Properties

Label 4598.2.a.bg.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{5} -1.61803 q^{6} +3.85410 q^{7} +1.00000 q^{8} -0.381966 q^{9} -1.61803 q^{10} -1.61803 q^{12} -0.618034 q^{13} +3.85410 q^{14} +2.61803 q^{15} +1.00000 q^{16} -3.23607 q^{17} -0.381966 q^{18} +1.00000 q^{19} -1.61803 q^{20} -6.23607 q^{21} -2.00000 q^{23} -1.61803 q^{24} -2.38197 q^{25} -0.618034 q^{26} +5.47214 q^{27} +3.85410 q^{28} +0.854102 q^{29} +2.61803 q^{30} -2.61803 q^{31} +1.00000 q^{32} -3.23607 q^{34} -6.23607 q^{35} -0.381966 q^{36} +1.23607 q^{37} +1.00000 q^{38} +1.00000 q^{39} -1.61803 q^{40} +0.618034 q^{41} -6.23607 q^{42} -12.0902 q^{43} +0.618034 q^{45} -2.00000 q^{46} -0.763932 q^{47} -1.61803 q^{48} +7.85410 q^{49} -2.38197 q^{50} +5.23607 q^{51} -0.618034 q^{52} -10.4721 q^{53} +5.47214 q^{54} +3.85410 q^{56} -1.61803 q^{57} +0.854102 q^{58} +12.9443 q^{59} +2.61803 q^{60} -5.70820 q^{61} -2.61803 q^{62} -1.47214 q^{63} +1.00000 q^{64} +1.00000 q^{65} +5.09017 q^{67} -3.23607 q^{68} +3.23607 q^{69} -6.23607 q^{70} +12.8541 q^{71} -0.381966 q^{72} -10.4721 q^{73} +1.23607 q^{74} +3.85410 q^{75} +1.00000 q^{76} +1.00000 q^{78} +4.47214 q^{79} -1.61803 q^{80} -7.70820 q^{81} +0.618034 q^{82} +2.38197 q^{83} -6.23607 q^{84} +5.23607 q^{85} -12.0902 q^{86} -1.38197 q^{87} +6.94427 q^{89} +0.618034 q^{90} -2.38197 q^{91} -2.00000 q^{92} +4.23607 q^{93} -0.763932 q^{94} -1.61803 q^{95} -1.61803 q^{96} -18.4721 q^{97} +7.85410 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + q^{7} + 2 q^{8} - 3 q^{9} - q^{10} - q^{12} + q^{13} + q^{14} + 3 q^{15} + 2 q^{16} - 2 q^{17} - 3 q^{18} + 2 q^{19} - q^{20} - 8 q^{21} - 4 q^{23} - q^{24} - 7 q^{25} + q^{26} + 2 q^{27} + q^{28} - 5 q^{29} + 3 q^{30} - 3 q^{31} + 2 q^{32} - 2 q^{34} - 8 q^{35} - 3 q^{36} - 2 q^{37} + 2 q^{38} + 2 q^{39} - q^{40} - q^{41} - 8 q^{42} - 13 q^{43} - q^{45} - 4 q^{46} - 6 q^{47} - q^{48} + 9 q^{49} - 7 q^{50} + 6 q^{51} + q^{52} - 12 q^{53} + 2 q^{54} + q^{56} - q^{57} - 5 q^{58} + 8 q^{59} + 3 q^{60} + 2 q^{61} - 3 q^{62} + 6 q^{63} + 2 q^{64} + 2 q^{65} - q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{70} + 19 q^{71} - 3 q^{72} - 12 q^{73} - 2 q^{74} + q^{75} + 2 q^{76} + 2 q^{78} - q^{80} - 2 q^{81} - q^{82} + 7 q^{83} - 8 q^{84} + 6 q^{85} - 13 q^{86} - 5 q^{87} - 4 q^{89} - q^{90} - 7 q^{91} - 4 q^{92} + 4 q^{93} - 6 q^{94} - q^{95} - q^{96} - 28 q^{97} + 9 q^{98}+O(q^{100}) \) 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
\(5\) −1.61803 −0.723607 −0.361803 0.932254i \(-0.617839\pi\)
−0.361803 + 0.932254i \(0.617839\pi\)
\(6\) −1.61803 −0.660560
\(7\) 3.85410 1.45671 0.728357 0.685198i \(-0.240284\pi\)
0.728357 + 0.685198i \(0.240284\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.381966 −0.127322
\(10\) −1.61803 −0.511667
\(11\) 0 0
\(12\) −1.61803 −0.467086
\(13\) −0.618034 −0.171412 −0.0857059 0.996320i \(-0.527315\pi\)
−0.0857059 + 0.996320i \(0.527315\pi\)
\(14\) 3.85410 1.03005
\(15\) 2.61803 0.675973
\(16\) 1.00000 0.250000
\(17\) −3.23607 −0.784862 −0.392431 0.919781i \(-0.628366\pi\)
−0.392431 + 0.919781i \(0.628366\pi\)
\(18\) −0.381966 −0.0900303
\(19\) 1.00000 0.229416
\(20\) −1.61803 −0.361803
\(21\) −6.23607 −1.36082
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) −1.61803 −0.330280
\(25\) −2.38197 −0.476393
\(26\) −0.618034 −0.121206
\(27\) 5.47214 1.05311
\(28\) 3.85410 0.728357
\(29\) 0.854102 0.158603 0.0793014 0.996851i \(-0.474731\pi\)
0.0793014 + 0.996851i \(0.474731\pi\)
\(30\) 2.61803 0.477985
\(31\) −2.61803 −0.470213 −0.235106 0.971970i \(-0.575544\pi\)
−0.235106 + 0.971970i \(0.575544\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −3.23607 −0.554981
\(35\) −6.23607 −1.05409
\(36\) −0.381966 −0.0636610
\(37\) 1.23607 0.203208 0.101604 0.994825i \(-0.467602\pi\)
0.101604 + 0.994825i \(0.467602\pi\)
\(38\) 1.00000 0.162221
\(39\) 1.00000 0.160128
\(40\) −1.61803 −0.255834
\(41\) 0.618034 0.0965207 0.0482603 0.998835i \(-0.484632\pi\)
0.0482603 + 0.998835i \(0.484632\pi\)
\(42\) −6.23607 −0.962246
\(43\) −12.0902 −1.84373 −0.921867 0.387507i \(-0.873336\pi\)
−0.921867 + 0.387507i \(0.873336\pi\)
\(44\) 0 0
\(45\) 0.618034 0.0921311
\(46\) −2.00000 −0.294884
\(47\) −0.763932 −0.111431 −0.0557155 0.998447i \(-0.517744\pi\)
−0.0557155 + 0.998447i \(0.517744\pi\)
\(48\) −1.61803 −0.233543
\(49\) 7.85410 1.12201
\(50\) −2.38197 −0.336861
\(51\) 5.23607 0.733196
\(52\) −0.618034 −0.0857059
\(53\) −10.4721 −1.43846 −0.719229 0.694773i \(-0.755505\pi\)
−0.719229 + 0.694773i \(0.755505\pi\)
\(54\) 5.47214 0.744663
\(55\) 0 0
\(56\) 3.85410 0.515026
\(57\) −1.61803 −0.214314
\(58\) 0.854102 0.112149
\(59\) 12.9443 1.68520 0.842600 0.538539i \(-0.181024\pi\)
0.842600 + 0.538539i \(0.181024\pi\)
\(60\) 2.61803 0.337987
\(61\) −5.70820 −0.730861 −0.365430 0.930839i \(-0.619078\pi\)
−0.365430 + 0.930839i \(0.619078\pi\)
\(62\) −2.61803 −0.332491
\(63\) −1.47214 −0.185472
\(64\) 1.00000 0.125000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 5.09017 0.621863 0.310932 0.950432i \(-0.399359\pi\)
0.310932 + 0.950432i \(0.399359\pi\)
\(68\) −3.23607 −0.392431
\(69\) 3.23607 0.389577
\(70\) −6.23607 −0.745353
\(71\) 12.8541 1.52550 0.762751 0.646693i \(-0.223848\pi\)
0.762751 + 0.646693i \(0.223848\pi\)
\(72\) −0.381966 −0.0450151
\(73\) −10.4721 −1.22567 −0.612835 0.790211i \(-0.709971\pi\)
−0.612835 + 0.790211i \(0.709971\pi\)
\(74\) 1.23607 0.143690
\(75\) 3.85410 0.445033
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) 4.47214 0.503155 0.251577 0.967837i \(-0.419051\pi\)
0.251577 + 0.967837i \(0.419051\pi\)
\(80\) −1.61803 −0.180902
\(81\) −7.70820 −0.856467
\(82\) 0.618034 0.0682504
\(83\) 2.38197 0.261455 0.130727 0.991418i \(-0.458269\pi\)
0.130727 + 0.991418i \(0.458269\pi\)
\(84\) −6.23607 −0.680411
\(85\) 5.23607 0.567931
\(86\) −12.0902 −1.30372
\(87\) −1.38197 −0.148162
\(88\) 0 0
\(89\) 6.94427 0.736091 0.368046 0.929808i \(-0.380027\pi\)
0.368046 + 0.929808i \(0.380027\pi\)
\(90\) 0.618034 0.0651465
\(91\) −2.38197 −0.249698
\(92\) −2.00000 −0.208514
\(93\) 4.23607 0.439260
\(94\) −0.763932 −0.0787936
\(95\) −1.61803 −0.166007
\(96\) −1.61803 −0.165140
\(97\) −18.4721 −1.87556 −0.937781 0.347228i \(-0.887123\pi\)
−0.937781 + 0.347228i \(0.887123\pi\)
\(98\) 7.85410 0.793384
\(99\) 0 0
\(100\) −2.38197 −0.238197
\(101\) −3.23607 −0.322001 −0.161000 0.986954i \(-0.551472\pi\)
−0.161000 + 0.986954i \(0.551472\pi\)
\(102\) 5.23607 0.518448
\(103\) −7.14590 −0.704106 −0.352053 0.935980i \(-0.614516\pi\)
−0.352053 + 0.935980i \(0.614516\pi\)
\(104\) −0.618034 −0.0606032
\(105\) 10.0902 0.984700
\(106\) −10.4721 −1.01714
\(107\) −6.18034 −0.597476 −0.298738 0.954335i \(-0.596566\pi\)
−0.298738 + 0.954335i \(0.596566\pi\)
\(108\) 5.47214 0.526557
\(109\) −12.4721 −1.19461 −0.597307 0.802013i \(-0.703763\pi\)
−0.597307 + 0.802013i \(0.703763\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 3.85410 0.364178
\(113\) −13.7082 −1.28956 −0.644780 0.764368i \(-0.723051\pi\)
−0.644780 + 0.764368i \(0.723051\pi\)
\(114\) −1.61803 −0.151543
\(115\) 3.23607 0.301765
\(116\) 0.854102 0.0793014
\(117\) 0.236068 0.0218245
\(118\) 12.9443 1.19162
\(119\) −12.4721 −1.14332
\(120\) 2.61803 0.238993
\(121\) 0 0
\(122\) −5.70820 −0.516797
\(123\) −1.00000 −0.0901670
\(124\) −2.61803 −0.235106
\(125\) 11.9443 1.06833
\(126\) −1.47214 −0.131148
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 1.00000 0.0883883
\(129\) 19.5623 1.72236
\(130\) 1.00000 0.0877058
\(131\) −1.67376 −0.146237 −0.0731186 0.997323i \(-0.523295\pi\)
−0.0731186 + 0.997323i \(0.523295\pi\)
\(132\) 0 0
\(133\) 3.85410 0.334193
\(134\) 5.09017 0.439724
\(135\) −8.85410 −0.762040
\(136\) −3.23607 −0.277491
\(137\) −0.326238 −0.0278724 −0.0139362 0.999903i \(-0.504436\pi\)
−0.0139362 + 0.999903i \(0.504436\pi\)
\(138\) 3.23607 0.275472
\(139\) −7.32624 −0.621403 −0.310702 0.950507i \(-0.600564\pi\)
−0.310702 + 0.950507i \(0.600564\pi\)
\(140\) −6.23607 −0.527044
\(141\) 1.23607 0.104096
\(142\) 12.8541 1.07869
\(143\) 0 0
\(144\) −0.381966 −0.0318305
\(145\) −1.38197 −0.114766
\(146\) −10.4721 −0.866680
\(147\) −12.7082 −1.04815
\(148\) 1.23607 0.101604
\(149\) 6.47214 0.530218 0.265109 0.964218i \(-0.414592\pi\)
0.265109 + 0.964218i \(0.414592\pi\)
\(150\) 3.85410 0.314686
\(151\) 6.00000 0.488273 0.244137 0.969741i \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 1.00000 0.0811107
\(153\) 1.23607 0.0999302
\(154\) 0 0
\(155\) 4.23607 0.340249
\(156\) 1.00000 0.0800641
\(157\) −12.8541 −1.02587 −0.512935 0.858428i \(-0.671442\pi\)
−0.512935 + 0.858428i \(0.671442\pi\)
\(158\) 4.47214 0.355784
\(159\) 16.9443 1.34377
\(160\) −1.61803 −0.127917
\(161\) −7.70820 −0.607492
\(162\) −7.70820 −0.605614
\(163\) 2.94427 0.230613 0.115307 0.993330i \(-0.463215\pi\)
0.115307 + 0.993330i \(0.463215\pi\)
\(164\) 0.618034 0.0482603
\(165\) 0 0
\(166\) 2.38197 0.184876
\(167\) 0.944272 0.0730700 0.0365350 0.999332i \(-0.488368\pi\)
0.0365350 + 0.999332i \(0.488368\pi\)
\(168\) −6.23607 −0.481123
\(169\) −12.6180 −0.970618
\(170\) 5.23607 0.401588
\(171\) −0.381966 −0.0292097
\(172\) −12.0902 −0.921867
\(173\) 12.0902 0.919199 0.459599 0.888126i \(-0.347993\pi\)
0.459599 + 0.888126i \(0.347993\pi\)
\(174\) −1.38197 −0.104767
\(175\) −9.18034 −0.693968
\(176\) 0 0
\(177\) −20.9443 −1.57427
\(178\) 6.94427 0.520495
\(179\) 11.2705 0.842397 0.421199 0.906968i \(-0.361609\pi\)
0.421199 + 0.906968i \(0.361609\pi\)
\(180\) 0.618034 0.0460655
\(181\) −19.8885 −1.47830 −0.739152 0.673539i \(-0.764773\pi\)
−0.739152 + 0.673539i \(0.764773\pi\)
\(182\) −2.38197 −0.176563
\(183\) 9.23607 0.682750
\(184\) −2.00000 −0.147442
\(185\) −2.00000 −0.147043
\(186\) 4.23607 0.310604
\(187\) 0 0
\(188\) −0.763932 −0.0557155
\(189\) 21.0902 1.53408
\(190\) −1.61803 −0.117385
\(191\) −10.0000 −0.723575 −0.361787 0.932261i \(-0.617833\pi\)
−0.361787 + 0.932261i \(0.617833\pi\)
\(192\) −1.61803 −0.116772
\(193\) −6.56231 −0.472365 −0.236183 0.971709i \(-0.575896\pi\)
−0.236183 + 0.971709i \(0.575896\pi\)
\(194\) −18.4721 −1.32622
\(195\) −1.61803 −0.115870
\(196\) 7.85410 0.561007
\(197\) 7.41641 0.528397 0.264199 0.964468i \(-0.414893\pi\)
0.264199 + 0.964468i \(0.414893\pi\)
\(198\) 0 0
\(199\) −12.1803 −0.863441 −0.431721 0.902007i \(-0.642093\pi\)
−0.431721 + 0.902007i \(0.642093\pi\)
\(200\) −2.38197 −0.168430
\(201\) −8.23607 −0.580927
\(202\) −3.23607 −0.227689
\(203\) 3.29180 0.231039
\(204\) 5.23607 0.366598
\(205\) −1.00000 −0.0698430
\(206\) −7.14590 −0.497878
\(207\) 0.763932 0.0530969
\(208\) −0.618034 −0.0428529
\(209\) 0 0
\(210\) 10.0902 0.696288
\(211\) −22.6525 −1.55946 −0.779730 0.626115i \(-0.784644\pi\)
−0.779730 + 0.626115i \(0.784644\pi\)
\(212\) −10.4721 −0.719229
\(213\) −20.7984 −1.42508
\(214\) −6.18034 −0.422479
\(215\) 19.5623 1.33414
\(216\) 5.47214 0.372332
\(217\) −10.0902 −0.684965
\(218\) −12.4721 −0.844720
\(219\) 16.9443 1.14499
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) −2.00000 −0.134231
\(223\) −10.4721 −0.701266 −0.350633 0.936513i \(-0.614034\pi\)
−0.350633 + 0.936513i \(0.614034\pi\)
\(224\) 3.85410 0.257513
\(225\) 0.909830 0.0606553
\(226\) −13.7082 −0.911856
\(227\) 10.9443 0.726397 0.363198 0.931712i \(-0.381685\pi\)
0.363198 + 0.931712i \(0.381685\pi\)
\(228\) −1.61803 −0.107157
\(229\) −1.85410 −0.122523 −0.0612613 0.998122i \(-0.519512\pi\)
−0.0612613 + 0.998122i \(0.519512\pi\)
\(230\) 3.23607 0.213380
\(231\) 0 0
\(232\) 0.854102 0.0560745
\(233\) −10.4721 −0.686052 −0.343026 0.939326i \(-0.611452\pi\)
−0.343026 + 0.939326i \(0.611452\pi\)
\(234\) 0.236068 0.0154322
\(235\) 1.23607 0.0806322
\(236\) 12.9443 0.842600
\(237\) −7.23607 −0.470033
\(238\) −12.4721 −0.808448
\(239\) −28.2705 −1.82867 −0.914334 0.404962i \(-0.867285\pi\)
−0.914334 + 0.404962i \(0.867285\pi\)
\(240\) 2.61803 0.168993
\(241\) −10.3820 −0.668761 −0.334381 0.942438i \(-0.608527\pi\)
−0.334381 + 0.942438i \(0.608527\pi\)
\(242\) 0 0
\(243\) −3.94427 −0.253025
\(244\) −5.70820 −0.365430
\(245\) −12.7082 −0.811897
\(246\) −1.00000 −0.0637577
\(247\) −0.618034 −0.0393246
\(248\) −2.61803 −0.166245
\(249\) −3.85410 −0.244244
\(250\) 11.9443 0.755422
\(251\) 8.47214 0.534756 0.267378 0.963592i \(-0.413843\pi\)
0.267378 + 0.963592i \(0.413843\pi\)
\(252\) −1.47214 −0.0927358
\(253\) 0 0
\(254\) −6.00000 −0.376473
\(255\) −8.47214 −0.530546
\(256\) 1.00000 0.0625000
\(257\) −9.88854 −0.616830 −0.308415 0.951252i \(-0.599799\pi\)
−0.308415 + 0.951252i \(0.599799\pi\)
\(258\) 19.5623 1.21790
\(259\) 4.76393 0.296016
\(260\) 1.00000 0.0620174
\(261\) −0.326238 −0.0201936
\(262\) −1.67376 −0.103405
\(263\) −25.7984 −1.59080 −0.795398 0.606088i \(-0.792738\pi\)
−0.795398 + 0.606088i \(0.792738\pi\)
\(264\) 0 0
\(265\) 16.9443 1.04088
\(266\) 3.85410 0.236310
\(267\) −11.2361 −0.687636
\(268\) 5.09017 0.310932
\(269\) −16.3607 −0.997528 −0.498764 0.866738i \(-0.666213\pi\)
−0.498764 + 0.866738i \(0.666213\pi\)
\(270\) −8.85410 −0.538843
\(271\) 16.1459 0.980793 0.490397 0.871499i \(-0.336852\pi\)
0.490397 + 0.871499i \(0.336852\pi\)
\(272\) −3.23607 −0.196215
\(273\) 3.85410 0.233261
\(274\) −0.326238 −0.0197088
\(275\) 0 0
\(276\) 3.23607 0.194788
\(277\) 9.05573 0.544106 0.272053 0.962282i \(-0.412297\pi\)
0.272053 + 0.962282i \(0.412297\pi\)
\(278\) −7.32624 −0.439399
\(279\) 1.00000 0.0598684
\(280\) −6.23607 −0.372676
\(281\) −29.2148 −1.74281 −0.871404 0.490566i \(-0.836790\pi\)
−0.871404 + 0.490566i \(0.836790\pi\)
\(282\) 1.23607 0.0736068
\(283\) 19.2705 1.14551 0.572756 0.819726i \(-0.305874\pi\)
0.572756 + 0.819726i \(0.305874\pi\)
\(284\) 12.8541 0.762751
\(285\) 2.61803 0.155079
\(286\) 0 0
\(287\) 2.38197 0.140603
\(288\) −0.381966 −0.0225076
\(289\) −6.52786 −0.383992
\(290\) −1.38197 −0.0811518
\(291\) 29.8885 1.75210
\(292\) −10.4721 −0.612835
\(293\) 20.0344 1.17042 0.585212 0.810880i \(-0.301011\pi\)
0.585212 + 0.810880i \(0.301011\pi\)
\(294\) −12.7082 −0.741158
\(295\) −20.9443 −1.21942
\(296\) 1.23607 0.0718450
\(297\) 0 0
\(298\) 6.47214 0.374921
\(299\) 1.23607 0.0714837
\(300\) 3.85410 0.222517
\(301\) −46.5967 −2.68579
\(302\) 6.00000 0.345261
\(303\) 5.23607 0.300804
\(304\) 1.00000 0.0573539
\(305\) 9.23607 0.528856
\(306\) 1.23607 0.0706613
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 11.5623 0.657757
\(310\) 4.23607 0.240592
\(311\) 21.1246 1.19787 0.598933 0.800799i \(-0.295591\pi\)
0.598933 + 0.800799i \(0.295591\pi\)
\(312\) 1.00000 0.0566139
\(313\) 11.3262 0.640197 0.320098 0.947384i \(-0.396284\pi\)
0.320098 + 0.947384i \(0.396284\pi\)
\(314\) −12.8541 −0.725399
\(315\) 2.38197 0.134209
\(316\) 4.47214 0.251577
\(317\) 8.00000 0.449325 0.224662 0.974437i \(-0.427872\pi\)
0.224662 + 0.974437i \(0.427872\pi\)
\(318\) 16.9443 0.950188
\(319\) 0 0
\(320\) −1.61803 −0.0904508
\(321\) 10.0000 0.558146
\(322\) −7.70820 −0.429561
\(323\) −3.23607 −0.180060
\(324\) −7.70820 −0.428234
\(325\) 1.47214 0.0816594
\(326\) 2.94427 0.163068
\(327\) 20.1803 1.11598
\(328\) 0.618034 0.0341252
\(329\) −2.94427 −0.162323
\(330\) 0 0
\(331\) −33.9787 −1.86764 −0.933820 0.357744i \(-0.883546\pi\)
−0.933820 + 0.357744i \(0.883546\pi\)
\(332\) 2.38197 0.130727
\(333\) −0.472136 −0.0258729
\(334\) 0.944272 0.0516683
\(335\) −8.23607 −0.449984
\(336\) −6.23607 −0.340205
\(337\) 19.0902 1.03991 0.519954 0.854194i \(-0.325949\pi\)
0.519954 + 0.854194i \(0.325949\pi\)
\(338\) −12.6180 −0.686331
\(339\) 22.1803 1.20467
\(340\) 5.23607 0.283966
\(341\) 0 0
\(342\) −0.381966 −0.0206544
\(343\) 3.29180 0.177740
\(344\) −12.0902 −0.651858
\(345\) −5.23607 −0.281900
\(346\) 12.0902 0.649972
\(347\) 22.4721 1.20637 0.603184 0.797602i \(-0.293899\pi\)
0.603184 + 0.797602i \(0.293899\pi\)
\(348\) −1.38197 −0.0740812
\(349\) 20.6525 1.10550 0.552751 0.833347i \(-0.313578\pi\)
0.552751 + 0.833347i \(0.313578\pi\)
\(350\) −9.18034 −0.490710
\(351\) −3.38197 −0.180516
\(352\) 0 0
\(353\) −15.8885 −0.845662 −0.422831 0.906209i \(-0.638964\pi\)
−0.422831 + 0.906209i \(0.638964\pi\)
\(354\) −20.9443 −1.11318
\(355\) −20.7984 −1.10386
\(356\) 6.94427 0.368046
\(357\) 20.1803 1.06806
\(358\) 11.2705 0.595665
\(359\) 35.2705 1.86151 0.930753 0.365648i \(-0.119153\pi\)
0.930753 + 0.365648i \(0.119153\pi\)
\(360\) 0.618034 0.0325733
\(361\) 1.00000 0.0526316
\(362\) −19.8885 −1.04532
\(363\) 0 0
\(364\) −2.38197 −0.124849
\(365\) 16.9443 0.886904
\(366\) 9.23607 0.482777
\(367\) 23.1246 1.20709 0.603547 0.797327i \(-0.293753\pi\)
0.603547 + 0.797327i \(0.293753\pi\)
\(368\) −2.00000 −0.104257
\(369\) −0.236068 −0.0122892
\(370\) −2.00000 −0.103975
\(371\) −40.3607 −2.09542
\(372\) 4.23607 0.219630
\(373\) −22.7426 −1.17757 −0.588785 0.808290i \(-0.700393\pi\)
−0.588785 + 0.808290i \(0.700393\pi\)
\(374\) 0 0
\(375\) −19.3262 −0.998003
\(376\) −0.763932 −0.0393968
\(377\) −0.527864 −0.0271864
\(378\) 21.0902 1.08476
\(379\) −13.0902 −0.672397 −0.336198 0.941791i \(-0.609141\pi\)
−0.336198 + 0.941791i \(0.609141\pi\)
\(380\) −1.61803 −0.0830034
\(381\) 9.70820 0.497366
\(382\) −10.0000 −0.511645
\(383\) −34.0344 −1.73908 −0.869539 0.493864i \(-0.835584\pi\)
−0.869539 + 0.493864i \(0.835584\pi\)
\(384\) −1.61803 −0.0825700
\(385\) 0 0
\(386\) −6.56231 −0.334013
\(387\) 4.61803 0.234748
\(388\) −18.4721 −0.937781
\(389\) 13.7984 0.699605 0.349803 0.936823i \(-0.386249\pi\)
0.349803 + 0.936823i \(0.386249\pi\)
\(390\) −1.61803 −0.0819323
\(391\) 6.47214 0.327310
\(392\) 7.85410 0.396692
\(393\) 2.70820 0.136611
\(394\) 7.41641 0.373633
\(395\) −7.23607 −0.364086
\(396\) 0 0
\(397\) −12.6180 −0.633281 −0.316640 0.948546i \(-0.602555\pi\)
−0.316640 + 0.948546i \(0.602555\pi\)
\(398\) −12.1803 −0.610545
\(399\) −6.23607 −0.312194
\(400\) −2.38197 −0.119098
\(401\) 17.2361 0.860728 0.430364 0.902655i \(-0.358385\pi\)
0.430364 + 0.902655i \(0.358385\pi\)
\(402\) −8.23607 −0.410778
\(403\) 1.61803 0.0806000
\(404\) −3.23607 −0.161000
\(405\) 12.4721 0.619745
\(406\) 3.29180 0.163369
\(407\) 0 0
\(408\) 5.23607 0.259224
\(409\) −0.270510 −0.0133759 −0.00668793 0.999978i \(-0.502129\pi\)
−0.00668793 + 0.999978i \(0.502129\pi\)
\(410\) −1.00000 −0.0493865
\(411\) 0.527864 0.0260376
\(412\) −7.14590 −0.352053
\(413\) 49.8885 2.45485
\(414\) 0.763932 0.0375452
\(415\) −3.85410 −0.189190
\(416\) −0.618034 −0.0303016
\(417\) 11.8541 0.580498
\(418\) 0 0
\(419\) −16.2918 −0.795906 −0.397953 0.917406i \(-0.630279\pi\)
−0.397953 + 0.917406i \(0.630279\pi\)
\(420\) 10.0902 0.492350
\(421\) −8.18034 −0.398685 −0.199343 0.979930i \(-0.563881\pi\)
−0.199343 + 0.979930i \(0.563881\pi\)
\(422\) −22.6525 −1.10271
\(423\) 0.291796 0.0141876
\(424\) −10.4721 −0.508572
\(425\) 7.70820 0.373903
\(426\) −20.7984 −1.00768
\(427\) −22.0000 −1.06465
\(428\) −6.18034 −0.298738
\(429\) 0 0
\(430\) 19.5623 0.943378
\(431\) −37.4164 −1.80228 −0.901142 0.433523i \(-0.857270\pi\)
−0.901142 + 0.433523i \(0.857270\pi\)
\(432\) 5.47214 0.263278
\(433\) 6.18034 0.297008 0.148504 0.988912i \(-0.452554\pi\)
0.148504 + 0.988912i \(0.452554\pi\)
\(434\) −10.0902 −0.484344
\(435\) 2.23607 0.107211
\(436\) −12.4721 −0.597307
\(437\) −2.00000 −0.0956730
\(438\) 16.9443 0.809629
\(439\) −20.0000 −0.954548 −0.477274 0.878755i \(-0.658375\pi\)
−0.477274 + 0.878755i \(0.658375\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 2.00000 0.0951303
\(443\) 17.7082 0.841342 0.420671 0.907213i \(-0.361795\pi\)
0.420671 + 0.907213i \(0.361795\pi\)
\(444\) −2.00000 −0.0949158
\(445\) −11.2361 −0.532641
\(446\) −10.4721 −0.495870
\(447\) −10.4721 −0.495315
\(448\) 3.85410 0.182089
\(449\) 16.1803 0.763597 0.381799 0.924245i \(-0.375305\pi\)
0.381799 + 0.924245i \(0.375305\pi\)
\(450\) 0.909830 0.0428898
\(451\) 0 0
\(452\) −13.7082 −0.644780
\(453\) −9.70820 −0.456131
\(454\) 10.9443 0.513640
\(455\) 3.85410 0.180683
\(456\) −1.61803 −0.0757714
\(457\) 37.2361 1.74183 0.870915 0.491434i \(-0.163527\pi\)
0.870915 + 0.491434i \(0.163527\pi\)
\(458\) −1.85410 −0.0866365
\(459\) −17.7082 −0.826548
\(460\) 3.23607 0.150882
\(461\) 13.4164 0.624864 0.312432 0.949940i \(-0.398856\pi\)
0.312432 + 0.949940i \(0.398856\pi\)
\(462\) 0 0
\(463\) −37.0132 −1.72015 −0.860074 0.510170i \(-0.829582\pi\)
−0.860074 + 0.510170i \(0.829582\pi\)
\(464\) 0.854102 0.0396507
\(465\) −6.85410 −0.317851
\(466\) −10.4721 −0.485112
\(467\) 26.8328 1.24167 0.620837 0.783939i \(-0.286793\pi\)
0.620837 + 0.783939i \(0.286793\pi\)
\(468\) 0.236068 0.0109122
\(469\) 19.6180 0.905877
\(470\) 1.23607 0.0570156
\(471\) 20.7984 0.958338
\(472\) 12.9443 0.595808
\(473\) 0 0
\(474\) −7.23607 −0.332364
\(475\) −2.38197 −0.109292
\(476\) −12.4721 −0.571659
\(477\) 4.00000 0.183147
\(478\) −28.2705 −1.29306
\(479\) 0.437694 0.0199988 0.00999938 0.999950i \(-0.496817\pi\)
0.00999938 + 0.999950i \(0.496817\pi\)
\(480\) 2.61803 0.119496
\(481\) −0.763932 −0.0348323
\(482\) −10.3820 −0.472886
\(483\) 12.4721 0.567502
\(484\) 0 0
\(485\) 29.8885 1.35717
\(486\) −3.94427 −0.178916
\(487\) −23.5066 −1.06518 −0.532592 0.846372i \(-0.678782\pi\)
−0.532592 + 0.846372i \(0.678782\pi\)
\(488\) −5.70820 −0.258398
\(489\) −4.76393 −0.215432
\(490\) −12.7082 −0.574098
\(491\) −21.4508 −0.968063 −0.484032 0.875050i \(-0.660828\pi\)
−0.484032 + 0.875050i \(0.660828\pi\)
\(492\) −1.00000 −0.0450835
\(493\) −2.76393 −0.124481
\(494\) −0.618034 −0.0278067
\(495\) 0 0
\(496\) −2.61803 −0.117553
\(497\) 49.5410 2.22222
\(498\) −3.85410 −0.172706
\(499\) −25.1246 −1.12473 −0.562366 0.826888i \(-0.690109\pi\)
−0.562366 + 0.826888i \(0.690109\pi\)
\(500\) 11.9443 0.534164
\(501\) −1.52786 −0.0682599
\(502\) 8.47214 0.378130
\(503\) −15.3262 −0.683363 −0.341682 0.939816i \(-0.610996\pi\)
−0.341682 + 0.939816i \(0.610996\pi\)
\(504\) −1.47214 −0.0655741
\(505\) 5.23607 0.233002
\(506\) 0 0
\(507\) 20.4164 0.906725
\(508\) −6.00000 −0.266207
\(509\) 17.7082 0.784902 0.392451 0.919773i \(-0.371627\pi\)
0.392451 + 0.919773i \(0.371627\pi\)
\(510\) −8.47214 −0.375152
\(511\) −40.3607 −1.78545
\(512\) 1.00000 0.0441942
\(513\) 5.47214 0.241601
\(514\) −9.88854 −0.436165
\(515\) 11.5623 0.509496
\(516\) 19.5623 0.861182
\(517\) 0 0
\(518\) 4.76393 0.209315
\(519\) −19.5623 −0.858690
\(520\) 1.00000 0.0438529
\(521\) 31.1246 1.36359 0.681797 0.731541i \(-0.261199\pi\)
0.681797 + 0.731541i \(0.261199\pi\)
\(522\) −0.326238 −0.0142790
\(523\) 21.8885 0.957119 0.478560 0.878055i \(-0.341159\pi\)
0.478560 + 0.878055i \(0.341159\pi\)
\(524\) −1.67376 −0.0731186
\(525\) 14.8541 0.648286
\(526\) −25.7984 −1.12486
\(527\) 8.47214 0.369052
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 16.9443 0.736012
\(531\) −4.94427 −0.214563
\(532\) 3.85410 0.167097
\(533\) −0.381966 −0.0165448
\(534\) −11.2361 −0.486232
\(535\) 10.0000 0.432338
\(536\) 5.09017 0.219862
\(537\) −18.2361 −0.786944
\(538\) −16.3607 −0.705359
\(539\) 0 0
\(540\) −8.85410 −0.381020
\(541\) 20.6525 0.887919 0.443960 0.896047i \(-0.353573\pi\)
0.443960 + 0.896047i \(0.353573\pi\)
\(542\) 16.1459 0.693526
\(543\) 32.1803 1.38099
\(544\) −3.23607 −0.138745
\(545\) 20.1803 0.864431
\(546\) 3.85410 0.164940
\(547\) 22.6525 0.968550 0.484275 0.874916i \(-0.339083\pi\)
0.484275 + 0.874916i \(0.339083\pi\)
\(548\) −0.326238 −0.0139362
\(549\) 2.18034 0.0930546
\(550\) 0 0
\(551\) 0.854102 0.0363860
\(552\) 3.23607 0.137736
\(553\) 17.2361 0.732952
\(554\) 9.05573 0.384741
\(555\) 3.23607 0.137363
\(556\) −7.32624 −0.310702
\(557\) −30.3607 −1.28642 −0.643212 0.765688i \(-0.722398\pi\)
−0.643212 + 0.765688i \(0.722398\pi\)
\(558\) 1.00000 0.0423334
\(559\) 7.47214 0.316038
\(560\) −6.23607 −0.263522
\(561\) 0 0
\(562\) −29.2148 −1.23235
\(563\) −1.34752 −0.0567914 −0.0283957 0.999597i \(-0.509040\pi\)
−0.0283957 + 0.999597i \(0.509040\pi\)
\(564\) 1.23607 0.0520479
\(565\) 22.1803 0.933134
\(566\) 19.2705 0.810000
\(567\) −29.7082 −1.24763
\(568\) 12.8541 0.539346
\(569\) 15.4508 0.647733 0.323867 0.946103i \(-0.395017\pi\)
0.323867 + 0.946103i \(0.395017\pi\)
\(570\) 2.61803 0.109657
\(571\) 36.2148 1.51554 0.757771 0.652521i \(-0.226289\pi\)
0.757771 + 0.652521i \(0.226289\pi\)
\(572\) 0 0
\(573\) 16.1803 0.675943
\(574\) 2.38197 0.0994213
\(575\) 4.76393 0.198670
\(576\) −0.381966 −0.0159153
\(577\) 23.1591 0.964124 0.482062 0.876137i \(-0.339888\pi\)
0.482062 + 0.876137i \(0.339888\pi\)
\(578\) −6.52786 −0.271523
\(579\) 10.6180 0.441270
\(580\) −1.38197 −0.0573830
\(581\) 9.18034 0.380865
\(582\) 29.8885 1.23892
\(583\) 0 0
\(584\) −10.4721 −0.433340
\(585\) −0.381966 −0.0157924
\(586\) 20.0344 0.827615
\(587\) −3.23607 −0.133567 −0.0667834 0.997767i \(-0.521274\pi\)
−0.0667834 + 0.997767i \(0.521274\pi\)
\(588\) −12.7082 −0.524077
\(589\) −2.61803 −0.107874
\(590\) −20.9443 −0.862262
\(591\) −12.0000 −0.493614
\(592\) 1.23607 0.0508021
\(593\) 35.7082 1.46636 0.733180 0.680035i \(-0.238035\pi\)
0.733180 + 0.680035i \(0.238035\pi\)
\(594\) 0 0
\(595\) 20.1803 0.827313
\(596\) 6.47214 0.265109
\(597\) 19.7082 0.806603
\(598\) 1.23607 0.0505466
\(599\) −25.2148 −1.03025 −0.515124 0.857116i \(-0.672254\pi\)
−0.515124 + 0.857116i \(0.672254\pi\)
\(600\) 3.85410 0.157343
\(601\) −27.4508 −1.11974 −0.559872 0.828579i \(-0.689150\pi\)
−0.559872 + 0.828579i \(0.689150\pi\)
\(602\) −46.5967 −1.89914
\(603\) −1.94427 −0.0791769
\(604\) 6.00000 0.244137
\(605\) 0 0
\(606\) 5.23607 0.212701
\(607\) 37.1246 1.50684 0.753421 0.657539i \(-0.228402\pi\)
0.753421 + 0.657539i \(0.228402\pi\)
\(608\) 1.00000 0.0405554
\(609\) −5.32624 −0.215830
\(610\) 9.23607 0.373957
\(611\) 0.472136 0.0191006
\(612\) 1.23607 0.0499651
\(613\) 42.9443 1.73450 0.867251 0.497870i \(-0.165885\pi\)
0.867251 + 0.497870i \(0.165885\pi\)
\(614\) 2.00000 0.0807134
\(615\) 1.61803 0.0652454
\(616\) 0 0
\(617\) 12.6180 0.507983 0.253991 0.967206i \(-0.418256\pi\)
0.253991 + 0.967206i \(0.418256\pi\)
\(618\) 11.5623 0.465104
\(619\) 49.0132 1.97001 0.985003 0.172540i \(-0.0551974\pi\)
0.985003 + 0.172540i \(0.0551974\pi\)
\(620\) 4.23607 0.170125
\(621\) −10.9443 −0.439179
\(622\) 21.1246 0.847020
\(623\) 26.7639 1.07227
\(624\) 1.00000 0.0400320
\(625\) −7.41641 −0.296656
\(626\) 11.3262 0.452688
\(627\) 0 0
\(628\) −12.8541 −0.512935
\(629\) −4.00000 −0.159490
\(630\) 2.38197 0.0948998
\(631\) 19.5967 0.780134 0.390067 0.920786i \(-0.372452\pi\)
0.390067 + 0.920786i \(0.372452\pi\)
\(632\) 4.47214 0.177892
\(633\) 36.6525 1.45681
\(634\) 8.00000 0.317721
\(635\) 9.70820 0.385258
\(636\) 16.9443 0.671884
\(637\) −4.85410 −0.192327
\(638\) 0 0
\(639\) −4.90983 −0.194230
\(640\) −1.61803 −0.0639584
\(641\) −18.9443 −0.748254 −0.374127 0.927378i \(-0.622058\pi\)
−0.374127 + 0.927378i \(0.622058\pi\)
\(642\) 10.0000 0.394669
\(643\) −30.0000 −1.18308 −0.591542 0.806274i \(-0.701481\pi\)
−0.591542 + 0.806274i \(0.701481\pi\)
\(644\) −7.70820 −0.303746
\(645\) −31.6525 −1.24632
\(646\) −3.23607 −0.127321
\(647\) −26.8328 −1.05491 −0.527453 0.849584i \(-0.676853\pi\)
−0.527453 + 0.849584i \(0.676853\pi\)
\(648\) −7.70820 −0.302807
\(649\) 0 0
\(650\) 1.47214 0.0577419
\(651\) 16.3262 0.639876
\(652\) 2.94427 0.115307
\(653\) 24.0344 0.940540 0.470270 0.882522i \(-0.344156\pi\)
0.470270 + 0.882522i \(0.344156\pi\)
\(654\) 20.1803 0.789114
\(655\) 2.70820 0.105818
\(656\) 0.618034 0.0241302
\(657\) 4.00000 0.156055
\(658\) −2.94427 −0.114780
\(659\) 1.88854 0.0735672 0.0367836 0.999323i \(-0.488289\pi\)
0.0367836 + 0.999323i \(0.488289\pi\)
\(660\) 0 0
\(661\) 41.2361 1.60390 0.801949 0.597393i \(-0.203797\pi\)
0.801949 + 0.597393i \(0.203797\pi\)
\(662\) −33.9787 −1.32062
\(663\) −3.23607 −0.125678
\(664\) 2.38197 0.0924382
\(665\) −6.23607 −0.241824
\(666\) −0.472136 −0.0182949
\(667\) −1.70820 −0.0661419
\(668\) 0.944272 0.0365350
\(669\) 16.9443 0.655103
\(670\) −8.23607 −0.318187
\(671\) 0 0
\(672\) −6.23607 −0.240562
\(673\) 9.27051 0.357352 0.178676 0.983908i \(-0.442819\pi\)
0.178676 + 0.983908i \(0.442819\pi\)
\(674\) 19.0902 0.735326
\(675\) −13.0344 −0.501696
\(676\) −12.6180 −0.485309
\(677\) −24.4508 −0.939722 −0.469861 0.882740i \(-0.655696\pi\)
−0.469861 + 0.882740i \(0.655696\pi\)
\(678\) 22.1803 0.851831
\(679\) −71.1935 −2.73216
\(680\) 5.23607 0.200794
\(681\) −17.7082 −0.678580
\(682\) 0 0
\(683\) 37.3050 1.42743 0.713717 0.700434i \(-0.247010\pi\)
0.713717 + 0.700434i \(0.247010\pi\)
\(684\) −0.381966 −0.0146048
\(685\) 0.527864 0.0201686
\(686\) 3.29180 0.125681
\(687\) 3.00000 0.114457
\(688\) −12.0902 −0.460933
\(689\) 6.47214 0.246569
\(690\) −5.23607 −0.199334
\(691\) 25.7082 0.977986 0.488993 0.872288i \(-0.337364\pi\)
0.488993 + 0.872288i \(0.337364\pi\)
\(692\) 12.0902 0.459599
\(693\) 0 0
\(694\) 22.4721 0.853031
\(695\) 11.8541 0.449652
\(696\) −1.38197 −0.0523833
\(697\) −2.00000 −0.0757554
\(698\) 20.6525 0.781708
\(699\) 16.9443 0.640891
\(700\) −9.18034 −0.346984
\(701\) 23.1246 0.873405 0.436702 0.899606i \(-0.356146\pi\)
0.436702 + 0.899606i \(0.356146\pi\)
\(702\) −3.38197 −0.127644
\(703\) 1.23607 0.0466192
\(704\) 0 0
\(705\) −2.00000 −0.0753244
\(706\) −15.8885 −0.597973
\(707\) −12.4721 −0.469063
\(708\) −20.9443 −0.787134
\(709\) −3.02129 −0.113467 −0.0567334 0.998389i \(-0.518069\pi\)
−0.0567334 + 0.998389i \(0.518069\pi\)
\(710\) −20.7984 −0.780549
\(711\) −1.70820 −0.0640627
\(712\) 6.94427 0.260248
\(713\) 5.23607 0.196092
\(714\) 20.1803 0.755230
\(715\) 0 0
\(716\) 11.2705 0.421199
\(717\) 45.7426 1.70829
\(718\) 35.2705 1.31628
\(719\) 20.2918 0.756756 0.378378 0.925651i \(-0.376482\pi\)
0.378378 + 0.925651i \(0.376482\pi\)
\(720\) 0.618034 0.0230328
\(721\) −27.5410 −1.02568
\(722\) 1.00000 0.0372161
\(723\) 16.7984 0.624738
\(724\) −19.8885 −0.739152
\(725\) −2.03444 −0.0755573
\(726\) 0 0
\(727\) 45.8885 1.70191 0.850956 0.525237i \(-0.176023\pi\)
0.850956 + 0.525237i \(0.176023\pi\)
\(728\) −2.38197 −0.0882815
\(729\) 29.5066 1.09284
\(730\) 16.9443 0.627136
\(731\) 39.1246 1.44708
\(732\) 9.23607 0.341375
\(733\) 4.36068 0.161065 0.0805327 0.996752i \(-0.474338\pi\)
0.0805327 + 0.996752i \(0.474338\pi\)
\(734\) 23.1246 0.853545
\(735\) 20.5623 0.758452
\(736\) −2.00000 −0.0737210
\(737\) 0 0
\(738\) −0.236068 −0.00868978
\(739\) 8.09017 0.297602 0.148801 0.988867i \(-0.452459\pi\)
0.148801 + 0.988867i \(0.452459\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 1.00000 0.0367359
\(742\) −40.3607 −1.48169
\(743\) 18.3607 0.673588 0.336794 0.941578i \(-0.390657\pi\)
0.336794 + 0.941578i \(0.390657\pi\)
\(744\) 4.23607 0.155302
\(745\) −10.4721 −0.383669
\(746\) −22.7426 −0.832667
\(747\) −0.909830 −0.0332889
\(748\) 0 0
\(749\) −23.8197 −0.870351
\(750\) −19.3262 −0.705694
\(751\) 11.0557 0.403429 0.201715 0.979444i \(-0.435349\pi\)
0.201715 + 0.979444i \(0.435349\pi\)
\(752\) −0.763932 −0.0278577
\(753\) −13.7082 −0.499555
\(754\) −0.527864 −0.0192237
\(755\) −9.70820 −0.353318
\(756\) 21.0902 0.767042
\(757\) −41.3951 −1.50453 −0.752266 0.658860i \(-0.771039\pi\)
−0.752266 + 0.658860i \(0.771039\pi\)
\(758\) −13.0902 −0.475456
\(759\) 0 0
\(760\) −1.61803 −0.0586923
\(761\) 31.0557 1.12577 0.562885 0.826535i \(-0.309692\pi\)
0.562885 + 0.826535i \(0.309692\pi\)
\(762\) 9.70820 0.351691
\(763\) −48.0689 −1.74021
\(764\) −10.0000 −0.361787
\(765\) −2.00000 −0.0723102
\(766\) −34.0344 −1.22971
\(767\) −8.00000 −0.288863
\(768\) −1.61803 −0.0583858
\(769\) 28.1803 1.01621 0.508105 0.861295i \(-0.330346\pi\)
0.508105 + 0.861295i \(0.330346\pi\)
\(770\) 0 0
\(771\) 16.0000 0.576226
\(772\) −6.56231 −0.236183
\(773\) 3.70820 0.133375 0.0666874 0.997774i \(-0.478757\pi\)
0.0666874 + 0.997774i \(0.478757\pi\)
\(774\) 4.61803 0.165992
\(775\) 6.23607 0.224006
\(776\) −18.4721 −0.663111
\(777\) −7.70820 −0.276530
\(778\) 13.7984 0.494696
\(779\) 0.618034 0.0221434
\(780\) −1.61803 −0.0579349
\(781\) 0 0
\(782\) 6.47214 0.231443
\(783\) 4.67376 0.167027
\(784\) 7.85410 0.280504
\(785\) 20.7984 0.742326
\(786\) 2.70820 0.0965984
\(787\) −45.2361 −1.61249 −0.806246 0.591581i \(-0.798504\pi\)
−0.806246 + 0.591581i \(0.798504\pi\)
\(788\) 7.41641 0.264199
\(789\) 41.7426 1.48608
\(790\) −7.23607 −0.257448
\(791\) −52.8328 −1.87852
\(792\) 0 0
\(793\) 3.52786 0.125278
\(794\) −12.6180 −0.447797
\(795\) −27.4164 −0.972360
\(796\) −12.1803 −0.431721
\(797\) −11.2361 −0.398002 −0.199001 0.979999i \(-0.563770\pi\)
−0.199001 + 0.979999i \(0.563770\pi\)
\(798\) −6.23607 −0.220754
\(799\) 2.47214 0.0874579
\(800\) −2.38197 −0.0842152
\(801\) −2.65248 −0.0937206
\(802\) 17.2361 0.608627
\(803\) 0 0
\(804\) −8.23607 −0.290464
\(805\) 12.4721 0.439585
\(806\) 1.61803 0.0569928
\(807\) 26.4721 0.931863
\(808\) −3.23607 −0.113844
\(809\) 45.2361 1.59042 0.795208 0.606337i \(-0.207362\pi\)
0.795208 + 0.606337i \(0.207362\pi\)
\(810\) 12.4721 0.438226
\(811\) −38.8328 −1.36360 −0.681802 0.731536i \(-0.738804\pi\)
−0.681802 + 0.731536i \(0.738804\pi\)
\(812\) 3.29180 0.115519
\(813\) −26.1246 −0.916230
\(814\) 0 0
\(815\) −4.76393 −0.166873
\(816\) 5.23607 0.183299
\(817\) −12.0902 −0.422982
\(818\) −0.270510 −0.00945815
\(819\) 0.909830 0.0317920
\(820\) −1.00000 −0.0349215
\(821\) −46.0000 −1.60541 −0.802706 0.596376i \(-0.796607\pi\)
−0.802706 + 0.596376i \(0.796607\pi\)
\(822\) 0.527864 0.0184114
\(823\) −11.7082 −0.408122 −0.204061 0.978958i \(-0.565414\pi\)
−0.204061 + 0.978958i \(0.565414\pi\)
\(824\) −7.14590 −0.248939
\(825\) 0 0
\(826\) 49.8885 1.73584
\(827\) −46.0689 −1.60197 −0.800986 0.598683i \(-0.795691\pi\)
−0.800986 + 0.598683i \(0.795691\pi\)
\(828\) 0.763932 0.0265485
\(829\) 49.3050 1.71243 0.856216 0.516618i \(-0.172809\pi\)
0.856216 + 0.516618i \(0.172809\pi\)
\(830\) −3.85410 −0.133778
\(831\) −14.6525 −0.508289
\(832\) −0.618034 −0.0214265
\(833\) −25.4164 −0.880626
\(834\) 11.8541 0.410474
\(835\) −1.52786 −0.0528739
\(836\) 0 0
\(837\) −14.3262 −0.495187
\(838\) −16.2918 −0.562791
\(839\) 43.3262 1.49579 0.747894 0.663818i \(-0.231065\pi\)
0.747894 + 0.663818i \(0.231065\pi\)
\(840\) 10.0902 0.348144
\(841\) −28.2705 −0.974845
\(842\) −8.18034 −0.281913
\(843\) 47.2705 1.62808
\(844\) −22.6525 −0.779730
\(845\) 20.4164 0.702346
\(846\) 0.291796 0.0100322
\(847\) 0 0
\(848\) −10.4721 −0.359615
\(849\) −31.1803 −1.07011
\(850\) 7.70820 0.264389
\(851\) −2.47214 −0.0847437
\(852\) −20.7984 −0.712541
\(853\) −25.5967 −0.876416 −0.438208 0.898874i \(-0.644387\pi\)
−0.438208 + 0.898874i \(0.644387\pi\)
\(854\) −22.0000 −0.752825
\(855\) 0.618034 0.0211363
\(856\) −6.18034 −0.211240
\(857\) 5.85410 0.199972 0.0999862 0.994989i \(-0.468120\pi\)
0.0999862 + 0.994989i \(0.468120\pi\)
\(858\) 0 0
\(859\) 35.1246 1.19844 0.599218 0.800586i \(-0.295478\pi\)
0.599218 + 0.800586i \(0.295478\pi\)
\(860\) 19.5623 0.667069
\(861\) −3.85410 −0.131347
\(862\) −37.4164 −1.27441
\(863\) −39.5623 −1.34672 −0.673358 0.739316i \(-0.735149\pi\)
−0.673358 + 0.739316i \(0.735149\pi\)
\(864\) 5.47214 0.186166
\(865\) −19.5623 −0.665138
\(866\) 6.18034 0.210016
\(867\) 10.5623 0.358715
\(868\) −10.0902 −0.342483
\(869\) 0 0
\(870\) 2.23607 0.0758098
\(871\) −3.14590 −0.106595
\(872\) −12.4721 −0.422360
\(873\) 7.05573 0.238800
\(874\) −2.00000 −0.0676510
\(875\) 46.0344 1.55625
\(876\) 16.9443 0.572494
\(877\) −14.1591 −0.478117 −0.239059 0.971005i \(-0.576839\pi\)
−0.239059 + 0.971005i \(0.576839\pi\)
\(878\) −20.0000 −0.674967
\(879\) −32.4164 −1.09338
\(880\) 0 0
\(881\) −3.74265 −0.126093 −0.0630465 0.998011i \(-0.520082\pi\)
−0.0630465 + 0.998011i \(0.520082\pi\)
\(882\) −3.00000 −0.101015
\(883\) −12.3607 −0.415970 −0.207985 0.978132i \(-0.566691\pi\)
−0.207985 + 0.978132i \(0.566691\pi\)
\(884\) 2.00000 0.0672673
\(885\) 33.8885 1.13915
\(886\) 17.7082 0.594919
\(887\) −24.0689 −0.808154 −0.404077 0.914725i \(-0.632407\pi\)
−0.404077 + 0.914725i \(0.632407\pi\)
\(888\) −2.00000 −0.0671156
\(889\) −23.1246 −0.775575
\(890\) −11.2361 −0.376634
\(891\) 0 0
\(892\) −10.4721 −0.350633
\(893\) −0.763932 −0.0255640
\(894\) −10.4721 −0.350241
\(895\) −18.2361 −0.609565
\(896\) 3.85410 0.128757
\(897\) −2.00000 −0.0667781
\(898\) 16.1803 0.539945
\(899\) −2.23607 −0.0745770
\(900\) 0.909830 0.0303277
\(901\) 33.8885 1.12899
\(902\) 0 0
\(903\) 75.3951 2.50899
\(904\) −13.7082 −0.455928
\(905\) 32.1803 1.06971
\(906\) −9.70820 −0.322533
\(907\) −22.4721 −0.746175 −0.373088 0.927796i \(-0.621701\pi\)
−0.373088 + 0.927796i \(0.621701\pi\)
\(908\) 10.9443 0.363198
\(909\) 1.23607 0.0409978
\(910\) 3.85410 0.127762
\(911\) 35.0557 1.16145 0.580724 0.814100i \(-0.302770\pi\)
0.580724 + 0.814100i \(0.302770\pi\)
\(912\) −1.61803 −0.0535785
\(913\) 0 0
\(914\) 37.2361 1.23166
\(915\) −14.9443 −0.494042
\(916\) −1.85410 −0.0612613
\(917\) −6.45085 −0.213026
\(918\) −17.7082 −0.584458
\(919\) −30.3820 −1.00221 −0.501104 0.865387i \(-0.667073\pi\)
−0.501104 + 0.865387i \(0.667073\pi\)
\(920\) 3.23607 0.106690
\(921\) −3.23607 −0.106632
\(922\) 13.4164 0.441846
\(923\) −7.94427 −0.261489
\(924\) 0 0
\(925\) −2.94427 −0.0968071
\(926\) −37.0132 −1.21633
\(927\) 2.72949 0.0896482
\(928\) 0.854102 0.0280373
\(929\) −14.1459 −0.464112 −0.232056 0.972702i \(-0.574545\pi\)
−0.232056 + 0.972702i \(0.574545\pi\)
\(930\) −6.85410 −0.224755
\(931\) 7.85410 0.257408
\(932\) −10.4721 −0.343026
\(933\) −34.1803 −1.11901
\(934\) 26.8328 0.877997
\(935\) 0 0
\(936\) 0.236068 0.00771612
\(937\) −36.5410 −1.19374 −0.596872 0.802337i \(-0.703590\pi\)
−0.596872 + 0.802337i \(0.703590\pi\)
\(938\) 19.6180 0.640552
\(939\) −18.3262 −0.598054
\(940\) 1.23607 0.0403161
\(941\) 29.4164 0.958947 0.479474 0.877556i \(-0.340828\pi\)
0.479474 + 0.877556i \(0.340828\pi\)
\(942\) 20.7984 0.677648
\(943\) −1.23607 −0.0402519
\(944\) 12.9443 0.421300
\(945\) −34.1246 −1.11007
\(946\) 0 0
\(947\) −49.7082 −1.61530 −0.807650 0.589662i \(-0.799261\pi\)
−0.807650 + 0.589662i \(0.799261\pi\)
\(948\) −7.23607 −0.235017
\(949\) 6.47214 0.210094
\(950\) −2.38197 −0.0772812
\(951\) −12.9443 −0.419747
\(952\) −12.4721 −0.404224
\(953\) 1.41641 0.0458820 0.0229410 0.999737i \(-0.492697\pi\)
0.0229410 + 0.999737i \(0.492697\pi\)
\(954\) 4.00000 0.129505
\(955\) 16.1803 0.523584
\(956\) −28.2705 −0.914334
\(957\) 0 0
\(958\) 0.437694 0.0141413
\(959\) −1.25735 −0.0406021
\(960\) 2.61803 0.0844967
\(961\) −24.1459 −0.778900
\(962\) −0.763932 −0.0246302
\(963\) 2.36068 0.0760718
\(964\) −10.3820 −0.334381
\(965\) 10.6180 0.341807
\(966\) 12.4721 0.401284
\(967\) −6.11146 −0.196531 −0.0982656 0.995160i \(-0.531329\pi\)
−0.0982656 + 0.995160i \(0.531329\pi\)
\(968\) 0 0
\(969\) 5.23607 0.168207
\(970\) 29.8885 0.959663
\(971\) 41.6180 1.33559 0.667793 0.744347i \(-0.267239\pi\)
0.667793 + 0.744347i \(0.267239\pi\)
\(972\) −3.94427 −0.126513
\(973\) −28.2361 −0.905207
\(974\) −23.5066 −0.753199
\(975\) −2.38197 −0.0762840
\(976\) −5.70820 −0.182715
\(977\) 20.4721 0.654962 0.327481 0.944858i \(-0.393800\pi\)
0.327481 + 0.944858i \(0.393800\pi\)
\(978\) −4.76393 −0.152334
\(979\) 0 0
\(980\) −12.7082 −0.405949
\(981\) 4.76393 0.152101
\(982\) −21.4508 −0.684524
\(983\) 9.09017 0.289931 0.144966 0.989437i \(-0.453693\pi\)
0.144966 + 0.989437i \(0.453693\pi\)
\(984\) −1.00000 −0.0318788
\(985\) −12.0000 −0.382352
\(986\) −2.76393 −0.0880215
\(987\) 4.76393 0.151638
\(988\) −0.618034 −0.0196623
\(989\) 24.1803 0.768890
\(990\) 0 0
\(991\) 8.14590 0.258763 0.129381 0.991595i \(-0.458701\pi\)
0.129381 + 0.991595i \(0.458701\pi\)
\(992\) −2.61803 −0.0831227
\(993\) 54.9787 1.74470
\(994\) 49.5410 1.57135
\(995\) 19.7082 0.624792
\(996\) −3.85410 −0.122122
\(997\) 53.7771 1.70314 0.851569 0.524243i \(-0.175652\pi\)
0.851569 + 0.524243i \(0.175652\pi\)
\(998\) −25.1246 −0.795306
\(999\) 6.76393 0.214001
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 4598.2.a.bg.1.1 yes 2
11.10 odd 2 4598.2.a.x.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.x.1.1 2 11.10 odd 2
4598.2.a.bg.1.1 yes 2 1.1 even 1 trivial