\pi\)
\(968\) 0.457123 0.0146925
\(969\) 4.93476 0.158527
\(970\) 29.6808 0.952992
\(971\) −7.29014 −0.233952 −0.116976 0.993135i \(-0.537320\pi\)
−0.116976 + 0.993135i \(0.537320\pi\)
\(972\) 1.00000 0.0320750
\(973\) 2.63433 0.0844527
\(974\) −4.79109 −0.153516
\(975\) 0 0
\(976\) 6.94297 0.222239
\(977\) 15.2936 0.489285 0.244643 0.969613i \(-0.421329\pi\)
0.244643 + 0.969613i \(0.421329\pi\)
\(978\) −6.79361 −0.217236
\(979\) 35.5092 1.13488
\(980\) 2.41496 0.0771430
\(981\) −3.84276 −0.122690
\(982\) 42.3139 1.35029
\(983\) 53.3268 1.70086 0.850430 0.526089i \(-0.176342\pi\)
0.850430 + 0.526089i \(0.176342\pi\)
\(984\) 9.15862 0.291966
\(985\) −40.7047 −1.29696
\(986\) −11.2139 −0.357122
\(987\) 9.77289 0.311075
\(988\) 0 0
\(989\) 26.0127 0.827155
\(990\) 7.84132 0.249213
\(991\) 31.4834 1.00010 0.500051 0.865996i \(-0.333314\pi\)
0.500051 + 0.865996i \(0.333314\pi\)
\(992\) 2.72294 0.0864533
\(993\) 19.0732 0.605271
\(994\) 1.50961 0.0478818
\(995\) 29.7948 0.944558
\(996\) 3.51468 0.111367
\(997\) −16.4135 −0.519819 −0.259910 0.965633i \(-0.583693\pi\)
−0.259910 + 0.965633i \(0.583693\pi\)
\(998\) 26.4820 0.838274
\(999\) −8.93878 −0.282811
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 7098.2.a.cr.1.6 6
13.12 even 2 7098.2.a.ct.1.1 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cr.1.6 6 1.1 even 1 trivial
7098.2.a.ct.1.1 yes 6 13.12 even 2