Properties

Label 3640.2.a.o.1.3
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $1$
Dimension $3$
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: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.254102\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.93543 q^{3} -1.00000 q^{5} -1.00000 q^{7} +0.745898 q^{9} +O(q^{10})\) \(q+1.93543 q^{3} -1.00000 q^{5} -1.00000 q^{7} +0.745898 q^{9} -3.18953 q^{11} +1.00000 q^{13} -1.93543 q^{15} +1.44364 q^{17} +2.93543 q^{19} -1.93543 q^{21} -0.173127 q^{23} +1.00000 q^{25} -4.36266 q^{27} -7.63317 q^{29} +2.06457 q^{31} -6.17313 q^{33} +1.00000 q^{35} -7.42723 q^{37} +1.93543 q^{39} +2.76231 q^{41} -7.87086 q^{43} -0.745898 q^{45} +9.53579 q^{47} +1.00000 q^{49} +2.79406 q^{51} -8.37907 q^{53} +3.18953 q^{55} +5.68133 q^{57} -11.9794 q^{59} -2.81047 q^{61} -0.745898 q^{63} -1.00000 q^{65} +3.74590 q^{67} -0.335076 q^{69} -10.2499 q^{71} +1.15672 q^{73} +1.93543 q^{75} +3.18953 q^{77} -2.12497 q^{79} -10.6813 q^{81} -4.98359 q^{83} -1.44364 q^{85} -14.7735 q^{87} +0.108560 q^{89} -1.00000 q^{91} +3.99583 q^{93} -2.93543 q^{95} +10.4231 q^{97} -2.37907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 2 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 2 q^{3} - 3 q^{5} - 3 q^{7} + 3 q^{9} - q^{11} + 3 q^{13} + 2 q^{15} - 5 q^{17} + q^{19} + 2 q^{21} + 5 q^{23} + 3 q^{25} + q^{27} - 5 q^{29} + 14 q^{31} - 13 q^{33} + 3 q^{35} - 16 q^{37} - 2 q^{39} + 6 q^{41} - 8 q^{43} - 3 q^{45} + 9 q^{47} + 3 q^{49} + 20 q^{51} - 8 q^{53} + q^{55} + 10 q^{57} - 7 q^{59} - 17 q^{61} - 3 q^{63} - 3 q^{65} + 12 q^{67} - 5 q^{69} + 2 q^{71} + q^{73} - 2 q^{75} + q^{77} + 10 q^{79} - 25 q^{81} - 18 q^{83} + 5 q^{85} - 27 q^{87} - 13 q^{89} - 3 q^{91} - 20 q^{93} - q^{95} - 7 q^{97} + 10 q^{99}+O(q^{100}) \) 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
\(3\) 1.93543 1.11742 0.558711 0.829362i \(-0.311296\pi\)
0.558711 + 0.829362i \(0.311296\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0.745898 0.248633
\(10\) 0 0
\(11\) −3.18953 −0.961681 −0.480840 0.876808i \(-0.659668\pi\)
−0.480840 + 0.876808i \(0.659668\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −1.93543 −0.499726
\(16\) 0 0
\(17\) 1.44364 0.350133 0.175067 0.984557i \(-0.443986\pi\)
0.175067 + 0.984557i \(0.443986\pi\)
\(18\) 0 0
\(19\) 2.93543 0.673434 0.336717 0.941606i \(-0.390683\pi\)
0.336717 + 0.941606i \(0.390683\pi\)
\(20\) 0 0
\(21\) −1.93543 −0.422346
\(22\) 0 0
\(23\) −0.173127 −0.0360995 −0.0180498 0.999837i \(-0.505746\pi\)
−0.0180498 + 0.999837i \(0.505746\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.36266 −0.839595
\(28\) 0 0
\(29\) −7.63317 −1.41744 −0.708722 0.705488i \(-0.750728\pi\)
−0.708722 + 0.705488i \(0.750728\pi\)
\(30\) 0 0
\(31\) 2.06457 0.370807 0.185404 0.982662i \(-0.440641\pi\)
0.185404 + 0.982662i \(0.440641\pi\)
\(32\) 0 0
\(33\) −6.17313 −1.07460
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −7.42723 −1.22103 −0.610514 0.792005i \(-0.709037\pi\)
−0.610514 + 0.792005i \(0.709037\pi\)
\(38\) 0 0
\(39\) 1.93543 0.309917
\(40\) 0 0
\(41\) 2.76231 0.431400 0.215700 0.976460i \(-0.430797\pi\)
0.215700 + 0.976460i \(0.430797\pi\)
\(42\) 0 0
\(43\) −7.87086 −1.20030 −0.600148 0.799889i \(-0.704892\pi\)
−0.600148 + 0.799889i \(0.704892\pi\)
\(44\) 0 0
\(45\) −0.745898 −0.111192
\(46\) 0 0
\(47\) 9.53579 1.39094 0.695469 0.718556i \(-0.255197\pi\)
0.695469 + 0.718556i \(0.255197\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 2.79406 0.391247
\(52\) 0 0
\(53\) −8.37907 −1.15095 −0.575477 0.817818i \(-0.695183\pi\)
−0.575477 + 0.817818i \(0.695183\pi\)
\(54\) 0 0
\(55\) 3.18953 0.430077
\(56\) 0 0
\(57\) 5.68133 0.752511
\(58\) 0 0
\(59\) −11.9794 −1.55959 −0.779794 0.626036i \(-0.784676\pi\)
−0.779794 + 0.626036i \(0.784676\pi\)
\(60\) 0 0
\(61\) −2.81047 −0.359843 −0.179922 0.983681i \(-0.557584\pi\)
−0.179922 + 0.983681i \(0.557584\pi\)
\(62\) 0 0
\(63\) −0.745898 −0.0939744
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 3.74590 0.457634 0.228817 0.973469i \(-0.426514\pi\)
0.228817 + 0.973469i \(0.426514\pi\)
\(68\) 0 0
\(69\) −0.335076 −0.0403384
\(70\) 0 0
\(71\) −10.2499 −1.21644 −0.608222 0.793767i \(-0.708117\pi\)
−0.608222 + 0.793767i \(0.708117\pi\)
\(72\) 0 0
\(73\) 1.15672 0.135384 0.0676919 0.997706i \(-0.478436\pi\)
0.0676919 + 0.997706i \(0.478436\pi\)
\(74\) 0 0
\(75\) 1.93543 0.223484
\(76\) 0 0
\(77\) 3.18953 0.363481
\(78\) 0 0
\(79\) −2.12497 −0.239077 −0.119539 0.992830i \(-0.538142\pi\)
−0.119539 + 0.992830i \(0.538142\pi\)
\(80\) 0 0
\(81\) −10.6813 −1.18681
\(82\) 0 0
\(83\) −4.98359 −0.547020 −0.273510 0.961869i \(-0.588185\pi\)
−0.273510 + 0.961869i \(0.588185\pi\)
\(84\) 0 0
\(85\) −1.44364 −0.156584
\(86\) 0 0
\(87\) −14.7735 −1.58388
\(88\) 0 0
\(89\) 0.108560 0.0115073 0.00575365 0.999983i \(-0.498169\pi\)
0.00575365 + 0.999983i \(0.498169\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 3.99583 0.414348
\(94\) 0 0
\(95\) −2.93543 −0.301169
\(96\) 0 0
\(97\) 10.4231 1.05830 0.529151 0.848528i \(-0.322511\pi\)
0.529151 + 0.848528i \(0.322511\pi\)
\(98\) 0 0
\(99\) −2.37907 −0.239105
\(100\) 0 0
\(101\) 1.15672 0.115098 0.0575490 0.998343i \(-0.481671\pi\)
0.0575490 + 0.998343i \(0.481671\pi\)
\(102\) 0 0
\(103\) −13.6608 −1.34603 −0.673017 0.739627i \(-0.735002\pi\)
−0.673017 + 0.739627i \(0.735002\pi\)
\(104\) 0 0
\(105\) 1.93543 0.188879
\(106\) 0 0
\(107\) 3.23353 0.312597 0.156298 0.987710i \(-0.450044\pi\)
0.156298 + 0.987710i \(0.450044\pi\)
\(108\) 0 0
\(109\) −11.7089 −1.12151 −0.560755 0.827982i \(-0.689489\pi\)
−0.560755 + 0.827982i \(0.689489\pi\)
\(110\) 0 0
\(111\) −14.3749 −1.36441
\(112\) 0 0
\(113\) −18.7693 −1.76567 −0.882834 0.469685i \(-0.844368\pi\)
−0.882834 + 0.469685i \(0.844368\pi\)
\(114\) 0 0
\(115\) 0.173127 0.0161442
\(116\) 0 0
\(117\) 0.745898 0.0689583
\(118\) 0 0
\(119\) −1.44364 −0.132338
\(120\) 0 0
\(121\) −0.826873 −0.0751702
\(122\) 0 0
\(123\) 5.34625 0.482056
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −13.9477 −1.23766 −0.618828 0.785527i \(-0.712392\pi\)
−0.618828 + 0.785527i \(0.712392\pi\)
\(128\) 0 0
\(129\) −15.2335 −1.34124
\(130\) 0 0
\(131\) −19.3627 −1.69172 −0.845862 0.533402i \(-0.820913\pi\)
−0.845862 + 0.533402i \(0.820913\pi\)
\(132\) 0 0
\(133\) −2.93543 −0.254534
\(134\) 0 0
\(135\) 4.36266 0.375478
\(136\) 0 0
\(137\) 18.3585 1.56847 0.784236 0.620463i \(-0.213055\pi\)
0.784236 + 0.620463i \(0.213055\pi\)
\(138\) 0 0
\(139\) 20.5962 1.74695 0.873473 0.486873i \(-0.161862\pi\)
0.873473 + 0.486873i \(0.161862\pi\)
\(140\) 0 0
\(141\) 18.4559 1.55426
\(142\) 0 0
\(143\) −3.18953 −0.266722
\(144\) 0 0
\(145\) 7.63317 0.633900
\(146\) 0 0
\(147\) 1.93543 0.159632
\(148\) 0 0
\(149\) −17.8820 −1.46495 −0.732477 0.680792i \(-0.761636\pi\)
−0.732477 + 0.680792i \(0.761636\pi\)
\(150\) 0 0
\(151\) 2.16195 0.175937 0.0879685 0.996123i \(-0.471963\pi\)
0.0879685 + 0.996123i \(0.471963\pi\)
\(152\) 0 0
\(153\) 1.07681 0.0870546
\(154\) 0 0
\(155\) −2.06457 −0.165830
\(156\) 0 0
\(157\) 0.660755 0.0527340 0.0263670 0.999652i \(-0.491606\pi\)
0.0263670 + 0.999652i \(0.491606\pi\)
\(158\) 0 0
\(159\) −16.2171 −1.28610
\(160\) 0 0
\(161\) 0.173127 0.0136443
\(162\) 0 0
\(163\) 14.9630 1.17199 0.585997 0.810313i \(-0.300703\pi\)
0.585997 + 0.810313i \(0.300703\pi\)
\(164\) 0 0
\(165\) 6.17313 0.480577
\(166\) 0 0
\(167\) 12.9753 1.00406 0.502028 0.864852i \(-0.332588\pi\)
0.502028 + 0.864852i \(0.332588\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.18953 0.167438
\(172\) 0 0
\(173\) 5.34209 0.406151 0.203076 0.979163i \(-0.434906\pi\)
0.203076 + 0.979163i \(0.434906\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0 0
\(177\) −23.1854 −1.74272
\(178\) 0 0
\(179\) 5.57277 0.416528 0.208264 0.978073i \(-0.433219\pi\)
0.208264 + 0.978073i \(0.433219\pi\)
\(180\) 0 0
\(181\) 11.0932 0.824552 0.412276 0.911059i \(-0.364734\pi\)
0.412276 + 0.911059i \(0.364734\pi\)
\(182\) 0 0
\(183\) −5.43947 −0.402097
\(184\) 0 0
\(185\) 7.42723 0.546061
\(186\) 0 0
\(187\) −4.60453 −0.336716
\(188\) 0 0
\(189\) 4.36266 0.317337
\(190\) 0 0
\(191\) −8.23769 −0.596059 −0.298029 0.954557i \(-0.596329\pi\)
−0.298029 + 0.954557i \(0.596329\pi\)
\(192\) 0 0
\(193\) 5.28169 0.380184 0.190092 0.981766i \(-0.439121\pi\)
0.190092 + 0.981766i \(0.439121\pi\)
\(194\) 0 0
\(195\) −1.93543 −0.138599
\(196\) 0 0
\(197\) −12.9190 −0.920442 −0.460221 0.887804i \(-0.652230\pi\)
−0.460221 + 0.887804i \(0.652230\pi\)
\(198\) 0 0
\(199\) −5.14554 −0.364758 −0.182379 0.983228i \(-0.558380\pi\)
−0.182379 + 0.983228i \(0.558380\pi\)
\(200\) 0 0
\(201\) 7.24993 0.511371
\(202\) 0 0
\(203\) 7.63317 0.535743
\(204\) 0 0
\(205\) −2.76231 −0.192928
\(206\) 0 0
\(207\) −0.129135 −0.00897553
\(208\) 0 0
\(209\) −9.36266 −0.647629
\(210\) 0 0
\(211\) 25.8227 1.77771 0.888854 0.458190i \(-0.151502\pi\)
0.888854 + 0.458190i \(0.151502\pi\)
\(212\) 0 0
\(213\) −19.8381 −1.35928
\(214\) 0 0
\(215\) 7.87086 0.536789
\(216\) 0 0
\(217\) −2.06457 −0.140152
\(218\) 0 0
\(219\) 2.23875 0.151281
\(220\) 0 0
\(221\) 1.44364 0.0971094
\(222\) 0 0
\(223\) 7.69774 0.515479 0.257739 0.966214i \(-0.417022\pi\)
0.257739 + 0.966214i \(0.417022\pi\)
\(224\) 0 0
\(225\) 0.745898 0.0497266
\(226\) 0 0
\(227\) −6.00000 −0.398234 −0.199117 0.979976i \(-0.563807\pi\)
−0.199117 + 0.979976i \(0.563807\pi\)
\(228\) 0 0
\(229\) −4.68550 −0.309627 −0.154813 0.987944i \(-0.549478\pi\)
−0.154813 + 0.987944i \(0.549478\pi\)
\(230\) 0 0
\(231\) 6.17313 0.406162
\(232\) 0 0
\(233\) 15.8820 1.04047 0.520234 0.854024i \(-0.325845\pi\)
0.520234 + 0.854024i \(0.325845\pi\)
\(234\) 0 0
\(235\) −9.53579 −0.622046
\(236\) 0 0
\(237\) −4.11273 −0.267150
\(238\) 0 0
\(239\) 6.75814 0.437147 0.218574 0.975820i \(-0.429860\pi\)
0.218574 + 0.975820i \(0.429860\pi\)
\(240\) 0 0
\(241\) −8.33091 −0.536641 −0.268320 0.963330i \(-0.586469\pi\)
−0.268320 + 0.963330i \(0.586469\pi\)
\(242\) 0 0
\(243\) −7.58501 −0.486579
\(244\) 0 0
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 2.93543 0.186777
\(248\) 0 0
\(249\) −9.64541 −0.611253
\(250\) 0 0
\(251\) 13.7857 0.870147 0.435074 0.900395i \(-0.356722\pi\)
0.435074 + 0.900395i \(0.356722\pi\)
\(252\) 0 0
\(253\) 0.552195 0.0347162
\(254\) 0 0
\(255\) −2.79406 −0.174971
\(256\) 0 0
\(257\) −14.3463 −0.894895 −0.447447 0.894310i \(-0.647667\pi\)
−0.447447 + 0.894310i \(0.647667\pi\)
\(258\) 0 0
\(259\) 7.42723 0.461506
\(260\) 0 0
\(261\) −5.69357 −0.352423
\(262\) 0 0
\(263\) −23.1044 −1.42468 −0.712339 0.701836i \(-0.752364\pi\)
−0.712339 + 0.701836i \(0.752364\pi\)
\(264\) 0 0
\(265\) 8.37907 0.514722
\(266\) 0 0
\(267\) 0.210110 0.0128585
\(268\) 0 0
\(269\) −6.23875 −0.380384 −0.190192 0.981747i \(-0.560911\pi\)
−0.190192 + 0.981747i \(0.560911\pi\)
\(270\) 0 0
\(271\) 26.9313 1.63596 0.817979 0.575248i \(-0.195095\pi\)
0.817979 + 0.575248i \(0.195095\pi\)
\(272\) 0 0
\(273\) −1.93543 −0.117138
\(274\) 0 0
\(275\) −3.18953 −0.192336
\(276\) 0 0
\(277\) −12.2583 −0.736528 −0.368264 0.929721i \(-0.620048\pi\)
−0.368264 + 0.929721i \(0.620048\pi\)
\(278\) 0 0
\(279\) 1.53996 0.0921948
\(280\) 0 0
\(281\) 1.14554 0.0683373 0.0341687 0.999416i \(-0.489122\pi\)
0.0341687 + 0.999416i \(0.489122\pi\)
\(282\) 0 0
\(283\) −30.4629 −1.81083 −0.905415 0.424527i \(-0.860440\pi\)
−0.905415 + 0.424527i \(0.860440\pi\)
\(284\) 0 0
\(285\) −5.68133 −0.336533
\(286\) 0 0
\(287\) −2.76231 −0.163054
\(288\) 0 0
\(289\) −14.9159 −0.877407
\(290\) 0 0
\(291\) 20.1731 1.18257
\(292\) 0 0
\(293\) −7.26634 −0.424504 −0.212252 0.977215i \(-0.568080\pi\)
−0.212252 + 0.977215i \(0.568080\pi\)
\(294\) 0 0
\(295\) 11.9794 0.697469
\(296\) 0 0
\(297\) 13.9149 0.807422
\(298\) 0 0
\(299\) −0.173127 −0.0100122
\(300\) 0 0
\(301\) 7.87086 0.453669
\(302\) 0 0
\(303\) 2.23875 0.128613
\(304\) 0 0
\(305\) 2.81047 0.160927
\(306\) 0 0
\(307\) 15.1044 0.862053 0.431027 0.902339i \(-0.358152\pi\)
0.431027 + 0.902339i \(0.358152\pi\)
\(308\) 0 0
\(309\) −26.4395 −1.50409
\(310\) 0 0
\(311\) 21.8709 1.24018 0.620091 0.784530i \(-0.287095\pi\)
0.620091 + 0.784530i \(0.287095\pi\)
\(312\) 0 0
\(313\) 16.8667 0.953362 0.476681 0.879076i \(-0.341840\pi\)
0.476681 + 0.879076i \(0.341840\pi\)
\(314\) 0 0
\(315\) 0.745898 0.0420266
\(316\) 0 0
\(317\) 14.6402 0.822274 0.411137 0.911573i \(-0.365132\pi\)
0.411137 + 0.911573i \(0.365132\pi\)
\(318\) 0 0
\(319\) 24.3463 1.36313
\(320\) 0 0
\(321\) 6.25827 0.349303
\(322\) 0 0
\(323\) 4.23769 0.235792
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −22.6618 −1.25320
\(328\) 0 0
\(329\) −9.53579 −0.525725
\(330\) 0 0
\(331\) 20.0357 1.10126 0.550630 0.834750i \(-0.314388\pi\)
0.550630 + 0.834750i \(0.314388\pi\)
\(332\) 0 0
\(333\) −5.53996 −0.303588
\(334\) 0 0
\(335\) −3.74590 −0.204660
\(336\) 0 0
\(337\) 13.4478 0.732549 0.366274 0.930507i \(-0.380633\pi\)
0.366274 + 0.930507i \(0.380633\pi\)
\(338\) 0 0
\(339\) −36.3267 −1.97300
\(340\) 0 0
\(341\) −6.58501 −0.356598
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0.335076 0.0180399
\(346\) 0 0
\(347\) 18.8461 1.01171 0.505856 0.862618i \(-0.331177\pi\)
0.505856 + 0.862618i \(0.331177\pi\)
\(348\) 0 0
\(349\) 2.39964 0.128450 0.0642250 0.997935i \(-0.479542\pi\)
0.0642250 + 0.997935i \(0.479542\pi\)
\(350\) 0 0
\(351\) −4.36266 −0.232862
\(352\) 0 0
\(353\) 7.56860 0.402836 0.201418 0.979505i \(-0.435445\pi\)
0.201418 + 0.979505i \(0.435445\pi\)
\(354\) 0 0
\(355\) 10.2499 0.544010
\(356\) 0 0
\(357\) −2.79406 −0.147877
\(358\) 0 0
\(359\) 33.4423 1.76502 0.882509 0.470296i \(-0.155853\pi\)
0.882509 + 0.470296i \(0.155853\pi\)
\(360\) 0 0
\(361\) −10.3832 −0.546486
\(362\) 0 0
\(363\) −1.60036 −0.0839969
\(364\) 0 0
\(365\) −1.15672 −0.0605455
\(366\) 0 0
\(367\) −3.24186 −0.169224 −0.0846120 0.996414i \(-0.526965\pi\)
−0.0846120 + 0.996414i \(0.526965\pi\)
\(368\) 0 0
\(369\) 2.06040 0.107260
\(370\) 0 0
\(371\) 8.37907 0.435020
\(372\) 0 0
\(373\) −13.2007 −0.683507 −0.341753 0.939790i \(-0.611021\pi\)
−0.341753 + 0.939790i \(0.611021\pi\)
\(374\) 0 0
\(375\) −1.93543 −0.0999453
\(376\) 0 0
\(377\) −7.63317 −0.393128
\(378\) 0 0
\(379\) −5.07158 −0.260509 −0.130255 0.991481i \(-0.541580\pi\)
−0.130255 + 0.991481i \(0.541580\pi\)
\(380\) 0 0
\(381\) −26.9948 −1.38298
\(382\) 0 0
\(383\) 18.9396 0.967768 0.483884 0.875132i \(-0.339226\pi\)
0.483884 + 0.875132i \(0.339226\pi\)
\(384\) 0 0
\(385\) −3.18953 −0.162554
\(386\) 0 0
\(387\) −5.87086 −0.298433
\(388\) 0 0
\(389\) −35.8144 −1.81586 −0.907930 0.419121i \(-0.862338\pi\)
−0.907930 + 0.419121i \(0.862338\pi\)
\(390\) 0 0
\(391\) −0.249933 −0.0126396
\(392\) 0 0
\(393\) −37.4751 −1.89037
\(394\) 0 0
\(395\) 2.12497 0.106919
\(396\) 0 0
\(397\) 4.62900 0.232323 0.116161 0.993230i \(-0.462941\pi\)
0.116161 + 0.993230i \(0.462941\pi\)
\(398\) 0 0
\(399\) −5.68133 −0.284422
\(400\) 0 0
\(401\) 32.0245 1.59923 0.799613 0.600516i \(-0.205038\pi\)
0.799613 + 0.600516i \(0.205038\pi\)
\(402\) 0 0
\(403\) 2.06457 0.102843
\(404\) 0 0
\(405\) 10.6813 0.530760
\(406\) 0 0
\(407\) 23.6894 1.17424
\(408\) 0 0
\(409\) −24.4014 −1.20657 −0.603286 0.797525i \(-0.706142\pi\)
−0.603286 + 0.797525i \(0.706142\pi\)
\(410\) 0 0
\(411\) 35.5316 1.75265
\(412\) 0 0
\(413\) 11.9794 0.589469
\(414\) 0 0
\(415\) 4.98359 0.244635
\(416\) 0 0
\(417\) 39.8625 1.95208
\(418\) 0 0
\(419\) 9.14838 0.446928 0.223464 0.974712i \(-0.428264\pi\)
0.223464 + 0.974712i \(0.428264\pi\)
\(420\) 0 0
\(421\) −4.84328 −0.236047 −0.118023 0.993011i \(-0.537656\pi\)
−0.118023 + 0.993011i \(0.537656\pi\)
\(422\) 0 0
\(423\) 7.11273 0.345833
\(424\) 0 0
\(425\) 1.44364 0.0700266
\(426\) 0 0
\(427\) 2.81047 0.136008
\(428\) 0 0
\(429\) −6.17313 −0.298041
\(430\) 0 0
\(431\) −31.3871 −1.51187 −0.755933 0.654649i \(-0.772816\pi\)
−0.755933 + 0.654649i \(0.772816\pi\)
\(432\) 0 0
\(433\) 22.1361 1.06380 0.531898 0.846809i \(-0.321479\pi\)
0.531898 + 0.846809i \(0.321479\pi\)
\(434\) 0 0
\(435\) 14.7735 0.708334
\(436\) 0 0
\(437\) −0.508203 −0.0243107
\(438\) 0 0
\(439\) 27.0716 1.29206 0.646028 0.763314i \(-0.276429\pi\)
0.646028 + 0.763314i \(0.276429\pi\)
\(440\) 0 0
\(441\) 0.745898 0.0355190
\(442\) 0 0
\(443\) 19.4506 0.924128 0.462064 0.886847i \(-0.347109\pi\)
0.462064 + 0.886847i \(0.347109\pi\)
\(444\) 0 0
\(445\) −0.108560 −0.00514622
\(446\) 0 0
\(447\) −34.6095 −1.63697
\(448\) 0 0
\(449\) −19.9037 −0.939313 −0.469656 0.882849i \(-0.655622\pi\)
−0.469656 + 0.882849i \(0.655622\pi\)
\(450\) 0 0
\(451\) −8.81047 −0.414869
\(452\) 0 0
\(453\) 4.18431 0.196596
\(454\) 0 0
\(455\) 1.00000 0.0468807
\(456\) 0 0
\(457\) −25.8831 −1.21076 −0.605380 0.795936i \(-0.706979\pi\)
−0.605380 + 0.795936i \(0.706979\pi\)
\(458\) 0 0
\(459\) −6.29809 −0.293970
\(460\) 0 0
\(461\) 16.6719 0.776489 0.388245 0.921556i \(-0.373082\pi\)
0.388245 + 0.921556i \(0.373082\pi\)
\(462\) 0 0
\(463\) 11.2817 0.524304 0.262152 0.965027i \(-0.415568\pi\)
0.262152 + 0.965027i \(0.415568\pi\)
\(464\) 0 0
\(465\) −3.99583 −0.185302
\(466\) 0 0
\(467\) 2.58918 0.119813 0.0599064 0.998204i \(-0.480920\pi\)
0.0599064 + 0.998204i \(0.480920\pi\)
\(468\) 0 0
\(469\) −3.74590 −0.172970
\(470\) 0 0
\(471\) 1.27885 0.0589261
\(472\) 0 0
\(473\) 25.1044 1.15430
\(474\) 0 0
\(475\) 2.93543 0.134687
\(476\) 0 0
\(477\) −6.24993 −0.286165
\(478\) 0 0
\(479\) −7.76231 −0.354669 −0.177334 0.984151i \(-0.556747\pi\)
−0.177334 + 0.984151i \(0.556747\pi\)
\(480\) 0 0
\(481\) −7.42723 −0.338652
\(482\) 0 0
\(483\) 0.335076 0.0152465
\(484\) 0 0
\(485\) −10.4231 −0.473287
\(486\) 0 0
\(487\) −33.9055 −1.53640 −0.768202 0.640208i \(-0.778848\pi\)
−0.768202 + 0.640208i \(0.778848\pi\)
\(488\) 0 0
\(489\) 28.9599 1.30961
\(490\) 0 0
\(491\) 23.7417 1.07145 0.535725 0.844393i \(-0.320039\pi\)
0.535725 + 0.844393i \(0.320039\pi\)
\(492\) 0 0
\(493\) −11.0195 −0.496294
\(494\) 0 0
\(495\) 2.37907 0.106931
\(496\) 0 0
\(497\) 10.2499 0.459772
\(498\) 0 0
\(499\) 27.9477 1.25111 0.625555 0.780180i \(-0.284873\pi\)
0.625555 + 0.780180i \(0.284873\pi\)
\(500\) 0 0
\(501\) 25.1127 1.12195
\(502\) 0 0
\(503\) −3.93437 −0.175425 −0.0877125 0.996146i \(-0.527956\pi\)
−0.0877125 + 0.996146i \(0.527956\pi\)
\(504\) 0 0
\(505\) −1.15672 −0.0514734
\(506\) 0 0
\(507\) 1.93543 0.0859556
\(508\) 0 0
\(509\) −19.8227 −0.878626 −0.439313 0.898334i \(-0.644778\pi\)
−0.439313 + 0.898334i \(0.644778\pi\)
\(510\) 0 0
\(511\) −1.15672 −0.0511703
\(512\) 0 0
\(513\) −12.8063 −0.565412
\(514\) 0 0
\(515\) 13.6608 0.601965
\(516\) 0 0
\(517\) −30.4147 −1.33764
\(518\) 0 0
\(519\) 10.3392 0.453842
\(520\) 0 0
\(521\) −43.3132 −1.89758 −0.948792 0.315901i \(-0.897693\pi\)
−0.948792 + 0.315901i \(0.897693\pi\)
\(522\) 0 0
\(523\) −21.3103 −0.931836 −0.465918 0.884828i \(-0.654276\pi\)
−0.465918 + 0.884828i \(0.654276\pi\)
\(524\) 0 0
\(525\) −1.93543 −0.0844692
\(526\) 0 0
\(527\) 2.98048 0.129832
\(528\) 0 0
\(529\) −22.9700 −0.998697
\(530\) 0 0
\(531\) −8.93543 −0.387765
\(532\) 0 0
\(533\) 2.76231 0.119649
\(534\) 0 0
\(535\) −3.23353 −0.139798
\(536\) 0 0
\(537\) 10.7857 0.465438
\(538\) 0 0
\(539\) −3.18953 −0.137383
\(540\) 0 0
\(541\) −2.16195 −0.0929494 −0.0464747 0.998919i \(-0.514799\pi\)
−0.0464747 + 0.998919i \(0.514799\pi\)
\(542\) 0 0
\(543\) 21.4702 0.921373
\(544\) 0 0
\(545\) 11.7089 0.501555
\(546\) 0 0
\(547\) 4.37907 0.187235 0.0936177 0.995608i \(-0.470157\pi\)
0.0936177 + 0.995608i \(0.470157\pi\)
\(548\) 0 0
\(549\) −2.09632 −0.0894688
\(550\) 0 0
\(551\) −22.4067 −0.954556
\(552\) 0 0
\(553\) 2.12497 0.0903628
\(554\) 0 0
\(555\) 14.3749 0.610180
\(556\) 0 0
\(557\) −21.9302 −0.929213 −0.464606 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(558\) 0 0
\(559\) −7.87086 −0.332902
\(560\) 0 0
\(561\) −8.91175 −0.376254
\(562\) 0 0
\(563\) −21.1086 −0.889620 −0.444810 0.895625i \(-0.646729\pi\)
−0.444810 + 0.895625i \(0.646729\pi\)
\(564\) 0 0
\(565\) 18.7693 0.789631
\(566\) 0 0
\(567\) 10.6813 0.448574
\(568\) 0 0
\(569\) −22.9742 −0.963128 −0.481564 0.876411i \(-0.659931\pi\)
−0.481564 + 0.876411i \(0.659931\pi\)
\(570\) 0 0
\(571\) 45.7540 1.91474 0.957372 0.288858i \(-0.0932755\pi\)
0.957372 + 0.288858i \(0.0932755\pi\)
\(572\) 0 0
\(573\) −15.9435 −0.666049
\(574\) 0 0
\(575\) −0.173127 −0.00721991
\(576\) 0 0
\(577\) −14.1208 −0.587856 −0.293928 0.955827i \(-0.594963\pi\)
−0.293928 + 0.955827i \(0.594963\pi\)
\(578\) 0 0
\(579\) 10.2223 0.424826
\(580\) 0 0
\(581\) 4.98359 0.206754
\(582\) 0 0
\(583\) 26.7253 1.10685
\(584\) 0 0
\(585\) −0.745898 −0.0308391
\(586\) 0 0
\(587\) −25.2663 −1.04285 −0.521427 0.853296i \(-0.674600\pi\)
−0.521427 + 0.853296i \(0.674600\pi\)
\(588\) 0 0
\(589\) 6.06040 0.249714
\(590\) 0 0
\(591\) −25.0039 −1.02852
\(592\) 0 0
\(593\) −5.36266 −0.220218 −0.110109 0.993920i \(-0.535120\pi\)
−0.110109 + 0.993920i \(0.535120\pi\)
\(594\) 0 0
\(595\) 1.44364 0.0591833
\(596\) 0 0
\(597\) −9.95885 −0.407589
\(598\) 0 0
\(599\) −16.4866 −0.673623 −0.336811 0.941572i \(-0.609348\pi\)
−0.336811 + 0.941572i \(0.609348\pi\)
\(600\) 0 0
\(601\) 7.40381 0.302008 0.151004 0.988533i \(-0.451749\pi\)
0.151004 + 0.988533i \(0.451749\pi\)
\(602\) 0 0
\(603\) 2.79406 0.113783
\(604\) 0 0
\(605\) 0.826873 0.0336172
\(606\) 0 0
\(607\) −1.57800 −0.0640490 −0.0320245 0.999487i \(-0.510195\pi\)
−0.0320245 + 0.999487i \(0.510195\pi\)
\(608\) 0 0
\(609\) 14.7735 0.598652
\(610\) 0 0
\(611\) 9.53579 0.385777
\(612\) 0 0
\(613\) 10.8105 0.436631 0.218315 0.975878i \(-0.429944\pi\)
0.218315 + 0.975878i \(0.429944\pi\)
\(614\) 0 0
\(615\) −5.34625 −0.215582
\(616\) 0 0
\(617\) 19.7571 0.795390 0.397695 0.917518i \(-0.369810\pi\)
0.397695 + 0.917518i \(0.369810\pi\)
\(618\) 0 0
\(619\) 0.713085 0.0286613 0.0143306 0.999897i \(-0.495438\pi\)
0.0143306 + 0.999897i \(0.495438\pi\)
\(620\) 0 0
\(621\) 0.755296 0.0303090
\(622\) 0 0
\(623\) −0.108560 −0.00434935
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −18.1208 −0.723675
\(628\) 0 0
\(629\) −10.7222 −0.427523
\(630\) 0 0
\(631\) −21.4423 −0.853605 −0.426802 0.904345i \(-0.640360\pi\)
−0.426802 + 0.904345i \(0.640360\pi\)
\(632\) 0 0
\(633\) 49.9781 1.98645
\(634\) 0 0
\(635\) 13.9477 0.553496
\(636\) 0 0
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −7.64541 −0.302448
\(640\) 0 0
\(641\) 42.0479 1.66079 0.830396 0.557174i \(-0.188114\pi\)
0.830396 + 0.557174i \(0.188114\pi\)
\(642\) 0 0
\(643\) −0.225457 −0.00889116 −0.00444558 0.999990i \(-0.501415\pi\)
−0.00444558 + 0.999990i \(0.501415\pi\)
\(644\) 0 0
\(645\) 15.2335 0.599819
\(646\) 0 0
\(647\) −28.5839 −1.12375 −0.561876 0.827222i \(-0.689920\pi\)
−0.561876 + 0.827222i \(0.689920\pi\)
\(648\) 0 0
\(649\) 38.2088 1.49983
\(650\) 0 0
\(651\) −3.99583 −0.156609
\(652\) 0 0
\(653\) −38.5962 −1.51039 −0.755193 0.655503i \(-0.772457\pi\)
−0.755193 + 0.655503i \(0.772457\pi\)
\(654\) 0 0
\(655\) 19.3627 0.756562
\(656\) 0 0
\(657\) 0.862796 0.0336609
\(658\) 0 0
\(659\) 14.8615 0.578921 0.289460 0.957190i \(-0.406524\pi\)
0.289460 + 0.957190i \(0.406524\pi\)
\(660\) 0 0
\(661\) 19.4988 0.758416 0.379208 0.925312i \(-0.376197\pi\)
0.379208 + 0.925312i \(0.376197\pi\)
\(662\) 0 0
\(663\) 2.79406 0.108512
\(664\) 0 0
\(665\) 2.93543 0.113831
\(666\) 0 0
\(667\) 1.32151 0.0511691
\(668\) 0 0
\(669\) 14.8984 0.576007
\(670\) 0 0
\(671\) 8.96408 0.346054
\(672\) 0 0
\(673\) −49.2280 −1.89760 −0.948801 0.315876i \(-0.897702\pi\)
−0.948801 + 0.315876i \(0.897702\pi\)
\(674\) 0 0
\(675\) −4.36266 −0.167919
\(676\) 0 0
\(677\) −17.5358 −0.673955 −0.336978 0.941513i \(-0.609405\pi\)
−0.336978 + 0.941513i \(0.609405\pi\)
\(678\) 0 0
\(679\) −10.4231 −0.400000
\(680\) 0 0
\(681\) −11.6126 −0.444996
\(682\) 0 0
\(683\) −36.1718 −1.38408 −0.692038 0.721861i \(-0.743287\pi\)
−0.692038 + 0.721861i \(0.743287\pi\)
\(684\) 0 0
\(685\) −18.3585 −0.701442
\(686\) 0 0
\(687\) −9.06847 −0.345984
\(688\) 0 0
\(689\) −8.37907 −0.319217
\(690\) 0 0
\(691\) 5.31973 0.202372 0.101186 0.994868i \(-0.467736\pi\)
0.101186 + 0.994868i \(0.467736\pi\)
\(692\) 0 0
\(693\) 2.37907 0.0903733
\(694\) 0 0
\(695\) −20.5962 −0.781258
\(696\) 0 0
\(697\) 3.98776 0.151047
\(698\) 0 0
\(699\) 30.7386 1.16264
\(700\) 0 0
\(701\) −9.78989 −0.369759 −0.184880 0.982761i \(-0.559189\pi\)
−0.184880 + 0.982761i \(0.559189\pi\)
\(702\) 0 0
\(703\) −21.8021 −0.822283
\(704\) 0 0
\(705\) −18.4559 −0.695088
\(706\) 0 0
\(707\) −1.15672 −0.0435030
\(708\) 0 0
\(709\) 2.51938 0.0946174 0.0473087 0.998880i \(-0.484936\pi\)
0.0473087 + 0.998880i \(0.484936\pi\)
\(710\) 0 0
\(711\) −1.58501 −0.0594425
\(712\) 0 0
\(713\) −0.357433 −0.0133860
\(714\) 0 0
\(715\) 3.18953 0.119282
\(716\) 0 0
\(717\) 13.0799 0.488478
\(718\) 0 0
\(719\) −17.1784 −0.640645 −0.320322 0.947309i \(-0.603791\pi\)
−0.320322 + 0.947309i \(0.603791\pi\)
\(720\) 0 0
\(721\) 13.6608 0.508753
\(722\) 0 0
\(723\) −16.1239 −0.599655
\(724\) 0 0
\(725\) −7.63317 −0.283489
\(726\) 0 0
\(727\) 53.2598 1.97530 0.987648 0.156689i \(-0.0500820\pi\)
0.987648 + 0.156689i \(0.0500820\pi\)
\(728\) 0 0
\(729\) 17.3637 0.643101
\(730\) 0 0
\(731\) −11.3627 −0.420263
\(732\) 0 0
\(733\) −0.379068 −0.0140012 −0.00700060 0.999975i \(-0.502228\pi\)
−0.00700060 + 0.999975i \(0.502228\pi\)
\(734\) 0 0
\(735\) −1.93543 −0.0713895
\(736\) 0 0
\(737\) −11.9477 −0.440098
\(738\) 0 0
\(739\) 27.8381 1.02404 0.512020 0.858974i \(-0.328897\pi\)
0.512020 + 0.858974i \(0.328897\pi\)
\(740\) 0 0
\(741\) 5.68133 0.208709
\(742\) 0 0
\(743\) 6.24292 0.229031 0.114515 0.993421i \(-0.463468\pi\)
0.114515 + 0.993421i \(0.463468\pi\)
\(744\) 0 0
\(745\) 17.8820 0.655147
\(746\) 0 0
\(747\) −3.71725 −0.136007
\(748\) 0 0
\(749\) −3.23353 −0.118150
\(750\) 0 0
\(751\) −17.9354 −0.654473 −0.327237 0.944942i \(-0.606117\pi\)
−0.327237 + 0.944942i \(0.606117\pi\)
\(752\) 0 0
\(753\) 26.6813 0.972322
\(754\) 0 0
\(755\) −2.16195 −0.0786814
\(756\) 0 0
\(757\) 15.6209 0.567752 0.283876 0.958861i \(-0.408380\pi\)
0.283876 + 0.958861i \(0.408380\pi\)
\(758\) 0 0
\(759\) 1.06874 0.0387927
\(760\) 0 0
\(761\) 27.0398 0.980193 0.490096 0.871668i \(-0.336962\pi\)
0.490096 + 0.871668i \(0.336962\pi\)
\(762\) 0 0
\(763\) 11.7089 0.423891
\(764\) 0 0
\(765\) −1.07681 −0.0389320
\(766\) 0 0
\(767\) −11.9794 −0.432552
\(768\) 0 0
\(769\) 8.49702 0.306411 0.153205 0.988194i \(-0.451040\pi\)
0.153205 + 0.988194i \(0.451040\pi\)
\(770\) 0 0
\(771\) −27.7662 −0.999975
\(772\) 0 0
\(773\) −26.2583 −0.944444 −0.472222 0.881480i \(-0.656548\pi\)
−0.472222 + 0.881480i \(0.656548\pi\)
\(774\) 0 0
\(775\) 2.06457 0.0741615
\(776\) 0 0
\(777\) 14.3749 0.515697
\(778\) 0 0
\(779\) 8.10856 0.290519
\(780\) 0 0
\(781\) 32.6925 1.16983
\(782\) 0 0
\(783\) 33.3009 1.19008
\(784\) 0 0
\(785\) −0.660755 −0.0235834
\(786\) 0 0
\(787\) 43.5058 1.55081 0.775407 0.631461i \(-0.217545\pi\)
0.775407 + 0.631461i \(0.217545\pi\)
\(788\) 0 0
\(789\) −44.7170 −1.59197
\(790\) 0 0
\(791\) 18.7693 0.667360
\(792\) 0 0
\(793\) −2.81047 −0.0998026
\(794\) 0 0
\(795\) 16.2171 0.575162
\(796\) 0 0
\(797\) −8.70191 −0.308237 −0.154119 0.988052i \(-0.549254\pi\)
−0.154119 + 0.988052i \(0.549254\pi\)
\(798\) 0 0
\(799\) 13.7662 0.487013
\(800\) 0 0
\(801\) 0.0809744 0.00286109
\(802\) 0 0
\(803\) −3.68940 −0.130196
\(804\) 0 0
\(805\) −0.173127 −0.00610193
\(806\) 0 0
\(807\) −12.0747 −0.425049
\(808\) 0 0
\(809\) −27.2182 −0.956940 −0.478470 0.878104i \(-0.658808\pi\)
−0.478470 + 0.878104i \(0.658808\pi\)
\(810\) 0 0
\(811\) 22.7253 0.797994 0.398997 0.916952i \(-0.369358\pi\)
0.398997 + 0.916952i \(0.369358\pi\)
\(812\) 0 0
\(813\) 52.1236 1.82806
\(814\) 0 0
\(815\) −14.9630 −0.524132
\(816\) 0 0
\(817\) −23.1044 −0.808320
\(818\) 0 0
\(819\) −0.745898 −0.0260638
\(820\) 0 0
\(821\) 2.22758 0.0777429 0.0388715 0.999244i \(-0.487624\pi\)
0.0388715 + 0.999244i \(0.487624\pi\)
\(822\) 0 0
\(823\) 23.6238 0.823473 0.411736 0.911303i \(-0.364922\pi\)
0.411736 + 0.911303i \(0.364922\pi\)
\(824\) 0 0
\(825\) −6.17313 −0.214921
\(826\) 0 0
\(827\) −38.2744 −1.33093 −0.665466 0.746428i \(-0.731767\pi\)
−0.665466 + 0.746428i \(0.731767\pi\)
\(828\) 0 0
\(829\) −39.8953 −1.38562 −0.692811 0.721119i \(-0.743628\pi\)
−0.692811 + 0.721119i \(0.743628\pi\)
\(830\) 0 0
\(831\) −23.7251 −0.823013
\(832\) 0 0
\(833\) 1.44364 0.0500190
\(834\) 0 0
\(835\) −12.9753 −0.449027
\(836\) 0 0
\(837\) −9.00701 −0.311328
\(838\) 0 0
\(839\) 20.2716 0.699852 0.349926 0.936777i \(-0.386207\pi\)
0.349926 + 0.936777i \(0.386207\pi\)
\(840\) 0 0
\(841\) 29.2653 1.00915
\(842\) 0 0
\(843\) 2.21712 0.0763616
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 0.826873 0.0284117
\(848\) 0 0
\(849\) −58.9588 −2.02346
\(850\) 0 0
\(851\) 1.28586 0.0440786
\(852\) 0 0
\(853\) −31.2252 −1.06913 −0.534565 0.845127i \(-0.679525\pi\)
−0.534565 + 0.845127i \(0.679525\pi\)
\(854\) 0 0
\(855\) −2.18953 −0.0748805
\(856\) 0 0
\(857\) 10.0534 0.343417 0.171709 0.985148i \(-0.445071\pi\)
0.171709 + 0.985148i \(0.445071\pi\)
\(858\) 0 0
\(859\) 47.9617 1.63643 0.818216 0.574911i \(-0.194963\pi\)
0.818216 + 0.574911i \(0.194963\pi\)
\(860\) 0 0
\(861\) −5.34625 −0.182200
\(862\) 0 0
\(863\) 3.72426 0.126775 0.0633877 0.997989i \(-0.479810\pi\)
0.0633877 + 0.997989i \(0.479810\pi\)
\(864\) 0 0
\(865\) −5.34209 −0.181636
\(866\) 0 0
\(867\) −28.8687 −0.980434
\(868\) 0 0
\(869\) 6.77765 0.229916
\(870\) 0 0
\(871\) 3.74590 0.126925
\(872\) 0 0
\(873\) 7.77454 0.263128
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −23.7787 −0.802950 −0.401475 0.915870i \(-0.631502\pi\)
−0.401475 + 0.915870i \(0.631502\pi\)
\(878\) 0 0
\(879\) −14.0635 −0.474350
\(880\) 0 0
\(881\) 55.6678 1.87549 0.937747 0.347318i \(-0.112908\pi\)
0.937747 + 0.347318i \(0.112908\pi\)
\(882\) 0 0
\(883\) 35.3955 1.19115 0.595576 0.803299i \(-0.296924\pi\)
0.595576 + 0.803299i \(0.296924\pi\)
\(884\) 0 0
\(885\) 23.1854 0.779368
\(886\) 0 0
\(887\) 23.5920 0.792142 0.396071 0.918220i \(-0.370373\pi\)
0.396071 + 0.918220i \(0.370373\pi\)
\(888\) 0 0
\(889\) 13.9477 0.467790
\(890\) 0 0
\(891\) 34.0685 1.14134
\(892\) 0 0
\(893\) 27.9917 0.936705
\(894\) 0 0
\(895\) −5.57277 −0.186277
\(896\) 0 0
\(897\) −0.335076 −0.0111879
\(898\) 0 0
\(899\) −15.7592 −0.525599
\(900\) 0 0
\(901\) −12.0963 −0.402987
\(902\) 0 0
\(903\) 15.2335 0.506940
\(904\) 0 0
\(905\) −11.0932 −0.368751
\(906\) 0 0
\(907\) 9.53295 0.316536 0.158268 0.987396i \(-0.449409\pi\)
0.158268 + 0.987396i \(0.449409\pi\)
\(908\) 0 0
\(909\) 0.862796 0.0286171
\(910\) 0 0
\(911\) 35.0234 1.16038 0.580189 0.814482i \(-0.302979\pi\)
0.580189 + 0.814482i \(0.302979\pi\)
\(912\) 0 0
\(913\) 15.8953 0.526059
\(914\) 0 0
\(915\) 5.43947 0.179823
\(916\) 0 0
\(917\) 19.3627 0.639411
\(918\) 0 0
\(919\) 3.21011 0.105892 0.0529459 0.998597i \(-0.483139\pi\)
0.0529459 + 0.998597i \(0.483139\pi\)
\(920\) 0 0
\(921\) 29.2335 0.963277
\(922\) 0 0
\(923\) −10.2499 −0.337381
\(924\) 0 0
\(925\) −7.42723 −0.244206
\(926\) 0 0
\(927\) −10.1895 −0.334668
\(928\) 0 0
\(929\) 38.4577 1.26175 0.630877 0.775883i \(-0.282695\pi\)
0.630877 + 0.775883i \(0.282695\pi\)
\(930\) 0 0
\(931\) 2.93543 0.0962049
\(932\) 0 0
\(933\) 42.3296 1.38581
\(934\) 0 0
\(935\) 4.60453 0.150584
\(936\) 0 0
\(937\) 14.1138 0.461077 0.230539 0.973063i \(-0.425951\pi\)
0.230539 + 0.973063i \(0.425951\pi\)
\(938\) 0 0
\(939\) 32.6443 1.06531
\(940\) 0 0
\(941\) 34.5397 1.12596 0.562981 0.826470i \(-0.309654\pi\)
0.562981 + 0.826470i \(0.309654\pi\)
\(942\) 0 0
\(943\) −0.478230 −0.0155733
\(944\) 0 0
\(945\) −4.36266 −0.141917
\(946\) 0 0
\(947\) −53.0562 −1.72410 −0.862048 0.506827i \(-0.830818\pi\)
−0.862048 + 0.506827i \(0.830818\pi\)
\(948\) 0 0
\(949\) 1.15672 0.0375487
\(950\) 0 0
\(951\) 28.3351 0.918828
\(952\) 0 0
\(953\) 28.1536 0.911985 0.455992 0.889984i \(-0.349284\pi\)
0.455992 + 0.889984i \(0.349284\pi\)
\(954\) 0 0
\(955\) 8.23769 0.266566
\(956\) 0 0
\(957\) 47.1205 1.52319
\(958\) 0 0
\(959\) −18.3585 −0.592827
\(960\) 0 0
\(961\) −26.7376 −0.862502
\(962\) 0 0
\(963\) 2.41188 0.0777218
\(964\) 0 0
\(965\) −5.28169 −0.170024
\(966\) 0 0
\(967\) 0.778712 0.0250417 0.0125208 0.999922i \(-0.496014\pi\)
0.0125208 + 0.999922i \(0.496014\pi\)
\(968\) 0 0
\(969\) 8.20177 0.263479
\(970\) 0 0
\(971\) −16.5522 −0.531185 −0.265593 0.964085i \(-0.585568\pi\)
−0.265593 + 0.964085i \(0.585568\pi\)
\(972\) 0 0
\(973\) −20.5962 −0.660283
\(974\) 0 0
\(975\) 1.93543 0.0619834
\(976\) 0 0
\(977\) −5.37801 −0.172058 −0.0860289 0.996293i \(-0.527418\pi\)
−0.0860289 + 0.996293i \(0.527418\pi\)
\(978\) 0 0
\(979\) −0.346255 −0.0110663
\(980\) 0 0
\(981\) −8.73366 −0.278844
\(982\) 0 0
\(983\) −15.3627 −0.489993 −0.244996 0.969524i \(-0.578787\pi\)
−0.244996 + 0.969524i \(0.578787\pi\)
\(984\) 0 0
\(985\) 12.9190 0.411634
\(986\) 0 0
\(987\) −18.4559 −0.587457
\(988\) 0 0
\(989\) 1.36266 0.0433301
\(990\) 0 0
\(991\) −4.09215 −0.129992 −0.0649958 0.997886i \(-0.520703\pi\)
−0.0649958 + 0.997886i \(0.520703\pi\)
\(992\) 0 0
\(993\) 38.7777 1.23057
\(994\) 0 0
\(995\) 5.14554 0.163125
\(996\) 0 0
\(997\) −12.9711 −0.410798 −0.205399 0.978678i \(-0.565849\pi\)
−0.205399 + 0.978678i \(0.565849\pi\)
\(998\) 0 0
\(999\) 32.4025 1.02517
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.o.1.3 3
4.3 odd 2 7280.2.a.bp.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.o.1.3 3 1.1 even 1 trivial
7280.2.a.bp.1.1 3 4.3 odd 2