Properties

Label 7098.2.a.cj.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Defining polynomial: \(x^{3} - x^{2} - 2 x + 1\)
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 \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.801938 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.801938 q^{10} +4.04892 q^{11} -1.00000 q^{12} -1.00000 q^{14} +0.801938 q^{15} +1.00000 q^{16} -0.753020 q^{17} +1.00000 q^{18} +0.664874 q^{19} -0.801938 q^{20} +1.00000 q^{21} +4.04892 q^{22} -3.80194 q^{23} -1.00000 q^{24} -4.35690 q^{25} -1.00000 q^{27} -1.00000 q^{28} -8.74094 q^{29} +0.801938 q^{30} +0.335126 q^{31} +1.00000 q^{32} -4.04892 q^{33} -0.753020 q^{34} +0.801938 q^{35} +1.00000 q^{36} -4.58211 q^{37} +0.664874 q^{38} -0.801938 q^{40} +6.89977 q^{41} +1.00000 q^{42} -1.30798 q^{43} +4.04892 q^{44} -0.801938 q^{45} -3.80194 q^{46} -5.49396 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.35690 q^{50} +0.753020 q^{51} +3.04892 q^{53} -1.00000 q^{54} -3.24698 q^{55} -1.00000 q^{56} -0.664874 q^{57} -8.74094 q^{58} -2.58211 q^{59} +0.801938 q^{60} +3.71379 q^{61} +0.335126 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.04892 q^{66} -8.86294 q^{67} -0.753020 q^{68} +3.80194 q^{69} +0.801938 q^{70} -10.1957 q^{71} +1.00000 q^{72} +9.44265 q^{73} -4.58211 q^{74} +4.35690 q^{75} +0.664874 q^{76} -4.04892 q^{77} +11.7899 q^{79} -0.801938 q^{80} +1.00000 q^{81} +6.89977 q^{82} +9.21313 q^{83} +1.00000 q^{84} +0.603875 q^{85} -1.30798 q^{86} +8.74094 q^{87} +4.04892 q^{88} +1.75302 q^{89} -0.801938 q^{90} -3.80194 q^{92} -0.335126 q^{93} -5.49396 q^{94} -0.533188 q^{95} -1.00000 q^{96} -8.18598 q^{97} +1.00000 q^{98} +4.04892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} + 2q^{5} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} + 2q^{5} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + 2q^{10} + 3q^{11} - 3q^{12} - 3q^{14} - 2q^{15} + 3q^{16} - 7q^{17} + 3q^{18} + 3q^{19} + 2q^{20} + 3q^{21} + 3q^{22} - 7q^{23} - 3q^{24} - 9q^{25} - 3q^{27} - 3q^{28} - 12q^{29} - 2q^{30} + 3q^{32} - 3q^{33} - 7q^{34} - 2q^{35} + 3q^{36} - 8q^{37} + 3q^{38} + 2q^{40} - 2q^{41} + 3q^{42} - 9q^{43} + 3q^{44} + 2q^{45} - 7q^{46} - 7q^{47} - 3q^{48} + 3q^{49} - 9q^{50} + 7q^{51} - 3q^{54} - 5q^{55} - 3q^{56} - 3q^{57} - 12q^{58} - 2q^{59} - 2q^{60} + 3q^{61} - 3q^{63} + 3q^{64} - 3q^{66} - 32q^{67} - 7q^{68} + 7q^{69} - 2q^{70} + 6q^{71} + 3q^{72} - 13q^{73} - 8q^{74} + 9q^{75} + 3q^{76} - 3q^{77} + 12q^{79} + 2q^{80} + 3q^{81} - 2q^{82} + 7q^{83} + 3q^{84} - 7q^{85} - 9q^{86} + 12q^{87} + 3q^{88} + 10q^{89} + 2q^{90} - 7q^{92} - 7q^{94} - 5q^{95} - 3q^{96} - 10q^{97} + 3q^{98} + 3q^{99} + O(q^{100}) \)

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
\(5\) −0.801938 −0.358637 −0.179319 0.983791i \(-0.557389\pi\)
−0.179319 + 0.983791i \(0.557389\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −0.801938 −0.253595
\(11\) 4.04892 1.22079 0.610397 0.792095i \(-0.291010\pi\)
0.610397 + 0.792095i \(0.291010\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 0.801938 0.207059
\(16\) 1.00000 0.250000
\(17\) −0.753020 −0.182634 −0.0913171 0.995822i \(-0.529108\pi\)
−0.0913171 + 0.995822i \(0.529108\pi\)
\(18\) 1.00000 0.235702
\(19\) 0.664874 0.152533 0.0762663 0.997087i \(-0.475700\pi\)
0.0762663 + 0.997087i \(0.475700\pi\)
\(20\) −0.801938 −0.179319
\(21\) 1.00000 0.218218
\(22\) 4.04892 0.863232
\(23\) −3.80194 −0.792759 −0.396379 0.918087i \(-0.629734\pi\)
−0.396379 + 0.918087i \(0.629734\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.35690 −0.871379
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) −8.74094 −1.62315 −0.811576 0.584247i \(-0.801390\pi\)
−0.811576 + 0.584247i \(0.801390\pi\)
\(30\) 0.801938 0.146413
\(31\) 0.335126 0.0601903 0.0300952 0.999547i \(-0.490419\pi\)
0.0300952 + 0.999547i \(0.490419\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.04892 −0.704826
\(34\) −0.753020 −0.129142
\(35\) 0.801938 0.135552
\(36\) 1.00000 0.166667
\(37\) −4.58211 −0.753293 −0.376647 0.926357i \(-0.622923\pi\)
−0.376647 + 0.926357i \(0.622923\pi\)
\(38\) 0.664874 0.107857
\(39\) 0 0
\(40\) −0.801938 −0.126797
\(41\) 6.89977 1.07756 0.538782 0.842445i \(-0.318885\pi\)
0.538782 + 0.842445i \(0.318885\pi\)
\(42\) 1.00000 0.154303
\(43\) −1.30798 −0.199465 −0.0997324 0.995014i \(-0.531799\pi\)
−0.0997324 + 0.995014i \(0.531799\pi\)
\(44\) 4.04892 0.610397
\(45\) −0.801938 −0.119546
\(46\) −3.80194 −0.560565
\(47\) −5.49396 −0.801376 −0.400688 0.916214i \(-0.631229\pi\)
−0.400688 + 0.916214i \(0.631229\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −4.35690 −0.616158
\(51\) 0.753020 0.105444
\(52\) 0 0
\(53\) 3.04892 0.418801 0.209401 0.977830i \(-0.432849\pi\)
0.209401 + 0.977830i \(0.432849\pi\)
\(54\) −1.00000 −0.136083
\(55\) −3.24698 −0.437823
\(56\) −1.00000 −0.133631
\(57\) −0.664874 −0.0880648
\(58\) −8.74094 −1.14774
\(59\) −2.58211 −0.336161 −0.168081 0.985773i \(-0.553757\pi\)
−0.168081 + 0.985773i \(0.553757\pi\)
\(60\) 0.801938 0.103530
\(61\) 3.71379 0.475502 0.237751 0.971326i \(-0.423590\pi\)
0.237751 + 0.971326i \(0.423590\pi\)
\(62\) 0.335126 0.0425610
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.04892 −0.498387
\(67\) −8.86294 −1.08278 −0.541390 0.840772i \(-0.682102\pi\)
−0.541390 + 0.840772i \(0.682102\pi\)
\(68\) −0.753020 −0.0913171
\(69\) 3.80194 0.457700
\(70\) 0.801938 0.0958499
\(71\) −10.1957 −1.21000 −0.605002 0.796224i \(-0.706828\pi\)
−0.605002 + 0.796224i \(0.706828\pi\)
\(72\) 1.00000 0.117851
\(73\) 9.44265 1.10518 0.552589 0.833454i \(-0.313640\pi\)
0.552589 + 0.833454i \(0.313640\pi\)
\(74\) −4.58211 −0.532659
\(75\) 4.35690 0.503091
\(76\) 0.664874 0.0762663
\(77\) −4.04892 −0.461417
\(78\) 0 0
\(79\) 11.7899 1.32646 0.663231 0.748415i \(-0.269185\pi\)
0.663231 + 0.748415i \(0.269185\pi\)
\(80\) −0.801938 −0.0896594
\(81\) 1.00000 0.111111
\(82\) 6.89977 0.761952
\(83\) 9.21313 1.01127 0.505636 0.862747i \(-0.331258\pi\)
0.505636 + 0.862747i \(0.331258\pi\)
\(84\) 1.00000 0.109109
\(85\) 0.603875 0.0654995
\(86\) −1.30798 −0.141043
\(87\) 8.74094 0.937127
\(88\) 4.04892 0.431616
\(89\) 1.75302 0.185820 0.0929099 0.995675i \(-0.470383\pi\)
0.0929099 + 0.995675i \(0.470383\pi\)
\(90\) −0.801938 −0.0845317
\(91\) 0 0
\(92\) −3.80194 −0.396379
\(93\) −0.335126 −0.0347509
\(94\) −5.49396 −0.566659
\(95\) −0.533188 −0.0547039
\(96\) −1.00000 −0.102062
\(97\) −8.18598 −0.831160 −0.415580 0.909557i \(-0.636421\pi\)
−0.415580 + 0.909557i \(0.636421\pi\)
\(98\) 1.00000 0.101015
\(99\) 4.04892 0.406932
\(100\) −4.35690 −0.435690
\(101\) 15.6189 1.55414 0.777071 0.629413i \(-0.216704\pi\)
0.777071 + 0.629413i \(0.216704\pi\)
\(102\) 0.753020 0.0745601
\(103\) −13.1347 −1.29420 −0.647099 0.762406i \(-0.724018\pi\)
−0.647099 + 0.762406i \(0.724018\pi\)
\(104\) 0 0
\(105\) −0.801938 −0.0782611
\(106\) 3.04892 0.296137
\(107\) −10.1642 −0.982611 −0.491306 0.870987i \(-0.663480\pi\)
−0.491306 + 0.870987i \(0.663480\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −13.4494 −1.28821 −0.644107 0.764935i \(-0.722771\pi\)
−0.644107 + 0.764935i \(0.722771\pi\)
\(110\) −3.24698 −0.309587
\(111\) 4.58211 0.434914
\(112\) −1.00000 −0.0944911
\(113\) −3.26444 −0.307092 −0.153546 0.988141i \(-0.549069\pi\)
−0.153546 + 0.988141i \(0.549069\pi\)
\(114\) −0.664874 −0.0622712
\(115\) 3.04892 0.284313
\(116\) −8.74094 −0.811576
\(117\) 0 0
\(118\) −2.58211 −0.237702
\(119\) 0.753020 0.0690293
\(120\) 0.801938 0.0732066
\(121\) 5.39373 0.490339
\(122\) 3.71379 0.336231
\(123\) −6.89977 −0.622132
\(124\) 0.335126 0.0300952
\(125\) 7.50365 0.671147
\(126\) −1.00000 −0.0890871
\(127\) 7.74094 0.686897 0.343449 0.939171i \(-0.388405\pi\)
0.343449 + 0.939171i \(0.388405\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.30798 0.115161
\(130\) 0 0
\(131\) 9.12498 0.797253 0.398627 0.917113i \(-0.369487\pi\)
0.398627 + 0.917113i \(0.369487\pi\)
\(132\) −4.04892 −0.352413
\(133\) −0.664874 −0.0576519
\(134\) −8.86294 −0.765641
\(135\) 0.801938 0.0690198
\(136\) −0.753020 −0.0645710
\(137\) −10.4722 −0.894699 −0.447350 0.894359i \(-0.647632\pi\)
−0.447350 + 0.894359i \(0.647632\pi\)
\(138\) 3.80194 0.323642
\(139\) 3.66487 0.310851 0.155425 0.987848i \(-0.450325\pi\)
0.155425 + 0.987848i \(0.450325\pi\)
\(140\) 0.801938 0.0677761
\(141\) 5.49396 0.462675
\(142\) −10.1957 −0.855602
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 7.00969 0.582123
\(146\) 9.44265 0.781479
\(147\) −1.00000 −0.0824786
\(148\) −4.58211 −0.376647
\(149\) −18.7385 −1.53512 −0.767561 0.640976i \(-0.778530\pi\)
−0.767561 + 0.640976i \(0.778530\pi\)
\(150\) 4.35690 0.355739
\(151\) −17.4209 −1.41769 −0.708846 0.705364i \(-0.750784\pi\)
−0.708846 + 0.705364i \(0.750784\pi\)
\(152\) 0.664874 0.0539284
\(153\) −0.753020 −0.0608781
\(154\) −4.04892 −0.326271
\(155\) −0.268750 −0.0215865
\(156\) 0 0
\(157\) 4.39612 0.350849 0.175424 0.984493i \(-0.443870\pi\)
0.175424 + 0.984493i \(0.443870\pi\)
\(158\) 11.7899 0.937951
\(159\) −3.04892 −0.241795
\(160\) −0.801938 −0.0633987
\(161\) 3.80194 0.299635
\(162\) 1.00000 0.0785674
\(163\) −11.8062 −0.924737 −0.462368 0.886688i \(-0.653000\pi\)
−0.462368 + 0.886688i \(0.653000\pi\)
\(164\) 6.89977 0.538782
\(165\) 3.24698 0.252777
\(166\) 9.21313 0.715077
\(167\) −8.05861 −0.623594 −0.311797 0.950149i \(-0.600931\pi\)
−0.311797 + 0.950149i \(0.600931\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 0.603875 0.0463151
\(171\) 0.664874 0.0508442
\(172\) −1.30798 −0.0997324
\(173\) −10.4940 −0.797841 −0.398920 0.916986i \(-0.630615\pi\)
−0.398920 + 0.916986i \(0.630615\pi\)
\(174\) 8.74094 0.662649
\(175\) 4.35690 0.329350
\(176\) 4.04892 0.305199
\(177\) 2.58211 0.194083
\(178\) 1.75302 0.131394
\(179\) 4.08575 0.305384 0.152692 0.988274i \(-0.451206\pi\)
0.152692 + 0.988274i \(0.451206\pi\)
\(180\) −0.801938 −0.0597729
\(181\) −13.1196 −0.975173 −0.487586 0.873075i \(-0.662123\pi\)
−0.487586 + 0.873075i \(0.662123\pi\)
\(182\) 0 0
\(183\) −3.71379 −0.274531
\(184\) −3.80194 −0.280283
\(185\) 3.67456 0.270159
\(186\) −0.335126 −0.0245726
\(187\) −3.04892 −0.222959
\(188\) −5.49396 −0.400688
\(189\) 1.00000 0.0727393
\(190\) −0.533188 −0.0386815
\(191\) −5.74094 −0.415400 −0.207700 0.978193i \(-0.566598\pi\)
−0.207700 + 0.978193i \(0.566598\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 11.3817 0.819269 0.409635 0.912250i \(-0.365656\pi\)
0.409635 + 0.912250i \(0.365656\pi\)
\(194\) −8.18598 −0.587719
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −8.63102 −0.614935 −0.307467 0.951559i \(-0.599482\pi\)
−0.307467 + 0.951559i \(0.599482\pi\)
\(198\) 4.04892 0.287744
\(199\) 3.87263 0.274523 0.137262 0.990535i \(-0.456170\pi\)
0.137262 + 0.990535i \(0.456170\pi\)
\(200\) −4.35690 −0.308079
\(201\) 8.86294 0.625143
\(202\) 15.6189 1.09894
\(203\) 8.74094 0.613494
\(204\) 0.753020 0.0527220
\(205\) −5.53319 −0.386455
\(206\) −13.1347 −0.915136
\(207\) −3.80194 −0.264253
\(208\) 0 0
\(209\) 2.69202 0.186211
\(210\) −0.801938 −0.0553390
\(211\) 0.533188 0.0367062 0.0183531 0.999832i \(-0.494158\pi\)
0.0183531 + 0.999832i \(0.494158\pi\)
\(212\) 3.04892 0.209401
\(213\) 10.1957 0.698596
\(214\) −10.1642 −0.694811
\(215\) 1.04892 0.0715356
\(216\) −1.00000 −0.0680414
\(217\) −0.335126 −0.0227498
\(218\) −13.4494 −0.910905
\(219\) −9.44265 −0.638075
\(220\) −3.24698 −0.218911
\(221\) 0 0
\(222\) 4.58211 0.307531
\(223\) −23.0640 −1.54448 −0.772239 0.635332i \(-0.780863\pi\)
−0.772239 + 0.635332i \(0.780863\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −4.35690 −0.290460
\(226\) −3.26444 −0.217147
\(227\) −28.8388 −1.91410 −0.957048 0.289928i \(-0.906368\pi\)
−0.957048 + 0.289928i \(0.906368\pi\)
\(228\) −0.664874 −0.0440324
\(229\) 16.3817 1.08253 0.541265 0.840852i \(-0.317946\pi\)
0.541265 + 0.840852i \(0.317946\pi\)
\(230\) 3.04892 0.201040
\(231\) 4.04892 0.266399
\(232\) −8.74094 −0.573871
\(233\) −10.0261 −0.656830 −0.328415 0.944533i \(-0.606515\pi\)
−0.328415 + 0.944533i \(0.606515\pi\)
\(234\) 0 0
\(235\) 4.40581 0.287404
\(236\) −2.58211 −0.168081
\(237\) −11.7899 −0.765833
\(238\) 0.753020 0.0488111
\(239\) −7.32975 −0.474122 −0.237061 0.971495i \(-0.576184\pi\)
−0.237061 + 0.971495i \(0.576184\pi\)
\(240\) 0.801938 0.0517649
\(241\) −9.00969 −0.580365 −0.290183 0.956971i \(-0.593716\pi\)
−0.290183 + 0.956971i \(0.593716\pi\)
\(242\) 5.39373 0.346722
\(243\) −1.00000 −0.0641500
\(244\) 3.71379 0.237751
\(245\) −0.801938 −0.0512339
\(246\) −6.89977 −0.439913
\(247\) 0 0
\(248\) 0.335126 0.0212805
\(249\) −9.21313 −0.583858
\(250\) 7.50365 0.474572
\(251\) −26.2978 −1.65990 −0.829952 0.557835i \(-0.811632\pi\)
−0.829952 + 0.557835i \(0.811632\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −15.3937 −0.967796
\(254\) 7.74094 0.485710
\(255\) −0.603875 −0.0378161
\(256\) 1.00000 0.0625000
\(257\) −21.4209 −1.33620 −0.668099 0.744073i \(-0.732892\pi\)
−0.668099 + 0.744073i \(0.732892\pi\)
\(258\) 1.30798 0.0814312
\(259\) 4.58211 0.284718
\(260\) 0 0
\(261\) −8.74094 −0.541051
\(262\) 9.12498 0.563743
\(263\) 7.50902 0.463026 0.231513 0.972832i \(-0.425632\pi\)
0.231513 + 0.972832i \(0.425632\pi\)
\(264\) −4.04892 −0.249194
\(265\) −2.44504 −0.150198
\(266\) −0.664874 −0.0407661
\(267\) −1.75302 −0.107283
\(268\) −8.86294 −0.541390
\(269\) −11.3870 −0.694279 −0.347140 0.937813i \(-0.612847\pi\)
−0.347140 + 0.937813i \(0.612847\pi\)
\(270\) 0.801938 0.0488044
\(271\) −17.4470 −1.05983 −0.529914 0.848052i \(-0.677776\pi\)
−0.529914 + 0.848052i \(0.677776\pi\)
\(272\) −0.753020 −0.0456586
\(273\) 0 0
\(274\) −10.4722 −0.632648
\(275\) −17.6407 −1.06377
\(276\) 3.80194 0.228850
\(277\) −20.5351 −1.23383 −0.616917 0.787028i \(-0.711619\pi\)
−0.616917 + 0.787028i \(0.711619\pi\)
\(278\) 3.66487 0.219805
\(279\) 0.335126 0.0200634
\(280\) 0.801938 0.0479249
\(281\) 10.2567 0.611862 0.305931 0.952054i \(-0.401032\pi\)
0.305931 + 0.952054i \(0.401032\pi\)
\(282\) 5.49396 0.327161
\(283\) −1.21744 −0.0723693 −0.0361846 0.999345i \(-0.511520\pi\)
−0.0361846 + 0.999345i \(0.511520\pi\)
\(284\) −10.1957 −0.605002
\(285\) 0.533188 0.0315833
\(286\) 0 0
\(287\) −6.89977 −0.407281
\(288\) 1.00000 0.0589256
\(289\) −16.4330 −0.966645
\(290\) 7.00969 0.411623
\(291\) 8.18598 0.479871
\(292\) 9.44265 0.552589
\(293\) −0.408206 −0.0238477 −0.0119238 0.999929i \(-0.503796\pi\)
−0.0119238 + 0.999929i \(0.503796\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 2.07069 0.120560
\(296\) −4.58211 −0.266329
\(297\) −4.04892 −0.234942
\(298\) −18.7385 −1.08549
\(299\) 0 0
\(300\) 4.35690 0.251546
\(301\) 1.30798 0.0753906
\(302\) −17.4209 −1.00246
\(303\) −15.6189 −0.897285
\(304\) 0.664874 0.0381332
\(305\) −2.97823 −0.170533
\(306\) −0.753020 −0.0430473
\(307\) 19.1540 1.09318 0.546590 0.837401i \(-0.315926\pi\)
0.546590 + 0.837401i \(0.315926\pi\)
\(308\) −4.04892 −0.230708
\(309\) 13.1347 0.747205
\(310\) −0.268750 −0.0152640
\(311\) 19.2513 1.09164 0.545820 0.837902i \(-0.316218\pi\)
0.545820 + 0.837902i \(0.316218\pi\)
\(312\) 0 0
\(313\) 26.4644 1.49586 0.747929 0.663779i \(-0.231048\pi\)
0.747929 + 0.663779i \(0.231048\pi\)
\(314\) 4.39612 0.248088
\(315\) 0.801938 0.0451841
\(316\) 11.7899 0.663231
\(317\) 1.19136 0.0669133 0.0334567 0.999440i \(-0.489348\pi\)
0.0334567 + 0.999440i \(0.489348\pi\)
\(318\) −3.04892 −0.170975
\(319\) −35.3913 −1.98153
\(320\) −0.801938 −0.0448297
\(321\) 10.1642 0.567311
\(322\) 3.80194 0.211874
\(323\) −0.500664 −0.0278577
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −11.8062 −0.653888
\(327\) 13.4494 0.743751
\(328\) 6.89977 0.380976
\(329\) 5.49396 0.302892
\(330\) 3.24698 0.178740
\(331\) 10.8847 0.598278 0.299139 0.954210i \(-0.403301\pi\)
0.299139 + 0.954210i \(0.403301\pi\)
\(332\) 9.21313 0.505636
\(333\) −4.58211 −0.251098
\(334\) −8.05861 −0.440947
\(335\) 7.10752 0.388325
\(336\) 1.00000 0.0545545
\(337\) −21.2717 −1.15875 −0.579373 0.815063i \(-0.696702\pi\)
−0.579373 + 0.815063i \(0.696702\pi\)
\(338\) 0 0
\(339\) 3.26444 0.177300
\(340\) 0.603875 0.0327497
\(341\) 1.35690 0.0734800
\(342\) 0.664874 0.0359523
\(343\) −1.00000 −0.0539949
\(344\) −1.30798 −0.0705215
\(345\) −3.04892 −0.164148
\(346\) −10.4940 −0.564159
\(347\) 3.18060 0.170744 0.0853719 0.996349i \(-0.472792\pi\)
0.0853719 + 0.996349i \(0.472792\pi\)
\(348\) 8.74094 0.468564
\(349\) 3.32736 0.178109 0.0890546 0.996027i \(-0.471615\pi\)
0.0890546 + 0.996027i \(0.471615\pi\)
\(350\) 4.35690 0.232886
\(351\) 0 0
\(352\) 4.04892 0.215808
\(353\) 21.1594 1.12620 0.563101 0.826388i \(-0.309608\pi\)
0.563101 + 0.826388i \(0.309608\pi\)
\(354\) 2.58211 0.137237
\(355\) 8.17629 0.433953
\(356\) 1.75302 0.0929099
\(357\) −0.753020 −0.0398541
\(358\) 4.08575 0.215939
\(359\) 26.4088 1.39380 0.696902 0.717167i \(-0.254561\pi\)
0.696902 + 0.717167i \(0.254561\pi\)
\(360\) −0.801938 −0.0422658
\(361\) −18.5579 −0.976734
\(362\) −13.1196 −0.689551
\(363\) −5.39373 −0.283097
\(364\) 0 0
\(365\) −7.57242 −0.396358
\(366\) −3.71379 −0.194123
\(367\) 14.4504 0.754306 0.377153 0.926151i \(-0.376903\pi\)
0.377153 + 0.926151i \(0.376903\pi\)
\(368\) −3.80194 −0.198190
\(369\) 6.89977 0.359188
\(370\) 3.67456 0.191031
\(371\) −3.04892 −0.158292
\(372\) −0.335126 −0.0173755
\(373\) 21.5719 1.11695 0.558476 0.829520i \(-0.311386\pi\)
0.558476 + 0.829520i \(0.311386\pi\)
\(374\) −3.04892 −0.157656
\(375\) −7.50365 −0.387487
\(376\) −5.49396 −0.283329
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −3.66056 −0.188030 −0.0940152 0.995571i \(-0.529970\pi\)
−0.0940152 + 0.995571i \(0.529970\pi\)
\(380\) −0.533188 −0.0273520
\(381\) −7.74094 −0.396580
\(382\) −5.74094 −0.293732
\(383\) 4.53989 0.231978 0.115989 0.993251i \(-0.462996\pi\)
0.115989 + 0.993251i \(0.462996\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 3.24698 0.165481
\(386\) 11.3817 0.579311
\(387\) −1.30798 −0.0664883
\(388\) −8.18598 −0.415580
\(389\) −5.90648 −0.299470 −0.149735 0.988726i \(-0.547842\pi\)
−0.149735 + 0.988726i \(0.547842\pi\)
\(390\) 0 0
\(391\) 2.86294 0.144785
\(392\) 1.00000 0.0505076
\(393\) −9.12498 −0.460294
\(394\) −8.63102 −0.434825
\(395\) −9.45473 −0.475719
\(396\) 4.04892 0.203466
\(397\) −35.4784 −1.78061 −0.890305 0.455364i \(-0.849509\pi\)
−0.890305 + 0.455364i \(0.849509\pi\)
\(398\) 3.87263 0.194117
\(399\) 0.664874 0.0332854
\(400\) −4.35690 −0.217845
\(401\) 9.60819 0.479810 0.239905 0.970796i \(-0.422884\pi\)
0.239905 + 0.970796i \(0.422884\pi\)
\(402\) 8.86294 0.442043
\(403\) 0 0
\(404\) 15.6189 0.777071
\(405\) −0.801938 −0.0398486
\(406\) 8.74094 0.433806
\(407\) −18.5526 −0.919617
\(408\) 0.753020 0.0372801
\(409\) −20.9812 −1.03745 −0.518727 0.854940i \(-0.673594\pi\)
−0.518727 + 0.854940i \(0.673594\pi\)
\(410\) −5.53319 −0.273265
\(411\) 10.4722 0.516555
\(412\) −13.1347 −0.647099
\(413\) 2.58211 0.127057
\(414\) −3.80194 −0.186855
\(415\) −7.38835 −0.362680
\(416\) 0 0
\(417\) −3.66487 −0.179470
\(418\) 2.69202 0.131671
\(419\) 14.1970 0.693569 0.346784 0.937945i \(-0.387274\pi\)
0.346784 + 0.937945i \(0.387274\pi\)
\(420\) −0.801938 −0.0391306
\(421\) −27.9269 −1.36107 −0.680537 0.732713i \(-0.738254\pi\)
−0.680537 + 0.732713i \(0.738254\pi\)
\(422\) 0.533188 0.0259552
\(423\) −5.49396 −0.267125
\(424\) 3.04892 0.148069
\(425\) 3.28083 0.159144
\(426\) 10.1957 0.493982
\(427\) −3.71379 −0.179723
\(428\) −10.1642 −0.491306
\(429\) 0 0
\(430\) 1.04892 0.0505833
\(431\) 31.7549 1.52958 0.764791 0.644279i \(-0.222842\pi\)
0.764791 + 0.644279i \(0.222842\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −16.4101 −0.788620 −0.394310 0.918977i \(-0.629016\pi\)
−0.394310 + 0.918977i \(0.629016\pi\)
\(434\) −0.335126 −0.0160865
\(435\) −7.00969 −0.336089
\(436\) −13.4494 −0.644107
\(437\) −2.52781 −0.120922
\(438\) −9.44265 −0.451187
\(439\) −6.83207 −0.326077 −0.163038 0.986620i \(-0.552129\pi\)
−0.163038 + 0.986620i \(0.552129\pi\)
\(440\) −3.24698 −0.154794
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 16.7114 0.793983 0.396991 0.917822i \(-0.370054\pi\)
0.396991 + 0.917822i \(0.370054\pi\)
\(444\) 4.58211 0.217457
\(445\) −1.40581 −0.0666419
\(446\) −23.0640 −1.09211
\(447\) 18.7385 0.886303
\(448\) −1.00000 −0.0472456
\(449\) 31.6668 1.49445 0.747224 0.664572i \(-0.231386\pi\)
0.747224 + 0.664572i \(0.231386\pi\)
\(450\) −4.35690 −0.205386
\(451\) 27.9366 1.31548
\(452\) −3.26444 −0.153546
\(453\) 17.4209 0.818504
\(454\) −28.8388 −1.35347
\(455\) 0 0
\(456\) −0.664874 −0.0311356
\(457\) −40.3260 −1.88637 −0.943186 0.332265i \(-0.892187\pi\)
−0.943186 + 0.332265i \(0.892187\pi\)
\(458\) 16.3817 0.765464
\(459\) 0.753020 0.0351480
\(460\) 3.04892 0.142157
\(461\) −25.1008 −1.16906 −0.584531 0.811371i \(-0.698721\pi\)
−0.584531 + 0.811371i \(0.698721\pi\)
\(462\) 4.04892 0.188373
\(463\) −25.4330 −1.18197 −0.590985 0.806683i \(-0.701261\pi\)
−0.590985 + 0.806683i \(0.701261\pi\)
\(464\) −8.74094 −0.405788
\(465\) 0.268750 0.0124630
\(466\) −10.0261 −0.464449
\(467\) 32.6829 1.51239 0.756193 0.654349i \(-0.227057\pi\)
0.756193 + 0.654349i \(0.227057\pi\)
\(468\) 0 0
\(469\) 8.86294 0.409252
\(470\) 4.40581 0.203225
\(471\) −4.39612 −0.202563
\(472\) −2.58211 −0.118851
\(473\) −5.29590 −0.243506
\(474\) −11.7899 −0.541526
\(475\) −2.89679 −0.132914
\(476\) 0.753020 0.0345146
\(477\) 3.04892 0.139600
\(478\) −7.32975 −0.335255
\(479\) −9.80864 −0.448168 −0.224084 0.974570i \(-0.571939\pi\)
−0.224084 + 0.974570i \(0.571939\pi\)
\(480\) 0.801938 0.0366033
\(481\) 0 0
\(482\) −9.00969 −0.410380
\(483\) −3.80194 −0.172994
\(484\) 5.39373 0.245170
\(485\) 6.56465 0.298085
\(486\) −1.00000 −0.0453609
\(487\) 16.0683 0.728124 0.364062 0.931375i \(-0.381390\pi\)
0.364062 + 0.931375i \(0.381390\pi\)
\(488\) 3.71379 0.168115
\(489\) 11.8062 0.533897
\(490\) −0.801938 −0.0362279
\(491\) 12.3676 0.558144 0.279072 0.960270i \(-0.409973\pi\)
0.279072 + 0.960270i \(0.409973\pi\)
\(492\) −6.89977 −0.311066
\(493\) 6.58211 0.296443
\(494\) 0 0
\(495\) −3.24698 −0.145941
\(496\) 0.335126 0.0150476
\(497\) 10.1957 0.457338
\(498\) −9.21313 −0.412850
\(499\) 32.4064 1.45071 0.725355 0.688375i \(-0.241676\pi\)
0.725355 + 0.688375i \(0.241676\pi\)
\(500\) 7.50365 0.335573
\(501\) 8.05861 0.360032
\(502\) −26.2978 −1.17373
\(503\) 31.9162 1.42307 0.711536 0.702650i \(-0.248000\pi\)
0.711536 + 0.702650i \(0.248000\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −12.5254 −0.557374
\(506\) −15.3937 −0.684335
\(507\) 0 0
\(508\) 7.74094 0.343449
\(509\) −11.3056 −0.501111 −0.250556 0.968102i \(-0.580613\pi\)
−0.250556 + 0.968102i \(0.580613\pi\)
\(510\) −0.603875 −0.0267401
\(511\) −9.44265 −0.417718
\(512\) 1.00000 0.0441942
\(513\) −0.664874 −0.0293549
\(514\) −21.4209 −0.944834
\(515\) 10.5332 0.464148
\(516\) 1.30798 0.0575805
\(517\) −22.2446 −0.978316
\(518\) 4.58211 0.201326
\(519\) 10.4940 0.460634
\(520\) 0 0
\(521\) 40.1213 1.75774 0.878872 0.477057i \(-0.158297\pi\)
0.878872 + 0.477057i \(0.158297\pi\)
\(522\) −8.74094 −0.382580
\(523\) 9.51679 0.416140 0.208070 0.978114i \(-0.433282\pi\)
0.208070 + 0.978114i \(0.433282\pi\)
\(524\) 9.12498 0.398627
\(525\) −4.35690 −0.190151
\(526\) 7.50902 0.327409
\(527\) −0.252356 −0.0109928
\(528\) −4.04892 −0.176207
\(529\) −8.54527 −0.371533
\(530\) −2.44504 −0.106206
\(531\) −2.58211 −0.112054
\(532\) −0.664874 −0.0288260
\(533\) 0 0
\(534\) −1.75302 −0.0758606
\(535\) 8.15106 0.352401
\(536\) −8.86294 −0.382821
\(537\) −4.08575 −0.176313
\(538\) −11.3870 −0.490930
\(539\) 4.04892 0.174399
\(540\) 0.801938 0.0345099
\(541\) −13.9675 −0.600509 −0.300254 0.953859i \(-0.597072\pi\)
−0.300254 + 0.953859i \(0.597072\pi\)
\(542\) −17.4470 −0.749411
\(543\) 13.1196 0.563016
\(544\) −0.753020 −0.0322855
\(545\) 10.7855 0.462002
\(546\) 0 0
\(547\) 17.6160 0.753204 0.376602 0.926375i \(-0.377092\pi\)
0.376602 + 0.926375i \(0.377092\pi\)
\(548\) −10.4722 −0.447350
\(549\) 3.71379 0.158501
\(550\) −17.6407 −0.752202
\(551\) −5.81163 −0.247584
\(552\) 3.80194 0.161821
\(553\) −11.7899 −0.501356
\(554\) −20.5351 −0.872453
\(555\) −3.67456 −0.155977
\(556\) 3.66487 0.155425
\(557\) 15.8950 0.673492 0.336746 0.941595i \(-0.390674\pi\)
0.336746 + 0.941595i \(0.390674\pi\)
\(558\) 0.335126 0.0141870
\(559\) 0 0
\(560\) 0.801938 0.0338881
\(561\) 3.04892 0.128725
\(562\) 10.2567 0.432651
\(563\) 4.29829 0.181151 0.0905757 0.995890i \(-0.471129\pi\)
0.0905757 + 0.995890i \(0.471129\pi\)
\(564\) 5.49396 0.231337
\(565\) 2.61788 0.110135
\(566\) −1.21744 −0.0511728
\(567\) −1.00000 −0.0419961
\(568\) −10.1957 −0.427801
\(569\) 3.03252 0.127130 0.0635650 0.997978i \(-0.479753\pi\)
0.0635650 + 0.997978i \(0.479753\pi\)
\(570\) 0.533188 0.0223328
\(571\) 38.1976 1.59852 0.799260 0.600986i \(-0.205225\pi\)
0.799260 + 0.600986i \(0.205225\pi\)
\(572\) 0 0
\(573\) 5.74094 0.239831
\(574\) −6.89977 −0.287991
\(575\) 16.5646 0.690794
\(576\) 1.00000 0.0416667
\(577\) −17.0761 −0.710886 −0.355443 0.934698i \(-0.615670\pi\)
−0.355443 + 0.934698i \(0.615670\pi\)
\(578\) −16.4330 −0.683521
\(579\) −11.3817 −0.473005
\(580\) 7.00969 0.291061
\(581\) −9.21313 −0.382225
\(582\) 8.18598 0.339320
\(583\) 12.3448 0.511270
\(584\) 9.44265 0.390740
\(585\) 0 0
\(586\) −0.408206 −0.0168628
\(587\) −43.9721 −1.81492 −0.907462 0.420135i \(-0.861983\pi\)
−0.907462 + 0.420135i \(0.861983\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 0.222816 0.00918099
\(590\) 2.07069 0.0852489
\(591\) 8.63102 0.355033
\(592\) −4.58211 −0.188323
\(593\) 16.5778 0.680768 0.340384 0.940286i \(-0.389443\pi\)
0.340384 + 0.940286i \(0.389443\pi\)
\(594\) −4.04892 −0.166129
\(595\) −0.603875 −0.0247565
\(596\) −18.7385 −0.767561
\(597\) −3.87263 −0.158496
\(598\) 0 0
\(599\) −2.05861 −0.0841124 −0.0420562 0.999115i \(-0.513391\pi\)
−0.0420562 + 0.999115i \(0.513391\pi\)
\(600\) 4.35690 0.177870
\(601\) 23.4620 0.957036 0.478518 0.878078i \(-0.341174\pi\)
0.478518 + 0.878078i \(0.341174\pi\)
\(602\) 1.30798 0.0533092
\(603\) −8.86294 −0.360927
\(604\) −17.4209 −0.708846
\(605\) −4.32544 −0.175854
\(606\) −15.6189 −0.634476
\(607\) 13.9095 0.564568 0.282284 0.959331i \(-0.408908\pi\)
0.282284 + 0.959331i \(0.408908\pi\)
\(608\) 0.664874 0.0269642
\(609\) −8.74094 −0.354201
\(610\) −2.97823 −0.120585
\(611\) 0 0
\(612\) −0.753020 −0.0304390
\(613\) −5.99462 −0.242121 −0.121060 0.992645i \(-0.538629\pi\)
−0.121060 + 0.992645i \(0.538629\pi\)
\(614\) 19.1540 0.772994
\(615\) 5.53319 0.223120
\(616\) −4.04892 −0.163136
\(617\) −39.4881 −1.58973 −0.794866 0.606785i \(-0.792459\pi\)
−0.794866 + 0.606785i \(0.792459\pi\)
\(618\) 13.1347 0.528354
\(619\) −24.5786 −0.987899 −0.493950 0.869491i \(-0.664447\pi\)
−0.493950 + 0.869491i \(0.664447\pi\)
\(620\) −0.268750 −0.0107933
\(621\) 3.80194 0.152567
\(622\) 19.2513 0.771906
\(623\) −1.75302 −0.0702333
\(624\) 0 0
\(625\) 15.7670 0.630681
\(626\) 26.4644 1.05773
\(627\) −2.69202 −0.107509
\(628\) 4.39612 0.175424
\(629\) 3.45042 0.137577
\(630\) 0.801938 0.0319500
\(631\) −17.2241 −0.685682 −0.342841 0.939393i \(-0.611389\pi\)
−0.342841 + 0.939393i \(0.611389\pi\)
\(632\) 11.7899 0.468975
\(633\) −0.533188 −0.0211923
\(634\) 1.19136 0.0473149
\(635\) −6.20775 −0.246347
\(636\) −3.04892 −0.120897
\(637\) 0 0
\(638\) −35.3913 −1.40116
\(639\) −10.1957 −0.403334
\(640\) −0.801938 −0.0316994
\(641\) −39.4631 −1.55870 −0.779349 0.626590i \(-0.784450\pi\)
−0.779349 + 0.626590i \(0.784450\pi\)
\(642\) 10.1642 0.401149
\(643\) 7.93661 0.312989 0.156495 0.987679i \(-0.449981\pi\)
0.156495 + 0.987679i \(0.449981\pi\)
\(644\) 3.80194 0.149817
\(645\) −1.04892 −0.0413011
\(646\) −0.500664 −0.0196984
\(647\) 34.9554 1.37424 0.687119 0.726545i \(-0.258875\pi\)
0.687119 + 0.726545i \(0.258875\pi\)
\(648\) 1.00000 0.0392837
\(649\) −10.4547 −0.410384
\(650\) 0 0
\(651\) 0.335126 0.0131346
\(652\) −11.8062 −0.462368
\(653\) −25.5609 −1.00028 −0.500138 0.865946i \(-0.666717\pi\)
−0.500138 + 0.865946i \(0.666717\pi\)
\(654\) 13.4494 0.525911
\(655\) −7.31767 −0.285925
\(656\) 6.89977 0.269391
\(657\) 9.44265 0.368393
\(658\) 5.49396 0.214177
\(659\) 18.4397 0.718307 0.359154 0.933278i \(-0.383065\pi\)
0.359154 + 0.933278i \(0.383065\pi\)
\(660\) 3.24698 0.126389
\(661\) −26.3201 −1.02373 −0.511866 0.859065i \(-0.671046\pi\)
−0.511866 + 0.859065i \(0.671046\pi\)
\(662\) 10.8847 0.423046
\(663\) 0 0
\(664\) 9.21313 0.357539
\(665\) 0.533188 0.0206761
\(666\) −4.58211 −0.177553
\(667\) 33.2325 1.28677
\(668\) −8.05861 −0.311797
\(669\) 23.0640 0.891705
\(670\) 7.10752 0.274588
\(671\) 15.0368 0.580491
\(672\) 1.00000 0.0385758
\(673\) 31.6732 1.22091 0.610457 0.792050i \(-0.290986\pi\)
0.610457 + 0.792050i \(0.290986\pi\)
\(674\) −21.2717 −0.819357
\(675\) 4.35690 0.167697
\(676\) 0 0
\(677\) 18.3187 0.704046 0.352023 0.935991i \(-0.385494\pi\)
0.352023 + 0.935991i \(0.385494\pi\)
\(678\) 3.26444 0.125370
\(679\) 8.18598 0.314149
\(680\) 0.603875 0.0231576
\(681\) 28.8388 1.10510
\(682\) 1.35690 0.0519582
\(683\) 9.86486 0.377468 0.188734 0.982028i \(-0.439562\pi\)
0.188734 + 0.982028i \(0.439562\pi\)
\(684\) 0.664874 0.0254221
\(685\) 8.39804 0.320873
\(686\) −1.00000 −0.0381802
\(687\) −16.3817 −0.624999
\(688\) −1.30798 −0.0498662
\(689\) 0 0
\(690\) −3.04892 −0.116070
\(691\) 45.5284 1.73198 0.865991 0.500060i \(-0.166689\pi\)
0.865991 + 0.500060i \(0.166689\pi\)
\(692\) −10.4940 −0.398920
\(693\) −4.04892 −0.153806
\(694\) 3.18060 0.120734
\(695\) −2.93900 −0.111483
\(696\) 8.74094 0.331324
\(697\) −5.19567 −0.196800
\(698\) 3.32736 0.125942
\(699\) 10.0261 0.379221
\(700\) 4.35690 0.164675
\(701\) 43.7821 1.65363 0.826813 0.562476i \(-0.190151\pi\)
0.826813 + 0.562476i \(0.190151\pi\)
\(702\) 0 0
\(703\) −3.04652 −0.114902
\(704\) 4.04892 0.152599
\(705\) −4.40581 −0.165933
\(706\) 21.1594 0.796345
\(707\) −15.6189 −0.587411
\(708\) 2.58211 0.0970415
\(709\) 3.89248 0.146185 0.0730925 0.997325i \(-0.476713\pi\)
0.0730925 + 0.997325i \(0.476713\pi\)
\(710\) 8.17629 0.306851
\(711\) 11.7899 0.442154
\(712\) 1.75302 0.0656972
\(713\) −1.27413 −0.0477164
\(714\) −0.753020 −0.0281811
\(715\) 0 0
\(716\) 4.08575 0.152692
\(717\) 7.32975 0.273734
\(718\) 26.4088 0.985568
\(719\) −40.9077 −1.52560 −0.762799 0.646636i \(-0.776175\pi\)
−0.762799 + 0.646636i \(0.776175\pi\)
\(720\) −0.801938 −0.0298865
\(721\) 13.1347 0.489161
\(722\) −18.5579 −0.690655
\(723\) 9.00969 0.335074
\(724\) −13.1196 −0.487586
\(725\) 38.0834 1.41438
\(726\) −5.39373 −0.200180
\(727\) −9.91962 −0.367898 −0.183949 0.982936i \(-0.558888\pi\)
−0.183949 + 0.982936i \(0.558888\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −7.57242 −0.280268
\(731\) 0.984935 0.0364291
\(732\) −3.71379 −0.137266
\(733\) −32.8471 −1.21324 −0.606618 0.794993i \(-0.707474\pi\)
−0.606618 + 0.794993i \(0.707474\pi\)
\(734\) 14.4504 0.533375
\(735\) 0.801938 0.0295799
\(736\) −3.80194 −0.140141
\(737\) −35.8853 −1.32185
\(738\) 6.89977 0.253984
\(739\) 18.5338 0.681776 0.340888 0.940104i \(-0.389272\pi\)
0.340888 + 0.940104i \(0.389272\pi\)
\(740\) 3.67456 0.135080
\(741\) 0 0
\(742\) −3.04892 −0.111929
\(743\) −10.8455 −0.397882 −0.198941 0.980011i \(-0.563750\pi\)
−0.198941 + 0.980011i \(0.563750\pi\)
\(744\) −0.335126 −0.0122863
\(745\) 15.0271 0.550552
\(746\) 21.5719 0.789805
\(747\) 9.21313 0.337091
\(748\) −3.04892 −0.111479
\(749\) 10.1642 0.371392
\(750\) −7.50365 −0.273994
\(751\) −16.3913 −0.598128 −0.299064 0.954233i \(-0.596674\pi\)
−0.299064 + 0.954233i \(0.596674\pi\)
\(752\) −5.49396 −0.200344
\(753\) 26.2978 0.958346
\(754\) 0 0
\(755\) 13.9705 0.508437
\(756\) 1.00000 0.0363696
\(757\) −39.2737 −1.42743 −0.713713 0.700439i \(-0.752988\pi\)
−0.713713 + 0.700439i \(0.752988\pi\)
\(758\) −3.66056 −0.132958
\(759\) 15.3937 0.558757
\(760\) −0.533188 −0.0193408
\(761\) 29.1752 1.05760 0.528801 0.848746i \(-0.322642\pi\)
0.528801 + 0.848746i \(0.322642\pi\)
\(762\) −7.74094 −0.280425
\(763\) 13.4494 0.486899
\(764\) −5.74094 −0.207700
\(765\) 0.603875 0.0218332
\(766\) 4.53989 0.164033
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 20.3134 0.732518 0.366259 0.930513i \(-0.380638\pi\)
0.366259 + 0.930513i \(0.380638\pi\)
\(770\) 3.24698 0.117013
\(771\) 21.4209 0.771454
\(772\) 11.3817 0.409635
\(773\) 7.57434 0.272430 0.136215 0.990679i \(-0.456506\pi\)
0.136215 + 0.990679i \(0.456506\pi\)
\(774\) −1.30798 −0.0470143
\(775\) −1.46011 −0.0524486
\(776\) −8.18598 −0.293860
\(777\) −4.58211 −0.164382
\(778\) −5.90648 −0.211757
\(779\) 4.58748 0.164364
\(780\) 0 0
\(781\) −41.2814 −1.47717
\(782\) 2.86294 0.102378
\(783\) 8.74094 0.312376
\(784\) 1.00000 0.0357143
\(785\) −3.52542 −0.125828
\(786\) −9.12498 −0.325477
\(787\) −10.8398 −0.386399 −0.193199 0.981160i \(-0.561886\pi\)
−0.193199 + 0.981160i \(0.561886\pi\)
\(788\) −8.63102 −0.307467
\(789\) −7.50902 −0.267328
\(790\) −9.45473 −0.336384
\(791\) 3.26444 0.116070
\(792\) 4.04892 0.143872
\(793\) 0 0
\(794\) −35.4784 −1.25908
\(795\) 2.44504 0.0867167
\(796\) 3.87263 0.137262
\(797\) 4.71917 0.167162 0.0835808 0.996501i \(-0.473364\pi\)
0.0835808 + 0.996501i \(0.473364\pi\)
\(798\) 0.664874 0.0235363
\(799\) 4.13706 0.146359
\(800\) −4.35690 −0.154040
\(801\) 1.75302 0.0619399
\(802\) 9.60819 0.339277
\(803\) 38.2325 1.34920
\(804\) 8.86294 0.312572
\(805\) −3.04892 −0.107460
\(806\) 0 0
\(807\) 11.3870 0.400842
\(808\) 15.6189 0.549472
\(809\) −3.73423 −0.131289 −0.0656443 0.997843i \(-0.520910\pi\)
−0.0656443 + 0.997843i \(0.520910\pi\)
\(810\) −0.801938 −0.0281772
\(811\) −31.1062 −1.09229 −0.546143 0.837692i \(-0.683905\pi\)
−0.546143 + 0.837692i \(0.683905\pi\)
\(812\) 8.74094 0.306747
\(813\) 17.4470 0.611892
\(814\) −18.5526 −0.650267
\(815\) 9.46788 0.331645
\(816\) 0.753020 0.0263610
\(817\) −0.869641 −0.0304249
\(818\) −20.9812 −0.733591
\(819\) 0 0
\(820\) −5.53319 −0.193227
\(821\) 37.8786 1.32197 0.660986 0.750398i \(-0.270138\pi\)
0.660986 + 0.750398i \(0.270138\pi\)
\(822\) 10.4722 0.365260
\(823\) 26.3773 0.919456 0.459728 0.888060i \(-0.347947\pi\)
0.459728 + 0.888060i \(0.347947\pi\)
\(824\) −13.1347 −0.457568
\(825\) 17.6407 0.614171
\(826\) 2.58211 0.0898429
\(827\) −2.49263 −0.0866773 −0.0433386 0.999060i \(-0.513799\pi\)
−0.0433386 + 0.999060i \(0.513799\pi\)
\(828\) −3.80194 −0.132126
\(829\) −47.8437 −1.66168 −0.830840 0.556512i \(-0.812139\pi\)
−0.830840 + 0.556512i \(0.812139\pi\)
\(830\) −7.38835 −0.256454
\(831\) 20.5351 0.712355
\(832\) 0 0
\(833\) −0.753020 −0.0260906
\(834\) −3.66487 −0.126904
\(835\) 6.46250 0.223644
\(836\) 2.69202 0.0931055
\(837\) −0.335126 −0.0115836
\(838\) 14.1970 0.490427
\(839\) 11.3773 0.392789 0.196395 0.980525i \(-0.437077\pi\)
0.196395 + 0.980525i \(0.437077\pi\)
\(840\) −0.801938 −0.0276695
\(841\) 47.4040 1.63462
\(842\) −27.9269 −0.962425
\(843\) −10.2567 −0.353258
\(844\) 0.533188 0.0183531
\(845\) 0 0
\(846\) −5.49396 −0.188886
\(847\) −5.39373 −0.185331
\(848\) 3.04892 0.104700
\(849\) 1.21744 0.0417824
\(850\) 3.28083 0.112532
\(851\) 17.4209 0.597180
\(852\) 10.1957 0.349298
\(853\) −13.2905 −0.455059 −0.227529 0.973771i \(-0.573065\pi\)
−0.227529 + 0.973771i \(0.573065\pi\)
\(854\) −3.71379 −0.127083
\(855\) −0.533188 −0.0182346
\(856\) −10.1642 −0.347406
\(857\) 21.5026 0.734514 0.367257 0.930119i \(-0.380297\pi\)
0.367257 + 0.930119i \(0.380297\pi\)
\(858\) 0 0
\(859\) −26.0398 −0.888467 −0.444234 0.895911i \(-0.646524\pi\)
−0.444234 + 0.895911i \(0.646524\pi\)
\(860\) 1.04892 0.0357678
\(861\) 6.89977 0.235144
\(862\) 31.7549 1.08158
\(863\) 21.4679 0.730775 0.365388 0.930856i \(-0.380936\pi\)
0.365388 + 0.930856i \(0.380936\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 8.41550 0.286136
\(866\) −16.4101 −0.557639
\(867\) 16.4330 0.558093
\(868\) −0.335126 −0.0113749
\(869\) 47.7362 1.61934
\(870\) −7.00969 −0.237651
\(871\) 0 0
\(872\) −13.4494 −0.455453
\(873\) −8.18598 −0.277053
\(874\) −2.52781 −0.0855045
\(875\) −7.50365 −0.253670
\(876\) −9.44265 −0.319038
\(877\) −40.5792 −1.37026 −0.685132 0.728419i \(-0.740255\pi\)
−0.685132 + 0.728419i \(0.740255\pi\)
\(878\) −6.83207 −0.230571
\(879\) 0.408206 0.0137685
\(880\) −3.24698 −0.109456
\(881\) −56.1680 −1.89235 −0.946175 0.323656i \(-0.895088\pi\)
−0.946175 + 0.323656i \(0.895088\pi\)
\(882\) 1.00000 0.0336718
\(883\) −45.7174 −1.53851 −0.769256 0.638941i \(-0.779373\pi\)
−0.769256 + 0.638941i \(0.779373\pi\)
\(884\) 0 0
\(885\) −2.07069 −0.0696054
\(886\) 16.7114 0.561430
\(887\) 5.37004 0.180308 0.0901542 0.995928i \(-0.471264\pi\)
0.0901542 + 0.995928i \(0.471264\pi\)
\(888\) 4.58211 0.153765
\(889\) −7.74094 −0.259623
\(890\) −1.40581 −0.0471230
\(891\) 4.04892 0.135644
\(892\) −23.0640 −0.772239
\(893\) −3.65279 −0.122236
\(894\) 18.7385 0.626711
\(895\) −3.27652 −0.109522
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 31.6668 1.05673
\(899\) −2.92931 −0.0976980
\(900\) −4.35690 −0.145230
\(901\) −2.29590 −0.0764874
\(902\) 27.9366 0.930187
\(903\) −1.30798 −0.0435268
\(904\) −3.26444 −0.108574
\(905\) 10.5211 0.349733
\(906\) 17.4209 0.578770
\(907\) 30.9065 1.02623 0.513116 0.858319i \(-0.328491\pi\)
0.513116 + 0.858319i \(0.328491\pi\)
\(908\) −28.8388 −0.957048
\(909\) 15.6189 0.518048
\(910\) 0 0
\(911\) −20.8267 −0.690019 −0.345010 0.938599i \(-0.612124\pi\)
−0.345010 + 0.938599i \(0.612124\pi\)
\(912\) −0.664874 −0.0220162
\(913\) 37.3032 1.23456
\(914\) −40.3260 −1.33387
\(915\) 2.97823 0.0984572
\(916\) 16.3817 0.541265
\(917\) −9.12498 −0.301333
\(918\) 0.753020 0.0248534
\(919\) 20.6316 0.680574 0.340287 0.940322i \(-0.389476\pi\)
0.340287 + 0.940322i \(0.389476\pi\)
\(920\) 3.04892 0.100520
\(921\) −19.1540 −0.631147
\(922\) −25.1008 −0.826651
\(923\) 0 0
\(924\) 4.04892 0.133200
\(925\) 19.9638 0.656404
\(926\) −25.4330 −0.835779
\(927\) −13.1347 −0.431399
\(928\) −8.74094 −0.286935
\(929\) 40.9982 1.34511 0.672554 0.740048i \(-0.265197\pi\)
0.672554 + 0.740048i \(0.265197\pi\)
\(930\) 0.268750 0.00881266
\(931\) 0.664874 0.0217904
\(932\) −10.0261 −0.328415
\(933\) −19.2513 −0.630259
\(934\) 32.6829 1.06942
\(935\) 2.44504 0.0799614
\(936\) 0 0
\(937\) −4.45042 −0.145389 −0.0726944 0.997354i \(-0.523160\pi\)
−0.0726944 + 0.997354i \(0.523160\pi\)
\(938\) 8.86294 0.289385
\(939\) −26.4644 −0.863634
\(940\) 4.40581 0.143702
\(941\) −21.8745 −0.713090 −0.356545 0.934278i \(-0.616045\pi\)
−0.356545 + 0.934278i \(0.616045\pi\)
\(942\) −4.39612 −0.143233
\(943\) −26.2325 −0.854248
\(944\) −2.58211 −0.0840404
\(945\) −0.801938 −0.0260870
\(946\) −5.29590 −0.172184
\(947\) 11.0546 0.359225 0.179612 0.983737i \(-0.442516\pi\)
0.179612 + 0.983737i \(0.442516\pi\)
\(948\) −11.7899 −0.382917
\(949\) 0 0
\(950\) −2.89679 −0.0939842
\(951\) −1.19136 −0.0386324
\(952\) 0.753020 0.0244055
\(953\) −1.52052 −0.0492543 −0.0246272 0.999697i \(-0.507840\pi\)
−0.0246272 + 0.999697i \(0.507840\pi\)
\(954\) 3.04892 0.0987123
\(955\) 4.60388 0.148978
\(956\) −7.32975 −0.237061
\(957\) 35.3913 1.14404
\(958\) −9.80864 −0.316903
\(959\) 10.4722 0.338165
\(960\) 0.801938 0.0258824
\(961\) −30.8877 −0.996377
\(962\) 0 0
\(963\) −10.1642 −0.327537
\(964\) −9.00969 −0.290183
\(965\) −9.12737 −0.293821
\(966\) −3.80194 −0.122325
\(967\) −33.7041 −1.08385 −0.541925 0.840427i \(-0.682304\pi\)
−0.541925 + 0.840427i \(0.682304\pi\)
\(968\) 5.39373 0.173361
\(969\) 0.500664 0.0160836
\(970\) 6.56465 0.210778
\(971\) −36.5357 −1.17249 −0.586243 0.810135i \(-0.699394\pi\)
−0.586243 + 0.810135i \(0.699394\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −3.66487 −0.117490
\(974\) 16.0683 0.514861
\(975\) 0 0
\(976\) 3.71379 0.118876
\(977\) −11.8933 −0.380501 −0.190251 0.981736i \(-0.560930\pi\)
−0.190251 + 0.981736i \(0.560930\pi\)
\(978\) 11.8062 0.377522
\(979\) 7.09783 0.226848
\(980\) −0.801938 −0.0256170
\(981\) −13.4494 −0.429405
\(982\) 12.3676 0.394668
\(983\) −47.0113 −1.49943 −0.749715 0.661761i \(-0.769809\pi\)
−0.749715 + 0.661761i \(0.769809\pi\)
\(984\) −6.89977 −0.219957
\(985\) 6.92154 0.220539
\(986\) 6.58211 0.209617
\(987\) −5.49396 −0.174875
\(988\) 0 0
\(989\) 4.97285 0.158128
\(990\) −3.24698 −0.103196
\(991\) −15.2097 −0.483151 −0.241576 0.970382i \(-0.577664\pi\)
−0.241576 + 0.970382i \(0.577664\pi\)
\(992\) 0.335126 0.0106402
\(993\) −10.8847 −0.345416
\(994\) 10.1957 0.323387
\(995\) −3.10560 −0.0984543
\(996\) −9.21313 −0.291929
\(997\) 44.4295 1.40710 0.703548 0.710648i \(-0.251598\pi\)
0.703548 + 0.710648i \(0.251598\pi\)
\(998\) 32.4064 1.02581
\(999\) 4.58211 0.144971
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.cj.1.1 yes 3
13.12 even 2 7098.2.a.cc.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cc.1.3 3 13.12 even 2
7098.2.a.cj.1.1 yes 3 1.1 even 1 trivial