Properties

Label 7098.2.a.bh.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
Defining polynomial: \(x^{2} - x - 10\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 546)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.70156\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.70156 q^{10} +0.701562 q^{11} -1.00000 q^{12} +1.00000 q^{14} +2.70156 q^{15} +1.00000 q^{16} -2.70156 q^{17} -1.00000 q^{18} +0.701562 q^{19} -2.70156 q^{20} +1.00000 q^{21} -0.701562 q^{22} +4.70156 q^{23} +1.00000 q^{24} +2.29844 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.70156 q^{29} -2.70156 q^{30} -1.00000 q^{32} -0.701562 q^{33} +2.70156 q^{34} +2.70156 q^{35} +1.00000 q^{36} -10.7016 q^{37} -0.701562 q^{38} +2.70156 q^{40} -3.40312 q^{41} -1.00000 q^{42} -10.1047 q^{43} +0.701562 q^{44} -2.70156 q^{45} -4.70156 q^{46} +8.00000 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.29844 q^{50} +2.70156 q^{51} -2.00000 q^{53} +1.00000 q^{54} -1.89531 q^{55} +1.00000 q^{56} -0.701562 q^{57} -2.70156 q^{58} +14.8062 q^{59} +2.70156 q^{60} +1.29844 q^{61} -1.00000 q^{63} +1.00000 q^{64} +0.701562 q^{66} -5.40312 q^{67} -2.70156 q^{68} -4.70156 q^{69} -2.70156 q^{70} +8.00000 q^{71} -1.00000 q^{72} +1.29844 q^{73} +10.7016 q^{74} -2.29844 q^{75} +0.701562 q^{76} -0.701562 q^{77} +9.40312 q^{79} -2.70156 q^{80} +1.00000 q^{81} +3.40312 q^{82} +13.4031 q^{83} +1.00000 q^{84} +7.29844 q^{85} +10.1047 q^{86} -2.70156 q^{87} -0.701562 q^{88} +8.80625 q^{89} +2.70156 q^{90} +4.70156 q^{92} -8.00000 q^{94} -1.89531 q^{95} +1.00000 q^{96} +8.80625 q^{97} -1.00000 q^{98} +0.701562 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 2q^{3} + 2q^{4} + q^{5} + 2q^{6} - 2q^{7} - 2q^{8} + 2q^{9} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{3} + 2q^{4} + q^{5} + 2q^{6} - 2q^{7} - 2q^{8} + 2q^{9} - q^{10} - 5q^{11} - 2q^{12} + 2q^{14} - q^{15} + 2q^{16} + q^{17} - 2q^{18} - 5q^{19} + q^{20} + 2q^{21} + 5q^{22} + 3q^{23} + 2q^{24} + 11q^{25} - 2q^{27} - 2q^{28} - q^{29} + q^{30} - 2q^{32} + 5q^{33} - q^{34} - q^{35} + 2q^{36} - 15q^{37} + 5q^{38} - q^{40} + 6q^{41} - 2q^{42} - q^{43} - 5q^{44} + q^{45} - 3q^{46} + 16q^{47} - 2q^{48} + 2q^{49} - 11q^{50} - q^{51} - 4q^{53} + 2q^{54} - 23q^{55} + 2q^{56} + 5q^{57} + q^{58} + 4q^{59} - q^{60} + 9q^{61} - 2q^{63} + 2q^{64} - 5q^{66} + 2q^{67} + q^{68} - 3q^{69} + q^{70} + 16q^{71} - 2q^{72} + 9q^{73} + 15q^{74} - 11q^{75} - 5q^{76} + 5q^{77} + 6q^{79} + q^{80} + 2q^{81} - 6q^{82} + 14q^{83} + 2q^{84} + 21q^{85} + q^{86} + q^{87} + 5q^{88} - 8q^{89} - q^{90} + 3q^{92} - 16q^{94} - 23q^{95} + 2q^{96} - 8q^{97} - 2q^{98} - 5q^{99} + O(q^{100}) \)

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
\(5\) −2.70156 −1.20818 −0.604088 0.796918i \(-0.706462\pi\)
−0.604088 + 0.796918i \(0.706462\pi\)
\(6\) 1.00000 0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.70156 0.854309
\(11\) 0.701562 0.211529 0.105764 0.994391i \(-0.466271\pi\)
0.105764 + 0.994391i \(0.466271\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) 2.70156 0.697540
\(16\) 1.00000 0.250000
\(17\) −2.70156 −0.655225 −0.327613 0.944812i \(-0.606244\pi\)
−0.327613 + 0.944812i \(0.606244\pi\)
\(18\) −1.00000 −0.235702
\(19\) 0.701562 0.160949 0.0804747 0.996757i \(-0.474356\pi\)
0.0804747 + 0.996757i \(0.474356\pi\)
\(20\) −2.70156 −0.604088
\(21\) 1.00000 0.218218
\(22\) −0.701562 −0.149574
\(23\) 4.70156 0.980343 0.490172 0.871626i \(-0.336934\pi\)
0.490172 + 0.871626i \(0.336934\pi\)
\(24\) 1.00000 0.204124
\(25\) 2.29844 0.459688
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) 2.70156 0.501667 0.250834 0.968030i \(-0.419295\pi\)
0.250834 + 0.968030i \(0.419295\pi\)
\(30\) −2.70156 −0.493236
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.701562 −0.122126
\(34\) 2.70156 0.463314
\(35\) 2.70156 0.456647
\(36\) 1.00000 0.166667
\(37\) −10.7016 −1.75933 −0.879663 0.475598i \(-0.842232\pi\)
−0.879663 + 0.475598i \(0.842232\pi\)
\(38\) −0.701562 −0.113808
\(39\) 0 0
\(40\) 2.70156 0.427154
\(41\) −3.40312 −0.531479 −0.265739 0.964045i \(-0.585616\pi\)
−0.265739 + 0.964045i \(0.585616\pi\)
\(42\) −1.00000 −0.154303
\(43\) −10.1047 −1.54095 −0.770475 0.637470i \(-0.779981\pi\)
−0.770475 + 0.637470i \(0.779981\pi\)
\(44\) 0.701562 0.105764
\(45\) −2.70156 −0.402725
\(46\) −4.70156 −0.693208
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −2.29844 −0.325048
\(51\) 2.70156 0.378294
\(52\) 0 0
\(53\) −2.00000 −0.274721 −0.137361 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.89531 −0.255564
\(56\) 1.00000 0.133631
\(57\) −0.701562 −0.0929242
\(58\) −2.70156 −0.354732
\(59\) 14.8062 1.92761 0.963805 0.266609i \(-0.0859033\pi\)
0.963805 + 0.266609i \(0.0859033\pi\)
\(60\) 2.70156 0.348770
\(61\) 1.29844 0.166248 0.0831240 0.996539i \(-0.473510\pi\)
0.0831240 + 0.996539i \(0.473510\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.701562 0.0863563
\(67\) −5.40312 −0.660097 −0.330048 0.943964i \(-0.607065\pi\)
−0.330048 + 0.943964i \(0.607065\pi\)
\(68\) −2.70156 −0.327613
\(69\) −4.70156 −0.566002
\(70\) −2.70156 −0.322898
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.29844 0.151971 0.0759853 0.997109i \(-0.475790\pi\)
0.0759853 + 0.997109i \(0.475790\pi\)
\(74\) 10.7016 1.24403
\(75\) −2.29844 −0.265401
\(76\) 0.701562 0.0804747
\(77\) −0.701562 −0.0799504
\(78\) 0 0
\(79\) 9.40312 1.05793 0.528967 0.848642i \(-0.322579\pi\)
0.528967 + 0.848642i \(0.322579\pi\)
\(80\) −2.70156 −0.302044
\(81\) 1.00000 0.111111
\(82\) 3.40312 0.375812
\(83\) 13.4031 1.47118 0.735592 0.677425i \(-0.236904\pi\)
0.735592 + 0.677425i \(0.236904\pi\)
\(84\) 1.00000 0.109109
\(85\) 7.29844 0.791627
\(86\) 10.1047 1.08962
\(87\) −2.70156 −0.289638
\(88\) −0.701562 −0.0747868
\(89\) 8.80625 0.933460 0.466730 0.884400i \(-0.345432\pi\)
0.466730 + 0.884400i \(0.345432\pi\)
\(90\) 2.70156 0.284770
\(91\) 0 0
\(92\) 4.70156 0.490172
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) −1.89531 −0.194455
\(96\) 1.00000 0.102062
\(97\) 8.80625 0.894139 0.447070 0.894499i \(-0.352468\pi\)
0.447070 + 0.894499i \(0.352468\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.701562 0.0705096
\(100\) 2.29844 0.229844
\(101\) −3.40312 −0.338624 −0.169312 0.985563i \(-0.554154\pi\)
−0.169312 + 0.985563i \(0.554154\pi\)
\(102\) −2.70156 −0.267495
\(103\) −3.29844 −0.325005 −0.162502 0.986708i \(-0.551957\pi\)
−0.162502 + 0.986708i \(0.551957\pi\)
\(104\) 0 0
\(105\) −2.70156 −0.263645
\(106\) 2.00000 0.194257
\(107\) −5.40312 −0.522340 −0.261170 0.965293i \(-0.584108\pi\)
−0.261170 + 0.965293i \(0.584108\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −9.29844 −0.890629 −0.445314 0.895374i \(-0.646908\pi\)
−0.445314 + 0.895374i \(0.646908\pi\)
\(110\) 1.89531 0.180711
\(111\) 10.7016 1.01575
\(112\) −1.00000 −0.0944911
\(113\) 4.80625 0.452134 0.226067 0.974112i \(-0.427413\pi\)
0.226067 + 0.974112i \(0.427413\pi\)
\(114\) 0.701562 0.0657073
\(115\) −12.7016 −1.18443
\(116\) 2.70156 0.250834
\(117\) 0 0
\(118\) −14.8062 −1.36303
\(119\) 2.70156 0.247652
\(120\) −2.70156 −0.246618
\(121\) −10.5078 −0.955256
\(122\) −1.29844 −0.117555
\(123\) 3.40312 0.306849
\(124\) 0 0
\(125\) 7.29844 0.652792
\(126\) 1.00000 0.0890871
\(127\) −6.59688 −0.585378 −0.292689 0.956208i \(-0.594550\pi\)
−0.292689 + 0.956208i \(0.594550\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.1047 0.889668
\(130\) 0 0
\(131\) −7.29844 −0.637667 −0.318834 0.947811i \(-0.603291\pi\)
−0.318834 + 0.947811i \(0.603291\pi\)
\(132\) −0.701562 −0.0610631
\(133\) −0.701562 −0.0608332
\(134\) 5.40312 0.466759
\(135\) 2.70156 0.232513
\(136\) 2.70156 0.231657
\(137\) 18.7016 1.59778 0.798891 0.601476i \(-0.205420\pi\)
0.798891 + 0.601476i \(0.205420\pi\)
\(138\) 4.70156 0.400224
\(139\) 6.80625 0.577298 0.288649 0.957435i \(-0.406794\pi\)
0.288649 + 0.957435i \(0.406794\pi\)
\(140\) 2.70156 0.228324
\(141\) −8.00000 −0.673722
\(142\) −8.00000 −0.671345
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −7.29844 −0.606102
\(146\) −1.29844 −0.107459
\(147\) −1.00000 −0.0824786
\(148\) −10.7016 −0.879663
\(149\) −15.4031 −1.26187 −0.630937 0.775834i \(-0.717329\pi\)
−0.630937 + 0.775834i \(0.717329\pi\)
\(150\) 2.29844 0.187667
\(151\) 4.70156 0.382608 0.191304 0.981531i \(-0.438728\pi\)
0.191304 + 0.981531i \(0.438728\pi\)
\(152\) −0.701562 −0.0569042
\(153\) −2.70156 −0.218408
\(154\) 0.701562 0.0565335
\(155\) 0 0
\(156\) 0 0
\(157\) 20.1047 1.60453 0.802264 0.596969i \(-0.203628\pi\)
0.802264 + 0.596969i \(0.203628\pi\)
\(158\) −9.40312 −0.748072
\(159\) 2.00000 0.158610
\(160\) 2.70156 0.213577
\(161\) −4.70156 −0.370535
\(162\) −1.00000 −0.0785674
\(163\) −5.40312 −0.423205 −0.211603 0.977356i \(-0.567868\pi\)
−0.211603 + 0.977356i \(0.567868\pi\)
\(164\) −3.40312 −0.265739
\(165\) 1.89531 0.147550
\(166\) −13.4031 −1.04028
\(167\) −3.29844 −0.255241 −0.127620 0.991823i \(-0.540734\pi\)
−0.127620 + 0.991823i \(0.540734\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 0 0
\(170\) −7.29844 −0.559765
\(171\) 0.701562 0.0536498
\(172\) −10.1047 −0.770475
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 2.70156 0.204805
\(175\) −2.29844 −0.173746
\(176\) 0.701562 0.0528822
\(177\) −14.8062 −1.11291
\(178\) −8.80625 −0.660056
\(179\) 14.8062 1.10667 0.553335 0.832958i \(-0.313355\pi\)
0.553335 + 0.832958i \(0.313355\pi\)
\(180\) −2.70156 −0.201363
\(181\) 8.80625 0.654563 0.327282 0.944927i \(-0.393867\pi\)
0.327282 + 0.944927i \(0.393867\pi\)
\(182\) 0 0
\(183\) −1.29844 −0.0959833
\(184\) −4.70156 −0.346604
\(185\) 28.9109 2.12557
\(186\) 0 0
\(187\) −1.89531 −0.138599
\(188\) 8.00000 0.583460
\(189\) 1.00000 0.0727393
\(190\) 1.89531 0.137501
\(191\) 12.7016 0.919053 0.459526 0.888164i \(-0.348019\pi\)
0.459526 + 0.888164i \(0.348019\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −11.4031 −0.820815 −0.410407 0.911902i \(-0.634614\pi\)
−0.410407 + 0.911902i \(0.634614\pi\)
\(194\) −8.80625 −0.632252
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 3.40312 0.242463 0.121231 0.992624i \(-0.461316\pi\)
0.121231 + 0.992624i \(0.461316\pi\)
\(198\) −0.701562 −0.0498578
\(199\) 22.1047 1.56696 0.783480 0.621417i \(-0.213443\pi\)
0.783480 + 0.621417i \(0.213443\pi\)
\(200\) −2.29844 −0.162524
\(201\) 5.40312 0.381107
\(202\) 3.40312 0.239443
\(203\) −2.70156 −0.189612
\(204\) 2.70156 0.189147
\(205\) 9.19375 0.642119
\(206\) 3.29844 0.229813
\(207\) 4.70156 0.326781
\(208\) 0 0
\(209\) 0.492189 0.0340455
\(210\) 2.70156 0.186425
\(211\) −24.7016 −1.70053 −0.850263 0.526358i \(-0.823557\pi\)
−0.850263 + 0.526358i \(0.823557\pi\)
\(212\) −2.00000 −0.137361
\(213\) −8.00000 −0.548151
\(214\) 5.40312 0.369350
\(215\) 27.2984 1.86174
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 9.29844 0.629770
\(219\) −1.29844 −0.0877403
\(220\) −1.89531 −0.127782
\(221\) 0 0
\(222\) −10.7016 −0.718242
\(223\) −9.40312 −0.629680 −0.314840 0.949145i \(-0.601951\pi\)
−0.314840 + 0.949145i \(0.601951\pi\)
\(224\) 1.00000 0.0668153
\(225\) 2.29844 0.153229
\(226\) −4.80625 −0.319707
\(227\) −21.4031 −1.42058 −0.710288 0.703912i \(-0.751435\pi\)
−0.710288 + 0.703912i \(0.751435\pi\)
\(228\) −0.701562 −0.0464621
\(229\) −6.00000 −0.396491 −0.198246 0.980152i \(-0.563524\pi\)
−0.198246 + 0.980152i \(0.563524\pi\)
\(230\) 12.7016 0.837516
\(231\) 0.701562 0.0461594
\(232\) −2.70156 −0.177366
\(233\) −18.2094 −1.19294 −0.596468 0.802637i \(-0.703430\pi\)
−0.596468 + 0.802637i \(0.703430\pi\)
\(234\) 0 0
\(235\) −21.6125 −1.40984
\(236\) 14.8062 0.963805
\(237\) −9.40312 −0.610799
\(238\) −2.70156 −0.175116
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 2.70156 0.174385
\(241\) 24.8062 1.59791 0.798955 0.601390i \(-0.205386\pi\)
0.798955 + 0.601390i \(0.205386\pi\)
\(242\) 10.5078 0.675468
\(243\) −1.00000 −0.0641500
\(244\) 1.29844 0.0831240
\(245\) −2.70156 −0.172596
\(246\) −3.40312 −0.216975
\(247\) 0 0
\(248\) 0 0
\(249\) −13.4031 −0.849388
\(250\) −7.29844 −0.461594
\(251\) 3.50781 0.221411 0.110706 0.993853i \(-0.464689\pi\)
0.110706 + 0.993853i \(0.464689\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 3.29844 0.207371
\(254\) 6.59688 0.413925
\(255\) −7.29844 −0.457046
\(256\) 1.00000 0.0625000
\(257\) −6.00000 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(258\) −10.1047 −0.629090
\(259\) 10.7016 0.664963
\(260\) 0 0
\(261\) 2.70156 0.167222
\(262\) 7.29844 0.450899
\(263\) −26.8062 −1.65294 −0.826472 0.562978i \(-0.809656\pi\)
−0.826472 + 0.562978i \(0.809656\pi\)
\(264\) 0.701562 0.0431782
\(265\) 5.40312 0.331911
\(266\) 0.701562 0.0430155
\(267\) −8.80625 −0.538934
\(268\) −5.40312 −0.330048
\(269\) −4.80625 −0.293042 −0.146521 0.989208i \(-0.546808\pi\)
−0.146521 + 0.989208i \(0.546808\pi\)
\(270\) −2.70156 −0.164412
\(271\) −12.2094 −0.741667 −0.370833 0.928699i \(-0.620928\pi\)
−0.370833 + 0.928699i \(0.620928\pi\)
\(272\) −2.70156 −0.163806
\(273\) 0 0
\(274\) −18.7016 −1.12980
\(275\) 1.61250 0.0972372
\(276\) −4.70156 −0.283001
\(277\) 27.6125 1.65907 0.829537 0.558452i \(-0.188604\pi\)
0.829537 + 0.558452i \(0.188604\pi\)
\(278\) −6.80625 −0.408212
\(279\) 0 0
\(280\) −2.70156 −0.161449
\(281\) −12.8062 −0.763957 −0.381978 0.924171i \(-0.624757\pi\)
−0.381978 + 0.924171i \(0.624757\pi\)
\(282\) 8.00000 0.476393
\(283\) 4.00000 0.237775 0.118888 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 8.00000 0.474713
\(285\) 1.89531 0.112269
\(286\) 0 0
\(287\) 3.40312 0.200880
\(288\) −1.00000 −0.0589256
\(289\) −9.70156 −0.570680
\(290\) 7.29844 0.428579
\(291\) −8.80625 −0.516231
\(292\) 1.29844 0.0759853
\(293\) 12.8062 0.748149 0.374075 0.927399i \(-0.377960\pi\)
0.374075 + 0.927399i \(0.377960\pi\)
\(294\) 1.00000 0.0583212
\(295\) −40.0000 −2.32889
\(296\) 10.7016 0.622016
\(297\) −0.701562 −0.0407088
\(298\) 15.4031 0.892279
\(299\) 0 0
\(300\) −2.29844 −0.132700
\(301\) 10.1047 0.582424
\(302\) −4.70156 −0.270544
\(303\) 3.40312 0.195504
\(304\) 0.701562 0.0402373
\(305\) −3.50781 −0.200857
\(306\) 2.70156 0.154438
\(307\) 6.80625 0.388453 0.194227 0.980957i \(-0.437780\pi\)
0.194227 + 0.980957i \(0.437780\pi\)
\(308\) −0.701562 −0.0399752
\(309\) 3.29844 0.187642
\(310\) 0 0
\(311\) 14.5969 0.827713 0.413856 0.910342i \(-0.364182\pi\)
0.413856 + 0.910342i \(0.364182\pi\)
\(312\) 0 0
\(313\) 22.2094 1.25535 0.627674 0.778476i \(-0.284007\pi\)
0.627674 + 0.778476i \(0.284007\pi\)
\(314\) −20.1047 −1.13457
\(315\) 2.70156 0.152216
\(316\) 9.40312 0.528967
\(317\) −7.40312 −0.415801 −0.207900 0.978150i \(-0.566663\pi\)
−0.207900 + 0.978150i \(0.566663\pi\)
\(318\) −2.00000 −0.112154
\(319\) 1.89531 0.106117
\(320\) −2.70156 −0.151022
\(321\) 5.40312 0.301573
\(322\) 4.70156 0.262008
\(323\) −1.89531 −0.105458
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 5.40312 0.299251
\(327\) 9.29844 0.514205
\(328\) 3.40312 0.187906
\(329\) −8.00000 −0.441054
\(330\) −1.89531 −0.104334
\(331\) −32.2094 −1.77039 −0.885194 0.465223i \(-0.845974\pi\)
−0.885194 + 0.465223i \(0.845974\pi\)
\(332\) 13.4031 0.735592
\(333\) −10.7016 −0.586442
\(334\) 3.29844 0.180482
\(335\) 14.5969 0.797513
\(336\) 1.00000 0.0545545
\(337\) −29.5078 −1.60739 −0.803696 0.595040i \(-0.797136\pi\)
−0.803696 + 0.595040i \(0.797136\pi\)
\(338\) 0 0
\(339\) −4.80625 −0.261040
\(340\) 7.29844 0.395813
\(341\) 0 0
\(342\) −0.701562 −0.0379361
\(343\) −1.00000 −0.0539949
\(344\) 10.1047 0.544808
\(345\) 12.7016 0.683829
\(346\) 18.0000 0.967686
\(347\) 4.00000 0.214731 0.107366 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) −2.70156 −0.144819
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 2.29844 0.122857
\(351\) 0 0
\(352\) −0.701562 −0.0373934
\(353\) −20.8062 −1.10740 −0.553702 0.832715i \(-0.686785\pi\)
−0.553702 + 0.832715i \(0.686785\pi\)
\(354\) 14.8062 0.786943
\(355\) −21.6125 −1.14707
\(356\) 8.80625 0.466730
\(357\) −2.70156 −0.142982
\(358\) −14.8062 −0.782535
\(359\) −26.8062 −1.41478 −0.707390 0.706824i \(-0.750127\pi\)
−0.707390 + 0.706824i \(0.750127\pi\)
\(360\) 2.70156 0.142385
\(361\) −18.5078 −0.974095
\(362\) −8.80625 −0.462846
\(363\) 10.5078 0.551517
\(364\) 0 0
\(365\) −3.50781 −0.183607
\(366\) 1.29844 0.0678704
\(367\) −29.6125 −1.54576 −0.772880 0.634552i \(-0.781184\pi\)
−0.772880 + 0.634552i \(0.781184\pi\)
\(368\) 4.70156 0.245086
\(369\) −3.40312 −0.177160
\(370\) −28.9109 −1.50301
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) −19.4031 −1.00466 −0.502328 0.864677i \(-0.667523\pi\)
−0.502328 + 0.864677i \(0.667523\pi\)
\(374\) 1.89531 0.0980043
\(375\) −7.29844 −0.376890
\(376\) −8.00000 −0.412568
\(377\) 0 0
\(378\) −1.00000 −0.0514344
\(379\) 17.6125 0.904693 0.452347 0.891842i \(-0.350587\pi\)
0.452347 + 0.891842i \(0.350587\pi\)
\(380\) −1.89531 −0.0972275
\(381\) 6.59688 0.337968
\(382\) −12.7016 −0.649868
\(383\) −16.9109 −0.864108 −0.432054 0.901848i \(-0.642211\pi\)
−0.432054 + 0.901848i \(0.642211\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.89531 0.0965941
\(386\) 11.4031 0.580404
\(387\) −10.1047 −0.513650
\(388\) 8.80625 0.447070
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) 0 0
\(391\) −12.7016 −0.642346
\(392\) −1.00000 −0.0505076
\(393\) 7.29844 0.368157
\(394\) −3.40312 −0.171447
\(395\) −25.4031 −1.27817
\(396\) 0.701562 0.0352548
\(397\) −0.806248 −0.0404645 −0.0202322 0.999795i \(-0.506441\pi\)
−0.0202322 + 0.999795i \(0.506441\pi\)
\(398\) −22.1047 −1.10801
\(399\) 0.701562 0.0351220
\(400\) 2.29844 0.114922
\(401\) −4.80625 −0.240013 −0.120006 0.992773i \(-0.538291\pi\)
−0.120006 + 0.992773i \(0.538291\pi\)
\(402\) −5.40312 −0.269483
\(403\) 0 0
\(404\) −3.40312 −0.169312
\(405\) −2.70156 −0.134242
\(406\) 2.70156 0.134076
\(407\) −7.50781 −0.372148
\(408\) −2.70156 −0.133747
\(409\) −5.29844 −0.261991 −0.130995 0.991383i \(-0.541817\pi\)
−0.130995 + 0.991383i \(0.541817\pi\)
\(410\) −9.19375 −0.454047
\(411\) −18.7016 −0.922480
\(412\) −3.29844 −0.162502
\(413\) −14.8062 −0.728568
\(414\) −4.70156 −0.231069
\(415\) −36.2094 −1.77745
\(416\) 0 0
\(417\) −6.80625 −0.333303
\(418\) −0.492189 −0.0240738
\(419\) 34.1047 1.66612 0.833061 0.553180i \(-0.186586\pi\)
0.833061 + 0.553180i \(0.186586\pi\)
\(420\) −2.70156 −0.131823
\(421\) −19.6125 −0.955855 −0.477927 0.878399i \(-0.658612\pi\)
−0.477927 + 0.878399i \(0.658612\pi\)
\(422\) 24.7016 1.20245
\(423\) 8.00000 0.388973
\(424\) 2.00000 0.0971286
\(425\) −6.20937 −0.301199
\(426\) 8.00000 0.387601
\(427\) −1.29844 −0.0628358
\(428\) −5.40312 −0.261170
\(429\) 0 0
\(430\) −27.2984 −1.31645
\(431\) 12.2094 0.588105 0.294052 0.955789i \(-0.404996\pi\)
0.294052 + 0.955789i \(0.404996\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 14.2094 0.682859 0.341429 0.939907i \(-0.389089\pi\)
0.341429 + 0.939907i \(0.389089\pi\)
\(434\) 0 0
\(435\) 7.29844 0.349933
\(436\) −9.29844 −0.445314
\(437\) 3.29844 0.157786
\(438\) 1.29844 0.0620418
\(439\) −0.492189 −0.0234909 −0.0117455 0.999931i \(-0.503739\pi\)
−0.0117455 + 0.999931i \(0.503739\pi\)
\(440\) 1.89531 0.0903555
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 0.209373 0.00994760 0.00497380 0.999988i \(-0.498417\pi\)
0.00497380 + 0.999988i \(0.498417\pi\)
\(444\) 10.7016 0.507874
\(445\) −23.7906 −1.12778
\(446\) 9.40312 0.445251
\(447\) 15.4031 0.728543
\(448\) −1.00000 −0.0472456
\(449\) 7.89531 0.372603 0.186301 0.982493i \(-0.440350\pi\)
0.186301 + 0.982493i \(0.440350\pi\)
\(450\) −2.29844 −0.108349
\(451\) −2.38750 −0.112423
\(452\) 4.80625 0.226067
\(453\) −4.70156 −0.220899
\(454\) 21.4031 1.00450
\(455\) 0 0
\(456\) 0.701562 0.0328537
\(457\) −0.596876 −0.0279207 −0.0139603 0.999903i \(-0.504444\pi\)
−0.0139603 + 0.999903i \(0.504444\pi\)
\(458\) 6.00000 0.280362
\(459\) 2.70156 0.126098
\(460\) −12.7016 −0.592213
\(461\) 20.3141 0.946120 0.473060 0.881030i \(-0.343149\pi\)
0.473060 + 0.881030i \(0.343149\pi\)
\(462\) −0.701562 −0.0326396
\(463\) 34.3141 1.59471 0.797355 0.603511i \(-0.206232\pi\)
0.797355 + 0.603511i \(0.206232\pi\)
\(464\) 2.70156 0.125417
\(465\) 0 0
\(466\) 18.2094 0.843533
\(467\) −4.49219 −0.207874 −0.103937 0.994584i \(-0.533144\pi\)
−0.103937 + 0.994584i \(0.533144\pi\)
\(468\) 0 0
\(469\) 5.40312 0.249493
\(470\) 21.6125 0.996910
\(471\) −20.1047 −0.926375
\(472\) −14.8062 −0.681513
\(473\) −7.08907 −0.325956
\(474\) 9.40312 0.431900
\(475\) 1.61250 0.0739864
\(476\) 2.70156 0.123826
\(477\) −2.00000 −0.0915737
\(478\) 16.0000 0.731823
\(479\) −7.50781 −0.343041 −0.171520 0.985181i \(-0.554868\pi\)
−0.171520 + 0.985181i \(0.554868\pi\)
\(480\) −2.70156 −0.123309
\(481\) 0 0
\(482\) −24.8062 −1.12989
\(483\) 4.70156 0.213928
\(484\) −10.5078 −0.477628
\(485\) −23.7906 −1.08028
\(486\) 1.00000 0.0453609
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) −1.29844 −0.0587775
\(489\) 5.40312 0.244338
\(490\) 2.70156 0.122044
\(491\) 26.5969 1.20030 0.600150 0.799887i \(-0.295108\pi\)
0.600150 + 0.799887i \(0.295108\pi\)
\(492\) 3.40312 0.153425
\(493\) −7.29844 −0.328705
\(494\) 0 0
\(495\) −1.89531 −0.0851880
\(496\) 0 0
\(497\) −8.00000 −0.358849
\(498\) 13.4031 0.600608
\(499\) 1.19375 0.0534397 0.0267198 0.999643i \(-0.491494\pi\)
0.0267198 + 0.999643i \(0.491494\pi\)
\(500\) 7.29844 0.326396
\(501\) 3.29844 0.147363
\(502\) −3.50781 −0.156561
\(503\) −33.4031 −1.48937 −0.744686 0.667415i \(-0.767401\pi\)
−0.744686 + 0.667415i \(0.767401\pi\)
\(504\) 1.00000 0.0445435
\(505\) 9.19375 0.409117
\(506\) −3.29844 −0.146633
\(507\) 0 0
\(508\) −6.59688 −0.292689
\(509\) −38.9109 −1.72470 −0.862348 0.506315i \(-0.831007\pi\)
−0.862348 + 0.506315i \(0.831007\pi\)
\(510\) 7.29844 0.323180
\(511\) −1.29844 −0.0574395
\(512\) −1.00000 −0.0441942
\(513\) −0.701562 −0.0309747
\(514\) 6.00000 0.264649
\(515\) 8.91093 0.392663
\(516\) 10.1047 0.444834
\(517\) 5.61250 0.246837
\(518\) −10.7016 −0.470200
\(519\) 18.0000 0.790112
\(520\) 0 0
\(521\) −1.29844 −0.0568856 −0.0284428 0.999595i \(-0.509055\pi\)
−0.0284428 + 0.999595i \(0.509055\pi\)
\(522\) −2.70156 −0.118244
\(523\) −33.6125 −1.46977 −0.734886 0.678191i \(-0.762764\pi\)
−0.734886 + 0.678191i \(0.762764\pi\)
\(524\) −7.29844 −0.318834
\(525\) 2.29844 0.100312
\(526\) 26.8062 1.16881
\(527\) 0 0
\(528\) −0.701562 −0.0305316
\(529\) −0.895314 −0.0389267
\(530\) −5.40312 −0.234697
\(531\) 14.8062 0.642536
\(532\) −0.701562 −0.0304166
\(533\) 0 0
\(534\) 8.80625 0.381084
\(535\) 14.5969 0.631078
\(536\) 5.40312 0.233379
\(537\) −14.8062 −0.638937
\(538\) 4.80625 0.207212
\(539\) 0.701562 0.0302184
\(540\) 2.70156 0.116257
\(541\) 6.70156 0.288123 0.144061 0.989569i \(-0.453984\pi\)
0.144061 + 0.989569i \(0.453984\pi\)
\(542\) 12.2094 0.524437
\(543\) −8.80625 −0.377912
\(544\) 2.70156 0.115829
\(545\) 25.1203 1.07604
\(546\) 0 0
\(547\) 9.61250 0.411001 0.205500 0.978657i \(-0.434118\pi\)
0.205500 + 0.978657i \(0.434118\pi\)
\(548\) 18.7016 0.798891
\(549\) 1.29844 0.0554160
\(550\) −1.61250 −0.0687571
\(551\) 1.89531 0.0807431
\(552\) 4.70156 0.200112
\(553\) −9.40312 −0.399862
\(554\) −27.6125 −1.17314
\(555\) −28.9109 −1.22720
\(556\) 6.80625 0.288649
\(557\) 24.5969 1.04220 0.521102 0.853495i \(-0.325521\pi\)
0.521102 + 0.853495i \(0.325521\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 2.70156 0.114162
\(561\) 1.89531 0.0800202
\(562\) 12.8062 0.540199
\(563\) 8.70156 0.366727 0.183364 0.983045i \(-0.441301\pi\)
0.183364 + 0.983045i \(0.441301\pi\)
\(564\) −8.00000 −0.336861
\(565\) −12.9844 −0.546257
\(566\) −4.00000 −0.168133
\(567\) −1.00000 −0.0419961
\(568\) −8.00000 −0.335673
\(569\) 26.0000 1.08998 0.544988 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) −1.89531 −0.0793860
\(571\) −1.19375 −0.0499569 −0.0249785 0.999688i \(-0.507952\pi\)
−0.0249785 + 0.999688i \(0.507952\pi\)
\(572\) 0 0
\(573\) −12.7016 −0.530615
\(574\) −3.40312 −0.142044
\(575\) 10.8062 0.450652
\(576\) 1.00000 0.0416667
\(577\) 8.80625 0.366609 0.183304 0.983056i \(-0.441321\pi\)
0.183304 + 0.983056i \(0.441321\pi\)
\(578\) 9.70156 0.403532
\(579\) 11.4031 0.473898
\(580\) −7.29844 −0.303051
\(581\) −13.4031 −0.556055
\(582\) 8.80625 0.365031
\(583\) −1.40312 −0.0581115
\(584\) −1.29844 −0.0537297
\(585\) 0 0
\(586\) −12.8062 −0.529021
\(587\) −35.0156 −1.44525 −0.722625 0.691241i \(-0.757064\pi\)
−0.722625 + 0.691241i \(0.757064\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 0 0
\(590\) 40.0000 1.64677
\(591\) −3.40312 −0.139986
\(592\) −10.7016 −0.439831
\(593\) 16.8062 0.690150 0.345075 0.938575i \(-0.387853\pi\)
0.345075 + 0.938575i \(0.387853\pi\)
\(594\) 0.701562 0.0287854
\(595\) −7.29844 −0.299207
\(596\) −15.4031 −0.630937
\(597\) −22.1047 −0.904685
\(598\) 0 0
\(599\) 11.2984 0.461642 0.230821 0.972996i \(-0.425859\pi\)
0.230821 + 0.972996i \(0.425859\pi\)
\(600\) 2.29844 0.0938333
\(601\) −15.4031 −0.628307 −0.314153 0.949372i \(-0.601721\pi\)
−0.314153 + 0.949372i \(0.601721\pi\)
\(602\) −10.1047 −0.411836
\(603\) −5.40312 −0.220032
\(604\) 4.70156 0.191304
\(605\) 28.3875 1.15412
\(606\) −3.40312 −0.138242
\(607\) 7.50781 0.304733 0.152366 0.988324i \(-0.451311\pi\)
0.152366 + 0.988324i \(0.451311\pi\)
\(608\) −0.701562 −0.0284521
\(609\) 2.70156 0.109473
\(610\) 3.50781 0.142027
\(611\) 0 0
\(612\) −2.70156 −0.109204
\(613\) −38.9109 −1.57160 −0.785799 0.618482i \(-0.787748\pi\)
−0.785799 + 0.618482i \(0.787748\pi\)
\(614\) −6.80625 −0.274678
\(615\) −9.19375 −0.370728
\(616\) 0.701562 0.0282667
\(617\) 30.9109 1.24443 0.622214 0.782847i \(-0.286233\pi\)
0.622214 + 0.782847i \(0.286233\pi\)
\(618\) −3.29844 −0.132683
\(619\) −7.29844 −0.293349 −0.146674 0.989185i \(-0.546857\pi\)
−0.146674 + 0.989185i \(0.546857\pi\)
\(620\) 0 0
\(621\) −4.70156 −0.188667
\(622\) −14.5969 −0.585281
\(623\) −8.80625 −0.352815
\(624\) 0 0
\(625\) −31.2094 −1.24837
\(626\) −22.2094 −0.887665
\(627\) −0.492189 −0.0196562
\(628\) 20.1047 0.802264
\(629\) 28.9109 1.15275
\(630\) −2.70156 −0.107633
\(631\) 7.50781 0.298881 0.149441 0.988771i \(-0.452253\pi\)
0.149441 + 0.988771i \(0.452253\pi\)
\(632\) −9.40312 −0.374036
\(633\) 24.7016 0.981799
\(634\) 7.40312 0.294016
\(635\) 17.8219 0.707239
\(636\) 2.00000 0.0793052
\(637\) 0 0
\(638\) −1.89531 −0.0750362
\(639\) 8.00000 0.316475
\(640\) 2.70156 0.106789
\(641\) −48.8062 −1.92773 −0.963865 0.266390i \(-0.914169\pi\)
−0.963865 + 0.266390i \(0.914169\pi\)
\(642\) −5.40312 −0.213244
\(643\) −46.3141 −1.82645 −0.913224 0.407458i \(-0.866415\pi\)
−0.913224 + 0.407458i \(0.866415\pi\)
\(644\) −4.70156 −0.185268
\(645\) −27.2984 −1.07487
\(646\) 1.89531 0.0745701
\(647\) −8.00000 −0.314512 −0.157256 0.987558i \(-0.550265\pi\)
−0.157256 + 0.987558i \(0.550265\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 10.3875 0.407745
\(650\) 0 0
\(651\) 0 0
\(652\) −5.40312 −0.211603
\(653\) −9.50781 −0.372069 −0.186035 0.982543i \(-0.559564\pi\)
−0.186035 + 0.982543i \(0.559564\pi\)
\(654\) −9.29844 −0.363598
\(655\) 19.7172 0.770414
\(656\) −3.40312 −0.132870
\(657\) 1.29844 0.0506569
\(658\) 8.00000 0.311872
\(659\) −35.0156 −1.36401 −0.682007 0.731345i \(-0.738893\pi\)
−0.682007 + 0.731345i \(0.738893\pi\)
\(660\) 1.89531 0.0737750
\(661\) 50.4187 1.96106 0.980531 0.196365i \(-0.0629136\pi\)
0.980531 + 0.196365i \(0.0629136\pi\)
\(662\) 32.2094 1.25185
\(663\) 0 0
\(664\) −13.4031 −0.520142
\(665\) 1.89531 0.0734971
\(666\) 10.7016 0.414677
\(667\) 12.7016 0.491806
\(668\) −3.29844 −0.127620
\(669\) 9.40312 0.363546
\(670\) −14.5969 −0.563927
\(671\) 0.910935 0.0351662
\(672\) −1.00000 −0.0385758
\(673\) 42.9109 1.65409 0.827047 0.562132i \(-0.190019\pi\)
0.827047 + 0.562132i \(0.190019\pi\)
\(674\) 29.5078 1.13660
\(675\) −2.29844 −0.0884669
\(676\) 0 0
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 4.80625 0.184583
\(679\) −8.80625 −0.337953
\(680\) −7.29844 −0.279882
\(681\) 21.4031 0.820170
\(682\) 0 0
\(683\) −11.5078 −0.440334 −0.220167 0.975462i \(-0.570660\pi\)
−0.220167 + 0.975462i \(0.570660\pi\)
\(684\) 0.701562 0.0268249
\(685\) −50.5234 −1.93040
\(686\) 1.00000 0.0381802
\(687\) 6.00000 0.228914
\(688\) −10.1047 −0.385238
\(689\) 0 0
\(690\) −12.7016 −0.483540
\(691\) −49.6125 −1.88735 −0.943674 0.330876i \(-0.892656\pi\)
−0.943674 + 0.330876i \(0.892656\pi\)
\(692\) −18.0000 −0.684257
\(693\) −0.701562 −0.0266501
\(694\) −4.00000 −0.151838
\(695\) −18.3875 −0.697478
\(696\) 2.70156 0.102402
\(697\) 9.19375 0.348238
\(698\) 30.0000 1.13552
\(699\) 18.2094 0.688742
\(700\) −2.29844 −0.0868728
\(701\) 3.19375 0.120626 0.0603132 0.998180i \(-0.480790\pi\)
0.0603132 + 0.998180i \(0.480790\pi\)
\(702\) 0 0
\(703\) −7.50781 −0.283162
\(704\) 0.701562 0.0264411
\(705\) 21.6125 0.813974
\(706\) 20.8062 0.783053
\(707\) 3.40312 0.127988
\(708\) −14.8062 −0.556453
\(709\) −51.6125 −1.93835 −0.969174 0.246377i \(-0.920760\pi\)
−0.969174 + 0.246377i \(0.920760\pi\)
\(710\) 21.6125 0.811103
\(711\) 9.40312 0.352645
\(712\) −8.80625 −0.330028
\(713\) 0 0
\(714\) 2.70156 0.101103
\(715\) 0 0
\(716\) 14.8062 0.553335
\(717\) 16.0000 0.597531
\(718\) 26.8062 1.00040
\(719\) −31.0156 −1.15669 −0.578344 0.815793i \(-0.696301\pi\)
−0.578344 + 0.815793i \(0.696301\pi\)
\(720\) −2.70156 −0.100681
\(721\) 3.29844 0.122840
\(722\) 18.5078 0.688789
\(723\) −24.8062 −0.922554
\(724\) 8.80625 0.327282
\(725\) 6.20937 0.230610
\(726\) −10.5078 −0.389981
\(727\) −22.1047 −0.819817 −0.409909 0.912127i \(-0.634439\pi\)
−0.409909 + 0.912127i \(0.634439\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 3.50781 0.129830
\(731\) 27.2984 1.00967
\(732\) −1.29844 −0.0479916
\(733\) −20.5969 −0.760763 −0.380381 0.924830i \(-0.624207\pi\)
−0.380381 + 0.924830i \(0.624207\pi\)
\(734\) 29.6125 1.09302
\(735\) 2.70156 0.0996486
\(736\) −4.70156 −0.173302
\(737\) −3.79063 −0.139630
\(738\) 3.40312 0.125271
\(739\) −40.2094 −1.47913 −0.739563 0.673088i \(-0.764968\pi\)
−0.739563 + 0.673088i \(0.764968\pi\)
\(740\) 28.9109 1.06279
\(741\) 0 0
\(742\) −2.00000 −0.0734223
\(743\) −23.0156 −0.844361 −0.422181 0.906512i \(-0.638735\pi\)
−0.422181 + 0.906512i \(0.638735\pi\)
\(744\) 0 0
\(745\) 41.6125 1.52456
\(746\) 19.4031 0.710399
\(747\) 13.4031 0.490395
\(748\) −1.89531 −0.0692995
\(749\) 5.40312 0.197426
\(750\) 7.29844 0.266501
\(751\) 34.8062 1.27010 0.635049 0.772472i \(-0.280980\pi\)
0.635049 + 0.772472i \(0.280980\pi\)
\(752\) 8.00000 0.291730
\(753\) −3.50781 −0.127832
\(754\) 0 0
\(755\) −12.7016 −0.462257
\(756\) 1.00000 0.0363696
\(757\) 30.4187 1.10559 0.552794 0.833318i \(-0.313562\pi\)
0.552794 + 0.833318i \(0.313562\pi\)
\(758\) −17.6125 −0.639715
\(759\) −3.29844 −0.119726
\(760\) 1.89531 0.0687503
\(761\) −32.5969 −1.18164 −0.590818 0.806805i \(-0.701195\pi\)
−0.590818 + 0.806805i \(0.701195\pi\)
\(762\) −6.59688 −0.238980
\(763\) 9.29844 0.336626
\(764\) 12.7016 0.459526
\(765\) 7.29844 0.263876
\(766\) 16.9109 0.611017
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −50.9109 −1.83590 −0.917948 0.396702i \(-0.870155\pi\)
−0.917948 + 0.396702i \(0.870155\pi\)
\(770\) −1.89531 −0.0683024
\(771\) 6.00000 0.216085
\(772\) −11.4031 −0.410407
\(773\) 28.3141 1.01839 0.509193 0.860652i \(-0.329944\pi\)
0.509193 + 0.860652i \(0.329944\pi\)
\(774\) 10.1047 0.363205
\(775\) 0 0
\(776\) −8.80625 −0.316126
\(777\) −10.7016 −0.383916
\(778\) −14.0000 −0.501924
\(779\) −2.38750 −0.0855412
\(780\) 0 0
\(781\) 5.61250 0.200831
\(782\) 12.7016 0.454207
\(783\) −2.70156 −0.0965460
\(784\) 1.00000 0.0357143
\(785\) −54.3141 −1.93855
\(786\) −7.29844 −0.260327
\(787\) −20.9109 −0.745394 −0.372697 0.927953i \(-0.621567\pi\)
−0.372697 + 0.927953i \(0.621567\pi\)
\(788\) 3.40312 0.121231
\(789\) 26.8062 0.954328
\(790\) 25.4031 0.903803
\(791\) −4.80625 −0.170891
\(792\) −0.701562 −0.0249289
\(793\) 0 0
\(794\) 0.806248 0.0286127
\(795\) −5.40312 −0.191629
\(796\) 22.1047 0.783480
\(797\) −40.5969 −1.43802 −0.719008 0.695002i \(-0.755403\pi\)
−0.719008 + 0.695002i \(0.755403\pi\)
\(798\) −0.701562 −0.0248350
\(799\) −21.6125 −0.764595
\(800\) −2.29844 −0.0812621
\(801\) 8.80625 0.311153
\(802\) 4.80625 0.169715
\(803\) 0.910935 0.0321462
\(804\) 5.40312 0.190553
\(805\) 12.7016 0.447671
\(806\) 0 0
\(807\) 4.80625 0.169188
\(808\) 3.40312 0.119721
\(809\) −11.6125 −0.408274 −0.204137 0.978942i \(-0.565439\pi\)
−0.204137 + 0.978942i \(0.565439\pi\)
\(810\) 2.70156 0.0949232
\(811\) 21.8953 0.768848 0.384424 0.923157i \(-0.374400\pi\)
0.384424 + 0.923157i \(0.374400\pi\)
\(812\) −2.70156 −0.0948062
\(813\) 12.2094 0.428201
\(814\) 7.50781 0.263149
\(815\) 14.5969 0.511306
\(816\) 2.70156 0.0945736
\(817\) −7.08907 −0.248015
\(818\) 5.29844 0.185256
\(819\) 0 0
\(820\) 9.19375 0.321060
\(821\) −28.5969 −0.998038 −0.499019 0.866591i \(-0.666306\pi\)
−0.499019 + 0.866591i \(0.666306\pi\)
\(822\) 18.7016 0.652292
\(823\) 5.19375 0.181043 0.0905214 0.995895i \(-0.471147\pi\)
0.0905214 + 0.995895i \(0.471147\pi\)
\(824\) 3.29844 0.114907
\(825\) −1.61250 −0.0561399
\(826\) 14.8062 0.515175
\(827\) −52.9109 −1.83989 −0.919947 0.392043i \(-0.871768\pi\)
−0.919947 + 0.392043i \(0.871768\pi\)
\(828\) 4.70156 0.163391
\(829\) −36.3141 −1.26124 −0.630620 0.776092i \(-0.717199\pi\)
−0.630620 + 0.776092i \(0.717199\pi\)
\(830\) 36.2094 1.25685
\(831\) −27.6125 −0.957867
\(832\) 0 0
\(833\) −2.70156 −0.0936036
\(834\) 6.80625 0.235681
\(835\) 8.91093 0.308376
\(836\) 0.492189 0.0170227
\(837\) 0 0
\(838\) −34.1047 −1.17813
\(839\) −34.8062 −1.20165 −0.600823 0.799382i \(-0.705160\pi\)
−0.600823 + 0.799382i \(0.705160\pi\)
\(840\) 2.70156 0.0932127
\(841\) −21.7016 −0.748330
\(842\) 19.6125 0.675891
\(843\) 12.8062 0.441071
\(844\) −24.7016 −0.850263
\(845\) 0 0
\(846\) −8.00000 −0.275046
\(847\) 10.5078 0.361053
\(848\) −2.00000 −0.0686803
\(849\) −4.00000 −0.137280
\(850\) 6.20937 0.212980
\(851\) −50.3141 −1.72474
\(852\) −8.00000 −0.274075
\(853\) 22.2094 0.760434 0.380217 0.924897i \(-0.375849\pi\)
0.380217 + 0.924897i \(0.375849\pi\)
\(854\) 1.29844 0.0444316
\(855\) −1.89531 −0.0648184
\(856\) 5.40312 0.184675
\(857\) −16.8062 −0.574091 −0.287045 0.957917i \(-0.592673\pi\)
−0.287045 + 0.957917i \(0.592673\pi\)
\(858\) 0 0
\(859\) 38.8062 1.32405 0.662026 0.749481i \(-0.269697\pi\)
0.662026 + 0.749481i \(0.269697\pi\)
\(860\) 27.2984 0.930869
\(861\) −3.40312 −0.115978
\(862\) −12.2094 −0.415853
\(863\) 22.5969 0.769207 0.384603 0.923082i \(-0.374338\pi\)
0.384603 + 0.923082i \(0.374338\pi\)
\(864\) 1.00000 0.0340207
\(865\) 48.6281 1.65341
\(866\) −14.2094 −0.482854
\(867\) 9.70156 0.329482
\(868\) 0 0
\(869\) 6.59688 0.223784
\(870\) −7.29844 −0.247440
\(871\) 0 0
\(872\) 9.29844 0.314885
\(873\) 8.80625 0.298046
\(874\) −3.29844 −0.111571
\(875\) −7.29844 −0.246732
\(876\) −1.29844 −0.0438702
\(877\) −0.387503 −0.0130850 −0.00654252 0.999979i \(-0.502083\pi\)
−0.00654252 + 0.999979i \(0.502083\pi\)
\(878\) 0.492189 0.0166106
\(879\) −12.8062 −0.431944
\(880\) −1.89531 −0.0638910
\(881\) −8.31406 −0.280108 −0.140054 0.990144i \(-0.544728\pi\)
−0.140054 + 0.990144i \(0.544728\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 13.8953 0.467615 0.233807 0.972283i \(-0.424882\pi\)
0.233807 + 0.972283i \(0.424882\pi\)
\(884\) 0 0
\(885\) 40.0000 1.34459
\(886\) −0.209373 −0.00703401
\(887\) −8.00000 −0.268614 −0.134307 0.990940i \(-0.542881\pi\)
−0.134307 + 0.990940i \(0.542881\pi\)
\(888\) −10.7016 −0.359121
\(889\) 6.59688 0.221252
\(890\) 23.7906 0.797464
\(891\) 0.701562 0.0235032
\(892\) −9.40312 −0.314840
\(893\) 5.61250 0.187815
\(894\) −15.4031 −0.515158
\(895\) −40.0000 −1.33705
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −7.89531 −0.263470
\(899\) 0 0
\(900\) 2.29844 0.0766146
\(901\) 5.40312 0.180004
\(902\) 2.38750 0.0794952
\(903\) −10.1047 −0.336263
\(904\) −4.80625 −0.159853
\(905\) −23.7906 −0.790827
\(906\) 4.70156 0.156199
\(907\) −25.6125 −0.850449 −0.425225 0.905088i \(-0.639805\pi\)
−0.425225 + 0.905088i \(0.639805\pi\)
\(908\) −21.4031 −0.710288
\(909\) −3.40312 −0.112875
\(910\) 0 0
\(911\) 40.9109 1.35544 0.677720 0.735320i \(-0.262968\pi\)
0.677720 + 0.735320i \(0.262968\pi\)
\(912\) −0.701562 −0.0232310
\(913\) 9.40312 0.311198
\(914\) 0.596876 0.0197429
\(915\) 3.50781 0.115965
\(916\) −6.00000 −0.198246
\(917\) 7.29844 0.241016
\(918\) −2.70156 −0.0891648
\(919\) −14.5969 −0.481507 −0.240753 0.970586i \(-0.577394\pi\)
−0.240753 + 0.970586i \(0.577394\pi\)
\(920\) 12.7016 0.418758
\(921\) −6.80625 −0.224274
\(922\) −20.3141 −0.669008
\(923\) 0 0
\(924\) 0.701562 0.0230797
\(925\) −24.5969 −0.808740
\(926\) −34.3141 −1.12763
\(927\) −3.29844 −0.108335
\(928\) −2.70156 −0.0886831
\(929\) −33.0156 −1.08321 −0.541604 0.840634i \(-0.682183\pi\)
−0.541604 + 0.840634i \(0.682183\pi\)
\(930\) 0 0
\(931\) 0.701562 0.0229928
\(932\) −18.2094 −0.596468
\(933\) −14.5969 −0.477880
\(934\) 4.49219 0.146989
\(935\) 5.12031 0.167452
\(936\) 0 0
\(937\) 28.8062 0.941059 0.470530 0.882384i \(-0.344063\pi\)
0.470530 + 0.882384i \(0.344063\pi\)
\(938\) −5.40312 −0.176418
\(939\) −22.2094 −0.724775
\(940\) −21.6125 −0.704922
\(941\) 50.0000 1.62995 0.814977 0.579494i \(-0.196750\pi\)
0.814977 + 0.579494i \(0.196750\pi\)
\(942\) 20.1047 0.655046
\(943\) −16.0000 −0.521032
\(944\) 14.8062 0.481902
\(945\) −2.70156 −0.0878818
\(946\) 7.08907 0.230485
\(947\) −4.49219 −0.145977 −0.0729883 0.997333i \(-0.523254\pi\)
−0.0729883 + 0.997333i \(0.523254\pi\)
\(948\) −9.40312 −0.305399
\(949\) 0 0
\(950\) −1.61250 −0.0523163
\(951\) 7.40312 0.240063
\(952\) −2.70156 −0.0875581
\(953\) −39.8219 −1.28996 −0.644978 0.764201i \(-0.723134\pi\)
−0.644978 + 0.764201i \(0.723134\pi\)
\(954\) 2.00000 0.0647524
\(955\) −34.3141 −1.11038
\(956\) −16.0000 −0.517477
\(957\) −1.89531 −0.0612668
\(958\) 7.50781 0.242566
\(959\) −18.7016 −0.603905
\(960\) 2.70156 0.0871925
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) −5.40312 −0.174113
\(964\) 24.8062 0.798955
\(965\) 30.8062 0.991688
\(966\) −4.70156 −0.151270
\(967\) 51.7172 1.66311 0.831556 0.555441i \(-0.187450\pi\)
0.831556 + 0.555441i \(0.187450\pi\)
\(968\) 10.5078 0.337734
\(969\) 1.89531 0.0608862
\(970\) 23.7906 0.763871
\(971\) 54.8062 1.75882 0.879408 0.476069i \(-0.157939\pi\)
0.879408 + 0.476069i \(0.157939\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −6.80625 −0.218198
\(974\) −8.00000 −0.256337
\(975\) 0 0
\(976\) 1.29844 0.0415620
\(977\) 41.7172 1.33465 0.667325 0.744766i \(-0.267439\pi\)
0.667325 + 0.744766i \(0.267439\pi\)
\(978\) −5.40312 −0.172773
\(979\) 6.17813 0.197454
\(980\) −2.70156 −0.0862982
\(981\) −9.29844 −0.296876
\(982\) −26.5969 −0.848740
\(983\) 38.1047 1.21535 0.607675 0.794186i \(-0.292102\pi\)
0.607675 + 0.794186i \(0.292102\pi\)
\(984\) −3.40312 −0.108488
\(985\) −9.19375 −0.292937
\(986\) 7.29844 0.232430
\(987\) 8.00000 0.254643
\(988\) 0 0
\(989\) −47.5078 −1.51066
\(990\) 1.89531 0.0602370
\(991\) −38.5969 −1.22607 −0.613035 0.790056i \(-0.710052\pi\)
−0.613035 + 0.790056i \(0.710052\pi\)
\(992\) 0 0
\(993\) 32.2094 1.02213
\(994\) 8.00000 0.253745
\(995\) −59.7172 −1.89316
\(996\) −13.4031 −0.424694
\(997\) −12.8062 −0.405578 −0.202789 0.979222i \(-0.565001\pi\)
−0.202789 + 0.979222i \(0.565001\pi\)
\(998\) −1.19375 −0.0377875
\(999\) 10.7016 0.338582
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.bh.1.1 2
13.12 even 2 546.2.a.i.1.2 2
39.38 odd 2 1638.2.a.w.1.1 2
52.51 odd 2 4368.2.a.bg.1.2 2
91.90 odd 2 3822.2.a.bt.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.a.i.1.2 2 13.12 even 2
1638.2.a.w.1.1 2 39.38 odd 2
3822.2.a.bt.1.1 2 91.90 odd 2
4368.2.a.bg.1.2 2 52.51 odd 2
7098.2.a.bh.1.1 2 1.1 even 1 trivial