Properties

Label 9036.2.a.i.1.3
Level 9036
Weight 2
Character 9036.1
Self dual yes
Analytic conductor 72.153
Analytic rank 1
Dimension 7
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 9036 = 2^{2} \cdot 3^{2} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9036.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(72.1528232664\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1004)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.85375\)
Character \(\chi\) = 9036.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.454452 q^{5} -2.18653 q^{7} +O(q^{10})\) \(q-0.454452 q^{5} -2.18653 q^{7} +1.15877 q^{11} +6.03215 q^{13} -0.0535246 q^{17} -2.08924 q^{19} -3.22849 q^{23} -4.79347 q^{25} +1.62034 q^{29} -2.01992 q^{31} +0.993671 q^{35} -3.49384 q^{37} -2.85650 q^{41} +2.78023 q^{43} +9.03663 q^{47} -2.21910 q^{49} +4.09037 q^{53} -0.526603 q^{55} +4.76605 q^{59} -14.6219 q^{61} -2.74132 q^{65} -4.98740 q^{67} +2.04056 q^{71} -0.0937424 q^{73} -2.53367 q^{77} -1.92521 q^{79} -7.96981 q^{83} +0.0243243 q^{85} +16.7462 q^{89} -13.1895 q^{91} +0.949460 q^{95} +3.00301 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 2q^{5} - 6q^{7} + O(q^{10}) \) \( 7q + 2q^{5} - 6q^{7} + 5q^{11} - q^{13} + 8q^{17} - 15q^{19} + 5q^{23} - 9q^{25} - 21q^{31} + 7q^{35} - q^{37} + 10q^{41} - 23q^{43} + 10q^{47} - 13q^{49} + q^{53} - 23q^{55} + 4q^{59} + 3q^{61} - 4q^{65} - 28q^{67} + 18q^{71} - 7q^{73} - 6q^{77} - 30q^{79} - 13q^{83} + q^{85} - 18q^{91} - 2q^{97} + O(q^{100}) \)

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
\(5\) −0.454452 −0.203237 −0.101618 0.994823i \(-0.532402\pi\)
−0.101618 + 0.994823i \(0.532402\pi\)
\(6\) 0 0
\(7\) −2.18653 −0.826429 −0.413215 0.910634i \(-0.635594\pi\)
−0.413215 + 0.910634i \(0.635594\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.15877 0.349381 0.174691 0.984623i \(-0.444107\pi\)
0.174691 + 0.984623i \(0.444107\pi\)
\(12\) 0 0
\(13\) 6.03215 1.67302 0.836509 0.547953i \(-0.184593\pi\)
0.836509 + 0.547953i \(0.184593\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.0535246 −0.0129816 −0.00649081 0.999979i \(-0.502066\pi\)
−0.00649081 + 0.999979i \(0.502066\pi\)
\(18\) 0 0
\(19\) −2.08924 −0.479305 −0.239653 0.970859i \(-0.577034\pi\)
−0.239653 + 0.970859i \(0.577034\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.22849 −0.673187 −0.336593 0.941650i \(-0.609275\pi\)
−0.336593 + 0.941650i \(0.609275\pi\)
\(24\) 0 0
\(25\) −4.79347 −0.958695
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1.62034 0.300889 0.150445 0.988618i \(-0.451929\pi\)
0.150445 + 0.988618i \(0.451929\pi\)
\(30\) 0 0
\(31\) −2.01992 −0.362788 −0.181394 0.983411i \(-0.558061\pi\)
−0.181394 + 0.983411i \(0.558061\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0.993671 0.167961
\(36\) 0 0
\(37\) −3.49384 −0.574383 −0.287192 0.957873i \(-0.592722\pi\)
−0.287192 + 0.957873i \(0.592722\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.85650 −0.446111 −0.223055 0.974806i \(-0.571603\pi\)
−0.223055 + 0.974806i \(0.571603\pi\)
\(42\) 0 0
\(43\) 2.78023 0.423980 0.211990 0.977272i \(-0.432005\pi\)
0.211990 + 0.977272i \(0.432005\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.03663 1.31813 0.659064 0.752087i \(-0.270953\pi\)
0.659064 + 0.752087i \(0.270953\pi\)
\(48\) 0 0
\(49\) −2.21910 −0.317014
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4.09037 0.561855 0.280927 0.959729i \(-0.409358\pi\)
0.280927 + 0.959729i \(0.409358\pi\)
\(54\) 0 0
\(55\) −0.526603 −0.0710072
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.76605 0.620487 0.310244 0.950657i \(-0.399589\pi\)
0.310244 + 0.950657i \(0.399589\pi\)
\(60\) 0 0
\(61\) −14.6219 −1.87214 −0.936068 0.351819i \(-0.885563\pi\)
−0.936068 + 0.351819i \(0.885563\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2.74132 −0.340019
\(66\) 0 0
\(67\) −4.98740 −0.609308 −0.304654 0.952463i \(-0.598541\pi\)
−0.304654 + 0.952463i \(0.598541\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.04056 0.242170 0.121085 0.992642i \(-0.461363\pi\)
0.121085 + 0.992642i \(0.461363\pi\)
\(72\) 0 0
\(73\) −0.0937424 −0.0109717 −0.00548586 0.999985i \(-0.501746\pi\)
−0.00548586 + 0.999985i \(0.501746\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.53367 −0.288739
\(78\) 0 0
\(79\) −1.92521 −0.216603 −0.108302 0.994118i \(-0.534541\pi\)
−0.108302 + 0.994118i \(0.534541\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −7.96981 −0.874801 −0.437400 0.899267i \(-0.644101\pi\)
−0.437400 + 0.899267i \(0.644101\pi\)
\(84\) 0 0
\(85\) 0.0243243 0.00263834
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 16.7462 1.77510 0.887549 0.460713i \(-0.152406\pi\)
0.887549 + 0.460713i \(0.152406\pi\)
\(90\) 0 0
\(91\) −13.1895 −1.38263
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.949460 0.0974125
\(96\) 0 0
\(97\) 3.00301 0.304910 0.152455 0.988310i \(-0.451282\pi\)
0.152455 + 0.988310i \(0.451282\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.55655 0.353890 0.176945 0.984221i \(-0.443379\pi\)
0.176945 + 0.984221i \(0.443379\pi\)
\(102\) 0 0
\(103\) −3.10568 −0.306011 −0.153006 0.988225i \(-0.548895\pi\)
−0.153006 + 0.988225i \(0.548895\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.8110 −1.04514 −0.522571 0.852596i \(-0.675027\pi\)
−0.522571 + 0.852596i \(0.675027\pi\)
\(108\) 0 0
\(109\) 7.53872 0.722078 0.361039 0.932551i \(-0.382422\pi\)
0.361039 + 0.932551i \(0.382422\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 3.30774 0.311166 0.155583 0.987823i \(-0.450274\pi\)
0.155583 + 0.987823i \(0.450274\pi\)
\(114\) 0 0
\(115\) 1.46719 0.136816
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.117033 0.0107284
\(120\) 0 0
\(121\) −9.65726 −0.877933
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.45066 0.398079
\(126\) 0 0
\(127\) −13.1951 −1.17087 −0.585437 0.810718i \(-0.699077\pi\)
−0.585437 + 0.810718i \(0.699077\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.18286 −0.365458 −0.182729 0.983163i \(-0.558493\pi\)
−0.182729 + 0.983163i \(0.558493\pi\)
\(132\) 0 0
\(133\) 4.56819 0.396112
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.2951 1.05044 0.525219 0.850967i \(-0.323983\pi\)
0.525219 + 0.850967i \(0.323983\pi\)
\(138\) 0 0
\(139\) 6.49640 0.551018 0.275509 0.961299i \(-0.411154\pi\)
0.275509 + 0.961299i \(0.411154\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.98985 0.584521
\(144\) 0 0
\(145\) −0.736365 −0.0611518
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.0170 −0.902548 −0.451274 0.892385i \(-0.649030\pi\)
−0.451274 + 0.892385i \(0.649030\pi\)
\(150\) 0 0
\(151\) −21.4320 −1.74411 −0.872055 0.489408i \(-0.837213\pi\)
−0.872055 + 0.489408i \(0.837213\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.917954 0.0737318
\(156\) 0 0
\(157\) 11.7026 0.933967 0.466984 0.884266i \(-0.345341\pi\)
0.466984 + 0.884266i \(0.345341\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.05918 0.556341
\(162\) 0 0
\(163\) −3.32371 −0.260333 −0.130167 0.991492i \(-0.541551\pi\)
−0.130167 + 0.991492i \(0.541551\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −23.4924 −1.81789 −0.908947 0.416913i \(-0.863112\pi\)
−0.908947 + 0.416913i \(0.863112\pi\)
\(168\) 0 0
\(169\) 23.3869 1.79899
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 4.48627 0.341085 0.170543 0.985350i \(-0.445448\pi\)
0.170543 + 0.985350i \(0.445448\pi\)
\(174\) 0 0
\(175\) 10.4811 0.792294
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.40995 0.479102 0.239551 0.970884i \(-0.423000\pi\)
0.239551 + 0.970884i \(0.423000\pi\)
\(180\) 0 0
\(181\) 6.25690 0.465072 0.232536 0.972588i \(-0.425298\pi\)
0.232536 + 0.972588i \(0.425298\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.58778 0.116736
\(186\) 0 0
\(187\) −0.0620225 −0.00453553
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11.8680 0.858738 0.429369 0.903129i \(-0.358736\pi\)
0.429369 + 0.903129i \(0.358736\pi\)
\(192\) 0 0
\(193\) 7.71261 0.555166 0.277583 0.960702i \(-0.410467\pi\)
0.277583 + 0.960702i \(0.410467\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −11.2830 −0.803881 −0.401941 0.915666i \(-0.631664\pi\)
−0.401941 + 0.915666i \(0.631664\pi\)
\(198\) 0 0
\(199\) −4.78352 −0.339095 −0.169547 0.985522i \(-0.554231\pi\)
−0.169547 + 0.985522i \(0.554231\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −3.54291 −0.248664
\(204\) 0 0
\(205\) 1.29814 0.0906661
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.42094 −0.167460
\(210\) 0 0
\(211\) 12.7879 0.880358 0.440179 0.897910i \(-0.354915\pi\)
0.440179 + 0.897910i \(0.354915\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.26348 −0.0861685
\(216\) 0 0
\(217\) 4.41660 0.299818
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −0.322868 −0.0217185
\(222\) 0 0
\(223\) −22.5770 −1.51187 −0.755933 0.654649i \(-0.772817\pi\)
−0.755933 + 0.654649i \(0.772817\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −23.7505 −1.57637 −0.788186 0.615437i \(-0.788980\pi\)
−0.788186 + 0.615437i \(0.788980\pi\)
\(228\) 0 0
\(229\) −6.30407 −0.416585 −0.208292 0.978067i \(-0.566791\pi\)
−0.208292 + 0.978067i \(0.566791\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 16.4538 1.07793 0.538963 0.842329i \(-0.318816\pi\)
0.538963 + 0.842329i \(0.318816\pi\)
\(234\) 0 0
\(235\) −4.10671 −0.267892
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.59054 0.102884 0.0514418 0.998676i \(-0.483618\pi\)
0.0514418 + 0.998676i \(0.483618\pi\)
\(240\) 0 0
\(241\) 3.38944 0.218333 0.109167 0.994023i \(-0.465182\pi\)
0.109167 + 0.994023i \(0.465182\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.00847 0.0644291
\(246\) 0 0
\(247\) −12.6026 −0.801886
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.00000 −0.0631194
\(252\) 0 0
\(253\) −3.74107 −0.235199
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −26.8858 −1.67709 −0.838546 0.544831i \(-0.816594\pi\)
−0.838546 + 0.544831i \(0.816594\pi\)
\(258\) 0 0
\(259\) 7.63937 0.474687
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.39336 −0.270906 −0.135453 0.990784i \(-0.543249\pi\)
−0.135453 + 0.990784i \(0.543249\pi\)
\(264\) 0 0
\(265\) −1.85887 −0.114190
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −22.6845 −1.38310 −0.691549 0.722329i \(-0.743072\pi\)
−0.691549 + 0.722329i \(0.743072\pi\)
\(270\) 0 0
\(271\) −15.0589 −0.914763 −0.457382 0.889271i \(-0.651213\pi\)
−0.457382 + 0.889271i \(0.651213\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.55452 −0.334950
\(276\) 0 0
\(277\) −10.7918 −0.648419 −0.324210 0.945985i \(-0.605098\pi\)
−0.324210 + 0.945985i \(0.605098\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 21.9382 1.30872 0.654362 0.756182i \(-0.272937\pi\)
0.654362 + 0.756182i \(0.272937\pi\)
\(282\) 0 0
\(283\) −12.1997 −0.725198 −0.362599 0.931945i \(-0.618111\pi\)
−0.362599 + 0.931945i \(0.618111\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.24582 0.368679
\(288\) 0 0
\(289\) −16.9971 −0.999831
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −29.4675 −1.72151 −0.860756 0.509017i \(-0.830009\pi\)
−0.860756 + 0.509017i \(0.830009\pi\)
\(294\) 0 0
\(295\) −2.16594 −0.126106
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −19.4747 −1.12625
\(300\) 0 0
\(301\) −6.07904 −0.350390
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 6.64492 0.380487
\(306\) 0 0
\(307\) −21.3436 −1.21814 −0.609072 0.793115i \(-0.708458\pi\)
−0.609072 + 0.793115i \(0.708458\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 30.9771 1.75655 0.878275 0.478155i \(-0.158694\pi\)
0.878275 + 0.478155i \(0.158694\pi\)
\(312\) 0 0
\(313\) −16.2372 −0.917783 −0.458892 0.888492i \(-0.651753\pi\)
−0.458892 + 0.888492i \(0.651753\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 27.5305 1.54627 0.773133 0.634244i \(-0.218688\pi\)
0.773133 + 0.634244i \(0.218688\pi\)
\(318\) 0 0
\(319\) 1.87759 0.105125
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0.111826 0.00622216
\(324\) 0 0
\(325\) −28.9150 −1.60391
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −19.7588 −1.08934
\(330\) 0 0
\(331\) −31.9237 −1.75469 −0.877344 0.479862i \(-0.840687\pi\)
−0.877344 + 0.479862i \(0.840687\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.26653 0.123834
\(336\) 0 0
\(337\) −18.7610 −1.02198 −0.510990 0.859587i \(-0.670721\pi\)
−0.510990 + 0.859587i \(0.670721\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.34061 −0.126751
\(342\) 0 0
\(343\) 20.1578 1.08842
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.43093 0.237865 0.118932 0.992902i \(-0.462053\pi\)
0.118932 + 0.992902i \(0.462053\pi\)
\(348\) 0 0
\(349\) −13.3203 −0.713018 −0.356509 0.934292i \(-0.616033\pi\)
−0.356509 + 0.934292i \(0.616033\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −21.3691 −1.13736 −0.568681 0.822558i \(-0.692546\pi\)
−0.568681 + 0.822558i \(0.692546\pi\)
\(354\) 0 0
\(355\) −0.927334 −0.0492178
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.72114 0.354728 0.177364 0.984145i \(-0.443243\pi\)
0.177364 + 0.984145i \(0.443243\pi\)
\(360\) 0 0
\(361\) −14.6351 −0.770267
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0.0426014 0.00222986
\(366\) 0 0
\(367\) 4.60106 0.240174 0.120087 0.992763i \(-0.461683\pi\)
0.120087 + 0.992763i \(0.461683\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.94369 −0.464333
\(372\) 0 0
\(373\) −25.0550 −1.29730 −0.648650 0.761087i \(-0.724666\pi\)
−0.648650 + 0.761087i \(0.724666\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.77412 0.503393
\(378\) 0 0
\(379\) −10.3050 −0.529333 −0.264666 0.964340i \(-0.585262\pi\)
−0.264666 + 0.964340i \(0.585262\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −9.92110 −0.506944 −0.253472 0.967343i \(-0.581573\pi\)
−0.253472 + 0.967343i \(0.581573\pi\)
\(384\) 0 0
\(385\) 1.15143 0.0586824
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 33.3777 1.69232 0.846158 0.532932i \(-0.178910\pi\)
0.846158 + 0.532932i \(0.178910\pi\)
\(390\) 0 0
\(391\) 0.172804 0.00873905
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.874915 0.0440218
\(396\) 0 0
\(397\) −2.43725 −0.122322 −0.0611611 0.998128i \(-0.519480\pi\)
−0.0611611 + 0.998128i \(0.519480\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −11.0399 −0.551306 −0.275653 0.961257i \(-0.588894\pi\)
−0.275653 + 0.961257i \(0.588894\pi\)
\(402\) 0 0
\(403\) −12.1844 −0.606950
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.04854 −0.200679
\(408\) 0 0
\(409\) −7.10281 −0.351211 −0.175606 0.984461i \(-0.556188\pi\)
−0.175606 + 0.984461i \(0.556188\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −10.4211 −0.512789
\(414\) 0 0
\(415\) 3.62189 0.177792
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −22.4900 −1.09871 −0.549354 0.835590i \(-0.685126\pi\)
−0.549354 + 0.835590i \(0.685126\pi\)
\(420\) 0 0
\(421\) −23.3162 −1.13636 −0.568180 0.822904i \(-0.692352\pi\)
−0.568180 + 0.822904i \(0.692352\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.256569 0.0124454
\(426\) 0 0
\(427\) 31.9711 1.54719
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.63794 −0.271570 −0.135785 0.990738i \(-0.543356\pi\)
−0.135785 + 0.990738i \(0.543356\pi\)
\(432\) 0 0
\(433\) 26.5522 1.27602 0.638009 0.770029i \(-0.279758\pi\)
0.638009 + 0.770029i \(0.279758\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.74510 0.322662
\(438\) 0 0
\(439\) 37.8832 1.80807 0.904034 0.427462i \(-0.140592\pi\)
0.904034 + 0.427462i \(0.140592\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −37.3614 −1.77509 −0.887547 0.460717i \(-0.847592\pi\)
−0.887547 + 0.460717i \(0.847592\pi\)
\(444\) 0 0
\(445\) −7.61036 −0.360766
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −3.53079 −0.166628 −0.0833141 0.996523i \(-0.526550\pi\)
−0.0833141 + 0.996523i \(0.526550\pi\)
\(450\) 0 0
\(451\) −3.31002 −0.155863
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 5.99397 0.281002
\(456\) 0 0
\(457\) 19.8957 0.930681 0.465341 0.885132i \(-0.345932\pi\)
0.465341 + 0.885132i \(0.345932\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −25.9530 −1.20875 −0.604375 0.796700i \(-0.706577\pi\)
−0.604375 + 0.796700i \(0.706577\pi\)
\(462\) 0 0
\(463\) −23.5757 −1.09566 −0.547828 0.836591i \(-0.684545\pi\)
−0.547828 + 0.836591i \(0.684545\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.93839 −0.182247 −0.0911234 0.995840i \(-0.529046\pi\)
−0.0911234 + 0.995840i \(0.529046\pi\)
\(468\) 0 0
\(469\) 10.9051 0.503550
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.22163 0.148131
\(474\) 0 0
\(475\) 10.0147 0.459507
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17.7826 −0.812506 −0.406253 0.913761i \(-0.633165\pi\)
−0.406253 + 0.913761i \(0.633165\pi\)
\(480\) 0 0
\(481\) −21.0754 −0.960954
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.36472 −0.0619689
\(486\) 0 0
\(487\) 38.4530 1.74247 0.871237 0.490863i \(-0.163319\pi\)
0.871237 + 0.490863i \(0.163319\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.93938 −0.222911 −0.111456 0.993769i \(-0.535551\pi\)
−0.111456 + 0.993769i \(0.535551\pi\)
\(492\) 0 0
\(493\) −0.0867279 −0.00390603
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.46173 −0.200136
\(498\) 0 0
\(499\) −9.78960 −0.438243 −0.219121 0.975698i \(-0.570319\pi\)
−0.219121 + 0.975698i \(0.570319\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −16.9870 −0.757412 −0.378706 0.925517i \(-0.623631\pi\)
−0.378706 + 0.925517i \(0.623631\pi\)
\(504\) 0 0
\(505\) −1.61628 −0.0719235
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −20.2558 −0.897822 −0.448911 0.893577i \(-0.648188\pi\)
−0.448911 + 0.893577i \(0.648188\pi\)
\(510\) 0 0
\(511\) 0.204970 0.00906735
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.41138 0.0621928
\(516\) 0 0
\(517\) 10.4713 0.460529
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 14.9138 0.653384 0.326692 0.945131i \(-0.394066\pi\)
0.326692 + 0.945131i \(0.394066\pi\)
\(522\) 0 0
\(523\) −30.4438 −1.33121 −0.665607 0.746302i \(-0.731827\pi\)
−0.665607 + 0.746302i \(0.731827\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.108115 0.00470957
\(528\) 0 0
\(529\) −12.5768 −0.546820
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −17.2308 −0.746351
\(534\) 0 0
\(535\) 4.91309 0.212412
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.57142 −0.110759
\(540\) 0 0
\(541\) 2.65322 0.114071 0.0570353 0.998372i \(-0.481835\pi\)
0.0570353 + 0.998372i \(0.481835\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.42598 −0.146753
\(546\) 0 0
\(547\) 18.8391 0.805500 0.402750 0.915310i \(-0.368054\pi\)
0.402750 + 0.915310i \(0.368054\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.38528 −0.144218
\(552\) 0 0
\(553\) 4.20952 0.179007
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.30321 0.139962 0.0699808 0.997548i \(-0.477706\pi\)
0.0699808 + 0.997548i \(0.477706\pi\)
\(558\) 0 0
\(559\) 16.7707 0.709327
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8.19333 −0.345308 −0.172654 0.984983i \(-0.555234\pi\)
−0.172654 + 0.984983i \(0.555234\pi\)
\(564\) 0 0
\(565\) −1.50321 −0.0632405
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 26.3058 1.10280 0.551398 0.834242i \(-0.314094\pi\)
0.551398 + 0.834242i \(0.314094\pi\)
\(570\) 0 0
\(571\) −29.5821 −1.23797 −0.618987 0.785401i \(-0.712457\pi\)
−0.618987 + 0.785401i \(0.712457\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 15.4757 0.645381
\(576\) 0 0
\(577\) 22.7949 0.948964 0.474482 0.880265i \(-0.342635\pi\)
0.474482 + 0.880265i \(0.342635\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 17.4262 0.722961
\(582\) 0 0
\(583\) 4.73978 0.196302
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.3149 0.879761 0.439881 0.898056i \(-0.355021\pi\)
0.439881 + 0.898056i \(0.355021\pi\)
\(588\) 0 0
\(589\) 4.22009 0.173886
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 4.84036 0.198770 0.0993850 0.995049i \(-0.468312\pi\)
0.0993850 + 0.995049i \(0.468312\pi\)
\(594\) 0 0
\(595\) −0.0531858 −0.00218040
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −43.7104 −1.78596 −0.892978 0.450100i \(-0.851388\pi\)
−0.892978 + 0.450100i \(0.851388\pi\)
\(600\) 0 0
\(601\) −16.0174 −0.653365 −0.326682 0.945134i \(-0.605931\pi\)
−0.326682 + 0.945134i \(0.605931\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.38876 0.178428
\(606\) 0 0
\(607\) −3.55146 −0.144149 −0.0720747 0.997399i \(-0.522962\pi\)
−0.0720747 + 0.997399i \(0.522962\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 54.5103 2.20525
\(612\) 0 0
\(613\) 20.6687 0.834801 0.417400 0.908723i \(-0.362941\pi\)
0.417400 + 0.908723i \(0.362941\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0094 1.36917 0.684583 0.728935i \(-0.259984\pi\)
0.684583 + 0.728935i \(0.259984\pi\)
\(618\) 0 0
\(619\) 1.90390 0.0765243 0.0382621 0.999268i \(-0.487818\pi\)
0.0382621 + 0.999268i \(0.487818\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −36.6161 −1.46699
\(624\) 0 0
\(625\) 21.9448 0.877790
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.187006 0.00745642
\(630\) 0 0
\(631\) 11.4055 0.454048 0.227024 0.973889i \(-0.427100\pi\)
0.227024 + 0.973889i \(0.427100\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.99652 0.237965
\(636\) 0 0
\(637\) −13.3860 −0.530371
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.81401 −0.0716491 −0.0358245 0.999358i \(-0.511406\pi\)
−0.0358245 + 0.999358i \(0.511406\pi\)
\(642\) 0 0
\(643\) −10.4605 −0.412523 −0.206261 0.978497i \(-0.566130\pi\)
−0.206261 + 0.978497i \(0.566130\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.7209 0.893249 0.446624 0.894722i \(-0.352626\pi\)
0.446624 + 0.894722i \(0.352626\pi\)
\(648\) 0 0
\(649\) 5.52274 0.216787
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −12.8539 −0.503013 −0.251507 0.967856i \(-0.580926\pi\)
−0.251507 + 0.967856i \(0.580926\pi\)
\(654\) 0 0
\(655\) 1.90091 0.0742746
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −33.7873 −1.31617 −0.658083 0.752946i \(-0.728632\pi\)
−0.658083 + 0.752946i \(0.728632\pi\)
\(660\) 0 0
\(661\) 27.6933 1.07714 0.538572 0.842580i \(-0.318964\pi\)
0.538572 + 0.842580i \(0.318964\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.07602 −0.0805046
\(666\) 0 0
\(667\) −5.23124 −0.202555
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −16.9433 −0.654089
\(672\) 0 0
\(673\) 17.1280 0.660237 0.330118 0.943940i \(-0.392911\pi\)
0.330118 + 0.943940i \(0.392911\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −10.9570 −0.421111 −0.210555 0.977582i \(-0.567527\pi\)
−0.210555 + 0.977582i \(0.567527\pi\)
\(678\) 0 0
\(679\) −6.56617 −0.251986
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.6594 1.32620 0.663102 0.748529i \(-0.269240\pi\)
0.663102 + 0.748529i \(0.269240\pi\)
\(684\) 0 0
\(685\) −5.58752 −0.213488
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.6737 0.939993
\(690\) 0 0
\(691\) 9.23393 0.351275 0.175638 0.984455i \(-0.443801\pi\)
0.175638 + 0.984455i \(0.443801\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.95230 −0.111987
\(696\) 0 0
\(697\) 0.152893 0.00579123
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −13.2605 −0.500842 −0.250421 0.968137i \(-0.580569\pi\)
−0.250421 + 0.968137i \(0.580569\pi\)
\(702\) 0 0
\(703\) 7.29947 0.275305
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.77649 −0.292465
\(708\) 0 0
\(709\) 46.0334 1.72882 0.864410 0.502787i \(-0.167692\pi\)
0.864410 + 0.502787i \(0.167692\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.52128 0.244224
\(714\) 0 0
\(715\) −3.17655 −0.118796
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.81518 0.0676949 0.0338474 0.999427i \(-0.489224\pi\)
0.0338474 + 0.999427i \(0.489224\pi\)
\(720\) 0 0
\(721\) 6.79064 0.252897
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.76705 −0.288461
\(726\) 0 0
\(727\) −34.6521 −1.28518 −0.642588 0.766212i \(-0.722139\pi\)
−0.642588 + 0.766212i \(0.722139\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.148810 −0.00550395
\(732\) 0 0
\(733\) 26.5655 0.981220 0.490610 0.871379i \(-0.336774\pi\)
0.490610 + 0.871379i \(0.336774\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −5.77923 −0.212881
\(738\) 0 0
\(739\) 14.3106 0.526424 0.263212 0.964738i \(-0.415218\pi\)
0.263212 + 0.964738i \(0.415218\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.40007 0.344855 0.172428 0.985022i \(-0.444839\pi\)
0.172428 + 0.985022i \(0.444839\pi\)
\(744\) 0 0
\(745\) 5.00670 0.183431
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 23.6386 0.863736
\(750\) 0 0
\(751\) 21.4083 0.781198 0.390599 0.920561i \(-0.372268\pi\)
0.390599 + 0.920561i \(0.372268\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.73980 0.354468
\(756\) 0 0
\(757\) −19.4330 −0.706304 −0.353152 0.935566i \(-0.614890\pi\)
−0.353152 + 0.935566i \(0.614890\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −36.1110 −1.30902 −0.654511 0.756053i \(-0.727125\pi\)
−0.654511 + 0.756053i \(0.727125\pi\)
\(762\) 0 0
\(763\) −16.4836 −0.596747
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.7496 1.03809
\(768\) 0 0
\(769\) 32.4205 1.16911 0.584556 0.811353i \(-0.301269\pi\)
0.584556 + 0.811353i \(0.301269\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 25.6367 0.922089 0.461045 0.887377i \(-0.347475\pi\)
0.461045 + 0.887377i \(0.347475\pi\)
\(774\) 0 0
\(775\) 9.68241 0.347803
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.96792 0.213823
\(780\) 0 0
\(781\) 2.36453 0.0846095
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −5.31826 −0.189817
\(786\) 0 0
\(787\) 2.24434 0.0800022 0.0400011 0.999200i \(-0.487264\pi\)
0.0400011 + 0.999200i \(0.487264\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −7.23247 −0.257157
\(792\) 0 0
\(793\) −88.2012 −3.13212
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 20.7390 0.734613 0.367307 0.930100i \(-0.380280\pi\)
0.367307 + 0.930100i \(0.380280\pi\)
\(798\) 0 0
\(799\) −0.483682 −0.0171114
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.108626 −0.00383331
\(804\) 0 0
\(805\) −3.20806 −0.113069
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 23.7671 0.835606 0.417803 0.908538i \(-0.362800\pi\)
0.417803 + 0.908538i \(0.362800\pi\)
\(810\) 0 0
\(811\) −6.35066 −0.223002 −0.111501 0.993764i \(-0.535566\pi\)
−0.111501 + 0.993764i \(0.535566\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.51047 0.0529093
\(816\) 0 0
\(817\) −5.80857 −0.203216
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10.6403 −0.371350 −0.185675 0.982611i \(-0.559447\pi\)
−0.185675 + 0.982611i \(0.559447\pi\)
\(822\) 0 0
\(823\) 31.4709 1.09701 0.548503 0.836149i \(-0.315198\pi\)
0.548503 + 0.836149i \(0.315198\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −11.2833 −0.392360 −0.196180 0.980568i \(-0.562854\pi\)
−0.196180 + 0.980568i \(0.562854\pi\)
\(828\) 0 0
\(829\) 2.17919 0.0756864 0.0378432 0.999284i \(-0.487951\pi\)
0.0378432 + 0.999284i \(0.487951\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0.118776 0.00411536
\(834\) 0 0
\(835\) 10.6761 0.369463
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −41.1253 −1.41980 −0.709901 0.704301i \(-0.751260\pi\)
−0.709901 + 0.704301i \(0.751260\pi\)
\(840\) 0 0
\(841\) −26.3745 −0.909466
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −10.6282 −0.365621
\(846\) 0 0
\(847\) 21.1159 0.725549
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 11.2798 0.386667
\(852\) 0 0
\(853\) 20.1056 0.688403 0.344202 0.938896i \(-0.388150\pi\)
0.344202 + 0.938896i \(0.388150\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 4.75122 0.162299 0.0811493 0.996702i \(-0.474141\pi\)
0.0811493 + 0.996702i \(0.474141\pi\)
\(858\) 0 0
\(859\) 27.2044 0.928203 0.464102 0.885782i \(-0.346377\pi\)
0.464102 + 0.885782i \(0.346377\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −43.0961 −1.46701 −0.733505 0.679684i \(-0.762117\pi\)
−0.733505 + 0.679684i \(0.762117\pi\)
\(864\) 0 0
\(865\) −2.03879 −0.0693211
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.23087 −0.0756771
\(870\) 0 0
\(871\) −30.0848 −1.01938
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −9.73149 −0.328984
\(876\) 0 0
\(877\) −37.2416 −1.25756 −0.628780 0.777583i \(-0.716445\pi\)
−0.628780 + 0.777583i \(0.716445\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −23.0353 −0.776079 −0.388039 0.921643i \(-0.626848\pi\)
−0.388039 + 0.921643i \(0.626848\pi\)
\(882\) 0 0
\(883\) 13.7702 0.463403 0.231701 0.972787i \(-0.425571\pi\)
0.231701 + 0.972787i \(0.425571\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 26.3219 0.883804 0.441902 0.897063i \(-0.354304\pi\)
0.441902 + 0.897063i \(0.354304\pi\)
\(888\) 0 0
\(889\) 28.8514 0.967644
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −18.8797 −0.631785
\(894\) 0 0
\(895\) −2.91301 −0.0973712
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.27295 −0.109159
\(900\) 0 0
\(901\) −0.218935 −0.00729378
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.84346 −0.0945198
\(906\) 0 0
\(907\) −32.6153 −1.08297 −0.541486 0.840710i \(-0.682138\pi\)
−0.541486 + 0.840710i \(0.682138\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −47.5936 −1.57685 −0.788423 0.615133i \(-0.789102\pi\)
−0.788423 + 0.615133i \(0.789102\pi\)
\(912\) 0 0
\(913\) −9.23515 −0.305639
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 9.14593 0.302025
\(918\) 0 0
\(919\) −16.4448 −0.542463 −0.271232 0.962514i \(-0.587431\pi\)
−0.271232 + 0.962514i \(0.587431\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 12.3089 0.405154
\(924\) 0 0
\(925\) 16.7476 0.550658
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −58.6216 −1.92331 −0.961657 0.274256i \(-0.911569\pi\)
−0.961657 + 0.274256i \(0.911569\pi\)
\(930\) 0 0
\(931\) 4.63624 0.151947
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.0281862 0.000921788 0
\(936\) 0 0
\(937\) 12.5654 0.410494 0.205247 0.978710i \(-0.434200\pi\)
0.205247 + 0.978710i \(0.434200\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.27635 0.139405 0.0697025 0.997568i \(-0.477795\pi\)
0.0697025 + 0.997568i \(0.477795\pi\)
\(942\) 0 0
\(943\) 9.22219 0.300316
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −28.9545 −0.940895 −0.470447 0.882428i \(-0.655907\pi\)
−0.470447 + 0.882428i \(0.655907\pi\)
\(948\) 0 0
\(949\) −0.565469 −0.0183559
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 11.0253 0.357144 0.178572 0.983927i \(-0.442852\pi\)
0.178572 + 0.983927i \(0.442852\pi\)
\(954\) 0 0
\(955\) −5.39343 −0.174527
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −26.8835 −0.868114
\(960\) 0 0
\(961\) −26.9199 −0.868385
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.50501 −0.112830
\(966\) 0 0
\(967\) −29.3057 −0.942409 −0.471205 0.882024i \(-0.656181\pi\)
−0.471205 + 0.882024i \(0.656181\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.75260 −0.0562437 −0.0281219 0.999605i \(-0.508953\pi\)
−0.0281219 + 0.999605i \(0.508953\pi\)
\(972\) 0 0
\(973\) −14.2046 −0.455377
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −19.9928 −0.639626 −0.319813 0.947481i \(-0.603620\pi\)
−0.319813 + 0.947481i \(0.603620\pi\)
\(978\) 0 0
\(979\) 19.4050 0.620186
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 33.6346 1.07278 0.536389 0.843971i \(-0.319788\pi\)
0.536389 + 0.843971i \(0.319788\pi\)
\(984\) 0 0
\(985\) 5.12758 0.163378
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −8.97593 −0.285418
\(990\) 0 0
\(991\) 54.2527 1.72339 0.861696 0.507424i \(-0.169402\pi\)
0.861696 + 0.507424i \(0.169402\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.17388 0.0689166
\(996\) 0 0
\(997\) 15.3787 0.487048 0.243524 0.969895i \(-0.421697\pi\)
0.243524 + 0.969895i \(0.421697\pi\)
\(998\) 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 9036.2.a.i.1.3 7
3.2 odd 2 1004.2.a.a.1.1 7
12.11 even 2 4016.2.a.g.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1004.2.a.a.1.1 7 3.2 odd 2
4016.2.a.g.1.7 7 12.11 even 2
9036.2.a.i.1.3 7 1.1 even 1 trivial