Properties

Label 4600.2.a.bi.1.7
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7311849298\)
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 1.7
Root \(2.98707\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-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 \(-0.169028\pi\)
0.862292 + 0.506411i \(0.169028\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.980560 −0.370617 −0.185308 0.982680i \(-0.559328\pi\)
−0.185308 + 0.982680i \(0.559328\pi\)
\(8\) 0 0
\(9\) 5.92257 1.97419
\(10\) 0 0
\(11\) −6.14721 −1.85345 −0.926727 0.375734i \(-0.877391\pi\)
−0.926727 + 0.375734i \(0.877391\pi\)
\(12\) 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 \(-0.460363\pi\)
0.124202 + 0.992257i \(0.460363\pi\)
\(20\) 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 \(-0.789028\pi\)
−0.788280 + 0.615316i \(0.789028\pi\)
\(32\) 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 \(-0.454273\pi\)
0.143163 + 0.989699i \(0.454273\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0.196089 0.0286026 0.0143013 0.999898i \(-0.495448\pi\)
0.0143013 + 0.999898i \(0.495448\pi\)
\(48\) 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 \(-0.178726\pi\)
0.846465 + 0.532444i \(0.178726\pi\)
\(60\) 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 \(-0.455750\pi\)
0.138569 + 0.990353i \(0.455750\pi\)
\(68\) 0 0
\(69\) −2.98707 −0.359601
\(70\) 0 0
\(71\) 10.2677 1.21855 0.609277 0.792958i \(-0.291460\pi\)
0.609277 + 0.792958i \(0.291460\pi\)
\(72\) 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 \(-0.584701\pi\)
−0.262966 + 0.964805i \(0.584701\pi\)
\(80\) 0 0
\(81\) 8.30917 0.923241
\(82\) 0 0
\(83\) −15.7171 −1.72517 −0.862587 0.505909i \(-0.831157\pi\)
−0.862587 + 0.505909i \(0.831157\pi\)
\(84\) 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 \(-0.622294\pi\)
−0.374817 + 0.927099i \(0.622294\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.3081 1.09320 0.546599 0.837395i \(-0.315922\pi\)
0.546599 + 0.837395i \(0.315922\pi\)
\(108\) 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 \(-0.516858\pi\)
−0.0529363 + 0.998598i \(0.516858\pi\)
\(128\) 0 0
\(129\) 5.60841 0.493793
\(130\) 0 0
\(131\) −11.7326 −1.02509 −0.512543 0.858662i \(-0.671296\pi\)
−0.512543 + 0.858662i \(0.671296\pi\)
\(132\) 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 \(-0.444185\pi\)
0.174451 + 0.984666i \(0.444185\pi\)
\(140\) 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 \(-0.545406\pi\)
−0.142162 + 0.989843i \(0.545406\pi\)
\(152\) 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 \(-0.608297\pi\)
−0.333698 + 0.942680i \(0.608297\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 15.6190 1.20864 0.604319 0.796742i \(-0.293445\pi\)
0.604319 + 0.796742i \(0.293445\pi\)
\(168\) 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 \(-0.367693\pi\)
0.403790 + 0.914852i \(0.367693\pi\)
\(180\) 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 \(-0.798083\pi\)
−0.805462 + 0.592648i \(0.798083\pi\)
\(192\) 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 \(-0.578869\pi\)
−0.245246 + 0.969461i \(0.578869\pi\)
\(200\) 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 \(-0.353338\pi\)
0.444623 + 0.895718i \(0.353338\pi\)
\(212\) 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 \(-0.148899\pi\)
0.892572 + 0.450905i \(0.148899\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.44407 −0.626825 −0.313412 0.949617i \(-0.601472\pi\)
−0.313412 + 0.949617i \(0.601472\pi\)
\(228\) 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 \(-0.666886\pi\)
−0.500597 + 0.865680i \(0.666886\pi\)
\(240\) 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 \(-0.768439\pi\)
−0.746859 + 0.664982i \(0.768439\pi\)
\(252\) 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 \(-0.281101\pi\)
0.634755 + 0.772714i \(0.281101\pi\)
\(264\) 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 \(-0.363703\pi\)
0.415225 + 0.909719i \(0.363703\pi\)
\(272\) 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 \(-0.435217\pi\)
0.202120 + 0.979361i \(0.435217\pi\)
\(284\) 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 \(-0.309806\pi\)
0.562587 + 0.826738i \(0.309806\pi\)
\(308\) 0 0
\(309\) −22.7255 −1.29281
\(310\) 0 0
\(311\) 15.1003 0.856258 0.428129 0.903718i \(-0.359173\pi\)
0.428129 + 0.903718i \(0.359173\pi\)
\(312\) 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 \(-0.491384\pi\)
0.0270635 + 0.999634i \(0.491384\pi\)
\(332\) 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 \(-0.253033\pi\)
0.700337 + 0.713813i \(0.253033\pi\)
\(348\) 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 \(-0.301679\pi\)
0.583510 + 0.812106i \(0.301679\pi\)
\(360\) 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 \(-0.433173\pi\)
0.208406 + 0.978043i \(0.433173\pi\)
\(368\) 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 \(-0.847722\pi\)
−0.887735 + 0.460355i \(0.847722\pi\)
\(380\) 0 0
\(381\) −3.56394 −0.182586
\(382\) 0 0
\(383\) 12.3139 0.629211 0.314606 0.949223i \(-0.398128\pi\)
0.314606 + 0.949223i \(0.398128\pi\)
\(384\) 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 \(-0.630066\pi\)
−0.397338 + 0.917672i \(0.630066\pi\)
\(420\) 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 \(-0.588601\pi\)
−0.274767 + 0.961511i \(0.588601\pi\)
\(432\) 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 \(-0.600870\pi\)
−0.311615 + 0.950208i \(0.600870\pi\)
\(440\) 0 0
\(441\) −35.7635 −1.70302
\(442\) 0 0
\(443\) −0.113844 −0.00540891 −0.00270446 0.999996i \(-0.500861\pi\)
−0.00270446 + 0.999996i \(0.500861\pi\)
\(444\) 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 \(-0.627147\pi\)
−0.388905 + 0.921278i \(0.627147\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.2260 −0.843399 −0.421699 0.906736i \(-0.638566\pi\)
−0.421699 + 0.906736i \(0.638566\pi\)
\(468\) 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 \(-0.475838\pi\)
0.0758355 + 0.997120i \(0.475838\pi\)
\(480\) 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 \(-0.647607\pi\)
−0.447279 + 0.894395i \(0.647607\pi\)
\(488\) 0 0
\(489\) −25.4521 −1.15098
\(490\) 0 0
\(491\) 18.1353 0.818432 0.409216 0.912437i \(-0.365802\pi\)
0.409216 + 0.912437i \(0.365802\pi\)
\(492\) 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 \(-0.391165\pi\)
0.335291 + 0.942115i \(0.391165\pi\)
\(500\) 0 0
\(501\) 46.6552 2.08440
\(502\) 0 0
\(503\) 7.90238 0.352350 0.176175 0.984359i \(-0.443628\pi\)
0.176175 + 0.984359i \(0.443628\pi\)
\(504\) 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 \(-0.384259\pi\)
0.355652 + 0.934618i \(0.384259\pi\)
\(524\) 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 \(-0.459630\pi\)
0.126485 + 0.991969i \(0.459630\pi\)
\(548\) 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 \(-0.732871\pi\)
−0.668050 + 0.744117i \(0.732871\pi\)
\(564\) 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 \(-0.402621\pi\)
0.301175 + 0.953569i \(0.402621\pi\)
\(572\) 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 \(-0.305584\pi\)
0.573502 + 0.819204i \(0.305584\pi\)
\(588\) 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 \(-0.399919\pi\)
0.309260 + 0.950977i \(0.399919\pi\)
\(600\) 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 \(-0.299780\pi\)
0.588345 + 0.808610i \(0.299780\pi\)
\(608\) 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 \(-0.403600\pi\)
0.298241 + 0.954490i \(0.403600\pi\)
\(620\) 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 \(-0.186765\pi\)
0.832751 + 0.553648i \(0.186765\pi\)
\(632\) 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 \(-0.502892\pi\)
−0.00908500 + 0.999959i \(0.502892\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15.5690 0.612079 0.306040 0.952019i \(-0.400996\pi\)
0.306040 + 0.952019i \(0.400996\pi\)
\(648\) 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 \(-0.355186\pi\)
0.439415 + 0.898284i \(0.355186\pi\)
\(660\) 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 \(-0.544152\pi\)
−0.138264 + 0.990395i \(0.544152\pi\)
\(684\) 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 \(-0.480020\pi\)
0.0627286 + 0.998031i \(0.480020\pi\)
\(692\) 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 \(-0.644801\pi\)
−0.439377 + 0.898303i \(0.644801\pi\)
\(720\) 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 \(-0.478911\pi\)
0.0662059 + 0.997806i \(0.478911\pi\)
\(728\) 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 \(-0.731962\pi\)
−0.665923 + 0.746021i \(0.731962\pi\)
\(740\) 0 0
\(741\) −20.6153 −0.757324
\(742\) 0 0
\(743\) −3.24466 −0.119035 −0.0595174 0.998227i \(-0.518956\pi\)
−0.0595174 + 0.998227i \(0.518956\pi\)
\(744\) 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 \(-0.336175\pi\)
0.492250 + 0.870454i \(0.336175\pi\)
\(752\) 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 \(-0.425964\pi\)
0.230498 + 0.973073i \(0.425964\pi\)
\(788\) 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 \(-0.787884\pi\)
−0.786064 + 0.618145i \(0.787884\pi\)
\(812\) 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 \(-0.512148\pi\)
−0.0381541 + 0.999272i \(0.512148\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −39.4367 −1.37135 −0.685674 0.727909i \(-0.740492\pi\)
−0.685674 + 0.727909i \(0.740492\pi\)
\(828\) 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 \(-0.726650\pi\)
−0.653381 + 0.757030i \(0.726650\pi\)
\(840\) 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 \(-0.230681\pi\)
0.748695 + 0.662914i \(0.230681\pi\)
\(860\) 0 0
\(861\) 14.2147 0.484434
\(862\) 0 0
\(863\) −22.1955 −0.755542 −0.377771 0.925899i \(-0.623309\pi\)
−0.377771 + 0.925899i \(0.623309\pi\)
\(864\) 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 \(-0.631120\pi\)
−0.400374 + 0.916352i \(0.631120\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 44.4300 1.49181 0.745907 0.666050i \(-0.232016\pi\)
0.745907 + 0.666050i \(0.232016\pi\)
\(888\) 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 \(-0.263448\pi\)
0.676611 + 0.736341i \(0.263448\pi\)
\(908\) 0 0
\(909\) −90.3934 −2.99816
\(910\) 0 0
\(911\) −2.71520 −0.0899587 −0.0449794 0.998988i \(-0.514322\pi\)
−0.0449794 + 0.998988i \(0.514322\pi\)
\(912\) 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 \(-0.443408\pi\)
0.176854 + 0.984237i \(0.443408\pi\)
\(920\) 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 \(-0.618449\pi\)
−0.363589 + 0.931559i \(0.618449\pi\)
\(948\) 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 \(-0.758670\pi\)
−0.726103 + 0.687586i \(0.758670\pi\)
\(968\) 0 0
\(969\) 10.8704 0.349207
\(970\) 0 0
\(971\) −34.3123 −1.10113 −0.550567 0.834791i \(-0.685588\pi\)
−0.550567 + 0.834791i \(0.685588\pi\)
\(972\) 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 \(-0.577786\pi\)
−0.241947 + 0.970289i \(0.577786\pi\)
\(984\) 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 \(-0.715528\pi\)
−0.626537 + 0.779392i \(0.715528\pi\)
\(992\) 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 4600.2.a.bi.1.7 7
4.3 odd 2 9200.2.a.cz.1.1 7
5.2 odd 4 920.2.e.b.369.1 14
5.3 odd 4 920.2.e.b.369.14 yes 14
5.4 even 2 4600.2.a.bh.1.1 7
20.3 even 4 1840.2.e.g.369.1 14
20.7 even 4 1840.2.e.g.369.14 14
20.19 odd 2 9200.2.a.dc.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.1 14 5.2 odd 4
920.2.e.b.369.14 yes 14 5.3 odd 4
1840.2.e.g.369.1 14 20.3 even 4
1840.2.e.g.369.14 14 20.7 even 4
4600.2.a.bh.1.1 7 5.4 even 2
4600.2.a.bi.1.7 7 1.1 even 1 trivial
9200.2.a.cz.1.1 7 4.3 odd 2
9200.2.a.dc.1.7 7 20.19 odd 2