Properties

Label 7098.2.a.ch.1.3
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 1.3
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.246980 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.246980 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.246980 q^{10} +5.40581 q^{11} -1.00000 q^{12} +1.00000 q^{14} -0.246980 q^{15} +1.00000 q^{16} -4.04892 q^{17} +1.00000 q^{18} -3.80194 q^{19} +0.246980 q^{20} -1.00000 q^{21} +5.40581 q^{22} -9.34481 q^{23} -1.00000 q^{24} -4.93900 q^{25} -1.00000 q^{27} +1.00000 q^{28} -3.26875 q^{29} -0.246980 q^{30} -1.41789 q^{31} +1.00000 q^{32} -5.40581 q^{33} -4.04892 q^{34} +0.246980 q^{35} +1.00000 q^{36} +1.35690 q^{37} -3.80194 q^{38} +0.246980 q^{40} -0.246980 q^{41} -1.00000 q^{42} -5.34481 q^{43} +5.40581 q^{44} +0.246980 q^{45} -9.34481 q^{46} -4.38404 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.93900 q^{50} +4.04892 q^{51} -8.67994 q^{53} -1.00000 q^{54} +1.33513 q^{55} +1.00000 q^{56} +3.80194 q^{57} -3.26875 q^{58} -0.466812 q^{59} -0.246980 q^{60} -7.00000 q^{61} -1.41789 q^{62} +1.00000 q^{63} +1.00000 q^{64} -5.40581 q^{66} -5.71917 q^{67} -4.04892 q^{68} +9.34481 q^{69} +0.246980 q^{70} +6.98792 q^{71} +1.00000 q^{72} -6.93900 q^{73} +1.35690 q^{74} +4.93900 q^{75} -3.80194 q^{76} +5.40581 q^{77} -5.75302 q^{79} +0.246980 q^{80} +1.00000 q^{81} -0.246980 q^{82} -11.8019 q^{83} -1.00000 q^{84} -1.00000 q^{85} -5.34481 q^{86} +3.26875 q^{87} +5.40581 q^{88} +17.9584 q^{89} +0.246980 q^{90} -9.34481 q^{92} +1.41789 q^{93} -4.38404 q^{94} -0.939001 q^{95} -1.00000 q^{96} -13.8509 q^{97} +1.00000 q^{98} +5.40581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 4q^{5} - 3q^{6} + 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 4q^{5} - 3q^{6} + 3q^{7} + 3q^{8} + 3q^{9} - 4q^{10} + 3q^{11} - 3q^{12} + 3q^{14} + 4q^{15} + 3q^{16} - 3q^{17} + 3q^{18} - 7q^{19} - 4q^{20} - 3q^{21} + 3q^{22} - 5q^{23} - 3q^{24} - 5q^{25} - 3q^{27} + 3q^{28} - 2q^{29} + 4q^{30} - 10q^{31} + 3q^{32} - 3q^{33} - 3q^{34} - 4q^{35} + 3q^{36} - 7q^{38} - 4q^{40} + 4q^{41} - 3q^{42} + 7q^{43} + 3q^{44} - 4q^{45} - 5q^{46} - 3q^{47} - 3q^{48} + 3q^{49} - 5q^{50} + 3q^{51} - 2q^{53} - 3q^{54} + 3q^{55} + 3q^{56} + 7q^{57} - 2q^{58} + 2q^{59} + 4q^{60} - 21q^{61} - 10q^{62} + 3q^{63} + 3q^{64} - 3q^{66} - 6q^{67} - 3q^{68} + 5q^{69} - 4q^{70} + 2q^{71} + 3q^{72} - 11q^{73} + 5q^{75} - 7q^{76} + 3q^{77} - 22q^{79} - 4q^{80} + 3q^{81} + 4q^{82} - 31q^{83} - 3q^{84} - 3q^{85} + 7q^{86} + 2q^{87} + 3q^{88} - 4q^{90} - 5q^{92} + 10q^{93} - 3q^{94} + 7q^{95} - 3q^{96} - 28q^{97} + 3q^{98} + 3q^{99} + O(q^{100}) \)

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
\(5\) 0.246980 0.110453 0.0552263 0.998474i \(-0.482412\pi\)
0.0552263 + 0.998474i \(0.482412\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0.246980 0.0781018
\(11\) 5.40581 1.62991 0.814957 0.579521i \(-0.196760\pi\)
0.814957 + 0.579521i \(0.196760\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) −0.246980 −0.0637699
\(16\) 1.00000 0.250000
\(17\) −4.04892 −0.982007 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.80194 −0.872224 −0.436112 0.899892i \(-0.643645\pi\)
−0.436112 + 0.899892i \(0.643645\pi\)
\(20\) 0.246980 0.0552263
\(21\) −1.00000 −0.218218
\(22\) 5.40581 1.15252
\(23\) −9.34481 −1.94853 −0.974264 0.225409i \(-0.927628\pi\)
−0.974264 + 0.225409i \(0.927628\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.93900 −0.987800
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) −3.26875 −0.606992 −0.303496 0.952833i \(-0.598154\pi\)
−0.303496 + 0.952833i \(0.598154\pi\)
\(30\) −0.246980 −0.0450921
\(31\) −1.41789 −0.254661 −0.127331 0.991860i \(-0.540641\pi\)
−0.127331 + 0.991860i \(0.540641\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.40581 −0.941031
\(34\) −4.04892 −0.694384
\(35\) 0.246980 0.0417472
\(36\) 1.00000 0.166667
\(37\) 1.35690 0.223072 0.111536 0.993760i \(-0.464423\pi\)
0.111536 + 0.993760i \(0.464423\pi\)
\(38\) −3.80194 −0.616756
\(39\) 0 0
\(40\) 0.246980 0.0390509
\(41\) −0.246980 −0.0385717 −0.0192859 0.999814i \(-0.506139\pi\)
−0.0192859 + 0.999814i \(0.506139\pi\)
\(42\) −1.00000 −0.154303
\(43\) −5.34481 −0.815077 −0.407538 0.913188i \(-0.633613\pi\)
−0.407538 + 0.913188i \(0.633613\pi\)
\(44\) 5.40581 0.814957
\(45\) 0.246980 0.0368175
\(46\) −9.34481 −1.37782
\(47\) −4.38404 −0.639478 −0.319739 0.947506i \(-0.603595\pi\)
−0.319739 + 0.947506i \(0.603595\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −4.93900 −0.698480
\(51\) 4.04892 0.566962
\(52\) 0 0
\(53\) −8.67994 −1.19228 −0.596141 0.802880i \(-0.703300\pi\)
−0.596141 + 0.802880i \(0.703300\pi\)
\(54\) −1.00000 −0.136083
\(55\) 1.33513 0.180028
\(56\) 1.00000 0.133631
\(57\) 3.80194 0.503579
\(58\) −3.26875 −0.429208
\(59\) −0.466812 −0.0607738 −0.0303869 0.999538i \(-0.509674\pi\)
−0.0303869 + 0.999538i \(0.509674\pi\)
\(60\) −0.246980 −0.0318849
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) −1.41789 −0.180073
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.40581 −0.665410
\(67\) −5.71917 −0.698708 −0.349354 0.936991i \(-0.613599\pi\)
−0.349354 + 0.936991i \(0.613599\pi\)
\(68\) −4.04892 −0.491003
\(69\) 9.34481 1.12498
\(70\) 0.246980 0.0295197
\(71\) 6.98792 0.829313 0.414657 0.909978i \(-0.363902\pi\)
0.414657 + 0.909978i \(0.363902\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.93900 −0.812149 −0.406074 0.913840i \(-0.633103\pi\)
−0.406074 + 0.913840i \(0.633103\pi\)
\(74\) 1.35690 0.157736
\(75\) 4.93900 0.570307
\(76\) −3.80194 −0.436112
\(77\) 5.40581 0.616050
\(78\) 0 0
\(79\) −5.75302 −0.647265 −0.323633 0.946183i \(-0.604904\pi\)
−0.323633 + 0.946183i \(0.604904\pi\)
\(80\) 0.246980 0.0276132
\(81\) 1.00000 0.111111
\(82\) −0.246980 −0.0272743
\(83\) −11.8019 −1.29543 −0.647715 0.761882i \(-0.724275\pi\)
−0.647715 + 0.761882i \(0.724275\pi\)
\(84\) −1.00000 −0.109109
\(85\) −1.00000 −0.108465
\(86\) −5.34481 −0.576346
\(87\) 3.26875 0.350447
\(88\) 5.40581 0.576262
\(89\) 17.9584 1.90358 0.951792 0.306744i \(-0.0992394\pi\)
0.951792 + 0.306744i \(0.0992394\pi\)
\(90\) 0.246980 0.0260339
\(91\) 0 0
\(92\) −9.34481 −0.974264
\(93\) 1.41789 0.147029
\(94\) −4.38404 −0.452180
\(95\) −0.939001 −0.0963395
\(96\) −1.00000 −0.102062
\(97\) −13.8509 −1.40634 −0.703171 0.711021i \(-0.748233\pi\)
−0.703171 + 0.711021i \(0.748233\pi\)
\(98\) 1.00000 0.101015
\(99\) 5.40581 0.543305
\(100\) −4.93900 −0.493900
\(101\) −13.6528 −1.35850 −0.679252 0.733905i \(-0.737696\pi\)
−0.679252 + 0.733905i \(0.737696\pi\)
\(102\) 4.04892 0.400903
\(103\) 7.00969 0.690685 0.345343 0.938477i \(-0.387763\pi\)
0.345343 + 0.938477i \(0.387763\pi\)
\(104\) 0 0
\(105\) −0.246980 −0.0241027
\(106\) −8.67994 −0.843070
\(107\) 7.89008 0.762763 0.381382 0.924418i \(-0.375448\pi\)
0.381382 + 0.924418i \(0.375448\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 17.6189 1.68759 0.843794 0.536667i \(-0.180317\pi\)
0.843794 + 0.536667i \(0.180317\pi\)
\(110\) 1.33513 0.127299
\(111\) −1.35690 −0.128791
\(112\) 1.00000 0.0944911
\(113\) 14.0586 1.32252 0.661261 0.750156i \(-0.270021\pi\)
0.661261 + 0.750156i \(0.270021\pi\)
\(114\) 3.80194 0.356084
\(115\) −2.30798 −0.215220
\(116\) −3.26875 −0.303496
\(117\) 0 0
\(118\) −0.466812 −0.0429735
\(119\) −4.04892 −0.371164
\(120\) −0.246980 −0.0225461
\(121\) 18.2228 1.65662
\(122\) −7.00000 −0.633750
\(123\) 0.246980 0.0222694
\(124\) −1.41789 −0.127331
\(125\) −2.45473 −0.219558
\(126\) 1.00000 0.0890871
\(127\) −7.25667 −0.643925 −0.321963 0.946752i \(-0.604343\pi\)
−0.321963 + 0.946752i \(0.604343\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.34481 0.470585
\(130\) 0 0
\(131\) −16.0248 −1.40009 −0.700045 0.714099i \(-0.746837\pi\)
−0.700045 + 0.714099i \(0.746837\pi\)
\(132\) −5.40581 −0.470516
\(133\) −3.80194 −0.329670
\(134\) −5.71917 −0.494061
\(135\) −0.246980 −0.0212566
\(136\) −4.04892 −0.347192
\(137\) −7.64310 −0.652994 −0.326497 0.945198i \(-0.605868\pi\)
−0.326497 + 0.945198i \(0.605868\pi\)
\(138\) 9.34481 0.795483
\(139\) 21.6571 1.83693 0.918466 0.395500i \(-0.129429\pi\)
0.918466 + 0.395500i \(0.129429\pi\)
\(140\) 0.246980 0.0208736
\(141\) 4.38404 0.369203
\(142\) 6.98792 0.586413
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −0.807315 −0.0670438
\(146\) −6.93900 −0.574276
\(147\) −1.00000 −0.0824786
\(148\) 1.35690 0.111536
\(149\) 8.69202 0.712078 0.356039 0.934471i \(-0.384127\pi\)
0.356039 + 0.934471i \(0.384127\pi\)
\(150\) 4.93900 0.403268
\(151\) 4.89977 0.398738 0.199369 0.979925i \(-0.436111\pi\)
0.199369 + 0.979925i \(0.436111\pi\)
\(152\) −3.80194 −0.308378
\(153\) −4.04892 −0.327336
\(154\) 5.40581 0.435613
\(155\) −0.350191 −0.0281280
\(156\) 0 0
\(157\) −14.1414 −1.12860 −0.564302 0.825568i \(-0.690855\pi\)
−0.564302 + 0.825568i \(0.690855\pi\)
\(158\) −5.75302 −0.457686
\(159\) 8.67994 0.688364
\(160\) 0.246980 0.0195255
\(161\) −9.34481 −0.736475
\(162\) 1.00000 0.0785674
\(163\) 6.99761 0.548095 0.274047 0.961716i \(-0.411637\pi\)
0.274047 + 0.961716i \(0.411637\pi\)
\(164\) −0.246980 −0.0192859
\(165\) −1.33513 −0.103939
\(166\) −11.8019 −0.916008
\(167\) −2.70841 −0.209583 −0.104792 0.994494i \(-0.533418\pi\)
−0.104792 + 0.994494i \(0.533418\pi\)
\(168\) −1.00000 −0.0771517
\(169\) 0 0
\(170\) −1.00000 −0.0766965
\(171\) −3.80194 −0.290741
\(172\) −5.34481 −0.407538
\(173\) 15.7453 1.19709 0.598545 0.801089i \(-0.295746\pi\)
0.598545 + 0.801089i \(0.295746\pi\)
\(174\) 3.26875 0.247803
\(175\) −4.93900 −0.373353
\(176\) 5.40581 0.407479
\(177\) 0.466812 0.0350877
\(178\) 17.9584 1.34604
\(179\) 19.7439 1.47573 0.737865 0.674948i \(-0.235834\pi\)
0.737865 + 0.674948i \(0.235834\pi\)
\(180\) 0.246980 0.0184088
\(181\) 1.79656 0.133537 0.0667687 0.997768i \(-0.478731\pi\)
0.0667687 + 0.997768i \(0.478731\pi\)
\(182\) 0 0
\(183\) 7.00000 0.517455
\(184\) −9.34481 −0.688909
\(185\) 0.335126 0.0246389
\(186\) 1.41789 0.103965
\(187\) −21.8877 −1.60059
\(188\) −4.38404 −0.319739
\(189\) −1.00000 −0.0727393
\(190\) −0.939001 −0.0681223
\(191\) 0.817003 0.0591163 0.0295581 0.999563i \(-0.490590\pi\)
0.0295581 + 0.999563i \(0.490590\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 20.1323 1.44915 0.724577 0.689194i \(-0.242035\pi\)
0.724577 + 0.689194i \(0.242035\pi\)
\(194\) −13.8509 −0.994433
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −3.47650 −0.247690 −0.123845 0.992302i \(-0.539523\pi\)
−0.123845 + 0.992302i \(0.539523\pi\)
\(198\) 5.40581 0.384174
\(199\) −15.8998 −1.12710 −0.563552 0.826080i \(-0.690566\pi\)
−0.563552 + 0.826080i \(0.690566\pi\)
\(200\) −4.93900 −0.349240
\(201\) 5.71917 0.403399
\(202\) −13.6528 −0.960607
\(203\) −3.26875 −0.229421
\(204\) 4.04892 0.283481
\(205\) −0.0609989 −0.00426035
\(206\) 7.00969 0.488388
\(207\) −9.34481 −0.649509
\(208\) 0 0
\(209\) −20.5526 −1.42165
\(210\) −0.246980 −0.0170432
\(211\) 12.3773 0.852091 0.426046 0.904702i \(-0.359906\pi\)
0.426046 + 0.904702i \(0.359906\pi\)
\(212\) −8.67994 −0.596141
\(213\) −6.98792 −0.478804
\(214\) 7.89008 0.539355
\(215\) −1.32006 −0.0900274
\(216\) −1.00000 −0.0680414
\(217\) −1.41789 −0.0962530
\(218\) 17.6189 1.19331
\(219\) 6.93900 0.468894
\(220\) 1.33513 0.0900141
\(221\) 0 0
\(222\) −1.35690 −0.0910689
\(223\) 11.1444 0.746281 0.373141 0.927775i \(-0.378281\pi\)
0.373141 + 0.927775i \(0.378281\pi\)
\(224\) 1.00000 0.0668153
\(225\) −4.93900 −0.329267
\(226\) 14.0586 0.935165
\(227\) −27.3424 −1.81478 −0.907390 0.420289i \(-0.861929\pi\)
−0.907390 + 0.420289i \(0.861929\pi\)
\(228\) 3.80194 0.251789
\(229\) −6.76510 −0.447051 −0.223525 0.974698i \(-0.571757\pi\)
−0.223525 + 0.974698i \(0.571757\pi\)
\(230\) −2.30798 −0.152184
\(231\) −5.40581 −0.355676
\(232\) −3.26875 −0.214604
\(233\) −16.0204 −1.04953 −0.524767 0.851246i \(-0.675848\pi\)
−0.524767 + 0.851246i \(0.675848\pi\)
\(234\) 0 0
\(235\) −1.08277 −0.0706321
\(236\) −0.466812 −0.0303869
\(237\) 5.75302 0.373699
\(238\) −4.04892 −0.262452
\(239\) 7.38404 0.477634 0.238817 0.971065i \(-0.423240\pi\)
0.238817 + 0.971065i \(0.423240\pi\)
\(240\) −0.246980 −0.0159425
\(241\) 15.4426 0.994748 0.497374 0.867536i \(-0.334298\pi\)
0.497374 + 0.867536i \(0.334298\pi\)
\(242\) 18.2228 1.17141
\(243\) −1.00000 −0.0641500
\(244\) −7.00000 −0.448129
\(245\) 0.246980 0.0157789
\(246\) 0.246980 0.0157468
\(247\) 0 0
\(248\) −1.41789 −0.0900364
\(249\) 11.8019 0.747917
\(250\) −2.45473 −0.155251
\(251\) 9.21313 0.581527 0.290764 0.956795i \(-0.406091\pi\)
0.290764 + 0.956795i \(0.406091\pi\)
\(252\) 1.00000 0.0629941
\(253\) −50.5163 −3.17593
\(254\) −7.25667 −0.455324
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 17.0519 1.06367 0.531834 0.846849i \(-0.321503\pi\)
0.531834 + 0.846849i \(0.321503\pi\)
\(258\) 5.34481 0.332754
\(259\) 1.35690 0.0843134
\(260\) 0 0
\(261\) −3.26875 −0.202331
\(262\) −16.0248 −0.990013
\(263\) 25.3773 1.56483 0.782417 0.622755i \(-0.213987\pi\)
0.782417 + 0.622755i \(0.213987\pi\)
\(264\) −5.40581 −0.332705
\(265\) −2.14377 −0.131691
\(266\) −3.80194 −0.233112
\(267\) −17.9584 −1.09903
\(268\) −5.71917 −0.349354
\(269\) −30.8726 −1.88234 −0.941169 0.337937i \(-0.890271\pi\)
−0.941169 + 0.337937i \(0.890271\pi\)
\(270\) −0.246980 −0.0150307
\(271\) −13.2862 −0.807080 −0.403540 0.914962i \(-0.632220\pi\)
−0.403540 + 0.914962i \(0.632220\pi\)
\(272\) −4.04892 −0.245502
\(273\) 0 0
\(274\) −7.64310 −0.461737
\(275\) −26.6993 −1.61003
\(276\) 9.34481 0.562492
\(277\) 4.97285 0.298790 0.149395 0.988778i \(-0.452267\pi\)
0.149395 + 0.988778i \(0.452267\pi\)
\(278\) 21.6571 1.29891
\(279\) −1.41789 −0.0848871
\(280\) 0.246980 0.0147599
\(281\) −23.0519 −1.37516 −0.687581 0.726108i \(-0.741327\pi\)
−0.687581 + 0.726108i \(0.741327\pi\)
\(282\) 4.38404 0.261066
\(283\) −17.2892 −1.02774 −0.513868 0.857869i \(-0.671788\pi\)
−0.513868 + 0.857869i \(0.671788\pi\)
\(284\) 6.98792 0.414657
\(285\) 0.939001 0.0556216
\(286\) 0 0
\(287\) −0.246980 −0.0145787
\(288\) 1.00000 0.0589256
\(289\) −0.606268 −0.0356628
\(290\) −0.807315 −0.0474071
\(291\) 13.8509 0.811952
\(292\) −6.93900 −0.406074
\(293\) 11.4590 0.669444 0.334722 0.942317i \(-0.391358\pi\)
0.334722 + 0.942317i \(0.391358\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −0.115293 −0.00671262
\(296\) 1.35690 0.0788680
\(297\) −5.40581 −0.313677
\(298\) 8.69202 0.503515
\(299\) 0 0
\(300\) 4.93900 0.285153
\(301\) −5.34481 −0.308070
\(302\) 4.89977 0.281950
\(303\) 13.6528 0.784332
\(304\) −3.80194 −0.218056
\(305\) −1.72886 −0.0989941
\(306\) −4.04892 −0.231461
\(307\) −15.9782 −0.911926 −0.455963 0.889999i \(-0.650705\pi\)
−0.455963 + 0.889999i \(0.650705\pi\)
\(308\) 5.40581 0.308025
\(309\) −7.00969 −0.398767
\(310\) −0.350191 −0.0198895
\(311\) −20.2741 −1.14964 −0.574820 0.818280i \(-0.694928\pi\)
−0.574820 + 0.818280i \(0.694928\pi\)
\(312\) 0 0
\(313\) −18.3937 −1.03968 −0.519838 0.854265i \(-0.674008\pi\)
−0.519838 + 0.854265i \(0.674008\pi\)
\(314\) −14.1414 −0.798044
\(315\) 0.246980 0.0139157
\(316\) −5.75302 −0.323633
\(317\) −6.98121 −0.392104 −0.196052 0.980593i \(-0.562812\pi\)
−0.196052 + 0.980593i \(0.562812\pi\)
\(318\) 8.67994 0.486747
\(319\) −17.6703 −0.989344
\(320\) 0.246980 0.0138066
\(321\) −7.89008 −0.440382
\(322\) −9.34481 −0.520766
\(323\) 15.3937 0.856530
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 6.99761 0.387562
\(327\) −17.6189 −0.974330
\(328\) −0.246980 −0.0136372
\(329\) −4.38404 −0.241700
\(330\) −1.33513 −0.0734962
\(331\) 1.81269 0.0996345 0.0498173 0.998758i \(-0.484136\pi\)
0.0498173 + 0.998758i \(0.484136\pi\)
\(332\) −11.8019 −0.647715
\(333\) 1.35690 0.0743574
\(334\) −2.70841 −0.148198
\(335\) −1.41252 −0.0771741
\(336\) −1.00000 −0.0545545
\(337\) −23.0344 −1.25477 −0.627383 0.778711i \(-0.715874\pi\)
−0.627383 + 0.778711i \(0.715874\pi\)
\(338\) 0 0
\(339\) −14.0586 −0.763559
\(340\) −1.00000 −0.0542326
\(341\) −7.66487 −0.415076
\(342\) −3.80194 −0.205585
\(343\) 1.00000 0.0539949
\(344\) −5.34481 −0.288173
\(345\) 2.30798 0.124257
\(346\) 15.7453 0.846470
\(347\) −28.2868 −1.51851 −0.759257 0.650790i \(-0.774438\pi\)
−0.759257 + 0.650790i \(0.774438\pi\)
\(348\) 3.26875 0.175223
\(349\) 5.79523 0.310212 0.155106 0.987898i \(-0.450428\pi\)
0.155106 + 0.987898i \(0.450428\pi\)
\(350\) −4.93900 −0.264001
\(351\) 0 0
\(352\) 5.40581 0.288131
\(353\) 11.5845 0.616581 0.308290 0.951292i \(-0.400243\pi\)
0.308290 + 0.951292i \(0.400243\pi\)
\(354\) 0.466812 0.0248108
\(355\) 1.72587 0.0915998
\(356\) 17.9584 0.951792
\(357\) 4.04892 0.214291
\(358\) 19.7439 1.04350
\(359\) −6.04461 −0.319022 −0.159511 0.987196i \(-0.550992\pi\)
−0.159511 + 0.987196i \(0.550992\pi\)
\(360\) 0.246980 0.0130170
\(361\) −4.54527 −0.239225
\(362\) 1.79656 0.0944251
\(363\) −18.2228 −0.956450
\(364\) 0 0
\(365\) −1.71379 −0.0897040
\(366\) 7.00000 0.365896
\(367\) 29.5555 1.54279 0.771394 0.636358i \(-0.219560\pi\)
0.771394 + 0.636358i \(0.219560\pi\)
\(368\) −9.34481 −0.487132
\(369\) −0.246980 −0.0128572
\(370\) 0.335126 0.0174224
\(371\) −8.67994 −0.450640
\(372\) 1.41789 0.0735144
\(373\) 6.38942 0.330832 0.165416 0.986224i \(-0.447103\pi\)
0.165416 + 0.986224i \(0.447103\pi\)
\(374\) −21.8877 −1.13179
\(375\) 2.45473 0.126762
\(376\) −4.38404 −0.226090
\(377\) 0 0
\(378\) −1.00000 −0.0514344
\(379\) 30.6612 1.57496 0.787479 0.616342i \(-0.211386\pi\)
0.787479 + 0.616342i \(0.211386\pi\)
\(380\) −0.939001 −0.0481697
\(381\) 7.25667 0.371770
\(382\) 0.817003 0.0418015
\(383\) −11.5453 −0.589936 −0.294968 0.955507i \(-0.595309\pi\)
−0.294968 + 0.955507i \(0.595309\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 1.33513 0.0680443
\(386\) 20.1323 1.02471
\(387\) −5.34481 −0.271692
\(388\) −13.8509 −0.703171
\(389\) 16.1903 0.820880 0.410440 0.911888i \(-0.365375\pi\)
0.410440 + 0.911888i \(0.365375\pi\)
\(390\) 0 0
\(391\) 37.8364 1.91347
\(392\) 1.00000 0.0505076
\(393\) 16.0248 0.808342
\(394\) −3.47650 −0.175144
\(395\) −1.42088 −0.0714922
\(396\) 5.40581 0.271652
\(397\) −28.0858 −1.40958 −0.704792 0.709414i \(-0.748960\pi\)
−0.704792 + 0.709414i \(0.748960\pi\)
\(398\) −15.8998 −0.796984
\(399\) 3.80194 0.190335
\(400\) −4.93900 −0.246950
\(401\) 14.3230 0.715259 0.357629 0.933864i \(-0.383585\pi\)
0.357629 + 0.933864i \(0.383585\pi\)
\(402\) 5.71917 0.285246
\(403\) 0 0
\(404\) −13.6528 −0.679252
\(405\) 0.246980 0.0122725
\(406\) −3.26875 −0.162225
\(407\) 7.33513 0.363589
\(408\) 4.04892 0.200451
\(409\) −33.4916 −1.65605 −0.828026 0.560690i \(-0.810536\pi\)
−0.828026 + 0.560690i \(0.810536\pi\)
\(410\) −0.0609989 −0.00301252
\(411\) 7.64310 0.377007
\(412\) 7.00969 0.345343
\(413\) −0.466812 −0.0229703
\(414\) −9.34481 −0.459273
\(415\) −2.91484 −0.143084
\(416\) 0 0
\(417\) −21.6571 −1.06055
\(418\) −20.5526 −1.00526
\(419\) −28.1159 −1.37355 −0.686775 0.726870i \(-0.740974\pi\)
−0.686775 + 0.726870i \(0.740974\pi\)
\(420\) −0.246980 −0.0120514
\(421\) −24.4131 −1.18982 −0.594911 0.803792i \(-0.702813\pi\)
−0.594911 + 0.803792i \(0.702813\pi\)
\(422\) 12.3773 0.602519
\(423\) −4.38404 −0.213159
\(424\) −8.67994 −0.421535
\(425\) 19.9976 0.970026
\(426\) −6.98792 −0.338566
\(427\) −7.00000 −0.338754
\(428\) 7.89008 0.381382
\(429\) 0 0
\(430\) −1.32006 −0.0636590
\(431\) −27.4983 −1.32455 −0.662273 0.749263i \(-0.730408\pi\)
−0.662273 + 0.749263i \(0.730408\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −21.5472 −1.03549 −0.517746 0.855534i \(-0.673229\pi\)
−0.517746 + 0.855534i \(0.673229\pi\)
\(434\) −1.41789 −0.0680611
\(435\) 0.807315 0.0387078
\(436\) 17.6189 0.843794
\(437\) 35.5284 1.69955
\(438\) 6.93900 0.331558
\(439\) −8.41849 −0.401792 −0.200896 0.979613i \(-0.564385\pi\)
−0.200896 + 0.979613i \(0.564385\pi\)
\(440\) 1.33513 0.0636496
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 20.7966 0.988074 0.494037 0.869441i \(-0.335521\pi\)
0.494037 + 0.869441i \(0.335521\pi\)
\(444\) −1.35690 −0.0643954
\(445\) 4.43535 0.210256
\(446\) 11.1444 0.527701
\(447\) −8.69202 −0.411119
\(448\) 1.00000 0.0472456
\(449\) 24.3370 1.14854 0.574268 0.818667i \(-0.305287\pi\)
0.574268 + 0.818667i \(0.305287\pi\)
\(450\) −4.93900 −0.232827
\(451\) −1.33513 −0.0628686
\(452\) 14.0586 0.661261
\(453\) −4.89977 −0.230211
\(454\) −27.3424 −1.28324
\(455\) 0 0
\(456\) 3.80194 0.178042
\(457\) −23.8194 −1.11422 −0.557112 0.830437i \(-0.688091\pi\)
−0.557112 + 0.830437i \(0.688091\pi\)
\(458\) −6.76510 −0.316112
\(459\) 4.04892 0.188987
\(460\) −2.30798 −0.107610
\(461\) 32.7278 1.52429 0.762143 0.647409i \(-0.224147\pi\)
0.762143 + 0.647409i \(0.224147\pi\)
\(462\) −5.40581 −0.251501
\(463\) −4.55065 −0.211486 −0.105743 0.994393i \(-0.533722\pi\)
−0.105743 + 0.994393i \(0.533722\pi\)
\(464\) −3.26875 −0.151748
\(465\) 0.350191 0.0162397
\(466\) −16.0204 −0.742133
\(467\) 8.67994 0.401660 0.200830 0.979626i \(-0.435636\pi\)
0.200830 + 0.979626i \(0.435636\pi\)
\(468\) 0 0
\(469\) −5.71917 −0.264087
\(470\) −1.08277 −0.0499444
\(471\) 14.1414 0.651600
\(472\) −0.466812 −0.0214868
\(473\) −28.8931 −1.32850
\(474\) 5.75302 0.264245
\(475\) 18.7778 0.861583
\(476\) −4.04892 −0.185582
\(477\) −8.67994 −0.397427
\(478\) 7.38404 0.337738
\(479\) 32.3532 1.47825 0.739127 0.673566i \(-0.235238\pi\)
0.739127 + 0.673566i \(0.235238\pi\)
\(480\) −0.246980 −0.0112730
\(481\) 0 0
\(482\) 15.4426 0.703393
\(483\) 9.34481 0.425204
\(484\) 18.2228 0.828310
\(485\) −3.42088 −0.155334
\(486\) −1.00000 −0.0453609
\(487\) −39.9734 −1.81137 −0.905685 0.423952i \(-0.860643\pi\)
−0.905685 + 0.423952i \(0.860643\pi\)
\(488\) −7.00000 −0.316875
\(489\) −6.99761 −0.316443
\(490\) 0.246980 0.0111574
\(491\) 10.3907 0.468928 0.234464 0.972125i \(-0.424667\pi\)
0.234464 + 0.972125i \(0.424667\pi\)
\(492\) 0.246980 0.0111347
\(493\) 13.2349 0.596070
\(494\) 0 0
\(495\) 1.33513 0.0600094
\(496\) −1.41789 −0.0636654
\(497\) 6.98792 0.313451
\(498\) 11.8019 0.528857
\(499\) −20.9148 −0.936277 −0.468138 0.883655i \(-0.655075\pi\)
−0.468138 + 0.883655i \(0.655075\pi\)
\(500\) −2.45473 −0.109779
\(501\) 2.70841 0.121003
\(502\) 9.21313 0.411202
\(503\) 16.5700 0.738821 0.369410 0.929266i \(-0.379560\pi\)
0.369410 + 0.929266i \(0.379560\pi\)
\(504\) 1.00000 0.0445435
\(505\) −3.37196 −0.150050
\(506\) −50.5163 −2.24572
\(507\) 0 0
\(508\) −7.25667 −0.321963
\(509\) −14.0194 −0.621398 −0.310699 0.950508i \(-0.600563\pi\)
−0.310699 + 0.950508i \(0.600563\pi\)
\(510\) 1.00000 0.0442807
\(511\) −6.93900 −0.306963
\(512\) 1.00000 0.0441942
\(513\) 3.80194 0.167860
\(514\) 17.0519 0.752127
\(515\) 1.73125 0.0762880
\(516\) 5.34481 0.235292
\(517\) −23.6993 −1.04229
\(518\) 1.35690 0.0596186
\(519\) −15.7453 −0.691140
\(520\) 0 0
\(521\) 6.95407 0.304663 0.152332 0.988329i \(-0.451322\pi\)
0.152332 + 0.988329i \(0.451322\pi\)
\(522\) −3.26875 −0.143069
\(523\) 6.62671 0.289766 0.144883 0.989449i \(-0.453719\pi\)
0.144883 + 0.989449i \(0.453719\pi\)
\(524\) −16.0248 −0.700045
\(525\) 4.93900 0.215556
\(526\) 25.3773 1.10650
\(527\) 5.74094 0.250079
\(528\) −5.40581 −0.235258
\(529\) 64.3256 2.79676
\(530\) −2.14377 −0.0931193
\(531\) −0.466812 −0.0202579
\(532\) −3.80194 −0.164835
\(533\) 0 0
\(534\) −17.9584 −0.777135
\(535\) 1.94869 0.0842492
\(536\) −5.71917 −0.247030
\(537\) −19.7439 −0.852013
\(538\) −30.8726 −1.33101
\(539\) 5.40581 0.232845
\(540\) −0.246980 −0.0106283
\(541\) −44.1021 −1.89610 −0.948050 0.318122i \(-0.896948\pi\)
−0.948050 + 0.318122i \(0.896948\pi\)
\(542\) −13.2862 −0.570692
\(543\) −1.79656 −0.0770978
\(544\) −4.04892 −0.173596
\(545\) 4.35152 0.186399
\(546\) 0 0
\(547\) 19.9530 0.853129 0.426564 0.904457i \(-0.359724\pi\)
0.426564 + 0.904457i \(0.359724\pi\)
\(548\) −7.64310 −0.326497
\(549\) −7.00000 −0.298753
\(550\) −26.6993 −1.13846
\(551\) 12.4276 0.529433
\(552\) 9.34481 0.397742
\(553\) −5.75302 −0.244643
\(554\) 4.97285 0.211276
\(555\) −0.335126 −0.0142253
\(556\) 21.6571 0.918466
\(557\) 36.3193 1.53890 0.769450 0.638708i \(-0.220531\pi\)
0.769450 + 0.638708i \(0.220531\pi\)
\(558\) −1.41789 −0.0600243
\(559\) 0 0
\(560\) 0.246980 0.0104368
\(561\) 21.8877 0.924099
\(562\) −23.0519 −0.972386
\(563\) 27.2814 1.14977 0.574887 0.818233i \(-0.305046\pi\)
0.574887 + 0.818233i \(0.305046\pi\)
\(564\) 4.38404 0.184602
\(565\) 3.47219 0.146076
\(566\) −17.2892 −0.726719
\(567\) 1.00000 0.0419961
\(568\) 6.98792 0.293207
\(569\) 35.6853 1.49601 0.748003 0.663695i \(-0.231013\pi\)
0.748003 + 0.663695i \(0.231013\pi\)
\(570\) 0.939001 0.0393304
\(571\) 10.3864 0.434659 0.217329 0.976098i \(-0.430265\pi\)
0.217329 + 0.976098i \(0.430265\pi\)
\(572\) 0 0
\(573\) −0.817003 −0.0341308
\(574\) −0.246980 −0.0103087
\(575\) 46.1540 1.92476
\(576\) 1.00000 0.0416667
\(577\) 15.7289 0.654801 0.327400 0.944886i \(-0.393827\pi\)
0.327400 + 0.944886i \(0.393827\pi\)
\(578\) −0.606268 −0.0252174
\(579\) −20.1323 −0.836669
\(580\) −0.807315 −0.0335219
\(581\) −11.8019 −0.489627
\(582\) 13.8509 0.574136
\(583\) −46.9221 −1.94332
\(584\) −6.93900 −0.287138
\(585\) 0 0
\(586\) 11.4590 0.473369
\(587\) 2.78448 0.114928 0.0574639 0.998348i \(-0.481699\pi\)
0.0574639 + 0.998348i \(0.481699\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 5.39075 0.222122
\(590\) −0.115293 −0.00474654
\(591\) 3.47650 0.143004
\(592\) 1.35690 0.0557681
\(593\) −3.08815 −0.126815 −0.0634075 0.997988i \(-0.520197\pi\)
−0.0634075 + 0.997988i \(0.520197\pi\)
\(594\) −5.40581 −0.221803
\(595\) −1.00000 −0.0409960
\(596\) 8.69202 0.356039
\(597\) 15.8998 0.650734
\(598\) 0 0
\(599\) 12.0054 0.490526 0.245263 0.969457i \(-0.421126\pi\)
0.245263 + 0.969457i \(0.421126\pi\)
\(600\) 4.93900 0.201634
\(601\) 39.4959 1.61107 0.805535 0.592548i \(-0.201878\pi\)
0.805535 + 0.592548i \(0.201878\pi\)
\(602\) −5.34481 −0.217838
\(603\) −5.71917 −0.232903
\(604\) 4.89977 0.199369
\(605\) 4.50066 0.182978
\(606\) 13.6528 0.554607
\(607\) −3.92021 −0.159117 −0.0795583 0.996830i \(-0.525351\pi\)
−0.0795583 + 0.996830i \(0.525351\pi\)
\(608\) −3.80194 −0.154189
\(609\) 3.26875 0.132456
\(610\) −1.72886 −0.0699994
\(611\) 0 0
\(612\) −4.04892 −0.163668
\(613\) −21.9191 −0.885306 −0.442653 0.896693i \(-0.645963\pi\)
−0.442653 + 0.896693i \(0.645963\pi\)
\(614\) −15.9782 −0.644829
\(615\) 0.0609989 0.00245971
\(616\) 5.40581 0.217806
\(617\) −6.80731 −0.274052 −0.137026 0.990567i \(-0.543754\pi\)
−0.137026 + 0.990567i \(0.543754\pi\)
\(618\) −7.00969 −0.281971
\(619\) 9.15777 0.368082 0.184041 0.982919i \(-0.441082\pi\)
0.184041 + 0.982919i \(0.441082\pi\)
\(620\) −0.350191 −0.0140640
\(621\) 9.34481 0.374994
\(622\) −20.2741 −0.812918
\(623\) 17.9584 0.719487
\(624\) 0 0
\(625\) 24.0887 0.963549
\(626\) −18.3937 −0.735161
\(627\) 20.5526 0.820790
\(628\) −14.1414 −0.564302
\(629\) −5.49396 −0.219058
\(630\) 0.246980 0.00983990
\(631\) 8.20237 0.326531 0.163266 0.986582i \(-0.447797\pi\)
0.163266 + 0.986582i \(0.447797\pi\)
\(632\) −5.75302 −0.228843
\(633\) −12.3773 −0.491955
\(634\) −6.98121 −0.277259
\(635\) −1.79225 −0.0711232
\(636\) 8.67994 0.344182
\(637\) 0 0
\(638\) −17.6703 −0.699572
\(639\) 6.98792 0.276438
\(640\) 0.246980 0.00976273
\(641\) −11.8127 −0.466573 −0.233287 0.972408i \(-0.574948\pi\)
−0.233287 + 0.972408i \(0.574948\pi\)
\(642\) −7.89008 −0.311397
\(643\) 13.2868 0.523980 0.261990 0.965071i \(-0.415621\pi\)
0.261990 + 0.965071i \(0.415621\pi\)
\(644\) −9.34481 −0.368237
\(645\) 1.32006 0.0519773
\(646\) 15.3937 0.605658
\(647\) 31.5840 1.24170 0.620848 0.783931i \(-0.286788\pi\)
0.620848 + 0.783931i \(0.286788\pi\)
\(648\) 1.00000 0.0392837
\(649\) −2.52350 −0.0990560
\(650\) 0 0
\(651\) 1.41789 0.0555717
\(652\) 6.99761 0.274047
\(653\) 8.85756 0.346623 0.173312 0.984867i \(-0.444553\pi\)
0.173312 + 0.984867i \(0.444553\pi\)
\(654\) −17.6189 −0.688955
\(655\) −3.95779 −0.154644
\(656\) −0.246980 −0.00964293
\(657\) −6.93900 −0.270716
\(658\) −4.38404 −0.170908
\(659\) −11.6233 −0.452778 −0.226389 0.974037i \(-0.572692\pi\)
−0.226389 + 0.974037i \(0.572692\pi\)
\(660\) −1.33513 −0.0519697
\(661\) −11.7651 −0.457609 −0.228805 0.973472i \(-0.573482\pi\)
−0.228805 + 0.973472i \(0.573482\pi\)
\(662\) 1.81269 0.0704523
\(663\) 0 0
\(664\) −11.8019 −0.458004
\(665\) −0.939001 −0.0364129
\(666\) 1.35690 0.0525786
\(667\) 30.5459 1.18274
\(668\) −2.70841 −0.104792
\(669\) −11.1444 −0.430866
\(670\) −1.41252 −0.0545703
\(671\) −37.8407 −1.46082
\(672\) −1.00000 −0.0385758
\(673\) 28.9390 1.11552 0.557758 0.830003i \(-0.311662\pi\)
0.557758 + 0.830003i \(0.311662\pi\)
\(674\) −23.0344 −0.887254
\(675\) 4.93900 0.190102
\(676\) 0 0
\(677\) −27.0538 −1.03976 −0.519881 0.854238i \(-0.674024\pi\)
−0.519881 + 0.854238i \(0.674024\pi\)
\(678\) −14.0586 −0.539918
\(679\) −13.8509 −0.531547
\(680\) −1.00000 −0.0383482
\(681\) 27.3424 1.04776
\(682\) −7.66487 −0.293503
\(683\) 24.4849 0.936887 0.468444 0.883493i \(-0.344815\pi\)
0.468444 + 0.883493i \(0.344815\pi\)
\(684\) −3.80194 −0.145371
\(685\) −1.88769 −0.0721250
\(686\) 1.00000 0.0381802
\(687\) 6.76510 0.258105
\(688\) −5.34481 −0.203769
\(689\) 0 0
\(690\) 2.30798 0.0878632
\(691\) −29.4752 −1.12129 −0.560644 0.828057i \(-0.689446\pi\)
−0.560644 + 0.828057i \(0.689446\pi\)
\(692\) 15.7453 0.598545
\(693\) 5.40581 0.205350
\(694\) −28.2868 −1.07375
\(695\) 5.34886 0.202894
\(696\) 3.26875 0.123902
\(697\) 1.00000 0.0378777
\(698\) 5.79523 0.219353
\(699\) 16.0204 0.605949
\(700\) −4.93900 −0.186677
\(701\) −22.3467 −0.844024 −0.422012 0.906590i \(-0.638676\pi\)
−0.422012 + 0.906590i \(0.638676\pi\)
\(702\) 0 0
\(703\) −5.15883 −0.194569
\(704\) 5.40581 0.203739
\(705\) 1.08277 0.0407794
\(706\) 11.5845 0.435988
\(707\) −13.6528 −0.513466
\(708\) 0.466812 0.0175439
\(709\) 36.6711 1.37721 0.688606 0.725136i \(-0.258223\pi\)
0.688606 + 0.725136i \(0.258223\pi\)
\(710\) 1.72587 0.0647709
\(711\) −5.75302 −0.215755
\(712\) 17.9584 0.673019
\(713\) 13.2500 0.496215
\(714\) 4.04892 0.151527
\(715\) 0 0
\(716\) 19.7439 0.737865
\(717\) −7.38404 −0.275762
\(718\) −6.04461 −0.225583
\(719\) 21.5080 0.802112 0.401056 0.916054i \(-0.368643\pi\)
0.401056 + 0.916054i \(0.368643\pi\)
\(720\) 0.246980 0.00920439
\(721\) 7.00969 0.261054
\(722\) −4.54527 −0.169157
\(723\) −15.4426 −0.574318
\(724\) 1.79656 0.0667687
\(725\) 16.1444 0.599586
\(726\) −18.2228 −0.676312
\(727\) 51.3260 1.90358 0.951789 0.306755i \(-0.0992432\pi\)
0.951789 + 0.306755i \(0.0992432\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.71379 −0.0634303
\(731\) 21.6407 0.800411
\(732\) 7.00000 0.258727
\(733\) −41.0726 −1.51705 −0.758526 0.651643i \(-0.774080\pi\)
−0.758526 + 0.651643i \(0.774080\pi\)
\(734\) 29.5555 1.09092
\(735\) −0.246980 −0.00910998
\(736\) −9.34481 −0.344454
\(737\) −30.9168 −1.13883
\(738\) −0.246980 −0.00909144
\(739\) 1.79656 0.0660876 0.0330438 0.999454i \(-0.489480\pi\)
0.0330438 + 0.999454i \(0.489480\pi\)
\(740\) 0.335126 0.0123195
\(741\) 0 0
\(742\) −8.67994 −0.318651
\(743\) 40.1444 1.47275 0.736377 0.676572i \(-0.236535\pi\)
0.736377 + 0.676572i \(0.236535\pi\)
\(744\) 1.41789 0.0519825
\(745\) 2.14675 0.0786509
\(746\) 6.38942 0.233933
\(747\) −11.8019 −0.431810
\(748\) −21.8877 −0.800293
\(749\) 7.89008 0.288297
\(750\) 2.45473 0.0896341
\(751\) −23.7948 −0.868283 −0.434142 0.900845i \(-0.642948\pi\)
−0.434142 + 0.900845i \(0.642948\pi\)
\(752\) −4.38404 −0.159870
\(753\) −9.21313 −0.335745
\(754\) 0 0
\(755\) 1.21014 0.0440416
\(756\) −1.00000 −0.0363696
\(757\) −19.0140 −0.691076 −0.345538 0.938405i \(-0.612303\pi\)
−0.345538 + 0.938405i \(0.612303\pi\)
\(758\) 30.6612 1.11366
\(759\) 50.5163 1.83363
\(760\) −0.939001 −0.0340611
\(761\) −0.576728 −0.0209064 −0.0104532 0.999945i \(-0.503327\pi\)
−0.0104532 + 0.999945i \(0.503327\pi\)
\(762\) 7.25667 0.262881
\(763\) 17.6189 0.637848
\(764\) 0.817003 0.0295581
\(765\) −1.00000 −0.0361551
\(766\) −11.5453 −0.417148
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −19.1696 −0.691273 −0.345636 0.938368i \(-0.612337\pi\)
−0.345636 + 0.938368i \(0.612337\pi\)
\(770\) 1.33513 0.0481146
\(771\) −17.0519 −0.614109
\(772\) 20.1323 0.724577
\(773\) 26.5157 0.953705 0.476852 0.878983i \(-0.341778\pi\)
0.476852 + 0.878983i \(0.341778\pi\)
\(774\) −5.34481 −0.192115
\(775\) 7.00298 0.251555
\(776\) −13.8509 −0.497217
\(777\) −1.35690 −0.0486784
\(778\) 16.1903 0.580450
\(779\) 0.939001 0.0336432
\(780\) 0 0
\(781\) 37.7754 1.35171
\(782\) 37.8364 1.35303
\(783\) 3.26875 0.116816
\(784\) 1.00000 0.0357143
\(785\) −3.49263 −0.124657
\(786\) 16.0248 0.571584
\(787\) 1.25236 0.0446417 0.0223208 0.999751i \(-0.492894\pi\)
0.0223208 + 0.999751i \(0.492894\pi\)
\(788\) −3.47650 −0.123845
\(789\) −25.3773 −0.903457
\(790\) −1.42088 −0.0505526
\(791\) 14.0586 0.499866
\(792\) 5.40581 0.192087
\(793\) 0 0
\(794\) −28.0858 −0.996726
\(795\) 2.14377 0.0760316
\(796\) −15.8998 −0.563552
\(797\) 21.3489 0.756216 0.378108 0.925762i \(-0.376575\pi\)
0.378108 + 0.925762i \(0.376575\pi\)
\(798\) 3.80194 0.134587
\(799\) 17.7506 0.627972
\(800\) −4.93900 −0.174620
\(801\) 17.9584 0.634528
\(802\) 14.3230 0.505764
\(803\) −37.5109 −1.32373
\(804\) 5.71917 0.201700
\(805\) −2.30798 −0.0813456
\(806\) 0 0
\(807\) 30.8726 1.08677
\(808\) −13.6528 −0.480304
\(809\) −7.30990 −0.257002 −0.128501 0.991709i \(-0.541017\pi\)
−0.128501 + 0.991709i \(0.541017\pi\)
\(810\) 0.246980 0.00867798
\(811\) 29.4849 1.03535 0.517677 0.855576i \(-0.326797\pi\)
0.517677 + 0.855576i \(0.326797\pi\)
\(812\) −3.26875 −0.114711
\(813\) 13.2862 0.465968
\(814\) 7.33513 0.257096
\(815\) 1.72827 0.0605385
\(816\) 4.04892 0.141740
\(817\) 20.3207 0.710930
\(818\) −33.4916 −1.17101
\(819\) 0 0
\(820\) −0.0609989 −0.00213017
\(821\) −27.6015 −0.963298 −0.481649 0.876364i \(-0.659962\pi\)
−0.481649 + 0.876364i \(0.659962\pi\)
\(822\) 7.64310 0.266584
\(823\) 28.3201 0.987175 0.493588 0.869696i \(-0.335685\pi\)
0.493588 + 0.869696i \(0.335685\pi\)
\(824\) 7.00969 0.244194
\(825\) 26.6993 0.929551
\(826\) −0.466812 −0.0162425
\(827\) −13.9987 −0.486782 −0.243391 0.969928i \(-0.578260\pi\)
−0.243391 + 0.969928i \(0.578260\pi\)
\(828\) −9.34481 −0.324755
\(829\) −52.2717 −1.81547 −0.907736 0.419541i \(-0.862191\pi\)
−0.907736 + 0.419541i \(0.862191\pi\)
\(830\) −2.91484 −0.101176
\(831\) −4.97285 −0.172506
\(832\) 0 0
\(833\) −4.04892 −0.140287
\(834\) −21.6571 −0.749924
\(835\) −0.668923 −0.0231490
\(836\) −20.5526 −0.710825
\(837\) 1.41789 0.0490096
\(838\) −28.1159 −0.971247
\(839\) 4.94810 0.170827 0.0854137 0.996346i \(-0.472779\pi\)
0.0854137 + 0.996346i \(0.472779\pi\)
\(840\) −0.246980 −0.00852161
\(841\) −18.3153 −0.631561
\(842\) −24.4131 −0.841331
\(843\) 23.0519 0.793950
\(844\) 12.3773 0.426046
\(845\) 0 0
\(846\) −4.38404 −0.150727
\(847\) 18.2228 0.626143
\(848\) −8.67994 −0.298070
\(849\) 17.2892 0.593364
\(850\) 19.9976 0.685912
\(851\) −12.6799 −0.434663
\(852\) −6.98792 −0.239402
\(853\) −11.4330 −0.391457 −0.195729 0.980658i \(-0.562707\pi\)
−0.195729 + 0.980658i \(0.562707\pi\)
\(854\) −7.00000 −0.239535
\(855\) −0.939001 −0.0321132
\(856\) 7.89008 0.269678
\(857\) −18.7366 −0.640031 −0.320015 0.947412i \(-0.603688\pi\)
−0.320015 + 0.947412i \(0.603688\pi\)
\(858\) 0 0
\(859\) 46.9172 1.60080 0.800398 0.599469i \(-0.204622\pi\)
0.800398 + 0.599469i \(0.204622\pi\)
\(860\) −1.32006 −0.0450137
\(861\) 0.246980 0.00841704
\(862\) −27.4983 −0.936595
\(863\) −4.08682 −0.139117 −0.0695585 0.997578i \(-0.522159\pi\)
−0.0695585 + 0.997578i \(0.522159\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 3.88876 0.132222
\(866\) −21.5472 −0.732203
\(867\) 0.606268 0.0205900
\(868\) −1.41789 −0.0481265
\(869\) −31.0998 −1.05499
\(870\) 0.807315 0.0273705
\(871\) 0 0
\(872\) 17.6189 0.596653
\(873\) −13.8509 −0.468780
\(874\) 35.5284 1.20177
\(875\) −2.45473 −0.0829850
\(876\) 6.93900 0.234447
\(877\) −15.3123 −0.517059 −0.258530 0.966003i \(-0.583238\pi\)
−0.258530 + 0.966003i \(0.583238\pi\)
\(878\) −8.41849 −0.284110
\(879\) −11.4590 −0.386504
\(880\) 1.33513 0.0450071
\(881\) 25.9965 0.875846 0.437923 0.899013i \(-0.355714\pi\)
0.437923 + 0.899013i \(0.355714\pi\)
\(882\) 1.00000 0.0336718
\(883\) −4.59478 −0.154627 −0.0773133 0.997007i \(-0.524634\pi\)
−0.0773133 + 0.997007i \(0.524634\pi\)
\(884\) 0 0
\(885\) 0.115293 0.00387553
\(886\) 20.7966 0.698674
\(887\) −33.2403 −1.11610 −0.558050 0.829808i \(-0.688450\pi\)
−0.558050 + 0.829808i \(0.688450\pi\)
\(888\) −1.35690 −0.0455344
\(889\) −7.25667 −0.243381
\(890\) 4.43535 0.148673
\(891\) 5.40581 0.181102
\(892\) 11.1444 0.373141
\(893\) 16.6679 0.557769
\(894\) −8.69202 −0.290705
\(895\) 4.87635 0.162998
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 24.3370 0.812138
\(899\) 4.63474 0.154577
\(900\) −4.93900 −0.164633
\(901\) 35.1444 1.17083
\(902\) −1.33513 −0.0444548
\(903\) 5.34481 0.177864
\(904\) 14.0586 0.467582
\(905\) 0.443714 0.0147495
\(906\) −4.89977 −0.162784
\(907\) −43.2398 −1.43575 −0.717877 0.696170i \(-0.754886\pi\)
−0.717877 + 0.696170i \(0.754886\pi\)
\(908\) −27.3424 −0.907390
\(909\) −13.6528 −0.452835
\(910\) 0 0
\(911\) 1.34588 0.0445910 0.0222955 0.999751i \(-0.492903\pi\)
0.0222955 + 0.999751i \(0.492903\pi\)
\(912\) 3.80194 0.125895
\(913\) −63.7991 −2.11144
\(914\) −23.8194 −0.787876
\(915\) 1.72886 0.0571543
\(916\) −6.76510 −0.223525
\(917\) −16.0248 −0.529184
\(918\) 4.04892 0.133634
\(919\) 0.336191 0.0110899 0.00554495 0.999985i \(-0.498235\pi\)
0.00554495 + 0.999985i \(0.498235\pi\)
\(920\) −2.30798 −0.0760918
\(921\) 15.9782 0.526501
\(922\) 32.7278 1.07783
\(923\) 0 0
\(924\) −5.40581 −0.177838
\(925\) −6.70171 −0.220351
\(926\) −4.55065 −0.149544
\(927\) 7.00969 0.230228
\(928\) −3.26875 −0.107302
\(929\) 0.103211 0.00338626 0.00169313 0.999999i \(-0.499461\pi\)
0.00169313 + 0.999999i \(0.499461\pi\)
\(930\) 0.350191 0.0114832
\(931\) −3.80194 −0.124603
\(932\) −16.0204 −0.524767
\(933\) 20.2741 0.663745
\(934\) 8.67994 0.284016
\(935\) −5.40581 −0.176789
\(936\) 0 0
\(937\) −0.309043 −0.0100960 −0.00504801 0.999987i \(-0.501607\pi\)
−0.00504801 + 0.999987i \(0.501607\pi\)
\(938\) −5.71917 −0.186737
\(939\) 18.3937 0.600257
\(940\) −1.08277 −0.0353160
\(941\) −58.7900 −1.91650 −0.958249 0.285934i \(-0.907696\pi\)
−0.958249 + 0.285934i \(0.907696\pi\)
\(942\) 14.1414 0.460751
\(943\) 2.30798 0.0751581
\(944\) −0.466812 −0.0151934
\(945\) −0.246980 −0.00803425
\(946\) −28.8931 −0.939395
\(947\) −31.4392 −1.02164 −0.510818 0.859689i \(-0.670657\pi\)
−0.510818 + 0.859689i \(0.670657\pi\)
\(948\) 5.75302 0.186849
\(949\) 0 0
\(950\) 18.7778 0.609231
\(951\) 6.98121 0.226381
\(952\) −4.04892 −0.131226
\(953\) −41.5284 −1.34524 −0.672618 0.739989i \(-0.734830\pi\)
−0.672618 + 0.739989i \(0.734830\pi\)
\(954\) −8.67994 −0.281023
\(955\) 0.201783 0.00652955
\(956\) 7.38404 0.238817
\(957\) 17.6703 0.571198
\(958\) 32.3532 1.04528
\(959\) −7.64310 −0.246809
\(960\) −0.246980 −0.00797123
\(961\) −28.9896 −0.935148
\(962\) 0 0
\(963\) 7.89008 0.254254
\(964\) 15.4426 0.497374
\(965\) 4.97226 0.160063
\(966\) 9.34481 0.300664
\(967\) 37.6297 1.21009 0.605045 0.796192i \(-0.293155\pi\)
0.605045 + 0.796192i \(0.293155\pi\)
\(968\) 18.2228 0.585704
\(969\) −15.3937 −0.494518
\(970\) −3.42088 −0.109838
\(971\) 14.9946 0.481200 0.240600 0.970624i \(-0.422656\pi\)
0.240600 + 0.970624i \(0.422656\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 21.6571 0.694295
\(974\) −39.9734 −1.28083
\(975\) 0 0
\(976\) −7.00000 −0.224065
\(977\) 47.8152 1.52974 0.764872 0.644182i \(-0.222802\pi\)
0.764872 + 0.644182i \(0.222802\pi\)
\(978\) −6.99761 −0.223759
\(979\) 97.0796 3.10268
\(980\) 0.246980 0.00788947
\(981\) 17.6189 0.562529
\(982\) 10.3907 0.331582
\(983\) 34.2790 1.09333 0.546666 0.837351i \(-0.315897\pi\)
0.546666 + 0.837351i \(0.315897\pi\)
\(984\) 0.246980 0.00787342
\(985\) −0.858625 −0.0273581
\(986\) 13.2349 0.421485
\(987\) 4.38404 0.139546
\(988\) 0 0
\(989\) 49.9463 1.58820
\(990\) 1.33513 0.0424331
\(991\) −61.3889 −1.95008 −0.975042 0.222020i \(-0.928735\pi\)
−0.975042 + 0.222020i \(0.928735\pi\)
\(992\) −1.41789 −0.0450182
\(993\) −1.81269 −0.0575240
\(994\) 6.98792 0.221643
\(995\) −3.92692 −0.124492
\(996\) 11.8019 0.373959
\(997\) −29.1027 −0.921693 −0.460846 0.887480i \(-0.652454\pi\)
−0.460846 + 0.887480i \(0.652454\pi\)
\(998\) −20.9148 −0.662048
\(999\) −1.35690 −0.0429303
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.ch.1.3 yes 3
13.12 even 2 7098.2.a.ce.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.ce.1.1 3 13.12 even 2
7098.2.a.ch.1.3 yes 3 1.1 even 1 trivial