Properties

Label 7098.2.a.cr.1.2
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 1.2
Root \(3.10863\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10863 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.10863 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.10863 q^{10} -1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} -3.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} -1.00000 q^{18} +4.73805 q^{19} -3.10863 q^{20} -1.00000 q^{21} +1.55496 q^{22} +5.10817 q^{23} -1.00000 q^{24} +4.66359 q^{25} +1.00000 q^{27} -1.00000 q^{28} -1.05926 q^{29} +3.10863 q^{30} +2.46553 q^{31} -1.00000 q^{32} -1.55496 q^{33} +1.24698 q^{34} +3.10863 q^{35} +1.00000 q^{36} -7.92429 q^{37} -4.73805 q^{38} +3.10863 q^{40} -2.71654 q^{41} +1.00000 q^{42} -2.63128 q^{43} -1.55496 q^{44} -3.10863 q^{45} -5.10817 q^{46} -5.06412 q^{47} +1.00000 q^{48} +1.00000 q^{49} -4.66359 q^{50} -1.24698 q^{51} -7.09392 q^{53} -1.00000 q^{54} +4.83379 q^{55} +1.00000 q^{56} +4.73805 q^{57} +1.05926 q^{58} +3.41870 q^{59} -3.10863 q^{60} +13.2814 q^{61} -2.46553 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} +8.48684 q^{67} -1.24698 q^{68} +5.10817 q^{69} -3.10863 q^{70} +5.31350 q^{71} -1.00000 q^{72} -9.45056 q^{73} +7.92429 q^{74} +4.66359 q^{75} +4.73805 q^{76} +1.55496 q^{77} +11.1942 q^{79} -3.10863 q^{80} +1.00000 q^{81} +2.71654 q^{82} +4.40061 q^{83} -1.00000 q^{84} +3.87640 q^{85} +2.63128 q^{86} -1.05926 q^{87} +1.55496 q^{88} -5.76399 q^{89} +3.10863 q^{90} +5.10817 q^{92} +2.46553 q^{93} +5.06412 q^{94} -14.7289 q^{95} -1.00000 q^{96} -10.8007 q^{97} -1.00000 q^{98} -1.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + 3q^{10} - 10q^{11} + 6q^{12} + 6q^{14} - 3q^{15} + 6q^{16} + 2q^{17} - 6q^{18} - 2q^{19} - 3q^{20} - 6q^{21} + 10q^{22} + 4q^{23} - 6q^{24} + 13q^{25} + 6q^{27} - 6q^{28} + 2q^{29} + 3q^{30} - 9q^{31} - 6q^{32} - 10q^{33} - 2q^{34} + 3q^{35} + 6q^{36} - 7q^{37} + 2q^{38} + 3q^{40} - 11q^{41} + 6q^{42} - 5q^{43} - 10q^{44} - 3q^{45} - 4q^{46} - 5q^{47} + 6q^{48} + 6q^{49} - 13q^{50} + 2q^{51} - 6q^{53} - 6q^{54} + 5q^{55} + 6q^{56} - 2q^{57} - 2q^{58} - 28q^{59} - 3q^{60} + 23q^{61} + 9q^{62} - 6q^{63} + 6q^{64} + 10q^{66} + 10q^{67} + 2q^{68} + 4q^{69} - 3q^{70} - 21q^{71} - 6q^{72} + 7q^{73} + 7q^{74} + 13q^{75} - 2q^{76} + 10q^{77} - 14q^{79} - 3q^{80} + 6q^{81} + 11q^{82} - 17q^{83} - 6q^{84} - q^{85} + 5q^{86} + 2q^{87} + 10q^{88} - 17q^{89} + 3q^{90} + 4q^{92} - 9q^{93} + 5q^{94} - 22q^{95} - 6q^{96} - 6q^{98} - 10q^{99} + O(q^{100}) \)

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
\(5\) −3.10863 −1.39022 −0.695111 0.718902i \(-0.744645\pi\)
−0.695111 + 0.718902i \(0.744645\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 3.10863 0.983036
\(11\) −1.55496 −0.468838 −0.234419 0.972136i \(-0.575319\pi\)
−0.234419 + 0.972136i \(0.575319\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) −3.10863 −0.802645
\(16\) 1.00000 0.250000
\(17\) −1.24698 −0.302437 −0.151218 0.988500i \(-0.548320\pi\)
−0.151218 + 0.988500i \(0.548320\pi\)
\(18\) −1.00000 −0.235702
\(19\) 4.73805 1.08698 0.543492 0.839414i \(-0.317102\pi\)
0.543492 + 0.839414i \(0.317102\pi\)
\(20\) −3.10863 −0.695111
\(21\) −1.00000 −0.218218
\(22\) 1.55496 0.331518
\(23\) 5.10817 1.06513 0.532564 0.846390i \(-0.321229\pi\)
0.532564 + 0.846390i \(0.321229\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.66359 0.932718
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) −1.05926 −0.196699 −0.0983494 0.995152i \(-0.531356\pi\)
−0.0983494 + 0.995152i \(0.531356\pi\)
\(30\) 3.10863 0.567556
\(31\) 2.46553 0.442822 0.221411 0.975181i \(-0.428934\pi\)
0.221411 + 0.975181i \(0.428934\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.55496 −0.270683
\(34\) 1.24698 0.213855
\(35\) 3.10863 0.525455
\(36\) 1.00000 0.166667
\(37\) −7.92429 −1.30274 −0.651372 0.758758i \(-0.725806\pi\)
−0.651372 + 0.758758i \(0.725806\pi\)
\(38\) −4.73805 −0.768614
\(39\) 0 0
\(40\) 3.10863 0.491518
\(41\) −2.71654 −0.424252 −0.212126 0.977242i \(-0.568039\pi\)
−0.212126 + 0.977242i \(0.568039\pi\)
\(42\) 1.00000 0.154303
\(43\) −2.63128 −0.401266 −0.200633 0.979666i \(-0.564300\pi\)
−0.200633 + 0.979666i \(0.564300\pi\)
\(44\) −1.55496 −0.234419
\(45\) −3.10863 −0.463407
\(46\) −5.10817 −0.753159
\(47\) −5.06412 −0.738678 −0.369339 0.929295i \(-0.620416\pi\)
−0.369339 + 0.929295i \(0.620416\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −4.66359 −0.659531
\(51\) −1.24698 −0.174612
\(52\) 0 0
\(53\) −7.09392 −0.974425 −0.487212 0.873284i \(-0.661986\pi\)
−0.487212 + 0.873284i \(0.661986\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.83379 0.651788
\(56\) 1.00000 0.133631
\(57\) 4.73805 0.627570
\(58\) 1.05926 0.139087
\(59\) 3.41870 0.445077 0.222539 0.974924i \(-0.428566\pi\)
0.222539 + 0.974924i \(0.428566\pi\)
\(60\) −3.10863 −0.401323
\(61\) 13.2814 1.70051 0.850254 0.526373i \(-0.176448\pi\)
0.850254 + 0.526373i \(0.176448\pi\)
\(62\) −2.46553 −0.313122
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.55496 0.191402
\(67\) 8.48684 1.03683 0.518416 0.855128i \(-0.326522\pi\)
0.518416 + 0.855128i \(0.326522\pi\)
\(68\) −1.24698 −0.151218
\(69\) 5.10817 0.614952
\(70\) −3.10863 −0.371553
\(71\) 5.31350 0.630596 0.315298 0.948993i \(-0.397896\pi\)
0.315298 + 0.948993i \(0.397896\pi\)
\(72\) −1.00000 −0.117851
\(73\) −9.45056 −1.10610 −0.553052 0.833147i \(-0.686537\pi\)
−0.553052 + 0.833147i \(0.686537\pi\)
\(74\) 7.92429 0.921180
\(75\) 4.66359 0.538505
\(76\) 4.73805 0.543492
\(77\) 1.55496 0.177204
\(78\) 0 0
\(79\) 11.1942 1.25945 0.629725 0.776818i \(-0.283167\pi\)
0.629725 + 0.776818i \(0.283167\pi\)
\(80\) −3.10863 −0.347556
\(81\) 1.00000 0.111111
\(82\) 2.71654 0.299991
\(83\) 4.40061 0.483030 0.241515 0.970397i \(-0.422356\pi\)
0.241515 + 0.970397i \(0.422356\pi\)
\(84\) −1.00000 −0.109109
\(85\) 3.87640 0.420455
\(86\) 2.63128 0.283738
\(87\) −1.05926 −0.113564
\(88\) 1.55496 0.165759
\(89\) −5.76399 −0.610982 −0.305491 0.952195i \(-0.598821\pi\)
−0.305491 + 0.952195i \(0.598821\pi\)
\(90\) 3.10863 0.327679
\(91\) 0 0
\(92\) 5.10817 0.532564
\(93\) 2.46553 0.255663
\(94\) 5.06412 0.522325
\(95\) −14.7289 −1.51115
\(96\) −1.00000 −0.102062
\(97\) −10.8007 −1.09664 −0.548322 0.836267i \(-0.684733\pi\)
−0.548322 + 0.836267i \(0.684733\pi\)
\(98\) −1.00000 −0.101015
\(99\) −1.55496 −0.156279
\(100\) 4.66359 0.466359
\(101\) 8.82958 0.878576 0.439288 0.898346i \(-0.355231\pi\)
0.439288 + 0.898346i \(0.355231\pi\)
\(102\) 1.24698 0.123469
\(103\) 1.89793 0.187009 0.0935044 0.995619i \(-0.470193\pi\)
0.0935044 + 0.995619i \(0.470193\pi\)
\(104\) 0 0
\(105\) 3.10863 0.303371
\(106\) 7.09392 0.689022
\(107\) −3.58727 −0.346795 −0.173397 0.984852i \(-0.555474\pi\)
−0.173397 + 0.984852i \(0.555474\pi\)
\(108\) 1.00000 0.0962250
\(109\) 20.3167 1.94599 0.972995 0.230826i \(-0.0741428\pi\)
0.972995 + 0.230826i \(0.0741428\pi\)
\(110\) −4.83379 −0.460884
\(111\) −7.92429 −0.752140
\(112\) −1.00000 −0.0944911
\(113\) −6.85060 −0.644450 −0.322225 0.946663i \(-0.604431\pi\)
−0.322225 + 0.946663i \(0.604431\pi\)
\(114\) −4.73805 −0.443759
\(115\) −15.8794 −1.48076
\(116\) −1.05926 −0.0983494
\(117\) 0 0
\(118\) −3.41870 −0.314717
\(119\) 1.24698 0.114310
\(120\) 3.10863 0.283778
\(121\) −8.58211 −0.780191
\(122\) −13.2814 −1.20244
\(123\) −2.71654 −0.244942
\(124\) 2.46553 0.221411
\(125\) 1.04578 0.0935370
\(126\) 1.00000 0.0890871
\(127\) 8.46378 0.751039 0.375520 0.926814i \(-0.377464\pi\)
0.375520 + 0.926814i \(0.377464\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −2.63128 −0.231671
\(130\) 0 0
\(131\) −5.07860 −0.443719 −0.221860 0.975079i \(-0.571213\pi\)
−0.221860 + 0.975079i \(0.571213\pi\)
\(132\) −1.55496 −0.135342
\(133\) −4.73805 −0.410841
\(134\) −8.48684 −0.733151
\(135\) −3.10863 −0.267548
\(136\) 1.24698 0.106928
\(137\) −20.8764 −1.78359 −0.891795 0.452440i \(-0.850554\pi\)
−0.891795 + 0.452440i \(0.850554\pi\)
\(138\) −5.10817 −0.434837
\(139\) 17.7255 1.50346 0.751729 0.659472i \(-0.229220\pi\)
0.751729 + 0.659472i \(0.229220\pi\)
\(140\) 3.10863 0.262727
\(141\) −5.06412 −0.426476
\(142\) −5.31350 −0.445899
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 3.29284 0.273455
\(146\) 9.45056 0.782134
\(147\) 1.00000 0.0824786
\(148\) −7.92429 −0.651372
\(149\) −0.829877 −0.0679862 −0.0339931 0.999422i \(-0.510822\pi\)
−0.0339931 + 0.999422i \(0.510822\pi\)
\(150\) −4.66359 −0.380780
\(151\) 3.39170 0.276012 0.138006 0.990431i \(-0.455931\pi\)
0.138006 + 0.990431i \(0.455931\pi\)
\(152\) −4.73805 −0.384307
\(153\) −1.24698 −0.100812
\(154\) −1.55496 −0.125302
\(155\) −7.66442 −0.615621
\(156\) 0 0
\(157\) −23.7381 −1.89450 −0.947251 0.320492i \(-0.896152\pi\)
−0.947251 + 0.320492i \(0.896152\pi\)
\(158\) −11.1942 −0.890566
\(159\) −7.09392 −0.562584
\(160\) 3.10863 0.245759
\(161\) −5.10817 −0.402580
\(162\) −1.00000 −0.0785674
\(163\) 6.35482 0.497748 0.248874 0.968536i \(-0.419940\pi\)
0.248874 + 0.968536i \(0.419940\pi\)
\(164\) −2.71654 −0.212126
\(165\) 4.83379 0.376310
\(166\) −4.40061 −0.341554
\(167\) 7.50114 0.580456 0.290228 0.956958i \(-0.406269\pi\)
0.290228 + 0.956958i \(0.406269\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) −3.87640 −0.297306
\(171\) 4.73805 0.362328
\(172\) −2.63128 −0.200633
\(173\) −16.1881 −1.23076 −0.615378 0.788232i \(-0.710997\pi\)
−0.615378 + 0.788232i \(0.710997\pi\)
\(174\) 1.05926 0.0803020
\(175\) −4.66359 −0.352534
\(176\) −1.55496 −0.117209
\(177\) 3.41870 0.256966
\(178\) 5.76399 0.432030
\(179\) 1.95421 0.146064 0.0730322 0.997330i \(-0.476732\pi\)
0.0730322 + 0.997330i \(0.476732\pi\)
\(180\) −3.10863 −0.231704
\(181\) −1.81969 −0.135256 −0.0676281 0.997711i \(-0.521543\pi\)
−0.0676281 + 0.997711i \(0.521543\pi\)
\(182\) 0 0
\(183\) 13.2814 0.981788
\(184\) −5.10817 −0.376580
\(185\) 24.6337 1.81110
\(186\) −2.46553 −0.180781
\(187\) 1.93900 0.141794
\(188\) −5.06412 −0.369339
\(189\) −1.00000 −0.0727393
\(190\) 14.7289 1.06854
\(191\) −23.3210 −1.68745 −0.843723 0.536779i \(-0.819641\pi\)
−0.843723 + 0.536779i \(0.819641\pi\)
\(192\) 1.00000 0.0721688
\(193\) −7.99277 −0.575332 −0.287666 0.957731i \(-0.592879\pi\)
−0.287666 + 0.957731i \(0.592879\pi\)
\(194\) 10.8007 0.775444
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 2.24858 0.160205 0.0801024 0.996787i \(-0.474475\pi\)
0.0801024 + 0.996787i \(0.474475\pi\)
\(198\) 1.55496 0.110506
\(199\) −25.4768 −1.80600 −0.903001 0.429638i \(-0.858641\pi\)
−0.903001 + 0.429638i \(0.858641\pi\)
\(200\) −4.66359 −0.329766
\(201\) 8.48684 0.598615
\(202\) −8.82958 −0.621247
\(203\) 1.05926 0.0743452
\(204\) −1.24698 −0.0873060
\(205\) 8.44471 0.589804
\(206\) −1.89793 −0.132235
\(207\) 5.10817 0.355043
\(208\) 0 0
\(209\) −7.36747 −0.509619
\(210\) −3.10863 −0.214516
\(211\) 2.01914 0.139003 0.0695016 0.997582i \(-0.477859\pi\)
0.0695016 + 0.997582i \(0.477859\pi\)
\(212\) −7.09392 −0.487212
\(213\) 5.31350 0.364075
\(214\) 3.58727 0.245221
\(215\) 8.17967 0.557849
\(216\) −1.00000 −0.0680414
\(217\) −2.46553 −0.167371
\(218\) −20.3167 −1.37602
\(219\) −9.45056 −0.638610
\(220\) 4.83379 0.325894
\(221\) 0 0
\(222\) 7.92429 0.531843
\(223\) 13.1491 0.880532 0.440266 0.897867i \(-0.354884\pi\)
0.440266 + 0.897867i \(0.354884\pi\)
\(224\) 1.00000 0.0668153
\(225\) 4.66359 0.310906
\(226\) 6.85060 0.455695
\(227\) −1.90722 −0.126587 −0.0632935 0.997995i \(-0.520160\pi\)
−0.0632935 + 0.997995i \(0.520160\pi\)
\(228\) 4.73805 0.313785
\(229\) 1.32344 0.0874554 0.0437277 0.999043i \(-0.486077\pi\)
0.0437277 + 0.999043i \(0.486077\pi\)
\(230\) 15.8794 1.04706
\(231\) 1.55496 0.102309
\(232\) 1.05926 0.0695435
\(233\) −23.7561 −1.55631 −0.778157 0.628069i \(-0.783845\pi\)
−0.778157 + 0.628069i \(0.783845\pi\)
\(234\) 0 0
\(235\) 15.7425 1.02693
\(236\) 3.41870 0.222539
\(237\) 11.1942 0.727144
\(238\) −1.24698 −0.0808297
\(239\) −27.3308 −1.76789 −0.883943 0.467595i \(-0.845121\pi\)
−0.883943 + 0.467595i \(0.845121\pi\)
\(240\) −3.10863 −0.200661
\(241\) −2.68328 −0.172846 −0.0864228 0.996259i \(-0.527544\pi\)
−0.0864228 + 0.996259i \(0.527544\pi\)
\(242\) 8.58211 0.551679
\(243\) 1.00000 0.0641500
\(244\) 13.2814 0.850254
\(245\) −3.10863 −0.198603
\(246\) 2.71654 0.173200
\(247\) 0 0
\(248\) −2.46553 −0.156561
\(249\) 4.40061 0.278877
\(250\) −1.04578 −0.0661407
\(251\) −30.8962 −1.95015 −0.975077 0.221867i \(-0.928785\pi\)
−0.975077 + 0.221867i \(0.928785\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −7.94300 −0.499372
\(254\) −8.46378 −0.531065
\(255\) 3.87640 0.242750
\(256\) 1.00000 0.0625000
\(257\) 27.6822 1.72677 0.863385 0.504546i \(-0.168340\pi\)
0.863385 + 0.504546i \(0.168340\pi\)
\(258\) 2.63128 0.163816
\(259\) 7.92429 0.492391
\(260\) 0 0
\(261\) −1.05926 −0.0655663
\(262\) 5.07860 0.313757
\(263\) 21.8601 1.34795 0.673975 0.738754i \(-0.264586\pi\)
0.673975 + 0.738754i \(0.264586\pi\)
\(264\) 1.55496 0.0957011
\(265\) 22.0524 1.35467
\(266\) 4.73805 0.290509
\(267\) −5.76399 −0.352751
\(268\) 8.48684 0.518416
\(269\) −17.0766 −1.04118 −0.520590 0.853807i \(-0.674288\pi\)
−0.520590 + 0.853807i \(0.674288\pi\)
\(270\) 3.10863 0.189185
\(271\) −27.8718 −1.69309 −0.846547 0.532315i \(-0.821322\pi\)
−0.846547 + 0.532315i \(0.821322\pi\)
\(272\) −1.24698 −0.0756092
\(273\) 0 0
\(274\) 20.8764 1.26119
\(275\) −7.25169 −0.437293
\(276\) 5.10817 0.307476
\(277\) −31.9253 −1.91820 −0.959102 0.283061i \(-0.908650\pi\)
−0.959102 + 0.283061i \(0.908650\pi\)
\(278\) −17.7255 −1.06311
\(279\) 2.46553 0.147607
\(280\) −3.10863 −0.185776
\(281\) 11.3692 0.678229 0.339114 0.940745i \(-0.389873\pi\)
0.339114 + 0.940745i \(0.389873\pi\)
\(282\) 5.06412 0.301564
\(283\) −16.6264 −0.988334 −0.494167 0.869367i \(-0.664527\pi\)
−0.494167 + 0.869367i \(0.664527\pi\)
\(284\) 5.31350 0.315298
\(285\) −14.7289 −0.872462
\(286\) 0 0
\(287\) 2.71654 0.160352
\(288\) −1.00000 −0.0589256
\(289\) −15.4450 −0.908532
\(290\) −3.29284 −0.193362
\(291\) −10.8007 −0.633147
\(292\) −9.45056 −0.553052
\(293\) 5.41358 0.316265 0.158132 0.987418i \(-0.449453\pi\)
0.158132 + 0.987418i \(0.449453\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −10.6275 −0.618757
\(296\) 7.92429 0.460590
\(297\) −1.55496 −0.0902278
\(298\) 0.829877 0.0480735
\(299\) 0 0
\(300\) 4.66359 0.269252
\(301\) 2.63128 0.151664
\(302\) −3.39170 −0.195170
\(303\) 8.82958 0.507246
\(304\) 4.73805 0.271746
\(305\) −41.2869 −2.36408
\(306\) 1.24698 0.0712851
\(307\) −6.53538 −0.372994 −0.186497 0.982456i \(-0.559713\pi\)
−0.186497 + 0.982456i \(0.559713\pi\)
\(308\) 1.55496 0.0886020
\(309\) 1.89793 0.107970
\(310\) 7.66442 0.435310
\(311\) −27.7921 −1.57595 −0.787973 0.615710i \(-0.788869\pi\)
−0.787973 + 0.615710i \(0.788869\pi\)
\(312\) 0 0
\(313\) −4.35209 −0.245995 −0.122997 0.992407i \(-0.539251\pi\)
−0.122997 + 0.992407i \(0.539251\pi\)
\(314\) 23.7381 1.33962
\(315\) 3.10863 0.175152
\(316\) 11.1942 0.629725
\(317\) −12.5835 −0.706761 −0.353381 0.935480i \(-0.614968\pi\)
−0.353381 + 0.935480i \(0.614968\pi\)
\(318\) 7.09392 0.397807
\(319\) 1.64710 0.0922198
\(320\) −3.10863 −0.173778
\(321\) −3.58727 −0.200222
\(322\) 5.10817 0.284667
\(323\) −5.90825 −0.328744
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −6.35482 −0.351961
\(327\) 20.3167 1.12352
\(328\) 2.71654 0.149996
\(329\) 5.06412 0.279194
\(330\) −4.83379 −0.266091
\(331\) −19.8866 −1.09307 −0.546533 0.837437i \(-0.684053\pi\)
−0.546533 + 0.837437i \(0.684053\pi\)
\(332\) 4.40061 0.241515
\(333\) −7.92429 −0.434248
\(334\) −7.50114 −0.410444
\(335\) −26.3825 −1.44143
\(336\) −1.00000 −0.0545545
\(337\) 0.500733 0.0272767 0.0136383 0.999907i \(-0.495659\pi\)
0.0136383 + 0.999907i \(0.495659\pi\)
\(338\) 0 0
\(339\) −6.85060 −0.372074
\(340\) 3.87640 0.210227
\(341\) −3.83379 −0.207611
\(342\) −4.73805 −0.256205
\(343\) −1.00000 −0.0539949
\(344\) 2.63128 0.141869
\(345\) −15.8794 −0.854920
\(346\) 16.1881 0.870276
\(347\) −24.7464 −1.32846 −0.664229 0.747530i \(-0.731240\pi\)
−0.664229 + 0.747530i \(0.731240\pi\)
\(348\) −1.05926 −0.0567821
\(349\) 4.30578 0.230483 0.115241 0.993338i \(-0.463236\pi\)
0.115241 + 0.993338i \(0.463236\pi\)
\(350\) 4.66359 0.249279
\(351\) 0 0
\(352\) 1.55496 0.0828795
\(353\) 4.18501 0.222746 0.111373 0.993779i \(-0.464475\pi\)
0.111373 + 0.993779i \(0.464475\pi\)
\(354\) −3.41870 −0.181702
\(355\) −16.5177 −0.876668
\(356\) −5.76399 −0.305491
\(357\) 1.24698 0.0659972
\(358\) −1.95421 −0.103283
\(359\) 6.33135 0.334156 0.167078 0.985944i \(-0.446567\pi\)
0.167078 + 0.985944i \(0.446567\pi\)
\(360\) 3.10863 0.163839
\(361\) 3.44914 0.181533
\(362\) 1.81969 0.0956406
\(363\) −8.58211 −0.450444
\(364\) 0 0
\(365\) 29.3783 1.53773
\(366\) −13.2814 −0.694229
\(367\) 19.8935 1.03843 0.519216 0.854643i \(-0.326224\pi\)
0.519216 + 0.854643i \(0.326224\pi\)
\(368\) 5.10817 0.266282
\(369\) −2.71654 −0.141417
\(370\) −24.6337 −1.28064
\(371\) 7.09392 0.368298
\(372\) 2.46553 0.127832
\(373\) −35.9969 −1.86385 −0.931923 0.362655i \(-0.881870\pi\)
−0.931923 + 0.362655i \(0.881870\pi\)
\(374\) −1.93900 −0.100263
\(375\) 1.04578 0.0540036
\(376\) 5.06412 0.261162
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −29.5252 −1.51661 −0.758304 0.651901i \(-0.773972\pi\)
−0.758304 + 0.651901i \(0.773972\pi\)
\(380\) −14.7289 −0.755574
\(381\) 8.46378 0.433613
\(382\) 23.3210 1.19320
\(383\) 0.770083 0.0393494 0.0196747 0.999806i \(-0.493737\pi\)
0.0196747 + 0.999806i \(0.493737\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.83379 −0.246353
\(386\) 7.99277 0.406821
\(387\) −2.63128 −0.133755
\(388\) −10.8007 −0.548322
\(389\) 18.6621 0.946208 0.473104 0.881006i \(-0.343133\pi\)
0.473104 + 0.881006i \(0.343133\pi\)
\(390\) 0 0
\(391\) −6.36979 −0.322134
\(392\) −1.00000 −0.0505076
\(393\) −5.07860 −0.256181
\(394\) −2.24858 −0.113282
\(395\) −34.7988 −1.75092
\(396\) −1.55496 −0.0781396
\(397\) −17.7403 −0.890360 −0.445180 0.895441i \(-0.646860\pi\)
−0.445180 + 0.895441i \(0.646860\pi\)
\(398\) 25.4768 1.27704
\(399\) −4.73805 −0.237199
\(400\) 4.66359 0.233179
\(401\) −18.1461 −0.906172 −0.453086 0.891467i \(-0.649677\pi\)
−0.453086 + 0.891467i \(0.649677\pi\)
\(402\) −8.48684 −0.423285
\(403\) 0 0
\(404\) 8.82958 0.439288
\(405\) −3.10863 −0.154469
\(406\) −1.05926 −0.0525700
\(407\) 12.3219 0.610776
\(408\) 1.24698 0.0617347
\(409\) −0.936649 −0.0463143 −0.0231572 0.999732i \(-0.507372\pi\)
−0.0231572 + 0.999732i \(0.507372\pi\)
\(410\) −8.44471 −0.417054
\(411\) −20.8764 −1.02976
\(412\) 1.89793 0.0935044
\(413\) −3.41870 −0.168223
\(414\) −5.10817 −0.251053
\(415\) −13.6799 −0.671519
\(416\) 0 0
\(417\) 17.7255 0.868022
\(418\) 7.36747 0.360355
\(419\) −10.0234 −0.489675 −0.244838 0.969564i \(-0.578735\pi\)
−0.244838 + 0.969564i \(0.578735\pi\)
\(420\) 3.10863 0.151686
\(421\) 19.7171 0.960951 0.480475 0.877008i \(-0.340464\pi\)
0.480475 + 0.877008i \(0.340464\pi\)
\(422\) −2.01914 −0.0982902
\(423\) −5.06412 −0.246226
\(424\) 7.09392 0.344511
\(425\) −5.81540 −0.282088
\(426\) −5.31350 −0.257440
\(427\) −13.2814 −0.642731
\(428\) −3.58727 −0.173397
\(429\) 0 0
\(430\) −8.17967 −0.394459
\(431\) 31.5252 1.51852 0.759259 0.650789i \(-0.225562\pi\)
0.759259 + 0.650789i \(0.225562\pi\)
\(432\) 1.00000 0.0481125
\(433\) 19.6284 0.943281 0.471641 0.881791i \(-0.343662\pi\)
0.471641 + 0.881791i \(0.343662\pi\)
\(434\) 2.46553 0.118349
\(435\) 3.29284 0.157879
\(436\) 20.3167 0.972995
\(437\) 24.2028 1.15778
\(438\) 9.45056 0.451565
\(439\) 34.8525 1.66342 0.831708 0.555213i \(-0.187363\pi\)
0.831708 + 0.555213i \(0.187363\pi\)
\(440\) −4.83379 −0.230442
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −9.65305 −0.458630 −0.229315 0.973352i \(-0.573649\pi\)
−0.229315 + 0.973352i \(0.573649\pi\)
\(444\) −7.92429 −0.376070
\(445\) 17.9181 0.849401
\(446\) −13.1491 −0.622630
\(447\) −0.829877 −0.0392518
\(448\) −1.00000 −0.0472456
\(449\) −15.2830 −0.721249 −0.360625 0.932711i \(-0.617436\pi\)
−0.360625 + 0.932711i \(0.617436\pi\)
\(450\) −4.66359 −0.219844
\(451\) 4.22410 0.198905
\(452\) −6.85060 −0.322225
\(453\) 3.39170 0.159356
\(454\) 1.90722 0.0895105
\(455\) 0 0
\(456\) −4.73805 −0.221880
\(457\) −16.0318 −0.749937 −0.374968 0.927038i \(-0.622346\pi\)
−0.374968 + 0.927038i \(0.622346\pi\)
\(458\) −1.32344 −0.0618403
\(459\) −1.24698 −0.0582040
\(460\) −15.8794 −0.740382
\(461\) −28.6119 −1.33259 −0.666294 0.745689i \(-0.732121\pi\)
−0.666294 + 0.745689i \(0.732121\pi\)
\(462\) −1.55496 −0.0723432
\(463\) 35.8620 1.66665 0.833325 0.552783i \(-0.186434\pi\)
0.833325 + 0.552783i \(0.186434\pi\)
\(464\) −1.05926 −0.0491747
\(465\) −7.66442 −0.355429
\(466\) 23.7561 1.10048
\(467\) −14.9263 −0.690708 −0.345354 0.938473i \(-0.612241\pi\)
−0.345354 + 0.938473i \(0.612241\pi\)
\(468\) 0 0
\(469\) −8.48684 −0.391886
\(470\) −15.7425 −0.726147
\(471\) −23.7381 −1.09379
\(472\) −3.41870 −0.157359
\(473\) 4.09153 0.188129
\(474\) −11.1942 −0.514169
\(475\) 22.0963 1.01385
\(476\) 1.24698 0.0571552
\(477\) −7.09392 −0.324808
\(478\) 27.3308 1.25008
\(479\) 14.4348 0.659541 0.329771 0.944061i \(-0.393029\pi\)
0.329771 + 0.944061i \(0.393029\pi\)
\(480\) 3.10863 0.141889
\(481\) 0 0
\(482\) 2.68328 0.122220
\(483\) −5.10817 −0.232430
\(484\) −8.58211 −0.390096
\(485\) 33.5754 1.52458
\(486\) −1.00000 −0.0453609
\(487\) 24.8740 1.12715 0.563575 0.826065i \(-0.309425\pi\)
0.563575 + 0.826065i \(0.309425\pi\)
\(488\) −13.2814 −0.601220
\(489\) 6.35482 0.287375
\(490\) 3.10863 0.140434
\(491\) −10.6142 −0.479014 −0.239507 0.970895i \(-0.576986\pi\)
−0.239507 + 0.970895i \(0.576986\pi\)
\(492\) −2.71654 −0.122471
\(493\) 1.32087 0.0594890
\(494\) 0 0
\(495\) 4.83379 0.217263
\(496\) 2.46553 0.110705
\(497\) −5.31350 −0.238343
\(498\) −4.40061 −0.197196
\(499\) −0.950418 −0.0425465 −0.0212733 0.999774i \(-0.506772\pi\)
−0.0212733 + 0.999774i \(0.506772\pi\)
\(500\) 1.04578 0.0467685
\(501\) 7.50114 0.335126
\(502\) 30.8962 1.37897
\(503\) 34.9853 1.55992 0.779958 0.625832i \(-0.215240\pi\)
0.779958 + 0.625832i \(0.215240\pi\)
\(504\) 1.00000 0.0445435
\(505\) −27.4479 −1.22142
\(506\) 7.94300 0.353109
\(507\) 0 0
\(508\) 8.46378 0.375520
\(509\) −26.0425 −1.15431 −0.577157 0.816634i \(-0.695838\pi\)
−0.577157 + 0.816634i \(0.695838\pi\)
\(510\) −3.87640 −0.171650
\(511\) 9.45056 0.418068
\(512\) −1.00000 −0.0441942
\(513\) 4.73805 0.209190
\(514\) −27.6822 −1.22101
\(515\) −5.89997 −0.259984
\(516\) −2.63128 −0.115836
\(517\) 7.87450 0.346320
\(518\) −7.92429 −0.348173
\(519\) −16.1881 −0.710578
\(520\) 0 0
\(521\) 39.0890 1.71252 0.856261 0.516544i \(-0.172782\pi\)
0.856261 + 0.516544i \(0.172782\pi\)
\(522\) 1.05926 0.0463624
\(523\) −6.41000 −0.280290 −0.140145 0.990131i \(-0.544757\pi\)
−0.140145 + 0.990131i \(0.544757\pi\)
\(524\) −5.07860 −0.221860
\(525\) −4.66359 −0.203536
\(526\) −21.8601 −0.953144
\(527\) −3.07446 −0.133926
\(528\) −1.55496 −0.0676709
\(529\) 3.09343 0.134497
\(530\) −22.0524 −0.957894
\(531\) 3.41870 0.148359
\(532\) −4.73805 −0.205421
\(533\) 0 0
\(534\) 5.76399 0.249432
\(535\) 11.1515 0.482122
\(536\) −8.48684 −0.366576
\(537\) 1.95421 0.0843303
\(538\) 17.0766 0.736225
\(539\) −1.55496 −0.0669768
\(540\) −3.10863 −0.133774
\(541\) −20.7891 −0.893792 −0.446896 0.894586i \(-0.647471\pi\)
−0.446896 + 0.894586i \(0.647471\pi\)
\(542\) 27.8718 1.19720
\(543\) −1.81969 −0.0780902
\(544\) 1.24698 0.0534638
\(545\) −63.1572 −2.70536
\(546\) 0 0
\(547\) 12.9402 0.553284 0.276642 0.960973i \(-0.410778\pi\)
0.276642 + 0.960973i \(0.410778\pi\)
\(548\) −20.8764 −0.891795
\(549\) 13.2814 0.566836
\(550\) 7.25169 0.309213
\(551\) −5.01881 −0.213808
\(552\) −5.10817 −0.217418
\(553\) −11.1942 −0.476028
\(554\) 31.9253 1.35637
\(555\) 24.6337 1.04564
\(556\) 17.7255 0.751729
\(557\) 24.0823 1.02040 0.510200 0.860056i \(-0.329571\pi\)
0.510200 + 0.860056i \(0.329571\pi\)
\(558\) −2.46553 −0.104374
\(559\) 0 0
\(560\) 3.10863 0.131364
\(561\) 1.93900 0.0818647
\(562\) −11.3692 −0.479580
\(563\) −27.0146 −1.13853 −0.569266 0.822154i \(-0.692772\pi\)
−0.569266 + 0.822154i \(0.692772\pi\)
\(564\) −5.06412 −0.213238
\(565\) 21.2960 0.895929
\(566\) 16.6264 0.698858
\(567\) −1.00000 −0.0419961
\(568\) −5.31350 −0.222949
\(569\) −17.1952 −0.720859 −0.360429 0.932787i \(-0.617370\pi\)
−0.360429 + 0.932787i \(0.617370\pi\)
\(570\) 14.7289 0.616924
\(571\) −21.5316 −0.901071 −0.450536 0.892758i \(-0.648767\pi\)
−0.450536 + 0.892758i \(0.648767\pi\)
\(572\) 0 0
\(573\) −23.3210 −0.974247
\(574\) −2.71654 −0.113386
\(575\) 23.8224 0.993464
\(576\) 1.00000 0.0416667
\(577\) 30.2104 1.25767 0.628837 0.777537i \(-0.283531\pi\)
0.628837 + 0.777537i \(0.283531\pi\)
\(578\) 15.4450 0.642429
\(579\) −7.99277 −0.332168
\(580\) 3.29284 0.136728
\(581\) −4.40061 −0.182568
\(582\) 10.8007 0.447703
\(583\) 11.0307 0.456847
\(584\) 9.45056 0.391067
\(585\) 0 0
\(586\) −5.41358 −0.223633
\(587\) 39.7362 1.64009 0.820045 0.572299i \(-0.193948\pi\)
0.820045 + 0.572299i \(0.193948\pi\)
\(588\) 1.00000 0.0412393
\(589\) 11.6818 0.481340
\(590\) 10.6275 0.437527
\(591\) 2.24858 0.0924943
\(592\) −7.92429 −0.325686
\(593\) −37.1150 −1.52413 −0.762066 0.647499i \(-0.775815\pi\)
−0.762066 + 0.647499i \(0.775815\pi\)
\(594\) 1.55496 0.0638007
\(595\) −3.87640 −0.158917
\(596\) −0.829877 −0.0339931
\(597\) −25.4768 −1.04270
\(598\) 0 0
\(599\) 10.5957 0.432928 0.216464 0.976291i \(-0.430548\pi\)
0.216464 + 0.976291i \(0.430548\pi\)
\(600\) −4.66359 −0.190390
\(601\) 0.577212 0.0235450 0.0117725 0.999931i \(-0.496253\pi\)
0.0117725 + 0.999931i \(0.496253\pi\)
\(602\) −2.63128 −0.107243
\(603\) 8.48684 0.345611
\(604\) 3.39170 0.138006
\(605\) 26.6786 1.08464
\(606\) −8.82958 −0.358677
\(607\) 3.75798 0.152532 0.0762659 0.997088i \(-0.475700\pi\)
0.0762659 + 0.997088i \(0.475700\pi\)
\(608\) −4.73805 −0.192153
\(609\) 1.05926 0.0429232
\(610\) 41.2869 1.67166
\(611\) 0 0
\(612\) −1.24698 −0.0504062
\(613\) −8.92496 −0.360476 −0.180238 0.983623i \(-0.557687\pi\)
−0.180238 + 0.983623i \(0.557687\pi\)
\(614\) 6.53538 0.263746
\(615\) 8.44471 0.340524
\(616\) −1.55496 −0.0626510
\(617\) 8.90864 0.358648 0.179324 0.983790i \(-0.442609\pi\)
0.179324 + 0.983790i \(0.442609\pi\)
\(618\) −1.89793 −0.0763460
\(619\) 8.63105 0.346911 0.173456 0.984842i \(-0.444507\pi\)
0.173456 + 0.984842i \(0.444507\pi\)
\(620\) −7.66442 −0.307810
\(621\) 5.10817 0.204984
\(622\) 27.7921 1.11436
\(623\) 5.76399 0.230930
\(624\) 0 0
\(625\) −26.5689 −1.06276
\(626\) 4.35209 0.173945
\(627\) −7.36747 −0.294229
\(628\) −23.7381 −0.947251
\(629\) 9.88142 0.393998
\(630\) −3.10863 −0.123851
\(631\) 22.0935 0.879528 0.439764 0.898113i \(-0.355062\pi\)
0.439764 + 0.898113i \(0.355062\pi\)
\(632\) −11.1942 −0.445283
\(633\) 2.01914 0.0802536
\(634\) 12.5835 0.499756
\(635\) −26.3108 −1.04411
\(636\) −7.09392 −0.281292
\(637\) 0 0
\(638\) −1.64710 −0.0652092
\(639\) 5.31350 0.210199
\(640\) 3.10863 0.122879
\(641\) 10.0871 0.398416 0.199208 0.979957i \(-0.436163\pi\)
0.199208 + 0.979957i \(0.436163\pi\)
\(642\) 3.58727 0.141578
\(643\) −8.84091 −0.348652 −0.174326 0.984688i \(-0.555775\pi\)
−0.174326 + 0.984688i \(0.555775\pi\)
\(644\) −5.10817 −0.201290
\(645\) 8.17967 0.322074
\(646\) 5.90825 0.232457
\(647\) 1.73856 0.0683497 0.0341748 0.999416i \(-0.489120\pi\)
0.0341748 + 0.999416i \(0.489120\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −5.31594 −0.208669
\(650\) 0 0
\(651\) −2.46553 −0.0966316
\(652\) 6.35482 0.248874
\(653\) −45.8052 −1.79250 −0.896248 0.443554i \(-0.853717\pi\)
−0.896248 + 0.443554i \(0.853717\pi\)
\(654\) −20.3167 −0.794447
\(655\) 15.7875 0.616868
\(656\) −2.71654 −0.106063
\(657\) −9.45056 −0.368701
\(658\) −5.06412 −0.197420
\(659\) 11.7599 0.458099 0.229050 0.973415i \(-0.426438\pi\)
0.229050 + 0.973415i \(0.426438\pi\)
\(660\) 4.83379 0.188155
\(661\) 13.5257 0.526089 0.263044 0.964784i \(-0.415273\pi\)
0.263044 + 0.964784i \(0.415273\pi\)
\(662\) 19.8866 0.772915
\(663\) 0 0
\(664\) −4.40061 −0.170777
\(665\) 14.7289 0.571161
\(666\) 7.92429 0.307060
\(667\) −5.41086 −0.209509
\(668\) 7.50114 0.290228
\(669\) 13.1491 0.508375
\(670\) 26.3825 1.01924
\(671\) −20.6520 −0.797262
\(672\) 1.00000 0.0385758
\(673\) 12.0762 0.465505 0.232752 0.972536i \(-0.425227\pi\)
0.232752 + 0.972536i \(0.425227\pi\)
\(674\) −0.500733 −0.0192875
\(675\) 4.66359 0.179502
\(676\) 0 0
\(677\) 4.22192 0.162262 0.0811308 0.996703i \(-0.474147\pi\)
0.0811308 + 0.996703i \(0.474147\pi\)
\(678\) 6.85060 0.263096
\(679\) 10.8007 0.414492
\(680\) −3.87640 −0.148653
\(681\) −1.90722 −0.0730850
\(682\) 3.83379 0.146803
\(683\) −46.8330 −1.79201 −0.896007 0.444039i \(-0.853545\pi\)
−0.896007 + 0.444039i \(0.853545\pi\)
\(684\) 4.73805 0.181164
\(685\) 64.8970 2.47959
\(686\) 1.00000 0.0381802
\(687\) 1.32344 0.0504924
\(688\) −2.63128 −0.100316
\(689\) 0 0
\(690\) 15.8794 0.604519
\(691\) 19.2883 0.733762 0.366881 0.930268i \(-0.380426\pi\)
0.366881 + 0.930268i \(0.380426\pi\)
\(692\) −16.1881 −0.615378
\(693\) 1.55496 0.0590680
\(694\) 24.7464 0.939361
\(695\) −55.1021 −2.09014
\(696\) 1.05926 0.0401510
\(697\) 3.38747 0.128309
\(698\) −4.30578 −0.162976
\(699\) −23.7561 −0.898539
\(700\) −4.66359 −0.176267
\(701\) −16.9306 −0.639459 −0.319729 0.947509i \(-0.603592\pi\)
−0.319729 + 0.947509i \(0.603592\pi\)
\(702\) 0 0
\(703\) −37.5457 −1.41606
\(704\) −1.55496 −0.0586047
\(705\) 15.7425 0.592897
\(706\) −4.18501 −0.157505
\(707\) −8.82958 −0.332070
\(708\) 3.41870 0.128483
\(709\) 7.93895 0.298153 0.149077 0.988826i \(-0.452370\pi\)
0.149077 + 0.988826i \(0.452370\pi\)
\(710\) 16.5177 0.619898
\(711\) 11.1942 0.419817
\(712\) 5.76399 0.216015
\(713\) 12.5943 0.471662
\(714\) −1.24698 −0.0466670
\(715\) 0 0
\(716\) 1.95421 0.0730322
\(717\) −27.3308 −1.02069
\(718\) −6.33135 −0.236284
\(719\) 31.5702 1.17737 0.588684 0.808363i \(-0.299646\pi\)
0.588684 + 0.808363i \(0.299646\pi\)
\(720\) −3.10863 −0.115852
\(721\) −1.89793 −0.0706827
\(722\) −3.44914 −0.128364
\(723\) −2.68328 −0.0997924
\(724\) −1.81969 −0.0676281
\(725\) −4.93993 −0.183465
\(726\) 8.58211 0.318512
\(727\) 10.8589 0.402733 0.201367 0.979516i \(-0.435462\pi\)
0.201367 + 0.979516i \(0.435462\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −29.3783 −1.08734
\(731\) 3.28115 0.121358
\(732\) 13.2814 0.490894
\(733\) −2.22682 −0.0822495 −0.0411247 0.999154i \(-0.513094\pi\)
−0.0411247 + 0.999154i \(0.513094\pi\)
\(734\) −19.8935 −0.734282
\(735\) −3.10863 −0.114664
\(736\) −5.10817 −0.188290
\(737\) −13.1967 −0.486106
\(738\) 2.71654 0.0999971
\(739\) −39.5399 −1.45450 −0.727249 0.686374i \(-0.759201\pi\)
−0.727249 + 0.686374i \(0.759201\pi\)
\(740\) 24.6337 0.905552
\(741\) 0 0
\(742\) −7.09392 −0.260426
\(743\) 35.0085 1.28434 0.642169 0.766563i \(-0.278035\pi\)
0.642169 + 0.766563i \(0.278035\pi\)
\(744\) −2.46553 −0.0903906
\(745\) 2.57978 0.0945159
\(746\) 35.9969 1.31794
\(747\) 4.40061 0.161010
\(748\) 1.93900 0.0708969
\(749\) 3.58727 0.131076
\(750\) −1.04578 −0.0381863
\(751\) 3.08816 0.112689 0.0563443 0.998411i \(-0.482056\pi\)
0.0563443 + 0.998411i \(0.482056\pi\)
\(752\) −5.06412 −0.184670
\(753\) −30.8962 −1.12592
\(754\) 0 0
\(755\) −10.5435 −0.383719
\(756\) −1.00000 −0.0363696
\(757\) −31.1069 −1.13060 −0.565300 0.824885i \(-0.691240\pi\)
−0.565300 + 0.824885i \(0.691240\pi\)
\(758\) 29.5252 1.07240
\(759\) −7.94300 −0.288312
\(760\) 14.7289 0.534272
\(761\) −34.3881 −1.24657 −0.623284 0.781996i \(-0.714202\pi\)
−0.623284 + 0.781996i \(0.714202\pi\)
\(762\) −8.46378 −0.306611
\(763\) −20.3167 −0.735515
\(764\) −23.3210 −0.843723
\(765\) 3.87640 0.140152
\(766\) −0.770083 −0.0278242
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −28.7352 −1.03622 −0.518109 0.855314i \(-0.673364\pi\)
−0.518109 + 0.855314i \(0.673364\pi\)
\(770\) 4.83379 0.174198
\(771\) 27.6822 0.996951
\(772\) −7.99277 −0.287666
\(773\) 43.0766 1.54936 0.774679 0.632354i \(-0.217911\pi\)
0.774679 + 0.632354i \(0.217911\pi\)
\(774\) 2.63128 0.0945793
\(775\) 11.4982 0.413028
\(776\) 10.8007 0.387722
\(777\) 7.92429 0.284282
\(778\) −18.6621 −0.669070
\(779\) −12.8711 −0.461155
\(780\) 0 0
\(781\) −8.26226 −0.295647
\(782\) 6.36979 0.227783
\(783\) −1.05926 −0.0378547
\(784\) 1.00000 0.0357143
\(785\) 73.7929 2.63378
\(786\) 5.07860 0.181148
\(787\) 12.5432 0.447117 0.223558 0.974691i \(-0.428233\pi\)
0.223558 + 0.974691i \(0.428233\pi\)
\(788\) 2.24858 0.0801024
\(789\) 21.8601 0.778239
\(790\) 34.7988 1.23808
\(791\) 6.85060 0.243579
\(792\) 1.55496 0.0552530
\(793\) 0 0
\(794\) 17.7403 0.629580
\(795\) 22.0524 0.782117
\(796\) −25.4768 −0.903001
\(797\) 35.9473 1.27332 0.636659 0.771146i \(-0.280316\pi\)
0.636659 + 0.771146i \(0.280316\pi\)
\(798\) 4.73805 0.167725
\(799\) 6.31486 0.223404
\(800\) −4.66359 −0.164883
\(801\) −5.76399 −0.203661
\(802\) 18.1461 0.640761
\(803\) 14.6952 0.518583
\(804\) 8.48684 0.299308
\(805\) 15.8794 0.559676
\(806\) 0 0
\(807\) −17.0766 −0.601125
\(808\) −8.82958 −0.310623
\(809\) 38.3283 1.34755 0.673776 0.738936i \(-0.264671\pi\)
0.673776 + 0.738936i \(0.264671\pi\)
\(810\) 3.10863 0.109226
\(811\) 55.4449 1.94693 0.973466 0.228831i \(-0.0734903\pi\)
0.973466 + 0.228831i \(0.0734903\pi\)
\(812\) 1.05926 0.0371726
\(813\) −27.8718 −0.977508
\(814\) −12.3219 −0.431884
\(815\) −19.7548 −0.691980
\(816\) −1.24698 −0.0436530
\(817\) −12.4671 −0.436170
\(818\) 0.936649 0.0327492
\(819\) 0 0
\(820\) 8.44471 0.294902
\(821\) −30.7208 −1.07216 −0.536082 0.844166i \(-0.680096\pi\)
−0.536082 + 0.844166i \(0.680096\pi\)
\(822\) 20.8764 0.728148
\(823\) −29.4586 −1.02686 −0.513431 0.858131i \(-0.671626\pi\)
−0.513431 + 0.858131i \(0.671626\pi\)
\(824\) −1.89793 −0.0661176
\(825\) −7.25169 −0.252471
\(826\) 3.41870 0.118952
\(827\) −39.5955 −1.37687 −0.688435 0.725298i \(-0.741702\pi\)
−0.688435 + 0.725298i \(0.741702\pi\)
\(828\) 5.10817 0.177521
\(829\) 52.6258 1.82777 0.913884 0.405975i \(-0.133068\pi\)
0.913884 + 0.405975i \(0.133068\pi\)
\(830\) 13.6799 0.474836
\(831\) −31.9253 −1.10748
\(832\) 0 0
\(833\) −1.24698 −0.0432053
\(834\) −17.7255 −0.613784
\(835\) −23.3183 −0.806962
\(836\) −7.36747 −0.254809
\(837\) 2.46553 0.0852211
\(838\) 10.0234 0.346253
\(839\) 31.0141 1.07073 0.535363 0.844622i \(-0.320175\pi\)
0.535363 + 0.844622i \(0.320175\pi\)
\(840\) −3.10863 −0.107258
\(841\) −27.8780 −0.961310
\(842\) −19.7171 −0.679495
\(843\) 11.3692 0.391576
\(844\) 2.01914 0.0695016
\(845\) 0 0
\(846\) 5.06412 0.174108
\(847\) 8.58211 0.294885
\(848\) −7.09392 −0.243606
\(849\) −16.6264 −0.570615
\(850\) 5.81540 0.199467
\(851\) −40.4786 −1.38759
\(852\) 5.31350 0.182037
\(853\) −55.8464 −1.91214 −0.956072 0.293133i \(-0.905302\pi\)
−0.956072 + 0.293133i \(0.905302\pi\)
\(854\) 13.2814 0.454480
\(855\) −14.7289 −0.503716
\(856\) 3.58727 0.122610
\(857\) 26.7950 0.915299 0.457650 0.889133i \(-0.348691\pi\)
0.457650 + 0.889133i \(0.348691\pi\)
\(858\) 0 0
\(859\) 13.5325 0.461724 0.230862 0.972986i \(-0.425845\pi\)
0.230862 + 0.972986i \(0.425845\pi\)
\(860\) 8.17967 0.278924
\(861\) 2.71654 0.0925793
\(862\) −31.5252 −1.07375
\(863\) −34.8946 −1.18783 −0.593914 0.804529i \(-0.702418\pi\)
−0.593914 + 0.804529i \(0.702418\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 50.3228 1.71103
\(866\) −19.6284 −0.667000
\(867\) −15.4450 −0.524541
\(868\) −2.46553 −0.0836855
\(869\) −17.4066 −0.590478
\(870\) −3.29284 −0.111638
\(871\) 0 0
\(872\) −20.3167 −0.688011
\(873\) −10.8007 −0.365548
\(874\) −24.2028 −0.818672
\(875\) −1.04578 −0.0353537
\(876\) −9.45056 −0.319305
\(877\) −51.7834 −1.74860 −0.874300 0.485386i \(-0.838679\pi\)
−0.874300 + 0.485386i \(0.838679\pi\)
\(878\) −34.8525 −1.17621
\(879\) 5.41358 0.182596
\(880\) 4.83379 0.162947
\(881\) −2.60278 −0.0876900 −0.0438450 0.999038i \(-0.513961\pi\)
−0.0438450 + 0.999038i \(0.513961\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −38.5127 −1.29605 −0.648027 0.761617i \(-0.724406\pi\)
−0.648027 + 0.761617i \(0.724406\pi\)
\(884\) 0 0
\(885\) −10.6275 −0.357239
\(886\) 9.65305 0.324300
\(887\) 15.6703 0.526156 0.263078 0.964775i \(-0.415262\pi\)
0.263078 + 0.964775i \(0.415262\pi\)
\(888\) 7.92429 0.265922
\(889\) −8.46378 −0.283866
\(890\) −17.9181 −0.600617
\(891\) −1.55496 −0.0520931
\(892\) 13.1491 0.440266
\(893\) −23.9941 −0.802931
\(894\) 0.829877 0.0277552
\(895\) −6.07491 −0.203062
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 15.2830 0.510000
\(899\) −2.61162 −0.0871025
\(900\) 4.66359 0.155453
\(901\) 8.84597 0.294702
\(902\) −4.22410 −0.140647
\(903\) 2.63128 0.0875634
\(904\) 6.85060 0.227848
\(905\) 5.65673 0.188036
\(906\) −3.39170 −0.112682
\(907\) −30.6745 −1.01853 −0.509265 0.860610i \(-0.670083\pi\)
−0.509265 + 0.860610i \(0.670083\pi\)
\(908\) −1.90722 −0.0632935
\(909\) 8.82958 0.292859
\(910\) 0 0
\(911\) 32.8588 1.08866 0.544331 0.838870i \(-0.316784\pi\)
0.544331 + 0.838870i \(0.316784\pi\)
\(912\) 4.73805 0.156893
\(913\) −6.84277 −0.226463
\(914\) 16.0318 0.530285
\(915\) −41.2869 −1.36490
\(916\) 1.32344 0.0437277
\(917\) 5.07860 0.167710
\(918\) 1.24698 0.0411565
\(919\) −10.6383 −0.350925 −0.175462 0.984486i \(-0.556142\pi\)
−0.175462 + 0.984486i \(0.556142\pi\)
\(920\) 15.8794 0.523529
\(921\) −6.53538 −0.215348
\(922\) 28.6119 0.942282
\(923\) 0 0
\(924\) 1.55496 0.0511544
\(925\) −36.9556 −1.21509
\(926\) −35.8620 −1.17850
\(927\) 1.89793 0.0623363
\(928\) 1.05926 0.0347718
\(929\) −3.54100 −0.116176 −0.0580882 0.998311i \(-0.518500\pi\)
−0.0580882 + 0.998311i \(0.518500\pi\)
\(930\) 7.66442 0.251326
\(931\) 4.73805 0.155283
\(932\) −23.7561 −0.778157
\(933\) −27.7921 −0.909873
\(934\) 14.9263 0.488404
\(935\) −6.02764 −0.197125
\(936\) 0 0
\(937\) −15.5489 −0.507959 −0.253980 0.967210i \(-0.581740\pi\)
−0.253980 + 0.967210i \(0.581740\pi\)
\(938\) 8.48684 0.277105
\(939\) −4.35209 −0.142025
\(940\) 15.7425 0.513464
\(941\) −34.3011 −1.11818 −0.559092 0.829106i \(-0.688850\pi\)
−0.559092 + 0.829106i \(0.688850\pi\)
\(942\) 23.7381 0.773427
\(943\) −13.8765 −0.451882
\(944\) 3.41870 0.111269
\(945\) 3.10863 0.101124
\(946\) −4.09153 −0.133027
\(947\) 45.7712 1.48737 0.743683 0.668533i \(-0.233077\pi\)
0.743683 + 0.668533i \(0.233077\pi\)
\(948\) 11.1942 0.363572
\(949\) 0 0
\(950\) −22.0963 −0.716900
\(951\) −12.5835 −0.408049
\(952\) −1.24698 −0.0404148
\(953\) 38.1938 1.23722 0.618609 0.785699i \(-0.287697\pi\)
0.618609 + 0.785699i \(0.287697\pi\)
\(954\) 7.09392 0.229674
\(955\) 72.4963 2.34592
\(956\) −27.3308 −0.883943
\(957\) 1.64710 0.0532431
\(958\) −14.4348 −0.466366
\(959\) 20.8764 0.674134
\(960\) −3.10863 −0.100331
\(961\) −24.9212 −0.803909
\(962\) 0 0
\(963\) −3.58727 −0.115598
\(964\) −2.68328 −0.0864228
\(965\) 24.8466 0.799839
\(966\) 5.10817 0.164353
\(967\) 1.46535 0.0471223 0.0235612 0.999722i \(-0.492500\pi\)
0.0235612 + 0.999722i \(0.492500\pi\)
\(968\) 8.58211 0.275839
\(969\) −5.90825 −0.189800
\(970\) −33.5754 −1.07804
\(971\) −15.1475 −0.486106 −0.243053 0.970013i \(-0.578149\pi\)
−0.243053 + 0.970013i \(0.578149\pi\)
\(972\) 1.00000 0.0320750
\(973\) −17.7255 −0.568254
\(974\) −24.8740 −0.797016
\(975\) 0 0
\(976\) 13.2814 0.425127
\(977\) −30.6974 −0.982098 −0.491049 0.871132i \(-0.663386\pi\)
−0.491049 + 0.871132i \(0.663386\pi\)
\(978\) −6.35482 −0.203205
\(979\) 8.96277 0.286451
\(980\) −3.10863 −0.0993016
\(981\) 20.3167 0.648663
\(982\) 10.6142 0.338714
\(983\) −13.4997 −0.430574 −0.215287 0.976551i \(-0.569069\pi\)
−0.215287 + 0.976551i \(0.569069\pi\)
\(984\) 2.71654 0.0866000
\(985\) −6.99001 −0.222720
\(986\) −1.32087 −0.0420651
\(987\) 5.06412 0.161193
\(988\) 0 0
\(989\) −13.4410 −0.427400
\(990\) −4.83379 −0.153628
\(991\) −39.7612 −1.26306 −0.631529 0.775352i \(-0.717572\pi\)
−0.631529 + 0.775352i \(0.717572\pi\)
\(992\) −2.46553 −0.0782806
\(993\) −19.8866 −0.631082
\(994\) 5.31350 0.168534
\(995\) 79.1980 2.51075
\(996\) 4.40061 0.139439
\(997\) 5.54069 0.175475 0.0877377 0.996144i \(-0.472036\pi\)
0.0877377 + 0.996144i \(0.472036\pi\)
\(998\) 0.950418 0.0300849
\(999\) −7.92429 −0.250713
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.1.2 6
13.12 even 2 7098.2.a.ct.1.5 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cr.1.2 6 1.1 even 1 trivial
7098.2.a.ct.1.5 yes 6 13.12 even 2