Properties

Label 3549.2.a.bh.1.14
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 1.14
Root \(2.78394\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.78394 q^{2} +1.00000 q^{3} +5.75034 q^{4} +1.59144 q^{5} +2.78394 q^{6} -1.00000 q^{7} +10.4407 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.78394 q^{2} +1.00000 q^{3} +5.75034 q^{4} +1.59144 q^{5} +2.78394 q^{6} -1.00000 q^{7} +10.4407 q^{8} +1.00000 q^{9} +4.43048 q^{10} -0.134788 q^{11} +5.75034 q^{12} -2.78394 q^{14} +1.59144 q^{15} +17.5657 q^{16} -7.07278 q^{17} +2.78394 q^{18} +5.94529 q^{19} +9.15132 q^{20} -1.00000 q^{21} -0.375242 q^{22} -7.87475 q^{23} +10.4407 q^{24} -2.46732 q^{25} +1.00000 q^{27} -5.75034 q^{28} +7.91488 q^{29} +4.43048 q^{30} -2.66844 q^{31} +28.0204 q^{32} -0.134788 q^{33} -19.6902 q^{34} -1.59144 q^{35} +5.75034 q^{36} -0.101235 q^{37} +16.5513 q^{38} +16.6158 q^{40} -3.72584 q^{41} -2.78394 q^{42} +0.825682 q^{43} -0.775076 q^{44} +1.59144 q^{45} -21.9228 q^{46} +2.58303 q^{47} +17.5657 q^{48} +1.00000 q^{49} -6.86886 q^{50} -7.07278 q^{51} +1.42870 q^{53} +2.78394 q^{54} -0.214507 q^{55} -10.4407 q^{56} +5.94529 q^{57} +22.0346 q^{58} -7.93495 q^{59} +9.15132 q^{60} -3.77939 q^{61} -7.42877 q^{62} -1.00000 q^{63} +42.8759 q^{64} -0.375242 q^{66} +4.56472 q^{67} -40.6709 q^{68} -7.87475 q^{69} -4.43048 q^{70} -10.6911 q^{71} +10.4407 q^{72} +1.49552 q^{73} -0.281832 q^{74} -2.46732 q^{75} +34.1874 q^{76} +0.134788 q^{77} +13.0892 q^{79} +27.9548 q^{80} +1.00000 q^{81} -10.3725 q^{82} -15.6291 q^{83} -5.75034 q^{84} -11.2559 q^{85} +2.29865 q^{86} +7.91488 q^{87} -1.40728 q^{88} -7.17174 q^{89} +4.43048 q^{90} -45.2824 q^{92} -2.66844 q^{93} +7.19100 q^{94} +9.46158 q^{95} +28.0204 q^{96} -13.9093 q^{97} +2.78394 q^{98} -0.134788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + O(q^{10}) \) \( 15q + 2q^{2} + 15q^{3} + 28q^{4} - 9q^{5} + 2q^{6} - 15q^{7} + 9q^{8} + 15q^{9} + 21q^{10} + 5q^{11} + 28q^{12} - 2q^{14} - 9q^{15} + 50q^{16} - q^{17} + 2q^{18} + 3q^{19} - 23q^{20} - 15q^{21} + 21q^{22} + 4q^{23} + 9q^{24} + 50q^{25} + 15q^{27} - 28q^{28} + 9q^{29} + 21q^{30} + 7q^{31} + 35q^{32} + 5q^{33} - 2q^{34} + 9q^{35} + 28q^{36} + 17q^{37} - 12q^{38} + 46q^{40} - 22q^{41} - 2q^{42} + 36q^{43} + 29q^{44} - 9q^{45} - q^{46} - 12q^{47} + 50q^{48} + 15q^{49} + 53q^{50} - q^{51} - 5q^{53} + 2q^{54} + 43q^{55} - 9q^{56} + 3q^{57} + 29q^{58} - 29q^{59} - 23q^{60} + 12q^{61} + 14q^{62} - 15q^{63} + 95q^{64} + 21q^{66} - 12q^{67} - 16q^{68} + 4q^{69} - 21q^{70} + 36q^{71} + 9q^{72} - 29q^{73} - 5q^{74} + 50q^{75} + 25q^{76} - 5q^{77} + 35q^{79} - 89q^{80} + 15q^{81} + 51q^{82} - 10q^{83} - 28q^{84} + 23q^{85} + 19q^{86} + 9q^{87} + 73q^{88} + 25q^{89} + 21q^{90} - 31q^{92} + 7q^{93} - 19q^{94} - 7q^{95} + 35q^{96} - 26q^{97} + 2q^{98} + 5q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.78394 1.96854 0.984272 0.176658i \(-0.0565286\pi\)
0.984272 + 0.176658i \(0.0565286\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.75034 2.87517
\(5\) 1.59144 0.711714 0.355857 0.934540i \(-0.384189\pi\)
0.355857 + 0.934540i \(0.384189\pi\)
\(6\) 2.78394 1.13654
\(7\) −1.00000 −0.377964
\(8\) 10.4407 3.69135
\(9\) 1.00000 0.333333
\(10\) 4.43048 1.40104
\(11\) −0.134788 −0.0406401 −0.0203200 0.999794i \(-0.506469\pi\)
−0.0203200 + 0.999794i \(0.506469\pi\)
\(12\) 5.75034 1.65998
\(13\) 0 0
\(14\) −2.78394 −0.744040
\(15\) 1.59144 0.410908
\(16\) 17.5657 4.39142
\(17\) −7.07278 −1.71540 −0.857701 0.514149i \(-0.828108\pi\)
−0.857701 + 0.514149i \(0.828108\pi\)
\(18\) 2.78394 0.656182
\(19\) 5.94529 1.36394 0.681971 0.731379i \(-0.261123\pi\)
0.681971 + 0.731379i \(0.261123\pi\)
\(20\) 9.15132 2.04630
\(21\) −1.00000 −0.218218
\(22\) −0.375242 −0.0800019
\(23\) −7.87475 −1.64200 −0.820999 0.570930i \(-0.806583\pi\)
−0.820999 + 0.570930i \(0.806583\pi\)
\(24\) 10.4407 2.13120
\(25\) −2.46732 −0.493463
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −5.75034 −1.08671
\(29\) 7.91488 1.46976 0.734878 0.678199i \(-0.237239\pi\)
0.734878 + 0.678199i \(0.237239\pi\)
\(30\) 4.43048 0.808891
\(31\) −2.66844 −0.479265 −0.239633 0.970864i \(-0.577027\pi\)
−0.239633 + 0.970864i \(0.577027\pi\)
\(32\) 28.0204 4.95336
\(33\) −0.134788 −0.0234636
\(34\) −19.6902 −3.37685
\(35\) −1.59144 −0.269003
\(36\) 5.75034 0.958389
\(37\) −0.101235 −0.0166429 −0.00832145 0.999965i \(-0.502649\pi\)
−0.00832145 + 0.999965i \(0.502649\pi\)
\(38\) 16.5513 2.68498
\(39\) 0 0
\(40\) 16.6158 2.62719
\(41\) −3.72584 −0.581878 −0.290939 0.956742i \(-0.593968\pi\)
−0.290939 + 0.956742i \(0.593968\pi\)
\(42\) −2.78394 −0.429572
\(43\) 0.825682 0.125915 0.0629577 0.998016i \(-0.479947\pi\)
0.0629577 + 0.998016i \(0.479947\pi\)
\(44\) −0.775076 −0.116847
\(45\) 1.59144 0.237238
\(46\) −21.9228 −3.23235
\(47\) 2.58303 0.376773 0.188387 0.982095i \(-0.439674\pi\)
0.188387 + 0.982095i \(0.439674\pi\)
\(48\) 17.5657 2.53539
\(49\) 1.00000 0.142857
\(50\) −6.86886 −0.971404
\(51\) −7.07278 −0.990388
\(52\) 0 0
\(53\) 1.42870 0.196247 0.0981235 0.995174i \(-0.468716\pi\)
0.0981235 + 0.995174i \(0.468716\pi\)
\(54\) 2.78394 0.378847
\(55\) −0.214507 −0.0289241
\(56\) −10.4407 −1.39520
\(57\) 5.94529 0.787473
\(58\) 22.0346 2.89328
\(59\) −7.93495 −1.03304 −0.516521 0.856274i \(-0.672773\pi\)
−0.516521 + 0.856274i \(0.672773\pi\)
\(60\) 9.15132 1.18143
\(61\) −3.77939 −0.483902 −0.241951 0.970289i \(-0.577787\pi\)
−0.241951 + 0.970289i \(0.577787\pi\)
\(62\) −7.42877 −0.943455
\(63\) −1.00000 −0.125988
\(64\) 42.8759 5.35949
\(65\) 0 0
\(66\) −0.375242 −0.0461891
\(67\) 4.56472 0.557670 0.278835 0.960339i \(-0.410052\pi\)
0.278835 + 0.960339i \(0.410052\pi\)
\(68\) −40.6709 −4.93207
\(69\) −7.87475 −0.948008
\(70\) −4.43048 −0.529544
\(71\) −10.6911 −1.26881 −0.634403 0.773003i \(-0.718754\pi\)
−0.634403 + 0.773003i \(0.718754\pi\)
\(72\) 10.4407 1.23045
\(73\) 1.49552 0.175038 0.0875189 0.996163i \(-0.472106\pi\)
0.0875189 + 0.996163i \(0.472106\pi\)
\(74\) −0.281832 −0.0327623
\(75\) −2.46732 −0.284901
\(76\) 34.1874 3.92156
\(77\) 0.134788 0.0153605
\(78\) 0 0
\(79\) 13.0892 1.47265 0.736323 0.676630i \(-0.236560\pi\)
0.736323 + 0.676630i \(0.236560\pi\)
\(80\) 27.9548 3.12544
\(81\) 1.00000 0.111111
\(82\) −10.3725 −1.14545
\(83\) −15.6291 −1.71552 −0.857760 0.514050i \(-0.828144\pi\)
−0.857760 + 0.514050i \(0.828144\pi\)
\(84\) −5.75034 −0.627413
\(85\) −11.2559 −1.22088
\(86\) 2.29865 0.247870
\(87\) 7.91488 0.848564
\(88\) −1.40728 −0.150017
\(89\) −7.17174 −0.760203 −0.380101 0.924945i \(-0.624111\pi\)
−0.380101 + 0.924945i \(0.624111\pi\)
\(90\) 4.43048 0.467014
\(91\) 0 0
\(92\) −45.2824 −4.72102
\(93\) −2.66844 −0.276704
\(94\) 7.19100 0.741695
\(95\) 9.46158 0.970737
\(96\) 28.0204 2.85982
\(97\) −13.9093 −1.41227 −0.706137 0.708076i \(-0.749564\pi\)
−0.706137 + 0.708076i \(0.749564\pi\)
\(98\) 2.78394 0.281221
\(99\) −0.134788 −0.0135467
\(100\) −14.1879 −1.41879
\(101\) 12.2952 1.22342 0.611709 0.791083i \(-0.290482\pi\)
0.611709 + 0.791083i \(0.290482\pi\)
\(102\) −19.6902 −1.94962
\(103\) 8.10004 0.798120 0.399060 0.916925i \(-0.369336\pi\)
0.399060 + 0.916925i \(0.369336\pi\)
\(104\) 0 0
\(105\) −1.59144 −0.155309
\(106\) 3.97742 0.386321
\(107\) −5.28792 −0.511202 −0.255601 0.966782i \(-0.582273\pi\)
−0.255601 + 0.966782i \(0.582273\pi\)
\(108\) 5.75034 0.553326
\(109\) 0.0300910 0.00288219 0.00144110 0.999999i \(-0.499541\pi\)
0.00144110 + 0.999999i \(0.499541\pi\)
\(110\) −0.597175 −0.0569384
\(111\) −0.101235 −0.00960879
\(112\) −17.5657 −1.65980
\(113\) −5.81240 −0.546785 −0.273392 0.961903i \(-0.588146\pi\)
−0.273392 + 0.961903i \(0.588146\pi\)
\(114\) 16.5513 1.55018
\(115\) −12.5322 −1.16863
\(116\) 45.5132 4.22579
\(117\) 0 0
\(118\) −22.0905 −2.03359
\(119\) 7.07278 0.648361
\(120\) 16.6158 1.51681
\(121\) −10.9818 −0.998348
\(122\) −10.5216 −0.952582
\(123\) −3.72584 −0.335948
\(124\) −15.3444 −1.37797
\(125\) −11.8838 −1.06292
\(126\) −2.78394 −0.248013
\(127\) 20.9759 1.86131 0.930654 0.365901i \(-0.119239\pi\)
0.930654 + 0.365901i \(0.119239\pi\)
\(128\) 63.3232 5.59703
\(129\) 0.825682 0.0726973
\(130\) 0 0
\(131\) 8.26962 0.722520 0.361260 0.932465i \(-0.382347\pi\)
0.361260 + 0.932465i \(0.382347\pi\)
\(132\) −0.775076 −0.0674617
\(133\) −5.94529 −0.515522
\(134\) 12.7079 1.09780
\(135\) 1.59144 0.136969
\(136\) −73.8450 −6.33215
\(137\) −10.0528 −0.858868 −0.429434 0.903098i \(-0.641287\pi\)
−0.429434 + 0.903098i \(0.641287\pi\)
\(138\) −21.9228 −1.86620
\(139\) −12.8728 −1.09186 −0.545928 0.837832i \(-0.683823\pi\)
−0.545928 + 0.837832i \(0.683823\pi\)
\(140\) −9.15132 −0.773428
\(141\) 2.58303 0.217530
\(142\) −29.7635 −2.49770
\(143\) 0 0
\(144\) 17.5657 1.46381
\(145\) 12.5961 1.04605
\(146\) 4.16345 0.344570
\(147\) 1.00000 0.0824786
\(148\) −0.582134 −0.0478512
\(149\) 22.7196 1.86126 0.930630 0.365962i \(-0.119260\pi\)
0.930630 + 0.365962i \(0.119260\pi\)
\(150\) −6.86886 −0.560840
\(151\) −2.67518 −0.217703 −0.108852 0.994058i \(-0.534717\pi\)
−0.108852 + 0.994058i \(0.534717\pi\)
\(152\) 62.0731 5.03479
\(153\) −7.07278 −0.571801
\(154\) 0.375242 0.0302379
\(155\) −4.24666 −0.341100
\(156\) 0 0
\(157\) 19.7016 1.57236 0.786178 0.618001i \(-0.212057\pi\)
0.786178 + 0.618001i \(0.212057\pi\)
\(158\) 36.4395 2.89897
\(159\) 1.42870 0.113303
\(160\) 44.5929 3.52538
\(161\) 7.87475 0.620617
\(162\) 2.78394 0.218727
\(163\) 5.99748 0.469759 0.234879 0.972025i \(-0.424531\pi\)
0.234879 + 0.972025i \(0.424531\pi\)
\(164\) −21.4248 −1.67300
\(165\) −0.214507 −0.0166994
\(166\) −43.5106 −3.37708
\(167\) −5.89546 −0.456204 −0.228102 0.973637i \(-0.573252\pi\)
−0.228102 + 0.973637i \(0.573252\pi\)
\(168\) −10.4407 −0.805519
\(169\) 0 0
\(170\) −31.3358 −2.40335
\(171\) 5.94529 0.454648
\(172\) 4.74795 0.362028
\(173\) 4.50959 0.342858 0.171429 0.985196i \(-0.445162\pi\)
0.171429 + 0.985196i \(0.445162\pi\)
\(174\) 22.0346 1.67044
\(175\) 2.46732 0.186511
\(176\) −2.36764 −0.178468
\(177\) −7.93495 −0.596428
\(178\) −19.9657 −1.49649
\(179\) 6.50536 0.486234 0.243117 0.969997i \(-0.421830\pi\)
0.243117 + 0.969997i \(0.421830\pi\)
\(180\) 9.15132 0.682099
\(181\) −11.5176 −0.856099 −0.428050 0.903755i \(-0.640799\pi\)
−0.428050 + 0.903755i \(0.640799\pi\)
\(182\) 0 0
\(183\) −3.77939 −0.279381
\(184\) −82.2180 −6.06119
\(185\) −0.161109 −0.0118450
\(186\) −7.42877 −0.544704
\(187\) 0.953326 0.0697141
\(188\) 14.8533 1.08329
\(189\) −1.00000 −0.0727393
\(190\) 26.3405 1.91094
\(191\) −22.6574 −1.63943 −0.819716 0.572771i \(-0.805868\pi\)
−0.819716 + 0.572771i \(0.805868\pi\)
\(192\) 42.8759 3.09430
\(193\) 12.8501 0.924972 0.462486 0.886627i \(-0.346958\pi\)
0.462486 + 0.886627i \(0.346958\pi\)
\(194\) −38.7226 −2.78012
\(195\) 0 0
\(196\) 5.75034 0.410738
\(197\) 6.15529 0.438546 0.219273 0.975664i \(-0.429631\pi\)
0.219273 + 0.975664i \(0.429631\pi\)
\(198\) −0.375242 −0.0266673
\(199\) −6.10499 −0.432771 −0.216386 0.976308i \(-0.569427\pi\)
−0.216386 + 0.976308i \(0.569427\pi\)
\(200\) −25.7605 −1.82155
\(201\) 4.56472 0.321971
\(202\) 34.2291 2.40835
\(203\) −7.91488 −0.555515
\(204\) −40.6709 −2.84753
\(205\) −5.92946 −0.414131
\(206\) 22.5500 1.57114
\(207\) −7.87475 −0.547333
\(208\) 0 0
\(209\) −0.801353 −0.0554308
\(210\) −4.43048 −0.305732
\(211\) 3.35021 0.230638 0.115319 0.993329i \(-0.463211\pi\)
0.115319 + 0.993329i \(0.463211\pi\)
\(212\) 8.21550 0.564243
\(213\) −10.6911 −0.732545
\(214\) −14.7213 −1.00632
\(215\) 1.31402 0.0896157
\(216\) 10.4407 0.710401
\(217\) 2.66844 0.181145
\(218\) 0.0837716 0.00567373
\(219\) 1.49552 0.101058
\(220\) −1.23349 −0.0831617
\(221\) 0 0
\(222\) −0.281832 −0.0189153
\(223\) −14.5203 −0.972350 −0.486175 0.873861i \(-0.661608\pi\)
−0.486175 + 0.873861i \(0.661608\pi\)
\(224\) −28.0204 −1.87219
\(225\) −2.46732 −0.164488
\(226\) −16.1814 −1.07637
\(227\) 14.8507 0.985676 0.492838 0.870121i \(-0.335959\pi\)
0.492838 + 0.870121i \(0.335959\pi\)
\(228\) 34.1874 2.26412
\(229\) −21.6278 −1.42920 −0.714602 0.699531i \(-0.753392\pi\)
−0.714602 + 0.699531i \(0.753392\pi\)
\(230\) −34.8889 −2.30051
\(231\) 0.134788 0.00886840
\(232\) 82.6370 5.42539
\(233\) 7.71618 0.505504 0.252752 0.967531i \(-0.418664\pi\)
0.252752 + 0.967531i \(0.418664\pi\)
\(234\) 0 0
\(235\) 4.11073 0.268155
\(236\) −45.6286 −2.97017
\(237\) 13.0892 0.850233
\(238\) 19.6902 1.27633
\(239\) 3.84302 0.248585 0.124292 0.992246i \(-0.460334\pi\)
0.124292 + 0.992246i \(0.460334\pi\)
\(240\) 27.9548 1.80447
\(241\) −4.88222 −0.314491 −0.157246 0.987560i \(-0.550261\pi\)
−0.157246 + 0.987560i \(0.550261\pi\)
\(242\) −30.5728 −1.96529
\(243\) 1.00000 0.0641500
\(244\) −21.7328 −1.39130
\(245\) 1.59144 0.101673
\(246\) −10.3725 −0.661328
\(247\) 0 0
\(248\) −27.8604 −1.76914
\(249\) −15.6291 −0.990456
\(250\) −33.0838 −2.09240
\(251\) 11.3686 0.717581 0.358791 0.933418i \(-0.383189\pi\)
0.358791 + 0.933418i \(0.383189\pi\)
\(252\) −5.75034 −0.362237
\(253\) 1.06142 0.0667310
\(254\) 58.3956 3.66407
\(255\) −11.2559 −0.704873
\(256\) 90.5363 5.65852
\(257\) 25.0640 1.56345 0.781723 0.623625i \(-0.214341\pi\)
0.781723 + 0.623625i \(0.214341\pi\)
\(258\) 2.29865 0.143108
\(259\) 0.101235 0.00629043
\(260\) 0 0
\(261\) 7.91488 0.489919
\(262\) 23.0221 1.42231
\(263\) 17.8501 1.10069 0.550343 0.834939i \(-0.314497\pi\)
0.550343 + 0.834939i \(0.314497\pi\)
\(264\) −1.40728 −0.0866123
\(265\) 2.27369 0.139672
\(266\) −16.5513 −1.01483
\(267\) −7.17174 −0.438903
\(268\) 26.2487 1.60339
\(269\) −6.75838 −0.412066 −0.206033 0.978545i \(-0.566055\pi\)
−0.206033 + 0.978545i \(0.566055\pi\)
\(270\) 4.43048 0.269630
\(271\) 7.27080 0.441670 0.220835 0.975311i \(-0.429122\pi\)
0.220835 + 0.975311i \(0.429122\pi\)
\(272\) −124.238 −7.53306
\(273\) 0 0
\(274\) −27.9864 −1.69072
\(275\) 0.332564 0.0200544
\(276\) −45.2824 −2.72568
\(277\) −13.1166 −0.788102 −0.394051 0.919089i \(-0.628927\pi\)
−0.394051 + 0.919089i \(0.628927\pi\)
\(278\) −35.8371 −2.14937
\(279\) −2.66844 −0.159755
\(280\) −16.6158 −0.992983
\(281\) 18.2095 1.08629 0.543143 0.839640i \(-0.317234\pi\)
0.543143 + 0.839640i \(0.317234\pi\)
\(282\) 7.19100 0.428218
\(283\) −22.5038 −1.33771 −0.668857 0.743391i \(-0.733216\pi\)
−0.668857 + 0.743391i \(0.733216\pi\)
\(284\) −61.4777 −3.64803
\(285\) 9.46158 0.560455
\(286\) 0 0
\(287\) 3.72584 0.219929
\(288\) 28.0204 1.65112
\(289\) 33.0243 1.94261
\(290\) 35.0667 2.05919
\(291\) −13.9093 −0.815376
\(292\) 8.59977 0.503263
\(293\) −10.6254 −0.620744 −0.310372 0.950615i \(-0.600454\pi\)
−0.310372 + 0.950615i \(0.600454\pi\)
\(294\) 2.78394 0.162363
\(295\) −12.6280 −0.735231
\(296\) −1.05696 −0.0614348
\(297\) −0.134788 −0.00782119
\(298\) 63.2500 3.66397
\(299\) 0 0
\(300\) −14.1879 −0.819138
\(301\) −0.825682 −0.0475915
\(302\) −7.44756 −0.428559
\(303\) 12.2952 0.706341
\(304\) 104.433 5.98965
\(305\) −6.01468 −0.344400
\(306\) −19.6902 −1.12562
\(307\) 25.4720 1.45377 0.726883 0.686761i \(-0.240968\pi\)
0.726883 + 0.686761i \(0.240968\pi\)
\(308\) 0.775076 0.0441641
\(309\) 8.10004 0.460795
\(310\) −11.8225 −0.671470
\(311\) −1.16454 −0.0660348 −0.0330174 0.999455i \(-0.510512\pi\)
−0.0330174 + 0.999455i \(0.510512\pi\)
\(312\) 0 0
\(313\) 1.26134 0.0712953 0.0356476 0.999364i \(-0.488651\pi\)
0.0356476 + 0.999364i \(0.488651\pi\)
\(314\) 54.8480 3.09525
\(315\) −1.59144 −0.0896675
\(316\) 75.2671 4.23410
\(317\) 4.95320 0.278200 0.139100 0.990278i \(-0.455579\pi\)
0.139100 + 0.990278i \(0.455579\pi\)
\(318\) 3.97742 0.223043
\(319\) −1.06683 −0.0597310
\(320\) 68.2345 3.81442
\(321\) −5.28792 −0.295143
\(322\) 21.9228 1.22171
\(323\) −42.0498 −2.33971
\(324\) 5.75034 0.319463
\(325\) 0 0
\(326\) 16.6966 0.924741
\(327\) 0.0300910 0.00166403
\(328\) −38.9005 −2.14792
\(329\) −2.58303 −0.142407
\(330\) −0.597175 −0.0328734
\(331\) −12.8190 −0.704597 −0.352298 0.935888i \(-0.614600\pi\)
−0.352298 + 0.935888i \(0.614600\pi\)
\(332\) −89.8728 −4.93241
\(333\) −0.101235 −0.00554764
\(334\) −16.4126 −0.898059
\(335\) 7.26449 0.396901
\(336\) −17.5657 −0.958287
\(337\) −4.17281 −0.227307 −0.113654 0.993520i \(-0.536255\pi\)
−0.113654 + 0.993520i \(0.536255\pi\)
\(338\) 0 0
\(339\) −5.81240 −0.315686
\(340\) −64.7253 −3.51022
\(341\) 0.359673 0.0194774
\(342\) 16.5513 0.894994
\(343\) −1.00000 −0.0539949
\(344\) 8.62072 0.464798
\(345\) −12.5322 −0.674711
\(346\) 12.5544 0.674931
\(347\) −2.68888 −0.144347 −0.0721733 0.997392i \(-0.522993\pi\)
−0.0721733 + 0.997392i \(0.522993\pi\)
\(348\) 45.5132 2.43976
\(349\) −1.62817 −0.0871537 −0.0435768 0.999050i \(-0.513875\pi\)
−0.0435768 + 0.999050i \(0.513875\pi\)
\(350\) 6.86886 0.367156
\(351\) 0 0
\(352\) −3.77682 −0.201305
\(353\) −21.5506 −1.14702 −0.573511 0.819198i \(-0.694419\pi\)
−0.573511 + 0.819198i \(0.694419\pi\)
\(354\) −22.0905 −1.17409
\(355\) −17.0143 −0.903027
\(356\) −41.2399 −2.18571
\(357\) 7.07278 0.374331
\(358\) 18.1106 0.957173
\(359\) 13.6959 0.722841 0.361421 0.932403i \(-0.382292\pi\)
0.361421 + 0.932403i \(0.382292\pi\)
\(360\) 16.6158 0.875729
\(361\) 16.3465 0.860340
\(362\) −32.0644 −1.68527
\(363\) −10.9818 −0.576397
\(364\) 0 0
\(365\) 2.38004 0.124577
\(366\) −10.5216 −0.549973
\(367\) −20.6517 −1.07801 −0.539005 0.842303i \(-0.681200\pi\)
−0.539005 + 0.842303i \(0.681200\pi\)
\(368\) −138.325 −7.21071
\(369\) −3.72584 −0.193959
\(370\) −0.448519 −0.0233174
\(371\) −1.42870 −0.0741744
\(372\) −15.3444 −0.795570
\(373\) −4.70300 −0.243512 −0.121756 0.992560i \(-0.538853\pi\)
−0.121756 + 0.992560i \(0.538853\pi\)
\(374\) 2.65401 0.137235
\(375\) −11.8838 −0.613676
\(376\) 26.9687 1.39080
\(377\) 0 0
\(378\) −2.78394 −0.143191
\(379\) 6.02884 0.309681 0.154840 0.987939i \(-0.450514\pi\)
0.154840 + 0.987939i \(0.450514\pi\)
\(380\) 54.4072 2.79103
\(381\) 20.9759 1.07463
\(382\) −63.0769 −3.22729
\(383\) −0.635311 −0.0324629 −0.0162314 0.999868i \(-0.505167\pi\)
−0.0162314 + 0.999868i \(0.505167\pi\)
\(384\) 63.3232 3.23145
\(385\) 0.214507 0.0109323
\(386\) 35.7740 1.82085
\(387\) 0.825682 0.0419718
\(388\) −79.9830 −4.06052
\(389\) −14.3172 −0.725908 −0.362954 0.931807i \(-0.618232\pi\)
−0.362954 + 0.931807i \(0.618232\pi\)
\(390\) 0 0
\(391\) 55.6964 2.81669
\(392\) 10.4407 0.527336
\(393\) 8.26962 0.417147
\(394\) 17.1360 0.863298
\(395\) 20.8306 1.04810
\(396\) −0.775076 −0.0389490
\(397\) −7.56097 −0.379474 −0.189737 0.981835i \(-0.560764\pi\)
−0.189737 + 0.981835i \(0.560764\pi\)
\(398\) −16.9959 −0.851930
\(399\) −5.94529 −0.297637
\(400\) −43.3401 −2.16701
\(401\) −9.40084 −0.469455 −0.234728 0.972061i \(-0.575420\pi\)
−0.234728 + 0.972061i \(0.575420\pi\)
\(402\) 12.7079 0.633814
\(403\) 0 0
\(404\) 70.7015 3.51753
\(405\) 1.59144 0.0790793
\(406\) −22.0346 −1.09356
\(407\) 0.0136452 0.000676369 0
\(408\) −73.8450 −3.65587
\(409\) −1.55862 −0.0770690 −0.0385345 0.999257i \(-0.512269\pi\)
−0.0385345 + 0.999257i \(0.512269\pi\)
\(410\) −16.5073 −0.815236
\(411\) −10.0528 −0.495868
\(412\) 46.5779 2.29473
\(413\) 7.93495 0.390453
\(414\) −21.9228 −1.07745
\(415\) −24.8728 −1.22096
\(416\) 0 0
\(417\) −12.8728 −0.630383
\(418\) −2.23092 −0.109118
\(419\) 29.7054 1.45120 0.725602 0.688115i \(-0.241562\pi\)
0.725602 + 0.688115i \(0.241562\pi\)
\(420\) −9.15132 −0.446539
\(421\) −38.8767 −1.89474 −0.947368 0.320146i \(-0.896268\pi\)
−0.947368 + 0.320146i \(0.896268\pi\)
\(422\) 9.32678 0.454021
\(423\) 2.58303 0.125591
\(424\) 14.9167 0.724417
\(425\) 17.4508 0.846488
\(426\) −29.7635 −1.44205
\(427\) 3.77939 0.182898
\(428\) −30.4073 −1.46979
\(429\) 0 0
\(430\) 3.65817 0.176413
\(431\) −22.2975 −1.07403 −0.537015 0.843572i \(-0.680448\pi\)
−0.537015 + 0.843572i \(0.680448\pi\)
\(432\) 17.5657 0.845130
\(433\) 34.2544 1.64616 0.823082 0.567923i \(-0.192253\pi\)
0.823082 + 0.567923i \(0.192253\pi\)
\(434\) 7.42877 0.356592
\(435\) 12.5961 0.603935
\(436\) 0.173033 0.00828679
\(437\) −46.8176 −2.23959
\(438\) 4.16345 0.198937
\(439\) 32.4533 1.54891 0.774455 0.632630i \(-0.218024\pi\)
0.774455 + 0.632630i \(0.218024\pi\)
\(440\) −2.23961 −0.106769
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −11.0332 −0.524205 −0.262103 0.965040i \(-0.584416\pi\)
−0.262103 + 0.965040i \(0.584416\pi\)
\(444\) −0.582134 −0.0276269
\(445\) −11.4134 −0.541047
\(446\) −40.4237 −1.91412
\(447\) 22.7196 1.07460
\(448\) −42.8759 −2.02570
\(449\) 20.3805 0.961816 0.480908 0.876771i \(-0.340307\pi\)
0.480908 + 0.876771i \(0.340307\pi\)
\(450\) −6.86886 −0.323801
\(451\) 0.502198 0.0236476
\(452\) −33.4232 −1.57210
\(453\) −2.67518 −0.125691
\(454\) 41.3435 1.94035
\(455\) 0 0
\(456\) 62.0731 2.90684
\(457\) 25.7914 1.20647 0.603234 0.797564i \(-0.293878\pi\)
0.603234 + 0.797564i \(0.293878\pi\)
\(458\) −60.2105 −2.81345
\(459\) −7.07278 −0.330129
\(460\) −72.0643 −3.36002
\(461\) 1.21019 0.0563640 0.0281820 0.999603i \(-0.491028\pi\)
0.0281820 + 0.999603i \(0.491028\pi\)
\(462\) 0.375242 0.0174578
\(463\) −21.3847 −0.993833 −0.496917 0.867798i \(-0.665535\pi\)
−0.496917 + 0.867798i \(0.665535\pi\)
\(464\) 139.030 6.45432
\(465\) −4.24666 −0.196934
\(466\) 21.4814 0.995106
\(467\) 15.8716 0.734450 0.367225 0.930132i \(-0.380308\pi\)
0.367225 + 0.930132i \(0.380308\pi\)
\(468\) 0 0
\(469\) −4.56472 −0.210779
\(470\) 11.4440 0.527875
\(471\) 19.7016 0.907800
\(472\) −82.8466 −3.81332
\(473\) −0.111292 −0.00511721
\(474\) 36.4395 1.67372
\(475\) −14.6689 −0.673055
\(476\) 40.6709 1.86415
\(477\) 1.42870 0.0654157
\(478\) 10.6988 0.489350
\(479\) 22.6704 1.03584 0.517919 0.855429i \(-0.326707\pi\)
0.517919 + 0.855429i \(0.326707\pi\)
\(480\) 44.5929 2.03538
\(481\) 0 0
\(482\) −13.5918 −0.619090
\(483\) 7.87475 0.358313
\(484\) −63.1492 −2.87042
\(485\) −22.1358 −1.00513
\(486\) 2.78394 0.126282
\(487\) 34.9729 1.58477 0.792386 0.610019i \(-0.208838\pi\)
0.792386 + 0.610019i \(0.208838\pi\)
\(488\) −39.4596 −1.78625
\(489\) 5.99748 0.271215
\(490\) 4.43048 0.200149
\(491\) −4.33486 −0.195629 −0.0978147 0.995205i \(-0.531185\pi\)
−0.0978147 + 0.995205i \(0.531185\pi\)
\(492\) −21.4248 −0.965906
\(493\) −55.9802 −2.52122
\(494\) 0 0
\(495\) −0.214507 −0.00964138
\(496\) −46.8729 −2.10466
\(497\) 10.6911 0.479563
\(498\) −43.5106 −1.94976
\(499\) 20.8879 0.935073 0.467536 0.883974i \(-0.345142\pi\)
0.467536 + 0.883974i \(0.345142\pi\)
\(500\) −68.3358 −3.05607
\(501\) −5.89546 −0.263390
\(502\) 31.6496 1.41259
\(503\) −35.1712 −1.56821 −0.784103 0.620631i \(-0.786877\pi\)
−0.784103 + 0.620631i \(0.786877\pi\)
\(504\) −10.4407 −0.465067
\(505\) 19.5671 0.870724
\(506\) 2.95493 0.131363
\(507\) 0 0
\(508\) 120.618 5.35157
\(509\) −40.6851 −1.80334 −0.901668 0.432429i \(-0.857657\pi\)
−0.901668 + 0.432429i \(0.857657\pi\)
\(510\) −31.3358 −1.38757
\(511\) −1.49552 −0.0661581
\(512\) 125.401 5.54201
\(513\) 5.94529 0.262491
\(514\) 69.7766 3.07771
\(515\) 12.8907 0.568034
\(516\) 4.74795 0.209017
\(517\) −0.348161 −0.0153121
\(518\) 0.281832 0.0123830
\(519\) 4.50959 0.197949
\(520\) 0 0
\(521\) −5.14269 −0.225305 −0.112653 0.993634i \(-0.535935\pi\)
−0.112653 + 0.993634i \(0.535935\pi\)
\(522\) 22.0346 0.964427
\(523\) 9.83526 0.430066 0.215033 0.976607i \(-0.431014\pi\)
0.215033 + 0.976607i \(0.431014\pi\)
\(524\) 47.5531 2.07737
\(525\) 2.46732 0.107682
\(526\) 49.6937 2.16675
\(527\) 18.8733 0.822133
\(528\) −2.36764 −0.103038
\(529\) 39.0116 1.69616
\(530\) 6.32983 0.274950
\(531\) −7.93495 −0.344348
\(532\) −34.1874 −1.48221
\(533\) 0 0
\(534\) −19.9657 −0.864001
\(535\) −8.41541 −0.363830
\(536\) 47.6590 2.05855
\(537\) 6.50536 0.280727
\(538\) −18.8149 −0.811170
\(539\) −0.134788 −0.00580573
\(540\) 9.15132 0.393810
\(541\) −12.6834 −0.545302 −0.272651 0.962113i \(-0.587900\pi\)
−0.272651 + 0.962113i \(0.587900\pi\)
\(542\) 20.2415 0.869447
\(543\) −11.5176 −0.494269
\(544\) −198.183 −8.49701
\(545\) 0.0478880 0.00205130
\(546\) 0 0
\(547\) 15.1082 0.645979 0.322990 0.946403i \(-0.395312\pi\)
0.322990 + 0.946403i \(0.395312\pi\)
\(548\) −57.8069 −2.46939
\(549\) −3.77939 −0.161301
\(550\) 0.925840 0.0394780
\(551\) 47.0562 2.00466
\(552\) −82.2180 −3.49943
\(553\) −13.0892 −0.556608
\(554\) −36.5160 −1.55141
\(555\) −0.161109 −0.00683871
\(556\) −74.0229 −3.13927
\(557\) 0.658544 0.0279034 0.0139517 0.999903i \(-0.495559\pi\)
0.0139517 + 0.999903i \(0.495559\pi\)
\(558\) −7.42877 −0.314485
\(559\) 0 0
\(560\) −27.9548 −1.18130
\(561\) 0.953326 0.0402495
\(562\) 50.6941 2.13840
\(563\) 4.87871 0.205613 0.102807 0.994701i \(-0.467218\pi\)
0.102807 + 0.994701i \(0.467218\pi\)
\(564\) 14.8533 0.625435
\(565\) −9.25009 −0.389154
\(566\) −62.6494 −2.63335
\(567\) −1.00000 −0.0419961
\(568\) −111.623 −4.68361
\(569\) −0.747003 −0.0313160 −0.0156580 0.999877i \(-0.504984\pi\)
−0.0156580 + 0.999877i \(0.504984\pi\)
\(570\) 26.3405 1.10328
\(571\) 26.2447 1.09831 0.549153 0.835722i \(-0.314950\pi\)
0.549153 + 0.835722i \(0.314950\pi\)
\(572\) 0 0
\(573\) −22.6574 −0.946526
\(574\) 10.3725 0.432941
\(575\) 19.4295 0.810265
\(576\) 42.8759 1.78650
\(577\) −34.6422 −1.44217 −0.721087 0.692844i \(-0.756357\pi\)
−0.721087 + 0.692844i \(0.756357\pi\)
\(578\) 91.9377 3.82410
\(579\) 12.8501 0.534033
\(580\) 72.4316 3.00756
\(581\) 15.6291 0.648406
\(582\) −38.7226 −1.60510
\(583\) −0.192572 −0.00797550
\(584\) 15.6143 0.646126
\(585\) 0 0
\(586\) −29.5806 −1.22196
\(587\) −17.7493 −0.732592 −0.366296 0.930498i \(-0.619374\pi\)
−0.366296 + 0.930498i \(0.619374\pi\)
\(588\) 5.75034 0.237140
\(589\) −15.8646 −0.653690
\(590\) −35.1557 −1.44734
\(591\) 6.15529 0.253195
\(592\) −1.77826 −0.0730860
\(593\) −24.5573 −1.00845 −0.504223 0.863573i \(-0.668221\pi\)
−0.504223 + 0.863573i \(0.668221\pi\)
\(594\) −0.375242 −0.0153964
\(595\) 11.2559 0.461448
\(596\) 130.645 5.35143
\(597\) −6.10499 −0.249861
\(598\) 0 0
\(599\) 28.0271 1.14516 0.572578 0.819850i \(-0.305943\pi\)
0.572578 + 0.819850i \(0.305943\pi\)
\(600\) −25.7605 −1.05167
\(601\) 30.6035 1.24834 0.624171 0.781288i \(-0.285437\pi\)
0.624171 + 0.781288i \(0.285437\pi\)
\(602\) −2.29865 −0.0936860
\(603\) 4.56472 0.185890
\(604\) −15.3832 −0.625934
\(605\) −17.4769 −0.710539
\(606\) 34.2291 1.39046
\(607\) −21.5723 −0.875593 −0.437797 0.899074i \(-0.644241\pi\)
−0.437797 + 0.899074i \(0.644241\pi\)
\(608\) 166.590 6.75610
\(609\) −7.91488 −0.320727
\(610\) −16.7445 −0.677966
\(611\) 0 0
\(612\) −40.6709 −1.64402
\(613\) 22.6684 0.915569 0.457784 0.889063i \(-0.348643\pi\)
0.457784 + 0.889063i \(0.348643\pi\)
\(614\) 70.9127 2.86180
\(615\) −5.92946 −0.239099
\(616\) 1.40728 0.0567011
\(617\) 11.7948 0.474841 0.237421 0.971407i \(-0.423698\pi\)
0.237421 + 0.971407i \(0.423698\pi\)
\(618\) 22.5500 0.907096
\(619\) −5.95151 −0.239211 −0.119606 0.992821i \(-0.538163\pi\)
−0.119606 + 0.992821i \(0.538163\pi\)
\(620\) −24.4197 −0.980719
\(621\) −7.87475 −0.316003
\(622\) −3.24200 −0.129992
\(623\) 7.17174 0.287330
\(624\) 0 0
\(625\) −6.57578 −0.263031
\(626\) 3.51150 0.140348
\(627\) −0.801353 −0.0320030
\(628\) 113.291 4.52079
\(629\) 0.716012 0.0285493
\(630\) −4.43048 −0.176515
\(631\) 1.30868 0.0520978 0.0260489 0.999661i \(-0.491707\pi\)
0.0260489 + 0.999661i \(0.491707\pi\)
\(632\) 136.660 5.43605
\(633\) 3.35021 0.133159
\(634\) 13.7894 0.547648
\(635\) 33.3819 1.32472
\(636\) 8.21550 0.325766
\(637\) 0 0
\(638\) −2.96999 −0.117583
\(639\) −10.6911 −0.422935
\(640\) 100.775 3.98349
\(641\) 32.0757 1.26691 0.633457 0.773778i \(-0.281635\pi\)
0.633457 + 0.773778i \(0.281635\pi\)
\(642\) −14.7213 −0.581002
\(643\) 14.3540 0.566067 0.283033 0.959110i \(-0.408659\pi\)
0.283033 + 0.959110i \(0.408659\pi\)
\(644\) 45.2824 1.78438
\(645\) 1.31402 0.0517397
\(646\) −117.064 −4.60582
\(647\) 26.7087 1.05003 0.525014 0.851094i \(-0.324060\pi\)
0.525014 + 0.851094i \(0.324060\pi\)
\(648\) 10.4407 0.410150
\(649\) 1.06954 0.0419830
\(650\) 0 0
\(651\) 2.66844 0.104584
\(652\) 34.4875 1.35064
\(653\) −18.9610 −0.742001 −0.371000 0.928633i \(-0.620985\pi\)
−0.371000 + 0.928633i \(0.620985\pi\)
\(654\) 0.0837716 0.00327573
\(655\) 13.1606 0.514227
\(656\) −65.4470 −2.55527
\(657\) 1.49552 0.0583460
\(658\) −7.19100 −0.280334
\(659\) −1.32694 −0.0516901 −0.0258451 0.999666i \(-0.508228\pi\)
−0.0258451 + 0.999666i \(0.508228\pi\)
\(660\) −1.23349 −0.0480135
\(661\) 33.0787 1.28661 0.643307 0.765608i \(-0.277562\pi\)
0.643307 + 0.765608i \(0.277562\pi\)
\(662\) −35.6874 −1.38703
\(663\) 0 0
\(664\) −163.179 −6.33259
\(665\) −9.46158 −0.366904
\(666\) −0.281832 −0.0109208
\(667\) −62.3276 −2.41334
\(668\) −33.9009 −1.31166
\(669\) −14.5203 −0.561387
\(670\) 20.2239 0.781318
\(671\) 0.509417 0.0196658
\(672\) −28.0204 −1.08091
\(673\) 6.08084 0.234399 0.117200 0.993108i \(-0.462608\pi\)
0.117200 + 0.993108i \(0.462608\pi\)
\(674\) −11.6169 −0.447465
\(675\) −2.46732 −0.0949670
\(676\) 0 0
\(677\) −14.2996 −0.549579 −0.274790 0.961504i \(-0.588608\pi\)
−0.274790 + 0.961504i \(0.588608\pi\)
\(678\) −16.1814 −0.621442
\(679\) 13.9093 0.533789
\(680\) −117.520 −4.50668
\(681\) 14.8507 0.569080
\(682\) 1.00131 0.0383421
\(683\) −40.8971 −1.56488 −0.782441 0.622724i \(-0.786026\pi\)
−0.782441 + 0.622724i \(0.786026\pi\)
\(684\) 34.1874 1.30719
\(685\) −15.9984 −0.611268
\(686\) −2.78394 −0.106291
\(687\) −21.6278 −0.825151
\(688\) 14.5037 0.552948
\(689\) 0 0
\(690\) −34.8889 −1.32820
\(691\) 37.7189 1.43489 0.717447 0.696613i \(-0.245311\pi\)
0.717447 + 0.696613i \(0.245311\pi\)
\(692\) 25.9317 0.985774
\(693\) 0.134788 0.00512017
\(694\) −7.48568 −0.284153
\(695\) −20.4863 −0.777089
\(696\) 82.6370 3.13235
\(697\) 26.3521 0.998156
\(698\) −4.53272 −0.171566
\(699\) 7.71618 0.291853
\(700\) 14.1879 0.536252
\(701\) 3.52274 0.133052 0.0665261 0.997785i \(-0.478808\pi\)
0.0665261 + 0.997785i \(0.478808\pi\)
\(702\) 0 0
\(703\) −0.601870 −0.0227000
\(704\) −5.77916 −0.217810
\(705\) 4.11073 0.154819
\(706\) −59.9956 −2.25797
\(707\) −12.2952 −0.462409
\(708\) −45.6286 −1.71483
\(709\) −2.41078 −0.0905388 −0.0452694 0.998975i \(-0.514415\pi\)
−0.0452694 + 0.998975i \(0.514415\pi\)
\(710\) −47.3669 −1.77765
\(711\) 13.0892 0.490882
\(712\) −74.8781 −2.80618
\(713\) 21.0133 0.786953
\(714\) 19.6902 0.736888
\(715\) 0 0
\(716\) 37.4080 1.39800
\(717\) 3.84302 0.143520
\(718\) 38.1286 1.42295
\(719\) 42.2743 1.57656 0.788282 0.615314i \(-0.210971\pi\)
0.788282 + 0.615314i \(0.210971\pi\)
\(720\) 27.9548 1.04181
\(721\) −8.10004 −0.301661
\(722\) 45.5076 1.69362
\(723\) −4.88222 −0.181572
\(724\) −66.2303 −2.46143
\(725\) −19.5285 −0.725270
\(726\) −30.5728 −1.13466
\(727\) 18.8872 0.700488 0.350244 0.936659i \(-0.386099\pi\)
0.350244 + 0.936659i \(0.386099\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.62589 0.245235
\(731\) −5.83987 −0.215995
\(732\) −21.7328 −0.803266
\(733\) −35.3689 −1.30638 −0.653191 0.757193i \(-0.726570\pi\)
−0.653191 + 0.757193i \(0.726570\pi\)
\(734\) −57.4931 −2.12211
\(735\) 1.59144 0.0587012
\(736\) −220.654 −8.13341
\(737\) −0.615270 −0.0226637
\(738\) −10.3725 −0.381818
\(739\) 18.9800 0.698191 0.349095 0.937087i \(-0.386489\pi\)
0.349095 + 0.937087i \(0.386489\pi\)
\(740\) −0.926433 −0.0340563
\(741\) 0 0
\(742\) −3.97742 −0.146016
\(743\) −41.4651 −1.52121 −0.760603 0.649217i \(-0.775097\pi\)
−0.760603 + 0.649217i \(0.775097\pi\)
\(744\) −27.8604 −1.02141
\(745\) 36.1569 1.32468
\(746\) −13.0929 −0.479365
\(747\) −15.6291 −0.571840
\(748\) 5.48195 0.200440
\(749\) 5.28792 0.193216
\(750\) −33.0838 −1.20805
\(751\) 7.35910 0.268537 0.134269 0.990945i \(-0.457132\pi\)
0.134269 + 0.990945i \(0.457132\pi\)
\(752\) 45.3726 1.65457
\(753\) 11.3686 0.414296
\(754\) 0 0
\(755\) −4.25740 −0.154943
\(756\) −5.75034 −0.209138
\(757\) −19.5518 −0.710623 −0.355311 0.934748i \(-0.615625\pi\)
−0.355311 + 0.934748i \(0.615625\pi\)
\(758\) 16.7840 0.609621
\(759\) 1.06142 0.0385271
\(760\) 98.7857 3.58333
\(761\) −37.1023 −1.34496 −0.672478 0.740117i \(-0.734770\pi\)
−0.672478 + 0.740117i \(0.734770\pi\)
\(762\) 58.3956 2.11545
\(763\) −0.0300910 −0.00108937
\(764\) −130.288 −4.71364
\(765\) −11.2559 −0.406959
\(766\) −1.76867 −0.0639046
\(767\) 0 0
\(768\) 90.5363 3.26695
\(769\) 30.7408 1.10854 0.554271 0.832337i \(-0.312997\pi\)
0.554271 + 0.832337i \(0.312997\pi\)
\(770\) 0.597175 0.0215207
\(771\) 25.0640 0.902656
\(772\) 73.8925 2.65945
\(773\) 1.97846 0.0711603 0.0355802 0.999367i \(-0.488672\pi\)
0.0355802 + 0.999367i \(0.488672\pi\)
\(774\) 2.29865 0.0826233
\(775\) 6.58387 0.236500
\(776\) −145.223 −5.21320
\(777\) 0.101235 0.00363178
\(778\) −39.8581 −1.42898
\(779\) −22.1512 −0.793649
\(780\) 0 0
\(781\) 1.44104 0.0515644
\(782\) 155.056 5.54477
\(783\) 7.91488 0.282855
\(784\) 17.5657 0.627346
\(785\) 31.3539 1.11907
\(786\) 23.0221 0.821172
\(787\) −9.71005 −0.346126 −0.173063 0.984911i \(-0.555366\pi\)
−0.173063 + 0.984911i \(0.555366\pi\)
\(788\) 35.3950 1.26089
\(789\) 17.8501 0.635481
\(790\) 57.9913 2.06324
\(791\) 5.81240 0.206665
\(792\) −1.40728 −0.0500056
\(793\) 0 0
\(794\) −21.0493 −0.747012
\(795\) 2.27369 0.0806395
\(796\) −35.1058 −1.24429
\(797\) −35.5792 −1.26028 −0.630140 0.776481i \(-0.717003\pi\)
−0.630140 + 0.776481i \(0.717003\pi\)
\(798\) −16.5513 −0.585911
\(799\) −18.2692 −0.646317
\(800\) −69.1353 −2.44430
\(801\) −7.17174 −0.253401
\(802\) −26.1714 −0.924144
\(803\) −0.201579 −0.00711356
\(804\) 26.2487 0.925720
\(805\) 12.5322 0.441702
\(806\) 0 0
\(807\) −6.75838 −0.237906
\(808\) 128.371 4.51607
\(809\) −22.4774 −0.790265 −0.395133 0.918624i \(-0.629301\pi\)
−0.395133 + 0.918624i \(0.629301\pi\)
\(810\) 4.43048 0.155671
\(811\) 3.81370 0.133917 0.0669586 0.997756i \(-0.478670\pi\)
0.0669586 + 0.997756i \(0.478670\pi\)
\(812\) −45.5132 −1.59720
\(813\) 7.27080 0.254998
\(814\) 0.0379876 0.00133146
\(815\) 9.54463 0.334334
\(816\) −124.238 −4.34921
\(817\) 4.90892 0.171741
\(818\) −4.33912 −0.151714
\(819\) 0 0
\(820\) −34.0964 −1.19070
\(821\) 13.8299 0.482668 0.241334 0.970442i \(-0.422415\pi\)
0.241334 + 0.970442i \(0.422415\pi\)
\(822\) −27.9864 −0.976137
\(823\) 37.3025 1.30028 0.650142 0.759813i \(-0.274709\pi\)
0.650142 + 0.759813i \(0.274709\pi\)
\(824\) 84.5702 2.94614
\(825\) 0.332564 0.0115784
\(826\) 22.0905 0.768625
\(827\) −30.2891 −1.05326 −0.526628 0.850096i \(-0.676544\pi\)
−0.526628 + 0.850096i \(0.676544\pi\)
\(828\) −45.2824 −1.57367
\(829\) 16.4068 0.569831 0.284916 0.958553i \(-0.408034\pi\)
0.284916 + 0.958553i \(0.408034\pi\)
\(830\) −69.2446 −2.40351
\(831\) −13.1166 −0.455011
\(832\) 0 0
\(833\) −7.07278 −0.245057
\(834\) −35.8371 −1.24094
\(835\) −9.38228 −0.324687
\(836\) −4.60805 −0.159373
\(837\) −2.66844 −0.0922346
\(838\) 82.6981 2.85676
\(839\) 6.43862 0.222286 0.111143 0.993804i \(-0.464549\pi\)
0.111143 + 0.993804i \(0.464549\pi\)
\(840\) −16.6158 −0.573299
\(841\) 33.6453 1.16018
\(842\) −108.231 −3.72987
\(843\) 18.2095 0.627167
\(844\) 19.2648 0.663122
\(845\) 0 0
\(846\) 7.19100 0.247232
\(847\) 10.9818 0.377340
\(848\) 25.0961 0.861804
\(849\) −22.5038 −0.772330
\(850\) 48.5820 1.66635
\(851\) 0.797199 0.0273276
\(852\) −61.4777 −2.10619
\(853\) 2.02935 0.0694836 0.0347418 0.999396i \(-0.488939\pi\)
0.0347418 + 0.999396i \(0.488939\pi\)
\(854\) 10.5216 0.360042
\(855\) 9.46158 0.323579
\(856\) −55.2097 −1.88703
\(857\) −49.1347 −1.67841 −0.839205 0.543815i \(-0.816979\pi\)
−0.839205 + 0.543815i \(0.816979\pi\)
\(858\) 0 0
\(859\) 18.4424 0.629246 0.314623 0.949217i \(-0.398122\pi\)
0.314623 + 0.949217i \(0.398122\pi\)
\(860\) 7.55608 0.257660
\(861\) 3.72584 0.126976
\(862\) −62.0748 −2.11428
\(863\) 44.9156 1.52894 0.764472 0.644657i \(-0.223000\pi\)
0.764472 + 0.644657i \(0.223000\pi\)
\(864\) 28.0204 0.953275
\(865\) 7.17675 0.244017
\(866\) 95.3624 3.24055
\(867\) 33.0243 1.12156
\(868\) 15.3444 0.520823
\(869\) −1.76426 −0.0598485
\(870\) 35.0667 1.18887
\(871\) 0 0
\(872\) 0.314171 0.0106392
\(873\) −13.9093 −0.470758
\(874\) −130.338 −4.40874
\(875\) 11.8838 0.401746
\(876\) 8.59977 0.290559
\(877\) −5.10048 −0.172231 −0.0861154 0.996285i \(-0.527445\pi\)
−0.0861154 + 0.996285i \(0.527445\pi\)
\(878\) 90.3480 3.04910
\(879\) −10.6254 −0.358387
\(880\) −3.76797 −0.127018
\(881\) −20.3571 −0.685849 −0.342925 0.939363i \(-0.611418\pi\)
−0.342925 + 0.939363i \(0.611418\pi\)
\(882\) 2.78394 0.0937402
\(883\) −58.6403 −1.97340 −0.986702 0.162538i \(-0.948032\pi\)
−0.986702 + 0.162538i \(0.948032\pi\)
\(884\) 0 0
\(885\) −12.6280 −0.424486
\(886\) −30.7159 −1.03192
\(887\) −24.1256 −0.810058 −0.405029 0.914304i \(-0.632739\pi\)
−0.405029 + 0.914304i \(0.632739\pi\)
\(888\) −1.05696 −0.0354694
\(889\) −20.9759 −0.703508
\(890\) −31.7742 −1.06508
\(891\) −0.134788 −0.00451557
\(892\) −83.4965 −2.79567
\(893\) 15.3568 0.513897
\(894\) 63.2500 2.11540
\(895\) 10.3529 0.346059
\(896\) −63.3232 −2.11548
\(897\) 0 0
\(898\) 56.7382 1.89338
\(899\) −21.1203 −0.704403
\(900\) −14.1879 −0.472930
\(901\) −10.1049 −0.336643
\(902\) 1.39809 0.0465514
\(903\) −0.825682 −0.0274770
\(904\) −60.6856 −2.01837
\(905\) −18.3296 −0.609298
\(906\) −7.44756 −0.247429
\(907\) 18.8848 0.627060 0.313530 0.949578i \(-0.398488\pi\)
0.313530 + 0.949578i \(0.398488\pi\)
\(908\) 85.3966 2.83398
\(909\) 12.2952 0.407806
\(910\) 0 0
\(911\) −15.0686 −0.499245 −0.249623 0.968343i \(-0.580307\pi\)
−0.249623 + 0.968343i \(0.580307\pi\)
\(912\) 104.433 3.45813
\(913\) 2.10662 0.0697189
\(914\) 71.8017 2.37499
\(915\) −6.01468 −0.198839
\(916\) −124.367 −4.10920
\(917\) −8.26962 −0.273087
\(918\) −19.6902 −0.649874
\(919\) 13.6354 0.449790 0.224895 0.974383i \(-0.427796\pi\)
0.224895 + 0.974383i \(0.427796\pi\)
\(920\) −130.845 −4.31384
\(921\) 25.4720 0.839332
\(922\) 3.36909 0.110955
\(923\) 0 0
\(924\) 0.775076 0.0254981
\(925\) 0.249778 0.00821266
\(926\) −59.5339 −1.95641
\(927\) 8.10004 0.266040
\(928\) 221.778 7.28023
\(929\) 26.0326 0.854103 0.427051 0.904227i \(-0.359552\pi\)
0.427051 + 0.904227i \(0.359552\pi\)
\(930\) −11.8225 −0.387674
\(931\) 5.94529 0.194849
\(932\) 44.3706 1.45341
\(933\) −1.16454 −0.0381252
\(934\) 44.1856 1.44580
\(935\) 1.51716 0.0496165
\(936\) 0 0
\(937\) −25.5354 −0.834206 −0.417103 0.908859i \(-0.636954\pi\)
−0.417103 + 0.908859i \(0.636954\pi\)
\(938\) −12.7079 −0.414928
\(939\) 1.26134 0.0411623
\(940\) 23.6381 0.770990
\(941\) −27.5605 −0.898446 −0.449223 0.893420i \(-0.648299\pi\)
−0.449223 + 0.893420i \(0.648299\pi\)
\(942\) 54.8480 1.78704
\(943\) 29.3400 0.955443
\(944\) −139.383 −4.53653
\(945\) −1.59144 −0.0517696
\(946\) −0.309831 −0.0100735
\(947\) −25.3044 −0.822281 −0.411141 0.911572i \(-0.634869\pi\)
−0.411141 + 0.911572i \(0.634869\pi\)
\(948\) 75.2671 2.44456
\(949\) 0 0
\(950\) −40.8374 −1.32494
\(951\) 4.95320 0.160619
\(952\) 73.8450 2.39333
\(953\) −40.8004 −1.32166 −0.660828 0.750537i \(-0.729795\pi\)
−0.660828 + 0.750537i \(0.729795\pi\)
\(954\) 3.97742 0.128774
\(955\) −36.0579 −1.16681
\(956\) 22.0987 0.714722
\(957\) −1.06683 −0.0344857
\(958\) 63.1132 2.03910
\(959\) 10.0528 0.324622
\(960\) 68.2345 2.20226
\(961\) −23.8794 −0.770305
\(962\) 0 0
\(963\) −5.28792 −0.170401
\(964\) −28.0744 −0.904215
\(965\) 20.4502 0.658315
\(966\) 21.9228 0.705356
\(967\) −0.377530 −0.0121406 −0.00607028 0.999982i \(-0.501932\pi\)
−0.00607028 + 0.999982i \(0.501932\pi\)
\(968\) −114.658 −3.68526
\(969\) −42.0498 −1.35083
\(970\) −61.6248 −1.97865
\(971\) 28.1109 0.902120 0.451060 0.892494i \(-0.351046\pi\)
0.451060 + 0.892494i \(0.351046\pi\)
\(972\) 5.75034 0.184442
\(973\) 12.8728 0.412683
\(974\) 97.3625 3.11970
\(975\) 0 0
\(976\) −66.3876 −2.12502
\(977\) −6.53388 −0.209037 −0.104519 0.994523i \(-0.533330\pi\)
−0.104519 + 0.994523i \(0.533330\pi\)
\(978\) 16.6966 0.533899
\(979\) 0.966664 0.0308947
\(980\) 9.15132 0.292328
\(981\) 0.0300910 0.000960731 0
\(982\) −12.0680 −0.385105
\(983\) −4.29547 −0.137004 −0.0685021 0.997651i \(-0.521822\pi\)
−0.0685021 + 0.997651i \(0.521822\pi\)
\(984\) −38.9005 −1.24010
\(985\) 9.79578 0.312119
\(986\) −155.846 −4.96314
\(987\) −2.58303 −0.0822186
\(988\) 0 0
\(989\) −6.50204 −0.206753
\(990\) −0.597175 −0.0189795
\(991\) −7.50668 −0.238458 −0.119229 0.992867i \(-0.538042\pi\)
−0.119229 + 0.992867i \(0.538042\pi\)
\(992\) −74.7707 −2.37397
\(993\) −12.8190 −0.406799
\(994\) 29.7635 0.944042
\(995\) −9.71573 −0.308009
\(996\) −89.8728 −2.84773
\(997\) −14.3663 −0.454985 −0.227493 0.973780i \(-0.573053\pi\)
−0.227493 + 0.973780i \(0.573053\pi\)
\(998\) 58.1508 1.84073
\(999\) −0.101235 −0.00320293
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.1.14 yes 15
13.12 even 2 3549.2.a.bg.1.2 15
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.bg.1.2 15 13.12 even 2
3549.2.a.bh.1.14 yes 15 1.1 even 1 trivial