Properties

Label 3549.2.a.h.1.1
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $1$
Dimension $3$
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: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.169.1
Defining polynomial: \(x^{3} - x^{2} - 4 x - 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 273)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.37720\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} -4.02830 q^{5} +2.37720 q^{6} -1.00000 q^{7} -3.92498 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.37720 q^{2} -1.00000 q^{3} +3.65109 q^{4} -4.02830 q^{5} +2.37720 q^{6} -1.00000 q^{7} -3.92498 q^{8} +1.00000 q^{9} +9.57608 q^{10} -3.27389 q^{11} -3.65109 q^{12} +2.37720 q^{14} +4.02830 q^{15} +2.02830 q^{16} -0.377203 q^{17} -2.37720 q^{18} -3.54778 q^{19} -14.7077 q^{20} +1.00000 q^{21} +7.78270 q^{22} +1.89669 q^{23} +3.92498 q^{24} +11.2272 q^{25} -1.00000 q^{27} -3.65109 q^{28} -8.67939 q^{29} -9.57608 q^{30} +6.33048 q^{31} +3.02830 q^{32} +3.27389 q^{33} +0.896688 q^{34} +4.02830 q^{35} +3.65109 q^{36} +4.02830 q^{37} +8.43380 q^{38} +15.8110 q^{40} +7.50881 q^{41} -2.37720 q^{42} -8.65109 q^{43} -11.9533 q^{44} -4.02830 q^{45} -4.50881 q^{46} -12.1239 q^{47} -2.02830 q^{48} +1.00000 q^{49} -26.6893 q^{50} +0.377203 q^{51} +7.75441 q^{53} +2.37720 q^{54} +13.1882 q^{55} +3.92498 q^{56} +3.54778 q^{57} +20.6327 q^{58} -2.10331 q^{59} +14.7077 q^{60} +7.75441 q^{61} -15.0488 q^{62} -1.00000 q^{63} -11.2555 q^{64} -7.78270 q^{66} +5.58383 q^{67} -1.37720 q^{68} -1.89669 q^{69} -9.57608 q^{70} +3.99225 q^{71} -3.92498 q^{72} +7.50106 q^{73} -9.57608 q^{74} -11.2272 q^{75} -12.9533 q^{76} +3.27389 q^{77} -1.16283 q^{79} -8.17058 q^{80} +1.00000 q^{81} -17.8500 q^{82} +15.1805 q^{83} +3.65109 q^{84} +1.51948 q^{85} +20.5654 q^{86} +8.67939 q^{87} +12.8500 q^{88} +6.35878 q^{89} +9.57608 q^{90} +6.92498 q^{92} -6.33048 q^{93} +28.8209 q^{94} +14.2915 q^{95} -3.02830 q^{96} +4.97170 q^{97} -2.37720 q^{98} -3.27389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{2} - 3q^{3} + 4q^{4} + 2q^{6} - 3q^{7} - 3q^{8} + 3q^{9} + O(q^{10}) \) \( 3q - 2q^{2} - 3q^{3} + 4q^{4} + 2q^{6} - 3q^{7} - 3q^{8} + 3q^{9} + 13q^{10} - 8q^{11} - 4q^{12} + 2q^{14} - 6q^{16} + 4q^{17} - 2q^{18} - 7q^{19} - 13q^{20} + 3q^{21} + q^{22} + 9q^{23} + 3q^{24} + 11q^{25} - 3q^{27} - 4q^{28} - 7q^{29} - 13q^{30} - 7q^{31} - 3q^{32} + 8q^{33} + 6q^{34} + 4q^{36} - 4q^{38} + 13q^{40} + 2q^{41} - 2q^{42} - 19q^{43} - 15q^{44} + 7q^{46} - 17q^{47} + 6q^{48} + 3q^{49} - 16q^{50} - 4q^{51} + 13q^{53} + 2q^{54} + 3q^{56} + 7q^{57} + 22q^{58} - 3q^{59} + 13q^{60} + 13q^{61} - 17q^{62} - 3q^{63} + q^{64} - q^{66} + 5q^{67} + q^{68} - 9q^{69} - 13q^{70} + 8q^{71} - 3q^{72} - 2q^{73} - 13q^{74} - 11q^{75} - 18q^{76} + 8q^{77} - q^{79} - 26q^{80} + 3q^{81} - 36q^{82} + 2q^{83} + 4q^{84} + 13q^{85} + 17q^{86} + 7q^{87} + 21q^{88} - 19q^{89} + 13q^{90} + 12q^{92} + 7q^{93} + 7q^{94} + 3q^{96} + 27q^{97} - 2q^{98} - 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.37720 −1.68094 −0.840468 0.541861i \(-0.817720\pi\)
−0.840468 + 0.541861i \(0.817720\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.65109 1.82555
\(5\) −4.02830 −1.80151 −0.900754 0.434329i \(-0.856986\pi\)
−0.900754 + 0.434329i \(0.856986\pi\)
\(6\) 2.37720 0.970489
\(7\) −1.00000 −0.377964
\(8\) −3.92498 −1.38769
\(9\) 1.00000 0.333333
\(10\) 9.57608 3.02822
\(11\) −3.27389 −0.987115 −0.493558 0.869713i \(-0.664304\pi\)
−0.493558 + 0.869713i \(0.664304\pi\)
\(12\) −3.65109 −1.05398
\(13\) 0 0
\(14\) 2.37720 0.635334
\(15\) 4.02830 1.04010
\(16\) 2.02830 0.507074
\(17\) −0.377203 −0.0914851 −0.0457426 0.998953i \(-0.514565\pi\)
−0.0457426 + 0.998953i \(0.514565\pi\)
\(18\) −2.37720 −0.560312
\(19\) −3.54778 −0.813917 −0.406958 0.913447i \(-0.633411\pi\)
−0.406958 + 0.913447i \(0.633411\pi\)
\(20\) −14.7077 −3.28874
\(21\) 1.00000 0.218218
\(22\) 7.78270 1.65928
\(23\) 1.89669 0.395487 0.197743 0.980254i \(-0.436639\pi\)
0.197743 + 0.980254i \(0.436639\pi\)
\(24\) 3.92498 0.801184
\(25\) 11.2272 2.24543
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) −3.65109 −0.689992
\(29\) −8.67939 −1.61172 −0.805861 0.592105i \(-0.798297\pi\)
−0.805861 + 0.592105i \(0.798297\pi\)
\(30\) −9.57608 −1.74834
\(31\) 6.33048 1.13699 0.568494 0.822687i \(-0.307526\pi\)
0.568494 + 0.822687i \(0.307526\pi\)
\(32\) 3.02830 0.535332
\(33\) 3.27389 0.569911
\(34\) 0.896688 0.153781
\(35\) 4.02830 0.680906
\(36\) 3.65109 0.608516
\(37\) 4.02830 0.662248 0.331124 0.943587i \(-0.392572\pi\)
0.331124 + 0.943587i \(0.392572\pi\)
\(38\) 8.43380 1.36814
\(39\) 0 0
\(40\) 15.8110 2.49994
\(41\) 7.50881 1.17268 0.586340 0.810065i \(-0.300568\pi\)
0.586340 + 0.810065i \(0.300568\pi\)
\(42\) −2.37720 −0.366810
\(43\) −8.65109 −1.31928 −0.659640 0.751582i \(-0.729291\pi\)
−0.659640 + 0.751582i \(0.729291\pi\)
\(44\) −11.9533 −1.80202
\(45\) −4.02830 −0.600503
\(46\) −4.50881 −0.664788
\(47\) −12.1239 −1.76845 −0.884223 0.467064i \(-0.845312\pi\)
−0.884223 + 0.467064i \(0.845312\pi\)
\(48\) −2.02830 −0.292759
\(49\) 1.00000 0.142857
\(50\) −26.6893 −3.77443
\(51\) 0.377203 0.0528190
\(52\) 0 0
\(53\) 7.75441 1.06515 0.532575 0.846383i \(-0.321225\pi\)
0.532575 + 0.846383i \(0.321225\pi\)
\(54\) 2.37720 0.323496
\(55\) 13.1882 1.77830
\(56\) 3.92498 0.524498
\(57\) 3.54778 0.469915
\(58\) 20.6327 2.70920
\(59\) −2.10331 −0.273828 −0.136914 0.990583i \(-0.543718\pi\)
−0.136914 + 0.990583i \(0.543718\pi\)
\(60\) 14.7077 1.89875
\(61\) 7.75441 0.992850 0.496425 0.868080i \(-0.334646\pi\)
0.496425 + 0.868080i \(0.334646\pi\)
\(62\) −15.0488 −1.91120
\(63\) −1.00000 −0.125988
\(64\) −11.2555 −1.40693
\(65\) 0 0
\(66\) −7.78270 −0.957984
\(67\) 5.58383 0.682173 0.341087 0.940032i \(-0.389205\pi\)
0.341087 + 0.940032i \(0.389205\pi\)
\(68\) −1.37720 −0.167010
\(69\) −1.89669 −0.228334
\(70\) −9.57608 −1.14456
\(71\) 3.99225 0.473793 0.236896 0.971535i \(-0.423870\pi\)
0.236896 + 0.971535i \(0.423870\pi\)
\(72\) −3.92498 −0.462564
\(73\) 7.50106 0.877933 0.438966 0.898503i \(-0.355345\pi\)
0.438966 + 0.898503i \(0.355345\pi\)
\(74\) −9.57608 −1.11320
\(75\) −11.2272 −1.29640
\(76\) −12.9533 −1.48584
\(77\) 3.27389 0.373094
\(78\) 0 0
\(79\) −1.16283 −0.130828 −0.0654142 0.997858i \(-0.520837\pi\)
−0.0654142 + 0.997858i \(0.520837\pi\)
\(80\) −8.17058 −0.913498
\(81\) 1.00000 0.111111
\(82\) −17.8500 −1.97120
\(83\) 15.1805 1.66627 0.833135 0.553069i \(-0.186543\pi\)
0.833135 + 0.553069i \(0.186543\pi\)
\(84\) 3.65109 0.398367
\(85\) 1.51948 0.164811
\(86\) 20.5654 2.21762
\(87\) 8.67939 0.930528
\(88\) 12.8500 1.36981
\(89\) 6.35878 0.674029 0.337015 0.941499i \(-0.390583\pi\)
0.337015 + 0.941499i \(0.390583\pi\)
\(90\) 9.57608 1.00941
\(91\) 0 0
\(92\) 6.92498 0.721979
\(93\) −6.33048 −0.656441
\(94\) 28.8209 2.97265
\(95\) 14.2915 1.46628
\(96\) −3.02830 −0.309074
\(97\) 4.97170 0.504800 0.252400 0.967623i \(-0.418780\pi\)
0.252400 + 0.967623i \(0.418780\pi\)
\(98\) −2.37720 −0.240134
\(99\) −3.27389 −0.329038
\(100\) 40.9914 4.09914
\(101\) 5.89669 0.586742 0.293371 0.955999i \(-0.405223\pi\)
0.293371 + 0.955999i \(0.405223\pi\)
\(102\) −0.896688 −0.0887853
\(103\) 10.5654 1.04104 0.520520 0.853849i \(-0.325738\pi\)
0.520520 + 0.853849i \(0.325738\pi\)
\(104\) 0 0
\(105\) −4.02830 −0.393121
\(106\) −18.4338 −1.79045
\(107\) −12.4055 −1.19928 −0.599642 0.800268i \(-0.704691\pi\)
−0.599642 + 0.800268i \(0.704691\pi\)
\(108\) −3.65109 −0.351327
\(109\) −12.1316 −1.16200 −0.580999 0.813905i \(-0.697338\pi\)
−0.580999 + 0.813905i \(0.697338\pi\)
\(110\) −31.3510 −2.98920
\(111\) −4.02830 −0.382349
\(112\) −2.02830 −0.191656
\(113\) −10.6716 −1.00390 −0.501952 0.864896i \(-0.667384\pi\)
−0.501952 + 0.864896i \(0.667384\pi\)
\(114\) −8.43380 −0.789897
\(115\) −7.64042 −0.712473
\(116\) −31.6893 −2.94227
\(117\) 0 0
\(118\) 5.00000 0.460287
\(119\) 0.377203 0.0345781
\(120\) −15.8110 −1.44334
\(121\) −0.281641 −0.0256037
\(122\) −18.4338 −1.66892
\(123\) −7.50881 −0.677047
\(124\) 23.1132 2.07563
\(125\) −25.0849 −2.24366
\(126\) 2.37720 0.211778
\(127\) 7.33048 0.650475 0.325238 0.945632i \(-0.394556\pi\)
0.325238 + 0.945632i \(0.394556\pi\)
\(128\) 20.6999 1.82963
\(129\) 8.65109 0.761686
\(130\) 0 0
\(131\) 11.4239 0.998113 0.499056 0.866570i \(-0.333680\pi\)
0.499056 + 0.866570i \(0.333680\pi\)
\(132\) 11.9533 1.04040
\(133\) 3.54778 0.307632
\(134\) −13.2739 −1.14669
\(135\) 4.02830 0.346701
\(136\) 1.48052 0.126953
\(137\) −3.19112 −0.272636 −0.136318 0.990665i \(-0.543527\pi\)
−0.136318 + 0.990665i \(0.543527\pi\)
\(138\) 4.50881 0.383816
\(139\) 5.37720 0.456088 0.228044 0.973651i \(-0.426767\pi\)
0.228044 + 0.973651i \(0.426767\pi\)
\(140\) 14.7077 1.24303
\(141\) 12.1239 1.02101
\(142\) −9.49039 −0.796416
\(143\) 0 0
\(144\) 2.02830 0.169025
\(145\) 34.9632 2.90353
\(146\) −17.8315 −1.47575
\(147\) −1.00000 −0.0824786
\(148\) 14.7077 1.20896
\(149\) −10.0283 −0.821550 −0.410775 0.911737i \(-0.634742\pi\)
−0.410775 + 0.911737i \(0.634742\pi\)
\(150\) 26.6893 2.17917
\(151\) −9.71544 −0.790631 −0.395315 0.918545i \(-0.629365\pi\)
−0.395315 + 0.918545i \(0.629365\pi\)
\(152\) 13.9250 1.12947
\(153\) −0.377203 −0.0304950
\(154\) −7.78270 −0.627148
\(155\) −25.5011 −2.04829
\(156\) 0 0
\(157\) 17.5761 1.40272 0.701362 0.712805i \(-0.252576\pi\)
0.701362 + 0.712805i \(0.252576\pi\)
\(158\) 2.76428 0.219914
\(159\) −7.75441 −0.614964
\(160\) −12.1989 −0.964406
\(161\) −1.89669 −0.149480
\(162\) −2.37720 −0.186771
\(163\) −5.49119 −0.430103 −0.215052 0.976603i \(-0.568992\pi\)
−0.215052 + 0.976603i \(0.568992\pi\)
\(164\) 27.4154 2.14078
\(165\) −13.1882 −1.02670
\(166\) −36.0870 −2.80090
\(167\) 4.43672 0.343324 0.171662 0.985156i \(-0.445086\pi\)
0.171662 + 0.985156i \(0.445086\pi\)
\(168\) −3.92498 −0.302819
\(169\) 0 0
\(170\) −3.61212 −0.277037
\(171\) −3.54778 −0.271306
\(172\) −31.5860 −2.40841
\(173\) 22.1599 1.68479 0.842393 0.538863i \(-0.181146\pi\)
0.842393 + 0.538863i \(0.181146\pi\)
\(174\) −20.6327 −1.56416
\(175\) −11.2272 −0.848694
\(176\) −6.64042 −0.500540
\(177\) 2.10331 0.158095
\(178\) −15.1161 −1.13300
\(179\) −1.94048 −0.145039 −0.0725193 0.997367i \(-0.523104\pi\)
−0.0725193 + 0.997367i \(0.523104\pi\)
\(180\) −14.7077 −1.09625
\(181\) −8.50106 −0.631879 −0.315939 0.948779i \(-0.602320\pi\)
−0.315939 + 0.948779i \(0.602320\pi\)
\(182\) 0 0
\(183\) −7.75441 −0.573222
\(184\) −7.44447 −0.548814
\(185\) −16.2272 −1.19305
\(186\) 15.0488 1.10343
\(187\) 1.23492 0.0903064
\(188\) −44.2653 −3.22838
\(189\) 1.00000 0.0727393
\(190\) −33.9738 −2.46472
\(191\) 0.651093 0.0471115 0.0235557 0.999723i \(-0.492501\pi\)
0.0235557 + 0.999723i \(0.492501\pi\)
\(192\) 11.2555 0.812293
\(193\) 19.0643 1.37228 0.686141 0.727469i \(-0.259303\pi\)
0.686141 + 0.727469i \(0.259303\pi\)
\(194\) −11.8187 −0.848537
\(195\) 0 0
\(196\) 3.65109 0.260792
\(197\) 24.7098 1.76050 0.880250 0.474509i \(-0.157374\pi\)
0.880250 + 0.474509i \(0.157374\pi\)
\(198\) 7.78270 0.553093
\(199\) 13.1444 0.931782 0.465891 0.884842i \(-0.345734\pi\)
0.465891 + 0.884842i \(0.345734\pi\)
\(200\) −44.0665 −3.11597
\(201\) −5.58383 −0.393853
\(202\) −14.0176 −0.986277
\(203\) 8.67939 0.609174
\(204\) 1.37720 0.0964235
\(205\) −30.2477 −2.11259
\(206\) −25.1161 −1.74992
\(207\) 1.89669 0.131829
\(208\) 0 0
\(209\) 11.6150 0.803430
\(210\) 9.57608 0.660812
\(211\) −19.5966 −1.34909 −0.674544 0.738235i \(-0.735660\pi\)
−0.674544 + 0.738235i \(0.735660\pi\)
\(212\) 28.3121 1.94448
\(213\) −3.99225 −0.273544
\(214\) 29.4904 2.01592
\(215\) 34.8492 2.37669
\(216\) 3.92498 0.267061
\(217\) −6.33048 −0.429741
\(218\) 28.8393 1.95324
\(219\) −7.50106 −0.506875
\(220\) 48.1514 3.24636
\(221\) 0 0
\(222\) 9.57608 0.642704
\(223\) −27.8676 −1.86615 −0.933076 0.359679i \(-0.882886\pi\)
−0.933076 + 0.359679i \(0.882886\pi\)
\(224\) −3.02830 −0.202337
\(225\) 11.2272 0.748478
\(226\) 25.3687 1.68750
\(227\) 12.0304 0.798487 0.399243 0.916845i \(-0.369273\pi\)
0.399243 + 0.916845i \(0.369273\pi\)
\(228\) 12.9533 0.857852
\(229\) −9.19887 −0.607879 −0.303939 0.952691i \(-0.598302\pi\)
−0.303939 + 0.952691i \(0.598302\pi\)
\(230\) 18.1628 1.19762
\(231\) −3.27389 −0.215406
\(232\) 34.0665 2.23657
\(233\) −12.4522 −0.815772 −0.407886 0.913033i \(-0.633734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(234\) 0 0
\(235\) 48.8385 3.18587
\(236\) −7.67939 −0.499886
\(237\) 1.16283 0.0755338
\(238\) −0.896688 −0.0581236
\(239\) −3.24559 −0.209940 −0.104970 0.994475i \(-0.533475\pi\)
−0.104970 + 0.994475i \(0.533475\pi\)
\(240\) 8.17058 0.527409
\(241\) 9.42605 0.607185 0.303592 0.952802i \(-0.401814\pi\)
0.303592 + 0.952802i \(0.401814\pi\)
\(242\) 0.669517 0.0430382
\(243\) −1.00000 −0.0641500
\(244\) 28.3121 1.81249
\(245\) −4.02830 −0.257358
\(246\) 17.8500 1.13807
\(247\) 0 0
\(248\) −24.8470 −1.57779
\(249\) −15.1805 −0.962022
\(250\) 59.6319 3.77145
\(251\) −11.9893 −0.756760 −0.378380 0.925650i \(-0.623519\pi\)
−0.378380 + 0.925650i \(0.623519\pi\)
\(252\) −3.65109 −0.229997
\(253\) −6.20955 −0.390391
\(254\) −17.4260 −1.09341
\(255\) −1.51948 −0.0951538
\(256\) −26.6970 −1.66856
\(257\) 14.5966 0.910512 0.455256 0.890360i \(-0.349548\pi\)
0.455256 + 0.890360i \(0.349548\pi\)
\(258\) −20.5654 −1.28035
\(259\) −4.02830 −0.250306
\(260\) 0 0
\(261\) −8.67939 −0.537241
\(262\) −27.1570 −1.67776
\(263\) 22.6532 1.39686 0.698429 0.715680i \(-0.253883\pi\)
0.698429 + 0.715680i \(0.253883\pi\)
\(264\) −12.8500 −0.790861
\(265\) −31.2370 −1.91888
\(266\) −8.43380 −0.517109
\(267\) −6.35878 −0.389151
\(268\) 20.3871 1.24534
\(269\) −27.9893 −1.70654 −0.853270 0.521470i \(-0.825384\pi\)
−0.853270 + 0.521470i \(0.825384\pi\)
\(270\) −9.57608 −0.582782
\(271\) −7.60730 −0.462110 −0.231055 0.972941i \(-0.574218\pi\)
−0.231055 + 0.972941i \(0.574218\pi\)
\(272\) −0.765079 −0.0463897
\(273\) 0 0
\(274\) 7.58595 0.458284
\(275\) −36.7565 −2.21650
\(276\) −6.92498 −0.416835
\(277\) −6.88894 −0.413916 −0.206958 0.978350i \(-0.566356\pi\)
−0.206958 + 0.978350i \(0.566356\pi\)
\(278\) −12.7827 −0.766656
\(279\) 6.33048 0.378996
\(280\) −15.8110 −0.944888
\(281\) 10.8062 0.644642 0.322321 0.946630i \(-0.395537\pi\)
0.322321 + 0.946630i \(0.395537\pi\)
\(282\) −28.8209 −1.71626
\(283\) −7.62492 −0.453254 −0.226627 0.973982i \(-0.572770\pi\)
−0.226627 + 0.973982i \(0.572770\pi\)
\(284\) 14.5761 0.864931
\(285\) −14.2915 −0.846556
\(286\) 0 0
\(287\) −7.50881 −0.443231
\(288\) 3.02830 0.178444
\(289\) −16.8577 −0.991630
\(290\) −83.1145 −4.88065
\(291\) −4.97170 −0.291446
\(292\) 27.3871 1.60271
\(293\) −22.2915 −1.30228 −0.651142 0.758956i \(-0.725710\pi\)
−0.651142 + 0.758956i \(0.725710\pi\)
\(294\) 2.37720 0.138641
\(295\) 8.47277 0.493303
\(296\) −15.8110 −0.918996
\(297\) 3.27389 0.189970
\(298\) 23.8393 1.38097
\(299\) 0 0
\(300\) −40.9914 −2.36664
\(301\) 8.65109 0.498641
\(302\) 23.0956 1.32900
\(303\) −5.89669 −0.338756
\(304\) −7.19595 −0.412716
\(305\) −31.2370 −1.78863
\(306\) 0.896688 0.0512602
\(307\) −28.2448 −1.61202 −0.806008 0.591905i \(-0.798376\pi\)
−0.806008 + 0.591905i \(0.798376\pi\)
\(308\) 11.9533 0.681101
\(309\) −10.5654 −0.601045
\(310\) 60.6212 3.44305
\(311\) −2.66177 −0.150935 −0.0754675 0.997148i \(-0.524045\pi\)
−0.0754675 + 0.997148i \(0.524045\pi\)
\(312\) 0 0
\(313\) −22.4826 −1.27079 −0.635397 0.772186i \(-0.719163\pi\)
−0.635397 + 0.772186i \(0.719163\pi\)
\(314\) −41.7819 −2.35789
\(315\) 4.02830 0.226969
\(316\) −4.24559 −0.238833
\(317\) 18.8315 1.05768 0.528842 0.848720i \(-0.322626\pi\)
0.528842 + 0.848720i \(0.322626\pi\)
\(318\) 18.4338 1.03372
\(319\) 28.4154 1.59096
\(320\) 45.3404 2.53460
\(321\) 12.4055 0.692407
\(322\) 4.50881 0.251266
\(323\) 1.33823 0.0744613
\(324\) 3.65109 0.202839
\(325\) 0 0
\(326\) 13.0537 0.722976
\(327\) 12.1316 0.670879
\(328\) −29.4720 −1.62732
\(329\) 12.1239 0.668410
\(330\) 31.3510 1.72582
\(331\) −17.8315 −0.980110 −0.490055 0.871691i \(-0.663023\pi\)
−0.490055 + 0.871691i \(0.663023\pi\)
\(332\) 55.4252 3.04186
\(333\) 4.02830 0.220749
\(334\) −10.5470 −0.577105
\(335\) −22.4933 −1.22894
\(336\) 2.02830 0.110653
\(337\) 7.57608 0.412695 0.206348 0.978479i \(-0.433842\pi\)
0.206348 + 0.978479i \(0.433842\pi\)
\(338\) 0 0
\(339\) 10.6716 0.579604
\(340\) 5.54778 0.300871
\(341\) −20.7253 −1.12234
\(342\) 8.43380 0.456047
\(343\) −1.00000 −0.0539949
\(344\) 33.9554 1.83075
\(345\) 7.64042 0.411346
\(346\) −52.6786 −2.83202
\(347\) 7.88814 0.423457 0.211729 0.977328i \(-0.432091\pi\)
0.211729 + 0.977328i \(0.432091\pi\)
\(348\) 31.6893 1.69872
\(349\) −11.7339 −0.628099 −0.314050 0.949407i \(-0.601686\pi\)
−0.314050 + 0.949407i \(0.601686\pi\)
\(350\) 26.6893 1.42660
\(351\) 0 0
\(352\) −9.91431 −0.528435
\(353\) −12.5371 −0.667283 −0.333641 0.942700i \(-0.608277\pi\)
−0.333641 + 0.942700i \(0.608277\pi\)
\(354\) −5.00000 −0.265747
\(355\) −16.0820 −0.853542
\(356\) 23.2165 1.23047
\(357\) −0.377203 −0.0199637
\(358\) 4.61292 0.243801
\(359\) −5.01762 −0.264820 −0.132410 0.991195i \(-0.542272\pi\)
−0.132410 + 0.991195i \(0.542272\pi\)
\(360\) 15.8110 0.833313
\(361\) −6.41325 −0.337539
\(362\) 20.2087 1.06215
\(363\) 0.281641 0.0147823
\(364\) 0 0
\(365\) −30.2165 −1.58160
\(366\) 18.4338 0.963550
\(367\) 23.7098 1.23764 0.618821 0.785532i \(-0.287611\pi\)
0.618821 + 0.785532i \(0.287611\pi\)
\(368\) 3.84704 0.200541
\(369\) 7.50881 0.390893
\(370\) 38.5753 2.00543
\(371\) −7.75441 −0.402589
\(372\) −23.1132 −1.19836
\(373\) −9.95328 −0.515361 −0.257681 0.966230i \(-0.582958\pi\)
−0.257681 + 0.966230i \(0.582958\pi\)
\(374\) −2.93566 −0.151799
\(375\) 25.0849 1.29538
\(376\) 47.5860 2.45406
\(377\) 0 0
\(378\) −2.37720 −0.122270
\(379\) −27.8500 −1.43056 −0.715278 0.698840i \(-0.753700\pi\)
−0.715278 + 0.698840i \(0.753700\pi\)
\(380\) 52.1797 2.67676
\(381\) −7.33048 −0.375552
\(382\) −1.54778 −0.0791914
\(383\) −6.90444 −0.352800 −0.176400 0.984319i \(-0.556445\pi\)
−0.176400 + 0.984319i \(0.556445\pi\)
\(384\) −20.6999 −1.05634
\(385\) −13.1882 −0.672133
\(386\) −45.3198 −2.30672
\(387\) −8.65109 −0.439760
\(388\) 18.1522 0.921536
\(389\) −28.3764 −1.43874 −0.719370 0.694627i \(-0.755570\pi\)
−0.719370 + 0.694627i \(0.755570\pi\)
\(390\) 0 0
\(391\) −0.715436 −0.0361812
\(392\) −3.92498 −0.198242
\(393\) −11.4239 −0.576261
\(394\) −58.7402 −2.95929
\(395\) 4.68422 0.235689
\(396\) −11.9533 −0.600675
\(397\) −4.76720 −0.239259 −0.119630 0.992819i \(-0.538171\pi\)
−0.119630 + 0.992819i \(0.538171\pi\)
\(398\) −31.2469 −1.56627
\(399\) −3.54778 −0.177611
\(400\) 22.7720 1.13860
\(401\) −8.26614 −0.412791 −0.206396 0.978469i \(-0.566173\pi\)
−0.206396 + 0.978469i \(0.566173\pi\)
\(402\) 13.2739 0.662041
\(403\) 0 0
\(404\) 21.5294 1.07113
\(405\) −4.02830 −0.200168
\(406\) −20.6327 −1.02398
\(407\) −13.1882 −0.653715
\(408\) −1.48052 −0.0732964
\(409\) 21.4338 1.05983 0.529916 0.848050i \(-0.322223\pi\)
0.529916 + 0.848050i \(0.322223\pi\)
\(410\) 71.9050 3.55113
\(411\) 3.19112 0.157407
\(412\) 38.5753 1.90047
\(413\) 2.10331 0.103497
\(414\) −4.50881 −0.221596
\(415\) −61.1514 −3.00180
\(416\) 0 0
\(417\) −5.37720 −0.263323
\(418\) −27.6113 −1.35051
\(419\) −2.29151 −0.111948 −0.0559739 0.998432i \(-0.517826\pi\)
−0.0559739 + 0.998432i \(0.517826\pi\)
\(420\) −14.7077 −0.717662
\(421\) 7.61292 0.371031 0.185516 0.982641i \(-0.440604\pi\)
0.185516 + 0.982641i \(0.440604\pi\)
\(422\) 46.5851 2.26773
\(423\) −12.1239 −0.589482
\(424\) −30.4359 −1.47810
\(425\) −4.23492 −0.205424
\(426\) 9.49039 0.459811
\(427\) −7.75441 −0.375262
\(428\) −45.2936 −2.18935
\(429\) 0 0
\(430\) −82.8435 −3.99507
\(431\) 20.8628 1.00492 0.502462 0.864599i \(-0.332428\pi\)
0.502462 + 0.864599i \(0.332428\pi\)
\(432\) −2.02830 −0.0975864
\(433\) −23.3764 −1.12340 −0.561699 0.827342i \(-0.689852\pi\)
−0.561699 + 0.827342i \(0.689852\pi\)
\(434\) 15.0488 0.722368
\(435\) −34.9632 −1.67635
\(436\) −44.2936 −2.12128
\(437\) −6.72903 −0.321893
\(438\) 17.8315 0.852024
\(439\) 9.15508 0.436948 0.218474 0.975843i \(-0.429892\pi\)
0.218474 + 0.975843i \(0.429892\pi\)
\(440\) −51.7635 −2.46773
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 11.2632 0.535132 0.267566 0.963540i \(-0.413781\pi\)
0.267566 + 0.963540i \(0.413781\pi\)
\(444\) −14.7077 −0.697996
\(445\) −25.6150 −1.21427
\(446\) 66.2469 3.13688
\(447\) 10.0283 0.474322
\(448\) 11.2555 0.531771
\(449\) −33.7848 −1.59440 −0.797202 0.603712i \(-0.793688\pi\)
−0.797202 + 0.603712i \(0.793688\pi\)
\(450\) −26.6893 −1.25814
\(451\) −24.5830 −1.15757
\(452\) −38.9632 −1.83267
\(453\) 9.71544 0.456471
\(454\) −28.5987 −1.34221
\(455\) 0 0
\(456\) −13.9250 −0.652097
\(457\) 34.2944 1.60423 0.802113 0.597172i \(-0.203709\pi\)
0.802113 + 0.597172i \(0.203709\pi\)
\(458\) 21.8676 1.02181
\(459\) 0.377203 0.0176063
\(460\) −27.8959 −1.30065
\(461\) 19.3326 0.900409 0.450205 0.892925i \(-0.351351\pi\)
0.450205 + 0.892925i \(0.351351\pi\)
\(462\) 7.78270 0.362084
\(463\) 6.29444 0.292527 0.146264 0.989246i \(-0.453275\pi\)
0.146264 + 0.989246i \(0.453275\pi\)
\(464\) −17.6044 −0.817263
\(465\) 25.5011 1.18258
\(466\) 29.6015 1.37126
\(467\) 24.2293 1.12120 0.560599 0.828087i \(-0.310571\pi\)
0.560599 + 0.828087i \(0.310571\pi\)
\(468\) 0 0
\(469\) −5.58383 −0.257837
\(470\) −116.099 −5.35525
\(471\) −17.5761 −0.809863
\(472\) 8.25547 0.379989
\(473\) 28.3227 1.30228
\(474\) −2.76428 −0.126968
\(475\) −39.8315 −1.82760
\(476\) 1.37720 0.0631240
\(477\) 7.75441 0.355050
\(478\) 7.71544 0.352896
\(479\) −33.6297 −1.53658 −0.768291 0.640101i \(-0.778893\pi\)
−0.768291 + 0.640101i \(0.778893\pi\)
\(480\) 12.1989 0.556800
\(481\) 0 0
\(482\) −22.4076 −1.02064
\(483\) 1.89669 0.0863023
\(484\) −1.02830 −0.0467407
\(485\) −20.0275 −0.909402
\(486\) 2.37720 0.107832
\(487\) −7.92498 −0.359115 −0.179558 0.983747i \(-0.557467\pi\)
−0.179558 + 0.983747i \(0.557467\pi\)
\(488\) −30.4359 −1.37777
\(489\) 5.49119 0.248320
\(490\) 9.57608 0.432603
\(491\) 2.43167 0.109740 0.0548699 0.998494i \(-0.482526\pi\)
0.0548699 + 0.998494i \(0.482526\pi\)
\(492\) −27.4154 −1.23598
\(493\) 3.27389 0.147449
\(494\) 0 0
\(495\) 13.1882 0.592766
\(496\) 12.8401 0.576537
\(497\) −3.99225 −0.179077
\(498\) 36.0870 1.61710
\(499\) −18.5838 −0.831926 −0.415963 0.909381i \(-0.636555\pi\)
−0.415963 + 0.909381i \(0.636555\pi\)
\(500\) −91.5873 −4.09591
\(501\) −4.43672 −0.198218
\(502\) 28.5011 1.27206
\(503\) −17.4543 −0.778251 −0.389125 0.921185i \(-0.627223\pi\)
−0.389125 + 0.921185i \(0.627223\pi\)
\(504\) 3.92498 0.174833
\(505\) −23.7536 −1.05702
\(506\) 14.7614 0.656222
\(507\) 0 0
\(508\) 26.7643 1.18747
\(509\) 2.76991 0.122774 0.0613870 0.998114i \(-0.480448\pi\)
0.0613870 + 0.998114i \(0.480448\pi\)
\(510\) 3.61212 0.159948
\(511\) −7.50106 −0.331827
\(512\) 22.0643 0.975115
\(513\) 3.54778 0.156638
\(514\) −34.6991 −1.53051
\(515\) −42.5606 −1.87544
\(516\) 31.5860 1.39049
\(517\) 39.6922 1.74566
\(518\) 9.57608 0.420749
\(519\) −22.1599 −0.972712
\(520\) 0 0
\(521\) −26.2816 −1.15142 −0.575710 0.817654i \(-0.695274\pi\)
−0.575710 + 0.817654i \(0.695274\pi\)
\(522\) 20.6327 0.903067
\(523\) 5.25042 0.229585 0.114792 0.993389i \(-0.463380\pi\)
0.114792 + 0.993389i \(0.463380\pi\)
\(524\) 41.7098 1.82210
\(525\) 11.2272 0.489994
\(526\) −53.8513 −2.34803
\(527\) −2.38788 −0.104018
\(528\) 6.64042 0.288987
\(529\) −19.4026 −0.843590
\(530\) 74.2568 3.22551
\(531\) −2.10331 −0.0912760
\(532\) 12.9533 0.561596
\(533\) 0 0
\(534\) 15.1161 0.654138
\(535\) 49.9730 2.16052
\(536\) −21.9164 −0.946646
\(537\) 1.94048 0.0837381
\(538\) 66.5363 2.86858
\(539\) −3.27389 −0.141016
\(540\) 14.7077 0.632918
\(541\) −0.111863 −0.00480937 −0.00240468 0.999997i \(-0.500765\pi\)
−0.00240468 + 0.999997i \(0.500765\pi\)
\(542\) 18.0841 0.776778
\(543\) 8.50106 0.364815
\(544\) −1.14228 −0.0489749
\(545\) 48.8697 2.09335
\(546\) 0 0
\(547\) −33.7515 −1.44311 −0.721555 0.692358i \(-0.756572\pi\)
−0.721555 + 0.692358i \(0.756572\pi\)
\(548\) −11.6511 −0.497710
\(549\) 7.75441 0.330950
\(550\) 87.3777 3.72580
\(551\) 30.7926 1.31181
\(552\) 7.44447 0.316858
\(553\) 1.16283 0.0494485
\(554\) 16.3764 0.695767
\(555\) 16.2272 0.688805
\(556\) 19.6327 0.832611
\(557\) 29.0147 1.22939 0.614696 0.788764i \(-0.289279\pi\)
0.614696 + 0.788764i \(0.289279\pi\)
\(558\) −15.0488 −0.637068
\(559\) 0 0
\(560\) 8.17058 0.345270
\(561\) −1.23492 −0.0521384
\(562\) −25.6885 −1.08360
\(563\) 1.43167 0.0603378 0.0301689 0.999545i \(-0.490395\pi\)
0.0301689 + 0.999545i \(0.490395\pi\)
\(564\) 44.2653 1.86391
\(565\) 42.9885 1.80854
\(566\) 18.1260 0.761892
\(567\) −1.00000 −0.0419961
\(568\) −15.6695 −0.657478
\(569\) −24.5011 −1.02714 −0.513569 0.858048i \(-0.671677\pi\)
−0.513569 + 0.858048i \(0.671677\pi\)
\(570\) 33.9738 1.42301
\(571\) −47.3735 −1.98252 −0.991259 0.131929i \(-0.957883\pi\)
−0.991259 + 0.131929i \(0.957883\pi\)
\(572\) 0 0
\(573\) −0.651093 −0.0271998
\(574\) 17.8500 0.745043
\(575\) 21.2944 0.888039
\(576\) −11.2555 −0.468978
\(577\) 27.4055 1.14091 0.570453 0.821330i \(-0.306768\pi\)
0.570453 + 0.821330i \(0.306768\pi\)
\(578\) 40.0742 1.66687
\(579\) −19.0643 −0.792287
\(580\) 127.654 5.30053
\(581\) −15.1805 −0.629791
\(582\) 11.8187 0.489903
\(583\) −25.3871 −1.05143
\(584\) −29.4415 −1.21830
\(585\) 0 0
\(586\) 52.9914 2.18906
\(587\) 27.8959 1.15139 0.575693 0.817666i \(-0.304732\pi\)
0.575693 + 0.817666i \(0.304732\pi\)
\(588\) −3.65109 −0.150569
\(589\) −22.4592 −0.925414
\(590\) −20.1415 −0.829212
\(591\) −24.7098 −1.01643
\(592\) 8.17058 0.335809
\(593\) −16.6015 −0.681740 −0.340870 0.940110i \(-0.610722\pi\)
−0.340870 + 0.940110i \(0.610722\pi\)
\(594\) −7.78270 −0.319328
\(595\) −1.51948 −0.0622928
\(596\) −36.6142 −1.49978
\(597\) −13.1444 −0.537965
\(598\) 0 0
\(599\) 11.7913 0.481778 0.240889 0.970553i \(-0.422561\pi\)
0.240889 + 0.970553i \(0.422561\pi\)
\(600\) 44.0665 1.79901
\(601\) 13.8217 0.563798 0.281899 0.959444i \(-0.409036\pi\)
0.281899 + 0.959444i \(0.409036\pi\)
\(602\) −20.5654 −0.838183
\(603\) 5.58383 0.227391
\(604\) −35.4720 −1.44333
\(605\) 1.13453 0.0461253
\(606\) 14.0176 0.569427
\(607\) −21.0948 −0.856210 −0.428105 0.903729i \(-0.640819\pi\)
−0.428105 + 0.903729i \(0.640819\pi\)
\(608\) −10.7437 −0.435716
\(609\) −8.67939 −0.351707
\(610\) 74.2568 3.00657
\(611\) 0 0
\(612\) −1.37720 −0.0556701
\(613\) 2.19383 0.0886079 0.0443039 0.999018i \(-0.485893\pi\)
0.0443039 + 0.999018i \(0.485893\pi\)
\(614\) 67.1436 2.70970
\(615\) 30.2477 1.21971
\(616\) −12.8500 −0.517740
\(617\) −6.34811 −0.255565 −0.127783 0.991802i \(-0.540786\pi\)
−0.127783 + 0.991802i \(0.540786\pi\)
\(618\) 25.1161 1.01032
\(619\) −7.77203 −0.312384 −0.156192 0.987727i \(-0.549922\pi\)
−0.156192 + 0.987727i \(0.549922\pi\)
\(620\) −93.1068 −3.73926
\(621\) −1.89669 −0.0761115
\(622\) 6.32756 0.253712
\(623\) −6.35878 −0.254759
\(624\) 0 0
\(625\) 44.9135 1.79654
\(626\) 53.4458 2.13612
\(627\) −11.6150 −0.463860
\(628\) 64.1719 2.56074
\(629\) −1.51948 −0.0605858
\(630\) −9.57608 −0.381520
\(631\) 34.2624 1.36397 0.681983 0.731368i \(-0.261118\pi\)
0.681983 + 0.731368i \(0.261118\pi\)
\(632\) 4.56408 0.181549
\(633\) 19.5966 0.778896
\(634\) −44.7664 −1.77790
\(635\) −29.5294 −1.17184
\(636\) −28.3121 −1.12265
\(637\) 0 0
\(638\) −67.5491 −2.67429
\(639\) 3.99225 0.157931
\(640\) −83.3855 −3.29610
\(641\) −23.2186 −0.917080 −0.458540 0.888674i \(-0.651627\pi\)
−0.458540 + 0.888674i \(0.651627\pi\)
\(642\) −29.4904 −1.16389
\(643\) 20.0801 0.791880 0.395940 0.918276i \(-0.370419\pi\)
0.395940 + 0.918276i \(0.370419\pi\)
\(644\) −6.92498 −0.272883
\(645\) −34.8492 −1.37218
\(646\) −3.18125 −0.125165
\(647\) −16.5294 −0.649836 −0.324918 0.945742i \(-0.605337\pi\)
−0.324918 + 0.945742i \(0.605337\pi\)
\(648\) −3.92498 −0.154188
\(649\) 6.88601 0.270300
\(650\) 0 0
\(651\) 6.33048 0.248111
\(652\) −20.0488 −0.785173
\(653\) −0.927907 −0.0363118 −0.0181559 0.999835i \(-0.505780\pi\)
−0.0181559 + 0.999835i \(0.505780\pi\)
\(654\) −28.8393 −1.12771
\(655\) −46.0189 −1.79811
\(656\) 15.2301 0.594635
\(657\) 7.50106 0.292644
\(658\) −28.8209 −1.12355
\(659\) 32.2568 1.25655 0.628273 0.777993i \(-0.283762\pi\)
0.628273 + 0.777993i \(0.283762\pi\)
\(660\) −48.1514 −1.87429
\(661\) −22.8569 −0.889031 −0.444516 0.895771i \(-0.646624\pi\)
−0.444516 + 0.895771i \(0.646624\pi\)
\(662\) 42.3892 1.64750
\(663\) 0 0
\(664\) −59.5830 −2.31227
\(665\) −14.2915 −0.554201
\(666\) −9.57608 −0.371065
\(667\) −16.4621 −0.637415
\(668\) 16.1989 0.626753
\(669\) 27.8676 1.07742
\(670\) 53.4712 2.06577
\(671\) −25.3871 −0.980057
\(672\) 3.02830 0.116819
\(673\) 1.08569 0.0418503 0.0209251 0.999781i \(-0.493339\pi\)
0.0209251 + 0.999781i \(0.493339\pi\)
\(674\) −18.0099 −0.693714
\(675\) −11.2272 −0.432134
\(676\) 0 0
\(677\) −8.60730 −0.330805 −0.165403 0.986226i \(-0.552892\pi\)
−0.165403 + 0.986226i \(0.552892\pi\)
\(678\) −25.3687 −0.974277
\(679\) −4.97170 −0.190796
\(680\) −5.96395 −0.228707
\(681\) −12.0304 −0.461007
\(682\) 49.2683 1.88658
\(683\) 33.4621 1.28039 0.640196 0.768212i \(-0.278853\pi\)
0.640196 + 0.768212i \(0.278853\pi\)
\(684\) −12.9533 −0.495281
\(685\) 12.8548 0.491156
\(686\) 2.37720 0.0907620
\(687\) 9.19887 0.350959
\(688\) −17.5470 −0.668972
\(689\) 0 0
\(690\) −18.1628 −0.691447
\(691\) −4.69219 −0.178499 −0.0892496 0.996009i \(-0.528447\pi\)
−0.0892496 + 0.996009i \(0.528447\pi\)
\(692\) 80.9079 3.07566
\(693\) 3.27389 0.124365
\(694\) −18.7517 −0.711805
\(695\) −21.6610 −0.821647
\(696\) −34.0665 −1.29129
\(697\) −2.83235 −0.107283
\(698\) 27.8938 1.05579
\(699\) 12.4522 0.470986
\(700\) −40.9914 −1.54933
\(701\) 41.4535 1.56568 0.782839 0.622224i \(-0.213771\pi\)
0.782839 + 0.622224i \(0.213771\pi\)
\(702\) 0 0
\(703\) −14.2915 −0.539015
\(704\) 36.8492 1.38881
\(705\) −48.8385 −1.83936
\(706\) 29.8032 1.12166
\(707\) −5.89669 −0.221768
\(708\) 7.67939 0.288609
\(709\) 3.84222 0.144298 0.0721488 0.997394i \(-0.477014\pi\)
0.0721488 + 0.997394i \(0.477014\pi\)
\(710\) 38.2301 1.43475
\(711\) −1.16283 −0.0436095
\(712\) −24.9581 −0.935345
\(713\) 12.0069 0.449664
\(714\) 0.896688 0.0335577
\(715\) 0 0
\(716\) −7.08489 −0.264775
\(717\) 3.24559 0.121209
\(718\) 11.9279 0.445146
\(719\) 8.91219 0.332369 0.166184 0.986095i \(-0.446855\pi\)
0.166184 + 0.986095i \(0.446855\pi\)
\(720\) −8.17058 −0.304499
\(721\) −10.5654 −0.393476
\(722\) 15.2456 0.567382
\(723\) −9.42605 −0.350558
\(724\) −31.0382 −1.15352
\(725\) −97.4450 −3.61902
\(726\) −0.669517 −0.0248481
\(727\) 29.6815 1.10083 0.550413 0.834892i \(-0.314470\pi\)
0.550413 + 0.834892i \(0.314470\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 71.8307 2.65858
\(731\) 3.26322 0.120694
\(732\) −28.3121 −1.04644
\(733\) 5.30299 0.195870 0.0979352 0.995193i \(-0.468776\pi\)
0.0979352 + 0.995193i \(0.468776\pi\)
\(734\) −56.3630 −2.08040
\(735\) 4.02830 0.148586
\(736\) 5.74373 0.211717
\(737\) −18.2808 −0.673383
\(738\) −17.8500 −0.657066
\(739\) −20.9143 −0.769345 −0.384673 0.923053i \(-0.625686\pi\)
−0.384673 + 0.923053i \(0.625686\pi\)
\(740\) −59.2469 −2.17796
\(741\) 0 0
\(742\) 18.4338 0.676726
\(743\) −0.318488 −0.0116842 −0.00584209 0.999983i \(-0.501860\pi\)
−0.00584209 + 0.999983i \(0.501860\pi\)
\(744\) 24.8470 0.910937
\(745\) 40.3969 1.48003
\(746\) 23.6610 0.866290
\(747\) 15.1805 0.555424
\(748\) 4.50881 0.164858
\(749\) 12.4055 0.453287
\(750\) −59.6319 −2.17745
\(751\) 39.5881 1.44459 0.722295 0.691585i \(-0.243087\pi\)
0.722295 + 0.691585i \(0.243087\pi\)
\(752\) −24.5908 −0.896733
\(753\) 11.9893 0.436915
\(754\) 0 0
\(755\) 39.1367 1.42433
\(756\) 3.65109 0.132789
\(757\) −10.2533 −0.372664 −0.186332 0.982487i \(-0.559660\pi\)
−0.186332 + 0.982487i \(0.559660\pi\)
\(758\) 66.2050 2.40467
\(759\) 6.20955 0.225392
\(760\) −56.0940 −2.03474
\(761\) −17.4784 −0.633591 −0.316796 0.948494i \(-0.602607\pi\)
−0.316796 + 0.948494i \(0.602607\pi\)
\(762\) 17.4260 0.631279
\(763\) 12.1316 0.439194
\(764\) 2.37720 0.0860042
\(765\) 1.51948 0.0549371
\(766\) 16.4132 0.593035
\(767\) 0 0
\(768\) 26.6970 0.963345
\(769\) 36.0566 1.30023 0.650117 0.759834i \(-0.274720\pi\)
0.650117 + 0.759834i \(0.274720\pi\)
\(770\) 31.3510 1.12981
\(771\) −14.5966 −0.525685
\(772\) 69.6057 2.50516
\(773\) −10.7184 −0.385513 −0.192756 0.981247i \(-0.561743\pi\)
−0.192756 + 0.981247i \(0.561743\pi\)
\(774\) 20.5654 0.739208
\(775\) 71.0734 2.55303
\(776\) −19.5139 −0.700507
\(777\) 4.02830 0.144514
\(778\) 67.4565 2.41843
\(779\) −26.6396 −0.954463
\(780\) 0 0
\(781\) −13.0702 −0.467688
\(782\) 1.70074 0.0608182
\(783\) 8.67939 0.310176
\(784\) 2.02830 0.0724392
\(785\) −70.8016 −2.52702
\(786\) 27.1570 0.968657
\(787\) −8.95811 −0.319322 −0.159661 0.987172i \(-0.551040\pi\)
−0.159661 + 0.987172i \(0.551040\pi\)
\(788\) 90.2178 3.21388
\(789\) −22.6532 −0.806476
\(790\) −11.1353 −0.396177
\(791\) 10.6716 0.379440
\(792\) 12.8500 0.456604
\(793\) 0 0
\(794\) 11.3326 0.402179
\(795\) 31.2370 1.10786
\(796\) 47.9914 1.70101
\(797\) −36.0686 −1.27761 −0.638807 0.769367i \(-0.720572\pi\)
−0.638807 + 0.769367i \(0.720572\pi\)
\(798\) 8.43380 0.298553
\(799\) 4.57315 0.161787
\(800\) 33.9992 1.20205
\(801\) 6.35878 0.224676
\(802\) 19.6503 0.693876
\(803\) −24.5577 −0.866621
\(804\) −20.3871 −0.718997
\(805\) 7.64042 0.269289
\(806\) 0 0
\(807\) 27.9893 0.985271
\(808\) −23.1444 −0.814217
\(809\) 47.5294 1.67104 0.835522 0.549458i \(-0.185166\pi\)
0.835522 + 0.549458i \(0.185166\pi\)
\(810\) 9.57608 0.336469
\(811\) −5.34678 −0.187751 −0.0938755 0.995584i \(-0.529926\pi\)
−0.0938755 + 0.995584i \(0.529926\pi\)
\(812\) 31.6893 1.11208
\(813\) 7.60730 0.266800
\(814\) 31.3510 1.09885
\(815\) 22.1201 0.774835
\(816\) 0.765079 0.0267831
\(817\) 30.6922 1.07378
\(818\) −50.9525 −1.78151
\(819\) 0 0
\(820\) −110.437 −3.85664
\(821\) −21.8697 −0.763258 −0.381629 0.924316i \(-0.624637\pi\)
−0.381629 + 0.924316i \(0.624637\pi\)
\(822\) −7.58595 −0.264590
\(823\) 22.9942 0.801526 0.400763 0.916182i \(-0.368745\pi\)
0.400763 + 0.916182i \(0.368745\pi\)
\(824\) −41.4690 −1.44464
\(825\) 36.7565 1.27970
\(826\) −5.00000 −0.173972
\(827\) 21.3425 0.742151 0.371075 0.928603i \(-0.378989\pi\)
0.371075 + 0.928603i \(0.378989\pi\)
\(828\) 6.92498 0.240660
\(829\) 27.4309 0.952714 0.476357 0.879252i \(-0.341957\pi\)
0.476357 + 0.879252i \(0.341957\pi\)
\(830\) 145.369 5.04584
\(831\) 6.88894 0.238975
\(832\) 0 0
\(833\) −0.377203 −0.0130693
\(834\) 12.7827 0.442629
\(835\) −17.8724 −0.618501
\(836\) 42.4076 1.46670
\(837\) −6.33048 −0.218814
\(838\) 5.44739 0.188177
\(839\) −4.43167 −0.152998 −0.0764992 0.997070i \(-0.524374\pi\)
−0.0764992 + 0.997070i \(0.524374\pi\)
\(840\) 15.8110 0.545531
\(841\) 46.3318 1.59765
\(842\) −18.0975 −0.623680
\(843\) −10.8062 −0.372184
\(844\) −71.5491 −2.46282
\(845\) 0 0
\(846\) 28.8209 0.990882
\(847\) 0.281641 0.00967729
\(848\) 15.7282 0.540110
\(849\) 7.62492 0.261687
\(850\) 10.0673 0.345304
\(851\) 7.64042 0.261910
\(852\) −14.5761 −0.499368
\(853\) 43.0040 1.47243 0.736215 0.676748i \(-0.236611\pi\)
0.736215 + 0.676748i \(0.236611\pi\)
\(854\) 18.4338 0.630791
\(855\) 14.2915 0.488759
\(856\) 48.6914 1.66424
\(857\) 0.866269 0.0295912 0.0147956 0.999891i \(-0.495290\pi\)
0.0147956 + 0.999891i \(0.495290\pi\)
\(858\) 0 0
\(859\) −15.3481 −0.523671 −0.261835 0.965113i \(-0.584328\pi\)
−0.261835 + 0.965113i \(0.584328\pi\)
\(860\) 127.238 4.33876
\(861\) 7.50881 0.255900
\(862\) −49.5950 −1.68921
\(863\) −37.0275 −1.26043 −0.630215 0.776420i \(-0.717033\pi\)
−0.630215 + 0.776420i \(0.717033\pi\)
\(864\) −3.02830 −0.103025
\(865\) −89.2667 −3.03516
\(866\) 55.5704 1.88836
\(867\) 16.8577 0.572518
\(868\) −23.1132 −0.784513
\(869\) 3.80697 0.129143
\(870\) 83.1145 2.81785
\(871\) 0 0
\(872\) 47.6164 1.61249
\(873\) 4.97170 0.168267
\(874\) 15.9963 0.541082
\(875\) 25.0849 0.848024
\(876\) −27.3871 −0.925324
\(877\) 23.0205 0.777349 0.388674 0.921375i \(-0.372933\pi\)
0.388674 + 0.921375i \(0.372933\pi\)
\(878\) −21.7635 −0.734482
\(879\) 22.2915 0.751874
\(880\) 26.7496 0.901728
\(881\) 38.0168 1.28082 0.640410 0.768034i \(-0.278765\pi\)
0.640410 + 0.768034i \(0.278765\pi\)
\(882\) −2.37720 −0.0800446
\(883\) −6.95620 −0.234095 −0.117047 0.993126i \(-0.537343\pi\)
−0.117047 + 0.993126i \(0.537343\pi\)
\(884\) 0 0
\(885\) −8.47277 −0.284809
\(886\) −26.7750 −0.899522
\(887\) −25.8131 −0.866720 −0.433360 0.901221i \(-0.642672\pi\)
−0.433360 + 0.901221i \(0.642672\pi\)
\(888\) 15.8110 0.530582
\(889\) −7.33048 −0.245857
\(890\) 60.8922 2.04111
\(891\) −3.27389 −0.109679
\(892\) −101.747 −3.40675
\(893\) 43.0128 1.43937
\(894\) −23.8393 −0.797305
\(895\) 7.81684 0.261288
\(896\) −20.6999 −0.691536
\(897\) 0 0
\(898\) 80.3134 2.68009
\(899\) −54.9447 −1.83251
\(900\) 40.9914 1.36638
\(901\) −2.92498 −0.0974453
\(902\) 58.4388 1.94580
\(903\) −8.65109 −0.287890
\(904\) 41.8860 1.39311
\(905\) 34.2448 1.13834
\(906\) −23.0956 −0.767299
\(907\) −2.59158 −0.0860519 −0.0430260 0.999074i \(-0.513700\pi\)
−0.0430260 + 0.999074i \(0.513700\pi\)
\(908\) 43.9242 1.45768
\(909\) 5.89669 0.195581
\(910\) 0 0
\(911\) 36.7507 1.21760 0.608802 0.793322i \(-0.291650\pi\)
0.608802 + 0.793322i \(0.291650\pi\)
\(912\) 7.19595 0.238282
\(913\) −49.6991 −1.64480
\(914\) −81.5248 −2.69660
\(915\) 31.2370 1.03266
\(916\) −33.5860 −1.10971
\(917\) −11.4239 −0.377251
\(918\) −0.896688 −0.0295951
\(919\) −3.16283 −0.104332 −0.0521660 0.998638i \(-0.516613\pi\)
−0.0521660 + 0.998638i \(0.516613\pi\)
\(920\) 29.9885 0.988692
\(921\) 28.2448 0.930698
\(922\) −45.9575 −1.51353
\(923\) 0 0
\(924\) −11.9533 −0.393234
\(925\) 45.2264 1.48703
\(926\) −14.9632 −0.491720
\(927\) 10.5654 0.347013
\(928\) −26.2838 −0.862807
\(929\) 39.5929 1.29900 0.649500 0.760361i \(-0.274978\pi\)
0.649500 + 0.760361i \(0.274978\pi\)
\(930\) −60.6212 −1.98785
\(931\) −3.54778 −0.116274
\(932\) −45.4642 −1.48923
\(933\) 2.66177 0.0871423
\(934\) −57.5979 −1.88466
\(935\) −4.97463 −0.162688
\(936\) 0 0
\(937\) 2.94553 0.0962263 0.0481131 0.998842i \(-0.484679\pi\)
0.0481131 + 0.998842i \(0.484679\pi\)
\(938\) 13.2739 0.433408
\(939\) 22.4826 0.733693
\(940\) 178.314 5.81596
\(941\) 20.9893 0.684232 0.342116 0.939658i \(-0.388856\pi\)
0.342116 + 0.939658i \(0.388856\pi\)
\(942\) 41.7819 1.36133
\(943\) 14.2419 0.463779
\(944\) −4.26614 −0.138851
\(945\) −4.02830 −0.131040
\(946\) −67.3289 −2.18905
\(947\) −6.36733 −0.206910 −0.103455 0.994634i \(-0.532990\pi\)
−0.103455 + 0.994634i \(0.532990\pi\)
\(948\) 4.24559 0.137890
\(949\) 0 0
\(950\) 94.6877 3.07207
\(951\) −18.8315 −0.610655
\(952\) −1.48052 −0.0479838
\(953\) 60.4535 1.95828 0.979141 0.203181i \(-0.0651281\pi\)
0.979141 + 0.203181i \(0.0651281\pi\)
\(954\) −18.4338 −0.596816
\(955\) −2.62280 −0.0848717
\(956\) −11.8500 −0.383255
\(957\) −28.4154 −0.918539
\(958\) 79.9447 2.58290
\(959\) 3.19112 0.103047
\(960\) −45.3404 −1.46335
\(961\) 9.07502 0.292742
\(962\) 0 0
\(963\) −12.4055 −0.399762
\(964\) 34.4154 1.10844
\(965\) −76.7968 −2.47218
\(966\) −4.50881 −0.145069
\(967\) 48.1719 1.54910 0.774552 0.632510i \(-0.217975\pi\)
0.774552 + 0.632510i \(0.217975\pi\)
\(968\) 1.10543 0.0355300
\(969\) −1.33823 −0.0429902
\(970\) 47.6094 1.52865
\(971\) 17.9653 0.576533 0.288267 0.957550i \(-0.406921\pi\)
0.288267 + 0.957550i \(0.406921\pi\)
\(972\) −3.65109 −0.117109
\(973\) −5.37720 −0.172385
\(974\) 18.8393 0.603650
\(975\) 0 0
\(976\) 15.7282 0.503448
\(977\) −2.82672 −0.0904347 −0.0452174 0.998977i \(-0.514398\pi\)
−0.0452174 + 0.998977i \(0.514398\pi\)
\(978\) −13.0537 −0.417410
\(979\) −20.8179 −0.665344
\(980\) −14.7077 −0.469820
\(981\) −12.1316 −0.387332
\(982\) −5.78058 −0.184466
\(983\) −29.8873 −0.953258 −0.476629 0.879105i \(-0.658141\pi\)
−0.476629 + 0.879105i \(0.658141\pi\)
\(984\) 29.4720 0.939532
\(985\) −99.5384 −3.17156
\(986\) −7.78270 −0.247852
\(987\) −12.1239 −0.385907
\(988\) 0 0
\(989\) −16.4084 −0.521757
\(990\) −31.3510 −0.996401
\(991\) 36.9469 1.17366 0.586828 0.809712i \(-0.300377\pi\)
0.586828 + 0.809712i \(0.300377\pi\)
\(992\) 19.1706 0.608666
\(993\) 17.8315 0.565867
\(994\) 9.49039 0.301017
\(995\) −52.9496 −1.67861
\(996\) −55.4252 −1.75622
\(997\) 10.7176 0.339428 0.169714 0.985493i \(-0.445716\pi\)
0.169714 + 0.985493i \(0.445716\pi\)
\(998\) 44.1775 1.39842
\(999\) −4.02830 −0.127450
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.h.1.1 3
13.3 even 3 273.2.k.d.22.3 6
13.9 even 3 273.2.k.d.211.3 yes 6
13.12 even 2 3549.2.a.s.1.3 3
39.29 odd 6 819.2.o.d.568.1 6
39.35 odd 6 819.2.o.d.757.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.k.d.22.3 6 13.3 even 3
273.2.k.d.211.3 yes 6 13.9 even 3
819.2.o.d.568.1 6 39.29 odd 6
819.2.o.d.757.1 6 39.35 odd 6
3549.2.a.h.1.1 3 1.1 even 1 trivial
3549.2.a.s.1.3 3 13.12 even 2