Properties

Label 3549.2.a.bh.1.1
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $15$
CM no
Inner twists $1$

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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 1.1
Root \(-2.61511\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61511 q^{2} +1.00000 q^{3} +4.83880 q^{4} -4.09685 q^{5} -2.61511 q^{6} -1.00000 q^{7} -7.42376 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.61511 q^{2} +1.00000 q^{3} +4.83880 q^{4} -4.09685 q^{5} -2.61511 q^{6} -1.00000 q^{7} -7.42376 q^{8} +1.00000 q^{9} +10.7137 q^{10} +5.70245 q^{11} +4.83880 q^{12} +2.61511 q^{14} -4.09685 q^{15} +9.73635 q^{16} -4.37843 q^{17} -2.61511 q^{18} +3.61201 q^{19} -19.8238 q^{20} -1.00000 q^{21} -14.9125 q^{22} +1.52889 q^{23} -7.42376 q^{24} +11.7842 q^{25} +1.00000 q^{27} -4.83880 q^{28} -8.65363 q^{29} +10.7137 q^{30} -2.53755 q^{31} -10.6141 q^{32} +5.70245 q^{33} +11.4501 q^{34} +4.09685 q^{35} +4.83880 q^{36} +0.399662 q^{37} -9.44580 q^{38} +30.4140 q^{40} +3.49412 q^{41} +2.61511 q^{42} +10.0663 q^{43} +27.5930 q^{44} -4.09685 q^{45} -3.99822 q^{46} +2.38790 q^{47} +9.73635 q^{48} +1.00000 q^{49} -30.8169 q^{50} -4.37843 q^{51} -4.72536 q^{53} -2.61511 q^{54} -23.3621 q^{55} +7.42376 q^{56} +3.61201 q^{57} +22.6302 q^{58} -3.98709 q^{59} -19.8238 q^{60} -1.11129 q^{61} +6.63598 q^{62} -1.00000 q^{63} +8.28433 q^{64} -14.9125 q^{66} -8.84355 q^{67} -21.1863 q^{68} +1.52889 q^{69} -10.7137 q^{70} -4.15260 q^{71} -7.42376 q^{72} -6.08083 q^{73} -1.04516 q^{74} +11.7842 q^{75} +17.4778 q^{76} -5.70245 q^{77} -0.225699 q^{79} -39.8884 q^{80} +1.00000 q^{81} -9.13750 q^{82} +9.32245 q^{83} -4.83880 q^{84} +17.9378 q^{85} -26.3246 q^{86} -8.65363 q^{87} -42.3336 q^{88} +9.60970 q^{89} +10.7137 q^{90} +7.39799 q^{92} -2.53755 q^{93} -6.24463 q^{94} -14.7979 q^{95} -10.6141 q^{96} -14.1480 q^{97} -2.61511 q^{98} +5.70245 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61511 −1.84916 −0.924581 0.380986i \(-0.875585\pi\)
−0.924581 + 0.380986i \(0.875585\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.83880 2.41940
\(5\) −4.09685 −1.83217 −0.916083 0.400988i \(-0.868667\pi\)
−0.916083 + 0.400988i \(0.868667\pi\)
\(6\) −2.61511 −1.06761
\(7\) −1.00000 −0.377964
\(8\) −7.42376 −2.62470
\(9\) 1.00000 0.333333
\(10\) 10.7137 3.38797
\(11\) 5.70245 1.71935 0.859677 0.510838i \(-0.170665\pi\)
0.859677 + 0.510838i \(0.170665\pi\)
\(12\) 4.83880 1.39684
\(13\) 0 0
\(14\) 2.61511 0.698917
\(15\) −4.09685 −1.05780
\(16\) 9.73635 2.43409
\(17\) −4.37843 −1.06192 −0.530962 0.847395i \(-0.678169\pi\)
−0.530962 + 0.847395i \(0.678169\pi\)
\(18\) −2.61511 −0.616387
\(19\) 3.61201 0.828652 0.414326 0.910128i \(-0.364017\pi\)
0.414326 + 0.910128i \(0.364017\pi\)
\(20\) −19.8238 −4.43274
\(21\) −1.00000 −0.218218
\(22\) −14.9125 −3.17936
\(23\) 1.52889 0.318796 0.159398 0.987214i \(-0.449045\pi\)
0.159398 + 0.987214i \(0.449045\pi\)
\(24\) −7.42376 −1.51537
\(25\) 11.7842 2.35683
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −4.83880 −0.914446
\(29\) −8.65363 −1.60694 −0.803470 0.595346i \(-0.797015\pi\)
−0.803470 + 0.595346i \(0.797015\pi\)
\(30\) 10.7137 1.95605
\(31\) −2.53755 −0.455758 −0.227879 0.973689i \(-0.573179\pi\)
−0.227879 + 0.973689i \(0.573179\pi\)
\(32\) −10.6141 −1.87633
\(33\) 5.70245 0.992669
\(34\) 11.4501 1.96367
\(35\) 4.09685 0.692494
\(36\) 4.83880 0.806466
\(37\) 0.399662 0.0657040 0.0328520 0.999460i \(-0.489541\pi\)
0.0328520 + 0.999460i \(0.489541\pi\)
\(38\) −9.44580 −1.53231
\(39\) 0 0
\(40\) 30.4140 4.80888
\(41\) 3.49412 0.545689 0.272845 0.962058i \(-0.412035\pi\)
0.272845 + 0.962058i \(0.412035\pi\)
\(42\) 2.61511 0.403520
\(43\) 10.0663 1.53510 0.767552 0.640987i \(-0.221475\pi\)
0.767552 + 0.640987i \(0.221475\pi\)
\(44\) 27.5930 4.15980
\(45\) −4.09685 −0.610722
\(46\) −3.99822 −0.589505
\(47\) 2.38790 0.348311 0.174156 0.984718i \(-0.444280\pi\)
0.174156 + 0.984718i \(0.444280\pi\)
\(48\) 9.73635 1.40532
\(49\) 1.00000 0.142857
\(50\) −30.8169 −4.35817
\(51\) −4.37843 −0.613102
\(52\) 0 0
\(53\) −4.72536 −0.649078 −0.324539 0.945872i \(-0.605209\pi\)
−0.324539 + 0.945872i \(0.605209\pi\)
\(54\) −2.61511 −0.355871
\(55\) −23.3621 −3.15014
\(56\) 7.42376 0.992042
\(57\) 3.61201 0.478423
\(58\) 22.6302 2.97149
\(59\) −3.98709 −0.519074 −0.259537 0.965733i \(-0.583570\pi\)
−0.259537 + 0.965733i \(0.583570\pi\)
\(60\) −19.8238 −2.55924
\(61\) −1.11129 −0.142287 −0.0711433 0.997466i \(-0.522665\pi\)
−0.0711433 + 0.997466i \(0.522665\pi\)
\(62\) 6.63598 0.842770
\(63\) −1.00000 −0.125988
\(64\) 8.28433 1.03554
\(65\) 0 0
\(66\) −14.9125 −1.83561
\(67\) −8.84355 −1.08041 −0.540206 0.841533i \(-0.681654\pi\)
−0.540206 + 0.841533i \(0.681654\pi\)
\(68\) −21.1863 −2.56922
\(69\) 1.52889 0.184057
\(70\) −10.7137 −1.28053
\(71\) −4.15260 −0.492823 −0.246411 0.969165i \(-0.579251\pi\)
−0.246411 + 0.969165i \(0.579251\pi\)
\(72\) −7.42376 −0.874899
\(73\) −6.08083 −0.711707 −0.355854 0.934542i \(-0.615810\pi\)
−0.355854 + 0.934542i \(0.615810\pi\)
\(74\) −1.04516 −0.121497
\(75\) 11.7842 1.36072
\(76\) 17.4778 2.00484
\(77\) −5.70245 −0.649855
\(78\) 0 0
\(79\) −0.225699 −0.0253931 −0.0126965 0.999919i \(-0.504042\pi\)
−0.0126965 + 0.999919i \(0.504042\pi\)
\(80\) −39.8884 −4.45965
\(81\) 1.00000 0.111111
\(82\) −9.13750 −1.00907
\(83\) 9.32245 1.02327 0.511636 0.859202i \(-0.329040\pi\)
0.511636 + 0.859202i \(0.329040\pi\)
\(84\) −4.83880 −0.527956
\(85\) 17.9378 1.94562
\(86\) −26.3246 −2.83865
\(87\) −8.65363 −0.927767
\(88\) −42.3336 −4.51278
\(89\) 9.60970 1.01863 0.509313 0.860581i \(-0.329899\pi\)
0.509313 + 0.860581i \(0.329899\pi\)
\(90\) 10.7137 1.12932
\(91\) 0 0
\(92\) 7.39799 0.771294
\(93\) −2.53755 −0.263132
\(94\) −6.24463 −0.644084
\(95\) −14.7979 −1.51823
\(96\) −10.6141 −1.08330
\(97\) −14.1480 −1.43651 −0.718254 0.695781i \(-0.755058\pi\)
−0.718254 + 0.695781i \(0.755058\pi\)
\(98\) −2.61511 −0.264166
\(99\) 5.70245 0.573118
\(100\) 57.0212 5.70212
\(101\) −10.1307 −1.00804 −0.504022 0.863691i \(-0.668147\pi\)
−0.504022 + 0.863691i \(0.668147\pi\)
\(102\) 11.4501 1.13373
\(103\) 1.94213 0.191363 0.0956817 0.995412i \(-0.469497\pi\)
0.0956817 + 0.995412i \(0.469497\pi\)
\(104\) 0 0
\(105\) 4.09685 0.399811
\(106\) 12.3573 1.20025
\(107\) −4.11614 −0.397922 −0.198961 0.980007i \(-0.563757\pi\)
−0.198961 + 0.980007i \(0.563757\pi\)
\(108\) 4.83880 0.465613
\(109\) 6.52500 0.624981 0.312491 0.949921i \(-0.398837\pi\)
0.312491 + 0.949921i \(0.398837\pi\)
\(110\) 61.0944 5.82512
\(111\) 0.399662 0.0379342
\(112\) −9.73635 −0.919999
\(113\) 0.829620 0.0780440 0.0390220 0.999238i \(-0.487576\pi\)
0.0390220 + 0.999238i \(0.487576\pi\)
\(114\) −9.44580 −0.884681
\(115\) −6.26363 −0.584087
\(116\) −41.8732 −3.88782
\(117\) 0 0
\(118\) 10.4267 0.959852
\(119\) 4.37843 0.401370
\(120\) 30.4140 2.77641
\(121\) 21.5180 1.95618
\(122\) 2.90616 0.263111
\(123\) 3.49412 0.315054
\(124\) −12.2787 −1.10266
\(125\) −27.7937 −2.48594
\(126\) 2.61511 0.232972
\(127\) −11.8157 −1.04848 −0.524239 0.851571i \(-0.675650\pi\)
−0.524239 + 0.851571i \(0.675650\pi\)
\(128\) −0.436221 −0.0385569
\(129\) 10.0663 0.886292
\(130\) 0 0
\(131\) 15.9488 1.39345 0.696726 0.717338i \(-0.254640\pi\)
0.696726 + 0.717338i \(0.254640\pi\)
\(132\) 27.5930 2.40166
\(133\) −3.61201 −0.313201
\(134\) 23.1268 1.99785
\(135\) −4.09685 −0.352601
\(136\) 32.5044 2.78723
\(137\) 13.2254 1.12992 0.564962 0.825117i \(-0.308891\pi\)
0.564962 + 0.825117i \(0.308891\pi\)
\(138\) −3.99822 −0.340351
\(139\) −3.88051 −0.329141 −0.164570 0.986365i \(-0.552624\pi\)
−0.164570 + 0.986365i \(0.552624\pi\)
\(140\) 19.8238 1.67542
\(141\) 2.38790 0.201098
\(142\) 10.8595 0.911308
\(143\) 0 0
\(144\) 9.73635 0.811363
\(145\) 35.4526 2.94418
\(146\) 15.9020 1.31606
\(147\) 1.00000 0.0824786
\(148\) 1.93388 0.158964
\(149\) 16.8716 1.38218 0.691089 0.722769i \(-0.257131\pi\)
0.691089 + 0.722769i \(0.257131\pi\)
\(150\) −30.8169 −2.51619
\(151\) 19.7463 1.60693 0.803467 0.595349i \(-0.202986\pi\)
0.803467 + 0.595349i \(0.202986\pi\)
\(152\) −26.8147 −2.17496
\(153\) −4.37843 −0.353975
\(154\) 14.9125 1.20169
\(155\) 10.3960 0.835024
\(156\) 0 0
\(157\) 17.9869 1.43551 0.717756 0.696294i \(-0.245169\pi\)
0.717756 + 0.696294i \(0.245169\pi\)
\(158\) 0.590227 0.0469559
\(159\) −4.72536 −0.374746
\(160\) 43.4844 3.43774
\(161\) −1.52889 −0.120493
\(162\) −2.61511 −0.205462
\(163\) 2.92694 0.229256 0.114628 0.993408i \(-0.463432\pi\)
0.114628 + 0.993408i \(0.463432\pi\)
\(164\) 16.9073 1.32024
\(165\) −23.3621 −1.81874
\(166\) −24.3792 −1.89220
\(167\) −15.6431 −1.21050 −0.605250 0.796036i \(-0.706927\pi\)
−0.605250 + 0.796036i \(0.706927\pi\)
\(168\) 7.42376 0.572756
\(169\) 0 0
\(170\) −46.9092 −3.59777
\(171\) 3.61201 0.276217
\(172\) 48.7090 3.71403
\(173\) −21.5961 −1.64192 −0.820959 0.570986i \(-0.806561\pi\)
−0.820959 + 0.570986i \(0.806561\pi\)
\(174\) 22.6302 1.71559
\(175\) −11.7842 −0.890799
\(176\) 55.5211 4.18506
\(177\) −3.98709 −0.299688
\(178\) −25.1304 −1.88360
\(179\) 3.42054 0.255663 0.127831 0.991796i \(-0.459198\pi\)
0.127831 + 0.991796i \(0.459198\pi\)
\(180\) −19.8238 −1.47758
\(181\) 11.5344 0.857346 0.428673 0.903460i \(-0.358981\pi\)
0.428673 + 0.903460i \(0.358981\pi\)
\(182\) 0 0
\(183\) −1.11129 −0.0821493
\(184\) −11.3501 −0.836742
\(185\) −1.63736 −0.120381
\(186\) 6.63598 0.486574
\(187\) −24.9678 −1.82582
\(188\) 11.5546 0.842704
\(189\) −1.00000 −0.0727393
\(190\) 38.6980 2.80745
\(191\) 5.79542 0.419342 0.209671 0.977772i \(-0.432761\pi\)
0.209671 + 0.977772i \(0.432761\pi\)
\(192\) 8.28433 0.597870
\(193\) −15.8937 −1.14405 −0.572026 0.820236i \(-0.693842\pi\)
−0.572026 + 0.820236i \(0.693842\pi\)
\(194\) 36.9985 2.65634
\(195\) 0 0
\(196\) 4.83880 0.345628
\(197\) −1.57741 −0.112386 −0.0561929 0.998420i \(-0.517896\pi\)
−0.0561929 + 0.998420i \(0.517896\pi\)
\(198\) −14.9125 −1.05979
\(199\) 4.31559 0.305924 0.152962 0.988232i \(-0.451119\pi\)
0.152962 + 0.988232i \(0.451119\pi\)
\(200\) −87.4828 −6.18597
\(201\) −8.84355 −0.623776
\(202\) 26.4929 1.86404
\(203\) 8.65363 0.607366
\(204\) −21.1863 −1.48334
\(205\) −14.3149 −0.999794
\(206\) −5.07887 −0.353862
\(207\) 1.52889 0.106265
\(208\) 0 0
\(209\) 20.5973 1.42475
\(210\) −10.7137 −0.739316
\(211\) −7.84846 −0.540310 −0.270155 0.962817i \(-0.587075\pi\)
−0.270155 + 0.962817i \(0.587075\pi\)
\(212\) −22.8651 −1.57038
\(213\) −4.15260 −0.284531
\(214\) 10.7642 0.735822
\(215\) −41.2403 −2.81256
\(216\) −7.42376 −0.505123
\(217\) 2.53755 0.172260
\(218\) −17.0636 −1.15569
\(219\) −6.08083 −0.410904
\(220\) −113.044 −7.62145
\(221\) 0 0
\(222\) −1.04516 −0.0701465
\(223\) 5.21856 0.349461 0.174730 0.984616i \(-0.444095\pi\)
0.174730 + 0.984616i \(0.444095\pi\)
\(224\) 10.6141 0.709184
\(225\) 11.7842 0.785611
\(226\) −2.16955 −0.144316
\(227\) −17.3482 −1.15144 −0.575720 0.817647i \(-0.695278\pi\)
−0.575720 + 0.817647i \(0.695278\pi\)
\(228\) 17.4778 1.15749
\(229\) 8.20358 0.542108 0.271054 0.962564i \(-0.412628\pi\)
0.271054 + 0.962564i \(0.412628\pi\)
\(230\) 16.3801 1.08007
\(231\) −5.70245 −0.375194
\(232\) 64.2425 4.21773
\(233\) 13.3917 0.877320 0.438660 0.898653i \(-0.355453\pi\)
0.438660 + 0.898653i \(0.355453\pi\)
\(234\) 0 0
\(235\) −9.78288 −0.638164
\(236\) −19.2927 −1.25585
\(237\) −0.225699 −0.0146607
\(238\) −11.4501 −0.742197
\(239\) −14.9556 −0.967400 −0.483700 0.875234i \(-0.660707\pi\)
−0.483700 + 0.875234i \(0.660707\pi\)
\(240\) −39.8884 −2.57478
\(241\) 23.0567 1.48521 0.742607 0.669727i \(-0.233589\pi\)
0.742607 + 0.669727i \(0.233589\pi\)
\(242\) −56.2718 −3.61729
\(243\) 1.00000 0.0641500
\(244\) −5.37733 −0.344248
\(245\) −4.09685 −0.261738
\(246\) −9.13750 −0.582586
\(247\) 0 0
\(248\) 18.8382 1.19623
\(249\) 9.32245 0.590786
\(250\) 72.6836 4.59691
\(251\) 18.9733 1.19759 0.598793 0.800904i \(-0.295647\pi\)
0.598793 + 0.800904i \(0.295647\pi\)
\(252\) −4.83880 −0.304815
\(253\) 8.71843 0.548123
\(254\) 30.8994 1.93880
\(255\) 17.9378 1.12331
\(256\) −15.4279 −0.964243
\(257\) 18.1751 1.13373 0.566867 0.823809i \(-0.308155\pi\)
0.566867 + 0.823809i \(0.308155\pi\)
\(258\) −26.3246 −1.63890
\(259\) −0.399662 −0.0248338
\(260\) 0 0
\(261\) −8.65363 −0.535646
\(262\) −41.7078 −2.57672
\(263\) 30.0127 1.85066 0.925331 0.379160i \(-0.123787\pi\)
0.925331 + 0.379160i \(0.123787\pi\)
\(264\) −42.3336 −2.60545
\(265\) 19.3591 1.18922
\(266\) 9.44580 0.579159
\(267\) 9.60970 0.588104
\(268\) −42.7921 −2.61394
\(269\) 15.2181 0.927864 0.463932 0.885871i \(-0.346438\pi\)
0.463932 + 0.885871i \(0.346438\pi\)
\(270\) 10.7137 0.652015
\(271\) −1.39762 −0.0848995 −0.0424497 0.999099i \(-0.513516\pi\)
−0.0424497 + 0.999099i \(0.513516\pi\)
\(272\) −42.6299 −2.58482
\(273\) 0 0
\(274\) −34.5859 −2.08941
\(275\) 67.1986 4.05223
\(276\) 7.39799 0.445307
\(277\) 9.68781 0.582084 0.291042 0.956710i \(-0.405998\pi\)
0.291042 + 0.956710i \(0.405998\pi\)
\(278\) 10.1480 0.608634
\(279\) −2.53755 −0.151919
\(280\) −30.4140 −1.81759
\(281\) 29.5572 1.76324 0.881619 0.471962i \(-0.156454\pi\)
0.881619 + 0.471962i \(0.156454\pi\)
\(282\) −6.24463 −0.371862
\(283\) 9.80289 0.582721 0.291361 0.956613i \(-0.405892\pi\)
0.291361 + 0.956613i \(0.405892\pi\)
\(284\) −20.0936 −1.19233
\(285\) −14.7979 −0.876550
\(286\) 0 0
\(287\) −3.49412 −0.206251
\(288\) −10.6141 −0.625442
\(289\) 2.17062 0.127684
\(290\) −92.7125 −5.44426
\(291\) −14.1480 −0.829368
\(292\) −29.4239 −1.72190
\(293\) −9.92535 −0.579845 −0.289923 0.957050i \(-0.593630\pi\)
−0.289923 + 0.957050i \(0.593630\pi\)
\(294\) −2.61511 −0.152516
\(295\) 16.3345 0.951031
\(296\) −2.96700 −0.172453
\(297\) 5.70245 0.330890
\(298\) −44.1212 −2.55587
\(299\) 0 0
\(300\) 57.0212 3.29212
\(301\) −10.0663 −0.580214
\(302\) −51.6388 −2.97148
\(303\) −10.1307 −0.581995
\(304\) 35.1678 2.01701
\(305\) 4.55281 0.260693
\(306\) 11.4501 0.654557
\(307\) −33.7537 −1.92643 −0.963213 0.268738i \(-0.913393\pi\)
−0.963213 + 0.268738i \(0.913393\pi\)
\(308\) −27.5930 −1.57226
\(309\) 1.94213 0.110484
\(310\) −27.1866 −1.54409
\(311\) 27.3331 1.54992 0.774959 0.632011i \(-0.217770\pi\)
0.774959 + 0.632011i \(0.217770\pi\)
\(312\) 0 0
\(313\) −12.6286 −0.713813 −0.356907 0.934140i \(-0.616169\pi\)
−0.356907 + 0.934140i \(0.616169\pi\)
\(314\) −47.0378 −2.65450
\(315\) 4.09685 0.230831
\(316\) −1.09211 −0.0614360
\(317\) 13.9653 0.784370 0.392185 0.919886i \(-0.371719\pi\)
0.392185 + 0.919886i \(0.371719\pi\)
\(318\) 12.3573 0.692965
\(319\) −49.3469 −2.76290
\(320\) −33.9396 −1.89728
\(321\) −4.11614 −0.229740
\(322\) 3.99822 0.222812
\(323\) −15.8149 −0.879966
\(324\) 4.83880 0.268822
\(325\) 0 0
\(326\) −7.65428 −0.423931
\(327\) 6.52500 0.360833
\(328\) −25.9395 −1.43227
\(329\) −2.38790 −0.131649
\(330\) 61.0944 3.36314
\(331\) 4.67384 0.256898 0.128449 0.991716i \(-0.459000\pi\)
0.128449 + 0.991716i \(0.459000\pi\)
\(332\) 45.1094 2.47570
\(333\) 0.399662 0.0219013
\(334\) 40.9084 2.23841
\(335\) 36.2307 1.97949
\(336\) −9.73635 −0.531162
\(337\) 19.4462 1.05930 0.529652 0.848215i \(-0.322323\pi\)
0.529652 + 0.848215i \(0.322323\pi\)
\(338\) 0 0
\(339\) 0.829620 0.0450588
\(340\) 86.7971 4.70723
\(341\) −14.4703 −0.783609
\(342\) −9.44580 −0.510771
\(343\) −1.00000 −0.0539949
\(344\) −74.7301 −4.02918
\(345\) −6.26363 −0.337223
\(346\) 56.4761 3.03617
\(347\) −23.9395 −1.28514 −0.642569 0.766228i \(-0.722131\pi\)
−0.642569 + 0.766228i \(0.722131\pi\)
\(348\) −41.8732 −2.24464
\(349\) −5.12046 −0.274092 −0.137046 0.990565i \(-0.543761\pi\)
−0.137046 + 0.990565i \(0.543761\pi\)
\(350\) 30.8169 1.64723
\(351\) 0 0
\(352\) −60.5264 −3.22607
\(353\) −7.74166 −0.412047 −0.206023 0.978547i \(-0.566052\pi\)
−0.206023 + 0.978547i \(0.566052\pi\)
\(354\) 10.4267 0.554171
\(355\) 17.0126 0.902933
\(356\) 46.4994 2.46446
\(357\) 4.37843 0.231731
\(358\) −8.94507 −0.472762
\(359\) 31.7337 1.67484 0.837420 0.546559i \(-0.184063\pi\)
0.837420 + 0.546559i \(0.184063\pi\)
\(360\) 30.4140 1.60296
\(361\) −5.95337 −0.313335
\(362\) −30.1637 −1.58537
\(363\) 21.5180 1.12940
\(364\) 0 0
\(365\) 24.9122 1.30397
\(366\) 2.90616 0.151907
\(367\) 13.1949 0.688769 0.344384 0.938829i \(-0.388088\pi\)
0.344384 + 0.938829i \(0.388088\pi\)
\(368\) 14.8858 0.775977
\(369\) 3.49412 0.181896
\(370\) 4.28186 0.222603
\(371\) 4.72536 0.245329
\(372\) −12.2787 −0.636621
\(373\) 30.9479 1.60242 0.801212 0.598381i \(-0.204189\pi\)
0.801212 + 0.598381i \(0.204189\pi\)
\(374\) 65.2934 3.37624
\(375\) −27.7937 −1.43526
\(376\) −17.7272 −0.914211
\(377\) 0 0
\(378\) 2.61511 0.134507
\(379\) −0.0568165 −0.00291847 −0.00145923 0.999999i \(-0.500464\pi\)
−0.00145923 + 0.999999i \(0.500464\pi\)
\(380\) −71.6038 −3.67320
\(381\) −11.8157 −0.605339
\(382\) −15.1557 −0.775431
\(383\) −2.47372 −0.126401 −0.0632005 0.998001i \(-0.520131\pi\)
−0.0632005 + 0.998001i \(0.520131\pi\)
\(384\) −0.436221 −0.0222608
\(385\) 23.3621 1.19064
\(386\) 41.5637 2.11554
\(387\) 10.0663 0.511701
\(388\) −68.4591 −3.47548
\(389\) 20.1130 1.01977 0.509884 0.860243i \(-0.329688\pi\)
0.509884 + 0.860243i \(0.329688\pi\)
\(390\) 0 0
\(391\) −6.69414 −0.338537
\(392\) −7.42376 −0.374957
\(393\) 15.9488 0.804509
\(394\) 4.12510 0.207819
\(395\) 0.924653 0.0465244
\(396\) 27.5930 1.38660
\(397\) 38.5811 1.93633 0.968164 0.250317i \(-0.0805347\pi\)
0.968164 + 0.250317i \(0.0805347\pi\)
\(398\) −11.2857 −0.565703
\(399\) −3.61201 −0.180827
\(400\) 114.735 5.73674
\(401\) 32.4962 1.62278 0.811390 0.584505i \(-0.198711\pi\)
0.811390 + 0.584505i \(0.198711\pi\)
\(402\) 23.1268 1.15346
\(403\) 0 0
\(404\) −49.0205 −2.43886
\(405\) −4.09685 −0.203574
\(406\) −22.6302 −1.12312
\(407\) 2.27905 0.112968
\(408\) 32.5044 1.60921
\(409\) −0.690530 −0.0341445 −0.0170723 0.999854i \(-0.505435\pi\)
−0.0170723 + 0.999854i \(0.505435\pi\)
\(410\) 37.4349 1.84878
\(411\) 13.2254 0.652362
\(412\) 9.39755 0.462984
\(413\) 3.98709 0.196192
\(414\) −3.99822 −0.196502
\(415\) −38.1927 −1.87480
\(416\) 0 0
\(417\) −3.88051 −0.190029
\(418\) −53.8642 −2.63459
\(419\) 30.5802 1.49394 0.746971 0.664857i \(-0.231507\pi\)
0.746971 + 0.664857i \(0.231507\pi\)
\(420\) 19.8238 0.967303
\(421\) −12.5119 −0.609792 −0.304896 0.952386i \(-0.598622\pi\)
−0.304896 + 0.952386i \(0.598622\pi\)
\(422\) 20.5246 0.999121
\(423\) 2.38790 0.116104
\(424\) 35.0800 1.70363
\(425\) −51.5961 −2.50278
\(426\) 10.8595 0.526144
\(427\) 1.11129 0.0537793
\(428\) −19.9172 −0.962732
\(429\) 0 0
\(430\) 107.848 5.20089
\(431\) 24.2411 1.16765 0.583827 0.811878i \(-0.301554\pi\)
0.583827 + 0.811878i \(0.301554\pi\)
\(432\) 9.73635 0.468440
\(433\) −14.7727 −0.709930 −0.354965 0.934880i \(-0.615507\pi\)
−0.354965 + 0.934880i \(0.615507\pi\)
\(434\) −6.63598 −0.318537
\(435\) 35.4526 1.69982
\(436\) 31.5731 1.51208
\(437\) 5.52237 0.264171
\(438\) 15.9020 0.759828
\(439\) −28.9217 −1.38036 −0.690178 0.723639i \(-0.742468\pi\)
−0.690178 + 0.723639i \(0.742468\pi\)
\(440\) 173.434 8.26816
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 38.5183 1.83006 0.915030 0.403385i \(-0.132166\pi\)
0.915030 + 0.403385i \(0.132166\pi\)
\(444\) 1.93388 0.0917780
\(445\) −39.3695 −1.86629
\(446\) −13.6471 −0.646210
\(447\) 16.8716 0.798001
\(448\) −8.28433 −0.391398
\(449\) 25.5939 1.20785 0.603926 0.797040i \(-0.293602\pi\)
0.603926 + 0.797040i \(0.293602\pi\)
\(450\) −30.8169 −1.45272
\(451\) 19.9250 0.938233
\(452\) 4.01436 0.188820
\(453\) 19.7463 0.927764
\(454\) 45.3674 2.12920
\(455\) 0 0
\(456\) −26.8147 −1.25571
\(457\) −5.16777 −0.241738 −0.120869 0.992668i \(-0.538568\pi\)
−0.120869 + 0.992668i \(0.538568\pi\)
\(458\) −21.4532 −1.00244
\(459\) −4.37843 −0.204367
\(460\) −30.3084 −1.41314
\(461\) −26.8777 −1.25182 −0.625909 0.779896i \(-0.715272\pi\)
−0.625909 + 0.779896i \(0.715272\pi\)
\(462\) 14.9125 0.693794
\(463\) 15.0113 0.697633 0.348817 0.937191i \(-0.386584\pi\)
0.348817 + 0.937191i \(0.386584\pi\)
\(464\) −84.2548 −3.91143
\(465\) 10.3960 0.482102
\(466\) −35.0208 −1.62231
\(467\) −26.6991 −1.23549 −0.617744 0.786379i \(-0.711953\pi\)
−0.617744 + 0.786379i \(0.711953\pi\)
\(468\) 0 0
\(469\) 8.84355 0.408357
\(470\) 25.5833 1.18007
\(471\) 17.9869 0.828794
\(472\) 29.5992 1.36241
\(473\) 57.4028 2.63939
\(474\) 0.590227 0.0271100
\(475\) 42.5645 1.95300
\(476\) 21.1863 0.971073
\(477\) −4.72536 −0.216359
\(478\) 39.1106 1.78888
\(479\) −8.99953 −0.411199 −0.205599 0.978636i \(-0.565914\pi\)
−0.205599 + 0.978636i \(0.565914\pi\)
\(480\) 43.4844 1.98478
\(481\) 0 0
\(482\) −60.2959 −2.74640
\(483\) −1.52889 −0.0695669
\(484\) 104.121 4.73277
\(485\) 57.9621 2.63192
\(486\) −2.61511 −0.118624
\(487\) −15.9943 −0.724772 −0.362386 0.932028i \(-0.618038\pi\)
−0.362386 + 0.932028i \(0.618038\pi\)
\(488\) 8.24998 0.373459
\(489\) 2.92694 0.132361
\(490\) 10.7137 0.483996
\(491\) 18.8654 0.851382 0.425691 0.904869i \(-0.360031\pi\)
0.425691 + 0.904869i \(0.360031\pi\)
\(492\) 16.9073 0.762241
\(493\) 37.8893 1.70645
\(494\) 0 0
\(495\) −23.3621 −1.05005
\(496\) −24.7065 −1.10935
\(497\) 4.15260 0.186269
\(498\) −24.3792 −1.09246
\(499\) 30.6858 1.37368 0.686841 0.726807i \(-0.258997\pi\)
0.686841 + 0.726807i \(0.258997\pi\)
\(500\) −134.488 −6.01449
\(501\) −15.6431 −0.698882
\(502\) −49.6173 −2.21453
\(503\) −22.4254 −0.999897 −0.499948 0.866055i \(-0.666648\pi\)
−0.499948 + 0.866055i \(0.666648\pi\)
\(504\) 7.42376 0.330681
\(505\) 41.5040 1.84691
\(506\) −22.7996 −1.01357
\(507\) 0 0
\(508\) −57.1739 −2.53668
\(509\) −24.6562 −1.09287 −0.546434 0.837502i \(-0.684015\pi\)
−0.546434 + 0.837502i \(0.684015\pi\)
\(510\) −46.9092 −2.07717
\(511\) 6.08083 0.269000
\(512\) 41.2181 1.82160
\(513\) 3.61201 0.159474
\(514\) −47.5300 −2.09646
\(515\) −7.95660 −0.350610
\(516\) 48.7090 2.14429
\(517\) 13.6169 0.598870
\(518\) 1.04516 0.0459217
\(519\) −21.5961 −0.947962
\(520\) 0 0
\(521\) −8.20050 −0.359271 −0.179635 0.983733i \(-0.557492\pi\)
−0.179635 + 0.983733i \(0.557492\pi\)
\(522\) 22.6302 0.990497
\(523\) −33.0519 −1.44526 −0.722630 0.691235i \(-0.757067\pi\)
−0.722630 + 0.691235i \(0.757067\pi\)
\(524\) 77.1729 3.37131
\(525\) −11.7842 −0.514303
\(526\) −78.4865 −3.42217
\(527\) 11.1105 0.483981
\(528\) 55.5211 2.41624
\(529\) −20.6625 −0.898369
\(530\) −50.6261 −2.19906
\(531\) −3.98709 −0.173025
\(532\) −17.4778 −0.757758
\(533\) 0 0
\(534\) −25.1304 −1.08750
\(535\) 16.8632 0.729060
\(536\) 65.6524 2.83575
\(537\) 3.42054 0.147607
\(538\) −39.7970 −1.71577
\(539\) 5.70245 0.245622
\(540\) −19.8238 −0.853081
\(541\) 1.79997 0.0773867 0.0386933 0.999251i \(-0.487680\pi\)
0.0386933 + 0.999251i \(0.487680\pi\)
\(542\) 3.65493 0.156993
\(543\) 11.5344 0.494989
\(544\) 46.4731 1.99252
\(545\) −26.7319 −1.14507
\(546\) 0 0
\(547\) −6.55618 −0.280322 −0.140161 0.990129i \(-0.544762\pi\)
−0.140161 + 0.990129i \(0.544762\pi\)
\(548\) 63.9952 2.73374
\(549\) −1.11129 −0.0474289
\(550\) −175.732 −7.49323
\(551\) −31.2570 −1.33159
\(552\) −11.3501 −0.483093
\(553\) 0.225699 0.00959768
\(554\) −25.3347 −1.07637
\(555\) −1.63736 −0.0695019
\(556\) −18.7770 −0.796322
\(557\) 15.2943 0.648039 0.324019 0.946050i \(-0.394966\pi\)
0.324019 + 0.946050i \(0.394966\pi\)
\(558\) 6.63598 0.280923
\(559\) 0 0
\(560\) 39.8884 1.68559
\(561\) −24.9678 −1.05414
\(562\) −77.2954 −3.26051
\(563\) 45.2000 1.90495 0.952477 0.304612i \(-0.0985267\pi\)
0.952477 + 0.304612i \(0.0985267\pi\)
\(564\) 11.5546 0.486535
\(565\) −3.39883 −0.142990
\(566\) −25.6356 −1.07755
\(567\) −1.00000 −0.0419961
\(568\) 30.8279 1.29351
\(569\) −9.68102 −0.405850 −0.202925 0.979194i \(-0.565045\pi\)
−0.202925 + 0.979194i \(0.565045\pi\)
\(570\) 38.6980 1.62088
\(571\) 27.8363 1.16491 0.582457 0.812861i \(-0.302091\pi\)
0.582457 + 0.812861i \(0.302091\pi\)
\(572\) 0 0
\(573\) 5.79542 0.242107
\(574\) 9.13750 0.381392
\(575\) 18.0167 0.751349
\(576\) 8.28433 0.345180
\(577\) −10.2332 −0.426016 −0.213008 0.977051i \(-0.568326\pi\)
−0.213008 + 0.977051i \(0.568326\pi\)
\(578\) −5.67641 −0.236108
\(579\) −15.8937 −0.660518
\(580\) 171.548 7.12314
\(581\) −9.32245 −0.386761
\(582\) 36.9985 1.53364
\(583\) −26.9461 −1.11600
\(584\) 45.1426 1.86801
\(585\) 0 0
\(586\) 25.9559 1.07223
\(587\) −29.9645 −1.23677 −0.618383 0.785877i \(-0.712212\pi\)
−0.618383 + 0.785877i \(0.712212\pi\)
\(588\) 4.83880 0.199549
\(589\) −9.16567 −0.377665
\(590\) −42.7165 −1.75861
\(591\) −1.57741 −0.0648860
\(592\) 3.89125 0.159929
\(593\) 12.9516 0.531857 0.265928 0.963993i \(-0.414321\pi\)
0.265928 + 0.963993i \(0.414321\pi\)
\(594\) −14.9125 −0.611869
\(595\) −17.9378 −0.735376
\(596\) 81.6384 3.34404
\(597\) 4.31559 0.176625
\(598\) 0 0
\(599\) 11.1867 0.457075 0.228538 0.973535i \(-0.426606\pi\)
0.228538 + 0.973535i \(0.426606\pi\)
\(600\) −87.4828 −3.57147
\(601\) −7.68718 −0.313566 −0.156783 0.987633i \(-0.550112\pi\)
−0.156783 + 0.987633i \(0.550112\pi\)
\(602\) 26.3246 1.07291
\(603\) −8.84355 −0.360137
\(604\) 95.5485 3.88781
\(605\) −88.1558 −3.58404
\(606\) 26.4929 1.07620
\(607\) −20.3771 −0.827082 −0.413541 0.910485i \(-0.635708\pi\)
−0.413541 + 0.910485i \(0.635708\pi\)
\(608\) −38.3383 −1.55482
\(609\) 8.65363 0.350663
\(610\) −11.9061 −0.482063
\(611\) 0 0
\(612\) −21.1863 −0.856406
\(613\) 40.7493 1.64585 0.822925 0.568150i \(-0.192341\pi\)
0.822925 + 0.568150i \(0.192341\pi\)
\(614\) 88.2697 3.56227
\(615\) −14.3149 −0.577231
\(616\) 42.3336 1.70567
\(617\) 25.3049 1.01874 0.509368 0.860549i \(-0.329879\pi\)
0.509368 + 0.860549i \(0.329879\pi\)
\(618\) −5.07887 −0.204302
\(619\) −21.6724 −0.871086 −0.435543 0.900168i \(-0.643444\pi\)
−0.435543 + 0.900168i \(0.643444\pi\)
\(620\) 50.3040 2.02026
\(621\) 1.52889 0.0613523
\(622\) −71.4791 −2.86605
\(623\) −9.60970 −0.385005
\(624\) 0 0
\(625\) 54.9458 2.19783
\(626\) 33.0253 1.31996
\(627\) 20.5973 0.822578
\(628\) 87.0351 3.47308
\(629\) −1.74989 −0.0697727
\(630\) −10.7137 −0.426844
\(631\) −29.7618 −1.18480 −0.592400 0.805644i \(-0.701819\pi\)
−0.592400 + 0.805644i \(0.701819\pi\)
\(632\) 1.67553 0.0666491
\(633\) −7.84846 −0.311948
\(634\) −36.5208 −1.45043
\(635\) 48.4073 1.92098
\(636\) −22.8651 −0.906659
\(637\) 0 0
\(638\) 129.048 5.10904
\(639\) −4.15260 −0.164274
\(640\) 1.78713 0.0706426
\(641\) −15.7964 −0.623920 −0.311960 0.950095i \(-0.600986\pi\)
−0.311960 + 0.950095i \(0.600986\pi\)
\(642\) 10.7642 0.424827
\(643\) −15.9937 −0.630732 −0.315366 0.948970i \(-0.602127\pi\)
−0.315366 + 0.948970i \(0.602127\pi\)
\(644\) −7.39799 −0.291522
\(645\) −41.2403 −1.62383
\(646\) 41.3578 1.62720
\(647\) 34.3302 1.34966 0.674829 0.737974i \(-0.264217\pi\)
0.674829 + 0.737974i \(0.264217\pi\)
\(648\) −7.42376 −0.291633
\(649\) −22.7362 −0.892473
\(650\) 0 0
\(651\) 2.53755 0.0994545
\(652\) 14.1629 0.554661
\(653\) 17.5804 0.687975 0.343988 0.938974i \(-0.388222\pi\)
0.343988 + 0.938974i \(0.388222\pi\)
\(654\) −17.0636 −0.667239
\(655\) −65.3397 −2.55303
\(656\) 34.0200 1.32826
\(657\) −6.08083 −0.237236
\(658\) 6.24463 0.243441
\(659\) −29.9239 −1.16567 −0.582835 0.812591i \(-0.698056\pi\)
−0.582835 + 0.812591i \(0.698056\pi\)
\(660\) −113.044 −4.40024
\(661\) 9.86053 0.383530 0.191765 0.981441i \(-0.438579\pi\)
0.191765 + 0.981441i \(0.438579\pi\)
\(662\) −12.2226 −0.475045
\(663\) 0 0
\(664\) −69.2077 −2.68578
\(665\) 14.7979 0.573837
\(666\) −1.04516 −0.0404991
\(667\) −13.2305 −0.512285
\(668\) −75.6938 −2.92868
\(669\) 5.21856 0.201761
\(670\) −94.7472 −3.66040
\(671\) −6.33710 −0.244641
\(672\) 10.6141 0.409448
\(673\) 40.3380 1.55492 0.777458 0.628935i \(-0.216509\pi\)
0.777458 + 0.628935i \(0.216509\pi\)
\(674\) −50.8540 −1.95882
\(675\) 11.7842 0.453573
\(676\) 0 0
\(677\) 29.8234 1.14621 0.573103 0.819483i \(-0.305739\pi\)
0.573103 + 0.819483i \(0.305739\pi\)
\(678\) −2.16955 −0.0833209
\(679\) 14.1480 0.542949
\(680\) −133.166 −5.10667
\(681\) −17.3482 −0.664784
\(682\) 37.8413 1.44902
\(683\) 12.8508 0.491722 0.245861 0.969305i \(-0.420929\pi\)
0.245861 + 0.969305i \(0.420929\pi\)
\(684\) 17.4778 0.668280
\(685\) −54.1826 −2.07021
\(686\) 2.61511 0.0998453
\(687\) 8.20358 0.312986
\(688\) 98.0095 3.73658
\(689\) 0 0
\(690\) 16.3801 0.623579
\(691\) 16.4674 0.626451 0.313225 0.949679i \(-0.398590\pi\)
0.313225 + 0.949679i \(0.398590\pi\)
\(692\) −104.499 −3.97246
\(693\) −5.70245 −0.216618
\(694\) 62.6043 2.37643
\(695\) 15.8979 0.603040
\(696\) 64.2425 2.43511
\(697\) −15.2987 −0.579481
\(698\) 13.3906 0.506840
\(699\) 13.3917 0.506521
\(700\) −57.0212 −2.15520
\(701\) −38.7459 −1.46341 −0.731705 0.681621i \(-0.761275\pi\)
−0.731705 + 0.681621i \(0.761275\pi\)
\(702\) 0 0
\(703\) 1.44358 0.0544458
\(704\) 47.2410 1.78046
\(705\) −9.78288 −0.368444
\(706\) 20.2453 0.761941
\(707\) 10.1307 0.381005
\(708\) −19.2927 −0.725064
\(709\) 51.1868 1.92236 0.961181 0.275918i \(-0.0889818\pi\)
0.961181 + 0.275918i \(0.0889818\pi\)
\(710\) −44.4897 −1.66967
\(711\) −0.225699 −0.00846436
\(712\) −71.3401 −2.67358
\(713\) −3.87964 −0.145294
\(714\) −11.4501 −0.428508
\(715\) 0 0
\(716\) 16.5513 0.618550
\(717\) −14.9556 −0.558529
\(718\) −82.9871 −3.09705
\(719\) −39.5817 −1.47615 −0.738074 0.674719i \(-0.764265\pi\)
−0.738074 + 0.674719i \(0.764265\pi\)
\(720\) −39.8884 −1.48655
\(721\) −1.94213 −0.0723286
\(722\) 15.5687 0.579408
\(723\) 23.0567 0.857489
\(724\) 55.8126 2.07426
\(725\) −101.976 −3.78729
\(726\) −56.2718 −2.08844
\(727\) 21.6125 0.801564 0.400782 0.916173i \(-0.368738\pi\)
0.400782 + 0.916173i \(0.368738\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −65.1482 −2.41124
\(731\) −44.0748 −1.63016
\(732\) −5.37733 −0.198752
\(733\) −11.8544 −0.437853 −0.218926 0.975741i \(-0.570255\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(734\) −34.5061 −1.27364
\(735\) −4.09685 −0.151115
\(736\) −16.2278 −0.598165
\(737\) −50.4299 −1.85761
\(738\) −9.13750 −0.336356
\(739\) −4.16606 −0.153251 −0.0766255 0.997060i \(-0.524415\pi\)
−0.0766255 + 0.997060i \(0.524415\pi\)
\(740\) −7.92283 −0.291249
\(741\) 0 0
\(742\) −12.3573 −0.453652
\(743\) 20.4996 0.752059 0.376029 0.926608i \(-0.377289\pi\)
0.376029 + 0.926608i \(0.377289\pi\)
\(744\) 18.8382 0.690641
\(745\) −69.1205 −2.53238
\(746\) −80.9322 −2.96314
\(747\) 9.32245 0.341091
\(748\) −120.814 −4.41739
\(749\) 4.11614 0.150400
\(750\) 72.6836 2.65403
\(751\) −9.35235 −0.341272 −0.170636 0.985334i \(-0.554582\pi\)
−0.170636 + 0.985334i \(0.554582\pi\)
\(752\) 23.2495 0.847821
\(753\) 18.9733 0.691426
\(754\) 0 0
\(755\) −80.8978 −2.94417
\(756\) −4.83880 −0.175985
\(757\) −24.3988 −0.886789 −0.443394 0.896327i \(-0.646226\pi\)
−0.443394 + 0.896327i \(0.646226\pi\)
\(758\) 0.148581 0.00539671
\(759\) 8.71843 0.316459
\(760\) 109.856 3.98489
\(761\) 48.1163 1.74421 0.872107 0.489316i \(-0.162754\pi\)
0.872107 + 0.489316i \(0.162754\pi\)
\(762\) 30.8994 1.11937
\(763\) −6.52500 −0.236221
\(764\) 28.0429 1.01456
\(765\) 17.9378 0.648541
\(766\) 6.46904 0.233736
\(767\) 0 0
\(768\) −15.4279 −0.556706
\(769\) 17.9764 0.648247 0.324123 0.946015i \(-0.394931\pi\)
0.324123 + 0.946015i \(0.394931\pi\)
\(770\) −61.0944 −2.20169
\(771\) 18.1751 0.654562
\(772\) −76.9062 −2.76792
\(773\) 0.803670 0.0289060 0.0144530 0.999896i \(-0.495399\pi\)
0.0144530 + 0.999896i \(0.495399\pi\)
\(774\) −26.3246 −0.946218
\(775\) −29.9030 −1.07415
\(776\) 105.031 3.77040
\(777\) −0.399662 −0.0143378
\(778\) −52.5976 −1.88572
\(779\) 12.6208 0.452187
\(780\) 0 0
\(781\) −23.6800 −0.847336
\(782\) 17.5059 0.626010
\(783\) −8.65363 −0.309256
\(784\) 9.73635 0.347727
\(785\) −73.6897 −2.63010
\(786\) −41.7078 −1.48767
\(787\) −21.4970 −0.766286 −0.383143 0.923689i \(-0.625158\pi\)
−0.383143 + 0.923689i \(0.625158\pi\)
\(788\) −7.63276 −0.271906
\(789\) 30.0127 1.06848
\(790\) −2.41807 −0.0860310
\(791\) −0.829620 −0.0294979
\(792\) −42.3336 −1.50426
\(793\) 0 0
\(794\) −100.894 −3.58058
\(795\) 19.3591 0.686596
\(796\) 20.8822 0.740152
\(797\) 1.61335 0.0571477 0.0285739 0.999592i \(-0.490903\pi\)
0.0285739 + 0.999592i \(0.490903\pi\)
\(798\) 9.44580 0.334378
\(799\) −10.4553 −0.369880
\(800\) −125.078 −4.42219
\(801\) 9.60970 0.339542
\(802\) −84.9810 −3.00078
\(803\) −34.6756 −1.22368
\(804\) −42.7921 −1.50916
\(805\) 6.26363 0.220764
\(806\) 0 0
\(807\) 15.2181 0.535703
\(808\) 75.2081 2.64581
\(809\) 4.21432 0.148168 0.0740838 0.997252i \(-0.476397\pi\)
0.0740838 + 0.997252i \(0.476397\pi\)
\(810\) 10.7137 0.376441
\(811\) 18.3325 0.643741 0.321871 0.946784i \(-0.395688\pi\)
0.321871 + 0.946784i \(0.395688\pi\)
\(812\) 41.8732 1.46946
\(813\) −1.39762 −0.0490167
\(814\) −5.95997 −0.208897
\(815\) −11.9912 −0.420035
\(816\) −42.6299 −1.49235
\(817\) 36.3598 1.27207
\(818\) 1.80581 0.0631387
\(819\) 0 0
\(820\) −69.2667 −2.41890
\(821\) −38.1069 −1.32994 −0.664970 0.746870i \(-0.731555\pi\)
−0.664970 + 0.746870i \(0.731555\pi\)
\(822\) −34.5859 −1.20632
\(823\) 11.3478 0.395559 0.197780 0.980246i \(-0.436627\pi\)
0.197780 + 0.980246i \(0.436627\pi\)
\(824\) −14.4179 −0.502271
\(825\) 67.1986 2.33956
\(826\) −10.4267 −0.362790
\(827\) −26.1746 −0.910181 −0.455091 0.890445i \(-0.650393\pi\)
−0.455091 + 0.890445i \(0.650393\pi\)
\(828\) 7.39799 0.257098
\(829\) 25.6170 0.889716 0.444858 0.895601i \(-0.353254\pi\)
0.444858 + 0.895601i \(0.353254\pi\)
\(830\) 99.8780 3.46682
\(831\) 9.68781 0.336066
\(832\) 0 0
\(833\) −4.37843 −0.151704
\(834\) 10.1480 0.351395
\(835\) 64.0874 2.21784
\(836\) 99.6662 3.44703
\(837\) −2.53755 −0.0877107
\(838\) −79.9706 −2.76254
\(839\) 6.23099 0.215118 0.107559 0.994199i \(-0.465697\pi\)
0.107559 + 0.994199i \(0.465697\pi\)
\(840\) −30.4140 −1.04938
\(841\) 45.8853 1.58225
\(842\) 32.7200 1.12760
\(843\) 29.5572 1.01801
\(844\) −37.9771 −1.30722
\(845\) 0 0
\(846\) −6.24463 −0.214695
\(847\) −21.5180 −0.739366
\(848\) −46.0078 −1.57991
\(849\) 9.80289 0.336434
\(850\) 134.929 4.62804
\(851\) 0.611040 0.0209462
\(852\) −20.0936 −0.688394
\(853\) −14.8238 −0.507558 −0.253779 0.967262i \(-0.581674\pi\)
−0.253779 + 0.967262i \(0.581674\pi\)
\(854\) −2.90616 −0.0994466
\(855\) −14.7979 −0.506076
\(856\) 30.5572 1.04442
\(857\) −48.0811 −1.64242 −0.821210 0.570626i \(-0.806701\pi\)
−0.821210 + 0.570626i \(0.806701\pi\)
\(858\) 0 0
\(859\) 9.03561 0.308291 0.154146 0.988048i \(-0.450738\pi\)
0.154146 + 0.988048i \(0.450738\pi\)
\(860\) −199.553 −6.80471
\(861\) −3.49412 −0.119079
\(862\) −63.3932 −2.15918
\(863\) 27.4629 0.934848 0.467424 0.884033i \(-0.345182\pi\)
0.467424 + 0.884033i \(0.345182\pi\)
\(864\) −10.6141 −0.361099
\(865\) 88.4758 3.00827
\(866\) 38.6322 1.31278
\(867\) 2.17062 0.0737182
\(868\) 12.2787 0.416766
\(869\) −1.28704 −0.0436597
\(870\) −92.7125 −3.14325
\(871\) 0 0
\(872\) −48.4400 −1.64039
\(873\) −14.1480 −0.478836
\(874\) −14.4416 −0.488495
\(875\) 27.7937 0.939599
\(876\) −29.4239 −0.994141
\(877\) 19.3933 0.654865 0.327433 0.944875i \(-0.393817\pi\)
0.327433 + 0.944875i \(0.393817\pi\)
\(878\) 75.6334 2.55250
\(879\) −9.92535 −0.334774
\(880\) −227.461 −7.66772
\(881\) −2.10868 −0.0710431 −0.0355215 0.999369i \(-0.511309\pi\)
−0.0355215 + 0.999369i \(0.511309\pi\)
\(882\) −2.61511 −0.0880553
\(883\) −7.70898 −0.259428 −0.129714 0.991551i \(-0.541406\pi\)
−0.129714 + 0.991551i \(0.541406\pi\)
\(884\) 0 0
\(885\) 16.3345 0.549078
\(886\) −100.730 −3.38408
\(887\) −3.93091 −0.131987 −0.0659936 0.997820i \(-0.521022\pi\)
−0.0659936 + 0.997820i \(0.521022\pi\)
\(888\) −2.96700 −0.0995659
\(889\) 11.8157 0.396287
\(890\) 102.956 3.45108
\(891\) 5.70245 0.191039
\(892\) 25.2516 0.845485
\(893\) 8.62513 0.288629
\(894\) −44.1212 −1.47563
\(895\) −14.0134 −0.468417
\(896\) 0.436221 0.0145731
\(897\) 0 0
\(898\) −66.9309 −2.23351
\(899\) 21.9591 0.732375
\(900\) 57.0212 1.90071
\(901\) 20.6897 0.689272
\(902\) −52.1061 −1.73494
\(903\) −10.0663 −0.334987
\(904\) −6.15890 −0.204842
\(905\) −47.2547 −1.57080
\(906\) −51.6388 −1.71559
\(907\) 19.4487 0.645784 0.322892 0.946436i \(-0.395345\pi\)
0.322892 + 0.946436i \(0.395345\pi\)
\(908\) −83.9444 −2.78579
\(909\) −10.1307 −0.336015
\(910\) 0 0
\(911\) −56.5453 −1.87343 −0.936714 0.350095i \(-0.886149\pi\)
−0.936714 + 0.350095i \(0.886149\pi\)
\(912\) 35.1678 1.16452
\(913\) 53.1608 1.75937
\(914\) 13.5143 0.447012
\(915\) 4.55281 0.150511
\(916\) 39.6954 1.31157
\(917\) −15.9488 −0.526675
\(918\) 11.4501 0.377908
\(919\) −6.22782 −0.205437 −0.102718 0.994710i \(-0.532754\pi\)
−0.102718 + 0.994710i \(0.532754\pi\)
\(920\) 46.4997 1.53305
\(921\) −33.7537 −1.11222
\(922\) 70.2880 2.31481
\(923\) 0 0
\(924\) −27.5930 −0.907743
\(925\) 4.70969 0.154853
\(926\) −39.2561 −1.29004
\(927\) 1.94213 0.0637878
\(928\) 91.8505 3.01514
\(929\) 28.7107 0.941969 0.470985 0.882141i \(-0.343899\pi\)
0.470985 + 0.882141i \(0.343899\pi\)
\(930\) −27.1866 −0.891484
\(931\) 3.61201 0.118379
\(932\) 64.7997 2.12259
\(933\) 27.3331 0.894846
\(934\) 69.8211 2.28462
\(935\) 102.289 3.34521
\(936\) 0 0
\(937\) 50.1310 1.63771 0.818855 0.574001i \(-0.194609\pi\)
0.818855 + 0.574001i \(0.194609\pi\)
\(938\) −23.1268 −0.755118
\(939\) −12.6286 −0.412120
\(940\) −47.3373 −1.54397
\(941\) −12.7241 −0.414795 −0.207398 0.978257i \(-0.566499\pi\)
−0.207398 + 0.978257i \(0.566499\pi\)
\(942\) −47.0378 −1.53257
\(943\) 5.34212 0.173963
\(944\) −38.8197 −1.26347
\(945\) 4.09685 0.133270
\(946\) −150.115 −4.88065
\(947\) −37.7169 −1.22564 −0.612818 0.790224i \(-0.709964\pi\)
−0.612818 + 0.790224i \(0.709964\pi\)
\(948\) −1.09211 −0.0354701
\(949\) 0 0
\(950\) −111.311 −3.61140
\(951\) 13.9653 0.452856
\(952\) −32.5044 −1.05347
\(953\) 40.0863 1.29852 0.649261 0.760566i \(-0.275078\pi\)
0.649261 + 0.760566i \(0.275078\pi\)
\(954\) 12.3573 0.400084
\(955\) −23.7430 −0.768304
\(956\) −72.3673 −2.34053
\(957\) −49.3469 −1.59516
\(958\) 23.5348 0.760373
\(959\) −13.2254 −0.427071
\(960\) −33.9396 −1.09540
\(961\) −24.5608 −0.792285
\(962\) 0 0
\(963\) −4.11614 −0.132641
\(964\) 111.567 3.59333
\(965\) 65.1139 2.09609
\(966\) 3.99822 0.128641
\(967\) 13.1830 0.423937 0.211968 0.977277i \(-0.432013\pi\)
0.211968 + 0.977277i \(0.432013\pi\)
\(968\) −159.744 −5.13437
\(969\) −15.8149 −0.508049
\(970\) −151.577 −4.86685
\(971\) 7.28316 0.233728 0.116864 0.993148i \(-0.462716\pi\)
0.116864 + 0.993148i \(0.462716\pi\)
\(972\) 4.83880 0.155204
\(973\) 3.88051 0.124403
\(974\) 41.8269 1.34022
\(975\) 0 0
\(976\) −10.8200 −0.346338
\(977\) −14.3070 −0.457721 −0.228860 0.973459i \(-0.573500\pi\)
−0.228860 + 0.973459i \(0.573500\pi\)
\(978\) −7.65428 −0.244757
\(979\) 54.7989 1.75138
\(980\) −19.8238 −0.633248
\(981\) 6.52500 0.208327
\(982\) −49.3350 −1.57434
\(983\) 25.9689 0.828280 0.414140 0.910213i \(-0.364082\pi\)
0.414140 + 0.910213i \(0.364082\pi\)
\(984\) −25.9395 −0.826921
\(985\) 6.46241 0.205909
\(986\) −99.0846 −3.15550
\(987\) −2.38790 −0.0760078
\(988\) 0 0
\(989\) 15.3903 0.489384
\(990\) 61.0944 1.94171
\(991\) −27.5093 −0.873862 −0.436931 0.899495i \(-0.643935\pi\)
−0.436931 + 0.899495i \(0.643935\pi\)
\(992\) 26.9338 0.855150
\(993\) 4.67384 0.148320
\(994\) −10.8595 −0.344442
\(995\) −17.6803 −0.560504
\(996\) 45.1094 1.42935
\(997\) 37.8645 1.19918 0.599590 0.800308i \(-0.295330\pi\)
0.599590 + 0.800308i \(0.295330\pi\)
\(998\) −80.2466 −2.54016
\(999\) 0.399662 0.0126447
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.bh.1.1 yes 15
13.12 even 2 3549.2.a.bg.1.15 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.15 15 13.12 even 2
3549.2.a.bh.1.1 yes 15 1.1 even 1 trivial