Properties

Label 7406.2.a.h.1.1
Level $7406$
Weight $2$
Character 7406.1
Self dual yes
Analytic conductor $59.137$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7406.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.1372077370\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7406.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +4.00000 q^{10} -1.00000 q^{12} +2.00000 q^{13} +1.00000 q^{14} -4.00000 q^{15} +1.00000 q^{16} -5.00000 q^{17} -2.00000 q^{18} +7.00000 q^{19} +4.00000 q^{20} -1.00000 q^{21} -1.00000 q^{24} +11.0000 q^{25} +2.00000 q^{26} +5.00000 q^{27} +1.00000 q^{28} +8.00000 q^{29} -4.00000 q^{30} -2.00000 q^{31} +1.00000 q^{32} -5.00000 q^{34} +4.00000 q^{35} -2.00000 q^{36} -8.00000 q^{37} +7.00000 q^{38} -2.00000 q^{39} +4.00000 q^{40} -2.00000 q^{41} -1.00000 q^{42} +3.00000 q^{43} -8.00000 q^{45} -1.00000 q^{48} +1.00000 q^{49} +11.0000 q^{50} +5.00000 q^{51} +2.00000 q^{52} +6.00000 q^{53} +5.00000 q^{54} +1.00000 q^{56} -7.00000 q^{57} +8.00000 q^{58} -9.00000 q^{59} -4.00000 q^{60} -6.00000 q^{61} -2.00000 q^{62} -2.00000 q^{63} +1.00000 q^{64} +8.00000 q^{65} -5.00000 q^{67} -5.00000 q^{68} +4.00000 q^{70} -2.00000 q^{71} -2.00000 q^{72} +17.0000 q^{73} -8.00000 q^{74} -11.0000 q^{75} +7.00000 q^{76} -2.00000 q^{78} +4.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +13.0000 q^{83} -1.00000 q^{84} -20.0000 q^{85} +3.00000 q^{86} -8.00000 q^{87} -6.00000 q^{89} -8.00000 q^{90} +2.00000 q^{91} +2.00000 q^{93} +28.0000 q^{95} -1.00000 q^{96} +14.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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 −0.288675 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.00000 1.78885 0.894427 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 4.00000 1.26491
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 1.00000 0.267261
\(15\) −4.00000 −1.03280
\(16\) 1.00000 0.250000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) −2.00000 −0.471405
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 4.00000 0.894427
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) 0 0
\(24\) −1.00000 −0.204124
\(25\) 11.0000 2.20000
\(26\) 2.00000 0.392232
\(27\) 5.00000 0.962250
\(28\) 1.00000 0.188982
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) −4.00000 −0.730297
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) 4.00000 0.676123
\(36\) −2.00000 −0.333333
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 7.00000 1.13555
\(39\) −2.00000 −0.320256
\(40\) 4.00000 0.632456
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) −1.00000 −0.154303
\(43\) 3.00000 0.457496 0.228748 0.973486i \(-0.426537\pi\)
0.228748 + 0.973486i \(0.426537\pi\)
\(44\) 0 0
\(45\) −8.00000 −1.19257
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −1.00000 −0.144338
\(49\) 1.00000 0.142857
\(50\) 11.0000 1.55563
\(51\) 5.00000 0.700140
\(52\) 2.00000 0.277350
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 5.00000 0.680414
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −7.00000 −0.927173
\(58\) 8.00000 1.05045
\(59\) −9.00000 −1.17170 −0.585850 0.810419i \(-0.699239\pi\)
−0.585850 + 0.810419i \(0.699239\pi\)
\(60\) −4.00000 −0.516398
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) −2.00000 −0.254000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) −5.00000 −0.610847 −0.305424 0.952217i \(-0.598798\pi\)
−0.305424 + 0.952217i \(0.598798\pi\)
\(68\) −5.00000 −0.606339
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) −2.00000 −0.235702
\(73\) 17.0000 1.98970 0.994850 0.101361i \(-0.0323196\pi\)
0.994850 + 0.101361i \(0.0323196\pi\)
\(74\) −8.00000 −0.929981
\(75\) −11.0000 −1.27017
\(76\) 7.00000 0.802955
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 4.00000 0.447214
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) 13.0000 1.42694 0.713468 0.700688i \(-0.247124\pi\)
0.713468 + 0.700688i \(0.247124\pi\)
\(84\) −1.00000 −0.109109
\(85\) −20.0000 −2.16930
\(86\) 3.00000 0.323498
\(87\) −8.00000 −0.857690
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −8.00000 −0.843274
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 28.0000 2.87274
\(96\) −1.00000 −0.102062
\(97\) 14.0000 1.42148 0.710742 0.703452i \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 11.0000 1.10000
\(101\) 14.0000 1.39305 0.696526 0.717532i \(-0.254728\pi\)
0.696526 + 0.717532i \(0.254728\pi\)
\(102\) 5.00000 0.495074
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 2.00000 0.196116
\(105\) −4.00000 −0.390360
\(106\) 6.00000 0.582772
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 5.00000 0.481125
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 8.00000 0.759326
\(112\) 1.00000 0.0944911
\(113\) −17.0000 −1.59923 −0.799613 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(114\) −7.00000 −0.655610
\(115\) 0 0
\(116\) 8.00000 0.742781
\(117\) −4.00000 −0.369800
\(118\) −9.00000 −0.828517
\(119\) −5.00000 −0.458349
\(120\) −4.00000 −0.365148
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) 2.00000 0.180334
\(124\) −2.00000 −0.179605
\(125\) 24.0000 2.14663
\(126\) −2.00000 −0.178174
\(127\) −22.0000 −1.95218 −0.976092 0.217357i \(-0.930256\pi\)
−0.976092 + 0.217357i \(0.930256\pi\)
\(128\) 1.00000 0.0883883
\(129\) −3.00000 −0.264135
\(130\) 8.00000 0.701646
\(131\) 1.00000 0.0873704 0.0436852 0.999045i \(-0.486090\pi\)
0.0436852 + 0.999045i \(0.486090\pi\)
\(132\) 0 0
\(133\) 7.00000 0.606977
\(134\) −5.00000 −0.431934
\(135\) 20.0000 1.72133
\(136\) −5.00000 −0.428746
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) 0 0
\(139\) −7.00000 −0.593732 −0.296866 0.954919i \(-0.595942\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) −2.00000 −0.167836
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 32.0000 2.65746
\(146\) 17.0000 1.40693
\(147\) −1.00000 −0.0824786
\(148\) −8.00000 −0.657596
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −11.0000 −0.898146
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) 7.00000 0.567775
\(153\) 10.0000 0.808452
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) −2.00000 −0.160128
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 4.00000 0.316228
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) 13.0000 1.00900
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −9.00000 −0.692308
\(170\) −20.0000 −1.53393
\(171\) −14.0000 −1.07061
\(172\) 3.00000 0.228748
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −8.00000 −0.606478
\(175\) 11.0000 0.831522
\(176\) 0 0
\(177\) 9.00000 0.676481
\(178\) −6.00000 −0.449719
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −8.00000 −0.596285
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) 2.00000 0.148250
\(183\) 6.00000 0.443533
\(184\) 0 0
\(185\) −32.0000 −2.35269
\(186\) 2.00000 0.146647
\(187\) 0 0
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 28.0000 2.03133
\(191\) 10.0000 0.723575 0.361787 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −11.0000 −0.791797 −0.395899 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 14.0000 1.00514
\(195\) −8.00000 −0.572892
\(196\) 1.00000 0.0714286
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 11.0000 0.777817
\(201\) 5.00000 0.352673
\(202\) 14.0000 0.985037
\(203\) 8.00000 0.561490
\(204\) 5.00000 0.350070
\(205\) −8.00000 −0.558744
\(206\) 16.0000 1.11477
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) −3.00000 −0.206529 −0.103264 0.994654i \(-0.532929\pi\)
−0.103264 + 0.994654i \(0.532929\pi\)
\(212\) 6.00000 0.412082
\(213\) 2.00000 0.137038
\(214\) 12.0000 0.820303
\(215\) 12.0000 0.818393
\(216\) 5.00000 0.340207
\(217\) −2.00000 −0.135769
\(218\) 4.00000 0.270914
\(219\) −17.0000 −1.14875
\(220\) 0 0
\(221\) −10.0000 −0.672673
\(222\) 8.00000 0.536925
\(223\) −2.00000 −0.133930 −0.0669650 0.997755i \(-0.521332\pi\)
−0.0669650 + 0.997755i \(0.521332\pi\)
\(224\) 1.00000 0.0668153
\(225\) −22.0000 −1.46667
\(226\) −17.0000 −1.13082
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) −7.00000 −0.463586
\(229\) 4.00000 0.264327 0.132164 0.991228i \(-0.457808\pi\)
0.132164 + 0.991228i \(0.457808\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.00000 0.525226
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) −9.00000 −0.585850
\(237\) 0 0
\(238\) −5.00000 −0.324102
\(239\) 30.0000 1.94054 0.970269 0.242028i \(-0.0778125\pi\)
0.970269 + 0.242028i \(0.0778125\pi\)
\(240\) −4.00000 −0.258199
\(241\) −21.0000 −1.35273 −0.676364 0.736567i \(-0.736446\pi\)
−0.676364 + 0.736567i \(0.736446\pi\)
\(242\) −11.0000 −0.707107
\(243\) −16.0000 −1.02640
\(244\) −6.00000 −0.384111
\(245\) 4.00000 0.255551
\(246\) 2.00000 0.127515
\(247\) 14.0000 0.890799
\(248\) −2.00000 −0.127000
\(249\) −13.0000 −0.823842
\(250\) 24.0000 1.51789
\(251\) 27.0000 1.70422 0.852112 0.523359i \(-0.175321\pi\)
0.852112 + 0.523359i \(0.175321\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −22.0000 −1.38040
\(255\) 20.0000 1.25245
\(256\) 1.00000 0.0625000
\(257\) −7.00000 −0.436648 −0.218324 0.975876i \(-0.570059\pi\)
−0.218324 + 0.975876i \(0.570059\pi\)
\(258\) −3.00000 −0.186772
\(259\) −8.00000 −0.497096
\(260\) 8.00000 0.496139
\(261\) −16.0000 −0.990375
\(262\) 1.00000 0.0617802
\(263\) −20.0000 −1.23325 −0.616626 0.787256i \(-0.711501\pi\)
−0.616626 + 0.787256i \(0.711501\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 7.00000 0.429198
\(267\) 6.00000 0.367194
\(268\) −5.00000 −0.305424
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 20.0000 1.21716
\(271\) 30.0000 1.82237 0.911185 0.411997i \(-0.135169\pi\)
0.911185 + 0.411997i \(0.135169\pi\)
\(272\) −5.00000 −0.303170
\(273\) −2.00000 −0.121046
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 0 0
\(277\) −26.0000 −1.56219 −0.781094 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) −7.00000 −0.419832
\(279\) 4.00000 0.239474
\(280\) 4.00000 0.239046
\(281\) −25.0000 −1.49137 −0.745687 0.666296i \(-0.767879\pi\)
−0.745687 + 0.666296i \(0.767879\pi\)
\(282\) 0 0
\(283\) −21.0000 −1.24832 −0.624160 0.781296i \(-0.714559\pi\)
−0.624160 + 0.781296i \(0.714559\pi\)
\(284\) −2.00000 −0.118678
\(285\) −28.0000 −1.65858
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) −2.00000 −0.117851
\(289\) 8.00000 0.470588
\(290\) 32.0000 1.87910
\(291\) −14.0000 −0.820695
\(292\) 17.0000 0.994850
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) −1.00000 −0.0583212
\(295\) −36.0000 −2.09600
\(296\) −8.00000 −0.464991
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) 0 0
\(300\) −11.0000 −0.635085
\(301\) 3.00000 0.172917
\(302\) 16.0000 0.920697
\(303\) −14.0000 −0.804279
\(304\) 7.00000 0.401478
\(305\) −24.0000 −1.37424
\(306\) 10.0000 0.571662
\(307\) −23.0000 −1.31268 −0.656340 0.754466i \(-0.727896\pi\)
−0.656340 + 0.754466i \(0.727896\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) −8.00000 −0.454369
\(311\) −8.00000 −0.453638 −0.226819 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) −2.00000 −0.113228
\(313\) 11.0000 0.621757 0.310878 0.950450i \(-0.399377\pi\)
0.310878 + 0.950450i \(0.399377\pi\)
\(314\) 12.0000 0.677199
\(315\) −8.00000 −0.450749
\(316\) 0 0
\(317\) 2.00000 0.112331 0.0561656 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) −6.00000 −0.336463
\(319\) 0 0
\(320\) 4.00000 0.223607
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) −35.0000 −1.94745
\(324\) 1.00000 0.0555556
\(325\) 22.0000 1.22034
\(326\) 20.0000 1.10770
\(327\) −4.00000 −0.221201
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) 1.00000 0.0549650 0.0274825 0.999622i \(-0.491251\pi\)
0.0274825 + 0.999622i \(0.491251\pi\)
\(332\) 13.0000 0.713468
\(333\) 16.0000 0.876795
\(334\) −24.0000 −1.31322
\(335\) −20.0000 −1.09272
\(336\) −1.00000 −0.0545545
\(337\) 27.0000 1.47078 0.735392 0.677642i \(-0.236998\pi\)
0.735392 + 0.677642i \(0.236998\pi\)
\(338\) −9.00000 −0.489535
\(339\) 17.0000 0.923313
\(340\) −20.0000 −1.08465
\(341\) 0 0
\(342\) −14.0000 −0.757033
\(343\) 1.00000 0.0539949
\(344\) 3.00000 0.161749
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 3.00000 0.161048 0.0805242 0.996753i \(-0.474341\pi\)
0.0805242 + 0.996753i \(0.474341\pi\)
\(348\) −8.00000 −0.428845
\(349\) −8.00000 −0.428230 −0.214115 0.976808i \(-0.568687\pi\)
−0.214115 + 0.976808i \(0.568687\pi\)
\(350\) 11.0000 0.587975
\(351\) 10.0000 0.533761
\(352\) 0 0
\(353\) −11.0000 −0.585471 −0.292735 0.956193i \(-0.594566\pi\)
−0.292735 + 0.956193i \(0.594566\pi\)
\(354\) 9.00000 0.478345
\(355\) −8.00000 −0.424596
\(356\) −6.00000 −0.317999
\(357\) 5.00000 0.264628
\(358\) −9.00000 −0.475665
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) −8.00000 −0.421637
\(361\) 30.0000 1.57895
\(362\) 10.0000 0.525588
\(363\) 11.0000 0.577350
\(364\) 2.00000 0.104828
\(365\) 68.0000 3.55928
\(366\) 6.00000 0.313625
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) 0 0
\(369\) 4.00000 0.208232
\(370\) −32.0000 −1.66360
\(371\) 6.00000 0.311504
\(372\) 2.00000 0.103695
\(373\) 26.0000 1.34623 0.673114 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) −24.0000 −1.23935
\(376\) 0 0
\(377\) 16.0000 0.824042
\(378\) 5.00000 0.257172
\(379\) 35.0000 1.79783 0.898915 0.438124i \(-0.144357\pi\)
0.898915 + 0.438124i \(0.144357\pi\)
\(380\) 28.0000 1.43637
\(381\) 22.0000 1.12709
\(382\) 10.0000 0.511645
\(383\) 2.00000 0.102195 0.0510976 0.998694i \(-0.483728\pi\)
0.0510976 + 0.998694i \(0.483728\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −11.0000 −0.559885
\(387\) −6.00000 −0.304997
\(388\) 14.0000 0.710742
\(389\) 14.0000 0.709828 0.354914 0.934899i \(-0.384510\pi\)
0.354914 + 0.934899i \(0.384510\pi\)
\(390\) −8.00000 −0.405096
\(391\) 0 0
\(392\) 1.00000 0.0505076
\(393\) −1.00000 −0.0504433
\(394\) 8.00000 0.403034
\(395\) 0 0
\(396\) 0 0
\(397\) −32.0000 −1.60603 −0.803017 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 8.00000 0.401004
\(399\) −7.00000 −0.350438
\(400\) 11.0000 0.550000
\(401\) 25.0000 1.24844 0.624220 0.781248i \(-0.285417\pi\)
0.624220 + 0.781248i \(0.285417\pi\)
\(402\) 5.00000 0.249377
\(403\) −4.00000 −0.199254
\(404\) 14.0000 0.696526
\(405\) 4.00000 0.198762
\(406\) 8.00000 0.397033
\(407\) 0 0
\(408\) 5.00000 0.247537
\(409\) −17.0000 −0.840596 −0.420298 0.907386i \(-0.638074\pi\)
−0.420298 + 0.907386i \(0.638074\pi\)
\(410\) −8.00000 −0.395092
\(411\) 3.00000 0.147979
\(412\) 16.0000 0.788263
\(413\) −9.00000 −0.442861
\(414\) 0 0
\(415\) 52.0000 2.55258
\(416\) 2.00000 0.0980581
\(417\) 7.00000 0.342791
\(418\) 0 0
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) −4.00000 −0.195180
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) −3.00000 −0.146038
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) −55.0000 −2.66789
\(426\) 2.00000 0.0969003
\(427\) −6.00000 −0.290360
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 12.0000 0.578691
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 5.00000 0.240563
\(433\) −10.0000 −0.480569 −0.240285 0.970702i \(-0.577241\pi\)
−0.240285 + 0.970702i \(0.577241\pi\)
\(434\) −2.00000 −0.0960031
\(435\) −32.0000 −1.53428
\(436\) 4.00000 0.191565
\(437\) 0 0
\(438\) −17.0000 −0.812291
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) −10.0000 −0.475651
\(443\) 7.00000 0.332580 0.166290 0.986077i \(-0.446821\pi\)
0.166290 + 0.986077i \(0.446821\pi\)
\(444\) 8.00000 0.379663
\(445\) −24.0000 −1.13771
\(446\) −2.00000 −0.0947027
\(447\) 10.0000 0.472984
\(448\) 1.00000 0.0472456
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) −22.0000 −1.03709
\(451\) 0 0
\(452\) −17.0000 −0.799613
\(453\) −16.0000 −0.751746
\(454\) −3.00000 −0.140797
\(455\) 8.00000 0.375046
\(456\) −7.00000 −0.327805
\(457\) 10.0000 0.467780 0.233890 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 4.00000 0.186908
\(459\) −25.0000 −1.16690
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) 8.00000 0.371391
\(465\) 8.00000 0.370991
\(466\) 3.00000 0.138972
\(467\) 16.0000 0.740392 0.370196 0.928954i \(-0.379291\pi\)
0.370196 + 0.928954i \(0.379291\pi\)
\(468\) −4.00000 −0.184900
\(469\) −5.00000 −0.230879
\(470\) 0 0
\(471\) −12.0000 −0.552931
\(472\) −9.00000 −0.414259
\(473\) 0 0
\(474\) 0 0
\(475\) 77.0000 3.53300
\(476\) −5.00000 −0.229175
\(477\) −12.0000 −0.549442
\(478\) 30.0000 1.37217
\(479\) −20.0000 −0.913823 −0.456912 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) −4.00000 −0.182574
\(481\) −16.0000 −0.729537
\(482\) −21.0000 −0.956524
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 56.0000 2.54283
\(486\) −16.0000 −0.725775
\(487\) 36.0000 1.63132 0.815658 0.578535i \(-0.196375\pi\)
0.815658 + 0.578535i \(0.196375\pi\)
\(488\) −6.00000 −0.271607
\(489\) −20.0000 −0.904431
\(490\) 4.00000 0.180702
\(491\) 4.00000 0.180517 0.0902587 0.995918i \(-0.471231\pi\)
0.0902587 + 0.995918i \(0.471231\pi\)
\(492\) 2.00000 0.0901670
\(493\) −40.0000 −1.80151
\(494\) 14.0000 0.629890
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −2.00000 −0.0897123
\(498\) −13.0000 −0.582544
\(499\) 15.0000 0.671492 0.335746 0.941953i \(-0.391012\pi\)
0.335746 + 0.941953i \(0.391012\pi\)
\(500\) 24.0000 1.07331
\(501\) 24.0000 1.07224
\(502\) 27.0000 1.20507
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 56.0000 2.49197
\(506\) 0 0
\(507\) 9.00000 0.399704
\(508\) −22.0000 −0.976092
\(509\) −16.0000 −0.709188 −0.354594 0.935020i \(-0.615381\pi\)
−0.354594 + 0.935020i \(0.615381\pi\)
\(510\) 20.0000 0.885615
\(511\) 17.0000 0.752036
\(512\) 1.00000 0.0441942
\(513\) 35.0000 1.54529
\(514\) −7.00000 −0.308757
\(515\) 64.0000 2.82018
\(516\) −3.00000 −0.132068
\(517\) 0 0
\(518\) −8.00000 −0.351500
\(519\) 6.00000 0.263371
\(520\) 8.00000 0.350823
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) −16.0000 −0.700301
\(523\) 24.0000 1.04945 0.524723 0.851273i \(-0.324169\pi\)
0.524723 + 0.851273i \(0.324169\pi\)
\(524\) 1.00000 0.0436852
\(525\) −11.0000 −0.480079
\(526\) −20.0000 −0.872041
\(527\) 10.0000 0.435607
\(528\) 0 0
\(529\) 0 0
\(530\) 24.0000 1.04249
\(531\) 18.0000 0.781133
\(532\) 7.00000 0.303488
\(533\) −4.00000 −0.173259
\(534\) 6.00000 0.259645
\(535\) 48.0000 2.07522
\(536\) −5.00000 −0.215967
\(537\) 9.00000 0.388379
\(538\) −24.0000 −1.03471
\(539\) 0 0
\(540\) 20.0000 0.860663
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 30.0000 1.28861
\(543\) −10.0000 −0.429141
\(544\) −5.00000 −0.214373
\(545\) 16.0000 0.685365
\(546\) −2.00000 −0.0855921
\(547\) −20.0000 −0.855138 −0.427569 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) −3.00000 −0.128154
\(549\) 12.0000 0.512148
\(550\) 0 0
\(551\) 56.0000 2.38568
\(552\) 0 0
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) 32.0000 1.35832
\(556\) −7.00000 −0.296866
\(557\) −6.00000 −0.254228 −0.127114 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 4.00000 0.169334
\(559\) 6.00000 0.253773
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) −25.0000 −1.05456
\(563\) −21.0000 −0.885044 −0.442522 0.896758i \(-0.645916\pi\)
−0.442522 + 0.896758i \(0.645916\pi\)
\(564\) 0 0
\(565\) −68.0000 −2.86078
\(566\) −21.0000 −0.882696
\(567\) 1.00000 0.0419961
\(568\) −2.00000 −0.0839181
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) −28.0000 −1.17279
\(571\) −13.0000 −0.544033 −0.272017 0.962293i \(-0.587691\pi\)
−0.272017 + 0.962293i \(0.587691\pi\)
\(572\) 0 0
\(573\) −10.0000 −0.417756
\(574\) −2.00000 −0.0834784
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) −27.0000 −1.12402 −0.562012 0.827129i \(-0.689973\pi\)
−0.562012 + 0.827129i \(0.689973\pi\)
\(578\) 8.00000 0.332756
\(579\) 11.0000 0.457144
\(580\) 32.0000 1.32873
\(581\) 13.0000 0.539331
\(582\) −14.0000 −0.580319
\(583\) 0 0
\(584\) 17.0000 0.703465
\(585\) −16.0000 −0.661519
\(586\) −14.0000 −0.578335
\(587\) −39.0000 −1.60970 −0.804851 0.593477i \(-0.797755\pi\)
−0.804851 + 0.593477i \(0.797755\pi\)
\(588\) −1.00000 −0.0412393
\(589\) −14.0000 −0.576860
\(590\) −36.0000 −1.48210
\(591\) −8.00000 −0.329076
\(592\) −8.00000 −0.328798
\(593\) 21.0000 0.862367 0.431183 0.902264i \(-0.358096\pi\)
0.431183 + 0.902264i \(0.358096\pi\)
\(594\) 0 0
\(595\) −20.0000 −0.819920
\(596\) −10.0000 −0.409616
\(597\) −8.00000 −0.327418
\(598\) 0 0
\(599\) −12.0000 −0.490307 −0.245153 0.969484i \(-0.578838\pi\)
−0.245153 + 0.969484i \(0.578838\pi\)
\(600\) −11.0000 −0.449073
\(601\) 2.00000 0.0815817 0.0407909 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 3.00000 0.122271
\(603\) 10.0000 0.407231
\(604\) 16.0000 0.651031
\(605\) −44.0000 −1.78885
\(606\) −14.0000 −0.568711
\(607\) 24.0000 0.974130 0.487065 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) 7.00000 0.283887
\(609\) −8.00000 −0.324176
\(610\) −24.0000 −0.971732
\(611\) 0 0
\(612\) 10.0000 0.404226
\(613\) 6.00000 0.242338 0.121169 0.992632i \(-0.461336\pi\)
0.121169 + 0.992632i \(0.461336\pi\)
\(614\) −23.0000 −0.928204
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) −21.0000 −0.845428 −0.422714 0.906263i \(-0.638923\pi\)
−0.422714 + 0.906263i \(0.638923\pi\)
\(618\) −16.0000 −0.643614
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) −8.00000 −0.320771
\(623\) −6.00000 −0.240385
\(624\) −2.00000 −0.0800641
\(625\) 41.0000 1.64000
\(626\) 11.0000 0.439648
\(627\) 0 0
\(628\) 12.0000 0.478852
\(629\) 40.0000 1.59490
\(630\) −8.00000 −0.318728
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 3.00000 0.119239
\(634\) 2.00000 0.0794301
\(635\) −88.0000 −3.49217
\(636\) −6.00000 −0.237915
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 4.00000 0.158238
\(640\) 4.00000 0.158114
\(641\) 45.0000 1.77739 0.888697 0.458496i \(-0.151612\pi\)
0.888697 + 0.458496i \(0.151612\pi\)
\(642\) −12.0000 −0.473602
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) −12.0000 −0.472500
\(646\) −35.0000 −1.37706
\(647\) 26.0000 1.02217 0.511083 0.859532i \(-0.329245\pi\)
0.511083 + 0.859532i \(0.329245\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 22.0000 0.862911
\(651\) 2.00000 0.0783862
\(652\) 20.0000 0.783260
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) −4.00000 −0.156412
\(655\) 4.00000 0.156293
\(656\) −2.00000 −0.0780869
\(657\) −34.0000 −1.32647
\(658\) 0 0
\(659\) −29.0000 −1.12968 −0.564840 0.825201i \(-0.691062\pi\)
−0.564840 + 0.825201i \(0.691062\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 1.00000 0.0388661
\(663\) 10.0000 0.388368
\(664\) 13.0000 0.504498
\(665\) 28.0000 1.08579
\(666\) 16.0000 0.619987
\(667\) 0 0
\(668\) −24.0000 −0.928588
\(669\) 2.00000 0.0773245
\(670\) −20.0000 −0.772667
\(671\) 0 0
\(672\) −1.00000 −0.0385758
\(673\) 1.00000 0.0385472 0.0192736 0.999814i \(-0.493865\pi\)
0.0192736 + 0.999814i \(0.493865\pi\)
\(674\) 27.0000 1.04000
\(675\) 55.0000 2.11695
\(676\) −9.00000 −0.346154
\(677\) −8.00000 −0.307465 −0.153732 0.988113i \(-0.549129\pi\)
−0.153732 + 0.988113i \(0.549129\pi\)
\(678\) 17.0000 0.652881
\(679\) 14.0000 0.537271
\(680\) −20.0000 −0.766965
\(681\) 3.00000 0.114960
\(682\) 0 0
\(683\) 19.0000 0.727015 0.363507 0.931591i \(-0.381579\pi\)
0.363507 + 0.931591i \(0.381579\pi\)
\(684\) −14.0000 −0.535303
\(685\) −12.0000 −0.458496
\(686\) 1.00000 0.0381802
\(687\) −4.00000 −0.152610
\(688\) 3.00000 0.114374
\(689\) 12.0000 0.457164
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 3.00000 0.113878
\(695\) −28.0000 −1.06210
\(696\) −8.00000 −0.303239
\(697\) 10.0000 0.378777
\(698\) −8.00000 −0.302804
\(699\) −3.00000 −0.113470
\(700\) 11.0000 0.415761
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 10.0000 0.377426
\(703\) −56.0000 −2.11208
\(704\) 0 0
\(705\) 0 0
\(706\) −11.0000 −0.413990
\(707\) 14.0000 0.526524
\(708\) 9.00000 0.338241
\(709\) 32.0000 1.20179 0.600893 0.799330i \(-0.294812\pi\)
0.600893 + 0.799330i \(0.294812\pi\)
\(710\) −8.00000 −0.300235
\(711\) 0 0
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 5.00000 0.187120
\(715\) 0 0
\(716\) −9.00000 −0.336346
\(717\) −30.0000 −1.12037
\(718\) 30.0000 1.11959
\(719\) −30.0000 −1.11881 −0.559406 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) −8.00000 −0.298142
\(721\) 16.0000 0.595871
\(722\) 30.0000 1.11648
\(723\) 21.0000 0.780998
\(724\) 10.0000 0.371647
\(725\) 88.0000 3.26824
\(726\) 11.0000 0.408248
\(727\) −46.0000 −1.70605 −0.853023 0.521874i \(-0.825233\pi\)
−0.853023 + 0.521874i \(0.825233\pi\)
\(728\) 2.00000 0.0741249
\(729\) 13.0000 0.481481
\(730\) 68.0000 2.51679
\(731\) −15.0000 −0.554795
\(732\) 6.00000 0.221766
\(733\) −22.0000 −0.812589 −0.406294 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 22.0000 0.812035
\(735\) −4.00000 −0.147542
\(736\) 0 0
\(737\) 0 0
\(738\) 4.00000 0.147242
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −32.0000 −1.17634
\(741\) −14.0000 −0.514303
\(742\) 6.00000 0.220267
\(743\) 30.0000 1.10059 0.550297 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) 2.00000 0.0733236
\(745\) −40.0000 −1.46549
\(746\) 26.0000 0.951928
\(747\) −26.0000 −0.951290
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) −24.0000 −0.876356
\(751\) 26.0000 0.948753 0.474377 0.880322i \(-0.342673\pi\)
0.474377 + 0.880322i \(0.342673\pi\)
\(752\) 0 0
\(753\) −27.0000 −0.983935
\(754\) 16.0000 0.582686
\(755\) 64.0000 2.32920
\(756\) 5.00000 0.181848
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) 35.0000 1.27126
\(759\) 0 0
\(760\) 28.0000 1.01567
\(761\) −33.0000 −1.19625 −0.598125 0.801403i \(-0.704087\pi\)
−0.598125 + 0.801403i \(0.704087\pi\)
\(762\) 22.0000 0.796976
\(763\) 4.00000 0.144810
\(764\) 10.0000 0.361787
\(765\) 40.0000 1.44620
\(766\) 2.00000 0.0722629
\(767\) −18.0000 −0.649942
\(768\) −1.00000 −0.0360844
\(769\) 30.0000 1.08183 0.540914 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 0 0
\(771\) 7.00000 0.252099
\(772\) −11.0000 −0.395899
\(773\) −38.0000 −1.36677 −0.683383 0.730061i \(-0.739492\pi\)
−0.683383 + 0.730061i \(0.739492\pi\)
\(774\) −6.00000 −0.215666
\(775\) −22.0000 −0.790263
\(776\) 14.0000 0.502571
\(777\) 8.00000 0.286998
\(778\) 14.0000 0.501924
\(779\) −14.0000 −0.501602
\(780\) −8.00000 −0.286446
\(781\) 0 0
\(782\) 0 0
\(783\) 40.0000 1.42948
\(784\) 1.00000 0.0357143
\(785\) 48.0000 1.71319
\(786\) −1.00000 −0.0356688
\(787\) −5.00000 −0.178231 −0.0891154 0.996021i \(-0.528404\pi\)
−0.0891154 + 0.996021i \(0.528404\pi\)
\(788\) 8.00000 0.284988
\(789\) 20.0000 0.712019
\(790\) 0 0
\(791\) −17.0000 −0.604450
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) −32.0000 −1.13564
\(795\) −24.0000 −0.851192
\(796\) 8.00000 0.283552
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) −7.00000 −0.247797
\(799\) 0 0
\(800\) 11.0000 0.388909
\(801\) 12.0000 0.423999
\(802\) 25.0000 0.882781
\(803\) 0 0
\(804\) 5.00000 0.176336
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) 24.0000 0.844840
\(808\) 14.0000 0.492518
\(809\) 17.0000 0.597688 0.298844 0.954302i \(-0.403399\pi\)
0.298844 + 0.954302i \(0.403399\pi\)
\(810\) 4.00000 0.140546
\(811\) −47.0000 −1.65039 −0.825197 0.564846i \(-0.808936\pi\)
−0.825197 + 0.564846i \(0.808936\pi\)
\(812\) 8.00000 0.280745
\(813\) −30.0000 −1.05215
\(814\) 0 0
\(815\) 80.0000 2.80228
\(816\) 5.00000 0.175035
\(817\) 21.0000 0.734697
\(818\) −17.0000 −0.594391
\(819\) −4.00000 −0.139771
\(820\) −8.00000 −0.279372
\(821\) −22.0000 −0.767805 −0.383903 0.923374i \(-0.625420\pi\)
−0.383903 + 0.923374i \(0.625420\pi\)
\(822\) 3.00000 0.104637
\(823\) −50.0000 −1.74289 −0.871445 0.490493i \(-0.836817\pi\)
−0.871445 + 0.490493i \(0.836817\pi\)
\(824\) 16.0000 0.557386
\(825\) 0 0
\(826\) −9.00000 −0.313150
\(827\) 29.0000 1.00843 0.504214 0.863579i \(-0.331782\pi\)
0.504214 + 0.863579i \(0.331782\pi\)
\(828\) 0 0
\(829\) −38.0000 −1.31979 −0.659897 0.751356i \(-0.729400\pi\)
−0.659897 + 0.751356i \(0.729400\pi\)
\(830\) 52.0000 1.80495
\(831\) 26.0000 0.901930
\(832\) 2.00000 0.0693375
\(833\) −5.00000 −0.173240
\(834\) 7.00000 0.242390
\(835\) −96.0000 −3.32222
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) −9.00000 −0.310900
\(839\) 28.0000 0.966667 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(840\) −4.00000 −0.138013
\(841\) 35.0000 1.20690
\(842\) −30.0000 −1.03387
\(843\) 25.0000 0.861046
\(844\) −3.00000 −0.103264
\(845\) −36.0000 −1.23844
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) 6.00000 0.206041
\(849\) 21.0000 0.720718
\(850\) −55.0000 −1.88648
\(851\) 0 0
\(852\) 2.00000 0.0685189
\(853\) −36.0000 −1.23262 −0.616308 0.787505i \(-0.711372\pi\)
−0.616308 + 0.787505i \(0.711372\pi\)
\(854\) −6.00000 −0.205316
\(855\) −56.0000 −1.91516
\(856\) 12.0000 0.410152
\(857\) −5.00000 −0.170797 −0.0853984 0.996347i \(-0.527216\pi\)
−0.0853984 + 0.996347i \(0.527216\pi\)
\(858\) 0 0
\(859\) −11.0000 −0.375315 −0.187658 0.982235i \(-0.560090\pi\)
−0.187658 + 0.982235i \(0.560090\pi\)
\(860\) 12.0000 0.409197
\(861\) 2.00000 0.0681598
\(862\) 12.0000 0.408722
\(863\) 36.0000 1.22545 0.612727 0.790295i \(-0.290072\pi\)
0.612727 + 0.790295i \(0.290072\pi\)
\(864\) 5.00000 0.170103
\(865\) −24.0000 −0.816024
\(866\) −10.0000 −0.339814
\(867\) −8.00000 −0.271694
\(868\) −2.00000 −0.0678844
\(869\) 0 0
\(870\) −32.0000 −1.08490
\(871\) −10.0000 −0.338837
\(872\) 4.00000 0.135457
\(873\) −28.0000 −0.947656
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) −17.0000 −0.574377
\(877\) −34.0000 −1.14810 −0.574049 0.818821i \(-0.694628\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(878\) 32.0000 1.07995
\(879\) 14.0000 0.472208
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 11.0000 0.370179 0.185090 0.982722i \(-0.440742\pi\)
0.185090 + 0.982722i \(0.440742\pi\)
\(884\) −10.0000 −0.336336
\(885\) 36.0000 1.21013
\(886\) 7.00000 0.235170
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 8.00000 0.268462
\(889\) −22.0000 −0.737856
\(890\) −24.0000 −0.804482
\(891\) 0 0
\(892\) −2.00000 −0.0669650
\(893\) 0 0
\(894\) 10.0000 0.334450
\(895\) −36.0000 −1.20335
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 9.00000 0.300334
\(899\) −16.0000 −0.533630
\(900\) −22.0000 −0.733333
\(901\) −30.0000 −0.999445
\(902\) 0 0
\(903\) −3.00000 −0.0998337
\(904\) −17.0000 −0.565412
\(905\) 40.0000 1.32964
\(906\) −16.0000 −0.531564
\(907\) −23.0000 −0.763702 −0.381851 0.924224i \(-0.624713\pi\)
−0.381851 + 0.924224i \(0.624713\pi\)
\(908\) −3.00000 −0.0995585
\(909\) −28.0000 −0.928701
\(910\) 8.00000 0.265197
\(911\) 28.0000 0.927681 0.463841 0.885919i \(-0.346471\pi\)
0.463841 + 0.885919i \(0.346471\pi\)
\(912\) −7.00000 −0.231793
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 24.0000 0.793416
\(916\) 4.00000 0.132164
\(917\) 1.00000 0.0330229
\(918\) −25.0000 −0.825123
\(919\) −4.00000 −0.131948 −0.0659739 0.997821i \(-0.521015\pi\)
−0.0659739 + 0.997821i \(0.521015\pi\)
\(920\) 0 0
\(921\) 23.0000 0.757876
\(922\) −10.0000 −0.329332
\(923\) −4.00000 −0.131662
\(924\) 0 0
\(925\) −88.0000 −2.89342
\(926\) 4.00000 0.131448
\(927\) −32.0000 −1.05102
\(928\) 8.00000 0.262613
\(929\) 50.0000 1.64045 0.820223 0.572043i \(-0.193849\pi\)
0.820223 + 0.572043i \(0.193849\pi\)
\(930\) 8.00000 0.262330
\(931\) 7.00000 0.229416
\(932\) 3.00000 0.0982683
\(933\) 8.00000 0.261908
\(934\) 16.0000 0.523536
\(935\) 0 0
\(936\) −4.00000 −0.130744
\(937\) −19.0000 −0.620703 −0.310351 0.950622i \(-0.600447\pi\)
−0.310351 + 0.950622i \(0.600447\pi\)
\(938\) −5.00000 −0.163256
\(939\) −11.0000 −0.358971
\(940\) 0 0
\(941\) 6.00000 0.195594 0.0977972 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) −12.0000 −0.390981
\(943\) 0 0
\(944\) −9.00000 −0.292925
\(945\) 20.0000 0.650600
\(946\) 0 0
\(947\) 27.0000 0.877382 0.438691 0.898638i \(-0.355442\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(948\) 0 0
\(949\) 34.0000 1.10369
\(950\) 77.0000 2.49821
\(951\) −2.00000 −0.0648544
\(952\) −5.00000 −0.162051
\(953\) −14.0000 −0.453504 −0.226752 0.973952i \(-0.572811\pi\)
−0.226752 + 0.973952i \(0.572811\pi\)
\(954\) −12.0000 −0.388514
\(955\) 40.0000 1.29437
\(956\) 30.0000 0.970269
\(957\) 0 0
\(958\) −20.0000 −0.646171
\(959\) −3.00000 −0.0968751
\(960\) −4.00000 −0.129099
\(961\) −27.0000 −0.870968
\(962\) −16.0000 −0.515861
\(963\) −24.0000 −0.773389
\(964\) −21.0000 −0.676364
\(965\) −44.0000 −1.41641
\(966\) 0 0
\(967\) 56.0000 1.80084 0.900419 0.435023i \(-0.143260\pi\)
0.900419 + 0.435023i \(0.143260\pi\)
\(968\) −11.0000 −0.353553
\(969\) 35.0000 1.12436
\(970\) 56.0000 1.79805
\(971\) 1.00000 0.0320915 0.0160458 0.999871i \(-0.494892\pi\)
0.0160458 + 0.999871i \(0.494892\pi\)
\(972\) −16.0000 −0.513200
\(973\) −7.00000 −0.224410
\(974\) 36.0000 1.15351
\(975\) −22.0000 −0.704564
\(976\) −6.00000 −0.192055
\(977\) −30.0000 −0.959785 −0.479893 0.877327i \(-0.659324\pi\)
−0.479893 + 0.877327i \(0.659324\pi\)
\(978\) −20.0000 −0.639529
\(979\) 0 0
\(980\) 4.00000 0.127775
\(981\) −8.00000 −0.255420
\(982\) 4.00000 0.127645
\(983\) 22.0000 0.701691 0.350846 0.936433i \(-0.385894\pi\)
0.350846 + 0.936433i \(0.385894\pi\)
\(984\) 2.00000 0.0637577
\(985\) 32.0000 1.01960
\(986\) −40.0000 −1.27386
\(987\) 0 0
\(988\) 14.0000 0.445399
\(989\) 0 0
\(990\) 0 0
\(991\) −30.0000 −0.952981 −0.476491 0.879180i \(-0.658091\pi\)
−0.476491 + 0.879180i \(0.658091\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −1.00000 −0.0317340
\(994\) −2.00000 −0.0634361
\(995\) 32.0000 1.01447
\(996\) −13.0000 −0.411921
\(997\) −54.0000 −1.71020 −0.855099 0.518465i \(-0.826503\pi\)
−0.855099 + 0.518465i \(0.826503\pi\)
\(998\) 15.0000 0.474817
\(999\) −40.0000 −1.26554
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 7406.2.a.h.1.1 yes 1
23.22 odd 2 7406.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7406.2.a.g.1.1 1 23.22 odd 2
7406.2.a.h.1.1 yes 1 1.1 even 1 trivial