Properties

Label 7098.2.a.ci.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

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.35690 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.35690 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.35690 q^{10} -4.29590 q^{11} -1.00000 q^{12} -1.00000 q^{14} -1.35690 q^{15} +1.00000 q^{16} +2.66487 q^{17} +1.00000 q^{18} -4.29590 q^{19} +1.35690 q^{20} +1.00000 q^{21} -4.29590 q^{22} -4.63102 q^{23} -1.00000 q^{24} -3.15883 q^{25} -1.00000 q^{27} -1.00000 q^{28} +5.54288 q^{29} -1.35690 q^{30} +5.51573 q^{31} +1.00000 q^{32} +4.29590 q^{33} +2.66487 q^{34} -1.35690 q^{35} +1.00000 q^{36} +3.53319 q^{37} -4.29590 q^{38} +1.35690 q^{40} +9.45473 q^{41} +1.00000 q^{42} -11.2470 q^{43} -4.29590 q^{44} +1.35690 q^{45} -4.63102 q^{46} +8.20775 q^{47} -1.00000 q^{48} +1.00000 q^{49} -3.15883 q^{50} -2.66487 q^{51} +10.1860 q^{53} -1.00000 q^{54} -5.82908 q^{55} -1.00000 q^{56} +4.29590 q^{57} +5.54288 q^{58} -1.75302 q^{59} -1.35690 q^{60} -2.20775 q^{61} +5.51573 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.29590 q^{66} -4.87263 q^{67} +2.66487 q^{68} +4.63102 q^{69} -1.35690 q^{70} +10.9879 q^{71} +1.00000 q^{72} +15.3110 q^{73} +3.53319 q^{74} +3.15883 q^{75} -4.29590 q^{76} +4.29590 q^{77} +16.0465 q^{79} +1.35690 q^{80} +1.00000 q^{81} +9.45473 q^{82} -5.62565 q^{83} +1.00000 q^{84} +3.61596 q^{85} -11.2470 q^{86} -5.54288 q^{87} -4.29590 q^{88} -9.81700 q^{89} +1.35690 q^{90} -4.63102 q^{92} -5.51573 q^{93} +8.20775 q^{94} -5.82908 q^{95} -1.00000 q^{96} +18.9366 q^{97} +1.00000 q^{98} -4.29590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q + 3q^{2} - 3q^{3} + 3q^{4} - 3q^{6} - 3q^{7} + 3q^{8} + 3q^{9} + q^{11} - 3q^{12} - 3q^{14} + 3q^{16} + 9q^{17} + 3q^{18} + q^{19} + 3q^{21} + q^{22} + q^{23} - 3q^{24} - q^{25} - 3q^{27} - 3q^{28} - 2q^{29} + 4q^{31} + 3q^{32} - q^{33} + 9q^{34} + 3q^{36} + 14q^{37} + q^{38} + 6q^{41} + 3q^{42} - 29q^{43} + q^{44} + q^{46} + 7q^{47} - 3q^{48} + 3q^{49} - q^{50} - 9q^{51} + 16q^{53} - 3q^{54} - 7q^{55} - 3q^{56} - q^{57} - 2q^{58} - 10q^{59} + 11q^{61} + 4q^{62} - 3q^{63} + 3q^{64} - q^{66} + 2q^{67} + 9q^{68} - q^{69} + 14q^{71} + 3q^{72} + 7q^{73} + 14q^{74} + q^{75} + q^{76} - q^{77} - 2q^{79} + 3q^{81} + 6q^{82} - 5q^{83} + 3q^{84} + 21q^{85} - 29q^{86} + 2q^{87} + q^{88} + q^{92} - 4q^{93} + 7q^{94} - 7q^{95} - 3q^{96} + 6q^{97} + 3q^{98} + q^{99} + O(q^{100}) \)

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
\(5\) 1.35690 0.606822 0.303411 0.952860i \(-0.401874\pi\)
0.303411 + 0.952860i \(0.401874\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.35690 0.429088
\(11\) −4.29590 −1.29526 −0.647631 0.761954i \(-0.724240\pi\)
−0.647631 + 0.761954i \(0.724240\pi\)
\(12\) −1.00000 −0.288675
\(13\) 0 0
\(14\) −1.00000 −0.267261
\(15\) −1.35690 −0.350349
\(16\) 1.00000 0.250000
\(17\) 2.66487 0.646327 0.323163 0.946343i \(-0.395254\pi\)
0.323163 + 0.946343i \(0.395254\pi\)
\(18\) 1.00000 0.235702
\(19\) −4.29590 −0.985546 −0.492773 0.870158i \(-0.664017\pi\)
−0.492773 + 0.870158i \(0.664017\pi\)
\(20\) 1.35690 0.303411
\(21\) 1.00000 0.218218
\(22\) −4.29590 −0.915888
\(23\) −4.63102 −0.965635 −0.482817 0.875721i \(-0.660387\pi\)
−0.482817 + 0.875721i \(0.660387\pi\)
\(24\) −1.00000 −0.204124
\(25\) −3.15883 −0.631767
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −1.00000 −0.188982
\(29\) 5.54288 1.02929 0.514643 0.857404i \(-0.327924\pi\)
0.514643 + 0.857404i \(0.327924\pi\)
\(30\) −1.35690 −0.247734
\(31\) 5.51573 0.990654 0.495327 0.868707i \(-0.335048\pi\)
0.495327 + 0.868707i \(0.335048\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.29590 0.747820
\(34\) 2.66487 0.457022
\(35\) −1.35690 −0.229357
\(36\) 1.00000 0.166667
\(37\) 3.53319 0.580853 0.290426 0.956897i \(-0.406203\pi\)
0.290426 + 0.956897i \(0.406203\pi\)
\(38\) −4.29590 −0.696887
\(39\) 0 0
\(40\) 1.35690 0.214544
\(41\) 9.45473 1.47658 0.738290 0.674483i \(-0.235633\pi\)
0.738290 + 0.674483i \(0.235633\pi\)
\(42\) 1.00000 0.154303
\(43\) −11.2470 −1.71515 −0.857574 0.514360i \(-0.828029\pi\)
−0.857574 + 0.514360i \(0.828029\pi\)
\(44\) −4.29590 −0.647631
\(45\) 1.35690 0.202274
\(46\) −4.63102 −0.682807
\(47\) 8.20775 1.19722 0.598612 0.801039i \(-0.295719\pi\)
0.598612 + 0.801039i \(0.295719\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) −3.15883 −0.446727
\(51\) −2.66487 −0.373157
\(52\) 0 0
\(53\) 10.1860 1.39915 0.699576 0.714558i \(-0.253372\pi\)
0.699576 + 0.714558i \(0.253372\pi\)
\(54\) −1.00000 −0.136083
\(55\) −5.82908 −0.785994
\(56\) −1.00000 −0.133631
\(57\) 4.29590 0.569005
\(58\) 5.54288 0.727815
\(59\) −1.75302 −0.228224 −0.114112 0.993468i \(-0.536402\pi\)
−0.114112 + 0.993468i \(0.536402\pi\)
\(60\) −1.35690 −0.175175
\(61\) −2.20775 −0.282674 −0.141337 0.989962i \(-0.545140\pi\)
−0.141337 + 0.989962i \(0.545140\pi\)
\(62\) 5.51573 0.700498
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 4.29590 0.528788
\(67\) −4.87263 −0.595286 −0.297643 0.954677i \(-0.596200\pi\)
−0.297643 + 0.954677i \(0.596200\pi\)
\(68\) 2.66487 0.323163
\(69\) 4.63102 0.557510
\(70\) −1.35690 −0.162180
\(71\) 10.9879 1.30403 0.652013 0.758208i \(-0.273925\pi\)
0.652013 + 0.758208i \(0.273925\pi\)
\(72\) 1.00000 0.117851
\(73\) 15.3110 1.79201 0.896006 0.444041i \(-0.146456\pi\)
0.896006 + 0.444041i \(0.146456\pi\)
\(74\) 3.53319 0.410725
\(75\) 3.15883 0.364751
\(76\) −4.29590 −0.492773
\(77\) 4.29590 0.489563
\(78\) 0 0
\(79\) 16.0465 1.80538 0.902688 0.430297i \(-0.141591\pi\)
0.902688 + 0.430297i \(0.141591\pi\)
\(80\) 1.35690 0.151706
\(81\) 1.00000 0.111111
\(82\) 9.45473 1.04410
\(83\) −5.62565 −0.617495 −0.308747 0.951144i \(-0.599910\pi\)
−0.308747 + 0.951144i \(0.599910\pi\)
\(84\) 1.00000 0.109109
\(85\) 3.61596 0.392206
\(86\) −11.2470 −1.21279
\(87\) −5.54288 −0.594259
\(88\) −4.29590 −0.457944
\(89\) −9.81700 −1.04060 −0.520300 0.853983i \(-0.674180\pi\)
−0.520300 + 0.853983i \(0.674180\pi\)
\(90\) 1.35690 0.143029
\(91\) 0 0
\(92\) −4.63102 −0.482817
\(93\) −5.51573 −0.571955
\(94\) 8.20775 0.846565
\(95\) −5.82908 −0.598051
\(96\) −1.00000 −0.102062
\(97\) 18.9366 1.92272 0.961361 0.275292i \(-0.0887746\pi\)
0.961361 + 0.275292i \(0.0887746\pi\)
\(98\) 1.00000 0.101015
\(99\) −4.29590 −0.431754
\(100\) −3.15883 −0.315883
\(101\) −0.00537681 −0.000535013 0 −0.000267506 1.00000i \(-0.500085\pi\)
−0.000267506 1.00000i \(0.500085\pi\)
\(102\) −2.66487 −0.263862
\(103\) −0.814019 −0.0802077 −0.0401039 0.999196i \(-0.512769\pi\)
−0.0401039 + 0.999196i \(0.512769\pi\)
\(104\) 0 0
\(105\) 1.35690 0.132419
\(106\) 10.1860 0.989350
\(107\) −5.05429 −0.488617 −0.244309 0.969698i \(-0.578561\pi\)
−0.244309 + 0.969698i \(0.578561\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −0.137063 −0.0131283 −0.00656414 0.999978i \(-0.502089\pi\)
−0.00656414 + 0.999978i \(0.502089\pi\)
\(110\) −5.82908 −0.555781
\(111\) −3.53319 −0.335355
\(112\) −1.00000 −0.0944911
\(113\) 11.4668 1.07871 0.539353 0.842079i \(-0.318669\pi\)
0.539353 + 0.842079i \(0.318669\pi\)
\(114\) 4.29590 0.402348
\(115\) −6.28382 −0.585969
\(116\) 5.54288 0.514643
\(117\) 0 0
\(118\) −1.75302 −0.161379
\(119\) −2.66487 −0.244289
\(120\) −1.35690 −0.123867
\(121\) 7.45473 0.677703
\(122\) −2.20775 −0.199880
\(123\) −9.45473 −0.852504
\(124\) 5.51573 0.495327
\(125\) −11.0707 −0.990192
\(126\) −1.00000 −0.0890871
\(127\) 10.8412 0.961998 0.480999 0.876721i \(-0.340274\pi\)
0.480999 + 0.876721i \(0.340274\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.2470 0.990241
\(130\) 0 0
\(131\) 15.0368 1.31377 0.656887 0.753989i \(-0.271873\pi\)
0.656887 + 0.753989i \(0.271873\pi\)
\(132\) 4.29590 0.373910
\(133\) 4.29590 0.372502
\(134\) −4.87263 −0.420931
\(135\) −1.35690 −0.116783
\(136\) 2.66487 0.228511
\(137\) 16.1806 1.38240 0.691201 0.722662i \(-0.257082\pi\)
0.691201 + 0.722662i \(0.257082\pi\)
\(138\) 4.63102 0.394219
\(139\) −7.63773 −0.647824 −0.323912 0.946087i \(-0.604998\pi\)
−0.323912 + 0.946087i \(0.604998\pi\)
\(140\) −1.35690 −0.114679
\(141\) −8.20775 −0.691217
\(142\) 10.9879 0.922086
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 7.52111 0.624594
\(146\) 15.3110 1.26714
\(147\) −1.00000 −0.0824786
\(148\) 3.53319 0.290426
\(149\) −7.72348 −0.632732 −0.316366 0.948637i \(-0.602463\pi\)
−0.316366 + 0.948637i \(0.602463\pi\)
\(150\) 3.15883 0.257918
\(151\) 12.4843 1.01596 0.507978 0.861370i \(-0.330393\pi\)
0.507978 + 0.861370i \(0.330393\pi\)
\(152\) −4.29590 −0.348443
\(153\) 2.66487 0.215442
\(154\) 4.29590 0.346173
\(155\) 7.48427 0.601151
\(156\) 0 0
\(157\) −3.28621 −0.262268 −0.131134 0.991365i \(-0.541862\pi\)
−0.131134 + 0.991365i \(0.541862\pi\)
\(158\) 16.0465 1.27659
\(159\) −10.1860 −0.807801
\(160\) 1.35690 0.107272
\(161\) 4.63102 0.364976
\(162\) 1.00000 0.0785674
\(163\) 15.0761 1.18085 0.590424 0.807093i \(-0.298960\pi\)
0.590424 + 0.807093i \(0.298960\pi\)
\(164\) 9.45473 0.738290
\(165\) 5.82908 0.453794
\(166\) −5.62565 −0.436635
\(167\) −9.84846 −0.762097 −0.381048 0.924555i \(-0.624437\pi\)
−0.381048 + 0.924555i \(0.624437\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 3.61596 0.277331
\(171\) −4.29590 −0.328515
\(172\) −11.2470 −0.857574
\(173\) −16.0978 −1.22390 −0.611948 0.790898i \(-0.709614\pi\)
−0.611948 + 0.790898i \(0.709614\pi\)
\(174\) −5.54288 −0.420204
\(175\) 3.15883 0.238785
\(176\) −4.29590 −0.323815
\(177\) 1.75302 0.131765
\(178\) −9.81700 −0.735816
\(179\) −1.39612 −0.104351 −0.0521756 0.998638i \(-0.516616\pi\)
−0.0521756 + 0.998638i \(0.516616\pi\)
\(180\) 1.35690 0.101137
\(181\) −18.4862 −1.37407 −0.687034 0.726625i \(-0.741088\pi\)
−0.687034 + 0.726625i \(0.741088\pi\)
\(182\) 0 0
\(183\) 2.20775 0.163202
\(184\) −4.63102 −0.341404
\(185\) 4.79417 0.352474
\(186\) −5.51573 −0.404433
\(187\) −11.4480 −0.837163
\(188\) 8.20775 0.598612
\(189\) 1.00000 0.0727393
\(190\) −5.82908 −0.422886
\(191\) −7.23251 −0.523326 −0.261663 0.965159i \(-0.584271\pi\)
−0.261663 + 0.965159i \(0.584271\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −11.2228 −0.807836 −0.403918 0.914795i \(-0.632352\pi\)
−0.403918 + 0.914795i \(0.632352\pi\)
\(194\) 18.9366 1.35957
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 4.42088 0.314975 0.157487 0.987521i \(-0.449661\pi\)
0.157487 + 0.987521i \(0.449661\pi\)
\(198\) −4.29590 −0.305296
\(199\) −2.73556 −0.193919 −0.0969594 0.995288i \(-0.530912\pi\)
−0.0969594 + 0.995288i \(0.530912\pi\)
\(200\) −3.15883 −0.223363
\(201\) 4.87263 0.343688
\(202\) −0.00537681 −0.000378311 0
\(203\) −5.54288 −0.389034
\(204\) −2.66487 −0.186579
\(205\) 12.8291 0.896022
\(206\) −0.814019 −0.0567154
\(207\) −4.63102 −0.321878
\(208\) 0 0
\(209\) 18.4547 1.27654
\(210\) 1.35690 0.0936347
\(211\) 2.44504 0.168324 0.0841618 0.996452i \(-0.473179\pi\)
0.0841618 + 0.996452i \(0.473179\pi\)
\(212\) 10.1860 0.699576
\(213\) −10.9879 −0.752880
\(214\) −5.05429 −0.345504
\(215\) −15.2610 −1.04079
\(216\) −1.00000 −0.0680414
\(217\) −5.51573 −0.374432
\(218\) −0.137063 −0.00928310
\(219\) −15.3110 −1.03462
\(220\) −5.82908 −0.392997
\(221\) 0 0
\(222\) −3.53319 −0.237132
\(223\) 2.27844 0.152576 0.0762878 0.997086i \(-0.475693\pi\)
0.0762878 + 0.997086i \(0.475693\pi\)
\(224\) −1.00000 −0.0668153
\(225\) −3.15883 −0.210589
\(226\) 11.4668 0.762761
\(227\) 3.39075 0.225052 0.112526 0.993649i \(-0.464106\pi\)
0.112526 + 0.993649i \(0.464106\pi\)
\(228\) 4.29590 0.284503
\(229\) −16.3884 −1.08297 −0.541486 0.840709i \(-0.682138\pi\)
−0.541486 + 0.840709i \(0.682138\pi\)
\(230\) −6.28382 −0.414343
\(231\) −4.29590 −0.282649
\(232\) 5.54288 0.363908
\(233\) 8.92394 0.584626 0.292313 0.956323i \(-0.405575\pi\)
0.292313 + 0.956323i \(0.405575\pi\)
\(234\) 0 0
\(235\) 11.1371 0.726502
\(236\) −1.75302 −0.114112
\(237\) −16.0465 −1.04233
\(238\) −2.66487 −0.172738
\(239\) −0.263373 −0.0170362 −0.00851809 0.999964i \(-0.502711\pi\)
−0.00851809 + 0.999964i \(0.502711\pi\)
\(240\) −1.35690 −0.0875873
\(241\) 14.0392 0.904346 0.452173 0.891930i \(-0.350649\pi\)
0.452173 + 0.891930i \(0.350649\pi\)
\(242\) 7.45473 0.479208
\(243\) −1.00000 −0.0641500
\(244\) −2.20775 −0.141337
\(245\) 1.35690 0.0866889
\(246\) −9.45473 −0.602812
\(247\) 0 0
\(248\) 5.51573 0.350249
\(249\) 5.62565 0.356511
\(250\) −11.0707 −0.700172
\(251\) 13.6635 0.862435 0.431218 0.902248i \(-0.358084\pi\)
0.431218 + 0.902248i \(0.358084\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 19.8944 1.25075
\(254\) 10.8412 0.680235
\(255\) −3.61596 −0.226440
\(256\) 1.00000 0.0625000
\(257\) 1.99031 0.124152 0.0620761 0.998071i \(-0.480228\pi\)
0.0620761 + 0.998071i \(0.480228\pi\)
\(258\) 11.2470 0.700206
\(259\) −3.53319 −0.219542
\(260\) 0 0
\(261\) 5.54288 0.343095
\(262\) 15.0368 0.928979
\(263\) −15.2446 −0.940021 −0.470011 0.882661i \(-0.655750\pi\)
−0.470011 + 0.882661i \(0.655750\pi\)
\(264\) 4.29590 0.264394
\(265\) 13.8213 0.849037
\(266\) 4.29590 0.263398
\(267\) 9.81700 0.600791
\(268\) −4.87263 −0.297643
\(269\) −6.15883 −0.375511 −0.187755 0.982216i \(-0.560121\pi\)
−0.187755 + 0.982216i \(0.560121\pi\)
\(270\) −1.35690 −0.0825781
\(271\) −0.737955 −0.0448276 −0.0224138 0.999749i \(-0.507135\pi\)
−0.0224138 + 0.999749i \(0.507135\pi\)
\(272\) 2.66487 0.161582
\(273\) 0 0
\(274\) 16.1806 0.977506
\(275\) 13.5700 0.818303
\(276\) 4.63102 0.278755
\(277\) −2.01507 −0.121074 −0.0605368 0.998166i \(-0.519281\pi\)
−0.0605368 + 0.998166i \(0.519281\pi\)
\(278\) −7.63773 −0.458080
\(279\) 5.51573 0.330218
\(280\) −1.35690 −0.0810900
\(281\) 11.1631 0.665937 0.332969 0.942938i \(-0.391950\pi\)
0.332969 + 0.942938i \(0.391950\pi\)
\(282\) −8.20775 −0.488764
\(283\) 12.2664 0.729159 0.364580 0.931172i \(-0.381213\pi\)
0.364580 + 0.931172i \(0.381213\pi\)
\(284\) 10.9879 0.652013
\(285\) 5.82908 0.345285
\(286\) 0 0
\(287\) −9.45473 −0.558095
\(288\) 1.00000 0.0589256
\(289\) −9.89844 −0.582261
\(290\) 7.52111 0.441655
\(291\) −18.9366 −1.11008
\(292\) 15.3110 0.896006
\(293\) −19.2935 −1.12714 −0.563569 0.826069i \(-0.690572\pi\)
−0.563569 + 0.826069i \(0.690572\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −2.37867 −0.138491
\(296\) 3.53319 0.205362
\(297\) 4.29590 0.249273
\(298\) −7.72348 −0.447409
\(299\) 0 0
\(300\) 3.15883 0.182375
\(301\) 11.2470 0.648265
\(302\) 12.4843 0.718389
\(303\) 0.00537681 0.000308890 0
\(304\) −4.29590 −0.246387
\(305\) −2.99569 −0.171533
\(306\) 2.66487 0.152341
\(307\) 17.8562 1.01911 0.509554 0.860438i \(-0.329810\pi\)
0.509554 + 0.860438i \(0.329810\pi\)
\(308\) 4.29590 0.244781
\(309\) 0.814019 0.0463079
\(310\) 7.48427 0.425078
\(311\) −0.957787 −0.0543111 −0.0271556 0.999631i \(-0.508645\pi\)
−0.0271556 + 0.999631i \(0.508645\pi\)
\(312\) 0 0
\(313\) −6.71140 −0.379351 −0.189675 0.981847i \(-0.560744\pi\)
−0.189675 + 0.981847i \(0.560744\pi\)
\(314\) −3.28621 −0.185451
\(315\) −1.35690 −0.0764524
\(316\) 16.0465 0.902688
\(317\) 32.5502 1.82820 0.914100 0.405489i \(-0.132899\pi\)
0.914100 + 0.405489i \(0.132899\pi\)
\(318\) −10.1860 −0.571201
\(319\) −23.8116 −1.33320
\(320\) 1.35690 0.0758528
\(321\) 5.05429 0.282103
\(322\) 4.63102 0.258077
\(323\) −11.4480 −0.636985
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 15.0761 0.834986
\(327\) 0.137063 0.00757962
\(328\) 9.45473 0.522050
\(329\) −8.20775 −0.452508
\(330\) 5.82908 0.320881
\(331\) 30.0761 1.65313 0.826565 0.562841i \(-0.190292\pi\)
0.826565 + 0.562841i \(0.190292\pi\)
\(332\) −5.62565 −0.308747
\(333\) 3.53319 0.193618
\(334\) −9.84846 −0.538884
\(335\) −6.61165 −0.361233
\(336\) 1.00000 0.0545545
\(337\) 0.477566 0.0260147 0.0130073 0.999915i \(-0.495860\pi\)
0.0130073 + 0.999915i \(0.495860\pi\)
\(338\) 0 0
\(339\) −11.4668 −0.622792
\(340\) 3.61596 0.196103
\(341\) −23.6950 −1.28316
\(342\) −4.29590 −0.232296
\(343\) −1.00000 −0.0539949
\(344\) −11.2470 −0.606397
\(345\) 6.28382 0.338309
\(346\) −16.0978 −0.865425
\(347\) 32.8243 1.76210 0.881050 0.473022i \(-0.156837\pi\)
0.881050 + 0.473022i \(0.156837\pi\)
\(348\) −5.54288 −0.297129
\(349\) 18.4789 0.989153 0.494576 0.869134i \(-0.335323\pi\)
0.494576 + 0.869134i \(0.335323\pi\)
\(350\) 3.15883 0.168847
\(351\) 0 0
\(352\) −4.29590 −0.228972
\(353\) 25.8431 1.37549 0.687744 0.725953i \(-0.258601\pi\)
0.687744 + 0.725953i \(0.258601\pi\)
\(354\) 1.75302 0.0931720
\(355\) 14.9095 0.791312
\(356\) −9.81700 −0.520300
\(357\) 2.66487 0.141040
\(358\) −1.39612 −0.0737875
\(359\) −2.74764 −0.145015 −0.0725075 0.997368i \(-0.523100\pi\)
−0.0725075 + 0.997368i \(0.523100\pi\)
\(360\) 1.35690 0.0715147
\(361\) −0.545269 −0.0286984
\(362\) −18.4862 −0.971613
\(363\) −7.45473 −0.391272
\(364\) 0 0
\(365\) 20.7754 1.08743
\(366\) 2.20775 0.115401
\(367\) −6.83579 −0.356825 −0.178413 0.983956i \(-0.557096\pi\)
−0.178413 + 0.983956i \(0.557096\pi\)
\(368\) −4.63102 −0.241409
\(369\) 9.45473 0.492194
\(370\) 4.79417 0.249237
\(371\) −10.1860 −0.528830
\(372\) −5.51573 −0.285977
\(373\) −7.48858 −0.387744 −0.193872 0.981027i \(-0.562105\pi\)
−0.193872 + 0.981027i \(0.562105\pi\)
\(374\) −11.4480 −0.591963
\(375\) 11.0707 0.571688
\(376\) 8.20775 0.423282
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 29.9909 1.54053 0.770265 0.637724i \(-0.220124\pi\)
0.770265 + 0.637724i \(0.220124\pi\)
\(380\) −5.82908 −0.299026
\(381\) −10.8412 −0.555410
\(382\) −7.23251 −0.370047
\(383\) −13.6625 −0.698120 −0.349060 0.937100i \(-0.613499\pi\)
−0.349060 + 0.937100i \(0.613499\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 5.82908 0.297078
\(386\) −11.2228 −0.571226
\(387\) −11.2470 −0.571716
\(388\) 18.9366 0.961361
\(389\) 21.9377 1.11228 0.556142 0.831087i \(-0.312281\pi\)
0.556142 + 0.831087i \(0.312281\pi\)
\(390\) 0 0
\(391\) −12.3411 −0.624116
\(392\) 1.00000 0.0505076
\(393\) −15.0368 −0.758508
\(394\) 4.42088 0.222721
\(395\) 21.7735 1.09554
\(396\) −4.29590 −0.215877
\(397\) −28.9168 −1.45129 −0.725645 0.688069i \(-0.758459\pi\)
−0.725645 + 0.688069i \(0.758459\pi\)
\(398\) −2.73556 −0.137121
\(399\) −4.29590 −0.215064
\(400\) −3.15883 −0.157942
\(401\) −32.8605 −1.64098 −0.820489 0.571663i \(-0.806299\pi\)
−0.820489 + 0.571663i \(0.806299\pi\)
\(402\) 4.87263 0.243024
\(403\) 0 0
\(404\) −0.00537681 −0.000267506 0
\(405\) 1.35690 0.0674247
\(406\) −5.54288 −0.275088
\(407\) −15.1782 −0.752356
\(408\) −2.66487 −0.131931
\(409\) 14.1618 0.700257 0.350128 0.936702i \(-0.386138\pi\)
0.350128 + 0.936702i \(0.386138\pi\)
\(410\) 12.8291 0.633583
\(411\) −16.1806 −0.798130
\(412\) −0.814019 −0.0401039
\(413\) 1.75302 0.0862605
\(414\) −4.63102 −0.227602
\(415\) −7.63342 −0.374710
\(416\) 0 0
\(417\) 7.63773 0.374021
\(418\) 18.4547 0.902650
\(419\) −34.3599 −1.67859 −0.839295 0.543676i \(-0.817032\pi\)
−0.839295 + 0.543676i \(0.817032\pi\)
\(420\) 1.35690 0.0662097
\(421\) −2.66786 −0.130023 −0.0650117 0.997884i \(-0.520708\pi\)
−0.0650117 + 0.997884i \(0.520708\pi\)
\(422\) 2.44504 0.119023
\(423\) 8.20775 0.399075
\(424\) 10.1860 0.494675
\(425\) −8.41789 −0.408328
\(426\) −10.9879 −0.532366
\(427\) 2.20775 0.106841
\(428\) −5.05429 −0.244309
\(429\) 0 0
\(430\) −15.2610 −0.735950
\(431\) −16.2577 −0.783107 −0.391554 0.920155i \(-0.628062\pi\)
−0.391554 + 0.920155i \(0.628062\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 2.77048 0.133141 0.0665704 0.997782i \(-0.478794\pi\)
0.0665704 + 0.997782i \(0.478794\pi\)
\(434\) −5.51573 −0.264763
\(435\) −7.52111 −0.360609
\(436\) −0.137063 −0.00656414
\(437\) 19.8944 0.951678
\(438\) −15.3110 −0.731586
\(439\) 28.3400 1.35260 0.676298 0.736628i \(-0.263583\pi\)
0.676298 + 0.736628i \(0.263583\pi\)
\(440\) −5.82908 −0.277891
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 14.2784 0.678389 0.339195 0.940716i \(-0.389846\pi\)
0.339195 + 0.940716i \(0.389846\pi\)
\(444\) −3.53319 −0.167678
\(445\) −13.3207 −0.631459
\(446\) 2.27844 0.107887
\(447\) 7.72348 0.365308
\(448\) −1.00000 −0.0472456
\(449\) 6.07846 0.286860 0.143430 0.989660i \(-0.454187\pi\)
0.143430 + 0.989660i \(0.454187\pi\)
\(450\) −3.15883 −0.148909
\(451\) −40.6165 −1.91256
\(452\) 11.4668 0.539353
\(453\) −12.4843 −0.586562
\(454\) 3.39075 0.159136
\(455\) 0 0
\(456\) 4.29590 0.201174
\(457\) −34.8702 −1.63116 −0.815580 0.578644i \(-0.803582\pi\)
−0.815580 + 0.578644i \(0.803582\pi\)
\(458\) −16.3884 −0.765778
\(459\) −2.66487 −0.124386
\(460\) −6.28382 −0.292984
\(461\) 35.4717 1.65208 0.826041 0.563610i \(-0.190588\pi\)
0.826041 + 0.563610i \(0.190588\pi\)
\(462\) −4.29590 −0.199863
\(463\) 11.6606 0.541912 0.270956 0.962592i \(-0.412660\pi\)
0.270956 + 0.962592i \(0.412660\pi\)
\(464\) 5.54288 0.257322
\(465\) −7.48427 −0.347075
\(466\) 8.92394 0.413393
\(467\) −19.3394 −0.894922 −0.447461 0.894303i \(-0.647672\pi\)
−0.447461 + 0.894303i \(0.647672\pi\)
\(468\) 0 0
\(469\) 4.87263 0.224997
\(470\) 11.1371 0.513714
\(471\) 3.28621 0.151420
\(472\) −1.75302 −0.0806893
\(473\) 48.3159 2.22157
\(474\) −16.0465 −0.737041
\(475\) 13.5700 0.622635
\(476\) −2.66487 −0.122144
\(477\) 10.1860 0.466384
\(478\) −0.263373 −0.0120464
\(479\) −7.88338 −0.360201 −0.180100 0.983648i \(-0.557642\pi\)
−0.180100 + 0.983648i \(0.557642\pi\)
\(480\) −1.35690 −0.0619335
\(481\) 0 0
\(482\) 14.0392 0.639469
\(483\) −4.63102 −0.210719
\(484\) 7.45473 0.338851
\(485\) 25.6950 1.16675
\(486\) −1.00000 −0.0453609
\(487\) 26.2524 1.18961 0.594804 0.803871i \(-0.297230\pi\)
0.594804 + 0.803871i \(0.297230\pi\)
\(488\) −2.20775 −0.0999402
\(489\) −15.0761 −0.681763
\(490\) 1.35690 0.0612983
\(491\) 39.7023 1.79174 0.895870 0.444316i \(-0.146553\pi\)
0.895870 + 0.444316i \(0.146553\pi\)
\(492\) −9.45473 −0.426252
\(493\) 14.7711 0.665256
\(494\) 0 0
\(495\) −5.82908 −0.261998
\(496\) 5.51573 0.247664
\(497\) −10.9879 −0.492876
\(498\) 5.62565 0.252091
\(499\) −6.89546 −0.308683 −0.154342 0.988018i \(-0.549326\pi\)
−0.154342 + 0.988018i \(0.549326\pi\)
\(500\) −11.0707 −0.495096
\(501\) 9.84846 0.439997
\(502\) 13.6635 0.609834
\(503\) 19.5036 0.869625 0.434812 0.900521i \(-0.356815\pi\)
0.434812 + 0.900521i \(0.356815\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −0.00729577 −0.000324658 0
\(506\) 19.8944 0.884414
\(507\) 0 0
\(508\) 10.8412 0.480999
\(509\) −39.4685 −1.74941 −0.874705 0.484657i \(-0.838945\pi\)
−0.874705 + 0.484657i \(0.838945\pi\)
\(510\) −3.61596 −0.160117
\(511\) −15.3110 −0.677317
\(512\) 1.00000 0.0441942
\(513\) 4.29590 0.189668
\(514\) 1.99031 0.0877889
\(515\) −1.10454 −0.0486718
\(516\) 11.2470 0.495121
\(517\) −35.2597 −1.55072
\(518\) −3.53319 −0.155239
\(519\) 16.0978 0.706617
\(520\) 0 0
\(521\) −16.8998 −0.740392 −0.370196 0.928954i \(-0.620710\pi\)
−0.370196 + 0.928954i \(0.620710\pi\)
\(522\) 5.54288 0.242605
\(523\) −26.4698 −1.15744 −0.578722 0.815525i \(-0.696448\pi\)
−0.578722 + 0.815525i \(0.696448\pi\)
\(524\) 15.0368 0.656887
\(525\) −3.15883 −0.137863
\(526\) −15.2446 −0.664696
\(527\) 14.6987 0.640287
\(528\) 4.29590 0.186955
\(529\) −1.55363 −0.0675491
\(530\) 13.8213 0.600360
\(531\) −1.75302 −0.0760746
\(532\) 4.29590 0.186251
\(533\) 0 0
\(534\) 9.81700 0.424823
\(535\) −6.85815 −0.296504
\(536\) −4.87263 −0.210465
\(537\) 1.39612 0.0602472
\(538\) −6.15883 −0.265526
\(539\) −4.29590 −0.185037
\(540\) −1.35690 −0.0583915
\(541\) −25.9667 −1.11640 −0.558199 0.829707i \(-0.688507\pi\)
−0.558199 + 0.829707i \(0.688507\pi\)
\(542\) −0.737955 −0.0316979
\(543\) 18.4862 0.793318
\(544\) 2.66487 0.114256
\(545\) −0.185981 −0.00796654
\(546\) 0 0
\(547\) −41.4155 −1.77080 −0.885399 0.464831i \(-0.846115\pi\)
−0.885399 + 0.464831i \(0.846115\pi\)
\(548\) 16.1806 0.691201
\(549\) −2.20775 −0.0942245
\(550\) 13.5700 0.578628
\(551\) −23.8116 −1.01441
\(552\) 4.63102 0.197109
\(553\) −16.0465 −0.682368
\(554\) −2.01507 −0.0856119
\(555\) −4.79417 −0.203501
\(556\) −7.63773 −0.323912
\(557\) 15.9500 0.675824 0.337912 0.941178i \(-0.390279\pi\)
0.337912 + 0.941178i \(0.390279\pi\)
\(558\) 5.51573 0.233499
\(559\) 0 0
\(560\) −1.35690 −0.0573393
\(561\) 11.4480 0.483336
\(562\) 11.1631 0.470889
\(563\) −21.9022 −0.923066 −0.461533 0.887123i \(-0.652700\pi\)
−0.461533 + 0.887123i \(0.652700\pi\)
\(564\) −8.20775 −0.345609
\(565\) 15.5593 0.654583
\(566\) 12.2664 0.515593
\(567\) −1.00000 −0.0419961
\(568\) 10.9879 0.461043
\(569\) −38.3159 −1.60628 −0.803142 0.595787i \(-0.796840\pi\)
−0.803142 + 0.595787i \(0.796840\pi\)
\(570\) 5.82908 0.244153
\(571\) 24.6752 1.03262 0.516312 0.856401i \(-0.327305\pi\)
0.516312 + 0.856401i \(0.327305\pi\)
\(572\) 0 0
\(573\) 7.23251 0.302142
\(574\) −9.45473 −0.394633
\(575\) 14.6286 0.610056
\(576\) 1.00000 0.0416667
\(577\) 3.57673 0.148901 0.0744506 0.997225i \(-0.476280\pi\)
0.0744506 + 0.997225i \(0.476280\pi\)
\(578\) −9.89844 −0.411721
\(579\) 11.2228 0.466404
\(580\) 7.52111 0.312297
\(581\) 5.62565 0.233391
\(582\) −18.9366 −0.784948
\(583\) −43.7579 −1.81227
\(584\) 15.3110 0.633572
\(585\) 0 0
\(586\) −19.2935 −0.797007
\(587\) 27.4741 1.13398 0.566989 0.823725i \(-0.308108\pi\)
0.566989 + 0.823725i \(0.308108\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −23.6950 −0.976336
\(590\) −2.37867 −0.0979281
\(591\) −4.42088 −0.181851
\(592\) 3.53319 0.145213
\(593\) 40.0954 1.64652 0.823261 0.567663i \(-0.192152\pi\)
0.823261 + 0.567663i \(0.192152\pi\)
\(594\) 4.29590 0.176263
\(595\) −3.61596 −0.148240
\(596\) −7.72348 −0.316366
\(597\) 2.73556 0.111959
\(598\) 0 0
\(599\) −25.6770 −1.04913 −0.524566 0.851370i \(-0.675772\pi\)
−0.524566 + 0.851370i \(0.675772\pi\)
\(600\) 3.15883 0.128959
\(601\) 33.7071 1.37494 0.687470 0.726212i \(-0.258721\pi\)
0.687470 + 0.726212i \(0.258721\pi\)
\(602\) 11.2470 0.458393
\(603\) −4.87263 −0.198429
\(604\) 12.4843 0.507978
\(605\) 10.1153 0.411245
\(606\) 0.00537681 0.000218418 0
\(607\) −24.8974 −1.01055 −0.505277 0.862957i \(-0.668610\pi\)
−0.505277 + 0.862957i \(0.668610\pi\)
\(608\) −4.29590 −0.174222
\(609\) 5.54288 0.224609
\(610\) −2.99569 −0.121292
\(611\) 0 0
\(612\) 2.66487 0.107721
\(613\) −5.05323 −0.204098 −0.102049 0.994779i \(-0.532540\pi\)
−0.102049 + 0.994779i \(0.532540\pi\)
\(614\) 17.8562 0.720619
\(615\) −12.8291 −0.517319
\(616\) 4.29590 0.173087
\(617\) −39.6577 −1.59656 −0.798279 0.602287i \(-0.794256\pi\)
−0.798279 + 0.602287i \(0.794256\pi\)
\(618\) 0.814019 0.0327447
\(619\) 48.8159 1.96208 0.981039 0.193810i \(-0.0620845\pi\)
0.981039 + 0.193810i \(0.0620845\pi\)
\(620\) 7.48427 0.300576
\(621\) 4.63102 0.185837
\(622\) −0.957787 −0.0384038
\(623\) 9.81700 0.393310
\(624\) 0 0
\(625\) 0.772398 0.0308959
\(626\) −6.71140 −0.268241
\(627\) −18.4547 −0.737011
\(628\) −3.28621 −0.131134
\(629\) 9.41550 0.375421
\(630\) −1.35690 −0.0540600
\(631\) 34.6829 1.38071 0.690353 0.723473i \(-0.257455\pi\)
0.690353 + 0.723473i \(0.257455\pi\)
\(632\) 16.0465 0.638296
\(633\) −2.44504 −0.0971817
\(634\) 32.5502 1.29273
\(635\) 14.7103 0.583762
\(636\) −10.1860 −0.403900
\(637\) 0 0
\(638\) −23.8116 −0.942711
\(639\) 10.9879 0.434675
\(640\) 1.35690 0.0536360
\(641\) 11.9326 0.471308 0.235654 0.971837i \(-0.424277\pi\)
0.235654 + 0.971837i \(0.424277\pi\)
\(642\) 5.05429 0.199477
\(643\) 22.0441 0.869336 0.434668 0.900591i \(-0.356866\pi\)
0.434668 + 0.900591i \(0.356866\pi\)
\(644\) 4.63102 0.182488
\(645\) 15.2610 0.600901
\(646\) −11.4480 −0.450417
\(647\) −48.2650 −1.89749 −0.948747 0.316036i \(-0.897648\pi\)
−0.948747 + 0.316036i \(0.897648\pi\)
\(648\) 1.00000 0.0392837
\(649\) 7.53079 0.295610
\(650\) 0 0
\(651\) 5.51573 0.216178
\(652\) 15.0761 0.590424
\(653\) 45.7730 1.79124 0.895618 0.444825i \(-0.146734\pi\)
0.895618 + 0.444825i \(0.146734\pi\)
\(654\) 0.137063 0.00535960
\(655\) 20.4034 0.797228
\(656\) 9.45473 0.369145
\(657\) 15.3110 0.597338
\(658\) −8.20775 −0.319971
\(659\) −10.1086 −0.393775 −0.196887 0.980426i \(-0.563083\pi\)
−0.196887 + 0.980426i \(0.563083\pi\)
\(660\) 5.82908 0.226897
\(661\) −3.05993 −0.119018 −0.0595088 0.998228i \(-0.518953\pi\)
−0.0595088 + 0.998228i \(0.518953\pi\)
\(662\) 30.0761 1.16894
\(663\) 0 0
\(664\) −5.62565 −0.218317
\(665\) 5.82908 0.226042
\(666\) 3.53319 0.136908
\(667\) −25.6692 −0.993915
\(668\) −9.84846 −0.381048
\(669\) −2.27844 −0.0880895
\(670\) −6.61165 −0.255430
\(671\) 9.48427 0.366136
\(672\) 1.00000 0.0385758
\(673\) 41.6829 1.60676 0.803379 0.595468i \(-0.203033\pi\)
0.803379 + 0.595468i \(0.203033\pi\)
\(674\) 0.477566 0.0183951
\(675\) 3.15883 0.121584
\(676\) 0 0
\(677\) −12.7216 −0.488929 −0.244465 0.969658i \(-0.578612\pi\)
−0.244465 + 0.969658i \(0.578612\pi\)
\(678\) −11.4668 −0.440380
\(679\) −18.9366 −0.726720
\(680\) 3.61596 0.138666
\(681\) −3.39075 −0.129934
\(682\) −23.6950 −0.907329
\(683\) −19.3254 −0.739467 −0.369734 0.929138i \(-0.620551\pi\)
−0.369734 + 0.929138i \(0.620551\pi\)
\(684\) −4.29590 −0.164258
\(685\) 21.9554 0.838873
\(686\) −1.00000 −0.0381802
\(687\) 16.3884 0.625255
\(688\) −11.2470 −0.428787
\(689\) 0 0
\(690\) 6.28382 0.239221
\(691\) −0.774791 −0.0294744 −0.0147372 0.999891i \(-0.504691\pi\)
−0.0147372 + 0.999891i \(0.504691\pi\)
\(692\) −16.0978 −0.611948
\(693\) 4.29590 0.163188
\(694\) 32.8243 1.24599
\(695\) −10.3636 −0.393114
\(696\) −5.54288 −0.210102
\(697\) 25.1957 0.954354
\(698\) 18.4789 0.699436
\(699\) −8.92394 −0.337534
\(700\) 3.15883 0.119393
\(701\) −1.06531 −0.0402362 −0.0201181 0.999798i \(-0.506404\pi\)
−0.0201181 + 0.999798i \(0.506404\pi\)
\(702\) 0 0
\(703\) −15.1782 −0.572457
\(704\) −4.29590 −0.161908
\(705\) −11.1371 −0.419446
\(706\) 25.8431 0.972617
\(707\) 0.00537681 0.000202216 0
\(708\) 1.75302 0.0658825
\(709\) −31.1672 −1.17051 −0.585254 0.810850i \(-0.699005\pi\)
−0.585254 + 0.810850i \(0.699005\pi\)
\(710\) 14.9095 0.559542
\(711\) 16.0465 0.601792
\(712\) −9.81700 −0.367908
\(713\) −25.5435 −0.956610
\(714\) 2.66487 0.0997304
\(715\) 0 0
\(716\) −1.39612 −0.0521756
\(717\) 0.263373 0.00983585
\(718\) −2.74764 −0.102541
\(719\) −31.7385 −1.18365 −0.591824 0.806067i \(-0.701592\pi\)
−0.591824 + 0.806067i \(0.701592\pi\)
\(720\) 1.35690 0.0505685
\(721\) 0.814019 0.0303157
\(722\) −0.545269 −0.0202928
\(723\) −14.0392 −0.522125
\(724\) −18.4862 −0.687034
\(725\) −17.5090 −0.650269
\(726\) −7.45473 −0.276671
\(727\) 47.0907 1.74650 0.873248 0.487276i \(-0.162010\pi\)
0.873248 + 0.487276i \(0.162010\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 20.7754 0.768931
\(731\) −29.9718 −1.10855
\(732\) 2.20775 0.0816008
\(733\) 48.8937 1.80593 0.902964 0.429716i \(-0.141386\pi\)
0.902964 + 0.429716i \(0.141386\pi\)
\(734\) −6.83579 −0.252314
\(735\) −1.35690 −0.0500499
\(736\) −4.63102 −0.170702
\(737\) 20.9323 0.771051
\(738\) 9.45473 0.348033
\(739\) 38.2723 1.40787 0.703935 0.710264i \(-0.251425\pi\)
0.703935 + 0.710264i \(0.251425\pi\)
\(740\) 4.79417 0.176237
\(741\) 0 0
\(742\) −10.1860 −0.373939
\(743\) −0.828020 −0.0303771 −0.0151886 0.999885i \(-0.504835\pi\)
−0.0151886 + 0.999885i \(0.504835\pi\)
\(744\) −5.51573 −0.202216
\(745\) −10.4800 −0.383956
\(746\) −7.48858 −0.274176
\(747\) −5.62565 −0.205832
\(748\) −11.4480 −0.418581
\(749\) 5.05429 0.184680
\(750\) 11.0707 0.404244
\(751\) 42.2586 1.54204 0.771019 0.636812i \(-0.219747\pi\)
0.771019 + 0.636812i \(0.219747\pi\)
\(752\) 8.20775 0.299306
\(753\) −13.6635 −0.497927
\(754\) 0 0
\(755\) 16.9399 0.616504
\(756\) 1.00000 0.0363696
\(757\) 24.5743 0.893169 0.446585 0.894741i \(-0.352640\pi\)
0.446585 + 0.894741i \(0.352640\pi\)
\(758\) 29.9909 1.08932
\(759\) −19.8944 −0.722121
\(760\) −5.82908 −0.211443
\(761\) −15.2798 −0.553891 −0.276946 0.960886i \(-0.589322\pi\)
−0.276946 + 0.960886i \(0.589322\pi\)
\(762\) −10.8412 −0.392734
\(763\) 0.137063 0.00496203
\(764\) −7.23251 −0.261663
\(765\) 3.61596 0.130735
\(766\) −13.6625 −0.493646
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 21.3002 0.768105 0.384053 0.923311i \(-0.374528\pi\)
0.384053 + 0.923311i \(0.374528\pi\)
\(770\) 5.82908 0.210066
\(771\) −1.99031 −0.0716793
\(772\) −11.2228 −0.403918
\(773\) 6.87907 0.247423 0.123711 0.992318i \(-0.460520\pi\)
0.123711 + 0.992318i \(0.460520\pi\)
\(774\) −11.2470 −0.404264
\(775\) −17.4233 −0.625862
\(776\) 18.9366 0.679785
\(777\) 3.53319 0.126752
\(778\) 21.9377 0.786504
\(779\) −40.6165 −1.45524
\(780\) 0 0
\(781\) −47.2030 −1.68905
\(782\) −12.3411 −0.441317
\(783\) −5.54288 −0.198086
\(784\) 1.00000 0.0357143
\(785\) −4.45904 −0.159150
\(786\) −15.0368 −0.536346
\(787\) −10.1967 −0.363474 −0.181737 0.983347i \(-0.558172\pi\)
−0.181737 + 0.983347i \(0.558172\pi\)
\(788\) 4.42088 0.157487
\(789\) 15.2446 0.542722
\(790\) 21.7735 0.774665
\(791\) −11.4668 −0.407713
\(792\) −4.29590 −0.152648
\(793\) 0 0
\(794\) −28.9168 −1.02622
\(795\) −13.8213 −0.490192
\(796\) −2.73556 −0.0969594
\(797\) −34.1041 −1.20803 −0.604014 0.796974i \(-0.706433\pi\)
−0.604014 + 0.796974i \(0.706433\pi\)
\(798\) −4.29590 −0.152073
\(799\) 21.8726 0.773798
\(800\) −3.15883 −0.111682
\(801\) −9.81700 −0.346867
\(802\) −32.8605 −1.16035
\(803\) −65.7743 −2.32113
\(804\) 4.87263 0.171844
\(805\) 6.28382 0.221475
\(806\) 0 0
\(807\) 6.15883 0.216801
\(808\) −0.00537681 −0.000189156 0
\(809\) 26.6853 0.938206 0.469103 0.883144i \(-0.344577\pi\)
0.469103 + 0.883144i \(0.344577\pi\)
\(810\) 1.35690 0.0476765
\(811\) 0.260389 0.00914350 0.00457175 0.999990i \(-0.498545\pi\)
0.00457175 + 0.999990i \(0.498545\pi\)
\(812\) −5.54288 −0.194517
\(813\) 0.737955 0.0258812
\(814\) −15.1782 −0.531996
\(815\) 20.4566 0.716565
\(816\) −2.66487 −0.0932893
\(817\) 48.3159 1.69036
\(818\) 14.1618 0.495156
\(819\) 0 0
\(820\) 12.8291 0.448011
\(821\) −28.5265 −0.995581 −0.497791 0.867297i \(-0.665855\pi\)
−0.497791 + 0.867297i \(0.665855\pi\)
\(822\) −16.1806 −0.564363
\(823\) −22.6980 −0.791202 −0.395601 0.918422i \(-0.629464\pi\)
−0.395601 + 0.918422i \(0.629464\pi\)
\(824\) −0.814019 −0.0283577
\(825\) −13.5700 −0.472448
\(826\) 1.75302 0.0609954
\(827\) −42.5206 −1.47859 −0.739294 0.673383i \(-0.764840\pi\)
−0.739294 + 0.673383i \(0.764840\pi\)
\(828\) −4.63102 −0.160939
\(829\) −28.4286 −0.987368 −0.493684 0.869641i \(-0.664350\pi\)
−0.493684 + 0.869641i \(0.664350\pi\)
\(830\) −7.63342 −0.264960
\(831\) 2.01507 0.0699018
\(832\) 0 0
\(833\) 2.66487 0.0923324
\(834\) 7.63773 0.264473
\(835\) −13.3633 −0.462457
\(836\) 18.4547 0.638270
\(837\) −5.51573 −0.190652
\(838\) −34.3599 −1.18694
\(839\) 6.64502 0.229412 0.114706 0.993400i \(-0.463407\pi\)
0.114706 + 0.993400i \(0.463407\pi\)
\(840\) 1.35690 0.0468174
\(841\) 1.72348 0.0594304
\(842\) −2.66786 −0.0919405
\(843\) −11.1631 −0.384479
\(844\) 2.44504 0.0841618
\(845\) 0 0
\(846\) 8.20775 0.282188
\(847\) −7.45473 −0.256148
\(848\) 10.1860 0.349788
\(849\) −12.2664 −0.420980
\(850\) −8.41789 −0.288731
\(851\) −16.3623 −0.560891
\(852\) −10.9879 −0.376440
\(853\) −21.9571 −0.751795 −0.375898 0.926661i \(-0.622666\pi\)
−0.375898 + 0.926661i \(0.622666\pi\)
\(854\) 2.20775 0.0755477
\(855\) −5.82908 −0.199350
\(856\) −5.05429 −0.172752
\(857\) −34.5060 −1.17870 −0.589352 0.807876i \(-0.700617\pi\)
−0.589352 + 0.807876i \(0.700617\pi\)
\(858\) 0 0
\(859\) −55.4693 −1.89259 −0.946294 0.323306i \(-0.895206\pi\)
−0.946294 + 0.323306i \(0.895206\pi\)
\(860\) −15.2610 −0.520395
\(861\) 9.45473 0.322216
\(862\) −16.2577 −0.553741
\(863\) 22.4808 0.765256 0.382628 0.923903i \(-0.375019\pi\)
0.382628 + 0.923903i \(0.375019\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −21.8431 −0.742687
\(866\) 2.77048 0.0941447
\(867\) 9.89844 0.336169
\(868\) −5.51573 −0.187216
\(869\) −68.9342 −2.33843
\(870\) −7.52111 −0.254989
\(871\) 0 0
\(872\) −0.137063 −0.00464155
\(873\) 18.9366 0.640907
\(874\) 19.8944 0.672938
\(875\) 11.0707 0.374258
\(876\) −15.3110 −0.517309
\(877\) 48.1406 1.62559 0.812797 0.582547i \(-0.197944\pi\)
0.812797 + 0.582547i \(0.197944\pi\)
\(878\) 28.3400 0.956430
\(879\) 19.2935 0.650754
\(880\) −5.82908 −0.196498
\(881\) −11.1521 −0.375725 −0.187862 0.982195i \(-0.560156\pi\)
−0.187862 + 0.982195i \(0.560156\pi\)
\(882\) 1.00000 0.0336718
\(883\) −53.4016 −1.79711 −0.898554 0.438863i \(-0.855381\pi\)
−0.898554 + 0.438863i \(0.855381\pi\)
\(884\) 0 0
\(885\) 2.37867 0.0799580
\(886\) 14.2784 0.479694
\(887\) −16.8963 −0.567323 −0.283661 0.958925i \(-0.591549\pi\)
−0.283661 + 0.958925i \(0.591549\pi\)
\(888\) −3.53319 −0.118566
\(889\) −10.8412 −0.363601
\(890\) −13.3207 −0.446509
\(891\) −4.29590 −0.143918
\(892\) 2.27844 0.0762878
\(893\) −35.2597 −1.17992
\(894\) 7.72348 0.258312
\(895\) −1.89440 −0.0633227
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) 6.07846 0.202841
\(899\) 30.5730 1.01967
\(900\) −3.15883 −0.105294
\(901\) 27.1444 0.904310
\(902\) −40.6165 −1.35238
\(903\) −11.2470 −0.374276
\(904\) 11.4668 0.381380
\(905\) −25.0838 −0.833815
\(906\) −12.4843 −0.414762
\(907\) 25.6359 0.851227 0.425613 0.904905i \(-0.360058\pi\)
0.425613 + 0.904905i \(0.360058\pi\)
\(908\) 3.39075 0.112526
\(909\) −0.00537681 −0.000178338 0
\(910\) 0 0
\(911\) 29.1782 0.966717 0.483359 0.875422i \(-0.339417\pi\)
0.483359 + 0.875422i \(0.339417\pi\)
\(912\) 4.29590 0.142251
\(913\) 24.1672 0.799817
\(914\) −34.8702 −1.15340
\(915\) 2.99569 0.0990344
\(916\) −16.3884 −0.541486
\(917\) −15.0368 −0.496560
\(918\) −2.66487 −0.0879540
\(919\) −21.2677 −0.701556 −0.350778 0.936459i \(-0.614083\pi\)
−0.350778 + 0.936459i \(0.614083\pi\)
\(920\) −6.28382 −0.207171
\(921\) −17.8562 −0.588383
\(922\) 35.4717 1.16820
\(923\) 0 0
\(924\) −4.29590 −0.141325
\(925\) −11.1608 −0.366963
\(926\) 11.6606 0.383190
\(927\) −0.814019 −0.0267359
\(928\) 5.54288 0.181954
\(929\) −17.1830 −0.563756 −0.281878 0.959450i \(-0.590957\pi\)
−0.281878 + 0.959450i \(0.590957\pi\)
\(930\) −7.48427 −0.245419
\(931\) −4.29590 −0.140792
\(932\) 8.92394 0.292313
\(933\) 0.957787 0.0313566
\(934\) −19.3394 −0.632806
\(935\) −15.5338 −0.508009
\(936\) 0 0
\(937\) 53.9323 1.76189 0.880946 0.473217i \(-0.156908\pi\)
0.880946 + 0.473217i \(0.156908\pi\)
\(938\) 4.87263 0.159097
\(939\) 6.71140 0.219018
\(940\) 11.1371 0.363251
\(941\) −33.1124 −1.07943 −0.539717 0.841846i \(-0.681469\pi\)
−0.539717 + 0.841846i \(0.681469\pi\)
\(942\) 3.28621 0.107070
\(943\) −43.7851 −1.42584
\(944\) −1.75302 −0.0570560
\(945\) 1.35690 0.0441398
\(946\) 48.3159 1.57088
\(947\) 47.6396 1.54808 0.774040 0.633136i \(-0.218233\pi\)
0.774040 + 0.633136i \(0.218233\pi\)
\(948\) −16.0465 −0.521167
\(949\) 0 0
\(950\) 13.5700 0.440270
\(951\) −32.5502 −1.05551
\(952\) −2.66487 −0.0863691
\(953\) −50.0901 −1.62258 −0.811288 0.584646i \(-0.801233\pi\)
−0.811288 + 0.584646i \(0.801233\pi\)
\(954\) 10.1860 0.329783
\(955\) −9.81376 −0.317566
\(956\) −0.263373 −0.00851809
\(957\) 23.8116 0.769721
\(958\) −7.88338 −0.254700
\(959\) −16.1806 −0.522499
\(960\) −1.35690 −0.0437936
\(961\) −0.576728 −0.0186041
\(962\) 0 0
\(963\) −5.05429 −0.162872
\(964\) 14.0392 0.452173
\(965\) −15.2282 −0.490213
\(966\) −4.63102 −0.149001
\(967\) −33.2094 −1.06794 −0.533971 0.845503i \(-0.679301\pi\)
−0.533971 + 0.845503i \(0.679301\pi\)
\(968\) 7.45473 0.239604
\(969\) 11.4480 0.367764
\(970\) 25.6950 0.825017
\(971\) −18.3593 −0.589178 −0.294589 0.955624i \(-0.595183\pi\)
−0.294589 + 0.955624i \(0.595183\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 7.63773 0.244854
\(974\) 26.2524 0.841180
\(975\) 0 0
\(976\) −2.20775 −0.0706684
\(977\) 25.6485 0.820568 0.410284 0.911958i \(-0.365430\pi\)
0.410284 + 0.911958i \(0.365430\pi\)
\(978\) −15.0761 −0.482079
\(979\) 42.1728 1.34785
\(980\) 1.35690 0.0433444
\(981\) −0.137063 −0.00437610
\(982\) 39.7023 1.26695
\(983\) 40.8864 1.30407 0.652036 0.758188i \(-0.273915\pi\)
0.652036 + 0.758188i \(0.273915\pi\)
\(984\) −9.45473 −0.301406
\(985\) 5.99867 0.191134
\(986\) 14.7711 0.470407
\(987\) 8.20775 0.261256
\(988\) 0 0
\(989\) 52.0850 1.65621
\(990\) −5.82908 −0.185260
\(991\) 52.4661 1.66664 0.833320 0.552791i \(-0.186437\pi\)
0.833320 + 0.552791i \(0.186437\pi\)
\(992\) 5.51573 0.175125
\(993\) −30.0761 −0.954435
\(994\) −10.9879 −0.348516
\(995\) −3.71187 −0.117674
\(996\) 5.62565 0.178255
\(997\) 40.2669 1.27527 0.637634 0.770340i \(-0.279913\pi\)
0.637634 + 0.770340i \(0.279913\pi\)
\(998\) −6.89546 −0.218272
\(999\) −3.53319 −0.111785
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.1.2 yes 3
13.12 even 2 7098.2.a.cd.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cd.1.2 3 13.12 even 2
7098.2.a.ci.1.2 yes 3 1.1 even 1 trivial