Properties

Label 3640.2.a.y.1.1
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $1$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.0655463357\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: 5.5.1194649.1
Defining polynomial: \( x^{5} - 8x^{3} - 3x^{2} + 10x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.75291\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.75291 q^{3} -1.00000 q^{5} +1.00000 q^{7} +4.57851 q^{9} +O(q^{10})\) \(q-2.75291 q^{3} -1.00000 q^{5} +1.00000 q^{7} +4.57851 q^{9} -0.480110 q^{11} -1.00000 q^{13} +2.75291 q^{15} -3.04559 q^{17} +4.05862 q^{19} -2.75291 q^{21} -5.17109 q^{23} +1.00000 q^{25} -4.34549 q^{27} -5.48402 q^{29} +7.19289 q^{31} +1.32170 q^{33} -1.00000 q^{35} -1.29990 q^{37} +2.75291 q^{39} +4.61829 q^{41} +8.76985 q^{43} -4.57851 q^{45} +4.03874 q^{47} +1.00000 q^{49} +8.38423 q^{51} -11.9458 q^{53} +0.480110 q^{55} -11.1730 q^{57} +1.43121 q^{59} -3.32170 q^{61} +4.57851 q^{63} +1.00000 q^{65} -12.6443 q^{67} +14.2355 q^{69} -7.70401 q^{71} +13.0785 q^{73} -2.75291 q^{75} -0.480110 q^{77} +15.8014 q^{79} -1.77279 q^{81} +15.7026 q^{83} +3.04559 q^{85} +15.0970 q^{87} +12.9356 q^{89} -1.00000 q^{91} -19.8014 q^{93} -4.05862 q^{95} +1.11828 q^{97} -2.19819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 5 q^{5} + 5 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 5 q^{5} + 5 q^{7} + q^{9} - 7 q^{11} - 5 q^{13} + q^{17} + 3 q^{19} - 5 q^{23} + 5 q^{25} - 9 q^{27} - 9 q^{29} + 6 q^{31} + q^{33} - 5 q^{35} - 10 q^{37} - 8 q^{41} + 6 q^{43} - q^{45} - 13 q^{47} + 5 q^{49} - 4 q^{51} - 16 q^{53} + 7 q^{55} - 10 q^{57} - q^{59} - 11 q^{61} + q^{63} + 5 q^{65} - 30 q^{67} - 15 q^{69} - 12 q^{71} + 23 q^{73} - 7 q^{77} + 2 q^{79} - 11 q^{81} - 2 q^{83} - q^{85} - 5 q^{87} - 25 q^{89} - 5 q^{91} - 22 q^{93} - 3 q^{95} - 5 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.75291 −1.58939 −0.794696 0.607007i \(-0.792370\pi\)
−0.794696 + 0.607007i \(0.792370\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 4.57851 1.52617
\(10\) 0 0
\(11\) −0.480110 −0.144759 −0.0723794 0.997377i \(-0.523059\pi\)
−0.0723794 + 0.997377i \(0.523059\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 2.75291 0.710798
\(16\) 0 0
\(17\) −3.04559 −0.738664 −0.369332 0.929298i \(-0.620413\pi\)
−0.369332 + 0.929298i \(0.620413\pi\)
\(18\) 0 0
\(19\) 4.05862 0.931111 0.465555 0.885019i \(-0.345855\pi\)
0.465555 + 0.885019i \(0.345855\pi\)
\(20\) 0 0
\(21\) −2.75291 −0.600734
\(22\) 0 0
\(23\) −5.17109 −1.07825 −0.539123 0.842227i \(-0.681244\pi\)
−0.539123 + 0.842227i \(0.681244\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.34549 −0.836290
\(28\) 0 0
\(29\) −5.48402 −1.01836 −0.509178 0.860661i \(-0.670051\pi\)
−0.509178 + 0.860661i \(0.670051\pi\)
\(30\) 0 0
\(31\) 7.19289 1.29188 0.645940 0.763388i \(-0.276465\pi\)
0.645940 + 0.763388i \(0.276465\pi\)
\(32\) 0 0
\(33\) 1.32170 0.230078
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −1.29990 −0.213702 −0.106851 0.994275i \(-0.534077\pi\)
−0.106851 + 0.994275i \(0.534077\pi\)
\(38\) 0 0
\(39\) 2.75291 0.440818
\(40\) 0 0
\(41\) 4.61829 0.721255 0.360628 0.932710i \(-0.382563\pi\)
0.360628 + 0.932710i \(0.382563\pi\)
\(42\) 0 0
\(43\) 8.76985 1.33739 0.668695 0.743537i \(-0.266853\pi\)
0.668695 + 0.743537i \(0.266853\pi\)
\(44\) 0 0
\(45\) −4.57851 −0.682524
\(46\) 0 0
\(47\) 4.03874 0.589110 0.294555 0.955634i \(-0.404829\pi\)
0.294555 + 0.955634i \(0.404829\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 8.38423 1.17403
\(52\) 0 0
\(53\) −11.9458 −1.64088 −0.820441 0.571732i \(-0.806272\pi\)
−0.820441 + 0.571732i \(0.806272\pi\)
\(54\) 0 0
\(55\) 0.480110 0.0647381
\(56\) 0 0
\(57\) −11.1730 −1.47990
\(58\) 0 0
\(59\) 1.43121 0.186328 0.0931638 0.995651i \(-0.470302\pi\)
0.0931638 + 0.995651i \(0.470302\pi\)
\(60\) 0 0
\(61\) −3.32170 −0.425300 −0.212650 0.977128i \(-0.568209\pi\)
−0.212650 + 0.977128i \(0.568209\pi\)
\(62\) 0 0
\(63\) 4.57851 0.576838
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −12.6443 −1.54475 −0.772376 0.635165i \(-0.780932\pi\)
−0.772376 + 0.635165i \(0.780932\pi\)
\(68\) 0 0
\(69\) 14.2355 1.71376
\(70\) 0 0
\(71\) −7.70401 −0.914297 −0.457149 0.889390i \(-0.651129\pi\)
−0.457149 + 0.889390i \(0.651129\pi\)
\(72\) 0 0
\(73\) 13.0785 1.53072 0.765362 0.643600i \(-0.222560\pi\)
0.765362 + 0.643600i \(0.222560\pi\)
\(74\) 0 0
\(75\) −2.75291 −0.317879
\(76\) 0 0
\(77\) −0.480110 −0.0547137
\(78\) 0 0
\(79\) 15.8014 1.77779 0.888896 0.458109i \(-0.151473\pi\)
0.888896 + 0.458109i \(0.151473\pi\)
\(80\) 0 0
\(81\) −1.77279 −0.196977
\(82\) 0 0
\(83\) 15.7026 1.72359 0.861793 0.507260i \(-0.169342\pi\)
0.861793 + 0.507260i \(0.169342\pi\)
\(84\) 0 0
\(85\) 3.04559 0.330340
\(86\) 0 0
\(87\) 15.0970 1.61857
\(88\) 0 0
\(89\) 12.9356 1.37117 0.685587 0.727991i \(-0.259546\pi\)
0.685587 + 0.727991i \(0.259546\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −19.8014 −2.05331
\(94\) 0 0
\(95\) −4.05862 −0.416405
\(96\) 0 0
\(97\) 1.11828 0.113544 0.0567720 0.998387i \(-0.481919\pi\)
0.0567720 + 0.998387i \(0.481919\pi\)
\(98\) 0 0
\(99\) −2.19819 −0.220926
\(100\) 0 0
\(101\) −17.3411 −1.72551 −0.862754 0.505625i \(-0.831262\pi\)
−0.862754 + 0.505625i \(0.831262\pi\)
\(102\) 0 0
\(103\) 5.63618 0.555349 0.277675 0.960675i \(-0.410436\pi\)
0.277675 + 0.960675i \(0.410436\pi\)
\(104\) 0 0
\(105\) 2.75291 0.268656
\(106\) 0 0
\(107\) 3.89299 0.376349 0.188175 0.982136i \(-0.439743\pi\)
0.188175 + 0.982136i \(0.439743\pi\)
\(108\) 0 0
\(109\) 16.3140 1.56260 0.781300 0.624155i \(-0.214557\pi\)
0.781300 + 0.624155i \(0.214557\pi\)
\(110\) 0 0
\(111\) 3.57851 0.339657
\(112\) 0 0
\(113\) −8.82752 −0.830423 −0.415212 0.909725i \(-0.636292\pi\)
−0.415212 + 0.909725i \(0.636292\pi\)
\(114\) 0 0
\(115\) 5.17109 0.482206
\(116\) 0 0
\(117\) −4.57851 −0.423283
\(118\) 0 0
\(119\) −3.04559 −0.279189
\(120\) 0 0
\(121\) −10.7695 −0.979045
\(122\) 0 0
\(123\) −12.7137 −1.14636
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −19.7863 −1.75575 −0.877877 0.478886i \(-0.841041\pi\)
−0.877877 + 0.478886i \(0.841041\pi\)
\(128\) 0 0
\(129\) −24.1426 −2.12564
\(130\) 0 0
\(131\) 1.54558 0.135038 0.0675189 0.997718i \(-0.478492\pi\)
0.0675189 + 0.997718i \(0.478492\pi\)
\(132\) 0 0
\(133\) 4.05862 0.351927
\(134\) 0 0
\(135\) 4.34549 0.374000
\(136\) 0 0
\(137\) −11.1672 −0.954078 −0.477039 0.878882i \(-0.658290\pi\)
−0.477039 + 0.878882i \(0.658290\pi\)
\(138\) 0 0
\(139\) −12.6192 −1.07035 −0.535175 0.844741i \(-0.679754\pi\)
−0.535175 + 0.844741i \(0.679754\pi\)
\(140\) 0 0
\(141\) −11.1183 −0.936328
\(142\) 0 0
\(143\) 0.480110 0.0401488
\(144\) 0 0
\(145\) 5.48402 0.455423
\(146\) 0 0
\(147\) −2.75291 −0.227056
\(148\) 0 0
\(149\) 1.66387 0.136310 0.0681550 0.997675i \(-0.478289\pi\)
0.0681550 + 0.997675i \(0.478289\pi\)
\(150\) 0 0
\(151\) 1.46745 0.119420 0.0597098 0.998216i \(-0.480982\pi\)
0.0597098 + 0.998216i \(0.480982\pi\)
\(152\) 0 0
\(153\) −13.9442 −1.12733
\(154\) 0 0
\(155\) −7.19289 −0.577747
\(156\) 0 0
\(157\) −23.7196 −1.89303 −0.946513 0.322665i \(-0.895421\pi\)
−0.946513 + 0.322665i \(0.895421\pi\)
\(158\) 0 0
\(159\) 32.8857 2.60800
\(160\) 0 0
\(161\) −5.17109 −0.407539
\(162\) 0 0
\(163\) −6.60716 −0.517513 −0.258756 0.965943i \(-0.583313\pi\)
−0.258756 + 0.965943i \(0.583313\pi\)
\(164\) 0 0
\(165\) −1.32170 −0.102894
\(166\) 0 0
\(167\) −4.33436 −0.335403 −0.167701 0.985838i \(-0.553634\pi\)
−0.167701 + 0.985838i \(0.553634\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 18.5824 1.42103
\(172\) 0 0
\(173\) −18.4696 −1.40422 −0.702109 0.712070i \(-0.747758\pi\)
−0.702109 + 0.712070i \(0.747758\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) −3.93999 −0.296148
\(178\) 0 0
\(179\) −13.9777 −1.04474 −0.522370 0.852719i \(-0.674952\pi\)
−0.522370 + 0.852719i \(0.674952\pi\)
\(180\) 0 0
\(181\) −12.7219 −0.945611 −0.472806 0.881167i \(-0.656759\pi\)
−0.472806 + 0.881167i \(0.656759\pi\)
\(182\) 0 0
\(183\) 9.14434 0.675969
\(184\) 0 0
\(185\) 1.29990 0.0955706
\(186\) 0 0
\(187\) 1.46222 0.106928
\(188\) 0 0
\(189\) −4.34549 −0.316088
\(190\) 0 0
\(191\) 4.29886 0.311055 0.155527 0.987832i \(-0.450292\pi\)
0.155527 + 0.987832i \(0.450292\pi\)
\(192\) 0 0
\(193\) 6.05722 0.436009 0.218004 0.975948i \(-0.430045\pi\)
0.218004 + 0.975948i \(0.430045\pi\)
\(194\) 0 0
\(195\) −2.75291 −0.197140
\(196\) 0 0
\(197\) −7.66032 −0.545775 −0.272888 0.962046i \(-0.587979\pi\)
−0.272888 + 0.962046i \(0.587979\pi\)
\(198\) 0 0
\(199\) −4.91383 −0.348332 −0.174166 0.984716i \(-0.555723\pi\)
−0.174166 + 0.984716i \(0.555723\pi\)
\(200\) 0 0
\(201\) 34.8087 2.45522
\(202\) 0 0
\(203\) −5.48402 −0.384903
\(204\) 0 0
\(205\) −4.61829 −0.322555
\(206\) 0 0
\(207\) −23.6759 −1.64559
\(208\) 0 0
\(209\) −1.94858 −0.134786
\(210\) 0 0
\(211\) −7.03189 −0.484095 −0.242048 0.970264i \(-0.577819\pi\)
−0.242048 + 0.970264i \(0.577819\pi\)
\(212\) 0 0
\(213\) 21.2084 1.45318
\(214\) 0 0
\(215\) −8.76985 −0.598099
\(216\) 0 0
\(217\) 7.19289 0.488285
\(218\) 0 0
\(219\) −36.0040 −2.43292
\(220\) 0 0
\(221\) 3.04559 0.204868
\(222\) 0 0
\(223\) −16.5843 −1.11057 −0.555285 0.831660i \(-0.687391\pi\)
−0.555285 + 0.831660i \(0.687391\pi\)
\(224\) 0 0
\(225\) 4.57851 0.305234
\(226\) 0 0
\(227\) −19.3062 −1.28140 −0.640700 0.767791i \(-0.721356\pi\)
−0.640700 + 0.767791i \(0.721356\pi\)
\(228\) 0 0
\(229\) −0.0339520 −0.00224361 −0.00112181 0.999999i \(-0.500357\pi\)
−0.00112181 + 0.999999i \(0.500357\pi\)
\(230\) 0 0
\(231\) 1.32170 0.0869615
\(232\) 0 0
\(233\) 18.2211 1.19370 0.596852 0.802352i \(-0.296418\pi\)
0.596852 + 0.802352i \(0.296418\pi\)
\(234\) 0 0
\(235\) −4.03874 −0.263458
\(236\) 0 0
\(237\) −43.4997 −2.82561
\(238\) 0 0
\(239\) −15.6642 −1.01324 −0.506618 0.862171i \(-0.669105\pi\)
−0.506618 + 0.862171i \(0.669105\pi\)
\(240\) 0 0
\(241\) −24.3596 −1.56914 −0.784571 0.620039i \(-0.787117\pi\)
−0.784571 + 0.620039i \(0.787117\pi\)
\(242\) 0 0
\(243\) 17.9168 1.14936
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −4.05862 −0.258244
\(248\) 0 0
\(249\) −43.2279 −2.73945
\(250\) 0 0
\(251\) 25.1697 1.58870 0.794348 0.607462i \(-0.207812\pi\)
0.794348 + 0.607462i \(0.207812\pi\)
\(252\) 0 0
\(253\) 2.48269 0.156086
\(254\) 0 0
\(255\) −8.38423 −0.525041
\(256\) 0 0
\(257\) 5.43616 0.339098 0.169549 0.985522i \(-0.445769\pi\)
0.169549 + 0.985522i \(0.445769\pi\)
\(258\) 0 0
\(259\) −1.29990 −0.0807719
\(260\) 0 0
\(261\) −25.1086 −1.55418
\(262\) 0 0
\(263\) 2.43929 0.150413 0.0752065 0.997168i \(-0.476038\pi\)
0.0752065 + 0.997168i \(0.476038\pi\)
\(264\) 0 0
\(265\) 11.9458 0.733824
\(266\) 0 0
\(267\) −35.6106 −2.17933
\(268\) 0 0
\(269\) 5.34113 0.325655 0.162827 0.986655i \(-0.447939\pi\)
0.162827 + 0.986655i \(0.447939\pi\)
\(270\) 0 0
\(271\) 29.5432 1.79462 0.897310 0.441402i \(-0.145519\pi\)
0.897310 + 0.441402i \(0.145519\pi\)
\(272\) 0 0
\(273\) 2.75291 0.166614
\(274\) 0 0
\(275\) −0.480110 −0.0289517
\(276\) 0 0
\(277\) −0.233460 −0.0140273 −0.00701363 0.999975i \(-0.502233\pi\)
−0.00701363 + 0.999975i \(0.502233\pi\)
\(278\) 0 0
\(279\) 32.9327 1.97163
\(280\) 0 0
\(281\) −17.9321 −1.06974 −0.534870 0.844935i \(-0.679639\pi\)
−0.534870 + 0.844935i \(0.679639\pi\)
\(282\) 0 0
\(283\) −25.6401 −1.52415 −0.762074 0.647490i \(-0.775819\pi\)
−0.762074 + 0.647490i \(0.775819\pi\)
\(284\) 0 0
\(285\) 11.1730 0.661832
\(286\) 0 0
\(287\) 4.61829 0.272609
\(288\) 0 0
\(289\) −7.72439 −0.454376
\(290\) 0 0
\(291\) −3.07852 −0.180466
\(292\) 0 0
\(293\) −7.23936 −0.422928 −0.211464 0.977386i \(-0.567823\pi\)
−0.211464 + 0.977386i \(0.567823\pi\)
\(294\) 0 0
\(295\) −1.43121 −0.0833282
\(296\) 0 0
\(297\) 2.08631 0.121060
\(298\) 0 0
\(299\) 5.17109 0.299052
\(300\) 0 0
\(301\) 8.76985 0.505486
\(302\) 0 0
\(303\) 47.7386 2.74251
\(304\) 0 0
\(305\) 3.32170 0.190200
\(306\) 0 0
\(307\) −2.04758 −0.116861 −0.0584307 0.998291i \(-0.518610\pi\)
−0.0584307 + 0.998291i \(0.518610\pi\)
\(308\) 0 0
\(309\) −15.5159 −0.882668
\(310\) 0 0
\(311\) −3.77436 −0.214024 −0.107012 0.994258i \(-0.534128\pi\)
−0.107012 + 0.994258i \(0.534128\pi\)
\(312\) 0 0
\(313\) −13.6332 −0.770596 −0.385298 0.922792i \(-0.625901\pi\)
−0.385298 + 0.922792i \(0.625901\pi\)
\(314\) 0 0
\(315\) −4.57851 −0.257970
\(316\) 0 0
\(317\) −7.18794 −0.403715 −0.201857 0.979415i \(-0.564698\pi\)
−0.201857 + 0.979415i \(0.564698\pi\)
\(318\) 0 0
\(319\) 2.63293 0.147416
\(320\) 0 0
\(321\) −10.7170 −0.598167
\(322\) 0 0
\(323\) −12.3609 −0.687778
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −44.9110 −2.48359
\(328\) 0 0
\(329\) 4.03874 0.222663
\(330\) 0 0
\(331\) 10.2436 0.563037 0.281518 0.959556i \(-0.409162\pi\)
0.281518 + 0.959556i \(0.409162\pi\)
\(332\) 0 0
\(333\) −5.95160 −0.326146
\(334\) 0 0
\(335\) 12.6443 0.690835
\(336\) 0 0
\(337\) −17.7160 −0.965052 −0.482526 0.875882i \(-0.660281\pi\)
−0.482526 + 0.875882i \(0.660281\pi\)
\(338\) 0 0
\(339\) 24.3014 1.31987
\(340\) 0 0
\(341\) −3.45338 −0.187011
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −14.2355 −0.766415
\(346\) 0 0
\(347\) −0.662334 −0.0355559 −0.0177780 0.999842i \(-0.505659\pi\)
−0.0177780 + 0.999842i \(0.505659\pi\)
\(348\) 0 0
\(349\) −26.7604 −1.43245 −0.716224 0.697870i \(-0.754131\pi\)
−0.716224 + 0.697870i \(0.754131\pi\)
\(350\) 0 0
\(351\) 4.34549 0.231945
\(352\) 0 0
\(353\) 5.69202 0.302956 0.151478 0.988461i \(-0.451597\pi\)
0.151478 + 0.988461i \(0.451597\pi\)
\(354\) 0 0
\(355\) 7.70401 0.408886
\(356\) 0 0
\(357\) 8.38423 0.443740
\(358\) 0 0
\(359\) −6.13307 −0.323691 −0.161846 0.986816i \(-0.551745\pi\)
−0.161846 + 0.986816i \(0.551745\pi\)
\(360\) 0 0
\(361\) −2.52762 −0.133033
\(362\) 0 0
\(363\) 29.6474 1.55609
\(364\) 0 0
\(365\) −13.0785 −0.684561
\(366\) 0 0
\(367\) 25.4203 1.32693 0.663465 0.748207i \(-0.269085\pi\)
0.663465 + 0.748207i \(0.269085\pi\)
\(368\) 0 0
\(369\) 21.1449 1.10076
\(370\) 0 0
\(371\) −11.9458 −0.620195
\(372\) 0 0
\(373\) −24.6484 −1.27625 −0.638123 0.769935i \(-0.720289\pi\)
−0.638123 + 0.769935i \(0.720289\pi\)
\(374\) 0 0
\(375\) 2.75291 0.142160
\(376\) 0 0
\(377\) 5.48402 0.282441
\(378\) 0 0
\(379\) −13.3988 −0.688250 −0.344125 0.938924i \(-0.611824\pi\)
−0.344125 + 0.938924i \(0.611824\pi\)
\(380\) 0 0
\(381\) 54.4700 2.79058
\(382\) 0 0
\(383\) −23.5438 −1.20303 −0.601517 0.798860i \(-0.705437\pi\)
−0.601517 + 0.798860i \(0.705437\pi\)
\(384\) 0 0
\(385\) 0.480110 0.0244687
\(386\) 0 0
\(387\) 40.1528 2.04108
\(388\) 0 0
\(389\) 22.7937 1.15569 0.577843 0.816148i \(-0.303895\pi\)
0.577843 + 0.816148i \(0.303895\pi\)
\(390\) 0 0
\(391\) 15.7490 0.796461
\(392\) 0 0
\(393\) −4.25484 −0.214628
\(394\) 0 0
\(395\) −15.8014 −0.795053
\(396\) 0 0
\(397\) −11.2880 −0.566526 −0.283263 0.959042i \(-0.591417\pi\)
−0.283263 + 0.959042i \(0.591417\pi\)
\(398\) 0 0
\(399\) −11.1730 −0.559350
\(400\) 0 0
\(401\) 17.7462 0.886204 0.443102 0.896471i \(-0.353878\pi\)
0.443102 + 0.896471i \(0.353878\pi\)
\(402\) 0 0
\(403\) −7.19289 −0.358303
\(404\) 0 0
\(405\) 1.77279 0.0880906
\(406\) 0 0
\(407\) 0.624096 0.0309353
\(408\) 0 0
\(409\) 7.57756 0.374686 0.187343 0.982295i \(-0.440012\pi\)
0.187343 + 0.982295i \(0.440012\pi\)
\(410\) 0 0
\(411\) 30.7423 1.51640
\(412\) 0 0
\(413\) 1.43121 0.0704252
\(414\) 0 0
\(415\) −15.7026 −0.770811
\(416\) 0 0
\(417\) 34.7396 1.70121
\(418\) 0 0
\(419\) −9.35867 −0.457201 −0.228601 0.973520i \(-0.573415\pi\)
−0.228601 + 0.973520i \(0.573415\pi\)
\(420\) 0 0
\(421\) 14.2277 0.693417 0.346708 0.937973i \(-0.387299\pi\)
0.346708 + 0.937973i \(0.387299\pi\)
\(422\) 0 0
\(423\) 18.4914 0.899082
\(424\) 0 0
\(425\) −3.04559 −0.147733
\(426\) 0 0
\(427\) −3.32170 −0.160748
\(428\) 0 0
\(429\) −1.32170 −0.0638123
\(430\) 0 0
\(431\) 20.1556 0.970861 0.485431 0.874275i \(-0.338663\pi\)
0.485431 + 0.874275i \(0.338663\pi\)
\(432\) 0 0
\(433\) 22.2801 1.07071 0.535356 0.844626i \(-0.320177\pi\)
0.535356 + 0.844626i \(0.320177\pi\)
\(434\) 0 0
\(435\) −15.0970 −0.723846
\(436\) 0 0
\(437\) −20.9875 −1.00397
\(438\) 0 0
\(439\) −14.6823 −0.700746 −0.350373 0.936610i \(-0.613945\pi\)
−0.350373 + 0.936610i \(0.613945\pi\)
\(440\) 0 0
\(441\) 4.57851 0.218024
\(442\) 0 0
\(443\) −5.28346 −0.251025 −0.125512 0.992092i \(-0.540057\pi\)
−0.125512 + 0.992092i \(0.540057\pi\)
\(444\) 0 0
\(445\) −12.9356 −0.613208
\(446\) 0 0
\(447\) −4.58050 −0.216650
\(448\) 0 0
\(449\) 11.8227 0.557947 0.278973 0.960299i \(-0.410006\pi\)
0.278973 + 0.960299i \(0.410006\pi\)
\(450\) 0 0
\(451\) −2.21729 −0.104408
\(452\) 0 0
\(453\) −4.03976 −0.189805
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) 17.0962 0.799725 0.399862 0.916575i \(-0.369058\pi\)
0.399862 + 0.916575i \(0.369058\pi\)
\(458\) 0 0
\(459\) 13.2346 0.617737
\(460\) 0 0
\(461\) −31.3834 −1.46167 −0.730836 0.682553i \(-0.760870\pi\)
−0.730836 + 0.682553i \(0.760870\pi\)
\(462\) 0 0
\(463\) 27.1224 1.26048 0.630241 0.776399i \(-0.282956\pi\)
0.630241 + 0.776399i \(0.282956\pi\)
\(464\) 0 0
\(465\) 19.8014 0.918266
\(466\) 0 0
\(467\) −30.5064 −1.41167 −0.705834 0.708377i \(-0.749428\pi\)
−0.705834 + 0.708377i \(0.749428\pi\)
\(468\) 0 0
\(469\) −12.6443 −0.583862
\(470\) 0 0
\(471\) 65.2978 3.00876
\(472\) 0 0
\(473\) −4.21049 −0.193599
\(474\) 0 0
\(475\) 4.05862 0.186222
\(476\) 0 0
\(477\) −54.6939 −2.50426
\(478\) 0 0
\(479\) 8.54273 0.390327 0.195164 0.980771i \(-0.437476\pi\)
0.195164 + 0.980771i \(0.437476\pi\)
\(480\) 0 0
\(481\) 1.29990 0.0592704
\(482\) 0 0
\(483\) 14.2355 0.647739
\(484\) 0 0
\(485\) −1.11828 −0.0507784
\(486\) 0 0
\(487\) 4.64312 0.210400 0.105200 0.994451i \(-0.466452\pi\)
0.105200 + 0.994451i \(0.466452\pi\)
\(488\) 0 0
\(489\) 18.1889 0.822531
\(490\) 0 0
\(491\) −15.8381 −0.714763 −0.357382 0.933958i \(-0.616330\pi\)
−0.357382 + 0.933958i \(0.616330\pi\)
\(492\) 0 0
\(493\) 16.7021 0.752223
\(494\) 0 0
\(495\) 2.19819 0.0988013
\(496\) 0 0
\(497\) −7.70401 −0.345572
\(498\) 0 0
\(499\) 36.2817 1.62419 0.812096 0.583523i \(-0.198326\pi\)
0.812096 + 0.583523i \(0.198326\pi\)
\(500\) 0 0
\(501\) 11.9321 0.533087
\(502\) 0 0
\(503\) 31.3669 1.39858 0.699290 0.714839i \(-0.253500\pi\)
0.699290 + 0.714839i \(0.253500\pi\)
\(504\) 0 0
\(505\) 17.3411 0.771670
\(506\) 0 0
\(507\) −2.75291 −0.122261
\(508\) 0 0
\(509\) 27.7239 1.22884 0.614420 0.788979i \(-0.289390\pi\)
0.614420 + 0.788979i \(0.289390\pi\)
\(510\) 0 0
\(511\) 13.0785 0.578560
\(512\) 0 0
\(513\) −17.6367 −0.778678
\(514\) 0 0
\(515\) −5.63618 −0.248360
\(516\) 0 0
\(517\) −1.93904 −0.0852789
\(518\) 0 0
\(519\) 50.8451 2.23185
\(520\) 0 0
\(521\) 2.71912 0.119127 0.0595634 0.998225i \(-0.481029\pi\)
0.0595634 + 0.998225i \(0.481029\pi\)
\(522\) 0 0
\(523\) −28.7118 −1.25548 −0.627740 0.778423i \(-0.716020\pi\)
−0.627740 + 0.778423i \(0.716020\pi\)
\(524\) 0 0
\(525\) −2.75291 −0.120147
\(526\) 0 0
\(527\) −21.9066 −0.954265
\(528\) 0 0
\(529\) 3.74014 0.162615
\(530\) 0 0
\(531\) 6.55280 0.284367
\(532\) 0 0
\(533\) −4.61829 −0.200040
\(534\) 0 0
\(535\) −3.89299 −0.168308
\(536\) 0 0
\(537\) 38.4792 1.66050
\(538\) 0 0
\(539\) −0.480110 −0.0206798
\(540\) 0 0
\(541\) 29.4731 1.26715 0.633574 0.773682i \(-0.281587\pi\)
0.633574 + 0.773682i \(0.281587\pi\)
\(542\) 0 0
\(543\) 35.0222 1.50295
\(544\) 0 0
\(545\) −16.3140 −0.698816
\(546\) 0 0
\(547\) 8.21762 0.351360 0.175680 0.984447i \(-0.443788\pi\)
0.175680 + 0.984447i \(0.443788\pi\)
\(548\) 0 0
\(549\) −15.2084 −0.649080
\(550\) 0 0
\(551\) −22.2575 −0.948203
\(552\) 0 0
\(553\) 15.8014 0.671942
\(554\) 0 0
\(555\) −3.57851 −0.151899
\(556\) 0 0
\(557\) 1.10376 0.0467678 0.0233839 0.999727i \(-0.492556\pi\)
0.0233839 + 0.999727i \(0.492556\pi\)
\(558\) 0 0
\(559\) −8.76985 −0.370925
\(560\) 0 0
\(561\) −4.02535 −0.169951
\(562\) 0 0
\(563\) 9.77670 0.412039 0.206019 0.978548i \(-0.433949\pi\)
0.206019 + 0.978548i \(0.433949\pi\)
\(564\) 0 0
\(565\) 8.82752 0.371376
\(566\) 0 0
\(567\) −1.77279 −0.0744502
\(568\) 0 0
\(569\) −26.4686 −1.10962 −0.554810 0.831977i \(-0.687209\pi\)
−0.554810 + 0.831977i \(0.687209\pi\)
\(570\) 0 0
\(571\) −22.6664 −0.948559 −0.474279 0.880374i \(-0.657291\pi\)
−0.474279 + 0.880374i \(0.657291\pi\)
\(572\) 0 0
\(573\) −11.8344 −0.494388
\(574\) 0 0
\(575\) −5.17109 −0.215649
\(576\) 0 0
\(577\) −26.8973 −1.11975 −0.559875 0.828577i \(-0.689151\pi\)
−0.559875 + 0.828577i \(0.689151\pi\)
\(578\) 0 0
\(579\) −16.6750 −0.692989
\(580\) 0 0
\(581\) 15.7026 0.651454
\(582\) 0 0
\(583\) 5.73530 0.237532
\(584\) 0 0
\(585\) 4.57851 0.189298
\(586\) 0 0
\(587\) −26.4855 −1.09317 −0.546587 0.837402i \(-0.684073\pi\)
−0.546587 + 0.837402i \(0.684073\pi\)
\(588\) 0 0
\(589\) 29.1932 1.20288
\(590\) 0 0
\(591\) 21.0882 0.867451
\(592\) 0 0
\(593\) −3.93917 −0.161762 −0.0808811 0.996724i \(-0.525773\pi\)
−0.0808811 + 0.996724i \(0.525773\pi\)
\(594\) 0 0
\(595\) 3.04559 0.124857
\(596\) 0 0
\(597\) 13.5273 0.553637
\(598\) 0 0
\(599\) −47.6048 −1.94508 −0.972540 0.232737i \(-0.925232\pi\)
−0.972540 + 0.232737i \(0.925232\pi\)
\(600\) 0 0
\(601\) −15.3439 −0.625891 −0.312946 0.949771i \(-0.601316\pi\)
−0.312946 + 0.949771i \(0.601316\pi\)
\(602\) 0 0
\(603\) −57.8922 −2.35755
\(604\) 0 0
\(605\) 10.7695 0.437842
\(606\) 0 0
\(607\) −7.06089 −0.286593 −0.143296 0.989680i \(-0.545770\pi\)
−0.143296 + 0.989680i \(0.545770\pi\)
\(608\) 0 0
\(609\) 15.0970 0.611761
\(610\) 0 0
\(611\) −4.03874 −0.163390
\(612\) 0 0
\(613\) −27.7702 −1.12163 −0.560814 0.827942i \(-0.689512\pi\)
−0.560814 + 0.827942i \(0.689512\pi\)
\(614\) 0 0
\(615\) 12.7137 0.512667
\(616\) 0 0
\(617\) −11.3617 −0.457405 −0.228702 0.973496i \(-0.573448\pi\)
−0.228702 + 0.973496i \(0.573448\pi\)
\(618\) 0 0
\(619\) 14.1288 0.567885 0.283942 0.958841i \(-0.408358\pi\)
0.283942 + 0.958841i \(0.408358\pi\)
\(620\) 0 0
\(621\) 22.4709 0.901726
\(622\) 0 0
\(623\) 12.9356 0.518255
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 5.36428 0.214229
\(628\) 0 0
\(629\) 3.95896 0.157854
\(630\) 0 0
\(631\) −44.1768 −1.75865 −0.879325 0.476222i \(-0.842006\pi\)
−0.879325 + 0.476222i \(0.842006\pi\)
\(632\) 0 0
\(633\) 19.3581 0.769417
\(634\) 0 0
\(635\) 19.7863 0.785197
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −35.2729 −1.39537
\(640\) 0 0
\(641\) 29.1197 1.15016 0.575080 0.818097i \(-0.304971\pi\)
0.575080 + 0.818097i \(0.304971\pi\)
\(642\) 0 0
\(643\) 46.6058 1.83795 0.918977 0.394310i \(-0.129016\pi\)
0.918977 + 0.394310i \(0.129016\pi\)
\(644\) 0 0
\(645\) 24.1426 0.950614
\(646\) 0 0
\(647\) −42.2035 −1.65919 −0.829595 0.558365i \(-0.811429\pi\)
−0.829595 + 0.558365i \(0.811429\pi\)
\(648\) 0 0
\(649\) −0.687138 −0.0269725
\(650\) 0 0
\(651\) −19.8014 −0.776077
\(652\) 0 0
\(653\) 43.4964 1.70215 0.851073 0.525048i \(-0.175952\pi\)
0.851073 + 0.525048i \(0.175952\pi\)
\(654\) 0 0
\(655\) −1.54558 −0.0603908
\(656\) 0 0
\(657\) 59.8801 2.33614
\(658\) 0 0
\(659\) −11.7287 −0.456887 −0.228444 0.973557i \(-0.573364\pi\)
−0.228444 + 0.973557i \(0.573364\pi\)
\(660\) 0 0
\(661\) 29.9391 1.16450 0.582248 0.813011i \(-0.302173\pi\)
0.582248 + 0.813011i \(0.302173\pi\)
\(662\) 0 0
\(663\) −8.38423 −0.325616
\(664\) 0 0
\(665\) −4.05862 −0.157386
\(666\) 0 0
\(667\) 28.3583 1.09804
\(668\) 0 0
\(669\) 45.6552 1.76513
\(670\) 0 0
\(671\) 1.59478 0.0615659
\(672\) 0 0
\(673\) −7.10458 −0.273861 −0.136931 0.990581i \(-0.543724\pi\)
−0.136931 + 0.990581i \(0.543724\pi\)
\(674\) 0 0
\(675\) −4.34549 −0.167258
\(676\) 0 0
\(677\) 39.3092 1.51077 0.755387 0.655278i \(-0.227449\pi\)
0.755387 + 0.655278i \(0.227449\pi\)
\(678\) 0 0
\(679\) 1.11828 0.0429156
\(680\) 0 0
\(681\) 53.1483 2.03665
\(682\) 0 0
\(683\) −11.7644 −0.450152 −0.225076 0.974341i \(-0.572263\pi\)
−0.225076 + 0.974341i \(0.572263\pi\)
\(684\) 0 0
\(685\) 11.1672 0.426677
\(686\) 0 0
\(687\) 0.0934668 0.00356598
\(688\) 0 0
\(689\) 11.9458 0.455099
\(690\) 0 0
\(691\) −15.3777 −0.584997 −0.292499 0.956266i \(-0.594487\pi\)
−0.292499 + 0.956266i \(0.594487\pi\)
\(692\) 0 0
\(693\) −2.19819 −0.0835023
\(694\) 0 0
\(695\) 12.6192 0.478675
\(696\) 0 0
\(697\) −14.0654 −0.532765
\(698\) 0 0
\(699\) −50.1610 −1.89726
\(700\) 0 0
\(701\) −9.31103 −0.351673 −0.175836 0.984419i \(-0.556263\pi\)
−0.175836 + 0.984419i \(0.556263\pi\)
\(702\) 0 0
\(703\) −5.27580 −0.198981
\(704\) 0 0
\(705\) 11.1183 0.418739
\(706\) 0 0
\(707\) −17.3411 −0.652180
\(708\) 0 0
\(709\) 7.05246 0.264861 0.132430 0.991192i \(-0.457722\pi\)
0.132430 + 0.991192i \(0.457722\pi\)
\(710\) 0 0
\(711\) 72.3467 2.71321
\(712\) 0 0
\(713\) −37.1950 −1.39297
\(714\) 0 0
\(715\) −0.480110 −0.0179551
\(716\) 0 0
\(717\) 43.1222 1.61043
\(718\) 0 0
\(719\) −24.1940 −0.902283 −0.451141 0.892452i \(-0.648983\pi\)
−0.451141 + 0.892452i \(0.648983\pi\)
\(720\) 0 0
\(721\) 5.63618 0.209902
\(722\) 0 0
\(723\) 67.0599 2.49398
\(724\) 0 0
\(725\) −5.48402 −0.203671
\(726\) 0 0
\(727\) −15.6579 −0.580718 −0.290359 0.956918i \(-0.593775\pi\)
−0.290359 + 0.956918i \(0.593775\pi\)
\(728\) 0 0
\(729\) −44.0049 −1.62981
\(730\) 0 0
\(731\) −26.7093 −0.987881
\(732\) 0 0
\(733\) −37.4320 −1.38258 −0.691291 0.722576i \(-0.742958\pi\)
−0.691291 + 0.722576i \(0.742958\pi\)
\(734\) 0 0
\(735\) 2.75291 0.101543
\(736\) 0 0
\(737\) 6.07068 0.223616
\(738\) 0 0
\(739\) −19.6276 −0.722012 −0.361006 0.932563i \(-0.617567\pi\)
−0.361006 + 0.932563i \(0.617567\pi\)
\(740\) 0 0
\(741\) 11.1730 0.410451
\(742\) 0 0
\(743\) −5.88857 −0.216031 −0.108015 0.994149i \(-0.534450\pi\)
−0.108015 + 0.994149i \(0.534450\pi\)
\(744\) 0 0
\(745\) −1.66387 −0.0609597
\(746\) 0 0
\(747\) 71.8945 2.63048
\(748\) 0 0
\(749\) 3.89299 0.142247
\(750\) 0 0
\(751\) 14.0324 0.512049 0.256025 0.966670i \(-0.417587\pi\)
0.256025 + 0.966670i \(0.417587\pi\)
\(752\) 0 0
\(753\) −69.2899 −2.52506
\(754\) 0 0
\(755\) −1.46745 −0.0534060
\(756\) 0 0
\(757\) −12.2366 −0.444745 −0.222373 0.974962i \(-0.571380\pi\)
−0.222373 + 0.974962i \(0.571380\pi\)
\(758\) 0 0
\(759\) −6.83463 −0.248081
\(760\) 0 0
\(761\) −17.7089 −0.641949 −0.320974 0.947088i \(-0.604010\pi\)
−0.320974 + 0.947088i \(0.604010\pi\)
\(762\) 0 0
\(763\) 16.3140 0.590608
\(764\) 0 0
\(765\) 13.9442 0.504155
\(766\) 0 0
\(767\) −1.43121 −0.0516780
\(768\) 0 0
\(769\) 34.6116 1.24813 0.624063 0.781374i \(-0.285481\pi\)
0.624063 + 0.781374i \(0.285481\pi\)
\(770\) 0 0
\(771\) −14.9652 −0.538960
\(772\) 0 0
\(773\) 28.1810 1.01360 0.506800 0.862063i \(-0.330828\pi\)
0.506800 + 0.862063i \(0.330828\pi\)
\(774\) 0 0
\(775\) 7.19289 0.258376
\(776\) 0 0
\(777\) 3.57851 0.128378
\(778\) 0 0
\(779\) 18.7439 0.671569
\(780\) 0 0
\(781\) 3.69877 0.132353
\(782\) 0 0
\(783\) 23.8307 0.851641
\(784\) 0 0
\(785\) 23.7196 0.846587
\(786\) 0 0
\(787\) 21.4594 0.764946 0.382473 0.923967i \(-0.375072\pi\)
0.382473 + 0.923967i \(0.375072\pi\)
\(788\) 0 0
\(789\) −6.71514 −0.239065
\(790\) 0 0
\(791\) −8.82752 −0.313870
\(792\) 0 0
\(793\) 3.32170 0.117957
\(794\) 0 0
\(795\) −32.8857 −1.16634
\(796\) 0 0
\(797\) 15.4647 0.547788 0.273894 0.961760i \(-0.411688\pi\)
0.273894 + 0.961760i \(0.411688\pi\)
\(798\) 0 0
\(799\) −12.3003 −0.435154
\(800\) 0 0
\(801\) 59.2259 2.09264
\(802\) 0 0
\(803\) −6.27913 −0.221586
\(804\) 0 0
\(805\) 5.17109 0.182257
\(806\) 0 0
\(807\) −14.7037 −0.517593
\(808\) 0 0
\(809\) −36.2656 −1.27503 −0.637516 0.770437i \(-0.720038\pi\)
−0.637516 + 0.770437i \(0.720038\pi\)
\(810\) 0 0
\(811\) 52.1033 1.82960 0.914798 0.403912i \(-0.132350\pi\)
0.914798 + 0.403912i \(0.132350\pi\)
\(812\) 0 0
\(813\) −81.3296 −2.85235
\(814\) 0 0
\(815\) 6.60716 0.231439
\(816\) 0 0
\(817\) 35.5935 1.24526
\(818\) 0 0
\(819\) −4.57851 −0.159986
\(820\) 0 0
\(821\) 10.7092 0.373754 0.186877 0.982383i \(-0.440163\pi\)
0.186877 + 0.982383i \(0.440163\pi\)
\(822\) 0 0
\(823\) −32.2825 −1.12530 −0.562648 0.826697i \(-0.690217\pi\)
−0.562648 + 0.826697i \(0.690217\pi\)
\(824\) 0 0
\(825\) 1.32170 0.0460157
\(826\) 0 0
\(827\) −10.6743 −0.371183 −0.185591 0.982627i \(-0.559420\pi\)
−0.185591 + 0.982627i \(0.559420\pi\)
\(828\) 0 0
\(829\) 47.6105 1.65358 0.826791 0.562509i \(-0.190164\pi\)
0.826791 + 0.562509i \(0.190164\pi\)
\(830\) 0 0
\(831\) 0.642694 0.0222948
\(832\) 0 0
\(833\) −3.04559 −0.105523
\(834\) 0 0
\(835\) 4.33436 0.149997
\(836\) 0 0
\(837\) −31.2566 −1.08039
\(838\) 0 0
\(839\) 13.6762 0.472154 0.236077 0.971734i \(-0.424138\pi\)
0.236077 + 0.971734i \(0.424138\pi\)
\(840\) 0 0
\(841\) 1.07446 0.0370502
\(842\) 0 0
\(843\) 49.3654 1.70024
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) −10.7695 −0.370044
\(848\) 0 0
\(849\) 70.5850 2.42247
\(850\) 0 0
\(851\) 6.72190 0.230424
\(852\) 0 0
\(853\) −36.8199 −1.26069 −0.630344 0.776316i \(-0.717086\pi\)
−0.630344 + 0.776316i \(0.717086\pi\)
\(854\) 0 0
\(855\) −18.5824 −0.635505
\(856\) 0 0
\(857\) −32.3429 −1.10481 −0.552406 0.833575i \(-0.686290\pi\)
−0.552406 + 0.833575i \(0.686290\pi\)
\(858\) 0 0
\(859\) 20.6611 0.704947 0.352473 0.935822i \(-0.385341\pi\)
0.352473 + 0.935822i \(0.385341\pi\)
\(860\) 0 0
\(861\) −12.7137 −0.433283
\(862\) 0 0
\(863\) 31.9507 1.08761 0.543807 0.839210i \(-0.316982\pi\)
0.543807 + 0.839210i \(0.316982\pi\)
\(864\) 0 0
\(865\) 18.4696 0.627985
\(866\) 0 0
\(867\) 21.2646 0.722182
\(868\) 0 0
\(869\) −7.58640 −0.257351
\(870\) 0 0
\(871\) 12.6443 0.428437
\(872\) 0 0
\(873\) 5.12004 0.173287
\(874\) 0 0
\(875\) −1.00000 −0.0338062
\(876\) 0 0
\(877\) 11.5911 0.391402 0.195701 0.980664i \(-0.437302\pi\)
0.195701 + 0.980664i \(0.437302\pi\)
\(878\) 0 0
\(879\) 19.9293 0.672199
\(880\) 0 0
\(881\) −12.7019 −0.427937 −0.213969 0.976841i \(-0.568639\pi\)
−0.213969 + 0.976841i \(0.568639\pi\)
\(882\) 0 0
\(883\) 29.0479 0.977540 0.488770 0.872413i \(-0.337446\pi\)
0.488770 + 0.872413i \(0.337446\pi\)
\(884\) 0 0
\(885\) 3.93999 0.132441
\(886\) 0 0
\(887\) −13.7994 −0.463340 −0.231670 0.972794i \(-0.574419\pi\)
−0.231670 + 0.972794i \(0.574419\pi\)
\(888\) 0 0
\(889\) −19.7863 −0.663613
\(890\) 0 0
\(891\) 0.851135 0.0285141
\(892\) 0 0
\(893\) 16.3917 0.548527
\(894\) 0 0
\(895\) 13.9777 0.467222
\(896\) 0 0
\(897\) −14.2355 −0.475311
\(898\) 0 0
\(899\) −39.4459 −1.31560
\(900\) 0 0
\(901\) 36.3820 1.21206
\(902\) 0 0
\(903\) −24.1426 −0.803415
\(904\) 0 0
\(905\) 12.7219 0.422890
\(906\) 0 0
\(907\) −2.52477 −0.0838336 −0.0419168 0.999121i \(-0.513346\pi\)
−0.0419168 + 0.999121i \(0.513346\pi\)
\(908\) 0 0
\(909\) −79.3965 −2.63342
\(910\) 0 0
\(911\) −18.5669 −0.615148 −0.307574 0.951524i \(-0.599517\pi\)
−0.307574 + 0.951524i \(0.599517\pi\)
\(912\) 0 0
\(913\) −7.53899 −0.249504
\(914\) 0 0
\(915\) −9.14434 −0.302303
\(916\) 0 0
\(917\) 1.54558 0.0510395
\(918\) 0 0
\(919\) −2.12755 −0.0701813 −0.0350907 0.999384i \(-0.511172\pi\)
−0.0350907 + 0.999384i \(0.511172\pi\)
\(920\) 0 0
\(921\) 5.63679 0.185739
\(922\) 0 0
\(923\) 7.70401 0.253580
\(924\) 0 0
\(925\) −1.29990 −0.0427405
\(926\) 0 0
\(927\) 25.8053 0.847557
\(928\) 0 0
\(929\) 36.9945 1.21375 0.606875 0.794797i \(-0.292423\pi\)
0.606875 + 0.794797i \(0.292423\pi\)
\(930\) 0 0
\(931\) 4.05862 0.133016
\(932\) 0 0
\(933\) 10.3905 0.340168
\(934\) 0 0
\(935\) −1.46222 −0.0478197
\(936\) 0 0
\(937\) 15.6718 0.511974 0.255987 0.966680i \(-0.417600\pi\)
0.255987 + 0.966680i \(0.417600\pi\)
\(938\) 0 0
\(939\) 37.5311 1.22478
\(940\) 0 0
\(941\) −41.6448 −1.35758 −0.678791 0.734332i \(-0.737496\pi\)
−0.678791 + 0.734332i \(0.737496\pi\)
\(942\) 0 0
\(943\) −23.8816 −0.777691
\(944\) 0 0
\(945\) 4.34549 0.141359
\(946\) 0 0
\(947\) −18.8055 −0.611097 −0.305548 0.952177i \(-0.598840\pi\)
−0.305548 + 0.952177i \(0.598840\pi\)
\(948\) 0 0
\(949\) −13.0785 −0.424547
\(950\) 0 0
\(951\) 19.7877 0.641661
\(952\) 0 0
\(953\) 18.0320 0.584113 0.292057 0.956401i \(-0.405660\pi\)
0.292057 + 0.956401i \(0.405660\pi\)
\(954\) 0 0
\(955\) −4.29886 −0.139108
\(956\) 0 0
\(957\) −7.24823 −0.234302
\(958\) 0 0
\(959\) −11.1672 −0.360608
\(960\) 0 0
\(961\) 20.7376 0.668956
\(962\) 0 0
\(963\) 17.8241 0.574373
\(964\) 0 0
\(965\) −6.05722 −0.194989
\(966\) 0 0
\(967\) −21.7343 −0.698928 −0.349464 0.936950i \(-0.613636\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(968\) 0 0
\(969\) 34.0284 1.09315
\(970\) 0 0
\(971\) 14.4643 0.464181 0.232090 0.972694i \(-0.425444\pi\)
0.232090 + 0.972694i \(0.425444\pi\)
\(972\) 0 0
\(973\) −12.6192 −0.404554
\(974\) 0 0
\(975\) 2.75291 0.0881636
\(976\) 0 0
\(977\) −12.4145 −0.397177 −0.198588 0.980083i \(-0.563636\pi\)
−0.198588 + 0.980083i \(0.563636\pi\)
\(978\) 0 0
\(979\) −6.21053 −0.198489
\(980\) 0 0
\(981\) 74.6939 2.38479
\(982\) 0 0
\(983\) 17.0057 0.542398 0.271199 0.962523i \(-0.412580\pi\)
0.271199 + 0.962523i \(0.412580\pi\)
\(984\) 0 0
\(985\) 7.66032 0.244078
\(986\) 0 0
\(987\) −11.1183 −0.353899
\(988\) 0 0
\(989\) −45.3496 −1.44203
\(990\) 0 0
\(991\) −15.3159 −0.486525 −0.243263 0.969960i \(-0.578218\pi\)
−0.243263 + 0.969960i \(0.578218\pi\)
\(992\) 0 0
\(993\) −28.1996 −0.894886
\(994\) 0 0
\(995\) 4.91383 0.155779
\(996\) 0 0
\(997\) 25.0386 0.792982 0.396491 0.918039i \(-0.370228\pi\)
0.396491 + 0.918039i \(0.370228\pi\)
\(998\) 0 0
\(999\) 5.64870 0.178717
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 3640.2.a.y.1.1 5
4.3 odd 2 7280.2.a.cc.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.y.1.1 5 1.1 even 1 trivial
7280.2.a.cc.1.5 5 4.3 odd 2