Properties

Label 3549.2.a.bh.1.13
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 1.13
Root \(2.49813\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.49813 q^{2} +1.00000 q^{3} +4.24068 q^{4} +2.35199 q^{5} +2.49813 q^{6} -1.00000 q^{7} +5.59751 q^{8} +1.00000 q^{9} +5.87558 q^{10} +5.16537 q^{11} +4.24068 q^{12} -2.49813 q^{14} +2.35199 q^{15} +5.50198 q^{16} -1.70559 q^{17} +2.49813 q^{18} -8.02484 q^{19} +9.97401 q^{20} -1.00000 q^{21} +12.9038 q^{22} +4.21818 q^{23} +5.59751 q^{24} +0.531841 q^{25} +1.00000 q^{27} -4.24068 q^{28} -5.24033 q^{29} +5.87558 q^{30} +1.11538 q^{31} +2.54966 q^{32} +5.16537 q^{33} -4.26078 q^{34} -2.35199 q^{35} +4.24068 q^{36} +8.21263 q^{37} -20.0471 q^{38} +13.1653 q^{40} -6.75466 q^{41} -2.49813 q^{42} -0.965145 q^{43} +21.9047 q^{44} +2.35199 q^{45} +10.5376 q^{46} +9.18662 q^{47} +5.50198 q^{48} +1.00000 q^{49} +1.32861 q^{50} -1.70559 q^{51} +11.9257 q^{53} +2.49813 q^{54} +12.1489 q^{55} -5.59751 q^{56} -8.02484 q^{57} -13.0910 q^{58} -2.98003 q^{59} +9.97401 q^{60} -14.6034 q^{61} +2.78637 q^{62} -1.00000 q^{63} -4.63456 q^{64} +12.9038 q^{66} -13.5464 q^{67} -7.23283 q^{68} +4.21818 q^{69} -5.87558 q^{70} +0.318196 q^{71} +5.59751 q^{72} -0.542709 q^{73} +20.5162 q^{74} +0.531841 q^{75} -34.0307 q^{76} -5.16537 q^{77} -13.2301 q^{79} +12.9406 q^{80} +1.00000 q^{81} -16.8740 q^{82} +5.79295 q^{83} -4.24068 q^{84} -4.01151 q^{85} -2.41106 q^{86} -5.24033 q^{87} +28.9132 q^{88} -7.80950 q^{89} +5.87558 q^{90} +17.8879 q^{92} +1.11538 q^{93} +22.9494 q^{94} -18.8743 q^{95} +2.54966 q^{96} -0.287042 q^{97} +2.49813 q^{98} +5.16537 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.49813 1.76645 0.883224 0.468952i \(-0.155368\pi\)
0.883224 + 0.468952i \(0.155368\pi\)
\(3\) 1.00000 0.577350
\(4\) 4.24068 2.12034
\(5\) 2.35199 1.05184 0.525920 0.850534i \(-0.323721\pi\)
0.525920 + 0.850534i \(0.323721\pi\)
\(6\) 2.49813 1.01986
\(7\) −1.00000 −0.377964
\(8\) 5.59751 1.97902
\(9\) 1.00000 0.333333
\(10\) 5.87558 1.85802
\(11\) 5.16537 1.55742 0.778709 0.627385i \(-0.215875\pi\)
0.778709 + 0.627385i \(0.215875\pi\)
\(12\) 4.24068 1.22418
\(13\) 0 0
\(14\) −2.49813 −0.667654
\(15\) 2.35199 0.607280
\(16\) 5.50198 1.37549
\(17\) −1.70559 −0.413665 −0.206833 0.978376i \(-0.566316\pi\)
−0.206833 + 0.978376i \(0.566316\pi\)
\(18\) 2.49813 0.588816
\(19\) −8.02484 −1.84102 −0.920512 0.390715i \(-0.872228\pi\)
−0.920512 + 0.390715i \(0.872228\pi\)
\(20\) 9.97401 2.23026
\(21\) −1.00000 −0.218218
\(22\) 12.9038 2.75110
\(23\) 4.21818 0.879552 0.439776 0.898108i \(-0.355058\pi\)
0.439776 + 0.898108i \(0.355058\pi\)
\(24\) 5.59751 1.14259
\(25\) 0.531841 0.106368
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −4.24068 −0.801412
\(29\) −5.24033 −0.973104 −0.486552 0.873652i \(-0.661746\pi\)
−0.486552 + 0.873652i \(0.661746\pi\)
\(30\) 5.87558 1.07273
\(31\) 1.11538 0.200328 0.100164 0.994971i \(-0.468063\pi\)
0.100164 + 0.994971i \(0.468063\pi\)
\(32\) 2.54966 0.450720
\(33\) 5.16537 0.899176
\(34\) −4.26078 −0.730718
\(35\) −2.35199 −0.397558
\(36\) 4.24068 0.706779
\(37\) 8.21263 1.35015 0.675074 0.737750i \(-0.264112\pi\)
0.675074 + 0.737750i \(0.264112\pi\)
\(38\) −20.0471 −3.25207
\(39\) 0 0
\(40\) 13.1653 2.08161
\(41\) −6.75466 −1.05490 −0.527450 0.849586i \(-0.676852\pi\)
−0.527450 + 0.849586i \(0.676852\pi\)
\(42\) −2.49813 −0.385470
\(43\) −0.965145 −0.147183 −0.0735916 0.997288i \(-0.523446\pi\)
−0.0735916 + 0.997288i \(0.523446\pi\)
\(44\) 21.9047 3.30225
\(45\) 2.35199 0.350613
\(46\) 10.5376 1.55368
\(47\) 9.18662 1.34001 0.670003 0.742358i \(-0.266293\pi\)
0.670003 + 0.742358i \(0.266293\pi\)
\(48\) 5.50198 0.794142
\(49\) 1.00000 0.142857
\(50\) 1.32861 0.187894
\(51\) −1.70559 −0.238830
\(52\) 0 0
\(53\) 11.9257 1.63812 0.819059 0.573709i \(-0.194496\pi\)
0.819059 + 0.573709i \(0.194496\pi\)
\(54\) 2.49813 0.339953
\(55\) 12.1489 1.63816
\(56\) −5.59751 −0.747998
\(57\) −8.02484 −1.06292
\(58\) −13.0910 −1.71894
\(59\) −2.98003 −0.387966 −0.193983 0.981005i \(-0.562141\pi\)
−0.193983 + 0.981005i \(0.562141\pi\)
\(60\) 9.97401 1.28764
\(61\) −14.6034 −1.86977 −0.934884 0.354954i \(-0.884497\pi\)
−0.934884 + 0.354954i \(0.884497\pi\)
\(62\) 2.78637 0.353869
\(63\) −1.00000 −0.125988
\(64\) −4.63456 −0.579320
\(65\) 0 0
\(66\) 12.9038 1.58835
\(67\) −13.5464 −1.65496 −0.827478 0.561499i \(-0.810225\pi\)
−0.827478 + 0.561499i \(0.810225\pi\)
\(68\) −7.23283 −0.877110
\(69\) 4.21818 0.507809
\(70\) −5.87558 −0.702266
\(71\) 0.318196 0.0377629 0.0188814 0.999822i \(-0.493989\pi\)
0.0188814 + 0.999822i \(0.493989\pi\)
\(72\) 5.59751 0.659673
\(73\) −0.542709 −0.0635193 −0.0317596 0.999496i \(-0.510111\pi\)
−0.0317596 + 0.999496i \(0.510111\pi\)
\(74\) 20.5162 2.38496
\(75\) 0.531841 0.0614117
\(76\) −34.0307 −3.90359
\(77\) −5.16537 −0.588649
\(78\) 0 0
\(79\) −13.2301 −1.48850 −0.744249 0.667903i \(-0.767192\pi\)
−0.744249 + 0.667903i \(0.767192\pi\)
\(80\) 12.9406 1.44680
\(81\) 1.00000 0.111111
\(82\) −16.8740 −1.86343
\(83\) 5.79295 0.635859 0.317930 0.948114i \(-0.397012\pi\)
0.317930 + 0.948114i \(0.397012\pi\)
\(84\) −4.24068 −0.462696
\(85\) −4.01151 −0.435110
\(86\) −2.41106 −0.259991
\(87\) −5.24033 −0.561822
\(88\) 28.9132 3.08216
\(89\) −7.80950 −0.827805 −0.413902 0.910321i \(-0.635835\pi\)
−0.413902 + 0.910321i \(0.635835\pi\)
\(90\) 5.87558 0.619340
\(91\) 0 0
\(92\) 17.8879 1.86495
\(93\) 1.11538 0.115660
\(94\) 22.9494 2.36705
\(95\) −18.8743 −1.93646
\(96\) 2.54966 0.260224
\(97\) −0.287042 −0.0291447 −0.0145723 0.999894i \(-0.504639\pi\)
−0.0145723 + 0.999894i \(0.504639\pi\)
\(98\) 2.49813 0.252350
\(99\) 5.16537 0.519140
\(100\) 2.25536 0.225536
\(101\) 12.9536 1.28893 0.644467 0.764632i \(-0.277079\pi\)
0.644467 + 0.764632i \(0.277079\pi\)
\(102\) −4.26078 −0.421880
\(103\) −6.53676 −0.644086 −0.322043 0.946725i \(-0.604370\pi\)
−0.322043 + 0.946725i \(0.604370\pi\)
\(104\) 0 0
\(105\) −2.35199 −0.229530
\(106\) 29.7919 2.89365
\(107\) −3.73899 −0.361462 −0.180731 0.983533i \(-0.557846\pi\)
−0.180731 + 0.983533i \(0.557846\pi\)
\(108\) 4.24068 0.408059
\(109\) −10.1278 −0.970066 −0.485033 0.874496i \(-0.661192\pi\)
−0.485033 + 0.874496i \(0.661192\pi\)
\(110\) 30.3496 2.89372
\(111\) 8.21263 0.779508
\(112\) −5.50198 −0.519888
\(113\) 16.5267 1.55471 0.777353 0.629065i \(-0.216562\pi\)
0.777353 + 0.629065i \(0.216562\pi\)
\(114\) −20.0471 −1.87758
\(115\) 9.92111 0.925148
\(116\) −22.2225 −2.06331
\(117\) 0 0
\(118\) −7.44450 −0.685322
\(119\) 1.70559 0.156351
\(120\) 13.1653 1.20182
\(121\) 15.6811 1.42555
\(122\) −36.4811 −3.30285
\(123\) −6.75466 −0.609047
\(124\) 4.72996 0.424763
\(125\) −10.5091 −0.939958
\(126\) −2.49813 −0.222551
\(127\) 13.8279 1.22703 0.613516 0.789682i \(-0.289755\pi\)
0.613516 + 0.789682i \(0.289755\pi\)
\(128\) −16.6771 −1.47406
\(129\) −0.965145 −0.0849762
\(130\) 0 0
\(131\) 9.92612 0.867249 0.433624 0.901094i \(-0.357234\pi\)
0.433624 + 0.901094i \(0.357234\pi\)
\(132\) 21.9047 1.90656
\(133\) 8.02484 0.695842
\(134\) −33.8407 −2.92339
\(135\) 2.35199 0.202427
\(136\) −9.54703 −0.818651
\(137\) 8.60954 0.735563 0.367781 0.929912i \(-0.380117\pi\)
0.367781 + 0.929912i \(0.380117\pi\)
\(138\) 10.5376 0.897019
\(139\) −9.92269 −0.841631 −0.420816 0.907146i \(-0.638256\pi\)
−0.420816 + 0.907146i \(0.638256\pi\)
\(140\) −9.97401 −0.842958
\(141\) 9.18662 0.773653
\(142\) 0.794896 0.0667062
\(143\) 0 0
\(144\) 5.50198 0.458498
\(145\) −12.3252 −1.02355
\(146\) −1.35576 −0.112203
\(147\) 1.00000 0.0824786
\(148\) 34.8271 2.86277
\(149\) −0.253154 −0.0207392 −0.0103696 0.999946i \(-0.503301\pi\)
−0.0103696 + 0.999946i \(0.503301\pi\)
\(150\) 1.32861 0.108481
\(151\) −19.1942 −1.56200 −0.780999 0.624532i \(-0.785290\pi\)
−0.780999 + 0.624532i \(0.785290\pi\)
\(152\) −44.9191 −3.64342
\(153\) −1.70559 −0.137888
\(154\) −12.9038 −1.03982
\(155\) 2.62336 0.210713
\(156\) 0 0
\(157\) −14.8981 −1.18900 −0.594500 0.804096i \(-0.702650\pi\)
−0.594500 + 0.804096i \(0.702650\pi\)
\(158\) −33.0505 −2.62935
\(159\) 11.9257 0.945768
\(160\) 5.99676 0.474086
\(161\) −4.21818 −0.332439
\(162\) 2.49813 0.196272
\(163\) −5.80688 −0.454830 −0.227415 0.973798i \(-0.573027\pi\)
−0.227415 + 0.973798i \(0.573027\pi\)
\(164\) −28.6443 −2.23674
\(165\) 12.1489 0.945790
\(166\) 14.4716 1.12321
\(167\) 21.4231 1.65777 0.828885 0.559419i \(-0.188976\pi\)
0.828885 + 0.559419i \(0.188976\pi\)
\(168\) −5.59751 −0.431857
\(169\) 0 0
\(170\) −10.0213 −0.768599
\(171\) −8.02484 −0.613675
\(172\) −4.09286 −0.312078
\(173\) 21.4128 1.62798 0.813991 0.580878i \(-0.197290\pi\)
0.813991 + 0.580878i \(0.197290\pi\)
\(174\) −13.0910 −0.992429
\(175\) −0.531841 −0.0402034
\(176\) 28.4198 2.14222
\(177\) −2.98003 −0.223992
\(178\) −19.5092 −1.46227
\(179\) 5.04689 0.377222 0.188611 0.982052i \(-0.439601\pi\)
0.188611 + 0.982052i \(0.439601\pi\)
\(180\) 9.97401 0.743419
\(181\) 15.8878 1.18093 0.590464 0.807064i \(-0.298945\pi\)
0.590464 + 0.807064i \(0.298945\pi\)
\(182\) 0 0
\(183\) −14.6034 −1.07951
\(184\) 23.6113 1.74065
\(185\) 19.3160 1.42014
\(186\) 2.78637 0.204306
\(187\) −8.80999 −0.644250
\(188\) 38.9575 2.84127
\(189\) −1.00000 −0.0727393
\(190\) −47.1506 −3.42066
\(191\) 13.3753 0.967801 0.483901 0.875123i \(-0.339220\pi\)
0.483901 + 0.875123i \(0.339220\pi\)
\(192\) −4.63456 −0.334471
\(193\) −6.66748 −0.479935 −0.239968 0.970781i \(-0.577137\pi\)
−0.239968 + 0.970781i \(0.577137\pi\)
\(194\) −0.717068 −0.0514825
\(195\) 0 0
\(196\) 4.24068 0.302905
\(197\) 12.3543 0.880210 0.440105 0.897946i \(-0.354941\pi\)
0.440105 + 0.897946i \(0.354941\pi\)
\(198\) 12.9038 0.917033
\(199\) −14.5437 −1.03098 −0.515488 0.856897i \(-0.672389\pi\)
−0.515488 + 0.856897i \(0.672389\pi\)
\(200\) 2.97698 0.210505
\(201\) −13.5464 −0.955489
\(202\) 32.3599 2.27683
\(203\) 5.24033 0.367799
\(204\) −7.23283 −0.506400
\(205\) −15.8869 −1.10959
\(206\) −16.3297 −1.13774
\(207\) 4.21818 0.293184
\(208\) 0 0
\(209\) −41.4513 −2.86725
\(210\) −5.87558 −0.405453
\(211\) 25.6088 1.76298 0.881491 0.472200i \(-0.156540\pi\)
0.881491 + 0.472200i \(0.156540\pi\)
\(212\) 50.5729 3.47336
\(213\) 0.318196 0.0218024
\(214\) −9.34050 −0.638503
\(215\) −2.27001 −0.154813
\(216\) 5.59751 0.380862
\(217\) −1.11538 −0.0757169
\(218\) −25.3006 −1.71357
\(219\) −0.542709 −0.0366729
\(220\) 51.5195 3.47344
\(221\) 0 0
\(222\) 20.5162 1.37696
\(223\) 8.99291 0.602210 0.301105 0.953591i \(-0.402645\pi\)
0.301105 + 0.953591i \(0.402645\pi\)
\(224\) −2.54966 −0.170356
\(225\) 0.531841 0.0354561
\(226\) 41.2860 2.74631
\(227\) 4.16233 0.276263 0.138132 0.990414i \(-0.455890\pi\)
0.138132 + 0.990414i \(0.455890\pi\)
\(228\) −34.0307 −2.25374
\(229\) 8.47202 0.559847 0.279924 0.960022i \(-0.409691\pi\)
0.279924 + 0.960022i \(0.409691\pi\)
\(230\) 24.7843 1.63423
\(231\) −5.16537 −0.339857
\(232\) −29.3328 −1.92579
\(233\) −18.5357 −1.21432 −0.607158 0.794581i \(-0.707691\pi\)
−0.607158 + 0.794581i \(0.707691\pi\)
\(234\) 0 0
\(235\) 21.6068 1.40947
\(236\) −12.6373 −0.822620
\(237\) −13.2301 −0.859384
\(238\) 4.26078 0.276185
\(239\) −0.176911 −0.0114434 −0.00572171 0.999984i \(-0.501821\pi\)
−0.00572171 + 0.999984i \(0.501821\pi\)
\(240\) 12.9406 0.835310
\(241\) −4.99572 −0.321803 −0.160901 0.986970i \(-0.551440\pi\)
−0.160901 + 0.986970i \(0.551440\pi\)
\(242\) 39.1735 2.51817
\(243\) 1.00000 0.0641500
\(244\) −61.9281 −3.96454
\(245\) 2.35199 0.150263
\(246\) −16.8740 −1.07585
\(247\) 0 0
\(248\) 6.24335 0.396453
\(249\) 5.79295 0.367113
\(250\) −26.2530 −1.66039
\(251\) 0.560900 0.0354037 0.0177019 0.999843i \(-0.494365\pi\)
0.0177019 + 0.999843i \(0.494365\pi\)
\(252\) −4.24068 −0.267137
\(253\) 21.7885 1.36983
\(254\) 34.5441 2.16749
\(255\) −4.01151 −0.251211
\(256\) −32.3924 −2.02453
\(257\) −16.9596 −1.05791 −0.528954 0.848650i \(-0.677416\pi\)
−0.528954 + 0.848650i \(0.677416\pi\)
\(258\) −2.41106 −0.150106
\(259\) −8.21263 −0.510308
\(260\) 0 0
\(261\) −5.24033 −0.324368
\(262\) 24.7968 1.53195
\(263\) 7.29257 0.449679 0.224839 0.974396i \(-0.427814\pi\)
0.224839 + 0.974396i \(0.427814\pi\)
\(264\) 28.9132 1.77949
\(265\) 28.0490 1.72304
\(266\) 20.0471 1.22917
\(267\) −7.80950 −0.477933
\(268\) −57.4459 −3.50906
\(269\) 1.71166 0.104362 0.0521809 0.998638i \(-0.483383\pi\)
0.0521809 + 0.998638i \(0.483383\pi\)
\(270\) 5.87558 0.357576
\(271\) −12.2573 −0.744575 −0.372288 0.928117i \(-0.621427\pi\)
−0.372288 + 0.928117i \(0.621427\pi\)
\(272\) −9.38409 −0.568994
\(273\) 0 0
\(274\) 21.5078 1.29933
\(275\) 2.74716 0.165660
\(276\) 17.8879 1.07673
\(277\) 32.0290 1.92444 0.962218 0.272279i \(-0.0877775\pi\)
0.962218 + 0.272279i \(0.0877775\pi\)
\(278\) −24.7882 −1.48670
\(279\) 1.11538 0.0667761
\(280\) −13.1653 −0.786775
\(281\) −25.3153 −1.51018 −0.755091 0.655620i \(-0.772408\pi\)
−0.755091 + 0.655620i \(0.772408\pi\)
\(282\) 22.9494 1.36662
\(283\) −8.29593 −0.493142 −0.246571 0.969125i \(-0.579304\pi\)
−0.246571 + 0.969125i \(0.579304\pi\)
\(284\) 1.34937 0.0800701
\(285\) −18.8743 −1.11802
\(286\) 0 0
\(287\) 6.75466 0.398715
\(288\) 2.54966 0.150240
\(289\) −14.0910 −0.828881
\(290\) −30.7900 −1.80805
\(291\) −0.287042 −0.0168267
\(292\) −2.30145 −0.134682
\(293\) −26.9892 −1.57672 −0.788362 0.615211i \(-0.789071\pi\)
−0.788362 + 0.615211i \(0.789071\pi\)
\(294\) 2.49813 0.145694
\(295\) −7.00898 −0.408079
\(296\) 45.9702 2.67197
\(297\) 5.16537 0.299725
\(298\) −0.632414 −0.0366348
\(299\) 0 0
\(300\) 2.25536 0.130214
\(301\) 0.965145 0.0556300
\(302\) −47.9496 −2.75919
\(303\) 12.9536 0.744166
\(304\) −44.1525 −2.53232
\(305\) −34.3469 −1.96670
\(306\) −4.26078 −0.243573
\(307\) −7.63819 −0.435935 −0.217967 0.975956i \(-0.569943\pi\)
−0.217967 + 0.975956i \(0.569943\pi\)
\(308\) −21.9047 −1.24813
\(309\) −6.53676 −0.371863
\(310\) 6.55350 0.372214
\(311\) −3.99085 −0.226301 −0.113150 0.993578i \(-0.536094\pi\)
−0.113150 + 0.993578i \(0.536094\pi\)
\(312\) 0 0
\(313\) 11.1267 0.628920 0.314460 0.949271i \(-0.398177\pi\)
0.314460 + 0.949271i \(0.398177\pi\)
\(314\) −37.2175 −2.10031
\(315\) −2.35199 −0.132519
\(316\) −56.1044 −3.15612
\(317\) 6.72186 0.377537 0.188769 0.982022i \(-0.439550\pi\)
0.188769 + 0.982022i \(0.439550\pi\)
\(318\) 29.7919 1.67065
\(319\) −27.0682 −1.51553
\(320\) −10.9004 −0.609352
\(321\) −3.73899 −0.208690
\(322\) −10.5376 −0.587237
\(323\) 13.6870 0.761567
\(324\) 4.24068 0.235593
\(325\) 0 0
\(326\) −14.5064 −0.803434
\(327\) −10.1278 −0.560068
\(328\) −37.8092 −2.08767
\(329\) −9.18662 −0.506475
\(330\) 30.3496 1.67069
\(331\) −19.4811 −1.07078 −0.535390 0.844605i \(-0.679835\pi\)
−0.535390 + 0.844605i \(0.679835\pi\)
\(332\) 24.5660 1.34824
\(333\) 8.21263 0.450049
\(334\) 53.5178 2.92836
\(335\) −31.8609 −1.74075
\(336\) −5.50198 −0.300157
\(337\) −6.57866 −0.358362 −0.179181 0.983816i \(-0.557345\pi\)
−0.179181 + 0.983816i \(0.557345\pi\)
\(338\) 0 0
\(339\) 16.5267 0.897609
\(340\) −17.0115 −0.922580
\(341\) 5.76136 0.311995
\(342\) −20.0471 −1.08402
\(343\) −1.00000 −0.0539949
\(344\) −5.40240 −0.291278
\(345\) 9.92111 0.534134
\(346\) 53.4920 2.87575
\(347\) 13.4028 0.719498 0.359749 0.933049i \(-0.382862\pi\)
0.359749 + 0.933049i \(0.382862\pi\)
\(348\) −22.2225 −1.19125
\(349\) −16.3285 −0.874045 −0.437022 0.899451i \(-0.643967\pi\)
−0.437022 + 0.899451i \(0.643967\pi\)
\(350\) −1.32861 −0.0710172
\(351\) 0 0
\(352\) 13.1699 0.701960
\(353\) −21.5374 −1.14632 −0.573161 0.819443i \(-0.694283\pi\)
−0.573161 + 0.819443i \(0.694283\pi\)
\(354\) −7.44450 −0.395671
\(355\) 0.748392 0.0397205
\(356\) −33.1175 −1.75523
\(357\) 1.70559 0.0902691
\(358\) 12.6078 0.666344
\(359\) 31.8829 1.68272 0.841358 0.540478i \(-0.181757\pi\)
0.841358 + 0.540478i \(0.181757\pi\)
\(360\) 13.1653 0.693870
\(361\) 45.3980 2.38937
\(362\) 39.6898 2.08605
\(363\) 15.6811 0.823044
\(364\) 0 0
\(365\) −1.27644 −0.0668122
\(366\) −36.4811 −1.90690
\(367\) 14.9500 0.780381 0.390191 0.920734i \(-0.372409\pi\)
0.390191 + 0.920734i \(0.372409\pi\)
\(368\) 23.2083 1.20982
\(369\) −6.75466 −0.351633
\(370\) 48.2539 2.50860
\(371\) −11.9257 −0.619150
\(372\) 4.72996 0.245237
\(373\) 1.74166 0.0901798 0.0450899 0.998983i \(-0.485643\pi\)
0.0450899 + 0.998983i \(0.485643\pi\)
\(374\) −22.0085 −1.13803
\(375\) −10.5091 −0.542685
\(376\) 51.4222 2.65190
\(377\) 0 0
\(378\) −2.49813 −0.128490
\(379\) −35.4778 −1.82237 −0.911186 0.411995i \(-0.864832\pi\)
−0.911186 + 0.411995i \(0.864832\pi\)
\(380\) −80.0398 −4.10596
\(381\) 13.8279 0.708427
\(382\) 33.4132 1.70957
\(383\) −22.1971 −1.13422 −0.567109 0.823642i \(-0.691938\pi\)
−0.567109 + 0.823642i \(0.691938\pi\)
\(384\) −16.6771 −0.851048
\(385\) −12.1489 −0.619165
\(386\) −16.6563 −0.847781
\(387\) −0.965145 −0.0490611
\(388\) −1.21725 −0.0617965
\(389\) 3.44035 0.174433 0.0872163 0.996189i \(-0.472203\pi\)
0.0872163 + 0.996189i \(0.472203\pi\)
\(390\) 0 0
\(391\) −7.19447 −0.363840
\(392\) 5.59751 0.282717
\(393\) 9.92612 0.500706
\(394\) 30.8628 1.55484
\(395\) −31.1169 −1.56566
\(396\) 21.9047 1.10075
\(397\) −17.9477 −0.900767 −0.450384 0.892835i \(-0.648713\pi\)
−0.450384 + 0.892835i \(0.648713\pi\)
\(398\) −36.3321 −1.82116
\(399\) 8.02484 0.401744
\(400\) 2.92618 0.146309
\(401\) 19.7564 0.986587 0.493293 0.869863i \(-0.335793\pi\)
0.493293 + 0.869863i \(0.335793\pi\)
\(402\) −33.8407 −1.68782
\(403\) 0 0
\(404\) 54.9321 2.73297
\(405\) 2.35199 0.116871
\(406\) 13.0910 0.649697
\(407\) 42.4213 2.10275
\(408\) −9.54703 −0.472648
\(409\) −20.3407 −1.00578 −0.502891 0.864350i \(-0.667730\pi\)
−0.502891 + 0.864350i \(0.667730\pi\)
\(410\) −39.6875 −1.96003
\(411\) 8.60954 0.424677
\(412\) −27.7203 −1.36568
\(413\) 2.98003 0.146637
\(414\) 10.5376 0.517894
\(415\) 13.6249 0.668822
\(416\) 0 0
\(417\) −9.92269 −0.485916
\(418\) −103.551 −5.06484
\(419\) 14.0084 0.684356 0.342178 0.939635i \(-0.388835\pi\)
0.342178 + 0.939635i \(0.388835\pi\)
\(420\) −9.97401 −0.486682
\(421\) −5.93566 −0.289286 −0.144643 0.989484i \(-0.546203\pi\)
−0.144643 + 0.989484i \(0.546203\pi\)
\(422\) 63.9742 3.11422
\(423\) 9.18662 0.446669
\(424\) 66.7541 3.24186
\(425\) −0.907100 −0.0440008
\(426\) 0.794896 0.0385128
\(427\) 14.6034 0.706706
\(428\) −15.8558 −0.766421
\(429\) 0 0
\(430\) −5.67078 −0.273469
\(431\) −10.9820 −0.528982 −0.264491 0.964388i \(-0.585204\pi\)
−0.264491 + 0.964388i \(0.585204\pi\)
\(432\) 5.50198 0.264714
\(433\) 6.59353 0.316865 0.158432 0.987370i \(-0.449356\pi\)
0.158432 + 0.987370i \(0.449356\pi\)
\(434\) −2.78637 −0.133750
\(435\) −12.3252 −0.590947
\(436\) −42.9487 −2.05687
\(437\) −33.8502 −1.61928
\(438\) −1.35576 −0.0647807
\(439\) −4.55826 −0.217554 −0.108777 0.994066i \(-0.534693\pi\)
−0.108777 + 0.994066i \(0.534693\pi\)
\(440\) 68.0035 3.24194
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 6.84511 0.325221 0.162610 0.986690i \(-0.448009\pi\)
0.162610 + 0.986690i \(0.448009\pi\)
\(444\) 34.8271 1.65282
\(445\) −18.3678 −0.870719
\(446\) 22.4655 1.06377
\(447\) −0.253154 −0.0119738
\(448\) 4.63456 0.218962
\(449\) 15.9302 0.751791 0.375896 0.926662i \(-0.377335\pi\)
0.375896 + 0.926662i \(0.377335\pi\)
\(450\) 1.32861 0.0626313
\(451\) −34.8903 −1.64292
\(452\) 70.0845 3.29650
\(453\) −19.1942 −0.901820
\(454\) 10.3981 0.488005
\(455\) 0 0
\(456\) −44.9191 −2.10353
\(457\) 11.3437 0.530638 0.265319 0.964161i \(-0.414523\pi\)
0.265319 + 0.964161i \(0.414523\pi\)
\(458\) 21.1643 0.988941
\(459\) −1.70559 −0.0796099
\(460\) 42.0722 1.96163
\(461\) −37.9495 −1.76749 −0.883743 0.467973i \(-0.844984\pi\)
−0.883743 + 0.467973i \(0.844984\pi\)
\(462\) −12.9038 −0.600339
\(463\) 33.4984 1.55680 0.778401 0.627767i \(-0.216031\pi\)
0.778401 + 0.627767i \(0.216031\pi\)
\(464\) −28.8322 −1.33850
\(465\) 2.62336 0.121655
\(466\) −46.3047 −2.14503
\(467\) 11.6371 0.538500 0.269250 0.963070i \(-0.413224\pi\)
0.269250 + 0.963070i \(0.413224\pi\)
\(468\) 0 0
\(469\) 13.5464 0.625514
\(470\) 53.9767 2.48976
\(471\) −14.8981 −0.686469
\(472\) −16.6807 −0.767792
\(473\) −4.98533 −0.229226
\(474\) −33.0505 −1.51806
\(475\) −4.26794 −0.195826
\(476\) 7.23283 0.331516
\(477\) 11.9257 0.546039
\(478\) −0.441948 −0.0202142
\(479\) −26.2836 −1.20093 −0.600465 0.799651i \(-0.705018\pi\)
−0.600465 + 0.799651i \(0.705018\pi\)
\(480\) 5.99676 0.273714
\(481\) 0 0
\(482\) −12.4800 −0.568448
\(483\) −4.21818 −0.191934
\(484\) 66.4984 3.02266
\(485\) −0.675118 −0.0306555
\(486\) 2.49813 0.113318
\(487\) 13.9247 0.630990 0.315495 0.948927i \(-0.397829\pi\)
0.315495 + 0.948927i \(0.397829\pi\)
\(488\) −81.7424 −3.70030
\(489\) −5.80688 −0.262596
\(490\) 5.87558 0.265432
\(491\) −23.3848 −1.05534 −0.527670 0.849449i \(-0.676934\pi\)
−0.527670 + 0.849449i \(0.676934\pi\)
\(492\) −28.6443 −1.29139
\(493\) 8.93782 0.402539
\(494\) 0 0
\(495\) 12.1489 0.546052
\(496\) 6.13679 0.275550
\(497\) −0.318196 −0.0142730
\(498\) 14.4716 0.648487
\(499\) 4.20079 0.188053 0.0940266 0.995570i \(-0.470026\pi\)
0.0940266 + 0.995570i \(0.470026\pi\)
\(500\) −44.5655 −1.99303
\(501\) 21.4231 0.957114
\(502\) 1.40120 0.0625388
\(503\) 5.60179 0.249772 0.124886 0.992171i \(-0.460144\pi\)
0.124886 + 0.992171i \(0.460144\pi\)
\(504\) −5.59751 −0.249333
\(505\) 30.4668 1.35575
\(506\) 54.4306 2.41973
\(507\) 0 0
\(508\) 58.6398 2.60172
\(509\) 7.88662 0.349568 0.174784 0.984607i \(-0.444077\pi\)
0.174784 + 0.984607i \(0.444077\pi\)
\(510\) −10.0213 −0.443751
\(511\) 0.542709 0.0240080
\(512\) −47.5665 −2.10216
\(513\) −8.02484 −0.354305
\(514\) −42.3673 −1.86874
\(515\) −15.3744 −0.677475
\(516\) −4.09286 −0.180178
\(517\) 47.4523 2.08695
\(518\) −20.5162 −0.901432
\(519\) 21.4128 0.939916
\(520\) 0 0
\(521\) 30.5215 1.33717 0.668585 0.743635i \(-0.266900\pi\)
0.668585 + 0.743635i \(0.266900\pi\)
\(522\) −13.0910 −0.572979
\(523\) 26.1984 1.14557 0.572787 0.819704i \(-0.305862\pi\)
0.572787 + 0.819704i \(0.305862\pi\)
\(524\) 42.0934 1.83886
\(525\) −0.531841 −0.0232114
\(526\) 18.2178 0.794334
\(527\) −1.90238 −0.0828688
\(528\) 28.4198 1.23681
\(529\) −5.20695 −0.226389
\(530\) 70.0703 3.04366
\(531\) −2.98003 −0.129322
\(532\) 34.0307 1.47542
\(533\) 0 0
\(534\) −19.5092 −0.844244
\(535\) −8.79405 −0.380200
\(536\) −75.8260 −3.27519
\(537\) 5.04689 0.217789
\(538\) 4.27596 0.184350
\(539\) 5.16537 0.222488
\(540\) 9.97401 0.429213
\(541\) −6.76840 −0.290996 −0.145498 0.989359i \(-0.546478\pi\)
−0.145498 + 0.989359i \(0.546478\pi\)
\(542\) −30.6203 −1.31525
\(543\) 15.8878 0.681810
\(544\) −4.34866 −0.186447
\(545\) −23.8204 −1.02035
\(546\) 0 0
\(547\) −39.8930 −1.70570 −0.852851 0.522155i \(-0.825128\pi\)
−0.852851 + 0.522155i \(0.825128\pi\)
\(548\) 36.5103 1.55964
\(549\) −14.6034 −0.623256
\(550\) 6.86277 0.292629
\(551\) 42.0528 1.79151
\(552\) 23.6113 1.00496
\(553\) 13.2301 0.562599
\(554\) 80.0128 3.39942
\(555\) 19.3160 0.819918
\(556\) −42.0789 −1.78454
\(557\) 20.7410 0.878825 0.439412 0.898285i \(-0.355187\pi\)
0.439412 + 0.898285i \(0.355187\pi\)
\(558\) 2.78637 0.117956
\(559\) 0 0
\(560\) −12.9406 −0.546839
\(561\) −8.80999 −0.371958
\(562\) −63.2410 −2.66766
\(563\) 46.2754 1.95027 0.975137 0.221602i \(-0.0711287\pi\)
0.975137 + 0.221602i \(0.0711287\pi\)
\(564\) 38.9575 1.64041
\(565\) 38.8707 1.63530
\(566\) −20.7243 −0.871109
\(567\) −1.00000 −0.0419961
\(568\) 1.78110 0.0747334
\(569\) −13.9515 −0.584879 −0.292439 0.956284i \(-0.594467\pi\)
−0.292439 + 0.956284i \(0.594467\pi\)
\(570\) −47.1506 −1.97492
\(571\) 25.4059 1.06320 0.531602 0.846994i \(-0.321590\pi\)
0.531602 + 0.846994i \(0.321590\pi\)
\(572\) 0 0
\(573\) 13.3753 0.558760
\(574\) 16.8740 0.704309
\(575\) 2.24340 0.0935563
\(576\) −4.63456 −0.193107
\(577\) −44.9472 −1.87118 −0.935588 0.353093i \(-0.885130\pi\)
−0.935588 + 0.353093i \(0.885130\pi\)
\(578\) −35.2012 −1.46418
\(579\) −6.66748 −0.277091
\(580\) −52.2671 −2.17027
\(581\) −5.79295 −0.240332
\(582\) −0.717068 −0.0297234
\(583\) 61.6006 2.55124
\(584\) −3.03782 −0.125706
\(585\) 0 0
\(586\) −67.4226 −2.78520
\(587\) 23.2272 0.958688 0.479344 0.877627i \(-0.340875\pi\)
0.479344 + 0.877627i \(0.340875\pi\)
\(588\) 4.24068 0.174882
\(589\) −8.95074 −0.368809
\(590\) −17.5094 −0.720850
\(591\) 12.3543 0.508189
\(592\) 45.1857 1.85712
\(593\) −9.16296 −0.376278 −0.188139 0.982142i \(-0.560245\pi\)
−0.188139 + 0.982142i \(0.560245\pi\)
\(594\) 12.9038 0.529449
\(595\) 4.01151 0.164456
\(596\) −1.07355 −0.0439742
\(597\) −14.5437 −0.595234
\(598\) 0 0
\(599\) 25.8168 1.05485 0.527424 0.849602i \(-0.323158\pi\)
0.527424 + 0.849602i \(0.323158\pi\)
\(600\) 2.97698 0.121535
\(601\) 17.8496 0.728102 0.364051 0.931379i \(-0.381393\pi\)
0.364051 + 0.931379i \(0.381393\pi\)
\(602\) 2.41106 0.0982675
\(603\) −13.5464 −0.551652
\(604\) −81.3962 −3.31196
\(605\) 36.8817 1.49946
\(606\) 32.3599 1.31453
\(607\) 34.2992 1.39216 0.696081 0.717963i \(-0.254925\pi\)
0.696081 + 0.717963i \(0.254925\pi\)
\(608\) −20.4606 −0.829787
\(609\) 5.24033 0.212349
\(610\) −85.8031 −3.47407
\(611\) 0 0
\(612\) −7.23283 −0.292370
\(613\) 0.143589 0.00579952 0.00289976 0.999996i \(-0.499077\pi\)
0.00289976 + 0.999996i \(0.499077\pi\)
\(614\) −19.0812 −0.770056
\(615\) −15.8869 −0.640620
\(616\) −28.9132 −1.16495
\(617\) −18.3135 −0.737272 −0.368636 0.929574i \(-0.620175\pi\)
−0.368636 + 0.929574i \(0.620175\pi\)
\(618\) −16.3297 −0.656877
\(619\) −0.301686 −0.0121258 −0.00606289 0.999982i \(-0.501930\pi\)
−0.00606289 + 0.999982i \(0.501930\pi\)
\(620\) 11.1248 0.446783
\(621\) 4.21818 0.169270
\(622\) −9.96969 −0.399748
\(623\) 7.80950 0.312881
\(624\) 0 0
\(625\) −27.3764 −1.09505
\(626\) 27.7961 1.11095
\(627\) −41.4513 −1.65540
\(628\) −63.1781 −2.52108
\(629\) −14.0073 −0.558509
\(630\) −5.87558 −0.234089
\(631\) 20.3829 0.811432 0.405716 0.913999i \(-0.367022\pi\)
0.405716 + 0.913999i \(0.367022\pi\)
\(632\) −74.0553 −2.94576
\(633\) 25.6088 1.01786
\(634\) 16.7921 0.666900
\(635\) 32.5231 1.29064
\(636\) 50.5729 2.00535
\(637\) 0 0
\(638\) −67.6201 −2.67711
\(639\) 0.318196 0.0125876
\(640\) −39.2243 −1.55047
\(641\) 20.7666 0.820233 0.410116 0.912033i \(-0.365488\pi\)
0.410116 + 0.912033i \(0.365488\pi\)
\(642\) −9.34050 −0.368640
\(643\) −11.0348 −0.435171 −0.217585 0.976041i \(-0.569818\pi\)
−0.217585 + 0.976041i \(0.569818\pi\)
\(644\) −17.8879 −0.704883
\(645\) −2.27001 −0.0893814
\(646\) 34.1921 1.34527
\(647\) −37.5007 −1.47430 −0.737152 0.675727i \(-0.763830\pi\)
−0.737152 + 0.675727i \(0.763830\pi\)
\(648\) 5.59751 0.219891
\(649\) −15.3929 −0.604226
\(650\) 0 0
\(651\) −1.11538 −0.0437152
\(652\) −24.6251 −0.964394
\(653\) −26.8688 −1.05146 −0.525729 0.850652i \(-0.676207\pi\)
−0.525729 + 0.850652i \(0.676207\pi\)
\(654\) −25.3006 −0.989331
\(655\) 23.3461 0.912207
\(656\) −37.1640 −1.45101
\(657\) −0.542709 −0.0211731
\(658\) −22.9494 −0.894662
\(659\) 10.8847 0.424008 0.212004 0.977269i \(-0.432001\pi\)
0.212004 + 0.977269i \(0.432001\pi\)
\(660\) 51.5195 2.00539
\(661\) −10.7257 −0.417181 −0.208590 0.978003i \(-0.566888\pi\)
−0.208590 + 0.978003i \(0.566888\pi\)
\(662\) −48.6665 −1.89148
\(663\) 0 0
\(664\) 32.4261 1.25838
\(665\) 18.8743 0.731914
\(666\) 20.5162 0.794988
\(667\) −22.1046 −0.855895
\(668\) 90.8485 3.51503
\(669\) 8.99291 0.347686
\(670\) −79.5929 −3.07494
\(671\) −75.4318 −2.91201
\(672\) −2.54966 −0.0983552
\(673\) −22.2093 −0.856104 −0.428052 0.903754i \(-0.640800\pi\)
−0.428052 + 0.903754i \(0.640800\pi\)
\(674\) −16.4344 −0.633028
\(675\) 0.531841 0.0204706
\(676\) 0 0
\(677\) 3.83321 0.147322 0.0736612 0.997283i \(-0.476532\pi\)
0.0736612 + 0.997283i \(0.476532\pi\)
\(678\) 41.2860 1.58558
\(679\) 0.287042 0.0110156
\(680\) −22.4545 −0.861090
\(681\) 4.16233 0.159501
\(682\) 14.3926 0.551123
\(683\) 6.80946 0.260557 0.130278 0.991477i \(-0.458413\pi\)
0.130278 + 0.991477i \(0.458413\pi\)
\(684\) −34.0307 −1.30120
\(685\) 20.2495 0.773695
\(686\) −2.49813 −0.0953792
\(687\) 8.47202 0.323228
\(688\) −5.31020 −0.202450
\(689\) 0 0
\(690\) 24.7843 0.943520
\(691\) 1.14161 0.0434288 0.0217144 0.999764i \(-0.493088\pi\)
0.0217144 + 0.999764i \(0.493088\pi\)
\(692\) 90.8046 3.45187
\(693\) −5.16537 −0.196216
\(694\) 33.4819 1.27096
\(695\) −23.3380 −0.885262
\(696\) −29.3328 −1.11186
\(697\) 11.5206 0.436375
\(698\) −40.7908 −1.54395
\(699\) −18.5357 −0.701086
\(700\) −2.25536 −0.0852448
\(701\) 8.44188 0.318845 0.159423 0.987210i \(-0.449037\pi\)
0.159423 + 0.987210i \(0.449037\pi\)
\(702\) 0 0
\(703\) −65.9050 −2.48565
\(704\) −23.9392 −0.902244
\(705\) 21.6068 0.813760
\(706\) −53.8034 −2.02492
\(707\) −12.9536 −0.487171
\(708\) −12.6373 −0.474940
\(709\) −7.11295 −0.267133 −0.133566 0.991040i \(-0.542643\pi\)
−0.133566 + 0.991040i \(0.542643\pi\)
\(710\) 1.86958 0.0701643
\(711\) −13.2301 −0.496166
\(712\) −43.7137 −1.63824
\(713\) 4.70487 0.176199
\(714\) 4.26078 0.159456
\(715\) 0 0
\(716\) 21.4022 0.799839
\(717\) −0.176911 −0.00660687
\(718\) 79.6478 2.97243
\(719\) 6.74382 0.251502 0.125751 0.992062i \(-0.459866\pi\)
0.125751 + 0.992062i \(0.459866\pi\)
\(720\) 12.9406 0.482267
\(721\) 6.53676 0.243442
\(722\) 113.410 4.22069
\(723\) −4.99572 −0.185793
\(724\) 67.3749 2.50397
\(725\) −2.78702 −0.103507
\(726\) 39.1735 1.45386
\(727\) −23.9650 −0.888811 −0.444406 0.895826i \(-0.646585\pi\)
−0.444406 + 0.895826i \(0.646585\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −3.18873 −0.118020
\(731\) 1.64614 0.0608846
\(732\) −61.9281 −2.28893
\(733\) 5.63526 0.208143 0.104072 0.994570i \(-0.466813\pi\)
0.104072 + 0.994570i \(0.466813\pi\)
\(734\) 37.3470 1.37850
\(735\) 2.35199 0.0867543
\(736\) 10.7549 0.396432
\(737\) −69.9722 −2.57746
\(738\) −16.8740 −0.621142
\(739\) 18.7986 0.691518 0.345759 0.938323i \(-0.387622\pi\)
0.345759 + 0.938323i \(0.387622\pi\)
\(740\) 81.9128 3.01118
\(741\) 0 0
\(742\) −29.7919 −1.09370
\(743\) 27.2365 0.999209 0.499604 0.866254i \(-0.333479\pi\)
0.499604 + 0.866254i \(0.333479\pi\)
\(744\) 6.24335 0.228892
\(745\) −0.595416 −0.0218144
\(746\) 4.35090 0.159298
\(747\) 5.79295 0.211953
\(748\) −37.3603 −1.36603
\(749\) 3.73899 0.136620
\(750\) −26.2530 −0.958625
\(751\) 17.2816 0.630615 0.315308 0.948989i \(-0.397892\pi\)
0.315308 + 0.948989i \(0.397892\pi\)
\(752\) 50.5446 1.84317
\(753\) 0.560900 0.0204403
\(754\) 0 0
\(755\) −45.1444 −1.64297
\(756\) −4.24068 −0.154232
\(757\) −10.1844 −0.370160 −0.185080 0.982723i \(-0.559254\pi\)
−0.185080 + 0.982723i \(0.559254\pi\)
\(758\) −88.6283 −3.21913
\(759\) 21.7885 0.790872
\(760\) −105.649 −3.83230
\(761\) 51.1035 1.85250 0.926251 0.376908i \(-0.123013\pi\)
0.926251 + 0.376908i \(0.123013\pi\)
\(762\) 34.5441 1.25140
\(763\) 10.1278 0.366651
\(764\) 56.7202 2.05206
\(765\) −4.01151 −0.145037
\(766\) −55.4513 −2.00354
\(767\) 0 0
\(768\) −32.3924 −1.16886
\(769\) 26.3949 0.951823 0.475911 0.879493i \(-0.342118\pi\)
0.475911 + 0.879493i \(0.342118\pi\)
\(770\) −30.3496 −1.09372
\(771\) −16.9596 −0.610784
\(772\) −28.2746 −1.01763
\(773\) −10.1413 −0.364758 −0.182379 0.983228i \(-0.558380\pi\)
−0.182379 + 0.983228i \(0.558380\pi\)
\(774\) −2.41106 −0.0866638
\(775\) 0.593205 0.0213085
\(776\) −1.60672 −0.0576778
\(777\) −8.21263 −0.294626
\(778\) 8.59445 0.308126
\(779\) 54.2050 1.94210
\(780\) 0 0
\(781\) 1.64360 0.0588127
\(782\) −17.9727 −0.642704
\(783\) −5.24033 −0.187274
\(784\) 5.50198 0.196499
\(785\) −35.0402 −1.25064
\(786\) 24.7968 0.884472
\(787\) 51.5981 1.83927 0.919636 0.392771i \(-0.128484\pi\)
0.919636 + 0.392771i \(0.128484\pi\)
\(788\) 52.3907 1.86634
\(789\) 7.29257 0.259622
\(790\) −77.7342 −2.76566
\(791\) −16.5267 −0.587623
\(792\) 28.9132 1.02739
\(793\) 0 0
\(794\) −44.8357 −1.59116
\(795\) 28.0490 0.994797
\(796\) −61.6751 −2.18602
\(797\) −15.1299 −0.535928 −0.267964 0.963429i \(-0.586351\pi\)
−0.267964 + 0.963429i \(0.586351\pi\)
\(798\) 20.0471 0.709660
\(799\) −15.6686 −0.554314
\(800\) 1.35601 0.0479423
\(801\) −7.80950 −0.275935
\(802\) 49.3541 1.74275
\(803\) −2.80330 −0.0989261
\(804\) −57.4459 −2.02596
\(805\) −9.92111 −0.349673
\(806\) 0 0
\(807\) 1.71166 0.0602533
\(808\) 72.5080 2.55082
\(809\) 4.43586 0.155956 0.0779782 0.996955i \(-0.475154\pi\)
0.0779782 + 0.996955i \(0.475154\pi\)
\(810\) 5.87558 0.206447
\(811\) −3.05676 −0.107337 −0.0536686 0.998559i \(-0.517091\pi\)
−0.0536686 + 0.998559i \(0.517091\pi\)
\(812\) 22.2225 0.779858
\(813\) −12.2573 −0.429881
\(814\) 105.974 3.71439
\(815\) −13.6577 −0.478409
\(816\) −9.38409 −0.328509
\(817\) 7.74513 0.270968
\(818\) −50.8138 −1.77666
\(819\) 0 0
\(820\) −67.3710 −2.35270
\(821\) 11.0373 0.385204 0.192602 0.981277i \(-0.438307\pi\)
0.192602 + 0.981277i \(0.438307\pi\)
\(822\) 21.5078 0.750170
\(823\) 49.7386 1.73378 0.866890 0.498499i \(-0.166115\pi\)
0.866890 + 0.498499i \(0.166115\pi\)
\(824\) −36.5895 −1.27466
\(825\) 2.74716 0.0956438
\(826\) 7.44450 0.259027
\(827\) 42.7670 1.48715 0.743577 0.668650i \(-0.233128\pi\)
0.743577 + 0.668650i \(0.233128\pi\)
\(828\) 17.8879 0.621649
\(829\) −11.5052 −0.399591 −0.199796 0.979838i \(-0.564028\pi\)
−0.199796 + 0.979838i \(0.564028\pi\)
\(830\) 34.0369 1.18144
\(831\) 32.0290 1.11107
\(832\) 0 0
\(833\) −1.70559 −0.0590950
\(834\) −24.7882 −0.858345
\(835\) 50.3869 1.74371
\(836\) −175.781 −6.07953
\(837\) 1.11538 0.0385532
\(838\) 34.9949 1.20888
\(839\) −10.5561 −0.364436 −0.182218 0.983258i \(-0.558328\pi\)
−0.182218 + 0.983258i \(0.558328\pi\)
\(840\) −13.1653 −0.454245
\(841\) −1.53898 −0.0530681
\(842\) −14.8281 −0.511009
\(843\) −25.3153 −0.871904
\(844\) 108.599 3.73812
\(845\) 0 0
\(846\) 22.9494 0.789017
\(847\) −15.6811 −0.538809
\(848\) 65.6148 2.25322
\(849\) −8.29593 −0.284715
\(850\) −2.26606 −0.0777251
\(851\) 34.6423 1.18752
\(852\) 1.34937 0.0462285
\(853\) −2.34131 −0.0801648 −0.0400824 0.999196i \(-0.512762\pi\)
−0.0400824 + 0.999196i \(0.512762\pi\)
\(854\) 36.4811 1.24836
\(855\) −18.8743 −0.645488
\(856\) −20.9290 −0.715339
\(857\) −47.5469 −1.62417 −0.812086 0.583537i \(-0.801668\pi\)
−0.812086 + 0.583537i \(0.801668\pi\)
\(858\) 0 0
\(859\) 49.5483 1.69057 0.845284 0.534318i \(-0.179431\pi\)
0.845284 + 0.534318i \(0.179431\pi\)
\(860\) −9.62636 −0.328256
\(861\) 6.75466 0.230198
\(862\) −27.4344 −0.934419
\(863\) 0.233810 0.00795899 0.00397949 0.999992i \(-0.498733\pi\)
0.00397949 + 0.999992i \(0.498733\pi\)
\(864\) 2.54966 0.0867412
\(865\) 50.3625 1.71238
\(866\) 16.4715 0.559725
\(867\) −14.0910 −0.478555
\(868\) −4.72996 −0.160545
\(869\) −68.3382 −2.31821
\(870\) −30.7900 −1.04388
\(871\) 0 0
\(872\) −56.6904 −1.91978
\(873\) −0.287042 −0.00971489
\(874\) −84.5624 −2.86037
\(875\) 10.5091 0.355271
\(876\) −2.30145 −0.0777589
\(877\) 21.2880 0.718845 0.359423 0.933175i \(-0.382974\pi\)
0.359423 + 0.933175i \(0.382974\pi\)
\(878\) −11.3872 −0.384298
\(879\) −26.9892 −0.910322
\(880\) 66.8429 2.25327
\(881\) 17.0535 0.574546 0.287273 0.957849i \(-0.407251\pi\)
0.287273 + 0.957849i \(0.407251\pi\)
\(882\) 2.49813 0.0841166
\(883\) 15.7586 0.530319 0.265160 0.964205i \(-0.414575\pi\)
0.265160 + 0.964205i \(0.414575\pi\)
\(884\) 0 0
\(885\) −7.00898 −0.235604
\(886\) 17.1000 0.574486
\(887\) −19.6096 −0.658425 −0.329212 0.944256i \(-0.606783\pi\)
−0.329212 + 0.944256i \(0.606783\pi\)
\(888\) 45.9702 1.54266
\(889\) −13.8279 −0.463774
\(890\) −45.8853 −1.53808
\(891\) 5.16537 0.173047
\(892\) 38.1360 1.27689
\(893\) −73.7212 −2.46698
\(894\) −0.632414 −0.0211511
\(895\) 11.8702 0.396778
\(896\) 16.6771 0.557142
\(897\) 0 0
\(898\) 39.7957 1.32800
\(899\) −5.84496 −0.194940
\(900\) 2.25536 0.0751788
\(901\) −20.3403 −0.677632
\(902\) −87.1607 −2.90214
\(903\) 0.965145 0.0321180
\(904\) 92.5086 3.07679
\(905\) 37.3678 1.24215
\(906\) −47.9496 −1.59302
\(907\) 8.16378 0.271074 0.135537 0.990772i \(-0.456724\pi\)
0.135537 + 0.990772i \(0.456724\pi\)
\(908\) 17.6511 0.585772
\(909\) 12.9536 0.429645
\(910\) 0 0
\(911\) 40.0348 1.32641 0.663206 0.748437i \(-0.269195\pi\)
0.663206 + 0.748437i \(0.269195\pi\)
\(912\) −44.1525 −1.46203
\(913\) 29.9228 0.990299
\(914\) 28.3382 0.937345
\(915\) −34.3469 −1.13547
\(916\) 35.9271 1.18706
\(917\) −9.92612 −0.327789
\(918\) −4.26078 −0.140627
\(919\) −34.0730 −1.12396 −0.561982 0.827149i \(-0.689961\pi\)
−0.561982 + 0.827149i \(0.689961\pi\)
\(920\) 55.5335 1.83088
\(921\) −7.63819 −0.251687
\(922\) −94.8030 −3.12217
\(923\) 0 0
\(924\) −21.9047 −0.720611
\(925\) 4.36781 0.143613
\(926\) 83.6835 2.75001
\(927\) −6.53676 −0.214695
\(928\) −13.3610 −0.438598
\(929\) −20.8776 −0.684972 −0.342486 0.939523i \(-0.611269\pi\)
−0.342486 + 0.939523i \(0.611269\pi\)
\(930\) 6.55350 0.214898
\(931\) −8.02484 −0.263003
\(932\) −78.6040 −2.57476
\(933\) −3.99085 −0.130655
\(934\) 29.0710 0.951232
\(935\) −20.7210 −0.677648
\(936\) 0 0
\(937\) 20.5927 0.672734 0.336367 0.941731i \(-0.390802\pi\)
0.336367 + 0.941731i \(0.390802\pi\)
\(938\) 33.8407 1.10494
\(939\) 11.1267 0.363107
\(940\) 91.6275 2.98856
\(941\) 18.7149 0.610089 0.305045 0.952338i \(-0.401329\pi\)
0.305045 + 0.952338i \(0.401329\pi\)
\(942\) −37.2175 −1.21261
\(943\) −28.4924 −0.927839
\(944\) −16.3960 −0.533645
\(945\) −2.35199 −0.0765101
\(946\) −12.4540 −0.404915
\(947\) −5.23110 −0.169988 −0.0849939 0.996381i \(-0.527087\pi\)
−0.0849939 + 0.996381i \(0.527087\pi\)
\(948\) −56.1044 −1.82218
\(949\) 0 0
\(950\) −10.6619 −0.345917
\(951\) 6.72186 0.217971
\(952\) 9.54703 0.309421
\(953\) −49.7229 −1.61068 −0.805341 0.592812i \(-0.798018\pi\)
−0.805341 + 0.592812i \(0.798018\pi\)
\(954\) 29.7919 0.964550
\(955\) 31.4585 1.01797
\(956\) −0.750222 −0.0242639
\(957\) −27.0682 −0.874992
\(958\) −65.6601 −2.12138
\(959\) −8.60954 −0.278017
\(960\) −10.9004 −0.351810
\(961\) −29.7559 −0.959869
\(962\) 0 0
\(963\) −3.73899 −0.120487
\(964\) −21.1852 −0.682330
\(965\) −15.6818 −0.504815
\(966\) −10.5376 −0.339041
\(967\) −4.55490 −0.146476 −0.0732379 0.997314i \(-0.523333\pi\)
−0.0732379 + 0.997314i \(0.523333\pi\)
\(968\) 87.7750 2.82120
\(969\) 13.6870 0.439691
\(970\) −1.68654 −0.0541514
\(971\) 33.4767 1.07432 0.537159 0.843481i \(-0.319497\pi\)
0.537159 + 0.843481i \(0.319497\pi\)
\(972\) 4.24068 0.136020
\(973\) 9.92269 0.318107
\(974\) 34.7859 1.11461
\(975\) 0 0
\(976\) −80.3473 −2.57185
\(977\) −48.7454 −1.55950 −0.779752 0.626089i \(-0.784655\pi\)
−0.779752 + 0.626089i \(0.784655\pi\)
\(978\) −14.5064 −0.463863
\(979\) −40.3390 −1.28924
\(980\) 9.97401 0.318608
\(981\) −10.1278 −0.323355
\(982\) −58.4183 −1.86420
\(983\) 5.57582 0.177841 0.0889205 0.996039i \(-0.471658\pi\)
0.0889205 + 0.996039i \(0.471658\pi\)
\(984\) −37.8092 −1.20531
\(985\) 29.0572 0.925840
\(986\) 22.3279 0.711065
\(987\) −9.18662 −0.292413
\(988\) 0 0
\(989\) −4.07115 −0.129455
\(990\) 30.3496 0.964572
\(991\) 39.8543 1.26601 0.633006 0.774147i \(-0.281821\pi\)
0.633006 + 0.774147i \(0.281821\pi\)
\(992\) 2.84384 0.0902920
\(993\) −19.4811 −0.618216
\(994\) −0.794896 −0.0252126
\(995\) −34.2066 −1.08442
\(996\) 24.5660 0.778404
\(997\) −39.1045 −1.23845 −0.619226 0.785213i \(-0.712554\pi\)
−0.619226 + 0.785213i \(0.712554\pi\)
\(998\) 10.4941 0.332186
\(999\) 8.21263 0.259836
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.1.13 yes 15
13.12 even 2 3549.2.a.bg.1.3 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.3 15 13.12 even 2
3549.2.a.bh.1.13 yes 15 1.1 even 1 trivial