Properties

Label 6012.2.a.c.1.1
Level $6012$
Weight $2$
Character 6012.1
Self dual yes
Analytic conductor $48.006$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6012.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0060616952\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
Defining polynomial: \(x^{3} - x^{2} - 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.311108\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.21432 q^{5} -4.42864 q^{7} +O(q^{10})\) \(q-2.21432 q^{5} -4.42864 q^{7} -0.903212 q^{11} +0.622216 q^{13} -4.21432 q^{17} -5.80642 q^{19} +1.24443 q^{23} -0.0967881 q^{25} -8.85728 q^{29} -3.05086 q^{31} +9.80642 q^{35} -1.18421 q^{37} -2.02074 q^{41} -8.83654 q^{43} -3.09679 q^{47} +12.6128 q^{49} +4.34767 q^{53} +2.00000 q^{55} +12.4286 q^{59} -2.90321 q^{61} -1.37778 q^{65} +5.59210 q^{67} +4.00000 q^{71} -7.80642 q^{73} +4.00000 q^{77} +1.72546 q^{79} -7.47949 q^{83} +9.33185 q^{85} -4.85728 q^{89} -2.75557 q^{91} +12.8573 q^{95} -7.28592 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + O(q^{10}) \) \( 3q + 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + 4q^{23} - 7q^{25} + 4q^{31} + 16q^{35} + 10q^{37} + 14q^{41} - 20q^{43} - 16q^{47} + 11q^{49} + 6q^{53} + 6q^{55} + 24q^{59} - 2q^{61} - 4q^{65} + 10q^{67} + 12q^{71} - 10q^{73} + 12q^{77} - 2q^{79} + 4q^{83} + 8q^{85} + 12q^{89} - 8q^{91} + 12q^{95} + 18q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −2.21432 −0.990274 −0.495137 0.868815i \(-0.664882\pi\)
−0.495137 + 0.868815i \(0.664882\pi\)
\(6\) 0 0
\(7\) −4.42864 −1.67387 −0.836934 0.547304i \(-0.815654\pi\)
−0.836934 + 0.547304i \(0.815654\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.903212 −0.272329 −0.136164 0.990686i \(-0.543478\pi\)
−0.136164 + 0.990686i \(0.543478\pi\)
\(12\) 0 0
\(13\) 0.622216 0.172572 0.0862858 0.996270i \(-0.472500\pi\)
0.0862858 + 0.996270i \(0.472500\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.21432 −1.02212 −0.511061 0.859544i \(-0.670748\pi\)
−0.511061 + 0.859544i \(0.670748\pi\)
\(18\) 0 0
\(19\) −5.80642 −1.33208 −0.666042 0.745914i \(-0.732013\pi\)
−0.666042 + 0.745914i \(0.732013\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.24443 0.259482 0.129741 0.991548i \(-0.458585\pi\)
0.129741 + 0.991548i \(0.458585\pi\)
\(24\) 0 0
\(25\) −0.0967881 −0.0193576
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −8.85728 −1.64476 −0.822378 0.568942i \(-0.807353\pi\)
−0.822378 + 0.568942i \(0.807353\pi\)
\(30\) 0 0
\(31\) −3.05086 −0.547950 −0.273975 0.961737i \(-0.588339\pi\)
−0.273975 + 0.961737i \(0.588339\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 9.80642 1.65759
\(36\) 0 0
\(37\) −1.18421 −0.194683 −0.0973413 0.995251i \(-0.531034\pi\)
−0.0973413 + 0.995251i \(0.531034\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.02074 −0.315587 −0.157794 0.987472i \(-0.550438\pi\)
−0.157794 + 0.987472i \(0.550438\pi\)
\(42\) 0 0
\(43\) −8.83654 −1.34756 −0.673780 0.738932i \(-0.735330\pi\)
−0.673780 + 0.738932i \(0.735330\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.09679 −0.451713 −0.225856 0.974161i \(-0.572518\pi\)
−0.225856 + 0.974161i \(0.572518\pi\)
\(48\) 0 0
\(49\) 12.6128 1.80184
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.34767 0.597199 0.298599 0.954379i \(-0.403481\pi\)
0.298599 + 0.954379i \(0.403481\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 12.4286 1.61807 0.809036 0.587760i \(-0.199990\pi\)
0.809036 + 0.587760i \(0.199990\pi\)
\(60\) 0 0
\(61\) −2.90321 −0.371718 −0.185859 0.982576i \(-0.559507\pi\)
−0.185859 + 0.982576i \(0.559507\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.37778 −0.170893
\(66\) 0 0
\(67\) 5.59210 0.683184 0.341592 0.939848i \(-0.389034\pi\)
0.341592 + 0.939848i \(0.389034\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.00000 0.474713 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(72\) 0 0
\(73\) −7.80642 −0.913673 −0.456836 0.889551i \(-0.651018\pi\)
−0.456836 + 0.889551i \(0.651018\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 1.72546 0.194129 0.0970646 0.995278i \(-0.469055\pi\)
0.0970646 + 0.995278i \(0.469055\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.47949 −0.820981 −0.410491 0.911865i \(-0.634643\pi\)
−0.410491 + 0.911865i \(0.634643\pi\)
\(84\) 0 0
\(85\) 9.33185 1.01218
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.85728 −0.514871 −0.257435 0.966296i \(-0.582877\pi\)
−0.257435 + 0.966296i \(0.582877\pi\)
\(90\) 0 0
\(91\) −2.75557 −0.288862
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 12.8573 1.31913
\(96\) 0 0
\(97\) −7.28592 −0.739773 −0.369886 0.929077i \(-0.620603\pi\)
−0.369886 + 0.929077i \(0.620603\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −13.2652 −1.31993 −0.659967 0.751294i \(-0.729430\pi\)
−0.659967 + 0.751294i \(0.729430\pi\)
\(102\) 0 0
\(103\) −4.64296 −0.457484 −0.228742 0.973487i \(-0.573461\pi\)
−0.228742 + 0.973487i \(0.573461\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.46520 0.915036 0.457518 0.889200i \(-0.348739\pi\)
0.457518 + 0.889200i \(0.348739\pi\)
\(108\) 0 0
\(109\) −6.42864 −0.615752 −0.307876 0.951426i \(-0.599618\pi\)
−0.307876 + 0.951426i \(0.599618\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.44938 −0.418563 −0.209281 0.977855i \(-0.567112\pi\)
−0.209281 + 0.977855i \(0.567112\pi\)
\(114\) 0 0
\(115\) −2.75557 −0.256958
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 18.6637 1.71090
\(120\) 0 0
\(121\) −10.1842 −0.925837
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 11.2859 1.00944
\(126\) 0 0
\(127\) 2.62222 0.232684 0.116342 0.993209i \(-0.462883\pi\)
0.116342 + 0.993209i \(0.462883\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 5.67307 0.495658 0.247829 0.968804i \(-0.420283\pi\)
0.247829 + 0.968804i \(0.420283\pi\)
\(132\) 0 0
\(133\) 25.7146 2.22973
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.4286 1.06185 0.530925 0.847419i \(-0.321845\pi\)
0.530925 + 0.847419i \(0.321845\pi\)
\(138\) 0 0
\(139\) −13.7857 −1.16929 −0.584643 0.811291i \(-0.698765\pi\)
−0.584643 + 0.811291i \(0.698765\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.561993 −0.0469962
\(144\) 0 0
\(145\) 19.6128 1.62876
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.5827 0.866972 0.433486 0.901160i \(-0.357283\pi\)
0.433486 + 0.901160i \(0.357283\pi\)
\(150\) 0 0
\(151\) 13.6938 1.11439 0.557193 0.830383i \(-0.311878\pi\)
0.557193 + 0.830383i \(0.311878\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 6.75557 0.542620
\(156\) 0 0
\(157\) 3.28592 0.262245 0.131122 0.991366i \(-0.458142\pi\)
0.131122 + 0.991366i \(0.458142\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.51114 −0.434338
\(162\) 0 0
\(163\) −8.31603 −0.651362 −0.325681 0.945480i \(-0.605594\pi\)
−0.325681 + 0.945480i \(0.605594\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −12.6128 −0.970219
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 21.8064 1.65791 0.828956 0.559314i \(-0.188935\pi\)
0.828956 + 0.559314i \(0.188935\pi\)
\(174\) 0 0
\(175\) 0.428639 0.0324021
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −25.9813 −1.94193 −0.970965 0.239220i \(-0.923108\pi\)
−0.970965 + 0.239220i \(0.923108\pi\)
\(180\) 0 0
\(181\) −19.1985 −1.42701 −0.713507 0.700649i \(-0.752894\pi\)
−0.713507 + 0.700649i \(0.752894\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.62222 0.192789
\(186\) 0 0
\(187\) 3.80642 0.278353
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.9541 0.864966 0.432483 0.901642i \(-0.357638\pi\)
0.432483 + 0.901642i \(0.357638\pi\)
\(192\) 0 0
\(193\) −20.6637 −1.48741 −0.743703 0.668510i \(-0.766932\pi\)
−0.743703 + 0.668510i \(0.766932\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 25.7353 1.83356 0.916782 0.399388i \(-0.130777\pi\)
0.916782 + 0.399388i \(0.130777\pi\)
\(198\) 0 0
\(199\) 16.3368 1.15808 0.579042 0.815298i \(-0.303427\pi\)
0.579042 + 0.815298i \(0.303427\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 39.2257 2.75310
\(204\) 0 0
\(205\) 4.47457 0.312518
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.24443 0.362765
\(210\) 0 0
\(211\) 19.9081 1.37053 0.685266 0.728293i \(-0.259686\pi\)
0.685266 + 0.728293i \(0.259686\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 19.5669 1.33445
\(216\) 0 0
\(217\) 13.5111 0.917196
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.62222 −0.176389
\(222\) 0 0
\(223\) 6.32693 0.423683 0.211841 0.977304i \(-0.432054\pi\)
0.211841 + 0.977304i \(0.432054\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.62222 0.439532 0.219766 0.975553i \(-0.429471\pi\)
0.219766 + 0.975553i \(0.429471\pi\)
\(228\) 0 0
\(229\) −18.9032 −1.24916 −0.624580 0.780961i \(-0.714730\pi\)
−0.624580 + 0.780961i \(0.714730\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −19.0923 −1.25078 −0.625390 0.780312i \(-0.715060\pi\)
−0.625390 + 0.780312i \(0.715060\pi\)
\(234\) 0 0
\(235\) 6.85728 0.447320
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 7.68736 0.497254 0.248627 0.968599i \(-0.420021\pi\)
0.248627 + 0.968599i \(0.420021\pi\)
\(240\) 0 0
\(241\) 11.1526 0.718400 0.359200 0.933261i \(-0.383050\pi\)
0.359200 + 0.933261i \(0.383050\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −27.9289 −1.78431
\(246\) 0 0
\(247\) −3.61285 −0.229880
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 15.8666 1.00149 0.500747 0.865594i \(-0.333059\pi\)
0.500747 + 0.865594i \(0.333059\pi\)
\(252\) 0 0
\(253\) −1.12399 −0.0706643
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.91903 −0.119706 −0.0598530 0.998207i \(-0.519063\pi\)
−0.0598530 + 0.998207i \(0.519063\pi\)
\(258\) 0 0
\(259\) 5.24443 0.325873
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.1334 0.994825 0.497413 0.867514i \(-0.334284\pi\)
0.497413 + 0.867514i \(0.334284\pi\)
\(264\) 0 0
\(265\) −9.62714 −0.591390
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.06223 −0.369621 −0.184810 0.982774i \(-0.559167\pi\)
−0.184810 + 0.982774i \(0.559167\pi\)
\(270\) 0 0
\(271\) 3.91903 0.238064 0.119032 0.992890i \(-0.462021\pi\)
0.119032 + 0.992890i \(0.462021\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.0874201 0.00527163
\(276\) 0 0
\(277\) 25.6543 1.54142 0.770710 0.637186i \(-0.219902\pi\)
0.770710 + 0.637186i \(0.219902\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 11.7462 0.700720 0.350360 0.936615i \(-0.386059\pi\)
0.350360 + 0.936615i \(0.386059\pi\)
\(282\) 0 0
\(283\) −0.295286 −0.0175530 −0.00877648 0.999961i \(-0.502794\pi\)
−0.00877648 + 0.999961i \(0.502794\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8.94914 0.528251
\(288\) 0 0
\(289\) 0.760491 0.0447348
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.24443 0.0727005 0.0363502 0.999339i \(-0.488427\pi\)
0.0363502 + 0.999339i \(0.488427\pi\)
\(294\) 0 0
\(295\) −27.5210 −1.60233
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.774305 0.0447792
\(300\) 0 0
\(301\) 39.1338 2.25564
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.42864 0.368103
\(306\) 0 0
\(307\) −15.7669 −0.899867 −0.449934 0.893062i \(-0.648552\pi\)
−0.449934 + 0.893062i \(0.648552\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 16.1334 0.914839 0.457419 0.889251i \(-0.348774\pi\)
0.457419 + 0.889251i \(0.348774\pi\)
\(312\) 0 0
\(313\) 25.2257 1.42584 0.712920 0.701245i \(-0.247372\pi\)
0.712920 + 0.701245i \(0.247372\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.4193 0.978364 0.489182 0.872182i \(-0.337295\pi\)
0.489182 + 0.872182i \(0.337295\pi\)
\(318\) 0 0
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 24.4701 1.36155
\(324\) 0 0
\(325\) −0.0602231 −0.00334057
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 13.7146 0.756108
\(330\) 0 0
\(331\) 7.65233 0.420610 0.210305 0.977636i \(-0.432554\pi\)
0.210305 + 0.977636i \(0.432554\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −12.3827 −0.676540
\(336\) 0 0
\(337\) 1.30465 0.0710690 0.0355345 0.999368i \(-0.488687\pi\)
0.0355345 + 0.999368i \(0.488687\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.75557 0.149222
\(342\) 0 0
\(343\) −24.8573 −1.34217
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.67307 0.519278 0.259639 0.965706i \(-0.416396\pi\)
0.259639 + 0.965706i \(0.416396\pi\)
\(348\) 0 0
\(349\) −17.1842 −0.919850 −0.459925 0.887958i \(-0.652124\pi\)
−0.459925 + 0.887958i \(0.652124\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.7239 −1.10302 −0.551512 0.834167i \(-0.685949\pi\)
−0.551512 + 0.834167i \(0.685949\pi\)
\(354\) 0 0
\(355\) −8.85728 −0.470096
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −19.3461 −1.02105 −0.510525 0.859863i \(-0.670549\pi\)
−0.510525 + 0.859863i \(0.670549\pi\)
\(360\) 0 0
\(361\) 14.7146 0.774450
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 17.2859 0.904786
\(366\) 0 0
\(367\) −13.6860 −0.714402 −0.357201 0.934027i \(-0.616269\pi\)
−0.357201 + 0.934027i \(0.616269\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −19.2543 −0.999632
\(372\) 0 0
\(373\) −17.4795 −0.905054 −0.452527 0.891751i \(-0.649477\pi\)
−0.452527 + 0.891751i \(0.649477\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −5.51114 −0.283838
\(378\) 0 0
\(379\) 18.7763 0.964474 0.482237 0.876041i \(-0.339824\pi\)
0.482237 + 0.876041i \(0.339824\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 21.3733 1.09213 0.546063 0.837744i \(-0.316126\pi\)
0.546063 + 0.837744i \(0.316126\pi\)
\(384\) 0 0
\(385\) −8.85728 −0.451409
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −9.65233 −0.489392 −0.244696 0.969600i \(-0.578688\pi\)
−0.244696 + 0.969600i \(0.578688\pi\)
\(390\) 0 0
\(391\) −5.24443 −0.265222
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.82071 −0.192241
\(396\) 0 0
\(397\) 22.5161 1.13005 0.565024 0.825074i \(-0.308867\pi\)
0.565024 + 0.825074i \(0.308867\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 30.0939 1.50282 0.751408 0.659838i \(-0.229375\pi\)
0.751408 + 0.659838i \(0.229375\pi\)
\(402\) 0 0
\(403\) −1.89829 −0.0945605
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.06959 0.0530177
\(408\) 0 0
\(409\) −17.3921 −0.859983 −0.429991 0.902833i \(-0.641483\pi\)
−0.429991 + 0.902833i \(0.641483\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −55.0420 −2.70844
\(414\) 0 0
\(415\) 16.5620 0.812996
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.9541 −0.974820 −0.487410 0.873173i \(-0.662058\pi\)
−0.487410 + 0.873173i \(0.662058\pi\)
\(420\) 0 0
\(421\) 15.0192 0.731992 0.365996 0.930616i \(-0.380728\pi\)
0.365996 + 0.930616i \(0.380728\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.407896 0.0197859
\(426\) 0 0
\(427\) 12.8573 0.622207
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 17.5812 0.846857 0.423428 0.905930i \(-0.360827\pi\)
0.423428 + 0.905930i \(0.360827\pi\)
\(432\) 0 0
\(433\) −10.2208 −0.491179 −0.245590 0.969374i \(-0.578982\pi\)
−0.245590 + 0.969374i \(0.578982\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.22570 −0.345652
\(438\) 0 0
\(439\) −5.91903 −0.282500 −0.141250 0.989974i \(-0.545112\pi\)
−0.141250 + 0.989974i \(0.545112\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −37.1022 −1.76278 −0.881389 0.472391i \(-0.843391\pi\)
−0.881389 + 0.472391i \(0.843391\pi\)
\(444\) 0 0
\(445\) 10.7556 0.509863
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.9398 −0.657859 −0.328929 0.944355i \(-0.606688\pi\)
−0.328929 + 0.944355i \(0.606688\pi\)
\(450\) 0 0
\(451\) 1.82516 0.0859434
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 6.10171 0.286053
\(456\) 0 0
\(457\) 2.47013 0.115548 0.0577738 0.998330i \(-0.481600\pi\)
0.0577738 + 0.998330i \(0.481600\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −21.8479 −1.01756 −0.508779 0.860897i \(-0.669903\pi\)
−0.508779 + 0.860897i \(0.669903\pi\)
\(462\) 0 0
\(463\) −38.1956 −1.77510 −0.887550 0.460712i \(-0.847594\pi\)
−0.887550 + 0.460712i \(0.847594\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −6.36842 −0.294695 −0.147348 0.989085i \(-0.547074\pi\)
−0.147348 + 0.989085i \(0.547074\pi\)
\(468\) 0 0
\(469\) −24.7654 −1.14356
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 7.98126 0.366979
\(474\) 0 0
\(475\) 0.561993 0.0257860
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −34.1847 −1.56194 −0.780969 0.624570i \(-0.785274\pi\)
−0.780969 + 0.624570i \(0.785274\pi\)
\(480\) 0 0
\(481\) −0.736833 −0.0335967
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 16.1334 0.732578
\(486\) 0 0
\(487\) −17.7540 −0.804512 −0.402256 0.915527i \(-0.631774\pi\)
−0.402256 + 0.915527i \(0.631774\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.32248 −0.104812 −0.0524061 0.998626i \(-0.516689\pi\)
−0.0524061 + 0.998626i \(0.516689\pi\)
\(492\) 0 0
\(493\) 37.3274 1.68114
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −17.7146 −0.794607
\(498\) 0 0
\(499\) 26.3289 1.17865 0.589323 0.807898i \(-0.299395\pi\)
0.589323 + 0.807898i \(0.299395\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.27163 −0.145875 −0.0729373 0.997337i \(-0.523237\pi\)
−0.0729373 + 0.997337i \(0.523237\pi\)
\(504\) 0 0
\(505\) 29.3733 1.30710
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.09234 −0.137066 −0.0685328 0.997649i \(-0.521832\pi\)
−0.0685328 + 0.997649i \(0.521832\pi\)
\(510\) 0 0
\(511\) 34.5718 1.52937
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 10.2810 0.453035
\(516\) 0 0
\(517\) 2.79706 0.123014
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.5605 0.681716 0.340858 0.940115i \(-0.389282\pi\)
0.340858 + 0.940115i \(0.389282\pi\)
\(522\) 0 0
\(523\) 4.82870 0.211144 0.105572 0.994412i \(-0.466333\pi\)
0.105572 + 0.994412i \(0.466333\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 12.8573 0.560072
\(528\) 0 0
\(529\) −21.4514 −0.932669
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.25734 −0.0544614
\(534\) 0 0
\(535\) −20.9590 −0.906136
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −11.3921 −0.490691
\(540\) 0 0
\(541\) −32.4385 −1.39464 −0.697320 0.716760i \(-0.745624\pi\)
−0.697320 + 0.716760i \(0.745624\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14.2351 0.609763
\(546\) 0 0
\(547\) 3.39853 0.145311 0.0726553 0.997357i \(-0.476853\pi\)
0.0726553 + 0.997357i \(0.476853\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 51.4291 2.19095
\(552\) 0 0
\(553\) −7.64143 −0.324947
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −37.9398 −1.60756 −0.803780 0.594927i \(-0.797181\pi\)
−0.803780 + 0.594927i \(0.797181\pi\)
\(558\) 0 0
\(559\) −5.49823 −0.232550
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −3.21279 −0.135403 −0.0677014 0.997706i \(-0.521567\pi\)
−0.0677014 + 0.997706i \(0.521567\pi\)
\(564\) 0 0
\(565\) 9.85236 0.414492
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −15.7255 −0.659245 −0.329623 0.944113i \(-0.606922\pi\)
−0.329623 + 0.944113i \(0.606922\pi\)
\(570\) 0 0
\(571\) −34.2973 −1.43530 −0.717649 0.696405i \(-0.754782\pi\)
−0.717649 + 0.696405i \(0.754782\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.120446 −0.00502295
\(576\) 0 0
\(577\) −29.9541 −1.24700 −0.623502 0.781822i \(-0.714291\pi\)
−0.623502 + 0.781822i \(0.714291\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 33.1240 1.37421
\(582\) 0 0
\(583\) −3.92687 −0.162634
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −26.8256 −1.10721 −0.553606 0.832779i \(-0.686749\pi\)
−0.553606 + 0.832779i \(0.686749\pi\)
\(588\) 0 0
\(589\) 17.7146 0.729916
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −21.5190 −0.883678 −0.441839 0.897094i \(-0.645674\pi\)
−0.441839 + 0.897094i \(0.645674\pi\)
\(594\) 0 0
\(595\) −41.3274 −1.69426
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.71456 −0.0700549 −0.0350275 0.999386i \(-0.511152\pi\)
−0.0350275 + 0.999386i \(0.511152\pi\)
\(600\) 0 0
\(601\) −0.488863 −0.0199411 −0.00997056 0.999950i \(-0.503174\pi\)
−0.00997056 + 0.999950i \(0.503174\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 22.5511 0.916832
\(606\) 0 0
\(607\) −31.9704 −1.29764 −0.648819 0.760943i \(-0.724737\pi\)
−0.648819 + 0.760943i \(0.724737\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.92687 −0.0779528
\(612\) 0 0
\(613\) −24.0558 −0.971604 −0.485802 0.874069i \(-0.661472\pi\)
−0.485802 + 0.874069i \(0.661472\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 45.1526 1.81777 0.908887 0.417043i \(-0.136933\pi\)
0.908887 + 0.417043i \(0.136933\pi\)
\(618\) 0 0
\(619\) 30.1037 1.20997 0.604985 0.796237i \(-0.293179\pi\)
0.604985 + 0.796237i \(0.293179\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 21.5111 0.861826
\(624\) 0 0
\(625\) −24.5067 −0.980268
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.99063 0.198990
\(630\) 0 0
\(631\) −33.7275 −1.34267 −0.671335 0.741154i \(-0.734279\pi\)
−0.671335 + 0.741154i \(0.734279\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −5.80642 −0.230421
\(636\) 0 0
\(637\) 7.84791 0.310946
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.2242 0.798806 0.399403 0.916775i \(-0.369217\pi\)
0.399403 + 0.916775i \(0.369217\pi\)
\(642\) 0 0
\(643\) 45.8084 1.80651 0.903254 0.429106i \(-0.141171\pi\)
0.903254 + 0.429106i \(0.141171\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 27.4291 1.07835 0.539175 0.842194i \(-0.318736\pi\)
0.539175 + 0.842194i \(0.318736\pi\)
\(648\) 0 0
\(649\) −11.2257 −0.440647
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.53972 0.0602538 0.0301269 0.999546i \(-0.490409\pi\)
0.0301269 + 0.999546i \(0.490409\pi\)
\(654\) 0 0
\(655\) −12.5620 −0.490838
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −28.7783 −1.12104 −0.560522 0.828139i \(-0.689400\pi\)
−0.560522 + 0.828139i \(0.689400\pi\)
\(660\) 0 0
\(661\) −12.2065 −0.474777 −0.237389 0.971415i \(-0.576291\pi\)
−0.237389 + 0.971415i \(0.576291\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −56.9403 −2.20805
\(666\) 0 0
\(667\) −11.0223 −0.426784
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.62222 0.101230
\(672\) 0 0
\(673\) −16.3684 −0.630956 −0.315478 0.948933i \(-0.602165\pi\)
−0.315478 + 0.948933i \(0.602165\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 41.7975 1.60641 0.803205 0.595703i \(-0.203126\pi\)
0.803205 + 0.595703i \(0.203126\pi\)
\(678\) 0 0
\(679\) 32.2667 1.23828
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −44.3368 −1.69650 −0.848250 0.529596i \(-0.822343\pi\)
−0.848250 + 0.529596i \(0.822343\pi\)
\(684\) 0 0
\(685\) −27.5210 −1.05152
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.70519 0.103060
\(690\) 0 0
\(691\) −21.4588 −0.816329 −0.408165 0.912908i \(-0.633831\pi\)
−0.408165 + 0.912908i \(0.633831\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 30.5259 1.15791
\(696\) 0 0
\(697\) 8.51606 0.322569
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.40006 −0.317266 −0.158633 0.987338i \(-0.550709\pi\)
−0.158633 + 0.987338i \(0.550709\pi\)
\(702\) 0 0
\(703\) 6.87601 0.259334
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 58.7467 2.20940
\(708\) 0 0
\(709\) −3.64449 −0.136872 −0.0684359 0.997656i \(-0.521801\pi\)
−0.0684359 + 0.997656i \(0.521801\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.79658 −0.142183
\(714\) 0 0
\(715\) 1.24443 0.0465391
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.48886 −0.0928189 −0.0464095 0.998923i \(-0.514778\pi\)
−0.0464095 + 0.998923i \(0.514778\pi\)
\(720\) 0 0
\(721\) 20.5620 0.765769
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.857279 0.0318385
\(726\) 0 0
\(727\) 10.8968 0.404138 0.202069 0.979371i \(-0.435233\pi\)
0.202069 + 0.979371i \(0.435233\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 37.2400 1.37737
\(732\) 0 0
\(733\) 13.0968 0.483741 0.241870 0.970309i \(-0.422239\pi\)
0.241870 + 0.970309i \(0.422239\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.05086 −0.186051
\(738\) 0 0
\(739\) −16.2973 −0.599506 −0.299753 0.954017i \(-0.596904\pi\)
−0.299753 + 0.954017i \(0.596904\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 14.3684 0.527126 0.263563 0.964642i \(-0.415102\pi\)
0.263563 + 0.964642i \(0.415102\pi\)
\(744\) 0 0
\(745\) −23.4336 −0.858539
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −41.9180 −1.53165
\(750\) 0 0
\(751\) −9.56046 −0.348866 −0.174433 0.984669i \(-0.555809\pi\)
−0.174433 + 0.984669i \(0.555809\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −30.3225 −1.10355
\(756\) 0 0
\(757\) −8.83854 −0.321242 −0.160621 0.987016i \(-0.551350\pi\)
−0.160621 + 0.987016i \(0.551350\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 11.9911 0.434677 0.217339 0.976096i \(-0.430262\pi\)
0.217339 + 0.976096i \(0.430262\pi\)
\(762\) 0 0
\(763\) 28.4701 1.03069
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.73329 0.279233
\(768\) 0 0
\(769\) 24.4889 0.883091 0.441545 0.897239i \(-0.354430\pi\)
0.441545 + 0.897239i \(0.354430\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.85881 −0.138792 −0.0693959 0.997589i \(-0.522107\pi\)
−0.0693959 + 0.997589i \(0.522107\pi\)
\(774\) 0 0
\(775\) 0.295286 0.0106070
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 11.7333 0.420389
\(780\) 0 0
\(781\) −3.61285 −0.129278
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.27607 −0.259694
\(786\) 0 0
\(787\) 37.8272 1.34839 0.674196 0.738552i \(-0.264490\pi\)
0.674196 + 0.738552i \(0.264490\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 19.7047 0.700619
\(792\) 0 0
\(793\) −1.80642 −0.0641480
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 27.4686 0.972988 0.486494 0.873684i \(-0.338276\pi\)
0.486494 + 0.873684i \(0.338276\pi\)
\(798\) 0 0
\(799\) 13.0509 0.461706
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.05086 0.248819
\(804\) 0 0
\(805\) 12.2034 0.430114
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −47.7748 −1.67967 −0.839836 0.542840i \(-0.817349\pi\)
−0.839836 + 0.542840i \(0.817349\pi\)
\(810\) 0 0
\(811\) −6.89676 −0.242178 −0.121089 0.992642i \(-0.538639\pi\)
−0.121089 + 0.992642i \(0.538639\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 18.4143 0.645027
\(816\) 0 0
\(817\) 51.3087 1.79506
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.734825 −0.0256456 −0.0128228 0.999918i \(-0.504082\pi\)
−0.0128228 + 0.999918i \(0.504082\pi\)
\(822\) 0 0
\(823\) 29.5288 1.02931 0.514655 0.857397i \(-0.327920\pi\)
0.514655 + 0.857397i \(0.327920\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 44.4197 1.54463 0.772313 0.635242i \(-0.219100\pi\)
0.772313 + 0.635242i \(0.219100\pi\)
\(828\) 0 0
\(829\) −13.5714 −0.471353 −0.235676 0.971832i \(-0.575731\pi\)
−0.235676 + 0.971832i \(0.575731\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −53.1546 −1.84170
\(834\) 0 0
\(835\) 2.21432 0.0766297
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 17.8524 0.616332 0.308166 0.951333i \(-0.400285\pi\)
0.308166 + 0.951333i \(0.400285\pi\)
\(840\) 0 0
\(841\) 49.4514 1.70522
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 27.9289 0.960783
\(846\) 0 0
\(847\) 45.1022 1.54973
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.47367 −0.0505166
\(852\) 0 0
\(853\) −16.1762 −0.553863 −0.276932 0.960890i \(-0.589318\pi\)
−0.276932 + 0.960890i \(0.589318\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −51.9081 −1.77315 −0.886574 0.462587i \(-0.846921\pi\)
−0.886574 + 0.462587i \(0.846921\pi\)
\(858\) 0 0
\(859\) 5.46076 0.186319 0.0931593 0.995651i \(-0.470303\pi\)
0.0931593 + 0.995651i \(0.470303\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 22.5018 0.765969 0.382985 0.923755i \(-0.374896\pi\)
0.382985 + 0.923755i \(0.374896\pi\)
\(864\) 0 0
\(865\) −48.2864 −1.64179
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.55845 −0.0528669
\(870\) 0 0
\(871\) 3.47949 0.117898
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −49.9813 −1.68968
\(876\) 0 0
\(877\) −38.7783 −1.30945 −0.654725 0.755867i \(-0.727216\pi\)
−0.654725 + 0.755867i \(0.727216\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.07160 0.103485 0.0517424 0.998660i \(-0.483523\pi\)
0.0517424 + 0.998660i \(0.483523\pi\)
\(882\) 0 0
\(883\) 19.7877 0.665909 0.332954 0.942943i \(-0.391954\pi\)
0.332954 + 0.942943i \(0.391954\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −33.5655 −1.12702 −0.563510 0.826109i \(-0.690549\pi\)
−0.563510 + 0.826109i \(0.690549\pi\)
\(888\) 0 0
\(889\) −11.6128 −0.389482
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 17.9813 0.601720
\(894\) 0 0
\(895\) 57.5308 1.92304
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 27.0223 0.901243
\(900\) 0 0
\(901\) −18.3225 −0.610410
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 42.5116 1.41313
\(906\) 0 0
\(907\) 19.8666 0.659661 0.329831 0.944040i \(-0.393008\pi\)
0.329831 + 0.944040i \(0.393008\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 11.0223 0.365184 0.182592 0.983189i \(-0.441551\pi\)
0.182592 + 0.983189i \(0.441551\pi\)
\(912\) 0 0
\(913\) 6.75557 0.223577
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −25.1240 −0.829667
\(918\) 0 0
\(919\) 14.7971 0.488110 0.244055 0.969761i \(-0.421522\pi\)
0.244055 + 0.969761i \(0.421522\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.48886 0.0819219
\(924\) 0 0
\(925\) 0.114617 0.00376859
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −30.5807 −1.00332 −0.501661 0.865065i \(-0.667277\pi\)
−0.501661 + 0.865065i \(0.667277\pi\)
\(930\) 0 0
\(931\) −73.2355 −2.40020
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −8.42864 −0.275646
\(936\) 0 0
\(937\) −31.3560 −1.02436 −0.512178 0.858880i \(-0.671161\pi\)
−0.512178 + 0.858880i \(0.671161\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −26.0020 −0.847641 −0.423821 0.905746i \(-0.639311\pi\)
−0.423821 + 0.905746i \(0.639311\pi\)
\(942\) 0 0
\(943\) −2.51468 −0.0818891
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 33.4938 1.08840 0.544201 0.838955i \(-0.316833\pi\)
0.544201 + 0.838955i \(0.316833\pi\)
\(948\) 0 0
\(949\) −4.85728 −0.157674
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −18.2429 −0.590945 −0.295473 0.955351i \(-0.595477\pi\)
−0.295473 + 0.955351i \(0.595477\pi\)
\(954\) 0 0
\(955\) −26.4701 −0.856553
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −55.0420 −1.77740
\(960\) 0 0
\(961\) −21.6923 −0.699751
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 45.7560 1.47294
\(966\) 0 0
\(967\) 31.2958 1.00640 0.503202 0.864169i \(-0.332155\pi\)
0.503202 + 0.864169i \(0.332155\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −41.9398 −1.34591 −0.672956 0.739683i \(-0.734976\pi\)
−0.672956 + 0.739683i \(0.734976\pi\)
\(972\) 0 0
\(973\) 61.0518 1.95723
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 11.4114 0.365084 0.182542 0.983198i \(-0.441567\pi\)
0.182542 + 0.983198i \(0.441567\pi\)
\(978\) 0 0
\(979\) 4.38715 0.140214
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 27.9911 0.892778 0.446389 0.894839i \(-0.352710\pi\)
0.446389 + 0.894839i \(0.352710\pi\)
\(984\) 0 0
\(985\) −56.9862 −1.81573
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −10.9965 −0.349667
\(990\) 0 0
\(991\) 5.33830 0.169577 0.0847884 0.996399i \(-0.472979\pi\)
0.0847884 + 0.996399i \(0.472979\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −36.1748 −1.14682
\(996\) 0 0
\(997\) −18.8399 −0.596666 −0.298333 0.954462i \(-0.596431\pi\)
−0.298333 + 0.954462i \(0.596431\pi\)
\(998\) 0 0
\(999\) 0 0
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 6012.2.a.c.1.1 yes 3
3.2 odd 2 6012.2.a.b.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.a.b.1.3 3 3.2 odd 2
6012.2.a.c.1.1 yes 3 1.1 even 1 trivial