Properties

Label 1815.2.a.o.1.4
Level $1815$
Weight $2$
Character 1815.1
Self dual yes
Analytic conductor $14.493$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1815.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(14.4928479669\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
Defining polynomial: \(x^{4} - x^{3} - 3 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.09529\) of defining polynomial
Character \(\chi\) \(=\) 1815.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.39026 q^{2} +1.00000 q^{3} -0.0671858 q^{4} -1.00000 q^{5} +1.39026 q^{6} -1.27759 q^{7} -2.87392 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.39026 q^{2} +1.00000 q^{3} -0.0671858 q^{4} -1.00000 q^{5} +1.39026 q^{6} -1.27759 q^{7} -2.87392 q^{8} +1.00000 q^{9} -1.39026 q^{10} -0.0671858 q^{12} +1.41837 q^{13} -1.77618 q^{14} -1.00000 q^{15} -3.86111 q^{16} -5.00000 q^{17} +1.39026 q^{18} -0.158146 q^{19} +0.0671858 q^{20} -1.27759 q^{21} -5.00829 q^{23} -2.87392 q^{24} +1.00000 q^{25} +1.97189 q^{26} +1.00000 q^{27} +0.0858360 q^{28} -6.27515 q^{29} -1.39026 q^{30} +3.04981 q^{31} +0.379898 q^{32} -6.95128 q^{34} +1.27759 q^{35} -0.0671858 q^{36} -4.69991 q^{37} -0.219863 q^{38} +1.41837 q^{39} +2.87392 q^{40} -7.58597 q^{41} -1.77618 q^{42} -5.41324 q^{43} -1.00000 q^{45} -6.96281 q^{46} -8.23211 q^{47} -3.86111 q^{48} -5.36776 q^{49} +1.39026 q^{50} -5.00000 q^{51} -0.0952940 q^{52} +9.36648 q^{53} +1.39026 q^{54} +3.67169 q^{56} -0.158146 q^{57} -8.72406 q^{58} +8.09846 q^{59} +0.0671858 q^{60} +14.2917 q^{61} +4.24002 q^{62} -1.27759 q^{63} +8.25038 q^{64} -1.41837 q^{65} -7.38362 q^{67} +0.335929 q^{68} -5.00829 q^{69} +1.77618 q^{70} -6.77618 q^{71} -2.87392 q^{72} -8.66107 q^{73} -6.53409 q^{74} +1.00000 q^{75} +0.0106252 q^{76} +1.97189 q^{78} +2.54572 q^{79} +3.86111 q^{80} +1.00000 q^{81} -10.5464 q^{82} -10.1221 q^{83} +0.0858360 q^{84} +5.00000 q^{85} -7.52580 q^{86} -6.27515 q^{87} +11.0447 q^{89} -1.39026 q^{90} -1.81209 q^{91} +0.336486 q^{92} +3.04981 q^{93} -11.4447 q^{94} +0.158146 q^{95} +0.379898 q^{96} +6.41196 q^{97} -7.46257 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 5q^{2} + 4q^{3} + 9q^{4} - 4q^{5} - 5q^{6} + 2q^{7} - 15q^{8} + 4q^{9} + O(q^{10}) \) \( 4q - 5q^{2} + 4q^{3} + 9q^{4} - 4q^{5} - 5q^{6} + 2q^{7} - 15q^{8} + 4q^{9} + 5q^{10} + 9q^{12} - 3q^{13} - 5q^{14} - 4q^{15} + 15q^{16} - 20q^{17} - 5q^{18} - 3q^{19} - 9q^{20} + 2q^{21} - 5q^{23} - 15q^{24} + 4q^{25} + 6q^{26} + 4q^{27} - 3q^{28} - 5q^{29} + 5q^{30} - q^{31} - 30q^{32} + 25q^{34} - 2q^{35} + 9q^{36} - 7q^{37} + q^{38} - 3q^{39} + 15q^{40} - 20q^{41} - 5q^{42} + 2q^{43} - 4q^{45} - 7q^{46} - 20q^{47} + 15q^{48} + 8q^{49} - 5q^{50} - 20q^{51} + 7q^{52} + 6q^{53} - 5q^{54} + 10q^{56} - 3q^{57} - 21q^{58} - 5q^{59} - 9q^{60} + 7q^{61} + 12q^{62} + 2q^{63} + 49q^{64} + 3q^{65} - 13q^{67} - 45q^{68} - 5q^{69} + 5q^{70} - 25q^{71} - 15q^{72} - 23q^{73} + 7q^{74} + 4q^{75} + 7q^{76} + 6q^{78} - 15q^{80} + 4q^{81} + 11q^{82} - 33q^{83} - 3q^{84} + 20q^{85} - 12q^{86} - 5q^{87} + 16q^{89} + 5q^{90} - 24q^{91} - q^{93} + 17q^{94} + 3q^{95} - 30q^{96} - 25q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.39026 0.983060 0.491530 0.870861i \(-0.336438\pi\)
0.491530 + 0.870861i \(0.336438\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.0671858 −0.0335929
\(5\) −1.00000 −0.447214
\(6\) 1.39026 0.567570
\(7\) −1.27759 −0.482884 −0.241442 0.970415i \(-0.577620\pi\)
−0.241442 + 0.970415i \(0.577620\pi\)
\(8\) −2.87392 −1.01608
\(9\) 1.00000 0.333333
\(10\) −1.39026 −0.439638
\(11\) 0 0
\(12\) −0.0671858 −0.0193949
\(13\) 1.41837 0.393384 0.196692 0.980465i \(-0.436980\pi\)
0.196692 + 0.980465i \(0.436980\pi\)
\(14\) −1.77618 −0.474704
\(15\) −1.00000 −0.258199
\(16\) −3.86111 −0.965279
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 1.39026 0.327687
\(19\) −0.158146 −0.0362811 −0.0181406 0.999835i \(-0.505775\pi\)
−0.0181406 + 0.999835i \(0.505775\pi\)
\(20\) 0.0671858 0.0150232
\(21\) −1.27759 −0.278793
\(22\) 0 0
\(23\) −5.00829 −1.04430 −0.522150 0.852853i \(-0.674870\pi\)
−0.522150 + 0.852853i \(0.674870\pi\)
\(24\) −2.87392 −0.586636
\(25\) 1.00000 0.200000
\(26\) 1.97189 0.386720
\(27\) 1.00000 0.192450
\(28\) 0.0858360 0.0162215
\(29\) −6.27515 −1.16527 −0.582633 0.812736i \(-0.697977\pi\)
−0.582633 + 0.812736i \(0.697977\pi\)
\(30\) −1.39026 −0.253825
\(31\) 3.04981 0.547763 0.273881 0.961763i \(-0.411692\pi\)
0.273881 + 0.961763i \(0.411692\pi\)
\(32\) 0.379898 0.0671570
\(33\) 0 0
\(34\) −6.95128 −1.19214
\(35\) 1.27759 0.215952
\(36\) −0.0671858 −0.0111976
\(37\) −4.69991 −0.772661 −0.386330 0.922360i \(-0.626258\pi\)
−0.386330 + 0.922360i \(0.626258\pi\)
\(38\) −0.219863 −0.0356665
\(39\) 1.41837 0.227120
\(40\) 2.87392 0.454407
\(41\) −7.58597 −1.18473 −0.592365 0.805670i \(-0.701806\pi\)
−0.592365 + 0.805670i \(0.701806\pi\)
\(42\) −1.77618 −0.274070
\(43\) −5.41324 −0.825512 −0.412756 0.910842i \(-0.635434\pi\)
−0.412756 + 0.910842i \(0.635434\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) −6.96281 −1.02661
\(47\) −8.23211 −1.20078 −0.600388 0.799709i \(-0.704987\pi\)
−0.600388 + 0.799709i \(0.704987\pi\)
\(48\) −3.86111 −0.557304
\(49\) −5.36776 −0.766823
\(50\) 1.39026 0.196612
\(51\) −5.00000 −0.700140
\(52\) −0.0952940 −0.0132149
\(53\) 9.36648 1.28659 0.643293 0.765620i \(-0.277568\pi\)
0.643293 + 0.765620i \(0.277568\pi\)
\(54\) 1.39026 0.189190
\(55\) 0 0
\(56\) 3.67169 0.490651
\(57\) −0.158146 −0.0209469
\(58\) −8.72406 −1.14553
\(59\) 8.09846 1.05433 0.527165 0.849763i \(-0.323255\pi\)
0.527165 + 0.849763i \(0.323255\pi\)
\(60\) 0.0671858 0.00867365
\(61\) 14.2917 1.82987 0.914934 0.403603i \(-0.132242\pi\)
0.914934 + 0.403603i \(0.132242\pi\)
\(62\) 4.24002 0.538484
\(63\) −1.27759 −0.160961
\(64\) 8.25038 1.03130
\(65\) −1.41837 −0.175927
\(66\) 0 0
\(67\) −7.38362 −0.902053 −0.451026 0.892511i \(-0.648942\pi\)
−0.451026 + 0.892511i \(0.648942\pi\)
\(68\) 0.335929 0.0407374
\(69\) −5.00829 −0.602927
\(70\) 1.77618 0.212294
\(71\) −6.77618 −0.804185 −0.402092 0.915599i \(-0.631717\pi\)
−0.402092 + 0.915599i \(0.631717\pi\)
\(72\) −2.87392 −0.338695
\(73\) −8.66107 −1.01370 −0.506851 0.862034i \(-0.669190\pi\)
−0.506851 + 0.862034i \(0.669190\pi\)
\(74\) −6.53409 −0.759572
\(75\) 1.00000 0.115470
\(76\) 0.0106252 0.00121879
\(77\) 0 0
\(78\) 1.97189 0.223273
\(79\) 2.54572 0.286416 0.143208 0.989693i \(-0.454258\pi\)
0.143208 + 0.989693i \(0.454258\pi\)
\(80\) 3.86111 0.431686
\(81\) 1.00000 0.111111
\(82\) −10.5464 −1.16466
\(83\) −10.1221 −1.11105 −0.555524 0.831501i \(-0.687482\pi\)
−0.555524 + 0.831501i \(0.687482\pi\)
\(84\) 0.0858360 0.00936547
\(85\) 5.00000 0.542326
\(86\) −7.52580 −0.811527
\(87\) −6.27515 −0.672766
\(88\) 0 0
\(89\) 11.0447 1.17073 0.585367 0.810768i \(-0.300950\pi\)
0.585367 + 0.810768i \(0.300950\pi\)
\(90\) −1.39026 −0.146546
\(91\) −1.81209 −0.189959
\(92\) 0.336486 0.0350811
\(93\) 3.04981 0.316251
\(94\) −11.4447 −1.18044
\(95\) 0.158146 0.0162254
\(96\) 0.379898 0.0387731
\(97\) 6.41196 0.651036 0.325518 0.945536i \(-0.394461\pi\)
0.325518 + 0.945536i \(0.394461\pi\)
\(98\) −7.46257 −0.753833
\(99\) 0 0
\(100\) −0.0671858 −0.00671858
\(101\) −8.77143 −0.872790 −0.436395 0.899755i \(-0.643745\pi\)
−0.436395 + 0.899755i \(0.643745\pi\)
\(102\) −6.95128 −0.688280
\(103\) 11.5666 1.13969 0.569847 0.821751i \(-0.307002\pi\)
0.569847 + 0.821751i \(0.307002\pi\)
\(104\) −4.07627 −0.399711
\(105\) 1.27759 0.124680
\(106\) 13.0218 1.26479
\(107\) −15.3467 −1.48362 −0.741809 0.670611i \(-0.766032\pi\)
−0.741809 + 0.670611i \(0.766032\pi\)
\(108\) −0.0671858 −0.00646496
\(109\) −14.4004 −1.37931 −0.689656 0.724137i \(-0.742238\pi\)
−0.689656 + 0.724137i \(0.742238\pi\)
\(110\) 0 0
\(111\) −4.69991 −0.446096
\(112\) 4.93293 0.466118
\(113\) 19.3645 1.82166 0.910831 0.412780i \(-0.135442\pi\)
0.910831 + 0.412780i \(0.135442\pi\)
\(114\) −0.219863 −0.0205921
\(115\) 5.00829 0.467026
\(116\) 0.421601 0.0391446
\(117\) 1.41837 0.131128
\(118\) 11.2589 1.03647
\(119\) 6.38796 0.585583
\(120\) 2.87392 0.262352
\(121\) 0 0
\(122\) 19.8692 1.79887
\(123\) −7.58597 −0.684004
\(124\) −0.204904 −0.0184009
\(125\) −1.00000 −0.0894427
\(126\) −1.77618 −0.158235
\(127\) 6.02415 0.534557 0.267278 0.963619i \(-0.413876\pi\)
0.267278 + 0.963619i \(0.413876\pi\)
\(128\) 10.7104 0.946671
\(129\) −5.41324 −0.476609
\(130\) −1.97189 −0.172946
\(131\) 18.7278 1.63626 0.818130 0.575034i \(-0.195011\pi\)
0.818130 + 0.575034i \(0.195011\pi\)
\(132\) 0 0
\(133\) 0.202046 0.0175196
\(134\) −10.2651 −0.886772
\(135\) −1.00000 −0.0860663
\(136\) 14.3696 1.23218
\(137\) 3.03719 0.259485 0.129742 0.991548i \(-0.458585\pi\)
0.129742 + 0.991548i \(0.458585\pi\)
\(138\) −6.96281 −0.592714
\(139\) 2.21192 0.187612 0.0938062 0.995590i \(-0.470097\pi\)
0.0938062 + 0.995590i \(0.470097\pi\)
\(140\) −0.0858360 −0.00725446
\(141\) −8.23211 −0.693269
\(142\) −9.42063 −0.790562
\(143\) 0 0
\(144\) −3.86111 −0.321760
\(145\) 6.27515 0.521122
\(146\) −12.0411 −0.996529
\(147\) −5.36776 −0.442725
\(148\) 0.315767 0.0259559
\(149\) −1.48122 −0.121346 −0.0606730 0.998158i \(-0.519325\pi\)
−0.0606730 + 0.998158i \(0.519325\pi\)
\(150\) 1.39026 0.113514
\(151\) 9.03395 0.735173 0.367586 0.929989i \(-0.380184\pi\)
0.367586 + 0.929989i \(0.380184\pi\)
\(152\) 0.454498 0.0368647
\(153\) −5.00000 −0.404226
\(154\) 0 0
\(155\) −3.04981 −0.244967
\(156\) −0.0952940 −0.00762962
\(157\) −17.6377 −1.40764 −0.703820 0.710379i \(-0.748524\pi\)
−0.703820 + 0.710379i \(0.748524\pi\)
\(158\) 3.53921 0.281564
\(159\) 9.36648 0.742810
\(160\) −0.379898 −0.0300335
\(161\) 6.39855 0.504276
\(162\) 1.39026 0.109229
\(163\) 23.5040 1.84098 0.920489 0.390770i \(-0.127791\pi\)
0.920489 + 0.390770i \(0.127791\pi\)
\(164\) 0.509669 0.0397985
\(165\) 0 0
\(166\) −14.0724 −1.09223
\(167\) −0.602731 −0.0466407 −0.0233203 0.999728i \(-0.507424\pi\)
−0.0233203 + 0.999728i \(0.507424\pi\)
\(168\) 3.67169 0.283277
\(169\) −10.9882 −0.845249
\(170\) 6.95128 0.533139
\(171\) −0.158146 −0.0120937
\(172\) 0.363693 0.0277313
\(173\) −9.66389 −0.734732 −0.367366 0.930076i \(-0.619740\pi\)
−0.367366 + 0.930076i \(0.619740\pi\)
\(174\) −8.72406 −0.661370
\(175\) −1.27759 −0.0965768
\(176\) 0 0
\(177\) 8.09846 0.608718
\(178\) 15.3550 1.15090
\(179\) −1.19571 −0.0893717 −0.0446859 0.999001i \(-0.514229\pi\)
−0.0446859 + 0.999001i \(0.514229\pi\)
\(180\) 0.0671858 0.00500773
\(181\) 15.5741 1.15761 0.578806 0.815466i \(-0.303519\pi\)
0.578806 + 0.815466i \(0.303519\pi\)
\(182\) −2.51927 −0.186741
\(183\) 14.2917 1.05647
\(184\) 14.3934 1.06110
\(185\) 4.69991 0.345544
\(186\) 4.24002 0.310894
\(187\) 0 0
\(188\) 0.553081 0.0403376
\(189\) −1.27759 −0.0929311
\(190\) 0.219863 0.0159506
\(191\) 18.4016 1.33149 0.665747 0.746178i \(-0.268113\pi\)
0.665747 + 0.746178i \(0.268113\pi\)
\(192\) 8.25038 0.595420
\(193\) −1.56799 −0.112866 −0.0564331 0.998406i \(-0.517973\pi\)
−0.0564331 + 0.998406i \(0.517973\pi\)
\(194\) 8.91428 0.640008
\(195\) −1.41837 −0.101571
\(196\) 0.360637 0.0257598
\(197\) −7.97000 −0.567839 −0.283920 0.958848i \(-0.591635\pi\)
−0.283920 + 0.958848i \(0.591635\pi\)
\(198\) 0 0
\(199\) 3.53141 0.250335 0.125167 0.992136i \(-0.460053\pi\)
0.125167 + 0.992136i \(0.460053\pi\)
\(200\) −2.87392 −0.203217
\(201\) −7.38362 −0.520801
\(202\) −12.1945 −0.858005
\(203\) 8.01707 0.562688
\(204\) 0.335929 0.0235197
\(205\) 7.58597 0.529827
\(206\) 16.0806 1.12039
\(207\) −5.00829 −0.348100
\(208\) −5.47647 −0.379725
\(209\) 0 0
\(210\) 1.77618 0.122568
\(211\) −20.2550 −1.39441 −0.697207 0.716870i \(-0.745574\pi\)
−0.697207 + 0.716870i \(0.745574\pi\)
\(212\) −0.629295 −0.0432201
\(213\) −6.77618 −0.464296
\(214\) −21.3358 −1.45849
\(215\) 5.41324 0.369180
\(216\) −2.87392 −0.195545
\(217\) −3.89642 −0.264506
\(218\) −20.0203 −1.35595
\(219\) −8.66107 −0.585261
\(220\) 0 0
\(221\) −7.09183 −0.477048
\(222\) −6.53409 −0.438539
\(223\) 22.5500 1.51006 0.755029 0.655691i \(-0.227623\pi\)
0.755029 + 0.655691i \(0.227623\pi\)
\(224\) −0.485354 −0.0324291
\(225\) 1.00000 0.0666667
\(226\) 26.9217 1.79080
\(227\) −18.8062 −1.24821 −0.624105 0.781341i \(-0.714536\pi\)
−0.624105 + 0.781341i \(0.714536\pi\)
\(228\) 0.0106252 0.000703668 0
\(229\) −23.8320 −1.57486 −0.787431 0.616403i \(-0.788589\pi\)
−0.787431 + 0.616403i \(0.788589\pi\)
\(230\) 6.96281 0.459114
\(231\) 0 0
\(232\) 18.0343 1.18401
\(233\) 10.0918 0.661137 0.330569 0.943782i \(-0.392759\pi\)
0.330569 + 0.943782i \(0.392759\pi\)
\(234\) 1.97189 0.128907
\(235\) 8.23211 0.537004
\(236\) −0.544102 −0.0354180
\(237\) 2.54572 0.165363
\(238\) 8.88090 0.575663
\(239\) −0.167227 −0.0108170 −0.00540850 0.999985i \(-0.501722\pi\)
−0.00540850 + 0.999985i \(0.501722\pi\)
\(240\) 3.86111 0.249234
\(241\) −0.965256 −0.0621776 −0.0310888 0.999517i \(-0.509897\pi\)
−0.0310888 + 0.999517i \(0.509897\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −0.960201 −0.0614706
\(245\) 5.36776 0.342934
\(246\) −10.5464 −0.672417
\(247\) −0.224308 −0.0142724
\(248\) −8.76492 −0.556573
\(249\) −10.1221 −0.641464
\(250\) −1.39026 −0.0879276
\(251\) −23.5102 −1.48395 −0.741975 0.670428i \(-0.766111\pi\)
−0.741975 + 0.670428i \(0.766111\pi\)
\(252\) 0.0858360 0.00540716
\(253\) 0 0
\(254\) 8.37512 0.525502
\(255\) 5.00000 0.313112
\(256\) −1.61062 −0.100664
\(257\) −6.58273 −0.410620 −0.205310 0.978697i \(-0.565820\pi\)
−0.205310 + 0.978697i \(0.565820\pi\)
\(258\) −7.52580 −0.468536
\(259\) 6.00457 0.373106
\(260\) 0.0952940 0.00590988
\(261\) −6.27515 −0.388422
\(262\) 26.0365 1.60854
\(263\) −12.4538 −0.767936 −0.383968 0.923346i \(-0.625443\pi\)
−0.383968 + 0.923346i \(0.625443\pi\)
\(264\) 0 0
\(265\) −9.36648 −0.575378
\(266\) 0.280895 0.0172228
\(267\) 11.0447 0.675924
\(268\) 0.496074 0.0303026
\(269\) 20.7729 1.26655 0.633274 0.773927i \(-0.281710\pi\)
0.633274 + 0.773927i \(0.281710\pi\)
\(270\) −1.39026 −0.0846083
\(271\) −14.3903 −0.874146 −0.437073 0.899426i \(-0.643985\pi\)
−0.437073 + 0.899426i \(0.643985\pi\)
\(272\) 19.3056 1.17057
\(273\) −1.81209 −0.109673
\(274\) 4.22247 0.255089
\(275\) 0 0
\(276\) 0.336486 0.0202541
\(277\) 17.4872 1.05070 0.525352 0.850885i \(-0.323934\pi\)
0.525352 + 0.850885i \(0.323934\pi\)
\(278\) 3.07513 0.184434
\(279\) 3.04981 0.182588
\(280\) −3.67169 −0.219426
\(281\) 18.8860 1.12664 0.563322 0.826238i \(-0.309523\pi\)
0.563322 + 0.826238i \(0.309523\pi\)
\(282\) −11.4447 −0.681525
\(283\) 13.5813 0.807326 0.403663 0.914908i \(-0.367737\pi\)
0.403663 + 0.914908i \(0.367737\pi\)
\(284\) 0.455263 0.0270149
\(285\) 0.158146 0.00936775
\(286\) 0 0
\(287\) 9.69177 0.572087
\(288\) 0.379898 0.0223857
\(289\) 8.00000 0.470588
\(290\) 8.72406 0.512295
\(291\) 6.41196 0.375876
\(292\) 0.581901 0.0340532
\(293\) −19.9023 −1.16271 −0.581353 0.813651i \(-0.697477\pi\)
−0.581353 + 0.813651i \(0.697477\pi\)
\(294\) −7.46257 −0.435226
\(295\) −8.09846 −0.471511
\(296\) 13.5072 0.785088
\(297\) 0 0
\(298\) −2.05927 −0.119290
\(299\) −7.10358 −0.410811
\(300\) −0.0671858 −0.00387897
\(301\) 6.91591 0.398626
\(302\) 12.5595 0.722719
\(303\) −8.77143 −0.503906
\(304\) 0.610619 0.0350214
\(305\) −14.2917 −0.818342
\(306\) −6.95128 −0.397378
\(307\) 14.9354 0.852410 0.426205 0.904627i \(-0.359850\pi\)
0.426205 + 0.904627i \(0.359850\pi\)
\(308\) 0 0
\(309\) 11.5666 0.658003
\(310\) −4.24002 −0.240817
\(311\) −4.99700 −0.283354 −0.141677 0.989913i \(-0.545249\pi\)
−0.141677 + 0.989913i \(0.545249\pi\)
\(312\) −4.07627 −0.230773
\(313\) 9.39648 0.531120 0.265560 0.964094i \(-0.414443\pi\)
0.265560 + 0.964094i \(0.414443\pi\)
\(314\) −24.5209 −1.38379
\(315\) 1.27759 0.0719841
\(316\) −0.171037 −0.00962155
\(317\) 2.15253 0.120898 0.0604492 0.998171i \(-0.480747\pi\)
0.0604492 + 0.998171i \(0.480747\pi\)
\(318\) 13.0218 0.730227
\(319\) 0 0
\(320\) −8.25038 −0.461210
\(321\) −15.3467 −0.856567
\(322\) 8.89563 0.495734
\(323\) 0.790729 0.0439973
\(324\) −0.0671858 −0.00373254
\(325\) 1.41837 0.0786767
\(326\) 32.6766 1.80979
\(327\) −14.4004 −0.796346
\(328\) 21.8015 1.20378
\(329\) 10.5173 0.579836
\(330\) 0 0
\(331\) −19.5116 −1.07245 −0.536227 0.844074i \(-0.680151\pi\)
−0.536227 + 0.844074i \(0.680151\pi\)
\(332\) 0.680063 0.0373233
\(333\) −4.69991 −0.257554
\(334\) −0.837950 −0.0458506
\(335\) 7.38362 0.403410
\(336\) 4.93293 0.269113
\(337\) −31.6047 −1.72162 −0.860809 0.508929i \(-0.830042\pi\)
−0.860809 + 0.508929i \(0.830042\pi\)
\(338\) −15.2765 −0.830931
\(339\) 19.3645 1.05174
\(340\) −0.335929 −0.0182183
\(341\) 0 0
\(342\) −0.219863 −0.0118888
\(343\) 15.8009 0.853171
\(344\) 15.5572 0.838789
\(345\) 5.00829 0.269637
\(346\) −13.4353 −0.722286
\(347\) −9.38313 −0.503713 −0.251856 0.967765i \(-0.581041\pi\)
−0.251856 + 0.967765i \(0.581041\pi\)
\(348\) 0.421601 0.0226002
\(349\) 24.8131 1.32822 0.664108 0.747637i \(-0.268812\pi\)
0.664108 + 0.747637i \(0.268812\pi\)
\(350\) −1.77618 −0.0949408
\(351\) 1.41837 0.0757067
\(352\) 0 0
\(353\) −19.4788 −1.03675 −0.518375 0.855153i \(-0.673463\pi\)
−0.518375 + 0.855153i \(0.673463\pi\)
\(354\) 11.2589 0.598406
\(355\) 6.77618 0.359642
\(356\) −0.742046 −0.0393284
\(357\) 6.38796 0.338086
\(358\) −1.66235 −0.0878578
\(359\) −29.7701 −1.57121 −0.785603 0.618732i \(-0.787647\pi\)
−0.785603 + 0.618732i \(0.787647\pi\)
\(360\) 2.87392 0.151469
\(361\) −18.9750 −0.998684
\(362\) 21.6520 1.13800
\(363\) 0 0
\(364\) 0.121747 0.00638126
\(365\) 8.66107 0.453341
\(366\) 19.8692 1.03858
\(367\) −6.43597 −0.335955 −0.167977 0.985791i \(-0.553724\pi\)
−0.167977 + 0.985791i \(0.553724\pi\)
\(368\) 19.3376 1.00804
\(369\) −7.58597 −0.394910
\(370\) 6.53409 0.339691
\(371\) −11.9665 −0.621272
\(372\) −0.204904 −0.0106238
\(373\) 20.8924 1.08177 0.540883 0.841098i \(-0.318090\pi\)
0.540883 + 0.841098i \(0.318090\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 23.6584 1.22009
\(377\) −8.90045 −0.458396
\(378\) −1.77618 −0.0913568
\(379\) −14.1991 −0.729359 −0.364680 0.931133i \(-0.618822\pi\)
−0.364680 + 0.931133i \(0.618822\pi\)
\(380\) −0.0106252 −0.000545059 0
\(381\) 6.02415 0.308627
\(382\) 25.5830 1.30894
\(383\) −26.4783 −1.35298 −0.676489 0.736453i \(-0.736499\pi\)
−0.676489 + 0.736453i \(0.736499\pi\)
\(384\) 10.7104 0.546561
\(385\) 0 0
\(386\) −2.17990 −0.110954
\(387\) −5.41324 −0.275171
\(388\) −0.430793 −0.0218702
\(389\) −36.4965 −1.85044 −0.925222 0.379427i \(-0.876121\pi\)
−0.925222 + 0.379427i \(0.876121\pi\)
\(390\) −1.97189 −0.0998506
\(391\) 25.0415 1.26640
\(392\) 15.4265 0.779157
\(393\) 18.7278 0.944695
\(394\) −11.0804 −0.558220
\(395\) −2.54572 −0.128089
\(396\) 0 0
\(397\) −8.03969 −0.403500 −0.201750 0.979437i \(-0.564663\pi\)
−0.201750 + 0.979437i \(0.564663\pi\)
\(398\) 4.90956 0.246094
\(399\) 0.202046 0.0101149
\(400\) −3.86111 −0.193056
\(401\) −28.0902 −1.40276 −0.701379 0.712788i \(-0.747432\pi\)
−0.701379 + 0.712788i \(0.747432\pi\)
\(402\) −10.2651 −0.511978
\(403\) 4.32575 0.215481
\(404\) 0.589316 0.0293196
\(405\) −1.00000 −0.0496904
\(406\) 11.1458 0.553156
\(407\) 0 0
\(408\) 14.3696 0.711401
\(409\) 5.97950 0.295667 0.147834 0.989012i \(-0.452770\pi\)
0.147834 + 0.989012i \(0.452770\pi\)
\(410\) 10.5464 0.520852
\(411\) 3.03719 0.149813
\(412\) −0.777114 −0.0382857
\(413\) −10.3465 −0.509119
\(414\) −6.96281 −0.342203
\(415\) 10.1221 0.496876
\(416\) 0.538833 0.0264185
\(417\) 2.21192 0.108318
\(418\) 0 0
\(419\) −15.4707 −0.755795 −0.377897 0.925847i \(-0.623353\pi\)
−0.377897 + 0.925847i \(0.623353\pi\)
\(420\) −0.0858360 −0.00418837
\(421\) 34.5746 1.68506 0.842532 0.538647i \(-0.181064\pi\)
0.842532 + 0.538647i \(0.181064\pi\)
\(422\) −28.1597 −1.37079
\(423\) −8.23211 −0.400259
\(424\) −26.9185 −1.30728
\(425\) −5.00000 −0.242536
\(426\) −9.42063 −0.456431
\(427\) −18.2590 −0.883614
\(428\) 1.03108 0.0498390
\(429\) 0 0
\(430\) 7.52580 0.362926
\(431\) −3.36052 −0.161870 −0.0809352 0.996719i \(-0.525791\pi\)
−0.0809352 + 0.996719i \(0.525791\pi\)
\(432\) −3.86111 −0.185768
\(433\) 3.67779 0.176744 0.0883718 0.996088i \(-0.471834\pi\)
0.0883718 + 0.996088i \(0.471834\pi\)
\(434\) −5.41702 −0.260025
\(435\) 6.27515 0.300870
\(436\) 0.967505 0.0463351
\(437\) 0.792040 0.0378884
\(438\) −12.0411 −0.575346
\(439\) 1.55432 0.0741835 0.0370917 0.999312i \(-0.488191\pi\)
0.0370917 + 0.999312i \(0.488191\pi\)
\(440\) 0 0
\(441\) −5.36776 −0.255608
\(442\) −9.85946 −0.468967
\(443\) 21.2059 1.00752 0.503761 0.863843i \(-0.331949\pi\)
0.503761 + 0.863843i \(0.331949\pi\)
\(444\) 0.315767 0.0149857
\(445\) −11.0447 −0.523569
\(446\) 31.3503 1.48448
\(447\) −1.48122 −0.0700592
\(448\) −10.5406 −0.497997
\(449\) 15.1106 0.713113 0.356557 0.934274i \(-0.383951\pi\)
0.356557 + 0.934274i \(0.383951\pi\)
\(450\) 1.39026 0.0655373
\(451\) 0 0
\(452\) −1.30102 −0.0611949
\(453\) 9.03395 0.424452
\(454\) −26.1454 −1.22707
\(455\) 1.81209 0.0849521
\(456\) 0.454498 0.0212838
\(457\) −41.3042 −1.93213 −0.966064 0.258303i \(-0.916837\pi\)
−0.966064 + 0.258303i \(0.916837\pi\)
\(458\) −33.1326 −1.54818
\(459\) −5.00000 −0.233380
\(460\) −0.336486 −0.0156887
\(461\) 16.3158 0.759901 0.379951 0.925007i \(-0.375941\pi\)
0.379951 + 0.925007i \(0.375941\pi\)
\(462\) 0 0
\(463\) 8.47904 0.394054 0.197027 0.980398i \(-0.436871\pi\)
0.197027 + 0.980398i \(0.436871\pi\)
\(464\) 24.2291 1.12481
\(465\) −3.04981 −0.141432
\(466\) 14.0302 0.649938
\(467\) −36.5669 −1.69212 −0.846058 0.533090i \(-0.821031\pi\)
−0.846058 + 0.533090i \(0.821031\pi\)
\(468\) −0.0952940 −0.00440497
\(469\) 9.43325 0.435587
\(470\) 11.4447 0.527907
\(471\) −17.6377 −0.812701
\(472\) −23.2743 −1.07129
\(473\) 0 0
\(474\) 3.53921 0.162561
\(475\) −0.158146 −0.00725623
\(476\) −0.429180 −0.0196714
\(477\) 9.36648 0.428862
\(478\) −0.232488 −0.0106338
\(479\) 38.9513 1.77973 0.889866 0.456222i \(-0.150798\pi\)
0.889866 + 0.456222i \(0.150798\pi\)
\(480\) −0.379898 −0.0173399
\(481\) −6.66619 −0.303952
\(482\) −1.34195 −0.0611243
\(483\) 6.39855 0.291144
\(484\) 0 0
\(485\) −6.41196 −0.291152
\(486\) 1.39026 0.0630633
\(487\) 8.27209 0.374844 0.187422 0.982279i \(-0.439987\pi\)
0.187422 + 0.982279i \(0.439987\pi\)
\(488\) −41.0733 −1.85930
\(489\) 23.5040 1.06289
\(490\) 7.46257 0.337124
\(491\) 12.1322 0.547518 0.273759 0.961798i \(-0.411733\pi\)
0.273759 + 0.961798i \(0.411733\pi\)
\(492\) 0.509669 0.0229777
\(493\) 31.3757 1.41309
\(494\) −0.311846 −0.0140306
\(495\) 0 0
\(496\) −11.7757 −0.528744
\(497\) 8.65719 0.388328
\(498\) −14.0724 −0.630597
\(499\) −28.3581 −1.26948 −0.634740 0.772725i \(-0.718893\pi\)
−0.634740 + 0.772725i \(0.718893\pi\)
\(500\) 0.0671858 0.00300464
\(501\) −0.602731 −0.0269280
\(502\) −32.6852 −1.45881
\(503\) 15.2800 0.681300 0.340650 0.940190i \(-0.389353\pi\)
0.340650 + 0.940190i \(0.389353\pi\)
\(504\) 3.67169 0.163550
\(505\) 8.77143 0.390324
\(506\) 0 0
\(507\) −10.9882 −0.488005
\(508\) −0.404737 −0.0179573
\(509\) −22.0494 −0.977321 −0.488661 0.872474i \(-0.662514\pi\)
−0.488661 + 0.872474i \(0.662514\pi\)
\(510\) 6.95128 0.307808
\(511\) 11.0653 0.489500
\(512\) −23.6599 −1.04563
\(513\) −0.158146 −0.00698231
\(514\) −9.15169 −0.403664
\(515\) −11.5666 −0.509687
\(516\) 0.363693 0.0160107
\(517\) 0 0
\(518\) 8.34789 0.366785
\(519\) −9.66389 −0.424198
\(520\) 4.07627 0.178756
\(521\) −23.9380 −1.04874 −0.524371 0.851490i \(-0.675700\pi\)
−0.524371 + 0.851490i \(0.675700\pi\)
\(522\) −8.72406 −0.381842
\(523\) 25.3421 1.10813 0.554066 0.832473i \(-0.313075\pi\)
0.554066 + 0.832473i \(0.313075\pi\)
\(524\) −1.25824 −0.0549667
\(525\) −1.27759 −0.0557586
\(526\) −17.3140 −0.754927
\(527\) −15.2491 −0.664260
\(528\) 0 0
\(529\) 2.08298 0.0905642
\(530\) −13.0218 −0.565632
\(531\) 8.09846 0.351443
\(532\) −0.0135746 −0.000588534 0
\(533\) −10.7597 −0.466053
\(534\) 15.3550 0.664474
\(535\) 15.3467 0.663494
\(536\) 21.2199 0.916561
\(537\) −1.19571 −0.0515988
\(538\) 28.8797 1.24509
\(539\) 0 0
\(540\) 0.0671858 0.00289122
\(541\) 35.0634 1.50749 0.753747 0.657165i \(-0.228245\pi\)
0.753747 + 0.657165i \(0.228245\pi\)
\(542\) −20.0062 −0.859338
\(543\) 15.5741 0.668347
\(544\) −1.89949 −0.0814399
\(545\) 14.4004 0.616847
\(546\) −2.51927 −0.107815
\(547\) 1.10787 0.0473689 0.0236845 0.999719i \(-0.492460\pi\)
0.0236845 + 0.999719i \(0.492460\pi\)
\(548\) −0.204056 −0.00871684
\(549\) 14.2917 0.609956
\(550\) 0 0
\(551\) 0.992388 0.0422771
\(552\) 14.3934 0.612625
\(553\) −3.25239 −0.138306
\(554\) 24.3117 1.03291
\(555\) 4.69991 0.199500
\(556\) −0.148609 −0.00630244
\(557\) 5.41988 0.229648 0.114824 0.993386i \(-0.463370\pi\)
0.114824 + 0.993386i \(0.463370\pi\)
\(558\) 4.24002 0.179495
\(559\) −7.67795 −0.324743
\(560\) −4.93293 −0.208454
\(561\) 0 0
\(562\) 26.2564 1.10756
\(563\) −32.7448 −1.38003 −0.690015 0.723795i \(-0.742396\pi\)
−0.690015 + 0.723795i \(0.742396\pi\)
\(564\) 0.553081 0.0232889
\(565\) −19.3645 −0.814672
\(566\) 18.8815 0.793650
\(567\) −1.27759 −0.0536538
\(568\) 19.4742 0.817119
\(569\) 3.51736 0.147455 0.0737277 0.997278i \(-0.476510\pi\)
0.0737277 + 0.997278i \(0.476510\pi\)
\(570\) 0.219863 0.00920906
\(571\) 36.0252 1.50761 0.753804 0.657099i \(-0.228217\pi\)
0.753804 + 0.657099i \(0.228217\pi\)
\(572\) 0 0
\(573\) 18.4016 0.768738
\(574\) 13.4740 0.562396
\(575\) −5.00829 −0.208860
\(576\) 8.25038 0.343766
\(577\) 15.5501 0.647357 0.323679 0.946167i \(-0.395080\pi\)
0.323679 + 0.946167i \(0.395080\pi\)
\(578\) 11.1221 0.462617
\(579\) −1.56799 −0.0651633
\(580\) −0.421601 −0.0175060
\(581\) 12.9319 0.536507
\(582\) 8.91428 0.369509
\(583\) 0 0
\(584\) 24.8912 1.03001
\(585\) −1.41837 −0.0586422
\(586\) −27.6694 −1.14301
\(587\) −24.2604 −1.00133 −0.500667 0.865640i \(-0.666912\pi\)
−0.500667 + 0.865640i \(0.666912\pi\)
\(588\) 0.360637 0.0148724
\(589\) −0.482315 −0.0198735
\(590\) −11.2589 −0.463523
\(591\) −7.97000 −0.327842
\(592\) 18.1469 0.745833
\(593\) −27.4019 −1.12526 −0.562630 0.826709i \(-0.690210\pi\)
−0.562630 + 0.826709i \(0.690210\pi\)
\(594\) 0 0
\(595\) −6.38796 −0.261881
\(596\) 0.0995167 0.00407636
\(597\) 3.53141 0.144531
\(598\) −9.87581 −0.403852
\(599\) 10.6773 0.436262 0.218131 0.975920i \(-0.430004\pi\)
0.218131 + 0.975920i \(0.430004\pi\)
\(600\) −2.87392 −0.117327
\(601\) −11.0663 −0.451403 −0.225701 0.974197i \(-0.572467\pi\)
−0.225701 + 0.974197i \(0.572467\pi\)
\(602\) 9.61489 0.391874
\(603\) −7.38362 −0.300684
\(604\) −0.606953 −0.0246966
\(605\) 0 0
\(606\) −12.1945 −0.495370
\(607\) 0.514518 0.0208836 0.0104418 0.999945i \(-0.496676\pi\)
0.0104418 + 0.999945i \(0.496676\pi\)
\(608\) −0.0600792 −0.00243653
\(609\) 8.01707 0.324868
\(610\) −19.8692 −0.804479
\(611\) −11.6761 −0.472366
\(612\) 0.335929 0.0135791
\(613\) −19.0977 −0.771348 −0.385674 0.922635i \(-0.626031\pi\)
−0.385674 + 0.922635i \(0.626031\pi\)
\(614\) 20.7641 0.837970
\(615\) 7.58597 0.305896
\(616\) 0 0
\(617\) −4.70745 −0.189515 −0.0947573 0.995500i \(-0.530208\pi\)
−0.0947573 + 0.995500i \(0.530208\pi\)
\(618\) 16.0806 0.646857
\(619\) 37.3691 1.50199 0.750996 0.660307i \(-0.229574\pi\)
0.750996 + 0.660307i \(0.229574\pi\)
\(620\) 0.204904 0.00822915
\(621\) −5.00829 −0.200976
\(622\) −6.94711 −0.278554
\(623\) −14.1106 −0.565329
\(624\) −5.47647 −0.219234
\(625\) 1.00000 0.0400000
\(626\) 13.0635 0.522123
\(627\) 0 0
\(628\) 1.18500 0.0472867
\(629\) 23.4996 0.936989
\(630\) 1.77618 0.0707647
\(631\) 35.5669 1.41590 0.707949 0.706264i \(-0.249621\pi\)
0.707949 + 0.706264i \(0.249621\pi\)
\(632\) −7.31621 −0.291023
\(633\) −20.2550 −0.805065
\(634\) 2.99257 0.118850
\(635\) −6.02415 −0.239061
\(636\) −0.629295 −0.0249532
\(637\) −7.61344 −0.301656
\(638\) 0 0
\(639\) −6.77618 −0.268062
\(640\) −10.7104 −0.423364
\(641\) 12.2098 0.482260 0.241130 0.970493i \(-0.422482\pi\)
0.241130 + 0.970493i \(0.422482\pi\)
\(642\) −21.3358 −0.842057
\(643\) −20.9596 −0.826565 −0.413282 0.910603i \(-0.635618\pi\)
−0.413282 + 0.910603i \(0.635618\pi\)
\(644\) −0.429892 −0.0169401
\(645\) 5.41324 0.213146
\(646\) 1.09932 0.0432520
\(647\) 14.8766 0.584859 0.292430 0.956287i \(-0.405536\pi\)
0.292430 + 0.956287i \(0.405536\pi\)
\(648\) −2.87392 −0.112898
\(649\) 0 0
\(650\) 1.97189 0.0773440
\(651\) −3.89642 −0.152713
\(652\) −1.57914 −0.0618438
\(653\) −12.1308 −0.474713 −0.237357 0.971423i \(-0.576281\pi\)
−0.237357 + 0.971423i \(0.576281\pi\)
\(654\) −20.0203 −0.782856
\(655\) −18.7278 −0.731757
\(656\) 29.2903 1.14359
\(657\) −8.66107 −0.337900
\(658\) 14.6217 0.570014
\(659\) −7.49994 −0.292156 −0.146078 0.989273i \(-0.546665\pi\)
−0.146078 + 0.989273i \(0.546665\pi\)
\(660\) 0 0
\(661\) 9.65248 0.375438 0.187719 0.982223i \(-0.439891\pi\)
0.187719 + 0.982223i \(0.439891\pi\)
\(662\) −27.1261 −1.05429
\(663\) −7.09183 −0.275424
\(664\) 29.0902 1.12892
\(665\) −0.202046 −0.00783500
\(666\) −6.53409 −0.253191
\(667\) 31.4278 1.21689
\(668\) 0.0404949 0.00156680
\(669\) 22.5500 0.871833
\(670\) 10.2651 0.396577
\(671\) 0 0
\(672\) −0.485354 −0.0187229
\(673\) −24.4496 −0.942463 −0.471231 0.882010i \(-0.656190\pi\)
−0.471231 + 0.882010i \(0.656190\pi\)
\(674\) −43.9386 −1.69245
\(675\) 1.00000 0.0384900
\(676\) 0.738254 0.0283944
\(677\) −46.7394 −1.79634 −0.898171 0.439646i \(-0.855104\pi\)
−0.898171 + 0.439646i \(0.855104\pi\)
\(678\) 26.9217 1.03392
\(679\) −8.19187 −0.314375
\(680\) −14.3696 −0.551049
\(681\) −18.8062 −0.720654
\(682\) 0 0
\(683\) −28.1941 −1.07882 −0.539408 0.842045i \(-0.681352\pi\)
−0.539408 + 0.842045i \(0.681352\pi\)
\(684\) 0.0106252 0.000406263 0
\(685\) −3.03719 −0.116045
\(686\) 21.9674 0.838718
\(687\) −23.8320 −0.909247
\(688\) 20.9011 0.796849
\(689\) 13.2851 0.506122
\(690\) 6.96281 0.265070
\(691\) 11.5971 0.441175 0.220587 0.975367i \(-0.429203\pi\)
0.220587 + 0.975367i \(0.429203\pi\)
\(692\) 0.649276 0.0246818
\(693\) 0 0
\(694\) −13.0450 −0.495180
\(695\) −2.21192 −0.0839028
\(696\) 18.0343 0.683587
\(697\) 37.9298 1.43670
\(698\) 34.4966 1.30572
\(699\) 10.0918 0.381708
\(700\) 0.0858360 0.00324429
\(701\) 36.7019 1.38621 0.693107 0.720835i \(-0.256241\pi\)
0.693107 + 0.720835i \(0.256241\pi\)
\(702\) 1.97189 0.0744243
\(703\) 0.743272 0.0280330
\(704\) 0 0
\(705\) 8.23211 0.310039
\(706\) −27.0805 −1.01919
\(707\) 11.2063 0.421456
\(708\) −0.544102 −0.0204486
\(709\) 36.4905 1.37043 0.685214 0.728341i \(-0.259708\pi\)
0.685214 + 0.728341i \(0.259708\pi\)
\(710\) 9.42063 0.353550
\(711\) 2.54572 0.0954721
\(712\) −31.7415 −1.18956
\(713\) −15.2744 −0.572029
\(714\) 8.88090 0.332359
\(715\) 0 0
\(716\) 0.0803349 0.00300225
\(717\) −0.167227 −0.00624520
\(718\) −41.3881 −1.54459
\(719\) −9.32888 −0.347909 −0.173954 0.984754i \(-0.555654\pi\)
−0.173954 + 0.984754i \(0.555654\pi\)
\(720\) 3.86111 0.143895
\(721\) −14.7774 −0.550340
\(722\) −26.3801 −0.981766
\(723\) −0.965256 −0.0358983
\(724\) −1.04636 −0.0388875
\(725\) −6.27515 −0.233053
\(726\) 0 0
\(727\) −8.46883 −0.314091 −0.157046 0.987591i \(-0.550197\pi\)
−0.157046 + 0.987591i \(0.550197\pi\)
\(728\) 5.20780 0.193014
\(729\) 1.00000 0.0370370
\(730\) 12.0411 0.445661
\(731\) 27.0662 1.00108
\(732\) −0.960201 −0.0354901
\(733\) −29.0470 −1.07288 −0.536438 0.843940i \(-0.680230\pi\)
−0.536438 + 0.843940i \(0.680230\pi\)
\(734\) −8.94765 −0.330264
\(735\) 5.36776 0.197993
\(736\) −1.90264 −0.0701322
\(737\) 0 0
\(738\) −10.5464 −0.388220
\(739\) 13.7551 0.505990 0.252995 0.967468i \(-0.418584\pi\)
0.252995 + 0.967468i \(0.418584\pi\)
\(740\) −0.315767 −0.0116078
\(741\) −0.224308 −0.00824018
\(742\) −16.6366 −0.610747
\(743\) 34.9135 1.28085 0.640427 0.768019i \(-0.278758\pi\)
0.640427 + 0.768019i \(0.278758\pi\)
\(744\) −8.76492 −0.321338
\(745\) 1.48122 0.0542676
\(746\) 29.0458 1.06344
\(747\) −10.1221 −0.370349
\(748\) 0 0
\(749\) 19.6068 0.716416
\(750\) −1.39026 −0.0507650
\(751\) 22.0992 0.806412 0.403206 0.915109i \(-0.367896\pi\)
0.403206 + 0.915109i \(0.367896\pi\)
\(752\) 31.7851 1.15908
\(753\) −23.5102 −0.856759
\(754\) −12.3739 −0.450631
\(755\) −9.03395 −0.328779
\(756\) 0.0858360 0.00312182
\(757\) −45.0300 −1.63664 −0.818321 0.574761i \(-0.805095\pi\)
−0.818321 + 0.574761i \(0.805095\pi\)
\(758\) −19.7404 −0.717004
\(759\) 0 0
\(760\) −0.454498 −0.0164864
\(761\) −33.6001 −1.21800 −0.609001 0.793169i \(-0.708430\pi\)
−0.609001 + 0.793169i \(0.708430\pi\)
\(762\) 8.37512 0.303399
\(763\) 18.3979 0.666048
\(764\) −1.23633 −0.0447287
\(765\) 5.00000 0.180775
\(766\) −36.8116 −1.33006
\(767\) 11.4866 0.414756
\(768\) −1.61062 −0.0581182
\(769\) −24.6086 −0.887408 −0.443704 0.896173i \(-0.646336\pi\)
−0.443704 + 0.896173i \(0.646336\pi\)
\(770\) 0 0
\(771\) −6.58273 −0.237071
\(772\) 0.105346 0.00379150
\(773\) −23.6816 −0.851768 −0.425884 0.904778i \(-0.640037\pi\)
−0.425884 + 0.904778i \(0.640037\pi\)
\(774\) −7.52580 −0.270509
\(775\) 3.04981 0.109553
\(776\) −18.4275 −0.661507
\(777\) 6.00457 0.215413
\(778\) −50.7394 −1.81910
\(779\) 1.19969 0.0429833
\(780\) 0.0952940 0.00341207
\(781\) 0 0
\(782\) 34.8141 1.24495
\(783\) −6.27515 −0.224255
\(784\) 20.7255 0.740198
\(785\) 17.6377 0.629515
\(786\) 26.0365 0.928692
\(787\) 18.4210 0.656639 0.328320 0.944567i \(-0.393518\pi\)
0.328320 + 0.944567i \(0.393518\pi\)
\(788\) 0.535471 0.0190754
\(789\) −12.4538 −0.443368
\(790\) −3.53921 −0.125919
\(791\) −24.7399 −0.879651
\(792\) 0 0
\(793\) 20.2709 0.719840
\(794\) −11.1772 −0.396665
\(795\) −9.36648 −0.332195
\(796\) −0.237260 −0.00840947
\(797\) −6.50665 −0.230477 −0.115239 0.993338i \(-0.536763\pi\)
−0.115239 + 0.993338i \(0.536763\pi\)
\(798\) 0.280895 0.00994359
\(799\) 41.1606 1.45616
\(800\) 0.379898 0.0134314
\(801\) 11.0447 0.390245
\(802\) −39.0526 −1.37900
\(803\) 0 0
\(804\) 0.496074 0.0174952
\(805\) −6.39855 −0.225519
\(806\) 6.01390 0.211831
\(807\) 20.7729 0.731242
\(808\) 25.2084 0.886828
\(809\) −11.8505 −0.416642 −0.208321 0.978060i \(-0.566800\pi\)
−0.208321 + 0.978060i \(0.566800\pi\)
\(810\) −1.39026 −0.0488486
\(811\) −7.51391 −0.263849 −0.131925 0.991260i \(-0.542116\pi\)
−0.131925 + 0.991260i \(0.542116\pi\)
\(812\) −0.538633 −0.0189023
\(813\) −14.3903 −0.504688
\(814\) 0 0
\(815\) −23.5040 −0.823310
\(816\) 19.3056 0.675830
\(817\) 0.856081 0.0299505
\(818\) 8.31305 0.290659
\(819\) −1.81209 −0.0633196
\(820\) −0.509669 −0.0177984
\(821\) 37.3365 1.30305 0.651527 0.758625i \(-0.274129\pi\)
0.651527 + 0.758625i \(0.274129\pi\)
\(822\) 4.22247 0.147276
\(823\) −43.0498 −1.50062 −0.750311 0.661085i \(-0.770096\pi\)
−0.750311 + 0.661085i \(0.770096\pi\)
\(824\) −33.2416 −1.15803
\(825\) 0 0
\(826\) −14.3843 −0.500495
\(827\) 20.0304 0.696524 0.348262 0.937397i \(-0.386772\pi\)
0.348262 + 0.937397i \(0.386772\pi\)
\(828\) 0.336486 0.0116937
\(829\) −47.9207 −1.66435 −0.832177 0.554510i \(-0.812906\pi\)
−0.832177 + 0.554510i \(0.812906\pi\)
\(830\) 14.0724 0.488458
\(831\) 17.4872 0.606624
\(832\) 11.7021 0.405696
\(833\) 26.8388 0.929909
\(834\) 3.07513 0.106483
\(835\) 0.602731 0.0208584
\(836\) 0 0
\(837\) 3.04981 0.105417
\(838\) −21.5083 −0.742992
\(839\) 2.22093 0.0766750 0.0383375 0.999265i \(-0.487794\pi\)
0.0383375 + 0.999265i \(0.487794\pi\)
\(840\) −3.67169 −0.126685
\(841\) 10.3775 0.357843
\(842\) 48.0676 1.65652
\(843\) 18.8860 0.650468
\(844\) 1.36085 0.0468424
\(845\) 10.9882 0.378007
\(846\) −11.4447 −0.393479
\(847\) 0 0
\(848\) −36.1651 −1.24191
\(849\) 13.5813 0.466110
\(850\) −6.95128 −0.238427
\(851\) 23.5385 0.806890
\(852\) 0.455263 0.0155971
\(853\) 6.37161 0.218160 0.109080 0.994033i \(-0.465210\pi\)
0.109080 + 0.994033i \(0.465210\pi\)
\(854\) −25.3847 −0.868646
\(855\) 0.158146 0.00540847
\(856\) 44.1051 1.50748
\(857\) −35.9060 −1.22653 −0.613263 0.789878i \(-0.710144\pi\)
−0.613263 + 0.789878i \(0.710144\pi\)
\(858\) 0 0
\(859\) 56.4697 1.92672 0.963360 0.268212i \(-0.0864328\pi\)
0.963360 + 0.268212i \(0.0864328\pi\)
\(860\) −0.363693 −0.0124018
\(861\) 9.69177 0.330295
\(862\) −4.67198 −0.159128
\(863\) −31.0742 −1.05778 −0.528888 0.848691i \(-0.677391\pi\)
−0.528888 + 0.848691i \(0.677391\pi\)
\(864\) 0.379898 0.0129244
\(865\) 9.66389 0.328582
\(866\) 5.11308 0.173749
\(867\) 8.00000 0.271694
\(868\) 0.261784 0.00888552
\(869\) 0 0
\(870\) 8.72406 0.295773
\(871\) −10.4727 −0.354853
\(872\) 41.3857 1.40150
\(873\) 6.41196 0.217012
\(874\) 1.10114 0.0372466
\(875\) 1.27759 0.0431905
\(876\) 0.581901 0.0196606
\(877\) −16.8224 −0.568053 −0.284026 0.958816i \(-0.591670\pi\)
−0.284026 + 0.958816i \(0.591670\pi\)
\(878\) 2.16090 0.0729268
\(879\) −19.9023 −0.671289
\(880\) 0 0
\(881\) 26.5633 0.894940 0.447470 0.894299i \(-0.352325\pi\)
0.447470 + 0.894299i \(0.352325\pi\)
\(882\) −7.46257 −0.251278
\(883\) −54.3742 −1.82984 −0.914919 0.403638i \(-0.867746\pi\)
−0.914919 + 0.403638i \(0.867746\pi\)
\(884\) 0.476470 0.0160254
\(885\) −8.09846 −0.272227
\(886\) 29.4816 0.990455
\(887\) 41.2262 1.38424 0.692120 0.721783i \(-0.256677\pi\)
0.692120 + 0.721783i \(0.256677\pi\)
\(888\) 13.5072 0.453271
\(889\) −7.69640 −0.258129
\(890\) −15.3550 −0.514699
\(891\) 0 0
\(892\) −1.51504 −0.0507273
\(893\) 1.30187 0.0435655
\(894\) −2.05927 −0.0688724
\(895\) 1.19571 0.0399682
\(896\) −13.6835 −0.457132
\(897\) −7.10358 −0.237182
\(898\) 21.0076 0.701033
\(899\) −19.1380 −0.638289
\(900\) −0.0671858 −0.00223953
\(901\) −46.8324 −1.56021
\(902\) 0 0
\(903\) 6.91591 0.230147
\(904\) −55.6521 −1.85096
\(905\) −15.5741 −0.517699
\(906\) 12.5595 0.417262
\(907\) 42.4046 1.40802 0.704010 0.710190i \(-0.251391\pi\)
0.704010 + 0.710190i \(0.251391\pi\)
\(908\) 1.26351 0.0419310
\(909\) −8.77143 −0.290930
\(910\) 2.51927 0.0835130
\(911\) −8.01199 −0.265449 −0.132725 0.991153i \(-0.542373\pi\)
−0.132725 + 0.991153i \(0.542373\pi\)
\(912\) 0.610619 0.0202196
\(913\) 0 0
\(914\) −57.4234 −1.89940
\(915\) −14.2917 −0.472470
\(916\) 1.60117 0.0529042
\(917\) −23.9265 −0.790123
\(918\) −6.95128 −0.229427
\(919\) −41.2336 −1.36017 −0.680086 0.733132i \(-0.738058\pi\)
−0.680086 + 0.733132i \(0.738058\pi\)
\(920\) −14.3934 −0.474537
\(921\) 14.9354 0.492139
\(922\) 22.6831 0.747028
\(923\) −9.61110 −0.316353
\(924\) 0 0
\(925\) −4.69991 −0.154532
\(926\) 11.7880 0.387379
\(927\) 11.5666 0.379898
\(928\) −2.38391 −0.0782558
\(929\) −15.1939 −0.498495 −0.249247 0.968440i \(-0.580183\pi\)
−0.249247 + 0.968440i \(0.580183\pi\)
\(930\) −4.24002 −0.139036
\(931\) 0.848889 0.0278212
\(932\) −0.678027 −0.0222095
\(933\) −4.99700 −0.163594
\(934\) −50.8375 −1.66345
\(935\) 0 0
\(936\) −4.07627 −0.133237
\(937\) −25.5213 −0.833746 −0.416873 0.908965i \(-0.636874\pi\)
−0.416873 + 0.908965i \(0.636874\pi\)
\(938\) 13.1146 0.428208
\(939\) 9.39648 0.306643
\(940\) −0.553081 −0.0180395
\(941\) −32.3673 −1.05514 −0.527572 0.849511i \(-0.676897\pi\)
−0.527572 + 0.849511i \(0.676897\pi\)
\(942\) −24.5209 −0.798934
\(943\) 37.9927 1.23721
\(944\) −31.2691 −1.01772
\(945\) 1.27759 0.0415600
\(946\) 0 0
\(947\) −40.1516 −1.30475 −0.652375 0.757896i \(-0.726227\pi\)
−0.652375 + 0.757896i \(0.726227\pi\)
\(948\) −0.171037 −0.00555501
\(949\) −12.2846 −0.398774
\(950\) −0.219863 −0.00713331
\(951\) 2.15253 0.0698007
\(952\) −18.3585 −0.595001
\(953\) −35.6513 −1.15486 −0.577429 0.816441i \(-0.695944\pi\)
−0.577429 + 0.816441i \(0.695944\pi\)
\(954\) 13.0218 0.421597
\(955\) −18.4016 −0.595462
\(956\) 0.0112353 0.000363374 0
\(957\) 0 0
\(958\) 54.1524 1.74958
\(959\) −3.88029 −0.125301
\(960\) −8.25038 −0.266280
\(961\) −21.6986 −0.699956
\(962\) −9.26772 −0.298803
\(963\) −15.3467 −0.494539
\(964\) 0.0648515 0.00208873
\(965\) 1.56799 0.0504753
\(966\) 8.89563 0.286212
\(967\) 20.0622 0.645156 0.322578 0.946543i \(-0.395451\pi\)
0.322578 + 0.946543i \(0.395451\pi\)
\(968\) 0 0
\(969\) 0.790729 0.0254019
\(970\) −8.91428 −0.286220
\(971\) −41.6307 −1.33599 −0.667996 0.744165i \(-0.732848\pi\)
−0.667996 + 0.744165i \(0.732848\pi\)
\(972\) −0.0671858 −0.00215499
\(973\) −2.82593 −0.0905950
\(974\) 11.5003 0.368494
\(975\) 1.41837 0.0454240
\(976\) −55.1820 −1.76633
\(977\) 19.0722 0.610173 0.305087 0.952325i \(-0.401315\pi\)
0.305087 + 0.952325i \(0.401315\pi\)
\(978\) 32.6766 1.04488
\(979\) 0 0
\(980\) −0.360637 −0.0115201
\(981\) −14.4004 −0.459771
\(982\) 16.8668 0.538243
\(983\) 26.5563 0.847015 0.423507 0.905893i \(-0.360799\pi\)
0.423507 + 0.905893i \(0.360799\pi\)
\(984\) 21.8015 0.695005
\(985\) 7.97000 0.253945
\(986\) 43.6203 1.38915
\(987\) 10.5173 0.334768
\(988\) 0.0150703 0.000479452 0
\(989\) 27.1111 0.862082
\(990\) 0 0
\(991\) −24.2494 −0.770307 −0.385153 0.922853i \(-0.625851\pi\)
−0.385153 + 0.922853i \(0.625851\pi\)
\(992\) 1.15862 0.0367861
\(993\) −19.5116 −0.619182
\(994\) 12.0357 0.381750
\(995\) −3.53141 −0.111953
\(996\) 0.680063 0.0215486
\(997\) −16.0616 −0.508675 −0.254338 0.967116i \(-0.581857\pi\)
−0.254338 + 0.967116i \(0.581857\pi\)
\(998\) −39.4250 −1.24798
\(999\) −4.69991 −0.148699
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 1815.2.a.o.1.4 4
3.2 odd 2 5445.2.a.bv.1.1 4
5.4 even 2 9075.2.a.dj.1.1 4
11.2 odd 10 165.2.m.a.136.2 yes 8
11.6 odd 10 165.2.m.a.91.2 8
11.10 odd 2 1815.2.a.x.1.1 4
33.2 even 10 495.2.n.d.136.1 8
33.17 even 10 495.2.n.d.91.1 8
33.32 even 2 5445.2.a.be.1.4 4
55.2 even 20 825.2.bx.h.499.2 16
55.13 even 20 825.2.bx.h.499.3 16
55.17 even 20 825.2.bx.h.124.3 16
55.24 odd 10 825.2.n.k.301.1 8
55.28 even 20 825.2.bx.h.124.2 16
55.39 odd 10 825.2.n.k.751.1 8
55.54 odd 2 9075.2.a.cl.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.a.91.2 8 11.6 odd 10
165.2.m.a.136.2 yes 8 11.2 odd 10
495.2.n.d.91.1 8 33.17 even 10
495.2.n.d.136.1 8 33.2 even 10
825.2.n.k.301.1 8 55.24 odd 10
825.2.n.k.751.1 8 55.39 odd 10
825.2.bx.h.124.2 16 55.28 even 20
825.2.bx.h.124.3 16 55.17 even 20
825.2.bx.h.499.2 16 55.2 even 20
825.2.bx.h.499.3 16 55.13 even 20
1815.2.a.o.1.4 4 1.1 even 1 trivial
1815.2.a.x.1.1 4 11.10 odd 2
5445.2.a.be.1.4 4 33.32 even 2
5445.2.a.bv.1.1 4 3.2 odd 2
9075.2.a.cl.1.4 4 55.54 odd 2
9075.2.a.dj.1.1 4 5.4 even 2