Properties

Label 9200.2.a.cz.1.3
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 1.3
Root \(1.58319\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.58319 q^{3} -2.84620 q^{7} -0.493499 q^{9} +O(q^{10})\) \(q-1.58319 q^{3} -2.84620 q^{7} -0.493499 q^{9} -1.98637 q^{11} -4.69204 q^{13} -3.16675 q^{17} +6.16110 q^{19} +4.50609 q^{21} +1.00000 q^{23} +5.53088 q^{27} -6.61816 q^{29} +8.29732 q^{31} +3.14481 q^{33} +1.71181 q^{37} +7.42840 q^{39} +6.72440 q^{41} -0.177968 q^{43} +11.4749 q^{47} +1.10086 q^{49} +5.01358 q^{51} -6.18762 q^{53} -9.75422 q^{57} +7.61559 q^{59} +11.8577 q^{61} +1.40460 q^{63} +3.07554 q^{67} -1.58319 q^{69} +1.96195 q^{71} -4.94732 q^{73} +5.65361 q^{77} -8.53182 q^{79} -7.27596 q^{81} +3.49429 q^{83} +10.4778 q^{87} +7.07506 q^{89} +13.3545 q^{91} -13.1363 q^{93} +7.00705 q^{97} +0.980272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + O(q^{10}) \) \( 7q - 3q^{3} - 4q^{7} + 2q^{9} + 7q^{11} - 7q^{13} + 7q^{19} - 6q^{21} + 7q^{23} - 11q^{29} + 10q^{31} - 19q^{33} - 19q^{37} + 24q^{39} - 16q^{41} - 6q^{43} - 6q^{47} - 17q^{49} + 7q^{51} - 15q^{53} - 8q^{57} + 11q^{59} + 5q^{61} - 13q^{63} - 9q^{67} - 3q^{69} + 14q^{71} - 10q^{73} - 6q^{77} + 32q^{79} - 5q^{81} - q^{83} - 10q^{87} - 24q^{89} + 7q^{91} - 26q^{93} + 7q^{97} + 61q^{99} + O(q^{100}) \)

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
\(3\) −1.58319 −0.914057 −0.457029 0.889452i \(-0.651086\pi\)
−0.457029 + 0.889452i \(0.651086\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.84620 −1.07576 −0.537881 0.843020i \(-0.680775\pi\)
−0.537881 + 0.843020i \(0.680775\pi\)
\(8\) 0 0
\(9\) −0.493499 −0.164500
\(10\) 0 0
\(11\) −1.98637 −0.598913 −0.299457 0.954110i \(-0.596805\pi\)
−0.299457 + 0.954110i \(0.596805\pi\)
\(12\) 0 0
\(13\) −4.69204 −1.30134 −0.650668 0.759362i \(-0.725511\pi\)
−0.650668 + 0.759362i \(0.725511\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.16675 −0.768050 −0.384025 0.923323i \(-0.625462\pi\)
−0.384025 + 0.923323i \(0.625462\pi\)
\(18\) 0 0
\(19\) 6.16110 1.41345 0.706727 0.707486i \(-0.250171\pi\)
0.706727 + 0.707486i \(0.250171\pi\)
\(20\) 0 0
\(21\) 4.50609 0.983309
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.53088 1.06442
\(28\) 0 0
\(29\) −6.61816 −1.22896 −0.614481 0.788932i \(-0.710635\pi\)
−0.614481 + 0.788932i \(0.710635\pi\)
\(30\) 0 0
\(31\) 8.29732 1.49024 0.745121 0.666929i \(-0.232392\pi\)
0.745121 + 0.666929i \(0.232392\pi\)
\(32\) 0 0
\(33\) 3.14481 0.547441
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.71181 0.281420 0.140710 0.990051i \(-0.455061\pi\)
0.140710 + 0.990051i \(0.455061\pi\)
\(38\) 0 0
\(39\) 7.42840 1.18950
\(40\) 0 0
\(41\) 6.72440 1.05018 0.525088 0.851048i \(-0.324033\pi\)
0.525088 + 0.851048i \(0.324033\pi\)
\(42\) 0 0
\(43\) −0.177968 −0.0271399 −0.0135700 0.999908i \(-0.504320\pi\)
−0.0135700 + 0.999908i \(0.504320\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.4749 1.67378 0.836891 0.547369i \(-0.184371\pi\)
0.836891 + 0.547369i \(0.184371\pi\)
\(48\) 0 0
\(49\) 1.10086 0.157266
\(50\) 0 0
\(51\) 5.01358 0.702042
\(52\) 0 0
\(53\) −6.18762 −0.849934 −0.424967 0.905209i \(-0.639714\pi\)
−0.424967 + 0.905209i \(0.639714\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −9.75422 −1.29198
\(58\) 0 0
\(59\) 7.61559 0.991465 0.495733 0.868475i \(-0.334900\pi\)
0.495733 + 0.868475i \(0.334900\pi\)
\(60\) 0 0
\(61\) 11.8577 1.51822 0.759109 0.650964i \(-0.225635\pi\)
0.759109 + 0.650964i \(0.225635\pi\)
\(62\) 0 0
\(63\) 1.40460 0.176963
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 3.07554 0.375737 0.187868 0.982194i \(-0.439842\pi\)
0.187868 + 0.982194i \(0.439842\pi\)
\(68\) 0 0
\(69\) −1.58319 −0.190594
\(70\) 0 0
\(71\) 1.96195 0.232840 0.116420 0.993200i \(-0.462858\pi\)
0.116420 + 0.993200i \(0.462858\pi\)
\(72\) 0 0
\(73\) −4.94732 −0.579041 −0.289520 0.957172i \(-0.593496\pi\)
−0.289520 + 0.957172i \(0.593496\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.65361 0.644289
\(78\) 0 0
\(79\) −8.53182 −0.959905 −0.479952 0.877295i \(-0.659346\pi\)
−0.479952 + 0.877295i \(0.659346\pi\)
\(80\) 0 0
\(81\) −7.27596 −0.808440
\(82\) 0 0
\(83\) 3.49429 0.383548 0.191774 0.981439i \(-0.438576\pi\)
0.191774 + 0.981439i \(0.438576\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 10.4778 1.12334
\(88\) 0 0
\(89\) 7.07506 0.749954 0.374977 0.927034i \(-0.377651\pi\)
0.374977 + 0.927034i \(0.377651\pi\)
\(90\) 0 0
\(91\) 13.3545 1.39993
\(92\) 0 0
\(93\) −13.1363 −1.36217
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 7.00705 0.711458 0.355729 0.934589i \(-0.384233\pi\)
0.355729 + 0.934589i \(0.384233\pi\)
\(98\) 0 0
\(99\) 0.980272 0.0985210
\(100\) 0 0
\(101\) 7.22362 0.718777 0.359389 0.933188i \(-0.382985\pi\)
0.359389 + 0.933188i \(0.382985\pi\)
\(102\) 0 0
\(103\) −12.8178 −1.26297 −0.631487 0.775386i \(-0.717555\pi\)
−0.631487 + 0.775386i \(0.717555\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −11.6841 −1.12954 −0.564772 0.825247i \(-0.691036\pi\)
−0.564772 + 0.825247i \(0.691036\pi\)
\(108\) 0 0
\(109\) −13.6019 −1.30283 −0.651413 0.758723i \(-0.725824\pi\)
−0.651413 + 0.758723i \(0.725824\pi\)
\(110\) 0 0
\(111\) −2.71013 −0.257234
\(112\) 0 0
\(113\) −1.44526 −0.135959 −0.0679795 0.997687i \(-0.521655\pi\)
−0.0679795 + 0.997687i \(0.521655\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.31552 0.214069
\(118\) 0 0
\(119\) 9.01322 0.826240
\(120\) 0 0
\(121\) −7.05433 −0.641303
\(122\) 0 0
\(123\) −10.6460 −0.959920
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.12328 −0.809561 −0.404780 0.914414i \(-0.632652\pi\)
−0.404780 + 0.914414i \(0.632652\pi\)
\(128\) 0 0
\(129\) 0.281758 0.0248074
\(130\) 0 0
\(131\) −9.33180 −0.815323 −0.407661 0.913133i \(-0.633656\pi\)
−0.407661 + 0.913133i \(0.633656\pi\)
\(132\) 0 0
\(133\) −17.5357 −1.52054
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 21.0013 1.79426 0.897129 0.441768i \(-0.145649\pi\)
0.897129 + 0.441768i \(0.145649\pi\)
\(138\) 0 0
\(139\) 16.1299 1.36812 0.684061 0.729425i \(-0.260212\pi\)
0.684061 + 0.729425i \(0.260212\pi\)
\(140\) 0 0
\(141\) −18.1669 −1.52993
\(142\) 0 0
\(143\) 9.32012 0.779388
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.74288 −0.143750
\(148\) 0 0
\(149\) −9.57227 −0.784191 −0.392096 0.919925i \(-0.628250\pi\)
−0.392096 + 0.919925i \(0.628250\pi\)
\(150\) 0 0
\(151\) −3.04120 −0.247489 −0.123745 0.992314i \(-0.539490\pi\)
−0.123745 + 0.992314i \(0.539490\pi\)
\(152\) 0 0
\(153\) 1.56279 0.126344
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.4786 0.995900 0.497950 0.867206i \(-0.334086\pi\)
0.497950 + 0.867206i \(0.334086\pi\)
\(158\) 0 0
\(159\) 9.79619 0.776889
\(160\) 0 0
\(161\) −2.84620 −0.224312
\(162\) 0 0
\(163\) −16.3939 −1.28407 −0.642034 0.766676i \(-0.721909\pi\)
−0.642034 + 0.766676i \(0.721909\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.13265 −0.629323 −0.314662 0.949204i \(-0.601891\pi\)
−0.314662 + 0.949204i \(0.601891\pi\)
\(168\) 0 0
\(169\) 9.01521 0.693477
\(170\) 0 0
\(171\) −3.04050 −0.232513
\(172\) 0 0
\(173\) 10.5256 0.800250 0.400125 0.916461i \(-0.368967\pi\)
0.400125 + 0.916461i \(0.368967\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −12.0570 −0.906256
\(178\) 0 0
\(179\) −20.5421 −1.53539 −0.767695 0.640816i \(-0.778596\pi\)
−0.767695 + 0.640816i \(0.778596\pi\)
\(180\) 0 0
\(181\) −22.0754 −1.64085 −0.820424 0.571756i \(-0.806263\pi\)
−0.820424 + 0.571756i \(0.806263\pi\)
\(182\) 0 0
\(183\) −18.7730 −1.38774
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 6.29034 0.459995
\(188\) 0 0
\(189\) −15.7420 −1.14506
\(190\) 0 0
\(191\) 4.50910 0.326267 0.163133 0.986604i \(-0.447840\pi\)
0.163133 + 0.986604i \(0.447840\pi\)
\(192\) 0 0
\(193\) −21.1534 −1.52266 −0.761329 0.648366i \(-0.775453\pi\)
−0.761329 + 0.648366i \(0.775453\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.1475 −0.722980 −0.361490 0.932376i \(-0.617732\pi\)
−0.361490 + 0.932376i \(0.617732\pi\)
\(198\) 0 0
\(199\) −6.57598 −0.466159 −0.233079 0.972458i \(-0.574880\pi\)
−0.233079 + 0.972458i \(0.574880\pi\)
\(200\) 0 0
\(201\) −4.86917 −0.343445
\(202\) 0 0
\(203\) 18.8366 1.32207
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.493499 −0.0343005
\(208\) 0 0
\(209\) −12.2382 −0.846536
\(210\) 0 0
\(211\) 26.5357 1.82680 0.913398 0.407069i \(-0.133449\pi\)
0.913398 + 0.407069i \(0.133449\pi\)
\(212\) 0 0
\(213\) −3.10614 −0.212829
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −23.6158 −1.60315
\(218\) 0 0
\(219\) 7.83257 0.529276
\(220\) 0 0
\(221\) 14.8585 0.999492
\(222\) 0 0
\(223\) −20.9231 −1.40111 −0.700557 0.713597i \(-0.747065\pi\)
−0.700557 + 0.713597i \(0.747065\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.32581 −0.618975 −0.309488 0.950903i \(-0.600158\pi\)
−0.309488 + 0.950903i \(0.600158\pi\)
\(228\) 0 0
\(229\) 29.5189 1.95066 0.975332 0.220742i \(-0.0708479\pi\)
0.975332 + 0.220742i \(0.0708479\pi\)
\(230\) 0 0
\(231\) −8.95076 −0.588917
\(232\) 0 0
\(233\) 28.9849 1.89886 0.949431 0.313974i \(-0.101661\pi\)
0.949431 + 0.313974i \(0.101661\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 13.5075 0.877408
\(238\) 0 0
\(239\) 9.62209 0.622401 0.311201 0.950344i \(-0.399269\pi\)
0.311201 + 0.950344i \(0.399269\pi\)
\(240\) 0 0
\(241\) 15.5745 1.00324 0.501621 0.865088i \(-0.332737\pi\)
0.501621 + 0.865088i \(0.332737\pi\)
\(242\) 0 0
\(243\) −5.07340 −0.325459
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −28.9081 −1.83938
\(248\) 0 0
\(249\) −5.53214 −0.350585
\(250\) 0 0
\(251\) 22.8066 1.43954 0.719770 0.694213i \(-0.244247\pi\)
0.719770 + 0.694213i \(0.244247\pi\)
\(252\) 0 0
\(253\) −1.98637 −0.124882
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −11.5591 −0.721038 −0.360519 0.932752i \(-0.617400\pi\)
−0.360519 + 0.932752i \(0.617400\pi\)
\(258\) 0 0
\(259\) −4.87216 −0.302742
\(260\) 0 0
\(261\) 3.26606 0.202164
\(262\) 0 0
\(263\) 6.57534 0.405453 0.202726 0.979235i \(-0.435020\pi\)
0.202726 + 0.979235i \(0.435020\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −11.2012 −0.685501
\(268\) 0 0
\(269\) −16.6536 −1.01539 −0.507694 0.861537i \(-0.669502\pi\)
−0.507694 + 0.861537i \(0.669502\pi\)
\(270\) 0 0
\(271\) 23.8675 1.44985 0.724925 0.688828i \(-0.241874\pi\)
0.724925 + 0.688828i \(0.241874\pi\)
\(272\) 0 0
\(273\) −21.1427 −1.27962
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −5.65369 −0.339697 −0.169849 0.985470i \(-0.554328\pi\)
−0.169849 + 0.985470i \(0.554328\pi\)
\(278\) 0 0
\(279\) −4.09472 −0.245144
\(280\) 0 0
\(281\) −31.7408 −1.89350 −0.946750 0.321971i \(-0.895655\pi\)
−0.946750 + 0.321971i \(0.895655\pi\)
\(282\) 0 0
\(283\) −0.998092 −0.0593304 −0.0296652 0.999560i \(-0.509444\pi\)
−0.0296652 + 0.999560i \(0.509444\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −19.1390 −1.12974
\(288\) 0 0
\(289\) −6.97168 −0.410099
\(290\) 0 0
\(291\) −11.0935 −0.650314
\(292\) 0 0
\(293\) −13.8947 −0.811739 −0.405869 0.913931i \(-0.633031\pi\)
−0.405869 + 0.913931i \(0.633031\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −10.9864 −0.637495
\(298\) 0 0
\(299\) −4.69204 −0.271347
\(300\) 0 0
\(301\) 0.506534 0.0291961
\(302\) 0 0
\(303\) −11.4364 −0.657003
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3.66633 0.209249 0.104624 0.994512i \(-0.466636\pi\)
0.104624 + 0.994512i \(0.466636\pi\)
\(308\) 0 0
\(309\) 20.2930 1.15443
\(310\) 0 0
\(311\) 14.4210 0.817741 0.408870 0.912593i \(-0.365923\pi\)
0.408870 + 0.912593i \(0.365923\pi\)
\(312\) 0 0
\(313\) 10.5046 0.593754 0.296877 0.954916i \(-0.404055\pi\)
0.296877 + 0.954916i \(0.404055\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −32.0818 −1.80189 −0.900946 0.433931i \(-0.857126\pi\)
−0.900946 + 0.433931i \(0.857126\pi\)
\(318\) 0 0
\(319\) 13.1461 0.736042
\(320\) 0 0
\(321\) 18.4982 1.03247
\(322\) 0 0
\(323\) −19.5107 −1.08560
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 21.5344 1.19086
\(328\) 0 0
\(329\) −32.6598 −1.80059
\(330\) 0 0
\(331\) −9.71307 −0.533879 −0.266939 0.963713i \(-0.586012\pi\)
−0.266939 + 0.963713i \(0.586012\pi\)
\(332\) 0 0
\(333\) −0.844778 −0.0462935
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.131832 −0.00718136 −0.00359068 0.999994i \(-0.501143\pi\)
−0.00359068 + 0.999994i \(0.501143\pi\)
\(338\) 0 0
\(339\) 2.28813 0.124274
\(340\) 0 0
\(341\) −16.4815 −0.892526
\(342\) 0 0
\(343\) 16.7901 0.906582
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 13.1981 0.708512 0.354256 0.935148i \(-0.384734\pi\)
0.354256 + 0.935148i \(0.384734\pi\)
\(348\) 0 0
\(349\) −34.0451 −1.82239 −0.911197 0.411971i \(-0.864841\pi\)
−0.911197 + 0.411971i \(0.864841\pi\)
\(350\) 0 0
\(351\) −25.9511 −1.38517
\(352\) 0 0
\(353\) 10.8593 0.577984 0.288992 0.957331i \(-0.406680\pi\)
0.288992 + 0.957331i \(0.406680\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −14.2697 −0.755231
\(358\) 0 0
\(359\) 20.3091 1.07188 0.535938 0.844257i \(-0.319958\pi\)
0.535938 + 0.844257i \(0.319958\pi\)
\(360\) 0 0
\(361\) 18.9592 0.997853
\(362\) 0 0
\(363\) 11.1684 0.586188
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 18.6731 0.974727 0.487364 0.873199i \(-0.337959\pi\)
0.487364 + 0.873199i \(0.337959\pi\)
\(368\) 0 0
\(369\) −3.31848 −0.172753
\(370\) 0 0
\(371\) 17.6112 0.914328
\(372\) 0 0
\(373\) 9.51979 0.492916 0.246458 0.969153i \(-0.420733\pi\)
0.246458 + 0.969153i \(0.420733\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 31.0527 1.59929
\(378\) 0 0
\(379\) −18.8304 −0.967251 −0.483625 0.875275i \(-0.660680\pi\)
−0.483625 + 0.875275i \(0.660680\pi\)
\(380\) 0 0
\(381\) 14.4439 0.739985
\(382\) 0 0
\(383\) 10.9401 0.559015 0.279507 0.960144i \(-0.409829\pi\)
0.279507 + 0.960144i \(0.409829\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0.0878272 0.00446451
\(388\) 0 0
\(389\) 22.2830 1.12979 0.564896 0.825162i \(-0.308916\pi\)
0.564896 + 0.825162i \(0.308916\pi\)
\(390\) 0 0
\(391\) −3.16675 −0.160150
\(392\) 0 0
\(393\) 14.7740 0.745252
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.8388 −0.543983 −0.271991 0.962300i \(-0.587682\pi\)
−0.271991 + 0.962300i \(0.587682\pi\)
\(398\) 0 0
\(399\) 27.7625 1.38986
\(400\) 0 0
\(401\) −2.71329 −0.135495 −0.0677476 0.997702i \(-0.521581\pi\)
−0.0677476 + 0.997702i \(0.521581\pi\)
\(402\) 0 0
\(403\) −38.9313 −1.93931
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.40029 −0.168546
\(408\) 0 0
\(409\) 21.6271 1.06939 0.534696 0.845044i \(-0.320426\pi\)
0.534696 + 0.845044i \(0.320426\pi\)
\(410\) 0 0
\(411\) −33.2490 −1.64005
\(412\) 0 0
\(413\) −21.6755 −1.06658
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −25.5368 −1.25054
\(418\) 0 0
\(419\) −4.00587 −0.195700 −0.0978498 0.995201i \(-0.531196\pi\)
−0.0978498 + 0.995201i \(0.531196\pi\)
\(420\) 0 0
\(421\) 25.4251 1.23914 0.619572 0.784940i \(-0.287306\pi\)
0.619572 + 0.784940i \(0.287306\pi\)
\(422\) 0 0
\(423\) −5.66284 −0.275337
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −33.7493 −1.63324
\(428\) 0 0
\(429\) −14.7556 −0.712405
\(430\) 0 0
\(431\) −1.07679 −0.0518673 −0.0259336 0.999664i \(-0.508256\pi\)
−0.0259336 + 0.999664i \(0.508256\pi\)
\(432\) 0 0
\(433\) −3.93871 −0.189283 −0.0946413 0.995511i \(-0.530170\pi\)
−0.0946413 + 0.995511i \(0.530170\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.16110 0.294726
\(438\) 0 0
\(439\) −13.1539 −0.627802 −0.313901 0.949456i \(-0.601636\pi\)
−0.313901 + 0.949456i \(0.601636\pi\)
\(440\) 0 0
\(441\) −0.543274 −0.0258702
\(442\) 0 0
\(443\) 8.95394 0.425415 0.212707 0.977116i \(-0.431772\pi\)
0.212707 + 0.977116i \(0.431772\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 15.1548 0.716795
\(448\) 0 0
\(449\) 8.23267 0.388524 0.194262 0.980950i \(-0.437769\pi\)
0.194262 + 0.980950i \(0.437769\pi\)
\(450\) 0 0
\(451\) −13.3571 −0.628964
\(452\) 0 0
\(453\) 4.81480 0.226219
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 36.3473 1.70026 0.850128 0.526576i \(-0.176524\pi\)
0.850128 + 0.526576i \(0.176524\pi\)
\(458\) 0 0
\(459\) −17.5149 −0.817527
\(460\) 0 0
\(461\) −15.2421 −0.709894 −0.354947 0.934886i \(-0.615501\pi\)
−0.354947 + 0.934886i \(0.615501\pi\)
\(462\) 0 0
\(463\) 5.57424 0.259057 0.129528 0.991576i \(-0.458654\pi\)
0.129528 + 0.991576i \(0.458654\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6.21488 0.287590 0.143795 0.989607i \(-0.454069\pi\)
0.143795 + 0.989607i \(0.454069\pi\)
\(468\) 0 0
\(469\) −8.75360 −0.404204
\(470\) 0 0
\(471\) −19.7560 −0.910309
\(472\) 0 0
\(473\) 0.353511 0.0162545
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 3.05358 0.139814
\(478\) 0 0
\(479\) 34.4168 1.57254 0.786272 0.617880i \(-0.212008\pi\)
0.786272 + 0.617880i \(0.212008\pi\)
\(480\) 0 0
\(481\) −8.03189 −0.366223
\(482\) 0 0
\(483\) 4.50609 0.205034
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −22.7752 −1.03204 −0.516021 0.856576i \(-0.672587\pi\)
−0.516021 + 0.856576i \(0.672587\pi\)
\(488\) 0 0
\(489\) 25.9547 1.17371
\(490\) 0 0
\(491\) −3.16911 −0.143020 −0.0715099 0.997440i \(-0.522782\pi\)
−0.0715099 + 0.997440i \(0.522782\pi\)
\(492\) 0 0
\(493\) 20.9581 0.943905
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.58410 −0.250481
\(498\) 0 0
\(499\) 14.0809 0.630346 0.315173 0.949034i \(-0.397937\pi\)
0.315173 + 0.949034i \(0.397937\pi\)
\(500\) 0 0
\(501\) 12.8756 0.575237
\(502\) 0 0
\(503\) −21.4946 −0.958399 −0.479199 0.877706i \(-0.659073\pi\)
−0.479199 + 0.877706i \(0.659073\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −14.2728 −0.633878
\(508\) 0 0
\(509\) −34.0952 −1.51124 −0.755622 0.655008i \(-0.772665\pi\)
−0.755622 + 0.655008i \(0.772665\pi\)
\(510\) 0 0
\(511\) 14.0811 0.622910
\(512\) 0 0
\(513\) 34.0764 1.50451
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −22.7933 −1.00245
\(518\) 0 0
\(519\) −16.6641 −0.731474
\(520\) 0 0
\(521\) −14.1367 −0.619339 −0.309669 0.950844i \(-0.600218\pi\)
−0.309669 + 0.950844i \(0.600218\pi\)
\(522\) 0 0
\(523\) 11.2020 0.489828 0.244914 0.969545i \(-0.421240\pi\)
0.244914 + 0.969545i \(0.421240\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −26.2756 −1.14458
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −3.75829 −0.163096
\(532\) 0 0
\(533\) −31.5511 −1.36663
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 32.5221 1.40343
\(538\) 0 0
\(539\) −2.18672 −0.0941887
\(540\) 0 0
\(541\) −33.6704 −1.44760 −0.723802 0.690008i \(-0.757607\pi\)
−0.723802 + 0.690008i \(0.757607\pi\)
\(542\) 0 0
\(543\) 34.9496 1.49983
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −23.1062 −0.987949 −0.493975 0.869476i \(-0.664456\pi\)
−0.493975 + 0.869476i \(0.664456\pi\)
\(548\) 0 0
\(549\) −5.85174 −0.249746
\(550\) 0 0
\(551\) −40.7752 −1.73708
\(552\) 0 0
\(553\) 24.2833 1.03263
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.48937 −0.147849 −0.0739246 0.997264i \(-0.523552\pi\)
−0.0739246 + 0.997264i \(0.523552\pi\)
\(558\) 0 0
\(559\) 0.835034 0.0353182
\(560\) 0 0
\(561\) −9.95883 −0.420462
\(562\) 0 0
\(563\) −38.8593 −1.63772 −0.818862 0.573991i \(-0.805394\pi\)
−0.818862 + 0.573991i \(0.805394\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 20.7089 0.869690
\(568\) 0 0
\(569\) −23.2055 −0.972823 −0.486412 0.873730i \(-0.661694\pi\)
−0.486412 + 0.873730i \(0.661694\pi\)
\(570\) 0 0
\(571\) 5.39836 0.225914 0.112957 0.993600i \(-0.463968\pi\)
0.112957 + 0.993600i \(0.463968\pi\)
\(572\) 0 0
\(573\) −7.13877 −0.298226
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 13.1082 0.545701 0.272850 0.962056i \(-0.412034\pi\)
0.272850 + 0.962056i \(0.412034\pi\)
\(578\) 0 0
\(579\) 33.4900 1.39180
\(580\) 0 0
\(581\) −9.94546 −0.412607
\(582\) 0 0
\(583\) 12.2909 0.509037
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 12.9646 0.535108 0.267554 0.963543i \(-0.413785\pi\)
0.267554 + 0.963543i \(0.413785\pi\)
\(588\) 0 0
\(589\) 51.1206 2.10639
\(590\) 0 0
\(591\) 16.0655 0.660845
\(592\) 0 0
\(593\) 17.0225 0.699030 0.349515 0.936931i \(-0.386346\pi\)
0.349515 + 0.936931i \(0.386346\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10.4110 0.426096
\(598\) 0 0
\(599\) 5.98111 0.244381 0.122191 0.992507i \(-0.461008\pi\)
0.122191 + 0.992507i \(0.461008\pi\)
\(600\) 0 0
\(601\) −21.3680 −0.871617 −0.435809 0.900039i \(-0.643538\pi\)
−0.435809 + 0.900039i \(0.643538\pi\)
\(602\) 0 0
\(603\) −1.51778 −0.0618086
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 17.5464 0.712186 0.356093 0.934450i \(-0.384109\pi\)
0.356093 + 0.934450i \(0.384109\pi\)
\(608\) 0 0
\(609\) −29.8220 −1.20845
\(610\) 0 0
\(611\) −53.8405 −2.17815
\(612\) 0 0
\(613\) −45.4601 −1.83612 −0.918059 0.396444i \(-0.870244\pi\)
−0.918059 + 0.396444i \(0.870244\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −25.8720 −1.04157 −0.520785 0.853688i \(-0.674360\pi\)
−0.520785 + 0.853688i \(0.674360\pi\)
\(618\) 0 0
\(619\) 3.20381 0.128772 0.0643859 0.997925i \(-0.479491\pi\)
0.0643859 + 0.997925i \(0.479491\pi\)
\(620\) 0 0
\(621\) 5.53088 0.221947
\(622\) 0 0
\(623\) −20.1370 −0.806773
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 19.3755 0.773783
\(628\) 0 0
\(629\) −5.42089 −0.216145
\(630\) 0 0
\(631\) −0.0248650 −0.000989858 0 −0.000494929 1.00000i \(-0.500158\pi\)
−0.000494929 1.00000i \(0.500158\pi\)
\(632\) 0 0
\(633\) −42.0112 −1.66980
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −5.16528 −0.204656
\(638\) 0 0
\(639\) −0.968219 −0.0383022
\(640\) 0 0
\(641\) −9.77145 −0.385949 −0.192975 0.981204i \(-0.561813\pi\)
−0.192975 + 0.981204i \(0.561813\pi\)
\(642\) 0 0
\(643\) −36.8211 −1.45208 −0.726041 0.687651i \(-0.758642\pi\)
−0.726041 + 0.687651i \(0.758642\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 46.5570 1.83034 0.915172 0.403064i \(-0.132055\pi\)
0.915172 + 0.403064i \(0.132055\pi\)
\(648\) 0 0
\(649\) −15.1274 −0.593802
\(650\) 0 0
\(651\) 37.3884 1.46537
\(652\) 0 0
\(653\) −2.76029 −0.108018 −0.0540092 0.998540i \(-0.517200\pi\)
−0.0540092 + 0.998540i \(0.517200\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.44150 0.0952520
\(658\) 0 0
\(659\) −39.3922 −1.53450 −0.767252 0.641346i \(-0.778376\pi\)
−0.767252 + 0.641346i \(0.778376\pi\)
\(660\) 0 0
\(661\) −17.7641 −0.690943 −0.345472 0.938429i \(-0.612281\pi\)
−0.345472 + 0.938429i \(0.612281\pi\)
\(662\) 0 0
\(663\) −23.5239 −0.913593
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.61816 −0.256256
\(668\) 0 0
\(669\) 33.1253 1.28070
\(670\) 0 0
\(671\) −23.5537 −0.909280
\(672\) 0 0
\(673\) 23.7072 0.913847 0.456923 0.889506i \(-0.348951\pi\)
0.456923 + 0.889506i \(0.348951\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −49.3507 −1.89670 −0.948352 0.317221i \(-0.897250\pi\)
−0.948352 + 0.317221i \(0.897250\pi\)
\(678\) 0 0
\(679\) −19.9435 −0.765361
\(680\) 0 0
\(681\) 14.7646 0.565779
\(682\) 0 0
\(683\) 15.6461 0.598682 0.299341 0.954146i \(-0.403233\pi\)
0.299341 + 0.954146i \(0.403233\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −46.7341 −1.78302
\(688\) 0 0
\(689\) 29.0325 1.10605
\(690\) 0 0
\(691\) −3.79498 −0.144368 −0.0721839 0.997391i \(-0.522997\pi\)
−0.0721839 + 0.997391i \(0.522997\pi\)
\(692\) 0 0
\(693\) −2.79005 −0.105985
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −21.2945 −0.806587
\(698\) 0 0
\(699\) −45.8887 −1.73567
\(700\) 0 0
\(701\) 0.751725 0.0283923 0.0141961 0.999899i \(-0.495481\pi\)
0.0141961 + 0.999899i \(0.495481\pi\)
\(702\) 0 0
\(703\) 10.5467 0.397775
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −20.5599 −0.773234
\(708\) 0 0
\(709\) 4.52035 0.169765 0.0848827 0.996391i \(-0.472948\pi\)
0.0848827 + 0.996391i \(0.472948\pi\)
\(710\) 0 0
\(711\) 4.21044 0.157904
\(712\) 0 0
\(713\) 8.29732 0.310737
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −15.2336 −0.568910
\(718\) 0 0
\(719\) 36.6742 1.36772 0.683859 0.729614i \(-0.260300\pi\)
0.683859 + 0.729614i \(0.260300\pi\)
\(720\) 0 0
\(721\) 36.4820 1.35866
\(722\) 0 0
\(723\) −24.6574 −0.917020
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −33.6449 −1.24782 −0.623910 0.781496i \(-0.714457\pi\)
−0.623910 + 0.781496i \(0.714457\pi\)
\(728\) 0 0
\(729\) 29.8601 1.10593
\(730\) 0 0
\(731\) 0.563582 0.0208448
\(732\) 0 0
\(733\) −47.5745 −1.75720 −0.878602 0.477555i \(-0.841523\pi\)
−0.878602 + 0.477555i \(0.841523\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.10916 −0.225034
\(738\) 0 0
\(739\) −28.8914 −1.06279 −0.531395 0.847124i \(-0.678332\pi\)
−0.531395 + 0.847124i \(0.678332\pi\)
\(740\) 0 0
\(741\) 45.7672 1.68130
\(742\) 0 0
\(743\) 3.61970 0.132794 0.0663969 0.997793i \(-0.478850\pi\)
0.0663969 + 0.997793i \(0.478850\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −1.72443 −0.0630936
\(748\) 0 0
\(749\) 33.2553 1.21512
\(750\) 0 0
\(751\) −19.2050 −0.700801 −0.350401 0.936600i \(-0.613955\pi\)
−0.350401 + 0.936600i \(0.613955\pi\)
\(752\) 0 0
\(753\) −36.1073 −1.31582
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 12.6638 0.460275 0.230137 0.973158i \(-0.426082\pi\)
0.230137 + 0.973158i \(0.426082\pi\)
\(758\) 0 0
\(759\) 3.14481 0.114149
\(760\) 0 0
\(761\) −38.9053 −1.41032 −0.705159 0.709050i \(-0.749124\pi\)
−0.705159 + 0.709050i \(0.749124\pi\)
\(762\) 0 0
\(763\) 38.7138 1.40153
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −35.7326 −1.29023
\(768\) 0 0
\(769\) 4.16816 0.150308 0.0751539 0.997172i \(-0.476055\pi\)
0.0751539 + 0.997172i \(0.476055\pi\)
\(770\) 0 0
\(771\) 18.3003 0.659070
\(772\) 0 0
\(773\) −26.6030 −0.956842 −0.478421 0.878131i \(-0.658791\pi\)
−0.478421 + 0.878131i \(0.658791\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 7.71358 0.276723
\(778\) 0 0
\(779\) 41.4297 1.48437
\(780\) 0 0
\(781\) −3.89716 −0.139451
\(782\) 0 0
\(783\) −36.6043 −1.30813
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 21.7538 0.775440 0.387720 0.921777i \(-0.373263\pi\)
0.387720 + 0.921777i \(0.373263\pi\)
\(788\) 0 0
\(789\) −10.4100 −0.370607
\(790\) 0 0
\(791\) 4.11351 0.146260
\(792\) 0 0
\(793\) −55.6366 −1.97571
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.2490 −0.363039 −0.181519 0.983387i \(-0.558102\pi\)
−0.181519 + 0.983387i \(0.558102\pi\)
\(798\) 0 0
\(799\) −36.3381 −1.28555
\(800\) 0 0
\(801\) −3.49153 −0.123367
\(802\) 0 0
\(803\) 9.82722 0.346795
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 26.3659 0.928123
\(808\) 0 0
\(809\) 37.0993 1.30434 0.652170 0.758072i \(-0.273859\pi\)
0.652170 + 0.758072i \(0.273859\pi\)
\(810\) 0 0
\(811\) −35.8084 −1.25740 −0.628701 0.777647i \(-0.716413\pi\)
−0.628701 + 0.777647i \(0.716413\pi\)
\(812\) 0 0
\(813\) −37.7869 −1.32525
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1.09648 −0.0383610
\(818\) 0 0
\(819\) −6.59042 −0.230288
\(820\) 0 0
\(821\) −21.5343 −0.751551 −0.375775 0.926711i \(-0.622624\pi\)
−0.375775 + 0.926711i \(0.622624\pi\)
\(822\) 0 0
\(823\) −41.1466 −1.43428 −0.717140 0.696929i \(-0.754549\pi\)
−0.717140 + 0.696929i \(0.754549\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.48319 −0.329763 −0.164881 0.986313i \(-0.552724\pi\)
−0.164881 + 0.986313i \(0.552724\pi\)
\(828\) 0 0
\(829\) 24.0091 0.833872 0.416936 0.908936i \(-0.363104\pi\)
0.416936 + 0.908936i \(0.363104\pi\)
\(830\) 0 0
\(831\) 8.95088 0.310503
\(832\) 0 0
\(833\) −3.48616 −0.120788
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 45.8915 1.58624
\(838\) 0 0
\(839\) −9.89039 −0.341454 −0.170727 0.985318i \(-0.554612\pi\)
−0.170727 + 0.985318i \(0.554612\pi\)
\(840\) 0 0
\(841\) 14.8001 0.510348
\(842\) 0 0
\(843\) 50.2519 1.73077
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 20.0781 0.689890
\(848\) 0 0
\(849\) 1.58017 0.0542314
\(850\) 0 0
\(851\) 1.71181 0.0586802
\(852\) 0 0
\(853\) −5.02358 −0.172004 −0.0860021 0.996295i \(-0.527409\pi\)
−0.0860021 + 0.996295i \(0.527409\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 26.8011 0.915509 0.457754 0.889079i \(-0.348654\pi\)
0.457754 + 0.889079i \(0.348654\pi\)
\(858\) 0 0
\(859\) −27.3018 −0.931525 −0.465763 0.884910i \(-0.654220\pi\)
−0.465763 + 0.884910i \(0.654220\pi\)
\(860\) 0 0
\(861\) 30.3007 1.03265
\(862\) 0 0
\(863\) 2.22910 0.0758796 0.0379398 0.999280i \(-0.487920\pi\)
0.0379398 + 0.999280i \(0.487920\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 11.0375 0.374854
\(868\) 0 0
\(869\) 16.9474 0.574900
\(870\) 0 0
\(871\) −14.4305 −0.488960
\(872\) 0 0
\(873\) −3.45797 −0.117035
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 46.4517 1.56856 0.784280 0.620407i \(-0.213032\pi\)
0.784280 + 0.620407i \(0.213032\pi\)
\(878\) 0 0
\(879\) 21.9980 0.741975
\(880\) 0 0
\(881\) −25.6878 −0.865444 −0.432722 0.901527i \(-0.642447\pi\)
−0.432722 + 0.901527i \(0.642447\pi\)
\(882\) 0 0
\(883\) 48.8481 1.64387 0.821934 0.569582i \(-0.192895\pi\)
0.821934 + 0.569582i \(0.192895\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 45.1121 1.51472 0.757358 0.653000i \(-0.226490\pi\)
0.757358 + 0.653000i \(0.226490\pi\)
\(888\) 0 0
\(889\) 25.9667 0.870895
\(890\) 0 0
\(891\) 14.4528 0.484185
\(892\) 0 0
\(893\) 70.6979 2.36581
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 7.42840 0.248027
\(898\) 0 0
\(899\) −54.9130 −1.83145
\(900\) 0 0
\(901\) 19.5947 0.652792
\(902\) 0 0
\(903\) −0.801941 −0.0266869
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 15.5516 0.516382 0.258191 0.966094i \(-0.416874\pi\)
0.258191 + 0.966094i \(0.416874\pi\)
\(908\) 0 0
\(909\) −3.56485 −0.118239
\(910\) 0 0
\(911\) 30.1283 0.998195 0.499097 0.866546i \(-0.333665\pi\)
0.499097 + 0.866546i \(0.333665\pi\)
\(912\) 0 0
\(913\) −6.94096 −0.229712
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 26.5602 0.877094
\(918\) 0 0
\(919\) −34.2483 −1.12975 −0.564874 0.825177i \(-0.691075\pi\)
−0.564874 + 0.825177i \(0.691075\pi\)
\(920\) 0 0
\(921\) −5.80452 −0.191265
\(922\) 0 0
\(923\) −9.20553 −0.303004
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 6.32556 0.207759
\(928\) 0 0
\(929\) −54.6989 −1.79461 −0.897307 0.441408i \(-0.854479\pi\)
−0.897307 + 0.441408i \(0.854479\pi\)
\(930\) 0 0
\(931\) 6.78252 0.222288
\(932\) 0 0
\(933\) −22.8312 −0.747462
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 12.1635 0.397364 0.198682 0.980064i \(-0.436334\pi\)
0.198682 + 0.980064i \(0.436334\pi\)
\(938\) 0 0
\(939\) −16.6308 −0.542725
\(940\) 0 0
\(941\) −27.9048 −0.909672 −0.454836 0.890575i \(-0.650302\pi\)
−0.454836 + 0.890575i \(0.650302\pi\)
\(942\) 0 0
\(943\) 6.72440 0.218977
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −10.5104 −0.341541 −0.170770 0.985311i \(-0.554626\pi\)
−0.170770 + 0.985311i \(0.554626\pi\)
\(948\) 0 0
\(949\) 23.2130 0.753527
\(950\) 0 0
\(951\) 50.7916 1.64703
\(952\) 0 0
\(953\) −11.7005 −0.379017 −0.189508 0.981879i \(-0.560689\pi\)
−0.189508 + 0.981879i \(0.560689\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −20.8129 −0.672784
\(958\) 0 0
\(959\) −59.7738 −1.93020
\(960\) 0 0
\(961\) 37.8455 1.22082
\(962\) 0 0
\(963\) 5.76609 0.185810
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −11.7133 −0.376673 −0.188337 0.982105i \(-0.560310\pi\)
−0.188337 + 0.982105i \(0.560310\pi\)
\(968\) 0 0
\(969\) 30.8892 0.992304
\(970\) 0 0
\(971\) 37.8963 1.21615 0.608075 0.793879i \(-0.291942\pi\)
0.608075 + 0.793879i \(0.291942\pi\)
\(972\) 0 0
\(973\) −45.9090 −1.47178
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.83500 −0.0906997 −0.0453499 0.998971i \(-0.514440\pi\)
−0.0453499 + 0.998971i \(0.514440\pi\)
\(978\) 0 0
\(979\) −14.0537 −0.449158
\(980\) 0 0
\(981\) 6.71253 0.214314
\(982\) 0 0
\(983\) 4.47696 0.142793 0.0713964 0.997448i \(-0.477254\pi\)
0.0713964 + 0.997448i \(0.477254\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 51.7068 1.64584
\(988\) 0 0
\(989\) −0.177968 −0.00565906
\(990\) 0 0
\(991\) 32.2466 1.02435 0.512173 0.858882i \(-0.328841\pi\)
0.512173 + 0.858882i \(0.328841\pi\)
\(992\) 0 0
\(993\) 15.3777 0.487996
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −27.5708 −0.873177 −0.436589 0.899661i \(-0.643813\pi\)
−0.436589 + 0.899661i \(0.643813\pi\)
\(998\) 0 0
\(999\) 9.46784 0.299549
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.1.3 7
4.3 odd 2 4600.2.a.bi.1.5 7
5.2 odd 4 1840.2.e.g.369.11 14
5.3 odd 4 1840.2.e.g.369.4 14
5.4 even 2 9200.2.a.dc.1.5 7
20.3 even 4 920.2.e.b.369.11 yes 14
20.7 even 4 920.2.e.b.369.4 14
20.19 odd 2 4600.2.a.bh.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.2.e.b.369.4 14 20.7 even 4
920.2.e.b.369.11 yes 14 20.3 even 4
1840.2.e.g.369.4 14 5.3 odd 4
1840.2.e.g.369.11 14 5.2 odd 4
4600.2.a.bh.1.3 7 20.19 odd 2
4600.2.a.bi.1.5 7 4.3 odd 2
9200.2.a.cz.1.3 7 1.1 even 1 trivial
9200.2.a.dc.1.5 7 5.4 even 2