Properties

Label 9200.2.a.cx.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $1$
Dimension $6$
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: \(6\)
Coefficient field: 6.6.143376304.1
Defining polynomial: \( x^{6} - 12x^{4} + 22x^{2} - 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 460)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.16223\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.21923 q^{3} +2.43185 q^{7} +7.36343 q^{9} +O(q^{10})\) \(q-3.21923 q^{3} +2.43185 q^{7} +7.36343 q^{9} +0.884969 q^{11} +5.10522 q^{13} +0.366626 q^{17} +2.79847 q^{19} -7.82867 q^{21} -1.00000 q^{23} -14.0469 q^{27} +8.02431 q^{29} -7.24179 q^{31} -2.84892 q^{33} -3.10036 q^{37} -16.4349 q^{39} -3.47185 q^{41} -8.56841 q^{43} -5.25528 q^{47} -1.08612 q^{49} -1.18025 q^{51} -11.6413 q^{53} -9.00892 q^{57} +9.33209 q^{59} +5.46699 q^{61} +17.9067 q^{63} -1.49020 q^{67} +3.21923 q^{69} -8.29949 q^{71} -10.2409 q^{73} +2.15211 q^{77} -6.06522 q^{79} +23.1298 q^{81} -16.2520 q^{83} -25.8321 q^{87} -17.6033 q^{89} +12.4151 q^{91} +23.3130 q^{93} -6.55618 q^{97} +6.51641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 4 q^{3} - 9 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 4 q^{3} - 9 q^{7} + 10 q^{9} - 2 q^{11} + 8 q^{13} + 5 q^{17} - 4 q^{19} - 6 q^{23} - 22 q^{27} + 5 q^{29} - 9 q^{31} - 10 q^{33} + 21 q^{37} + 8 q^{39} - q^{41} - 16 q^{43} - 16 q^{47} + 19 q^{49} + 12 q^{51} - q^{53} + 12 q^{57} + 11 q^{59} - 4 q^{61} - 19 q^{63} - 25 q^{67} + 4 q^{69} + 17 q^{71} - 14 q^{73} + 20 q^{77} - 10 q^{79} + 14 q^{81} - 21 q^{83} - 64 q^{87} - 24 q^{89} + 4 q^{91} + 4 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) −3.21923 −1.85862 −0.929311 0.369298i \(-0.879598\pi\)
−0.929311 + 0.369298i \(0.879598\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.43185 0.919152 0.459576 0.888138i \(-0.348001\pi\)
0.459576 + 0.888138i \(0.348001\pi\)
\(8\) 0 0
\(9\) 7.36343 2.45448
\(10\) 0 0
\(11\) 0.884969 0.266828 0.133414 0.991060i \(-0.457406\pi\)
0.133414 + 0.991060i \(0.457406\pi\)
\(12\) 0 0
\(13\) 5.10522 1.41593 0.707967 0.706245i \(-0.249612\pi\)
0.707967 + 0.706245i \(0.249612\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.366626 0.0889198 0.0444599 0.999011i \(-0.485843\pi\)
0.0444599 + 0.999011i \(0.485843\pi\)
\(18\) 0 0
\(19\) 2.79847 0.642014 0.321007 0.947077i \(-0.395979\pi\)
0.321007 + 0.947077i \(0.395979\pi\)
\(20\) 0 0
\(21\) −7.82867 −1.70836
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −14.0469 −2.70332
\(28\) 0 0
\(29\) 8.02431 1.49008 0.745038 0.667022i \(-0.232431\pi\)
0.745038 + 0.667022i \(0.232431\pi\)
\(30\) 0 0
\(31\) −7.24179 −1.30066 −0.650332 0.759650i \(-0.725370\pi\)
−0.650332 + 0.759650i \(0.725370\pi\)
\(32\) 0 0
\(33\) −2.84892 −0.495933
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.10036 −0.509697 −0.254848 0.966981i \(-0.582026\pi\)
−0.254848 + 0.966981i \(0.582026\pi\)
\(38\) 0 0
\(39\) −16.4349 −2.63169
\(40\) 0 0
\(41\) −3.47185 −0.542212 −0.271106 0.962550i \(-0.587389\pi\)
−0.271106 + 0.962550i \(0.587389\pi\)
\(42\) 0 0
\(43\) −8.56841 −1.30667 −0.653335 0.757069i \(-0.726631\pi\)
−0.653335 + 0.757069i \(0.726631\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.25528 −0.766561 −0.383281 0.923632i \(-0.625206\pi\)
−0.383281 + 0.923632i \(0.625206\pi\)
\(48\) 0 0
\(49\) −1.08612 −0.155160
\(50\) 0 0
\(51\) −1.18025 −0.165268
\(52\) 0 0
\(53\) −11.6413 −1.59905 −0.799526 0.600632i \(-0.794916\pi\)
−0.799526 + 0.600632i \(0.794916\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.00892 −1.19326
\(58\) 0 0
\(59\) 9.33209 1.21493 0.607467 0.794345i \(-0.292186\pi\)
0.607467 + 0.794345i \(0.292186\pi\)
\(60\) 0 0
\(61\) 5.46699 0.699976 0.349988 0.936754i \(-0.386186\pi\)
0.349988 + 0.936754i \(0.386186\pi\)
\(62\) 0 0
\(63\) 17.9067 2.25604
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.49020 −0.182057 −0.0910285 0.995848i \(-0.529015\pi\)
−0.0910285 + 0.995848i \(0.529015\pi\)
\(68\) 0 0
\(69\) 3.21923 0.387549
\(70\) 0 0
\(71\) −8.29949 −0.984969 −0.492484 0.870321i \(-0.663911\pi\)
−0.492484 + 0.870321i \(0.663911\pi\)
\(72\) 0 0
\(73\) −10.2409 −1.19860 −0.599302 0.800523i \(-0.704555\pi\)
−0.599302 + 0.800523i \(0.704555\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.15211 0.245256
\(78\) 0 0
\(79\) −6.06522 −0.682391 −0.341195 0.939992i \(-0.610832\pi\)
−0.341195 + 0.939992i \(0.610832\pi\)
\(80\) 0 0
\(81\) 23.1298 2.56998
\(82\) 0 0
\(83\) −16.2520 −1.78389 −0.891943 0.452148i \(-0.850658\pi\)
−0.891943 + 0.452148i \(0.850658\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −25.8321 −2.76949
\(88\) 0 0
\(89\) −17.6033 −1.86594 −0.932972 0.359949i \(-0.882794\pi\)
−0.932972 + 0.359949i \(0.882794\pi\)
\(90\) 0 0
\(91\) 12.4151 1.30146
\(92\) 0 0
\(93\) 23.3130 2.41744
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.55618 −0.665679 −0.332839 0.942984i \(-0.608007\pi\)
−0.332839 + 0.942984i \(0.608007\pi\)
\(98\) 0 0
\(99\) 6.51641 0.654924
\(100\) 0 0
\(101\) 13.4912 1.34243 0.671213 0.741265i \(-0.265774\pi\)
0.671213 + 0.741265i \(0.265774\pi\)
\(102\) 0 0
\(103\) −12.5460 −1.23619 −0.618096 0.786103i \(-0.712096\pi\)
−0.618096 + 0.786103i \(0.712096\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.46269 −0.141404 −0.0707020 0.997497i \(-0.522524\pi\)
−0.0707020 + 0.997497i \(0.522524\pi\)
\(108\) 0 0
\(109\) −19.2173 −1.84069 −0.920343 0.391113i \(-0.872090\pi\)
−0.920343 + 0.391113i \(0.872090\pi\)
\(110\) 0 0
\(111\) 9.98078 0.947334
\(112\) 0 0
\(113\) −0.834901 −0.0785409 −0.0392705 0.999229i \(-0.512503\pi\)
−0.0392705 + 0.999229i \(0.512503\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 37.5920 3.47538
\(118\) 0 0
\(119\) 0.891578 0.0817308
\(120\) 0 0
\(121\) −10.2168 −0.928803
\(122\) 0 0
\(123\) 11.1767 1.00777
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −7.87453 −0.698751 −0.349376 0.936983i \(-0.613606\pi\)
−0.349376 + 0.936983i \(0.613606\pi\)
\(128\) 0 0
\(129\) 27.5837 2.42861
\(130\) 0 0
\(131\) 12.8740 1.12481 0.562403 0.826863i \(-0.309877\pi\)
0.562403 + 0.826863i \(0.309877\pi\)
\(132\) 0 0
\(133\) 6.80546 0.590108
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.26675 0.279097 0.139549 0.990215i \(-0.455435\pi\)
0.139549 + 0.990215i \(0.455435\pi\)
\(138\) 0 0
\(139\) 12.5578 1.06514 0.532570 0.846386i \(-0.321226\pi\)
0.532570 + 0.846386i \(0.321226\pi\)
\(140\) 0 0
\(141\) 16.9179 1.42475
\(142\) 0 0
\(143\) 4.51797 0.377811
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 3.49647 0.288384
\(148\) 0 0
\(149\) −0.188265 −0.0154233 −0.00771164 0.999970i \(-0.502455\pi\)
−0.00771164 + 0.999970i \(0.502455\pi\)
\(150\) 0 0
\(151\) 18.6708 1.51941 0.759704 0.650269i \(-0.225344\pi\)
0.759704 + 0.650269i \(0.225344\pi\)
\(152\) 0 0
\(153\) 2.69962 0.218252
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 20.0277 1.59839 0.799193 0.601074i \(-0.205260\pi\)
0.799193 + 0.601074i \(0.205260\pi\)
\(158\) 0 0
\(159\) 37.4759 2.97203
\(160\) 0 0
\(161\) −2.43185 −0.191656
\(162\) 0 0
\(163\) −3.35607 −0.262867 −0.131434 0.991325i \(-0.541958\pi\)
−0.131434 + 0.991325i \(0.541958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.57745 0.199449 0.0997246 0.995015i \(-0.468204\pi\)
0.0997246 + 0.995015i \(0.468204\pi\)
\(168\) 0 0
\(169\) 13.0633 1.00487
\(170\) 0 0
\(171\) 20.6064 1.57581
\(172\) 0 0
\(173\) −19.4182 −1.47634 −0.738170 0.674615i \(-0.764310\pi\)
−0.738170 + 0.674615i \(0.764310\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −30.0421 −2.25810
\(178\) 0 0
\(179\) 20.3628 1.52199 0.760993 0.648760i \(-0.224712\pi\)
0.760993 + 0.648760i \(0.224712\pi\)
\(180\) 0 0
\(181\) −22.5629 −1.67709 −0.838543 0.544835i \(-0.816592\pi\)
−0.838543 + 0.544835i \(0.816592\pi\)
\(182\) 0 0
\(183\) −17.5995 −1.30099
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0.324453 0.0237263
\(188\) 0 0
\(189\) −34.1598 −2.48476
\(190\) 0 0
\(191\) 16.6554 1.20514 0.602571 0.798065i \(-0.294143\pi\)
0.602571 + 0.798065i \(0.294143\pi\)
\(192\) 0 0
\(193\) 14.5214 1.04527 0.522636 0.852556i \(-0.324949\pi\)
0.522636 + 0.852556i \(0.324949\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.3479 −0.950995 −0.475498 0.879717i \(-0.657732\pi\)
−0.475498 + 0.879717i \(0.657732\pi\)
\(198\) 0 0
\(199\) −18.7856 −1.33168 −0.665838 0.746097i \(-0.731926\pi\)
−0.665838 + 0.746097i \(0.731926\pi\)
\(200\) 0 0
\(201\) 4.79730 0.338375
\(202\) 0 0
\(203\) 19.5139 1.36961
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.36343 −0.511794
\(208\) 0 0
\(209\) 2.47656 0.171307
\(210\) 0 0
\(211\) −17.1078 −1.17775 −0.588874 0.808225i \(-0.700429\pi\)
−0.588874 + 0.808225i \(0.700429\pi\)
\(212\) 0 0
\(213\) 26.7180 1.83068
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −17.6109 −1.19551
\(218\) 0 0
\(219\) 32.9677 2.22775
\(220\) 0 0
\(221\) 1.87171 0.125905
\(222\) 0 0
\(223\) 13.5184 0.905262 0.452631 0.891698i \(-0.350485\pi\)
0.452631 + 0.891698i \(0.350485\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −8.29581 −0.550612 −0.275306 0.961357i \(-0.588779\pi\)
−0.275306 + 0.961357i \(0.588779\pi\)
\(228\) 0 0
\(229\) −6.22318 −0.411239 −0.205620 0.978632i \(-0.565921\pi\)
−0.205620 + 0.978632i \(0.565921\pi\)
\(230\) 0 0
\(231\) −6.92813 −0.455838
\(232\) 0 0
\(233\) −13.6347 −0.893242 −0.446621 0.894723i \(-0.647373\pi\)
−0.446621 + 0.894723i \(0.647373\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 19.5253 1.26831
\(238\) 0 0
\(239\) −11.5281 −0.745693 −0.372847 0.927893i \(-0.621618\pi\)
−0.372847 + 0.927893i \(0.621618\pi\)
\(240\) 0 0
\(241\) −17.5952 −1.13341 −0.566704 0.823921i \(-0.691782\pi\)
−0.566704 + 0.823921i \(0.691782\pi\)
\(242\) 0 0
\(243\) −32.3195 −2.07329
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 14.2868 0.909049
\(248\) 0 0
\(249\) 52.3188 3.31557
\(250\) 0 0
\(251\) −12.5471 −0.791968 −0.395984 0.918257i \(-0.629596\pi\)
−0.395984 + 0.918257i \(0.629596\pi\)
\(252\) 0 0
\(253\) −0.884969 −0.0556375
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.88072 0.304451 0.152225 0.988346i \(-0.451356\pi\)
0.152225 + 0.988346i \(0.451356\pi\)
\(258\) 0 0
\(259\) −7.53961 −0.468489
\(260\) 0 0
\(261\) 59.0864 3.65736
\(262\) 0 0
\(263\) 11.6045 0.715566 0.357783 0.933805i \(-0.383533\pi\)
0.357783 + 0.933805i \(0.383533\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 56.6690 3.46808
\(268\) 0 0
\(269\) −6.04327 −0.368465 −0.184232 0.982883i \(-0.558980\pi\)
−0.184232 + 0.982883i \(0.558980\pi\)
\(270\) 0 0
\(271\) −3.93401 −0.238974 −0.119487 0.992836i \(-0.538125\pi\)
−0.119487 + 0.992836i \(0.538125\pi\)
\(272\) 0 0
\(273\) −39.9671 −2.41892
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.92174 0.475971 0.237986 0.971269i \(-0.423513\pi\)
0.237986 + 0.971269i \(0.423513\pi\)
\(278\) 0 0
\(279\) −53.3244 −3.19245
\(280\) 0 0
\(281\) −6.00419 −0.358180 −0.179090 0.983833i \(-0.557315\pi\)
−0.179090 + 0.983833i \(0.557315\pi\)
\(282\) 0 0
\(283\) −7.65299 −0.454923 −0.227461 0.973787i \(-0.573043\pi\)
−0.227461 + 0.973787i \(0.573043\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.44301 −0.498375
\(288\) 0 0
\(289\) −16.8656 −0.992093
\(290\) 0 0
\(291\) 21.1058 1.23725
\(292\) 0 0
\(293\) −13.5480 −0.791485 −0.395743 0.918361i \(-0.629513\pi\)
−0.395743 + 0.918361i \(0.629513\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −12.4310 −0.721323
\(298\) 0 0
\(299\) −5.10522 −0.295243
\(300\) 0 0
\(301\) −20.8371 −1.20103
\(302\) 0 0
\(303\) −43.4313 −2.49506
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −10.0870 −0.575697 −0.287848 0.957676i \(-0.592940\pi\)
−0.287848 + 0.957676i \(0.592940\pi\)
\(308\) 0 0
\(309\) 40.3883 2.29761
\(310\) 0 0
\(311\) 28.2481 1.60180 0.800902 0.598795i \(-0.204354\pi\)
0.800902 + 0.598795i \(0.204354\pi\)
\(312\) 0 0
\(313\) −14.4504 −0.816786 −0.408393 0.912806i \(-0.633911\pi\)
−0.408393 + 0.912806i \(0.633911\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 14.7835 0.830324 0.415162 0.909748i \(-0.363725\pi\)
0.415162 + 0.909748i \(0.363725\pi\)
\(318\) 0 0
\(319\) 7.10127 0.397595
\(320\) 0 0
\(321\) 4.70875 0.262817
\(322\) 0 0
\(323\) 1.02599 0.0570877
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 61.8649 3.42114
\(328\) 0 0
\(329\) −12.7800 −0.704586
\(330\) 0 0
\(331\) 20.1494 1.10751 0.553757 0.832679i \(-0.313194\pi\)
0.553757 + 0.832679i \(0.313194\pi\)
\(332\) 0 0
\(333\) −22.8293 −1.25104
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 24.0660 1.31096 0.655479 0.755214i \(-0.272467\pi\)
0.655479 + 0.755214i \(0.272467\pi\)
\(338\) 0 0
\(339\) 2.68774 0.145978
\(340\) 0 0
\(341\) −6.40876 −0.347054
\(342\) 0 0
\(343\) −19.6642 −1.06177
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 26.3788 1.41609 0.708045 0.706168i \(-0.249578\pi\)
0.708045 + 0.706168i \(0.249578\pi\)
\(348\) 0 0
\(349\) 0.535518 0.0286656 0.0143328 0.999897i \(-0.495438\pi\)
0.0143328 + 0.999897i \(0.495438\pi\)
\(350\) 0 0
\(351\) −71.7124 −3.82773
\(352\) 0 0
\(353\) −5.27606 −0.280816 −0.140408 0.990094i \(-0.544841\pi\)
−0.140408 + 0.990094i \(0.544841\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −2.87019 −0.151907
\(358\) 0 0
\(359\) −20.4351 −1.07852 −0.539261 0.842139i \(-0.681296\pi\)
−0.539261 + 0.842139i \(0.681296\pi\)
\(360\) 0 0
\(361\) −11.1685 −0.587818
\(362\) 0 0
\(363\) 32.8903 1.72629
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −12.4382 −0.649268 −0.324634 0.945840i \(-0.605241\pi\)
−0.324634 + 0.945840i \(0.605241\pi\)
\(368\) 0 0
\(369\) −25.5647 −1.33085
\(370\) 0 0
\(371\) −28.3098 −1.46977
\(372\) 0 0
\(373\) 2.99999 0.155334 0.0776669 0.996979i \(-0.475253\pi\)
0.0776669 + 0.996979i \(0.475253\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 40.9659 2.10985
\(378\) 0 0
\(379\) 3.02165 0.155212 0.0776059 0.996984i \(-0.475272\pi\)
0.0776059 + 0.996984i \(0.475272\pi\)
\(380\) 0 0
\(381\) 25.3499 1.29871
\(382\) 0 0
\(383\) −8.15719 −0.416813 −0.208406 0.978042i \(-0.566828\pi\)
−0.208406 + 0.978042i \(0.566828\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −63.0929 −3.20719
\(388\) 0 0
\(389\) 11.7789 0.597214 0.298607 0.954376i \(-0.403478\pi\)
0.298607 + 0.954376i \(0.403478\pi\)
\(390\) 0 0
\(391\) −0.366626 −0.0185411
\(392\) 0 0
\(393\) −41.4443 −2.09059
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −16.7004 −0.838167 −0.419083 0.907948i \(-0.637649\pi\)
−0.419083 + 0.907948i \(0.637649\pi\)
\(398\) 0 0
\(399\) −21.9083 −1.09679
\(400\) 0 0
\(401\) 9.99936 0.499344 0.249672 0.968330i \(-0.419677\pi\)
0.249672 + 0.968330i \(0.419677\pi\)
\(402\) 0 0
\(403\) −36.9710 −1.84165
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.74373 −0.136002
\(408\) 0 0
\(409\) 2.20305 0.108934 0.0544668 0.998516i \(-0.482654\pi\)
0.0544668 + 0.998516i \(0.482654\pi\)
\(410\) 0 0
\(411\) −10.5164 −0.518736
\(412\) 0 0
\(413\) 22.6942 1.11671
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −40.4264 −1.97969
\(418\) 0 0
\(419\) −4.12814 −0.201673 −0.100836 0.994903i \(-0.532152\pi\)
−0.100836 + 0.994903i \(0.532152\pi\)
\(420\) 0 0
\(421\) −15.7354 −0.766899 −0.383449 0.923562i \(-0.625264\pi\)
−0.383449 + 0.923562i \(0.625264\pi\)
\(422\) 0 0
\(423\) −38.6969 −1.88151
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 13.2949 0.643385
\(428\) 0 0
\(429\) −14.5444 −0.702209
\(430\) 0 0
\(431\) 1.35158 0.0651034 0.0325517 0.999470i \(-0.489637\pi\)
0.0325517 + 0.999470i \(0.489637\pi\)
\(432\) 0 0
\(433\) 39.4114 1.89399 0.946996 0.321244i \(-0.104101\pi\)
0.946996 + 0.321244i \(0.104101\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.79847 −0.133869
\(438\) 0 0
\(439\) −10.1059 −0.482326 −0.241163 0.970485i \(-0.577529\pi\)
−0.241163 + 0.970485i \(0.577529\pi\)
\(440\) 0 0
\(441\) −7.99756 −0.380836
\(442\) 0 0
\(443\) −6.25526 −0.297197 −0.148598 0.988898i \(-0.547476\pi\)
−0.148598 + 0.988898i \(0.547476\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.606068 0.0286660
\(448\) 0 0
\(449\) 2.28779 0.107968 0.0539839 0.998542i \(-0.482808\pi\)
0.0539839 + 0.998542i \(0.482808\pi\)
\(450\) 0 0
\(451\) −3.07248 −0.144677
\(452\) 0 0
\(453\) −60.1055 −2.82400
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −14.3062 −0.669217 −0.334609 0.942357i \(-0.608604\pi\)
−0.334609 + 0.942357i \(0.608604\pi\)
\(458\) 0 0
\(459\) −5.14995 −0.240379
\(460\) 0 0
\(461\) −2.38995 −0.111311 −0.0556556 0.998450i \(-0.517725\pi\)
−0.0556556 + 0.998450i \(0.517725\pi\)
\(462\) 0 0
\(463\) 9.52232 0.442540 0.221270 0.975213i \(-0.428980\pi\)
0.221270 + 0.975213i \(0.428980\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.14501 0.284357 0.142178 0.989841i \(-0.454589\pi\)
0.142178 + 0.989841i \(0.454589\pi\)
\(468\) 0 0
\(469\) −3.62394 −0.167338
\(470\) 0 0
\(471\) −64.4738 −2.97080
\(472\) 0 0
\(473\) −7.58278 −0.348657
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −85.7197 −3.92483
\(478\) 0 0
\(479\) 1.40986 0.0644180 0.0322090 0.999481i \(-0.489746\pi\)
0.0322090 + 0.999481i \(0.489746\pi\)
\(480\) 0 0
\(481\) −15.8281 −0.721697
\(482\) 0 0
\(483\) 7.82867 0.356217
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −31.2993 −1.41831 −0.709154 0.705054i \(-0.750923\pi\)
−0.709154 + 0.705054i \(0.750923\pi\)
\(488\) 0 0
\(489\) 10.8039 0.488571
\(490\) 0 0
\(491\) 25.9254 1.17000 0.584999 0.811034i \(-0.301095\pi\)
0.584999 + 0.811034i \(0.301095\pi\)
\(492\) 0 0
\(493\) 2.94192 0.132497
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −20.1831 −0.905336
\(498\) 0 0
\(499\) 8.04562 0.360172 0.180086 0.983651i \(-0.442362\pi\)
0.180086 + 0.983651i \(0.442362\pi\)
\(500\) 0 0
\(501\) −8.29740 −0.370701
\(502\) 0 0
\(503\) 5.50490 0.245451 0.122726 0.992441i \(-0.460836\pi\)
0.122726 + 0.992441i \(0.460836\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −42.0538 −1.86767
\(508\) 0 0
\(509\) −8.26586 −0.366378 −0.183189 0.983078i \(-0.558642\pi\)
−0.183189 + 0.983078i \(0.558642\pi\)
\(510\) 0 0
\(511\) −24.9043 −1.10170
\(512\) 0 0
\(513\) −39.3098 −1.73557
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −4.65076 −0.204540
\(518\) 0 0
\(519\) 62.5116 2.74396
\(520\) 0 0
\(521\) 11.9776 0.524747 0.262374 0.964966i \(-0.415495\pi\)
0.262374 + 0.964966i \(0.415495\pi\)
\(522\) 0 0
\(523\) 0.711546 0.0311137 0.0155569 0.999879i \(-0.495048\pi\)
0.0155569 + 0.999879i \(0.495048\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.65503 −0.115655
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 68.7162 2.98203
\(532\) 0 0
\(533\) −17.7246 −0.767737
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −65.5524 −2.82880
\(538\) 0 0
\(539\) −0.961182 −0.0414011
\(540\) 0 0
\(541\) 34.9533 1.50276 0.751381 0.659869i \(-0.229388\pi\)
0.751381 + 0.659869i \(0.229388\pi\)
\(542\) 0 0
\(543\) 72.6351 3.11707
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17.8478 −0.763118 −0.381559 0.924345i \(-0.624613\pi\)
−0.381559 + 0.924345i \(0.624613\pi\)
\(548\) 0 0
\(549\) 40.2558 1.71808
\(550\) 0 0
\(551\) 22.4558 0.956650
\(552\) 0 0
\(553\) −14.7497 −0.627221
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.29661 0.139682 0.0698410 0.997558i \(-0.477751\pi\)
0.0698410 + 0.997558i \(0.477751\pi\)
\(558\) 0 0
\(559\) −43.7437 −1.85016
\(560\) 0 0
\(561\) −1.04449 −0.0440983
\(562\) 0 0
\(563\) −4.44153 −0.187188 −0.0935941 0.995610i \(-0.529836\pi\)
−0.0935941 + 0.995610i \(0.529836\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 56.2481 2.36220
\(568\) 0 0
\(569\) −6.00088 −0.251570 −0.125785 0.992058i \(-0.540145\pi\)
−0.125785 + 0.992058i \(0.540145\pi\)
\(570\) 0 0
\(571\) −18.1609 −0.760008 −0.380004 0.924985i \(-0.624077\pi\)
−0.380004 + 0.924985i \(0.624077\pi\)
\(572\) 0 0
\(573\) −53.6175 −2.23990
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −10.0474 −0.418279 −0.209140 0.977886i \(-0.567066\pi\)
−0.209140 + 0.977886i \(0.567066\pi\)
\(578\) 0 0
\(579\) −46.7476 −1.94277
\(580\) 0 0
\(581\) −39.5223 −1.63966
\(582\) 0 0
\(583\) −10.3022 −0.426672
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 42.3593 1.74836 0.874178 0.485605i \(-0.161401\pi\)
0.874178 + 0.485605i \(0.161401\pi\)
\(588\) 0 0
\(589\) −20.2660 −0.835044
\(590\) 0 0
\(591\) 42.9698 1.76754
\(592\) 0 0
\(593\) 19.6741 0.807917 0.403958 0.914777i \(-0.367634\pi\)
0.403958 + 0.914777i \(0.367634\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 60.4751 2.47508
\(598\) 0 0
\(599\) 18.2740 0.746655 0.373328 0.927700i \(-0.378217\pi\)
0.373328 + 0.927700i \(0.378217\pi\)
\(600\) 0 0
\(601\) −8.17793 −0.333585 −0.166792 0.985992i \(-0.553341\pi\)
−0.166792 + 0.985992i \(0.553341\pi\)
\(602\) 0 0
\(603\) −10.9730 −0.446855
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −21.7927 −0.884538 −0.442269 0.896883i \(-0.645826\pi\)
−0.442269 + 0.896883i \(0.645826\pi\)
\(608\) 0 0
\(609\) −62.8197 −2.54558
\(610\) 0 0
\(611\) −26.8294 −1.08540
\(612\) 0 0
\(613\) −15.2379 −0.615455 −0.307727 0.951475i \(-0.599568\pi\)
−0.307727 + 0.951475i \(0.599568\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20.2945 0.817024 0.408512 0.912753i \(-0.366048\pi\)
0.408512 + 0.912753i \(0.366048\pi\)
\(618\) 0 0
\(619\) −2.08510 −0.0838073 −0.0419037 0.999122i \(-0.513342\pi\)
−0.0419037 + 0.999122i \(0.513342\pi\)
\(620\) 0 0
\(621\) 14.0469 0.563681
\(622\) 0 0
\(623\) −42.8085 −1.71509
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −7.97262 −0.318396
\(628\) 0 0
\(629\) −1.13667 −0.0453221
\(630\) 0 0
\(631\) −39.0512 −1.55461 −0.777303 0.629127i \(-0.783413\pi\)
−0.777303 + 0.629127i \(0.783413\pi\)
\(632\) 0 0
\(633\) 55.0738 2.18899
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.54488 −0.219696
\(638\) 0 0
\(639\) −61.1127 −2.41758
\(640\) 0 0
\(641\) −21.8361 −0.862475 −0.431238 0.902238i \(-0.641923\pi\)
−0.431238 + 0.902238i \(0.641923\pi\)
\(642\) 0 0
\(643\) 16.3727 0.645676 0.322838 0.946454i \(-0.395363\pi\)
0.322838 + 0.946454i \(0.395363\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.9991 0.825560 0.412780 0.910831i \(-0.364558\pi\)
0.412780 + 0.910831i \(0.364558\pi\)
\(648\) 0 0
\(649\) 8.25861 0.324179
\(650\) 0 0
\(651\) 56.6936 2.22200
\(652\) 0 0
\(653\) −23.2756 −0.910846 −0.455423 0.890275i \(-0.650512\pi\)
−0.455423 + 0.890275i \(0.650512\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −75.4080 −2.94195
\(658\) 0 0
\(659\) 2.09639 0.0816637 0.0408318 0.999166i \(-0.486999\pi\)
0.0408318 + 0.999166i \(0.486999\pi\)
\(660\) 0 0
\(661\) −31.3184 −1.21814 −0.609072 0.793115i \(-0.708458\pi\)
−0.609072 + 0.793115i \(0.708458\pi\)
\(662\) 0 0
\(663\) −6.02545 −0.234009
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −8.02431 −0.310703
\(668\) 0 0
\(669\) −43.5190 −1.68254
\(670\) 0 0
\(671\) 4.83812 0.186773
\(672\) 0 0
\(673\) 44.3377 1.70909 0.854545 0.519377i \(-0.173836\pi\)
0.854545 + 0.519377i \(0.173836\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.03772 0.116749 0.0583746 0.998295i \(-0.481408\pi\)
0.0583746 + 0.998295i \(0.481408\pi\)
\(678\) 0 0
\(679\) −15.9436 −0.611860
\(680\) 0 0
\(681\) 26.7061 1.02338
\(682\) 0 0
\(683\) 22.6750 0.867635 0.433817 0.901001i \(-0.357166\pi\)
0.433817 + 0.901001i \(0.357166\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 20.0338 0.764338
\(688\) 0 0
\(689\) −59.4313 −2.26415
\(690\) 0 0
\(691\) 18.2394 0.693860 0.346930 0.937891i \(-0.387224\pi\)
0.346930 + 0.937891i \(0.387224\pi\)
\(692\) 0 0
\(693\) 15.8469 0.601974
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −1.27287 −0.0482134
\(698\) 0 0
\(699\) 43.8934 1.66020
\(700\) 0 0
\(701\) 17.4315 0.658378 0.329189 0.944264i \(-0.393225\pi\)
0.329189 + 0.944264i \(0.393225\pi\)
\(702\) 0 0
\(703\) −8.67629 −0.327232
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 32.8086 1.23389
\(708\) 0 0
\(709\) −32.4207 −1.21758 −0.608792 0.793330i \(-0.708346\pi\)
−0.608792 + 0.793330i \(0.708346\pi\)
\(710\) 0 0
\(711\) −44.6608 −1.67491
\(712\) 0 0
\(713\) 7.24179 0.271207
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 37.1117 1.38596
\(718\) 0 0
\(719\) −0.494269 −0.0184331 −0.00921656 0.999958i \(-0.502934\pi\)
−0.00921656 + 0.999958i \(0.502934\pi\)
\(720\) 0 0
\(721\) −30.5099 −1.13625
\(722\) 0 0
\(723\) 56.6430 2.10658
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 4.25774 0.157911 0.0789555 0.996878i \(-0.474842\pi\)
0.0789555 + 0.996878i \(0.474842\pi\)
\(728\) 0 0
\(729\) 34.6543 1.28349
\(730\) 0 0
\(731\) −3.14140 −0.116189
\(732\) 0 0
\(733\) 14.8525 0.548589 0.274295 0.961646i \(-0.411556\pi\)
0.274295 + 0.961646i \(0.411556\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.31878 −0.0485780
\(738\) 0 0
\(739\) 42.1389 1.55010 0.775052 0.631898i \(-0.217724\pi\)
0.775052 + 0.631898i \(0.217724\pi\)
\(740\) 0 0
\(741\) −45.9926 −1.68958
\(742\) 0 0
\(743\) −3.97014 −0.145650 −0.0728252 0.997345i \(-0.523202\pi\)
−0.0728252 + 0.997345i \(0.523202\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −119.670 −4.37851
\(748\) 0 0
\(749\) −3.55705 −0.129972
\(750\) 0 0
\(751\) −51.5382 −1.88066 −0.940328 0.340269i \(-0.889482\pi\)
−0.940328 + 0.340269i \(0.889482\pi\)
\(752\) 0 0
\(753\) 40.3921 1.47197
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −39.9808 −1.45313 −0.726564 0.687099i \(-0.758884\pi\)
−0.726564 + 0.687099i \(0.758884\pi\)
\(758\) 0 0
\(759\) 2.84892 0.103409
\(760\) 0 0
\(761\) −20.6683 −0.749226 −0.374613 0.927181i \(-0.622224\pi\)
−0.374613 + 0.927181i \(0.622224\pi\)
\(762\) 0 0
\(763\) −46.7336 −1.69187
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 47.6424 1.72027
\(768\) 0 0
\(769\) −0.0670558 −0.00241809 −0.00120905 0.999999i \(-0.500385\pi\)
−0.00120905 + 0.999999i \(0.500385\pi\)
\(770\) 0 0
\(771\) −15.7121 −0.565859
\(772\) 0 0
\(773\) 21.2074 0.762778 0.381389 0.924415i \(-0.375446\pi\)
0.381389 + 0.924415i \(0.375446\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 24.2717 0.870744
\(778\) 0 0
\(779\) −9.71588 −0.348108
\(780\) 0 0
\(781\) −7.34480 −0.262817
\(782\) 0 0
\(783\) −112.716 −4.02816
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −19.1047 −0.681010 −0.340505 0.940243i \(-0.610598\pi\)
−0.340505 + 0.940243i \(0.610598\pi\)
\(788\) 0 0
\(789\) −37.3577 −1.32997
\(790\) 0 0
\(791\) −2.03035 −0.0721910
\(792\) 0 0
\(793\) 27.9102 0.991121
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −51.0751 −1.80917 −0.904587 0.426290i \(-0.859820\pi\)
−0.904587 + 0.426290i \(0.859820\pi\)
\(798\) 0 0
\(799\) −1.92672 −0.0681625
\(800\) 0 0
\(801\) −129.621 −4.57992
\(802\) 0 0
\(803\) −9.06286 −0.319822
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 19.4547 0.684837
\(808\) 0 0
\(809\) −5.02800 −0.176775 −0.0883876 0.996086i \(-0.528171\pi\)
−0.0883876 + 0.996086i \(0.528171\pi\)
\(810\) 0 0
\(811\) −51.3571 −1.80339 −0.901696 0.432371i \(-0.857677\pi\)
−0.901696 + 0.432371i \(0.857677\pi\)
\(812\) 0 0
\(813\) 12.6645 0.444162
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −23.9785 −0.838900
\(818\) 0 0
\(819\) 91.4179 3.19440
\(820\) 0 0
\(821\) 13.7483 0.479818 0.239909 0.970795i \(-0.422882\pi\)
0.239909 + 0.970795i \(0.422882\pi\)
\(822\) 0 0
\(823\) 9.07220 0.316237 0.158119 0.987420i \(-0.449457\pi\)
0.158119 + 0.987420i \(0.449457\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 48.2010 1.67611 0.838057 0.545583i \(-0.183692\pi\)
0.838057 + 0.545583i \(0.183692\pi\)
\(828\) 0 0
\(829\) 41.0601 1.42608 0.713038 0.701125i \(-0.247319\pi\)
0.713038 + 0.701125i \(0.247319\pi\)
\(830\) 0 0
\(831\) −25.5019 −0.884651
\(832\) 0 0
\(833\) −0.398199 −0.0137968
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 101.724 3.51611
\(838\) 0 0
\(839\) −29.3970 −1.01490 −0.507449 0.861682i \(-0.669412\pi\)
−0.507449 + 0.861682i \(0.669412\pi\)
\(840\) 0 0
\(841\) 35.3895 1.22033
\(842\) 0 0
\(843\) 19.3288 0.665721
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −24.8458 −0.853711
\(848\) 0 0
\(849\) 24.6367 0.845530
\(850\) 0 0
\(851\) 3.10036 0.106279
\(852\) 0 0
\(853\) −1.39913 −0.0479053 −0.0239527 0.999713i \(-0.507625\pi\)
−0.0239527 + 0.999713i \(0.507625\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −3.68808 −0.125982 −0.0629912 0.998014i \(-0.520064\pi\)
−0.0629912 + 0.998014i \(0.520064\pi\)
\(858\) 0 0
\(859\) −16.0281 −0.546871 −0.273435 0.961890i \(-0.588160\pi\)
−0.273435 + 0.961890i \(0.588160\pi\)
\(860\) 0 0
\(861\) 27.1800 0.926291
\(862\) 0 0
\(863\) 35.0979 1.19475 0.597374 0.801963i \(-0.296211\pi\)
0.597374 + 0.801963i \(0.296211\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 54.2942 1.84393
\(868\) 0 0
\(869\) −5.36753 −0.182081
\(870\) 0 0
\(871\) −7.60781 −0.257781
\(872\) 0 0
\(873\) −48.2759 −1.63389
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 53.2491 1.79809 0.899046 0.437853i \(-0.144261\pi\)
0.899046 + 0.437853i \(0.144261\pi\)
\(878\) 0 0
\(879\) 43.6142 1.47107
\(880\) 0 0
\(881\) 40.8449 1.37610 0.688050 0.725663i \(-0.258467\pi\)
0.688050 + 0.725663i \(0.258467\pi\)
\(882\) 0 0
\(883\) 14.9288 0.502393 0.251196 0.967936i \(-0.419176\pi\)
0.251196 + 0.967936i \(0.419176\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −34.9975 −1.17510 −0.587550 0.809188i \(-0.699908\pi\)
−0.587550 + 0.809188i \(0.699908\pi\)
\(888\) 0 0
\(889\) −19.1496 −0.642259
\(890\) 0 0
\(891\) 20.4692 0.685742
\(892\) 0 0
\(893\) −14.7068 −0.492143
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 16.4349 0.548745
\(898\) 0 0
\(899\) −58.1104 −1.93809
\(900\) 0 0
\(901\) −4.26799 −0.142187
\(902\) 0 0
\(903\) 67.0793 2.23226
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 16.3920 0.544288 0.272144 0.962257i \(-0.412267\pi\)
0.272144 + 0.962257i \(0.412267\pi\)
\(908\) 0 0
\(909\) 99.3416 3.29495
\(910\) 0 0
\(911\) 44.1111 1.46147 0.730733 0.682663i \(-0.239178\pi\)
0.730733 + 0.682663i \(0.239178\pi\)
\(912\) 0 0
\(913\) −14.3825 −0.475991
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 31.3076 1.03387
\(918\) 0 0
\(919\) −28.5629 −0.942203 −0.471101 0.882079i \(-0.656143\pi\)
−0.471101 + 0.882079i \(0.656143\pi\)
\(920\) 0 0
\(921\) 32.4724 1.07000
\(922\) 0 0
\(923\) −42.3708 −1.39465
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −92.3813 −3.03420
\(928\) 0 0
\(929\) 16.2273 0.532400 0.266200 0.963918i \(-0.414232\pi\)
0.266200 + 0.963918i \(0.414232\pi\)
\(930\) 0 0
\(931\) −3.03948 −0.0996148
\(932\) 0 0
\(933\) −90.9372 −2.97715
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −5.65418 −0.184714 −0.0923571 0.995726i \(-0.529440\pi\)
−0.0923571 + 0.995726i \(0.529440\pi\)
\(938\) 0 0
\(939\) 46.5192 1.51810
\(940\) 0 0
\(941\) −25.6246 −0.835338 −0.417669 0.908599i \(-0.637153\pi\)
−0.417669 + 0.908599i \(0.637153\pi\)
\(942\) 0 0
\(943\) 3.47185 0.113059
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.248718 −0.00808223 −0.00404112 0.999992i \(-0.501286\pi\)
−0.00404112 + 0.999992i \(0.501286\pi\)
\(948\) 0 0
\(949\) −52.2820 −1.69715
\(950\) 0 0
\(951\) −47.5914 −1.54326
\(952\) 0 0
\(953\) −39.1737 −1.26896 −0.634481 0.772939i \(-0.718786\pi\)
−0.634481 + 0.772939i \(0.718786\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −22.8606 −0.738978
\(958\) 0 0
\(959\) 7.94423 0.256533
\(960\) 0 0
\(961\) 21.4435 0.691726
\(962\) 0 0
\(963\) −10.7704 −0.347073
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −2.04114 −0.0656386 −0.0328193 0.999461i \(-0.510449\pi\)
−0.0328193 + 0.999461i \(0.510449\pi\)
\(968\) 0 0
\(969\) −3.30290 −0.106105
\(970\) 0 0
\(971\) 13.6713 0.438734 0.219367 0.975642i \(-0.429601\pi\)
0.219367 + 0.975642i \(0.429601\pi\)
\(972\) 0 0
\(973\) 30.5387 0.979025
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 45.8777 1.46776 0.733878 0.679281i \(-0.237708\pi\)
0.733878 + 0.679281i \(0.237708\pi\)
\(978\) 0 0
\(979\) −15.5784 −0.497887
\(980\) 0 0
\(981\) −141.505 −4.51792
\(982\) 0 0
\(983\) 59.6356 1.90208 0.951039 0.309070i \(-0.100018\pi\)
0.951039 + 0.309070i \(0.100018\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 41.1418 1.30956
\(988\) 0 0
\(989\) 8.56841 0.272460
\(990\) 0 0
\(991\) 42.3396 1.34496 0.672480 0.740115i \(-0.265229\pi\)
0.672480 + 0.740115i \(0.265229\pi\)
\(992\) 0 0
\(993\) −64.8656 −2.05845
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −7.02379 −0.222446 −0.111223 0.993795i \(-0.535477\pi\)
−0.111223 + 0.993795i \(0.535477\pi\)
\(998\) 0 0
\(999\) 43.5504 1.37787
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.cx.1.1 6
4.3 odd 2 2300.2.a.o.1.6 6
5.2 odd 4 1840.2.e.f.369.12 12
5.3 odd 4 1840.2.e.f.369.1 12
5.4 even 2 9200.2.a.cy.1.6 6
20.3 even 4 460.2.c.a.369.12 yes 12
20.7 even 4 460.2.c.a.369.1 12
20.19 odd 2 2300.2.a.n.1.1 6
60.23 odd 4 4140.2.f.b.829.4 12
60.47 odd 4 4140.2.f.b.829.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
460.2.c.a.369.1 12 20.7 even 4
460.2.c.a.369.12 yes 12 20.3 even 4
1840.2.e.f.369.1 12 5.3 odd 4
1840.2.e.f.369.12 12 5.2 odd 4
2300.2.a.n.1.1 6 20.19 odd 2
2300.2.a.o.1.6 6 4.3 odd 2
4140.2.f.b.829.3 12 60.47 odd 4
4140.2.f.b.829.4 12 60.23 odd 4
9200.2.a.cx.1.1 6 1.1 even 1 trivial
9200.2.a.cy.1.6 6 5.4 even 2