Properties

Label 3549.2.a.bg.1.10
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Defining polynomial: \(x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + 4553 x^{7} - 6393 x^{6} - 6785 x^{5} + 7806 x^{4} + 4632 x^{3} - 3811 x^{2} - 1041 x + 281\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-1.08127\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} +1.66920 q^{5} +1.08127 q^{6} +1.00000 q^{7} -3.06092 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.08127 q^{2} +1.00000 q^{3} -0.830866 q^{4} +1.66920 q^{5} +1.08127 q^{6} +1.00000 q^{7} -3.06092 q^{8} +1.00000 q^{9} +1.80485 q^{10} -4.63545 q^{11} -0.830866 q^{12} +1.08127 q^{14} +1.66920 q^{15} -1.64793 q^{16} +4.03225 q^{17} +1.08127 q^{18} -0.793678 q^{19} -1.38688 q^{20} +1.00000 q^{21} -5.01215 q^{22} +4.31595 q^{23} -3.06092 q^{24} -2.21376 q^{25} +1.00000 q^{27} -0.830866 q^{28} +4.61741 q^{29} +1.80485 q^{30} +5.75711 q^{31} +4.33998 q^{32} -4.63545 q^{33} +4.35994 q^{34} +1.66920 q^{35} -0.830866 q^{36} +5.73497 q^{37} -0.858176 q^{38} -5.10929 q^{40} +7.33613 q^{41} +1.08127 q^{42} +11.4344 q^{43} +3.85144 q^{44} +1.66920 q^{45} +4.66668 q^{46} -5.10901 q^{47} -1.64793 q^{48} +1.00000 q^{49} -2.39366 q^{50} +4.03225 q^{51} -6.41614 q^{53} +1.08127 q^{54} -7.73752 q^{55} -3.06092 q^{56} -0.793678 q^{57} +4.99264 q^{58} +12.2304 q^{59} -1.38688 q^{60} +10.3412 q^{61} +6.22497 q^{62} +1.00000 q^{63} +7.98853 q^{64} -5.01215 q^{66} -1.86971 q^{67} -3.35026 q^{68} +4.31595 q^{69} +1.80485 q^{70} +6.08759 q^{71} -3.06092 q^{72} -3.11657 q^{73} +6.20102 q^{74} -2.21376 q^{75} +0.659440 q^{76} -4.63545 q^{77} +2.28592 q^{79} -2.75073 q^{80} +1.00000 q^{81} +7.93230 q^{82} +0.655507 q^{83} -0.830866 q^{84} +6.73066 q^{85} +12.3636 q^{86} +4.61741 q^{87} +14.1887 q^{88} -10.8262 q^{89} +1.80485 q^{90} -3.58597 q^{92} +5.75711 q^{93} -5.52419 q^{94} -1.32481 q^{95} +4.33998 q^{96} -14.7169 q^{97} +1.08127 q^{98} -4.63545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - 2q^{2} + 15q^{3} + 28q^{4} + 9q^{5} - 2q^{6} + 15q^{7} - 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q - 2q^{2} + 15q^{3} + 28q^{4} + 9q^{5} - 2q^{6} + 15q^{7} - 9q^{8} + 15q^{9} + 21q^{10} - 5q^{11} + 28q^{12} - 2q^{14} + 9q^{15} + 50q^{16} - q^{17} - 2q^{18} - 3q^{19} + 23q^{20} + 15q^{21} + 21q^{22} + 4q^{23} - 9q^{24} + 50q^{25} + 15q^{27} + 28q^{28} + 9q^{29} + 21q^{30} - 7q^{31} - 35q^{32} - 5q^{33} + 2q^{34} + 9q^{35} + 28q^{36} - 17q^{37} - 12q^{38} + 46q^{40} + 22q^{41} - 2q^{42} + 36q^{43} - 29q^{44} + 9q^{45} + q^{46} + 12q^{47} + 50q^{48} + 15q^{49} - 53q^{50} - q^{51} - 5q^{53} - 2q^{54} + 43q^{55} - 9q^{56} - 3q^{57} - 29q^{58} + 29q^{59} + 23q^{60} + 12q^{61} + 14q^{62} + 15q^{63} + 95q^{64} + 21q^{66} + 12q^{67} - 16q^{68} + 4q^{69} + 21q^{70} - 36q^{71} - 9q^{72} + 29q^{73} - 5q^{74} + 50q^{75} - 25q^{76} - 5q^{77} + 35q^{79} + 89q^{80} + 15q^{81} + 51q^{82} + 10q^{83} + 28q^{84} - 23q^{85} - 19q^{86} + 9q^{87} + 73q^{88} - 25q^{89} + 21q^{90} - 31q^{92} - 7q^{93} - 19q^{94} - 7q^{95} - 35q^{96} + 26q^{97} - 2q^{98} - 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.08127 0.764570 0.382285 0.924044i \(-0.375137\pi\)
0.382285 + 0.924044i \(0.375137\pi\)
\(3\) 1.00000 0.577350
\(4\) −0.830866 −0.415433
\(5\) 1.66920 0.746491 0.373245 0.927733i \(-0.378245\pi\)
0.373245 + 0.927733i \(0.378245\pi\)
\(6\) 1.08127 0.441425
\(7\) 1.00000 0.377964
\(8\) −3.06092 −1.08220
\(9\) 1.00000 0.333333
\(10\) 1.80485 0.570744
\(11\) −4.63545 −1.39764 −0.698821 0.715297i \(-0.746291\pi\)
−0.698821 + 0.715297i \(0.746291\pi\)
\(12\) −0.830866 −0.239850
\(13\) 0 0
\(14\) 1.08127 0.288980
\(15\) 1.66920 0.430987
\(16\) −1.64793 −0.411983
\(17\) 4.03225 0.977965 0.488983 0.872294i \(-0.337368\pi\)
0.488983 + 0.872294i \(0.337368\pi\)
\(18\) 1.08127 0.254857
\(19\) −0.793678 −0.182082 −0.0910411 0.995847i \(-0.529019\pi\)
−0.0910411 + 0.995847i \(0.529019\pi\)
\(20\) −1.38688 −0.310117
\(21\) 1.00000 0.218218
\(22\) −5.01215 −1.06859
\(23\) 4.31595 0.899937 0.449969 0.893044i \(-0.351435\pi\)
0.449969 + 0.893044i \(0.351435\pi\)
\(24\) −3.06092 −0.624807
\(25\) −2.21376 −0.442752
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −0.830866 −0.157019
\(29\) 4.61741 0.857431 0.428716 0.903439i \(-0.358966\pi\)
0.428716 + 0.903439i \(0.358966\pi\)
\(30\) 1.80485 0.329519
\(31\) 5.75711 1.03401 0.517004 0.855983i \(-0.327047\pi\)
0.517004 + 0.855983i \(0.327047\pi\)
\(32\) 4.33998 0.767208
\(33\) −4.63545 −0.806929
\(34\) 4.35994 0.747723
\(35\) 1.66920 0.282147
\(36\) −0.830866 −0.138478
\(37\) 5.73497 0.942823 0.471412 0.881913i \(-0.343745\pi\)
0.471412 + 0.881913i \(0.343745\pi\)
\(38\) −0.858176 −0.139215
\(39\) 0 0
\(40\) −5.10929 −0.807850
\(41\) 7.33613 1.14571 0.572855 0.819657i \(-0.305836\pi\)
0.572855 + 0.819657i \(0.305836\pi\)
\(42\) 1.08127 0.166843
\(43\) 11.4344 1.74373 0.871863 0.489750i \(-0.162912\pi\)
0.871863 + 0.489750i \(0.162912\pi\)
\(44\) 3.85144 0.580626
\(45\) 1.66920 0.248830
\(46\) 4.66668 0.688065
\(47\) −5.10901 −0.745226 −0.372613 0.927987i \(-0.621538\pi\)
−0.372613 + 0.927987i \(0.621538\pi\)
\(48\) −1.64793 −0.237858
\(49\) 1.00000 0.142857
\(50\) −2.39366 −0.338514
\(51\) 4.03225 0.564629
\(52\) 0 0
\(53\) −6.41614 −0.881325 −0.440663 0.897673i \(-0.645256\pi\)
−0.440663 + 0.897673i \(0.645256\pi\)
\(54\) 1.08127 0.147142
\(55\) −7.73752 −1.04333
\(56\) −3.06092 −0.409032
\(57\) −0.793678 −0.105125
\(58\) 4.99264 0.655566
\(59\) 12.2304 1.59227 0.796133 0.605122i \(-0.206876\pi\)
0.796133 + 0.605122i \(0.206876\pi\)
\(60\) −1.38688 −0.179046
\(61\) 10.3412 1.32406 0.662029 0.749478i \(-0.269695\pi\)
0.662029 + 0.749478i \(0.269695\pi\)
\(62\) 6.22497 0.790571
\(63\) 1.00000 0.125988
\(64\) 7.98853 0.998567
\(65\) 0 0
\(66\) −5.01215 −0.616953
\(67\) −1.86971 −0.228422 −0.114211 0.993457i \(-0.536434\pi\)
−0.114211 + 0.993457i \(0.536434\pi\)
\(68\) −3.35026 −0.406279
\(69\) 4.31595 0.519579
\(70\) 1.80485 0.215721
\(71\) 6.08759 0.722464 0.361232 0.932476i \(-0.382356\pi\)
0.361232 + 0.932476i \(0.382356\pi\)
\(72\) −3.06092 −0.360732
\(73\) −3.11657 −0.364767 −0.182384 0.983227i \(-0.558381\pi\)
−0.182384 + 0.983227i \(0.558381\pi\)
\(74\) 6.20102 0.720854
\(75\) −2.21376 −0.255623
\(76\) 0.659440 0.0756429
\(77\) −4.63545 −0.528259
\(78\) 0 0
\(79\) 2.28592 0.257186 0.128593 0.991697i \(-0.458954\pi\)
0.128593 + 0.991697i \(0.458954\pi\)
\(80\) −2.75073 −0.307541
\(81\) 1.00000 0.111111
\(82\) 7.93230 0.875976
\(83\) 0.655507 0.0719513 0.0359756 0.999353i \(-0.488546\pi\)
0.0359756 + 0.999353i \(0.488546\pi\)
\(84\) −0.830866 −0.0906549
\(85\) 6.73066 0.730042
\(86\) 12.3636 1.33320
\(87\) 4.61741 0.495038
\(88\) 14.1887 1.51252
\(89\) −10.8262 −1.14758 −0.573788 0.819004i \(-0.694527\pi\)
−0.573788 + 0.819004i \(0.694527\pi\)
\(90\) 1.80485 0.190248
\(91\) 0 0
\(92\) −3.58597 −0.373864
\(93\) 5.75711 0.596985
\(94\) −5.52419 −0.569777
\(95\) −1.32481 −0.135923
\(96\) 4.33998 0.442948
\(97\) −14.7169 −1.49427 −0.747136 0.664671i \(-0.768572\pi\)
−0.747136 + 0.664671i \(0.768572\pi\)
\(98\) 1.08127 0.109224
\(99\) −4.63545 −0.465880
\(100\) 1.83934 0.183934
\(101\) −7.83185 −0.779298 −0.389649 0.920963i \(-0.627404\pi\)
−0.389649 + 0.920963i \(0.627404\pi\)
\(102\) 4.35994 0.431698
\(103\) −14.2990 −1.40892 −0.704461 0.709743i \(-0.748811\pi\)
−0.704461 + 0.709743i \(0.748811\pi\)
\(104\) 0 0
\(105\) 1.66920 0.162898
\(106\) −6.93755 −0.673835
\(107\) −13.6120 −1.31592 −0.657960 0.753053i \(-0.728580\pi\)
−0.657960 + 0.753053i \(0.728580\pi\)
\(108\) −0.830866 −0.0799501
\(109\) −1.08293 −0.103726 −0.0518631 0.998654i \(-0.516516\pi\)
−0.0518631 + 0.998654i \(0.516516\pi\)
\(110\) −8.36630 −0.797696
\(111\) 5.73497 0.544339
\(112\) −1.64793 −0.155715
\(113\) 14.7313 1.38581 0.692903 0.721031i \(-0.256331\pi\)
0.692903 + 0.721031i \(0.256331\pi\)
\(114\) −0.858176 −0.0803755
\(115\) 7.20420 0.671795
\(116\) −3.83645 −0.356205
\(117\) 0 0
\(118\) 13.2243 1.21740
\(119\) 4.03225 0.369636
\(120\) −5.10929 −0.466413
\(121\) 10.4874 0.953401
\(122\) 11.1816 1.01234
\(123\) 7.33613 0.661476
\(124\) −4.78339 −0.429561
\(125\) −12.0412 −1.07700
\(126\) 1.08127 0.0963267
\(127\) 19.2838 1.71116 0.855582 0.517667i \(-0.173199\pi\)
0.855582 + 0.517667i \(0.173199\pi\)
\(128\) −0.0422458 −0.00373404
\(129\) 11.4344 1.00674
\(130\) 0 0
\(131\) 0.626566 0.0547433 0.0273717 0.999625i \(-0.491286\pi\)
0.0273717 + 0.999625i \(0.491286\pi\)
\(132\) 3.85144 0.335225
\(133\) −0.793678 −0.0688206
\(134\) −2.02166 −0.174644
\(135\) 1.66920 0.143662
\(136\) −12.3424 −1.05835
\(137\) 1.27827 0.109210 0.0546052 0.998508i \(-0.482610\pi\)
0.0546052 + 0.998508i \(0.482610\pi\)
\(138\) 4.66668 0.397254
\(139\) 17.3701 1.47331 0.736656 0.676268i \(-0.236404\pi\)
0.736656 + 0.676268i \(0.236404\pi\)
\(140\) −1.38688 −0.117213
\(141\) −5.10901 −0.430256
\(142\) 6.58230 0.552375
\(143\) 0 0
\(144\) −1.64793 −0.137328
\(145\) 7.70740 0.640065
\(146\) −3.36984 −0.278890
\(147\) 1.00000 0.0824786
\(148\) −4.76499 −0.391680
\(149\) −2.06250 −0.168967 −0.0844834 0.996425i \(-0.526924\pi\)
−0.0844834 + 0.996425i \(0.526924\pi\)
\(150\) −2.39366 −0.195441
\(151\) 10.6932 0.870199 0.435100 0.900382i \(-0.356713\pi\)
0.435100 + 0.900382i \(0.356713\pi\)
\(152\) 2.42938 0.197049
\(153\) 4.03225 0.325988
\(154\) −5.01215 −0.403891
\(155\) 9.60980 0.771878
\(156\) 0 0
\(157\) −9.91978 −0.791685 −0.395842 0.918318i \(-0.629547\pi\)
−0.395842 + 0.918318i \(0.629547\pi\)
\(158\) 2.47169 0.196637
\(159\) −6.41614 −0.508833
\(160\) 7.24432 0.572714
\(161\) 4.31595 0.340144
\(162\) 1.08127 0.0849522
\(163\) −20.9575 −1.64152 −0.820759 0.571275i \(-0.806449\pi\)
−0.820759 + 0.571275i \(0.806449\pi\)
\(164\) −6.09534 −0.475966
\(165\) −7.73752 −0.602365
\(166\) 0.708777 0.0550118
\(167\) −8.36605 −0.647384 −0.323692 0.946162i \(-0.604924\pi\)
−0.323692 + 0.946162i \(0.604924\pi\)
\(168\) −3.06092 −0.236155
\(169\) 0 0
\(170\) 7.27762 0.558168
\(171\) −0.793678 −0.0606940
\(172\) −9.50043 −0.724401
\(173\) 5.93501 0.451230 0.225615 0.974217i \(-0.427561\pi\)
0.225615 + 0.974217i \(0.427561\pi\)
\(174\) 4.99264 0.378491
\(175\) −2.21376 −0.167344
\(176\) 7.63890 0.575804
\(177\) 12.2304 0.919295
\(178\) −11.7060 −0.877403
\(179\) 14.5930 1.09073 0.545365 0.838199i \(-0.316391\pi\)
0.545365 + 0.838199i \(0.316391\pi\)
\(180\) −1.38688 −0.103372
\(181\) −2.33617 −0.173646 −0.0868232 0.996224i \(-0.527672\pi\)
−0.0868232 + 0.996224i \(0.527672\pi\)
\(182\) 0 0
\(183\) 10.3412 0.764446
\(184\) −13.2108 −0.973910
\(185\) 9.57283 0.703809
\(186\) 6.22497 0.456437
\(187\) −18.6913 −1.36684
\(188\) 4.24490 0.309591
\(189\) 1.00000 0.0727393
\(190\) −1.43247 −0.103922
\(191\) 2.92459 0.211616 0.105808 0.994387i \(-0.466257\pi\)
0.105808 + 0.994387i \(0.466257\pi\)
\(192\) 7.98853 0.576523
\(193\) −24.0430 −1.73065 −0.865327 0.501207i \(-0.832889\pi\)
−0.865327 + 0.501207i \(0.832889\pi\)
\(194\) −15.9128 −1.14248
\(195\) 0 0
\(196\) −0.830866 −0.0593476
\(197\) −14.6055 −1.04060 −0.520299 0.853984i \(-0.674180\pi\)
−0.520299 + 0.853984i \(0.674180\pi\)
\(198\) −5.01215 −0.356198
\(199\) −15.4843 −1.09765 −0.548827 0.835936i \(-0.684925\pi\)
−0.548827 + 0.835936i \(0.684925\pi\)
\(200\) 6.77613 0.479145
\(201\) −1.86971 −0.131879
\(202\) −8.46830 −0.595828
\(203\) 4.61741 0.324079
\(204\) −3.35026 −0.234565
\(205\) 12.2455 0.855262
\(206\) −15.4610 −1.07722
\(207\) 4.31595 0.299979
\(208\) 0 0
\(209\) 3.67905 0.254486
\(210\) 1.80485 0.124547
\(211\) 19.8268 1.36493 0.682467 0.730917i \(-0.260907\pi\)
0.682467 + 0.730917i \(0.260907\pi\)
\(212\) 5.33095 0.366131
\(213\) 6.08759 0.417115
\(214\) −14.7182 −1.00611
\(215\) 19.0863 1.30168
\(216\) −3.06092 −0.208269
\(217\) 5.75711 0.390818
\(218\) −1.17094 −0.0793059
\(219\) −3.11657 −0.210599
\(220\) 6.42884 0.433432
\(221\) 0 0
\(222\) 6.20102 0.416185
\(223\) 27.3639 1.83242 0.916211 0.400695i \(-0.131231\pi\)
0.916211 + 0.400695i \(0.131231\pi\)
\(224\) 4.33998 0.289977
\(225\) −2.21376 −0.147584
\(226\) 15.9285 1.05955
\(227\) −15.1297 −1.00419 −0.502096 0.864812i \(-0.667438\pi\)
−0.502096 + 0.864812i \(0.667438\pi\)
\(228\) 0.659440 0.0436725
\(229\) −10.6735 −0.705322 −0.352661 0.935751i \(-0.614723\pi\)
−0.352661 + 0.935751i \(0.614723\pi\)
\(230\) 7.78965 0.513634
\(231\) −4.63545 −0.304990
\(232\) −14.1335 −0.927910
\(233\) −10.6341 −0.696660 −0.348330 0.937372i \(-0.613251\pi\)
−0.348330 + 0.937372i \(0.613251\pi\)
\(234\) 0 0
\(235\) −8.52798 −0.556304
\(236\) −10.1618 −0.661479
\(237\) 2.28592 0.148487
\(238\) 4.35994 0.282613
\(239\) −14.5524 −0.941315 −0.470658 0.882316i \(-0.655983\pi\)
−0.470658 + 0.882316i \(0.655983\pi\)
\(240\) −2.75073 −0.177559
\(241\) −21.0486 −1.35586 −0.677929 0.735127i \(-0.737123\pi\)
−0.677929 + 0.735127i \(0.737123\pi\)
\(242\) 11.3397 0.728942
\(243\) 1.00000 0.0641500
\(244\) −8.59218 −0.550058
\(245\) 1.66920 0.106642
\(246\) 7.93230 0.505745
\(247\) 0 0
\(248\) −17.6220 −1.11900
\(249\) 0.655507 0.0415411
\(250\) −13.0198 −0.823442
\(251\) −16.3957 −1.03489 −0.517443 0.855718i \(-0.673116\pi\)
−0.517443 + 0.855718i \(0.673116\pi\)
\(252\) −0.830866 −0.0523396
\(253\) −20.0064 −1.25779
\(254\) 20.8509 1.30830
\(255\) 6.73066 0.421490
\(256\) −16.0227 −1.00142
\(257\) −14.2261 −0.887400 −0.443700 0.896175i \(-0.646334\pi\)
−0.443700 + 0.896175i \(0.646334\pi\)
\(258\) 12.3636 0.769724
\(259\) 5.73497 0.356354
\(260\) 0 0
\(261\) 4.61741 0.285810
\(262\) 0.677484 0.0418551
\(263\) 17.0566 1.05175 0.525876 0.850561i \(-0.323737\pi\)
0.525876 + 0.850561i \(0.323737\pi\)
\(264\) 14.1887 0.873256
\(265\) −10.7099 −0.657901
\(266\) −0.858176 −0.0526181
\(267\) −10.8262 −0.662554
\(268\) 1.55348 0.0948940
\(269\) 17.2732 1.05317 0.526583 0.850124i \(-0.323473\pi\)
0.526583 + 0.850124i \(0.323473\pi\)
\(270\) 1.80485 0.109840
\(271\) 7.90154 0.479985 0.239992 0.970775i \(-0.422855\pi\)
0.239992 + 0.970775i \(0.422855\pi\)
\(272\) −6.64487 −0.402905
\(273\) 0 0
\(274\) 1.38215 0.0834990
\(275\) 10.2618 0.618808
\(276\) −3.58597 −0.215850
\(277\) 4.50995 0.270977 0.135488 0.990779i \(-0.456740\pi\)
0.135488 + 0.990779i \(0.456740\pi\)
\(278\) 18.7817 1.12645
\(279\) 5.75711 0.344669
\(280\) −5.10929 −0.305339
\(281\) 20.7726 1.23919 0.619594 0.784922i \(-0.287297\pi\)
0.619594 + 0.784922i \(0.287297\pi\)
\(282\) −5.52419 −0.328961
\(283\) −2.02320 −0.120267 −0.0601335 0.998190i \(-0.519153\pi\)
−0.0601335 + 0.998190i \(0.519153\pi\)
\(284\) −5.05797 −0.300136
\(285\) −1.32481 −0.0784750
\(286\) 0 0
\(287\) 7.33613 0.433038
\(288\) 4.33998 0.255736
\(289\) −0.740925 −0.0435838
\(290\) 8.33374 0.489374
\(291\) −14.7169 −0.862719
\(292\) 2.58946 0.151536
\(293\) 25.9848 1.51805 0.759024 0.651063i \(-0.225677\pi\)
0.759024 + 0.651063i \(0.225677\pi\)
\(294\) 1.08127 0.0630607
\(295\) 20.4151 1.18861
\(296\) −17.5543 −1.02032
\(297\) −4.63545 −0.268976
\(298\) −2.23011 −0.129187
\(299\) 0 0
\(300\) 1.83934 0.106194
\(301\) 11.4344 0.659067
\(302\) 11.5622 0.665328
\(303\) −7.83185 −0.449928
\(304\) 1.30793 0.0750147
\(305\) 17.2616 0.988398
\(306\) 4.35994 0.249241
\(307\) 24.6185 1.40505 0.702526 0.711658i \(-0.252055\pi\)
0.702526 + 0.711658i \(0.252055\pi\)
\(308\) 3.85144 0.219456
\(309\) −14.2990 −0.813441
\(310\) 10.3907 0.590154
\(311\) 33.1216 1.87815 0.939076 0.343711i \(-0.111684\pi\)
0.939076 + 0.343711i \(0.111684\pi\)
\(312\) 0 0
\(313\) −7.05477 −0.398759 −0.199380 0.979922i \(-0.563893\pi\)
−0.199380 + 0.979922i \(0.563893\pi\)
\(314\) −10.7259 −0.605298
\(315\) 1.66920 0.0940490
\(316\) −1.89930 −0.106844
\(317\) 13.0084 0.730622 0.365311 0.930886i \(-0.380963\pi\)
0.365311 + 0.930886i \(0.380963\pi\)
\(318\) −6.93755 −0.389039
\(319\) −21.4038 −1.19838
\(320\) 13.3345 0.745421
\(321\) −13.6120 −0.759747
\(322\) 4.66668 0.260064
\(323\) −3.20031 −0.178070
\(324\) −0.830866 −0.0461592
\(325\) 0 0
\(326\) −22.6606 −1.25506
\(327\) −1.08293 −0.0598863
\(328\) −22.4553 −1.23988
\(329\) −5.10901 −0.281669
\(330\) −8.36630 −0.460550
\(331\) 17.9368 0.985894 0.492947 0.870059i \(-0.335920\pi\)
0.492947 + 0.870059i \(0.335920\pi\)
\(332\) −0.544638 −0.0298909
\(333\) 5.73497 0.314274
\(334\) −9.04592 −0.494970
\(335\) −3.12093 −0.170515
\(336\) −1.64793 −0.0899020
\(337\) 28.3388 1.54371 0.771856 0.635797i \(-0.219328\pi\)
0.771856 + 0.635797i \(0.219328\pi\)
\(338\) 0 0
\(339\) 14.7313 0.800095
\(340\) −5.59227 −0.303284
\(341\) −26.6868 −1.44517
\(342\) −0.858176 −0.0464048
\(343\) 1.00000 0.0539949
\(344\) −34.9997 −1.88706
\(345\) 7.20420 0.387861
\(346\) 6.41732 0.344997
\(347\) −8.49524 −0.456048 −0.228024 0.973655i \(-0.573227\pi\)
−0.228024 + 0.973655i \(0.573227\pi\)
\(348\) −3.83645 −0.205655
\(349\) −11.0479 −0.591381 −0.295691 0.955284i \(-0.595550\pi\)
−0.295691 + 0.955284i \(0.595550\pi\)
\(350\) −2.39366 −0.127946
\(351\) 0 0
\(352\) −20.1178 −1.07228
\(353\) 11.0968 0.590621 0.295310 0.955401i \(-0.404577\pi\)
0.295310 + 0.955401i \(0.404577\pi\)
\(354\) 13.2243 0.702865
\(355\) 10.1614 0.539313
\(356\) 8.99514 0.476741
\(357\) 4.03225 0.213410
\(358\) 15.7789 0.833940
\(359\) −16.3104 −0.860830 −0.430415 0.902631i \(-0.641633\pi\)
−0.430415 + 0.902631i \(0.641633\pi\)
\(360\) −5.10929 −0.269283
\(361\) −18.3701 −0.966846
\(362\) −2.52602 −0.132765
\(363\) 10.4874 0.550446
\(364\) 0 0
\(365\) −5.20220 −0.272296
\(366\) 11.1816 0.584472
\(367\) 15.3843 0.803056 0.401528 0.915847i \(-0.368479\pi\)
0.401528 + 0.915847i \(0.368479\pi\)
\(368\) −7.11238 −0.370758
\(369\) 7.33613 0.381903
\(370\) 10.3508 0.538111
\(371\) −6.41614 −0.333110
\(372\) −4.78339 −0.248007
\(373\) 21.1348 1.09432 0.547160 0.837028i \(-0.315709\pi\)
0.547160 + 0.837028i \(0.315709\pi\)
\(374\) −20.2103 −1.04505
\(375\) −12.0412 −0.621807
\(376\) 15.6382 0.806481
\(377\) 0 0
\(378\) 1.08127 0.0556143
\(379\) −27.2340 −1.39892 −0.699458 0.714674i \(-0.746575\pi\)
−0.699458 + 0.714674i \(0.746575\pi\)
\(380\) 1.10074 0.0564667
\(381\) 19.2838 0.987941
\(382\) 3.16226 0.161795
\(383\) 15.5635 0.795257 0.397629 0.917546i \(-0.369833\pi\)
0.397629 + 0.917546i \(0.369833\pi\)
\(384\) −0.0422458 −0.00215585
\(385\) −7.73752 −0.394340
\(386\) −25.9969 −1.32321
\(387\) 11.4344 0.581242
\(388\) 12.2278 0.620770
\(389\) −25.1109 −1.27317 −0.636586 0.771206i \(-0.719654\pi\)
−0.636586 + 0.771206i \(0.719654\pi\)
\(390\) 0 0
\(391\) 17.4030 0.880107
\(392\) −3.06092 −0.154600
\(393\) 0.626566 0.0316061
\(394\) −15.7924 −0.795610
\(395\) 3.81567 0.191987
\(396\) 3.85144 0.193542
\(397\) 3.55580 0.178461 0.0892304 0.996011i \(-0.471559\pi\)
0.0892304 + 0.996011i \(0.471559\pi\)
\(398\) −16.7426 −0.839233
\(399\) −0.793678 −0.0397336
\(400\) 3.64812 0.182406
\(401\) −31.3198 −1.56403 −0.782017 0.623257i \(-0.785809\pi\)
−0.782017 + 0.623257i \(0.785809\pi\)
\(402\) −2.02166 −0.100831
\(403\) 0 0
\(404\) 6.50721 0.323746
\(405\) 1.66920 0.0829434
\(406\) 4.99264 0.247781
\(407\) −26.5842 −1.31773
\(408\) −12.3424 −0.611040
\(409\) −10.2735 −0.507991 −0.253996 0.967205i \(-0.581745\pi\)
−0.253996 + 0.967205i \(0.581745\pi\)
\(410\) 13.2406 0.653908
\(411\) 1.27827 0.0630527
\(412\) 11.8805 0.585312
\(413\) 12.2304 0.601820
\(414\) 4.66668 0.229355
\(415\) 1.09418 0.0537109
\(416\) 0 0
\(417\) 17.3701 0.850617
\(418\) 3.97803 0.194572
\(419\) 5.29913 0.258879 0.129440 0.991587i \(-0.458682\pi\)
0.129440 + 0.991587i \(0.458682\pi\)
\(420\) −1.38688 −0.0676730
\(421\) −17.2903 −0.842677 −0.421339 0.906903i \(-0.638440\pi\)
−0.421339 + 0.906903i \(0.638440\pi\)
\(422\) 21.4380 1.04359
\(423\) −5.10901 −0.248409
\(424\) 19.6393 0.953768
\(425\) −8.92643 −0.432996
\(426\) 6.58230 0.318914
\(427\) 10.3412 0.500447
\(428\) 11.3097 0.546676
\(429\) 0 0
\(430\) 20.6374 0.995222
\(431\) −19.2244 −0.926008 −0.463004 0.886356i \(-0.653229\pi\)
−0.463004 + 0.886356i \(0.653229\pi\)
\(432\) −1.64793 −0.0792861
\(433\) −9.23571 −0.443840 −0.221920 0.975065i \(-0.571232\pi\)
−0.221920 + 0.975065i \(0.571232\pi\)
\(434\) 6.22497 0.298808
\(435\) 7.70740 0.369542
\(436\) 0.899772 0.0430912
\(437\) −3.42547 −0.163862
\(438\) −3.36984 −0.161017
\(439\) 36.8646 1.75945 0.879726 0.475480i \(-0.157726\pi\)
0.879726 + 0.475480i \(0.157726\pi\)
\(440\) 23.6839 1.12909
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −20.1394 −0.956850 −0.478425 0.878128i \(-0.658792\pi\)
−0.478425 + 0.878128i \(0.658792\pi\)
\(444\) −4.76499 −0.226136
\(445\) −18.0712 −0.856656
\(446\) 29.5876 1.40102
\(447\) −2.06250 −0.0975530
\(448\) 7.98853 0.377423
\(449\) 33.2197 1.56774 0.783868 0.620927i \(-0.213244\pi\)
0.783868 + 0.620927i \(0.213244\pi\)
\(450\) −2.39366 −0.112838
\(451\) −34.0063 −1.60129
\(452\) −12.2398 −0.575709
\(453\) 10.6932 0.502410
\(454\) −16.3592 −0.767776
\(455\) 0 0
\(456\) 2.42938 0.113766
\(457\) −25.1540 −1.17665 −0.588327 0.808623i \(-0.700213\pi\)
−0.588327 + 0.808623i \(0.700213\pi\)
\(458\) −11.5408 −0.539268
\(459\) 4.03225 0.188210
\(460\) −5.98572 −0.279086
\(461\) −23.1849 −1.07983 −0.539915 0.841720i \(-0.681543\pi\)
−0.539915 + 0.841720i \(0.681543\pi\)
\(462\) −5.01215 −0.233186
\(463\) 12.8679 0.598022 0.299011 0.954250i \(-0.403343\pi\)
0.299011 + 0.954250i \(0.403343\pi\)
\(464\) −7.60917 −0.353247
\(465\) 9.60980 0.445644
\(466\) −11.4982 −0.532645
\(467\) −25.5865 −1.18400 −0.592000 0.805938i \(-0.701661\pi\)
−0.592000 + 0.805938i \(0.701661\pi\)
\(468\) 0 0
\(469\) −1.86971 −0.0863353
\(470\) −9.22101 −0.425333
\(471\) −9.91978 −0.457079
\(472\) −37.4363 −1.72315
\(473\) −53.0035 −2.43710
\(474\) 2.47169 0.113528
\(475\) 1.75701 0.0806171
\(476\) −3.35026 −0.153559
\(477\) −6.41614 −0.293775
\(478\) −15.7350 −0.719701
\(479\) −25.2752 −1.15485 −0.577426 0.816443i \(-0.695943\pi\)
−0.577426 + 0.816443i \(0.695943\pi\)
\(480\) 7.24432 0.330656
\(481\) 0 0
\(482\) −22.7591 −1.03665
\(483\) 4.31595 0.196382
\(484\) −8.71363 −0.396074
\(485\) −24.5655 −1.11546
\(486\) 1.08127 0.0490472
\(487\) 42.4961 1.92568 0.962841 0.270068i \(-0.0870462\pi\)
0.962841 + 0.270068i \(0.0870462\pi\)
\(488\) −31.6536 −1.43289
\(489\) −20.9575 −0.947731
\(490\) 1.80485 0.0815349
\(491\) −40.3541 −1.82116 −0.910578 0.413337i \(-0.864363\pi\)
−0.910578 + 0.413337i \(0.864363\pi\)
\(492\) −6.09534 −0.274799
\(493\) 18.6186 0.838538
\(494\) 0 0
\(495\) −7.73752 −0.347775
\(496\) −9.48732 −0.425993
\(497\) 6.08759 0.273066
\(498\) 0.708777 0.0317611
\(499\) −5.56698 −0.249212 −0.124606 0.992206i \(-0.539767\pi\)
−0.124606 + 0.992206i \(0.539767\pi\)
\(500\) 10.0047 0.447422
\(501\) −8.36605 −0.373767
\(502\) −17.7281 −0.791242
\(503\) 18.0562 0.805085 0.402542 0.915401i \(-0.368127\pi\)
0.402542 + 0.915401i \(0.368127\pi\)
\(504\) −3.06092 −0.136344
\(505\) −13.0729 −0.581739
\(506\) −21.6322 −0.961668
\(507\) 0 0
\(508\) −16.0223 −0.710874
\(509\) −9.76430 −0.432795 −0.216397 0.976305i \(-0.569431\pi\)
−0.216397 + 0.976305i \(0.569431\pi\)
\(510\) 7.27762 0.322259
\(511\) −3.11657 −0.137869
\(512\) −17.2403 −0.761923
\(513\) −0.793678 −0.0350417
\(514\) −15.3822 −0.678480
\(515\) −23.8679 −1.05175
\(516\) −9.50043 −0.418233
\(517\) 23.6826 1.04156
\(518\) 6.20102 0.272457
\(519\) 5.93501 0.260518
\(520\) 0 0
\(521\) 19.4225 0.850914 0.425457 0.904979i \(-0.360113\pi\)
0.425457 + 0.904979i \(0.360113\pi\)
\(522\) 4.99264 0.218522
\(523\) 15.4560 0.675845 0.337923 0.941174i \(-0.390276\pi\)
0.337923 + 0.941174i \(0.390276\pi\)
\(524\) −0.520592 −0.0227422
\(525\) −2.21376 −0.0966163
\(526\) 18.4427 0.804138
\(527\) 23.2141 1.01122
\(528\) 7.63890 0.332440
\(529\) −4.37260 −0.190113
\(530\) −11.5802 −0.503011
\(531\) 12.2304 0.530755
\(532\) 0.659440 0.0285903
\(533\) 0 0
\(534\) −11.7060 −0.506569
\(535\) −22.7212 −0.982322
\(536\) 5.72304 0.247197
\(537\) 14.5930 0.629733
\(538\) 18.6769 0.805219
\(539\) −4.63545 −0.199663
\(540\) −1.38688 −0.0596820
\(541\) −3.65437 −0.157114 −0.0785569 0.996910i \(-0.525031\pi\)
−0.0785569 + 0.996910i \(0.525031\pi\)
\(542\) 8.54366 0.366982
\(543\) −2.33617 −0.100255
\(544\) 17.4999 0.750303
\(545\) −1.80764 −0.0774306
\(546\) 0 0
\(547\) 41.0035 1.75318 0.876592 0.481235i \(-0.159812\pi\)
0.876592 + 0.481235i \(0.159812\pi\)
\(548\) −1.06208 −0.0453696
\(549\) 10.3412 0.441353
\(550\) 11.0957 0.473122
\(551\) −3.66473 −0.156123
\(552\) −13.2108 −0.562287
\(553\) 2.28592 0.0972074
\(554\) 4.87645 0.207181
\(555\) 9.57283 0.406344
\(556\) −14.4322 −0.612062
\(557\) −6.55475 −0.277734 −0.138867 0.990311i \(-0.544346\pi\)
−0.138867 + 0.990311i \(0.544346\pi\)
\(558\) 6.22497 0.263524
\(559\) 0 0
\(560\) −2.75073 −0.116240
\(561\) −18.6913 −0.789148
\(562\) 22.4607 0.947446
\(563\) −25.4130 −1.07103 −0.535516 0.844525i \(-0.679883\pi\)
−0.535516 + 0.844525i \(0.679883\pi\)
\(564\) 4.24490 0.178743
\(565\) 24.5896 1.03449
\(566\) −2.18762 −0.0919526
\(567\) 1.00000 0.0419961
\(568\) −18.6336 −0.781849
\(569\) 21.8432 0.915713 0.457857 0.889026i \(-0.348617\pi\)
0.457857 + 0.889026i \(0.348617\pi\)
\(570\) −1.43247 −0.0599996
\(571\) 28.7510 1.20319 0.601596 0.798800i \(-0.294532\pi\)
0.601596 + 0.798800i \(0.294532\pi\)
\(572\) 0 0
\(573\) 2.92459 0.122177
\(574\) 7.93230 0.331088
\(575\) −9.55446 −0.398449
\(576\) 7.98853 0.332856
\(577\) −46.2811 −1.92671 −0.963353 0.268238i \(-0.913559\pi\)
−0.963353 + 0.268238i \(0.913559\pi\)
\(578\) −0.801136 −0.0333229
\(579\) −24.0430 −0.999194
\(580\) −6.40382 −0.265904
\(581\) 0.655507 0.0271950
\(582\) −15.9128 −0.659609
\(583\) 29.7417 1.23178
\(584\) 9.53957 0.394750
\(585\) 0 0
\(586\) 28.0965 1.16065
\(587\) 1.61084 0.0664866 0.0332433 0.999447i \(-0.489416\pi\)
0.0332433 + 0.999447i \(0.489416\pi\)
\(588\) −0.830866 −0.0342643
\(589\) −4.56929 −0.188274
\(590\) 22.0741 0.908776
\(591\) −14.6055 −0.600790
\(592\) −9.45083 −0.388427
\(593\) −36.9127 −1.51582 −0.757912 0.652357i \(-0.773780\pi\)
−0.757912 + 0.652357i \(0.773780\pi\)
\(594\) −5.01215 −0.205651
\(595\) 6.73066 0.275930
\(596\) 1.71366 0.0701944
\(597\) −15.4843 −0.633730
\(598\) 0 0
\(599\) −13.4868 −0.551054 −0.275527 0.961293i \(-0.588852\pi\)
−0.275527 + 0.961293i \(0.588852\pi\)
\(600\) 6.77613 0.276634
\(601\) 47.7912 1.94945 0.974723 0.223418i \(-0.0717214\pi\)
0.974723 + 0.223418i \(0.0717214\pi\)
\(602\) 12.3636 0.503902
\(603\) −1.86971 −0.0761406
\(604\) −8.88460 −0.361509
\(605\) 17.5056 0.711705
\(606\) −8.46830 −0.344001
\(607\) −31.8176 −1.29144 −0.645718 0.763576i \(-0.723442\pi\)
−0.645718 + 0.763576i \(0.723442\pi\)
\(608\) −3.44455 −0.139695
\(609\) 4.61741 0.187107
\(610\) 18.6644 0.755699
\(611\) 0 0
\(612\) −3.35026 −0.135426
\(613\) 35.4524 1.43191 0.715955 0.698146i \(-0.245991\pi\)
0.715955 + 0.698146i \(0.245991\pi\)
\(614\) 26.6191 1.07426
\(615\) 12.2455 0.493786
\(616\) 14.1887 0.571680
\(617\) −49.4752 −1.99180 −0.995899 0.0904759i \(-0.971161\pi\)
−0.995899 + 0.0904759i \(0.971161\pi\)
\(618\) −15.4610 −0.621933
\(619\) 11.7993 0.474253 0.237126 0.971479i \(-0.423794\pi\)
0.237126 + 0.971479i \(0.423794\pi\)
\(620\) −7.98445 −0.320663
\(621\) 4.31595 0.173193
\(622\) 35.8132 1.43598
\(623\) −10.8262 −0.433743
\(624\) 0 0
\(625\) −9.03049 −0.361220
\(626\) −7.62807 −0.304879
\(627\) 3.67905 0.146927
\(628\) 8.24201 0.328892
\(629\) 23.1249 0.922048
\(630\) 1.80485 0.0719070
\(631\) −5.14719 −0.204906 −0.102453 0.994738i \(-0.532669\pi\)
−0.102453 + 0.994738i \(0.532669\pi\)
\(632\) −6.99702 −0.278327
\(633\) 19.8268 0.788045
\(634\) 14.0655 0.558611
\(635\) 32.1887 1.27737
\(636\) 5.33095 0.211386
\(637\) 0 0
\(638\) −23.1432 −0.916246
\(639\) 6.08759 0.240821
\(640\) −0.0705168 −0.00278742
\(641\) −13.5685 −0.535924 −0.267962 0.963429i \(-0.586350\pi\)
−0.267962 + 0.963429i \(0.586350\pi\)
\(642\) −14.7182 −0.580879
\(643\) −11.1073 −0.438030 −0.219015 0.975721i \(-0.570284\pi\)
−0.219015 + 0.975721i \(0.570284\pi\)
\(644\) −3.58597 −0.141307
\(645\) 19.0863 0.751523
\(646\) −3.46038 −0.136147
\(647\) −9.09478 −0.357553 −0.178776 0.983890i \(-0.557214\pi\)
−0.178776 + 0.983890i \(0.557214\pi\)
\(648\) −3.06092 −0.120244
\(649\) −56.6935 −2.22542
\(650\) 0 0
\(651\) 5.75711 0.225639
\(652\) 17.4129 0.681941
\(653\) 3.37219 0.131964 0.0659819 0.997821i \(-0.478982\pi\)
0.0659819 + 0.997821i \(0.478982\pi\)
\(654\) −1.17094 −0.0457873
\(655\) 1.04587 0.0408654
\(656\) −12.0894 −0.472013
\(657\) −3.11657 −0.121589
\(658\) −5.52419 −0.215355
\(659\) −20.0281 −0.780185 −0.390092 0.920776i \(-0.627557\pi\)
−0.390092 + 0.920776i \(0.627557\pi\)
\(660\) 6.42884 0.250242
\(661\) 25.9859 1.01073 0.505367 0.862905i \(-0.331357\pi\)
0.505367 + 0.862905i \(0.331357\pi\)
\(662\) 19.3944 0.753785
\(663\) 0 0
\(664\) −2.00645 −0.0778655
\(665\) −1.32481 −0.0513739
\(666\) 6.20102 0.240285
\(667\) 19.9285 0.771634
\(668\) 6.95106 0.268945
\(669\) 27.3639 1.05795
\(670\) −3.37456 −0.130370
\(671\) −47.9363 −1.85056
\(672\) 4.33998 0.167418
\(673\) −26.8919 −1.03661 −0.518303 0.855197i \(-0.673436\pi\)
−0.518303 + 0.855197i \(0.673436\pi\)
\(674\) 30.6417 1.18028
\(675\) −2.21376 −0.0852076
\(676\) 0 0
\(677\) −23.0492 −0.885853 −0.442927 0.896558i \(-0.646060\pi\)
−0.442927 + 0.896558i \(0.646060\pi\)
\(678\) 15.9285 0.611729
\(679\) −14.7169 −0.564782
\(680\) −20.6020 −0.790050
\(681\) −15.1297 −0.579771
\(682\) −28.8555 −1.10494
\(683\) −35.3125 −1.35119 −0.675597 0.737271i \(-0.736114\pi\)
−0.675597 + 0.737271i \(0.736114\pi\)
\(684\) 0.659440 0.0252143
\(685\) 2.13370 0.0815246
\(686\) 1.08127 0.0412829
\(687\) −10.6735 −0.407218
\(688\) −18.8431 −0.718385
\(689\) 0 0
\(690\) 7.78965 0.296547
\(691\) 29.9975 1.14116 0.570580 0.821242i \(-0.306718\pi\)
0.570580 + 0.821242i \(0.306718\pi\)
\(692\) −4.93120 −0.187456
\(693\) −4.63545 −0.176086
\(694\) −9.18560 −0.348681
\(695\) 28.9942 1.09981
\(696\) −14.1335 −0.535729
\(697\) 29.5811 1.12046
\(698\) −11.9457 −0.452152
\(699\) −10.6341 −0.402217
\(700\) 1.83934 0.0695204
\(701\) −32.8331 −1.24009 −0.620045 0.784566i \(-0.712886\pi\)
−0.620045 + 0.784566i \(0.712886\pi\)
\(702\) 0 0
\(703\) −4.55172 −0.171671
\(704\) −37.0305 −1.39564
\(705\) −8.52798 −0.321182
\(706\) 11.9985 0.451571
\(707\) −7.83185 −0.294547
\(708\) −10.1618 −0.381905
\(709\) −0.735973 −0.0276400 −0.0138200 0.999904i \(-0.504399\pi\)
−0.0138200 + 0.999904i \(0.504399\pi\)
\(710\) 10.9872 0.412343
\(711\) 2.28592 0.0857288
\(712\) 33.1382 1.24190
\(713\) 24.8474 0.930542
\(714\) 4.35994 0.163166
\(715\) 0 0
\(716\) −12.1248 −0.453125
\(717\) −14.5524 −0.543469
\(718\) −17.6359 −0.658165
\(719\) −12.0005 −0.447544 −0.223772 0.974642i \(-0.571837\pi\)
−0.223772 + 0.974642i \(0.571837\pi\)
\(720\) −2.75073 −0.102514
\(721\) −14.2990 −0.532522
\(722\) −19.8629 −0.739221
\(723\) −21.0486 −0.782805
\(724\) 1.94105 0.0721384
\(725\) −10.2218 −0.379629
\(726\) 11.3397 0.420855
\(727\) −37.0876 −1.37550 −0.687751 0.725947i \(-0.741402\pi\)
−0.687751 + 0.725947i \(0.741402\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −5.62496 −0.208189
\(731\) 46.1063 1.70530
\(732\) −8.59218 −0.317576
\(733\) −29.3473 −1.08397 −0.541983 0.840390i \(-0.682326\pi\)
−0.541983 + 0.840390i \(0.682326\pi\)
\(734\) 16.6345 0.613992
\(735\) 1.66920 0.0615695
\(736\) 18.7311 0.690439
\(737\) 8.66697 0.319252
\(738\) 7.93230 0.291992
\(739\) 14.5291 0.534463 0.267231 0.963632i \(-0.413891\pi\)
0.267231 + 0.963632i \(0.413891\pi\)
\(740\) −7.95374 −0.292385
\(741\) 0 0
\(742\) −6.93755 −0.254686
\(743\) −17.9329 −0.657896 −0.328948 0.944348i \(-0.606694\pi\)
−0.328948 + 0.944348i \(0.606694\pi\)
\(744\) −17.6220 −0.646055
\(745\) −3.44274 −0.126132
\(746\) 22.8523 0.836684
\(747\) 0.655507 0.0239838
\(748\) 15.5300 0.567832
\(749\) −13.6120 −0.497371
\(750\) −13.0198 −0.475415
\(751\) −21.4043 −0.781055 −0.390527 0.920591i \(-0.627707\pi\)
−0.390527 + 0.920591i \(0.627707\pi\)
\(752\) 8.41929 0.307020
\(753\) −16.3957 −0.597491
\(754\) 0 0
\(755\) 17.8491 0.649596
\(756\) −0.830866 −0.0302183
\(757\) 43.6768 1.58746 0.793730 0.608270i \(-0.208136\pi\)
0.793730 + 0.608270i \(0.208136\pi\)
\(758\) −29.4472 −1.06957
\(759\) −20.0064 −0.726185
\(760\) 4.05513 0.147095
\(761\) 31.4196 1.13896 0.569479 0.822006i \(-0.307145\pi\)
0.569479 + 0.822006i \(0.307145\pi\)
\(762\) 20.8509 0.755350
\(763\) −1.08293 −0.0392048
\(764\) −2.42994 −0.0879122
\(765\) 6.73066 0.243347
\(766\) 16.8283 0.608030
\(767\) 0 0
\(768\) −16.0227 −0.578171
\(769\) −5.48923 −0.197947 −0.0989733 0.995090i \(-0.531556\pi\)
−0.0989733 + 0.995090i \(0.531556\pi\)
\(770\) −8.36630 −0.301501
\(771\) −14.2261 −0.512341
\(772\) 19.9765 0.718971
\(773\) 31.3794 1.12864 0.564319 0.825557i \(-0.309139\pi\)
0.564319 + 0.825557i \(0.309139\pi\)
\(774\) 12.3636 0.444400
\(775\) −12.7449 −0.457809
\(776\) 45.0471 1.61710
\(777\) 5.73497 0.205741
\(778\) −27.1515 −0.973429
\(779\) −5.82252 −0.208613
\(780\) 0 0
\(781\) −28.2187 −1.00975
\(782\) 18.8173 0.672904
\(783\) 4.61741 0.165013
\(784\) −1.64793 −0.0588546
\(785\) −16.5581 −0.590985
\(786\) 0.677484 0.0241651
\(787\) −7.84245 −0.279553 −0.139777 0.990183i \(-0.544638\pi\)
−0.139777 + 0.990183i \(0.544638\pi\)
\(788\) 12.1352 0.432299
\(789\) 17.0566 0.607230
\(790\) 4.12575 0.146788
\(791\) 14.7313 0.523785
\(792\) 14.1887 0.504175
\(793\) 0 0
\(794\) 3.84477 0.136446
\(795\) −10.7099 −0.379839
\(796\) 12.8654 0.456001
\(797\) 5.01412 0.177609 0.0888047 0.996049i \(-0.471695\pi\)
0.0888047 + 0.996049i \(0.471695\pi\)
\(798\) −0.858176 −0.0303791
\(799\) −20.6008 −0.728805
\(800\) −9.60767 −0.339682
\(801\) −10.8262 −0.382526
\(802\) −33.8650 −1.19581
\(803\) 14.4467 0.509814
\(804\) 1.55348 0.0547870
\(805\) 7.20420 0.253915
\(806\) 0 0
\(807\) 17.2732 0.608046
\(808\) 23.9726 0.843354
\(809\) −30.4281 −1.06980 −0.534898 0.844917i \(-0.679650\pi\)
−0.534898 + 0.844917i \(0.679650\pi\)
\(810\) 1.80485 0.0634160
\(811\) 49.4527 1.73652 0.868260 0.496109i \(-0.165238\pi\)
0.868260 + 0.496109i \(0.165238\pi\)
\(812\) −3.83645 −0.134633
\(813\) 7.90154 0.277119
\(814\) −28.7445 −1.00750
\(815\) −34.9823 −1.22538
\(816\) −6.64487 −0.232617
\(817\) −9.07521 −0.317501
\(818\) −11.1084 −0.388395
\(819\) 0 0
\(820\) −10.1744 −0.355304
\(821\) 15.7133 0.548398 0.274199 0.961673i \(-0.411587\pi\)
0.274199 + 0.961673i \(0.411587\pi\)
\(822\) 1.38215 0.0482082
\(823\) 9.09400 0.316997 0.158499 0.987359i \(-0.449335\pi\)
0.158499 + 0.987359i \(0.449335\pi\)
\(824\) 43.7680 1.52473
\(825\) 10.2618 0.357269
\(826\) 13.2243 0.460133
\(827\) 8.35927 0.290680 0.145340 0.989382i \(-0.453572\pi\)
0.145340 + 0.989382i \(0.453572\pi\)
\(828\) −3.58597 −0.124621
\(829\) −6.13514 −0.213082 −0.106541 0.994308i \(-0.533978\pi\)
−0.106541 + 0.994308i \(0.533978\pi\)
\(830\) 1.18309 0.0410658
\(831\) 4.50995 0.156449
\(832\) 0 0
\(833\) 4.03225 0.139709
\(834\) 18.7817 0.650356
\(835\) −13.9646 −0.483266
\(836\) −3.05680 −0.105722
\(837\) 5.75711 0.198995
\(838\) 5.72976 0.197931
\(839\) −38.5294 −1.33018 −0.665091 0.746762i \(-0.731607\pi\)
−0.665091 + 0.746762i \(0.731607\pi\)
\(840\) −5.10929 −0.176287
\(841\) −7.67953 −0.264811
\(842\) −18.6954 −0.644286
\(843\) 20.7726 0.715446
\(844\) −16.4734 −0.567038
\(845\) 0 0
\(846\) −5.52419 −0.189926
\(847\) 10.4874 0.360352
\(848\) 10.5734 0.363091
\(849\) −2.02320 −0.0694362
\(850\) −9.65184 −0.331055
\(851\) 24.7518 0.848482
\(852\) −5.05797 −0.173283
\(853\) −27.8326 −0.952969 −0.476485 0.879183i \(-0.658089\pi\)
−0.476485 + 0.879183i \(0.658089\pi\)
\(854\) 11.1816 0.382627
\(855\) −1.32481 −0.0453075
\(856\) 41.6651 1.42408
\(857\) −24.6902 −0.843400 −0.421700 0.906735i \(-0.638566\pi\)
−0.421700 + 0.906735i \(0.638566\pi\)
\(858\) 0 0
\(859\) 31.2546 1.06639 0.533197 0.845991i \(-0.320990\pi\)
0.533197 + 0.845991i \(0.320990\pi\)
\(860\) −15.8582 −0.540759
\(861\) 7.33613 0.250014
\(862\) −20.7867 −0.707998
\(863\) −4.20143 −0.143018 −0.0715091 0.997440i \(-0.522782\pi\)
−0.0715091 + 0.997440i \(0.522782\pi\)
\(864\) 4.33998 0.147649
\(865\) 9.90674 0.336839
\(866\) −9.98625 −0.339346
\(867\) −0.740925 −0.0251631
\(868\) −4.78339 −0.162359
\(869\) −10.5963 −0.359454
\(870\) 8.33374 0.282540
\(871\) 0 0
\(872\) 3.31477 0.112252
\(873\) −14.7169 −0.498091
\(874\) −3.70384 −0.125284
\(875\) −12.0412 −0.407068
\(876\) 2.58946 0.0874896
\(877\) 46.1765 1.55927 0.779635 0.626234i \(-0.215404\pi\)
0.779635 + 0.626234i \(0.215404\pi\)
\(878\) 39.8604 1.34522
\(879\) 25.9848 0.876445
\(880\) 12.7509 0.429832
\(881\) 23.6571 0.797028 0.398514 0.917162i \(-0.369526\pi\)
0.398514 + 0.917162i \(0.369526\pi\)
\(882\) 1.08127 0.0364081
\(883\) 28.4713 0.958134 0.479067 0.877778i \(-0.340975\pi\)
0.479067 + 0.877778i \(0.340975\pi\)
\(884\) 0 0
\(885\) 20.4151 0.686245
\(886\) −21.7760 −0.731579
\(887\) −9.79667 −0.328940 −0.164470 0.986382i \(-0.552591\pi\)
−0.164470 + 0.986382i \(0.552591\pi\)
\(888\) −17.5543 −0.589082
\(889\) 19.2838 0.646759
\(890\) −19.5397 −0.654973
\(891\) −4.63545 −0.155293
\(892\) −22.7357 −0.761249
\(893\) 4.05491 0.135692
\(894\) −2.23011 −0.0745861
\(895\) 24.3587 0.814220
\(896\) −0.0422458 −0.00141133
\(897\) 0 0
\(898\) 35.9194 1.19864
\(899\) 26.5830 0.886591
\(900\) 1.83934 0.0613112
\(901\) −25.8715 −0.861905
\(902\) −36.7698 −1.22430
\(903\) 11.4344 0.380512
\(904\) −45.0913 −1.49972
\(905\) −3.89955 −0.129625
\(906\) 11.5622 0.384127
\(907\) −32.9274 −1.09334 −0.546669 0.837349i \(-0.684104\pi\)
−0.546669 + 0.837349i \(0.684104\pi\)
\(908\) 12.5707 0.417175
\(909\) −7.83185 −0.259766
\(910\) 0 0
\(911\) −19.3453 −0.640940 −0.320470 0.947259i \(-0.603841\pi\)
−0.320470 + 0.947259i \(0.603841\pi\)
\(912\) 1.30793 0.0433097
\(913\) −3.03857 −0.100562
\(914\) −27.1981 −0.899635
\(915\) 17.2616 0.570652
\(916\) 8.86822 0.293014
\(917\) 0.626566 0.0206910
\(918\) 4.35994 0.143899
\(919\) −26.9673 −0.889568 −0.444784 0.895638i \(-0.646720\pi\)
−0.444784 + 0.895638i \(0.646720\pi\)
\(920\) −22.0514 −0.727015
\(921\) 24.6185 0.811208
\(922\) −25.0690 −0.825605
\(923\) 0 0
\(924\) 3.85144 0.126703
\(925\) −12.6958 −0.417436
\(926\) 13.9136 0.457229
\(927\) −14.2990 −0.469640
\(928\) 20.0395 0.657828
\(929\) 37.9175 1.24403 0.622017 0.783004i \(-0.286313\pi\)
0.622017 + 0.783004i \(0.286313\pi\)
\(930\) 10.3907 0.340726
\(931\) −0.793678 −0.0260117
\(932\) 8.83547 0.289415
\(933\) 33.1216 1.08435
\(934\) −27.6657 −0.905251
\(935\) −31.1996 −1.02034
\(936\) 0 0
\(937\) 33.3091 1.08816 0.544080 0.839033i \(-0.316879\pi\)
0.544080 + 0.839033i \(0.316879\pi\)
\(938\) −2.02166 −0.0660094
\(939\) −7.05477 −0.230224
\(940\) 7.08561 0.231107
\(941\) 9.43451 0.307556 0.153778 0.988105i \(-0.450856\pi\)
0.153778 + 0.988105i \(0.450856\pi\)
\(942\) −10.7259 −0.349469
\(943\) 31.6623 1.03107
\(944\) −20.1549 −0.655985
\(945\) 1.66920 0.0542992
\(946\) −57.3108 −1.86334
\(947\) −8.18143 −0.265861 −0.132930 0.991125i \(-0.542439\pi\)
−0.132930 + 0.991125i \(0.542439\pi\)
\(948\) −1.89930 −0.0616863
\(949\) 0 0
\(950\) 1.89979 0.0616374
\(951\) 13.0084 0.421825
\(952\) −12.3424 −0.400019
\(953\) −35.7424 −1.15781 −0.578905 0.815395i \(-0.696520\pi\)
−0.578905 + 0.815395i \(0.696520\pi\)
\(954\) −6.93755 −0.224612
\(955\) 4.88174 0.157969
\(956\) 12.0911 0.391053
\(957\) −21.4038 −0.691886
\(958\) −27.3291 −0.882964
\(959\) 1.27827 0.0412777
\(960\) 13.3345 0.430369
\(961\) 2.14436 0.0691728
\(962\) 0 0
\(963\) −13.6120 −0.438640
\(964\) 17.4886 0.563268
\(965\) −40.1327 −1.29192
\(966\) 4.66668 0.150148
\(967\) −33.9787 −1.09268 −0.546341 0.837563i \(-0.683980\pi\)
−0.546341 + 0.837563i \(0.683980\pi\)
\(968\) −32.1011 −1.03177
\(969\) −3.20031 −0.102809
\(970\) −26.5618 −0.852848
\(971\) 37.6727 1.20897 0.604487 0.796615i \(-0.293378\pi\)
0.604487 + 0.796615i \(0.293378\pi\)
\(972\) −0.830866 −0.0266500
\(973\) 17.3701 0.556860
\(974\) 45.9496 1.47232
\(975\) 0 0
\(976\) −17.0416 −0.545489
\(977\) −25.7786 −0.824730 −0.412365 0.911019i \(-0.635297\pi\)
−0.412365 + 0.911019i \(0.635297\pi\)
\(978\) −22.6606 −0.724606
\(979\) 50.1844 1.60390
\(980\) −1.38688 −0.0443024
\(981\) −1.08293 −0.0345754
\(982\) −43.6335 −1.39240
\(983\) 31.8264 1.01510 0.507552 0.861621i \(-0.330550\pi\)
0.507552 + 0.861621i \(0.330550\pi\)
\(984\) −22.4553 −0.715848
\(985\) −24.3795 −0.776797
\(986\) 20.1316 0.641121
\(987\) −5.10901 −0.162622
\(988\) 0 0
\(989\) 49.3502 1.56924
\(990\) −8.36630 −0.265899
\(991\) 22.3388 0.709616 0.354808 0.934939i \(-0.384546\pi\)
0.354808 + 0.934939i \(0.384546\pi\)
\(992\) 24.9858 0.793299
\(993\) 17.9368 0.569206
\(994\) 6.58230 0.208778
\(995\) −25.8465 −0.819388
\(996\) −0.544638 −0.0172575
\(997\) 22.7194 0.719532 0.359766 0.933043i \(-0.382857\pi\)
0.359766 + 0.933043i \(0.382857\pi\)
\(998\) −6.01938 −0.190540
\(999\) 5.73497 0.181446
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 3549.2.a.bg.1.10 15
13.12 even 2 3549.2.a.bh.1.6 yes 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.10 15 1.1 even 1 trivial
3549.2.a.bh.1.6 yes 15 13.12 even 2