Properties

Label 7098.2.a.cc.1.2
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 1.2
Root \(-1.24698\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.554958 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.554958 q^{10} +0.356896 q^{11} -1.00000 q^{12} -1.00000 q^{14} +0.554958 q^{15} +1.00000 q^{16} -3.80194 q^{17} -1.00000 q^{18} -5.74094 q^{19} -0.554958 q^{20} -1.00000 q^{21} -0.356896 q^{22} -2.44504 q^{23} +1.00000 q^{24} -4.69202 q^{25} -1.00000 q^{27} +1.00000 q^{28} +0.405813 q^{29} -0.554958 q^{30} +4.74094 q^{31} -1.00000 q^{32} -0.356896 q^{33} +3.80194 q^{34} -0.554958 q^{35} +1.00000 q^{36} -3.54288 q^{37} +5.74094 q^{38} +0.554958 q^{40} +3.26875 q^{41} +1.00000 q^{42} -6.04892 q^{43} +0.356896 q^{44} -0.554958 q^{45} +2.44504 q^{46} -0.603875 q^{47} -1.00000 q^{48} +1.00000 q^{49} +4.69202 q^{50} +3.80194 q^{51} -1.35690 q^{53} +1.00000 q^{54} -0.198062 q^{55} -1.00000 q^{56} +5.74094 q^{57} -0.405813 q^{58} -5.54288 q^{59} +0.554958 q^{60} +4.38404 q^{61} -4.74094 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.356896 q^{66} +15.2959 q^{67} -3.80194 q^{68} +2.44504 q^{69} +0.554958 q^{70} -7.42758 q^{71} -1.00000 q^{72} +11.2295 q^{73} +3.54288 q^{74} +4.69202 q^{75} -5.74094 q^{76} +0.356896 q^{77} -1.76271 q^{79} -0.554958 q^{80} +1.00000 q^{81} -3.26875 q^{82} +11.4426 q^{83} -1.00000 q^{84} +2.10992 q^{85} +6.04892 q^{86} -0.405813 q^{87} -0.356896 q^{88} -4.80194 q^{89} +0.554958 q^{90} -2.44504 q^{92} -4.74094 q^{93} +0.603875 q^{94} +3.18598 q^{95} +1.00000 q^{96} -2.65279 q^{97} -1.00000 q^{98} +0.356896 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 3q^{2} - 3q^{3} + 3q^{4} - 2q^{5} + 3q^{6} + 3q^{7} - 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 3q^{2} - 3q^{3} + 3q^{4} - 2q^{5} + 3q^{6} + 3q^{7} - 3q^{8} + 3q^{9} + 2q^{10} - 3q^{11} - 3q^{12} - 3q^{14} + 2q^{15} + 3q^{16} - 7q^{17} - 3q^{18} - 3q^{19} - 2q^{20} - 3q^{21} + 3q^{22} - 7q^{23} + 3q^{24} - 9q^{25} - 3q^{27} + 3q^{28} - 12q^{29} - 2q^{30} - 3q^{32} + 3q^{33} + 7q^{34} - 2q^{35} + 3q^{36} + 8q^{37} + 3q^{38} + 2q^{40} + 2q^{41} + 3q^{42} - 9q^{43} - 3q^{44} - 2q^{45} + 7q^{46} + 7q^{47} - 3q^{48} + 3q^{49} + 9q^{50} + 7q^{51} + 3q^{54} - 5q^{55} - 3q^{56} + 3q^{57} + 12q^{58} + 2q^{59} + 2q^{60} + 3q^{61} + 3q^{63} + 3q^{64} - 3q^{66} + 32q^{67} - 7q^{68} + 7q^{69} + 2q^{70} - 6q^{71} - 3q^{72} + 13q^{73} - 8q^{74} + 9q^{75} - 3q^{76} - 3q^{77} + 12q^{79} - 2q^{80} + 3q^{81} - 2q^{82} - 7q^{83} - 3q^{84} + 7q^{85} + 9q^{86} + 12q^{87} + 3q^{88} - 10q^{89} + 2q^{90} - 7q^{92} - 7q^{94} - 5q^{95} + 3q^{96} + 10q^{97} - 3q^{98} - 3q^{99} + O(q^{100}) \)

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
\(5\) −0.554958 −0.248185 −0.124092 0.992271i \(-0.539602\pi\)
−0.124092 + 0.992271i \(0.539602\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.554958 0.175493
\(11\) 0.356896 0.107608 0.0538041 0.998552i \(-0.482865\pi\)
0.0538041 + 0.998552i \(0.482865\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 0.554958 0.143290
\(16\) 1.00000 0.250000
\(17\) −3.80194 −0.922105 −0.461053 0.887373i \(-0.652528\pi\)
−0.461053 + 0.887373i \(0.652528\pi\)
\(18\) −1.00000 −0.235702
\(19\) −5.74094 −1.31706 −0.658531 0.752554i \(-0.728822\pi\)
−0.658531 + 0.752554i \(0.728822\pi\)
\(20\) −0.554958 −0.124092
\(21\) −1.00000 −0.218218
\(22\) −0.356896 −0.0760905
\(23\) −2.44504 −0.509826 −0.254913 0.966964i \(-0.582047\pi\)
−0.254913 + 0.966964i \(0.582047\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.69202 −0.938404
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.00000 0.188982
\(29\) 0.405813 0.0753576 0.0376788 0.999290i \(-0.488004\pi\)
0.0376788 + 0.999290i \(0.488004\pi\)
\(30\) −0.554958 −0.101321
\(31\) 4.74094 0.851498 0.425749 0.904841i \(-0.360011\pi\)
0.425749 + 0.904841i \(0.360011\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.356896 −0.0621276
\(34\) 3.80194 0.652027
\(35\) −0.554958 −0.0938050
\(36\) 1.00000 0.166667
\(37\) −3.54288 −0.582445 −0.291223 0.956655i \(-0.594062\pi\)
−0.291223 + 0.956655i \(0.594062\pi\)
\(38\) 5.74094 0.931303
\(39\) 0 0
\(40\) 0.554958 0.0877466
\(41\) 3.26875 0.510493 0.255246 0.966876i \(-0.417843\pi\)
0.255246 + 0.966876i \(0.417843\pi\)
\(42\) 1.00000 0.154303
\(43\) −6.04892 −0.922451 −0.461226 0.887283i \(-0.652590\pi\)
−0.461226 + 0.887283i \(0.652590\pi\)
\(44\) 0.356896 0.0538041
\(45\) −0.554958 −0.0827283
\(46\) 2.44504 0.360502
\(47\) −0.603875 −0.0880843 −0.0440421 0.999030i \(-0.514024\pi\)
−0.0440421 + 0.999030i \(0.514024\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) 4.69202 0.663552
\(51\) 3.80194 0.532378
\(52\) 0 0
\(53\) −1.35690 −0.186384 −0.0931920 0.995648i \(-0.529707\pi\)
−0.0931920 + 0.995648i \(0.529707\pi\)
\(54\) 1.00000 0.136083
\(55\) −0.198062 −0.0267067
\(56\) −1.00000 −0.133631
\(57\) 5.74094 0.760406
\(58\) −0.405813 −0.0532859
\(59\) −5.54288 −0.721621 −0.360811 0.932639i \(-0.617500\pi\)
−0.360811 + 0.932639i \(0.617500\pi\)
\(60\) 0.554958 0.0716448
\(61\) 4.38404 0.561319 0.280660 0.959807i \(-0.409447\pi\)
0.280660 + 0.959807i \(0.409447\pi\)
\(62\) −4.74094 −0.602100
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0.356896 0.0439308
\(67\) 15.2959 1.86869 0.934346 0.356368i \(-0.115985\pi\)
0.934346 + 0.356368i \(0.115985\pi\)
\(68\) −3.80194 −0.461053
\(69\) 2.44504 0.294348
\(70\) 0.554958 0.0663302
\(71\) −7.42758 −0.881492 −0.440746 0.897632i \(-0.645286\pi\)
−0.440746 + 0.897632i \(0.645286\pi\)
\(72\) −1.00000 −0.117851
\(73\) 11.2295 1.31432 0.657158 0.753753i \(-0.271758\pi\)
0.657158 + 0.753753i \(0.271758\pi\)
\(74\) 3.54288 0.411851
\(75\) 4.69202 0.541788
\(76\) −5.74094 −0.658531
\(77\) 0.356896 0.0406721
\(78\) 0 0
\(79\) −1.76271 −0.198320 −0.0991601 0.995071i \(-0.531616\pi\)
−0.0991601 + 0.995071i \(0.531616\pi\)
\(80\) −0.554958 −0.0620462
\(81\) 1.00000 0.111111
\(82\) −3.26875 −0.360973
\(83\) 11.4426 1.25599 0.627997 0.778216i \(-0.283875\pi\)
0.627997 + 0.778216i \(0.283875\pi\)
\(84\) −1.00000 −0.109109
\(85\) 2.10992 0.228853
\(86\) 6.04892 0.652272
\(87\) −0.405813 −0.0435077
\(88\) −0.356896 −0.0380452
\(89\) −4.80194 −0.509004 −0.254502 0.967072i \(-0.581912\pi\)
−0.254502 + 0.967072i \(0.581912\pi\)
\(90\) 0.554958 0.0584977
\(91\) 0 0
\(92\) −2.44504 −0.254913
\(93\) −4.74094 −0.491612
\(94\) 0.603875 0.0622850
\(95\) 3.18598 0.326875
\(96\) 1.00000 0.102062
\(97\) −2.65279 −0.269350 −0.134675 0.990890i \(-0.542999\pi\)
−0.134675 + 0.990890i \(0.542999\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0.356896 0.0358694
\(100\) −4.69202 −0.469202
\(101\) −9.10752 −0.906232 −0.453116 0.891451i \(-0.649688\pi\)
−0.453116 + 0.891451i \(0.649688\pi\)
\(102\) −3.80194 −0.376448
\(103\) 12.2784 1.20983 0.604915 0.796290i \(-0.293207\pi\)
0.604915 + 0.796290i \(0.293207\pi\)
\(104\) 0 0
\(105\) 0.554958 0.0541584
\(106\) 1.35690 0.131793
\(107\) 6.08575 0.588332 0.294166 0.955754i \(-0.404958\pi\)
0.294166 + 0.955754i \(0.404958\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 20.2010 1.93491 0.967455 0.253044i \(-0.0814319\pi\)
0.967455 + 0.253044i \(0.0814319\pi\)
\(110\) 0.198062 0.0188845
\(111\) 3.54288 0.336275
\(112\) 1.00000 0.0944911
\(113\) 2.81700 0.265001 0.132501 0.991183i \(-0.457699\pi\)
0.132501 + 0.991183i \(0.457699\pi\)
\(114\) −5.74094 −0.537688
\(115\) 1.35690 0.126531
\(116\) 0.405813 0.0376788
\(117\) 0 0
\(118\) 5.54288 0.510263
\(119\) −3.80194 −0.348523
\(120\) −0.554958 −0.0506605
\(121\) −10.8726 −0.988420
\(122\) −4.38404 −0.396913
\(123\) −3.26875 −0.294733
\(124\) 4.74094 0.425749
\(125\) 5.37867 0.481083
\(126\) −1.00000 −0.0890871
\(127\) −1.40581 −0.124746 −0.0623729 0.998053i \(-0.519867\pi\)
−0.0623729 + 0.998053i \(0.519867\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 6.04892 0.532577
\(130\) 0 0
\(131\) −9.50365 −0.830338 −0.415169 0.909744i \(-0.636277\pi\)
−0.415169 + 0.909744i \(0.636277\pi\)
\(132\) −0.356896 −0.0310638
\(133\) −5.74094 −0.497803
\(134\) −15.2959 −1.32136
\(135\) 0.554958 0.0477632
\(136\) 3.80194 0.326013
\(137\) −1.03684 −0.0885829 −0.0442914 0.999019i \(-0.514103\pi\)
−0.0442914 + 0.999019i \(0.514103\pi\)
\(138\) −2.44504 −0.208136
\(139\) 8.74094 0.741397 0.370698 0.928753i \(-0.379118\pi\)
0.370698 + 0.928753i \(0.379118\pi\)
\(140\) −0.554958 −0.0469025
\(141\) 0.603875 0.0508555
\(142\) 7.42758 0.623309
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −0.225209 −0.0187026
\(146\) −11.2295 −0.929362
\(147\) −1.00000 −0.0824786
\(148\) −3.54288 −0.291223
\(149\) −9.38835 −0.769124 −0.384562 0.923099i \(-0.625648\pi\)
−0.384562 + 0.923099i \(0.625648\pi\)
\(150\) −4.69202 −0.383102
\(151\) −8.66248 −0.704943 −0.352471 0.935823i \(-0.614659\pi\)
−0.352471 + 0.935823i \(0.614659\pi\)
\(152\) 5.74094 0.465652
\(153\) −3.80194 −0.307368
\(154\) −0.356896 −0.0287595
\(155\) −2.63102 −0.211329
\(156\) 0 0
\(157\) 7.10992 0.567433 0.283717 0.958908i \(-0.408433\pi\)
0.283717 + 0.958908i \(0.408433\pi\)
\(158\) 1.76271 0.140234
\(159\) 1.35690 0.107609
\(160\) 0.554958 0.0438733
\(161\) −2.44504 −0.192696
\(162\) −1.00000 −0.0785674
\(163\) 18.8931 1.47982 0.739910 0.672706i \(-0.234868\pi\)
0.739910 + 0.672706i \(0.234868\pi\)
\(164\) 3.26875 0.255246
\(165\) 0.198062 0.0154191
\(166\) −11.4426 −0.888122
\(167\) −3.13169 −0.242337 −0.121169 0.992632i \(-0.538664\pi\)
−0.121169 + 0.992632i \(0.538664\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) −2.10992 −0.161823
\(171\) −5.74094 −0.439021
\(172\) −6.04892 −0.461226
\(173\) −4.39612 −0.334231 −0.167116 0.985937i \(-0.553445\pi\)
−0.167116 + 0.985937i \(0.553445\pi\)
\(174\) 0.405813 0.0307646
\(175\) −4.69202 −0.354683
\(176\) 0.356896 0.0269020
\(177\) 5.54288 0.416628
\(178\) 4.80194 0.359920
\(179\) −16.9215 −1.26478 −0.632388 0.774652i \(-0.717925\pi\)
−0.632388 + 0.774652i \(0.717925\pi\)
\(180\) −0.554958 −0.0413641
\(181\) −9.71917 −0.722420 −0.361210 0.932484i \(-0.617636\pi\)
−0.361210 + 0.932484i \(0.617636\pi\)
\(182\) 0 0
\(183\) −4.38404 −0.324078
\(184\) 2.44504 0.180251
\(185\) 1.96615 0.144554
\(186\) 4.74094 0.347622
\(187\) −1.35690 −0.0992261
\(188\) −0.603875 −0.0440421
\(189\) −1.00000 −0.0727393
\(190\) −3.18598 −0.231135
\(191\) 3.40581 0.246436 0.123218 0.992380i \(-0.460679\pi\)
0.123218 + 0.992380i \(0.460679\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 17.0804 1.22947 0.614736 0.788733i \(-0.289262\pi\)
0.614736 + 0.788733i \(0.289262\pi\)
\(194\) 2.65279 0.190459
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −3.89977 −0.277847 −0.138924 0.990303i \(-0.544364\pi\)
−0.138924 + 0.990303i \(0.544364\pi\)
\(198\) −0.356896 −0.0253635
\(199\) 3.52111 0.249605 0.124802 0.992182i \(-0.460170\pi\)
0.124802 + 0.992182i \(0.460170\pi\)
\(200\) 4.69202 0.331776
\(201\) −15.2959 −1.07889
\(202\) 9.10752 0.640803
\(203\) 0.405813 0.0284825
\(204\) 3.80194 0.266189
\(205\) −1.81402 −0.126697
\(206\) −12.2784 −0.855479
\(207\) −2.44504 −0.169942
\(208\) 0 0
\(209\) −2.04892 −0.141727
\(210\) −0.554958 −0.0382957
\(211\) −3.18598 −0.219332 −0.109666 0.993968i \(-0.534978\pi\)
−0.109666 + 0.993968i \(0.534978\pi\)
\(212\) −1.35690 −0.0931920
\(213\) 7.42758 0.508930
\(214\) −6.08575 −0.416014
\(215\) 3.35690 0.228938
\(216\) 1.00000 0.0680414
\(217\) 4.74094 0.321836
\(218\) −20.2010 −1.36819
\(219\) −11.2295 −0.758821
\(220\) −0.198062 −0.0133534
\(221\) 0 0
\(222\) −3.54288 −0.237782
\(223\) −3.35450 −0.224634 −0.112317 0.993672i \(-0.535827\pi\)
−0.112317 + 0.993672i \(0.535827\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −4.69202 −0.312801
\(226\) −2.81700 −0.187384
\(227\) 10.8804 0.722157 0.361079 0.932535i \(-0.382409\pi\)
0.361079 + 0.932535i \(0.382409\pi\)
\(228\) 5.74094 0.380203
\(229\) 12.0804 0.798294 0.399147 0.916887i \(-0.369306\pi\)
0.399147 + 0.916887i \(0.369306\pi\)
\(230\) −1.35690 −0.0894711
\(231\) −0.356896 −0.0234820
\(232\) −0.405813 −0.0266429
\(233\) −23.8810 −1.56450 −0.782248 0.622968i \(-0.785927\pi\)
−0.782248 + 0.622968i \(0.785927\pi\)
\(234\) 0 0
\(235\) 0.335126 0.0218612
\(236\) −5.54288 −0.360811
\(237\) 1.76271 0.114500
\(238\) 3.80194 0.246443
\(239\) 17.4819 1.13081 0.565404 0.824814i \(-0.308720\pi\)
0.565404 + 0.824814i \(0.308720\pi\)
\(240\) 0.554958 0.0358224
\(241\) 2.22521 0.143338 0.0716692 0.997428i \(-0.477167\pi\)
0.0716692 + 0.997428i \(0.477167\pi\)
\(242\) 10.8726 0.698919
\(243\) −1.00000 −0.0641500
\(244\) 4.38404 0.280660
\(245\) −0.554958 −0.0354550
\(246\) 3.26875 0.208408
\(247\) 0 0
\(248\) −4.74094 −0.301050
\(249\) −11.4426 −0.725148
\(250\) −5.37867 −0.340177
\(251\) −8.30665 −0.524311 −0.262156 0.965026i \(-0.584433\pi\)
−0.262156 + 0.965026i \(0.584433\pi\)
\(252\) 1.00000 0.0629941
\(253\) −0.872625 −0.0548615
\(254\) 1.40581 0.0882086
\(255\) −2.10992 −0.132128
\(256\) 1.00000 0.0625000
\(257\) 4.66248 0.290838 0.145419 0.989370i \(-0.453547\pi\)
0.145419 + 0.989370i \(0.453547\pi\)
\(258\) −6.04892 −0.376589
\(259\) −3.54288 −0.220144
\(260\) 0 0
\(261\) 0.405813 0.0251192
\(262\) 9.50365 0.587137
\(263\) −20.6015 −1.27034 −0.635171 0.772372i \(-0.719070\pi\)
−0.635171 + 0.772372i \(0.719070\pi\)
\(264\) 0.356896 0.0219654
\(265\) 0.753020 0.0462577
\(266\) 5.74094 0.352000
\(267\) 4.80194 0.293874
\(268\) 15.2959 0.934346
\(269\) 32.3032 1.96956 0.984780 0.173804i \(-0.0556060\pi\)
0.984780 + 0.173804i \(0.0556060\pi\)
\(270\) −0.554958 −0.0337737
\(271\) 5.21850 0.317002 0.158501 0.987359i \(-0.449334\pi\)
0.158501 + 0.987359i \(0.449334\pi\)
\(272\) −3.80194 −0.230526
\(273\) 0 0
\(274\) 1.03684 0.0626375
\(275\) −1.67456 −0.100980
\(276\) 2.44504 0.147174
\(277\) −6.27950 −0.377299 −0.188649 0.982045i \(-0.560411\pi\)
−0.188649 + 0.982045i \(0.560411\pi\)
\(278\) −8.74094 −0.524247
\(279\) 4.74094 0.283833
\(280\) 0.554958 0.0331651
\(281\) −0.423272 −0.0252503 −0.0126251 0.999920i \(-0.504019\pi\)
−0.0126251 + 0.999920i \(0.504019\pi\)
\(282\) −0.603875 −0.0359603
\(283\) 10.9946 0.653563 0.326781 0.945100i \(-0.394036\pi\)
0.326781 + 0.945100i \(0.394036\pi\)
\(284\) −7.42758 −0.440746
\(285\) −3.18598 −0.188721
\(286\) 0 0
\(287\) 3.26875 0.192948
\(288\) −1.00000 −0.0589256
\(289\) −2.54527 −0.149722
\(290\) 0.225209 0.0132247
\(291\) 2.65279 0.155509
\(292\) 11.2295 0.657158
\(293\) 15.3177 0.894868 0.447434 0.894317i \(-0.352338\pi\)
0.447434 + 0.894317i \(0.352338\pi\)
\(294\) 1.00000 0.0583212
\(295\) 3.07606 0.179095
\(296\) 3.54288 0.205926
\(297\) −0.356896 −0.0207092
\(298\) 9.38835 0.543853
\(299\) 0 0
\(300\) 4.69202 0.270894
\(301\) −6.04892 −0.348654
\(302\) 8.66248 0.498470
\(303\) 9.10752 0.523214
\(304\) −5.74094 −0.329265
\(305\) −2.43296 −0.139311
\(306\) 3.80194 0.217342
\(307\) 19.8280 1.13164 0.565822 0.824527i \(-0.308559\pi\)
0.565822 + 0.824527i \(0.308559\pi\)
\(308\) 0.356896 0.0203360
\(309\) −12.2784 −0.698496
\(310\) 2.63102 0.149432
\(311\) 24.6461 1.39755 0.698776 0.715341i \(-0.253729\pi\)
0.698776 + 0.715341i \(0.253729\pi\)
\(312\) 0 0
\(313\) 11.2034 0.633256 0.316628 0.948550i \(-0.397449\pi\)
0.316628 + 0.948550i \(0.397449\pi\)
\(314\) −7.10992 −0.401236
\(315\) −0.554958 −0.0312683
\(316\) −1.76271 −0.0991601
\(317\) 24.8756 1.39715 0.698577 0.715535i \(-0.253817\pi\)
0.698577 + 0.715535i \(0.253817\pi\)
\(318\) −1.35690 −0.0760909
\(319\) 0.144833 0.00810909
\(320\) −0.554958 −0.0310231
\(321\) −6.08575 −0.339674
\(322\) 2.44504 0.136257
\(323\) 21.8267 1.21447
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −18.8931 −1.04639
\(327\) −20.2010 −1.11712
\(328\) −3.26875 −0.180487
\(329\) −0.603875 −0.0332927
\(330\) −0.198062 −0.0109030
\(331\) −22.7289 −1.24929 −0.624645 0.780908i \(-0.714757\pi\)
−0.624645 + 0.780908i \(0.714757\pi\)
\(332\) 11.4426 0.627997
\(333\) −3.54288 −0.194148
\(334\) 3.13169 0.171358
\(335\) −8.48858 −0.463781
\(336\) −1.00000 −0.0545545
\(337\) 10.5743 0.576021 0.288010 0.957627i \(-0.407006\pi\)
0.288010 + 0.957627i \(0.407006\pi\)
\(338\) 0 0
\(339\) −2.81700 −0.152999
\(340\) 2.10992 0.114426
\(341\) 1.69202 0.0916281
\(342\) 5.74094 0.310434
\(343\) 1.00000 0.0539949
\(344\) 6.04892 0.326136
\(345\) −1.35690 −0.0730528
\(346\) 4.39612 0.236337
\(347\) 7.57002 0.406380 0.203190 0.979139i \(-0.434869\pi\)
0.203190 + 0.979139i \(0.434869\pi\)
\(348\) −0.405813 −0.0217539
\(349\) 5.50066 0.294444 0.147222 0.989103i \(-0.452967\pi\)
0.147222 + 0.989103i \(0.452967\pi\)
\(350\) 4.69202 0.250799
\(351\) 0 0
\(352\) −0.356896 −0.0190226
\(353\) 33.0508 1.75912 0.879559 0.475789i \(-0.157838\pi\)
0.879559 + 0.475789i \(0.157838\pi\)
\(354\) −5.54288 −0.294601
\(355\) 4.12200 0.218773
\(356\) −4.80194 −0.254502
\(357\) 3.80194 0.201220
\(358\) 16.9215 0.894331
\(359\) 11.8702 0.626487 0.313243 0.949673i \(-0.398584\pi\)
0.313243 + 0.949673i \(0.398584\pi\)
\(360\) 0.554958 0.0292489
\(361\) 13.9584 0.734651
\(362\) 9.71917 0.510828
\(363\) 10.8726 0.570665
\(364\) 0 0
\(365\) −6.23191 −0.326193
\(366\) 4.38404 0.229158
\(367\) −2.46980 −0.128922 −0.0644612 0.997920i \(-0.520533\pi\)
−0.0644612 + 0.997920i \(0.520533\pi\)
\(368\) −2.44504 −0.127457
\(369\) 3.26875 0.170164
\(370\) −1.96615 −0.102215
\(371\) −1.35690 −0.0704465
\(372\) −4.74094 −0.245806
\(373\) −9.28514 −0.480766 −0.240383 0.970678i \(-0.577273\pi\)
−0.240383 + 0.970678i \(0.577273\pi\)
\(374\) 1.35690 0.0701634
\(375\) −5.37867 −0.277753
\(376\) 0.603875 0.0311425
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 0.292913 0.0150459 0.00752297 0.999972i \(-0.497605\pi\)
0.00752297 + 0.999972i \(0.497605\pi\)
\(380\) 3.18598 0.163437
\(381\) 1.40581 0.0720220
\(382\) −3.40581 −0.174257
\(383\) −28.2446 −1.44323 −0.721615 0.692294i \(-0.756600\pi\)
−0.721615 + 0.692294i \(0.756600\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.198062 −0.0100942
\(386\) −17.0804 −0.869368
\(387\) −6.04892 −0.307484
\(388\) −2.65279 −0.134675
\(389\) −23.1618 −1.17435 −0.587175 0.809460i \(-0.699760\pi\)
−0.587175 + 0.809460i \(0.699760\pi\)
\(390\) 0 0
\(391\) 9.29590 0.470114
\(392\) −1.00000 −0.0505076
\(393\) 9.50365 0.479396
\(394\) 3.89977 0.196468
\(395\) 0.978230 0.0492201
\(396\) 0.356896 0.0179347
\(397\) 21.8767 1.09796 0.548979 0.835836i \(-0.315017\pi\)
0.548979 + 0.835836i \(0.315017\pi\)
\(398\) −3.52111 −0.176497
\(399\) 5.74094 0.287406
\(400\) −4.69202 −0.234601
\(401\) −15.3381 −0.765949 −0.382974 0.923759i \(-0.625100\pi\)
−0.382974 + 0.923759i \(0.625100\pi\)
\(402\) 15.2959 0.762890
\(403\) 0 0
\(404\) −9.10752 −0.453116
\(405\) −0.554958 −0.0275761
\(406\) −0.405813 −0.0201402
\(407\) −1.26444 −0.0626759
\(408\) −3.80194 −0.188224
\(409\) −18.6383 −0.921606 −0.460803 0.887503i \(-0.652438\pi\)
−0.460803 + 0.887503i \(0.652438\pi\)
\(410\) 1.81402 0.0895880
\(411\) 1.03684 0.0511433
\(412\) 12.2784 0.604915
\(413\) −5.54288 −0.272747
\(414\) 2.44504 0.120167
\(415\) −6.35019 −0.311719
\(416\) 0 0
\(417\) −8.74094 −0.428046
\(418\) 2.04892 0.100216
\(419\) 39.2258 1.91631 0.958153 0.286257i \(-0.0924111\pi\)
0.958153 + 0.286257i \(0.0924111\pi\)
\(420\) 0.554958 0.0270792
\(421\) 7.94139 0.387040 0.193520 0.981096i \(-0.438010\pi\)
0.193520 + 0.981096i \(0.438010\pi\)
\(422\) 3.18598 0.155091
\(423\) −0.603875 −0.0293614
\(424\) 1.35690 0.0658967
\(425\) 17.8388 0.865308
\(426\) −7.42758 −0.359868
\(427\) 4.38404 0.212159
\(428\) 6.08575 0.294166
\(429\) 0 0
\(430\) −3.35690 −0.161884
\(431\) −24.2674 −1.16892 −0.584460 0.811422i \(-0.698694\pi\)
−0.584460 + 0.811422i \(0.698694\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −20.7832 −0.998775 −0.499387 0.866379i \(-0.666441\pi\)
−0.499387 + 0.866379i \(0.666441\pi\)
\(434\) −4.74094 −0.227572
\(435\) 0.225209 0.0107980
\(436\) 20.2010 0.967455
\(437\) 14.0368 0.671473
\(438\) 11.2295 0.536567
\(439\) 38.5502 1.83990 0.919950 0.392036i \(-0.128229\pi\)
0.919950 + 0.392036i \(0.128229\pi\)
\(440\) 0.198062 0.00944225
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −1.59850 −0.0759470 −0.0379735 0.999279i \(-0.512090\pi\)
−0.0379735 + 0.999279i \(0.512090\pi\)
\(444\) 3.54288 0.168137
\(445\) 2.66487 0.126327
\(446\) 3.35450 0.158840
\(447\) 9.38835 0.444054
\(448\) 1.00000 0.0472456
\(449\) −26.2064 −1.23676 −0.618379 0.785880i \(-0.712210\pi\)
−0.618379 + 0.785880i \(0.712210\pi\)
\(450\) 4.69202 0.221184
\(451\) 1.16660 0.0549332
\(452\) 2.81700 0.132501
\(453\) 8.66248 0.406999
\(454\) −10.8804 −0.510642
\(455\) 0 0
\(456\) −5.74094 −0.268844
\(457\) −11.1540 −0.521764 −0.260882 0.965371i \(-0.584013\pi\)
−0.260882 + 0.965371i \(0.584013\pi\)
\(458\) −12.0804 −0.564479
\(459\) 3.80194 0.177459
\(460\) 1.35690 0.0632656
\(461\) −17.9191 −0.834578 −0.417289 0.908774i \(-0.637020\pi\)
−0.417289 + 0.908774i \(0.637020\pi\)
\(462\) 0.356896 0.0166043
\(463\) 11.5453 0.536554 0.268277 0.963342i \(-0.413546\pi\)
0.268277 + 0.963342i \(0.413546\pi\)
\(464\) 0.405813 0.0188394
\(465\) 2.63102 0.122011
\(466\) 23.8810 1.10627
\(467\) −18.4620 −0.854321 −0.427160 0.904176i \(-0.640486\pi\)
−0.427160 + 0.904176i \(0.640486\pi\)
\(468\) 0 0
\(469\) 15.2959 0.706299
\(470\) −0.335126 −0.0154582
\(471\) −7.10992 −0.327608
\(472\) 5.54288 0.255132
\(473\) −2.15883 −0.0992633
\(474\) −1.76271 −0.0809639
\(475\) 26.9366 1.23594
\(476\) −3.80194 −0.174262
\(477\) −1.35690 −0.0621280
\(478\) −17.4819 −0.799602
\(479\) 35.8756 1.63920 0.819599 0.572937i \(-0.194196\pi\)
0.819599 + 0.572937i \(0.194196\pi\)
\(480\) −0.554958 −0.0253303
\(481\) 0 0
\(482\) −2.22521 −0.101356
\(483\) 2.44504 0.111253
\(484\) −10.8726 −0.494210
\(485\) 1.47219 0.0668487
\(486\) 1.00000 0.0453609
\(487\) 1.90648 0.0863907 0.0431954 0.999067i \(-0.486246\pi\)
0.0431954 + 0.999067i \(0.486246\pi\)
\(488\) −4.38404 −0.198456
\(489\) −18.8931 −0.854374
\(490\) 0.554958 0.0250705
\(491\) −17.7536 −0.801209 −0.400605 0.916251i \(-0.631200\pi\)
−0.400605 + 0.916251i \(0.631200\pi\)
\(492\) −3.26875 −0.147367
\(493\) −1.54288 −0.0694877
\(494\) 0 0
\(495\) −0.198062 −0.00890224
\(496\) 4.74094 0.212874
\(497\) −7.42758 −0.333173
\(498\) 11.4426 0.512757
\(499\) 24.8528 1.11256 0.556281 0.830994i \(-0.312228\pi\)
0.556281 + 0.830994i \(0.312228\pi\)
\(500\) 5.37867 0.240541
\(501\) 3.13169 0.139913
\(502\) 8.30665 0.370744
\(503\) 42.3870 1.88994 0.944972 0.327151i \(-0.106089\pi\)
0.944972 + 0.327151i \(0.106089\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 5.05429 0.224913
\(506\) 0.872625 0.0387929
\(507\) 0 0
\(508\) −1.40581 −0.0623729
\(509\) −2.93362 −0.130031 −0.0650153 0.997884i \(-0.520710\pi\)
−0.0650153 + 0.997884i \(0.520710\pi\)
\(510\) 2.10992 0.0934287
\(511\) 11.2295 0.496765
\(512\) −1.00000 −0.0441942
\(513\) 5.74094 0.253469
\(514\) −4.66248 −0.205653
\(515\) −6.81402 −0.300262
\(516\) 6.04892 0.266289
\(517\) −0.215521 −0.00947859
\(518\) 3.54288 0.155665
\(519\) 4.39612 0.192968
\(520\) 0 0
\(521\) −40.1396 −1.75855 −0.879273 0.476318i \(-0.841971\pi\)
−0.879273 + 0.476318i \(0.841971\pi\)
\(522\) −0.405813 −0.0177620
\(523\) −14.8418 −0.648985 −0.324492 0.945888i \(-0.605193\pi\)
−0.324492 + 0.945888i \(0.605193\pi\)
\(524\) −9.50365 −0.415169
\(525\) 4.69202 0.204777
\(526\) 20.6015 0.898267
\(527\) −18.0248 −0.785171
\(528\) −0.356896 −0.0155319
\(529\) −17.0218 −0.740077
\(530\) −0.753020 −0.0327091
\(531\) −5.54288 −0.240540
\(532\) −5.74094 −0.248901
\(533\) 0 0
\(534\) −4.80194 −0.207800
\(535\) −3.37734 −0.146015
\(536\) −15.2959 −0.660682
\(537\) 16.9215 0.730218
\(538\) −32.3032 −1.39269
\(539\) 0.356896 0.0153726
\(540\) 0.554958 0.0238816
\(541\) 39.0127 1.67729 0.838643 0.544682i \(-0.183350\pi\)
0.838643 + 0.544682i \(0.183350\pi\)
\(542\) −5.21850 −0.224154
\(543\) 9.71917 0.417089
\(544\) 3.80194 0.163007
\(545\) −11.2107 −0.480215
\(546\) 0 0
\(547\) 27.0978 1.15862 0.579310 0.815107i \(-0.303322\pi\)
0.579310 + 0.815107i \(0.303322\pi\)
\(548\) −1.03684 −0.0442914
\(549\) 4.38404 0.187106
\(550\) 1.67456 0.0714036
\(551\) −2.32975 −0.0992506
\(552\) −2.44504 −0.104068
\(553\) −1.76271 −0.0749580
\(554\) 6.27950 0.266791
\(555\) −1.96615 −0.0834583
\(556\) 8.74094 0.370698
\(557\) 32.2338 1.36579 0.682896 0.730516i \(-0.260720\pi\)
0.682896 + 0.730516i \(0.260720\pi\)
\(558\) −4.74094 −0.200700
\(559\) 0 0
\(560\) −0.554958 −0.0234513
\(561\) 1.35690 0.0572882
\(562\) 0.423272 0.0178546
\(563\) 15.8237 0.666890 0.333445 0.942770i \(-0.391789\pi\)
0.333445 + 0.942770i \(0.391789\pi\)
\(564\) 0.603875 0.0254277
\(565\) −1.56332 −0.0657693
\(566\) −10.9946 −0.462138
\(567\) 1.00000 0.0419961
\(568\) 7.42758 0.311654
\(569\) −22.0127 −0.922819 −0.461410 0.887187i \(-0.652656\pi\)
−0.461410 + 0.887187i \(0.652656\pi\)
\(570\) 3.18598 0.133446
\(571\) 10.0379 0.420073 0.210037 0.977694i \(-0.432642\pi\)
0.210037 + 0.977694i \(0.432642\pi\)
\(572\) 0 0
\(573\) −3.40581 −0.142280
\(574\) −3.26875 −0.136435
\(575\) 11.4722 0.478423
\(576\) 1.00000 0.0416667
\(577\) 2.85325 0.118782 0.0593911 0.998235i \(-0.481084\pi\)
0.0593911 + 0.998235i \(0.481084\pi\)
\(578\) 2.54527 0.105869
\(579\) −17.0804 −0.709836
\(580\) −0.225209 −0.00935131
\(581\) 11.4426 0.474721
\(582\) −2.65279 −0.109962
\(583\) −0.484271 −0.0200564
\(584\) −11.2295 −0.464681
\(585\) 0 0
\(586\) −15.3177 −0.632767
\(587\) −42.0514 −1.73565 −0.867824 0.496872i \(-0.834482\pi\)
−0.867824 + 0.496872i \(0.834482\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −27.2174 −1.12148
\(590\) −3.07606 −0.126640
\(591\) 3.89977 0.160415
\(592\) −3.54288 −0.145611
\(593\) −0.00909768 −0.000373597 0 −0.000186798 1.00000i \(-0.500059\pi\)
−0.000186798 1.00000i \(0.500059\pi\)
\(594\) 0.356896 0.0146436
\(595\) 2.10992 0.0864981
\(596\) −9.38835 −0.384562
\(597\) −3.52111 −0.144109
\(598\) 0 0
\(599\) 9.13169 0.373111 0.186555 0.982444i \(-0.440268\pi\)
0.186555 + 0.982444i \(0.440268\pi\)
\(600\) −4.69202 −0.191551
\(601\) −10.7791 −0.439689 −0.219844 0.975535i \(-0.570555\pi\)
−0.219844 + 0.975535i \(0.570555\pi\)
\(602\) 6.04892 0.246535
\(603\) 15.2959 0.622897
\(604\) −8.66248 −0.352471
\(605\) 6.03385 0.245311
\(606\) −9.10752 −0.369968
\(607\) −3.04354 −0.123533 −0.0617667 0.998091i \(-0.519673\pi\)
−0.0617667 + 0.998091i \(0.519673\pi\)
\(608\) 5.74094 0.232826
\(609\) −0.405813 −0.0164444
\(610\) 2.43296 0.0985077
\(611\) 0 0
\(612\) −3.80194 −0.153684
\(613\) 21.2228 0.857181 0.428591 0.903499i \(-0.359010\pi\)
0.428591 + 0.903499i \(0.359010\pi\)
\(614\) −19.8280 −0.800194
\(615\) 1.81402 0.0731483
\(616\) −0.356896 −0.0143797
\(617\) 19.1019 0.769013 0.384506 0.923122i \(-0.374372\pi\)
0.384506 + 0.923122i \(0.374372\pi\)
\(618\) 12.2784 0.493911
\(619\) 21.1454 0.849906 0.424953 0.905215i \(-0.360291\pi\)
0.424953 + 0.905215i \(0.360291\pi\)
\(620\) −2.63102 −0.105664
\(621\) 2.44504 0.0981162
\(622\) −24.6461 −0.988218
\(623\) −4.80194 −0.192386
\(624\) 0 0
\(625\) 20.4752 0.819007
\(626\) −11.2034 −0.447779
\(627\) 2.04892 0.0818259
\(628\) 7.10992 0.283717
\(629\) 13.4698 0.537076
\(630\) 0.554958 0.0221101
\(631\) 32.4359 1.29125 0.645627 0.763653i \(-0.276596\pi\)
0.645627 + 0.763653i \(0.276596\pi\)
\(632\) 1.76271 0.0701168
\(633\) 3.18598 0.126631
\(634\) −24.8756 −0.987937
\(635\) 0.780167 0.0309600
\(636\) 1.35690 0.0538044
\(637\) 0 0
\(638\) −0.144833 −0.00573400
\(639\) −7.42758 −0.293831
\(640\) 0.554958 0.0219366
\(641\) 18.4499 0.728729 0.364365 0.931256i \(-0.381286\pi\)
0.364365 + 0.931256i \(0.381286\pi\)
\(642\) 6.08575 0.240186
\(643\) 18.8334 0.742717 0.371358 0.928490i \(-0.378892\pi\)
0.371358 + 0.928490i \(0.378892\pi\)
\(644\) −2.44504 −0.0963481
\(645\) −3.35690 −0.132178
\(646\) −21.8267 −0.858760
\(647\) 47.8049 1.87941 0.939703 0.341992i \(-0.111102\pi\)
0.939703 + 0.341992i \(0.111102\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −1.97823 −0.0776523
\(650\) 0 0
\(651\) −4.74094 −0.185812
\(652\) 18.8931 0.739910
\(653\) 41.1637 1.61086 0.805431 0.592690i \(-0.201934\pi\)
0.805431 + 0.592690i \(0.201934\pi\)
\(654\) 20.2010 0.789923
\(655\) 5.27413 0.206077
\(656\) 3.26875 0.127623
\(657\) 11.2295 0.438105
\(658\) 0.603875 0.0235415
\(659\) 31.9758 1.24560 0.622801 0.782380i \(-0.285995\pi\)
0.622801 + 0.782380i \(0.285995\pi\)
\(660\) 0.198062 0.00770956
\(661\) 43.2567 1.68249 0.841245 0.540655i \(-0.181823\pi\)
0.841245 + 0.540655i \(0.181823\pi\)
\(662\) 22.7289 0.883382
\(663\) 0 0
\(664\) −11.4426 −0.444061
\(665\) 3.18598 0.123547
\(666\) 3.54288 0.137284
\(667\) −0.992230 −0.0384193
\(668\) −3.13169 −0.121169
\(669\) 3.35450 0.129693
\(670\) 8.48858 0.327943
\(671\) 1.56465 0.0604025
\(672\) 1.00000 0.0385758
\(673\) −12.6872 −0.489057 −0.244528 0.969642i \(-0.578633\pi\)
−0.244528 + 0.969642i \(0.578633\pi\)
\(674\) −10.5743 −0.407308
\(675\) 4.69202 0.180596
\(676\) 0 0
\(677\) −7.39672 −0.284279 −0.142139 0.989847i \(-0.545398\pi\)
−0.142139 + 0.989847i \(0.545398\pi\)
\(678\) 2.81700 0.108186
\(679\) −2.65279 −0.101805
\(680\) −2.10992 −0.0809116
\(681\) −10.8804 −0.416938
\(682\) −1.69202 −0.0647909
\(683\) −5.76138 −0.220453 −0.110227 0.993906i \(-0.535158\pi\)
−0.110227 + 0.993906i \(0.535158\pi\)
\(684\) −5.74094 −0.219510
\(685\) 0.575400 0.0219849
\(686\) −1.00000 −0.0381802
\(687\) −12.0804 −0.460895
\(688\) −6.04892 −0.230613
\(689\) 0 0
\(690\) 1.35690 0.0516561
\(691\) −3.84894 −0.146420 −0.0732102 0.997317i \(-0.523324\pi\)
−0.0732102 + 0.997317i \(0.523324\pi\)
\(692\) −4.39612 −0.167116
\(693\) 0.356896 0.0135574
\(694\) −7.57002 −0.287354
\(695\) −4.85086 −0.184003
\(696\) 0.405813 0.0153823
\(697\) −12.4276 −0.470728
\(698\) −5.50066 −0.208203
\(699\) 23.8810 0.903262
\(700\) −4.69202 −0.177342
\(701\) 26.4776 1.00004 0.500022 0.866013i \(-0.333325\pi\)
0.500022 + 0.866013i \(0.333325\pi\)
\(702\) 0 0
\(703\) 20.3394 0.767116
\(704\) 0.356896 0.0134510
\(705\) −0.335126 −0.0126216
\(706\) −33.0508 −1.24388
\(707\) −9.10752 −0.342524
\(708\) 5.54288 0.208314
\(709\) −19.4886 −0.731909 −0.365955 0.930633i \(-0.619257\pi\)
−0.365955 + 0.930633i \(0.619257\pi\)
\(710\) −4.12200 −0.154696
\(711\) −1.76271 −0.0661068
\(712\) 4.80194 0.179960
\(713\) −11.5918 −0.434116
\(714\) −3.80194 −0.142284
\(715\) 0 0
\(716\) −16.9215 −0.632388
\(717\) −17.4819 −0.652873
\(718\) −11.8702 −0.442993
\(719\) 48.2140 1.79808 0.899039 0.437868i \(-0.144266\pi\)
0.899039 + 0.437868i \(0.144266\pi\)
\(720\) −0.554958 −0.0206821
\(721\) 12.2784 0.457273
\(722\) −13.9584 −0.519477
\(723\) −2.22521 −0.0827564
\(724\) −9.71917 −0.361210
\(725\) −1.90408 −0.0707159
\(726\) −10.8726 −0.403521
\(727\) −15.6987 −0.582234 −0.291117 0.956688i \(-0.594027\pi\)
−0.291117 + 0.956688i \(0.594027\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.23191 0.230653
\(731\) 22.9976 0.850597
\(732\) −4.38404 −0.162039
\(733\) −34.5478 −1.27605 −0.638026 0.770015i \(-0.720249\pi\)
−0.638026 + 0.770015i \(0.720249\pi\)
\(734\) 2.46980 0.0911618
\(735\) 0.554958 0.0204699
\(736\) 2.44504 0.0901254
\(737\) 5.45904 0.201086
\(738\) −3.26875 −0.120324
\(739\) 38.3739 1.41161 0.705803 0.708408i \(-0.250586\pi\)
0.705803 + 0.708408i \(0.250586\pi\)
\(740\) 1.96615 0.0722770
\(741\) 0 0
\(742\) 1.35690 0.0498132
\(743\) 20.3110 0.745137 0.372568 0.928005i \(-0.378477\pi\)
0.372568 + 0.928005i \(0.378477\pi\)
\(744\) 4.74094 0.173811
\(745\) 5.21014 0.190885
\(746\) 9.28514 0.339953
\(747\) 11.4426 0.418665
\(748\) −1.35690 −0.0496130
\(749\) 6.08575 0.222369
\(750\) 5.37867 0.196401
\(751\) 18.8552 0.688035 0.344017 0.938963i \(-0.388212\pi\)
0.344017 + 0.938963i \(0.388212\pi\)
\(752\) −0.603875 −0.0220211
\(753\) 8.30665 0.302711
\(754\) 0 0
\(755\) 4.80731 0.174956
\(756\) −1.00000 −0.0363696
\(757\) 3.10885 0.112993 0.0564966 0.998403i \(-0.482007\pi\)
0.0564966 + 0.998403i \(0.482007\pi\)
\(758\) −0.292913 −0.0106391
\(759\) 0.872625 0.0316743
\(760\) −3.18598 −0.115568
\(761\) −48.7928 −1.76874 −0.884370 0.466787i \(-0.845411\pi\)
−0.884370 + 0.466787i \(0.845411\pi\)
\(762\) −1.40581 −0.0509272
\(763\) 20.2010 0.731327
\(764\) 3.40581 0.123218
\(765\) 2.10992 0.0762842
\(766\) 28.2446 1.02052
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −9.82610 −0.354338 −0.177169 0.984180i \(-0.556694\pi\)
−0.177169 + 0.984180i \(0.556694\pi\)
\(770\) 0.198062 0.00713767
\(771\) −4.66248 −0.167915
\(772\) 17.0804 0.614736
\(773\) 4.30260 0.154754 0.0773769 0.997002i \(-0.475346\pi\)
0.0773769 + 0.997002i \(0.475346\pi\)
\(774\) 6.04892 0.217424
\(775\) −22.2446 −0.799049
\(776\) 2.65279 0.0952297
\(777\) 3.54288 0.127100
\(778\) 23.1618 0.830391
\(779\) −18.7657 −0.672351
\(780\) 0 0
\(781\) −2.65087 −0.0948557
\(782\) −9.29590 −0.332421
\(783\) −0.405813 −0.0145026
\(784\) 1.00000 0.0357143
\(785\) −3.94571 −0.140828
\(786\) −9.50365 −0.338984
\(787\) −30.7904 −1.09756 −0.548780 0.835967i \(-0.684908\pi\)
−0.548780 + 0.835967i \(0.684908\pi\)
\(788\) −3.89977 −0.138924
\(789\) 20.6015 0.733432
\(790\) −0.978230 −0.0348039
\(791\) 2.81700 0.100161
\(792\) −0.356896 −0.0126817
\(793\) 0 0
\(794\) −21.8767 −0.776374
\(795\) −0.753020 −0.0267069
\(796\) 3.52111 0.124802
\(797\) −9.83877 −0.348507 −0.174254 0.984701i \(-0.555751\pi\)
−0.174254 + 0.984701i \(0.555751\pi\)
\(798\) −5.74094 −0.203227
\(799\) 2.29590 0.0812230
\(800\) 4.69202 0.165888
\(801\) −4.80194 −0.169668
\(802\) 15.3381 0.541607
\(803\) 4.00777 0.141431
\(804\) −15.2959 −0.539445
\(805\) 1.35690 0.0478243
\(806\) 0 0
\(807\) −32.3032 −1.13713
\(808\) 9.10752 0.320402
\(809\) 32.8364 1.15447 0.577233 0.816580i \(-0.304133\pi\)
0.577233 + 0.816580i \(0.304133\pi\)
\(810\) 0.554958 0.0194992
\(811\) −27.1420 −0.953083 −0.476542 0.879152i \(-0.658110\pi\)
−0.476542 + 0.879152i \(0.658110\pi\)
\(812\) 0.405813 0.0142413
\(813\) −5.21850 −0.183021
\(814\) 1.26444 0.0443185
\(815\) −10.4849 −0.367269
\(816\) 3.80194 0.133094
\(817\) 34.7265 1.21493
\(818\) 18.6383 0.651674
\(819\) 0 0
\(820\) −1.81402 −0.0633483
\(821\) 30.8896 1.07805 0.539027 0.842288i \(-0.318792\pi\)
0.539027 + 0.842288i \(0.318792\pi\)
\(822\) −1.03684 −0.0361638
\(823\) −10.5284 −0.366997 −0.183499 0.983020i \(-0.558742\pi\)
−0.183499 + 0.983020i \(0.558742\pi\)
\(824\) −12.2784 −0.427740
\(825\) 1.67456 0.0583008
\(826\) 5.54288 0.192861
\(827\) −46.2573 −1.60852 −0.804261 0.594276i \(-0.797439\pi\)
−0.804261 + 0.594276i \(0.797439\pi\)
\(828\) −2.44504 −0.0849711
\(829\) 14.8595 0.516091 0.258046 0.966133i \(-0.416922\pi\)
0.258046 + 0.966133i \(0.416922\pi\)
\(830\) 6.35019 0.220418
\(831\) 6.27950 0.217834
\(832\) 0 0
\(833\) −3.80194 −0.131729
\(834\) 8.74094 0.302674
\(835\) 1.73795 0.0601444
\(836\) −2.04892 −0.0708633
\(837\) −4.74094 −0.163871
\(838\) −39.2258 −1.35503
\(839\) 25.5284 0.881338 0.440669 0.897670i \(-0.354741\pi\)
0.440669 + 0.897670i \(0.354741\pi\)
\(840\) −0.554958 −0.0191479
\(841\) −28.8353 −0.994321
\(842\) −7.94139 −0.273679
\(843\) 0.423272 0.0145782
\(844\) −3.18598 −0.109666
\(845\) 0 0
\(846\) 0.603875 0.0207617
\(847\) −10.8726 −0.373588
\(848\) −1.35690 −0.0465960
\(849\) −10.9946 −0.377334
\(850\) −17.8388 −0.611865
\(851\) 8.66248 0.296946
\(852\) 7.42758 0.254465
\(853\) 21.0640 0.721217 0.360609 0.932717i \(-0.382569\pi\)
0.360609 + 0.932717i \(0.382569\pi\)
\(854\) −4.38404 −0.150019
\(855\) 3.18598 0.108958
\(856\) −6.08575 −0.208007
\(857\) 32.2922 1.10308 0.551540 0.834149i \(-0.314040\pi\)
0.551540 + 0.834149i \(0.314040\pi\)
\(858\) 0 0
\(859\) 24.7700 0.845142 0.422571 0.906330i \(-0.361128\pi\)
0.422571 + 0.906330i \(0.361128\pi\)
\(860\) 3.35690 0.114469
\(861\) −3.26875 −0.111399
\(862\) 24.2674 0.826552
\(863\) −1.51514 −0.0515759 −0.0257880 0.999667i \(-0.508209\pi\)
−0.0257880 + 0.999667i \(0.508209\pi\)
\(864\) 1.00000 0.0340207
\(865\) 2.43967 0.0829511
\(866\) 20.7832 0.706240
\(867\) 2.54527 0.0864419
\(868\) 4.74094 0.160918
\(869\) −0.629104 −0.0213409
\(870\) −0.225209 −0.00763531
\(871\) 0 0
\(872\) −20.2010 −0.684094
\(873\) −2.65279 −0.0897834
\(874\) −14.0368 −0.474803
\(875\) 5.37867 0.181832
\(876\) −11.2295 −0.379410
\(877\) −16.0425 −0.541716 −0.270858 0.962619i \(-0.587307\pi\)
−0.270858 + 0.962619i \(0.587307\pi\)
\(878\) −38.5502 −1.30101
\(879\) −15.3177 −0.516652
\(880\) −0.198062 −0.00667668
\(881\) −18.8452 −0.634911 −0.317456 0.948273i \(-0.602828\pi\)
−0.317456 + 0.948273i \(0.602828\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 41.0092 1.38007 0.690035 0.723776i \(-0.257595\pi\)
0.690035 + 0.723776i \(0.257595\pi\)
\(884\) 0 0
\(885\) −3.07606 −0.103401
\(886\) 1.59850 0.0537026
\(887\) −5.77107 −0.193774 −0.0968868 0.995295i \(-0.530888\pi\)
−0.0968868 + 0.995295i \(0.530888\pi\)
\(888\) −3.54288 −0.118891
\(889\) −1.40581 −0.0471495
\(890\) −2.66487 −0.0893268
\(891\) 0.356896 0.0119565
\(892\) −3.35450 −0.112317
\(893\) 3.46681 0.116012
\(894\) −9.38835 −0.313994
\(895\) 9.39075 0.313898
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 26.2064 0.874520
\(899\) 1.92394 0.0641668
\(900\) −4.69202 −0.156401
\(901\) 5.15883 0.171866
\(902\) −1.16660 −0.0388436
\(903\) 6.04892 0.201295
\(904\) −2.81700 −0.0936921
\(905\) 5.39373 0.179294
\(906\) −8.66248 −0.287792
\(907\) 48.1618 1.59919 0.799593 0.600542i \(-0.205048\pi\)
0.799593 + 0.600542i \(0.205048\pi\)
\(908\) 10.8804 0.361079
\(909\) −9.10752 −0.302077
\(910\) 0 0
\(911\) 9.32736 0.309029 0.154515 0.987991i \(-0.450619\pi\)
0.154515 + 0.987991i \(0.450619\pi\)
\(912\) 5.74094 0.190101
\(913\) 4.08383 0.135155
\(914\) 11.1540 0.368943
\(915\) 2.43296 0.0804312
\(916\) 12.0804 0.399147
\(917\) −9.50365 −0.313838
\(918\) −3.80194 −0.125483
\(919\) −45.0877 −1.48731 −0.743653 0.668566i \(-0.766908\pi\)
−0.743653 + 0.668566i \(0.766908\pi\)
\(920\) −1.35690 −0.0447355
\(921\) −19.8280 −0.653355
\(922\) 17.9191 0.590136
\(923\) 0 0
\(924\) −0.356896 −0.0117410
\(925\) 16.6233 0.546569
\(926\) −11.5453 −0.379401
\(927\) 12.2784 0.403277
\(928\) −0.405813 −0.0133215
\(929\) 31.1704 1.02267 0.511335 0.859382i \(-0.329151\pi\)
0.511335 + 0.859382i \(0.329151\pi\)
\(930\) −2.63102 −0.0862746
\(931\) −5.74094 −0.188152
\(932\) −23.8810 −0.782248
\(933\) −24.6461 −0.806877
\(934\) 18.4620 0.604096
\(935\) 0.753020 0.0246264
\(936\) 0 0
\(937\) 12.4698 0.407370 0.203685 0.979036i \(-0.434708\pi\)
0.203685 + 0.979036i \(0.434708\pi\)
\(938\) −15.2959 −0.499429
\(939\) −11.2034 −0.365610
\(940\) 0.335126 0.0109306
\(941\) 10.9866 0.358153 0.179076 0.983835i \(-0.442689\pi\)
0.179076 + 0.983835i \(0.442689\pi\)
\(942\) 7.10992 0.231654
\(943\) −7.99223 −0.260263
\(944\) −5.54288 −0.180405
\(945\) 0.554958 0.0180528
\(946\) 2.15883 0.0701897
\(947\) −57.7445 −1.87644 −0.938222 0.346033i \(-0.887528\pi\)
−0.938222 + 0.346033i \(0.887528\pi\)
\(948\) 1.76271 0.0572501
\(949\) 0 0
\(950\) −26.9366 −0.873939
\(951\) −24.8756 −0.806647
\(952\) 3.80194 0.123222
\(953\) −38.7942 −1.25667 −0.628333 0.777944i \(-0.716263\pi\)
−0.628333 + 0.777944i \(0.716263\pi\)
\(954\) 1.35690 0.0439311
\(955\) −1.89008 −0.0611617
\(956\) 17.4819 0.565404
\(957\) −0.144833 −0.00468179
\(958\) −35.8756 −1.15909
\(959\) −1.03684 −0.0334812
\(960\) 0.554958 0.0179112
\(961\) −8.52350 −0.274952
\(962\) 0 0
\(963\) 6.08575 0.196111
\(964\) 2.22521 0.0716692
\(965\) −9.47889 −0.305136
\(966\) −2.44504 −0.0786679
\(967\) 41.1588 1.32358 0.661789 0.749690i \(-0.269797\pi\)
0.661789 + 0.749690i \(0.269797\pi\)
\(968\) 10.8726 0.349459
\(969\) −21.8267 −0.701174
\(970\) −1.47219 −0.0472691
\(971\) 30.9084 0.991898 0.495949 0.868352i \(-0.334820\pi\)
0.495949 + 0.868352i \(0.334820\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 8.74094 0.280222
\(974\) −1.90648 −0.0610875
\(975\) 0 0
\(976\) 4.38404 0.140330
\(977\) 40.6249 1.29971 0.649853 0.760060i \(-0.274830\pi\)
0.649853 + 0.760060i \(0.274830\pi\)
\(978\) 18.8931 0.604134
\(979\) −1.71379 −0.0547730
\(980\) −0.554958 −0.0177275
\(981\) 20.2010 0.644970
\(982\) 17.7536 0.566541
\(983\) −36.6335 −1.16843 −0.584214 0.811600i \(-0.698597\pi\)
−0.584214 + 0.811600i \(0.698597\pi\)
\(984\) 3.26875 0.104204
\(985\) 2.16421 0.0689575
\(986\) 1.54288 0.0491352
\(987\) 0.603875 0.0192216
\(988\) 0 0
\(989\) 14.7899 0.470290
\(990\) 0.198062 0.00629483
\(991\) 0.754348 0.0239627 0.0119813 0.999928i \(-0.496186\pi\)
0.0119813 + 0.999928i \(0.496186\pi\)
\(992\) −4.74094 −0.150525
\(993\) 22.7289 0.721278
\(994\) 7.42758 0.235589
\(995\) −1.95407 −0.0619481
\(996\) −11.4426 −0.362574
\(997\) 35.2336 1.11586 0.557929 0.829889i \(-0.311596\pi\)
0.557929 + 0.829889i \(0.311596\pi\)
\(998\) −24.8528 −0.786701
\(999\) 3.54288 0.112092
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.cc.1.2 3
13.12 even 2 7098.2.a.cj.1.2 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cc.1.2 3 1.1 even 1 trivial
7098.2.a.cj.1.2 yes 3 13.12 even 2