Properties

Label 6012.2.a.c.1.3
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 1.3
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.67513 q^{5} +3.35026 q^{7} +O(q^{10})\) \(q+1.67513 q^{5} +3.35026 q^{7} +1.19394 q^{11} -2.96239 q^{13} -0.324869 q^{17} -1.61213 q^{19} -5.92478 q^{23} -2.19394 q^{25} +6.70052 q^{29} +8.31265 q^{31} +5.61213 q^{35} -0.574515 q^{37} +6.06300 q^{41} -1.36248 q^{43} -5.19394 q^{47} +4.22425 q^{49} +11.2120 q^{53} +2.00000 q^{55} +4.64974 q^{59} -0.806063 q^{61} -4.96239 q^{65} +5.28726 q^{67} +4.00000 q^{71} -3.61213 q^{73} +4.00000 q^{77} +12.1744 q^{79} +11.6629 q^{83} -0.544198 q^{85} +10.7005 q^{89} -9.92478 q^{91} -2.70052 q^{95} +16.0508 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + O(q^{10}) \) \( 3q + 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + 4q^{23} - 7q^{25} + 4q^{31} + 16q^{35} + 10q^{37} + 14q^{41} - 20q^{43} - 16q^{47} + 11q^{49} + 6q^{53} + 6q^{55} + 24q^{59} - 2q^{61} - 4q^{65} + 10q^{67} + 12q^{71} - 10q^{73} + 12q^{77} - 2q^{79} + 4q^{83} + 8q^{85} + 12q^{89} - 8q^{91} + 12q^{95} + 18q^{97} + O(q^{100}) \)

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
\(5\) 1.67513 0.749141 0.374571 0.927198i \(-0.377790\pi\)
0.374571 + 0.927198i \(0.377790\pi\)
\(6\) 0 0
\(7\) 3.35026 1.26628 0.633140 0.774037i \(-0.281766\pi\)
0.633140 + 0.774037i \(0.281766\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.19394 0.359985 0.179993 0.983668i \(-0.442393\pi\)
0.179993 + 0.983668i \(0.442393\pi\)
\(12\) 0 0
\(13\) −2.96239 −0.821619 −0.410809 0.911721i \(-0.634754\pi\)
−0.410809 + 0.911721i \(0.634754\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.324869 −0.0787923 −0.0393962 0.999224i \(-0.512543\pi\)
−0.0393962 + 0.999224i \(0.512543\pi\)
\(18\) 0 0
\(19\) −1.61213 −0.369847 −0.184924 0.982753i \(-0.559204\pi\)
−0.184924 + 0.982753i \(0.559204\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −5.92478 −1.23540 −0.617701 0.786413i \(-0.711936\pi\)
−0.617701 + 0.786413i \(0.711936\pi\)
\(24\) 0 0
\(25\) −2.19394 −0.438787
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 6.70052 1.24426 0.622128 0.782916i \(-0.286268\pi\)
0.622128 + 0.782916i \(0.286268\pi\)
\(30\) 0 0
\(31\) 8.31265 1.49300 0.746498 0.665388i \(-0.231734\pi\)
0.746498 + 0.665388i \(0.231734\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 5.61213 0.948623
\(36\) 0 0
\(37\) −0.574515 −0.0944498 −0.0472249 0.998884i \(-0.515038\pi\)
−0.0472249 + 0.998884i \(0.515038\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.06300 0.946882 0.473441 0.880825i \(-0.343012\pi\)
0.473441 + 0.880825i \(0.343012\pi\)
\(42\) 0 0
\(43\) −1.36248 −0.207776 −0.103888 0.994589i \(-0.533128\pi\)
−0.103888 + 0.994589i \(0.533128\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.19394 −0.757614 −0.378807 0.925476i \(-0.623665\pi\)
−0.378807 + 0.925476i \(0.623665\pi\)
\(48\) 0 0
\(49\) 4.22425 0.603465
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11.2120 1.54009 0.770046 0.637989i \(-0.220233\pi\)
0.770046 + 0.637989i \(0.220233\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.64974 0.605344 0.302672 0.953095i \(-0.402121\pi\)
0.302672 + 0.953095i \(0.402121\pi\)
\(60\) 0 0
\(61\) −0.806063 −0.103206 −0.0516029 0.998668i \(-0.516433\pi\)
−0.0516029 + 0.998668i \(0.516433\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.96239 −0.615509
\(66\) 0 0
\(67\) 5.28726 0.645941 0.322971 0.946409i \(-0.395318\pi\)
0.322971 + 0.946409i \(0.395318\pi\)
\(68\) 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
\(73\) −3.61213 −0.422767 −0.211384 0.977403i \(-0.567797\pi\)
−0.211384 + 0.977403i \(0.567797\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 12.1744 1.36973 0.684865 0.728670i \(-0.259861\pi\)
0.684865 + 0.728670i \(0.259861\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 11.6629 1.28017 0.640085 0.768304i \(-0.278899\pi\)
0.640085 + 0.768304i \(0.278899\pi\)
\(84\) 0 0
\(85\) −0.544198 −0.0590266
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10.7005 1.13425 0.567127 0.823631i \(-0.308055\pi\)
0.567127 + 0.823631i \(0.308055\pi\)
\(90\) 0 0
\(91\) −9.92478 −1.04040
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.70052 −0.277068
\(96\) 0 0
\(97\) 16.0508 1.62971 0.814855 0.579665i \(-0.196816\pi\)
0.814855 + 0.579665i \(0.196816\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.98778 0.197792 0.0988958 0.995098i \(-0.468469\pi\)
0.0988958 + 0.995098i \(0.468469\pi\)
\(102\) 0 0
\(103\) 7.02539 0.692233 0.346116 0.938192i \(-0.387500\pi\)
0.346116 + 0.938192i \(0.387500\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.3430 0.999892 0.499946 0.866056i \(-0.333353\pi\)
0.499946 + 0.866056i \(0.333353\pi\)
\(108\) 0 0
\(109\) 1.35026 0.129332 0.0646658 0.997907i \(-0.479402\pi\)
0.0646658 + 0.997907i \(0.479402\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.4133 1.07367 0.536835 0.843687i \(-0.319620\pi\)
0.536835 + 0.843687i \(0.319620\pi\)
\(114\) 0 0
\(115\) −9.92478 −0.925490
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.08840 −0.0997732
\(120\) 0 0
\(121\) −9.57452 −0.870410
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.0508 −1.07785
\(126\) 0 0
\(127\) −0.962389 −0.0853982 −0.0426991 0.999088i \(-0.513596\pi\)
−0.0426991 + 0.999088i \(0.513596\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −9.27504 −0.810364 −0.405182 0.914236i \(-0.632792\pi\)
−0.405182 + 0.914236i \(0.632792\pi\)
\(132\) 0 0
\(133\) −5.40105 −0.468330
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.64974 0.397254 0.198627 0.980075i \(-0.436352\pi\)
0.198627 + 0.980075i \(0.436352\pi\)
\(138\) 0 0
\(139\) −17.6751 −1.49919 −0.749593 0.661900i \(-0.769751\pi\)
−0.749593 + 0.661900i \(0.769751\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.53690 −0.295771
\(144\) 0 0
\(145\) 11.2243 0.932124
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.47390 0.448439 0.224220 0.974539i \(-0.428017\pi\)
0.224220 + 0.974539i \(0.428017\pi\)
\(150\) 0 0
\(151\) −9.33804 −0.759919 −0.379960 0.925003i \(-0.624062\pi\)
−0.379960 + 0.925003i \(0.624062\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 13.9248 1.11847
\(156\) 0 0
\(157\) −20.0508 −1.60023 −0.800113 0.599849i \(-0.795227\pi\)
−0.800113 + 0.599849i \(0.795227\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −19.8496 −1.56436
\(162\) 0 0
\(163\) 18.3004 1.43340 0.716700 0.697381i \(-0.245652\pi\)
0.716700 + 0.697381i \(0.245652\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) −4.22425 −0.324943
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 17.6121 1.33903 0.669513 0.742801i \(-0.266503\pi\)
0.669513 + 0.742801i \(0.266503\pi\)
\(174\) 0 0
\(175\) −7.35026 −0.555628
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −16.3733 −1.22380 −0.611898 0.790936i \(-0.709594\pi\)
−0.611898 + 0.790936i \(0.709594\pi\)
\(180\) 0 0
\(181\) 1.43136 0.106392 0.0531962 0.998584i \(-0.483059\pi\)
0.0531962 + 0.998584i \(0.483059\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.962389 −0.0707562
\(186\) 0 0
\(187\) −0.387873 −0.0283641
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50659 −0.109013 −0.0545064 0.998513i \(-0.517359\pi\)
−0.0545064 + 0.998513i \(0.517359\pi\)
\(192\) 0 0
\(193\) −0.911603 −0.0656186 −0.0328093 0.999462i \(-0.510445\pi\)
−0.0328093 + 0.999462i \(0.510445\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.4641 −0.959274 −0.479637 0.877467i \(-0.659232\pi\)
−0.479637 + 0.877467i \(0.659232\pi\)
\(198\) 0 0
\(199\) −18.3634 −1.30175 −0.650875 0.759185i \(-0.725598\pi\)
−0.650875 + 0.759185i \(0.725598\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 22.4485 1.57558
\(204\) 0 0
\(205\) 10.1563 0.709349
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.92478 −0.133140
\(210\) 0 0
\(211\) −7.01317 −0.482807 −0.241403 0.970425i \(-0.577608\pi\)
−0.241403 + 0.970425i \(0.577608\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.28233 −0.155654
\(216\) 0 0
\(217\) 27.8496 1.89055
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.962389 0.0647373
\(222\) 0 0
\(223\) 21.2750 1.42468 0.712341 0.701834i \(-0.247635\pi\)
0.712341 + 0.701834i \(0.247635\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.03761 0.201613 0.100807 0.994906i \(-0.467858\pi\)
0.100807 + 0.994906i \(0.467858\pi\)
\(228\) 0 0
\(229\) −16.8061 −1.11058 −0.555288 0.831658i \(-0.687392\pi\)
−0.555288 + 0.831658i \(0.687392\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.43866 0.552835 0.276417 0.961038i \(-0.410853\pi\)
0.276417 + 0.961038i \(0.410853\pi\)
\(234\) 0 0
\(235\) −8.70052 −0.567560
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −27.2809 −1.76466 −0.882328 0.470635i \(-0.844025\pi\)
−0.882328 + 0.470635i \(0.844025\pi\)
\(240\) 0 0
\(241\) −22.9380 −1.47756 −0.738782 0.673945i \(-0.764599\pi\)
−0.738782 + 0.673945i \(0.764599\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 7.07618 0.452080
\(246\) 0 0
\(247\) 4.77575 0.303873
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 5.11283 0.322719 0.161360 0.986896i \(-0.448412\pi\)
0.161360 + 0.986896i \(0.448412\pi\)
\(252\) 0 0
\(253\) −7.07381 −0.444727
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −16.5623 −1.03313 −0.516564 0.856249i \(-0.672789\pi\)
−0.516564 + 0.856249i \(0.672789\pi\)
\(258\) 0 0
\(259\) −1.92478 −0.119600
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 26.8872 1.65793 0.828967 0.559298i \(-0.188929\pi\)
0.828967 + 0.559298i \(0.188929\pi\)
\(264\) 0 0
\(265\) 18.7816 1.15375
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 18.1890 1.10900 0.554502 0.832183i \(-0.312909\pi\)
0.554502 + 0.832183i \(0.312909\pi\)
\(270\) 0 0
\(271\) 18.5623 1.12758 0.563790 0.825918i \(-0.309343\pi\)
0.563790 + 0.825918i \(0.309343\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.61942 −0.157957
\(276\) 0 0
\(277\) 1.09825 0.0659872 0.0329936 0.999456i \(-0.489496\pi\)
0.0329936 + 0.999456i \(0.489496\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.1114 0.841817 0.420908 0.907103i \(-0.361711\pi\)
0.420908 + 0.907103i \(0.361711\pi\)
\(282\) 0 0
\(283\) 18.2374 1.08410 0.542051 0.840345i \(-0.317648\pi\)
0.542051 + 0.840345i \(0.317648\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 20.3127 1.19902
\(288\) 0 0
\(289\) −16.8945 −0.993792
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5.92478 −0.346129 −0.173065 0.984910i \(-0.555367\pi\)
−0.173065 + 0.984910i \(0.555367\pi\)
\(294\) 0 0
\(295\) 7.78892 0.453488
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 17.5515 1.01503
\(300\) 0 0
\(301\) −4.56467 −0.263103
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.35026 −0.0773158
\(306\) 0 0
\(307\) −10.0484 −0.573493 −0.286747 0.958006i \(-0.592574\pi\)
−0.286747 + 0.958006i \(0.592574\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 26.8872 1.52463 0.762316 0.647205i \(-0.224062\pi\)
0.762316 + 0.647205i \(0.224062\pi\)
\(312\) 0 0
\(313\) 8.44851 0.477538 0.238769 0.971076i \(-0.423256\pi\)
0.238769 + 0.971076i \(0.423256\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.83638 0.271638 0.135819 0.990734i \(-0.456633\pi\)
0.135819 + 0.990734i \(0.456633\pi\)
\(318\) 0 0
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.523730 0.0291411
\(324\) 0 0
\(325\) 6.49929 0.360516
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −17.4010 −0.959351
\(330\) 0 0
\(331\) 0.787965 0.0433105 0.0216552 0.999765i \(-0.493106\pi\)
0.0216552 + 0.999765i \(0.493106\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 8.85685 0.483901
\(336\) 0 0
\(337\) −12.4241 −0.676782 −0.338391 0.941006i \(-0.609883\pi\)
−0.338391 + 0.941006i \(0.609883\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.92478 0.537457
\(342\) 0 0
\(343\) −9.29948 −0.502125
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.27504 −0.283179 −0.141589 0.989925i \(-0.545221\pi\)
−0.141589 + 0.989925i \(0.545221\pi\)
\(348\) 0 0
\(349\) −16.5745 −0.887213 −0.443607 0.896222i \(-0.646301\pi\)
−0.443607 + 0.896222i \(0.646301\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 5.58769 0.297403 0.148701 0.988882i \(-0.452491\pi\)
0.148701 + 0.988882i \(0.452491\pi\)
\(354\) 0 0
\(355\) 6.70052 0.355627
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 10.5501 0.556812 0.278406 0.960464i \(-0.410194\pi\)
0.278406 + 0.960464i \(0.410194\pi\)
\(360\) 0 0
\(361\) −16.4010 −0.863213
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6.05079 −0.316713
\(366\) 0 0
\(367\) −22.6107 −1.18027 −0.590135 0.807305i \(-0.700925\pi\)
−0.590135 + 0.807305i \(0.700925\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 37.5633 1.95019
\(372\) 0 0
\(373\) 1.66291 0.0861023 0.0430512 0.999073i \(-0.486292\pi\)
0.0430512 + 0.999073i \(0.486292\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −19.8496 −1.02230
\(378\) 0 0
\(379\) 17.8618 0.917498 0.458749 0.888566i \(-0.348298\pi\)
0.458749 + 0.888566i \(0.348298\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.67021 −0.238636 −0.119318 0.992856i \(-0.538071\pi\)
−0.119318 + 0.992856i \(0.538071\pi\)
\(384\) 0 0
\(385\) 6.70052 0.341490
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2.78797 −0.141355 −0.0706777 0.997499i \(-0.522516\pi\)
−0.0706777 + 0.997499i \(0.522516\pi\)
\(390\) 0 0
\(391\) 1.92478 0.0973402
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 20.3938 1.02612
\(396\) 0 0
\(397\) 12.0303 0.603784 0.301892 0.953342i \(-0.402382\pi\)
0.301892 + 0.953342i \(0.402382\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 39.3235 1.96372 0.981860 0.189608i \(-0.0607218\pi\)
0.981860 + 0.189608i \(0.0607218\pi\)
\(402\) 0 0
\(403\) −24.6253 −1.22667
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.685935 −0.0340005
\(408\) 0 0
\(409\) −0.956509 −0.0472963 −0.0236482 0.999720i \(-0.507528\pi\)
−0.0236482 + 0.999720i \(0.507528\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 15.5778 0.766535
\(414\) 0 0
\(415\) 19.5369 0.959029
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.49341 −0.317224 −0.158612 0.987341i \(-0.550702\pi\)
−0.158612 + 0.987341i \(0.550702\pi\)
\(420\) 0 0
\(421\) −29.8251 −1.45359 −0.726794 0.686856i \(-0.758990\pi\)
−0.726794 + 0.686856i \(0.758990\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.712742 0.0345731
\(426\) 0 0
\(427\) −2.70052 −0.130687
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −24.2882 −1.16992 −0.584961 0.811061i \(-0.698890\pi\)
−0.584961 + 0.811061i \(0.698890\pi\)
\(432\) 0 0
\(433\) −18.2677 −0.877892 −0.438946 0.898513i \(-0.644648\pi\)
−0.438946 + 0.898513i \(0.644648\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 9.55149 0.456910
\(438\) 0 0
\(439\) −20.5623 −0.981385 −0.490692 0.871333i \(-0.663256\pi\)
−0.490692 + 0.871333i \(0.663256\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 40.0771 1.90412 0.952061 0.305908i \(-0.0989601\pi\)
0.952061 + 0.305908i \(0.0989601\pi\)
\(444\) 0 0
\(445\) 17.9248 0.849716
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −20.4993 −0.967421 −0.483711 0.875228i \(-0.660711\pi\)
−0.483711 + 0.875228i \(0.660711\pi\)
\(450\) 0 0
\(451\) 7.23884 0.340864
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −16.6253 −0.779406
\(456\) 0 0
\(457\) −21.4763 −1.00462 −0.502309 0.864688i \(-0.667516\pi\)
−0.502309 + 0.864688i \(0.667516\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.48612 −0.0692155 −0.0346077 0.999401i \(-0.511018\pi\)
−0.0346077 + 0.999401i \(0.511018\pi\)
\(462\) 0 0
\(463\) −24.6982 −1.14782 −0.573910 0.818918i \(-0.694574\pi\)
−0.573910 + 0.818918i \(0.694574\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.14903 −0.238269 −0.119134 0.992878i \(-0.538012\pi\)
−0.119134 + 0.992878i \(0.538012\pi\)
\(468\) 0 0
\(469\) 17.7137 0.817943
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.62672 −0.0747964
\(474\) 0 0
\(475\) 3.53690 0.162284
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 20.8773 0.953909 0.476954 0.878928i \(-0.341741\pi\)
0.476954 + 0.878928i \(0.341741\pi\)
\(480\) 0 0
\(481\) 1.70194 0.0776017
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 26.8872 1.22088
\(486\) 0 0
\(487\) 11.8373 0.536401 0.268200 0.963363i \(-0.413571\pi\)
0.268200 + 0.963363i \(0.413571\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 12.3576 0.557689 0.278844 0.960336i \(-0.410049\pi\)
0.278844 + 0.960336i \(0.410049\pi\)
\(492\) 0 0
\(493\) −2.17679 −0.0980378
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 13.4010 0.601119
\(498\) 0 0
\(499\) 23.5853 1.05582 0.527912 0.849299i \(-0.322975\pi\)
0.527912 + 0.849299i \(0.322975\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0.0449056 0.00200224 0.00100112 0.999999i \(-0.499681\pi\)
0.00100112 + 0.999999i \(0.499681\pi\)
\(504\) 0 0
\(505\) 3.32979 0.148174
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 24.4387 1.08322 0.541612 0.840628i \(-0.317814\pi\)
0.541612 + 0.840628i \(0.317814\pi\)
\(510\) 0 0
\(511\) −12.1016 −0.535342
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 11.7685 0.518580
\(516\) 0 0
\(517\) −6.20123 −0.272730
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −18.2252 −0.798461 −0.399230 0.916851i \(-0.630723\pi\)
−0.399230 + 0.916851i \(0.630723\pi\)
\(522\) 0 0
\(523\) 29.3112 1.28169 0.640845 0.767670i \(-0.278584\pi\)
0.640845 + 0.767670i \(0.278584\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.70052 −0.117637
\(528\) 0 0
\(529\) 12.1030 0.526217
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −17.9610 −0.777976
\(534\) 0 0
\(535\) 17.3258 0.749061
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 5.04349 0.217239
\(540\) 0 0
\(541\) 24.9887 1.07435 0.537175 0.843471i \(-0.319492\pi\)
0.537175 + 0.843471i \(0.319492\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.26187 0.0968877
\(546\) 0 0
\(547\) −1.10062 −0.0470589 −0.0235295 0.999723i \(-0.507490\pi\)
−0.0235295 + 0.999723i \(0.507490\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −10.8021 −0.460185
\(552\) 0 0
\(553\) 40.7875 1.73446
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −44.4993 −1.88550 −0.942748 0.333507i \(-0.891768\pi\)
−0.942748 + 0.333507i \(0.891768\pi\)
\(558\) 0 0
\(559\) 4.03620 0.170713
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 37.4372 1.57779 0.788896 0.614527i \(-0.210653\pi\)
0.788896 + 0.614527i \(0.210653\pi\)
\(564\) 0 0
\(565\) 19.1187 0.804330
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −26.1744 −1.09729 −0.548644 0.836056i \(-0.684856\pi\)
−0.548644 + 0.836056i \(0.684856\pi\)
\(570\) 0 0
\(571\) 1.92715 0.0806486 0.0403243 0.999187i \(-0.487161\pi\)
0.0403243 + 0.999187i \(0.487161\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 12.9986 0.542078
\(576\) 0 0
\(577\) −16.4934 −0.686630 −0.343315 0.939220i \(-0.611550\pi\)
−0.343315 + 0.939220i \(0.611550\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 39.0738 1.62105
\(582\) 0 0
\(583\) 13.3865 0.554410
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 22.2130 0.916828 0.458414 0.888739i \(-0.348418\pi\)
0.458414 + 0.888739i \(0.348418\pi\)
\(588\) 0 0
\(589\) −13.4010 −0.552181
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.90080 −0.160187 −0.0800933 0.996787i \(-0.525522\pi\)
−0.0800933 + 0.996787i \(0.525522\pi\)
\(594\) 0 0
\(595\) −1.82321 −0.0747442
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 29.4010 1.20129 0.600647 0.799514i \(-0.294910\pi\)
0.600647 + 0.799514i \(0.294910\pi\)
\(600\) 0 0
\(601\) 13.8496 0.564935 0.282468 0.959277i \(-0.408847\pi\)
0.282468 + 0.959277i \(0.408847\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −16.0386 −0.652060
\(606\) 0 0
\(607\) 19.2022 0.779393 0.389696 0.920943i \(-0.372580\pi\)
0.389696 + 0.920943i \(0.372580\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 15.3865 0.622469
\(612\) 0 0
\(613\) 12.1319 0.490002 0.245001 0.969523i \(-0.421212\pi\)
0.245001 + 0.969523i \(0.421212\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.0620 0.445341 0.222671 0.974894i \(-0.428523\pi\)
0.222671 + 0.974894i \(0.428523\pi\)
\(618\) 0 0
\(619\) −10.3150 −0.414596 −0.207298 0.978278i \(-0.566467\pi\)
−0.207298 + 0.978278i \(0.566467\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 35.8496 1.43628
\(624\) 0 0
\(625\) −9.21696 −0.368678
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.186642 0.00744192
\(630\) 0 0
\(631\) −26.4847 −1.05434 −0.527170 0.849760i \(-0.676747\pi\)
−0.527170 + 0.849760i \(0.676747\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.61213 −0.0639753
\(636\) 0 0
\(637\) −12.5139 −0.495818
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −33.3136 −1.31581 −0.657904 0.753102i \(-0.728557\pi\)
−0.657904 + 0.753102i \(0.728557\pi\)
\(642\) 0 0
\(643\) 23.9224 0.943408 0.471704 0.881757i \(-0.343639\pi\)
0.471704 + 0.881757i \(0.343639\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −34.8021 −1.36821 −0.684106 0.729383i \(-0.739807\pi\)
−0.684106 + 0.729383i \(0.739807\pi\)
\(648\) 0 0
\(649\) 5.55149 0.217915
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.1622 −0.945540 −0.472770 0.881186i \(-0.656746\pi\)
−0.472770 + 0.881186i \(0.656746\pi\)
\(654\) 0 0
\(655\) −15.5369 −0.607077
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −10.1721 −0.396247 −0.198123 0.980177i \(-0.563485\pi\)
−0.198123 + 0.980177i \(0.563485\pi\)
\(660\) 0 0
\(661\) −40.2736 −1.56646 −0.783231 0.621731i \(-0.786430\pi\)
−0.783231 + 0.621731i \(0.786430\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.04746 −0.350845
\(666\) 0 0
\(667\) −39.6991 −1.53716
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.962389 −0.0371526
\(672\) 0 0
\(673\) −15.1490 −0.583952 −0.291976 0.956426i \(-0.594313\pi\)
−0.291976 + 0.956426i \(0.594313\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −21.6531 −0.832195 −0.416097 0.909320i \(-0.636602\pi\)
−0.416097 + 0.909320i \(0.636602\pi\)
\(678\) 0 0
\(679\) 53.7743 2.06367
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.63656 −0.368733 −0.184366 0.982858i \(-0.559023\pi\)
−0.184366 + 0.982858i \(0.559023\pi\)
\(684\) 0 0
\(685\) 7.78892 0.297599
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −33.2144 −1.26537
\(690\) 0 0
\(691\) −10.4001 −0.395638 −0.197819 0.980239i \(-0.563386\pi\)
−0.197819 + 0.980239i \(0.563386\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −29.6082 −1.12310
\(696\) 0 0
\(697\) −1.96968 −0.0746071
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −40.6615 −1.53576 −0.767882 0.640592i \(-0.778689\pi\)
−0.767882 + 0.640592i \(0.778689\pi\)
\(702\) 0 0
\(703\) 0.926192 0.0349320
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.65959 0.250460
\(708\) 0 0
\(709\) −28.7367 −1.07923 −0.539615 0.841912i \(-0.681430\pi\)
−0.539615 + 0.841912i \(0.681430\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −49.2506 −1.84445
\(714\) 0 0
\(715\) −5.92478 −0.221574
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 11.8496 0.441914 0.220957 0.975284i \(-0.429082\pi\)
0.220957 + 0.975284i \(0.429082\pi\)
\(720\) 0 0
\(721\) 23.5369 0.876560
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −14.7005 −0.545964
\(726\) 0 0
\(727\) −3.13681 −0.116338 −0.0581690 0.998307i \(-0.518526\pi\)
−0.0581690 + 0.998307i \(0.518526\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.442628 0.0163712
\(732\) 0 0
\(733\) 15.1939 0.561201 0.280600 0.959825i \(-0.409466\pi\)
0.280600 + 0.959825i \(0.409466\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.31265 0.232529
\(738\) 0 0
\(739\) 19.9271 0.733032 0.366516 0.930412i \(-0.380551\pi\)
0.366516 + 0.930412i \(0.380551\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 13.1490 0.482391 0.241196 0.970477i \(-0.422460\pi\)
0.241196 + 0.970477i \(0.422460\pi\)
\(744\) 0 0
\(745\) 9.16950 0.335944
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 34.6516 1.26614
\(750\) 0 0
\(751\) 24.2252 0.883990 0.441995 0.897017i \(-0.354271\pi\)
0.441995 + 0.897017i \(0.354271\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −15.6424 −0.569287
\(756\) 0 0
\(757\) 16.3272 0.593424 0.296712 0.954967i \(-0.404110\pi\)
0.296712 + 0.954967i \(0.404110\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −47.2652 −1.71336 −0.856681 0.515847i \(-0.827477\pi\)
−0.856681 + 0.515847i \(0.827477\pi\)
\(762\) 0 0
\(763\) 4.52373 0.163770
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −13.7743 −0.497362
\(768\) 0 0
\(769\) 10.1504 0.366034 0.183017 0.983110i \(-0.441414\pi\)
0.183017 + 0.983110i \(0.441414\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −25.0616 −0.901403 −0.450701 0.892675i \(-0.648826\pi\)
−0.450701 + 0.892675i \(0.648826\pi\)
\(774\) 0 0
\(775\) −18.2374 −0.655108
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.77433 −0.350202
\(780\) 0 0
\(781\) 4.77575 0.170890
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −33.5877 −1.19880
\(786\) 0 0
\(787\) 25.5491 0.910728 0.455364 0.890305i \(-0.349509\pi\)
0.455364 + 0.890305i \(0.349509\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 38.2374 1.35957
\(792\) 0 0
\(793\) 2.38787 0.0847959
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −33.2384 −1.17736 −0.588682 0.808365i \(-0.700353\pi\)
−0.588682 + 0.808365i \(0.700353\pi\)
\(798\) 0 0
\(799\) 1.68735 0.0596941
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.31265 −0.152190
\(804\) 0 0
\(805\) −33.2506 −1.17193
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −10.0997 −0.355085 −0.177543 0.984113i \(-0.556815\pi\)
−0.177543 + 0.984113i \(0.556815\pi\)
\(810\) 0 0
\(811\) 7.13681 0.250607 0.125304 0.992118i \(-0.460009\pi\)
0.125304 + 0.992118i \(0.460009\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 30.6556 1.07382
\(816\) 0 0
\(817\) 2.19649 0.0768455
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −15.9878 −0.557977 −0.278989 0.960294i \(-0.589999\pi\)
−0.278989 + 0.960294i \(0.589999\pi\)
\(822\) 0 0
\(823\) −37.7377 −1.31545 −0.657726 0.753257i \(-0.728482\pi\)
−0.657726 + 0.753257i \(0.728482\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −22.6155 −0.786416 −0.393208 0.919449i \(-0.628635\pi\)
−0.393208 + 0.919449i \(0.628635\pi\)
\(828\) 0 0
\(829\) −21.3503 −0.741525 −0.370763 0.928728i \(-0.620904\pi\)
−0.370763 + 0.928728i \(0.620904\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.37233 −0.0475484
\(834\) 0 0
\(835\) −1.67513 −0.0579703
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 27.1187 0.936242 0.468121 0.883664i \(-0.344931\pi\)
0.468121 + 0.883664i \(0.344931\pi\)
\(840\) 0 0
\(841\) 15.8970 0.548173
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −7.07618 −0.243428
\(846\) 0 0
\(847\) −32.0771 −1.10218
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.40388 0.116683
\(852\) 0 0
\(853\) 33.1305 1.13437 0.567183 0.823592i \(-0.308033\pi\)
0.567183 + 0.823592i \(0.308033\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −24.9868 −0.853534 −0.426767 0.904362i \(-0.640348\pi\)
−0.426767 + 0.904362i \(0.640348\pi\)
\(858\) 0 0
\(859\) −23.2896 −0.794632 −0.397316 0.917682i \(-0.630058\pi\)
−0.397316 + 0.917682i \(0.630058\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 32.0362 1.09052 0.545262 0.838265i \(-0.316430\pi\)
0.545262 + 0.838265i \(0.316430\pi\)
\(864\) 0 0
\(865\) 29.5026 1.00312
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 14.5355 0.493083
\(870\) 0 0
\(871\) −15.6629 −0.530718
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −40.3733 −1.36487
\(876\) 0 0
\(877\) −20.1721 −0.681162 −0.340581 0.940215i \(-0.610624\pi\)
−0.340581 + 0.940215i \(0.610624\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −16.3757 −0.551710 −0.275855 0.961199i \(-0.588961\pi\)
−0.275855 + 0.961199i \(0.588961\pi\)
\(882\) 0 0
\(883\) 5.98541 0.201425 0.100713 0.994916i \(-0.467888\pi\)
0.100713 + 0.994916i \(0.467888\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −55.6093 −1.86718 −0.933589 0.358346i \(-0.883341\pi\)
−0.933589 + 0.358346i \(0.883341\pi\)
\(888\) 0 0
\(889\) −3.22425 −0.108138
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.37328 0.280201
\(894\) 0 0
\(895\) −27.4274 −0.916797
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 55.6991 1.85767
\(900\) 0 0
\(901\) −3.64244 −0.121347
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.39772 0.0797030
\(906\) 0 0
\(907\) 9.11283 0.302587 0.151293 0.988489i \(-0.451656\pi\)
0.151293 + 0.988489i \(0.451656\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 39.6991 1.31529 0.657645 0.753328i \(-0.271553\pi\)
0.657645 + 0.753328i \(0.271553\pi\)
\(912\) 0 0
\(913\) 13.9248 0.460843
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −31.0738 −1.02615
\(918\) 0 0
\(919\) 5.79877 0.191284 0.0956419 0.995416i \(-0.469510\pi\)
0.0956419 + 0.995416i \(0.469510\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −11.8496 −0.390033
\(924\) 0 0
\(925\) 1.26045 0.0414434
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −43.1636 −1.41615 −0.708076 0.706136i \(-0.750437\pi\)
−0.708076 + 0.706136i \(0.750437\pi\)
\(930\) 0 0
\(931\) −6.81003 −0.223190
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −0.649738 −0.0212487
\(936\) 0 0
\(937\) 48.1886 1.57425 0.787126 0.616793i \(-0.211568\pi\)
0.787126 + 0.616793i \(0.211568\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −8.31028 −0.270907 −0.135454 0.990784i \(-0.543249\pi\)
−0.135454 + 0.990784i \(0.543249\pi\)
\(942\) 0 0
\(943\) −35.9219 −1.16978
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −5.66879 −0.184211 −0.0921055 0.995749i \(-0.529360\pi\)
−0.0921055 + 0.995749i \(0.529360\pi\)
\(948\) 0 0
\(949\) 10.7005 0.347354
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 25.6869 0.832080 0.416040 0.909346i \(-0.363418\pi\)
0.416040 + 0.909346i \(0.363418\pi\)
\(954\) 0 0
\(955\) −2.52373 −0.0816660
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 15.5778 0.503035
\(960\) 0 0
\(961\) 38.1002 1.22904
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.52705 −0.0491576
\(966\) 0 0
\(967\) −41.6893 −1.34064 −0.670318 0.742074i \(-0.733842\pi\)
−0.670318 + 0.742074i \(0.733842\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −48.4993 −1.55642 −0.778208 0.628006i \(-0.783871\pi\)
−0.778208 + 0.628006i \(0.783871\pi\)
\(972\) 0 0
\(973\) −59.2163 −1.89839
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 30.7851 0.984904 0.492452 0.870340i \(-0.336101\pi\)
0.492452 + 0.870340i \(0.336101\pi\)
\(978\) 0 0
\(979\) 12.7757 0.408315
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −31.2652 −0.997205 −0.498602 0.866831i \(-0.666153\pi\)
−0.498602 + 0.866831i \(0.666153\pi\)
\(984\) 0 0
\(985\) −22.5540 −0.718632
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.07239 0.256687
\(990\) 0 0
\(991\) 7.39868 0.235027 0.117513 0.993071i \(-0.462508\pi\)
0.117513 + 0.993071i \(0.462508\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −30.7612 −0.975194
\(996\) 0 0
\(997\) 50.2189 1.59045 0.795224 0.606316i \(-0.207353\pi\)
0.795224 + 0.606316i \(0.207353\pi\)
\(998\) 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.1.3 yes 3
3.2 odd 2 6012.2.a.b.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.a.b.1.1 3 3.2 odd 2
6012.2.a.c.1.3 yes 3 1.1 even 1 trivial