Properties

Label 9200.2.a.cz.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.4623698596\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Defining polynomial: \(x^{7} - 3 x^{6} - 7 x^{5} + 24 x^{4} + x^{3} - 35 x^{2} + 17 x - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 920)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.98707\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.98707 q^{3} +0.980560 q^{7} +5.92257 q^{9} +O(q^{10})\) \(q-2.98707 q^{3} +0.980560 q^{7} +5.92257 q^{9} +6.14721 q^{11} -6.37400 q^{13} +3.36098 q^{17} -1.08276 q^{19} -2.92900 q^{21} +1.00000 q^{23} -8.72993 q^{27} -0.271042 q^{29} +8.77792 q^{31} -18.3621 q^{33} -8.84665 q^{37} +19.0396 q^{39} -4.85308 q^{41} -1.87756 q^{43} -0.196089 q^{47} -6.03850 q^{49} -10.0395 q^{51} -1.93157 q^{53} +3.23429 q^{57} -13.0036 q^{59} +6.00189 q^{61} +5.80744 q^{63} -2.26847 q^{67} -2.98707 q^{69} -10.2677 q^{71} +1.38188 q^{73} +6.02771 q^{77} +4.67459 q^{79} +8.30917 q^{81} +15.7171 q^{83} +0.809622 q^{87} -11.1548 q^{89} -6.25008 q^{91} -26.2202 q^{93} -10.2868 q^{97} +36.4073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + 7q^{11} - 7q^{13} + 7q^{19} - 6q^{21} + 7q^{23} - 11q^{29} + 10q^{31} - 19q^{33} - 19q^{37} + 24q^{39} - 16q^{41} - 6q^{43} - 6q^{47} - 17q^{49} + 7q^{51} - 15q^{53} - 8q^{57} + 11q^{59} + 5q^{61} - 13q^{63} - 9q^{67} - 3q^{69} + 14q^{71} - 10q^{73} - 6q^{77} + 32q^{79} - 5q^{81} - q^{83} - 10q^{87} - 24q^{89} + 7q^{91} - 26q^{93} + 7q^{97} + 61q^{99} + O(q^{100}) \)

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
\(3\) −2.98707 −1.72458 −0.862292 0.506411i \(-0.830972\pi\)
−0.862292 + 0.506411i \(0.830972\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0.980560 0.370617 0.185308 0.982680i \(-0.440672\pi\)
0.185308 + 0.982680i \(0.440672\pi\)
\(8\) 0 0
\(9\) 5.92257 1.97419
\(10\) 0 0
\(11\) 6.14721 1.85345 0.926727 0.375734i \(-0.122609\pi\)
0.926727 + 0.375734i \(0.122609\pi\)
\(12\) 0 0
\(13\) −6.37400 −1.76783 −0.883914 0.467649i \(-0.845101\pi\)
−0.883914 + 0.467649i \(0.845101\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.36098 0.815157 0.407579 0.913170i \(-0.366373\pi\)
0.407579 + 0.913170i \(0.366373\pi\)
\(18\) 0 0
\(19\) −1.08276 −0.248403 −0.124202 0.992257i \(-0.539637\pi\)
−0.124202 + 0.992257i \(0.539637\pi\)
\(20\) 0 0
\(21\) −2.92900 −0.639160
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −8.72993 −1.68008
\(28\) 0 0
\(29\) −0.271042 −0.0503313 −0.0251657 0.999683i \(-0.508011\pi\)
−0.0251657 + 0.999683i \(0.508011\pi\)
\(30\) 0 0
\(31\) 8.77792 1.57656 0.788280 0.615316i \(-0.210972\pi\)
0.788280 + 0.615316i \(0.210972\pi\)
\(32\) 0 0
\(33\) −18.3621 −3.19644
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.84665 −1.45438 −0.727190 0.686436i \(-0.759174\pi\)
−0.727190 + 0.686436i \(0.759174\pi\)
\(38\) 0 0
\(39\) 19.0396 3.04877
\(40\) 0 0
\(41\) −4.85308 −0.757923 −0.378962 0.925412i \(-0.623719\pi\)
−0.378962 + 0.925412i \(0.623719\pi\)
\(42\) 0 0
\(43\) −1.87756 −0.286326 −0.143163 0.989699i \(-0.545727\pi\)
−0.143163 + 0.989699i \(0.545727\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −0.196089 −0.0286026 −0.0143013 0.999898i \(-0.504552\pi\)
−0.0143013 + 0.999898i \(0.504552\pi\)
\(48\) 0 0
\(49\) −6.03850 −0.862643
\(50\) 0 0
\(51\) −10.0395 −1.40581
\(52\) 0 0
\(53\) −1.93157 −0.265321 −0.132661 0.991162i \(-0.542352\pi\)
−0.132661 + 0.991162i \(0.542352\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.23429 0.428392
\(58\) 0 0
\(59\) −13.0036 −1.69293 −0.846465 0.532444i \(-0.821274\pi\)
−0.846465 + 0.532444i \(0.821274\pi\)
\(60\) 0 0
\(61\) 6.00189 0.768464 0.384232 0.923237i \(-0.374466\pi\)
0.384232 + 0.923237i \(0.374466\pi\)
\(62\) 0 0
\(63\) 5.80744 0.731668
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.26847 −0.277138 −0.138569 0.990353i \(-0.544250\pi\)
−0.138569 + 0.990353i \(0.544250\pi\)
\(68\) 0 0
\(69\) −2.98707 −0.359601
\(70\) 0 0
\(71\) −10.2677 −1.21855 −0.609277 0.792958i \(-0.708540\pi\)
−0.609277 + 0.792958i \(0.708540\pi\)
\(72\) 0 0
\(73\) 1.38188 0.161737 0.0808685 0.996725i \(-0.474231\pi\)
0.0808685 + 0.996725i \(0.474231\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.02771 0.686921
\(78\) 0 0
\(79\) 4.67459 0.525932 0.262966 0.964805i \(-0.415299\pi\)
0.262966 + 0.964805i \(0.415299\pi\)
\(80\) 0 0
\(81\) 8.30917 0.923241
\(82\) 0 0
\(83\) 15.7171 1.72517 0.862587 0.505909i \(-0.168843\pi\)
0.862587 + 0.505909i \(0.168843\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.809622 0.0868006
\(88\) 0 0
\(89\) −11.1548 −1.18241 −0.591206 0.806521i \(-0.701348\pi\)
−0.591206 + 0.806521i \(0.701348\pi\)
\(90\) 0 0
\(91\) −6.25008 −0.655187
\(92\) 0 0
\(93\) −26.2202 −2.71891
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −10.2868 −1.04447 −0.522234 0.852802i \(-0.674901\pi\)
−0.522234 + 0.852802i \(0.674901\pi\)
\(98\) 0 0
\(99\) 36.4073 3.65908
\(100\) 0 0
\(101\) −15.2625 −1.51868 −0.759339 0.650695i \(-0.774478\pi\)
−0.759339 + 0.650695i \(0.774478\pi\)
\(102\) 0 0
\(103\) 7.60795 0.749634 0.374817 0.927099i \(-0.377706\pi\)
0.374817 + 0.927099i \(0.377706\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.3081 −1.09320 −0.546599 0.837395i \(-0.684078\pi\)
−0.546599 + 0.837395i \(0.684078\pi\)
\(108\) 0 0
\(109\) 3.45336 0.330772 0.165386 0.986229i \(-0.447113\pi\)
0.165386 + 0.986229i \(0.447113\pi\)
\(110\) 0 0
\(111\) 26.4256 2.50820
\(112\) 0 0
\(113\) 14.6889 1.38181 0.690907 0.722944i \(-0.257212\pi\)
0.690907 + 0.722944i \(0.257212\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −37.7505 −3.49003
\(118\) 0 0
\(119\) 3.29564 0.302111
\(120\) 0 0
\(121\) 26.7882 2.43530
\(122\) 0 0
\(123\) 14.4965 1.30710
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 1.19312 0.105873 0.0529363 0.998598i \(-0.483142\pi\)
0.0529363 + 0.998598i \(0.483142\pi\)
\(128\) 0 0
\(129\) 5.60841 0.493793
\(130\) 0 0
\(131\) 11.7326 1.02509 0.512543 0.858662i \(-0.328704\pi\)
0.512543 + 0.858662i \(0.328704\pi\)
\(132\) 0 0
\(133\) −1.06171 −0.0920623
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.4665 −0.894210 −0.447105 0.894481i \(-0.647545\pi\)
−0.447105 + 0.894481i \(0.647545\pi\)
\(138\) 0 0
\(139\) −4.11349 −0.348902 −0.174451 0.984666i \(-0.555815\pi\)
−0.174451 + 0.984666i \(0.555815\pi\)
\(140\) 0 0
\(141\) 0.585732 0.0493275
\(142\) 0 0
\(143\) −39.1823 −3.27659
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 18.0374 1.48770
\(148\) 0 0
\(149\) 1.37793 0.112885 0.0564424 0.998406i \(-0.482024\pi\)
0.0564424 + 0.998406i \(0.482024\pi\)
\(150\) 0 0
\(151\) 3.49384 0.284325 0.142162 0.989843i \(-0.454594\pi\)
0.142162 + 0.989843i \(0.454594\pi\)
\(152\) 0 0
\(153\) 19.9057 1.60928
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −3.32373 −0.265262 −0.132631 0.991165i \(-0.542343\pi\)
−0.132631 + 0.991165i \(0.542343\pi\)
\(158\) 0 0
\(159\) 5.76973 0.457569
\(160\) 0 0
\(161\) 0.980560 0.0772789
\(162\) 0 0
\(163\) 8.52075 0.667397 0.333698 0.942680i \(-0.391703\pi\)
0.333698 + 0.942680i \(0.391703\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −15.6190 −1.20864 −0.604319 0.796742i \(-0.706555\pi\)
−0.604319 + 0.796742i \(0.706555\pi\)
\(168\) 0 0
\(169\) 27.6278 2.12522
\(170\) 0 0
\(171\) −6.41275 −0.490395
\(172\) 0 0
\(173\) −8.42727 −0.640713 −0.320357 0.947297i \(-0.603803\pi\)
−0.320357 + 0.947297i \(0.603803\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 38.8428 2.91960
\(178\) 0 0
\(179\) −10.8047 −0.807580 −0.403790 0.914852i \(-0.632307\pi\)
−0.403790 + 0.914852i \(0.632307\pi\)
\(180\) 0 0
\(181\) −15.4282 −1.14677 −0.573385 0.819286i \(-0.694370\pi\)
−0.573385 + 0.819286i \(0.694370\pi\)
\(182\) 0 0
\(183\) −17.9281 −1.32528
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 20.6607 1.51086
\(188\) 0 0
\(189\) −8.56022 −0.622664
\(190\) 0 0
\(191\) 22.2634 1.61092 0.805462 0.592648i \(-0.201917\pi\)
0.805462 + 0.592648i \(0.201917\pi\)
\(192\) 0 0
\(193\) 16.1399 1.16178 0.580889 0.813983i \(-0.302705\pi\)
0.580889 + 0.813983i \(0.302705\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.9936 0.997004 0.498502 0.866889i \(-0.333884\pi\)
0.498502 + 0.866889i \(0.333884\pi\)
\(198\) 0 0
\(199\) 6.91926 0.490493 0.245246 0.969461i \(-0.421131\pi\)
0.245246 + 0.969461i \(0.421131\pi\)
\(200\) 0 0
\(201\) 6.77608 0.477948
\(202\) 0 0
\(203\) −0.265773 −0.0186536
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 5.92257 0.411647
\(208\) 0 0
\(209\) −6.65598 −0.460404
\(210\) 0 0
\(211\) −12.9170 −0.889246 −0.444623 0.895718i \(-0.646662\pi\)
−0.444623 + 0.895718i \(0.646662\pi\)
\(212\) 0 0
\(213\) 30.6704 2.10150
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 8.60728 0.584300
\(218\) 0 0
\(219\) −4.12777 −0.278929
\(220\) 0 0
\(221\) −21.4229 −1.44106
\(222\) 0 0
\(223\) −26.6579 −1.78514 −0.892572 0.450905i \(-0.851101\pi\)
−0.892572 + 0.450905i \(0.851101\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.44407 0.626825 0.313412 0.949617i \(-0.398528\pi\)
0.313412 + 0.949617i \(0.398528\pi\)
\(228\) 0 0
\(229\) 14.1994 0.938322 0.469161 0.883113i \(-0.344556\pi\)
0.469161 + 0.883113i \(0.344556\pi\)
\(230\) 0 0
\(231\) −18.0052 −1.18465
\(232\) 0 0
\(233\) −9.41134 −0.616557 −0.308279 0.951296i \(-0.599753\pi\)
−0.308279 + 0.951296i \(0.599753\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −13.9633 −0.907014
\(238\) 0 0
\(239\) 15.4781 1.00119 0.500597 0.865680i \(-0.333114\pi\)
0.500597 + 0.865680i \(0.333114\pi\)
\(240\) 0 0
\(241\) −3.51052 −0.226133 −0.113066 0.993587i \(-0.536067\pi\)
−0.113066 + 0.993587i \(0.536067\pi\)
\(242\) 0 0
\(243\) 1.36974 0.0878689
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.90153 0.439134
\(248\) 0 0
\(249\) −46.9480 −2.97521
\(250\) 0 0
\(251\) 23.6649 1.49372 0.746859 0.664982i \(-0.231561\pi\)
0.746859 + 0.664982i \(0.231561\pi\)
\(252\) 0 0
\(253\) 6.14721 0.386472
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 30.8326 1.92328 0.961641 0.274311i \(-0.0884497\pi\)
0.961641 + 0.274311i \(0.0884497\pi\)
\(258\) 0 0
\(259\) −8.67467 −0.539018
\(260\) 0 0
\(261\) −1.60527 −0.0993636
\(262\) 0 0
\(263\) −20.5880 −1.26951 −0.634755 0.772714i \(-0.718899\pi\)
−0.634755 + 0.772714i \(0.718899\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 33.3203 2.03917
\(268\) 0 0
\(269\) −17.0277 −1.03820 −0.519099 0.854714i \(-0.673732\pi\)
−0.519099 + 0.854714i \(0.673732\pi\)
\(270\) 0 0
\(271\) −13.6709 −0.830450 −0.415225 0.909719i \(-0.636297\pi\)
−0.415225 + 0.909719i \(0.636297\pi\)
\(272\) 0 0
\(273\) 18.6694 1.12993
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.2380 0.975647 0.487824 0.872942i \(-0.337791\pi\)
0.487824 + 0.872942i \(0.337791\pi\)
\(278\) 0 0
\(279\) 51.9879 3.11243
\(280\) 0 0
\(281\) −0.362407 −0.0216194 −0.0108097 0.999942i \(-0.503441\pi\)
−0.0108097 + 0.999942i \(0.503441\pi\)
\(282\) 0 0
\(283\) −6.80039 −0.404241 −0.202120 0.979361i \(-0.564783\pi\)
−0.202120 + 0.979361i \(0.564783\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.75873 −0.280899
\(288\) 0 0
\(289\) −5.70382 −0.335519
\(290\) 0 0
\(291\) 30.7274 1.80127
\(292\) 0 0
\(293\) −26.2172 −1.53162 −0.765812 0.643065i \(-0.777663\pi\)
−0.765812 + 0.643065i \(0.777663\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −53.6647 −3.11394
\(298\) 0 0
\(299\) −6.37400 −0.368618
\(300\) 0 0
\(301\) −1.84106 −0.106117
\(302\) 0 0
\(303\) 45.5902 2.61909
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −19.7146 −1.12517 −0.562587 0.826738i \(-0.690194\pi\)
−0.562587 + 0.826738i \(0.690194\pi\)
\(308\) 0 0
\(309\) −22.7255 −1.29281
\(310\) 0 0
\(311\) −15.1003 −0.856258 −0.428129 0.903718i \(-0.640827\pi\)
−0.428129 + 0.903718i \(0.640827\pi\)
\(312\) 0 0
\(313\) 12.9813 0.733747 0.366874 0.930271i \(-0.380428\pi\)
0.366874 + 0.930271i \(0.380428\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.3503 0.974489 0.487244 0.873266i \(-0.338002\pi\)
0.487244 + 0.873266i \(0.338002\pi\)
\(318\) 0 0
\(319\) −1.66616 −0.0932868
\(320\) 0 0
\(321\) 33.7781 1.88531
\(322\) 0 0
\(323\) −3.63915 −0.202488
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −10.3154 −0.570444
\(328\) 0 0
\(329\) −0.192277 −0.0106006
\(330\) 0 0
\(331\) −0.984756 −0.0541271 −0.0270635 0.999634i \(-0.508616\pi\)
−0.0270635 + 0.999634i \(0.508616\pi\)
\(332\) 0 0
\(333\) −52.3950 −2.87123
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 23.5575 1.28326 0.641629 0.767015i \(-0.278259\pi\)
0.641629 + 0.767015i \(0.278259\pi\)
\(338\) 0 0
\(339\) −43.8767 −2.38305
\(340\) 0 0
\(341\) 53.9598 2.92208
\(342\) 0 0
\(343\) −12.7850 −0.690327
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −26.0916 −1.40067 −0.700337 0.713813i \(-0.746967\pi\)
−0.700337 + 0.713813i \(0.746967\pi\)
\(348\) 0 0
\(349\) −17.8609 −0.956070 −0.478035 0.878341i \(-0.658651\pi\)
−0.478035 + 0.878341i \(0.658651\pi\)
\(350\) 0 0
\(351\) 55.6445 2.97009
\(352\) 0 0
\(353\) −13.1080 −0.697667 −0.348833 0.937185i \(-0.613422\pi\)
−0.348833 + 0.937185i \(0.613422\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −9.84430 −0.521016
\(358\) 0 0
\(359\) −22.1119 −1.16702 −0.583510 0.812106i \(-0.698321\pi\)
−0.583510 + 0.812106i \(0.698321\pi\)
\(360\) 0 0
\(361\) −17.8276 −0.938296
\(362\) 0 0
\(363\) −80.0183 −4.19987
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −7.98495 −0.416811 −0.208406 0.978043i \(-0.566827\pi\)
−0.208406 + 0.978043i \(0.566827\pi\)
\(368\) 0 0
\(369\) −28.7427 −1.49629
\(370\) 0 0
\(371\) −1.89402 −0.0983326
\(372\) 0 0
\(373\) 23.8712 1.23600 0.618002 0.786177i \(-0.287942\pi\)
0.618002 + 0.786177i \(0.287942\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.72762 0.0889771
\(378\) 0 0
\(379\) 34.5647 1.77547 0.887735 0.460355i \(-0.152278\pi\)
0.887735 + 0.460355i \(0.152278\pi\)
\(380\) 0 0
\(381\) −3.56394 −0.182586
\(382\) 0 0
\(383\) −12.3139 −0.629211 −0.314606 0.949223i \(-0.601872\pi\)
−0.314606 + 0.949223i \(0.601872\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11.1200 −0.565262
\(388\) 0 0
\(389\) −27.0447 −1.37122 −0.685611 0.727968i \(-0.740465\pi\)
−0.685611 + 0.727968i \(0.740465\pi\)
\(390\) 0 0
\(391\) 3.36098 0.169972
\(392\) 0 0
\(393\) −35.0462 −1.76785
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −9.07631 −0.455527 −0.227763 0.973717i \(-0.573141\pi\)
−0.227763 + 0.973717i \(0.573141\pi\)
\(398\) 0 0
\(399\) 3.17141 0.158769
\(400\) 0 0
\(401\) 6.73762 0.336461 0.168230 0.985748i \(-0.446195\pi\)
0.168230 + 0.985748i \(0.446195\pi\)
\(402\) 0 0
\(403\) −55.9504 −2.78709
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −54.3823 −2.69563
\(408\) 0 0
\(409\) 25.7205 1.27180 0.635898 0.771773i \(-0.280630\pi\)
0.635898 + 0.771773i \(0.280630\pi\)
\(410\) 0 0
\(411\) 31.2640 1.54214
\(412\) 0 0
\(413\) −12.7509 −0.627428
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 12.2873 0.601711
\(418\) 0 0
\(419\) 16.2666 0.794676 0.397338 0.917672i \(-0.369934\pi\)
0.397338 + 0.917672i \(0.369934\pi\)
\(420\) 0 0
\(421\) −18.9106 −0.921645 −0.460822 0.887492i \(-0.652445\pi\)
−0.460822 + 0.887492i \(0.652445\pi\)
\(422\) 0 0
\(423\) −1.16135 −0.0564669
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 5.88522 0.284806
\(428\) 0 0
\(429\) 117.040 5.65076
\(430\) 0 0
\(431\) 11.4086 0.549535 0.274767 0.961511i \(-0.411399\pi\)
0.274767 + 0.961511i \(0.411399\pi\)
\(432\) 0 0
\(433\) −23.2756 −1.11856 −0.559278 0.828980i \(-0.688922\pi\)
−0.559278 + 0.828980i \(0.688922\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.08276 −0.0517956
\(438\) 0 0
\(439\) 13.0581 0.623231 0.311615 0.950208i \(-0.399130\pi\)
0.311615 + 0.950208i \(0.399130\pi\)
\(440\) 0 0
\(441\) −35.7635 −1.70302
\(442\) 0 0
\(443\) 0.113844 0.00540891 0.00270446 0.999996i \(-0.499139\pi\)
0.00270446 + 0.999996i \(0.499139\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.11598 −0.194679
\(448\) 0 0
\(449\) −11.0371 −0.520874 −0.260437 0.965491i \(-0.583867\pi\)
−0.260437 + 0.965491i \(0.583867\pi\)
\(450\) 0 0
\(451\) −29.8329 −1.40478
\(452\) 0 0
\(453\) −10.4363 −0.490342
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −30.1638 −1.41100 −0.705501 0.708709i \(-0.749278\pi\)
−0.705501 + 0.708709i \(0.749278\pi\)
\(458\) 0 0
\(459\) −29.3411 −1.36953
\(460\) 0 0
\(461\) −37.3908 −1.74146 −0.870732 0.491759i \(-0.836354\pi\)
−0.870732 + 0.491759i \(0.836354\pi\)
\(462\) 0 0
\(463\) 16.7365 0.777810 0.388905 0.921278i \(-0.372853\pi\)
0.388905 + 0.921278i \(0.372853\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 18.2260 0.843399 0.421699 0.906736i \(-0.361434\pi\)
0.421699 + 0.906736i \(0.361434\pi\)
\(468\) 0 0
\(469\) −2.22437 −0.102712
\(470\) 0 0
\(471\) 9.92820 0.457467
\(472\) 0 0
\(473\) −11.5418 −0.530692
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −11.4399 −0.523795
\(478\) 0 0
\(479\) −3.31948 −0.151671 −0.0758355 0.997120i \(-0.524162\pi\)
−0.0758355 + 0.997120i \(0.524162\pi\)
\(480\) 0 0
\(481\) 56.3885 2.57110
\(482\) 0 0
\(483\) −2.92900 −0.133274
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 19.7412 0.894558 0.447279 0.894395i \(-0.352393\pi\)
0.447279 + 0.894395i \(0.352393\pi\)
\(488\) 0 0
\(489\) −25.4521 −1.15098
\(490\) 0 0
\(491\) −18.1353 −0.818432 −0.409216 0.912437i \(-0.634198\pi\)
−0.409216 + 0.912437i \(0.634198\pi\)
\(492\) 0 0
\(493\) −0.910968 −0.0410279
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.0681 −0.451616
\(498\) 0 0
\(499\) −14.9797 −0.670582 −0.335291 0.942115i \(-0.608835\pi\)
−0.335291 + 0.942115i \(0.608835\pi\)
\(500\) 0 0
\(501\) 46.6552 2.08440
\(502\) 0 0
\(503\) −7.90238 −0.352350 −0.176175 0.984359i \(-0.556372\pi\)
−0.176175 + 0.984359i \(0.556372\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −82.5262 −3.66512
\(508\) 0 0
\(509\) −21.1882 −0.939152 −0.469576 0.882892i \(-0.655593\pi\)
−0.469576 + 0.882892i \(0.655593\pi\)
\(510\) 0 0
\(511\) 1.35502 0.0599425
\(512\) 0 0
\(513\) 9.45245 0.417336
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −1.20540 −0.0530136
\(518\) 0 0
\(519\) 25.1728 1.10496
\(520\) 0 0
\(521\) −11.1210 −0.487219 −0.243610 0.969873i \(-0.578332\pi\)
−0.243610 + 0.969873i \(0.578332\pi\)
\(522\) 0 0
\(523\) −16.2670 −0.711304 −0.355652 0.934618i \(-0.615741\pi\)
−0.355652 + 0.934618i \(0.615741\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 29.5024 1.28515
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −77.0151 −3.34217
\(532\) 0 0
\(533\) 30.9335 1.33988
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 32.2743 1.39274
\(538\) 0 0
\(539\) −37.1200 −1.59887
\(540\) 0 0
\(541\) −13.8797 −0.596733 −0.298367 0.954451i \(-0.596442\pi\)
−0.298367 + 0.954451i \(0.596442\pi\)
\(542\) 0 0
\(543\) 46.0851 1.97770
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −5.91647 −0.252970 −0.126485 0.991969i \(-0.540370\pi\)
−0.126485 + 0.991969i \(0.540370\pi\)
\(548\) 0 0
\(549\) 35.5467 1.51709
\(550\) 0 0
\(551\) 0.293475 0.0125025
\(552\) 0 0
\(553\) 4.58371 0.194919
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.2857 −1.19850 −0.599252 0.800560i \(-0.704535\pi\)
−0.599252 + 0.800560i \(0.704535\pi\)
\(558\) 0 0
\(559\) 11.9676 0.506175
\(560\) 0 0
\(561\) −61.7148 −2.60560
\(562\) 0 0
\(563\) 31.7025 1.33610 0.668050 0.744117i \(-0.267129\pi\)
0.668050 + 0.744117i \(0.267129\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 8.14763 0.342169
\(568\) 0 0
\(569\) −24.0702 −1.00907 −0.504537 0.863390i \(-0.668337\pi\)
−0.504537 + 0.863390i \(0.668337\pi\)
\(570\) 0 0
\(571\) −14.3935 −0.602349 −0.301175 0.953569i \(-0.597379\pi\)
−0.301175 + 0.953569i \(0.597379\pi\)
\(572\) 0 0
\(573\) −66.5023 −2.77817
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −5.77998 −0.240624 −0.120312 0.992736i \(-0.538389\pi\)
−0.120312 + 0.992736i \(0.538389\pi\)
\(578\) 0 0
\(579\) −48.2111 −2.00358
\(580\) 0 0
\(581\) 15.4115 0.639378
\(582\) 0 0
\(583\) −11.8738 −0.491761
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −27.7897 −1.14700 −0.573502 0.819204i \(-0.694416\pi\)
−0.573502 + 0.819204i \(0.694416\pi\)
\(588\) 0 0
\(589\) −9.50441 −0.391623
\(590\) 0 0
\(591\) −41.7999 −1.71942
\(592\) 0 0
\(593\) −22.1872 −0.911118 −0.455559 0.890205i \(-0.650561\pi\)
−0.455559 + 0.890205i \(0.650561\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −20.6683 −0.845897
\(598\) 0 0
\(599\) −15.1380 −0.618521 −0.309260 0.950977i \(-0.600081\pi\)
−0.309260 + 0.950977i \(0.600081\pi\)
\(600\) 0 0
\(601\) 20.5353 0.837652 0.418826 0.908067i \(-0.362442\pi\)
0.418826 + 0.908067i \(0.362442\pi\)
\(602\) 0 0
\(603\) −13.4352 −0.547123
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −28.9906 −1.17669 −0.588345 0.808610i \(-0.700220\pi\)
−0.588345 + 0.808610i \(0.700220\pi\)
\(608\) 0 0
\(609\) 0.793883 0.0321698
\(610\) 0 0
\(611\) 1.24987 0.0505644
\(612\) 0 0
\(613\) −9.03621 −0.364969 −0.182485 0.983209i \(-0.558414\pi\)
−0.182485 + 0.983209i \(0.558414\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.42741 −0.178241 −0.0891203 0.996021i \(-0.528406\pi\)
−0.0891203 + 0.996021i \(0.528406\pi\)
\(618\) 0 0
\(619\) −14.8403 −0.596483 −0.298241 0.954490i \(-0.596400\pi\)
−0.298241 + 0.954490i \(0.596400\pi\)
\(620\) 0 0
\(621\) −8.72993 −0.350320
\(622\) 0 0
\(623\) −10.9380 −0.438222
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 19.8819 0.794005
\(628\) 0 0
\(629\) −29.7334 −1.18555
\(630\) 0 0
\(631\) −41.8369 −1.66550 −0.832751 0.553648i \(-0.813235\pi\)
−0.832751 + 0.553648i \(0.813235\pi\)
\(632\) 0 0
\(633\) 38.5841 1.53358
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 38.4894 1.52501
\(638\) 0 0
\(639\) −60.8113 −2.40566
\(640\) 0 0
\(641\) 5.86478 0.231645 0.115822 0.993270i \(-0.463050\pi\)
0.115822 + 0.993270i \(0.463050\pi\)
\(642\) 0 0
\(643\) 0.460745 0.0181700 0.00908500 0.999959i \(-0.497108\pi\)
0.00908500 + 0.999959i \(0.497108\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −15.5690 −0.612079 −0.306040 0.952019i \(-0.599004\pi\)
−0.306040 + 0.952019i \(0.599004\pi\)
\(648\) 0 0
\(649\) −79.9362 −3.13777
\(650\) 0 0
\(651\) −25.7105 −1.00767
\(652\) 0 0
\(653\) 29.4538 1.15262 0.576308 0.817233i \(-0.304493\pi\)
0.576308 + 0.817233i \(0.304493\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 8.18430 0.319300
\(658\) 0 0
\(659\) −22.5604 −0.878829 −0.439415 0.898284i \(-0.644814\pi\)
−0.439415 + 0.898284i \(0.644814\pi\)
\(660\) 0 0
\(661\) −39.7530 −1.54621 −0.773106 0.634277i \(-0.781298\pi\)
−0.773106 + 0.634277i \(0.781298\pi\)
\(662\) 0 0
\(663\) 63.9916 2.48523
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.271042 −0.0104948
\(668\) 0 0
\(669\) 79.6289 3.07863
\(670\) 0 0
\(671\) 36.8949 1.42431
\(672\) 0 0
\(673\) −11.5047 −0.443475 −0.221737 0.975106i \(-0.571173\pi\)
−0.221737 + 0.975106i \(0.571173\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −31.7703 −1.22103 −0.610515 0.792005i \(-0.709038\pi\)
−0.610515 + 0.792005i \(0.709038\pi\)
\(678\) 0 0
\(679\) −10.0868 −0.387098
\(680\) 0 0
\(681\) −28.2101 −1.08101
\(682\) 0 0
\(683\) 7.22683 0.276527 0.138264 0.990395i \(-0.455848\pi\)
0.138264 + 0.990395i \(0.455848\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −42.4145 −1.61822
\(688\) 0 0
\(689\) 12.3118 0.469043
\(690\) 0 0
\(691\) −3.29788 −0.125457 −0.0627286 0.998031i \(-0.519980\pi\)
−0.0627286 + 0.998031i \(0.519980\pi\)
\(692\) 0 0
\(693\) 35.6996 1.35611
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16.3111 −0.617827
\(698\) 0 0
\(699\) 28.1123 1.06331
\(700\) 0 0
\(701\) 18.7936 0.709824 0.354912 0.934900i \(-0.384511\pi\)
0.354912 + 0.934900i \(0.384511\pi\)
\(702\) 0 0
\(703\) 9.57884 0.361273
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14.9658 −0.562848
\(708\) 0 0
\(709\) 14.1039 0.529685 0.264842 0.964292i \(-0.414680\pi\)
0.264842 + 0.964292i \(0.414680\pi\)
\(710\) 0 0
\(711\) 27.6856 1.03829
\(712\) 0 0
\(713\) 8.77792 0.328736
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −46.2341 −1.72664
\(718\) 0 0
\(719\) 23.5631 0.878754 0.439377 0.898303i \(-0.355199\pi\)
0.439377 + 0.898303i \(0.355199\pi\)
\(720\) 0 0
\(721\) 7.46005 0.277827
\(722\) 0 0
\(723\) 10.4862 0.389985
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −3.57021 −0.132412 −0.0662059 0.997806i \(-0.521089\pi\)
−0.0662059 + 0.997806i \(0.521089\pi\)
\(728\) 0 0
\(729\) −29.0190 −1.07478
\(730\) 0 0
\(731\) −6.31045 −0.233401
\(732\) 0 0
\(733\) −10.3158 −0.381022 −0.190511 0.981685i \(-0.561015\pi\)
−0.190511 + 0.981685i \(0.561015\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −13.9448 −0.513663
\(738\) 0 0
\(739\) 36.2056 1.33185 0.665923 0.746021i \(-0.268038\pi\)
0.665923 + 0.746021i \(0.268038\pi\)
\(740\) 0 0
\(741\) −20.6153 −0.757324
\(742\) 0 0
\(743\) 3.24466 0.119035 0.0595174 0.998227i \(-0.481044\pi\)
0.0595174 + 0.998227i \(0.481044\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 93.0856 3.40582
\(748\) 0 0
\(749\) −11.0883 −0.405157
\(750\) 0 0
\(751\) −26.9796 −0.984499 −0.492250 0.870454i \(-0.663825\pi\)
−0.492250 + 0.870454i \(0.663825\pi\)
\(752\) 0 0
\(753\) −70.6888 −2.57604
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 11.7249 0.426148 0.213074 0.977036i \(-0.431652\pi\)
0.213074 + 0.977036i \(0.431652\pi\)
\(758\) 0 0
\(759\) −18.3621 −0.666504
\(760\) 0 0
\(761\) −24.4303 −0.885599 −0.442800 0.896621i \(-0.646015\pi\)
−0.442800 + 0.896621i \(0.646015\pi\)
\(762\) 0 0
\(763\) 3.38623 0.122590
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 82.8852 2.99281
\(768\) 0 0
\(769\) 0.804588 0.0290142 0.0145071 0.999895i \(-0.495382\pi\)
0.0145071 + 0.999895i \(0.495382\pi\)
\(770\) 0 0
\(771\) −92.0989 −3.31686
\(772\) 0 0
\(773\) −6.02477 −0.216696 −0.108348 0.994113i \(-0.534556\pi\)
−0.108348 + 0.994113i \(0.534556\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 25.9118 0.929582
\(778\) 0 0
\(779\) 5.25474 0.188270
\(780\) 0 0
\(781\) −63.1179 −2.25853
\(782\) 0 0
\(783\) 2.36618 0.0845604
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −12.9326 −0.460996 −0.230498 0.973073i \(-0.574036\pi\)
−0.230498 + 0.973073i \(0.574036\pi\)
\(788\) 0 0
\(789\) 61.4977 2.18938
\(790\) 0 0
\(791\) 14.4033 0.512123
\(792\) 0 0
\(793\) −38.2561 −1.35851
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −36.3660 −1.28815 −0.644075 0.764962i \(-0.722758\pi\)
−0.644075 + 0.764962i \(0.722758\pi\)
\(798\) 0 0
\(799\) −0.659052 −0.0233156
\(800\) 0 0
\(801\) −66.0654 −2.33431
\(802\) 0 0
\(803\) 8.49472 0.299772
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 50.8629 1.79046
\(808\) 0 0
\(809\) 26.5840 0.934642 0.467321 0.884088i \(-0.345219\pi\)
0.467321 + 0.884088i \(0.345219\pi\)
\(810\) 0 0
\(811\) 44.7712 1.57213 0.786064 0.618145i \(-0.212116\pi\)
0.786064 + 0.618145i \(0.212116\pi\)
\(812\) 0 0
\(813\) 40.8360 1.43218
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.03296 0.0711242
\(818\) 0 0
\(819\) −37.0166 −1.29346
\(820\) 0 0
\(821\) 22.3949 0.781587 0.390794 0.920478i \(-0.372201\pi\)
0.390794 + 0.920478i \(0.372201\pi\)
\(822\) 0 0
\(823\) 2.18913 0.0763081 0.0381541 0.999272i \(-0.487852\pi\)
0.0381541 + 0.999272i \(0.487852\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 39.4367 1.37135 0.685674 0.727909i \(-0.259508\pi\)
0.685674 + 0.727909i \(0.259508\pi\)
\(828\) 0 0
\(829\) −11.0629 −0.384229 −0.192115 0.981373i \(-0.561535\pi\)
−0.192115 + 0.981373i \(0.561535\pi\)
\(830\) 0 0
\(831\) −48.5040 −1.68259
\(832\) 0 0
\(833\) −20.2953 −0.703190
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −76.6306 −2.64874
\(838\) 0 0
\(839\) 37.8510 1.30676 0.653381 0.757030i \(-0.273350\pi\)
0.653381 + 0.757030i \(0.273350\pi\)
\(840\) 0 0
\(841\) −28.9265 −0.997467
\(842\) 0 0
\(843\) 1.08254 0.0372845
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 26.2675 0.902561
\(848\) 0 0
\(849\) 20.3132 0.697148
\(850\) 0 0
\(851\) −8.84665 −0.303259
\(852\) 0 0
\(853\) −28.9770 −0.992155 −0.496078 0.868278i \(-0.665227\pi\)
−0.496078 + 0.868278i \(0.665227\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 56.0462 1.91450 0.957250 0.289261i \(-0.0934095\pi\)
0.957250 + 0.289261i \(0.0934095\pi\)
\(858\) 0 0
\(859\) −43.8866 −1.49739 −0.748695 0.662914i \(-0.769319\pi\)
−0.748695 + 0.662914i \(0.769319\pi\)
\(860\) 0 0
\(861\) 14.2147 0.484434
\(862\) 0 0
\(863\) 22.1955 0.755542 0.377771 0.925899i \(-0.376691\pi\)
0.377771 + 0.925899i \(0.376691\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 17.0377 0.578630
\(868\) 0 0
\(869\) 28.7357 0.974791
\(870\) 0 0
\(871\) 14.4592 0.489932
\(872\) 0 0
\(873\) −60.9245 −2.06198
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5.44979 0.184026 0.0920131 0.995758i \(-0.470670\pi\)
0.0920131 + 0.995758i \(0.470670\pi\)
\(878\) 0 0
\(879\) 78.3125 2.64141
\(880\) 0 0
\(881\) −11.7854 −0.397060 −0.198530 0.980095i \(-0.563617\pi\)
−0.198530 + 0.980095i \(0.563617\pi\)
\(882\) 0 0
\(883\) 23.7945 0.800748 0.400374 0.916352i \(-0.368880\pi\)
0.400374 + 0.916352i \(0.368880\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −44.4300 −1.49181 −0.745907 0.666050i \(-0.767984\pi\)
−0.745907 + 0.666050i \(0.767984\pi\)
\(888\) 0 0
\(889\) 1.16993 0.0392381
\(890\) 0 0
\(891\) 51.0782 1.71119
\(892\) 0 0
\(893\) 0.212318 0.00710496
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 19.0396 0.635712
\(898\) 0 0
\(899\) −2.37919 −0.0793504
\(900\) 0 0
\(901\) −6.49196 −0.216279
\(902\) 0 0
\(903\) 5.49938 0.183008
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −40.7542 −1.35322 −0.676611 0.736341i \(-0.736552\pi\)
−0.676611 + 0.736341i \(0.736552\pi\)
\(908\) 0 0
\(909\) −90.3934 −2.99816
\(910\) 0 0
\(911\) 2.71520 0.0899587 0.0449794 0.998988i \(-0.485678\pi\)
0.0449794 + 0.998988i \(0.485678\pi\)
\(912\) 0 0
\(913\) 96.6163 3.19753
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.5046 0.379914
\(918\) 0 0
\(919\) −10.7227 −0.353708 −0.176854 0.984237i \(-0.556592\pi\)
−0.176854 + 0.984237i \(0.556592\pi\)
\(920\) 0 0
\(921\) 58.8890 1.94046
\(922\) 0 0
\(923\) 65.4464 2.15419
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 45.0587 1.47992
\(928\) 0 0
\(929\) 38.8670 1.27518 0.637592 0.770374i \(-0.279930\pi\)
0.637592 + 0.770374i \(0.279930\pi\)
\(930\) 0 0
\(931\) 6.53827 0.214283
\(932\) 0 0
\(933\) 45.1055 1.47669
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 38.6117 1.26139 0.630694 0.776032i \(-0.282770\pi\)
0.630694 + 0.776032i \(0.282770\pi\)
\(938\) 0 0
\(939\) −38.7761 −1.26541
\(940\) 0 0
\(941\) 26.3928 0.860381 0.430191 0.902738i \(-0.358446\pi\)
0.430191 + 0.902738i \(0.358446\pi\)
\(942\) 0 0
\(943\) −4.85308 −0.158038
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 22.3777 0.727179 0.363589 0.931559i \(-0.381551\pi\)
0.363589 + 0.931559i \(0.381551\pi\)
\(948\) 0 0
\(949\) −8.80811 −0.285923
\(950\) 0 0
\(951\) −51.8265 −1.68059
\(952\) 0 0
\(953\) −17.4362 −0.564815 −0.282407 0.959295i \(-0.591133\pi\)
−0.282407 + 0.959295i \(0.591133\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 4.97692 0.160881
\(958\) 0 0
\(959\) −10.2630 −0.331409
\(960\) 0 0
\(961\) 46.0519 1.48554
\(962\) 0 0
\(963\) −66.9732 −2.15818
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 45.1587 1.45221 0.726103 0.687586i \(-0.241330\pi\)
0.726103 + 0.687586i \(0.241330\pi\)
\(968\) 0 0
\(969\) 10.8704 0.349207
\(970\) 0 0
\(971\) 34.3123 1.10113 0.550567 0.834791i \(-0.314412\pi\)
0.550567 + 0.834791i \(0.314412\pi\)
\(972\) 0 0
\(973\) −4.03353 −0.129309
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.51320 −0.0484115 −0.0242058 0.999707i \(-0.507706\pi\)
−0.0242058 + 0.999707i \(0.507706\pi\)
\(978\) 0 0
\(979\) −68.5713 −2.19155
\(980\) 0 0
\(981\) 20.4528 0.653007
\(982\) 0 0
\(983\) 15.1715 0.483895 0.241947 0.970289i \(-0.422214\pi\)
0.241947 + 0.970289i \(0.422214\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0.574345 0.0182816
\(988\) 0 0
\(989\) −1.87756 −0.0597031
\(990\) 0 0
\(991\) 39.4470 1.25307 0.626537 0.779392i \(-0.284472\pi\)
0.626537 + 0.779392i \(0.284472\pi\)
\(992\) 0 0
\(993\) 2.94153 0.0933467
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.33319 0.0738928 0.0369464 0.999317i \(-0.488237\pi\)
0.0369464 + 0.999317i \(0.488237\pi\)
\(998\) 0 0
\(999\) 77.2307 2.44347
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 9200.2.a.cz.1.1 7
4.3 odd 2 4600.2.a.bi.1.7 7
5.2 odd 4 1840.2.e.g.369.14 14
5.3 odd 4 1840.2.e.g.369.1 14
5.4 even 2 9200.2.a.dc.1.7 7
20.3 even 4 920.2.e.b.369.14 yes 14
20.7 even 4 920.2.e.b.369.1 14
20.19 odd 2 4600.2.a.bh.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.1 14 20.7 even 4
920.2.e.b.369.14 yes 14 20.3 even 4
1840.2.e.g.369.1 14 5.3 odd 4
1840.2.e.g.369.14 14 5.2 odd 4
4600.2.a.bh.1.1 7 20.19 odd 2
4600.2.a.bi.1.7 7 4.3 odd 2
9200.2.a.cz.1.1 7 1.1 even 1 trivial
9200.2.a.dc.1.7 7 5.4 even 2