Properties

Label 5054.2.a.f.1.1
Level $5054$
Weight $2$
Character 5054.1
Self dual yes
Analytic conductor $40.356$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.3563931816\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 5054.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.61803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.381966 q^{9} -1.00000 q^{10} -5.00000 q^{11} -1.61803 q^{12} +1.85410 q^{13} +1.00000 q^{14} -1.61803 q^{15} +1.00000 q^{16} +0.145898 q^{17} +0.381966 q^{18} +1.00000 q^{20} +1.61803 q^{21} +5.00000 q^{22} -8.23607 q^{23} +1.61803 q^{24} -4.00000 q^{25} -1.85410 q^{26} +5.47214 q^{27} -1.00000 q^{28} +3.76393 q^{29} +1.61803 q^{30} -6.70820 q^{31} -1.00000 q^{32} +8.09017 q^{33} -0.145898 q^{34} -1.00000 q^{35} -0.381966 q^{36} +11.9443 q^{37} -3.00000 q^{39} -1.00000 q^{40} -10.0902 q^{41} -1.61803 q^{42} -0.145898 q^{43} -5.00000 q^{44} -0.381966 q^{45} +8.23607 q^{46} -9.94427 q^{47} -1.61803 q^{48} +1.00000 q^{49} +4.00000 q^{50} -0.236068 q^{51} +1.85410 q^{52} -0.708204 q^{53} -5.47214 q^{54} -5.00000 q^{55} +1.00000 q^{56} -3.76393 q^{58} -11.0000 q^{59} -1.61803 q^{60} -1.47214 q^{61} +6.70820 q^{62} +0.381966 q^{63} +1.00000 q^{64} +1.85410 q^{65} -8.09017 q^{66} -1.14590 q^{67} +0.145898 q^{68} +13.3262 q^{69} +1.00000 q^{70} +10.0000 q^{71} +0.381966 q^{72} +5.56231 q^{73} -11.9443 q^{74} +6.47214 q^{75} +5.00000 q^{77} +3.00000 q^{78} +2.14590 q^{79} +1.00000 q^{80} -7.70820 q^{81} +10.0902 q^{82} +11.4164 q^{83} +1.61803 q^{84} +0.145898 q^{85} +0.145898 q^{86} -6.09017 q^{87} +5.00000 q^{88} +1.85410 q^{89} +0.381966 q^{90} -1.85410 q^{91} -8.23607 q^{92} +10.8541 q^{93} +9.94427 q^{94} +1.61803 q^{96} +0.527864 q^{97} -1.00000 q^{98} +1.90983 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - q^{3} + 2 q^{4} + 2 q^{5} + q^{6} - 2 q^{7} - 2 q^{8} - 3 q^{9} - 2 q^{10} - 10 q^{11} - q^{12} - 3 q^{13} + 2 q^{14} - q^{15} + 2 q^{16} + 7 q^{17} + 3 q^{18} + 2 q^{20} + q^{21} + 10 q^{22} - 12 q^{23} + q^{24} - 8 q^{25} + 3 q^{26} + 2 q^{27} - 2 q^{28} + 12 q^{29} + q^{30} - 2 q^{32} + 5 q^{33} - 7 q^{34} - 2 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 2 q^{40} - 9 q^{41} - q^{42} - 7 q^{43} - 10 q^{44} - 3 q^{45} + 12 q^{46} - 2 q^{47} - q^{48} + 2 q^{49} + 8 q^{50} + 4 q^{51} - 3 q^{52} + 12 q^{53} - 2 q^{54} - 10 q^{55} + 2 q^{56} - 12 q^{58} - 22 q^{59} - q^{60} + 6 q^{61} + 3 q^{63} + 2 q^{64} - 3 q^{65} - 5 q^{66} - 9 q^{67} + 7 q^{68} + 11 q^{69} + 2 q^{70} + 20 q^{71} + 3 q^{72} - 9 q^{73} - 6 q^{74} + 4 q^{75} + 10 q^{77} + 6 q^{78} + 11 q^{79} + 2 q^{80} - 2 q^{81} + 9 q^{82} - 4 q^{83} + q^{84} + 7 q^{85} + 7 q^{86} - q^{87} + 10 q^{88} - 3 q^{89} + 3 q^{90} + 3 q^{91} - 12 q^{92} + 15 q^{93} + 2 q^{94} + q^{96} + 10 q^{97} - 2 q^{98} + 15 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −1.61803 −0.934172 −0.467086 0.884212i \(-0.654696\pi\)
−0.467086 + 0.884212i \(0.654696\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 1.61803 0.660560
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) −0.381966 −0.127322
\(10\) −1.00000 −0.316228
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) −1.61803 −0.467086
\(13\) 1.85410 0.514235 0.257118 0.966380i \(-0.417227\pi\)
0.257118 + 0.966380i \(0.417227\pi\)
\(14\) 1.00000 0.267261
\(15\) −1.61803 −0.417775
\(16\) 1.00000 0.250000
\(17\) 0.145898 0.0353855 0.0176927 0.999843i \(-0.494368\pi\)
0.0176927 + 0.999843i \(0.494368\pi\)
\(18\) 0.381966 0.0900303
\(19\) 0 0
\(20\) 1.00000 0.223607
\(21\) 1.61803 0.353084
\(22\) 5.00000 1.06600
\(23\) −8.23607 −1.71734 −0.858669 0.512530i \(-0.828708\pi\)
−0.858669 + 0.512530i \(0.828708\pi\)
\(24\) 1.61803 0.330280
\(25\) −4.00000 −0.800000
\(26\) −1.85410 −0.363619
\(27\) 5.47214 1.05311
\(28\) −1.00000 −0.188982
\(29\) 3.76393 0.698945 0.349472 0.936947i \(-0.386361\pi\)
0.349472 + 0.936947i \(0.386361\pi\)
\(30\) 1.61803 0.295411
\(31\) −6.70820 −1.20483 −0.602414 0.798183i \(-0.705795\pi\)
−0.602414 + 0.798183i \(0.705795\pi\)
\(32\) −1.00000 −0.176777
\(33\) 8.09017 1.40832
\(34\) −0.145898 −0.0250213
\(35\) −1.00000 −0.169031
\(36\) −0.381966 −0.0636610
\(37\) 11.9443 1.96363 0.981813 0.189850i \(-0.0608002\pi\)
0.981813 + 0.189850i \(0.0608002\pi\)
\(38\) 0 0
\(39\) −3.00000 −0.480384
\(40\) −1.00000 −0.158114
\(41\) −10.0902 −1.57582 −0.787910 0.615791i \(-0.788837\pi\)
−0.787910 + 0.615791i \(0.788837\pi\)
\(42\) −1.61803 −0.249668
\(43\) −0.145898 −0.0222492 −0.0111246 0.999938i \(-0.503541\pi\)
−0.0111246 + 0.999938i \(0.503541\pi\)
\(44\) −5.00000 −0.753778
\(45\) −0.381966 −0.0569401
\(46\) 8.23607 1.21434
\(47\) −9.94427 −1.45052 −0.725261 0.688474i \(-0.758281\pi\)
−0.725261 + 0.688474i \(0.758281\pi\)
\(48\) −1.61803 −0.233543
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) −0.236068 −0.0330561
\(52\) 1.85410 0.257118
\(53\) −0.708204 −0.0972793 −0.0486396 0.998816i \(-0.515489\pi\)
−0.0486396 + 0.998816i \(0.515489\pi\)
\(54\) −5.47214 −0.744663
\(55\) −5.00000 −0.674200
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −3.76393 −0.494228
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) −1.61803 −0.208887
\(61\) −1.47214 −0.188488 −0.0942438 0.995549i \(-0.530043\pi\)
−0.0942438 + 0.995549i \(0.530043\pi\)
\(62\) 6.70820 0.851943
\(63\) 0.381966 0.0481232
\(64\) 1.00000 0.125000
\(65\) 1.85410 0.229973
\(66\) −8.09017 −0.995831
\(67\) −1.14590 −0.139994 −0.0699969 0.997547i \(-0.522299\pi\)
−0.0699969 + 0.997547i \(0.522299\pi\)
\(68\) 0.145898 0.0176927
\(69\) 13.3262 1.60429
\(70\) 1.00000 0.119523
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0.381966 0.0450151
\(73\) 5.56231 0.651019 0.325509 0.945539i \(-0.394464\pi\)
0.325509 + 0.945539i \(0.394464\pi\)
\(74\) −11.9443 −1.38849
\(75\) 6.47214 0.747338
\(76\) 0 0
\(77\) 5.00000 0.569803
\(78\) 3.00000 0.339683
\(79\) 2.14590 0.241432 0.120716 0.992687i \(-0.461481\pi\)
0.120716 + 0.992687i \(0.461481\pi\)
\(80\) 1.00000 0.111803
\(81\) −7.70820 −0.856467
\(82\) 10.0902 1.11427
\(83\) 11.4164 1.25311 0.626557 0.779376i \(-0.284464\pi\)
0.626557 + 0.779376i \(0.284464\pi\)
\(84\) 1.61803 0.176542
\(85\) 0.145898 0.0158249
\(86\) 0.145898 0.0157326
\(87\) −6.09017 −0.652935
\(88\) 5.00000 0.533002
\(89\) 1.85410 0.196534 0.0982672 0.995160i \(-0.468670\pi\)
0.0982672 + 0.995160i \(0.468670\pi\)
\(90\) 0.381966 0.0402628
\(91\) −1.85410 −0.194363
\(92\) −8.23607 −0.858669
\(93\) 10.8541 1.12552
\(94\) 9.94427 1.02567
\(95\) 0 0
\(96\) 1.61803 0.165140
\(97\) 0.527864 0.0535965 0.0267982 0.999641i \(-0.491469\pi\)
0.0267982 + 0.999641i \(0.491469\pi\)
\(98\) −1.00000 −0.101015
\(99\) 1.90983 0.191945
\(100\) −4.00000 −0.400000
\(101\) 10.8541 1.08002 0.540012 0.841657i \(-0.318420\pi\)
0.540012 + 0.841657i \(0.318420\pi\)
\(102\) 0.236068 0.0233742
\(103\) 3.90983 0.385247 0.192624 0.981273i \(-0.438300\pi\)
0.192624 + 0.981273i \(0.438300\pi\)
\(104\) −1.85410 −0.181810
\(105\) 1.61803 0.157904
\(106\) 0.708204 0.0687868
\(107\) −3.94427 −0.381307 −0.190654 0.981657i \(-0.561061\pi\)
−0.190654 + 0.981657i \(0.561061\pi\)
\(108\) 5.47214 0.526557
\(109\) −6.56231 −0.628555 −0.314277 0.949331i \(-0.601762\pi\)
−0.314277 + 0.949331i \(0.601762\pi\)
\(110\) 5.00000 0.476731
\(111\) −19.3262 −1.83437
\(112\) −1.00000 −0.0944911
\(113\) 2.85410 0.268491 0.134246 0.990948i \(-0.457139\pi\)
0.134246 + 0.990948i \(0.457139\pi\)
\(114\) 0 0
\(115\) −8.23607 −0.768017
\(116\) 3.76393 0.349472
\(117\) −0.708204 −0.0654735
\(118\) 11.0000 1.01263
\(119\) −0.145898 −0.0133745
\(120\) 1.61803 0.147706
\(121\) 14.0000 1.27273
\(122\) 1.47214 0.133281
\(123\) 16.3262 1.47209
\(124\) −6.70820 −0.602414
\(125\) −9.00000 −0.804984
\(126\) −0.381966 −0.0340282
\(127\) −8.32624 −0.738834 −0.369417 0.929264i \(-0.620443\pi\)
−0.369417 + 0.929264i \(0.620443\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.236068 0.0207846
\(130\) −1.85410 −0.162615
\(131\) −6.61803 −0.578220 −0.289110 0.957296i \(-0.593359\pi\)
−0.289110 + 0.957296i \(0.593359\pi\)
\(132\) 8.09017 0.704159
\(133\) 0 0
\(134\) 1.14590 0.0989905
\(135\) 5.47214 0.470966
\(136\) −0.145898 −0.0125107
\(137\) −19.1246 −1.63393 −0.816963 0.576690i \(-0.804344\pi\)
−0.816963 + 0.576690i \(0.804344\pi\)
\(138\) −13.3262 −1.13440
\(139\) 4.23607 0.359299 0.179649 0.983731i \(-0.442504\pi\)
0.179649 + 0.983731i \(0.442504\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 16.0902 1.35504
\(142\) −10.0000 −0.839181
\(143\) −9.27051 −0.775239
\(144\) −0.381966 −0.0318305
\(145\) 3.76393 0.312578
\(146\) −5.56231 −0.460340
\(147\) −1.61803 −0.133453
\(148\) 11.9443 0.981813
\(149\) 3.61803 0.296401 0.148200 0.988957i \(-0.452652\pi\)
0.148200 + 0.988957i \(0.452652\pi\)
\(150\) −6.47214 −0.528448
\(151\) 9.76393 0.794578 0.397289 0.917694i \(-0.369951\pi\)
0.397289 + 0.917694i \(0.369951\pi\)
\(152\) 0 0
\(153\) −0.0557281 −0.00450535
\(154\) −5.00000 −0.402911
\(155\) −6.70820 −0.538816
\(156\) −3.00000 −0.240192
\(157\) 6.67376 0.532624 0.266312 0.963887i \(-0.414195\pi\)
0.266312 + 0.963887i \(0.414195\pi\)
\(158\) −2.14590 −0.170718
\(159\) 1.14590 0.0908756
\(160\) −1.00000 −0.0790569
\(161\) 8.23607 0.649093
\(162\) 7.70820 0.605614
\(163\) −8.47214 −0.663589 −0.331794 0.943352i \(-0.607654\pi\)
−0.331794 + 0.943352i \(0.607654\pi\)
\(164\) −10.0902 −0.787910
\(165\) 8.09017 0.629819
\(166\) −11.4164 −0.886085
\(167\) −24.1803 −1.87113 −0.935565 0.353153i \(-0.885109\pi\)
−0.935565 + 0.353153i \(0.885109\pi\)
\(168\) −1.61803 −0.124834
\(169\) −9.56231 −0.735562
\(170\) −0.145898 −0.0111899
\(171\) 0 0
\(172\) −0.145898 −0.0111246
\(173\) −6.23607 −0.474119 −0.237060 0.971495i \(-0.576184\pi\)
−0.237060 + 0.971495i \(0.576184\pi\)
\(174\) 6.09017 0.461695
\(175\) 4.00000 0.302372
\(176\) −5.00000 −0.376889
\(177\) 17.7984 1.33781
\(178\) −1.85410 −0.138971
\(179\) 20.0344 1.49744 0.748722 0.662884i \(-0.230668\pi\)
0.748722 + 0.662884i \(0.230668\pi\)
\(180\) −0.381966 −0.0284701
\(181\) 20.2361 1.50414 0.752068 0.659086i \(-0.229057\pi\)
0.752068 + 0.659086i \(0.229057\pi\)
\(182\) 1.85410 0.137435
\(183\) 2.38197 0.176080
\(184\) 8.23607 0.607171
\(185\) 11.9443 0.878160
\(186\) −10.8541 −0.795861
\(187\) −0.729490 −0.0533456
\(188\) −9.94427 −0.725261
\(189\) −5.47214 −0.398039
\(190\) 0 0
\(191\) 25.1803 1.82199 0.910993 0.412422i \(-0.135317\pi\)
0.910993 + 0.412422i \(0.135317\pi\)
\(192\) −1.61803 −0.116772
\(193\) −12.1803 −0.876760 −0.438380 0.898790i \(-0.644448\pi\)
−0.438380 + 0.898790i \(0.644448\pi\)
\(194\) −0.527864 −0.0378984
\(195\) −3.00000 −0.214834
\(196\) 1.00000 0.0714286
\(197\) 12.5623 0.895027 0.447514 0.894277i \(-0.352310\pi\)
0.447514 + 0.894277i \(0.352310\pi\)
\(198\) −1.90983 −0.135726
\(199\) −16.0902 −1.14060 −0.570301 0.821436i \(-0.693173\pi\)
−0.570301 + 0.821436i \(0.693173\pi\)
\(200\) 4.00000 0.282843
\(201\) 1.85410 0.130778
\(202\) −10.8541 −0.763692
\(203\) −3.76393 −0.264176
\(204\) −0.236068 −0.0165281
\(205\) −10.0902 −0.704728
\(206\) −3.90983 −0.272411
\(207\) 3.14590 0.218655
\(208\) 1.85410 0.128559
\(209\) 0 0
\(210\) −1.61803 −0.111655
\(211\) 21.9443 1.51071 0.755353 0.655318i \(-0.227465\pi\)
0.755353 + 0.655318i \(0.227465\pi\)
\(212\) −0.708204 −0.0486396
\(213\) −16.1803 −1.10866
\(214\) 3.94427 0.269625
\(215\) −0.145898 −0.00995016
\(216\) −5.47214 −0.372332
\(217\) 6.70820 0.455383
\(218\) 6.56231 0.444455
\(219\) −9.00000 −0.608164
\(220\) −5.00000 −0.337100
\(221\) 0.270510 0.0181965
\(222\) 19.3262 1.29709
\(223\) 25.6525 1.71782 0.858908 0.512129i \(-0.171143\pi\)
0.858908 + 0.512129i \(0.171143\pi\)
\(224\) 1.00000 0.0668153
\(225\) 1.52786 0.101858
\(226\) −2.85410 −0.189852
\(227\) 9.76393 0.648055 0.324027 0.946048i \(-0.394963\pi\)
0.324027 + 0.946048i \(0.394963\pi\)
\(228\) 0 0
\(229\) 1.09017 0.0720405 0.0360202 0.999351i \(-0.488532\pi\)
0.0360202 + 0.999351i \(0.488532\pi\)
\(230\) 8.23607 0.543070
\(231\) −8.09017 −0.532294
\(232\) −3.76393 −0.247114
\(233\) 18.0344 1.18148 0.590738 0.806864i \(-0.298837\pi\)
0.590738 + 0.806864i \(0.298837\pi\)
\(234\) 0.708204 0.0462967
\(235\) −9.94427 −0.648693
\(236\) −11.0000 −0.716039
\(237\) −3.47214 −0.225539
\(238\) 0.145898 0.00945716
\(239\) −17.8541 −1.15489 −0.577443 0.816431i \(-0.695949\pi\)
−0.577443 + 0.816431i \(0.695949\pi\)
\(240\) −1.61803 −0.104444
\(241\) −19.0902 −1.22971 −0.614853 0.788642i \(-0.710785\pi\)
−0.614853 + 0.788642i \(0.710785\pi\)
\(242\) −14.0000 −0.899954
\(243\) −3.94427 −0.253025
\(244\) −1.47214 −0.0942438
\(245\) 1.00000 0.0638877
\(246\) −16.3262 −1.04092
\(247\) 0 0
\(248\) 6.70820 0.425971
\(249\) −18.4721 −1.17062
\(250\) 9.00000 0.569210
\(251\) −2.47214 −0.156040 −0.0780199 0.996952i \(-0.524860\pi\)
−0.0780199 + 0.996952i \(0.524860\pi\)
\(252\) 0.381966 0.0240616
\(253\) 41.1803 2.58899
\(254\) 8.32624 0.522435
\(255\) −0.236068 −0.0147832
\(256\) 1.00000 0.0625000
\(257\) −25.9443 −1.61836 −0.809180 0.587561i \(-0.800088\pi\)
−0.809180 + 0.587561i \(0.800088\pi\)
\(258\) −0.236068 −0.0146970
\(259\) −11.9443 −0.742181
\(260\) 1.85410 0.114987
\(261\) −1.43769 −0.0889910
\(262\) 6.61803 0.408864
\(263\) −2.81966 −0.173868 −0.0869338 0.996214i \(-0.527707\pi\)
−0.0869338 + 0.996214i \(0.527707\pi\)
\(264\) −8.09017 −0.497916
\(265\) −0.708204 −0.0435046
\(266\) 0 0
\(267\) −3.00000 −0.183597
\(268\) −1.14590 −0.0699969
\(269\) 13.1803 0.803620 0.401810 0.915723i \(-0.368381\pi\)
0.401810 + 0.915723i \(0.368381\pi\)
\(270\) −5.47214 −0.333024
\(271\) −29.6525 −1.80126 −0.900630 0.434587i \(-0.856894\pi\)
−0.900630 + 0.434587i \(0.856894\pi\)
\(272\) 0.145898 0.00884637
\(273\) 3.00000 0.181568
\(274\) 19.1246 1.15536
\(275\) 20.0000 1.20605
\(276\) 13.3262 0.802145
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) −4.23607 −0.254062
\(279\) 2.56231 0.153401
\(280\) 1.00000 0.0597614
\(281\) 7.76393 0.463157 0.231579 0.972816i \(-0.425611\pi\)
0.231579 + 0.972816i \(0.425611\pi\)
\(282\) −16.0902 −0.958156
\(283\) 26.5623 1.57897 0.789483 0.613773i \(-0.210349\pi\)
0.789483 + 0.613773i \(0.210349\pi\)
\(284\) 10.0000 0.593391
\(285\) 0 0
\(286\) 9.27051 0.548177
\(287\) 10.0902 0.595604
\(288\) 0.381966 0.0225076
\(289\) −16.9787 −0.998748
\(290\) −3.76393 −0.221026
\(291\) −0.854102 −0.0500683
\(292\) 5.56231 0.325509
\(293\) −11.7639 −0.687256 −0.343628 0.939106i \(-0.611656\pi\)
−0.343628 + 0.939106i \(0.611656\pi\)
\(294\) 1.61803 0.0943657
\(295\) −11.0000 −0.640445
\(296\) −11.9443 −0.694247
\(297\) −27.3607 −1.58763
\(298\) −3.61803 −0.209587
\(299\) −15.2705 −0.883116
\(300\) 6.47214 0.373669
\(301\) 0.145898 0.00840942
\(302\) −9.76393 −0.561851
\(303\) −17.5623 −1.00893
\(304\) 0 0
\(305\) −1.47214 −0.0842943
\(306\) 0.0557281 0.00318576
\(307\) 12.9443 0.738769 0.369384 0.929277i \(-0.379569\pi\)
0.369384 + 0.929277i \(0.379569\pi\)
\(308\) 5.00000 0.284901
\(309\) −6.32624 −0.359887
\(310\) 6.70820 0.381000
\(311\) 24.2361 1.37430 0.687151 0.726515i \(-0.258861\pi\)
0.687151 + 0.726515i \(0.258861\pi\)
\(312\) 3.00000 0.169842
\(313\) 30.0902 1.70080 0.850398 0.526139i \(-0.176361\pi\)
0.850398 + 0.526139i \(0.176361\pi\)
\(314\) −6.67376 −0.376622
\(315\) 0.381966 0.0215213
\(316\) 2.14590 0.120716
\(317\) 18.4164 1.03437 0.517184 0.855874i \(-0.326980\pi\)
0.517184 + 0.855874i \(0.326980\pi\)
\(318\) −1.14590 −0.0642588
\(319\) −18.8197 −1.05370
\(320\) 1.00000 0.0559017
\(321\) 6.38197 0.356207
\(322\) −8.23607 −0.458978
\(323\) 0 0
\(324\) −7.70820 −0.428234
\(325\) −7.41641 −0.411388
\(326\) 8.47214 0.469228
\(327\) 10.6180 0.587179
\(328\) 10.0902 0.557136
\(329\) 9.94427 0.548245
\(330\) −8.09017 −0.445349
\(331\) −3.52786 −0.193909 −0.0969545 0.995289i \(-0.530910\pi\)
−0.0969545 + 0.995289i \(0.530910\pi\)
\(332\) 11.4164 0.626557
\(333\) −4.56231 −0.250013
\(334\) 24.1803 1.32309
\(335\) −1.14590 −0.0626071
\(336\) 1.61803 0.0882710
\(337\) −22.4508 −1.22298 −0.611488 0.791254i \(-0.709429\pi\)
−0.611488 + 0.791254i \(0.709429\pi\)
\(338\) 9.56231 0.520121
\(339\) −4.61803 −0.250817
\(340\) 0.145898 0.00791243
\(341\) 33.5410 1.81635
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0.145898 0.00786629
\(345\) 13.3262 0.717461
\(346\) 6.23607 0.335253
\(347\) −22.9443 −1.23171 −0.615857 0.787858i \(-0.711190\pi\)
−0.615857 + 0.787858i \(0.711190\pi\)
\(348\) −6.09017 −0.326467
\(349\) 6.70820 0.359082 0.179541 0.983750i \(-0.442539\pi\)
0.179541 + 0.983750i \(0.442539\pi\)
\(350\) −4.00000 −0.213809
\(351\) 10.1459 0.541548
\(352\) 5.00000 0.266501
\(353\) 1.90983 0.101650 0.0508250 0.998708i \(-0.483815\pi\)
0.0508250 + 0.998708i \(0.483815\pi\)
\(354\) −17.7984 −0.945973
\(355\) 10.0000 0.530745
\(356\) 1.85410 0.0982672
\(357\) 0.236068 0.0124940
\(358\) −20.0344 −1.05885
\(359\) 10.0557 0.530721 0.265361 0.964149i \(-0.414509\pi\)
0.265361 + 0.964149i \(0.414509\pi\)
\(360\) 0.381966 0.0201314
\(361\) 0 0
\(362\) −20.2361 −1.06358
\(363\) −22.6525 −1.18895
\(364\) −1.85410 −0.0971813
\(365\) 5.56231 0.291144
\(366\) −2.38197 −0.124507
\(367\) 25.3262 1.32202 0.661009 0.750378i \(-0.270128\pi\)
0.661009 + 0.750378i \(0.270128\pi\)
\(368\) −8.23607 −0.429335
\(369\) 3.85410 0.200637
\(370\) −11.9443 −0.620953
\(371\) 0.708204 0.0367681
\(372\) 10.8541 0.562759
\(373\) 0.145898 0.00755431 0.00377716 0.999993i \(-0.498798\pi\)
0.00377716 + 0.999993i \(0.498798\pi\)
\(374\) 0.729490 0.0377210
\(375\) 14.5623 0.751994
\(376\) 9.94427 0.512837
\(377\) 6.97871 0.359422
\(378\) 5.47214 0.281456
\(379\) 17.0344 0.875001 0.437500 0.899218i \(-0.355864\pi\)
0.437500 + 0.899218i \(0.355864\pi\)
\(380\) 0 0
\(381\) 13.4721 0.690198
\(382\) −25.1803 −1.28834
\(383\) 11.9443 0.610324 0.305162 0.952300i \(-0.401289\pi\)
0.305162 + 0.952300i \(0.401289\pi\)
\(384\) 1.61803 0.0825700
\(385\) 5.00000 0.254824
\(386\) 12.1803 0.619963
\(387\) 0.0557281 0.00283282
\(388\) 0.527864 0.0267982
\(389\) 13.6180 0.690462 0.345231 0.938518i \(-0.387801\pi\)
0.345231 + 0.938518i \(0.387801\pi\)
\(390\) 3.00000 0.151911
\(391\) −1.20163 −0.0607688
\(392\) −1.00000 −0.0505076
\(393\) 10.7082 0.540157
\(394\) −12.5623 −0.632880
\(395\) 2.14590 0.107972
\(396\) 1.90983 0.0959726
\(397\) 1.27051 0.0637651 0.0318825 0.999492i \(-0.489850\pi\)
0.0318825 + 0.999492i \(0.489850\pi\)
\(398\) 16.0902 0.806527
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) 33.4164 1.66874 0.834368 0.551208i \(-0.185833\pi\)
0.834368 + 0.551208i \(0.185833\pi\)
\(402\) −1.85410 −0.0924742
\(403\) −12.4377 −0.619566
\(404\) 10.8541 0.540012
\(405\) −7.70820 −0.383024
\(406\) 3.76393 0.186801
\(407\) −59.7214 −2.96028
\(408\) 0.236068 0.0116871
\(409\) 34.2148 1.69181 0.845906 0.533332i \(-0.179060\pi\)
0.845906 + 0.533332i \(0.179060\pi\)
\(410\) 10.0902 0.498318
\(411\) 30.9443 1.52637
\(412\) 3.90983 0.192624
\(413\) 11.0000 0.541275
\(414\) −3.14590 −0.154612
\(415\) 11.4164 0.560409
\(416\) −1.85410 −0.0909048
\(417\) −6.85410 −0.335647
\(418\) 0 0
\(419\) 16.7426 0.817932 0.408966 0.912550i \(-0.365890\pi\)
0.408966 + 0.912550i \(0.365890\pi\)
\(420\) 1.61803 0.0789520
\(421\) 25.9443 1.26445 0.632223 0.774786i \(-0.282143\pi\)
0.632223 + 0.774786i \(0.282143\pi\)
\(422\) −21.9443 −1.06823
\(423\) 3.79837 0.184683
\(424\) 0.708204 0.0343934
\(425\) −0.583592 −0.0283084
\(426\) 16.1803 0.783940
\(427\) 1.47214 0.0712417
\(428\) −3.94427 −0.190654
\(429\) 15.0000 0.724207
\(430\) 0.145898 0.00703583
\(431\) 14.9443 0.719840 0.359920 0.932983i \(-0.382804\pi\)
0.359920 + 0.932983i \(0.382804\pi\)
\(432\) 5.47214 0.263278
\(433\) 25.3820 1.21978 0.609890 0.792486i \(-0.291214\pi\)
0.609890 + 0.792486i \(0.291214\pi\)
\(434\) −6.70820 −0.322004
\(435\) −6.09017 −0.292001
\(436\) −6.56231 −0.314277
\(437\) 0 0
\(438\) 9.00000 0.430037
\(439\) 39.9443 1.90644 0.953218 0.302284i \(-0.0977490\pi\)
0.953218 + 0.302284i \(0.0977490\pi\)
\(440\) 5.00000 0.238366
\(441\) −0.381966 −0.0181889
\(442\) −0.270510 −0.0128668
\(443\) −34.2148 −1.62559 −0.812797 0.582547i \(-0.802056\pi\)
−0.812797 + 0.582547i \(0.802056\pi\)
\(444\) −19.3262 −0.917183
\(445\) 1.85410 0.0878929
\(446\) −25.6525 −1.21468
\(447\) −5.85410 −0.276890
\(448\) −1.00000 −0.0472456
\(449\) −0.180340 −0.00851077 −0.00425538 0.999991i \(-0.501355\pi\)
−0.00425538 + 0.999991i \(0.501355\pi\)
\(450\) −1.52786 −0.0720242
\(451\) 50.4508 2.37564
\(452\) 2.85410 0.134246
\(453\) −15.7984 −0.742272
\(454\) −9.76393 −0.458244
\(455\) −1.85410 −0.0869216
\(456\) 0 0
\(457\) −5.88854 −0.275454 −0.137727 0.990470i \(-0.543980\pi\)
−0.137727 + 0.990470i \(0.543980\pi\)
\(458\) −1.09017 −0.0509403
\(459\) 0.798374 0.0372649
\(460\) −8.23607 −0.384009
\(461\) −24.5410 −1.14299 −0.571495 0.820606i \(-0.693636\pi\)
−0.571495 + 0.820606i \(0.693636\pi\)
\(462\) 8.09017 0.376389
\(463\) 6.56231 0.304976 0.152488 0.988305i \(-0.451271\pi\)
0.152488 + 0.988305i \(0.451271\pi\)
\(464\) 3.76393 0.174736
\(465\) 10.8541 0.503347
\(466\) −18.0344 −0.835429
\(467\) 24.5279 1.13501 0.567507 0.823369i \(-0.307908\pi\)
0.567507 + 0.823369i \(0.307908\pi\)
\(468\) −0.708204 −0.0327367
\(469\) 1.14590 0.0529127
\(470\) 9.94427 0.458695
\(471\) −10.7984 −0.497563
\(472\) 11.0000 0.506316
\(473\) 0.729490 0.0335420
\(474\) 3.47214 0.159480
\(475\) 0 0
\(476\) −0.145898 −0.00668723
\(477\) 0.270510 0.0123858
\(478\) 17.8541 0.816628
\(479\) 22.1803 1.01345 0.506723 0.862109i \(-0.330857\pi\)
0.506723 + 0.862109i \(0.330857\pi\)
\(480\) 1.61803 0.0738528
\(481\) 22.1459 1.00977
\(482\) 19.0902 0.869533
\(483\) −13.3262 −0.606365
\(484\) 14.0000 0.636364
\(485\) 0.527864 0.0239691
\(486\) 3.94427 0.178916
\(487\) 11.1803 0.506630 0.253315 0.967384i \(-0.418479\pi\)
0.253315 + 0.967384i \(0.418479\pi\)
\(488\) 1.47214 0.0666405
\(489\) 13.7082 0.619906
\(490\) −1.00000 −0.0451754
\(491\) 29.5967 1.33568 0.667841 0.744304i \(-0.267218\pi\)
0.667841 + 0.744304i \(0.267218\pi\)
\(492\) 16.3262 0.736044
\(493\) 0.549150 0.0247325
\(494\) 0 0
\(495\) 1.90983 0.0858405
\(496\) −6.70820 −0.301207
\(497\) −10.0000 −0.448561
\(498\) 18.4721 0.827756
\(499\) −10.4164 −0.466302 −0.233151 0.972440i \(-0.574904\pi\)
−0.233151 + 0.972440i \(0.574904\pi\)
\(500\) −9.00000 −0.402492
\(501\) 39.1246 1.74796
\(502\) 2.47214 0.110337
\(503\) −39.7771 −1.77357 −0.886786 0.462180i \(-0.847068\pi\)
−0.886786 + 0.462180i \(0.847068\pi\)
\(504\) −0.381966 −0.0170141
\(505\) 10.8541 0.483001
\(506\) −41.1803 −1.83069
\(507\) 15.4721 0.687142
\(508\) −8.32624 −0.369417
\(509\) 25.4164 1.12656 0.563281 0.826265i \(-0.309539\pi\)
0.563281 + 0.826265i \(0.309539\pi\)
\(510\) 0.236068 0.0104533
\(511\) −5.56231 −0.246062
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 25.9443 1.14435
\(515\) 3.90983 0.172288
\(516\) 0.236068 0.0103923
\(517\) 49.7214 2.18674
\(518\) 11.9443 0.524801
\(519\) 10.0902 0.442909
\(520\) −1.85410 −0.0813077
\(521\) 5.65248 0.247639 0.123820 0.992305i \(-0.460486\pi\)
0.123820 + 0.992305i \(0.460486\pi\)
\(522\) 1.43769 0.0629262
\(523\) −34.1591 −1.49367 −0.746836 0.665009i \(-0.768428\pi\)
−0.746836 + 0.665009i \(0.768428\pi\)
\(524\) −6.61803 −0.289110
\(525\) −6.47214 −0.282467
\(526\) 2.81966 0.122943
\(527\) −0.978714 −0.0426334
\(528\) 8.09017 0.352079
\(529\) 44.8328 1.94925
\(530\) 0.708204 0.0307624
\(531\) 4.20163 0.182335
\(532\) 0 0
\(533\) −18.7082 −0.810342
\(534\) 3.00000 0.129823
\(535\) −3.94427 −0.170526
\(536\) 1.14590 0.0494953
\(537\) −32.4164 −1.39887
\(538\) −13.1803 −0.568245
\(539\) −5.00000 −0.215365
\(540\) 5.47214 0.235483
\(541\) 32.3050 1.38890 0.694449 0.719542i \(-0.255648\pi\)
0.694449 + 0.719542i \(0.255648\pi\)
\(542\) 29.6525 1.27368
\(543\) −32.7426 −1.40512
\(544\) −0.145898 −0.00625533
\(545\) −6.56231 −0.281098
\(546\) −3.00000 −0.128388
\(547\) 13.1803 0.563551 0.281775 0.959480i \(-0.409077\pi\)
0.281775 + 0.959480i \(0.409077\pi\)
\(548\) −19.1246 −0.816963
\(549\) 0.562306 0.0239986
\(550\) −20.0000 −0.852803
\(551\) 0 0
\(552\) −13.3262 −0.567202
\(553\) −2.14590 −0.0912529
\(554\) 8.00000 0.339887
\(555\) −19.3262 −0.820353
\(556\) 4.23607 0.179649
\(557\) −32.2361 −1.36589 −0.682943 0.730472i \(-0.739300\pi\)
−0.682943 + 0.730472i \(0.739300\pi\)
\(558\) −2.56231 −0.108471
\(559\) −0.270510 −0.0114413
\(560\) −1.00000 −0.0422577
\(561\) 1.18034 0.0498340
\(562\) −7.76393 −0.327502
\(563\) 22.0689 0.930093 0.465046 0.885286i \(-0.346038\pi\)
0.465046 + 0.885286i \(0.346038\pi\)
\(564\) 16.0902 0.677518
\(565\) 2.85410 0.120073
\(566\) −26.5623 −1.11650
\(567\) 7.70820 0.323714
\(568\) −10.0000 −0.419591
\(569\) −3.27051 −0.137107 −0.0685535 0.997647i \(-0.521838\pi\)
−0.0685535 + 0.997647i \(0.521838\pi\)
\(570\) 0 0
\(571\) −45.0132 −1.88374 −0.941871 0.335975i \(-0.890934\pi\)
−0.941871 + 0.335975i \(0.890934\pi\)
\(572\) −9.27051 −0.387619
\(573\) −40.7426 −1.70205
\(574\) −10.0902 −0.421156
\(575\) 32.9443 1.37387
\(576\) −0.381966 −0.0159153
\(577\) −16.7082 −0.695572 −0.347786 0.937574i \(-0.613066\pi\)
−0.347786 + 0.937574i \(0.613066\pi\)
\(578\) 16.9787 0.706221
\(579\) 19.7082 0.819045
\(580\) 3.76393 0.156289
\(581\) −11.4164 −0.473632
\(582\) 0.854102 0.0354037
\(583\) 3.54102 0.146654
\(584\) −5.56231 −0.230170
\(585\) −0.708204 −0.0292806
\(586\) 11.7639 0.485964
\(587\) −24.0557 −0.992886 −0.496443 0.868069i \(-0.665361\pi\)
−0.496443 + 0.868069i \(0.665361\pi\)
\(588\) −1.61803 −0.0667266
\(589\) 0 0
\(590\) 11.0000 0.452863
\(591\) −20.3262 −0.836110
\(592\) 11.9443 0.490907
\(593\) 25.5623 1.04972 0.524859 0.851189i \(-0.324118\pi\)
0.524859 + 0.851189i \(0.324118\pi\)
\(594\) 27.3607 1.12262
\(595\) −0.145898 −0.00598124
\(596\) 3.61803 0.148200
\(597\) 26.0344 1.06552
\(598\) 15.2705 0.624458
\(599\) −17.0000 −0.694601 −0.347301 0.937754i \(-0.612902\pi\)
−0.347301 + 0.937754i \(0.612902\pi\)
\(600\) −6.47214 −0.264224
\(601\) 26.1246 1.06565 0.532823 0.846227i \(-0.321131\pi\)
0.532823 + 0.846227i \(0.321131\pi\)
\(602\) −0.145898 −0.00594636
\(603\) 0.437694 0.0178243
\(604\) 9.76393 0.397289
\(605\) 14.0000 0.569181
\(606\) 17.5623 0.713420
\(607\) 0.944272 0.0383268 0.0191634 0.999816i \(-0.493900\pi\)
0.0191634 + 0.999816i \(0.493900\pi\)
\(608\) 0 0
\(609\) 6.09017 0.246786
\(610\) 1.47214 0.0596050
\(611\) −18.4377 −0.745909
\(612\) −0.0557281 −0.00225267
\(613\) 20.6525 0.834146 0.417073 0.908873i \(-0.363056\pi\)
0.417073 + 0.908873i \(0.363056\pi\)
\(614\) −12.9443 −0.522388
\(615\) 16.3262 0.658337
\(616\) −5.00000 −0.201456
\(617\) −8.67376 −0.349193 −0.174596 0.984640i \(-0.555862\pi\)
−0.174596 + 0.984640i \(0.555862\pi\)
\(618\) 6.32624 0.254479
\(619\) −10.2016 −0.410038 −0.205019 0.978758i \(-0.565726\pi\)
−0.205019 + 0.978758i \(0.565726\pi\)
\(620\) −6.70820 −0.269408
\(621\) −45.0689 −1.80855
\(622\) −24.2361 −0.971778
\(623\) −1.85410 −0.0742830
\(624\) −3.00000 −0.120096
\(625\) 11.0000 0.440000
\(626\) −30.0902 −1.20265
\(627\) 0 0
\(628\) 6.67376 0.266312
\(629\) 1.74265 0.0694838
\(630\) −0.381966 −0.0152179
\(631\) −4.94427 −0.196828 −0.0984142 0.995146i \(-0.531377\pi\)
−0.0984142 + 0.995146i \(0.531377\pi\)
\(632\) −2.14590 −0.0853592
\(633\) −35.5066 −1.41126
\(634\) −18.4164 −0.731409
\(635\) −8.32624 −0.330417
\(636\) 1.14590 0.0454378
\(637\) 1.85410 0.0734622
\(638\) 18.8197 0.745077
\(639\) −3.81966 −0.151103
\(640\) −1.00000 −0.0395285
\(641\) −30.0902 −1.18849 −0.594245 0.804284i \(-0.702549\pi\)
−0.594245 + 0.804284i \(0.702549\pi\)
\(642\) −6.38197 −0.251876
\(643\) −8.65248 −0.341220 −0.170610 0.985339i \(-0.554574\pi\)
−0.170610 + 0.985339i \(0.554574\pi\)
\(644\) 8.23607 0.324547
\(645\) 0.236068 0.00929517
\(646\) 0 0
\(647\) 46.1033 1.81251 0.906254 0.422733i \(-0.138929\pi\)
0.906254 + 0.422733i \(0.138929\pi\)
\(648\) 7.70820 0.302807
\(649\) 55.0000 2.15894
\(650\) 7.41641 0.290895
\(651\) −10.8541 −0.425406
\(652\) −8.47214 −0.331794
\(653\) −36.6869 −1.43567 −0.717835 0.696213i \(-0.754867\pi\)
−0.717835 + 0.696213i \(0.754867\pi\)
\(654\) −10.6180 −0.415198
\(655\) −6.61803 −0.258588
\(656\) −10.0902 −0.393955
\(657\) −2.12461 −0.0828890
\(658\) −9.94427 −0.387668
\(659\) 33.5410 1.30657 0.653286 0.757111i \(-0.273390\pi\)
0.653286 + 0.757111i \(0.273390\pi\)
\(660\) 8.09017 0.314909
\(661\) −41.8328 −1.62711 −0.813554 0.581489i \(-0.802470\pi\)
−0.813554 + 0.581489i \(0.802470\pi\)
\(662\) 3.52786 0.137114
\(663\) −0.437694 −0.0169986
\(664\) −11.4164 −0.443043
\(665\) 0 0
\(666\) 4.56231 0.176786
\(667\) −31.0000 −1.20032
\(668\) −24.1803 −0.935565
\(669\) −41.5066 −1.60474
\(670\) 1.14590 0.0442699
\(671\) 7.36068 0.284156
\(672\) −1.61803 −0.0624170
\(673\) −32.0902 −1.23699 −0.618493 0.785791i \(-0.712256\pi\)
−0.618493 + 0.785791i \(0.712256\pi\)
\(674\) 22.4508 0.864774
\(675\) −21.8885 −0.842490
\(676\) −9.56231 −0.367781
\(677\) 9.70820 0.373117 0.186558 0.982444i \(-0.440267\pi\)
0.186558 + 0.982444i \(0.440267\pi\)
\(678\) 4.61803 0.177355
\(679\) −0.527864 −0.0202576
\(680\) −0.145898 −0.00559493
\(681\) −15.7984 −0.605395
\(682\) −33.5410 −1.28435
\(683\) −13.2705 −0.507782 −0.253891 0.967233i \(-0.581710\pi\)
−0.253891 + 0.967233i \(0.581710\pi\)
\(684\) 0 0
\(685\) −19.1246 −0.730714
\(686\) 1.00000 0.0381802
\(687\) −1.76393 −0.0672982
\(688\) −0.145898 −0.00556231
\(689\) −1.31308 −0.0500245
\(690\) −13.3262 −0.507321
\(691\) 0.527864 0.0200809 0.0100404 0.999950i \(-0.496804\pi\)
0.0100404 + 0.999950i \(0.496804\pi\)
\(692\) −6.23607 −0.237060
\(693\) −1.90983 −0.0725484
\(694\) 22.9443 0.870953
\(695\) 4.23607 0.160683
\(696\) 6.09017 0.230847
\(697\) −1.47214 −0.0557611
\(698\) −6.70820 −0.253909
\(699\) −29.1803 −1.10370
\(700\) 4.00000 0.151186
\(701\) 35.2705 1.33215 0.666074 0.745885i \(-0.267973\pi\)
0.666074 + 0.745885i \(0.267973\pi\)
\(702\) −10.1459 −0.382932
\(703\) 0 0
\(704\) −5.00000 −0.188445
\(705\) 16.0902 0.605991
\(706\) −1.90983 −0.0718774
\(707\) −10.8541 −0.408211
\(708\) 17.7984 0.668904
\(709\) 8.34752 0.313498 0.156749 0.987638i \(-0.449899\pi\)
0.156749 + 0.987638i \(0.449899\pi\)
\(710\) −10.0000 −0.375293
\(711\) −0.819660 −0.0307397
\(712\) −1.85410 −0.0694854
\(713\) 55.2492 2.06910
\(714\) −0.236068 −0.00883462
\(715\) −9.27051 −0.346697
\(716\) 20.0344 0.748722
\(717\) 28.8885 1.07886
\(718\) −10.0557 −0.375276
\(719\) −13.8328 −0.515877 −0.257938 0.966161i \(-0.583043\pi\)
−0.257938 + 0.966161i \(0.583043\pi\)
\(720\) −0.381966 −0.0142350
\(721\) −3.90983 −0.145610
\(722\) 0 0
\(723\) 30.8885 1.14876
\(724\) 20.2361 0.752068
\(725\) −15.0557 −0.559156
\(726\) 22.6525 0.840712
\(727\) 48.1246 1.78484 0.892422 0.451203i \(-0.149005\pi\)
0.892422 + 0.451203i \(0.149005\pi\)
\(728\) 1.85410 0.0687176
\(729\) 29.5066 1.09284
\(730\) −5.56231 −0.205870
\(731\) −0.0212862 −0.000787300 0
\(732\) 2.38197 0.0880400
\(733\) 43.6525 1.61234 0.806170 0.591683i \(-0.201536\pi\)
0.806170 + 0.591683i \(0.201536\pi\)
\(734\) −25.3262 −0.934808
\(735\) −1.61803 −0.0596821
\(736\) 8.23607 0.303585
\(737\) 5.72949 0.211048
\(738\) −3.85410 −0.141871
\(739\) −15.4164 −0.567102 −0.283551 0.958957i \(-0.591512\pi\)
−0.283551 + 0.958957i \(0.591512\pi\)
\(740\) 11.9443 0.439080
\(741\) 0 0
\(742\) −0.708204 −0.0259990
\(743\) 12.4934 0.458339 0.229170 0.973387i \(-0.426399\pi\)
0.229170 + 0.973387i \(0.426399\pi\)
\(744\) −10.8541 −0.397931
\(745\) 3.61803 0.132555
\(746\) −0.145898 −0.00534171
\(747\) −4.36068 −0.159549
\(748\) −0.729490 −0.0266728
\(749\) 3.94427 0.144121
\(750\) −14.5623 −0.531740
\(751\) 10.1803 0.371486 0.185743 0.982598i \(-0.440531\pi\)
0.185743 + 0.982598i \(0.440531\pi\)
\(752\) −9.94427 −0.362630
\(753\) 4.00000 0.145768
\(754\) −6.97871 −0.254150
\(755\) 9.76393 0.355346
\(756\) −5.47214 −0.199020
\(757\) 29.8885 1.08632 0.543159 0.839630i \(-0.317228\pi\)
0.543159 + 0.839630i \(0.317228\pi\)
\(758\) −17.0344 −0.618719
\(759\) −66.6312 −2.41856
\(760\) 0 0
\(761\) −39.8328 −1.44394 −0.721969 0.691925i \(-0.756763\pi\)
−0.721969 + 0.691925i \(0.756763\pi\)
\(762\) −13.4721 −0.488044
\(763\) 6.56231 0.237571
\(764\) 25.1803 0.910993
\(765\) −0.0557281 −0.00201485
\(766\) −11.9443 −0.431564
\(767\) −20.3951 −0.736425
\(768\) −1.61803 −0.0583858
\(769\) 12.5836 0.453776 0.226888 0.973921i \(-0.427145\pi\)
0.226888 + 0.973921i \(0.427145\pi\)
\(770\) −5.00000 −0.180187
\(771\) 41.9787 1.51183
\(772\) −12.1803 −0.438380
\(773\) −20.5623 −0.739575 −0.369787 0.929116i \(-0.620569\pi\)
−0.369787 + 0.929116i \(0.620569\pi\)
\(774\) −0.0557281 −0.00200310
\(775\) 26.8328 0.963863
\(776\) −0.527864 −0.0189492
\(777\) 19.3262 0.693325
\(778\) −13.6180 −0.488230
\(779\) 0 0
\(780\) −3.00000 −0.107417
\(781\) −50.0000 −1.78914
\(782\) 1.20163 0.0429701
\(783\) 20.5967 0.736068
\(784\) 1.00000 0.0357143
\(785\) 6.67376 0.238197
\(786\) −10.7082 −0.381949
\(787\) 34.3262 1.22360 0.611799 0.791013i \(-0.290446\pi\)
0.611799 + 0.791013i \(0.290446\pi\)
\(788\) 12.5623 0.447514
\(789\) 4.56231 0.162422
\(790\) −2.14590 −0.0763476
\(791\) −2.85410 −0.101480
\(792\) −1.90983 −0.0678629
\(793\) −2.72949 −0.0969270
\(794\) −1.27051 −0.0450887
\(795\) 1.14590 0.0406408
\(796\) −16.0902 −0.570301
\(797\) 11.7984 0.417920 0.208960 0.977924i \(-0.432992\pi\)
0.208960 + 0.977924i \(0.432992\pi\)
\(798\) 0 0
\(799\) −1.45085 −0.0513274
\(800\) 4.00000 0.141421
\(801\) −0.708204 −0.0250232
\(802\) −33.4164 −1.17997
\(803\) −27.8115 −0.981448
\(804\) 1.85410 0.0653891
\(805\) 8.23607 0.290283
\(806\) 12.4377 0.438099
\(807\) −21.3262 −0.750719
\(808\) −10.8541 −0.381846
\(809\) −32.8541 −1.15509 −0.577544 0.816359i \(-0.695989\pi\)
−0.577544 + 0.816359i \(0.695989\pi\)
\(810\) 7.70820 0.270839
\(811\) −26.5410 −0.931981 −0.465991 0.884790i \(-0.654302\pi\)
−0.465991 + 0.884790i \(0.654302\pi\)
\(812\) −3.76393 −0.132088
\(813\) 47.9787 1.68269
\(814\) 59.7214 2.09323
\(815\) −8.47214 −0.296766
\(816\) −0.236068 −0.00826403
\(817\) 0 0
\(818\) −34.2148 −1.19629
\(819\) 0.708204 0.0247466
\(820\) −10.0902 −0.352364
\(821\) 14.2361 0.496842 0.248421 0.968652i \(-0.420088\pi\)
0.248421 + 0.968652i \(0.420088\pi\)
\(822\) −30.9443 −1.07931
\(823\) −38.2361 −1.33283 −0.666413 0.745583i \(-0.732171\pi\)
−0.666413 + 0.745583i \(0.732171\pi\)
\(824\) −3.90983 −0.136205
\(825\) −32.3607 −1.12665
\(826\) −11.0000 −0.382739
\(827\) −15.6180 −0.543092 −0.271546 0.962425i \(-0.587535\pi\)
−0.271546 + 0.962425i \(0.587535\pi\)
\(828\) 3.14590 0.109328
\(829\) 28.8885 1.00334 0.501670 0.865059i \(-0.332719\pi\)
0.501670 + 0.865059i \(0.332719\pi\)
\(830\) −11.4164 −0.396269
\(831\) 12.9443 0.449032
\(832\) 1.85410 0.0642794
\(833\) 0.145898 0.00505507
\(834\) 6.85410 0.237338
\(835\) −24.1803 −0.836795
\(836\) 0 0
\(837\) −36.7082 −1.26882
\(838\) −16.7426 −0.578365
\(839\) −18.8197 −0.649727 −0.324863 0.945761i \(-0.605318\pi\)
−0.324863 + 0.945761i \(0.605318\pi\)
\(840\) −1.61803 −0.0558275
\(841\) −14.8328 −0.511476
\(842\) −25.9443 −0.894099
\(843\) −12.5623 −0.432669
\(844\) 21.9443 0.755353
\(845\) −9.56231 −0.328953
\(846\) −3.79837 −0.130591
\(847\) −14.0000 −0.481046
\(848\) −0.708204 −0.0243198
\(849\) −42.9787 −1.47503
\(850\) 0.583592 0.0200170
\(851\) −98.3738 −3.37221
\(852\) −16.1803 −0.554329
\(853\) −54.9574 −1.88171 −0.940853 0.338814i \(-0.889974\pi\)
−0.940853 + 0.338814i \(0.889974\pi\)
\(854\) −1.47214 −0.0503755
\(855\) 0 0
\(856\) 3.94427 0.134812
\(857\) 24.7426 0.845193 0.422596 0.906318i \(-0.361119\pi\)
0.422596 + 0.906318i \(0.361119\pi\)
\(858\) −15.0000 −0.512092
\(859\) 53.0689 1.81069 0.905343 0.424680i \(-0.139613\pi\)
0.905343 + 0.424680i \(0.139613\pi\)
\(860\) −0.145898 −0.00497508
\(861\) −16.3262 −0.556397
\(862\) −14.9443 −0.509004
\(863\) 20.7082 0.704915 0.352458 0.935828i \(-0.385346\pi\)
0.352458 + 0.935828i \(0.385346\pi\)
\(864\) −5.47214 −0.186166
\(865\) −6.23607 −0.212033
\(866\) −25.3820 −0.862514
\(867\) 27.4721 0.933003
\(868\) 6.70820 0.227691
\(869\) −10.7295 −0.363973
\(870\) 6.09017 0.206476
\(871\) −2.12461 −0.0719897
\(872\) 6.56231 0.222228
\(873\) −0.201626 −0.00682401
\(874\) 0 0
\(875\) 9.00000 0.304256
\(876\) −9.00000 −0.304082
\(877\) 10.3262 0.348692 0.174346 0.984684i \(-0.444219\pi\)
0.174346 + 0.984684i \(0.444219\pi\)
\(878\) −39.9443 −1.34805
\(879\) 19.0344 0.642016
\(880\) −5.00000 −0.168550
\(881\) 20.8541 0.702593 0.351296 0.936264i \(-0.385741\pi\)
0.351296 + 0.936264i \(0.385741\pi\)
\(882\) 0.381966 0.0128615
\(883\) −57.9787 −1.95114 −0.975570 0.219691i \(-0.929495\pi\)
−0.975570 + 0.219691i \(0.929495\pi\)
\(884\) 0.270510 0.00909823
\(885\) 17.7984 0.598286
\(886\) 34.2148 1.14947
\(887\) 32.8328 1.10242 0.551209 0.834367i \(-0.314167\pi\)
0.551209 + 0.834367i \(0.314167\pi\)
\(888\) 19.3262 0.648546
\(889\) 8.32624 0.279253
\(890\) −1.85410 −0.0621496
\(891\) 38.5410 1.29117
\(892\) 25.6525 0.858908
\(893\) 0 0
\(894\) 5.85410 0.195790
\(895\) 20.0344 0.669678
\(896\) 1.00000 0.0334077
\(897\) 24.7082 0.824983
\(898\) 0.180340 0.00601802
\(899\) −25.2492 −0.842109
\(900\) 1.52786 0.0509288
\(901\) −0.103326 −0.00344227
\(902\) −50.4508 −1.67983
\(903\) −0.236068 −0.00785585
\(904\) −2.85410 −0.0949260
\(905\) 20.2361 0.672670
\(906\) 15.7984 0.524866
\(907\) −32.3262 −1.07338 −0.536688 0.843781i \(-0.680325\pi\)
−0.536688 + 0.843781i \(0.680325\pi\)
\(908\) 9.76393 0.324027
\(909\) −4.14590 −0.137511
\(910\) 1.85410 0.0614629
\(911\) 23.1591 0.767294 0.383647 0.923480i \(-0.374668\pi\)
0.383647 + 0.923480i \(0.374668\pi\)
\(912\) 0 0
\(913\) −57.0820 −1.88914
\(914\) 5.88854 0.194776
\(915\) 2.38197 0.0787454
\(916\) 1.09017 0.0360202
\(917\) 6.61803 0.218547
\(918\) −0.798374 −0.0263503
\(919\) −19.0344 −0.627888 −0.313944 0.949441i \(-0.601650\pi\)
−0.313944 + 0.949441i \(0.601650\pi\)
\(920\) 8.23607 0.271535
\(921\) −20.9443 −0.690137
\(922\) 24.5410 0.808215
\(923\) 18.5410 0.610285
\(924\) −8.09017 −0.266147
\(925\) −47.7771 −1.57090
\(926\) −6.56231 −0.215651
\(927\) −1.49342 −0.0490504
\(928\) −3.76393 −0.123557
\(929\) 8.88854 0.291624 0.145812 0.989312i \(-0.453421\pi\)
0.145812 + 0.989312i \(0.453421\pi\)
\(930\) −10.8541 −0.355920
\(931\) 0 0
\(932\) 18.0344 0.590738
\(933\) −39.2148 −1.28383
\(934\) −24.5279 −0.802576
\(935\) −0.729490 −0.0238569
\(936\) 0.708204 0.0231484
\(937\) −33.3951 −1.09097 −0.545486 0.838120i \(-0.683655\pi\)
−0.545486 + 0.838120i \(0.683655\pi\)
\(938\) −1.14590 −0.0374149
\(939\) −48.6869 −1.58884
\(940\) −9.94427 −0.324346
\(941\) 24.2148 0.789379 0.394690 0.918814i \(-0.370852\pi\)
0.394690 + 0.918814i \(0.370852\pi\)
\(942\) 10.7984 0.351830
\(943\) 83.1033 2.70622
\(944\) −11.0000 −0.358020
\(945\) −5.47214 −0.178009
\(946\) −0.729490 −0.0237178
\(947\) 14.1115 0.458561 0.229280 0.973360i \(-0.426363\pi\)
0.229280 + 0.973360i \(0.426363\pi\)
\(948\) −3.47214 −0.112770
\(949\) 10.3131 0.334777
\(950\) 0 0
\(951\) −29.7984 −0.966278
\(952\) 0.145898 0.00472858
\(953\) −40.7771 −1.32090 −0.660450 0.750870i \(-0.729634\pi\)
−0.660450 + 0.750870i \(0.729634\pi\)
\(954\) −0.270510 −0.00875808
\(955\) 25.1803 0.814817
\(956\) −17.8541 −0.577443
\(957\) 30.4508 0.984336
\(958\) −22.1803 −0.716614
\(959\) 19.1246 0.617566
\(960\) −1.61803 −0.0522218
\(961\) 14.0000 0.451613
\(962\) −22.1459 −0.714012
\(963\) 1.50658 0.0485488
\(964\) −19.0902 −0.614853
\(965\) −12.1803 −0.392099
\(966\) 13.3262 0.428765
\(967\) −21.7295 −0.698773 −0.349387 0.936979i \(-0.613610\pi\)
−0.349387 + 0.936979i \(0.613610\pi\)
\(968\) −14.0000 −0.449977
\(969\) 0 0
\(970\) −0.527864 −0.0169487
\(971\) 7.58359 0.243369 0.121685 0.992569i \(-0.461170\pi\)
0.121685 + 0.992569i \(0.461170\pi\)
\(972\) −3.94427 −0.126513
\(973\) −4.23607 −0.135802
\(974\) −11.1803 −0.358241
\(975\) 12.0000 0.384308
\(976\) −1.47214 −0.0471219
\(977\) −22.7771 −0.728704 −0.364352 0.931261i \(-0.618709\pi\)
−0.364352 + 0.931261i \(0.618709\pi\)
\(978\) −13.7082 −0.438340
\(979\) −9.27051 −0.296287
\(980\) 1.00000 0.0319438
\(981\) 2.50658 0.0800289
\(982\) −29.5967 −0.944470
\(983\) −47.5066 −1.51522 −0.757612 0.652705i \(-0.773634\pi\)
−0.757612 + 0.652705i \(0.773634\pi\)
\(984\) −16.3262 −0.520461
\(985\) 12.5623 0.400268
\(986\) −0.549150 −0.0174885
\(987\) −16.0902 −0.512156
\(988\) 0 0
\(989\) 1.20163 0.0382095
\(990\) −1.90983 −0.0606984
\(991\) −1.41641 −0.0449937 −0.0224968 0.999747i \(-0.507162\pi\)
−0.0224968 + 0.999747i \(0.507162\pi\)
\(992\) 6.70820 0.212986
\(993\) 5.70820 0.181144
\(994\) 10.0000 0.317181
\(995\) −16.0902 −0.510093
\(996\) −18.4721 −0.585312
\(997\) 1.96556 0.0622499 0.0311249 0.999516i \(-0.490091\pi\)
0.0311249 + 0.999516i \(0.490091\pi\)
\(998\) 10.4164 0.329726
\(999\) 65.3607 2.06792
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 5054.2.a.f.1.1 2
19.18 odd 2 5054.2.a.p.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5054.2.a.f.1.1 2 1.1 even 1 trivial
5054.2.a.p.1.2 yes 2 19.18 odd 2