Properties

Label 7098.2.a.ck.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 \(0.445042\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.356896 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.356896 q^{10} +3.40581 q^{11} -1.00000 q^{12} -1.00000 q^{14} +0.356896 q^{15} +1.00000 q^{16} -2.66487 q^{17} +1.00000 q^{18} +8.63102 q^{19} -0.356896 q^{20} +1.00000 q^{21} +3.40581 q^{22} +8.29590 q^{23} -1.00000 q^{24} -4.87263 q^{25} -1.00000 q^{27} -1.00000 q^{28} +2.21983 q^{29} +0.356896 q^{30} -3.89977 q^{31} +1.00000 q^{32} -3.40581 q^{33} -2.66487 q^{34} +0.356896 q^{35} +1.00000 q^{36} -11.5308 q^{37} +8.63102 q^{38} -0.356896 q^{40} -6.66487 q^{41} +1.00000 q^{42} +5.82371 q^{43} +3.40581 q^{44} -0.356896 q^{45} +8.29590 q^{46} +4.59179 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.87263 q^{50} +2.66487 q^{51} +13.0858 q^{53} -1.00000 q^{54} -1.21552 q^{55} -1.00000 q^{56} -8.63102 q^{57} +2.21983 q^{58} +13.6039 q^{59} +0.356896 q^{60} -13.5254 q^{61} -3.89977 q^{62} -1.00000 q^{63} +1.00000 q^{64} -3.40581 q^{66} +3.78017 q^{67} -2.66487 q^{68} -8.29590 q^{69} +0.356896 q^{70} -14.1032 q^{71} +1.00000 q^{72} +1.72587 q^{73} -11.5308 q^{74} +4.87263 q^{75} +8.63102 q^{76} -3.40581 q^{77} +4.49396 q^{79} -0.356896 q^{80} +1.00000 q^{81} -6.66487 q^{82} +10.4940 q^{83} +1.00000 q^{84} +0.951083 q^{85} +5.82371 q^{86} -2.21983 q^{87} +3.40581 q^{88} -13.4330 q^{89} -0.356896 q^{90} +8.29590 q^{92} +3.89977 q^{93} +4.59179 q^{94} -3.08038 q^{95} -1.00000 q^{96} +9.28621 q^{97} +1.00000 q^{98} +3.40581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} + 3q^{5} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} + 3q^{5} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + 3q^{10} - 3q^{11} - 3q^{12} - 3q^{14} - 3q^{15} + 3q^{16} - 9q^{17} + 3q^{18} + 11q^{19} + 3q^{20} + 3q^{21} - 3q^{22} + 11q^{23} - 3q^{24} + 2q^{25} - 3q^{27} - 3q^{28} + 8q^{29} - 3q^{30} + 11q^{31} + 3q^{32} + 3q^{33} - 9q^{34} - 3q^{35} + 3q^{36} + 3q^{37} + 11q^{38} + 3q^{40} - 21q^{41} + 3q^{42} + 10q^{43} - 3q^{44} + 3q^{45} + 11q^{46} - 14q^{47} - 3q^{48} + 3q^{49} + 2q^{50} + 9q^{51} + 2q^{53} - 3q^{54} - 24q^{55} - 3q^{56} - 11q^{57} + 8q^{58} + 32q^{59} - 3q^{60} - 6q^{61} + 11q^{62} - 3q^{63} + 3q^{64} + 3q^{66} + 10q^{67} - 9q^{68} - 11q^{69} - 3q^{70} - 21q^{71} + 3q^{72} + 16q^{73} + 3q^{74} - 2q^{75} + 11q^{76} + 3q^{77} + 4q^{79} + 3q^{80} + 3q^{81} - 21q^{82} + 22q^{83} + 3q^{84} + 12q^{85} + 10q^{86} - 8q^{87} - 3q^{88} - 21q^{89} + 3q^{90} + 11q^{92} - 11q^{93} - 14q^{94} + 25q^{95} - 3q^{96} + 36q^{97} + 3q^{98} - 3q^{99} + O(q^{100}) \)

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
\(5\) −0.356896 −0.159609 −0.0798043 0.996811i \(-0.525430\pi\)
−0.0798043 + 0.996811i \(0.525430\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −0.356896 −0.112860
\(11\) 3.40581 1.02689 0.513446 0.858122i \(-0.328369\pi\)
0.513446 + 0.858122i \(0.328369\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) 0.356896 0.0921501
\(16\) 1.00000 0.250000
\(17\) −2.66487 −0.646327 −0.323163 0.946343i \(-0.604746\pi\)
−0.323163 + 0.946343i \(0.604746\pi\)
\(18\) 1.00000 0.235702
\(19\) 8.63102 1.98009 0.990046 0.140743i \(-0.0449491\pi\)
0.990046 + 0.140743i \(0.0449491\pi\)
\(20\) −0.356896 −0.0798043
\(21\) 1.00000 0.218218
\(22\) 3.40581 0.726122
\(23\) 8.29590 1.72981 0.864907 0.501932i \(-0.167377\pi\)
0.864907 + 0.501932i \(0.167377\pi\)
\(24\) −1.00000 −0.204124
\(25\) −4.87263 −0.974525
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) 2.21983 0.412213 0.206106 0.978530i \(-0.433921\pi\)
0.206106 + 0.978530i \(0.433921\pi\)
\(30\) 0.356896 0.0651600
\(31\) −3.89977 −0.700420 −0.350210 0.936671i \(-0.613890\pi\)
−0.350210 + 0.936671i \(0.613890\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.40581 −0.592876
\(34\) −2.66487 −0.457022
\(35\) 0.356896 0.0603264
\(36\) 1.00000 0.166667
\(37\) −11.5308 −1.89565 −0.947826 0.318790i \(-0.896724\pi\)
−0.947826 + 0.318790i \(0.896724\pi\)
\(38\) 8.63102 1.40014
\(39\) 0 0
\(40\) −0.356896 −0.0564302
\(41\) −6.66487 −1.04088 −0.520439 0.853899i \(-0.674232\pi\)
−0.520439 + 0.853899i \(0.674232\pi\)
\(42\) 1.00000 0.154303
\(43\) 5.82371 0.888107 0.444054 0.896000i \(-0.353540\pi\)
0.444054 + 0.896000i \(0.353540\pi\)
\(44\) 3.40581 0.513446
\(45\) −0.356896 −0.0532029
\(46\) 8.29590 1.22316
\(47\) 4.59179 0.669782 0.334891 0.942257i \(-0.391301\pi\)
0.334891 + 0.942257i \(0.391301\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −4.87263 −0.689093
\(51\) 2.66487 0.373157
\(52\) 0 0
\(53\) 13.0858 1.79747 0.898733 0.438496i \(-0.144489\pi\)
0.898733 + 0.438496i \(0.144489\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.21552 −0.163901
\(56\) −1.00000 −0.133631
\(57\) −8.63102 −1.14321
\(58\) 2.21983 0.291478
\(59\) 13.6039 1.77107 0.885537 0.464569i \(-0.153791\pi\)
0.885537 + 0.464569i \(0.153791\pi\)
\(60\) 0.356896 0.0460751
\(61\) −13.5254 −1.73175 −0.865876 0.500258i \(-0.833238\pi\)
−0.865876 + 0.500258i \(0.833238\pi\)
\(62\) −3.89977 −0.495272
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.40581 −0.419227
\(67\) 3.78017 0.461821 0.230910 0.972975i \(-0.425830\pi\)
0.230910 + 0.972975i \(0.425830\pi\)
\(68\) −2.66487 −0.323163
\(69\) −8.29590 −0.998709
\(70\) 0.356896 0.0426572
\(71\) −14.1032 −1.67374 −0.836872 0.547399i \(-0.815618\pi\)
−0.836872 + 0.547399i \(0.815618\pi\)
\(72\) 1.00000 0.117851
\(73\) 1.72587 0.201998 0.100999 0.994887i \(-0.467796\pi\)
0.100999 + 0.994887i \(0.467796\pi\)
\(74\) −11.5308 −1.34043
\(75\) 4.87263 0.562642
\(76\) 8.63102 0.990046
\(77\) −3.40581 −0.388128
\(78\) 0 0
\(79\) 4.49396 0.505610 0.252805 0.967517i \(-0.418647\pi\)
0.252805 + 0.967517i \(0.418647\pi\)
\(80\) −0.356896 −0.0399022
\(81\) 1.00000 0.111111
\(82\) −6.66487 −0.736012
\(83\) 10.4940 1.15186 0.575931 0.817498i \(-0.304640\pi\)
0.575931 + 0.817498i \(0.304640\pi\)
\(84\) 1.00000 0.109109
\(85\) 0.951083 0.103159
\(86\) 5.82371 0.627987
\(87\) −2.21983 −0.237991
\(88\) 3.40581 0.363061
\(89\) −13.4330 −1.42389 −0.711945 0.702235i \(-0.752186\pi\)
−0.711945 + 0.702235i \(0.752186\pi\)
\(90\) −0.356896 −0.0376201
\(91\) 0 0
\(92\) 8.29590 0.864907
\(93\) 3.89977 0.404388
\(94\) 4.59179 0.473607
\(95\) −3.08038 −0.316040
\(96\) −1.00000 −0.102062
\(97\) 9.28621 0.942872 0.471436 0.881900i \(-0.343736\pi\)
0.471436 + 0.881900i \(0.343736\pi\)
\(98\) 1.00000 0.101015
\(99\) 3.40581 0.342297
\(100\) −4.87263 −0.487263
\(101\) −6.33273 −0.630130 −0.315065 0.949070i \(-0.602026\pi\)
−0.315065 + 0.949070i \(0.602026\pi\)
\(102\) 2.66487 0.263862
\(103\) −11.9433 −1.17681 −0.588405 0.808567i \(-0.700244\pi\)
−0.588405 + 0.808567i \(0.700244\pi\)
\(104\) 0 0
\(105\) −0.356896 −0.0348295
\(106\) 13.0858 1.27100
\(107\) −0.356896 −0.0345024 −0.0172512 0.999851i \(-0.505492\pi\)
−0.0172512 + 0.999851i \(0.505492\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 18.5429 1.77609 0.888043 0.459761i \(-0.152065\pi\)
0.888043 + 0.459761i \(0.152065\pi\)
\(110\) −1.21552 −0.115895
\(111\) 11.5308 1.09445
\(112\) −1.00000 −0.0944911
\(113\) −0.274127 −0.0257877 −0.0128938 0.999917i \(-0.504104\pi\)
−0.0128938 + 0.999917i \(0.504104\pi\)
\(114\) −8.63102 −0.808369
\(115\) −2.96077 −0.276093
\(116\) 2.21983 0.206106
\(117\) 0 0
\(118\) 13.6039 1.25234
\(119\) 2.66487 0.244289
\(120\) 0.356896 0.0325800
\(121\) 0.599564 0.0545058
\(122\) −13.5254 −1.22453
\(123\) 6.66487 0.600951
\(124\) −3.89977 −0.350210
\(125\) 3.52350 0.315151
\(126\) −1.00000 −0.0890871
\(127\) 5.42758 0.481620 0.240810 0.970572i \(-0.422587\pi\)
0.240810 + 0.970572i \(0.422587\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.82371 −0.512749
\(130\) 0 0
\(131\) −5.78017 −0.505016 −0.252508 0.967595i \(-0.581255\pi\)
−0.252508 + 0.967595i \(0.581255\pi\)
\(132\) −3.40581 −0.296438
\(133\) −8.63102 −0.748405
\(134\) 3.78017 0.326557
\(135\) 0.356896 0.0307167
\(136\) −2.66487 −0.228511
\(137\) −18.1957 −1.55456 −0.777280 0.629154i \(-0.783401\pi\)
−0.777280 + 0.629154i \(0.783401\pi\)
\(138\) −8.29590 −0.706194
\(139\) 3.21014 0.272281 0.136140 0.990690i \(-0.456530\pi\)
0.136140 + 0.990690i \(0.456530\pi\)
\(140\) 0.356896 0.0301632
\(141\) −4.59179 −0.386699
\(142\) −14.1032 −1.18352
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −0.792249 −0.0657927
\(146\) 1.72587 0.142834
\(147\) −1.00000 −0.0824786
\(148\) −11.5308 −0.947826
\(149\) 18.4698 1.51310 0.756552 0.653933i \(-0.226882\pi\)
0.756552 + 0.653933i \(0.226882\pi\)
\(150\) 4.87263 0.397848
\(151\) 19.2814 1.56910 0.784550 0.620066i \(-0.212894\pi\)
0.784550 + 0.620066i \(0.212894\pi\)
\(152\) 8.63102 0.700068
\(153\) −2.66487 −0.215442
\(154\) −3.40581 −0.274448
\(155\) 1.39181 0.111793
\(156\) 0 0
\(157\) 16.7681 1.33824 0.669119 0.743155i \(-0.266671\pi\)
0.669119 + 0.743155i \(0.266671\pi\)
\(158\) 4.49396 0.357520
\(159\) −13.0858 −1.03777
\(160\) −0.356896 −0.0282151
\(161\) −8.29590 −0.653808
\(162\) 1.00000 0.0785674
\(163\) 5.15346 0.403650 0.201825 0.979422i \(-0.435313\pi\)
0.201825 + 0.979422i \(0.435313\pi\)
\(164\) −6.66487 −0.520439
\(165\) 1.21552 0.0946282
\(166\) 10.4940 0.814489
\(167\) −13.3599 −1.03382 −0.516909 0.856040i \(-0.672918\pi\)
−0.516909 + 0.856040i \(0.672918\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 0.951083 0.0729447
\(171\) 8.63102 0.660031
\(172\) 5.82371 0.444054
\(173\) 14.8509 1.12909 0.564545 0.825402i \(-0.309052\pi\)
0.564545 + 0.825402i \(0.309052\pi\)
\(174\) −2.21983 −0.168285
\(175\) 4.87263 0.368336
\(176\) 3.40581 0.256723
\(177\) −13.6039 −1.02253
\(178\) −13.4330 −1.00684
\(179\) 2.21983 0.165918 0.0829590 0.996553i \(-0.473563\pi\)
0.0829590 + 0.996553i \(0.473563\pi\)
\(180\) −0.356896 −0.0266014
\(181\) 17.2271 1.28048 0.640241 0.768174i \(-0.278834\pi\)
0.640241 + 0.768174i \(0.278834\pi\)
\(182\) 0 0
\(183\) 13.5254 0.999828
\(184\) 8.29590 0.611582
\(185\) 4.11529 0.302562
\(186\) 3.89977 0.285945
\(187\) −9.07606 −0.663708
\(188\) 4.59179 0.334891
\(189\) 1.00000 0.0727393
\(190\) −3.08038 −0.223474
\(191\) 6.58748 0.476653 0.238327 0.971185i \(-0.423401\pi\)
0.238327 + 0.971185i \(0.423401\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 22.4373 1.61507 0.807535 0.589820i \(-0.200801\pi\)
0.807535 + 0.589820i \(0.200801\pi\)
\(194\) 9.28621 0.666711
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 22.8659 1.62913 0.814565 0.580073i \(-0.196976\pi\)
0.814565 + 0.580073i \(0.196976\pi\)
\(198\) 3.40581 0.242041
\(199\) −11.2373 −0.796590 −0.398295 0.917257i \(-0.630398\pi\)
−0.398295 + 0.917257i \(0.630398\pi\)
\(200\) −4.87263 −0.344547
\(201\) −3.78017 −0.266632
\(202\) −6.33273 −0.445570
\(203\) −2.21983 −0.155802
\(204\) 2.66487 0.186579
\(205\) 2.37867 0.166133
\(206\) −11.9433 −0.832130
\(207\) 8.29590 0.576605
\(208\) 0 0
\(209\) 29.3957 2.03334
\(210\) −0.356896 −0.0246282
\(211\) −0.219833 −0.0151339 −0.00756695 0.999971i \(-0.502409\pi\)
−0.00756695 + 0.999971i \(0.502409\pi\)
\(212\) 13.0858 0.898733
\(213\) 14.1032 0.966336
\(214\) −0.356896 −0.0243969
\(215\) −2.07846 −0.141750
\(216\) −1.00000 −0.0680414
\(217\) 3.89977 0.264734
\(218\) 18.5429 1.25588
\(219\) −1.72587 −0.116624
\(220\) −1.21552 −0.0819504
\(221\) 0 0
\(222\) 11.5308 0.773896
\(223\) 19.8562 1.32967 0.664836 0.746990i \(-0.268501\pi\)
0.664836 + 0.746990i \(0.268501\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −4.87263 −0.324842
\(226\) −0.274127 −0.0182346
\(227\) 0.537500 0.0356751 0.0178376 0.999841i \(-0.494322\pi\)
0.0178376 + 0.999841i \(0.494322\pi\)
\(228\) −8.63102 −0.571603
\(229\) 16.2741 1.07542 0.537712 0.843128i \(-0.319289\pi\)
0.537712 + 0.843128i \(0.319289\pi\)
\(230\) −2.96077 −0.195227
\(231\) 3.40581 0.224086
\(232\) 2.21983 0.145739
\(233\) 5.43834 0.356277 0.178139 0.984005i \(-0.442992\pi\)
0.178139 + 0.984005i \(0.442992\pi\)
\(234\) 0 0
\(235\) −1.63879 −0.106903
\(236\) 13.6039 0.885537
\(237\) −4.49396 −0.291914
\(238\) 2.66487 0.172738
\(239\) 24.1323 1.56099 0.780494 0.625164i \(-0.214968\pi\)
0.780494 + 0.625164i \(0.214968\pi\)
\(240\) 0.356896 0.0230375
\(241\) −16.9095 −1.08923 −0.544617 0.838685i \(-0.683325\pi\)
−0.544617 + 0.838685i \(0.683325\pi\)
\(242\) 0.599564 0.0385414
\(243\) −1.00000 −0.0641500
\(244\) −13.5254 −0.865876
\(245\) −0.356896 −0.0228012
\(246\) 6.66487 0.424937
\(247\) 0 0
\(248\) −3.89977 −0.247636
\(249\) −10.4940 −0.665028
\(250\) 3.52350 0.222846
\(251\) −5.62804 −0.355239 −0.177619 0.984099i \(-0.556840\pi\)
−0.177619 + 0.984099i \(0.556840\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 28.2543 1.77633
\(254\) 5.42758 0.340557
\(255\) −0.951083 −0.0595591
\(256\) 1.00000 0.0625000
\(257\) −5.56033 −0.346844 −0.173422 0.984848i \(-0.555482\pi\)
−0.173422 + 0.984848i \(0.555482\pi\)
\(258\) −5.82371 −0.362568
\(259\) 11.5308 0.716489
\(260\) 0 0
\(261\) 2.21983 0.137404
\(262\) −5.78017 −0.357100
\(263\) −3.50365 −0.216044 −0.108022 0.994148i \(-0.534452\pi\)
−0.108022 + 0.994148i \(0.534452\pi\)
\(264\) −3.40581 −0.209613
\(265\) −4.67025 −0.286891
\(266\) −8.63102 −0.529202
\(267\) 13.4330 0.822084
\(268\) 3.78017 0.230910
\(269\) −2.54288 −0.155042 −0.0775210 0.996991i \(-0.524700\pi\)
−0.0775210 + 0.996991i \(0.524700\pi\)
\(270\) 0.356896 0.0217200
\(271\) 2.83148 0.172000 0.0860000 0.996295i \(-0.472591\pi\)
0.0860000 + 0.996295i \(0.472591\pi\)
\(272\) −2.66487 −0.161582
\(273\) 0 0
\(274\) −18.1957 −1.09924
\(275\) −16.5953 −1.00073
\(276\) −8.29590 −0.499354
\(277\) −12.4655 −0.748978 −0.374489 0.927231i \(-0.622182\pi\)
−0.374489 + 0.927231i \(0.622182\pi\)
\(278\) 3.21014 0.192532
\(279\) −3.89977 −0.233473
\(280\) 0.356896 0.0213286
\(281\) −0.493959 −0.0294671 −0.0147336 0.999891i \(-0.504690\pi\)
−0.0147336 + 0.999891i \(0.504690\pi\)
\(282\) −4.59179 −0.273437
\(283\) −15.4058 −0.915781 −0.457890 0.889009i \(-0.651395\pi\)
−0.457890 + 0.889009i \(0.651395\pi\)
\(284\) −14.1032 −0.836872
\(285\) 3.08038 0.182466
\(286\) 0 0
\(287\) 6.66487 0.393415
\(288\) 1.00000 0.0589256
\(289\) −9.89844 −0.582261
\(290\) −0.792249 −0.0465225
\(291\) −9.28621 −0.544367
\(292\) 1.72587 0.100999
\(293\) 22.4450 1.31125 0.655627 0.755085i \(-0.272405\pi\)
0.655627 + 0.755085i \(0.272405\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −4.85517 −0.282679
\(296\) −11.5308 −0.670214
\(297\) −3.40581 −0.197625
\(298\) 18.4698 1.06993
\(299\) 0 0
\(300\) 4.87263 0.281321
\(301\) −5.82371 −0.335673
\(302\) 19.2814 1.10952
\(303\) 6.33273 0.363806
\(304\) 8.63102 0.495023
\(305\) 4.82717 0.276403
\(306\) −2.66487 −0.152341
\(307\) −25.7265 −1.46829 −0.734143 0.678994i \(-0.762416\pi\)
−0.734143 + 0.678994i \(0.762416\pi\)
\(308\) −3.40581 −0.194064
\(309\) 11.9433 0.679431
\(310\) 1.39181 0.0790496
\(311\) 9.70171 0.550134 0.275067 0.961425i \(-0.411300\pi\)
0.275067 + 0.961425i \(0.411300\pi\)
\(312\) 0 0
\(313\) −8.74392 −0.494236 −0.247118 0.968985i \(-0.579483\pi\)
−0.247118 + 0.968985i \(0.579483\pi\)
\(314\) 16.7681 0.946278
\(315\) 0.356896 0.0201088
\(316\) 4.49396 0.252805
\(317\) −1.10992 −0.0623391 −0.0311696 0.999514i \(-0.509923\pi\)
−0.0311696 + 0.999514i \(0.509923\pi\)
\(318\) −13.0858 −0.733813
\(319\) 7.56033 0.423297
\(320\) −0.356896 −0.0199511
\(321\) 0.356896 0.0199200
\(322\) −8.29590 −0.462312
\(323\) −23.0006 −1.27979
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 5.15346 0.285424
\(327\) −18.5429 −1.02542
\(328\) −6.66487 −0.368006
\(329\) −4.59179 −0.253154
\(330\) 1.21552 0.0669122
\(331\) 17.0073 0.934806 0.467403 0.884044i \(-0.345190\pi\)
0.467403 + 0.884044i \(0.345190\pi\)
\(332\) 10.4940 0.575931
\(333\) −11.5308 −0.631884
\(334\) −13.3599 −0.731020
\(335\) −1.34913 −0.0737106
\(336\) 1.00000 0.0545545
\(337\) −8.72886 −0.475491 −0.237746 0.971327i \(-0.576408\pi\)
−0.237746 + 0.971327i \(0.576408\pi\)
\(338\) 0 0
\(339\) 0.274127 0.0148885
\(340\) 0.951083 0.0515797
\(341\) −13.2819 −0.719255
\(342\) 8.63102 0.466712
\(343\) −1.00000 −0.0539949
\(344\) 5.82371 0.313993
\(345\) 2.96077 0.159403
\(346\) 14.8509 0.798387
\(347\) −11.7560 −0.631095 −0.315548 0.948910i \(-0.602188\pi\)
−0.315548 + 0.948910i \(0.602188\pi\)
\(348\) −2.21983 −0.118996
\(349\) −23.9758 −1.28340 −0.641699 0.766957i \(-0.721770\pi\)
−0.641699 + 0.766957i \(0.721770\pi\)
\(350\) 4.87263 0.260453
\(351\) 0 0
\(352\) 3.40581 0.181530
\(353\) 17.8019 0.947502 0.473751 0.880659i \(-0.342900\pi\)
0.473751 + 0.880659i \(0.342900\pi\)
\(354\) −13.6039 −0.723038
\(355\) 5.03338 0.267144
\(356\) −13.4330 −0.711945
\(357\) −2.66487 −0.141040
\(358\) 2.21983 0.117322
\(359\) −4.93123 −0.260260 −0.130130 0.991497i \(-0.541540\pi\)
−0.130130 + 0.991497i \(0.541540\pi\)
\(360\) −0.356896 −0.0188101
\(361\) 55.4946 2.92077
\(362\) 17.2271 0.905438
\(363\) −0.599564 −0.0314689
\(364\) 0 0
\(365\) −0.615957 −0.0322407
\(366\) 13.5254 0.706985
\(367\) −26.0694 −1.36081 −0.680405 0.732837i \(-0.738196\pi\)
−0.680405 + 0.732837i \(0.738196\pi\)
\(368\) 8.29590 0.432454
\(369\) −6.66487 −0.346960
\(370\) 4.11529 0.213944
\(371\) −13.0858 −0.679378
\(372\) 3.89977 0.202194
\(373\) −17.7506 −0.919093 −0.459546 0.888154i \(-0.651988\pi\)
−0.459546 + 0.888154i \(0.651988\pi\)
\(374\) −9.07606 −0.469312
\(375\) −3.52350 −0.181953
\(376\) 4.59179 0.236804
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) −4.85517 −0.249393 −0.124697 0.992195i \(-0.539796\pi\)
−0.124697 + 0.992195i \(0.539796\pi\)
\(380\) −3.08038 −0.158020
\(381\) −5.42758 −0.278064
\(382\) 6.58748 0.337045
\(383\) 9.20775 0.470494 0.235247 0.971936i \(-0.424410\pi\)
0.235247 + 0.971936i \(0.424410\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 1.21552 0.0619487
\(386\) 22.4373 1.14203
\(387\) 5.82371 0.296036
\(388\) 9.28621 0.471436
\(389\) 11.7802 0.597278 0.298639 0.954366i \(-0.403467\pi\)
0.298639 + 0.954366i \(0.403467\pi\)
\(390\) 0 0
\(391\) −22.1075 −1.11803
\(392\) 1.00000 0.0505076
\(393\) 5.78017 0.291571
\(394\) 22.8659 1.15197
\(395\) −1.60388 −0.0806997
\(396\) 3.40581 0.171149
\(397\) 5.12929 0.257432 0.128716 0.991682i \(-0.458914\pi\)
0.128716 + 0.991682i \(0.458914\pi\)
\(398\) −11.2373 −0.563274
\(399\) 8.63102 0.432092
\(400\) −4.87263 −0.243631
\(401\) −26.8611 −1.34138 −0.670691 0.741737i \(-0.734002\pi\)
−0.670691 + 0.741737i \(0.734002\pi\)
\(402\) −3.78017 −0.188538
\(403\) 0 0
\(404\) −6.33273 −0.315065
\(405\) −0.356896 −0.0177343
\(406\) −2.21983 −0.110168
\(407\) −39.2717 −1.94663
\(408\) 2.66487 0.131931
\(409\) 27.2513 1.34749 0.673745 0.738964i \(-0.264685\pi\)
0.673745 + 0.738964i \(0.264685\pi\)
\(410\) 2.37867 0.117474
\(411\) 18.1957 0.897526
\(412\) −11.9433 −0.588405
\(413\) −13.6039 −0.669403
\(414\) 8.29590 0.407721
\(415\) −3.74525 −0.183847
\(416\) 0 0
\(417\) −3.21014 −0.157201
\(418\) 29.3957 1.43779
\(419\) −28.8418 −1.40901 −0.704506 0.709698i \(-0.748831\pi\)
−0.704506 + 0.709698i \(0.748831\pi\)
\(420\) −0.356896 −0.0174147
\(421\) 15.2121 0.741391 0.370695 0.928755i \(-0.379119\pi\)
0.370695 + 0.928755i \(0.379119\pi\)
\(422\) −0.219833 −0.0107013
\(423\) 4.59179 0.223261
\(424\) 13.0858 0.635500
\(425\) 12.9849 0.629862
\(426\) 14.1032 0.683303
\(427\) 13.5254 0.654541
\(428\) −0.356896 −0.0172512
\(429\) 0 0
\(430\) −2.07846 −0.100232
\(431\) 4.45473 0.214577 0.107288 0.994228i \(-0.465783\pi\)
0.107288 + 0.994228i \(0.465783\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 36.6655 1.76203 0.881015 0.473089i \(-0.156861\pi\)
0.881015 + 0.473089i \(0.156861\pi\)
\(434\) 3.89977 0.187195
\(435\) 0.792249 0.0379854
\(436\) 18.5429 0.888043
\(437\) 71.6021 3.42519
\(438\) −1.72587 −0.0824654
\(439\) 7.41849 0.354065 0.177033 0.984205i \(-0.443350\pi\)
0.177033 + 0.984205i \(0.443350\pi\)
\(440\) −1.21552 −0.0579477
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 34.2747 1.62844 0.814220 0.580556i \(-0.197165\pi\)
0.814220 + 0.580556i \(0.197165\pi\)
\(444\) 11.5308 0.547227
\(445\) 4.79417 0.227265
\(446\) 19.8562 0.940220
\(447\) −18.4698 −0.873591
\(448\) −1.00000 −0.0472456
\(449\) −9.70171 −0.457852 −0.228926 0.973444i \(-0.573521\pi\)
−0.228926 + 0.973444i \(0.573521\pi\)
\(450\) −4.87263 −0.229698
\(451\) −22.6993 −1.06887
\(452\) −0.274127 −0.0128938
\(453\) −19.2814 −0.905920
\(454\) 0.537500 0.0252261
\(455\) 0 0
\(456\) −8.63102 −0.404185
\(457\) −7.58402 −0.354766 −0.177383 0.984142i \(-0.556763\pi\)
−0.177383 + 0.984142i \(0.556763\pi\)
\(458\) 16.2741 0.760440
\(459\) 2.66487 0.124386
\(460\) −2.96077 −0.138047
\(461\) −4.51573 −0.210318 −0.105159 0.994455i \(-0.533535\pi\)
−0.105159 + 0.994455i \(0.533535\pi\)
\(462\) 3.40581 0.158453
\(463\) 13.0556 0.606746 0.303373 0.952872i \(-0.401887\pi\)
0.303373 + 0.952872i \(0.401887\pi\)
\(464\) 2.21983 0.103053
\(465\) −1.39181 −0.0645438
\(466\) 5.43834 0.251926
\(467\) 23.9711 1.10925 0.554624 0.832101i \(-0.312862\pi\)
0.554624 + 0.832101i \(0.312862\pi\)
\(468\) 0 0
\(469\) −3.78017 −0.174552
\(470\) −1.63879 −0.0755919
\(471\) −16.7681 −0.772633
\(472\) 13.6039 0.626169
\(473\) 19.8345 0.911990
\(474\) −4.49396 −0.206414
\(475\) −42.0557 −1.92965
\(476\) 2.66487 0.122144
\(477\) 13.0858 0.599155
\(478\) 24.1323 1.10378
\(479\) −2.84654 −0.130062 −0.0650309 0.997883i \(-0.520715\pi\)
−0.0650309 + 0.997883i \(0.520715\pi\)
\(480\) 0.356896 0.0162900
\(481\) 0 0
\(482\) −16.9095 −0.770205
\(483\) 8.29590 0.377476
\(484\) 0.599564 0.0272529
\(485\) −3.31421 −0.150490
\(486\) −1.00000 −0.0453609
\(487\) 13.7694 0.623952 0.311976 0.950090i \(-0.399009\pi\)
0.311976 + 0.950090i \(0.399009\pi\)
\(488\) −13.5254 −0.612267
\(489\) −5.15346 −0.233047
\(490\) −0.356896 −0.0161229
\(491\) −38.2825 −1.72766 −0.863832 0.503780i \(-0.831942\pi\)
−0.863832 + 0.503780i \(0.831942\pi\)
\(492\) 6.66487 0.300476
\(493\) −5.91557 −0.266424
\(494\) 0 0
\(495\) −1.21552 −0.0546336
\(496\) −3.89977 −0.175105
\(497\) 14.1032 0.632615
\(498\) −10.4940 −0.470246
\(499\) 32.2828 1.44517 0.722587 0.691280i \(-0.242953\pi\)
0.722587 + 0.691280i \(0.242953\pi\)
\(500\) 3.52350 0.157576
\(501\) 13.3599 0.596875
\(502\) −5.62804 −0.251192
\(503\) −3.47112 −0.154770 −0.0773849 0.997001i \(-0.524657\pi\)
−0.0773849 + 0.997001i \(0.524657\pi\)
\(504\) −1.00000 −0.0445435
\(505\) 2.26013 0.100574
\(506\) 28.2543 1.25606
\(507\) 0 0
\(508\) 5.42758 0.240810
\(509\) −6.25236 −0.277131 −0.138565 0.990353i \(-0.544249\pi\)
−0.138565 + 0.990353i \(0.544249\pi\)
\(510\) −0.951083 −0.0421146
\(511\) −1.72587 −0.0763481
\(512\) 1.00000 0.0441942
\(513\) −8.63102 −0.381069
\(514\) −5.56033 −0.245256
\(515\) 4.26252 0.187829
\(516\) −5.82371 −0.256374
\(517\) 15.6388 0.687793
\(518\) 11.5308 0.506634
\(519\) −14.8509 −0.651880
\(520\) 0 0
\(521\) −28.2174 −1.23623 −0.618114 0.786088i \(-0.712103\pi\)
−0.618114 + 0.786088i \(0.712103\pi\)
\(522\) 2.21983 0.0971594
\(523\) −4.27844 −0.187083 −0.0935415 0.995615i \(-0.529819\pi\)
−0.0935415 + 0.995615i \(0.529819\pi\)
\(524\) −5.78017 −0.252508
\(525\) −4.87263 −0.212659
\(526\) −3.50365 −0.152766
\(527\) 10.3924 0.452700
\(528\) −3.40581 −0.148219
\(529\) 45.8219 1.99226
\(530\) −4.67025 −0.202863
\(531\) 13.6039 0.590358
\(532\) −8.63102 −0.374202
\(533\) 0 0
\(534\) 13.4330 0.581301
\(535\) 0.127375 0.00550689
\(536\) 3.78017 0.163278
\(537\) −2.21983 −0.0957928
\(538\) −2.54288 −0.109631
\(539\) 3.40581 0.146699
\(540\) 0.356896 0.0153584
\(541\) −10.3026 −0.442943 −0.221472 0.975167i \(-0.571086\pi\)
−0.221472 + 0.975167i \(0.571086\pi\)
\(542\) 2.83148 0.121622
\(543\) −17.2271 −0.739287
\(544\) −2.66487 −0.114256
\(545\) −6.61788 −0.283479
\(546\) 0 0
\(547\) 29.4276 1.25823 0.629116 0.777311i \(-0.283417\pi\)
0.629116 + 0.777311i \(0.283417\pi\)
\(548\) −18.1957 −0.777280
\(549\) −13.5254 −0.577251
\(550\) −16.5953 −0.707624
\(551\) 19.1594 0.816219
\(552\) −8.29590 −0.353097
\(553\) −4.49396 −0.191103
\(554\) −12.4655 −0.529608
\(555\) −4.11529 −0.174684
\(556\) 3.21014 0.136140
\(557\) −11.7802 −0.499142 −0.249571 0.968357i \(-0.580290\pi\)
−0.249571 + 0.968357i \(0.580290\pi\)
\(558\) −3.89977 −0.165091
\(559\) 0 0
\(560\) 0.356896 0.0150816
\(561\) 9.07606 0.383192
\(562\) −0.493959 −0.0208364
\(563\) −21.3163 −0.898377 −0.449188 0.893437i \(-0.648287\pi\)
−0.449188 + 0.893437i \(0.648287\pi\)
\(564\) −4.59179 −0.193349
\(565\) 0.0978347 0.00411594
\(566\) −15.4058 −0.647555
\(567\) −1.00000 −0.0419961
\(568\) −14.1032 −0.591758
\(569\) −39.1159 −1.63982 −0.819912 0.572490i \(-0.805977\pi\)
−0.819912 + 0.572490i \(0.805977\pi\)
\(570\) 3.08038 0.129023
\(571\) −22.0629 −0.923304 −0.461652 0.887061i \(-0.652743\pi\)
−0.461652 + 0.887061i \(0.652743\pi\)
\(572\) 0 0
\(573\) −6.58748 −0.275196
\(574\) 6.66487 0.278186
\(575\) −40.4228 −1.68575
\(576\) 1.00000 0.0416667
\(577\) 23.2078 0.966151 0.483076 0.875579i \(-0.339520\pi\)
0.483076 + 0.875579i \(0.339520\pi\)
\(578\) −9.89844 −0.411721
\(579\) −22.4373 −0.932461
\(580\) −0.792249 −0.0328964
\(581\) −10.4940 −0.435363
\(582\) −9.28621 −0.384926
\(583\) 44.5676 1.84580
\(584\) 1.72587 0.0714171
\(585\) 0 0
\(586\) 22.4450 0.927196
\(587\) 41.7754 1.72425 0.862127 0.506692i \(-0.169132\pi\)
0.862127 + 0.506692i \(0.169132\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −33.6590 −1.38690
\(590\) −4.85517 −0.199884
\(591\) −22.8659 −0.940578
\(592\) −11.5308 −0.473913
\(593\) −14.4397 −0.592966 −0.296483 0.955038i \(-0.595814\pi\)
−0.296483 + 0.955038i \(0.595814\pi\)
\(594\) −3.40581 −0.139742
\(595\) −0.951083 −0.0389906
\(596\) 18.4698 0.756552
\(597\) 11.2373 0.459912
\(598\) 0 0
\(599\) −6.85517 −0.280095 −0.140047 0.990145i \(-0.544725\pi\)
−0.140047 + 0.990145i \(0.544725\pi\)
\(600\) 4.87263 0.198924
\(601\) 0.914247 0.0372929 0.0186465 0.999826i \(-0.494064\pi\)
0.0186465 + 0.999826i \(0.494064\pi\)
\(602\) −5.82371 −0.237357
\(603\) 3.78017 0.153940
\(604\) 19.2814 0.784550
\(605\) −0.213982 −0.00869960
\(606\) 6.33273 0.257250
\(607\) −19.5791 −0.794692 −0.397346 0.917669i \(-0.630069\pi\)
−0.397346 + 0.917669i \(0.630069\pi\)
\(608\) 8.63102 0.350034
\(609\) 2.21983 0.0899522
\(610\) 4.82717 0.195446
\(611\) 0 0
\(612\) −2.66487 −0.107721
\(613\) 26.3394 1.06384 0.531920 0.846795i \(-0.321471\pi\)
0.531920 + 0.846795i \(0.321471\pi\)
\(614\) −25.7265 −1.03824
\(615\) −2.37867 −0.0959171
\(616\) −3.40581 −0.137224
\(617\) −6.24400 −0.251374 −0.125687 0.992070i \(-0.540113\pi\)
−0.125687 + 0.992070i \(0.540113\pi\)
\(618\) 11.9433 0.480431
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 1.39181 0.0558965
\(621\) −8.29590 −0.332903
\(622\) 9.70171 0.389003
\(623\) 13.4330 0.538180
\(624\) 0 0
\(625\) 23.1056 0.924224
\(626\) −8.74392 −0.349477
\(627\) −29.3957 −1.17395
\(628\) 16.7681 0.669119
\(629\) 30.7281 1.22521
\(630\) 0.356896 0.0142191
\(631\) 20.0629 0.798692 0.399346 0.916800i \(-0.369237\pi\)
0.399346 + 0.916800i \(0.369237\pi\)
\(632\) 4.49396 0.178760
\(633\) 0.219833 0.00873756
\(634\) −1.10992 −0.0440804
\(635\) −1.93708 −0.0768708
\(636\) −13.0858 −0.518884
\(637\) 0 0
\(638\) 7.56033 0.299317
\(639\) −14.1032 −0.557914
\(640\) −0.356896 −0.0141075
\(641\) −13.1535 −0.519530 −0.259765 0.965672i \(-0.583645\pi\)
−0.259765 + 0.965672i \(0.583645\pi\)
\(642\) 0.356896 0.0140856
\(643\) 43.2006 1.70366 0.851832 0.523815i \(-0.175492\pi\)
0.851832 + 0.523815i \(0.175492\pi\)
\(644\) −8.29590 −0.326904
\(645\) 2.07846 0.0818392
\(646\) −23.0006 −0.904946
\(647\) 7.10513 0.279332 0.139666 0.990199i \(-0.455397\pi\)
0.139666 + 0.990199i \(0.455397\pi\)
\(648\) 1.00000 0.0392837
\(649\) 46.3323 1.81870
\(650\) 0 0
\(651\) −3.89977 −0.152844
\(652\) 5.15346 0.201825
\(653\) 18.9422 0.741267 0.370634 0.928779i \(-0.379141\pi\)
0.370634 + 0.928779i \(0.379141\pi\)
\(654\) −18.5429 −0.725084
\(655\) 2.06292 0.0806049
\(656\) −6.66487 −0.260220
\(657\) 1.72587 0.0673327
\(658\) −4.59179 −0.179007
\(659\) 20.8286 0.811367 0.405684 0.914014i \(-0.367033\pi\)
0.405684 + 0.914014i \(0.367033\pi\)
\(660\) 1.21552 0.0473141
\(661\) −33.7995 −1.31465 −0.657325 0.753607i \(-0.728312\pi\)
−0.657325 + 0.753607i \(0.728312\pi\)
\(662\) 17.0073 0.661007
\(663\) 0 0
\(664\) 10.4940 0.407245
\(665\) 3.08038 0.119452
\(666\) −11.5308 −0.446809
\(667\) 18.4155 0.713051
\(668\) −13.3599 −0.516909
\(669\) −19.8562 −0.767686
\(670\) −1.34913 −0.0521213
\(671\) −46.0650 −1.77832
\(672\) 1.00000 0.0385758
\(673\) 18.3521 0.707422 0.353711 0.935355i \(-0.384920\pi\)
0.353711 + 0.935355i \(0.384920\pi\)
\(674\) −8.72886 −0.336223
\(675\) 4.87263 0.187547
\(676\) 0 0
\(677\) −11.0750 −0.425647 −0.212823 0.977091i \(-0.568266\pi\)
−0.212823 + 0.977091i \(0.568266\pi\)
\(678\) 0.274127 0.0105278
\(679\) −9.28621 −0.356372
\(680\) 0.951083 0.0364724
\(681\) −0.537500 −0.0205970
\(682\) −13.2819 −0.508590
\(683\) −26.8015 −1.02553 −0.512765 0.858529i \(-0.671379\pi\)
−0.512765 + 0.858529i \(0.671379\pi\)
\(684\) 8.63102 0.330015
\(685\) 6.49396 0.248121
\(686\) −1.00000 −0.0381802
\(687\) −16.2741 −0.620897
\(688\) 5.82371 0.222027
\(689\) 0 0
\(690\) 2.96077 0.112715
\(691\) −21.5338 −0.819184 −0.409592 0.912269i \(-0.634329\pi\)
−0.409592 + 0.912269i \(0.634329\pi\)
\(692\) 14.8509 0.564545
\(693\) −3.40581 −0.129376
\(694\) −11.7560 −0.446252
\(695\) −1.14569 −0.0434584
\(696\) −2.21983 −0.0841425
\(697\) 17.7611 0.672748
\(698\) −23.9758 −0.907499
\(699\) −5.43834 −0.205697
\(700\) 4.87263 0.184168
\(701\) −28.9724 −1.09427 −0.547136 0.837044i \(-0.684282\pi\)
−0.547136 + 0.837044i \(0.684282\pi\)
\(702\) 0 0
\(703\) −99.5226 −3.75356
\(704\) 3.40581 0.128361
\(705\) 1.63879 0.0617205
\(706\) 17.8019 0.669985
\(707\) 6.33273 0.238167
\(708\) −13.6039 −0.511265
\(709\) 34.6069 1.29969 0.649844 0.760068i \(-0.274834\pi\)
0.649844 + 0.760068i \(0.274834\pi\)
\(710\) 5.03338 0.188899
\(711\) 4.49396 0.168537
\(712\) −13.4330 −0.503421
\(713\) −32.3521 −1.21160
\(714\) −2.66487 −0.0997304
\(715\) 0 0
\(716\) 2.21983 0.0829590
\(717\) −24.1323 −0.901236
\(718\) −4.93123 −0.184032
\(719\) −5.78017 −0.215564 −0.107782 0.994175i \(-0.534375\pi\)
−0.107782 + 0.994175i \(0.534375\pi\)
\(720\) −0.356896 −0.0133007
\(721\) 11.9433 0.444792
\(722\) 55.4946 2.06529
\(723\) 16.9095 0.628870
\(724\) 17.2271 0.640241
\(725\) −10.8164 −0.401711
\(726\) −0.599564 −0.0222519
\(727\) −19.4668 −0.721984 −0.360992 0.932569i \(-0.617562\pi\)
−0.360992 + 0.932569i \(0.617562\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −0.615957 −0.0227976
\(731\) −15.5195 −0.574008
\(732\) 13.5254 0.499914
\(733\) −13.3948 −0.494748 −0.247374 0.968920i \(-0.579568\pi\)
−0.247374 + 0.968920i \(0.579568\pi\)
\(734\) −26.0694 −0.962238
\(735\) 0.356896 0.0131643
\(736\) 8.29590 0.305791
\(737\) 12.8745 0.474240
\(738\) −6.66487 −0.245337
\(739\) −19.2814 −0.709279 −0.354639 0.935003i \(-0.615396\pi\)
−0.354639 + 0.935003i \(0.615396\pi\)
\(740\) 4.11529 0.151281
\(741\) 0 0
\(742\) −13.0858 −0.480393
\(743\) 21.9842 0.806522 0.403261 0.915085i \(-0.367877\pi\)
0.403261 + 0.915085i \(0.367877\pi\)
\(744\) 3.89977 0.142973
\(745\) −6.59179 −0.241505
\(746\) −17.7506 −0.649897
\(747\) 10.4940 0.383954
\(748\) −9.07606 −0.331854
\(749\) 0.356896 0.0130407
\(750\) −3.52350 −0.128660
\(751\) 10.8659 0.396503 0.198252 0.980151i \(-0.436474\pi\)
0.198252 + 0.980151i \(0.436474\pi\)
\(752\) 4.59179 0.167445
\(753\) 5.62804 0.205097
\(754\) 0 0
\(755\) −6.88146 −0.250442
\(756\) 1.00000 0.0363696
\(757\) 31.0320 1.12788 0.563940 0.825816i \(-0.309285\pi\)
0.563940 + 0.825816i \(0.309285\pi\)
\(758\) −4.85517 −0.176348
\(759\) −28.2543 −1.02557
\(760\) −3.08038 −0.111737
\(761\) −25.5211 −0.925139 −0.462570 0.886583i \(-0.653072\pi\)
−0.462570 + 0.886583i \(0.653072\pi\)
\(762\) −5.42758 −0.196621
\(763\) −18.5429 −0.671297
\(764\) 6.58748 0.238327
\(765\) 0.951083 0.0343865
\(766\) 9.20775 0.332690
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) −17.8780 −0.644697 −0.322349 0.946621i \(-0.604472\pi\)
−0.322349 + 0.946621i \(0.604472\pi\)
\(770\) 1.21552 0.0438043
\(771\) 5.56033 0.200251
\(772\) 22.4373 0.807535
\(773\) −42.5870 −1.53175 −0.765874 0.642991i \(-0.777693\pi\)
−0.765874 + 0.642991i \(0.777693\pi\)
\(774\) 5.82371 0.209329
\(775\) 19.0021 0.682577
\(776\) 9.28621 0.333355
\(777\) −11.5308 −0.413665
\(778\) 11.7802 0.422339
\(779\) −57.5247 −2.06104
\(780\) 0 0
\(781\) −48.0329 −1.71875
\(782\) −22.1075 −0.790563
\(783\) −2.21983 −0.0793303
\(784\) 1.00000 0.0357143
\(785\) −5.98446 −0.213595
\(786\) 5.78017 0.206172
\(787\) 41.4902 1.47897 0.739484 0.673175i \(-0.235070\pi\)
0.739484 + 0.673175i \(0.235070\pi\)
\(788\) 22.8659 0.814565
\(789\) 3.50365 0.124733
\(790\) −1.60388 −0.0570633
\(791\) 0.274127 0.00974682
\(792\) 3.40581 0.121020
\(793\) 0 0
\(794\) 5.12929 0.182032
\(795\) 4.67025 0.165637
\(796\) −11.2373 −0.398295
\(797\) 16.1661 0.572634 0.286317 0.958135i \(-0.407569\pi\)
0.286317 + 0.958135i \(0.407569\pi\)
\(798\) 8.63102 0.305535
\(799\) −12.2366 −0.432898
\(800\) −4.87263 −0.172273
\(801\) −13.4330 −0.474630
\(802\) −26.8611 −0.948500
\(803\) 5.87800 0.207430
\(804\) −3.78017 −0.133316
\(805\) 2.96077 0.104353
\(806\) 0 0
\(807\) 2.54288 0.0895135
\(808\) −6.33273 −0.222785
\(809\) −15.0905 −0.530555 −0.265278 0.964172i \(-0.585464\pi\)
−0.265278 + 0.964172i \(0.585464\pi\)
\(810\) −0.356896 −0.0125400
\(811\) −9.42221 −0.330858 −0.165429 0.986222i \(-0.552901\pi\)
−0.165429 + 0.986222i \(0.552901\pi\)
\(812\) −2.21983 −0.0779009
\(813\) −2.83148 −0.0993043
\(814\) −39.2717 −1.37647
\(815\) −1.83925 −0.0644260
\(816\) 2.66487 0.0932893
\(817\) 50.2646 1.75853
\(818\) 27.2513 0.952819
\(819\) 0 0
\(820\) 2.37867 0.0830666
\(821\) −0.640120 −0.0223403 −0.0111702 0.999938i \(-0.503556\pi\)
−0.0111702 + 0.999938i \(0.503556\pi\)
\(822\) 18.1957 0.634647
\(823\) −32.1715 −1.12143 −0.560714 0.828009i \(-0.689473\pi\)
−0.560714 + 0.828009i \(0.689473\pi\)
\(824\) −11.9433 −0.416065
\(825\) 16.5953 0.577773
\(826\) −13.6039 −0.473339
\(827\) 15.3002 0.532040 0.266020 0.963967i \(-0.414291\pi\)
0.266020 + 0.963967i \(0.414291\pi\)
\(828\) 8.29590 0.288302
\(829\) 17.3491 0.602560 0.301280 0.953536i \(-0.402586\pi\)
0.301280 + 0.953536i \(0.402586\pi\)
\(830\) −3.74525 −0.130000
\(831\) 12.4655 0.432423
\(832\) 0 0
\(833\) −2.66487 −0.0923324
\(834\) −3.21014 −0.111158
\(835\) 4.76809 0.165006
\(836\) 29.3957 1.01667
\(837\) 3.89977 0.134796
\(838\) −28.8418 −0.996322
\(839\) −3.10992 −0.107366 −0.0536831 0.998558i \(-0.517096\pi\)
−0.0536831 + 0.998558i \(0.517096\pi\)
\(840\) −0.356896 −0.0123141
\(841\) −24.0723 −0.830081
\(842\) 15.2121 0.524242
\(843\) 0.493959 0.0170129
\(844\) −0.219833 −0.00756695
\(845\) 0 0
\(846\) 4.59179 0.157869
\(847\) −0.599564 −0.0206012
\(848\) 13.0858 0.449367
\(849\) 15.4058 0.528726
\(850\) 12.9849 0.445380
\(851\) −95.6583 −3.27912
\(852\) 14.1032 0.483168
\(853\) 42.3961 1.45162 0.725808 0.687898i \(-0.241466\pi\)
0.725808 + 0.687898i \(0.241466\pi\)
\(854\) 13.5254 0.462830
\(855\) −3.08038 −0.105347
\(856\) −0.356896 −0.0121984
\(857\) −10.3918 −0.354978 −0.177489 0.984123i \(-0.556797\pi\)
−0.177489 + 0.984123i \(0.556797\pi\)
\(858\) 0 0
\(859\) −47.4862 −1.62021 −0.810104 0.586286i \(-0.800589\pi\)
−0.810104 + 0.586286i \(0.800589\pi\)
\(860\) −2.07846 −0.0708748
\(861\) −6.66487 −0.227138
\(862\) 4.45473 0.151729
\(863\) −22.8364 −0.777359 −0.388680 0.921373i \(-0.627069\pi\)
−0.388680 + 0.921373i \(0.627069\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −5.30021 −0.180213
\(866\) 36.6655 1.24594
\(867\) 9.89844 0.336169
\(868\) 3.89977 0.132367
\(869\) 15.3056 0.519206
\(870\) 0.792249 0.0268598
\(871\) 0 0
\(872\) 18.5429 0.627941
\(873\) 9.28621 0.314291
\(874\) 71.6021 2.42198
\(875\) −3.52350 −0.119116
\(876\) −1.72587 −0.0583119
\(877\) 52.8122 1.78334 0.891671 0.452684i \(-0.149533\pi\)
0.891671 + 0.452684i \(0.149533\pi\)
\(878\) 7.41849 0.250362
\(879\) −22.4450 −0.757052
\(880\) −1.21552 −0.0409752
\(881\) −14.1564 −0.476943 −0.238471 0.971150i \(-0.576646\pi\)
−0.238471 + 0.971150i \(0.576646\pi\)
\(882\) 1.00000 0.0336718
\(883\) −22.0785 −0.742999 −0.371500 0.928433i \(-0.621156\pi\)
−0.371500 + 0.928433i \(0.621156\pi\)
\(884\) 0 0
\(885\) 4.85517 0.163205
\(886\) 34.2747 1.15148
\(887\) −28.4397 −0.954910 −0.477455 0.878656i \(-0.658441\pi\)
−0.477455 + 0.878656i \(0.658441\pi\)
\(888\) 11.5308 0.386948
\(889\) −5.42758 −0.182035
\(890\) 4.79417 0.160701
\(891\) 3.40581 0.114099
\(892\) 19.8562 0.664836
\(893\) 39.6319 1.32623
\(894\) −18.4698 −0.617722
\(895\) −0.792249 −0.0264820
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −9.70171 −0.323750
\(899\) −8.65684 −0.288722
\(900\) −4.87263 −0.162421
\(901\) −34.8719 −1.16175
\(902\) −22.6993 −0.755805
\(903\) 5.82371 0.193801
\(904\) −0.274127 −0.00911732
\(905\) −6.14829 −0.204376
\(906\) −19.2814 −0.640582
\(907\) −30.2828 −1.00552 −0.502761 0.864425i \(-0.667682\pi\)
−0.502761 + 0.864425i \(0.667682\pi\)
\(908\) 0.537500 0.0178376
\(909\) −6.33273 −0.210043
\(910\) 0 0
\(911\) −14.0392 −0.465140 −0.232570 0.972580i \(-0.574714\pi\)
−0.232570 + 0.972580i \(0.574714\pi\)
\(912\) −8.63102 −0.285802
\(913\) 35.7405 1.18284
\(914\) −7.58402 −0.250857
\(915\) −4.82717 −0.159581
\(916\) 16.2741 0.537712
\(917\) 5.78017 0.190878
\(918\) 2.66487 0.0879540
\(919\) −5.06425 −0.167054 −0.0835270 0.996506i \(-0.526618\pi\)
−0.0835270 + 0.996506i \(0.526618\pi\)
\(920\) −2.96077 −0.0976137
\(921\) 25.7265 0.847716
\(922\) −4.51573 −0.148718
\(923\) 0 0
\(924\) 3.40581 0.112043
\(925\) 56.1852 1.84736
\(926\) 13.0556 0.429034
\(927\) −11.9433 −0.392270
\(928\) 2.21983 0.0728696
\(929\) −34.1957 −1.12192 −0.560962 0.827842i \(-0.689569\pi\)
−0.560962 + 0.827842i \(0.689569\pi\)
\(930\) −1.39181 −0.0456393
\(931\) 8.63102 0.282870
\(932\) 5.43834 0.178139
\(933\) −9.70171 −0.317620
\(934\) 23.9711 0.784357
\(935\) 3.23921 0.105933
\(936\) 0 0
\(937\) 10.6052 0.346457 0.173228 0.984882i \(-0.444580\pi\)
0.173228 + 0.984882i \(0.444580\pi\)
\(938\) −3.78017 −0.123427
\(939\) 8.74392 0.285347
\(940\) −1.63879 −0.0534515
\(941\) −5.10082 −0.166282 −0.0831410 0.996538i \(-0.526495\pi\)
−0.0831410 + 0.996538i \(0.526495\pi\)
\(942\) −16.7681 −0.546334
\(943\) −55.2911 −1.80053
\(944\) 13.6039 0.442768
\(945\) −0.356896 −0.0116098
\(946\) 19.8345 0.644874
\(947\) −41.6577 −1.35369 −0.676847 0.736124i \(-0.736654\pi\)
−0.676847 + 0.736124i \(0.736654\pi\)
\(948\) −4.49396 −0.145957
\(949\) 0 0
\(950\) −42.0557 −1.36447
\(951\) 1.10992 0.0359915
\(952\) 2.66487 0.0863691
\(953\) −6.55901 −0.212467 −0.106234 0.994341i \(-0.533879\pi\)
−0.106234 + 0.994341i \(0.533879\pi\)
\(954\) 13.0858 0.423667
\(955\) −2.35105 −0.0760780
\(956\) 24.1323 0.780494
\(957\) −7.56033 −0.244391
\(958\) −2.84654 −0.0919676
\(959\) 18.1957 0.587569
\(960\) 0.356896 0.0115188
\(961\) −15.7918 −0.509412
\(962\) 0 0
\(963\) −0.356896 −0.0115008
\(964\) −16.9095 −0.544617
\(965\) −8.00777 −0.257779
\(966\) 8.29590 0.266916
\(967\) −36.7042 −1.18033 −0.590164 0.807283i \(-0.700937\pi\)
−0.590164 + 0.807283i \(0.700937\pi\)
\(968\) 0.599564 0.0192707
\(969\) 23.0006 0.738885
\(970\) −3.31421 −0.106413
\(971\) 34.8853 1.11952 0.559761 0.828654i \(-0.310893\pi\)
0.559761 + 0.828654i \(0.310893\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −3.21014 −0.102912
\(974\) 13.7694 0.441200
\(975\) 0 0
\(976\) −13.5254 −0.432938
\(977\) −43.0461 −1.37717 −0.688583 0.725158i \(-0.741767\pi\)
−0.688583 + 0.725158i \(0.741767\pi\)
\(978\) −5.15346 −0.164789
\(979\) −45.7502 −1.46218
\(980\) −0.356896 −0.0114006
\(981\) 18.5429 0.592028
\(982\) −38.2825 −1.22164
\(983\) 36.9724 1.17924 0.589618 0.807682i \(-0.299278\pi\)
0.589618 + 0.807682i \(0.299278\pi\)
\(984\) 6.66487 0.212468
\(985\) −8.16075 −0.260023
\(986\) −5.91557 −0.188390
\(987\) 4.59179 0.146158
\(988\) 0 0
\(989\) 48.3129 1.53626
\(990\) −1.21552 −0.0386318
\(991\) −6.03875 −0.191827 −0.0959137 0.995390i \(-0.530577\pi\)
−0.0959137 + 0.995390i \(0.530577\pi\)
\(992\) −3.89977 −0.123818
\(993\) −17.0073 −0.539710
\(994\) 14.1032 0.447327
\(995\) 4.01054 0.127143
\(996\) −10.4940 −0.332514
\(997\) −49.9866 −1.58309 −0.791546 0.611110i \(-0.790723\pi\)
−0.791546 + 0.611110i \(0.790723\pi\)
\(998\) 32.2828 1.02189
\(999\) 11.5308 0.364818
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.ck.1.2 yes 3
13.12 even 2 7098.2.a.cb.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cb.1.2 3 13.12 even 2
7098.2.a.ck.1.2 yes 3 1.1 even 1 trivial