Properties

Label 7098.2.a.ci.1.1
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.04892 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.04892 q^{10} +2.13706 q^{11} -1.00000 q^{12} -1.00000 q^{14} +3.04892 q^{15} +1.00000 q^{16} -1.40581 q^{17} +1.00000 q^{18} +2.13706 q^{19} -3.04892 q^{20} +1.00000 q^{21} +2.13706 q^{22} -2.26875 q^{23} -1.00000 q^{24} +4.29590 q^{25} -1.00000 q^{27} -1.00000 q^{28} -2.58211 q^{29} +3.04892 q^{30} -6.34481 q^{31} +1.00000 q^{32} -2.13706 q^{33} -1.40581 q^{34} +3.04892 q^{35} +1.00000 q^{36} +10.6528 q^{37} +2.13706 q^{38} -3.04892 q^{40} -4.43296 q^{41} +1.00000 q^{42} -9.55496 q^{43} +2.13706 q^{44} -3.04892 q^{45} -2.26875 q^{46} -3.98792 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.29590 q^{50} +1.40581 q^{51} +6.46681 q^{53} -1.00000 q^{54} -6.51573 q^{55} -1.00000 q^{56} -2.13706 q^{57} -2.58211 q^{58} -3.44504 q^{59} +3.04892 q^{60} +9.98792 q^{61} -6.34481 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.13706 q^{66} +11.3937 q^{67} -1.40581 q^{68} +2.26875 q^{69} +3.04892 q^{70} +4.21983 q^{71} +1.00000 q^{72} +5.84548 q^{73} +10.6528 q^{74} -4.29590 q^{75} +2.13706 q^{76} -2.13706 q^{77} -10.7071 q^{79} -3.04892 q^{80} +1.00000 q^{81} -4.43296 q^{82} +8.94869 q^{83} +1.00000 q^{84} +4.28621 q^{85} -9.55496 q^{86} +2.58211 q^{87} +2.13706 q^{88} -3.73556 q^{89} -3.04892 q^{90} -2.26875 q^{92} +6.34481 q^{93} -3.98792 q^{94} -6.51573 q^{95} -1.00000 q^{96} -5.10321 q^{97} +1.00000 q^{98} +2.13706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + q^{11} - 3q^{12} - 3q^{14} + 3q^{16} + 9q^{17} + 3q^{18} + q^{19} + 3q^{21} + q^{22} + q^{23} - 3q^{24} - q^{25} - 3q^{27} - 3q^{28} - 2q^{29} + 4q^{31} + 3q^{32} - q^{33} + 9q^{34} + 3q^{36} + 14q^{37} + q^{38} + 6q^{41} + 3q^{42} - 29q^{43} + q^{44} + q^{46} + 7q^{47} - 3q^{48} + 3q^{49} - q^{50} - 9q^{51} + 16q^{53} - 3q^{54} - 7q^{55} - 3q^{56} - q^{57} - 2q^{58} - 10q^{59} + 11q^{61} + 4q^{62} - 3q^{63} + 3q^{64} - q^{66} + 2q^{67} + 9q^{68} - q^{69} + 14q^{71} + 3q^{72} + 7q^{73} + 14q^{74} + q^{75} + q^{76} - q^{77} - 2q^{79} + 3q^{81} + 6q^{82} - 5q^{83} + 3q^{84} + 21q^{85} - 29q^{86} + 2q^{87} + q^{88} + q^{92} - 4q^{93} + 7q^{94} - 7q^{95} - 3q^{96} + 6q^{97} + 3q^{98} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −3.04892 −1.36352 −0.681759 0.731577i \(-0.738785\pi\)
−0.681759 + 0.731577i \(0.738785\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −3.04892 −0.964152
\(11\) 2.13706 0.644349 0.322174 0.946680i \(-0.395586\pi\)
0.322174 + 0.946680i \(0.395586\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 3.04892 0.787227
\(16\) 1.00000 0.250000
\(17\) −1.40581 −0.340960 −0.170480 0.985361i \(-0.554532\pi\)
−0.170480 + 0.985361i \(0.554532\pi\)
\(18\) 1.00000 0.235702
\(19\) 2.13706 0.490276 0.245138 0.969488i \(-0.421167\pi\)
0.245138 + 0.969488i \(0.421167\pi\)
\(20\) −3.04892 −0.681759
\(21\) 1.00000 0.218218
\(22\) 2.13706 0.455623
\(23\) −2.26875 −0.473067 −0.236534 0.971623i \(-0.576011\pi\)
−0.236534 + 0.971623i \(0.576011\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.29590 0.859179
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) −2.58211 −0.479485 −0.239742 0.970837i \(-0.577063\pi\)
−0.239742 + 0.970837i \(0.577063\pi\)
\(30\) 3.04892 0.556654
\(31\) −6.34481 −1.13956 −0.569781 0.821796i \(-0.692972\pi\)
−0.569781 + 0.821796i \(0.692972\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.13706 −0.372015
\(34\) −1.40581 −0.241095
\(35\) 3.04892 0.515361
\(36\) 1.00000 0.166667
\(37\) 10.6528 1.75131 0.875654 0.482939i \(-0.160431\pi\)
0.875654 + 0.482939i \(0.160431\pi\)
\(38\) 2.13706 0.346677
\(39\) 0 0
\(40\) −3.04892 −0.482076
\(41\) −4.43296 −0.692312 −0.346156 0.938177i \(-0.612513\pi\)
−0.346156 + 0.938177i \(0.612513\pi\)
\(42\) 1.00000 0.154303
\(43\) −9.55496 −1.45712 −0.728559 0.684983i \(-0.759809\pi\)
−0.728559 + 0.684983i \(0.759809\pi\)
\(44\) 2.13706 0.322174
\(45\) −3.04892 −0.454506
\(46\) −2.26875 −0.334509
\(47\) −3.98792 −0.581698 −0.290849 0.956769i \(-0.593938\pi\)
−0.290849 + 0.956769i \(0.593938\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) 4.29590 0.607532
\(51\) 1.40581 0.196853
\(52\) 0 0
\(53\) 6.46681 0.888285 0.444142 0.895956i \(-0.353508\pi\)
0.444142 + 0.895956i \(0.353508\pi\)
\(54\) −1.00000 −0.136083
\(55\) −6.51573 −0.878581
\(56\) −1.00000 −0.133631
\(57\) −2.13706 −0.283061
\(58\) −2.58211 −0.339047
\(59\) −3.44504 −0.448506 −0.224253 0.974531i \(-0.571994\pi\)
−0.224253 + 0.974531i \(0.571994\pi\)
\(60\) 3.04892 0.393614
\(61\) 9.98792 1.27882 0.639411 0.768865i \(-0.279178\pi\)
0.639411 + 0.768865i \(0.279178\pi\)
\(62\) −6.34481 −0.805792
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.13706 −0.263054
\(67\) 11.3937 1.39197 0.695983 0.718058i \(-0.254969\pi\)
0.695983 + 0.718058i \(0.254969\pi\)
\(68\) −1.40581 −0.170480
\(69\) 2.26875 0.273125
\(70\) 3.04892 0.364415
\(71\) 4.21983 0.500802 0.250401 0.968142i \(-0.419438\pi\)
0.250401 + 0.968142i \(0.419438\pi\)
\(72\) 1.00000 0.117851
\(73\) 5.84548 0.684161 0.342081 0.939671i \(-0.388868\pi\)
0.342081 + 0.939671i \(0.388868\pi\)
\(74\) 10.6528 1.23836
\(75\) −4.29590 −0.496047
\(76\) 2.13706 0.245138
\(77\) −2.13706 −0.243541
\(78\) 0 0
\(79\) −10.7071 −1.20464 −0.602321 0.798254i \(-0.705757\pi\)
−0.602321 + 0.798254i \(0.705757\pi\)
\(80\) −3.04892 −0.340879
\(81\) 1.00000 0.111111
\(82\) −4.43296 −0.489539
\(83\) 8.94869 0.982246 0.491123 0.871090i \(-0.336586\pi\)
0.491123 + 0.871090i \(0.336586\pi\)
\(84\) 1.00000 0.109109
\(85\) 4.28621 0.464905
\(86\) −9.55496 −1.03034
\(87\) 2.58211 0.276831
\(88\) 2.13706 0.227812
\(89\) −3.73556 −0.395969 −0.197984 0.980205i \(-0.563440\pi\)
−0.197984 + 0.980205i \(0.563440\pi\)
\(90\) −3.04892 −0.321384
\(91\) 0 0
\(92\) −2.26875 −0.236534
\(93\) 6.34481 0.657927
\(94\) −3.98792 −0.411322
\(95\) −6.51573 −0.668500
\(96\) −1.00000 −0.102062
\(97\) −5.10321 −0.518153 −0.259076 0.965857i \(-0.583418\pi\)
−0.259076 + 0.965857i \(0.583418\pi\)
\(98\) 1.00000 0.101015
\(99\) 2.13706 0.214783
\(100\) 4.29590 0.429590
\(101\) −12.2174 −1.21568 −0.607840 0.794059i \(-0.707964\pi\)
−0.607840 + 0.794059i \(0.707964\pi\)
\(102\) 1.40581 0.139196
\(103\) −4.53319 −0.446668 −0.223334 0.974742i \(-0.571694\pi\)
−0.223334 + 0.974742i \(0.571694\pi\)
\(104\) 0 0
\(105\) −3.04892 −0.297544
\(106\) 6.46681 0.628112
\(107\) −12.5254 −1.21088 −0.605439 0.795892i \(-0.707002\pi\)
−0.605439 + 0.795892i \(0.707002\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −1.15883 −0.110996 −0.0554981 0.998459i \(-0.517675\pi\)
−0.0554981 + 0.998459i \(0.517675\pi\)
\(110\) −6.51573 −0.621250
\(111\) −10.6528 −1.01112
\(112\) −1.00000 −0.0944911
\(113\) 4.34721 0.408951 0.204475 0.978872i \(-0.434451\pi\)
0.204475 + 0.978872i \(0.434451\pi\)
\(114\) −2.13706 −0.200154
\(115\) 6.91723 0.645035
\(116\) −2.58211 −0.239742
\(117\) 0 0
\(118\) −3.44504 −0.317142
\(119\) 1.40581 0.128871
\(120\) 3.04892 0.278327
\(121\) −6.43296 −0.584815
\(122\) 9.98792 0.904264
\(123\) 4.43296 0.399707
\(124\) −6.34481 −0.569781
\(125\) 2.14675 0.192011
\(126\) −1.00000 −0.0890871
\(127\) 18.2959 1.62350 0.811749 0.584006i \(-0.198516\pi\)
0.811749 + 0.584006i \(0.198516\pi\)
\(128\) 1.00000 0.0883883
\(129\) 9.55496 0.841267
\(130\) 0 0
\(131\) 3.52781 0.308226 0.154113 0.988053i \(-0.450748\pi\)
0.154113 + 0.988053i \(0.450748\pi\)
\(132\) −2.13706 −0.186007
\(133\) −2.13706 −0.185307
\(134\) 11.3937 0.984268
\(135\) 3.04892 0.262409
\(136\) −1.40581 −0.120547
\(137\) 0.249373 0.0213053 0.0106527 0.999943i \(-0.496609\pi\)
0.0106527 + 0.999943i \(0.496609\pi\)
\(138\) 2.26875 0.193129
\(139\) 0.168522 0.0142939 0.00714694 0.999974i \(-0.497725\pi\)
0.00714694 + 0.999974i \(0.497725\pi\)
\(140\) 3.04892 0.257681
\(141\) 3.98792 0.335843
\(142\) 4.21983 0.354120
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 7.87263 0.653786
\(146\) 5.84548 0.483775
\(147\) −1.00000 −0.0824786
\(148\) 10.6528 0.875654
\(149\) 16.3327 1.33803 0.669015 0.743249i \(-0.266716\pi\)
0.669015 + 0.743249i \(0.266716\pi\)
\(150\) −4.29590 −0.350759
\(151\) 24.3448 1.98115 0.990576 0.136961i \(-0.0437335\pi\)
0.990576 + 0.136961i \(0.0437335\pi\)
\(152\) 2.13706 0.173339
\(153\) −1.40581 −0.113653
\(154\) −2.13706 −0.172209
\(155\) 19.3448 1.55381
\(156\) 0 0
\(157\) −12.0978 −0.965512 −0.482756 0.875755i \(-0.660364\pi\)
−0.482756 + 0.875755i \(0.660364\pi\)
\(158\) −10.7071 −0.851810
\(159\) −6.46681 −0.512852
\(160\) −3.04892 −0.241038
\(161\) 2.26875 0.178803
\(162\) 1.00000 0.0785674
\(163\) 14.0707 1.10210 0.551051 0.834472i \(-0.314227\pi\)
0.551051 + 0.834472i \(0.314227\pi\)
\(164\) −4.43296 −0.346156
\(165\) 6.51573 0.507249
\(166\) 8.94869 0.694553
\(167\) 19.9541 1.54409 0.772046 0.635567i \(-0.219233\pi\)
0.772046 + 0.635567i \(0.219233\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 4.28621 0.328737
\(171\) 2.13706 0.163425
\(172\) −9.55496 −0.728559
\(173\) −6.61596 −0.503002 −0.251501 0.967857i \(-0.580924\pi\)
−0.251501 + 0.967857i \(0.580924\pi\)
\(174\) 2.58211 0.195749
\(175\) −4.29590 −0.324739
\(176\) 2.13706 0.161087
\(177\) 3.44504 0.258945
\(178\) −3.73556 −0.279992
\(179\) −7.49396 −0.560125 −0.280062 0.959982i \(-0.590355\pi\)
−0.280062 + 0.959982i \(0.590355\pi\)
\(180\) −3.04892 −0.227253
\(181\) 19.1226 1.42137 0.710685 0.703510i \(-0.248385\pi\)
0.710685 + 0.703510i \(0.248385\pi\)
\(182\) 0 0
\(183\) −9.98792 −0.738328
\(184\) −2.26875 −0.167254
\(185\) −32.4795 −2.38794
\(186\) 6.34481 0.465224
\(187\) −3.00431 −0.219697
\(188\) −3.98792 −0.290849
\(189\) 1.00000 0.0727393
\(190\) −6.51573 −0.472701
\(191\) 23.2403 1.68161 0.840804 0.541340i \(-0.182083\pi\)
0.840804 + 0.541340i \(0.182083\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 4.00538 0.288313 0.144157 0.989555i \(-0.453953\pi\)
0.144157 + 0.989555i \(0.453953\pi\)
\(194\) −5.10321 −0.366389
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −7.75840 −0.552763 −0.276381 0.961048i \(-0.589135\pi\)
−0.276381 + 0.961048i \(0.589135\pi\)
\(198\) 2.13706 0.151874
\(199\) 14.5526 1.03160 0.515802 0.856708i \(-0.327494\pi\)
0.515802 + 0.856708i \(0.327494\pi\)
\(200\) 4.29590 0.303766
\(201\) −11.3937 −0.803652
\(202\) −12.2174 −0.859616
\(203\) 2.58211 0.181228
\(204\) 1.40581 0.0984266
\(205\) 13.5157 0.943979
\(206\) −4.53319 −0.315842
\(207\) −2.26875 −0.157689
\(208\) 0 0
\(209\) 4.56704 0.315909
\(210\) −3.04892 −0.210395
\(211\) 3.80194 0.261736 0.130868 0.991400i \(-0.458224\pi\)
0.130868 + 0.991400i \(0.458224\pi\)
\(212\) 6.46681 0.444142
\(213\) −4.21983 −0.289138
\(214\) −12.5254 −0.856220
\(215\) 29.1323 1.98680
\(216\) −1.00000 −0.0680414
\(217\) 6.34481 0.430714
\(218\) −1.15883 −0.0784861
\(219\) −5.84548 −0.395001
\(220\) −6.51573 −0.439290
\(221\) 0 0
\(222\) −10.6528 −0.714969
\(223\) −23.1347 −1.54921 −0.774606 0.632444i \(-0.782052\pi\)
−0.774606 + 0.632444i \(0.782052\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 4.29590 0.286393
\(226\) 4.34721 0.289172
\(227\) −2.72348 −0.180764 −0.0903819 0.995907i \(-0.528809\pi\)
−0.0903819 + 0.995907i \(0.528809\pi\)
\(228\) −2.13706 −0.141530
\(229\) 11.7385 0.775705 0.387852 0.921721i \(-0.373217\pi\)
0.387852 + 0.921721i \(0.373217\pi\)
\(230\) 6.91723 0.456109
\(231\) 2.13706 0.140608
\(232\) −2.58211 −0.169524
\(233\) 9.92931 0.650491 0.325245 0.945630i \(-0.394553\pi\)
0.325245 + 0.945630i \(0.394553\pi\)
\(234\) 0 0
\(235\) 12.1588 0.793155
\(236\) −3.44504 −0.224253
\(237\) 10.7071 0.695500
\(238\) 1.40581 0.0911253
\(239\) 22.1172 1.43064 0.715322 0.698795i \(-0.246280\pi\)
0.715322 + 0.698795i \(0.246280\pi\)
\(240\) 3.04892 0.196807
\(241\) 24.5429 1.58095 0.790473 0.612497i \(-0.209835\pi\)
0.790473 + 0.612497i \(0.209835\pi\)
\(242\) −6.43296 −0.413526
\(243\) −1.00000 −0.0641500
\(244\) 9.98792 0.639411
\(245\) −3.04892 −0.194788
\(246\) 4.43296 0.282635
\(247\) 0 0
\(248\) −6.34481 −0.402896
\(249\) −8.94869 −0.567100
\(250\) 2.14675 0.135773
\(251\) 27.2489 1.71994 0.859968 0.510349i \(-0.170484\pi\)
0.859968 + 0.510349i \(0.170484\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −4.84846 −0.304820
\(254\) 18.2959 1.14799
\(255\) −4.28621 −0.268413
\(256\) 1.00000 0.0625000
\(257\) 17.2349 1.07508 0.537542 0.843237i \(-0.319353\pi\)
0.537542 + 0.843237i \(0.319353\pi\)
\(258\) 9.55496 0.594866
\(259\) −10.6528 −0.661932
\(260\) 0 0
\(261\) −2.58211 −0.159828
\(262\) 3.52781 0.217949
\(263\) 8.46011 0.521673 0.260836 0.965383i \(-0.416002\pi\)
0.260836 + 0.965383i \(0.416002\pi\)
\(264\) −2.13706 −0.131527
\(265\) −19.7168 −1.21119
\(266\) −2.13706 −0.131032
\(267\) 3.73556 0.228613
\(268\) 11.3937 0.695983
\(269\) 1.29590 0.0790122 0.0395061 0.999219i \(-0.487422\pi\)
0.0395061 + 0.999219i \(0.487422\pi\)
\(270\) 3.04892 0.185551
\(271\) −5.46250 −0.331823 −0.165912 0.986141i \(-0.553057\pi\)
−0.165912 + 0.986141i \(0.553057\pi\)
\(272\) −1.40581 −0.0852399
\(273\) 0 0
\(274\) 0.249373 0.0150651
\(275\) 9.18060 0.553611
\(276\) 2.26875 0.136563
\(277\) 1.01746 0.0611332 0.0305666 0.999533i \(-0.490269\pi\)
0.0305666 + 0.999533i \(0.490269\pi\)
\(278\) 0.168522 0.0101073
\(279\) −6.34481 −0.379854
\(280\) 3.04892 0.182208
\(281\) −23.7482 −1.41670 −0.708350 0.705861i \(-0.750560\pi\)
−0.708350 + 0.705861i \(0.750560\pi\)
\(282\) 3.98792 0.237477
\(283\) −19.9148 −1.18381 −0.591907 0.806006i \(-0.701625\pi\)
−0.591907 + 0.806006i \(0.701625\pi\)
\(284\) 4.21983 0.250401
\(285\) 6.51573 0.385959
\(286\) 0 0
\(287\) 4.43296 0.261669
\(288\) 1.00000 0.0589256
\(289\) −15.0237 −0.883746
\(290\) 7.87263 0.462296
\(291\) 5.10321 0.299156
\(292\) 5.84548 0.342081
\(293\) 9.15213 0.534673 0.267337 0.963603i \(-0.413856\pi\)
0.267337 + 0.963603i \(0.413856\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 10.5036 0.611546
\(296\) 10.6528 0.619181
\(297\) −2.13706 −0.124005
\(298\) 16.3327 0.946130
\(299\) 0 0
\(300\) −4.29590 −0.248024
\(301\) 9.55496 0.550739
\(302\) 24.3448 1.40089
\(303\) 12.2174 0.701874
\(304\) 2.13706 0.122569
\(305\) −30.4523 −1.74370
\(306\) −1.40581 −0.0803650
\(307\) 22.2784 1.27150 0.635749 0.771896i \(-0.280691\pi\)
0.635749 + 0.771896i \(0.280691\pi\)
\(308\) −2.13706 −0.121770
\(309\) 4.53319 0.257884
\(310\) 19.3448 1.09871
\(311\) −0.254749 −0.0144455 −0.00722275 0.999974i \(-0.502299\pi\)
−0.00722275 + 0.999974i \(0.502299\pi\)
\(312\) 0 0
\(313\) 24.1129 1.36294 0.681471 0.731845i \(-0.261341\pi\)
0.681471 + 0.731845i \(0.261341\pi\)
\(314\) −12.0978 −0.682720
\(315\) 3.04892 0.171787
\(316\) −10.7071 −0.602321
\(317\) −12.8321 −0.720721 −0.360360 0.932813i \(-0.617346\pi\)
−0.360360 + 0.932813i \(0.617346\pi\)
\(318\) −6.46681 −0.362641
\(319\) −5.51812 −0.308956
\(320\) −3.04892 −0.170440
\(321\) 12.5254 0.699101
\(322\) 2.26875 0.126432
\(323\) −3.00431 −0.167164
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.0707 0.779303
\(327\) 1.15883 0.0640836
\(328\) −4.43296 −0.244769
\(329\) 3.98792 0.219861
\(330\) 6.51573 0.358679
\(331\) 29.0707 1.59787 0.798935 0.601418i \(-0.205397\pi\)
0.798935 + 0.601418i \(0.205397\pi\)
\(332\) 8.94869 0.491123
\(333\) 10.6528 0.583769
\(334\) 19.9541 1.09184
\(335\) −34.7385 −1.89797
\(336\) 1.00000 0.0545545
\(337\) 17.7821 0.968652 0.484326 0.874888i \(-0.339065\pi\)
0.484326 + 0.874888i \(0.339065\pi\)
\(338\) 0 0
\(339\) −4.34721 −0.236108
\(340\) 4.28621 0.232452
\(341\) −13.5593 −0.734276
\(342\) 2.13706 0.115559
\(343\) −1.00000 −0.0539949
\(344\) −9.55496 −0.515169
\(345\) −6.91723 −0.372411
\(346\) −6.61596 −0.355676
\(347\) −10.5144 −0.564443 −0.282221 0.959349i \(-0.591071\pi\)
−0.282221 + 0.959349i \(0.591071\pi\)
\(348\) 2.58211 0.138415
\(349\) 18.1274 0.970336 0.485168 0.874421i \(-0.338758\pi\)
0.485168 + 0.874421i \(0.338758\pi\)
\(350\) −4.29590 −0.229625
\(351\) 0 0
\(352\) 2.13706 0.113906
\(353\) −16.1715 −0.860722 −0.430361 0.902657i \(-0.641614\pi\)
−0.430361 + 0.902657i \(0.641614\pi\)
\(354\) 3.44504 0.183102
\(355\) −12.8659 −0.682852
\(356\) −3.73556 −0.197984
\(357\) −1.40581 −0.0744035
\(358\) −7.49396 −0.396068
\(359\) 7.77240 0.410211 0.205106 0.978740i \(-0.434246\pi\)
0.205106 + 0.978740i \(0.434246\pi\)
\(360\) −3.04892 −0.160692
\(361\) −14.4330 −0.759629
\(362\) 19.1226 1.00506
\(363\) 6.43296 0.337643
\(364\) 0 0
\(365\) −17.8224 −0.932866
\(366\) −9.98792 −0.522077
\(367\) −2.07846 −0.108495 −0.0542473 0.998528i \(-0.517276\pi\)
−0.0542473 + 0.998528i \(0.517276\pi\)
\(368\) −2.26875 −0.118267
\(369\) −4.43296 −0.230771
\(370\) −32.4795 −1.68853
\(371\) −6.46681 −0.335740
\(372\) 6.34481 0.328963
\(373\) 8.10752 0.419792 0.209896 0.977724i \(-0.432688\pi\)
0.209896 + 0.977724i \(0.432688\pi\)
\(374\) −3.00431 −0.155349
\(375\) −2.14675 −0.110858
\(376\) −3.98792 −0.205661
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 13.4222 0.689452 0.344726 0.938703i \(-0.387972\pi\)
0.344726 + 0.938703i \(0.387972\pi\)
\(380\) −6.51573 −0.334250
\(381\) −18.2959 −0.937327
\(382\) 23.2403 1.18908
\(383\) 12.4209 0.634677 0.317339 0.948312i \(-0.397211\pi\)
0.317339 + 0.948312i \(0.397211\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 6.51573 0.332072
\(386\) 4.00538 0.203868
\(387\) −9.55496 −0.485706
\(388\) −5.10321 −0.259076
\(389\) 37.5666 1.90470 0.952350 0.305007i \(-0.0986587\pi\)
0.952350 + 0.305007i \(0.0986587\pi\)
\(390\) 0 0
\(391\) 3.18944 0.161297
\(392\) 1.00000 0.0505076
\(393\) −3.52781 −0.177955
\(394\) −7.75840 −0.390862
\(395\) 32.6450 1.64255
\(396\) 2.13706 0.107391
\(397\) 36.1159 1.81260 0.906302 0.422630i \(-0.138893\pi\)
0.906302 + 0.422630i \(0.138893\pi\)
\(398\) 14.5526 0.729454
\(399\) 2.13706 0.106987
\(400\) 4.29590 0.214795
\(401\) −9.82610 −0.490692 −0.245346 0.969436i \(-0.578902\pi\)
−0.245346 + 0.969436i \(0.578902\pi\)
\(402\) −11.3937 −0.568268
\(403\) 0 0
\(404\) −12.2174 −0.607840
\(405\) −3.04892 −0.151502
\(406\) 2.58211 0.128148
\(407\) 22.7657 1.12845
\(408\) 1.40581 0.0695981
\(409\) −3.09352 −0.152965 −0.0764824 0.997071i \(-0.524369\pi\)
−0.0764824 + 0.997071i \(0.524369\pi\)
\(410\) 13.5157 0.667494
\(411\) −0.249373 −0.0123006
\(412\) −4.53319 −0.223334
\(413\) 3.44504 0.169519
\(414\) −2.26875 −0.111503
\(415\) −27.2838 −1.33931
\(416\) 0 0
\(417\) −0.168522 −0.00825257
\(418\) 4.56704 0.223381
\(419\) −20.1535 −0.984561 −0.492280 0.870437i \(-0.663837\pi\)
−0.492280 + 0.870437i \(0.663837\pi\)
\(420\) −3.04892 −0.148772
\(421\) 11.2034 0.546022 0.273011 0.962011i \(-0.411980\pi\)
0.273011 + 0.962011i \(0.411980\pi\)
\(422\) 3.80194 0.185075
\(423\) −3.98792 −0.193899
\(424\) 6.46681 0.314056
\(425\) −6.03923 −0.292946
\(426\) −4.21983 −0.204452
\(427\) −9.98792 −0.483349
\(428\) −12.5254 −0.605439
\(429\) 0 0
\(430\) 29.1323 1.40488
\(431\) −38.9898 −1.87807 −0.939037 0.343816i \(-0.888280\pi\)
−0.939037 + 0.343816i \(0.888280\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 23.4426 1.12658 0.563291 0.826259i \(-0.309535\pi\)
0.563291 + 0.826259i \(0.309535\pi\)
\(434\) 6.34481 0.304561
\(435\) −7.87263 −0.377463
\(436\) −1.15883 −0.0554981
\(437\) −4.84846 −0.231933
\(438\) −5.84548 −0.279308
\(439\) −26.8592 −1.28192 −0.640960 0.767574i \(-0.721464\pi\)
−0.640960 + 0.767574i \(0.721464\pi\)
\(440\) −6.51573 −0.310625
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −11.1347 −0.529024 −0.264512 0.964382i \(-0.585211\pi\)
−0.264512 + 0.964382i \(0.585211\pi\)
\(444\) −10.6528 −0.505559
\(445\) 11.3894 0.539910
\(446\) −23.1347 −1.09546
\(447\) −16.3327 −0.772512
\(448\) −1.00000 −0.0472456
\(449\) 27.0858 1.27826 0.639128 0.769100i \(-0.279295\pi\)
0.639128 + 0.769100i \(0.279295\pi\)
\(450\) 4.29590 0.202511
\(451\) −9.47352 −0.446090
\(452\) 4.34721 0.204475
\(453\) −24.3448 −1.14382
\(454\) −2.72348 −0.127819
\(455\) 0 0
\(456\) −2.13706 −0.100077
\(457\) 3.40880 0.159457 0.0797284 0.996817i \(-0.474595\pi\)
0.0797284 + 0.996817i \(0.474595\pi\)
\(458\) 11.7385 0.548506
\(459\) 1.40581 0.0656177
\(460\) 6.91723 0.322518
\(461\) −30.9178 −1.43999 −0.719993 0.693981i \(-0.755855\pi\)
−0.719993 + 0.693981i \(0.755855\pi\)
\(462\) 2.13706 0.0994252
\(463\) 35.0465 1.62875 0.814375 0.580339i \(-0.197080\pi\)
0.814375 + 0.580339i \(0.197080\pi\)
\(464\) −2.58211 −0.119871
\(465\) −19.3448 −0.897094
\(466\) 9.92931 0.459967
\(467\) 4.04652 0.187251 0.0936254 0.995607i \(-0.470154\pi\)
0.0936254 + 0.995607i \(0.470154\pi\)
\(468\) 0 0
\(469\) −11.3937 −0.526114
\(470\) 12.1588 0.560845
\(471\) 12.0978 0.557439
\(472\) −3.44504 −0.158571
\(473\) −20.4196 −0.938892
\(474\) 10.7071 0.491793
\(475\) 9.18060 0.421235
\(476\) 1.40581 0.0644353
\(477\) 6.46681 0.296095
\(478\) 22.1172 1.01162
\(479\) −16.0411 −0.732939 −0.366469 0.930430i \(-0.619434\pi\)
−0.366469 + 0.930430i \(0.619434\pi\)
\(480\) 3.04892 0.139163
\(481\) 0 0
\(482\) 24.5429 1.11790
\(483\) −2.26875 −0.103232
\(484\) −6.43296 −0.292407
\(485\) 15.5593 0.706510
\(486\) −1.00000 −0.0453609
\(487\) 36.7724 1.66632 0.833158 0.553035i \(-0.186530\pi\)
0.833158 + 0.553035i \(0.186530\pi\)
\(488\) 9.98792 0.452132
\(489\) −14.0707 −0.636298
\(490\) −3.04892 −0.137736
\(491\) −7.69069 −0.347076 −0.173538 0.984827i \(-0.555520\pi\)
−0.173538 + 0.984827i \(0.555520\pi\)
\(492\) 4.43296 0.199853
\(493\) 3.62996 0.163485
\(494\) 0 0
\(495\) −6.51573 −0.292860
\(496\) −6.34481 −0.284891
\(497\) −4.21983 −0.189285
\(498\) −8.94869 −0.401000
\(499\) −21.8213 −0.976856 −0.488428 0.872604i \(-0.662430\pi\)
−0.488428 + 0.872604i \(0.662430\pi\)
\(500\) 2.14675 0.0960057
\(501\) −19.9541 −0.891482
\(502\) 27.2489 1.21618
\(503\) 0.875018 0.0390151 0.0195076 0.999810i \(-0.493790\pi\)
0.0195076 + 0.999810i \(0.493790\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 37.2500 1.65760
\(506\) −4.84846 −0.215540
\(507\) 0 0
\(508\) 18.2959 0.811749
\(509\) −40.2043 −1.78202 −0.891012 0.453980i \(-0.850004\pi\)
−0.891012 + 0.453980i \(0.850004\pi\)
\(510\) −4.28621 −0.189796
\(511\) −5.84548 −0.258589
\(512\) 1.00000 0.0441942
\(513\) −2.13706 −0.0943537
\(514\) 17.2349 0.760199
\(515\) 13.8213 0.609040
\(516\) 9.55496 0.420634
\(517\) −8.52243 −0.374816
\(518\) −10.6528 −0.468057
\(519\) 6.61596 0.290408
\(520\) 0 0
\(521\) −4.36898 −0.191408 −0.0957042 0.995410i \(-0.530510\pi\)
−0.0957042 + 0.995410i \(0.530510\pi\)
\(522\) −2.58211 −0.113016
\(523\) −9.54958 −0.417574 −0.208787 0.977961i \(-0.566952\pi\)
−0.208787 + 0.977961i \(0.566952\pi\)
\(524\) 3.52781 0.154113
\(525\) 4.29590 0.187488
\(526\) 8.46011 0.368878
\(527\) 8.91962 0.388545
\(528\) −2.13706 −0.0930037
\(529\) −17.8528 −0.776208
\(530\) −19.7168 −0.856442
\(531\) −3.44504 −0.149502
\(532\) −2.13706 −0.0926534
\(533\) 0 0
\(534\) 3.73556 0.161654
\(535\) 38.1890 1.65105
\(536\) 11.3937 0.492134
\(537\) 7.49396 0.323388
\(538\) 1.29590 0.0558701
\(539\) 2.13706 0.0920498
\(540\) 3.04892 0.131205
\(541\) 4.13813 0.177912 0.0889560 0.996036i \(-0.471647\pi\)
0.0889560 + 0.996036i \(0.471647\pi\)
\(542\) −5.46250 −0.234634
\(543\) −19.1226 −0.820629
\(544\) −1.40581 −0.0602737
\(545\) 3.53319 0.151345
\(546\) 0 0
\(547\) −17.0242 −0.727901 −0.363950 0.931418i \(-0.618572\pi\)
−0.363950 + 0.931418i \(0.618572\pi\)
\(548\) 0.249373 0.0106527
\(549\) 9.98792 0.426274
\(550\) 9.18060 0.391462
\(551\) −5.51812 −0.235080
\(552\) 2.26875 0.0965644
\(553\) 10.7071 0.455312
\(554\) 1.01746 0.0432277
\(555\) 32.4795 1.37868
\(556\) 0.168522 0.00714694
\(557\) −18.9778 −0.804113 −0.402057 0.915615i \(-0.631705\pi\)
−0.402057 + 0.915615i \(0.631705\pi\)
\(558\) −6.34481 −0.268597
\(559\) 0 0
\(560\) 3.04892 0.128840
\(561\) 3.00431 0.126842
\(562\) −23.7482 −1.00176
\(563\) −31.3840 −1.32268 −0.661340 0.750086i \(-0.730012\pi\)
−0.661340 + 0.750086i \(0.730012\pi\)
\(564\) 3.98792 0.167922
\(565\) −13.2543 −0.557612
\(566\) −19.9148 −0.837083
\(567\) −1.00000 −0.0419961
\(568\) 4.21983 0.177060
\(569\) 30.4196 1.27525 0.637627 0.770345i \(-0.279916\pi\)
0.637627 + 0.770345i \(0.279916\pi\)
\(570\) 6.51573 0.272914
\(571\) −26.4534 −1.10704 −0.553520 0.832836i \(-0.686716\pi\)
−0.553520 + 0.832836i \(0.686716\pi\)
\(572\) 0 0
\(573\) −23.2403 −0.970876
\(574\) 4.43296 0.185028
\(575\) −9.74632 −0.406449
\(576\) 1.00000 0.0416667
\(577\) −6.25667 −0.260469 −0.130234 0.991483i \(-0.541573\pi\)
−0.130234 + 0.991483i \(0.541573\pi\)
\(578\) −15.0237 −0.624903
\(579\) −4.00538 −0.166458
\(580\) 7.87263 0.326893
\(581\) −8.94869 −0.371254
\(582\) 5.10321 0.211535
\(583\) 13.8200 0.572365
\(584\) 5.84548 0.241888
\(585\) 0 0
\(586\) 9.15213 0.378071
\(587\) −16.9028 −0.697651 −0.348826 0.937188i \(-0.613419\pi\)
−0.348826 + 0.937188i \(0.613419\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −13.5593 −0.558700
\(590\) 10.5036 0.432428
\(591\) 7.75840 0.319138
\(592\) 10.6528 0.437827
\(593\) 8.60089 0.353196 0.176598 0.984283i \(-0.443491\pi\)
0.176598 + 0.984283i \(0.443491\pi\)
\(594\) −2.13706 −0.0876848
\(595\) −4.28621 −0.175717
\(596\) 16.3327 0.669015
\(597\) −14.5526 −0.595597
\(598\) 0 0
\(599\) −28.3744 −1.15934 −0.579672 0.814850i \(-0.696819\pi\)
−0.579672 + 0.814850i \(0.696819\pi\)
\(600\) −4.29590 −0.175379
\(601\) 30.3394 1.23757 0.618786 0.785560i \(-0.287625\pi\)
0.618786 + 0.785560i \(0.287625\pi\)
\(602\) 9.55496 0.389431
\(603\) 11.3937 0.463989
\(604\) 24.3448 0.990576
\(605\) 19.6136 0.797405
\(606\) 12.2174 0.496300
\(607\) 9.64609 0.391523 0.195761 0.980652i \(-0.437282\pi\)
0.195761 + 0.980652i \(0.437282\pi\)
\(608\) 2.13706 0.0866694
\(609\) −2.58211 −0.104632
\(610\) −30.4523 −1.23298
\(611\) 0 0
\(612\) −1.40581 −0.0568266
\(613\) 27.1444 1.09635 0.548175 0.836364i \(-0.315323\pi\)
0.548175 + 0.836364i \(0.315323\pi\)
\(614\) 22.2784 0.899085
\(615\) −13.5157 −0.545007
\(616\) −2.13706 −0.0861047
\(617\) 30.4510 1.22591 0.612956 0.790117i \(-0.289980\pi\)
0.612956 + 0.790117i \(0.289980\pi\)
\(618\) 4.53319 0.182352
\(619\) 3.06578 0.123224 0.0616121 0.998100i \(-0.480376\pi\)
0.0616121 + 0.998100i \(0.480376\pi\)
\(620\) 19.3448 0.776906
\(621\) 2.26875 0.0910418
\(622\) −0.254749 −0.0102145
\(623\) 3.73556 0.149662
\(624\) 0 0
\(625\) −28.0248 −1.12099
\(626\) 24.1129 0.963745
\(627\) −4.56704 −0.182390
\(628\) −12.0978 −0.482756
\(629\) −14.9758 −0.597126
\(630\) 3.04892 0.121472
\(631\) 17.7791 0.707775 0.353887 0.935288i \(-0.384860\pi\)
0.353887 + 0.935288i \(0.384860\pi\)
\(632\) −10.7071 −0.425905
\(633\) −3.80194 −0.151113
\(634\) −12.8321 −0.509627
\(635\) −55.7827 −2.21367
\(636\) −6.46681 −0.256426
\(637\) 0 0
\(638\) −5.51812 −0.218465
\(639\) 4.21983 0.166934
\(640\) −3.04892 −0.120519
\(641\) −41.9754 −1.65793 −0.828964 0.559303i \(-0.811069\pi\)
−0.828964 + 0.559303i \(0.811069\pi\)
\(642\) 12.5254 0.494339
\(643\) −26.7222 −1.05382 −0.526909 0.849921i \(-0.676649\pi\)
−0.526909 + 0.849921i \(0.676649\pi\)
\(644\) 2.26875 0.0894013
\(645\) −29.1323 −1.14708
\(646\) −3.00431 −0.118203
\(647\) −33.7399 −1.32645 −0.663226 0.748419i \(-0.730813\pi\)
−0.663226 + 0.748419i \(0.730813\pi\)
\(648\) 1.00000 0.0392837
\(649\) −7.36227 −0.288994
\(650\) 0 0
\(651\) −6.34481 −0.248673
\(652\) 14.0707 0.551051
\(653\) −14.8374 −0.580634 −0.290317 0.956931i \(-0.593761\pi\)
−0.290317 + 0.956931i \(0.593761\pi\)
\(654\) 1.15883 0.0453140
\(655\) −10.7560 −0.420272
\(656\) −4.43296 −0.173078
\(657\) 5.84548 0.228054
\(658\) 3.98792 0.155465
\(659\) −25.0508 −0.975842 −0.487921 0.872888i \(-0.662245\pi\)
−0.487921 + 0.872888i \(0.662245\pi\)
\(660\) 6.51573 0.253624
\(661\) 34.5816 1.34507 0.672535 0.740066i \(-0.265206\pi\)
0.672535 + 0.740066i \(0.265206\pi\)
\(662\) 29.0707 1.12986
\(663\) 0 0
\(664\) 8.94869 0.347277
\(665\) 6.51573 0.252669
\(666\) 10.6528 0.412787
\(667\) 5.85815 0.226829
\(668\) 19.9541 0.772046
\(669\) 23.1347 0.894438
\(670\) −34.7385 −1.34207
\(671\) 21.3448 0.824007
\(672\) 1.00000 0.0385758
\(673\) 24.7791 0.955164 0.477582 0.878587i \(-0.341513\pi\)
0.477582 + 0.878587i \(0.341513\pi\)
\(674\) 17.7821 0.684940
\(675\) −4.29590 −0.165349
\(676\) 0 0
\(677\) −38.1347 −1.46563 −0.732817 0.680426i \(-0.761795\pi\)
−0.732817 + 0.680426i \(0.761795\pi\)
\(678\) −4.34721 −0.166953
\(679\) 5.10321 0.195843
\(680\) 4.28621 0.164369
\(681\) 2.72348 0.104364
\(682\) −13.5593 −0.519211
\(683\) −38.6407 −1.47855 −0.739273 0.673406i \(-0.764831\pi\)
−0.739273 + 0.673406i \(0.764831\pi\)
\(684\) 2.13706 0.0817127
\(685\) −0.760316 −0.0290502
\(686\) −1.00000 −0.0381802
\(687\) −11.7385 −0.447853
\(688\) −9.55496 −0.364279
\(689\) 0 0
\(690\) −6.91723 −0.263334
\(691\) 6.00969 0.228619 0.114310 0.993445i \(-0.463534\pi\)
0.114310 + 0.993445i \(0.463534\pi\)
\(692\) −6.61596 −0.251501
\(693\) −2.13706 −0.0811803
\(694\) −10.5144 −0.399121
\(695\) −0.513811 −0.0194899
\(696\) 2.58211 0.0978744
\(697\) 6.23191 0.236051
\(698\) 18.1274 0.686131
\(699\) −9.92931 −0.375561
\(700\) −4.29590 −0.162370
\(701\) 24.3642 0.920223 0.460111 0.887861i \(-0.347809\pi\)
0.460111 + 0.887861i \(0.347809\pi\)
\(702\) 0 0
\(703\) 22.7657 0.858624
\(704\) 2.13706 0.0805436
\(705\) −12.1588 −0.457928
\(706\) −16.1715 −0.608623
\(707\) 12.2174 0.459484
\(708\) 3.44504 0.129473
\(709\) −26.1239 −0.981104 −0.490552 0.871412i \(-0.663205\pi\)
−0.490552 + 0.871412i \(0.663205\pi\)
\(710\) −12.8659 −0.482849
\(711\) −10.7071 −0.401547
\(712\) −3.73556 −0.139996
\(713\) 14.3948 0.539089
\(714\) −1.40581 −0.0526112
\(715\) 0 0
\(716\) −7.49396 −0.280062
\(717\) −22.1172 −0.825982
\(718\) 7.77240 0.290063
\(719\) −4.64981 −0.173409 −0.0867043 0.996234i \(-0.527634\pi\)
−0.0867043 + 0.996234i \(0.527634\pi\)
\(720\) −3.04892 −0.113626
\(721\) 4.53319 0.168825
\(722\) −14.4330 −0.537139
\(723\) −24.5429 −0.912759
\(724\) 19.1226 0.710685
\(725\) −11.0925 −0.411964
\(726\) 6.43296 0.238750
\(727\) −28.4292 −1.05438 −0.527191 0.849747i \(-0.676755\pi\)
−0.527191 + 0.849747i \(0.676755\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −17.8224 −0.659636
\(731\) 13.4325 0.496818
\(732\) −9.98792 −0.369164
\(733\) 9.99356 0.369120 0.184560 0.982821i \(-0.440914\pi\)
0.184560 + 0.982821i \(0.440914\pi\)
\(734\) −2.07846 −0.0767173
\(735\) 3.04892 0.112461
\(736\) −2.26875 −0.0836272
\(737\) 24.3491 0.896912
\(738\) −4.43296 −0.163180
\(739\) −13.5101 −0.496977 −0.248488 0.968635i \(-0.579934\pi\)
−0.248488 + 0.968635i \(0.579934\pi\)
\(740\) −32.4795 −1.19397
\(741\) 0 0
\(742\) −6.46681 −0.237404
\(743\) 38.1540 1.39974 0.699868 0.714272i \(-0.253242\pi\)
0.699868 + 0.714272i \(0.253242\pi\)
\(744\) 6.34481 0.232612
\(745\) −49.7972 −1.82443
\(746\) 8.10752 0.296838
\(747\) 8.94869 0.327415
\(748\) −3.00431 −0.109849
\(749\) 12.5254 0.457669
\(750\) −2.14675 −0.0783883
\(751\) −24.1473 −0.881149 −0.440575 0.897716i \(-0.645225\pi\)
−0.440575 + 0.897716i \(0.645225\pi\)
\(752\) −3.98792 −0.145424
\(753\) −27.2489 −0.993005
\(754\) 0 0
\(755\) −74.2253 −2.70134
\(756\) 1.00000 0.0363696
\(757\) −7.27173 −0.264296 −0.132148 0.991230i \(-0.542187\pi\)
−0.132148 + 0.991230i \(0.542187\pi\)
\(758\) 13.4222 0.487516
\(759\) 4.84846 0.175988
\(760\) −6.51573 −0.236350
\(761\) 27.7894 1.00736 0.503682 0.863889i \(-0.331978\pi\)
0.503682 + 0.863889i \(0.331978\pi\)
\(762\) −18.2959 −0.662790
\(763\) 1.15883 0.0419526
\(764\) 23.2403 0.840804
\(765\) 4.28621 0.154968
\(766\) 12.4209 0.448785
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −12.5894 −0.453985 −0.226993 0.973896i \(-0.572889\pi\)
−0.226993 + 0.973896i \(0.572889\pi\)
\(770\) 6.51573 0.234811
\(771\) −17.2349 −0.620700
\(772\) 4.00538 0.144157
\(773\) 42.4935 1.52838 0.764192 0.644989i \(-0.223138\pi\)
0.764192 + 0.644989i \(0.223138\pi\)
\(774\) −9.55496 −0.343446
\(775\) −27.2567 −0.979088
\(776\) −5.10321 −0.183195
\(777\) 10.6528 0.382167
\(778\) 37.5666 1.34683
\(779\) −9.47352 −0.339424
\(780\) 0 0
\(781\) 9.01805 0.322691
\(782\) 3.18944 0.114054
\(783\) 2.58211 0.0922769
\(784\) 1.00000 0.0357143
\(785\) 36.8853 1.31649
\(786\) −3.52781 −0.125833
\(787\) −30.9017 −1.10153 −0.550763 0.834662i \(-0.685663\pi\)
−0.550763 + 0.834662i \(0.685663\pi\)
\(788\) −7.75840 −0.276381
\(789\) −8.46011 −0.301188
\(790\) 32.6450 1.16146
\(791\) −4.34721 −0.154569
\(792\) 2.13706 0.0759372
\(793\) 0 0
\(794\) 36.1159 1.28170
\(795\) 19.7168 0.699282
\(796\) 14.5526 0.515802
\(797\) 52.3038 1.85270 0.926348 0.376670i \(-0.122931\pi\)
0.926348 + 0.376670i \(0.122931\pi\)
\(798\) 2.13706 0.0756512
\(799\) 5.60627 0.198336
\(800\) 4.29590 0.151883
\(801\) −3.73556 −0.131990
\(802\) −9.82610 −0.346972
\(803\) 12.4922 0.440839
\(804\) −11.3937 −0.401826
\(805\) −6.91723 −0.243800
\(806\) 0 0
\(807\) −1.29590 −0.0456177
\(808\) −12.2174 −0.429808
\(809\) 31.7942 1.11782 0.558912 0.829227i \(-0.311219\pi\)
0.558912 + 0.829227i \(0.311219\pi\)
\(810\) −3.04892 −0.107128
\(811\) −12.3196 −0.432599 −0.216300 0.976327i \(-0.569399\pi\)
−0.216300 + 0.976327i \(0.569399\pi\)
\(812\) 2.58211 0.0906141
\(813\) 5.46250 0.191578
\(814\) 22.7657 0.797937
\(815\) −42.9004 −1.50273
\(816\) 1.40581 0.0492133
\(817\) −20.4196 −0.714390
\(818\) −3.09352 −0.108162
\(819\) 0 0
\(820\) 13.5157 0.471990
\(821\) −41.0901 −1.43405 −0.717027 0.697046i \(-0.754497\pi\)
−0.717027 + 0.697046i \(0.754497\pi\)
\(822\) −0.249373 −0.00869787
\(823\) −2.76164 −0.0962649 −0.0481324 0.998841i \(-0.515327\pi\)
−0.0481324 + 0.998841i \(0.515327\pi\)
\(824\) −4.53319 −0.157921
\(825\) −9.18060 −0.319628
\(826\) 3.44504 0.119868
\(827\) 28.6098 0.994862 0.497431 0.867504i \(-0.334277\pi\)
0.497431 + 0.867504i \(0.334277\pi\)
\(828\) −2.26875 −0.0788445
\(829\) −50.4741 −1.75304 −0.876519 0.481367i \(-0.840140\pi\)
−0.876519 + 0.481367i \(0.840140\pi\)
\(830\) −27.2838 −0.947035
\(831\) −1.01746 −0.0352952
\(832\) 0 0
\(833\) −1.40581 −0.0487085
\(834\) −0.168522 −0.00583545
\(835\) −60.8383 −2.10540
\(836\) 4.56704 0.157954
\(837\) 6.34481 0.219309
\(838\) −20.1535 −0.696190
\(839\) −38.4185 −1.32635 −0.663177 0.748463i \(-0.730792\pi\)
−0.663177 + 0.748463i \(0.730792\pi\)
\(840\) −3.04892 −0.105198
\(841\) −22.3327 −0.770094
\(842\) 11.2034 0.386096
\(843\) 23.7482 0.817933
\(844\) 3.80194 0.130868
\(845\) 0 0
\(846\) −3.98792 −0.137107
\(847\) 6.43296 0.221039
\(848\) 6.46681 0.222071
\(849\) 19.9148 0.683475
\(850\) −6.03923 −0.207144
\(851\) −24.1685 −0.828486
\(852\) −4.21983 −0.144569
\(853\) −7.09677 −0.242989 −0.121494 0.992592i \(-0.538769\pi\)
−0.121494 + 0.992592i \(0.538769\pi\)
\(854\) −9.98792 −0.341780
\(855\) −6.51573 −0.222833
\(856\) −12.5254 −0.428110
\(857\) −37.8901 −1.29430 −0.647150 0.762362i \(-0.724039\pi\)
−0.647150 + 0.762362i \(0.724039\pi\)
\(858\) 0 0
\(859\) 32.9329 1.12366 0.561828 0.827254i \(-0.310098\pi\)
0.561828 + 0.827254i \(0.310098\pi\)
\(860\) 29.1323 0.993402
\(861\) −4.43296 −0.151075
\(862\) −38.9898 −1.32800
\(863\) −27.3400 −0.930665 −0.465333 0.885136i \(-0.654065\pi\)
−0.465333 + 0.885136i \(0.654065\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 20.1715 0.685852
\(866\) 23.4426 0.796614
\(867\) 15.0237 0.510231
\(868\) 6.34481 0.215357
\(869\) −22.8817 −0.776209
\(870\) −7.87263 −0.266907
\(871\) 0 0
\(872\) −1.15883 −0.0392431
\(873\) −5.10321 −0.172718
\(874\) −4.84846 −0.164002
\(875\) −2.14675 −0.0725735
\(876\) −5.84548 −0.197500
\(877\) 7.54852 0.254895 0.127448 0.991845i \(-0.459322\pi\)
0.127448 + 0.991845i \(0.459322\pi\)
\(878\) −26.8592 −0.906455
\(879\) −9.15213 −0.308694
\(880\) −6.51573 −0.219645
\(881\) −9.14138 −0.307981 −0.153990 0.988072i \(-0.549212\pi\)
−0.153990 + 0.988072i \(0.549212\pi\)
\(882\) 1.00000 0.0336718
\(883\) 31.5838 1.06288 0.531439 0.847097i \(-0.321651\pi\)
0.531439 + 0.847097i \(0.321651\pi\)
\(884\) 0 0
\(885\) −10.5036 −0.353076
\(886\) −11.1347 −0.374077
\(887\) 57.3159 1.92448 0.962239 0.272205i \(-0.0877530\pi\)
0.962239 + 0.272205i \(0.0877530\pi\)
\(888\) −10.6528 −0.357484
\(889\) −18.2959 −0.613625
\(890\) 11.3894 0.381774
\(891\) 2.13706 0.0715943
\(892\) −23.1347 −0.774606
\(893\) −8.52243 −0.285192
\(894\) −16.3327 −0.546248
\(895\) 22.8485 0.763740
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 27.0858 0.903863
\(899\) 16.3830 0.546403
\(900\) 4.29590 0.143197
\(901\) −9.09113 −0.302869
\(902\) −9.47352 −0.315434
\(903\) −9.55496 −0.317969
\(904\) 4.34721 0.144586
\(905\) −58.3032 −1.93806
\(906\) −24.3448 −0.808802
\(907\) −35.9963 −1.19524 −0.597618 0.801781i \(-0.703886\pi\)
−0.597618 + 0.801781i \(0.703886\pi\)
\(908\) −2.72348 −0.0903819
\(909\) −12.2174 −0.405227
\(910\) 0 0
\(911\) −8.76569 −0.290420 −0.145210 0.989401i \(-0.546386\pi\)
−0.145210 + 0.989401i \(0.546386\pi\)
\(912\) −2.13706 −0.0707652
\(913\) 19.1239 0.632909
\(914\) 3.40880 0.112753
\(915\) 30.4523 1.00672
\(916\) 11.7385 0.387852
\(917\) −3.52781 −0.116499
\(918\) 1.40581 0.0463987
\(919\) 28.5695 0.942422 0.471211 0.882020i \(-0.343817\pi\)
0.471211 + 0.882020i \(0.343817\pi\)
\(920\) 6.91723 0.228054
\(921\) −22.2784 −0.734100
\(922\) −30.9178 −1.01822
\(923\) 0 0
\(924\) 2.13706 0.0703042
\(925\) 45.7633 1.50469
\(926\) 35.0465 1.15170
\(927\) −4.53319 −0.148889
\(928\) −2.58211 −0.0847618
\(929\) −23.2644 −0.763281 −0.381641 0.924311i \(-0.624641\pi\)
−0.381641 + 0.924311i \(0.624641\pi\)
\(930\) −19.3448 −0.634341
\(931\) 2.13706 0.0700394
\(932\) 9.92931 0.325245
\(933\) 0.254749 0.00834012
\(934\) 4.04652 0.132406
\(935\) 9.15990 0.299561
\(936\) 0 0
\(937\) 57.3491 1.87351 0.936757 0.349980i \(-0.113812\pi\)
0.936757 + 0.349980i \(0.113812\pi\)
\(938\) −11.3937 −0.372019
\(939\) −24.1129 −0.786895
\(940\) 12.1588 0.396577
\(941\) 50.8840 1.65877 0.829385 0.558677i \(-0.188691\pi\)
0.829385 + 0.558677i \(0.188691\pi\)
\(942\) 12.0978 0.394169
\(943\) 10.0573 0.327510
\(944\) −3.44504 −0.112127
\(945\) −3.04892 −0.0991813
\(946\) −20.4196 −0.663897
\(947\) −9.63593 −0.313126 −0.156563 0.987668i \(-0.550041\pi\)
−0.156563 + 0.987668i \(0.550041\pi\)
\(948\) 10.7071 0.347750
\(949\) 0 0
\(950\) 9.18060 0.297858
\(951\) 12.8321 0.416108
\(952\) 1.40581 0.0455627
\(953\) −6.38345 −0.206780 −0.103390 0.994641i \(-0.532969\pi\)
−0.103390 + 0.994641i \(0.532969\pi\)
\(954\) 6.46681 0.209371
\(955\) −70.8577 −2.29290
\(956\) 22.1172 0.715322
\(957\) 5.51812 0.178376
\(958\) −16.0411 −0.518266
\(959\) −0.249373 −0.00805266
\(960\) 3.04892 0.0984034
\(961\) 9.25667 0.298602
\(962\) 0 0
\(963\) −12.5254 −0.403626
\(964\) 24.5429 0.790473
\(965\) −12.2121 −0.393120
\(966\) −2.26875 −0.0729958
\(967\) −28.8692 −0.928370 −0.464185 0.885738i \(-0.653653\pi\)
−0.464185 + 0.885738i \(0.653653\pi\)
\(968\) −6.43296 −0.206763
\(969\) 3.00431 0.0965124
\(970\) 15.5593 0.499578
\(971\) −35.9661 −1.15421 −0.577104 0.816670i \(-0.695817\pi\)
−0.577104 + 0.816670i \(0.695817\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −0.168522 −0.00540258
\(974\) 36.7724 1.17826
\(975\) 0 0
\(976\) 9.98792 0.319705
\(977\) 42.2664 1.35222 0.676110 0.736800i \(-0.263664\pi\)
0.676110 + 0.736800i \(0.263664\pi\)
\(978\) −14.0707 −0.449931
\(979\) −7.98313 −0.255142
\(980\) −3.04892 −0.0973941
\(981\) −1.15883 −0.0369987
\(982\) −7.69069 −0.245420
\(983\) 39.2435 1.25167 0.625837 0.779954i \(-0.284758\pi\)
0.625837 + 0.779954i \(0.284758\pi\)
\(984\) 4.43296 0.141318
\(985\) 23.6547 0.753702
\(986\) 3.62996 0.115601
\(987\) −3.98792 −0.126937
\(988\) 0 0
\(989\) 21.6778 0.689314
\(990\) −6.51573 −0.207083
\(991\) 31.1892 0.990758 0.495379 0.868677i \(-0.335029\pi\)
0.495379 + 0.868677i \(0.335029\pi\)
\(992\) −6.34481 −0.201448
\(993\) −29.0707 −0.922530
\(994\) −4.21983 −0.133845
\(995\) −44.3696 −1.40661
\(996\) −8.94869 −0.283550
\(997\) −23.7275 −0.751458 −0.375729 0.926730i \(-0.622608\pi\)
−0.375729 + 0.926730i \(0.622608\pi\)
\(998\) −21.8213 −0.690742
\(999\) −10.6528 −0.337039
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.ci.1.1 yes 3
13.12 even 2 7098.2.a.cd.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cd.1.3 3 13.12 even 2
7098.2.a.ci.1.1 yes 3 1.1 even 1 trivial