Properties

Label 7098.2.a.cr.1.5
Level $7098$
Weight $2$
Character 7098.1
Self dual yes
Analytic conductor $56.678$
Analytic rank $1$
Dimension $6$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7098.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(56.6778153547\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.48406561.1
Defining polynomial: \(x^{6} - 3 x^{5} - 17 x^{4} + 39 x^{3} + 111 x^{2} - 131 x - 281\)
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 1.5
Root \(-2.10863\) of defining polynomial
Character \(\chi\) \(=\) 7098.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.10863 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.10863 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.10863 q^{10} -1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} +2.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} -1.00000 q^{18} -6.98503 q^{19} +2.10863 q^{20} -1.00000 q^{21} +1.55496 q^{22} -1.97111 q^{23} -1.00000 q^{24} -0.553673 q^{25} +1.00000 q^{27} -1.00000 q^{28} +6.02003 q^{29} -2.10863 q^{30} -2.75174 q^{31} -1.00000 q^{32} -1.55496 q^{33} +1.24698 q^{34} -2.10863 q^{35} +1.00000 q^{36} +2.76545 q^{37} +6.98503 q^{38} -2.10863 q^{40} +7.97320 q^{41} +1.00000 q^{42} -3.66462 q^{43} -1.55496 q^{44} +2.10863 q^{45} +1.97111 q^{46} -5.63759 q^{47} +1.00000 q^{48} +1.00000 q^{49} +0.553673 q^{50} -1.24698 q^{51} +8.81309 q^{53} -1.00000 q^{54} -3.27883 q^{55} +1.00000 q^{56} -6.98503 q^{57} -6.02003 q^{58} -5.40902 q^{59} +2.10863 q^{60} +3.42032 q^{61} +2.75174 q^{62} -1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} +1.40756 q^{67} -1.24698 q^{68} -1.97111 q^{69} +2.10863 q^{70} -11.6269 q^{71} -1.00000 q^{72} +7.48979 q^{73} -2.76545 q^{74} -0.553673 q^{75} -6.98503 q^{76} +1.55496 q^{77} -16.4358 q^{79} +2.10863 q^{80} +1.00000 q^{81} -7.97320 q^{82} -16.7237 q^{83} -1.00000 q^{84} -2.62942 q^{85} +3.66462 q^{86} +6.02003 q^{87} +1.55496 q^{88} -10.9813 q^{89} -2.10863 q^{90} -1.97111 q^{92} -2.75174 q^{93} +5.63759 q^{94} -14.7289 q^{95} -1.00000 q^{96} +6.39487 q^{97} -1.00000 q^{98} -1.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + O(q^{10}) \) \( 6q - 6q^{2} + 6q^{3} + 6q^{4} - 3q^{5} - 6q^{6} - 6q^{7} - 6q^{8} + 6q^{9} + 3q^{10} - 10q^{11} + 6q^{12} + 6q^{14} - 3q^{15} + 6q^{16} + 2q^{17} - 6q^{18} - 2q^{19} - 3q^{20} - 6q^{21} + 10q^{22} + 4q^{23} - 6q^{24} + 13q^{25} + 6q^{27} - 6q^{28} + 2q^{29} + 3q^{30} - 9q^{31} - 6q^{32} - 10q^{33} - 2q^{34} + 3q^{35} + 6q^{36} - 7q^{37} + 2q^{38} + 3q^{40} - 11q^{41} + 6q^{42} - 5q^{43} - 10q^{44} - 3q^{45} - 4q^{46} - 5q^{47} + 6q^{48} + 6q^{49} - 13q^{50} + 2q^{51} - 6q^{53} - 6q^{54} + 5q^{55} + 6q^{56} - 2q^{57} - 2q^{58} - 28q^{59} - 3q^{60} + 23q^{61} + 9q^{62} - 6q^{63} + 6q^{64} + 10q^{66} + 10q^{67} + 2q^{68} + 4q^{69} - 3q^{70} - 21q^{71} - 6q^{72} + 7q^{73} + 7q^{74} + 13q^{75} - 2q^{76} + 10q^{77} - 14q^{79} - 3q^{80} + 6q^{81} + 11q^{82} - 17q^{83} - 6q^{84} - q^{85} + 5q^{86} + 2q^{87} + 10q^{88} - 17q^{89} + 3q^{90} + 4q^{92} - 9q^{93} + 5q^{94} - 22q^{95} - 6q^{96} - 6q^{98} - 10q^{99} + O(q^{100}) \)

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
\(5\) 2.10863 0.943009 0.471504 0.881864i \(-0.343711\pi\)
0.471504 + 0.881864i \(0.343711\pi\)
\(6\) −1.00000 −0.408248
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −2.10863 −0.666808
\(11\) −1.55496 −0.468838 −0.234419 0.972136i \(-0.575319\pi\)
−0.234419 + 0.972136i \(0.575319\pi\)
\(12\) 1.00000 0.288675
\(13\) 0 0
\(14\) 1.00000 0.267261
\(15\) 2.10863 0.544446
\(16\) 1.00000 0.250000
\(17\) −1.24698 −0.302437 −0.151218 0.988500i \(-0.548320\pi\)
−0.151218 + 0.988500i \(0.548320\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.98503 −1.60248 −0.801238 0.598346i \(-0.795825\pi\)
−0.801238 + 0.598346i \(0.795825\pi\)
\(20\) 2.10863 0.471504
\(21\) −1.00000 −0.218218
\(22\) 1.55496 0.331518
\(23\) −1.97111 −0.411005 −0.205502 0.978657i \(-0.565883\pi\)
−0.205502 + 0.978657i \(0.565883\pi\)
\(24\) −1.00000 −0.204124
\(25\) −0.553673 −0.110735
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 6.02003 1.11789 0.558945 0.829204i \(-0.311206\pi\)
0.558945 + 0.829204i \(0.311206\pi\)
\(30\) −2.10863 −0.384982
\(31\) −2.75174 −0.494226 −0.247113 0.968987i \(-0.579482\pi\)
−0.247113 + 0.968987i \(0.579482\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.55496 −0.270683
\(34\) 1.24698 0.213855
\(35\) −2.10863 −0.356424
\(36\) 1.00000 0.166667
\(37\) 2.76545 0.454638 0.227319 0.973820i \(-0.427004\pi\)
0.227319 + 0.973820i \(0.427004\pi\)
\(38\) 6.98503 1.13312
\(39\) 0 0
\(40\) −2.10863 −0.333404
\(41\) 7.97320 1.24521 0.622603 0.782538i \(-0.286075\pi\)
0.622603 + 0.782538i \(0.286075\pi\)
\(42\) 1.00000 0.154303
\(43\) −3.66462 −0.558849 −0.279425 0.960168i \(-0.590144\pi\)
−0.279425 + 0.960168i \(0.590144\pi\)
\(44\) −1.55496 −0.234419
\(45\) 2.10863 0.314336
\(46\) 1.97111 0.290624
\(47\) −5.63759 −0.822326 −0.411163 0.911562i \(-0.634877\pi\)
−0.411163 + 0.911562i \(0.634877\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 0.553673 0.0783012
\(51\) −1.24698 −0.174612
\(52\) 0 0
\(53\) 8.81309 1.21057 0.605285 0.796009i \(-0.293059\pi\)
0.605285 + 0.796009i \(0.293059\pi\)
\(54\) −1.00000 −0.136083
\(55\) −3.27883 −0.442118
\(56\) 1.00000 0.133631
\(57\) −6.98503 −0.925190
\(58\) −6.02003 −0.790468
\(59\) −5.40902 −0.704194 −0.352097 0.935964i \(-0.614531\pi\)
−0.352097 + 0.935964i \(0.614531\pi\)
\(60\) 2.10863 0.272223
\(61\) 3.42032 0.437928 0.218964 0.975733i \(-0.429732\pi\)
0.218964 + 0.975733i \(0.429732\pi\)
\(62\) 2.75174 0.349471
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 1.55496 0.191402
\(67\) 1.40756 0.171960 0.0859802 0.996297i \(-0.472598\pi\)
0.0859802 + 0.996297i \(0.472598\pi\)
\(68\) −1.24698 −0.151218
\(69\) −1.97111 −0.237294
\(70\) 2.10863 0.252030
\(71\) −11.6269 −1.37985 −0.689927 0.723879i \(-0.742357\pi\)
−0.689927 + 0.723879i \(0.742357\pi\)
\(72\) −1.00000 −0.117851
\(73\) 7.48979 0.876613 0.438307 0.898825i \(-0.355578\pi\)
0.438307 + 0.898825i \(0.355578\pi\)
\(74\) −2.76545 −0.321477
\(75\) −0.553673 −0.0639327
\(76\) −6.98503 −0.801238
\(77\) 1.55496 0.177204
\(78\) 0 0
\(79\) −16.4358 −1.84918 −0.924589 0.380967i \(-0.875591\pi\)
−0.924589 + 0.380967i \(0.875591\pi\)
\(80\) 2.10863 0.235752
\(81\) 1.00000 0.111111
\(82\) −7.97320 −0.880493
\(83\) −16.7237 −1.83566 −0.917830 0.396974i \(-0.870060\pi\)
−0.917830 + 0.396974i \(0.870060\pi\)
\(84\) −1.00000 −0.109109
\(85\) −2.62942 −0.285201
\(86\) 3.66462 0.395166
\(87\) 6.02003 0.645415
\(88\) 1.55496 0.165759
\(89\) −10.9813 −1.16401 −0.582005 0.813185i \(-0.697732\pi\)
−0.582005 + 0.813185i \(0.697732\pi\)
\(90\) −2.10863 −0.222269
\(91\) 0 0
\(92\) −1.97111 −0.205502
\(93\) −2.75174 −0.285342
\(94\) 5.63759 0.581473
\(95\) −14.7289 −1.51115
\(96\) −1.00000 −0.102062
\(97\) 6.39487 0.649301 0.324651 0.945834i \(-0.394753\pi\)
0.324651 + 0.945834i \(0.394753\pi\)
\(98\) −1.00000 −0.101015
\(99\) −1.55496 −0.156279
\(100\) −0.553673 −0.0553673
\(101\) −1.28670 −0.128032 −0.0640158 0.997949i \(-0.520391\pi\)
−0.0640158 + 0.997949i \(0.520391\pi\)
\(102\) 1.24698 0.123469
\(103\) 6.54173 0.644576 0.322288 0.946642i \(-0.395548\pi\)
0.322288 + 0.946642i \(0.395548\pi\)
\(104\) 0 0
\(105\) −2.10863 −0.205781
\(106\) −8.81309 −0.856003
\(107\) 2.66334 0.257474 0.128737 0.991679i \(-0.458908\pi\)
0.128737 + 0.991679i \(0.458908\pi\)
\(108\) 1.00000 0.0962250
\(109\) 4.40973 0.422376 0.211188 0.977446i \(-0.432267\pi\)
0.211188 + 0.977446i \(0.432267\pi\)
\(110\) 3.27883 0.312625
\(111\) 2.76545 0.262485
\(112\) −1.00000 −0.0944911
\(113\) −5.81726 −0.547242 −0.273621 0.961838i \(-0.588221\pi\)
−0.273621 + 0.961838i \(0.588221\pi\)
\(114\) 6.98503 0.654208
\(115\) −4.15634 −0.387581
\(116\) 6.02003 0.558945
\(117\) 0 0
\(118\) 5.40902 0.497940
\(119\) 1.24698 0.114310
\(120\) −2.10863 −0.192491
\(121\) −8.58211 −0.780191
\(122\) −3.42032 −0.309662
\(123\) 7.97320 0.718920
\(124\) −2.75174 −0.247113
\(125\) −11.7107 −1.04743
\(126\) 1.00000 0.0890871
\(127\) −3.83276 −0.340103 −0.170051 0.985435i \(-0.554393\pi\)
−0.170051 + 0.985435i \(0.554393\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −3.66462 −0.322652
\(130\) 0 0
\(131\) 11.8617 1.03637 0.518183 0.855270i \(-0.326609\pi\)
0.518183 + 0.855270i \(0.326609\pi\)
\(132\) −1.55496 −0.135342
\(133\) 6.98503 0.605679
\(134\) −1.40756 −0.121594
\(135\) 2.10863 0.181482
\(136\) 1.24698 0.106928
\(137\) −2.18760 −0.186899 −0.0934496 0.995624i \(-0.529789\pi\)
−0.0934496 + 0.995624i \(0.529789\pi\)
\(138\) 1.97111 0.167792
\(139\) 4.14041 0.351185 0.175592 0.984463i \(-0.443816\pi\)
0.175592 + 0.984463i \(0.443816\pi\)
\(140\) −2.10863 −0.178212
\(141\) −5.63759 −0.474770
\(142\) 11.6269 0.975704
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 12.6940 1.05418
\(146\) −7.48979 −0.619859
\(147\) 1.00000 0.0824786
\(148\) 2.76545 0.227319
\(149\) −16.1634 −1.32416 −0.662079 0.749434i \(-0.730326\pi\)
−0.662079 + 0.749434i \(0.730326\pi\)
\(150\) 0.553673 0.0452072
\(151\) −14.5820 −1.18667 −0.593333 0.804957i \(-0.702188\pi\)
−0.593333 + 0.804957i \(0.702188\pi\)
\(152\) 6.98503 0.566561
\(153\) −1.24698 −0.100812
\(154\) −1.55496 −0.125302
\(155\) −5.80240 −0.466060
\(156\) 0 0
\(157\) 5.49884 0.438855 0.219428 0.975629i \(-0.429581\pi\)
0.219428 + 0.975629i \(0.429581\pi\)
\(158\) 16.4358 1.30757
\(159\) 8.81309 0.698923
\(160\) −2.10863 −0.166702
\(161\) 1.97111 0.155345
\(162\) −1.00000 −0.0785674
\(163\) −14.1960 −1.11192 −0.555958 0.831211i \(-0.687648\pi\)
−0.555958 + 0.831211i \(0.687648\pi\)
\(164\) 7.97320 0.622603
\(165\) −3.27883 −0.255257
\(166\) 16.7237 1.29801
\(167\) −24.5175 −1.89722 −0.948612 0.316442i \(-0.897512\pi\)
−0.948612 + 0.316442i \(0.897512\pi\)
\(168\) 1.00000 0.0771517
\(169\) 0 0
\(170\) 2.62942 0.201667
\(171\) −6.98503 −0.534159
\(172\) −3.66462 −0.279425
\(173\) −12.5776 −0.956259 −0.478129 0.878289i \(-0.658685\pi\)
−0.478129 + 0.878289i \(0.658685\pi\)
\(174\) −6.02003 −0.456377
\(175\) 0.553673 0.0418538
\(176\) −1.55496 −0.117209
\(177\) −5.40902 −0.406567
\(178\) 10.9813 0.823080
\(179\) 2.52767 0.188927 0.0944635 0.995528i \(-0.469886\pi\)
0.0944635 + 0.995528i \(0.469886\pi\)
\(180\) 2.10863 0.157168
\(181\) −12.7141 −0.945031 −0.472516 0.881322i \(-0.656654\pi\)
−0.472516 + 0.881322i \(0.656654\pi\)
\(182\) 0 0
\(183\) 3.42032 0.252838
\(184\) 1.97111 0.145312
\(185\) 5.83132 0.428727
\(186\) 2.75174 0.201767
\(187\) 1.93900 0.141794
\(188\) −5.63759 −0.411163
\(189\) −1.00000 −0.0727393
\(190\) 14.7289 1.06854
\(191\) −2.77016 −0.200442 −0.100221 0.994965i \(-0.531955\pi\)
−0.100221 + 0.994965i \(0.531955\pi\)
\(192\) 1.00000 0.0721688
\(193\) −22.2930 −1.60468 −0.802341 0.596865i \(-0.796413\pi\)
−0.802341 + 0.596865i \(0.796413\pi\)
\(194\) −6.39487 −0.459125
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 8.75440 0.623725 0.311863 0.950127i \(-0.399047\pi\)
0.311863 + 0.950127i \(0.399047\pi\)
\(198\) 1.55496 0.110506
\(199\) −14.5824 −1.03372 −0.516859 0.856070i \(-0.672899\pi\)
−0.516859 + 0.856070i \(0.672899\pi\)
\(200\) 0.553673 0.0391506
\(201\) 1.40756 0.0992814
\(202\) 1.28670 0.0905320
\(203\) −6.02003 −0.422523
\(204\) −1.24698 −0.0873060
\(205\) 16.8125 1.17424
\(206\) −6.54173 −0.455784
\(207\) −1.97111 −0.137002
\(208\) 0 0
\(209\) 10.8614 0.751301
\(210\) 2.10863 0.145509
\(211\) 13.1688 0.906575 0.453287 0.891364i \(-0.350251\pi\)
0.453287 + 0.891364i \(0.350251\pi\)
\(212\) 8.81309 0.605285
\(213\) −11.6269 −0.796659
\(214\) −2.66334 −0.182062
\(215\) −7.72733 −0.527000
\(216\) −1.00000 −0.0680414
\(217\) 2.75174 0.186800
\(218\) −4.40973 −0.298665
\(219\) 7.48979 0.506113
\(220\) −3.27883 −0.221059
\(221\) 0 0
\(222\) −2.76545 −0.185605
\(223\) −4.36466 −0.292280 −0.146140 0.989264i \(-0.546685\pi\)
−0.146140 + 0.989264i \(0.546685\pi\)
\(224\) 1.00000 0.0668153
\(225\) −0.553673 −0.0369116
\(226\) 5.81726 0.386958
\(227\) −0.618667 −0.0410624 −0.0205312 0.999789i \(-0.506536\pi\)
−0.0205312 + 0.999789i \(0.506536\pi\)
\(228\) −6.98503 −0.462595
\(229\) 2.93024 0.193636 0.0968180 0.995302i \(-0.469134\pi\)
0.0968180 + 0.995302i \(0.469134\pi\)
\(230\) 4.15634 0.274061
\(231\) 1.55496 0.102309
\(232\) −6.02003 −0.395234
\(233\) −18.7941 −1.23124 −0.615620 0.788043i \(-0.711094\pi\)
−0.615620 + 0.788043i \(0.711094\pi\)
\(234\) 0 0
\(235\) −11.8876 −0.775461
\(236\) −5.40902 −0.352097
\(237\) −16.4358 −1.06762
\(238\) −1.24698 −0.0808297
\(239\) 19.6751 1.27267 0.636337 0.771411i \(-0.280449\pi\)
0.636337 + 0.771411i \(0.280449\pi\)
\(240\) 2.10863 0.136112
\(241\) 5.57097 0.358858 0.179429 0.983771i \(-0.442575\pi\)
0.179429 + 0.983771i \(0.442575\pi\)
\(242\) 8.58211 0.551679
\(243\) 1.00000 0.0641500
\(244\) 3.42032 0.218964
\(245\) 2.10863 0.134716
\(246\) −7.97320 −0.508353
\(247\) 0 0
\(248\) 2.75174 0.174735
\(249\) −16.7237 −1.05982
\(250\) 11.7107 0.740647
\(251\) 10.6372 0.671413 0.335707 0.941967i \(-0.391025\pi\)
0.335707 + 0.941967i \(0.391025\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 3.06499 0.192694
\(254\) 3.83276 0.240489
\(255\) −2.62942 −0.164661
\(256\) 1.00000 0.0625000
\(257\) −2.38334 −0.148669 −0.0743345 0.997233i \(-0.523683\pi\)
−0.0743345 + 0.997233i \(0.523683\pi\)
\(258\) 3.66462 0.228149
\(259\) −2.76545 −0.171837
\(260\) 0 0
\(261\) 6.02003 0.372630
\(262\) −11.8617 −0.732821
\(263\) 7.81509 0.481899 0.240949 0.970538i \(-0.422541\pi\)
0.240949 + 0.970538i \(0.422541\pi\)
\(264\) 1.55496 0.0957011
\(265\) 18.5836 1.14158
\(266\) −6.98503 −0.428280
\(267\) −10.9813 −0.672042
\(268\) 1.40756 0.0859802
\(269\) −7.21556 −0.439940 −0.219970 0.975507i \(-0.570596\pi\)
−0.219970 + 0.975507i \(0.570596\pi\)
\(270\) −2.10863 −0.128327
\(271\) 4.97552 0.302241 0.151121 0.988515i \(-0.451712\pi\)
0.151121 + 0.988515i \(0.451712\pi\)
\(272\) −1.24698 −0.0756092
\(273\) 0 0
\(274\) 2.18760 0.132158
\(275\) 0.860939 0.0519166
\(276\) −1.97111 −0.118647
\(277\) −13.1229 −0.788479 −0.394240 0.919008i \(-0.628992\pi\)
−0.394240 + 0.919008i \(0.628992\pi\)
\(278\) −4.14041 −0.248325
\(279\) −2.75174 −0.164742
\(280\) 2.10863 0.126015
\(281\) 0.105985 0.00632254 0.00316127 0.999995i \(-0.498994\pi\)
0.00316127 + 0.999995i \(0.498994\pi\)
\(282\) 5.63759 0.335713
\(283\) 29.5509 1.75662 0.878309 0.478094i \(-0.158672\pi\)
0.878309 + 0.478094i \(0.158672\pi\)
\(284\) −11.6269 −0.689927
\(285\) −14.7289 −0.872462
\(286\) 0 0
\(287\) −7.97320 −0.470643
\(288\) −1.00000 −0.0589256
\(289\) −15.4450 −0.908532
\(290\) −12.6940 −0.745418
\(291\) 6.39487 0.374874
\(292\) 7.48979 0.438307
\(293\) −12.1002 −0.706903 −0.353451 0.935453i \(-0.614992\pi\)
−0.353451 + 0.935453i \(0.614992\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −11.4056 −0.664061
\(296\) −2.76545 −0.160739
\(297\) −1.55496 −0.0902278
\(298\) 16.1634 0.936322
\(299\) 0 0
\(300\) −0.553673 −0.0319663
\(301\) 3.66462 0.211225
\(302\) 14.5820 0.839099
\(303\) −1.28670 −0.0739190
\(304\) −6.98503 −0.400619
\(305\) 7.21220 0.412969
\(306\) 1.24698 0.0712851
\(307\) 11.8071 0.673867 0.336934 0.941528i \(-0.390610\pi\)
0.336934 + 0.941528i \(0.390610\pi\)
\(308\) 1.55496 0.0886020
\(309\) 6.54173 0.372146
\(310\) 5.80240 0.329554
\(311\) 2.36454 0.134080 0.0670402 0.997750i \(-0.478644\pi\)
0.0670402 + 0.997750i \(0.478644\pi\)
\(312\) 0 0
\(313\) −6.67399 −0.377236 −0.188618 0.982051i \(-0.560401\pi\)
−0.188618 + 0.982051i \(0.560401\pi\)
\(314\) −5.49884 −0.310318
\(315\) −2.10863 −0.118808
\(316\) −16.4358 −0.924589
\(317\) −0.860447 −0.0483275 −0.0241638 0.999708i \(-0.507692\pi\)
−0.0241638 + 0.999708i \(0.507692\pi\)
\(318\) −8.81309 −0.494213
\(319\) −9.36089 −0.524109
\(320\) 2.10863 0.117876
\(321\) 2.66334 0.148653
\(322\) −1.97111 −0.109846
\(323\) 8.71019 0.484648
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 14.1960 0.786243
\(327\) 4.40973 0.243859
\(328\) −7.97320 −0.440247
\(329\) 5.63759 0.310810
\(330\) 3.27883 0.180494
\(331\) −15.4980 −0.851848 −0.425924 0.904759i \(-0.640051\pi\)
−0.425924 + 0.904759i \(0.640051\pi\)
\(332\) −16.7237 −0.917830
\(333\) 2.76545 0.151546
\(334\) 24.5175 1.34154
\(335\) 2.96802 0.162160
\(336\) −1.00000 −0.0545545
\(337\) −15.6615 −0.853135 −0.426568 0.904456i \(-0.640277\pi\)
−0.426568 + 0.904456i \(0.640277\pi\)
\(338\) 0 0
\(339\) −5.81726 −0.315950
\(340\) −2.62942 −0.142600
\(341\) 4.27883 0.231712
\(342\) 6.98503 0.377707
\(343\) −1.00000 −0.0539949
\(344\) 3.66462 0.197583
\(345\) −4.15634 −0.223770
\(346\) 12.5776 0.676177
\(347\) −13.0233 −0.699129 −0.349564 0.936912i \(-0.613670\pi\)
−0.349564 + 0.936912i \(0.613670\pi\)
\(348\) 6.02003 0.322707
\(349\) −26.4749 −1.41717 −0.708584 0.705626i \(-0.750666\pi\)
−0.708584 + 0.705626i \(0.750666\pi\)
\(350\) −0.553673 −0.0295951
\(351\) 0 0
\(352\) 1.55496 0.0828795
\(353\) −21.5831 −1.14875 −0.574375 0.818592i \(-0.694755\pi\)
−0.574375 + 0.818592i \(0.694755\pi\)
\(354\) 5.40902 0.287486
\(355\) −24.5167 −1.30121
\(356\) −10.9813 −0.582005
\(357\) 1.24698 0.0659972
\(358\) −2.52767 −0.133592
\(359\) −4.67664 −0.246824 −0.123412 0.992356i \(-0.539384\pi\)
−0.123412 + 0.992356i \(0.539384\pi\)
\(360\) −2.10863 −0.111135
\(361\) 29.7907 1.56793
\(362\) 12.7141 0.668238
\(363\) −8.58211 −0.450444
\(364\) 0 0
\(365\) 15.7932 0.826654
\(366\) −3.42032 −0.178783
\(367\) 31.3614 1.63705 0.818525 0.574471i \(-0.194792\pi\)
0.818525 + 0.574471i \(0.194792\pi\)
\(368\) −1.97111 −0.102751
\(369\) 7.97320 0.415068
\(370\) −5.83132 −0.303156
\(371\) −8.81309 −0.457553
\(372\) −2.75174 −0.142671
\(373\) 28.2046 1.46038 0.730190 0.683244i \(-0.239432\pi\)
0.730190 + 0.683244i \(0.239432\pi\)
\(374\) −1.93900 −0.100263
\(375\) −11.7107 −0.604735
\(376\) 5.63759 0.290736
\(377\) 0 0
\(378\) 1.00000 0.0514344
\(379\) 32.5590 1.67245 0.836223 0.548390i \(-0.184759\pi\)
0.836223 + 0.548390i \(0.184759\pi\)
\(380\) −14.7289 −0.755574
\(381\) −3.83276 −0.196358
\(382\) 2.77016 0.141734
\(383\) −8.63110 −0.441029 −0.220514 0.975384i \(-0.570774\pi\)
−0.220514 + 0.975384i \(0.570774\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 3.27883 0.167105
\(386\) 22.2930 1.13468
\(387\) −3.66462 −0.186283
\(388\) 6.39487 0.324651
\(389\) −26.3682 −1.33692 −0.668460 0.743748i \(-0.733046\pi\)
−0.668460 + 0.743748i \(0.733046\pi\)
\(390\) 0 0
\(391\) 2.45793 0.124303
\(392\) −1.00000 −0.0505076
\(393\) 11.8617 0.598346
\(394\) −8.75440 −0.441040
\(395\) −34.6571 −1.74379
\(396\) −1.55496 −0.0781396
\(397\) 12.0701 0.605779 0.302889 0.953026i \(-0.402049\pi\)
0.302889 + 0.953026i \(0.402049\pi\)
\(398\) 14.5824 0.730949
\(399\) 6.98503 0.349689
\(400\) −0.553673 −0.0276837
\(401\) 18.5164 0.924664 0.462332 0.886707i \(-0.347013\pi\)
0.462332 + 0.886707i \(0.347013\pi\)
\(402\) −1.40756 −0.0702025
\(403\) 0 0
\(404\) −1.28670 −0.0640158
\(405\) 2.10863 0.104779
\(406\) 6.02003 0.298769
\(407\) −4.30016 −0.213151
\(408\) 1.24698 0.0617347
\(409\) 35.8394 1.77214 0.886072 0.463547i \(-0.153424\pi\)
0.886072 + 0.463547i \(0.153424\pi\)
\(410\) −16.8125 −0.830313
\(411\) −2.18760 −0.107906
\(412\) 6.54173 0.322288
\(413\) 5.40902 0.266160
\(414\) 1.97111 0.0968748
\(415\) −35.2640 −1.73104
\(416\) 0 0
\(417\) 4.14041 0.202757
\(418\) −10.8614 −0.531250
\(419\) 27.0079 1.31942 0.659710 0.751520i \(-0.270679\pi\)
0.659710 + 0.751520i \(0.270679\pi\)
\(420\) −2.10863 −0.102891
\(421\) 26.2859 1.28110 0.640549 0.767918i \(-0.278707\pi\)
0.640549 + 0.767918i \(0.278707\pi\)
\(422\) −13.1688 −0.641045
\(423\) −5.63759 −0.274109
\(424\) −8.81309 −0.428001
\(425\) 0.690419 0.0334903
\(426\) 11.6269 0.563323
\(427\) −3.42032 −0.165521
\(428\) 2.66334 0.128737
\(429\) 0 0
\(430\) 7.72733 0.372645
\(431\) 6.58585 0.317229 0.158615 0.987341i \(-0.449297\pi\)
0.158615 + 0.987341i \(0.449297\pi\)
\(432\) 1.00000 0.0481125
\(433\) 25.4472 1.22291 0.611457 0.791278i \(-0.290584\pi\)
0.611457 + 0.791278i \(0.290584\pi\)
\(434\) −2.75174 −0.132088
\(435\) 12.6940 0.608632
\(436\) 4.40973 0.211188
\(437\) 13.7683 0.658625
\(438\) −7.48979 −0.357876
\(439\) 23.8445 1.13803 0.569017 0.822326i \(-0.307324\pi\)
0.569017 + 0.822326i \(0.307324\pi\)
\(440\) 3.27883 0.156312
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −0.966959 −0.0459416 −0.0229708 0.999736i \(-0.507312\pi\)
−0.0229708 + 0.999736i \(0.507312\pi\)
\(444\) 2.76545 0.131243
\(445\) −23.1554 −1.09767
\(446\) 4.36466 0.206673
\(447\) −16.1634 −0.764503
\(448\) −1.00000 −0.0472456
\(449\) 32.7563 1.54586 0.772932 0.634489i \(-0.218790\pi\)
0.772932 + 0.634489i \(0.218790\pi\)
\(450\) 0.553673 0.0261004
\(451\) −12.3980 −0.583799
\(452\) −5.81726 −0.273621
\(453\) −14.5820 −0.685122
\(454\) 0.618667 0.0290355
\(455\) 0 0
\(456\) 6.98503 0.327104
\(457\) −2.38368 −0.111504 −0.0557520 0.998445i \(-0.517756\pi\)
−0.0557520 + 0.998445i \(0.517756\pi\)
\(458\) −2.93024 −0.136921
\(459\) −1.24698 −0.0582040
\(460\) −4.15634 −0.193791
\(461\) −36.9292 −1.71996 −0.859982 0.510325i \(-0.829525\pi\)
−0.859982 + 0.510325i \(0.829525\pi\)
\(462\) −1.55496 −0.0723432
\(463\) 29.8161 1.38567 0.692836 0.721095i \(-0.256361\pi\)
0.692836 + 0.721095i \(0.256361\pi\)
\(464\) 6.02003 0.279473
\(465\) −5.80240 −0.269080
\(466\) 18.7941 0.870618
\(467\) 9.34853 0.432598 0.216299 0.976327i \(-0.430601\pi\)
0.216299 + 0.976327i \(0.430601\pi\)
\(468\) 0 0
\(469\) −1.40756 −0.0649949
\(470\) 11.8876 0.548334
\(471\) 5.49884 0.253373
\(472\) 5.40902 0.248970
\(473\) 5.69833 0.262010
\(474\) 16.4358 0.754923
\(475\) 3.86743 0.177450
\(476\) 1.24698 0.0571552
\(477\) 8.81309 0.403523
\(478\) −19.6751 −0.899917
\(479\) −17.5839 −0.803429 −0.401715 0.915765i \(-0.631586\pi\)
−0.401715 + 0.915765i \(0.631586\pi\)
\(480\) −2.10863 −0.0962454
\(481\) 0 0
\(482\) −5.57097 −0.253751
\(483\) 1.97111 0.0896886
\(484\) −8.58211 −0.390096
\(485\) 13.4844 0.612297
\(486\) −1.00000 −0.0453609
\(487\) −35.9216 −1.62776 −0.813882 0.581030i \(-0.802650\pi\)
−0.813882 + 0.581030i \(0.802650\pi\)
\(488\) −3.42032 −0.154831
\(489\) −14.1960 −0.641965
\(490\) −2.10863 −0.0952583
\(491\) −28.4463 −1.28376 −0.641882 0.766804i \(-0.721846\pi\)
−0.641882 + 0.766804i \(0.721846\pi\)
\(492\) 7.97320 0.359460
\(493\) −7.50685 −0.338092
\(494\) 0 0
\(495\) −3.27883 −0.147373
\(496\) −2.75174 −0.123557
\(497\) 11.6269 0.521536
\(498\) 16.7237 0.749405
\(499\) 41.0934 1.83960 0.919798 0.392393i \(-0.128353\pi\)
0.919798 + 0.392393i \(0.128353\pi\)
\(500\) −11.7107 −0.523716
\(501\) −24.5175 −1.09536
\(502\) −10.6372 −0.474761
\(503\) −39.3325 −1.75375 −0.876874 0.480720i \(-0.840375\pi\)
−0.876874 + 0.480720i \(0.840375\pi\)
\(504\) 1.00000 0.0445435
\(505\) −2.71318 −0.120735
\(506\) −3.06499 −0.136256
\(507\) 0 0
\(508\) −3.83276 −0.170051
\(509\) 39.3970 1.74624 0.873121 0.487504i \(-0.162093\pi\)
0.873121 + 0.487504i \(0.162093\pi\)
\(510\) 2.62942 0.116433
\(511\) −7.48979 −0.331329
\(512\) −1.00000 −0.0441942
\(513\) −6.98503 −0.308397
\(514\) 2.38334 0.105125
\(515\) 13.7941 0.607841
\(516\) −3.66462 −0.161326
\(517\) 8.76621 0.385537
\(518\) 2.76545 0.121507
\(519\) −12.5776 −0.552096
\(520\) 0 0
\(521\) −14.1675 −0.620689 −0.310344 0.950624i \(-0.600444\pi\)
−0.310344 + 0.950624i \(0.600444\pi\)
\(522\) −6.02003 −0.263489
\(523\) −35.5333 −1.55376 −0.776882 0.629647i \(-0.783200\pi\)
−0.776882 + 0.629647i \(0.783200\pi\)
\(524\) 11.8617 0.518183
\(525\) 0.553673 0.0241643
\(526\) −7.81509 −0.340754
\(527\) 3.43136 0.149472
\(528\) −1.55496 −0.0676709
\(529\) −19.1147 −0.831075
\(530\) −18.5836 −0.807218
\(531\) −5.40902 −0.234731
\(532\) 6.98503 0.302840
\(533\) 0 0
\(534\) 10.9813 0.475205
\(535\) 5.61599 0.242801
\(536\) −1.40756 −0.0607972
\(537\) 2.52767 0.109077
\(538\) 7.21556 0.311085
\(539\) −1.55496 −0.0669768
\(540\) 2.10863 0.0907411
\(541\) 26.1033 1.12227 0.561134 0.827725i \(-0.310365\pi\)
0.561134 + 0.827725i \(0.310365\pi\)
\(542\) −4.97552 −0.213717
\(543\) −12.7141 −0.545614
\(544\) 1.24698 0.0534638
\(545\) 9.29850 0.398304
\(546\) 0 0
\(547\) 30.0222 1.28366 0.641828 0.766848i \(-0.278176\pi\)
0.641828 + 0.766848i \(0.278176\pi\)
\(548\) −2.18760 −0.0934496
\(549\) 3.42032 0.145976
\(550\) −0.860939 −0.0367106
\(551\) −42.0501 −1.79139
\(552\) 1.97111 0.0838960
\(553\) 16.4358 0.698923
\(554\) 13.1229 0.557539
\(555\) 5.83132 0.247526
\(556\) 4.14041 0.175592
\(557\) −2.05456 −0.0870546 −0.0435273 0.999052i \(-0.513860\pi\)
−0.0435273 + 0.999052i \(0.513860\pi\)
\(558\) 2.75174 0.116490
\(559\) 0 0
\(560\) −2.10863 −0.0891059
\(561\) 1.93900 0.0818647
\(562\) −0.105985 −0.00447071
\(563\) −2.42156 −0.102057 −0.0510283 0.998697i \(-0.516250\pi\)
−0.0510283 + 0.998697i \(0.516250\pi\)
\(564\) −5.63759 −0.237385
\(565\) −12.2665 −0.516054
\(566\) −29.5509 −1.24212
\(567\) −1.00000 −0.0419961
\(568\) 11.6269 0.487852
\(569\) 6.71089 0.281335 0.140668 0.990057i \(-0.455075\pi\)
0.140668 + 0.990057i \(0.455075\pi\)
\(570\) 14.7289 0.616924
\(571\) 2.23277 0.0934384 0.0467192 0.998908i \(-0.485123\pi\)
0.0467192 + 0.998908i \(0.485123\pi\)
\(572\) 0 0
\(573\) −2.77016 −0.115725
\(574\) 7.97320 0.332795
\(575\) 1.09135 0.0455125
\(576\) 1.00000 0.0416667
\(577\) 38.5277 1.60393 0.801964 0.597372i \(-0.203788\pi\)
0.801964 + 0.597372i \(0.203788\pi\)
\(578\) 15.4450 0.642429
\(579\) −22.2930 −0.926464
\(580\) 12.6940 0.527090
\(581\) 16.7237 0.693814
\(582\) −6.39487 −0.265076
\(583\) −13.7040 −0.567561
\(584\) −7.48979 −0.309930
\(585\) 0 0
\(586\) 12.1002 0.499856
\(587\) −24.0684 −0.993409 −0.496704 0.867920i \(-0.665457\pi\)
−0.496704 + 0.867920i \(0.665457\pi\)
\(588\) 1.00000 0.0412393
\(589\) 19.2210 0.791986
\(590\) 11.4056 0.469562
\(591\) 8.75440 0.360108
\(592\) 2.76545 0.113659
\(593\) −18.5679 −0.762492 −0.381246 0.924474i \(-0.624505\pi\)
−0.381246 + 0.924474i \(0.624505\pi\)
\(594\) 1.55496 0.0638007
\(595\) 2.62942 0.107796
\(596\) −16.1634 −0.662079
\(597\) −14.5824 −0.596818
\(598\) 0 0
\(599\) 38.4810 1.57229 0.786145 0.618042i \(-0.212074\pi\)
0.786145 + 0.618042i \(0.212074\pi\)
\(600\) 0.553673 0.0226036
\(601\) −46.5198 −1.89758 −0.948791 0.315905i \(-0.897692\pi\)
−0.948791 + 0.315905i \(0.897692\pi\)
\(602\) −3.66462 −0.149359
\(603\) 1.40756 0.0573201
\(604\) −14.5820 −0.593333
\(605\) −18.0965 −0.735727
\(606\) 1.28670 0.0522687
\(607\) −3.32130 −0.134807 −0.0674037 0.997726i \(-0.521472\pi\)
−0.0674037 + 0.997726i \(0.521472\pi\)
\(608\) 6.98503 0.283280
\(609\) −6.02003 −0.243944
\(610\) −7.21220 −0.292013
\(611\) 0 0
\(612\) −1.24698 −0.0504062
\(613\) −6.34784 −0.256387 −0.128193 0.991749i \(-0.540918\pi\)
−0.128193 + 0.991749i \(0.540918\pi\)
\(614\) −11.8071 −0.476496
\(615\) 16.8125 0.677947
\(616\) −1.55496 −0.0626510
\(617\) −31.3868 −1.26358 −0.631792 0.775138i \(-0.717680\pi\)
−0.631792 + 0.775138i \(0.717680\pi\)
\(618\) −6.54173 −0.263147
\(619\) 8.74463 0.351476 0.175738 0.984437i \(-0.443769\pi\)
0.175738 + 0.984437i \(0.443769\pi\)
\(620\) −5.80240 −0.233030
\(621\) −1.97111 −0.0790979
\(622\) −2.36454 −0.0948092
\(623\) 10.9813 0.439955
\(624\) 0 0
\(625\) −21.9251 −0.877003
\(626\) 6.67399 0.266746
\(627\) 10.8614 0.433764
\(628\) 5.49884 0.219428
\(629\) −3.44846 −0.137499
\(630\) 2.10863 0.0840099
\(631\) 37.0302 1.47415 0.737074 0.675812i \(-0.236207\pi\)
0.737074 + 0.675812i \(0.236207\pi\)
\(632\) 16.4358 0.653783
\(633\) 13.1688 0.523411
\(634\) 0.860447 0.0341727
\(635\) −8.08188 −0.320720
\(636\) 8.81309 0.349462
\(637\) 0 0
\(638\) 9.36089 0.370601
\(639\) −11.6269 −0.459951
\(640\) −2.10863 −0.0833510
\(641\) −4.96318 −0.196034 −0.0980169 0.995185i \(-0.531250\pi\)
−0.0980169 + 0.995185i \(0.531250\pi\)
\(642\) −2.66334 −0.105113
\(643\) −0.0131905 −0.000520184 0 −0.000260092 1.00000i \(-0.500083\pi\)
−0.000260092 1.00000i \(0.500083\pi\)
\(644\) 1.97111 0.0776726
\(645\) −7.72733 −0.304263
\(646\) −8.71019 −0.342698
\(647\) 16.2940 0.640582 0.320291 0.947319i \(-0.396219\pi\)
0.320291 + 0.947319i \(0.396219\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 8.41079 0.330153
\(650\) 0 0
\(651\) 2.75174 0.107849
\(652\) −14.1960 −0.555958
\(653\) −29.3247 −1.14756 −0.573782 0.819008i \(-0.694524\pi\)
−0.573782 + 0.819008i \(0.694524\pi\)
\(654\) −4.40973 −0.172434
\(655\) 25.0121 0.977302
\(656\) 7.97320 0.311301
\(657\) 7.48979 0.292204
\(658\) −5.63759 −0.219776
\(659\) −33.7303 −1.31395 −0.656974 0.753914i \(-0.728164\pi\)
−0.656974 + 0.753914i \(0.728164\pi\)
\(660\) −3.27883 −0.127628
\(661\) −11.4642 −0.445907 −0.222953 0.974829i \(-0.571570\pi\)
−0.222953 + 0.974829i \(0.571570\pi\)
\(662\) 15.4980 0.602348
\(663\) 0 0
\(664\) 16.7237 0.649004
\(665\) 14.7289 0.571161
\(666\) −2.76545 −0.107159
\(667\) −11.8661 −0.459458
\(668\) −24.5175 −0.948612
\(669\) −4.36466 −0.168748
\(670\) −2.96802 −0.114665
\(671\) −5.31846 −0.205317
\(672\) 1.00000 0.0385758
\(673\) −16.8424 −0.649227 −0.324614 0.945847i \(-0.605234\pi\)
−0.324614 + 0.945847i \(0.605234\pi\)
\(674\) 15.6615 0.603258
\(675\) −0.553673 −0.0213109
\(676\) 0 0
\(677\) −14.5299 −0.558429 −0.279215 0.960229i \(-0.590074\pi\)
−0.279215 + 0.960229i \(0.590074\pi\)
\(678\) 5.81726 0.223410
\(679\) −6.39487 −0.245413
\(680\) 2.62942 0.100834
\(681\) −0.618667 −0.0237074
\(682\) −4.27883 −0.163845
\(683\) 0.888021 0.0339792 0.0169896 0.999856i \(-0.494592\pi\)
0.0169896 + 0.999856i \(0.494592\pi\)
\(684\) −6.98503 −0.267079
\(685\) −4.61284 −0.176248
\(686\) 1.00000 0.0381802
\(687\) 2.93024 0.111796
\(688\) −3.66462 −0.139712
\(689\) 0 0
\(690\) 4.15634 0.158229
\(691\) 32.1864 1.22443 0.612214 0.790692i \(-0.290279\pi\)
0.612214 + 0.790692i \(0.290279\pi\)
\(692\) −12.5776 −0.478129
\(693\) 1.55496 0.0590680
\(694\) 13.0233 0.494359
\(695\) 8.73060 0.331170
\(696\) −6.02003 −0.228189
\(697\) −9.94242 −0.376596
\(698\) 26.4749 1.00209
\(699\) −18.7941 −0.710857
\(700\) 0.553673 0.0209269
\(701\) −29.3407 −1.10818 −0.554091 0.832456i \(-0.686934\pi\)
−0.554091 + 0.832456i \(0.686934\pi\)
\(702\) 0 0
\(703\) −19.3168 −0.728546
\(704\) −1.55496 −0.0586047
\(705\) −11.8876 −0.447713
\(706\) 21.5831 0.812289
\(707\) 1.28670 0.0483914
\(708\) −5.40902 −0.203283
\(709\) 34.9450 1.31239 0.656194 0.754592i \(-0.272165\pi\)
0.656194 + 0.754592i \(0.272165\pi\)
\(710\) 24.5167 0.920097
\(711\) −16.4358 −0.616392
\(712\) 10.9813 0.411540
\(713\) 5.42397 0.203129
\(714\) −1.24698 −0.0466670
\(715\) 0 0
\(716\) 2.52767 0.0944635
\(717\) 19.6751 0.734779
\(718\) 4.67664 0.174531
\(719\) −39.7736 −1.48331 −0.741653 0.670784i \(-0.765958\pi\)
−0.741653 + 0.670784i \(0.765958\pi\)
\(720\) 2.10863 0.0785841
\(721\) −6.54173 −0.243627
\(722\) −29.7907 −1.10869
\(723\) 5.57097 0.207187
\(724\) −12.7141 −0.472516
\(725\) −3.33313 −0.123789
\(726\) 8.58211 0.318512
\(727\) 28.3096 1.04995 0.524973 0.851119i \(-0.324075\pi\)
0.524973 + 0.851119i \(0.324075\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −15.7932 −0.584533
\(731\) 4.56971 0.169017
\(732\) 3.42032 0.126419
\(733\) −15.4937 −0.572272 −0.286136 0.958189i \(-0.592371\pi\)
−0.286136 + 0.958189i \(0.592371\pi\)
\(734\) −31.3614 −1.15757
\(735\) 2.10863 0.0777780
\(736\) 1.97111 0.0726561
\(737\) −2.18869 −0.0806215
\(738\) −7.97320 −0.293498
\(739\) −46.7102 −1.71826 −0.859132 0.511755i \(-0.828996\pi\)
−0.859132 + 0.511755i \(0.828996\pi\)
\(740\) 5.83132 0.214364
\(741\) 0 0
\(742\) 8.81309 0.323539
\(743\) −37.7024 −1.38317 −0.691584 0.722296i \(-0.743087\pi\)
−0.691584 + 0.722296i \(0.743087\pi\)
\(744\) 2.75174 0.100884
\(745\) −34.0827 −1.24869
\(746\) −28.2046 −1.03264
\(747\) −16.7237 −0.611887
\(748\) 1.93900 0.0708969
\(749\) −2.66334 −0.0973161
\(750\) 11.7107 0.427612
\(751\) −30.7925 −1.12364 −0.561818 0.827261i \(-0.689898\pi\)
−0.561818 + 0.827261i \(0.689898\pi\)
\(752\) −5.63759 −0.205582
\(753\) 10.6372 0.387641
\(754\) 0 0
\(755\) −30.7480 −1.11904
\(756\) −1.00000 −0.0363696
\(757\) 8.21818 0.298695 0.149347 0.988785i \(-0.452283\pi\)
0.149347 + 0.988785i \(0.452283\pi\)
\(758\) −32.5590 −1.18260
\(759\) 3.06499 0.111252
\(760\) 14.7289 0.534272
\(761\) 42.8880 1.55469 0.777345 0.629074i \(-0.216566\pi\)
0.777345 + 0.629074i \(0.216566\pi\)
\(762\) 3.83276 0.138846
\(763\) −4.40973 −0.159643
\(764\) −2.77016 −0.100221
\(765\) −2.62942 −0.0950669
\(766\) 8.63110 0.311854
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −49.1724 −1.77320 −0.886602 0.462534i \(-0.846940\pi\)
−0.886602 + 0.462534i \(0.846940\pi\)
\(770\) −3.27883 −0.118161
\(771\) −2.38334 −0.0858340
\(772\) −22.2930 −0.802341
\(773\) 10.3709 0.373016 0.186508 0.982453i \(-0.440283\pi\)
0.186508 + 0.982453i \(0.440283\pi\)
\(774\) 3.66462 0.131722
\(775\) 1.52356 0.0547280
\(776\) −6.39487 −0.229563
\(777\) −2.76545 −0.0992101
\(778\) 26.3682 0.945345
\(779\) −55.6931 −1.99541
\(780\) 0 0
\(781\) 18.0793 0.646927
\(782\) −2.45793 −0.0878955
\(783\) 6.02003 0.215138
\(784\) 1.00000 0.0357143
\(785\) 11.5950 0.413844
\(786\) −11.8617 −0.423095
\(787\) 23.5512 0.839509 0.419754 0.907638i \(-0.362116\pi\)
0.419754 + 0.907638i \(0.362116\pi\)
\(788\) 8.75440 0.311863
\(789\) 7.81509 0.278224
\(790\) 34.6571 1.23305
\(791\) 5.81726 0.206838
\(792\) 1.55496 0.0552530
\(793\) 0 0
\(794\) −12.0701 −0.428350
\(795\) 18.5836 0.659091
\(796\) −14.5824 −0.516859
\(797\) −26.7104 −0.946132 −0.473066 0.881027i \(-0.656853\pi\)
−0.473066 + 0.881027i \(0.656853\pi\)
\(798\) −6.98503 −0.247267
\(799\) 7.02995 0.248702
\(800\) 0.553673 0.0195753
\(801\) −10.9813 −0.388004
\(802\) −18.5164 −0.653836
\(803\) −11.6463 −0.410989
\(804\) 1.40756 0.0496407
\(805\) 4.15634 0.146492
\(806\) 0 0
\(807\) −7.21556 −0.254000
\(808\) 1.28670 0.0452660
\(809\) −3.80663 −0.133834 −0.0669169 0.997759i \(-0.521316\pi\)
−0.0669169 + 0.997759i \(0.521316\pi\)
\(810\) −2.10863 −0.0740898
\(811\) 0.849234 0.0298206 0.0149103 0.999889i \(-0.495254\pi\)
0.0149103 + 0.999889i \(0.495254\pi\)
\(812\) −6.02003 −0.211262
\(813\) 4.97552 0.174499
\(814\) 4.30016 0.150721
\(815\) −29.9341 −1.04855
\(816\) −1.24698 −0.0436530
\(817\) 25.5975 0.895543
\(818\) −35.8394 −1.25310
\(819\) 0 0
\(820\) 16.8125 0.587120
\(821\) −20.0311 −0.699090 −0.349545 0.936919i \(-0.613664\pi\)
−0.349545 + 0.936919i \(0.613664\pi\)
\(822\) 2.18760 0.0763013
\(823\) 36.6174 1.27640 0.638201 0.769870i \(-0.279679\pi\)
0.638201 + 0.769870i \(0.279679\pi\)
\(824\) −6.54173 −0.227892
\(825\) 0.860939 0.0299740
\(826\) −5.40902 −0.188204
\(827\) 14.3761 0.499907 0.249953 0.968258i \(-0.419585\pi\)
0.249953 + 0.968258i \(0.419585\pi\)
\(828\) −1.97111 −0.0685008
\(829\) −6.10322 −0.211974 −0.105987 0.994368i \(-0.533800\pi\)
−0.105987 + 0.994368i \(0.533800\pi\)
\(830\) 35.2640 1.22403
\(831\) −13.1229 −0.455229
\(832\) 0 0
\(833\) −1.24698 −0.0432053
\(834\) −4.14041 −0.143371
\(835\) −51.6984 −1.78910
\(836\) 10.8614 0.375650
\(837\) −2.75174 −0.0951139
\(838\) −27.0079 −0.932971
\(839\) 53.2223 1.83744 0.918718 0.394914i \(-0.129226\pi\)
0.918718 + 0.394914i \(0.129226\pi\)
\(840\) 2.10863 0.0727547
\(841\) 7.24072 0.249680
\(842\) −26.2859 −0.905873
\(843\) 0.105985 0.00365032
\(844\) 13.1688 0.453287
\(845\) 0 0
\(846\) 5.63759 0.193824
\(847\) 8.58211 0.294885
\(848\) 8.81309 0.302643
\(849\) 29.5509 1.01418
\(850\) −0.690419 −0.0236812
\(851\) −5.45101 −0.186858
\(852\) −11.6269 −0.398329
\(853\) −13.3932 −0.458573 −0.229287 0.973359i \(-0.573639\pi\)
−0.229287 + 0.973359i \(0.573639\pi\)
\(854\) 3.42032 0.117041
\(855\) −14.7289 −0.503716
\(856\) −2.66334 −0.0910309
\(857\) −3.82155 −0.130541 −0.0652707 0.997868i \(-0.520791\pi\)
−0.0652707 + 0.997868i \(0.520791\pi\)
\(858\) 0 0
\(859\) −44.8782 −1.53122 −0.765612 0.643302i \(-0.777564\pi\)
−0.765612 + 0.643302i \(0.777564\pi\)
\(860\) −7.72733 −0.263500
\(861\) −7.97320 −0.271726
\(862\) −6.58585 −0.224315
\(863\) −8.69475 −0.295973 −0.147986 0.988989i \(-0.547279\pi\)
−0.147986 + 0.988989i \(0.547279\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −26.5216 −0.901760
\(866\) −25.4472 −0.864731
\(867\) −15.4450 −0.524541
\(868\) 2.75174 0.0934000
\(869\) 25.5571 0.866964
\(870\) −12.6940 −0.430368
\(871\) 0 0
\(872\) −4.40973 −0.149332
\(873\) 6.39487 0.216434
\(874\) −13.7683 −0.465718
\(875\) 11.7107 0.395892
\(876\) 7.48979 0.253056
\(877\) −21.9730 −0.741976 −0.370988 0.928638i \(-0.620981\pi\)
−0.370988 + 0.928638i \(0.620981\pi\)
\(878\) −23.8445 −0.804712
\(879\) −12.1002 −0.408131
\(880\) −3.27883 −0.110529
\(881\) −29.7224 −1.00137 −0.500687 0.865628i \(-0.666919\pi\)
−0.500687 + 0.865628i \(0.666919\pi\)
\(882\) −1.00000 −0.0336718
\(883\) 35.0900 1.18087 0.590436 0.807084i \(-0.298956\pi\)
0.590436 + 0.807084i \(0.298956\pi\)
\(884\) 0 0
\(885\) −11.4056 −0.383396
\(886\) 0.966959 0.0324856
\(887\) 25.4402 0.854200 0.427100 0.904204i \(-0.359535\pi\)
0.427100 + 0.904204i \(0.359535\pi\)
\(888\) −2.76545 −0.0928025
\(889\) 3.83276 0.128547
\(890\) 23.1554 0.776172
\(891\) −1.55496 −0.0520931
\(892\) −4.36466 −0.146140
\(893\) 39.3787 1.31776
\(894\) 16.1634 0.540586
\(895\) 5.32992 0.178160
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −32.7563 −1.09309
\(899\) −16.5655 −0.552491
\(900\) −0.553673 −0.0184558
\(901\) −10.9897 −0.366121
\(902\) 12.3980 0.412808
\(903\) 3.66462 0.121951
\(904\) 5.81726 0.193479
\(905\) −26.8093 −0.891172
\(906\) 14.5820 0.484454
\(907\) 52.5340 1.74436 0.872181 0.489183i \(-0.162705\pi\)
0.872181 + 0.489183i \(0.162705\pi\)
\(908\) −0.618667 −0.0205312
\(909\) −1.28670 −0.0426772
\(910\) 0 0
\(911\) −15.7819 −0.522879 −0.261439 0.965220i \(-0.584197\pi\)
−0.261439 + 0.965220i \(0.584197\pi\)
\(912\) −6.98503 −0.231298
\(913\) 26.0046 0.860626
\(914\) 2.38368 0.0788452
\(915\) 7.21220 0.238428
\(916\) 2.93024 0.0968180
\(917\) −11.8617 −0.391709
\(918\) 1.24698 0.0411565
\(919\) −49.8498 −1.64439 −0.822197 0.569203i \(-0.807252\pi\)
−0.822197 + 0.569203i \(0.807252\pi\)
\(920\) 4.15634 0.137031
\(921\) 11.8071 0.389057
\(922\) 36.9292 1.21620
\(923\) 0 0
\(924\) 1.55496 0.0511544
\(925\) −1.53116 −0.0503442
\(926\) −29.8161 −0.979818
\(927\) 6.54173 0.214859
\(928\) −6.02003 −0.197617
\(929\) 19.1901 0.629606 0.314803 0.949157i \(-0.398062\pi\)
0.314803 + 0.949157i \(0.398062\pi\)
\(930\) 5.80240 0.190268
\(931\) −6.98503 −0.228925
\(932\) −18.7941 −0.615620
\(933\) 2.36454 0.0774114
\(934\) −9.34853 −0.305893
\(935\) 4.08864 0.133713
\(936\) 0 0
\(937\) −23.4063 −0.764650 −0.382325 0.924028i \(-0.624876\pi\)
−0.382325 + 0.924028i \(0.624876\pi\)
\(938\) 1.40756 0.0459584
\(939\) −6.67399 −0.217797
\(940\) −11.8876 −0.387730
\(941\) −3.86671 −0.126051 −0.0630256 0.998012i \(-0.520075\pi\)
−0.0630256 + 0.998012i \(0.520075\pi\)
\(942\) −5.49884 −0.179162
\(943\) −15.7161 −0.511785
\(944\) −5.40902 −0.176048
\(945\) −2.10863 −0.0685938
\(946\) −5.69833 −0.185269
\(947\) 48.4114 1.57316 0.786579 0.617489i \(-0.211850\pi\)
0.786579 + 0.617489i \(0.211850\pi\)
\(948\) −16.4358 −0.533811
\(949\) 0 0
\(950\) −3.86743 −0.125476
\(951\) −0.860447 −0.0279019
\(952\) −1.24698 −0.0404148
\(953\) 22.6556 0.733885 0.366943 0.930244i \(-0.380405\pi\)
0.366943 + 0.930244i \(0.380405\pi\)
\(954\) −8.81309 −0.285334
\(955\) −5.84125 −0.189018
\(956\) 19.6751 0.636337
\(957\) −9.36089 −0.302595
\(958\) 17.5839 0.568110
\(959\) 2.18760 0.0706413
\(960\) 2.10863 0.0680558
\(961\) −23.4280 −0.755740
\(962\) 0 0
\(963\) 2.66334 0.0858248
\(964\) 5.57097 0.179429
\(965\) −47.0077 −1.51323
\(966\) −1.97111 −0.0634194
\(967\) 19.7448 0.634950 0.317475 0.948267i \(-0.397165\pi\)
0.317475 + 0.948267i \(0.397165\pi\)
\(968\) 8.58211 0.275839
\(969\) 8.71019 0.279812
\(970\) −13.4844 −0.432959
\(971\) −12.7120 −0.407947 −0.203974 0.978976i \(-0.565386\pi\)
−0.203974 + 0.978976i \(0.565386\pi\)
\(972\) 1.00000 0.0320750
\(973\) −4.14041 −0.132735
\(974\) 35.9216 1.15100
\(975\) 0 0
\(976\) 3.42032 0.109482
\(977\) 41.1062 1.31510 0.657552 0.753409i \(-0.271592\pi\)
0.657552 + 0.753409i \(0.271592\pi\)
\(978\) 14.1960 0.453938
\(979\) 17.0754 0.545732
\(980\) 2.10863 0.0673578
\(981\) 4.40973 0.140792
\(982\) 28.4463 0.907758
\(983\) −12.6710 −0.404144 −0.202072 0.979371i \(-0.564767\pi\)
−0.202072 + 0.979371i \(0.564767\pi\)
\(984\) −7.97320 −0.254176
\(985\) 18.4598 0.588178
\(986\) 7.50685 0.239067
\(987\) 5.63759 0.179446
\(988\) 0 0
\(989\) 7.22337 0.229690
\(990\) 3.27883 0.104208
\(991\) 42.4770 1.34932 0.674662 0.738126i \(-0.264289\pi\)
0.674662 + 0.738126i \(0.264289\pi\)
\(992\) 2.75174 0.0873677
\(993\) −15.4980 −0.491815
\(994\) −11.6269 −0.368781
\(995\) −30.7489 −0.974806
\(996\) −16.7237 −0.529909
\(997\) 8.78235 0.278140 0.139070 0.990283i \(-0.455589\pi\)
0.139070 + 0.990283i \(0.455589\pi\)
\(998\) −41.0934 −1.30079
\(999\) 2.76545 0.0874951
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.cr.1.5 6
13.12 even 2 7098.2.a.ct.1.2 yes 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7098.2.a.cr.1.5 6 1.1 even 1 trivial
7098.2.a.ct.1.2 yes 6 13.12 even 2