Properties

Label 7098.2.a.cr.1.1
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 1.1
Root \(3.41496\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.41496 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.41496 q^{10} -3.24698 q^{11} +1.00000 q^{12} +1.00000 q^{14} -3.41496 q^{15} +1.00000 q^{16} +1.80194 q^{17} -1.00000 q^{18} -1.93665 q^{19} -3.41496 q^{20} -1.00000 q^{21} +3.24698 q^{22} +3.28422 q^{23} -1.00000 q^{24} +6.66194 q^{25} +1.00000 q^{27} -1.00000 q^{28} -3.64112 q^{29} +3.41496 q^{30} +3.10698 q^{31} -1.00000 q^{32} -3.24698 q^{33} -1.80194 q^{34} +3.41496 q^{35} +1.00000 q^{36} +4.80172 q^{37} +1.93665 q^{38} +3.41496 q^{40} +4.58189 q^{41} +1.00000 q^{42} +5.11205 q^{43} -3.24698 q^{44} -3.41496 q^{45} -3.28422 q^{46} +10.5966 q^{47} +1.00000 q^{48} +1.00000 q^{49} -6.66194 q^{50} +1.80194 q^{51} -2.46409 q^{53} -1.00000 q^{54} +11.0883 q^{55} +1.00000 q^{56} -1.93665 q^{57} +3.64112 q^{58} -13.2749 q^{59} -3.41496 q^{60} -1.76668 q^{61} -3.10698 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.24698 q^{66} +12.4092 q^{67} +1.80194 q^{68} +3.28422 q^{69} -3.41496 q^{70} +2.66429 q^{71} -1.00000 q^{72} -0.368396 q^{73} -4.80172 q^{74} +6.66194 q^{75} -1.93665 q^{76} +3.24698 q^{77} -15.0033 q^{79} -3.41496 q^{80} +1.00000 q^{81} -4.58189 q^{82} +1.43401 q^{83} -1.00000 q^{84} -6.15354 q^{85} -5.11205 q^{86} -3.64112 q^{87} +3.24698 q^{88} -5.10615 q^{89} +3.41496 q^{90} +3.28422 q^{92} +3.10698 q^{93} -10.5966 q^{94} +6.61356 q^{95} -1.00000 q^{96} +11.9553 q^{97} -1.00000 q^{98} -3.24698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + 3q^{10} - 10q^{11} + 6q^{12} + 6q^{14} - 3q^{15} + 6q^{16} + 2q^{17} - 6q^{18} - 2q^{19} - 3q^{20} - 6q^{21} + 10q^{22} + 4q^{23} - 6q^{24} + 13q^{25} + 6q^{27} - 6q^{28} + 2q^{29} + 3q^{30} - 9q^{31} - 6q^{32} - 10q^{33} - 2q^{34} + 3q^{35} + 6q^{36} - 7q^{37} + 2q^{38} + 3q^{40} - 11q^{41} + 6q^{42} - 5q^{43} - 10q^{44} - 3q^{45} - 4q^{46} - 5q^{47} + 6q^{48} + 6q^{49} - 13q^{50} + 2q^{51} - 6q^{53} - 6q^{54} + 5q^{55} + 6q^{56} - 2q^{57} - 2q^{58} - 28q^{59} - 3q^{60} + 23q^{61} + 9q^{62} - 6q^{63} + 6q^{64} + 10q^{66} + 10q^{67} + 2q^{68} + 4q^{69} - 3q^{70} - 21q^{71} - 6q^{72} + 7q^{73} + 7q^{74} + 13q^{75} - 2q^{76} + 10q^{77} - 14q^{79} - 3q^{80} + 6q^{81} + 11q^{82} - 17q^{83} - 6q^{84} - q^{85} + 5q^{86} + 2q^{87} + 10q^{88} - 17q^{89} + 3q^{90} + 4q^{92} - 9q^{93} + 5q^{94} - 22q^{95} - 6q^{96} - 6q^{98} - 10q^{99} + O(q^{100}) \)

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
\(5\) −3.41496 −1.52722 −0.763608 0.645680i \(-0.776574\pi\)
−0.763608 + 0.645680i \(0.776574\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.41496 1.07990
\(11\) −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
\(15\) −3.41496 −0.881738
\(16\) 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
\(19\) −1.93665 −0.444297 −0.222149 0.975013i \(-0.571307\pi\)
−0.222149 + 0.975013i \(0.571307\pi\)
\(20\) −3.41496 −0.763608
\(21\) −1.00000 −0.218218
\(22\) 3.24698 0.692258
\(23\) 3.28422 0.684808 0.342404 0.939553i \(-0.388759\pi\)
0.342404 + 0.939553i \(0.388759\pi\)
\(24\) −1.00000 −0.204124
\(25\) 6.66194 1.33239
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) −3.64112 −0.676139 −0.338069 0.941121i \(-0.609774\pi\)
−0.338069 + 0.941121i \(0.609774\pi\)
\(30\) 3.41496 0.623483
\(31\) 3.10698 0.558030 0.279015 0.960287i \(-0.409992\pi\)
0.279015 + 0.960287i \(0.409992\pi\)
\(32\) −1.00000 −0.176777
\(33\) −3.24698 −0.565227
\(34\) −1.80194 −0.309030
\(35\) 3.41496 0.577233
\(36\) 1.00000 0.166667
\(37\) 4.80172 0.789398 0.394699 0.918810i \(-0.370849\pi\)
0.394699 + 0.918810i \(0.370849\pi\)
\(38\) 1.93665 0.314165
\(39\) 0 0
\(40\) 3.41496 0.539952
\(41\) 4.58189 0.715571 0.357785 0.933804i \(-0.383532\pi\)
0.357785 + 0.933804i \(0.383532\pi\)
\(42\) 1.00000 0.154303
\(43\) 5.11205 0.779581 0.389790 0.920904i \(-0.372547\pi\)
0.389790 + 0.920904i \(0.372547\pi\)
\(44\) −3.24698 −0.489501
\(45\) −3.41496 −0.509072
\(46\) −3.28422 −0.484232
\(47\) 10.5966 1.54567 0.772836 0.634605i \(-0.218837\pi\)
0.772836 + 0.634605i \(0.218837\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −6.66194 −0.942140
\(51\) 1.80194 0.252322
\(52\) 0 0
\(53\) −2.46409 −0.338469 −0.169235 0.985576i \(-0.554130\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(54\) −1.00000 −0.136083
\(55\) 11.0883 1.49515
\(56\) 1.00000 0.133631
\(57\) −1.93665 −0.256515
\(58\) 3.64112 0.478102
\(59\) −13.2749 −1.72824 −0.864120 0.503286i \(-0.832124\pi\)
−0.864120 + 0.503286i \(0.832124\pi\)
\(60\) −3.41496 −0.440869
\(61\) −1.76668 −0.226200 −0.113100 0.993584i \(-0.536078\pi\)
−0.113100 + 0.993584i \(0.536078\pi\)
\(62\) −3.10698 −0.394587
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 3.24698 0.399676
\(67\) 12.4092 1.51603 0.758013 0.652240i \(-0.226170\pi\)
0.758013 + 0.652240i \(0.226170\pi\)
\(68\) 1.80194 0.218517
\(69\) 3.28422 0.395374
\(70\) −3.41496 −0.408166
\(71\) 2.66429 0.316193 0.158097 0.987424i \(-0.449464\pi\)
0.158097 + 0.987424i \(0.449464\pi\)
\(72\) −1.00000 −0.117851
\(73\) −0.368396 −0.0431175 −0.0215587 0.999768i \(-0.506863\pi\)
−0.0215587 + 0.999768i \(0.506863\pi\)
\(74\) −4.80172 −0.558189
\(75\) 6.66194 0.769254
\(76\) −1.93665 −0.222149
\(77\) 3.24698 0.370028
\(78\) 0 0
\(79\) −15.0033 −1.68801 −0.844004 0.536336i \(-0.819808\pi\)
−0.844004 + 0.536336i \(0.819808\pi\)
\(80\) −3.41496 −0.381804
\(81\) 1.00000 0.111111
\(82\) −4.58189 −0.505985
\(83\) 1.43401 0.157403 0.0787014 0.996898i \(-0.474923\pi\)
0.0787014 + 0.996898i \(0.474923\pi\)
\(84\) −1.00000 −0.109109
\(85\) −6.15354 −0.667445
\(86\) −5.11205 −0.551247
\(87\) −3.64112 −0.390369
\(88\) 3.24698 0.346129
\(89\) −5.10615 −0.541251 −0.270625 0.962685i \(-0.587230\pi\)
−0.270625 + 0.962685i \(0.587230\pi\)
\(90\) 3.41496 0.359968
\(91\) 0 0
\(92\) 3.28422 0.342404
\(93\) 3.10698 0.322179
\(94\) −10.5966 −1.09296
\(95\) 6.61356 0.678537
\(96\) −1.00000 −0.102062
\(97\) 11.9553 1.21387 0.606936 0.794750i \(-0.292398\pi\)
0.606936 + 0.794750i \(0.292398\pi\)
\(98\) −1.00000 −0.101015
\(99\) −3.24698 −0.326334
\(100\) 6.66194 0.666194
\(101\) −18.5354 −1.84434 −0.922170 0.386785i \(-0.873585\pi\)
−0.922170 + 0.386785i \(0.873585\pi\)
\(102\) −1.80194 −0.178418
\(103\) 18.2577 1.79899 0.899493 0.436936i \(-0.143936\pi\)
0.899493 + 0.436936i \(0.143936\pi\)
\(104\) 0 0
\(105\) 3.41496 0.333266
\(106\) 2.46409 0.239334
\(107\) −15.0210 −1.45213 −0.726066 0.687625i \(-0.758653\pi\)
−0.726066 + 0.687625i \(0.758653\pi\)
\(108\) 1.00000 0.0962250
\(109\) −11.7533 −1.12577 −0.562883 0.826536i \(-0.690308\pi\)
−0.562883 + 0.826536i \(0.690308\pi\)
\(110\) −11.0883 −1.05723
\(111\) 4.80172 0.455759
\(112\) −1.00000 −0.0944911
\(113\) 3.69957 0.348026 0.174013 0.984743i \(-0.444326\pi\)
0.174013 + 0.984743i \(0.444326\pi\)
\(114\) 1.93665 0.181384
\(115\) −11.2155 −1.04585
\(116\) −3.64112 −0.338069
\(117\) 0 0
\(118\) 13.2749 1.22205
\(119\) −1.80194 −0.165183
\(120\) 3.41496 0.311742
\(121\) −0.457123 −0.0415567
\(122\) 1.76668 0.159948
\(123\) 4.58189 0.413135
\(124\) 3.10698 0.279015
\(125\) −5.67545 −0.507627
\(126\) 1.00000 0.0890871
\(127\) 3.89724 0.345824 0.172912 0.984937i \(-0.444682\pi\)
0.172912 + 0.984937i \(0.444682\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 5.11205 0.450091
\(130\) 0 0
\(131\) −17.6740 −1.54418 −0.772091 0.635511i \(-0.780789\pi\)
−0.772091 + 0.635511i \(0.780789\pi\)
\(132\) −3.24698 −0.282613
\(133\) 1.93665 0.167928
\(134\) −12.4092 −1.07199
\(135\) −3.41496 −0.293913
\(136\) −1.80194 −0.154515
\(137\) 14.9195 1.27466 0.637331 0.770590i \(-0.280038\pi\)
0.637331 + 0.770590i \(0.280038\pi\)
\(138\) −3.28422 −0.279572
\(139\) −3.27513 −0.277793 −0.138897 0.990307i \(-0.544356\pi\)
−0.138897 + 0.990307i \(0.544356\pi\)
\(140\) 3.41496 0.288617
\(141\) 10.5966 0.892395
\(142\) −2.66429 −0.223582
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 12.4343 1.03261
\(146\) 0.368396 0.0304887
\(147\) 1.00000 0.0824786
\(148\) 4.80172 0.394699
\(149\) −8.92475 −0.731144 −0.365572 0.930783i \(-0.619127\pi\)
−0.365572 + 0.930783i \(0.619127\pi\)
\(150\) −6.66194 −0.543945
\(151\) 0.712364 0.0579714 0.0289857 0.999580i \(-0.490772\pi\)
0.0289857 + 0.999580i \(0.490772\pi\)
\(152\) 1.93665 0.157083
\(153\) 1.80194 0.145678
\(154\) −3.24698 −0.261649
\(155\) −10.6102 −0.852232
\(156\) 0 0
\(157\) −14.1436 −1.12879 −0.564393 0.825506i \(-0.690890\pi\)
−0.564393 + 0.825506i \(0.690890\pi\)
\(158\) 15.0033 1.19360
\(159\) −2.46409 −0.195415
\(160\) 3.41496 0.269976
\(161\) −3.28422 −0.258833
\(162\) −1.00000 −0.0785674
\(163\) −15.6565 −1.22632 −0.613158 0.789960i \(-0.710101\pi\)
−0.613158 + 0.789960i \(0.710101\pi\)
\(164\) 4.58189 0.357785
\(165\) 11.0883 0.863223
\(166\) −1.43401 −0.111301
\(167\) −19.6904 −1.52369 −0.761845 0.647759i \(-0.775706\pi\)
−0.761845 + 0.647759i \(0.775706\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 6.15354 0.471955
\(171\) −1.93665 −0.148099
\(172\) 5.11205 0.389790
\(173\) 16.3915 1.24622 0.623112 0.782132i \(-0.285868\pi\)
0.623112 + 0.782132i \(0.285868\pi\)
\(174\) 3.64112 0.276033
\(175\) −6.66194 −0.503595
\(176\) −3.24698 −0.244750
\(177\) −13.2749 −0.997800
\(178\) 5.10615 0.382722
\(179\) −17.0906 −1.27741 −0.638704 0.769452i \(-0.720529\pi\)
−0.638704 + 0.769452i \(0.720529\pi\)
\(180\) −3.41496 −0.254536
\(181\) 21.3647 1.58803 0.794015 0.607899i \(-0.207987\pi\)
0.794015 + 0.607899i \(0.207987\pi\)
\(182\) 0 0
\(183\) −1.76668 −0.130597
\(184\) −3.28422 −0.242116
\(185\) −16.3977 −1.20558
\(186\) −3.10698 −0.227815
\(187\) −5.85086 −0.427857
\(188\) 10.5966 0.772836
\(189\) −1.00000 −0.0727393
\(190\) −6.61356 −0.479798
\(191\) 16.2973 1.17923 0.589614 0.807685i \(-0.299280\pi\)
0.589614 + 0.807685i \(0.299280\pi\)
\(192\) 1.00000 0.0721688
\(193\) −18.7221 −1.34765 −0.673824 0.738892i \(-0.735349\pi\)
−0.673824 + 0.738892i \(0.735349\pi\)
\(194\) −11.9553 −0.858338
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −6.35011 −0.452426 −0.226213 0.974078i \(-0.572635\pi\)
−0.226213 + 0.974078i \(0.572635\pi\)
\(198\) 3.24698 0.230753
\(199\) 11.9820 0.849380 0.424690 0.905339i \(-0.360383\pi\)
0.424690 + 0.905339i \(0.360383\pi\)
\(200\) −6.66194 −0.471070
\(201\) 12.4092 0.875278
\(202\) 18.5354 1.30414
\(203\) 3.64112 0.255556
\(204\) 1.80194 0.126161
\(205\) −15.6470 −1.09283
\(206\) −18.2577 −1.27207
\(207\) 3.28422 0.228269
\(208\) 0 0
\(209\) 6.28825 0.434967
\(210\) −3.41496 −0.235654
\(211\) 9.42870 0.649099 0.324549 0.945869i \(-0.394787\pi\)
0.324549 + 0.945869i \(0.394787\pi\)
\(212\) −2.46409 −0.169235
\(213\) 2.66429 0.182554
\(214\) 15.0210 1.02681
\(215\) −17.4575 −1.19059
\(216\) −1.00000 −0.0680414
\(217\) −3.10698 −0.210916
\(218\) 11.7533 0.796037
\(219\) −0.368396 −0.0248939
\(220\) 11.0883 0.747573
\(221\) 0 0
\(222\) −4.80172 −0.322270
\(223\) 15.9921 1.07091 0.535456 0.844563i \(-0.320140\pi\)
0.535456 + 0.844563i \(0.320140\pi\)
\(224\) 1.00000 0.0668153
\(225\) 6.66194 0.444129
\(226\) −3.69957 −0.246092
\(227\) −4.11815 −0.273331 −0.136665 0.990617i \(-0.543639\pi\)
−0.136665 + 0.990617i \(0.543639\pi\)
\(228\) −1.93665 −0.128258
\(229\) −0.403067 −0.0266354 −0.0133177 0.999911i \(-0.504239\pi\)
−0.0133177 + 0.999911i \(0.504239\pi\)
\(230\) 11.2155 0.739527
\(231\) 3.24698 0.213636
\(232\) 3.64112 0.239051
\(233\) −18.7561 −1.22875 −0.614376 0.789014i \(-0.710592\pi\)
−0.614376 + 0.789014i \(0.710592\pi\)
\(234\) 0 0
\(235\) −36.1869 −2.36058
\(236\) −13.2749 −0.864120
\(237\) −15.0033 −0.974572
\(238\) 1.80194 0.116802
\(239\) 10.3497 0.669466 0.334733 0.942313i \(-0.391354\pi\)
0.334733 + 0.942313i \(0.391354\pi\)
\(240\) −3.41496 −0.220435
\(241\) 9.33396 0.601253 0.300627 0.953742i \(-0.402804\pi\)
0.300627 + 0.953742i \(0.402804\pi\)
\(242\) 0.457123 0.0293850
\(243\) 1.00000 0.0641500
\(244\) −1.76668 −0.113100
\(245\) −3.41496 −0.218174
\(246\) −4.58189 −0.292131
\(247\) 0 0
\(248\) −3.10698 −0.197293
\(249\) 1.43401 0.0908766
\(250\) 5.67545 0.358947
\(251\) −30.9745 −1.95509 −0.977547 0.210718i \(-0.932420\pi\)
−0.977547 + 0.210718i \(0.932420\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −10.6638 −0.670428
\(254\) −3.89724 −0.244535
\(255\) −6.15354 −0.385350
\(256\) 1.00000 0.0625000
\(257\) −2.27305 −0.141789 −0.0708944 0.997484i \(-0.522585\pi\)
−0.0708944 + 0.997484i \(0.522585\pi\)
\(258\) −5.11205 −0.318263
\(259\) −4.80172 −0.298364
\(260\) 0 0
\(261\) −3.64112 −0.225380
\(262\) 17.6740 1.09190
\(263\) −18.5834 −1.14590 −0.572950 0.819590i \(-0.694201\pi\)
−0.572950 + 0.819590i \(0.694201\pi\)
\(264\) 3.24698 0.199838
\(265\) 8.41477 0.516915
\(266\) −1.93665 −0.118743
\(267\) −5.10615 −0.312491
\(268\) 12.4092 0.758013
\(269\) 26.7522 1.63111 0.815555 0.578679i \(-0.196432\pi\)
0.815555 + 0.578679i \(0.196432\pi\)
\(270\) 3.41496 0.207828
\(271\) −5.33182 −0.323885 −0.161943 0.986800i \(-0.551776\pi\)
−0.161943 + 0.986800i \(0.551776\pi\)
\(272\) 1.80194 0.109259
\(273\) 0 0
\(274\) −14.9195 −0.901323
\(275\) −21.6312 −1.30441
\(276\) 3.28422 0.197687
\(277\) 25.0045 1.50238 0.751188 0.660088i \(-0.229481\pi\)
0.751188 + 0.660088i \(0.229481\pi\)
\(278\) 3.27513 0.196429
\(279\) 3.10698 0.186010
\(280\) −3.41496 −0.204083
\(281\) −13.8066 −0.823633 −0.411817 0.911267i \(-0.635106\pi\)
−0.411817 + 0.911267i \(0.635106\pi\)
\(282\) −10.5966 −0.631018
\(283\) −22.0224 −1.30910 −0.654548 0.756021i \(-0.727141\pi\)
−0.654548 + 0.756021i \(0.727141\pi\)
\(284\) 2.66429 0.158097
\(285\) 6.61356 0.391754
\(286\) 0 0
\(287\) −4.58189 −0.270460
\(288\) −1.00000 −0.0589256
\(289\) −13.7530 −0.809001
\(290\) −12.4343 −0.730165
\(291\) 11.9553 0.700830
\(292\) −0.368396 −0.0215587
\(293\) 2.17514 0.127073 0.0635364 0.997980i \(-0.479762\pi\)
0.0635364 + 0.997980i \(0.479762\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 45.3331 2.63939
\(296\) −4.80172 −0.279094
\(297\) −3.24698 −0.188409
\(298\) 8.92475 0.516997
\(299\) 0 0
\(300\) 6.66194 0.384627
\(301\) −5.11205 −0.294654
\(302\) −0.712364 −0.0409920
\(303\) −18.5354 −1.06483
\(304\) −1.93665 −0.111074
\(305\) 6.03315 0.345457
\(306\) −1.80194 −0.103010
\(307\) −21.5338 −1.22900 −0.614500 0.788917i \(-0.710642\pi\)
−0.614500 + 0.788917i \(0.710642\pi\)
\(308\) 3.24698 0.185014
\(309\) 18.2577 1.03864
\(310\) 10.6102 0.602619
\(311\) −10.5043 −0.595644 −0.297822 0.954621i \(-0.596260\pi\)
−0.297822 + 0.954621i \(0.596260\pi\)
\(312\) 0 0
\(313\) −16.0754 −0.908635 −0.454317 0.890840i \(-0.650117\pi\)
−0.454317 + 0.890840i \(0.650117\pi\)
\(314\) 14.1436 0.798172
\(315\) 3.41496 0.192411
\(316\) −15.0033 −0.844004
\(317\) −15.3743 −0.863508 −0.431754 0.901991i \(-0.642105\pi\)
−0.431754 + 0.901991i \(0.642105\pi\)
\(318\) 2.46409 0.138179
\(319\) 11.8226 0.661941
\(320\) −3.41496 −0.190902
\(321\) −15.0210 −0.838389
\(322\) 3.28422 0.183023
\(323\) −3.48972 −0.194173
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 15.6565 0.867136
\(327\) −11.7533 −0.649962
\(328\) −4.58189 −0.252992
\(329\) −10.5966 −0.584209
\(330\) −11.0883 −0.610391
\(331\) 8.21249 0.451399 0.225700 0.974197i \(-0.427533\pi\)
0.225700 + 0.974197i \(0.427533\pi\)
\(332\) 1.43401 0.0787014
\(333\) 4.80172 0.263133
\(334\) 19.6904 1.07741
\(335\) −42.3769 −2.31530
\(336\) −1.00000 −0.0545545
\(337\) −18.4567 −1.00540 −0.502701 0.864460i \(-0.667660\pi\)
−0.502701 + 0.864460i \(0.667660\pi\)
\(338\) 0 0
\(339\) 3.69957 0.200933
\(340\) −6.15354 −0.333723
\(341\) −10.0883 −0.546312
\(342\) 1.93665 0.104722
\(343\) −1.00000 −0.0539949
\(344\) −5.11205 −0.275623
\(345\) −11.2155 −0.603821
\(346\) −16.3915 −0.881214
\(347\) 31.3648 1.68375 0.841876 0.539671i \(-0.181451\pi\)
0.841876 + 0.539671i \(0.181451\pi\)
\(348\) −3.64112 −0.195184
\(349\) 6.96959 0.373073 0.186537 0.982448i \(-0.440274\pi\)
0.186537 + 0.982448i \(0.440274\pi\)
\(350\) 6.66194 0.356096
\(351\) 0 0
\(352\) 3.24698 0.173065
\(353\) −13.0978 −0.697127 −0.348563 0.937285i \(-0.613330\pi\)
−0.348563 + 0.937285i \(0.613330\pi\)
\(354\) 13.2749 0.705551
\(355\) −9.09845 −0.482895
\(356\) −5.10615 −0.270625
\(357\) −1.80194 −0.0953687
\(358\) 17.0906 0.903264
\(359\) 8.01400 0.422963 0.211481 0.977382i \(-0.432171\pi\)
0.211481 + 0.977382i \(0.432171\pi\)
\(360\) 3.41496 0.179984
\(361\) −15.2494 −0.802600
\(362\) −21.3647 −1.12291
\(363\) −0.457123 −0.0239928
\(364\) 0 0
\(365\) 1.25806 0.0658497
\(366\) 1.76668 0.0923460
\(367\) −25.7361 −1.34342 −0.671708 0.740816i \(-0.734439\pi\)
−0.671708 + 0.740816i \(0.734439\pi\)
\(368\) 3.28422 0.171202
\(369\) 4.58189 0.238524
\(370\) 16.3977 0.852474
\(371\) 2.46409 0.127929
\(372\) 3.10698 0.161089
\(373\) −0.973483 −0.0504050 −0.0252025 0.999682i \(-0.508023\pi\)
−0.0252025 + 0.999682i \(0.508023\pi\)
\(374\) 5.85086 0.302541
\(375\) −5.67545 −0.293079
\(376\) −10.5966 −0.546478
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 5.27383 0.270899 0.135449 0.990784i \(-0.456752\pi\)
0.135449 + 0.990784i \(0.456752\pi\)
\(380\) 6.61356 0.339269
\(381\) 3.89724 0.199662
\(382\) −16.2973 −0.833840
\(383\) −11.1179 −0.568100 −0.284050 0.958810i \(-0.591678\pi\)
−0.284050 + 0.958810i \(0.591678\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −11.0883 −0.565112
\(386\) 18.7221 0.952931
\(387\) 5.11205 0.259860
\(388\) 11.9553 0.606936
\(389\) −13.6798 −0.693595 −0.346797 0.937940i \(-0.612731\pi\)
−0.346797 + 0.937940i \(0.612731\pi\)
\(390\) 0 0
\(391\) 5.91797 0.299284
\(392\) −1.00000 −0.0505076
\(393\) −17.6740 −0.891534
\(394\) 6.35011 0.319914
\(395\) 51.2358 2.57795
\(396\) −3.24698 −0.163167
\(397\) −16.3683 −0.821500 −0.410750 0.911748i \(-0.634733\pi\)
−0.410750 + 0.911748i \(0.634733\pi\)
\(398\) −11.9820 −0.600603
\(399\) 1.93665 0.0969536
\(400\) 6.66194 0.333097
\(401\) 35.9089 1.79320 0.896602 0.442837i \(-0.146028\pi\)
0.896602 + 0.442837i \(0.146028\pi\)
\(402\) −12.4092 −0.618915
\(403\) 0 0
\(404\) −18.5354 −0.922170
\(405\) −3.41496 −0.169691
\(406\) −3.64112 −0.180706
\(407\) −15.5911 −0.772822
\(408\) −1.80194 −0.0892092
\(409\) −12.4416 −0.615197 −0.307599 0.951516i \(-0.599525\pi\)
−0.307599 + 0.951516i \(0.599525\pi\)
\(410\) 15.6470 0.772748
\(411\) 14.9195 0.735927
\(412\) 18.2577 0.899493
\(413\) 13.2749 0.653213
\(414\) −3.28422 −0.161411
\(415\) −4.89708 −0.240388
\(416\) 0 0
\(417\) −3.27513 −0.160384
\(418\) −6.28825 −0.307568
\(419\) 9.73591 0.475630 0.237815 0.971310i \(-0.423569\pi\)
0.237815 + 0.971310i \(0.423569\pi\)
\(420\) 3.41496 0.166633
\(421\) −24.4352 −1.19090 −0.595449 0.803393i \(-0.703026\pi\)
−0.595449 + 0.803393i \(0.703026\pi\)
\(422\) −9.42870 −0.458982
\(423\) 10.5966 0.515224
\(424\) 2.46409 0.119667
\(425\) 12.0044 0.582299
\(426\) −2.66429 −0.129085
\(427\) 1.76668 0.0854957
\(428\) −15.0210 −0.726066
\(429\) 0 0
\(430\) 17.4575 0.841873
\(431\) −38.2356 −1.84174 −0.920872 0.389864i \(-0.872522\pi\)
−0.920872 + 0.389864i \(0.872522\pi\)
\(432\) 1.00000 0.0481125
\(433\) 31.9423 1.53505 0.767524 0.641021i \(-0.221489\pi\)
0.767524 + 0.641021i \(0.221489\pi\)
\(434\) 3.10698 0.149140
\(435\) 12.4343 0.596177
\(436\) −11.7533 −0.562883
\(437\) −6.36038 −0.304258
\(438\) 0.368396 0.0176026
\(439\) 20.6203 0.984152 0.492076 0.870552i \(-0.336238\pi\)
0.492076 + 0.870552i \(0.336238\pi\)
\(440\) −11.0883 −0.528614
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −0.760370 −0.0361263 −0.0180631 0.999837i \(-0.505750\pi\)
−0.0180631 + 0.999837i \(0.505750\pi\)
\(444\) 4.80172 0.227880
\(445\) 17.4373 0.826606
\(446\) −15.9921 −0.757250
\(447\) −8.92475 −0.422126
\(448\) −1.00000 −0.0472456
\(449\) −19.8729 −0.937859 −0.468929 0.883236i \(-0.655360\pi\)
−0.468929 + 0.883236i \(0.655360\pi\)
\(450\) −6.66194 −0.314047
\(451\) −14.8773 −0.700545
\(452\) 3.69957 0.174013
\(453\) 0.712364 0.0334698
\(454\) 4.11815 0.193274
\(455\) 0 0
\(456\) 1.93665 0.0906918
\(457\) −39.0448 −1.82644 −0.913220 0.407466i \(-0.866413\pi\)
−0.913220 + 0.407466i \(0.866413\pi\)
\(458\) 0.403067 0.0188341
\(459\) 1.80194 0.0841073
\(460\) −11.2155 −0.522925
\(461\) 25.0785 1.16802 0.584011 0.811746i \(-0.301483\pi\)
0.584011 + 0.811746i \(0.301483\pi\)
\(462\) −3.24698 −0.151063
\(463\) −11.3140 −0.525807 −0.262904 0.964822i \(-0.584680\pi\)
−0.262904 + 0.964822i \(0.584680\pi\)
\(464\) −3.64112 −0.169035
\(465\) −10.6102 −0.492036
\(466\) 18.7561 0.868858
\(467\) 12.6861 0.587043 0.293521 0.955952i \(-0.405173\pi\)
0.293521 + 0.955952i \(0.405173\pi\)
\(468\) 0 0
\(469\) −12.4092 −0.573004
\(470\) 36.1869 1.66918
\(471\) −14.1436 −0.651705
\(472\) 13.2749 0.611025
\(473\) −16.5987 −0.763211
\(474\) 15.0033 0.689127
\(475\) −12.9018 −0.591976
\(476\) −1.80194 −0.0825917
\(477\) −2.46409 −0.112823
\(478\) −10.3497 −0.473384
\(479\) −5.31845 −0.243006 −0.121503 0.992591i \(-0.538771\pi\)
−0.121503 + 0.992591i \(0.538771\pi\)
\(480\) 3.41496 0.155871
\(481\) 0 0
\(482\) −9.33396 −0.425150
\(483\) −3.28422 −0.149437
\(484\) −0.457123 −0.0207783
\(485\) −40.8267 −1.85385
\(486\) −1.00000 −0.0453609
\(487\) 31.2192 1.41468 0.707338 0.706875i \(-0.249896\pi\)
0.707338 + 0.706875i \(0.249896\pi\)
\(488\) 1.76668 0.0799739
\(489\) −15.6565 −0.708014
\(490\) 3.41496 0.154272
\(491\) 24.9801 1.12734 0.563668 0.826001i \(-0.309390\pi\)
0.563668 + 0.826001i \(0.309390\pi\)
\(492\) 4.58189 0.206567
\(493\) −6.56107 −0.295496
\(494\) 0 0
\(495\) 11.0883 0.498382
\(496\) 3.10698 0.139507
\(497\) −2.66429 −0.119510
\(498\) −1.43401 −0.0642595
\(499\) −8.22457 −0.368182 −0.184091 0.982909i \(-0.558934\pi\)
−0.184091 + 0.982909i \(0.558934\pi\)
\(500\) −5.67545 −0.253814
\(501\) −19.6904 −0.879703
\(502\) 30.9745 1.38246
\(503\) −28.4248 −1.26740 −0.633700 0.773579i \(-0.718465\pi\)
−0.633700 + 0.773579i \(0.718465\pi\)
\(504\) 1.00000 0.0445435
\(505\) 63.2975 2.81670
\(506\) 10.6638 0.474064
\(507\) 0 0
\(508\) 3.89724 0.172912
\(509\) −8.58953 −0.380724 −0.190362 0.981714i \(-0.560966\pi\)
−0.190362 + 0.981714i \(0.560966\pi\)
\(510\) 6.15354 0.272483
\(511\) 0.368396 0.0162969
\(512\) −1.00000 −0.0441942
\(513\) −1.93665 −0.0855050
\(514\) 2.27305 0.100260
\(515\) −62.3493 −2.74744
\(516\) 5.11205 0.225046
\(517\) −34.4069 −1.51322
\(518\) 4.80172 0.210975
\(519\) 16.3915 0.719508
\(520\) 0 0
\(521\) 24.0161 1.05216 0.526082 0.850434i \(-0.323660\pi\)
0.526082 + 0.850434i \(0.323660\pi\)
\(522\) 3.64112 0.159367
\(523\) −28.7110 −1.25544 −0.627721 0.778438i \(-0.716012\pi\)
−0.627721 + 0.778438i \(0.716012\pi\)
\(524\) −17.6740 −0.772091
\(525\) −6.66194 −0.290751
\(526\) 18.5834 0.810274
\(527\) 5.59858 0.243878
\(528\) −3.24698 −0.141307
\(529\) −12.2139 −0.531038
\(530\) −8.41477 −0.365514
\(531\) −13.2749 −0.576080
\(532\) 1.93665 0.0839642
\(533\) 0 0
\(534\) 5.10615 0.220965
\(535\) 51.2960 2.21772
\(536\) −12.4092 −0.535996
\(537\) −17.0906 −0.737512
\(538\) −26.7522 −1.15337
\(539\) −3.24698 −0.139857
\(540\) −3.41496 −0.146956
\(541\) 13.3317 0.573173 0.286587 0.958054i \(-0.407479\pi\)
0.286587 + 0.958054i \(0.407479\pi\)
\(542\) 5.33182 0.229021
\(543\) 21.3647 0.916849
\(544\) −1.80194 −0.0772574
\(545\) 40.1372 1.71929
\(546\) 0 0
\(547\) 9.82136 0.419931 0.209965 0.977709i \(-0.432665\pi\)
0.209965 + 0.977709i \(0.432665\pi\)
\(548\) 14.9195 0.637331
\(549\) −1.76668 −0.0754002
\(550\) 21.6312 0.922356
\(551\) 7.05156 0.300406
\(552\) −3.28422 −0.139786
\(553\) 15.0033 0.638007
\(554\) −25.0045 −1.06234
\(555\) −16.3977 −0.696042
\(556\) −3.27513 −0.138897
\(557\) −25.6623 −1.08735 −0.543674 0.839297i \(-0.682967\pi\)
−0.543674 + 0.839297i \(0.682967\pi\)
\(558\) −3.10698 −0.131529
\(559\) 0 0
\(560\) 3.41496 0.144308
\(561\) −5.85086 −0.247023
\(562\) 13.8066 0.582396
\(563\) −39.5263 −1.66584 −0.832918 0.553396i \(-0.813331\pi\)
−0.832918 + 0.553396i \(0.813331\pi\)
\(564\) 10.5966 0.446197
\(565\) −12.6339 −0.531511
\(566\) 22.0224 0.925670
\(567\) −1.00000 −0.0419961
\(568\) −2.66429 −0.111791
\(569\) 4.74188 0.198790 0.0993949 0.995048i \(-0.468309\pi\)
0.0993949 + 0.995048i \(0.468309\pi\)
\(570\) −6.61356 −0.277012
\(571\) −7.02759 −0.294095 −0.147048 0.989129i \(-0.546977\pi\)
−0.147048 + 0.989129i \(0.546977\pi\)
\(572\) 0 0
\(573\) 16.2973 0.680828
\(574\) 4.58189 0.191244
\(575\) 21.8793 0.912429
\(576\) 1.00000 0.0416667
\(577\) −10.9656 −0.456503 −0.228251 0.973602i \(-0.573301\pi\)
−0.228251 + 0.973602i \(0.573301\pi\)
\(578\) 13.7530 0.572050
\(579\) −18.7221 −0.778065
\(580\) 12.4343 0.516305
\(581\) −1.43401 −0.0594927
\(582\) −11.9553 −0.495562
\(583\) 8.00086 0.331362
\(584\) 0.368396 0.0152443
\(585\) 0 0
\(586\) −2.17514 −0.0898541
\(587\) 28.8685 1.19153 0.595766 0.803158i \(-0.296849\pi\)
0.595766 + 0.803158i \(0.296849\pi\)
\(588\) 1.00000 0.0412393
\(589\) −6.01712 −0.247931
\(590\) −45.3331 −1.86633
\(591\) −6.35011 −0.261208
\(592\) 4.80172 0.197350
\(593\) −17.5637 −0.721255 −0.360628 0.932710i \(-0.617437\pi\)
−0.360628 + 0.932710i \(0.617437\pi\)
\(594\) 3.24698 0.133225
\(595\) 6.15354 0.252271
\(596\) −8.92475 −0.365572
\(597\) 11.9820 0.490390
\(598\) 0 0
\(599\) 9.82575 0.401469 0.200735 0.979646i \(-0.435667\pi\)
0.200735 + 0.979646i \(0.435667\pi\)
\(600\) −6.66194 −0.271972
\(601\) 22.3197 0.910438 0.455219 0.890380i \(-0.349561\pi\)
0.455219 + 0.890380i \(0.349561\pi\)
\(602\) 5.11205 0.208352
\(603\) 12.4092 0.505342
\(604\) 0.712364 0.0289857
\(605\) 1.56106 0.0634660
\(606\) 18.5354 0.752948
\(607\) 29.0228 1.17800 0.588999 0.808134i \(-0.299522\pi\)
0.588999 + 0.808134i \(0.299522\pi\)
\(608\) 1.93665 0.0785414
\(609\) 3.64112 0.147546
\(610\) −6.03315 −0.244275
\(611\) 0 0
\(612\) 1.80194 0.0728390
\(613\) 36.4576 1.47251 0.736255 0.676704i \(-0.236592\pi\)
0.736255 + 0.676704i \(0.236592\pi\)
\(614\) 21.5338 0.869035
\(615\) −15.6470 −0.630946
\(616\) −3.24698 −0.130825
\(617\) 33.4147 1.34522 0.672612 0.739995i \(-0.265172\pi\)
0.672612 + 0.739995i \(0.265172\pi\)
\(618\) −18.2577 −0.734433
\(619\) 12.8283 0.515614 0.257807 0.966196i \(-0.417000\pi\)
0.257807 + 0.966196i \(0.417000\pi\)
\(620\) −10.6102 −0.426116
\(621\) 3.28422 0.131791
\(622\) 10.5043 0.421184
\(623\) 5.10615 0.204574
\(624\) 0 0
\(625\) −13.9283 −0.557131
\(626\) 16.0754 0.642502
\(627\) 6.28825 0.251129
\(628\) −14.1436 −0.564393
\(629\) 8.65240 0.344994
\(630\) −3.41496 −0.136055
\(631\) −28.1757 −1.12166 −0.560828 0.827933i \(-0.689517\pi\)
−0.560828 + 0.827933i \(0.689517\pi\)
\(632\) 15.0033 0.596801
\(633\) 9.42870 0.374757
\(634\) 15.3743 0.610592
\(635\) −13.3089 −0.528148
\(636\) −2.46409 −0.0977076
\(637\) 0 0
\(638\) −11.8226 −0.468063
\(639\) 2.66429 0.105398
\(640\) 3.41496 0.134988
\(641\) 48.0176 1.89658 0.948291 0.317404i \(-0.102811\pi\)
0.948291 + 0.317404i \(0.102811\pi\)
\(642\) 15.0210 0.592830
\(643\) −8.71604 −0.343727 −0.171864 0.985121i \(-0.554979\pi\)
−0.171864 + 0.985121i \(0.554979\pi\)
\(644\) −3.28422 −0.129417
\(645\) −17.4575 −0.687386
\(646\) 3.48972 0.137301
\(647\) 27.8665 1.09555 0.547773 0.836627i \(-0.315476\pi\)
0.547773 + 0.836627i \(0.315476\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 43.1032 1.69195
\(650\) 0 0
\(651\) −3.10698 −0.121772
\(652\) −15.6565 −0.613158
\(653\) −12.1077 −0.473810 −0.236905 0.971533i \(-0.576133\pi\)
−0.236905 + 0.971533i \(0.576133\pi\)
\(654\) 11.7533 0.459592
\(655\) 60.3559 2.35830
\(656\) 4.58189 0.178893
\(657\) −0.368396 −0.0143725
\(658\) 10.5966 0.413098
\(659\) −23.4234 −0.912448 −0.456224 0.889865i \(-0.650798\pi\)
−0.456224 + 0.889865i \(0.650798\pi\)
\(660\) 11.0883 0.431611
\(661\) −5.85897 −0.227888 −0.113944 0.993487i \(-0.536348\pi\)
−0.113944 + 0.993487i \(0.536348\pi\)
\(662\) −8.21249 −0.319187
\(663\) 0 0
\(664\) −1.43401 −0.0556503
\(665\) −6.61356 −0.256463
\(666\) −4.80172 −0.186063
\(667\) −11.9582 −0.463025
\(668\) −19.6904 −0.761845
\(669\) 15.9921 0.618292
\(670\) 42.3769 1.63716
\(671\) 5.73638 0.221451
\(672\) 1.00000 0.0385758
\(673\) −12.6299 −0.486845 −0.243423 0.969920i \(-0.578270\pi\)
−0.243423 + 0.969920i \(0.578270\pi\)
\(674\) 18.4567 0.710927
\(675\) 6.66194 0.256418
\(676\) 0 0
\(677\) 14.8183 0.569515 0.284757 0.958600i \(-0.408087\pi\)
0.284757 + 0.958600i \(0.408087\pi\)
\(678\) −3.69957 −0.142081
\(679\) −11.9553 −0.458801
\(680\) 6.15354 0.235978
\(681\) −4.11815 −0.157808
\(682\) 10.0883 0.386301
\(683\) 26.9967 1.03300 0.516499 0.856288i \(-0.327235\pi\)
0.516499 + 0.856288i \(0.327235\pi\)
\(684\) −1.93665 −0.0740495
\(685\) −50.9496 −1.94668
\(686\) 1.00000 0.0381802
\(687\) −0.403067 −0.0153780
\(688\) 5.11205 0.194895
\(689\) 0 0
\(690\) 11.2155 0.426966
\(691\) 14.4624 0.550174 0.275087 0.961419i \(-0.411293\pi\)
0.275087 + 0.961419i \(0.411293\pi\)
\(692\) 16.3915 0.623112
\(693\) 3.24698 0.123343
\(694\) −31.3648 −1.19059
\(695\) 11.1844 0.424250
\(696\) 3.64112 0.138016
\(697\) 8.25628 0.312729
\(698\) −6.96959 −0.263803
\(699\) −18.7561 −0.709420
\(700\) −6.66194 −0.251798
\(701\) 31.2297 1.17953 0.589764 0.807575i \(-0.299221\pi\)
0.589764 + 0.807575i \(0.299221\pi\)
\(702\) 0 0
\(703\) −9.29923 −0.350727
\(704\) −3.24698 −0.122375
\(705\) −36.1869 −1.36288
\(706\) 13.0978 0.492943
\(707\) 18.5354 0.697095
\(708\) −13.2749 −0.498900
\(709\) −23.8268 −0.894834 −0.447417 0.894325i \(-0.647656\pi\)
−0.447417 + 0.894325i \(0.647656\pi\)
\(710\) 9.09845 0.341459
\(711\) −15.0033 −0.562670
\(712\) 5.10615 0.191361
\(713\) 10.2040 0.382143
\(714\) 1.80194 0.0674358
\(715\) 0 0
\(716\) −17.0906 −0.638704
\(717\) 10.3497 0.386516
\(718\) −8.01400 −0.299080
\(719\) 37.7147 1.40652 0.703261 0.710931i \(-0.251726\pi\)
0.703261 + 0.710931i \(0.251726\pi\)
\(720\) −3.41496 −0.127268
\(721\) −18.2577 −0.679952
\(722\) 15.2494 0.567524
\(723\) 9.33396 0.347134
\(724\) 21.3647 0.794015
\(725\) −24.2569 −0.900879
\(726\) 0.457123 0.0169654
\(727\) 40.5041 1.50222 0.751108 0.660180i \(-0.229520\pi\)
0.751108 + 0.660180i \(0.229520\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.25806 −0.0465627
\(731\) 9.21160 0.340703
\(732\) −1.76668 −0.0652985
\(733\) −46.1126 −1.70321 −0.851604 0.524185i \(-0.824370\pi\)
−0.851604 + 0.524185i \(0.824370\pi\)
\(734\) 25.7361 0.949938
\(735\) −3.41496 −0.125963
\(736\) −3.28422 −0.121058
\(737\) −40.2924 −1.48419
\(738\) −4.58189 −0.168662
\(739\) 12.9995 0.478195 0.239097 0.970996i \(-0.423148\pi\)
0.239097 + 0.970996i \(0.423148\pi\)
\(740\) −16.3977 −0.602790
\(741\) 0 0
\(742\) −2.46409 −0.0904597
\(743\) −31.1171 −1.14158 −0.570788 0.821098i \(-0.693362\pi\)
−0.570788 + 0.821098i \(0.693362\pi\)
\(744\) −3.10698 −0.113907
\(745\) 30.4777 1.11662
\(746\) 0.973483 0.0356417
\(747\) 1.43401 0.0524676
\(748\) −5.85086 −0.213928
\(749\) 15.0210 0.548854
\(750\) 5.67545 0.207238
\(751\) −49.5868 −1.80945 −0.904725 0.425997i \(-0.859924\pi\)
−0.904725 + 0.425997i \(0.859924\pi\)
\(752\) 10.5966 0.386418
\(753\) −30.9745 −1.12877
\(754\) 0 0
\(755\) −2.43269 −0.0885348
\(756\) −1.00000 −0.0363696
\(757\) −24.1697 −0.878462 −0.439231 0.898374i \(-0.644749\pi\)
−0.439231 + 0.898374i \(0.644749\pi\)
\(758\) −5.27383 −0.191554
\(759\) −10.6638 −0.387072
\(760\) −6.61356 −0.239899
\(761\) −52.4508 −1.90134 −0.950670 0.310204i \(-0.899603\pi\)
−0.950670 + 0.310204i \(0.899603\pi\)
\(762\) −3.89724 −0.141182
\(763\) 11.7533 0.425500
\(764\) 16.2973 0.589614
\(765\) −6.15354 −0.222482
\(766\) 11.1179 0.401707
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −21.4549 −0.773685 −0.386842 0.922146i \(-0.626434\pi\)
−0.386842 + 0.922146i \(0.626434\pi\)
\(770\) 11.0883 0.399595
\(771\) −2.27305 −0.0818618
\(772\) −18.7221 −0.673824
\(773\) 19.1744 0.689654 0.344827 0.938666i \(-0.387938\pi\)
0.344827 + 0.938666i \(0.387938\pi\)
\(774\) −5.11205 −0.183749
\(775\) 20.6985 0.743512
\(776\) −11.9553 −0.429169
\(777\) −4.80172 −0.172261
\(778\) 13.6798 0.490446
\(779\) −8.87349 −0.317926
\(780\) 0 0
\(781\) −8.65090 −0.309554
\(782\) −5.91797 −0.211626
\(783\) −3.64112 −0.130123
\(784\) 1.00000 0.0357143
\(785\) 48.2999 1.72390
\(786\) 17.6740 0.630410
\(787\) −0.0274054 −0.000976897 0 −0.000488449 1.00000i \(-0.500155\pi\)
−0.000488449 1.00000i \(0.500155\pi\)
\(788\) −6.35011 −0.226213
\(789\) −18.5834 −0.661586
\(790\) −51.2358 −1.82289
\(791\) −3.69957 −0.131542
\(792\) 3.24698 0.115376
\(793\) 0 0
\(794\) 16.3683 0.580888
\(795\) 8.41477 0.298441
\(796\) 11.9820 0.424690
\(797\) 6.95916 0.246506 0.123253 0.992375i \(-0.460667\pi\)
0.123253 + 0.992375i \(0.460667\pi\)
\(798\) −1.93665 −0.0685565
\(799\) 19.0944 0.675512
\(800\) −6.66194 −0.235535
\(801\) −5.10615 −0.180417
\(802\) −35.9089 −1.26799
\(803\) 1.19617 0.0422120
\(804\) 12.4092 0.437639
\(805\) 11.2155 0.395294
\(806\) 0 0
\(807\) 26.7522 0.941722
\(808\) 18.5354 0.652072
\(809\) −35.2083 −1.23786 −0.618930 0.785446i \(-0.712433\pi\)
−0.618930 + 0.785446i \(0.712433\pi\)
\(810\) 3.41496 0.119989
\(811\) −25.6464 −0.900567 −0.450284 0.892886i \(-0.648677\pi\)
−0.450284 + 0.892886i \(0.648677\pi\)
\(812\) 3.64112 0.127778
\(813\) −5.33182 −0.186995
\(814\) 15.5911 0.546467
\(815\) 53.4665 1.87285
\(816\) 1.80194 0.0630804
\(817\) −9.90024 −0.346366
\(818\) 12.4416 0.435010
\(819\) 0 0
\(820\) −15.6470 −0.546415
\(821\) −31.8661 −1.11214 −0.556068 0.831137i \(-0.687691\pi\)
−0.556068 + 0.831137i \(0.687691\pi\)
\(822\) −14.9195 −0.520379
\(823\) −48.6456 −1.69568 −0.847839 0.530254i \(-0.822097\pi\)
−0.847839 + 0.530254i \(0.822097\pi\)
\(824\) −18.2577 −0.636037
\(825\) −21.6312 −0.753101
\(826\) −13.2749 −0.461891
\(827\) 3.18286 0.110679 0.0553394 0.998468i \(-0.482376\pi\)
0.0553394 + 0.998468i \(0.482376\pi\)
\(828\) 3.28422 0.114135
\(829\) −0.573876 −0.0199315 −0.00996576 0.999950i \(-0.503172\pi\)
−0.00996576 + 0.999950i \(0.503172\pi\)
\(830\) 4.89708 0.169980
\(831\) 25.0045 0.867398
\(832\) 0 0
\(833\) 1.80194 0.0624334
\(834\) 3.27513 0.113409
\(835\) 67.2419 2.32700
\(836\) 6.28825 0.217484
\(837\) 3.10698 0.107393
\(838\) −9.73591 −0.336321
\(839\) 30.7253 1.06076 0.530378 0.847762i \(-0.322050\pi\)
0.530378 + 0.847762i \(0.322050\pi\)
\(840\) −3.41496 −0.117827
\(841\) −15.7423 −0.542836
\(842\) 24.4352 0.842092
\(843\) −13.8066 −0.475525
\(844\) 9.42870 0.324549
\(845\) 0 0
\(846\) −10.5966 −0.364319
\(847\) 0.457123 0.0157069
\(848\) −2.46409 −0.0846173
\(849\) −22.0224 −0.755806
\(850\) −12.0044 −0.411747
\(851\) 15.7699 0.540586
\(852\) 2.66429 0.0912772
\(853\) 23.5695 0.807005 0.403502 0.914979i \(-0.367793\pi\)
0.403502 + 0.914979i \(0.367793\pi\)
\(854\) −1.76668 −0.0604546
\(855\) 6.61356 0.226179
\(856\) 15.0210 0.513406
\(857\) −18.7309 −0.639834 −0.319917 0.947446i \(-0.603655\pi\)
−0.319917 + 0.947446i \(0.603655\pi\)
\(858\) 0 0
\(859\) −35.0464 −1.19577 −0.597884 0.801582i \(-0.703992\pi\)
−0.597884 + 0.801582i \(0.703992\pi\)
\(860\) −17.4575 −0.595294
\(861\) −4.58189 −0.156150
\(862\) 38.2356 1.30231
\(863\) −35.2615 −1.20032 −0.600158 0.799881i \(-0.704896\pi\)
−0.600158 + 0.799881i \(0.704896\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −55.9764 −1.90325
\(866\) −31.9423 −1.08544
\(867\) −13.7530 −0.467077
\(868\) −3.10698 −0.105458
\(869\) 48.7156 1.65256
\(870\) −12.4343 −0.421561
\(871\) 0 0
\(872\) 11.7533 0.398019
\(873\) 11.9553 0.404624
\(874\) 6.36038 0.215143
\(875\) 5.67545 0.191865
\(876\) −0.368396 −0.0124469
\(877\) −31.7171 −1.07101 −0.535506 0.844532i \(-0.679879\pi\)
−0.535506 + 0.844532i \(0.679879\pi\)
\(878\) −20.6203 −0.695900
\(879\) 2.17514 0.0733656
\(880\) 11.0883 0.373786
\(881\) −16.3131 −0.549602 −0.274801 0.961501i \(-0.588612\pi\)
−0.274801 + 0.961501i \(0.588612\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −20.4148 −0.687014 −0.343507 0.939150i \(-0.611615\pi\)
−0.343507 + 0.939150i \(0.611615\pi\)
\(884\) 0 0
\(885\) 45.3331 1.52386
\(886\) 0.760370 0.0255451
\(887\) −8.78093 −0.294835 −0.147417 0.989074i \(-0.547096\pi\)
−0.147417 + 0.989074i \(0.547096\pi\)
\(888\) −4.80172 −0.161135
\(889\) −3.89724 −0.130709
\(890\) −17.4373 −0.584499
\(891\) −3.24698 −0.108778
\(892\) 15.9921 0.535456
\(893\) −20.5219 −0.686738
\(894\) 8.92475 0.298488
\(895\) 58.3635 1.95088
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 19.8729 0.663166
\(899\) −11.3129 −0.377306
\(900\) 6.66194 0.222065
\(901\) −4.44014 −0.147923
\(902\) 14.8773 0.495360
\(903\) −5.11205 −0.170119
\(904\) −3.69957 −0.123046
\(905\) −72.9597 −2.42526
\(906\) −0.712364 −0.0236667
\(907\) 12.4859 0.414588 0.207294 0.978279i \(-0.433534\pi\)
0.207294 + 0.978279i \(0.433534\pi\)
\(908\) −4.11815 −0.136665
\(909\) −18.5354 −0.614780
\(910\) 0 0
\(911\) −15.1753 −0.502780 −0.251390 0.967886i \(-0.580888\pi\)
−0.251390 + 0.967886i \(0.580888\pi\)
\(912\) −1.93665 −0.0641288
\(913\) −4.65620 −0.154098
\(914\) 39.0448 1.29149
\(915\) 6.03315 0.199450
\(916\) −0.403067 −0.0133177
\(917\) 17.6740 0.583646
\(918\) −1.80194 −0.0594728
\(919\) −0.144447 −0.00476487 −0.00238243 0.999997i \(-0.500758\pi\)
−0.00238243 + 0.999997i \(0.500758\pi\)
\(920\) 11.2155 0.369764
\(921\) −21.5338 −0.709564
\(922\) −25.0785 −0.825916
\(923\) 0 0
\(924\) 3.24698 0.106818
\(925\) 31.9888 1.05178
\(926\) 11.3140 0.371802
\(927\) 18.2577 0.599662
\(928\) 3.64112 0.119526
\(929\) −40.2284 −1.31985 −0.659926 0.751331i \(-0.729412\pi\)
−0.659926 + 0.751331i \(0.729412\pi\)
\(930\) 10.6102 0.347922
\(931\) −1.93665 −0.0634710
\(932\) −18.7561 −0.614376
\(933\) −10.5043 −0.343895
\(934\) −12.6861 −0.415102
\(935\) 19.9804 0.653430
\(936\) 0 0
\(937\) 29.4246 0.961261 0.480630 0.876923i \(-0.340408\pi\)
0.480630 + 0.876923i \(0.340408\pi\)
\(938\) 12.4092 0.405175
\(939\) −16.0754 −0.524600
\(940\) −36.1869 −1.18029
\(941\) 23.6938 0.772395 0.386197 0.922416i \(-0.373788\pi\)
0.386197 + 0.922416i \(0.373788\pi\)
\(942\) 14.1436 0.460825
\(943\) 15.0479 0.490028
\(944\) −13.2749 −0.432060
\(945\) 3.41496 0.111089
\(946\) 16.5987 0.539671
\(947\) −16.5847 −0.538932 −0.269466 0.963010i \(-0.586847\pi\)
−0.269466 + 0.963010i \(0.586847\pi\)
\(948\) −15.0033 −0.487286
\(949\) 0 0
\(950\) 12.9018 0.418590
\(951\) −15.3743 −0.498546
\(952\) 1.80194 0.0584011
\(953\) 17.5290 0.567820 0.283910 0.958851i \(-0.408368\pi\)
0.283910 + 0.958851i \(0.408368\pi\)
\(954\) 2.46409 0.0797779
\(955\) −55.6545 −1.80094
\(956\) 10.3497 0.334733
\(957\) 11.8226 0.382172
\(958\) 5.31845 0.171831
\(959\) −14.9195 −0.481777
\(960\) −3.41496 −0.110217
\(961\) −21.3467 −0.688603
\(962\) 0 0
\(963\) −15.0210 −0.484044
\(964\) 9.33396 0.300627
\(965\) 63.9353 2.05815
\(966\) 3.28422 0.105668
\(967\) 44.7198 1.43809 0.719045 0.694963i \(-0.244579\pi\)
0.719045 + 0.694963i \(0.244579\pi\)
\(968\) 0.457123 0.0146925
\(969\) −3.48972 −0.112106
\(970\) 40.8267 1.31087
\(971\) −31.6941 −1.01711 −0.508555 0.861029i \(-0.669820\pi\)
−0.508555 + 0.861029i \(0.669820\pi\)
\(972\) 1.00000 0.0320750
\(973\) 3.27513 0.104996
\(974\) −31.2192 −1.00033
\(975\) 0 0
\(976\) −1.76668 −0.0565501
\(977\) −43.1638 −1.38093 −0.690467 0.723364i \(-0.742595\pi\)
−0.690467 + 0.723364i \(0.742595\pi\)
\(978\) 15.6565 0.500641
\(979\) 16.5796 0.529885
\(980\) −3.41496 −0.109087
\(981\) −11.7533 −0.375255
\(982\) −24.9801 −0.797147
\(983\) 58.3576 1.86132 0.930659 0.365887i \(-0.119234\pi\)
0.930659 + 0.365887i \(0.119234\pi\)
\(984\) −4.58189 −0.146065
\(985\) 21.6853 0.690953
\(986\) 6.56107 0.208947
\(987\) −10.5966 −0.337293
\(988\) 0 0
\(989\) 16.7891 0.533863
\(990\) −11.0883 −0.352409
\(991\) −38.6339 −1.22725 −0.613623 0.789599i \(-0.710288\pi\)
−0.613623 + 0.789599i \(0.710288\pi\)
\(992\) −3.10698 −0.0986467
\(993\) 8.21249 0.260615
\(994\) 2.66429 0.0845062
\(995\) −40.9180 −1.29719
\(996\) 1.43401 0.0454383
\(997\) 13.4648 0.426433 0.213217 0.977005i \(-0.431606\pi\)
0.213217 + 0.977005i \(0.431606\pi\)
\(998\) 8.22457 0.260344
\(999\) 4.80172 0.151920
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.1.1 6
13.12 even 2 7098.2.a.ct.1.6 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cr.1.1 6 1.1 even 1 trivial
7098.2.a.ct.1.6 yes 6 13.12 even 2