Properties

Label 6012.2.a.c.1.2
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 1.2
Root \(2.17009\) of defining polynomial
Character \(\chi\) \(=\) 6012.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.539189 q^{5} +1.07838 q^{7} +O(q^{10})\) \(q+0.539189 q^{5} +1.07838 q^{7} +3.70928 q^{11} +4.34017 q^{13} -1.46081 q^{17} +3.41855 q^{19} +8.68035 q^{23} -4.70928 q^{25} +2.15676 q^{29} -1.26180 q^{31} +0.581449 q^{35} +11.7587 q^{37} +9.95774 q^{41} -9.80098 q^{43} -7.70928 q^{47} -5.83710 q^{49} -9.55971 q^{53} +2.00000 q^{55} +6.92162 q^{59} +1.70928 q^{61} +2.34017 q^{65} -0.879362 q^{67} +4.00000 q^{71} +1.41855 q^{73} +4.00000 q^{77} -15.8999 q^{79} -0.183417 q^{83} -0.787653 q^{85} +6.15676 q^{89} +4.68035 q^{91} +1.84324 q^{95} +9.23513 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + O(q^{10}) \) \( 3q + 4q^{11} + 2q^{13} - 6q^{17} - 4q^{19} + 4q^{23} - 7q^{25} + 4q^{31} + 16q^{35} + 10q^{37} + 14q^{41} - 20q^{43} - 16q^{47} + 11q^{49} + 6q^{53} + 6q^{55} + 24q^{59} - 2q^{61} - 4q^{65} + 10q^{67} + 12q^{71} - 10q^{73} + 12q^{77} - 2q^{79} + 4q^{83} + 8q^{85} + 12q^{89} - 8q^{91} + 12q^{95} + 18q^{97} + O(q^{100}) \)

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
\(5\) 0.539189 0.241133 0.120566 0.992705i \(-0.461529\pi\)
0.120566 + 0.992705i \(0.461529\pi\)
\(6\) 0 0
\(7\) 1.07838 0.407588 0.203794 0.979014i \(-0.434673\pi\)
0.203794 + 0.979014i \(0.434673\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.70928 1.11839 0.559194 0.829037i \(-0.311111\pi\)
0.559194 + 0.829037i \(0.311111\pi\)
\(12\) 0 0
\(13\) 4.34017 1.20375 0.601874 0.798591i \(-0.294421\pi\)
0.601874 + 0.798591i \(0.294421\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.46081 −0.354299 −0.177149 0.984184i \(-0.556688\pi\)
−0.177149 + 0.984184i \(0.556688\pi\)
\(18\) 0 0
\(19\) 3.41855 0.784269 0.392135 0.919908i \(-0.371737\pi\)
0.392135 + 0.919908i \(0.371737\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 8.68035 1.80998 0.904989 0.425436i \(-0.139879\pi\)
0.904989 + 0.425436i \(0.139879\pi\)
\(24\) 0 0
\(25\) −4.70928 −0.941855
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2.15676 0.400499 0.200250 0.979745i \(-0.435825\pi\)
0.200250 + 0.979745i \(0.435825\pi\)
\(30\) 0 0
\(31\) −1.26180 −0.226625 −0.113313 0.993559i \(-0.536146\pi\)
−0.113313 + 0.993559i \(0.536146\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.581449 0.0982829
\(36\) 0 0
\(37\) 11.7587 1.93312 0.966561 0.256436i \(-0.0825484\pi\)
0.966561 + 0.256436i \(0.0825484\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 9.95774 1.55514 0.777569 0.628798i \(-0.216453\pi\)
0.777569 + 0.628798i \(0.216453\pi\)
\(42\) 0 0
\(43\) −9.80098 −1.49464 −0.747318 0.664467i \(-0.768659\pi\)
−0.747318 + 0.664467i \(0.768659\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.70928 −1.12451 −0.562257 0.826963i \(-0.690067\pi\)
−0.562257 + 0.826963i \(0.690067\pi\)
\(48\) 0 0
\(49\) −5.83710 −0.833872
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −9.55971 −1.31313 −0.656563 0.754271i \(-0.727991\pi\)
−0.656563 + 0.754271i \(0.727991\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.92162 0.901118 0.450559 0.892747i \(-0.351225\pi\)
0.450559 + 0.892747i \(0.351225\pi\)
\(60\) 0 0
\(61\) 1.70928 0.218850 0.109425 0.993995i \(-0.465099\pi\)
0.109425 + 0.993995i \(0.465099\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.34017 0.290263
\(66\) 0 0
\(67\) −0.879362 −0.107431 −0.0537156 0.998556i \(-0.517106\pi\)
−0.0537156 + 0.998556i \(0.517106\pi\)
\(68\) 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
\(73\) 1.41855 0.166029 0.0830144 0.996548i \(-0.473545\pi\)
0.0830144 + 0.996548i \(0.473545\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −15.8999 −1.78888 −0.894438 0.447192i \(-0.852424\pi\)
−0.894438 + 0.447192i \(0.852424\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.183417 −0.0201327 −0.0100663 0.999949i \(-0.503204\pi\)
−0.0100663 + 0.999949i \(0.503204\pi\)
\(84\) 0 0
\(85\) −0.787653 −0.0854330
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.15676 0.652615 0.326307 0.945264i \(-0.394196\pi\)
0.326307 + 0.945264i \(0.394196\pi\)
\(90\) 0 0
\(91\) 4.68035 0.490634
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.84324 0.189113
\(96\) 0 0
\(97\) 9.23513 0.937686 0.468843 0.883282i \(-0.344671\pi\)
0.468843 + 0.883282i \(0.344671\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −8.72261 −0.867932 −0.433966 0.900929i \(-0.642886\pi\)
−0.433966 + 0.900929i \(0.642886\pi\)
\(102\) 0 0
\(103\) 3.61757 0.356449 0.178225 0.983990i \(-0.442965\pi\)
0.178225 + 0.983990i \(0.442965\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.8082 −1.14154 −0.570770 0.821110i \(-0.693355\pi\)
−0.570770 + 0.821110i \(0.693355\pi\)
\(108\) 0 0
\(109\) −0.921622 −0.0882754 −0.0441377 0.999025i \(-0.514054\pi\)
−0.0441377 + 0.999025i \(0.514054\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.0361 1.22633 0.613167 0.789953i \(-0.289895\pi\)
0.613167 + 0.789953i \(0.289895\pi\)
\(114\) 0 0
\(115\) 4.68035 0.436445
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.57531 −0.144408
\(120\) 0 0
\(121\) 2.75872 0.250793
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −5.23513 −0.468245
\(126\) 0 0
\(127\) 6.34017 0.562599 0.281300 0.959620i \(-0.409235\pi\)
0.281300 + 0.959620i \(0.409235\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.60197 0.664187 0.332094 0.943246i \(-0.392245\pi\)
0.332094 + 0.943246i \(0.392245\pi\)
\(132\) 0 0
\(133\) 3.68649 0.319659
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.92162 0.591354 0.295677 0.955288i \(-0.404455\pi\)
0.295677 + 0.955288i \(0.404455\pi\)
\(138\) 0 0
\(139\) −16.5392 −1.40284 −0.701418 0.712750i \(-0.747449\pi\)
−0.701418 + 0.712750i \(0.747449\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 16.0989 1.34626
\(144\) 0 0
\(145\) 1.16290 0.0965735
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −18.0566 −1.47926 −0.739629 0.673015i \(-0.764999\pi\)
−0.739629 + 0.673015i \(0.764999\pi\)
\(150\) 0 0
\(151\) 3.64423 0.296563 0.148282 0.988945i \(-0.452626\pi\)
0.148282 + 0.988945i \(0.452626\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.680346 −0.0546467
\(156\) 0 0
\(157\) −13.2351 −1.05628 −0.528139 0.849158i \(-0.677110\pi\)
−0.528139 + 0.849158i \(0.677110\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 9.36069 0.737726
\(162\) 0 0
\(163\) −1.98440 −0.155430 −0.0777152 0.996976i \(-0.524762\pi\)
−0.0777152 + 0.996976i \(0.524762\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.00000 −0.0773823
\(168\) 0 0
\(169\) 5.83710 0.449008
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 12.5814 0.956550 0.478275 0.878210i \(-0.341262\pi\)
0.478275 + 0.878210i \(0.341262\pi\)
\(174\) 0 0
\(175\) −5.07838 −0.383889
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.3545 1.37188 0.685942 0.727657i \(-0.259390\pi\)
0.685942 + 0.727657i \(0.259390\pi\)
\(180\) 0 0
\(181\) −20.2329 −1.50390 −0.751949 0.659222i \(-0.770886\pi\)
−0.751949 + 0.659222i \(0.770886\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.34017 0.466139
\(186\) 0 0
\(187\) −5.41855 −0.396244
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.55252 0.401766 0.200883 0.979615i \(-0.435619\pi\)
0.200883 + 0.979615i \(0.435619\pi\)
\(192\) 0 0
\(193\) −0.424694 −0.0305701 −0.0152851 0.999883i \(-0.504866\pi\)
−0.0152851 + 0.999883i \(0.504866\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −8.27125 −0.589302 −0.294651 0.955605i \(-0.595203\pi\)
−0.294651 + 0.955605i \(0.595203\pi\)
\(198\) 0 0
\(199\) −1.97334 −0.139886 −0.0699431 0.997551i \(-0.522282\pi\)
−0.0699431 + 0.997551i \(0.522282\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 2.32580 0.163239
\(204\) 0 0
\(205\) 5.36910 0.374994
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.6803 0.877118
\(210\) 0 0
\(211\) 7.10504 0.489131 0.244566 0.969633i \(-0.421355\pi\)
0.244566 + 0.969633i \(0.421355\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −5.28458 −0.360405
\(216\) 0 0
\(217\) −1.36069 −0.0923698
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.34017 −0.426486
\(222\) 0 0
\(223\) 4.39803 0.294514 0.147257 0.989098i \(-0.452956\pi\)
0.147257 + 0.989098i \(0.452956\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.3402 0.686301 0.343151 0.939280i \(-0.388506\pi\)
0.343151 + 0.939280i \(0.388506\pi\)
\(228\) 0 0
\(229\) −14.2907 −0.944358 −0.472179 0.881503i \(-0.656532\pi\)
−0.472179 + 0.881503i \(0.656532\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6.65368 0.435897 0.217949 0.975960i \(-0.430063\pi\)
0.217949 + 0.975960i \(0.430063\pi\)
\(234\) 0 0
\(235\) −4.15676 −0.271157
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 23.5936 1.52614 0.763070 0.646316i \(-0.223691\pi\)
0.763070 + 0.646316i \(0.223691\pi\)
\(240\) 0 0
\(241\) 5.78539 0.372669 0.186335 0.982486i \(-0.440339\pi\)
0.186335 + 0.982486i \(0.440339\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −3.14730 −0.201074
\(246\) 0 0
\(247\) 14.8371 0.944062
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.0205 1.70552 0.852760 0.522303i \(-0.174927\pi\)
0.852760 + 0.522303i \(0.174927\pi\)
\(252\) 0 0
\(253\) 32.1978 2.02426
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.48133 0.404294 0.202147 0.979355i \(-0.435208\pi\)
0.202147 + 0.979355i \(0.435208\pi\)
\(258\) 0 0
\(259\) 12.6803 0.787918
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.97948 0.307048 0.153524 0.988145i \(-0.450938\pi\)
0.153524 + 0.988145i \(0.450938\pi\)
\(264\) 0 0
\(265\) −5.15449 −0.316638
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 29.8732 1.82140 0.910701 0.413066i \(-0.135542\pi\)
0.910701 + 0.413066i \(0.135542\pi\)
\(270\) 0 0
\(271\) −4.48133 −0.272221 −0.136111 0.990694i \(-0.543460\pi\)
−0.136111 + 0.990694i \(0.543460\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −17.4680 −1.05336
\(276\) 0 0
\(277\) −16.7526 −1.00657 −0.503283 0.864122i \(-0.667874\pi\)
−0.503283 + 0.864122i \(0.667874\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −17.8576 −1.06530 −0.532648 0.846337i \(-0.678803\pi\)
−0.532648 + 0.846337i \(0.678803\pi\)
\(282\) 0 0
\(283\) −5.94214 −0.353224 −0.176612 0.984281i \(-0.556514\pi\)
−0.176612 + 0.984281i \(0.556514\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 10.7382 0.633856
\(288\) 0 0
\(289\) −14.8660 −0.874472
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 8.68035 0.507111 0.253556 0.967321i \(-0.418400\pi\)
0.253556 + 0.967321i \(0.418400\pi\)
\(294\) 0 0
\(295\) 3.73206 0.217289
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 37.6742 2.17876
\(300\) 0 0
\(301\) −10.5692 −0.609196
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.921622 0.0527719
\(306\) 0 0
\(307\) 25.8154 1.47336 0.736680 0.676241i \(-0.236392\pi\)
0.736680 + 0.676241i \(0.236392\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.97948 0.282360 0.141180 0.989984i \(-0.454910\pi\)
0.141180 + 0.989984i \(0.454910\pi\)
\(312\) 0 0
\(313\) −11.6742 −0.659865 −0.329932 0.944005i \(-0.607026\pi\)
−0.329932 + 0.944005i \(0.607026\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −10.2557 −0.576015 −0.288007 0.957628i \(-0.592993\pi\)
−0.288007 + 0.957628i \(0.592993\pi\)
\(318\) 0 0
\(319\) 8.00000 0.447914
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.99386 −0.277866
\(324\) 0 0
\(325\) −20.4391 −1.13376
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8.31351 −0.458339
\(330\) 0 0
\(331\) 21.5597 1.18503 0.592514 0.805560i \(-0.298135\pi\)
0.592514 + 0.805560i \(0.298135\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.474142 −0.0259052
\(336\) 0 0
\(337\) 29.1194 1.58624 0.793118 0.609068i \(-0.208456\pi\)
0.793118 + 0.609068i \(0.208456\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.68035 −0.253455
\(342\) 0 0
\(343\) −13.8432 −0.747465
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.6020 0.622826 0.311413 0.950275i \(-0.399198\pi\)
0.311413 + 0.950275i \(0.399198\pi\)
\(348\) 0 0
\(349\) −4.24128 −0.227030 −0.113515 0.993536i \(-0.536211\pi\)
−0.113515 + 0.993536i \(0.536211\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −20.8638 −1.11047 −0.555233 0.831695i \(-0.687371\pi\)
−0.555233 + 0.831695i \(0.687371\pi\)
\(354\) 0 0
\(355\) 2.15676 0.114469
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −23.2039 −1.22466 −0.612328 0.790603i \(-0.709767\pi\)
−0.612328 + 0.790603i \(0.709767\pi\)
\(360\) 0 0
\(361\) −7.31351 −0.384922
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.764867 0.0400350
\(366\) 0 0
\(367\) 36.2967 1.89467 0.947336 0.320242i \(-0.103764\pi\)
0.947336 + 0.320242i \(0.103764\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −10.3090 −0.535215
\(372\) 0 0
\(373\) −10.1834 −0.527277 −0.263639 0.964622i \(-0.584923\pi\)
−0.263639 + 0.964622i \(0.584923\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.36069 0.482100
\(378\) 0 0
\(379\) −0.638086 −0.0327763 −0.0163881 0.999866i \(-0.505217\pi\)
−0.0163881 + 0.999866i \(0.505217\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −12.7031 −0.649100 −0.324550 0.945869i \(-0.605213\pi\)
−0.324550 + 0.945869i \(0.605213\pi\)
\(384\) 0 0
\(385\) 2.15676 0.109918
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −23.5597 −1.19452 −0.597262 0.802046i \(-0.703745\pi\)
−0.597262 + 0.802046i \(0.703745\pi\)
\(390\) 0 0
\(391\) −12.6803 −0.641273
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.57304 −0.431356
\(396\) 0 0
\(397\) −0.546377 −0.0274219 −0.0137109 0.999906i \(-0.504364\pi\)
−0.0137109 + 0.999906i \(0.504364\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.4173 −0.670029 −0.335015 0.942213i \(-0.608741\pi\)
−0.335015 + 0.942213i \(0.608741\pi\)
\(402\) 0 0
\(403\) −5.47641 −0.272799
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 43.6163 2.16198
\(408\) 0 0
\(409\) −27.6514 −1.36727 −0.683637 0.729822i \(-0.739603\pi\)
−0.683637 + 0.729822i \(0.739603\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.46412 0.367286
\(414\) 0 0
\(415\) −0.0988967 −0.00485465
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13.5525 −0.662084 −0.331042 0.943616i \(-0.607400\pi\)
−0.331042 + 0.943616i \(0.607400\pi\)
\(420\) 0 0
\(421\) 20.8059 1.01402 0.507009 0.861941i \(-0.330751\pi\)
0.507009 + 0.861941i \(0.330751\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 6.87936 0.333698
\(426\) 0 0
\(427\) 1.84324 0.0892009
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.70701 0.323065 0.161533 0.986867i \(-0.448356\pi\)
0.161533 + 0.986867i \(0.448356\pi\)
\(432\) 0 0
\(433\) 18.4885 0.888501 0.444251 0.895902i \(-0.353470\pi\)
0.444251 + 0.895902i \(0.353470\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 29.6742 1.41951
\(438\) 0 0
\(439\) 2.48133 0.118427 0.0592137 0.998245i \(-0.481141\pi\)
0.0592137 + 0.998245i \(0.481141\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.02505 0.238748 0.119374 0.992849i \(-0.461911\pi\)
0.119374 + 0.992849i \(0.461911\pi\)
\(444\) 0 0
\(445\) 3.31965 0.157367
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.43907 0.303878 0.151939 0.988390i \(-0.451448\pi\)
0.151939 + 0.988390i \(0.451448\pi\)
\(450\) 0 0
\(451\) 36.9360 1.73925
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.52359 0.118308
\(456\) 0 0
\(457\) −26.9939 −1.26272 −0.631360 0.775490i \(-0.717503\pi\)
−0.631360 + 0.775490i \(0.717503\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 11.3340 0.527878 0.263939 0.964539i \(-0.414978\pi\)
0.263939 + 0.964539i \(0.414978\pi\)
\(462\) 0 0
\(463\) 8.89374 0.413327 0.206664 0.978412i \(-0.433739\pi\)
0.206664 + 0.978412i \(0.433739\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.5174 0.903160 0.451580 0.892231i \(-0.350861\pi\)
0.451580 + 0.892231i \(0.350861\pi\)
\(468\) 0 0
\(469\) −0.948284 −0.0437877
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −36.3545 −1.67158
\(474\) 0 0
\(475\) −16.0989 −0.738668
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 17.3074 0.790794 0.395397 0.918510i \(-0.370607\pi\)
0.395397 + 0.918510i \(0.370607\pi\)
\(480\) 0 0
\(481\) 51.0349 2.32699
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.97948 0.226107
\(486\) 0 0
\(487\) −28.0833 −1.27258 −0.636288 0.771452i \(-0.719531\pi\)
−0.636288 + 0.771452i \(0.719531\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 29.9649 1.35230 0.676149 0.736765i \(-0.263648\pi\)
0.676149 + 0.736765i \(0.263648\pi\)
\(492\) 0 0
\(493\) −3.15061 −0.141896
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.31351 0.193487
\(498\) 0 0
\(499\) −31.9143 −1.42868 −0.714339 0.699800i \(-0.753273\pi\)
−0.714339 + 0.699800i \(0.753273\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.2267 1.21398 0.606990 0.794710i \(-0.292377\pi\)
0.606990 + 0.794710i \(0.292377\pi\)
\(504\) 0 0
\(505\) −4.70313 −0.209287
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22.6537 1.00411 0.502053 0.864837i \(-0.332578\pi\)
0.502053 + 0.864837i \(0.332578\pi\)
\(510\) 0 0
\(511\) 1.52973 0.0676714
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.95055 0.0859516
\(516\) 0 0
\(517\) −28.5958 −1.25764
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16.6647 0.730096 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(522\) 0 0
\(523\) −34.1399 −1.49284 −0.746418 0.665478i \(-0.768228\pi\)
−0.746418 + 0.665478i \(0.768228\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.84324 0.0802930
\(528\) 0 0
\(529\) 52.3484 2.27602
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 43.2183 1.87199
\(534\) 0 0
\(535\) −6.36683 −0.275262
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −21.6514 −0.932593
\(540\) 0 0
\(541\) −10.5503 −0.453591 −0.226795 0.973942i \(-0.572825\pi\)
−0.226795 + 0.973942i \(0.572825\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −0.496928 −0.0212861
\(546\) 0 0
\(547\) −12.2979 −0.525821 −0.262910 0.964820i \(-0.584682\pi\)
−0.262910 + 0.964820i \(0.584682\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.37298 0.314099
\(552\) 0 0
\(553\) −17.1461 −0.729125
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −17.5609 −0.744080 −0.372040 0.928217i \(-0.621342\pi\)
−0.372040 + 0.928217i \(0.621342\pi\)
\(558\) 0 0
\(559\) −42.5380 −1.79916
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −18.2245 −0.768069 −0.384035 0.923319i \(-0.625466\pi\)
−0.384035 + 0.923319i \(0.625466\pi\)
\(564\) 0 0
\(565\) 7.02893 0.295709
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 1.89988 0.0796471 0.0398236 0.999207i \(-0.487320\pi\)
0.0398236 + 0.999207i \(0.487320\pi\)
\(570\) 0 0
\(571\) 16.3701 0.685069 0.342535 0.939505i \(-0.388715\pi\)
0.342535 + 0.939505i \(0.388715\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −40.8781 −1.70474
\(576\) 0 0
\(577\) −23.5525 −0.980504 −0.490252 0.871581i \(-0.663095\pi\)
−0.490252 + 0.871581i \(0.663095\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −0.197793 −0.00820585
\(582\) 0 0
\(583\) −35.4596 −1.46859
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −23.3874 −0.965299 −0.482650 0.875813i \(-0.660326\pi\)
−0.482650 + 0.875813i \(0.660326\pi\)
\(588\) 0 0
\(589\) −4.31351 −0.177735
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −46.5802 −1.91282 −0.956410 0.292026i \(-0.905671\pi\)
−0.956410 + 0.292026i \(0.905671\pi\)
\(594\) 0 0
\(595\) −0.849388 −0.0348215
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 20.3135 0.829988 0.414994 0.909824i \(-0.363784\pi\)
0.414994 + 0.909824i \(0.363784\pi\)
\(600\) 0 0
\(601\) −15.3607 −0.626576 −0.313288 0.949658i \(-0.601430\pi\)
−0.313288 + 0.949658i \(0.601430\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.48747 0.0604744
\(606\) 0 0
\(607\) 16.7682 0.680599 0.340300 0.940317i \(-0.389471\pi\)
0.340300 + 0.940317i \(0.389471\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −33.4596 −1.35363
\(612\) 0 0
\(613\) −14.0761 −0.568529 −0.284264 0.958746i \(-0.591749\pi\)
−0.284264 + 0.958746i \(0.591749\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 39.7854 1.60170 0.800850 0.598865i \(-0.204382\pi\)
0.800850 + 0.598865i \(0.204382\pi\)
\(618\) 0 0
\(619\) −29.7887 −1.19731 −0.598654 0.801007i \(-0.704298\pi\)
−0.598654 + 0.801007i \(0.704298\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.63931 0.265998
\(624\) 0 0
\(625\) 20.7237 0.828946
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −17.1773 −0.684903
\(630\) 0 0
\(631\) 40.2122 1.60082 0.800411 0.599452i \(-0.204615\pi\)
0.800411 + 0.599452i \(0.204615\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.41855 0.135661
\(636\) 0 0
\(637\) −25.3340 −1.00377
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.08944 0.0430303 0.0215152 0.999769i \(-0.493151\pi\)
0.0215152 + 0.999769i \(0.493151\pi\)
\(642\) 0 0
\(643\) −19.7308 −0.778108 −0.389054 0.921215i \(-0.627198\pi\)
−0.389054 + 0.921215i \(0.627198\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −16.6270 −0.653676 −0.326838 0.945080i \(-0.605983\pi\)
−0.326838 + 0.945080i \(0.605983\pi\)
\(648\) 0 0
\(649\) 25.6742 1.00780
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 14.6225 0.572222 0.286111 0.958196i \(-0.407637\pi\)
0.286111 + 0.958196i \(0.407637\pi\)
\(654\) 0 0
\(655\) 4.09890 0.160157
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 46.9504 1.82893 0.914463 0.404669i \(-0.132613\pi\)
0.914463 + 0.404669i \(0.132613\pi\)
\(660\) 0 0
\(661\) 30.4801 1.18554 0.592769 0.805372i \(-0.298035\pi\)
0.592769 + 0.805372i \(0.298035\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.98771 0.0770802
\(666\) 0 0
\(667\) 18.7214 0.724895
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 6.34017 0.244760
\(672\) 0 0
\(673\) 9.51745 0.366871 0.183435 0.983032i \(-0.441278\pi\)
0.183435 + 0.983032i \(0.441278\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −28.1445 −1.08168 −0.540840 0.841126i \(-0.681894\pi\)
−0.540840 + 0.841126i \(0.681894\pi\)
\(678\) 0 0
\(679\) 9.95896 0.382190
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −26.0267 −0.995883 −0.497941 0.867211i \(-0.665910\pi\)
−0.497941 + 0.867211i \(0.665910\pi\)
\(684\) 0 0
\(685\) 3.73206 0.142595
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −41.4908 −1.58067
\(690\) 0 0
\(691\) −26.1412 −0.994456 −0.497228 0.867620i \(-0.665649\pi\)
−0.497228 + 0.867620i \(0.665649\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −8.91775 −0.338269
\(696\) 0 0
\(697\) −14.5464 −0.550983
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25.0616 0.946562 0.473281 0.880912i \(-0.343070\pi\)
0.473281 + 0.880912i \(0.343070\pi\)
\(702\) 0 0
\(703\) 40.1978 1.51609
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.40626 −0.353759
\(708\) 0 0
\(709\) 22.3812 0.840544 0.420272 0.907398i \(-0.361935\pi\)
0.420272 + 0.907398i \(0.361935\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −10.9528 −0.410186
\(714\) 0 0
\(715\) 8.68035 0.324627
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −17.3607 −0.647445 −0.323722 0.946152i \(-0.604934\pi\)
−0.323722 + 0.946152i \(0.604934\pi\)
\(720\) 0 0
\(721\) 3.90110 0.145285
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −10.1568 −0.377212
\(726\) 0 0
\(727\) 32.2401 1.19572 0.597859 0.801602i \(-0.296018\pi\)
0.597859 + 0.801602i \(0.296018\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 14.3174 0.529548
\(732\) 0 0
\(733\) 17.7093 0.654107 0.327054 0.945006i \(-0.393944\pi\)
0.327054 + 0.945006i \(0.393944\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −3.26180 −0.120150
\(738\) 0 0
\(739\) 34.3701 1.26433 0.632163 0.774835i \(-0.282167\pi\)
0.632163 + 0.774835i \(0.282167\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −11.5174 −0.422534 −0.211267 0.977428i \(-0.567759\pi\)
−0.211267 + 0.977428i \(0.567759\pi\)
\(744\) 0 0
\(745\) −9.73594 −0.356697
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −12.7337 −0.465278
\(750\) 0 0
\(751\) −10.6647 −0.389162 −0.194581 0.980886i \(-0.562335\pi\)
−0.194581 + 0.980886i \(0.562335\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.96493 0.0715110
\(756\) 0 0
\(757\) 46.5113 1.69048 0.845241 0.534385i \(-0.179457\pi\)
0.845241 + 0.534385i \(0.179457\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −48.7259 −1.76631 −0.883157 0.469078i \(-0.844586\pi\)
−0.883157 + 0.469078i \(0.844586\pi\)
\(762\) 0 0
\(763\) −0.993857 −0.0359800
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 30.0410 1.08472
\(768\) 0 0
\(769\) 39.3607 1.41938 0.709691 0.704513i \(-0.248834\pi\)
0.709691 + 0.704513i \(0.248834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 24.9204 0.896324 0.448162 0.893952i \(-0.352079\pi\)
0.448162 + 0.893952i \(0.352079\pi\)
\(774\) 0 0
\(775\) 5.94214 0.213448
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 34.0410 1.21965
\(780\) 0 0
\(781\) 14.8371 0.530913
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.13624 −0.254703
\(786\) 0 0
\(787\) 16.6237 0.592571 0.296286 0.955099i \(-0.404252\pi\)
0.296286 + 0.955099i \(0.404252\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 14.0579 0.499840
\(792\) 0 0
\(793\) 7.41855 0.263440
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 15.7698 0.558595 0.279297 0.960205i \(-0.409899\pi\)
0.279297 + 0.960205i \(0.409899\pi\)
\(798\) 0 0
\(799\) 11.2618 0.398414
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5.26180 0.185685
\(804\) 0 0
\(805\) 5.04718 0.177890
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −46.1256 −1.62169 −0.810844 0.585262i \(-0.800992\pi\)
−0.810844 + 0.585262i \(0.800992\pi\)
\(810\) 0 0
\(811\) −28.2401 −0.991642 −0.495821 0.868425i \(-0.665133\pi\)
−0.495821 + 0.868425i \(0.665133\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.06997 −0.0374793
\(816\) 0 0
\(817\) −33.5052 −1.17220
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −5.27739 −0.184182 −0.0920912 0.995751i \(-0.529355\pi\)
−0.0920912 + 0.995751i \(0.529355\pi\)
\(822\) 0 0
\(823\) 38.2089 1.33188 0.665939 0.746007i \(-0.268031\pi\)
0.665939 + 0.746007i \(0.268031\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −21.8043 −0.758210 −0.379105 0.925354i \(-0.623768\pi\)
−0.379105 + 0.925354i \(0.623768\pi\)
\(828\) 0 0
\(829\) −19.0784 −0.662619 −0.331310 0.943522i \(-0.607490\pi\)
−0.331310 + 0.943522i \(0.607490\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 8.52690 0.295440
\(834\) 0 0
\(835\) −0.539189 −0.0186594
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15.0289 0.518856 0.259428 0.965762i \(-0.416466\pi\)
0.259428 + 0.965762i \(0.416466\pi\)
\(840\) 0 0
\(841\) −24.3484 −0.839600
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 3.14730 0.108270
\(846\) 0 0
\(847\) 2.97495 0.102220
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 102.070 3.49891
\(852\) 0 0
\(853\) −46.9542 −1.60768 −0.803841 0.594844i \(-0.797214\pi\)
−0.803841 + 0.594844i \(0.797214\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −39.1050 −1.33580 −0.667901 0.744250i \(-0.732807\pi\)
−0.667901 + 0.744250i \(0.732807\pi\)
\(858\) 0 0
\(859\) −46.1711 −1.57534 −0.787669 0.616098i \(-0.788712\pi\)
−0.787669 + 0.616098i \(0.788712\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −14.5380 −0.494878 −0.247439 0.968903i \(-0.579589\pi\)
−0.247439 + 0.968903i \(0.579589\pi\)
\(864\) 0 0
\(865\) 6.78378 0.230655
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −58.9770 −2.00066
\(870\) 0 0
\(871\) −3.81658 −0.129320
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −5.64545 −0.190851
\(876\) 0 0
\(877\) 36.9504 1.24773 0.623863 0.781534i \(-0.285562\pi\)
0.623863 + 0.781534i \(0.285562\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −10.6959 −0.360356 −0.180178 0.983634i \(-0.557667\pi\)
−0.180178 + 0.983634i \(0.557667\pi\)
\(882\) 0 0
\(883\) −33.7731 −1.13656 −0.568278 0.822837i \(-0.692390\pi\)
−0.568278 + 0.822837i \(0.692390\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 57.1748 1.91974 0.959871 0.280440i \(-0.0904805\pi\)
0.959871 + 0.280440i \(0.0904805\pi\)
\(888\) 0 0
\(889\) 6.83710 0.229309
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −26.3545 −0.881921
\(894\) 0 0
\(895\) 9.89657 0.330806
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −2.72138 −0.0907632
\(900\) 0 0
\(901\) 13.9649 0.465239
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −10.9093 −0.362639
\(906\) 0 0
\(907\) 31.0205 1.03002 0.515010 0.857184i \(-0.327788\pi\)
0.515010 + 0.857184i \(0.327788\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −18.7214 −0.620267 −0.310134 0.950693i \(-0.600374\pi\)
−0.310134 + 0.950693i \(0.600374\pi\)
\(912\) 0 0
\(913\) −0.680346 −0.0225162
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 8.19779 0.270715
\(918\) 0 0
\(919\) −16.5958 −0.547446 −0.273723 0.961809i \(-0.588255\pi\)
−0.273723 + 0.961809i \(0.588255\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 17.3607 0.571434
\(924\) 0 0
\(925\) −55.3751 −1.82072
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −58.2557 −1.91131 −0.955653 0.294495i \(-0.904849\pi\)
−0.955653 + 0.294495i \(0.904849\pi\)
\(930\) 0 0
\(931\) −19.9544 −0.653980
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.92162 −0.0955473
\(936\) 0 0
\(937\) −18.8326 −0.615233 −0.307617 0.951510i \(-0.599531\pi\)
−0.307617 + 0.951510i \(0.599531\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 30.3123 0.988152 0.494076 0.869419i \(-0.335506\pi\)
0.494076 + 0.869419i \(0.335506\pi\)
\(942\) 0 0
\(943\) 86.4366 2.81476
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 40.1750 1.30551 0.652756 0.757568i \(-0.273613\pi\)
0.652756 + 0.757568i \(0.273613\pi\)
\(948\) 0 0
\(949\) 6.15676 0.199857
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −43.4440 −1.40729 −0.703644 0.710552i \(-0.748445\pi\)
−0.703644 + 0.710552i \(0.748445\pi\)
\(954\) 0 0
\(955\) 2.99386 0.0968789
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 7.46412 0.241029
\(960\) 0 0
\(961\) −29.4079 −0.948641
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.228990 −0.00737145
\(966\) 0 0
\(967\) −1.60650 −0.0516617 −0.0258308 0.999666i \(-0.508223\pi\)
−0.0258308 + 0.999666i \(0.508223\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −21.5609 −0.691923 −0.345962 0.938249i \(-0.612447\pi\)
−0.345962 + 0.938249i \(0.612447\pi\)
\(972\) 0 0
\(973\) −17.8355 −0.571780
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −56.1966 −1.79789 −0.898944 0.438064i \(-0.855664\pi\)
−0.898944 + 0.438064i \(0.855664\pi\)
\(978\) 0 0
\(979\) 22.8371 0.729877
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −32.7259 −1.04379 −0.521897 0.853008i \(-0.674776\pi\)
−0.521897 + 0.853008i \(0.674776\pi\)
\(984\) 0 0
\(985\) −4.45977 −0.142100
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −85.0759 −2.70526
\(990\) 0 0
\(991\) −30.7370 −0.976392 −0.488196 0.872734i \(-0.662345\pi\)
−0.488196 + 0.872734i \(0.662345\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.06400 −0.0337311
\(996\) 0 0
\(997\) −29.3789 −0.930440 −0.465220 0.885195i \(-0.654025\pi\)
−0.465220 + 0.885195i \(0.654025\pi\)
\(998\) 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.1.2 yes 3
3.2 odd 2 6012.2.a.b.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6012.2.a.b.1.2 3 3.2 odd 2
6012.2.a.c.1.2 yes 3 1.1 even 1 trivial