Properties

Label 1441.2.a.e.1.3
Level $1441$
Weight $2$
Character 1441.1
Self dual yes
Analytic conductor $11.506$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(11.5064429313\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) \(=\) 1441.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.33619 q^{2} +2.29063 q^{3} +3.45776 q^{4} -0.314509 q^{5} -5.35135 q^{6} +0.543204 q^{7} -3.40560 q^{8} +2.24701 q^{9} +O(q^{10})\) \(q-2.33619 q^{2} +2.29063 q^{3} +3.45776 q^{4} -0.314509 q^{5} -5.35135 q^{6} +0.543204 q^{7} -3.40560 q^{8} +2.24701 q^{9} +0.734752 q^{10} +1.00000 q^{11} +7.92047 q^{12} +6.37371 q^{13} -1.26903 q^{14} -0.720426 q^{15} +1.04060 q^{16} +7.80692 q^{17} -5.24942 q^{18} -4.51268 q^{19} -1.08750 q^{20} +1.24428 q^{21} -2.33619 q^{22} +3.63556 q^{23} -7.80099 q^{24} -4.90108 q^{25} -14.8902 q^{26} -1.72483 q^{27} +1.87827 q^{28} +1.45649 q^{29} +1.68305 q^{30} -3.82273 q^{31} +4.38018 q^{32} +2.29063 q^{33} -18.2384 q^{34} -0.170843 q^{35} +7.76961 q^{36} -1.07120 q^{37} +10.5425 q^{38} +14.5998 q^{39} +1.07109 q^{40} +4.72274 q^{41} -2.90687 q^{42} +0.536888 q^{43} +3.45776 q^{44} -0.706705 q^{45} -8.49333 q^{46} +2.22765 q^{47} +2.38362 q^{48} -6.70493 q^{49} +11.4498 q^{50} +17.8828 q^{51} +22.0388 q^{52} -3.76717 q^{53} +4.02953 q^{54} -0.314509 q^{55} -1.84994 q^{56} -10.3369 q^{57} -3.40263 q^{58} +9.78696 q^{59} -2.49106 q^{60} -4.79737 q^{61} +8.93061 q^{62} +1.22058 q^{63} -12.3141 q^{64} -2.00459 q^{65} -5.35135 q^{66} +15.1411 q^{67} +26.9945 q^{68} +8.32773 q^{69} +0.399121 q^{70} +8.17140 q^{71} -7.65241 q^{72} +10.2037 q^{73} +2.50252 q^{74} -11.2266 q^{75} -15.6038 q^{76} +0.543204 q^{77} -34.1079 q^{78} -14.4673 q^{79} -0.327277 q^{80} -10.6920 q^{81} -11.0332 q^{82} +2.12709 q^{83} +4.30243 q^{84} -2.45535 q^{85} -1.25427 q^{86} +3.33629 q^{87} -3.40560 q^{88} -7.45804 q^{89} +1.65099 q^{90} +3.46223 q^{91} +12.5709 q^{92} -8.75648 q^{93} -5.20420 q^{94} +1.41928 q^{95} +10.0334 q^{96} -0.288063 q^{97} +15.6640 q^{98} +2.24701 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + O(q^{10}) \) \( 28 q + 7 q^{2} - 2 q^{3} + 27 q^{4} + 3 q^{5} - q^{6} + 7 q^{7} + 21 q^{8} + 28 q^{9} + 14 q^{10} + 28 q^{11} - 6 q^{12} + 3 q^{13} - q^{14} + 19 q^{15} + 29 q^{16} + 9 q^{17} - 2 q^{18} + 20 q^{19} + 6 q^{20} + 6 q^{21} + 7 q^{22} + 24 q^{23} + 20 q^{24} + 23 q^{25} + 10 q^{26} - 20 q^{27} - 3 q^{28} + 43 q^{29} + 11 q^{30} + 3 q^{31} + 44 q^{32} - 2 q^{33} - 28 q^{34} + 32 q^{35} + 24 q^{36} - 4 q^{37} + 24 q^{38} + 37 q^{39} + 22 q^{40} + 32 q^{41} - 27 q^{42} + 25 q^{43} + 27 q^{44} - 36 q^{45} + 10 q^{46} + 19 q^{47} + 42 q^{48} + 17 q^{49} + q^{50} + 39 q^{51} - 19 q^{52} + 5 q^{53} + 6 q^{54} + 3 q^{55} + 8 q^{56} + 2 q^{57} + 21 q^{58} + 44 q^{59} + 65 q^{60} + 28 q^{61} + 60 q^{62} - 8 q^{63} + 5 q^{64} + 33 q^{65} - q^{66} + 7 q^{67} + 13 q^{68} - 22 q^{69} + 9 q^{70} + 117 q^{71} - 17 q^{72} + 7 q^{73} + 41 q^{74} - 40 q^{75} + 34 q^{76} + 7 q^{77} - 97 q^{78} + 48 q^{79} + 41 q^{80} + 40 q^{81} + 2 q^{82} + 22 q^{83} + 27 q^{84} + 30 q^{85} + 24 q^{86} + 37 q^{87} + 21 q^{88} - 6 q^{89} + 4 q^{90} - 33 q^{91} + 18 q^{92} + 5 q^{93} - 43 q^{94} + 64 q^{95} + 55 q^{96} - 50 q^{97} + 97 q^{98} + 28 q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.33619 −1.65193 −0.825966 0.563720i \(-0.809370\pi\)
−0.825966 + 0.563720i \(0.809370\pi\)
\(3\) 2.29063 1.32250 0.661249 0.750166i \(-0.270027\pi\)
0.661249 + 0.750166i \(0.270027\pi\)
\(4\) 3.45776 1.72888
\(5\) −0.314509 −0.140653 −0.0703265 0.997524i \(-0.522404\pi\)
−0.0703265 + 0.997524i \(0.522404\pi\)
\(6\) −5.35135 −2.18468
\(7\) 0.543204 0.205312 0.102656 0.994717i \(-0.467266\pi\)
0.102656 + 0.994717i \(0.467266\pi\)
\(8\) −3.40560 −1.20406
\(9\) 2.24701 0.749002
\(10\) 0.734752 0.232349
\(11\) 1.00000 0.301511
\(12\) 7.92047 2.28644
\(13\) 6.37371 1.76775 0.883875 0.467723i \(-0.154926\pi\)
0.883875 + 0.467723i \(0.154926\pi\)
\(14\) −1.26903 −0.339161
\(15\) −0.720426 −0.186013
\(16\) 1.04060 0.260149
\(17\) 7.80692 1.89346 0.946728 0.322035i \(-0.104367\pi\)
0.946728 + 0.322035i \(0.104367\pi\)
\(18\) −5.24942 −1.23730
\(19\) −4.51268 −1.03528 −0.517640 0.855599i \(-0.673189\pi\)
−0.517640 + 0.855599i \(0.673189\pi\)
\(20\) −1.08750 −0.243172
\(21\) 1.24428 0.271525
\(22\) −2.33619 −0.498076
\(23\) 3.63556 0.758066 0.379033 0.925383i \(-0.376257\pi\)
0.379033 + 0.925383i \(0.376257\pi\)
\(24\) −7.80099 −1.59237
\(25\) −4.90108 −0.980217
\(26\) −14.8902 −2.92020
\(27\) −1.72483 −0.331944
\(28\) 1.87827 0.354960
\(29\) 1.45649 0.270464 0.135232 0.990814i \(-0.456822\pi\)
0.135232 + 0.990814i \(0.456822\pi\)
\(30\) 1.68305 0.307281
\(31\) −3.82273 −0.686583 −0.343291 0.939229i \(-0.611542\pi\)
−0.343291 + 0.939229i \(0.611542\pi\)
\(32\) 4.38018 0.774314
\(33\) 2.29063 0.398748
\(34\) −18.2384 −3.12786
\(35\) −0.170843 −0.0288777
\(36\) 7.76961 1.29494
\(37\) −1.07120 −0.176104 −0.0880520 0.996116i \(-0.528064\pi\)
−0.0880520 + 0.996116i \(0.528064\pi\)
\(38\) 10.5425 1.71021
\(39\) 14.5998 2.33785
\(40\) 1.07109 0.169355
\(41\) 4.72274 0.737568 0.368784 0.929515i \(-0.379774\pi\)
0.368784 + 0.929515i \(0.379774\pi\)
\(42\) −2.90687 −0.448540
\(43\) 0.536888 0.0818747 0.0409373 0.999162i \(-0.486966\pi\)
0.0409373 + 0.999162i \(0.486966\pi\)
\(44\) 3.45776 0.521277
\(45\) −0.706705 −0.105349
\(46\) −8.49333 −1.25227
\(47\) 2.22765 0.324936 0.162468 0.986714i \(-0.448055\pi\)
0.162468 + 0.986714i \(0.448055\pi\)
\(48\) 2.38362 0.344046
\(49\) −6.70493 −0.957847
\(50\) 11.4498 1.61925
\(51\) 17.8828 2.50409
\(52\) 22.0388 3.05623
\(53\) −3.76717 −0.517461 −0.258731 0.965950i \(-0.583304\pi\)
−0.258731 + 0.965950i \(0.583304\pi\)
\(54\) 4.02953 0.548349
\(55\) −0.314509 −0.0424085
\(56\) −1.84994 −0.247208
\(57\) −10.3369 −1.36916
\(58\) −3.40263 −0.446788
\(59\) 9.78696 1.27415 0.637077 0.770800i \(-0.280143\pi\)
0.637077 + 0.770800i \(0.280143\pi\)
\(60\) −2.49106 −0.321595
\(61\) −4.79737 −0.614240 −0.307120 0.951671i \(-0.599365\pi\)
−0.307120 + 0.951671i \(0.599365\pi\)
\(62\) 8.93061 1.13419
\(63\) 1.22058 0.153779
\(64\) −12.3141 −1.53926
\(65\) −2.00459 −0.248639
\(66\) −5.35135 −0.658705
\(67\) 15.1411 1.84978 0.924888 0.380240i \(-0.124159\pi\)
0.924888 + 0.380240i \(0.124159\pi\)
\(68\) 26.9945 3.27356
\(69\) 8.32773 1.00254
\(70\) 0.399121 0.0477040
\(71\) 8.17140 0.969767 0.484883 0.874579i \(-0.338862\pi\)
0.484883 + 0.874579i \(0.338862\pi\)
\(72\) −7.65241 −0.901845
\(73\) 10.2037 1.19425 0.597126 0.802147i \(-0.296309\pi\)
0.597126 + 0.802147i \(0.296309\pi\)
\(74\) 2.50252 0.290912
\(75\) −11.2266 −1.29634
\(76\) −15.6038 −1.78988
\(77\) 0.543204 0.0619039
\(78\) −34.1079 −3.86196
\(79\) −14.4673 −1.62769 −0.813847 0.581079i \(-0.802631\pi\)
−0.813847 + 0.581079i \(0.802631\pi\)
\(80\) −0.327277 −0.0365907
\(81\) −10.6920 −1.18800
\(82\) −11.0332 −1.21841
\(83\) 2.12709 0.233479 0.116739 0.993163i \(-0.462756\pi\)
0.116739 + 0.993163i \(0.462756\pi\)
\(84\) 4.30243 0.469434
\(85\) −2.45535 −0.266320
\(86\) −1.25427 −0.135251
\(87\) 3.33629 0.357688
\(88\) −3.40560 −0.363038
\(89\) −7.45804 −0.790551 −0.395275 0.918563i \(-0.629351\pi\)
−0.395275 + 0.918563i \(0.629351\pi\)
\(90\) 1.65099 0.174030
\(91\) 3.46223 0.362940
\(92\) 12.5709 1.31061
\(93\) −8.75648 −0.908004
\(94\) −5.20420 −0.536772
\(95\) 1.41928 0.145615
\(96\) 10.0334 1.02403
\(97\) −0.288063 −0.0292484 −0.0146242 0.999893i \(-0.504655\pi\)
−0.0146242 + 0.999893i \(0.504655\pi\)
\(98\) 15.6640 1.58230
\(99\) 2.24701 0.225833
\(100\) −16.9468 −1.69468
\(101\) −5.67036 −0.564222 −0.282111 0.959382i \(-0.591035\pi\)
−0.282111 + 0.959382i \(0.591035\pi\)
\(102\) −41.7775 −4.13659
\(103\) 0.0917267 0.00903810 0.00451905 0.999990i \(-0.498562\pi\)
0.00451905 + 0.999990i \(0.498562\pi\)
\(104\) −21.7063 −2.12848
\(105\) −0.391339 −0.0381907
\(106\) 8.80082 0.854811
\(107\) 6.80587 0.657949 0.328974 0.944339i \(-0.393297\pi\)
0.328974 + 0.944339i \(0.393297\pi\)
\(108\) −5.96406 −0.573892
\(109\) 5.44692 0.521721 0.260860 0.965377i \(-0.415994\pi\)
0.260860 + 0.965377i \(0.415994\pi\)
\(110\) 0.734752 0.0700559
\(111\) −2.45372 −0.232897
\(112\) 0.565256 0.0534116
\(113\) −17.5873 −1.65448 −0.827238 0.561851i \(-0.810089\pi\)
−0.827238 + 0.561851i \(0.810089\pi\)
\(114\) 24.1489 2.26175
\(115\) −1.14342 −0.106624
\(116\) 5.03620 0.467599
\(117\) 14.3218 1.32405
\(118\) −22.8641 −2.10482
\(119\) 4.24075 0.388749
\(120\) 2.45349 0.223972
\(121\) 1.00000 0.0909091
\(122\) 11.2075 1.01468
\(123\) 10.8181 0.975432
\(124\) −13.2181 −1.18702
\(125\) 3.11398 0.278523
\(126\) −2.85151 −0.254033
\(127\) 11.8787 1.05406 0.527030 0.849846i \(-0.323305\pi\)
0.527030 + 0.849846i \(0.323305\pi\)
\(128\) 20.0077 1.76845
\(129\) 1.22981 0.108279
\(130\) 4.68310 0.410735
\(131\) −1.00000 −0.0873704
\(132\) 7.92047 0.689388
\(133\) −2.45131 −0.212555
\(134\) −35.3723 −3.05570
\(135\) 0.542476 0.0466889
\(136\) −26.5873 −2.27984
\(137\) 9.56395 0.817103 0.408552 0.912735i \(-0.366034\pi\)
0.408552 + 0.912735i \(0.366034\pi\)
\(138\) −19.4551 −1.65613
\(139\) 16.4826 1.39804 0.699019 0.715103i \(-0.253620\pi\)
0.699019 + 0.715103i \(0.253620\pi\)
\(140\) −0.590734 −0.0499261
\(141\) 5.10273 0.429727
\(142\) −19.0899 −1.60199
\(143\) 6.37371 0.532997
\(144\) 2.33822 0.194852
\(145\) −0.458080 −0.0380415
\(146\) −23.8377 −1.97283
\(147\) −15.3585 −1.26675
\(148\) −3.70395 −0.304463
\(149\) 4.34525 0.355977 0.177988 0.984033i \(-0.443041\pi\)
0.177988 + 0.984033i \(0.443041\pi\)
\(150\) 26.2274 2.14146
\(151\) −1.55343 −0.126416 −0.0632082 0.998000i \(-0.520133\pi\)
−0.0632082 + 0.998000i \(0.520133\pi\)
\(152\) 15.3684 1.24654
\(153\) 17.5422 1.41820
\(154\) −1.26903 −0.102261
\(155\) 1.20228 0.0965698
\(156\) 50.4828 4.04186
\(157\) 3.81663 0.304600 0.152300 0.988334i \(-0.451332\pi\)
0.152300 + 0.988334i \(0.451332\pi\)
\(158\) 33.7982 2.68884
\(159\) −8.62922 −0.684342
\(160\) −1.37761 −0.108910
\(161\) 1.97485 0.155640
\(162\) 24.9784 1.96249
\(163\) −20.0385 −1.56953 −0.784766 0.619792i \(-0.787217\pi\)
−0.784766 + 0.619792i \(0.787217\pi\)
\(164\) 16.3301 1.27517
\(165\) −0.720426 −0.0560851
\(166\) −4.96928 −0.385691
\(167\) 25.4400 1.96861 0.984304 0.176483i \(-0.0564722\pi\)
0.984304 + 0.176483i \(0.0564722\pi\)
\(168\) −4.23753 −0.326933
\(169\) 27.6242 2.12494
\(170\) 5.73615 0.439943
\(171\) −10.1400 −0.775427
\(172\) 1.85643 0.141552
\(173\) −24.6773 −1.87618 −0.938088 0.346396i \(-0.887405\pi\)
−0.938088 + 0.346396i \(0.887405\pi\)
\(174\) −7.79419 −0.590876
\(175\) −2.66229 −0.201250
\(176\) 1.04060 0.0784378
\(177\) 22.4183 1.68507
\(178\) 17.4234 1.30594
\(179\) −10.3609 −0.774411 −0.387205 0.921994i \(-0.626560\pi\)
−0.387205 + 0.921994i \(0.626560\pi\)
\(180\) −2.44362 −0.182137
\(181\) −11.3881 −0.846474 −0.423237 0.906019i \(-0.639106\pi\)
−0.423237 + 0.906019i \(0.639106\pi\)
\(182\) −8.08840 −0.599552
\(183\) −10.9890 −0.812332
\(184\) −12.3813 −0.912759
\(185\) 0.336902 0.0247695
\(186\) 20.4568 1.49996
\(187\) 7.80692 0.570898
\(188\) 7.70268 0.561776
\(189\) −0.936936 −0.0681521
\(190\) −3.31570 −0.240546
\(191\) 3.38638 0.245030 0.122515 0.992467i \(-0.460904\pi\)
0.122515 + 0.992467i \(0.460904\pi\)
\(192\) −28.2071 −2.03567
\(193\) −4.21318 −0.303271 −0.151636 0.988436i \(-0.548454\pi\)
−0.151636 + 0.988436i \(0.548454\pi\)
\(194\) 0.672969 0.0483163
\(195\) −4.59179 −0.328825
\(196\) −23.1841 −1.65600
\(197\) 23.3051 1.66042 0.830210 0.557451i \(-0.188220\pi\)
0.830210 + 0.557451i \(0.188220\pi\)
\(198\) −5.24942 −0.373060
\(199\) 17.4522 1.23715 0.618576 0.785725i \(-0.287710\pi\)
0.618576 + 0.785725i \(0.287710\pi\)
\(200\) 16.6911 1.18024
\(201\) 34.6826 2.44633
\(202\) 13.2470 0.932057
\(203\) 0.791172 0.0555294
\(204\) 61.8344 4.32928
\(205\) −1.48535 −0.103741
\(206\) −0.214291 −0.0149303
\(207\) 8.16912 0.567793
\(208\) 6.63245 0.459878
\(209\) −4.51268 −0.312149
\(210\) 0.914239 0.0630885
\(211\) 10.3257 0.710849 0.355424 0.934705i \(-0.384336\pi\)
0.355424 + 0.934705i \(0.384336\pi\)
\(212\) −13.0260 −0.894629
\(213\) 18.7177 1.28252
\(214\) −15.8998 −1.08689
\(215\) −0.168856 −0.0115159
\(216\) 5.87409 0.399681
\(217\) −2.07652 −0.140964
\(218\) −12.7250 −0.861847
\(219\) 23.3730 1.57940
\(220\) −1.08750 −0.0733192
\(221\) 49.7590 3.34716
\(222\) 5.73236 0.384731
\(223\) 20.5939 1.37907 0.689533 0.724254i \(-0.257816\pi\)
0.689533 + 0.724254i \(0.257816\pi\)
\(224\) 2.37933 0.158976
\(225\) −11.0128 −0.734185
\(226\) 41.0873 2.73308
\(227\) −18.6562 −1.23826 −0.619128 0.785290i \(-0.712514\pi\)
−0.619128 + 0.785290i \(0.712514\pi\)
\(228\) −35.7425 −2.36711
\(229\) 3.48451 0.230263 0.115131 0.993350i \(-0.463271\pi\)
0.115131 + 0.993350i \(0.463271\pi\)
\(230\) 2.67123 0.176136
\(231\) 1.24428 0.0818678
\(232\) −4.96023 −0.325655
\(233\) −21.7891 −1.42745 −0.713727 0.700424i \(-0.752994\pi\)
−0.713727 + 0.700424i \(0.752994\pi\)
\(234\) −33.4583 −2.18724
\(235\) −0.700617 −0.0457032
\(236\) 33.8410 2.20286
\(237\) −33.1392 −2.15262
\(238\) −9.90718 −0.642187
\(239\) −3.75514 −0.242900 −0.121450 0.992598i \(-0.538754\pi\)
−0.121450 + 0.992598i \(0.538754\pi\)
\(240\) −0.749672 −0.0483911
\(241\) −1.40733 −0.0906542 −0.0453271 0.998972i \(-0.514433\pi\)
−0.0453271 + 0.998972i \(0.514433\pi\)
\(242\) −2.33619 −0.150176
\(243\) −19.3169 −1.23918
\(244\) −16.5882 −1.06195
\(245\) 2.10876 0.134724
\(246\) −25.2730 −1.61135
\(247\) −28.7625 −1.83012
\(248\) 13.0187 0.826688
\(249\) 4.87239 0.308775
\(250\) −7.27485 −0.460102
\(251\) 11.9983 0.757325 0.378663 0.925535i \(-0.376384\pi\)
0.378663 + 0.925535i \(0.376384\pi\)
\(252\) 4.22049 0.265866
\(253\) 3.63556 0.228565
\(254\) −27.7508 −1.74124
\(255\) −5.62431 −0.352208
\(256\) −22.1134 −1.38209
\(257\) 11.9080 0.742800 0.371400 0.928473i \(-0.378878\pi\)
0.371400 + 0.928473i \(0.378878\pi\)
\(258\) −2.87307 −0.178870
\(259\) −0.581880 −0.0361562
\(260\) −6.93141 −0.429868
\(261\) 3.27274 0.202578
\(262\) 2.33619 0.144330
\(263\) −22.2094 −1.36949 −0.684746 0.728782i \(-0.740087\pi\)
−0.684746 + 0.728782i \(0.740087\pi\)
\(264\) −7.80099 −0.480118
\(265\) 1.18481 0.0727824
\(266\) 5.72671 0.351127
\(267\) −17.0836 −1.04550
\(268\) 52.3542 3.19804
\(269\) −12.4304 −0.757898 −0.378949 0.925418i \(-0.623714\pi\)
−0.378949 + 0.925418i \(0.623714\pi\)
\(270\) −1.26732 −0.0771269
\(271\) −18.2743 −1.11009 −0.555043 0.831822i \(-0.687298\pi\)
−0.555043 + 0.831822i \(0.687298\pi\)
\(272\) 8.12384 0.492580
\(273\) 7.93070 0.479988
\(274\) −22.3432 −1.34980
\(275\) −4.90108 −0.295546
\(276\) 28.7953 1.73327
\(277\) 21.3833 1.28480 0.642400 0.766370i \(-0.277939\pi\)
0.642400 + 0.766370i \(0.277939\pi\)
\(278\) −38.5065 −2.30946
\(279\) −8.58970 −0.514252
\(280\) 0.581823 0.0347706
\(281\) 1.85893 0.110894 0.0554471 0.998462i \(-0.482342\pi\)
0.0554471 + 0.998462i \(0.482342\pi\)
\(282\) −11.9209 −0.709880
\(283\) −25.1027 −1.49220 −0.746102 0.665832i \(-0.768077\pi\)
−0.746102 + 0.665832i \(0.768077\pi\)
\(284\) 28.2548 1.67661
\(285\) 3.25105 0.192576
\(286\) −14.8902 −0.880474
\(287\) 2.56541 0.151431
\(288\) 9.84230 0.579963
\(289\) 43.9480 2.58517
\(290\) 1.07016 0.0628420
\(291\) −0.659847 −0.0386809
\(292\) 35.2820 2.06472
\(293\) −12.5964 −0.735891 −0.367946 0.929847i \(-0.619939\pi\)
−0.367946 + 0.929847i \(0.619939\pi\)
\(294\) 35.8804 2.09259
\(295\) −3.07809 −0.179213
\(296\) 3.64808 0.212040
\(297\) −1.72483 −0.100085
\(298\) −10.1513 −0.588049
\(299\) 23.1720 1.34007
\(300\) −38.8189 −2.24121
\(301\) 0.291640 0.0168098
\(302\) 3.62910 0.208831
\(303\) −12.9887 −0.746183
\(304\) −4.69587 −0.269327
\(305\) 1.50882 0.0863947
\(306\) −40.9818 −2.34277
\(307\) −10.6504 −0.607852 −0.303926 0.952696i \(-0.598298\pi\)
−0.303926 + 0.952696i \(0.598298\pi\)
\(308\) 1.87827 0.107024
\(309\) 0.210112 0.0119529
\(310\) −2.80876 −0.159527
\(311\) −17.1880 −0.974643 −0.487322 0.873223i \(-0.662026\pi\)
−0.487322 + 0.873223i \(0.662026\pi\)
\(312\) −49.7213 −2.81491
\(313\) −24.9637 −1.41103 −0.705516 0.708694i \(-0.749285\pi\)
−0.705516 + 0.708694i \(0.749285\pi\)
\(314\) −8.91635 −0.503179
\(315\) −0.383885 −0.0216295
\(316\) −50.0243 −2.81409
\(317\) −1.60050 −0.0898933 −0.0449466 0.998989i \(-0.514312\pi\)
−0.0449466 + 0.998989i \(0.514312\pi\)
\(318\) 20.1595 1.13049
\(319\) 1.45649 0.0815478
\(320\) 3.87290 0.216502
\(321\) 15.5898 0.870136
\(322\) −4.61361 −0.257107
\(323\) −35.2301 −1.96026
\(324\) −36.9703 −2.05391
\(325\) −31.2381 −1.73278
\(326\) 46.8135 2.59276
\(327\) 12.4769 0.689975
\(328\) −16.0838 −0.888078
\(329\) 1.21007 0.0667132
\(330\) 1.68305 0.0926488
\(331\) −19.3992 −1.06628 −0.533138 0.846028i \(-0.678987\pi\)
−0.533138 + 0.846028i \(0.678987\pi\)
\(332\) 7.35498 0.403657
\(333\) −2.40699 −0.131902
\(334\) −59.4326 −3.25201
\(335\) −4.76201 −0.260176
\(336\) 1.29479 0.0706368
\(337\) −26.6789 −1.45329 −0.726647 0.687011i \(-0.758923\pi\)
−0.726647 + 0.687011i \(0.758923\pi\)
\(338\) −64.5353 −3.51026
\(339\) −40.2861 −2.18804
\(340\) −8.49001 −0.460436
\(341\) −3.82273 −0.207012
\(342\) 23.6890 1.28095
\(343\) −7.44457 −0.401969
\(344\) −1.82843 −0.0985822
\(345\) −2.61915 −0.141010
\(346\) 57.6506 3.09932
\(347\) 22.1118 1.18703 0.593513 0.804825i \(-0.297741\pi\)
0.593513 + 0.804825i \(0.297741\pi\)
\(348\) 11.5361 0.618399
\(349\) −8.51031 −0.455546 −0.227773 0.973714i \(-0.573144\pi\)
−0.227773 + 0.973714i \(0.573144\pi\)
\(350\) 6.21960 0.332452
\(351\) −10.9936 −0.586794
\(352\) 4.38018 0.233465
\(353\) 28.5988 1.52216 0.761080 0.648658i \(-0.224670\pi\)
0.761080 + 0.648658i \(0.224670\pi\)
\(354\) −52.3734 −2.78362
\(355\) −2.56998 −0.136401
\(356\) −25.7881 −1.36677
\(357\) 9.71401 0.514120
\(358\) 24.2050 1.27927
\(359\) 12.0731 0.637196 0.318598 0.947890i \(-0.396788\pi\)
0.318598 + 0.947890i \(0.396788\pi\)
\(360\) 2.40676 0.126847
\(361\) 1.36428 0.0718042
\(362\) 26.6048 1.39832
\(363\) 2.29063 0.120227
\(364\) 11.9716 0.627480
\(365\) −3.20916 −0.167975
\(366\) 25.6724 1.34192
\(367\) 27.2886 1.42445 0.712227 0.701949i \(-0.247687\pi\)
0.712227 + 0.701949i \(0.247687\pi\)
\(368\) 3.78314 0.197210
\(369\) 10.6120 0.552440
\(370\) −0.787066 −0.0409176
\(371\) −2.04634 −0.106241
\(372\) −30.2778 −1.56983
\(373\) −20.0361 −1.03743 −0.518716 0.854947i \(-0.673590\pi\)
−0.518716 + 0.854947i \(0.673590\pi\)
\(374\) −18.2384 −0.943085
\(375\) 7.13300 0.368347
\(376\) −7.58649 −0.391243
\(377\) 9.28325 0.478112
\(378\) 2.18886 0.112583
\(379\) −4.54617 −0.233521 −0.116761 0.993160i \(-0.537251\pi\)
−0.116761 + 0.993160i \(0.537251\pi\)
\(380\) 4.90753 0.251751
\(381\) 27.2097 1.39399
\(382\) −7.91121 −0.404773
\(383\) 2.20834 0.112841 0.0564204 0.998407i \(-0.482031\pi\)
0.0564204 + 0.998407i \(0.482031\pi\)
\(384\) 45.8303 2.33877
\(385\) −0.170843 −0.00870696
\(386\) 9.84277 0.500984
\(387\) 1.20639 0.0613243
\(388\) −0.996054 −0.0505670
\(389\) −20.1882 −1.02358 −0.511791 0.859110i \(-0.671018\pi\)
−0.511791 + 0.859110i \(0.671018\pi\)
\(390\) 10.7273 0.543197
\(391\) 28.3825 1.43536
\(392\) 22.8343 1.15331
\(393\) −2.29063 −0.115547
\(394\) −54.4451 −2.74290
\(395\) 4.55009 0.228940
\(396\) 7.76961 0.390438
\(397\) −30.8583 −1.54873 −0.774367 0.632737i \(-0.781931\pi\)
−0.774367 + 0.632737i \(0.781931\pi\)
\(398\) −40.7715 −2.04369
\(399\) −5.61505 −0.281104
\(400\) −5.10004 −0.255002
\(401\) −17.0035 −0.849113 −0.424556 0.905401i \(-0.639570\pi\)
−0.424556 + 0.905401i \(0.639570\pi\)
\(402\) −81.0251 −4.04116
\(403\) −24.3650 −1.21371
\(404\) −19.6068 −0.975473
\(405\) 3.36273 0.167095
\(406\) −1.84832 −0.0917308
\(407\) −1.07120 −0.0530974
\(408\) −60.9017 −3.01508
\(409\) −3.98834 −0.197211 −0.0986053 0.995127i \(-0.531438\pi\)
−0.0986053 + 0.995127i \(0.531438\pi\)
\(410\) 3.47004 0.171373
\(411\) 21.9075 1.08062
\(412\) 0.317169 0.0156258
\(413\) 5.31632 0.261599
\(414\) −19.0846 −0.937956
\(415\) −0.668991 −0.0328395
\(416\) 27.9180 1.36879
\(417\) 37.7557 1.84890
\(418\) 10.5425 0.515648
\(419\) −17.9681 −0.877801 −0.438900 0.898536i \(-0.644632\pi\)
−0.438900 + 0.898536i \(0.644632\pi\)
\(420\) −1.35316 −0.0660272
\(421\) −17.6538 −0.860392 −0.430196 0.902736i \(-0.641556\pi\)
−0.430196 + 0.902736i \(0.641556\pi\)
\(422\) −24.1227 −1.17427
\(423\) 5.00554 0.243378
\(424\) 12.8295 0.623056
\(425\) −38.2624 −1.85600
\(426\) −43.7280 −2.11863
\(427\) −2.60595 −0.126111
\(428\) 23.5331 1.13751
\(429\) 14.5998 0.704887
\(430\) 0.394480 0.0190235
\(431\) 29.4012 1.41621 0.708104 0.706109i \(-0.249551\pi\)
0.708104 + 0.706109i \(0.249551\pi\)
\(432\) −1.79485 −0.0863549
\(433\) 15.5782 0.748639 0.374320 0.927300i \(-0.377876\pi\)
0.374320 + 0.927300i \(0.377876\pi\)
\(434\) 4.85114 0.232862
\(435\) −1.04929 −0.0503098
\(436\) 18.8342 0.901993
\(437\) −16.4061 −0.784810
\(438\) −54.6035 −2.60906
\(439\) 33.0192 1.57592 0.787961 0.615725i \(-0.211137\pi\)
0.787961 + 0.615725i \(0.211137\pi\)
\(440\) 1.07109 0.0510624
\(441\) −15.0660 −0.717430
\(442\) −116.246 −5.52927
\(443\) −3.91943 −0.186218 −0.0931088 0.995656i \(-0.529680\pi\)
−0.0931088 + 0.995656i \(0.529680\pi\)
\(444\) −8.48440 −0.402652
\(445\) 2.34562 0.111193
\(446\) −48.1111 −2.27812
\(447\) 9.95338 0.470779
\(448\) −6.68907 −0.316029
\(449\) −38.1005 −1.79807 −0.899036 0.437874i \(-0.855732\pi\)
−0.899036 + 0.437874i \(0.855732\pi\)
\(450\) 25.7279 1.21282
\(451\) 4.72274 0.222385
\(452\) −60.8128 −2.86039
\(453\) −3.55834 −0.167186
\(454\) 43.5844 2.04552
\(455\) −1.08890 −0.0510486
\(456\) 35.2034 1.64855
\(457\) −24.5233 −1.14715 −0.573576 0.819152i \(-0.694444\pi\)
−0.573576 + 0.819152i \(0.694444\pi\)
\(458\) −8.14045 −0.380378
\(459\) −13.4656 −0.628521
\(460\) −3.95366 −0.184341
\(461\) 14.3001 0.666024 0.333012 0.942923i \(-0.391935\pi\)
0.333012 + 0.942923i \(0.391935\pi\)
\(462\) −2.90687 −0.135240
\(463\) −28.1884 −1.31003 −0.655013 0.755618i \(-0.727337\pi\)
−0.655013 + 0.755618i \(0.727337\pi\)
\(464\) 1.51562 0.0703608
\(465\) 2.75400 0.127713
\(466\) 50.9035 2.35806
\(467\) 31.4165 1.45378 0.726891 0.686753i \(-0.240964\pi\)
0.726891 + 0.686753i \(0.240964\pi\)
\(468\) 49.5213 2.28912
\(469\) 8.22469 0.379781
\(470\) 1.63677 0.0754986
\(471\) 8.74250 0.402833
\(472\) −33.3305 −1.53416
\(473\) 0.536888 0.0246861
\(474\) 77.4193 3.55599
\(475\) 22.1170 1.01480
\(476\) 14.6635 0.672101
\(477\) −8.46487 −0.387580
\(478\) 8.77271 0.401255
\(479\) −41.4746 −1.89502 −0.947512 0.319720i \(-0.896411\pi\)
−0.947512 + 0.319720i \(0.896411\pi\)
\(480\) −3.15560 −0.144033
\(481\) −6.82751 −0.311308
\(482\) 3.28779 0.149755
\(483\) 4.52366 0.205834
\(484\) 3.45776 0.157171
\(485\) 0.0905986 0.00411387
\(486\) 45.1279 2.04704
\(487\) −16.2605 −0.736832 −0.368416 0.929661i \(-0.620100\pi\)
−0.368416 + 0.929661i \(0.620100\pi\)
\(488\) 16.3379 0.739583
\(489\) −45.9008 −2.07570
\(490\) −4.92646 −0.222555
\(491\) −20.6771 −0.933144 −0.466572 0.884483i \(-0.654511\pi\)
−0.466572 + 0.884483i \(0.654511\pi\)
\(492\) 37.4063 1.68641
\(493\) 11.3707 0.512111
\(494\) 67.1946 3.02323
\(495\) −0.706705 −0.0317640
\(496\) −3.97791 −0.178614
\(497\) 4.43874 0.199105
\(498\) −11.3828 −0.510076
\(499\) −0.843697 −0.0377691 −0.0188845 0.999822i \(-0.506011\pi\)
−0.0188845 + 0.999822i \(0.506011\pi\)
\(500\) 10.7674 0.481534
\(501\) 58.2738 2.60348
\(502\) −28.0302 −1.25105
\(503\) 25.3863 1.13192 0.565959 0.824433i \(-0.308506\pi\)
0.565959 + 0.824433i \(0.308506\pi\)
\(504\) −4.15682 −0.185160
\(505\) 1.78338 0.0793595
\(506\) −8.49333 −0.377575
\(507\) 63.2770 2.81023
\(508\) 41.0736 1.82235
\(509\) 36.9272 1.63677 0.818384 0.574672i \(-0.194870\pi\)
0.818384 + 0.574672i \(0.194870\pi\)
\(510\) 13.1394 0.581824
\(511\) 5.54269 0.245194
\(512\) 11.6457 0.514672
\(513\) 7.78362 0.343655
\(514\) −27.8193 −1.22706
\(515\) −0.0288489 −0.00127124
\(516\) 4.25241 0.187202
\(517\) 2.22765 0.0979719
\(518\) 1.35938 0.0597277
\(519\) −56.5266 −2.48124
\(520\) 6.82685 0.299377
\(521\) −29.8608 −1.30822 −0.654112 0.756398i \(-0.726958\pi\)
−0.654112 + 0.756398i \(0.726958\pi\)
\(522\) −7.64574 −0.334645
\(523\) 14.2719 0.624066 0.312033 0.950071i \(-0.398990\pi\)
0.312033 + 0.950071i \(0.398990\pi\)
\(524\) −3.45776 −0.151053
\(525\) −6.09833 −0.266153
\(526\) 51.8853 2.26231
\(527\) −29.8437 −1.30001
\(528\) 2.38362 0.103734
\(529\) −9.78273 −0.425336
\(530\) −2.76794 −0.120232
\(531\) 21.9914 0.954344
\(532\) −8.47603 −0.367483
\(533\) 30.1014 1.30384
\(534\) 39.9106 1.72710
\(535\) −2.14051 −0.0925424
\(536\) −51.5645 −2.22725
\(537\) −23.7331 −1.02416
\(538\) 29.0398 1.25200
\(539\) −6.70493 −0.288802
\(540\) 1.87575 0.0807196
\(541\) 27.5187 1.18312 0.591560 0.806261i \(-0.298512\pi\)
0.591560 + 0.806261i \(0.298512\pi\)
\(542\) 42.6922 1.83379
\(543\) −26.0861 −1.11946
\(544\) 34.1957 1.46613
\(545\) −1.71311 −0.0733815
\(546\) −18.5276 −0.792907
\(547\) −42.6872 −1.82517 −0.912586 0.408885i \(-0.865918\pi\)
−0.912586 + 0.408885i \(0.865918\pi\)
\(548\) 33.0699 1.41267
\(549\) −10.7797 −0.460067
\(550\) 11.4498 0.488223
\(551\) −6.57268 −0.280005
\(552\) −28.3609 −1.20712
\(553\) −7.85867 −0.334185
\(554\) −49.9554 −2.12240
\(555\) 0.771720 0.0327577
\(556\) 56.9930 2.41704
\(557\) 22.0904 0.936002 0.468001 0.883728i \(-0.344974\pi\)
0.468001 + 0.883728i \(0.344974\pi\)
\(558\) 20.0671 0.849509
\(559\) 3.42197 0.144734
\(560\) −0.177778 −0.00751250
\(561\) 17.8828 0.755012
\(562\) −4.34279 −0.183190
\(563\) 27.6699 1.16615 0.583074 0.812419i \(-0.301850\pi\)
0.583074 + 0.812419i \(0.301850\pi\)
\(564\) 17.6440 0.742947
\(565\) 5.53138 0.232707
\(566\) 58.6447 2.46502
\(567\) −5.80793 −0.243910
\(568\) −27.8285 −1.16766
\(569\) −20.7074 −0.868098 −0.434049 0.900889i \(-0.642916\pi\)
−0.434049 + 0.900889i \(0.642916\pi\)
\(570\) −7.59506 −0.318122
\(571\) 38.7837 1.62305 0.811523 0.584320i \(-0.198639\pi\)
0.811523 + 0.584320i \(0.198639\pi\)
\(572\) 22.0388 0.921488
\(573\) 7.75695 0.324051
\(574\) −5.99328 −0.250155
\(575\) −17.8182 −0.743069
\(576\) −27.6699 −1.15291
\(577\) −25.7724 −1.07292 −0.536460 0.843926i \(-0.680239\pi\)
−0.536460 + 0.843926i \(0.680239\pi\)
\(578\) −102.671 −4.27053
\(579\) −9.65086 −0.401076
\(580\) −1.58393 −0.0657692
\(581\) 1.15545 0.0479359
\(582\) 1.54153 0.0638983
\(583\) −3.76717 −0.156020
\(584\) −34.7498 −1.43796
\(585\) −4.50433 −0.186231
\(586\) 29.4276 1.21564
\(587\) −1.73455 −0.0715925 −0.0357963 0.999359i \(-0.511397\pi\)
−0.0357963 + 0.999359i \(0.511397\pi\)
\(588\) −53.1062 −2.19006
\(589\) 17.2508 0.710805
\(590\) 7.19099 0.296048
\(591\) 53.3835 2.19590
\(592\) −1.11468 −0.0458132
\(593\) 33.8954 1.39192 0.695958 0.718082i \(-0.254980\pi\)
0.695958 + 0.718082i \(0.254980\pi\)
\(594\) 4.02953 0.165334
\(595\) −1.33376 −0.0546787
\(596\) 15.0248 0.615441
\(597\) 39.9766 1.63613
\(598\) −54.1341 −2.21371
\(599\) 10.0090 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(600\) 38.2333 1.56087
\(601\) −16.6990 −0.681167 −0.340583 0.940214i \(-0.610625\pi\)
−0.340583 + 0.940214i \(0.610625\pi\)
\(602\) −0.681325 −0.0277687
\(603\) 34.0221 1.38549
\(604\) −5.37140 −0.218559
\(605\) −0.314509 −0.0127866
\(606\) 30.3441 1.23264
\(607\) 19.0334 0.772540 0.386270 0.922386i \(-0.373763\pi\)
0.386270 + 0.922386i \(0.373763\pi\)
\(608\) −19.7664 −0.801632
\(609\) 1.81229 0.0734375
\(610\) −3.52488 −0.142718
\(611\) 14.1984 0.574405
\(612\) 60.6567 2.45190
\(613\) −35.1293 −1.41886 −0.709429 0.704777i \(-0.751047\pi\)
−0.709429 + 0.704777i \(0.751047\pi\)
\(614\) 24.8814 1.00413
\(615\) −3.40239 −0.137197
\(616\) −1.84994 −0.0745361
\(617\) −19.0192 −0.765684 −0.382842 0.923814i \(-0.625055\pi\)
−0.382842 + 0.923814i \(0.625055\pi\)
\(618\) −0.490862 −0.0197454
\(619\) −26.6743 −1.07213 −0.536065 0.844177i \(-0.680090\pi\)
−0.536065 + 0.844177i \(0.680090\pi\)
\(620\) 4.15721 0.166958
\(621\) −6.27073 −0.251636
\(622\) 40.1544 1.61004
\(623\) −4.05124 −0.162309
\(624\) 15.1925 0.608188
\(625\) 23.5260 0.941042
\(626\) 58.3199 2.33093
\(627\) −10.3369 −0.412816
\(628\) 13.1970 0.526617
\(629\) −8.36276 −0.333445
\(630\) 0.896827 0.0357304
\(631\) −47.6453 −1.89673 −0.948365 0.317181i \(-0.897264\pi\)
−0.948365 + 0.317181i \(0.897264\pi\)
\(632\) 49.2697 1.95984
\(633\) 23.6523 0.940096
\(634\) 3.73907 0.148498
\(635\) −3.73595 −0.148257
\(636\) −29.8378 −1.18315
\(637\) −42.7353 −1.69323
\(638\) −3.40263 −0.134712
\(639\) 18.3612 0.726357
\(640\) −6.29260 −0.248737
\(641\) −1.18002 −0.0466082 −0.0233041 0.999728i \(-0.507419\pi\)
−0.0233041 + 0.999728i \(0.507419\pi\)
\(642\) −36.4206 −1.43741
\(643\) −18.6281 −0.734620 −0.367310 0.930099i \(-0.619721\pi\)
−0.367310 + 0.930099i \(0.619721\pi\)
\(644\) 6.82856 0.269083
\(645\) −0.386788 −0.0152298
\(646\) 82.3041 3.23821
\(647\) −1.04305 −0.0410065 −0.0205032 0.999790i \(-0.506527\pi\)
−0.0205032 + 0.999790i \(0.506527\pi\)
\(648\) 36.4126 1.43042
\(649\) 9.78696 0.384172
\(650\) 72.9780 2.86243
\(651\) −4.75655 −0.186424
\(652\) −69.2882 −2.71354
\(653\) −17.3841 −0.680292 −0.340146 0.940373i \(-0.610476\pi\)
−0.340146 + 0.940373i \(0.610476\pi\)
\(654\) −29.1484 −1.13979
\(655\) 0.314509 0.0122889
\(656\) 4.91446 0.191877
\(657\) 22.9278 0.894498
\(658\) −2.82694 −0.110206
\(659\) −3.23750 −0.126115 −0.0630575 0.998010i \(-0.520085\pi\)
−0.0630575 + 0.998010i \(0.520085\pi\)
\(660\) −2.49106 −0.0969645
\(661\) 15.3210 0.595920 0.297960 0.954578i \(-0.403694\pi\)
0.297960 + 0.954578i \(0.403694\pi\)
\(662\) 45.3201 1.76142
\(663\) 113.980 4.42661
\(664\) −7.24403 −0.281123
\(665\) 0.770959 0.0298965
\(666\) 5.62318 0.217894
\(667\) 5.29516 0.205029
\(668\) 87.9655 3.40349
\(669\) 47.1730 1.82381
\(670\) 11.1249 0.429794
\(671\) −4.79737 −0.185200
\(672\) 5.45018 0.210245
\(673\) −26.4810 −1.02077 −0.510384 0.859946i \(-0.670497\pi\)
−0.510384 + 0.859946i \(0.670497\pi\)
\(674\) 62.3270 2.40074
\(675\) 8.45355 0.325377
\(676\) 95.5179 3.67377
\(677\) −17.9841 −0.691186 −0.345593 0.938385i \(-0.612322\pi\)
−0.345593 + 0.938385i \(0.612322\pi\)
\(678\) 94.1159 3.61450
\(679\) −0.156477 −0.00600504
\(680\) 8.36194 0.320666
\(681\) −42.7346 −1.63759
\(682\) 8.93061 0.341971
\(683\) −7.47119 −0.285877 −0.142939 0.989732i \(-0.545655\pi\)
−0.142939 + 0.989732i \(0.545655\pi\)
\(684\) −35.0618 −1.34062
\(685\) −3.00795 −0.114928
\(686\) 17.3919 0.664026
\(687\) 7.98173 0.304522
\(688\) 0.558683 0.0212996
\(689\) −24.0109 −0.914742
\(690\) 6.11882 0.232940
\(691\) −17.2576 −0.656511 −0.328255 0.944589i \(-0.606461\pi\)
−0.328255 + 0.944589i \(0.606461\pi\)
\(692\) −85.3281 −3.24369
\(693\) 1.22058 0.0463661
\(694\) −51.6573 −1.96089
\(695\) −5.18394 −0.196638
\(696\) −11.3621 −0.430678
\(697\) 36.8700 1.39655
\(698\) 19.8817 0.752532
\(699\) −49.9110 −1.88781
\(700\) −9.20556 −0.347938
\(701\) 15.4973 0.585324 0.292662 0.956216i \(-0.405459\pi\)
0.292662 + 0.956216i \(0.405459\pi\)
\(702\) 25.6831 0.969344
\(703\) 4.83398 0.182317
\(704\) −12.3141 −0.464105
\(705\) −1.60486 −0.0604424
\(706\) −66.8120 −2.51450
\(707\) −3.08016 −0.115841
\(708\) 77.5173 2.91328
\(709\) 19.0070 0.713823 0.356911 0.934138i \(-0.383830\pi\)
0.356911 + 0.934138i \(0.383830\pi\)
\(710\) 6.00396 0.225324
\(711\) −32.5080 −1.21915
\(712\) 25.3991 0.951872
\(713\) −13.8977 −0.520475
\(714\) −22.6937 −0.849291
\(715\) −2.00459 −0.0749675
\(716\) −35.8256 −1.33886
\(717\) −8.60166 −0.321235
\(718\) −28.2051 −1.05261
\(719\) −26.8539 −1.00148 −0.500740 0.865597i \(-0.666939\pi\)
−0.500740 + 0.865597i \(0.666939\pi\)
\(720\) −0.735394 −0.0274065
\(721\) 0.0498263 0.00185563
\(722\) −3.18721 −0.118616
\(723\) −3.22368 −0.119890
\(724\) −39.3775 −1.46345
\(725\) −7.13838 −0.265113
\(726\) −5.35135 −0.198607
\(727\) −7.95940 −0.295198 −0.147599 0.989047i \(-0.547154\pi\)
−0.147599 + 0.989047i \(0.547154\pi\)
\(728\) −11.7910 −0.437002
\(729\) −12.1721 −0.450817
\(730\) 7.49720 0.277484
\(731\) 4.19144 0.155026
\(732\) −37.9974 −1.40442
\(733\) −23.0074 −0.849797 −0.424898 0.905241i \(-0.639690\pi\)
−0.424898 + 0.905241i \(0.639690\pi\)
\(734\) −63.7513 −2.35310
\(735\) 4.83041 0.178172
\(736\) 15.9244 0.586981
\(737\) 15.1411 0.557728
\(738\) −24.7917 −0.912594
\(739\) −13.9978 −0.514917 −0.257459 0.966289i \(-0.582885\pi\)
−0.257459 + 0.966289i \(0.582885\pi\)
\(740\) 1.16493 0.0428236
\(741\) −65.8844 −2.42032
\(742\) 4.78064 0.175503
\(743\) −4.46936 −0.163965 −0.0819825 0.996634i \(-0.526125\pi\)
−0.0819825 + 0.996634i \(0.526125\pi\)
\(744\) 29.8211 1.09329
\(745\) −1.36662 −0.0500692
\(746\) 46.8081 1.71377
\(747\) 4.77959 0.174876
\(748\) 26.9945 0.987015
\(749\) 3.69698 0.135085
\(750\) −16.6640 −0.608484
\(751\) 26.2771 0.958864 0.479432 0.877579i \(-0.340843\pi\)
0.479432 + 0.877579i \(0.340843\pi\)
\(752\) 2.31808 0.0845317
\(753\) 27.4837 1.00156
\(754\) −21.6874 −0.789809
\(755\) 0.488569 0.0177808
\(756\) −3.23970 −0.117827
\(757\) −8.29482 −0.301480 −0.150740 0.988573i \(-0.548166\pi\)
−0.150740 + 0.988573i \(0.548166\pi\)
\(758\) 10.6207 0.385761
\(759\) 8.32773 0.302278
\(760\) −4.83351 −0.175330
\(761\) −10.6435 −0.385828 −0.192914 0.981216i \(-0.561794\pi\)
−0.192914 + 0.981216i \(0.561794\pi\)
\(762\) −63.5668 −2.30278
\(763\) 2.95879 0.107115
\(764\) 11.7093 0.423627
\(765\) −5.51719 −0.199474
\(766\) −5.15909 −0.186405
\(767\) 62.3793 2.25238
\(768\) −50.6538 −1.82781
\(769\) −28.8981 −1.04209 −0.521046 0.853528i \(-0.674458\pi\)
−0.521046 + 0.853528i \(0.674458\pi\)
\(770\) 0.399121 0.0143833
\(771\) 27.2769 0.982352
\(772\) −14.5682 −0.524320
\(773\) 19.4491 0.699534 0.349767 0.936837i \(-0.386261\pi\)
0.349767 + 0.936837i \(0.386261\pi\)
\(774\) −2.81835 −0.101304
\(775\) 18.7355 0.673000
\(776\) 0.981029 0.0352169
\(777\) −1.33287 −0.0478166
\(778\) 47.1634 1.69089
\(779\) −21.3122 −0.763589
\(780\) −15.8773 −0.568499
\(781\) 8.17140 0.292396
\(782\) −66.3068 −2.37112
\(783\) −2.51220 −0.0897788
\(784\) −6.97712 −0.249183
\(785\) −1.20037 −0.0428429
\(786\) 5.35135 0.190876
\(787\) −33.7652 −1.20360 −0.601800 0.798647i \(-0.705549\pi\)
−0.601800 + 0.798647i \(0.705549\pi\)
\(788\) 80.5835 2.87067
\(789\) −50.8737 −1.81115
\(790\) −10.6299 −0.378193
\(791\) −9.55351 −0.339684
\(792\) −7.65241 −0.271917
\(793\) −30.5770 −1.08582
\(794\) 72.0907 2.55840
\(795\) 2.71397 0.0962547
\(796\) 60.3455 2.13889
\(797\) 29.9480 1.06081 0.530406 0.847744i \(-0.322040\pi\)
0.530406 + 0.847744i \(0.322040\pi\)
\(798\) 13.1178 0.464365
\(799\) 17.3911 0.615252
\(800\) −21.4676 −0.758996
\(801\) −16.7583 −0.592124
\(802\) 39.7233 1.40268
\(803\) 10.2037 0.360081
\(804\) 119.924 4.22941
\(805\) −0.621109 −0.0218912
\(806\) 56.9211 2.00496
\(807\) −28.4736 −1.00232
\(808\) 19.3110 0.679358
\(809\) −13.7240 −0.482510 −0.241255 0.970462i \(-0.577559\pi\)
−0.241255 + 0.970462i \(0.577559\pi\)
\(810\) −7.85596 −0.276030
\(811\) −55.3907 −1.94503 −0.972516 0.232837i \(-0.925199\pi\)
−0.972516 + 0.232837i \(0.925199\pi\)
\(812\) 2.73568 0.0960037
\(813\) −41.8598 −1.46809
\(814\) 2.50252 0.0877132
\(815\) 6.30228 0.220759
\(816\) 18.6087 0.651436
\(817\) −2.42280 −0.0847632
\(818\) 9.31749 0.325779
\(819\) 7.77965 0.271843
\(820\) −5.13597 −0.179356
\(821\) 6.34584 0.221471 0.110736 0.993850i \(-0.464679\pi\)
0.110736 + 0.993850i \(0.464679\pi\)
\(822\) −51.1800 −1.78511
\(823\) −48.8338 −1.70224 −0.851120 0.524972i \(-0.824076\pi\)
−0.851120 + 0.524972i \(0.824076\pi\)
\(824\) −0.312385 −0.0108824
\(825\) −11.2266 −0.390860
\(826\) −12.4199 −0.432144
\(827\) −40.3974 −1.40476 −0.702378 0.711804i \(-0.747878\pi\)
−0.702378 + 0.711804i \(0.747878\pi\)
\(828\) 28.2469 0.981647
\(829\) 8.82269 0.306425 0.153212 0.988193i \(-0.451038\pi\)
0.153212 + 0.988193i \(0.451038\pi\)
\(830\) 1.56289 0.0542486
\(831\) 48.9814 1.69915
\(832\) −78.4866 −2.72103
\(833\) −52.3448 −1.81364
\(834\) −88.2042 −3.05426
\(835\) −8.00113 −0.276890
\(836\) −15.6038 −0.539668
\(837\) 6.59357 0.227907
\(838\) 41.9769 1.45007
\(839\) 43.1858 1.49094 0.745470 0.666539i \(-0.232225\pi\)
0.745470 + 0.666539i \(0.232225\pi\)
\(840\) 1.33274 0.0459840
\(841\) −26.8786 −0.926849
\(842\) 41.2425 1.42131
\(843\) 4.25812 0.146657
\(844\) 35.7037 1.22897
\(845\) −8.68808 −0.298879
\(846\) −11.6939 −0.402044
\(847\) 0.543204 0.0186647
\(848\) −3.92010 −0.134617
\(849\) −57.5012 −1.97344
\(850\) 89.3880 3.06598
\(851\) −3.89440 −0.133498
\(852\) 64.7213 2.21732
\(853\) 36.8173 1.26060 0.630301 0.776351i \(-0.282932\pi\)
0.630301 + 0.776351i \(0.282932\pi\)
\(854\) 6.08798 0.208326
\(855\) 3.18913 0.109066
\(856\) −23.1781 −0.792211
\(857\) −44.1996 −1.50983 −0.754915 0.655822i \(-0.772322\pi\)
−0.754915 + 0.655822i \(0.772322\pi\)
\(858\) −34.1079 −1.16443
\(859\) −17.6542 −0.602352 −0.301176 0.953569i \(-0.597379\pi\)
−0.301176 + 0.953569i \(0.597379\pi\)
\(860\) −0.583865 −0.0199096
\(861\) 5.87642 0.200268
\(862\) −68.6867 −2.33948
\(863\) −8.93498 −0.304150 −0.152075 0.988369i \(-0.548596\pi\)
−0.152075 + 0.988369i \(0.548596\pi\)
\(864\) −7.55508 −0.257029
\(865\) 7.76123 0.263890
\(866\) −36.3935 −1.23670
\(867\) 100.669 3.41889
\(868\) −7.18012 −0.243709
\(869\) −14.4673 −0.490768
\(870\) 2.45135 0.0831084
\(871\) 96.5048 3.26994
\(872\) −18.5501 −0.628184
\(873\) −0.647280 −0.0219071
\(874\) 38.3277 1.29645
\(875\) 1.69153 0.0571841
\(876\) 80.8181 2.73059
\(877\) 11.8641 0.400621 0.200310 0.979732i \(-0.435805\pi\)
0.200310 + 0.979732i \(0.435805\pi\)
\(878\) −77.1390 −2.60332
\(879\) −28.8538 −0.973215
\(880\) −0.327277 −0.0110325
\(881\) −7.19783 −0.242501 −0.121251 0.992622i \(-0.538690\pi\)
−0.121251 + 0.992622i \(0.538690\pi\)
\(882\) 35.1970 1.18515
\(883\) −13.1306 −0.441878 −0.220939 0.975288i \(-0.570912\pi\)
−0.220939 + 0.975288i \(0.570912\pi\)
\(884\) 172.055 5.78683
\(885\) −7.05078 −0.237009
\(886\) 9.15651 0.307619
\(887\) 24.9610 0.838110 0.419055 0.907961i \(-0.362362\pi\)
0.419055 + 0.907961i \(0.362362\pi\)
\(888\) 8.35641 0.280423
\(889\) 6.45254 0.216411
\(890\) −5.47981 −0.183684
\(891\) −10.6920 −0.358195
\(892\) 71.2087 2.38424
\(893\) −10.0527 −0.336400
\(894\) −23.2529 −0.777695
\(895\) 3.25860 0.108923
\(896\) 10.8683 0.363083
\(897\) 53.0786 1.77224
\(898\) 89.0098 2.97029
\(899\) −5.56777 −0.185696
\(900\) −38.0795 −1.26932
\(901\) −29.4100 −0.979790
\(902\) −11.0332 −0.367365
\(903\) 0.668040 0.0222310
\(904\) 59.8955 1.99209
\(905\) 3.58168 0.119059
\(906\) 8.31295 0.276179
\(907\) 31.1653 1.03483 0.517414 0.855735i \(-0.326895\pi\)
0.517414 + 0.855735i \(0.326895\pi\)
\(908\) −64.5087 −2.14080
\(909\) −12.7413 −0.422604
\(910\) 2.54388 0.0843288
\(911\) −7.55230 −0.250219 −0.125109 0.992143i \(-0.539928\pi\)
−0.125109 + 0.992143i \(0.539928\pi\)
\(912\) −10.7565 −0.356184
\(913\) 2.12709 0.0703965
\(914\) 57.2910 1.89502
\(915\) 3.45615 0.114257
\(916\) 12.0486 0.398097
\(917\) −0.543204 −0.0179382
\(918\) 31.4582 1.03828
\(919\) 20.0776 0.662300 0.331150 0.943578i \(-0.392563\pi\)
0.331150 + 0.943578i \(0.392563\pi\)
\(920\) 3.89402 0.128382
\(921\) −24.3962 −0.803884
\(922\) −33.4078 −1.10023
\(923\) 52.0821 1.71430
\(924\) 4.30243 0.141540
\(925\) 5.25004 0.172620
\(926\) 65.8533 2.16407
\(927\) 0.206111 0.00676956
\(928\) 6.37970 0.209424
\(929\) −36.4399 −1.19555 −0.597777 0.801662i \(-0.703949\pi\)
−0.597777 + 0.801662i \(0.703949\pi\)
\(930\) −6.43384 −0.210974
\(931\) 30.2572 0.991640
\(932\) −75.3417 −2.46790
\(933\) −39.3715 −1.28896
\(934\) −73.3948 −2.40155
\(935\) −2.45535 −0.0802985
\(936\) −48.7743 −1.59424
\(937\) −22.7359 −0.742750 −0.371375 0.928483i \(-0.621114\pi\)
−0.371375 + 0.928483i \(0.621114\pi\)
\(938\) −19.2144 −0.627372
\(939\) −57.1828 −1.86609
\(940\) −2.42257 −0.0790154
\(941\) −1.59355 −0.0519483 −0.0259741 0.999663i \(-0.508269\pi\)
−0.0259741 + 0.999663i \(0.508269\pi\)
\(942\) −20.4241 −0.665453
\(943\) 17.1698 0.559125
\(944\) 10.1843 0.331469
\(945\) 0.294675 0.00958579
\(946\) −1.25427 −0.0407798
\(947\) 45.0572 1.46416 0.732081 0.681218i \(-0.238549\pi\)
0.732081 + 0.681218i \(0.238549\pi\)
\(948\) −114.587 −3.72163
\(949\) 65.0355 2.11114
\(950\) −51.6695 −1.67638
\(951\) −3.66617 −0.118884
\(952\) −14.4423 −0.468078
\(953\) 11.6770 0.378256 0.189128 0.981952i \(-0.439434\pi\)
0.189128 + 0.981952i \(0.439434\pi\)
\(954\) 19.7755 0.640255
\(955\) −1.06505 −0.0344641
\(956\) −12.9844 −0.419945
\(957\) 3.33629 0.107847
\(958\) 96.8924 3.13045
\(959\) 5.19518 0.167761
\(960\) 8.87141 0.286323
\(961\) −16.3867 −0.528604
\(962\) 15.9503 0.514259
\(963\) 15.2928 0.492805
\(964\) −4.86622 −0.156730
\(965\) 1.32509 0.0426560
\(966\) −10.5681 −0.340023
\(967\) 26.3853 0.848495 0.424247 0.905546i \(-0.360539\pi\)
0.424247 + 0.905546i \(0.360539\pi\)
\(968\) −3.40560 −0.109460
\(969\) −80.6993 −2.59244
\(970\) −0.211655 −0.00679584
\(971\) −32.2931 −1.03633 −0.518167 0.855279i \(-0.673386\pi\)
−0.518167 + 0.855279i \(0.673386\pi\)
\(972\) −66.7933 −2.14240
\(973\) 8.95343 0.287034
\(974\) 37.9875 1.21720
\(975\) −71.5551 −2.29160
\(976\) −4.99212 −0.159794
\(977\) −19.9381 −0.637875 −0.318938 0.947776i \(-0.603326\pi\)
−0.318938 + 0.947776i \(0.603326\pi\)
\(978\) 107.233 3.42892
\(979\) −7.45804 −0.238360
\(980\) 7.29160 0.232922
\(981\) 12.2393 0.390770
\(982\) 48.3055 1.54149
\(983\) 14.6538 0.467382 0.233691 0.972311i \(-0.424920\pi\)
0.233691 + 0.972311i \(0.424920\pi\)
\(984\) −36.8420 −1.17448
\(985\) −7.32968 −0.233543
\(986\) −26.5641 −0.845972
\(987\) 2.77182 0.0882281
\(988\) −99.4540 −3.16405
\(989\) 1.95189 0.0620664
\(990\) 1.65099 0.0524720
\(991\) 29.2410 0.928871 0.464435 0.885607i \(-0.346257\pi\)
0.464435 + 0.885607i \(0.346257\pi\)
\(992\) −16.7443 −0.531631
\(993\) −44.4365 −1.41015
\(994\) −10.3697 −0.328907
\(995\) −5.48888 −0.174009
\(996\) 16.8476 0.533836
\(997\) 40.5825 1.28526 0.642631 0.766176i \(-0.277843\pi\)
0.642631 + 0.766176i \(0.277843\pi\)
\(998\) 1.97103 0.0623919
\(999\) 1.84764 0.0584567
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 1441.2.a.e.1.3 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1441.2.a.e.1.3 28 1.1 even 1 trivial