Properties

Label 5733.2.a.x.1.2
Level $5733$
Weight $2$
Character 5733.1
Self dual yes
Analytic conductor $45.778$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 5733 = 3^{2} \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5733.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(45.7782354788\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 2\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.470683\) of defining polynomial
Character \(\chi\) \(=\) 5733.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.470683 q^{2} -1.77846 q^{4} +0.529317 q^{5} +1.77846 q^{8} +O(q^{10})\) \(q-0.470683 q^{2} -1.77846 q^{4} +0.529317 q^{5} +1.77846 q^{8} -0.249141 q^{10} +2.24914 q^{11} -1.00000 q^{13} +2.71982 q^{16} -1.30777 q^{17} +1.47068 q^{19} -0.941367 q^{20} -1.05863 q^{22} -5.83709 q^{23} -4.71982 q^{25} +0.470683 q^{26} -5.22154 q^{29} +7.02760 q^{31} -4.83709 q^{32} +0.615547 q^{34} -2.36641 q^{37} -0.692226 q^{38} +0.941367 q^{40} +6.49828 q^{41} +11.3940 q^{43} -4.00000 q^{44} +2.74742 q^{46} +8.58451 q^{47} +2.22154 q^{50} +1.77846 q^{52} -11.2767 q^{53} +1.19051 q^{55} +2.45769 q^{58} -12.1725 q^{59} +2.00000 q^{61} -3.30777 q^{62} -3.16291 q^{64} -0.529317 q^{65} -15.9379 q^{67} +2.32582 q^{68} -1.19051 q^{71} -7.64315 q^{73} +1.11383 q^{74} -2.61555 q^{76} -1.33881 q^{79} +1.43965 q^{80} -3.05863 q^{82} -16.3500 q^{83} -0.692226 q^{85} -5.36297 q^{86} +4.00000 q^{88} +6.91033 q^{89} +10.3810 q^{92} -4.04059 q^{94} +0.778457 q^{95} +3.47068 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 3q^{4} + 2q^{5} - 3q^{8} + O(q^{10}) \) \( 3q - q^{2} + 3q^{4} + 2q^{5} - 3q^{8} + 8q^{10} - 2q^{11} - 3q^{13} - q^{16} + 4q^{17} + 4q^{19} - 2q^{20} - 4q^{22} - 10q^{23} - 5q^{25} + q^{26} - 24q^{29} + 4q^{31} - 7q^{32} - 14q^{34} - 10q^{38} + 2q^{40} + 2q^{41} + 10q^{43} - 12q^{44} - 18q^{46} - 8q^{47} + 15q^{50} - 3q^{52} - 8q^{53} - 6q^{55} + 12q^{58} - 4q^{59} + 6q^{61} - 2q^{62} - 17q^{64} - 2q^{65} - 12q^{67} + 22q^{68} + 6q^{71} + 10q^{73} - 30q^{74} + 8q^{76} - 14q^{79} - 14q^{80} - 10q^{82} - 12q^{83} - 10q^{85} + 26q^{86} + 12q^{88} + 2q^{89} + 12q^{92} + 10q^{94} - 6q^{95} + 10q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.470683 −0.332823 −0.166412 0.986056i \(-0.553218\pi\)
−0.166412 + 0.986056i \(0.553218\pi\)
\(3\) 0 0
\(4\) −1.77846 −0.889229
\(5\) 0.529317 0.236718 0.118359 0.992971i \(-0.462237\pi\)
0.118359 + 0.992971i \(0.462237\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.77846 0.628780
\(9\) 0 0
\(10\) −0.249141 −0.0787852
\(11\) 2.24914 0.678141 0.339071 0.940761i \(-0.389887\pi\)
0.339071 + 0.940761i \(0.389887\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 2.71982 0.679956
\(17\) −1.30777 −0.317182 −0.158591 0.987344i \(-0.550695\pi\)
−0.158591 + 0.987344i \(0.550695\pi\)
\(18\) 0 0
\(19\) 1.47068 0.337398 0.168699 0.985668i \(-0.446043\pi\)
0.168699 + 0.985668i \(0.446043\pi\)
\(20\) −0.941367 −0.210496
\(21\) 0 0
\(22\) −1.05863 −0.225701
\(23\) −5.83709 −1.21712 −0.608559 0.793509i \(-0.708252\pi\)
−0.608559 + 0.793509i \(0.708252\pi\)
\(24\) 0 0
\(25\) −4.71982 −0.943965
\(26\) 0.470683 0.0923086
\(27\) 0 0
\(28\) 0 0
\(29\) −5.22154 −0.969616 −0.484808 0.874621i \(-0.661111\pi\)
−0.484808 + 0.874621i \(0.661111\pi\)
\(30\) 0 0
\(31\) 7.02760 1.26219 0.631097 0.775704i \(-0.282605\pi\)
0.631097 + 0.775704i \(0.282605\pi\)
\(32\) −4.83709 −0.855085
\(33\) 0 0
\(34\) 0.615547 0.105566
\(35\) 0 0
\(36\) 0 0
\(37\) −2.36641 −0.389035 −0.194517 0.980899i \(-0.562314\pi\)
−0.194517 + 0.980899i \(0.562314\pi\)
\(38\) −0.692226 −0.112294
\(39\) 0 0
\(40\) 0.941367 0.148843
\(41\) 6.49828 1.01486 0.507431 0.861693i \(-0.330595\pi\)
0.507431 + 0.861693i \(0.330595\pi\)
\(42\) 0 0
\(43\) 11.3940 1.73757 0.868785 0.495190i \(-0.164902\pi\)
0.868785 + 0.495190i \(0.164902\pi\)
\(44\) −4.00000 −0.603023
\(45\) 0 0
\(46\) 2.74742 0.405085
\(47\) 8.58451 1.25218 0.626090 0.779751i \(-0.284654\pi\)
0.626090 + 0.779751i \(0.284654\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.22154 0.314174
\(51\) 0 0
\(52\) 1.77846 0.246628
\(53\) −11.2767 −1.54898 −0.774490 0.632587i \(-0.781993\pi\)
−0.774490 + 0.632587i \(0.781993\pi\)
\(54\) 0 0
\(55\) 1.19051 0.160528
\(56\) 0 0
\(57\) 0 0
\(58\) 2.45769 0.322711
\(59\) −12.1725 −1.58472 −0.792360 0.610054i \(-0.791148\pi\)
−0.792360 + 0.610054i \(0.791148\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −3.30777 −0.420088
\(63\) 0 0
\(64\) −3.16291 −0.395364
\(65\) −0.529317 −0.0656536
\(66\) 0 0
\(67\) −15.9379 −1.94713 −0.973564 0.228415i \(-0.926646\pi\)
−0.973564 + 0.228415i \(0.926646\pi\)
\(68\) 2.32582 0.282047
\(69\) 0 0
\(70\) 0 0
\(71\) −1.19051 −0.141287 −0.0706436 0.997502i \(-0.522505\pi\)
−0.0706436 + 0.997502i \(0.522505\pi\)
\(72\) 0 0
\(73\) −7.64315 −0.894562 −0.447281 0.894393i \(-0.647608\pi\)
−0.447281 + 0.894393i \(0.647608\pi\)
\(74\) 1.11383 0.129480
\(75\) 0 0
\(76\) −2.61555 −0.300024
\(77\) 0 0
\(78\) 0 0
\(79\) −1.33881 −0.150628 −0.0753139 0.997160i \(-0.523996\pi\)
−0.0753139 + 0.997160i \(0.523996\pi\)
\(80\) 1.43965 0.160958
\(81\) 0 0
\(82\) −3.05863 −0.337770
\(83\) −16.3500 −1.79464 −0.897322 0.441377i \(-0.854490\pi\)
−0.897322 + 0.441377i \(0.854490\pi\)
\(84\) 0 0
\(85\) −0.692226 −0.0750825
\(86\) −5.36297 −0.578304
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) 6.91033 0.732494 0.366247 0.930518i \(-0.380643\pi\)
0.366247 + 0.930518i \(0.380643\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.3810 1.08230
\(93\) 0 0
\(94\) −4.04059 −0.416755
\(95\) 0.778457 0.0798680
\(96\) 0 0
\(97\) 3.47068 0.352395 0.176197 0.984355i \(-0.443620\pi\)
0.176197 + 0.984355i \(0.443620\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 8.39400 0.839400
\(101\) 7.75086 0.771239 0.385620 0.922658i \(-0.373988\pi\)
0.385620 + 0.922658i \(0.373988\pi\)
\(102\) 0 0
\(103\) 16.9966 1.67472 0.837361 0.546651i \(-0.184098\pi\)
0.837361 + 0.546651i \(0.184098\pi\)
\(104\) −1.77846 −0.174392
\(105\) 0 0
\(106\) 5.30777 0.515537
\(107\) 5.55691 0.537207 0.268604 0.963251i \(-0.413438\pi\)
0.268604 + 0.963251i \(0.413438\pi\)
\(108\) 0 0
\(109\) 7.92332 0.758917 0.379458 0.925209i \(-0.376110\pi\)
0.379458 + 0.925209i \(0.376110\pi\)
\(110\) −0.560352 −0.0534275
\(111\) 0 0
\(112\) 0 0
\(113\) 9.89229 0.930588 0.465294 0.885156i \(-0.345949\pi\)
0.465294 + 0.885156i \(0.345949\pi\)
\(114\) 0 0
\(115\) −3.08967 −0.288113
\(116\) 9.28629 0.862210
\(117\) 0 0
\(118\) 5.72938 0.527432
\(119\) 0 0
\(120\) 0 0
\(121\) −5.94137 −0.540124
\(122\) −0.941367 −0.0852273
\(123\) 0 0
\(124\) −12.4983 −1.12238
\(125\) −5.14486 −0.460171
\(126\) 0 0
\(127\) 0.824101 0.0731271 0.0365635 0.999331i \(-0.488359\pi\)
0.0365635 + 0.999331i \(0.488359\pi\)
\(128\) 11.1629 0.986671
\(129\) 0 0
\(130\) 0.249141 0.0218511
\(131\) 10.6155 0.927485 0.463742 0.885970i \(-0.346506\pi\)
0.463742 + 0.885970i \(0.346506\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.50172 0.648050
\(135\) 0 0
\(136\) −2.32582 −0.199437
\(137\) −11.3630 −0.970804 −0.485402 0.874291i \(-0.661327\pi\)
−0.485402 + 0.874291i \(0.661327\pi\)
\(138\) 0 0
\(139\) 13.9233 1.18096 0.590480 0.807052i \(-0.298938\pi\)
0.590480 + 0.807052i \(0.298938\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.560352 0.0470237
\(143\) −2.24914 −0.188083
\(144\) 0 0
\(145\) −2.76385 −0.229525
\(146\) 3.59750 0.297731
\(147\) 0 0
\(148\) 4.20855 0.345941
\(149\) −9.30777 −0.762523 −0.381261 0.924467i \(-0.624510\pi\)
−0.381261 + 0.924467i \(0.624510\pi\)
\(150\) 0 0
\(151\) 7.07324 0.575612 0.287806 0.957689i \(-0.407074\pi\)
0.287806 + 0.957689i \(0.407074\pi\)
\(152\) 2.61555 0.212149
\(153\) 0 0
\(154\) 0 0
\(155\) 3.71982 0.298783
\(156\) 0 0
\(157\) 6.04059 0.482091 0.241046 0.970514i \(-0.422510\pi\)
0.241046 + 0.970514i \(0.422510\pi\)
\(158\) 0.630155 0.0501325
\(159\) 0 0
\(160\) −2.56035 −0.202414
\(161\) 0 0
\(162\) 0 0
\(163\) 6.38101 0.499800 0.249900 0.968272i \(-0.419602\pi\)
0.249900 + 0.968272i \(0.419602\pi\)
\(164\) −11.5569 −0.902443
\(165\) 0 0
\(166\) 7.69566 0.597299
\(167\) −16.5845 −1.28335 −0.641674 0.766977i \(-0.721760\pi\)
−0.641674 + 0.766977i \(0.721760\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0.325819 0.0249892
\(171\) 0 0
\(172\) −20.2637 −1.54510
\(173\) −23.3009 −1.77153 −0.885767 0.464130i \(-0.846367\pi\)
−0.885767 + 0.464130i \(0.846367\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 6.11727 0.461106
\(177\) 0 0
\(178\) −3.25258 −0.243791
\(179\) −21.0422 −1.57277 −0.786384 0.617738i \(-0.788049\pi\)
−0.786384 + 0.617738i \(0.788049\pi\)
\(180\) 0 0
\(181\) −16.7474 −1.24483 −0.622413 0.782689i \(-0.713848\pi\)
−0.622413 + 0.782689i \(0.713848\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −10.3810 −0.765299
\(185\) −1.25258 −0.0920914
\(186\) 0 0
\(187\) −2.94137 −0.215094
\(188\) −15.2672 −1.11347
\(189\) 0 0
\(190\) −0.366407 −0.0265819
\(191\) 7.43965 0.538314 0.269157 0.963096i \(-0.413255\pi\)
0.269157 + 0.963096i \(0.413255\pi\)
\(192\) 0 0
\(193\) −1.50172 −0.108096 −0.0540480 0.998538i \(-0.517212\pi\)
−0.0540480 + 0.998538i \(0.517212\pi\)
\(194\) −1.63359 −0.117285
\(195\) 0 0
\(196\) 0 0
\(197\) −23.9931 −1.70944 −0.854720 0.519090i \(-0.826271\pi\)
−0.854720 + 0.519090i \(0.826271\pi\)
\(198\) 0 0
\(199\) 2.01461 0.142812 0.0714059 0.997447i \(-0.477251\pi\)
0.0714059 + 0.997447i \(0.477251\pi\)
\(200\) −8.39400 −0.593546
\(201\) 0 0
\(202\) −3.64820 −0.256687
\(203\) 0 0
\(204\) 0 0
\(205\) 3.43965 0.240235
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) −2.71982 −0.188586
\(209\) 3.30777 0.228803
\(210\) 0 0
\(211\) 10.1008 0.695370 0.347685 0.937611i \(-0.386968\pi\)
0.347685 + 0.937611i \(0.386968\pi\)
\(212\) 20.0552 1.37740
\(213\) 0 0
\(214\) −2.61555 −0.178795
\(215\) 6.03104 0.411313
\(216\) 0 0
\(217\) 0 0
\(218\) −3.72938 −0.252585
\(219\) 0 0
\(220\) −2.11727 −0.142746
\(221\) 1.30777 0.0879704
\(222\) 0 0
\(223\) −10.1414 −0.679120 −0.339560 0.940584i \(-0.610278\pi\)
−0.339560 + 0.940584i \(0.610278\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.65613 −0.309721
\(227\) −5.38445 −0.357379 −0.178689 0.983906i \(-0.557186\pi\)
−0.178689 + 0.983906i \(0.557186\pi\)
\(228\) 0 0
\(229\) −3.32238 −0.219549 −0.109775 0.993957i \(-0.535013\pi\)
−0.109775 + 0.993957i \(0.535013\pi\)
\(230\) 1.45426 0.0958908
\(231\) 0 0
\(232\) −9.28629 −0.609675
\(233\) −13.7198 −0.898816 −0.449408 0.893327i \(-0.648365\pi\)
−0.449408 + 0.893327i \(0.648365\pi\)
\(234\) 0 0
\(235\) 4.54392 0.296413
\(236\) 21.6482 1.40918
\(237\) 0 0
\(238\) 0 0
\(239\) 3.50172 0.226507 0.113254 0.993566i \(-0.463873\pi\)
0.113254 + 0.993566i \(0.463873\pi\)
\(240\) 0 0
\(241\) −1.58795 −0.102289 −0.0511444 0.998691i \(-0.516287\pi\)
−0.0511444 + 0.998691i \(0.516287\pi\)
\(242\) 2.79650 0.179766
\(243\) 0 0
\(244\) −3.55691 −0.227708
\(245\) 0 0
\(246\) 0 0
\(247\) −1.47068 −0.0935773
\(248\) 12.4983 0.793642
\(249\) 0 0
\(250\) 2.42160 0.153156
\(251\) −4.92676 −0.310974 −0.155487 0.987838i \(-0.549695\pi\)
−0.155487 + 0.987838i \(0.549695\pi\)
\(252\) 0 0
\(253\) −13.1284 −0.825378
\(254\) −0.387890 −0.0243384
\(255\) 0 0
\(256\) 1.07162 0.0669764
\(257\) −8.01461 −0.499938 −0.249969 0.968254i \(-0.580420\pi\)
−0.249969 + 0.968254i \(0.580420\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.941367 0.0583811
\(261\) 0 0
\(262\) −4.99656 −0.308689
\(263\) −1.60256 −0.0988179 −0.0494090 0.998779i \(-0.515734\pi\)
−0.0494090 + 0.998779i \(0.515734\pi\)
\(264\) 0 0
\(265\) −5.96896 −0.366671
\(266\) 0 0
\(267\) 0 0
\(268\) 28.3449 1.73144
\(269\) −11.8207 −0.720719 −0.360359 0.932814i \(-0.617346\pi\)
−0.360359 + 0.932814i \(0.617346\pi\)
\(270\) 0 0
\(271\) −21.8827 −1.32928 −0.664641 0.747163i \(-0.731415\pi\)
−0.664641 + 0.747163i \(0.731415\pi\)
\(272\) −3.55691 −0.215670
\(273\) 0 0
\(274\) 5.34836 0.323106
\(275\) −10.6155 −0.640142
\(276\) 0 0
\(277\) −10.2181 −0.613946 −0.306973 0.951718i \(-0.599316\pi\)
−0.306973 + 0.951718i \(0.599316\pi\)
\(278\) −6.55348 −0.393051
\(279\) 0 0
\(280\) 0 0
\(281\) −1.54231 −0.0920063 −0.0460031 0.998941i \(-0.514648\pi\)
−0.0460031 + 0.998941i \(0.514648\pi\)
\(282\) 0 0
\(283\) −15.8466 −0.941985 −0.470993 0.882137i \(-0.656104\pi\)
−0.470993 + 0.882137i \(0.656104\pi\)
\(284\) 2.11727 0.125637
\(285\) 0 0
\(286\) 1.05863 0.0625983
\(287\) 0 0
\(288\) 0 0
\(289\) −15.2897 −0.899396
\(290\) 1.30090 0.0763914
\(291\) 0 0
\(292\) 13.5930 0.795470
\(293\) 11.0828 0.647464 0.323732 0.946149i \(-0.395062\pi\)
0.323732 + 0.946149i \(0.395062\pi\)
\(294\) 0 0
\(295\) −6.44309 −0.375131
\(296\) −4.20855 −0.244617
\(297\) 0 0
\(298\) 4.38101 0.253785
\(299\) 5.83709 0.337568
\(300\) 0 0
\(301\) 0 0
\(302\) −3.32926 −0.191577
\(303\) 0 0
\(304\) 4.00000 0.229416
\(305\) 1.05863 0.0606172
\(306\) 0 0
\(307\) −20.4121 −1.16498 −0.582489 0.812839i \(-0.697921\pi\)
−0.582489 + 0.812839i \(0.697921\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.75086 −0.0994421
\(311\) −1.92332 −0.109062 −0.0545308 0.998512i \(-0.517366\pi\)
−0.0545308 + 0.998512i \(0.517366\pi\)
\(312\) 0 0
\(313\) 14.3664 0.812037 0.406019 0.913865i \(-0.366917\pi\)
0.406019 + 0.913865i \(0.366917\pi\)
\(314\) −2.84320 −0.160451
\(315\) 0 0
\(316\) 2.38101 0.133943
\(317\) −15.5569 −0.873763 −0.436882 0.899519i \(-0.643917\pi\)
−0.436882 + 0.899519i \(0.643917\pi\)
\(318\) 0 0
\(319\) −11.7440 −0.657537
\(320\) −1.67418 −0.0935895
\(321\) 0 0
\(322\) 0 0
\(323\) −1.92332 −0.107016
\(324\) 0 0
\(325\) 4.71982 0.261809
\(326\) −3.00344 −0.166345
\(327\) 0 0
\(328\) 11.5569 0.638124
\(329\) 0 0
\(330\) 0 0
\(331\) 31.5500 1.73415 0.867073 0.498180i \(-0.165998\pi\)
0.867073 + 0.498180i \(0.165998\pi\)
\(332\) 29.0777 1.59585
\(333\) 0 0
\(334\) 7.80605 0.427128
\(335\) −8.43621 −0.460919
\(336\) 0 0
\(337\) −8.42666 −0.459029 −0.229515 0.973305i \(-0.573714\pi\)
−0.229515 + 0.973305i \(0.573714\pi\)
\(338\) −0.470683 −0.0256018
\(339\) 0 0
\(340\) 1.23109 0.0667655
\(341\) 15.8061 0.855946
\(342\) 0 0
\(343\) 0 0
\(344\) 20.2637 1.09255
\(345\) 0 0
\(346\) 10.9673 0.589608
\(347\) −19.3484 −1.03867 −0.519337 0.854569i \(-0.673821\pi\)
−0.519337 + 0.854569i \(0.673821\pi\)
\(348\) 0 0
\(349\) −27.2553 −1.45894 −0.729470 0.684013i \(-0.760233\pi\)
−0.729470 + 0.684013i \(0.760233\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −10.8793 −0.579868
\(353\) −25.6742 −1.36650 −0.683249 0.730185i \(-0.739434\pi\)
−0.683249 + 0.730185i \(0.739434\pi\)
\(354\) 0 0
\(355\) −0.630155 −0.0334452
\(356\) −12.2897 −0.651354
\(357\) 0 0
\(358\) 9.90422 0.523454
\(359\) 23.4182 1.23596 0.617982 0.786192i \(-0.287951\pi\)
0.617982 + 0.786192i \(0.287951\pi\)
\(360\) 0 0
\(361\) −16.8371 −0.886163
\(362\) 7.88273 0.414307
\(363\) 0 0
\(364\) 0 0
\(365\) −4.04564 −0.211759
\(366\) 0 0
\(367\) 14.6854 0.766569 0.383285 0.923630i \(-0.374793\pi\)
0.383285 + 0.923630i \(0.374793\pi\)
\(368\) −15.8759 −0.827586
\(369\) 0 0
\(370\) 0.589568 0.0306502
\(371\) 0 0
\(372\) 0 0
\(373\) −23.6673 −1.22545 −0.612723 0.790298i \(-0.709926\pi\)
−0.612723 + 0.790298i \(0.709926\pi\)
\(374\) 1.38445 0.0715883
\(375\) 0 0
\(376\) 15.2672 0.787345
\(377\) 5.22154 0.268923
\(378\) 0 0
\(379\) −32.7405 −1.68177 −0.840884 0.541215i \(-0.817965\pi\)
−0.840884 + 0.541215i \(0.817965\pi\)
\(380\) −1.38445 −0.0710209
\(381\) 0 0
\(382\) −3.50172 −0.179164
\(383\) −22.6155 −1.15560 −0.577800 0.816178i \(-0.696089\pi\)
−0.577800 + 0.816178i \(0.696089\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.706834 0.0359769
\(387\) 0 0
\(388\) −6.17246 −0.313359
\(389\) −38.0483 −1.92913 −0.964563 0.263852i \(-0.915007\pi\)
−0.964563 + 0.263852i \(0.915007\pi\)
\(390\) 0 0
\(391\) 7.63359 0.386047
\(392\) 0 0
\(393\) 0 0
\(394\) 11.2932 0.568941
\(395\) −0.708654 −0.0356562
\(396\) 0 0
\(397\) 11.7052 0.587468 0.293734 0.955887i \(-0.405102\pi\)
0.293734 + 0.955887i \(0.405102\pi\)
\(398\) −0.948243 −0.0475311
\(399\) 0 0
\(400\) −12.8371 −0.641855
\(401\) −3.55691 −0.177624 −0.0888119 0.996048i \(-0.528307\pi\)
−0.0888119 + 0.996048i \(0.528307\pi\)
\(402\) 0 0
\(403\) −7.02760 −0.350070
\(404\) −13.7846 −0.685808
\(405\) 0 0
\(406\) 0 0
\(407\) −5.32238 −0.263821
\(408\) 0 0
\(409\) −5.26213 −0.260196 −0.130098 0.991501i \(-0.541529\pi\)
−0.130098 + 0.991501i \(0.541529\pi\)
\(410\) −1.61899 −0.0799560
\(411\) 0 0
\(412\) −30.2277 −1.48921
\(413\) 0 0
\(414\) 0 0
\(415\) −8.65432 −0.424824
\(416\) 4.83709 0.237158
\(417\) 0 0
\(418\) −1.55691 −0.0761512
\(419\) 26.0337 1.27183 0.635915 0.771759i \(-0.280623\pi\)
0.635915 + 0.771759i \(0.280623\pi\)
\(420\) 0 0
\(421\) 22.2423 1.08402 0.542011 0.840372i \(-0.317663\pi\)
0.542011 + 0.840372i \(0.317663\pi\)
\(422\) −4.75430 −0.231436
\(423\) 0 0
\(424\) −20.0552 −0.973966
\(425\) 6.17246 0.299408
\(426\) 0 0
\(427\) 0 0
\(428\) −9.88273 −0.477700
\(429\) 0 0
\(430\) −2.83871 −0.136895
\(431\) −27.6742 −1.33302 −0.666509 0.745497i \(-0.732212\pi\)
−0.666509 + 0.745497i \(0.732212\pi\)
\(432\) 0 0
\(433\) 12.7880 0.614552 0.307276 0.951620i \(-0.400582\pi\)
0.307276 + 0.951620i \(0.400582\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −14.0913 −0.674850
\(437\) −8.58451 −0.410653
\(438\) 0 0
\(439\) 18.1656 0.866996 0.433498 0.901155i \(-0.357279\pi\)
0.433498 + 0.901155i \(0.357279\pi\)
\(440\) 2.11727 0.100937
\(441\) 0 0
\(442\) −0.615547 −0.0292786
\(443\) −0.107714 −0.00511767 −0.00255883 0.999997i \(-0.500815\pi\)
−0.00255883 + 0.999997i \(0.500815\pi\)
\(444\) 0 0
\(445\) 3.65775 0.173394
\(446\) 4.77340 0.226027
\(447\) 0 0
\(448\) 0 0
\(449\) 22.1725 1.04638 0.523192 0.852215i \(-0.324741\pi\)
0.523192 + 0.852215i \(0.324741\pi\)
\(450\) 0 0
\(451\) 14.6155 0.688219
\(452\) −17.5930 −0.827505
\(453\) 0 0
\(454\) 2.53437 0.118944
\(455\) 0 0
\(456\) 0 0
\(457\) 4.35953 0.203930 0.101965 0.994788i \(-0.467487\pi\)
0.101965 + 0.994788i \(0.467487\pi\)
\(458\) 1.56379 0.0730711
\(459\) 0 0
\(460\) 5.49484 0.256198
\(461\) 32.3810 1.50813 0.754067 0.656797i \(-0.228089\pi\)
0.754067 + 0.656797i \(0.228089\pi\)
\(462\) 0 0
\(463\) 8.36641 0.388820 0.194410 0.980920i \(-0.437721\pi\)
0.194410 + 0.980920i \(0.437721\pi\)
\(464\) −14.2017 −0.659296
\(465\) 0 0
\(466\) 6.45769 0.299147
\(467\) −19.5423 −0.904310 −0.452155 0.891939i \(-0.649345\pi\)
−0.452155 + 0.891939i \(0.649345\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −2.13875 −0.0986532
\(471\) 0 0
\(472\) −21.6482 −0.996439
\(473\) 25.6267 1.17832
\(474\) 0 0
\(475\) −6.94137 −0.318492
\(476\) 0 0
\(477\) 0 0
\(478\) −1.64820 −0.0753870
\(479\) −28.5224 −1.30322 −0.651612 0.758553i \(-0.725907\pi\)
−0.651612 + 0.758553i \(0.725907\pi\)
\(480\) 0 0
\(481\) 2.36641 0.107899
\(482\) 0.747422 0.0340441
\(483\) 0 0
\(484\) 10.5665 0.480294
\(485\) 1.83709 0.0834180
\(486\) 0 0
\(487\) 24.8241 1.12489 0.562444 0.826836i \(-0.309861\pi\)
0.562444 + 0.826836i \(0.309861\pi\)
\(488\) 3.55691 0.161014
\(489\) 0 0
\(490\) 0 0
\(491\) −29.1690 −1.31638 −0.658190 0.752852i \(-0.728678\pi\)
−0.658190 + 0.752852i \(0.728678\pi\)
\(492\) 0 0
\(493\) 6.82860 0.307545
\(494\) 0.692226 0.0311447
\(495\) 0 0
\(496\) 19.1138 0.858236
\(497\) 0 0
\(498\) 0 0
\(499\) −33.3009 −1.49075 −0.745376 0.666644i \(-0.767730\pi\)
−0.745376 + 0.666644i \(0.767730\pi\)
\(500\) 9.14992 0.409197
\(501\) 0 0
\(502\) 2.31894 0.103500
\(503\) −12.3258 −0.549581 −0.274791 0.961504i \(-0.588609\pi\)
−0.274791 + 0.961504i \(0.588609\pi\)
\(504\) 0 0
\(505\) 4.10266 0.182566
\(506\) 6.17934 0.274705
\(507\) 0 0
\(508\) −1.46563 −0.0650267
\(509\) 23.7052 1.05072 0.525358 0.850882i \(-0.323932\pi\)
0.525358 + 0.850882i \(0.323932\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.8302 −1.00896
\(513\) 0 0
\(514\) 3.77234 0.166391
\(515\) 8.99656 0.396436
\(516\) 0 0
\(517\) 19.3078 0.849155
\(518\) 0 0
\(519\) 0 0
\(520\) −0.941367 −0.0412817
\(521\) 43.9018 1.92337 0.961687 0.274149i \(-0.0883962\pi\)
0.961687 + 0.274149i \(0.0883962\pi\)
\(522\) 0 0
\(523\) −37.4328 −1.63682 −0.818410 0.574634i \(-0.805144\pi\)
−0.818410 + 0.574634i \(0.805144\pi\)
\(524\) −18.8793 −0.824746
\(525\) 0 0
\(526\) 0.754297 0.0328889
\(527\) −9.19051 −0.400345
\(528\) 0 0
\(529\) 11.0716 0.481375
\(530\) 2.80949 0.122037
\(531\) 0 0
\(532\) 0 0
\(533\) −6.49828 −0.281472
\(534\) 0 0
\(535\) 2.94137 0.127166
\(536\) −28.3449 −1.22431
\(537\) 0 0
\(538\) 5.56379 0.239872
\(539\) 0 0
\(540\) 0 0
\(541\) −34.9751 −1.50370 −0.751848 0.659336i \(-0.770837\pi\)
−0.751848 + 0.659336i \(0.770837\pi\)
\(542\) 10.2998 0.442416
\(543\) 0 0
\(544\) 6.32582 0.271217
\(545\) 4.19395 0.179649
\(546\) 0 0
\(547\) 6.50783 0.278255 0.139127 0.990274i \(-0.455570\pi\)
0.139127 + 0.990274i \(0.455570\pi\)
\(548\) 20.2086 0.863267
\(549\) 0 0
\(550\) 4.99656 0.213054
\(551\) −7.67924 −0.327146
\(552\) 0 0
\(553\) 0 0
\(554\) 4.80949 0.204336
\(555\) 0 0
\(556\) −24.7620 −1.05014
\(557\) 43.4328 1.84031 0.920153 0.391559i \(-0.128064\pi\)
0.920153 + 0.391559i \(0.128064\pi\)
\(558\) 0 0
\(559\) −11.3940 −0.481915
\(560\) 0 0
\(561\) 0 0
\(562\) 0.725938 0.0306218
\(563\) −33.8827 −1.42799 −0.713993 0.700152i \(-0.753115\pi\)
−0.713993 + 0.700152i \(0.753115\pi\)
\(564\) 0 0
\(565\) 5.23615 0.220287
\(566\) 7.45875 0.313515
\(567\) 0 0
\(568\) −2.11727 −0.0888385
\(569\) −19.2147 −0.805521 −0.402760 0.915305i \(-0.631949\pi\)
−0.402760 + 0.915305i \(0.631949\pi\)
\(570\) 0 0
\(571\) 20.8268 0.871573 0.435787 0.900050i \(-0.356470\pi\)
0.435787 + 0.900050i \(0.356470\pi\)
\(572\) 4.00000 0.167248
\(573\) 0 0
\(574\) 0 0
\(575\) 27.5500 1.14892
\(576\) 0 0
\(577\) −28.6448 −1.19250 −0.596249 0.802800i \(-0.703343\pi\)
−0.596249 + 0.802800i \(0.703343\pi\)
\(578\) 7.19662 0.299340
\(579\) 0 0
\(580\) 4.91539 0.204100
\(581\) 0 0
\(582\) 0 0
\(583\) −25.3630 −1.05043
\(584\) −13.5930 −0.562483
\(585\) 0 0
\(586\) −5.21649 −0.215491
\(587\) −4.32076 −0.178337 −0.0891685 0.996017i \(-0.528421\pi\)
−0.0891685 + 0.996017i \(0.528421\pi\)
\(588\) 0 0
\(589\) 10.3354 0.425862
\(590\) 3.03265 0.124852
\(591\) 0 0
\(592\) −6.43621 −0.264527
\(593\) −15.9690 −0.655767 −0.327883 0.944718i \(-0.606335\pi\)
−0.327883 + 0.944718i \(0.606335\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.5535 0.678057
\(597\) 0 0
\(598\) −2.74742 −0.112350
\(599\) 16.8697 0.689279 0.344640 0.938735i \(-0.388001\pi\)
0.344640 + 0.938735i \(0.388001\pi\)
\(600\) 0 0
\(601\) 15.3415 0.625792 0.312896 0.949787i \(-0.398701\pi\)
0.312896 + 0.949787i \(0.398701\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −12.5795 −0.511851
\(605\) −3.14486 −0.127857
\(606\) 0 0
\(607\) −35.8353 −1.45451 −0.727254 0.686368i \(-0.759204\pi\)
−0.727254 + 0.686368i \(0.759204\pi\)
\(608\) −7.11383 −0.288504
\(609\) 0 0
\(610\) −0.498281 −0.0201748
\(611\) −8.58451 −0.347292
\(612\) 0 0
\(613\) 19.6673 0.794355 0.397177 0.917742i \(-0.369990\pi\)
0.397177 + 0.917742i \(0.369990\pi\)
\(614\) 9.60761 0.387732
\(615\) 0 0
\(616\) 0 0
\(617\) 41.4588 1.66907 0.834533 0.550958i \(-0.185737\pi\)
0.834533 + 0.550958i \(0.185737\pi\)
\(618\) 0 0
\(619\) −10.8793 −0.437276 −0.218638 0.975806i \(-0.570161\pi\)
−0.218638 + 0.975806i \(0.570161\pi\)
\(620\) −6.61555 −0.265687
\(621\) 0 0
\(622\) 0.905275 0.0362982
\(623\) 0 0
\(624\) 0 0
\(625\) 20.8759 0.835034
\(626\) −6.76203 −0.270265
\(627\) 0 0
\(628\) −10.7429 −0.428689
\(629\) 3.09472 0.123395
\(630\) 0 0
\(631\) −31.4396 −1.25159 −0.625796 0.779987i \(-0.715226\pi\)
−0.625796 + 0.779987i \(0.715226\pi\)
\(632\) −2.38101 −0.0947117
\(633\) 0 0
\(634\) 7.32238 0.290809
\(635\) 0.436210 0.0173105
\(636\) 0 0
\(637\) 0 0
\(638\) 5.52770 0.218844
\(639\) 0 0
\(640\) 5.90871 0.233562
\(641\) −3.04221 −0.120160 −0.0600799 0.998194i \(-0.519136\pi\)
−0.0600799 + 0.998194i \(0.519136\pi\)
\(642\) 0 0
\(643\) −8.02922 −0.316641 −0.158321 0.987388i \(-0.550608\pi\)
−0.158321 + 0.987388i \(0.550608\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.905275 0.0356176
\(647\) 7.07324 0.278078 0.139039 0.990287i \(-0.455599\pi\)
0.139039 + 0.990287i \(0.455599\pi\)
\(648\) 0 0
\(649\) −27.3776 −1.07466
\(650\) −2.22154 −0.0871361
\(651\) 0 0
\(652\) −11.3484 −0.444436
\(653\) 15.7586 0.616681 0.308341 0.951276i \(-0.400226\pi\)
0.308341 + 0.951276i \(0.400226\pi\)
\(654\) 0 0
\(655\) 5.61899 0.219552
\(656\) 17.6742 0.690061
\(657\) 0 0
\(658\) 0 0
\(659\) 12.2181 0.475950 0.237975 0.971271i \(-0.423516\pi\)
0.237975 + 0.971271i \(0.423516\pi\)
\(660\) 0 0
\(661\) −3.73443 −0.145253 −0.0726263 0.997359i \(-0.523138\pi\)
−0.0726263 + 0.997359i \(0.523138\pi\)
\(662\) −14.8501 −0.577165
\(663\) 0 0
\(664\) −29.0777 −1.12844
\(665\) 0 0
\(666\) 0 0
\(667\) 30.4786 1.18014
\(668\) 29.4948 1.14119
\(669\) 0 0
\(670\) 3.97078 0.153405
\(671\) 4.49828 0.173654
\(672\) 0 0
\(673\) −5.65775 −0.218090 −0.109045 0.994037i \(-0.534779\pi\)
−0.109045 + 0.994037i \(0.534779\pi\)
\(674\) 3.96629 0.152776
\(675\) 0 0
\(676\) −1.77846 −0.0684022
\(677\) 9.39906 0.361235 0.180618 0.983553i \(-0.442190\pi\)
0.180618 + 0.983553i \(0.442190\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.23109 −0.0472103
\(681\) 0 0
\(682\) −7.43965 −0.284879
\(683\) 20.7328 0.793319 0.396660 0.917966i \(-0.370169\pi\)
0.396660 + 0.917966i \(0.370169\pi\)
\(684\) 0 0
\(685\) −6.01461 −0.229806
\(686\) 0 0
\(687\) 0 0
\(688\) 30.9897 1.18147
\(689\) 11.2767 0.429610
\(690\) 0 0
\(691\) −16.0862 −0.611949 −0.305975 0.952040i \(-0.598982\pi\)
−0.305975 + 0.952040i \(0.598982\pi\)
\(692\) 41.4396 1.57530
\(693\) 0 0
\(694\) 9.10695 0.345695
\(695\) 7.36984 0.279554
\(696\) 0 0
\(697\) −8.49828 −0.321895
\(698\) 12.8286 0.485570
\(699\) 0 0
\(700\) 0 0
\(701\) 6.98013 0.263636 0.131818 0.991274i \(-0.457919\pi\)
0.131818 + 0.991274i \(0.457919\pi\)
\(702\) 0 0
\(703\) −3.48024 −0.131260
\(704\) −7.11383 −0.268112
\(705\) 0 0
\(706\) 12.0844 0.454803
\(707\) 0 0
\(708\) 0 0
\(709\) 8.39239 0.315183 0.157591 0.987504i \(-0.449627\pi\)
0.157591 + 0.987504i \(0.449627\pi\)
\(710\) 0.296604 0.0111313
\(711\) 0 0
\(712\) 12.2897 0.460577
\(713\) −41.0207 −1.53624
\(714\) 0 0
\(715\) −1.19051 −0.0445225
\(716\) 37.4227 1.39855
\(717\) 0 0
\(718\) −11.0225 −0.411358
\(719\) −5.16129 −0.192484 −0.0962418 0.995358i \(-0.530682\pi\)
−0.0962418 + 0.995358i \(0.530682\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 7.92494 0.294936
\(723\) 0 0
\(724\) 29.7846 1.10693
\(725\) 24.6448 0.915284
\(726\) 0 0
\(727\) 40.4362 1.49970 0.749848 0.661610i \(-0.230127\pi\)
0.749848 + 0.661610i \(0.230127\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 1.90422 0.0704782
\(731\) −14.9008 −0.551125
\(732\) 0 0
\(733\) 39.1311 1.44534 0.722670 0.691193i \(-0.242915\pi\)
0.722670 + 0.691193i \(0.242915\pi\)
\(734\) −6.91215 −0.255132
\(735\) 0 0
\(736\) 28.2345 1.04074
\(737\) −35.8466 −1.32043
\(738\) 0 0
\(739\) −7.13531 −0.262477 −0.131238 0.991351i \(-0.541895\pi\)
−0.131238 + 0.991351i \(0.541895\pi\)
\(740\) 2.22766 0.0818903
\(741\) 0 0
\(742\) 0 0
\(743\) −13.8827 −0.509308 −0.254654 0.967032i \(-0.581962\pi\)
−0.254654 + 0.967032i \(0.581962\pi\)
\(744\) 0 0
\(745\) −4.92676 −0.180502
\(746\) 11.1398 0.407857
\(747\) 0 0
\(748\) 5.23109 0.191268
\(749\) 0 0
\(750\) 0 0
\(751\) −37.3251 −1.36201 −0.681005 0.732278i \(-0.738457\pi\)
−0.681005 + 0.732278i \(0.738457\pi\)
\(752\) 23.3484 0.851427
\(753\) 0 0
\(754\) −2.45769 −0.0895039
\(755\) 3.74398 0.136258
\(756\) 0 0
\(757\) −7.10428 −0.258209 −0.129105 0.991631i \(-0.541210\pi\)
−0.129105 + 0.991631i \(0.541210\pi\)
\(758\) 15.4104 0.559732
\(759\) 0 0
\(760\) 1.38445 0.0502194
\(761\) −25.9621 −0.941125 −0.470562 0.882367i \(-0.655949\pi\)
−0.470562 + 0.882367i \(0.655949\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −13.2311 −0.478684
\(765\) 0 0
\(766\) 10.6448 0.384611
\(767\) 12.1725 0.439522
\(768\) 0 0
\(769\) 21.4638 0.774005 0.387002 0.922079i \(-0.373511\pi\)
0.387002 + 0.922079i \(0.373511\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.67074 0.0961221
\(773\) −40.4914 −1.45637 −0.728187 0.685378i \(-0.759637\pi\)
−0.728187 + 0.685378i \(0.759637\pi\)
\(774\) 0 0
\(775\) −33.1690 −1.19147
\(776\) 6.17246 0.221578
\(777\) 0 0
\(778\) 17.9087 0.642058
\(779\) 9.55691 0.342412
\(780\) 0 0
\(781\) −2.67762 −0.0958127
\(782\) −3.59301 −0.128486
\(783\) 0 0
\(784\) 0 0
\(785\) 3.19738 0.114119
\(786\) 0 0
\(787\) 5.02072 0.178969 0.0894847 0.995988i \(-0.471478\pi\)
0.0894847 + 0.995988i \(0.471478\pi\)
\(788\) 42.6707 1.52008
\(789\) 0 0
\(790\) 0.333552 0.0118672
\(791\) 0 0
\(792\) 0 0
\(793\) −2.00000 −0.0710221
\(794\) −5.50945 −0.195523
\(795\) 0 0
\(796\) −3.58289 −0.126992
\(797\) 19.7002 0.697815 0.348908 0.937157i \(-0.386553\pi\)
0.348908 + 0.937157i \(0.386553\pi\)
\(798\) 0 0
\(799\) −11.2266 −0.397169
\(800\) 22.8302 0.807170
\(801\) 0 0
\(802\) 1.67418 0.0591174
\(803\) −17.1905 −0.606640
\(804\) 0 0
\(805\) 0 0
\(806\) 3.30777 0.116511
\(807\) 0 0
\(808\) 13.7846 0.484940
\(809\) 2.57678 0.0905947 0.0452974 0.998974i \(-0.485576\pi\)
0.0452974 + 0.998974i \(0.485576\pi\)
\(810\) 0 0
\(811\) −41.2311 −1.44782 −0.723910 0.689895i \(-0.757657\pi\)
−0.723910 + 0.689895i \(0.757657\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 2.50516 0.0878057
\(815\) 3.37758 0.118311
\(816\) 0 0
\(817\) 16.7570 0.586252
\(818\) 2.47680 0.0865992
\(819\) 0 0
\(820\) −6.11727 −0.213624
\(821\) −5.26719 −0.183826 −0.0919130 0.995767i \(-0.529298\pi\)
−0.0919130 + 0.995767i \(0.529298\pi\)
\(822\) 0 0
\(823\) 36.0191 1.25555 0.627774 0.778396i \(-0.283966\pi\)
0.627774 + 0.778396i \(0.283966\pi\)
\(824\) 30.2277 1.05303
\(825\) 0 0
\(826\) 0 0
\(827\) 16.3157 0.567353 0.283676 0.958920i \(-0.408446\pi\)
0.283676 + 0.958920i \(0.408446\pi\)
\(828\) 0 0
\(829\) 30.3956 1.05568 0.527842 0.849343i \(-0.323001\pi\)
0.527842 + 0.849343i \(0.323001\pi\)
\(830\) 4.07344 0.141391
\(831\) 0 0
\(832\) 3.16291 0.109654
\(833\) 0 0
\(834\) 0 0
\(835\) −8.77846 −0.303791
\(836\) −5.88273 −0.203459
\(837\) 0 0
\(838\) −12.2536 −0.423295
\(839\) 29.8398 1.03018 0.515092 0.857135i \(-0.327758\pi\)
0.515092 + 0.857135i \(0.327758\pi\)
\(840\) 0 0
\(841\) −1.73549 −0.0598445
\(842\) −10.4691 −0.360788
\(843\) 0 0
\(844\) −17.9639 −0.618343
\(845\) 0.529317 0.0182090
\(846\) 0 0
\(847\) 0 0
\(848\) −30.6707 −1.05324
\(849\) 0 0
\(850\) −2.90528 −0.0996501
\(851\) 13.8129 0.473501
\(852\) 0 0
\(853\) 0.203497 0.00696761 0.00348380 0.999994i \(-0.498891\pi\)
0.00348380 + 0.999994i \(0.498891\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 9.88273 0.337785
\(857\) −12.6155 −0.430939 −0.215469 0.976511i \(-0.569128\pi\)
−0.215469 + 0.976511i \(0.569128\pi\)
\(858\) 0 0
\(859\) 27.9671 0.954227 0.477113 0.878842i \(-0.341683\pi\)
0.477113 + 0.878842i \(0.341683\pi\)
\(860\) −10.7259 −0.365751
\(861\) 0 0
\(862\) 13.0258 0.443660
\(863\) 2.76891 0.0942546 0.0471273 0.998889i \(-0.484993\pi\)
0.0471273 + 0.998889i \(0.484993\pi\)
\(864\) 0 0
\(865\) −12.3336 −0.419353
\(866\) −6.01910 −0.204537
\(867\) 0 0
\(868\) 0 0
\(869\) −3.01117 −0.102147
\(870\) 0 0
\(871\) 15.9379 0.540036
\(872\) 14.0913 0.477191
\(873\) 0 0
\(874\) 4.04059 0.136675
\(875\) 0 0
\(876\) 0 0
\(877\) 6.71133 0.226626 0.113313 0.993559i \(-0.463854\pi\)
0.113313 + 0.993559i \(0.463854\pi\)
\(878\) −8.55024 −0.288557
\(879\) 0 0
\(880\) 3.23797 0.109152
\(881\) −18.3741 −0.619040 −0.309520 0.950893i \(-0.600168\pi\)
−0.309520 + 0.950893i \(0.600168\pi\)
\(882\) 0 0
\(883\) 9.93105 0.334207 0.167103 0.985939i \(-0.446559\pi\)
0.167103 + 0.985939i \(0.446559\pi\)
\(884\) −2.32582 −0.0782258
\(885\) 0 0
\(886\) 0.0506994 0.00170328
\(887\) −51.3776 −1.72509 −0.862545 0.505980i \(-0.831131\pi\)
−0.862545 + 0.505980i \(0.831131\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1.72164 −0.0577096
\(891\) 0 0
\(892\) 18.0361 0.603893
\(893\) 12.6251 0.422483
\(894\) 0 0
\(895\) −11.1380 −0.372302
\(896\) 0 0
\(897\) 0 0
\(898\) −10.4362 −0.348261
\(899\) −36.6949 −1.22384
\(900\) 0 0
\(901\) 14.7474 0.491308
\(902\) −6.87930 −0.229055
\(903\) 0 0
\(904\) 17.5930 0.585135
\(905\) −8.86469 −0.294672
\(906\) 0 0
\(907\) 4.34225 0.144182 0.0720910 0.997398i \(-0.477033\pi\)
0.0720910 + 0.997398i \(0.477033\pi\)
\(908\) 9.57602 0.317791
\(909\) 0 0
\(910\) 0 0
\(911\) −31.4853 −1.04315 −0.521577 0.853204i \(-0.674656\pi\)
−0.521577 + 0.853204i \(0.674656\pi\)
\(912\) 0 0
\(913\) −36.7734 −1.21702
\(914\) −2.05196 −0.0678728
\(915\) 0 0
\(916\) 5.90871 0.195229
\(917\) 0 0
\(918\) 0 0
\(919\) 43.4588 1.43357 0.716786 0.697293i \(-0.245612\pi\)
0.716786 + 0.697293i \(0.245612\pi\)
\(920\) −5.49484 −0.181160
\(921\) 0 0
\(922\) −15.2412 −0.501942
\(923\) 1.19051 0.0391860
\(924\) 0 0
\(925\) 11.1690 0.367235
\(926\) −3.93793 −0.129408
\(927\) 0 0
\(928\) 25.2571 0.829104
\(929\) 4.40517 0.144529 0.0722645 0.997385i \(-0.476977\pi\)
0.0722645 + 0.997385i \(0.476977\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 24.4001 0.799252
\(933\) 0 0
\(934\) 9.19824 0.300976
\(935\) −1.55691 −0.0509165
\(936\) 0 0
\(937\) 34.0990 1.11397 0.556983 0.830524i \(-0.311959\pi\)
0.556983 + 0.830524i \(0.311959\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −8.08117 −0.263579
\(941\) 44.4672 1.44959 0.724795 0.688964i \(-0.241934\pi\)
0.724795 + 0.688964i \(0.241934\pi\)
\(942\) 0 0
\(943\) −37.9311 −1.23521
\(944\) −33.1070 −1.07754
\(945\) 0 0
\(946\) −12.0621 −0.392172
\(947\) −57.9311 −1.88251 −0.941253 0.337702i \(-0.890350\pi\)
−0.941253 + 0.337702i \(0.890350\pi\)
\(948\) 0 0
\(949\) 7.64315 0.248107
\(950\) 3.26719 0.106002
\(951\) 0 0
\(952\) 0 0
\(953\) −35.3060 −1.14367 −0.571836 0.820368i \(-0.693769\pi\)
−0.571836 + 0.820368i \(0.693769\pi\)
\(954\) 0 0
\(955\) 3.93793 0.127428
\(956\) −6.22766 −0.201417
\(957\) 0 0
\(958\) 13.4250 0.433743
\(959\) 0 0
\(960\) 0 0
\(961\) 18.3871 0.593133
\(962\) −1.11383 −0.0359113
\(963\) 0 0
\(964\) 2.82410 0.0909582
\(965\) −0.794885 −0.0255882
\(966\) 0 0
\(967\) 23.7148 0.762616 0.381308 0.924448i \(-0.375474\pi\)
0.381308 + 0.924448i \(0.375474\pi\)
\(968\) −10.5665 −0.339619
\(969\) 0 0
\(970\) −0.864688 −0.0277635
\(971\) −23.9379 −0.768205 −0.384102 0.923291i \(-0.625489\pi\)
−0.384102 + 0.923291i \(0.625489\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −11.6843 −0.374389
\(975\) 0 0
\(976\) 5.43965 0.174119
\(977\) 16.1871 0.517870 0.258935 0.965895i \(-0.416628\pi\)
0.258935 + 0.965895i \(0.416628\pi\)
\(978\) 0 0
\(979\) 15.5423 0.496734
\(980\) 0 0
\(981\) 0 0
\(982\) 13.7294 0.438122
\(983\) 45.7243 1.45838 0.729190 0.684312i \(-0.239897\pi\)
0.729190 + 0.684312i \(0.239897\pi\)
\(984\) 0 0
\(985\) −12.7000 −0.404654
\(986\) −3.21411 −0.102358
\(987\) 0 0
\(988\) 2.61555 0.0832116
\(989\) −66.5078 −2.11483
\(990\) 0 0
\(991\) −5.40356 −0.171650 −0.0858248 0.996310i \(-0.527353\pi\)
−0.0858248 + 0.996310i \(0.527353\pi\)
\(992\) −33.9931 −1.07928
\(993\) 0 0
\(994\) 0 0
\(995\) 1.06637 0.0338061
\(996\) 0 0
\(997\) −6.04832 −0.191552 −0.0957761 0.995403i \(-0.530533\pi\)
−0.0957761 + 0.995403i \(0.530533\pi\)
\(998\) 15.6742 0.496158
\(999\) 0 0
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 5733.2.a.x.1.2 3
3.2 odd 2 637.2.a.j.1.2 3
7.6 odd 2 819.2.a.i.1.2 3
21.2 odd 6 637.2.e.i.508.2 6
21.5 even 6 637.2.e.j.508.2 6
21.11 odd 6 637.2.e.i.79.2 6
21.17 even 6 637.2.e.j.79.2 6
21.20 even 2 91.2.a.d.1.2 3
39.38 odd 2 8281.2.a.bg.1.2 3
84.83 odd 2 1456.2.a.t.1.1 3
105.104 even 2 2275.2.a.m.1.2 3
168.83 odd 2 5824.2.a.bs.1.3 3
168.125 even 2 5824.2.a.by.1.1 3
273.83 odd 4 1183.2.c.f.337.3 6
273.125 odd 4 1183.2.c.f.337.4 6
273.272 even 2 1183.2.a.i.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.a.d.1.2 3 21.20 even 2
637.2.a.j.1.2 3 3.2 odd 2
637.2.e.i.79.2 6 21.11 odd 6
637.2.e.i.508.2 6 21.2 odd 6
637.2.e.j.79.2 6 21.17 even 6
637.2.e.j.508.2 6 21.5 even 6
819.2.a.i.1.2 3 7.6 odd 2
1183.2.a.i.1.2 3 273.272 even 2
1183.2.c.f.337.3 6 273.83 odd 4
1183.2.c.f.337.4 6 273.125 odd 4
1456.2.a.t.1.1 3 84.83 odd 2
2275.2.a.m.1.2 3 105.104 even 2
5733.2.a.x.1.2 3 1.1 even 1 trivial
5824.2.a.bs.1.3 3 168.83 odd 2
5824.2.a.by.1.1 3 168.125 even 2
8281.2.a.bg.1.2 3 39.38 odd 2